LMFDB - Embedded newform 966.2.y.d.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	966.25
Dual form			966.2.y.d.541.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.968835 + 3.99359i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64295 - 0.121825i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.968835 + 3.99359i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64295 - 0.121825i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(4.03517 - 0.777715i) q^{10} +(-0.100127 - 2.10191i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(1.31651 + 1.51934i) q^{13} +(0.00406904 - 2.64575i) q^{14} +(-0.584833 + 4.06760i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.565045 + 0.793495i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-3.47958 + 4.88639i) q^{19} +(-0.584833 - 4.06760i) q^{20} +(2.49890 + 0.869185i) q^{21} -2.10430 q^{22} +(-3.93662 - 2.73917i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-10.5660 + 5.44714i) q^{25} +(1.58026 - 1.24273i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.64256 - 0.129954i) q^{28} +(4.16895 - 9.12872i) q^{29} +(4.03517 + 0.777715i) q^{30} +(5.57839 + 4.38689i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.688248 - 1.98856i) q^{33} +(0.819482 - 0.526649i) q^{34} +(3.04710 + 10.4368i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.324531 - 0.309440i) q^{37} +(4.71529 + 3.70815i) q^{38} +(0.657528 + 1.89980i) q^{39} +(-4.09082 + 0.390626i) q^{40} +(-8.81935 - 2.58959i) q^{41} +(0.987103 - 2.45472i) q^{42} +(0.808301 + 5.62186i) q^{43} +(-0.100127 + 2.10191i) q^{44} +(-2.05472 + 3.55887i) q^{45} +(-2.92338 + 3.80183i) q^{46} +(6.58820 + 11.4111i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.97032 - 0.643955i) q^{49} +(4.93822 + 10.8132i) q^{50} +(0.229658 + 0.946661i) q^{51} +(-1.16613 - 1.63760i) q^{52} +(-1.89075 - 5.46295i) q^{53} +(0.928368 - 0.371662i) q^{54} +(8.29719 - 2.43627i) q^{55} +(-0.255545 + 2.63338i) q^{56} +(-5.04642 + 3.24314i) q^{57} +(-8.92002 - 4.59859i) q^{58} +(-9.57940 + 1.84628i) q^{59} +(0.968835 - 3.99359i) q^{60} +(6.00423 - 2.40373i) q^{61} +(4.64735 - 5.36333i) q^{62} +(1.99686 + 1.73567i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-4.79213 + 6.72960i) q^{65} +(-1.95356 - 0.782088i) q^{66} +(8.09769 - 4.17465i) q^{67} +(-0.487060 - 0.843613i) q^{68} +(-2.63659 - 4.00605i) q^{69} +(10.5700 - 2.54704i) q^{70} +(1.09785 + 0.705547i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(1.20555 + 0.115116i) q^{73} +(-0.324531 + 0.309440i) q^{74} +(-11.8336 + 1.12997i) q^{75} +(3.92831 - 4.53351i) q^{76} +(-0.520695 - 5.54305i) q^{77} +(1.92894 - 0.566387i) q^{78} +(2.64770 - 7.65003i) q^{79} +(0.195535 + 4.10478i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-3.00630 + 8.68614i) q^{82} +(10.6639 - 3.13121i) q^{83} +(-2.40497 - 1.10278i) q^{84} +(-2.62146 + 3.02533i) q^{85} +(5.65395 - 0.539887i) q^{86} +(7.26312 - 6.92537i) q^{87} +(2.09477 + 0.200026i) q^{88} +(1.88389 - 1.48150i) q^{89} +(3.45707 + 2.22173i) q^{90} +(3.66456 + 3.85514i) q^{91} +(3.65842 + 3.10096i) q^{92} +(3.54835 + 6.14592i) q^{93} +(11.7117 - 6.03778i) q^{94} +(-22.8854 - 9.16193i) q^{95} +(0.580057 - 0.814576i) q^{96} +(8.90942 + 2.61604i) q^{97} +(-0.311565 - 6.99306i) q^{98} +(1.37802 - 1.59032i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$2$	0.0475819	−	0.998867i	0.0336455	−	0.706306i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.968835	+	3.99359i	0.433276	+	1.78599i	0.600015	+	0.799988i	$0.295161\pi$
$5$	0.968835	+	3.99359i	0.433276	+	1.78599i	−0.166739	+	0.986001i	$0.553324\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	2.64295	−	0.121825i	0.998939	−	0.0460457i
$7$	2.64295	−	0.121825i	0.998939	−	0.0460457i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	4.03517	−	0.777715i	1.27603	−	0.245935i
$11$	−0.100127	−	2.10191i	−0.0301893	−	0.633751i	−0.962368	−	0.271751i	$-0.912397\pi$
$11$	−0.100127	−	2.10191i	−0.0301893	−	0.633751i	0.932178	−	0.362000i	$-0.117906\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	1.31651	+	1.51934i	0.365135	+	0.421388i	0.908353	−	0.418203i	$-0.137340\pi$
$13$	1.31651	+	1.51934i	0.365135	+	0.421388i	−0.543219	+	0.839591i	$0.682795\pi$
$14$	0.00406904	−	2.64575i	0.00108750	−	0.707106i
$15$	−0.584833	+	4.06760i	−0.151003	+	1.05025i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	0.565045	+	0.793495i	0.137044	+	0.192451i	0.877394	−	0.479770i	$-0.159280\pi$
$17$	0.565045	+	0.793495i	0.137044	+	0.192451i	−0.740351	+	0.672221i	$0.765341\pi$
$18$	0.723734	−	0.690079i	0.170586	−	0.162653i
$19$	−3.47958	+	4.88639i	−0.798271	+	1.12102i	0.191936	+	0.981407i	$0.438523\pi$
$19$	−3.47958	+	4.88639i	−0.798271	+	1.12102i	−0.990207	+	0.139608i	$0.955416\pi$
$20$	−0.584833	−	4.06760i	−0.130773	−	0.909544i
$21$	2.49890	+	0.869185i	0.545305	+	0.189672i
$22$	−2.10430			−0.448638
$23$	−3.93662	−	2.73917i	−0.820842	−	0.571156i
$23$	−3.93662	−	2.73917i	−0.820842	−	0.571156i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−10.5660	+	5.44714i	−2.11319	+	1.08943i
$26$	1.58026	−	1.24273i	0.309914	−	0.243719i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−2.64256	−	0.129954i	−0.499396	−	0.0245590i
$29$	4.16895	−	9.12872i	0.774154	−	1.69516i	0.0568692	−	0.998382i	$-0.481888\pi$
$29$	4.16895	−	9.12872i	0.774154	−	1.69516i	0.717285	−	0.696780i	$-0.245385\pi$
$30$	4.03517	+	0.777715i	0.736718	+	0.141991i
$31$	5.57839	+	4.38689i	1.00191	+	0.787909i	0.977315	−	0.211789i	$-0.0679289\pi$
$31$	5.57839	+	4.38689i	1.00191	+	0.787909i	0.0245921	+	0.999698i	$0.492171\pi$
$32$	0.235759	−	0.971812i	0.0416767	−	0.171794i
$33$	0.688248	−	1.98856i	0.119809	−	0.346164i
$34$	0.819482	−	0.526649i	0.140540	−	0.0903196i
$35$	3.04710	+	10.4368i	0.515054	+	1.76414i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−0.324531	−	0.309440i	−0.0533525	−	0.0508715i	0.662934	−	0.748678i	$-0.269311\pi$
$37$	−0.324531	−	0.309440i	−0.0533525	−	0.0508715i	−0.716286	+	0.697806i	$0.754160\pi$
$38$	4.71529	+	3.70815i	0.764921	+	0.601541i
$39$	0.657528	+	1.89980i	0.105289	+	0.304212i
$40$	−4.09082	+	0.390626i	−0.646816	+	0.0617635i
$41$	−8.81935	−	2.58959i	−1.37735	−	0.404427i	−0.492504	−	0.870310i	$-0.663918\pi$
$41$	−8.81935	−	2.58959i	−1.37735	−	0.404427i	−0.884846	+	0.465883i	$0.845737\pi$
$42$	0.987103	−	2.45472i	0.152313	−	0.378771i
$43$	0.808301	+	5.62186i	0.123265	+	0.857326i	0.953818	+	0.300386i	$0.0971155\pi$
$43$	0.808301	+	5.62186i	0.123265	+	0.857326i	−0.830553	+	0.556940i	$0.811975\pi$
$44$	−0.100127	+	2.10191i	−0.0150946	+	0.316875i
$45$	−2.05472	+	3.55887i	−0.306299	+	0.530525i
$46$	−2.92338	+	3.80183i	−0.431028	+	0.560549i
$47$	6.58820	+	11.4111i	0.960988	+	1.66448i	0.720028	+	0.693945i	$0.244129\pi$
$47$	6.58820	+	11.4111i	0.960988	+	1.66448i	0.240960	+	0.970535i	$0.422538\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	6.97032	−	0.643955i	0.995760	−	0.0919936i
$50$	4.93822	+	10.8132i	0.698370	+	1.52922i
$51$	0.229658	+	0.946661i	0.0321585	+	0.132559i
$52$	−1.16613	−	1.63760i	−0.161713	−	0.227094i
$53$	−1.89075	−	5.46295i	−0.259714	−	0.750394i	−0.997183	−	0.0750127i	$-0.976100\pi$
$53$	−1.89075	−	5.46295i	−0.259714	−	0.750394i	0.737469	−	0.675381i	$-0.236021\pi$
$54$	0.928368	−	0.371662i	0.126335	−	0.0505769i
$55$	8.29719	−	2.43627i	1.11879	−	0.328507i
$56$	−0.255545	+	2.63338i	−0.0341486	+	0.351900i
$57$	−5.04642	+	3.24314i	−0.668415	+	0.429564i
$58$	−8.92002	−	4.59859i	−1.17126	−	0.603824i
$59$	−9.57940	+	1.84628i	−1.24713	+	0.240365i	−0.769758	−	0.638336i	$-0.779623\pi$
$59$	−9.57940	+	1.84628i	−1.24713	+	0.240365i	−0.477373	+	0.878701i	$0.658411\pi$
$60$	0.968835	−	3.99359i	0.125076	−	0.515571i
$61$	6.00423	−	2.40373i	0.768763	−	0.307766i	0.0460725	−	0.998938i	$-0.485329\pi$
$61$	6.00423	−	2.40373i	0.768763	−	0.307766i	0.722690	+	0.691172i	$0.242905\pi$
$62$	4.64735	−	5.36333i	0.590214	−	0.681144i
$63$	1.99686	+	1.73567i	0.251581	+	0.218674i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−4.79213	+	6.72960i	−0.594390	+	0.834704i
$66$	−1.95356	−	0.782088i	−0.240467	−	0.0962684i
$67$	8.09769	−	4.17465i	0.989291	−	0.510015i	0.113932	−	0.993489i	$-0.463655\pi$
$67$	8.09769	−	4.17465i	0.989291	−	0.510015i	0.875359	+	0.483474i	$0.160625\pi$
$68$	−0.487060	−	0.843613i	−0.0590647	−	0.102303i
$69$	−2.63659	−	4.00605i	−0.317408	−	0.482271i
$70$	10.5700	−	2.54704i	1.26336	−	0.304430i
$71$	1.09785	+	0.705547i	0.130291	+	0.0837331i	0.604163	−	0.796861i	$-0.293508\pi$
$71$	1.09785	+	0.705547i	0.130291	+	0.0837331i	−0.473872	+	0.880594i	$0.657144\pi$
$72$	−0.786053	+	0.618159i	−0.0926372	+	0.0728507i
$73$	1.20555	+	0.115116i	0.141099	+	0.0134733i	0.165366	−	0.986232i	$-0.447119\pi$
$73$	1.20555	+	0.115116i	0.141099	+	0.0134733i	−0.0242678	+	0.999705i	$0.507725\pi$
$74$	−0.324531	+	0.309440i	−0.0377259	+	0.0359716i
$75$	−11.8336	+	1.12997i	−1.36643	+	0.130478i
$76$	3.92831	−	4.53351i	0.450608	−	0.520029i
$77$	−0.520695	−	5.54305i	−0.0593387	−	0.631689i
$78$	1.92894	−	0.566387i	0.218409	−	0.0641307i
$79$	2.64770	−	7.65003i	0.297890	−	0.860695i	−0.692380	−	0.721533i	$-0.743438\pi$
$79$	2.64770	−	7.65003i	0.297890	−	0.860695i	0.990270	−	0.139162i	$-0.0444410\pi$
$80$	0.195535	+	4.10478i	0.0218614	+	0.458928i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	−3.00630	+	8.68614i	−0.331991	+	0.959224i
$83$	10.6639	−	3.13121i	1.17052	−	0.343695i	0.362006	−	0.932176i	$-0.382092\pi$
$83$	10.6639	−	3.13121i	1.17052	−	0.343695i	0.808511	+	0.588481i	$0.200274\pi$
$84$	−2.40497	−	1.10278i	−0.262403	−	0.120324i
$85$	−2.62146	+	3.02533i	−0.284337	+	0.328143i
$86$	5.65395	−	0.539887i	0.609681	−	0.0582175i
$87$	7.26312	−	6.92537i	0.778688	−	0.742478i
$88$	2.09477	+	0.200026i	0.223303	+	0.0213229i
$89$	1.88389	−	1.48150i	0.199691	−	0.157039i	−0.513306	−	0.858206i	$-0.671579\pi$
$89$	1.88389	−	1.48150i	0.199691	−	0.157039i	0.712998	+	0.701166i	$0.247337\pi$
$90$	3.45707	+	2.22173i	0.364408	+	0.234191i
$91$	3.66456	+	3.85514i	0.384151	+	0.404128i
$92$	3.65842	+	3.10096i	0.381417	+	0.323298i
$93$	3.54835	+	6.14592i	0.367947	+	0.637303i
$94$	11.7117	−	6.03778i	1.20797	−	0.622749i
$95$	−22.8854	−	9.16193i	−2.34799	−	0.939995i
$96$	0.580057	−	0.814576i	0.0592018	−	0.0831373i
$97$	8.90942	+	2.61604i	0.904615	+	0.265619i	0.700772	−	0.713385i	$-0.252839\pi$
$97$	8.90942	+	2.61604i	0.904615	+	0.265619i	0.203842	+	0.979004i	$0.434657\pi$
$98$	−0.311565	−	6.99306i	−0.0314728	−	0.706406i
$99$	1.37802	−	1.59032i	0.138496	−	0.159833i
$100$	11.0359	−	4.41811i	1.10359	−	0.441811i
$101$	0.585441	−	2.41322i	0.0582535	−	0.240124i	−0.935240	−	0.354015i	$-0.884816\pi$
$101$	0.585441	−	2.41322i	0.0582535	−	0.240124i	0.993493	+	0.113891i	$0.0363314\pi$
$102$	0.956517	−	0.184353i	0.0947093	−	0.0182537i
$103$	−6.03639	−	3.11197i	−0.594783	−	0.306632i	0.134425	−	0.990924i	$-0.457081\pi$
$103$	−6.03639	−	3.11197i	−0.594783	−	0.306632i	−0.729208	+	0.684292i	$0.760111\pi$
$104$	−1.69123	+	1.08689i	−0.165839	+	0.106578i
$105$	−1.05014	+	10.8217i	−0.102484	+	1.05609i
$106$	−5.54673	+	1.62867i	−0.538746	+	0.158190i
$107$	1.20778	−	0.483520i	0.116760	−	0.0467437i	−0.312547	−	0.949902i	$-0.601182\pi$
$107$	1.20778	−	0.483520i	0.116760	−	0.0467437i	0.429307	+	0.903159i	$0.358758\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	−10.1666	−	14.2769i	−0.973780	−	1.36748i	−0.929645	−	0.368457i	$-0.879886\pi$
$109$	−10.1666	−	14.2769i	−0.973780	−	1.36748i	−0.0441348	−	0.999026i	$-0.514053\pi$
$110$	−2.03872	−	8.40371i	−0.194384	−	0.801262i
$111$	−0.186277	−	0.407890i	−0.0176806	−	0.0387152i
$112$	2.61824	+	0.380557i	0.247400	+	0.0359592i
$113$	−14.3591	−	9.22805i	−1.35079	−	0.868102i	−0.353073	−	0.935596i	$-0.614863\pi$
$113$	−14.3591	−	9.22805i	−1.35079	−	0.868102i	−0.997720	+	0.0674943i	$0.978500\pi$
$114$	2.99935	+	5.19502i	0.280915	+	0.486558i
$115$	7.12518	−	18.3751i	0.664427	−	1.71348i
$116$	−5.01781	+	8.69110i	−0.465892	+	0.806949i
$117$	−0.0956572	+	2.00809i	−0.00884352	+	0.185648i
$118$	1.38838	+	9.65640i	0.127811	+	0.888943i
$119$	1.59005	+	2.02833i	0.145760	+	0.185936i
$120$	−3.94297	−	1.15776i	−0.359942	−	0.105689i
$121$	6.54217	−	0.624702i	0.594743	−	0.0567911i
$122$	−2.11532	−	6.11180i	−0.191512	−	0.553337i
$123$	−7.22514	−	5.68192i	−0.651469	−	0.512321i
$124$	−5.13613	−	4.89729i	−0.461238	−	0.439789i
$125$	−18.5348	−	21.3903i	−1.65780	−	1.91321i
$126$	1.82872	−	1.91201i	0.162915	−	0.170335i
$127$	−15.2815	+	9.82080i	−1.35601	+	0.871455i	−0.998058	−	0.0622853i	$-0.980161\pi$
$127$	−15.2815	+	9.82080i	−1.35601	+	0.871455i	−0.357952	+	0.933740i	$0.616525\pi$
$128$	−0.327068	+	0.945001i	−0.0289090	+	0.0835271i
$129$	−1.33903	+	5.51957i	−0.117895	+	0.485971i
$130$	6.49396	+	5.10691i	0.569558	+	0.447905i
$131$	1.50116	+	0.289325i	0.131157	+	0.0252785i	0.254407	−	0.967097i	$-0.418120\pi$
$131$	1.50116	+	0.289325i	0.131157	+	0.0252785i	−0.123250	+	0.992376i	$0.539332\pi$
$132$	−0.874157	+	1.91414i	−0.0760856	+	0.166604i
$133$	−8.60106	+	13.3384i	−0.745807	+	1.15658i
$134$	−3.78462	−	8.28716i	−0.326941	−	0.715901i
$135$	−3.23023	+	2.54028i	−0.278014	+	0.218633i
$136$	−0.865833	+	0.446368i	−0.0742445	+	0.0382757i
$137$	8.30212	−	14.3797i	0.709298	−	1.22854i	−0.255820	−	0.966724i	$-0.582345\pi$
$137$	8.30212	−	14.3797i	0.709298	−	1.22854i	0.965118	−	0.261816i	$-0.0843212\pi$
$138$	−4.12696	+	2.44298i	−0.351310	+	0.207961i
$139$	3.91694			0.332231			0.166115	−	0.986106i	$-0.446878\pi$
$139$	3.91694			0.332231			0.166115	+	0.986106i	$0.446878\pi$
$140$	−2.04122	−	10.6792i	−0.172515	−	0.902558i
$141$	1.87520	+	13.0423i	0.157920	+	1.09836i
$142$	0.756986	−	1.06304i	0.0635249	−	0.0892082i
$143$	3.06170	−	2.91932i	0.256032	−	0.244126i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	40.4954	+	7.80486i	3.36296	+	0.648158i
$146$	0.172348	−	1.19870i	0.0142636	−	0.0992054i
$147$	6.71035	+	1.99278i	0.553461	+	0.164362i
$148$	0.293647	+	0.338887i	0.0241377	+	0.0278563i
$149$	6.02048	+	3.10377i	0.493217	+	0.254271i	0.686845	−	0.726804i	$-0.258995\pi$
$149$	6.02048	+	3.10377i	0.493217	+	0.254271i	−0.193628	+	0.981075i	$0.562025\pi$
$150$	0.565627	+	11.8740i	0.0461832	+	0.969506i
$151$	15.2879	−	2.94649i	1.24411	−	0.239782i	0.475623	−	0.879649i	$-0.342223\pi$
$151$	15.2879	−	2.94649i	1.24411	−	0.239782i	0.768486	+	0.639867i	$0.221011\pi$
$152$	−4.34146	−	4.13957i	−0.352139	−	0.335764i
$153$	−0.138632	+	0.964205i	−0.0112077	+	0.0779514i
$154$	−5.56154	+	0.256357i	−0.448162	+	0.0206578i
$155$	−12.1149	+	26.5280i	−0.973094	+	2.13078i
$156$	−0.473963	−	1.95370i	−0.0379474	−	0.156421i
$157$	−8.13400	−	0.776703i	−0.649164	−	0.0619876i	−0.234721	−	0.972063i	$-0.575418\pi$
$157$	−8.13400	−	0.776703i	−0.649164	−	0.0619876i	−0.414443	+	0.910075i	$0.636024\pi$
$158$	−7.51538	−	3.00870i	−0.597891	−	0.239360i
$159$	0.275066	−	5.77435i	0.0218142	−	0.457936i
$160$	4.10943			0.324879
$161$	−10.7380	−	6.75989i	−0.846270	−	0.532754i
$162$	1.00000			0.0785674
$163$	0.501432	−	10.5263i	0.0392752	−	0.824487i	−0.890193	−	0.455584i	$-0.849430\pi$
$163$	0.501432	−	10.5263i	0.0392752	−	0.824487i	0.929468	−	0.368903i	$-0.120267\pi$
$164$	8.53326	+	3.41620i	0.666335	+	0.266760i
$165$	8.60831	+	0.821994i	0.670156	+	0.0639922i
$166$	−2.62025	−	10.8008i	−0.203371	−	0.838307i
$167$	−6.62926	+	14.5161i	−0.512988	+	1.12329i	0.459039	+	0.888416i	$0.348194\pi$
$167$	−6.62926	+	14.5161i	−0.512988	+	1.12329i	−0.972027	+	0.234871i	$0.924533\pi$
$168$	−1.21597	+	2.34977i	−0.0938140	+	0.181289i
$169$	1.27492	−	8.86723i	0.0980704	−	0.682095i
$170$	2.89717	+	2.76244i	0.222203	+	0.211870i
$171$	−5.89029	+	1.13526i	−0.450442	+	0.0868155i
$172$	−0.270250	−	5.67324i	−0.0206063	−	0.432580i
$173$	−13.7984	−	7.11358i	−1.04907	−	0.540835i	−0.154610	−	0.987976i	$-0.549412\pi$
$173$	−13.7984	−	7.11358i	−1.04907	−	0.540835i	−0.894464	+	0.447140i	$0.852442\pi$
$174$	−6.57194	−	7.58442i	−0.498217	−	0.574973i
$175$	−27.2617	+	15.6837i	−2.06079	+	1.18558i
$176$	0.299473	−	2.08288i	0.0225736	−	0.157003i
$177$	−9.57940	−	1.84628i	−0.720032	−	0.138775i
$178$	−1.39019	−	1.95224i	−0.104199	−	0.146327i
$179$	−5.88551	+	5.61182i	−0.439903	+	0.419447i	−0.877390	−	0.479778i	$-0.840717\pi$
$179$	−5.88551	+	5.61182i	−0.439903	+	0.419447i	0.437487	+	0.899225i	$0.355869\pi$
$180$	2.38370	−	3.34744i	0.177671	−	0.249504i
$181$	1.66661	+	11.5915i	0.123878	+	0.861591i	0.953097	+	0.302666i	$0.0978768\pi$
$181$	1.66661	+	11.5915i	0.123878	+	0.861591i	−0.829218	+	0.558925i	$0.811214\pi$
$182$	4.02514	−	3.47698i	0.298363	−	0.257731i
$183$	6.46751			0.478092
$184$	3.27152	−	3.50673i	0.241180	−	0.258519i
$185$	0.921359	−	1.59584i	0.0677396	−	0.117329i
$186$	6.30780	−	3.25190i	0.462510	−	0.238441i
$187$	1.61128	−	1.26713i	0.117829	−	0.0926615i
$188$	−5.47368	−	11.9857i	−0.399209	−	0.874145i
$189$	1.20874	+	2.35350i	0.0879226	+	0.171192i
$190$	−10.2405	+	22.4235i	−0.742923	+	1.62677i
$191$	11.2912	+	2.17621i	0.817006	+	0.157465i	0.580599	−	0.814189i	$-0.302818\pi$
$191$	11.2912	+	2.17621i	0.817006	+	0.157465i	0.236406	+	0.971654i	$0.424030\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	−4.62147	+	19.0500i	−0.332661	+	1.37125i	0.522392	+	0.852706i	$0.325040\pi$
$193$	−4.62147	+	19.0500i	−0.332661	+	1.37125i	−0.855053	+	0.518541i	$0.826475\pi$
$194$	3.03701	−	8.77485i	0.218044	−	0.629998i
$195$	−6.95000	+	4.46649i	−0.497700	+	0.319852i
$196$	−6.99997	−	0.0215313i	−0.499998	−	0.00153795i
$197$	0.0284968	+	0.0328871i	0.00203032	+	0.00234311i	0.756764	−	0.653688i	$-0.226779\pi$
$197$	0.0284968	+	0.0328871i	0.00203032	+	0.00234311i	−0.754734	+	0.656032i	$0.772234\pi$
$198$	−1.52295	−	1.45213i	−0.108231	−	0.103198i
$199$	−8.05067	−	6.33111i	−0.570697	−	0.448801i	0.290642	−	0.956832i	$-0.406131\pi$
$199$	−8.05067	−	6.33111i	−0.570697	−	0.448801i	−0.861339	+	0.508031i	$0.830374\pi$
$200$	−3.88800	−	11.2336i	−0.274923	−	0.794338i
$201$	9.06920	−	0.866004i	0.639692	−	0.0610832i
$202$	−2.38263	−	0.699603i	−0.167641	−	0.0492239i
$203$	9.90619	−	24.6346i	0.695278	−	1.72901i
$204$	−0.138632	−	0.964205i	−0.00970617	−	0.0675079i
$205$	1.79729	−	37.7298i	0.125528	−	2.63516i
$206$	−3.39567	+	5.88148i	−0.236588	+	0.409782i
$207$	−0.958824	−	4.69901i	−0.0666429	−	0.326603i
$208$	1.00518	+	1.74103i	0.0696970	+	0.120719i
$209$	10.6192	+	6.82453i	0.734544	+	0.472062i
$210$	10.7595	+	1.56387i	0.742474	+	0.107917i
$211$	10.3354	+	22.6315i	0.711521	+	1.55801i	0.825418	+	0.564522i	$0.190940\pi$
$211$	10.3354	+	22.6315i	0.711521	+	1.55801i	−0.113896	+	0.993493i	$0.536333\pi$
$212$	1.36290	+	5.61794i	0.0936042	+	0.385842i
$213$	0.756986	+	1.06304i	0.0518678	+	0.0728382i
$214$	−0.425504	−	1.22941i	−0.0290869	−	0.0840410i
$215$	−21.6683	+	8.67468i	−1.47777	+	0.591609i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	15.2778	+	10.9147i	1.03712	+	0.740940i
$218$	−14.7445	+	9.47572i	−0.998624	+	0.641777i
$219$	1.07641	+	0.554926i	0.0727368	+	0.0374984i
$220$	−8.49120	+	1.63654i	−0.572476	+	0.110336i
$221$	−0.461697	+	1.90314i	−0.0310571	+	0.128019i
$222$	−0.416291	+	0.166658i	−0.0279396	+	0.0111853i
$223$	0.551696	−	0.636692i	0.0369443	−	0.0426360i	−0.736977	−	0.675918i	$-0.763747\pi$
$223$	0.551696	−	0.636692i	0.0369443	−	0.0426360i	0.773921	+	0.633282i	$0.218293\pi$
$224$	0.504707	−	2.59717i	0.0337221	−	0.173530i
$225$	−11.4059	−	3.34908i	−0.760394	−	0.223272i
$226$	−9.90083	+	13.9038i	−0.658593	+	0.924865i
$227$	−6.30386	−	2.52368i	−0.418402	−	0.167503i	0.152902	−	0.988241i	$-0.451138\pi$
$227$	−6.30386	−	2.52368i	−0.418402	−	0.167503i	−0.571304	+	0.820739i	$0.693562\pi$
$228$	5.33185	−	2.74876i	0.353110	−	0.182041i
$229$	−2.56262	−	4.43859i	−0.169343	−	0.293310i	0.768846	−	0.639434i	$-0.220831\pi$
$229$	−2.56262	−	4.43859i	−0.169343	−	0.293310i	−0.938189	+	0.346124i	$0.887498\pi$
$230$	−18.0152	−	7.99143i	−1.18789	−	0.526939i
$231$	1.57675	−	5.33951i	0.103742	−	0.351314i
$232$	8.44250	+	5.42567i	0.554277	+	0.356213i
$233$	4.27558	−	3.36236i	0.280103	−	0.220275i	−0.468217	−	0.883614i	$-0.655103\pi$
$233$	4.27558	−	3.36236i	0.280103	−	0.220275i	0.748320	+	0.663338i	$0.230861\pi$
$234$	2.00127	+	0.191098i	0.130827	+	0.0124925i
$235$	−39.1884	+	37.3661i	−2.55637	+	2.43749i
$236$	9.71152	−	0.927338i	0.632166	−	0.0603645i
$237$	5.30127	−	6.11799i	0.344354	−	0.397406i
$238$	2.10169	−	1.49174i	0.136232	−	0.0966951i
$239$	16.7401	−	4.91534i	1.08283	−	0.317947i	0.308818	−	0.951121i	$-0.400067\pi$
$239$	16.7401	−	4.91534i	1.08283	−	0.317947i	0.774009	+	0.633174i	$0.218248\pi$
$240$	−1.34406	+	3.88342i	−0.0867589	+	0.250673i
$241$	−0.717786	−	15.0682i	−0.0462367	−	0.970627i	−0.896163	−	0.443725i	$-0.853657\pi$
$241$	−0.717786	−	15.0682i	−0.0462367	−	0.970627i	0.849926	−	0.526902i	$-0.176646\pi$
$242$	−0.312705	−	6.56449i	−0.0201014	−	0.421981i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	−6.20553	+	1.82211i	−0.397268	+	0.116649i
$245$	9.32479	+	27.2127i	0.595739	+	1.73856i
$246$	−6.01927	+	6.94660i	−0.383774	+	0.442899i
$247$	−12.0050	+	1.14634i	−0.763859	+	0.0729397i
$248$	−5.13613	+	4.89729i	−0.326144	+	0.310978i
$249$	11.0638	+	1.05646i	0.701139	+	0.0669507i
$250$	−22.2480	+	17.4960i	−1.40709	+	1.10655i
$251$	−26.2753	−	16.8861i	−1.65848	−	1.06584i	−0.920277	−	0.391267i	$-0.872037\pi$
$251$	−26.2753	−	16.8861i	−1.65848	−	1.06584i	−0.738206	−	0.674575i	$-0.764327\pi$
$252$	−1.82283	−	1.91763i	−0.114828	−	0.120799i
$253$	−5.36333	+	8.54870i	−0.337190	+	0.537452i
$254$	9.08255	+	15.7314i	0.569890	+	0.987078i
$255$	−3.55808	+	1.83432i	−0.222816	+	0.114869i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	3.74683	−	5.26168i	0.233721	−	0.328215i	−0.681014	−	0.732271i	$-0.738461\pi$
$257$	3.74683	−	5.26168i	0.233721	−	0.328215i	0.914734	+	0.404056i	$0.132400\pi$
$258$	5.44960	+	1.60015i	0.339278	+	0.0996209i
$259$	−0.895415	−	0.778296i	−0.0556384	−	0.0483609i
$260$	5.41012	−	6.24361i	0.335521	−	0.387212i
$261$	9.31675	−	3.72986i	0.576692	−	0.230873i
$262$	0.360426	−	1.48569i	0.0222672	−	0.0917865i
$263$	20.5060	−	3.95220i	1.26445	−	0.243703i	0.487421	−	0.873167i	$-0.337938\pi$
$263$	20.5060	−	3.95220i	1.26445	−	0.243703i	0.777030	+	0.629464i	$0.216725\pi$
$264$	1.87037	+	0.964245i	0.115114	+	0.0593452i
$265$	19.9850	−	12.8436i	1.22767	−	0.788974i
$266$	12.9140	+	9.22598i	0.791808	+	0.565681i
$267$	2.29956	−	0.675211i	0.140731	−	0.0413223i
$268$	−8.45785	+	3.38601i	−0.516646	+	0.206834i
$269$	−10.5687	−	30.5364i	−0.644388	−	1.86184i	−0.484729	−	0.874664i	$-0.661082\pi$
$269$	−10.5687	−	30.5364i	−0.644388	−	1.86184i	−0.159659	−	0.987172i	$-0.551039\pi$
$270$	2.38370	+	3.34744i	0.145068	+	0.203719i
$271$	−0.764805	−	3.15257i	−0.0464586	−	0.191505i	0.943854	−	0.330364i	$-0.107172\pi$
$271$	−0.764805	−	3.15257i	−0.0464586	−	0.191505i	−0.990312	+	0.138859i	$0.955656\pi$
$272$	0.404664	+	0.886091i	0.0245364	+	0.0537272i
$273$	1.96925	+	4.94097i	0.119185	+	0.299041i
$274$	−13.9684	−	8.97693i	−0.843860	−	0.542316i
$275$	12.5074	+	21.6634i	0.754222	+	1.30635i
$276$	2.24385	+	4.23853i	0.135064	+	0.255130i
$277$	−2.87380	+	4.97757i	−0.172670	+	0.299073i	−0.939353	−	0.342953i	$-0.888573\pi$
$277$	−2.87380	+	4.97757i	−0.172670	+	0.299073i	0.766682	+	0.642027i	$0.221906\pi$
$278$	0.186376	−	3.91251i	0.0111781	−	0.234657i
$279$	1.00997	+	7.02447i	0.0604651	+	0.420544i
$280$	−10.7642	+	1.53077i	−0.643286	+	0.0914810i
$281$	7.11396	+	2.08885i	0.424383	+	0.124610i	0.486948	−	0.873431i	$-0.338110\pi$
$281$	7.11396	+	2.08885i	0.424383	+	0.124610i	−0.0625653	+	0.998041i	$0.519928\pi$
$282$	13.1167	−	1.25250i	0.781091	−	0.0745851i
$283$	−6.57723	−	19.0036i	−0.390975	−	1.12965i	−0.953115	−	0.302607i	$-0.902143\pi$
$283$	−6.57723	−	19.0036i	−0.390975	−	1.12965i	0.562140	−	0.827042i	$-0.309978\pi$
$284$	−1.02582	−	0.806710i	−0.0608709	−	0.0478694i
$285$	−17.8409	−	17.0113i	−1.05681	−	1.00766i
$286$	−2.77033	−	3.19714i	−0.163813	−	0.189051i
$287$	−23.6245	−	5.76973i	−1.39451	−	0.340577i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	5.24980	−	15.1683i	0.308812	−	0.892253i
$290$	9.72287	−	40.0782i	0.570946	−	2.35347i
$291$	7.29894	+	5.73995i	0.427871	+	0.336482i
$292$	−1.18915	−	0.229189i	−0.0695895	−	0.0134123i
$293$	−7.36927	+	16.1364i	−0.430517	+	0.942701i	0.562725	+	0.826644i	$0.309753\pi$
$293$	−7.36927	+	16.1364i	−0.430517	+	0.942701i	−0.993243	+	0.116057i	$0.962974\pi$
$294$	2.30981	−	6.60793i	0.134711	−	0.385382i
$295$	−16.6541	−	36.4675i	−0.969642	−	2.12322i
$296$	0.352475	−	0.277190i	0.0204872	−	0.0161113i
$297$	1.87037	−	0.964245i	0.108530	−	0.0559512i
$298$	3.38672	−	5.86598i	0.196188	−	0.339807i
$299$	−1.02089	−	9.58719i	−0.0590398	−	0.554442i
$300$	11.8874			0.686321
$301$	2.82118	+	14.7598i	0.162610	+	0.850740i
$302$	−2.21573	−	15.4107i	−0.127501	−	0.886789i
$303$	1.44041	−	2.02277i	0.0827492	−	0.116205i
$304$	−4.34146	+	4.13957i	−0.249000	+	0.237421i
$305$	15.4166	+	21.6496i	0.882754	+	1.23965i
$306$	0.956517	+	0.184353i	0.0546804	+	0.0105388i
$307$	0.0155291	−	0.108007i	0.000886291	−	0.00616429i	−0.989373	−	0.145396i	$-0.953554\pi$
$307$	0.0155291	−	0.108007i	0.000886291	−	0.00616429i	0.990260	+	0.139232i	$0.0444634\pi$
$308$	−0.00856246	+	5.56744i	−0.000487891	+	0.317234i
$309$	−4.44738	−	5.13255i	−0.253003	−	0.291981i
$310$	25.9215	+	13.3635i	1.47224	+	0.758993i
$311$	−0.425755	−	8.93771i	−0.0241424	−	0.506811i	−0.978260	−	0.207380i	$-0.933506\pi$
$311$	−0.425755	−	8.93771i	−0.0241424	−	0.506811i	0.954118	−	0.299431i	$-0.0967967\pi$
$312$	−1.97404	+	0.380465i	−0.111758	+	0.0215396i
$313$	13.3548	+	12.7338i	0.754857	+	0.719755i	0.966239	−	0.257649i	$-0.0829477\pi$
$313$	13.3548	+	12.7338i	0.754857	+	0.719755i	−0.211381	+	0.977404i	$0.567796\pi$
$314$	−1.16285	+	8.08783i	−0.0656237	+	0.456423i
$315$	−4.99694	+	9.65622i	−0.281546	+	0.544066i
$316$	−3.36289	+	7.36371i	−0.189177	+	0.414241i
$317$	−1.70258	−	7.01812i	−0.0956263	−	0.394177i	0.903803	−	0.427948i	$-0.140763\pi$
$317$	−1.70258	−	7.01812i	−0.0956263	−	0.394177i	−0.999430	+	0.0337711i	$0.989248\pi$
$318$	−5.75472	−	0.549509i	−0.322709	−	0.0308149i
$319$	−19.6052	−	7.84874i	−1.09768	−	0.439445i
$320$	0.195535	−	4.10478i	0.0109307	−	0.229464i
$321$	1.30097			0.0726129
$322$	−7.26316	+	10.4042i	−0.404760	+	0.579801i
$323$	−5.84345			−0.325138
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	−22.1863	−	8.88204i	−1.23067	−	0.492687i
$326$	−10.4906	−	1.00173i	−0.581019	−	0.0554805i
$327$	−4.13211	−	17.0328i	−0.228506	−	0.941915i
$328$	3.81836	−	8.36104i	0.210834	−	0.461661i
$329$	18.8024	+	29.3563i	1.03661	+	1.61847i
$330$	1.23066	−	8.55945i	0.0677458	−	0.471182i
$331$	−10.9508	−	10.4416i	−0.601912	−	0.573922i	0.326629	−	0.945153i	$-0.394087\pi$
$331$	−10.9508	−	10.4416i	−0.601912	−	0.573922i	−0.928541	+	0.371231i	$0.878936\pi$
$332$	−10.9133	+	2.10336i	−0.598944	+	0.115437i
$333$	−0.0213363	−	0.447904i	−0.00116922	−	0.0245450i
$334$	14.1842	+	7.31246i	0.776124	+	0.400120i
$335$	24.5172	+	28.2943i	1.33952	+	1.54589i
$336$	2.28925	+	1.32640i	0.124889	+	0.0723609i
$337$	1.46529	−	10.1913i	0.0798192	−	0.555155i	−0.910194	−	0.414182i	$-0.864068\pi$
$337$	1.46529	−	10.1913i	0.0798192	−	0.555155i	0.990013	−	0.140973i	$-0.0450231\pi$
$338$	−8.79652	−	1.69539i	−0.478468	−	0.0922171i
$339$	−9.90083	−	13.9038i	−0.537739	−	0.755149i
$340$	2.89717	−	2.76244i	0.157121	−	0.149815i
$341$	8.66232	−	12.1645i	0.469091	−	0.658746i
$342$	0.853703	+	5.93764i	0.0461630	+	0.321071i
$343$	18.3437	−	2.55110i	0.990468	−	0.137746i
$344$	−5.67967			−0.306227
$345$	13.4441	−	14.4107i	0.723807	−	0.775844i
$346$	−7.76207	+	13.4443i	−0.417292	+	0.722770i
$347$	−2.94740	+	1.51949i	−0.158224	+	0.0815704i	−0.535520	−	0.844523i	$-0.679884\pi$
$347$	−2.94740	+	1.51949i	−0.158224	+	0.0815704i	0.377296	+	0.926093i	$0.376854\pi$
$348$	−7.88853	+	6.20361i	−0.422870	+	0.332548i
$349$	4.57721	+	10.0227i	0.245013	+	0.536503i	0.991685	−	0.128689i	$-0.0410770\pi$
$349$	4.57721	+	10.0227i	0.245013	+	0.536503i	−0.746672	+	0.665192i	$0.768350\pi$
$350$	14.3688	+	27.9771i	0.768043	+	1.49544i
$351$	−0.835138	+	1.82870i	−0.0445764	+	0.0976086i
$352$	−2.06627	−	0.398241i	−0.110133	−	0.0212263i
$353$	−4.86596	−	3.82663i	−0.258989	−	0.203671i	0.480219	−	0.877149i	$-0.340557\pi$
$353$	−4.86596	−	3.82663i	−0.258989	−	0.203671i	−0.739208	+	0.673478i	$0.764800\pi$
$354$	−2.29999	+	9.48070i	−0.122243	+	0.503893i
$355$	−1.75403	+	5.06794i	−0.0930943	+	0.268978i
$356$	−2.01618	+	1.29572i	−0.106857	+	0.0686731i
$357$	0.722300	+	2.47400i	0.0382282	+	0.130938i
$358$	5.32542	+	6.14586i	0.281457	+	0.324819i
$359$	2.81805	+	2.68700i	0.148731	+	0.141814i	0.760792	−	0.648996i	$-0.224811\pi$
$359$	2.81805	+	2.68700i	0.148731	+	0.141814i	−0.612061	+	0.790811i	$0.709659\pi$
$360$	−3.23023	−	2.54028i	−0.170248	−	0.133885i
$361$	−5.55503	−	16.0502i	−0.292370	−	0.844747i
$362$	11.6577	−	1.11317i	0.612715	−	0.0585072i
$363$	6.30572	+	1.85153i	0.330965	+	0.0971800i
$364$	−3.28152	−	4.18602i	−0.171998	−	0.219407i
$365$	0.708251	+	4.92599i	0.0370715	+	0.257838i
$366$	0.307737	−	6.46019i	0.0160856	−	0.337679i
$367$	5.68120	−	9.84013i	0.296556	−	0.513651i	−0.678789	−	0.734333i	$-0.737495\pi$
$367$	5.68120	−	9.84013i	0.296556	−	0.513651i	0.975346	+	0.220682i	$0.0708284\pi$
$368$	−3.34709	−	3.43468i	−0.174479	−	0.179045i
$369$	−4.59584	−	7.96022i	−0.239250	−	0.414393i
$370$	−1.55019	−	0.996248i	−0.0805907	−	0.0517925i
$371$	−5.66266	−	14.2079i	−0.293991	−	0.737639i
$372$	−2.94808	−	6.45539i	−0.152851	−	0.334696i
$373$	−3.44117	−	14.1847i	−0.178177	−	0.734456i	−0.988845	−	0.148950i	$-0.952411\pi$
$373$	−3.44117	−	14.1847i	−0.178177	−	0.734456i	0.810668	−	0.585507i	$-0.199104\pi$
$374$	−1.18902	−	1.66975i	−0.0614829	−	0.0863407i
$375$	−9.25715	−	26.7468i	−0.478037	−	1.38120i
$376$	−12.2326	+	4.89717i	−0.630846	+	0.252553i
$377$	19.3581	−	5.68404i	0.996991	−	0.292743i
$378$	2.40835	−	1.09538i	0.123872	−	0.0563404i
$379$	−10.7722	+	6.92287i	−0.553331	+	0.355604i	−0.787233	−	0.616656i	$-0.788487\pi$
$379$	−10.7722	+	6.92287i	−0.553331	+	0.355604i	0.233902	+	0.972260i	$0.424851\pi$
$380$	21.9109	+	11.2958i	1.12400	+	0.579465i
$381$	−17.8368	+	3.43777i	−0.913809	+	0.176122i
$382$	2.71100	−	11.1749i	0.138707	−	0.571758i
$383$	−27.2947	+	10.9271i	−1.39469	+	0.558350i	−0.942691	−	0.333667i	$-0.891714\pi$
$383$	−27.2947	+	10.9271i	−1.39469	+	0.558350i	−0.452001	+	0.892017i	$0.649290\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	21.6322	−	7.44974i	1.10248	−	0.379674i
$386$	18.8085	+	5.52267i	0.957327	+	0.281097i
$387$	−3.29453	+	4.62652i	−0.167470	+	0.235179i
$388$	−8.62041	−	3.45109i	−0.437635	−	0.175203i
$389$	24.4026	−	12.5804i	1.23726	−	0.637852i	0.289605	−	0.957146i	$-0.406476\pi$
$389$	24.4026	−	12.5804i	1.23726	−	0.637852i	0.947656	+	0.319294i	$0.103446\pi$
$390$	4.13074	+	7.15465i	0.209168	+	0.362290i
$391$	−0.0508532	−	4.67144i	−0.00257176	−	0.236245i
$392$	−0.354579	+	6.99101i	−0.0179089	+	0.353100i
$393$	1.28610	+	0.826526i	0.0648751	+	0.0416927i
$394$	0.0342058	−	0.0268997i	0.00172326	−	0.00135519i
$395$	33.1163	+	3.16222i	1.66626	+	0.159109i
$396$	−1.52295	+	1.45213i	−0.0765312	+	0.0729724i
$397$	−23.1574	+	2.21127i	−1.16224	+	0.110980i	−0.658298	−	0.752758i	$-0.728723\pi$
$397$	−23.1574	+	2.21127i	−1.16224	+	0.110980i	−0.503941	+	0.863738i	$0.668117\pi$
$398$	−6.70701	+	7.74030i	−0.336192	+	0.387986i
$399$	−12.9423	+	9.18622i	−0.647926	+	0.459886i
$400$	−11.4059	+	3.34908i	−0.570296	+	0.167454i
$401$	0.702384	−	2.02941i	0.0350754	−	0.101344i	−0.926104	−	0.377269i	$-0.876863\pi$
$401$	0.702384	−	2.02941i	0.0350754	−	0.101344i	0.961179	+	0.275926i	$0.0889843\pi$
$402$	−0.433493	−	9.10013i	−0.0216207	−	0.453873i
$403$	0.678851	+	14.2508i	0.0338160	+	0.709885i
$404$	−0.812181	+	2.34664i	−0.0404075	+	0.116750i
$405$	−3.94297	+	1.15776i	−0.195928	+	0.0575296i
$406$	−24.1353	−	11.0671i	−1.19782	−	0.549253i
$407$	−0.617921	+	0.713119i	−0.0306292	+	0.0353480i
$408$	−0.969709	+	0.0925960i	−0.0480078	+	0.00458419i
$409$	−3.32962	+	3.17479i	−0.164639	+	0.156983i	−0.767920	−	0.640546i	$-0.778708\pi$
$409$	−3.32962	+	3.17479i	−0.164639	+	0.156983i	0.603281	+	0.797529i	$0.293860\pi$
$410$	−37.6015	−	3.59051i	−1.85701	−	0.177323i
$411$	13.0518	−	10.2641i	0.643798	−	0.506289i
$412$	5.71324	+	3.67168i	0.281471	+	0.180891i
$413$	−25.0929	+	6.04662i	−1.23474	+	0.297535i
$414$	−4.73931	+	0.734150i	−0.232924	+	0.0360815i
$415$	22.8364	+	39.5537i	1.12099	+	1.94162i
$416$	1.78689	−	0.921205i	0.0876094	−	0.0451658i
$417$	3.63637	+	1.45578i	0.178074	+	0.0712899i
$418$	7.32208	−	10.2824i	0.358135	−	0.502930i
$419$	−30.5414	−	8.96775i	−1.49204	−	0.438103i	−0.568851	−	0.822441i	$-0.692612\pi$
$419$	−30.5414	−	8.96775i	−1.49204	−	0.438103i	−0.923193	+	0.384337i	$0.874430\pi$
$420$	2.07406	−	10.6729i	0.101204	−	0.520783i
$421$	−4.41909	+	5.09990i	−0.215373	+	0.248554i	−0.853148	−	0.521669i	$-0.825310\pi$
$421$	−4.41909	+	5.09990i	−0.215373	+	0.248554i	0.637775	+	0.770223i	$0.279855\pi$
$422$	23.0976	−	9.24689i	1.12437	−	0.450132i
$423$	−3.10646	+	12.8050i	−0.151041	+	0.622600i
$424$	5.67643	−	1.09404i	0.275672	−	0.0531314i
$425$	−10.2925	−	5.30617i	−0.499261	−	0.257387i
$426$	1.09785	−	0.705547i	0.0531912	−	0.0341839i
$427$	15.5760	−	7.08440i	0.753776	−	0.342838i
$428$	−1.24827	+	0.366525i	−0.0603373	+	0.0177166i
$429$	3.92738	−	1.57229i	0.189616	−	0.0759107i
$430$	7.63384	+	22.0565i	0.368136	+	1.06366i
$431$	8.72761	+	12.2562i	0.420394	+	0.590361i	0.969409	−	0.245452i	$-0.0789363\pi$
$431$	8.72761	+	12.2562i	0.420394	+	0.590361i	−0.549015	+	0.835813i	$0.684997\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	0.923300	+	2.02174i	0.0443710	+	0.0971588i	0.930519	−	0.366243i	$-0.119356\pi$
$433$	0.923300	+	2.02174i	0.0443710	+	0.0971588i	−0.886148	+	0.463402i	$0.846629\pi$
$434$	11.6293	−	14.7412i	0.558225	−	0.707598i
$435$	34.6939	+	22.2964i	1.66345	+	1.06903i
$436$	8.76341	+	15.1787i	0.419691	+	0.726927i
$437$	27.0824	−	9.70470i	1.29553	−	0.464239i
$438$	0.605515	−	1.04878i	0.0289326	−	0.0501128i
$439$	−0.674108	+	14.1513i	−0.0321734	+	0.675404i	0.923963	+	0.382482i	$0.124931\pi$
$439$	−0.674108	+	14.1513i	−0.0321734	+	0.675404i	−0.956136	+	0.292922i	$0.905372\pi$
$440$	1.23066	+	8.55945i	0.0586696	+	0.408056i
$441$	5.48904	+	4.34402i	0.261383	+	0.206858i
$442$	1.87902	+	0.551729i	0.0893757	+	0.0262431i
$443$	−5.25045	+	0.501358i	−0.249457	+	0.0238202i	−0.219035	−	0.975717i	$-0.570291\pi$
$443$	−5.25045	+	0.501358i	−0.249457	+	0.0238202i	−0.0304214	+	0.999537i	$0.509685\pi$
$444$	0.146661	+	0.423749i	0.00696023	+	0.0201103i
$445$	7.74170	+	6.08814i	0.366992	+	0.288606i
$446$	−0.609720	−	0.581367i	−0.0288711	−	0.0275285i
$447$	4.43567	+	5.11903i	0.209800	+	0.242122i
$448$	−2.57021	−	0.627713i	−0.121431	−	0.0296567i
$449$	−14.4456	+	9.28363i	−0.681731	+	0.438122i	−0.835137	−	0.550041i	$-0.814612\pi$
$449$	−14.4456	+	9.28363i	−0.681731	+	0.438122i	0.153407	+	0.988163i	$0.450976\pi$
$450$	−3.88800	+	11.2336i	−0.183282	+	0.529559i
$451$	−4.56005	+	18.7968i	−0.214725	+	0.885107i
$452$	13.4169	+	10.5512i	0.631079	+	0.496286i
$453$	15.2879	+	2.94649i	0.718286	+	0.138438i
$454$	−2.82078	+	6.17664i	−0.132386	+	0.289884i
$455$	−11.8455	+	18.3698i	−0.555325	+	0.861188i
$456$	−2.49195	−	5.45660i	−0.116696	−	0.255529i
$457$	−2.45413	+	1.92995i	−0.114799	+	0.0902792i	−0.673908	−	0.738815i	$-0.735386\pi$
$457$	−2.45413	+	1.92995i	−0.114799	+	0.0902792i	0.559109	+	0.829094i	$0.311143\pi$
$458$	−4.55550	+	2.34852i	−0.212864	+	0.109739i
$459$	−0.487060	+	0.843613i	−0.0227340	+	0.0393765i
$460$	−8.83958	+	17.6146i	−0.412147	+	0.821283i
$461$	11.8189			0.550461			0.275231	−	0.961378i	$-0.411246\pi$
$461$	11.8189			0.550461			0.275231	+	0.961378i	$0.411246\pi$
$462$	−5.25844	−	1.82902i	−0.244645	−	0.0850939i
$463$	1.03505	+	7.19893i	0.0481029	+	0.334563i	0.999635	+	0.0270137i	$0.00859976\pi$
$463$	1.03505	+	7.19893i	0.0481029	+	0.334563i	−0.951532	+	0.307549i	$0.900491\pi$
$464$	5.82123	−	8.17478i	0.270244	−	0.379504i
$465$	−21.1066	+	20.1251i	−0.978793	+	0.933278i
$466$	−3.15511	−	4.43073i	−0.146157	−	0.205249i
$467$	26.0144	+	5.01386i	1.20380	+	0.232014i	0.751428	−	0.659815i	$-0.229366\pi$
$467$	26.0144	+	5.01386i	1.20380	+	0.232014i	0.452373	+	0.891829i	$0.350578\pi$
$468$	0.286105	−	1.98991i	0.0132252	−	0.0919835i
$469$	20.8932	−	12.0199i	0.964757	−	0.555026i
$470$	35.4591	+	40.9220i	1.63561	+	1.88759i
$471$	−7.26267	−	3.74417i	−0.334646	−	0.172522i
$472$	−0.464195	−	9.74465i	−0.0213663	−	0.448534i
$473$	11.7357	−	2.26188i	0.539610	−	0.104001i
$474$	−5.85881	−	5.58637i	−0.269104	−	0.256590i
$475$	10.1483	−	70.5833i	0.465638	−	3.23858i
$476$	−1.39005	−	2.17029i	−0.0637127	−	0.0994749i
$477$	2.40147	−	5.25849i	0.109956	−	0.240770i
$478$	−4.11324	−	16.9550i	−0.188135	−	0.775505i
$479$	−2.21729	−	0.211725i	−0.101310	−	0.00967398i	0.0442777	−	0.999019i	$-0.485901\pi$
$479$	−2.21729	−	0.211725i	−0.101310	−	0.00967398i	−0.145588	+	0.989345i	$0.546507\pi$
$480$	3.81507	+	1.52732i	0.174133	+	0.0697124i
$481$	0.0428938	−	0.900452i	0.00195579	−	0.0410571i
$482$	−15.0853			−0.687115
$483$	−7.45639	−	10.2666i	−0.339277	−	0.467145i
$484$	−6.57193			−0.298724
$485$	−1.81565	+	38.1151i	−0.0824443	+	1.73072i
$486$	0.928368	+	0.371662i	0.0421116	+	0.0168590i
$487$	41.5530	+	3.96783i	1.88295	+	0.179800i	0.972356	−	0.233505i	$-0.0750196\pi$
$487$	41.5530	+	3.96783i	1.88295	+	0.179800i	0.910593	+	0.413305i	$0.135626\pi$
$488$	1.52477	+	6.28520i	0.0690233	+	0.284518i
$489$	4.37776	−	9.58596i	0.197969	−	0.433492i
$490$	27.6256	−	8.01939i	1.24800	−	0.362279i
$491$	−2.34781	+	16.3294i	−0.105955	+	0.736936i	0.865705	+	0.500555i	$0.166871\pi$
$491$	−2.34781	+	16.3294i	−0.105955	+	0.736936i	−0.971660	+	0.236381i	$0.924039\pi$
$492$	6.65233	+	6.34298i	0.299910	+	0.285964i
$493$	9.59924	−	1.85010i	0.432328	−	0.0833244i
$494$	0.573818	+	12.0459i	0.0258173	+	0.541972i
$495$	7.68618	+	3.96250i	0.345468	+	0.178101i
$496$	4.64735	+	5.36333i	0.208672	+	0.240821i
$497$	2.98752	+	1.73098i	0.134009	+	0.0776449i
$498$	1.58170	−	11.0010i	0.0708779	−	0.492966i
$499$	8.70960	+	1.67864i	0.389895	+	0.0751461i	0.380431	−	0.924809i	$-0.375775\pi$
$499$	8.70960	+	1.67864i	0.389895	+	0.0751461i	0.00946356	+	0.999955i	$0.496988\pi$
$500$	16.4176	+	23.0553i	0.734218	+	1.03106i
$501$	−11.5495	+	11.0124i	−0.515992	+	0.491998i
$502$	−18.1172	+	25.4421i	−0.808611	+	1.13554i
$503$	0.143098	+	0.995270i	0.00638043	+	0.0443769i	0.992763	−	0.120091i	$-0.0383185\pi$
$503$	0.143098	+	0.995270i	0.00638043	+	0.0443769i	−0.986382	+	0.164468i	$0.947409\pi$
$504$	−2.00219	+	1.72952i	−0.0891845	+	0.0770390i
$505$	10.2046			0.454099
$506$	8.28382	+	5.76402i	0.368261	+	0.256242i
$507$	4.47921	−	7.75821i	0.198929	−	0.344554i
$508$	16.1458	−	8.32373i	0.716354	−	0.369306i
$509$	−5.87139	+	4.61732i	−0.260245	+	0.204659i	−0.739753	−	0.672879i	$-0.765058\pi$
$509$	−5.87139	+	4.61732i	−0.260245	+	0.204659i	0.479508	+	0.877538i	$0.340815\pi$
$510$	1.66294	+	3.64133i	0.0736362	+	0.161241i
$511$	3.20022	+	0.157378i	0.141569	+	0.00696201i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−5.89029	−	1.13526i	−0.260063	−	0.0501230i
$514$	−5.07744	−	3.99294i	−0.223956	−	0.176121i
$515$	6.57969	−	27.1219i	0.289936	−	1.19513i
$516$	1.85764	−	5.36729i	0.0817780	−	0.236282i
$517$	23.3255	−	14.9904i	1.02585	−	0.659277i
$518$	−0.820020	+	0.857368i	−0.0360296	+	0.0376706i
$519$	−10.1662	−	11.7324i	−0.446245	−	0.514994i
$520$	−5.97911	−	5.70107i	−0.262201	−	0.250009i
$521$	−25.5806	−	20.1168i	−1.12071	−	0.881333i	−0.126840	−	0.991923i	$-0.540483\pi$
$521$	−25.5806	−	20.1168i	−1.12071	−	0.881333i	−0.993866	+	0.110590i	$0.964726\pi$
$522$	−3.28233	−	9.48367i	−0.143664	−	0.415089i
$523$	4.69269	−	0.448098i	0.205197	−	0.0195939i	0.00804870	−	0.999968i	$-0.497438\pi$
$523$	4.69269	−	0.448098i	0.205197	−	0.0195939i	0.197148	+	0.980374i	$0.436832\pi$
$524$	−1.46686	−	0.430710i	−0.0640802	−	0.0188156i
$525$	−31.1379	+	4.42809i	−1.35897	+	0.193258i
$526$	−2.97201	−	20.6708i	−0.129586	−	0.901289i
$527$	−0.328936	+	6.90521i	−0.0143287	+	0.300796i
$528$	1.05215	−	1.82238i	0.0457889	−	0.0793087i
$529$	7.99394	+	21.5661i	0.347563	+	0.937657i
$530$	−11.8781	−	20.5735i	−0.515952	−	0.893654i
$531$	−8.20701	−	5.27433i	−0.356154	−	0.228886i
$532$	9.83001	−	12.4604i	0.426185	−	0.540226i
$533$	−7.67631	−	16.8088i	−0.332498	−	0.728069i
$534$	−0.565029	−	2.32908i	−0.0244512	−	0.100789i
$535$	3.10112	+	4.35491i	0.134073	+	0.188279i
$536$	2.97974	+	8.60938i	0.128705	+	0.371869i
$537$	−7.54962	+	3.02241i	−0.325790	+	0.130427i
$538$	−31.0047	+	9.10380i	−1.33671	+	0.392493i
$539$	−2.05145	−	14.5865i	−0.0883623	−	0.628286i
$540$	3.45707	−	2.22173i	0.148769	−	0.0956079i
$541$	13.4395	+	6.92852i	0.577808	+	0.297881i	0.722249	−	0.691633i	$-0.243108\pi$
$541$	13.4395	+	6.92852i	0.577808	+	0.297881i	−0.144442	+	0.989513i	$0.546139\pi$
$542$	−3.18539	+	0.613933i	−0.136824	+	0.0263707i
$543$	−2.76091	+	11.3806i	−0.118482	+	0.488389i
$544$	0.904342	−	0.362044i	0.0387733	−	0.0155225i
$545$	47.1666	−	54.4331i	2.02039	−	2.33166i
$546$	5.02907	−	1.73192i	0.215224	−	0.0741194i
$547$	36.2272	+	10.6373i	1.54896	+	0.454817i	0.940791	−	0.338987i	$-0.110084\pi$
$547$	36.2272	+	10.6373i	1.54896	+	0.454817i	0.608174	+	0.793804i	$0.291902\pi$
$548$	−9.63140	+	13.5254i	−0.411433	+	0.577777i
$549$	6.00423	+	2.40373i	0.256254	+	0.102589i
$550$	22.2340	−	11.4624i	0.948059	−	0.488758i
$551$	30.1003	+	52.1353i	1.28232	+	2.22104i
$552$	4.34050	−	2.03963i	0.184744	−	0.0868124i
$553$	6.06576	−	20.5412i	0.257942	−	0.873499i
$554$	4.83520	+	3.10739i	0.205428	+	0.132020i
$555$	1.44847	−	1.13909i	0.0614843	−	0.0483518i
$556$	−3.89921	−	0.372329i	−0.165363	−	0.0157903i
$557$	27.4704	−	26.1930i	1.16396	−	1.10983i	0.171764	−	0.985138i	$-0.445053\pi$
$557$	27.4704	−	26.1930i	1.16396	−	1.10983i	0.992195	−	0.124695i	$-0.0397951\pi$
$558$	7.06457	−	0.674584i	0.299067	−	0.0285574i
$559$	−7.47735	+	8.62933i	−0.316258	+	0.364982i
$560$	1.01685	+	10.8249i	0.0429699	+	0.457435i
$561$	1.96681	−	0.577506i	0.0830386	−	0.0243823i
$562$	2.42498	−	7.00651i	0.102291	−	0.295552i
$563$	−1.77226	−	37.2042i	−0.0746917	−	1.56797i	−0.656299	−	0.754501i	$-0.727879\pi$
$563$	−1.77226	−	37.2042i	−0.0746917	−	1.56797i	0.581607	−	0.813470i	$-0.302424\pi$
$564$	−0.626959	−	13.1615i	−0.0263997	−	0.554198i
$565$	22.9414	−	66.2850i	0.965154	−	2.78863i
$566$	−19.2951	+	5.66555i	−0.811033	+	0.238141i
$567$	0.247444	+	2.63415i	0.0103917	+	0.110624i
$568$	−0.854607	+	0.986269i	−0.0358585	+	0.0413829i
$569$	−32.9958	+	3.15072i	−1.38326	+	0.132085i	−0.759995	−	0.649929i	$-0.774798\pi$
$569$	−32.9958	+	3.15072i	−1.38326	+	0.132085i	−0.623261	+	0.782014i	$0.714192\pi$
$570$	−17.8409	+	17.0113i	−0.747274	+	0.712525i
$571$	2.29087	+	0.218751i	0.0958698	+	0.00915446i	0.142881	−	0.989740i	$-0.454363\pi$
$571$	2.29087	+	0.218751i	0.0958698	+	0.00915446i	−0.0470109	+	0.998894i	$0.514970\pi$
$572$	−3.32533	+	2.61507i	−0.139039	+	0.109342i
$573$	9.67361	+	6.21685i	0.404121	+	0.259713i
$574$	−6.88730	+	23.3232i	−0.287470	+	0.973493i
$575$	56.5148	+	7.49865i	2.35683	+	0.312715i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	33.4428	−	17.2410i	1.39224	−	0.717751i	0.411201	−	0.911545i	$-0.365110\pi$
$577$	33.4428	−	17.2410i	1.39224	−	0.717751i	0.981042	+	0.193794i	$0.0620792\pi$
$578$	−14.9013	−	5.96559i	−0.619813	−	0.248136i
$579$	−11.3706	+	15.9678i	−0.472545	+	0.663597i
$580$	−39.5702	−	11.6189i	−1.64306	−	0.482447i
$581$	27.8027	−	9.57475i	1.15345	−	0.397228i
$582$	6.08074	−	7.01755i	0.252055	−	0.290887i
$583$	−11.2933	+	4.52117i	−0.467722	+	0.187248i
$584$	−0.285511	+	1.17689i	−0.0118145	+	0.0487002i
$585$	−8.11218	+	1.56350i	−0.335397	+	0.0646426i
$586$	15.7675	+	8.12873i	0.651351	+	0.335795i
$587$	26.6939	−	17.1551i	1.10177	−	0.708067i	0.142288	−	0.989825i	$-0.454554\pi$
$587$	26.6939	−	17.1551i	1.10177	−	0.708067i	0.959485	+	0.281759i	$0.0909177\pi$
$588$	−6.49054	−	2.62161i	−0.267665	−	0.108114i
$589$	−40.8465	+	11.9936i	−1.68305	+	0.494189i
$590$	−37.2186	+	14.9001i	−1.53227	+	0.613427i
$591$	0.0142326	+	0.0411225i	0.000585453	+	0.00169155i
$592$	−0.260104	−	0.365265i	−0.0106902	−	0.0150123i
$593$	5.87740	+	24.2270i	0.241356	+	0.994883i	0.955525	+	0.294910i	$0.0952897\pi$
$593$	5.87740	+	24.2270i	0.241356	+	0.994883i	−0.714169	+	0.699973i	$0.753195\pi$
$594$	−0.874157	−	1.91414i	−0.0358671	−	0.0785380i
$595$	−6.55982	+	8.31513i	−0.268926	+	0.340887i
$596$	−5.69819	−	3.66200i	−0.233407	−	0.150001i
$597$	−5.12094	−	8.86973i	−0.209586	−	0.363014i
$598$	−9.62491	+	0.563560i	−0.393592	+	0.0230457i
$599$	−16.3714	+	28.3560i	−0.668915	+	1.15860i	0.309292	+	0.950967i	$0.399908\pi$
$599$	−16.3714	+	28.3560i	−0.668915	+	1.15860i	−0.978208	+	0.207628i	$0.933426\pi$
$600$	0.565627	−	11.8740i	0.0230916	−	0.484753i
$601$	5.08959	+	35.3989i	0.207609	+	1.44395i	0.780929	+	0.624620i	$0.214746\pi$
$601$	5.08959	+	35.3989i	0.207609	+	1.44395i	−0.573320	+	0.819332i	$0.694345\pi$
$602$	14.8773	−	2.11569i	0.606354	−	0.0862289i
$603$	8.74141	+	2.56671i	0.355978	+	0.104525i
$604$	−15.4987	+	1.47995i	−0.630634	+	0.0602182i
$605$	8.83310	+	25.5216i	0.359116	+	1.03760i
$606$	−1.95194	−	1.53502i	−0.0792922	−	0.0623560i
$607$	−1.57325	−	1.50009i	−0.0638560	−	0.0608866i	0.657479	−	0.753473i	$-0.271623\pi$
$607$	−1.57325	−	1.50009i	−0.0638560	−	0.0608866i	−0.721335	+	0.692586i	$0.756471\pi$
$608$	3.92831	+	4.53351i	0.159314	+	0.183858i
$609$	18.3523	−	19.1882i	0.743675	−	0.777546i
$610$	22.3587	−	14.3690i	0.905276	−	0.581786i
$611$	−8.66385	+	25.0325i	−0.350502	+	1.01271i
$612$	0.229658	−	0.946661i	0.00928336	−	0.0382665i
$613$	−11.9873	−	9.42695i	−0.484164	−	0.380751i	0.346032	−	0.938223i	$-0.387529\pi$
$613$	−11.9873	−	9.42695i	−0.484164	−	0.380751i	−0.830196	+	0.557472i	$0.811771\pi$
$614$	−0.107146	−	0.0206507i	−0.00432406	−	0.000833393i
$615$	15.6913	−	34.3591i	0.632734	−	1.38549i
$616$	5.56073	+	0.273462i	0.224048	+	0.0110181i
$617$	15.3289	+	33.5656i	0.617117	+	1.35130i	0.917598	+	0.397510i	$0.130126\pi$
$617$	15.3289	+	33.5656i	0.617117	+	1.35130i	−0.300480	+	0.953788i	$0.597147\pi$
$618$	−5.33836	+	4.19813i	−0.214740	+	0.168874i
$619$	−25.1765	+	12.9794i	−1.01193	+	0.521686i	−0.882704	−	0.469930i	$-0.844279\pi$
$619$	−25.1765	+	12.9794i	−1.01193	+	0.521686i	−0.129225	+	0.991615i	$0.541249\pi$
$620$	14.5817	−	25.2563i	0.585616	−	1.01432i
$621$	0.856303	−	4.71877i	0.0343622	−	0.189358i
$622$	−8.94784			−0.358776
$623$	4.79852	−	4.14504i	0.192249	−	0.166067i
$624$	0.286105	+	1.98991i	0.0114534	+	0.0796600i
$625$	32.9901	−	46.3282i	1.31961	−	1.85313i
$626$	13.3548	−	12.7338i	0.533765	−	0.508944i
$627$	7.32208	+	10.2824i	0.292416	+	0.410640i
$628$	8.02334	+	1.54637i	0.320166	+	0.0617070i
$629$	0.0621641	−	0.432361i	0.00247865	−	0.0172394i
$630$	9.40752	+	5.45074i	0.374805	+	0.217163i
$631$	−20.0209	−	23.1054i	−0.797020	−	0.919810i	0.201194	−	0.979551i	$-0.435518\pi$
$631$	−20.0209	−	23.1054i	−0.797020	−	0.919810i	−0.998214	+	0.0597415i	$0.980972\pi$
$632$	7.19535	+	3.70946i	0.286216	+	0.147554i
$633$	1.18383	+	24.8516i	0.0470530	+	0.987764i
$634$	−7.09119	+	1.36671i	−0.281627	+	0.0542792i
$635$	−54.0255	−	51.5132i	−2.14394	−	2.04424i
$636$	−0.822707	+	5.72205i	−0.0326225	+	0.226894i
$637$	10.1549	+	9.74248i	0.402351	+	0.386011i
$638$	−8.77271	+	19.2096i	−0.347315	+	0.760513i
$639$	0.307670	+	1.26823i	0.0121712	+	0.0501706i
$640$	−4.09082	−	0.390626i	−0.161704	−	0.0154409i
$641$	−4.91288	−	1.96682i	−0.194047	−	0.0776848i	0.272604	−	0.962126i	$-0.412115\pi$
$641$	−4.91288	−	1.96682i	−0.194047	−	0.0776848i	−0.466651	+	0.884442i	$0.654540\pi$
$642$	0.0619025	−	1.29949i	0.00244310	−	0.0512869i
$643$	−27.8706			−1.09911			−0.549555	−	0.835458i	$-0.685203\pi$
$643$	−27.8706			−1.09911			−0.549555	+	0.835458i	$0.685203\pi$
$644$	10.0468	+	7.74999i	0.395898	+	0.305392i
$645$	−23.3402			−0.919020
$646$	−0.278043	+	5.83683i	−0.0109394	+	0.229647i
$647$	15.8205	+	6.33357i	0.621967	+	0.248998i	0.661174	−	0.750233i	$-0.270059\pi$
$647$	15.8205	+	6.33357i	0.621967	+	0.248998i	−0.0392061	+	0.999231i	$0.512483\pi$
$648$	−0.995472	−	0.0950560i	−0.0391058	−	0.00373415i
$649$	4.83987	+	19.9502i	0.189981	+	0.783114i
$650$	−9.92765	+	21.7385i	−0.389394	+	0.852655i
$651$	10.1268	+	15.8111i	0.396902	+	0.619684i
$652$	−1.49975	+	10.4310i	−0.0587349	+	0.408510i
$653$	−9.65537	−	9.20638i	−0.377844	−	0.360274i	0.477231	−	0.878778i	$-0.341641\pi$
$653$	−9.65537	−	9.20638i	−0.377844	−	0.360274i	−0.855075	+	0.518504i	$0.826489\pi$
$654$	−17.2101	+	3.31697i	−0.672968	+	0.129704i
$655$	0.298931	+	6.27534i	0.0116802	+	0.245198i
$656$	−8.16989	−	4.21187i	−0.318980	−	0.164446i
$657$	0.793056	+	0.915236i	0.0309401	+	0.0357067i
$658$	30.2177	−	17.3843i	1.17801	−	0.677710i
$659$	−2.40464	+	16.7246i	−0.0936714	+	0.651499i	0.887848	+	0.460137i	$0.152200\pi$
$659$	−2.40464	+	16.7246i	−0.0936714	+	0.651499i	−0.981519	+	0.191362i	$0.938709\pi$
$660$	−8.49120	−	1.63654i	−0.330519	−	0.0637024i
$661$	−1.36442	−	1.91606i	−0.0530699	−	0.0745262i	0.787188	−	0.616713i	$-0.211536\pi$
$661$	−1.36442	−	1.91606i	−0.0530699	−	0.0745262i	−0.840258	+	0.542187i	$0.817597\pi$
$662$	−10.9508	+	10.4416i	−0.425616	+	0.405824i
$663$	−1.13595	+	1.59522i	−0.0441166	+	0.0619531i
$664$	1.58170	+	11.0010i	0.0613820	+	0.426921i
$665$	−61.6010	−	21.4265i	−2.38879	−	0.830883i
$666$	−0.448412			−0.0173756
$667$	−41.4167	+	24.5169i	−1.60366	+	0.949297i
$668$	7.97909	−	13.8202i	0.308720	−	0.534719i
$669$	0.748812	−	0.386039i	0.0289507	−	0.0149251i
$670$	29.4289	−	23.1431i	1.13694	−	0.894097i
$671$	−5.65362	−	12.3797i	−0.218256	−	0.477913i
$672$	1.43382	−	2.22355i	0.0553109	−	0.0857751i
$673$	3.77351	−	8.26284i	0.145458	−	0.318509i	−0.822854	−	0.568253i	$-0.807619\pi$
$673$	3.77351	−	8.26284i	0.145458	−	0.318509i	0.968312	+	0.249744i	$0.0803466\pi$
$674$	−10.1100	−	1.94855i	−0.389424	−	0.0750552i
$675$	−9.34416	−	7.34833i	−0.359657	−	0.282837i
$676$	−2.11203	+	8.70589i	−0.0812318	+	0.334842i
$677$	−5.32183	+	15.3764i	−0.204534	+	0.590963i	−0.999885	−	0.0151867i	$-0.995166\pi$
$677$	−5.32183	+	15.3764i	−0.204534	+	0.590963i	0.795350	+	0.606150i	$0.207287\pi$
$678$	−14.3591	+	9.22805i	−0.551459	+	0.354401i
$679$	23.8658	+	5.82866i	0.915886	+	0.223684i
$680$	−2.62146	−	3.02533i	−0.100528	−	0.116016i
$681$	−4.91434	−	4.68581i	−0.188318	−	0.179561i
$682$	−11.7386	−	9.23132i	−0.449494	−	0.353486i
$683$	−2.02432	−	5.84889i	−0.0774584	−	0.223801i	0.899623	−	0.436668i	$-0.143841\pi$
$683$	−2.02432	−	5.84889i	−0.0774584	−	0.223801i	−0.977081	+	0.212866i	$0.931720\pi$
$684$	5.97153	−	0.570212i	0.228327	−	0.0218026i
$685$	65.4700	+	19.2237i	2.50148	+	0.734501i
$686$	−1.67538	−	18.4443i	−0.0639664	−	0.704208i
$687$	−0.729398	−	5.07307i	−0.0278283	−	0.193550i
$688$	−0.270250	+	5.67324i	−0.0103032	+	0.216290i
$689$	5.81087	−	10.0647i	0.221376	−	0.383435i
$690$	−13.7546	−	14.1146i	−0.523630	−	0.537332i
$691$	−1.28888	−	2.23241i	−0.0490314	−	0.0849248i	0.840468	−	0.541861i	$-0.182280\pi$
$691$	−1.28888	−	2.23241i	−0.0490314	−	0.0849248i	−0.889499	+	0.456936i	$0.848947\pi$
$692$	13.0597	+	8.39299i	0.496457	+	0.319053i
$693$	3.44829	−	4.37101i	0.130990	−	0.166041i
$694$	1.37752	+	3.01636i	0.0522901	+	0.114499i
$695$	3.79487	+	15.6427i	0.143948	+	0.593361i
$696$	5.82123	+	8.17478i	0.220653	+	0.309864i
$697$	−2.92850	−	8.46135i	−0.110925	−	0.320496i
$698$	10.2291	−	4.09513i	0.387179	−	0.155003i
$699$	5.21897	−	1.53243i	0.197400	−	0.0579618i
$700$	28.6291	−	13.0213i	1.08208	−	0.492158i
$701$	−34.6217	+	22.2500i	−1.30764	+	0.840371i	−0.994022	−	0.109177i	$-0.965178\pi$
$701$	−34.6217	+	22.2500i	−1.30764	+	0.840371i	−0.313621	+	0.949548i	$0.601542\pi$
$702$	1.78689	+	0.921205i	0.0674417	+	0.0347686i
$703$	2.64127	−	0.509064i	0.0996176	−	0.0191997i
$704$	−0.496107	+	2.04498i	−0.0186977	+	0.0770731i
$705$	−50.2688	+	20.1246i	−1.89323	+	0.757937i
$706$	−4.05383	+	4.67837i	−0.152568	+	0.176073i
$707$	1.25330	−	6.44933i	0.0471351	−	0.242552i
$708$	9.36052	+	2.74850i	0.351790	+	0.103295i
$709$	−4.64000	+	6.51596i	−0.174259	+	0.244712i	−0.892463	−	0.451120i	$-0.851025\pi$
$709$	−4.64000	+	6.51596i	−0.174259	+	0.244712i	0.718205	+	0.695832i	$0.244964\pi$
$710$	4.97874	+	1.99319i	0.186849	+	0.0748029i
$711$	7.19535	−	3.70946i	0.269847	−	0.139116i
$712$	1.19832	+	2.07555i	0.0449089	+	0.0777845i
$713$	−9.94355	−	32.5496i	−0.372389	−	1.21899i
$714$	2.50556	−	0.603764i	0.0937683	−	0.0225953i
$715$	14.6249	+	9.39883i	0.546939	+	0.351496i
$716$	6.39229	−	5.02696i	0.238891	−	0.187866i
$717$	17.3678	+	1.65843i	0.648613	+	0.0619350i
$718$	2.81805	−	2.68700i	0.105169	−	0.100278i
$719$	−35.8490	+	3.42317i	−1.33694	+	0.127663i	−0.738908	−	0.673806i	$-0.764658\pi$
$719$	−35.8490	+	3.42317i	−1.33694	+	0.127663i	−0.598036	+	0.801469i	$0.704052\pi$
$720$	−2.69111	+	3.10570i	−0.100292	+	0.115743i
$721$	−16.3330	−	7.48939i	−0.608271	−	0.278919i
$722$	−16.2963	+	4.78504i	−0.606487	+	0.178081i
$723$	4.93391	−	14.2556i	0.183494	−	0.530171i
$724$	−0.557218	−	11.6975i	−0.0207089	−	0.434732i
$725$	5.67642	+	119.163i	0.210817	+	4.42559i
$726$	2.14947	−	6.21048i	0.0797743	−	0.230493i
$727$	−34.2177	+	10.0472i	−1.26907	+	0.372631i	−0.845861	−	0.533403i	$-0.820913\pi$
$727$	−34.2177	+	10.0472i	−1.26907	+	0.372631i	−0.423204	+	0.906034i	$0.639095\pi$
$728$	−4.33742	+	3.07862i	−0.160755	+	0.114101i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	4.95411	−	0.473060i	0.183360	−	0.0175087i
$731$	−4.00419	+	3.81799i	−0.148100	+	0.141213i
$732$	−6.43823	−	0.614776i	−0.237964	−	0.0227228i
$733$	6.34825	−	4.99232i	0.234478	−	0.184396i	−0.494006	−	0.869459i	$-0.664468\pi$
$733$	6.34825	−	4.99232i	0.234478	−	0.184396i	0.728484	+	0.685063i	$0.240225\pi$
$734$	−9.55866	−	6.14298i	−0.352817	−	0.226741i
$735$	−1.45712	+	28.7291i	−0.0537466	+	1.05969i
$736$	−3.59005	+	3.17987i	−0.132331	+	0.117212i
$737$	−9.58555	−	16.6027i	−0.353088	−	0.611567i
$738$	−8.16989	+	4.21187i	−0.300738	+	0.155041i
$739$	2.86304	+	1.14619i	0.105319	+	0.0421632i	0.423723	−	0.905792i	$-0.360723\pi$
$739$	2.86304	+	1.14619i	0.105319	+	0.0421632i	−0.318405	+	0.947955i	$0.603147\pi$
$740$	−1.06888	+	1.50103i	−0.0392929	+	0.0551791i
$741$	−11.5711	−	3.39758i	−0.425075	−	0.124813i
$742$	−14.4613	+	4.98021i	−0.530890	+	0.182829i
$743$	−24.7830	+	28.6011i	−0.909200	+	1.04927i	0.0893794	+	0.995998i	$0.471512\pi$
$743$	−24.7830	+	28.6011i	−0.909200	+	1.04927i	−0.998580	+	0.0532755i	$0.983034\pi$
$744$	−6.58835	+	2.63758i	−0.241541	+	0.0966983i
$745$	−6.56236	+	27.0504i	−0.240426	+	0.991050i
$746$	−14.3324	+	2.76234i	−0.524746	+	0.101136i
$747$	9.87862	+	5.09278i	0.361440	+	0.186335i
$748$	−1.72443	+	1.10823i	−0.0630516	+	0.0405208i
$749$	3.13318	−	1.42506i	0.114484	−	0.0520704i
$750$	−27.1570	+	7.97400i	−0.991632	+	0.291169i
$751$	−2.72880	+	1.09245i	−0.0995752	+	0.0398639i	−0.420915	−	0.907100i	$-0.638291\pi$
$751$	−2.72880	+	1.09245i	−0.0995752	+	0.0398639i	0.321340	+	0.946964i	$0.395867\pi$
$752$	4.30958	+	12.4517i	0.157154	+	0.454067i
$753$	−18.1172	−	25.4421i	−0.660228	−	0.927161i
$754$	−4.75651	−	19.6066i	−0.173222	−	0.714030i
$755$	26.5785	+	58.1988i	0.967291	+	2.11807i
$756$	−0.979548	−	2.45774i	−0.0356258	−	0.0893871i
$757$	−2.14092	−	1.37589i	−0.0778131	−	0.0500075i	0.501156	−	0.865357i	$-0.332908\pi$
$757$	−2.14092	−	1.37589i	−0.0778131	−	0.0500075i	−0.578969	+	0.815350i	$0.696545\pi$
$758$	6.40247	+	11.0894i	0.232548	+	0.402785i
$759$	−8.15638	+	5.94299i	−0.296058	+	0.215717i
$760$	12.3256	−	21.3486i	0.447097	−	0.774395i
$761$	−0.0398989	+	0.837580i	−0.00144633	+	0.0303623i	−0.999475	−	0.0323953i	$-0.989686\pi$
$761$	−0.0398989	+	0.837580i	−0.00144633	+	0.0303623i	0.998029	+	0.0627575i	$0.0199895\pi$
$762$	2.58516	+	17.9802i	0.0936506	+	0.651354i
$763$	−28.6089	−	36.4946i	−1.03571	−	1.32119i
$764$	−11.0333	−	3.23965i	−0.399169	−	0.117207i
$765$	−3.98496	+	0.380517i	−0.144076	+	0.0137576i
$766$	9.61602	+	27.7837i	0.347441	+	1.00387i
$767$	−15.4165	−	12.1237i	−0.556658	−	0.437761i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	10.6088	+	12.2433i	0.382565	+	0.441503i	0.914073	−	0.405550i	$-0.132920\pi$
$769$	10.6088	+	12.2433i	0.382565	+	0.441503i	−0.531508	+	0.847053i	$0.678374\pi$
$770$	−6.41200	−	21.9622i	−0.231073	−	0.791462i
$771$	5.43400	−	3.49222i	0.195701	−	0.125769i
$772$	6.41136	−	18.5244i	0.230750	−	0.666708i
$773$	−6.70966	+	27.6576i	−0.241330	+	0.994774i	0.714215	+	0.699927i	$0.246784\pi$
$773$	−6.70966	+	27.6576i	−0.241330	+	0.994774i	−0.955544	+	0.294848i	$0.904731\pi$
$774$	4.46452	+	3.51094i	0.160474	+	0.126198i
$775$	−82.8371	−	15.9655i	−2.97560	−	0.573499i
$776$	−3.85736	+	8.44643i	−0.138471	+	0.303209i
$777$	−0.542011	−	1.05534i	−0.0194445	−	0.0378600i
$778$	−11.4050	−	24.9736i	−0.408891	−	0.895346i
$779$	43.3414	−	34.0841i	1.55287	−	1.22119i
$780$	7.34310	−	3.78563i	0.262925	−	0.135547i
$781$	1.37308	−	2.37824i	0.0491325	−	0.0851000i
$782$	−4.66857	−	0.171481i	−0.166948	−	0.00613213i
$783$	10.0356			0.358644
$784$	6.96622	+	0.686823i	0.248794	+	0.0245294i
$785$	−4.77867	−	33.2364i	−0.170558	−	1.18626i
$786$	0.886784	−	1.24531i	0.0316306	−	0.0444189i
$787$	−33.2015	+	31.6576i	−1.18351	+	1.12847i	−0.194454	+	0.980912i	$0.562293\pi$
$787$	−33.2015	+	31.6576i	−1.18351	+	1.12847i	−0.989053	+	0.147560i	$0.952858\pi$
$788$	−0.0252417	−	0.0354470i	−0.000899198	−	0.00126275i
$789$	20.5060	+	3.95220i	0.730031	+	0.140702i
$790$	4.73438	−	32.9283i	0.168442	−	1.17154i
$791$	−39.0746	−	22.6399i	−1.38933	−	0.804983i
$792$	1.37802	+	1.59032i	0.0489659	+	0.0565096i
$793$	11.5567	+	5.95790i	0.410391	+	0.211571i
$794$	1.10689	+	23.2364i	0.0392820	+	0.824630i
$795$	23.3269	−	4.49589i	0.827320	−	0.159453i
$796$	7.41240	+	7.06771i	0.262726	+	0.250508i
$797$	−1.19977	+	8.34460i	−0.0424981	+	0.295581i	0.957477	+	0.288510i	$0.0931598\pi$
$797$	−1.19977	+	8.34460i	−0.0424981	+	0.295581i	−0.999975	+	0.00707087i	$0.997749\pi$
$798$	8.55999	+	13.3648i	0.303020	+	0.473107i
$799$	−5.33202	+	11.6755i	−0.188633	+	0.413049i
$800$	2.80257	+	11.5523i	0.0990858	+	0.408437i
$801$	2.38579	+	0.227815i	0.0842976	+	0.00804945i
$802$	−1.99369	−	0.798151i	−0.0703995	−	0.0281837i
$803$	0.121256	−	2.54548i	0.00427904	−	0.0898281i
$804$	−9.11045			−0.321301
$805$	16.5929	−	49.4323i	0.584823	−	1.74226i
$806$	14.2670			0.502533
$807$	1.53754	−	32.2770i	0.0541241	−	1.13620i
$808$	2.30534	+	0.922919i	0.0811015	+	0.0324682i
$809$	12.9647	+	1.23798i	0.455814	+	0.0435250i	0.320438	−	0.947269i	$-0.396170\pi$
$809$	12.9647	+	1.23798i	0.455814	+	0.0435250i	0.135376	+	0.990794i	$0.456776\pi$
$810$	0.968835	+	3.99359i	0.0340414	+	0.140321i
$811$	−20.5932	+	45.0928i	−0.723124	+	1.58342i	0.0863500	+	0.996265i	$0.472480\pi$
$811$	−20.5932	+	45.0928i	−0.723124	+	1.58342i	−0.809474	+	0.587156i	$0.800248\pi$
$812$	−12.2030	+	23.5814i	−0.428241	+	0.827545i
$813$	0.461671	−	3.21099i	0.0161915	−	0.112614i
$814$	0.682909	+	0.651153i	0.0239360	+	0.0228229i
$815$	42.5238	−	8.19578i	1.48954	−	0.287086i
$816$	0.0463505	+	0.973017i	0.00162259	+	0.0340624i
$817$	−30.2832	−	15.6121i	−1.05947	−	0.546197i
$818$	3.01276	+	3.47691i	0.105339	+	0.121567i
$819$	−0.00818027	+	5.31893i	−0.000285842	+	0.185859i
$820$	−5.37560	+	37.3881i	−0.187724	+	1.30565i
$821$	−55.6468	−	10.7250i	−1.94209	−	0.374307i	−0.999145	−	0.0413500i	$-0.986834\pi$
$821$	−55.6468	−	10.7250i	−1.94209	−	0.374307i	−0.942942	−	0.332957i	$-0.891954\pi$
$822$	−9.63140	−	13.5254i	−0.335934	−	0.471753i
$823$	−23.7283	+	22.6249i	−0.827118	+	0.788655i	−0.979876	−	0.199609i	$-0.936033\pi$
$823$	−23.7283	+	22.6249i	−0.827118	+	0.788655i	0.152758	+	0.988264i	$0.451184\pi$
$824$	3.93937	−	5.53206i	0.137234	−	0.192719i
$825$	3.55996	+	24.7601i	0.123942	+	0.862036i
$826$	4.84581	+	25.3522i	0.168607	+	0.882115i
$827$	41.5802			1.44588			0.722942	−	0.690908i	$-0.242789\pi$
$827$	41.5802			1.44588			0.722942	+	0.690908i	$0.242789\pi$
$828$	0.507814	+	4.76887i	0.0176477	+	0.165730i
$829$	−6.16547	+	10.6789i	−0.214135	+	0.370893i	−0.953005	−	0.302955i	$-0.902027\pi$
$829$	−6.16547	+	10.6789i	−0.214135	+	0.370893i	0.738869	+	0.673849i	$0.235360\pi$
$830$	40.5955	−	20.9285i	1.40909	−	0.726437i
$831$	−4.51793	+	3.55294i	−0.156725	+	0.123250i
$832$	−0.835138	−	1.82870i	−0.0289532	−	0.0633986i
$833$	4.44952	+	5.16705i	0.154167	+	0.179028i
$834$	1.62716	−	3.56298i	0.0563439	−	0.123376i
$835$	−64.3939	−	12.4109i	−2.22844	−	0.429497i
$836$	−9.92238	−	7.80304i	−0.343173	−	0.269874i
$837$	−1.67311	+	6.89666i	−0.0578312	+	0.238383i
$838$	−10.4108	+	30.0801i	−0.359636	+	1.03910i
$839$	−10.3426	+	6.64681i	−0.357068	+	0.229474i	−0.706860	−	0.707354i	$-0.749889\pi$
$839$	−10.3426	+	6.64681i	−0.357068	+	0.229474i	0.349792	+	0.936827i	$0.386252\pi$
$840$	−10.5621	−	2.57954i	−0.364427	−	0.0890027i
$841$	−46.9625	−	54.1976i	−1.61940	−	1.86888i
$842$	4.88386	+	4.65675i	0.168309	+	0.160482i
$843$	5.82802	+	4.58321i	0.200728	+	0.157854i
$844$	−8.13739	−	23.5114i	−0.280100	−	0.809297i
$845$	36.6473	−	3.49939i	1.26071	−	0.120383i
$846$	12.6427	+	3.71222i	0.434664	+	0.127629i
$847$	17.2145	−	2.44806i	0.591497	−	0.0841162i
$848$	−0.822707	−	5.72205i	−0.0282519	−	0.196496i
$849$	0.956856	−	20.0869i	0.0328392	−	0.689380i
$850$	−5.78990	+	10.0284i	−0.198592	+	0.343971i
$851$	0.429948	+	2.10709i	0.0147384	+	0.0722301i
$852$	−0.652510	−	1.13018i	−0.0223546	−	0.0387194i
$853$	−18.9032	−	12.1483i	−0.647232	−	0.415951i	0.175422	−	0.984493i	$-0.443871\pi$
$853$	−18.9032	−	12.1483i	−0.647232	−	0.415951i	−0.822654	+	0.568543i	$0.807507\pi$
$854$	−6.33524	−	15.8955i	−0.216787	−	0.543932i
$855$	−10.2405	−	22.4235i	−0.350217	−	0.766869i
$856$	0.306714	+	1.26429i	0.0104833	+	0.0432127i
$857$	2.86136	+	4.01821i	0.0977420	+	0.137259i	0.860551	−	0.509365i	$-0.170120\pi$
$857$	2.86136	+	4.01821i	0.0977420	+	0.137259i	−0.762809	+	0.646624i	$0.776180\pi$
$858$	−1.38363	−	3.99775i	−0.0472365	−	0.136481i
$859$	34.0787	−	13.6431i	1.16275	−	0.465495i	0.291615	−	0.956536i	$-0.405808\pi$
$859$	34.0787	−	13.6431i	1.16275	−	0.465495i	0.871137	+	0.491041i	$0.163383\pi$
$860$	22.3948	−	6.57570i	0.763656	−	0.224230i
$861$	−19.7879	−	14.1368i	−0.674368	−	0.481780i
$862$	12.6576	−	8.13455i	0.431120	−	0.277064i
$863$	27.0798	+	13.9606i	0.921806	+	0.475224i	0.852709	−	0.522386i	$-0.174958\pi$
$863$	27.0798	+	13.9606i	0.921806	+	0.475224i	0.0690966	+	0.997610i	$0.477988\pi$
$864$	0.981929	−	0.189251i	0.0334059	−	0.00643846i
$865$	15.0403	−	61.9971i	0.511387	−	2.10797i
$866$	2.06339	−	0.826056i	0.0701167	−	0.0280705i
$867$	10.5112	−	12.1306i	0.356980	−	0.411977i
$868$	−14.1711	−	12.3175i	−0.480999	−	0.418085i
$869$	−16.3448	−	4.79927i	−0.554459	−	0.162804i
$870$	23.9220	−	33.5937i	0.811030	−	1.13893i
$871$	17.0034	+	6.80714i	0.576139	+	0.230651i
$872$	15.5785	−	8.03126i	0.527553	−	0.271973i
$873$	4.64278	+	8.04152i	0.157134	+	0.272164i
$874$	−8.40508	−	27.5135i	−0.284306	−	0.930659i
$875$	−51.5924	−	54.2754i	−1.74414	−	1.83484i
$876$	−1.01878	−	0.654732i	−0.0344215	−	0.0221214i
$877$	−30.9616	+	24.3485i	−1.04550	+	0.822190i	−0.984401	−	0.175941i	$-0.943703\pi$
$877$	−30.9616	+	24.3485i	−1.04550	+	0.822190i	−0.0610995	+	0.998132i	$0.519461\pi$
$878$	14.1032	+	1.34669i	0.475959	+	0.0454486i
$879$	−12.8387	+	12.2417i	−0.433039	+	0.412902i
$880$	8.60831	−	0.821994i	0.290186	−	0.0277094i
$881$	−2.51610	+	2.90373i	−0.0847695	+	0.0978292i	−0.796550	−	0.604573i	$-0.793344\pi$
$881$	−2.51610	+	2.90373i	−0.0847695	+	0.0978292i	0.711780	+	0.702402i	$0.247889\pi$
$882$	4.60028	−	5.27612i	0.154899	−	0.177656i
$883$	−35.1411	+	10.3183i	−1.18259	+	0.347240i	−0.813172	−	0.582023i	$-0.802261\pi$
$883$	−35.1411	+	10.3183i	−1.18259	+	0.347240i	−0.369419	+	0.929263i	$0.620443\pi$
$884$	0.640511	−	1.85063i	0.0215427	−	0.0622436i
$885$	−1.90758	−	40.0450i	−0.0641225	−	1.34610i
$886$	0.250963	+	5.26836i	0.00843127	+	0.176994i
$887$	7.85971	−	22.7091i	0.263903	−	0.762498i	−0.732731	−	0.680519i	$-0.761755\pi$
$887$	7.85971	−	22.7091i	0.263903	−	0.762498i	0.996634	−	0.0819796i	$-0.0261242\pi$
$888$	0.430248	−	0.126332i	0.0144382	−	0.00423943i
$889$	−39.1916	+	27.8175i	−1.31445	+	0.932969i
$890$	6.44961	−	7.44325i	0.216191	−	0.249498i
$891$	2.09477	−	0.200026i	0.0701774	−	0.00670113i
$892$	−0.609720	+	0.581367i	−0.0204149	+	0.0194656i
$893$	−78.6833	−	7.51334i	−2.63304	−	0.251424i
$894$	5.32429	−	4.18707i	0.178071	−	0.140037i
$895$	−28.1134	−	18.0674i	−0.939728	−	0.603926i
$896$	−0.749298	+	2.53743i	−0.0250323	+	0.0847696i
$897$	2.61544	−	9.27987i	0.0873268	−	0.309846i
$898$	8.58577	+	14.8710i	0.286511	+	0.496251i
$899$	63.3027	−	32.6348i	2.11126	−	1.08843i
$900$	11.0359	+	4.41811i	0.367864	+	0.147270i
$901$	3.26647	−	4.58711i	0.108822	−	0.152819i
$902$	18.5585	+	5.44928i	0.617931	+	0.181441i
$903$	−2.86657	+	14.7510i	−0.0953934	+	0.490884i
$904$	11.1776	−	12.8997i	0.371763	−	0.429037i
$905$	−44.6772	+	17.8860i	−1.48512	+	0.594552i
$906$	3.67058	−	15.1303i	0.121947	−	0.502672i
$907$	4.60859	−	0.888232i	0.153026	−	0.0294933i	−0.112163	−	0.993690i	$-0.535778\pi$
$907$	4.60859	−	0.888232i	0.153026	−	0.0294933i	0.265189	+	0.964197i	$0.414566\pi$
$908$	6.03542	+	3.11148i	0.200293	+	0.103258i
$909$	2.08902	−	1.34253i	0.0692883	−	0.0445289i
$910$	17.7853	+	12.7061i	0.589578	+	0.421205i
$911$	37.5450	−	11.0242i	1.24392	−	0.365249i	0.407435	−	0.913234i	$-0.366423\pi$
$911$	37.5450	−	11.0242i	1.24392	−	0.365249i	0.836488	+	0.547986i	$0.184605\pi$
$912$	−5.56899	+	2.22949i	−0.184408	+	0.0738258i
$913$	−7.64927	−	22.1011i	−0.253154	−	0.731440i
$914$	1.81099	+	2.54318i	0.0599023	+	0.0841209i
$915$	6.26595	+	25.8286i	0.207146	+	0.853868i
$916$	2.12910	+	4.66208i	0.0703475	+	0.154040i
$917$	4.00273	+	0.581791i	0.132182	+	0.0192124i
$918$	0.819482	+	0.526649i	0.0270469	+	0.0173820i
$919$	−0.150779	−	0.261157i	−0.00497373	−	0.00861476i	0.863528	−	0.504301i	$-0.168250\pi$
$919$	−0.150779	−	0.261157i	−0.00497373	−	0.00861476i	−0.868502	+	0.495686i	$0.834917\pi$
$920$	17.1740	+	9.66770i	0.566210	+	0.318735i
$921$	0.0545589	−	0.0944988i	0.00179778	−	0.00311384i
$922$	0.562366	−	11.8055i	0.0185205	−	0.388794i
$923$	0.373373	+	2.59687i	0.0122897	+	0.0854770i
$924$	−2.07716	+	5.16545i	−0.0683335	+	0.169931i
$925$	5.11454	+	1.50177i	0.168165	+	0.0493778i
$926$	7.24003	−	0.691339i	0.237922	−	0.0227188i
$927$	−2.22123	−	6.41782i	−0.0729548	−	0.210789i
$928$	−7.88853	−	6.20361i	−0.258954	−	0.203643i
$929$	34.2078	+	32.6171i	1.12232	+	1.07013i	0.996952	+	0.0780230i	$0.0248607\pi$
$929$	34.2078	+	32.6171i	1.12232	+	1.07013i	0.125371	+	0.992110i	$0.459988\pi$
$930$	19.0980	+	22.0402i	0.626247	+	0.722728i
$931$	−21.1072	+	36.3004i	−0.691760	+	1.18970i
$932$	−4.57583	+	2.94071i	−0.149886	+	0.0963262i
$933$	2.92655	−	8.45572i	0.0958110	−	0.276828i
$934$	6.24599	−	25.7463i	0.204375	−	0.842445i
$935$	6.62146	+	5.20717i	0.216545	+	0.170293i
$936$	−1.97404	−	0.380465i	−0.0645235	−	0.0124359i
$937$	7.92638	−	17.3564i	0.258944	−	0.567007i	−0.734852	−	0.678227i	$-0.762749\pi$
$937$	7.92638	−	17.3564i	0.258944	−	0.567007i	0.993796	+	0.111220i	$0.0354758\pi$
$938$	−11.0121	−	21.4414i	−0.359559	−	0.700088i
$939$	7.66550	+	16.7851i	0.250154	+	0.547761i
$940$	42.5628	−	33.4718i	1.38825	−	1.09173i
$941$	−18.1435	+	9.35363i	−0.591461	+	0.304920i	−0.727851	−	0.685736i	$-0.759481\pi$
$941$	−18.1435	+	9.35363i	−0.591461	+	0.304920i	0.136389	+	0.990655i	$0.456450\pi$
$942$	−4.08550	+	7.07629i	−0.133113	+	0.230558i
$943$	27.6251	+	34.3519i	0.899596	+	1.11865i
$944$	−9.75569			−0.317521
$945$	−8.22786	+	7.10735i	−0.267652	+	0.231202i
$946$	−1.70091	−	11.8301i	−0.0553012	−	0.384629i
$947$	32.3917	−	45.4878i	1.05259	−	1.47816i	0.183806	−	0.982962i	$-0.441158\pi$
$947$	32.3917	−	45.4878i	1.05259	−	1.47816i	0.868783	−	0.495193i	$-0.164903\pi$
$948$	−5.85881	+	5.58637i	−0.190285	+	0.181437i
$949$	1.41222	+	1.98318i	0.0458425	+	0.0643768i
$950$	−70.0204	−	13.4953i	−2.27176	−	0.437846i
$951$	1.02775	−	7.14819i	0.0333272	−	0.231796i
$952$	−2.23397	+	1.28521i	−0.0724034	+	0.0416538i
$953$	0.369257	+	0.426145i	0.0119614	+	0.0138042i	0.761699	−	0.647931i	$-0.224366\pi$
$953$	0.369257	+	0.426145i	0.0119614	+	0.0138042i	−0.749737	+	0.661736i	$0.769820\pi$
$954$	−5.13826	−	2.64896i	−0.166357	−	0.0857632i
$955$	2.24846	+	47.2010i	0.0727585	+	1.52739i
$956$	−17.1315	+	3.30183i	−0.554073	+	0.106789i
$957$	−15.2838	−	14.5730i	−0.494054	−	0.471080i
$958$	−0.316988	+	2.20470i	−0.0102414	+	0.0712307i
$959$	20.1902	−	39.0161i	0.651977	−	1.25990i
$960$	1.70712	−	3.73807i	0.0550971	−	0.120646i
$961$	4.56504	+	18.8174i	0.147260	+	0.607012i
$962$	−0.897391	−	0.0856905i	−0.0289331	−	0.00276277i
$963$	1.20778	+	0.483520i	0.0389200	+	0.0155812i
$964$	−0.717786	+	15.0682i	−0.0231183	+	0.485313i
$965$	−80.5553			−2.59317
$966$	−10.6097	+	6.95944i	−0.341362	+	0.223916i
$967$	12.2606			0.394274			0.197137	−	0.980376i	$-0.436836\pi$
$967$	12.2606			0.394274			0.197137	+	0.980376i	$0.436836\pi$
$968$	−0.312705	+	6.56449i	−0.0100507	+	0.210991i
$969$	−5.42487	−	2.17179i	−0.174272	−	0.0697680i
$970$	37.9856	+	3.62718i	1.21964	+	0.116462i
$971$	8.62603	+	35.5570i	0.276822	+	1.14108i	0.925115	+	0.379686i	$0.123968\pi$
$971$	8.62603	+	35.5570i	0.276822	+	1.14108i	−0.648293	+	0.761391i	$0.724517\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	10.3523	−	0.477183i	0.331879	−	0.0152978i
$974$	5.94051	−	41.3172i	0.190346	−	1.32389i
$975$	−17.2959	−	16.4916i	−0.553912	−	0.528154i
$976$	6.35064	−	1.22398i	0.203279	−	0.0391788i
$977$	2.36845	+	49.7198i	0.0757733	+	1.59068i	0.642181	+	0.766553i	$0.278030\pi$
$977$	2.36845	+	49.7198i	0.0757733	+	1.59068i	−0.566408	+	0.824125i	$0.691667\pi$
$978$	−9.36680	−	4.82892i	−0.299517	−	0.154412i
$979$	−3.30262	−	3.81143i	−0.105552	−	0.121814i
$980$	−6.69583	−	27.9759i	−0.213890	−	0.893657i
$981$	2.49433	−	17.3484i	0.0796378	−	0.553893i
$982$	16.1992	+	3.12214i	0.516937	+	0.0996315i
$983$	21.9319	+	30.7991i	0.699520	+	0.982338i	0.999596	+	0.0284230i	$0.00904854\pi$
$983$	21.9319	+	30.7991i	0.699520	+	0.982338i	−0.300076	+	0.953915i	$0.597012\pi$
$984$	6.65233	−	6.34298i	0.212068	−	0.202207i
$985$	−0.103729	+	0.145667i	−0.00330508	+	0.00464134i
$986$	−1.39126	−	9.67640i	−0.0443066	−	0.308159i
$987$	6.54493	+	34.2416i	0.208327	+	1.08992i
$988$	12.0596			0.383667
$989$	12.2172	−	24.3452i	0.388485	−	0.774132i
$990$	4.32373	−	7.48893i	0.137417	−	0.238014i
$991$	−13.7463	+	7.08672i	−0.436666	+	0.225117i	−0.662520	−	0.749044i	$-0.730513\pi$
$991$	−13.7463	+	7.08672i	−0.436666	+	0.225117i	0.225854	+	0.974161i	$0.427483\pi$
$992$	5.57839	−	4.38689i	0.177114	−	0.139284i
$993$	−6.28565	−	13.7637i	−0.199469	−	0.436776i
$994$	1.87117	−	2.90177i	0.0593498	−	0.0920386i
$995$	17.4841	−	38.2849i	0.554284	−	1.21371i
$996$	−10.9133	−	2.10336i	−0.345800	−	0.0666475i
$997$	−13.8613	−	10.9007i	−0.438992	−	0.345228i	0.374073	−	0.927399i	$-0.377961\pi$
$997$	−13.8613	−	10.9007i	−0.438992	−	0.345228i	−0.813066	+	0.582172i	$0.802203\pi$
$998$	2.09115	−	8.61986i	0.0661943	−	0.272857i
$999$	0.146661	−	0.423749i	0.00464015	−	0.0134068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.25.8	✓	160
7.2	even	3	inner	966.2.y.d.163.8	yes	160
23.12	even	11	inner	966.2.y.d.403.8	yes	160
161.58	even	33	inner	966.2.y.d.541.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.25.8	✓	160	1.1	even	1	trivial
966.2.y.d.163.8	yes	160	7.2	even	3	inner
966.2.y.d.403.8	yes	160	23.12	even	11	inner
966.2.y.d.541.8	yes	160	161.58	even	33	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.968835 + 3.99359i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64295 - 0.121825i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(0.0475819 - 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.968835 + 3.99359i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64295 - 0.121825i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(4.03517 - 0.777715i) q^{10} +(-0.100127 - 2.10191i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(1.31651 + 1.51934i) q^{13} +(0.00406904 - 2.64575i) q^{14} +(-0.584833 + 4.06760i) q^{15} +(0.981929 + 0.189251i) q^{16} +(0.565045 + 0.793495i) q^{17} +(0.723734 - 0.690079i) q^{18} +(-3.47958 + 4.88639i) q^{19} +(-0.584833 - 4.06760i) q^{20} +(2.49890 + 0.869185i) q^{21} -2.10430 q^{22} +(-3.93662 - 2.73917i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-10.5660 + 5.44714i) q^{25} +(1.58026 - 1.24273i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.64256 - 0.129954i) q^{28} +(4.16895 - 9.12872i) q^{29} +(4.03517 + 0.777715i) q^{30} +(5.57839 + 4.38689i) q^{31} +(0.235759 - 0.971812i) q^{32} +(0.688248 - 1.98856i) q^{33} +(0.819482 - 0.526649i) q^{34} +(3.04710 + 10.4368i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.324531 - 0.309440i) q^{37} +(4.71529 + 3.70815i) q^{38} +(0.657528 + 1.89980i) q^{39} +(-4.09082 + 0.390626i) q^{40} +(-8.81935 - 2.58959i) q^{41} +(0.987103 - 2.45472i) q^{42} +(0.808301 + 5.62186i) q^{43} +(-0.100127 + 2.10191i) q^{44} +(-2.05472 + 3.55887i) q^{45} +(-2.92338 + 3.80183i) q^{46} +(6.58820 + 11.4111i) q^{47} +(0.841254 + 0.540641i) q^{48} +(6.97032 - 0.643955i) q^{49} +(4.93822 + 10.8132i) q^{50} +(0.229658 + 0.946661i) q^{51} +(-1.16613 - 1.63760i) q^{52} +(-1.89075 - 5.46295i) q^{53} +(0.928368 - 0.371662i) q^{54} +(8.29719 - 2.43627i) q^{55} +(-0.255545 + 2.63338i) q^{56} +(-5.04642 + 3.24314i) q^{57} +(-8.92002 - 4.59859i) q^{58} +(-9.57940 + 1.84628i) q^{59} +(0.968835 - 3.99359i) q^{60} +(6.00423 - 2.40373i) q^{61} +(4.64735 - 5.36333i) q^{62} +(1.99686 + 1.73567i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-4.79213 + 6.72960i) q^{65} +(-1.95356 - 0.782088i) q^{66} +(8.09769 - 4.17465i) q^{67} +(-0.487060 - 0.843613i) q^{68} +(-2.63659 - 4.00605i) q^{69} +(10.5700 - 2.54704i) q^{70} +(1.09785 + 0.705547i) q^{71} +(-0.786053 + 0.618159i) q^{72} +(1.20555 + 0.115116i) q^{73} +(-0.324531 + 0.309440i) q^{74} +(-11.8336 + 1.12997i) q^{75} +(3.92831 - 4.53351i) q^{76} +(-0.520695 - 5.54305i) q^{77} +(1.92894 - 0.566387i) q^{78} +(2.64770 - 7.65003i) q^{79} +(0.195535 + 4.10478i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-3.00630 + 8.68614i) q^{82} +(10.6639 - 3.13121i) q^{83} +(-2.40497 - 1.10278i) q^{84} +(-2.62146 + 3.02533i) q^{85} +(5.65395 - 0.539887i) q^{86} +(7.26312 - 6.92537i) q^{87} +(2.09477 + 0.200026i) q^{88} +(1.88389 - 1.48150i) q^{89} +(3.45707 + 2.22173i) q^{90} +(3.66456 + 3.85514i) q^{91} +(3.65842 + 3.10096i) q^{92} +(3.54835 + 6.14592i) q^{93} +(11.7117 - 6.03778i) q^{94} +(-22.8854 - 9.16193i) q^{95} +(0.580057 - 0.814576i) q^{96} +(8.90942 + 2.61604i) q^{97} +(-0.311565 - 6.99306i) q^{98} +(1.37802 - 1.59032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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