LMFDB - Embedded newform 33.7.b.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(23,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("33.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.b (of order $2$, degree $1$, 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:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$20$
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} + 1026 x^{18} + 441321 x^{16} + 103808124 x^{14} + 14594358456 x^{12} + 1256133373152 x^{10} + \cdots + 32\!\cdots\!64 $ x^20 + 1026x^18 + 441321x^16 + 103808124x^14 + 14594358456x^12 + 1256133373152x^10 + 64843235559312x^8 + 1864534894961472x^6 + 25120735435348224x^4 + 103653954147713024*x^2 + 32367107232497664
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{17}\cdot 11^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.11
Root			$0.582665i$ of defining polynomial
Character	$\chi$	$=$	33.23
Dual form			33.7.b.a.23.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.582665i q^{2} +(12.1539 + 24.1098i) q^{3} +63.6605 q^{4} -147.782i q^{5} +(-14.0479 + 7.08168i) q^{6} +326.963 q^{7} +74.3834i q^{8} +(-433.563 + 586.058i) q^{9} +O(q^{10})$	\(q+0.582665i q^{2} +(12.1539 + 24.1098i) q^{3} +63.6605 q^{4} -147.782i q^{5} +(-14.0479 + 7.08168i) q^{6} +326.963 q^{7} +74.3834i q^{8} +(-433.563 + 586.058i) q^{9} +86.1076 q^{10} +401.312i q^{11} +(773.726 + 1534.84i) q^{12} +2279.33 q^{13} +190.510i q^{14} +(3563.00 - 1796.14i) q^{15} +4030.93 q^{16} +2067.89i q^{17} +(-341.476 - 252.622i) q^{18} -8558.98 q^{19} -9407.90i q^{20} +(3973.90 + 7883.02i) q^{21} -233.830 q^{22} +8323.40i q^{23} +(-1793.37 + 904.051i) q^{24} -6214.61 q^{25} +1328.09i q^{26} +(-19399.2 - 3330.19i) q^{27} +20814.7 q^{28} -40568.3i q^{29} +(1046.55 + 2076.04i) q^{30} -51064.4 q^{31} +7109.22i q^{32} +(-9675.53 + 4877.52i) q^{33} -1204.89 q^{34} -48319.4i q^{35} +(-27600.8 + 37308.7i) q^{36} +33778.4 q^{37} -4987.02i q^{38} +(27702.9 + 54954.2i) q^{39} +10992.5 q^{40} -109117. i q^{41} +(-4593.16 + 2315.45i) q^{42} -39239.5 q^{43} +25547.7i q^{44} +(86609.0 + 64073.0i) q^{45} -4849.76 q^{46} +35386.9i q^{47} +(48991.7 + 97184.9i) q^{48} -10743.9 q^{49} -3621.04i q^{50} +(-49856.3 + 25133.0i) q^{51} +145104. q^{52} -10819.6i q^{53} +(1940.39 - 11303.3i) q^{54} +59306.8 q^{55} +24320.6i q^{56} +(-104025. - 206355. i) q^{57} +23637.8 q^{58} +155338. i q^{59} +(226822. - 114343. i) q^{60} +103691. q^{61} -29753.4i q^{62} +(-141759. + 191620. i) q^{63} +253837. q^{64} -336845. i q^{65} +(-2841.96 - 5637.60i) q^{66} -392370. q^{67} +131643. i q^{68} +(-200675. + 101162. i) q^{69} +28154.0 q^{70} +260839. i q^{71} +(-43593.0 - 32249.9i) q^{72} -398815. q^{73} +19681.5i q^{74} +(-75532.1 - 149833. i) q^{75} -544869. q^{76} +131214. i q^{77} +(-32019.9 + 16141.5i) q^{78} -260579. q^{79} -595700. i q^{80} +(-155487. - 508186. i) q^{81} +63578.7 q^{82} -612098. i q^{83} +(252980. + 501837. i) q^{84} +305597. q^{85} -22863.5i q^{86} +(978093. - 493065. i) q^{87} -29850.9 q^{88} +1.03603e6i q^{89} +(-37333.1 + 50464.1i) q^{90} +745259. q^{91} +529872. i q^{92} +(-620634. - 1.23115e6i) q^{93} -20618.7 q^{94} +1.26487e6i q^{95} +(-171402. + 86405.1i) q^{96} +825727. q^{97} -6260.10i q^{98} +(-235192. - 173994. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	$ 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) $ 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.582665i			0.0728332i	0.999337	+	0.0364166i	$0.0115943\pi$
$2$			0.582665i			0.0728332i	−0.999337	+	0.0364166i	$0.988406\pi$
$3$	12.1539	+	24.1098i	0.450146	+	0.892955i
$3$	12.1539	+	24.1098i	0.450146	+	0.892955i
$4$	63.6605			0.994695
$5$		−	147.782i		−	1.18226i	−0.806577	−	0.591129i	$-0.798682\pi$
$5$		−	147.782i		−	1.18226i	0.806577	−	0.591129i	$-0.201318\pi$
$6$	−14.0479	+	7.08168i	−0.0650367	+	0.0327856i
$7$	326.963			0.953246			0.476623	−	0.879108i	$-0.341861\pi$
$7$	326.963			0.953246			0.476623	+	0.879108i	$0.341861\pi$
$8$			74.3834i			0.145280i
$9$	−433.563	+	586.058i	−0.594737	+	0.803921i
$10$	86.1076			0.0861076
$11$			401.312i			0.301511i
$11$			401.312i			0.301511i
$12$	773.726	+	1534.84i	0.447758	+	0.888218i
$13$	2279.33			1.03748			0.518738	−	0.854933i	$-0.326402\pi$
$13$	2279.33			1.03748			0.518738	+	0.854933i	$0.326402\pi$
$14$			190.510i			0.0694279i
$15$	3563.00	−	1796.14i	1.05570	−	0.532189i
$16$	4030.93			0.984114
$17$			2067.89i			0.420901i	0.977604	+	0.210451i	$0.0674931\pi$
$17$			2067.89i			0.420901i	−0.977604	+	0.210451i	$0.932507\pi$
$18$	−341.476	−	252.622i	−0.0585521	−	0.0433166i
$19$	−8558.98			−1.24785			−0.623923	−	0.781485i	$-0.714462\pi$
$19$	−8558.98			−1.24785			−0.623923	+	0.781485i	$0.714462\pi$
$20$		−	9407.90i		−	1.17599i
$21$	3973.90	+	7883.02i	0.429100	+	0.851206i
$22$	−233.830			−0.0219600
$23$			8323.40i			0.684097i	0.939682	+	0.342048i	$0.111121\pi$
$23$			8323.40i			0.684097i	−0.939682	+	0.342048i	$0.888879\pi$
$24$	−1793.37	+	904.051i	−0.129728	+	0.0653972i
$25$	−6214.61			−0.397735
$26$			1328.09i			0.0755626i
$27$	−19399.2	−	3330.19i	−0.985583	−	0.169191i
$28$	20814.7			0.948190
$29$		−	40568.3i		−	1.66339i	−0.555236	−	0.831693i	$-0.687372\pi$
$29$		−	40568.3i		−	1.66339i	0.555236	−	0.831693i	$-0.312628\pi$
$30$	1046.55	+	2076.04i	0.0387610	+	0.0768902i
$31$	−51064.4			−1.71409			−0.857044	−	0.515244i	$-0.827701\pi$
$31$	−51064.4			−1.71409			−0.857044	+	0.515244i	$0.827701\pi$
$32$			7109.22i			0.216956i
$33$	−9675.53	+	4877.52i	−0.269236	+	0.135724i
$34$	−1204.89			−0.0306556
$35$		−	48319.4i		−	1.12698i
$36$	−27600.8	+	37308.7i	−0.591582	+	0.799656i
$37$	33778.4			0.666858			0.333429	−	0.942775i	$-0.391794\pi$
$37$	33778.4			0.666858			0.333429	+	0.942775i	$0.391794\pi$
$38$		−	4987.02i		−	0.0908846i
$39$	27702.9	+	54954.2i	0.467016	+	0.926419i
$40$	10992.5			0.171758
$41$		−	109117.i		−	1.58322i	−0.611028	−	0.791609i	$-0.709244\pi$
$41$		−	109117.i		−	1.58322i	0.611028	−	0.791609i	$-0.290756\pi$
$42$	−4593.16	+	2315.45i	−0.0619960	+	0.0312527i
$43$	−39239.5			−0.493535			−0.246768	−	0.969075i	$-0.579368\pi$
$43$	−39239.5			−0.493535			−0.246768	+	0.969075i	$0.579368\pi$
$44$			25547.7i			0.299912i
$45$	86609.0	+	64073.0i	0.950442	+	0.703133i
$46$	−4849.76			−0.0498249
$47$			35386.9i			0.340838i	0.985372	+	0.170419i	$0.0545122\pi$
$47$			35386.9i			0.340838i	−0.985372	+	0.170419i	$0.945488\pi$
$48$	48991.7	+	97184.9i	0.442995	+	0.878769i
$49$	−10743.9			−0.0913217
$50$		−	3621.04i		−	0.0289683i
$51$	−49856.3	+	25133.0i	−0.375846	+	0.189467i
$52$	145104.			1.03197
$53$		−	10819.6i		−	0.0726747i	−0.999340	−	0.0363374i	$-0.988431\pi$
$53$		−	10819.6i		−	0.0726747i	0.999340	−	0.0363374i	$-0.0115691\pi$
$54$	1940.39	−	11303.3i	0.0123227	−	0.0717832i
$55$	59306.8			0.356464
$56$			24320.6i			0.138488i
$57$	−104025.	−	206355.i	−0.561714	−	1.11427i
$58$	23637.8			0.121150
$59$			155338.i			0.756348i	0.925734	+	0.378174i	$0.123448\pi$
$59$			155338.i			0.756348i	−0.925734	+	0.378174i	$0.876552\pi$
$60$	226822.	−	114343.i	1.05010	−	0.529366i
$61$	103691.			0.456828			0.228414	−	0.973564i	$-0.426646\pi$
$61$	103691.			0.456828			0.228414	+	0.973564i	$0.426646\pi$
$62$		−	29753.4i		−	0.124842i
$63$	−141759.	+	191620.i	−0.566931	+	0.766334i
$64$	253837.			0.968313
$65$		−	336845.i		−	1.22656i
$66$	−2841.96	−	5637.60i	−0.00988522	−	0.0196093i
$67$	−392370.			−1.30458			−0.652291	−	0.757969i	$-0.726192\pi$
$67$	−392370.			−1.30458			−0.652291	+	0.757969i	$0.726192\pi$
$68$			131643.i			0.418669i
$69$	−200675.	+	101162.i	−0.610867	+	0.307944i
$70$	28154.0			0.0820818
$71$			260839.i			0.728782i	0.931246	+	0.364391i	$0.118723\pi$
$71$			260839.i			0.728782i	−0.931246	+	0.364391i	$0.881277\pi$
$72$	−43593.0	−	32249.9i	−0.116794	−	0.0864033i
$73$	−398815.			−1.02519			−0.512593	−	0.858632i	$-0.671315\pi$
$73$	−398815.			−1.02519			−0.512593	+	0.858632i	$0.671315\pi$
$74$			19681.5i			0.0485694i
$75$	−75532.1	−	149833.i	−0.179039	−	0.355160i
$76$	−544869.			−1.24123
$77$			131214.i			0.287415i
$78$	−32019.9	+	16141.5i	−0.0674740	+	0.0340142i
$79$	−260579.			−0.528517			−0.264258	−	0.964452i	$-0.585127\pi$
$79$	−260579.			−0.528517			−0.264258	+	0.964452i	$0.585127\pi$
$80$		−	595700.i		−	1.16348i
$81$	−155487.	−	508186.i	−0.292576	−	0.956242i
$82$	63578.7			0.115311
$83$		−	612098.i		−	1.07050i	−0.844694	−	0.535250i	$-0.820217\pi$
$83$		−	612098.i		−	1.07050i	0.844694	−	0.535250i	$-0.179783\pi$
$84$	252980.	+	501837.i	0.426824	+	0.846690i
$85$	305597.			0.497614
$86$		−	22863.5i		−	0.0359458i
$87$	978093.	−	493065.i	1.48533	−	0.748767i
$88$	−29850.9			−0.0438036
$89$			1.03603e6i			1.46960i	0.678282	+	0.734802i	$0.262725\pi$
$89$			1.03603e6i			1.46960i	−0.678282	+	0.734802i	$0.737275\pi$
$90$	−37333.1	+	50464.1i	−0.0512114	+	0.0692237i
$91$	745259.			0.988970
$92$			529872.i			0.680468i
$93$	−620634.	−	1.23115e6i	−0.771590	−	1.53060i
$94$	−20618.7			−0.0248243
$95$			1.26487e6i			1.47528i
$96$	−171402.	+	86405.1i	−0.193732	+	0.0976620i
$97$	825727.			0.904735			0.452368	−	0.891832i	$-0.350579\pi$
$97$	825727.			0.904735			0.452368	+	0.891832i	$0.350579\pi$
$98$		−	6260.10i		−	0.00665125i
$99$	−235192.	−	173994.i	−0.242391	−	0.179320i
$100$	−395625.			−0.395625
$101$			1.66768e6i			1.61864i	0.587369	+	0.809319i	$0.300164\pi$
$101$			1.66768e6i			1.61864i	−0.587369	+	0.809319i	$0.699836\pi$
$102$	−14644.1	−	29049.6i	−0.0137995	−	0.0273740i
$103$	−986637.			−0.902913			−0.451456	−	0.892293i	$-0.649095\pi$
$103$	−986637.			−0.902913			−0.451456	+	0.892293i	$0.649095\pi$
$104$			169544.i			0.150724i
$105$	1.16497e6	−	587272.i	1.00635	−	0.507307i
$106$	6304.20			0.00529313
$107$		−	1.61557e6i		−	1.31879i	−0.751797	−	0.659395i	$-0.770812\pi$
$107$		−	1.61557e6i		−	1.31879i	0.751797	−	0.659395i	$-0.229188\pi$
$108$	−1.23497e6	−	212002.i	−0.980355	−	0.168294i
$109$	1.59329e6			1.23031			0.615156	−	0.788405i	$-0.289093\pi$
$109$	1.59329e6			1.23031			0.615156	+	0.788405i	$0.289093\pi$
$110$			34556.0i			0.0259624i
$111$	410541.	+	814389.i	0.300184	+	0.595474i
$112$	1.31797e6			0.938103
$113$			2.04277e6i			1.41574i	0.706342	+	0.707871i	$0.250344\pi$
$113$			2.04277e6i			1.41574i	−0.706342	+	0.707871i	$0.749656\pi$
$114$	120236.	−	60612.0i	0.0811559	−	0.0409114i
$115$	1.23005e6			0.808779
$116$		−	2.58260e6i		−	1.65456i
$117$	−988235.	+	1.33582e6i	−0.617025	+	0.834048i
$118$	−90510.1			−0.0550873
$119$			676124.i			0.401223i
$120$	133603.	+	265028.i	0.0773164	+	0.153373i
$121$	−161051.			−0.0909091
$122$			60417.3i			0.0332722i
$123$	2.63079e6	−	1.32620e6i	1.41374	−	0.712679i
$124$	−3.25078e6			−1.70499
$125$		−	1.39069e6i		−	0.712033i
$126$	−111650.	−	82598.2i	−0.0558145	−	0.0412913i
$127$	−310970.			−0.151812			−0.0759061	−	0.997115i	$-0.524185\pi$
$127$	−310970.			−0.151812			−0.0759061	+	0.997115i	$0.524185\pi$
$128$			602892.i			0.287481i
$129$	−476915.	−	946056.i	−0.222163	−	0.440705i
$130$	196268.			0.0893346
$131$			337515.i			0.150134i	0.997178	+	0.0750671i	$0.0239171\pi$
$131$			337515.i			0.150134i	−0.997178	+	0.0750671i	$0.976083\pi$
$132$	−615949.	+	310505.i	−0.267808	+	0.135004i
$133$	−2.79847e6			−1.18951
$134$		−	228620.i		−	0.0950169i
$135$	−492143.	+	2.86686e6i	−0.200028	+	1.16521i
$136$	−153816.			−0.0611485
$137$		−	4.13445e6i		−	1.60789i	−0.594704	−	0.803945i	$-0.702731\pi$
$137$		−	4.13445e6i		−	1.60789i	0.594704	−	0.803945i	$-0.297269\pi$
$138$	−58943.7	−	116927.i	−0.0224285	−	0.0444914i
$139$	−524465.			−0.195287			−0.0976433	−	0.995221i	$-0.531130\pi$
$139$	−524465.			−0.195287			−0.0976433	+	0.995221i	$0.531130\pi$
$140$		−	3.07604e6i		−	1.12101i
$141$	−853170.	+	430090.i	−0.304353	+	0.153427i
$142$	−151982.			−0.0530795
$143$			914723.i			0.312811i
$144$	−1.74766e6	+	2.36236e6i	−0.585289	+	0.791150i
$145$	−5.99528e6			−1.96655
$146$		−	232375.i		−	0.0746675i
$147$	−130581.	−	259033.i	−0.0411081	−	0.0815461i
$148$	2.15035e6			0.663321
$149$		−	3.24462e6i		−	0.980856i	−0.871482	−	0.490428i	$-0.836840\pi$
$149$		−	3.24462e6i		−	0.980856i	0.871482	−	0.490428i	$-0.163160\pi$
$150$	87302.5	−	44009.9i	0.0258674	−	0.0130400i
$151$	4.85640e6			1.41053			0.705267	−	0.708942i	$-0.250827\pi$
$151$	4.85640e6			1.41053			0.705267	+	0.708942i	$0.250827\pi$
$152$		−	636646.i		−	0.181287i
$153$	−1.21190e6	−	896560.i	−0.338371	−	0.250325i
$154$	−76454.0			−0.0209333
$155$			7.54641e6i			2.02649i
$156$	1.76358e6	+	3.49841e6i	0.464538	+	0.921504i
$157$	3.33617e6			0.862083			0.431042	−	0.902332i	$-0.358146\pi$
$157$	3.33617e6			0.862083			0.431042	+	0.902332i	$0.358146\pi$
$158$		−	151831.i		−	0.0384936i
$159$	260858.	−	131501.i	0.0648953	−	0.0327143i
$160$	1.05062e6			0.256498
$161$			2.72145e6i			0.652113i
$162$	296103.	−	90597.0i	0.0696461	−	0.0213093i
$163$	4.61273e6			1.06511			0.532556	−	0.846395i	$-0.321232\pi$
$163$	4.61273e6			1.06511			0.532556	+	0.846395i	$0.321232\pi$
$164$		−	6.94644e6i		−	1.57482i
$165$	720811.	+	1.42987e6i	0.160461	+	0.318307i
$166$	356648.			0.0779679
$167$		−	6.28385e6i		−	1.34920i	−0.738183	−	0.674601i	$-0.764316\pi$
$167$		−	6.28385e6i		−	1.34920i	0.738183	−	0.674601i	$-0.235684\pi$
$168$	−586365.	+	295592.i	−0.123663	+	0.0623397i
$169$	368554.			0.0763555
$170$			178061.i			0.0362428i
$171$	3.71086e6	−	5.01606e6i	0.742140	−	1.00317i
$172$	−2.49801e6			−0.490917
$173$			4.36123e6i			0.842307i	0.906989	+	0.421153i	$0.138375\pi$
$173$			4.36123e6i			0.842307i	−0.906989	+	0.421153i	$0.861625\pi$
$174$	287292.	+	569901.i	0.0545351	+	0.108181i
$175$	−2.03195e6			−0.379140
$176$			1.61766e6i			0.296722i
$177$	−3.74517e6	+	1.88797e6i	−0.675385	+	0.340467i
$178$	−603656.			−0.107036
$179$			5.02976e6i			0.876977i	0.898737	+	0.438489i	$0.144486\pi$
$179$			5.02976e6i			0.876977i	−0.898737	+	0.438489i	$0.855514\pi$
$180$	5.51357e6	+	4.07892e6i	0.945400	+	0.699403i
$181$	46941.7			0.00791631			0.00395815	−	0.999992i	$-0.498740\pi$
$181$	46941.7			0.00791631			0.00395815	+	0.999992i	$0.498740\pi$
$182$			434237.i			0.0720298i
$183$	1.26026e6	+	2.49997e6i	0.205639	+	0.407927i
$184$	−619123.			−0.0993856
$185$		−	4.99185e6i		−	0.788399i
$186$	717349.	−	361622.i	0.111479	−	0.0561973i
$187$	−829868.			−0.126907
$188$			2.25275e6i			0.339030i
$189$	−6.34284e6	−	1.08885e6i	−0.939503	−	0.161281i
$190$	−736994.			−0.107449
$191$			7.46810e6i			1.07179i	0.844284	+	0.535895i	$0.180026\pi$
$191$			7.46810e6i			1.07179i	−0.844284	+	0.535895i	$0.819974\pi$
$192$	3.08513e6	+	6.11996e6i	0.435882	+	0.864659i
$193$	7.07956e6			0.984768			0.492384	−	0.870378i	$-0.336126\pi$
$193$	7.07956e6			0.984768			0.492384	+	0.870378i	$0.336126\pi$
$194$			481123.i			0.0658947i
$195$	8.12126e6	−	4.09400e6i	1.09527	−	0.552133i
$196$	−683962.			−0.0908372
$197$		−	3.77806e6i		−	0.494163i	−0.968995	−	0.247082i	$-0.920528\pi$
$197$		−	3.77806e6i		−	0.494163i	0.968995	−	0.247082i	$-0.0794716\pi$
$198$	101380.	−	137038.i	0.0130604	−	0.0176541i
$199$	67509.1			0.00856650			0.00428325	−	0.999991i	$-0.498637\pi$
$199$	67509.1			0.00856650			0.00428325	+	0.999991i	$0.498637\pi$
$200$		−	462264.i		−	0.0577830i
$201$	−4.76885e6	−	9.45996e6i	−0.587253	−	1.16493i
$202$	−971702.			−0.117891
$203$		−	1.32644e7i		−	1.58562i
$204$	−3.17388e6	+	1.59998e6i	−0.373852	+	0.188462i
$205$	−1.61256e7			−1.87177
$206$		−	574879.i		−	0.0657620i
$207$	−4.87800e6	−	3.60872e6i	−0.549959	−	0.406857i
$208$	9.18784e6			1.02099
$209$		−	3.43482e6i		−	0.376240i
$210$	342183.	+	678788.i	0.0369488	+	0.0732953i
$211$	5.62387e6			0.598670			0.299335	−	0.954148i	$-0.403235\pi$
$211$	5.62387e6			0.598670			0.299335	+	0.954148i	$0.403235\pi$
$212$		−	688781.i		−	0.0722892i
$213$	−6.28877e6	+	3.17022e6i	−0.650769	+	0.328058i
$214$	941340.			0.0960517
$215$			5.79891e6i			0.583486i
$216$	247711.	−	1.44298e6i	0.0245801	−	0.143186i
$217$	−1.66962e7			−1.63395
$218$			928355.i			0.0896076i
$219$	−4.84717e6	−	9.61533e6i	−0.461483	−	0.915444i
$220$	3.77550e6			0.354573
$221$			4.71341e6i			0.436675i
$222$	−474516.	+	239208.i	−0.0433703	+	0.0218633i
$223$	4.46626e6			0.402744			0.201372	−	0.979515i	$-0.435460\pi$
$223$	4.46626e6			0.402744			0.201372	+	0.979515i	$0.435460\pi$
$224$			2.32445e6i			0.206813i
$225$	2.69443e6	−	3.64212e6i	0.236548	−	0.319747i
$226$	−1.19025e6			−0.103113
$227$			2.20720e7i			1.88696i	0.331425	+	0.943482i	$0.392471\pi$
$227$			2.20720e7i			1.88696i	−0.331425	+	0.943482i	$0.607529\pi$
$228$	−6.62231e6	−	1.31367e7i	−0.558734	−	1.10836i
$229$	−1.78562e7			−1.48691			−0.743453	−	0.668788i	$-0.766813\pi$
$229$	−1.78562e7			−1.48691			−0.743453	+	0.668788i	$0.766813\pi$
$230$			716709.i			0.0589059i
$231$	−3.16355e6	+	1.59477e6i	−0.256648	+	0.129379i
$232$	3.01761e6			0.241657
$233$			6.13944e6i			0.485357i	0.970107	+	0.242678i	$0.0780260\pi$
$233$			6.13944e6i			0.485357i	−0.970107	+	0.242678i	$0.921974\pi$
$234$	−778337.	−	575810.i	−0.0607464	−	0.0449399i
$235$	5.22955e6			0.402959
$236$			9.88890e6i			0.752336i
$237$	−3.16707e6	−	6.28251e6i	−0.237910	−	0.471942i
$238$	−393954.			−0.0292223
$239$			3.91518e6i			0.286786i	0.989666	+	0.143393i	$0.0458013\pi$
$239$			3.91518e6i			0.286786i	−0.989666	+	0.143393i	$0.954199\pi$
$240$	1.43622e7	−	7.24011e6i	1.03893	−	0.523735i
$241$	1.93049e7			1.37916			0.689581	−	0.724208i	$-0.257795\pi$
$241$	1.93049e7			1.37916			0.689581	+	0.724208i	$0.257795\pi$
$242$		−	93838.8i		−	0.00662120i
$243$	1.03625e7	−	9.92523e6i	0.722179	−	0.691706i
$244$	6.60103e6			0.454404
$245$			1.58776e6i			0.107966i
$246$	772732.	+	1.53287e6i	0.0519067	+	0.102967i
$247$	−1.95088e7			−1.29461
$248$		−	3.79834e6i		−	0.249023i
$249$	1.47576e7	−	7.43941e6i	0.955908	−	0.481882i
$250$	810306.			0.0518596
$251$			3.57950e6i			0.226361i	0.993574	+	0.113180i	$0.0361038\pi$
$251$			3.57950e6i			0.226361i	−0.993574	+	0.113180i	$0.963896\pi$
$252$	−9.02447e6	+	1.21986e7i	−0.563923	+	0.762269i
$253$	−3.34028e6			−0.206263
$254$		−	181191.i		−	0.0110570i
$255$	3.71421e6	+	7.36788e6i	0.223999	+	0.444347i
$256$	1.58943e7			0.947374
$257$		−	2.09948e7i		−	1.23684i	−0.785849	−	0.618418i	$-0.787774\pi$
$257$		−	2.09948e7i		−	1.23684i	0.785849	−	0.618418i	$-0.212226\pi$
$258$	551234.	−	277882.i	0.0320979	−	0.0161808i
$259$	1.10443e7			0.635680
$260$		−	2.14437e7i		−	1.22006i
$261$	2.37754e7	+	1.75889e7i	1.33723	+	0.989277i
$262$	−196658.			−0.0109347
$263$			2.18326e7i			1.20016i	0.799942	+	0.600078i	$0.204864\pi$
$263$			2.18326e7i			1.20016i	−0.799942	+	0.600078i	$0.795136\pi$
$264$	−362806.	−	719699.i	−0.0197180	−	0.0391146i
$265$	−1.59895e6			−0.0859203
$266$		−	1.63057e6i		−	0.0866354i
$267$	−2.49783e7	+	1.25918e7i	−1.31229	+	0.661537i
$268$	−2.49785e7			−1.29766
$269$			587121.i			0.0301628i	0.999886	+	0.0150814i	$0.00480073\pi$
$269$			587121.i			0.0301628i	−0.999886	+	0.0150814i	$0.995199\pi$
$270$	−1.67042e6	−	286755.i	−0.0848662	−	0.0145687i
$271$	3.44813e7			1.73251			0.866255	−	0.499603i	$-0.166521\pi$
$271$	3.44813e7			1.73251			0.866255	+	0.499603i	$0.166521\pi$
$272$			8.33552e6i			0.414215i
$273$	9.05784e6	+	1.79680e7i	0.445181	+	0.883105i
$274$	2.40900e6			0.117108
$275$		−	2.49400e6i		−	0.119922i
$276$	−1.27751e7	+	6.44004e6i	−0.607627	+	0.306310i
$277$	−2.35553e6			−0.110828			−0.0554139	−	0.998463i	$-0.517648\pi$
$277$	−2.35553e6			−0.110828			−0.0554139	+	0.998463i	$0.517648\pi$
$278$		−	305588.i		−	0.0142233i
$279$	2.21396e7	−	2.99267e7i	1.01943	−	1.37799i
$280$	3.59416e6			0.163728
$281$			9.15412e6i			0.412570i	0.978492	+	0.206285i	$0.0661374\pi$
$281$			9.15412e6i			0.412570i	−0.978492	+	0.206285i	$0.933863\pi$
$282$	−250599.	−	497112.i	−0.0111746	−	0.0221670i
$283$	−1.19341e7			−0.526539			−0.263270	−	0.964722i	$-0.584801\pi$
$283$	−1.19341e7			−0.526539			−0.263270	+	0.964722i	$0.584801\pi$
$284$			1.66051e7i			0.724916i
$285$	−3.04956e7	+	1.53731e7i	−1.31736	+	0.664091i
$286$	−532977.			−0.0227830
$287$		−	3.56772e7i		−	1.50920i
$288$	−4.16641e6	−	3.08229e6i	−0.174415	−	0.129032i
$289$	1.98614e7			0.822842
$290$		−	3.49324e6i		−	0.143230i
$291$	1.00358e7	+	1.99081e7i	0.407263	+	0.807888i
$292$	−2.53887e7			−1.01975
$293$		−	4.42536e7i		−	1.75932i	−0.475601	−	0.879661i	$-0.657769\pi$
$293$		−	4.42536e7i		−	1.75932i	0.475601	−	0.879661i	$-0.342231\pi$
$294$	150930.	−	76084.9i	0.00593926	−	0.00299403i
$295$	2.29562e7			0.894199
$296$			2.51255e6i			0.0968811i
$297$	1.33644e6	−	7.78514e6i	0.0510131	−	0.297165i
$298$	1.89053e6			0.0714389
$299$			1.89718e7i			0.709734i
$300$	−4.80841e6	−	9.53844e6i	−0.178089	−	0.353276i
$301$	−1.28299e7			−0.470461
$302$			2.82966e6i			0.102734i
$303$	−4.02075e7	+	2.02690e7i	−1.44537	+	0.728624i
$304$	−3.45007e7			−1.22802
$305$		−	1.53237e7i		−	0.540088i
$306$	522394.	−	706134.i	0.0182320	−	0.0246446i
$307$	−1.89255e7			−0.654082			−0.327041	−	0.945010i	$-0.606052\pi$
$307$	−1.89255e7			−0.654082			−0.327041	+	0.945010i	$0.606052\pi$
$308$			8.35316e6i			0.285890i
$309$	−1.19915e7	−	2.37876e7i	−0.406443	−	0.806260i
$310$	−4.39703e6			−0.147596
$311$		−	2.23816e7i		−	0.744064i	−0.928220	−	0.372032i	$-0.878661\pi$
$311$		−	2.23816e7i		−	0.744064i	0.928220	−	0.372032i	$-0.121339\pi$
$312$	−4.08768e6	+	2.06063e6i	−0.134590	+	0.0678480i
$313$	−5.01701e6			−0.163611			−0.0818053	−	0.996648i	$-0.526069\pi$
$313$	−5.01701e6			−0.163611			−0.0818053	+	0.996648i	$0.526069\pi$
$314$			1.94387e6i			0.0627883i
$315$	2.83180e7	+	2.09495e7i	0.906005	+	0.670258i
$316$	−1.65886e7			−0.525713
$317$			4.53612e6i			0.142399i	0.997462	+	0.0711994i	$0.0226827\pi$
$317$			4.53612e6i			0.142399i	−0.997462	+	0.0711994i	$0.977317\pi$
$318$	76621.0	+	151993.i	0.00238268	+	0.00472653i
$319$	1.62805e7			0.501530
$320$		−	3.75127e7i		−	1.14480i
$321$	3.89512e7	−	1.96356e7i	1.17762	−	0.593648i
$322$	−1.58569e6			−0.0474954
$323$		−	1.76990e7i		−	0.525220i
$324$	−9.89839e6	−	3.23514e7i	−0.291024	−	0.951170i
$325$	−1.41652e7			−0.412640
$326$			2.68768e6i			0.0775755i
$327$	1.93648e7	+	3.84139e7i	0.553821	+	1.09861i
$328$	8.11648e6			0.230010
$329$			1.15702e7i			0.324903i
$330$	−833137.	+	419992.i	−0.0231833	+	0.0116869i
$331$	5.04608e7			1.39146			0.695729	−	0.718304i	$-0.255081\pi$
$331$	5.04608e7			1.39146			0.695729	+	0.718304i	$0.255081\pi$
$332$		−	3.89665e7i		−	1.06482i
$333$	−1.46451e7	+	1.97961e7i	−0.396605	+	0.536101i
$334$	3.66138e6			0.0982666
$335$			5.79854e7i			1.54235i
$336$	1.60185e7	+	3.17759e7i	0.422284	+	0.837684i
$337$	−2.61450e7			−0.683124			−0.341562	−	0.939859i	$-0.610956\pi$
$337$	−2.61450e7			−0.683124			−0.341562	+	0.939859i	$0.610956\pi$
$338$			214743.i			0.00556122i
$339$	−4.92507e7	+	2.48277e7i	−1.26419	+	0.637291i
$340$	1.94545e7			0.494974
$341$		−	2.04927e7i		−	0.516817i
$342$	2.92268e6	+	2.16219e6i	0.0730640	+	0.0540524i
$343$	−4.19798e7			−1.04030
$344$		−	2.91877e6i		−	0.0717008i
$345$	1.49500e7	+	2.96563e7i	0.364069	+	0.722203i
$346$	−2.54114e6			−0.0613479
$347$			518595.i			0.0124120i	0.999981	+	0.00620598i	$0.00197544\pi$
$347$			518595.i			0.0124120i	−0.999981	+	0.00620598i	$0.998025\pi$
$348$	6.22659e7	−	3.13888e7i	1.47745	−	0.744795i
$349$	−2.34373e7			−0.551354			−0.275677	−	0.961250i	$-0.588902\pi$
$349$	−2.34373e7			−0.551354			−0.275677	+	0.961250i	$0.588902\pi$
$350$		−	1.18395e6i		−	0.0276139i
$351$	−4.42173e7	−	7.59062e6i	−1.02252	−	0.175532i
$352$	−2.85301e6			−0.0654147
$353$		−	2.25397e7i		−	0.512419i	−0.966621	−	0.256209i	$-0.917526\pi$
$353$		−	2.25397e7i		−	0.512419i	0.966621	−	0.256209i	$-0.0824736\pi$
$354$	−1.10006e6	−	2.18218e6i	−0.0247973	−	0.0491904i
$355$	3.85474e7			0.861608
$356$			6.59539e7i			1.46181i
$357$	−1.63012e7	+	8.21757e6i	−0.358274	+	0.180609i
$358$	−2.93067e6			−0.0638730
$359$		−	4.05040e7i		−	0.875416i	−0.899117	−	0.437708i	$-0.855790\pi$
$359$		−	4.05040e7i		−	0.875416i	0.899117	−	0.437708i	$-0.144210\pi$
$360$	−4.76596e6	+	6.44227e6i	−0.102151	+	0.138080i
$361$	2.62103e7			0.557122
$362$			27351.3i			0.000576570i
$363$	−1.95741e6	−	3.88290e6i	−0.0409224	−	0.0811777i
$364$	4.74436e7			0.983723
$365$			5.89377e7i			1.21203i
$366$	−1.45665e6	+	734308.i	−0.0297106	+	0.0149774i
$367$	1.77915e7			0.359927			0.179964	−	0.983673i	$-0.442402\pi$
$367$	1.77915e7			0.359927			0.179964	+	0.983673i	$0.442402\pi$
$368$			3.35511e7i			0.673229i
$369$	6.39489e7	+	4.73091e7i	1.27278	+	0.941598i
$370$	2.90858e6			0.0574216
$371$		−	3.53761e6i		−	0.0692769i
$372$	−3.95099e7	−	7.83757e7i	−0.767497	−	1.52248i
$373$	7.79015e7			1.50113			0.750567	−	0.660795i	$-0.229781\pi$
$373$	7.79015e7			1.50113			0.750567	+	0.660795i	$0.229781\pi$
$374$		−	483535.i		−	0.00924300i
$375$	3.35292e7	−	1.69024e7i	0.635813	−	0.320519i
$376$	−2.63219e6			−0.0495170
$377$		−	9.24687e7i		−	1.72572i
$378$	634436.	−	3.69575e6i	0.0117466	−	0.0684270i
$379$	−1.03818e7			−0.190702			−0.0953508	−	0.995444i	$-0.530397\pi$
$379$	−1.03818e7			−0.190702			−0.0953508	+	0.995444i	$0.530397\pi$
$380$			8.05220e7i			1.46745i
$381$	−3.77951e6	−	7.49741e6i	−0.0683377	−	0.135562i
$382$	−4.35140e6			−0.0780619
$383$		−	5.54090e7i		−	0.986243i	−0.869960	−	0.493122i	$-0.835856\pi$
$383$		−	5.54090e7i		−	0.986243i	0.869960	−	0.493122i	$-0.164144\pi$
$384$	−1.45356e7	+	7.32752e6i	−0.256708	+	0.129409i
$385$	1.93911e7			0.339798
$386$			4.12501e6i			0.0717238i
$387$	1.70128e7	−	2.29966e7i	0.293524	−	0.396763i
$388$	5.25662e7			0.899936
$389$			2.58378e7i			0.438942i	0.975619	+	0.219471i	$0.0704331\pi$
$389$			2.58378e7i			0.438942i	−0.975619	+	0.219471i	$0.929567\pi$
$390$	2.38543e6	+	4.73198e6i	0.0402136	+	0.0797717i
$391$	−1.72119e7			−0.287937
$392$		−	799167.i		−	0.0132672i
$393$	−8.13742e6	+	4.10214e6i	−0.134063	+	0.0675823i
$394$	2.20135e6			0.0359915
$395$			3.85090e7i			0.624843i
$396$	−1.49724e7	−	1.10765e7i	−0.241105	−	0.178369i
$397$	−2.33415e7			−0.373042			−0.186521	−	0.982451i	$-0.559721\pi$
$397$	−2.33415e7			−0.373042			−0.186521	+	0.982451i	$0.559721\pi$
$398$			39335.2i			0.000623925i
$399$	−3.40125e7	−	6.74706e7i	−0.535451	−	1.06217i
$400$	−2.50507e7			−0.391417
$401$			85511.9i			0.00132615i	1.00000		0.000663076i	$0.000211064\pi$
$401$			85511.9i			0.00132615i	−1.00000		0.000663076i	$0.999789\pi$
$402$	5.51199e6	−	2.77864e6i	0.0848458	−	0.0427715i
$403$	−1.16393e8			−1.77832
$404$			1.06166e8i			1.61005i
$405$	−7.51009e7	+	2.29782e7i	−1.13053	+	0.345901i
$406$	7.72868e6			0.115485
$407$			1.35557e7i			0.201065i
$408$	−1.86948e6	−	3.70848e6i	−0.0275258	−	0.0546029i
$409$	−1.26678e8			−1.85153			−0.925764	−	0.378103i	$-0.876577\pi$
$409$	−1.26678e8			−1.85153			−0.925764	+	0.378103i	$0.876577\pi$
$410$		−	9.39580e6i		−	0.136327i
$411$	9.96807e7	−	5.02499e7i	1.43577	−	0.723785i
$412$	−6.28098e7			−0.898123
$413$			5.07899e7i			0.720986i
$414$	2.10268e6	−	2.84224e6i	0.0296327	−	0.0400553i
$415$	−9.04573e7			−1.26561
$416$			1.62043e7i			0.225087i
$417$	−6.37433e6	−	1.26447e7i	−0.0879075	−	0.174382i
$418$	2.00135e6			0.0274028
$419$		−	1.66138e7i		−	0.225853i	−0.993603	−	0.112927i	$-0.963977\pi$
$419$		−	1.66138e7i		−	0.225853i	0.993603	−	0.112927i	$-0.0360225\pi$
$420$	7.41626e7	−	3.73860e7i	1.00101	−	0.504616i
$421$	8.29220e7			1.11128			0.555640	−	0.831423i	$-0.312473\pi$
$421$	8.29220e7			1.11128			0.555640	+	0.831423i	$0.312473\pi$
$422$			3.27683e6i			0.0436031i
$423$	−2.07388e7	−	1.53424e7i	−0.274007	−	0.202709i
$424$	804798.			0.0105582
$425$		−	1.28511e7i		−	0.167407i
$426$	−1.84718e6	−	3.66425e6i	−0.0238935	−	0.0473976i
$427$	3.39032e7			0.435469
$428$		−	1.02848e8i		−	1.31179i
$429$	−2.20538e7	+	1.11175e7i	−0.279326	+	0.140811i
$430$	−3.37882e6			−0.0424972
$431$		−	4.44527e6i		−	0.0555221i	−0.999615	−	0.0277611i	$-0.991162\pi$
$431$		−	4.44527e6i		−	0.0555221i	0.999615	−	0.0277611i	$-0.00883776\pi$
$432$	−7.81970e7	−	1.34238e7i	−0.969926	−	0.166504i
$433$	−7.77854e7			−0.958151			−0.479076	−	0.877774i	$-0.659028\pi$
$433$	−7.77854e7			−0.958151			−0.479076	+	0.877774i	$0.659028\pi$
$434$		−	9.72829e6i		−	0.119006i
$435$	−7.28663e7	−	1.44545e8i	−0.885236	−	1.75604i
$436$	1.01430e8			1.22379
$437$		−	7.12399e7i		−	0.853648i
$438$	5.60252e6	−	2.82428e6i	0.0666747	−	0.0336113i
$439$	−9.07327e7			−1.07243			−0.536217	−	0.844080i	$-0.680147\pi$
$439$	−9.07327e7			−1.07243			−0.536217	+	0.844080i	$0.680147\pi$
$440$			4.41144e6i			0.0517871i
$441$	4.65816e6	−	6.29655e6i	0.0543123	−	0.0734153i
$442$	−2.74634e6			−0.0318044
$443$			1.56071e8i			1.79520i	0.440814	+	0.897598i	$0.354690\pi$
$443$			1.56071e8i			1.79520i	−0.440814	+	0.897598i	$0.645310\pi$
$444$	2.61352e7	+	5.18444e7i	0.298591	+	0.592315i
$445$	1.53106e8			1.73745
$446$			2.60233e6i			0.0293331i
$447$	7.82271e7	−	3.94350e7i	0.875860	−	0.441529i
$448$	8.29955e7			0.923040
$449$			3.66108e7i			0.404455i	0.979339	+	0.202227i	$0.0648180\pi$
$449$			3.66108e7i			0.404455i	−0.979339	+	0.202227i	$0.935182\pi$
$450$	2.12214e6	+	1.56995e6i	0.0232882	+	0.0172285i
$451$	4.37899e7			0.477358
$452$			1.30044e8i			1.40823i
$453$	5.90244e7	+	1.17087e8i	0.634947	+	1.25954i
$454$	−1.28606e7			−0.137434
$455$		−	1.10136e8i		−	1.16922i
$456$	1.53494e7	−	7.73776e6i	0.161881	−	0.0816057i
$457$	7.33486e6			0.0768499			0.0384250	−	0.999261i	$-0.487766\pi$
$457$	7.33486e6			0.0768499			0.0384250	+	0.999261i	$0.487766\pi$
$458$		−	1.04042e7i		−	0.108296i
$459$	6.88646e6	−	4.01155e7i	0.0712128	−	0.414833i
$460$	7.83057e7			0.804489
$461$			1.31526e8i			1.34248i	0.741238	+	0.671242i	$0.234239\pi$
$461$			1.31526e8i			1.34248i	−0.741238	+	0.671242i	$0.765761\pi$
$462$	−929218.	−	1.84329e6i	−0.00942305	−	0.0186925i
$463$	−4.52546e7			−0.455953			−0.227976	−	0.973667i	$-0.573211\pi$
$463$	−4.52546e7			−0.455953			−0.227976	+	0.973667i	$0.573211\pi$
$464$		−	1.63528e8i		−	1.63696i
$465$	−1.81942e8	+	9.17187e7i	−1.80957	+	0.912219i
$466$	−3.57724e6			−0.0353501
$467$		−	4.27275e7i		−	0.419524i	−0.977752	−	0.209762i	$-0.932731\pi$
$467$		−	4.27275e7i		−	0.419524i	0.977752	−	0.209762i	$-0.0672690\pi$
$468$	−6.29115e7	+	8.50391e7i	−0.613752	+	0.829624i
$469$	−1.28291e8			−1.24359
$470$			3.04708e6i			0.0293488i
$471$	4.05476e7	+	8.04343e7i	0.388064	+	0.769802i
$472$	−1.15546e7			−0.109882
$473$		−	1.57473e7i		−	0.148807i
$474$	3.66060e6	−	1.84534e6i	0.0343730	−	0.0173277i
$475$	5.31907e7			0.496313
$476$			4.30424e7i			0.399094i
$477$	6.34091e6	+	4.69098e6i	0.0584247	+	0.0432223i
$478$	−2.28124e6			−0.0208875
$479$		−	2.17056e8i		−	1.97499i	−0.157646	−	0.987496i	$-0.550390\pi$
$479$		−	2.17056e8i		−	1.97499i	0.157646	−	0.987496i	$-0.449610\pi$
$480$	1.27691e7	+	2.53301e7i	0.115462	+	0.229041i
$481$	7.69922e7			0.691849
$482$			1.12483e7i			0.100449i
$483$	−6.56135e7	+	3.30764e7i	−0.582307	+	0.293546i
$484$	−1.02526e7			−0.0904268
$485$		−	1.22028e8i		−	1.06963i
$486$	5.78309e6	+	6.03786e6i	0.0503792	+	0.0525986i
$487$	1.92097e8			1.66316			0.831578	−	0.555408i	$-0.187438\pi$
$487$	1.92097e8			1.66316			0.831578	+	0.555408i	$0.187438\pi$
$488$			7.71290e6i			0.0663679i
$489$	5.60629e7	+	1.11212e8i	0.479456	+	0.951097i
$490$	−925132.			−0.00786349
$491$			2.02023e8i			1.70670i	0.521339	+	0.853350i	$0.325433\pi$
$491$			2.02023e8i			1.70670i	−0.521339	+	0.853350i	$0.674567\pi$
$492$	1.67477e8	−	8.44266e7i	1.40624	−	0.708899i
$493$	8.38907e7			0.700121
$494$		−	1.13671e7i		−	0.0942906i
$495$	−2.57132e7	+	3.47572e7i	−0.212002	+	0.286569i
$496$	−2.05837e8			−1.68686
$497$			8.52848e7i			0.694708i
$498$	4.33469e6	+	8.59872e6i	0.0350970	+	0.0696218i
$499$	−1.11112e8			−0.894250			−0.447125	−	0.894471i	$-0.647552\pi$
$499$	−1.11112e8			−0.894250			−0.447125	+	0.894471i	$0.647552\pi$
$500$		−	8.85320e7i		−	0.708256i
$501$	1.51502e8	−	7.63736e7i	1.20478	−	0.607338i
$502$	−2.08565e6			−0.0164866
$503$		−	2.38784e7i		−	0.187629i	−0.995590	−	0.0938146i	$-0.970094\pi$
$503$		−	2.38784e7i		−	0.187629i	0.995590	−	0.0938146i	$-0.0299061\pi$
$504$	−1.42533e7	−	1.05445e7i	−0.111333	−	0.0823637i
$505$	2.46454e8			1.91365
$506$		−	1.94626e6i		−	0.0150228i
$507$	4.47938e6	+	8.88575e6i	0.0343712	+	0.0681820i
$508$	−1.97965e7			−0.151007
$509$			4.44980e7i			0.337433i	0.985665	+	0.168716i	$0.0539622\pi$
$509$			4.44980e7i			0.337433i	−0.985665	+	0.168716i	$0.946038\pi$
$510$	−4.29301e6	+	2.16414e6i	−0.0323632	+	0.0163146i
$511$	−1.30398e8			−0.977254
$512$			4.78462e7i			0.356482i
$513$	1.66038e8	+	2.85030e7i	1.22986	+	0.211125i
$514$	1.22329e7			0.0900827
$515$			1.45807e8i			1.06748i
$516$	−3.03607e7	−	6.02264e7i	−0.220985	−	0.438367i
$517$	−1.42012e7			−0.102767
$518$			6.43513e6i			0.0462986i
$519$	−1.05148e8	+	5.30061e7i	−0.752142	+	0.379161i
$520$	2.50557e7			0.178195
$521$		−	1.53589e8i		−	1.08604i	−0.839719	−	0.543022i	$-0.817280\pi$
$521$		−	1.53589e8i		−	1.08604i	0.839719	−	0.543022i	$-0.182720\pi$
$522$	−1.02485e7	+	1.38531e7i	−0.0720522	+	0.0973947i
$523$	2.47233e6			0.0172823			0.00864115	−	0.999963i	$-0.497249\pi$
$523$	2.47233e6			0.0172823			0.00864115	+	0.999963i	$0.497249\pi$
$524$			2.14864e7i			0.149338i
$525$	−2.46962e7	−	4.89899e7i	−0.170668	−	0.338554i
$526$	−1.27211e7			−0.0874111
$527$		−	1.05595e8i		−	0.721462i
$528$	−3.90014e7	+	1.96610e7i	−0.264959	+	0.133568i
$529$	7.87568e7			0.532012
$530$		−	931650.i		−	0.00625785i
$531$	−9.10371e7	−	6.73489e7i	−0.608044	−	0.449828i
$532$	−1.78152e8			−1.18320
$533$		−	2.48714e8i		−	1.64255i
$534$	−7.33680e6	−	1.45540e7i	−0.0481818	−	0.0955782i
$535$	−2.38753e8			−1.55915
$536$		−	2.91858e7i		−	0.189530i
$537$	−1.21266e8	+	6.11315e7i	−0.783101	+	0.394768i
$538$	−342095.			−0.00219685
$539$		−	4.31165e6i		−	0.0275345i
$540$	−3.13301e7	+	1.82506e8i	−0.198967	+	1.15903i
$541$	1.05393e8			0.665610			0.332805	−	0.942996i	$-0.392005\pi$
$541$	1.05393e8			0.665610			0.332805	+	0.942996i	$0.392005\pi$
$542$			2.00911e7i			0.126184i
$543$	570527.	+	1.13175e6i	0.00356350	+	0.00706891i
$544$	−1.47011e7			−0.0913171
$545$		−	2.35460e8i		−	1.45455i
$546$	−1.04693e7	+	5.27769e6i	−0.0643194	+	0.0324239i
$547$	−1.78974e8			−1.09353			−0.546763	−	0.837288i	$-0.684140\pi$
$547$	−1.78974e8			−1.09353			−0.546763	+	0.837288i	$0.684140\pi$
$548$		−	2.63201e8i		−	1.59936i
$549$	−4.49567e7	+	6.07691e7i	−0.271692	+	0.367253i
$550$	1.45316e6			0.00873427
$551$			3.47223e8i			2.07565i
$552$	−7.52479e6	−	1.49269e7i	−0.0447380	−	0.0887468i
$553$	−8.51999e7			−0.503807
$554$		−	1.37248e6i		−	0.00807194i
$555$	1.20352e8	−	6.06706e7i	0.704004	−	0.354895i
$556$	−3.33877e7			−0.194251
$557$			1.42960e8i			0.827275i	0.910442	+	0.413638i	$0.135742\pi$
$557$			1.42960e8i			0.827275i	−0.910442	+	0.413638i	$0.864258\pi$
$558$	1.74372e7	+	1.29000e7i	0.100363	+	0.0742484i
$559$	−8.94400e7			−0.512031
$560$		−	1.94772e8i		−	1.10908i
$561$	−1.00862e7	−	2.00079e7i	−0.0571265	−	0.113322i
$562$	−5.33379e6			−0.0300488
$563$			1.32358e8i			0.741692i	0.928694	+	0.370846i	$0.120932\pi$
$563$			1.32358e8i			0.741692i	−0.928694	+	0.370846i	$0.879068\pi$
$564$	−5.43132e7	+	2.73798e7i	−0.302739	+	0.152613i
$565$	3.01885e8			1.67377
$566$		−	6.95359e6i		−	0.0383495i
$567$	−5.08386e7	−	1.66158e8i	−0.278897	−	0.911534i
$568$	−1.94021e7			−0.105877
$569$		−	3.62808e7i		−	0.196943i	−0.995140	−	0.0984713i	$-0.968605\pi$
$569$		−	3.62808e7i		−	0.196943i	0.995140	−	0.0984713i	$-0.0313953\pi$
$570$	−8.95738e6	−	1.77688e7i	−0.0483678	−	0.0959472i
$571$	2.08819e8			1.12166			0.560830	−	0.827931i	$-0.310482\pi$
$571$	2.08819e8			1.12166			0.560830	+	0.827931i	$0.310482\pi$
$572$			5.82317e7i			0.311151i
$573$	−1.80054e8	+	9.07669e7i	−0.957061	+	0.482463i
$574$	2.07879e7			0.109920
$575$		−	5.17267e7i		−	0.272089i
$576$	−1.10054e8	+	1.48763e8i	−0.575891	+	0.778446i
$577$	3.81698e6			0.0198698			0.00993489	−	0.999951i	$-0.496838\pi$
$577$	3.81698e6			0.0198698			0.00993489	+	0.999951i	$0.496838\pi$
$578$			1.15726e7i			0.0599302i
$579$	8.60445e7	+	1.70687e8i	0.443290	+	0.879354i
$580$	−3.81662e8			−1.95612
$581$		−	2.00134e8i		−	1.02045i
$582$	−1.15998e7	+	5.84754e6i	−0.0588410	+	0.0296623i
$583$	4.34203e6			0.0219123
$584$		−	2.96652e7i		−	0.148939i
$585$	1.97411e8	+	1.46044e8i	0.986060	+	0.729483i
$586$	2.57850e7			0.128137
$587$			1.00262e8i			0.495705i	0.968798	+	0.247853i	$0.0797249\pi$
$587$			1.00262e8i			0.495705i	−0.968798	+	0.247853i	$0.920275\pi$
$588$	−8.31284e6	−	1.64902e7i	−0.0408900	−	0.0811135i
$589$	4.37059e8			2.13892
$590$			1.33758e7i			0.0651274i
$591$	9.10883e7	−	4.59184e7i	0.441266	−	0.222446i
$592$	1.36158e8			0.656265
$593$			6.33376e7i			0.303737i	0.988401	+	0.151869i	$0.0485290\pi$
$593$			6.33376e7i			0.303737i	−0.988401	+	0.151869i	$0.951471\pi$
$594$	4.53613e6	+	778700.i	0.0216434	+	0.00371544i
$595$	9.99192e7			0.474349
$596$		−	2.06554e8i		−	0.975653i
$597$	820502.	+	1.62763e6i	0.00385618	+	0.00764949i
$598$	−1.10542e7			−0.0516921
$599$			6.97579e7i			0.324574i	0.986744	+	0.162287i	$0.0518870\pi$
$599$			6.97579e7i			0.324574i	−0.986744	+	0.162287i	$0.948113\pi$
$600$	1.11451e7	−	5.61833e6i	0.0515976	−	0.0260108i
$601$	−3.19227e8			−1.47054			−0.735270	−	0.677775i	$-0.762944\pi$
$601$	−3.19227e8			−1.47054			−0.735270	+	0.677775i	$0.762944\pi$
$602$		−	7.47553e6i		−	0.0342652i
$603$	1.70117e8	−	2.29952e8i	0.775883	−	1.04878i
$604$	3.09161e8			1.40305
$605$			2.38005e7i			0.107478i
$606$	−1.18100e7	−	2.34275e7i	−0.0530680	−	0.105271i
$607$	−2.95834e8			−1.32276			−0.661380	−	0.750051i	$-0.730029\pi$
$607$	−2.95834e8			−1.32276			−0.661380	+	0.750051i	$0.730029\pi$
$608$		−	6.08477e7i		−	0.270728i
$609$	3.19801e8	−	1.61214e8i	1.41588	−	0.713759i
$610$	8.92860e6			0.0393364
$611$			8.06585e7i			0.353612i
$612$	−7.71503e7	−	5.70755e7i	−0.336576	−	0.248998i
$613$	2.04858e8			0.889347			0.444673	−	0.895693i	$-0.353320\pi$
$613$	2.04858e8			0.889347			0.444673	+	0.895693i	$0.353320\pi$
$614$		−	1.10272e7i		−	0.0476389i
$615$	−1.95989e8	−	3.88784e8i	−0.842571	−	1.67141i
$616$	−9.76015e6			−0.0417556
$617$			3.55623e8i			1.51403i	0.653399	+	0.757014i	$0.273342\pi$
$617$			3.55623e8i			1.51403i	−0.653399	+	0.757014i	$0.726658\pi$
$618$	1.38602e7	−	6.98705e6i	0.0587225	−	0.0296025i
$619$	7.84718e7			0.330858			0.165429	−	0.986222i	$-0.447099\pi$
$619$	7.84718e7			0.330858			0.165429	+	0.986222i	$0.447099\pi$
$620$			4.80408e8i			2.01574i
$621$	2.77185e7	−	1.61468e8i	0.115743	−	0.674234i
$622$	1.30410e7			0.0541925
$623$			3.38742e8i			1.40089i
$624$	1.11669e8	+	2.21517e8i	0.459597	+	0.911702i
$625$	−3.02623e8			−1.23954
$626$		−	2.92324e6i		−	0.0119163i
$627$	8.28127e7	−	4.17466e7i	0.335965	−	0.169363i
$628$	2.12382e8			0.857510
$629$			6.98499e7i			0.280681i
$630$	−1.22066e7	+	1.64999e7i	−0.0488170	+	0.0659872i
$631$	−3.53089e8			−1.40539			−0.702693	−	0.711493i	$-0.748019\pi$
$631$	−3.53089e8			−1.40539			−0.702693	+	0.711493i	$0.748019\pi$
$632$		−	1.93828e7i		−	0.0767829i
$633$	6.83522e7	+	1.35590e8i	0.269489	+	0.534586i
$634$	−2.64304e6			−0.0103714
$635$			4.59558e7i			0.179481i
$636$	1.66064e7	−	8.37141e6i	0.0645510	−	0.0325407i
$637$	−2.44889e7			−0.0947440
$638$			9.48610e6i			0.0365280i
$639$	−1.52867e8	−	1.13090e8i	−0.585882	−	0.433433i
$640$	8.90968e7			0.339877
$641$		−	1.77468e7i		−	0.0673825i	−0.999432	−	0.0336912i	$-0.989274\pi$
$641$		−	1.77468e7i		−	0.0673825i	0.999432	−	0.0336912i	$-0.0107263\pi$
$642$	1.14410e7	+	2.26955e7i	0.0432373	+	0.0857698i
$643$	2.38112e8			0.895672			0.447836	−	0.894116i	$-0.352195\pi$
$643$	2.38112e8			0.895672			0.447836	+	0.894116i	$0.352195\pi$
$644$			1.73249e8i			0.648653i
$645$	−1.39810e8	+	7.04796e7i	−0.521027	+	0.262654i
$646$	1.03126e7			0.0382535
$647$			4.72843e8i			1.74584i	0.487864	+	0.872920i	$0.337776\pi$
$647$			4.72843e8i			1.74584i	−0.487864	+	0.872920i	$0.662224\pi$
$648$	3.78006e7	−	1.15657e7i	0.138923	−	0.0425055i
$649$	−6.23390e7			−0.228048
$650$		−	8.25356e6i		−	0.0300539i
$651$	−2.02925e8	−	4.02541e8i	−0.735515	−	1.45904i
$652$	2.93649e8			1.05946
$653$			2.82767e7i			0.101552i	0.998710	+	0.0507760i	$0.0161695\pi$
$653$			2.82767e7i			0.101552i	−0.998710	+	0.0507760i	$0.983831\pi$
$654$	−2.23824e7	+	1.12832e7i	−0.0800155	+	0.0403365i
$655$	4.98788e7			0.177497
$656$		−	4.39843e8i		−	1.55807i
$657$	1.72911e8	−	2.33728e8i	0.609715	−	0.824167i
$658$	−6.74156e6			−0.0236637
$659$		−	3.49085e8i		−	1.21976i	−0.792493	−	0.609880i	$-0.791217\pi$
$659$		−	3.49085e8i		−	1.21976i	0.792493	−	0.609880i	$-0.208783\pi$
$660$	4.58872e7	+	9.10264e7i	0.159610	+	0.316618i
$661$	−1.72721e8			−0.598056			−0.299028	−	0.954244i	$-0.596662\pi$
$661$	−1.72721e8			−0.598056			−0.299028	+	0.954244i	$0.596662\pi$
$662$			2.94018e7i			0.101344i
$663$	−1.13639e8	+	5.72865e7i	−0.389931	+	0.196568i
$664$	4.55299e7			0.155522
$665$			4.13565e8i			1.40630i
$666$	−1.15345e7	−	8.53317e6i	−0.0390459	−	0.0288860i
$667$	3.37666e8			1.13792
$668$		−	4.00033e8i		−	1.34204i
$669$	5.42827e7	+	1.07681e8i	0.181294	+	0.359632i
$670$	−3.37861e7			−0.112334
$671$			4.16125e7i			0.137739i
$672$	−5.60421e7	+	2.82513e7i	−0.184674	+	0.0930959i
$673$	−4.67477e8			−1.53361			−0.766806	−	0.641879i	$-0.778155\pi$
$673$	−4.67477e8			−1.53361			−0.766806	+	0.641879i	$0.778155\pi$
$674$		−	1.52338e7i		−	0.0497541i
$675$	1.20559e8	+	2.06958e7i	0.392001	+	0.0672933i
$676$	2.34623e7			0.0759505
$677$		−	3.97447e8i		−	1.28089i	−0.768002	−	0.640447i	$-0.778749\pi$
$677$		−	3.97447e8i		−	1.28089i	0.768002	−	0.640447i	$-0.221251\pi$
$678$	−1.44663e7	−	2.86967e7i	−0.0464159	−	0.0920753i
$679$	2.69983e8			0.862436
$680$			2.27314e7i			0.0722934i
$681$	−5.32150e8	+	2.68262e8i	−1.68497	+	0.849409i
$682$	1.19404e7			0.0376414
$683$		−	4.80399e8i		−	1.50779i	−0.656996	−	0.753894i	$-0.728173\pi$
$683$		−	4.80399e8i		−	1.50779i	0.656996	−	0.753894i	$-0.271827\pi$
$684$	2.36235e8	−	3.19325e8i	0.738204	−	0.997848i
$685$	−6.10999e8			−1.90094
$686$		−	2.44602e7i		−	0.0757682i
$687$	−2.17024e8	−	4.30510e8i	−0.669325	−	1.32774i
$688$	−1.58172e8			−0.485695
$689$		−	2.46615e7i		−	0.0753983i
$690$	−1.72797e7	+	8.71084e6i	−0.0526004	+	0.0265163i
$691$	1.42412e8			0.431630			0.215815	−	0.976434i	$-0.430759\pi$
$691$	1.42412e8			0.431630			0.215815	+	0.976434i	$0.430759\pi$
$692$			2.77638e8i			0.837839i
$693$	−7.68992e7	−	5.68896e7i	−0.231058	−	0.170936i
$694$	−302168.			−0.000904002
$695$			7.75067e7i			0.230879i
$696$	3.66758e7	+	7.27539e7i	0.108781	+	0.215788i
$697$	2.25642e8			0.666378
$698$		−	1.36561e7i		−	0.0401569i
$699$	−1.48021e8	+	7.46184e7i	−0.433402	+	0.218482i
$700$	−1.29355e8			−0.377128
$701$			3.58347e7i			0.104028i	0.998646	+	0.0520139i	$0.0165640\pi$
$701$			3.58347e7i			0.104028i	−0.998646	+	0.0520139i	$0.983436\pi$
$702$	4.42279e6	−	2.57639e7i	0.0127845	−	0.0744733i
$703$	−2.89108e8			−0.832137
$704$			1.01868e8i			0.291957i
$705$	6.35597e7	+	1.26083e8i	0.181391	+	0.359824i
$706$	1.31331e7			0.0373211
$707$			5.45272e8i			1.54296i
$708$	−2.38419e8	+	1.20189e8i	−0.671802	+	0.338661i
$709$	−3.38395e8			−0.949478			−0.474739	−	0.880127i	$-0.657458\pi$
$709$	−3.38395e8			−0.949478			−0.474739	+	0.880127i	$0.657458\pi$
$710$			2.24602e7i			0.0627537i
$711$	1.12978e8	−	1.52715e8i	0.314328	−	0.424886i
$712$	−7.70630e7			−0.213504
$713$		−	4.25029e8i		−	1.17260i
$714$	−4.78810e6	−	9.49814e6i	−0.0131543	−	0.0260942i
$715$	1.35180e8			0.369823
$716$			3.20197e8i			0.872325i
$717$	−9.43942e7	+	4.75849e7i	−0.256087	+	0.129096i
$718$	2.36003e7			0.0637593
$719$		−	4.89502e8i		−	1.31695i	−0.752604	−	0.658473i	$-0.771203\pi$
$719$		−	4.89502e8i		−	1.31695i	0.752604	−	0.658473i	$-0.228797\pi$
$720$	3.49115e8	+	2.58274e8i	0.935343	+	0.691963i
$721$	−3.22594e8			−0.860698
$722$			1.52718e7i			0.0405769i
$723$	2.34630e8	+	4.65436e8i	0.620825	+	1.23153i
$724$	2.98833e6			0.00787432
$725$			2.52116e8i			0.661587i
$726$	2.26243e6	−	1.14051e6i	0.00591243	−	0.00298051i
$727$	7.93952e7			0.206629			0.103314	−	0.994649i	$-0.467055\pi$
$727$	7.93952e7			0.206629			0.103314	+	0.994649i	$0.467055\pi$
$728$			5.54349e7i			0.143677i
$729$	3.65240e8	+	1.29206e8i	0.942749	+	0.333504i
$730$	−3.43410e7			−0.0882763
$731$		−	8.11429e7i		−	0.207730i
$732$	8.02286e7	+	1.59149e8i	0.204548	+	0.405763i
$733$	2.83896e8			0.720854			0.360427	−	0.932787i	$-0.382631\pi$
$733$	2.83896e8			0.720854			0.360427	+	0.932787i	$0.382631\pi$
$734$			1.03665e7i			0.0262146i
$735$	−3.82805e7	+	1.92975e7i	−0.0964086	+	0.0486004i
$736$	−5.91729e7			−0.148419
$737$		−	1.57463e8i		−	0.393346i
$738$	−2.75654e7	+	3.72608e7i	−0.0685795	+	0.0927007i
$739$	5.36905e8			1.33035			0.665173	−	0.746689i	$-0.268358\pi$
$739$	5.36905e8			1.33035			0.665173	+	0.746689i	$0.268358\pi$
$740$		−	3.17783e8i		−	0.784217i
$741$	−2.37109e8	−	4.70352e8i	−0.582764	−	1.15603i
$742$	2.06124e6			0.00504566
$743$		−	9.93548e6i		−	0.0242227i	−0.999927	−	0.0121114i	$-0.996145\pi$
$743$		−	9.93548e6i		−	0.0242227i	0.999927	−	0.0121114i	$-0.00385526\pi$
$744$	9.15771e7	−	4.61648e7i	0.222366	−	0.112097i
$745$	−4.79498e8			−1.15963
$746$			4.53905e7i			0.109332i
$747$	3.58725e8	+	2.65383e8i	0.860597	+	0.636666i
$748$	−5.28298e7			−0.126233
$749$		−	5.28234e8i		−	1.25713i
$750$	9.84842e6	+	1.95363e7i	0.0233444	+	0.0463083i
$751$	1.20239e8			0.283875			0.141937	−	0.989876i	$-0.454667\pi$
$751$	1.20239e8			0.283875			0.141937	+	0.989876i	$0.454667\pi$
$752$			1.42642e8i			0.335424i
$753$	−8.63009e7	+	4.35050e7i	−0.202130	+	0.101895i
$754$	5.38783e7			0.125690
$755$		−	7.17690e8i		−	1.66762i
$756$	−4.03788e8	−	6.93168e7i	−0.934520	−	0.160425i
$757$	1.71781e7			0.0395992			0.0197996	−	0.999804i	$-0.493697\pi$
$757$	1.71781e7			0.0395992			0.0197996	+	0.999804i	$0.493697\pi$
$758$		−	6.04911e6i		−	0.0138894i
$759$	−4.05976e7	−	8.05334e7i	−0.0928485	−	0.184183i
$760$	−9.40850e7			−0.214328
$761$			2.00013e8i			0.453841i	0.973913	+	0.226921i	$0.0728658\pi$
$761$			2.00013e8i			0.453841i	−0.973913	+	0.226921i	$0.927134\pi$
$762$	4.36848e6	−	2.20219e6i	0.00987338	−	0.00497725i
$763$	5.20948e8			1.17279
$764$			4.75423e8i			1.06611i
$765$	−1.32496e8	+	1.79098e8i	−0.295949	+	0.400042i
$766$	3.22849e7			0.0718312
$767$			3.54067e8i			0.784693i
$768$	1.93179e8	+	3.83208e8i	0.426457	+	0.845963i
$769$	1.74167e8			0.382990			0.191495	−	0.981494i	$-0.438666\pi$
$769$	1.74167e8			0.382990			0.191495	+	0.981494i	$0.438666\pi$
$770$			1.12985e7i			0.0247486i
$771$	5.06180e8	−	2.55170e8i	1.10444	−	0.556757i
$772$	4.50688e8			0.979544
$773$		−	6.53580e8i		−	1.41501i	−0.706707	−	0.707506i	$-0.749820\pi$
$773$		−	6.53580e8i		−	1.41501i	0.706707	−	0.707506i	$-0.250180\pi$
$774$	1.33993e7	+	9.91277e6i	0.0288975	+	0.0213783i
$775$	3.17345e8			0.681753
$776$			6.14204e7i			0.131440i
$777$	1.34232e8	+	2.66275e8i	0.286149	+	0.567634i
$778$	−1.50548e7			−0.0319695
$779$			9.33930e8i			1.97561i
$780$	5.17004e8	−	2.60626e8i	1.08946	−	0.549204i
$781$	−1.04678e8			−0.219736
$782$		−	1.00288e7i		−	0.0209714i
$783$	−1.35100e8	+	7.86994e8i	−0.281430	+	1.63941i
$784$	−4.33079e7			−0.0898709
$785$		−	4.93027e8i		−	1.01921i
$786$	−2.39018e6	−	4.74139e6i	−0.00492223	−	0.00976423i
$787$	3.77368e7			0.0774177			0.0387089	−	0.999251i	$-0.487676\pi$
$787$	3.77368e7			0.0774177			0.0387089	+	0.999251i	$0.487676\pi$
$788$		−	2.40513e8i		−	0.491542i
$789$	−5.26378e8	+	2.65352e8i	−1.07168	+	0.540245i
$790$	−2.24379e7			−0.0455093
$791$			6.67911e8i			1.34955i
$792$	1.29422e7	−	1.74944e7i	0.0260516	−	0.0352146i
$793$	2.36347e8			0.473948
$794$		−	1.36003e7i		−	0.0271698i
$795$	−1.94335e7	−	3.85502e7i	−0.0386767	−	0.0767230i
$796$	4.29766e6			0.00852105
$797$		−	2.93888e8i		−	0.580506i	−0.956950	−	0.290253i	$-0.906261\pi$
$797$		−	2.93888e8i		−	0.580506i	0.956950	−	0.290253i	$-0.0937395\pi$
$798$	3.93128e7	−	1.98179e7i	0.0773615	−	0.0389986i
$799$	−7.31761e7			−0.143459
$800$		−	4.41810e7i		−	0.0862911i
$801$	−6.07171e8	−	4.49182e8i	−1.18144	−	0.874027i
$802$	−49824.8			−9.65879e−5
$803$		−	1.60049e8i		−	0.309105i
$804$	−3.03587e8	−	6.02226e8i	−0.584138	−	1.15875i
$805$	4.02182e8			0.770966
$806$		−	6.78180e7i		−	0.129521i
$807$	−1.41554e7	+	7.13584e6i	−0.0269340	+	0.0135777i
$808$	−1.24048e8			−0.235156
$809$			8.88657e8i			1.67837i	0.543844	+	0.839187i	$0.316968\pi$
$809$			8.88657e8i			1.67837i	−0.543844	+	0.839187i	$0.683032\pi$
$810$	−1.33886e7	−	4.37587e7i	−0.0251931	−	0.0823397i
$811$	4.74095e8			0.888798			0.444399	−	0.895829i	$-0.353417\pi$
$811$	4.74095e8			0.888798			0.444399	+	0.895829i	$0.353417\pi$
$812$		−	8.44416e8i		−	1.57721i
$813$	4.19084e8	+	8.31336e8i	0.779883	+	1.54705i
$814$	−7.89841e6			−0.0146442
$815$		−	6.81680e8i		−	1.25924i
$816$	−2.00967e8	+	1.01309e8i	−0.369875	+	0.186457i
$817$	3.35850e8			0.615857
$818$		−	7.38107e7i		−	0.134853i
$819$	−3.23117e8	+	4.36765e8i	−0.588177	+	0.795053i
$820$	−1.02656e9			−1.86184
$821$			3.26757e8i			0.590467i	0.955425	+	0.295233i	$0.0953974\pi$
$821$			3.26757e8i			0.590467i	−0.955425	+	0.295233i	$0.904603\pi$
$822$	2.92789e7	+	5.80805e7i	0.0527156	+	0.104572i
$823$	−1.61640e8			−0.289968			−0.144984	−	0.989434i	$-0.546313\pi$
$823$	−1.61640e8			−0.289968			−0.144984	+	0.989434i	$0.546313\pi$
$824$		−	7.33894e7i		−	0.131175i
$825$	6.01297e7	−	3.03119e7i	0.107085	−	0.0539823i
$826$	−2.95935e7			−0.0525117
$827$		−	2.62384e8i		−	0.463896i	−0.972728	−	0.231948i	$-0.925490\pi$
$827$		−	2.62384e8i		−	0.463896i	0.972728	−	0.231948i	$-0.0745099\pi$
$828$	−3.10536e8	−	2.29733e8i	−0.547042	−	0.404699i
$829$	−1.00648e9			−1.76661			−0.883306	−	0.468796i	$-0.844688\pi$
$829$	−1.00648e9			−1.76661			−0.883306	+	0.468796i	$0.844688\pi$
$830$		−	5.27063e7i		−	0.0921783i
$831$	−2.86290e7	−	5.67912e7i	−0.0498887	−	0.0989642i
$832$	5.78580e8			1.00460
$833$		−	2.22172e7i		−	0.0384374i
$834$	7.36766e6	−	3.71410e6i	0.0127008	−	0.00640258i
$835$	−9.28642e8			−1.59510
$836$		−	2.18662e8i		−	0.374244i
$837$	9.90610e8	+	1.70054e8i	1.68938	+	0.290009i
$838$	9.68028e6			0.0164496
$839$		−	1.25339e8i		−	0.212227i	−0.994354	−	0.106114i	$-0.966159\pi$
$839$		−	1.25339e8i		−	0.212227i	0.994354	−	0.106114i	$-0.0338407\pi$
$840$	4.36832e7	+	8.66544e7i	0.0737016	+	0.146202i
$841$	−1.05096e9			−1.76685
$842$			4.83158e7i			0.0809380i
$843$	−2.20704e8	+	1.11259e8i	−0.368406	+	0.185717i
$844$	3.58018e8			0.595495
$845$		−	5.44657e7i		−	0.0902720i
$846$	8.93951e6	−	1.20838e7i	0.0147639	−	0.0199568i
$847$	−5.26578e7			−0.0866587
$848$		−	4.36131e7i		−	0.0715202i
$849$	−1.45047e8	−	2.87729e8i	−0.237020	−	0.470176i
$850$	7.48790e6			0.0121928
$851$			2.81151e8i			0.456195i
$852$	−4.00346e8	+	2.01818e8i	−0.647317	+	0.326318i
$853$	6.34131e8			1.02172			0.510860	−	0.859664i	$-0.329327\pi$
$853$	6.34131e8			1.02172			0.510860	+	0.859664i	$0.329327\pi$
$854$			1.97542e7i			0.0317166i
$855$	−7.41285e8	−	5.48399e8i	−1.18601	−	0.877402i
$856$	1.20172e8			0.191594
$857$		−	5.73783e8i		−	0.911602i	−0.890082	−	0.455801i	$-0.849353\pi$
$857$		−	5.73783e8i		−	0.911602i	0.890082	−	0.455801i	$-0.150647\pi$
$858$	−6.47778e6	−	1.28500e7i	−0.0102557	−	0.0203442i
$859$	−2.34727e8			−0.370325			−0.185163	−	0.982708i	$-0.559281\pi$
$859$	−2.34727e8			−0.370325			−0.185163	+	0.982708i	$0.559281\pi$
$860$			3.69161e8i			0.580391i
$861$	8.60171e8	−	4.33619e8i	1.34764	−	0.679359i
$862$	2.59010e6			0.00404385
$863$		−	8.61041e6i		−	0.0133965i	−0.999978	−	0.00669825i	$-0.997868\pi$
$863$		−	8.61041e6i		−	0.0133965i	0.999978	−	0.00669825i	$-0.00213214\pi$
$864$	2.36751e7	−	1.37913e8i	0.0367071	−	0.213828i
$865$	6.44512e8			0.995824
$866$		−	4.53228e7i		−	0.0697852i
$867$	2.41395e8	+	4.78854e8i	0.370399	+	0.734761i
$868$	−1.06289e9			−1.62528
$869$		−	1.04574e8i		−	0.159354i
$870$	8.42213e7	−	4.24567e7i	0.127898	−	0.0644745i
$871$	−8.94342e8			−1.35347
$872$			1.18514e8i			0.178740i
$873$	−3.58005e8	+	4.83924e8i	−0.538079	+	0.727335i
$874$	4.15090e7			0.0621739
$875$		−	4.54704e8i		−	0.678743i
$876$	−3.08573e8	−	6.12117e8i	−0.459035	−	0.910588i
$877$	1.28749e8			0.190873			0.0954363	−	0.995436i	$-0.469575\pi$
$877$	1.28749e8			0.190873			0.0954363	+	0.995436i	$0.469575\pi$
$878$		−	5.28668e7i		−	0.0781087i
$879$	1.06694e9	−	5.37855e8i	1.57100	−	0.791952i
$880$	2.39061e8			0.350802
$881$		−	1.06318e9i		−	1.55482i	−0.628994	−	0.777410i	$-0.716533\pi$
$881$		−	1.06318e9i		−	1.55482i	0.628994	−	0.777410i	$-0.283467\pi$
$882$	3.66878e6	+	2.71415e6i	0.00534707	+	0.00395574i
$883$	2.75225e8			0.399767			0.199883	−	0.979820i	$-0.435944\pi$
$883$	2.75225e8			0.399767			0.199883	+	0.979820i	$0.435944\pi$
$884$			3.00058e8i			0.434358i
$885$	2.79009e8	+	5.53469e8i	0.402520	+	0.798480i
$886$	−9.09374e7			−0.130750
$887$			3.00397e8i			0.430452i	0.976564	+	0.215226i	$0.0690488\pi$
$887$			3.00397e8i			0.430452i	−0.976564	+	0.215226i	$0.930951\pi$
$888$	−6.05770e7	+	3.05374e7i	−0.0865105	+	0.0436107i
$889$	−1.01676e8			−0.144714
$890$			8.92097e7i			0.126544i
$891$	2.03941e8	−	6.23988e7i	0.288318	−	0.0882151i
$892$	2.84324e8			0.400608
$893$		−	3.02876e8i		−	0.425314i
$894$	2.29774e7	+	4.55802e7i	0.0321579	+	0.0637917i
$895$	7.43310e8			1.03681
$896$			1.97124e8i			0.274041i
$897$	−4.57406e8	+	2.30582e8i	−0.633760	+	0.319484i
$898$	−2.13318e7			−0.0294577
$899$			2.07160e9i			2.85119i
$900$	1.71529e8	−	2.31859e8i	0.235293	−	0.318051i
$901$	2.23737e7			0.0305889
$902$			2.55149e7i			0.0347675i
$903$	−1.55934e8	−	3.09326e8i	−0.211776	−	0.420100i
$904$	−1.51948e8			−0.205679
$905$		−	6.93715e6i		−	0.00935912i
$906$	−6.82224e7	+	3.43915e7i	−0.0917366	+	0.0462452i
$907$	1.28430e9			1.72126			0.860628	−	0.509234i	$-0.170071\pi$
$907$	1.28430e9			1.72126			0.860628	+	0.509234i	$0.170071\pi$
$908$			1.40511e9i			1.87695i
$909$	−9.77360e8	−	7.23046e8i	−1.30126	−	0.962664i
$910$	6.41725e7			0.0851578
$911$			5.73694e8i			0.758796i	0.925233	+	0.379398i	$0.123869\pi$
$911$			5.73694e8i			0.758796i	−0.925233	+	0.379398i	$0.876131\pi$
$912$	−4.19319e8	−	8.31804e8i	−0.552790	−	1.09657i
$913$	2.45642e8			0.322768
$914$			4.27377e6i			0.00559722i
$915$	3.69452e8	−	1.86244e8i	0.482275	−	0.243119i
$916$	−1.13674e9			−1.47902
$917$			1.10355e8i			0.143115i
$918$	2.33739e7	+	4.01250e6i	0.0302136	+	0.00518666i
$919$	−1.67764e8			−0.216148			−0.108074	−	0.994143i	$-0.534468\pi$
$919$	−1.67764e8			−0.216148			−0.108074	+	0.994143i	$0.534468\pi$
$920$			9.14954e7i			0.117499i
$921$	−2.30020e8	−	4.56290e8i	−0.294433	−	0.584066i
$922$	−7.66357e7			−0.0977774
$923$			5.94539e8i			0.756093i
$924$	−2.01393e8	+	1.01524e8i	−0.255287	+	0.128692i
$925$	−2.09919e8			−0.265233
$926$		−	2.63683e7i		−	0.0332085i
$927$	4.27769e8	−	5.78226e8i	0.536995	−	0.725870i
$928$	2.88409e8			0.360882
$929$		−	3.25935e7i		−	0.0406522i	−0.999793	−	0.0203261i	$-0.993530\pi$
$929$		−	3.25935e7i		−	0.0406522i	0.999793	−	0.0203261i	$-0.00647044\pi$
$930$	−5.34413e7	−	1.06011e8i	−0.0664398	−	0.131797i
$931$	9.19568e7			0.113955
$932$			3.90840e8i			0.482782i
$933$	5.39616e8	−	2.72025e8i	0.664416	−	0.334938i
$934$	2.48959e7			0.0305553
$935$			1.22640e8i			0.150036i
$936$	−9.93629e7	−	7.35082e7i	−0.121170	−	0.0896414i
$937$	3.39083e8			0.412180			0.206090	−	0.978533i	$-0.433926\pi$
$937$	3.39083e8			0.412180			0.206090	+	0.978533i	$0.433926\pi$
$938$		−	7.47505e7i		−	0.0905745i
$939$	−6.09764e7	−	1.20959e8i	−0.0736487	−	0.146097i
$940$	3.32916e8			0.400822
$941$			3.63683e8i			0.436470i	0.975896	+	0.218235i	$0.0700300\pi$
$941$			3.63683e8i			0.436470i	−0.975896	+	0.218235i	$0.929970\pi$
$942$	−4.68663e7	+	2.36257e7i	−0.0560671	+	0.0282639i
$943$	9.08224e8			1.08307
$944$			6.26157e8i			0.744333i
$945$	−1.60913e8	+	9.37360e8i	−0.190676	+	1.11074i
$946$	9.17539e6			0.0108381
$947$			1.23933e9i			1.45927i	0.683836	+	0.729636i	$0.260310\pi$
$947$			1.23933e9i			1.45927i	−0.683836	+	0.729636i	$0.739690\pi$
$948$	−2.01617e8	−	3.99948e8i	−0.236648	−	0.469438i
$949$	−9.09031e8			−1.06360
$950$			3.09924e7i			0.0361480i
$951$	−1.09365e8	+	5.51317e7i	−0.127156	+	0.0641003i
$952$	−5.02924e7			−0.0582896
$953$		−	1.12365e9i		−	1.29823i	−0.760689	−	0.649116i	$-0.775139\pi$
$953$		−	1.12365e9i		−	1.29823i	0.760689	−	0.649116i	$-0.224861\pi$
$954$	−2.73327e6	+	3.69463e6i	−0.00314802	+	0.00425526i
$955$	1.10365e9			1.26713
$956$			2.49242e8i			0.285265i
$957$	1.97873e8	+	3.92520e8i	0.225762	+	0.447843i
$958$	1.26471e8			0.143845
$959$		−	1.35181e9i		−	1.53271i
$960$	9.04422e8	−	4.55927e8i	1.02225	−	0.515325i
$961$	1.72007e9			1.93809
$962$			4.48607e7i			0.0503896i
$963$	9.46821e8	+	7.00454e8i	1.06020	+	0.784333i
$964$	1.22896e9			1.37185
$965$		−	1.04623e9i		−	1.16425i
$966$	−1.92724e7	−	3.82307e7i	−0.0213799	−	0.0424113i
$967$	−1.27609e9			−1.41124			−0.705621	−	0.708590i	$-0.749332\pi$
$967$	−1.27609e9			−1.41124			−0.705621	+	0.708590i	$0.749332\pi$
$968$		−	1.19795e7i		−	0.0132073i
$969$	4.26719e8	−	2.15113e8i	0.468998	−	0.236426i
$970$	7.11014e7			0.0779046
$971$			8.71577e8i			0.952024i	0.879439	+	0.476012i	$0.157918\pi$
$971$			8.71577e8i			0.952024i	−0.879439	+	0.476012i	$0.842082\pi$
$972$	6.59681e8	−	6.31845e8i	0.718348	−	0.688037i
$973$	−1.71481e8			−0.186156
$974$			1.11928e8i			0.121133i
$975$	−1.72163e8	−	3.41519e8i	−0.185749	−	0.368469i
$976$	4.17972e8			0.449571
$977$		−	9.19146e8i		−	0.985600i	−0.870143	−	0.492800i	$-0.835973\pi$
$977$		−	9.19146e8i		−	0.985600i	0.870143	−	0.492800i	$-0.164027\pi$
$978$	−6.47993e7	+	3.26659e7i	−0.0692714	+	0.0349203i
$979$	−4.15769e8			−0.443102
$980$			1.01078e8i			0.107393i
$981$	−6.90792e8	+	9.33761e8i	−0.731712	+	0.989074i
$982$	−1.17712e8			−0.124304
$983$		−	5.76928e8i		−	0.607381i	−0.952771	−	0.303690i	$-0.901781\pi$
$983$		−	5.76928e8i		−	0.607381i	0.952771	−	0.303690i	$-0.0982188\pi$
$984$	9.86473e7	+	1.95687e8i	0.103538	+	0.205388i
$985$	−5.58331e8			−0.584229
$986$			4.88802e7i			0.0509921i
$987$	−2.78955e8	+	1.40624e8i	−0.290124	+	0.146254i
$988$	−1.24194e9			−1.28774
$989$		−	3.26606e8i		−	0.337626i
$990$	−2.02518e7	−	1.49822e7i	−0.0208717	−	0.0154408i
$991$	−1.27105e9			−1.30599			−0.652996	−	0.757361i	$-0.726488\pi$
$991$	−1.27105e9			−1.30599			−0.652996	+	0.757361i	$0.726488\pi$
$992$		−	3.63028e8i		−	0.371882i
$993$	6.13298e8	+	1.21660e9i	0.626360	+	1.24251i
$994$	−4.96925e7			−0.0505978
$995$		−	9.97665e6i		−	0.0101278i
$996$	9.39473e8	−	4.73597e8i	0.950838	−	0.479325i
$997$	1.48068e8			0.149409			0.0747043	−	0.997206i	$-0.476199\pi$
$997$	1.48068e8			0.149409			0.0747043	+	0.997206i	$0.476199\pi$
$998$		−	6.47411e7i		−	0.0651311i
$999$	−6.55274e8	−	1.12488e8i	−0.657244	−	0.112827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.b.a.23.11	yes	20
3.2	odd	2	inner	33.7.b.a.23.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.b.a.23.10	✓	20	3.2	odd	2	inner
33.7.b.a.23.11	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.582665i q^{2} +(12.1539 + 24.1098i) q^{3} +63.6605 q^{4} -147.782i q^{5} +(-14.0479 + 7.08168i) q^{6} +326.963 q^{7} +74.3834i q^{8} +(-433.563 + 586.058i) q^{9} +O(q^{10})\)	\(q+0.582665i q^{2} +(12.1539 + 24.1098i) q^{3} +63.6605 q^{4} -147.782i q^{5} +(-14.0479 + 7.08168i) q^{6} +326.963 q^{7} +74.3834i q^{8} +(-433.563 + 586.058i) q^{9} +86.1076 q^{10} +401.312i q^{11} +(773.726 + 1534.84i) q^{12} +2279.33 q^{13} +190.510i q^{14} +(3563.00 - 1796.14i) q^{15} +4030.93 q^{16} +2067.89i q^{17} +(-341.476 - 252.622i) q^{18} -8558.98 q^{19} -9407.90i q^{20} +(3973.90 + 7883.02i) q^{21} -233.830 q^{22} +8323.40i q^{23} +(-1793.37 + 904.051i) q^{24} -6214.61 q^{25} +1328.09i q^{26} +(-19399.2 - 3330.19i) q^{27} +20814.7 q^{28} -40568.3i q^{29} +(1046.55 + 2076.04i) q^{30} -51064.4 q^{31} +7109.22i q^{32} +(-9675.53 + 4877.52i) q^{33} -1204.89 q^{34} -48319.4i q^{35} +(-27600.8 + 37308.7i) q^{36} +33778.4 q^{37} -4987.02i q^{38} +(27702.9 + 54954.2i) q^{39} +10992.5 q^{40} -109117. i q^{41} +(-4593.16 + 2315.45i) q^{42} -39239.5 q^{43} +25547.7i q^{44} +(86609.0 + 64073.0i) q^{45} -4849.76 q^{46} +35386.9i q^{47} +(48991.7 + 97184.9i) q^{48} -10743.9 q^{49} -3621.04i q^{50} +(-49856.3 + 25133.0i) q^{51} +145104. q^{52} -10819.6i q^{53} +(1940.39 - 11303.3i) q^{54} +59306.8 q^{55} +24320.6i q^{56} +(-104025. - 206355. i) q^{57} +23637.8 q^{58} +155338. i q^{59} +(226822. - 114343. i) q^{60} +103691. q^{61} -29753.4i q^{62} +(-141759. + 191620. i) q^{63} +253837. q^{64} -336845. i q^{65} +(-2841.96 - 5637.60i) q^{66} -392370. q^{67} +131643. i q^{68} +(-200675. + 101162. i) q^{69} +28154.0 q^{70} +260839. i q^{71} +(-43593.0 - 32249.9i) q^{72} -398815. q^{73} +19681.5i q^{74} +(-75532.1 - 149833. i) q^{75} -544869. q^{76} +131214. i q^{77} +(-32019.9 + 16141.5i) q^{78} -260579. q^{79} -595700. i q^{80} +(-155487. - 508186. i) q^{81} +63578.7 q^{82} -612098. i q^{83} +(252980. + 501837. i) q^{84} +305597. q^{85} -22863.5i q^{86} +(978093. - 493065. i) q^{87} -29850.9 q^{88} +1.03603e6i q^{89} +(-37333.1 + 50464.1i) q^{90} +745259. q^{91} +529872. i q^{92} +(-620634. - 1.23115e6i) q^{93} -20618.7 q^{94} +1.26487e6i q^{95} +(-171402. + 86405.1i) q^{96} +825727. q^{97} -6260.10i q^{98} +(-235192. - 173994. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9}+O(q^{10}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9	\( 20 q + 16 q^{3} - 772 q^{4} + 286 q^{6} + 160 q^{7} - 1072 q^{9} + 996 q^{10} + 6092 q^{12} + 808 q^{13} - 3032 q^{15} + 28004 q^{16} + 18686 q^{18} + 5920 q^{19} - 20888 q^{21} - 48096 q^{24} - 100612 q^{25} - 17624 q^{27} - 33296 q^{28} + 109582 q^{30} - 90896 q^{31} - 21296 q^{33} + 68928 q^{34} - 28988 q^{36} + 239656 q^{37} - 15416 q^{39} + 34632 q^{40} + 150364 q^{42} - 125840 q^{43} - 242428 q^{45} + 244380 q^{46} + 305492 q^{48} - 186204 q^{49} - 21992 q^{51} - 120368 q^{52} - 777728 q^{54} - 191664 q^{55} - 255840 q^{57} + 601176 q^{58} + 970736 q^{60} + 1108360 q^{61} + 574088 q^{63} - 2533132 q^{64} + 465850 q^{66} + 617728 q^{67} + 323804 q^{69} - 238680 q^{70} - 2031648 q^{72} - 1379960 q^{73} + 2481512 q^{75} + 4678408 q^{76} - 1556840 q^{78} + 347152 q^{79} - 1086136 q^{81} - 1760328 q^{82} - 345760 q^{84} - 4097232 q^{85} - 2983056 q^{87} - 622908 q^{88} - 4093630 q^{90} + 979616 q^{91} + 2363236 q^{93} - 217752 q^{94} + 8811824 q^{96} - 3139256 q^{97} + 212960 q^{99}+O(q^{100}) \) 20 * q + 16 * q^3 - 772 * q^4 + 286 * q^6 + 160 * q^7 - 1072 * q^9 + 996 * q^10 + 6092 * q^12 + 808 * q^13 - 3032 * q^15 + 28004 * q^16 + 18686 * q^18 + 5920 * q^19 - 20888 * q^21 - 48096 * q^24 - 100612 * q^25 - 17624 * q^27 - 33296 * q^28 + 109582 * q^30 - 90896 * q^31 - 21296 * q^33 + 68928 * q^34 - 28988 * q^36 + 239656 * q^37 - 15416 * q^39 + 34632 * q^40 + 150364 * q^42 - 125840 * q^43 - 242428 * q^45 + 244380 * q^46 + 305492 * q^48 - 186204 * q^49 - 21992 * q^51 - 120368 * q^52 - 777728 * q^54 - 191664 * q^55 - 255840 * q^57 + 601176 * q^58 + 970736 * q^60 + 1108360 * q^61 + 574088 * q^63 - 2533132 * q^64 + 465850 * q^66 + 617728 * q^67 + 323804 * q^69 - 238680 * q^70 - 2031648 * q^72 - 1379960 * q^73 + 2481512 * q^75 + 4678408 * q^76 - 1556840 * q^78 + 347152 * q^79 - 1086136 * q^81 - 1760328 * q^82 - 345760 * q^84 - 4097232 * q^85 - 2983056 * q^87 - 622908 * q^88 - 4093630 * q^90 + 979616 * q^91 + 2363236 * q^93 - 217752 * q^94 + 8811824 * q^96 - 3139256 * q^97 + 212960 * q^99

Introduction

L-functions

Modular forms

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