LMFDB - Embedded newform 552.2.bf.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

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

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

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26748 + 0.627300i) q^{2} +(-1.72666 + 0.136498i) q^{3} +(1.21299 - 1.59018i) q^{4} +(1.70656 + 0.245367i) q^{5} +(2.10288 - 1.25614i) q^{6} +(4.42418 - 2.02045i) q^{7} +(-0.539916 + 2.77642i) q^{8} +(2.96274 - 0.471373i) q^{9} +O(q^{10})$	\(q+(-1.26748 + 0.627300i) q^{2} +(-1.72666 + 0.136498i) q^{3} +(1.21299 - 1.59018i) q^{4} +(1.70656 + 0.245367i) q^{5} +(2.10288 - 1.25614i) q^{6} +(4.42418 - 2.02045i) q^{7} +(-0.539916 + 2.77642i) q^{8} +(2.96274 - 0.471373i) q^{9} +(-2.31695 + 0.759532i) q^{10} +(-1.04171 - 3.54775i) q^{11} +(-1.87737 + 2.91127i) q^{12} +(-0.139816 - 0.0638519i) q^{13} +(-4.34011 + 5.33617i) q^{14} +(-2.98015 - 0.190723i) q^{15} +(-1.05732 - 3.85773i) q^{16} +(-2.85642 + 1.83571i) q^{17} +(-3.45950 + 2.45598i) q^{18} +(-3.15372 - 2.02677i) q^{19} +(2.46022 - 2.41611i) q^{20} +(-7.36328 + 4.09254i) q^{21} +(3.54585 + 3.84321i) q^{22} +(2.81381 - 3.88361i) q^{23} +(0.553277 - 4.86764i) q^{24} +(-1.94531 - 0.571194i) q^{25} +(0.217268 - 0.00677600i) q^{26} +(-5.05131 + 1.21831i) q^{27} +(2.15360 - 9.48601i) q^{28} +(5.19619 - 3.33939i) q^{29} +(3.89691 - 1.62771i) q^{30} +(2.04424 + 2.35917i) q^{31} +(3.76008 + 4.22632i) q^{32} +(2.28295 + 5.98357i) q^{33} +(2.46890 - 4.11856i) q^{34} +(8.04590 - 2.36249i) q^{35} +(2.84420 - 5.28304i) q^{36} +(0.751692 + 5.22813i) q^{37} +(5.26866 + 0.590556i) q^{38} +(0.250131 + 0.0911661i) q^{39} +(-1.60264 + 4.60566i) q^{40} +(-8.13898 - 1.17021i) q^{41} +(6.76553 - 9.80618i) q^{42} +(6.49227 - 7.49248i) q^{43} +(-6.90512 - 2.64687i) q^{44} +(5.17176 - 0.0774704i) q^{45} +(-1.13025 + 6.68749i) q^{46} -4.59284i q^{47} +(2.35220 + 6.51668i) q^{48} +(10.9071 - 12.5875i) q^{49} +(2.82394 - 0.496318i) q^{50} +(4.68151 - 3.55955i) q^{51} +(-0.271131 + 0.144881i) q^{52} +(-2.55912 + 1.16871i) q^{53} +(5.63816 - 4.71287i) q^{54} +(-0.907249 - 6.31006i) q^{55} +(3.22094 + 13.3742i) q^{56} +(5.72207 + 3.06908i) q^{57} +(-4.49125 + 7.49217i) q^{58} +(-3.43267 + 7.51649i) q^{59} +(-3.91818 + 4.50762i) q^{60} +(3.14182 + 3.62585i) q^{61} +(-4.07093 - 1.70785i) q^{62} +(12.1553 - 8.07151i) q^{63} +(-7.41698 - 2.99806i) q^{64} +(-0.222938 - 0.143274i) q^{65} +(-6.64708 - 6.15194i) q^{66} +(5.42635 + 1.59332i) q^{67} +(-0.545705 + 6.76891i) q^{68} +(-4.32840 + 7.08978i) q^{69} +(-8.71599 + 8.04159i) q^{70} +(2.55546 - 8.70311i) q^{71} +(-0.290900 + 8.48029i) q^{72} +(12.7459 + 8.19127i) q^{73} +(-4.23236 - 6.15499i) q^{74} +(3.43686 + 0.720729i) q^{75} +(-7.04836 + 2.55652i) q^{76} +(-11.7768 - 13.5911i) q^{77} +(-0.374224 + 0.0413565i) q^{78} +(-14.7505 - 6.73631i) q^{79} +(-0.857821 - 6.84289i) q^{80} +(8.55562 - 2.79311i) q^{81} +(11.0500 - 3.62237i) q^{82} +(8.15748 - 1.17287i) q^{83} +(-2.42372 + 16.6731i) q^{84} +(-5.32509 + 2.43189i) q^{85} +(-3.52876 + 13.5691i) q^{86} +(-8.51626 + 6.47528i) q^{87} +(10.4125 - 0.976744i) q^{88} +(-2.16000 + 2.49277i) q^{89} +(-6.50648 + 3.34244i) q^{90} -0.747581 q^{91} +(-2.76251 - 9.18524i) q^{92} +(-3.85173 - 3.79447i) q^{93} +(2.88109 + 5.82131i) q^{94} +(-4.88473 - 4.23264i) q^{95} +(-7.06928 - 6.78420i) q^{96} +(-4.91572 - 0.706774i) q^{97} +(-5.92836 + 22.7963i) q^{98} +(-4.75863 - 10.0200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.26748	+	0.627300i	−0.896241	+	0.443568i
$2$	−1.26748	+	0.627300i	−0.896241	+	0.443568i
$3$	−1.72666	+	0.136498i	−0.996890	+	0.0788072i
$3$	−1.72666	+	0.136498i	−0.996890	+	0.0788072i
$4$	1.21299	−	1.59018i	0.606494	−	0.795088i
$5$	1.70656	+	0.245367i	0.763199	+	0.109731i	0.512913	−	0.858441i	$-0.328566\pi$
$5$	1.70656	+	0.245367i	0.763199	+	0.109731i	0.250286	+	0.968172i	$0.419475\pi$
$6$	2.10288	−	1.25614i	0.858497	−	0.512819i
$7$	4.42418	−	2.02045i	1.67218	−	0.763660i	0.672459	−	0.740134i	$-0.265238\pi$
$7$	4.42418	−	2.02045i	1.67218	−	0.763660i	0.999723	−	0.0235260i	$-0.00748923\pi$
$8$	−0.539916	+	2.77642i	−0.190889	+	0.981612i
$9$	2.96274	−	0.471373i	0.987579	−	0.157124i
$10$	−2.31695	+	0.759532i	−0.732683	+	0.240185i
$11$	−1.04171	−	3.54775i	−0.314088	−	1.06969i	−0.953643	−	0.300940i	$-0.902700\pi$
$11$	−1.04171	−	3.54775i	−0.314088	−	1.06969i	0.639555	−	0.768745i	$-0.279119\pi$
$12$	−1.87737	+	2.91127i	−0.541949	+	0.840411i
$13$	−0.139816	−	0.0638519i	−0.0387780	−	0.0177093i	0.395932	−	0.918280i	$-0.370422\pi$
$13$	−0.139816	−	0.0638519i	−0.0387780	−	0.0177093i	−0.434710	+	0.900571i	$0.643149\pi$
$14$	−4.34011	+	5.33617i	−1.15994	+	1.42615i
$15$	−2.98015	−	0.190723i	−0.769473	−	0.0492446i
$16$	−1.05732	−	3.85773i	−0.264329	−	0.964432i
$17$	−2.85642	+	1.83571i	−0.692784	+	0.445225i	−0.839075	−	0.544016i	$-0.816903\pi$
$17$	−2.85642	+	1.83571i	−0.692784	+	0.445225i	0.146290	+	0.989242i	$0.453267\pi$
$18$	−3.45950	+	2.45598i	−0.815413	+	0.578880i
$19$	−3.15372	−	2.02677i	−0.723513	−	0.464974i	0.126344	−	0.991986i	$-0.459676\pi$
$19$	−3.15372	−	2.02677i	−0.723513	−	0.464974i	−0.849857	+	0.527013i	$0.823312\pi$
$20$	2.46022	−	2.41611i	0.550122	−	0.540259i
$21$	−7.36328	+	4.09254i	−1.60680	+	0.893065i
$22$	3.54585	+	3.84321i	0.755977	+	0.819376i
$23$	2.81381	−	3.88361i	0.586720	−	0.809790i
$23$	2.81381	−	3.88361i	0.586720	−	0.809790i
$24$	0.553277	−	4.86764i	0.112937	−	0.993602i
$25$	−1.94531	−	0.571194i	−0.389062	−	0.114239i
$26$	0.217268	−	0.00677600i	0.0426097	−	0.00132888i
$27$	−5.05131	+	1.21831i	−0.972125	+	0.234464i
$28$	2.15360	−	9.48601i	0.406992	−	1.79269i
$29$	5.19619	−	3.33939i	0.964909	−	0.620109i	0.0395565	−	0.999217i	$-0.487405\pi$
$29$	5.19619	−	3.33939i	0.964909	−	0.620109i	0.925352	+	0.379108i	$0.123769\pi$
$30$	3.89691	−	1.62771i	0.711476	−	0.297179i
$31$	2.04424	+	2.35917i	0.367156	+	0.423720i	0.909024	−	0.416743i	$-0.136829\pi$
$31$	2.04424	+	2.35917i	0.367156	+	0.423720i	−0.541869	+	0.840463i	$0.682283\pi$
$32$	3.76008	+	4.22632i	0.664694	+	0.747115i
$33$	2.28295	+	5.98357i	0.397410	+	1.04161i
$34$	2.46890	−	4.11856i	0.423414	−	0.706326i
$35$	8.04590	−	2.36249i	1.36000	−	0.399333i
$36$	2.84420	−	5.28304i	0.474033	−	0.880507i
$37$	0.751692	+	5.22813i	0.123577	+	0.859499i	0.953451	+	0.301548i	$0.0975033\pi$
$37$	0.751692	+	5.22813i	0.123577	+	0.859499i	−0.829874	+	0.557951i	$0.811588\pi$
$38$	5.26866	+	0.590556i	0.854690	+	0.0958008i
$39$	0.250131	+	0.0911661i	0.0400530	+	0.0145983i
$40$	−1.60264	+	4.60566i	−0.253400	+	0.728218i
$41$	−8.13898	−	1.17021i	−1.27110	−	0.182756i	−0.526444	−	0.850210i	$-0.676475\pi$
$41$	−8.13898	−	1.17021i	−1.27110	−	0.182756i	−0.744651	+	0.667454i	$0.767384\pi$
$42$	6.76553	−	9.80618i	1.04394	−	1.51313i
$43$	6.49227	−	7.49248i	0.990063	−	1.14259i	0.000281200	−	1.00000i	$-0.499910\pi$
$43$	6.49227	−	7.49248i	0.990063	−	1.14259i	0.989781	−	0.142593i	$-0.0455441\pi$
$44$	−6.90512	−	2.64687i	−1.04099	−	0.399031i
$45$	5.17176	−	0.0774704i	0.770960	−	0.0115486i
$46$	−1.13025	+	6.68749i	−0.166646	+	0.986017i
$47$		−	4.59284i		−	0.669934i	−0.942230	−	0.334967i	$-0.891275\pi$
$47$		−	4.59284i		−	0.669934i	0.942230	−	0.334967i	$-0.108725\pi$
$48$	2.35220	+	6.51668i	0.339512	+	0.940602i
$49$	10.9071	−	12.5875i	1.55816	−	1.79821i
$50$	2.82394	−	0.496318i	0.399366	−	0.0701900i
$51$	4.68151	−	3.55955i	0.655543	−	0.498437i
$52$	−0.271131	+	0.144881i	−0.0375991	+	0.0200913i
$53$	−2.55912	+	1.16871i	−0.351522	+	0.160535i	−0.583347	−	0.812223i	$-0.698257\pi$
$53$	−2.55912	+	1.16871i	−0.351522	+	0.160535i	0.231826	+	0.972757i	$0.425530\pi$
$54$	5.63816	−	4.71287i	0.767257	−	0.641340i
$55$	−0.907249	−	6.31006i	−0.122333	−	0.850848i
$56$	3.22094	+	13.3742i	0.430416	+	1.78721i
$57$	5.72207	+	3.06908i	0.757907	+	0.406510i
$58$	−4.49125	+	7.49217i	−0.589730	+	0.983770i
$59$	−3.43267	+	7.51649i	−0.446895	+	0.978564i	0.543386	+	0.839483i	$0.317142\pi$
$59$	−3.43267	+	7.51649i	−0.446895	+	0.978564i	−0.990281	+	0.139081i	$0.955585\pi$
$60$	−3.91818	+	4.50762i	−0.505835	+	0.581932i
$61$	3.14182	+	3.62585i	0.402268	+	0.464242i	0.920354	−	0.391086i	$-0.127901\pi$
$61$	3.14182	+	3.62585i	0.402268	+	0.464242i	−0.518086	+	0.855329i	$0.673355\pi$
$62$	−4.07093	−	1.70785i	−0.517008	−	0.216897i
$63$	12.1553	−	8.07151i	1.53142	−	1.01691i
$64$	−7.41698	−	2.99806i	−0.927123	−	0.374758i
$65$	−0.222938	−	0.143274i	−0.0276521	−	0.0177709i
$66$	−6.64708	−	6.15194i	−0.818199	−	0.757251i
$67$	5.42635	+	1.59332i	0.662934	+	0.194655i	0.595854	−	0.803093i	$-0.296814\pi$
$67$	5.42635	+	1.59332i	0.662934	+	0.194655i	0.0670799	+	0.997748i	$0.478632\pi$
$68$	−0.545705	+	6.76891i	−0.0661764	+	0.820851i
$69$	−4.32840	+	7.08978i	−0.521078	+	0.853509i
$70$	−8.71599	+	8.04159i	−1.04176	+	0.961154i
$71$	2.55546	−	8.70311i	0.303278	−	1.03287i	−0.657016	−	0.753877i	$-0.728181\pi$
$71$	2.55546	−	8.70311i	0.303278	−	1.03287i	0.960293	−	0.278992i	$-0.0900004\pi$
$72$	−0.290900	+	8.48029i	−0.0342829	+	0.999412i
$73$	12.7459	+	8.19127i	1.49179	+	0.958716i	0.995912	+	0.0903247i	$0.0287905\pi$
$73$	12.7459	+	8.19127i	1.49179	+	0.958716i	0.495879	+	0.868392i	$0.334846\pi$
$74$	−4.23236	−	6.15499i	−0.492002	−	0.715503i
$75$	3.43686	+	0.720729i	0.396855	+	0.0832227i
$76$	−7.04836	+	2.55652i	−0.808502	+	0.293253i
$77$	−11.7768	−	13.5911i	−1.34209	−	1.54885i
$78$	−0.374224	+	0.0413565i	−0.0423725	+	0.00468270i
$79$	−14.7505	−	6.73631i	−1.65956	−	0.757894i	−0.999980	−	0.00625534i	$-0.998009\pi$
$79$	−14.7505	−	6.73631i	−1.65956	−	0.757894i	−0.659575	−	0.751638i	$-0.729264\pi$
$80$	−0.857821	−	6.84289i	−0.0959073	−	0.765059i
$81$	8.55562	−	2.79311i	0.950624	−	0.310345i
$82$	11.0500	−	3.62237i	1.22027	−	0.400024i
$83$	8.15748	−	1.17287i	0.895399	−	0.128739i	0.320774	−	0.947156i	$-0.396057\pi$
$83$	8.15748	−	1.17287i	0.895399	−	0.128739i	0.574625	+	0.818417i	$0.305148\pi$
$84$	−2.42372	+	16.6731i	−0.264450	+	1.81919i
$85$	−5.32509	+	2.43189i	−0.577587	+	0.263775i
$86$	−3.52876	+	13.5691i	−0.380516	+	1.46320i
$87$	−8.51626	+	6.47528i	−0.913039	+	0.694222i
$88$	10.4125	−	0.976744i	1.10997	−	0.104121i
$89$	−2.16000	+	2.49277i	−0.228959	+	0.264233i	−0.858592	−	0.512660i	$-0.828660\pi$
$89$	−2.16000	+	2.49277i	−0.228959	+	0.264233i	0.629632	+	0.776893i	$0.283206\pi$
$90$	−6.50648	+	3.34244i	−0.685843	+	0.352324i
$91$	−0.747581			−0.0783678
$92$	−2.76251	−	9.18524i	−0.288011	−	0.957627i
$93$	−3.85173	−	3.79447i	−0.399406	−	0.393468i
$94$	2.88109	+	5.82131i	0.297162	+	0.600422i
$95$	−4.88473	−	4.23264i	−0.501162	−	0.434260i
$96$	−7.06928	−	6.78420i	−0.721505	−	0.692409i
$97$	−4.91572	−	0.706774i	−0.499116	−	0.0717620i	−0.111840	−	0.993726i	$-0.535675\pi$
$97$	−4.91572	−	0.706774i	−0.499116	−	0.0717620i	−0.387275	+	0.921964i	$0.626584\pi$
$98$	−5.92836	+	22.7963i	−0.598855	+	2.30278i
$99$	−4.75863	−	10.0200i	−0.478260	−	1.00705i
$100$	−3.26794	+	2.40053i	−0.326794	+	0.240053i
$101$	1.50575	+	10.4727i	0.149828	+	1.04208i	0.916499	+	0.400036i	$0.131002\pi$
$101$	1.50575	+	10.4727i	0.149828	+	1.04208i	−0.766671	+	0.642040i	$0.778088\pi$
$102$	−3.70079	+	7.44836i	−0.366433	+	0.737498i
$103$	0.966749	+	3.29244i	0.0952566	+	0.324414i	0.993311	−	0.115470i	$-0.0368375\pi$
$103$	0.966749	+	3.29244i	0.0952566	+	0.324414i	−0.898054	+	0.439885i	$0.855019\pi$
$104$	0.252768	−	0.353713i	0.0247860	−	0.0346844i
$105$	−13.5701	+	5.17747i	−1.32430	+	0.505270i
$106$	2.51049	−	3.08664i	0.243840	−	0.299801i
$107$	−0.241758	+	0.209484i	−0.0233716	+	0.0202516i	−0.666468	−	0.745533i	$-0.732195\pi$
$107$	−0.241758	+	0.209484i	−0.0233716	+	0.0202516i	0.643097	+	0.765785i	$0.277649\pi$
$108$	−4.18985	+	9.51026i	−0.403169	+	0.915126i
$109$	7.68472	−	4.93867i	0.736062	−	0.473039i	−0.118128	−	0.992998i	$-0.537689\pi$
$109$	7.68472	−	4.93867i	0.736062	−	0.473039i	0.854191	+	0.519960i	$0.174053\pi$
$110$	5.10822	+	7.42873i	0.487049	+	0.708301i
$111$	−2.01155	−	8.92462i	−0.190928	−	0.847087i
$112$	−12.4721	−	14.9310i	−1.17851	−	1.41085i
$113$	7.99381	+	2.34720i	0.751995	+	0.220806i	0.635197	−	0.772350i	$-0.280919\pi$
$113$	7.99381	+	2.34720i	0.751995	+	0.220806i	0.116798	+	0.993156i	$0.462737\pi$
$114$	−9.17782	−	0.300529i	−0.859581	−	0.0281471i
$115$	5.75486	−	5.93722i	0.536644	−	0.553649i
$116$	0.992705	−	12.3135i	0.0921704	−	1.14328i
$117$	−0.444336	−	0.123271i	−0.0410789	−	0.0113964i
$118$	−0.364277	−	11.6803i	−0.0335344	−	1.07526i
$119$	−8.92835	+	13.8928i	−0.818461	+	1.27355i
$120$	2.13856	−	8.17118i	0.195223	−	0.745923i
$121$	−2.24755	+	1.44441i	−0.204322	+	0.131310i
$122$	−6.25667	−	2.62481i	−0.566452	−	0.237639i
$123$	14.2130	+	0.909602i	1.28154	+	0.0820160i
$124$	6.23113	−	0.389043i	0.559572	−	0.0349371i
$125$	−11.0212	−	5.03321i	−0.985765	−	0.450184i
$126$	−10.3433	+	17.8555i	−0.921452	+	1.59069i
$127$	0.512454	−	0.150470i	0.0454729	−	0.0133521i	−0.258917	−	0.965900i	$-0.583366\pi$
$127$	0.512454	−	0.150470i	0.0454729	−	0.0133521i	0.304390	+	0.952548i	$0.401547\pi$
$128$	11.2815	−	0.852705i	0.997156	−	0.0753692i
$129$	−10.1873	+	13.8232i	−0.896939	+	1.21706i
$130$	0.372444	+	0.0417466i	0.0326655	+	0.00366142i
$131$	−5.35742	−	11.7311i	−0.468080	−	1.02495i	−0.985571	−	0.169263i	$-0.945861\pi$
$131$	−5.35742	−	11.7311i	−0.468080	−	1.02495i	0.517491	−	0.855689i	$-0.326866\pi$
$132$	12.2841	+	3.62772i	1.06920	+	0.315752i
$133$	−18.0476	−	2.59486i	−1.56493	−	0.225003i
$134$	−7.87726	+	1.38446i	−0.680491	+	0.119599i
$135$	−8.91932	+	0.839701i	−0.767652	+	0.0722699i
$136$	−3.55447	−	8.92175i	−0.304794	−	0.765034i
$137$	11.1808			0.955237			0.477619	−	0.878567i	$-0.341500\pi$
$137$	11.1808			0.955237			0.477619	+	0.878567i	$0.341500\pi$
$138$	1.03872	−	11.7013i	0.0884221	−	0.996083i
$139$			10.4551i			0.886793i	0.896326	+	0.443397i	$0.146227\pi$
$139$			10.4551i			0.886793i	−0.896326	+	0.443397i	$0.853773\pi$
$140$	6.00281	−	15.6601i	0.507330	−	1.32352i
$141$	0.626914	+	7.93029i	0.0527957	+	0.667851i
$142$	2.22048	+	12.6340i	0.186338	+	1.06022i
$143$	−0.0808821	+	0.562547i	−0.00676370	+	0.0470426i
$144$	−4.95098	−	10.9310i	−0.412582	−	0.910921i
$145$	9.68701	−	4.42391i	0.804463	−	0.367386i
$146$	−21.2935	−	2.38675i	−1.76226	−	0.197529i
$147$	−17.1147	+	23.2231i	−1.41160	+	1.91541i
$148$	9.22544	+	5.14634i	0.758326	+	0.423027i
$149$	−0.841739	−	2.86670i	−0.0689580	−	0.234849i	0.917802	−	0.397039i	$-0.129962\pi$
$149$	−0.841739	−	2.86670i	−0.0689580	−	0.234849i	−0.986760	+	0.162190i	$0.948144\pi$
$150$	−4.80825	+	1.24244i	−0.392592	+	0.101445i
$151$	−8.34416	+	18.2712i	−0.679038	+	1.48689i	0.184621	+	0.982810i	$0.440894\pi$
$151$	−8.34416	+	18.2712i	−0.679038	+	1.48689i	−0.863659	+	0.504076i	$0.831833\pi$
$152$	7.32991	−	7.66176i	0.594534	−	0.621451i
$153$	−7.59752	+	6.78517i	−0.614223	+	0.548549i
$154$	23.4525	+	9.83885i	1.88986	+	0.792837i
$155$	2.90976	+	4.52767i	0.233717	+	0.363671i
$156$	0.448376	−	0.287169i	0.0358988	−	0.0229919i
$157$	7.20932	+	4.63315i	0.575367	+	0.369766i	0.795729	−	0.605652i	$-0.207088\pi$
$157$	7.20932	+	4.63315i	0.575367	+	0.369766i	−0.220363	+	0.975418i	$0.570724\pi$
$158$	22.9215	−	0.714861i	1.82354	−	0.0568713i
$159$	4.25921	−	2.36728i	0.337777	−	0.187738i
$160$	5.37982	+	8.13509i	0.425312	+	0.643135i
$161$	4.60214	−	22.8670i	0.362700	−	1.80217i
$162$	−9.09192	+	8.90713i	−0.714328	+	0.699811i
$163$	−5.71169	+	19.4522i	−0.447374	+	1.52362i	0.359644	+	0.933090i	$0.382898\pi$
$163$	−5.71169	+	19.4522i	−0.447374	+	1.52362i	−0.807018	+	0.590527i	$0.798920\pi$
$164$	−11.7333	+	11.5230i	−0.916219	+	0.899792i
$165$	2.42783	+	10.7715i	0.189006	+	0.838561i
$166$	−9.60366	+	6.60377i	−0.745389	+	0.512552i
$167$	−3.44485	−	5.36029i	−0.266570	−	0.414791i	0.682003	−	0.731349i	$-0.261109\pi$
$167$	−3.44485	−	5.36029i	−0.266570	−	0.414791i	−0.948573	+	0.316558i	$0.897473\pi$
$168$	−7.38704	−	22.6532i	−0.569923	−	1.74773i
$169$	−8.49772	−	9.80689i	−0.653671	−	0.754376i
$170$	5.22390	−	6.42279i	0.400655	−	0.492606i
$171$	−10.2990	−	4.51822i	−0.787585	−	0.345517i
$172$	−4.03931	−	19.4122i	−0.307995	−	1.48016i
$173$	13.7974	−	4.05128i	1.04900	−	0.308013i	0.288585	−	0.957454i	$-0.406815\pi$
$173$	13.7974	−	4.05128i	1.04900	−	0.308013i	0.760412	+	0.649441i	$0.224997\pi$
$174$	6.73221	−	13.5495i	0.510367	−	1.02719i
$175$	−9.76047	+	1.40334i	−0.737822	+	0.106083i
$176$	−12.5848	+	7.76974i	−0.948617	+	0.585666i
$177$	4.90107	−	13.4470i	0.368387	−	1.01074i
$178$	1.17403	−	4.51449i	0.0879972	−	0.338375i
$179$	−1.13428	+	7.88908i	−0.0847800	+	0.589658i	0.902503	+	0.430684i	$0.141728\pi$
$179$	−1.13428	+	7.88908i	−0.0847800	+	0.589658i	−0.987283	+	0.158974i	$0.949181\pi$
$180$	6.15009	−	8.31798i	0.458401	−	0.619985i
$181$	12.8807	−	14.8651i	0.957413	−	1.10491i	−0.0369960	−	0.999315i	$-0.511779\pi$
$181$	12.8807	−	14.8651i	0.957413	−	1.10491i	0.994409	−	0.105598i	$-0.0336757\pi$
$182$	0.947541	−	0.468958i	0.0702364	−	0.0347615i
$183$	−5.91978	−	5.83177i	−0.437603	−	0.431097i
$184$	9.26331	+	9.90914i	0.682900	+	0.730512i
$185$			9.10658i			0.669529i
$186$	7.26224	+	2.39320i	0.532494	+	0.175478i
$187$	9.48821	+	8.22158i	0.693847	+	0.601221i
$188$	−7.30342	−	5.57106i	−0.532657	−	0.406311i
$189$	−19.8864	+	15.5960i	−1.44652	+	1.13444i
$190$	8.84641	+	2.30058i	0.641786	+	0.166901i
$191$	8.56084	+	18.7456i	0.619441	+	1.35639i	0.915925	+	0.401349i	$0.131458\pi$
$191$	8.56084	+	18.7456i	0.619441	+	1.35639i	−0.296484	+	0.955038i	$0.595814\pi$
$192$	13.2159	+	4.16424i	0.953773	+	0.300528i
$193$	0.395580	+	2.75132i	0.0284745	+	0.198044i	0.999093	−	0.0425788i	$-0.0135573\pi$
$193$	0.395580	+	2.75132i	0.0284745	+	0.198044i	−0.970619	+	0.240623i	$0.922648\pi$
$194$	6.67391	−	2.18781i	0.479159	−	0.157076i
$195$	0.404496	+	0.216955i	0.0289665	+	0.0155364i
$196$	−6.78609	−	32.6126i	−0.484721	−	2.32947i
$197$	−2.01216	+	4.40603i	−0.143361	+	0.313916i	−0.967668	−	0.252226i	$-0.918837\pi$
$197$	−2.01216	+	4.40603i	−0.143361	+	0.313916i	0.824308	+	0.566142i	$0.191565\pi$
$198$	12.3170	+	9.71502i	0.875331	+	0.690416i
$199$	−14.7390	+	12.7714i	−1.04482	+	0.905342i	−0.995624	−	0.0934468i	$-0.970211\pi$
$199$	−14.7390	+	12.7714i	−1.04482	+	0.905342i	−0.0491964	+	0.998789i	$0.515666\pi$
$200$	2.63618	−	5.09259i	0.186406	−	0.360101i
$201$	−9.58697	−	2.01044i	−0.676213	−	0.141806i
$202$	−8.47805	−	12.3294i	−0.596514	−	0.867492i
$203$	16.2418	−	25.2727i	1.13995	−	1.77380i
$204$	0.0183046	−	11.7621i	0.00128158	−	0.823513i
$205$	−13.6026	−	3.99407i	−0.950044	−	0.278958i
$206$	−3.29068	−	3.56665i	−0.229273	−	0.248500i
$207$	6.50595	−	12.8325i	0.452195	−	0.891919i
$208$	−0.0984933	+	0.606884i	−0.00682928	+	0.0420799i
$209$	−3.90521	+	13.2999i	−0.270129	+	0.919975i
$210$	13.9519	−	15.0748i	0.962774	−	1.04026i
$211$	2.48206	−	3.86216i	0.170872	−	0.265882i	−0.745247	−	0.666788i	$-0.767668\pi$
$211$	2.48206	−	3.86216i	0.170872	−	0.265882i	0.916119	+	0.400907i	$0.131305\pi$
$212$	−1.24573	+	5.48707i	−0.0855568	+	0.376854i
$213$	−3.22447	+	15.3762i	−0.220937	+	1.05356i
$214$	0.175012	−	0.417171i	0.0119636	−	0.0285172i
$215$	12.9179	−	11.1934i	0.880993	−	0.763385i
$216$	−0.655257	−	14.6823i	−0.0445846	−	0.999006i
$217$	13.8107	+	6.30712i	0.937529	+	0.428155i
$218$	−6.64216	+	11.0803i	−0.449864	+	0.750450i
$219$	−23.1259	−	12.4038i	−1.56271	−	0.838171i
$220$	−11.1346	−	6.21134i	−0.750693	−	0.418769i
$221$	0.516588	−	0.0742741i	0.0347494	−	0.00499621i
$222$	8.14801	+	10.0499i	0.546858	+	0.674505i
$223$	0.152511	+	0.333954i	0.0102129	+	0.0223632i	0.914670	−	0.404202i	$-0.132451\pi$
$223$	0.152511	+	0.333954i	0.0102129	+	0.0223632i	−0.904457	+	0.426565i	$0.859723\pi$
$224$	25.1744	+	11.1009i	1.68203	+	0.741713i
$225$	−6.03268	−	0.775332i	−0.402179	−	0.0516888i
$226$	−11.6044	+	2.03951i	−0.771910	+	0.135666i
$227$	7.72922	+	6.69741i	0.513006	+	0.444523i	0.872492	−	0.488628i	$-0.162502\pi$
$227$	7.72922	+	6.69741i	0.513006	+	0.444523i	−0.359486	+	0.933151i	$0.617048\pi$
$228$	11.8212	−	5.37633i	0.782877	−	0.356056i
$229$	−14.7852			−0.977032			−0.488516	−	0.872555i	$-0.662462\pi$
$229$	−14.7852			−0.977032			−0.488516	+	0.872555i	$0.662462\pi$
$230$	−3.56973	+	11.1353i	−0.235381	+	0.734240i
$231$	22.1897	+	21.8598i	1.45998	+	1.43827i
$232$	6.46604	+	16.2298i	0.424516	+	1.06554i
$233$	13.8254	+	11.9798i	0.905732	+	0.784821i	0.977134	−	0.212626i	$-0.0682017\pi$
$233$	13.8254	+	11.9798i	0.905732	+	0.784821i	−0.0714014	+	0.997448i	$0.522747\pi$
$234$	0.640513	−	0.122490i	0.0418717	−	0.00800740i
$235$	1.12693	−	7.83797i	0.0735128	−	0.511293i
$236$	7.78876	+	14.5760i	0.507005	+	0.948814i
$237$	26.3886	+	9.61793i	1.71412	+	0.624752i
$238$	2.60152	−	23.2095i	0.168631	−	1.50445i
$239$	12.0127	−	1.72717i	0.777039	−	0.111721i	0.257626	−	0.966245i	$-0.417060\pi$
$239$	12.0127	−	1.72717i	0.777039	−	0.111721i	0.519413	+	0.854523i	$0.326151\pi$
$240$	2.41521	+	11.6983i	0.155901	+	0.755121i
$241$	−1.85712	−	6.32477i	−0.119628	−	0.407414i	0.877806	−	0.479017i	$-0.159007\pi$
$241$	−1.85712	−	6.32477i	−0.119628	−	0.407414i	−0.997433	+	0.0716029i	$0.977189\pi$
$242$	1.94263	−	3.24064i	0.124877	−	0.208316i
$243$	−14.3914	+	5.99058i	−0.923210	+	0.384296i
$244$	9.57672	−	0.597926i	0.613087	−	0.0382783i
$245$	21.7022	−	18.8051i	1.38650	−	1.20141i
$246$	−18.5852	+	7.76293i	−1.18495	+	0.494947i
$247$	0.311528	+	0.484747i	0.0198220	+	0.0308437i
$248$	−7.65376	+	4.40190i	−0.486014	+	0.279521i
$249$	−13.9251	+	3.13863i	−0.882469	+	0.198903i
$250$	17.1264	−	0.534127i	1.08317	−	0.0337811i
$251$	4.73397	−	16.1224i	0.298805	−	1.01764i	−0.664065	−	0.747674i	$-0.731170\pi$
$251$	4.73397	−	16.1224i	0.298805	−	1.01764i	0.962871	−	0.269963i	$-0.0870115\pi$
$252$	1.90910	−	29.1197i	0.120262	−	1.83437i
$253$	−16.7093	−	5.93708i	−1.05050	−	0.373261i
$254$	−0.555133	+	0.512180i	−0.0348321	+	0.0321370i
$255$	8.86270	−	4.92592i	0.555004	−	0.308473i
$256$	−13.7642	+	8.15769i	−0.860260	+	0.509856i
$257$	−8.95508	+	13.9344i	−0.558603	+	0.869203i	−0.999599	−	0.0283060i	$-0.990989\pi$
$257$	−8.95508	+	13.9344i	−0.558603	+	0.869203i	0.440997	+	0.897509i	$0.354625\pi$
$258$	4.24082	−	23.9110i	0.264022	−	1.48864i
$259$	13.8888	+	21.6114i	0.863009	+	1.34287i
$260$	−0.498251	+	0.180721i	−0.0309002	+	0.0112079i
$261$	13.8209	−	12.3431i	0.855489	−	0.764017i
$262$	14.1493	+	11.5082i	0.874148	+	0.710978i
$263$	2.04068	−	4.46846i	0.125834	−	0.275537i	−0.836222	−	0.548391i	$-0.815240\pi$
$263$	2.04068	−	4.46846i	0.125834	−	0.275537i	0.962055	+	0.272854i	$0.0879677\pi$
$264$	−17.8455	+	3.10779i	−1.09831	+	0.191271i
$265$	−4.65406	+	1.36655i	−0.285896	+	0.0839468i
$266$	24.5027	−	8.03237i	1.50236	−	0.492496i
$267$	3.38933	−	4.59901i	0.207424	−	0.281455i
$268$	9.11576	−	6.69617i	0.556834	−	0.409034i
$269$	1.71601	+	3.75754i	0.104627	+	0.229101i	0.954704	−	0.297557i	$-0.0961720\pi$
$269$	1.71601	+	3.75754i	0.104627	+	0.229101i	−0.850077	+	0.526658i	$0.823445\pi$
$270$	10.7783	−	6.65939i	0.655945	−	0.405278i
$271$	−1.32021	+	9.18229i	−0.0801973	+	0.557785i	0.909620	+	0.415441i	$0.136373\pi$
$271$	−1.32021	+	9.18229i	−0.0801973	+	0.557785i	−0.989817	+	0.142343i	$0.954536\pi$
$272$	10.1018	+	9.07838i	0.612513	+	0.550458i
$273$	1.29082	−	0.102043i	0.0781241	−	0.00617595i
$274$	−14.1713	+	7.01370i	−0.856122	+	0.423713i
$275$			7.49648i			0.452055i
$276$	6.02369	+	15.4827i	0.362583	+	0.931951i
$277$			26.4781i			1.59092i	0.606009	+	0.795458i	$0.292769\pi$
$277$			26.4781i			1.59092i	−0.606009	+	0.795458i	$0.707231\pi$
$278$	−6.55851	−	13.2516i	−0.393353	−	0.794780i
$279$	7.16858	+	6.02601i	0.429172	+	0.360768i
$280$	2.21515	+	23.6143i	0.132380	+	1.41122i
$281$	−1.84530	+	12.8343i	−0.110081	+	0.765632i	0.857756	+	0.514057i	$0.171858\pi$
$281$	−1.84530	+	12.8343i	−0.110081	+	0.765632i	−0.967838	+	0.251576i	$0.919051\pi$
$282$	−5.76927	−	9.65818i	−0.343555	−	0.575137i
$283$	−11.3435	−	24.8387i	−0.674299	−	1.47651i	−0.868573	−	0.495561i	$-0.834963\pi$
$283$	−11.3435	−	24.8387i	−0.674299	−	1.47651i	0.194274	−	0.980947i	$-0.437765\pi$
$284$	−10.7397	−	14.6204i	−0.637286	−	0.867562i
$285$	9.01203	+	6.64159i	0.533826	+	0.393414i
$286$	−0.250370	−	0.763752i	−0.0148047	−	0.0451616i
$287$	−38.3727	+	11.2672i	−2.26507	+	0.665084i
$288$	13.1323	+	10.7491i	0.773828	+	0.633396i
$289$	−2.27274	+	4.97660i	−0.133691	+	0.292741i
$290$	−9.50293	+	11.6839i	−0.558031	+	0.686100i
$291$	8.58427	+	0.549374i	0.503219	+	0.0322049i
$292$	28.4862	−	10.3323i	1.66703	−	0.604649i
$293$	−11.8709	−	18.4715i	−0.693505	−	1.07912i	−0.992187	−	0.124762i	$-0.960183\pi$
$293$	−11.8709	−	18.4715i	−0.693505	−	1.07912i	0.298681	−	0.954353i	$-0.403453\pi$
$294$	7.12463	−	40.1708i	0.415517	−	2.34281i
$295$	−7.70236	+	11.9851i	−0.448449	+	0.697800i
$296$	−14.9213	−	0.735740i	−0.867284	−	0.0427640i
$297$	9.58426	+	16.6516i	0.556135	+	0.966226i
$298$	2.86517	+	3.10545i	0.165975	+	0.179894i
$299$	−0.641392	+	0.363325i	−0.0370927	+	0.0210116i
$300$	5.31496	−	4.59098i	0.306859	−	0.265060i
$301$	13.5848	−	46.2654i	0.783012	−	2.66670i
$302$	−0.885487	−	28.3925i	−0.0509541	−	1.63381i
$303$	−4.02944	−	17.8774i	−0.231485	−	1.02703i
$304$	−4.48426	+	14.3092i	−0.257190	+	0.820686i
$305$	4.47205	+	6.95864i	0.256069	+	0.398451i
$306$	5.37334	−	13.3660i	0.307173	−	0.764082i
$307$	−13.0972	+	11.3488i	−0.747495	+	0.647708i	−0.942923	−	0.333010i	$-0.891936\pi$
$307$	−13.0972	+	11.3488i	−0.747495	+	0.647708i	0.195429	+	0.980718i	$0.437390\pi$
$308$	−35.8974	+	2.24127i	−2.04544	+	0.127708i
$309$	−2.11866	−	5.55299i	−0.120527	−	0.315898i
$310$	−6.52825	−	3.91342i	−0.370780	−	0.222267i
$311$	−0.248069	−	0.844845i	−0.0140667	−	0.0479068i	0.952161	−	0.305598i	$-0.0988564\pi$
$311$	−0.248069	−	0.844845i	−0.0140667	−	0.0479068i	−0.966227	+	0.257691i	$0.917038\pi$
$312$	−0.388165	+	0.645246i	−0.0219755	+	0.0365299i
$313$	3.81364	−	0.548318i	0.215560	−	0.0309928i	−0.0336889	−	0.999432i	$-0.510726\pi$
$313$	3.81364	−	0.548318i	0.215560	−	0.0309928i	0.249248	+	0.968440i	$0.419816\pi$
$314$	−12.0440	−	1.34999i	−0.679683	−	0.0761846i
$315$	22.7243	−	10.7920i	1.28037	−	0.608063i
$316$	−28.6040	+	15.2848i	−1.60910	+	0.859834i
$317$	0.766384	−	5.33032i	0.0430444	−	0.299381i	−0.956915	−	0.290368i	$-0.906222\pi$
$317$	0.766384	−	5.33032i	0.0430444	−	0.299381i	0.999959	−	0.00901226i	$-0.00286873\pi$
$318$	−3.91344	+	5.67227i	−0.219455	+	0.318085i
$319$	−17.2602	−	14.9561i	−0.966388	−	0.837380i
$320$	−11.9219	−	6.93627i	−0.666456	−	0.387749i
$321$	0.388840	−	0.394708i	0.0217029	−	0.0220305i
$322$	8.51137	+	31.8703i	0.474320	+	1.77606i
$323$	12.7289			0.708257
$324$	5.93633	−	16.9929i	0.329796	−	0.944052i
$325$	0.235514	+	0.204074i	0.0130639	+	0.0113200i
$326$	−4.96296	−	28.2382i	−0.274873	−	1.56397i
$327$	−12.5948	+	9.57637i	−0.696494	+	0.529574i
$328$	7.64335	−	21.9654i	0.422033	−	1.21284i
$329$	−9.27962	−	20.3195i	−0.511602	−	1.12025i
$330$	−9.83418	−	12.1297i	−0.541354	−	0.667715i
$331$	14.5945	−	2.09837i	0.802186	−	0.115337i	0.270986	−	0.962583i	$-0.412650\pi$
$331$	14.5945	−	2.09837i	0.802186	−	0.115337i	0.531200	+	0.847247i	$0.321741\pi$
$332$	8.02986	−	14.3945i	0.440696	−	0.790001i
$333$	4.69146	+	15.1352i	0.257091	+	0.829406i
$334$	7.72877	+	4.63308i	0.422899	+	0.253511i
$335$	8.86947	+	4.05055i	0.484591	+	0.221305i
$336$	23.5732	+	24.0784i	1.28603	+	1.31359i
$337$	4.90539	−	4.25054i	0.267214	−	0.231542i	−0.510939	−	0.859617i	$-0.670702\pi$
$337$	4.90539	−	4.25054i	0.267214	−	0.231542i	0.778153	+	0.628075i	$0.216157\pi$
$338$	16.9225	+	7.09937i	0.920463	+	0.386155i
$339$	−14.1230	−	2.96168i	−0.767057	−	0.160856i
$340$	−2.59215	+	11.4177i	−0.140579	+	0.619211i
$341$	6.24024	−	9.71001i	0.337928	−	0.525826i
$342$	15.8880	−	0.733842i	0.859126	−	0.0396817i
$343$	13.2307	−	45.0597i	0.714391	−	2.43299i
$344$	17.2970	+	22.0706i	0.932591	+	1.18997i
$345$	−9.12629	+	11.0371i	−0.491343	+	0.594218i
$346$	−14.9465	+	13.7900i	−0.803528	+	0.741355i
$347$	−4.85013	−	1.42413i	−0.260369	−	0.0764511i	0.148943	−	0.988846i	$-0.452413\pi$
$347$	−4.85013	−	1.42413i	−0.260369	−	0.0764511i	−0.409312	+	0.912395i	$0.634231\pi$
$348$	−0.0332984	+	21.3968i	−0.00178498	+	1.14699i
$349$	−7.44538	+	11.5852i	−0.398542	+	0.620143i	−0.981296	−	0.192505i	$-0.938339\pi$
$349$	−7.44538	+	11.5852i	−0.398542	+	0.620143i	0.582754	+	0.812649i	$0.301975\pi$
$350$	11.4908	−	7.90145i	0.614211	−	0.422350i
$351$	0.784046	+	0.152196i	0.0418493	+	0.00812363i
$352$	11.0770	−	17.7424i	0.590406	−	0.945674i
$353$	−16.5529	+	14.3432i	−0.881024	+	0.763412i	−0.972624	−	0.232384i	$-0.925347\pi$
$353$	−16.5529	+	14.3432i	−0.881024	+	0.763412i	0.0916002	+	0.995796i	$0.470802\pi$
$354$	2.22332	+	20.1182i	0.118168	+	1.06927i
$355$	6.49652	−	14.2254i	0.344799	−	0.755005i
$356$	1.34389	+	6.45848i	0.0712260	+	0.342299i
$357$	13.5199	−	25.2069i	0.715550	−	1.33409i
$358$	−3.51115	−	10.7108i	−0.185570	−	0.566081i
$359$	−0.808089	−	5.62038i	−0.0426493	−	0.296632i	−0.999971	−	0.00760813i	$-0.997578\pi$
$359$	−0.808089	−	5.62038i	−0.0426493	−	0.296632i	0.957322	−	0.289024i	$-0.0933309\pi$
$360$	−2.57722	+	14.4008i	−0.135832	+	0.758988i
$361$	−2.05474	−	4.49924i	−0.108144	−	0.236802i
$362$	−7.00106	+	26.9212i	−0.367968	+	1.41495i
$363$	3.68360	−	2.80080i	0.193339	−	0.147004i
$364$	−0.906807	+	1.18879i	−0.0475296	+	0.0623093i
$365$	19.7418	+	17.1064i	1.03333	+	0.895387i
$366$	11.1614	+	3.67814i	0.583418	+	0.192260i
$367$			20.6389i			1.07734i	0.842516	+	0.538672i	$0.181074\pi$
$367$			20.6389i			1.07734i	−0.842516	+	0.538672i	$0.818926\pi$
$368$	−17.9570	−	6.74871i	−0.936075	−	0.351801i
$369$	−24.6653	+	0.369473i	−1.28402	+	0.0192340i
$370$	−5.71256	−	11.5424i	−0.296982	−	0.600059i
$371$	−8.96066	+	10.3412i	−0.465214	+	0.536886i
$372$	−10.7060	+	1.52228i	−0.555079	+	0.0789268i
$373$	1.10928	−	7.71520i	0.0574362	−	0.399478i	−0.940741	−	0.339126i	$-0.889869\pi$
$373$	1.10928	−	7.71520i	0.0574362	−	0.399478i	0.998177	−	0.0603517i	$-0.0192222\pi$
$374$	−17.1835	−	4.46870i	−0.888536	−	0.231071i
$375$	19.7169	+	7.18628i	1.01818	+	0.371098i
$376$	12.7516	+	2.47975i	0.657615	+	0.127883i
$377$	−0.939738	+	0.135114i	−0.0483990	+	0.00695872i
$378$	15.4221	−	32.2422i	0.793228	−	1.65836i
$379$	−22.9665	+	6.74356i	−1.17971	+	0.346394i	−0.812061	−	0.583572i	$-0.801655\pi$
$379$	−22.9665	+	6.74356i	−1.17971	+	0.346394i	−0.367647	+	0.929966i	$0.619836\pi$
$380$	−12.6558	+	2.63343i	−0.649227	+	0.135092i
$381$	−0.864297	+	0.329760i	−0.0442793	+	0.0168941i
$382$	−22.6098	−	18.3894i	−1.15682	−	0.940884i
$383$	13.4915	+	15.5700i	0.689382	+	0.795589i	0.987277	−	0.159009i	$-0.0508300\pi$
$383$	13.4915	+	15.5700i	0.689382	+	0.795589i	−0.297895	+	0.954599i	$0.596285\pi$
$384$	−19.3630	+	3.01224i	−0.988115	+	0.153718i
$385$	−16.7630	−	26.0838i	−0.854323	−	1.32935i
$386$	−2.22729	−	3.23908i	−0.113366	−	0.164865i
$387$	15.7031	−	25.2585i	0.798236	−	1.28396i
$388$	−7.08661	+	6.95955i	−0.359768	+	0.353318i
$389$	−10.1146	+	34.4471i	−0.512830	+	1.74654i	0.141113	+	0.989993i	$0.454932\pi$
$389$	−10.1146	+	34.4471i	−0.512830	+	1.74654i	−0.653943	+	0.756544i	$0.726886\pi$
$390$	−0.648784	−	0.0212445i	−0.0328524	−	0.00107576i
$391$	−0.908242	+	16.2586i	−0.0459318	+	0.822232i
$392$	29.0591	+	37.0788i	1.46771	+	1.87276i
$393$	10.8517	+	19.5244i	0.547398	+	0.984876i
$394$	−0.213532	−	6.84676i	−0.0107576	−	0.344935i
$395$	−23.5197	−	15.1152i	−1.18341	−	0.760529i
$396$	−21.7057	−	4.58709i	−1.09075	−	0.230510i
$397$	−16.6073	−	25.8414i	−0.833494	−	1.29694i	−0.952651	−	0.304067i	$-0.901655\pi$
$397$	−16.6073	−	25.8414i	−0.833494	−	1.29694i	0.119156	−	0.992876i	$-0.461981\pi$
$398$	10.6698	−	25.4333i	0.534830	−	1.27485i
$399$	31.5164	+	2.01698i	1.57779	+	0.100975i
$400$	−0.146704	+	8.10841i	−0.00733520	+	0.405420i
$401$	13.3871	−	29.3136i	0.668518	−	1.46385i	−0.205848	−	0.978584i	$-0.565995\pi$
$401$	13.3871	−	29.3136i	0.668518	−	1.46385i	0.874366	−	0.485266i	$-0.161277\pi$
$402$	13.4124	−	3.46572i	0.668950	−	0.172855i
$403$	−0.135179	−	0.460379i	−0.00673376	−	0.0229331i
$404$	18.4799	+	10.3089i	0.919412	+	0.512887i
$405$	15.2860	−	2.66735i	0.759570	−	0.132542i
$406$	−4.73249	+	42.2211i	−0.234870	+	2.09540i
$407$	17.7650	−	8.11302i	0.880580	−	0.402147i
$408$	7.35518	+	14.9197i	0.364136	+	0.738635i
$409$	−1.18870	+	8.26757i	−0.0587773	+	0.408805i	0.939098	+	0.343650i	$0.111663\pi$
$409$	−1.18870	+	8.26757i	−0.0587773	+	0.408805i	−0.997875	+	0.0651551i	$0.979246\pi$
$410$	19.7464	−	3.47050i	0.975205	−	0.171396i
$411$	−19.3054	+	1.52615i	−0.952266	+	0.0752796i
$412$	6.40822	+	2.45640i	0.315710	+	0.121018i
$413$			40.1898i			1.97761i
$414$	−0.196319	+	20.3460i	−0.00964855	+	0.999953i
$415$	14.2090			0.697494
$416$	−0.255861	−	0.830996i	−0.0125446	−	0.0407429i
$417$	−1.42711	−	18.0525i	−0.0698857	−	0.884035i
$418$	−3.39329	−	19.3071i	−0.165971	−	0.944339i
$419$	−4.15370	−	0.597212i	−0.202922	−	0.0291757i	0.0401044	−	0.999195i	$-0.487231\pi$
$419$	−4.15370	−	0.597212i	−0.202922	−	0.0291757i	−0.243026	+	0.970020i	$0.578140\pi$
$420$	−8.22727	+	27.8590i	−0.401449	+	1.35938i
$421$	−6.03418	−	13.2130i	−0.294088	−	0.643963i	0.703696	−	0.710501i	$-0.251532\pi$
$421$	−6.03418	−	13.2130i	−0.294088	−	0.643963i	−0.997784	+	0.0665386i	$0.978804\pi$
$422$	−0.723215	+	6.45218i	−0.0352056	+	0.314087i
$423$	−2.16494	−	13.6074i	−0.105263	−	0.661613i
$424$	−1.86312	−	7.73618i	−0.0904810	−	0.375702i
$425$	6.60517	−	1.93945i	0.320398	−	0.0940773i
$426$	−5.55854	−	21.5116i	−0.269312	−	1.04224i
$427$	21.2258	+	9.69351i	1.02719	+	0.469102i
$428$	0.0398674	+	0.638539i	0.00192706	+	0.0308649i
$429$	0.0628695	−	0.982370i	0.00303537	−	0.0474293i
$430$	−9.35148	+	22.2908i	−0.450968	+	1.07496i
$431$	−18.3977	+	11.8235i	−0.886187	+	0.569518i	−0.902664	−	0.430346i	$-0.858391\pi$
$431$	−18.3977	+	11.8235i	−0.886187	+	0.569518i	0.0164768	+	0.999864i	$0.494755\pi$
$432$	10.0407	+	18.1984i	0.483086	+	0.875573i
$433$	−5.12944	+	7.98157i	−0.246505	+	0.383570i	−0.942353	−	0.334619i	$-0.891392\pi$
$433$	−5.12944	+	7.98157i	−0.246505	+	0.383570i	0.695848	+	0.718189i	$0.255029\pi$
$434$	−21.4611	+	0.669315i	−1.03017	+	0.0321282i
$435$	−16.1224	+	8.96087i	−0.773008	+	0.429641i
$436$	1.46812	−	18.2106i	0.0703104	−	0.872130i
$437$	−16.7452	+	6.54488i	−0.801031	+	0.313084i
$438$	37.0925	+	1.21460i	1.77235	+	0.0580357i
$439$	29.4647	+	8.65161i	1.40627	+	0.412919i	0.894833	−	0.446400i	$-0.147294\pi$
$439$	29.4647	+	8.65161i	1.40627	+	0.412919i	0.511439	+	0.859319i	$0.329112\pi$
$440$	18.0092	+	0.887996i	0.858554	+	0.0423336i
$441$	26.3815	−	42.4346i	1.25626	−	2.02070i
$442$	−0.608170	+	0.418196i	−0.0289277	+	0.0198916i
$443$	−13.0206	+	8.36785i	−0.618629	+	0.397568i	−0.812084	−	0.583541i	$-0.801667\pi$
$443$	−13.0206	+	8.36785i	−0.618629	+	0.397568i	0.193455	+	0.981109i	$0.438031\pi$
$444$	−16.6317	−	7.62674i	−0.789305	−	0.361949i
$445$	−4.29782	+	3.72408i	−0.203736	+	0.176538i
$446$	−0.402794	−	0.327607i	−0.0190728	−	0.0155127i
$447$	1.84470	+	4.83493i	0.0872513	+	0.228684i
$448$	−38.8715	+	1.72172i	−1.83651	+	0.0813434i
$449$	−6.12846	−	20.8716i	−0.289220	−	0.984993i	−0.968062	−	0.250709i	$-0.919336\pi$
$449$	−6.12846	−	20.8716i	−0.289220	−	0.984993i	0.678842	−	0.734284i	$-0.262482\pi$
$450$	8.13264	−	2.80159i	0.383377	−	0.132068i
$451$	4.32687	+	30.0941i	0.203744	+	1.41707i
$452$	13.4289	−	9.86445i	0.631640	−	0.463985i
$453$	11.9136	−	32.6871i	0.559749	−	1.53577i
$454$	−13.9979	−	3.64026i	−0.656953	−	0.170846i
$455$	−1.27580	−	0.183432i	−0.0598102	−	0.00859941i
$456$	−11.6105	+	14.2298i	−0.543711	+	0.666372i
$457$	17.4650	+	15.1335i	0.816977	+	0.707915i	0.959448	−	0.281884i	$-0.0909594\pi$
$457$	17.4650	+	15.1335i	0.816977	+	0.707915i	−0.142471	+	0.989799i	$0.545505\pi$
$458$	18.7399	−	9.27475i	0.875656	−	0.433381i
$459$	12.1922	−	12.7528i	0.569084	−	0.595248i
$460$	−2.46064	−	16.3530i	−0.114728	−	0.762464i
$461$	7.97989			0.371660			0.185830	−	0.982582i	$-0.440503\pi$
$461$	7.97989			0.371660			0.185830	+	0.982582i	$0.440503\pi$
$462$	−41.8376	−	13.7872i	−1.94646	−	0.641437i
$463$	−21.4721	+	24.7801i	−0.997893	+	1.15163i	−0.00946296	+	0.999955i	$0.503012\pi$
$463$	−21.4721	+	24.7801i	−0.997893	+	1.15163i	−0.988430	+	0.151675i	$0.951533\pi$
$464$	−18.3765	−	16.5147i	−0.853107	−	0.766676i
$465$	−5.64219	−	7.42059i	−0.261650	−	0.344121i
$466$	−25.0383	−	6.51140i	−1.15988	−	0.301635i
$467$	−27.0717	+	12.3632i	−1.25273	+	0.572103i	−0.927603	−	0.373568i	$-0.878134\pi$
$467$	−27.0717	+	12.3632i	−1.25273	+	0.572103i	−0.325127	+	0.945670i	$0.605407\pi$
$468$	−0.734997	+	0.557047i	−0.0339752	+	0.0257495i
$469$	27.2264	−	3.91456i	1.25720	−	0.180758i
$470$	3.48841	+	10.6414i	0.160908	+	0.490850i
$471$	−13.0805	−	7.01584i	−0.602717	−	0.323273i
$472$	−19.0156	−	13.5888i	−0.875262	−	0.625475i
$473$	−33.3445	−	15.2279i	−1.53318	−	0.700181i
$474$	−39.4802	+	4.36307i	−1.81339	+	0.200402i
$475$	4.97728	+	5.74409i	0.228373	+	0.263557i
$476$	11.2620	+	31.0494i	0.516192	+	1.42315i
$477$	−7.03109	+	4.66887i	−0.321931	+	0.213773i
$478$	−14.1424	+	9.72473i	−0.646858	+	0.444799i
$479$	−0.0159470	−	0.0102485i	−0.000728638	−	0.000468267i	0.540276	−	0.841488i	$-0.318320\pi$
$479$	−0.0159470	−	0.0102485i	−0.000728638	−	0.000468267i	−0.541005	+	0.841019i	$0.681956\pi$
$480$	−10.3996	−	13.3122i	−0.474673	−	0.607617i
$481$	0.228727	−	0.778974i	0.0104291	−	0.0355181i
$482$	6.32138	+	6.85152i	0.287931	+	0.312078i
$483$	−4.82505	+	40.1118i	−0.219547	+	1.82515i
$484$	−0.429382	+	5.32605i	−0.0195174	+	0.242093i
$485$	−8.21557	−	2.41231i	−0.373050	−	0.109537i
$486$	14.4829	−	16.6207i	0.656957	−	0.753928i
$487$	−0.574711	−	0.369344i	−0.0260426	−	0.0167366i	0.527555	−	0.849521i	$-0.323109\pi$
$487$	−0.574711	−	0.369344i	−0.0260426	−	0.0167366i	−0.553597	+	0.832784i	$0.686745\pi$
$488$	−11.7632	+	6.76534i	−0.532494	+	0.306252i
$489$	7.20698	−	34.3671i	0.325911	−	1.55413i
$490$	−15.7106	+	37.4488i	−0.709732	+	1.69176i
$491$	−0.446282	−	0.515036i	−0.0201404	−	0.0232433i	0.745590	−	0.666405i	$-0.232168\pi$
$491$	−0.446282	−	0.515036i	−0.0201404	−	0.0232433i	−0.765730	+	0.643162i	$0.777622\pi$
$492$	18.6867	−	21.4979i	0.842459	−	0.969198i
$493$	−8.71237	+	19.0774i	−0.392385	+	0.859204i
$494$	−0.698936	−	0.418983i	−0.0314466	−	0.0188509i
$495$	−5.66233	−	18.2674i	−0.254503	−	0.821058i
$496$	6.93965	−	10.3805i	0.311599	−	0.466098i
$497$	−6.27841	−	43.6673i	−0.281625	−	1.95875i
$498$	15.6809	−	12.7134i	0.702678	−	0.569700i
$499$	−28.8646	+	13.1820i	−1.29216	+	0.590109i	−0.938504	−	0.345268i	$-0.887788\pi$
$499$	−28.8646	+	13.1820i	−1.29216	+	0.590109i	−0.353654	+	0.935377i	$0.615061\pi$
$500$	−21.3723	+	11.4204i	−0.955796	+	0.510736i
$501$	6.67976	+	8.78520i	0.298430	+	0.392494i
$502$	4.11341	+	23.4044i	0.183590	+	1.04459i
$503$	−3.22184	+	3.71820i	−0.143655	+	0.165786i	−0.823017	−	0.568016i	$-0.807711\pi$
$503$	−3.22184	+	3.71820i	−0.143655	+	0.165786i	0.679362	+	0.733803i	$0.262256\pi$
$504$	15.8471	+	38.1061i	0.705884	+	1.69738i
$505$			18.2418i			0.811752i
$506$	24.9029	−	2.95662i	1.10707	−	0.131438i
$507$	16.0113	+	15.7733i	0.711088	+	0.700516i
$508$	0.382327	−	0.997410i	0.0169630	−	0.0442529i
$509$	−3.42713	+	3.95512i	−0.151905	+	0.175308i	−0.826602	−	0.562787i	$-0.809729\pi$
$509$	−3.42713	+	3.95512i	−0.151905	+	0.175308i	0.674697	+	0.738095i	$0.264274\pi$
$510$	−8.14322	+	11.8031i	−0.360588	+	0.522648i
$511$	72.9401	+	10.4872i	3.22668	+	0.463927i
$512$	12.3284	−	18.9739i	0.544844	−	0.838537i
$513$	18.3997	+	6.39565i	0.812365	+	0.282375i
$514$	2.60931	−	23.2790i	0.115092	−	1.02679i
$515$	0.841962	+	5.85598i	0.0371013	+	0.258045i
$516$	9.62426	+	32.9669i	0.423684	+	1.45129i
$517$	−16.2942	+	4.78442i	−0.716619	+	0.210418i
$518$	−31.1606	−	18.6795i	−1.36912	−	0.820730i
$519$	−23.2705	+	8.87852i	−1.02146	+	0.389724i
$520$	0.518155	−	0.541613i	0.0227226	−	0.0237513i
$521$	21.7187	+	25.0647i	0.951514	+	1.09811i	0.995082	+	0.0990550i	$0.0315820\pi$
$521$	21.7187	+	25.0647i	0.951514	+	1.09811i	−0.0435681	+	0.999050i	$0.513873\pi$
$522$	−9.77478	+	24.3144i	−0.427830	+	1.06421i
$523$	11.4707	−	7.37175i	0.501577	−	0.322344i	−0.265270	−	0.964174i	$-0.585461\pi$
$523$	11.4707	−	7.37175i	0.501577	−	0.322344i	0.766847	+	0.641830i	$0.221825\pi$
$524$	−25.1530	−	5.71047i	−1.09881	−	0.249463i
$525$	16.6615	−	3.75539i	0.727167	−	0.163899i
$526$	0.216558	+	6.94379i	0.00944238	+	0.302764i
$527$	−10.1700	−	2.98617i	−0.443011	−	0.130080i
$528$	20.6692	−	15.1335i	0.899512	−	0.658602i
$529$	−7.16492	−	21.8555i	−0.311518	−	0.950240i
$530$	5.04166	−	4.65157i	0.218996	−	0.202051i
$531$	−6.62702	+	23.8874i	−0.287588	+	1.03663i
$532$	−26.0179	+	25.5514i	−1.12802	+	1.10779i
$533$	1.06324	+	0.683303i	0.0460541	+	0.0295971i
$534$	−1.41093	+	7.95526i	−0.0610570	+	0.344258i
$535$	−0.463975	+	0.298179i	−0.0200594	+	0.0128914i
$536$	−7.35349	+	14.2056i	−0.317623	+	0.613586i
$537$	0.881674	−	13.7766i	0.0380470	−	0.594505i
$538$	−4.53210	−	3.68613i	−0.195393	−	0.158920i
$539$	−56.0192	−	25.5831i	−2.41292	−	1.10194i
$540$	−9.48376	+	15.2018i	−0.408116	+	0.654182i
$541$	−0.0520051	−	0.177113i	−0.00223587	−	0.00761468i	0.958367	−	0.285538i	$-0.0921722\pi$
$541$	−0.0520051	−	0.177113i	−0.00223587	−	0.00761468i	−0.960603	+	0.277923i	$0.910354\pi$
$542$	−4.08672	−	12.4665i	−0.175540	−	0.535482i
$543$	−20.2115	+	27.4252i	−0.867360	+	1.17693i
$544$	−18.4987	−	5.16974i	−0.793125	−	0.221651i
$545$	14.3262	−	6.54258i	0.613669	−	0.280253i
$546$	−1.57207	+	0.939070i	−0.0672785	+	0.0401885i
$547$	−45.4157	−	6.52979i	−1.94183	−	0.279194i	−0.943236	−	0.332122i	$-0.892235\pi$
$547$	−45.4157	−	6.52979i	−1.94183	−	0.279194i	−0.998598	+	0.0529284i	$0.983144\pi$
$548$	13.5621	−	17.7794i	0.579346	−	0.759498i
$549$	11.0175	+	9.26147i	0.470215	+	0.395270i
$550$	−4.70255	−	9.50161i	−0.200517	−	0.405150i
$551$	−23.1555			−0.986459
$552$	−17.3472	−	15.8453i	−0.738346	−	0.674422i
$553$	−78.8691			−3.35385
$554$	−16.6097	−	33.5604i	−0.705680	−	1.42584i
$555$	−1.24303	−	15.7240i	−0.0527637	−	0.667447i
$556$	16.6255	+	12.6820i	0.705078	+	0.537835i
$557$	−6.58577	−	0.946891i	−0.279048	−	0.0401211i	0.00136984	−	0.999999i	$-0.499564\pi$
$557$	−6.58577	−	0.946891i	−0.279048	−	0.0401211i	−0.280418	+	0.959878i	$0.590473\pi$
$558$	−12.8661	−	3.14097i	−0.544666	−	0.132968i
$559$	−1.38613	+	0.633026i	−0.0586272	+	0.0267741i
$560$	−17.6209	−	28.5410i	−0.744619	−	1.20608i
$561$	−17.5052	−	12.9008i	−0.739069	−	0.544671i
$562$	−5.71211	−	17.4248i	−0.240951	−	0.735019i
$563$	11.5156	+	39.2186i	0.485326	+	1.65287i	0.730139	+	0.683299i	$0.239455\pi$
$563$	11.5156	+	39.2186i	0.485326	+	1.65287i	−0.244813	+	0.969570i	$0.578727\pi$
$564$	13.3710	+	8.62245i	0.563020	+	0.363071i
$565$	13.0660	+	5.96706i	0.549692	+	0.251036i
$566$	29.9589	+	24.3667i	1.25927	+	1.02421i
$567$	32.2082	−	29.6434i	1.35262	−	1.24491i
$568$	22.7837	+	11.7940i	0.955984	+	0.494864i
$569$	−13.0191	+	8.36687i	−0.545789	+	0.350758i	−0.784299	−	0.620382i	$-0.786977\pi$
$569$	−13.0191	+	8.36687i	−0.545789	+	0.350758i	0.238510	+	0.971140i	$0.423341\pi$
$570$	−15.5888	−	2.76480i	−0.652943	−	0.115805i
$571$	12.3138	+	7.91363i	0.515318	+	0.331175i	0.772318	−	0.635237i	$-0.219097\pi$
$571$	12.3138	+	7.91363i	0.515318	+	0.331175i	−0.256999	+	0.966412i	$0.582734\pi$
$572$	0.796440	+	0.810980i	0.0333008	+	0.0339088i
$573$	−17.3404	−	31.1989i	−0.724407	−	1.30335i
$574$	41.5685	−	38.3521i	1.73503	−	1.60079i
$575$	−7.69203	+	5.94760i	−0.320780	+	0.248032i
$576$	−23.3878	−	5.38630i	−0.974490	−	0.224429i
$577$	20.9966	+	6.16515i	0.874099	+	0.256659i	0.687858	−	0.725846i	$-0.258551\pi$
$577$	20.9966	+	6.16515i	0.874099	+	0.256659i	0.186241	+	0.982504i	$0.440369\pi$
$578$	−0.241184	−	7.73341i	−0.0100319	−	0.321668i
$579$	−1.05858	−	4.69661i	−0.0439932	−	0.195184i
$580$	4.71544	−	20.7702i	0.195798	−	0.862436i
$581$	33.7204	−	21.6708i	1.39896	−	0.899056i
$582$	−11.2250	+	4.68860i	−0.465290	+	0.194349i
$583$	6.81214	+	7.86163i	0.282130	+	0.325596i
$584$	−29.6241	+	30.9653i	−1.22585	+	1.28135i
$585$	−0.728042	−	0.319395i	−0.0301008	−	0.0132054i
$586$	26.6332	+	15.9655i	1.10021	+	0.659530i
$587$	14.9987	−	4.40402i	0.619064	−	0.181774i	0.0428620	−	0.999081i	$-0.486352\pi$
$587$	14.9987	−	4.40402i	0.619064	−	0.181774i	0.576202	+	0.817307i	$0.304534\pi$
$588$	16.1689	+	55.3848i	0.666793	+	2.28403i
$589$	−1.66544	−	11.5834i	−0.0686232	−	0.477285i
$590$	2.24429	−	20.0225i	0.0923961	−	0.824315i
$591$	2.87292	−	7.88238i	0.118176	−	0.324238i
$592$	19.3739	−	8.42762i	0.796264	−	0.346373i
$593$	−5.18599	−	0.745633i	−0.212963	−	0.0306195i	0.0350075	−	0.999387i	$-0.488855\pi$
$593$	−5.18599	−	0.745633i	−0.212963	−	0.0306195i	−0.247970	+	0.968768i	$0.579764\pi$
$594$	−22.5934	−	15.0933i	−0.927018	−	0.619287i
$595$	−18.6456	+	21.5182i	−0.764397	+	0.882161i
$596$	−5.57958	−	2.13876i	−0.228548	−	0.0876071i
$597$	23.7060	−	24.0638i	0.970224	−	0.984866i
$598$	0.585035	−	0.862851i	0.0239239	−	0.0352846i
$599$		−	40.1375i		−	1.63998i	−0.572381	−	0.819988i	$-0.693980\pi$
$599$		−	40.1375i		−	1.63998i	0.572381	−	0.819988i	$-0.306020\pi$
$600$	−3.85666	+	9.15303i	−0.157448	+	0.373671i
$601$	−0.00833239	+	0.00961609i	−0.000339885	+	0.000392249i	−0.755919	−	0.654665i	$-0.772810\pi$
$601$	−0.00833239	+	0.00961609i	−0.000339885	+	0.000392249i	0.755580	+	0.655057i	$0.227355\pi$
$602$	11.8040	+	67.1620i	0.481094	+	2.73732i
$603$	16.8279	+	2.16275i	0.685285	+	0.0880742i
$604$	18.9330	+	35.4314i	0.770372	+	1.44168i
$605$	−4.18999	+	1.91351i	−0.170347	+	0.0777951i
$606$	16.3217	+	20.1314i	0.663023	+	0.817784i
$607$	−1.79281	−	12.4693i	−0.0727678	−	0.506111i	−0.993311	−	0.115470i	$-0.963162\pi$
$607$	−1.79281	−	12.4693i	−0.0727678	−	0.506111i	0.920543	−	0.390641i	$-0.127747\pi$
$608$	−3.29244	−	20.9495i	−0.133526	−	0.849614i
$609$	−24.5945	+	45.8545i	−0.996617	+	1.85812i
$610$	−10.0334	−	6.01459i	−0.406239	−	0.243524i
$611$	−0.293261	+	0.642153i	−0.0118641	+	0.0259787i
$612$	1.57390	+	20.3117i	0.0636212	+	0.821053i
$613$	25.0955	+	28.9617i	1.01360	+	1.16975i	0.985418	+	0.170150i	$0.0544252\pi$
$613$	25.0955	+	28.9617i	1.01360	+	1.16975i	0.0281784	+	0.999603i	$0.491029\pi$
$614$	9.48126	−	22.6001i	0.382632	−	0.912067i
$615$	24.0322	+	5.03970i	0.969073	+	0.203220i
$616$	44.0931	−	25.3592i	1.77656	−	1.02175i
$617$	13.1376	+	8.44302i	0.528900	+	0.339903i	0.777684	−	0.628656i	$-0.216395\pi$
$617$	13.1376	+	8.44302i	0.528900	+	0.339903i	−0.248784	+	0.968559i	$0.580031\pi$
$618$	6.16874	+	5.70924i	0.248143	+	0.229659i
$619$	17.2868	+	5.07586i	0.694814	+	0.204016i	0.610024	−	0.792383i	$-0.291160\pi$
$619$	17.2868	+	5.07586i	0.694814	+	0.204016i	0.0847903	+	0.996399i	$0.472978\pi$
$620$	10.7293	+	0.864987i	0.430899	+	0.0347387i
$621$	−9.48199	+	23.0454i	−0.380499	+	0.924781i
$622$	0.844393	+	0.915207i	0.0338571	+	0.0366964i
$623$	−4.51969	+	15.3926i	−0.181077	+	0.616693i
$624$	0.0872262	−	1.06133i	0.00349184	−	0.0424872i
$625$	−9.04544	−	5.81315i	−0.361818	−	0.232526i
$626$	−4.48973	+	3.08728i	−0.179446	+	0.123392i
$627$	4.92757	−	23.4975i	0.196788	−	0.938401i
$628$	16.1124	−	5.84413i	0.642953	−	0.233206i
$629$	−11.7445	−	13.5539i	−0.468283	−	0.540428i
$630$	−22.0326	+	27.9336i	−0.877799	+	1.11290i
$631$	−12.6030	−	5.75561i	−0.501719	−	0.229127i	0.148446	−	0.988921i	$-0.452573\pi$
$631$	−12.6030	−	5.75561i	−0.501719	−	0.229127i	−0.650165	+	0.759793i	$0.725300\pi$
$632$	26.6668	−	37.3164i	1.06075	−	1.48437i
$633$	−3.75850	+	7.00744i	−0.149387	+	0.278521i
$634$	2.37234	+	7.23680i	0.0942176	+	0.287410i
$635$	0.911456	−	0.131048i	0.0361700	−	0.00520046i
$636$	1.40197	−	9.64437i	0.0555919	−	0.382424i
$637$	−2.32872	+	1.06349i	−0.0922673	+	0.0421370i
$638$	31.2589	+	8.12912i	1.23755	+	0.321835i
$639$	3.46876	−	26.9896i	0.137222	−	1.06769i
$640$	19.4619	+	1.31292i	0.769298	+	0.0518976i
$641$	31.4900	−	36.3414i	1.24378	−	1.43540i	0.385113	−	0.922869i	$-0.374162\pi$
$641$	31.4900	−	36.3414i	1.24378	−	1.43540i	0.858668	−	0.512532i	$-0.171292\pi$
$642$	−0.245244	+	0.744202i	−0.00967903	+	0.0293713i
$643$	40.3353			1.59067			0.795335	−	0.606170i	$-0.207295\pi$
$643$	40.3353			1.59067			0.795335	+	0.606170i	$0.207295\pi$
$644$	−30.7802	−	35.0556i	−1.21291	−	1.38138i
$645$	−20.7770	+	21.0905i	−0.818093	+	0.830439i
$646$	−16.1336	+	7.98487i	−0.634769	+	0.314160i
$647$	30.4731	+	26.4051i	1.19802	+	1.03809i	0.998303	+	0.0582378i	$0.0185482\pi$
$647$	30.4731	+	26.4051i	1.19802	+	1.03809i	0.199718	+	0.979853i	$0.435997\pi$
$648$	3.13552	+	25.2620i	0.123175	+	0.992385i
$649$	30.2425	+	4.34821i	1.18712	+	0.170682i
$650$	−0.426523	−	0.110921i	−0.0167296	−	0.00435067i
$651$	−24.7073	−	9.00515i	−0.968355	−	0.352940i
$652$	24.0043	+	32.6779i	0.940079	+	1.27977i
$653$	−0.673484	−	4.68418i	−0.0263555	−	0.183306i	0.972391	−	0.233357i	$-0.0749709\pi$
$653$	−0.673484	−	4.68418i	−0.0263555	−	0.183306i	−0.998747	+	0.0500503i	$0.984062\pi$
$654$	9.95635	−	20.0385i	0.389324	−	0.783569i
$655$	−6.26435	−	21.3344i	−0.244769	−	0.833605i
$656$	4.09114	+	32.6353i	0.159732	+	1.27419i
$657$	41.6238	+	18.2605i	1.62390	+	0.712411i
$658$	24.5082	+	19.9334i	0.955427	+	0.777085i
$659$	11.0220	−	9.55065i	0.429358	−	0.372041i	−0.413206	−	0.910638i	$-0.635591\pi$
$659$	11.0220	−	9.55065i	0.429358	−	0.372041i	0.842563	+	0.538597i	$0.181046\pi$
$660$	20.0735	+	9.20505i	0.781361	+	0.358306i
$661$	4.72452	−	3.03626i	0.183762	−	0.118097i	−0.445525	−	0.895269i	$-0.646983\pi$
$661$	4.72452	−	3.03626i	0.183762	−	0.118097i	0.629288	+	0.777172i	$0.283347\pi$
$662$	−17.1818	+	11.8148i	−0.667791	+	0.459194i
$663$	−0.881835	+	0.198760i	−0.0342476	+	0.00771918i
$664$	−1.14798	+	23.2818i	−0.0445502	+	0.903509i
$665$	−30.1628	−	8.85658i	−1.16966	−	0.343444i
$666$	−15.4407	−	16.2406i	−0.598313	−	0.629310i
$667$	1.65221	−	29.5764i	0.0639737	−	1.14520i
$668$	−12.7024	−	1.02405i	−0.491469	−	0.0396219i
$669$	−0.308920	−	0.555808i	−0.0119435	−	0.0214888i
$670$	−13.7827	+	0.429847i	−0.532474	+	0.0166064i
$671$	9.59072	−	14.9235i	0.370246	−	0.576113i
$672$	−44.9829	−	15.7313i	−1.73525	−	0.606849i
$673$	20.2824	−	13.0347i	0.781828	−	0.502451i	−0.0878115	−	0.996137i	$-0.527987\pi$
$673$	20.2824	−	13.0347i	0.781828	−	0.502451i	0.869640	+	0.493686i	$0.164351\pi$
$674$	−3.55109	+	8.46461i	−0.136783	+	0.326045i
$675$	10.5222	+	0.515289i	0.405001	+	0.0198335i
$676$	−25.9023	+	1.61722i	−0.996243	+	0.0622008i
$677$	18.0572	+	8.24647i	0.693996	+	0.316938i	0.731000	−	0.682378i	$-0.239054\pi$
$677$	18.0572	+	8.24647i	0.693996	+	0.316938i	−0.0370035	+	0.999315i	$0.511781\pi$
$678$	19.7584	−	5.10552i	0.758818	−	0.196076i
$679$	−23.1760	+	6.80510i	−0.889414	+	0.261156i
$680$	−3.87683	−	16.0977i	−0.148670	−	0.617318i
$681$	−14.2600	−	10.5091i	−0.546443	−	0.402711i
$682$	−1.81826	+	16.2217i	−0.0696249	+	0.621161i
$683$	−2.20335	−	4.82466i	−0.0843087	−	0.184610i	0.862782	−	0.505576i	$-0.168720\pi$
$683$	−2.20335	−	4.82466i	−0.0843087	−	0.184610i	−0.947091	+	0.320965i	$0.895993\pi$
$684$	−19.6773	+	10.8967i	−0.752382	+	0.416645i
$685$	19.0807	+	2.74339i	0.729036	+	0.104820i
$686$	11.4963	+	65.4116i	0.438932	+	2.49743i
$687$	25.5290	−	2.01815i	0.973994	−	0.0769972i
$688$	−35.7684	−	17.1235i	−1.36366	−	0.652828i
$689$	0.432430			0.0164743
$690$	4.64377	−	19.7142i	0.176785	−	0.750507i
$691$		−	29.5562i		−	1.12437i	−0.827011	−	0.562185i	$-0.809961\pi$
$691$		−	29.5562i		−	1.12437i	0.827011	−	0.562185i	$-0.190039\pi$
$692$	10.2938	−	26.8544i	0.391313	−	1.02085i
$693$	−41.2980	−	34.7157i	−1.56878	−	1.31874i
$694$	7.04077	−	1.23744i	0.267264	−	0.0469727i
$695$	−2.56534	+	17.8424i	−0.0973091	+	0.676799i
$696$	−13.3800	−	27.1408i	−0.507168	−	1.02877i
$697$	25.3965	−	11.5982i	0.961963	−	0.439314i
$698$	2.16941	−	19.3545i	0.0821135	−	0.732578i
$699$	−25.5070	−	18.7979i	−0.964765	−	0.711002i
$700$	−9.60777	+	17.2231i	−0.363140	+	0.650972i
$701$	−1.48964	−	5.07323i	−0.0562628	−	0.191613i	0.926566	−	0.376131i	$-0.122746\pi$
$701$	−1.48964	−	5.07323i	−0.0562628	−	0.191613i	−0.982829	+	0.184518i	$0.940928\pi$
$702$	−1.08923	+	0.298927i	−0.0411104	+	0.0112823i
$703$	8.22561	−	18.0116i	0.310235	−	0.679319i
$704$	−2.91000	+	29.4367i	−0.109675	+	1.10944i
$705$	−0.875962	+	13.6874i	−0.0329906	+	0.515496i
$706$	11.9829	−	28.5633i	0.450984	−	1.07499i
$707$	27.8214	+	43.2909i	1.04633	+	1.62812i
$708$	−15.4382	−	24.1046i	−0.580201	−	0.905908i
$709$	−16.8590	−	10.8346i	−0.633152	−	0.406902i	0.184324	−	0.982866i	$-0.440991\pi$
$709$	−16.8590	−	10.8346i	−0.633152	−	0.406902i	−0.817475	+	0.575964i	$0.804627\pi$
$710$	0.689414	+	22.1056i	0.0258733	+	0.829609i
$711$	−46.8770	−	13.0049i	−1.75803	−	0.487723i
$712$	−5.75475	−	7.34294i	−0.215668	−	0.275188i
$713$	14.9142	−	1.30075i	0.558542	−	0.0487135i
$714$	−1.32389	+	40.4302i	−0.0495454	+	1.51306i
$715$	−0.276061	+	0.940177i	−0.0103241	+	0.0351606i
$716$	11.1692	+	11.3731i	0.417411	+	0.425032i
$717$	−20.5062	+	4.62196i	−0.765818	+	0.172610i
$718$	4.54990	+	6.61678i	0.169801	+	0.246936i
$719$	−13.2378	−	20.5984i	−0.493686	−	0.768190i	0.501608	−	0.865095i	$-0.332742\pi$
$719$	−13.2378	−	20.5984i	−0.493686	−	0.768190i	−0.995294	+	0.0969050i	$0.969106\pi$
$720$	−5.76705	−	19.8693i	−0.214925	−	0.740487i
$721$	10.9293	+	12.6131i	0.407029	+	0.469736i
$722$	5.42671	+	4.41375i	0.201961	+	0.164263i
$723$	4.06994	+	10.6673i	0.151363	+	0.396719i
$724$	−8.01399	−	38.5137i	−0.297838	−	1.43135i
$725$	−12.0156	+	3.52811i	−0.446250	+	0.131031i
$726$	−2.91193	+	5.86067i	−0.108072	+	0.217510i
$727$	−15.9819	+	2.29785i	−0.592735	+	0.0852225i	−0.432154	−	0.901800i	$-0.642246\pi$
$727$	−15.9819	+	2.29785i	−0.592735	+	0.0852225i	−0.160582	+	0.987023i	$0.551337\pi$
$728$	0.403631	−	2.07560i	0.0149596	−	0.0769267i
$729$	24.0314	−	12.3081i	0.890053	−	0.455856i
$730$	−35.7530	−	9.29786i	−1.32328	−	0.344129i
$731$	−4.79064	+	33.3197i	−0.177188	+	1.23237i
$732$	−16.4542	+	2.33962i	−0.608163	+	0.0864749i
$733$	−2.47696	+	2.85857i	−0.0914887	+	0.105584i	−0.799648	−	0.600469i	$-0.794980\pi$
$733$	−2.47696	+	2.85857i	−0.0914887	+	0.105584i	0.708159	+	0.706053i	$0.249526\pi$
$734$	−12.9468	−	26.1593i	−0.477876	−	0.965559i
$735$	−34.9056	+	35.4323i	−1.28751	+	1.30694i
$736$	26.9936	−	2.71062i	0.994996	−	0.0999147i
$737$		−	20.9111i		−	0.770270i
$738$	31.0308	−	15.9408i	1.14226	−	0.586790i
$739$	26.9615	+	23.3622i	0.991793	+	0.859394i	0.990066	−	0.140605i	$-0.0449047\pi$
$739$	26.9615	+	23.3622i	0.991793	+	0.859394i	0.00172748	+	0.999999i	$0.499450\pi$
$740$	14.4811	+	11.0462i	0.532334	+	0.406066i
$741$	−0.604071	−	0.794472i	−0.0221911	−	0.0291856i
$742$	4.87041	−	18.7282i	0.178798	−	0.687533i
$743$	−1.99943	−	4.37815i	−0.0733521	−	0.160619i	0.869404	−	0.494102i	$-0.164503\pi$
$743$	−1.99943	−	4.37815i	−0.0733521	−	0.160619i	−0.942756	+	0.333484i	$0.891776\pi$
$744$	12.6146	−	8.64532i	0.462475	−	0.316953i
$745$	−0.733089	−	5.09874i	−0.0268583	−	0.186803i
$746$	3.43376	+	10.4747i	0.125719	+	0.383505i
$747$	23.6156	−	7.32011i	0.864049	−	0.267829i
$748$	24.5828	−	5.11524i	0.898838	−	0.187032i
$749$	−0.646325	+	1.41526i	−0.0236162	+	0.0517123i
$750$	−29.4987	+	3.25998i	−1.07714	+	0.119038i
$751$	34.4203	−	29.8253i	1.25601	−	1.08834i	0.263698	−	0.964605i	$-0.415058\pi$
$751$	34.4203	−	29.8253i	1.25601	−	1.08834i	0.992315	−	0.123736i	$-0.0394877\pi$
$752$	−17.7179	+	4.85609i	−0.646106	+	0.177083i
$753$	−5.97329	+	28.4842i	−0.217679	+	1.03802i
$754$	1.10634	−	0.760751i	0.0402904	−	0.0277049i
$755$	−18.7230	+	29.1335i	−0.681399	+	1.06028i
$756$	0.678403	+	50.5405i	0.0246733	+	1.83814i
$757$	8.10677	+	2.38036i	0.294645	+	0.0865157i	0.425715	−	0.904858i	$-0.360023\pi$
$757$	8.10677	+	2.38036i	0.294645	+	0.0865157i	−0.131069	+	0.991373i	$0.541841\pi$
$758$	24.8792	−	22.9542i	0.903653	−	0.833733i
$759$	29.6617	+	7.97056i	1.07665	+	0.289313i
$760$	14.3889	−	11.2768i	0.521941	−	0.409051i
$761$	−6.77754	+	23.0822i	−0.245686	+	0.836728i	0.740637	+	0.671905i	$0.234524\pi$
$761$	−6.77754	+	23.0822i	−0.245686	+	0.836728i	−0.986323	+	0.164824i	$0.947295\pi$
$762$	0.888617	−	0.960137i	0.0321912	−	0.0347821i
$763$	24.0202	−	37.3762i	0.869590	−	1.35311i
$764$	40.1931	+	9.12499i	1.45413	+	0.330131i
$765$	−14.6305	+	9.71515i	−0.528968	+	0.351252i
$766$	−26.8672	−	11.2714i	−0.970750	−	0.407251i
$767$	0.959884	−	0.831744i	0.0346594	−	0.0300325i
$768$	22.6526	−	15.9644i	0.817404	−	0.576065i
$769$	26.4421	+	12.0757i	0.953528	+	0.435462i	0.830548	−	0.556948i	$-0.188028\pi$
$769$	26.4421	+	12.0757i	0.953528	+	0.435462i	0.122980	+	0.992409i	$0.460755\pi$
$770$	37.6091	+	22.5451i	1.35534	+	0.812469i
$771$	13.5604	−	25.2823i	0.488366	−	0.910521i
$772$	4.85491	+	2.70828i	0.174732	+	0.0974730i
$773$	24.4429	−	3.51436i	0.879149	−	0.126403i	0.312063	−	0.950061i	$-0.398980\pi$
$773$	24.4429	−	3.51436i	0.879149	−	0.126403i	0.567086	+	0.823659i	$0.308071\pi$
$774$	−4.05866	+	41.8652i	−0.145886	+	1.50481i
$775$	−2.62912	−	5.75698i	−0.0944409	−	0.206797i
$776$	4.61637	−	13.2665i	0.165718	−	0.476239i
$777$	−26.9312	−	35.4199i	−0.966153	−	1.27068i
$778$	−8.78869	−	50.0057i	−0.315090	−	1.79279i
$779$	23.2963	+	20.1864i	0.834678	+	0.723252i
$780$	0.835644	−	0.380055i	0.0299209	−	0.0136082i
$781$	−33.5385			−1.20010
$782$	−9.04785	−	21.1771i	−0.323550	−	0.757292i
$783$	−22.1792	+	23.1989i	−0.792619	+	0.829060i
$784$	−60.0913	−	28.7677i	−2.14612	−	1.02742i
$785$	11.1664	+	9.67570i	0.398544	+	0.345340i
$786$	−26.0020	−	17.9394i	−0.927460	−	0.639878i
$787$	0.579521	−	4.03066i	0.0206577	−	0.143677i	−0.976882	−	0.213778i	$-0.931423\pi$
$787$	0.579521	−	4.03066i	0.0206577	−	0.143677i	0.997540	+	0.0701008i	$0.0223321\pi$
$788$	4.56562	+	8.54415i	0.162644	+	0.304373i
$789$	−2.91363	+	7.99408i	−0.103728	+	0.284597i
$790$	39.2925	+	4.40423i	1.39796	+	0.156695i
$791$	40.1085	−	5.76673i	1.42609	−	0.205041i
$792$	30.3890	−	7.80198i	1.07982	−	0.277231i
$793$	−0.207759	−	0.707563i	−0.00737774	−	0.0251263i
$794$	37.2596	+	22.3356i	1.32229	+	0.792661i
$795$	7.84946	−	2.99485i	0.278392	−	0.106216i
$796$	2.43056	+	38.9292i	0.0861489	+	1.37981i
$797$	−4.06010	+	3.51809i	−0.143816	+	0.124617i	−0.723798	−	0.690012i	$-0.757605\pi$
$797$	−4.06010	+	3.51809i	−0.143816	+	0.124617i	0.579982	+	0.814629i	$0.303060\pi$
$798$	−41.2115	+	17.2138i	−1.45887	+	0.609361i
$799$	8.43113	+	13.1191i	0.298272	+	0.464120i
$800$	−4.90046	−	10.3692i	−0.173258	−	0.366608i
$801$	−5.22448	+	8.40358i	−0.184598	+	0.296926i
$802$	1.42064	+	45.5520i	0.0501646	+	1.60850i
$803$	15.7830	−	53.7521i	0.556971	−	1.89687i
$804$	−14.8258	+	12.8063i	−0.522867	+	0.451644i
$805$	13.4647	−	37.8948i	0.474567	−	1.33561i
$806$	0.460132	+	0.498721i	0.0162075	+	0.0175667i
$807$	−3.47587	−	6.25377i	−0.122356	−	0.220143i
$808$	−29.8896	−	1.47380i	−1.05151	−	0.0518480i
$809$	18.7342	−	29.1509i	0.658658	−	1.02489i	−0.337834	−	0.941206i	$-0.609694\pi$
$809$	18.7342	−	29.1509i	0.658658	−	1.02489i	0.996492	−	0.0836862i	$-0.0266693\pi$
$810$	−17.7015	+	12.9697i	−0.621966	+	0.455710i
$811$	2.87007	+	4.46592i	0.100782	+	0.156820i	0.887982	−	0.459877i	$-0.152107\pi$
$811$	2.87007	+	4.46592i	0.100782	+	0.156820i	−0.787200	+	0.616697i	$0.788470\pi$
$812$	−20.4870	−	56.4829i	−0.718952	−	1.98216i
$813$	1.02620	−	16.0349i	0.0359904	−	0.562370i
$814$	−17.4274	+	21.4271i	−0.610832	+	0.751018i
$815$	−14.5203	+	31.7950i	−0.508624	+	1.11373i
$816$	−18.6816	−	14.2964i	−0.653988	−	0.500475i
$817$	−35.6604	+	10.4708i	−1.24760	+	0.366328i
$818$	−3.67960	−	11.2246i	−0.128654	−	0.392459i
$819$	−2.21489	+	0.352389i	−0.0773944	+	0.0123135i
$820$	−22.8510	+	16.7857i	−0.797993	+	0.586182i
$821$	−5.49118	−	12.0240i	−0.191643	−	0.419640i	0.789281	−	0.614033i	$-0.210454\pi$
$821$	−5.49118	−	12.0240i	−0.191643	−	0.419640i	−0.980924	+	0.194392i	$0.937726\pi$
$822$	23.5118	−	14.0447i	0.820068	−	0.489864i
$823$	1.61350	−	11.2221i	0.0562431	−	0.391179i	−0.942183	−	0.335098i	$-0.891230\pi$
$823$	1.61350	−	11.2221i	0.0562431	−	0.391179i	0.998426	−	0.0560808i	$-0.0178605\pi$
$824$	−9.66316	+	0.906456i	−0.336632	+	0.0315779i
$825$	−1.02326	−	12.9439i	−0.0356252	−	0.450649i
$826$	−25.2111	−	50.9397i	−0.877207	−	1.77242i
$827$		−	25.3661i		−	0.882065i	−0.897491	−	0.441032i	$-0.854612\pi$
$827$		−	25.3661i		−	0.882065i	0.897491	−	0.441032i	$-0.145388\pi$
$828$	−12.5142	−	25.9113i	−0.434900	−	0.900479i
$829$			6.96281i			0.241828i	0.992663	+	0.120914i	$0.0385826\pi$
$829$			6.96281i			0.241828i	−0.992663	+	0.120914i	$0.961417\pi$
$830$	−18.0096	+	8.91334i	−0.625123	+	0.309386i
$831$	−3.61421	−	45.7188i	−0.125376	−	1.58597i
$832$	0.845582	+	0.892765i	0.0293153	+	0.0309511i
$833$	−8.04833	+	55.9774i	−0.278858	+	1.93950i
$834$	13.1332	+	21.9859i	0.454764	+	0.761309i
$835$	−4.56362	−	9.99292i	−0.157930	−	0.345819i
$836$	16.4122	+	22.3426i	0.567629	+	0.772736i
$837$	−13.2003	−	9.42640i	−0.456268	−	0.325824i
$838$	5.63935	−	1.84867i	0.194808	−	0.0638611i
$839$	32.2532	−	9.47040i	1.11350	−	0.326954i	0.327300	−	0.944921i	$-0.393861\pi$
$839$	32.2532	−	9.47040i	1.11350	−	0.326954i	0.786205	+	0.617966i	$0.212043\pi$
$840$	−7.04812	−	40.4716i	−0.243183	−	1.39640i
$841$	3.80186	−	8.32492i	0.131099	−	0.287066i
$842$	15.9367	+	12.9619i	0.549215	+	0.446697i
$843$	1.43435	−	22.4125i	0.0494016	−	0.771926i
$844$	−3.13080	−	8.63166i	−0.107767	−	0.297114i
$845$	−12.0956	−	18.8211i	−0.416102	−	0.647467i
$846$	11.2799	+	15.8889i	0.387812	+	0.546273i
$847$	−7.02518	+	10.9314i	−0.241388	+	0.375607i
$848$	7.21436	+	8.63668i	0.247742	+	0.296585i
$849$	22.9768	+	41.3397i	0.788561	+	1.41878i
$850$	−7.15528	+	6.60164i	−0.245424	+	0.226434i
$851$	22.4192	+	11.7917i	0.768519	+	0.404214i
$852$	20.5396	+	23.7786i	0.703674	+	0.814641i
$853$	3.84778	−	13.1043i	0.131745	−	0.448684i	−0.867025	−	0.498265i	$-0.833971\pi$
$853$	3.84778	−	13.1043i	0.131745	−	0.448684i	0.998770	+	0.0495815i	$0.0157887\pi$
$854$	−32.9839	+	1.02868i	−1.12869	+	0.0352007i
$855$	−16.4673	−	10.2377i	−0.563170	−	0.350121i
$856$	−0.451086	−	0.784323i	−0.0154178	−	0.0268076i
$857$	5.50051	+	8.55895i	0.187894	+	0.292368i	0.922402	−	0.386232i	$-0.126223\pi$
$857$	5.50051	+	8.55895i	0.187894	+	0.292368i	−0.734508	+	0.678600i	$0.762587\pi$
$858$	0.536556	+	1.28457i	0.0183177	+	0.0438544i
$859$	12.9589	−	11.2289i	0.442151	−	0.383126i	−0.405140	−	0.914255i	$-0.632777\pi$
$859$	12.9589	−	11.2289i	0.442151	−	0.383126i	0.847291	+	0.531128i	$0.178232\pi$
$860$	−2.13024	−	34.1192i	−0.0726407	−	1.16346i
$861$	64.7187	−	24.6925i	2.20561	−	0.841519i
$862$	15.9018	−	26.5269i	0.541617	−	0.903509i
$863$	2.57888	+	8.78284i	0.0877859	+	0.298971i	0.991670	−	0.128807i	$-0.0411147\pi$
$863$	2.57888	+	8.78284i	0.0877859	+	0.298971i	−0.903884	+	0.427778i	$0.859296\pi$
$864$	−24.1423	−	16.7675i	−0.821338	−	0.570443i
$865$	24.5402	−	3.52835i	0.834391	−	0.119967i
$866$	1.49460	−	13.3341i	0.0507886	−	0.453112i
$867$	3.24496	−	8.90315i	0.110205	−	0.302367i
$868$	26.7816	−	14.3109i	0.909027	−	0.485744i
$869$	−8.53298	+	59.3482i	−0.289461	+	2.01325i
$870$	14.8135	−	21.4712i	0.502226	−	0.727943i
$871$	−0.656955	−	0.569254i	−0.0222601	−	0.0192885i
$872$	9.56270	+	24.0024i	0.323834	+	0.812825i
$873$	−14.8971	+	0.223152i	−0.504192	+	0.00755254i
$874$	17.1185	−	18.7997i	0.579042	−	0.635911i
$875$	−58.9291			−1.99217
$876$	−47.7757	+	21.7286i	−1.61419	+	0.734143i
$877$	−15.5812	−	13.5012i	−0.526138	−	0.455901i	0.350837	−	0.936436i	$-0.385897\pi$
$877$	−15.5812	−	13.5012i	−0.526138	−	0.455901i	−0.876976	+	0.480535i	$0.840442\pi$
$878$	−42.7729	+	7.51750i	−1.44352	+	0.253703i
$879$	23.0184	+	30.2737i	0.776390	+	1.02111i
$880$	−23.3832	+	10.1717i	−0.788249	+	0.342886i
$881$	6.32385	+	13.8473i	0.213056	+	0.466527i	0.985743	−	0.168260i	$-0.0538149\pi$
$881$	6.32385	+	13.8473i	0.213056	+	0.466527i	−0.772687	+	0.634788i	$0.781088\pi$
$882$	−6.81860	+	70.3340i	−0.229594	+	2.36827i
$883$	−57.1265	+	8.21355i	−1.92246	+	0.276408i	−0.995188	−	0.0979813i	$-0.968761\pi$
$883$	−57.1265	+	8.21355i	−1.92246	+	0.276408i	−0.927272	+	0.374389i	$0.877852\pi$
$884$	0.508506	−	0.911559i	0.0171029	−	0.0306590i
$885$	11.6634	−	21.7456i	0.392063	−	0.730971i
$886$	11.2542	−	18.7739i	0.378091	−	0.630721i
$887$	−40.2655	−	18.3886i	−1.35198	−	0.617430i	−0.398026	−	0.917374i	$-0.630305\pi$
$887$	−40.2655	−	18.3886i	−1.35198	−	0.617430i	−0.953957	+	0.299944i	$0.903032\pi$
$888$	25.8645	−	0.766357i	0.867957	−	0.0257172i
$889$	1.96317	−	1.70110i	0.0658426	−	0.0570530i
$890$	3.11126	−	7.41620i	0.104290	−	0.248592i
$891$	−18.8217	−	27.4435i	−0.630551	−	0.919393i
$892$	0.716040	+	0.162562i	0.0239748	+	0.00544297i
$893$	−9.30865	+	14.4845i	−0.311502	+	0.484707i
$894$	−5.37107	−	4.97098i	−0.179635	−	0.166254i
$895$	−3.87144	+	13.1849i	−0.129408	+	0.440723i
$896$	48.1886	−	26.5663i	1.60987	−	0.887519i
$897$	1.05788	−	0.714888i	0.0353214	−	0.0238694i
$898$	20.8605	+	22.6099i	0.696122	+	0.754502i
$899$	18.5004	+	5.43222i	0.617024	+	0.181175i
$900$	−8.55049	+	8.65256i	−0.285016	+	0.288419i
$901$	5.16450	−	8.03613i	0.172055	−	0.267722i
$902$	−24.3622	−	35.4292i	−0.811173	−	1.17966i
$903$	−17.1412	+	81.7392i	−0.570422	+	2.72011i
$904$	−10.8328	+	20.9269i	−0.360293	+	0.696017i
$905$	25.6291	−	22.2077i	0.851940	−	0.738210i
$906$	5.40447	+	48.9035i	0.179551	+	1.62471i
$907$	−9.85817	+	21.5864i	−0.327335	+	0.716764i	−0.999725	−	0.0234327i	$-0.992540\pi$
$907$	−9.85817	+	21.5864i	−0.327335	+	0.716764i	0.672390	+	0.740197i	$0.265268\pi$
$908$	20.0255	−	4.16694i	0.664570	−	0.138285i
$909$	9.39771	+	30.3182i	0.311702	+	1.00559i
$910$	1.73211	−	0.567812i	0.0574188	−	0.0188228i
$911$	3.61075	+	25.1133i	0.119630	+	0.832042i	0.957965	+	0.286886i	$0.0926202\pi$
$911$	3.61075	+	25.1133i	0.119630	+	0.832042i	−0.838335	+	0.545155i	$0.816471\pi$
$912$	5.78964	−	25.3192i	0.191714	−	0.838402i
$913$	−12.6588	−	27.7189i	−0.418944	−	0.917360i
$914$	−31.6297	−	8.22554i	−1.04622	−	0.272077i
$915$	−8.67156	−	11.4048i	−0.286673	−	0.377031i
$916$	−17.9343	+	23.5110i	−0.592564	+	0.776826i
$917$	−47.4044	−	41.0761i	−1.56543	−	1.35645i
$918$	−7.45352	+	23.8120i	−0.246003	+	0.785913i
$919$		−	8.51361i		−	0.280838i	−0.990092	−	0.140419i	$-0.955155\pi$
$919$		−	8.51361i		−	0.280838i	0.990092	−	0.140419i	$-0.0448450\pi$
$920$	13.3771	+	19.1835i	0.441029	+	0.632461i
$921$	21.0653	−	21.3832i	0.694126	−	0.704601i
$922$	−10.1143	+	5.00578i	−0.333097	+	0.164857i
$923$	−0.913005	+	1.05366i	−0.0300519	+	0.0346818i
$924$	61.6768	−	8.76984i	2.02902	−	0.288506i
$925$	1.52401	−	10.5997i	0.0501090	−	0.348516i
$926$	11.6708	−	44.8777i	0.383526	−	1.47477i
$927$	4.41619	+	9.29895i	0.145047	+	0.305417i
$928$	33.6514	+	9.40442i	1.10466	+	0.308715i
$929$	−32.5416	+	4.67877i	−1.06765	+	0.153505i	−0.653671	−	0.756779i	$-0.726772\pi$
$929$	−32.5416	+	4.67877i	−1.06765	+	0.153505i	−0.413983	+	0.910285i	$0.635863\pi$
$930$	11.8063	+	5.86606i	0.387143	+	0.192356i
$931$	−59.9099	+	17.5911i	−1.96347	+	0.576526i
$932$	35.8200	−	7.45348i	1.17332	−	0.244147i
$933$	0.543651	+	1.42490i	0.0177983	+	0.0466492i
$934$	26.5573	−	32.6522i	0.868981	−	1.06841i
$935$	14.1749	+	16.3587i	0.463570	+	0.534988i
$936$	0.582155	−	1.16711i	0.0190283	−	0.0381481i
$937$	−22.1936	−	34.5339i	−0.725033	−	1.12817i	−0.986627	−	0.162996i	$-0.947884\pi$
$937$	−22.1936	−	34.5339i	−0.725033	−	1.12817i	0.261593	−	0.965178i	$-0.415752\pi$
$938$	−32.0532	+	22.0407i	−1.04657	+	0.719655i
$939$	−6.51003	+	1.46732i	−0.212447	+	0.0478840i
$940$	−11.0968	−	11.2994i	−0.361938	−	0.368545i
$941$	−10.3313	+	35.1851i	−0.336790	+	1.14700i	0.600841	+	0.799369i	$0.294833\pi$
$941$	−10.3313	+	35.1851i	−0.336790	+	1.14700i	−0.937631	+	0.347633i	$0.886986\pi$
$942$	20.9802	+	0.687001i	0.683573	+	0.0223837i
$943$	−27.4462	+	28.3159i	−0.893771	+	0.922093i
$944$	32.6260	+	5.29498i	1.06189	+	0.172337i
$945$	−37.7641	+	21.7361i	−1.22847	+	0.707074i
$946$	51.8158	−	1.61600i	1.68468	−	0.0525406i
$947$	33.2066	+	21.3406i	1.07907	+	0.693476i	0.954342	−	0.298715i	$-0.0965580\pi$
$947$	33.2066	+	21.3406i	1.07907	+	0.693476i	0.124727	+	0.992191i	$0.460194\pi$
$948$	47.3032	−	30.2960i	1.53634	−	0.983969i
$949$	−1.25905	−	1.95912i	−0.0408705	−	0.0635957i
$950$	−9.91185	−	4.15824i	−0.321583	−	0.134911i
$951$	−0.595709	+	9.30828i	−0.0193172	+	0.301842i
$952$	−33.7516	−	32.2898i	−1.09390	−	1.04652i
$953$	−21.3181	+	46.6800i	−0.690560	+	1.51211i	0.160495	+	0.987037i	$0.448691\pi$
$953$	−21.3181	+	46.6800i	−0.690560	+	1.51211i	−0.851054	+	0.525078i	$0.824036\pi$
$954$	5.98295	−	10.3283i	0.193705	−	0.334391i
$955$	10.0101	+	34.0912i	0.323918	+	1.10316i
$956$	11.8248	−	21.1974i	0.382441	−	0.685573i
$957$	31.8441	+	23.4681i	1.02937	+	0.758618i
$958$	0.0266414	+	0.00298619i	0.000860744	+	9.64793e-5i
$959$	49.4657	−	22.5902i	1.59733	−	0.729477i
$960$	21.5320	+	10.3493i	0.694941	+	0.334022i
$961$	3.02496	−	21.0391i	0.0975793	−	0.678679i
$962$	0.198744	+	1.13081i	0.00640777	+	0.0364588i
$963$	−0.617519	+	0.734604i	−0.0198993	+	0.0236723i
$964$	−12.3102	−	4.71872i	−0.396483	−	0.151980i
$965$			4.79236i			0.154272i
$966$	−19.0465	−	53.8675i	−0.612811	−	1.73316i
$967$	−61.0162			−1.96215			−0.981075	−	0.193629i	$-0.937974\pi$
$967$	−61.0162			−1.96215			−0.981075	+	0.193629i	$0.937974\pi$
$968$	−2.79680	−	7.01999i	−0.0898926	−	0.225631i
$969$	−21.9786	+	1.73748i	−0.706054	+	0.0558158i
$970$	11.9263	−	2.09609i	0.382930	−	0.0673013i
$971$	−57.4209	−	8.25587i	−1.84272	−	0.264944i	−0.869354	−	0.494189i	$-0.835465\pi$
$971$	−57.4209	−	8.25587i	−1.84272	−	0.264944i	−0.973369	+	0.229246i	$0.926374\pi$
$972$	−7.93055	+	30.1514i	−0.254372	+	0.967106i
$973$	21.1241	+	46.2554i	0.677209	+	1.48288i
$974$	0.960121	+	0.107618i	0.0307643	+	0.00344832i
$975$	−0.434509	−	0.320220i	−0.0139154	−	0.0102552i
$976$	10.6656	−	15.9539i	0.341399	−	0.510673i
$977$	−26.0064	+	7.63618i	−0.832020	+	0.244303i	−0.669884	−	0.742465i	$-0.733656\pi$
$977$	−26.0064	+	7.63618i	−0.832020	+	0.244303i	−0.162136	+	0.986768i	$0.551838\pi$
$978$	12.4238	+	48.0804i	0.397270	+	1.53744i
$979$	11.0938	+	5.06637i	0.354560	+	0.161922i
$980$	−3.57883	−	57.3206i	−0.114322	−	1.83104i
$981$	20.4398	−	18.2543i	0.652594	−	0.582816i
$982$	0.888733	+	0.372843i	0.0283606	+	0.0118979i
$983$	−47.2541	+	30.3684i	−1.50717	+	0.968600i	−0.513282	+	0.858220i	$0.671570\pi$
$983$	−47.2541	+	30.3684i	−1.50717	+	0.968600i	−0.993889	+	0.110380i	$0.964793\pi$
$984$	−10.1993	+	38.9702i	−0.325141	+	1.24232i
$985$	−4.51498	+	7.02545i	−0.143859	+	0.223849i
$986$	−0.924562	−	29.6454i	−0.0294440	−	0.944103i
$987$	18.7964	+	33.8184i	0.598295	+	1.07645i
$988$	1.14871	+	0.0926083i	0.0365454	+	0.00294626i
$989$	−10.8299	−	46.2959i	−0.344370	−	1.47213i
$990$	18.6360	+	19.6015i	0.592291	+	0.622976i
$991$	−14.3849	−	4.22378i	−0.456951	−	0.134173i	0.0451533	−	0.998980i	$-0.485622\pi$
$991$	−14.3849	−	4.22378i	−0.456951	−	0.134173i	−0.502104	+	0.864807i	$0.667441\pi$
$992$	−2.28414	+	17.5103i	−0.0725216	+	0.555952i
$993$	−24.9134	+	5.61530i	−0.790601	+	0.178196i
$994$	35.3503	+	51.4088i	1.12124	+	1.63059i
$995$	−28.2867	+	18.1788i	−0.896750	+	0.576306i
$996$	−11.9000	+	25.9505i	−0.377067	+	0.822274i
$997$	−5.24189	+	4.54213i	−0.166012	+	0.143851i	−0.733905	−	0.679252i	$-0.762304\pi$
$997$	−5.24189	+	4.54213i	−0.166012	+	0.143851i	0.567893	+	0.823103i	$0.307759\pi$
$998$	28.3161	−	34.8147i	0.896331	−	1.10204i
$999$	−10.1665	−	25.4931i	−0.321654	−	0.806566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.12	✓	920
3.2	odd	2	inner	552.2.bf.a.5.81	yes	920
8.5	even	2	inner	552.2.bf.a.5.64	yes	920
23.14	odd	22	inner	552.2.bf.a.221.29	yes	920
24.5	odd	2	inner	552.2.bf.a.5.29	yes	920
69.14	even	22	inner	552.2.bf.a.221.64	yes	920
184.37	odd	22	inner	552.2.bf.a.221.81	yes	920
552.221	even	22	inner	552.2.bf.a.221.12	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.12	✓	920	1.1	even	1	trivial
552.2.bf.a.5.29	yes	920	24.5	odd	2	inner
552.2.bf.a.5.64	yes	920	8.5	even	2	inner
552.2.bf.a.5.81	yes	920	3.2	odd	2	inner
552.2.bf.a.221.12	yes	920	552.221	even	22	inner
552.2.bf.a.221.29	yes	920	23.14	odd	22	inner
552.2.bf.a.221.64	yes	920	69.14	even	22	inner
552.2.bf.a.221.81	yes	920	184.37	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26748 + 0.627300i) q^{2} +(-1.72666 + 0.136498i) q^{3} +(1.21299 - 1.59018i) q^{4} +(1.70656 + 0.245367i) q^{5} +(2.10288 - 1.25614i) q^{6} +(4.42418 - 2.02045i) q^{7} +(-0.539916 + 2.77642i) q^{8} +(2.96274 - 0.471373i) q^{9} +O(q^{10})\)	\(q+(-1.26748 + 0.627300i) q^{2} +(-1.72666 + 0.136498i) q^{3} +(1.21299 - 1.59018i) q^{4} +(1.70656 + 0.245367i) q^{5} +(2.10288 - 1.25614i) q^{6} +(4.42418 - 2.02045i) q^{7} +(-0.539916 + 2.77642i) q^{8} +(2.96274 - 0.471373i) q^{9} +(-2.31695 + 0.759532i) q^{10} +(-1.04171 - 3.54775i) q^{11} +(-1.87737 + 2.91127i) q^{12} +(-0.139816 - 0.0638519i) q^{13} +(-4.34011 + 5.33617i) q^{14} +(-2.98015 - 0.190723i) q^{15} +(-1.05732 - 3.85773i) q^{16} +(-2.85642 + 1.83571i) q^{17} +(-3.45950 + 2.45598i) q^{18} +(-3.15372 - 2.02677i) q^{19} +(2.46022 - 2.41611i) q^{20} +(-7.36328 + 4.09254i) q^{21} +(3.54585 + 3.84321i) q^{22} +(2.81381 - 3.88361i) q^{23} +(0.553277 - 4.86764i) q^{24} +(-1.94531 - 0.571194i) q^{25} +(0.217268 - 0.00677600i) q^{26} +(-5.05131 + 1.21831i) q^{27} +(2.15360 - 9.48601i) q^{28} +(5.19619 - 3.33939i) q^{29} +(3.89691 - 1.62771i) q^{30} +(2.04424 + 2.35917i) q^{31} +(3.76008 + 4.22632i) q^{32} +(2.28295 + 5.98357i) q^{33} +(2.46890 - 4.11856i) q^{34} +(8.04590 - 2.36249i) q^{35} +(2.84420 - 5.28304i) q^{36} +(0.751692 + 5.22813i) q^{37} +(5.26866 + 0.590556i) q^{38} +(0.250131 + 0.0911661i) q^{39} +(-1.60264 + 4.60566i) q^{40} +(-8.13898 - 1.17021i) q^{41} +(6.76553 - 9.80618i) q^{42} +(6.49227 - 7.49248i) q^{43} +(-6.90512 - 2.64687i) q^{44} +(5.17176 - 0.0774704i) q^{45} +(-1.13025 + 6.68749i) q^{46} -4.59284i q^{47} +(2.35220 + 6.51668i) q^{48} +(10.9071 - 12.5875i) q^{49} +(2.82394 - 0.496318i) q^{50} +(4.68151 - 3.55955i) q^{51} +(-0.271131 + 0.144881i) q^{52} +(-2.55912 + 1.16871i) q^{53} +(5.63816 - 4.71287i) q^{54} +(-0.907249 - 6.31006i) q^{55} +(3.22094 + 13.3742i) q^{56} +(5.72207 + 3.06908i) q^{57} +(-4.49125 + 7.49217i) q^{58} +(-3.43267 + 7.51649i) q^{59} +(-3.91818 + 4.50762i) q^{60} +(3.14182 + 3.62585i) q^{61} +(-4.07093 - 1.70785i) q^{62} +(12.1553 - 8.07151i) q^{63} +(-7.41698 - 2.99806i) q^{64} +(-0.222938 - 0.143274i) q^{65} +(-6.64708 - 6.15194i) q^{66} +(5.42635 + 1.59332i) q^{67} +(-0.545705 + 6.76891i) q^{68} +(-4.32840 + 7.08978i) q^{69} +(-8.71599 + 8.04159i) q^{70} +(2.55546 - 8.70311i) q^{71} +(-0.290900 + 8.48029i) q^{72} +(12.7459 + 8.19127i) q^{73} +(-4.23236 - 6.15499i) q^{74} +(3.43686 + 0.720729i) q^{75} +(-7.04836 + 2.55652i) q^{76} +(-11.7768 - 13.5911i) q^{77} +(-0.374224 + 0.0413565i) q^{78} +(-14.7505 - 6.73631i) q^{79} +(-0.857821 - 6.84289i) q^{80} +(8.55562 - 2.79311i) q^{81} +(11.0500 - 3.62237i) q^{82} +(8.15748 - 1.17287i) q^{83} +(-2.42372 + 16.6731i) q^{84} +(-5.32509 + 2.43189i) q^{85} +(-3.52876 + 13.5691i) q^{86} +(-8.51626 + 6.47528i) q^{87} +(10.4125 - 0.976744i) q^{88} +(-2.16000 + 2.49277i) q^{89} +(-6.50648 + 3.34244i) q^{90} -0.747581 q^{91} +(-2.76251 - 9.18524i) q^{92} +(-3.85173 - 3.79447i) q^{93} +(2.88109 + 5.82131i) q^{94} +(-4.88473 - 4.23264i) q^{95} +(-7.06928 - 6.78420i) q^{96} +(-4.91572 - 0.706774i) q^{97} +(-5.92836 + 22.7963i) q^{98} +(-4.75863 - 10.0200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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