LMFDB - Embedded newform 69.6.g.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(5,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("69.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.g (of order $22$, degree $10$, 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:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$380$
Relative dimension:	$38$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	69.5
Dual form			69.6.g.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79794 + 9.52891i) q^{2} +(-3.60982 - 15.1647i) q^{3} +(-56.0515 - 36.0221i) q^{4} +(-6.21680 + 43.2388i) q^{5} +(154.603 + 8.03237i) q^{6} +(210.991 - 96.3564i) q^{7} +(259.904 - 225.208i) q^{8} +(-216.938 + 109.484i) q^{9} +O(q^{10})$	\(q+(-2.79794 + 9.52891i) q^{2} +(-3.60982 - 15.1647i) q^{3} +(-56.0515 - 36.0221i) q^{4} +(-6.21680 + 43.2388i) q^{5} +(154.603 + 8.03237i) q^{6} +(210.991 - 96.3564i) q^{7} +(259.904 - 225.208i) q^{8} +(-216.938 + 109.484i) q^{9} +(-394.624 - 180.219i) q^{10} +(300.233 - 88.1565i) q^{11} +(-343.930 + 980.039i) q^{12} +(-312.127 + 683.464i) q^{13} +(327.831 + 2280.11i) q^{14} +(678.146 - 61.8082i) q^{15} +(533.081 + 1167.28i) q^{16} +(24.8839 - 15.9919i) q^{17} +(-436.282 - 2373.52i) q^{18} +(-871.245 + 1355.68i) q^{19} +(1906.01 - 2199.66i) q^{20} +(-2222.86 - 2851.80i) q^{21} +3107.55i q^{22} +(990.238 + 2335.76i) q^{23} +(-4353.43 - 3128.42i) q^{24} +(1167.47 + 342.800i) q^{25} +(-5639.35 - 4886.52i) q^{26} +(2443.40 + 2894.60i) q^{27} +(-15297.3 - 2199.42i) q^{28} +(440.825 + 685.937i) q^{29} +(-1308.45 + 6634.93i) q^{30} +(1985.33 + 2291.19i) q^{31} +(-1721.61 + 247.530i) q^{32} +(-2420.66 - 4234.73i) q^{33} +(82.7617 + 281.861i) q^{34} +(2854.65 + 9722.03i) q^{35} +(16103.6 + 1677.84i) q^{36} +(3996.03 - 574.542i) q^{37} +(-10480.5 - 12095.1i) q^{38} +(11491.3 + 2266.15i) q^{39} +(8121.97 + 12638.0i) q^{40} +(-10681.6 - 1535.79i) q^{41} +(33393.9 - 13202.3i) q^{42} +(17146.3 + 14857.3i) q^{43} +(-20004.1 - 5873.74i) q^{44} +(-3385.29 - 10060.8i) q^{45} +(-25027.9 + 2900.57i) q^{46} +6812.71i q^{47} +(15777.2 - 12297.7i) q^{48} +(24226.5 - 27958.8i) q^{49} +(-6533.02 + 10165.6i) q^{50} +(-332.339 - 319.630i) q^{51} +(42115.0 - 27065.7i) q^{52} +(11339.3 + 24829.6i) q^{53} +(-34418.8 + 15184.1i) q^{54} +(1945.29 + 13529.8i) q^{55} +(33137.2 - 72560.4i) q^{56} +(23703.6 + 8318.42i) q^{57} +(-7769.64 + 2281.37i) q^{58} +(4986.67 + 2277.33i) q^{59} +(-40237.6 - 20963.8i) q^{60} +(-34667.5 + 30039.6i) q^{61} +(-27387.4 + 12507.4i) q^{62} +(-35222.6 + 44003.6i) q^{63} +(-3385.75 + 23548.4i) q^{64} +(-27611.7 - 17745.0i) q^{65} +(47125.2 - 11217.7i) q^{66} +(14366.9 - 48929.2i) q^{67} -1970.84 q^{68} +(31846.6 - 23448.4i) q^{69} -100627. q^{70} +(18930.7 - 64472.1i) q^{71} +(-31726.5 + 77311.7i) q^{72} +(-40387.3 - 25955.3i) q^{73} +(-5705.88 + 39685.3i) q^{74} +(984.116 - 18941.8i) q^{75} +(97669.2 - 44604.0i) q^{76} +(54852.1 - 47529.7i) q^{77} +(-53745.8 + 103159. i) q^{78} +(-20719.2 - 9462.16i) q^{79} +(-53786.1 + 15793.0i) q^{80} +(35075.5 - 47502.5i) q^{81} +(44520.9 - 97487.1i) q^{82} +(-4872.18 - 33886.8i) q^{83} +(21866.9 + 239920. i) q^{84} +(536.772 + 1175.37i) q^{85} +(-189548. + 121815. i) q^{86} +(8810.76 - 9161.11i) q^{87} +(58178.4 - 90527.3i) q^{88} +(-41428.5 + 47811.0i) q^{89} +(105340. - 4108.63i) q^{90} +174280. i q^{91} +(28634.7 - 166593. i) q^{92} +(27578.6 - 38377.8i) q^{93} +(-64917.7 - 19061.6i) q^{94} +(-53201.8 - 46099.6i) q^{95} +(9968.41 + 25214.2i) q^{96} +(75686.6 + 10882.1i) q^{97} +(198633. + 309079. i) q^{98} +(-55480.4 + 51995.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9}+O(q^{10}) $ 380 * q - 11 * q^3 + 578 * q^4 + 64 * q^6 - 22 * q^7 + 433 * q^9	$ 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9} - 22 q^{10} + 148 q^{12} - 542 q^{13} + 4620 q^{15} - 11102 q^{16} - 11526 q^{18} - 22 q^{19} + 12496 q^{21} + 15878 q^{24} - 17304 q^{25} - 21014 q^{27} - 22 q^{28} - 33627 q^{30} - 6566 q^{31} + 41250 q^{33} + 75988 q^{34} + 12154 q^{36} - 72138 q^{37} + 45205 q^{39} - 119372 q^{40} - 11 q^{42} + 59334 q^{43} + 119802 q^{46} + 5138 q^{48} + 147060 q^{49} - 11 q^{51} - 246042 q^{52} - 172143 q^{54} - 95048 q^{55} + 92422 q^{57} + 277528 q^{58} + 420629 q^{60} + 125158 q^{61} + 7194 q^{63} - 100196 q^{64} - 312378 q^{66} - 94380 q^{67} - 136956 q^{69} - 395908 q^{70} - 507803 q^{72} + 83336 q^{73} + 577756 q^{75} + 415338 q^{76} - 361512 q^{78} + 342958 q^{79} - 420607 q^{81} + 247868 q^{82} - 978505 q^{84} - 634728 q^{85} + 354721 q^{87} + 22506 q^{88} + 1636316 q^{90} + 1162112 q^{93} + 40940 q^{94} - 102479 q^{96} + 582824 q^{97} - 674663 q^{99}+O(q^{100}) $ 380 * q - 11 * q^3 + 578 * q^4 + 64 * q^6 - 22 * q^7 + 433 * q^9 - 22 * q^10 + 148 * q^12 - 542 * q^13 + 4620 * q^15 - 11102 * q^16 - 11526 * q^18 - 22 * q^19 + 12496 * q^21 + 15878 * q^24 - 17304 * q^25 - 21014 * q^27 - 22 * q^28 - 33627 * q^30 - 6566 * q^31 + 41250 * q^33 + 75988 * q^34 + 12154 * q^36 - 72138 * q^37 + 45205 * q^39 - 119372 * q^40 - 11 * q^42 + 59334 * q^43 + 119802 * q^46 + 5138 * q^48 + 147060 * q^49 - 11 * q^51 - 246042 * q^52 - 172143 * q^54 - 95048 * q^55 + 92422 * q^57 + 277528 * q^58 + 420629 * q^60 + 125158 * q^61 + 7194 * q^63 - 100196 * q^64 - 312378 * q^66 - 94380 * q^67 - 136956 * q^69 - 395908 * q^70 - 507803 * q^72 + 83336 * q^73 + 577756 * q^75 + 415338 * q^76 - 361512 * q^78 + 342958 * q^79 - 420607 * q^81 + 247868 * q^82 - 978505 * q^84 - 634728 * q^85 + 354721 * q^87 + 22506 * q^88 + 1636316 * q^90 + 1162112 * q^93 + 40940 * q^94 - 102479 * q^96 + 582824 * q^97 - 674663 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$

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 $

$2$	−2.79794	+	9.52891i	−0.494611	+	1.68449i	0.212315	+	0.977201i	$0.431900\pi$
$2$	−2.79794	+	9.52891i	−0.494611	+	1.68449i	−0.706926	+	0.707288i	$0.749919\pi$
$3$	−3.60982	−	15.1647i	−0.231570	−	0.972818i
$3$	−3.60982	−	15.1647i	−0.231570	−	0.972818i
$4$	−56.0515	−	36.0221i	−1.75161	−	1.12569i
$5$	−6.21680	+	43.2388i	−0.111210	+	0.773479i	0.855537	+	0.517742i	$0.173227\pi$
$5$	−6.21680	+	43.2388i	−0.111210	+	0.773479i	−0.966746	+	0.255737i	$0.917682\pi$
$6$	154.603	+	8.03237i	1.75324	+	0.0910889i
$7$	210.991	−	96.3564i	1.62749	−	0.743251i	0.628102	−	0.778131i	$-0.283832\pi$
$7$	210.991	−	96.3564i	1.62749	−	0.743251i	0.999392	+	0.0348800i	$0.0111049\pi$
$8$	259.904	−	225.208i	1.43578	−	1.24411i
$9$	−216.938	+	109.484i	−0.892751	+	0.450551i
$10$	−394.624	−	180.219i	−1.24791	−	0.569902i
$11$	300.233	−	88.1565i	0.748130	−	0.219671i	0.114625	−	0.993409i	$-0.463433\pi$
$11$	300.233	−	88.1565i	0.748130	−	0.219671i	0.633506	+	0.773738i	$0.281615\pi$
$12$	−343.930	+	980.039i	−0.689472	+	1.96467i
$13$	−312.127	+	683.464i	−0.512240	+	1.12165i	0.460055	+	0.887891i	$0.347830\pi$
$13$	−312.127	+	683.464i	−0.512240	+	1.12165i	−0.972295	+	0.233759i	$0.924897\pi$
$14$	327.831	+	2280.11i	0.447023	+	3.10911i
$15$	678.146	−	61.8082i	0.778207	−	0.0709280i
$16$	533.081	+	1167.28i	0.520587	+	1.13993i
$17$	24.8839	−	15.9919i	0.0208831	−	0.0134208i	−0.530158	−	0.847899i	$-0.677867\pi$
$17$	24.8839	−	15.9919i	0.0208831	−	0.0134208i	0.551041	+	0.834478i	$0.314231\pi$
$18$	−436.282	−	2373.52i	−0.317385	−	1.72668i
$19$	−871.245	+	1355.68i	−0.553677	+	0.861538i	−0.999435	−	0.0336157i	$-0.989298\pi$
$19$	−871.245	+	1355.68i	−0.553677	+	0.861538i	0.445758	+	0.895153i	$0.352934\pi$
$20$	1906.01	−	2199.66i	1.06549	−	1.22965i
$21$	−2222.86	−	2851.80i	−1.09993	−	1.41114i
$22$			3107.55i			1.36887i
$23$	990.238	+	2335.76i	0.390319	+	0.920680i
$23$	990.238	+	2335.76i	0.390319	+	0.920680i
$24$	−4353.43	−	3128.42i	−1.54278	−	1.10866i
$25$	1167.47	+	342.800i	0.373591	+	0.109696i
$26$	−5639.35	−	4886.52i	−1.63605	−	1.41764i
$27$	2443.40	+	2894.60i	0.645039	+	0.764150i
$28$	−15297.3	−	2199.42i	−3.68740	−	0.530169i
$29$	440.825	+	685.937i	0.0973355	+	0.151457i	0.886506	−	0.462717i	$-0.153126\pi$
$29$	440.825	+	685.937i	0.0973355	+	0.151457i	−0.789170	+	0.614174i	$0.789489\pi$
$30$	−1308.45	+	6634.93i	−0.265432	+	1.34596i
$31$	1985.33	+	2291.19i	0.371046	+	0.428210i	0.910310	−	0.413927i	$-0.135843\pi$
$31$	1985.33	+	2291.19i	0.371046	+	0.428210i	−0.539264	+	0.842137i	$0.681298\pi$
$32$	−1721.61	+	247.530i	−0.297207	+	0.0427319i
$33$	−2420.66	−	4234.73i	−0.386944	−	0.676926i
$34$	82.7617	+	281.861i	0.0122781	+	0.0418155i
$35$	2854.65	+	9722.03i	0.393897	+	1.34149i
$36$	16103.6	+	1677.84i	2.07093	+	0.215772i
$37$	3996.03	−	574.542i	0.479870	−	0.0689950i	0.101865	−	0.994798i	$-0.467519\pi$
$37$	3996.03	−	574.542i	0.479870	−	0.0689950i	0.378006	+	0.925803i	$0.376610\pi$
$38$	−10480.5	−	12095.1i	−1.17740	−	1.35879i
$39$	11491.3	+	2266.15i	1.20978	+	0.238576i
$40$	8121.97	+	12638.0i	0.802622	+	1.24890i
$41$	−10681.6	−	1535.79i	−0.992379	−	0.142683i	−0.373048	−	0.927812i	$-0.621687\pi$
$41$	−10681.6	−	1535.79i	−0.992379	−	0.142683i	−0.619331	+	0.785130i	$0.712596\pi$
$42$	33393.9	−	13202.3i	2.92109	−	1.15485i
$43$	17146.3	+	14857.3i	1.41416	+	1.22538i	0.938284	+	0.345865i	$0.112414\pi$
$43$	17146.3	+	14857.3i	1.41416	+	1.22538i	0.475876	+	0.879512i	$0.342131\pi$
$44$	−20004.1	−	5873.74i	−1.55771	−	0.457386i
$45$	−3385.29	−	10060.8i	−0.249210	−	0.740630i
$46$	−25027.9	+	2900.57i	−1.74393	+	0.202110i
$47$			6812.71i			0.449858i	0.974375	+	0.224929i	$0.0722150\pi$
$47$			6812.71i			0.449858i	−0.974375	+	0.224929i	$0.927785\pi$
$48$	15777.2	−	12297.7i	0.988389	−	0.770409i
$49$	24226.5	−	27958.8i	1.44145	−	1.66352i
$50$	−6533.02	+	10165.6i	−0.369564	+	0.575052i
$51$	−332.339	−	319.630i	−0.0178919	−	0.0172077i
$52$	42115.0	−	27065.7i	2.15987	−	1.38807i
$53$	11339.3	+	24829.6i	0.554494	+	1.21417i	0.954651	+	0.297726i	$0.0962282\pi$
$53$	11339.3	+	24829.6i	0.554494	+	1.21417i	−0.400157	+	0.916446i	$0.631045\pi$
$54$	−34418.8	+	15184.1i	−1.60624	+	0.708604i
$55$	1945.29	+	13529.8i	0.0867116	+	0.603093i
$56$	33137.2	−	72560.4i	1.41204	−	3.09193i
$57$	23703.6	+	8318.42i	0.966335	+	0.339120i
$58$	−7769.64	+	2281.37i	−0.303271	+	0.0890484i
$59$	4986.67	+	2277.33i	0.186501	+	0.0851720i	0.506477	−	0.862254i	$-0.330948\pi$
$59$	4986.67	+	2277.33i	0.186501	+	0.0851720i	−0.319976	+	0.947426i	$0.603675\pi$
$60$	−40237.6	−	20963.8i	−1.44296	−	0.751783i
$61$	−34667.5	+	30039.6i	−1.19288	+	1.03364i	−0.194272	+	0.980948i	$0.562235\pi$
$61$	−34667.5	+	30039.6i	−1.19288	+	1.03364i	−0.998611	+	0.0526915i	$0.983220\pi$
$62$	−27387.4	+	12507.4i	−0.904839	+	0.413226i
$63$	−35222.6	+	44003.6i	−1.11807	+	1.39681i
$64$	−3385.75	+	23548.4i	−0.103325	+	0.718640i
$65$	−27611.7	−	17745.0i	−0.810606	−	0.520945i
$66$	47125.2	−	11217.7i	1.33166	−	0.316989i
$67$	14366.9	−	48929.2i	0.391000	−	1.33162i	−0.495384	−	0.868674i	$-0.664973\pi$
$67$	14366.9	−	48929.2i	0.391000	−	1.33162i	0.886384	−	0.462950i	$-0.153209\pi$
$68$	−1970.84			−0.0516868
$69$	31846.6	−	23448.4i	0.805268	−	0.592911i
$70$	−100627.			−2.45455
$71$	18930.7	−	64472.1i	0.445678	−	1.51784i	−0.364245	−	0.931303i	$-0.618673\pi$
$71$	18930.7	−	64472.1i	0.445678	−	1.51784i	0.809923	−	0.586536i	$-0.199509\pi$
$72$	−31726.5	+	77311.7i	−0.721259	+	1.75758i
$73$	−40387.3	−	25955.3i	−0.887028	−	0.570058i	0.0158886	−	0.999874i	$-0.494942\pi$
$73$	−40387.3	−	25955.3i	−0.887028	−	0.570058i	−0.902917	+	0.429815i	$0.858579\pi$
$74$	−5705.88	+	39685.3i	−0.121128	+	0.842462i
$75$	984.116	−	18941.8i	0.0202020	−	0.388838i
$76$	97669.2	−	44604.0i	1.93965	−	0.885809i
$77$	54852.1	−	47529.7i	1.05431	−	0.913562i
$78$	−53745.8	+	103159.i	−1.00025	+	1.91986i
$79$	−20719.2	−	9462.16i	−0.373513	−	0.170578i	0.219809	−	0.975543i	$-0.429457\pi$
$79$	−20719.2	−	9462.16i	−0.373513	−	0.170578i	−0.593322	+	0.804965i	$0.702184\pi$
$80$	−53786.1	+	15793.0i	−0.939604	+	0.275893i
$81$	35075.5	−	47502.5i	0.594007	−	0.804460i
$82$	44520.9	−	97487.1i	0.731188	−	1.60108i
$83$	−4872.18	−	33886.8i	−0.0776297	−	0.539927i	−0.991110	−	0.133044i	$-0.957525\pi$
$83$	−4872.18	−	33886.8i	−0.0776297	−	0.539927i	0.913480	−	0.406883i	$-0.133384\pi$
$84$	21866.9	+	239920.i	0.338135	+	3.70994i
$85$	536.772	+	1175.37i	0.00805829	+	0.0176452i
$86$	−189548.	+	121815.i	−2.76359	+	1.77605i
$87$	8810.76	−	9161.11i	0.124800	−	0.129763i
$88$	58178.4	−	90527.3i	0.800857	−	1.24616i
$89$	−41428.5	+	47811.0i	−0.554401	+	0.639813i	−0.961903	−	0.273391i	$-0.911855\pi$
$89$	−41428.5	+	47811.0i	−0.554401	+	0.639813i	0.407502	+	0.913204i	$0.366400\pi$
$90$	105340.	−	4108.63i	1.37084	−	0.0534676i
$91$			174280.i			2.20620i
$92$	28634.7	−	166593.i	0.352714	−	2.05205i
$93$	27578.6	−	38377.8i	0.330648	−	0.460121i
$94$	−64917.7	−	19061.6i	−0.757781	−	0.222505i
$95$	−53201.8	−	46099.6i	−0.604807	−	0.524069i
$96$	9968.41	+	25214.2i	0.110395	+	0.279233i
$97$	75686.6	+	10882.1i	0.816751	+	0.117431i	0.538014	−	0.842936i	$-0.319175\pi$
$97$	75686.6	+	10882.1i	0.816751	+	0.117431i	0.278738	+	0.960367i	$0.410084\pi$
$98$	198633.	+	309079.i	2.08923	+	3.25090i
$99$	−55480.4	+	51995.3i	−0.568921	+	0.533182i
$100$	−53090.1	−	61269.2i	−0.530901	−	0.612692i
$101$	197833.	−	28444.1i	1.92972	−	0.277452i	0.933103	−	0.359609i	$-0.117090\pi$
$101$	197833.	−	28444.1i	1.92972	−	0.277452i	0.996619	+	0.0821570i	$0.0261809\pi$
$102$	3975.59	−	2272.53i	0.0378356	−	0.0216276i
$103$	6119.47	+	20841.0i	0.0568357	+	0.193565i	0.983017	−	0.183513i	$-0.0587471\pi$
$103$	6119.47	+	20841.0i	0.0568357	+	0.193565i	−0.926182	+	0.377078i	$0.876929\pi$
$104$	72798.5	+	247929.i	0.659992	+	2.24773i
$105$	137127.	−	78384.8i	1.21381	−	0.693838i
$106$	−268326.	+	38579.4i	−2.31952	+	0.333496i
$107$	−49046.9	−	56603.2i	−0.414145	−	0.477949i	0.509899	−	0.860234i	$-0.329683\pi$
$107$	−49046.9	−	56603.2i	−0.414145	−	0.477949i	−0.924044	+	0.382285i	$0.875137\pi$
$108$	−32687.0	−	250263.i	−0.269659	−	2.06461i
$109$	5889.92	+	9164.89i	0.0474835	+	0.0738858i	0.864184	−	0.503176i	$-0.167835\pi$
$109$	5889.92	+	9164.89i	0.0474835	+	0.0738858i	−0.816700	+	0.577062i	$0.804199\pi$
$110$	−134367.	−	19319.0i	−1.05879	−	0.152231i
$111$	−23137.7	−	58524.7i	−0.178243	−	0.450850i
$112$	224951.	+	194921.i	1.69450	+	1.46830i
$113$	−115771.	−	33993.4i	−0.852910	−	0.250437i	−0.174079	−	0.984732i	$-0.555695\pi$
$113$	−115771.	−	33993.4i	−0.852910	−	0.250437i	−0.678831	+	0.734295i	$0.737513\pi$
$114$	−145587.	+	202595.i	−1.04920	+	1.46005i
$115$	−107152.	+	28295.7i	−0.755534	+	0.199515i
$116$		−	54327.3i		−	0.374863i
$117$	−7115.88	−	182442.i	−0.0480578	−	1.23214i
$118$	−35652.9	+	41145.6i	−0.235716	+	0.272031i
$119$	3709.36	−	5771.87i	0.0240122	−	0.0373637i
$120$	162333.	−	168788.i	1.02909	−	1.07001i
$121$	−53116.2	+	34135.7i	−0.329810	+	0.211956i
$122$	−189247.	−	414392.i	−1.15114	−	2.52065i
$123$	15269.0	+	167528.i	0.0910011	+	0.998445i
$124$	−28747.1	−	199940.i	−0.167896	−	1.16774i
$125$	−78788.8	+	172523.i	−0.451013	+	0.987582i
$126$	−320755.	−	458752.i	−1.79990	−	2.57426i
$127$	143345.	−	42089.8i	0.788629	−	0.231562i	0.137472	−	0.990506i	$-0.456102\pi$
$127$	143345.	−	42089.8i	0.788629	−	0.231562i	0.651157	+	0.758943i	$0.274284\pi$
$128$	−265546.	−	121271.i	−1.43257	−	0.654231i
$129$	163413.	−	313651.i	0.864592	−	1.65948i
$130$	246346.	−	213460.i	1.27846	−	1.10779i
$131$	281117.	−	128382.i	1.43123	−	0.653619i	0.459166	−	0.888351i	$-0.348148\pi$
$131$	281117.	−	128382.i	1.43123	−	0.653619i	0.972060	+	0.234732i	$0.0754212\pi$
$132$	−16862.4	+	324560.i	−0.0842335	+	1.62129i
$133$	−53196.1	+	369987.i	−0.260766	+	1.81367i
$134$	426045.	+	273802.i	2.04971	+	1.31727i
$135$	−140349.	+	87654.7i	−0.662788	+	0.413943i
$136$	2865.92	−	9760.42i	0.0132867	−	0.0452503i
$137$	−111360.			−0.506906			−0.253453	−	0.967348i	$-0.581566\pi$
$137$	−111360.			−0.506906			−0.253453	+	0.967348i	$0.581566\pi$
$138$	134332.	+	369070.i	0.600459	+	1.64972i
$139$	−326112.			−1.43163			−0.715814	−	0.698291i	$-0.753944\pi$
$139$	−326112.			−1.43163			−0.715814	+	0.698291i	$0.753944\pi$
$140$	190201.	−	647765.i	0.820149	−	2.79317i
$141$	103313.	−	24592.7i	0.437630	−	0.104174i
$142$	561381.	+	360778.i	2.33635	+	1.50148i
$143$	−33459.3	+	232715.i	−0.136829	+	0.951664i
$144$	−243445.	−	194865.i	−0.978350	−	0.783119i
$145$	−32399.6	+	14796.4i	−0.127974	+	0.0584435i
$146$	360327.	−	312225.i	1.39899	−	1.21223i
$147$	−511441.	−	266462.i	−1.95210	−	1.01705i
$148$	−244679.	−	111741.i	−0.918213	−	0.419334i
$149$	−57403.1	+	16855.1i	−0.211821	+	0.0621964i	−0.385922	−	0.922532i	$-0.626117\pi$
$149$	−57403.1	+	16855.1i	−0.211821	+	0.0621964i	0.174100	+	0.984728i	$0.444298\pi$
$150$	177741.	+	62375.6i	0.645001	+	0.226353i
$151$	19279.4	−	42216.1i	0.0688101	−	0.150673i	−0.872102	−	0.489324i	$-0.837243\pi$
$151$	19279.4	−	42216.1i	0.0688101	−	0.150673i	0.940912	+	0.338651i	$0.109971\pi$
$152$	78871.0	+	548560.i	0.276891	+	1.92582i
$153$	−3647.41	+	6193.64i	−0.0125967	+	0.0213903i
$154$	299433.	+	655666.i	1.01741	+	2.22782i
$155$	−111411.	+	71599.3i	−0.372476	+	0.239376i
$156$	−562471.	−	540961.i	−1.85050	−	1.77973i
$157$	−112345.	+	174812.i	−0.363751	+	0.566007i	−0.974098	−	0.226127i	$-0.927394\pi$
$157$	−112345.	+	174812.i	−0.363751	+	0.566007i	0.610347	+	0.792134i	$0.291030\pi$
$158$	148135.	−	170957.i	0.472080	−	0.544809i
$159$	335602.	−	261588.i	1.05276	−	0.820588i
$160$		−	75979.1i		−	0.234636i
$161$	433997.	+	397409.i	1.31954	+	1.20829i
$162$	354508.	+	467141.i	1.06130	+	1.39849i
$163$	−76360.9	−	22421.6i	−0.225114	−	0.0660993i	0.167231	−	0.985918i	$-0.446518\pi$
$163$	−76360.9	−	22421.6i	−0.225114	−	0.0660993i	−0.392344	+	0.919818i	$0.628336\pi$
$164$	543399.	+	470858.i	1.57764	+	1.36704i
$165$	198153.	−	78339.9i	0.566620	−	0.224013i
$166$	336536.	+	48386.6i	0.947897	+	0.136287i
$167$	81340.9	+	126569.i	0.225693	+	0.351185i	0.935570	−	0.353140i	$-0.114886\pi$
$167$	81340.9	+	126569.i	0.225693	+	0.351185i	−0.709878	+	0.704325i	$0.751250\pi$
$168$	−1.21998e6	−	240587.i	−3.33487	−	0.657657i
$169$	−126554.	−	146051.i	−0.340846	−	0.393358i
$170$	−12701.8	+	1826.25i	−0.0337088	+	0.00484660i
$171$	40580.9	−	389487.i	0.106128	−	1.01860i
$172$	−425882.	−	1.45042e6i	−1.09766	−	3.73829i
$173$	2006.10	+	6832.15i	0.00509609	+	0.0173557i	0.962002	−	0.273043i	$-0.0880302\pi$
$173$	2006.10	+	6832.15i	0.00509609	+	0.0173557i	−0.956906	+	0.290399i	$0.906212\pi$
$174$	62643.4	+	109589.i	0.156856	+	0.274407i
$175$	279357.	−	40165.5i	0.689548	−	0.0991420i
$176$	262952.	+	303463.i	0.639876	+	0.738456i
$177$	16534.2	−	83842.3i	0.0396689	−	0.201155i
$178$	−339673.	−	528541.i	−0.803545	−	1.25034i
$179$	−128384.	−	18458.8i	−0.299486	−	0.0430596i	−0.00906629	−	0.999959i	$-0.502886\pi$
$179$	−128384.	−	18458.8i	−0.299486	−	0.0430596i	−0.290420	+	0.956899i	$0.593795\pi$
$180$	−172660.	+	685868.i	−0.397202	+	1.57783i
$181$	501.952	+	434.944i	0.00113885	+	0.000986817i	0.655430	−	0.755256i	$-0.272487\pi$
$181$	501.952	+	434.944i	0.00113885	+	0.000986817i	−0.654291	+	0.756243i	$0.727033\pi$
$182$	−1.66070e6	−	487626.i	−3.71632	−	1.09121i
$183$	580685.	+	417286.i	1.28178	+	0.921099i
$184$	783400.	+	384064.i	1.70584	+	0.836294i
$185$			176355.i			0.378843i
$186$	288535.	+	370173.i	0.611527	+	0.784553i
$187$	6061.18	−	6994.98i	0.0126752	−	0.0146279i
$188$	245408.	−	381863.i	0.506401	−	0.787976i
$189$	794450.	+	375297.i	1.61775	+	0.764223i
$190$	588134.	−	377971.i	1.18193	−	0.759581i
$191$	51309.4	+	112352.i	0.101769	+	0.222842i	0.953666	−	0.300866i	$-0.0972756\pi$
$191$	51309.4	+	112352.i	0.101769	+	0.222842i	−0.851898	+	0.523708i	$0.824548\pi$
$192$	369327.	−	33661.5i	0.723033	−	0.0658993i
$193$	−68842.5	−	478810.i	−0.133034	−	0.925273i	−0.941568	−	0.336823i	$-0.890647\pi$
$193$	−68842.5	−	478810.i	−0.133034	−	0.925273i	0.808534	−	0.588450i	$-0.200262\pi$
$194$	−315461.	+	690763.i	−0.601785	+	1.31773i
$195$	−169424.	+	482781.i	−0.319073	+	0.909208i
$196$	−2.36507e6	+	694446.i	−4.39747	+	1.29121i
$197$	178824.	+	81666.0i	0.328291	+	0.149926i	0.572741	−	0.819736i	$-0.305880\pi$
$197$	178824.	+	81666.0i	0.328291	+	0.149926i	−0.244450	+	0.969662i	$0.578607\pi$
$198$	−340227.	−	674147.i	−0.616745	−	1.22206i
$199$	−311672.	+	270066.i	−0.557912	+	0.483433i	−0.887574	−	0.460666i	$-0.847611\pi$
$199$	−311672.	+	270066.i	−0.557912	+	0.483433i	0.329662	+	0.944099i	$0.393065\pi$
$200$	380632.	−	173829.i	0.672869	−	0.307289i
$201$	−793861.	−	41244.8i	−1.38597	−	0.0720077i
$202$	−282483.	+	1.96472e6i	−0.487096	+	3.38783i
$203$	159105.	+	102250.i	0.270984	+	0.174151i
$204$	7114.38	+	29887.3i	0.0119691	+	0.0502818i
$205$	132811.	−	452313.i	0.220724	−	0.751717i
$206$	−215714.			−0.354169
$207$	−470549.	−	398301.i	−0.763271	−	0.646079i
$208$	−964186.			−1.54526
$209$	−142065.	+	483827.i	−0.224968	+	0.766169i
$210$	363247.	+	1.52599e6i	0.568400	+	2.38783i
$211$	145388.	+	93435.0i	0.224813	+	0.144479i	0.648199	−	0.761471i	$-0.275522\pi$
$211$	145388.	+	93435.0i	0.224813	+	0.144479i	−0.423386	+	0.905949i	$0.639159\pi$
$212$	258830.	−	1.80020e6i	0.395526	−	2.75094i
$213$	−1.04604e6	−	54346.6i	−1.57979	−	0.0820773i
$214$	676597.	−	308991.i	1.00994	−	0.461224i
$215$	−749008.	+	649019.i	−1.10507	+	0.957550i
$216$	1.28694e6	+	202043.i	1.87682	+	0.294652i
$217$	639658.	+	292122.i	0.922143	+	0.421129i
$218$	−103811.	+	30481.7i	−0.147946	+	0.0434408i
$219$	−247815.	+	706156.i	−0.349154	+	0.994926i
$220$	378335.	−	828438.i	0.527011	−	1.15399i
$221$	3162.94	+	21998.7i	0.00435623	+	0.0302982i
$222$	622414.	−	56728.6i	0.847612	−	0.0772537i
$223$	−288064.	−	630773.i	−0.387907	−	0.849397i	−0.998355	−	0.0573409i	$-0.981738\pi$
$223$	−288064.	−	630773.i	−0.387907	−	0.849397i	0.610448	−	0.792056i	$-0.290989\pi$
$224$	−339393.	+	218114.i	−0.451942	+	0.290445i
$225$	−290800.	+	53452.7i	−0.382947	+	0.0703904i
$226$	647840.	−	1.00806e6i	0.843717	−	1.31285i
$227$	30100.9	−	34738.2i	0.0387716	−	0.0447449i	−0.736033	−	0.676946i	$-0.763303\pi$
$227$	30100.9	−	34738.2i	0.0387716	−	0.0447449i	0.774804	+	0.632201i	$0.217848\pi$
$228$	−1.02898e6	−	1.32011e6i	−1.31090	−	1.68180i
$229$		−	301237.i		−	0.379594i	−0.981823	−	0.189797i	$-0.939217\pi$
$229$		−	301237.i		−	0.379594i	0.981823	−	0.189797i	$-0.0607830\pi$
$230$	30176.2	−	1.10021e6i	0.0376135	−	1.37137i
$231$	−918781.	−	660245.i	−1.13288	−	0.814095i
$232$	269051.	+	79000.6i	0.328182	+	0.0963630i
$233$	−983152.	−	851906.i	−1.18640	−	1.02802i	−0.998953	−	0.0457453i	$-0.985434\pi$
$233$	−983152.	−	851906.i	−1.18640	−	1.02802i	−0.187446	−	0.982275i	$-0.560021\pi$
$234$	1.75839e6	+	442656.i	2.09930	+	0.528478i
$235$	−294574.	−	42353.3i	−0.347956	−	0.0500285i
$236$	−197476.	−	307278.i	−0.230799	−	0.359130i
$237$	−68698.4	+	348358.i	−0.0794467	+	0.402861i
$238$	44621.1	+	51495.5i	0.0510620	+	0.0589287i
$239$	1.32875e6	−	191046.i	1.50470	−	0.216343i	0.659870	−	0.751379i	$-0.270611\pi$
$239$	1.32875e6	−	191046.i	1.50470	−	0.216343i	0.844829	+	0.535036i	$0.179702\pi$
$240$	433655.	+	758641.i	0.485977	+	0.850175i
$241$	190214.	+	647808.i	0.210959	+	0.718462i	0.995187	+	0.0979891i	$0.0312410\pi$
$241$	190214.	+	647808.i	0.210959	+	0.718462i	−0.784228	+	0.620473i	$0.786941\pi$
$242$	−176660.	−	601649.i	−0.193910	−	0.660397i
$243$	−846980.	−	360436.i	−0.920147	−	0.391572i
$244$	3.02525e6	−	434966.i	3.25302	−	0.467714i
$245$	1.05830e6	+	1.22134e6i	1.12640	+	1.29993i
$246$	−1.63908e6	−	323236.i	−1.72688	−	0.340551i
$247$	−654621.	−	1.01861e6i	−0.682728	−	1.06235i
$248$	1.03199e6	+	148378.i	1.06548	+	0.153193i
$249$	−496296.	+	196210.i	−0.507274	+	0.200551i
$250$	−1.42351e6	−	1.23348e6i	−1.44049	−	1.24820i
$251$	48032.3	+	14103.5i	0.0481226	+	0.0141301i	0.305705	−	0.952126i	$-0.401108\pi$
$251$	48032.3	+	14103.5i	0.0481226	+	0.0141301i	−0.257583	+	0.966256i	$0.582926\pi$
$252$	3.55938e6	−	1.19767e6i	3.53080	−	1.18806i
$253$	503215.	+	613977.i	0.494256	+	0.603047i
$254$			1.48368e6i			1.44297i
$255$	15886.5	−	12382.9i	0.0152995	−	0.0119254i
$256$	1.40001e6	−	1.61570e6i	1.33516	−	1.54085i
$257$	−13897.2	+	21624.4i	−0.0131248	+	0.0204226i	−0.847754	−	0.530390i	$-0.822046\pi$
$257$	−13897.2	+	21624.4i	−0.0131248	+	0.0204226i	0.834629	+	0.550812i	$0.185682\pi$
$258$	2.53153e6	+	2.43472e6i	2.36774	+	2.27719i
$259$	787765.	−	506266.i	0.729705	−	0.468953i
$260$	908467.	+	1.98926e6i	0.833443	+	1.82498i
$261$	−170731.	−	100543.i	−0.155136	−	0.0913587i
$262$	436789.	+	3.03794e6i	0.393114	+	2.73417i
$263$	−250003.	+	547431.i	−0.222872	+	0.488023i	−0.987729	−	0.156178i	$-0.950083\pi$
$263$	−250003.	+	547431.i	−0.222872	+	0.488023i	0.764856	+	0.644201i	$0.222810\pi$
$264$	−1.58284e6	−	555472.i	−1.39774	−	0.490515i
$265$	−1.14410e6	+	335937.i	−1.00080	+	0.293862i
$266$	−3.37674e6	−	1.54210e6i	−2.92613	−	1.33632i
$267$	874591.	+	455663.i	0.750805	+	0.391170i
$268$	−2.56782e6	+	2.22503e6i	−2.18388	+	1.89234i
$269$	1.59513e6	−	728469.i	1.34405	−	0.613805i	0.392058	−	0.919941i	$-0.371763\pi$
$269$	1.59513e6	−	728469.i	1.34405	−	0.613805i	0.951988	+	0.306135i	$0.0990360\pi$
$270$	−442566.	−	1.58263e6i	−0.369461	−	1.32120i
$271$	−20347.2	+	141518.i	−0.0168299	+	0.117054i	−0.996505	−	0.0835387i	$-0.973378\pi$
$271$	−20347.2	+	141518.i	−0.0168299	+	0.117054i	0.979675	+	0.200593i	$0.0642869\pi$
$272$	31932.2	+	20521.6i	0.0261702	+	0.0168186i
$273$	2.64291e6	−	629121.i	2.14623	−	0.510890i
$274$	311578.	−	1.06114e6i	0.250721	−	0.853877i
$275$	380734.			0.303591
$276$	−2.62971e6	+	167134.i	−2.07795	+	0.132067i
$277$	−2.15842e6			−1.69020			−0.845099	−	0.534611i	$-0.820458\pi$
$277$	−2.15842e6			−1.69020			−0.845099	+	0.534611i	$0.820458\pi$
$278$	912442.	−	3.10749e6i	0.708098	−	2.41156i
$279$	−681543.	−	279686.i	−0.524182	−	0.215110i
$280$	2.93142e6	+	1.88391e6i	2.23451	+	1.43603i
$281$	366859.	−	2.55156e6i	0.277162	−	1.92770i	−0.0866674	−	0.996237i	$-0.527622\pi$
$281$	366859.	−	2.55156e6i	0.277162	−	1.92770i	0.363829	−	0.931466i	$-0.381469\pi$
$282$	−54722.2	+	1.05327e6i	−0.0409771	+	0.788708i
$283$	965638.	−	440992.i	0.716718	−	0.327314i	−0.0234605	−	0.999725i	$-0.507468\pi$
$283$	965638.	−	440992.i	0.716718	−	0.327314i	0.740178	+	0.672411i	$0.234741\pi$
$284$	−3.38352e6	+	2.93183e6i	−2.48927	+	2.15697i
$285$	−507039.	+	973202.i	−0.369768	+	0.709726i
$286$	−2.12390e6	−	969952.i	−1.53539	−	0.701189i
$287$	−2.40171e6	+	705206.i	−1.72114	+	0.505372i
$288$	346382.	−	242187.i	0.246079	−	0.172056i
$289$	−589466.	+	1.29075e6i	−0.415159	+	0.909071i
$290$	−50341.5	−	350133.i	−0.0351505	−	0.244477i
$291$	−108191.	−	1.18705e6i	−0.0748961	−	0.821744i
$292$	1.32880e6	+	2.90967e6i	0.912017	+	1.99704i
$293$	1.36601e6	−	877883.i	0.929578	−	0.597403i	0.0141562	−	0.999900i	$-0.495494\pi$
$293$	1.36601e6	−	877883.i	0.929578	−	0.597403i	0.915422	+	0.402496i	$0.131857\pi$
$294$	3.97007e6	−	4.12794e6i	2.67874	−	2.78525i
$295$	−129470.	+	201460.i	−0.0866194	+	0.134782i
$296$	909193.	−	1.04926e6i	0.603152	−	0.696074i
$297$	988769.	+	653652.i	0.650434	+	0.429987i
$298$		−	594149.i		−	0.387574i
$299$	−1.90549e6	−	52263.1i	−1.23262	−	0.0338079i
$300$	−737486.	+	1.02627e6i	−0.473097	+	0.658351i
$301$	5.04931e6	+	1.48261e6i	3.21230	+	0.943216i
$302$	348330.	+	301830.i	0.219773	+	0.190434i
$303$	−1.14549e6	−	2.89740e6i	−0.716777	−	1.81302i
$304$	−2.04691e6	−	294302.i	−1.27033	−	0.182645i
$305$	−1.08335e6	−	1.68573e6i	−0.666838	−	1.03762i
$306$	−48813.4	−	52085.3i	−0.0298013	−	0.0317989i
$307$	−1.90632e6	−	2.20001e6i	−1.15438	−	1.33223i	−0.934192	−	0.356771i	$-0.883878\pi$
$307$	−1.90632e6	−	2.20001e6i	−1.15438	−	1.33223i	−0.220190	−	0.975457i	$-0.570668\pi$
$308$	−4.78666e6	+	688218.i	−2.87512	+	0.413380i
$309$	293958.	−	168032.i	0.175142	−	0.100115i
$310$	−370543.	−	1.26195e6i	−0.218995	−	0.745829i
$311$	464706.	+	1.58264e6i	0.272444	+	0.927859i	0.976101	+	0.217319i	$0.0697312\pi$
$311$	464706.	+	1.58264e6i	0.272444	+	0.927859i	−0.703657	+	0.710540i	$0.748451\pi$
$312$	3.49699e6	−	1.99895e6i	2.03380	−	1.16256i
$313$	−1.56925e6	+	225623.i	−0.905378	+	0.130174i	−0.579248	−	0.815151i	$-0.696654\pi$
$313$	−1.56925e6	+	225623.i	−0.905378	+	0.130174i	−0.326130	+	0.945325i	$0.605745\pi$
$314$	−1.35143e6	−	1.55964e6i	−0.773518	−	0.892687i
$315$	−1.68369e6	−	1.79654e6i	−0.956061	−	1.02014i
$316$	820497.	+	1.27672e6i	0.462231	+	0.719246i
$317$	−10069.2	−	1447.73i	−0.00562788	−	0.000809167i	0.139500	−	0.990222i	$-0.455450\pi$
$317$	−10069.2	−	1447.73i	−0.00562788	−	0.000809167i	−0.145128	+	0.989413i	$0.546359\pi$
$318$	1.55365e6	+	3.92983e6i	0.861562	+	2.17924i
$319$	192820.	+	167080.i	0.106090	+	0.0919278i
$320$	−997156.	−	292792.i	−0.544363	−	0.159839i
$321$	−681322.	+	948111.i	−0.369054	+	0.513567i
$322$	−5.00117e6	+	3.02359e6i	−2.68802	+	1.62511i
$323$			47667.5i			0.0254224i
$324$	−3.67718e6	+	1.39909e6i	−1.94604	+	0.740431i
$325$	−598691.	+	690926.i	−0.314409	+	0.362847i
$326$	427306.	−	664901.i	0.222687	−	0.346508i
$327$	117722.	−	122403.i	0.0608817	−	0.0633026i
$328$	−3.12207e6	+	2.00643e6i	−1.60235	+	1.02977i
$329$	656449.	+	1.43742e6i	0.334358	+	0.732141i
$330$	192072.	+	2.10738e6i	0.0970911	+	1.06526i
$331$	6679.54	+	46457.3i	0.00335102	+	0.0233068i	0.991428	−	0.130652i	$-0.0417069\pi$
$331$	6679.54	+	46457.3i	0.00335102	+	0.0233068i	−0.988077	+	0.153958i	$0.950798\pi$
$332$	−947580.	+	2.07491e6i	−0.471814	+	1.03313i
$333$	−803988.	+	562141.i	−0.397319	+	0.277801i
$334$	−1.43365e6	+	420957.i	−0.703197	+	0.206477i
$335$	2.02633e6	+	925392.i	0.986500	+	0.450520i
$336$	2.14389e6	−	4.11495e6i	1.03599	−	1.98846i
$337$	2.19452e6	−	1.90156e6i	1.05260	−	0.912085i	0.0563356	−	0.998412i	$-0.482058\pi$
$337$	2.19452e6	−	1.90156e6i	1.05260	−	0.912085i	0.996267	+	0.0863266i	$0.0275129\pi$
$338$	1.74580e6	−	797279.i	0.831193	−	0.379593i
$339$	−97588.8	+	1.87835e6i	−0.0461212	+	0.887720i
$340$	12252.3	−	85216.8i	0.00574806	−	0.0399786i
$341$	798045.	+	512872.i	0.371656	+	0.238849i
$342$	3.59784e6	+	1.47645e6i	1.66332	+	0.682581i
$343$	1.31924e6	−	4.49293e6i	0.605466	−	2.06203i
$344$	7.80239e6			3.55493
$345$	815895.	+	1.52278e6i	0.369051	+	0.688795i
$346$	−70715.8			−0.0317560
$347$	−1.09350e6	+	3.72412e6i	−0.487523	+	1.66035i	0.237315	+	0.971433i	$0.423733\pi$
$347$	−1.09350e6	+	3.72412e6i	−0.487523	+	1.66035i	−0.724838	+	0.688919i	$0.758085\pi$
$348$	−823859.	+	196112.i	−0.364674	+	0.0868071i
$349$	698776.	+	449076.i	0.307096	+	0.197359i	0.685107	−	0.728442i	$-0.259755\pi$
$349$	698776.	+	449076.i	0.307096	+	0.197359i	−0.378011	+	0.925801i	$0.623392\pi$
$350$	−398891.	+	2.77435e6i	−0.174054	+	1.21057i
$351$	−2.74100e6	+	766495.i	−1.18752	+	0.332079i
$352$	−495062.	+	226087.i	−0.212963	+	0.0972568i
$353$	−1.37326e6	+	1.18994e6i	−0.586565	+	0.508261i	−0.896822	−	0.442391i	$-0.854130\pi$
$353$	−1.37326e6	+	1.18994e6i	−0.586565	+	0.508261i	0.310257	+	0.950653i	$0.399585\pi$
$354$	752663.	+	392139.i	0.319222	+	0.166315i
$355$	2.67001e6	+	1.21935e6i	1.12445	+	0.513521i
$356$	4.04438e6	−	1.18754e6i	1.69133	−	0.496618i
$357$	−100919.	−	35416.0i	−0.0419085	−	0.0147072i
$358$	535102.	−	1.17171e6i	0.220663	−	0.483184i
$359$	−52690.8	−	366473.i	−0.0215774	−	0.150074i	0.976184	−	0.216942i	$-0.0696084\pi$
$359$	−52690.8	−	366473.i	−0.0215774	−	0.150074i	−0.997762	+	0.0668683i	$0.978699\pi$
$360$	−3.14563e6	−	1.85245e6i	−1.27924	−	0.753338i
$361$	−50201.4	−	109926.i	−0.0202744	−	0.0443947i
$362$	−5548.97	+	3566.11i	−0.00222557	+	0.00143029i
$363$	709399.	+	682270.i	0.282569	+	0.271762i
$364$	6.27794e6	−	9.76867e6i	2.48350	−	3.86440i
$365$	1.37336e6	−	1.58494e6i	0.539574	−	0.622702i
$366$	−5.60100e6	+	4.36576e6i	−2.18556	+	1.70356i
$367$		−	1.71313e6i		−	0.663934i	−0.943291	−	0.331967i	$-0.892288\pi$
$367$		−	1.71313e6i		−	0.663934i	0.943291	−	0.331967i	$-0.107712\pi$
$368$	−2.19862e6	+	2.40104e6i	−0.846312	+	0.924229i
$369$	2.48540e6	−	836295.i	0.950233	−	0.319738i
$370$	−1.68047e6	−	493431.i	−0.638156	−	0.187380i
$371$	4.78499e6	+	4.14621e6i	1.80487	+	1.56393i
$372$	−2.92827e6	+	1.15769e6i	−1.09712	+	0.433746i
$373$	2.52214e6	+	362630.i	0.938637	+	0.134956i	0.594619	−	0.804007i	$-0.297303\pi$
$373$	2.52214e6	+	362630.i	0.938637	+	0.134956i	0.344018	+	0.938963i	$0.388212\pi$
$374$	49695.7	+	77328.0i	0.0183713	+	0.0285863i
$375$	2.90069e6	+	572033.i	1.06518	+	0.210060i
$376$	1.53428e6	+	1.77065e6i	0.559674	+	0.645898i
$377$	−606407.	+	87188.2i	−0.219741	+	0.0315940i
$378$	−5.79899e6	+	6.52018e6i	−2.08748	+	2.34709i
$379$	−832785.	−	2.83621e6i	−0.297807	−	1.01424i	−0.963432	−	0.267951i	$-0.913653\pi$
$379$	−832785.	−	2.83621e6i	−0.297807	−	1.01424i	0.665625	−	0.746286i	$-0.268165\pi$
$380$	1.32143e6	+	4.50039e6i	0.469447	+	1.59879i
$381$	−1.15573e6	−	2.02185e6i	−0.407891	−	0.713569i
$382$	−1.21415e6	+	174569.i	−0.425711	+	0.0612080i
$383$	−3.08549e6	−	3.56085e6i	−1.07480	−	1.24038i	−0.969278	−	0.245968i	$-0.920894\pi$
$383$	−3.08549e6	−	3.56085e6i	−1.07480	−	1.24038i	−0.105521	−	0.994417i	$-0.533651\pi$
$384$	−880465.	+	4.46470e6i	−0.304708	+	1.54513i
$385$	1.71412e6	+	2.66722e6i	0.589372	+	0.917081i
$386$	4.75515e6	+	683688.i	1.62441	+	0.233555i
$387$	−5.34633e6	−	1.34588e6i	−1.81459	−	0.456804i
$388$	−3.85035e6	−	3.33635e6i	−1.29844	−	1.12510i
$389$	139659.	+	41007.7i	0.0467947	+	0.0137402i	0.305046	−	0.952338i	$-0.401328\pi$
$389$	139659.	+	41007.7i	0.0467947	+	0.0137402i	−0.258251	+	0.966078i	$0.583146\pi$
$390$	−4.12633e6	−	2.96522e6i	−1.37373	−	0.987178i
$391$	61994.2	+	42287.0i	0.0205073	+	0.0139883i
$392$		−	1.27226e7i		−	4.18178i
$393$	−2.96165e6	−	3.79962e6i	−0.967281	−	1.24096i
$394$	−1.27853e6	+	1.47550e6i	−0.414924	+	0.478848i
$395$	537940.	−	837051.i	0.173477	−	0.269935i
$396$	4.98274e6	−	915890.i	1.59673	−	0.293498i
$397$	1.97250e6	−	1.26765e6i	0.628117	−	0.403666i	−0.187495	−	0.982266i	$-0.560037\pi$
$397$	1.97250e6	−	1.26765e6i	0.628117	−	0.403666i	0.815612	+	0.578599i	$0.196401\pi$
$398$	−1.70139e6	−	3.72552e6i	−0.538389	−	1.17891i
$399$	5.80279e6	−	528882.i	1.82475	−	0.166313i
$400$	222211.	+	1.54551e6i	0.0694409	+	0.482972i
$401$	1.76896e6	−	3.87348e6i	0.549359	−	1.20293i	−0.407721	−	0.913106i	$-0.633677\pi$
$401$	1.76896e6	−	3.87348e6i	0.549359	−	1.20293i	0.957080	−	0.289822i	$-0.0935962\pi$
$402$	2.61419e6	−	7.44923e6i	0.806812	−	2.29904i
$403$	−2.18562e6	+	641756.i	−0.670366	+	0.196837i
$404$	−1.21134e7	−	5.53202e6i	−3.69245	−	1.68628i
$405$	1.83590e6	+	1.81194e6i	0.556174	+	0.548916i
$406$	−1.41950e6	+	1.23000e6i	−0.427386	+	0.370332i
$407$	1.14909e6	−	524772.i	0.343849	−	0.157031i
$408$	−158360.	−	8227.53i	−0.0470971	−	0.00244691i
$409$	−592169.	+	4.11863e6i	−0.175040	+	1.21743i	0.693000	+	0.720937i	$0.256288\pi$
$409$	−592169.	+	4.11863e6i	−0.175040	+	1.21743i	−0.868041	+	0.496493i	$0.834621\pi$
$410$	3.93845e6	+	2.53109e6i	1.15709	+	0.743614i
$411$	401989.	+	1.68874e6i	0.117384	+	0.493127i
$412$	407732.	−	1.38861e6i	0.118340	−	0.403029i
$413$	1.27158e6			0.366833
$414$	5.11194e6	−	3.36939e6i	1.46583	−	0.966164i
$415$	1.49551e6			0.426255
$416$	368183.	−	1.25392e6i	0.104311	−	0.355251i
$417$	1.17721e6	+	4.94541e6i	0.331522	+	1.39271i
$418$	−4.21286e6	−	2.70744e6i	−1.17933	−	0.757911i
$419$	−64574.6	+	449126.i	−0.0179691	+	0.124978i	−0.996832	−	0.0795420i	$-0.974654\pi$
$419$	−64574.6	+	449126.i	−0.0179691	+	0.124978i	0.978862	+	0.204520i	$0.0655633\pi$
$420$	−1.05098e7	−	546032.i	−2.90717	−	0.151041i
$421$	5.22105e6	−	2.38437e6i	1.43566	−	0.655645i	0.462681	−	0.886525i	$-0.346888\pi$
$421$	5.22105e6	−	2.38437e6i	1.43566	−	0.655645i	0.972982	+	0.230880i	$0.0741604\pi$
$422$	−1.29712e6	+	1.12396e6i	−0.354568	+	0.307235i
$423$	−745883.	−	1.47794e6i	−0.202684	−	0.401611i
$424$	8.53897e6	+	3.89962e6i	2.30670	+	1.05343i
$425$	34533.2	−	10139.9i	0.00927395	−	0.00272308i
$426$	3.44462e6	−	9.81555e6i	0.919638	−	2.62054i
$427$	−4.42003e6	+	9.67852e6i	−1.17316	+	2.56885i
$428$	710188.	+	4.93947e6i	0.187398	+	1.30338i
$429$	3.64984e6	−	332656.i	0.957481	−	0.0872675i
$430$	−4.08877e6	−	8.95315e6i	−1.06640	−	2.33510i
$431$	−2.37835e6	+	1.52848e6i	−0.616713	+	0.396338i	−0.811369	−	0.584534i	$-0.801277\pi$
$431$	−2.37835e6	+	1.52848e6i	−0.616713	+	0.396338i	0.194656	+	0.980872i	$0.437641\pi$
$432$	−2.07629e6	+	4.39520e6i	−0.535276	+	1.13310i
$433$	−418376.	+	651006.i	−0.107238	+	0.166865i	−0.890725	−	0.454543i	$-0.849803\pi$
$433$	−418376.	+	651006.i	−0.107238	+	0.166865i	0.783487	+	0.621408i	$0.213439\pi$
$434$	−4.57333e6	+	5.27790e6i	−1.16549	+	1.34505i
$435$	341341.	+	437919.i	0.0864898	+	0.110961i
$436$		−	725873.i		−	0.182871i
$437$	−4.02929e6	−	692570.i	−1.00931	−	0.173484i
$438$	−6.03553e6	−	4.33719e6i	−1.50325	−	1.08025i
$439$	−1.68244e6	−	494008.i	−0.416656	−	0.122341i	0.0666838	−	0.997774i	$-0.478758\pi$
$439$	−1.68244e6	−	494008.i	−0.416656	−	0.122341i	−0.483339	+	0.875433i	$0.660576\pi$
$440$	3.55261e6	+	3.07835e6i	0.874814	+	0.758031i
$441$	−2.19461e6	+	8.71775e6i	−0.537354	+	2.13456i
$442$	−218474.	−	31411.8i	−0.0531917	−	0.00764781i
$443$	1.89081e6	+	2.94215e6i	0.457760	+	0.712288i	0.991027	−	0.133658i	$-0.0426725\pi$
$443$	1.89081e6	+	2.94215e6i	0.457760	+	0.712288i	−0.533268	+	0.845947i	$0.679036\pi$
$444$	−811279.	+	4.11387e6i	−0.195305	+	0.990359i
$445$	−1.80974e6	−	2.08855e6i	−0.433227	−	0.499971i
$446$	6.81656e6	−	980074.i	1.62266	−	0.233304i
$447$	462818.	+	809659.i	0.109557	+	0.191661i
$448$	1.55468e6	+	5.29475e6i	0.365970	+	1.24638i
$449$	9670.90	+	32936.1i	0.00226387	+	0.00771003i	0.960617	−	0.277875i	$-0.0896302\pi$
$449$	9670.90	+	32936.1i	0.00226387	+	0.00771003i	−0.958353	+	0.285585i	$0.907812\pi$
$450$	304296.	−	2.92057e6i	0.0708377	−	0.679886i
$451$	−3.34237e6	+	480560.i	−0.773772	+	0.111252i
$452$	5.26462e6	+	6.07569e6i	1.21205	+	1.39878i
$453$	−709791.	−	139975.i	−0.162512	−	0.0320483i
$454$	246797.	+	384024.i	0.0561954	+	0.0874417i
$455$	−7.53567e6	−	1.08347e6i	−1.70645	−	0.245350i
$456$	8.03405e6	−	3.17626e6i	1.80935	−	0.715326i
$457$	−26491.2	−	22954.8i	−0.00593350	−	0.00514141i	0.651889	−	0.758314i	$-0.273977\pi$
$457$	−26491.2	−	22954.8i	−0.00593350	−	0.00514141i	−0.657822	+	0.753173i	$0.728522\pi$
$458$	2.87046e6	+	842843.i	0.639422	+	0.187751i
$459$	107091.	+	32954.1i	0.0237259	+	0.00730093i
$460$	7.02528e6	+	2.27381e6i	1.54799	+	0.501025i
$461$		−	2.08712e6i		−	0.457400i	−0.973497	−	0.228700i	$-0.926553\pi$
$461$		−	2.08712e6i		−	0.457400i	0.973497	−	0.228700i	$-0.0734475\pi$
$462$	8.86210e6	−	6.90765e6i	1.93167	−	1.50566i
$463$	2.60517e6	−	3.00653e6i	0.564786	−	0.651798i	−0.399478	−	0.916743i	$-0.630808\pi$
$463$	2.60517e6	−	3.00653e6i	0.564786	−	0.651798i	0.964263	+	0.264945i	$0.0853539\pi$
$464$	−565689.	+	880229.i	−0.121978	+	0.189802i
$465$	1.48796e6	+	1.43105e6i	0.319123	+	0.306919i
$466$	1.08685e7	−	6.98478e6i	2.31849	−	1.49001i
$467$	−2.44398e6	−	5.35158e6i	−0.518569	−	1.13551i	−0.969979	−	0.243190i	$-0.921806\pi$
$467$	−2.44398e6	−	5.35158e6i	−0.518569	−	1.13551i	0.451410	−	0.892317i	$-0.350921\pi$
$468$	−6.17311e6	+	1.04825e7i	−1.30283	+	2.21233i
$469$	−1.68335e6	−	1.17080e7i	−0.353381	−	2.45782i
$470$	1.22778e6	−	2.68846e6i	0.256375	−	0.561383i
$471$	3.05652e6	+	1.07264e6i	0.634856	+	0.222793i
$472$	1.80893e6	−	531150.i	0.373738	−	0.109739i
$473$	6.45765e6	+	2.94911e6i	1.32716	+	0.606092i
$474$	−3.12726e6	−	1.62931e6i	−0.639320	−	0.333086i
$475$	−1.48188e6	+	1.28406e6i	−0.301356	+	0.261126i
$476$	−415830.	+	189903.i	−0.0841199	+	0.0384163i
$477$	−5.17837e6	−	4.14503e6i	−1.04207	−	0.834125i
$478$	−1.89731e6	+	1.31961e7i	−0.379813	+	2.64166i
$479$	2.12939e6	+	1.36848e6i	0.424050	+	0.272520i	0.735213	−	0.677836i	$-0.237082\pi$
$479$	2.12939e6	+	1.36848e6i	0.424050	+	0.272520i	−0.311163	+	0.950356i	$0.600719\pi$
$480$	−1.15220e6	+	274271.i	−0.228258	+	0.0543346i
$481$	−854591.	+	2.91047e6i	−0.168421	+	0.573588i
$482$	−6.70511e6			−1.31458
$483$	4.45995e6	−	8.01602e6i	0.869886	−	1.56348i
$484$	4.20688e6			0.816295
$485$	−941057.	+	3.20495e6i	−0.181661	+	0.618681i
$486$	5.80436e6	−	7.06232e6i	1.11471	−	1.35630i
$487$	−632562.	−	406523.i	−0.120860	−	0.0776717i	0.478814	−	0.877916i	$-0.341067\pi$
$487$	−632562.	−	406523.i	−0.120860	−	0.0776717i	−0.599674	+	0.800244i	$0.704703\pi$
$488$	−2.24507e6	+	1.56148e7i	−0.426757	+	2.96816i
$489$	−64368.2	+	1.23893e6i	−0.0121730	+	0.234301i
$490$	−1.45991e7	+	6.66717e6i	−2.74685	+	1.25444i
$491$	−447320.	+	387605.i	−0.0837365	+	0.0725581i	−0.695723	−	0.718310i	$-0.744916\pi$
$491$	−447320.	+	387605.i	−0.0837365	+	0.0725581i	0.611987	+	0.790868i	$0.290371\pi$
$492$	5.17886e6	−	9.94021e6i	0.964542	−	1.85133i
$493$	21938.9	+	10019.2i	0.00406534	+	0.00185658i
$494$	1.15378e7	−	3.38781e6i	2.12719	−	0.624600i
$495$	−1.90330e6	−	2.72215e6i	−0.349136	−	0.499343i
$496$	−1.61613e6	+	3.53883e6i	−0.294966	+	0.645886i
$497$	−2.21809e6	−	1.54271e7i	−0.402798	−	2.80152i
$498$	−481065.	−	5.27814e6i	−0.0869221	−	0.953691i
$499$	2.46967e6	+	5.40783e6i	0.444005	+	0.972235i	0.990846	+	0.134999i	$0.0431030\pi$
$499$	2.46967e6	+	5.40783e6i	0.444005	+	0.972235i	−0.546841	+	0.837237i	$0.684170\pi$
$500$	1.06309e7	−	6.83206e6i	1.90171	−	1.22216i
$501$	1.62576e6	−	1.69040e6i	0.289375	−	0.300882i
$502$	−268783.	+	418234.i	−0.0476039	+	0.0740730i
$503$	−6.27856e6	+	7.24585e6i	−1.10647	+	1.27694i	−0.148865	+	0.988858i	$0.547562\pi$
$503$	−6.27856e6	+	7.24585e6i	−1.10647	+	1.27694i	−0.957607	+	0.288079i	$0.906984\pi$
$504$	755463.	+	1.93691e7i	0.132476	+	3.39652i
$505$			8.73088e6i			1.52346i
$506$	−7.25849e6	+	3.07722e6i	−1.26029	+	0.534296i
$507$	−1.75799e6	+	2.44637e6i	−0.303736	+	0.422672i
$508$	−9.55085e6	−	2.80438e6i	−1.64204	−	0.482146i
$509$	−2.17399e6	−	1.88377e6i	−0.371932	−	0.322281i	0.448760	−	0.893653i	$-0.351866\pi$
$509$	−2.17399e6	−	1.88377e6i	−0.371932	−	0.322281i	−0.820691	+	0.571372i	$0.806411\pi$
$510$	73545.9	+	186027.i	0.0125208	+	0.0316703i
$511$	−1.10223e7	−	1.58477e6i	−1.86733	−	0.268481i
$512$	6.42824e6	+	1.00025e7i	1.08372	+	1.68630i
$513$	−6.05296e6	+	790580.i	−1.01549	+	0.132633i
$514$	−167173.	−	192928.i	−0.0279100	−	0.0322098i
$515$	−939184.	+	135034.i	−0.156039	+	0.0224350i
$516$	−2.04579e7	+	1.16941e7i	−3.38249	+	1.93350i
$517$	600585.	+	2.04540e6i	0.0988207	+	0.336552i
$518$	2.62004e6	+	8.92305e6i	0.429026	+	1.46113i
$519$	96366.0	−	55084.8i	0.0157038	−	0.00897663i
$520$	−1.11727e7	+	1.60639e6i	−1.81197	+	0.260522i
$521$	5.62991e6	+	6.49726e6i	0.908672	+	1.04866i	0.998610	+	0.0527155i	$0.0167877\pi$
$521$	5.62991e6	+	6.49726e6i	0.908672	+	1.04866i	−0.0899380	+	0.995947i	$0.528667\pi$
$522$	1.43576e6	−	1.34557e6i	0.230624	−	0.216137i
$523$	2.08719e6	+	3.24773e6i	0.333662	+	0.519188i	0.967030	−	0.254662i	$-0.0819643\pi$
$523$	2.08719e6	+	3.24773e6i	0.333662	+	0.519188i	−0.633368	+	0.773851i	$0.718328\pi$
$524$	−2.03816e7	−	2.93043e6i	−3.24272	−	0.466233i
$525$	−1.61753e6	−	4.09138e6i	−0.256126	−	0.647846i
$526$	−4.51692e6	−	3.91394e6i	−0.711833	−	0.616807i
$527$	86043.2	+	25264.6i	0.0134955	+	0.00396265i
$528$	3.65273e6	−	5.08305e6i	0.570207	−	0.793487i
$529$	−4.47520e6	+	4.62591e6i	−0.695302	+	0.718718i
$530$		−	1.18419e7i		−	1.83119i
$531$	−1.33113e6	+	51918.7i	−0.204873	+	0.00799075i
$532$	1.63094e7	−	1.88221e7i	2.49839	−	2.88330i
$533$	4.38368e6	−	6.82114e6i	0.668376	−	1.04001i
$534$	−6.78902e6	+	7.05898e6i	−1.03028	+	1.07125i
$535$	2.75237e6	−	1.76884e6i	0.415740	−	0.267180i
$536$	−7.28525e6	−	1.59525e7i	−1.09530	−	2.39837i
$537$	183519.	+	2.01354e6i	0.0274629	+	0.301317i
$538$	2.47845e6	+	1.72380e7i	0.369169	+	2.56763i
$539$	4.80884e6	−	1.05299e7i	0.712966	−	1.56118i
$540$	1.10243e7	+	142489.i	1.62692	+	0.0210280i
$541$	3.01949e6	−	886602.i	0.443548	−	0.130237i	−0.0523296	−	0.998630i	$-0.516665\pi$
$541$	3.01949e6	−	886602.i	0.443548	−	0.130237i	0.495878	+	0.868392i	$0.334846\pi$
$542$	−1.29158e6	−	589844.i	−0.188852	−	0.0862460i
$543$	4783.85	−	9182.03i	0.000696271	−	0.00133641i
$544$	−38881.8	+	33691.3i	−0.00563312	+	0.00488113i
$545$	−432895.	+	197697.i	−0.0624298	+	0.0285107i
$546$	−1.39988e6	+	2.69443e7i	−0.200960	+	3.86799i
$547$	1.53789e6	−	1.06962e7i	0.219764	−	1.52849i	−0.519145	−	0.854686i	$-0.673750\pi$
$547$	1.53789e6	−	1.06962e7i	0.219764	−	1.52849i	0.738909	−	0.673805i	$-0.235341\pi$
$548$	6.24189e6	+	4.01142e6i	0.887901	+	0.570619i
$549$	4.23186e6	−	1.03123e7i	0.599240	−	1.46024i
$550$	−1.06527e6	+	3.62798e6i	−0.150160	+	0.511396i
$551$	−1.31398e6			−0.184378
$552$	2.99630e6	−	1.32665e7i	0.418541	−	1.85313i
$553$	−5.28332e6			−0.734672
$554$	6.03914e6	−	2.05674e7i	0.835989	−	2.84712i
$555$	2.67438e6	−	636610.i	0.368545	−	0.0877286i
$556$	1.82791e7	+	1.17473e7i	2.50765	+	1.61157i
$557$	−1.21849e6	+	8.47475e6i	−0.166411	+	1.15741i	0.719816	+	0.694165i	$0.244226\pi$
$557$	−1.21849e6	+	8.47475e6i	−0.166411	+	1.15741i	−0.886228	+	0.463250i	$0.846683\pi$
$558$	4.57201e6	−	5.71181e6i	0.621616	−	0.776584i
$559$	−1.55063e7	+	7.08148e6i	−2.09883	+	0.958505i
$560$	−9.82662e6	+	8.51482e6i	−1.32414	+	1.14737i
$561$	−127957.	−	66665.6i	−0.0171655	−	0.00894324i
$562$	2.32871e7	+	1.06349e7i	3.11011	+	1.42034i
$563$	4.09609e6	−	1.20272e6i	0.544627	−	0.159917i	0.00216536	−	0.999998i	$-0.499311\pi$
$563$	4.09609e6	−	1.20272e6i	0.544627	−	0.159917i	0.542461	+	0.840081i	$0.317493\pi$
$564$	−6.67673e6	−	2.34310e6i	−0.883824	−	0.310165i
$565$	2.18956e6	−	4.79446e6i	0.288560	−	0.631857i
$566$	1.50038e6	+	1.04353e7i	0.196861	+	1.36920i
$567$	2.82345e6	−	1.34024e7i	0.368827	−	1.75075i
$568$	−9.59948e6	−	2.10199e7i	−1.24847	−	2.73376i
$569$	−6.59751e6	+	4.23996e6i	−0.854279	+	0.549011i	−0.892906	−	0.450242i	$-0.851338\pi$
$569$	−6.59751e6	+	4.23996e6i	−0.854279	+	0.549011i	0.0386279	+	0.999254i	$0.487701\pi$
$570$	−7.85489e6	−	7.55449e6i	−1.01263	−	0.973908i
$571$	−2.29925e6	+	3.57770e6i	−0.295118	+	0.459212i	−0.956873	−	0.290508i	$-0.906176\pi$
$571$	−2.29925e6	+	3.57770e6i	−0.295118	+	0.459212i	0.661755	+	0.749720i	$0.269812\pi$
$572$	1.02583e7	−	1.18387e7i	1.31095	−	1.51292i
$573$	1.51857e6	−	1.18366e6i	0.193218	−	0.150606i
$574$		−	2.48588e7i		−	3.14920i
$575$	355374.	+	3.06638e6i	0.0448246	+	0.386774i
$576$	−1.84367e6	−	5.47924e6i	−0.231541	−	0.688120i
$577$	−1.36488e7	−	4.00765e6i	−1.70669	−	0.501130i	−0.724541	−	0.689231i	$-0.757948\pi$
$577$	−1.36488e7	−	4.00765e6i	−1.70669	−	0.501130i	−0.982150	+	0.188102i	$0.939766\pi$
$578$	−1.06502e7	−	9.22842e6i	−1.32598	−	1.14897i
$579$	−7.01252e6	+	2.77240e6i	−0.869316	+	0.343684i
$580$	2.34905e6	+	337742.i	0.289949	+	0.0416884i
$581$	−4.29319e6	−	6.68034e6i	−0.527643	−	0.821029i
$582$	1.16140e7	+	2.29035e6i	1.42126	+	0.280282i
$583$	5.59333e6	+	6.45505e6i	0.681552	+	0.786553i
$584$	−1.63422e7	+	2.34965e6i	−1.98280	+	0.285083i
$585$	7.93283e6	+	826526.i	0.958382	+	0.0998544i
$586$	4.54325e6	+	1.54729e7i	0.546540	+	1.86135i
$587$	−1.10389e6	−	3.75949e6i	−0.132230	−	0.450333i	0.866584	−	0.499032i	$-0.166311\pi$
$587$	−1.10389e6	−	3.75949e6i	−0.132230	−	0.450333i	−0.998814	+	0.0486983i	$0.984493\pi$
$588$	1.90686e7	+	3.33588e7i	2.27444	+	3.97893i
$589$	−4.83584e6	+	695288.i	−0.574359	+	0.0825804i
$590$	−1.55744e6	−	1.79738e6i	−0.184197	−	0.212574i
$591$	592922.	−	3.00661e6i	0.0698279	−	0.354086i
$592$	2.80086e6	+	4.35822e6i	0.328464	+	0.511099i
$593$	6.99215e6	+	1.00532e6i	0.816534	+	0.117400i	0.537912	−	0.843001i	$-0.319213\pi$
$593$	6.99215e6	+	1.00532e6i	0.816534	+	0.117400i	0.278622	+	0.960401i	$0.410122\pi$
$594$	−8.99511e6	+	7.59300e6i	−1.04602	+	0.882973i
$595$	226509.	+	196271.i	0.0262296	+	0.0227281i
$596$	3.82469e6	+	1.12303e6i	0.441042	+	0.129502i
$597$	5.22056e6	+	3.75154e6i	0.599489	+	0.430798i
$598$	5.82945e6	−	1.80110e7i	0.666614	−	2.05961i
$599$			6.87594e6i			0.783006i	0.920177	+	0.391503i	$0.128045\pi$
$599$			6.87594e6i			0.783006i	−0.920177	+	0.391503i	$0.871955\pi$
$600$	−4.01008e6	−	5.14469e6i	−0.454753	−	0.583420i
$601$	4.34782e6	−	5.01765e6i	0.491004	−	0.566649i	−0.455129	−	0.890425i	$-0.650407\pi$
$601$	4.34782e6	−	5.01765e6i	0.491004	−	0.566649i	0.946134	+	0.323776i	$0.104952\pi$
$602$	−2.82553e7	+	4.39662e7i	−3.17767	+	4.94456i
$603$	2.24023e6	+	1.21876e7i	0.250899	+	1.36497i
$604$	−2.60135e6	+	1.67179e6i	−0.290140	+	0.186461i
$605$	−1.14577e6	−	2.50890e6i	−0.127266	−	0.278673i
$606$	3.08141e7	−	2.80848e6i	3.40854	−	0.310663i
$607$	−944747.	−	6.57086e6i	−0.104074	−	0.723853i	−0.973317	−	0.229467i	$-0.926302\pi$
$607$	−944747.	−	6.57086e6i	−0.104074	−	0.723853i	0.869242	−	0.494387i	$-0.164607\pi$
$608$	1.16437e6	−	2.54961e6i	0.127741	−	0.279715i
$609$	976261.	−	2.78189e6i	0.106665	−	0.303946i
$610$	1.90943e7	−	5.60660e6i	2.07769	−	0.610064i
$611$	−4.65624e6	−	2.12643e6i	−0.504583	−	0.230435i
$612$	427551.	−	215775.i	0.0461434	−	0.0232875i
$613$	4.09306e6	−	3.54666e6i	0.439944	−	0.381214i	−0.406535	−	0.913635i	$-0.633263\pi$
$613$	4.09306e6	−	3.54666e6i	0.439944	−	0.381214i	0.846479	+	0.532421i	$0.178718\pi$
$614$	2.62974e7	−	1.20096e7i	2.81509	−	1.28561i
$615$	−7.33863e6	−	381276.i	−0.782397	−	0.0406492i
$616$	3.55223e6	−	2.47063e7i	0.377181	−	2.62335i
$617$	7.82920e6	+	5.03152e6i	0.827950	+	0.532091i	0.884626	−	0.466301i	$-0.154414\pi$
$617$	7.82920e6	+	5.03152e6i	0.827950	+	0.532091i	−0.0566757	+	0.998393i	$0.518050\pi$
$618$	778689.	+	3.27125e6i	0.0820149	+	0.344542i
$619$	−1.02784e6	+	3.50051e6i	−0.107820	+	0.367202i	−0.995673	−	0.0929257i	$-0.970378\pi$
$619$	−1.02784e6	+	3.50051e6i	−0.107820	+	0.367202i	0.887853	+	0.460127i	$0.152196\pi$
$620$	8.82390e6			0.921895
$621$	−4.34153e6	+	8.57354e6i	−0.451766	+	0.892136i
$622$	−1.63811e7			−1.69772
$623$	−4.13415e6	+	1.40796e7i	−0.426742	+	1.45335i
$624$	3.48054e6	+	1.46216e7i	0.357837	+	1.50326i
$625$	−3.77114e6	−	2.42356e6i	−0.386164	−	0.248173i
$626$	2.24071e6	−	1.55845e7i	0.228533	−	1.58948i
$627$	7.84994e6	+	407841.i	0.797439	+	0.0414307i
$628$	1.25942e7	−	5.75157e6i	1.27430	−	0.581953i
$629$	90248.6	−	78200.9i	0.00909524	−	0.00788107i
$630$	2.18300e7	−	1.10171e7i	2.19130	−	1.10590i
$631$	−5.49693e6	−	2.51037e6i	−0.549601	−	0.250994i	0.121205	−	0.992628i	$-0.461324\pi$
$631$	−5.49693e6	−	2.51037e6i	−0.549601	−	0.250994i	−0.670805	+	0.741633i	$0.734051\pi$
$632$	−7.51598e6	+	2.20689e6i	−0.748501	+	0.219780i
$633$	892094.	−	2.54205e6i	0.0884915	−	0.252159i
$634$	41968.1	−	91897.4i	0.00414664	−	0.00907988i
$635$	928767.	+	6.45972e6i	0.0914056	+	0.635740i
$636$	−2.82339e7	+	2.57332e6i	−2.76776	+	0.252261i
$637$	1.15471e7	+	2.52846e7i	1.12752	+	2.46893i
$638$	−2.13159e6	+	1.36989e6i	−0.207325	+	0.133240i
$639$	2.95186e6	+	1.60591e7i	0.285985	+	1.55585i
$640$	6.89444e6	−	1.07280e7i	0.665349	−	1.03530i
$641$	−2.78494e6	+	3.21399e6i	−0.267714	+	0.308958i	−0.873650	−	0.486555i	$-0.838253\pi$
$641$	−2.78494e6	+	3.21399e6i	−0.267714	+	0.308958i	0.605936	+	0.795513i	$0.292799\pi$
$642$	−7.12817e6	−	9.14501e6i	−0.682559	−	0.875682i
$643$		−	7.18996e6i		−	0.685802i	−0.939372	−	0.342901i	$-0.888590\pi$
$643$		−	7.18996e6i		−	0.685802i	0.939372	−	0.342901i	$-0.111410\pi$
$644$	−1.00107e7	−	3.79088e7i	−0.951149	−	3.60185i
$645$	1.25460e7	+	9.01567e6i	1.18742	+	0.853294i
$646$	−454220.	−	133371.i	−0.0428237	−	0.0125742i
$647$	−817513.	−	708379.i	−0.0767775	−	0.0665281i	0.615627	−	0.788038i	$-0.288903\pi$
$647$	−817513.	−	708379.i	−0.0767775	−	0.0665281i	−0.692404	+	0.721510i	$0.743448\pi$
$648$	−1.58169e6	−	2.02454e7i	−0.147973	−	1.89404i
$649$	1.69793e6	+	244125.i	0.158237	+	0.0227510i
$650$	−4.90867e6	−	7.63804e6i	−0.455702	−	0.709086i
$651$	2.12090e6	−	1.07547e7i	0.196141	−	0.994598i
$652$	3.47247e6	+	4.00744e6i	0.319904	+	0.369189i
$653$	−1.52334e7	+	2.19023e6i	−1.39802	+	0.201005i	−0.799771	−	0.600306i	$-0.795046\pi$
$653$	−1.52334e7	+	2.19023e6i	−1.39802	+	0.201005i	−0.598249	+	0.801310i	$0.704137\pi$
$654$	836986.	+	1.46423e6i	0.0765198	+	0.133865i
$655$	3.80342e6	+	1.29533e7i	0.346395	+	1.17971i
$656$	−3.90147e6	−	1.32872e7i	−0.353972	−	1.20552i
$657$	1.16032e7	+	1.20895e6i	1.04874	+	0.109268i
$658$	−1.55338e7	+	2.23342e6i	−1.39866	+	0.201097i
$659$	−2.42443e6	−	2.79794e6i	−0.217468	−	0.250972i	0.636525	−	0.771256i	$-0.280371\pi$
$659$	−2.42443e6	−	2.79794e6i	−0.217468	−	0.250972i	−0.853993	+	0.520285i	$0.825826\pi$
$660$	−1.39288e7	−	2.74684e6i	−1.24467	−	0.245456i
$661$	−6.89312e6	−	1.07259e7i	−0.613638	−	0.954840i	−0.999479	−	0.0322743i	$-0.989725\pi$
$661$	−6.89312e6	−	1.07259e7i	−0.613638	−	0.954840i	0.385841	−	0.922565i	$-0.373911\pi$
$662$	−461376.	−	66335.8i	−0.0409176	−	0.00588306i
$663$	322187.	−	127377.i	0.0284659	−	0.0112540i
$664$	−8.89788e6	−	7.71006e6i	−0.783189	−	0.678637i
$665$	−1.56671e7	−	4.60027e6i	−1.37383	−	0.403394i
$666$	−3.10708e6	−	9.23397e6i	−0.271435	−	0.806683i
$667$	−1.16566e6	+	1.70890e6i	−0.101452	+	0.148731i
$668$		−	1.00244e7i		−	0.869199i
$669$	−8.52564e6	+	6.64540e6i	−0.736482	+	0.574058i
$670$	−1.44875e7	+	1.67195e7i	−1.24683	+	1.43892i
$671$	−7.76016e6	+	1.20750e7i	−0.665372	+	1.03534i
$672$	4.53280e6	+	4.35945e6i	0.387207	+	0.372399i
$673$	6.14124e6	−	3.94674e6i	0.522659	−	0.335893i	−0.252564	−	0.967580i	$-0.581274\pi$
$673$	6.14124e6	−	3.94674e6i	0.522659	−	0.335893i	0.775223	+	0.631688i	$0.217637\pi$
$674$	1.19797e7	+	2.62318e7i	1.01577	+	2.22422i
$675$	1.86033e6	+	4.21695e6i	0.157156	+	0.356237i
$676$	1.83247e6	+	1.27451e7i	0.154231	+	1.07270i
$677$	4.94315e6	−	1.08240e7i	0.414507	−	0.907644i	−0.581084	−	0.813844i	$-0.697371\pi$
$677$	4.94315e6	−	1.08240e7i	0.414507	−	0.907644i	0.995591	−	0.0938001i	$-0.0299015\pi$
$678$	−1.76255e7	−	6.18541e6i	−1.47254	−	0.516766i
$679$	1.70178e7	−	4.99687e6i	1.41654	−	0.415933i
$680$	404212.	+	184597.i	0.0335226	+	0.0153092i
$681$	−635455.	−	331073.i	−0.0525070	−	0.0273562i
$682$	−7.12000e6	+	6.16951e6i	−0.586164	+	0.507914i
$683$	1.63760e7	−	7.47865e6i	1.34324	−	0.613439i	0.391457	−	0.920196i	$-0.371971\pi$
$683$	1.63760e7	−	7.47865e6i	1.34324	−	0.613439i	0.951788	+	0.306757i	$0.0992440\pi$
$684$	−1.63048e7	+	2.03695e7i	−1.33252	+	1.66472i
$685$	692302.	−	4.81507e6i	0.0563727	−	0.392081i
$686$	3.91216e7	+	2.51419e7i	3.17400	+	2.03980i
$687$	−4.56818e6	+	1.08741e6i	−0.369276	+	0.0879027i
$688$	−8.20238e6	+	2.79348e7i	−0.660646	+	2.24995i
$689$	−2.05094e7			−1.64591
$690$	−1.67933e7	+	3.51394e6i	−1.34280	+	0.280977i
$691$	1.79981e7			1.43394			0.716969	−	0.697105i	$-0.245529\pi$
$691$	1.79981e7			1.43394			0.716969	+	0.697105i	$0.245529\pi$
$692$	133663.	−	455216.i	0.0106108	−	0.0361370i
$693$	−6.69580e6	+	1.63164e7i	−0.529626	+	1.29060i
$694$	−3.24273e7	−	2.08397e7i	−2.55571	−	1.64246i
$695$	2.02738e6	−	1.41007e7i	0.159211	−	1.10733i
$696$	226796.	−	4.36527e6i	0.0177465	−	0.341576i
$697$	−290360.	+	132603.i	−0.0226389	+	0.0103388i
$698$	−6.23434e6	+	5.40208e6i	−0.484342	+	0.419684i
$699$	−9.36992e6	+	1.79845e7i	−0.725342	+	1.39221i
$700$	−1.71052e7	−	7.81169e6i	−1.31942	−	0.602560i
$701$	1.25993e7	−	3.69948e6i	0.968390	−	0.284345i	0.240966	−	0.970534i	$-0.422536\pi$
$701$	1.25993e7	−	3.69948e6i	0.968390	−	0.284345i	0.727424	+	0.686189i	$0.240718\pi$
$702$	365306.	−	2.82634e7i	0.0279778	−	2.16462i
$703$	−2.70262e6	+	5.91791e6i	−0.206251	+	0.451627i
$704$	1.05943e6	+	7.36849e6i	0.0805639	+	0.560334i
$705$	421081.	+	4.62002e6i	0.0319075	+	0.350083i
$706$	−7.49649e6	−	1.64150e7i	−0.566039	−	1.23945i
$707$	3.90002e7	−	2.50639e7i	2.93439	−	1.88582i
$708$	−3.94694e6	+	4.10389e6i	−0.295922	+	0.307689i
$709$	−1.99595e6	+	3.10575e6i	−0.149119	+	0.232034i	−0.907775	−	0.419458i	$-0.862220\pi$
$709$	−1.99595e6	+	3.10575e6i	−0.149119	+	0.232034i	0.758656	+	0.651492i	$0.225857\pi$
$710$	−1.90896e7	+	2.20306e7i	−1.42119	+	1.64014i
$711$	5.53075e6	−	215718.i	0.410308	−	0.0160034i
$712$			2.17563e7i			1.60837i
$713$	−3.38572e6	+	6.90607e6i	−0.249418	+	0.508753i
$714$	619841.	−	862556.i	0.0455025	−	0.0633202i
$715$	−9.85429e6	−	2.89348e6i	−0.720876	−	0.211668i
$716$	6.53117e6	+	5.65929e6i	0.476111	+	0.412553i
$717$	−7.69372e6	−	1.94606e7i	−0.558906	−	1.41370i
$718$	3.63951e6	+	523282.i	0.263470	+	0.0378813i
$719$	−1.64815e6	−	2.56457e6i	−0.118898	−	0.185009i	0.776703	−	0.629867i	$-0.216891\pi$
$719$	−1.64815e6	−	2.56457e6i	−0.118898	−	0.185009i	−0.895601	+	0.444858i	$0.853254\pi$
$720$	9.93918e6	−	9.31482e6i	0.714528	−	0.669643i
$721$	3.29932e6	+	3.80762e6i	0.236367	+	0.272782i
$722$	1.18793e6	−	170799.i	0.0848104	−	0.0121939i
$723$	9.13720e6	−	5.22301e6i	0.650081	−	0.371599i
$724$	−12467.6	−	42460.6i	−0.000883965	−	0.00301051i
$725$	279511.	+	951927.i	0.0197494	+	0.0672603i
$726$	−8.48614e6	+	4.85085e6i	−0.597542	+	0.341567i
$727$	2.44381e7	−	3.51366e6i	1.71487	−	0.246561i	0.786333	−	0.617804i	$-0.211977\pi$
$727$	2.44381e7	−	3.51366e6i	1.71487	−	0.246561i	0.928536	+	0.371243i	$0.121068\pi$
$728$	3.92494e7	+	4.52962e7i	2.74476	+	3.16762i
$729$	−2.40846e6	+	1.41453e7i	−0.167850	+	0.985813i
$730$	1.12602e7	+	1.75212e7i	0.782055	+	1.21690i
$731$	664263.	+	95506.6i	0.0459776	+	0.00661059i
$732$	−1.75168e7	−	4.43070e7i	−1.20830	−	3.05629i
$733$	1.02729e7	+	8.90148e6i	0.706206	+	0.611931i	0.932091	−	0.362223i	$-0.117982\pi$
$733$	1.02729e7	+	8.90148e6i	0.706206	+	0.611931i	−0.225886	+	0.974154i	$0.572528\pi$
$734$	1.63242e7	+	4.79323e6i	1.11839	+	0.328389i
$735$	1.47010e7	−	2.04576e7i	1.00376	−	1.39681i
$736$	−2.28297e6	−	3.77615e6i	−0.155348	−	0.256953i
$737$		−	1.59567e7i		−	1.08212i
$738$	1.01499e6	+	2.60230e7i	0.0685993	+	1.75880i
$739$	−4.03631e6	+	4.65815e6i	−0.271878	+	0.313764i	−0.875226	−	0.483714i	$-0.839287\pi$
$739$	−4.03631e6	+	4.65815e6i	−0.271878	+	0.313764i	0.603348	+	0.797478i	$0.293833\pi$
$740$	6.35269e6	−	9.88497e6i	0.426460	−	0.663584i
$741$	−1.30839e7	+	1.36042e7i	−0.875369	+	0.910177i
$742$	−5.28970e7	+	3.39948e7i	−3.52713	+	2.26675i
$743$	−178626.	−	391137.i	−0.0118706	−	0.0259930i	0.903604	−	0.428369i	$-0.140912\pi$
$743$	−178626.	−	391137.i	−0.0118706	−	0.0259930i	−0.915474	+	0.402376i	$0.868184\pi$
$744$	−1.47519e6	−	1.61855e7i	−0.0977047	−	1.07200i
$745$	−371930.	−	2.58683e6i	−0.0245510	−	0.170756i
$746$	−1.05123e7	+	2.30187e7i	−0.691591	+	1.51437i
$747$	4.76702e6	+	6.81791e6i	0.312569	+	0.447044i
$748$	−591712.	+	173742.i	−0.0386684	+	0.0113541i
$749$	−1.58026e7	−	7.21678e6i	−1.02925	−	0.470045i
$750$	−1.35668e7	+	2.60399e7i	−0.880692	+	1.69038i
$751$	3.23822e6	−	2.80594e6i	0.209511	−	0.181542i	−0.543784	−	0.839225i	$-0.683009\pi$
$751$	3.23822e6	−	2.80594e6i	0.209511	−	0.181542i	0.753295	+	0.657683i	$0.228463\pi$
$752$	−7.95238e6	+	3.63173e6i	−0.512805	+	0.234190i
$753$	40488.7	−	779308.i	0.00260223	−	0.0500866i
$754$	865882.	−	6.02234e6i	0.0554665	−	0.385778i
$755$	1.70552e6	+	1.09607e6i	0.108890	+	0.0699794i
$756$	−3.10111e7	−	4.96537e7i	−1.97339	−	3.15971i
$757$	−1.20611e6	+	4.10762e6i	−0.0764972	+	0.260526i	−0.988858	−	0.148861i	$-0.952439\pi$
$757$	−1.20611e6	+	4.10762e6i	−0.0764972	+	0.260526i	0.912361	+	0.409387i	$0.134257\pi$
$758$	2.93560e7			1.85577
$759$	7.49429e6	−	9.84746e6i	0.472200	−	0.620469i
$760$	−2.42094e7			−1.52037
$761$	167074.	−	569003.i	0.0104580	−	0.0356166i	−0.954099	−	0.299492i	$-0.903183\pi$
$761$	167074.	−	569003.i	0.0104580	−	0.0356166i	0.964557	+	0.263876i	$0.0850009\pi$
$762$	2.24997e7	−	5.35583e6i	1.40375	−	0.334149i
$763$	2.12582e6	+	1.36618e6i	0.132195	+	0.0849565i
$764$	1.17118e6	−	8.14577e6i	0.0725926	−	0.504892i
$765$	−245130.	−	196214.i	−0.0151441	−	0.0121221i
$766$	4.25640e7	−	1.94383e7i	2.62102	−	1.19698i
$767$	−3.11295e6	+	2.69739e6i	−0.191066	+	0.165560i
$768$	−2.95555e7	−	1.53984e7i	−1.80815	−	0.942050i
$769$	−1.48511e6	−	678227.i	−0.0905613	−	0.0413580i	0.369619	−	0.929183i	$-0.379488\pi$
$769$	−1.48511e6	−	678227.i	−0.0905613	−	0.0413580i	−0.460181	+	0.887825i	$0.652215\pi$
$770$	−3.02117e7	+	8.87096e6i	−1.83632	+	0.539193i
$771$	378094.	+	132686.i	0.0229068	+	0.00803879i
$772$	−1.33890e7	+	2.93179e7i	−0.808548	+	1.77047i
$773$	4.42085e6	+	3.07477e7i	0.266107	+	1.85082i	0.484289	+	0.874908i	$0.339078\pi$
$773$	4.42085e6	+	3.07477e7i	0.266107	+	1.85082i	−0.218182	+	0.975908i	$0.570013\pi$
$774$	2.77835e7	−	4.71789e7i	1.66700	−	2.83071i
$775$	1.53239e6	+	3.35547e6i	0.0916464	+	0.200678i
$776$	2.21220e7	−	1.42170e7i	1.31877	−	0.847525i
$777$	−1.05211e7	−	1.01187e7i	−0.625184	−	0.601275i
$778$	−781517.	+	1.21606e6i	−0.0462903	+	0.0720291i
$779$	1.13883e7	−	1.31429e7i	0.672383	−	0.775972i
$780$	2.68873e7	−	2.09575e7i	1.58238	−	1.23340i
$781$		−	2.10255e7i		−	1.23344i
$782$	−576405.	+	472421.i	−0.0337063	+	0.0276256i
$783$	−908398.	+	2.95203e6i	−0.0529507	+	0.172075i
$784$	4.55506e7	+	1.33749e7i	2.64669	+	0.777140i
$785$	−6.86023e6	−	5.94443e6i	−0.397342	−	0.344299i
$786$	4.44928e7	−	1.75902e7i	2.56882	−	1.01558i
$787$	6.03379e6	+	867528.i	0.347259	+	0.0499283i	0.313738	−	0.949510i	$-0.398419\pi$
$787$	6.03379e6	+	867528.i	0.347259	+	0.0499283i	0.0335213	+	0.999438i	$0.489328\pi$
$788$	−7.08155e6	−	1.10191e7i	−0.406268	−	0.632165i
$789$	9.20411e6	+	1.81511e6i	0.526368	+	0.103803i
$790$	6.47105e6	+	7.46799e6i	0.368899	+	0.425732i
$791$	−2.77021e7	+	3.98296e6i	−1.57424	+	0.226342i
$792$	−2.70984e6	+	2.60084e7i	−0.153508	+	1.47333i
$793$	−9.71027e6	−	3.30701e7i	−0.548338	−	1.86747i
$794$	6.56037e6	+	2.23426e7i	0.369298	+	1.25771i
$795$	9.22438e6	+	1.61373e7i	0.517630	+	0.905549i
$796$	2.71980e7	−	3.91049e6i	1.52144	−	0.218750i
$797$	−3.37219e6	−	3.89171e6i	−0.188047	−	0.217018i	0.653896	−	0.756585i	$-0.273133\pi$
$797$	−3.37219e6	−	3.89171e6i	−0.188047	−	0.217018i	−0.841943	+	0.539567i	$0.818588\pi$
$798$	−1.11962e7	+	5.67740e7i	−0.622390	+	3.15604i
$799$	108948.	+	169527.i	0.00603745	+	0.00939445i
$800$	−2.09478e6	−	301184.i	−0.115721	−	0.0166382i
$801$	3.75289e6	−	1.49078e7i	0.206673	−	0.820980i
$802$	3.19606e7	+	2.76940e7i	1.75460	+	1.52037i
$803$	−1.44137e7	−	4.23226e6i	−0.788838	−	0.231624i
$804$	4.30114e7	+	3.09084e7i	2.34662	+	1.68631i
$805$	−1.98816e7	+	1.62949e7i	−1.08134	+	0.886261i
$806$		−	2.26222e7i		−	1.22658i
$807$	−1.68052e7	−	2.15600e7i	−0.908362	−	1.16537i
$808$	4.50118e7	−	5.19463e7i	2.42548	−	2.79915i
$809$	1.24676e7	−	1.94000e7i	0.669751	−	1.04215i	−0.325569	−	0.945518i	$-0.605556\pi$
$809$	1.24676e7	−	1.94000e7i	0.669751	−	1.04215i	0.995320	−	0.0966342i	$-0.0308077\pi$
$810$	−2.24025e7	+	1.24244e7i	−1.19973	+	0.665369i
$811$	1.51219e7	−	9.71827e6i	0.807337	−	0.518844i	−0.0706653	−	0.997500i	$-0.522512\pi$
$811$	1.51219e7	−	9.71827e6i	0.807337	−	0.518844i	0.878003	+	0.478656i	$0.158876\pi$
$812$	−5.23478e6	−	1.14626e7i	−0.278618	−	0.610088i
$813$	2.21953e6	−	202294.i	0.117770	−	0.0107339i
$814$	1.78542e6	+	1.24179e7i	0.0944450	+	0.656880i
$815$	1.44420e6	−	3.16236e6i	0.0761612	−	0.166770i
$816$	195935.	−	558323.i	0.0103012	−	0.0293535i
$817$	−3.50804e7	+	1.03005e7i	−1.83870	+	0.539890i
$818$	−3.75892e7	−	1.71664e7i	−1.96417	−	0.897007i
$819$	−1.90809e7	−	3.78081e7i	−0.994006	−	1.96959i
$820$	−2.37375e7	+	2.05687e7i	−1.23282	+	1.06825i
$821$	−1.05264e7	+	4.80725e6i	−0.545033	+	0.248908i	−0.668851	−	0.743397i	$-0.733213\pi$
$821$	−1.05264e7	+	4.80725e6i	−0.545033	+	0.248908i	0.123818	+	0.992305i	$0.460486\pi$
$822$	−1.72166e7	−	894483.i	−0.888726	−	0.0461735i
$823$	3.73334e6	−	2.59660e7i	0.192131	−	1.33630i	−0.634222	−	0.773151i	$-0.718680\pi$
$823$	3.73334e6	−	2.59660e7i	0.192131	−	1.33630i	0.826353	−	0.563152i	$-0.190411\pi$
$824$	6.28405e6	+	4.03851e6i	0.322420	+	0.207206i
$825$	−1.37438e6	−	5.77372e6i	−0.0703027	−	0.295339i
$826$	−3.55780e6	+	1.21168e7i	−0.181439	+	0.617926i
$827$	2.24897e7			1.14346			0.571729	−	0.820442i	$-0.306273\pi$
$827$	2.24897e7			1.14346			0.571729	+	0.820442i	$0.306273\pi$
$828$	1.20273e7	+	3.92755e7i	0.609668	+	1.99088i
$829$	−5.94962e6			−0.300679			−0.150339	−	0.988634i	$-0.548037\pi$
$829$	−5.94962e6			−0.300679			−0.150339	+	0.988634i	$0.548037\pi$
$830$	−4.18435e6	+	1.42506e7i	−0.210830	+	0.718022i
$831$	7.79152e6	+	3.27319e7i	0.391399	+	1.64425i
$832$	−1.50377e7	−	9.66414e6i	−0.753135	−	0.484011i
$833$	155734.	−	1.08315e6i	0.00777625	−	0.0540850i
$834$	−5.04181e7	−	2.61945e6i	−2.50998	−	0.130405i
$835$	−5.97836e6	+	2.73023e6i	−0.296733	+	0.135514i
$836$	2.53914e7	−	2.20018e7i	1.25652	−	1.08879i
$837$	−1.78111e6	+	1.13450e7i	−0.0878776	+	0.559747i
$838$	−4.09901e6	−	1.87195e6i	−0.201636	−	0.0920842i
$839$	−1.81252e6	+	532205.i	−0.0888953	+	0.0261020i	−0.325878	−	0.945412i	$-0.605660\pi$
$839$	−1.81252e6	+	532205.i	−0.0888953	+	0.0261020i	0.236982	+	0.971514i	$0.423842\pi$
$840$	1.79871e7	−	5.12548e7i	0.879554	−	2.50632i
$841$	8.24446e6	−	1.80528e7i	0.401950	−	0.880148i
$842$	8.11229e6	+	5.64222e7i	0.394333	+	2.74265i
$843$	−4.00180e7	+	3.64736e6i	−1.93949	+	0.176770i
$844$	−4.78347e6	−	1.04743e7i	−0.231147	−	0.506140i
$845$	7.10183e6	−	4.56407e6i	0.342159	−	0.219893i
$846$	1.61701e7	−	2.97226e6i	0.776759	−	0.142778i
$847$	−7.91786e6	+	1.23204e7i	−0.379227	+	0.590089i
$848$	−2.29385e7	+	2.64724e7i	−1.09541	+	1.26416i
$849$	−1.01733e7	−	1.30517e7i	−0.484387	−	0.621440i
$850$			357435.i			0.0169687i
$851$	5.29901e6	+	8.76482e6i	0.250825	+	0.414877i
$852$	5.66743e7	+	4.07267e7i	2.67478	+	1.92212i
$853$	2.21722e7	+	6.51034e6i	1.04336	+	0.306359i	0.758133	−	0.652100i	$-0.226112\pi$
$853$	2.21722e7	+	6.51034e6i	1.04336	+	0.306359i	0.285231	+	0.958459i	$0.407930\pi$
$854$	−7.98587e7	−	6.91980e7i	−3.74695	−	3.24675i
$855$	1.65887e7	+	4.17603e6i	0.776062	+	0.195366i
$856$	−2.54950e7	−	3.66563e6i	−1.18924	−	0.170987i
$857$	1.61847e6	+	2.51839e6i	0.0752754	+	0.117131i	0.876850	−	0.480764i	$-0.159641\pi$
$857$	1.61847e6	+	2.51839e6i	0.0752754	+	0.117131i	−0.801575	+	0.597895i	$0.796004\pi$
$858$	−7.04217e6	+	3.57097e7i	−0.326579	+	1.65603i
$859$	2.06710e6	+	2.38556e6i	0.0955824	+	0.110308i	0.801526	−	0.597961i	$-0.204022\pi$
$859$	2.06710e6	+	2.38556e6i	0.0955824	+	0.110308i	−0.705943	+	0.708269i	$0.749477\pi$
$860$	6.53621e7	−	9.39765e6i	3.01356	−	0.433284i
$861$	1.93640e7	+	3.38756e7i	0.890199	+	1.55733i
$862$	−7.91021e6	−	2.69397e7i	−0.362593	−	1.23488i
$863$	−2.58327e6	−	8.79781e6i	−0.118071	−	0.402113i	0.879156	−	0.476534i	$-0.158107\pi$
$863$	−2.58327e6	−	8.79781e6i	−0.118071	−	0.402113i	−0.997227	+	0.0744215i	$0.976289\pi$
$864$	−4.92308e6	−	4.37854e6i	−0.224364	−	0.199547i
$865$	−307885.	+	44267.2i	−0.0139910	+	0.00201160i
$866$	−5.03278e6	−	5.80814e6i	−0.228041	−	0.263174i
$867$	2.17018e7	+	4.27972e6i	0.980500	+	0.193361i
$868$	−2.53309e7	−	3.94157e7i	−1.14117	−	1.77570i
$869$	−7.05476e6	−	1.01432e6i	−0.316908	−	0.0455644i
$870$	−5.12794e6	+	2.02733e6i	−0.229692	+	0.0908085i
$871$	2.89571e7	+	2.50914e7i	1.29333	+	1.12068i
$872$	3.59483e6	+	1.05554e6i	0.160098	+	0.0470091i
$873$	−1.76108e7	+	5.92573e6i	−0.782064	+	0.263152i
$874$	1.78731e7	−	3.64570e7i	0.791448	−	1.61437i
$875$			4.39927e7i			1.94250i
$876$	3.93276e7	−	3.06543e7i	1.73156	−	1.34968i
$877$	−1.47595e7	+	1.70334e7i	−0.647997	+	0.747828i	−0.980767	−	0.195180i	$-0.937471\pi$
$877$	−1.47595e7	+	1.70334e7i	−0.647997	+	0.747828i	0.332771	+	0.943008i	$0.392016\pi$
$878$	9.41471e6	−	1.46496e7i	0.412165	−	0.641341i
$879$	−1.82439e7	−	1.75462e7i	−0.796427	−	0.765969i
$880$	−1.47561e7	+	9.48318e6i	−0.642340	+	0.412807i
$881$	−6.09442e6	−	1.33449e7i	−0.264541	−	0.579263i	0.730019	−	0.683426i	$-0.239511\pi$
$881$	−6.09442e6	−	1.33449e7i	−0.264541	−	0.579263i	−0.994560	+	0.104163i	$0.966784\pi$
$882$	−7.69303e7	−	4.53040e7i	−3.32986	−	1.96094i
$883$	−3.62423e6	−	2.52070e7i	−0.156428	−	1.08798i	−0.905149	−	0.425094i	$-0.860241\pi$
$883$	−3.62423e6	−	2.52070e7i	−0.156428	−	1.08798i	0.748722	−	0.662884i	$-0.230668\pi$
$884$	615154.	−	1.34700e6i	0.0264760	−	0.0579744i
$885$	3.52245e6	+	1.23615e6i	0.151177	+	0.0530534i
$886$	−3.33259e7	+	9.78535e6i	−1.42625	+	0.418786i
$887$	1.65057e7	+	7.53788e6i	0.704407	+	0.321692i	0.735216	−	0.677833i	$-0.237081\pi$
$887$	1.65057e7	+	7.53788e6i	0.704407	+	0.321692i	−0.0308084	+	0.999525i	$0.509808\pi$
$888$	−1.91938e7	−	1.00000e7i	−0.816826	−	0.425567i
$889$	2.61889e7	−	2.26928e7i	1.11138	−	0.963015i
$890$	2.49651e7	−	1.14012e7i	1.05647	−	0.482476i
$891$	6.34319e6	−	1.73540e7i	0.267678	−	0.732327i
$892$	−6.57533e6	+	4.57325e7i	−0.276698	+	1.92448i
$893$	−9.23588e6	−	5.93554e6i	−0.387570	−	0.249076i
$894$	−9.01011e6	+	2.14477e6i	−0.377039	+	0.0897505i
$895$	1.59627e6	−	5.43640e6i	0.0666115	−	0.226858i
$896$	−6.77130e7			−2.81775
$897$	6.08591e6	+	2.90849e7i	0.252548	+	1.20694i
$898$	−340903.			−0.0141072
$899$	−696431.	+	2.37183e6i	−0.0287395	+	0.0978777i
$900$	1.82253e7	+	7.47913e6i	0.750011	+	0.307783i
$901$	679239.	+	436520.i	0.0278747	+	0.0179140i
$902$	4.77253e6	−	3.31937e7i	0.195314	−	1.35844i
$903$	4.25631e6	−	8.19235e7i	0.173705	−	3.34340i
$904$	−3.77450e7	+	1.72375e7i	−1.53616	+	0.701543i
$905$	−21927.0	+	18999.8i	−0.000889933	+	0.000771131i
$906$	3.31976e6	−	6.37189e6i	0.134365	−	0.257898i
$907$	3.33069e7	+	1.52108e7i	1.34436	+	0.613950i	0.952067	−	0.305890i	$-0.0989539\pi$
$907$	3.33069e7	+	1.52108e7i	1.34436	+	0.613950i	0.392295	+	0.919839i	$0.371681\pi$
$908$	−2.93854e6	+	862834.i	−0.118282	+	0.0347306i
$909$	−3.98034e7	+	2.78301e7i	−1.59775	+	1.11713i
$910$	3.14086e7	−	6.87752e7i	1.25732	−	2.75314i
$911$	786314.	+	5.46893e6i	0.0313906	+	0.218327i	0.999479	−	0.0322834i	$-0.0102779\pi$
$911$	786314.	+	5.46893e6i	0.0313906	+	0.218327i	−0.968088	+	0.250610i	$0.919369\pi$
$912$	2.92598e6	+	3.21033e7i	0.116489	+	1.27809i
$913$	−4.45013e6	−	9.74442e6i	−0.176683	−	0.386883i
$914$	292855.	−	188206.i	0.0115954	−	0.00745193i
$915$	−2.16530e7	+	2.25140e7i	−0.854997	+	0.888994i
$916$	−1.08512e7	+	1.68848e7i	−0.427306	+	0.664901i
$917$	4.69427e7	−	5.41748e7i	1.84351	−	2.12752i
$918$	−613652.	+	928261.i	−0.0240334	+	0.0363549i
$919$		−	4.20918e7i		−	1.64403i	−0.569469	−	0.822013i	$-0.692851\pi$
$919$		−	4.20918e7i		−	1.64403i	0.569469	−	0.822013i	$-0.307149\pi$
$920$	−2.14767e7	+	3.14856e7i	−0.836562	+	1.22643i
$921$	−2.64811e7	+	3.68504e7i	−1.02869	+	1.43151i
$922$	1.98880e7	+	5.83965e6i	0.770485	+	0.226235i
$923$	3.81555e7	+	3.30620e7i	1.47419	+	1.27739i
$924$	2.77156e7	+	7.01041e7i	1.06794	+	2.70124i
$925$	4.86220e6	+	699078.i	0.186844	+	0.0268640i
$926$	2.13598e7	+	3.32365e7i	0.818597	+	1.27376i
$927$	−3.60930e6	−	3.85123e6i	−0.137951	−	0.147197i
$928$	−928718.	−	1.07180e6i	−0.0354009	−	0.0408548i
$929$	2.12485e7	−	3.05507e6i	0.807771	−	0.116140i	0.273957	−	0.961742i	$-0.411667\pi$
$929$	2.12485e7	−	3.05507e6i	0.807771	−	0.116140i	0.533814	+	0.845602i	$0.320758\pi$
$930$	−1.77996e7	+	1.01746e7i	−0.674843	+	0.385754i
$931$	1.67961e7	+	5.72024e7i	0.635090	+	2.16292i
$932$	2.44197e7	+	8.31658e7i	0.920874	+	3.13621i
$933$	2.23229e7	−	1.27602e7i	0.839549	−	0.479903i
$934$	5.78328e7	−	8.31510e6i	2.16924	−	0.311889i
$935$	264773.	+	305565.i	0.00990479	+	0.0114307i
$936$	−4.29370e7	−	4.58150e7i	−1.60193	−	1.70930i
$937$	−5.51487e6	−	8.58130e6i	−0.205204	−	0.319304i	0.723363	−	0.690468i	$-0.242595\pi$
$937$	−5.51487e6	−	8.58130e6i	−0.205204	−	0.319304i	−0.928567	+	0.371164i	$0.878959\pi$
$938$	1.16274e8	+	1.67177e7i	4.31496	+	0.620397i
$939$	9.08622e6	+	2.29827e7i	0.336294	+	0.850624i
$940$	1.49856e7	+	1.29851e7i	0.553166	+	0.479321i
$941$	−1.14031e7	−	3.34824e6i	−0.419805	−	0.123266i	0.0650060	−	0.997885i	$-0.479293\pi$
$941$	−1.14031e7	−	3.34824e6i	−0.419805	−	0.123266i	−0.484811	+	0.874619i	$0.661112\pi$
$942$	−1.87730e7	+	2.61241e7i	−0.689299	+	0.959212i
$943$	−6.99012e6	−	2.64705e7i	−0.255980	−	0.969355i
$944$			7.03487e6i			0.256937i
$945$	−2.11663e7	+	3.20179e7i	−0.771020	+	1.16631i
$946$	−4.61699e7	+	5.32830e7i	−1.67738	+	1.93580i
$947$	−2.40641e7	+	3.74445e7i	−0.871957	+	1.35679i	0.0615014	+	0.998107i	$0.480411\pi$
$947$	−2.40641e7	+	3.74445e7i	−0.871957	+	1.35679i	−0.933459	+	0.358685i	$0.883225\pi$
$948$	1.63993e7	−	1.70514e7i	0.592657	−	0.616223i
$949$	3.03455e7	−	1.95019e7i	1.09378	−	0.702928i
$950$	−8.08945e6	−	1.77134e7i	−0.290810	−	0.636786i
$951$	14393.5	+	157922.i	0.000516076	+	0.00566228i
$952$	−335796.	−	2.33551e6i	−0.0120083	−	0.0835199i
$953$	1.29190e7	−	2.82887e7i	0.460785	−	1.00898i	−0.526523	−	0.850161i	$-0.676505\pi$
$953$	1.29190e7	−	2.82887e7i	0.460785	−	1.00898i	0.987308	−	0.158817i	$-0.0507680\pi$
$954$	5.39863e7	−	3.77467e7i	1.92049	−	1.34279i
$955$	−5.17694e6	+	1.52009e6i	−0.183681	+	0.0539337i
$956$	−8.13605e7	−	3.71561e7i	−2.87918	−	1.31488i
$957$	1.83767e6	−	3.52720e6i	0.0648617	−	0.124494i
$958$	−1.89980e7	+	1.64619e7i	−0.668796	+	0.579515i
$959$	−2.34959e7	+	1.07302e7i	−0.824985	+	0.376758i
$960$	−840551.	+	1.61785e7i	−0.0294365	+	0.566580i
$961$	2.76633e6	−	1.92402e7i	0.0966262	−	0.672050i
$962$	−2.53425e7	−	1.62866e7i	−0.882900	−	0.567406i
$963$	1.68373e7	+	6.90955e6i	0.585069	+	0.240096i
$964$	1.26737e7	−	4.31625e7i	0.439247	−	1.49594i
$965$	2.11312e7			0.730474
$966$	6.39053e7	+	6.49268e7i	2.20340	+	2.23862i
$967$	−2.15667e7			−0.741680			−0.370840	−	0.928697i	$-0.620930\pi$
$967$	−2.15667e7			−0.741680			−0.370840	+	0.928697i	$0.620930\pi$
$968$	−6.11748e6	+	2.08342e7i	−0.209838	+	0.714643i
$969$	722866.	−	172071.i	0.0247314	−	0.00588707i
$970$	−2.79066e7	−	1.79345e7i	−0.952309	−	0.612012i
$971$	−4.13875e6	+	2.87856e7i	−0.140871	+	0.979778i	0.789655	+	0.613551i	$0.210260\pi$
$971$	−4.13875e6	+	2.87856e7i	−0.140871	+	0.979778i	−0.930526	+	0.366227i	$0.880650\pi$
$972$	3.44908e7	+	5.07130e7i	1.17095	+	1.72168i
$973$	−6.88068e7	+	3.14230e7i	−2.32996	+	1.06406i
$974$	5.64359e6	−	4.89020e6i	0.190616	−	0.165169i
$975$	1.26389e7	+	6.58487e6i	0.425792	+	0.221838i
$976$	−5.35453e7	−	2.44533e7i	−1.79927	−	0.821700i
$977$	−2.63513e7	+	7.73743e6i	−0.883213	+	0.259335i	−0.691726	−	0.722160i	$-0.743149\pi$
$977$	−2.63513e7	+	7.73743e6i	−0.883213	+	0.259335i	−0.191487	+	0.981495i	$0.561331\pi$
$978$	−1.16256e7	−	4.07981e6i	−0.388657	−	0.136393i
$979$	−8.22337e6	+	1.80067e7i	−0.274216	+	0.600449i
$980$	−1.53239e7	−	1.06580e8i	−0.509687	−	3.54495i
$981$	−2.28116e6	−	1.34337e6i	−0.0756803	−	0.0445679i
$982$	−2.44188e6	−	5.34697e6i	−0.0808064	−	0.176941i
$983$	−3.09601e7	+	1.98968e7i	−1.02192	+	0.656750i	−0.940452	−	0.339926i	$-0.889598\pi$
$983$	−3.09601e7	+	1.98968e7i	−1.02192	+	0.656750i	−0.0814708	+	0.996676i	$0.525962\pi$
$984$	4.16971e7	+	4.01025e7i	1.37284	+	1.32033i
$985$	−4.64285e6	+	7.22441e6i	−0.152473	+	0.237253i
$986$	−156855.	+	181021.i	−0.00513815	+	0.00592974i
$987$	1.94285e7	−	1.51437e7i	0.634813	−	0.494811i
$988$			8.06755e7i			2.62935i
$989$	−1.77243e7	+	5.47619e7i	−0.576206	+	1.78028i
$990$	3.12644e7	−	1.05200e7i	1.01382	−	0.341135i
$991$	−4.58228e7	−	1.34548e7i	−1.48217	−	0.435204i	−0.562135	−	0.827045i	$-0.690020\pi$
$991$	−4.58228e7	−	1.34548e7i	−1.48217	−	0.435204i	−0.920033	+	0.391842i	$0.871838\pi$
$992$	−3.98509e6	−	3.45310e6i	−0.128576	−	0.111412i
$993$	680400.	−	268996.i	0.0218973	−	0.00865710i
$994$	1.53210e8	+	2.20282e7i	4.91836	+	0.707154i
$995$	−9.73971e6	−	1.51553e7i	−0.311881	−	0.485296i
$996$	3.48861e7	+	6.87974e6i	1.11430	+	0.219747i
$997$	3.23140e6	+	3.72924e6i	0.102956	+	0.118818i	0.804889	−	0.593425i	$-0.202225\pi$
$997$	3.23140e6	+	3.72924e6i	0.102956	+	0.118818i	−0.701933	+	0.712243i	$0.747679\pi$
$998$	−5.84407e7	+	8.40250e6i	−1.85733	+	0.267044i
$999$	1.14270e7	+	1.01630e7i	0.362257	+	0.322188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.g.a.5.3	✓	380
3.2	odd	2	inner	69.6.g.a.5.36	yes	380
23.14	odd	22	inner	69.6.g.a.14.36	yes	380
69.14	even	22	inner	69.6.g.a.14.3	yes	380

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.g.a.5.3	✓	380	1.1	even	1	trivial
69.6.g.a.5.36	yes	380	3.2	odd	2	inner
69.6.g.a.14.3	yes	380	69.14	even	22	inner
69.6.g.a.14.36	yes	380	23.14	odd	22	inner

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.79794 + 9.52891i) q^{2} +(-3.60982 - 15.1647i) q^{3} +(-56.0515 - 36.0221i) q^{4} +(-6.21680 + 43.2388i) q^{5} +(154.603 + 8.03237i) q^{6} +(210.991 - 96.3564i) q^{7} +(259.904 - 225.208i) q^{8} +(-216.938 + 109.484i) q^{9} +O(q^{10})\)	\(q+(-2.79794 + 9.52891i) q^{2} +(-3.60982 - 15.1647i) q^{3} +(-56.0515 - 36.0221i) q^{4} +(-6.21680 + 43.2388i) q^{5} +(154.603 + 8.03237i) q^{6} +(210.991 - 96.3564i) q^{7} +(259.904 - 225.208i) q^{8} +(-216.938 + 109.484i) q^{9} +(-394.624 - 180.219i) q^{10} +(300.233 - 88.1565i) q^{11} +(-343.930 + 980.039i) q^{12} +(-312.127 + 683.464i) q^{13} +(327.831 + 2280.11i) q^{14} +(678.146 - 61.8082i) q^{15} +(533.081 + 1167.28i) q^{16} +(24.8839 - 15.9919i) q^{17} +(-436.282 - 2373.52i) q^{18} +(-871.245 + 1355.68i) q^{19} +(1906.01 - 2199.66i) q^{20} +(-2222.86 - 2851.80i) q^{21} +3107.55i q^{22} +(990.238 + 2335.76i) q^{23} +(-4353.43 - 3128.42i) q^{24} +(1167.47 + 342.800i) q^{25} +(-5639.35 - 4886.52i) q^{26} +(2443.40 + 2894.60i) q^{27} +(-15297.3 - 2199.42i) q^{28} +(440.825 + 685.937i) q^{29} +(-1308.45 + 6634.93i) q^{30} +(1985.33 + 2291.19i) q^{31} +(-1721.61 + 247.530i) q^{32} +(-2420.66 - 4234.73i) q^{33} +(82.7617 + 281.861i) q^{34} +(2854.65 + 9722.03i) q^{35} +(16103.6 + 1677.84i) q^{36} +(3996.03 - 574.542i) q^{37} +(-10480.5 - 12095.1i) q^{38} +(11491.3 + 2266.15i) q^{39} +(8121.97 + 12638.0i) q^{40} +(-10681.6 - 1535.79i) q^{41} +(33393.9 - 13202.3i) q^{42} +(17146.3 + 14857.3i) q^{43} +(-20004.1 - 5873.74i) q^{44} +(-3385.29 - 10060.8i) q^{45} +(-25027.9 + 2900.57i) q^{46} +6812.71i q^{47} +(15777.2 - 12297.7i) q^{48} +(24226.5 - 27958.8i) q^{49} +(-6533.02 + 10165.6i) q^{50} +(-332.339 - 319.630i) q^{51} +(42115.0 - 27065.7i) q^{52} +(11339.3 + 24829.6i) q^{53} +(-34418.8 + 15184.1i) q^{54} +(1945.29 + 13529.8i) q^{55} +(33137.2 - 72560.4i) q^{56} +(23703.6 + 8318.42i) q^{57} +(-7769.64 + 2281.37i) q^{58} +(4986.67 + 2277.33i) q^{59} +(-40237.6 - 20963.8i) q^{60} +(-34667.5 + 30039.6i) q^{61} +(-27387.4 + 12507.4i) q^{62} +(-35222.6 + 44003.6i) q^{63} +(-3385.75 + 23548.4i) q^{64} +(-27611.7 - 17745.0i) q^{65} +(47125.2 - 11217.7i) q^{66} +(14366.9 - 48929.2i) q^{67} -1970.84 q^{68} +(31846.6 - 23448.4i) q^{69} -100627. q^{70} +(18930.7 - 64472.1i) q^{71} +(-31726.5 + 77311.7i) q^{72} +(-40387.3 - 25955.3i) q^{73} +(-5705.88 + 39685.3i) q^{74} +(984.116 - 18941.8i) q^{75} +(97669.2 - 44604.0i) q^{76} +(54852.1 - 47529.7i) q^{77} +(-53745.8 + 103159. i) q^{78} +(-20719.2 - 9462.16i) q^{79} +(-53786.1 + 15793.0i) q^{80} +(35075.5 - 47502.5i) q^{81} +(44520.9 - 97487.1i) q^{82} +(-4872.18 - 33886.8i) q^{83} +(21866.9 + 239920. i) q^{84} +(536.772 + 1175.37i) q^{85} +(-189548. + 121815. i) q^{86} +(8810.76 - 9161.11i) q^{87} +(58178.4 - 90527.3i) q^{88} +(-41428.5 + 47811.0i) q^{89} +(105340. - 4108.63i) q^{90} +174280. i q^{91} +(28634.7 - 166593. i) q^{92} +(27578.6 - 38377.8i) q^{93} +(-64917.7 - 19061.6i) q^{94} +(-53201.8 - 46099.6i) q^{95} +(9968.41 + 25214.2i) q^{96} +(75686.6 + 10882.1i) q^{97} +(198633. + 309079. i) q^{98} +(-55480.4 + 51995.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9}+O(q^{10}) \) 380 * q - 11 * q^3 + 578 * q^4 + 64 * q^6 - 22 * q^7 + 433 * q^9	\( 380 q - 11 q^{3} + 578 q^{4} + 64 q^{6} - 22 q^{7} + 433 q^{9} - 22 q^{10} + 148 q^{12} - 542 q^{13} + 4620 q^{15} - 11102 q^{16} - 11526 q^{18} - 22 q^{19} + 12496 q^{21} + 15878 q^{24} - 17304 q^{25} - 21014 q^{27} - 22 q^{28} - 33627 q^{30} - 6566 q^{31} + 41250 q^{33} + 75988 q^{34} + 12154 q^{36} - 72138 q^{37} + 45205 q^{39} - 119372 q^{40} - 11 q^{42} + 59334 q^{43} + 119802 q^{46} + 5138 q^{48} + 147060 q^{49} - 11 q^{51} - 246042 q^{52} - 172143 q^{54} - 95048 q^{55} + 92422 q^{57} + 277528 q^{58} + 420629 q^{60} + 125158 q^{61} + 7194 q^{63} - 100196 q^{64} - 312378 q^{66} - 94380 q^{67} - 136956 q^{69} - 395908 q^{70} - 507803 q^{72} + 83336 q^{73} + 577756 q^{75} + 415338 q^{76} - 361512 q^{78} + 342958 q^{79} - 420607 q^{81} + 247868 q^{82} - 978505 q^{84} - 634728 q^{85} + 354721 q^{87} + 22506 q^{88} + 1636316 q^{90} + 1162112 q^{93} + 40940 q^{94} - 102479 q^{96} + 582824 q^{97} - 674663 q^{99}+O(q^{100}) \) 380 * q - 11 * q^3 + 578 * q^4 + 64 * q^6 - 22 * q^7 + 433 * q^9 - 22 * q^10 + 148 * q^12 - 542 * q^13 + 4620 * q^15 - 11102 * q^16 - 11526 * q^18 - 22 * q^19 + 12496 * q^21 + 15878 * q^24 - 17304 * q^25 - 21014 * q^27 - 22 * q^28 - 33627 * q^30 - 6566 * q^31 + 41250 * q^33 + 75988 * q^34 + 12154 * q^36 - 72138 * q^37 + 45205 * q^39 - 119372 * q^40 - 11 * q^42 + 59334 * q^43 + 119802 * q^46 + 5138 * q^48 + 147060 * q^49 - 11 * q^51 - 246042 * q^52 - 172143 * q^54 - 95048 * q^55 + 92422 * q^57 + 277528 * q^58 + 420629 * q^60 + 125158 * q^61 + 7194 * q^63 - 100196 * q^64 - 312378 * q^66 - 94380 * q^67 - 136956 * q^69 - 395908 * q^70 - 507803 * q^72 + 83336 * q^73 + 577756 * q^75 + 415338 * q^76 - 361512 * q^78 + 342958 * q^79 - 420607 * q^81 + 247868 * q^82 - 978505 * q^84 - 634728 * q^85 + 354721 * q^87 + 22506 * q^88 + 1636316 * q^90 + 1162112 * q^93 + 40940 * q^94 - 102479 * q^96 + 582824 * q^97 - 674663 * q^99

Introduction

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