LMFDB - Embedded newform 760.2.f.b.381.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.15
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.676154 - 1.24210i) q^{2} +1.70163i q^{3} +(-1.08563 + 1.67970i) q^{4} +1.00000i q^{5} +(2.11360 - 1.15057i) q^{6} +1.91794 q^{7} +(2.82042 + 0.212725i) q^{8} +0.104446 q^{9} +(1.24210 - 0.676154i) q^{10} -4.53978i q^{11} +(-2.85824 - 1.84735i) q^{12} -3.96750i q^{13} +(-1.29683 - 2.38228i) q^{14} -1.70163 q^{15} +(-1.64281 - 3.64708i) q^{16} +1.87557 q^{17} +(-0.0706218 - 0.129733i) q^{18} +1.00000i q^{19} +(-1.67970 - 1.08563i) q^{20} +3.26364i q^{21} +(-5.63886 + 3.06959i) q^{22} +5.88514 q^{23} +(-0.361980 + 4.79931i) q^{24} -1.00000 q^{25} +(-4.92804 + 2.68264i) q^{26} +5.28263i q^{27} +(-2.08218 + 3.22158i) q^{28} +9.11883i q^{29} +(1.15057 + 2.11360i) q^{30} +10.2385 q^{31} +(-3.41925 + 4.50652i) q^{32} +7.72503 q^{33} +(-1.26817 - 2.32964i) q^{34} +1.91794i q^{35} +(-0.113390 + 0.175439i) q^{36} -4.77120i q^{37} +(1.24210 - 0.676154i) q^{38} +6.75123 q^{39} +(-0.212725 + 2.82042i) q^{40} +1.03479 q^{41} +(4.05377 - 2.20672i) q^{42} -6.88595i q^{43} +(7.62548 + 4.92852i) q^{44} +0.104446i q^{45} +(-3.97926 - 7.30994i) q^{46} -8.52598 q^{47} +(6.20599 - 2.79546i) q^{48} -3.32149 q^{49} +(0.676154 + 1.24210i) q^{50} +3.19153i q^{51} +(6.66423 + 4.30724i) q^{52} +4.21648i q^{53} +(6.56156 - 3.57187i) q^{54} +4.53978 q^{55} +(5.40940 + 0.407994i) q^{56} -1.70163 q^{57} +(11.3265 - 6.16573i) q^{58} +5.57956i q^{59} +(1.84735 - 2.85824i) q^{60} +1.67139i q^{61} +(-6.92281 - 12.7173i) q^{62} +0.200322 q^{63} +(7.90950 + 1.19995i) q^{64} +3.96750 q^{65} +(-5.22331 - 9.59527i) q^{66} +8.44650i q^{67} +(-2.03617 + 3.15040i) q^{68} +10.0143i q^{69} +(2.38228 - 1.29683i) q^{70} +13.9445 q^{71} +(0.294582 + 0.0222183i) q^{72} -7.89229 q^{73} +(-5.92631 + 3.22607i) q^{74} -1.70163i q^{75} +(-1.67970 - 1.08563i) q^{76} -8.70703i q^{77} +(-4.56487 - 8.38571i) q^{78} +6.65433 q^{79} +(3.64708 - 1.64281i) q^{80} -8.67575 q^{81} +(-0.699679 - 1.28532i) q^{82} -8.65418i q^{83} +(-5.48194 - 3.54310i) q^{84} +1.87557i q^{85} +(-8.55305 + 4.65597i) q^{86} -15.5169 q^{87} +(0.965723 - 12.8041i) q^{88} -4.77053 q^{89} +(0.129733 - 0.0706218i) q^{90} -7.60944i q^{91} +(-6.38909 + 9.88529i) q^{92} +17.4222i q^{93} +(5.76488 + 10.5901i) q^{94} -1.00000 q^{95} +(-7.66845 - 5.81830i) q^{96} -3.50972 q^{97} +(2.24584 + 4.12563i) q^{98} -0.474163i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.676154	−	1.24210i	−0.478113	−	0.878298i
$2$	−0.676154	−	1.24210i	−0.478113	−	0.878298i
$3$			1.70163i			0.982438i	0.871036	+	0.491219i	$0.163449\pi$
$3$			1.70163i			0.982438i	−0.871036	+	0.491219i	$0.836551\pi$
$4$	−1.08563	+	1.67970i	−0.542816	+	0.839852i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	2.11360	−	1.15057i	0.862874	−	0.469717i
$7$	1.91794			0.724915			0.362457	−	0.932000i	$-0.381938\pi$
$7$	1.91794			0.724915			0.362457	+	0.932000i	$0.381938\pi$
$8$	2.82042	+	0.212725i	0.997168	+	0.0752096i
$9$	0.104446			0.0348155
$10$	1.24210	−	0.676154i	0.392787	−	0.213819i
$11$		−	4.53978i		−	1.36879i	−0.729110	−	0.684397i	$-0.760066\pi$
$11$		−	4.53978i		−	1.36879i	0.729110	−	0.684397i	$-0.239934\pi$
$12$	−2.85824	−	1.84735i	−0.825103	−	0.533283i
$13$		−	3.96750i		−	1.10039i	−0.835037	−	0.550193i	$-0.814554\pi$
$13$		−	3.96750i		−	1.10039i	0.835037	−	0.550193i	$-0.185446\pi$
$14$	−1.29683	−	2.38228i	−0.346591	−	0.636691i
$15$	−1.70163			−0.439360
$16$	−1.64281	−	3.64708i	−0.410703	−	0.911769i
$17$	1.87557			0.454892			0.227446	−	0.973791i	$-0.426963\pi$
$17$	1.87557			0.454892			0.227446	+	0.973791i	$0.426963\pi$
$18$	−0.0706218	−	0.129733i	−0.0166457	−	0.0305784i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.67970	−	1.08563i	−0.375593	−	0.242754i
$21$			3.26364i			0.712184i
$22$	−5.63886	+	3.06959i	−1.20221	+	0.654438i
$23$	5.88514			1.22714			0.613568	−	0.789642i	$-0.289734\pi$
$23$	5.88514			1.22714			0.613568	+	0.789642i	$0.289734\pi$
$24$	−0.361980	+	4.79931i	−0.0738888	+	0.979656i
$25$	−1.00000			−0.200000
$26$	−4.92804	+	2.68264i	−0.966468	+	0.526110i
$27$			5.28263i			1.01664i
$28$	−2.08218	+	3.22158i	−0.393495	+	0.608821i
$29$			9.11883i			1.69332i	0.532131	+	0.846662i	$0.321391\pi$
$29$			9.11883i			1.69332i	−0.532131	+	0.846662i	$0.678609\pi$
$30$	1.15057	+	2.11360i	0.210064	+	0.385889i
$31$	10.2385			1.83889			0.919446	−	0.393217i	$-0.128638\pi$
$31$	10.2385			1.83889			0.919446	+	0.393217i	$0.128638\pi$
$32$	−3.41925	+	4.50652i	−0.604443	+	0.796648i
$33$	7.72503			1.34476
$34$	−1.26817	−	2.32964i	−0.217490	−	0.399531i
$35$			1.91794i			0.324192i
$36$	−0.113390	+	0.175439i	−0.0188984	+	0.0292398i
$37$		−	4.77120i		−	0.784381i	−0.919884	−	0.392190i	$-0.871717\pi$
$37$		−	4.77120i		−	0.784381i	0.919884	−	0.392190i	$-0.128283\pi$
$38$	1.24210	−	0.676154i	0.201495	−	0.109687i
$39$	6.75123			1.08106
$40$	−0.212725	+	2.82042i	−0.0336348	+	0.445947i
$41$	1.03479			0.161607			0.0808037	−	0.996730i	$-0.474251\pi$
$41$	1.03479			0.161607			0.0808037	+	0.996730i	$0.474251\pi$
$42$	4.05377	−	2.20672i	0.625510	−	0.340504i
$43$		−	6.88595i		−	1.05010i	−0.851072	−	0.525049i	$-0.824047\pi$
$43$		−	6.88595i		−	1.05010i	0.851072	−	0.525049i	$-0.175953\pi$
$44$	7.62548	+	4.92852i	1.14958	+	0.743002i
$45$			0.104446i			0.0155699i
$46$	−3.97926	−	7.30994i	−0.586710	−	1.07779i
$47$	−8.52598			−1.24364			−0.621821	−	0.783159i	$-0.713607\pi$
$47$	−8.52598			−1.24364			−0.621821	+	0.783159i	$0.713607\pi$
$48$	6.20599	−	2.79546i	0.895757	−	0.403490i
$49$	−3.32149			−0.474499
$50$	0.676154	+	1.24210i	0.0956226	+	0.175660i
$51$			3.19153i			0.446903i
$52$	6.66423	+	4.30724i	0.924162	+	0.597307i
$53$			4.21648i			0.579177i	0.957151	+	0.289589i	$0.0935185\pi$
$53$			4.21648i			0.579177i	−0.957151	+	0.289589i	$0.906481\pi$
$54$	6.56156	−	3.57187i	0.892915	−	0.486070i
$55$	4.53978			0.612143
$56$	5.40940	+	0.407994i	0.722861	+	0.0545206i
$57$	−1.70163			−0.225387
$58$	11.3265	−	6.16573i	1.48724	−	0.809600i
$59$			5.57956i			0.726397i	0.931712	+	0.363199i	$0.118315\pi$
$59$			5.57956i			0.726397i	−0.931712	+	0.363199i	$0.881685\pi$
$60$	1.84735	−	2.85824i	0.238491	−	0.368997i
$61$			1.67139i			0.214000i	0.994259	+	0.107000i	$0.0341245\pi$
$61$			1.67139i			0.214000i	−0.994259	+	0.107000i	$0.965876\pi$
$62$	−6.92281	−	12.7173i	−0.879198	−	1.61509i
$63$	0.200322			0.0252382
$64$	7.90950	+	1.19995i	0.988687	+	0.149993i
$65$	3.96750			0.492108
$66$	−5.22331	−	9.59527i	−0.642945	−	1.18110i
$67$			8.44650i			1.03190i	0.856617	+	0.515952i	$0.172562\pi$
$67$			8.44650i			1.03190i	−0.856617	+	0.515952i	$0.827438\pi$
$68$	−2.03617	+	3.15040i	−0.246922	+	0.382042i
$69$			10.0143i			1.20559i
$70$	2.38228	−	1.29683i	0.284737	−	0.155000i
$71$	13.9445			1.65491			0.827456	−	0.561531i	$-0.189788\pi$
$71$	13.9445			1.65491			0.827456	+	0.561531i	$0.189788\pi$
$72$	0.294582	+	0.0222183i	0.0347169	+	0.00261846i
$73$	−7.89229			−0.923722			−0.461861	−	0.886952i	$-0.652818\pi$
$73$	−7.89229			−0.923722			−0.461861	+	0.886952i	$0.652818\pi$
$74$	−5.92631	+	3.22607i	−0.688920	+	0.375023i
$75$		−	1.70163i		−	0.196488i
$76$	−1.67970	−	1.08563i	−0.192675	−	0.124530i
$77$		−	8.70703i		−	0.992259i
$78$	−4.56487	−	8.38571i	−0.516870	−	0.949495i
$79$	6.65433			0.748671			0.374335	−	0.927293i	$-0.377871\pi$
$79$	6.65433			0.748671			0.374335	+	0.927293i	$0.377871\pi$
$80$	3.64708	−	1.64281i	0.407756	−	0.183672i
$81$	−8.67575			−0.963972
$82$	−0.699679	−	1.28532i	−0.0772667	−	0.141940i
$83$		−	8.65418i		−	0.949920i	−0.880007	−	0.474960i	$-0.842463\pi$
$83$		−	8.65418i		−	0.949920i	0.880007	−	0.474960i	$-0.157537\pi$
$84$	−5.48194	−	3.54310i	−0.598129	−	0.386584i
$85$			1.87557i			0.203434i
$86$	−8.55305	+	4.65597i	−0.922299	+	0.502066i
$87$	−15.5169			−1.66359
$88$	0.965723	−	12.8041i	0.102946	−	1.36492i
$89$	−4.77053			−0.505675			−0.252838	−	0.967509i	$-0.581364\pi$
$89$	−4.77053			−0.505675			−0.252838	+	0.967509i	$0.581364\pi$
$90$	0.129733	−	0.0706218i	0.0136751	−	0.00744420i
$91$		−	7.60944i		−	0.797687i
$92$	−6.38909	+	9.88529i	−0.666109	+	1.03061i
$93$			17.4222i			1.80660i
$94$	5.76488	+	10.5901i	0.594602	+	1.09229i
$95$	−1.00000			−0.102598
$96$	−7.66845	−	5.81830i	−0.782658	−	0.593828i
$97$	−3.50972			−0.356358			−0.178179	−	0.983998i	$-0.557021\pi$
$97$	−3.50972			−0.356358			−0.178179	+	0.983998i	$0.557021\pi$
$98$	2.24584	+	4.12563i	0.226864	+	0.416751i
$99$		−	0.474163i		−	0.0476552i
$100$	1.08563	−	1.67970i	0.108563	−	0.167970i
$101$			15.7112i			1.56332i	0.623705	+	0.781660i	$0.285627\pi$
$101$			15.7112i			1.56332i	−0.623705	+	0.781660i	$0.714373\pi$
$102$	3.96420	−	2.15796i	0.392514	−	0.213670i
$103$	3.48138			0.343030			0.171515	−	0.985181i	$-0.445134\pi$
$103$	3.48138			0.343030			0.171515	+	0.985181i	$0.445134\pi$
$104$	0.843987	−	11.1900i	0.0827597	−	1.09727i
$105$	−3.26364			−0.318498
$106$	5.23729	−	2.85099i	0.508690	−	0.276912i
$107$		−	19.2252i		−	1.85857i	−0.369358	−	0.929287i	$-0.620422\pi$
$107$		−	19.2252i		−	1.85857i	0.369358	−	0.929287i	$-0.379578\pi$
$108$	−8.87325	−	5.73498i	−0.853829	−	0.551849i
$109$		−	7.74845i		−	0.742167i	−0.928599	−	0.371084i	$-0.878986\pi$
$109$		−	7.74845i		−	0.742167i	0.928599	−	0.371084i	$-0.121014\pi$
$110$	−3.06959	−	5.63886i	−0.292674	−	0.537644i
$111$	8.11883			0.770605
$112$	−3.15082	−	6.99489i	−0.297724	−	0.660955i
$113$	−8.87248			−0.834652			−0.417326	−	0.908757i	$-0.637033\pi$
$113$	−8.87248			−0.834652			−0.417326	+	0.908757i	$0.637033\pi$
$114$	1.15057	+	2.11360i	0.107760	+	0.197957i
$115$			5.88514i			0.548792i
$116$	−15.3169	−	9.89968i	−1.42214	−	0.919162i
$117$		−	0.414391i		−	0.0383105i
$118$	6.93038	−	3.77264i	0.637993	−	0.347300i
$119$	3.59723			0.329758
$120$	−4.79931	−	0.361980i	−0.438115	−	0.0330441i
$121$	−9.60956			−0.873596
$122$	2.07604	−	1.13012i	0.187956	−	0.102316i
$123$			1.76084i			0.158769i
$124$	−11.1152	+	17.1977i	−0.998179	+	1.54440i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.135449	−	0.248821i	−0.0120667	−	0.0221667i
$127$	12.2054			1.08306			0.541528	−	0.840683i	$-0.317846\pi$
$127$	12.2054			1.08306			0.541528	+	0.840683i	$0.317846\pi$
$128$	−3.85758	−	10.6357i	−0.340966	−	0.940076i
$129$	11.7174			1.03166
$130$	−2.68264	−	4.92804i	−0.235283	−	0.432218i
$131$			13.1495i			1.14888i	0.818547	+	0.574440i	$0.194780\pi$
$131$			13.1495i			1.14888i	−0.818547	+	0.574440i	$0.805220\pi$
$132$	−8.38653	+	12.9758i	−0.729954	+	1.12940i
$133$			1.91794i			0.166307i
$134$	10.4914	−	5.71114i	0.906320	−	0.493367i
$135$	−5.28263			−0.454656
$136$	5.28988	+	0.398980i	0.453603	+	0.0342122i
$137$	7.99518			0.683075			0.341537	−	0.939868i	$-0.389052\pi$
$137$	7.99518			0.683075			0.341537	+	0.939868i	$0.389052\pi$
$138$	12.4388	−	6.77124i	1.05886	−	0.576406i
$139$		−	22.8758i		−	1.94030i	−0.242508	−	0.970149i	$-0.577970\pi$
$139$		−	22.8758i		−	1.94030i	0.242508	−	0.970149i	$-0.422030\pi$
$140$	−3.22158	−	2.08218i	−0.272273	−	0.175976i
$141$		−	14.5081i		−	1.22180i
$142$	−9.42865	−	17.3205i	−0.791235	−	1.45351i
$143$	−18.0116			−1.50620
$144$	−0.171586	−	0.380924i	−0.0142988	−	0.0317437i
$145$	−9.11883			−0.757277
$146$	5.33640	+	9.80302i	0.441644	+	0.811303i
$147$		−	5.65196i		−	0.466166i
$148$	8.01420	+	5.17976i	0.658764	+	0.425774i
$149$			23.8712i			1.95560i	0.209531	+	0.977802i	$0.432806\pi$
$149$			23.8712i			1.95560i	−0.209531	+	0.977802i	$0.567194\pi$
$150$	−2.11360	+	1.15057i	−0.172575	+	0.0939433i
$151$	10.1896			0.829215			0.414608	−	0.910000i	$-0.363919\pi$
$151$	10.1896			0.829215			0.414608	+	0.910000i	$0.363919\pi$
$152$	−0.212725	+	2.82042i	−0.0172543	+	0.228766i
$153$	0.195896			0.0158373
$154$	−10.8150	+	5.88730i	−0.871499	+	0.474412i
$155$			10.2385i			0.822377i
$156$	−7.32935	+	11.3401i	−0.586817	+	0.907932i
$157$		−	0.576523i		−	0.0460116i	−0.999735	−	0.0230058i	$-0.992676\pi$
$157$		−	0.576523i		−	0.0460116i	0.999735	−	0.0230058i	$-0.00732362\pi$
$158$	−4.49935	−	8.26535i	−0.357949	−	0.657556i
$159$	−7.17489			−0.569006
$160$	−4.50652	−	3.41925i	−0.356272	−	0.270315i
$161$	11.2874			0.889569
$162$	5.86615	+	10.7762i	0.460888	+	0.846655i
$163$		−	17.1008i		−	1.33944i	−0.742613	−	0.669720i	$-0.766414\pi$
$163$		−	17.1008i		−	1.33944i	0.742613	−	0.669720i	$-0.233586\pi$
$164$	−1.12340	+	1.73815i	−0.0877230	+	0.135726i
$165$			7.72503i			0.601393i
$166$	−10.7494	+	5.85156i	−0.834313	+	0.454169i
$167$	−9.12743			−0.706302			−0.353151	−	0.935566i	$-0.614890\pi$
$167$	−9.12743			−0.706302			−0.353151	+	0.935566i	$0.614890\pi$
$168$	−0.694257	+	9.20481i	−0.0535631	+	0.710167i
$169$	−2.74107			−0.210851
$170$	2.32964	−	1.26817i	0.178676	−	0.0972644i
$171$			0.104446i			0.00798721i
$172$	11.5664	+	7.47561i	0.881927	+	0.570010i
$173$			6.52631i			0.496186i	0.968736	+	0.248093i	$0.0798039\pi$
$173$			6.52631i			0.496186i	−0.968736	+	0.248093i	$0.920196\pi$
$174$	10.4918	+	19.2736i	0.795382	+	1.46112i
$175$	−1.91794			−0.144983
$176$	−16.5569	+	7.45799i	−1.24802	+	0.562167i
$177$	−9.49437			−0.713640
$178$	3.22561	+	5.92548i	0.241770	+	0.444134i
$179$			17.4355i			1.30319i	0.758568	+	0.651594i	$0.225899\pi$
$179$			17.4355i			1.30319i	−0.758568	+	0.651594i	$0.774101\pi$
$180$	−0.175439	−	0.113390i	−0.0130764	−	0.00845161i
$181$		−	6.35322i		−	0.472231i	−0.971725	−	0.236116i	$-0.924126\pi$
$181$		−	6.35322i		−	0.472231i	0.971725	−	0.236116i	$-0.0758744\pi$
$182$	−9.45170	+	5.14516i	−0.700607	+	0.381384i
$183$	−2.84410			−0.210242
$184$	16.5985	+	1.25192i	1.22366	+	0.0922925i
$185$	4.77120			0.350786
$186$	21.6401	−	11.7801i	1.58673	−	0.863758i
$187$		−	8.51465i		−	0.622653i
$188$	9.25607	−	14.3211i	0.675068	−	1.04448i
$189$			10.1318i			0.736979i
$190$	0.676154	+	1.24210i	0.0490534	+	0.0901115i
$191$	−19.9186			−1.44126			−0.720631	−	0.693319i	$-0.756148\pi$
$191$	−19.9186			−1.44126			−0.720631	+	0.693319i	$0.756148\pi$
$192$	−2.04187	+	13.4591i	−0.147359	+	0.971324i
$193$	3.18031			0.228923			0.114462	−	0.993428i	$-0.463486\pi$
$193$	3.18031			0.228923			0.114462	+	0.993428i	$0.463486\pi$
$194$	2.37311	+	4.35942i	0.170379	+	0.312988i
$195$			6.75123i			0.483466i
$196$	3.60591	−	5.57912i	0.257565	−	0.398509i
$197$		−	11.3656i		−	0.809768i	−0.914368	−	0.404884i	$-0.867312\pi$
$197$		−	11.3656i		−	0.809768i	0.914368	−	0.404884i	$-0.132688\pi$
$198$	−0.588958	+	0.320607i	−0.0418555	+	0.0227846i
$199$	−18.3116			−1.29807			−0.649037	−	0.760757i	$-0.724828\pi$
$199$	−18.3116			−1.29807			−0.649037	+	0.760757i	$0.724828\pi$
$200$	−2.82042	−	0.212725i	−0.199434	−	0.0150419i
$201$	−14.3728			−1.01378
$202$	19.5149	−	10.6232i	1.37306	−	0.747444i
$203$			17.4894i			1.22751i
$204$	−5.36082	−	3.46482i	−0.375332	−	0.242586i
$205$			1.03479i			0.0722731i
$206$	−2.35395	−	4.32422i	−0.164007	−	0.301283i
$207$	0.614681			0.0427233
$208$	−14.4698	+	6.51785i	−1.00330	+	0.451932i
$209$	4.53978			0.314023
$210$	2.20672	+	4.05377i	0.152278	+	0.279736i
$211$			7.65690i			0.527122i	0.964643	+	0.263561i	$0.0848971\pi$
$211$			7.65690i			0.527122i	−0.964643	+	0.263561i	$0.915103\pi$
$212$	−7.08243	−	4.57754i	−0.486423	−	0.314387i
$213$			23.7285i			1.62585i
$214$	−23.8797	+	12.9992i	−1.63238	+	0.888609i
$215$	6.88595			0.469618
$216$	−1.12375	+	14.8992i	−0.0764613	+	1.01376i
$217$	19.6369			1.33304
$218$	−9.62436	+	5.23915i	−0.651844	+	0.354840i
$219$		−	13.4298i		−	0.907500i
$220$	−4.92852	+	7.62548i	−0.332281	+	0.514110i
$221$		−	7.44131i		−	0.500557i
$222$	−5.48958	−	10.0844i	−0.368437	−	0.676821i
$223$	−21.1092			−1.41358			−0.706788	−	0.707425i	$-0.749857\pi$
$223$	−21.1092			−1.41358			−0.706788	+	0.707425i	$0.749857\pi$
$224$	−6.55792	+	8.64326i	−0.438170	+	0.577502i
$225$	−0.104446			−0.00696309
$226$	5.99916	+	11.0205i	0.399058	+	0.733074i
$227$		−	10.3489i		−	0.686877i	−0.939175	−	0.343439i	$-0.888408\pi$
$227$		−	10.3489i		−	0.686877i	0.939175	−	0.343439i	$-0.111592\pi$
$228$	1.84735	−	2.85824i	0.122343	−	0.189291i
$229$		−	1.52423i		−	0.100724i	−0.998731	−	0.0503621i	$-0.983962\pi$
$229$		−	1.52423i		−	0.100724i	0.998731	−	0.0503621i	$-0.0160375\pi$
$230$	7.30994	−	3.97926i	0.482003	−	0.262385i
$231$	14.8162			0.974833
$232$	−1.93980	+	25.7189i	−0.127354	+	1.68853i
$233$	−25.5868			−1.67625			−0.838123	−	0.545481i	$-0.816347\pi$
$233$	−25.5868			−1.67625			−0.838123	+	0.545481i	$0.816347\pi$
$234$	−0.514716	+	0.280192i	−0.0336480	+	0.0183167i
$235$		−	8.52598i		−	0.556174i
$236$	−9.37201	−	6.05735i	−0.610066	−	0.394300i
$237$			11.3232i			0.735523i
$238$	−2.43228	−	4.46813i	−0.157662	−	0.289626i
$239$	6.58822			0.426157			0.213078	−	0.977035i	$-0.431651\pi$
$239$	6.58822			0.426157			0.213078	+	0.977035i	$0.431651\pi$
$240$	2.79546	+	6.20599i	0.180446	+	0.400595i
$241$	15.0024			0.966387			0.483194	−	0.875514i	$-0.339477\pi$
$241$	15.0024			0.966387			0.483194	+	0.875514i	$0.339477\pi$
$242$	6.49754	+	11.9360i	0.417678	+	0.767278i
$243$			1.08494i			0.0695989i
$244$	−2.80745	−	1.81452i	−0.179728	−	0.116163i
$245$		−	3.32149i		−	0.212202i
$246$	2.18714	−	1.19060i	0.139447	−	0.0759097i
$247$	3.96750			0.252446
$248$	28.8769	+	2.17799i	1.83368	+	0.138302i
$249$	14.7262			0.933237
$250$	−1.24210	+	0.676154i	−0.0785574	+	0.0427637i
$251$		−	22.6661i		−	1.43067i	−0.698782	−	0.715334i	$-0.746274\pi$
$251$		−	22.6661i		−	1.43067i	0.698782	−	0.715334i	$-0.253726\pi$
$252$	−0.217476	+	0.336482i	−0.0136997	+	0.0211964i
$253$		−	26.7172i		−	1.67970i
$254$	−8.25275	−	15.1604i	−0.517824	−	0.951247i
$255$	−3.19153			−0.199861
$256$	−10.6023	+	11.9829i	−0.662647	+	0.748932i
$257$	−19.7457			−1.23170			−0.615851	−	0.787862i	$-0.711188\pi$
$257$	−19.7457			−1.23170			−0.615851	+	0.787862i	$0.711188\pi$
$258$	−7.92274	−	14.5542i	−0.493248	−	0.906102i
$259$		−	9.15089i		−	0.568609i
$260$	−4.30724	+	6.66423i	−0.267124	+	0.413298i
$261$			0.952428i			0.0589538i
$262$	16.3330	−	8.89111i	1.00906	−	0.549295i
$263$	7.50344			0.462682			0.231341	−	0.972873i	$-0.425689\pi$
$263$	7.50344			0.462682			0.231341	+	0.972873i	$0.425689\pi$
$264$	21.7878	+	1.64331i	1.34095	+	0.101139i
$265$	−4.21648			−0.259016
$266$	2.38228	−	1.29683i	0.146067	−	0.0795135i
$267$		−	8.11769i		−	0.496794i
$268$	−14.1876	−	9.16978i	−0.866647	−	0.560134i
$269$		−	0.0408937i		−	0.00249333i	−0.999999	−	0.00124667i	$-0.999603\pi$
$269$		−	0.0408937i		−	0.00249333i	0.999999	−	0.00124667i	$-0.000396826\pi$
$270$	3.57187	+	6.56156i	0.217377	+	0.399324i
$271$	8.31371			0.505022			0.252511	−	0.967594i	$-0.418744\pi$
$271$	8.31371			0.505022			0.252511	+	0.967594i	$0.418744\pi$
$272$	−3.08120	−	6.84034i	−0.186825	−	0.414756i
$273$	12.9485			0.783678
$274$	−5.40598	−	9.93083i	−0.326587	−	0.599943i
$275$			4.53978i			0.273759i
$276$	−16.8211	−	10.8719i	−1.01251	−	0.654411i
$277$		−	8.11160i		−	0.487379i	−0.969853	−	0.243689i	$-0.921642\pi$
$277$		−	8.11160i		−	0.487379i	0.969853	−	0.243689i	$-0.0783578\pi$
$278$	−28.4140	+	15.4676i	−1.70416	+	0.927682i
$279$	1.06938			0.0640218
$280$	−0.407994	+	5.40940i	−0.0243823	+	0.323273i
$281$	−13.4028			−0.799546			−0.399773	−	0.916614i	$-0.630911\pi$
$281$	−13.4028			−0.799546			−0.399773	+	0.916614i	$0.630911\pi$
$282$	−18.0205	+	9.80970i	−1.07311	+	0.584159i
$283$			0.522506i			0.0310598i	0.999879	+	0.0155299i	$0.00494351\pi$
$283$			0.522506i			0.0310598i	−0.999879	+	0.0155299i	$0.995056\pi$
$284$	−15.1386	+	23.4227i	−0.898311	+	1.38988i
$285$		−	1.70163i		−	0.100796i
$286$	12.1786	+	22.3722i	0.720135	+	1.32290i
$287$	1.98467			0.117152
$288$	−0.357128	+	0.470690i	−0.0210440	+	0.0277357i
$289$	−13.4822			−0.793073
$290$	6.16573	+	11.3265i	0.362064	+	0.665115i
$291$		−	5.97225i		−	0.350099i
$292$	8.56811	−	13.2567i	0.501411	−	0.775790i
$293$		−	20.2544i		−	1.18327i	−0.806205	−	0.591637i	$-0.798482\pi$
$293$		−	20.2544i		−	1.18327i	0.806205	−	0.591637i	$-0.201518\pi$
$294$	−7.02031	+	3.82160i	−0.409433	+	0.222880i
$295$	−5.57956			−0.324855
$296$	1.01495	−	13.4568i	0.0589930	−	0.782159i
$297$	23.9819			1.39157
$298$	29.6504	−	16.1406i	1.71760	−	0.935000i
$299$		−	23.3493i		−	1.35032i
$300$	2.85824	+	1.84735i	0.165021	+	0.106657i
$301$		−	13.2069i		−	0.761231i
$302$	−6.88972	−	12.6565i	−0.396459	−	0.728298i
$303$	−26.7346			−1.53587
$304$	3.64708	−	1.64281i	0.209174	−	0.0942216i
$305$	−1.67139			−0.0957037
$306$	−0.132456	−	0.243323i	−0.00757201	−	0.0139098i
$307$			9.17726i			0.523774i	0.965099	+	0.261887i	$0.0843448\pi$
$307$			9.17726i			0.523774i	−0.965099	+	0.261887i	$0.915655\pi$
$308$	14.6252	+	9.45263i	0.833350	+	0.538613i
$309$			5.92402i			0.337006i
$310$	12.7173	−	6.92281i	0.722292	−	0.393189i
$311$	−4.99647			−0.283324			−0.141662	−	0.989915i	$-0.545245\pi$
$311$	−4.99647			−0.283324			−0.141662	+	0.989915i	$0.545245\pi$
$312$	19.0413	+	1.43616i	1.07800	+	0.0813063i
$313$	−8.99280			−0.508303			−0.254152	−	0.967164i	$-0.581796\pi$
$313$	−8.99280			−0.508303			−0.254152	+	0.967164i	$0.581796\pi$
$314$	−0.716100	+	0.389819i	−0.0404119	+	0.0219987i
$315$			0.200322i			0.0112869i
$316$	−7.22415	+	11.1773i	−0.406390	+	0.628773i
$317$			29.7313i			1.66987i	0.550346	+	0.834937i	$0.314496\pi$
$317$			29.7313i			1.66987i	−0.550346	+	0.834937i	$0.685504\pi$
$318$	4.85133	+	8.91194i	0.272049	+	0.499757i
$319$	41.3974			2.31781
$320$	−1.19995	+	7.90950i	−0.0670790	+	0.442154i
$321$	32.7143			1.82593
$322$	−7.63200	−	14.0201i	−0.425315	−	0.781307i
$323$			1.87557i			0.104359i
$324$	9.41867	−	14.5727i	0.523259	−	0.809594i
$325$			3.96750i			0.220077i
$326$	−21.2410	+	11.5628i	−1.17643	+	0.640404i
$327$	13.1850			0.729133
$328$	2.91855	+	0.220126i	0.161150	+	0.0121544i
$329$	−16.3523			−0.901534
$330$	9.59527	−	5.22331i	0.528202	−	0.287534i
$331$		−	15.0825i		−	0.829011i	−0.910047	−	0.414505i	$-0.863955\pi$
$331$		−	15.0825i		−	0.829011i	0.910047	−	0.414505i	$-0.136045\pi$
$332$	14.5365	+	9.39525i	0.797792	+	0.515631i
$333$		−	0.498335i		−	0.0273086i
$334$	6.17155	+	11.3372i	0.337692	+	0.620344i
$335$	−8.44650			−0.461482
$336$	11.9027	−	5.36153i	0.649347	−	0.292496i
$337$	25.6306			1.39619			0.698093	−	0.716007i	$-0.254032\pi$
$337$	25.6306			1.39619			0.698093	+	0.716007i	$0.254032\pi$
$338$	1.85338	+	3.40468i	0.100811	+	0.185190i
$339$		−	15.0977i		−	0.819994i
$340$	−3.15040	−	2.03617i	−0.170854	−	0.110427i
$341$		−	46.4805i		−	2.51706i
$342$	0.129733	−	0.0706218i	0.00701516	−	0.00381879i
$343$	−19.7960			−1.06889
$344$	1.46481	−	19.4213i	0.0789775	−	1.04712i
$345$	−10.0143			−0.539154
$346$	8.10634	−	4.41279i	0.435800	−	0.237233i
$347$			8.17009i			0.438594i	0.975658	+	0.219297i	$0.0703763\pi$
$347$			8.17009i			0.438594i	−0.975658	+	0.219297i	$0.929624\pi$
$348$	16.8456	−	26.0638i	0.903020	−	1.39717i
$349$			26.9479i			1.44249i	0.692681	+	0.721244i	$0.256430\pi$
$349$			26.9479i			1.44249i	−0.692681	+	0.721244i	$0.743570\pi$
$350$	1.29683	+	2.38228i	0.0693182	+	0.127338i
$351$	20.9588			1.11870
$352$	20.4586	+	15.5226i	1.09045	+	0.827358i
$353$	−17.8408			−0.949570			−0.474785	−	0.880102i	$-0.657474\pi$
$353$	−17.8408			−0.949570			−0.474785	+	0.880102i	$0.657474\pi$
$354$	6.41965	+	11.7930i	0.341201	+	0.626789i
$355$			13.9445i			0.740099i
$356$	5.17903	−	8.01308i	0.274488	−	0.424692i
$357$			6.12117i			0.323967i
$358$	21.6566	−	11.7891i	1.14459	−	0.623071i
$359$	−17.1567			−0.905497			−0.452748	−	0.891638i	$-0.649556\pi$
$359$	−17.1567			−0.905497			−0.452748	+	0.891638i	$0.649556\pi$
$360$	−0.0222183	+	0.294582i	−0.00117101	+	0.0155258i
$361$	−1.00000			−0.0526316
$362$	−7.89135	+	4.29576i	−0.414760	+	0.225780i
$363$		−	16.3519i		−	0.858254i
$364$	12.7816	+	8.26105i	0.669939	+	0.432997i
$365$		−	7.89229i		−	0.413101i
$366$	1.92305	+	3.53266i	0.100519	+	0.184655i
$367$	8.13127			0.424449			0.212224	−	0.977221i	$-0.431929\pi$
$367$	8.13127			0.424449			0.212224	+	0.977221i	$0.431929\pi$
$368$	−9.66817	−	21.4636i	−0.503988	−	1.11887i
$369$	0.108080			0.00562644
$370$	−3.22607	−	5.92631i	−0.167715	−	0.308094i
$371$			8.08696i			0.419854i
$372$	−29.2641	−	18.9141i	−1.51727	−	0.980649i
$373$		−	13.9581i		−	0.722722i	−0.932426	−	0.361361i	$-0.882312\pi$
$373$		−	13.9581i		−	0.722722i	0.932426	−	0.361361i	$-0.117688\pi$
$374$	−10.5761	+	5.75722i	−0.546875	+	0.297699i
$375$	1.70163			0.0878719
$376$	−24.0468	−	1.81369i	−1.24012	−	0.0935338i
$377$	36.1790			1.86331
$378$	12.5847	−	6.85065i	0.647287	−	0.352359i
$379$			19.5799i			1.00575i	0.864359	+	0.502875i	$0.167724\pi$
$379$			19.5799i			1.00575i	−0.864359	+	0.502875i	$0.832276\pi$
$380$	1.08563	−	1.67970i	0.0556917	−	0.0861670i
$381$			20.7692i			1.06404i
$382$	13.4681	+	24.7410i	0.689086	+	1.26586i
$383$	5.33999			0.272861			0.136430	−	0.990650i	$-0.456437\pi$
$383$	5.33999			0.272861			0.136430	+	0.990650i	$0.456437\pi$
$384$	18.0981	−	6.56419i	0.923566	−	0.334978i
$385$	8.70703			0.443751
$386$	−2.15038	−	3.95026i	−0.109451	−	0.201063i
$387$		−	0.719213i		−	0.0365596i
$388$	3.81026	−	5.89529i	0.193437	−	0.299288i
$389$		−	34.6720i		−	1.75794i	−0.476875	−	0.878971i	$-0.658231\pi$
$389$		−	34.6720i		−	1.75794i	0.476875	−	0.878971i	$-0.341769\pi$
$390$	8.38571	−	4.56487i	0.424627	−	0.231151i
$391$	11.0380			0.558214
$392$	−9.36799	−	0.706564i	−0.473155	−	0.0356869i
$393$	−22.3757			−1.12870
$394$	−14.1173	+	7.68492i	−0.711218	+	0.387161i
$395$			6.65433i			0.334816i
$396$	0.796453	+	0.514766i	0.0400233	+	0.0258680i
$397$		−	13.3397i		−	0.669503i	−0.942306	−	0.334751i	$-0.891348\pi$
$397$		−	13.3397i		−	0.669503i	0.942306	−	0.334751i	$-0.108652\pi$
$398$	12.3815	+	22.7448i	0.620626	+	1.14010i
$399$	−3.26364			−0.163386
$400$	1.64281	+	3.64708i	0.0821405	+	0.182354i
$401$	−14.5196			−0.725076			−0.362538	−	0.931969i	$-0.618090\pi$
$401$	−14.5196			−0.725076			−0.362538	+	0.931969i	$0.618090\pi$
$402$	9.71826	+	17.8525i	0.484703	+	0.890403i
$403$		−	40.6213i		−	2.02349i
$404$	−26.3901	−	17.0565i	−1.31296	−	0.848595i
$405$		−	8.67575i		−	0.431102i
$406$	21.7236	−	11.8255i	1.07812	−	0.586891i
$407$	−21.6602			−1.07366
$408$	−0.678917	+	9.00143i	−0.0336114	+	0.445637i
$409$	−17.3406			−0.857438			−0.428719	−	0.903438i	$-0.641035\pi$
$409$	−17.3406			−0.857438			−0.428719	+	0.903438i	$0.641035\pi$
$410$	1.28532	−	0.699679i	0.0634773	−	0.0345547i
$411$			13.6049i			0.671078i
$412$	−3.77949	+	5.84768i	−0.186202	+	0.288095i
$413$			10.7013i			0.526576i
$414$	−0.415619	−	0.763497i	−0.0204266	−	0.0375238i
$415$	8.65418			0.424817
$416$	17.8796	+	13.5659i	0.876621	+	0.665121i
$417$	38.9262			1.90622
$418$	−3.06959	−	5.63886i	−0.150138	−	0.275806i
$419$			21.8769i			1.06876i	0.845245	+	0.534379i	$0.179454\pi$
$419$			21.8769i			1.06876i	−0.845245	+	0.534379i	$0.820546\pi$
$420$	3.54310	−	5.48194i	0.172886	−	0.267491i
$421$		−	24.8520i		−	1.21121i	−0.795764	−	0.605607i	$-0.792930\pi$
$421$		−	24.8520i		−	1.21121i	0.795764	−	0.605607i	$-0.207070\pi$
$422$	9.51064	−	5.17724i	0.462971	−	0.252024i
$423$	−0.890508			−0.0432980
$424$	−0.896949	+	11.8922i	−0.0435597	+	0.577537i
$425$	−1.87557			−0.0909784
$426$	29.4732	−	16.0441i	1.42798	−	0.777339i
$427$			3.20564i			0.155132i
$428$	32.2927	+	20.8715i	1.56093	+	1.00886i
$429$		−	30.6491i		−	1.47975i
$430$	−4.65597	−	8.55305i	−0.224531	−	0.412465i
$431$	34.9062			1.68137			0.840687	−	0.541521i	$-0.182152\pi$
$431$	34.9062			1.68137			0.840687	+	0.541521i	$0.182152\pi$
$432$	19.2662	−	8.67835i	0.926943	−	0.417538i
$433$	−8.13382			−0.390886			−0.195443	−	0.980715i	$-0.562615\pi$
$433$	−8.13382			−0.390886			−0.195443	+	0.980715i	$0.562615\pi$
$434$	−13.2776	−	24.3910i	−0.637344	−	1.17081i
$435$		−	15.5169i		−	0.743978i
$436$	13.0151	+	8.41196i	0.623311	+	0.402860i
$437$			5.88514i			0.281524i
$438$	−16.6811	+	9.08060i	−0.797055	+	0.433888i
$439$	−28.3815			−1.35457			−0.677287	−	0.735719i	$-0.736844\pi$
$439$	−28.3815			−1.35457			−0.677287	+	0.735719i	$0.736844\pi$
$440$	12.8041	+	0.965723i	0.610409	+	0.0460391i
$441$	−0.346918			−0.0165199
$442$	−9.24287	+	5.03148i	−0.439638	+	0.239323i
$443$			7.03515i			0.334250i	0.985936	+	0.167125i	$0.0534483\pi$
$443$			7.03515i			0.334250i	−0.985936	+	0.167125i	$0.946552\pi$
$444$	−8.81406	+	13.6372i	−0.418297	+	0.647194i
$445$		−	4.77053i		−	0.226145i
$446$	14.2731	+	26.2198i	0.675850	+	1.24154i
$447$	−40.6200			−1.92126
$448$	15.1700	+	2.30143i	0.716714	+	0.108732i
$449$	30.0184			1.41666			0.708328	−	0.705884i	$-0.249450\pi$
$449$	30.0184			1.41666			0.708328	+	0.705884i	$0.249450\pi$
$450$	0.0706218	+	0.129733i	0.00332915	+	0.00611567i
$451$		−	4.69773i		−	0.221207i
$452$	9.63224	−	14.9031i	0.453062	−	0.700985i
$453$			17.3389i			0.814652i
$454$	−12.8543	+	6.99742i	−0.603283	+	0.328405i
$455$	7.60944			0.356736
$456$	−4.79931	−	0.361980i	−0.224748	−	0.0169513i
$457$	−3.70017			−0.173087			−0.0865433	−	0.996248i	$-0.527582\pi$
$457$	−3.70017			−0.173087			−0.0865433	+	0.996248i	$0.527582\pi$
$458$	−1.89325	+	1.03062i	−0.0884659	+	0.0481576i
$459$			9.90792i			0.462462i
$460$	−9.88529	−	6.38909i	−0.460904	−	0.297893i
$461$			6.34216i			0.295384i	0.989033	+	0.147692i	$0.0471844\pi$
$461$			6.34216i			0.295384i	−0.989033	+	0.147692i	$0.952816\pi$
$462$	−10.0180	−	18.4032i	−0.466080	−	0.856194i
$463$	12.0989			0.562285			0.281143	−	0.959666i	$-0.409287\pi$
$463$	12.0989			0.562285			0.281143	+	0.959666i	$0.409287\pi$
$464$	33.2571	−	14.9805i	1.54392	−	0.695452i
$465$	−17.4222			−0.807935
$466$	17.3006	+	31.7814i	0.801435	+	1.47224i
$467$		−	20.5836i		−	0.952494i	−0.879311	−	0.476247i	$-0.841997\pi$
$467$		−	20.5836i		−	0.952494i	0.879311	−	0.476247i	$-0.158003\pi$
$468$	0.696054	+	0.449876i	0.0321751	+	0.0207955i
$469$			16.1999i			0.748042i
$470$	−10.5901	+	5.76488i	−0.488486	+	0.265914i
$471$	0.981031			0.0452035
$472$	−1.18691	+	15.7367i	−0.0546321	+	0.724340i
$473$	−31.2607			−1.43737
$474$	14.0646	−	7.65625i	0.646008	−	0.351663i
$475$		−	1.00000i		−	0.0458831i
$476$	−3.90527	+	6.04228i	−0.178998	+	0.276948i
$477$			0.440396i			0.0201643i
$478$	−4.45466	−	8.18324i	−0.203751	−	0.374293i
$479$	−8.55049			−0.390682			−0.195341	−	0.980735i	$-0.562581\pi$
$479$	−8.55049			−0.390682			−0.195341	+	0.980735i	$0.562581\pi$
$480$	5.81830	−	7.66845i	0.265568	−	0.350015i
$481$	−18.9297			−0.863122
$482$	−10.1439	−	18.6345i	−0.462042	−	0.848776i
$483$			19.2070i			0.873947i
$484$	10.4324	−	16.1412i	0.474202	−	0.733691i
$485$		−	3.50972i		−	0.159368i
$486$	1.34760	−	0.733586i	0.0611286	−	0.0332761i
$487$	−8.59813			−0.389619			−0.194809	−	0.980841i	$-0.562409\pi$
$487$	−8.59813			−0.389619			−0.194809	+	0.980841i	$0.562409\pi$
$488$	−0.355547	+	4.71403i	−0.0160949	+	0.213394i
$489$	29.0993			1.31592
$490$	−4.12563	+	2.24584i	−0.186377	+	0.101457i
$491$			8.36945i			0.377708i	0.982005	+	0.188854i	$0.0604773\pi$
$491$			8.36945i			0.377708i	−0.982005	+	0.188854i	$0.939523\pi$
$492$	−2.95768	−	1.91162i	−0.133343	−	0.0861825i
$493$			17.1030i			0.770279i
$494$	−2.68264	−	4.92804i	−0.120698	−	0.221723i
$495$	0.474163			0.0213120
$496$	−16.8199	−	37.3407i	−0.755237	−	1.67664i
$497$	26.7448			1.19967
$498$	−9.95721	−	18.2915i	−0.446193	−	0.819661i
$499$		−	19.8968i		−	0.890705i	−0.895355	−	0.445352i	$-0.853078\pi$
$499$		−	19.8968i		−	0.890705i	0.895355	−	0.445352i	$-0.146922\pi$
$500$	1.67970	+	1.08563i	0.0751186	+	0.0485509i
$501$		−	15.5315i		−	0.693898i
$502$	−28.1535	+	15.3257i	−1.25655	+	0.684022i
$503$	22.8495			1.01881			0.509405	−	0.860527i	$-0.329865\pi$
$503$	22.8495			1.01881			0.509405	+	0.860527i	$0.329865\pi$
$504$	0.564992	+	0.0426135i	0.0251668	+	0.00189816i
$505$	−15.7112			−0.699138
$506$	−33.1855	+	18.0650i	−1.47527	+	0.803085i
$507$		−	4.66429i		−	0.207148i
$508$	−13.2506	+	20.5015i	−0.587900	+	0.909607i
$509$			12.3733i			0.548435i	0.961668	+	0.274218i	$0.0884189\pi$
$509$			12.3733i			0.548435i	−0.961668	+	0.274218i	$0.911581\pi$
$510$	2.15796	+	3.96420i	0.0955562	+	0.175538i
$511$	−15.1370			−0.669620
$512$	22.0528	+	5.06689i	0.974606	+	0.223927i
$513$	−5.28263			−0.233234
$514$	13.3511	+	24.5262i	0.588893	+	1.08180i
$515$			3.48138i			0.153408i
$516$	−12.7207	+	19.6817i	−0.559999	+	0.866439i
$517$			38.7060i			1.70229i
$518$	−11.3663	+	6.18742i	−0.499408	+	0.271859i
$519$	−11.1054			−0.487472
$520$	11.1900	+	0.843987i	0.490714	+	0.0370113i
$521$	−6.60286			−0.289277			−0.144638	−	0.989485i	$-0.546202\pi$
$521$	−6.60286			−0.289277			−0.144638	+	0.989485i	$0.546202\pi$
$522$	1.18301	−	0.643988i	0.0517790	−	0.0281866i
$523$			38.7033i			1.69238i	0.532884	+	0.846189i	$0.321108\pi$
$523$			38.7033i			1.69238i	−0.532884	+	0.846189i	$0.678892\pi$
$524$	−22.0873	−	14.2755i	−0.964889	−	0.623630i
$525$		−	3.26364i		−	0.142437i
$526$	−5.07349	−	9.32004i	−0.221214	−	0.406373i
$527$	19.2030			0.836497
$528$	−12.6908	−	28.1738i	−0.552294	−	1.22611i
$529$	11.6349			0.505864
$530$	2.85099	+	5.23729i	0.123839	+	0.227493i
$531$			0.582765i			0.0252898i
$532$	−3.22158	−	2.08218i	−0.139673	−	0.0902739i
$533$		−	4.10554i		−	0.177831i
$534$	−10.0830	+	5.48881i	−0.436334	+	0.237524i
$535$	19.2252			0.831180
$536$	−1.79678	+	23.8226i	−0.0776091	+	1.02898i
$537$	−29.6688			−1.28030
$538$	−0.0507941	+	0.0276504i	−0.00218989	+	0.00119209i
$539$			15.0788i			0.649491i
$540$	5.73498	−	8.87325i	0.246794	−	0.381844i
$541$		−	22.2218i		−	0.955389i	−0.878526	−	0.477694i	$-0.841473\pi$
$541$		−	22.2218i		−	0.955389i	0.878526	−	0.477694i	$-0.158527\pi$
$542$	−5.62135	−	10.3265i	−0.241458	−	0.443560i
$543$	10.8109			0.463938
$544$	−6.41303	+	8.45229i	−0.274956	+	0.362389i
$545$	7.74845			0.331907
$546$	−8.75517	−	16.0833i	−0.374687	−	0.688303i
$547$			17.9175i			0.766097i	0.923728	+	0.383048i	$0.125126\pi$
$547$			17.9175i			0.766097i	−0.923728	+	0.383048i	$0.874874\pi$
$548$	−8.67982	+	13.4295i	−0.370783	+	0.573682i
$549$			0.174571i			0.00745051i
$550$	5.63886	−	3.06959i	0.240442	−	0.130888i
$551$	−9.11883			−0.388475
$552$	−2.13030	+	28.2446i	−0.0906716	+	1.20217i
$553$	12.7626			0.542722
$554$	−10.0754	+	5.48469i	−0.428064	+	0.233022i
$555$			8.11883i			0.344625i
$556$	38.4245	+	24.8347i	1.62956	+	1.05322i
$557$		−	40.4579i		−	1.71426i	−0.515104	−	0.857128i	$-0.672247\pi$
$557$		−	40.4579i		−	1.71426i	0.515104	−	0.857128i	$-0.327753\pi$
$558$	−0.723063	−	1.32827i	−0.0306097	−	0.0562303i
$559$	−27.3200			−1.15551
$560$	6.99489	−	3.15082i	0.295588	−	0.133146i
$561$	14.4888			0.611718
$562$	9.06238	+	16.6477i	0.382273	+	0.702240i
$563$			44.1290i			1.85982i	0.367793	+	0.929908i	$0.380113\pi$
$563$			44.1290i			1.85982i	−0.367793	+	0.929908i	$0.619887\pi$
$564$	24.3693	+	15.7504i	1.02613	+	0.663213i
$565$		−	8.87248i		−	0.373268i
$566$	0.649005	−	0.353295i	0.0272797	−	0.0148501i
$567$	−16.6396			−0.698798
$568$	39.3294	+	2.96635i	1.65022	+	0.124465i
$569$	−40.9226			−1.71556			−0.857782	−	0.514014i	$-0.828158\pi$
$569$	−40.9226			−1.71556			−0.857782	+	0.514014i	$0.828158\pi$
$570$	−2.11360	+	1.15057i	−0.0885290	+	0.0481919i
$571$		−	17.5592i		−	0.734832i	−0.930057	−	0.367416i	$-0.880243\pi$
$571$		−	17.5592i		−	0.734832i	0.930057	−	0.367416i	$-0.119757\pi$
$572$	19.5539	−	30.2541i	0.817590	−	1.26499i
$573$		−	33.8942i		−	1.41595i
$574$	−1.34195	−	2.46517i	−0.0560117	−	0.102894i
$575$	−5.88514			−0.245427
$576$	0.826118	+	0.125330i	0.0344216	+	0.00522208i
$577$	−9.76320			−0.406447			−0.203224	−	0.979132i	$-0.565142\pi$
$577$	−9.76320			−0.406447			−0.203224	+	0.979132i	$0.565142\pi$
$578$	9.11608	+	16.7463i	0.379179	+	0.696555i
$579$			5.41171i			0.224903i
$580$	9.89968	−	15.3169i	0.411062	−	0.636001i
$581$		−	16.5982i		−	0.688611i
$582$	−7.41814	+	4.03816i	−0.307492	+	0.167387i
$583$	19.1418			0.792774
$584$	−22.2595	−	1.67889i	−0.921106	−	0.0694728i
$585$	0.414391			0.0171330
$586$	−25.1580	+	13.6951i	−1.03927	+	0.565739i
$587$			25.4596i			1.05083i	0.850845	+	0.525416i	$0.176090\pi$
$587$			25.4596i			1.05083i	−0.850845	+	0.525416i	$0.823910\pi$
$588$	9.49362	+	6.13594i	0.391510	+	0.253042i
$589$			10.2385i			0.421871i
$590$	3.77264	+	6.93038i	0.155317	+	0.285319i
$591$	19.3401			0.795547
$592$	−17.4009	+	7.83818i	−0.715174	+	0.322147i
$593$	44.8209			1.84057			0.920287	−	0.391244i	$-0.127955\pi$
$593$	44.8209			1.84057			0.920287	+	0.391244i	$0.127955\pi$
$594$	−16.2155	−	29.7880i	−0.665330	−	1.22222i
$595$			3.59723i			0.147472i
$596$	−40.0965	−	25.9153i	−1.64242	−	1.06153i
$597$		−	31.1596i		−	1.27528i
$598$	−29.0022	+	15.7877i	−1.18599	+	0.645608i
$599$	11.5281			0.471025			0.235512	−	0.971871i	$-0.424323\pi$
$599$	11.5281			0.471025			0.235512	+	0.971871i	$0.424323\pi$
$600$	0.361980	−	4.79931i	0.0147778	−	0.195931i
$601$	−35.1911			−1.43548			−0.717738	−	0.696313i	$-0.754822\pi$
$601$	−35.1911			−1.43548			−0.717738	+	0.696313i	$0.754822\pi$
$602$	−16.4043	+	8.92988i	−0.668588	+	0.363955i
$603$			0.882206i			0.0359262i
$604$	−11.0621	+	17.1155i	−0.450111	+	0.696418i
$605$		−	9.60956i		−	0.390684i
$606$	18.0767	+	33.2071i	0.734317	+	1.34895i
$607$	8.60565			0.349292			0.174646	−	0.984631i	$-0.444122\pi$
$607$	8.60565			0.349292			0.174646	+	0.984631i	$0.444122\pi$
$608$	−4.50652	−	3.41925i	−0.182764	−	0.138669i
$609$	−29.7605			−1.20596
$610$	1.13012	+	2.07604i	0.0457572	+	0.0840564i
$611$			33.8268i			1.36849i
$612$	−0.212671	+	0.329048i	−0.00859671	+	0.0133010i
$613$			46.2101i			1.86641i	0.359345	+	0.933205i	$0.383000\pi$
$613$			46.2101i			1.86641i	−0.359345	+	0.933205i	$0.617000\pi$
$614$	11.3991	−	6.20525i	0.460030	−	0.250423i
$615$	−1.76084			−0.0710038
$616$	1.85220	−	24.5575i	0.0746274	−	0.989448i
$617$	−15.2660			−0.614588			−0.307294	−	0.951615i	$-0.599423\pi$
$617$	−15.2660			−0.614588			−0.307294	+	0.951615i	$0.599423\pi$
$618$	7.35824	−	4.00555i	0.295992	−	0.161127i
$619$		−	5.30696i		−	0.213305i	−0.994296	−	0.106652i	$-0.965987\pi$
$619$		−	5.30696i		−	0.213305i	0.994296	−	0.106652i	$-0.0340132\pi$
$620$	−17.1977	−	11.1152i	−0.690675	−	0.446399i
$621$			31.0890i			1.24756i
$622$	3.37839	+	6.20613i	0.135461	+	0.248843i
$623$	−9.14961			−0.366571
$624$	−11.0910	−	24.6223i	−0.443995	−	0.985679i
$625$	1.00000			0.0400000
$626$	6.08052	+	11.1700i	0.243027	+	0.446442i
$627$			7.72503i			0.308508i
$628$	0.968389	+	0.625892i	0.0386429	+	0.0249758i
$629$		−	8.94871i		−	0.356808i
$630$	0.248821	−	0.135449i	0.00991325	−	0.00539641i
$631$	10.8330			0.431254			0.215627	−	0.976476i	$-0.430821\pi$
$631$	10.8330			0.431254			0.215627	+	0.976476i	$0.430821\pi$
$632$	18.7680	+	1.41554i	0.746550	+	0.0563072i
$633$	−13.0292			−0.517865
$634$	36.9292	−	20.1029i	1.46665	−	0.798389i
$635$			12.2054i			0.484358i
$636$	7.78929	−	12.0517i	0.308865	−	0.477881i
$637$			13.1780i			0.522132i
$638$	−27.9910	−	51.4198i	−1.10818	−	2.03573i
$639$	1.45646			0.0576165
$640$	10.6357	−	3.85758i	0.420415	−	0.152484i
$641$	−43.5708			−1.72094			−0.860472	−	0.509498i	$-0.829831\pi$
$641$	−43.5708			−1.72094			−0.860472	+	0.509498i	$0.829831\pi$
$642$	−22.1199	−	40.6345i	−0.873003	−	1.60372i
$643$			24.5170i			0.966857i	0.875384	+	0.483428i	$0.160609\pi$
$643$			24.5170i			0.966857i	−0.875384	+	0.483428i	$0.839391\pi$
$644$	−12.2539	+	18.9594i	−0.482872	+	0.747106i
$645$			11.7174i			0.461371i
$646$	2.32964	−	1.26817i	0.0916586	−	0.0498956i
$647$	−13.3298			−0.524048			−0.262024	−	0.965061i	$-0.584390\pi$
$647$	−13.3298			−0.524048			−0.262024	+	0.965061i	$0.584390\pi$
$648$	−24.4692	−	1.84555i	−0.961242	−	0.0725000i
$649$	25.3300			0.994288
$650$	4.92804	−	2.68264i	0.193294	−	0.105222i
$651$			33.4148i			1.30963i
$652$	28.7243	+	18.5652i	1.12493	+	0.727069i
$653$			11.3684i			0.444879i	0.974947	+	0.222439i	$0.0714020\pi$
$653$			11.3684i			0.444879i	−0.974947	+	0.222439i	$0.928598\pi$
$654$	−8.91511	−	16.3771i	−0.348608	−	0.640396i
$655$	−13.1495			−0.513795
$656$	−1.69997	−	3.77397i	−0.0663726	−	0.147349i
$657$	−0.824321			−0.0321598
$658$	11.0567	+	20.3113i	0.431035	+	0.791816i
$659$			16.3793i			0.638049i	0.947747	+	0.319024i	$0.103355\pi$
$659$			16.3793i			0.638049i	−0.947747	+	0.319024i	$0.896645\pi$
$660$	−12.9758	−	8.38653i	−0.505081	−	0.326445i
$661$		−	2.05089i		−	0.0797705i	−0.999204	−	0.0398852i	$-0.987301\pi$
$661$		−	2.05089i		−	0.0797705i	0.999204	−	0.0398852i	$-0.0126992\pi$
$662$	−18.7340	+	10.1981i	−0.728119	+	0.396361i
$663$	12.6624			0.491766
$664$	1.84096	−	24.4084i	0.0714431	−	0.947229i
$665$	−1.91794			−0.0743747
$666$	−0.618982	+	0.336951i	−0.0239851	+	0.0130566i
$667$			53.6656i			2.07794i
$668$	9.90902	−	15.3314i	0.383392	−	0.593189i
$669$		−	35.9201i		−	1.38875i
$670$	5.71114	+	10.4914i	0.220640	+	0.405318i
$671$	7.58775			0.292922
$672$	−14.7077	−	11.1592i	−0.567360	−	0.430475i
$673$	−12.5634			−0.484285			−0.242143	−	0.970241i	$-0.577850\pi$
$673$	−12.5634			−0.484285			−0.242143	+	0.970241i	$0.577850\pi$
$674$	−17.3302	−	31.8358i	−0.667535	−	1.22627i
$675$		−	5.28263i		−	0.203328i
$676$	2.97579	−	4.60418i	0.114453	−	0.177084i
$677$		−	0.535951i		−	0.0205983i	−0.999947	−	0.0102991i	$-0.996722\pi$
$677$		−	0.535951i		−	0.0205983i	0.999947	−	0.0102991i	$-0.00327837\pi$
$678$	−18.7529	+	10.2084i	−0.720200	+	0.392050i
$679$	−6.73144			−0.258329
$680$	−0.398980	+	5.28988i	−0.0153002	+	0.202858i
$681$	17.6099			0.674815
$682$	−57.7335	+	31.4280i	−2.21073	+	1.20344i
$683$			11.5114i			0.440470i	0.975447	+	0.220235i	$0.0706825\pi$
$683$			11.5114i			0.440470i	−0.975447	+	0.220235i	$0.929318\pi$
$684$	−0.175439	−	0.113390i	−0.00670808	−	0.00433558i
$685$			7.99518i			0.305480i
$686$	13.3852	+	24.5887i	0.511048	+	0.938800i
$687$	2.59369			0.0989554
$688$	−25.1136	+	11.3123i	−0.957447	+	0.431278i
$689$	16.7289			0.637319
$690$	6.77124	+	12.4388i	0.257777	+	0.473538i
$691$		−	12.7408i		−	0.484681i	−0.970191	−	0.242341i	$-0.922085\pi$
$691$		−	12.7408i		−	0.484681i	0.970191	−	0.242341i	$-0.0779151\pi$
$692$	−10.9623	−	7.08517i	−0.416723	−	0.269338i
$693$		−	0.909418i		−	0.0345459i
$694$	10.1481	−	5.52424i	0.385216	−	0.209697i
$695$	22.8758			0.867728
$696$	−43.7641	−	3.30083i	−1.65887	−	0.125118i
$697$	1.94082			0.0735139
$698$	33.4720	−	18.2209i	1.26694	−	0.689673i
$699$		−	43.5393i		−	1.64681i
$700$	2.08218	−	3.22158i	0.0786990	−	0.121764i
$701$		−	1.28507i		−	0.0485366i	−0.999705	−	0.0242683i	$-0.992274\pi$
$701$		−	1.28507i		−	0.0485366i	0.999705	−	0.0242683i	$-0.00772559\pi$
$702$	−14.1714	−	26.0330i	−0.534865	−	0.982552i
$703$	4.77120			0.179949
$704$	5.44748	−	35.9073i	0.205310	−	1.35331i
$705$	14.5081			0.546406
$706$	12.0631	+	22.1601i	0.454002	+	0.834005i
$707$			30.1331i			1.13327i
$708$	10.3074	−	15.9477i	0.387375	−	0.599352i
$709$		−	7.21375i		−	0.270918i	−0.990783	−	0.135459i	$-0.956749\pi$
$709$		−	7.21375i		−	0.270918i	0.990783	−	0.135459i	$-0.0432509\pi$
$710$	17.3205	−	9.42865i	0.650027	−	0.353851i
$711$	0.695021			0.0260653
$712$	−13.4549	−	1.01481i	−0.504243	−	0.0380316i
$713$	60.2551			2.25657
$714$	7.60311	−	4.13885i	0.284539	−	0.154893i
$715$		−	18.0116i		−	0.673594i
$716$	−29.2864	−	18.9285i	−1.09448	−	0.707391i
$717$			11.2107i			0.418673i
$718$	11.6006	+	21.3104i	0.432930	+	0.795296i
$719$	−39.5034			−1.47323			−0.736613	−	0.676314i	$-0.763576\pi$
$719$	−39.5034			−1.47323			−0.736613	+	0.676314i	$0.763576\pi$
$720$	0.380924	−	0.171586i	0.0141962	−	0.00639462i
$721$	6.67709			0.248668
$722$	0.676154	+	1.24210i	0.0251639	+	0.0462262i
$723$			25.5285i			0.949415i
$724$	10.6715	+	6.89726i	0.396604	+	0.256334i
$725$		−	9.11883i		−	0.338665i
$726$	−20.3108	+	11.0564i	−0.753803	+	0.410343i
$727$	−8.48094			−0.314541			−0.157270	−	0.987556i	$-0.550269\pi$
$727$	−8.48094			−0.314541			−0.157270	+	0.987556i	$0.550269\pi$
$728$	1.61872	−	21.4618i	0.0599937	−	0.795427i
$729$	−27.8734			−1.03235
$730$	−9.80302	+	5.33640i	−0.362826	+	0.197509i
$731$		−	12.9151i		−	0.477681i
$732$	3.08764	−	4.77724i	0.114123	−	0.176572i
$733$		−	7.62376i		−	0.281590i	−0.990039	−	0.140795i	$-0.955034\pi$
$733$		−	7.62376i		−	0.281590i	0.990039	−	0.140795i	$-0.0449658\pi$
$734$	−5.49799	−	10.0999i	−0.202935	−	0.372793i
$735$	5.65196			0.208476
$736$	−20.1227	+	26.5215i	−0.741734	+	0.977596i
$737$	38.3452			1.41246
$738$	−0.0730790	−	0.134247i	−0.00269007	−	0.00494169i
$739$		−	24.3473i		−	0.895630i	−0.894126	−	0.447815i	$-0.852202\pi$
$739$		−	24.3473i		−	0.895630i	0.894126	−	0.447815i	$-0.147798\pi$
$740$	−5.17976	+	8.01420i	−0.190412	+	0.294608i
$741$			6.75123i			0.248013i
$742$	10.0448	−	5.46803i	0.368757	−	0.200738i
$743$	−41.5194			−1.52320			−0.761599	−	0.648048i	$-0.775586\pi$
$743$	−41.5194			−1.52320			−0.761599	+	0.648048i	$0.775586\pi$
$744$	−3.70613	+	49.1378i	−0.135873	+	1.80148i
$745$	−23.8712			−0.874573
$746$	−17.3373	+	9.43781i	−0.634765	+	0.345543i
$747$		−	0.903898i		−	0.0330719i
$748$	14.3021	+	9.24377i	0.522936	+	0.337986i
$749$		−	36.8729i		−	1.34731i
$750$	−1.15057	−	2.11360i	−0.0420127	−	0.0771778i
$751$	−24.8532			−0.906906			−0.453453	−	0.891280i	$-0.649808\pi$
$751$	−24.8532			−0.906906			−0.453453	+	0.891280i	$0.649808\pi$
$752$	14.0066	+	31.0949i	0.510767	+	1.13391i
$753$	38.5693			1.40554
$754$	−24.4626	−	44.9379i	−0.890874	−	1.63654i
$755$			10.1896i			0.370836i
$756$	−17.0184	−	10.9994i	−0.618953	−	0.400043i
$757$		−	25.6490i		−	0.932227i	−0.884725	−	0.466114i	$-0.845654\pi$
$757$		−	25.6490i		−	0.932227i	0.884725	−	0.466114i	$-0.154346\pi$
$758$	24.3202	−	13.2390i	0.883348	−	0.480862i
$759$	45.4629			1.65020
$760$	−2.82042	−	0.212725i	−0.102307	−	0.00771634i
$761$	12.5388			0.454530			0.227265	−	0.973833i	$-0.427022\pi$
$761$	12.5388			0.454530			0.227265	+	0.973833i	$0.427022\pi$
$762$	25.7974	−	14.0431i	0.934541	−	0.508730i
$763$		−	14.8611i		−	0.538008i
$764$	21.6243	−	33.4574i	0.782339	−	1.21045i
$765$			0.195896i			0.00708264i
$766$	−3.61065	−	6.63281i	−0.130458	−	0.239653i
$767$	22.1369			0.799318
$768$	−20.3905	−	18.0413i	−0.735779	−	0.651009i
$769$	38.0665			1.37271			0.686356	−	0.727266i	$-0.259209\pi$
$769$	38.0665			1.37271			0.686356	+	0.727266i	$0.259209\pi$
$770$	−5.88730	−	10.8150i	−0.212163	−	0.389746i
$771$		−	33.5999i		−	1.21007i
$772$	−3.45264	+	5.34197i	−0.124263	+	0.192262i
$773$			4.22947i			0.152123i	0.997103	+	0.0760617i	$0.0242346\pi$
$773$			4.22947i			0.152123i	−0.997103	+	0.0760617i	$0.975765\pi$
$774$	−0.893335	+	0.486299i	−0.0321103	+	0.0174796i
$775$	−10.2385			−0.367778
$776$	−9.89886	−	0.746604i	−0.355349	−	0.0268015i
$777$	15.5715			0.558623
$778$	−43.0662	+	23.4436i	−1.54400	+	0.840495i
$779$			1.03479i			0.0370753i
$780$	−11.3401	−	7.32935i	−0.406040	−	0.262433i
$781$		−	63.3050i		−	2.26523i
$782$	−7.46337	−	13.7103i	−0.266890	−	0.490279i
$783$	−48.1714			−1.72150
$784$	5.45658	+	12.1137i	0.194878	+	0.432634i
$785$	0.576523			0.0205770
$786$	15.1294	+	27.7928i	0.539648	+	0.991338i
$787$		−	28.3598i		−	1.01092i	−0.862850	−	0.505460i	$-0.831323\pi$
$787$		−	28.3598i		−	1.01092i	0.862850	−	0.505460i	$-0.168677\pi$
$788$	19.0909	+	12.3389i	0.680085	+	0.439555i
$789$			12.7681i			0.454557i
$790$	8.26535	−	4.49935i	0.294068	−	0.160080i
$791$	−17.0169			−0.605052
$792$	0.100866	−	1.33734i	0.00358413	−	0.0475202i
$793$	6.63126			0.235483
$794$	−16.5693	+	9.01973i	−0.588023	+	0.320098i
$795$		−	7.17489i		−	0.254467i
$796$	19.8796	−	30.7580i	0.704615	−	1.09019i
$797$		−	28.4360i		−	1.00726i	−0.863921	−	0.503628i	$-0.831998\pi$
$797$		−	28.4360i		−	1.00726i	0.863921	−	0.503628i	$-0.168002\pi$
$798$	2.20672	+	4.05377i	0.0781171	+	0.143502i
$799$	−15.9910			−0.565723
$800$	3.41925	−	4.50652i	0.120889	−	0.159330i
$801$	−0.498264			−0.0176053
$802$	9.81751	+	18.0349i	0.346668	+	0.636833i
$803$			35.8292i			1.26439i
$804$	15.6036	−	24.1421i	0.550297	−	0.851427i
$805$			11.2874i			0.397827i
$806$	−50.4558	+	27.4663i	−1.77723	+	0.967458i
$807$	0.0695860			0.00244954
$808$	−3.34216	+	44.3121i	−0.117577	+	1.55889i
$809$	54.9575			1.93220			0.966101	−	0.258164i	$-0.0831176\pi$
$809$	54.9575			1.93220			0.966101	+	0.258164i	$0.0831176\pi$
$810$	−10.7762	+	5.86615i	−0.378636	+	0.206115i
$811$			27.7581i			0.974717i	0.873202	+	0.487359i	$0.162040\pi$
$811$			27.7581i			0.974717i	−0.873202	+	0.487359i	$0.837960\pi$
$812$	−29.3770	−	18.9870i	−1.03093	−	0.666314i
$813$			14.1469i			0.496153i
$814$	14.6456	+	26.9041i	0.513329	+	0.942989i
$815$	17.1008			0.599016
$816$	11.6397	−	5.24307i	0.407473	−	0.183544i
$817$	6.88595			0.240909
$818$	11.7249	+	21.5388i	0.409953	+	0.753087i
$819$		−	0.794779i		−	0.0277718i
$820$	−1.73815	−	1.12340i	−0.0606987	−	0.0392309i
$821$			1.68746i			0.0588927i	0.999566	+	0.0294463i	$0.00937441\pi$
$821$			1.68746i			0.0588927i	−0.999566	+	0.0294463i	$0.990626\pi$
$822$	16.8986	−	9.19899i	0.589407	−	0.320851i
$823$	−15.9961			−0.557591			−0.278795	−	0.960351i	$-0.589935\pi$
$823$	−15.9961			−0.557591			−0.278795	+	0.960351i	$0.589935\pi$
$824$	9.81893	+	0.740576i	0.342059	+	0.0257992i
$825$	−7.72503			−0.268951
$826$	13.2921	−	7.23572i	0.462491	−	0.251763i
$827$		−	23.8803i		−	0.830398i	−0.909731	−	0.415199i	$-0.863712\pi$
$827$		−	23.8803i		−	0.830398i	0.909731	−	0.415199i	$-0.136288\pi$
$828$	−0.667317	+	1.03248i	−0.0231909	+	0.0358813i
$829$			41.1168i			1.42805i	0.700122	+	0.714023i	$0.253129\pi$
$829$			41.1168i			1.42805i	−0.700122	+	0.714023i	$0.746871\pi$
$830$	−5.85156	−	10.7494i	−0.203111	−	0.373116i
$831$	13.8030			0.478820
$832$	4.76079	−	31.3809i	0.165051	−	1.08794i
$833$	−6.22968			−0.215846
$834$	−26.3201	−	48.3503i	−0.911391	−	1.67423i
$835$		−	9.12743i		−	0.315868i
$836$	−4.92852	+	7.62548i	−0.170456	+	0.263733i
$837$			54.0863i			1.86949i
$838$	27.1734	−	14.7922i	0.938688	−	0.510987i
$839$	13.5553			0.467981			0.233990	−	0.972239i	$-0.424822\pi$
$839$	13.5553			0.467981			0.233990	+	0.972239i	$0.424822\pi$
$840$	−9.20481	−	0.694257i	−0.317596	−	0.0239541i
$841$	−54.1530			−1.86734
$842$	−30.8688	+	16.8038i	−1.06381	+	0.579098i
$843$		−	22.8067i		−	0.785504i
$844$	−12.8613	−	8.31256i	−0.442705	−	0.286130i
$845$		−	2.74107i		−	0.0942956i
$846$	0.602120	+	1.10610i	0.0207013	+	0.0380285i
$847$	−18.4306			−0.633283
$848$	15.3778	−	6.92687i	0.528076	−	0.237870i
$849$	−0.889113			−0.0305143
$850$	1.26817	+	2.32964i	0.0434980	+	0.0799061i
$851$		−	28.0792i		−	0.962542i
$852$	−39.8568	−	25.7604i	−1.36547	−	0.882535i
$853$		−	4.56005i		−	0.156133i	−0.996948	−	0.0780665i	$-0.975125\pi$
$853$		−	4.56005i		−	0.156133i	0.996948	−	0.0780665i	$-0.0248746\pi$
$854$	3.98173	−	2.16751i	0.136252	−	0.0741705i
$855$	−0.104446			−0.00357199
$856$	4.08969	−	54.2232i	0.139783	−	1.85331i
$857$	5.48833			0.187478			0.0937389	−	0.995597i	$-0.470118\pi$
$857$	5.48833			0.187478			0.0937389	+	0.995597i	$0.470118\pi$
$858$	−38.0692	+	20.7235i	−1.29966	+	0.707488i
$859$		−	8.03552i		−	0.274168i	−0.990559	−	0.137084i	$-0.956227\pi$
$859$		−	8.03552i		−	0.274168i	0.990559	−	0.137084i	$-0.0437731\pi$
$860$	−7.47561	+	11.5664i	−0.254916	+	0.394410i
$861$			3.37719i			0.115094i
$862$	−23.6020	−	43.3571i	−0.803887	−	1.47675i
$863$	0.335470			0.0114195			0.00570976	−	0.999984i	$-0.498183\pi$
$863$	0.335470			0.0114195			0.00570976	+	0.999984i	$0.498183\pi$
$864$	−23.8063	−	18.0626i	−0.809906	−	0.614502i
$865$	−6.52631			−0.221901
$866$	5.49972	+	10.1030i	0.186888	+	0.343315i
$867$		−	22.9418i		−	0.779146i
$868$	−21.3184	+	32.9842i	−0.723594	+	1.11956i
$869$		−	30.2092i		−	1.02478i
$870$	−19.2736	+	10.4918i	−0.653435	+	0.355706i
$871$	33.5115			1.13549
$872$	1.64829	−	21.8539i	0.0558181	−	0.740065i
$873$	−0.366577			−0.0124068
$874$	7.30994	−	3.97926i	0.247262	−	0.134601i
$875$		−	1.91794i		−	0.0648383i
$876$	22.5580	+	14.5798i	0.762165	+	0.492605i
$877$			17.0173i			0.574633i	0.957836	+	0.287317i	$0.0927632\pi$
$877$			17.0173i			0.574633i	−0.957836	+	0.287317i	$0.907237\pi$
$878$	19.1902	+	35.2527i	0.647640	+	1.18972i
$879$	34.4655			1.16249
$880$	−7.45799	−	16.5569i	−0.251409	−	0.558133i
$881$	−5.24994			−0.176875			−0.0884375	−	0.996082i	$-0.528187\pi$
$881$	−5.24994			−0.176875			−0.0884375	+	0.996082i	$0.528187\pi$
$882$	0.234570	+	0.430907i	0.00789838	+	0.0145094i
$883$			12.9814i			0.436860i	0.975853	+	0.218430i	$0.0700936\pi$
$883$			12.9814i			0.436860i	−0.975853	+	0.218430i	$0.929906\pi$
$884$	12.4992	+	8.07852i	0.420394	+	0.271710i
$885$		−	9.49437i		−	0.319150i
$886$	8.73836	−	4.75684i	0.293571	−	0.159809i
$887$	−14.0639			−0.472220			−0.236110	−	0.971726i	$-0.575873\pi$
$887$	−14.0639			−0.472220			−0.236110	+	0.971726i	$0.575873\pi$
$888$	22.8985	+	1.72708i	0.768423	+	0.0579569i
$889$	23.4093			0.785123
$890$	−5.92548	+	3.22561i	−0.198623	+	0.108123i
$891$			39.3860i			1.31948i
$892$	22.9168	−	35.4572i	0.767311	−	1.18720i
$893$		−	8.52598i		−	0.285311i
$894$	27.4654	+	50.4541i	0.918580	+	1.68744i
$895$	−17.4355			−0.582803
$896$	−7.39863	−	20.3988i	−0.247171	−	0.681475i
$897$	39.7319			1.32661
$898$	−20.2971	−	37.2859i	−0.677322	−	1.24425i
$899$			93.3632i			3.11384i
$900$	0.113390	−	0.175439i	0.00377967	−	0.00584797i
$901$			7.90828i			0.263463i
$902$	−5.83505	+	3.17639i	−0.194286	+	0.105762i
$903$	22.4732			0.747863
$904$	−25.0241	−	1.88740i	−0.832289	−	0.0627739i
$905$	6.35322			0.211188
$906$	21.5367	−	11.7238i	0.715508	−	0.389496i
$907$		−	35.0794i		−	1.16479i	−0.812905	−	0.582396i	$-0.802115\pi$
$907$		−	35.0794i		−	1.16479i	0.812905	−	0.582396i	$-0.197885\pi$
$908$	17.3830	+	11.2350i	0.576875	+	0.372848i
$909$			1.64098i			0.0544277i
$910$	−5.14516	−	9.45170i	−0.170560	−	0.313321i
$911$	15.6792			0.519474			0.259737	−	0.965679i	$-0.416364\pi$
$911$	15.6792			0.519474			0.259737	+	0.965679i	$0.416364\pi$
$912$	2.79546	+	6.20599i	0.0925669	+	0.205501i
$913$	−39.2880			−1.30024
$914$	2.50188	+	4.59598i	0.0827550	+	0.152022i
$915$		−	2.84410i		−	0.0940230i
$916$	2.56026	+	1.65476i	0.0845935	+	0.0546747i
$917$			25.2201i			0.832840i
$918$	12.3066	−	6.69928i	0.406180	−	0.221109i
$919$	−34.2297			−1.12913			−0.564566	−	0.825388i	$-0.690956\pi$
$919$	−34.2297			−1.12913			−0.564566	+	0.825388i	$0.690956\pi$
$920$	−1.25192	+	16.5985i	−0.0412744	+	0.547238i
$921$	−15.6163			−0.514576
$922$	7.87761	−	4.28828i	0.259435	−	0.141227i
$923$		−	55.3249i		−	1.82104i
$924$	−16.0849	+	24.8868i	−0.529154	+	0.818715i
$925$			4.77120i			0.156876i
$926$	−8.18074	−	15.0281i	−0.268836	−	0.493854i
$927$	0.363617			0.0119428
$928$	−41.0942	−	31.1795i	−1.34898	−	1.02352i
$929$	20.9733			0.688113			0.344056	−	0.938949i	$-0.388199\pi$
$929$	20.9733			0.688113			0.344056	+	0.938949i	$0.388199\pi$
$930$	11.7801	+	21.6401i	0.386284	+	0.709608i
$931$		−	3.32149i		−	0.108858i
$932$	27.7778	−	42.9782i	0.909892	−	1.40780i
$933$		−	8.50216i		−	0.278348i
$934$	−25.5669	+	13.9177i	−0.836574	+	0.455400i
$935$	8.51465			0.278459
$936$	0.0881513	−	1.16876i	0.00288132	−	0.0382020i
$937$	−46.8424			−1.53027			−0.765137	−	0.643868i	$-0.777329\pi$
$937$	−46.8424			−1.53027			−0.765137	+	0.643868i	$0.777329\pi$
$938$	20.1219	−	10.9536i	0.657004	−	0.357649i
$939$		−	15.3024i		−	0.499376i
$940$	14.3211	+	9.25607i	0.467103	+	0.301900i
$941$			59.6047i			1.94306i	0.236919	+	0.971529i	$0.423862\pi$
$941$			59.6047i			1.94306i	−0.236919	+	0.971529i	$0.576138\pi$
$942$	−0.663328	−	1.21854i	−0.0216124	−	0.0397022i
$943$	6.08990			0.198314
$944$	20.3491	−	9.16616i	0.662307	−	0.298333i
$945$	−10.1318			−0.329587
$946$	21.1370	+	38.8289i	0.687224	+	1.26244i
$947$		−	14.1256i		−	0.459020i	−0.973306	−	0.229510i	$-0.926288\pi$
$947$		−	14.1256i		−	0.459020i	0.973306	−	0.229510i	$-0.0737124\pi$
$948$	−19.0197	−	12.2928i	−0.617730	−	0.399253i
$949$			31.3127i			1.01645i
$950$	−1.24210	+	0.676154i	−0.0402991	+	0.0219373i
$951$	−50.5917			−1.64055
$952$	10.1457	+	0.765221i	0.328824	+	0.0248010i
$953$	51.9713			1.68351			0.841757	−	0.539856i	$-0.181521\pi$
$953$	51.9713			1.68351			0.841757	+	0.539856i	$0.181521\pi$
$954$	0.547016	−	0.297775i	0.0177103	−	0.00964083i
$955$		−	19.9186i		−	0.644552i
$956$	−7.15238	+	11.0663i	−0.231325	+	0.357909i
$957$			70.4432i			2.27711i
$958$	5.78145	+	10.6206i	0.186790	+	0.343135i
$959$	15.3343			0.495171
$960$	−13.4591	−	2.04187i	−0.434389	−	0.0659010i
$961$	73.8272			2.38152
$962$	12.7994	+	23.5127i	0.412670	+	0.758079i
$963$		−	2.00801i		−	0.0647071i
$964$	−16.2870	+	25.1995i	−0.524570	+	0.811622i
$965$			3.18031i			0.102378i
$966$	23.8570	−	12.9869i	0.767586	−	0.417845i
$967$	−39.6770			−1.27593			−0.637963	−	0.770067i	$-0.720223\pi$
$967$	−39.6770			−1.27593			−0.637963	+	0.770067i	$0.720223\pi$
$968$	−27.1030	−	2.04419i	−0.871122	−	0.0657028i
$969$	−3.19153			−0.102527
$970$	−4.35942	+	2.37311i	−0.139973	+	0.0761960i
$971$			40.1418i			1.28821i	0.764936	+	0.644106i	$0.222771\pi$
$971$			40.1418i			1.28821i	−0.764936	+	0.644106i	$0.777229\pi$
$972$	−1.82238	−	1.17784i	−0.0584528	−	0.0377794i
$973$		−	43.8745i		−	1.40655i
$974$	5.81366	+	10.6798i	0.186282	+	0.342201i
$975$	−6.75123			−0.216212
$976$	6.09570	−	2.74578i	0.195119	−	0.0878904i
$977$	13.4151			0.429187			0.214594	−	0.976703i	$-0.431157\pi$
$977$	13.4151			0.429187			0.214594	+	0.976703i	$0.431157\pi$
$978$	−19.6756	−	36.1443i	−0.629158	−	1.15577i
$979$			21.6571i			0.692165i
$980$	5.57912	+	3.60591i	0.178219	+	0.115187i
$981$		−	0.809298i		−	0.0258389i
$982$	10.3957	−	5.65904i	0.331740	−	0.180587i
$983$	−20.7083			−0.660494			−0.330247	−	0.943895i	$-0.607132\pi$
$983$	−20.7083			−0.660494			−0.330247	+	0.943895i	$0.607132\pi$
$984$	−0.374574	+	4.96629i	−0.0119410	+	0.158320i
$985$	11.3656			0.362139
$986$	21.2436	−	11.5642i	0.676535	−	0.368281i
$987$		−	27.8257i		−	0.885702i
$988$	−4.30724	+	6.66423i	−0.137032	+	0.212017i
$989$		−	40.5248i		−	1.28861i
$990$	−0.320607	−	0.588958i	−0.0101896	−	0.0187183i
$991$	−0.521289			−0.0165593			−0.00827965	−	0.999966i	$-0.502636\pi$
$991$	−0.521289			−0.0165593			−0.00827965	+	0.999966i	$0.502636\pi$
$992$	−35.0080	+	46.1401i	−1.11151	+	1.46495i
$993$	25.6649			0.814452
$994$	−18.0836	−	33.2198i	−0.573578	−	1.05367i
$995$		−	18.3116i		−	0.580516i
$996$	−15.9873	+	24.7357i	−0.506576	+	0.783781i
$997$			8.52842i			0.270098i	0.990839	+	0.135049i	$0.0431191\pi$
$997$			8.52842i			0.270098i	−0.990839	+	0.135049i	$0.956881\pi$
$998$	−24.7139	+	13.4533i	−0.782305	+	0.425858i
$999$	25.2045			0.797434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.15	✓	44
4.3	odd	2		3040.2.f.b.1521.13		44
8.3	odd	2		3040.2.f.b.1521.32		44
8.5	even	2	inner	760.2.f.b.381.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.15	✓	44	1.1	even	1	trivial
760.2.f.b.381.16	yes	44	8.5	even	2	inner
3040.2.f.b.1521.13		44	4.3	odd	2
3040.2.f.b.1521.32		44	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.676154 - 1.24210i) q^{2} +1.70163i q^{3} +(-1.08563 + 1.67970i) q^{4} +1.00000i q^{5} +(2.11360 - 1.15057i) q^{6} +1.91794 q^{7} +(2.82042 + 0.212725i) q^{8} +0.104446 q^{9} +(1.24210 - 0.676154i) q^{10} -4.53978i q^{11} +(-2.85824 - 1.84735i) q^{12} -3.96750i q^{13} +(-1.29683 - 2.38228i) q^{14} -1.70163 q^{15} +(-1.64281 - 3.64708i) q^{16} +1.87557 q^{17} +(-0.0706218 - 0.129733i) q^{18} +1.00000i q^{19} +(-1.67970 - 1.08563i) q^{20} +3.26364i q^{21} +(-5.63886 + 3.06959i) q^{22} +5.88514 q^{23} +(-0.361980 + 4.79931i) q^{24} -1.00000 q^{25} +(-4.92804 + 2.68264i) q^{26} +5.28263i q^{27} +(-2.08218 + 3.22158i) q^{28} +9.11883i q^{29} +(1.15057 + 2.11360i) q^{30} +10.2385 q^{31} +(-3.41925 + 4.50652i) q^{32} +7.72503 q^{33} +(-1.26817 - 2.32964i) q^{34} +1.91794i q^{35} +(-0.113390 + 0.175439i) q^{36} -4.77120i q^{37} +(1.24210 - 0.676154i) q^{38} +6.75123 q^{39} +(-0.212725 + 2.82042i) q^{40} +1.03479 q^{41} +(4.05377 - 2.20672i) q^{42} -6.88595i q^{43} +(7.62548 + 4.92852i) q^{44} +0.104446i q^{45} +(-3.97926 - 7.30994i) q^{46} -8.52598 q^{47} +(6.20599 - 2.79546i) q^{48} -3.32149 q^{49} +(0.676154 + 1.24210i) q^{50} +3.19153i q^{51} +(6.66423 + 4.30724i) q^{52} +4.21648i q^{53} +(6.56156 - 3.57187i) q^{54} +4.53978 q^{55} +(5.40940 + 0.407994i) q^{56} -1.70163 q^{57} +(11.3265 - 6.16573i) q^{58} +5.57956i q^{59} +(1.84735 - 2.85824i) q^{60} +1.67139i q^{61} +(-6.92281 - 12.7173i) q^{62} +0.200322 q^{63} +(7.90950 + 1.19995i) q^{64} +3.96750 q^{65} +(-5.22331 - 9.59527i) q^{66} +8.44650i q^{67} +(-2.03617 + 3.15040i) q^{68} +10.0143i q^{69} +(2.38228 - 1.29683i) q^{70} +13.9445 q^{71} +(0.294582 + 0.0222183i) q^{72} -7.89229 q^{73} +(-5.92631 + 3.22607i) q^{74} -1.70163i q^{75} +(-1.67970 - 1.08563i) q^{76} -8.70703i q^{77} +(-4.56487 - 8.38571i) q^{78} +6.65433 q^{79} +(3.64708 - 1.64281i) q^{80} -8.67575 q^{81} +(-0.699679 - 1.28532i) q^{82} -8.65418i q^{83} +(-5.48194 - 3.54310i) q^{84} +1.87557i q^{85} +(-8.55305 + 4.65597i) q^{86} -15.5169 q^{87} +(0.965723 - 12.8041i) q^{88} -4.77053 q^{89} +(0.129733 - 0.0706218i) q^{90} -7.60944i q^{91} +(-6.38909 + 9.88529i) q^{92} +17.4222i q^{93} +(5.76488 + 10.5901i) q^{94} -1.00000 q^{95} +(-7.66845 - 5.81830i) q^{96} -3.50972 q^{97} +(2.24584 + 4.12563i) q^{98} -0.474163i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

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