LMFDB - Embedded newform 668.2.e.a.9.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.9
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.174236 + 1.30752i) q^{3} +(-3.98478 - 1.76210i) q^{5} +(-0.546271 + 1.17470i) q^{7} +(1.21607 - 0.329959i) q^{9} +O(q^{10})$	\(q+(0.174236 + 1.30752i) q^{3} +(-3.98478 - 1.76210i) q^{5} +(-0.546271 + 1.17470i) q^{7} +(1.21607 - 0.329959i) q^{9} +(3.11275 - 3.99106i) q^{11} +(-1.14839 + 2.24333i) q^{13} +(1.60969 - 5.51720i) q^{15} +(7.71084 + 0.584836i) q^{17} +(-0.906296 + 1.36334i) q^{19} +(-1.63113 - 0.509583i) q^{21} +(-3.47141 - 1.38051i) q^{23} +(9.40909 + 10.3444i) q^{25} +(2.17496 + 5.18134i) q^{27} +(7.05769 - 2.80671i) q^{29} +(5.68575 - 1.31392i) q^{31} +(5.76074 + 3.37460i) q^{33} +(4.24672 - 3.71835i) q^{35} +(-3.15074 - 0.854899i) q^{37} +(-3.13328 - 1.11067i) q^{39} +(-0.194636 + 0.0950317i) q^{41} +(1.23599 - 13.0228i) q^{43} +(-5.42718 - 0.828023i) q^{45} +(0.121934 + 6.44215i) q^{47} +(3.42926 + 4.06942i) q^{49} +(0.578825 + 10.1840i) q^{51} +(-0.180484 - 1.04936i) q^{53} +(-19.4363 + 10.4185i) q^{55} +(-1.94050 - 0.947455i) q^{57} +(-2.30974 + 0.175185i) q^{59} +(10.7678 - 10.9735i) q^{61} +(-0.276698 + 1.60877i) q^{63} +(8.52904 - 6.91559i) q^{65} +(-10.0430 + 4.44111i) q^{67} +(1.20020 - 4.77946i) q^{69} +(7.67608 - 0.875397i) q^{71} +(-5.53782 + 4.15300i) q^{73} +(-11.8861 + 14.1049i) q^{75} +(2.98791 + 5.83676i) q^{77} +(1.08069 - 2.87477i) q^{79} +(-3.13406 + 1.83591i) q^{81} +(1.49389 - 2.07261i) q^{83} +(-29.6955 - 15.9177i) q^{85} +(4.89953 + 8.73903i) q^{87} +(-1.31598 - 4.51051i) q^{89} +(-2.00792 - 2.57448i) q^{91} +(2.70864 + 7.20529i) q^{93} +(6.01373 - 3.83561i) q^{95} +(-12.7207 - 2.93962i) q^{97} +(2.46843 - 5.88047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.174236	+	1.30752i	0.100595	+	0.754896i	0.966859	+	0.255310i	$0.0821774\pi$
$3$	0.174236	+	1.30752i	0.100595	+	0.754896i	−0.866264	+	0.499587i	$0.833485\pi$
$4$		0			0
$5$	−3.98478	−	1.76210i	−1.78205	−	0.788036i	−0.982201	−	0.187831i	$-0.939854\pi$
$5$	−3.98478	−	1.76210i	−1.78205	−	0.788036i	−0.799846	−	0.600206i	$-0.795085\pi$
$6$		0			0
$7$	−0.546271	+	1.17470i	−0.206471	+	0.443997i	−0.982391	−	0.186834i	$-0.940177\pi$
$7$	−0.546271	+	1.17470i	−0.206471	+	0.443997i	0.775921	+	0.630831i	$0.217286\pi$
$8$		0			0
$9$	1.21607	−	0.329959i	0.405356	−	0.109986i
$10$		0			0
$11$	3.11275	−	3.99106i	0.938530	−	1.20335i	−0.0404058	−	0.999183i	$-0.512865\pi$
$11$	3.11275	−	3.99106i	0.938530	−	1.20335i	0.978936	−	0.204166i	$-0.0654482\pi$
$12$		0			0
$13$	−1.14839	+	2.24333i	−0.318505	+	0.622187i	−0.993267	−	0.115848i	$-0.963041\pi$
$13$	−1.14839	+	2.24333i	−0.318505	+	0.622187i	0.674762	+	0.738035i	$0.264246\pi$
$14$		0			0
$15$	1.60969	−	5.51720i	0.415620	−	1.42453i
$16$		0			0
$17$	7.71084	+	0.584836i	1.87015	+	0.141844i	0.961341	−	0.275361i	$-0.0887973\pi$
$17$	7.71084	+	0.584836i	1.87015	+	0.141844i	0.908813	+	0.417204i	$0.136990\pi$
$18$		0			0
$19$	−0.906296	+	1.36334i	−0.207918	+	0.312771i	−0.921925	−	0.387367i	$-0.873384\pi$
$19$	−0.906296	+	1.36334i	−0.207918	+	0.312771i	0.714007	+	0.700139i	$0.246878\pi$
$20$		0			0
$21$	−1.63113	−	0.509583i	−0.355941	−	0.111200i
$22$		0			0
$23$	−3.47141	−	1.38051i	−0.723838	−	0.287856i	−0.0215685	−	0.999767i	$-0.506866\pi$
$23$	−3.47141	−	1.38051i	−0.723838	−	0.287856i	−0.702270	+	0.711911i	$0.747830\pi$
$24$		0			0
$25$	9.40909	+	10.3444i	1.88182	+	2.06888i
$26$		0			0
$27$	2.17496	+	5.18134i	0.418571	+	0.997149i
$28$		0			0
$29$	7.05769	−	2.80671i	1.31058	−	0.521192i	0.393291	−	0.919414i	$-0.371336\pi$
$29$	7.05769	−	2.80671i	1.31058	−	0.521192i	0.917289	+	0.398222i	$0.130373\pi$
$30$		0			0
$31$	5.68575	−	1.31392i	1.02119	−	0.235987i	0.318833	−	0.947811i	$-0.396709\pi$
$31$	5.68575	−	1.31392i	1.02119	−	0.235987i	0.702358	+	0.711824i	$0.252131\pi$
$32$		0			0
$33$	5.76074	+	3.37460i	1.00282	+	0.587442i
$34$		0			0
$35$	4.24672	−	3.71835i	0.717826	−	0.628516i
$36$		0			0
$37$	−3.15074	−	0.854899i	−0.517979	−	0.140545i	−0.00672997	−	0.999977i	$-0.502142\pi$
$37$	−3.15074	−	0.854899i	−0.517979	−	0.140545i	−0.511249	+	0.859433i	$0.670817\pi$
$38$		0			0
$39$	−3.13328	−	1.11067i	−0.501727	−	0.177849i
$40$		0			0
$41$	−0.194636	+	0.0950317i	−0.0303971	+	0.0148415i	−0.453885	−	0.891060i	$-0.649962\pi$
$41$	−0.194636	+	0.0950317i	−0.0303971	+	0.0148415i	0.423488	+	0.905902i	$0.360806\pi$
$42$		0			0
$43$	1.23599	−	13.0228i	0.188487	−	1.98596i	0.0230645	−	0.999734i	$-0.492658\pi$
$43$	1.23599	−	13.0228i	0.188487	−	1.98596i	0.165422	−	0.986223i	$-0.447101\pi$
$44$		0			0
$45$	−5.42718	−	0.828023i	−0.809036	−	0.123434i
$46$		0			0
$47$	0.121934	+	6.44215i	0.0177859	+	0.939685i	0.891440	+	0.453138i	$0.149696\pi$
$47$	0.121934	+	6.44215i	0.0177859	+	0.939685i	−0.873654	+	0.486547i	$0.838256\pi$
$48$		0			0
$49$	3.42926	+	4.06942i	0.489894	+	0.581346i
$50$		0			0
$51$	0.578825	+	10.1840i	0.0810517	+	1.42604i
$52$		0			0
$53$	−0.180484	−	1.04936i	−0.0247914	−	0.144141i	0.970495	−	0.241122i	$-0.0775153\pi$
$53$	−0.180484	−	1.04936i	−0.0247914	−	0.144141i	−0.995286	+	0.0969806i	$0.969082\pi$
$54$		0			0
$55$	−19.4363	+	10.4185i	−2.62079	+	1.40483i
$56$		0			0
$57$	−1.94050	−	0.947455i	−0.257025	−	0.125494i
$58$		0			0
$59$	−2.30974	+	0.175185i	−0.300703	+	0.0228071i	−0.225116	−	0.974332i	$-0.572276\pi$
$59$	−2.30974	+	0.175185i	−0.300703	+	0.0228071i	−0.0755875	+	0.997139i	$0.524083\pi$
$60$		0			0
$61$	10.7678	−	10.9735i	1.37867	−	1.40501i	0.563050	−	0.826423i	$-0.309628\pi$
$61$	10.7678	−	10.9735i	1.37867	−	1.40501i	0.815620	−	0.578588i	$-0.196396\pi$
$62$		0			0
$63$	−0.276698	+	1.60877i	−0.0348606	+	0.202685i
$64$		0			0
$65$	8.52904	−	6.91559i	1.05790	−	0.857773i
$66$		0			0
$67$	−10.0430	+	4.44111i	−1.22695	+	0.542567i	−0.913423	−	0.407012i	$-0.866571\pi$
$67$	−10.0430	+	4.44111i	−1.22695	+	0.542567i	−0.313526	+	0.949579i	$0.601510\pi$
$68$		0			0
$69$	1.20020	−	4.77946i	0.144487	−	0.575380i
$70$		0			0
$71$	7.67608	−	0.875397i	0.910983	−	0.103890i	0.354792	−	0.934945i	$-0.384552\pi$
$71$	7.67608	−	0.875397i	0.910983	−	0.103890i	0.556191	+	0.831055i	$0.312262\pi$
$72$		0			0
$73$	−5.53782	+	4.15300i	−0.648153	+	0.486072i	−0.872614	−	0.488411i	$-0.837577\pi$
$73$	−5.53782	+	4.15300i	−0.648153	+	0.486072i	0.224460	+	0.974483i	$0.427938\pi$
$74$		0			0
$75$	−11.8861	+	14.1049i	−1.37249	+	1.62870i
$76$		0			0
$77$	2.98791	+	5.83676i	0.340504	+	0.665161i
$78$		0			0
$79$	1.08069	−	2.87477i	0.121587	−	0.323437i	−0.861175	−	0.508308i	$-0.830271\pi$
$79$	1.08069	−	2.87477i	0.121587	−	0.323437i	0.982763	+	0.184871i	$0.0591868\pi$
$80$		0			0
$81$	−3.13406	+	1.83591i	−0.348229	+	0.203990i
$82$		0			0
$83$	1.49389	−	2.07261i	0.163976	−	0.227499i	−0.721234	−	0.692692i	$-0.756425\pi$
$83$	1.49389	−	2.07261i	0.163976	−	0.227499i	0.885209	+	0.465193i	$0.154015\pi$
$84$		0			0
$85$	−29.6955	−	15.9177i	−3.22092	−	1.72652i
$86$		0			0
$87$	4.89953	+	8.73903i	0.525284	+	0.936923i
$88$		0			0
$89$	−1.31598	−	4.51051i	−0.139493	−	0.478113i	0.859988	−	0.510314i	$-0.170471\pi$
$89$	−1.31598	−	4.51051i	−0.139493	−	0.478113i	−0.999481	+	0.0322018i	$0.989748\pi$
$90$		0			0
$91$	−2.00792	−	2.57448i	−0.210487	−	0.269879i
$92$		0			0
$93$	2.70864	+	7.20529i	0.280873	+	0.747154i
$94$		0			0
$95$	6.01373	−	3.83561i	0.616996	−	0.393526i
$96$		0			0
$97$	−12.7207	−	2.93962i	−1.29159	−	0.298473i	−0.477202	−	0.878794i	$-0.658349\pi$
$97$	−12.7207	−	2.93962i	−1.29159	−	0.298473i	−0.814388	+	0.580320i	$0.802927\pi$
$98$		0			0
$99$	2.46843	−	5.88047i	0.248087	−	0.591010i
$100$		0			0
$101$	−0.585876	−	6.17298i	−0.0582968	−	0.614234i	−0.976118	−	0.217241i	$-0.930294\pi$
$101$	−0.585876	−	6.17298i	−0.0582968	−	0.614234i	0.917821	−	0.396994i	$-0.129947\pi$
$102$		0			0
$103$	3.66609	−	2.53841i	0.361231	−	0.250117i	−0.374740	−	0.927130i	$-0.622268\pi$
$103$	3.66609	−	2.53841i	0.361231	−	0.250117i	0.735971	+	0.677013i	$0.236726\pi$
$104$		0			0
$105$	5.60175	+	4.90479i	0.546675	+	0.478659i
$106$		0			0
$107$	12.7727	+	8.84386i	1.23479	+	0.854968i	0.993314	−	0.115440i	$-0.0368278\pi$
$107$	12.7727	+	8.84386i	1.23479	+	0.854968i	0.241472	+	0.970408i	$0.422370\pi$
$108$		0			0
$109$	10.8163	+	6.89871i	1.03601	+	0.660777i	0.942282	−	0.334821i	$-0.108676\pi$
$109$	10.8163	+	6.89871i	1.03601	+	0.660777i	0.0937278	+	0.995598i	$0.470122\pi$
$110$		0			0
$111$	0.568823	−	4.26861i	0.0539903	−	0.405158i
$112$		0			0
$113$	3.76472	−	6.15653i	0.354155	−	0.579157i	−0.625408	−	0.780298i	$-0.715067\pi$
$113$	3.76472	−	6.15653i	0.354155	−	0.579157i	0.979562	+	0.201141i	$0.0644649\pi$
$114$		0			0
$115$	11.4002	+	11.6180i	1.06307	+	1.08338i
$116$		0			0
$117$	−0.656308	+	3.10696i	−0.0606757	+	0.287238i
$118$		0			0
$119$	−4.89922	+	8.73848i	−0.449110	+	0.801055i
$120$		0			0
$121$	−3.56022	−	14.1776i	−0.323656	−	1.28887i
$122$		0			0
$123$	−0.158168	−	0.237932i	−0.0142616	−	0.0214536i
$124$		0			0
$125$	−12.3767	−	37.1327i	−1.10700	−	3.32125i
$126$		0			0
$127$	−13.2453	−	1.51052i	−1.17533	−	0.134037i	−0.496303	−	0.868150i	$-0.665309\pi$
$127$	−13.2453	−	1.51052i	−1.17533	−	0.134037i	−0.679028	+	0.734112i	$0.737598\pi$
$128$		0			0
$129$	17.2429	−	0.652964i	1.51815	−	0.0574903i
$130$		0			0
$131$	−0.307833	+	5.41608i	−0.0268955	+	0.473205i	0.956500	+	0.291731i	$0.0942314\pi$
$131$	−0.307833	+	5.41608i	−0.0268955	+	0.473205i	−0.983396	+	0.181474i	$0.941913\pi$
$132$		0			0
$133$	−1.10644	−	1.80938i	−0.0959402	−	0.156893i
$134$		0			0
$135$	0.463326	−	24.4790i	0.0398768	−	2.10682i
$136$		0			0
$137$	12.2435	−	4.34000i	1.04603	−	0.370791i	0.245070	−	0.969505i	$-0.421189\pi$
$137$	12.2435	−	4.34000i	1.04603	−	0.370791i	0.800963	+	0.598714i	$0.204321\pi$
$138$		0			0
$139$	2.03764	+	1.92512i	0.172830	+	0.163286i	0.768296	−	0.640094i	$-0.221105\pi$
$139$	2.03764	+	1.92512i	0.172830	+	0.163286i	−0.595466	+	0.803381i	$0.703033\pi$
$140$		0			0
$141$	−8.40199	+	1.28189i	−0.707575	+	0.107955i
$142$		0			0
$143$	5.37861	+	11.5662i	0.449782	+	0.967214i
$144$		0			0
$145$	−33.0690	−	1.25228i	−2.74623	−	0.103996i
$146$		0			0
$147$	−4.72335	+	5.19286i	−0.389575	+	0.428300i
$148$		0			0
$149$	7.03516	+	5.70431i	0.576343	+	0.467315i	0.873035	−	0.487658i	$-0.162149\pi$
$149$	7.03516	+	5.70431i	0.576343	+	0.467315i	−0.296692	+	0.954973i	$0.595884\pi$
$150$		0			0
$151$	−9.18791	−	6.89033i	−0.747702	−	0.560727i	0.156579	−	0.987665i	$-0.449953\pi$
$151$	−9.18791	−	6.89033i	−0.747702	−	0.560727i	−0.904281	+	0.426939i	$0.859592\pi$
$152$		0			0
$153$	9.56987	−	1.83306i	0.773678	−	0.148194i
$154$		0			0
$155$	−24.9717	−	4.78320i	−2.00578	−	0.384196i
$156$		0			0
$157$	2.51398	+	11.9012i	0.200638	+	0.949818i	0.955740	+	0.294211i	$0.0950569\pi$
$157$	2.51398	+	11.9012i	0.200638	+	0.949818i	−0.755103	+	0.655607i	$0.772413\pi$
$158$		0			0
$159$	1.34061	−	0.418823i	0.106318	−	0.0332148i
$160$		0			0
$161$	3.51802	−	3.32374i	0.277259	−	0.261948i
$162$		0			0
$163$	−4.74113	+	14.2244i	−0.371354	+	1.11414i	0.582233	+	0.813022i	$0.302179\pi$
$163$	−4.74113	+	14.2244i	−0.371354	+	1.11414i	−0.953587	+	0.301118i	$0.902640\pi$
$164$		0			0
$165$	−17.0089	−	23.5980i	−1.32414	−	1.83710i
$166$		0			0
$167$	−5.93515	+	11.4793i	−0.459276	+	0.888294i
$167$	−5.93515	+	11.4793i	−0.459276	+	0.888294i
$168$		0			0
$169$	3.88762	+	5.39366i	0.299047	+	0.414897i
$170$		0			0
$171$	−0.652271	+	1.95695i	−0.0498804	+	0.149652i
$172$		0			0
$173$	−5.96118	+	5.63198i	−0.453220	+	0.428192i	−0.879136	−	0.476571i	$-0.841880\pi$
$173$	−5.96118	+	5.63198i	−0.453220	+	0.428192i	0.425916	+	0.904763i	$0.359952\pi$
$174$		0			0
$175$	−17.2915	+	5.40206i	−1.30712	+	0.408358i
$176$		0			0
$177$	−0.631499	−	2.98951i	−0.0474664	−	0.224705i
$178$		0			0
$179$	−20.7487	−	3.97430i	−1.55083	−	0.297053i	−0.659955	−	0.751305i	$-0.729425\pi$
$179$	−20.7487	−	3.97430i	−1.55083	−	0.297053i	−0.890873	+	0.454252i	$0.849906\pi$
$180$		0			0
$181$	−7.63092	+	1.46166i	−0.567202	+	0.108645i	−0.463712	−	0.885986i	$-0.653483\pi$
$181$	−7.63092	+	1.46166i	−0.567202	+	0.108645i	−0.103490	+	0.994631i	$0.533001\pi$
$182$		0			0
$183$	16.2242	+	12.1671i	1.19933	+	0.899415i
$184$		0			0
$185$	11.0486	+	8.95852i	0.812308	+	0.658643i
$186$		0			0
$187$	26.3361	−	28.9540i	1.92588	−	2.11732i
$188$		0			0
$189$	−7.27466	−	0.275481i	−0.529153	−	0.0200383i
$190$		0			0
$191$	4.88711	+	10.5093i	0.353619	+	0.760425i	0.999997	−	0.00259297i	$-0.000825368\pi$
$191$	4.88711	+	10.5093i	0.353619	+	0.760425i	−0.646378	+	0.763018i	$0.723717\pi$
$192$		0			0
$193$	9.78002	−	1.49213i	0.703981	−	0.107406i	0.211051	−	0.977475i	$-0.432311\pi$
$193$	9.78002	−	1.49213i	0.703981	−	0.107406i	0.492930	+	0.870069i	$0.335926\pi$
$194$		0			0
$195$	10.5283	+	9.94693i	0.753949	+	0.712314i
$196$		0			0
$197$	−5.69293	+	2.01799i	−0.405604	+	0.143776i	−0.529081	−	0.848572i	$-0.677463\pi$
$197$	−5.69293	+	2.01799i	−0.405604	+	0.143776i	0.123477	+	0.992347i	$0.460596\pi$
$198$		0			0
$199$	−0.219270	+	11.5847i	−0.0155437	+	0.821220i	0.903843	+	0.427865i	$0.140734\pi$
$199$	−0.219270	+	11.5847i	−0.0155437	+	0.821220i	−0.919387	+	0.393355i	$0.871314\pi$
$200$		0			0
$201$	−7.55669	−	12.3576i	−0.533008	−	0.871640i
$202$		0			0
$203$	−0.558361	+	9.82392i	−0.0391892	+	0.689504i
$204$		0			0
$205$	0.943038	−	0.0357115i	0.0658646	−	0.00249420i
$206$		0			0
$207$	−4.67697	−	0.533372i	−0.325072	−	0.0370719i
$208$		0			0
$209$	2.62009	+	7.86081i	0.181235	+	0.543744i
$210$		0			0
$211$	−13.7557	−	20.6927i	−0.946984	−	1.42455i	−0.904992	−	0.425428i	$-0.860124\pi$
$211$	−13.7557	−	20.6927i	−0.946984	−	1.42455i	−0.0419918	−	0.999118i	$-0.513370\pi$
$212$		0			0
$213$	2.48205	+	9.88410i	0.170067	+	0.677247i
$214$		0			0
$215$	−27.8726	+	49.7150i	−1.90090	+	3.39053i
$216$		0			0
$217$	−1.56249	+	7.39683i	−0.106069	+	0.502130i
$218$		0			0
$219$	−6.39502	−	6.51720i	−0.432135	−	0.440392i
$220$		0			0
$221$	−10.1670	+	16.6263i	−0.683906	+	1.11841i
$222$		0			0
$223$	0.208190	−	1.56232i	0.0139414	−	0.104620i	−0.982886	−	0.184216i	$-0.941025\pi$
$223$	0.208190	−	1.56232i	0.0139414	−	0.104620i	0.996827	+	0.0795954i	$0.0253628\pi$
$224$		0			0
$225$	14.8553	+	9.47486i	0.990354	+	0.631657i
$226$		0			0
$227$	−16.7872	−	11.6235i	−1.11421	−	0.771479i	−0.138457	−	0.990368i	$-0.544214\pi$
$227$	−16.7872	−	11.6235i	−1.11421	−	0.771479i	−0.975750	+	0.218890i	$0.929757\pi$
$228$		0			0
$229$	8.88245	+	7.77732i	0.586969	+	0.513940i	0.900050	−	0.435787i	$-0.143530\pi$
$229$	8.88245	+	7.77732i	0.586969	+	0.513940i	−0.313081	+	0.949726i	$0.601361\pi$
$230$		0			0
$231$	−7.11108	+	4.92372i	−0.467874	+	0.323957i
$232$		0			0
$233$	−1.60043	−	16.8626i	−0.104848	−	1.10471i	−0.880661	−	0.473747i	$-0.842901\pi$
$233$	−1.60043	−	16.8626i	−0.104848	−	1.10471i	0.775814	−	0.630962i	$-0.217340\pi$
$234$		0			0
$235$	10.8659	−	25.8854i	0.708811	−	1.68858i
$236$		0			0
$237$	3.94711	+	0.912137i	0.256392	+	0.0592496i
$238$		0			0
$239$	−6.26008	+	3.99274i	−0.404931	+	0.258269i	−0.724473	−	0.689303i	$-0.757917\pi$
$239$	−6.26008	+	3.99274i	−0.404931	+	0.258269i	0.319542	+	0.947572i	$0.396471\pi$
$240$		0			0
$241$	5.13676	+	13.6644i	0.330888	+	0.880201i	0.991574	+	0.129539i	$0.0413496\pi$
$241$	5.13676	+	13.6644i	0.330888	+	0.880201i	−0.660686	+	0.750662i	$0.729735\pi$
$242$		0			0
$243$	7.42106	+	9.51501i	0.476061	+	0.610388i
$244$		0			0
$245$	−6.49410	−	22.2585i	−0.414893	−	1.42204i
$246$		0			0
$247$	−2.01764	−	3.59876i	−0.128379	−	0.228983i
$248$		0			0
$249$	2.97027	+	1.59216i	0.188233	+	0.100899i
$250$		0			0
$251$	−1.25651	+	1.74328i	−0.0793104	+	0.110035i	−0.849023	−	0.528355i	$-0.822809\pi$
$251$	−1.25651	+	1.74328i	−0.0793104	+	0.110035i	0.769713	+	0.638390i	$0.220399\pi$
$252$		0			0
$253$	−16.3153	+	9.55739i	−1.02574	+	0.600868i
$254$		0			0
$255$	15.6387	−	41.6008i	0.979334	−	2.60514i
$256$		0			0
$257$	−1.86754	−	3.64816i	−0.116494	−	0.227566i	0.824597	−	0.565721i	$-0.191402\pi$
$257$	−1.86754	−	3.64816i	−0.116494	−	0.227566i	−0.941091	+	0.338155i	$0.890197\pi$
$258$		0			0
$259$	2.72541	−	3.23418i	0.169349	−	0.200962i
$260$		0			0
$261$	7.65653	−	5.74189i	0.473927	−	0.355414i
$262$		0			0
$263$	−11.7734	+	1.34266i	−0.725979	+	0.0827921i	−0.468464	−	0.883482i	$-0.655193\pi$
$263$	−11.7734	+	1.34266i	−0.725979	+	0.0827921i	−0.257514	+	0.966275i	$0.582903\pi$
$264$		0			0
$265$	−1.12990	+	4.49951i	−0.0694090	+	0.276403i
$266$		0			0
$267$	5.66828	−	2.50656i	0.346893	−	0.153399i
$268$		0			0
$269$	10.0287	−	8.13160i	0.611463	−	0.495792i	−0.273240	−	0.961946i	$-0.588095\pi$
$269$	10.0287	−	8.13160i	0.611463	−	0.495792i	0.884704	+	0.466153i	$0.154361\pi$
$270$		0			0
$271$	−0.360619	+	2.09670i	−0.0219060	+	0.127365i	−0.994423	−	0.105468i	$-0.966366\pi$
$271$	−0.360619	+	2.09670i	−0.0219060	+	0.127365i	0.972517	+	0.232833i	$0.0747997\pi$
$272$		0			0
$273$	3.01633	−	3.07396i	0.182556	−	0.186044i
$274$		0			0
$275$	70.5732	−	5.35269i	4.25573	−	0.322780i
$276$		0			0
$277$	−14.8712	−	7.26093i	−0.893526	−	0.436267i	−0.0660810	−	0.997814i	$-0.521050\pi$
$277$	−14.8712	−	7.26093i	−0.893526	−	0.436267i	−0.827445	+	0.561547i	$0.810206\pi$
$278$		0			0
$279$	6.48072	−	3.47388i	0.387990	−	0.207976i
$280$		0			0
$281$	−2.95668	−	17.1906i	−0.176381	−	1.02551i	−0.929827	−	0.367998i	$-0.880043\pi$
$281$	−2.95668	−	17.1906i	−0.176381	−	1.02551i	0.753446	−	0.657510i	$-0.228390\pi$
$282$		0			0
$283$	0.0579623	+	1.01980i	0.00344550	+	0.0606209i	0.999651	−	0.0264087i	$-0.00840711\pi$
$283$	0.0579623	+	1.01980i	0.00344550	+	0.0606209i	−0.996206	+	0.0870296i	$0.972263\pi$
$284$		0			0
$285$	6.06295	+	7.19476i	0.359138	+	0.426181i
$286$		0			0
$287$	−0.00531017	−	0.280553i	−0.000313450	−	0.0165605i
$288$		0			0
$289$	42.3095	+	6.45514i	2.48879	+	0.379714i
$290$		0			0
$291$	1.62720	−	17.1447i	0.0953882	−	1.00504i
$292$		0			0
$293$	18.1167	−	8.84555i	1.05839	−	0.516762i	0.174597	−	0.984640i	$-0.444138\pi$
$293$	18.1167	−	8.84555i	1.05839	−	0.516762i	0.883793	+	0.467878i	$0.154981\pi$
$294$		0			0
$295$	9.51251	+	3.37193i	0.553840	+	0.196322i
$296$		0			0
$297$	27.4491	+	7.44785i	1.59276	+	0.432168i
$298$		0			0
$299$	7.08345	−	6.20214i	0.409646	−	0.358679i
$300$		0			0
$301$	14.6227	+	8.56589i	0.842841	+	0.493730i
$302$		0			0
$303$	7.96920	−	1.84160i	0.457819	−	0.105797i
$304$		0			0
$305$	−62.2435	+	24.7530i	−3.56405	+	1.41735i
$306$		0			0
$307$	10.7682	+	25.6528i	0.614574	+	1.46408i	0.867919	+	0.496706i	$0.165457\pi$
$307$	10.7682	+	25.6528i	0.614574	+	1.46408i	−0.253345	+	0.967376i	$0.581531\pi$
$308$		0			0
$309$	3.95778	+	4.35120i	0.225150	+	0.247531i
$310$		0			0
$311$	3.58263	+	1.42474i	0.203152	+	0.0807897i	0.468893	−	0.883255i	$-0.344653\pi$
$311$	3.58263	+	1.42474i	0.203152	+	0.0807897i	−0.265741	+	0.964044i	$0.585617\pi$
$312$		0			0
$313$	17.8758	+	5.58461i	1.01040	+	0.315661i	0.758205	−	0.652016i	$-0.226076\pi$
$313$	17.8758	+	5.58461i	1.01040	+	0.315661i	0.252195	+	0.967676i	$0.418848\pi$
$314$		0			0
$315$	3.93739	−	5.92301i	0.221847	−	0.333724i
$316$		0			0
$317$	6.61079	+	0.501402i	0.371299	+	0.0281615i	0.259956	−	0.965620i	$-0.416292\pi$
$317$	6.61079	+	0.501402i	0.371299	+	0.0281615i	0.111343	+	0.993782i	$0.464485\pi$
$318$		0			0
$319$	10.7671	−	36.9042i	0.602843	−	2.06624i
$320$		0			0
$321$	−9.33804	+	18.2415i	−0.521198	+	1.01814i
$322$		0			0
$323$	−7.78563	+	9.98245i	−0.433204	+	0.555438i
$324$		0			0
$325$	−34.0111	+	9.22833i	−1.88660	+	0.511896i
$326$		0			0
$327$	−7.13561	+	15.3445i	−0.394600	+	0.848551i
$328$		0			0
$329$	−7.63424	−	3.37592i	−0.420889	−	0.186121i
$330$		0			0
$331$	−0.0159784	−	0.119907i	−0.000878254	−	0.00659067i	0.990793	−	0.135384i	$-0.0432269\pi$
$331$	−0.0159784	−	0.119907i	−0.000878254	−	0.00659067i	−0.991671	+	0.128794i	$0.958890\pi$
$332$		0			0
$333$	−4.11359			−0.225424
$334$		0			0
$335$	47.8449			2.61404
$336$		0			0
$337$	0.766722	+	5.75370i	0.0417660	+	0.313424i	0.999655	+	0.0262835i	$0.00836725\pi$
$337$	0.766722	+	5.75370i	0.0417660	+	0.313424i	−0.957889	+	0.287140i	$0.907295\pi$
$338$		0			0
$339$	8.70573	+	3.84975i	0.472830	+	0.209090i
$340$		0			0
$341$	12.4544	−	26.7821i	0.674444	−	1.45033i
$342$		0			0
$343$	−15.4058	+	4.18009i	−0.831834	+	0.225704i
$344$		0			0
$345$	−13.2044	+	16.9302i	−0.710902	+	0.911493i
$346$		0			0
$347$	9.47843	−	18.5157i	0.508829	−	0.993977i	−0.484072	−	0.875028i	$-0.660843\pi$
$347$	9.47843	−	18.5157i	0.508829	−	0.993977i	0.992900	−	0.118949i	$-0.0379525\pi$
$348$		0			0
$349$	−0.198407	+	0.680037i	−0.0106205	+	0.0364015i	−0.965114	−	0.261830i	$-0.915674\pi$
$349$	−0.198407	+	0.680037i	−0.0106205	+	0.0364015i	0.954493	+	0.298232i	$0.0963968\pi$
$350$		0			0
$351$	−14.1211	−	1.07103i	−0.753730	−	0.0571674i
$352$		0			0
$353$	9.37835	−	14.1078i	0.499159	−	0.750884i	−0.493770	−	0.869593i	$-0.664381\pi$
$353$	9.37835	−	14.1078i	0.499159	−	0.750884i	0.992929	+	0.118709i	$0.0378755\pi$
$354$		0			0
$355$	−32.1300	−	10.0378i	−1.70528	−	0.532750i
$356$		0			0
$357$	−12.2793	−	4.88326i	−0.649892	−	0.258449i
$358$		0			0
$359$	2.52386	+	2.77474i	0.133204	+	0.146445i	0.802728	−	0.596346i	$-0.203381\pi$
$359$	2.52386	+	2.77474i	0.133204	+	0.146445i	−0.669524	+	0.742791i	$0.733502\pi$
$360$		0			0
$361$	6.31664	+	15.0479i	0.332455	+	0.791997i
$362$		0			0
$363$	17.9172	−	7.12530i	0.940407	−	0.373981i
$364$		0			0
$365$	29.3850	−	6.79057i	1.53808	−	0.355435i
$366$		0			0
$367$	13.3064	+	7.79477i	0.694587	+	0.406884i	0.809997	−	0.586434i	$-0.199469\pi$
$367$	13.3064	+	7.79477i	0.694587	+	0.406884i	−0.115410	+	0.993318i	$0.536818\pi$
$368$		0			0
$369$	−0.205334	+	0.179787i	−0.0106893	+	0.00935933i
$370$		0			0
$371$	1.33128	+	0.361221i	0.0691168	+	0.0187537i
$372$		0			0
$373$	−5.14742	−	1.82462i	−0.266523	−	0.0944755i	0.197486	−	0.980306i	$-0.436722\pi$
$373$	−5.14742	−	1.82462i	−0.266523	−	0.0944755i	−0.464010	+	0.885830i	$0.653590\pi$
$374$		0			0
$375$	46.3952	−	22.6526i	2.39584	−	1.16978i
$376$		0			0
$377$	−1.80859	+	19.0559i	−0.0931471	+	0.981428i
$378$		0			0
$379$	−26.4022	−	4.02817i	−1.35619	−	0.206913i	−0.568346	−	0.822790i	$-0.692417\pi$
$379$	−26.4022	−	4.02817i	−1.35619	−	0.206913i	−0.787843	+	0.615876i	$0.788802\pi$
$380$		0			0
$381$	−0.332777	−	17.5817i	−0.0170487	−	0.900736i
$382$		0			0
$383$	−14.8124	−	17.5775i	−0.756877	−	0.898168i	0.240493	−	0.970651i	$-0.422691\pi$
$383$	−14.8124	−	17.5775i	−0.756877	−	0.898168i	−0.997370	+	0.0724826i	$0.976908\pi$
$384$		0			0
$385$	−1.62117	−	28.5232i	−0.0826224	−	1.45368i
$386$		0			0
$387$	−2.79394	−	16.2444i	−0.142024	−	0.825750i
$388$		0			0
$389$	5.65210	−	3.02971i	0.286573	−	0.153612i	−0.322868	−	0.946444i	$-0.604647\pi$
$389$	5.65210	−	3.02971i	0.286573	−	0.153612i	0.609441	+	0.792832i	$0.291394\pi$
$390$		0			0
$391$	−25.9601	−	12.6751i	−1.31286	−	0.641007i
$392$		0			0
$393$	−7.13526	+	0.541181i	−0.359926	+	0.0272990i
$394$		0			0
$395$	−9.37196	+	9.55103i	−0.471554	+	0.480564i
$396$		0			0
$397$	−3.86340	+	22.4624i	−0.193898	+	1.12736i	0.711466	+	0.702720i	$0.248032\pi$
$397$	−3.86340	+	22.4624i	−0.193898	+	1.12736i	−0.905364	+	0.424636i	$0.860402\pi$
$398$		0			0
$399$	2.17302	−	1.76195i	0.108787	−	0.0882077i
$400$		0			0
$401$	−23.7003	+	10.4805i	−1.18354	+	0.523370i	−0.900126	−	0.435629i	$-0.856526\pi$
$401$	−23.7003	+	10.4805i	−1.18354	+	0.523370i	−0.283410	+	0.958999i	$0.591466\pi$
$402$		0			0
$403$	−3.58188	+	14.2639i	−0.178426	+	0.710535i
$404$		0			0
$405$	15.7236	−	1.79315i	0.781311	−	0.0891024i
$406$		0			0
$407$	−13.2194	+	9.91370i	−0.655263	+	0.491404i
$408$		0			0
$409$	−20.4651	+	24.2854i	−1.01193	+	1.20084i	−0.0324161	+	0.999474i	$0.510320\pi$
$409$	−20.4651	+	24.2854i	−1.01193	+	1.20084i	−0.979517	+	0.201363i	$0.935463\pi$
$410$		0			0
$411$	7.80789	+	15.2524i	0.385135	+	0.752347i
$412$		0			0
$413$	1.05596	−	2.80896i	0.0519602	−	0.138220i
$414$		0			0
$415$	−9.60498	+	5.62652i	−0.471490	+	0.276195i
$416$		0			0
$417$	−2.16209	+	2.99968i	−0.105878	+	0.146895i
$418$		0			0
$419$	−10.5627	−	5.66197i	−0.516023	−	0.276605i	0.193731	−	0.981055i	$-0.437941\pi$
$419$	−10.5627	−	5.66197i	−0.516023	−	0.276605i	−0.709754	+	0.704449i	$0.751194\pi$
$420$		0			0
$421$	−3.78641	−	6.75363i	−0.184539	−	0.329152i	0.764329	−	0.644827i	$-0.223070\pi$
$421$	−3.78641	−	6.75363i	−0.184539	−	0.329152i	−0.948867	+	0.315675i	$0.897769\pi$
$422$		0			0
$423$	2.27393	+	7.79386i	0.110562	+	0.378950i
$424$		0			0
$425$	66.5022	+	85.2667i	3.22583	+	4.13604i
$426$		0			0
$427$	7.00850	+	18.6434i	0.339165	+	0.902218i
$428$		0			0
$429$	−14.1859	+	9.04788i	−0.684900	+	0.436836i
$430$		0			0
$431$	9.32339	+	2.15454i	0.449092	+	0.103780i	0.443641	−	0.896205i	$-0.353687\pi$
$431$	9.32339	+	2.15454i	0.449092	+	0.103780i	0.00545093	+	0.999985i	$0.498265\pi$
$432$		0			0
$433$	11.9589	−	28.4894i	0.574710	−	1.36911i	−0.330361	−	0.943855i	$-0.607171\pi$
$433$	11.9589	−	28.4894i	0.574710	−	1.36911i	0.905071	−	0.425260i	$-0.139817\pi$
$434$		0			0
$435$	−4.12445	−	43.4566i	−0.197752	−	2.08358i
$436$		0			0
$437$	5.02822	−	3.48155i	0.240532	−	0.166545i
$438$		0			0
$439$	5.03138	+	4.40539i	0.240135	+	0.210258i	0.770377	−	0.637588i	$-0.220068\pi$
$439$	5.03138	+	4.40539i	0.240135	+	0.210258i	−0.530243	+	0.847846i	$0.677899\pi$
$440$		0			0
$441$	5.51295	+	3.81718i	0.262522	+	0.181770i
$442$		0			0
$443$	−13.9991	−	8.92879i	−0.665119	−	0.424220i	0.161583	−	0.986859i	$-0.448340\pi$
$443$	−13.9991	−	8.92879i	−0.665119	−	0.424220i	−0.826702	+	0.562640i	$0.809786\pi$
$444$		0			0
$445$	−2.70409	+	20.2923i	−0.128186	+	0.961945i
$446$		0			0
$447$	−6.23271	+	10.1925i	−0.294797	+	0.482089i
$448$		0			0
$449$	−1.87996	−	1.91588i	−0.0887208	−	0.0904160i	0.667973	−	0.744186i	$-0.267162\pi$
$449$	−1.87996	−	1.91588i	−0.0887208	−	0.0904160i	−0.756693	+	0.653770i	$0.773186\pi$
$450$		0			0
$451$	−0.226577	+	1.07261i	−0.0106691	+	0.0505074i
$452$		0			0
$453$	7.40836	−	13.2139i	0.348075	−	0.620844i
$454$		0			0
$455$	3.46461	+	13.7969i	0.162423	+	0.646808i
$456$		0			0
$457$	−3.21092	−	4.83018i	−0.150200	−	0.225946i	0.749983	−	0.661457i	$-0.230062\pi$
$457$	−3.21092	−	4.83018i	−0.150200	−	0.225946i	−0.900183	+	0.435511i	$0.856568\pi$
$458$		0			0
$459$	13.7405	+	41.2245i	0.641352	+	1.92419i
$460$		0			0
$461$	−1.69531	−	0.193336i	−0.0789583	−	0.00900457i	0.0737390	−	0.997278i	$-0.476507\pi$
$461$	−1.69531	−	0.193336i	−0.0789583	−	0.00900457i	−0.152697	+	0.988273i	$0.548796\pi$
$462$		0			0
$463$	−18.8307	+	0.713092i	−0.875137	+	0.0331402i	−0.471589	−	0.881818i	$-0.656319\pi$
$463$	−18.8307	+	0.713092i	−0.875137	+	0.0331402i	−0.403548	+	0.914959i	$0.632223\pi$
$464$		0			0
$465$	1.90315	−	33.4844i	0.0882564	−	1.55280i
$466$		0			0
$467$	−3.65864	−	5.98307i	−0.169302	−	0.276863i	0.757177	−	0.653209i	$-0.226578\pi$
$467$	−3.65864	−	5.98307i	−0.169302	−	0.276863i	−0.926479	+	0.376346i	$0.877180\pi$
$468$		0			0
$469$	0.269218	−	14.2236i	0.0124313	−	0.656786i
$470$		0			0
$471$	−15.1230	+	5.36070i	−0.696831	+	0.247008i
$472$		0			0
$473$	−48.1274	−	45.4696i	−2.21290	−	2.09070i
$474$		0			0
$475$	−22.6303	+	3.45270i	−1.03835	+	0.158421i
$476$		0			0
$477$	−0.565727	−	1.21654i	−0.0259029	−	0.0557017i
$478$		0			0
$479$	6.79378	+	0.257271i	0.310416	+	0.0117550i	0.192590	−	0.981279i	$-0.438311\pi$
$479$	6.79378	+	0.257271i	0.310416	+	0.0117550i	0.117826	+	0.993034i	$0.462408\pi$
$480$		0			0
$481$	5.53609	−	6.08639i	0.252424	−	0.277516i
$482$		0			0
$483$	4.95882	+	4.02076i	0.225634	+	0.182951i
$484$		0			0
$485$	45.5092	+	34.1289i	2.06647	+	1.54971i
$486$		0			0
$487$	32.8709	−	6.29626i	1.48952	−	0.285311i	0.622123	−	0.782919i	$-0.286270\pi$
$487$	32.8709	−	6.29626i	1.48952	−	0.285311i	0.867402	+	0.497609i	$0.165788\pi$
$488$		0			0
$489$	−19.4247	−	3.72071i	−0.878416	−	0.168256i
$490$		0			0
$491$	−0.176438	−	0.835258i	−0.00796255	−	0.0376947i	0.974246	−	0.225486i	$-0.0723971\pi$
$491$	−0.176438	−	0.835258i	−0.00796255	−	0.0376947i	−0.982209	+	0.187792i	$0.939867\pi$
$492$		0			0
$493$	56.0622	−	17.5145i	2.52491	−	0.788812i
$494$		0			0
$495$	−20.1982	+	19.0828i	−0.907840	+	0.857706i
$496$		0			0
$497$	−3.16489	+	9.49533i	−0.141965	+	0.425924i
$498$		0			0
$499$	9.63634	+	13.3694i	0.431382	+	0.598497i	0.969716	−	0.244234i	$-0.0785366\pi$
$499$	9.63634	+	13.3694i	0.431382	+	0.598497i	−0.538334	+	0.842731i	$0.680946\pi$
$500$		0			0
$501$	−16.0435	−	5.76021i	−0.716771	−	0.257347i
$502$		0			0
$503$	9.60865	+	13.3310i	0.428428	+	0.594399i	0.969049	−	0.246867i	$-0.0794011\pi$
$503$	9.60865	+	13.3310i	0.428428	+	0.594399i	−0.540621	+	0.841266i	$0.681811\pi$
$504$		0			0
$505$	−8.54284	+	25.6303i	−0.380151	+	1.14053i
$506$		0			0
$507$	−6.37495	+	6.02290i	−0.283121	+	0.267487i
$508$		0			0
$509$	1.94487	−	0.607601i	0.0862050	−	0.0269314i	−0.254791	−	0.966996i	$-0.582007\pi$
$509$	1.94487	−	0.607601i	0.0862050	−	0.0269314i	0.340996	+	0.940065i	$0.389236\pi$
$510$		0			0
$511$	−1.85340	−	8.77397i	−0.0819895	−	0.388137i
$512$		0			0
$513$	−9.03507	−	1.73062i	−0.398908	−	0.0764088i
$514$		0			0
$515$	−19.0815	+	3.65496i	−0.840832	+	0.161057i
$516$		0			0
$517$	26.0906	+	19.5662i	1.14746	+	0.860520i
$518$		0			0
$519$	−8.40258	−	6.81306i	−0.368832	−	0.299060i
$520$		0			0
$521$	0.867367	−	0.953586i	0.0380000	−	0.0417774i	−0.720463	−	0.693493i	$-0.756071\pi$
$521$	0.867367	−	0.953586i	0.0380000	−	0.0417774i	0.758463	+	0.651716i	$0.225950\pi$
$522$		0			0
$523$	−11.5744	−	0.438308i	−0.506115	−	0.0191659i	−0.216450	−	0.976294i	$-0.569448\pi$
$523$	−11.5744	−	0.438308i	−0.506115	−	0.0191659i	−0.289666	+	0.957128i	$0.593544\pi$
$524$		0			0
$525$	−10.0761	−	21.6677i	−0.439757	−	0.945658i
$526$		0			0
$527$	44.6103	−	6.80618i	1.94326	−	0.296482i
$528$		0			0
$529$	−6.57368	−	6.21066i	−0.285812	−	0.270029i
$530$		0			0
$531$	−2.75100	+	0.975157i	−0.119383	+	0.0423182i
$532$		0			0
$533$	0.0103300	−	0.545766i	0.000447442	−	0.0236397i
$534$		0			0
$535$	−35.3127	−	57.7477i	−1.52670	−	2.49665i
$536$		0			0
$537$	1.58130	−	27.8217i	0.0682381	−	1.20060i
$538$		0			0
$539$	26.9157	−	1.01926i	1.15934	−	0.0439027i
$540$		0			0
$541$	−13.9912	−	1.59559i	−0.601529	−	0.0685996i	−0.192773	−	0.981243i	$-0.561748\pi$
$541$	−13.9912	−	1.59559i	−0.601529	−	0.0685996i	−0.408756	+	0.912644i	$0.634037\pi$
$542$		0			0
$543$	−3.24074	−	9.72289i	−0.139073	−	0.417249i
$544$		0			0
$545$	−30.9441	−	46.5492i	−1.32550	−	1.99395i
$546$		0			0
$547$	0.0239711	+	0.0954586i	0.00102493	+	0.00408152i	0.970398	−	0.241513i	$-0.0776435\pi$
$547$	0.0239711	+	0.0954586i	0.00102493	+	0.00408152i	−0.969373	+	0.245594i	$0.921017\pi$
$548$		0			0
$549$	9.47351	−	16.8974i	0.404320	−	0.721164i
$550$		0			0
$551$	−2.56987	+	12.1657i	−0.109480	+	0.518277i
$552$		0			0
$553$	2.78665	+	2.83990i	0.118501	+	0.120765i
$554$		0			0
$555$	−9.78836	+	16.0071i	−0.415493	+	0.679465i
$556$		0			0
$557$	0.509702	−	3.82495i	0.0215968	−	0.162068i	−0.977122	−	0.212682i	$-0.931780\pi$
$557$	0.509702	−	3.82495i	0.0215968	−	0.162068i	0.998718	+	0.0506134i	$0.0161176\pi$
$558$		0			0
$559$	27.7950	+	17.7279i	1.17560	+	0.749811i
$560$		0			0
$561$	42.4465	+	29.3901i	1.79209	+	1.24085i
$562$		0			0
$563$	−2.62166	−	2.29548i	−0.110490	−	0.0967429i	0.601730	−	0.798700i	$-0.294479\pi$
$563$	−2.62166	−	2.29548i	−0.110490	−	0.0967429i	−0.712219	+	0.701957i	$0.752310\pi$
$564$		0			0
$565$	−25.8500	+	17.8986i	−1.08752	+	0.752999i
$566$		0			0
$567$	−0.444604	−	4.68449i	−0.0186716	−	0.196730i
$568$		0			0
$569$	−7.60096	+	18.1075i	−0.318649	+	0.759108i	0.680991	+	0.732291i	$0.261549\pi$
$569$	−7.60096	+	18.1075i	−0.318649	+	0.759108i	−0.999640	+	0.0268166i	$0.991463\pi$
$570$		0			0
$571$	24.5157	+	5.66532i	1.02595	+	0.237086i	0.704398	−	0.709806i	$-0.251217\pi$
$571$	24.5157	+	5.66532i	1.02595	+	0.237086i	0.321552	+	0.946892i	$0.395796\pi$
$572$		0			0
$573$	−12.8896	+	8.22109i	−0.538469	+	0.343441i
$574$		0			0
$575$	−18.3822	−	48.8989i	−0.766592	−	2.03923i
$576$		0			0
$577$	−12.4608	−	15.9768i	−0.518751	−	0.665123i	0.455593	−	0.890188i	$-0.349427\pi$
$577$	−12.4608	−	15.9768i	−0.518751	−	0.665123i	−0.974344	+	0.225065i	$0.927741\pi$
$578$		0			0
$579$	3.65503	+	12.5276i	0.151898	+	0.520628i
$580$		0			0
$581$	1.61864	+	2.88709i	0.0671526	+	0.119777i
$582$		0			0
$583$	−4.74987	−	2.54609i	−0.196719	−	0.105448i
$584$		0			0
$585$	8.09002	−	11.2241i	0.334481	−	0.464057i
$586$		0			0
$587$	−21.0538	+	12.3332i	−0.868984	+	0.509044i	−0.871186	−	0.490954i	$-0.836648\pi$
$587$	−21.0538	+	12.3332i	−0.868984	+	0.509044i	0.00220214	+	0.999998i	$0.499299\pi$
$588$		0			0
$589$	−3.36166	+	8.94240i	−0.138515	+	0.368465i
$590$		0			0
$591$	−3.63048	−	7.09200i	−0.149338	−	0.291726i
$592$		0			0
$593$	12.2711	−	14.5619i	0.503915	−	0.597984i	−0.451858	−	0.892090i	$-0.649239\pi$
$593$	12.2711	−	14.5619i	0.503915	−	0.597984i	0.955773	+	0.294106i	$0.0950218\pi$
$594$		0			0
$595$	34.9204	−	26.1880i	1.43160	−	1.07360i
$596$		0			0
$597$	−15.1855	+	1.73178i	−0.621499	+	0.0708771i
$598$		0			0
$599$	−1.35107	+	5.38026i	−0.0552031	+	0.219831i	−0.991241	−	0.132069i	$-0.957838\pi$
$599$	−1.35107	+	5.38026i	−0.0552031	+	0.219831i	0.936037	+	0.351900i	$0.114464\pi$
$600$		0			0
$601$	−15.1558	+	6.70203i	−0.618218	+	0.273381i	−0.689739	−	0.724058i	$-0.742275\pi$
$601$	−15.1558	+	6.70203i	−0.618218	+	0.273381i	0.0715211	+	0.997439i	$0.477215\pi$
$602$		0			0
$603$	−10.7476	+	8.71446i	−0.437676	+	0.354880i
$604$		0			0
$605$	−10.7957	+	62.7680i	−0.438908	+	2.55188i
$606$		0			0
$607$	4.87332	−	4.96643i	0.197802	−	0.201581i	−0.607713	−	0.794157i	$-0.707913\pi$
$607$	4.87332	−	4.96643i	0.197802	−	0.201581i	0.805515	+	0.592576i	$0.201889\pi$
$608$		0			0
$609$	−12.9422	+	0.981617i	−0.524446	+	0.0397771i
$610$		0			0
$611$	−14.5919	−	7.12454i	−0.590325	−	0.288228i
$612$		0			0
$613$	−22.2598	+	11.9320i	−0.899063	+	0.481927i	−0.855900	−	0.517141i	$-0.826996\pi$
$613$	−22.2598	+	11.9320i	−0.899063	+	0.481927i	−0.0431625	+	0.999068i	$0.513743\pi$
$614$		0			0
$615$	0.211005	+	1.22682i	0.00850854	+	0.0494700i
$616$		0			0
$617$	1.55272	+	27.3188i	0.0625100	+	1.09981i	0.864551	+	0.502545i	$0.167603\pi$
$617$	1.55272	+	27.3188i	0.0625100	+	1.09981i	−0.802041	+	0.597269i	$0.796252\pi$
$618$		0			0
$619$	−13.3351	−	15.8244i	−0.535982	−	0.636038i	0.427434	−	0.904046i	$-0.359418\pi$
$619$	−13.3351	−	15.8244i	−0.535982	−	0.636038i	−0.963416	+	0.268009i	$0.913634\pi$
$620$		0			0
$621$	−0.397271	−	20.9891i	−0.0159419	−	0.842263i
$622$		0			0
$623$	6.01739	+	0.918071i	0.241082	+	0.0367817i
$624$		0			0
$625$	−9.50710	+	100.170i	−0.380284	+	4.00679i
$626$		0			0
$627$	−9.82165	+	4.79545i	−0.392239	+	0.191512i
$628$		0			0
$629$	−23.7949	−	8.43466i	−0.948765	−	0.336312i
$630$		0			0
$631$	−32.2294	−	8.74488i	−1.28303	−	0.348128i	−0.445876	−	0.895095i	$-0.647108\pi$
$631$	−32.2294	−	8.74488i	−1.28303	−	0.348128i	−0.837155	+	0.546966i	$0.815783\pi$
$632$		0			0
$633$	24.6594	−	21.5913i	0.980122	−	0.858178i
$634$		0			0
$635$	50.1179	+	29.3587i	1.98887	+	1.16506i
$636$		0			0
$637$	−13.0672	+	3.01969i	−0.517740	+	0.119644i
$638$		0			0
$639$	9.04579	−	3.59733i	0.357846	−	0.142308i
$640$		0			0
$641$	−14.4179	−	34.3473i	−0.569472	−	1.35664i	−0.909297	−	0.416147i	$-0.863380\pi$
$641$	−14.4179	−	34.3473i	−0.569472	−	1.35664i	0.339825	−	0.940489i	$-0.389632\pi$
$642$		0			0
$643$	−6.78982	−	7.46475i	−0.267764	−	0.294381i	0.591085	−	0.806609i	$-0.298700\pi$
$643$	−6.78982	−	7.46475i	−0.267764	−	0.294381i	−0.858849	+	0.512228i	$0.828820\pi$
$644$		0			0
$645$	−69.8597	−	27.7818i	−2.75072	−	1.09391i
$646$		0			0
$647$	19.8746	+	6.20905i	0.781351	+	0.244103i	0.662752	−	0.748839i	$-0.269389\pi$
$647$	19.8746	+	6.20905i	0.781351	+	0.244103i	0.118599	+	0.992942i	$0.462160\pi$
$648$		0			0
$649$	−6.49049	+	9.76363i	−0.254774	+	0.383256i
$650$		0			0
$651$	−9.94374	−	0.754193i	−0.389726	−	0.0295591i
$652$		0			0
$653$	5.45814	−	18.7077i	0.213594	−	0.732090i	−0.780652	−	0.624966i	$-0.785113\pi$
$653$	5.45814	−	18.7077i	0.213594	−	0.732090i	0.994246	−	0.107124i	$-0.0341643\pi$
$654$		0			0
$655$	10.7703	−	21.0395i	0.420832	−	0.822080i
$656$		0			0
$657$	−5.36404	+	6.87758i	−0.209271	+	0.268320i
$658$		0			0
$659$	−31.1393	+	8.44911i	−1.21301	+	0.329131i	−0.810201	−	0.586152i	$-0.800642\pi$
$659$	−31.1393	+	8.44911i	−1.21301	+	0.329131i	−0.402813	+	0.915282i	$0.631968\pi$
$660$		0			0
$661$	−20.9019	+	44.9477i	−0.812991	+	1.74826i	−0.165471	+	0.986215i	$0.552914\pi$
$661$	−20.9019	+	44.9477i	−0.812991	+	1.74826i	−0.647521	+	0.762048i	$0.724194\pi$
$662$		0			0
$663$	−23.5107	−	10.3966i	−0.913080	−	0.403772i
$664$		0			0
$665$	1.22059	+	9.15964i	0.0473324	+	0.355196i
$666$		0			0
$667$	−28.3748			−1.09868
$668$		0			0
$669$	2.07903			0.0803800
$670$		0			0
$671$	−10.2785	−	77.1325i	−0.396796	−	2.97767i
$672$		0			0
$673$	13.1582	+	5.81869i	0.507213	+	0.224294i	0.642177	−	0.766557i	$-0.278031\pi$
$673$	13.1582	+	5.81869i	0.507213	+	0.224294i	−0.134964	+	0.990851i	$0.543092\pi$
$674$		0			0
$675$	−33.1334	+	71.2503i	−1.27530	+	2.74242i
$676$		0			0
$677$	21.3374	−	5.78955i	0.820065	−	0.222510i	0.172977	−	0.984926i	$-0.444661\pi$
$677$	21.3374	−	5.78955i	0.820065	−	0.222510i	0.647088	+	0.762416i	$0.275987\pi$
$678$		0			0
$679$	10.4021	−	13.3372i	0.399197	−	0.511836i
$680$		0			0
$681$	12.2730	−	23.9748i	0.470302	−	0.918718i
$682$		0			0
$683$	12.8439	−	44.0223i	0.491458	−	1.68447i	−0.214920	−	0.976632i	$-0.568949\pi$
$683$	12.8439	−	44.0223i	0.491458	−	1.68447i	0.706378	−	0.707835i	$-0.250328\pi$
$684$		0			0
$685$	−56.4352	−	4.28038i	−2.15628	−	0.163545i
$686$		0			0
$687$	−8.62135	+	12.9691i	−0.328925	+	0.494801i
$688$		0			0
$689$	2.56133	+	0.800188i	0.0975789	+	0.0304847i
$690$		0			0
$691$	−39.1930	−	15.5863i	−1.49097	−	0.592931i	−0.524892	−	0.851169i	$-0.675894\pi$
$691$	−39.1930	−	15.5863i	−1.49097	−	0.592931i	−0.966081	+	0.258238i	$0.916858\pi$
$692$		0			0
$693$	5.55939	+	6.11201i	0.211184	+	0.232176i
$694$		0			0
$695$	−4.72729	−	11.2617i	−0.179316	−	0.427180i
$696$		0			0
$697$	−1.55639	+	0.618944i	−0.0589523	+	0.0234442i
$698$		0			0
$699$	21.7694	−	5.03068i	0.823393	−	0.190278i
$700$		0			0
$701$	−25.6464	−	15.0234i	−0.968650	−	0.567428i	−0.0660076	−	0.997819i	$-0.521026\pi$
$701$	−25.6464	−	15.0234i	−0.968650	−	0.567428i	−0.902642	+	0.430391i	$0.858376\pi$
$702$		0			0
$703$	4.02102	−	3.52073i	0.151656	−	0.132787i
$704$		0			0
$705$	35.7389	+	9.69713i	1.34600	+	0.365215i
$706$		0			0
$707$	7.57147	+	2.68389i	0.284754	+	0.100938i
$708$		0			0
$709$	42.7003	−	20.8486i	1.60364	−	0.782985i	0.603745	−	0.797177i	$-0.293674\pi$
$709$	42.7003	−	20.8486i	1.60364	−	0.782985i	0.999899	+	0.0141927i	$0.00451782\pi$
$710$		0			0
$711$	0.365639	−	3.85250i	0.0137125	−	0.144480i
$712$		0			0
$713$	−21.5514	−	3.28809i	−0.807107	−	0.123140i
$714$		0			0
$715$	−1.05173	−	55.5664i	−0.0393326	−	2.07807i
$716$		0			0
$717$	−6.31131	−	7.48949i	−0.235700	−	0.279700i
$718$		0			0
$719$	−0.570696	−	10.0409i	−0.0212834	−	0.374464i	−0.991317	−	0.131494i	$-0.958023\pi$
$719$	−0.570696	−	10.0409i	−0.0212834	−	0.374464i	0.970034	−	0.242971i	$-0.0781218\pi$
$720$		0			0
$721$	0.979201	+	5.69323i	0.0364673	+	0.212027i
$722$		0			0
$723$	−16.9714	+	9.09725i	−0.631174	+	0.338330i
$724$		0			0
$725$	95.4401	+	46.5989i	3.54456	+	1.73064i
$726$		0			0
$727$	−19.9078	+	1.50993i	−0.738340	+	0.0560001i	−0.439424	−	0.898280i	$-0.644818\pi$
$727$	−19.9078	+	1.50993i	−0.738340	+	0.0560001i	−0.298915	+	0.954280i	$0.596625\pi$
$728$		0			0
$729$	−18.7798	+	19.1387i	−0.695550	+	0.708839i
$730$		0			0
$731$	17.1467	−	99.6938i	0.634194	−	3.68731i
$732$		0			0
$733$	−5.06161	+	4.10410i	−0.186955	+	0.151588i	−0.718711	−	0.695309i	$-0.755267\pi$
$733$	−5.06161	+	4.10410i	−0.186955	+	0.151588i	0.531756	+	0.846898i	$0.321532\pi$
$734$		0			0
$735$	27.9719	−	12.3694i	1.03176	−	0.456252i
$736$		0			0
$737$	−13.5367	+	53.9063i	−0.498631	+	1.98566i
$738$		0			0
$739$	20.3755	−	2.32366i	0.749525	−	0.0854774i	0.269824	−	0.962910i	$-0.413034\pi$
$739$	20.3755	−	2.32366i	0.749525	−	0.0854774i	0.479701	+	0.877432i	$0.340745\pi$
$740$		0			0
$741$	4.35389	−	3.26513i	0.159944	−	0.119948i
$742$		0			0
$743$	−18.0833	+	21.4591i	−0.663413	+	0.787256i	−0.987305	−	0.158838i	$-0.949225\pi$
$743$	−18.0833	+	21.4591i	−0.663413	+	0.787256i	0.323892	+	0.946094i	$0.395008\pi$
$744$		0			0
$745$	−17.9820	−	35.1271i	−0.658808	−	1.28696i
$746$		0			0
$747$	1.13279	−	3.01336i	0.0414467	−	0.110253i
$748$		0			0
$749$	−17.3663	+	10.1730i	−0.634550	+	0.371715i
$750$		0			0
$751$	−9.57647	+	13.2863i	−0.349450	+	0.484826i	−0.948896	−	0.315590i	$-0.897798\pi$
$751$	−9.57647	+	13.2863i	−0.349450	+	0.484826i	0.599445	+	0.800416i	$0.295388\pi$
$752$		0			0
$753$	−2.49830	−	1.33917i	−0.0910431	−	0.0488021i
$754$		0			0
$755$	24.4703	+	43.6465i	0.890567	+	1.58846i
$756$		0			0
$757$	−7.38929	−	25.3267i	−0.268568	−	0.920516i	−0.976731	−	0.214467i	$-0.931199\pi$
$757$	−7.38929	−	25.3267i	−0.268568	−	0.920516i	0.708163	−	0.706049i	$-0.249524\pi$
$758$		0			0
$759$	−15.3392	−	19.6673i	−0.556777	−	0.713879i
$760$		0			0
$761$	−13.1259	−	34.9165i	−0.475814	−	1.26572i	−0.927593	−	0.373592i	$-0.878126\pi$
$761$	−13.1259	−	34.9165i	−0.475814	−	1.26572i	0.451779	−	0.892130i	$-0.350790\pi$
$762$		0			0
$763$	−14.0126	+	8.93734i	−0.507288	+	0.323553i
$764$		0			0
$765$	−41.3639	−	9.55876i	−1.49551	−	0.345598i
$766$		0			0
$767$	2.25948	−	5.38269i	0.0815851	−	0.194358i
$768$		0			0
$769$	−0.0977317	−	1.02973i	−0.00352430	−	0.0371331i	0.993591	−	0.113035i	$-0.0360573\pi$
$769$	−0.0977317	−	1.02973i	−0.00352430	−	0.0371331i	−0.997115	+	0.0759021i	$0.975816\pi$
$770$		0			0
$771$	4.44465	−	3.07748i	0.160070	−	0.110833i
$772$		0			0
$773$	14.6081	+	12.7906i	0.525417	+	0.460046i	0.879997	−	0.474980i	$-0.157545\pi$
$773$	14.6081	+	12.7906i	0.525417	+	0.460046i	−0.354579	+	0.935026i	$0.615376\pi$
$774$		0			0
$775$	67.0894	+	46.4528i	2.40992	+	1.66864i
$776$		0			0
$777$	4.70362	+	3.00002i	0.168741	+	0.107625i
$778$		0			0
$779$	0.0468375	−	0.351482i	0.00167813	−	0.0125931i
$780$		0			0
$781$	20.4000	−	33.3606i	0.729969	−	1.19374i
$782$		0			0
$783$	29.8927	+	30.4638i	1.06828	+	1.08869i
$784$		0			0
$785$	10.9534	−	51.8535i	0.390945	−	1.85073i
$786$		0			0
$787$	−22.2301	+	39.6507i	−0.792418	+	1.41340i	0.115087	+	0.993355i	$0.463285\pi$
$787$	−22.2301	+	39.6507i	−0.792418	+	1.41340i	−0.907505	+	0.420040i	$0.862016\pi$
$788$		0			0
$789$	−3.80691	−	15.1600i	−0.135530	−	0.539710i
$790$		0			0
$791$	5.17555	+	7.78556i	0.184021	+	0.276823i
$792$		0			0
$793$	12.2516	+	36.7574i	0.435067	+	1.30529i
$794$		0			0
$795$	−6.08006	−	0.693383i	−0.215638	−	0.0245918i
$796$		0			0
$797$	−13.2176	+	0.500531i	−0.468190	+	0.0177297i	−0.270884	−	0.962612i	$-0.587316\pi$
$797$	−13.2176	+	0.500531i	−0.468190	+	0.0177297i	−0.197307	+	0.980342i	$0.563219\pi$
$798$		0			0
$799$	−2.82739	+	49.7457i	−0.100026	+	1.75988i
$800$		0			0
$801$	−3.08860	−	5.05086i	−0.109130	−	0.178463i
$802$		0			0
$803$	−0.663013	+	35.0290i	−0.0233972	+	1.23615i
$804$		0			0
$805$	−19.8753	+	7.04527i	−0.700512	+	0.248313i
$806$		0			0
$807$	12.3796	+	11.6960i	0.435782	+	0.411717i
$808$		0			0
$809$	−13.1635	+	2.00835i	−0.462803	+	0.0706097i	−0.378036	−	0.925791i	$-0.623400\pi$
$809$	−13.1635	+	2.00835i	−0.462803	+	0.0706097i	−0.0847677	+	0.996401i	$0.527015\pi$
$810$		0			0
$811$	−0.168324	−	0.361965i	−0.00591065	−	0.0127103i	0.903774	−	0.428010i	$-0.140785\pi$
$811$	−0.168324	−	0.361965i	−0.00591065	−	0.0127103i	−0.909685	+	0.415300i	$0.863677\pi$
$812$		0			0
$813$	−2.80430	−	0.106195i	−0.0983512	−	0.00372442i
$814$		0			0
$815$	43.9572	−	48.3267i	1.53975	−	1.69281i
$816$		0			0
$817$	16.6343	+	13.4876i	0.581960	+	0.471870i
$818$		0			0
$819$	−3.29123	−	2.46821i	−0.115005	−	0.0862461i
$820$		0			0
$821$	−39.6780	+	7.60013i	−1.38477	+	0.265246i	−0.825811	−	0.563947i	$-0.809282\pi$
$821$	−39.6780	+	7.60013i	−1.38477	+	0.265246i	−0.558962	+	0.829193i	$0.688800\pi$
$822$		0			0
$823$	12.2437	+	2.34522i	0.426790	+	0.0817494i	0.397025	−	0.917808i	$-0.370042\pi$
$823$	12.2437	+	2.34522i	0.426790	+	0.0817494i	0.0297641	+	0.999557i	$0.490524\pi$
$824$		0			0
$825$	19.2952	+	91.3432i	0.671772	+	3.18016i
$826$		0			0
$827$	−47.2231	+	14.7530i	−1.64211	+	0.513014i	−0.973128	−	0.230266i	$-0.926041\pi$
$827$	−47.2231	+	14.7530i	−1.64211	+	0.513014i	−0.668981	+	0.743279i	$0.733269\pi$
$828$		0			0
$829$	−16.5068	+	15.5952i	−0.573304	+	0.541645i	−0.917748	−	0.397162i	$-0.869995\pi$
$829$	−16.5068	+	15.5952i	−0.573304	+	0.541645i	0.344444	+	0.938807i	$0.388067\pi$
$830$		0			0
$831$	6.90269	−	20.7095i	0.239452	−	0.718406i
$832$		0			0
$833$	24.0625	+	33.3842i	0.833717	+	1.15670i
$834$		0			0
$835$	43.8779	−	35.2841i	1.51846	−	1.22106i
$836$		0			0
$837$	19.1741	+	26.6021i	0.662755	+	0.919502i
$838$		0			0
$839$	15.5398	−	46.6227i	0.536494	−	1.60960i	−0.234061	−	0.972222i	$-0.575201\pi$
$839$	15.5398	−	46.6227i	0.536494	−	1.60960i	0.770555	−	0.637374i	$-0.219979\pi$
$840$		0			0
$841$	20.8535	−	19.7019i	0.719087	−	0.679377i
$842$		0			0
$843$	21.9619	−	6.86116i	0.756409	−	0.236311i
$844$		0			0
$845$	−5.98711	−	28.3429i	−0.205963	−	0.975026i
$846$		0			0
$847$	18.5993	+	3.56261i	0.639080	+	0.122413i
$848$		0			0
$849$	−1.32331	+	0.253473i	−0.0454159	+	0.00869918i
$850$		0			0
$851$	9.75731	+	7.31733i	0.334476	+	0.250835i
$852$		0			0
$853$	26.0184	+	21.0964i	0.890852	+	0.722328i	0.961393	−	0.275180i	$-0.0887376\pi$
$853$	26.0184	+	21.0964i	0.890852	+	0.722328i	−0.0705409	+	0.997509i	$0.522473\pi$
$854$		0			0
$855$	6.04750	−	6.64865i	0.206820	−	0.227379i
$856$		0			0
$857$	15.4795	+	0.586188i	0.528770	+	0.0200238i	0.300878	−	0.953663i	$-0.402720\pi$
$857$	15.4795	+	0.586188i	0.528770	+	0.0200238i	0.227892	+	0.973686i	$0.426817\pi$
$858$		0			0
$859$	14.4928	+	31.1653i	0.494487	+	1.06335i	0.981765	+	0.190100i	$0.0608814\pi$
$859$	14.4928	+	31.1653i	0.494487	+	1.06335i	−0.487278	+	0.873247i	$0.662010\pi$
$860$		0			0
$861$	0.365903	−	0.0558257i	0.0124699	−	0.00190253i
$862$		0			0
$863$	−11.2339	−	10.6136i	−0.382408	−	0.361290i	0.471363	−	0.881939i	$-0.343762\pi$
$863$	−11.2339	−	10.6136i	−0.382408	−	0.361290i	−0.853771	+	0.520649i	$0.825690\pi$
$864$		0			0
$865$	33.6781	−	11.9380i	1.14509	−	0.405904i
$866$		0			0
$867$	−1.06837	+	56.4452i	−0.0362837	+	1.91698i
$868$		0			0
$869$	−8.10944	−	13.2616i	−0.275094	−	0.449867i
$870$		0			0
$871$	1.57039	−	27.6299i	0.0532108	−	0.936202i
$872$		0			0
$873$	−16.4392	+	0.622528i	−0.556381	+	0.0210694i
$874$		0			0
$875$	50.3809	+	5.74555i	1.70319	+	0.194235i
$876$		0			0
$877$	−12.3342	−	37.0053i	−0.416497	−	1.24958i	−0.922146	−	0.386841i	$-0.873566\pi$
$877$	−12.3342	−	37.0053i	−0.416497	−	1.24958i	0.505649	−	0.862739i	$-0.331253\pi$
$878$		0			0
$879$	14.7223	+	22.1467i	0.496571	+	0.746991i
$880$		0			0
$881$	0.321379	+	1.27980i	0.0108275	+	0.0431177i	0.975062	−	0.221935i	$-0.0712372\pi$
$881$	0.321379	+	1.27980i	0.0108275	+	0.0431177i	−0.964234	+	0.265053i	$0.914611\pi$
$882$		0			0
$883$	11.5793	−	20.6533i	0.389673	−	0.695040i	−0.605211	−	0.796065i	$-0.706911\pi$
$883$	11.5793	−	20.6533i	0.389673	−	0.695040i	0.994884	+	0.101025i	$0.0322123\pi$
$884$		0			0
$885$	−2.75144	+	13.0253i	−0.0924887	+	0.437841i
$886$		0			0
$887$	−15.8477	−	16.1505i	−0.532114	−	0.542281i	0.394204	−	0.919023i	$-0.371020\pi$
$887$	−15.8477	−	16.1505i	−0.532114	−	0.542281i	−0.926318	+	0.376742i	$0.877044\pi$
$888$		0			0
$889$	9.00994	−	14.7342i	0.302184	−	0.494168i
$890$		0			0
$891$	−2.42834	+	18.2229i	−0.0813524	+	0.610491i
$892$		0			0
$893$	−8.89334	−	5.67226i	−0.297604	−	0.189815i
$894$		0			0
$895$	75.6757	+	52.3980i	2.52956	+	1.75147i
$896$		0			0
$897$	9.34361	+	8.18110i	0.311974	+	0.273159i
$898$		0			0
$899$	36.4405	−	25.2315i	1.21536	−	0.841516i
$900$		0			0
$901$	−0.777977	−	8.19702i	−0.0259182	−	0.273082i
$902$		0			0
$903$	−8.65225	+	20.6120i	−0.287929	+	0.685924i
$904$		0			0
$905$	32.9831	+	7.62206i	1.09640	+	0.253366i
$906$		0			0
$907$	−26.8170	+	17.1042i	−0.890445	+	0.567934i	−0.901873	−	0.432001i	$-0.857808\pi$
$907$	−26.8170	+	17.1042i	−0.890445	+	0.567934i	0.0114288	+	0.999935i	$0.496362\pi$
$908$		0			0
$909$	−2.74929	−	7.31344i	−0.0911883	−	0.242572i
$910$		0			0
$911$	−12.8062	−	16.4197i	−0.424290	−	0.544008i	0.527984	−	0.849254i	$-0.322948\pi$
$911$	−12.8062	−	16.4197i	−0.424290	−	0.544008i	−0.952274	+	0.305246i	$0.901261\pi$
$912$		0			0
$913$	−3.62181	−	12.4137i	−0.119865	−	0.410835i
$914$		0			0
$915$	−43.2101	−	77.0717i	−1.42848	−	2.54791i
$916$		0			0
$917$	−6.19414	−	3.32026i	−0.204548	−	0.109645i
$918$		0			0
$919$	22.0262	−	30.5590i	0.726576	−	1.00805i	−0.272372	−	0.962192i	$-0.587808\pi$
$919$	22.0262	−	30.5590i	0.726576	−	1.00805i	0.998948	−	0.0458559i	$-0.0146015\pi$
$920$		0			0
$921$	−31.6653	+	18.5493i	−1.04341	+	0.611220i
$922$		0			0
$923$	−6.85130	+	18.2253i	−0.225513	+	0.599892i
$924$		0			0
$925$	−20.8022	−	40.6363i	−0.683972	−	1.33611i
$926$		0			0
$927$	3.62064	−	4.29653i	0.118918	−	0.141117i
$928$		0			0
$929$	−29.6131	+	22.2079i	−0.971574	+	0.728616i	−0.962483	−	0.271342i	$-0.912532\pi$
$929$	−29.6131	+	22.2079i	−0.971574	+	0.728616i	−0.00909135	+	0.999959i	$0.502894\pi$
$930$		0			0
$931$	−8.65592	+	0.987140i	−0.283686	+	0.0323522i
$932$		0			0
$933$	−1.23865	+	4.93260i	−0.0405516	+	0.161486i
$934$		0			0
$935$	−155.963	+	68.9683i	−5.10054	+	2.25550i
$936$		0			0
$937$	27.3415	−	22.1693i	0.893208	−	0.724239i	−0.0686928	−	0.997638i	$-0.521883\pi$
$937$	27.3415	−	22.1693i	0.893208	−	0.724239i	0.961901	+	0.273399i	$0.0881479\pi$
$938$		0			0
$939$	−4.18736	+	24.3460i	−0.136649	+	0.794502i
$940$		0			0
$941$	−11.8816	+	12.1086i	−0.387328	+	0.394728i	−0.879601	−	0.475713i	$-0.842190\pi$
$941$	−11.8816	+	12.1086i	−0.387328	+	0.394728i	0.492273	+	0.870441i	$0.336166\pi$
$942$		0			0
$943$	0.806853	−	0.0611966i	0.0262748	−	0.00199283i
$944$		0			0
$945$	28.5025	+	13.9164i	0.927185	+	0.452701i
$946$		0			0
$947$	6.70763	−	3.59551i	0.217969	−	0.116838i	−0.359829	−	0.933018i	$-0.617165\pi$
$947$	6.70763	−	3.59551i	0.217969	−	0.116838i	0.577798	+	0.816180i	$0.303912\pi$
$948$		0			0
$949$	−2.95698	−	17.1924i	−0.0959878	−	0.558089i
$950$		0			0
$951$	0.496248	+	8.73109i	0.0160919	+	0.283125i
$952$		0			0
$953$	−5.79642	−	6.87848i	−0.187765	−	0.222816i	0.662650	−	0.748929i	$-0.269432\pi$
$953$	−5.79642	−	6.87848i	−0.187765	−	0.222816i	−0.850414	+	0.526114i	$0.823649\pi$
$954$		0			0
$955$	−0.955626	−	50.4887i	−0.0309233	−	1.63378i
$956$		0			0
$957$	50.1290	+	7.64816i	1.62044	+	0.247230i
$958$		0			0
$959$	−1.59005	+	16.7533i	−0.0513455	+	0.540993i
$960$		0			0
$961$	2.74448	−	1.34000i	0.0885317	−	0.0432259i
$962$		0			0
$963$	18.4506	+	6.54025i	0.594562	+	0.210757i
$964$		0			0
$965$	−41.6005	−	11.2876i	−1.33917	−	0.363360i
$966$		0			0
$967$	19.1205	−	16.7415i	0.614873	−	0.538372i	−0.293808	−	0.955865i	$-0.594922\pi$
$967$	19.1205	−	16.7415i	0.614873	−	0.538372i	0.908680	+	0.417493i	$0.137091\pi$
$968$		0			0
$969$	−14.4088	−	8.44055i	−0.462877	−	0.271150i
$970$		0			0
$971$	−36.9189	+	8.53158i	−1.18478	+	0.273791i	−0.771151	−	0.636652i	$-0.780319\pi$
$971$	−36.9189	+	8.53158i	−1.18478	+	0.273791i	−0.413633	+	0.910444i	$0.635740\pi$
$972$		0			0
$973$	−3.37454	+	1.34199i	−0.108183	+	0.0430222i
$974$		0			0
$975$	−17.9922	−	42.8623i	−0.576211	−	1.37269i
$976$		0			0
$977$	27.8380	+	30.6052i	0.890617	+	0.979148i	0.999890	−	0.0148643i	$-0.00473161\pi$
$977$	27.8380	+	30.6052i	0.890617	+	0.979148i	−0.109272	+	0.994012i	$0.534852\pi$
$978$		0			0
$979$	−22.0980	−	8.78794i	−0.706255	−	0.280864i
$980$		0			0
$981$	15.4296	+	4.82038i	0.492629	+	0.153903i
$982$		0			0
$983$	−11.6765	+	17.5649i	−0.372421	+	0.560232i	−0.970468	−	0.241229i	$-0.922450\pi$
$983$	−11.6765	+	17.5649i	−0.372421	+	0.560232i	0.598047	+	0.801461i	$0.295944\pi$
$984$		0			0
$985$	26.2410	+	1.99027i	0.836106	+	0.0634153i
$986$		0			0
$987$	3.08392	−	10.5701i	0.0981623	−	0.336451i
$988$		0			0
$989$	−22.2687	+	43.5011i	−0.708104	+	1.38325i
$990$		0			0
$991$	−30.4633	+	39.0590i	−0.967700	+	1.24075i	0.00288620	+	0.999996i	$0.499081\pi$
$991$	−30.4633	+	39.0590i	−0.967700	+	1.24075i	−0.970586	+	0.240754i	$0.922605\pi$
$992$		0			0
$993$	0.153996	−	0.0417842i	0.00488692	−	0.00132598i
$994$		0			0
$995$	21.2872	−	45.7762i	0.674851	−	1.45120i
$996$		0			0
$997$	28.6067	+	12.6501i	0.905983	+	0.400633i	0.804328	−	0.594186i	$-0.202526\pi$
$997$	28.6067	+	12.6501i	0.905983	+	0.400633i	0.101656	+	0.994820i	$0.467586\pi$
$998$		0			0
$999$	−2.42321	−	18.1844i	−0.0766669	−	0.575330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.9	✓	1148
167.130	even	83	inner	668.2.e.a.297.9	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.9	✓	1148	1.1	even	1	trivial
668.2.e.a.297.9	yes	1148	167.130	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(0.174236 + 1.30752i) q^{3} +(-3.98478 - 1.76210i) q^{5} +(-0.546271 + 1.17470i) q^{7} +(1.21607 - 0.329959i) q^{9} +O(q^{10})\)	\(q+(0.174236 + 1.30752i) q^{3} +(-3.98478 - 1.76210i) q^{5} +(-0.546271 + 1.17470i) q^{7} +(1.21607 - 0.329959i) q^{9} +(3.11275 - 3.99106i) q^{11} +(-1.14839 + 2.24333i) q^{13} +(1.60969 - 5.51720i) q^{15} +(7.71084 + 0.584836i) q^{17} +(-0.906296 + 1.36334i) q^{19} +(-1.63113 - 0.509583i) q^{21} +(-3.47141 - 1.38051i) q^{23} +(9.40909 + 10.3444i) q^{25} +(2.17496 + 5.18134i) q^{27} +(7.05769 - 2.80671i) q^{29} +(5.68575 - 1.31392i) q^{31} +(5.76074 + 3.37460i) q^{33} +(4.24672 - 3.71835i) q^{35} +(-3.15074 - 0.854899i) q^{37} +(-3.13328 - 1.11067i) q^{39} +(-0.194636 + 0.0950317i) q^{41} +(1.23599 - 13.0228i) q^{43} +(-5.42718 - 0.828023i) q^{45} +(0.121934 + 6.44215i) q^{47} +(3.42926 + 4.06942i) q^{49} +(0.578825 + 10.1840i) q^{51} +(-0.180484 - 1.04936i) q^{53} +(-19.4363 + 10.4185i) q^{55} +(-1.94050 - 0.947455i) q^{57} +(-2.30974 + 0.175185i) q^{59} +(10.7678 - 10.9735i) q^{61} +(-0.276698 + 1.60877i) q^{63} +(8.52904 - 6.91559i) q^{65} +(-10.0430 + 4.44111i) q^{67} +(1.20020 - 4.77946i) q^{69} +(7.67608 - 0.875397i) q^{71} +(-5.53782 + 4.15300i) q^{73} +(-11.8861 + 14.1049i) q^{75} +(2.98791 + 5.83676i) q^{77} +(1.08069 - 2.87477i) q^{79} +(-3.13406 + 1.83591i) q^{81} +(1.49389 - 2.07261i) q^{83} +(-29.6955 - 15.9177i) q^{85} +(4.89953 + 8.73903i) q^{87} +(-1.31598 - 4.51051i) q^{89} +(-2.00792 - 2.57448i) q^{91} +(2.70864 + 7.20529i) q^{93} +(6.01373 - 3.83561i) q^{95} +(-12.7207 - 2.93962i) q^{97} +(2.46843 - 5.88047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more