LMFDB - Embedded newform 96.2.o.a.35.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(11,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("96.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.o (of order $8$, degree $4$, 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:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			35.13
Character	$\chi$	$=$	96.35
Dual form			96.2.o.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12377 + 0.858568i) q^{2} +(1.25135 - 1.19755i) q^{3} +(0.525721 + 1.92967i) q^{4} +(-2.18808 + 0.906333i) q^{5} +(2.43441 - 0.271409i) q^{6} +(-1.93241 - 1.93241i) q^{7} +(-1.06596 + 2.61987i) q^{8} +(0.131733 - 2.99711i) q^{9} +O(q^{10})$	\(q+(1.12377 + 0.858568i) q^{2} +(1.25135 - 1.19755i) q^{3} +(0.525721 + 1.92967i) q^{4} +(-2.18808 + 0.906333i) q^{5} +(2.43441 - 0.271409i) q^{6} +(-1.93241 - 1.93241i) q^{7} +(-1.06596 + 2.61987i) q^{8} +(0.131733 - 2.99711i) q^{9} +(-3.23705 - 0.860107i) q^{10} +(1.42447 - 0.590036i) q^{11} +(2.96874 + 1.78510i) q^{12} +(-0.110405 + 0.266541i) q^{13} +(-0.512479 - 3.83069i) q^{14} +(-1.65266 + 3.75448i) q^{15} +(-3.44724 + 2.02893i) q^{16} -6.17031 q^{17} +(2.72126 - 3.25496i) q^{18} +(7.34269 + 3.04144i) q^{19} +(-2.89924 - 3.74579i) q^{20} +(-4.73227 - 0.103949i) q^{21} +(2.10737 + 0.559943i) q^{22} +(1.85295 + 1.85295i) q^{23} +(1.80355 + 4.55491i) q^{24} +(0.430727 - 0.430727i) q^{25} +(-0.352914 + 0.204741i) q^{26} +(-3.42435 - 3.90817i) q^{27} +(2.71300 - 4.74481i) q^{28} +(2.11574 - 5.10784i) q^{29} +(-5.08069 + 2.80025i) q^{30} -3.42046i q^{31} +(-5.61588 - 0.679633i) q^{32} +(1.07591 - 2.44422i) q^{33} +(-6.93401 - 5.29763i) q^{34} +(5.97967 + 2.47686i) q^{35} +(5.85267 - 1.32144i) q^{36} +(2.52377 + 6.09293i) q^{37} +(5.64022 + 9.72209i) q^{38} +(0.181042 + 0.465751i) q^{39} +(-0.0420633 - 6.69861i) q^{40} +(-0.753641 + 0.753641i) q^{41} +(-5.22874 - 4.17979i) q^{42} +(1.57129 + 3.79343i) q^{43} +(1.88745 + 2.43857i) q^{44} +(2.42813 + 6.67731i) q^{45} +(0.491405 + 3.67317i) q^{46} -1.54798i q^{47} +(-1.88393 + 6.66714i) q^{48} +0.468394i q^{49} +(0.853846 - 0.114230i) q^{50} +(-7.72119 + 7.38927i) q^{51} +(-0.572378 - 0.0729187i) q^{52} +(5.12700 + 12.3777i) q^{53} +(-0.492750 - 7.33193i) q^{54} +(-2.58210 + 2.58210i) q^{55} +(7.12253 - 3.00278i) q^{56} +(12.8305 - 4.98737i) q^{57} +(6.76303 - 3.92353i) q^{58} +(-3.08775 - 7.45449i) q^{59} +(-8.11374 - 1.21529i) q^{60} +(-4.28571 - 1.77520i) q^{61} +(2.93670 - 3.84381i) q^{62} +(-6.04619 + 5.53707i) q^{63} +(-5.72745 - 5.58537i) q^{64} -0.683277i q^{65} +(3.30761 - 1.82300i) q^{66} +(-0.531731 + 1.28371i) q^{67} +(-3.24386 - 11.9066i) q^{68} +(4.53768 + 0.0996750i) q^{69} +(4.59322 + 7.91738i) q^{70} +(8.72539 - 8.72539i) q^{71} +(7.71161 + 3.53993i) q^{72} +(-2.73022 - 2.73022i) q^{73} +(-2.39505 + 9.01389i) q^{74} +(0.0231699 - 1.05481i) q^{75} +(-2.00877 + 15.7679i) q^{76} +(-3.89285 - 1.61247i) q^{77} +(-0.196429 + 0.678834i) q^{78} -2.76080 q^{79} +(5.70394 - 7.56381i) q^{80} +(-8.96529 - 0.789635i) q^{81} +(-1.49397 + 0.199867i) q^{82} +(2.53133 - 6.11116i) q^{83} +(-2.28726 - 9.18636i) q^{84} +(13.5011 - 5.59235i) q^{85} +(-1.49115 + 5.61200i) q^{86} +(-3.46939 - 8.92538i) q^{87} +(0.0273838 + 4.36089i) q^{88} +(4.14369 + 4.14369i) q^{89} +(-3.00426 + 9.58848i) q^{90} +(0.728413 - 0.301719i) q^{91} +(-2.60144 + 4.54970i) q^{92} +(-4.09618 - 4.28017i) q^{93} +(1.32905 - 1.73957i) q^{94} -18.8230 q^{95} +(-7.84130 + 5.87486i) q^{96} -10.3656 q^{97} +(-0.402149 + 0.526368i) q^{98} +(-1.58075 - 4.34703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9	$ 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 16 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 24 q^{22} + 16 q^{24} - 8 q^{25} - 28 q^{27} - 8 q^{28} + 44 q^{30} - 8 q^{33} - 24 q^{34} + 48 q^{36} - 8 q^{37} - 28 q^{39} + 24 q^{40} + 56 q^{42} - 8 q^{43} - 4 q^{45} + 24 q^{46} + 48 q^{48} - 16 q^{51} + 48 q^{52} + 40 q^{54} + 24 q^{55} - 4 q^{57} + 96 q^{58} + 8 q^{60} - 40 q^{61} + 40 q^{64} - 28 q^{66} + 56 q^{67} - 4 q^{69} + 40 q^{70} - 64 q^{72} - 8 q^{73} + 16 q^{75} + 48 q^{76} - 92 q^{78} + 16 q^{79} - 48 q^{82} - 136 q^{84} - 48 q^{85} + 52 q^{87} - 48 q^{88} - 136 q^{90} + 40 q^{91} + 8 q^{93} - 64 q^{94} - 104 q^{96} - 16 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 - 16 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 40 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 - 24 * q^22 + 16 * q^24 - 8 * q^25 - 28 * q^27 - 8 * q^28 + 44 * q^30 - 8 * q^33 - 24 * q^34 + 48 * q^36 - 8 * q^37 - 28 * q^39 + 24 * q^40 + 56 * q^42 - 8 * q^43 - 4 * q^45 + 24 * q^46 + 48 * q^48 - 16 * q^51 + 48 * q^52 + 40 * q^54 + 24 * q^55 - 4 * q^57 + 96 * q^58 + 8 * q^60 - 40 * q^61 + 40 * q^64 - 28 * q^66 + 56 * q^67 - 4 * q^69 + 40 * q^70 - 64 * q^72 - 8 * q^73 + 16 * q^75 + 48 * q^76 - 92 * q^78 + 16 * q^79 - 48 * q^82 - 136 * q^84 - 48 * q^85 + 52 * q^87 - 48 * q^88 - 136 * q^90 + 40 * q^91 + 8 * q^93 - 64 * q^94 - 104 * q^96 - 16 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.12377	+	0.858568i	0.794626	+	0.607100i
$2$	1.12377	+	0.858568i	0.794626	+	0.607100i
$3$	1.25135	−	1.19755i	0.722465	−	0.691408i
$3$	1.25135	−	1.19755i	0.722465	−	0.691408i
$4$	0.525721	+	1.92967i	0.262860	+	0.964834i
$5$	−2.18808	+	0.906333i	−0.978540	+	0.405324i	−0.813884	−	0.581027i	$-0.802651\pi$
$5$	−2.18808	+	0.906333i	−0.978540	+	0.405324i	−0.164655	+	0.986351i	$0.552651\pi$
$6$	2.43441	−	0.271409i	0.993842	−	0.110802i
$7$	−1.93241	−	1.93241i	−0.730381	−	0.730381i	0.240314	−	0.970695i	$-0.422750\pi$
$7$	−1.93241	−	1.93241i	−0.730381	−	0.730381i	−0.970695	+	0.240314i	$0.922750\pi$
$8$	−1.06596	+	2.61987i	−0.376875	+	0.926264i
$9$	0.131733	−	2.99711i	0.0439110	−	0.999035i
$10$	−3.23705	−	0.860107i	−1.02365	−	0.271990i
$11$	1.42447	−	0.590036i	0.429495	−	0.177903i	−0.157454	−	0.987526i	$-0.550329\pi$
$11$	1.42447	−	0.590036i	0.429495	−	0.177903i	0.586949	+	0.809624i	$0.300329\pi$
$12$	2.96874	+	1.78510i	0.857001	+	0.515315i
$13$	−0.110405	+	0.266541i	−0.0306208	+	0.0739252i	−0.938450	−	0.345414i	$-0.887738\pi$
$13$	−0.110405	+	0.266541i	−0.0306208	+	0.0739252i	0.907829	+	0.419340i	$0.137738\pi$
$14$	−0.512479	−	3.83069i	−0.136966	−	1.02379i
$15$	−1.65266	+	3.75448i	−0.426716	+	0.969402i
$16$	−3.44724	+	2.02893i	−0.861809	+	0.507233i
$17$	−6.17031			−1.49652			−0.748260	−	0.663406i	$-0.769110\pi$
$17$	−6.17031			−1.49652			−0.748260	+	0.663406i	$0.769110\pi$
$18$	2.72126	−	3.25496i	0.641407	−	0.767201i
$19$	7.34269	+	3.04144i	1.68453	+	0.697755i	0.999526	−	0.0307845i	$-0.00980057\pi$
$19$	7.34269	+	3.04144i	1.68453	+	0.697755i	0.685004	+	0.728540i	$0.259801\pi$
$20$	−2.89924	−	3.74579i	−0.648290	−	0.837585i
$21$	−4.73227	−	0.103949i	−1.03267	−	0.0226836i
$22$	2.10737	+	0.559943i	0.449292	+	0.119380i
$23$	1.85295	+	1.85295i	0.386366	+	0.386366i	0.873389	−	0.487023i	$-0.161917\pi$
$23$	1.85295	+	1.85295i	0.386366	+	0.386366i	−0.487023	+	0.873389i	$0.661917\pi$
$24$	1.80355	+	4.55491i	0.368148	+	0.929767i
$25$	0.430727	−	0.430727i	0.0861453	−	0.0861453i
$26$	−0.352914	+	0.204741i	−0.0692121	+	0.0401530i
$27$	−3.42435	−	3.90817i	−0.659017	−	0.752128i
$28$	2.71300	−	4.74481i	0.512708	−	0.896685i
$29$	2.11574	−	5.10784i	0.392882	−	0.948501i	−0.596427	−	0.802667i	$-0.703413\pi$
$29$	2.11574	−	5.10784i	0.392882	−	0.948501i	0.989309	−	0.145834i	$-0.0465866\pi$
$30$	−5.08069	+	2.80025i	−0.927603	+	0.511253i
$31$		−	3.42046i		−	0.614332i	−0.951656	−	0.307166i	$-0.900619\pi$
$31$		−	3.42046i		−	0.614332i	0.951656	−	0.307166i	$-0.0993807\pi$
$32$	−5.61588	−	0.679633i	−0.992757	−	0.120143i
$33$	1.07591	−	2.44422i	0.187292	−	0.425485i
$34$	−6.93401	−	5.29763i	−1.18917	−	0.908536i
$35$	5.97967	+	2.47686i	1.01075	+	0.418666i
$36$	5.85267	−	1.32144i	0.975446	−	0.220240i
$37$	2.52377	+	6.09293i	0.414906	+	1.00167i	0.983801	+	0.179262i	$0.0573709\pi$
$37$	2.52377	+	6.09293i	0.414906	+	1.00167i	−0.568895	+	0.822410i	$0.692629\pi$
$38$	5.64022	+	9.72209i	0.914964	+	1.57713i
$39$	0.181042	+	0.465751i	0.0289900	+	0.0745798i
$40$	−0.0420633	−	6.69861i	−0.00665079	−	1.05914i
$41$	−0.753641	+	0.753641i	−0.117699	+	0.117699i	−0.763503	−	0.645804i	$-0.776522\pi$
$41$	−0.753641	+	0.753641i	−0.117699	+	0.117699i	0.645804	+	0.763503i	$0.276522\pi$
$42$	−5.22874	−	4.17979i	−0.806812	−	0.644956i
$43$	1.57129	+	3.79343i	0.239619	+	0.578492i	0.997243	−	0.0741989i	$-0.0236400\pi$
$43$	1.57129	+	3.79343i	0.239619	+	0.578492i	−0.757624	+	0.652691i	$0.773640\pi$
$44$	1.88745	+	2.43857i	0.284544	+	0.367628i
$45$	2.42813	+	6.67731i	0.361965	+	0.995394i
$46$	0.491405	+	3.67317i	0.0724538	+	0.541579i
$47$		−	1.54798i		−	0.225796i	−0.993607	−	0.112898i	$-0.963987\pi$
$47$		−	1.54798i		−	0.225796i	0.993607	−	0.112898i	$-0.0360133\pi$
$48$	−1.88393	+	6.66714i	−0.271922	+	0.962319i
$49$			0.468394i			0.0669135i
$50$	0.853846	−	0.114230i	0.120752	−	0.0161545i
$51$	−7.72119	+	7.38927i	−1.08118	+	1.03471i
$52$	−0.572378	−	0.0729187i	−0.0793745	−	0.0101120i
$53$	5.12700	+	12.3777i	0.704248	+	1.70020i	0.713897	+	0.700251i	$0.246928\pi$
$53$	5.12700	+	12.3777i	0.704248	+	1.70020i	−0.00964932	+	0.999953i	$0.503072\pi$
$54$	−0.492750	−	7.33193i	−0.0670548	−	0.997749i
$55$	−2.58210	+	2.58210i	−0.348170	+	0.348170i
$56$	7.12253	−	3.00278i	0.951788	−	0.401264i
$57$	12.8305	−	4.98737i	1.69945	−	0.660593i
$58$	6.76303	−	3.92353i	0.888029	−	0.515185i
$59$	−3.08775	−	7.45449i	−0.401991	−	0.970492i	−0.987182	−	0.159597i	$-0.948981\pi$
$59$	−3.08775	−	7.45449i	−0.401991	−	0.970492i	0.585191	−	0.810895i	$-0.301019\pi$
$60$	−8.11374	−	1.21529i	−1.04748	−	0.156893i
$61$	−4.28571	−	1.77520i	−0.548728	−	0.227291i	0.0910552	−	0.995846i	$-0.470976\pi$
$61$	−4.28571	−	1.77520i	−0.548728	−	0.227291i	−0.639784	+	0.768555i	$0.720976\pi$
$62$	2.93670	−	3.84381i	0.372961	−	0.488164i
$63$	−6.04619	+	5.53707i	−0.761748	+	0.697605i
$64$	−5.72745	−	5.58537i	−0.715931	−	0.698171i
$65$		−	0.683277i		−	0.0847501i
$66$	3.30761	−	1.82300i	0.407138	−	0.224396i
$67$	−0.531731	+	1.28371i	−0.0649613	+	0.156831i	−0.953026	−	0.302887i	$-0.902049\pi$
$67$	−0.531731	+	1.28371i	−0.0649613	+	0.156831i	0.888065	+	0.459718i	$0.152049\pi$
$68$	−3.24386	−	11.9066i	−0.393376	−	1.44389i
$69$	4.53768	+	0.0996750i	0.546272	+	0.0119995i
$70$	4.59322	+	7.91738i	0.548995	+	0.946307i
$71$	8.72539	−	8.72539i	1.03551	−	1.03551i	0.0361678	−	0.999346i	$-0.488485\pi$
$71$	8.72539	−	8.72539i	1.03551	−	1.03551i	0.999346	−	0.0361678i	$-0.0115151\pi$
$72$	7.71161	+	3.53993i	0.908822	+	0.417184i
$73$	−2.73022	−	2.73022i	−0.319548	−	0.319548i	0.529046	−	0.848593i	$-0.322550\pi$
$73$	−2.73022	−	2.73022i	−0.319548	−	0.319548i	−0.848593	+	0.529046i	$0.822550\pi$
$74$	−2.39505	+	9.01389i	−0.278419	+	1.04784i
$75$	0.0231699	−	1.05481i	0.00267543	−	0.121799i
$76$	−2.00877	+	15.7679i	−0.230422	+	1.80870i
$77$	−3.89285	−	1.61247i	−0.443632	−	0.183758i
$78$	−0.196429	+	0.678834i	−0.0222412	+	0.0768629i
$79$	−2.76080			−0.310614			−0.155307	−	0.987866i	$-0.549637\pi$
$79$	−2.76080			−0.310614			−0.155307	+	0.987866i	$0.549637\pi$
$80$	5.70394	−	7.56381i	0.637720	−	0.845660i
$81$	−8.96529	−	0.789635i	−0.996144	−	0.0877372i
$82$	−1.49397	+	0.199867i	−0.164982	+	0.0220716i
$83$	2.53133	−	6.11116i	0.277849	−	0.670787i	−0.721927	−	0.691970i	$-0.756743\pi$
$83$	2.53133	−	6.11116i	0.277849	−	0.670787i	0.999776	+	0.0211827i	$0.00674318\pi$
$84$	−2.28726	−	9.18636i	−0.249561	−	1.00231i
$85$	13.5011	−	5.59235i	1.46440	−	0.606576i
$86$	−1.49115	+	5.61200i	−0.160795	+	0.605158i
$87$	−3.46939	−	8.92538i	−0.371958	−	0.956901i
$88$	0.0273838	+	4.36089i	0.00291913	+	0.464873i
$89$	4.14369	+	4.14369i	0.439230	+	0.439230i	0.891753	−	0.452523i	$-0.149476\pi$
$89$	4.14369	+	4.14369i	0.439230	+	0.439230i	−0.452523	+	0.891753i	$0.649476\pi$
$90$	−3.00426	+	9.58848i	−0.316677	+	1.01071i
$91$	0.728413	−	0.301719i	0.0763585	−	0.0316287i
$92$	−2.60144	+	4.54970i	−0.271219	+	0.474339i
$93$	−4.09618	−	4.28017i	−0.424754	−	0.443833i
$94$	1.32905	−	1.73957i	0.137081	−	0.179423i
$95$	−18.8230			−1.93120
$96$	−7.84130	+	5.87486i	−0.800300	+	0.599600i
$97$	−10.3656			−1.05246			−0.526232	−	0.850341i	$-0.676396\pi$
$97$	−10.3656			−1.05246			−0.526232	+	0.850341i	$0.676396\pi$
$98$	−0.402149	+	0.526368i	−0.0406231	+	0.0531712i
$99$	−1.58075	−	4.34703i	−0.158872	−	0.436893i
$100$	1.05760	+	0.604717i	0.105760	+	0.0604717i
$101$	−10.5700	+	4.37825i	−1.05176	+	0.435652i	−0.840519	−	0.541783i	$-0.817750\pi$
$101$	−10.5700	+	4.37825i	−1.05176	+	0.435652i	−0.211238	+	0.977435i	$0.567750\pi$
$102$	−15.0210	+	1.67468i	−1.48730	+	0.165818i
$103$	−10.4823	−	10.4823i	−1.03285	−	1.03285i	−0.999442	−	0.0334101i	$-0.989363\pi$
$103$	−10.4823	−	10.4823i	−1.03285	−	1.03285i	−0.0334101	−	0.999442i	$-0.510637\pi$
$104$	−0.580616	−	0.573370i	−0.0569341	−	0.0562235i
$105$	10.4488	−	4.06156i	1.01970	−	0.396368i
$106$	−4.86551	+	18.3115i	−0.472580	+	1.77857i
$107$	−9.39578	+	3.89186i	−0.908325	+	0.376240i	−0.787415	−	0.616423i	$-0.788581\pi$
$107$	−9.39578	+	3.89186i	−0.908325	+	0.376240i	−0.120910	+	0.992664i	$0.538581\pi$
$108$	5.74122	−	8.66247i	0.552450	−	0.833546i
$109$	3.00588	−	7.25683i	0.287911	−	0.695078i	−0.712064	−	0.702114i	$-0.752240\pi$
$109$	3.00588	−	7.25683i	0.287911	−	0.695078i	0.999975	+	0.00703600i	$0.00223965\pi$
$110$	−5.11859	+	0.684777i	−0.488038	+	0.0652910i
$111$	10.4547	+	4.60201i	0.992318	+	0.436803i
$112$	10.5822	+	2.74074i	0.999923	+	0.258975i
$113$	13.6372			1.28288			0.641438	−	0.767175i	$-0.278338\pi$
$113$	13.6372			1.28288			0.641438	+	0.767175i	$0.278338\pi$
$114$	18.7006	+	5.41124i	1.75147	+	0.506809i
$115$	−5.73378	−	2.37501i	−0.534678	−	0.221471i
$116$	10.9687	+	1.39737i	1.01842	+	0.129743i
$117$	0.784308	+	0.366008i	0.0725093	+	0.0338374i
$118$	2.93027	−	11.0282i	0.269753	−	1.01523i
$119$	11.9235	+	11.9235i	1.09303	+	1.09303i
$120$	−8.07457	−	8.33190i	−0.737104	−	0.760595i
$121$	−6.09719	+	6.09719i	−0.554290	+	0.554290i
$122$	−3.29202	−	5.67449i	−0.298046	−	0.513744i
$123$	−0.0405404	+	1.84559i	−0.00365540	+	0.166411i
$124$	6.60035	−	1.79821i	0.592729	−	0.161484i
$125$	3.97958	−	9.60756i	0.355945	−	0.859326i
$126$	−11.5485	+	1.03133i	−1.02882	+	0.0918778i
$127$			7.75395i			0.688052i	0.938960	+	0.344026i	$0.111791\pi$
$127$			7.75395i			0.688052i	−0.938960	+	0.344026i	$0.888209\pi$
$128$	−1.64092	−	11.1941i	−0.145038	−	0.989426i
$129$	6.50906	+	2.86519i	0.573090	+	0.252266i
$130$	0.586640	−	0.767847i	0.0514518	−	0.0673446i
$131$	−1.16782	−	0.483728i	−0.102033	−	0.0422635i	0.331083	−	0.943602i	$-0.392586\pi$
$131$	−1.16782	−	0.483728i	−0.102033	−	0.0422635i	−0.433116	+	0.901338i	$0.642586\pi$
$132$	5.28217	+	0.791169i	0.459753	+	0.0688625i
$133$	−8.31177	−	20.0664i	−0.720722	−	1.73998i
$134$	−1.69970	+	0.986071i	−0.146832	+	0.0851836i
$135$	11.0349	+	5.44780i	0.949730	+	0.468872i
$136$	6.57732	−	16.1654i	0.564000	−	1.38617i
$137$	−7.54494	+	7.54494i	−0.644608	+	0.644608i	−0.951685	−	0.307077i	$-0.900649\pi$
$137$	−7.54494	+	7.54494i	−0.644608	+	0.644608i	0.307077	+	0.951685i	$0.400649\pi$
$138$	5.01373	+	4.00792i	0.426797	+	0.341177i
$139$	0.412435	+	0.995705i	0.0349822	+	0.0844546i	0.940405	−	0.340056i	$-0.110446\pi$
$139$	0.412435	+	0.995705i	0.0349822	+	0.0844546i	−0.905423	+	0.424511i	$0.860446\pi$
$140$	−1.63588	+	12.8409i	−0.138257	+	1.08525i
$141$	−1.85379	−	1.93706i	−0.156117	−	0.163130i
$142$	17.2967	−	2.31399i	1.45151	−	0.194186i
$143$			0.444824i			0.0371980i
$144$	5.62681	+	10.5990i	0.468901	+	0.883251i
$145$			13.0939i			1.08739i
$146$	−0.724059	−	5.41221i	−0.0599236	−	0.447918i
$147$	0.560927	+	0.586123i	0.0462645	+	0.0483426i
$148$	−10.4305	+	8.07323i	−0.857384	+	0.663615i
$149$	−0.458938	−	1.10798i	−0.0375977	−	0.0907689i	0.903965	−	0.427606i	$-0.140643\pi$
$149$	−0.458938	−	1.10798i	−0.0375977	−	0.0907689i	−0.941563	+	0.336837i	$0.890643\pi$
$150$	0.931661	−	1.16547i	0.0760698	−	0.0951600i
$151$	9.80869	−	9.80869i	0.798220	−	0.798220i	−0.184595	−	0.982815i	$-0.559097\pi$
$151$	9.80869	−	9.80869i	0.798220	−	0.798220i	0.982815	+	0.184595i	$0.0590974\pi$
$152$	−15.7952	+	15.9948i	−1.28116	+	1.29735i
$153$	−0.812833	+	18.4931i	−0.0657136	+	1.49508i
$154$	−2.99026	−	5.15433i	−0.240962	−	0.415348i
$155$	3.10007	+	7.48424i	0.249004	+	0.601148i
$156$	−0.803567	+	0.594207i	−0.0643368	+	0.0475746i
$157$	8.28207	+	3.43055i	0.660981	+	0.273787i	0.687851	−	0.725852i	$-0.258554\pi$
$157$	8.28207	+	3.43055i	0.660981	+	0.273787i	−0.0268702	+	0.999639i	$0.508554\pi$
$158$	−3.10250	−	2.37033i	−0.246822	−	0.188574i
$159$	21.2386	+	9.34890i	1.68433	+	0.741416i
$160$	12.9040	−	3.60276i	1.02015	−	0.284824i
$161$		−	7.16129i		−	0.564389i
$162$	−9.39698	−	8.58469i	−0.738296	−	0.674477i
$163$	−1.15049	+	2.77752i	−0.0901131	+	0.217552i	−0.962510	−	0.271246i	$-0.912564\pi$
$163$	−1.15049	+	2.77752i	−0.0901131	+	0.217552i	0.872397	+	0.488798i	$0.162564\pi$
$164$	−1.85048	−	1.05807i	−0.144498	−	0.0826215i
$165$	−0.138898	+	6.32329i	−0.0108132	+	0.492267i
$166$	8.09148	−	4.69423i	0.628020	−	0.364343i
$167$	−1.86833	+	1.86833i	−0.144576	+	0.144576i	−0.775690	−	0.631114i	$-0.782598\pi$
$167$	−1.86833	+	1.86833i	−0.144576	+	0.144576i	0.631114	+	0.775690i	$0.282598\pi$
$168$	5.31676	−	12.2871i	0.410197	−	0.947973i
$169$	9.13353	+	9.13353i	0.702579	+	0.702579i
$170$	19.9736	+	5.30713i	1.53191	+	0.407038i
$171$	10.0828	−	21.6062i	0.771051	−	1.65227i
$172$	−6.49399	+	5.02635i	−0.495162	+	0.383255i
$173$	−9.59196	−	3.97312i	−0.729263	−	0.302071i	−0.0130138	−	0.999915i	$-0.504143\pi$
$173$	−9.59196	−	3.97312i	−0.729263	−	0.302071i	−0.716249	+	0.697845i	$0.754143\pi$
$174$	3.76425	−	13.0088i	0.285367	−	0.986193i
$175$	−1.66468			−0.125838
$176$	−3.71335	+	4.92416i	−0.279904	+	0.371172i
$177$	−12.7910	−	5.63040i	−0.961430	−	0.423207i
$178$	1.09892	+	8.21420i	0.0823672	+	0.615680i
$179$	0.00532113	−	0.0128464i	0.000397720	−	0.000960181i	−0.923681	−	0.383163i	$-0.874835\pi$
$179$	0.00532113	−	0.0128464i	0.000397720	−	0.000960181i	0.924078	+	0.382203i	$0.124835\pi$
$180$	−11.6085	+	8.19589i	−0.865244	+	0.610886i
$181$	−9.45181	+	3.91507i	−0.702547	+	0.291005i	−0.705217	−	0.708992i	$-0.749150\pi$
$181$	−9.45181	+	3.91507i	−0.702547	+	0.291005i	0.00266940	+	0.999996i	$0.499150\pi$
$182$	1.07762	+	0.286330i	0.0798782	+	0.0212242i
$183$	−7.48879	+	2.91097i	−0.553588	+	0.215185i
$184$	−6.82965	+	2.87931i	−0.503489	+	0.212266i
$185$	−11.0444	−	11.0444i	−0.812004	−	0.812004i
$186$	−0.928343	−	8.32678i	−0.0680694	−	0.610549i
$187$	−8.78944	+	3.64071i	−0.642748	+	0.266235i
$188$	2.98709	−	0.813805i	0.217856	−	0.0593528i
$189$	−0.934943	+	14.1694i	−0.0680071	+	1.03067i
$190$	−21.1527	−	16.1608i	−1.53458	−	1.17243i
$191$	7.77941			0.562898			0.281449	−	0.959576i	$-0.409185\pi$
$191$	7.77941			0.562898			0.281449	+	0.959576i	$0.409185\pi$
$192$	−13.8558	−	0.130302i	−0.999956	−	0.00940375i
$193$	−6.23528			−0.448825			−0.224413	−	0.974494i	$-0.572046\pi$
$193$	−6.23528			−0.448825			−0.224413	+	0.974494i	$0.572046\pi$
$194$	−11.6485	−	8.89956i	−0.836316	−	0.638951i
$195$	−0.818261	−	0.855016i	−0.0585969	−	0.0612290i
$196$	−0.903846	+	0.246245i	−0.0645604	+	0.0175889i
$197$	6.90773	−	2.86128i	0.492156	−	0.203858i	−0.122781	−	0.992434i	$-0.539181\pi$
$197$	6.90773	−	2.86128i	0.492156	−	0.203858i	0.614937	+	0.788576i	$0.289181\pi$
$198$	1.95582	−	6.24224i	0.138994	−	0.443617i
$199$	12.4517	+	12.4517i	0.882681	+	0.882681i	0.993806	−	0.111125i	$-0.0354455\pi$
$199$	12.4517	+	12.4517i	0.882681	+	0.882681i	−0.111125	+	0.993806i	$0.535445\pi$
$200$	0.669310	+	1.58759i	0.0473274	+	0.112259i
$201$	0.871935	+	2.24315i	0.0615015	+	0.158219i
$202$	−15.6373	−	4.15494i	−1.10024	−	0.292341i
$203$	−13.9589	+	5.78196i	−0.979721	+	0.405814i
$204$	−18.3180	−	11.0146i	−1.28252	−	0.771179i
$205$	0.965978	−	2.33208i	0.0674668	−	0.162879i
$206$	−2.77993	−	20.7795i	−0.193687	−	1.44777i
$207$	5.79757	−	5.30938i	0.402959	−	0.369028i
$208$	−0.160202	−	1.14283i	−0.0111080	−	0.0792413i
$209$	12.2540			0.847630
$210$	15.2292	+	4.40675i	1.05091	+	0.304095i
$211$	−1.16851	−	0.484011i	−0.0804432	−	0.0333207i	0.342099	−	0.939664i	$-0.388862\pi$
$211$	−1.16851	−	0.484011i	−0.0804432	−	0.0333207i	−0.422542	+	0.906343i	$0.638862\pi$
$212$	−21.1894	+	16.4006i	−1.45530	+	1.12640i
$213$	0.469362	−	21.3676i	0.0321602	−	1.46408i
$214$	−13.9001	−	3.69336i	−0.950194	−	0.252473i
$215$	−6.87622	−	6.87622i	−0.468954	−	0.468954i
$216$	13.8891	−	4.80539i	0.945036	−	0.326965i
$217$	−6.60972	+	6.60972i	−0.448697	+	0.448697i
$218$	9.60840	−	5.57426i	0.650763	−	0.377536i
$219$	−6.68602	−	0.146866i	−0.451800	−	0.00992426i
$220$	−6.34005	−	3.62512i	−0.427446	−	0.244406i
$221$	0.681233	−	1.64464i	0.0458247	−	0.110631i
$222$	7.79757	+	14.1477i	0.523339	+	0.949531i
$223$		−	10.5047i		−	0.703449i	−0.936104	−	0.351724i	$-0.885595\pi$
$223$		−	10.5047i		−	0.703449i	0.936104	−	0.351724i	$-0.114405\pi$
$224$	9.53884	+	12.1655i	0.637340	+	0.812841i
$225$	−1.23419	−	1.34767i	−0.0822795	−	0.0898450i
$226$	15.3250	+	11.7084i	1.01941	+	0.778833i
$227$	16.7869	+	6.95334i	1.11418	+	0.461509i	0.862376	−	0.506268i	$-0.168975\pi$
$227$	16.7869	+	6.95334i	1.11418	+	0.461509i	0.251806	+	0.967778i	$0.418975\pi$
$228$	16.3692	+	22.1367i	1.08408	+	1.46604i
$229$	5.87646	+	14.1870i	0.388327	+	0.937505i	0.990295	+	0.138984i	$0.0443838\pi$
$229$	5.87646	+	14.1870i	0.388327	+	0.937505i	−0.601967	+	0.798521i	$0.705616\pi$
$230$	−4.40435	−	7.59181i	−0.290414	−	0.500589i
$231$	−6.80233	+	2.64414i	−0.447560	+	0.173972i
$232$	11.1266	+	10.9877i	0.730496	+	0.721379i
$233$	2.54073	−	2.54073i	0.166449	−	0.166449i	−0.618968	−	0.785416i	$-0.712449\pi$
$233$	2.54073	−	2.54073i	0.166449	−	0.166449i	0.785416	+	0.618968i	$0.212449\pi$
$234$	0.567140	+	1.08469i	0.0370751	+	0.0709085i
$235$	1.40298	+	3.38711i	0.0915206	+	0.220950i
$236$	12.7614	−	9.87732i	0.830696	−	0.642959i
$237$	−3.45471	+	3.30620i	−0.224408	+	0.214761i
$238$	3.16215	+	23.6365i	0.204972	+	1.53213i
$239$		−	17.6107i		−	1.13914i	−0.821943	−	0.569570i	$-0.807110\pi$
$239$		−	17.6107i		−	1.13914i	0.821943	−	0.569570i	$-0.192890\pi$
$240$	−1.92046	−	16.2957i	−0.123965	−	1.05188i
$241$			6.18628i			0.398493i	0.979949	+	0.199247i	$0.0638495\pi$
$241$			6.18628i			0.398493i	−0.979949	+	0.199247i	$0.936151\pi$
$242$	−12.0867	+	1.61699i	−0.776963	+	0.103944i
$243$	−12.1643	+	9.74831i	−0.780341	+	0.625354i
$244$	1.17246	−	9.20325i	0.0750589	−	0.589177i
$245$	−0.424521	−	1.02489i	−0.0271217	−	0.0654775i
$246$	−1.63012	+	2.03921i	−0.103933	+	0.130015i
$247$	−1.62134	+	1.62134i	−0.103163	+	0.103163i
$248$	8.96116	+	3.64608i	0.569034	+	0.231526i
$249$	−4.15088	−	10.6786i	−0.263051	−	0.676727i
$250$	12.7209	−	7.37995i	0.804539	−	0.466749i
$251$	9.18840	+	22.1828i	0.579967	+	1.40016i	0.892842	+	0.450369i	$0.148708\pi$
$251$	9.18840	+	22.1828i	0.579967	+	1.40016i	−0.312876	+	0.949794i	$0.601292\pi$
$252$	−13.8633	−	8.75619i	−0.873306	−	0.551588i
$253$	3.73278	+	1.54617i	0.234678	+	0.0972067i
$254$	−6.65729	+	8.71366i	−0.417716	+	0.546744i
$255$	10.1975	−	23.1663i	0.638589	−	1.45073i
$256$	7.76687	−	13.9884i	0.485429	−	0.874276i
$257$			11.8836i			0.741276i	0.928777	+	0.370638i	$0.120861\pi$
$257$			11.8836i			0.741276i	−0.928777	+	0.370638i	$0.879139\pi$
$258$	4.85473	+	8.80828i	0.302242	+	0.548380i
$259$	6.89706	−	16.6510i	0.428563	−	1.03464i
$260$	1.31850	−	0.359213i	0.0817698	−	0.0222774i
$261$	−15.0300	−	7.01395i	−0.930335	−	0.434153i
$262$	−0.897051	−	1.54626i	−0.0554200	−	0.0955280i
$263$	−11.6191	+	11.6191i	−0.716464	+	0.716464i	−0.967879	−	0.251415i	$-0.919104\pi$
$263$	−11.6191	+	11.6191i	−0.716464	+	0.716464i	0.251415	+	0.967879i	$0.419104\pi$
$264$	5.25667	+	5.42419i	0.323526	+	0.333836i
$265$	−22.4366	−	22.4366i	−1.37827	−	1.37827i
$266$	7.88784	−	29.6862i	0.483635	−	1.82018i
$267$	10.1475	+	0.222900i	0.621015	+	0.0136413i
$268$	−2.75668	−	0.351190i	−0.168391	−	0.0214524i
$269$	13.7480	+	5.69459i	0.838228	+	0.347205i	0.760155	−	0.649742i	$-0.225123\pi$
$269$	13.7480	+	5.69459i	0.838228	+	0.347205i	0.0780733	+	0.996948i	$0.475123\pi$
$270$	7.72335	+	15.5963i	0.470028	+	0.949158i
$271$	7.07297			0.429652			0.214826	−	0.976652i	$-0.431081\pi$
$271$	7.07297			0.429652			0.214826	+	0.976652i	$0.431081\pi$
$272$	21.2705	−	12.5191i	1.28971	−	0.759084i
$273$	0.550173	−	1.24987i	0.0332980	−	0.0756455i
$274$	−14.9566	+	2.00093i	−0.903563	+	0.120881i
$275$	0.359414	−	0.867703i	0.0216735	−	0.0523245i
$276$	2.19321	+	8.80861i	0.132016	+	0.530216i
$277$	−1.13397	+	0.469705i	−0.0681335	+	0.0282218i	−0.416490	−	0.909140i	$-0.636740\pi$
$277$	−1.13397	+	0.469705i	−0.0681335	+	0.0282218i	0.348356	+	0.937362i	$0.386740\pi$
$278$	−0.391399	+	1.47305i	−0.0234746	+	0.0883475i
$279$	−10.2515	−	0.450587i	−0.613740	−	0.0269759i
$280$	−12.8632	+	13.0257i	−0.768720	+	0.778436i
$281$	−12.0212	−	12.0212i	−0.717122	−	0.717122i	0.250893	−	0.968015i	$-0.419276\pi$
$281$	−12.0212	−	12.0212i	−0.717122	−	0.717122i	−0.968015	+	0.250893i	$0.919276\pi$
$282$	−0.420136	−	3.76841i	−0.0250187	−	0.224406i
$283$	12.8158	−	5.30848i	0.761821	−	0.315557i	0.0322666	−	0.999479i	$-0.489727\pi$
$283$	12.8158	−	5.30848i	0.761821	−	0.315557i	0.729555	+	0.683923i	$0.239727\pi$
$284$	21.4242	+	12.2500i	1.27129	+	0.726903i
$285$	−23.5541	+	22.5415i	−1.39522	+	1.33524i
$286$	−0.381912	+	0.499880i	−0.0225829	+	0.0295585i
$287$	2.91268			0.171930
$288$	−2.77673	+	16.7419i	−0.163620	+	0.986523i
$289$	21.0727			1.23957
$290$	−11.2420	+	14.7146i	−0.660155	+	0.864069i
$291$	−12.9709	+	12.4133i	−0.760369	+	0.727682i
$292$	3.83308	−	6.70374i	0.224314	−	0.392307i
$293$	24.7412	−	10.2481i	1.44539	−	0.598702i	0.484295	−	0.874905i	$-0.339076\pi$
$293$	24.7412	−	10.2481i	1.44539	−	0.598702i	0.961099	+	0.276203i	$0.0890763\pi$
$294$	0.127126	+	1.14026i	0.00741417	+	0.0665015i
$295$	13.5125	+	13.5125i	0.786729	+	0.786729i
$296$	−18.6529	+	0.117129i	−1.08418	+	0.00680801i
$297$	−7.18386	−	3.54660i	−0.416850	−	0.205795i
$298$	0.435531	−	1.63914i	0.0252296	−	0.0949529i
$299$	−0.698461	+	0.289312i	−0.0403930	+	0.0167313i
$300$	2.04761	−	0.509823i	0.118219	−	0.0294346i
$301$	4.29408	−	10.3668i	0.247506	−	0.597533i
$302$	19.4441	−	2.60129i	1.11888	−	0.149687i
$303$	−7.98357	+	18.1369i	−0.458644	+	1.04194i
$304$	−31.4829	+	4.41326i	−1.80567	+	0.253118i
$305$	10.9864			0.629079
$306$	−16.7910	+	20.0841i	−0.959878	+	1.14813i
$307$	−0.664375	−	0.275193i	−0.0379179	−	0.0157061i	0.363644	−	0.931538i	$-0.381532\pi$
$307$	−0.664375	−	0.275193i	−0.0379179	−	0.0157061i	−0.401562	+	0.915832i	$0.631532\pi$
$308$	1.06498	−	8.35962i	0.0606830	−	0.476334i
$309$	−25.6701	−	0.563871i	−1.46032	−	0.0320775i
$310$	−2.94196	+	11.0722i	−0.167092	+	0.628858i
$311$	3.60638	+	3.60638i	0.204499	+	0.204499i	0.801924	−	0.597425i	$-0.203810\pi$
$311$	3.60638	+	3.60638i	0.204499	+	0.204499i	−0.597425	+	0.801924i	$0.703810\pi$
$312$	−1.41319	−	0.0221652i	−0.0800062	−	0.00125486i
$313$	23.2233	−	23.2233i	1.31266	−	1.31266i	0.393210	−	0.919449i	$-0.371365\pi$
$313$	23.2233	−	23.2233i	1.31266	−	1.31266i	0.919449	−	0.393210i	$-0.128635\pi$
$314$	6.36179	+	10.9659i	0.359017	+	0.618840i
$315$	8.21113	−	17.5954i	0.462645	−	0.991389i
$316$	−1.45141	−	5.32742i	−0.0816481	−	0.299691i
$317$	1.42053	−	3.42947i	0.0797850	−	0.192618i	−0.878954	−	0.476907i	$-0.841758\pi$
$317$	1.42053	−	3.42947i	0.0797850	−	0.192618i	0.958738	+	0.284289i	$0.0917577\pi$
$318$	15.8406	+	28.7408i	0.888298	+	1.61170i
$319$		−	8.52434i		−	0.477271i
$320$	17.5943	+	7.03026i	0.983553	+	0.393004i
$321$	−7.09666	+	16.1220i	−0.396097	+	0.899843i
$322$	6.14846	−	8.04765i	0.342640	−	0.448478i
$323$	−45.3067	−	18.7666i	−2.52093	−	1.04420i
$324$	−3.18951	−	17.7152i	−0.177195	−	0.984176i
$325$	0.0672520	+	0.162361i	0.00373047	+	0.00900615i
$326$	−3.67758	+	2.13353i	−0.203682	+	0.118165i
$327$	−4.92905	−	12.6805i	−0.272577	−	0.701233i
$328$	−1.17109	−	2.77779i	−0.0646626	−	0.153378i
$329$	−2.99133	+	2.99133i	−0.164917	+	0.164917i
$330$	−5.58507	+	6.98667i	−0.307448	+	0.384604i
$331$	−3.25086	−	7.84826i	−0.178683	−	0.431380i	0.809008	−	0.587798i	$-0.200005\pi$
$331$	−3.25086	−	7.84826i	−0.178683	−	0.431380i	−0.987691	+	0.156419i	$0.950005\pi$
$332$	13.1233	+	1.67185i	0.720233	+	0.0917549i
$333$	18.5936	−	6.76138i	1.01892	−	0.370521i
$334$	−3.70366	+	0.495485i	−0.202655	+	0.0271117i
$335$		−	3.29079i		−	0.179795i
$336$	16.5242	−	9.24312i	0.901467	−	0.504253i
$337$		−	24.2771i		−	1.32246i	−0.750183	−	0.661230i	$-0.770035\pi$
$337$		−	24.2771i		−	1.32246i	0.750183	−	0.661230i	$-0.229965\pi$
$338$	2.42223	+	18.1058i	0.131752	+	0.984823i
$339$	17.0648	−	16.3312i	0.926833	−	0.886990i
$340$	17.8892	+	23.1127i	0.970179	+	1.25346i
$341$	−2.01819	−	4.87235i	−0.109291	−	0.263853i
$342$	29.8811	−	15.6236i	1.61579	−	0.844828i
$343$	−12.6217	+	12.6217i	−0.681509	+	0.681509i
$344$	−11.6132	+	0.0729242i	−0.626143	+	0.00393181i
$345$	−10.0191	+	3.89455i	−0.539413	+	0.209676i
$346$	−7.36796	−	12.7002i	−0.396104	−	0.682768i
$347$	−1.37907	−	3.32937i	−0.0740325	−	0.178730i	0.882531	−	0.470254i	$-0.155838\pi$
$347$	−1.37907	−	3.32937i	−0.0740325	−	0.178730i	−0.956564	+	0.291524i	$0.905838\pi$
$348$	15.3991	−	11.3870i	0.825477	−	0.610409i
$349$	10.7378	+	4.44775i	0.574782	+	0.238083i	0.651089	−	0.759002i	$-0.274313\pi$
$349$	10.7378	+	4.44775i	0.574782	+	0.238083i	−0.0763062	+	0.997084i	$0.524313\pi$
$350$	−1.87072	−	1.42924i	−0.0999940	−	0.0763961i
$351$	1.41975	−	0.481249i	0.0757809	−	0.0256871i
$352$	−8.40068	+	2.34545i	−0.447758	+	0.125013i
$353$			5.62531i			0.299405i	0.988731	+	0.149703i	$0.0478316\pi$
$353$			5.62531i			0.299405i	−0.988731	+	0.149703i	$0.952168\pi$
$354$	−9.54006	−	17.3092i	−0.507049	−	0.919975i
$355$	−11.1838	+	27.0000i	−0.593572	+	1.43301i
$356$	−5.81752	+	10.1744i	−0.308328	+	0.539240i
$357$	29.1996	+	0.641400i	1.54540	+	0.0339465i
$358$	0.0170092	−	0.00986780i	0.000898964	−	0.000521529i
$359$	−22.3781	+	22.3781i	−1.18107	+	1.18107i	−0.201603	+	0.979467i	$0.564615\pi$
$359$	−22.3781	+	22.3781i	−1.18107	+	1.18107i	−0.979467	+	0.201603i	$0.935385\pi$
$360$	−20.0820	−	0.756359i	−1.05841	−	0.0398636i
$361$	31.2298	+	31.2298i	1.64367	+	1.64367i
$362$	−13.9830	−	3.71539i	−0.734931	−	0.195276i
$363$	−0.327984	+	14.9314i	−0.0172147	+	0.783696i
$364$	0.965159	+	1.24698i	0.0505881	+	0.0653593i
$365$	8.44842	+	3.49945i	0.442211	+	0.183170i
$366$	−10.9150	−	3.15837i	−0.570534	−	0.165091i
$367$	−26.0135			−1.35789			−0.678946	−	0.734188i	$-0.737563\pi$
$367$	−26.0135			−1.35789			−0.678946	+	0.734188i	$0.737563\pi$
$368$	−10.1470	−	2.62804i	−0.528951	−	0.136996i
$369$	2.15946	+	2.35802i	0.112417	+	0.122754i
$370$	−2.92901	−	21.8938i	−0.152272	−	1.13821i
$371$	14.0113	−	33.8262i	0.727428	−	1.75617i
$372$	6.10587	−	10.1544i	0.316575	−	0.526483i
$373$	−16.7694	+	6.94611i	−0.868286	+	0.359656i	−0.771942	−	0.635692i	$-0.780715\pi$
$373$	−16.7694	+	6.94611i	−0.868286	+	0.359656i	−0.0963434	+	0.995348i	$0.530715\pi$
$374$	−13.0031	−	3.45502i	−0.672375	−	0.178655i
$375$	−6.52573	−	16.7881i	−0.336987	−	0.866936i
$376$	4.05551	+	1.65009i	0.209147	+	0.0850968i
$377$	1.12786	+	1.12786i	0.0580878	+	0.0580878i
$378$	−13.2161	+	15.1205i	−0.679762	+	0.777713i
$379$	11.8673	−	4.91559i	0.609582	−	0.252497i	−0.0564681	−	0.998404i	$-0.517984\pi$
$379$	11.8673	−	4.91559i	0.609582	−	0.252497i	0.666050	+	0.745907i	$0.267984\pi$
$380$	−9.89563	−	36.3221i	−0.507635	−	1.86328i
$381$	9.28576	+	9.70287i	0.475724	+	0.497093i
$382$	8.74227	+	6.67916i	0.447294	+	0.341735i
$383$	−5.25906			−0.268725			−0.134363	−	0.990932i	$-0.542899\pi$
$383$	−5.25906			−0.268725			−0.134363	+	0.990932i	$0.542899\pi$
$384$	−15.4589	−	12.0426i	−0.788882	−	0.614545i
$385$	9.97932			0.508593
$386$	−7.00702	−	5.35341i	−0.356648	−	0.272482i
$387$	11.5763	−	4.20960i	0.588456	−	0.213986i
$388$	−5.44940	−	20.0021i	−0.276651	−	1.01545i
$389$	−25.9373	+	10.7436i	−1.31507	+	0.544721i	−0.926360	−	0.376639i	$-0.877080\pi$
$389$	−25.9373	+	10.7436i	−1.31507	+	0.544721i	−0.388712	+	0.921359i	$0.627080\pi$
$390$	−0.185448	−	1.66338i	−0.00939051	−	0.0842283i
$391$	−11.4333	−	11.4333i	−0.578204	−	0.578204i
$392$	−1.22713	−	0.499291i	−0.0619796	−	0.0252180i
$393$	−2.04064	+	0.793219i	−0.102937	+	0.0400126i
$394$	10.2193	+	2.71534i	0.514841	+	0.136797i
$395$	6.04085	−	2.50220i	0.303948	−	0.125899i
$396$	7.55728	−	5.33565i	0.379768	−	0.268126i
$397$	−14.4580	+	34.9046i	−0.725624	+	1.75181i	−0.0689699	+	0.997619i	$0.521971\pi$
$397$	−14.4580	+	34.9046i	−0.725624	+	1.75181i	−0.656654	+	0.754192i	$0.728029\pi$
$398$	3.30223	+	24.6836i	0.165526	+	1.23728i
$399$	−34.4315	−	15.1562i	−1.72373	−	0.758759i
$400$	−0.610901	+	2.35873i	−0.0305450	+	0.117937i
$401$	31.7191			1.58397			0.791987	−	0.610537i	$-0.209046\pi$
$401$	31.7191			1.58397			0.791987	+	0.610537i	$0.209046\pi$
$402$	−0.946039	+	3.26940i	−0.0471841	+	0.163063i
$403$	0.911693	+	0.377635i	0.0454146	+	0.0188114i
$404$	−14.0054	−	18.0949i	−0.696797	−	0.900255i
$405$	20.3325	−	6.39776i	1.01033	−	0.317907i
$406$	−20.6508	−	5.48706i	−1.02488	−	0.272318i
$407$	7.19010	+	7.19010i	0.356400	+	0.356400i
$408$	−11.1284	−	28.1052i	−0.550940	−	1.39142i
$409$	−17.8308	+	17.8308i	−0.881677	+	0.881677i	−0.993705	−	0.112028i	$-0.964265\pi$
$409$	−17.8308	+	17.8308i	−0.881677	+	0.881677i	0.112028	+	0.993705i	$0.464265\pi$
$410$	3.08779	−	1.79136i	0.152495	−	0.0884690i
$411$	−0.405863	+	18.4768i	−0.0200197	+	0.911393i
$412$	14.7166	−	25.7381i	0.725035	−	1.26803i
$413$	−8.43832	+	20.3719i	−0.415223	+	1.00244i
$414$	11.0736	−	0.988918i	0.544238	−	0.0486026i
$415$			15.6659i			0.769011i
$416$	0.801171	−	1.42183i	0.0392806	−	0.0697109i
$417$	1.70851	+	0.752059i	0.0836660	+	0.0368285i
$418$	13.7707	+	10.5209i	0.673548	+	0.514596i
$419$	−2.10652	−	0.872548i	−0.102910	−	0.0426268i	0.330634	−	0.943759i	$-0.392737\pi$
$419$	−2.10652	−	0.872548i	−0.102910	−	0.0426268i	−0.433544	+	0.901132i	$0.642737\pi$
$420$	13.3306	+	18.0275i	0.650468	+	0.879651i
$421$	−0.169965	−	0.410331i	−0.00828357	−	0.0199983i	0.919684	−	0.392660i	$-0.128445\pi$
$421$	−0.169965	−	0.410331i	−0.00828357	−	0.0199983i	−0.927967	+	0.372662i	$0.878445\pi$
$422$	−0.897576	−	1.54716i	−0.0436933	−	0.0753145i
$423$	−4.63946	−	0.203920i	−0.225578	−	0.00991492i
$424$	−37.8931	+	0.237946i	−1.84025	+	0.0115557i
$425$	−2.65772	+	2.65772i	−0.128918	+	0.128918i
$426$	18.8730	−	23.6093i	0.914400	−	1.14387i
$427$	4.85132	+	11.7121i	0.234772	+	0.566790i
$428$	−12.4496	−	16.0847i	−0.601772	−	0.777484i
$429$	0.532700	+	0.556628i	0.0257190	+	0.0268743i
$430$	−1.82359	−	13.6310i	−0.0879412	−	0.657345i
$431$		−	2.95351i		−	0.142266i	−0.997467	−	0.0711329i	$-0.977339\pi$
$431$		−	2.95351i		−	0.142266i	0.997467	−	0.0711329i	$-0.0226614\pi$
$432$	19.7340	+	6.52462i	0.949451	+	0.313916i
$433$		−	31.3472i		−	1.50645i	−0.657764	−	0.753224i	$-0.728497\pi$
$433$		−	31.3472i		−	1.50645i	0.657764	−	0.753224i	$-0.271503\pi$
$434$	−13.1027	+	1.75291i	−0.628950	+	0.0841424i
$435$	15.6807	+	16.3850i	0.751830	+	0.785602i
$436$	15.5835	+	1.98528i	0.746315	+	0.0950776i
$437$	7.96999	+	19.2413i	0.381256	+	0.920434i
$438$	−7.38746	−	5.90545i	−0.352987	−	0.282173i
$439$	−7.44392	+	7.44392i	−0.355279	+	0.355279i	−0.862069	−	0.506791i	$-0.830832\pi$
$439$	−7.44392	+	7.44392i	−0.355279	+	0.355279i	0.506791	+	0.862069i	$0.330832\pi$
$440$	−4.01234	−	9.51717i	−0.191281	−	0.453713i
$441$	1.40383	+	0.0617029i	0.0668489	+	0.00293824i
$442$	2.17759	−	1.26331i	0.103577	−	0.0600897i
$443$	3.50021	+	8.45026i	0.166300	+	0.401484i	0.984957	−	0.172799i	$-0.0552810\pi$
$443$	3.50021	+	8.45026i	0.166300	+	0.401484i	−0.818657	+	0.574283i	$0.805281\pi$
$444$	−3.38409	+	22.5935i	−0.160602	+	1.07224i
$445$	−12.8223	−	5.31117i	−0.607835	−	0.251773i
$446$	9.01903	−	11.8049i	0.427064	−	0.558979i
$447$	−1.90115	−	0.836857i	−0.0899213	−	0.0395820i
$448$	0.274559	+	21.8610i	0.0129717	+	1.03283i
$449$		−	24.0900i		−	1.13688i	−0.822725	−	0.568439i	$-0.807547\pi$
$449$		−	24.0900i		−	1.13688i	0.822725	−	0.568439i	$-0.192453\pi$
$450$	−0.229879	−	2.57412i	−0.0108366	−	0.121345i
$451$	−0.628866	+	1.51822i	−0.0296121	+	0.0714901i
$452$	7.16934	+	26.3152i	0.337217	+	1.23776i
$453$	0.527636	−	24.0205i	0.0247905	−	1.12858i
$454$	12.8947	+	22.2266i	0.605176	+	1.04315i
$455$	−1.32037	+	1.32037i	−0.0618999	+	0.0618999i
$456$	−0.610609	+	38.9307i	−0.0285944	+	1.82310i
$457$	−13.8807	−	13.8807i	−0.649311	−	0.649311i	0.303515	−	0.952827i	$-0.401840\pi$
$457$	−13.8807	−	13.8807i	−0.649311	−	0.649311i	−0.952827	+	0.303515i	$0.901840\pi$
$458$	−5.57674	+	20.9883i	−0.260584	+	0.980719i
$459$	21.1293	+	24.1146i	0.986231	+	1.12557i
$460$	1.56861	−	12.3129i	0.0731370	−	0.574091i
$461$	−26.4361	−	10.9502i	−1.23125	−	0.510001i	−0.330282	−	0.943882i	$-0.607144\pi$
$461$	−26.4361	−	10.9502i	−1.23125	−	0.510001i	−0.900970	+	0.433881i	$0.857144\pi$
$462$	−9.91443	−	2.86886i	−0.461261	−	0.133471i
$463$	35.7558			1.66171			0.830857	−	0.556485i	$-0.187850\pi$
$463$	35.7558			1.66171			0.830857	+	0.556485i	$0.187850\pi$
$464$	3.07002	+	21.9006i	0.142522	+	1.01671i
$465$	12.8420	+	5.65287i	0.595535	+	0.262145i
$466$	5.03658	−	0.673807i	0.233315	−	0.0312135i
$467$	1.84875	−	4.46327i	0.0855498	−	0.206536i	−0.875315	−	0.483553i	$-0.839346\pi$
$467$	1.84875	−	4.46327i	0.0855498	−	0.206536i	0.960865	+	0.277018i	$0.0893460\pi$
$468$	−0.293946	+	1.70587i	−0.0135877	+	0.0788540i
$469$	3.50818	−	1.45313i	0.161993	−	0.0670995i
$470$	−1.33143	+	5.01089i	−0.0614142	+	0.231135i
$471$	14.4720	−	5.62542i	0.666834	−	0.259206i
$472$	22.8212	−	0.143304i	1.05043	−	0.00659610i
$473$	4.47652	+	4.47652i	0.205831	+	0.205831i
$474$	−6.72090	+	0.749305i	−0.308701	+	0.0344167i
$475$	4.47273	−	1.85266i	0.205223	−	0.0850060i
$476$	−16.7400	+	29.2769i	−0.767278	+	1.34191i
$477$	37.7726	−	13.7356i	1.72949	−	0.628911i
$478$	15.1200	−	19.7904i	0.691572	−	0.905190i
$479$	15.8988			0.726433			0.363216	−	0.931705i	$-0.381679\pi$
$479$	15.8988			0.726433			0.363216	+	0.931705i	$0.381679\pi$
$480$	11.8328	−	19.9615i	0.540092	−	0.911114i
$481$	−1.90265			−0.0867535
$482$	−5.31134	+	6.95196i	−0.241925	+	0.316653i
$483$	−8.57603	−	8.96126i	−0.390223	−	0.407751i
$484$	−14.9710	−	8.56013i	−0.680499	−	0.389097i
$485$	22.6807	−	9.39466i	1.02988	−	0.426590i
$486$	−22.0395	+	0.510969i	−0.999731	+	0.0231780i
$487$	−10.4283	−	10.4283i	−0.472552	−	0.472552i	0.430187	−	0.902740i	$-0.358448\pi$
$487$	−10.4283	−	10.4283i	−0.472552	−	0.472552i	−0.902740	+	0.430187i	$0.858448\pi$
$488$	9.21919	−	9.33570i	0.417333	−	0.422607i
$489$	1.88657	+	4.85341i	0.0853138	+	0.219479i
$490$	0.402869	−	1.51622i	0.0181998	−	0.0684957i
$491$	0.306137	−	0.126806i	0.0138158	−	0.00572268i	−0.375765	−	0.926715i	$-0.622620\pi$
$491$	0.306137	−	0.126806i	0.0138158	−	0.00572268i	0.389581	+	0.920992i	$0.372620\pi$
$492$	−3.58269	+	0.892036i	−0.161520	+	0.0402161i
$493$	−13.0547	+	31.5169i	−0.587956	+	1.41945i
$494$	−3.21404	+	0.429983i	−0.144607	+	0.0193458i
$495$	7.39867	+	8.07896i	0.332545	+	0.363122i
$496$	6.93988	+	11.7911i	0.311610	+	0.529437i
$497$	−33.7220			−1.51264
$498$	4.50365	−	15.5641i	0.201813	−	0.697443i
$499$	5.62549	+	2.33015i	0.251831	+	0.104312i	0.505028	−	0.863103i	$-0.331482\pi$
$499$	5.62549	+	2.33015i	0.251831	+	0.104312i	−0.253197	+	0.967415i	$0.581482\pi$
$500$	20.6315	+	2.62838i	0.922671	+	0.117545i
$501$	−0.100502	+	4.57535i	−0.00449012	+	0.204411i
$502$	−8.71976	+	32.8172i	−0.389182	+	1.46470i
$503$	−10.6198	−	10.6198i	−0.473513	−	0.473513i	0.429536	−	0.903050i	$-0.358677\pi$
$503$	−10.6198	−	10.6198i	−0.473513	−	0.473513i	−0.903050	+	0.429536i	$0.858677\pi$
$504$	−8.06139	−	21.7425i	−0.359083	−	0.968490i
$505$	19.1599	−	19.1599i	0.852605	−	0.852605i
$506$	2.86730	+	4.94238i	0.127467	+	0.219716i
$507$	22.3671	+	0.491317i	0.993358	+	0.0218202i
$508$	−14.9625	+	4.07641i	−0.663855	+	0.180861i
$509$	−2.01172	+	4.85673i	−0.0891681	+	0.215271i	−0.962172	−	0.272442i	$-0.912169\pi$
$509$	−2.01172	+	4.85673i	−0.0891681	+	0.215271i	0.873004	+	0.487713i	$0.162169\pi$
$510$	31.3494	−	17.2784i	1.38818	−	0.765100i
$511$			10.5518i			0.466783i
$512$	20.7382	−	9.05139i	0.916507	−	0.400019i
$513$	−13.2575	−	39.1115i	−0.585332	−	1.72681i
$514$	−10.2028	+	13.3544i	−0.450028	+	0.589037i
$515$	32.4366	+	13.4357i	1.42933	+	0.592046i
$516$	−2.10691	+	14.0666i	−0.0927517	+	0.619248i
$517$	−0.913364	−	2.20506i	−0.0401697	−	0.0969783i
$518$	22.0467	−	12.7903i	0.968677	−	0.561973i
$519$	−16.7609	+	6.51513i	−0.735721	+	0.285983i
$520$	1.79010	+	0.728348i	0.0785010	+	0.0319402i
$521$	−19.9974	+	19.9974i	−0.876102	+	0.876102i	−0.993129	−	0.117027i	$-0.962664\pi$
$521$	−19.9974	+	19.9974i	−0.876102	+	0.876102i	0.117027	+	0.993129i	$0.462664\pi$
$522$	−10.8683	−	20.7864i	−0.475694	−	0.909795i
$523$	−15.2948	−	36.9248i	−0.668793	−	1.61461i	−0.783632	−	0.621225i	$-0.786635\pi$
$523$	−15.2948	−	36.9248i	−0.668793	−	1.61461i	0.114839	−	0.993384i	$-0.463365\pi$
$524$	0.319486	−	2.50782i	0.0139568	−	0.109554i
$525$	−2.08309	+	1.99354i	−0.0909134	+	0.0870053i
$526$	−23.0330	+	3.08141i	−1.00429	+	0.134356i
$527$			21.1053i			0.919360i
$528$	1.25025	+	10.6088i	0.0544101	+	0.461687i
$529$		−	16.1332i		−	0.701443i
$530$	−5.95023	−	44.4769i	−0.258462	−	1.93195i
$531$	−22.7487	+	8.27232i	−0.987208	+	0.358988i
$532$	34.3518	−	26.5883i	1.48934	−	1.15275i
$533$	−0.117671	−	0.284082i	−0.00509688	−	0.0123050i
$534$	11.2121	+	8.96279i	0.485193	+	0.387858i
$535$	17.0314	−	17.0314i	0.736332	−	0.736332i
$536$	−2.79636	−	2.76146i	−0.120784	−	0.119277i
$537$	−0.00872561	−	0.0224476i	−0.000376538	−	0.000968684i
$538$	10.5604	+	18.2030i	0.455289	+	0.784786i
$539$	0.276370	+	0.667216i	0.0119041	+	0.0287390i
$540$	−4.71119	+	24.1576i	−0.202737	+	1.03958i
$541$	−35.6786	−	14.7786i	−1.53394	−	0.635380i	−0.553618	−	0.832771i	$-0.686753\pi$
$541$	−35.6786	−	14.7786i	−1.53394	−	0.635380i	−0.980325	+	0.197391i	$0.936753\pi$
$542$	7.94840	+	6.07263i	0.341413	+	0.260842i
$543$	−7.13898	+	16.2181i	−0.306363	+	0.695987i
$544$	34.6517	+	4.19354i	1.48568	+	0.179797i
$545$			18.6029i			0.796859i
$546$	1.69137	−	0.932204i	0.0723837	−	0.0398946i
$547$	12.4112	−	29.9634i	0.530666	−	1.28114i	−0.400416	−	0.916333i	$-0.631135\pi$
$547$	12.4112	−	29.9634i	0.530666	−	1.28114i	0.931083	−	0.364808i	$-0.118865\pi$
$548$	−18.5258	−	10.5927i	−0.791381	−	0.452498i
$549$	−5.88502	+	12.6109i	−0.251167	+	0.538219i
$550$	1.14888	−	0.666517i	0.0489885	−	0.0284204i
$551$	31.0704	−	31.0704i	1.32364	−	1.32364i
$552$	−5.09813	+	11.7819i	−0.216991	+	0.501470i
$553$	5.33499	+	5.33499i	0.226867	+	0.226867i
$554$	−1.67759	−	0.445748i	−0.0712741	−	0.0189380i
$555$	−27.0467	−	0.594111i	−1.14807	−	0.0252186i
$556$	−1.70455	+	1.31932i	−0.0722892	+	0.0559518i
$557$	−9.30090	−	3.85256i	−0.394092	−	0.163238i	0.176832	−	0.984241i	$-0.443415\pi$
$557$	−9.30090	−	3.85256i	−0.394092	−	0.163238i	−0.570924	+	0.821003i	$0.693415\pi$
$558$	−11.1334	−	9.30795i	−0.471316	−	0.394037i
$559$	−1.18458			−0.0501025
$560$	−25.6387	+	3.59402i	−1.08343	+	0.151875i
$561$	−6.63869	+	15.0816i	−0.280286	+	0.636746i
$562$	−3.18804	−	23.8300i	−0.134479	−	1.00521i
$563$	−1.24166	+	2.99763i	−0.0523297	+	0.126335i	−0.947882	−	0.318620i	$-0.896780\pi$
$563$	−1.24166	+	2.99763i	−0.0523297	+	0.126335i	0.895553	+	0.444955i	$0.146780\pi$
$564$	2.76330	−	4.59555i	0.116356	−	0.193507i
$565$	−29.8392	+	12.3598i	−1.25535	+	0.519981i
$566$	18.9597	+	5.03773i	0.796937	+	0.211752i
$567$	15.7987	+	18.8505i	0.663483	+	0.791646i
$568$	13.5585	+	32.1603i	0.568900	+	1.34942i
$569$	−28.3250	−	28.3250i	−1.18745	−	1.18745i	−0.977771	−	0.209674i	$-0.932760\pi$
$569$	−28.3250	−	28.3250i	−1.18745	−	1.18745i	−0.209674	−	0.977771i	$-0.567240\pi$
$570$	−45.8228	+	5.10873i	−1.91931	+	0.213981i
$571$	−37.5476	+	15.5527i	−1.57132	+	0.650862i	−0.987008	−	0.160669i	$-0.948635\pi$
$571$	−37.5476	+	15.5527i	−1.57132	+	0.650862i	−0.584310	+	0.811530i	$0.698635\pi$
$572$	−0.858362	+	0.233853i	−0.0358899	+	0.00977789i
$573$	9.73473	−	9.31626i	0.406674	−	0.389192i
$574$	3.27319	+	2.50074i	0.136620	+	0.104379i
$575$	1.59623			0.0665673
$576$	−17.4944	+	16.4300i	−0.728935	+	0.684583i
$577$	5.37886			0.223925			0.111962	−	0.993712i	$-0.464286\pi$
$577$	5.37886			0.223925			0.111962	+	0.993712i	$0.464286\pi$
$578$	23.6809	+	18.0924i	0.984995	+	0.752543i
$579$	−7.80249	+	7.46708i	−0.324260	+	0.310321i
$580$	−25.2669	+	6.88375i	−1.04915	+	0.285832i
$581$	−16.7008	+	6.91770i	−0.692866	+	0.286994i
$582$	−25.2340	+	2.81331i	−1.04598	+	0.116616i
$583$	14.6066	+	14.6066i	0.604942	+	0.604942i
$584$	10.0631	−	4.24251i	0.416415	−	0.175556i
$585$	−2.04785	−	0.0900101i	−0.0846684	−	0.00372146i
$586$	36.6021	+	9.72544i	1.51202	+	0.401754i
$587$	−1.77252	+	0.734203i	−0.0731599	+	0.0303038i	−0.418963	−	0.908003i	$-0.637606\pi$
$587$	−1.77252	+	0.734203i	−0.0731599	+	0.0303038i	0.345803	+	0.938307i	$0.387606\pi$
$588$	−0.836132	+	1.39054i	−0.0344815	+	0.0573449i
$589$	10.4031	−	25.1154i	0.428653	−	1.03486i
$590$	3.58355	+	26.7864i	0.147532	+	1.10278i
$591$	5.21743	−	11.8528i	0.214616	−	0.487560i
$592$	−21.0622	−	15.8832i	−0.865651	−	0.652795i
$593$	−24.1664			−0.992394			−0.496197	−	0.868210i	$-0.665271\pi$
$593$	−24.1664			−0.992394			−0.496197	+	0.868210i	$0.665271\pi$
$594$	−5.02802	−	10.1534i	−0.206302	−	0.416599i
$595$	−36.8964	−	15.2830i	−1.51260	−	0.626541i
$596$	1.89675	−	1.46808i	0.0776940	−	0.0601351i
$597$	30.4931	+	0.669813i	1.24800	+	0.0274136i
$598$	−1.03330	−	0.274556i	−0.0422549	−	0.0112274i
$599$	11.6692	+	11.6692i	0.476789	+	0.476789i	0.904103	−	0.427314i	$-0.140540\pi$
$599$	11.6692	+	11.6692i	0.476789	+	0.476789i	−0.427314	+	0.904103i	$0.640540\pi$
$600$	2.73876	+	1.18509i	0.111809	+	0.0483809i
$601$	−8.80143	+	8.80143i	−0.359018	+	0.359018i	−0.863451	−	0.504433i	$-0.831702\pi$
$601$	−8.80143	+	8.80143i	−0.359018	+	0.359018i	0.504433	+	0.863451i	$0.331702\pi$
$602$	13.7262	−	7.96316i	0.559437	−	0.324554i
$603$	3.77738	+	1.76276i	0.153827	+	0.0717852i
$604$	24.0841	+	13.7709i	0.979970	+	0.560329i
$605$	7.81507	−	18.8672i	0.317728	−	0.767062i
$606$	−24.5434	+	13.5272i	−0.997009	+	0.549506i
$607$		−	31.9215i		−	1.29565i	−0.761788	−	0.647826i	$-0.775678\pi$
$607$		−	31.9215i		−	1.29565i	0.761788	−	0.647826i	$-0.224322\pi$
$608$	−39.1686	−	22.0707i	−1.58850	−	0.895086i
$609$	−10.5432	+	23.9517i	−0.427231	+	0.970573i
$610$	12.3462	+	9.43257i	0.499882	+	0.381914i
$611$	0.412600	+	0.170905i	0.0166920	+	0.00691406i
$612$	−36.1128	+	8.15369i	−1.45977	+	0.329594i
$613$	7.35458	+	17.7555i	0.297049	+	0.717139i	0.999983	+	0.00588391i	$0.00187292\pi$
$613$	7.35458	+	17.7555i	0.297049	+	0.717139i	−0.702934	+	0.711255i	$0.748127\pi$
$614$	−0.510333	−	0.879665i	−0.0205954	−	0.0355004i
$615$	−1.58401	−	4.07504i	−0.0638736	−	0.164322i
$616$	8.37411	−	8.47994i	0.337402	−	0.341667i
$617$	13.5933	−	13.5933i	0.547246	−	0.547246i	−0.378397	−	0.925643i	$-0.623525\pi$
$617$	13.5933	−	13.5933i	0.547246	−	0.547246i	0.925643	+	0.378397i	$0.123525\pi$
$618$	−28.3632	−	22.6732i	−1.14093	−	0.912050i
$619$	−3.75210	−	9.05838i	−0.150810	−	0.364087i	0.830362	−	0.557224i	$-0.188134\pi$
$619$	−3.75210	−	9.05838i	−0.150810	−	0.364087i	−0.981172	+	0.193137i	$0.938134\pi$
$620$	−12.8123	+	9.91673i	−0.514555	+	0.398265i
$621$	0.896498	−	13.5868i	0.0359752	−	0.545219i
$622$	0.956420	+	7.14907i	0.0383489	+	0.286651i
$623$		−	16.0146i		−	0.641611i
$624$	−1.56907	−	1.23823i	−0.0628132	−	0.0495689i
$625$			27.6746i			1.10699i
$626$	46.0365	−	6.15887i	1.83999	−	0.246158i
$627$	15.3340	−	14.6749i	0.612383	−	0.586058i
$628$	−2.26576	+	17.7852i	−0.0904136	+	0.709705i
$629$	−15.5725	−	37.5953i	−0.620915	−	1.49902i
$630$	24.3343	−	12.7234i	0.969502	−	0.506912i
$631$	5.39207	−	5.39207i	0.214655	−	0.214655i	−0.591587	−	0.806242i	$-0.701498\pi$
$631$	5.39207	−	5.39207i	0.214655	−	0.214655i	0.806242	+	0.591587i	$0.201498\pi$
$632$	2.94291	−	7.23293i	0.117063	−	0.287711i
$633$	−2.04183	+	0.793682i	−0.0811556	+	0.0315460i
$634$	4.54078	−	2.63431i	0.180337	−	0.104622i
$635$	−7.02766	−	16.9663i	−0.278884	−	0.673286i
$636$	−6.87470	+	45.8983i	−0.272600	+	1.81999i
$637$	−0.124846	−	0.0517131i	−0.00494659	−	0.00204895i
$638$	7.31873	−	9.57940i	0.289751	−	0.379252i
$639$	−25.0015	−	27.3003i	−0.989044	−	1.07999i
$640$	13.7360	+	23.0063i	0.542964	+	0.909405i
$641$			1.82203i			0.0719659i	0.999352	+	0.0359830i	$0.0114562\pi$
$641$			1.82203i			0.0719659i	−0.999352	+	0.0359830i	$0.988544\pi$
$642$	−21.8169	+	12.0245i	−0.861043	+	0.474568i
$643$	−10.4095	+	25.1308i	−0.410511	+	0.991062i	0.574489	+	0.818512i	$0.305201\pi$
$643$	−10.4095	+	25.1308i	−0.410511	+	0.991062i	−0.985001	+	0.172550i	$0.944799\pi$
$644$	13.8189	−	3.76484i	0.544542	−	0.148355i
$645$	−16.8392	−	0.369890i	−0.663041	−	0.0145644i
$646$	−34.8019	−	59.9883i	−1.36926	−	2.36021i
$647$	27.3258	−	27.3258i	1.07429	−	1.07429i	0.0772785	−	0.997010i	$-0.475377\pi$
$647$	27.3258	−	27.3258i	1.07429	−	1.07429i	0.997010	−	0.0772785i	$-0.0246231\pi$
$648$	11.6254	−	22.6462i	0.456689	−	0.889626i
$649$	−8.79684	−	8.79684i	−0.345306	−	0.345306i
$650$	−0.0638219	+	0.240197i	−0.00250330	+	0.00942129i
$651$	−0.355554	+	16.1865i	−0.0139353	+	0.634400i
$652$	−5.96453	−	0.759858i	−0.233589	−	0.0297583i
$653$	21.5061	+	8.90811i	0.841598	+	0.348601i	0.761483	−	0.648184i	$-0.224471\pi$
$653$	21.5061	+	8.90811i	0.841598	+	0.348601i	0.0801145	+	0.996786i	$0.474471\pi$
$654$	5.34796	−	18.4819i	0.209122	−	0.722699i
$655$	2.99371			0.116974
$656$	1.06889	−	4.12706i	0.0417332	−	0.161135i
$657$	−8.54241	+	7.82309i	−0.333271	+	0.305208i
$658$	−5.92982	+	0.793306i	−0.231169	+	0.0309263i
$659$	−17.2778	+	41.7123i	−0.673048	+	1.62488i	0.103355	+	0.994644i	$0.467042\pi$
$659$	−17.2778	+	41.7123i	−0.673048	+	1.62488i	−0.776403	+	0.630237i	$0.782958\pi$
$660$	−12.2749	+	3.05626i	−0.477799	+	0.118965i
$661$	44.7407	−	18.5322i	1.74021	−	0.720819i	0.741453	−	0.671005i	$-0.234137\pi$
$661$	44.7407	−	18.5322i	1.74021	−	0.720819i	0.998759	−	0.0498140i	$-0.0158629\pi$
$662$	3.08505	−	11.6107i	0.119904	−	0.451264i
$663$	−1.11709	−	2.87383i	−0.0433841	−	0.111610i
$664$	13.3122	+	13.1460i	0.516612	+	0.510164i
$665$	36.3736	+	36.3736i	1.41051	+	1.41051i
$666$	26.7001	+	8.36566i	1.03461	+	0.324163i
$667$	13.3849	−	5.54420i	0.518265	−	0.214672i
$668$	−4.58747	−	2.62303i	−0.177495	−	0.101488i
$669$	−12.5800	−	13.1451i	−0.486370	−	0.508217i
$670$	2.82537	−	3.69810i	0.109154	−	0.142870i
$671$	−7.15231			−0.276112
$672$	26.5052	+	3.79997i	1.02246	+	0.146587i
$673$	−10.8139			−0.416844			−0.208422	−	0.978039i	$-0.566833\pi$
$673$	−10.8139			−0.416844			−0.208422	+	0.978039i	$0.566833\pi$
$674$	20.8436	−	27.2819i	0.802865	−	1.05086i
$675$	−3.15831	−	0.208395i	−0.121564	−	0.00802114i
$676$	−12.8230	+	22.4264i	−0.493192	+	0.862553i
$677$	−16.7436	+	6.93541i	−0.643507	+	0.266549i	−0.680480	−	0.732767i	$-0.738229\pi$
$677$	−16.7436	+	6.93541i	−0.643507	+	0.266549i	0.0369727	+	0.999316i	$0.488229\pi$
$678$	33.1984	−	3.70125i	1.27498	−	0.142146i
$679$	20.0305	+	20.0305i	0.768701	+	0.768701i
$680$	0.259543	+	41.3325i	0.00995304	+	1.58503i
$681$	29.3332	−	11.4021i	1.12405	−	0.436930i
$682$	1.91526	−	7.20816i	0.0733391	−	0.276015i
$683$	43.5660	−	18.0456i	1.66701	−	0.690497i	0.668428	−	0.743777i	$-0.266968\pi$
$683$	43.5660	−	18.0456i	1.66701	−	0.690497i	0.998580	+	0.0532798i	$0.0169675\pi$
$684$	46.9935	+	8.09765i	1.79684	+	0.309621i
$685$	9.67071	−	23.3472i	0.369499	−	0.892049i
$686$	−25.0205	+	3.34731i	−0.955288	+	0.127801i
$687$	24.3432	+	10.7155i	0.928751	+	0.408822i
$688$	−13.1132	−	9.88880i	−0.499936	−	0.377007i
$689$	−3.86521			−0.147253
$690$	−14.6030	−	4.22554i	−0.555925	−	0.160864i
$691$	−5.29763	−	2.19435i	−0.201531	−	0.0834771i	0.279635	−	0.960106i	$-0.409787\pi$
$691$	−5.29763	−	2.19435i	−0.201531	−	0.0834771i	−0.481166	+	0.876629i	$0.659787\pi$
$692$	2.62411	−	20.5980i	0.0997536	−	0.783020i
$693$	−5.34557	+	11.4549i	−0.203061	+	0.435135i
$694$	1.30873	−	4.92548i	0.0496789	−	0.186969i
$695$	−1.80488	−	1.80488i	−0.0684630	−	0.0684630i
$696$	27.0816	+	0.424761i	1.02652	+	0.0161005i
$697$	4.65020	−	4.65020i	0.176139	−	0.176139i
$698$	8.24815	+	14.2174i	0.312197	+	0.538137i
$699$	0.136673	−	6.22199i	0.00516943	−	0.235337i
$700$	−0.875156	−	3.21228i	−0.0330778	−	0.121413i
$701$	−13.7184	+	33.1190i	−0.518135	+	1.25089i	0.420912	+	0.907101i	$0.361710\pi$
$701$	−13.7184	+	33.1190i	−0.518135	+	1.25089i	−0.939047	+	0.343787i	$0.888290\pi$
$702$	2.00866	+	0.678143i	0.0758121	+	0.0255949i
$703$			52.4144i			1.97685i
$704$	−11.4542	−	4.57681i	−0.431695	−	0.172495i
$705$	5.81186	+	2.55829i	0.218887	+	0.0963508i
$706$	−4.82971	+	6.32156i	−0.181769	+	0.237915i
$707$	28.8861	+	11.9650i	1.08638	+	0.449991i
$708$	4.14031	−	27.6424i	0.155602	−	1.03886i
$709$	−1.39804	−	3.37516i	−0.0525044	−	0.126757i	0.895451	−	0.445160i	$-0.146853\pi$
$709$	−1.39804	−	3.37516i	−0.0525044	−	0.126757i	−0.947955	+	0.318403i	$0.896853\pi$
$710$	−35.7493	+	20.7398i	−1.34165	+	0.778349i
$711$	−0.363688	+	8.27440i	−0.0136394	+	0.310314i
$712$	−15.2729	+	6.43891i	−0.572378	+	0.241309i
$713$	6.33792	−	6.33792i	0.237357	−	0.237357i
$714$	32.2629	+	25.7906i	1.20741	+	0.965189i
$715$	−0.403158	−	0.973311i	−0.0150773	−	0.0363998i
$716$	0.0275866	+	0.00351443i	0.00103096	+	0.000131340i
$717$	−21.0897	−	22.0371i	−0.787610	−	0.822989i
$718$	−44.3610	+	5.93472i	−1.65554	+	0.221482i
$719$			25.3851i			0.946706i	0.880873	+	0.473353i	$0.156956\pi$
$719$			25.3851i			0.946706i	−0.880873	+	0.473353i	$0.843044\pi$
$720$	−21.9182	−	18.0917i	−0.816841	−	0.674239i
$721$			40.5121i			1.50875i
$722$	8.28220	+	61.9080i	0.308232	+	2.30398i
$723$	7.40840	+	7.74117i	0.275521	+	0.287897i
$724$	−12.5238	−	16.1806i	−0.465443	−	0.601348i
$725$	−1.28878	−	3.11138i	−0.0478640	−	0.115554i
$726$	−13.1882	+	16.4979i	−0.489461	+	0.612294i
$727$	−32.5294	+	32.5294i	−1.20645	+	1.20645i	−0.234280	+	0.972169i	$0.575273\pi$
$727$	−32.5294	+	32.5294i	−1.20645	+	1.20645i	−0.972169	+	0.234280i	$0.924727\pi$
$728$	0.0140029	+	2.22997i	0.000518982	+	0.0826482i
$729$	−3.54764	+	26.7659i	−0.131394	+	0.991330i
$730$	6.48957	+	11.1861i	0.240190	+	0.414017i
$731$	−9.69534	−	23.4066i	−0.358595	−	0.865725i
$732$	−9.55423	−	12.9205i	−0.353134	−	0.477556i
$733$	26.3419	+	10.9112i	0.972961	+	0.403014i	0.811814	−	0.583917i	$-0.198481\pi$
$733$	26.3419	+	10.9112i	0.972961	+	0.403014i	0.161147	+	0.986930i	$0.448481\pi$
$734$	−29.2332	−	22.3343i	−1.07902	−	0.824376i
$735$	−1.75858	−	0.774099i	−0.0648661	−	0.0285531i
$736$	−9.14660	−	11.6652i	−0.337148	−	0.429987i
$737$			2.14236i			0.0789147i
$738$	0.402218	+	4.50392i	0.0148059	+	0.165792i
$739$	13.4201	−	32.3991i	0.493668	−	1.19182i	−0.459172	−	0.888347i	$-0.651854\pi$
$739$	13.4201	−	32.3991i	0.493668	−	1.19182i	0.952840	−	0.303473i	$-0.0981461\pi$
$740$	15.5058	−	27.1184i	0.570005	−	0.996893i
$741$	−0.0872162	+	3.97050i	−0.00320397	+	0.145860i
$742$	44.7875	−	25.9832i	1.64420	−	0.953874i
$743$	5.42669	−	5.42669i	0.199086	−	0.199086i	−0.600522	−	0.799608i	$-0.705041\pi$
$743$	5.42669	−	5.42669i	0.199086	−	0.199086i	0.799608	+	0.600522i	$0.205041\pi$
$744$	15.5799	−	6.16896i	0.571186	−	0.226165i
$745$	2.00839	+	2.00839i	0.0735817	+	0.0735817i
$746$	−24.8087	−	6.59183i	−0.908309	−	0.241344i
$747$	−17.9823	−	8.39169i	−0.657939	−	0.307036i
$748$	−11.6461	−	15.0467i	−0.425825	−	0.550162i
$749$	25.6771	+	10.6358i	0.938222	+	0.388624i
$750$	7.08034	−	24.4688i	0.258538	−	0.893474i
$751$	3.67683			0.134170			0.0670848	−	0.997747i	$-0.478630\pi$
$751$	3.67683			0.134170			0.0670848	+	0.997747i	$0.478630\pi$
$752$	3.14075	+	5.33625i	0.114531	+	0.194593i
$753$	38.0629	+	16.7547i	1.38709	+	0.610576i
$754$	0.299111	+	2.23580i	0.0108930	+	0.0814231i
$755$	−12.5723	+	30.3521i	−0.457552	+	1.10463i
$756$	−27.8338	+	5.64503i	−1.01231	+	0.205308i
$757$	−13.0816	+	5.41857i	−0.475458	+	0.196941i	−0.607526	−	0.794299i	$-0.707838\pi$
$757$	−13.0816	+	5.41857i	−0.475458	+	0.196941i	0.132068	+	0.991241i	$0.457838\pi$
$758$	17.5565	+	4.66488i	0.637680	+	0.169436i
$759$	6.52262	−	2.53541i	0.236756	−	0.0920296i
$760$	20.0646	−	49.3138i	0.727819	−	1.78880i
$761$	25.8277	+	25.8277i	0.936254	+	0.936254i	0.998087	−	0.0618325i	$-0.0196945\pi$
$761$	25.8277	+	25.8277i	0.936254	+	0.936254i	−0.0618325	+	0.998087i	$0.519694\pi$
$762$	2.10449	+	18.8763i	0.0762377	+	0.683815i
$763$	−19.8317	+	8.21457i	−0.717957	+	0.297387i
$764$	4.08980	+	15.0117i	0.147964	+	0.543104i
$765$	−14.9823	−	41.2010i	−0.541688	−	1.48963i
$766$	−5.90997	−	4.51526i	−0.213536	−	0.163143i
$767$	2.32783			0.0840532
$768$	−7.03284	−	26.8056i	−0.253776	−	0.967263i
$769$	−22.8386			−0.823580			−0.411790	−	0.911279i	$-0.635096\pi$
$769$	−22.8386			−0.823580			−0.411790	+	0.911279i	$0.635096\pi$
$770$	11.2145	+	8.56793i	0.404141	+	0.308767i
$771$	14.2312	+	14.8704i	0.512524	+	0.535546i
$772$	−3.27802	−	12.0320i	−0.117978	−	0.433042i
$773$	−8.07057	+	3.34294i	−0.290278	+	0.120237i	−0.523071	−	0.852289i	$-0.675214\pi$
$773$	−8.07057	+	3.34294i	−0.290278	+	0.120237i	0.232793	+	0.972526i	$0.425214\pi$
$774$	16.6233	+	5.20841i	0.597513	+	0.187213i
$775$	−1.47328	−	1.47328i	−0.0529219	−	0.0529219i
$776$	11.0493	−	27.1565i	0.396647	−	0.974861i
$777$	−11.3098	−	29.0957i	−0.405738	−	1.04380i
$778$	−38.3716	−	10.1956i	−1.37569	−	0.365531i
$779$	−7.82591	+	3.24160i	−0.280392	+	0.116142i
$780$	1.21972	−	2.02847i	0.0436730	−	0.0726309i
$781$	7.28079	−	17.5774i	0.260527	−	0.628968i
$782$	−3.03212	−	22.6646i	−0.108429	−	0.810484i
$783$	−27.2073	+	9.22236i	−0.972311	+	0.329580i
$784$	−0.950341	−	1.61467i	−0.0339407	−	0.0576666i
$785$	−21.2311			−0.757769
$786$	−2.97424	−	0.860633i	−0.106088	−	0.0306978i
$787$	23.1792	+	9.60114i	0.826249	+	0.342244i	0.755417	−	0.655245i	$-0.227434\pi$
$787$	23.1792	+	9.60114i	0.826249	+	0.342244i	0.0708325	+	0.997488i	$0.477434\pi$
$788$	9.15285	+	11.8254i	0.326057	+	0.421262i
$789$	−0.625023	+	28.4540i	−0.0222514	+	1.01299i
$790$	8.93684	+	2.37458i	0.317959	+	0.0844838i
$791$	−26.3525	−	26.3525i	−0.936989	−	0.936989i
$792$	13.0737	+	0.492401i	0.464553	+	0.0174967i
$793$	0.946326	−	0.946326i	0.0336050	−	0.0336050i
$794$	−46.2154	+	26.8116i	−1.64012	+	0.951508i
$795$	−54.9449	−	1.20692i	−1.94870	−	0.0428052i
$796$	−17.4816	+	30.5739i	−0.619619	+	1.08366i
$797$	9.64229	−	23.2785i	0.341547	−	0.824568i	−0.656012	−	0.754750i	$-0.727758\pi$
$797$	9.64229	−	23.2785i	0.341547	−	0.824568i	0.997560	−	0.0698182i	$-0.0222419\pi$
$798$	−25.6804	−	46.5939i	−0.909077	−	1.64940i
$799$			9.55151i			0.337908i
$800$	−2.71164	+	2.12617i	−0.0958711	+	0.0751716i
$801$	12.9649	−	11.8732i	0.458093	−	0.419519i
$802$	35.6450	+	27.2330i	1.25867	+	0.961630i
$803$	−5.50005	−	2.27819i	−0.194092	−	0.0803957i
$804$	−3.87013	+	2.86181i	−0.136489	+	0.100928i
$805$	6.49052	+	15.6695i	0.228761	+	0.552277i
$806$	0.700307	+	1.20713i	0.0246673	+	0.0425192i
$807$	24.0230	−	9.33801i	0.845651	−	0.328713i
$808$	−0.203196	−	32.3591i	−0.00714842	−	1.13839i
$809$	24.9240	−	24.9240i	0.876282	−	0.876282i	−0.116866	−	0.993148i	$-0.537285\pi$
$809$	24.9240	−	24.9240i	0.876282	−	0.876282i	0.993148	+	0.116866i	$0.0372847\pi$
$810$	28.3419	+	10.2672i	0.995834	+	0.360753i
$811$	6.09225	+	14.7080i	0.213928	+	0.516467i	0.994020	−	0.109197i	$-0.0348280\pi$
$811$	6.09225	+	14.7080i	0.213928	+	0.516467i	−0.780092	+	0.625664i	$0.784828\pi$
$812$	−18.4957	−	23.8963i	−0.649073	−	0.838596i
$813$	8.85073	−	8.47026i	0.310409	−	0.297065i
$814$	1.90683	+	14.2532i	0.0668344	+	0.499575i
$815$		−	7.12017i		−	0.249409i
$816$	11.6244	−	41.1383i	0.406936	−	1.44013i
$817$			32.6330i			1.14168i
$818$	−35.3467	+	4.72877i	−1.23587	+	0.165338i
$819$	−0.808327	−	2.22288i	−0.0282452	−	0.0776737i
$820$	5.00797	+	0.637995i	0.174886	+	0.0222798i
$821$	9.49765	+	22.9294i	0.331470	+	0.800240i	0.998476	+	0.0551876i	$0.0175757\pi$
$821$	9.49765	+	22.9294i	0.331470	+	0.800240i	−0.667006	+	0.745053i	$0.732424\pi$
$822$	−16.3197	+	20.4152i	−0.569214	+	0.712062i
$823$	27.2557	−	27.2557i	0.950072	−	0.950072i	−0.0487391	−	0.998812i	$-0.515520\pi$
$823$	27.2557	−	27.2557i	0.950072	−	0.950072i	0.998812	+	0.0487391i	$0.0155203\pi$
$824$	38.6360	−	16.2885i	1.34595	−	0.567438i
$825$	−0.589369	−	1.51621i	−0.0205192	−	0.0527878i
$826$	−26.9734	+	15.6485i	−0.938525	+	0.544480i
$827$	−20.6867	−	49.9420i	−0.719345	−	1.73665i	−0.675207	−	0.737628i	$-0.735946\pi$
$827$	−20.6867	−	49.9420i	−0.719345	−	1.73665i	−0.0441379	−	0.999025i	$-0.514054\pi$
$828$	13.2932	+	8.39613i	0.461972	+	0.291786i
$829$	−0.359915	−	0.149082i	−0.0125004	−	0.00517782i	0.376424	−	0.926447i	$-0.377153\pi$
$829$	−0.359915	−	0.149082i	−0.0125004	−	0.00517782i	−0.388925	+	0.921269i	$0.627153\pi$
$830$	−13.4503	+	17.6049i	−0.466866	+	0.611076i
$831$	−0.856489	+	1.94575i	−0.0297113	+	0.0674973i
$832$	2.12107	−	0.909948i	0.0735348	−	0.0315468i
$833$		−	2.89014i		−	0.100137i
$834$	1.27428	+	2.31201i	0.0441246	+	0.0800585i
$835$	2.39473	−	5.78138i	0.0828730	−	0.200073i
$836$	6.44220	+	23.6462i	0.222808	+	0.817822i
$837$	−13.3677	+	11.7128i	−0.462057	+	0.404855i
$838$	−1.61810	−	2.78913i	−0.0558963	−	0.0963490i
$839$	−27.7697	+	27.7697i	−0.958717	+	0.958717i	−0.999181	−	0.0404644i	$-0.987116\pi$
$839$	−27.7697	+	27.7697i	−0.958717	+	0.958717i	0.0404644	+	0.999181i	$0.487116\pi$
$840$	−0.497261	+	31.7040i	−0.0171571	+	1.09389i
$841$	−1.10756	−	1.10756i	−0.0381918	−	0.0381918i
$842$	0.161296	−	0.607044i	0.00555862	−	0.0209201i
$843$	−29.4386	−	0.646651i	−1.01392	−	0.0222718i
$844$	0.319673	−	2.50928i	0.0110036	−	0.0863730i
$845$	−28.2629	−	11.7069i	−0.972275	−	0.402729i
$846$	−5.03861	−	4.21245i	−0.173231	−	0.144827i
$847$	23.5645			0.809686
$848$	−42.7874	−	32.2664i	−1.46933	−	1.10803i
$849$	9.67982	−	21.9904i	0.332211	−	0.754707i
$850$	−5.26849	+	0.704832i	−0.180708	+	0.0241755i
$851$	−6.61346	+	15.9663i	−0.226706	+	0.547317i
$852$	41.4791	−	10.3277i	1.42105	−	0.353820i
$853$	20.4516	−	8.47133i	0.700250	−	0.290053i	−0.00401354	−	0.999992i	$-0.501278\pi$
$853$	20.4516	−	8.47133i	0.700250	−	0.290053i	0.704263	+	0.709939i	$0.251278\pi$
$854$	−4.60389	+	17.3269i	−0.157542	+	0.592916i
$855$	−2.47960	+	56.4145i	−0.0848007	+	1.92933i
$856$	−0.180623	−	28.7643i	−0.00617356	−	0.983144i
$857$	13.1734	+	13.1734i	0.449996	+	0.449996i	0.895353	−	0.445357i	$-0.146923\pi$
$857$	13.1734	+	13.1734i	0.449996	+	0.449996i	−0.445357	+	0.895353i	$0.646923\pi$
$858$	0.120729	+	1.08288i	0.00412163	+	0.0369690i
$859$	−7.55122	+	3.12782i	−0.257644	+	0.106720i	−0.507767	−	0.861494i	$-0.669529\pi$
$859$	−7.55122	+	3.12782i	−0.257644	+	0.106720i	0.250123	+	0.968214i	$0.419529\pi$
$860$	9.65384	−	16.8838i	0.329193	−	0.575732i
$861$	3.64477	−	3.48809i	0.124214	−	0.118874i
$862$	2.53579	−	3.31907i	0.0863695	−	0.113048i
$863$	−19.3590			−0.658989			−0.329494	−	0.944158i	$-0.606878\pi$
$863$	−19.3590			−0.658989			−0.329494	+	0.944158i	$0.606878\pi$
$864$	16.5746	+	24.2751i	0.563880	+	0.825857i
$865$	24.5889			0.836049
$866$	26.9137	−	35.2270i	0.914564	−	1.19706i
$867$	26.3692	−	25.2357i	0.895547	−	0.857049i
$868$	−16.2294	−	9.27969i	−0.550862	−	0.314973i
$869$	−3.93268	+	1.62897i	−0.133407	+	0.0552591i
$870$	3.55381	+	31.8759i	0.120485	+	1.08070i
$871$	−0.283457	−	0.283457i	−0.00960456	−	0.00960456i
$872$	15.8078	+	15.6105i	0.535320	+	0.528639i
$873$	−1.36549	+	31.0667i	−0.0462147	+	1.05145i
$874$	−7.56349	+	28.4655i	−0.255839	+	0.962861i
$875$	−26.2559	+	10.8755i	−0.887611	+	0.367661i
$876$	−3.23158	−	12.9790i	−0.109185	−	0.438520i
$877$	−6.24223	+	15.0701i	−0.210785	+	0.508880i	−0.993544	−	0.113444i	$-0.963812\pi$
$877$	−6.24223	+	15.0701i	−0.210785	+	0.508880i	0.782759	+	0.622325i	$0.213812\pi$
$878$	−14.7564	+	1.97414i	−0.498003	+	0.0666241i
$879$	18.6871	−	42.4528i	0.630299	−	1.43190i
$880$	3.66219	−	14.1400i	0.123453	−	0.476659i
$881$	−36.6844			−1.23593			−0.617964	−	0.786207i	$-0.712042\pi$
$881$	−36.6844			−1.23593			−0.617964	+	0.786207i	$0.712042\pi$
$882$	1.52460	+	1.27462i	0.0513361	+	0.0429188i
$883$	11.4178	+	4.72942i	0.384240	+	0.159158i	0.566438	−	0.824104i	$-0.308321\pi$
$883$	11.4178	+	4.72942i	0.384240	+	0.159158i	−0.182198	+	0.983262i	$0.558321\pi$
$884$	3.53175	+	0.449931i	0.118786	+	0.0151328i
$885$	33.0908	+	0.726874i	1.11233	+	0.0244336i
$886$	−3.32169	+	12.5013i	−0.111594	+	0.419990i
$887$	−34.3135	−	34.3135i	−1.15213	−	1.15213i	−0.986124	−	0.166009i	$-0.946912\pi$
$887$	−34.3135	−	34.3135i	−1.15213	−	1.15213i	−0.166009	−	0.986124i	$-0.553088\pi$
$888$	−23.2010	+	22.4845i	−0.778575	+	0.754529i
$889$	14.9838	−	14.9838i	0.502540	−	0.502540i
$890$	−9.84931	−	16.9773i	−0.330150	−	0.569082i
$891$	−13.2367	+	4.16503i	−0.443447	+	0.139534i
$892$	20.2706	−	5.52256i	0.678711	−	0.184909i
$893$	4.70809	−	11.3663i	0.157550	−	0.380360i
$894$	−1.41796	−	2.57270i	−0.0474236	−	0.0860441i
$895$			0.0329316i			0.00110078i
$896$	−18.4606	+	24.8024i	−0.616725	+	0.828591i
$897$	−0.527550	+	1.19847i	−0.0176144	+	0.0400159i
$898$	20.6829	−	27.0717i	0.690199	−	0.903393i
$899$	−17.4711	−	7.23678i	−0.582695	−	0.241360i
$900$	1.95172	−	3.09008i	0.0650574	−	0.103003i
$901$	−31.6352	−	76.3741i	−1.05392	−	2.54439i
$902$	−2.01019	+	1.16620i	−0.0669322	+	0.0388303i
$903$	−7.04144	−	18.1149i	−0.234324	−	0.602825i
$904$	−14.5367	+	35.7276i	−0.483483	+	1.18828i
$905$	17.1330	−	17.1330i	0.569519	−	0.569519i
$906$	21.2162	−	26.5405i	0.704860	−	0.881749i
$907$	5.32554	+	12.8570i	0.176832	+	0.426910i	0.987299	−	0.158875i	$-0.0507866\pi$
$907$	5.32554	+	12.8570i	0.176832	+	0.426910i	−0.810467	+	0.585784i	$0.800787\pi$
$908$	−4.59244	+	36.0486i	−0.152406	+	1.19631i
$909$	11.7297	+	32.2562i	0.389048	+	1.06987i
$910$	−2.61742	+	0.350165i	−0.0867667	+	0.0116079i
$911$		−	10.5385i		−	0.349157i	−0.984643	−	0.174579i	$-0.944144\pi$
$911$		−	10.5385i		−	0.349157i	0.984643	−	0.174579i	$-0.0558563\pi$
$912$	−34.1109	+	43.2249i	−1.12952	+	1.43132i
$913$		−	10.1988i		−	0.337530i
$914$	−3.68119	−	27.5162i	−0.121763	−	0.910156i
$915$	13.7478	−	13.1568i	0.454488	−	0.434950i
$916$	−24.2869	+	18.7980i	−0.802461	+	0.621104i
$917$	1.32195	+	3.19147i	0.0436546	+	0.105392i
$918$	3.04042	+	45.2403i	0.100349	+	1.49315i
$919$	11.9849	−	11.9849i	0.395346	−	0.395346i	−0.481242	−	0.876588i	$-0.659814\pi$
$919$	11.9849	−	11.9849i	0.395346	−	0.395346i	0.876588	+	0.481242i	$0.159814\pi$
$920$	12.3342	−	12.4901i	0.406647	−	0.411786i
$921$	−1.16092	+	0.451262i	−0.0382536	+	0.0148696i
$922$	−20.3066	−	35.0027i	−0.668763	−	1.15275i
$923$	1.36235	+	3.28900i	0.0448423	+	0.108259i
$924$	−8.67843	−	11.7362i	−0.285499	−	0.386091i
$925$	3.71144	+	1.53733i	0.122032	+	0.0505471i
$926$	40.1814	+	30.6988i	1.32044	+	1.00883i
$927$	−32.7974	+	30.0357i	−1.07721	+	0.986502i
$928$	−15.3532	+	27.2471i	−0.503992	+	0.894429i
$929$			0.514845i			0.0168915i	0.999964	+	0.00844575i	$0.00268840\pi$
$929$			0.514845i			0.0168915i	−0.999964	+	0.00844575i	$0.997312\pi$
$930$	9.57813	+	17.3783i	0.314079	+	0.569857i
$931$	−1.42460	+	3.43928i	−0.0466892	+	0.112718i
$932$	6.23848	+	3.56705i	0.204348	+	0.116843i
$933$	8.83166	+	0.193997i	0.289136	+	0.00635117i
$934$	5.90959	−	3.42842i	0.193368	−	0.112181i
$935$	15.9323	−	15.9323i	0.521043	−	0.521043i
$936$	−1.79494	+	1.66464i	−0.0586693	+	0.0544103i
$937$	−15.6989	−	15.6989i	−0.512862	−	0.512862i	0.402540	−	0.915402i	$-0.368127\pi$
$937$	−15.6989	−	15.6989i	−0.512862	−	0.512862i	−0.915402	+	0.402540i	$0.868127\pi$
$938$	5.19000	+	1.37902i	0.169460	+	0.0450266i
$939$	1.24924	−	56.8715i	0.0407675	−	1.85593i
$940$	−5.79841	+	4.48797i	−0.189123	+	0.146381i
$941$	8.26022	+	3.42149i	0.269275	+	0.111538i	0.513236	−	0.858248i	$-0.328447\pi$
$941$	8.26022	+	3.42149i	0.269275	+	0.111538i	−0.243960	+	0.969785i	$0.578447\pi$
$942$	21.0930	+	6.10352i	0.687247	+	0.198863i
$943$	−2.79291			−0.0909497
$944$	25.7689	+	19.4326i	0.838705	+	0.632476i
$945$	−10.7965	−	31.8512i	−0.351210	−	1.03612i
$946$	1.18718	+	8.87398i	0.0385986	+	0.288518i
$947$	−1.67384	+	4.04101i	−0.0543926	+	0.131315i	−0.948740	−	0.316058i	$-0.897641\pi$
$947$	−1.67384	+	4.04101i	−0.0543926	+	0.131315i	0.894347	+	0.447373i	$0.147641\pi$
$948$	−8.19609	−	4.92831i	−0.266196	−	0.160064i
$949$	1.02914	−	0.426286i	0.0334074	−	0.0138378i
$950$	6.61696	+	1.75817i	0.214682	+	0.0570426i
$951$	−2.32939	−	5.99261i	−0.0755357	−	0.194324i
$952$	−43.9482	+	18.5281i	−1.42437	+	0.600499i
$953$	32.0579	+	32.0579i	1.03846	+	1.03846i	0.999230	+	0.0392279i	$0.0124898\pi$
$953$	32.0579	+	32.0579i	1.03846	+	1.03846i	0.0392279	+	0.999230i	$0.487510\pi$
$954$	54.2407	+	16.9947i	1.75611	+	0.550223i
$955$	−17.0220	+	7.05074i	−0.550819	+	0.228157i
$956$	33.9828	−	9.25830i	1.09908	−	0.299435i
$957$	−10.2083	−	10.6669i	−0.329989	−	0.344812i
$958$	17.8666	+	13.6502i	0.577242	+	0.441017i
$959$	29.1598			0.941619
$960$	30.4357	−	12.2729i	0.982308	−	0.396105i
$961$	19.3005			0.622596
$962$	−2.13815	−	1.63356i	−0.0689366	−	0.0526680i
$963$	10.4266	+	28.6728i	0.335992	+	0.923970i
$964$	−11.9375	+	3.25225i	−0.384480	+	0.104748i
$965$	13.6433	−	5.65124i	0.439193	−	0.181920i
$966$	−1.94364	−	17.4335i	−0.0625356	−	0.560914i
$967$	−37.4258	−	37.4258i	−1.20353	−	1.20353i	−0.973085	−	0.230448i	$-0.925981\pi$
$967$	−37.4258	−	37.4258i	−1.20353	−	1.20353i	−0.230448	−	0.973085i	$-0.574019\pi$
$968$	−9.47448	−	22.4732i	−0.304521	−	0.722317i
$969$	−79.1684	+	30.7736i	−2.54326	+	0.988591i
$970$	33.5539	+	8.91551i	1.07735	+	0.286260i
$971$	33.0754	−	13.7003i	1.06144	−	0.439663i	0.217478	−	0.976065i	$-0.430217\pi$
$971$	33.0754	−	13.7003i	1.06144	−	0.439663i	0.843962	+	0.536402i	$0.180217\pi$
$972$	−25.2060	−	18.3482i	−0.808484	−	0.588519i
$973$	1.12712	−	2.72110i	0.0361337	−	0.0872344i
$974$	−2.76561	−	20.6725i	−0.0886160	−	0.662389i
$975$	0.278591	+	0.122632i	0.00892206	+	0.00392735i
$976$	18.3756	−	2.57588i	0.588188	−	0.0824520i
$977$	−39.7489			−1.27168			−0.635839	−	0.771821i	$-0.719346\pi$
$977$	−39.7489			−1.27168			−0.635839	+	0.771821i	$0.719346\pi$
$978$	−2.04691	+	7.07387i	−0.0654530	+	0.226198i
$979$	8.34750	+	3.45765i	0.266787	+	0.110507i
$980$	1.75451	−	1.35799i	0.0560457	−	0.0433793i
$981$	−21.3535	−	9.96489i	−0.681765	−	0.318155i
$982$	0.452899	+	0.120339i	0.0144526	+	0.00384016i
$983$	29.8565	+	29.8565i	0.952276	+	0.952276i	0.998912	−	0.0466360i	$-0.0148501\pi$
$983$	29.8565	+	29.8565i	0.952276	+	0.952276i	−0.0466360	+	0.998912i	$0.514850\pi$
$984$	−4.79199	−	2.07354i	−0.152763	−	0.0661020i
$985$	−12.5214	+	12.5214i	−0.398965	+	0.398965i
$986$	−41.7300	+	24.2094i	−1.32895	+	0.770985i
$987$	−0.160912	+	7.32546i	−0.00512187	+	0.233172i
$988$	−3.98102	−	2.27628i	−0.126653	−	0.0724180i
$989$	−4.11750	+	9.94053i	−0.130929	+	0.316091i
$990$	1.37806	+	15.4312i	0.0437978	+	0.490434i
$991$		−	56.2662i		−	1.78736i	−0.448710	−	0.893678i	$-0.648116\pi$
$991$		−	56.2662i		−	1.78736i	0.448710	−	0.893678i	$-0.351884\pi$
$992$	−2.32465	+	19.2089i	−0.0738079	+	0.609882i
$993$	−13.4667	−	5.92782i	−0.427352	−	0.188114i
$994$	−37.8958	−	28.9527i	−1.20198	−	0.918323i
$995$	−38.5309	−	15.9600i	−1.22151	−	0.505966i
$996$	18.4239	−	13.6238i	0.583783	−	0.431685i
$997$	13.8797	+	33.5085i	0.439574	+	1.06122i	0.976096	+	0.217339i	$0.0697376\pi$
$997$	13.8797	+	33.5085i	0.439574	+	1.06122i	−0.536523	+	0.843886i	$0.680262\pi$
$998$	4.32116	+	7.44842i	0.136784	+	0.235776i
$999$	15.1699	−	30.7277i	0.479956	−	0.972181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.o.a.35.13	yes	56
3.2	odd	2	inner	96.2.o.a.35.2	yes	56
4.3	odd	2		384.2.o.a.47.3		56
8.3	odd	2		768.2.o.a.95.12		56
8.5	even	2		768.2.o.b.95.3		56
12.11	even	2		384.2.o.a.47.8		56
24.5	odd	2		768.2.o.b.95.8		56
24.11	even	2		768.2.o.a.95.7		56
32.5	even	8		768.2.o.a.671.7		56
32.11	odd	8	inner	96.2.o.a.11.2	✓	56
32.21	even	8		384.2.o.a.335.8		56
32.27	odd	8		768.2.o.b.671.8		56
96.5	odd	8		768.2.o.a.671.12		56
96.11	even	8	inner	96.2.o.a.11.13	yes	56
96.53	odd	8		384.2.o.a.335.3		56
96.59	even	8		768.2.o.b.671.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.2	✓	56	32.11	odd	8	inner
96.2.o.a.11.13	yes	56	96.11	even	8	inner
96.2.o.a.35.2	yes	56	3.2	odd	2	inner
96.2.o.a.35.13	yes	56	1.1	even	1	trivial
384.2.o.a.47.3		56	4.3	odd	2
384.2.o.a.47.8		56	12.11	even	2
384.2.o.a.335.3		56	96.53	odd	8
384.2.o.a.335.8		56	32.21	even	8
768.2.o.a.95.7		56	24.11	even	2
768.2.o.a.95.12		56	8.3	odd	2
768.2.o.a.671.7		56	32.5	even	8
768.2.o.a.671.12		56	96.5	odd	8
768.2.o.b.95.3		56	8.5	even	2
768.2.o.b.95.8		56	24.5	odd	2
768.2.o.b.671.3		56	96.59	even	8
768.2.o.b.671.8		56	32.27	odd	8

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.o (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12377 + 0.858568i) q^{2} +(1.25135 - 1.19755i) q^{3} +(0.525721 + 1.92967i) q^{4} +(-2.18808 + 0.906333i) q^{5} +(2.43441 - 0.271409i) q^{6} +(-1.93241 - 1.93241i) q^{7} +(-1.06596 + 2.61987i) q^{8} +(0.131733 - 2.99711i) q^{9} +O(q^{10})\)	\(q+(1.12377 + 0.858568i) q^{2} +(1.25135 - 1.19755i) q^{3} +(0.525721 + 1.92967i) q^{4} +(-2.18808 + 0.906333i) q^{5} +(2.43441 - 0.271409i) q^{6} +(-1.93241 - 1.93241i) q^{7} +(-1.06596 + 2.61987i) q^{8} +(0.131733 - 2.99711i) q^{9} +(-3.23705 - 0.860107i) q^{10} +(1.42447 - 0.590036i) q^{11} +(2.96874 + 1.78510i) q^{12} +(-0.110405 + 0.266541i) q^{13} +(-0.512479 - 3.83069i) q^{14} +(-1.65266 + 3.75448i) q^{15} +(-3.44724 + 2.02893i) q^{16} -6.17031 q^{17} +(2.72126 - 3.25496i) q^{18} +(7.34269 + 3.04144i) q^{19} +(-2.89924 - 3.74579i) q^{20} +(-4.73227 - 0.103949i) q^{21} +(2.10737 + 0.559943i) q^{22} +(1.85295 + 1.85295i) q^{23} +(1.80355 + 4.55491i) q^{24} +(0.430727 - 0.430727i) q^{25} +(-0.352914 + 0.204741i) q^{26} +(-3.42435 - 3.90817i) q^{27} +(2.71300 - 4.74481i) q^{28} +(2.11574 - 5.10784i) q^{29} +(-5.08069 + 2.80025i) q^{30} -3.42046i q^{31} +(-5.61588 - 0.679633i) q^{32} +(1.07591 - 2.44422i) q^{33} +(-6.93401 - 5.29763i) q^{34} +(5.97967 + 2.47686i) q^{35} +(5.85267 - 1.32144i) q^{36} +(2.52377 + 6.09293i) q^{37} +(5.64022 + 9.72209i) q^{38} +(0.181042 + 0.465751i) q^{39} +(-0.0420633 - 6.69861i) q^{40} +(-0.753641 + 0.753641i) q^{41} +(-5.22874 - 4.17979i) q^{42} +(1.57129 + 3.79343i) q^{43} +(1.88745 + 2.43857i) q^{44} +(2.42813 + 6.67731i) q^{45} +(0.491405 + 3.67317i) q^{46} -1.54798i q^{47} +(-1.88393 + 6.66714i) q^{48} +0.468394i q^{49} +(0.853846 - 0.114230i) q^{50} +(-7.72119 + 7.38927i) q^{51} +(-0.572378 - 0.0729187i) q^{52} +(5.12700 + 12.3777i) q^{53} +(-0.492750 - 7.33193i) q^{54} +(-2.58210 + 2.58210i) q^{55} +(7.12253 - 3.00278i) q^{56} +(12.8305 - 4.98737i) q^{57} +(6.76303 - 3.92353i) q^{58} +(-3.08775 - 7.45449i) q^{59} +(-8.11374 - 1.21529i) q^{60} +(-4.28571 - 1.77520i) q^{61} +(2.93670 - 3.84381i) q^{62} +(-6.04619 + 5.53707i) q^{63} +(-5.72745 - 5.58537i) q^{64} -0.683277i q^{65} +(3.30761 - 1.82300i) q^{66} +(-0.531731 + 1.28371i) q^{67} +(-3.24386 - 11.9066i) q^{68} +(4.53768 + 0.0996750i) q^{69} +(4.59322 + 7.91738i) q^{70} +(8.72539 - 8.72539i) q^{71} +(7.71161 + 3.53993i) q^{72} +(-2.73022 - 2.73022i) q^{73} +(-2.39505 + 9.01389i) q^{74} +(0.0231699 - 1.05481i) q^{75} +(-2.00877 + 15.7679i) q^{76} +(-3.89285 - 1.61247i) q^{77} +(-0.196429 + 0.678834i) q^{78} -2.76080 q^{79} +(5.70394 - 7.56381i) q^{80} +(-8.96529 - 0.789635i) q^{81} +(-1.49397 + 0.199867i) q^{82} +(2.53133 - 6.11116i) q^{83} +(-2.28726 - 9.18636i) q^{84} +(13.5011 - 5.59235i) q^{85} +(-1.49115 + 5.61200i) q^{86} +(-3.46939 - 8.92538i) q^{87} +(0.0273838 + 4.36089i) q^{88} +(4.14369 + 4.14369i) q^{89} +(-3.00426 + 9.58848i) q^{90} +(0.728413 - 0.301719i) q^{91} +(-2.60144 + 4.54970i) q^{92} +(-4.09618 - 4.28017i) q^{93} +(1.32905 - 1.73957i) q^{94} -18.8230 q^{95} +(-7.84130 + 5.87486i) q^{96} -10.3656 q^{97} +(-0.402149 + 0.526368i) q^{98} +(-1.58075 - 4.34703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9	\( 56 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} - 16 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 40 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} - 24 q^{22} + 16 q^{24} - 8 q^{25} - 28 q^{27} - 8 q^{28} + 44 q^{30} - 8 q^{33} - 24 q^{34} + 48 q^{36} - 8 q^{37} - 28 q^{39} + 24 q^{40} + 56 q^{42} - 8 q^{43} - 4 q^{45} + 24 q^{46} + 48 q^{48} - 16 q^{51} + 48 q^{52} + 40 q^{54} + 24 q^{55} - 4 q^{57} + 96 q^{58} + 8 q^{60} - 40 q^{61} + 40 q^{64} - 28 q^{66} + 56 q^{67} - 4 q^{69} + 40 q^{70} - 64 q^{72} - 8 q^{73} + 16 q^{75} + 48 q^{76} - 92 q^{78} + 16 q^{79} - 48 q^{82} - 136 q^{84} - 48 q^{85} + 52 q^{87} - 48 q^{88} - 136 q^{90} + 40 q^{91} + 8 q^{93} - 64 q^{94} - 104 q^{96} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 - 16 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 40 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 - 24 * q^22 + 16 * q^24 - 8 * q^25 - 28 * q^27 - 8 * q^28 + 44 * q^30 - 8 * q^33 - 24 * q^34 + 48 * q^36 - 8 * q^37 - 28 * q^39 + 24 * q^40 + 56 * q^42 - 8 * q^43 - 4 * q^45 + 24 * q^46 + 48 * q^48 - 16 * q^51 + 48 * q^52 + 40 * q^54 + 24 * q^55 - 4 * q^57 + 96 * q^58 + 8 * q^60 - 40 * q^61 + 40 * q^64 - 28 * q^66 + 56 * q^67 - 4 * q^69 + 40 * q^70 - 64 * q^72 - 8 * q^73 + 16 * q^75 + 48 * q^76 - 92 * q^78 + 16 * q^79 - 48 * q^82 - 136 * q^84 - 48 * q^85 + 52 * q^87 - 48 * q^88 - 136 * q^90 + 40 * q^91 + 8 * q^93 - 64 * q^94 - 104 * q^96 - 16 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more