LMFDB - Embedded newform 690.2.w.b.217.9

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			217.9
Character	$\chi$	$=$	690.217
Dual form			690.2.w.b.283.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0962341 + 2.23400i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.35425 + 1.83156i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0962341 + 2.23400i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.35425 + 1.83156i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(2.22144 + 0.255360i) q^{10} +(1.05421 + 0.913477i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(2.41058 - 4.41465i) q^{13} +(1.58760 + 3.47637i) q^{14} +(-0.380835 - 2.20340i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-6.18092 - 4.62698i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(0.753219 - 5.23875i) q^{19} +(0.413185 - 2.19756i) q^{20} +(2.88827 - 2.50270i) q^{21} +(0.986355 - 0.986355i) q^{22} +(-0.367647 - 4.78172i) q^{23} -1.00000i q^{24} +(-4.98148 - 0.429973i) q^{25} +(-4.23143 - 2.71937i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(3.58077 - 1.33556i) q^{28} +(5.88683 - 0.846398i) q^{29} +(-2.22495 + 0.222676i) q^{30} +(-8.20400 + 5.27239i) q^{31} +(0.349464 - 0.936950i) q^{32} +(-1.22429 - 0.668513i) q^{33} +(-5.05613 + 5.83508i) q^{34} +(-3.76891 - 7.66965i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.31954 + 0.492162i) q^{37} +(-5.17167 - 1.12503i) q^{38} +(-1.41709 + 4.82616i) q^{39} +(-2.16249 - 0.568905i) q^{40} +(2.71326 - 5.94121i) q^{41} +(-2.29028 - 3.05945i) q^{42} +(-0.905943 - 4.16455i) q^{43} +(-0.913477 - 1.05421i) q^{44} +(0.840498 + 2.07209i) q^{45} +(-4.79576 + 0.0255868i) q^{46} +(7.10477 + 7.10477i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(4.11192 - 6.39827i) q^{49} +(-0.784252 + 4.93811i) q^{50} +(7.02320 + 3.20739i) q^{51} +(-3.01431 + 4.02665i) q^{52} +(-1.36051 - 2.49158i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-2.14215 + 2.26719i) q^{55} +(-1.07671 - 3.66692i) q^{56} +(0.377572 + 5.27914i) q^{57} +(-0.424280 - 5.93221i) q^{58} +(1.11079 + 3.78300i) q^{59} +(0.0633826 + 2.23517i) q^{60} +(-1.03298 - 1.60735i) q^{61} +(4.67369 + 8.55923i) q^{62} +(-2.29028 + 3.05945i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(9.63032 + 5.81006i) q^{65} +(-0.754149 + 1.17348i) q^{66} +(-11.5329 - 0.824851i) q^{67} +(5.45952 + 5.45952i) q^{68} +(1.37567 + 4.59429i) q^{69} +(-7.91898 + 3.21216i) q^{70} +(-2.57260 - 2.96894i) q^{71} +(0.212565 + 0.977147i) q^{72} +(-4.69436 - 6.27093i) q^{73} +(0.585043 - 1.28107i) q^{74} +(4.95903 - 0.638742i) q^{75} +(-1.49111 + 5.07824i) q^{76} +(-5.20917 - 1.13319i) q^{77} +(4.71277 + 1.75777i) q^{78} +(-7.27596 + 2.13642i) q^{79} +(-0.721725 + 2.11639i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-5.73251 - 3.13019i) q^{82} +(3.07677 - 8.24914i) q^{83} +(-3.21505 + 2.06618i) q^{84} +(10.9315 - 13.3629i) q^{85} +(-4.21857 + 0.606539i) q^{86} +(-5.57238 + 2.07839i) q^{87} +(-1.11669 + 0.835943i) q^{88} +(0.749222 + 0.481496i) q^{89} +(2.12677 - 0.690535i) q^{90} +19.2230i q^{91} +(-0.316604 + 4.78537i) q^{92} +(6.89579 - 6.89579i) q^{93} +(7.59352 - 6.57982i) q^{94} +(11.6309 + 2.18684i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-1.71270 - 4.59194i) q^{97} +(-6.08862 - 4.55789i) q^{98} +(1.33841 + 0.392994i) 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} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−0.0962341	+	2.23400i	−0.0430372	+	0.999073i
$5$	−0.0962341	+	2.23400i	−0.0430372	+	0.999073i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−3.35425	+	1.83156i	−1.26779	+	0.692265i	−0.965364	−	0.260908i	$-0.915978\pi$
$7$	−3.35425	+	1.83156i	−1.26779	+	0.692265i	−0.302425	+	0.953173i	$0.597796\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	2.22144	+	0.255360i	0.702481	+	0.0807520i
$11$	1.05421	+	0.913477i	0.317856	+	0.275424i	0.799145	−	0.601138i	$-0.205286\pi$
$11$	1.05421	+	0.913477i	0.317856	+	0.275424i	−0.481289	+	0.876562i	$0.659831\pi$
$12$	0.997452	−	0.0713392i	0.287940	−	0.0205938i
$13$	2.41058	−	4.41465i	0.668574	−	1.22440i	−0.294625	−	0.955613i	$-0.595195\pi$
$13$	2.41058	−	4.41465i	0.668574	−	1.22440i	0.963199	−	0.268789i	$-0.0866236\pi$
$14$	1.58760	+	3.47637i	0.424305	+	0.929099i
$15$	−0.380835	−	2.20340i	−0.0983312	−	0.568915i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−6.18092	−	4.62698i	−1.49909	−	1.12221i	−0.960014	−	0.279951i	$-0.909682\pi$
$17$	−6.18092	−	4.62698i	−1.49909	−	1.12221i	−0.539079	−	0.842255i	$-0.681227\pi$
$18$	−0.349464	−	0.936950i	−0.0823695	−	0.220841i
$19$	0.753219	−	5.23875i	0.172800	−	1.20185i	−0.700133	−	0.714013i	$-0.746876\pi$
$19$	0.753219	−	5.23875i	0.172800	−	1.20185i	0.872933	−	0.487840i	$-0.162215\pi$
$20$	0.413185	−	2.19756i	0.0923911	−	0.491390i
$21$	2.88827	−	2.50270i	0.630273	−	0.546134i
$22$	0.986355	−	0.986355i	0.210292	−	0.210292i
$23$	−0.367647	−	4.78172i	−0.0766598	−	0.997057i
$23$	−0.367647	−	4.78172i	−0.0766598	−	0.997057i
$24$		−	1.00000i		−	0.204124i
$25$	−4.98148	−	0.429973i	−0.996296	−	0.0859946i
$26$	−4.23143	−	2.71937i	−0.829852	−	0.533313i
$27$	−0.800541	+	0.599278i	−0.154064	+	0.115331i
$28$	3.58077	−	1.33556i	0.676702	−	0.252397i
$29$	5.88683	−	0.846398i	1.09316	−	0.157172i	0.427928	−	0.903813i	$-0.359244\pi$
$29$	5.88683	−	0.846398i	1.09316	−	0.157172i	0.665228	+	0.746640i	$0.268334\pi$
$30$	−2.22495	+	0.222676i	−0.406219	+	0.0406549i
$31$	−8.20400	+	5.27239i	−1.47348	+	0.946949i	−0.475754	+	0.879578i	$0.657825\pi$
$31$	−8.20400	+	5.27239i	−1.47348	+	0.946949i	−0.997728	+	0.0673712i	$0.978539\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	−1.22429	−	0.668513i	−0.213121	−	0.116373i
$34$	−5.05613	+	5.83508i	−0.867119	+	1.00071i
$35$	−3.76891	−	7.66965i	−0.637062	−	1.29641i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	1.31954	+	0.492162i	0.216931	+	0.0809110i	0.455580	−	0.890195i	$-0.349432\pi$
$37$	1.31954	+	0.492162i	0.216931	+	0.0809110i	−0.238649	+	0.971106i	$0.576705\pi$
$38$	−5.17167	−	1.12503i	−0.838956	−	0.182504i
$39$	−1.41709	+	4.82616i	−0.226916	+	0.772805i
$40$	−2.16249	−	0.568905i	−0.341919	−	0.0899518i
$41$	2.71326	−	5.94121i	0.423740	−	0.927860i	−0.570562	−	0.821255i	$-0.693274\pi$
$41$	2.71326	−	5.94121i	0.423740	−	0.927860i	0.994301	−	0.106606i	$-0.0339983\pi$
$42$	−2.29028	−	3.05945i	−0.353398	−	0.472084i
$43$	−0.905943	−	4.16455i	−0.138155	−	0.635088i	−0.993189	−	0.116516i	$-0.962827\pi$
$43$	−0.905943	−	4.16455i	−0.138155	−	0.635088i	0.855034	−	0.518572i	$-0.173536\pi$
$44$	−0.913477	−	1.05421i	−0.137712	−	0.158928i
$45$	0.840498	+	2.07209i	0.125294	+	0.308889i
$46$	−4.79576	+	0.0255868i	−0.707097	+	0.00377256i
$47$	7.10477	+	7.10477i	1.03634	+	1.03634i	0.999314	+	0.0370233i	$0.0117876\pi$
$47$	7.10477	+	7.10477i	1.03634	+	1.03634i	0.0370233	+	0.999314i	$0.488212\pi$
$48$	−0.997452	−	0.0713392i	−0.143970	−	0.0102969i
$49$	4.11192	−	6.39827i	0.587417	−	0.914038i
$50$	−0.784252	+	4.93811i	−0.110910	+	0.698354i
$51$	7.02320	+	3.20739i	0.983445	+	0.449124i
$52$	−3.01431	+	4.02665i	−0.418010	+	0.558396i
$53$	−1.36051	−	2.49158i	−0.186880	−	0.342245i	0.767395	−	0.641174i	$-0.221552\pi$
$53$	−1.36051	−	2.49158i	−0.186880	−	0.342245i	−0.954275	+	0.298929i	$0.903371\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	−2.14215	+	2.26719i	−0.288848	+	0.305708i
$56$	−1.07671	−	3.66692i	−0.143881	−	0.490013i
$57$	0.377572	+	5.27914i	0.0500106	+	0.699239i
$58$	−0.424280	−	5.93221i	−0.0557107	−	0.778937i
$59$	1.11079	+	3.78300i	0.144612	+	0.492505i	0.999661	−	0.0260435i	$-0.00829085\pi$
$59$	1.11079	+	3.78300i	0.144612	+	0.492505i	−0.855048	+	0.518548i	$0.826473\pi$
$60$	0.0633826	+	2.23517i	0.00818265	+	0.288559i
$61$	−1.03298	−	1.60735i	−0.132259	−	0.205800i	0.768807	−	0.639481i	$-0.220851\pi$
$61$	−1.03298	−	1.60735i	−0.132259	−	0.205800i	−0.901066	+	0.433681i	$0.857214\pi$
$62$	4.67369	+	8.55923i	0.593559	+	1.08702i
$63$	−2.29028	+	3.05945i	−0.288548	+	0.385455i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	9.63032	+	5.81006i	1.19449	+	0.720650i
$66$	−0.754149	+	1.17348i	−0.0928294	+	0.144445i
$67$	−11.5329	−	0.824851i	−1.40897	−	0.100772i	−0.653983	−	0.756510i	$-0.726903\pi$
$67$	−11.5329	−	0.824851i	−1.40897	−	0.100772i	−0.754989	+	0.655738i	$0.772358\pi$
$68$	5.45952	+	5.45952i	0.662064	+	0.662064i
$69$	1.37567	+	4.59429i	0.165612	+	0.553088i
$70$	−7.91898	+	3.21216i	−0.946499	+	0.383926i
$71$	−2.57260	−	2.96894i	−0.305312	−	0.352348i	0.582273	−	0.812993i	$-0.302164\pi$
$71$	−2.57260	−	2.96894i	−0.305312	−	0.352348i	−0.887584	+	0.460645i	$0.847618\pi$
$72$	0.212565	+	0.977147i	0.0250511	+	0.115158i
$73$	−4.69436	−	6.27093i	−0.549434	−	0.733957i	0.436756	−	0.899580i	$-0.356127\pi$
$73$	−4.69436	−	6.27093i	−0.549434	−	0.733957i	−0.986189	+	0.165623i	$0.947037\pi$
$74$	0.585043	−	1.28107i	0.0680099	−	0.148921i
$75$	4.95903	−	0.638742i	0.572620	−	0.0737556i
$76$	−1.49111	+	5.07824i	−0.171041	+	0.582514i
$77$	−5.20917	−	1.13319i	−0.593640	−	0.129138i
$78$	4.71277	+	1.75777i	0.533616	+	0.199029i
$79$	−7.27596	+	2.13642i	−0.818610	+	0.240366i	−0.664117	−	0.747628i	$-0.731192\pi$
$79$	−7.27596	+	2.13642i	−0.818610	+	0.240366i	−0.154493	+	0.987994i	$0.549374\pi$
$80$	−0.721725	+	2.11639i	−0.0806914	+	0.236620i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−5.73251	−	3.13019i	−0.633049	−	0.345671i
$83$	3.07677	−	8.24914i	0.337720	−	0.905461i	−0.651451	−	0.758691i	$-0.725839\pi$
$83$	3.07677	−	8.24914i	0.337720	−	0.905461i	0.989171	−	0.146771i	$-0.0468879\pi$
$84$	−3.21505	+	2.06618i	−0.350790	+	0.225439i
$85$	10.9315	−	13.3629i	1.18568	−	1.44941i
$86$	−4.21857	+	0.606539i	−0.454900	+	0.0654048i
$87$	−5.57238	+	2.07839i	−0.597422	+	0.222827i
$88$	−1.11669	+	0.835943i	−0.119039	+	0.0891118i
$89$	0.749222	+	0.481496i	0.0794174	+	0.0510384i	0.579747	−	0.814797i	$-0.303151\pi$
$89$	0.749222	+	0.481496i	0.0794174	+	0.0510384i	−0.500330	+	0.865835i	$0.666788\pi$
$90$	2.12677	−	0.690535i	0.224182	−	0.0727888i
$91$			19.2230i			2.01511i
$92$	−0.316604	+	4.78537i	−0.0330083	+	0.498909i
$93$	6.89579	−	6.89579i	0.715060	−	0.715060i
$94$	7.59352	−	6.57982i	0.783212	−	0.678657i
$95$	11.6309	+	2.18684i	1.19330	+	0.224365i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−1.71270	−	4.59194i	−0.173899	−	0.466241i	0.820536	−	0.571595i	$-0.193675\pi$
$97$	−1.71270	−	4.59194i	−0.173899	−	0.466241i	−0.994435	+	0.105354i	$0.966402\pi$
$98$	−6.08862	−	4.55789i	−0.615044	−	0.460416i
$99$	1.33841	+	0.392994i	0.134516	+	0.0394973i
$100$	4.86958	+	1.13453i	0.486958	+	0.113453i
$101$	−6.92270	−	15.1586i	−0.688835	−	1.50834i	−0.853003	−	0.521905i	$-0.825221\pi$
$101$	−6.92270	−	15.1586i	−0.688835	−	1.50834i	0.164169	−	0.986432i	$-0.447506\pi$
$102$	3.70024	−	6.77649i	0.366379	−	0.670973i
$103$	−18.2766	+	1.30717i	−1.80085	+	0.128799i	−0.931117	−	0.364721i	$-0.881164\pi$
$103$	−18.2766	+	1.30717i	−1.80085	+	0.128799i	−0.869734	+	0.493520i	$0.835710\pi$
$104$	3.80135	+	3.29389i	0.372753	+	0.322993i
$105$	5.31308	+	6.69323i	0.518503	+	0.653193i
$106$	−2.58229	+	1.17929i	−0.250815	+	0.114543i
$107$	−0.762205	+	3.50380i	−0.0736852	+	0.338725i	−0.999200	−	0.0399855i	$-0.987269\pi$
$107$	−0.762205	+	3.50380i	−0.0736852	+	0.338725i	0.925515	+	0.378711i	$0.123632\pi$
$108$	0.877679	−	0.479249i	0.0844547	−	0.0461158i
$109$	1.71969	+	11.9607i	0.164717	+	1.14563i	0.889594	+	0.456752i	$0.150987\pi$
$109$	1.71969	+	11.9607i	0.164717	+	1.14563i	−0.724877	+	0.688878i	$0.758103\pi$
$110$	2.10859	+	2.29844i	0.201046	+	0.219147i
$111$	−1.39400	−	0.200427i	−0.132313	−	0.0190237i
$112$	−3.73439	+	0.812368i	−0.352867	+	0.0767615i
$113$	−0.583582	+	8.15955i	−0.0548988	+	0.767585i	0.893210	+	0.449640i	$0.148448\pi$
$113$	−0.583582	+	8.15955i	−0.0548988	+	0.767585i	−0.948109	+	0.317946i	$0.897007\pi$
$114$	5.29263			0.495700
$115$	10.7177	−	0.361159i	0.999433	−	0.0336782i
$116$	−5.94736			−0.552199
$117$	0.358830	−	5.01709i	0.0331738	−	0.463831i
$118$	3.85260	−	0.838083i	0.354661	−	0.0771518i
$119$	29.2070	+	4.19933i	2.67740	+	0.384952i
$120$	2.23400	+	0.0962341i	0.203935	+	0.00878493i
$121$	−1.28855	−	8.96205i	−0.117141	−	0.814732i
$122$	−1.67694	+	0.915681i	−0.151823	+	0.0829018i
$123$	−1.38836	+	6.38218i	−0.125184	+	0.575461i
$124$	8.87084	−	4.05118i	0.796625	−	0.363806i
$125$	1.43995	−	11.0872i	0.128793	−	0.991672i
$126$	2.88827	+	2.50270i	0.257308	+	0.222958i
$127$	−4.98149	+	0.356283i	−0.442036	+	0.0316150i	−0.290584	−	0.956850i	$-0.593850\pi$
$127$	−4.98149	+	0.356283i	−0.442036	+	0.0316150i	−0.151452	+	0.988465i	$0.548395\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	1.77048	+	3.87681i	0.155882	+	0.341334i
$130$	6.48228	−	9.19130i	0.568534	−	0.806130i
$131$	9.01082	+	2.64582i	0.787279	+	0.231166i	0.650571	−	0.759445i	$-0.274530\pi$
$131$	9.01082	+	2.64582i	0.787279	+	0.231166i	0.136708	+	0.990611i	$0.456348\pi$
$132$	1.11669	+	0.835943i	0.0971953	+	0.0727595i
$133$	7.06861	+	18.9517i	0.612926	+	1.64332i
$134$	−1.64550	+	11.4447i	−0.142149	+	0.988671i
$135$	−1.26174	−	1.84608i	−0.108594	−	0.158885i
$136$	5.83508	−	5.05613i	0.500354	−	0.433560i
$137$	−1.70416	+	1.70416i	−0.145597	+	0.145597i	−0.776148	−	0.630551i	$-0.782829\pi$
$137$	−1.70416	+	1.70416i	−0.145597	+	0.145597i	0.630551	+	0.776148i	$0.282829\pi$
$138$	4.68073	−	1.04441i	0.398450	−	0.0889065i
$139$			10.4039i			0.882443i	0.897398	+	0.441222i	$0.145455\pi$
$139$			10.4039i			0.882443i	−0.897398	+	0.441222i	$0.854545\pi$
$140$	2.63904	+	8.12795i	0.223040	+	0.686938i
$141$	−8.45264	−	5.43218i	−0.711840	−	0.457472i
$142$	−3.14490	+	2.35424i	−0.263914	+	0.197564i
$143$	6.57393	−	2.45195i	0.549739	−	0.205042i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	1.32434	+	13.2326i	0.109980	+	1.09891i
$146$	−6.58985	+	4.23504i	−0.545380	+	0.350494i
$147$	−2.65790	+	7.12610i	−0.219220	+	0.587751i
$148$	−1.23606	−	0.674943i	−0.101604	−	0.0554799i
$149$	9.78309	−	11.2903i	0.801462	−	0.924936i	−0.196999	−	0.980404i	$-0.563119\pi$
$149$	9.78309	−	11.2903i	0.801462	−	0.924936i	0.998460	+	0.0554674i	$0.0176649\pi$
$150$	−0.283342	−	4.99197i	−0.0231347	−	0.407592i
$151$	17.5211	−	5.14465i	1.42585	−	0.418666i	0.524368	−	0.851492i	$-0.324302\pi$
$151$	17.5211	−	5.14465i	1.42585	−	0.418666i	0.901478	+	0.432826i	$0.142483\pi$
$152$	4.95892	+	1.84958i	0.402222	+	0.150021i
$153$	−7.54448	−	1.64120i	−0.609935	−	0.132683i
$154$	−1.50192	+	5.11506i	−0.121028	+	0.412183i
$155$	−10.9890	−	18.8351i	−0.882658	−	1.51287i
$156$	2.08950	−	4.57537i	0.167294	−	0.366323i
$157$	−2.62750	−	3.50993i	−0.209697	−	0.280123i	0.683345	−	0.730096i	$-0.260525\pi$
$157$	−2.62750	−	3.50993i	−0.209697	−	0.280123i	−0.893042	+	0.449973i	$0.851434\pi$
$158$	1.61191	+	7.40984i	0.128237	+	0.589495i
$159$	1.85904	+	2.14545i	0.147431	+	0.170145i
$160$	2.05951	+	0.870868i	0.162819	+	0.0688482i
$161$	9.99119	+	15.3657i	0.787416	+	1.21099i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−16.4267	−	1.17486i	−1.28664	−	0.0920223i	−0.588802	−	0.808277i	$-0.700400\pi$
$163$	−16.4267	−	1.17486i	−1.28664	−	0.0920223i	−0.697839	+	0.716255i	$0.745855\pi$
$164$	−3.53116	+	5.49460i	−0.275737	+	0.429056i
$165$	1.61127	−	2.67072i	0.125437	−	0.207916i
$166$	−8.00863	−	3.65742i	−0.621590	−	0.283871i
$167$	8.14738	−	10.8836i	0.630463	−	0.842201i	−0.365607	−	0.930769i	$-0.619138\pi$
$167$	8.14738	−	10.8836i	0.630463	−	0.842201i	0.996070	+	0.0885689i	$0.0282293\pi$
$168$	1.83156	+	3.35425i	0.141308	+	0.258786i
$169$	−6.64988	−	10.3474i	−0.511529	−	0.795955i
$170$	−12.5490	−	11.8569i	−0.962463	−	0.909383i
$171$	−1.49111	−	5.07824i	−0.114028	−	0.388343i
$172$	0.304044	+	4.25109i	0.0231831	+	0.324143i
$173$	0.850021	+	11.8848i	0.0646259	+	0.903588i	0.921578	+	0.388193i	$0.126900\pi$
$173$	0.850021	+	11.8848i	0.0646259	+	0.903588i	−0.856952	+	0.515396i	$0.827645\pi$
$174$	1.67557	+	5.70645i	0.127024	+	0.432605i
$175$	17.4967	−	7.68164i	1.32262	−	0.580678i
$176$	0.754149	+	1.17348i	0.0568461	+	0.0884543i
$177$	−1.88954	−	3.46043i	−0.142026	−	0.260102i
$178$	0.533718	−	0.712964i	0.0400038	−	0.0534389i
$179$	−2.43174	−	1.11054i	−0.181757	−	0.0830057i	0.322458	−	0.946584i	$-0.395491\pi$
$179$	−2.43174	−	1.11054i	−0.181757	−	0.0830057i	−0.504215	+	0.863578i	$0.668218\pi$
$180$	−0.537054	−	2.17062i	−0.0400296	−	0.161788i
$181$	−8.67364	+	13.4965i	−0.644707	+	1.00318i	0.353008	+	0.935620i	$0.385159\pi$
$181$	−8.67364	+	13.4965i	−0.644707	+	1.00318i	−0.997715	+	0.0675630i	$0.978478\pi$
$182$	19.1740	+	1.37135i	1.42127	+	0.101651i
$183$	1.35104	+	1.35104i	0.0998717	+	0.0998717i
$184$	4.75059	+	0.657182i	0.350218	+	0.0484481i
$185$	−1.22647	+	2.90048i	−0.0901721	+	0.213248i
$186$	−6.38628	−	7.37016i	−0.468265	−	0.540406i
$187$	−2.28934	−	10.5239i	−0.167413	−	0.769585i
$188$	−6.02134	−	8.04357i	−0.439152	−	0.586638i
$189$	1.58760	−	3.47637i	0.115481	−	0.252869i
$190$	3.01100	−	11.4452i	0.218441	−	0.830324i
$191$	0.451628	−	1.53810i	0.0326786	−	0.111293i	−0.941539	−	0.336905i	$-0.890620\pi$
$191$	0.451628	−	1.53810i	0.0326786	−	0.111293i	0.974217	+	0.225612i	$0.0724381\pi$
$192$	0.977147	+	0.212565i	0.0705195	+	0.0153406i
$193$	14.8744	+	5.54786i	1.07068	+	0.399344i	0.822145	−	0.569278i	$-0.192777\pi$
$193$	14.8744	+	5.54786i	1.07068	+	0.399344i	0.248537	+	0.968622i	$0.420050\pi$
$194$	−4.70242	+	1.38076i	−0.337614	+	0.0991324i
$195$	−10.6453	−	3.63021i	−0.762323	−	0.259965i
$196$	−4.98063	+	5.74796i	−0.355759	+	0.410568i
$197$	4.39393	+	2.39927i	0.313054	+	0.170941i	0.628093	−	0.778138i	$-0.283836\pi$
$197$	4.39393	+	2.39927i	0.313054	+	0.170941i	−0.315039	+	0.949079i	$0.602018\pi$
$198$	0.487474	−	1.30697i	0.0346432	−	0.0928821i
$199$	−11.1390	+	7.15862i	−0.789625	+	0.507461i	−0.872215	−	0.489122i	$-0.837317\pi$
$199$	−11.1390	+	7.15862i	−0.789625	+	0.507461i	0.0825900	+	0.996584i	$0.473681\pi$
$200$	1.47904	−	4.77624i	0.104584	−	0.337731i
$201$	11.4447	−	1.64550i	0.807247	−	0.116065i
$202$	−15.6138	+	5.82366i	−1.09859	+	0.409751i
$203$	−18.1957	+	13.6211i	−1.27709	+	0.956015i
$204$	−6.49525	−	4.17425i	−0.454759	−	0.292256i
$205$	13.0115	+	6.63315i	0.908764	+	0.463280i
$206$			18.3233i			1.27665i
$207$	−2.32082	−	4.19688i	−0.161308	−	0.291703i
$208$	3.55668	−	3.55668i	0.246612	−	0.246612i
$209$	5.57953	−	4.83469i	0.385944	−	0.334422i
$210$	7.05521	−	4.82205i	0.486856	−	0.332753i
$211$	−0.908813	+	6.32093i	−0.0625653	+	0.435151i	0.934330	+	0.356410i	$0.115999\pi$
$211$	−0.908813	+	6.32093i	−0.0625653	+	0.435151i	−0.996895	+	0.0787414i	$0.974910\pi$
$212$	0.992071	+	2.65984i	0.0681357	+	0.182679i
$213$	3.14490	+	2.35424i	0.215485	+	0.161310i
$214$	3.44050	+	1.01022i	0.235188	+	0.0690573i
$215$	9.39078	−	1.62310i	0.640446	−	0.110695i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	17.8616	−	32.7111i	1.21252	−	2.22057i
$218$	12.0529	−	0.862043i	0.816328	−	0.0583849i
$219$	5.92006	+	5.12976i	0.400041	+	0.346637i
$220$	2.44300	−	1.93925i	0.164707	−	0.130744i
$221$	−35.3261	+	16.1329i	−2.37629	+	1.08521i
$222$	−0.299363	+	1.37615i	−0.0200919	+	0.0923611i
$223$	22.2653	−	12.1577i	1.49099	−	0.814143i	0.492568	−	0.870274i	$-0.336058\pi$
$223$	22.2653	−	12.1577i	1.49099	−	0.814143i	0.998423	+	0.0561306i	$0.0178763\pi$
$224$	0.543889	+	3.78283i	0.0363401	+	0.252751i
$225$	−4.70993	+	1.67826i	−0.313995	+	0.111884i
$226$	8.09712	+	1.16419i	0.538613	+	0.0774408i
$227$	−17.7057	+	3.85164i	−1.17517	+	0.255642i	−0.757425	−	0.652923i	$-0.773543\pi$
$227$	−17.7057	+	3.85164i	−1.17517	+	0.255642i	−0.417744	+	0.908565i	$0.637179\pi$
$228$	0.377572	−	5.27914i	0.0250053	−	0.349620i
$229$	−0.366279			−0.0242044			−0.0121022	−	0.999927i	$-0.503852\pi$
$229$	−0.366279			−0.0242044			−0.0121022	+	0.999927i	$0.503852\pi$
$230$	0.404355	−	10.7162i	0.0266624	−	0.706604i
$231$	5.33100			0.350754
$232$	−0.424280	+	5.93221i	−0.0278553	+	0.389469i
$233$	−21.1597	+	4.60301i	−1.38622	+	0.301553i	−0.842944	−	0.538001i	$-0.819180\pi$
$233$	−21.1597	+	4.60301i	−1.38622	+	0.301553i	−0.543275	+	0.839555i	$0.682816\pi$
$234$	−4.97871	−	0.715831i	−0.325469	−	0.0467953i
$235$	−16.5558	+	15.1883i	−1.07998	+	0.990776i
$236$	−0.561106	−	3.90258i	−0.0365249	−	0.254036i
$237$	6.65556	−	3.63421i	0.432325	−	0.236067i
$238$	6.27223	−	28.8330i	0.406568	−	1.86896i
$239$	−13.2378	+	6.04551i	−0.856284	+	0.391052i	−0.794665	−	0.607048i	$-0.792354\pi$
$239$	−13.2378	+	6.04551i	−0.856284	+	0.391052i	−0.0616189	+	0.998100i	$0.519626\pi$
$240$	0.255360	−	2.22144i	0.0164834	−	0.143393i
$241$	−17.1441	−	14.8555i	−1.10435	−	0.956926i	−0.105056	−	0.994466i	$-0.533502\pi$
$241$	−17.1441	−	14.8555i	−1.10435	−	0.956926i	−0.999295	+	0.0375404i	$0.988048\pi$
$242$	−9.03114	+	0.645920i	−0.580543	+	0.0415213i
$243$	−0.479249	+	0.877679i	−0.0307438	+	0.0563031i
$244$	0.793716	+	1.73800i	0.0508124	+	0.111264i
$245$	13.8980	+	9.80174i	0.887911	+	0.626210i
$246$	6.26687	+	1.84012i	0.399561	+	0.117322i
$247$	−21.3116	−	15.9536i	−1.35602	−	1.01511i
$248$	−3.40801	−	9.13724i	−0.216409	−	0.580215i
$249$	−1.25298	+	8.71464i	−0.0794041	+	0.552268i
$250$	−10.9563	−	2.22723i	−0.692934	−	0.140862i
$251$	−15.6793	+	13.5862i	−0.989668	+	0.857552i	−0.989802	−	0.142448i	$-0.954503\pi$
$251$	−15.6793	+	13.5862i	−0.989668	+	0.857552i	0.000134070		1.00000i	$0.499957\pi$
$252$	2.70237	−	2.70237i	0.170233	−	0.170233i
$253$	3.98041	−	5.37676i	0.250246	−	0.338034i
$254$			4.99422i			0.313365i
$255$	−7.84116	+	15.3811i	−0.491033	+	0.963204i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	0.706045	−	0.528538i	0.0440419	−	0.0329693i	−0.577030	−	0.816723i	$-0.695788\pi$
$257$	0.706045	−	0.528538i	0.0440419	−	0.0329693i	0.621072	+	0.783754i	$0.286698\pi$
$258$	3.99323	−	1.48940i	0.248608	−	0.0927259i
$259$	−5.32749	+	0.765977i	−0.331034	+	0.0475955i
$260$	−8.70544	−	7.12146i	−0.539889	−	0.441654i
$261$	5.00324	−	3.21539i	0.309693	−	0.199027i
$262$	3.28190	−	8.79911i	0.202756	−	0.543611i
$263$	18.0033	+	9.83056i	1.11013	+	0.606178i	0.926303	−	0.376780i	$-0.122969\pi$
$263$	18.0033	+	9.83056i	1.11013	+	0.606178i	0.183829	+	0.982958i	$0.441151\pi$
$264$	0.913477	−	1.05421i	0.0562206	−	0.0648820i
$265$	5.69712	−	2.79959i	0.349971	−	0.171978i
$266$	19.4077	−	5.69860i	1.18996	−	0.349404i
$267$	−0.834449	−	0.311233i	−0.0510675	−	0.0190472i
$268$	11.2981	+	2.45776i	0.690144	+	0.150132i
$269$	5.70171	−	19.4183i	0.347640	−	1.18395i	−0.581290	−	0.813696i	$-0.697452\pi$
$269$	5.70171	−	19.4183i	0.347640	−	1.18395i	0.928930	−	0.370256i	$-0.120730\pi$
$270$	−1.93139	+	1.12683i	−0.117540	+	0.0685768i
$271$	−0.723593	+	1.58445i	−0.0439552	+	0.0962484i	−0.930336	−	0.366709i	$-0.880484\pi$
$271$	−0.723593	+	1.58445i	−0.0439552	+	0.0962484i	0.886381	+	0.462957i	$0.153212\pi$
$272$	−4.62698	−	6.18092i	−0.280552	−	0.374773i
$273$	−4.08614	−	18.7837i	−0.247304	−	1.13684i
$274$	1.57825	+	1.82140i	0.0953455	+	0.110035i
$275$	−4.85874	−	5.00374i	−0.292993	−	0.301737i
$276$	−0.707835	−	4.74331i	−0.0426066	−	0.285514i
$277$	18.8888	+	18.8888i	1.13492	+	1.13492i	0.989348	+	0.145567i	$0.0465008\pi$
$277$	18.8888	+	18.8888i	1.13492	+	1.13492i	0.145567	+	0.989348i	$0.453499\pi$
$278$	10.3773	+	0.742202i	0.622392	+	0.0445143i
$279$	−5.27239	+	8.20400i	−0.315650	+	0.491161i
$280$	8.29551	−	2.05247i	0.495752	−	0.122659i
$281$	27.0868	+	12.3701i	1.61586	+	0.737939i	0.998800	−	0.0489760i	$-0.0155958\pi$
$281$	27.0868	+	12.3701i	1.61586	+	0.737939i	0.617061	+	0.786915i	$0.288323\pi$
$282$	−6.02134	+	8.04357i	−0.358566	+	0.478988i
$283$	−6.30665	−	11.5498i	−0.374891	−	0.686562i	0.620316	−	0.784352i	$-0.287004\pi$
$283$	−6.30665	−	11.5498i	−0.374891	−	0.686562i	−0.995207	+	0.0977901i	$0.968823\pi$
$284$	2.12389	+	3.30484i	0.126030	+	0.196106i
$285$	−11.8299	+	0.335460i	−0.700744	+	0.0198709i
$286$	−1.97672	−	6.73210i	−0.116886	−	0.398077i
$287$	1.78073	+	24.8978i	0.105113	+	1.46967i
$288$	−0.0713392	−	0.997452i	−0.00420370	−	0.0587754i
$289$	12.0054	+	40.8866i	0.706199	+	2.40509i
$290$	13.2934	−	0.376959i	0.780613	−	0.0221358i
$291$	2.64965	+	4.12294i	0.155325	+	0.241691i
$292$	3.75413	+	6.87518i	0.219694	+	0.402340i
$293$	1.24632	−	1.66489i	0.0728107	−	0.0972637i	−0.762657	−	0.646803i	$-0.776106\pi$
$293$	1.24632	−	1.66489i	0.0728107	−	0.0972637i	0.835468	+	0.549539i	$0.185197\pi$
$294$	6.91833	+	3.15950i	0.403485	+	0.184265i
$295$	−8.55810	+	2.11744i	−0.498272	+	0.123282i
$296$	−0.761403	+	1.18477i	−0.0442556	+	0.0688631i
$297$	−1.39136	−	0.0995123i	−0.0807351	−	0.00577429i
$298$	−10.5636	−	10.5636i	−0.611933	−	0.611933i
$299$	−21.9958	−	9.90368i	−1.27205	−	0.572745i
$300$	−4.99946	−	0.0735031i	−0.288644	−	0.00424370i
$301$	10.6664	+	12.3097i	0.614801	+	0.709518i
$302$	−3.88161	−	17.8435i	−0.223361	−	1.02678i
$303$	9.98669	+	13.3407i	0.573720	+	0.766401i
$304$	2.19864	−	4.81434i	0.126100	−	0.276121i
$305$	3.69022	−	2.15299i	0.211301	−	0.123280i
$306$	−2.17524	+	7.40817i	−0.124350	+	0.423497i
$307$	−5.85432	−	1.27353i	−0.334123	−	0.0726841i	0.0423738	−	0.999102i	$-0.486508\pi$
$307$	−5.85432	−	1.27353i	−0.334123	−	0.0726841i	−0.376497	+	0.926418i	$0.622872\pi$
$308$	4.99488	+	1.86299i	0.284610	+	0.106154i
$309$	17.5811	−	5.16228i	1.00015	−	0.293672i
$310$	−19.5710	+	9.61732i	−1.11156	+	0.546227i
$311$	12.3051	−	14.2008i	0.697758	−	0.805256i	−0.290690	−	0.956817i	$-0.593885\pi$
$311$	12.3051	−	14.2008i	0.697758	−	0.805256i	0.988448	+	0.151562i	$0.0484302\pi$
$312$	−4.41465	−	2.41058i	−0.249930	−	0.136472i
$313$	3.38891	−	9.08601i	0.191552	−	0.513572i	−0.805299	−	0.592869i	$-0.797995\pi$
$313$	3.38891	−	9.08601i	0.191552	−	0.513572i	0.996851	+	0.0792976i	$0.0252677\pi$
$314$	−3.68843	+	2.37041i	−0.208150	+	0.133770i
$315$	−6.61441	−	5.41090i	−0.372680	−	0.304870i
$316$	7.50595	−	1.07919i	0.422243	−	0.0607093i
$317$	−12.7949	+	4.77226i	−0.718634	+	0.268037i	−0.682062	−	0.731294i	$-0.738917\pi$
$317$	−12.7949	+	4.77226i	−0.718634	+	0.268037i	−0.0365721	+	0.999331i	$0.511644\pi$
$318$	2.27260	−	1.70125i	0.127441	−	0.0954013i
$319$	6.97911	+	4.48520i	0.390755	+	0.251123i
$320$	1.01557	−	1.99214i	0.0567723	−	0.111364i
$321$		−	3.58575i		−	0.200137i
$322$	16.0393	−	8.86956i	0.893838	−	0.494281i
$323$	−28.8952	+	28.8952i	−1.60777	+	1.60777i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	−13.9064	+	20.9550i	−0.771390	+	1.16237i
$326$	−2.34374	+	16.3011i	−0.129808	+	0.902832i
$327$	−4.22283	−	11.3218i	−0.233523	−	0.626099i
$328$	5.22869	+	3.91415i	0.288706	+	0.216123i
$329$	−36.8440	−	10.8184i	−2.03128	−	0.596437i
$330$	−2.54897	−	1.79770i	−0.140316	−	0.0989599i
$331$	−6.46452	−	14.1553i	−0.355322	−	0.778047i	−0.999909	−	0.0135156i	$-0.995698\pi$
$331$	−6.46452	−	14.1553i	−0.355322	−	0.778047i	0.644586	−	0.764531i	$-0.277030\pi$
$332$	−4.21943	+	7.72731i	−0.231571	+	0.424091i
$333$	1.40475	−	0.100469i	0.0769796	−	0.00550569i
$334$	−10.2747	−	8.90305i	−0.562205	−	0.487153i
$335$	2.95257	−	25.6851i	0.161316	−	1.40333i
$336$	3.47637	−	1.58760i	0.189652	−	0.0866109i
$337$	−2.03853	+	9.37096i	−0.111046	+	0.510469i	0.887701	+	0.460420i	$0.152301\pi$
$337$	−2.03853	+	9.37096i	−0.111046	+	0.510469i	−0.998747	+	0.0500486i	$0.984062\pi$
$338$	−10.7954	+	5.89476i	−0.587195	+	0.320633i
$339$	−1.16419	−	8.09712i	−0.0632302	−	0.439775i
$340$	−12.7219	+	11.6711i	−0.689944	+	0.632957i
$341$	−13.4649	−	1.93596i	−0.729167	−	0.104838i
$342$	−5.17167	+	1.12503i	−0.279652	+	0.0608346i
$343$	−0.165120	+	2.30868i	−0.00891564	+	0.124657i
$344$	4.26195			0.229789
$345$	−10.3960	+	2.63112i	−0.559703	+	0.141655i
$346$	11.9152			0.640565
$347$	−0.293598	+	4.10504i	−0.0157612	+	0.220370i	0.983467	+	0.181087i	$0.0579617\pi$
$347$	−0.293598	+	4.10504i	−0.0157612	+	0.220370i	−0.999228	+	0.0392823i	$0.987493\pi$
$348$	5.81145	−	1.26420i	0.311526	−	0.0677684i
$349$	−16.7696	−	2.41111i	−0.897658	−	0.129064i	−0.321986	−	0.946745i	$-0.604350\pi$
$349$	−16.7696	−	2.41111i	−0.897658	−	0.129064i	−0.575672	+	0.817681i	$0.695259\pi$
$350$	−6.41387	−	18.0001i	−0.342836	−	0.962145i
$351$	0.715831	+	4.97871i	0.0382082	+	0.265744i
$352$	1.22429	−	0.668513i	0.0652549	−	0.0356318i
$353$	1.99441	−	9.16815i	0.106152	−	0.487971i	−0.893120	−	0.449818i	$-0.851489\pi$
$353$	1.99441	−	9.16815i	0.106152	−	0.487971i	0.999272	−	0.0381533i	$-0.0121475\pi$
$354$	−3.58641	+	1.63786i	−0.190616	+	0.0870513i
$355$	6.88017	−	5.46147i	0.365162	−	0.289865i
$356$	−0.673072	−	0.583220i	−0.0356727	−	0.0309106i
$357$	−29.4321	+	2.10503i	−1.55771	+	0.111410i
$358$	−1.28119	+	2.34632i	−0.0677130	+	0.124007i
$359$	−9.75099	−	21.3517i	−0.514638	−	1.12690i	−0.971430	−	0.237326i	$-0.923729\pi$
$359$	−9.75099	−	21.3517i	−0.514638	−	1.12690i	0.456792	−	0.889573i	$-0.348998\pi$
$360$	−2.20340	+	0.380835i	−0.116129	+	0.0200718i
$361$	−8.64684	−	2.53894i	−0.455097	−	0.133629i
$362$	12.8433	+	9.61437i	0.675028	+	0.505320i
$363$	3.16412	+	8.48334i	0.166073	+	0.445260i
$364$	2.73571	−	19.0273i	0.143390	−	0.997302i
$365$	14.4610	−	9.88371i	0.756923	−	0.517337i
$366$	1.44398	−	1.25121i	0.0754780	−	0.0654020i
$367$	−6.63213	+	6.63213i	−0.346194	+	0.346194i	−0.858690	−	0.512496i	$-0.828721\pi$
$367$	−6.63213	+	6.63213i	−0.346194	+	0.346194i	0.512496	+	0.858690i	$0.328721\pi$
$368$	0.994411	−	4.69160i	0.0518372	−	0.244567i
$369$		−	6.53144i		−	0.340013i
$370$	2.80559	+	1.43027i	0.145856	+	0.0743560i
$371$	9.12698	+	5.86555i	0.473849	+	0.304524i
$372$	−7.80697	+	5.84422i	−0.404773	+	0.303009i
$373$	6.89321	−	2.57103i	0.356917	−	0.133123i	−0.164608	−	0.986359i	$-0.552636\pi$
$373$	6.89321	−	2.57103i	0.356917	−	0.133123i	0.521525	+	0.853236i	$0.325363\pi$
$374$	−10.6604	+	1.53274i	−0.551238	+	0.0792560i
$375$	0.949720	+	11.1399i	0.0490433	+	0.575263i
$376$	−8.45264	+	5.43218i	−0.435911	+	0.280143i
$377$	10.4541	−	28.0286i	0.538414	−	1.44354i
$378$	−3.35425	−	1.83156i	−0.172524	−	0.0942053i
$379$	1.91720	−	2.21257i	0.0984800	−	0.113652i	−0.704370	−	0.709833i	$-0.748770\pi$
$379$	1.91720	−	2.21257i	0.0984800	−	0.113652i	0.802850	+	0.596181i	$0.203316\pi$
$380$	−11.2013	−	3.81982i	−0.574613	−	0.195953i
$381$	4.79192	−	1.40703i	0.245497	−	0.0720845i
$382$	−1.50196	−	0.560204i	−0.0768472	−	0.0286625i
$383$	−12.6716	−	2.75654i	−0.647488	−	0.140852i	−0.123184	−	0.992384i	$-0.539311\pi$
$383$	−12.6716	−	2.75654i	−0.647488	−	0.140852i	−0.524304	+	0.851531i	$0.675674\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	3.03283	−	11.5282i	0.154567	−	0.587532i
$386$	6.59485	−	14.4407i	0.335669	−	0.735013i
$387$	−2.55409	−	3.41187i	−0.129832	−	0.173435i
$388$	1.04177	+	4.78894i	0.0528879	+	0.243122i
$389$	12.1918	+	14.0701i	0.618148	+	0.713381i	0.975354	−	0.220645i	$-0.0708161\pi$
$389$	12.1918	+	14.0701i	0.618148	+	0.713381i	−0.357206	+	0.934026i	$0.616271\pi$
$390$	−4.38039	+	10.3592i	−0.221810	+	0.524556i
$391$	−19.8525	+	31.2565i	−1.00398	+	1.58071i
$392$	5.37800	+	5.37800i	0.271630	+	0.271630i
$393$	−9.36731	−	0.669963i	−0.472518	−	0.0337952i
$394$	2.70661	−	4.21157i	0.136357	−	0.212176i
$395$	−4.07255	−	16.4601i	−0.204912	−	0.828196i
$396$	−1.26886	−	0.579470i	−0.0637627	−	0.0291194i
$397$	−4.34140	+	5.79943i	−0.217889	+	0.291065i	−0.896146	−	0.443759i	$-0.853644\pi$
$397$	−4.34140	+	5.79943i	−0.217889	+	0.291065i	0.678257	+	0.734824i	$0.262735\pi$
$398$	6.34573	+	11.6213i	0.318083	+	0.582525i
$399$	−10.9355	−	17.0160i	−0.547462	−	0.851867i
$400$	−4.65856	−	1.81600i	−0.232928	−	0.0908000i
$401$	−3.07335	−	10.4669i	−0.153476	−	0.522690i	0.846477	−	0.532425i	$-0.178719\pi$
$401$	−3.07335	−	10.4669i	−0.153476	−	0.522690i	−0.999953	+	0.00973520i	$0.996901\pi$
$402$	−0.824851	−	11.5329i	−0.0411398	−	0.575210i
$403$	3.49935	+	48.9273i	0.174315	+	2.43724i
$404$	4.69495	+	15.9895i	0.233582	+	0.795508i
$405$	1.62532	+	1.53569i	0.0807629	+	0.0763088i
$406$	12.2883	+	19.1210i	0.609860	+	0.948961i
$407$	0.941489	+	1.72421i	0.0466679	+	0.0854658i
$408$	−4.62698	+	6.18092i	−0.229070	+	0.306001i
$409$	−32.8264	−	14.9913i	−1.62316	−	0.741272i	−0.623967	−	0.781451i	$-0.714480\pi$
$409$	−32.8264	−	14.9913i	−1.62316	−	0.741272i	−0.999193	+	0.0401786i	$0.987207\pi$
$410$	7.54448	−	12.5052i	0.372596	−	0.617586i
$411$	1.30297	−	2.02746i	0.0642709	−	0.100007i
$412$	18.2766	+	1.30717i	0.900426	+	0.0643997i
$413$	−10.6547	−	10.6547i	−0.524282	−	0.524282i
$414$	−4.35175	+	2.01551i	−0.213877	+	0.0990567i
$415$	18.1325	+	7.66735i	0.890088	+	0.376375i
$416$	−3.29389	−	3.80135i	−0.161496	−	0.186377i
$417$	−2.21150	−	10.1661i	−0.108297	−	0.497836i
$418$	−4.42433	−	5.91022i	−0.216401	−	0.289078i
$419$	6.92937	−	15.1732i	0.338522	−	0.741259i	−0.661440	−	0.749998i	$-0.730054\pi$
$419$	6.92937	−	15.1732i	0.338522	−	0.741259i	0.999962	+	0.00873890i	$0.00278171\pi$
$420$	−4.30645	−	7.38124i	−0.210133	−	0.360167i
$421$	10.3965	−	35.4072i	0.506694	−	1.72564i	−0.166377	−	0.986062i	$-0.553207\pi$
$421$	10.3965	−	35.4072i	0.506694	−	1.72564i	0.673071	−	0.739578i	$-0.264975\pi$
$422$	6.24000	+	1.35743i	0.303758	+	0.0660786i
$423$	9.41416	+	3.51130i	0.457732	+	0.170725i
$424$	2.72384	−	0.799792i	0.132281	−	0.0388413i
$425$	28.8006	+	25.7068i	1.39704	+	1.24696i
$426$	2.57260	−	2.96894i	0.124643	−	0.143846i
$427$	6.40883	+	3.49949i	0.310145	+	0.169352i
$428$	1.25309	−	3.35966i	0.0605704	−	0.162395i
$429$	−5.90249	+	3.79330i	−0.284975	+	0.183142i
$430$	−0.949035	−	9.48264i	−0.0457665	−	0.457293i
$431$	−19.0513	+	2.73916i	−0.917667	+	0.131941i	−0.584934	−	0.811081i	$-0.698880\pi$
$431$	−19.0513	+	2.73916i	−0.917667	+	0.131941i	−0.332733	+	0.943021i	$0.607971\pi$
$432$	−0.936950	+	0.349464i	−0.0450790	+	0.0168136i
$433$	−8.47665	+	6.34554i	−0.407362	+	0.304947i	−0.783237	−	0.621723i	$-0.786433\pi$
$433$	−8.47665	+	6.34554i	−0.407362	+	0.304947i	0.375875	+	0.926670i	$0.377342\pi$
$434$	−31.3535	−	20.1497i	−1.50502	−	0.967215i
$435$	−4.10686	−	12.6487i	−0.196909	−	0.606458i
$436$		−	12.0837i		−	0.578706i
$437$	−25.3272	−	1.67567i	−1.21156	−	0.0801581i
$438$	5.53903	−	5.53903i	0.264665	−	0.264665i
$439$	15.0857	−	13.0718i	0.720002	−	0.623885i	−0.215789	−	0.976440i	$-0.569232\pi$
$439$	15.0857	−	13.0718i	0.720002	−	0.623885i	0.935791	+	0.352555i	$0.114687\pi$
$440$	−1.76003	−	2.57512i	−0.0839061	−	0.122764i
$441$	1.08239	−	7.52822i	0.0515426	−	0.358487i
$442$	13.5716	+	36.3870i	0.645537	+	1.73075i
$443$	3.53709	+	2.64784i	0.168052	+	0.125802i	0.679994	−	0.733218i	$-0.261983\pi$
$443$	3.53709	+	2.64784i	0.168052	+	0.125802i	−0.511941	+	0.859020i	$0.671073\pi$
$444$	1.35129	+	0.396773i	0.0641292	+	0.0188300i
$445$	−1.14776	+	1.62742i	−0.0544091	+	0.0771472i
$446$	−10.5384	−	23.0759i	−0.499007	−	1.09267i
$447$	−7.15959	+	13.1118i	−0.338637	+	0.620168i
$448$	3.81199	−	0.272639i	0.180100	−	0.0128810i
$449$	18.6300	+	16.1430i	0.879206	+	0.761837i	0.972279	−	0.233823i	$-0.0751235\pi$
$449$	18.6300	+	16.1430i	0.879206	+	0.761837i	−0.0930729	+	0.995659i	$0.529669\pi$
$450$	1.33798	+	4.81765i	0.0630732	+	0.227106i
$451$	8.28749	−	3.78477i	0.390243	−	0.178218i
$452$	1.73887	−	7.99344i	0.0817894	−	0.375980i
$453$	−16.0271	+	8.75146i	−0.753019	+	0.411179i
$454$	2.57872	+	17.9354i	0.121025	+	0.841748i
$455$	−42.9440	−	1.84990i	−2.01325	−	0.0867249i
$456$	−5.23875	−	0.753219i	−0.245327	−	0.0352727i
$457$	4.61921	−	1.00485i	0.216078	−	0.0470048i	−0.103223	−	0.994658i	$-0.532916\pi$
$457$	4.61921	−	1.00485i	0.216078	−	0.0470048i	0.319301	+	0.947653i	$0.396552\pi$
$458$	−0.0261300	+	0.365346i	−0.00122098	+	0.0170715i
$459$	7.72092			0.360382
$460$	−10.6600	−	1.16781i	−0.497026	−	0.0544493i
$461$	−12.8598			−0.598939			−0.299469	−	0.954106i	$-0.596810\pi$
$461$	−12.8598			−0.598939			−0.299469	+	0.954106i	$0.596810\pi$
$462$	0.380309	−	5.31742i	0.0176936	−	0.247389i
$463$	22.1468	−	4.81774i	1.02925	−	0.223899i	0.333927	−	0.942599i	$-0.391626\pi$
$463$	22.1468	−	4.81774i	1.02925	−	0.223899i	0.695321	+	0.718700i	$0.255262\pi$
$464$	5.88683	+	0.846398i	0.273289	+	0.0392930i
$465$	14.7416	+	16.0688i	0.683623	+	0.745171i
$466$	3.08177	+	21.4342i	0.142760	+	0.992919i
$467$	35.5244	−	19.3978i	1.64387	−	0.897622i	0.653863	−	0.756613i	$-0.273147\pi$
$467$	35.5244	−	19.3978i	1.64387	−	0.897622i	0.990008	−	0.141009i	$-0.0450346\pi$
$468$	−1.06918	+	4.91496i	−0.0494231	+	0.227194i
$469$	40.1951	−	18.3565i	1.85604	−	0.847624i
$470$	13.9685	+	17.5971i	0.644321	+	0.811694i
$471$	3.31354	+	2.87120i	0.152680	+	0.132298i
$472$	−3.93266	+	0.281270i	−0.181015	+	0.0129465i
$473$	2.84917	−	5.21786i	0.131005	−	0.239918i
$474$	−3.15015	−	6.89786i	−0.144691	−	0.316829i
$475$	−6.00467	+	25.7729i	−0.275513	+	1.18254i
$476$	−28.3120	−	8.31317i	−1.29768	−	0.381033i
$477$	−2.27260	−	1.70125i	−0.104055	−	0.0778949i
$478$	5.08574	+	13.6354i	0.232616	+	0.623668i
$479$	−0.331832	+	2.30795i	−0.0151618	+	0.105453i	−0.995997	−	0.0893864i	$-0.971509\pi$
$479$	−0.331832	+	2.30795i	−0.0151618	+	0.105453i	0.980835	+	0.194839i	$0.0624185\pi$
$480$	−2.19756	−	0.413185i	−0.100305	−	0.0188592i
$481$	5.35357	−	4.63890i	0.244102	−	0.211515i
$482$	−16.0407	+	16.0407i	−0.730633	+	0.730633i
$483$	−13.0291	−	12.8908i	−0.592844	−	0.586551i
$484$			9.05421i			0.411555i
$485$	10.4232	−	3.38427i	0.473293	−	0.153672i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	12.7491	−	9.54385i	0.577717	−	0.432473i	−0.270047	−	0.962847i	$-0.587039\pi$
$487$	12.7491	−	9.54385i	0.577717	−	0.432473i	0.847764	+	0.530374i	$0.177948\pi$
$488$	1.79019	−	0.667706i	0.0810381	−	0.0302256i
$489$	16.3011	−	2.34374i	0.737159	−	0.105988i
$490$	10.7682	−	13.1633i	0.486459	−	0.594659i
$491$	−31.8873	+	20.4927i	−1.43905	+	0.924823i	−0.439405	+	0.898289i	$0.644811\pi$
$491$	−31.8873	+	20.4927i	−1.43905	+	0.924823i	−0.999648	+	0.0265345i	$0.991553\pi$
$492$	2.28250	−	6.11963i	0.102903	−	0.275894i
$493$	−40.3023	−	22.0067i	−1.81512	−	0.991132i
$494$	−17.4333	+	20.1191i	−0.784363	+	0.905203i
$495$	−1.00675	+	2.95219i	−0.0452499	+	0.132691i
$496$	−9.35709	+	2.74749i	−0.420146	+	0.123366i
$497$	14.0670	+	5.24670i	0.630989	+	0.235347i
$498$	8.60305	+	1.87148i	0.385512	+	0.0838630i
$499$	−1.34884	+	4.59374i	−0.0603826	+	0.205644i	−0.984159	−	0.177288i	$-0.943268\pi$
$499$	−1.34884	+	4.59374i	−0.0603826	+	0.205644i	0.923776	+	0.382932i	$0.125086\pi$
$500$	−3.00317	+	10.7694i	−0.134306	+	0.481624i
$501$	−5.64771	+	12.3668i	−0.252321	+	0.552506i
$502$	12.4330	+	16.6086i	0.554913	+	0.741277i
$503$	−2.17473	−	9.99707i	−0.0969664	−	0.445748i	−0.999873	−	0.0159115i	$-0.994935\pi$
$503$	−2.17473	−	9.99707i	−0.0969664	−	0.445748i	0.902907	−	0.429836i	$-0.141429\pi$
$504$	−2.50270	−	2.88827i	−0.111479	−	0.128654i
$505$	34.5305	−	14.0065i	1.53659	−	0.623282i
$506$	−5.07911	−	4.35384i	−0.225794	−	0.193552i
$507$	8.69741	+	8.69741i	0.386265	+	0.386265i
$508$	4.98149	+	0.356283i	0.221018	+	0.0158075i
$509$	15.0692	−	23.4482i	0.667932	−	1.03932i	−0.327593	−	0.944819i	$-0.606237\pi$
$509$	15.0692	−	23.4482i	0.667932	−	1.03932i	0.995525	−	0.0945033i	$-0.0301263\pi$
$510$	14.7826	+	8.91846i	0.654583	+	0.394916i
$511$	27.2317	+	12.4363i	1.20466	+	0.550149i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	2.53649	+	4.64523i	0.111989	+	0.205092i
$514$	−0.476823	−	0.741951i	−0.0210318	−	0.0327261i
$515$	−1.16138	−	40.9557i	−0.0511765	−	1.80473i
$516$	−1.20073	−	4.08931i	−0.0528592	−	0.180022i
$517$	0.999866	+	13.9800i	0.0439741	+	0.614838i
$518$	0.383967	+	5.36856i	0.0168705	+	0.235881i
$519$	−3.35690	−	11.4326i	−0.147352	−	0.501833i
$520$	−7.72436	+	8.17522i	−0.338736	+	0.358507i
$521$	5.91309	+	9.20095i	0.259057	+	0.403101i	0.946281	−	0.323345i	$-0.104807\pi$
$521$	5.91309	+	9.20095i	0.259057	+	0.403101i	−0.687224	+	0.726446i	$0.741171\pi$
$522$	−2.85027	−	5.21987i	−0.124753	−	0.228468i
$523$	−4.05853	+	5.42156i	−0.177467	+	0.237068i	−0.880451	−	0.474138i	$-0.842760\pi$
$523$	−4.05853	+	5.42156i	−0.177467	+	0.237068i	0.702983	+	0.711206i	$0.251851\pi$
$524$	−8.54257	−	3.90126i	−0.373184	−	0.170427i
$525$	−15.4640	+	11.2253i	−0.674903	+	0.489911i
$526$	11.0899	−	17.2561i	0.483540	−	0.752404i
$527$	75.1035	+	5.37151i	3.27156	+	0.233987i
$528$	−0.986355	−	0.986355i	−0.0429256	−	0.0429256i
$529$	−22.7297	+	3.51597i	−0.988247	+	0.152868i
$530$	−2.38603	−	5.88232i	−0.103643	−	0.255512i
$531$	2.58192	+	2.97970i	0.112046	+	0.129308i
$532$	−4.29956	−	19.7647i	−0.186409	−	0.856910i
$533$	−19.6878	−	26.2998i	−0.852773	−	1.13917i
$534$	−0.369969	+	0.810120i	−0.0160101	+	0.0350573i
$535$	−7.75413	−	2.03995i	−0.335240	−	0.0881947i
$536$	3.25750	−	11.0940i	0.140703	−	0.479189i
$537$	2.61223	+	0.568257i	0.112726	+	0.0245221i
$538$	−18.9620	−	7.07247i	−0.817511	−	0.304916i
$539$	10.1795	−	2.98897i	0.438461	−	0.128744i
$540$	0.986178	+	2.00685i	0.0424383	+	0.0863611i
$541$	18.6433	−	21.5155i	0.801538	−	0.925024i	−0.196927	−	0.980418i	$-0.563096\pi$
$541$	18.6433	−	21.5155i	0.801538	−	0.925024i	0.998465	+	0.0553944i	$0.0176416\pi$
$542$	1.52879	+	0.834783i	0.0656672	+	0.0358570i
$543$	5.60655	−	15.0317i	0.240600	−	0.645073i
$544$	−6.49525	+	4.17425i	−0.278482	+	0.178969i
$545$	−26.8857	+	2.69076i	−1.15166	+	0.115259i
$546$	−19.0273	+	2.73571i	−0.814293	+	0.117078i
$547$	22.3591	−	8.33951i	0.956006	−	0.356572i	0.177438	−	0.984132i	$-0.443219\pi$
$547$	22.3591	−	8.33951i	0.956006	−	0.356572i	0.778568	+	0.627560i	$0.215946\pi$
$548$	1.92935	−	1.44429i	0.0824176	−	0.0616970i
$549$	−1.60735	−	1.03298i	−0.0685999	−	0.0440865i
$550$	−5.33761	+	4.48940i	−0.227597	+	0.191429i
$551$		−	31.4772i		−	1.34097i
$552$	−4.78172	+	0.367647i	−0.203523	+	0.0156481i
$553$	20.4925	−	20.4925i	0.871428	−	0.871428i
$554$	20.1881	−	17.4931i	0.857712	−	0.743212i
$555$	0.581903	−	3.09490i	0.0247004	−	0.131371i
$556$	1.48062	−	10.2980i	0.0627924	−	0.436731i
$557$	5.90566	+	15.8337i	0.250231	+	0.670894i	0.999958	+	0.00914772i	$0.00291185\pi$
$557$	5.90566	+	15.8337i	0.250231	+	0.670894i	−0.749727	+	0.661747i	$0.769815\pi$
$558$	7.80697	+	5.84422i	0.330495	+	0.247406i
$559$	−20.5689	−	6.03956i	−0.869970	−	0.255446i
$560$	−1.45545	−	8.42080i	−0.0615040	−	0.355844i
$561$	4.47404	+	9.79678i	0.188894	+	0.413620i
$562$	14.2709	−	26.1353i	0.601983	−	1.10245i
$563$	20.9360	−	1.49737i	0.882348	−	0.0631068i	0.377192	−	0.926135i	$-0.376890\pi$
$563$	20.9360	−	1.49737i	0.882348	−	0.0631068i	0.505156	+	0.863028i	$0.331435\pi$
$564$	7.59352	+	6.57982i	0.319745	+	0.277061i
$565$	−18.1722	−	2.08895i	−0.764512	−	0.0878827i
$566$	−11.9702	+	5.46663i	−0.503147	+	0.229779i
$567$	−0.812368	+	3.73439i	−0.0341162	+	0.156830i
$568$	3.44794	−	1.88272i	0.144672	−	0.0789970i
$569$	−1.18212	−	8.22183i	−0.0495571	−	0.344677i	−0.999482	−	0.0321973i	$-0.989750\pi$
$569$	−1.18212	−	8.22183i	−0.0495571	−	0.344677i	0.949924	−	0.312480i	$-0.101160\pi$
$570$	−0.509331	+	11.8237i	−0.0213335	+	0.495241i
$571$	−1.91743	−	0.275685i	−0.0802420	−	0.0115371i	0.102077	−	0.994777i	$-0.467451\pi$
$571$	−1.91743	−	0.275685i	−0.0802420	−	0.0115371i	−0.182319	+	0.983239i	$0.558360\pi$
$572$	−6.85596	+	1.49142i	−0.286662	+	0.0623596i
$573$	−0.114359	+	1.59895i	−0.00477743	+	0.0667972i
$574$	24.9614			1.04187
$575$	−0.224583	+	23.9781i	−0.00936578	+	0.999956i
$576$	−1.00000			−0.0416667
$577$	0.457066	−	6.39062i	0.0190279	−	0.266045i	−0.979028	−	0.203724i	$-0.934695\pi$
$577$	0.457066	−	6.39062i	0.0190279	−	0.266045i	0.998056	−	0.0623206i	$-0.0198501\pi$
$578$	41.6388	−	9.05797i	1.73195	−	0.376762i
$579$	−15.7137	−	2.25930i	−0.653041	−	0.0938931i
$580$	0.572339	−	13.2864i	0.0237651	−	0.551687i
$581$	4.78854	+	33.3050i	0.198662	+	1.38173i
$582$	4.30145	−	2.34877i	0.178301	−	0.0973597i
$583$	0.841745	−	3.86944i	0.0348615	−	0.160256i
$584$	7.12548	−	3.25410i	0.294855	−	0.134656i
$585$	11.1736	+	1.28444i	0.461973	+	0.0531050i
$586$	−1.57173	−	1.36191i	−0.0649277	−	0.0562602i
$587$	−31.6974	+	2.26704i	−1.30829	+	0.0935709i	−0.708002	−	0.706211i	$-0.750403\pi$
$587$	−31.6974	+	2.26704i	−1.30829	+	0.0935709i	−0.600291	+	0.799782i	$0.704949\pi$
$588$	3.64499	−	6.67531i	0.150317	−	0.275285i
$589$	21.4414	+	46.9500i	0.883476	+	1.93454i
$590$	1.50152	+	8.68736i	0.0618167	+	0.357653i
$591$	−4.80351	−	1.41044i	−0.197590	−	0.0580177i
$592$	1.12743	+	0.843983i	0.0463371	+	0.0346875i
$593$	16.6259	+	44.5759i	0.682745	+	1.83051i	0.541827	+	0.840490i	$0.317733\pi$
$593$	16.6259	+	44.5759i	0.682745	+	1.83051i	0.140918	+	0.990021i	$0.454995\pi$
$594$	−0.198517	+	1.38072i	−0.00814527	+	0.0566516i
$595$	−12.1920	+	64.8441i	−0.499823	+	2.65835i
$596$	−11.2903	+	9.78309i	−0.462468	+	0.400731i
$597$	9.36280	−	9.36280i	0.383194	−	0.383194i
$598$	−11.4476	+	21.2333i	−0.468128	+	0.868293i
$599$			2.85376i			0.116601i	0.998299	+	0.0583007i	$0.0185682\pi$
$599$			2.85376i			0.116601i	−0.998299	+	0.0583007i	$0.981432\pi$
$600$	−0.429973	+	4.98148i	−0.0175536	+	0.203368i
$601$	−31.1743	−	20.0345i	−1.27163	−	0.817225i	−0.281796	−	0.959474i	$-0.590930\pi$
$601$	−31.1743	−	20.0345i	−1.27163	−	0.817225i	−0.989831	+	0.142250i	$0.954566\pi$
$602$	13.0392	−	9.76105i	0.531440	−	0.397831i
$603$	−10.8334	+	4.04064i	−0.441169	+	0.164548i
$604$	−18.0749	+	2.59878i	−0.735457	+	0.105743i
$605$	20.1452	−	2.01616i	0.819018	−	0.0819684i
$606$	14.0191	−	9.00953i	0.569487	−	0.365987i
$607$	7.88709	−	21.1461i	0.320127	−	0.858294i	−0.672828	−	0.739799i	$-0.734920\pi$
$607$	7.88709	−	21.1461i	0.320127	−	0.858294i	0.992955	−	0.118494i	$-0.0378068\pi$
$608$	−4.64523	−	2.53649i	−0.188389	−	0.102868i
$609$	14.8845	−	17.1776i	0.603149	−	0.696072i
$610$	−1.88425	−	3.83441i	−0.0762910	−	0.155251i
$611$	48.4917	−	14.2384i	1.96176	−	0.576026i
$612$	7.23412	+	2.69819i	0.292422	+	0.109068i
$613$	−26.9253	−	5.85724i	−1.08750	−	0.236572i	−0.367137	−	0.930167i	$-0.619662\pi$
$613$	−26.9253	−	5.85724i	−1.08750	−	0.236572i	−0.720365	+	0.693595i	$0.756026\pi$
$614$	−1.68793	+	5.74855i	−0.0681191	+	0.231992i
$615$	−14.1241	−	3.71577i	−0.569541	−	0.149834i
$616$	2.21458	−	4.84925i	0.0892279	−	0.195382i
$617$	13.5528	+	18.1044i	0.545616	+	0.728858i	0.985590	−	0.169153i	$-0.0541032\pi$
$617$	13.5528	+	18.1044i	0.545616	+	0.728858i	−0.439974	+	0.898011i	$0.645012\pi$
$618$	−3.89490	−	17.9046i	−0.156676	−	0.720228i
$619$	−3.75792	−	4.33687i	−0.151044	−	0.174314i	0.675185	−	0.737648i	$-0.264064\pi$
$619$	−3.75792	−	4.33687i	−0.151044	−	0.174314i	−0.826229	+	0.563335i	$0.809518\pi$
$620$	8.19663	+	20.2073i	0.329185	+	0.811544i
$621$	3.15989	+	3.60764i	0.126802	+	0.144770i
$622$	−13.2868	−	13.2868i	−0.532753	−	0.532753i
$623$	−3.39497	−	0.242813i	−0.136017	−	0.00972810i
$624$	−2.71937	+	4.23143i	−0.108862	+	0.169393i
$625$	24.6302	+	4.28380i	0.985210	+	0.171352i
$626$	−8.82110	−	4.02846i	−0.352562	−	0.161010i
$627$	−4.42433	+	5.91022i	−0.176691	+	0.236031i
$628$	2.10124	+	3.84814i	0.0838487	+	0.153557i
$629$	−5.87873	−	9.14749i	−0.234400	−	0.364734i
$630$	−5.86898	+	6.21154i	−0.233826	+	0.247474i
$631$	6.51467	+	22.1869i	0.259345	+	0.883248i	0.981491	+	0.191507i	$0.0613375\pi$
$631$	6.51467	+	22.1869i	0.259345	+	0.883248i	−0.722146	+	0.691740i	$0.756844\pi$
$632$	−0.540975	−	7.56381i	−0.0215188	−	0.300872i
$633$	−0.455567	−	6.36966i	−0.0181072	−	0.253171i
$634$	3.84732	+	13.1028i	0.152797	+	0.520377i
$635$	−0.316546	−	11.1629i	−0.0125618	−	0.442987i
$636$	−1.53479	−	2.38818i	−0.0608583	−	0.0946974i
$637$	−18.3340	−	33.5762i	−0.726419	−	1.33034i
$638$	4.97165	−	6.64135i	0.196830	−	0.262934i
$639$	−3.57346	−	1.63195i	−0.141364	−	0.0645588i
$640$	−1.91461	−	1.15510i	−0.0756817	−	0.0456595i
$641$	6.27206	−	9.75951i	0.247731	−	0.385477i	−0.695011	−	0.718999i	$-0.744601\pi$
$641$	6.27206	−	9.75951i	0.247731	−	0.385477i	0.942742	+	0.333521i	$0.108237\pi$
$642$	−3.57661	−	0.255804i	−0.141158	−	0.0100958i
$643$	4.24802	+	4.24802i	0.167526	+	0.167526i	0.785891	−	0.618365i	$-0.212205\pi$
$643$	4.24802	+	4.24802i	0.167526	+	0.167526i	−0.618365	+	0.785891i	$0.712205\pi$
$644$	−7.70273	−	16.6312i	−0.303530	−	0.655362i
$645$	−8.83115	+	3.58216i	−0.347726	+	0.141047i
$646$	26.7602	+	30.8829i	1.05287	+	1.21507i
$647$	−3.58206	−	16.4665i	−0.140825	−	0.647364i	−0.992392	−	0.123118i	$-0.960711\pi$
$647$	−3.58206	−	16.4665i	−0.140825	−	0.647364i	0.851567	−	0.524246i	$-0.175653\pi$
$648$	0.599278	+	0.800541i	0.0235419	+	0.0314482i
$649$	−2.28468	+	5.00275i	−0.0896815	+	0.196375i
$650$	19.9095	+	15.3659i	0.780915	+	0.602700i
$651$	−10.5002	+	35.7603i	−0.411534	+	1.40156i
$652$	16.0923	+	3.50067i	0.630224	+	0.137097i
$653$	7.44947	+	2.77851i	0.291520	+	0.108731i	0.490970	−	0.871177i	$-0.336643\pi$
$653$	7.44947	+	2.77851i	0.291520	+	0.108731i	−0.199449	+	0.979908i	$0.563915\pi$
$654$	−11.5943	+	3.40438i	−0.453371	+	0.133122i
$655$	−6.77789	+	19.8755i	−0.264834	+	0.776601i
$656$	4.27718	−	4.93613i	0.166996	−	0.192724i
$657$	−6.87518	−	3.75413i	−0.268226	−	0.146463i
$658$	−13.4192	+	35.9784i	−0.523137	+	1.40258i
$659$	−1.93175	+	1.24146i	−0.0752505	+	0.0483605i	−0.577725	−	0.816231i	$-0.696059\pi$
$659$	−1.93175	+	1.24146i	−0.0752505	+	0.0483605i	0.502475	+	0.864592i	$0.332423\pi$
$660$	−1.97496	+	2.41423i	−0.0768751	+	0.0939739i
$661$	−5.92726	+	0.852211i	−0.230544	+	0.0331472i	−0.256618	−	0.966513i	$-0.582608\pi$
$661$	−5.92726	+	0.852211i	−0.230544	+	0.0331472i	0.0260746	+	0.999660i	$0.491699\pi$
$662$	−14.5804	+	5.43822i	−0.566685	+	0.211362i
$663$	31.0895	−	23.2733i	1.20741	−	0.903859i
$664$	7.40661	+	4.75994i	0.287432	+	0.184721i
$665$	−43.0182	+	13.9675i	−1.66818	+	0.541635i
$666$		−	1.40833i		−	0.0545718i
$667$	−6.21151	−	27.8380i	−0.240511	−	1.07789i
$668$	−9.61336	+	9.61336i	−0.371952	+	0.371952i
$669$	−19.1721	+	16.6127i	−0.741237	+	0.642285i
$670$	−25.4091	−	4.77741i	−0.981637	−	0.184567i
$671$	0.379299	−	2.63808i	0.0146427	−	0.101842i
$672$	−1.33556	−	3.58077i	−0.0515203	−	0.138131i
$673$	35.6792	+	26.7091i	1.37533	+	1.02956i	0.994480	+	0.104926i	$0.0334605\pi$
$673$	35.6792	+	26.7091i	1.37533	+	1.02956i	0.380853	+	0.924636i	$0.375630\pi$
$674$	9.20166	+	2.70185i	0.354435	+	0.104071i
$675$	4.24555	−	2.64108i	0.163411	−	0.101655i
$676$	5.10960	+	11.1885i	0.196523	+	0.430326i
$677$	−12.9924	+	23.7938i	−0.499337	+	0.914468i	0.499502	+	0.866313i	$0.333516\pi$
$677$	−12.9924	+	23.7938i	−0.499337	+	0.914468i	−0.998840	+	0.0481557i	$0.984666\pi$
$678$	−8.15955	+	0.583582i	−0.313365	+	0.0224123i
$679$	14.1553	+	12.2656i	0.543229	+	0.470711i
$680$	10.7338	+	13.5221i	0.411624	+	0.518550i
$681$	16.4823	−	7.52723i	0.631605	−	0.288444i
$682$	−2.89161	+	13.2925i	−0.110725	+	0.508997i
$683$	−15.9098	+	8.68739i	−0.608770	+	0.332414i	−0.753890	−	0.657000i	$-0.771825\pi$
$683$	−15.9098	+	8.68739i	−0.608770	+	0.332414i	0.145120	+	0.989414i	$0.453643\pi$
$684$	0.753219	+	5.23875i	0.0288001	+	0.200309i
$685$	−3.64310	−	3.97109i	−0.139196	−	0.151728i
$686$	2.29102	+	0.329398i	0.0874714	+	0.0125765i
$687$	0.357908	−	0.0778582i	0.0136550	−	0.00297047i
$688$	0.304044	−	4.25109i	0.0115916	−	0.162071i
$689$	−14.2791			−0.543989
$690$	1.88277	+	10.5572i	0.0716760	+	0.401907i
$691$	34.8359			1.32522			0.662609	−	0.748965i	$-0.269449\pi$
$691$	34.8359			1.32522			0.662609	+	0.748965i	$0.269449\pi$
$692$	0.850021	−	11.8848i	0.0323129	−	0.451794i
$693$	−5.20917	+	1.13319i	−0.197880	+	0.0430462i
$694$	4.07363	+	0.585700i	0.154633	+	0.0222329i
$695$	−23.2422	−	1.00121i	−0.881625	−	0.0379779i
$696$	−0.846398	−	5.88683i	−0.0320826	−	0.223140i
$697$	−44.2602	+	24.1679i	−1.67648	+	0.915425i
$698$	−3.60130	+	16.5549i	−0.136311	+	0.626612i
$699$	19.6977	−	8.99564i	0.745036	−	0.340246i
$700$	−18.4118	+	5.11342i	−0.695900	+	0.193269i
$701$	−14.5710	−	12.6258i	−0.550337	−	0.476870i	0.334742	−	0.942310i	$-0.391351\pi$
$701$	−14.5710	−	12.6258i	−0.550337	−	0.476870i	−0.885080	+	0.465440i	$0.845896\pi$
$702$	5.01709	−	0.358830i	0.189358	−	0.0135432i
$703$	3.57222	−	6.54203i	0.134729	−	0.246737i
$704$	−0.579470	−	1.26886i	−0.0218396	−	0.0478220i
$705$	12.9489	−	18.3604i	0.487684	−	0.691492i
$706$	−9.00251	−	2.64338i	−0.338814	−	0.0994847i
$707$	50.9844	+	38.1665i	1.91747	+	1.43540i
$708$	1.37784	+	3.69412i	0.0517822	+	0.138833i
$709$	−3.17038	+	22.0505i	−0.119066	+	0.828123i	0.839522	+	0.543326i	$0.182835\pi$
$709$	−3.17038	+	22.0505i	−0.119066	+	0.828123i	−0.958588	+	0.284797i	$0.908074\pi$
$710$	−4.95673	−	7.25226i	−0.186023	−	0.272172i
$711$	−5.73095	+	4.96590i	−0.214927	+	0.186236i
$712$	−0.629751	+	0.629751i	−0.0236009	+	0.0236009i
$713$	28.2273	+	37.2908i	1.05712	+	1.39655i
$714$			29.5073i			1.10428i
$715$	4.84501	+	14.9221i	0.181193	+	0.558055i
$716$	2.24895	+	1.44531i	0.0840471	+	0.0540138i
$717$	11.6502	−	8.72126i	0.435086	−	0.325701i
$718$	−21.9929	+	8.20294i	−0.820769	+	0.306131i
$719$	19.5296	−	2.80793i	0.728331	−	0.104718i	0.231832	−	0.972756i	$-0.425528\pi$
$719$	19.5296	−	2.80793i	0.728331	−	0.104718i	0.496499	+	0.868038i	$0.334619\pi$
$720$	0.222676	+	2.22495i	0.00829865	+	0.0829191i
$721$	58.9103	−	37.8594i	2.19394	−	1.40996i
$722$	−3.14933	+	8.44369i	−0.117206	+	0.314241i
$723$	19.9101	+	10.8717i	0.740465	+	0.404324i
$724$	10.5061	−	12.1247i	0.390456	−	0.450610i
$725$	−29.6890	+	1.68513i	−1.10262	+	0.0625843i
$726$	8.68745	−	2.55086i	0.322421	−	0.0946715i
$727$	22.3610	+	8.34024i	0.829325	+	0.309322i	0.728040	−	0.685535i	$-0.240432\pi$
$727$	22.3610	+	8.34024i	0.829325	+	0.309322i	0.101286	+	0.994857i	$0.467704\pi$
$728$	−18.7837	−	4.08614i	−0.696169	−	0.151442i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−8.82689	−	15.1293i	−0.326698	−	0.559959i
$731$	−13.6697	+	29.9325i	−0.505593	+	1.10709i
$732$	−1.14501	−	1.52956i	−0.0423209	−	0.0565342i
$733$	−5.24195	−	24.0969i	−0.193616	−	0.890038i	−0.966736	−	0.255778i	$-0.917668\pi$
$733$	−5.24195	−	24.0969i	−0.193616	−	0.890038i	0.773120	−	0.634260i	$-0.218695\pi$
$734$	6.14210	+	7.08836i	0.226709	+	0.261636i
$735$	−15.6639	−	6.62351i	−0.577771	−	0.244312i
$736$	−4.60871	−	1.32657i	−0.169879	−	0.0488981i
$737$	−11.4046	−	11.4046i	−0.420095	−	0.420095i
$738$	−6.51480	−	0.465948i	−0.239813	−	0.0171518i
$739$	12.3075	−	19.1509i	0.452740	−	0.704477i	−0.537590	−	0.843206i	$-0.680665\pi$
$739$	12.3075	−	19.1509i	0.452740	−	0.704477i	0.990330	+	0.138729i	$0.0443016\pi$
$740$	1.62677	−	2.69641i	0.0598013	−	0.0991221i
$741$	24.2157	+	11.0589i	0.889586	+	0.406260i
$742$	6.50172	−	8.68528i	0.238686	−	0.318847i
$743$	15.3822	+	28.1704i	0.564319	+	1.03347i	0.991599	+	0.129353i	$0.0412901\pi$
$743$	15.3822	+	28.1704i	0.564319	+	1.03347i	−0.427280	+	0.904119i	$0.640528\pi$
$744$	5.27239	+	8.20400i	0.193295	+	0.300773i
$745$	24.2810	+	22.9419i	0.889587	+	0.840526i
$746$	−2.07273	−	7.05906i	−0.0758880	−	0.258451i
$747$	−0.628088	−	8.78182i	−0.0229806	−	0.321310i
$748$	0.768327	+	10.7426i	0.0280928	+	0.392789i
$749$	−3.86080	−	13.1487i	−0.141070	−	0.480442i
$750$	11.1793	−	0.152587i	0.408210	−	0.00557168i
$751$	11.5537	+	17.9778i	0.421599	+	0.656020i	0.985471	−	0.169841i	$-0.0543255\pi$
$751$	11.5537	+	17.9778i	0.421599	+	0.656020i	−0.563873	+	0.825862i	$0.690689\pi$
$752$	4.81533	+	8.81863i	0.175597	+	0.321582i
$753$	12.4330	−	16.6086i	0.453085	−	0.605250i
$754$	−27.2114	−	12.4270i	−0.990979	−	0.452565i
$755$	9.80701	+	39.6371i	0.356914	+	1.44254i
$756$	−2.06618	+	3.21505i	−0.0751464	+	0.116930i
$757$	25.8024	+	1.84542i	0.937803	+	0.0670730i	0.531866	−	0.846828i	$-0.321491\pi$
$757$	25.8024	+	1.84542i	0.937803	+	0.0670730i	0.405937	+	0.913901i	$0.366945\pi$
$758$	−2.07016	−	2.07016i	−0.0751916	−	0.0751916i
$759$	−2.74653	+	6.09999i	−0.0996928	+	0.221415i
$760$	−4.60918	+	10.9002i	−0.167193	+	0.395393i
$761$	−25.2040	−	29.0870i	−0.913645	−	1.05440i	−0.998317	−	0.0579935i	$-0.981530\pi$
$761$	−25.2040	−	29.0870i	−0.913645	−	1.05440i	0.0846721	−	0.996409i	$-0.473016\pi$
$762$	−1.06160	−	4.88008i	−0.0384576	−	0.176787i
$763$	−27.6751	−	36.9696i	−1.00191	−	1.33839i
$764$	−0.665925	+	1.45817i	−0.0240923	+	0.0527549i
$765$	4.39247	−	16.6964i	0.158810	−	0.603659i
$766$	−3.65349	+	12.4427i	−0.132006	+	0.449571i
$767$	19.3783	+	4.21548i	0.699708	+	0.152212i
$768$	−0.936950	−	0.349464i	−0.0338093	−	0.0126102i
$769$	3.15622	−	0.926749i	0.113816	−	0.0334194i	−0.224329	−	0.974514i	$-0.572019\pi$
$769$	3.15622	−	0.926749i	0.113816	−	0.0334194i	0.338145	+	0.941094i	$0.390201\pi$
$770$	−11.2825	−	3.84752i	−0.406592	−	0.138655i
$771$	−0.577560	+	0.666540i	−0.0208003	+	0.0240049i
$772$	−13.9335	−	7.60824i	−0.501476	−	0.273827i
$773$	−16.9880	+	45.5467i	−0.611018	+	1.63820i	0.149407	+	0.988776i	$0.452263\pi$
$773$	−16.9880	+	45.5467i	−0.611018	+	1.63820i	−0.760425	+	0.649426i	$0.775009\pi$
$774$	−3.58538	+	2.30418i	−0.128874	+	0.0828222i
$775$	43.1350	−	22.7368i	1.54946	−	0.816730i
$776$	4.85106	−	0.697477i	0.174143	−	0.0250380i
$777$	5.04292	−	1.88091i	0.180914	−	0.0674773i
$778$	14.9040	−	11.1570i	0.534333	−	0.399997i
$779$	−29.0808	−	18.6891i	−1.04193	−	0.669607i
$780$	10.0203	+	5.10824i	0.358783	+	0.182904i
$781$		−	5.47989i		−	0.196086i
$782$	29.7606	+	22.0317i	1.06424	+	0.787853i
$783$	−4.20542	+	4.20542i	−0.150289	+	0.150289i
$784$	5.74796	−	4.98063i	0.205284	−	0.177880i
$785$	8.09403	−	5.53205i	0.288888	−	0.197447i
$786$	−1.33651	+	9.29565i	−0.0476718	+	0.331565i
$787$	−5.92375	−	15.8822i	−0.211159	−	0.566139i	0.787587	−	0.616203i	$-0.211330\pi$
$787$	−5.92375	−	15.8822i	−0.211159	−	0.566139i	−0.998746	+	0.0500646i	$0.984057\pi$
$788$	−4.00775	−	3.00017i	−0.142770	−	0.106876i
$789$	−19.6815	−	5.77902i	−0.700681	−	0.205738i
$790$	−16.7087	+	2.88792i	−0.594468	+	0.102748i
$791$	−12.9872	−	28.4381i	−0.461773	−	1.01114i
$792$	−0.668513	+	1.22429i	−0.0237546	+	0.0435032i
$793$	−9.58595	+	0.685601i	−0.340407	+	0.0243464i
$794$	5.47494	+	4.74406i	0.194298	+	0.168360i
$795$	−4.97182	+	3.94662i	−0.176332	+	0.139972i
$796$	12.0444	−	5.50051i	0.426904	−	0.194960i
$797$	−7.43203	+	34.1645i	−0.263256	+	1.21017i	0.635633	+	0.771992i	$0.280739\pi$
$797$	−7.43203	+	34.1645i	−0.263256	+	1.21017i	−0.898889	+	0.438177i	$0.855624\pi$
$798$	−17.7528	+	9.69377i	−0.628443	+	0.343156i
$799$	−11.0404	−	76.7876i	−0.390581	−	2.71655i
$800$	−2.14371	+	4.51713i	−0.0757916	+	0.159705i
$801$	0.881537	+	0.126746i	0.0311476	+	0.00447834i
$802$	−10.6594	+	2.31882i	−0.376398	+	0.0818804i
$803$	0.779516	−	10.8991i	0.0275085	−	0.384619i
$804$	−11.5624			−0.407774
$805$	−35.2885	+	20.8416i	−1.24376	+	0.734569i
$806$	49.0523			1.72779
$807$	−1.44377	+	20.1865i	−0.0508229	+	0.710598i
$808$	16.2837	−	3.54230i	0.572859	−	0.124618i
$809$	−38.3326	−	5.51140i	−1.34770	−	0.193770i	−0.569607	−	0.821917i	$-0.692905\pi$
$809$	−38.3326	−	5.51140i	−1.34770	−	0.193770i	−0.778095	+	0.628147i	$0.783814\pi$
$810$	1.64772	−	1.51163i	0.0578950	−	0.0531131i
$811$	−3.63626	−	25.2907i	−0.127686	−	0.888077i	−0.948476	−	0.316848i	$-0.897376\pi$
$811$	−3.63626	−	25.2907i	−0.127686	−	0.888077i	0.820790	−	0.571230i	$-0.193533\pi$
$812$	19.9490	−	10.8930i	0.700071	−	0.382268i
$813$	0.370258	−	1.70205i	0.0129855	−	0.0596935i
$814$	1.78698	−	0.816087i	0.0626336	−	0.0286038i
$815$	4.20545	−	36.5842i	0.147310	−	1.28149i
$816$	5.83508	+	5.05613i	0.204269	+	0.177000i
$817$	−22.4994	+	1.60919i	−0.787156	+	0.0562985i
$818$	−17.2949	+	31.6733i	−0.604702	+	1.10743i
$819$	7.98551	+	17.4858i	0.279036	+	0.611004i
$820$	−11.9351	−	8.41737i	−0.416791	−	0.293947i
$821$	38.4407	+	11.2872i	1.34159	+	0.393926i	0.872236	−	0.489085i	$-0.162669\pi$
$821$	38.4407	+	11.2872i	1.34159	+	0.393926i	0.469353	+	0.883011i	$0.344487\pi$
$822$	−1.92935	−	1.44429i	−0.0672937	−	0.0503754i
$823$	11.7979	+	31.6314i	0.411249	+	1.10260i	0.963215	+	0.268734i	$0.0866051\pi$
$823$	11.7979	+	31.6314i	0.411249	+	1.10260i	−0.551966	+	0.833867i	$0.686122\pi$
$824$	2.60768	−	18.1368i	0.0908429	−	0.631826i
$825$	5.81133	+	3.85659i	0.202325	+	0.134269i
$826$	−11.3876	+	9.86742i	−0.396226	+	0.343332i
$827$	5.47322	−	5.47322i	0.190323	−	0.190323i	−0.605513	−	0.795835i	$-0.707032\pi$
$827$	5.47322	−	5.47322i	0.190323	−	0.190323i	0.795835	+	0.605513i	$0.207032\pi$
$828$	1.69992	+	4.48445i	0.0590763	+	0.155845i
$829$			5.14955i			0.178851i	0.995993	+	0.0894257i	$0.0285031\pi$
$829$			5.14955i			0.178851i	−0.995993	+	0.0894257i	$0.971497\pi$
$830$	8.94137	−	17.5393i	0.310359	−	0.608798i
$831$	−22.4722	−	14.4420i	−0.779552	−	0.500987i
$832$	−4.02665	+	3.01431i	−0.139599	+	0.104502i
$833$	−55.0201	+	20.5214i	−1.90633	+	0.711025i
$834$	−10.2980	+	1.48062i	−0.356589	+	0.0512698i
$835$	23.5299	+	19.2486i	0.814287	+	0.666125i
$836$	−6.21079	+	3.99143i	−0.214805	+	0.138046i
$837$	3.40801	−	9.13724i	0.117798	−	0.315829i
$838$	−14.6402	−	7.99415i	−0.505737	−	0.276153i
$839$	25.6253	−	29.5732i	0.884683	−	1.02098i	−0.114936	−	0.993373i	$-0.536666\pi$
$839$	25.6253	−	29.5732i	0.884683	−	1.02098i	0.999619	−	0.0276059i	$-0.00878834\pi$
$840$	−7.66965	+	3.76891i	−0.264628	+	0.130040i
$841$	6.11304	−	1.79495i	0.210795	−	0.0618949i
$842$	−34.5753	−	12.8959i	−1.19154	−	0.444423i
$843$	−29.0972	−	6.32971i	−1.00216	−	0.218007i
$844$	1.79913	−	6.12726i	0.0619285	−	0.210909i
$845$	23.7560	−	13.8600i	0.817232	−	0.476799i
$846$	4.17395	−	9.13968i	0.143503	−	0.314229i
$847$	20.7367	+	27.7009i	0.712520	+	0.951815i
$848$	−0.603437	−	2.77396i	−0.0207221	−	0.0952581i
$849$	8.61760	+	9.94524i	0.295755	+	0.341320i
$850$	27.6959	−	26.8933i	0.949963	−	0.922434i
$851$	1.86826	−	6.49060i	0.0640430	−	0.222495i
$852$	−2.77785	−	2.77785i	−0.0951675	−	0.0951675i
$853$	50.2469	+	3.59373i	1.72042	+	0.123047i	0.896323	−	0.443402i	$-0.146229\pi$
$853$	50.2469	+	3.59373i	1.72042	+	0.123047i	0.824097	+	0.566449i	$0.191683\pi$
$854$	3.94777	−	6.14285i	0.135090	−	0.210204i
$855$	11.4883	−	2.84242i	0.392890	−	0.0972088i
$856$	−3.26171	−	1.48957i	−0.111483	−	0.0509126i
$857$	3.13675	−	4.19021i	0.107149	−	0.143135i	−0.743761	−	0.668446i	$-0.766960\pi$
$857$	3.13675	−	4.19021i	0.107149	−	0.143135i	0.850911	+	0.525311i	$0.176051\pi$
$858$	3.36256	+	6.15807i	0.114796	+	0.210233i
$859$	−0.870484	−	1.35450i	−0.0297005	−	0.0462149i	0.826086	−	0.563544i	$-0.190563\pi$
$859$	−0.870484	−	1.35450i	−0.0297005	−	0.0462149i	−0.855786	+	0.517329i	$0.826926\pi$
$860$	−9.52618	+	0.270133i	−0.324840	+	0.00921147i
$861$	−7.03244	−	23.9503i	−0.239665	−	0.816224i
$862$	1.37308	+	19.1981i	0.0467672	+	0.653891i
$863$	−3.04202	−	42.5330i	−0.103552	−	1.44784i	−0.737961	−	0.674843i	$-0.764211\pi$
$863$	−3.04202	−	42.5330i	−0.103552	−	1.44784i	0.634409	−	0.772997i	$-0.281243\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	−26.6325	+	0.755216i	−0.905532	+	0.0256781i
$866$	5.72465	+	8.90774i	0.194532	+	0.302697i
$867$	−20.4221	−	37.4002i	−0.693570	−	1.27018i
$868$	−22.3351	+	29.8361i	−0.758101	+	1.01270i
$869$	−9.62195	−	4.39420i	−0.326402	−	0.149063i
$870$	−12.9094	+	3.19405i	−0.437671	+	0.108288i
$871$	−31.4425	+	48.9254i	−1.06539	+	1.65777i
$872$	−12.0529	−	0.862043i	−0.408164	−	0.0291925i
$873$	−3.46549	−	3.46549i	−0.117289	−	0.117289i
$874$	−3.47822	+	25.1431i	−0.117652	+	0.850478i
$875$	15.4770	+	39.8267i	0.523218	+	1.34639i
$876$	−5.12976	−	5.92006i	−0.173319	−	0.200020i
$877$	−0.895540	−	4.11673i	−0.0302402	−	0.139012i	0.959552	−	0.281533i	$-0.0908429\pi$
$877$	−0.895540	−	4.11673i	−0.0302402	−	0.139012i	−0.989792	+	0.142521i	$0.954479\pi$
$878$	−11.9623	−	15.9798i	−0.403709	−	0.539293i
$879$	−0.863939	+	1.89176i	−0.0291399	+	0.0638075i
$880$	−2.69412	+	1.57184i	−0.0908189	+	0.0529866i
$881$	1.79177	−	6.10220i	0.0603662	−	0.205588i	−0.923788	−	0.382905i	$-0.874924\pi$
$881$	1.79177	−	6.10220i	0.0603662	−	0.205588i	0.984154	+	0.177317i	$0.0567417\pi$
$882$	−7.43182	−	1.61669i	−0.250242	−	0.0544369i
$883$	1.08467	+	0.404560i	0.0365020	+	0.0136145i	0.367649	−	0.929965i	$-0.380163\pi$
$883$	1.08467	+	0.404560i	0.0365020	+	0.0136145i	−0.331147	+	0.943579i	$0.607436\pi$
$884$	37.2624	−	10.9412i	1.25327	−	0.367994i
$885$	7.91243	−	3.88821i	0.265973	−	0.130701i
$886$	2.89342	−	3.33919i	0.0972064	−	0.112182i
$887$	14.0111	+	7.65067i	0.470448	+	0.256884i	0.696941	−	0.717129i	$-0.254544\pi$
$887$	14.0111	+	7.65067i	0.470448	+	0.256884i	−0.226492	+	0.974013i	$0.572726\pi$
$888$	0.492162	−	1.31954i	0.0165159	−	0.0442808i
$889$	16.0566	−	10.3190i	0.538522	−	0.346087i
$890$	1.54140	+	1.26093i	0.0516677	+	0.0422666i
$891$	1.38072	−	0.198517i	0.0462558	−	0.00665058i
$892$	−23.7689	+	8.86532i	−0.795840	+	0.296833i
$893$	42.5716	−	31.8687i	1.42460	−	1.06645i
$894$	12.5676	+	8.07674i	0.420325	+	0.270126i
$895$	2.71496	−	5.32564i	0.0907511	−	0.178016i
$896$		−	3.82173i		−	0.127675i
$897$	23.5983	+	5.00180i	0.787926	+	0.167005i
$898$	17.4310	−	17.4310i	0.581678	−	0.581678i
$899$	−43.8330	+	37.9815i	−1.46191	+	1.26675i
$900$	4.90083	−	0.990888i	0.163361	−	0.0330296i
$901$	−3.11932	+	21.6953i	−0.103919	+	0.722776i
$902$	−3.18390	−	8.53638i	−0.106012	−	0.284230i
$903$	−13.0392	−	9.76105i	−0.433919	−	0.324828i
$904$	−7.84903	−	2.30468i	−0.261055	−	0.0766526i
$905$	−29.3163	−	20.6757i	−0.974507	−	0.687284i
$906$	7.58580	+	16.6106i	0.252021	+	0.551850i
$907$	12.9342	−	23.6872i	0.429473	−	0.786521i	−0.569908	−	0.821709i	$-0.693021\pi$
$907$	12.9342	−	23.6872i	0.429473	−	0.786521i	0.999381	+	0.0351876i	$0.0112029\pi$
$908$	18.0736	−	1.29265i	0.599794	−	0.0428981i
$909$	−12.5942	−	10.9130i	−0.417724	−	0.361960i
$910$	−4.90878	+	42.7026i	−0.162725	+	1.41558i
$911$	13.5044	−	6.16726i	0.447421	−	0.204330i	−0.178945	−	0.983859i	$-0.557269\pi$
$911$	13.5044	−	6.16726i	0.447421	−	0.204330i	0.626367	+	0.779529i	$0.284541\pi$
$912$	−1.12503	+	5.17167i	−0.0372534	+	0.171251i
$913$	10.7790	−	5.88576i	0.356731	−	0.194790i
$914$	−0.672757	−	4.67913i	−0.0222528	−	0.154772i
$915$	−3.14823	+	2.88820i	−0.104077	+	0.0954809i
$916$	0.362551	+	0.0521269i	0.0119790	+	0.00172232i
$917$	−35.0706	+	7.62913i	−1.15813	+	0.251936i
$918$	0.550804	−	7.70125i	0.0181793	−	0.254179i
$919$	−51.5573			−1.70072			−0.850359	−	0.526203i	$-0.823615\pi$
$919$	−51.5573			−1.70072			−0.850359	+	0.526203i	$0.823615\pi$
$920$	−1.92531	+	10.5496i	−0.0634756	+	0.347809i
$921$	5.99123			0.197418
$922$	−0.917405	+	12.8270i	−0.0302131	+	0.422435i
$923$	−19.3083	+	4.20026i	−0.635540	+	0.138253i
$924$	−5.27674	−	0.758680i	−0.173592	−	0.0249588i
$925$	−6.36163	−	3.01906i	−0.209169	−	0.0992661i
$926$	−3.22553	−	22.4340i	−0.105997	−	0.737229i
$927$	−16.0820	+	8.78144i	−0.528202	+	0.288420i
$928$	1.26420	−	5.81145i	0.0414995	−	0.190770i
$929$	2.92603	−	1.33627i	0.0960000	−	0.0438417i	−0.366836	−	0.930286i	$-0.619559\pi$
$929$	2.92603	−	1.33627i	0.0960000	−	0.0438417i	0.462836	+	0.886444i	$0.346832\pi$
$930$	17.0795	−	13.5577i	0.560058	−	0.444573i
$931$	−30.4218	−	26.3606i	−0.997034	−	0.863934i
$932$	21.5994	−	1.54482i	0.707512	−	0.0506023i
$933$	−9.00528	+	16.4919i	−0.294820	+	0.539922i
$934$	−16.8141	−	36.8177i	−0.550173	−	1.20471i
$935$	23.7307	−	4.10161i	0.776077	−	0.134137i
$936$	4.82616	+	1.41709i	0.157748	+	0.0463190i
$937$	−27.1822	−	20.3483i	−0.888003	−	0.664750i	0.0546574	−	0.998505i	$-0.482593\pi$
$937$	−27.1822	−	20.3483i	−0.888003	−	0.664750i	−0.942660	+	0.333755i	$0.891684\pi$
$938$	−15.4422	−	41.4023i	−0.504207	−	1.35183i
$939$	−1.38009	+	9.59873i	−0.0450375	+	0.313243i
$940$	18.5488	−	12.6776i	0.604994	−	0.413497i
$941$	18.0952	−	15.6796i	0.589888	−	0.511141i	−0.307987	−	0.951390i	$-0.599655\pi$
$941$	18.0952	−	15.6796i	0.589888	−	0.511141i	0.897875	+	0.440249i	$0.145110\pi$
$942$	3.10027	−	3.10027i	0.101012	−	0.101012i
$943$	−29.4067	−	10.7898i	−0.957614	−	0.351363i
$944$			3.94271i			0.128324i
$945$	7.61341	+	3.88125i	0.247664	+	0.126257i
$946$	−5.00131	−	3.21415i	−0.162607	−	0.104501i
$947$	11.4740	−	8.58935i	0.372856	−	0.279117i	−0.396373	−	0.918089i	$-0.629731\pi$
$947$	11.4740	−	8.58935i	0.372856	−	0.279117i	0.769229	+	0.638973i	$0.220640\pi$
$948$	−7.10502	+	2.65003i	−0.230760	+	0.0860691i
$949$	−39.0001	+	5.60737i	−1.26600	+	0.182023i
$950$	25.2788	+	7.82799i	0.820154	+	0.253973i
$951$	11.4881	−	7.38295i	0.372527	−	0.239409i
$952$	−10.3117	+	27.6469i	−0.334206	+	0.896040i
$953$	−25.6292	−	13.9946i	−0.830211	−	0.453330i	0.00715329	−	0.999974i	$-0.497723\pi$
$953$	−25.6292	−	13.9946i	−0.830211	−	0.453330i	−0.837365	+	0.546645i	$0.815905\pi$
$954$	−1.85904	+	2.14545i	−0.0601887	+	0.0694614i
$955$	3.39265	+	1.15695i	0.109784	+	0.0374381i
$956$	13.9635	−	4.10004i	0.451610	−	0.132605i
$957$	−7.77301	−	2.89918i	−0.251266	−	0.0937173i
$958$	2.27839	+	0.495634i	0.0736115	+	0.0160132i
$959$	2.59492	−	8.83748i	0.0837943	−	0.285377i
$960$	−0.568905	+	2.16249i	−0.0183613	+	0.0697939i
$961$	26.6297	−	58.3108i	0.859021	−	1.88099i
$962$	−4.24516	−	5.67087i	−0.136869	−	0.182836i
$963$	0.762205	+	3.50380i	0.0245617	+	0.112908i
$964$	14.8555	+	17.1441i	0.478463	+	0.552176i
$965$	−13.8253	+	32.6954i	−0.445053	+	1.05250i
$966$	−13.7874	+	12.0763i	−0.443603	+	0.388548i
$967$	−7.77763	−	7.77763i	−0.250112	−	0.250112i	0.570905	−	0.821016i	$-0.306593\pi$
$967$	−7.77763	−	7.77763i	−0.250112	−	0.250112i	−0.821016	+	0.570905i	$0.806593\pi$
$968$	9.03114	+	0.645920i	0.290272	+	0.0207606i
$969$	22.0927	−	34.3770i	0.709721	−	1.10435i
$970$	−2.63207	−	10.6381i	−0.0845106	−	0.341568i
$971$	−34.8195	−	15.9015i	−1.11741	−	0.510304i	−0.230883	−	0.972982i	$-0.574161\pi$
$971$	−34.8195	−	15.9015i	−1.11741	−	0.510304i	−0.886527	+	0.462678i	$0.846889\pi$
$972$	0.599278	−	0.800541i	0.0192218	−	0.0256774i
$973$	−19.0553	−	34.8972i	−0.610885	−	1.11875i
$974$	−8.61002	−	13.3975i	−0.275883	−	0.429282i
$975$	9.13432	−	23.4321i	0.292532	−	0.750428i
$976$	−0.538294	−	1.83326i	−0.0172304	−	0.0586813i
$977$	2.85669	+	39.9418i	0.0913937	+	1.27785i	0.811650	+	0.584144i	$0.198570\pi$
$977$	2.85669	+	39.9418i	0.0913937	+	1.27785i	−0.720256	+	0.693708i	$0.755976\pi$
$978$	−1.17486	−	16.4267i	−0.0375680	−	0.525269i
$979$	0.350001	+	1.19199i	0.0111861	+	0.0380963i
$980$	−12.3616	−	11.6799i	−0.394877	−	0.373100i
$981$	6.53296	+	10.1655i	0.208581	+	0.324559i
$982$	18.1657	+	33.2680i	0.579691	+	1.06162i
$983$	30.2517	−	40.4115i	0.964878	−	1.28893i	0.00753557	−	0.999972i	$-0.497601\pi$
$983$	30.2517	−	40.4115i	0.964878	−	1.28893i	0.957343	−	0.288955i	$-0.0933078\pi$
$984$	−5.94121	−	2.71326i	−0.189399	−	0.0864955i
$985$	−5.78280	+	9.58513i	−0.184255	+	0.305407i
$986$	−24.8258	+	38.6296i	−0.790613	+	1.23022i
$987$	38.3017	+	2.73939i	1.21916	+	0.0871957i
$988$	18.8242	+	18.8242i	0.598877	+	0.598877i
$989$	−19.5806	+	5.86305i	−0.622628	+	0.186434i
$990$	2.87285	+	1.21479i	0.0913051	+	0.0386085i
$991$	−27.5733	−	31.8212i	−0.875893	−	1.01083i	−0.999828	−	0.0185444i	$-0.994097\pi$
$991$	−27.5733	−	31.8212i	−0.875893	−	1.01083i	0.123935	−	0.992290i	$-0.460449\pi$
$992$	2.07296	+	9.52925i	0.0658166	+	0.302554i
$993$	9.32572	+	12.4577i	0.295943	+	0.395333i
$994$	6.23686	−	13.6568i	0.197821	−	0.433168i
$995$	−14.9204	−	25.5735i	−0.473008	−	0.810733i
$996$	2.48045	−	8.44762i	0.0785959	−	0.267673i
$997$	−21.3457	−	4.64348i	−0.676026	−	0.147060i	−0.138570	−	0.990353i	$-0.544251\pi$
$997$	−21.3457	−	4.64348i	−0.676026	−	0.147060i	−0.537455	+	0.843292i	$0.680614\pi$
$998$	4.48581	+	1.67312i	0.141996	+	0.0529617i
$999$	−1.35129	+	0.396773i	−0.0427528	+	0.0125534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.217.9	yes	240
5.3	odd	4	inner	690.2.w.b.493.4	yes	240
23.7	odd	22	inner	690.2.w.b.7.4	✓	240
115.53	even	44	inner	690.2.w.b.283.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.4	✓	240	23.7	odd	22	inner
690.2.w.b.217.9	yes	240	1.1	even	1	trivial
690.2.w.b.283.9	yes	240	115.53	even	44	inner
690.2.w.b.493.4	yes	240	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0962341 + 2.23400i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.35425 + 1.83156i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.0962341 + 2.23400i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.35425 + 1.83156i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(2.22144 + 0.255360i) q^{10} +(1.05421 + 0.913477i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(2.41058 - 4.41465i) q^{13} +(1.58760 + 3.47637i) q^{14} +(-0.380835 - 2.20340i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-6.18092 - 4.62698i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(0.753219 - 5.23875i) q^{19} +(0.413185 - 2.19756i) q^{20} +(2.88827 - 2.50270i) q^{21} +(0.986355 - 0.986355i) q^{22} +(-0.367647 - 4.78172i) q^{23} -1.00000i q^{24} +(-4.98148 - 0.429973i) q^{25} +(-4.23143 - 2.71937i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(3.58077 - 1.33556i) q^{28} +(5.88683 - 0.846398i) q^{29} +(-2.22495 + 0.222676i) q^{30} +(-8.20400 + 5.27239i) q^{31} +(0.349464 - 0.936950i) q^{32} +(-1.22429 - 0.668513i) q^{33} +(-5.05613 + 5.83508i) q^{34} +(-3.76891 - 7.66965i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.31954 + 0.492162i) q^{37} +(-5.17167 - 1.12503i) q^{38} +(-1.41709 + 4.82616i) q^{39} +(-2.16249 - 0.568905i) q^{40} +(2.71326 - 5.94121i) q^{41} +(-2.29028 - 3.05945i) q^{42} +(-0.905943 - 4.16455i) q^{43} +(-0.913477 - 1.05421i) q^{44} +(0.840498 + 2.07209i) q^{45} +(-4.79576 + 0.0255868i) q^{46} +(7.10477 + 7.10477i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(4.11192 - 6.39827i) q^{49} +(-0.784252 + 4.93811i) q^{50} +(7.02320 + 3.20739i) q^{51} +(-3.01431 + 4.02665i) q^{52} +(-1.36051 - 2.49158i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-2.14215 + 2.26719i) q^{55} +(-1.07671 - 3.66692i) q^{56} +(0.377572 + 5.27914i) q^{57} +(-0.424280 - 5.93221i) q^{58} +(1.11079 + 3.78300i) q^{59} +(0.0633826 + 2.23517i) q^{60} +(-1.03298 - 1.60735i) q^{61} +(4.67369 + 8.55923i) q^{62} +(-2.29028 + 3.05945i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(9.63032 + 5.81006i) q^{65} +(-0.754149 + 1.17348i) q^{66} +(-11.5329 - 0.824851i) q^{67} +(5.45952 + 5.45952i) q^{68} +(1.37567 + 4.59429i) q^{69} +(-7.91898 + 3.21216i) q^{70} +(-2.57260 - 2.96894i) q^{71} +(0.212565 + 0.977147i) q^{72} +(-4.69436 - 6.27093i) q^{73} +(0.585043 - 1.28107i) q^{74} +(4.95903 - 0.638742i) q^{75} +(-1.49111 + 5.07824i) q^{76} +(-5.20917 - 1.13319i) q^{77} +(4.71277 + 1.75777i) q^{78} +(-7.27596 + 2.13642i) q^{79} +(-0.721725 + 2.11639i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-5.73251 - 3.13019i) q^{82} +(3.07677 - 8.24914i) q^{83} +(-3.21505 + 2.06618i) q^{84} +(10.9315 - 13.3629i) q^{85} +(-4.21857 + 0.606539i) q^{86} +(-5.57238 + 2.07839i) q^{87} +(-1.11669 + 0.835943i) q^{88} +(0.749222 + 0.481496i) q^{89} +(2.12677 - 0.690535i) q^{90} +19.2230i q^{91} +(-0.316604 + 4.78537i) q^{92} +(6.89579 - 6.89579i) q^{93} +(7.59352 - 6.57982i) q^{94} +(11.6309 + 2.18684i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-1.71270 - 4.59194i) q^{97} +(-6.08862 - 4.55789i) q^{98} +(1.33841 + 0.392994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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