LMFDB - Embedded newform 322.2.i.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	322.127
Dual form			322.2.i.d.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(-0.473601 + 3.29397i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.68725 + 0.789049i) q^{5} +(1.38243 + 3.02711i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-7.74745 - 2.27486i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(-0.473601 + 3.29397i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.68725 + 0.789049i) q^{5} +(1.38243 + 3.02711i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-7.74745 - 2.27486i) q^{9} +(-1.83407 + 2.11663i) q^{10} +(2.03893 + 1.31034i) q^{11} +(2.79956 + 1.79917i) q^{12} +(-1.56505 + 1.80616i) q^{13} +(0.959493 + 0.281733i) q^{14} +(-1.32642 - 9.22542i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.04126 - 2.28005i) q^{17} +(-7.74745 + 2.27486i) q^{18} +(-2.73211 + 5.98248i) q^{19} +(-0.398581 + 2.77219i) q^{20} +(-2.79956 + 1.79917i) q^{21} +2.42368 q^{22} +(4.38057 - 1.95208i) q^{23} +3.32784 q^{24} +(2.39246 - 1.53754i) q^{25} +(-0.340118 + 2.36557i) q^{26} +(7.01520 - 15.3611i) q^{27} +(0.959493 - 0.281733i) q^{28} +(2.32836 + 5.09840i) q^{29} +(-6.10349 - 7.04380i) q^{30} +(0.688945 + 4.79171i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-5.28186 + 6.09559i) q^{33} +(-2.10865 - 1.35515i) q^{34} +(-2.35610 - 1.51417i) q^{35} +(-5.28769 + 6.10232i) q^{36} +(-2.54083 - 0.746055i) q^{37} +(0.935979 + 6.50987i) q^{38} +(-5.20824 - 6.01062i) q^{39} +(1.16345 + 2.54761i) q^{40} +(10.2748 - 3.01695i) q^{41} +(-1.38243 + 3.02711i) q^{42} +(-0.540218 + 3.75730i) q^{43} +(2.03893 - 1.31034i) q^{44} +22.6143 q^{45} +(2.62979 - 4.01051i) q^{46} +4.68422 q^{47} +(2.79956 - 1.79917i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(1.18141 - 2.58693i) q^{50} +(8.00354 - 2.35005i) q^{51} +(0.992799 + 2.17393i) q^{52} +(9.27553 + 10.7045i) q^{53} +(-2.40330 - 16.7153i) q^{54} +(-6.51304 - 1.91240i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-18.4122 - 11.8328i) q^{57} +(4.71515 + 3.03024i) q^{58} +(7.89747 - 9.11417i) q^{59} +(-8.94275 - 2.62583i) q^{60} +(0.362182 + 2.51903i) q^{61} +(3.17017 + 3.65858i) q^{62} +(-3.35428 - 7.34485i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.78053 - 6.08852i) q^{65} +(-1.14786 + 7.98352i) q^{66} +(-3.50857 + 2.25482i) q^{67} -2.50656 q^{68} +(4.35546 + 15.3540i) q^{69} -2.80070 q^{70} +(-6.22677 + 4.00170i) q^{71} +(-1.14912 + 7.99234i) q^{72} +(1.08217 - 2.36963i) q^{73} +(-2.54083 + 0.746055i) q^{74} +(3.93154 + 8.60888i) q^{75} +(4.30690 + 4.97043i) q^{76} +(0.344926 + 2.39901i) q^{77} +(-7.63104 - 2.24067i) q^{78} +(5.38873 - 6.21893i) q^{79} +(2.35610 + 1.51417i) q^{80} +(26.8985 + 17.2866i) q^{81} +(7.01262 - 8.09300i) q^{82} +(-16.2144 - 4.76098i) q^{83} +(0.473601 + 3.29397i) q^{84} +(4.59720 + 5.30545i) q^{85} +(1.57689 + 3.45290i) q^{86} +(-17.8967 + 5.25494i) q^{87} +(1.00683 - 2.20466i) q^{88} +(0.504383 - 3.50806i) q^{89} +(19.0244 - 12.2262i) q^{90} -2.38990 q^{91} +(0.0440769 - 4.79563i) q^{92} -16.1100 q^{93} +(3.94062 - 2.53248i) q^{94} +(2.62140 - 18.2322i) q^{95} +(1.38243 - 3.02711i) q^{96} +(-8.20917 + 2.41043i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-12.8157 - 14.7901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	−0.473601	+	3.29397i	−0.273434	+	1.90177i	0.138167	+	0.990409i	$0.455879\pi$
$3$	−0.473601	+	3.29397i	−0.273434	+	1.90177i	−0.411601	+	0.911364i	$0.635030\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−2.68725	+	0.789049i	−1.20178	+	0.352873i	−0.820532	−	0.571601i	$-0.806323\pi$
$5$	−2.68725	+	0.789049i	−1.20178	+	0.352873i	−0.381244	+	0.924474i	$0.624504\pi$
$6$	1.38243	+	3.02711i	0.564377	+	1.23581i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$7$	0.654861	+	0.755750i	0.247514	+	0.285646i
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−7.74745	−	2.27486i	−2.58248	−	0.758285i
$10$	−1.83407	+	2.11663i	−0.579984	+	0.669337i
$11$	2.03893	+	1.31034i	0.614760	+	0.395082i	0.810640	−	0.585546i	$-0.199120\pi$
$11$	2.03893	+	1.31034i	0.614760	+	0.395082i	−0.195879	+	0.980628i	$0.562756\pi$
$12$	2.79956	+	1.79917i	0.808163	+	0.519375i
$13$	−1.56505	+	1.80616i	−0.434067	+	0.500940i	−0.930071	−	0.367381i	$-0.880255\pi$
$13$	−1.56505	+	1.80616i	−0.434067	+	0.500940i	0.496004	+	0.868320i	$0.334800\pi$
$14$	0.959493	+	0.281733i	0.256435	+	0.0752962i
$15$	−1.32642	−	9.22542i	−0.342479	−	2.38199i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.04126	−	2.28005i	−0.252543	−	0.552992i	0.740320	−	0.672255i	$-0.234674\pi$
$17$	−1.04126	−	2.28005i	−0.252543	−	0.552992i	−0.992863	+	0.119263i	$0.961947\pi$
$18$	−7.74745	+	2.27486i	−1.82609	+	0.536189i
$19$	−2.73211	+	5.98248i	−0.626789	+	1.37248i	0.283688	+	0.958917i	$0.408442\pi$
$19$	−2.73211	+	5.98248i	−0.626789	+	1.37248i	−0.910477	+	0.413559i	$0.864285\pi$
$20$	−0.398581	+	2.77219i	−0.0891255	+	0.619881i
$21$	−2.79956	+	1.79917i	−0.610914	+	0.392610i
$22$	2.42368			0.516730
$23$	4.38057	−	1.95208i	0.913412	−	0.407037i
$23$	4.38057	−	1.95208i	0.913412	−	0.407037i
$24$	3.32784			0.679293
$25$	2.39246	−	1.53754i	0.478492	−	0.307508i
$26$	−0.340118	+	2.36557i	−0.0667026	+	0.463927i
$27$	7.01520	−	15.3611i	1.35008	−	2.95625i
$28$	0.959493	−	0.281733i	0.181327	−	0.0532424i
$29$	2.32836	+	5.09840i	0.432366	+	0.946749i	0.992937	+	0.118643i	$0.0378544\pi$
$29$	2.32836	+	5.09840i	0.432366	+	0.946749i	−0.560571	+	0.828106i	$0.689418\pi$
$30$	−6.10349	−	7.04380i	−1.11434	−	1.28602i
$31$	0.688945	+	4.79171i	0.123738	+	0.860617i	0.953262	+	0.302146i	$0.0977029\pi$
$31$	0.688945	+	4.79171i	0.123738	+	0.860617i	−0.829524	+	0.558472i	$0.811388\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−5.28186	+	6.09559i	−0.919454	+	1.06111i
$34$	−2.10865	−	1.35515i	−0.361631	−	0.232406i
$35$	−2.35610	−	1.51417i	−0.398254	−	0.255942i
$36$	−5.28769	+	6.10232i	−0.881281	+	1.01705i
$37$	−2.54083	−	0.746055i	−0.417710	−	0.122651i	0.0661223	−	0.997812i	$-0.478937\pi$
$37$	−2.54083	−	0.746055i	−0.417710	−	0.122651i	−0.483832	+	0.875161i	$0.660755\pi$
$38$	0.935979	+	6.50987i	0.151836	+	1.05604i
$39$	−5.20824	−	6.01062i	−0.833985	−	0.962470i
$40$	1.16345	+	2.54761i	0.183958	+	0.402812i
$41$	10.2748	−	3.01695i	1.60465	−	0.471169i	0.647817	−	0.761796i	$-0.275682\pi$
$41$	10.2748	−	3.01695i	1.60465	−	0.471169i	0.956836	+	0.290627i	$0.0938639\pi$
$42$	−1.38243	+	3.02711i	−0.213314	+	0.467093i
$43$	−0.540218	+	3.75730i	−0.0823824	+	0.572982i	0.906263	+	0.422715i	$0.138923\pi$
$43$	−0.540218	+	3.75730i	−0.0823824	+	0.572982i	−0.988645	+	0.150268i	$0.951986\pi$
$44$	2.03893	−	1.31034i	0.307380	−	0.197541i
$45$	22.6143			3.37114
$46$	2.62979	−	4.01051i	0.387742	−	0.591317i
$47$	4.68422			0.683264			0.341632	−	0.939834i	$-0.389020\pi$
$47$	4.68422			0.683264			0.341632	+	0.939834i	$0.389020\pi$
$48$	2.79956	−	1.79917i	0.404081	−	0.259687i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	1.18141	−	2.58693i	0.167076	−	0.365846i
$51$	8.00354	−	2.35005i	1.12072	−	0.329073i
$52$	0.992799	+	2.17393i	0.137676	+	0.301469i
$53$	9.27553	+	10.7045i	1.27409	+	1.47038i	0.812125	+	0.583484i	$0.198311\pi$
$53$	9.27553	+	10.7045i	1.27409	+	1.47038i	0.461968	+	0.886897i	$0.347144\pi$
$54$	−2.40330	−	16.7153i	−0.327048	−	2.27467i
$55$	−6.51304	−	1.91240i	−0.878218	−	0.257868i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	−18.4122	−	11.8328i	−2.43875	−	1.56729i
$58$	4.71515	+	3.03024i	0.619129	+	0.397890i
$59$	7.89747	−	9.11417i	1.02816	−	1.18656i	0.0459210	−	0.998945i	$-0.485378\pi$
$59$	7.89747	−	9.11417i	1.02816	−	1.18656i	0.982242	−	0.187618i	$-0.0600768\pi$
$60$	−8.94275	−	2.62583i	−1.15450	−	0.338993i
$61$	0.362182	+	2.51903i	0.0463727	+	0.322529i	0.999783	+	0.0208513i	$0.00663765\pi$
$61$	0.362182	+	2.51903i	0.0463727	+	0.322529i	−0.953410	+	0.301678i	$0.902453\pi$
$62$	3.17017	+	3.65858i	0.402612	+	0.464640i
$63$	−3.35428	−	7.34485i	−0.422599	−	0.925363i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	2.78053	−	6.08852i	0.344883	−	0.755188i
$66$	−1.14786	+	7.98352i	−0.141291	+	0.982704i
$67$	−3.50857	+	2.25482i	−0.428641	+	0.275471i	−0.737122	−	0.675760i	$-0.763816\pi$
$67$	−3.50857	+	2.25482i	−0.428641	+	0.275471i	0.308481	+	0.951230i	$0.400179\pi$
$68$	−2.50656			−0.303965
$69$	4.35546	+	15.3540i	0.524335	+	1.84840i
$70$	−2.80070			−0.334748
$71$	−6.22677	+	4.00170i	−0.738981	+	0.474914i	−0.855193	−	0.518310i	$-0.826561\pi$
$71$	−6.22677	+	4.00170i	−0.738981	+	0.474914i	0.116211	+	0.993224i	$0.462925\pi$
$72$	−1.14912	+	7.99234i	−0.135426	+	0.941906i
$73$	1.08217	−	2.36963i	0.126659	−	0.277345i	−0.835670	−	0.549232i	$-0.814920\pi$
$73$	1.08217	−	2.36963i	0.126659	−	0.277345i	0.962329	+	0.271887i	$0.0876477\pi$
$74$	−2.54083	+	0.746055i	−0.295365	+	0.0867271i
$75$	3.93154	+	8.60888i	0.453975	+	0.994067i
$76$	4.30690	+	4.97043i	0.494035	+	0.570147i
$77$	0.344926	+	2.39901i	0.0393079	+	0.273393i
$78$	−7.63104	−	2.24067i	−0.864045	−	0.253706i
$79$	5.38873	−	6.21893i	0.606280	−	0.699684i	−0.366761	−	0.930315i	$-0.619533\pi$
$79$	5.38873	−	6.21893i	0.606280	−	0.699684i	0.973041	+	0.230631i	$0.0740789\pi$
$80$	2.35610	+	1.51417i	0.263420	+	0.169290i
$81$	26.8985	+	17.2866i	2.98873	+	1.92074i
$82$	7.01262	−	8.09300i	0.774414	−	0.893722i
$83$	−16.2144	−	4.76098i	−1.77976	−	0.522586i	−0.784529	−	0.620092i	$-0.787095\pi$
$83$	−16.2144	−	4.76098i	−1.77976	−	0.522586i	−0.995235	+	0.0975066i	$0.968913\pi$
$84$	0.473601	+	3.29397i	0.0516741	+	0.359401i
$85$	4.59720	+	5.30545i	0.498637	+	0.575457i
$86$	1.57689	+	3.45290i	0.170040	+	0.372336i
$87$	−17.8967	+	5.25494i	−1.91873	+	0.563389i
$88$	1.00683	−	2.20466i	0.107329	−	0.235017i
$89$	0.504383	−	3.50806i	0.0534645	−	0.371854i	−0.945470	−	0.325708i	$-0.894397\pi$
$89$	0.504383	−	3.50806i	0.0534645	−	0.371854i	0.998935	−	0.0461452i	$-0.0146937\pi$
$90$	19.0244	−	12.2262i	2.00535	−	1.28876i
$91$	−2.38990			−0.250529
$92$	0.0440769	−	4.79563i	0.00459534	−	0.499979i
$93$	−16.1100			−1.67053
$94$	3.94062	−	2.53248i	0.406444	−	0.261206i
$95$	2.62140	−	18.2322i	0.268950	−	1.87059i
$96$	1.38243	−	3.02711i	0.141094	−	0.308953i
$97$	−8.20917	+	2.41043i	−0.833515	+	0.244742i	−0.670526	−	0.741886i	$-0.733932\pi$
$97$	−8.20917	+	2.41043i	−0.833515	+	0.244742i	−0.162989	+	0.986628i	$0.552113\pi$
$98$	0.415415	+	0.909632i	0.0419633	+	0.0918867i
$99$	−12.8157	−	14.7901i	−1.28802	−	1.48646i
$100$	−0.404733	−	2.81498i	−0.0404733	−	0.281498i
$101$	−4.91130	−	1.44209i	−0.488692	−	0.143493i	0.0280977	−	0.999605i	$-0.491055\pi$
$101$	−4.91130	−	1.44209i	−0.488692	−	0.143493i	−0.516790	+	0.856112i	$0.672873\pi$
$102$	5.46247	−	6.30403i	0.540866	−	0.624192i
$103$	−8.08945	−	5.19878i	−0.797078	−	0.512251i	0.0775834	−	0.996986i	$-0.475280\pi$
$103$	−8.08945	−	5.19878i	−0.797078	−	0.512251i	−0.874661	+	0.484735i	$0.838916\pi$
$104$	2.01051	+	1.29208i	0.197147	+	0.126698i
$105$	6.10349	−	7.04380i	0.595640	−	0.687405i
$106$	13.5904	+	3.99050i	1.32001	+	0.387591i
$107$	−0.492919	−	3.42833i	−0.0476523	−	0.331429i	−0.999677	−	0.0254083i	$-0.991911\pi$
$107$	−0.492919	−	3.42833i	−0.0476523	−	0.331429i	0.952025	−	0.306021i	$-0.0989977\pi$
$108$	−11.0588	−	12.7625i	−1.06413	−	1.22807i
$109$	−2.38747	−	5.22783i	−0.228678	−	0.500735i	0.760159	−	0.649737i	$-0.225121\pi$
$109$	−2.38747	−	5.22783i	−0.228678	−	0.500735i	−0.988837	+	0.149002i	$0.952394\pi$
$110$	−6.51304	+	1.91240i	−0.620994	+	0.182340i
$111$	3.66082	−	8.01608i	0.347470	−	0.760852i
$112$	0.142315	−	0.989821i	0.0134475	−	0.0935293i
$113$	−3.58932	+	2.30671i	−0.337655	+	0.216997i	−0.698469	−	0.715640i	$-0.746135\pi$
$113$	−3.58932	+	2.30671i	−0.337655	+	0.216997i	0.360815	+	0.932638i	$0.382499\pi$
$114$	−21.8866			−2.04987
$115$	−10.2314	+	8.70222i	−0.954083	+	0.811486i
$116$	5.60490			0.520402
$117$	16.2339	−	10.4329i	1.50082	−	0.964522i
$118$	1.71628	−	11.9370i	0.157997	−	1.09889i
$119$	1.04126	−	2.28005i	0.0954524	−	0.209012i
$120$	−8.94275	+	2.62583i	−0.816358	+	0.239704i
$121$	−2.12932	−	4.66257i	−0.193575	−	0.423870i
$122$	1.66658	+	1.92334i	0.150885	+	0.174131i
$123$	5.07159	+	35.2737i	0.457290	+	3.18052i
$124$	4.64490	+	1.36386i	0.417124	+	0.122479i
$125$	3.95439	−	4.56361i	0.353691	−	0.408182i
$126$	−6.79272	−	4.36542i	−0.605144	−	0.388902i
$127$	15.0594	+	9.67811i	1.33631	+	0.858793i	0.996652	−	0.0817561i	$-0.0260529\pi$
$127$	15.0594	+	9.67811i	1.33631	+	0.858793i	0.339656	+	0.940550i	$0.389689\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−12.1206	−	3.55892i	−1.06716	−	0.313345i
$130$	−0.952568	−	6.62526i	−0.0835458	−	0.581074i
$131$	−6.95672	−	8.02848i	−0.607811	−	0.701451i	0.365534	−	0.930798i	$-0.380887\pi$
$131$	−6.95672	−	8.02848i	−0.607811	−	0.701451i	−0.973345	+	0.229347i	$0.926341\pi$
$132$	3.35058	+	7.33675i	0.291631	+	0.638582i
$133$	−6.31041	+	1.85290i	−0.547182	+	0.160667i
$134$	−1.73255	+	3.79376i	−0.149670	+	0.327731i
$135$	−6.73092	+	46.8146i	−0.579306	+	4.02916i
$136$	−2.10865	+	1.35515i	−0.180815	+	0.116203i
$137$	−6.85681			−0.585817			−0.292908	−	0.956140i	$-0.594623\pi$
$137$	−6.85681			−0.585817			−0.292908	+	0.956140i	$0.594623\pi$
$138$	11.9650	+	10.5618i	1.01853	+	0.899083i
$139$	16.3847			1.38973			0.694867	−	0.719139i	$-0.255463\pi$
$139$	16.3847			1.38973			0.694867	+	0.719139i	$0.255463\pi$
$140$	−2.35610	+	1.51417i	−0.199127	+	0.127971i
$141$	−2.21845	+	15.4297i	−0.186827	+	1.29941i
$142$	−3.07481	+	6.73289i	−0.258032	+	0.565011i
$143$	−5.55771	+	1.63189i	−0.464759	+	0.136466i
$144$	3.35428	+	7.34485i	0.279523	+	0.612070i
$145$	−10.2798	−	11.8635i	−0.853689	−	0.985210i
$146$	−0.370737	−	2.57853i	−0.0306824	−	0.213401i
$147$	−3.19304	−	0.937561i	−0.263357	−	0.0773287i
$148$	−1.73413	+	2.00130i	−0.142545	+	0.164506i
$149$	3.84794	+	2.47292i	0.315236	+	0.202590i	0.688685	−	0.725061i	$-0.258188\pi$
$149$	3.84794	+	2.47292i	0.315236	+	0.202590i	−0.373449	+	0.927651i	$0.621825\pi$
$150$	7.96173	+	5.11670i	0.650073	+	0.417776i
$151$	8.47637	−	9.78225i	0.689797	−	0.796068i	−0.297539	−	0.954710i	$-0.596166\pi$
$151$	8.47637	−	9.78225i	0.689797	−	0.796068i	0.987336	+	0.158642i	$0.0507114\pi$
$152$	6.31041	+	1.85290i	0.511842	+	0.150290i
$153$	2.88035	+	20.0333i	0.232862	+	1.61959i
$154$	1.58717	+	1.83170i	0.127898	+	0.147602i
$155$	−5.63226	−	12.3329i	−0.452394	−	0.990605i
$156$	−7.63104	+	2.24067i	−0.610972	+	0.179398i
$157$	−2.32368	+	5.08814i	−0.185450	+	0.406078i	−0.979407	−	0.201895i	$-0.935290\pi$
$157$	−2.32368	+	5.08814i	−0.185450	+	0.406078i	0.793958	+	0.607973i	$0.208017\pi$
$158$	1.17108	−	8.14507i	0.0931664	−	0.647987i
$159$	−39.6533	+	25.4836i	−3.14471	+	2.02098i
$160$	2.80070			0.221415
$161$	4.34395	+	2.03227i	0.342351	+	0.160165i
$162$	31.9744			2.51214
$163$	5.00243	−	3.21487i	0.391820	−	0.251808i	−0.329866	−	0.944028i	$-0.607004\pi$
$163$	5.00243	−	3.21487i	0.391820	−	0.251808i	0.721687	+	0.692220i	$0.243367\pi$
$164$	1.52399	−	10.5996i	0.119003	−	0.827687i
$165$	9.38397	−	20.5480i	0.730541	−	1.59966i
$166$	−16.2144	+	4.76098i	−1.25848	+	0.369524i
$167$	9.69635	+	21.2321i	0.750326	+	1.64299i	0.765778	+	0.643105i	$0.222354\pi$
$167$	9.69635	+	21.2321i	0.750326	+	1.64299i	−0.0154518	+	0.999881i	$0.504919\pi$
$168$	2.17927	+	2.51501i	0.168134	+	0.194038i
$169$	1.03725	+	7.21421i	0.0797882	+	0.554939i
$170$	6.73576	+	1.97780i	0.516609	+	0.151690i
$171$	34.7762	−	40.1338i	2.65940	−	3.06911i
$172$	3.19334	+	2.05224i	0.243490	+	0.156482i
$173$	−1.98537	−	1.27592i	−0.150945	−	0.0970065i	0.462988	−	0.886364i	$-0.346777\pi$
$173$	−1.98537	−	1.27592i	−0.150945	−	0.0970065i	−0.613933	+	0.789358i	$0.710414\pi$
$174$	−12.2146	+	14.0964i	−0.925987	+	1.06865i
$175$	2.72873	+	0.801226i	0.206272	+	0.0605670i
$176$	−0.344926	−	2.39901i	−0.0259997	−	0.180832i
$177$	26.2815	+	30.3305i	1.97544	+	2.27978i
$178$	−1.47229	−	3.22386i	−0.110353	−	0.241638i
$179$	13.3295	−	3.91388i	0.996291	−	0.292537i	0.257358	−	0.966316i	$-0.417148\pi$
$179$	13.3295	−	3.91388i	0.996291	−	0.292537i	0.738933	+	0.673779i	$0.235330\pi$
$180$	9.39433	−	20.5707i	0.700212	−	1.53325i
$181$	−0.666970	+	4.63888i	−0.0495755	+	0.344805i	0.949904	+	0.312542i	$0.101181\pi$
$181$	−0.666970	+	4.63888i	−0.0495755	+	0.344805i	−0.999479	+	0.0322632i	$0.989729\pi$
$182$	−2.01051	+	1.29208i	−0.149029	+	0.0957750i
$183$	−8.46915			−0.626057
$184$	−2.55563	−	4.05817i	−0.188404	−	0.299172i
$185$	7.41652			0.545274
$186$	−13.5526	+	8.70975i	−0.993727	+	0.638630i
$187$	0.864576	−	6.01326i	0.0632241	−	0.439733i
$188$	1.94590	−	4.26092i	0.141919	−	0.310759i
$189$	16.2032	−	4.75768i	1.17861	−	0.346070i
$190$	−7.65182	−	16.7551i	−0.555121	−	1.21555i
$191$	−5.33339	−	6.15506i	−0.385911	−	0.445365i	0.529243	−	0.848471i	$-0.322476\pi$
$191$	−5.33339	−	6.15506i	−0.385911	−	0.445365i	−0.915153	+	0.403106i	$0.867931\pi$
$192$	−0.473601	−	3.29397i	−0.0341792	−	0.237722i
$193$	−1.63080	−	0.478847i	−0.117388	−	0.0344681i	0.222511	−	0.974930i	$-0.428575\pi$
$193$	−1.63080	−	0.478847i	−0.117388	−	0.0344681i	−0.339899	+	0.940462i	$0.610393\pi$
$194$	−5.60282	+	6.46600i	−0.402259	+	0.464232i
$195$	18.7385	+	12.0425i	1.34189	+	0.862383i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	2.48513	−	2.86799i	0.177058	−	0.204336i	−0.660283	−	0.751017i	$-0.729564\pi$
$197$	2.48513	−	2.86799i	0.177058	−	0.204336i	0.837341	+	0.546681i	$0.184109\pi$
$198$	−18.7773	−	5.51352i	−1.33445	−	0.391829i
$199$	3.12374	+	21.7261i	0.221436	+	1.54012i	0.732613	+	0.680645i	$0.238301\pi$
$199$	3.12374	+	21.7261i	0.221436	+	1.54012i	−0.511177	+	0.859475i	$0.670790\pi$
$200$	−1.86237	−	2.14930i	−0.131690	−	0.151978i
$201$	−5.76565	−	12.6250i	−0.406678	−	0.890500i
$202$	−4.91130	+	1.44209i	−0.345558	+	0.101465i
$203$	−2.32836	+	5.09840i	−0.163419	+	0.357838i
$204$	1.18711	−	8.25653i	0.0831143	−	0.578072i
$205$	−25.2305	+	16.2146i	−1.76217	+	1.13248i
$206$	−9.61595			−0.669975
$207$	−38.3789	+	5.15850i	−2.66752	+	0.358540i
$208$	2.38990			0.165710
$209$	−13.4097	+	8.61787i	−0.927566	+	0.596110i
$210$	1.32642	−	9.22542i	0.0915313	−	0.636614i
$211$	−1.67468	+	3.66703i	−0.115290	+	0.252449i	−0.958477	−	0.285172i	$-0.907949\pi$
$211$	−1.67468	+	3.66703i	−0.115290	+	0.252449i	0.843187	+	0.537621i	$0.180677\pi$
$212$	13.5904	−	3.99050i	0.933391	−	0.274068i
$213$	−10.2325	−	22.4060i	−0.701117	−	1.53523i
$214$	−2.26816	−	2.61760i	−0.155049	−	0.178936i
$215$	−1.51299	−	10.5231i	−0.103185	−	0.717667i
$216$	−16.2032	−	4.75768i	−1.10249	−	0.323719i
$217$	−3.17017	+	3.65858i	−0.215205	+	0.248360i
$218$	−4.83484	−	3.10716i	−0.327457	−	0.210444i
$219$	7.29297	+	4.68691i	0.492814	+	0.316712i
$220$	−4.44520	+	5.13003i	−0.299695	+	0.345867i
$221$	5.74776	+	1.68770i	0.386636	+	0.113527i
$222$	−1.25414	−	8.72274i	−0.0841724	−	0.585432i
$223$	−3.89712	−	4.49752i	−0.260971	−	0.301176i	0.610109	−	0.792317i	$-0.291125\pi$
$223$	−3.89712	−	4.49752i	−0.260971	−	0.301176i	−0.871080	+	0.491141i	$0.836580\pi$
$224$	−0.415415	−	0.909632i	−0.0277561	−	0.0607773i
$225$	−22.0332	+	6.46952i	−1.46888	+	0.431301i
$226$	−1.77242	+	3.88106i	−0.117900	+	0.258165i
$227$	1.83817	−	12.7847i	0.122003	−	0.848552i	−0.833278	−	0.552854i	$-0.813539\pi$
$227$	1.83817	−	12.7847i	0.122003	−	0.848552i	0.955281	−	0.295698i	$-0.0955523\pi$
$228$	−18.4122	+	11.8328i	−1.21938	+	0.783646i
$229$	12.5774			0.831139			0.415569	−	0.909562i	$-0.363582\pi$
$229$	12.5774			0.831139			0.415569	+	0.909562i	$0.363582\pi$
$230$	−3.90243	+	12.8523i	−0.257319	+	0.847455i
$231$	−8.06562			−0.530679
$232$	4.71515	−	3.03024i	0.309564	−	0.198945i
$233$	1.77601	−	12.3524i	0.116350	−	0.809232i	−0.845170	−	0.534498i	$-0.820501\pi$
$233$	1.77601	−	12.3524i	0.116350	−	0.809232i	0.961520	−	0.274735i	$-0.0885900\pi$
$234$	8.01638	−	17.5534i	0.524047	−	1.14750i
$235$	−12.5877	+	3.69608i	−0.821130	+	0.241106i
$236$	−5.00981	−	10.9700i	−0.326111	−	0.714083i
$237$	17.9328	+	20.6956i	1.16486	+	1.34432i
$238$	−0.356721	−	2.48105i	−0.0231228	−	0.160822i
$239$	0.770307	+	0.226183i	0.0498270	+	0.0146305i	0.306551	−	0.951854i	$-0.400825\pi$
$239$	0.770307	+	0.226183i	0.0498270	+	0.0146305i	−0.256724	+	0.966485i	$0.582643\pi$
$240$	−6.10349	+	7.04380i	−0.393979	+	0.454675i
$241$	11.9454	+	7.67683i	0.769470	+	0.494508i	0.865524	−	0.500868i	$-0.166986\pi$
$241$	11.9454	+	7.67683i	0.769470	+	0.494508i	−0.0960539	+	0.995376i	$0.530622\pi$
$242$	−4.31208	−	2.77120i	−0.277191	−	0.178140i
$243$	−36.5045	+	42.1285i	−2.34177	+	2.70254i
$244$	2.44185	+	0.716992i	0.156323	+	0.0459007i
$245$	−0.398581	−	2.77219i	−0.0254644	−	0.177109i
$246$	23.3369	+	26.9322i	1.48791	+	1.71713i
$247$	−6.52946	−	14.2975i	−0.415459	−	0.909729i
$248$	4.64490	−	1.36386i	0.294951	−	0.0866055i
$249$	23.3617	−	51.1550i	1.48049	−	3.24181i
$250$	0.859371	−	5.97706i	0.0543514	−	0.378022i
$251$	21.2732	−	13.6715i	1.34275	−	0.862935i	0.345603	−	0.938381i	$-0.387675\pi$
$251$	21.2732	−	13.6715i	1.34275	−	0.862935i	0.997150	+	0.0754464i	$0.0240382\pi$
$252$	−8.07452			−0.508647
$253$	11.4896	+	1.75988i	0.722343	+	0.110642i
$254$	17.9012			1.12322
$255$	−19.6532	+	12.6304i	−1.23073	+	0.790944i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	6.46479	−	14.1559i	0.403263	−	0.883022i	−0.593666	−	0.804711i	$-0.702320\pi$
$257$	6.46479	−	14.1559i	0.403263	−	0.883022i	0.996929	−	0.0783109i	$-0.0249527\pi$
$258$	−12.1206	+	3.55892i	−0.754594	+	0.221569i
$259$	−1.10006	−	2.40879i	−0.0683543	−	0.149675i
$260$	−4.38324	−	5.05852i	−0.271837	−	0.313716i
$261$	−6.44073	−	44.7963i	−0.398671	−	2.77282i
$262$	−10.1929	−	2.99290i	−0.629719	−	0.184902i
$263$	−4.23623	+	4.88887i	−0.261217	+	0.301461i	−0.871174	−	0.490974i	$-0.836641\pi$
$263$	−4.23623	+	4.88887i	−0.261217	+	0.301461i	0.609957	+	0.792434i	$0.291187\pi$
$264$	6.78523	+	4.36060i	0.417602	+	0.268377i
$265$	−33.3721	−	21.4469i	−2.05003	−	1.31748i
$266$	−4.30690	+	4.97043i	−0.264073	+	0.304756i
$267$	11.3166	+	3.32284i	0.692562	+	0.203355i
$268$	0.593545	+	4.12820i	0.0362566	+	0.252170i
$269$	10.0263	+	11.5710i	0.611316	+	0.705496i	0.974034	−	0.226403i	$-0.0726966\pi$
$269$	10.0263	+	11.5710i	0.611316	+	0.705496i	−0.362718	+	0.931899i	$0.618151\pi$
$270$	19.6475	+	43.0220i	1.19571	+	2.61823i
$271$	−2.29255	+	0.673153i	−0.139262	+	0.0408911i	−0.350621	−	0.936517i	$-0.614029\pi$
$271$	−2.29255	+	0.673153i	−0.139262	+	0.0408911i	0.211359	+	0.977409i	$0.432211\pi$
$272$	−1.04126	+	2.28005i	−0.0631358	+	0.138248i
$273$	1.13186	−	7.87224i	0.0685032	−	0.476450i
$274$	−5.76832	+	3.70707i	−0.348477	+	0.223952i
$275$	6.89276			0.415649
$276$	15.7758	+	2.41640i	0.949590	+	0.145450i
$277$	−31.0003			−1.86263			−0.931315	−	0.364215i	$-0.881337\pi$
$277$	−31.0003			−1.86263			−0.931315	+	0.364215i	$0.881337\pi$
$278$	13.7837	−	8.85825i	0.826691	−	0.531282i
$279$	5.56290	−	38.6908i	0.333042	−	2.31636i
$280$	−1.16345	+	2.54761i	−0.0695296	+	0.152249i
$281$	−13.0781	+	3.84008i	−0.780175	+	0.229080i	−0.647486	−	0.762078i	$-0.724179\pi$
$281$	−13.0781	+	3.84008i	−0.780175	+	0.229080i	−0.132689	+	0.991158i	$0.542361\pi$
$282$	6.47563	+	14.1797i	0.385618	+	0.844386i
$283$	−14.3580	−	16.5700i	−0.853492	−	0.984982i	0.146499	−	0.989211i	$-0.453199\pi$
$283$	−14.3580	−	16.5700i	−0.853492	−	0.984982i	−0.999991	+	0.00422863i	$0.998654\pi$
$284$	1.05338	+	7.32643i	0.0625067	+	0.434744i
$285$	58.8148	+	17.2696i	3.48389	+	1.02296i
$286$	−3.79318	+	4.37756i	−0.224295	+	0.258851i
$287$	9.00862	+	5.78949i	0.531762	+	0.341743i
$288$	6.79272	+	4.36542i	0.400265	+	0.257235i
$289$	7.01825	−	8.09949i	0.412838	−	0.476441i
$290$	−15.0618	−	4.42254i	−0.884459	−	0.259701i
$291$	−4.05201	−	28.1823i	−0.237533	−	1.65208i
$292$	−1.70594	−	1.96876i	−0.0998327	−	0.115213i
$293$	9.47619	+	20.7500i	0.553605	+	1.21223i	0.955078	+	0.296355i	$0.0957711\pi$
$293$	9.47619	+	20.7500i	0.553605	+	1.21223i	−0.401473	+	0.915871i	$0.631502\pi$
$294$	−3.19304	+	0.937561i	−0.186222	+	0.0546797i
$295$	−14.0310	+	30.7236i	−0.816915	+	1.78879i
$296$	−0.376863	+	2.62114i	−0.0219047	+	0.152351i
$297$	34.4318	−	22.1280i	1.99794	−	1.28400i
$298$	4.57406			0.264968
$299$	−3.33003	+	10.9671i	−0.192580	+	0.634245i
$300$	9.46413			0.546412
$301$	−3.19334	+	2.05224i	−0.184061	+	0.118289i
$302$	1.84209	−	12.8120i	0.106000	−	0.737249i
$303$	7.07618	−	15.4947i	0.406516	−	0.890146i
$304$	6.31041	−	1.85290i	0.361927	−	0.106271i
$305$	−2.96092	−	6.48350i	−0.169542	−	0.371244i
$306$	13.2539	+	15.2958i	0.757675	+	0.874404i
$307$	−0.980452	−	6.81919i	−0.0559574	−	0.389192i	−0.998483	−	0.0550585i	$-0.982465\pi$
$307$	−0.980452	−	6.81919i	−0.0559574	−	0.389192i	0.942526	−	0.334133i	$-0.108444\pi$
$308$	2.32550	+	0.682830i	0.132508	+	0.0389078i
$309$	20.9558	−	24.1843i	1.19213	−	1.37579i
$310$	−11.4059	−	7.33010i	−0.647809	−	0.416321i
$311$	−0.299362	−	0.192388i	−0.0169753	−	0.0109093i	0.532126	−	0.846665i	$-0.321393\pi$
$311$	−0.299362	−	0.192388i	−0.0169753	−	0.0109093i	−0.549101	+	0.835756i	$0.685030\pi$
$312$	−5.20824	+	6.01062i	−0.294858	+	0.340285i
$313$	−3.67851	−	1.08011i	−0.207922	−	0.0610513i	0.176113	−	0.984370i	$-0.443648\pi$
$313$	−3.67851	−	1.08011i	−0.207922	−	0.0610513i	−0.384035	+	0.923319i	$0.625466\pi$
$314$	0.796056	+	5.53669i	0.0449241	+	0.312454i
$315$	14.8092	+	17.0908i	0.834406	+	0.962956i
$316$	−3.41838	−	7.48520i	−0.192299	−	0.421076i
$317$	−22.2916	+	6.54540i	−1.25202	+	0.367626i	−0.839518	−	0.543331i	$-0.817163\pi$
$317$	−22.2916	+	6.54540i	−1.25202	+	0.367626i	−0.412501	+	0.910957i	$0.635345\pi$
$318$	−19.5810	+	42.8764i	−1.09805	+	2.40439i
$319$	−1.93328	+	13.4462i	−0.108243	+	0.752844i
$320$	2.35610	−	1.51417i	0.131710	−	0.0846449i
$321$	11.5263			0.643333
$322$	4.75309	−	0.638861i	0.264879	−	0.0356023i
$323$	16.4852			0.917260
$324$	26.8985	−	17.2866i	1.49436	−	0.960369i
$325$	−0.967270	+	6.72751i	−0.0536545	+	0.373175i
$326$	2.47022	−	5.40903i	0.136813	−	0.299579i
$327$	18.3510	−	5.38834i	1.01481	−	0.297976i
$328$	−4.44850	−	9.74086i	−0.245627	−	0.537849i
$329$	3.06751	+	3.54010i	0.169117	+	0.195172i
$330$	−3.21481	−	22.3595i	−0.176969	−	1.23085i
$331$	21.9911	+	6.45717i	1.20874	+	0.354918i	0.823189	−	0.567768i	$-0.192193\pi$
$331$	21.9911	+	6.45717i	1.20874	+	0.354918i	0.385552	+	0.922686i	$0.374011\pi$
$332$	−11.0665	+	12.7714i	−0.607351	+	0.700920i
$333$	17.9878	+	11.5600i	0.985724	+	0.633486i
$334$	19.6360	+	12.6193i	1.07443	+	0.690497i
$335$	7.64926	−	8.82772i	0.417924	−	0.482310i
$336$	3.19304	+	0.937561i	0.174195	+	0.0511481i
$337$	−0.206330	−	1.43505i	−0.0112395	−	0.0781724i	0.983430	−	0.181290i	$-0.0580273\pi$
$337$	−0.206330	−	1.43505i	−0.0112395	−	0.0781724i	−0.994669	+	0.103118i	$0.967118\pi$
$338$	4.77288	+	5.50820i	0.259611	+	0.299607i
$339$	−5.89834	−	12.9156i	−0.320354	−	0.701477i
$340$	6.73576	−	1.97780i	0.365298	−	0.107261i
$341$	−4.87407	+	10.6727i	−0.263946	+	0.577960i
$342$	7.55758	−	52.5641i	0.408667	−	2.84234i
$343$	−0.841254	+	0.540641i	−0.0454234	+	0.0291919i
$344$	3.79593			0.204663
$345$	−23.8192	−	37.8233i	−1.28238	−	2.03634i
$346$	−2.36002			−0.126875
$347$	27.8088	−	17.8717i	1.49286	−	0.959401i	0.497070	−	0.867711i	$-0.334409\pi$
$347$	27.8088	−	17.8717i	1.49286	−	0.959401i	0.995788	−	0.0916905i	$-0.0292270\pi$
$348$	−2.65449	+	18.4624i	−0.142296	+	0.989687i
$349$	−1.48259	+	3.24642i	−0.0793612	+	0.173777i	−0.945153	−	0.326627i	$-0.894088\pi$
$349$	−1.48259	+	3.24642i	−0.0793612	+	0.173777i	0.865792	+	0.500404i	$0.166815\pi$
$350$	2.72873	−	0.801226i	0.145857	−	0.0428273i
$351$	16.7656	+	36.7115i	0.894882	+	1.95952i
$352$	−1.58717	−	1.83170i	−0.0845966	−	0.0976297i
$353$	5.16924	+	35.9529i	0.275131	+	1.91358i	0.391143	+	0.920330i	$0.372080\pi$
$353$	5.16924	+	35.9529i	0.275131	+	1.91358i	−0.116012	+	0.993248i	$0.537011\pi$
$354$	38.5073	+	11.3068i	2.04664	+	0.600948i
$355$	13.5754	−	15.6668i	0.720505	−	0.831508i
$356$	−2.98152	−	1.91610i	−0.158020	−	0.101553i
$357$	7.01726	+	4.50972i	0.371393	+	0.238680i
$358$	9.09745	−	10.4990i	0.480815	−	0.554890i
$359$	4.70224	+	1.38070i	0.248175	+	0.0728707i	0.403454	−	0.915000i	$-0.367810\pi$
$359$	4.70224	+	1.38070i	0.248175	+	0.0728707i	−0.155279	+	0.987871i	$0.549628\pi$
$360$	−3.21835	−	22.3841i	−0.169622	−	1.17975i
$361$	−15.8833	−	18.3303i	−0.835965	−	0.964755i
$362$	1.94688	+	4.26307i	0.102326	+	0.224062i
$363$	16.3668	−	4.80573i	0.859034	−	0.252235i
$364$	−0.992799	+	2.17393i	−0.0520368	+	0.113945i
$365$	−1.03832	+	7.22169i	−0.0543483	+	0.378001i
$366$	−7.12470	+	4.57877i	−0.372414	+	0.239336i
$367$	−6.33730			−0.330804			−0.165402	−	0.986226i	$-0.552892\pi$
$367$	−6.33730			−0.330804			−0.165402	+	0.986226i	$0.552892\pi$
$368$	−4.34395	−	2.03227i	−0.226444	−	0.105939i
$369$	−86.4666			−4.50127
$370$	6.23918	−	4.00967i	0.324359	−	0.208453i
$371$	−2.01577	+	14.0200i	−0.104653	+	0.727880i
$372$	−6.69235	+	14.6542i	−0.346982	+	0.759785i
$373$	−4.96384	+	1.45752i	−0.257018	+	0.0754673i	−0.407703	−	0.913114i	$-0.633670\pi$
$373$	−4.96384	+	1.45752i	−0.257018	+	0.0754673i	0.150685	+	0.988582i	$0.451852\pi$
$374$	−2.52369	−	5.52610i	−0.130497	−	0.285748i
$375$	13.1596	+	15.1870i	0.679558	+	0.784251i
$376$	−0.666634	−	4.63654i	−0.0343790	−	0.239111i
$377$	−12.8525	−	3.77385i	−0.661940	−	0.194363i
$378$	11.0588	−	12.7625i	0.568802	−	0.656432i
$379$	−7.78275	−	5.00167i	−0.399773	−	0.256918i	0.325271	−	0.945621i	$-0.394544\pi$
$379$	−7.78275	−	5.00167i	−0.399773	−	0.256918i	−0.725044	+	0.688702i	$0.758181\pi$
$380$	−15.4956	−	9.95844i	−0.794909	−	0.510857i
$381$	−39.0116	+	45.0217i	−1.99862	+	2.30653i
$382$	−7.81441	−	2.29452i	−0.399820	−	0.117398i
$383$	−4.39565	−	30.5724i	−0.224607	−	1.56218i	−0.720289	−	0.693675i	$-0.755991\pi$
$383$	−4.39565	−	30.5724i	−0.224607	−	1.56218i	0.495681	−	0.868505i	$-0.334918\pi$
$384$	−2.17927	−	2.51501i	−0.111211	−	0.128344i
$385$	−2.81984	−	6.17458i	−0.143712	−	0.314686i
$386$	−1.63080	+	0.478847i	−0.0830057	+	0.0243727i
$387$	12.7326	−	27.8806i	0.647235	−	1.41725i
$388$	−1.21761	+	8.46866i	−0.0618147	+	0.429931i
$389$	13.4057	−	8.61531i	0.679695	−	0.436813i	−0.154714	−	0.987959i	$-0.549446\pi$
$389$	13.4057	−	8.61531i	0.679695	−	0.436813i	0.834409	+	0.551146i	$0.185809\pi$
$390$	22.2745			1.12791
$391$	−9.01216	−	7.95527i	−0.455764	−	0.402315i
$392$	1.00000			0.0505076
$393$	29.7403	−	19.1129i	1.50020	−	0.964119i
$394$	0.540069	−	3.75626i	0.0272083	−	0.189238i
$395$	−9.57385	+	20.9638i	−0.481713	+	1.05480i
$396$	−18.7773	+	5.51352i	−0.943597	+	0.277065i
$397$	6.83155	+	14.9590i	0.342866	+	0.750772i	0.999995	−	0.00300606i	$-0.000956860\pi$
$397$	6.83155	+	14.9590i	0.342866	+	0.750772i	−0.657130	+	0.753778i	$0.728230\pi$
$398$	14.3739	+	16.5883i	0.720496	+	0.831497i
$399$	−3.11479	−	21.6638i	−0.155934	−	1.08455i
$400$	−2.72873	−	0.801226i	−0.136436	−	0.0400613i
$401$	−4.61191	+	5.32242i	−0.230308	+	0.265789i	−0.859127	−	0.511762i	$-0.828993\pi$
$401$	−4.61191	+	5.32242i	−0.230308	+	0.265789i	0.628820	+	0.777551i	$0.283538\pi$
$402$	−11.6760	−	7.50369i	−0.582345	−	0.374250i
$403$	−9.73285	−	6.25493i	−0.484828	−	0.311580i
$404$	−3.35200	+	3.86841i	−0.166768	+	0.192461i
$405$	−85.9232	−	25.2293i	−4.26956	−	1.25366i
$406$	0.797661	+	5.54785i	0.0395873	+	0.275335i
$407$	−4.20298	−	4.85050i	−0.208334	−	0.240431i
$408$	−3.46516	−	7.58763i	−0.171551	−	0.375644i
$409$	0.191659	−	0.0562763i	0.00947694	−	0.00278268i	−0.276991	−	0.960873i	$-0.589337\pi$
$409$	0.191659	−	0.0562763i	0.00947694	−	0.00278268i	0.286468	+	0.958090i	$0.407519\pi$
$410$	−12.4589	+	27.2812i	−0.615302	+	1.34732i
$411$	3.24739	−	22.5861i	0.160182	−	1.11409i
$412$	−8.08945	+	5.19878i	−0.398539	+	0.256125i
$413$	12.0598			0.593423
$414$	−29.4975	+	25.0888i	−1.44972	+	1.23305i
$415$	47.3289			2.32328
$416$	2.01051	−	1.29208i	0.0985733	−	0.0633492i
$417$	−7.75982	+	53.9707i	−0.380000	+	2.64296i
$418$	−6.62176	+	14.4996i	−0.323881	+	0.709200i
$419$	−17.8542	+	5.24248i	−0.872237	+	0.256112i	−0.687066	−	0.726595i	$-0.741102\pi$
$419$	−17.8542	+	5.24248i	−0.872237	+	0.256112i	−0.185170	+	0.982706i	$0.559284\pi$
$420$	−3.87179	−	8.47803i	−0.188924	−	0.413686i
$421$	21.2509	+	24.5249i	1.03571	+	1.19527i	0.980444	+	0.196797i	$0.0630541\pi$
$421$	21.2509	+	24.5249i	1.03571	+	1.19527i	0.0552626	+	0.998472i	$0.482400\pi$
$422$	0.573719	+	3.99031i	0.0279282	+	0.194245i
$423$	−36.2908	−	10.6559i	−1.76452	−	0.518109i
$424$	9.27553	−	10.7045i	0.450460	−	0.519858i
$425$	−5.99685	−	3.85394i	−0.290890	−	0.186944i
$426$	−20.7217	−	13.3170i	−1.00397	−	0.645212i
$427$	−1.66658	+	1.92334i	−0.0806515	+	0.0930767i
$428$	−3.32328	−	0.975804i	−0.160637	−	0.0471673i
$429$	−2.74326	−	19.0798i	−0.132446	−	0.921181i
$430$	−6.96201	−	8.03458i	−0.335738	−	0.387462i
$431$	12.6292	+	27.6541i	0.608328	+	1.33205i	0.923712	+	0.383088i	$0.125139\pi$
$431$	12.6292	+	27.6541i	0.608328	+	1.33205i	−0.315384	+	0.948964i	$0.602133\pi$
$432$	−16.2032	+	4.75768i	−0.779575	+	0.228904i
$433$	−5.28841	+	11.5800i	−0.254145	+	0.556499i	−0.993102	−	0.117253i	$-0.962591\pi$
$433$	−5.28841	+	11.5800i	−0.254145	+	0.556499i	0.738957	+	0.673752i	$0.235318\pi$
$434$	−0.688945	+	4.79171i	−0.0330704	+	0.230010i
$435$	43.9465	−	28.2427i	2.10707	−	1.35413i
$436$	−5.74719			−0.275240
$437$	−0.289886	+	31.5400i	−0.0138671	+	1.50876i
$438$	8.66918			0.414229
$439$	4.79394	−	3.08088i	0.228802	−	0.147042i	−0.421217	−	0.906960i	$-0.638397\pi$
$439$	4.79394	−	3.08088i	0.228802	−	0.147042i	0.650020	+	0.759917i	$0.274761\pi$
$440$	−0.966034	+	6.71891i	−0.0460538	+	0.320311i
$441$	3.35428	−	7.34485i	0.159728	−	0.349755i
$442$	5.74776	−	1.68770i	0.273393	−	0.0802755i
$443$	−12.7805	−	27.9853i	−0.607218	−	1.32962i	−0.924461	−	0.381278i	$-0.875484\pi$
$443$	−12.7805	−	27.9853i	−0.607218	−	1.32962i	0.317242	−	0.948344i	$-0.397243\pi$
$444$	−5.77092	−	6.66000i	−0.273876	−	0.316069i
$445$	1.41263	+	9.82503i	0.0669649	+	0.465751i
$446$	−5.71001	−	1.67661i	−0.270377	−	0.0793898i
$447$	−9.96812	+	11.5038i	−0.471476	+	0.544112i
$448$	−0.841254	−	0.540641i	−0.0397455	−	0.0255429i
$449$	−21.3574	−	13.7256i	−1.00792	−	0.647750i	−0.0710651	−	0.997472i	$-0.522640\pi$
$449$	−21.3574	−	13.7256i	−1.00792	−	0.647750i	−0.936854	+	0.349722i	$0.886276\pi$
$450$	−15.0378	+	17.3545i	−0.708888	+	0.818101i
$451$	24.9028	+	7.31213i	1.17263	+	0.344315i
$452$	0.607205	+	4.22320i	0.0285605	+	0.198643i
$453$	28.2080	+	32.5538i	1.32533	+	1.52951i
$454$	−5.36558	−	11.7490i	−0.251819	−	0.551407i
$455$	6.42226	−	1.88574i	0.301080	−	0.0884051i
$456$	−9.09202	+	19.9088i	−0.425773	+	0.932313i
$457$	0.563105	−	3.91648i	0.0263409	−	0.183205i	−0.972403	−	0.233307i	$-0.925045\pi$
$457$	0.563105	−	3.91648i	0.0263409	−	0.183205i	0.998744	+	0.0501015i	$0.0159545\pi$
$458$	10.5808	−	6.79986i	0.494408	−	0.317737i
$459$	−42.3288			−1.97574
$460$	3.66554	+	12.9218i	0.170907	+	0.602484i
$461$	−25.0839			−1.16827			−0.584137	−	0.811655i	$-0.698567\pi$
$461$	−25.0839			−1.16827			−0.584137	+	0.811655i	$0.698567\pi$
$462$	−6.78523	+	4.36060i	−0.315678	+	0.202874i
$463$	−3.51988	+	24.4813i	−0.163583	+	1.13774i	0.728228	+	0.685335i	$0.240344\pi$
$463$	−3.51988	+	24.4813i	−0.163583	+	1.13774i	−0.891811	+	0.452408i	$0.850565\pi$
$464$	2.32836	−	5.09840i	0.108091	−	0.236687i
$465$	43.2918	−	12.7116i	2.00761	−	0.589487i
$466$	−5.18414	−	11.3517i	−0.240150	−	0.525856i
$467$	−6.82419	−	7.87553i	−0.315786	−	0.364436i	0.575561	−	0.817759i	$-0.304784\pi$
$467$	−6.82419	−	7.87553i	−0.315786	−	0.364436i	−0.891346	+	0.453323i	$0.850238\pi$
$468$	−2.74629	−	19.1009i	−0.126947	−	0.882938i
$469$	−4.00171	−	1.17501i	−0.184782	−	0.0542568i
$470$	−8.59119	+	9.91476i	−0.396282	+	0.457334i
$471$	−15.6597	−	10.0639i	−0.721560	−	0.463719i
$472$	−10.1453	−	6.52000i	−0.466976	−	0.300108i
$473$	−6.02480	+	6.95299i	−0.277021	+	0.319699i
$474$	26.2750	+	7.71503i	1.20685	+	0.354363i
$475$	2.66185	+	18.5136i	0.122134	+	0.849462i
$476$	−1.64145	−	1.89433i	−0.0752356	−	0.0868265i
$477$	−47.5104	−	104.033i	−2.17535	−	4.76336i
$478$	0.770307	−	0.226183i	0.0352330	−	0.0103454i
$479$	13.1442	−	28.7819i	0.600575	−	1.31508i	−0.328261	−	0.944587i	$-0.606463\pi$
$479$	13.1442	−	28.7819i	0.600575	−	1.31508i	0.928837	−	0.370490i	$-0.120810\pi$
$480$	−1.32642	+	9.22542i	−0.0605423	+	0.421081i
$481$	5.32402	−	3.42154i	0.242754	−	0.156009i
$482$	14.1995			0.646770
$483$	−8.75153	+	13.3463i	−0.398208	+	0.607279i
$484$	−5.12578			−0.232990
$485$	20.1582	−	12.9549i	0.915336	−	0.588250i
$486$	−7.93319	+	55.1766i	−0.359857	+	2.50286i
$487$	12.7768	−	27.9772i	0.578970	−	1.26777i	−0.362912	−	0.931823i	$-0.618217\pi$
$487$	12.7768	−	27.9772i	0.578970	−	1.26777i	0.941882	−	0.335944i	$-0.109055\pi$
$488$	2.44185	−	0.716992i	0.110537	−	0.0324567i
$489$	8.22051	+	18.0004i	0.371744	+	0.814006i
$490$	−1.83407	−	2.11663i	−0.0828548	−	0.0956195i
$491$	1.67747	+	11.6670i	0.0757030	+	0.526526i	0.992021	+	0.126074i	$0.0402377\pi$
$491$	1.67747	+	11.6670i	0.0757030	+	0.526526i	−0.916318	+	0.400452i	$0.868853\pi$
$492$	34.1929	+	10.0399i	1.54153	+	0.452635i
$493$	9.20015	−	10.6175i	0.414354	−	0.478190i
$494$	−13.2228	−	8.49775i	−0.594920	−	0.382332i
$495$	46.1090	+	29.6325i	2.07245	+	1.33188i
$496$	3.17017	−	3.65858i	0.142345	−	0.164275i
$497$	−7.10195	−	2.08532i	−0.318566	−	0.0935394i
$498$	−8.00336	−	55.6646i	−0.358639	−	2.49439i
$499$	27.3368	+	31.5484i	1.22376	+	1.41230i	0.881160	+	0.472819i	$0.156763\pi$
$499$	27.3368	+	31.5484i	1.22376	+	1.41230i	0.342604	+	0.939480i	$0.388691\pi$
$500$	−2.50849	−	5.49283i	−0.112183	−	0.245647i
$501$	−74.5299	+	21.8840i	−3.32975	+	0.977703i
$502$	10.5048	−	23.0023i	0.468852	−	1.02664i
$503$	0.853005	−	5.93278i	0.0380336	−	0.264530i	−0.961928	−	0.273303i	$-0.911884\pi$
$503$	0.853005	−	5.93278i	0.0380336	−	0.264530i	0.999962	+	0.00877377i	$0.00279281\pi$
$504$	−6.79272	+	4.36542i	−0.302572	+	0.194451i
$505$	14.3358			0.637934
$506$	10.6171	−	4.73122i	0.471987	−	0.210329i
$507$	−24.2546			−1.07719
$508$	15.0594	−	9.67811i	0.668154	−	0.429397i
$509$	3.26117	−	22.6820i	0.144549	−	1.00536i	−0.780403	−	0.625277i	$-0.784986\pi$
$509$	3.26117	−	22.6820i	0.144549	−	1.00536i	0.924952	−	0.380083i	$-0.124105\pi$
$510$	−9.70486	+	21.2507i	−0.429739	+	0.940996i
$511$	2.49952	−	0.733926i	0.110572	−	0.0324670i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	72.7315	+	83.9366i	3.21117	+	3.70589i
$514$	−2.21474	−	15.4039i	−0.0976880	−	0.679435i
$515$	25.8405	+	7.58745i	1.13867	+	0.334343i
$516$	−8.27237	+	9.54683i	−0.364171	+	0.420276i
$517$	9.55080	+	6.13793i	0.420044	+	0.269946i
$518$	−2.22772	−	1.43167i	−0.0978804	−	0.0629039i
$519$	5.14312	−	5.93547i	0.225758	−	0.260538i
$520$	−6.42226	−	1.88574i	−0.281635	−	0.0826954i
$521$	2.14759	+	14.9368i	0.0940878	+	0.654395i	0.981222	+	0.192883i	$0.0617838\pi$
$521$	2.14759	+	14.9368i	0.0940878	+	0.654395i	−0.887134	+	0.461512i	$0.847307\pi$
$522$	−29.6370	−	34.2029i	−1.29718	−	1.49702i
$523$	13.1533	+	28.8018i	0.575155	+	1.25941i	0.944007	+	0.329925i	$0.107023\pi$
$523$	13.1533	+	28.8018i	0.575155	+	1.25941i	−0.368853	+	0.929488i	$0.620249\pi$
$524$	−10.1929	+	2.99290i	−0.445278	+	0.130745i
$525$	−3.93154	+	8.60888i	−0.171587	+	0.375722i
$526$	−0.920621	+	6.40306i	−0.0401410	+	0.279187i
$527$	10.2080	−	6.56026i	0.444666	−	0.285769i
$528$	8.06562			0.351011
$529$	15.3787	−	17.1025i	0.668641	−	0.743585i
$530$	−39.6695			−1.72313
$531$	−81.9187	+	52.6459i	−3.55497	+	2.28464i
$532$	−0.935979	+	6.50987i	−0.0405798	+	0.282239i
$533$	−10.6315	+	23.2796i	−0.460499	+	1.00835i
$534$	11.3166	−	3.32284i	0.489716	−	0.143793i
$535$	4.02972	+	8.82385i	0.174220	+	0.381488i
$536$	2.73120	+	3.15197i	0.117970	+	0.136144i
$537$	6.57936	+	45.7604i	0.283920	+	1.97471i
$538$	14.6904	+	4.31350i	0.633350	+	0.185968i
$539$	−1.58717	+	1.83170i	−0.0683644	+	0.0788967i
$540$	39.7879	+	25.5702i	1.71220	+	1.10036i
$541$	−28.3278	−	18.2052i	−1.21791	−	0.782702i	−0.235944	−	0.971767i	$-0.575818\pi$
$541$	−28.3278	−	18.2052i	−1.21791	−	0.782702i	−0.981965	+	0.189064i	$0.939455\pi$
$542$	−1.56468	+	1.80574i	−0.0672088	+	0.0775631i
$543$	−14.9644	−	4.39396i	−0.642186	−	0.188563i
$544$	0.356721	+	2.48105i	0.0152943	+	0.106374i
$545$	10.5407	+	12.1647i	0.451516	+	0.521077i
$546$	−3.30388	−	7.23448i	−0.141393	−	0.309607i
$547$	−3.31116	+	0.972246i	−0.141575	+	0.0415702i	−0.351752	−	0.936093i	$-0.614414\pi$
$547$	−3.31116	+	0.972246i	−0.141575	+	0.0415702i	0.210177	+	0.977663i	$0.432596\pi$
$548$	−2.84842	+	6.23717i	−0.121679	+	0.266439i
$549$	2.92445	−	20.3400i	0.124813	−	0.868090i
$550$	5.79856	−	3.72651i	0.247252	−	0.158899i
$551$	−36.8624			−1.57039
$552$	14.5778	−	6.49622i	0.620474	−	0.276497i
$553$	8.22883			0.349925
$554$	−26.0791	+	16.7601i	−1.10800	+	0.712066i
$555$	−3.51247	+	24.4298i	−0.149096	+	1.03699i
$556$	6.80646	−	14.9041i	0.288658	−	0.632073i
$557$	−0.907330	+	0.266416i	−0.0384448	+	0.0112884i	−0.300898	−	0.953656i	$-0.597287\pi$
$557$	−0.907330	+	0.266416i	−0.0384448	+	0.0112884i	0.262454	+	0.964945i	$0.415468\pi$
$558$	−16.2380	−	35.5563i	−0.687410	−	1.50522i
$559$	−5.94083	−	6.85608i	−0.251270	−	0.289981i
$560$	0.398581	+	2.77219i	0.0168431	+	0.117147i
$561$	19.3980	+	5.69577i	0.818985	+	0.240476i
$562$	−8.92591	+	10.3010i	−0.376517	+	0.434523i
$563$	27.1638	+	17.4571i	1.14482	+	0.735729i	0.968600	−	0.248623i	$-0.0799780\pi$
$563$	27.1638	+	17.4571i	1.14482	+	0.735729i	0.176216	+	0.984352i	$0.443614\pi$
$564$	13.1138	+	8.42770i	0.552189	+	0.354870i
$565$	7.82529	−	9.03087i	0.329213	−	0.379932i
$566$	−21.0371	−	6.17704i	−0.884254	−	0.259641i
$567$	4.55043	+	31.6489i	0.191100	+	1.32913i
$568$	4.84713	+	5.59389i	0.203381	+	0.234714i
$569$	8.01056	+	17.5407i	0.335820	+	0.735344i	0.999924	−	0.0122962i	$-0.00391410\pi$
$569$	8.01056	+	17.5407i	0.335820	+	0.735344i	−0.664104	+	0.747640i	$0.731187\pi$
$570$	58.8148	−	17.2696i	2.46348	−	0.723344i
$571$	7.29393	−	15.9715i	0.305242	−	0.668386i	−0.693397	−	0.720556i	$-0.743887\pi$
$571$	7.29393	−	15.9715i	0.305242	−	0.668386i	0.998638	+	0.0521703i	$0.0166139\pi$
$572$	−0.824337	+	5.73339i	−0.0344672	+	0.239725i
$573$	22.8005	−	14.6530i	0.952504	−	0.612137i
$574$	10.7086			0.446967
$575$	7.47893	−	11.4056i	0.311893	−	0.475646i
$576$	8.07452			0.336438
$577$	11.0001	−	7.06933i	0.457940	−	0.294300i	−0.291260	−	0.956644i	$-0.594075\pi$
$577$	11.0001	−	7.06933i	0.457940	−	0.294300i	0.749200	+	0.662344i	$0.230438\pi$
$578$	1.52521	−	10.6081i	0.0634404	−	0.441238i
$579$	2.34966	−	5.14503i	0.0976484	−	0.213820i
$580$	−15.0618	+	4.42254i	−0.625407	+	0.183636i
$581$	−7.02008	−	15.3718i	−0.291242	−	0.637731i
$582$	−18.6453	−	21.5178i	−0.772872	−	0.891942i
$583$	4.88557	+	33.9799i	0.202340	+	1.40730i
$584$	−2.49952	−	0.733926i	−0.103431	−	0.0303701i
$585$	−35.3925	+	40.8452i	−1.46330	+	1.68874i
$586$	19.1902	+	12.3328i	0.792738	+	0.509462i
$587$	−20.5676	−	13.2180i	−0.848915	−	0.545565i	0.0423210	−	0.999104i	$-0.486525\pi$
$587$	−20.5676	−	13.2180i	−0.848915	−	0.545565i	−0.891236	+	0.453539i	$0.850161\pi$
$588$	−2.17927	+	2.51501i	−0.0898717	+	0.103717i
$589$	−30.5486	−	8.96989i	−1.25873	−	0.369598i
$590$	4.80680	+	33.4320i	0.197893	+	1.37637i
$591$	8.27010	+	9.54420i	0.340186	+	0.392596i
$592$	1.10006	+	2.40879i	0.0452121	+	0.0990007i
$593$	9.89773	−	2.90624i	0.406451	−	0.119345i	−0.0721151	−	0.997396i	$-0.522975\pi$
$593$	9.89773	−	2.90624i	0.406451	−	0.119345i	0.478566	+	0.878052i	$0.341157\pi$
$594$	17.0026	−	37.2305i	0.697625	−	1.52759i
$595$	−0.999068	+	6.94867i	−0.0409578	+	0.284868i
$596$	3.84794	−	2.47292i	0.157618	−	0.101295i
$597$	−73.0444			−2.98951
$598$	3.12788	+	11.0265i	0.127909	+	0.450906i
$599$	17.6636			0.721714			0.360857	−	0.932621i	$-0.382484\pi$
$599$	17.6636			0.721714			0.360857	+	0.932621i	$0.382484\pi$
$600$	7.96173	−	5.11670i	0.325036	−	0.208888i
$601$	0.164226	−	1.14222i	0.00669891	−	0.0465920i	−0.986198	−	0.165571i	$-0.947053\pi$
$601$	0.164226	−	1.14222i	0.00669891	−	0.0465920i	0.992897	+	0.118979i	$0.0379623\pi$
$602$	−1.57689	+	3.45290i	−0.0642692	+	0.140730i
$603$	32.3119	−	9.48763i	1.31584	−	0.386366i
$604$	−5.37704	−	11.7741i	−0.218788	−	0.479080i
$605$	9.40103	+	10.8494i	0.382206	+	0.441089i
$606$	−2.42419	−	16.8606i	−0.0984761	−	0.684916i
$607$	12.6775	+	3.72246i	0.514565	+	0.151090i	0.528698	−	0.848810i	$-0.322680\pi$
$607$	12.6775	+	3.72246i	0.514565	+	0.151090i	−0.0141324	+	0.999900i	$0.504499\pi$
$608$	4.30690	−	4.97043i	0.174668	−	0.201577i
$609$	−15.6913	−	10.0842i	−0.635842	−	0.408631i
$610$	−5.99613	−	3.85348i	−0.242776	−	0.156023i
$611$	−7.33104	+	8.46047i	−0.296582	+	0.342274i
$612$	19.4194	+	5.70206i	0.784984	+	0.230492i
$613$	−2.59518	−	18.0499i	−0.104818	−	0.729028i	−0.972668	−	0.232201i	$-0.925407\pi$
$613$	−2.59518	−	18.0499i	−0.104818	−	0.729028i	0.867850	−	0.496827i	$-0.165502\pi$
$614$	−4.51154	−	5.20660i	−0.182071	−	0.210121i
$615$	−41.4613	−	90.7876i	−1.67188	−	3.66091i
$616$	2.32550	−	0.682830i	0.0936972	−	0.0275120i
$617$	−15.0109	+	32.8692i	−0.604315	+	1.32326i	0.322080	+	0.946712i	$0.395618\pi$
$617$	−15.0109	+	32.8692i	−0.604315	+	1.32326i	−0.926395	+	0.376553i	$0.877109\pi$
$618$	4.55413	−	31.6746i	0.183194	−	1.27414i
$619$	−15.8562	+	10.1901i	−0.637312	+	0.409576i	−0.819011	−	0.573779i	$-0.805477\pi$
$619$	−15.8562	+	10.1901i	−0.637312	+	0.409576i	0.181698	+	0.983354i	$0.441841\pi$
$620$	−13.5582			−0.544509
$621$	0.744336	−	80.9848i	0.0298692	−	3.24981i
$622$	−0.355853			−0.0142684
$623$	2.98152	−	1.91610i	0.119452	−	0.0767671i
$624$	−1.13186	+	7.87224i	−0.0453106	+	0.315142i
$625$	−12.9326	+	28.3184i	−0.517303	+	1.13274i
$626$	−3.67851	+	1.08011i	−0.147023	+	0.0431698i
$627$	−22.0362	−	48.2524i	−0.880039	−	1.92702i
$628$	3.66305	+	4.22738i	0.146171	+	0.168691i
$629$	0.944630	+	6.57005i	0.0376649	+	0.261965i
$630$	21.6983	+	6.37119i	0.864480	+	0.253834i
$631$	4.45135	−	5.13713i	0.177205	−	0.204506i	−0.660198	−	0.751092i	$-0.729527\pi$
$631$	4.45135	−	5.13713i	0.177205	−	0.204506i	0.837403	+	0.546586i	$0.184073\pi$
$632$	−6.92253	−	4.44884i	−0.275363	−	0.176965i
$633$	−11.2860	−	7.25305i	−0.448577	−	0.288283i
$634$	−15.2142	+	17.5581i	−0.604231	+	0.697320i
$635$	−48.1050	−	14.1249i	−1.90899	−	0.560530i
$636$	6.70815	+	46.6562i	0.265995	+	1.85004i
$637$	−1.56505	−	1.80616i	−0.0620095	−	0.0715628i
$638$	5.64320	+	12.3569i	0.223417	+	0.489214i
$639$	57.3449	−	16.8380i	2.26853	−	0.666100i
$640$	1.16345	−	2.54761i	0.0459895	−	0.100703i
$641$	3.81176	−	26.5114i	0.150555	−	1.04714i	−0.764736	−	0.644344i	$-0.777131\pi$
$641$	3.81176	−	26.5114i	0.150555	−	1.04714i	0.915291	−	0.402792i	$-0.131960\pi$
$642$	9.69650	−	6.23156i	0.382690	−	0.245940i
$643$	15.6295			0.616367			0.308184	−	0.951327i	$-0.400279\pi$
$643$	15.6295			0.616367			0.308184	+	0.951327i	$0.400279\pi$
$644$	3.65316	−	3.10716i	0.143955	−	0.122439i
$645$	35.3792			1.39305
$646$	13.8682	−	8.91256i	0.545638	−	0.350660i
$647$	1.76065	−	12.2456i	0.0692184	−	0.481425i	−0.925497	−	0.378755i	$-0.876352\pi$
$647$	1.76065	−	12.2456i	0.0692184	−	0.481425i	0.994715	−	0.102670i	$-0.0327386\pi$
$648$	13.2826	−	29.0849i	0.521791	−	1.14256i
$649$	28.0450	−	8.23477i	1.10086	−	0.323243i
$650$	2.82345	+	6.18249i	0.110745	+	0.242497i
$651$	−10.5498	−	12.1752i	−0.413481	−	0.477182i
$652$	−0.846261	−	5.88587i	−0.0331421	−	0.230509i
$653$	−3.50121	−	1.02805i	−0.137013	−	0.0402307i	0.212507	−	0.977160i	$-0.431837\pi$
$653$	−3.50121	−	1.02805i	−0.137013	−	0.0402307i	−0.349520	+	0.936929i	$0.613655\pi$
$654$	12.5247	−	14.4543i	0.489754	−	0.565206i
$655$	25.0293	+	16.0854i	0.977976	+	0.628507i
$656$	−9.00862	−	5.78949i	−0.351728	−	0.226042i
$657$	−13.7747	+	15.8968i	−0.537401	+	0.620194i
$658$	4.49448	+	1.31970i	0.175213	+	0.0514472i
$659$	1.66938	+	11.6108i	0.0650296	+	0.452291i	0.996156	+	0.0875948i	$0.0279181\pi$
$659$	1.66938	+	11.6108i	0.0650296	+	0.452291i	−0.931127	+	0.364696i	$0.881173\pi$
$660$	−14.7929	−	17.0719i	−0.575813	−	0.664524i
$661$	−14.6495	−	32.0778i	−0.569798	−	1.24768i	−0.946905	−	0.321513i	$-0.895809\pi$
$661$	−14.6495	−	32.0778i	−0.569798	−	1.24768i	0.377107	−	0.926170i	$-0.376919\pi$
$662$	21.9911	−	6.45717i	0.854709	−	0.250965i
$663$	−8.28136	+	18.1337i	−0.321622	+	0.704253i
$664$	−2.40497	+	16.7269i	−0.0933310	+	0.649131i
$665$	15.4956	−	9.95844i	0.600895	−	0.386172i
$666$	21.3821			0.828540
$667$	20.1520	+	17.7887i	0.780290	+	0.688783i
$668$	23.3414			0.903104
$669$	16.6604	−	10.7070i	0.644127	−	0.413955i
$670$	1.66234	−	11.5619i	0.0642219	−	0.446673i
$671$	−2.56233	+	5.61071i	−0.0989176	+	0.216599i
$672$	3.19304	−	0.937561i	0.123174	−	0.0361672i
$673$	7.64239	+	16.7345i	0.294593	+	0.645068i	0.997827	−	0.0658904i	$-0.0209888\pi$
$673$	7.64239	+	16.7345i	0.294593	+	0.645068i	−0.703234	+	0.710958i	$0.748262\pi$
$674$	−0.949424	−	1.09569i	−0.0365705	−	0.0422046i
$675$	−6.83481	−	47.5371i	−0.263072	−	1.82970i
$676$	6.99316	+	2.05338i	0.268968	+	0.0789761i
$677$	−13.5695	+	15.6601i	−0.521519	+	0.601865i	−0.954011	−	0.299773i	$-0.903089\pi$
$677$	−13.5695	+	15.6601i	−0.521519	+	0.601865i	0.432492	+	0.901638i	$0.357635\pi$
$678$	−11.9447	−	7.67638i	−0.458733	−	0.294810i
$679$	−7.19755	−	4.62558i	−0.276217	−	0.177514i
$680$	4.59720	−	5.30545i	0.176295	−	0.203455i
$681$	41.2419	+	12.1097i	1.58039	+	0.464046i
$682$	1.66978	+	11.6136i	0.0639392	+	0.444707i
$683$	−25.7905	−	29.7639i	−0.986848	−	1.13888i	−0.990308	−	0.138889i	$-0.955647\pi$
$683$	−25.7905	−	29.7639i	−0.986848	−	1.13888i	0.00346034	−	0.999994i	$-0.498899\pi$
$684$	−22.0605	−	48.3057i	−0.843503	−	1.84701i
$685$	18.4260	−	5.41036i	0.704021	−	0.206719i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	−5.95667	+	41.4296i	−0.227261	+	1.58064i
$688$	3.19334	−	2.05224i	0.121745	−	0.0782408i
$689$	−33.8508			−1.28961
$690$	−40.4868	−	18.9413i	−1.54131	−	0.721084i
$691$	9.46095			0.359912			0.179956	−	0.983675i	$-0.442405\pi$
$691$	9.46095			0.359912			0.179956	+	0.983675i	$0.442405\pi$
$692$	−1.98537	+	1.27592i	−0.0754725	+	0.0485032i
$693$	2.78511	−	19.3709i	0.105798	−	0.735838i
$694$	13.7321	−	30.0692i	0.521265	−	1.14141i
$695$	−44.0299	+	12.9283i	−1.67015	+	0.490400i
$696$	7.74842	+	16.9667i	0.293703	+	0.643120i
$697$	−17.5775	−	20.2856i	−0.665797	−	0.768371i
$698$	0.507913	+	3.53261i	0.0192248	+	0.133711i
$699$	39.8473	+	11.7002i	1.50716	+	0.442543i
$700$	1.86237	−	2.14930i	0.0703912	−	0.0812357i
$701$	8.39684	+	5.39632i	0.317144	+	0.203816i	0.689522	−	0.724265i	$-0.257821\pi$
$701$	8.39684	+	5.39632i	0.317144	+	0.203816i	−0.372377	+	0.928081i	$0.621457\pi$
$702$	33.9519	+	21.8196i	1.28143	+	0.823526i
$703$	11.4051	−	13.1622i	0.430151	−	0.496420i
$704$	−2.32550	−	0.682830i	−0.0876457	−	0.0257351i
$705$	−6.21322	−	43.2139i	−0.234004	−	1.62753i
$706$	23.7862	+	27.4508i	0.895206	+	1.03312i
$707$	−2.12636	−	4.65608i	−0.0799700	−	0.175110i
$708$	38.5073	−	11.3068i	1.44719	−	0.424934i
$709$	−2.66252	+	5.83011i	−0.0999931	+	0.218954i	−0.953017	−	0.302918i	$-0.902039\pi$
$709$	−2.66252	+	5.83011i	−0.0999931	+	0.218954i	0.853023	+	0.521873i	$0.174766\pi$
$710$	2.95021	−	20.5191i	0.110719	−	0.770070i
$711$	−55.8961	+	35.9223i	−2.09627	+	1.34719i
$712$	−3.54413			−0.132822
$713$	12.3718	+	19.6456i	0.463327	+	0.735732i
$714$	8.34143			0.312170
$715$	13.6473	−	8.77061i	0.510382	−	0.328002i
$716$	1.97706	−	13.7508i	0.0738864	−	0.513891i
$717$	−1.10986	+	2.43025i	−0.0414484	+	0.0907593i
$718$	4.70224	−	1.38070i	0.175486	−	0.0515274i
$719$	−6.11427	−	13.3884i	−0.228024	−	0.499302i	0.760691	−	0.649114i	$-0.224860\pi$
$719$	−6.11427	−	13.3884i	−0.228024	−	0.499302i	−0.988714	+	0.149812i	$0.952133\pi$
$720$	−14.8092	−	17.0908i	−0.551908	−	0.636935i
$721$	−1.36849	−	9.51808i	−0.0509653	−	0.354472i
$722$	−23.2720	−	6.83329i	−0.866096	−	0.254309i
$723$	−30.9446	+	35.7120i	−1.15084	+	1.32814i
$724$	3.94261	+	2.53376i	0.146526	+	0.0941664i
$725$	13.4095	+	8.61778i	0.498017	+	0.320056i
$726$	11.1705	−	12.8914i	0.414575	−	0.478445i
$727$	−5.09809	−	1.49693i	−0.189078	−	0.0555182i	0.185823	−	0.982583i	$-0.440505\pi$
$727$	−5.09809	−	1.49693i	−0.189078	−	0.0555182i	−0.374901	+	0.927065i	$0.622323\pi$
$728$	0.340118	+	2.36557i	0.0126056	+	0.0876739i
$729$	−58.6650	−	67.7030i	−2.17278	−	2.50752i
$730$	3.03085	+	6.63663i	0.112177	+	0.245633i
$731$	9.12932	−	2.68061i	0.337660	−	0.0991460i
$732$	−3.51821	+	7.70381i	−0.130037	+	0.284741i
$733$	−6.22433	+	43.2912i	−0.229901	+	1.59900i	0.468615	+	0.883402i	$0.344753\pi$
$733$	−6.22433	+	43.2912i	−0.229901	+	1.59900i	−0.698516	+	0.715594i	$0.746156\pi$
$734$	−5.33127	+	3.42620i	−0.196781	+	0.126463i
$735$	9.32029			0.343784
$736$	−4.75309	+	0.638861i	−0.175201	+	0.0235487i
$737$	−10.1083			−0.372345
$738$	−72.7403	+	46.7474i	−2.67761	+	1.72079i
$739$	−4.33325	+	30.1384i	−0.159401	+	1.10866i	0.740339	+	0.672233i	$0.234665\pi$
$739$	−4.33325	+	30.1384i	−0.159401	+	1.10866i	−0.899740	+	0.436425i	$0.856244\pi$
$740$	3.08093	−	6.74631i	0.113257	−	0.247999i
$741$	50.1879	−	14.7365i	1.84370	−	0.541359i
$742$	5.88399	+	12.8841i	0.216008	+	0.472992i
$743$	8.93234	+	10.3085i	0.327696	+	0.378181i	0.895560	−	0.444941i	$-0.146775\pi$
$743$	8.93234	+	10.3085i	0.327696	+	0.378181i	−0.567864	+	0.823123i	$0.692230\pi$
$744$	2.29270	+	15.9461i	0.0840544	+	0.584611i
$745$	−12.2917	−	3.60916i	−0.450331	−	0.132229i
$746$	−3.38786	+	3.90980i	−0.124038	+	0.143148i
$747$	114.790	+	73.7709i	4.19994	+	2.69914i
$748$	−5.11070	−	3.28445i	−0.186866	−	0.120091i
$749$	2.26816	−	2.61760i	0.0828769	−	0.0956451i
$750$	19.2812	+	5.66148i	0.704051	+	0.206728i
$751$	−3.54246	−	24.6384i	−0.129266	−	0.899067i	−0.946487	−	0.322742i	$-0.895395\pi$
$751$	−3.54246	−	24.6384i	−0.129266	−	0.899067i	0.817221	−	0.576325i	$-0.195514\pi$
$752$	−3.06751	−	3.54010i	−0.111861	−	0.129094i
$753$	34.9583	+	76.5481i	1.27395	+	2.78957i
$754$	−12.8525	+	3.77385i	−0.468062	+	0.137435i
$755$	−15.0595	+	32.9756i	−0.548070	+	1.20011i
$756$	2.40330	−	16.7153i	0.0874072	−	0.607930i
$757$	15.6588	−	10.0633i	0.569130	−	0.365758i	−0.224206	−	0.974542i	$-0.571979\pi$
$757$	15.6588	−	10.0633i	0.569130	−	0.365758i	0.793336	+	0.608784i	$0.208342\pi$
$758$	−9.25137			−0.336025
$759$	−11.2384	+	37.0128i	−0.407930	+	1.34348i
$760$	−18.4197			−0.668153
$761$	−13.9980	+	8.99597i	−0.507427	+	0.326104i	−0.769181	−	0.639031i	$-0.779336\pi$
$761$	−13.9980	+	8.99597i	−0.507427	+	0.326104i	0.261754	+	0.965135i	$0.415699\pi$
$762$	−8.47802	+	58.9659i	−0.307126	+	2.13611i
$763$	2.38747	−	5.22783i	0.0864322	−	0.189260i
$764$	−7.81441	+	2.29452i	−0.282716	+	0.0830128i
$765$	−23.5474	−	51.5617i	−0.851360	−	1.86422i
$766$	−20.2266	−	23.3427i	−0.730816	−	0.843406i
$767$	4.10174	+	28.5282i	0.148105	+	1.03010i
$768$	−3.19304	−	0.937561i	−0.115219	−	0.0338313i
$769$	18.2848	−	21.1018i	0.659367	−	0.760950i	−0.323307	−	0.946294i	$-0.604795\pi$
$769$	18.2848	−	21.1018i	0.659367	−	0.760950i	0.982674	+	0.185344i	$0.0593400\pi$
$770$	−5.71043	−	3.66987i	−0.205790	−	0.132253i
$771$	43.5674	+	27.9991i	1.56904	+	1.00836i
$772$	−1.11303	+	1.28451i	−0.0400590	+	0.0462305i
$773$	7.34432	+	2.15649i	0.264157	+	0.0775634i	0.411129	−	0.911577i	$-0.365135\pi$
$773$	7.34432	+	2.15649i	0.264157	+	0.0775634i	−0.146972	+	0.989141i	$0.546953\pi$
$774$	−4.36200	−	30.3384i	−0.156789	−	1.09049i
$775$	9.01574	+	10.4047i	0.323855	+	0.373748i
$776$	3.55418	+	7.78258i	0.127588	+	0.279378i
$777$	8.45547	−	2.48275i	0.303338	−	0.0890682i
$778$	6.61979	−	14.4953i	0.237331	−	0.519682i
$779$	−10.0230	+	69.7114i	−0.359111	+	2.49767i
$780$	18.7385	−	12.0425i	0.670947	−	0.431191i
$781$	−17.9395			−0.641927
$782$	−11.8825	−	1.82006i	−0.424916	−	0.0650851i
$783$	94.6512			3.38256
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	2.22952	−	15.5066i	0.0795748	−	0.553455i
$786$	14.6859	−	32.1576i	0.523828	−	1.14702i
$787$	−2.50303	+	0.734956i	−0.0892234	+	0.0261984i	−0.326040	−	0.945356i	$-0.605714\pi$
$787$	−2.50303	+	0.734956i	−0.0892234	+	0.0261984i	0.236816	+	0.971554i	$0.423896\pi$
$788$	−1.57645	−	3.45195i	−0.0561589	−	0.122971i
$789$	−14.0975	−	16.2694i	−0.501884	−	0.579205i
$790$	3.27986	+	22.8119i	0.116692	+	0.811611i
$791$	−4.09380	−	1.20205i	−0.145559	−	0.0427399i
$792$	−12.8157	+	14.7901i	−0.455385	+	0.525542i
$793$	−5.11662	−	3.28825i	−0.181697	−	0.116769i
$794$	13.8345	+	8.89091i	0.490969	+	0.315527i
$795$	86.4506	−	99.7693i	3.06609	−	3.53845i
$796$	21.0604	+	6.18389i	0.746465	+	0.219182i
$797$	−6.08892	−	42.3494i	−0.215681	−	1.50009i	−0.753733	−	0.657181i	$-0.771749\pi$
$797$	−6.08892	−	42.3494i	−0.215681	−	1.50009i	0.538052	−	0.842912i	$-0.319160\pi$
$798$	−14.3327	−	16.5408i	−0.507371	−	0.585538i
$799$	−4.87750	−	10.6802i	−0.172554	−	0.377840i
$800$	−2.72873	+	0.801226i	−0.0964750	+	0.0283276i
$801$	−11.8880	+	26.0311i	−0.420042	+	0.919764i
$802$	−1.00226	+	6.97089i	−0.0353911	+	0.246151i
$803$	5.31150	−	3.41350i	0.187439	−	0.120460i
$804$	−13.8793			−0.489484
$805$	−13.2768	−	2.03364i	−0.467947	−	0.0716763i
$806$	−11.5695			−0.407517
$807$	−42.8630	+	27.5464i	−1.50885	+	0.969678i
$808$	−0.728458	+	5.06654i	−0.0256271	+	0.178240i
$809$	2.95511	−	6.47079i	0.103896	−	0.227501i	−0.850544	−	0.525905i	$-0.823727\pi$
$809$	2.95511	−	6.47079i	0.103896	−	0.227501i	0.954440	+	0.298404i	$0.0964541\pi$
$810$	−85.9232	+	25.2293i	−3.01903	+	0.886468i
$811$	−17.1789	−	37.6166i	−0.603233	−	1.32090i	−0.927107	−	0.374796i	$-0.877713\pi$
$811$	−17.1789	−	37.6166i	−0.603233	−	1.32090i	0.323874	−	0.946100i	$-0.395014\pi$
$812$	3.67043	+	4.23590i	0.128807	+	0.148651i
$813$	−1.13159	−	7.87039i	−0.0396866	−	0.276027i
$814$	−6.15816	−	1.80820i	−0.215843	−	0.0633773i
$815$	−10.9061	+	12.5863i	−0.382024	+	0.440879i
$816$	−7.01726	−	4.50972i	−0.245653	−	0.157872i
$817$	−21.0020	−	13.4972i	−0.734768	−	0.472207i
$818$	0.130809	−	0.150961i	0.00457362	−	0.00527824i
$819$	18.5156	+	5.43667i	0.646988	+	0.189973i
$820$	4.26823	+	29.6862i	0.149053	+	1.03669i
$821$	−11.1622	−	12.8819i	−0.389564	−	0.449581i	0.526763	−	0.850012i	$-0.323406\pi$
$821$	−11.1622	−	12.8819i	−0.389564	−	0.449581i	−0.916327	+	0.400432i	$0.868860\pi$
$822$	−9.47909	−	20.7563i	−0.330621	−	0.723960i
$823$	−7.32675	+	2.15133i	−0.255394	+	0.0749905i	−0.406923	−	0.913462i	$-0.633398\pi$
$823$	−7.32675	+	2.15133i	−0.255394	+	0.0749905i	0.151529	+	0.988453i	$0.451580\pi$
$824$	−3.99461	+	8.74698i	−0.139159	+	0.304715i
$825$	−3.26442	+	22.7045i	−0.113653	+	0.790471i
$826$	10.1453	−	6.52000i	0.353001	−	0.226860i
$827$	−45.0115			−1.56520			−0.782601	−	0.622523i	$-0.786108\pi$
$827$	−45.0115			−1.56520			−0.782601	+	0.622523i	$0.786108\pi$
$828$	−11.2508	+	37.0536i	−0.390994	+	1.28770i
$829$	41.2142			1.43143			0.715714	−	0.698394i	$-0.246102\pi$
$829$	41.2142			1.43143			0.715714	+	0.698394i	$0.246102\pi$
$830$	39.8156	−	25.5879i	1.38202	−	0.888170i
$831$	14.6818	−	102.114i	0.509306	−	3.54230i
$832$	0.992799	−	2.17393i	0.0344191	−	0.0753673i
$833$	2.40503	−	0.706179i	0.0833292	−	0.0244677i
$834$	22.6508	+	49.5983i	0.784333	+	1.71745i
$835$	−42.8097	−	49.4050i	−1.48149	−	1.70973i
$836$	2.26851	+	15.7779i	0.0784582	+	0.545688i
$837$	78.4393	+	23.0319i	2.71126	+	0.796097i
$838$	−12.1856	+	14.0630i	−0.420946	+	0.485798i
$839$	−3.39211	−	2.17998i	−0.117109	−	0.0752612i	0.480775	−	0.876844i	$-0.340355\pi$
$839$	−3.39211	−	2.17998i	−0.117109	−	0.0752612i	−0.597884	+	0.801583i	$0.703992\pi$
$840$	−7.84072	−	5.03893i	−0.270531	−	0.173860i
$841$	−1.58146	+	1.82510i	−0.0545331	+	0.0629345i
$842$	31.1366	+	9.14252i	1.07304	+	0.315072i
$843$	−6.45530	−	44.8976i	−0.222332	−	1.54635i
$844$	2.63997	+	3.04668i	0.0908714	+	0.104871i
$845$	−8.47970	−	18.5680i	−0.291711	−	0.638757i
$846$	−36.2908	+	10.6559i	−1.24770	+	0.366359i
$847$	2.12932	−	4.66257i	0.0731644	−	0.160208i
$848$	2.01577	−	14.0200i	0.0692217	−	0.481447i
$849$	61.3809	−	39.4471i	2.10659	−	1.35382i
$850$	−7.12847			−0.244504
$851$	−12.5866	+	1.69176i	−0.431464	+	0.0579929i
$852$	−24.6319			−0.843876
$853$	0.606069	−	0.389497i	0.0207514	−	0.0133361i	−0.530224	−	0.847858i	$-0.677892\pi$
$853$	0.606069	−	0.389497i	0.0207514	−	0.0133361i	0.550975	+	0.834521i	$0.314256\pi$
$854$	−0.362182	+	2.51903i	−0.0123936	+	0.0861996i
$855$	−61.7848	+	135.290i	−2.11300	+	4.62681i
$856$	−3.32328	+	0.975804i	−0.113587	+	0.0333523i
$857$	−14.3481	−	31.4180i	−0.490123	−	1.07322i	−0.979555	−	0.201177i	$-0.935523\pi$
$857$	−14.3481	−	31.4180i	−0.490123	−	1.07322i	0.489432	−	0.872041i	$-0.337204\pi$
$858$	−12.6231	−	14.5678i	−0.430945	−	0.497338i
$859$	5.80418	+	40.3690i	0.198036	+	1.37737i	0.809974	+	0.586466i	$0.199481\pi$
$859$	5.80418	+	40.3690i	0.198036	+	1.37737i	−0.611938	+	0.790906i	$0.709610\pi$
$860$	−10.2006	−	2.99518i	−0.347839	−	0.102135i
$861$	−23.3369	+	26.9322i	−0.795319	+	0.917847i
$862$	25.5753	+	16.4363i	0.871098	+	0.559821i
$863$	34.5508	+	22.2045i	1.17612	+	0.755849i	0.974670	−	0.223649i	$-0.0717969\pi$
$863$	34.5508	+	22.2045i	1.17612	+	0.755849i	0.201454	+	0.979498i	$0.435433\pi$
$864$	−11.0588	+	12.7625i	−0.376227	+	0.434189i
$865$	6.34196	+	1.86217i	0.215633	+	0.0633156i
$866$	1.81173	+	12.6008i	0.0615650	+	0.428194i
$867$	23.3556	+	26.9538i	0.793198	+	0.915399i
$868$	2.01102	+	4.40352i	0.0682585	+	0.149465i
$869$	19.1362	−	5.61889i	0.649150	−	0.190608i
$870$	21.7010	−	47.5186i	0.735733	−	1.61103i
$871$	1.41851	−	9.86597i	0.0480645	−	0.334296i
$872$	−4.83484	+	3.10716i	−0.163728	+	0.105222i
$873$	69.0835			2.33812
$874$	16.8079	+	26.6898i	0.568537	+	0.902797i
$875$	6.03852			0.204139
$876$	7.29297	−	4.68691i	0.246407	−	0.158356i
$877$	−0.976555	+	6.79209i	−0.0329759	+	0.229353i	−0.999644	−	0.0266802i	$-0.991506\pi$
$877$	−0.976555	+	6.79209i	−0.0329759	+	0.229353i	0.966668	+	0.256033i	$0.0824155\pi$
$878$	2.36727	−	5.18360i	0.0798915	−	0.174938i
$879$	−72.8377	+	21.3871i	−2.45675	+	0.721368i
$880$	2.81984	+	6.17458i	0.0950567	+	0.208145i
$881$	−35.6230	−	41.1112i	−1.20017	−	1.38507i	−0.902661	−	0.430352i	$-0.858390\pi$
$881$	−35.6230	−	41.1112i	−1.20017	−	1.38507i	−0.297509	−	0.954719i	$-0.596156\pi$
$882$	−1.14912	−	7.99234i	−0.0386930	−	0.269116i
$883$	−52.5289	−	15.4239i	−1.76774	−	0.519055i	−0.774238	−	0.632894i	$-0.781867\pi$
$883$	−52.5289	−	15.4239i	−1.76774	−	0.519055i	−0.993499	+	0.113839i	$0.963685\pi$
$884$	3.92289	−	4.52726i	0.131941	−	0.152268i
$885$	−94.5573	−	60.7683i	−3.17851	−	2.04270i
$886$	−25.8816	−	16.6331i	−0.869510	−	0.558800i
$887$	−3.68191	+	4.24915i	−0.123626	+	0.142672i	−0.814188	−	0.580601i	$-0.802818\pi$
$887$	−3.68191	+	4.24915i	−0.123626	+	0.142672i	0.690562	+	0.723273i	$0.257363\pi$
$888$	−8.45547	−	2.48275i	−0.283747	−	0.0833157i
$889$	2.54760	+	17.7190i	0.0854439	+	0.594275i
$890$	6.50019	+	7.50162i	0.217887	+	0.251455i
$891$	32.1928	+	70.4925i	1.07850	+	2.36159i
$892$	−5.71001	+	1.67661i	−0.191185	+	0.0561371i
$893$	−12.7978	+	28.0233i	−0.428262	+	0.937763i
$894$	−2.16628	+	15.0668i	−0.0724512	+	0.503909i
$895$	−32.7314	+	21.0352i	−1.09409	+	0.703129i
$896$	−1.00000			−0.0334077
$897$	−34.5483	−	16.1630i	−1.15353	−	0.539668i
$898$	−25.3876			−0.847195
$899$	−22.8260	+	14.6694i	−0.761289	+	0.489251i
$900$	−3.26802	+	22.7296i	−0.108934	+	0.757654i
$901$	14.7486	−	32.2949i	0.491346	−	1.07590i
$902$	24.9028	−	7.31213i	0.829173	−	0.243467i
$903$	−5.24763	−	11.4907i	−0.174630	−	0.382387i
$904$	2.79405	+	3.22450i	0.0929287	+	0.107245i
$905$	−1.86798	−	12.9921i	−0.0620939	−	0.431873i
$906$	41.3300	+	12.1356i	1.37310	+	0.403177i
$907$	25.8584	−	29.8422i	0.858615	−	0.990895i	−0.141384	−	0.989955i	$-0.545155\pi$
$907$	25.8584	−	29.8422i	0.858615	−	0.990895i	1.00000		0.000939896i	$-0.000299178\pi$
$908$	−10.8658	−	6.98302i	−0.360594	−	0.231740i
$909$	34.7695	+	22.3450i	1.15323	+	0.741137i
$910$	4.38324	−	5.05852i	0.145303	−	0.167688i
$911$	−0.385140	−	0.113087i	−0.0127603	−	0.00374675i	0.275346	−	0.961345i	$-0.411208\pi$
$911$	−0.385140	−	0.113087i	−0.0127603	−	0.00374675i	−0.288106	+	0.957598i	$0.593026\pi$
$912$	3.11479	+	21.6638i	0.103141	+	0.717361i
$913$	−26.8215	−	30.9537i	−0.887664	−	1.02442i
$914$	−1.64369	−	3.59919i	−0.0543686	−	0.119051i
$915$	22.7587	−	6.68257i	0.752381	−	0.220919i
$916$	5.22484	−	11.4408i	0.172634	−	0.378015i
$917$	1.51184	−	10.5151i	0.0499253	−	0.347238i
$918$	−35.6092	+	22.8847i	−1.17528	+	0.755307i
$919$	23.5549			0.777005			0.388502	−	0.921448i	$-0.372993\pi$
$919$	23.5549			0.777005			0.388502	+	0.921448i	$0.372993\pi$
$920$	10.0697	+	8.88881i	0.331989	+	0.293055i
$921$	22.9265			0.755455
$922$	−21.1019	+	13.5614i	−0.694955	+	0.446621i
$923$	2.51747	−	17.5094i	0.0828637	−	0.576330i
$924$	−3.35058	+	7.33675i	−0.110226	+	0.241361i
$925$	−7.22593	+	2.12172i	−0.237587	+	0.0697618i
$926$	10.2745	+	22.4980i	0.337640	+	0.739329i
$927$	50.8462	+	58.6796i	1.67001	+	1.92729i
$928$	−0.797661	−	5.54785i	−0.0261845	−	0.182117i
$929$	−2.71314	−	0.796649i	−0.0890151	−	0.0261372i	0.236922	−	0.971529i	$-0.423861\pi$
$929$	−2.71314	−	0.796649i	−0.0890151	−	0.0261372i	−0.325937	+	0.945392i	$0.605680\pi$
$930$	29.5469	−	34.0990i	0.968882	−	1.11815i
$931$	−5.53277	−	3.55570i	−0.181329	−	0.116533i
$932$	−10.4984	−	6.74688i	−0.343885	−	0.221001i
$933$	0.775500	−	0.894974i	0.0253887	−	0.0293001i
$934$	−9.99871	−	2.93589i	−0.327168	−	0.0960651i
$935$	2.42142	+	16.8413i	0.0791889	+	0.550771i
$936$	−12.6370	−	14.5839i	−0.413054	−	0.476690i
$937$	6.64289	+	14.5459i	0.217014	+	0.475194i	0.986560	−	0.163397i	$-0.0522450\pi$
$937$	6.64289	+	14.5459i	0.217014	+	0.475194i	−0.769547	+	0.638591i	$0.779518\pi$
$938$	−4.00171	+	1.17501i	−0.130660	+	0.0383654i
$939$	5.29999	−	11.6054i	0.172959	−	0.378726i
$940$	−1.86704	+	12.9856i	−0.0608962	+	0.423543i
$941$	31.7621	−	20.4122i	1.03541	−	0.665420i	0.0915653	−	0.995799i	$-0.470813\pi$
$941$	31.7621	−	20.4122i	1.03541	−	0.665420i	0.943848	+	0.330379i	$0.107177\pi$
$942$	−18.6147			−0.606500
$943$	39.1201	−	33.2732i	1.27393	−	1.08352i
$944$	−12.0598			−0.392512
$945$	−39.7879	+	25.5702i	−1.29430	+	0.831797i
$946$	−1.30932	+	9.10649i	−0.0425695	+	0.296077i
$947$	8.85053	−	19.3800i	0.287604	−	0.629764i	−0.709591	−	0.704614i	$-0.751120\pi$
$947$	8.85053	−	19.3800i	0.287604	−	0.629764i	0.997195	+	0.0748494i	$0.0238476\pi$
$948$	26.2750	−	7.71503i	0.853371	−	0.250572i
$949$	2.58629	+	5.66318i	0.0839544	+	0.183835i
$950$	12.2485	+	14.1355i	0.397394	+	0.458617i
$951$	−11.0030	−	76.5276i	−0.356797	−	2.48158i
$952$	−2.40503	−	0.706179i	−0.0779473	−	0.0228874i
$953$	29.6192	−	34.1824i	0.959460	−	1.10728i	−0.0347040	−	0.999398i	$-0.511049\pi$
$953$	29.6192	−	34.1824i	0.959460	−	1.10728i	0.994164	−	0.107878i	$-0.0344057\pi$
$954$	−96.2130	−	61.8323i	−3.11501	−	2.00190i
$955$	19.1888	+	12.3319i	0.620936	+	0.399051i
$956$	0.525740	−	0.606737i	0.0170037	−	0.0196233i
$957$	−43.3758	−	12.7363i	−1.40214	−	0.411706i
$958$	−4.50301	−	31.3191i	−0.145486	−	1.01188i
$959$	−4.49026	−	5.18203i	−0.144998	−	0.167337i
$960$	3.87179	+	8.47803i	0.124961	+	0.273627i
$961$	7.25839	−	2.13126i	0.234142	−	0.0687502i
$962$	2.62903	−	5.75676i	0.0847632	−	0.185606i
$963$	−3.98009	+	27.6821i	−0.128257	+	0.892044i
$964$	11.9454	−	7.67683i	0.384735	−	0.247254i
$965$	4.76021			0.153237
$966$	−0.146681	+	15.9591i	−0.00471938	+	0.513475i
$967$	−38.6632			−1.24332			−0.621662	−	0.783285i	$-0.713542\pi$
$967$	−38.6632			−1.24332			−0.621662	+	0.783285i	$0.713542\pi$
$968$	−4.31208	+	2.77120i	−0.138595	+	0.0890698i
$969$	−7.80740	+	54.3017i	−0.250810	+	1.74442i
$970$	9.95420	−	21.7967i	0.319610	−	0.699849i
$971$	−42.6398	+	12.5202i	−1.36838	+	0.401792i	−0.881709	−	0.471794i	$-0.843606\pi$
$971$	−42.6398	+	12.5202i	−1.36838	+	0.401792i	−0.486669	+	0.873586i	$0.661788\pi$
$972$	23.1569	+	50.7065i	0.742757	+	1.62641i
$973$	10.7297	+	12.3827i	0.343979	+	0.396972i
$974$	−4.37712	−	30.4435i	−0.140252	−	0.975474i
$975$	−21.7021	−	6.37231i	−0.695023	−	0.204077i
$976$	1.66658	−	1.92334i	0.0533459	−	0.0615645i
$977$	−12.8112	−	8.23327i	−0.409867	−	0.263406i	0.319420	−	0.947613i	$-0.396512\pi$
$977$	−12.8112	−	8.23327i	−0.409867	−	0.263406i	−0.729287	+	0.684208i	$0.760148\pi$
$978$	16.6473	+	10.6986i	0.532322	+	0.342102i
$979$	5.62515	−	6.49177i	0.179781	−	0.207478i
$980$	−2.68725	−	0.789049i	−0.0858411	−	0.0252052i
$981$	6.60424	+	45.9335i	0.210857	+	1.46654i
$982$	7.71885	+	8.90803i	0.246318	+	0.284267i
$983$	5.92707	+	12.9785i	0.189044	+	0.413949i	0.980294	−	0.197544i	$-0.0632965\pi$
$983$	5.92707	+	12.9785i	0.189044	+	0.413949i	−0.791250	+	0.611493i	$0.790569\pi$
$984$	34.1929	−	10.0399i	1.09003	−	0.320061i
$985$	−4.41518	+	9.66789i	−0.140679	+	0.308045i
$986$	1.99938	−	13.9060i	0.0636734	−	0.442858i
$987$	−13.1138	+	8.42770i	−0.417415	+	0.268257i
$988$	−15.7179			−0.500054
$989$	4.96809	+	17.5136i	0.157976	+	0.556902i
$990$	54.8099			1.74197
$991$	3.78277	−	2.43104i	0.120164	−	0.0772245i	−0.479178	−	0.877718i	$-0.659065\pi$
$991$	3.78277	−	2.43104i	0.120164	−	0.0772245i	0.599342	+	0.800493i	$0.295429\pi$
$992$	0.688945	−	4.79171i	0.0218740	−	0.152137i
$993$	−31.6847	+	69.3799i	−1.00548	+	2.20170i
$994$	−7.10195	+	2.08532i	−0.225260	+	0.0661423i
$995$	−25.5372	−	55.9187i	−0.809584	−	1.77274i
$996$	−36.8274	−	42.5011i	−1.16692	−	1.34670i
$997$	−3.91037	−	27.1972i	−0.123843	−	0.861345i	−0.953138	−	0.302535i	$-0.902167\pi$
$997$	−3.91037	−	27.1972i	−0.123843	−	0.861345i	0.829296	−	0.558810i	$-0.188742\pi$
$998$	40.0535	+	11.7608i	1.26787	+	0.372281i
$999$	−29.2847	+	33.7963i	−0.926526	+	1.06927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.127.1	yes	40
23.2	even	11	inner	322.2.i.d.71.1	✓	40
23.5	odd	22		7406.2.a.bv.1.20		20
23.18	even	11		7406.2.a.bu.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.71.1	✓	40	23.2	even	11	inner
322.2.i.d.127.1	yes	40	1.1	even	1	trivial
7406.2.a.bu.1.20		20	23.18	even	11
7406.2.a.bv.1.20		20	23.5	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.473601 + 3.29397i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.68725 + 0.789049i) q^{5} +(1.38243 + 3.02711i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-7.74745 - 2.27486i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.473601 + 3.29397i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.68725 + 0.789049i) q^{5} +(1.38243 + 3.02711i) q^{6} +(0.654861 + 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-7.74745 - 2.27486i) q^{9} +(-1.83407 + 2.11663i) q^{10} +(2.03893 + 1.31034i) q^{11} +(2.79956 + 1.79917i) q^{12} +(-1.56505 + 1.80616i) q^{13} +(0.959493 + 0.281733i) q^{14} +(-1.32642 - 9.22542i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.04126 - 2.28005i) q^{17} +(-7.74745 + 2.27486i) q^{18} +(-2.73211 + 5.98248i) q^{19} +(-0.398581 + 2.77219i) q^{20} +(-2.79956 + 1.79917i) q^{21} +2.42368 q^{22} +(4.38057 - 1.95208i) q^{23} +3.32784 q^{24} +(2.39246 - 1.53754i) q^{25} +(-0.340118 + 2.36557i) q^{26} +(7.01520 - 15.3611i) q^{27} +(0.959493 - 0.281733i) q^{28} +(2.32836 + 5.09840i) q^{29} +(-6.10349 - 7.04380i) q^{30} +(0.688945 + 4.79171i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-5.28186 + 6.09559i) q^{33} +(-2.10865 - 1.35515i) q^{34} +(-2.35610 - 1.51417i) q^{35} +(-5.28769 + 6.10232i) q^{36} +(-2.54083 - 0.746055i) q^{37} +(0.935979 + 6.50987i) q^{38} +(-5.20824 - 6.01062i) q^{39} +(1.16345 + 2.54761i) q^{40} +(10.2748 - 3.01695i) q^{41} +(-1.38243 + 3.02711i) q^{42} +(-0.540218 + 3.75730i) q^{43} +(2.03893 - 1.31034i) q^{44} +22.6143 q^{45} +(2.62979 - 4.01051i) q^{46} +4.68422 q^{47} +(2.79956 - 1.79917i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(1.18141 - 2.58693i) q^{50} +(8.00354 - 2.35005i) q^{51} +(0.992799 + 2.17393i) q^{52} +(9.27553 + 10.7045i) q^{53} +(-2.40330 - 16.7153i) q^{54} +(-6.51304 - 1.91240i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-18.4122 - 11.8328i) q^{57} +(4.71515 + 3.03024i) q^{58} +(7.89747 - 9.11417i) q^{59} +(-8.94275 - 2.62583i) q^{60} +(0.362182 + 2.51903i) q^{61} +(3.17017 + 3.65858i) q^{62} +(-3.35428 - 7.34485i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(2.78053 - 6.08852i) q^{65} +(-1.14786 + 7.98352i) q^{66} +(-3.50857 + 2.25482i) q^{67} -2.50656 q^{68} +(4.35546 + 15.3540i) q^{69} -2.80070 q^{70} +(-6.22677 + 4.00170i) q^{71} +(-1.14912 + 7.99234i) q^{72} +(1.08217 - 2.36963i) q^{73} +(-2.54083 + 0.746055i) q^{74} +(3.93154 + 8.60888i) q^{75} +(4.30690 + 4.97043i) q^{76} +(0.344926 + 2.39901i) q^{77} +(-7.63104 - 2.24067i) q^{78} +(5.38873 - 6.21893i) q^{79} +(2.35610 + 1.51417i) q^{80} +(26.8985 + 17.2866i) q^{81} +(7.01262 - 8.09300i) q^{82} +(-16.2144 - 4.76098i) q^{83} +(0.473601 + 3.29397i) q^{84} +(4.59720 + 5.30545i) q^{85} +(1.57689 + 3.45290i) q^{86} +(-17.8967 + 5.25494i) q^{87} +(1.00683 - 2.20466i) q^{88} +(0.504383 - 3.50806i) q^{89} +(19.0244 - 12.2262i) q^{90} -2.38990 q^{91} +(0.0440769 - 4.79563i) q^{92} -16.1100 q^{93} +(3.94062 - 2.53248i) q^{94} +(2.62140 - 18.2322i) q^{95} +(1.38243 - 3.02711i) q^{96} +(-8.20917 + 2.41043i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-12.8157 - 14.7901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

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