LMFDB - Embedded newform 690.2.w.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.20400 + 0.377364i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(2.34384 - 4.29243i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.20400 + 0.377364i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(2.34384 - 4.29243i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(2.17146 - 0.533633i) q^{10} +(1.50612 - 1.30506i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(-0.244830 + 0.133687i) q^{13} +(-2.03165 + 4.44870i) q^{14} +(-0.0997532 + 2.23384i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-1.82271 - 2.43486i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.800012 + 5.56421i) q^{19} +(-2.12786 + 0.687184i) q^{20} +(-3.69611 - 3.20270i) q^{21} +(-1.40918 + 1.40918i) q^{22} +(-4.79141 - 0.205848i) q^{23} +1.00000i q^{24} +(4.71519 - 1.66342i) q^{25} +(0.234669 - 0.150813i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(1.70911 - 4.58230i) q^{28} +(-1.36321 - 0.196000i) q^{29} +(-0.0598614 - 2.23527i) q^{30} +(-4.02938 - 2.58953i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-0.955089 - 1.74912i) q^{33} +(1.99177 + 2.29863i) q^{34} +(-3.54601 + 10.3450i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.26626 - 8.75718i) q^{37} +(-1.19492 - 5.49296i) q^{38} +(0.0785898 + 0.267652i) q^{39} +(2.07341 - 0.837233i) q^{40} +(-3.49392 - 7.65063i) q^{41} +(3.91517 + 2.93086i) q^{42} +(1.89412 + 0.412041i) q^{43} +(1.30506 - 1.50612i) q^{44} +(2.16159 + 0.572311i) q^{45} +(4.79389 - 0.136492i) q^{46} +(1.51427 + 1.51427i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(-9.14684 - 14.2328i) q^{49} +(-4.58451 + 1.99556i) q^{50} +(-2.76666 + 1.26349i) q^{51} +(-0.223312 + 0.167169i) q^{52} +(4.69085 + 2.56140i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-2.82701 + 3.44471i) q^{55} +(-1.37786 + 4.69255i) q^{56} +(5.60710 + 0.401028i) q^{57} +(1.37372 + 0.0982503i) q^{58} +(-1.00990 + 3.43939i) q^{59} +(0.219171 + 2.22530i) q^{60} +(-8.04008 + 12.5106i) q^{61} +(4.20385 + 2.29548i) q^{62} +(-3.91517 + 2.93086i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.489156 - 0.387036i) q^{65} +(1.07744 + 1.67652i) q^{66} +(-1.04123 - 14.5583i) q^{67} +(-2.15068 - 2.15068i) q^{68} +(-1.21963 + 4.63816i) q^{69} +(2.79897 - 10.5716i) q^{70} +(-2.87789 + 3.32126i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-3.85745 - 2.88765i) q^{73} +(3.88267 + 8.50186i) q^{74} +(-0.623115 - 4.96102i) q^{75} +(1.58374 + 5.39372i) q^{76} +(-2.07177 - 9.52378i) q^{77} +(-0.0974836 - 0.261364i) q^{78} +(-7.25291 - 2.12965i) q^{79} +(-2.00840 + 0.983015i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.03081 + 7.38188i) q^{82} +(4.13083 - 1.54072i) q^{83} +(-4.11428 - 2.64409i) q^{84} +(4.93608 + 4.67860i) q^{85} +(-1.91869 - 0.275866i) q^{86} +(-0.481292 + 1.29039i) q^{87} +(-1.19429 + 1.59539i) q^{88} +(-1.70958 + 1.09868i) q^{89} +(-2.19691 - 0.416647i) q^{90} +1.36426i q^{91} +(-4.77194 + 0.478136i) q^{92} +(-3.38685 + 3.38685i) q^{93} +(-1.61844 - 1.40238i) q^{94} +(-3.86295 - 11.9616i) q^{95} +(0.142315 + 0.989821i) q^{96} +(12.7250 + 4.74617i) q^{97} +(10.1389 + 13.5440i) q^{98} +(-1.91216 + 0.561461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.20400	+	0.377364i	−0.985657	+	0.168762i
$5$	−2.20400	+	0.377364i	−0.985657	+	0.168762i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	2.34384	−	4.29243i	0.885889	−	1.62238i	0.107851	−	0.994167i	$-0.465603\pi$
$7$	2.34384	−	4.29243i	0.885889	−	1.62238i	0.778038	−	0.628217i	$-0.216215\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	2.17146	−	0.533633i	0.686676	−	0.168750i
$11$	1.50612	−	1.30506i	0.454113	−	0.393491i	−0.397550	−	0.917580i	$-0.630140\pi$
$11$	1.50612	−	1.30506i	0.454113	−	0.393491i	0.851664	+	0.524089i	$0.175594\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	−0.244830	+	0.133687i	−0.0679036	+	0.0370782i	−0.512842	−	0.858483i	$-0.671407\pi$
$13$	−0.244830	+	0.133687i	−0.0679036	+	0.0370782i	0.444938	+	0.895561i	$0.353226\pi$
$14$	−2.03165	+	4.44870i	−0.542982	+	1.18896i
$15$	−0.0997532	+	2.23384i	−0.0257562	+	0.576775i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−1.82271	−	2.43486i	−0.442073	−	0.590540i	0.523061	−	0.852295i	$-0.324790\pi$
$17$	−1.82271	−	2.43486i	−0.442073	−	0.590540i	−0.965134	+	0.261755i	$0.915699\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	0.800012	+	5.56421i	0.183535	+	1.27652i	0.848321	+	0.529482i	$0.177614\pi$
$19$	0.800012	+	5.56421i	0.183535	+	1.27652i	−0.664785	+	0.747034i	$0.731477\pi$
$20$	−2.12786	+	0.687184i	−0.475803	+	0.153659i
$21$	−3.69611	−	3.20270i	−0.806557	−	0.698886i
$22$	−1.40918	+	1.40918i	−0.300439	+	0.300439i
$23$	−4.79141	−	0.205848i	−0.999078	−	0.0429223i
$23$	−4.79141	−	0.205848i	−0.999078	−	0.0429223i
$24$			1.00000i			0.204124i
$25$	4.71519	−	1.66342i	0.943039	−	0.332683i
$26$	0.234669	−	0.150813i	0.0460224	−	0.0295768i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	1.70911	−	4.58230i	0.322991	−	0.865973i
$29$	−1.36321	−	0.196000i	−0.253142	−	0.0363963i	0.0145757	−	0.999894i	$-0.495360\pi$
$29$	−1.36321	−	0.196000i	−0.253142	−	0.0363963i	−0.267717	+	0.963498i	$0.586269\pi$
$30$	−0.0598614	−	2.23527i	−0.0109291	−	0.408102i
$31$	−4.02938	−	2.58953i	−0.723698	−	0.465093i	0.126223	−	0.992002i	$-0.459714\pi$
$31$	−4.02938	−	2.58953i	−0.723698	−	0.465093i	−0.849922	+	0.526909i	$0.823351\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−0.955089	−	1.74912i	−0.166260	−	0.304482i
$34$	1.99177	+	2.29863i	0.341586	+	0.394211i
$35$	−3.54601	+	10.3450i	−0.599385	+	1.74862i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−3.26626	−	8.75718i	−0.536970	−	1.43967i	−0.868244	−	0.496137i	$-0.834751\pi$
$37$	−3.26626	−	8.75718i	−0.536970	−	1.43967i	0.331275	−	0.943534i	$-0.392521\pi$
$38$	−1.19492	−	5.49296i	−0.193842	−	0.891076i
$39$	0.0785898	+	0.267652i	0.0125844	+	0.0428586i
$40$	2.07341	−	0.837233i	0.327835	−	0.132378i
$41$	−3.49392	−	7.65063i	−0.545659	−	1.19483i	−0.958780	−	0.284151i	$-0.908288\pi$
$41$	−3.49392	−	7.65063i	−0.545659	−	1.19483i	0.413120	−	0.910676i	$-0.364439\pi$
$42$	3.91517	+	2.93086i	0.604124	+	0.452242i
$43$	1.89412	+	0.412041i	0.288851	+	0.0628357i	0.354656	−	0.934997i	$-0.384598\pi$
$43$	1.89412	+	0.412041i	0.288851	+	0.0628357i	−0.0658051	+	0.997832i	$0.520962\pi$
$44$	1.30506	−	1.50612i	0.196746	−	0.227057i
$45$	2.16159	+	0.572311i	0.322230	+	0.0853151i
$46$	4.79389	−	0.136492i	0.706820	−	0.0201246i
$47$	1.51427	+	1.51427i	0.220879	+	0.220879i	0.808868	−	0.587990i	$-0.200080\pi$
$47$	1.51427	+	1.51427i	0.220879	+	0.220879i	−0.587990	+	0.808868i	$0.700080\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	−9.14684	−	14.2328i	−1.30669	−	2.03325i
$50$	−4.58451	+	1.99556i	−0.648348	+	0.282214i
$51$	−2.76666	+	1.26349i	−0.387410	+	0.176924i
$52$	−0.223312	+	0.167169i	−0.0309678	+	0.0231822i
$53$	4.69085	+	2.56140i	0.644337	+	0.351835i	0.767963	−	0.640494i	$-0.221270\pi$
$53$	4.69085	+	2.56140i	0.644337	+	0.351835i	−0.123626	+	0.992329i	$0.539452\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	−2.82701	+	3.44471i	−0.381193	+	0.464485i
$56$	−1.37786	+	4.69255i	−0.184124	+	0.627068i
$57$	5.60710	+	0.401028i	0.742679	+	0.0531174i
$58$	1.37372	+	0.0982503i	0.180378	+	0.0129009i
$59$	−1.00990	+	3.43939i	−0.131477	+	0.447770i	−0.998746	−	0.0500704i	$-0.984055\pi$
$59$	−1.00990	+	3.43939i	−0.131477	+	0.447770i	0.867268	+	0.497841i	$0.165874\pi$
$60$	0.219171	+	2.22530i	0.0282949	+	0.287285i
$61$	−8.04008	+	12.5106i	−1.02943	+	1.60182i	−0.257320	+	0.966326i	$0.582839\pi$
$61$	−8.04008	+	12.5106i	−1.02943	+	1.60182i	−0.772107	+	0.635493i	$0.780797\pi$
$62$	4.20385	+	2.29548i	0.533889	+	0.291526i
$63$	−3.91517	+	2.93086i	−0.493265	+	0.369254i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	0.489156	−	0.387036i	0.0606723	−	0.0480059i
$66$	1.07744	+	1.67652i	0.132623	+	0.206366i
$67$	−1.04123	−	14.5583i	−0.127207	−	1.77858i	−0.515347	−	0.856981i	$-0.672337\pi$
$67$	−1.04123	−	14.5583i	−0.127207	−	1.77858i	0.388141	−	0.921600i	$-0.373118\pi$
$68$	−2.15068	−	2.15068i	−0.260808	−	0.260808i
$69$	−1.21963	+	4.63816i	−0.146826	+	0.558368i
$70$	2.79897	−	10.5716i	0.334541	−	1.26355i
$71$	−2.87789	+	3.32126i	−0.341543	+	0.394161i	−0.900372	−	0.435122i	$-0.856705\pi$
$71$	−2.87789	+	3.32126i	−0.341543	+	0.394161i	0.558829	+	0.829283i	$0.311251\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	−3.85745	−	2.88765i	−0.451481	−	0.337974i	0.349218	−	0.937041i	$-0.386447\pi$
$73$	−3.85745	−	2.88765i	−0.451481	−	0.337974i	−0.800699	+	0.599067i	$0.795538\pi$
$74$	3.88267	+	8.50186i	0.451351	+	0.988321i
$75$	−0.623115	−	4.96102i	−0.0719511	−	0.572849i
$76$	1.58374	+	5.39372i	0.181667	+	0.618702i
$77$	−2.07177	−	9.52378i	−0.236100	−	1.08534i
$78$	−0.0974836	−	0.261364i	−0.0110378	−	0.0295936i
$79$	−7.25291	−	2.12965i	−0.816016	−	0.239604i	−0.153016	−	0.988224i	$-0.548899\pi$
$79$	−7.25291	−	2.12965i	−0.816016	−	0.239604i	−0.663000	+	0.748620i	$0.730717\pi$
$80$	−2.00840	+	0.983015i	−0.224546	+	0.109904i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	4.03081	+	7.38188i	0.445129	+	0.815192i
$83$	4.13083	−	1.54072i	0.453418	−	0.169116i	−0.112371	−	0.993666i	$-0.535845\pi$
$83$	4.13083	−	1.54072i	0.453418	−	0.169116i	0.565789	+	0.824550i	$0.308572\pi$
$84$	−4.11428	−	2.64409i	−0.448905	−	0.288494i
$85$	4.93608	+	4.67860i	0.535393	+	0.507465i
$86$	−1.91869	−	0.275866i	−0.206898	−	0.0297474i
$87$	−0.481292	+	1.29039i	−0.0515999	+	0.138345i
$88$	−1.19429	+	1.59539i	−0.127312	+	0.170069i
$89$	−1.70958	+	1.09868i	−0.181215	+	0.116460i	−0.628103	−	0.778130i	$-0.716168\pi$
$89$	−1.70958	+	1.09868i	−0.181215	+	0.116460i	0.446889	+	0.894590i	$0.352532\pi$
$90$	−2.19691	−	0.416647i	−0.231574	−	0.0439184i
$91$			1.36426i			0.143013i
$92$	−4.77194	+	0.478136i	−0.497509	+	0.0498491i
$93$	−3.38685	+	3.38685i	−0.351200	+	0.351200i
$94$	−1.61844	−	1.40238i	−0.166929	−	0.144645i
$95$	−3.86295	−	11.9616i	−0.396331	−	1.22723i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	12.7250	+	4.74617i	1.29202	+	0.481900i	0.899129	−	0.437683i	$-0.144201\pi$
$97$	12.7250	+	4.74617i	1.29202	+	0.481900i	0.392895	+	0.919583i	$0.371473\pi$
$98$	10.1389	+	13.5440i	1.02418	+	1.36815i
$99$	−1.91216	+	0.561461i	−0.192179	+	0.0564290i
$100$	4.43047	−	2.31753i	0.443047	−	0.231753i
$101$	6.27379	−	13.7377i	0.624266	−	1.36695i	−0.288110	−	0.957597i	$-0.593027\pi$
$101$	6.27379	−	13.7377i	0.624266	−	1.36695i	0.912376	−	0.409354i	$-0.134246\pi$
$102$	2.66948	−	1.45764i	0.264318	−	0.144328i
$103$	−0.436546	+	6.10371i	−0.0430141	+	0.601416i	0.929537	+	0.368728i	$0.120207\pi$
$103$	−0.436546	+	6.10371i	−0.0430141	+	0.601416i	−0.972551	+	0.232688i	$0.925248\pi$
$104$	0.210818	−	0.182674i	0.0206724	−	0.0179127i
$105$	9.35479	+	5.66395i	0.912934	+	0.552745i
$106$	−4.86162	−	2.22023i	−0.472202	−	0.215648i
$107$	0.838508	−	0.182406i	0.0810616	−	0.0176339i	−0.171852	−	0.985123i	$-0.554975\pi$
$107$	0.838508	−	0.182406i	0.0810616	−	0.0176339i	0.252913	+	0.967489i	$0.418611\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	0.651483	−	4.53117i	0.0624008	−	0.434007i	−0.934541	−	0.355856i	$-0.884189\pi$
$109$	0.651483	−	4.53117i	0.0624008	−	0.434007i	0.996942	−	0.0781509i	$-0.0249016\pi$
$110$	2.57406	−	3.63761i	0.245427	−	0.346833i
$111$	−9.25134	+	1.33014i	−0.878099	+	0.126252i
$112$	1.03958	−	4.77889i	0.0982314	−	0.451563i
$113$	4.54141	−	0.324808i	0.427219	−	0.0305553i	0.143926	−	0.989589i	$-0.454027\pi$
$113$	4.54141	−	0.324808i	0.427219	−	0.0305553i	0.283294	+	0.959033i	$0.408573\pi$
$114$	−5.62143			−0.526495
$115$	10.6379	−	1.35442i	0.991992	−	0.126300i
$116$	−1.37723			−0.127872
$117$	0.278241	−	0.0199002i	0.0257234	−	0.00183977i
$118$	0.761960	−	3.50267i	0.0701441	−	0.322447i
$119$	−14.7236	+	2.11694i	−1.34971	+	0.194059i
$120$	−0.377364	−	2.20400i	−0.0344484	−	0.201196i
$121$	−1.00025	+	6.95686i	−0.0909314	+	0.632442i
$122$	7.12710	−	13.0523i	0.645257	−	1.18170i
$123$	−8.21847	+	1.78782i	−0.741035	+	0.161202i
$124$	−4.35690	−	1.98973i	−0.391261	−	0.178683i
$125$	−9.76455	+	5.44550i	−0.873368	+	0.487061i
$126$	3.69611	−	3.20270i	0.329276	−	0.285319i
$127$	1.01714	−	14.2215i	0.0902566	−	1.26195i	−0.727387	−	0.686227i	$-0.759266\pi$
$127$	1.01714	−	14.2215i	0.0902566	−	1.26195i	0.817644	−	0.575725i	$-0.195280\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	0.805250	−	1.76325i	0.0708983	−	0.155246i
$130$	−0.460298	+	0.420946i	−0.0403708	+	0.0369194i
$131$	15.7201	−	4.61585i	1.37348	−	0.403289i	0.489982	−	0.871732i	$-0.337003\pi$
$131$	15.7201	−	4.61585i	1.37348	−	0.403289i	0.883493	+	0.468443i	$0.155185\pi$
$132$	−1.19429	−	1.59539i	−0.103950	−	0.138861i
$133$	25.7590	+	9.60763i	2.23359	+	0.833087i
$134$	2.07716	+	14.4469i	0.179439	+	1.24803i
$135$	1.01871	−	1.99054i	0.0876766	−	0.171318i
$136$	2.29863	+	1.99177i	0.197106	+	0.170793i
$137$	3.33155	−	3.33155i	0.284633	−	0.284633i	−0.550320	−	0.834954i	$-0.685494\pi$
$137$	3.33155	−	3.33155i	0.284633	−	0.284633i	0.834954	+	0.550320i	$0.185494\pi$
$138$	0.885642	−	4.71335i	0.0753908	−	0.401227i
$139$			1.19039i			0.100968i	0.998725	+	0.0504838i	$0.0160763\pi$
$139$			1.19039i			0.100968i	−0.998725	+	0.0504838i	$0.983924\pi$
$140$	−2.03768	+	10.7443i	−0.172215	+	0.908061i
$141$	1.80154	−	1.15778i	0.151717	−	0.0975028i
$142$	2.63362	−	3.51811i	0.221009	−	0.295233i
$143$	−0.194274	+	0.520868i	−0.0162460	+	0.0435572i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	3.07847	−	0.0824428i	0.255653	−	0.00684650i
$146$	4.05363	+	2.60511i	0.335480	+	0.215600i
$147$	−15.8518	+	5.91241i	−1.30743	+	0.487648i
$148$	−4.47929	−	8.20321i	−0.368195	−	0.674299i
$149$	7.75232	+	8.94665i	0.635094	+	0.732938i	0.978499	−	0.206249i	$-0.0661258\pi$
$149$	7.75232	+	8.94665i	0.635094	+	0.732938i	−0.343405	+	0.939187i	$0.611580\pi$
$150$	0.975443	+	4.90393i	0.0796446	+	0.400404i
$151$	9.50239	+	2.79015i	0.773293	+	0.227059i	0.644492	−	0.764611i	$-0.277069\pi$
$151$	9.50239	+	2.79015i	0.773293	+	0.227059i	0.128801	+	0.991670i	$0.458887\pi$
$152$	−1.96449	−	5.26699i	−0.159341	−	0.427210i
$153$	0.646521	+	2.97201i	0.0522681	+	0.240273i
$154$	2.74591	+	9.35172i	0.221272	+	0.753583i
$155$	9.85793	+	4.18676i	0.791808	+	0.336289i
$156$	0.115881	+	0.253743i	0.00927788	+	0.0203157i
$157$	12.4401	+	9.31251i	0.992824	+	0.743219i	0.966561	−	0.256436i	$-0.0825483\pi$
$157$	12.4401	+	9.31251i	0.992824	+	0.743219i	0.0262631	+	0.999655i	$0.491639\pi$
$158$	7.38636	+	1.60680i	0.587627	+	0.127830i
$159$	3.49997	−	4.03918i	0.277566	−	0.320328i
$160$	1.93316	−	1.12379i	0.152830	−	0.0888433i
$161$	−12.1139	+	20.0843i	−0.954709	+	1.58286i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	0.0904249	+	1.26431i	0.00708263	+	0.0990281i	0.999764	−	0.0217372i	$-0.00691971\pi$
$163$	0.0904249	+	1.26431i	0.00708263	+	0.0990281i	−0.992681	+	0.120765i	$0.961465\pi$
$164$	−4.54716	−	7.07552i	−0.355073	−	0.552505i
$165$	2.76506	+	3.49463i	0.215260	+	0.272056i
$166$	−4.01039	+	1.83148i	−0.311267	+	0.142151i
$167$	−9.34047	+	6.99218i	−0.722787	+	0.541072i	−0.896131	−	0.443790i	$-0.853634\pi$
$167$	−9.34047	+	6.99218i	−0.722787	+	0.541072i	0.173344	+	0.984861i	$0.444543\pi$
$168$	4.29243	+	2.34384i	0.331168	+	0.180831i
$169$	−6.98626	+	10.8708i	−0.537405	+	0.836218i
$170$	−5.25727	−	4.31454i	−0.403214	−	0.330910i
$171$	1.58374	−	5.39372i	0.121112	−	0.412468i
$172$	1.93348	+	0.138285i	0.147427	+	0.0105442i
$173$	8.09225	+	0.578769i	0.615242	+	0.0440030i	0.375483	−	0.926829i	$-0.377477\pi$
$173$	8.09225	+	0.578769i	0.615242	+	0.0440030i	0.239760	+	0.970832i	$0.422931\pi$
$174$	0.388010	−	1.32144i	0.0294149	−	0.100178i
$175$	3.91158	−	24.1384i	0.295687	−	1.82469i
$176$	1.07744	−	1.67652i	0.0812148	−	0.126373i
$177$	3.14612	+	1.71791i	0.236477	+	0.129126i
$178$	1.62684	−	1.21784i	0.121937	−	0.0912808i
$179$	14.0404	−	6.41204i	1.04943	−	0.479259i	0.185381	−	0.982667i	$-0.440648\pi$
$179$	14.0404	−	6.41204i	1.04943	−	0.479259i	0.864049	+	0.503408i	$0.167921\pi$
$180$	2.22103	+	0.258859i	0.165546	+	0.0192942i
$181$	−4.57070	−	7.11216i	−0.339738	−	0.528642i	0.628781	−	0.777582i	$-0.283554\pi$
$181$	−4.57070	−	7.11216i	−0.339738	−	0.528642i	−0.968519	+	0.248940i	$0.919918\pi$
$182$	−0.0973249	−	1.36078i	−0.00721420	−	0.100868i
$183$	10.5157	+	10.5157i	0.777340	+	0.777340i
$184$	4.72567	−	0.817344i	0.348381	−	0.0602554i
$185$	10.5035	+	18.0682i	0.772230	+	1.32840i
$186$	3.13661	−	3.61984i	0.229987	−	0.265420i
$187$	−5.92288	−	1.28844i	−0.433124	−	0.0942203i
$188$	1.71436	+	1.28335i	0.125032	+	0.0935981i
$189$	2.03165	+	4.44870i	0.147781	+	0.323595i
$190$	4.70644	+	11.6555i	0.341441	+	0.845582i
$191$	−4.74498	−	16.1599i	−0.343334	−	1.16929i	−0.932468	−	0.361254i	$-0.882349\pi$
$191$	−4.74498	−	16.1599i	−0.343334	−	1.16929i	0.589133	−	0.808036i	$-0.299469\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	6.77690	+	18.1696i	0.487812	+	1.30787i	0.914906	+	0.403667i	$0.132264\pi$
$193$	6.77690	+	18.1696i	0.487812	+	1.30787i	−0.427094	+	0.904207i	$0.640463\pi$
$194$	−13.0311	−	3.82629i	−0.935581	−	0.274711i
$195$	−0.274214	−	0.560247i	−0.0196369	−	0.0401201i
$196$	−11.0793	−	12.7862i	−0.791376	−	0.913297i
$197$	−6.94387	−	12.7168i	−0.494730	−	0.906031i	−0.999095	−	0.0425401i	$-0.986455\pi$
$197$	−6.94387	−	12.7168i	−0.494730	−	0.906031i	0.504364	−	0.863491i	$-0.331727\pi$
$198$	1.86723	−	0.696443i	0.132699	−	0.0494940i
$199$	15.9551	+	10.2537i	1.13102	+	0.726865i	0.965773	−	0.259387i	$-0.0835205\pi$
$199$	15.9551	+	10.2537i	1.13102	+	0.726865i	0.165250	+	0.986252i	$0.447157\pi$
$200$	−4.25385	+	2.62769i	−0.300793	+	0.185806i
$201$	−14.4469	−	2.07716i	−1.01901	−	0.146511i
$202$	−5.27777	+	14.1503i	−0.371343	+	0.995609i
$203$	−4.03646	+	5.39208i	−0.283304	+	0.378450i
$204$	−2.55869	+	1.64437i	−0.179144	+	0.115129i
$205$	10.5877	+	15.5435i	0.739474	+	1.08560i
$206$		−	6.11930i		−	0.426352i
$207$	4.27291	+	2.17767i	0.296988	+	0.151359i
$208$	−0.197249	+	0.197249i	−0.0136767	+	0.0136767i
$209$	8.46656	+	7.33632i	0.585644	+	0.507464i
$210$	−9.73502	−	4.98216i	−0.671780	−	0.343802i
$211$	2.08477	+	14.4999i	0.143522	+	0.998215i	0.926535	+	0.376210i	$0.122773\pi$
$211$	2.08477	+	14.4999i	0.143522	+	0.998215i	−0.783013	+	0.622006i	$0.786318\pi$
$212$	5.00762	+	1.86775i	0.343925	+	0.128277i
$213$	2.63362	+	3.51811i	0.180453	+	0.241057i
$214$	−0.823359	+	0.241760i	−0.0562837	+	0.0165264i
$215$	−4.33013	−	0.193364i	−0.295312	−	0.0131873i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−20.5596	+	11.2264i	−1.39568	+	0.762096i
$218$	−0.326574	+	4.56610i	−0.0221184	+	0.309255i
$219$	−3.64162	+	3.15548i	−0.246078	+	0.213228i
$220$	−2.30800	+	3.81197i	−0.155605	+	0.257003i
$221$	0.771765	+	0.352453i	0.0519145	+	0.0237086i
$222$	9.13288	−	1.98674i	0.612959	−	0.133341i
$223$	3.97564	−	7.28085i	0.266229	−	0.487562i	−0.710029	−	0.704172i	$-0.751318\pi$
$223$	3.97564	−	7.28085i	0.266229	−	0.487562i	0.976258	+	0.216611i	$0.0695002\pi$
$224$	−0.696013	+	4.84088i	−0.0465043	+	0.323445i
$225$	−4.98010	−	0.445666i	−0.332007	−	0.0297110i
$226$	−4.50666	+	0.647960i	−0.299779	+	0.0431017i
$227$	−2.48336	+	11.4158i	−0.164826	+	0.757695i	0.818303	+	0.574786i	$0.194915\pi$
$227$	−2.48336	+	11.4158i	−0.164826	+	0.757695i	−0.983130	+	0.182909i	$0.941449\pi$
$228$	5.60710	−	0.401028i	0.371339	−	0.0265587i
$229$	15.2432			1.00730			0.503648	−	0.863909i	$-0.331991\pi$
$229$	15.2432			1.00730			0.503648	+	0.863909i	$0.331991\pi$
$230$	−10.5142	+	2.10987i	−0.693286	+	0.139121i
$231$	−9.74652			−0.641274
$232$	1.37372	−	0.0982503i	0.0901890	−	0.00645045i
$233$	2.97475	−	13.6747i	0.194883	−	0.895860i	−0.770991	−	0.636846i	$-0.780239\pi$
$233$	2.97475	−	13.6747i	0.194883	−	0.895860i	0.965873	−	0.259014i	$-0.0833977\pi$
$234$	−0.276112	+	0.0396990i	−0.0180500	+	0.00259520i
$235$	−3.90887	−	2.76601i	−0.254987	−	0.180435i
$236$	−0.510140	+	3.54810i	−0.0332073	+	0.230962i
$237$	−3.62269	+	6.63447i	−0.235319	+	0.430955i
$238$	14.5351	−	3.16191i	0.942169	−	0.204956i
$239$	−1.45787	−	0.665786i	−0.0943016	−	0.0430661i	0.367706	−	0.929942i	$-0.380143\pi$
$239$	−1.45787	−	0.665786i	−0.0943016	−	0.0430661i	−0.462007	+	0.886876i	$0.652871\pi$
$240$	0.533633	+	2.17146i	0.0344459	+	0.140167i
$241$	18.6512	−	16.1613i	1.20143	−	1.04104i	0.203347	−	0.979107i	$-0.434818\pi$
$241$	18.6512	−	16.1613i	1.20143	−	1.04104i	0.998080	−	0.0619357i	$-0.0197274\pi$
$242$	0.501400	−	7.01049i	0.0322312	−	0.450652i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	−6.17780	+	13.5275i	−0.395493	+	0.866009i
$245$	25.5305	+	27.9172i	1.63108	+	1.78357i
$246$	8.06999	−	2.36956i	0.514524	−	0.151078i
$247$	−0.939731	−	1.25533i	−0.0597936	−	0.0798750i
$248$	4.48774	+	1.67384i	0.284972	+	0.106289i
$249$	−0.627439	−	4.36393i	−0.0397623	−	0.276553i
$250$	9.35120	−	6.12822i	0.591422	−	0.387583i
$251$	19.8769	+	17.2235i	1.25462	+	1.08713i	0.992518	+	0.122095i	$0.0389611\pi$
$251$	19.8769	+	17.2235i	1.25462	+	1.08713i	0.262102	+	0.965040i	$0.415584\pi$
$252$	−3.45822	+	3.45822i	−0.217847	+	0.217847i
$253$	−7.48510	+	5.94306i	−0.470584	+	0.373637i
$254$			14.2578i			0.894614i
$255$	5.62092	−	3.82877i	0.351995	−	0.239767i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	11.0118	−	14.7100i	0.686894	−	0.917584i	−0.312584	−	0.949890i	$-0.601194\pi$
$257$	11.0118	−	14.7100i	0.686894	−	0.917584i	0.999478	+	0.0323067i	$0.0102853\pi$
$258$	−0.677409	+	1.81620i	−0.0421737	+	0.113072i
$259$	−45.2451	−	6.50527i	−2.81140	−	0.404218i
$260$	0.429096	−	0.452711i	0.0266114	−	0.0280759i
$261$	1.15860	+	0.744585i	0.0717154	+	0.0460887i
$262$	−15.3508	+	5.72555i	−0.948376	+	0.353726i
$263$	−12.8323	−	23.5006i	−0.791273	−	1.44911i	−0.890957	−	0.454089i	$-0.849965\pi$
$263$	−12.8323	−	23.5006i	−0.791273	−	1.44911i	0.0996838	−	0.995019i	$-0.468217\pi$
$264$	1.30506	+	1.50612i	0.0803211	+	0.0926955i
$265$	−11.3052	−	3.87515i	−0.694472	−	0.238049i
$266$	−26.3788	−	7.74552i	−1.61739	−	0.474908i
$267$	0.710173	+	1.90405i	0.0434619	+	0.116526i
$268$	−3.10250	−	14.2620i	−0.189515	−	0.871187i
$269$	−4.67026	−	15.9054i	−0.284751	−	0.969772i	−0.970332	−	0.241776i	$-0.922270\pi$
$269$	−4.67026	−	15.9054i	−0.284751	−	0.969772i	0.685581	−	0.727996i	$-0.259548\pi$
$270$	−0.874111	+	2.05814i	−0.0531967	+	0.125254i
$271$	−4.23459	−	9.27246i	−0.257233	−	0.563262i	0.736320	−	0.676634i	$-0.236562\pi$
$271$	−4.23459	−	9.27246i	−0.257233	−	0.563262i	−0.993553	+	0.113372i	$0.963835\pi$
$272$	−2.43486	−	1.82271i	−0.147635	−	0.110518i
$273$	1.33308	+	0.289994i	0.0806816	+	0.0175512i
$274$	−3.08539	+	3.56073i	−0.186395	+	0.215112i
$275$	4.93080	−	8.65894i	0.297338	−	0.522154i
$276$	−0.547139	+	4.76452i	−0.0329339	+	0.286790i
$277$	−11.1432	−	11.1432i	−0.669530	−	0.669530i	0.288077	−	0.957607i	$-0.406984\pi$
$277$	−11.1432	−	11.1432i	−0.669530	−	0.669530i	−0.957607	+	0.288077i	$0.906984\pi$
$278$	−0.0849215	−	1.18736i	−0.00509325	−	0.0712129i
$279$	2.58953	+	4.02938i	0.155031	+	0.241233i
$280$	1.26599	−	10.8623i	0.0756575	−	0.649147i
$281$	15.9541	−	7.28602i	0.951745	−	0.434647i	0.121838	−	0.992550i	$-0.461121\pi$
$281$	15.9541	−	7.28602i	0.951745	−	0.434647i	0.829906	+	0.557903i	$0.188394\pi$
$282$	−1.71436	+	1.28335i	−0.102089	+	0.0764226i
$283$	−24.1808	−	13.2037i	−1.43740	−	0.784881i	−0.443619	−	0.896216i	$-0.646305\pi$
$283$	−24.1808	−	13.2037i	−1.43740	−	0.784881i	−0.993783	+	0.111335i	$0.964487\pi$
$284$	−2.37593	+	3.69702i	−0.140986	+	0.219378i
$285$	−12.5094	+	1.23205i	−0.740991	+	0.0729805i
$286$	0.156621	−	0.533400i	0.00926117	−	0.0315406i
$287$	−41.0289	−	2.93445i	−2.42186	−	0.173215i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	2.18319	−	7.43527i	0.128423	−	0.437369i
$290$	−3.06474	+	0.301848i	−0.179968	+	0.0177251i
$291$	7.34259	−	11.4253i	0.430430	−	0.669762i
$292$	−4.22914	−	2.30929i	−0.247492	−	0.135141i
$293$	22.5626	−	16.8901i	1.31812	−	0.986732i	0.318878	−	0.947796i	$-0.396694\pi$
$293$	22.5626	−	16.8901i	1.31812	−	0.986732i	0.999242	−	0.0389366i	$-0.0123970\pi$
$294$	15.3896	−	7.02820i	0.897541	−	0.409893i
$295$	0.927905	−	7.96150i	0.0540247	−	0.463536i
$296$	5.05309	+	7.86276i	0.293705	+	0.457013i
$297$	0.142171	+	1.98781i	0.00824959	+	0.115344i
$298$	−8.37081	−	8.37081i	−0.484908	−	0.484908i
$299$	1.20060	−	0.590153i	0.0694325	−	0.0341294i
$300$	−1.32280	−	4.82185i	−0.0763719	−	0.278389i
$301$	6.20818	−	7.16463i	0.357834	−	0.412962i
$302$	−9.67722	−	2.10515i	−0.556862	−	0.121138i
$303$	−12.0902	−	9.05058i	−0.694561	−	0.519942i
$304$	2.33522	+	5.11343i	0.133934	+	0.293275i
$305$	12.9993	−	30.6074i	0.744335	−	1.75257i
$306$	−0.856895	−	2.91832i	−0.0489854	−	0.166829i
$307$	4.28838	+	19.7134i	0.244751	+	1.12510i	0.921345	+	0.388745i	$0.127091\pi$
$307$	4.28838	+	19.7134i	0.244751	+	1.12510i	−0.676594	+	0.736356i	$0.736545\pi$
$308$	−3.40606	−	9.13200i	−0.194078	−	0.520344i
$309$	5.87142	+	1.72401i	0.334014	+	0.0980752i
$310$	−10.1315	−	3.47284i	−0.575430	−	0.197244i
$311$	−3.65443	−	4.21744i	−0.207224	−	0.239149i	0.642618	−	0.766187i	$-0.277848\pi$
$311$	−3.65443	−	4.21744i	−0.207224	−	0.239149i	−0.849842	+	0.527037i	$0.823303\pi$
$312$	−0.133687	−	0.244830i	−0.00756855	−	0.0138608i
$313$	−16.0822	+	5.99833i	−0.909017	+	0.339046i	−0.760102	−	0.649804i	$-0.774851\pi$
$313$	−16.0822	+	5.99833i	−0.909017	+	0.339046i	−0.148915	+	0.988850i	$0.547578\pi$
$314$	−13.0727	−	8.40132i	−0.737735	−	0.474114i
$315$	7.52302	−	7.93705i	0.423874	−	0.447202i
$316$	−7.48217	−	1.07577i	−0.420905	−	0.0605170i
$317$	10.1313	−	27.1630i	0.569030	−	1.52563i	−0.259535	−	0.965734i	$-0.583569\pi$
$317$	10.1313	−	27.1630i	0.569030	−	1.52563i	0.828565	−	0.559894i	$-0.189158\pi$
$318$	−3.20290	+	4.27857i	−0.179610	+	0.239931i
$319$	−2.30895	+	1.48387i	−0.129277	+	0.0830810i
$320$	−1.84806	+	1.25883i	−0.103310	+	0.0703710i
$321$		−	0.858119i		−	0.0478955i
$322$	10.6502	−	20.8973i	0.593514	−	1.16456i
$323$	12.0899	−	12.0899i	0.672699	−	0.672699i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−0.932043	+	1.03762i	−0.0517005	+	0.0575566i
$326$	−0.180389	−	1.25463i	−0.00999083	−	0.0694877i
$327$	−4.28913	−	1.59976i	−0.237190	−	0.0884671i
$328$	5.04033	+	6.73310i	0.278306	+	0.371773i
$329$	10.0491	−	2.95068i	0.554024	−	0.162676i
$330$	−3.00732	−	3.28846i	−0.165548	−	0.181024i
$331$	12.7284	−	27.8713i	0.699617	−	1.53195i	−0.140818	−	0.990035i	$-0.544973\pi$
$331$	12.7284	−	27.8713i	0.699617	−	1.53195i	0.840435	−	0.541912i	$-0.182299\pi$
$332$	3.86952	−	2.11292i	0.212367	−	0.115961i
$333$	−0.666770	+	9.32266i	−0.0365388	+	0.510879i
$334$	8.81785	−	7.64071i	0.482491	−	0.418081i
$335$	7.78865	+	31.6935i	0.425539	+	1.73160i
$336$	−4.44870	−	2.03165i	−0.242696	−	0.110836i
$337$	−1.36578	+	0.297107i	−0.0743986	+	0.0161844i	−0.249611	−	0.968346i	$-0.580303\pi$
$337$	−1.36578	+	0.297107i	−0.0743986	+	0.0161844i	0.175212	+	0.984531i	$0.443939\pi$
$338$	6.19294	−	11.3415i	0.336852	−	0.616898i
$339$	0.647960	−	4.50666i	0.0351924	−	0.244768i
$340$	5.55167	+	3.92850i	0.301082	+	0.213053i
$341$	−9.44824	+	1.35845i	−0.511651	+	0.0735643i
$342$	−1.19492	+	5.49296i	−0.0646139	+	0.297025i
$343$	−48.3844	+	3.46052i	−2.61251	+	0.186851i
$344$	−1.93842			−0.104513
$345$	0.937791	−	10.6827i	0.0504890	−	0.575138i
$346$	−8.11292			−0.436153
$347$	−9.19452	+	0.657605i	−0.493588	+	0.0353021i	−0.315915	−	0.948788i	$-0.602311\pi$
$347$	−9.19452	+	0.657605i	−0.493588	+	0.0353021i	−0.177673	+	0.984090i	$0.556857\pi$
$348$	−0.292751	+	1.34575i	−0.0156931	+	0.0721399i
$349$	−32.8330	+	4.72067i	−1.75751	+	0.252692i	−0.944254	−	0.329217i	$-0.893215\pi$
$349$	−32.8330	+	4.72067i	−1.75751	+	0.252692i	−0.813254	+	0.581909i	$0.802306\pi$
$350$	−2.17960	+	24.3559i	−0.116504	+	1.30188i
$351$	0.0396990	−	0.276112i	0.00211897	−	0.0147378i
$352$	−0.955089	+	1.74912i	−0.0509064	+	0.0932281i
$353$	−1.72616	+	0.375503i	−0.0918741	+	0.0199860i	−0.258267	−	0.966073i	$-0.583152\pi$
$353$	−1.72616	+	0.375503i	−0.0918741	+	0.0199860i	0.166393	+	0.986059i	$0.446788\pi$
$354$	−3.26066	−	1.48909i	−0.173302	−	0.0791444i
$355$	5.08954	−	8.40606i	0.270124	−	0.446147i
$356$	−1.53582	+	1.33079i	−0.0813981	+	0.0705318i
$357$	−1.06117	+	14.8371i	−0.0561632	+	0.785264i
$358$	−13.5472	+	7.39734i	−0.715992	+	0.390961i
$359$	−14.9637	+	32.7660i	−0.789755	+	1.72932i	−0.112403	+	0.993663i	$0.535855\pi$
$359$	−14.9637	+	32.7660i	−0.789755	+	1.72932i	−0.677352	+	0.735659i	$0.736872\pi$
$360$	−2.23384	−	0.0997532i	−0.117734	−	0.00525746i
$361$	−12.0900	+	3.54995i	−0.636317	+	0.186839i
$362$	5.06643	+	6.76796i	0.266286	+	0.355716i
$363$	6.58526	+	2.45617i	0.345636	+	0.128916i
$364$	0.194154	+	1.35037i	0.0101764	+	0.0707786i
$365$	9.59150	+	4.90871i	0.502042	+	0.256934i
$366$	−11.2390	−	9.73869i	−0.587474	−	0.509049i
$367$	−6.79128	+	6.79128i	−0.354502	+	0.354502i	−0.861781	−	0.507280i	$-0.830651\pi$
$367$	−6.79128	+	6.79128i	−0.354502	+	0.354502i	0.507280	+	0.861781i	$0.330651\pi$
$368$	−4.65532	+	1.15239i	−0.242675	+	0.0600723i
$369$			8.41068i			0.437843i
$370$	−11.7657	−	17.2729i	−0.611668	−	0.897974i
$371$	21.9892	−	14.1316i	1.14162	−	0.733676i
$372$	−2.87038	+	3.83438i	−0.148822	+	0.198803i
$373$	−8.63094	+	23.1405i	−0.446893	+	1.19817i	0.496952	+	0.867778i	$0.334453\pi$
$373$	−8.63094	+	23.1405i	−0.446893	+	1.19817i	−0.943845	+	0.330389i	$0.892820\pi$
$374$	5.99971	+	0.862627i	0.310237	+	0.0446054i
$375$	3.24545	+	10.6989i	0.167594	+	0.552490i
$376$	−1.80154	−	1.15778i	−0.0929076	−	0.0597081i
$377$	0.359957	−	0.134257i	0.0185387	−	0.00691459i
$378$	−2.34384	−	4.29243i	−0.120554	−	0.220779i
$379$	9.71585	+	11.2127i	0.499069	+	0.575957i	0.948266	−	0.317476i	$-0.102835\pi$
$379$	9.71585	+	11.2127i	0.499069	+	0.575957i	−0.449197	+	0.893433i	$0.648290\pi$
$380$	−5.52595	−	11.2901i	−0.283475	−	0.579169i
$381$	−13.6803	−	4.01689i	−0.700861	−	0.205791i
$382$	5.88572	+	15.7802i	0.301140	+	0.807387i
$383$	0.636313	+	2.92508i	0.0325141	+	0.149465i	0.990542	−	0.137210i	$-0.0438136\pi$
$383$	0.636313	+	2.92508i	0.0325141	+	0.149465i	−0.958028	+	0.286675i	$0.907450\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	8.16011	+	20.2086i	0.415878	+	1.02992i
$386$	−8.05583	−	17.6398i	−0.410031	−	0.897843i
$387$	−1.55179	−	1.16165i	−0.0788818	−	0.0590502i
$388$	13.2709	+	2.88691i	0.673728	+	0.146560i
$389$	−15.7625	+	18.1909i	−0.799189	+	0.922313i	−0.998336	−	0.0576563i	$-0.981637\pi$
$389$	−15.7625	+	18.1909i	−0.799189	+	0.922313i	0.199148	+	0.979970i	$0.436183\pi$
$390$	0.313483	+	0.539258i	0.0158738	+	0.0273064i
$391$	8.23216	+	12.0416i	0.416318	+	0.608971i
$392$	11.9632	+	11.9632i	0.604232	+	0.604232i
$393$	−1.16881	−	16.3421i	−0.0589585	−	0.824348i
$394$	7.83338	+	12.1890i	0.394640	+	0.614072i
$395$	16.7890	+	1.95675i	0.844748	+	0.0984546i
$396$	−1.81279	+	0.827875i	−0.0910963	+	0.0416023i
$397$	26.6173	−	19.9254i	1.33588	−	1.00003i	0.337609	−	0.941286i	$-0.390382\pi$
$397$	26.6173	−	19.9254i	1.33588	−	1.00003i	0.998273	−	0.0587424i	$-0.0187091\pi$
$398$	−16.6459	−	9.08934i	−0.834383	−	0.455608i
$399$	14.8635	−	23.1281i	0.744108	−	1.15785i
$400$	4.05556	−	2.92446i	0.202778	−	0.146223i
$401$	−8.24920	+	28.0942i	−0.411945	+	1.40296i	0.448668	+	0.893699i	$0.351899\pi$
$401$	−8.24920	+	28.0942i	−0.411945	+	1.40296i	−0.860613	+	0.509259i	$0.829920\pi$
$402$	14.5583	+	1.04123i	0.726103	+	0.0519319i
$403$	1.33270	+	0.0953166i	0.0663865	+	0.00474806i
$404$	4.25486	−	14.4907i	0.211687	−	0.720940i
$405$	−1.72850	−	1.41855i	−0.0858900	−	0.0704882i
$406$	3.64151	−	5.66630i	0.180725	−	0.281214i
$407$	−16.3481	−	8.92672i	−0.810343	−	0.442481i
$408$	2.43486	−	1.82271i	0.120544	−	0.0902378i
$409$	23.9524	−	10.9387i	1.18437	−	0.540884i	0.276859	−	0.960911i	$-0.410707\pi$
$409$	23.9524	−	10.9387i	1.18437	−	0.540884i	0.907512	+	0.420027i	$0.137979\pi$
$410$	−11.6695	−	14.7485i	−0.576318	−	0.728379i
$411$	−2.54724	−	3.96358i	−0.125646	−	0.195509i
$412$	0.436546	+	6.10371i	0.0215071	+	0.300708i
$413$	12.3963	+	12.3963i	0.609981	+	0.609981i
$414$	−4.41738	−	1.86730i	−0.217102	−	0.0917726i
$415$	−8.52292	+	4.95457i	−0.418374	+	0.243210i
$416$	0.182674	−	0.210818i	0.00895635	−	0.0103362i
$417$	1.16319	+	0.253036i	0.0569615	+	0.0123912i
$418$	−8.96836	−	6.71363i	−0.438657	−	0.328374i
$419$	−5.20648	−	11.4006i	−0.254353	−	0.556956i	0.738780	−	0.673947i	$-0.235402\pi$
$419$	−5.20648	−	11.4006i	−0.254353	−	0.556956i	−0.993133	+	0.116991i	$0.962675\pi$
$420$	10.0656	+	4.27498i	0.491153	+	0.208598i
$421$	4.66714	+	15.8948i	0.227462	+	0.774666i	0.991569	+	0.129576i	$0.0413618\pi$
$421$	4.66714	+	15.8948i	0.227462	+	0.774666i	−0.764107	+	0.645090i	$0.776820\pi$
$422$	−3.11387	−	14.3142i	−0.151581	−	0.696806i
$423$	−0.748377	−	2.00648i	−0.0363874	−	0.0975583i
$424$	−5.12811	−	1.50575i	−0.249043	−	0.0731256i
$425$	−12.6446	−	8.44891i	−0.613355	−	0.409832i
$426$	−2.87789	−	3.32126i	−0.139434	−	0.160916i
$427$	34.8562	+	63.8343i	1.68681	+	3.08916i
$428$	0.804014	−	0.299882i	0.0388635	−	0.0144953i
$429$	0.467669	+	0.300553i	0.0225793	+	0.0145108i
$430$	4.33289	−	0.116037i	0.208951	−	0.00559579i
$431$	−19.7481	−	2.83935i	−0.951233	−	0.136767i	−0.350808	−	0.936448i	$-0.614093\pi$
$431$	−19.7481	−	2.83935i	−0.951233	−	0.136767i	−0.600425	+	0.799681i	$0.705002\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	−22.4975	+	30.0531i	−1.08116	+	1.44426i	−0.195043	+	0.980795i	$0.562485\pi$
$433$	−22.4975	+	30.0531i	−1.08116	+	1.44426i	−0.886116	+	0.463464i	$0.846606\pi$
$434$	19.7063	−	12.6645i	0.945933	−	0.607915i
$435$	0.573817	−	3.02564i	0.0275124	−	0.145068i
$436$		−	4.57776i		−	0.219235i
$437$	−2.68781	−	26.8251i	−0.128575	−	1.28322i
$438$	3.40723	−	3.40723i	0.162804	−	0.162804i
$439$	22.8921	+	19.8361i	1.09258	+	0.946726i	0.998805	−	0.0488675i	$-0.0155612\pi$
$439$	22.8921	+	19.8361i	1.09258	+	0.946726i	0.0937747	+	0.995593i	$0.470107\pi$
$440$	2.03017	−	3.96691i	0.0967848	−	0.189115i
$441$	2.40775	+	16.7463i	0.114655	+	0.797443i
$442$	−0.794942	−	0.296498i	−0.0378116	−	0.0141030i
$443$	4.08473	+	5.45656i	0.194071	+	0.259249i	0.887013	−	0.461745i	$-0.152776\pi$
$443$	4.08473	+	5.45656i	0.194071	+	0.259249i	−0.692941	+	0.720994i	$0.743686\pi$
$444$	−8.96788	+	2.63321i	−0.425597	+	0.124966i
$445$	3.35330	−	3.06661i	0.158961	−	0.145371i
$446$	−3.44610	+	7.54592i	−0.163178	+	0.357309i
$447$	10.3901	−	5.67340i	0.491433	−	0.268343i
$448$	0.348895	−	4.87819i	0.0164838	−	0.230473i
$449$	10.2132	−	8.84983i	0.481993	−	0.417649i	−0.379677	−	0.925119i	$-0.623965\pi$
$449$	10.2132	−	8.84983i	0.481993	−	0.417649i	0.861669	+	0.507470i	$0.169419\pi$
$450$	4.99920	+	0.0892541i	0.235665	+	0.00420748i
$451$	−15.2468	−	6.96300i	−0.717945	−	0.327875i
$452$	4.44896	−	0.967811i	0.209261	−	0.0455220i
$453$	4.74627	−	8.69214i	0.222999	−	0.408392i
$454$	1.66264	−	11.5639i	0.0780315	−	0.542721i
$455$	−0.514821	−	3.00681i	−0.0241352	−	0.140962i
$456$	−5.56421	+	0.800012i	−0.260568	+	0.0374640i
$457$	1.41200	−	6.49086i	0.0660506	−	0.303630i	−0.932256	−	0.361799i	$-0.882163\pi$
$457$	1.41200	−	6.49086i	0.0660506	−	0.303630i	0.998307	+	0.0581693i	$0.0185263\pi$
$458$	−15.2043	+	1.08743i	−0.710452	+	0.0508125i
$459$	3.04152			0.141966
$460$	10.3369	−	2.85457i	0.481960	−	0.133095i
$461$	38.0333			1.77139			0.885693	−	0.464271i	$-0.153683\pi$
$461$	38.0333			1.77139			0.885693	+	0.464271i	$0.153683\pi$
$462$	9.72169	−	0.695309i	0.452294	−	0.0323487i
$463$	3.84298	−	17.6659i	0.178598	−	0.821003i	−0.797439	−	0.603400i	$-0.793812\pi$
$463$	3.84298	−	17.6659i	0.178598	−	0.821003i	0.976037	−	0.217603i	$-0.0698239\pi$
$464$	−1.36321	+	0.196000i	−0.0632854	+	0.00909907i
$465$	6.18654	−	8.74269i	0.286894	−	0.405432i
$466$	−1.99163	+	13.8521i	−0.0922605	+	0.641686i
$467$	−2.09423	+	3.83530i	−0.0969095	+	0.177476i	−0.921636	−	0.388055i	$-0.873147\pi$
$467$	−2.09423	+	3.83530i	−0.0969095	+	0.177476i	0.824727	+	0.565531i	$0.191329\pi$
$468$	0.272577	−	0.0592954i	0.0125999	−	0.00274093i
$469$	−64.9310	−	29.6530i	−2.99823	−	1.36925i
$470$	4.09624	+	2.48011i	0.188945	+	0.114399i
$471$	11.7440	−	10.1762i	0.541135	−	0.468897i
$472$	0.255722	−	3.57546i	0.0117705	−	0.164574i
$473$	3.39052	−	1.85137i	0.155896	−	0.0851259i
$474$	3.14017	−	6.87600i	0.144233	−	0.315825i
$475$	13.0278	+	24.9056i	0.597757	+	1.14275i
$476$	−14.2725	+	4.19078i	−0.654178	+	0.192084i
$477$	−3.20290	−	4.27857i	−0.146651	−	0.195902i
$478$	1.50165	+	0.560087i	0.0686839	+	0.0256178i
$479$	−5.15566	−	35.8584i	−0.235568	−	1.63841i	−0.673344	−	0.739329i	$-0.735143\pi$
$479$	−5.15566	−	35.8584i	−0.235568	−	1.63841i	0.437776	−	0.899084i	$-0.355766\pi$
$480$	−0.687184	−	2.12786i	−0.0313655	−	0.0971230i
$481$	1.97040	+	1.70736i	0.0898426	+	0.0778490i
$482$	−17.4507	+	17.4507i	−0.794858	+	0.794858i
$483$	17.0503	+	16.1063i	0.775816	+	0.732861i
$484$			7.02840i			0.319473i
$485$	−29.8368	−	5.65859i	−1.35482	−	0.256943i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	0.360651	−	0.481773i	0.0163427	−	0.0218312i	−0.792295	−	0.610138i	$-0.791114\pi$
$487$	0.360651	−	0.481773i	0.0163427	−	0.0218312i	0.808638	+	0.588306i	$0.200205\pi$
$488$	5.19702	−	13.9337i	0.235258	−	0.630751i
$489$	1.25463	+	0.180389i	0.0567365	+	0.00815748i
$490$	−27.4571	−	26.0248i	−1.24038	−	1.17568i
$491$	7.29833	+	4.69035i	0.329369	+	0.211673i	0.694865	−	0.719140i	$-0.255464\pi$
$491$	7.29833	+	4.69035i	0.329369	+	0.211673i	−0.365496	+	0.930813i	$0.619101\pi$
$492$	−7.88039	+	2.93923i	−0.355275	+	0.132511i
$493$	2.00751	+	3.67648i	0.0904136	+	0.165580i
$494$	1.02689	+	1.18510i	0.0462020	+	0.0533200i
$495$	4.00252	−	1.95904i	0.179900	−	0.0880522i
$496$	−4.59572	−	1.34942i	−0.206354	−	0.0605909i
$497$	7.51095	+	20.1376i	0.336912	+	0.903297i
$498$	0.937159	+	4.30805i	0.0419951	+	0.193048i
$499$	−6.88494	−	23.4479i	−0.308212	−	1.04967i	−0.957333	−	0.288989i	$-0.906681\pi$
$499$	−6.88494	−	23.4479i	−0.308212	−	1.04967i	0.649120	−	0.760686i	$-0.275137\pi$
$500$	−8.89019	+	6.77972i	−0.397581	+	0.303198i
$501$	4.84693	+	10.6133i	0.216545	+	0.474167i
$502$	−21.0550	−	15.7616i	−0.939730	−	0.703473i
$503$	−32.2912	−	7.02451i	−1.43979	−	0.313208i	−0.576163	−	0.817335i	$-0.695451\pi$
$503$	−32.2912	−	7.02451i	−1.43979	−	0.313208i	−0.863629	+	0.504127i	$0.831814\pi$
$504$	3.20270	−	3.69611i	0.142660	−	0.164638i
$505$	−8.64331	+	32.6453i	−0.384622	+	1.45270i
$506$	7.04206	−	6.46190i	0.313058	−	0.287267i
$507$	9.13737	+	9.13737i	0.405805	+	0.405805i
$508$	−1.01714	−	14.2215i	−0.0451283	−	0.630976i
$509$	12.1415	+	18.8925i	0.538162	+	0.837396i	0.998738	−	0.0502239i	$-0.0159935\pi$
$509$	12.1415	+	18.8925i	0.538162	+	0.837396i	−0.460576	+	0.887620i	$0.652357\pi$
$510$	−5.33345	+	4.22001i	−0.236169	+	0.186865i
$511$	−21.4363	+	9.78962i	−0.948285	+	0.433067i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	−4.93381	−	2.69406i	−0.217833	−	0.118946i
$514$	−9.93430	+	15.4581i	−0.438183	+	0.681826i
$515$	−1.34117	−	13.6173i	−0.0590991	−	0.600049i
$516$	0.546117	−	1.85990i	0.0240415	−	0.0818777i
$517$	4.25689	+	0.304459i	0.187218	+	0.0133901i
$518$	45.5939	+	3.26094i	2.00328	+	0.143278i
$519$	2.28567	−	7.78429i	0.100330	−	0.341692i
$520$	−0.395706	+	0.482169i	−0.0173529	+	0.0211445i
$521$	−12.8390	+	19.9778i	−0.562486	+	0.875245i	−0.999709	−	0.0241077i	$-0.992326\pi$
$521$	−12.8390	+	19.9778i	−0.562486	+	0.875245i	0.437223	+	0.899353i	$0.355962\pi$
$522$	−1.20876	−	0.660035i	−0.0529061	−	0.0288889i
$523$	−0.545904	+	0.408658i	−0.0238707	+	0.0178694i	−0.611146	−	0.791518i	$-0.709291\pi$
$523$	−0.545904	+	0.408658i	−0.0238707	+	0.0178694i	0.587276	+	0.809387i	$0.300200\pi$
$524$	14.9032	−	6.80608i	0.651051	−	0.297325i
$525$	−22.7553	−	8.95317i	−0.993122	−	0.390748i
$526$	14.4761	+	22.5253i	0.631188	+	0.982148i
$527$	1.03927	+	14.5309i	0.0452715	+	0.632978i
$528$	−1.40918	−	1.40918i	−0.0613269	−	0.0613269i
$529$	22.9153	+	1.97261i	0.996315	+	0.0857655i
$530$	11.5528	+	3.05877i	0.501823	+	0.132865i
$531$	2.34741	−	2.70905i	0.101869	−	0.117563i
$532$	26.8642	+	5.84394i	1.16471	+	0.253367i
$533$	1.87821	+	1.40601i	0.0813543	+	0.0609010i
$534$	−0.844196	−	1.84853i	−0.0365320	−	0.0799938i
$535$	−1.77923	+	0.718445i	−0.0769230	+	0.0310611i
$536$	4.11203	+	14.0043i	0.177613	+	0.604893i
$537$	−3.28100	−	15.0825i	−0.141586	−	0.650859i
$538$	5.79304	+	15.5318i	0.249756	+	0.669621i
$539$	−32.3509	−	9.49909i	−1.39345	−	0.409155i
$540$	0.725058	−	2.11525i	0.0312015	−	0.0910259i
$541$	−23.5002	−	27.1207i	−1.01035	−	1.16601i	−0.986075	−	0.166304i	$-0.946817\pi$
$541$	−23.5002	−	27.1207i	−1.01035	−	1.16601i	−0.0242779	−	0.999705i	$-0.507729\pi$
$542$	4.88529	+	8.94674i	0.209841	+	0.384295i
$543$	−7.92119	+	2.95445i	−0.339931	+	0.126788i
$544$	2.55869	+	1.64437i	0.109703	+	0.0705017i
$545$	0.274031	+	10.2325i	0.0117382	+	0.438313i
$546$	−1.35037	−	0.194154i	−0.0577905	−	0.00830902i
$547$	6.01310	−	16.1218i	0.257102	−	0.689316i	−0.742704	−	0.669620i	$-0.766457\pi$
$547$	6.01310	−	16.1218i	0.257102	−	0.689316i	0.999806	−	0.0196969i	$-0.00627011\pi$
$548$	2.82351	−	3.77177i	0.120614	−	0.161122i
$549$	12.5106	−	8.04008i	0.533940	−	0.343142i
$550$	−4.30052	+	8.98863i	−0.183375	+	0.383277i
$551$		−	7.74198i		−	0.329819i
$552$	0.205848	−	4.79141i	0.00876148	−	0.203936i
$553$	−26.1410	+	26.1410i	−1.11163	+	1.11163i
$554$	11.9098	+	10.3199i	0.505997	+	0.438449i
$555$	19.8880	−	6.42275i	0.844197	−	0.272631i
$556$	0.169410	+	1.17827i	0.00718459	+	0.0499699i
$557$	28.4323	+	10.6047i	1.20471	+	0.449335i	0.870031	−	0.492996i	$-0.164098\pi$
$557$	28.4323	+	10.6047i	1.20471	+	0.449335i	0.334682	+	0.942331i	$0.391371\pi$
$558$	−2.87038	−	3.83438i	−0.121513	−	0.162322i
$559$	−0.518823	+	0.152340i	−0.0219439	+	0.00644330i
$560$	−0.487859	+	10.9250i	−0.0206158	+	0.461663i
$561$	−2.51800	+	5.51365i	−0.106310	+	0.232786i
$562$	−15.3937	+	8.40561i	−0.649345	+	0.354569i
$563$	−1.90899	+	26.6912i	−0.0804544	+	1.12490i	0.783521	+	0.621365i	$0.213422\pi$
$563$	−1.90899	+	26.6912i	−0.0804544	+	1.12490i	−0.863975	+	0.503534i	$0.832033\pi$
$564$	1.61844	−	1.40238i	0.0681485	−	0.0590510i
$565$	−9.88667	+	2.42964i	−0.415935	+	0.102216i
$566$	25.0612	+	11.4451i	1.05340	+	0.481071i
$567$	4.77889	−	1.03958i	0.200694	−	0.0436584i
$568$	2.10614	−	3.85710i	0.0883715	−	0.161840i
$569$	4.97655	−	34.6126i	0.208628	−	1.45104i	−0.569013	−	0.822329i	$-0.692675\pi$
$569$	4.97655	−	34.6126i	0.208628	−	1.45104i	0.777641	−	0.628709i	$-0.216416\pi$
$570$	12.3896	−	2.12132i	0.518943	−	0.0888524i
$571$	11.5736	−	1.66403i	0.484339	−	0.0696375i	0.104180	−	0.994558i	$-0.466778\pi$
$571$	11.5736	−	1.66403i	0.484339	−	0.0696375i	0.380159	+	0.924921i	$0.375869\pi$
$572$	−0.118169	+	0.543215i	−0.00494090	+	0.0227129i
$573$	−16.7992	+	1.20150i	−0.701797	+	0.0501935i
$574$	41.1337			1.71689
$575$	−22.9348	+	6.99950i	−0.956449	+	0.291899i
$576$	−1.00000			−0.0416667
$577$	1.06238	−	0.0759827i	0.0442273	−	0.00316320i	−0.0492080	−	0.998789i	$-0.515670\pi$
$577$	1.06238	−	0.0759827i	0.0442273	−	0.00316320i	0.0934353	+	0.995625i	$0.470215\pi$
$578$	−1.64720	+	7.57207i	−0.0685147	+	0.314957i
$579$	19.1949	−	2.75980i	0.797711	−	0.114694i
$580$	3.03540	−	0.519716i	0.126038	−	0.0215800i
$581$	3.06859	−	21.3425i	0.127306	−	0.885435i
$582$	−6.50881	+	11.9200i	−0.269799	+	0.494100i
$583$	10.4078	−	2.26407i	0.431046	−	0.0937683i
$584$	4.38311	+	2.00170i	0.181374	+	0.0828309i
$585$	−0.605732	+	0.148858i	−0.0250439	+	0.00615452i
$586$	−21.3002	+	18.4567i	−0.879902	+	0.762439i
$587$	−1.10485	+	15.4478i	−0.0456018	+	0.637597i	0.922333	+	0.386396i	$0.126280\pi$
$587$	−1.10485	+	15.4478i	−0.0456018	+	0.637597i	−0.967935	+	0.251201i	$0.919174\pi$
$588$	−14.8490	+	8.10818i	−0.612363	+	0.334376i
$589$	11.1851	−	24.4920i	0.460874	−	1.00917i
$590$	−0.357574	+	8.00741i	−0.0147211	+	0.329660i
$591$	−13.9022	+	4.08204i	−0.571858	+	0.167913i
$592$	−5.60114	−	7.48224i	−0.230205	−	0.307518i
$593$	30.3012	+	11.3018i	1.24432	+	0.464107i	0.883457	−	0.468512i	$-0.155210\pi$
$593$	30.3012	+	11.3018i	1.24432	+	0.464107i	0.360862	+	0.932619i	$0.382482\pi$
$594$	−0.283617	−	1.97260i	−0.0116370	−	0.0809369i
$595$	31.6519	−	10.2219i	1.29760	−	0.419056i
$596$	8.94665	+	7.75232i	0.366469	+	0.317547i
$597$	13.4109	−	13.4109i	0.548870	−	0.548870i
$598$	−1.15544	+	0.674299i	−0.0472495	+	0.0275741i
$599$			13.4493i			0.549523i	0.961512	+	0.274761i	$0.0885988\pi$
$599$			13.4493i			0.549523i	−0.961512	+	0.274761i	$0.911401\pi$
$600$	1.66342	+	4.71519i	0.0679087	+	0.192497i
$601$	6.59225	−	4.23658i	0.268904	−	0.172814i	−0.399239	−	0.916847i	$-0.630726\pi$
$601$	6.59225	−	4.23658i	0.268904	−	0.172814i	0.668143	+	0.744033i	$0.267089\pi$
$602$	−5.68125	+	7.58926i	−0.231550	+	0.309315i
$603$	−5.10061	+	13.6753i	−0.207713	+	0.556899i
$604$	9.80275	+	1.40942i	0.398868	+	0.0573486i
$605$	−0.420730	−	15.7104i	−0.0171051	−	0.638717i
$606$	12.7050	+	8.16501i	0.516106	+	0.331681i
$607$	−14.4685	+	5.39649i	−0.587260	+	0.219037i	−0.625490	−	0.780232i	$-0.715101\pi$
$607$	−14.4685	+	5.39649i	−0.587260	+	0.219037i	0.0382297	+	0.999269i	$0.487828\pi$
$608$	−2.69406	−	4.93381i	−0.109259	−	0.200092i
$609$	4.41084	+	5.09038i	0.178736	+	0.206273i
$610$	−10.7826	+	31.4567i	−0.436576	+	1.27365i
$611$	−0.573177	−	0.168300i	−0.0231883	−	0.00680869i
$612$	1.06290	+	2.84975i	0.0429653	+	0.115194i
$613$	−4.31434	−	19.8327i	−0.174255	−	0.801036i	−0.978419	−	0.206629i	$-0.933751\pi$
$613$	−4.31434	−	19.8327i	−0.174255	−	0.801036i	0.804165	−	0.594407i	$-0.202613\pi$
$614$	−5.68379	−	19.3572i	−0.229379	−	0.781193i
$615$	17.4388	−	7.04170i	0.703201	−	0.283949i
$616$	4.04885	+	8.86575i	0.163133	+	0.357211i
$617$	−9.44357	−	7.06937i	−0.380184	−	0.284602i	0.392046	−	0.919946i	$-0.371768\pi$
$617$	−9.44357	−	7.06937i	−0.380184	−	0.284602i	−0.772230	+	0.635344i	$0.780858\pi$
$618$	−5.97945	−	1.30075i	−0.240529	−	0.0523239i
$619$	−0.388252	+	0.448067i	−0.0156052	+	0.0180093i	−0.763499	−	0.645810i	$-0.776520\pi$
$619$	−0.388252	+	0.448067i	−0.0156052	+	0.0180093i	0.747893	+	0.663819i	$0.231065\pi$
$620$	10.3534	+	2.74122i	0.415804	+	0.110090i
$621$	3.03618	−	3.71236i	0.121838	−	0.148972i
$622$	3.94599	+	3.94599i	0.158220	+	0.158220i
$623$	0.709017	+	9.91335i	0.0284062	+	0.397170i
$624$	0.150813	+	0.234669i	0.00603734	+	0.00939428i
$625$	19.4661	−	15.6867i	0.778644	−	0.627466i
$626$	15.6133	−	7.13034i	0.624031	−	0.284986i
$627$	8.96836	−	6.71363i	0.358162	−	0.268116i
$628$	13.6387	+	7.44732i	0.544245	+	0.297180i
$629$	−15.3691	+	23.9147i	−0.612804	+	0.953542i
$630$	−6.93763	+	8.45351i	−0.276402	+	0.336796i
$631$	2.69895	−	9.19177i	0.107443	−	0.365919i	−0.888166	−	0.459522i	$-0.848021\pi$
$631$	2.69895	−	9.19177i	0.107443	−	0.365919i	0.995610	+	0.0936040i	$0.0298387\pi$
$632$	7.53985	+	0.539260i	0.299919	+	0.0214506i
$633$	14.6117	+	1.04505i	0.580763	+	0.0415370i
$634$	−8.16768	+	27.8166i	−0.324380	+	1.10474i
$635$	3.12490	+	31.7279i	0.124008	+	1.25908i
$636$	2.88951	−	4.49617i	0.114577	−	0.178285i
$637$	4.14216	+	2.26179i	0.164118	+	0.0896154i
$638$	2.19721	−	1.64481i	0.0869885	−	0.0651187i
$639$	3.99752	−	1.82561i	0.158140	−	0.0722200i
$640$	1.75355	−	1.38747i	0.0693151	−	0.0548444i
$641$	15.2922	+	23.7951i	0.604004	+	0.939849i	0.999769	+	0.0214968i	$0.00684317\pi$
$641$	15.2922	+	23.7951i	0.604004	+	0.939849i	−0.395765	+	0.918352i	$0.629520\pi$
$642$	0.0612175	+	0.855932i	0.00241606	+	0.0337810i
$643$	−15.3919	−	15.3919i	−0.606997	−	0.606997i	0.335163	−	0.942160i	$-0.391209\pi$
$643$	−15.3919	−	15.3919i	−0.606997	−	0.606997i	−0.942160	+	0.335163i	$0.891209\pi$
$644$	−9.13230	+	21.6039i	−0.359863	+	0.851311i
$645$	−1.10938	+	4.19007i	−0.0436818	+	0.164984i
$646$	−11.1966	+	12.9216i	−0.440524	+	0.508392i
$647$	−31.2422	−	6.79633i	−1.22826	−	0.267191i	−0.448793	−	0.893636i	$-0.648146\pi$
$647$	−31.2422	−	6.79633i	−1.22826	−	0.267191i	−0.779466	+	0.626444i	$0.784510\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	2.96759	+	6.49812i	0.116488	+	0.255074i
$650$	0.855646	−	1.10146i	0.0335612	−	0.0432029i
$651$	6.59957	+	22.4761i	0.258658	+	0.880907i
$652$	0.269434	+	1.23857i	0.0105519	+	0.0485061i
$653$	−12.8986	−	34.5826i	−0.504763	−	1.35332i	−0.900459	−	0.434940i	$-0.856770\pi$
$653$	−12.8986	−	34.5826i	−0.504763	−	1.35332i	0.395697	−	0.918381i	$-0.370503\pi$
$654$	4.39233	+	1.28970i	0.171754	+	0.0504314i
$655$	−32.9053	+	16.1055i	−1.28572	+	0.629295i
$656$	−5.50783	−	6.35637i	−0.215044	−	0.248175i
$657$	2.30929	+	4.22914i	0.0900939	+	0.164995i
$658$	−9.81299	+	3.66006i	−0.382550	+	0.142684i
$659$	34.9409	+	22.4551i	1.36110	+	0.874728i	0.998365	−	0.0571628i	$-0.0182054\pi$
$659$	34.9409	+	22.4551i	1.36110	+	0.874728i	0.362739	+	0.931891i	$0.381842\pi$
$660$	3.23426	+	3.06555i	0.125893	+	0.119326i
$661$	47.2393	+	6.79199i	1.83740	+	0.264178i	0.971670	−	0.236341i	$-0.0759482\pi$
$661$	47.2393	+	6.79199i	1.83740	+	0.264178i	0.865726	+	0.500518i	$0.166857\pi$
$662$	−10.7077	+	28.7084i	−0.416165	+	1.11578i
$663$	0.508449	−	0.679208i	0.0197465	−	0.0263783i
$664$	−3.70892	+	2.38358i	−0.143934	+	0.0925009i
$665$	−60.3984	−	11.4546i	−2.34215	−	0.444192i
$666$		−	9.34648i		−	0.362169i
$667$	6.49135	+	1.21973i	0.251346	+	0.0472281i
$668$	−8.25030	+	8.25030i	−0.319214	+	0.319214i
$669$	−6.26937	−	5.43244i	−0.242388	−	0.210030i
$670$	−10.0298	−	31.0572i	−0.387485	−	1.19984i
$671$	4.21778	+	29.3353i	0.162826	+	1.13248i
$672$	4.58230	+	1.70911i	0.176766	+	0.0659303i
$673$	−8.14730	−	10.8835i	−0.314055	−	0.419529i	0.615543	−	0.788103i	$-0.288937\pi$
$673$	−8.14730	−	10.8835i	−0.314055	−	0.419529i	−0.929598	+	0.368575i	$0.879846\pi$
$674$	1.34110	−	0.393783i	0.0516573	−	0.0151680i
$675$	−1.49408	+	4.77155i	−0.0575070	+	0.183657i
$676$	−5.36807	+	11.7544i	−0.206464	+	0.452094i
$677$	−9.76962	+	5.33462i	−0.375477	+	0.205026i	−0.655895	−	0.754852i	$-0.727709\pi$
$677$	−9.76962	+	5.33462i	−0.375477	+	0.205026i	0.280418	+	0.959878i	$0.409527\pi$
$678$	−0.324808	+	4.54141i	−0.0124742	+	0.174412i
$679$	50.1979	−	43.4967i	1.92642	−	1.66925i
$680$	−5.81778	−	3.52244i	−0.223102	−	0.135079i
$681$	10.6271	+	4.85322i	0.407230	+	0.185976i
$682$	9.32726	−	2.02902i	0.357159	−	0.0776952i
$683$	−5.00761	+	9.17075i	−0.191611	+	0.350909i	−0.955768	−	0.294121i	$-0.904973\pi$
$683$	−5.00761	+	9.17075i	−0.191611	+	0.350909i	0.764157	+	0.645030i	$0.223155\pi$
$684$	0.800012	−	5.56421i	0.0305892	−	0.212753i
$685$	−6.08551	+	8.59992i	−0.232515	+	0.328586i
$686$	48.0143	−	6.90341i	1.83319	−	0.263573i
$687$	3.24017	−	14.8948i	0.123620	−	0.568272i
$688$	1.93348	−	0.138285i	0.0737134	−	0.00527209i
$689$	−1.49089			−0.0567982
$690$	−0.173305	+	10.7224i	−0.00659760	+	0.408195i
$691$	−38.8202			−1.47679			−0.738394	−	0.674369i	$-0.764416\pi$
$691$	−38.8202			−1.47679			−0.738394	+	0.674369i	$0.764416\pi$
$692$	8.09225	−	0.578769i	0.307621	−	0.0220015i
$693$	−2.07177	+	9.52378i	−0.0787001	+	0.361779i
$694$	9.12418	−	1.31186i	0.346349	−	0.0497975i
$695$	−0.449210	−	2.62361i	−0.0170395	−	0.0995194i
$696$	0.196000	−	1.36321i	0.00742936	−	0.0516723i
$697$	−12.2598	+	22.4521i	−0.464372	+	0.850435i
$698$	32.4125	−	7.05092i	1.22683	−	0.266881i
$699$	−12.7299	−	5.81354i	−0.481488	−	0.219888i
$700$	0.436511	−	24.4494i	0.0164986	−	0.924100i
$701$	14.2151	−	12.3174i	0.536896	−	0.465223i	−0.343708	−	0.939077i	$-0.611683\pi$
$701$	14.2151	−	12.3174i	0.536896	−	0.465223i	0.880603	+	0.473854i	$0.157138\pi$
$702$	−0.0199002	+	0.278241i	−0.000751084	+	0.0105015i
$703$	46.1137	−	25.1800i	1.73921	−	0.949682i
$704$	0.827875	−	1.81279i	0.0312017	−	0.0683222i
$705$	−3.53369	+	3.23158i	−0.133086	+	0.121709i
$706$	1.69497	−	0.497689i	0.0637911	−	0.0187308i
$707$	−44.2632	−	59.1288i	−1.66469	−	2.22377i
$708$	3.35858	+	1.25269i	0.126223	+	0.0470788i
$709$	0.727329	+	5.05869i	0.0273154	+	0.189983i	0.998911	−	0.0466665i	$-0.0148598\pi$
$709$	0.727329	+	5.05869i	0.0273154	+	0.189983i	−0.971595	+	0.236649i	$0.923951\pi$
$710$	−4.47689	+	8.74773i	−0.168015	+	0.328296i
$711$	5.71279	+	4.95016i	0.214246	+	0.185646i
$712$	1.43697	−	1.43697i	0.0538526	−	0.0538526i
$713$	18.7734	+	13.2369i	0.703068	+	0.495727i
$714$		−	14.8750i		−	0.556684i
$715$	0.231622	−	1.22130i	0.00866217	−	0.0456742i
$716$	12.9850	−	8.34494i	0.485271	−	0.311865i
$717$	−0.960463	+	1.28303i	−0.0358691	+	0.0479156i
$718$	12.5881	−	33.7500i	0.469784	−	1.25954i
$719$	12.3343	+	1.77340i	0.459991	+	0.0661367i	0.368415	−	0.929661i	$-0.379900\pi$
$719$	12.3343	+	1.77340i	0.459991	+	0.0661367i	0.0915760	+	0.995798i	$0.470810\pi$
$720$	2.23527	−	0.0598614i	0.0833035	−	0.00223090i
$721$	25.1765	+	16.1800i	0.937622	+	0.602573i
$722$	11.8060	−	4.40340i	0.439373	−	0.163877i
$723$	−11.8274	−	21.6603i	−0.439866	−	0.805554i
$724$	−5.53635	−	6.38928i	−0.205757	−	0.237456i
$725$	−6.75382	+	1.34341i	−0.250831	+	0.0498929i
$726$	−6.74370	−	1.98013i	−0.250282	−	0.0734895i
$727$	−1.70806	−	4.57949i	−0.0633485	−	0.169844i	0.901419	−	0.432948i	$-0.142527\pi$
$727$	−1.70806	−	4.57949i	−0.0633485	−	0.169844i	−0.964768	+	0.263104i	$0.915254\pi$
$728$	−0.289994	−	1.33308i	−0.0107479	−	0.0494072i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−9.91725	−	4.21195i	−0.367054	−	0.155891i
$731$	−2.44918	−	5.36296i	−0.0905863	−	0.198356i
$732$	11.9052	+	8.91209i	0.440027	+	0.329400i
$733$	32.5908	+	7.08970i	1.20377	+	0.261864i	0.769338	−	0.638841i	$-0.220586\pi$
$733$	32.5908	+	7.08970i	1.20377	+	0.261864i	0.434430	+	0.900705i	$0.356950\pi$
$734$	6.28949	−	7.25846i	0.232149	−	0.267915i
$735$	32.7062	−	19.0128i	1.20638	−	0.701299i
$736$	4.56125	−	1.48156i	0.168130	−	0.0546109i
$737$	−20.5678	−	20.5678i	−0.757623	−	0.757623i
$738$	−0.600011	−	8.38925i	−0.0220867	−	0.308813i
$739$	7.81964	+	12.1676i	0.287650	+	0.447592i	0.954764	−	0.297363i	$-0.0961072\pi$
$739$	7.81964	+	12.1676i	0.287650	+	0.447592i	−0.667114	+	0.744955i	$0.732471\pi$
$740$	12.9679	+	16.3895i	0.476711	+	0.602490i
$741$	−1.42640	+	0.651415i	−0.0524001	+	0.0239303i
$742$	−20.9250	+	15.6643i	−0.768182	+	0.575054i
$743$	28.4894	+	15.5564i	1.04518	+	0.570709i	0.907624	−	0.419785i	$-0.137895\pi$
$743$	28.4894	+	15.5564i	1.04518	+	0.570709i	0.137553	+	0.990494i	$0.456076\pi$
$744$	2.58953	−	4.02938i	0.0949366	−	0.147724i
$745$	−20.4622	−	16.7929i	−0.749677	−	0.615245i
$746$	6.95813	−	23.6972i	0.254755	−	0.867617i
$747$	−4.39757	−	0.314521i	−0.160899	−	0.0115077i
$748$	−6.04596	−	0.432415i	−0.221062	−	0.0158107i
$749$	1.18236	−	4.02676i	0.0432027	−	0.147135i
$750$	−4.00044	−	10.4401i	−0.146075	−	0.381220i
$751$	−5.98070	+	9.30615i	−0.218239	+	0.339586i	−0.933060	−	0.359721i	$-0.882872\pi$
$751$	−5.98070	+	9.30615i	−0.218239	+	0.339586i	0.714821	+	0.699307i	$0.246508\pi$
$752$	1.87955	+	1.02631i	0.0685401	+	0.0374257i
$753$	21.0550	−	15.7616i	0.767286	−	0.574383i
$754$	−0.349462	+	0.159594i	−0.0127267	+	0.00581207i
$755$	−21.9961	−	2.56363i	−0.800521	−	0.0933000i
$756$	2.64409	+	4.11428i	0.0961645	+	0.149635i
$757$	1.09953	+	15.3735i	0.0399632	+	0.558758i	0.977509	+	0.210896i	$0.0676380\pi$
$757$	1.09953	+	15.3735i	0.0399632	+	0.558758i	−0.937545	+	0.347863i	$0.886907\pi$
$758$	−10.4910	−	10.4910i	−0.381050	−	0.381050i
$759$	4.21617	+	8.57733i	0.153037	+	0.311337i
$760$	6.31729	+	10.8671i	0.229152	+	0.394191i
$761$	4.94377	−	5.70541i	0.179211	−	0.206821i	−0.659036	−	0.752112i	$-0.729035\pi$
$761$	4.94377	−	5.70541i	0.179211	−	0.206821i	0.838247	+	0.545291i	$0.183581\pi$
$762$	13.9320	+	3.03071i	0.504702	+	0.109791i
$763$	−17.9227	−	13.4168i	−0.648846	−	0.485720i
$764$	−6.99647	−	15.3201i	−0.253124	−	0.554263i
$765$	−2.54646	−	6.30632i	−0.0920674	−	0.228006i
$766$	−0.843364	−	2.87224i	−0.0304720	−	0.103778i
$767$	−0.212550	−	0.977076i	−0.00767473	−	0.0352802i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	−3.97264	−	1.16647i	−0.143257	−	0.0420640i	0.209318	−	0.977848i	$-0.432876\pi$
$769$	−3.97264	−	1.16647i	−0.143257	−	0.0420640i	−0.352575	+	0.935784i	$0.614694\pi$
$770$	−9.58098	−	19.5749i	−0.345275	−	0.705432i
$771$	−12.0331	−	13.8869i	−0.433361	−	0.500126i
$772$	9.29372	+	17.0202i	0.334488	+	0.612569i
$773$	−44.6251	+	16.6443i	−1.60505	+	0.598654i	−0.982884	−	0.184228i	$-0.941022\pi$
$773$	−44.6251	+	16.6443i	−1.60505	+	0.598654i	−0.622170	+	0.782882i	$0.713749\pi$
$774$	1.63071	+	1.04799i	0.0586145	+	0.0376692i
$775$	−23.3068	−	5.50758i	−0.837204	−	0.197838i
$776$	−13.4430	−	1.93282i	−0.482577	−	0.0693841i
$777$	−15.9741	+	42.8283i	−0.573069	+	1.53646i
$778$	14.4246	−	19.2690i	0.517147	−	0.690827i
$779$	39.7745	−	25.5615i	1.42507	−	0.915836i
$780$	−0.351154	−	0.515520i	−0.0125733	−	0.0184586i
$781$			8.75806i			0.313388i
$782$	−9.07023	−	11.4237i	−0.324351	−	0.408509i
$783$	0.973847	−	0.973847i	0.0348024	−	0.0348024i
$784$	−12.7862	−	11.0793i	−0.456648	−	0.395688i
$785$	−30.9320	−	15.8303i	−1.10401	−	0.565008i
$786$	2.33166	+	16.2170i	0.0831675	+	0.578443i
$787$	27.0209	+	10.0783i	0.963190	+	0.359251i	0.781361	−	0.624079i	$-0.214526\pi$
$787$	27.0209	+	10.0783i	0.963190	+	0.359251i	0.181829	+	0.983330i	$0.441798\pi$
$788$	−8.68297	−	11.5991i	−0.309318	−	0.413201i
$789$	−25.6912	+	7.54362i	−0.914632	+	0.268560i
$790$	−16.8858	−	0.754045i	−0.600771	−	0.0268277i
$791$	9.25012	−	20.2549i	0.328896	−	0.720183i
$792$	1.74912	−	0.955089i	0.0621521	−	0.0339376i
$793$	0.295943	−	4.13783i	0.0105093	−	0.146939i
$794$	−25.1280	+	21.7735i	−0.891759	+	0.772713i
$795$	−6.18968	+	10.2231i	−0.219525	+	0.362576i
$796$	17.2519	+	7.87868i	0.611478	+	0.279252i
$797$	−30.5388	+	6.64331i	−1.08174	+	0.235318i	−0.717902	−	0.696144i	$-0.754897\pi$
$797$	−30.5388	+	6.64331i	−1.08174	+	0.235318i	−0.363838	+	0.931462i	$0.618534\pi$
$798$	−13.1757	+	24.1295i	−0.466416	+	0.854177i
$799$	0.926955	−	6.44711i	0.0327933	−	0.228082i
$800$	−3.83659	+	3.20633i	−0.135644	+	0.113361i
$801$	2.01149	−	0.289209i	0.0710726	−	0.0102187i
$802$	6.22397	−	28.6111i	0.219776	−	1.01029i
$803$	−9.57837	+	0.685058i	−0.338013	+	0.0241752i
$804$	−14.5955			−0.514744
$805$	19.1199	−	48.8371i	0.673888	−	1.72128i
$806$	−1.33610			−0.0470623
$807$	−16.5347	+	1.18258i	−0.582049	+	0.0416290i
$808$	−3.21026	+	14.7573i	−0.112937	+	0.519161i
$809$	20.0206	−	2.87853i	0.703887	−	0.101204i	0.218929	−	0.975741i	$-0.429744\pi$
$809$	20.0206	−	2.87853i	0.703887	−	0.101204i	0.484958	+	0.874537i	$0.338835\pi$
$810$	1.82530	+	1.29162i	0.0641344	+	0.0453830i
$811$	−3.26494	+	22.7082i	−0.114648	+	0.797392i	0.848650	+	0.528955i	$0.177416\pi$
$811$	−3.26494	+	22.7082i	−0.114648	+	0.797392i	−0.963297	+	0.268437i	$0.913493\pi$
$812$	−3.22800	+	5.91164i	−0.113281	+	0.207458i
$813$	−9.96068	+	2.16681i	−0.349336	+	0.0759935i
$814$	16.9432	+	7.73772i	0.593860	+	0.271207i
$815$	−0.676399	−	2.75240i	−0.0236932	−	0.0964124i
$816$	−2.29863	+	1.99177i	−0.0804680	+	0.0697259i
$817$	−0.777362	+	10.8689i	−0.0271964	+	0.380256i
$818$	−23.1110	+	12.6196i	−0.808058	+	0.441233i
$819$	0.566733	−	1.24097i	0.0198032	−	0.0433630i
$820$	12.6920	+	13.8785i	0.443222	+	0.484657i
$821$	35.5660	−	10.4431i	1.24126	−	0.364468i	0.405773	−	0.913974i	$-0.367002\pi$
$821$	35.5660	−	10.4431i	1.24126	−	0.364468i	0.835490	+	0.549506i	$0.185184\pi$
$822$	2.82351	+	3.77177i	0.0984812	+	0.131555i
$823$	−29.0163	−	10.8225i	−1.01144	−	0.377249i	−0.211535	−	0.977370i	$-0.567846\pi$
$823$	−29.0163	−	10.8225i	−1.01144	−	0.377249i	−0.799909	+	0.600121i	$0.795119\pi$
$824$	−0.870867	−	6.05701i	−0.0303381	−	0.211006i
$825$	−7.41294	−	6.65871i	−0.258085	−	0.231826i
$826$	−13.2490	−	11.4804i	−0.460993	−	0.399453i
$827$	−17.1328	+	17.1328i	−0.595764	+	0.595764i	−0.939183	−	0.343418i	$-0.888415\pi$
$827$	−17.1328	+	17.1328i	−0.595764	+	0.595764i	0.343418	+	0.939183i	$0.388415\pi$
$828$	4.53933	+	1.54741i	0.157753	+	0.0537761i
$829$			0.451620i			0.0156854i	0.999969	+	0.00784270i	$0.00249644\pi$
$829$			0.451620i			0.0156854i	−0.999969	+	0.00784270i	$0.997504\pi$
$830$	8.14775	−	5.54996i	0.282813	−	0.192642i
$831$	−13.2572	+	8.51989i	−0.459887	+	0.295552i
$832$	−0.167169	+	0.223312i	−0.00579556	+	0.00774196i
$833$	−17.9827	+	48.2135i	−0.623064	+	1.67050i
$834$	−1.17827	−	0.169410i	−0.0408003	−	0.00586619i
$835$	17.9477	−	18.9355i	0.621107	−	0.655290i
$836$	9.42445	+	6.05673i	0.325951	+	0.209476i
$837$	4.48774	−	1.67384i	0.155119	−	0.0578564i
$838$	6.00653	+	11.0001i	0.207492	+	0.379993i
$839$	31.2729	+	36.0909i	1.07966	+	1.24600i	0.967652	+	0.252288i	$0.0811830\pi$
$839$	31.2729	+	36.0909i	1.07966	+	1.24600i	0.112009	+	0.993707i	$0.464271\pi$
$840$	−10.3450	−	3.54601i	−0.356935	−	0.122349i
$841$	−26.0054	−	7.63587i	−0.896737	−	0.263306i
$842$	−5.78917	−	15.5214i	−0.199508	−	0.534902i
$843$	−3.72821	−	17.1383i	−0.128406	−	0.590274i
$844$	4.12711	+	14.0556i	0.142061	+	0.483815i
$845$	11.2954	−	26.5956i	0.388575	−	0.914918i
$846$	0.889611	+	1.94798i	0.0305855	+	0.0669728i
$847$	27.5174	+	20.5993i	0.945509	+	0.707799i
$848$	5.22246	+	1.13608i	0.179340	+	0.0390130i
$849$	−18.0420	+	20.8216i	−0.619200	+	0.714594i
$850$	13.2152	+	7.52532i	0.453276	+	0.258116i
$851$	13.8473	+	42.6316i	0.474681	+	1.46139i
$852$	3.10749	+	3.10749i	0.106461	+	0.106461i
$853$	0.666179	+	9.31440i	0.0228095	+	0.318919i	0.996028	+	0.0890378i	$0.0283792\pi$
$853$	0.666179	+	9.31440i	0.0228095	+	0.318919i	−0.973219	+	0.229881i	$0.926166\pi$
$854$	−39.3213	−	61.1851i	−1.34555	−	2.09371i
$855$	−1.45516	+	12.4854i	−0.0497654	+	0.426991i
$856$	−0.780572	+	0.356475i	−0.0266794	+	0.0121841i
$857$	22.1283	−	16.5650i	0.755887	−	0.565850i	−0.150343	−	0.988634i	$-0.548038\pi$
$857$	22.1283	−	16.5650i	0.755887	−	0.565850i	0.906231	+	0.422784i	$0.138947\pi$
$858$	−0.487919	−	0.266424i	−0.0166573	−	0.00909555i
$859$	25.1268	−	39.0981i	0.857316	−	1.33401i	−0.0839936	−	0.996466i	$-0.526768\pi$
$859$	25.1268	−	39.0981i	0.857316	−	1.33401i	0.941310	−	0.337544i	$-0.109596\pi$
$860$	−4.31357	+	0.424846i	−0.147092	+	0.0144871i
$861$	−11.5887	+	39.4675i	−0.394942	+	1.34505i
$862$	19.9004	+	1.42330i	0.677809	+	0.0484778i
$863$	−14.4407	−	1.03282i	−0.491567	−	0.0351576i	−0.176644	−	0.984275i	$-0.556524\pi$
$863$	−14.4407	−	1.03282i	−0.491567	−	0.0351576i	−0.314923	+	0.949117i	$0.601979\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	−18.0537	+	1.77812i	−0.613844	+	0.0604578i
$866$	20.2962	−	31.5815i	0.689692	−	1.07318i
$867$	−6.80128	−	3.71378i	−0.230984	−	0.126127i
$868$	−18.7526	+	14.0380i	−0.636506	+	0.476482i
$869$	−13.7031	+	6.25800i	−0.464846	+	0.212288i
$870$	−0.356508	+	3.05887i	−0.0120868	+	0.103705i
$871$	2.20119	+	3.42511i	0.0745844	+	0.116056i
$872$	0.326574	+	4.56610i	0.0110592	+	0.154628i
$873$	−9.60341	−	9.60341i	−0.325026	−	0.325026i
$874$	4.59464	+	26.5650i	0.155416	+	0.898574i
$875$	0.487856	+	54.6770i	0.0164926	+	1.84842i
$876$	−3.15548	+	3.64162i	−0.106614	+	0.123039i
$877$	−15.1749	−	3.30111i	−0.512422	−	0.111470i	−0.0510826	−	0.998694i	$-0.516267\pi$
$877$	−15.1749	−	3.30111i	−0.512422	−	0.111470i	−0.461339	+	0.887224i	$0.652631\pi$
$878$	−24.2489	−	18.1525i	−0.818359	−	0.612616i
$879$	−11.7081	−	25.6372i	−0.394905	−	0.864722i
$880$	−1.74201	+	4.10164i	−0.0587230	+	0.138266i
$881$	9.48142	+	32.2907i	0.319437	+	1.08790i	0.950126	+	0.311867i	$0.100954\pi$
$881$	9.48142	+	32.2907i	0.319437	+	1.08790i	−0.630689	+	0.776036i	$0.717228\pi$
$882$	−3.59629	−	16.5319i	−0.121093	−	0.556657i
$883$	−0.134351	−	0.360208i	−0.00452126	−	0.0121220i	0.934669	−	0.355518i	$-0.115695\pi$
$883$	−0.134351	−	0.360208i	−0.00452126	−	0.0121220i	−0.939191	+	0.343396i	$0.888423\pi$
$884$	0.814069	+	0.239032i	0.0273801	+	0.00803952i
$885$	−7.58231	−	2.59904i	−0.254877	−	0.0873657i
$886$	−4.46359	−	5.15126i	−0.149957	−	0.173060i
$887$	23.1373	+	42.3727i	0.776873	+	1.42274i	0.902514	+	0.430661i	$0.141720\pi$
$887$	23.1373	+	42.3727i	0.776873	+	1.42274i	−0.125640	+	0.992076i	$0.540099\pi$
$888$	8.75718	−	3.26626i	0.293872	−	0.109608i
$889$	−58.6606	−	37.6989i	−1.96741	−	1.26438i
$890$	−3.12598	+	3.29802i	−0.104783	+	0.110550i
$891$	1.97260	+	0.283617i	0.0660847	+	0.00950154i
$892$	2.89900	−	7.77253i	0.0970658	−	0.260244i
$893$	−7.21427	+	9.63714i	−0.241416	+	0.322495i
$894$	−9.95885	+	6.40017i	−0.333074	+	0.214054i
$895$	−28.5253	+	19.4305i	−0.953497	+	0.649489i
$896$			4.89066i			0.163385i
$897$	−0.321460	−	1.29861i	−0.0107332	−	0.0433593i
$898$	−9.55588	+	9.55588i	−0.318884	+	0.318884i
$899$	4.98534	+	4.31982i	0.166270	+	0.144074i
$900$	−4.99283	+	0.267612i	−0.166428	+	0.00892041i
$901$	−2.31343	−	16.0902i	−0.0770715	−	0.536044i
$902$	15.7047	+	5.85756i	0.522910	+	0.195035i
$903$	−5.68125	−	7.58926i	−0.189060	−	0.252555i
$904$	−4.36858	+	1.28273i	−0.145297	+	0.0426630i
$905$	12.7577	+	13.9503i	0.424080	+	0.463725i
$906$	−4.11408	+	9.00859i	−0.136681	+	0.299290i
$907$	−19.3754	+	10.5798i	−0.643349	+	0.351295i	−0.767575	−	0.640959i	$-0.778537\pi$
$907$	−19.3754	+	10.5798i	−0.643349	+	0.351295i	0.124226	+	0.992254i	$0.460355\pi$
$908$	−0.833442	+	11.6530i	−0.0276588	+	0.386720i
$909$	−11.4137	+	9.89002i	−0.378568	+	0.328031i
$910$	0.728013	+	2.96243i	0.0241334	+	0.0982035i
$911$	−35.2081	−	16.0790i	−1.16650	−	0.532721i	−0.264467	−	0.964395i	$-0.585196\pi$
$911$	−35.2081	−	16.0790i	−1.16650	−	0.532721i	−0.902030	+	0.431673i	$0.857923\pi$
$912$	5.49296	−	1.19492i	0.181890	−	0.0395678i
$913$	4.21080	−	7.71151i	0.139357	−	0.255214i
$914$	−0.945350	+	6.57506i	−0.0312694	+	0.217483i
$915$	−27.1447	−	19.2082i	−0.897376	−	0.635005i
$916$	15.0880	−	2.16933i	0.498522	−	0.0716766i
$917$	17.0323	−	78.2964i	0.562457	−	2.58557i
$918$	−3.03377	+	0.216979i	−0.100129	+	0.00716139i
$919$	12.9002			0.425538			0.212769	−	0.977103i	$-0.431752\pi$
$919$	12.9002			0.425538			0.212769	+	0.977103i	$0.431752\pi$
$920$	−10.1069	+	3.58472i	−0.333215	+	0.118185i
$921$	20.1744			0.664770
$922$	−37.9364	+	2.71326i	−1.24937	+	0.0893566i
$923$	0.260583	−	1.19788i	0.00857721	−	0.0394288i
$924$	−9.64732	+	1.38707i	−0.317373	+	0.0456314i
$925$	−29.9679	−	35.8586i	−0.985338	−	1.17903i
$926$	−2.57292	+	17.8950i	−0.0845513	+	0.588067i
$927$	2.93267	−	5.37078i	0.0963214	−	0.176400i
$928$	1.34575	−	0.292751i	0.0441765	−	0.00961001i
$929$	49.6568	+	22.6775i	1.62919	+	0.744025i	0.999462	−	0.0327940i	$-0.0104405\pi$
$929$	49.6568	+	22.6775i	1.62919	+	0.744025i	0.629724	+	0.776819i	$0.283168\pi$
$930$	−5.54708	+	9.16175i	−0.181896	+	0.300426i
$931$	71.8764	−	62.2813i	2.35565	−	2.04119i
$932$	0.998359	−	13.9589i	0.0327023	−	0.457238i
$933$	−4.89787	+	2.67444i	−0.160349	+	0.0875571i
$934$	1.81529	−	3.97493i	0.0593980	−	0.130064i
$935$	13.5402	+	0.604644i	0.442812	+	0.0197740i
$936$	−0.267652	+	0.0785898i	−0.00874848	+	0.00256879i
$937$	16.6912	+	22.2969i	0.545278	+	0.728407i	0.985536	−	0.169465i	$-0.0542039\pi$
$937$	16.6912	+	22.2969i	0.545278	+	0.728407i	−0.440258	+	0.897871i	$0.645113\pi$
$938$	66.8810	+	24.9453i	2.18374	+	0.814493i
$939$	2.44274	+	16.9897i	0.0797160	+	0.554437i
$940$	−4.26273	−	2.18157i	−0.139035	−	0.0711549i
$941$	−15.4959	−	13.4273i	−0.505152	−	0.437717i	0.364630	−	0.931152i	$-0.381195\pi$
$941$	−15.4959	−	13.4273i	−0.505152	−	0.437717i	−0.869782	+	0.493436i	$0.835741\pi$
$942$	−10.9881	+	10.9881i	−0.358012	+	0.358012i
$943$	15.1660	+	37.3765i	0.493872	+	1.21715i
$944$			3.58459i			0.116668i
$945$	−6.15653	−	9.03824i	−0.200272	−	0.294014i
$946$	−3.24981	+	2.08853i	−0.105660	+	0.0679039i
$947$	5.94758	−	7.94503i	0.193270	−	0.258179i	−0.693430	−	0.720524i	$-0.743901\pi$
$947$	5.94758	−	7.94503i	0.193270	−	0.258179i	0.886700	+	0.462346i	$0.152992\pi$
$948$	−2.64164	+	7.08250i	−0.0857964	+	0.230029i
$949$	1.33046	+	0.191292i	0.0431886	+	0.00620959i
$950$	−14.7714	−	23.9127i	−0.479246	−	0.775831i
$951$	−24.3887	−	15.6737i	−0.790858	−	0.508253i
$952$	13.9371	−	5.19829i	0.451705	−	0.168477i
$953$	−15.3159	−	28.0491i	−0.496132	−	0.908598i	−0.999021	−	0.0442468i	$-0.985911\pi$
$953$	−15.3159	−	28.0491i	−0.496132	−	0.908598i	0.502889	−	0.864351i	$-0.332271\pi$
$954$	3.49997	+	4.03918i	0.113316	+	0.130773i
$955$	16.5561	+	33.8258i	0.535742	+	1.09458i
$956$	−1.53778	−	0.451533i	−0.0497354	−	0.0146036i
$957$	0.959160	+	2.57161i	0.0310052	+	0.0831282i
$958$	7.70064	+	35.3993i	0.248796	+	1.14370i
$959$	−6.49180	−	22.1090i	−0.209631	−	0.713938i
$960$	0.837233	+	2.07341i	0.0270216	+	0.0669191i
$961$	−3.34760	−	7.33021i	−0.107987	−	0.236458i
$962$	−2.08718	−	1.56245i	−0.0672935	−	0.0503753i
$963$	−0.838508	−	0.182406i	−0.0270205	−	0.00587796i
$964$	16.1613	−	18.6512i	0.520521	−	0.600714i
$965$	−21.7928	−	37.4883i	−0.701535	−	1.20679i
$966$	−18.1559	−	14.8489i	−0.584156	−	0.477755i
$967$	−14.1553	−	14.1553i	−0.455204	−	0.455204i	0.441874	−	0.897077i	$-0.354314\pi$
$967$	−14.1553	−	14.1553i	−0.455204	−	0.455204i	−0.897077	+	0.441874i	$0.854314\pi$
$968$	−0.501400	−	7.01049i	−0.0161156	−	0.225326i
$969$	−9.24370	−	14.3835i	−0.296950	−	0.462064i
$970$	30.1645	+	3.51564i	0.968523	+	0.112880i
$971$	−37.7870	+	17.2568i	−1.21264	+	0.553796i	−0.915994	−	0.401191i	$-0.868596\pi$
$971$	−37.7870	+	17.2568i	−1.21264	+	0.553796i	−0.296649	+	0.954987i	$0.595869\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	5.10966	+	2.79009i	0.163808	+	0.0894460i
$974$	−0.325363	+	0.506274i	−0.0104253	+	0.0162221i
$975$	0.815783	+	1.13130i	0.0261260	+	0.0362307i
$976$	−4.18975	+	14.2690i	−0.134111	+	0.456739i
$977$	−10.1623	−	0.726825i	−0.325122	−	0.0232532i	−0.0921756	−	0.995743i	$-0.529382\pi$
$977$	−10.1623	−	0.726825i	−0.325122	−	0.0232532i	−0.232946	+	0.972490i	$0.574837\pi$
$978$	−1.26431	−	0.0904249i	−0.0404280	−	0.00289147i
$979$	−1.14099	+	3.88585i	−0.0364661	+	0.124192i
$980$	29.2437	+	23.9997i	0.934155	+	0.766643i
$981$	−2.47492	+	3.85106i	−0.0790183	+	0.122955i
$982$	−7.61434	−	4.15775i	−0.242984	−	0.132679i
$983$	33.5305	−	25.1006i	1.06946	−	0.800585i	0.0887470	−	0.996054i	$-0.471714\pi$
$983$	33.5305	−	25.1006i	1.06946	−	0.800585i	0.980710	+	0.195469i	$0.0626228\pi$
$984$	7.65063	−	3.49392i	0.243893	−	0.111382i
$985$	20.1031	+	25.4073i	0.640538	+	0.809544i
$986$	−2.26467	−	3.52389i	−0.0721218	−	0.112224i
$987$	−0.747159	−	10.4467i	−0.0237823	−	0.332521i
$988$	−1.10882	−	1.10882i	−0.0352762	−	0.0352762i
$989$	−8.99071	−	2.36416i	−0.285888	−	0.0751760i
$990$	−3.85257	+	2.23958i	−0.122443	+	0.0711786i
$991$	−29.3818	+	33.9084i	−0.933344	+	1.07714i	0.0635181	+	0.997981i	$0.479768\pi$
$991$	−29.3818	+	33.9084i	−0.933344	+	1.07714i	−0.996862	+	0.0791558i	$0.974778\pi$
$992$	4.68027	+	1.01813i	0.148599	+	0.0323257i
$993$	−24.5288	−	18.3620i	−0.778397	−	0.582701i
$994$	−8.92842	−	19.5505i	−0.283192	−	0.620105i
$995$	−39.0342	−	16.5782i	−1.23747	−	0.525565i
$996$	−1.24210	−	4.23022i	−0.0393576	−	0.134040i
$997$	−1.17950	−	5.42208i	−0.0373552	−	0.171719i	0.954690	−	0.297603i	$-0.0961871\pi$
$997$	−1.17950	−	5.42208i	−0.0373552	−	0.171719i	−0.992045	+	0.125884i	$0.959823\pi$
$998$	8.54015	+	22.8970i	0.270334	+	0.724793i
$999$	8.96788	+	2.63321i	0.283731	+	0.0833110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.1	✓	240
5.3	odd	4	inner	690.2.w.a.283.8	yes	240
23.10	odd	22	inner	690.2.w.a.217.8	yes	240
115.33	even	44	inner	690.2.w.a.493.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.1	✓	240	1.1	even	1	trivial
690.2.w.a.217.8	yes	240	23.10	odd	22	inner
690.2.w.a.283.8	yes	240	5.3	odd	4	inner
690.2.w.a.493.1	yes	240	115.33	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.20400 + 0.377364i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(2.34384 - 4.29243i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.20400 + 0.377364i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(2.34384 - 4.29243i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(2.17146 - 0.533633i) q^{10} +(1.50612 - 1.30506i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(-0.244830 + 0.133687i) q^{13} +(-2.03165 + 4.44870i) q^{14} +(-0.0997532 + 2.23384i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-1.82271 - 2.43486i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.800012 + 5.56421i) q^{19} +(-2.12786 + 0.687184i) q^{20} +(-3.69611 - 3.20270i) q^{21} +(-1.40918 + 1.40918i) q^{22} +(-4.79141 - 0.205848i) q^{23} +1.00000i q^{24} +(4.71519 - 1.66342i) q^{25} +(0.234669 - 0.150813i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(1.70911 - 4.58230i) q^{28} +(-1.36321 - 0.196000i) q^{29} +(-0.0598614 - 2.23527i) q^{30} +(-4.02938 - 2.58953i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-0.955089 - 1.74912i) q^{33} +(1.99177 + 2.29863i) q^{34} +(-3.54601 + 10.3450i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.26626 - 8.75718i) q^{37} +(-1.19492 - 5.49296i) q^{38} +(0.0785898 + 0.267652i) q^{39} +(2.07341 - 0.837233i) q^{40} +(-3.49392 - 7.65063i) q^{41} +(3.91517 + 2.93086i) q^{42} +(1.89412 + 0.412041i) q^{43} +(1.30506 - 1.50612i) q^{44} +(2.16159 + 0.572311i) q^{45} +(4.79389 - 0.136492i) q^{46} +(1.51427 + 1.51427i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(-9.14684 - 14.2328i) q^{49} +(-4.58451 + 1.99556i) q^{50} +(-2.76666 + 1.26349i) q^{51} +(-0.223312 + 0.167169i) q^{52} +(4.69085 + 2.56140i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-2.82701 + 3.44471i) q^{55} +(-1.37786 + 4.69255i) q^{56} +(5.60710 + 0.401028i) q^{57} +(1.37372 + 0.0982503i) q^{58} +(-1.00990 + 3.43939i) q^{59} +(0.219171 + 2.22530i) q^{60} +(-8.04008 + 12.5106i) q^{61} +(4.20385 + 2.29548i) q^{62} +(-3.91517 + 2.93086i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.489156 - 0.387036i) q^{65} +(1.07744 + 1.67652i) q^{66} +(-1.04123 - 14.5583i) q^{67} +(-2.15068 - 2.15068i) q^{68} +(-1.21963 + 4.63816i) q^{69} +(2.79897 - 10.5716i) q^{70} +(-2.87789 + 3.32126i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-3.85745 - 2.88765i) q^{73} +(3.88267 + 8.50186i) q^{74} +(-0.623115 - 4.96102i) q^{75} +(1.58374 + 5.39372i) q^{76} +(-2.07177 - 9.52378i) q^{77} +(-0.0974836 - 0.261364i) q^{78} +(-7.25291 - 2.12965i) q^{79} +(-2.00840 + 0.983015i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.03081 + 7.38188i) q^{82} +(4.13083 - 1.54072i) q^{83} +(-4.11428 - 2.64409i) q^{84} +(4.93608 + 4.67860i) q^{85} +(-1.91869 - 0.275866i) q^{86} +(-0.481292 + 1.29039i) q^{87} +(-1.19429 + 1.59539i) q^{88} +(-1.70958 + 1.09868i) q^{89} +(-2.19691 - 0.416647i) q^{90} +1.36426i q^{91} +(-4.77194 + 0.478136i) q^{92} +(-3.38685 + 3.38685i) q^{93} +(-1.61844 - 1.40238i) q^{94} +(-3.86295 - 11.9616i) q^{95} +(0.142315 + 0.989821i) q^{96} +(12.7250 + 4.74617i) q^{97} +(10.1389 + 13.5440i) q^{98} +(-1.91216 + 0.561461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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