LMFDB - Embedded newform 11.7.d.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,7,Mod(2,11)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.53059491982$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.3
Root			$-2.50105i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.7.d.a.7.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58811 - 3.56223i) q^{2} +(-1.49018 - 4.58631i) q^{3} +(13.7859 - 42.4287i) q^{4} +(-177.805 - 129.183i) q^{5} +(-12.4807 + 17.1783i) q^{6} +(410.475 + 133.371i) q^{7} +(-454.830 + 147.783i) q^{8} +(570.960 - 414.827i) q^{9} +O(q^{10})$	\(q+(-2.58811 - 3.56223i) q^{2} +(-1.49018 - 4.58631i) q^{3} +(13.7859 - 42.4287i) q^{4} +(-177.805 - 129.183i) q^{5} +(-12.4807 + 17.1783i) q^{6} +(410.475 + 133.371i) q^{7} +(-454.830 + 147.783i) q^{8} +(570.960 - 414.827i) q^{9} +967.721i q^{10} +(555.888 + 1209.36i) q^{11} -215.135 q^{12} +(-731.150 - 1006.34i) q^{13} +(-587.255 - 1807.39i) q^{14} +(-327.510 + 1007.97i) q^{15} +(-606.298 - 440.502i) q^{16} +(2611.74 - 3594.75i) q^{17} +(-2955.42 - 960.273i) q^{18} +(5208.19 - 1692.24i) q^{19} +(-7932.25 + 5763.12i) q^{20} -2081.31i q^{21} +(2869.32 - 5110.16i) q^{22} -1527.75 q^{23} +(1355.56 + 1865.77i) q^{24} +(10097.9 + 31078.3i) q^{25} +(-1692.52 + 5209.05i) q^{26} +(-5597.44 - 4066.78i) q^{27} +(11317.5 - 15577.3i) q^{28} +(-12422.7 - 4036.37i) q^{29} +(4438.27 - 1442.08i) q^{30} +(21546.0 - 15654.1i) q^{31} +33907.0i q^{32} +(4718.12 - 4351.64i) q^{33} -19564.8 q^{34} +(-55755.1 - 76740.3i) q^{35} +(-9729.35 - 29943.9i) q^{36} +(-13771.9 + 42385.5i) q^{37} +(-19507.6 - 14173.1i) q^{38} +(-3525.85 + 4852.91i) q^{39} +(99962.0 + 32479.6i) q^{40} +(56183.8 - 18255.2i) q^{41} +(-7414.12 + 5386.67i) q^{42} +75353.2i q^{43} +(58975.0 - 6913.49i) q^{44} -155108. q^{45} +(3953.99 + 5442.21i) q^{46} +(31948.0 + 98325.7i) q^{47} +(-1116.78 + 3437.10i) q^{48} +(55521.6 + 40338.8i) q^{49} +(84573.4 - 116405. i) q^{50} +(-20378.6 - 6621.40i) q^{51} +(-52777.3 + 17148.4i) q^{52} +(-65433.1 + 47539.9i) q^{53} +30464.7i q^{54} +(57388.7 - 286841. i) q^{55} -206406. q^{56} +(-15522.3 - 21364.6i) q^{57} +(17772.8 + 54699.0i) q^{58} +(31634.5 - 97361.1i) q^{59} +(38252.0 + 27791.7i) q^{60} +(-18853.7 + 25950.0i) q^{61} +(-111527. - 36237.3i) q^{62} +(289691. - 94126.2i) q^{63} +(81981.5 - 59563.0i) q^{64} +273384. i q^{65} +(-27712.6 - 5544.50i) q^{66} -81451.8 q^{67} +(-116515. - 160369. i) q^{68} +(2276.63 + 7006.74i) q^{69} +(-129066. + 397225. i) q^{70} +(-42876.5 - 31151.6i) q^{71} +(-198385. + 273054. i) q^{72} +(445412. + 144723. i) q^{73} +(186630. - 60639.8i) q^{74} +(127487. - 92624.7i) q^{75} -244306. i q^{76} +(66884.3 + 570551. i) q^{77} +26412.5 q^{78} +(-252611. - 347689. i) q^{79} +(50897.5 + 156646. i) q^{80} +(148675. - 457576. i) q^{81} +(-210439. - 152893. i) q^{82} +(233446. - 321311. i) q^{83} +(-88307.4 - 28692.8i) q^{84} +(-928758. + 301772. i) q^{85} +(268425. - 195022. i) q^{86} +62989.2i q^{87} +(-431558. - 467902. i) q^{88} +552369. q^{89} +(401436. + 552530. i) q^{90} +(-165901. - 510592. i) q^{91} +(-21061.5 + 64820.5i) q^{92} +(-103902. - 75489.1i) q^{93} +(267574. - 368284. i) q^{94} +(-1.14465e6 - 371919. i) q^{95} +(155508. - 50527.6i) q^{96} +(-1.22017e6 + 886505. i) q^{97} -302182. i q^{98} +(819064. + 459898. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.58811	−	3.56223i	−0.323514	−	0.445279i	0.616022	−	0.787729i	$-0.288743\pi$
$2$	−2.58811	−	3.56223i	−0.323514	−	0.445279i	−0.939536	+	0.342450i	$0.888743\pi$
$3$	−1.49018	−	4.58631i	−0.0551919	−	0.169863i	0.919661	−	0.392714i	$-0.128464\pi$
$3$	−1.49018	−	4.58631i	−0.0551919	−	0.169863i	−0.974853	+	0.222851i	$0.928464\pi$
$4$	13.7859	−	42.4287i	0.215405	−	0.662948i
$5$	−177.805	−	129.183i	−1.42244	−	1.03346i	−0.991363	−	0.131145i	$-0.958135\pi$
$5$	−177.805	−	129.183i	−1.42244	−	1.03346i	−0.431074	−	0.902317i	$-0.641865\pi$
$6$	−12.4807	+	17.1783i	−0.0577812	+	0.0795290i
$7$	410.475	+	133.371i	1.19672	+	0.388838i	0.838553	−	0.544820i	$-0.183402\pi$
$7$	410.475	+	133.371i	1.19672	+	0.388838i	0.358167	+	0.933658i	$0.383402\pi$
$8$	−454.830	+	147.783i	−0.888340	+	0.288639i
$9$	570.960	−	414.827i	0.783210	−	0.569035i
$10$			967.721i			0.967721i
$11$	555.888	+	1209.36i	0.417647	+	0.908609i
$11$	555.888	+	1209.36i	0.417647	+	0.908609i
$12$	−215.135			−0.124499
$13$	−731.150	−	1006.34i	−0.332795	−	0.458053i	0.609525	−	0.792767i	$-0.291360\pi$
$13$	−731.150	−	1006.34i	−0.332795	−	0.458053i	−0.942320	+	0.334714i	$0.891360\pi$
$14$	−587.255	−	1807.39i	−0.214014	−	0.658669i
$15$	−327.510	+	1007.97i	−0.0970401	+	0.298659i
$16$	−606.298	−	440.502i	−0.148022	−	0.107544i
$17$	2611.74	−	3594.75i	0.531597	−	0.731680i	−0.455776	−	0.890095i	$-0.650638\pi$
$17$	2611.74	−	3594.75i	0.531597	−	0.731680i	0.987373	+	0.158414i	$0.0506381\pi$
$18$	−2955.42	−	960.273i	−0.506759	−	0.164656i
$19$	5208.19	−	1692.24i	0.759322	−	0.246719i	0.0963346	−	0.995349i	$-0.469288\pi$
$19$	5208.19	−	1692.24i	0.759322	−	0.246719i	0.662988	+	0.748630i	$0.269288\pi$
$20$	−7932.25	+	5763.12i	−0.991532	+	0.720390i
$21$		−	2081.31i		−	0.224739i
$22$	2869.32	−	5110.16i	0.269470	−	0.479917i
$23$	−1527.75			−0.125565			−0.0627826	−	0.998027i	$-0.519997\pi$
$23$	−1527.75			−0.125565			−0.0627826	+	0.998027i	$0.519997\pi$
$24$	1355.56	+	1865.77i	0.0980585	+	0.134966i
$25$	10097.9	+	31078.3i	0.646269	+	1.98901i
$26$	−1692.52	+	5209.05i	−0.0962974	+	0.296373i
$27$	−5597.44	−	4066.78i	−0.284379	−	0.206614i
$28$	11317.5	−	15577.3i	0.515559	−	0.709606i
$29$	−12422.7	−	4036.37i	−0.509356	−	0.165500i	0.0430535	−	0.999073i	$-0.486291\pi$
$29$	−12422.7	−	4036.37i	−0.509356	−	0.165500i	−0.552409	+	0.833573i	$0.686291\pi$
$30$	4438.27	−	1442.08i	0.164380	−	0.0534104i
$31$	21546.0	−	15654.1i	0.723238	−	0.525463i	−0.164179	−	0.986431i	$-0.552497\pi$
$31$	21546.0	−	15654.1i	0.723238	−	0.525463i	0.887417	+	0.460967i	$0.152497\pi$
$32$			33907.0i			1.03476i
$33$	4718.12	−	4351.64i	0.131289	−	0.121091i
$34$	−19564.8			−0.497781
$35$	−55755.1	−	76740.3i	−1.30041	−	1.78986i
$36$	−9729.35	−	29943.9i	−0.208534	−	0.641801i
$37$	−13771.9	+	42385.5i	−0.271887	+	0.836782i	0.718139	+	0.695899i	$0.244994\pi$
$37$	−13771.9	+	42385.5i	−0.271887	+	0.836782i	−0.990026	+	0.140882i	$0.955006\pi$
$38$	−19507.6	−	14173.1i	−0.355510	−	0.258293i
$39$	−3525.85	+	4852.91i	−0.0594388	+	0.0818104i
$40$	99962.0	+	32479.6i	1.56191	+	0.507494i
$41$	56183.8	−	18255.2i	0.815191	−	0.264872i	0.128396	−	0.991723i	$-0.459017\pi$
$41$	56183.8	−	18255.2i	0.815191	−	0.264872i	0.686795	+	0.726851i	$0.259017\pi$
$42$	−7414.12	+	5386.67i	−0.100072	+	0.0727064i
$43$			75353.2i			0.947755i	0.880591	+	0.473878i	$0.157146\pi$
$43$			75353.2i			0.947755i	−0.880591	+	0.473878i	$0.842854\pi$
$44$	58975.0	−	6913.49i	0.692324	−	0.0811595i
$45$	−155108.			−1.70214
$46$	3953.99	+	5442.21i	0.0406221	+	0.0559115i
$47$	31948.0	+	98325.7i	0.307716	+	0.947051i	0.978650	+	0.205534i	$0.0658932\pi$
$47$	31948.0	+	98325.7i	0.307716	+	0.947051i	−0.670934	+	0.741517i	$0.734107\pi$
$48$	−1116.78	+	3437.10i	−0.0100982	+	0.0310791i
$49$	55521.6	+	40338.8i	0.471926	+	0.342874i
$50$	84573.4	−	116405.i	0.676588	−	0.931243i
$51$	−20378.6	−	6621.40i	−0.153626	−	0.0499160i
$52$	−52777.3	+	17148.4i	−0.375351	+	0.121959i
$53$	−65433.1	+	47539.9i	−0.439511	+	0.319323i	−0.785441	−	0.618937i	$-0.787564\pi$
$53$	−65433.1	+	47539.9i	−0.439511	+	0.319323i	0.345930	+	0.938260i	$0.387564\pi$
$54$			30464.7i			0.193471i
$55$	57388.7	−	286841.i	0.344936	−	1.72406i
$56$	−206406.			−1.17533
$57$	−15522.3	−	21364.6i	−0.0838170	−	0.115364i
$58$	17772.8	+	54699.0i	0.0910902	+	0.280347i
$59$	31634.5	−	97361.1i	0.154030	−	0.474056i	−0.844031	−	0.536294i	$-0.819824\pi$
$59$	31634.5	−	97361.1i	0.154030	−	0.474056i	0.998061	+	0.0622383i	$0.0198239\pi$
$60$	38252.0	+	27791.7i	0.177092	+	0.128665i
$61$	−18853.7	+	25950.0i	−0.0830631	+	0.114327i	−0.848527	−	0.529153i	$-0.822510\pi$
$61$	−18853.7	+	25950.0i	−0.0830631	+	0.114327i	0.765463	+	0.643479i	$0.222510\pi$
$62$	−111527.	−	36237.3i	−0.467955	−	0.152048i
$63$	289691.	−	94126.2i	1.15854	−	0.376434i
$64$	81981.5	−	59563.0i	0.312735	−	0.227215i
$65$			273384.i			0.995481i
$66$	−27712.6	−	5544.50i	−0.0963929	−	0.0192855i
$67$	−81451.8			−0.270817			−0.135409	−	0.990790i	$-0.543235\pi$
$67$	−81451.8			−0.270817			−0.135409	+	0.990790i	$0.543235\pi$
$68$	−116515.	−	160369.i	−0.370558	−	0.510029i
$69$	2276.63	+	7006.74i	0.00693019	+	0.0213289i
$70$	−129066.	+	397225.i	−0.376286	+	1.15809i
$71$	−42876.5	−	31151.6i	−0.119796	−	0.0870372i	0.526274	−	0.850315i	$-0.323589\pi$
$71$	−42876.5	−	31151.6i	−0.119796	−	0.0870372i	−0.646070	+	0.763278i	$0.723589\pi$
$72$	−198385.	+	273054.i	−0.531511	+	0.731562i
$73$	445412.	+	144723.i	1.14497	+	0.372023i	0.819246	−	0.573442i	$-0.194392\pi$
$73$	445412.	+	144723.i	1.14497	+	0.372023i	0.325723	+	0.945465i	$0.394392\pi$
$74$	186630.	−	60639.8i	0.460560	−	0.149645i
$75$	127487.	−	92624.7i	0.302191	−	0.219555i
$76$		−	244306.i		−	0.556536i
$77$	66884.3	+	570551.i	0.146505	+	1.24975i
$78$	26412.5			0.0556577
$79$	−252611.	−	347689.i	−0.512354	−	0.705195i	0.471960	−	0.881620i	$-0.343547\pi$
$79$	−252611.	−	347689.i	−0.512354	−	0.705195i	−0.984314	+	0.176425i	$0.943547\pi$
$80$	50897.5	+	156646.i	0.0994092	+	0.305950i
$81$	148675.	−	457576.i	0.279759	−	0.861009i
$82$	−210439.	−	152893.i	−0.381668	−	0.277298i
$83$	233446.	−	321311.i	0.408275	−	0.561942i	−0.554522	−	0.832169i	$-0.687099\pi$
$83$	233446.	−	321311.i	0.408275	−	0.561942i	0.962797	+	0.270227i	$0.0870988\pi$
$84$	−88307.4	−	28692.8i	−0.148991	−	0.0484100i
$85$	−928758.	+	301772.i	−1.51233	+	0.491385i
$86$	268425.	−	195022.i	0.422015	−	0.306612i
$87$			62989.2i			0.0956551i
$88$	−431558.	−	467902.i	−0.633273	−	0.686605i
$89$	552369.			0.783537			0.391768	−	0.920064i	$-0.371863\pi$
$89$	552369.			0.783537			0.391768	+	0.920064i	$0.371863\pi$
$90$	401436.	+	552530.i	0.550667	+	0.757928i
$91$	−165901.	−	510592.i	−0.220154	−	0.677564i
$92$	−21061.5	+	64820.5i	−0.0270474	+	0.0832433i
$93$	−103902.	−	75489.1i	−0.129174	−	0.0938503i
$94$	267574.	−	368284.i	0.322152	−	0.443404i
$95$	−1.14465e6	−	371919.i	−1.33506	−	0.433788i
$96$	155508.	−	50527.6i	0.175768	−	0.0571104i
$97$	−1.22017e6	+	886505.i	−1.33692	+	0.971328i	−0.337367	+	0.941373i	$0.609536\pi$
$97$	−1.22017e6	+	886505.i	−1.33692	+	0.971328i	−0.999551	+	0.0299552i	$0.990464\pi$
$98$		−	302182.i		−	0.321063i
$99$	819064.	+	459898.i	0.844136	+	0.473976i
$100$	1.45782e6			1.45782
$101$	1.02132e6	+	1.40572e6i	0.991280	+	1.36438i	0.930526	+	0.366227i	$0.119351\pi$
$101$	1.02132e6	+	1.40572e6i	0.991280	+	1.36438i	0.0607542	+	0.998153i	$0.480649\pi$
$102$	29155.1	+	89730.2i	0.0274735	+	0.0845547i
$103$	−95794.5	+	294825.i	−0.0876655	+	0.269807i	−0.985273	−	0.170989i	$-0.945304\pi$
$103$	−95794.5	+	294825.i	−0.0876655	+	0.269807i	0.897607	+	0.440796i	$0.145304\pi$
$104$	481270.	+	349663.i	0.427847	+	0.310849i
$105$	−268869.	+	370067.i	−0.232260	+	0.319678i
$106$	338696.	+	110049.i	0.284376	+	0.0923993i
$107$	−188927.	+	61386.1i	−0.154221	+	0.0501094i	−0.385110	−	0.922871i	$-0.625837\pi$
$107$	−188927.	+	61386.1i	−0.154221	+	0.0501094i	0.230889	+	0.972980i	$0.425837\pi$
$108$	−249714.	+	181428.i	−0.198231	+	0.144023i
$109$		−	2.10994e6i		−	1.62926i	−0.579979	−	0.814631i	$-0.696939\pi$
$109$		−	2.10994e6i		−	1.62926i	0.579979	−	0.814631i	$-0.303061\pi$
$110$	−1.17032e6	+	537944.i	−0.879280	+	0.404166i
$111$	214916.			0.157145
$112$	−190120.	−	261678.i	−0.135324	−	0.186257i
$113$	−278283.	−	856466.i	−0.192864	−	0.593574i	−0.999995	−	0.00320155i	$-0.998981\pi$
$113$	−278283.	−	856466.i	−0.192864	−	0.593574i	0.807131	−	0.590372i	$-0.201019\pi$
$114$	−35932.3	+	110588.i	−0.0242533	+	0.0746439i
$115$	271641.	+	197359.i	0.178609	+	0.129767i
$116$	−342516.	+	471433.i	−0.219436	+	0.302027i
$117$	−834914.	−	271280.i	−0.521296	−	0.169379i
$118$	−428696.	+	139292.i	−0.260918	+	0.0847773i
$119$	1.55149e6	−	1.12722e6i	0.920677	−	0.668911i
$120$		−	506857.i		−	0.293320i
$121$	−1.15354e6	+	1.34454e6i	−0.651142	+	0.758956i
$122$	141235.			0.0777793
$123$	−167448.	−	230473.i	−0.0899840	−	0.123852i
$124$	−367151.	−	1.12997e6i	−0.192566	−	0.592657i
$125$	1.15814e6	−	3.56438e6i	0.592966	−	1.82496i
$126$	−1.08505e6	−	788336.i	−0.542424	−	0.394094i
$127$	−1.80200e6	+	2.48024e6i	−0.879719	+	1.21083i	0.0967796	+	0.995306i	$0.469146\pi$
$127$	−1.80200e6	+	2.48024e6i	−0.879719	+	1.21083i	−0.976499	+	0.215524i	$0.930854\pi$
$128$	1.63948e6	+	532701.i	0.781767	+	0.254011i
$129$	345593.	−	112290.i	0.160989	−	0.0523084i
$130$	973857.	−	707549.i	0.443267	−	0.322052i
$131$			2.01342e6i			0.895611i	0.894131	+	0.447806i	$0.147794\pi$
$131$			2.01342e6i			0.895611i	−0.894131	+	0.447806i	$0.852206\pi$
$132$	−119591.	−	260175.i	−0.0519968	−	0.113121i
$133$	2.36353e6			1.00463
$134$	210806.	+	290150.i	0.0876132	+	0.120589i
$135$	469894.	+	1.44618e6i	0.190985	+	0.587790i
$136$	−656653.	+	2.02097e6i	−0.261047	+	0.803421i
$137$	312961.	+	227380.i	0.121711	+	0.0884280i	0.646975	−	0.762511i	$-0.276034\pi$
$137$	312961.	+	227380.i	0.121711	+	0.0884280i	−0.525265	+	0.850939i	$0.676034\pi$
$138$	19067.5	−	26244.1i	0.00725531	−	0.00998607i
$139$	−380583.	−	123659.i	−0.141712	−	0.0460449i	0.237302	−	0.971436i	$-0.423737\pi$
$139$	−380583.	−	123659.i	−0.141712	−	0.0460449i	−0.379014	+	0.925391i	$0.623737\pi$
$140$	−4.02462e6	+	1.30768e6i	−1.46670	+	0.476560i
$141$	403344.	−	293046.i	0.143886	−	0.104539i
$142$			233360.i			0.0815006i
$143$	810591.	−	1.44364e6i	0.277200	−	0.493685i
$144$	−528904.			−0.177129
$145$	1.68738e6	+	2.32248e6i	0.553489	+	0.761812i
$146$	−637240.	−	1.96122e6i	−0.204760	−	0.630185i
$147$	102269.	−	314752.i	0.0321953	−	0.0990868i
$148$	1.60850e6	+	1.16865e6i	0.496177	+	0.360494i
$149$	−1.06140e6	+	1.46089e6i	−0.320864	+	0.441631i	−0.938731	−	0.344651i	$-0.887997\pi$
$149$	−1.06140e6	+	1.46089e6i	−0.320864	+	0.441631i	0.617867	+	0.786283i	$0.287997\pi$
$150$	−659901.	−	214415.i	−0.195526	−	0.0635303i
$151$	5.93241e6	−	1.92756e6i	1.72306	−	0.559856i	0.730642	−	0.682761i	$-0.239221\pi$
$151$	5.93241e6	−	1.92756e6i	1.72306	−	0.559856i	0.992418	+	0.122905i	$0.0392210\pi$
$152$	−2.11876e6	+	1.53937e6i	−0.603324	+	0.438341i
$153$		−	3.13587e6i		−	0.875556i
$154$	1.85933e6	−	1.71491e6i	0.509090	−	0.469546i
$155$	−5.85321e6			−1.57181
$156$	157296.	+	216499.i	0.0414327	+	0.0570272i
$157$	80884.7	+	248938.i	0.0209010	+	0.0643267i	0.960963	−	0.276677i	$-0.0892332\pi$
$157$	80884.7	+	248938.i	0.0209010	+	0.0643267i	−0.940062	+	0.341004i	$0.889233\pi$
$158$	−584763.	+	1.79971e6i	−0.148255	+	0.456281i
$159$	315540.	+	229253.i	0.0784988	+	0.0570327i
$160$	4.38020e6	−	6.02882e6i	1.06938	−	1.47188i
$161$	−627104.	−	203758.i	−0.150266	−	0.0488245i
$162$	−2.01478e6	+	654641.i	−0.473895	+	0.153978i
$163$	−4.04432e6	+	2.93837e6i	−0.933861	+	0.678490i	−0.946935	−	0.321425i	$-0.895838\pi$
$163$	−4.04432e6	+	2.93837e6i	−0.933861	+	0.678490i	0.0130740	+	0.999915i	$0.495838\pi$
$164$		−	2.63547e6i		−	0.597485i
$165$	−1.40106e6	+	164243.i	−0.311893	+	0.0365624i
$166$	−1.74877e6			−0.382304
$167$	−3.27567e6	−	4.50858e6i	−0.703317	−	0.968033i	−0.999915	−	0.0130308i	$-0.995852\pi$
$167$	−3.27567e6	−	4.50858e6i	−0.703317	−	0.968033i	0.296598	−	0.955003i	$-0.404148\pi$
$168$	307583.	+	946644.i	0.0648686	+	0.199645i
$169$	1.01342e6	−	3.11900e6i	0.209957	−	0.646182i
$170$	3.47871e6	+	2.52743e6i	0.708062	+	0.514437i
$171$	2.27168e6	−	3.12670e6i	0.454317	−	0.625314i
$172$	3.19714e6	+	1.03881e6i	0.628313	+	0.204151i
$173$	2.10357e6	−	683491.i	0.406273	−	0.132006i	−0.0987493	−	0.995112i	$-0.531484\pi$
$173$	2.10357e6	−	683491.i	0.406273	−	0.132006i	0.505023	+	0.863106i	$0.331484\pi$
$174$	224382.	−	163023.i	0.0425932	−	0.0309458i
$175$			1.41036e7i			2.63158i
$176$	195690.	−	978102.i	0.0358948	−	0.179410i
$177$	−493669.			−0.0890259
$178$	−1.42959e6	−	1.96767e6i	−0.253485	−	0.348892i
$179$	1.52287e6	+	4.68691e6i	0.265524	+	0.817198i	0.991572	+	0.129555i	$0.0413548\pi$
$179$	1.52287e6	+	4.68691e6i	0.265524	+	0.817198i	−0.726048	+	0.687644i	$0.758645\pi$
$180$	−2.13830e6	+	6.58102e6i	−0.366650	+	1.12843i
$181$	−8.76651e6	−	6.36925e6i	−1.47840	−	1.07412i	−0.978069	−	0.208283i	$-0.933212\pi$
$181$	−8.76651e6	−	6.36925e6i	−1.47840	−	1.07412i	−0.500329	−	0.865835i	$-0.666788\pi$
$182$	−1.38948e6	+	1.91245e6i	−0.230482	+	0.317231i
$183$	147110.	+	47799.0i	0.0240043	+	0.00779947i
$184$	694868.	−	225776.i	0.111545	−	0.0362430i
$185$	7.92418e6	−	5.75725e6i	1.25152	−	0.909285i
$186$			565497.i			0.0878803i
$187$	5.79917e6	+	1.16025e6i	0.886832	+	0.177430i
$188$	4.61226e6			0.694130
$189$	−1.75522e6	−	2.41585e6i	−0.259983	−	0.357836i
$190$	1.63762e6	+	5.04007e6i	0.238755	+	0.734812i
$191$	−1.92860e6	+	5.93561e6i	−0.276784	+	0.851854i	0.711958	+	0.702222i	$0.247809\pi$
$191$	−1.92860e6	+	5.93561e6i	−0.276784	+	0.851854i	−0.988742	+	0.149631i	$0.952191\pi$
$192$	−395342.	−	287233.i	−0.0558559	−	0.0405817i
$193$	−833999.	+	1.14790e6i	−0.116010	+	0.159673i	−0.863073	−	0.505079i	$-0.831463\pi$
$193$	−833999.	+	1.14790e6i	−0.116010	+	0.159673i	0.747063	+	0.664753i	$0.231463\pi$
$194$	6.31587e6	+	2.05215e6i	0.865024	+	0.281063i
$195$	1.25382e6	−	407392.i	0.169096	−	0.0549426i
$196$	2.47694e6	−	1.79960e6i	0.328963	−	0.239006i
$197$			1.16779e6i			0.152745i	0.997079	+	0.0763726i	$0.0243338\pi$
$197$			1.16779e6i			0.152745i	−0.997079	+	0.0763726i	$0.975666\pi$
$198$	−481566.	−	4.10796e6i	−0.0620384	−	0.529214i
$199$	−1.25085e7			−1.58726			−0.793629	−	0.608402i	$-0.791811\pi$
$199$	−1.25085e7			−1.58726			−0.793629	+	0.608402i	$0.791811\pi$
$200$	−9.18571e6	−	1.26430e7i	−1.14821	−	1.58038i
$201$	121378.	+	373563.i	0.0149469	+	0.0460019i
$202$	2.36422e6	−	7.27633e6i	0.286837	−	0.882792i
$203$	−4.56086e6	−	3.31366e6i	−0.545203	−	0.396114i
$204$	−561875.	+	773355.i	−0.0661834	+	0.0910937i
$205$	−1.23480e7	−	4.01211e6i	−1.43329	−	0.465705i
$206$	1.29816e6	−	421798.i	0.148500	−	0.0482507i
$207$	−872285.	+	633752.i	−0.0983439	+	0.0714510i
$208$			932216.i			0.103592i
$209$	4.94170e6	+	5.35788e6i	0.541300	+	0.586886i
$210$	2.01413e6			0.217485
$211$	4.66667e6	+	6.42312e6i	0.496775	+	0.683752i	0.981620	−	0.190848i	$-0.0611238\pi$
$211$	4.66667e6	+	6.42312e6i	0.496775	+	0.683752i	−0.484845	+	0.874600i	$0.661124\pi$
$212$	1.11500e6	+	3.43162e6i	0.117022	+	0.360157i
$213$	−78977.1	+	243066.i	−0.00817264	+	0.0251528i
$214$	707636.	+	514128.i	0.0722053	+	0.0524602i
$215$	9.73432e6	−	1.33981e7i	0.979468	−	1.34812i
$216$	3.14689e6	+	1.02249e6i	0.312263	+	0.101460i
$217$	1.09319e7	−	3.55199e6i	1.06983	−	0.347610i
$218$	−7.51610e6	+	5.46077e6i	−0.725476	+	0.527089i
$219$		−	2.25846e6i		−	0.215021i
$220$	−1.13791e7	−	6.38929e6i	−1.06866	−	0.600046i
$221$	−5.52711e6			−0.512061
$222$	−556226.	−	765579.i	−0.0508385	−	0.0699731i
$223$	−1.37086e6	−	4.21907e6i	−0.123617	−	0.380454i	0.870030	−	0.493000i	$-0.164100\pi$
$223$	−1.37086e6	−	4.21907e6i	−0.123617	−	0.380454i	−0.993647	+	0.112545i	$0.964100\pi$
$224$	−4.52222e6	+	1.39180e7i	−0.402354	+	1.23832i
$225$	1.86576e7	+	1.35556e7i	1.63798	+	1.19006i
$226$	−2.33070e6	+	3.20794e6i	−0.201912	+	0.277908i
$227$	6.61204e6	+	2.14838e6i	0.565272	+	0.183668i	0.577692	−	0.816255i	$-0.303953\pi$
$227$	6.61204e6	+	2.14838e6i	0.565272	+	0.183668i	−0.0124198	+	0.999923i	$0.503953\pi$
$228$	−1.12046e6	+	364061.i	−0.0945351	+	0.0307163i
$229$	−1.25652e7	+	9.12917e6i	−1.04632	+	0.760195i	−0.971509	−	0.237003i	$-0.923835\pi$
$229$	−1.25652e7	+	9.12917e6i	−1.04632	+	0.760195i	−0.0748094	+	0.997198i	$0.523835\pi$
$230$		−	1.47844e6i		−	0.121512i
$231$	2.51705e6	−	1.15698e6i	0.204200	−	0.0938618i
$232$	6.24672e6			0.500251
$233$	1.18712e7	+	1.63392e7i	0.938481	+	1.29171i	0.956458	+	0.291869i	$0.0942773\pi$
$233$	1.18712e7	+	1.63392e7i	0.938481	+	1.29171i	−0.0179775	+	0.999838i	$0.505723\pi$
$234$	1.19449e6	+	3.67626e6i	0.0932255	+	0.286919i
$235$	7.02148e6	−	2.16099e7i	0.541034	−	1.66513i
$236$	−3.69479e6	−	2.68442e6i	−0.281096	−	0.204228i
$237$	−1.21817e6	+	1.67667e6i	−0.0915090	+	0.125951i
$238$	−8.03085e6	−	2.60938e6i	−0.595704	−	0.193556i
$239$	−8.86804e6	+	2.88140e6i	−0.649582	+	0.211062i	−0.615230	−	0.788348i	$-0.710937\pi$
$239$	−8.86804e6	+	2.88140e6i	−0.649582	+	0.211062i	−0.0343520	+	0.999410i	$0.510937\pi$
$240$	642583.	−	466864.i	0.0464831	−	0.0337720i
$241$			3.27194e6i			0.233752i	0.993147	+	0.116876i	$0.0372879\pi$
$241$			3.27194e6i			0.233752i	−0.993147	+	0.116876i	$0.962712\pi$
$242$	7.77504e6	+	629355.i	0.548601	+	0.0444068i
$243$	−7.36395e6			−0.513207
$244$	841107.	+	1.15768e6i	0.0579004	+	0.0796931i
$245$	−4.66093e6	−	1.43449e7i	−0.316938	−	0.975434i
$246$	−387622.	+	1.19298e6i	−0.0260378	+	0.0801360i
$247$	−5.51094e6	−	4.00394e6i	−0.365709	−	0.265703i
$248$	−7.48636e6	+	1.03041e7i	−0.490812	+	0.675545i
$249$	−1.82151e6	−	591845.i	−0.117987	−	0.0383363i
$250$	−1.56945e7	+	5.09946e6i	−1.00445	+	0.326365i
$251$	2.20784e7	−	1.60409e7i	1.39620	−	1.01440i	0.401044	−	0.916059i	$-0.368647\pi$
$251$	2.20784e7	−	1.60409e7i	1.39620	−	1.01440i	0.995153	−	0.0983378i	$-0.0313526\pi$
$252$		−	1.35888e7i		−	0.849141i
$253$	−849259.	−	1.84760e6i	−0.0524419	−	0.114090i
$254$	1.34990e7			0.823758
$255$	2.76804e6	+	3.80988e6i	0.166936	+	0.229768i
$256$	−4.34967e6	−	1.33869e7i	−0.259261	−	0.797922i
$257$	−49372.2	+	151952.i	−0.00290859	+	0.00895172i	−0.952500	−	0.304538i	$-0.901498\pi$
$257$	−49372.2	+	151952.i	−0.00290859	+	0.00895172i	0.949592	+	0.313489i	$0.101498\pi$
$258$	−1.29444e6	−	940463.i	−0.0753740	−	0.0547624i
$259$	−1.13060e7	+	1.55614e7i	−0.650745	+	0.895673i
$260$	1.15993e7	+	3.76885e6i	0.659953	+	0.214432i
$261$	−8.76724e6	+	2.84865e6i	−0.493107	+	0.160220i
$262$	7.17225e6	−	5.21095e6i	0.398797	−	0.289743i
$263$		−	7.88255e6i		−	0.433311i	−0.976248	−	0.216655i	$-0.930485\pi$
$263$		−	7.88255e6i		−	0.433311i	0.976248	−	0.216655i	$-0.0695148\pi$
$264$	−1.50284e6	+	2.67652e6i	−0.0816774	+	0.145465i
$265$	1.77756e7			0.955185
$266$	−6.11708e6	−	8.41944e6i	−0.325012	−	0.447340i
$267$	−823131.	−	2.53334e6i	−0.0432449	−	0.133094i
$268$	−1.12289e6	+	3.45589e6i	−0.0583354	+	0.179538i
$269$	−1.87407e7	−	1.36159e7i	−0.962783	−	0.699503i	−0.00898758	−	0.999960i	$-0.502861\pi$
$269$	−1.87407e7	−	1.36159e7i	−0.962783	−	0.699503i	−0.953795	+	0.300457i	$0.902861\pi$
$270$	3.93551e6	−	5.41676e6i	0.199944	−	0.275200i
$271$	6.95544e6	+	2.25996e6i	0.349475	+	0.113551i	0.478494	−	0.878091i	$-0.341183\pi$
$271$	6.95544e6	+	2.25996e6i	0.349475	+	0.113551i	−0.129019	+	0.991642i	$0.541183\pi$
$272$	−3.16698e6	+	1.02901e6i	−0.157376	+	0.0511346i
$273$	−2.09451e6	+	1.52175e6i	−0.102943	+	0.0747921i
$274$		−	1.70332e6i		−	0.0828030i
$275$	−3.19715e7	+	2.94881e7i	−1.53732	+	1.41791i
$276$	328672.			0.0156328
$277$	1.36455e6	+	1.87814e6i	0.0642023	+	0.0883669i	0.839911	−	0.542725i	$-0.182607\pi$
$277$	1.36455e6	+	1.87814e6i	0.0642023	+	0.0883669i	−0.775708	+	0.631091i	$0.782607\pi$
$278$	544490.	+	1.67577e6i	0.0253429	+	0.0779974i
$279$	5.80817e6	−	1.78757e7i	0.267440	−	0.823096i
$280$	3.67000e7	+	2.66641e7i	1.67183	+	1.21466i
$281$	−2.04506e7	+	2.81478e7i	−0.921693	+	1.26860i	0.0413202	+	0.999146i	$0.486844\pi$
$281$	−2.04506e7	+	2.81478e7i	−0.921693	+	1.26860i	−0.963013	+	0.269455i	$0.913156\pi$
$282$	−2.08780e6	−	678367.i	−0.0930982	−	0.0302494i
$283$	1.60928e7	−	5.22887e6i	0.710023	−	0.230700i	0.0683307	−	0.997663i	$-0.478233\pi$
$283$	1.60928e7	−	5.22887e6i	0.710023	−	0.230700i	0.641692	+	0.766962i	$0.278233\pi$
$284$	−1.91281e6	+	1.38974e6i	−0.0835060	+	0.0606706i
$285$			5.80394e6i			0.250720i
$286$	−7.24047e6	+	848782.i	−0.309506	+	0.0362826i
$287$	2.54968e7			1.07855
$288$	1.40655e7	+	1.93595e7i	0.588814	+	0.810434i
$289$	1.35789e6	+	4.17914e6i	0.0562561	+	0.173138i
$290$	3.90608e6	−	1.20217e7i	0.160157	−	0.492914i
$291$	5.88406e6	+	4.27502e6i	0.238780	+	0.173484i
$292$	1.22808e7	−	1.69031e7i	0.493264	−	0.678920i
$293$	−2.08451e7	−	6.77297e6i	−0.828706	−	0.269263i	−0.136206	−	0.990681i	$-0.543491\pi$
$293$	−2.08451e7	−	6.77297e6i	−0.828706	−	0.269263i	−0.692500	+	0.721418i	$0.743491\pi$
$294$	−1.38590e6	+	450307.i	−0.0545369	+	0.0177201i
$295$	−1.82021e7	+	1.32246e7i	−0.709016	+	0.515130i
$296$		−	2.13135e7i		−	0.821824i
$297$	1.80664e6	−	9.02999e6i	0.0689610	−	0.344681i
$298$	7.95107e6			0.300453
$299$	1.11702e6	+	1.53744e6i	0.0417874	+	0.0575155i
$300$	−2.17242e6	−	6.68602e6i	−0.0804600	−	0.247630i
$301$	−1.00500e7	+	3.09306e7i	−0.368523	+	1.13420i
$302$	−2.22202e7	−	1.61439e7i	−0.806726	−	0.586121i
$303$	4.92513e6	−	6.77886e6i	0.177047	−	0.243685i
$304$	−3.90315e6	−	1.26821e6i	−0.138930	−	0.0451410i
$305$	6.70457e6	−	2.17845e6i	0.236304	−	0.0767799i
$306$	−1.11707e7	+	8.11599e6i	−0.389867	+	0.283255i
$307$		−	4.05672e7i		−	1.40204i	−0.713143	−	0.701018i	$-0.752729\pi$
$307$		−	4.05672e7i		−	1.40204i	0.713143	−	0.701018i	$-0.247271\pi$
$308$	2.51298e7	+	5.02776e6i	0.860076	+	0.172077i
$309$	1.49491e6			0.0506687
$310$	1.51488e7	+	2.08505e7i	0.508502	+	0.699892i
$311$	−36417.8	−	112082.i	−0.00121069	−	0.00372611i	0.950449	−	0.310879i	$-0.100624\pi$
$311$	−36417.8	−	112082.i	−0.00121069	−	0.00372611i	−0.951660	+	0.307153i	$0.900624\pi$
$312$	886483.	−	2.72831e6i	0.0291881	−	0.0898319i
$313$	−2.92669e6	−	2.12636e6i	−0.0954428	−	0.0693432i	0.539040	−	0.842280i	$-0.318787\pi$
$313$	−2.92669e6	−	2.12636e6i	−0.0954428	−	0.0693432i	−0.634483	+	0.772937i	$0.718787\pi$
$314$	677434.	−	932408.i	0.0218816	−	0.0301174i
$315$	−6.36678e7	−	2.06869e7i	−2.03699	−	0.661857i
$316$	−1.82344e7	+	5.92473e6i	−0.577872	+	0.187762i
$317$	1.80750e7	−	1.31322e7i	0.567414	−	0.412251i	−0.266751	−	0.963766i	$-0.585950\pi$
$317$	1.80750e7	−	1.31322e7i	0.567414	−	0.412251i	0.834165	+	0.551515i	$0.185950\pi$
$318$		−	1.71736e6i		−	0.0534047i
$319$	−2.02420e6	−	1.72673e7i	−0.0623564	−	0.531926i
$320$	−2.22712e7			−0.679663
$321$	563072.	+	775002.i	0.0170235	+	0.0234308i
$322$	897181.	+	2.76124e6i	0.0268728	+	0.0827058i
$323$	7.51923e6	−	2.31418e7i	0.223134	−	0.686736i
$324$	−1.73647e7	−	1.26162e7i	−0.510543	−	0.370931i
$325$	2.38923e7	−	3.28849e7i	0.695997	−	0.957957i
$326$	2.09343e7	+	6.80196e6i	0.604235	+	0.196328i
$327$	−9.67685e6	+	3.14420e6i	−0.276752	+	0.0899222i
$328$	−2.28563e7	+	1.66061e7i	−0.647715	+	0.470593i
$329$			4.46212e7i			1.25301i
$330$	4.21117e6	+	4.56582e6i	0.117182	+	0.127051i
$331$	5.24977e7			1.44763			0.723813	−	0.689996i	$-0.242388\pi$
$331$	5.24977e7			1.44763			0.723813	+	0.689996i	$0.242388\pi$
$332$	−1.04145e7	−	1.43344e7i	−0.284594	−	0.391710i
$333$	9.71944e6	+	2.99134e7i	0.263214	+	0.810089i
$334$	−7.58279e6	+	2.33374e7i	−0.203512	+	0.626345i
$335$	1.44825e7	+	1.05222e7i	0.385221	+	0.279879i
$336$	−916821.	+	1.26190e6i	−0.0241695	+	0.0332664i
$337$	5.64793e7	+	1.83512e7i	1.47570	+	0.479485i	0.932826	−	0.360326i	$-0.117335\pi$
$337$	5.64793e7	+	1.83512e7i	1.47570	+	0.479485i	0.542878	+	0.839811i	$0.317335\pi$
$338$	−1.37334e7	+	4.46226e6i	−0.355655	+	0.115559i
$339$	−3.51333e6	+	2.55258e6i	−0.0901819	+	0.0655210i
$340$			4.35662e7i			1.10844i
$341$	3.09086e7	+	1.73549e7i	0.779499	+	0.437683i
$342$	−1.70174e7			−0.425417
$343$	−1.24359e7	−	1.71165e7i	−0.308173	−	0.424164i
$344$	−1.11359e7	−	3.42729e7i	−0.273559	−	0.841929i
$345$	500354.	−	1.53993e6i	0.0121849	−	0.0375011i
$346$	−7.87902e6	−	5.72444e6i	−0.190215	−	0.138199i
$347$	−1.84118e7	+	2.53416e7i	−0.440663	+	0.606521i	−0.970359	−	0.241667i	$-0.922306\pi$
$347$	−1.84118e7	+	2.53416e7i	−0.440663	+	0.606521i	0.529696	+	0.848187i	$0.322306\pi$
$348$	2.67255e6	+	868364.i	0.0634144	+	0.0206046i
$349$	1.40794e7	−	4.57468e6i	0.331214	−	0.107618i	−0.138689	−	0.990336i	$-0.544289\pi$
$349$	1.40794e7	−	4.57468e6i	0.331214	−	0.107618i	0.469903	+	0.882718i	$0.344289\pi$
$350$	5.02404e7	−	3.65018e7i	1.17179	−	0.851354i
$351$			8.60636e6i			0.199021i
$352$	−4.10057e7	+	1.88485e7i	−0.940192	+	0.432164i
$353$	−7.93118e7			−1.80307			−0.901537	−	0.432702i	$-0.857560\pi$
$353$	−7.93118e7			−1.80307			−0.901537	+	0.432702i	$0.857560\pi$
$354$	1.27767e6	+	1.75856e6i	0.0288011	+	0.0396413i
$355$	3.59939e6	+	1.10778e7i	0.0804534	+	0.247610i
$356$	7.61492e6	−	2.34363e7i	0.168778	−	0.519444i
$357$	−7.48179e6	−	5.43584e6i	−0.164437	−	0.119471i
$358$	1.27545e7	−	1.75551e7i	0.277981	−	0.382607i
$359$	6.16902e7	+	2.00444e7i	1.33332	+	0.433220i	0.887047	−	0.461679i	$-0.152753\pi$
$359$	6.16902e7	+	2.00444e7i	1.33332	+	0.433220i	0.446268	+	0.894899i	$0.352753\pi$
$360$	7.05477e7	−	2.29223e7i	1.51208	−	0.491305i
$361$	−1.37993e7	+	1.00258e7i	−0.293317	+	0.213107i
$362$			4.77127e7i			1.00579i
$363$	7.88545e6	+	3.28688e6i	0.164857	+	0.0687169i
$364$	−2.39509e7			−0.496612
$365$	−6.05007e7	−	8.32720e7i	−1.24418	−	1.71246i
$366$	−210467.	−	647749.i	−0.00429279	−	0.0132119i
$367$	−1.88121e7	+	5.78976e7i	−0.380574	+	1.17129i	0.559067	+	0.829122i	$0.311159\pi$
$367$	−1.88121e7	+	5.78976e7i	−0.380574	+	1.17129i	−0.939641	+	0.342163i	$0.888841\pi$
$368$	926273.	+	672977.i	0.0185864	+	0.0135038i
$369$	2.45059e7	−	3.37295e7i	0.487744	−	0.671323i
$370$	−4.10173e7	−	1.33273e7i	−0.809771	−	0.263111i
$371$	−3.31991e7	+	1.07870e7i	−0.650136	+	0.211242i
$372$	−4.63529e6	+	3.36774e6i	−0.0900426	+	0.0654198i
$373$		−	8.30651e7i		−	1.60063i	−0.599577	−	0.800317i	$-0.704665\pi$
$373$		−	8.30651e7i		−	1.60063i	0.599577	−	0.800317i	$-0.295335\pi$
$374$	−1.08758e7	−	2.36608e7i	−0.207897	−	0.452288i
$375$	−1.80732e7			−0.342721
$376$	−2.90618e7	−	4.00001e7i	−0.546712	−	0.752485i
$377$	5.02087e6	+	1.54526e7i	0.0937033	+	0.288389i
$378$	−4.06311e6	+	1.25050e7i	−0.0752287	+	0.231530i
$379$	2.44463e7	+	1.77613e7i	0.449051	+	0.326254i	0.789221	−	0.614109i	$-0.210485\pi$
$379$	2.44463e7	+	1.77613e7i	0.449051	+	0.326254i	−0.340170	+	0.940364i	$0.610485\pi$
$380$	−3.15601e7	+	4.34387e7i	−0.575158	+	0.791638i
$381$	1.40605e7	+	4.56852e6i	0.254229	+	0.0826040i
$382$	2.61354e7	−	8.49192e6i	0.468856	−	0.152341i
$383$	2.82748e7	−	2.05429e7i	0.503273	−	0.365649i	−0.306993	−	0.951712i	$-0.599323\pi$
$383$	2.82748e7	−	2.05429e7i	0.503273	−	0.365649i	0.810266	+	0.586063i	$0.199323\pi$
$384$		−	8.31300e6i		−	0.146813i
$385$	6.18129e7	−	1.10087e8i	1.08317	−	1.92909i
$386$	6.24757e6			0.108630
$387$	3.12585e7	+	4.30236e7i	0.539306	+	0.742291i
$388$	2.07921e7	+	6.39915e7i	0.355962	+	1.09554i
$389$	−3.46526e6	+	1.06650e7i	−0.0588691	+	0.181180i	−0.976167	−	0.217022i	$-0.930366\pi$
$389$	−3.46526e6	+	1.06650e7i	−0.0588691	+	0.181180i	0.917298	+	0.398202i	$0.130366\pi$
$390$	−4.69626e6	−	3.41204e6i	−0.0791696	−	0.0575201i
$391$	−3.99008e6	+	5.49188e6i	−0.0667501	+	0.0918736i
$392$	−3.12143e7	−	1.01421e7i	−0.518198	−	0.168373i
$393$	9.23415e6	−	3.00036e6i	0.152132	−	0.0494305i
$394$	4.15995e6	−	3.02238e6i	0.0680142	−	0.0494152i
$395$			9.44536e7i			1.53259i
$396$	3.08044e7	−	2.84117e7i	0.496053	−	0.457522i
$397$	−9.00645e7			−1.43940			−0.719701	−	0.694284i	$-0.755721\pi$
$397$	−9.00645e7			−1.43940			−0.719701	+	0.694284i	$0.755721\pi$
$398$	3.23735e7	+	4.45583e7i	0.513500	+	0.706773i
$399$	−3.52209e6	−	1.08399e7i	−0.0554475	−	0.170650i
$400$	7.56767e6	−	2.32909e7i	0.118245	−	0.363920i
$401$	1.19697e7	+	8.69650e6i	0.185631	+	0.134869i	0.676720	−	0.736241i	$-0.263401\pi$
$401$	1.19697e7	+	8.69650e6i	0.185631	+	0.134869i	−0.491089	+	0.871110i	$0.663401\pi$
$402$	1.01658e6	−	1.39920e6i	0.0156481	−	0.0215378i
$403$	−3.15067e7	−	1.02371e7i	−0.481380	−	0.156410i
$404$	7.37227e7	−	2.39540e7i	1.11804	−	0.363273i
$405$	−8.55460e7	+	6.21528e7i	−1.28776	+	0.935611i
$406$			2.48230e7i			0.370916i
$407$	−5.89149e7	+	6.90645e6i	−0.873860	+	0.102440i
$408$	1.02473e7			0.150879
$409$	9.97836e6	+	1.37340e7i	0.145844	+	0.200737i	0.875689	−	0.482876i	$-0.160408\pi$
$409$	9.97836e6	+	1.37340e7i	0.145844	+	0.200737i	−0.729845	+	0.683613i	$0.760408\pi$
$410$	1.76660e7	+	5.43702e7i	0.256322	+	0.788877i
$411$	576464.	−	1.77417e6i	0.00830323	−	0.0255547i
$412$	1.11884e7	+	8.12887e6i	0.159984	+	0.116235i
$413$	2.59704e7	−	3.57451e7i	0.368661	−	0.507419i
$414$	4.51514e6	+	1.46706e6i	0.0636313	+	0.0206750i
$415$	−8.30157e7	+	2.69734e7i	−1.16149	+	0.377391i
$416$	3.41220e7	−	2.47911e7i	0.473974	−	0.344362i
$417$			1.92975e6i			0.0266129i
$418$	6.29631e6	−	3.14703e7i	0.0862099	−	0.430895i
$419$	2.56959e7			0.349318			0.174659	−	0.984629i	$-0.444118\pi$
$419$	2.56959e7			0.349318			0.174659	+	0.984629i	$0.444118\pi$
$420$	1.19949e7	+	1.65095e7i	0.161900	+	0.222836i
$421$	−3.07935e6	−	9.47727e6i	−0.0412680	−	0.127010i	0.928300	−	0.371832i	$-0.121270\pi$
$421$	−3.07935e6	−	9.47727e6i	−0.0412680	−	0.127010i	−0.969568	+	0.244822i	$0.921270\pi$
$422$	1.08028e7	−	3.32475e7i	0.143747	−	0.442407i
$423$	5.90291e7	+	4.28872e7i	0.779911	+	0.566639i
$424$	2.27353e7	−	3.12925e7i	0.298266	−	0.410528i
$425$	1.38092e8	+	4.48687e7i	1.79887	+	0.584490i
$426$	1.07026e6	−	347749.i	0.0138440	−	0.00449818i
$427$	−1.12000e7	+	8.13725e6i	−0.143858	+	0.104519i
$428$			8.86220e6i			0.113034i
$429$	−7.82889e6	−	1.56634e6i	−0.0991581	−	0.0198387i
$430$	−7.29208e7			−0.917162
$431$	−8.21900e7	−	1.13125e8i	−1.02657	−	1.41295i	−0.907496	−	0.420061i	$-0.862009\pi$
$431$	−8.21900e7	−	1.13125e8i	−1.02657	−	1.41295i	−0.119070	−	0.992886i	$-0.537991\pi$
$432$	1.60230e6	+	4.93136e6i	0.0198743	+	0.0611668i
$433$	2.66302e6	−	8.19593e6i	0.0328028	−	0.100957i	−0.933315	−	0.359060i	$-0.883097\pi$
$433$	2.66302e6	−	8.19593e6i	0.0328028	−	0.100957i	0.966117	+	0.258103i	$0.0830974\pi$
$434$	−4.09460e7	−	2.97490e7i	−0.500889	−	0.363917i
$435$	8.13711e6	−	1.11998e7i	0.0988559	−	0.136063i
$436$	−8.95221e7	−	2.90875e7i	−1.08012	−	0.350951i
$437$	−7.95683e6	+	2.58533e6i	−0.0953445	+	0.0309793i
$438$	−8.04517e6	+	5.84516e6i	−0.0957443	+	0.0695623i
$439$		−	2.28257e7i		−	0.269793i	−0.990860	−	0.134897i	$-0.956930\pi$
$439$		−	2.28257e7i		−	0.269793i	0.990860	−	0.134897i	$-0.0430703\pi$
$440$	1.62882e7	+	1.38945e8i	0.191212	+	1.63112i
$441$	4.84342e7			0.564724
$442$	1.43048e7	+	1.96889e7i	0.165659	+	0.228010i
$443$	−4.89646e7	−	1.50697e8i	−0.563210	−	1.73338i	−0.673210	−	0.739452i	$-0.735085\pi$
$443$	−4.89646e7	−	1.50697e8i	−0.563210	−	1.73338i	0.109999	−	0.993932i	$-0.464915\pi$
$444$	2.96281e6	−	9.11859e6i	0.0338497	−	0.104179i
$445$	−9.82138e7	−	7.13565e7i	−1.11453	−	0.809755i
$446$	−1.14814e7	+	1.58028e7i	−0.129416	+	0.178126i
$447$	8.28180e6	+	2.69092e6i	0.0927261	+	0.0301285i
$448$	4.15953e7	−	1.35151e7i	0.462605	−	0.150310i
$449$	6.40803e7	−	4.65571e7i	0.707922	−	0.514336i	−0.174580	−	0.984643i	$-0.555857\pi$
$449$	6.40803e7	−	4.65571e7i	0.707922	−	0.514336i	0.882503	+	0.470307i	$0.155857\pi$
$450$		−	1.01546e8i		−	1.11436i
$451$	5.33090e7	+	5.77985e7i	0.581127	+	0.630068i
$452$	−4.01751e7			−0.435053
$453$	−1.76808e7	−	2.43355e7i	−0.190198	−	0.261785i
$454$	−9.45967e6	−	2.91139e7i	−0.101090	−	0.311123i
$455$	−3.64616e7	+	1.12217e8i	−0.387081	+	1.19131i
$456$	1.02174e7	+	7.42334e6i	0.107757	+	0.0782898i
$457$	−5.36779e7	+	7.38813e7i	−0.562402	+	0.774080i	−0.991629	−	0.129116i	$-0.958786\pi$
$457$	−5.36779e7	+	7.38813e7i	−0.562402	+	0.774080i	0.429227	+	0.903196i	$0.358786\pi$
$458$	6.50404e7	+	2.11329e7i	0.676997	+	0.219970i
$459$	−2.92381e7	+	9.50003e6i	−0.302350	+	0.0982396i
$460$	1.21185e7	−	8.80462e6i	0.124502	−	0.0904559i
$461$			3.30074e7i			0.336906i	0.985710	+	0.168453i	$0.0538772\pi$
$461$			3.30074e7i			0.336906i	−0.985710	+	0.168453i	$0.946123\pi$
$462$	−1.06358e7	−	5.97194e6i	−0.107856	−	0.0605605i
$463$	1.16798e8			1.17677			0.588385	−	0.808581i	$-0.299764\pi$
$463$	1.16798e8			1.17677			0.588385	+	0.808581i	$0.299764\pi$
$464$	5.75382e6	+	7.91946e6i	0.0575973	+	0.0792759i
$465$	8.72235e6	+	2.68446e7i	0.0867511	+	0.266992i
$466$	2.74803e7	−	8.45756e7i	0.271559	−	0.835771i
$467$	−8.86108e6	−	6.43795e6i	−0.0870034	−	0.0632116i	0.543433	−	0.839452i	$-0.317124\pi$
$467$	−8.86108e6	−	6.43795e6i	−0.0870034	−	0.0632116i	−0.630437	+	0.776241i	$0.717124\pi$
$468$	−2.30201e7	+	3.16845e7i	−0.224580	+	0.309107i
$469$	−3.34339e7	−	1.08633e7i	−0.324092	−	0.105304i
$470$	−9.51518e7	+	3.09167e7i	−0.916481	+	0.297783i
$471$	1.02117e6	−	741925.i	0.00977318	−	0.00710063i
$472$			4.89578e7i			0.465582i
$473$	−9.11290e7	+	4.18879e7i	−0.861139	+	0.395827i
$474$	9.12545e6			0.0856879
$475$	1.05184e8	+	1.44774e8i	0.981453	+	1.35085i
$476$	−2.64379e7	−	8.13674e7i	−0.245135	−	0.754449i
$477$	−1.76388e7	+	5.42867e7i	−0.162523	+	0.500194i
$478$	3.32157e7	+	2.41326e7i	0.304130	+	0.220964i
$479$	6.24833e7	−	8.60009e7i	0.568535	−	0.782522i	−0.423845	−	0.905735i	$-0.639320\pi$
$479$	6.24833e7	−	8.60009e7i	0.568535	−	0.782522i	0.992380	+	0.123213i	$0.0393198\pi$
$480$	−3.41773e7	−	1.11049e7i	−0.309040	−	0.100413i
$481$	5.27236e7	−	1.71309e7i	0.473772	−	0.153938i
$482$	1.16554e7	−	8.46816e6i	0.104085	−	0.0756219i
$483$			3.17973e6i			0.0282195i
$484$	4.11444e7	+	6.74788e7i	0.362890	+	0.595156i
$485$	3.31473e8			2.90551
$486$	1.90587e7	+	2.62321e7i	0.166030	+	0.228520i
$487$	5.59915e7	+	1.72324e8i	0.484769	+	1.49197i	0.832315	+	0.554303i	$0.187015\pi$
$487$	5.59915e7	+	1.72324e8i	0.484769	+	1.49197i	−0.347545	+	0.937663i	$0.612985\pi$
$488$	4.74028e6	−	1.45891e7i	0.0407892	−	0.125536i
$489$	1.95030e7	+	1.41698e7i	0.166792	+	0.121182i
$490$	−3.90367e7	+	5.37294e7i	−0.331806	+	0.456692i
$491$	−1.30913e8	−	4.25364e7i	−1.10596	−	0.359348i	−0.301567	−	0.953445i	$-0.597510\pi$
$491$	−1.30913e8	−	4.25364e7i	−1.10596	−	0.359348i	−0.804394	+	0.594097i	$0.797510\pi$
$492$	−1.20871e7	+	3.92733e6i	−0.101491	+	0.0329763i
$493$	−4.69545e7	+	3.41144e7i	−0.391865	+	0.284707i
$494$			2.99939e7i			0.248801i
$495$	−8.62225e7	−	1.87581e8i	−0.710895	−	1.54658i
$496$	−1.99589e7			−0.163566
$497$	−1.34450e7	−	1.85054e7i	−0.109519	−	0.150741i
$498$	2.60599e6	+	8.02040e6i	0.0211001	+	0.0649394i
$499$	4.60144e7	−	1.41618e8i	0.370333	−	1.13977i	−0.576241	−	0.817280i	$-0.695481\pi$
$499$	4.60144e7	−	1.41618e8i	0.370333	−	1.13977i	0.946574	−	0.322488i	$-0.104519\pi$
$500$	−1.35266e8	−	9.82764e7i	−1.08213	−	0.786212i
$501$	−1.57964e7	+	2.17419e7i	−0.125616	+	0.172895i
$502$	−1.14283e8	−	3.71328e7i	−0.903379	−	0.293526i
$503$	−1.29801e8	+	4.21749e7i	−1.01994	+	0.331398i	−0.770805	−	0.637071i	$-0.780146\pi$
$503$	−1.29801e8	+	4.21749e7i	−1.01994	+	0.331398i	−0.249133	+	0.968469i	$0.580146\pi$
$504$	−1.17850e8	+	8.56229e7i	−0.920528	+	0.668803i
$505$		−	3.81880e8i		−	2.96519i
$506$	−4.38360e6	+	7.80706e6i	−0.0338360	+	0.0602609i
$507$	−1.58149e7			−0.121351
$508$	8.03912e7	+	1.10649e8i	0.613222	+	0.844027i
$509$	1.91519e7	+	5.89435e7i	0.145231	+	0.446974i	0.997041	−	0.0768770i	$-0.0244949\pi$
$509$	1.91519e7	+	5.89435e7i	0.145231	+	0.446974i	−0.851810	+	0.523851i	$0.824495\pi$
$510$	6.40767e6	−	1.97208e7i	0.0483047	−	0.148667i
$511$	1.63529e8	+	1.18810e8i	1.22555	+	0.890414i
$512$	2.84186e7	−	3.91148e7i	0.211735	−	0.291428i
$513$	−3.60345e7	−	1.17083e7i	−0.266911	−	0.0867247i
$514$	669068.	−	217394.i	0.00492698	−	0.00160087i
$515$	5.51190e7	−	4.00463e7i	0.403533	−	0.293184i
$516$		−	1.62111e7i		−	0.117995i
$517$	−1.01152e8	+	9.32946e7i	−0.731983	+	0.675126i
$518$	8.46946e7			0.609349
$519$	−6.26940e6	−	8.62909e6i	−0.0448460	−	0.0617253i
$520$	−4.04016e7	−	1.24343e8i	−0.287335	−	0.884326i
$521$	−3.02270e7	+	9.30291e7i	−0.213738	+	0.657818i	0.785503	+	0.618858i	$0.212404\pi$
$521$	−3.02270e7	+	9.30291e7i	−0.213738	+	0.657818i	−0.999241	+	0.0389599i	$0.987596\pi$
$522$	3.28382e7	+	2.38583e7i	0.230870	+	0.167737i
$523$	4.58380e7	−	6.30906e7i	0.320421	−	0.441021i	−0.618175	−	0.786041i	$-0.712128\pi$
$523$	4.58380e7	−	6.30906e7i	0.320421	−	0.441021i	0.938596	+	0.345019i	$0.112128\pi$
$524$	8.54266e7	+	2.77568e7i	0.593744	+	0.192919i
$525$	6.46836e7	−	2.10170e7i	0.447009	−	0.145242i
$526$	−2.80795e7	+	2.04009e7i	−0.192944	+	0.140182i
$527$		−	1.18337e8i		−	0.808514i
$528$	−4.77749e6	+	560054.i	−0.0324563	+	0.00380477i
$529$	−1.45702e8			−0.984233
$530$	−4.60053e7	−	6.33209e7i	−0.309016	−	0.425324i
$531$	−2.23259e7	−	6.87121e7i	−0.149116	−	0.458933i
$532$	3.25834e7	−	1.00281e8i	0.216402	−	0.666018i
$533$	−5.94498e7	−	4.31928e7i	−0.392617	−	0.285253i
$534$	−6.89397e6	+	9.48874e6i	−0.0452737	+	0.0623139i
$535$	4.15221e7	+	1.34914e7i	0.271156	+	0.0881038i
$536$	3.70467e7	−	1.20372e7i	0.240578	−	0.0781685i
$537$	1.92263e7	−	1.39687e7i	0.124157	−	0.0902055i
$538$			1.01998e8i			0.655006i
$539$	−1.79203e7	+	8.95694e7i	−0.114440	+	0.571997i
$540$	6.78376e7			0.430814
$541$	1.36789e8	+	1.88273e8i	0.863889	+	1.18904i	0.980628	+	0.195879i	$0.0627559\pi$
$541$	1.36789e8	+	1.88273e8i	0.863889	+	1.18904i	−0.116739	+	0.993163i	$0.537244\pi$
$542$	−9.95096e6	−	3.06259e7i	−0.0624982	−	0.192350i
$543$	−1.61476e7	+	4.96973e7i	−0.100858	+	0.310408i
$544$	1.21887e8	+	8.85561e7i	0.757113	+	0.550075i
$545$	−2.72568e8	+	3.75157e8i	−1.68378	+	2.31752i
$546$	1.08417e7	+	3.52267e6i	0.0666067	+	0.0216418i
$547$	5.89868e7	−	1.91660e7i	0.360407	−	0.117103i	−0.123216	−	0.992380i	$-0.539321\pi$
$547$	5.89868e7	−	1.91660e7i	0.360407	−	0.117103i	0.483623	+	0.875277i	$0.339321\pi$
$548$	1.39619e7	−	1.01439e7i	0.0848403	−	0.0616401i
$549$			2.26374e7i			0.136807i
$550$	1.87789e8	+	3.75713e7i	1.12871	+	0.225823i
$551$	−7.15302e7			−0.427597
$552$	−2.07096e6	−	2.85043e6i	−0.0123127	−	0.0169470i
$553$	−5.73186e7	−	1.76408e8i	−0.338938	−	1.04314i
$554$	3.15877e6	−	9.72170e6i	0.0185776	−	0.0571759i
$555$	−3.82130e7	−	2.77634e7i	−0.223528	−	0.162403i
$556$	−1.04934e7	+	1.44429e7i	−0.0610508	+	0.0840292i
$557$	1.97657e8	+	6.42228e7i	1.14379	+	0.371641i	0.818802	−	0.574076i	$-0.194639\pi$
$557$	1.97657e8	+	6.42228e7i	1.14379	+	0.371641i	0.324991	+	0.945717i	$0.394639\pi$
$558$	−7.87095e7	+	2.55743e7i	−0.453028	+	0.147198i
$559$	7.58310e7	−	5.50945e7i	0.434122	−	0.315408i
$560$			7.10877e7i			0.404790i
$561$	−3.32056e6	−	2.83258e7i	−0.0188071	−	0.160433i
$562$	1.53197e8			0.863062
$563$	−1.51399e8	−	2.08383e8i	−0.848396	−	1.16772i	−0.984214	−	0.176983i	$-0.943366\pi$
$563$	−1.51399e8	−	2.08383e8i	−0.848396	−	1.16772i	0.135818	−	0.990734i	$-0.456634\pi$
$564$	−6.87311e6	−	2.11533e7i	−0.0383104	−	0.117907i
$565$	−6.11606e7	+	1.88233e8i	−0.339099	+	1.04364i
$566$	−6.02764e7	−	4.37934e7i	−0.332428	−	0.241523i
$567$	1.22055e8	−	1.67994e8i	0.669586	−	0.921606i
$568$	2.41052e7	+	7.83226e6i	0.131542	+	0.0427407i
$569$	−2.84806e8	+	9.25390e7i	−1.54601	+	0.502329i	−0.953027	−	0.302887i	$-0.902050\pi$
$569$	−2.84806e8	+	9.25390e7i	−1.54601	+	0.502329i	−0.592982	+	0.805215i	$0.702050\pi$
$570$	2.06750e7	−	1.50213e7i	0.111640	−	0.0811114i
$571$			3.52614e8i			1.89405i	0.321164	+	0.947024i	$0.395926\pi$
$571$			3.52614e8i			1.89405i	−0.321164	+	0.947024i	$0.604074\pi$
$572$	−5.00769e7	−	5.42942e7i	−0.267577	−	0.290112i
$573$	3.00965e7			0.159975
$574$	−6.59885e7	−	9.08254e7i	−0.348925	−	0.480255i
$575$	−1.54272e7	−	4.74799e7i	−0.0811489	−	0.249751i
$576$	2.20998e7	−	6.80162e7i	0.115643	−	0.355914i
$577$	−5.09564e7	−	3.70220e7i	−0.265260	−	0.192723i	0.447203	−	0.894433i	$-0.352420\pi$
$577$	−5.09564e7	−	3.70220e7i	−0.265260	−	0.192723i	−0.712463	+	0.701710i	$0.752420\pi$
$578$	1.13727e7	−	1.56532e7i	0.0588953	−	0.0810624i
$579$	6.50744e6	+	2.11440e6i	0.0335255	+	0.0108931i
$580$	1.21802e8	−	3.95758e7i	0.624267	−	0.202837i
$581$	1.38678e8	−	1.00755e8i	0.707095	−	0.513734i
$582$		−	3.20246e7i		−	0.162448i
$583$	−9.38663e7	−	5.27052e7i	−0.473701	−	0.265979i
$584$	−2.23975e8			−1.12450
$585$	1.13407e8	+	1.56091e8i	0.566464	+	0.779671i
$586$	2.98225e7	+	9.17842e7i	0.148201	+	0.456116i
$587$	1.16032e8	−	3.57109e8i	0.573671	−	1.76558i	−0.0669893	−	0.997754i	$-0.521339\pi$
$587$	1.16032e8	−	3.57109e8i	0.573671	−	1.76558i	0.640660	−	0.767824i	$-0.278661\pi$
$588$	−1.19446e7	−	8.67828e6i	−0.0587544	−	0.0426876i
$589$	8.57251e7	−	1.17991e8i	0.419529	−	0.577432i
$590$	9.42183e7	+	3.06134e7i	0.458753	+	0.149058i
$591$	5.35586e6	−	1.74023e6i	0.0259458	−	0.00843030i
$592$	2.70207e7	−	1.96317e7i	0.130236	−	0.0946223i
$593$			8.28216e7i			0.397173i	0.980083	+	0.198586i	$0.0636351\pi$
$593$			8.28216e7i			0.397173i	−0.980083	+	0.198586i	$0.936365\pi$
$594$	−3.68427e7	+	1.69349e7i	−0.175789	+	0.0808024i
$595$	−4.21479e8			−2.00090
$596$	4.73515e7	+	6.51737e7i	0.223663	+	0.307846i
$597$	1.86400e7	+	5.73681e7i	0.0876039	+	0.269617i
$598$	2.58576e6	−	7.95814e6i	0.0120916	−	0.0372141i
$599$	4.46105e7	+	3.24114e7i	0.207566	+	0.150806i	0.686712	−	0.726930i	$-0.259053\pi$
$599$	4.46105e7	+	3.24114e7i	0.207566	+	0.150806i	−0.479146	+	0.877735i	$0.659053\pi$
$600$	−4.42965e7	+	6.09689e7i	−0.205076	+	0.282264i
$601$	−1.96185e8	−	6.37444e7i	−0.903738	−	0.293642i	−0.179959	−	0.983674i	$-0.557596\pi$
$601$	−1.96185e8	−	6.37444e7i	−0.903738	−	0.293642i	−0.723779	+	0.690032i	$0.757596\pi$
$602$	1.36192e8	−	4.42516e7i	0.624256	−	0.202833i
$603$	−4.65057e7	+	3.37884e7i	−0.212107	+	0.154105i
$604$		−	2.78278e8i		−	1.26290i
$605$	3.78795e8	−	9.00479e7i	1.71056	−	0.406638i
$606$	−3.68946e7			−0.165785
$607$	−1.69681e8	−	2.33546e8i	−0.758695	−	1.04425i	−0.997321	−	0.0731426i	$-0.976697\pi$
$607$	−1.69681e8	−	2.33546e8i	−0.758695	−	1.04425i	0.238627	−	0.971111i	$-0.423303\pi$
$608$	5.73789e7	+	1.76594e8i	0.255295	+	0.785716i
$609$	−8.40095e6	+	2.58555e7i	−0.0371943	+	0.114472i
$610$	−2.51123e7	−	1.82452e7i	−0.110636	−	0.0803819i
$611$	7.55905e7	−	1.04041e8i	0.331393	−	0.456123i
$612$	−1.33051e8	−	4.32309e7i	−0.580449	−	0.188599i
$613$	1.61876e7	−	5.25966e6i	0.0702748	−	0.0228337i	−0.273669	−	0.961824i	$-0.588237\pi$
$613$	1.61876e7	−	5.25966e6i	0.0702748	−	0.0228337i	0.343943	+	0.938990i	$0.388237\pi$
$614$	−1.44510e8	+	1.04992e8i	−0.624297	+	0.453579i
$615$			6.26105e7i			0.269167i
$616$	−1.14739e8	−	2.49619e8i	−0.490872	−	1.06791i
$617$	5.45778e7			0.232360			0.116180	−	0.993228i	$-0.462935\pi$
$617$	5.45778e7			0.232360			0.116180	+	0.993228i	$0.462935\pi$
$618$	−3.86900e6	−	5.32522e6i	−0.0163920	−	0.0225617i
$619$	8.67108e7	+	2.66869e8i	0.365596	+	1.12519i	0.949607	+	0.313443i	$0.101483\pi$
$619$	8.67108e7	+	2.66869e8i	0.365596	+	1.12519i	−0.584011	+	0.811746i	$0.698517\pi$
$620$	−8.06919e7	+	2.48344e8i	−0.338575	+	1.04203i
$621$	8.55150e6	+	6.21303e6i	0.0357082	+	0.0259435i
$622$	−305010.	+	419810.i	−0.00126749	+	0.00174454i
$623$	2.26734e8	+	7.36702e7i	0.937674	+	0.304669i
$624$	4.27543e6	−	1.38917e6i	0.0175965	−	0.00571745i
$625$	−2.53303e8	+	1.84035e8i	−1.03753	+	0.753809i
$626$			1.59288e7i			0.0649322i
$627$	1.72088e7	−	3.06484e7i	0.0698150	−	0.124338i
$628$	1.16772e7			0.0471475
$629$	1.16397e8	+	1.60206e8i	0.467723	+	0.643765i
$630$	9.10878e7	+	2.80340e8i	0.364283	+	1.12115i
$631$	−1.10980e8	+	3.41561e8i	−0.441729	+	1.35950i	0.444302	+	0.895877i	$0.353452\pi$
$631$	−1.10980e8	+	3.41561e8i	−0.441729	+	1.35950i	−0.886031	+	0.463626i	$0.846548\pi$
$632$	1.66278e8	+	1.20808e8i	0.658692	+	0.478568i
$633$	2.25042e7	−	3.09744e7i	0.0887265	−	0.122121i
$634$	−9.35602e7	−	3.03996e7i	−0.367133	−	0.119289i
$635$	6.40808e8	−	2.08211e8i	2.50269	−	0.813173i
$636$	1.40769e7	−	1.02275e7i	0.0547188	−	0.0397555i
$637$		−	8.53674e7i		−	0.330274i
$638$	−5.62711e7	+	5.19002e7i	−0.216682	+	0.199851i
$639$	−3.74033e7			−0.143353
$640$	−2.22692e8	−	3.06509e8i	−0.849503	−	1.16924i
$641$	−9.80928e7	−	3.01899e8i	−0.372446	−	1.14627i	−0.945186	−	0.326533i	$-0.894120\pi$
$641$	−9.80928e7	−	3.01899e8i	−0.372446	−	1.14627i	0.572740	−	0.819737i	$-0.305880\pi$
$642$	1.30344e6	−	4.01158e6i	0.00492591	−	0.0151604i
$643$	6.53068e7	+	4.74482e7i	0.245655	+	0.178479i	0.703799	−	0.710399i	$-0.251486\pi$
$643$	6.53068e7	+	4.74482e7i	0.245655	+	0.178479i	−0.458144	+	0.888878i	$0.651486\pi$
$644$	−1.72904e7	+	2.37982e7i	−0.0647362	+	0.0891018i
$645$	−7.59540e7	−	2.46789e7i	−0.283055	−	0.0919702i
$646$	−1.01897e8	+	3.31084e7i	−0.377976	+	0.122812i
$647$	−5.88912e7	+	4.27869e7i	−0.217439	+	0.157979i	−0.691173	−	0.722689i	$-0.742906\pi$
$647$	−5.88912e7	+	4.27869e7i	−0.217439	+	0.157979i	0.473734	+	0.880668i	$0.342906\pi$
$648$			2.30091e8i			0.845618i
$649$	1.35330e8	−	1.58644e7i	0.495061	−	0.0580348i
$650$	−1.78979e8			−0.651723
$651$	−3.25810e7	−	4.48439e7i	−0.118092	−	0.162540i
$652$	6.89165e7	+	2.12103e8i	0.248645	+	0.765252i
$653$	−3.83937e6	+	1.18164e7i	−0.0137886	+	0.0424369i	−0.957714	−	0.287722i	$-0.907102\pi$
$653$	−3.83937e6	+	1.18164e7i	−0.0137886	+	0.0424369i	0.943925	+	0.330159i	$0.107102\pi$
$654$	3.62451e7	+	2.63336e7i	0.129574	+	0.0941407i
$655$	2.60098e8	−	3.57995e8i	0.925579	−	1.27395i
$656$	−4.21056e7	−	1.36809e7i	−0.149152	−	0.0484623i
$657$	3.14348e8	−	1.02138e8i	1.10844	−	0.360156i
$658$	1.58951e8	−	1.15485e8i	0.557937	−	0.405365i
$659$			4.91181e8i			1.71627i	0.513425	+	0.858134i	$0.328376\pi$
$659$			4.91181e8i			1.71627i	−0.513425	+	0.858134i	$0.671624\pi$
$660$	−1.23463e7	+	6.17094e7i	−0.0429442	+	0.214644i
$661$	1.87537e8			0.649355			0.324677	−	0.945825i	$-0.394744\pi$
$661$	1.87537e8			0.649355			0.324677	+	0.945825i	$0.394744\pi$
$662$	−1.35870e8	−	1.87009e8i	−0.468328	−	0.644598i
$663$	8.23641e6	+	2.53491e7i	0.0282616	+	0.0869803i
$664$	−5.86940e7	+	1.80642e8i	−0.200488	+	0.617040i
$665$	−4.20246e8	−	3.05327e8i	−1.42902	−	1.03825i
$666$	8.14033e7	−	1.12042e8i	0.275562	−	0.379279i
$667$	1.89788e7	+	6.16658e6i	0.0639574	+	0.0207810i
$668$	−2.36451e8	+	7.68277e7i	−0.793254	+	0.257744i
$669$	−1.73071e7	+	1.25744e7i	−0.0578026	+	0.0419960i
$670$		−	7.88226e7i		−	0.262075i
$671$	−4.18634e7	−	8.37567e6i	−0.138569	−	0.0277238i
$672$	7.05711e7			0.232551
$673$	−1.39767e8	−	1.92373e8i	−0.458522	−	0.631101i	0.515680	−	0.856782i	$-0.327540\pi$
$673$	−1.39767e8	−	1.92373e8i	−0.458522	−	0.631101i	−0.974201	+	0.225680i	$0.927540\pi$
$674$	−8.08034e7	−	2.48687e8i	−0.263906	−	0.812220i
$675$	6.98659e7	−	2.15025e8i	0.227171	−	0.699162i
$676$	−1.18364e8	−	8.59964e7i	−0.383159	−	0.278382i
$677$	−1.60046e8	+	2.20284e8i	−0.515796	+	0.709933i	−0.984883	−	0.173219i	$-0.944583\pi$
$677$	−1.60046e8	+	2.20284e8i	−0.515796	+	0.709933i	0.469087	+	0.883152i	$0.344583\pi$
$678$	1.81858e7	+	5.90892e6i	0.0583502	+	0.0189591i
$679$	−6.19083e8	+	2.01152e8i	−1.97761	+	0.642563i
$680$	3.77830e8	−	2.74510e8i	1.20163	−	0.873034i
$681$		−	3.35263e7i		−	0.106156i
$682$	−1.81726e7	−	1.55020e8i	−0.0572880	−	0.488691i
$683$	−4.00959e8			−1.25846			−0.629228	−	0.777221i	$-0.716629\pi$
$683$	−4.00959e8			−1.25846			−0.629228	+	0.777221i	$0.716629\pi$
$684$	−1.01345e8	−	1.39489e8i	−0.316689	−	0.435884i
$685$	−2.62725e7	−	8.08583e7i	−0.0817390	−	0.251567i
$686$	−2.87876e7	+	8.85990e7i	−0.0891728	+	0.274446i
$687$	6.05937e7	+	4.40239e7i	0.186878	+	0.135774i
$688$	3.31932e7	−	4.56865e7i	0.101926	−	0.140289i
$689$	9.56828e7	+	3.10892e7i	0.292534	+	0.0950500i
$690$	−6.78057e6	+	2.20314e6i	−0.0206404	+	0.00670649i
$691$	6.57449e7	−	4.77665e7i	0.199264	−	0.144773i	−0.483679	−	0.875245i	$-0.660700\pi$
$691$	6.57449e7	−	4.77665e7i	0.199264	−	0.144773i	0.682943	+	0.730472i	$0.260700\pi$
$692$		−	9.86742e7i		−	0.297773i
$693$	2.74868e8	+	2.98016e8i	0.825894	+	0.895448i
$694$	1.37924e8			0.412632
$695$	5.16949e7	+	7.11519e7i	0.153990	+	0.211949i
$696$	−9.30875e6	−	2.86494e7i	−0.0276098	−	0.0849743i
$697$	8.11144e7	−	2.49644e8i	0.239552	−	0.737265i
$698$	−5.27352e7	−	3.83144e7i	−0.155072	−	0.112667i
$699$	5.72467e7	−	7.87933e7i	0.167617	−	0.230705i
$700$	5.98399e8	+	1.94432e8i	1.74460	+	0.566856i
$701$	1.14828e8	−	3.73100e7i	0.333346	−	0.108311i	−0.137562	−	0.990493i	$-0.543927\pi$
$701$	1.14828e8	−	3.73100e7i	0.333346	−	0.108311i	0.470907	+	0.882183i	$0.343927\pi$
$702$	3.06579e7	−	2.22742e7i	0.0886197	−	0.0643860i
$703$			2.44057e8i			0.702467i
$704$	1.17606e8	+	6.60347e7i	0.337062	+	0.189258i
$705$	−1.09573e8			−0.312706
$706$	2.05268e8	+	2.82527e8i	0.583320	+	0.802871i
$707$	2.31742e8	+	7.13228e8i	0.655762	+	2.01823i
$708$	−6.80569e6	+	2.09457e7i	−0.0191766	+	0.0590196i
$709$	−1.59808e8	−	1.16107e8i	−0.448393	−	0.325776i	0.340568	−	0.940220i	$-0.389381\pi$
$709$	−1.59808e8	−	1.16107e8i	−0.448393	−	0.325776i	−0.788961	+	0.614443i	$0.789381\pi$
$710$	3.01460e7	−	4.14925e7i	0.0842277	−	0.115930i
$711$	−2.88461e8	−	9.37267e7i	−0.802561	−	0.260768i
$712$	−2.51234e8	+	8.16309e7i	−0.696047	+	0.226159i
$713$	−3.29169e7	+	2.39155e7i	−0.0908135	+	0.0659799i
$714$			4.07204e7i			0.111871i
$715$	−3.30619e8	+	1.51971e8i	−0.904504	+	0.415760i
$716$	2.19854e8			0.598956
$717$	2.64300e7	+	3.63778e7i	0.0717033	+	0.0986912i
$718$	−8.82586e7	−	2.71632e8i	−0.238442	−	0.733850i
$719$	4.45804e7	−	1.37204e8i	0.119938	−	0.369131i	−0.873007	−	0.487708i	$-0.837833\pi$
$719$	4.45804e7	−	1.37204e8i	0.119938	−	0.369131i	0.992945	+	0.118577i	$0.0378331\pi$
$720$	9.40415e7	+	6.83252e7i	0.251955	+	0.183056i
$721$	−7.86424e7	+	1.08242e8i	−0.209822	+	0.288795i
$722$	7.14285e7	+	2.32085e7i	0.189784	+	0.0616646i
$723$	1.50061e7	−	4.87579e6i	0.0397058	−	0.0129012i
$724$	−3.91093e8	+	2.84146e8i	−1.03054	+	0.748731i
$725$		−	4.26835e8i		−	1.12007i
$726$	−8.69981e6	−	3.65966e7i	−0.0227353	−	0.0956380i
$727$	2.81996e8			0.733904			0.366952	−	0.930240i	$-0.380401\pi$
$727$	2.81996e8			0.733904			0.366952	+	0.930240i	$0.380401\pi$
$728$	1.50914e8	+	2.07715e8i	0.391143	+	0.538362i
$729$	−9.74107e7	−	2.99799e8i	−0.251434	−	0.773834i
$730$	−1.40052e8	+	4.31035e8i	−0.360014	+	1.10801i
$731$	2.70875e8	+	1.96803e8i	0.693454	+	0.503824i
$732$	4.05610e6	−	5.58274e6i	0.0103413	−	0.0142336i
$733$	1.26784e8	+	4.11947e7i	0.321924	+	0.104599i	0.465521	−	0.885037i	$-0.345867\pi$
$733$	1.26784e8	+	4.11947e7i	0.321924	+	0.104599i	−0.143597	+	0.989636i	$0.545867\pi$
$734$	2.54933e8	−	8.28326e7i	0.644670	−	0.209466i
$735$	−5.88443e7	+	4.27529e7i	−0.148198	+	0.107672i
$736$		−	5.18015e7i		−	0.129930i
$737$	−4.52781e7	−	9.85045e7i	−0.113106	−	0.246067i
$738$	−1.83577e8			−0.456718
$739$	1.82304e8	+	2.50919e8i	0.451712	+	0.621728i	0.972764	−	0.231796i	$-0.0744603\pi$
$739$	1.82304e8	+	2.50919e8i	0.451712	+	0.621728i	−0.521052	+	0.853525i	$0.674460\pi$
$740$	−1.35031e8	−	4.15582e8i	−0.333225	−	1.02556i
$741$	−1.01510e7	+	3.12415e7i	−0.0249490	+	0.0767851i
$742$	1.24349e8	+	9.03448e7i	0.304390	+	0.221152i
$743$	−2.21503e8	+	3.04872e8i	−0.540023	+	0.743278i	−0.988616	−	0.150458i	$-0.951925\pi$
$743$	−2.21503e8	+	3.04872e8i	−0.540023	+	0.743278i	0.448593	+	0.893736i	$0.351925\pi$
$744$	5.84138e7	+	1.89798e7i	0.141839	+	0.0460864i
$745$	3.77444e8	−	1.22639e8i	0.912818	−	0.296593i
$746$	−2.95897e8	+	2.14982e8i	−0.712728	+	0.517828i
$747$		−	2.80296e8i		−	0.672441i
$748$	1.29175e8	−	2.30056e8i	0.308655	−	0.549704i
$749$	−8.57370e7			−0.204043
$750$	4.67754e7	+	6.43808e7i	0.110875	+	0.152606i
$751$	−5.63303e7	−	1.73367e8i	−0.132991	−	0.409305i	0.862281	−	0.506430i	$-0.169035\pi$
$751$	−5.63303e7	−	1.73367e8i	−0.132991	−	0.409305i	−0.995272	+	0.0971255i	$0.969035\pi$
$752$	2.39426e7	−	7.36878e7i	0.0563013	−	0.173278i
$753$	−1.06469e8	−	7.73546e7i	−0.249368	−	0.181176i
$754$	4.20513e7	−	5.78787e7i	0.0980993	−	0.135022i
$755$	−1.30382e9	−	4.23636e8i	−3.02953	−	0.984355i
$756$	−1.26699e8	+	4.11669e7i	−0.293229	+	0.0952758i
$757$	4.46035e7	−	3.24063e7i	0.102821	−	0.0747037i	−0.535187	−	0.844734i	$-0.679759\pi$
$757$	4.46035e7	−	3.24063e7i	0.102821	−	0.0747037i	0.638008	+	0.770030i	$0.279759\pi$
$758$		−	1.33052e8i		−	0.305501i
$759$	−7.20812e6	+	6.64823e6i	−0.0164853	+	0.0152048i
$760$	5.75585e8			1.31120
$761$	5.65755e7	+	7.78694e7i	0.128373	+	0.176690i	0.868365	−	0.495925i	$-0.165171\pi$
$761$	5.65755e7	+	7.78694e7i	0.128373	+	0.176690i	−0.739992	+	0.672615i	$0.765171\pi$
$762$	−2.01159e7	−	6.19105e7i	−0.0454648	−	0.139926i
$763$	2.81406e8	−	8.66078e8i	0.633519	−	1.94977i
$764$	2.25253e8	+	1.63656e8i	0.505114	+	0.366987i
$765$	−4.05100e8	+	5.57573e8i	−0.904854	+	1.24542i
$766$	−1.46357e8	−	4.75542e7i	−0.325632	−	0.105804i
$767$	−1.21108e8	+	3.93504e7i	−0.268403	+	0.0872093i
$768$	−5.49147e7	+	3.98979e7i	−0.121229	+	0.0880777i
$769$		−	1.92663e8i		−	0.423661i	−0.977306	−	0.211831i	$-0.932057\pi$
$769$		−	1.92663e8i		−	0.423661i	0.977306	−	0.211831i	$-0.0679425\pi$
$770$	−5.52134e8	+	6.47253e7i	−1.20941	+	0.141776i
$771$	770472.			0.00168110
$772$	3.72065e7	+	5.12104e7i	0.0808662	+	0.111303i
$773$	3.80694e7	+	1.17166e8i	0.0824210	+	0.253666i	0.983772	−	0.179424i	$-0.0574234\pi$
$773$	3.80694e7	+	1.17166e8i	0.0824210	+	0.253666i	−0.901351	+	0.433090i	$0.857423\pi$
$774$	7.23596e7	−	2.22700e8i	0.156053	−	0.480283i
$775$	7.04072e8	+	5.11538e8i	1.51256	+	1.09894i
$776$	4.23959e8	−	5.83530e8i	0.907275	−	1.24876i
$777$	8.82175e7	+	2.86636e7i	0.188058	+	0.0611037i
$778$	4.69596e7	−	1.52581e7i	0.0997208	−	0.0324013i
$779$	2.61724e8	−	1.90153e8i	0.553644	−	0.402246i
$780$		−	5.88144e7i		−	0.123937i
$781$	1.38389e7	−	6.91699e7i	0.0290502	−	0.145199i
$782$	2.98901e7			0.0625040
$783$	5.31202e7	+	7.31136e7i	0.110656	+	0.152305i
$784$	−1.58934e7	−	4.89147e7i	−0.0329813	−	0.101506i
$785$	1.77767e7	−	5.47111e7i	0.0367488	−	0.113101i
$786$	−3.45870e7	−	2.51289e7i	−0.0712271	−	0.0517495i
$787$	−5.20234e8	+	7.16041e8i	−1.06727	+	1.46897i	−0.194463	+	0.980910i	$0.562296\pi$
$787$	−5.20234e8	+	7.16041e8i	−1.06727	+	1.46897i	−0.872808	+	0.488063i	$0.837704\pi$
$788$	4.95480e7	+	1.60991e7i	0.101262	+	0.0329021i
$789$	−3.61518e7	+	1.17464e7i	−0.0736036	+	0.0239153i
$790$	3.36465e8	−	2.44456e8i	0.682432	−	0.495816i
$791$		−	3.88673e8i		−	0.785334i
$792$	−4.40500e8	−	8.81316e7i	−0.886688	−	0.177401i
$793$	3.98994e7			0.0800105
$794$	2.33097e8	+	3.20831e8i	0.465667	+	0.640935i
$795$	−2.64889e7	−	8.15246e7i	−0.0527185	−	0.162251i
$796$	−1.72442e8	+	5.30721e8i	−0.341903	+	1.05227i
$797$	−2.88112e8	−	2.09326e8i	−0.569097	−	0.413473i	0.265680	−	0.964061i	$-0.414404\pi$
$797$	−2.88112e8	−	2.09326e8i	−0.569097	−	0.413473i	−0.834777	+	0.550588i	$0.814404\pi$
$798$	−2.94986e7	+	4.06013e7i	−0.0580487	+	0.0798972i
$799$	4.36895e8	+	1.41956e8i	0.856519	+	0.278300i
$800$	−1.05377e9	+	3.42391e8i	−2.05815	+	0.668733i
$801$	3.15380e8	−	2.29137e8i	0.613673	−	0.445860i
$802$		−	6.51464e7i		−	0.126290i
$803$	7.25771e7	+	6.19113e8i	0.140169	+	1.19570i
$804$	1.75231e7			0.0337166
$805$	8.51799e7	+	1.17240e8i	0.163286	+	0.224744i
$806$	4.50758e7	+	1.38729e8i	0.0860871	+	0.264949i
$807$	−3.45197e7	+	1.06241e8i	−0.0656820	+	0.202148i
$808$	−6.72268e8	−	4.88431e8i	−1.27441	−	0.925911i
$809$	1.42171e7	−	1.95682e7i	0.0268513	−	0.0369577i	−0.795380	−	0.606111i	$-0.792729\pi$
$809$	1.42171e7	−	1.95682e7i	0.0268513	−	0.0369577i	0.822232	+	0.569153i	$0.192729\pi$
$810$	4.42805e8	+	1.43876e8i	0.833216	+	0.270728i
$811$	−3.16543e7	+	1.02851e7i	−0.0593430	+	0.0192817i	−0.338538	−	0.940953i	$-0.609932\pi$
$811$	−3.16543e7	+	1.02851e7i	−0.0593430	+	0.0192817i	0.279195	+	0.960234i	$0.409932\pi$
$812$	−2.03470e8	+	1.47830e8i	−0.380042	+	0.276117i
$813$		−	3.52676e7i		−	0.0656302i
$814$	1.77081e8	+	1.91994e8i	0.328321	+	0.355971i
$815$	1.09868e9			2.02955
$816$	9.43876e6	+	1.29913e7i	0.0173718	+	0.0239102i
$817$	1.27516e8	+	3.92454e8i	0.233829	+	0.719652i
$818$	2.30987e7	−	7.10904e7i	0.0422014	−	0.129883i
$819$	−3.06530e8	−	2.22707e8i	−0.557984	−	0.405399i
$820$	−3.40457e8	+	4.68599e8i	−0.617477	+	0.849884i
$821$	2.27775e8	+	7.40085e7i	0.411601	+	0.133737i	0.507496	−	0.861654i	$-0.330571\pi$
$821$	2.27775e8	+	7.40085e7i	0.411601	+	0.133737i	−0.0958951	+	0.995391i	$0.530571\pi$
$822$	−7.81198e6	+	2.53827e6i	−0.0140652	+	0.00457006i
$823$	3.35884e8	−	2.44034e8i	0.602545	−	0.437774i	−0.244237	−	0.969716i	$-0.578537\pi$
$823$	3.35884e8	−	2.44034e8i	0.602545	−	0.437774i	0.846781	+	0.531941i	$0.178537\pi$
$824$		−	1.48252e8i		−	0.264984i
$825$	1.82885e8	+	1.02688e8i	0.325699	+	0.182877i
$826$	−1.94547e8			−0.345210
$827$	7.44382e6	+	1.02455e7i	0.0131607	+	0.0181142i	0.815547	−	0.578691i	$-0.196436\pi$
$827$	7.44382e6	+	1.02455e7i	0.0131607	+	0.0181142i	−0.802386	+	0.596805i	$0.796436\pi$
$828$	1.48640e7	+	4.57468e7i	0.0261846	+	0.0805878i
$829$	1.70484e8	−	5.24697e8i	0.299241	−	0.920969i	−0.682523	−	0.730864i	$-0.739117\pi$
$829$	1.70484e8	−	5.24697e8i	0.299241	−	0.920969i	0.981764	−	0.190105i	$-0.0608828\pi$
$830$	3.10939e8	+	2.25911e8i	0.543803	+	0.395096i
$831$	6.58032e6	−	9.05704e6i	0.0114669	−	0.0157828i
$832$	−1.19882e8	−	3.89519e7i	−0.208153	−	0.0676329i
$833$	2.90016e8	−	9.42318e7i	0.501749	−	0.163028i
$834$	6.87421e6	−	4.99440e6i	0.0118502	−	0.00860965i
$835$			1.22481e9i			2.10382i
$836$	2.95454e8	−	1.35807e8i	0.505674	−	0.232436i
$837$	−1.84264e8			−0.314242
$838$	−6.65039e7	−	9.15347e7i	−0.113009	−	0.155544i
$839$	−3.16518e8	−	9.74144e8i	−0.535936	−	1.64944i	−0.741617	−	0.670823i	$-0.765941\pi$
$839$	−3.16518e8	−	9.74144e8i	−0.535936	−	1.64944i	0.205681	−	0.978619i	$-0.434059\pi$
$840$	6.76002e7	−	2.08052e8i	0.114054	−	0.351022i
$841$	−3.43192e8	−	2.49343e8i	−0.576964	−	0.419189i
$842$	−2.57905e7	+	3.54976e7i	−0.0432040	+	0.0594652i
$843$	1.59569e8	+	5.18473e7i	0.266359	+	0.0865452i
$844$	3.36859e8	−	1.09452e8i	0.560300	−	0.182053i
$845$	−5.83111e8	+	4.23655e8i	−0.966454	+	0.702170i
$846$		−	3.21272e8i		−	0.530594i
$847$	−6.52821e8	+	3.98050e8i	−1.07434	+	0.655069i
$848$	6.06134e7			0.0993987
$849$	−4.79624e7	−	6.60146e7i	−0.0783751	−	0.107874i
$850$	−1.97564e8	−	6.08040e8i	−0.321700	−	0.990092i
$851$	2.10400e7	−	6.47545e7i	0.0341395	−	0.105071i
$852$	9.22422e6	+	6.70179e6i	0.0149146	+	0.0108361i
$853$	3.18095e8	−	4.37820e8i	0.512518	−	0.705421i	−0.471823	−	0.881693i	$-0.656404\pi$
$853$	3.18095e8	−	4.37820e8i	0.512518	−	0.705421i	0.984341	+	0.176272i	$0.0564040\pi$
$854$	5.79736e7	+	1.88368e7i	0.0930800	+	0.0302435i
$855$	−8.07831e8	+	2.62480e8i	−1.29247	+	0.419950i
$856$	7.68579e7	−	5.58406e7i	0.122537	−	0.0890284i
$857$		−	4.96898e8i		−	0.789450i	−0.918799	−	0.394725i	$-0.870840\pi$
$857$		−	4.96898e8i		−	0.789450i	0.918799	−	0.394725i	$-0.129160\pi$
$858$	1.46824e7	+	3.19422e7i	0.0232453	+	0.0505711i
$859$	1.78440e8			0.281523			0.140761	−	0.990044i	$-0.455045\pi$
$859$	1.78440e8			0.281523			0.140761	+	0.990044i	$0.455045\pi$
$860$	−4.34269e8	−	5.97720e8i	−0.682753	−	0.939729i
$861$	−3.79948e7	−	1.16936e8i	−0.0595271	−	0.183206i
$862$	−1.90260e8	+	5.85559e8i	−0.297047	+	0.914217i
$863$	5.28735e8	+	3.84148e8i	0.822631	+	0.597677i	0.917465	−	0.397816i	$-0.130232\pi$
$863$	5.28735e8	+	3.84148e8i	0.822631	+	0.597677i	−0.0948336	+	0.995493i	$0.530232\pi$
$864$	1.37892e8	−	1.89792e8i	0.213796	−	0.294264i
$865$	−4.62319e8	−	1.50217e8i	−0.714321	−	0.232097i
$866$	−3.60880e7	+	1.17257e7i	−0.0555660	+	0.0180545i
$867$	1.71433e7	−	1.24554e7i	0.0263050	−	0.0191117i
$868$		−	5.12793e8i		−	0.784121i
$869$	2.80057e8	−	4.98773e8i	0.426764	−	0.760052i
$870$	−6.09559e7			−0.0925674
$871$	5.95535e7	+	8.19683e7i	0.0901265	+	0.124049i
$872$	3.11814e8	+	9.59665e8i	0.470269	+	1.44734i
$873$	−3.28922e8	+	1.01232e9i	−0.494368	+	1.52151i
$874$	2.98027e7	+	2.16529e7i	0.0446397	+	0.0324326i
$875$	9.50772e8	−	1.30862e9i	1.41923	−	1.95340i
$876$	−9.58237e7	−	3.11350e7i	−0.142548	−	0.0463166i
$877$	1.07291e9	−	3.48610e8i	1.59062	−	0.516822i	0.625853	−	0.779941i	$-0.284751\pi$
$877$	1.07291e9	−	3.48610e8i	1.59062	−	0.516822i	0.964763	+	0.263119i	$0.0847512\pi$
$878$	−8.13106e7	+	5.90756e7i	−0.120133	+	0.0872820i
$879$			1.05695e8i			0.155628i
$880$	−1.61148e8	+	1.48631e8i	−0.236471	+	0.218103i
$881$	−5.40451e8			−0.790366			−0.395183	−	0.918602i	$-0.629319\pi$
$881$	−5.40451e8			−0.790366			−0.395183	+	0.918602i	$0.629319\pi$
$882$	−1.25353e8	−	1.72534e8i	−0.182696	−	0.251460i
$883$	−2.90938e8	−	8.95414e8i	−0.422589	−	1.30059i	−0.905284	−	0.424806i	$-0.860342\pi$
$883$	−2.90938e8	−	8.95414e8i	−0.422589	−	1.30059i	0.482695	−	0.875788i	$-0.339658\pi$
$884$	−7.61963e7	+	2.34508e8i	−0.110300	+	0.339470i
$885$	8.77767e7	+	6.37735e7i	0.126634	+	0.0920048i
$886$	−4.10093e8	+	5.64445e8i	−0.589633	+	0.811560i
$887$	−1.19204e9	−	3.87317e8i	−1.70812	−	0.555003i	−0.718105	−	0.695935i	$-0.754990\pi$
$887$	−1.19204e9	−	3.87317e8i	−1.70812	−	0.555003i	−0.990019	+	0.140931i	$0.954990\pi$
$888$	−9.77502e7	+	3.17610e7i	−0.139598	+	0.0453581i
$889$	−1.07047e9	+	7.77742e8i	−1.52359	+	1.10696i
$890$			5.34539e8i			0.758244i
$891$	6.36020e8	−	7.45590e7i	0.899161	−	0.105406i
$892$	−1.97908e8			−0.278849
$893$	3.32782e8	+	4.58035e8i	0.467311	+	0.643198i
$894$	−1.18485e7	−	3.64661e7i	−0.0165826	−	0.0510360i
$895$	3.34694e8	−	1.03008e9i	0.466852	−	1.43682i
$896$	6.01920e8	+	4.37320e8i	0.836786	+	0.607961i
$897$	5.38662e6	−	7.41405e6i	0.00746344	−	0.0102725i
$898$	−3.31694e8	−	1.07774e8i	−0.458046	−	0.148828i
$899$	−3.30845e8	+	1.07498e8i	−0.455350	+	0.147952i
$900$	8.32357e8	−	6.04743e8i	1.14178	−	0.829551i
$901$			3.59377e8i			0.491333i
$902$	6.79219e7	−	3.39488e8i	0.0925530	−	0.462599i
$903$	1.56833e8			0.212998
$904$	2.53143e8	+	3.48421e8i	0.342657	+	0.471628i
$905$	7.35931e8	+	2.26496e9i	0.992868	+	3.05573i
$906$	−4.09288e7	+	1.25966e8i	−0.0550357	+	0.169382i
$907$	−4.79416e8	−	3.48316e8i	−0.642526	−	0.466823i	0.218191	−	0.975906i	$-0.429984\pi$
$907$	−4.79416e8	−	3.48316e8i	−0.642526	−	0.466823i	−0.860717	+	0.509083i	$0.829984\pi$
$908$	1.82306e8	−	2.50923e8i	0.243525	−	0.335183i
$909$	1.16626e9	+	3.78941e8i	1.55276	+	0.504522i
$910$	4.94111e8	−	1.60546e8i	0.655692	−	0.213047i
$911$	−5.83596e8	+	4.24008e8i	−0.771894	+	0.560813i	−0.902535	−	0.430616i	$-0.858296\pi$
$911$	−5.83596e8	+	4.24008e8i	−0.771894	+	0.560813i	0.130642	+	0.991430i	$0.458296\pi$
$912$			1.97909e7i			0.0260905i
$913$	5.18351e8	+	1.03707e8i	0.681101	+	0.136269i
$914$	4.02107e8			0.526627
$915$	−1.99821e7	−	2.75029e7i	−0.0260842	−	0.0359018i
$916$	2.14116e8	+	6.58980e8i	0.278588	+	0.857405i
$917$	−2.68532e8	+	8.26456e8i	−0.348247	+	1.07180i
$918$	1.09513e8	+	7.95656e7i	0.141559	+	0.102848i
$919$	5.48446e8	−	7.54871e8i	0.706622	−	0.972582i	−0.293241	−	0.956039i	$-0.594734\pi$
$919$	5.48446e8	−	7.54871e8i	0.706622	−	0.972582i	0.999863	−	0.0165436i	$-0.00526623\pi$
$920$	−1.52717e8	−	4.96208e7i	−0.196121	−	0.0637236i
$921$	−1.86054e8	+	6.04525e7i	−0.238155	+	0.0773811i
$922$	1.17580e8	−	8.54269e7i	0.150017	−	0.108994i
$923$			6.59249e7i			0.0838386i
$924$	−1.43891e7	−	1.22745e8i	−0.0182397	−	0.155593i
$925$	−1.45634e9			−1.84008
$926$	−3.02286e8	−	4.16061e8i	−0.380702	−	0.523991i
$927$	6.76065e7	+	2.08071e8i	0.0848690	+	0.261200i
$928$	1.36861e8	−	4.21216e8i	0.171252	−	0.527061i
$929$	−5.21066e8	−	3.78577e8i	−0.649899	−	0.472179i	0.213338	−	0.976978i	$-0.431566\pi$
$929$	−5.21066e8	−	3.78577e8i	−0.649899	−	0.472179i	−0.863237	+	0.504799i	$0.831566\pi$
$930$	7.30524e7	−	1.00548e8i	0.0908209	−	0.125004i
$931$	3.57430e8	+	1.16136e8i	0.442937	+	0.143919i
$932$	8.56908e8	−	2.78426e8i	1.05849	−	0.343924i
$933$	−459775.	+	334046.i	−0.000566110	+	0.000411303i
$934$			4.82274e7i			0.0591906i
$935$	−8.81236e8	−	9.55450e8i	−1.07810	−	1.16889i
$936$	4.19835e8			0.511978
$937$	−6.83767e8	−	9.41125e8i	−0.831169	−	1.14401i	−0.987704	−	0.156334i	$-0.950032\pi$
$937$	−6.83767e8	−	9.41125e8i	−0.831169	−	1.14401i	0.156535	−	0.987672i	$-0.449968\pi$
$938$	4.78330e7	+	1.47215e8i	0.0579588	+	0.178379i
$939$	−5.39086e6	+	1.65914e7i	−0.00651120	+	0.0200394i
$940$	−8.20082e8	−	5.95824e8i	−0.987356	−	0.717356i
$941$	−6.03769e8	+	8.31016e8i	−0.724606	+	0.997334i	0.274753	+	0.961515i	$0.411404\pi$
$941$	−6.03769e8	+	8.31016e8i	−0.724606	+	0.997334i	−0.999358	+	0.0358190i	$0.988596\pi$
$942$	−5.28581e6	−	1.71747e6i	−0.00632352	−	0.00205464i
$943$	−8.58349e7	+	2.78895e7i	−0.102360	+	0.0332587i
$944$	−6.20677e7	+	4.50948e7i	−0.0737818	+	0.0536056i
$945$			6.56293e8i			0.777682i
$946$	3.85067e8	+	2.16212e8i	0.454844	+	0.255391i
$947$	−8.25669e8			−0.972200			−0.486100	−	0.873903i	$-0.661581\pi$
$947$	−8.25669e8			−0.972200			−0.486100	+	0.873903i	$0.661581\pi$
$948$	5.43453e7	+	7.47999e7i	0.0637877	+	0.0877963i
$949$	−1.80022e8	−	5.54051e8i	−0.210633	−	0.648263i
$950$	2.43488e8	−	7.49380e8i	0.283993	−	0.874040i
$951$	−8.71636e7	−	6.33281e7i	−0.101343	−	0.0736300i
$952$	−5.39079e8	+	7.41979e8i	−0.624801	+	0.859965i
$953$	7.12743e8	+	2.31584e8i	0.823482	+	0.267565i	0.690297	−	0.723526i	$-0.257480\pi$
$953$	7.12743e8	+	2.31584e8i	0.823482	+	0.267565i	0.133185	+	0.991091i	$0.457480\pi$
$954$	2.39033e8	−	7.76666e7i	0.275304	−	0.0894518i
$955$	1.10969e9	−	8.06237e8i	1.27407	−	0.925663i
$956$			4.15982e8i			0.476103i
$957$	−7.61765e7	+	3.50150e7i	−0.0869131	+	0.0399501i
$958$	−4.68069e8			−0.532370
$959$	9.81368e7	+	1.35074e8i	0.111269	+	0.153149i
$960$	3.31882e7	+	1.02143e8i	0.0375119	+	0.115450i
$961$	−5.50743e7	+	1.69501e8i	−0.0620553	+	0.190987i
$962$	−1.97479e8	−	1.43477e8i	−0.221817	−	0.161160i
$963$	−8.24052e7	+	1.13421e8i	−0.0922732	+	0.127003i
$964$	1.38824e8	+	4.51068e7i	0.154965	+	0.0503513i
$965$	2.96578e8	−	9.63640e7i	0.330033	−	0.107234i
$966$	1.13269e7	−	8.22950e6i	0.0125655	−	0.00912939i
$967$			4.94016e8i			0.546338i	0.961966	+	0.273169i	$0.0880719\pi$
$967$			4.94016e8i			0.546338i	−0.961966	+	0.273169i	$0.911928\pi$
$968$	3.25964e8	−	7.82010e8i	0.359371	−	0.862156i
$969$	−1.17341e8			−0.128967
$970$	−8.57889e8	−	1.18078e9i	−0.939974	−	1.29376i
$971$	−3.33340e8	−	1.02592e9i	−0.364108	−	1.12061i	−0.950538	−	0.310609i	$-0.899467\pi$
$971$	−3.33340e8	−	1.02592e9i	−0.364108	−	1.12061i	0.586430	−	0.810000i	$-0.300533\pi$
$972$	−1.01519e8	+	3.12443e8i	−0.110547	+	0.340230i
$973$	−1.39727e8	−	1.01518e8i	−0.151685	−	0.110206i
$974$	4.68946e8	−	6.45449e8i	0.507512	−	0.698530i
$975$	−1.86424e8	−	6.05728e7i	−0.201135	−	0.0653528i
$976$	2.28620e7	−	7.42831e6i	0.0245903	−	0.00798989i
$977$	1.16119e9	−	8.43652e8i	1.24514	−	0.904648i	0.247211	−	0.968962i	$-0.420486\pi$
$977$	1.16119e9	−	8.43652e8i	1.24514	−	0.904648i	0.997930	+	0.0643138i	$0.0204859\pi$
$978$		−	1.06147e8i		−	0.113473i
$979$	3.07055e8	+	6.68012e8i	0.327242	+	0.711929i
$980$	−6.72889e8			−0.714933
$981$	−8.75260e8	−	1.20469e9i	−0.927107	−	1.27605i
$982$	1.87294e8	+	5.76433e8i	0.197784	+	0.608715i
$983$	−3.87685e8	+	1.19317e9i	−0.408148	+	1.25615i	0.510089	+	0.860121i	$0.329612\pi$
$983$	−3.87685e8	+	1.19317e9i	−0.408148	+	1.25615i	−0.918238	+	0.396030i	$0.870388\pi$
$984$	1.10221e8	+	8.00799e7i	0.115685	+	0.0840501i
$985$	1.50859e8	−	2.07639e8i	0.157856	−	0.217270i
$986$	2.43047e8	+	7.89708e7i	0.253548	+	0.0823826i
$987$	2.04646e8	−	6.64937e7i	0.212840	−	0.0691558i
$988$	−2.45855e8	+	1.78624e8i	−0.254923	+	0.185212i
$989$		−	1.15121e8i		−	0.119005i
$990$	−4.45053e8	+	7.92625e8i	−0.458676	+	0.816888i
$991$	2.23866e8			0.230021			0.115010	−	0.993364i	$-0.463310\pi$
$991$	2.23866e8			0.230021			0.115010	+	0.993364i	$0.463310\pi$
$992$	5.30783e8	+	7.30560e8i	0.543728	+	0.748377i
$993$	−7.82312e7	−	2.40771e8i	−0.0798973	−	0.245899i
$994$	−3.11235e7	+	9.57883e7i	−0.0316905	+	0.0975334i
$995$	2.22408e9	+	1.61589e9i	2.25778	+	1.64037i
$996$	−5.02224e7	+	6.91252e7i	−0.0508299	+	0.0699614i
$997$	6.29260e8	+	2.04459e8i	0.634957	+	0.206310i	0.608770	−	0.793347i	$-0.291663\pi$
$997$	6.29260e8	+	2.04459e8i	0.634957	+	0.206310i	0.0261873	+	0.999657i	$0.491663\pi$
$998$	−6.23566e8	+	2.02609e8i	−0.627322	+	0.203829i
$999$	2.49460e8	−	1.81243e8i	0.250210	−	0.181788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.8.3	yes	20
3.2	odd	2		99.7.k.a.19.3		20
11.2	odd	10		121.7.b.c.120.8		20
11.7	odd	10	inner	11.7.d.a.7.3	✓	20
11.9	even	5		121.7.b.c.120.13		20
33.29	even	10		99.7.k.a.73.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.7.3	✓	20	11.7	odd	10	inner
11.7.d.a.8.3	yes	20	1.1	even	1	trivial
99.7.k.a.19.3		20	3.2	odd	2
99.7.k.a.73.3		20	33.29	even	10
121.7.b.c.120.8		20	11.2	odd	10
121.7.b.c.120.13		20	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.58811 - 3.56223i) q^{2} +(-1.49018 - 4.58631i) q^{3} +(13.7859 - 42.4287i) q^{4} +(-177.805 - 129.183i) q^{5} +(-12.4807 + 17.1783i) q^{6} +(410.475 + 133.371i) q^{7} +(-454.830 + 147.783i) q^{8} +(570.960 - 414.827i) q^{9} +O(q^{10})\)	\(q+(-2.58811 - 3.56223i) q^{2} +(-1.49018 - 4.58631i) q^{3} +(13.7859 - 42.4287i) q^{4} +(-177.805 - 129.183i) q^{5} +(-12.4807 + 17.1783i) q^{6} +(410.475 + 133.371i) q^{7} +(-454.830 + 147.783i) q^{8} +(570.960 - 414.827i) q^{9} +967.721i q^{10} +(555.888 + 1209.36i) q^{11} -215.135 q^{12} +(-731.150 - 1006.34i) q^{13} +(-587.255 - 1807.39i) q^{14} +(-327.510 + 1007.97i) q^{15} +(-606.298 - 440.502i) q^{16} +(2611.74 - 3594.75i) q^{17} +(-2955.42 - 960.273i) q^{18} +(5208.19 - 1692.24i) q^{19} +(-7932.25 + 5763.12i) q^{20} -2081.31i q^{21} +(2869.32 - 5110.16i) q^{22} -1527.75 q^{23} +(1355.56 + 1865.77i) q^{24} +(10097.9 + 31078.3i) q^{25} +(-1692.52 + 5209.05i) q^{26} +(-5597.44 - 4066.78i) q^{27} +(11317.5 - 15577.3i) q^{28} +(-12422.7 - 4036.37i) q^{29} +(4438.27 - 1442.08i) q^{30} +(21546.0 - 15654.1i) q^{31} +33907.0i q^{32} +(4718.12 - 4351.64i) q^{33} -19564.8 q^{34} +(-55755.1 - 76740.3i) q^{35} +(-9729.35 - 29943.9i) q^{36} +(-13771.9 + 42385.5i) q^{37} +(-19507.6 - 14173.1i) q^{38} +(-3525.85 + 4852.91i) q^{39} +(99962.0 + 32479.6i) q^{40} +(56183.8 - 18255.2i) q^{41} +(-7414.12 + 5386.67i) q^{42} +75353.2i q^{43} +(58975.0 - 6913.49i) q^{44} -155108. q^{45} +(3953.99 + 5442.21i) q^{46} +(31948.0 + 98325.7i) q^{47} +(-1116.78 + 3437.10i) q^{48} +(55521.6 + 40338.8i) q^{49} +(84573.4 - 116405. i) q^{50} +(-20378.6 - 6621.40i) q^{51} +(-52777.3 + 17148.4i) q^{52} +(-65433.1 + 47539.9i) q^{53} +30464.7i q^{54} +(57388.7 - 286841. i) q^{55} -206406. q^{56} +(-15522.3 - 21364.6i) q^{57} +(17772.8 + 54699.0i) q^{58} +(31634.5 - 97361.1i) q^{59} +(38252.0 + 27791.7i) q^{60} +(-18853.7 + 25950.0i) q^{61} +(-111527. - 36237.3i) q^{62} +(289691. - 94126.2i) q^{63} +(81981.5 - 59563.0i) q^{64} +273384. i q^{65} +(-27712.6 - 5544.50i) q^{66} -81451.8 q^{67} +(-116515. - 160369. i) q^{68} +(2276.63 + 7006.74i) q^{69} +(-129066. + 397225. i) q^{70} +(-42876.5 - 31151.6i) q^{71} +(-198385. + 273054. i) q^{72} +(445412. + 144723. i) q^{73} +(186630. - 60639.8i) q^{74} +(127487. - 92624.7i) q^{75} -244306. i q^{76} +(66884.3 + 570551. i) q^{77} +26412.5 q^{78} +(-252611. - 347689. i) q^{79} +(50897.5 + 156646. i) q^{80} +(148675. - 457576. i) q^{81} +(-210439. - 152893. i) q^{82} +(233446. - 321311. i) q^{83} +(-88307.4 - 28692.8i) q^{84} +(-928758. + 301772. i) q^{85} +(268425. - 195022. i) q^{86} +62989.2i q^{87} +(-431558. - 467902. i) q^{88} +552369. q^{89} +(401436. + 552530. i) q^{90} +(-165901. - 510592. i) q^{91} +(-21061.5 + 64820.5i) q^{92} +(-103902. - 75489.1i) q^{93} +(267574. - 368284. i) q^{94} +(-1.14465e6 - 371919. i) q^{95} +(155508. - 50527.6i) q^{96} +(-1.22017e6 + 886505. i) q^{97} -302182. i q^{98} +(819064. + 459898. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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