LMFDB - Embedded newform 770.2.bg.e.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(81,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("770.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bg (of order $15$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			191.3
Character	$\chi$	$=$	770.191
Dual form			770.2.bg.e.641.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(-1.76210 + 0.374545i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.45741 - 1.05887i) q^{6} +(2.59531 - 0.514179i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.224066 - 0.0997608i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.76210 + 0.374545i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.45741 - 1.05887i) q^{6} +(2.59531 - 0.514179i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.224066 - 0.0997608i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.61493 + 2.04014i) q^{11} +(-0.900732 + 1.56011i) q^{12} +(1.72311 + 1.25191i) q^{13} +(-2.16180 + 1.52533i) q^{14} +(0.556683 + 1.71329i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-2.51772 - 1.12096i) q^{17} +(-0.164118 + 0.182272i) q^{18} +(1.07610 + 1.19513i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-4.38060 + 1.87809i) q^{21} +(1.55906 - 2.92734i) q^{22} +(4.07823 - 7.06369i) q^{23} +(0.188304 - 1.79160i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-2.08334 - 0.442827i) q^{26} +(4.01478 - 2.91691i) q^{27} +(1.35449 - 2.27274i) q^{28} +(-0.673586 - 2.07309i) q^{29} +(-1.20541 - 1.33875i) q^{30} +(-0.412165 + 3.92149i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.84363 - 4.57433i) q^{33} +2.75598 q^{34} +(-0.782645 - 2.52734i) q^{35} +(0.0757930 - 0.233267i) q^{36} +(5.54398 + 1.17841i) q^{37} +(-1.46917 - 0.654115i) q^{38} +(-3.50519 - 1.56061i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-1.99208 + 6.13100i) q^{41} +(3.23799 - 3.49747i) q^{42} +5.84878 q^{43} +(-0.233611 + 3.30839i) q^{44} +(-0.122636 - 0.212411i) q^{45} +(-0.852581 + 8.11177i) q^{46} +(5.29846 + 5.88454i) q^{47} +(0.556683 + 1.71329i) q^{48} +(6.47124 - 2.66890i) q^{49} +(0.809017 - 0.587785i) q^{50} +(4.85631 + 1.03224i) q^{51} +(2.08334 - 0.442827i) q^{52} +(-0.121351 + 1.15458i) q^{53} +(-2.48127 + 4.29769i) q^{54} +(2.30229 + 2.38735i) q^{55} +(-0.312981 + 2.62717i) q^{56} +(-2.34382 - 1.70288i) q^{57} +(1.45855 + 1.61989i) q^{58} +(2.63256 - 2.92376i) q^{59} +(1.64572 + 0.732721i) q^{60} +(1.08606 + 10.3332i) q^{61} +(-1.21848 - 3.75010i) q^{62} +(0.530226 - 0.374120i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.06494 - 1.84453i) q^{65} +(-1.65079 + 5.74220i) q^{66} +(4.41627 + 7.64921i) q^{67} +(-2.51772 + 1.12096i) q^{68} +(-4.54056 + 13.9744i) q^{69} +(1.74295 + 1.99051i) q^{70} +(11.8340 - 8.59790i) q^{71} +(0.0256378 + 0.243928i) q^{72} +(6.04355 - 6.71204i) q^{73} +(-5.54398 + 1.17841i) q^{74} +(1.64572 - 0.732721i) q^{75} +1.60820 q^{76} +(-5.73754 + 6.63932i) q^{77} +3.83691 q^{78} +(9.12036 - 4.06064i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-6.47428 + 7.19041i) q^{81} +(-0.673844 - 6.41120i) q^{82} +(7.00436 - 5.08896i) q^{83} +(-1.53550 + 4.51211i) q^{84} +(-0.851646 + 2.62110i) q^{85} +(-5.34313 + 2.37891i) q^{86} +(1.96339 + 3.40069i) q^{87} +(-1.13223 - 3.11738i) q^{88} +(-3.15388 + 5.46269i) q^{89} +(0.198429 + 0.144167i) q^{90} +(5.11571 + 2.36311i) q^{91} +(-2.52048 - 7.75725i) q^{92} +(-0.742500 - 7.06442i) q^{93} +(-7.23384 - 3.22071i) q^{94} +(1.07610 - 1.19513i) q^{95} +(-1.20541 - 1.33875i) q^{96} +(-2.45289 - 1.78213i) q^{97} +(-4.82623 + 5.07025i) q^{98} +(-0.382392 + 0.717993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) $ 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9} + 36 q^{10} - 2 q^{12} + 28 q^{13} - 2 q^{14} - 6 q^{15} + 9 q^{16} - 4 q^{17} - 7 q^{18} - q^{19} - 18 q^{20} - 32 q^{21} - 20 q^{22} - 30 q^{23} + 2 q^{24} + 9 q^{25} - 11 q^{26} + 18 q^{27} + 6 q^{28} + 22 q^{29} - 3 q^{30} - 8 q^{31} + 36 q^{32} - 24 q^{33} + 32 q^{34} - 3 q^{35} - 14 q^{36} + 20 q^{37} - 4 q^{38} - 25 q^{39} - 9 q^{40} + 34 q^{41} + 22 q^{42} + 12 q^{43} - 58 q^{45} - 20 q^{46} - 13 q^{47} - 6 q^{48} + 6 q^{49} + 18 q^{50} - 37 q^{51} + 11 q^{52} + 2 q^{53} + 14 q^{54} - 10 q^{55} - 2 q^{56} - 18 q^{57} + 11 q^{58} + 29 q^{59} - 2 q^{60} + 21 q^{61} + 44 q^{62} + 31 q^{63} - 18 q^{64} + 6 q^{65} - q^{66} - 20 q^{67} - 4 q^{68} - 104 q^{69} + 4 q^{70} - 70 q^{71} - 22 q^{72} - 28 q^{73} - 20 q^{74} - 2 q^{75} + 12 q^{76} - 47 q^{77} + 20 q^{78} - 24 q^{79} + 9 q^{80} + 44 q^{81} - 28 q^{82} - 56 q^{83} - 46 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} - 5 q^{88} - 20 q^{89} + 44 q^{90} - 36 q^{91} + 10 q^{92} + 77 q^{93} - 22 q^{94} - q^{95} - 3 q^{96} - 178 q^{97} - 68 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9 + 36 * q^10 - 2 * q^12 + 28 * q^13 - 2 * q^14 - 6 * q^15 + 9 * q^16 - 4 * q^17 - 7 * q^18 - q^19 - 18 * q^20 - 32 * q^21 - 20 * q^22 - 30 * q^23 + 2 * q^24 + 9 * q^25 - 11 * q^26 + 18 * q^27 + 6 * q^28 + 22 * q^29 - 3 * q^30 - 8 * q^31 + 36 * q^32 - 24 * q^33 + 32 * q^34 - 3 * q^35 - 14 * q^36 + 20 * q^37 - 4 * q^38 - 25 * q^39 - 9 * q^40 + 34 * q^41 + 22 * q^42 + 12 * q^43 - 58 * q^45 - 20 * q^46 - 13 * q^47 - 6 * q^48 + 6 * q^49 + 18 * q^50 - 37 * q^51 + 11 * q^52 + 2 * q^53 + 14 * q^54 - 10 * q^55 - 2 * q^56 - 18 * q^57 + 11 * q^58 + 29 * q^59 - 2 * q^60 + 21 * q^61 + 44 * q^62 + 31 * q^63 - 18 * q^64 + 6 * q^65 - q^66 - 20 * q^67 - 4 * q^68 - 104 * q^69 + 4 * q^70 - 70 * q^71 - 22 * q^72 - 28 * q^73 - 20 * q^74 - 2 * q^75 + 12 * q^76 - 47 * q^77 + 20 * q^78 - 24 * q^79 + 9 * q^80 + 44 * q^81 - 28 * q^82 - 56 * q^83 - 46 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 - 5 * q^88 - 20 * q^89 + 44 * q^90 - 36 * q^91 + 10 * q^92 + 77 * q^93 - 22 * q^94 - q^95 - 3 * q^96 - 178 * q^97 - 68 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	−1.76210	+	0.374545i	−1.01735	+	0.216244i	−0.686260	−	0.727356i	$-0.740749\pi$
$3$	−1.76210	+	0.374545i	−1.01735	+	0.216244i	−0.331087	+	0.943600i	$0.607415\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$6$	1.45741	−	1.05887i	0.594987	−	0.432283i
$7$	2.59531	−	0.514179i	0.980934	−	0.194341i
$7$	2.59531	−	0.514179i	0.980934	−	0.194341i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.224066	−	0.0997608i	0.0746888	−	0.0332536i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.61493	+	2.04014i	−0.788430	+	0.615124i
$11$	−2.61493	+	2.04014i	−0.788430	+	0.615124i
$12$	−0.900732	+	1.56011i	−0.260019	+	0.450366i
$13$	1.72311	+	1.25191i	0.477905	+	0.347218i	0.800514	−	0.599314i	$-0.204560\pi$
$13$	1.72311	+	1.25191i	0.477905	+	0.347218i	−0.322609	+	0.946532i	$0.604560\pi$
$14$	−2.16180	+	1.52533i	−0.577764	+	0.407662i
$15$	0.556683	+	1.71329i	0.143735	+	0.442371i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−2.51772	−	1.12096i	−0.610636	−	0.271873i	0.0780306	−	0.996951i	$-0.475137\pi$
$17$	−2.51772	−	1.12096i	−0.610636	−	0.271873i	−0.688666	+	0.725078i	$0.741803\pi$
$18$	−0.164118	+	0.182272i	−0.0386831	+	0.0429619i
$19$	1.07610	+	1.19513i	0.246874	+	0.274181i	0.853827	−	0.520556i	$-0.174275\pi$
$19$	1.07610	+	1.19513i	0.246874	+	0.274181i	−0.606954	+	0.794737i	$0.707609\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	−4.38060	+	1.87809i	−0.955926	+	0.409834i
$22$	1.55906	−	2.92734i	0.332392	−	0.624112i
$23$	4.07823	−	7.06369i	0.850369	−	1.47288i	−0.0305069	−	0.999535i	$-0.509712\pi$
$23$	4.07823	−	7.06369i	0.850369	−	1.47288i	0.880876	−	0.473348i	$-0.156955\pi$
$24$	0.188304	−	1.79160i	0.0384374	−	0.365708i
$25$	−0.978148	+	0.207912i	−0.195630	+	0.0415823i
$26$	−2.08334	−	0.442827i	−0.408576	−	0.0868456i
$27$	4.01478	−	2.91691i	0.772645	−	0.561360i
$28$	1.35449	−	2.27274i	0.255975	−	0.429508i
$29$	−0.673586	−	2.07309i	−0.125082	−	0.384962i	0.868834	−	0.495103i	$-0.164870\pi$
$29$	−0.673586	−	2.07309i	−0.125082	−	0.384962i	−0.993916	+	0.110141i	$0.964870\pi$
$30$	−1.20541	−	1.33875i	−0.220078	−	0.244421i
$31$	−0.412165	+	3.92149i	−0.0740270	+	0.704320i	0.893071	+	0.449916i	$0.148546\pi$
$31$	−0.412165	+	3.92149i	−0.0740270	+	0.704320i	−0.967098	+	0.254404i	$0.918121\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.84363	−	4.57433i	0.669090	−	0.796288i
$34$	2.75598			0.472647
$35$	−0.782645	−	2.52734i	−0.132291	−	0.427199i
$36$	0.0757930	−	0.233267i	0.0126322	−	0.0388778i
$37$	5.54398	+	1.17841i	0.911425	+	0.193729i	0.639681	−	0.768640i	$-0.279066\pi$
$37$	5.54398	+	1.17841i	0.911425	+	0.193729i	0.271744	+	0.962370i	$0.412400\pi$
$38$	−1.46917	−	0.654115i	−0.238330	−	0.106111i
$39$	−3.50519	−	1.56061i	−0.561279	−	0.249898i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	−1.99208	+	6.13100i	−0.311111	+	0.957501i	0.666215	+	0.745760i	$0.267913\pi$
$41$	−1.99208	+	6.13100i	−0.311111	+	0.957501i	−0.977326	+	0.211741i	$0.932087\pi$
$42$	3.23799	−	3.49747i	0.499633	−	0.539672i
$43$	5.84878			0.891931			0.445965	−	0.895050i	$-0.352860\pi$
$43$	5.84878			0.891931			0.445965	+	0.895050i	$0.352860\pi$
$44$	−0.233611	+	3.30839i	−0.0352181	+	0.498758i
$45$	−0.122636	−	0.212411i	−0.0182814	−	0.0316644i
$46$	−0.852581	+	8.11177i	−0.125706	+	1.19602i
$47$	5.29846	+	5.88454i	0.772860	+	0.858348i	0.993121	−	0.117093i	$-0.0373576\pi$
$47$	5.29846	+	5.88454i	0.772860	+	0.858348i	−0.220261	+	0.975441i	$0.570691\pi$
$48$	0.556683	+	1.71329i	0.0803503	+	0.247293i
$49$	6.47124	−	2.66890i	0.924463	−	0.381272i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	4.85631	+	1.03224i	0.680019	+	0.144543i
$52$	2.08334	−	0.442827i	0.288907	−	0.0614091i
$53$	−0.121351	+	1.15458i	−0.0166688	+	0.158593i	−0.999690	−	0.0248989i	$-0.992074\pi$
$53$	−0.121351	+	1.15458i	−0.0166688	+	0.158593i	0.983021	+	0.183492i	$0.0587403\pi$
$54$	−2.48127	+	4.29769i	−0.337658	+	0.584841i
$55$	2.30229	+	2.38735i	0.310441	+	0.321910i
$56$	−0.312981	+	2.62717i	−0.0418239	+	0.351071i
$57$	−2.34382	−	1.70288i	−0.310446	−	0.225552i
$58$	1.45855	+	1.61989i	0.191517	+	0.212701i
$59$	2.63256	−	2.92376i	0.342731	−	0.380641i	−0.546996	−	0.837136i	$-0.684229\pi$
$59$	2.63256	−	2.92376i	0.342731	−	0.380641i	0.889726	+	0.456495i	$0.150895\pi$
$60$	1.64572	+	0.732721i	0.212461	+	0.0945939i
$61$	1.08606	+	10.3332i	0.139056	+	1.32303i	0.812141	+	0.583461i	$0.198302\pi$
$61$	1.08606	+	10.3332i	0.139056	+	1.32303i	−0.673085	+	0.739565i	$0.735031\pi$
$62$	−1.21848	−	3.75010i	−0.154747	−	0.476263i
$63$	0.530226	−	0.374120i	0.0668022	−	0.0471347i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.06494	−	1.84453i	0.132090	−	0.228786i
$66$	−1.65079	+	5.74220i	−0.203198	+	0.706816i
$67$	4.41627	+	7.64921i	0.539533	+	0.934499i	0.998929	+	0.0462676i	$0.0147327\pi$
$67$	4.41627	+	7.64921i	0.539533	+	0.934499i	−0.459396	+	0.888232i	$0.651934\pi$
$68$	−2.51772	+	1.12096i	−0.305318	+	0.135936i
$69$	−4.54056	+	13.9744i	−0.546619	+	1.68232i
$70$	1.74295	+	1.99051i	0.208322	+	0.237912i
$71$	11.8340	−	8.59790i	1.40444	−	1.02038i	0.410335	−	0.911935i	$-0.365412\pi$
$71$	11.8340	−	8.59790i	1.40444	−	1.02038i	0.994102	−	0.108449i	$-0.0345883\pi$
$72$	0.0256378	+	0.243928i	0.00302145	+	0.0287471i
$73$	6.04355	−	6.71204i	0.707344	−	0.785585i	−0.277183	−	0.960817i	$-0.589401\pi$
$73$	6.04355	−	6.71204i	0.707344	−	0.785585i	0.984527	+	0.175232i	$0.0560676\pi$
$74$	−5.54398	+	1.17841i	−0.644475	+	0.136987i
$75$	1.64572	−	0.732721i	0.190031	−	0.0846074i
$76$	1.60820			0.184473
$77$	−5.73754	+	6.63932i	−0.653854	+	0.756621i
$78$	3.83691			0.434444
$79$	9.12036	−	4.06064i	1.02612	−	0.456858i	0.176527	−	0.984296i	$-0.443514\pi$
$79$	9.12036	−	4.06064i	1.02612	−	0.456858i	0.849594	+	0.527438i	$0.176847\pi$
$80$	−0.978148	+	0.207912i	−0.109360	+	0.0232452i
$81$	−6.47428	+	7.19041i	−0.719364	+	0.798935i
$82$	−0.673844	−	6.41120i	−0.0744136	−	0.707998i
$83$	7.00436	−	5.08896i	0.768828	−	0.558586i	−0.132777	−	0.991146i	$-0.542390\pi$
$83$	7.00436	−	5.08896i	0.768828	−	0.558586i	0.901605	+	0.432560i	$0.142390\pi$
$84$	−1.53550	+	4.51211i	−0.167537	+	0.492312i
$85$	−0.851646	+	2.62110i	−0.0923739	+	0.284298i
$86$	−5.34313	+	2.37891i	−0.576164	+	0.256525i
$87$	1.96339	+	3.40069i	0.210497	+	0.364592i
$88$	−1.13223	−	3.11738i	−0.120696	−	0.332314i
$89$	−3.15388	+	5.46269i	−0.334311	+	0.579044i	−0.983352	−	0.181710i	$-0.941837\pi$
$89$	−3.15388	+	5.46269i	−0.334311	+	0.579044i	0.649041	+	0.760753i	$0.275170\pi$
$90$	0.198429	+	0.144167i	0.0209162	+	0.0151965i
$91$	5.11571	+	2.36311i	0.536272	+	0.247722i
$92$	−2.52048	−	7.75725i	−0.262778	−	0.808749i
$93$	−0.742500	−	7.06442i	−0.0769937	−	0.732546i
$94$	−7.23384	−	3.22071i	−0.746114	−	0.332191i
$95$	1.07610	−	1.19513i	0.110405	−	0.122617i
$96$	−1.20541	−	1.33875i	−0.123027	−	0.136635i
$97$	−2.45289	−	1.78213i	−0.249053	−	0.180948i	0.456254	−	0.889850i	$-0.349191\pi$
$97$	−2.45289	−	1.78213i	−0.249053	−	0.180948i	−0.705307	+	0.708902i	$0.749191\pi$
$98$	−4.82623	+	5.07025i	−0.487523	+	0.512173i
$99$	−0.382392	+	0.717993i	−0.0384318	+	0.0721610i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.0609755	−	0.580143i	0.00606729	−	0.0577264i	−0.991069	−	0.133348i	$-0.957427\pi$
$101$	0.0609755	−	0.580143i	0.00606729	−	0.0577264i	0.997137	+	0.0756212i	$0.0240940\pi$
$102$	−4.85631	+	1.03224i	−0.480846	+	0.102207i
$103$	−8.99563	−	1.91208i	−0.886366	−	0.188403i	−0.257836	−	0.966189i	$-0.583010\pi$
$103$	−8.99563	−	1.91208i	−0.886366	−	0.188403i	−0.628530	+	0.777786i	$0.716343\pi$
$104$	−1.72311	+	1.25191i	−0.168965	+	0.122760i
$105$	2.32570	+	4.16029i	0.226965	+	0.406003i
$106$	−0.358749	−	1.10412i	−0.0348448	−	0.107241i
$107$	1.96123	+	2.17817i	0.189599	+	0.210571i	0.830448	−	0.557095i	$-0.188084\pi$
$107$	1.96123	+	2.17817i	0.189599	+	0.210571i	−0.640849	+	0.767667i	$0.721418\pi$
$108$	0.518727	−	4.93536i	0.0499145	−	0.474905i
$109$	5.91837	+	10.2509i	0.566877	+	0.981861i	0.996872	+	0.0790292i	$0.0251820\pi$
$109$	5.91837	+	10.2509i	0.566877	+	0.981861i	−0.429995	+	0.902831i	$0.641485\pi$
$110$	−3.07427	−	1.24452i	−0.293120	−	0.118661i
$111$	−10.2104			−0.969129
$112$	−0.782645	−	2.52734i	−0.0739530	−	0.238812i
$113$	5.50108	−	16.9306i	0.517498	−	1.59269i	−0.261193	−	0.965287i	$-0.584116\pi$
$113$	5.50108	−	16.9306i	0.517498	−	1.59269i	0.778691	−	0.627408i	$-0.215884\pi$
$114$	2.83381	+	0.602344i	0.265410	+	0.0564147i
$115$	−7.45129	−	3.31753i	−0.694836	−	0.309361i
$116$	−1.99132	−	0.886593i	−0.184889	−	0.0823181i
$117$	0.510983	+	0.108613i	0.0472404	+	0.0100413i
$118$	−1.21577	+	3.74175i	−0.111920	+	0.344456i
$119$	−7.11062	−	1.61468i	−0.651829	−	0.148017i
$120$	−1.80146			−0.164450
$121$	2.67568	−	10.6696i	0.243244	−	0.969965i
$122$	−5.19504	−	8.99808i	−0.470337	−	0.814647i
$123$	1.21391	−	11.5495i	0.109454	−	1.04139i
$124$	2.63844	+	2.93029i	0.236939	+	0.263147i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−0.332218	+	0.557438i	−0.0295963	+	0.0496605i
$127$	−0.0368746	+	0.0267910i	−0.00327209	+	0.00237732i	−0.589420	−	0.807827i	$-0.700644\pi$
$127$	−0.0368746	+	0.0267910i	−0.00327209	+	0.00237732i	0.586148	+	0.810204i	$0.300644\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	−10.3061	+	2.19063i	−0.907403	+	0.192875i
$130$	−0.222633	+	2.11821i	−0.0195262	+	0.185780i
$131$	−2.82422	+	4.89170i	−0.246754	+	0.427390i	−0.962623	−	0.270844i	$-0.912697\pi$
$131$	−2.82422	+	4.89170i	−0.246754	+	0.427390i	0.715870	+	0.698234i	$0.246030\pi$
$132$	−0.827497	−	5.91720i	−0.0720243	−	0.515026i
$133$	3.40731	+	2.54842i	0.295451	+	0.220976i
$134$	−7.14568	−	5.19164i	−0.617292	−	0.448489i
$135$	−3.32059	−	3.68789i	−0.285791	−	0.317403i
$136$	1.84411	−	2.04809i	0.158131	−	0.175623i
$137$	11.9517	+	5.32125i	1.02110	+	0.454625i	0.847841	−	0.530251i	$-0.177902\pi$
$137$	11.9517	+	5.32125i	1.02110	+	0.454625i	0.173263	+	0.984876i	$0.444569\pi$
$138$	−1.53589	−	14.6131i	−0.130744	−	1.24395i
$139$	−4.65840	−	14.3371i	−0.395120	−	1.21606i	−0.928868	−	0.370411i	$-0.879217\pi$
$139$	−4.65840	−	14.3371i	−0.395120	−	1.21606i	0.533748	−	0.845644i	$-0.320783\pi$
$140$	−2.40187	−	1.10950i	−0.202995	−	0.0937702i
$141$	−11.5404	−	8.38461i	−0.971880	−	0.706112i
$142$	−7.31381	+	12.6679i	−0.613762	+	1.06307i
$143$	−7.05988	+	0.241720i	−0.590377	+	0.0202136i
$144$	−0.122636	−	0.212411i	−0.0102196	−	0.0177009i
$145$	−1.99132	+	0.886593i	−0.165370	+	0.0736275i
$146$	−2.79102	+	8.58989i	−0.230987	+	0.710904i
$147$	−10.4033	+	7.12664i	−0.858052	+	0.587795i
$148$	4.58538	−	3.33147i	0.376916	−	0.273845i
$149$	2.23083	+	21.2249i	0.182757	+	1.73881i	0.574292	+	0.818651i	$0.305277\pi$
$149$	2.23083	+	21.2249i	0.182757	+	1.73881i	−0.391535	+	0.920163i	$0.628056\pi$
$150$	−1.20541	+	1.33875i	−0.0984217	+	0.109308i
$151$	18.2583	−	3.88092i	1.48584	−	0.315824i	0.607674	−	0.794186i	$-0.292103\pi$
$151$	18.2583	−	3.88092i	1.48584	−	0.315824i	0.878163	+	0.478362i	$0.158769\pi$
$152$	−1.46917	+	0.654115i	−0.119165	+	0.0530557i
$153$	−0.675963			−0.0546484
$154$	2.54105	−	8.39899i	0.204764	−	0.676810i
$155$	3.94309			0.316717
$156$	−3.50519	+	1.56061i	−0.280640	+	0.124949i
$157$	−19.8194	+	4.21275i	−1.58176	+	0.336214i	−0.913223	−	0.407461i	$-0.866414\pi$
$157$	−19.8194	+	4.21275i	−1.58176	+	0.336214i	−0.668541	+	0.743675i	$0.733081\pi$
$158$	−6.68025	+	7.41917i	−0.531452	+	0.590237i
$159$	−0.218609	−	2.07993i	−0.0173369	−	0.164949i
$160$	0.809017	−	0.587785i	0.0639584	−	0.0464685i
$161$	6.95225	−	20.4294i	0.547914	−	1.61006i
$162$	2.98994	−	9.20210i	0.234912	−	0.722985i
$163$	14.6626	−	6.52821i	1.14846	−	0.511329i	0.257892	−	0.966174i	$-0.416972\pi$
$163$	14.6626	−	6.52821i	1.14846	−	0.511329i	0.890571	+	0.454845i	$0.150305\pi$
$164$	3.22326	+	5.58284i	0.251694	+	0.435947i
$165$	−4.95104	−	3.34443i	−0.385438	−	0.260363i
$166$	−4.32893	+	7.49793i	−0.335990	+	0.581952i
$167$	7.07567	+	5.14078i	0.547532	+	0.397805i	0.826875	−	0.562386i	$-0.190117\pi$
$167$	7.07567	+	5.14078i	0.547532	+	0.397805i	−0.279343	+	0.960191i	$0.590117\pi$
$168$	−0.432492	−	4.74656i	−0.0333675	−	0.366205i
$169$	−2.61540	−	8.04936i	−0.201184	−	0.619182i
$170$	−0.288079	−	2.74089i	−0.0220946	−	0.210216i
$171$	0.360344	+	0.160435i	0.0275562	+	0.0122688i
$172$	3.91360	−	4.34649i	0.298409	−	0.331417i
$173$	5.83766	+	6.48337i	0.443829	+	0.492922i	0.923000	−	0.384800i	$-0.125729\pi$
$173$	5.83766	+	6.48337i	0.443829	+	0.492922i	−0.479171	+	0.877721i	$0.659063\pi$
$174$	−3.17683	−	2.30810i	−0.240835	−	0.174977i
$175$	−2.43169	+	1.04254i	−0.183818	+	0.0788084i
$176$	2.30229	+	2.38735i	0.173542	+	0.179953i
$177$	−3.54375	+	6.13796i	−0.266365	+	0.461357i
$178$	0.659341	−	6.27321i	0.0494197	−	0.470197i
$179$	−18.2361	+	3.87621i	−1.36303	+	0.289721i	−0.830656	−	0.556786i	$-0.812034\pi$
$179$	−18.2361	+	3.87621i	−1.36303	+	0.289721i	−0.532376	+	0.846508i	$0.678701\pi$
$180$	−0.239911	−	0.0509948i	−0.0178819	−	0.00380092i
$181$	−15.2452	+	11.0763i	−1.13317	+	0.823296i	−0.986153	−	0.165838i	$-0.946967\pi$
$181$	−15.2452	+	11.0763i	−1.13317	+	0.823296i	−0.147017	+	0.989134i	$0.546967\pi$
$182$	−5.63460	−	0.0780648i	−0.417664	−	0.00578655i
$183$	−5.78398	−	17.8013i	−0.427564	−	1.31591i
$184$	5.45773	+	6.06142i	0.402349	+	0.446854i
$185$	0.592450	−	5.63679i	0.0435578	−	0.414425i
$186$	3.55167	+	6.15166i	0.260421	+	0.451062i
$187$	8.87055	−	2.20526i	0.648679	−	0.161264i
$188$	7.91843			0.577511
$189$	8.91978	−	9.63459i	0.648819	−	0.700814i
$190$	−0.496962	+	1.52949i	−0.0360534	+	0.110961i
$191$	−3.79346	−	0.806325i	−0.274485	−	0.0583436i	0.0686124	−	0.997643i	$-0.478143\pi$
$191$	−3.79346	−	0.806325i	−0.274485	−	0.0583436i	−0.343098	+	0.939300i	$0.611476\pi$
$192$	1.64572	+	0.732721i	0.118770	+	0.0528796i
$193$	−12.2061	−	5.43451i	−0.878615	−	0.391184i	−0.0826866	−	0.996576i	$-0.526350\pi$
$193$	−12.2061	−	5.43451i	−0.878615	−	0.391184i	−0.795928	+	0.605391i	$0.793017\pi$
$194$	2.96568	+	0.630375i	0.212923	+	0.0452583i
$195$	−1.18567	+	3.64911i	−0.0849075	+	0.261318i
$196$	2.34672	−	6.59491i	0.167623	−	0.471065i
$197$	−12.7532			−0.908624			−0.454312	−	0.890843i	$-0.650115\pi$
$197$	−12.7532			−0.908624			−0.454312	+	0.890843i	$0.650115\pi$
$198$	0.0572979	−	0.811452i	0.00407199	−	0.0576674i
$199$	−6.51791	−	11.2893i	−0.462042	−	0.800281i	0.537020	−	0.843569i	$-0.319550\pi$
$199$	−6.51791	−	11.2893i	−0.462042	−	0.800281i	−0.999063	+	0.0432886i	$0.986217\pi$
$200$	0.104528	−	0.994522i	0.00739128	−	0.0703233i
$201$	−10.6469	−	11.8246i	−0.750973	−	0.834040i
$202$	0.180262	+	0.554788i	0.0126832	+	0.0390348i
$203$	−2.81410	−	5.03395i	−0.197511	−	0.353314i
$204$	4.01661	−	2.91824i	0.281219	−	0.204318i
$205$	6.30564	+	1.34030i	0.440405	+	0.0936110i
$206$	8.99563	−	1.91208i	0.626755	−	0.133221i
$207$	0.209114	−	1.98958i	0.0145344	−	0.138286i
$208$	1.06494	−	1.84453i	0.0738404	−	0.127895i
$209$	−5.25214	−	0.929784i	−0.363298	−	0.0643145i
$210$	−3.81678	−	2.85467i	−0.263383	−	0.196991i
$211$	4.51374	+	3.27943i	0.310739	+	0.225765i	0.732214	−	0.681075i	$-0.238487\pi$
$211$	4.51374	+	3.27943i	0.310739	+	0.225765i	−0.421475	+	0.906840i	$0.638487\pi$
$212$	0.776819	+	0.862745i	0.0533521	+	0.0592535i
$213$	−17.6324	+	19.5827i	−1.20815	+	1.34179i
$214$	−2.67761	−	1.19215i	−0.183038	−	0.0814937i
$215$	−0.611364	−	5.81674i	−0.0416947	−	0.396698i
$216$	1.53351	+	4.71966i	0.104342	+	0.321132i
$217$	0.946650	+	10.3894i	0.0642628	+	0.705278i
$218$	−9.57613	−	6.95747i	−0.648577	−	0.471219i
$219$	−8.13536	+	14.0909i	−0.549737	+	0.952172i
$220$	3.31468	−	0.113490i	0.223476	−	0.00765148i
$221$	−2.93496	−	5.08350i	−0.197427	−	0.341953i
$222$	9.32767	−	4.15295i	0.626032	−	0.278727i
$223$	−3.88282	+	11.9501i	−0.260013	+	0.800238i	0.732787	+	0.680458i	$0.238219\pi$
$223$	−3.88282	+	11.9501i	−0.260013	+	0.800238i	−0.992800	+	0.119780i	$0.961781\pi$
$224$	1.74295	+	1.99051i	0.116455	+	0.132997i
$225$	−0.198429	+	0.144167i	−0.0132286	+	0.00961112i
$226$	1.86080	+	17.7043i	0.123779	+	1.17768i
$227$	−8.42893	+	9.36127i	−0.559448	+	0.621330i	−0.954818	−	0.297192i	$-0.903950\pi$
$227$	−8.42893	+	9.36127i	−0.559448	+	0.621330i	0.395370	+	0.918522i	$0.370616\pi$
$228$	−2.83381	+	0.602344i	−0.187673	+	0.0398912i
$229$	4.45995	−	1.98570i	0.294722	−	0.131219i	−0.254049	−	0.967191i	$-0.581763\pi$
$229$	4.45995	−	1.98570i	0.294722	−	0.131219i	0.548771	+	0.835973i	$0.315096\pi$
$230$	8.15645			0.537820
$231$	7.62338	−	13.8481i	0.501582	−	0.911138i
$232$	2.17977			0.143109
$233$	−1.45729	+	0.648828i	−0.0954704	+	0.0425061i	−0.453916	−	0.891044i	$-0.649973\pi$
$233$	−1.45729	+	0.648828i	−0.0954704	+	0.0425061i	0.358446	+	0.933551i	$0.383307\pi$
$234$	−0.510983	+	0.108613i	−0.0334040	+	0.00710024i
$235$	5.29846	−	5.88454i	0.345633	−	0.383865i
$236$	−0.411247	−	3.91275i	−0.0267699	−	0.254698i
$237$	−14.5501	+	10.5712i	−0.945128	+	0.686676i
$238$	7.15262	−	1.41707i	0.463636	−	0.0918548i
$239$	7.71549	−	23.7458i	0.499073	−	1.53599i	−0.311438	−	0.950267i	$-0.600811\pi$
$239$	7.71549	−	23.7458i	0.499073	−	1.53599i	0.810511	−	0.585723i	$-0.199189\pi$
$240$	1.64572	−	0.732721i	0.106231	−	0.0472970i
$241$	2.52882	+	4.38004i	0.162896	+	0.282143i	0.935906	−	0.352250i	$-0.114583\pi$
$241$	2.52882	+	4.38004i	0.162896	+	0.282143i	−0.773010	+	0.634393i	$0.781250\pi$
$242$	1.89536	+	10.8355i	0.121839	+	0.696531i
$243$	1.27136	−	2.20205i	0.0815575	−	0.141262i
$244$	8.40575	+	6.10714i	0.538123	+	0.390969i
$245$	−3.33071	−	6.15681i	−0.212791	−	0.393344i
$246$	3.58866	+	11.0448i	0.228805	+	0.704189i
$247$	0.358039	+	3.40652i	0.0227815	+	0.216751i
$248$	−3.60219	−	1.60380i	−0.228739	−	0.101841i
$249$	−10.4363	+	11.5907i	−0.661374	+	0.734531i
$250$	−0.669131	−	0.743145i	−0.0423195	−	0.0470006i
$251$	−14.1520	−	10.2821i	−0.893268	−	0.648997i	0.0434598	−	0.999055i	$-0.486162\pi$
$251$	−14.1520	−	10.2821i	−0.893268	−	0.648997i	−0.936728	+	0.350058i	$0.886162\pi$
$252$	0.0767653	−	0.644370i	0.00483576	−	0.0405915i
$253$	3.74664	+	26.7912i	0.235549	+	1.68435i
$254$	0.0227898	−	0.0394730i	0.00142996	−	0.00247676i
$255$	0.518963	−	4.93761i	0.0324987	−	0.309205i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−24.4842	−	5.20429i	−1.52729	−	0.324634i	−0.633718	−	0.773564i	$-0.718472\pi$
$257$	−24.4842	−	5.20429i	−1.52729	−	0.324634i	−0.893567	+	0.448930i	$0.851805\pi$
$258$	8.52410	−	6.19312i	0.530687	−	0.385567i
$259$	14.9943	+	0.207739i	0.931697	+	0.0129082i
$260$	−0.658170	−	2.02564i	−0.0408180	−	0.125625i
$261$	−0.357741	−	0.397311i	−0.0221436	−	0.0245930i
$262$	0.590423	−	5.61750i	0.0364765	−	0.347051i
$263$	−4.23081	−	7.32798i	−0.260883	−	0.451862i	0.705594	−	0.708616i	$-0.250680\pi$
$263$	−4.23081	−	7.32798i	−0.260883	−	0.451862i	−0.966477	+	0.256754i	$0.917347\pi$
$264$	3.16270	+	5.06906i	0.194651	+	0.311979i
$265$	1.16094			0.0713158
$266$	−4.14927	−	0.942215i	−0.254408	−	0.0577709i
$267$	3.51143	−	10.8071i	0.214896	−	0.661381i
$268$	8.63953	+	1.83639i	0.527743	+	0.112175i
$269$	8.77928	+	3.90879i	0.535282	+	0.238323i	0.656531	−	0.754299i	$-0.272023\pi$
$269$	8.77928	+	3.90879i	0.535282	+	0.238323i	−0.121249	+	0.992622i	$0.538690\pi$
$270$	4.53351	+	2.01845i	0.275901	+	0.122839i
$271$	11.9083	+	2.53118i	0.723376	+	0.153758i	0.554864	−	0.831941i	$-0.312770\pi$
$271$	11.9083	+	2.53118i	0.723376	+	0.153758i	0.168512	+	0.985700i	$0.446104\pi$
$272$	−0.851646	+	2.62110i	−0.0516386	+	0.158927i
$273$	−9.89947	−	2.24797i	−0.599143	−	0.136053i
$274$	−13.0828			−0.790360
$275$	2.13362	−	2.53923i	0.128662	−	0.153121i
$276$	7.34678	+	12.7250i	0.442224	+	0.765954i
$277$	0.368719	−	3.50813i	0.0221542	−	0.210783i	−0.977845	−	0.209331i	$-0.932871\pi$
$277$	0.368719	−	3.50813i	0.0221542	−	0.210783i	0.999999	−	0.00145160i	$-0.000462057\pi$
$278$	10.0871	+	11.2028i	0.604983	+	0.671901i
$279$	0.298858	+	0.919792i	0.0178922	+	0.0550665i
$280$	2.64550	+	0.0366522i	0.158099	+	0.00219039i
$281$	−19.9333	+	14.4824i	−1.18912	+	0.863946i	−0.993171	−	0.116668i	$-0.962779\pi$
$281$	−19.9333	+	14.4824i	−1.18912	+	0.863946i	−0.195949	+	0.980614i	$0.562779\pi$
$282$	13.9530	+	2.96581i	0.830891	+	0.176611i
$283$	14.1523	−	3.00816i	0.841267	−	0.178817i	0.232928	−	0.972494i	$-0.425169\pi$
$283$	14.1523	−	3.00816i	0.841267	−	0.178817i	0.608339	+	0.793677i	$0.291836\pi$
$284$	1.52900	−	14.5475i	0.0907297	−	0.863235i
$285$	−1.44856	+	2.50898i	−0.0858052	+	0.148619i
$286$	6.35121	−	3.09234i	0.375555	−	0.182854i
$287$	−2.01764	+	16.9361i	−0.119097	+	0.999707i
$288$	0.198429	+	0.144167i	0.0116925	+	0.00849511i
$289$	−6.29288	−	6.98895i	−0.370169	−	0.411115i
$290$	1.45855	−	1.61989i	0.0856491	−	0.0951230i
$291$	4.98971	+	2.22156i	0.292502	+	0.130230i
$292$	−0.944095	−	8.98246i	−0.0552490	−	0.525659i
$293$	−0.274100	−	0.843593i	−0.0160131	−	0.0492833i	0.942731	−	0.333555i	$-0.108248\pi$
$293$	−0.274100	−	0.843593i	−0.0160131	−	0.0492833i	−0.958744	+	0.284272i	$0.908248\pi$
$294$	6.60525	−	10.7419i	0.385226	−	0.626482i
$295$	−3.18292	−	2.31253i	−0.185317	−	0.134640i
$296$	−2.83392	+	4.90849i	−0.164718	+	0.285300i
$297$	−4.54747	+	15.8182i	−0.263871	+	0.917866i
$298$	−10.6709	−	18.4826i	−0.618150	−	1.07067i
$299$	15.8704	−	7.06594i	0.917807	−	0.408634i
$300$	0.556683	−	1.71329i	0.0321401	−	0.0989171i
$301$	15.1794	−	3.00732i	0.874925	−	0.173339i
$302$	−15.1013	+	10.9717i	−0.868979	+	0.631350i
$303$	0.109845	+	1.04511i	0.00631044	+	0.0600398i
$304$	1.07610	−	1.19513i	0.0617184	−	0.0685452i
$305$	10.1630	−	2.16022i	0.581934	−	0.123694i
$306$	0.617523	−	0.274939i	0.0353015	−	0.0157172i
$307$	31.8773			1.81933			0.909667	−	0.415339i	$-0.136337\pi$
$307$	31.8773			1.81933			0.909667	+	0.415339i	$0.136337\pi$
$308$	1.09481	+	8.70640i	0.0623826	+	0.496093i
$309$	16.5673			0.942483
$310$	−3.60219	+	1.60380i	−0.204591	+	0.0910896i
$311$	−9.62162	+	2.04514i	−0.545592	+	0.115969i	−0.472458	−	0.881353i	$-0.656633\pi$
$311$	−9.62162	+	2.04514i	−0.545592	+	0.115969i	−0.0731338	+	0.997322i	$0.523300\pi$
$312$	2.56739	−	2.85138i	0.145350	−	0.161427i
$313$	−0.391347	−	3.72342i	−0.0221202	−	0.210460i	−0.999999	−	0.00128836i	$-0.999590\pi$
$313$	−0.391347	−	3.72342i	−0.0221202	−	0.210460i	0.977879	−	0.209172i	$-0.0670768\pi$
$314$	16.3925	−	11.9098i	0.925081	−	0.672111i
$315$	−0.427494	−	0.488216i	−0.0240866	−	0.0275078i
$316$	3.08506	−	9.49485i	0.173548	−	0.534127i
$317$	−5.20631	+	2.31800i	−0.292415	+	0.130192i	−0.547701	−	0.836674i	$-0.684497\pi$
$317$	−5.20631	+	2.31800i	−0.292415	+	0.130192i	0.255286	+	0.966866i	$0.417830\pi$
$318$	1.04569	+	1.81119i	0.0586396	+	0.101567i
$319$	5.99076	+	4.04676i	0.335418	+	0.226575i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−4.27170	−	3.10357i	−0.238423	−	0.173225i
$322$	1.95819	+	21.4909i	0.109126	+	1.19764i
$323$	−1.36962	−	4.21525i	−0.0762076	−	0.234543i
$324$	1.01138	+	9.62265i	0.0561879	+	0.534592i
$325$	−1.94574	−	0.866301i	−0.107930	−	0.0480537i
$326$	−10.7397	+	11.9276i	−0.594816	+	0.660610i
$327$	−14.2682	−	15.8464i	−0.789033	−	0.876310i
$328$	−5.21534	−	3.78916i	−0.287969	−	0.209222i
$329$	16.7768	+	12.5478i	0.924937	+	0.691784i
$330$	5.88330	+	1.04152i	0.323865	+	0.0573337i
$331$	−10.0048	+	17.3288i	−0.549911	+	0.952475i	0.448369	+	0.893849i	$0.352005\pi$
$331$	−10.0048	+	17.3288i	−0.549911	+	0.952475i	−0.998280	+	0.0586258i	$0.981328\pi$
$332$	0.904993	−	8.61043i	0.0496679	−	0.472559i
$333$	1.35978	−	0.289030i	0.0745154	−	0.0158387i
$334$	−8.55489	−	1.81840i	−0.468103	−	0.0994983i
$335$	7.14568	−	5.19164i	0.390410	−	0.283650i
$336$	2.32570	+	4.16029i	0.126877	+	0.226962i
$337$	1.85410	+	5.70635i	0.101000	+	0.310845i	0.988771	−	0.149440i	$-0.0477472\pi$
$337$	1.85410	+	5.70635i	0.101000	+	0.310845i	−0.887771	+	0.460285i	$0.847747\pi$
$338$	5.66325	+	6.28968i	0.308040	+	0.342114i
$339$	−3.35217	+	31.8937i	−0.182065	+	1.73223i
$340$	1.37799	+	2.38675i	0.0747321	+	0.129440i
$341$	−6.92259	−	11.0953i	−0.374879	−	0.600843i
$342$	−0.394446			−0.0213292
$343$	15.4226	−	10.2540i	0.832740	−	0.553664i
$344$	−1.80737	+	5.56252i	−0.0974470	+	0.299911i
$345$	14.3725	+	3.05496i	0.773787	+	0.164474i
$346$	−7.96999	−	3.54847i	−0.428469	−	0.190767i
$347$	7.84310	+	3.49197i	0.421040	+	0.187459i	0.606309	−	0.795229i	$-0.292649\pi$
$347$	7.84310	+	3.49197i	0.421040	+	0.187459i	−0.185270	+	0.982688i	$0.559316\pi$
$348$	3.84097	+	0.816423i	0.205898	+	0.0437649i
$349$	−5.02962	+	15.4796i	−0.269229	+	0.828603i	0.721459	+	0.692457i	$0.243472\pi$
$349$	−5.02962	+	15.4796i	−0.269229	+	0.828603i	−0.990689	+	0.136146i	$0.956528\pi$
$350$	1.79742	−	1.94146i	0.0960762	−	0.103776i
$351$	10.5696			0.564165
$352$	−3.07427	−	1.24452i	−0.163859	−	0.0663334i
$353$	8.64213	+	14.9686i	0.459974	+	0.796699i	0.998959	−	0.0456168i	$-0.0145253\pi$
$353$	8.64213	+	14.9686i	0.459974	+	0.796699i	−0.538985	+	0.842315i	$0.681192\pi$
$354$	0.740846	−	7.04868i	0.0393755	−	0.374633i
$355$	−9.78779	−	10.8704i	−0.519482	−	0.576943i
$356$	1.94921	+	5.99904i	0.103308	+	0.317949i
$357$	13.1344	+	0.181971i	0.695145	+	0.00963092i
$358$	15.0829	−	10.9584i	0.797158	−	0.579169i
$359$	−34.9961	−	7.43866i	−1.84703	−	0.392598i	−0.855000	−	0.518628i	$-0.826443\pi$
$359$	−34.9961	−	7.43866i	−1.84703	−	0.392598i	−0.992026	+	0.126031i	$0.959776\pi$
$360$	0.239911	−	0.0509948i	0.0126444	−	0.00268766i
$361$	1.71570	−	16.3238i	0.0902999	−	0.859146i
$362$	9.42208	−	16.3195i	0.495213	−	0.857735i
$363$	−0.718562	+	19.8031i	−0.0377147	+	1.03939i
$364$	5.17921	−	2.22048i	0.271465	−	0.116385i
$365$	−7.30699	−	5.30884i	−0.382466	−	0.277878i
$366$	12.5244	+	13.9097i	0.654659	+	0.727072i
$367$	−25.2088	+	27.9972i	−1.31589	+	1.46144i	−0.522618	+	0.852567i	$0.675045\pi$
$367$	−25.2088	+	27.9972i	−1.31589	+	1.46144i	−0.793268	+	0.608873i	$0.791622\pi$
$368$	−7.45129	−	3.31753i	−0.388425	−	0.172938i
$369$	0.165275	+	1.57248i	0.00860385	+	0.0818601i
$370$	1.75146	+	5.39043i	0.0910540	+	0.280235i
$371$	0.278716	+	3.05888i	0.0144702	+	0.158809i
$372$	−5.74672	−	4.17523i	−0.297953	−	0.216476i
$373$	9.43807	−	16.3472i	0.488685	−	0.846427i	−0.511231	−	0.859444i	$-0.670810\pi$
$373$	9.43807	−	16.3472i	0.488685	−	0.846427i	0.999915	+	0.0130169i	$0.00414353\pi$
$374$	−7.20669	+	5.62258i	−0.372649	+	0.290737i
$375$	−0.900732	−	1.56011i	−0.0465136	−	0.0805639i
$376$	−7.23384	+	3.22071i	−0.373057	+	0.166096i
$377$	1.43466	−	4.41543i	0.0738887	−	0.227406i
$378$	−4.22988	+	12.4296i	−0.217562	+	0.639312i
$379$	19.1304	−	13.8991i	0.982665	−	0.713948i	0.0243620	−	0.999703i	$-0.492245\pi$
$379$	19.1304	−	13.8991i	0.982665	−	0.713948i	0.958303	+	0.285756i	$0.0922446\pi$
$380$	−0.168103	−	1.59939i	−0.00862349	−	0.0820471i
$381$	0.0549422	−	0.0610195i	0.00281478	−	0.00312613i
$382$	3.79346	−	0.806325i	0.194090	−	0.0412552i
$383$	14.1628	−	6.30571i	0.723688	−	0.322207i	−0.0116269	−	0.999932i	$-0.503701\pi$
$383$	14.1628	−	6.30571i	0.723688	−	0.322207i	0.735315	+	0.677726i	$0.237034\pi$
$384$	−1.80146			−0.0919306
$385$	7.20269	+	5.01212i	0.367083	+	0.255441i
$386$	13.3612			0.680070
$387$	1.31052	−	0.583479i	0.0666172	−	0.0296599i
$388$	−2.96568	+	0.630375i	−0.150560	+	0.0320024i
$389$	3.81823	−	4.24058i	0.193592	−	0.215006i	−0.638532	−	0.769595i	$-0.720458\pi$
$389$	3.81823	−	4.24058i	0.193592	−	0.215006i	0.832124	+	0.554589i	$0.187125\pi$
$390$	−0.401066	−	3.81589i	−0.0203088	−	0.193225i
$391$	−18.1859	+	13.2128i	−0.919702	+	0.668202i
$392$	0.538554	+	6.97925i	0.0272011	+	0.352505i
$393$	3.14439	−	9.67745i	0.158614	−	0.488163i
$394$	11.6506	−	5.18717i	0.586948	−	0.261326i
$395$	−4.99174	−	8.64594i	−0.251162	−	0.435025i
$396$	0.277703	+	0.764604i	0.0139551	+	0.0384228i
$397$	6.47752	−	11.2194i	0.325098	−	0.563086i	−0.656434	−	0.754383i	$-0.727936\pi$
$397$	6.47752	−	11.2194i	0.325098	−	0.563086i	0.981532	+	0.191297i	$0.0612695\pi$
$398$	10.5462	+	7.66226i	0.528633	+	0.384074i
$399$	−6.95851	−	3.21436i	−0.348361	−	0.160919i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−0.655492	−	6.23659i	−0.0327337	−	0.311440i	−0.998622	−	0.0524810i	$-0.983287\pi$
$401$	−0.655492	−	6.23659i	−0.0327337	−	0.311440i	0.965888	−	0.258959i	$-0.0833796\pi$
$402$	14.5359	+	6.47179i	0.724984	+	0.322784i
$403$	−5.61957	+	6.24116i	−0.279931	+	0.310895i
$404$	−0.390330	−	0.433505i	−0.0194196	−	0.0215677i
$405$	7.82777	+	5.68721i	0.388965	+	0.282600i
$406$	4.61830	+	3.45415i	0.229202	+	0.171426i
$407$	−16.9012	+	8.22903i	−0.837763	+	0.407898i
$408$	−2.48240	+	4.29965i	−0.122897	+	0.212864i
$409$	1.70319	−	16.2048i	0.0842174	−	0.801275i	−0.868146	−	0.496309i	$-0.834688\pi$
$409$	1.70319	−	16.2048i	0.0842174	−	0.801275i	0.952363	−	0.304966i	$-0.0986451\pi$
$410$	−6.30564	+	1.34030i	−0.311413	+	0.0661929i
$411$	−23.0531	−	4.90010i	−1.13713	−	0.241704i
$412$	−7.44020	+	5.40562i	−0.366553	+	0.266316i
$413$	5.32898	−	8.94166i	0.262222	−	0.439990i
$414$	0.618202	+	1.90263i	0.0303830	+	0.0935091i
$415$	−5.79324	−	6.43404i	−0.284379	−	0.315835i
$416$	−0.222633	+	2.11821i	−0.0109155	+	0.103854i
$417$	13.5784	+	23.5185i	0.664939	+	1.15171i
$418$	5.17624	−	1.28684i	0.253178	−	0.0629412i
$419$	10.8508			0.530096			0.265048	−	0.964235i	$-0.414612\pi$
$419$	10.8508			0.530096			0.265048	+	0.964235i	$0.414612\pi$
$420$	4.64790	+	1.05544i	0.226794	+	0.0515004i
$421$	−3.12628	+	9.62171i	−0.152366	+	0.468933i	−0.997884	−	0.0650123i	$-0.979291\pi$
$421$	−3.12628	+	9.62171i	−0.152366	+	0.468933i	0.845519	+	0.533946i	$0.179291\pi$
$422$	−5.45737	−	1.16000i	−0.265661	−	0.0564679i
$423$	1.77425	+	0.789948i	0.0862671	+	0.0384086i
$424$	−1.06057	−	0.472196i	−0.0515058	−	0.0229319i
$425$	2.69576	+	0.573001i	0.130763	+	0.0277946i
$426$	8.14295	−	25.0614i	0.394527	−	1.21423i
$427$	8.13175	+	26.2593i	0.393523	+	1.27078i
$428$	2.93101			0.141676
$429$	12.3497	−	3.07018i	0.596248	−	0.148230i
$430$	2.92439	+	5.06519i	0.141027	+	0.244265i
$431$	−1.72216	+	16.3853i	−0.0829537	+	0.789252i	0.871400	+	0.490573i	$0.163213\pi$
$431$	−1.72216	+	16.3853i	−0.0829537	+	0.789252i	−0.954354	+	0.298679i	$0.903454\pi$
$432$	−3.32059	−	3.68789i	−0.159762	−	0.177434i
$433$	4.68385	+	14.4154i	0.225091	+	0.692760i	0.998282	+	0.0585867i	$0.0186594\pi$
$433$	4.68385	+	14.4154i	0.225091	+	0.692760i	−0.773191	+	0.634173i	$0.781341\pi$
$434$	−5.09056	−	9.10615i	−0.244354	−	0.437109i
$435$	3.17683	−	2.30810i	0.152317	−	0.110665i
$436$	11.5781	+	2.46100i	0.554490	+	0.117860i
$437$	12.8306	−	2.72722i	0.613770	−	0.130461i
$438$	1.70075	−	16.1816i	0.0812651	−	0.773186i
$439$	−1.62899	+	2.82150i	−0.0777476	+	0.134663i	−0.902278	−	0.431155i	$-0.858106\pi$
$439$	−1.62899	+	2.82150i	−0.0777476	+	0.134663i	0.824530	+	0.565818i	$0.191439\pi$
$440$	−2.98195	+	1.45188i	−0.142159	+	0.0692157i
$441$	1.18374	−	1.24359i	0.0563684	−	0.0592185i
$442$	4.74886	+	3.45025i	0.225880	+	0.164112i
$443$	−10.9908	−	12.2065i	−0.522189	−	0.579950i	0.423141	−	0.906064i	$-0.360927\pi$
$443$	−10.9908	−	12.2065i	−0.522189	−	0.579950i	−0.945330	+	0.326114i	$0.894261\pi$
$444$	−6.83209	+	7.58781i	−0.324237	+	0.360101i
$445$	5.76243	+	2.56560i	0.273166	+	0.121621i
$446$	−1.31341	−	12.4962i	−0.0621917	−	0.591715i
$447$	−11.8806	−	36.5648i	−0.561935	−	1.72946i
$448$	−2.40187	−	1.10950i	−0.113478	−	0.0524191i
$449$	6.27866	+	4.56171i	0.296308	+	0.215281i	0.725999	−	0.687695i	$-0.241378\pi$
$449$	6.27866	+	4.56171i	0.296308	+	0.215281i	−0.429691	+	0.902976i	$0.641378\pi$
$450$	0.122636	−	0.212411i	0.00578110	−	0.0100132i
$451$	−7.29892	−	20.0962i	−0.343693	−	0.946294i
$452$	−8.90093	−	15.4169i	−0.418665	−	0.725148i
$453$	−30.7193	+	13.6771i	−1.44332	+	0.642606i
$454$	3.89264	−	11.9803i	0.182690	−	0.562263i
$455$	1.81543	−	5.33470i	0.0851087	−	0.250094i
$456$	2.34382	−	1.70288i	0.109759	−	0.0797448i
$457$	−2.92484	−	27.8280i	−0.136818	−	1.30174i	−0.820368	−	0.571836i	$-0.806231\pi$
$457$	−2.92484	−	27.8280i	−0.136818	−	1.30174i	0.683549	−	0.729904i	$-0.260435\pi$
$458$	−3.26671	+	3.62805i	−0.152643	+	0.169528i
$459$	−13.3778	+	2.84354i	−0.624423	+	0.132725i
$460$	−7.45129	+	3.31753i	−0.347418	+	0.154681i
$461$	31.7364			1.47811			0.739057	−	0.673643i	$-0.235271\pi$
$461$	31.7364			1.47811			0.739057	+	0.673643i	$0.235271\pi$
$462$	−1.33178	+	15.7516i	−0.0619599	+	0.732830i
$463$	−28.0165			−1.30204			−0.651019	−	0.759061i	$-0.725658\pi$
$463$	−28.0165			−1.30204			−0.651019	+	0.759061i	$0.725658\pi$
$464$	−1.99132	+	0.886593i	−0.0924447	+	0.0411590i
$465$	−6.94811	+	1.47687i	−0.322211	+	0.0684880i
$466$	1.06740	−	1.18547i	0.0494464	−	0.0549157i
$467$	3.68030	+	35.0157i	0.170304	+	1.62033i	0.661957	+	0.749542i	$0.269726\pi$
$467$	3.68030	+	35.0157i	0.170304	+	1.62033i	−0.491653	+	0.870791i	$0.663607\pi$
$468$	0.422630	−	0.307058i	0.0195361	−	0.0141938i
$469$	15.3946	+	17.5813i	0.710858	+	0.811829i
$470$	−2.44693	+	7.53087i	−0.112868	+	0.347373i
$471$	33.3459	−	14.8466i	1.53650	−	0.684093i
$472$	1.96715	+	3.40721i	0.0905455	+	0.156829i
$473$	−15.2941	+	11.9323i	−0.703225	+	0.548648i
$474$	8.99243	−	15.5753i	0.413036	−	0.715399i
$475$	−1.30106	−	0.945277i	−0.0596968	−	0.0433723i
$476$	−5.95787	+	4.20379i	−0.273079	+	0.192680i
$477$	0.0879909	+	0.270808i	0.00402883	+	0.0123995i
$478$	2.60985	+	24.8311i	0.119372	+	1.13575i
$479$	5.52522	+	2.45998i	0.252454	+	0.112400i	0.529062	−	0.848583i	$-0.322544\pi$
$479$	5.52522	+	2.45998i	0.252454	+	0.112400i	−0.276609	+	0.960983i	$0.589211\pi$
$480$	−1.20541	+	1.33875i	−0.0550194	+	0.0611052i
$481$	8.07763	+	8.97112i	0.368308	+	0.409048i
$482$	−4.09171	−	2.97280i	−0.186372	−	0.135408i
$483$	−4.59880	+	38.6025i	−0.209253	+	1.75648i
$484$	−6.13869	−	9.12779i	−0.279031	−	0.414899i
$485$	−1.51597	+	2.62573i	−0.0688365	+	0.119228i
$486$	−0.265786	+	2.52878i	−0.0120563	+	0.114708i
$487$	10.9915	−	2.33633i	0.498075	−	0.105869i	0.0479771	−	0.998848i	$-0.484723\pi$
$487$	10.9915	−	2.33633i	0.498075	−	0.105869i	0.450098	+	0.892979i	$0.351389\pi$
$488$	−10.1630	−	2.16022i	−0.460059	−	0.0977885i
$489$	−23.3918	+	16.9951i	−1.05781	+	0.768547i
$490$	5.54696	+	4.26981i	0.250586	+	0.192890i
$491$	5.92412	+	18.2326i	0.267352	+	0.822824i	0.991142	+	0.132804i	$0.0423982\pi$
$491$	5.92412	+	18.2326i	0.267352	+	0.822824i	−0.723790	+	0.690020i	$0.757602\pi$
$492$	−7.77072	−	8.63026i	−0.350331	−	0.389082i
$493$	−0.627946	+	5.97450i	−0.0282813	+	0.269078i
$494$	−1.71264	−	2.96638i	−0.0770553	−	0.133464i
$495$	0.754031	+	0.305246i	0.0338912	+	0.0137198i
$496$	3.94309			0.177050
$497$	26.2920	−	28.3990i	1.17936	−	1.27387i
$498$	4.81968	−	14.8335i	0.215975	−	0.664703i
$499$	−16.0902	−	3.42007i	−0.720294	−	0.153103i	−0.166841	−	0.985984i	$-0.553357\pi$
$499$	−16.0902	−	3.42007i	−0.720294	−	0.153103i	−0.553453	+	0.832880i	$0.686690\pi$
$500$	0.913545	+	0.406737i	0.0408550	+	0.0181898i
$501$	−14.3935	−	6.40839i	−0.643053	−	0.286306i
$502$	17.1106	+	3.63697i	0.763684	+	0.162326i
$503$	−2.58015	+	7.94090i	−0.115043	+	0.354067i	−0.991956	−	0.126583i	$-0.959599\pi$
$503$	−2.58015	+	7.94090i	−0.115043	+	0.354067i	0.876913	+	0.480650i	$0.159599\pi$
$504$	0.191960	+	0.619885i	0.00855060	+	0.0276119i
$505$	−0.583339			−0.0259582
$506$	−14.3197	−	22.9511i	−0.636587	−	1.02030i
$507$	7.62344	+	13.2042i	0.338569	+	0.586418i
$508$	−0.00476436	+	0.0453299i	−0.000211384	+	0.00201119i
$509$	6.68830	+	7.42811i	0.296454	+	0.329245i	0.872909	−	0.487884i	$-0.162231\pi$
$509$	6.68830	+	7.42811i	0.296454	+	0.329245i	−0.576455	+	0.817129i	$0.695564\pi$
$510$	1.53421	+	4.72181i	0.0679359	+	0.209085i
$511$	12.2337	−	20.5273i	0.541186	−	0.908073i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	7.80637	+	1.65930i	0.344660	+	0.0732597i
$514$	24.4842	−	5.20429i	1.07995	−	0.229551i
$515$	−0.961306	+	9.14622i	−0.0423602	+	0.403031i
$516$	−5.26818	+	9.12476i	−0.231919	+	0.401695i
$517$	−25.8603	−	4.57805i	−1.13734	−	0.201342i
$518$	−13.7824	+	5.90893i	−0.605565	+	0.259624i
$519$	−12.7148	−	9.23787i	−0.558119	−	0.405498i
$520$	1.42517	+	1.58281i	0.0624978	+	0.0694109i
$521$	26.7965	−	29.7605i	1.17397	−	1.30383i	0.230237	−	0.973135i	$-0.426050\pi$
$521$	26.7965	−	29.7605i	1.17397	−	1.30383i	0.943737	−	0.330696i	$-0.107284\pi$
$522$	0.488414	+	0.217456i	0.0213773	+	0.00951778i
$523$	0.253601	+	2.41285i	0.0110892	+	0.105507i	0.998666	−	0.0516280i	$-0.0164410\pi$
$523$	0.253601	+	2.41285i	0.0110892	+	0.105507i	−0.987577	+	0.157135i	$0.949774\pi$
$524$	1.74547	+	5.37199i	0.0762510	+	0.234677i
$525$	3.89440	−	2.74783i	0.169965	−	0.119925i
$526$	6.84559	+	4.97361i	0.298482	+	0.216860i
$527$	5.43354	−	9.41117i	0.236689	−	0.409957i
$528$	−4.95104	−	3.34443i	−0.215466	−	0.145548i
$529$	−21.7639	−	37.6961i	−0.946254	−	1.63896i
$530$	−1.06057	+	0.472196i	−0.0460682	+	0.0205109i
$531$	0.298193	−	0.917743i	0.0129405	−	0.0398266i
$532$	4.17378	−	0.826903i	0.180956	−	0.0358508i
$533$	−11.1081	+	8.07047i	−0.481143	+	0.349571i
$534$	1.18778	+	11.3010i	0.0514002	+	0.489041i
$535$	1.96123	−	2.17817i	0.0847914	−	0.0941704i
$536$	−8.63953	+	1.83639i	−0.373171	+	0.0793199i
$537$	30.6820	−	13.6605i	1.32403	−	0.589495i
$538$	−9.61012			−0.414322
$539$	−11.4769	+	20.1812i	−0.494345	+	0.869266i
$540$	−4.96254			−0.213554
$541$	−26.1698	+	11.6516i	−1.12513	+	0.500940i	−0.883032	−	0.469312i	$-0.844502\pi$
$541$	−26.1698	+	11.6516i	−1.12513	+	0.500940i	−0.242097	+	0.970252i	$0.577835\pi$
$542$	−11.9083	+	2.53118i	−0.511504	+	0.108724i
$543$	22.7150	−	25.2276i	0.974795	−	1.08262i
$544$	−0.288079	−	2.74089i	−0.0123513	−	0.117514i
$545$	9.57613	−	6.95747i	0.410196	−	0.298025i
$546$	9.95795	−	1.97285i	0.426161	−	0.0844304i
$547$	10.3878	−	31.9703i	0.444149	−	1.36695i	−0.439265	−	0.898357i	$-0.644761\pi$
$547$	10.3878	−	31.9703i	0.444149	−	1.36695i	0.883414	−	0.468593i	$-0.155239\pi$
$548$	11.9517	−	5.32125i	0.510552	−	0.227313i
$549$	1.27419	+	2.20697i	0.0543813	+	0.0941911i
$550$	−0.916358	+	3.18752i	−0.0390736	+	0.135916i
$551$	1.75276	−	3.03586i	0.0746699	−	0.129332i
$552$	−11.8873	−	8.63665i	−0.505958	−	0.367600i
$553$	21.5822	−	15.2281i	0.917770	−	0.647565i
$554$	1.09004	+	3.35481i	0.0463115	+	0.142532i
$555$	1.06728	+	10.1545i	0.0453034	+	0.431033i
$556$	−13.7716	−	6.13151i	−0.584046	−	0.260034i
$557$	9.93021	−	11.0286i	0.420757	−	0.467297i	−0.495081	−	0.868847i	$-0.664862\pi$
$557$	9.93021	−	11.0286i	0.420757	−	0.467297i	0.915837	+	0.401549i	$0.131528\pi$
$558$	−0.647134	−	0.718715i	−0.0273954	−	0.0304256i
$559$	10.0781	+	7.32217i	0.426258	+	0.309695i
$560$	−2.43169	+	1.04254i	−0.102758	+	0.0440552i
$561$	−14.8048	+	7.20830i	−0.625059	+	0.304335i
$562$	12.3194	−	21.3379i	0.519664	−	0.900085i
$563$	−0.488306	+	4.64593i	−0.0205797	+	0.195802i	−0.999981	−	0.00611956i	$-0.998052\pi$
$563$	−0.488306	+	4.64593i	−0.0205797	+	0.195802i	0.979402	+	0.201922i	$0.0647187\pi$
$564$	−13.9530	+	2.96581i	−0.587529	+	0.124883i
$565$	−17.4128	−	3.70122i	−0.732564	−	0.155711i
$566$	−11.7052	+	8.50436i	−0.492008	+	0.357465i
$567$	−13.1056	+	21.9903i	−0.550383	+	0.923504i
$568$	4.52019	+	13.9117i	0.189663	+	0.583722i
$569$	11.0700	+	12.2945i	0.464080	+	0.515413i	0.929070	−	0.369903i	$-0.120609\pi$
$569$	11.0700	+	12.2945i	0.464080	+	0.515413i	−0.464991	+	0.885316i	$0.653942\pi$
$570$	0.302831	−	2.88125i	0.0126842	−	0.120682i
$571$	21.9000	+	37.9319i	0.916485	+	1.58740i	0.804712	+	0.593665i	$0.202320\pi$
$571$	21.9000	+	37.9319i	0.916485	+	1.58740i	0.111773	+	0.993734i	$0.464347\pi$
$572$	−4.54435	+	5.40826i	−0.190009	+	0.226131i
$573$	6.98645			0.291863
$574$	−5.04533	−	16.2925i	−0.210588	−	0.680038i
$575$	−2.52048	+	7.75725i	−0.105111	+	0.323500i
$576$	−0.239911	−	0.0509948i	−0.00999631	−	0.00212478i
$577$	−0.563202	−	0.250754i	−0.0234464	−	0.0104390i	0.394980	−	0.918690i	$-0.370752\pi$
$577$	−0.563202	−	0.250754i	−0.0234464	−	0.0104390i	−0.418426	+	0.908251i	$0.637418\pi$
$578$	8.59149	+	3.82518i	0.357359	+	0.159106i
$579$	23.5438	+	5.00439i	0.978448	+	0.207975i
$580$	−0.673586	+	2.07309i	−0.0279692	+	0.0860802i
$581$	15.5618	−	16.8089i	0.645613	−	0.697351i
$582$	−5.46192			−0.226404
$583$	−2.03817	−	3.26671i	−0.0844125	−	0.135293i
$584$	4.51597	+	7.82189i	0.186872	+	0.323672i
$585$	0.0546055	−	0.519537i	0.00225766	−	0.0214802i
$586$	0.593523	+	0.659174i	0.0245182	+	0.0272302i
$587$	−9.70335	−	29.8638i	−0.400500	−	1.23261i	−0.924595	−	0.380953i	$-0.875596\pi$
$587$	−9.70335	−	29.8638i	−0.400500	−	1.23261i	0.524094	−	0.851660i	$-0.324404\pi$
$588$	−1.66506	+	12.4998i	−0.0686660	+	0.515484i
$589$	−5.13020	+	3.72731i	−0.211386	+	0.153581i
$590$	3.84833	+	0.817988i	0.158433	+	0.0336760i
$591$	22.4723	−	4.77663i	0.924387	−	0.196484i
$592$	0.592450	−	5.63679i	0.0243496	−	0.231671i
$593$	−20.6883	+	35.8332i	−0.849568	+	1.47149i	0.0320268	+	0.999487i	$0.489804\pi$
$593$	−20.6883	+	35.8332i	−0.849568	+	1.47149i	−0.881595	+	0.472008i	$0.843530\pi$
$594$	−2.27953	−	16.3003i	−0.0935302	−	0.668808i
$595$	−0.862571	+	7.24045i	−0.0353620	+	0.296829i
$596$	17.2659	+	12.5444i	0.707239	+	0.513839i
$597$	15.7136	+	17.4517i	0.643113	+	0.714250i
$598$	−11.6243	+	12.9101i	−0.475354	+	0.527934i
$599$	21.9502	+	9.77284i	0.896859	+	0.399307i	0.802792	−	0.596259i	$-0.203347\pi$
$599$	21.9502	+	9.77284i	0.896859	+	0.399307i	0.0940665	+	0.995566i	$0.470013\pi$
$600$	0.188304	+	1.79160i	0.00768749	+	0.0731416i
$601$	4.71364	+	14.5071i	0.192273	+	0.591757i	0.999998	+	0.00219617i	$0.000699064\pi$
$601$	4.71364	+	14.5071i	0.192273	+	0.591757i	−0.807724	+	0.589561i	$0.799301\pi$
$602$	−12.6439	+	8.92133i	−0.515326	+	0.363606i
$603$	1.75263	+	1.27336i	0.0713726	+	0.0518552i
$604$	9.33309	−	16.1654i	0.379758	−	0.657760i
$605$	−10.8909	−	1.54575i	−0.442776	−	0.0628436i
$606$	−0.525432	−	0.910075i	−0.0213442	−	0.0369693i
$607$	44.1524	−	19.6579i	1.79209	−	0.797891i	0.816817	−	0.576897i	$-0.195737\pi$
$607$	44.1524	−	19.6579i	1.79209	−	0.797891i	0.975275	−	0.220994i	$-0.0709301\pi$
$608$	−0.496962	+	1.52949i	−0.0201545	+	0.0620290i
$609$	6.84416	+	7.81630i	0.277339	+	0.316733i
$610$	−8.40575	+	6.10714i	−0.340339	+	0.247271i
$611$	1.76291	+	16.7729i	0.0713195	+	0.678560i
$612$	−0.452308	+	0.502339i	−0.0182835	+	0.0203058i
$613$	1.87888	−	0.399368i	0.0758871	−	0.0161303i	−0.169812	−	0.985477i	$-0.554316\pi$
$613$	1.87888	−	0.399368i	0.0758871	−	0.0161303i	0.245699	+	0.969346i	$0.420983\pi$
$614$	−29.1214	+	12.9657i	−1.17524	+	0.523252i
$615$	−11.6132			−0.468288
$616$	−4.54137	−	7.50839i	−0.182977	−	0.302522i
$617$	−13.1873			−0.530902			−0.265451	−	0.964124i	$-0.585521\pi$
$617$	−13.1873			−0.530902			−0.265451	+	0.964124i	$0.585521\pi$
$618$	−15.1350	+	6.73854i	−0.608820	+	0.271064i
$619$	−39.7312	+	8.44512i	−1.59693	+	0.339438i	−0.918560	−	0.395281i	$-0.870647\pi$
$619$	−39.7312	+	8.44512i	−1.59693	+	0.339438i	−0.678371	+	0.734720i	$0.737314\pi$
$620$	2.63844	−	2.93029i	0.105962	−	0.117683i
$621$	−4.23097	−	40.2550i	−0.169783	−	1.61538i
$622$	7.95796	−	5.78179i	0.319085	−	0.231829i
$623$	−5.37650	+	15.7990i	−0.215405	+	0.632974i
$624$	−1.18567	+	3.64911i	−0.0474647	+	0.146081i
$625$	0.913545	−	0.406737i	0.0365418	−	0.0162695i
$626$	1.87196	+	3.24234i	0.0748187	+	0.129590i
$627$	9.60302	−	0.328793i	0.383508	−	0.0131307i
$628$	−10.1311	+	17.5476i	−0.404275	+	0.700225i
$629$	−12.6372	−	9.18148i	−0.503879	−	0.366090i
$630$	0.589111	+	0.272129i	0.0234707	+	0.0108419i
$631$	7.28804	+	22.4303i	0.290132	+	0.892936i	0.984813	+	0.173618i	$0.0555457\pi$
$631$	7.28804	+	22.4303i	0.290132	+	0.892936i	−0.694681	+	0.719318i	$0.744454\pi$
$632$	1.04356	+	9.92878i	0.0415105	+	0.394946i
$633$	−9.18195	−	4.08807i	−0.364950	−	0.162486i
$634$	3.81338	−	4.23519i	0.151449	−	0.168201i
$635$	0.0304987	+	0.0338722i	0.00121030	+	0.00134418i
$636$	−1.69197	−	1.22929i	−0.0670909	−	0.0487444i
$637$	14.4919	+	3.50262i	0.574190	+	0.138779i
$638$	−7.11880	−	1.26024i	−0.281836	−	0.0498933i
$639$	1.79387	−	3.10707i	0.0709643	−	0.122914i
$640$	0.104528	−	0.994522i	0.00413185	−	0.0393119i
$641$	−31.5146	+	6.69864i	−1.24475	+	0.264580i	−0.782771	−	0.622310i	$-0.786194\pi$
$641$	−31.5146	+	6.69864i	−1.24475	+	0.264580i	−0.461981	+	0.886890i	$0.652861\pi$
$642$	5.16473	+	1.09780i	0.203836	+	0.0433266i
$643$	−28.4827	+	20.6939i	−1.12325	+	0.816088i	−0.984698	−	0.174267i	$-0.944244\pi$
$643$	−28.4827	+	20.6939i	−1.12325	+	0.816088i	−0.138551	+	0.990355i	$0.544244\pi$
$644$	−10.5300	−	18.8365i	−0.414942	−	0.742261i
$645$	3.25592	+	10.0207i	0.128202	+	0.394564i
$646$	2.96570	+	3.29375i	0.116684	+	0.129591i
$647$	3.65763	−	34.8000i	0.143796	−	1.36813i	−0.649994	−	0.759939i	$-0.725229\pi$
$647$	3.65763	−	34.8000i	0.143796	−	1.36813i	0.793790	−	0.608191i	$-0.208105\pi$
$648$	−4.83783	−	8.37936i	−0.190048	−	0.329172i
$649$	−0.919095	+	13.0162i	−0.0360776	+	0.510931i
$650$	2.12988			0.0835409
$651$	−5.55939	−	17.9526i	−0.217890	−	0.703616i
$652$	4.95979	−	15.2647i	0.194240	−	0.597810i
$653$	−1.77775	−	0.377872i	−0.0695686	−	0.0147873i	0.172996	−	0.984923i	$-0.444655\pi$
$653$	−1.77775	−	0.377872i	−0.0695686	−	0.0147873i	−0.242565	+	0.970135i	$0.577989\pi$
$654$	19.4800	+	8.67304i	0.761727	+	0.339143i
$655$	5.16011	+	2.29743i	0.201622	+	0.0897680i
$656$	6.30564	+	1.34030i	0.246194	+	0.0523301i
$657$	0.684558	−	2.10685i	0.0267071	−	0.0821961i
$658$	−20.4301	−	4.63926i	−0.796447	−	0.180857i
$659$	31.7206			1.23566			0.617829	−	0.786313i	$-0.288012\pi$
$659$	31.7206			1.23566			0.617829	+	0.786313i	$0.288012\pi$
$660$	−5.79829	+	1.44148i	−0.225698	+	0.0561095i
$661$	−20.2556	−	35.0837i	−0.787850	−	1.36460i	−0.927281	−	0.374365i	$-0.877861\pi$
$661$	−20.2556	−	35.0837i	−0.787850	−	1.36460i	0.139431	−	0.990232i	$-0.455473\pi$
$662$	2.09156	−	19.8999i	0.0812910	−	0.773432i
$663$	7.07569	+	7.85834i	0.274797	+	0.305193i
$664$	2.67543	+	8.23411i	0.103827	+	0.319546i
$665$	2.17829	−	3.65503i	0.0844706	−	0.141736i
$666$	−1.12466	+	0.817114i	−0.0435797	+	0.0316625i
$667$	−17.3907	−	3.69650i	−0.673370	−	0.143129i
$668$	8.55489	−	1.81840i	0.330999	−	0.0703560i
$669$	2.36606	−	22.5115i	0.0914771	−	0.870346i
$670$	−4.41627	+	7.64921i	−0.170615	+	0.295515i
$671$	−23.9210	−	24.8048i	−0.923461	−	0.957577i
$672$	−3.81678	−	2.85467i	−0.147235	−	0.110121i
$673$	−25.6968	−	18.6698i	−0.990537	−	0.719667i	−0.0304984	−	0.999535i	$-0.509709\pi$
$673$	−25.6968	−	18.6698i	−0.990537	−	0.719667i	−0.960039	+	0.279868i	$0.909709\pi$
$674$	−4.01479	−	4.45888i	−0.154644	−	0.171749i
$675$	−3.32059	+	3.68789i	−0.127810	+	0.141947i
$676$	−7.73188	−	3.44246i	−0.297380	−	0.132402i
$677$	−3.97978	−	37.8651i	−0.152955	−	1.45527i	−0.754430	−	0.656381i	$-0.772086\pi$
$677$	−3.97978	−	37.8651i	−0.152955	−	1.45527i	0.601474	−	0.798892i	$-0.294580\pi$
$678$	−9.90999	−	30.4998i	−0.380591	−	1.17134i
$679$	−7.28233	−	3.36394i	−0.279470	−	0.129096i
$680$	−2.22964	−	1.61993i	−0.0855027	−	0.0621213i
$681$	11.3464	−	19.6525i	0.434794	−	0.753085i
$682$	10.8370	+	7.32037i	0.414969	+	0.280311i
$683$	−17.6953	−	30.6492i	−0.677093	−	1.17276i	−0.975852	−	0.218431i	$-0.929906\pi$
$683$	−17.6953	−	30.6492i	−0.677093	−	1.17276i	0.298760	−	0.954328i	$-0.403427\pi$
$684$	0.360344	−	0.160435i	0.0137781	−	0.00613440i
$685$	4.04280	−	12.4425i	0.154468	−	0.475402i
$686$	−9.91854	+	15.6404i	−0.378692	+	0.597154i
$687$	−7.11513	+	5.16945i	−0.271459	+	0.197227i
$688$	−0.611364	−	5.81674i	−0.0233080	−	0.221761i
$689$	−1.65453	+	1.83754i	−0.0630327	+	0.0700049i
$690$	−14.3725	+	3.05496i	−0.547150	+	0.116300i
$691$	−23.6977	+	10.5509i	−0.901502	+	0.401375i	−0.804530	−	0.593912i	$-0.797583\pi$
$691$	−23.6977	+	10.5509i	−0.901502	+	0.401375i	−0.0969725	+	0.995287i	$0.530916\pi$
$692$	8.72424			0.331646
$693$	−0.623247	+	2.06003i	−0.0236752	+	0.0782541i
$694$	−8.58534			−0.325895
$695$	−13.7716	+	6.13151i	−0.522387	+	0.232582i
$696$	−3.84097	+	0.816423i	−0.145592	+	0.0309464i
$697$	11.8881	−	13.2031i	0.450294	−	0.500102i
$698$	−1.70133	−	16.1870i	−0.0643961	−	0.612688i
$699$	2.32487	−	1.68912i	0.0879348	−	0.0638884i
$700$	−0.852362	+	2.50469i	−0.0322163	+	0.0946684i
$701$	−6.04567	+	18.6066i	−0.228342	+	0.702763i	0.769594	+	0.638534i	$0.220459\pi$
$701$	−6.04567	+	18.6066i	−0.228342	+	0.702763i	−0.997935	+	0.0642292i	$0.979541\pi$
$702$	−9.65584	+	4.29906i	−0.364436	+	0.162257i
$703$	4.55751	+	7.89384i	0.171890	+	0.297722i
$704$	3.31468	−	0.113490i	0.124927	−	0.00427731i
$705$	−7.13238	+	12.3536i	−0.268621	+	0.465265i
$706$	−13.9833	−	10.1594i	−0.526267	−	0.382355i
$707$	−0.140047	−	1.53700i	−0.00526701	−	0.0578049i
$708$	2.19016	+	6.74062i	0.0823113	+	0.253328i
$709$	−1.09665	−	10.4340i	−0.0411857	−	0.391856i	−0.995624	−	0.0934481i	$-0.970211\pi$
$709$	−1.09665	−	10.4340i	−0.0411857	−	0.391856i	0.954438	−	0.298408i	$-0.0964556\pi$
$710$	13.3630	+	5.94959i	0.501505	+	0.223284i
$711$	1.63847	−	1.81971i	0.0614475	−	0.0682444i
$712$	−4.22072	−	4.68759i	−0.158178	−	0.175675i
$713$	26.0193	+	18.9041i	0.974430	+	0.707965i
$714$	−12.0729	+	5.17599i	−0.451815	+	0.193707i
$715$	0.978355	+	6.99594i	0.0365884	+	0.261633i
$716$	−9.32177	+	16.1458i	−0.348371	+	0.603396i
$717$	−4.70155	+	44.7323i	−0.175583	+	1.67056i
$718$	34.9961	−	7.43866i	1.30604	−	0.277608i
$719$	−12.3850	−	2.63252i	−0.461884	−	0.0981766i	−0.0289085	−	0.999582i	$-0.509203\pi$
$719$	−12.3850	−	2.63252i	−0.461884	−	0.0981766i	−0.432976	+	0.901406i	$0.642536\pi$
$720$	−0.198429	+	0.144167i	−0.00739500	+	0.00537278i
$721$	−24.3296	−	0.337075i	−0.906081	−	0.0125533i
$722$	5.07211	+	15.6103i	0.188764	+	0.580957i
$723$	−6.09655	−	6.77090i	−0.226733	−	0.251813i
$724$	−1.96975	+	18.7409i	−0.0732052	+	0.696501i
$725$	1.08989	+	1.88774i	0.0404773	+	0.0701088i
$726$	−7.39819	−	18.3833i	−0.274573	−	0.682267i
$727$	−29.4616			−1.09267			−0.546336	−	0.837566i	$-0.683978\pi$
$727$	−29.4616			−1.09267			−0.546336	+	0.837566i	$0.683978\pi$
$728$	−3.82830	+	4.13509i	−0.141886	+	0.153257i
$729$	7.55434	−	23.2499i	0.279790	−	0.861107i
$730$	8.83457	+	1.87785i	0.326982	+	0.0695022i
$731$	−14.7256	−	6.55625i	−0.544645	−	0.242492i
$732$	−17.0992	−	7.61303i	−0.632003	−	0.281386i
$733$	−38.0910	−	8.09649i	−1.40692	−	0.299051i	−0.558999	−	0.829169i	$-0.688814\pi$
$733$	−38.0910	−	8.09649i	−1.40692	−	0.299051i	−0.847924	+	0.530118i	$0.822148\pi$
$734$	11.6419	−	35.8300i	0.429709	−	1.32251i
$735$	8.17504	+	9.60140i	0.301541	+	0.354153i
$736$	8.15645			0.300651
$737$	−27.1537	−	10.9923i	−1.00022	−	0.404907i
$738$	−0.790572	−	1.36931i	−0.0291014	−	0.0504050i
$739$	3.60597	−	34.3085i	0.132648	−	1.26206i	−0.702360	−	0.711822i	$-0.747870\pi$
$739$	3.60597	−	34.3085i	0.132648	−	1.26206i	0.835008	−	0.550238i	$-0.185463\pi$
$740$	−3.79252	−	4.21202i	−0.139416	−	0.154837i
$741$	−1.90679	−	5.86851i	−0.0700479	−	0.215585i
$742$	−1.49878	−	2.68106i	−0.0550219	−	0.0984249i
$743$	9.42547	−	6.84800i	0.345787	−	0.251229i	−0.401313	−	0.915941i	$-0.631446\pi$
$743$	9.42547	−	6.84800i	0.345787	−	0.251229i	0.747099	+	0.664712i	$0.231446\pi$
$744$	6.94811	+	1.47687i	0.254730	+	0.0541445i
$745$	20.8755	−	4.43722i	0.764818	−	0.162567i
$746$	−1.97309	+	18.7727i	−0.0722401	+	0.687319i
$747$	1.06176	−	1.83903i	0.0388478	−	0.0672864i
$748$	4.29673	−	8.06771i	0.157104	−	0.294985i
$749$	6.20996	+	4.64459i	0.226907	+	0.169710i
$750$	1.45741	+	1.05887i	0.0532173	+	0.0386646i
$751$	−20.0016	−	22.2141i	−0.729870	−	0.810603i	0.257957	−	0.966156i	$-0.416951\pi$
$751$	−20.0016	−	22.2141i	−0.729870	−	0.810603i	−0.987827	+	0.155553i	$0.950284\pi$
$752$	5.29846	−	5.88454i	0.193215	−	0.214587i
$753$	28.7884	+	12.8174i	1.04911	+	0.467092i
$754$	0.485290	+	4.61722i	0.0176732	+	0.168149i
$755$	−5.76816	−	17.7526i	−0.209925	−	0.646083i
$756$	−1.19140	−	13.0755i	−0.0433308	−	0.475551i
$757$	−2.79703	−	2.03216i	−0.101660	−	0.0738601i	0.535794	−	0.844349i	$-0.320012\pi$
$757$	−2.79703	−	2.03216i	−0.101660	−	0.0738601i	−0.637454	+	0.770489i	$0.720012\pi$
$758$	−11.8233	+	20.4785i	−0.429440	+	0.743812i
$759$	−16.6365	−	45.8054i	−0.603865	−	1.66263i
$760$	0.804101	+	1.39274i	0.0291678	+	0.0505201i
$761$	−31.5514	+	14.0476i	−1.14374	+	0.509224i	−0.889055	−	0.457801i	$-0.848637\pi$
$761$	−31.5514	+	14.0476i	−1.14374	+	0.509224i	−0.254681	+	0.967025i	$0.581971\pi$
$762$	−0.0253734	+	0.0780912i	−0.000919180	+	0.00282894i
$763$	20.6308	+	23.5612i	0.746885	+	0.852973i
$764$	−3.13754	+	2.27955i	−0.113512	+	0.0824714i
$765$	0.0706574	+	0.672260i	0.00255462	+	0.0243056i
$766$	−10.3736	+	11.5211i	−0.374815	+	0.416274i
$767$	8.19649	−	1.74222i	0.295958	−	0.0629079i
$768$	1.64572	−	0.732721i	0.0593848	−	0.0264398i
$769$	−0.460799			−0.0166169			−0.00830843	−	0.999965i	$-0.502645\pi$
$769$	−0.460799			−0.0166169			−0.00830843	+	0.999965i	$0.502645\pi$
$770$	−8.61859	−	1.64920i	−0.310593	−	0.0594330i
$771$	45.0929			1.62398
$772$	−12.2061	+	5.43451i	−0.439307	+	0.195592i
$773$	40.0685	−	8.51683i	1.44116	−	0.306329i	0.579984	−	0.814628i	$-0.303059\pi$
$773$	40.0685	−	8.51683i	1.44116	−	0.306329i	0.861181	+	0.508299i	$0.169726\pi$
$774$	−0.959893	+	1.06607i	−0.0345026	+	0.0383191i
$775$	−0.412165	−	3.92149i	−0.0148054	−	0.140864i
$776$	2.45289	−	1.78213i	0.0880535	−	0.0639746i
$777$	−26.4991	+	5.24997i	−0.950651	+	0.188342i
$778$	−1.76333	+	5.42697i	−0.0632185	+	0.194566i
$779$	−9.47099	+	4.21676i	−0.339333	+	0.151081i
$780$	1.91845	+	3.32286i	0.0686916	+	0.118977i
$781$	−13.4041	+	46.6259i	−0.479638	+	1.66840i
$782$	11.2395	−	19.4674i	0.401924	−	0.696154i
$783$	−8.75131	−	6.35820i	−0.312746	−	0.227223i
$784$	−3.33071	−	6.15681i	−0.118954	−	0.219886i
$785$	6.26137	+	19.2705i	0.223478	+	0.687794i
$786$	1.06363	+	10.1197i	0.0379383	+	0.360959i
$787$	−40.0762	−	17.8431i	−1.42856	−	0.636037i	−0.460708	−	0.887552i	$-0.652404\pi$
$787$	−40.0762	−	17.8431i	−1.42856	−	0.636037i	−0.967853	+	0.251515i	$0.919071\pi$
$788$	−8.53352	+	9.47744i	−0.303994	+	0.337620i
$789$	10.1998	+	11.3280i	0.363121	+	0.403287i
$790$	8.07680	+	5.86814i	0.287360	+	0.208779i
$791$	5.57165	−	46.7686i	0.198105	−	1.66290i
$792$	−0.564687	−	0.585548i	−0.0200653	−	0.0208065i
$793$	−11.0648	+	19.1648i	−0.392923	+	0.680563i
$794$	−1.35417	+	12.8841i	−0.0480577	+	0.457239i
$795$	−2.04568	+	0.434824i	−0.0725530	+	0.0154216i
$796$	−12.7510	−	2.71030i	−0.451946	−	0.0960640i
$797$	−10.6030	+	7.70355i	−0.375578	+	0.272874i	−0.759520	−	0.650484i	$-0.774566\pi$
$797$	−10.6030	+	7.70355i	−0.375578	+	0.272874i	0.383942	+	0.923357i	$0.374566\pi$
$798$	7.66431	+	0.106186i	0.271314	+	0.00375893i
$799$	−6.74369	−	20.7549i	−0.238575	−	0.734257i
$800$	−0.669131	−	0.743145i	−0.0236573	−	0.0262741i
$801$	−0.161717	+	1.53864i	−0.00571401	+	0.0543651i
$802$	3.13547	+	5.43079i	0.110717	+	0.191768i
$803$	−2.10996	+	29.8812i	−0.0744588	+	1.05448i
$804$	−15.9115			−0.561155
$805$	−21.0442	−	4.77871i	−0.741710	−	0.168427i
$806$	2.59522	−	7.98727i	0.0914128	−	0.281340i
$807$	−16.9340	−	3.59943i	−0.596104	−	0.126706i
$808$	0.532907	+	0.237265i	0.0187476	+	0.00834696i
$809$	34.7029	+	15.4507i	1.22009	+	0.543219i	0.912804	−	0.408398i	$-0.133912\pi$
$809$	34.7029	+	15.4507i	1.22009	+	0.543219i	0.307286	+	0.951617i	$0.400579\pi$
$810$	−9.46422	−	2.01168i	−0.332539	−	0.0706833i
$811$	−2.17083	+	6.68114i	−0.0762283	+	0.234606i	−0.981909	−	0.189354i	$-0.939361\pi$
$811$	−2.17083	+	6.68114i	−0.0762283	+	0.234606i	0.905681	+	0.423961i	$0.139361\pi$
$812$	−5.62396	−	1.27709i	−0.197362	−	0.0448170i
$813$	−21.9316			−0.769174
$814$	12.0930	−	14.3919i	0.423859	−	0.504437i
$815$	−8.02510	−	13.8999i	−0.281107	−	0.486892i
$816$	0.518963	−	4.93761i	0.0181673	−	0.172851i
$817$	6.29386	+	6.99003i	0.220194	+	0.244550i
$818$	5.03514	+	15.4966i	0.176049	+	0.541825i
$819$	1.38200	+	0.0191471i	0.0482912	+	0.000669052i
$820$	5.21534	−	3.78916i	0.182127	−	0.132323i
$821$	28.9614	+	6.15594i	1.01076	+	0.214844i	0.683391	−	0.730053i	$-0.260504\pi$
$821$	28.9614	+	6.15594i	1.01076	+	0.214844i	0.327370	+	0.944896i	$0.393838\pi$
$822$	23.0531	−	4.90010i	0.804071	−	0.170911i
$823$	0.0613925	−	0.584110i	0.00214001	−	0.0203608i	−0.993400	−	0.114703i	$-0.963408\pi$
$823$	0.0613925	−	0.584110i	0.00214001	−	0.0203608i	0.995540	+	0.0943426i	$0.0300749\pi$
$824$	4.59830	−	7.96449i	0.160189	−	0.277456i
$825$	−2.80858	+	5.27350i	−0.0977823	+	0.183600i
$826$	−1.23136	+	10.3361i	−0.0428446	+	0.359639i
$827$	27.9385	+	20.2985i	0.971516	+	0.705848i	0.955797	−	0.294029i	$-0.0949962\pi$
$827$	27.9385	+	20.2985i	0.971516	+	0.705848i	0.0157193	+	0.999876i	$0.494996\pi$
$828$	−1.33862	−	1.48669i	−0.0465204	−	0.0516662i
$829$	34.0174	−	37.7801i	1.18147	−	1.31216i	0.241702	−	0.970351i	$-0.422294\pi$
$829$	34.0174	−	37.7801i	1.18147	−	1.31216i	0.939770	−	0.341807i	$-0.111039\pi$
$830$	7.90935	+	3.52147i	0.274538	+	0.122232i
$831$	0.664234	+	6.31976i	0.0230420	+	0.219230i
$832$	−0.658170	−	2.02564i	−0.0228179	−	0.0702264i
$833$	−19.2845	−	0.534458i	−0.668167	−	0.0185179i
$834$	−21.9704	−	15.9624i	−0.760772	−	0.552733i
$835$	4.37301	−	7.57427i	0.151334	−	0.262118i
$836$	−4.20533	+	3.28095i	−0.145444	+	0.113474i
$837$	9.78387	+	16.9462i	0.338180	+	0.585745i
$838$	−9.91270	+	4.41342i	−0.342429	+	0.152459i
$839$	−17.5782	+	54.1003i	−0.606868	+	1.86775i	−0.123470	+	0.992348i	$0.539402\pi$
$839$	−17.5782	+	54.1003i	−0.606868	+	1.86775i	−0.483398	+	0.875400i	$0.660598\pi$
$840$	−4.67535	+	0.926274i	−0.161315	+	0.0319595i
$841$	19.6175	−	14.2530i	0.676466	−	0.491482i
$842$	−1.05750	−	10.0614i	−0.0364439	−	0.346740i
$843$	29.7001	−	32.9853i	1.02293	−	1.13607i
$844$	5.45737	−	1.16000i	0.187851	−	0.0399289i
$845$	−7.73188	+	3.44246i	−0.265985	+	0.118424i
$846$	−1.94216			−0.0667729
$847$	1.45814	−	29.0667i	0.0501021	−	0.998744i
$848$	1.16094			0.0398668
$849$	−23.8110	+	10.6014i	−0.817193	+	0.363838i
$850$	−2.69576	+	0.573001i	−0.0924637	+	0.0196538i
$851$	30.9335	−	34.3552i	1.06039	−	1.17768i
$852$	2.75444	+	26.2068i	0.0943657	+	0.897830i
$853$	12.7568	−	9.26832i	0.436783	−	0.317341i	−0.347572	−	0.937653i	$-0.612994\pi$
$853$	12.7568	−	9.26832i	0.436783	−	0.317341i	0.784355	+	0.620312i	$0.212994\pi$
$854$	−18.1093	−	20.6816i	−0.619689	−	0.707710i
$855$	0.121890	−	0.375140i	0.00416856	−	0.0128295i
$856$	−2.67761	+	1.19215i	−0.0915189	+	0.0407469i
$857$	−17.6501	−	30.5708i	−0.602915	−	1.04428i	−0.992377	−	0.123237i	$-0.960672\pi$
$857$	−17.6501	−	30.5708i	−0.602915	−	1.04428i	0.389462	−	0.921043i	$-0.372661\pi$
$858$	−10.0332	+	7.82781i	−0.342529	+	0.267237i
$859$	−15.1690	+	26.2735i	−0.517560	+	0.896440i	0.482232	+	0.876044i	$0.339826\pi$
$859$	−15.1690	+	26.2735i	−0.517560	+	0.896440i	−0.999792	+	0.0203966i	$0.993507\pi$
$860$	−4.73176	−	3.43783i	−0.161352	−	0.117229i
$861$	−2.78807	−	30.5988i	−0.0950171	−	1.04280i
$862$	−5.09123	−	15.6692i	−0.173408	−	0.533695i
$863$	1.65270	+	15.7244i	0.0562585	+	0.535264i	0.985964	+	0.166960i	$0.0533949\pi$
$863$	1.65270	+	15.7244i	0.0562585	+	0.535264i	−0.929705	+	0.368304i	$0.879938\pi$
$864$	4.53351	+	2.01845i	0.154233	+	0.0686690i
$865$	5.83766	−	6.48337i	0.198486	−	0.220441i
$866$	−10.1422	−	11.2640i	−0.344645	−	0.382767i
$867$	13.7063	+	9.95824i	0.465492	+	0.338200i
$868$	8.35426	+	6.24836i	0.283562	+	0.212083i
$869$	−15.5648	+	29.2251i	−0.528000	+	0.991392i
$870$	−1.96339	+	3.40069i	−0.0665651	+	0.115294i
$871$	−1.96642	+	18.7092i	−0.0666295	+	0.633938i
$872$	−11.5781	+	2.46100i	−0.392084	+	0.0833399i
$873$	−0.727396	−	0.154613i	−0.0246186	−	0.00523285i
$874$	−10.6121	+	7.71011i	−0.358958	+	0.260798i
$875$	1.29101	+	2.30939i	0.0436440	+	0.0780718i
$876$	5.02793	+	15.4744i	0.169878	+	0.522831i
$877$	−5.50752	−	6.11672i	−0.185976	−	0.206547i	0.642946	−	0.765911i	$-0.277712\pi$
$877$	−5.50752	−	6.11672i	−0.185976	−	0.206547i	−0.828922	+	0.559364i	$0.811045\pi$
$878$	0.340552	−	3.24014i	0.0114931	−	0.109349i
$879$	0.798955	+	1.38383i	0.0269481	+	0.0466755i
$880$	2.13362	−	2.53923i	0.0719242	−	0.0855974i
$881$	33.4534			1.12707			0.563536	−	0.826091i	$-0.309441\pi$
$881$	33.4534			1.12707			0.563536	+	0.826091i	$0.309441\pi$
$882$	−0.575584	+	1.61754i	−0.0193809	+	0.0544655i
$883$	−11.5709	+	35.6114i	−0.389390	+	1.19842i	0.543855	+	0.839179i	$0.316964\pi$
$883$	−11.5709	+	35.6114i	−0.389390	+	1.19842i	−0.933245	+	0.359240i	$0.883036\pi$
$884$	−5.74165	−	1.22042i	−0.193112	−	0.0410473i
$885$	6.47476	+	2.88275i	0.217647	+	0.0969025i
$886$	15.0054	+	6.68085i	0.504118	+	0.224448i
$887$	47.8853	+	10.1783i	1.60783	+	0.341755i	0.922356	−	0.386340i	$-0.126261\pi$
$887$	47.8853	+	10.1783i	1.60783	+	0.341755i	0.685476	+	0.728095i	$0.259594\pi$
$888$	3.15519	−	9.71067i	0.105881	−	0.325869i
$889$	−0.0819256	+	0.0884910i	−0.00274770	+	0.00296789i
$890$	−6.30777			−0.211437
$891$	2.26034	−	32.0108i	0.0757241	−	1.07240i
$892$	6.28254	+	10.8817i	0.210355	+	0.364346i
$893$	−1.33111	+	12.6647i	−0.0445439	+	0.423807i
$894$	25.7258	+	28.5714i	0.860398	+	0.955569i
$895$	5.76117	+	17.7311i	0.192575	+	0.592684i
$896$	2.64550	+	0.0366522i	0.0883799	+	0.00122446i
$897$	−25.3186	+	18.3951i	−0.845364	+	0.614193i
$898$	−7.59126	−	1.61357i	−0.253324	−	0.0538456i
$899$	8.40721	−	1.78701i	0.280396	−	0.0596000i
$900$	−0.0256378	+	0.243928i	−0.000854594	+	0.00813092i
$901$	1.59976	−	2.77087i	0.0532958	−	0.0923110i
$902$	14.8418	+	15.3901i	0.494177	+	0.512433i
$903$	−25.6212	+	10.9846i	−0.852619	+	0.365543i
$904$	14.4020	+	10.4637i	0.479004	+	0.348017i
$905$	12.6092	+	14.0039i	0.419144	+	0.465507i
$906$	22.5005	−	24.9893i	0.747528	−	0.830214i
$907$	43.6289	+	19.4248i	1.44867	+	0.644990i	0.972190	−	0.234194i	$-0.0752449\pi$
$907$	43.6289	+	19.4248i	1.44867	+	0.644990i	0.476482	+	0.879184i	$0.341912\pi$
$908$	1.31673	+	12.5278i	0.0436971	+	0.415751i
$909$	−0.0442130	−	0.136074i	−0.00146645	−	0.00451328i
$910$	0.511339	+	5.61189i	0.0169507	+	0.186032i
$911$	31.2415	+	22.6983i	1.03508	+	0.752027i	0.969318	−	0.245808i	$-0.0790534\pi$
$911$	31.2415	+	22.6983i	1.03508	+	0.752027i	0.0657582	+	0.997836i	$0.479053\pi$
$912$	−1.44856	+	2.50898i	−0.0479666	+	0.0830805i
$913$	−7.93370	+	27.5971i	−0.262567	+	0.913331i
$914$	13.9907	+	24.2325i	0.462770	+	0.801541i
$915$	−17.0992	+	7.61303i	−0.565281	+	0.251679i
$916$	1.50863	−	4.64308i	0.0498465	−	0.153412i
$917$	−4.81452	+	14.1476i	−0.158989	+	0.467195i
$918$	11.0647	−	8.03895i	0.365189	−	0.265325i
$919$	−0.113600	−	1.08083i	−0.00374732	−	0.0356533i	0.992488	−	0.122338i	$-0.0390393\pi$
$919$	−0.113600	−	1.08083i	−0.00374732	−	0.0356533i	−0.996236	+	0.0866850i	$0.972373\pi$
$920$	5.45773	−	6.06142i	0.179936	−	0.199839i
$921$	−56.1709	+	11.9395i	−1.85089	+	0.393420i
$922$	−28.9927	+	12.9084i	−0.954823	+	0.425115i
$923$	31.1551			1.02548
$924$	−5.19010	−	14.9315i	−0.170742	−	0.491209i
$925$	−5.66784			−0.186357
$926$	25.5944	−	11.3954i	0.841083	−	0.374474i
$927$	−2.20637	+	0.468978i	−0.0724667	+	0.0154033i
$928$	1.45855	−	1.61989i	0.0478793	−	0.0531754i
$929$	1.38777	+	13.2037i	0.0455312	+	0.433200i	0.993414	+	0.114581i	$0.0365525\pi$
$929$	1.38777	+	13.2037i	0.0455312	+	0.433200i	−0.947883	+	0.318619i	$0.896781\pi$
$930$	5.74672	−	4.17523i	0.188442	−	0.136911i
$931$	10.1534	+	4.86195i	0.332763	+	0.159344i
$932$	−0.492945	+	1.51713i	−0.0161470	+	0.0496952i
$933$	16.1882	−	7.20747i	0.529979	−	0.235962i
$934$	−17.6043	−	30.4915i	−0.576030	−	0.997713i
$935$	−3.12040	−	8.59145i	−0.102048	−	0.280970i
$936$	−0.261199	+	0.452411i	−0.00853757	+	0.0147875i
$937$	19.0742	+	13.8582i	0.623127	+	0.452728i	0.854012	−	0.520253i	$-0.174162\pi$
$937$	19.0742	+	13.8582i	0.623127	+	0.452728i	−0.230885	+	0.972981i	$0.574162\pi$
$938$	−21.2147	−	9.79974i	−0.692683	−	0.319973i
$939$	2.08418	+	6.41445i	0.0680147	+	0.209328i
$940$	−0.827701	−	7.87505i	−0.0269966	−	0.256856i
$941$	27.7825	+	12.3696i	0.905685	+	0.403237i	0.806091	−	0.591791i	$-0.201579\pi$
$941$	27.7825	+	12.3696i	0.905685	+	0.403237i	0.0995936	+	0.995028i	$0.468246\pi$
$942$	−24.4244	+	27.1260i	−0.795789	+	0.883813i
$943$	35.1833	+	39.0750i	1.14573	+	1.27246i
$944$	−3.18292	−	2.31253i	−0.103595	−	0.0752663i
$945$	−10.5142	−	7.86383i	−0.342026	−	0.255810i
$946$	9.11858	−	17.1214i	0.296471	−	0.556665i
$947$	6.30305	−	10.9172i	0.204821	−	0.354761i	−0.745254	−	0.666780i	$-0.767672\pi$
$947$	6.30305	−	10.9172i	0.204821	−	0.354761i	0.950076	+	0.312019i	$0.101005\pi$
$948$	−1.87993	+	17.8863i	−0.0610573	+	0.580921i
$949$	18.8166	−	3.99959i	0.610813	−	0.129832i
$950$	1.57306	+	0.334364i	0.0510368	+	0.0108482i
$951$	8.30582	−	6.03453i	0.269335	−	0.195683i
$952$	3.73295	−	6.26364i	0.120986	−	0.203006i
$953$	−10.2164	−	31.4428i	−0.330942	−	1.01853i	−0.968687	−	0.248286i	$-0.920133\pi$
$953$	−10.2164	−	31.4428i	−0.330942	−	1.01853i	0.637745	−	0.770247i	$-0.279867\pi$
$954$	−0.190531	−	0.211606i	−0.00616868	−	0.00685101i
$955$	−0.405383	+	3.85696i	−0.0131179	+	0.124808i
$956$	−12.4839	−	21.6228i	−0.403759	−	0.699331i
$957$	−12.0720	−	4.88697i	−0.390232	−	0.157973i
$958$	−6.04810			−0.195405
$959$	33.7545	+	7.66496i	1.08999	+	0.247514i
$960$	0.556683	−	1.71329i	0.0179669	−	0.0552963i
$961$	15.1144	+	3.21266i	0.487561	+	0.103634i
$962$	−11.0282	−	4.91005i	−0.355562	−	0.158307i
$963$	0.656742	+	0.292400i	0.0211632	+	0.00942246i
$964$	4.94712	+	1.05154i	0.159336	+	0.0338679i
$965$	−4.12885	+	12.7073i	−0.132912	+	0.409062i
$966$	−11.4998	−	37.1357i	−0.370001	−	1.19482i
$967$	−23.0371			−0.740824			−0.370412	−	0.928868i	$-0.620784\pi$
$967$	−23.0371			−0.740824			−0.370412	+	0.928868i	$0.620784\pi$
$968$	9.32058	+	5.84182i	0.299575	+	0.187763i
$969$	3.99220	+	6.91470i	0.128248	+	0.222132i
$970$	0.316923	−	3.01533i	0.0101758	−	0.0968163i
$971$	12.7304	+	14.1386i	0.408538	+	0.453728i	0.911939	−	0.410325i	$-0.134585\pi$
$971$	12.7304	+	14.1386i	0.408538	+	0.453728i	−0.503401	+	0.864053i	$0.667918\pi$
$972$	−0.785741	−	2.41826i	−0.0252026	−	0.0775658i
$973$	−19.4618	−	34.8139i	−0.623917	−	1.11608i
$974$	−9.09101	+	6.60501i	−0.291295	+	0.211638i
$975$	3.75306	+	0.797737i	0.120194	+	0.0255480i
$976$	10.1630	−	2.16022i	0.325311	−	0.0691469i
$977$	3.86103	−	36.7353i	0.123525	−	1.17527i	−0.740585	−	0.671963i	$-0.765451\pi$
$977$	3.86103	−	36.7353i	0.123525	−	1.17527i	0.864110	−	0.503303i	$-0.167882\pi$
$978$	14.4569	−	25.0401i	0.462282	−	0.800695i
$979$	−2.89745	−	20.7189i	−0.0926030	−	0.662178i
$980$	−6.80409	−	1.64451i	−0.217349	−	0.0525320i
$981$	2.34875	+	1.70647i	0.0749898	+	0.0544833i
$982$	−12.8278	−	14.2467i	−0.409352	−	0.454631i
$983$	16.5024	−	18.3278i	0.526345	−	0.584566i	−0.420081	−	0.907487i	$-0.637998\pi$
$983$	16.5024	−	18.3278i	0.526345	−	0.584566i	0.946426	+	0.322921i	$0.104665\pi$
$984$	10.6091	+	4.72350i	0.338207	+	0.150580i
$985$	1.33307	+	12.6833i	0.0424751	+	0.404123i
$986$	−1.85639	−	5.71339i	−0.0591196	−	0.181951i
$987$	−34.2622	−	15.8268i	−1.09058	−	0.503773i
$988$	2.77111	+	2.01333i	0.0881607	+	0.0640525i
$989$	23.8527	−	41.3140i	0.758470	−	1.31371i
$990$	−0.812996	+	0.0278358i	−0.0258387	+	0.000884679i
$991$	−10.5940	−	18.3494i	−0.336530	−	0.582887i	0.647248	−	0.762280i	$-0.275920\pi$
$991$	−10.5940	−	18.3494i	−0.336530	−	0.582887i	−0.983777	+	0.179393i	$0.942587\pi$
$992$	−3.60219	+	1.60380i	−0.114370	+	0.0509207i
$993$	11.1390	−	34.2822i	0.353484	−	1.08791i
$994$	−12.4680	+	36.6377i	−0.395462	+	1.16208i
$995$	−10.5462	+	7.66226i	−0.334337	+	0.242910i
$996$	1.63031	+	15.5114i	0.0516584	+	0.491497i
$997$	−11.9431	+	13.2642i	−0.378242	+	0.420080i	−0.901965	−	0.431808i	$-0.857876\pi$
$997$	−11.9431	+	13.2642i	−0.378242	+	0.420080i	0.523724	+	0.851888i	$0.324542\pi$
$998$	16.0902	−	3.42007i	0.509325	−	0.108260i
$999$	25.6952	−	11.4402i	0.812960	−	0.361953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bg.e.191.3	yes	72
7.4	even	3	inner	770.2.bg.e.81.7	✓	72
11.3	even	5	inner	770.2.bg.e.751.7	yes	72
77.25	even	15	inner	770.2.bg.e.641.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bg.e.81.7	✓	72	7.4	even	3	inner
770.2.bg.e.191.3	yes	72	1.1	even	1	trivial
770.2.bg.e.641.3	yes	72	77.25	even	15	inner
770.2.bg.e.751.7	yes	72	11.3	even	5	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.76210 + 0.374545i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.45741 - 1.05887i) q^{6} +(2.59531 - 0.514179i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.224066 - 0.0997608i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-1.76210 + 0.374545i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(1.45741 - 1.05887i) q^{6} +(2.59531 - 0.514179i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.224066 - 0.0997608i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.61493 + 2.04014i) q^{11} +(-0.900732 + 1.56011i) q^{12} +(1.72311 + 1.25191i) q^{13} +(-2.16180 + 1.52533i) q^{14} +(0.556683 + 1.71329i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-2.51772 - 1.12096i) q^{17} +(-0.164118 + 0.182272i) q^{18} +(1.07610 + 1.19513i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(-4.38060 + 1.87809i) q^{21} +(1.55906 - 2.92734i) q^{22} +(4.07823 - 7.06369i) q^{23} +(0.188304 - 1.79160i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(-2.08334 - 0.442827i) q^{26} +(4.01478 - 2.91691i) q^{27} +(1.35449 - 2.27274i) q^{28} +(-0.673586 - 2.07309i) q^{29} +(-1.20541 - 1.33875i) q^{30} +(-0.412165 + 3.92149i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.84363 - 4.57433i) q^{33} +2.75598 q^{34} +(-0.782645 - 2.52734i) q^{35} +(0.0757930 - 0.233267i) q^{36} +(5.54398 + 1.17841i) q^{37} +(-1.46917 - 0.654115i) q^{38} +(-3.50519 - 1.56061i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-1.99208 + 6.13100i) q^{41} +(3.23799 - 3.49747i) q^{42} +5.84878 q^{43} +(-0.233611 + 3.30839i) q^{44} +(-0.122636 - 0.212411i) q^{45} +(-0.852581 + 8.11177i) q^{46} +(5.29846 + 5.88454i) q^{47} +(0.556683 + 1.71329i) q^{48} +(6.47124 - 2.66890i) q^{49} +(0.809017 - 0.587785i) q^{50} +(4.85631 + 1.03224i) q^{51} +(2.08334 - 0.442827i) q^{52} +(-0.121351 + 1.15458i) q^{53} +(-2.48127 + 4.29769i) q^{54} +(2.30229 + 2.38735i) q^{55} +(-0.312981 + 2.62717i) q^{56} +(-2.34382 - 1.70288i) q^{57} +(1.45855 + 1.61989i) q^{58} +(2.63256 - 2.92376i) q^{59} +(1.64572 + 0.732721i) q^{60} +(1.08606 + 10.3332i) q^{61} +(-1.21848 - 3.75010i) q^{62} +(0.530226 - 0.374120i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.06494 - 1.84453i) q^{65} +(-1.65079 + 5.74220i) q^{66} +(4.41627 + 7.64921i) q^{67} +(-2.51772 + 1.12096i) q^{68} +(-4.54056 + 13.9744i) q^{69} +(1.74295 + 1.99051i) q^{70} +(11.8340 - 8.59790i) q^{71} +(0.0256378 + 0.243928i) q^{72} +(6.04355 - 6.71204i) q^{73} +(-5.54398 + 1.17841i) q^{74} +(1.64572 - 0.732721i) q^{75} +1.60820 q^{76} +(-5.73754 + 6.63932i) q^{77} +3.83691 q^{78} +(9.12036 - 4.06064i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-6.47428 + 7.19041i) q^{81} +(-0.673844 - 6.41120i) q^{82} +(7.00436 - 5.08896i) q^{83} +(-1.53550 + 4.51211i) q^{84} +(-0.851646 + 2.62110i) q^{85} +(-5.34313 + 2.37891i) q^{86} +(1.96339 + 3.40069i) q^{87} +(-1.13223 - 3.11738i) q^{88} +(-3.15388 + 5.46269i) q^{89} +(0.198429 + 0.144167i) q^{90} +(5.11571 + 2.36311i) q^{91} +(-2.52048 - 7.75725i) q^{92} +(-0.742500 - 7.06442i) q^{93} +(-7.23384 - 3.22071i) q^{94} +(1.07610 - 1.19513i) q^{95} +(-1.20541 - 1.33875i) q^{96} +(-2.45289 - 1.78213i) q^{97} +(-4.82623 + 5.07025i) q^{98} +(-0.382392 + 0.717993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9} + 36 q^{10} - 2 q^{12} + 28 q^{13} - 2 q^{14} - 6 q^{15} + 9 q^{16} - 4 q^{17} - 7 q^{18} - q^{19} - 18 q^{20} - 32 q^{21} - 20 q^{22} - 30 q^{23} + 2 q^{24} + 9 q^{25} - 11 q^{26} + 18 q^{27} + 6 q^{28} + 22 q^{29} - 3 q^{30} - 8 q^{31} + 36 q^{32} - 24 q^{33} + 32 q^{34} - 3 q^{35} - 14 q^{36} + 20 q^{37} - 4 q^{38} - 25 q^{39} - 9 q^{40} + 34 q^{41} + 22 q^{42} + 12 q^{43} - 58 q^{45} - 20 q^{46} - 13 q^{47} - 6 q^{48} + 6 q^{49} + 18 q^{50} - 37 q^{51} + 11 q^{52} + 2 q^{53} + 14 q^{54} - 10 q^{55} - 2 q^{56} - 18 q^{57} + 11 q^{58} + 29 q^{59} - 2 q^{60} + 21 q^{61} + 44 q^{62} + 31 q^{63} - 18 q^{64} + 6 q^{65} - q^{66} - 20 q^{67} - 4 q^{68} - 104 q^{69} + 4 q^{70} - 70 q^{71} - 22 q^{72} - 28 q^{73} - 20 q^{74} - 2 q^{75} + 12 q^{76} - 47 q^{77} + 20 q^{78} - 24 q^{79} + 9 q^{80} + 44 q^{81} - 28 q^{82} - 56 q^{83} - 46 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} - 5 q^{88} - 20 q^{89} + 44 q^{90} - 36 q^{91} + 10 q^{92} + 77 q^{93} - 22 q^{94} - q^{95} - 3 q^{96} - 178 q^{97} - 68 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9 + 36 * q^10 - 2 * q^12 + 28 * q^13 - 2 * q^14 - 6 * q^15 + 9 * q^16 - 4 * q^17 - 7 * q^18 - q^19 - 18 * q^20 - 32 * q^21 - 20 * q^22 - 30 * q^23 + 2 * q^24 + 9 * q^25 - 11 * q^26 + 18 * q^27 + 6 * q^28 + 22 * q^29 - 3 * q^30 - 8 * q^31 + 36 * q^32 - 24 * q^33 + 32 * q^34 - 3 * q^35 - 14 * q^36 + 20 * q^37 - 4 * q^38 - 25 * q^39 - 9 * q^40 + 34 * q^41 + 22 * q^42 + 12 * q^43 - 58 * q^45 - 20 * q^46 - 13 * q^47 - 6 * q^48 + 6 * q^49 + 18 * q^50 - 37 * q^51 + 11 * q^52 + 2 * q^53 + 14 * q^54 - 10 * q^55 - 2 * q^56 - 18 * q^57 + 11 * q^58 + 29 * q^59 - 2 * q^60 + 21 * q^61 + 44 * q^62 + 31 * q^63 - 18 * q^64 + 6 * q^65 - q^66 - 20 * q^67 - 4 * q^68 - 104 * q^69 + 4 * q^70 - 70 * q^71 - 22 * q^72 - 28 * q^73 - 20 * q^74 - 2 * q^75 + 12 * q^76 - 47 * q^77 + 20 * q^78 - 24 * q^79 + 9 * q^80 + 44 * q^81 - 28 * q^82 - 56 * q^83 - 46 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 - 5 * q^88 - 20 * q^89 + 44 * q^90 - 36 * q^91 + 10 * q^92 + 77 * q^93 - 22 * q^94 - q^95 - 3 * q^96 - 178 * q^97 - 68 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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