LMFDB - Embedded newform 833.2.l.b.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(246,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("833.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			491.1
Character	$\chi$	$=$	833.491
Dual form			833.2.l.b.246.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61504 - 1.61504i) q^{2} +(-0.678714 - 1.63856i) q^{3} +3.21670i q^{4} +(1.74157 - 0.721382i) q^{5} +(-1.55019 + 3.74249i) q^{6} +(1.96501 - 1.96501i) q^{8} +(-0.102907 + 0.102907i) q^{9} +O(q^{10})$	\(q+(-1.61504 - 1.61504i) q^{2} +(-0.678714 - 1.63856i) q^{3} +3.21670i q^{4} +(1.74157 - 0.721382i) q^{5} +(-1.55019 + 3.74249i) q^{6} +(1.96501 - 1.96501i) q^{8} +(-0.102907 + 0.102907i) q^{9} +(-3.97776 - 1.64764i) q^{10} +(0.942148 - 2.27455i) q^{11} +(5.27075 - 2.18322i) q^{12} +3.98367i q^{13} +(-2.36406 - 2.36406i) q^{15} +0.0862625 q^{16} +(3.87974 - 1.39558i) q^{17} +0.332399 q^{18} +(-3.97083 - 3.97083i) q^{19} +(2.32047 + 5.60210i) q^{20} +(-5.19508 + 2.15187i) q^{22} +(2.23264 - 5.39006i) q^{23} +(-4.55346 - 1.88611i) q^{24} +(-1.02286 + 1.02286i) q^{25} +(6.43378 - 6.43378i) q^{26} +(-4.67722 - 1.93737i) q^{27} +(-0.946086 + 0.391882i) q^{29} +7.63608i q^{30} +(-0.859202 - 2.07430i) q^{31} +(-4.06934 - 4.06934i) q^{32} -4.36643 q^{33} +(-8.51984 - 4.01200i) q^{34} +(-0.331022 - 0.331022i) q^{36} +(-0.0997033 - 0.240705i) q^{37} +12.8261i q^{38} +(6.52748 - 2.70377i) q^{39} +(2.00468 - 4.83972i) q^{40} +(-6.97038 - 2.88722i) q^{41} +(6.88208 - 6.88208i) q^{43} +(7.31652 + 3.03060i) q^{44} +(-0.104985 + 0.253456i) q^{45} +(-12.3109 + 5.09936i) q^{46} -8.05197i q^{47} +(-0.0585476 - 0.141346i) q^{48} +3.30392 q^{50} +(-4.91998 - 5.40998i) q^{51} -12.8143 q^{52} +(1.54243 + 1.54243i) q^{53} +(4.42496 + 10.6828i) q^{54} -4.64093i q^{55} +(-3.81138 + 9.20149i) q^{57} +(2.16087 + 0.895061i) q^{58} +(-5.29521 + 5.29521i) q^{59} +(7.60445 - 7.60445i) q^{60} +(-13.0633 - 5.41099i) q^{61} +(-1.96242 + 4.73771i) q^{62} +12.9717i q^{64} +(2.87375 + 6.93784i) q^{65} +(7.05195 + 7.05195i) q^{66} +13.6463 q^{67} +(4.48917 + 12.4799i) q^{68} -10.3473 q^{69} +(4.40277 + 10.6292i) q^{71} +0.404428i q^{72} +(-3.47743 + 1.44040i) q^{73} +(-0.227723 + 0.549773i) q^{74} +(2.37025 + 0.981789i) q^{75} +(12.7729 - 12.7729i) q^{76} +(-14.9088 - 6.17544i) q^{78} +(-1.15715 + 2.79362i) q^{79} +(0.150232 - 0.0622282i) q^{80} +9.41542i q^{81} +(6.59444 + 15.9204i) q^{82} +(8.14920 + 8.14920i) q^{83} +(5.75008 - 5.22928i) q^{85} -22.2296 q^{86} +(1.28424 + 1.28424i) q^{87} +(-2.61818 - 6.32083i) q^{88} +8.47176i q^{89} +(0.578896 - 0.239786i) q^{90} +(17.3382 + 7.18171i) q^{92} +(-2.81571 + 2.81571i) q^{93} +(-13.0042 + 13.0042i) q^{94} +(-9.77995 - 4.05099i) q^{95} +(-3.90594 + 9.42977i) q^{96} +(2.92175 - 1.21023i) q^{97} +(0.137114 + 0.331022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 24 q^{9}+O(q^{10}) $ 32 * q + 24 * q^9	$ 32 q + 24 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 24 q^{18} + 8 q^{23} + 8 q^{25} - 16 q^{29} - 40 q^{32} - 8 q^{36} - 8 q^{37} + 8 q^{39} - 24 q^{43} + 64 q^{44} - 80 q^{46} + 16 q^{50} + 8 q^{51} + 32 q^{53} - 8 q^{57} - 104 q^{58} + 152 q^{60} - 64 q^{65} + 96 q^{67} - 48 q^{71} - 24 q^{74} - 136 q^{78} - 80 q^{79} + 72 q^{85} - 72 q^{86} + 56 q^{88} + 8 q^{92} - 48 q^{93} - 32 q^{95} + 8 q^{99}+O(q^{100}) $ 32 * q + 24 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 24 * q^18 + 8 * q^23 + 8 * q^25 - 16 * q^29 - 40 * q^32 - 8 * q^36 - 8 * q^37 + 8 * q^39 - 24 * q^43 + 64 * q^44 - 80 * q^46 + 16 * q^50 + 8 * q^51 + 32 * q^53 - 8 * q^57 - 104 * q^58 + 152 * q^60 - 64 * q^65 + 96 * q^67 - 48 * q^71 - 24 * q^74 - 136 * q^78 - 80 * q^79 + 72 * q^85 - 72 * q^86 + 56 * q^88 + 8 * q^92 - 48 * q^93 - 32 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−1.61504	−	1.61504i	−1.14200	−	1.14200i	−0.988083	−	0.153921i	$-0.950810\pi$
$2$	−1.61504	−	1.61504i	−1.14200	−	1.14200i	−0.153921	−	0.988083i	$-0.549190\pi$
$3$	−0.678714	−	1.63856i	−0.391856	−	0.946023i	−0.989536	−	0.144289i	$-0.953911\pi$
$3$	−0.678714	−	1.63856i	−0.391856	−	0.946023i	0.597680	−	0.801735i	$-0.296089\pi$
$4$			3.21670i			1.60835i
$5$	1.74157	−	0.721382i	0.778854	−	0.322612i	0.0424008	−	0.999101i	$-0.486499\pi$
$5$	1.74157	−	0.721382i	0.778854	−	0.322612i	0.736453	+	0.676489i	$0.236499\pi$
$6$	−1.55019	+	3.74249i	−0.632862	+	1.52786i
$7$		0			0
$7$		0			0
$8$	1.96501	−	1.96501i	0.694736	−	0.694736i
$9$	−0.102907	+	0.102907i	−0.0343025	+	0.0343025i
$10$	−3.97776	−	1.64764i	−1.25788	−	0.521030i
$11$	0.942148	−	2.27455i	0.284068	−	0.685802i	−0.715854	−	0.698250i	$-0.753962\pi$
$11$	0.942148	−	2.27455i	0.284068	−	0.685802i	0.999923	+	0.0124481i	$0.00396246\pi$
$12$	5.27075	−	2.18322i	1.52153	−	0.630240i
$13$			3.98367i			1.10487i	0.833556	+	0.552436i	$0.186301\pi$
$13$			3.98367i			1.10487i	−0.833556	+	0.552436i	$0.813699\pi$
$14$		0			0
$15$	−2.36406	−	2.36406i	−0.610396	−	0.610396i
$16$	0.0862625			0.0215656
$17$	3.87974	−	1.39558i	0.940974	−	0.338479i
$17$	3.87974	−	1.39558i	0.940974	−	0.338479i
$18$	0.332399			0.0783471
$19$	−3.97083	−	3.97083i	−0.910970	−	0.910970i	0.0853786	−	0.996349i	$-0.472790\pi$
$19$	−3.97083	−	3.97083i	−0.910970	−	0.910970i	−0.996349	+	0.0853786i	$0.972790\pi$
$20$	2.32047	+	5.60210i	0.518872	+	1.25267i
$21$		0			0
$22$	−5.19508	+	2.15187i	−1.10760	+	0.458781i
$23$	2.23264	−	5.39006i	0.465537	−	1.12391i	−0.500555	−	0.865705i	$-0.666871\pi$
$23$	2.23264	−	5.39006i	0.465537	−	1.12391i	0.966091	−	0.258200i	$-0.0831295\pi$
$24$	−4.55346	−	1.88611i	−0.929472	−	0.385000i
$25$	−1.02286	+	1.02286i	−0.204572	+	0.204572i
$26$	6.43378	−	6.43378i	1.26177	−	1.26177i
$27$	−4.67722	−	1.93737i	−0.900131	−	0.372846i
$28$		0			0
$29$	−0.946086	+	0.391882i	−0.175684	+	0.0727706i	−0.468792	−	0.883309i	$-0.655310\pi$
$29$	−0.946086	+	0.391882i	−0.175684	+	0.0727706i	0.293108	+	0.956079i	$0.405310\pi$
$30$			7.63608i			1.39415i
$31$	−0.859202	−	2.07430i	−0.154317	−	0.372555i	0.827747	−	0.561102i	$-0.189622\pi$
$31$	−0.859202	−	2.07430i	−0.154317	−	0.372555i	−0.982064	+	0.188547i	$0.939622\pi$
$32$	−4.06934	−	4.06934i	−0.719364	−	0.719364i
$33$	−4.36643			−0.760098
$34$	−8.51984	−	4.01200i	−1.46114	−	0.688052i
$35$		0			0
$36$	−0.331022	−	0.331022i	−0.0551703	−	0.0551703i
$37$	−0.0997033	−	0.240705i	−0.0163911	−	0.0395717i	0.915472	−	0.402382i	$-0.131817\pi$
$37$	−0.0997033	−	0.240705i	−0.0163911	−	0.0395717i	−0.931863	+	0.362810i	$0.881817\pi$
$38$			12.8261i			2.08066i
$39$	6.52748	−	2.70377i	1.04523	−	0.432950i
$40$	2.00468	−	4.83972i	0.316967	−	0.765227i
$41$	−6.97038	−	2.88722i	−1.08859	−	0.450909i	−0.235075	−	0.971977i	$-0.575534\pi$
$41$	−6.97038	−	2.88722i	−1.08859	−	0.450909i	−0.853515	+	0.521069i	$0.825534\pi$
$42$		0			0
$43$	6.88208	−	6.88208i	1.04951	−	1.04951i	0.0507980	−	0.998709i	$-0.483824\pi$
$43$	6.88208	−	6.88208i	1.04951	−	1.04951i	0.998709	−	0.0507980i	$-0.0161765\pi$
$44$	7.31652	+	3.03060i	1.10301	+	0.456881i
$45$	−0.104985	+	0.253456i	−0.0156502	+	0.0377830i
$46$	−12.3109	+	5.09936i	−1.81515	+	0.751860i
$47$		−	8.05197i		−	1.17450i	−0.809406	−	0.587250i	$-0.800211\pi$
$47$		−	8.05197i		−	1.17450i	0.809406	−	0.587250i	$-0.199789\pi$
$48$	−0.0585476	−	0.141346i	−0.00845062	−	0.0204016i
$49$		0			0
$50$	3.30392			0.467245
$51$	−4.91998	−	5.40998i	−0.688935	−	0.757549i
$52$	−12.8143			−1.77702
$53$	1.54243	+	1.54243i	0.211869	+	0.211869i	0.805061	−	0.593192i	$-0.202133\pi$
$53$	1.54243	+	1.54243i	0.211869	+	0.211869i	−0.593192	+	0.805061i	$0.702133\pi$
$54$	4.42496	+	10.6828i	0.602161	+	1.45375i
$55$		−	4.64093i		−	0.625783i
$56$		0			0
$57$	−3.81138	+	9.20149i	−0.504830	+	1.21877i
$58$	2.16087	+	0.895061i	0.283736	+	0.117527i
$59$	−5.29521	+	5.29521i	−0.689378	+	0.689378i	−0.962094	−	0.272717i	$-0.912078\pi$
$59$	−5.29521	+	5.29521i	−0.689378	+	0.689378i	0.272717	+	0.962094i	$0.412078\pi$
$60$	7.60445	−	7.60445i	0.981730	−	0.981730i
$61$	−13.0633	−	5.41099i	−1.67258	−	0.692807i	−0.673653	−	0.739048i	$-0.735276\pi$
$61$	−13.0633	−	5.41099i	−1.67258	−	0.692807i	−0.998930	+	0.0462413i	$0.985276\pi$
$62$	−1.96242	+	4.73771i	−0.249228	+	0.601690i
$63$		0			0
$64$			12.9717i			1.62147i
$65$	2.87375	+	6.93784i	0.356444	+	0.860533i
$66$	7.05195	+	7.05195i	0.868035	+	0.868035i
$67$	13.6463			1.66716			0.833582	−	0.552396i	$-0.186286\pi$
$67$	13.6463			1.66716			0.833582	+	0.552396i	$0.186286\pi$
$68$	4.48917	+	12.4799i	0.544391	+	1.51341i
$69$	−10.3473			−1.24566
$70$		0			0
$71$	4.40277	+	10.6292i	0.522512	+	1.26146i	0.936338	+	0.351100i	$0.114192\pi$
$71$	4.40277	+	10.6292i	0.522512	+	1.26146i	−0.413825	+	0.910356i	$0.635808\pi$
$72$			0.404428i			0.0476623i
$73$	−3.47743	+	1.44040i	−0.407002	+	0.168586i	−0.576786	−	0.816895i	$-0.695693\pi$
$73$	−3.47743	+	1.44040i	−0.407002	+	0.168586i	0.169783	+	0.985481i	$0.445693\pi$
$74$	−0.227723	+	0.549773i	−0.0264723	+	0.0639098i
$75$	2.37025	+	0.981789i	0.273693	+	0.113367i
$76$	12.7729	−	12.7729i	1.46516	−	1.46516i
$77$		0			0
$78$	−14.9088	−	6.17544i	−1.68809	−	0.699231i
$79$	−1.15715	+	2.79362i	−0.130190	+	0.314306i	−0.975510	−	0.219953i	$-0.929410\pi$
$79$	−1.15715	+	2.79362i	−0.130190	+	0.314306i	0.845320	+	0.534260i	$0.179410\pi$
$80$	0.150232	−	0.0622282i	0.0167965	−	0.00695733i
$81$			9.41542i			1.04616i
$82$	6.59444	+	15.9204i	0.728235	+	1.75811i
$83$	8.14920	+	8.14920i	0.894490	+	0.894490i	0.994942	−	0.100452i	$-0.0320287\pi$
$83$	8.14920	+	8.14920i	0.894490	+	0.894490i	−0.100452	+	0.994942i	$0.532029\pi$
$84$		0			0
$85$	5.75008	−	5.22928i	0.623684	−	0.567195i
$86$	−22.2296			−2.39708
$87$	1.28424	+	1.28424i	0.137685	+	0.137685i
$88$	−2.61818	−	6.32083i	−0.279098	−	0.673803i
$89$			8.47176i			0.898005i	0.893530	+	0.449003i	$0.148221\pi$
$89$			8.47176i			0.898005i	−0.893530	+	0.449003i	$0.851779\pi$
$90$	0.578896	−	0.239786i	0.0610210	−	0.0252757i
$91$		0			0
$92$	17.3382	+	7.18171i	1.80763	+	0.748745i
$93$	−2.81571	+	2.81571i	−0.291975	+	0.291975i
$94$	−13.0042	+	13.0042i	−1.34128	+	1.34128i
$95$	−9.77995	−	4.05099i	−1.00340	−	0.415623i
$96$	−3.90594	+	9.42977i	−0.398648	+	0.962421i
$97$	2.92175	−	1.21023i	0.296659	−	0.122880i	−0.229390	−	0.973335i	$-0.573673\pi$
$97$	2.92175	−	1.21023i	0.296659	−	0.122880i	0.526049	+	0.850454i	$0.323673\pi$
$98$		0			0
$99$	0.137114	+	0.331022i	0.0137804	+	0.0332689i
$100$	−3.29023	−	3.29023i	−0.329023	−	0.329023i
$101$	13.3170			1.32509			0.662543	−	0.749024i	$-0.269477\pi$
$101$	13.3170			1.32509			0.662543	+	0.749024i	$0.269477\pi$
$102$	−0.791371	+	16.6833i	−0.0783574	+	1.65189i
$103$	−11.6429			−1.14721			−0.573605	−	0.819132i	$-0.694455\pi$
$103$	−11.6429			−1.14721			−0.573605	+	0.819132i	$0.694455\pi$
$104$	7.82795	+	7.82795i	0.767593	+	0.767593i
$105$		0			0
$106$		−	4.98216i		−	0.483910i
$107$	−4.53845	+	1.87989i	−0.438748	+	0.181735i	−0.591113	−	0.806589i	$-0.701311\pi$
$107$	−4.53845	+	1.87989i	−0.438748	+	0.181735i	0.152365	+	0.988324i	$0.451311\pi$
$108$	6.23192	−	15.0452i	0.599667	−	1.44772i
$109$	−16.1195	−	6.67690i	−1.54396	−	0.639531i	−0.561752	−	0.827305i	$-0.689873\pi$
$109$	−16.1195	−	6.67690i	−1.54396	−	0.639531i	−0.982212	+	0.187774i	$0.939873\pi$
$110$	−7.49528	+	7.49528i	−0.714647	+	0.714647i
$111$	−0.326740	+	0.326740i	−0.0310128	+	0.0310128i
$112$		0			0
$113$	7.42051	−	17.9147i	0.698063	−	1.68527i	−0.0298046	−	0.999556i	$-0.509489\pi$
$113$	7.42051	−	17.9147i	0.698063	−	1.68527i	0.727868	−	0.685718i	$-0.240511\pi$
$114$	21.0163	−	8.70523i	1.96836	−	0.815320i
$115$		−	10.9977i		−	1.02555i
$116$	−1.26056	−	3.04327i	−0.117040	−	0.282560i
$117$	−0.409949	−	0.409949i	−0.0378998	−	0.0378998i
$118$	17.1039			1.57454
$119$		0			0
$120$	−9.29078			−0.848128
$121$	3.49225	+	3.49225i	0.317478	+	0.317478i
$122$	12.3588	+	29.8367i	1.11891	+	2.70129i
$123$			13.3810i			1.20652i
$124$	6.67238	−	2.76379i	0.599198	−	0.248196i
$125$	−4.65042	+	11.2271i	−0.415946	+	1.00418i
$126$		0			0
$127$	0.0196127	−	0.0196127i	0.00174035	−	0.00174035i	−0.706236	−	0.707976i	$-0.749608\pi$
$127$	0.0196127	−	0.0196127i	0.00174035	−	0.00174035i	0.707976	+	0.706236i	$0.249608\pi$
$128$	12.8112	−	12.8112i	1.13236	−	1.13236i
$129$	−15.9477	−	6.60574i	−1.40411	−	0.581603i
$130$	6.56366	−	15.8461i	0.575671	−	1.38979i
$131$	−0.870950	+	0.360759i	−0.0760952	+	0.0315197i	−0.420406	−	0.907336i	$-0.638112\pi$
$131$	−0.870950	+	0.360759i	−0.0760952	+	0.0315197i	0.344311	+	0.938856i	$0.388112\pi$
$132$		−	14.0455i		−	1.22250i
$133$		0			0
$134$	−22.0393	−	22.0393i	−1.90391	−	1.90391i
$135$	−9.54328			−0.821355
$136$	4.88138	−	10.3660i	0.418575	−	0.888881i
$137$	12.4714			1.06550			0.532752	−	0.846271i	$-0.321158\pi$
$137$	12.4714			1.06550			0.532752	+	0.846271i	$0.321158\pi$
$138$	16.7112	+	16.7112i	1.42255	+	1.42255i
$139$	−5.06257	−	12.2221i	−0.429401	−	1.03667i	−0.979478	−	0.201552i	$-0.935401\pi$
$139$	−5.06257	−	12.2221i	−0.429401	−	1.03667i	0.550076	−	0.835114i	$-0.314599\pi$
$140$		0			0
$141$	−13.1936	+	5.46498i	−1.11110	+	0.460235i
$142$	10.0560	−	24.2772i	0.843877	−	2.03730i
$143$	9.06104	+	3.75321i	0.757723	+	0.313859i
$144$	−0.00887705	+	0.00887705i	−0.000739755	+	0.000739755i
$145$	−1.36498	+	1.36498i	−0.113355	+	0.113355i
$146$	7.94248	+	3.28988i	0.657324	+	0.272273i
$147$		0			0
$148$	0.774275	−	0.320715i	0.0636450	−	0.0263626i
$149$			10.2194i			0.837205i	0.908170	+	0.418602i	$0.137480\pi$
$149$			10.2194i			0.837205i	−0.908170	+	0.418602i	$0.862520\pi$
$150$	−2.24242	−	5.41367i	−0.183092	−	0.442024i
$151$	−15.1405	−	15.1405i	−1.23212	−	1.23212i	−0.963149	−	0.268968i	$-0.913318\pi$
$151$	−15.1405	−	15.1405i	−1.23212	−	1.23212i	−0.268968	−	0.963149i	$-0.586682\pi$
$152$	−15.6054			−1.26577
$153$	−0.255638	+	0.542869i	−0.0206671	+	0.0438884i
$154$		0			0
$155$	−2.99272	−	2.99272i	−0.240381	−	0.240381i
$156$	8.69721	+	20.9969i	0.696334	+	1.68110i
$157$		−	8.48840i		−	0.677448i	−0.940886	−	0.338724i	$-0.890005\pi$
$157$		−	8.48840i		−	0.677448i	0.940886	−	0.338724i	$-0.109995\pi$
$158$	6.38064	−	2.64295i	0.507617	−	0.210262i
$159$	1.48049	−	3.57423i	0.117411	−	0.283455i
$160$	−10.0226	−	4.15149i	−0.792354	−	0.328204i
$161$		0			0
$162$	15.2063	−	15.2063i	1.19472	−	1.19472i
$163$	1.59290	+	0.659802i	0.124766	+	0.0516796i	0.444193	−	0.895931i	$-0.353490\pi$
$163$	1.59290	+	0.659802i	0.124766	+	0.0516796i	−0.319427	+	0.947611i	$0.603490\pi$
$164$	9.28732	−	22.4216i	0.725218	−	1.75083i
$165$	−7.60445	+	3.14986i	−0.592005	+	0.245217i
$166$		−	26.3225i		−	2.04302i
$167$	2.94038	+	7.09870i	0.227533	+	0.549314i	0.995876	−	0.0907249i	$-0.0289184\pi$
$167$	2.94038	+	7.09870i	0.227533	+	0.549314i	−0.768343	+	0.640039i	$0.778918\pi$
$168$		0			0
$169$	−2.86962			−0.220740
$170$	−17.7321	−	0.841121i	−1.35999	−	0.0645110i
$171$	0.817255			0.0624970
$172$	22.1375	+	22.1375i	1.68797	+	1.68797i
$173$	−4.30487	−	10.3929i	−0.327293	−	0.790155i	−0.998791	−	0.0491493i	$-0.984349\pi$
$173$	−4.30487	−	10.3929i	−0.327293	−	0.790155i	0.671498	−	0.741006i	$-0.265651\pi$
$174$		−	4.14820i		−	0.314474i
$175$		0			0
$176$	0.0812721	−	0.196208i	0.00612611	−	0.0147897i
$177$	12.2705	+	5.08259i	0.922304	+	0.382031i
$178$	13.6822	−	13.6822i	1.02553	−	1.02553i
$179$	4.53146	−	4.53146i	0.338698	−	0.338698i	−0.517179	−	0.855877i	$-0.673018\pi$
$179$	4.53146	−	4.53146i	0.338698	−	0.338698i	0.855877	+	0.517179i	$0.173018\pi$
$180$	−0.815291	−	0.337704i	−0.0607682	−	0.0251710i
$181$	4.34393	−	10.4872i	0.322882	−	0.779505i	−0.676202	−	0.736716i	$-0.736376\pi$
$181$	4.34393	−	10.4872i	0.322882	−	0.779505i	0.999084	−	0.0427894i	$-0.0136244\pi$
$182$		0			0
$183$			25.0775i			1.85378i
$184$	−6.20437	−	14.9787i	−0.457392	−	1.10424i
$185$	−0.347281	−	0.347281i	−0.0255326	−	0.0255326i
$186$	9.09495			0.666874
$187$	0.480966	−	10.1395i	0.0351717	−	0.741473i
$188$	25.9007			1.88900
$189$		0			0
$190$	9.25249	+	22.3375i	0.671246	+	1.62053i
$191$		−	9.43064i		−	0.682377i	−0.939995	−	0.341189i	$-0.889170\pi$
$191$		−	9.43064i		−	0.682377i	0.939995	−	0.341189i	$-0.110830\pi$
$192$	21.2550	−	8.80410i	1.53395	−	0.635381i
$193$	−5.51498	+	13.3143i	−0.396977	+	0.958387i	0.591402	+	0.806377i	$0.298575\pi$
$193$	−5.51498	+	13.3143i	−0.396977	+	0.958387i	−0.988379	+	0.152010i	$0.951425\pi$
$194$	−6.67331	−	2.76418i	−0.479116	−	0.198456i
$195$	9.41762	−	9.41762i	0.674409	−	0.674409i
$196$		0			0
$197$	−15.3090	−	6.34118i	−1.09072	−	0.451791i	−0.236462	−	0.971641i	$-0.575988\pi$
$197$	−15.3090	−	6.34118i	−1.09072	−	0.451791i	−0.854257	+	0.519850i	$0.825988\pi$
$198$	0.313169	−	0.756057i	0.0222559	−	0.0537306i
$199$	−16.3296	+	6.76393i	−1.15757	+	0.479482i	−0.877066	−	0.480369i	$-0.840503\pi$
$199$	−16.3296	+	6.76393i	−1.15757	+	0.479482i	−0.280507	+	0.959852i	$0.590503\pi$
$200$			4.01986i			0.284247i
$201$	−9.26195	−	22.3603i	−0.653288	−	1.57718i
$202$	−21.5074	−	21.5074i	−1.51325	−	1.51325i
$203$		0			0
$204$	17.4023	−	15.8261i	1.21840	−	1.10805i
$205$	−14.2222			−0.993321
$206$	18.8037	+	18.8037i	1.31012	+	1.31012i
$207$	0.324922	+	0.784432i	0.0225837	+	0.0545218i
$208$			0.343641i			0.0238272i
$209$	−12.7729	+	5.29072i	−0.883523	+	0.365967i
$210$		0			0
$211$	8.48319	+	3.51385i	0.584007	+	0.241904i	0.655070	−	0.755568i	$-0.272639\pi$
$211$	8.48319	+	3.51385i	0.584007	+	0.241904i	−0.0710631	+	0.997472i	$0.522639\pi$
$212$	−4.96152	+	4.96152i	−0.340759	+	0.340759i
$213$	14.4284	−	14.4284i	0.988618	−	0.988618i
$214$	10.3659	+	4.29368i	0.708595	+	0.293510i
$215$	7.02101	−	16.9502i	0.478829	−	1.15600i
$216$	−12.9977	+	5.38383i	−0.884382	+	0.366323i
$217$		0			0
$218$	15.2501	+	36.8170i	1.03287	+	2.49356i
$219$	4.72036	+	4.72036i	0.318972	+	0.318972i
$220$	14.9285			1.00648
$221$	5.55954	+	15.4556i	0.373975	+	1.03966i
$222$	1.05539			0.0708335
$223$	16.6584	+	16.6584i	1.11553	+	1.11553i	0.992389	+	0.123142i	$0.0392969\pi$
$223$	16.6584	+	16.6584i	1.11553	+	1.11553i	0.123142	+	0.992389i	$0.460703\pi$
$224$		0			0
$225$		−	0.210520i		−	0.0140347i
$226$	−40.9173	+	16.9485i	−2.72178	+	1.12740i
$227$	9.51265	−	22.9656i	0.631377	−	1.52428i	−0.206516	−	0.978443i	$-0.566213\pi$
$227$	9.51265	−	22.9656i	0.631377	−	1.52428i	0.837893	−	0.545835i	$-0.183787\pi$
$228$	−29.5984	−	12.2601i	−1.96020	−	0.811942i
$229$	−3.74433	+	3.74433i	−0.247432	+	0.247432i	−0.819916	−	0.572484i	$-0.805980\pi$
$229$	−3.74433	+	3.74433i	−0.247432	+	0.247432i	0.572484	+	0.819916i	$0.305980\pi$
$230$	−17.7618	+	17.7618i	−1.17118	+	1.17118i
$231$		0			0
$232$	−1.08902	+	2.62912i	−0.0714974	+	0.172610i
$233$	16.0137	−	6.63310i	1.04909	−	0.434549i	0.209526	−	0.977803i	$-0.432808\pi$
$233$	16.0137	−	6.63310i	1.04909	−	0.434549i	0.839568	+	0.543254i	$0.182808\pi$
$234$			1.32417i			0.0865635i
$235$	−5.80854	−	14.0231i	−0.378908	−	0.914764i
$236$	−17.0331	−	17.0331i	−1.10876	−	1.10876i
$237$	5.36288			0.348357
$238$		0			0
$239$	−4.73382			−0.306205			−0.153103	−	0.988210i	$-0.548926\pi$
$239$	−4.73382			−0.306205			−0.153103	+	0.988210i	$0.548926\pi$
$240$	−0.203929	−	0.203929i	−0.0131636	−	0.0131636i
$241$	−0.173022	−	0.417712i	−0.0111453	−	0.0269072i	0.918209	−	0.396096i	$-0.129635\pi$
$241$	−0.173022	−	0.417712i	−0.0111453	−	0.0269072i	−0.929354	+	0.369189i	$0.879635\pi$
$242$		−	11.2802i		−	0.725122i
$243$	1.39608	−	0.578277i	0.0895588	−	0.0370965i
$244$	17.4055	−	42.0206i	1.11427	−	2.69010i
$245$		0			0
$246$	21.6108	−	21.6108i	1.37785	−	1.37785i
$247$	15.8185	−	15.8185i	1.00650	−	1.00650i
$248$	−5.76435	−	2.38767i	−0.366037	−	0.151617i
$249$	7.82198	−	18.8839i	0.495698	−	1.19672i
$250$	25.6428	−	10.6216i	1.62179	−	0.671769i
$251$			2.42543i			0.153092i	0.997066	+	0.0765458i	$0.0243891\pi$
$251$			2.42543i			0.153092i	−0.997066	+	0.0765458i	$0.975611\pi$
$252$		0			0
$253$	−10.1565	−	10.1565i	−0.638532	−	0.638532i
$254$	−0.0633505			−0.00397496
$255$	−12.4711	−	5.87267i	−0.780973	−	0.367761i
$256$	−15.4376			−0.964850
$257$	−7.29692	−	7.29692i	−0.455169	−	0.455169i	0.441897	−	0.897066i	$-0.354306\pi$
$257$	−7.29692	−	7.29692i	−0.455169	−	0.455169i	−0.897066	+	0.441897i	$0.854306\pi$
$258$	15.0876	+	36.4246i	0.939311	+	2.26770i
$259$		0			0
$260$	−22.3169	+	9.24397i	−1.38404	+	0.573286i
$261$	0.0570317	−	0.137687i	0.00353017	−	0.00852260i
$262$	1.98926	+	0.823977i	0.122897	+	0.0509055i
$263$	−0.930424	+	0.930424i	−0.0573724	+	0.0573724i	−0.735211	−	0.677838i	$-0.762917\pi$
$263$	−0.930424	+	0.930424i	−0.0573724	+	0.0573724i	0.677838	+	0.735211i	$0.262917\pi$
$264$	−8.58008	+	8.58008i	−0.528067	+	0.528067i
$265$	3.79893	+	1.57357i	0.233366	+	0.0966634i
$266$		0			0
$267$	13.8815	−	5.74990i	0.849534	−	0.351888i
$268$			43.8961i			2.68138i
$269$	−0.971411	−	2.34519i	−0.0592280	−	0.142989i	0.891495	−	0.453030i	$-0.149657\pi$
$269$	−0.971411	−	2.34519i	−0.0592280	−	0.142989i	−0.950723	+	0.310041i	$0.899657\pi$
$270$	15.4128	+	15.4128i	0.937991	+	0.937991i
$271$	22.1108			1.34314			0.671569	−	0.740942i	$-0.265621\pi$
$271$	22.1108			1.34314			0.671569	+	0.740942i	$0.265621\pi$
$272$	0.334676	−	0.120387i	0.0202927	−	0.00729951i
$273$		0			0
$274$	−20.1418	−	20.1418i	−1.21681	−	1.21681i
$275$	1.36286	+	3.29023i	0.0821834	+	0.198408i
$276$		−	33.2840i		−	2.00346i
$277$	14.0806	−	5.83239i	0.846024	−	0.350435i	0.0827980	−	0.996566i	$-0.473614\pi$
$277$	14.0806	−	5.83239i	0.846024	−	0.350435i	0.763226	+	0.646132i	$0.223614\pi$
$278$	−11.5629	+	27.9154i	−0.693499	+	1.67426i
$279$	0.301879	+	0.125042i	0.0180730	+	0.00748609i
$280$		0			0
$281$	3.03475	−	3.03475i	0.181038	−	0.181038i	−0.610770	−	0.791808i	$-0.709140\pi$
$281$	3.03475	−	3.03475i	0.181038	−	0.181038i	0.791808	+	0.610770i	$0.209140\pi$
$282$	30.1344	+	12.4821i	1.79448	+	0.743296i
$283$	−4.80512	+	11.6006i	−0.285634	+	0.689583i	−0.999948	−	0.0102437i	$-0.996739\pi$
$283$	−4.80512	+	11.6006i	−0.285634	+	0.689583i	0.714313	+	0.699826i	$0.246739\pi$
$284$	−34.1910	+	14.1624i	−2.02886	+	0.840382i
$285$			18.7745i			1.11211i
$286$	−8.57236	−	20.6955i	−0.506894	−	1.22375i
$287$		0			0
$288$	0.837530			0.0493519
$289$	13.1047	−	10.8290i	0.770864	−	0.636999i
$290$	4.40898			0.258904
$291$	−3.96607	−	3.96607i	−0.232495	−	0.232495i
$292$	−4.63332	−	11.1858i	−0.271145	−	0.654601i
$293$			29.5459i			1.72609i	0.505129	+	0.863044i	$0.331445\pi$
$293$			29.5459i			1.72609i	−0.505129	+	0.863044i	$0.668555\pi$
$294$		0			0
$295$	−5.40211	+	13.0418i	−0.314523	+	0.759326i
$296$	−0.668906	−	0.277070i	−0.0388794	−	0.0161044i
$297$	−8.81326	+	8.81326i	−0.511397	+	0.511397i
$298$	16.5047	−	16.5047i	0.956091	−	0.956091i
$299$	21.4722	+	8.89409i	1.24177	+	0.514358i
$300$	−3.15812	+	7.62437i	−0.182334	+	0.440193i
$301$		0			0
$302$			48.9050i			2.81417i
$303$	−9.03840	−	21.8206i	−0.519243	−	1.25356i
$304$	−0.342534	−	0.342534i	−0.0196456	−	0.0196456i
$305$	−26.6540			−1.52621
$306$	1.28962	−	0.463890i	0.0737226	−	0.0265188i
$307$	12.5831			0.718156			0.359078	−	0.933307i	$-0.383091\pi$
$307$	12.5831			0.718156			0.359078	+	0.933307i	$0.383091\pi$
$308$		0			0
$309$	7.90220	+	19.0776i	0.449540	+	1.08529i
$310$			9.66671i			0.549032i
$311$	−6.99922	+	2.89917i	−0.396889	+	0.164397i	−0.572196	−	0.820117i	$-0.693908\pi$
$311$	−6.99922	+	2.89917i	−0.396889	+	0.164397i	0.175307	+	0.984514i	$0.443908\pi$
$312$	7.51363	−	18.1395i	0.425375	−	1.02695i
$313$	12.7766	+	5.29225i	0.722177	+	0.299135i	0.713333	−	0.700826i	$-0.247185\pi$
$313$	12.7766	+	5.29225i	0.722177	+	0.299135i	0.00884394	+	0.999961i	$0.497185\pi$
$314$	−13.7091	+	13.7091i	−0.773648	+	0.773648i
$315$		0			0
$316$	−8.98621	−	3.72221i	−0.505514	−	0.209391i
$317$	−4.13627	+	9.98583i	−0.232316	+	0.560860i	−0.996449	−	0.0841984i	$-0.973167\pi$
$317$	−4.13627	+	9.98583i	−0.232316	+	0.560860i	0.764133	+	0.645059i	$0.223167\pi$
$318$	−8.16357	+	3.38146i	−0.457790	+	0.189623i
$319$			2.52113i			0.141156i
$320$	9.35757	+	22.5912i	0.523104	+	1.26289i
$321$	6.16061	+	6.16061i	0.343852	+	0.343852i
$322$		0			0
$323$	−20.9474	−	9.86414i	−1.16554	−	0.548855i
$324$	−30.2865			−1.68259
$325$	−4.07474	−	4.07474i	−0.226026	−	0.226026i
$326$	−1.50699	−	3.63820i	−0.0834646	−	0.201501i
$327$			30.9444i			1.71123i
$328$	−19.3703	+	8.02343i	−1.06954	+	0.443020i
$329$		0			0
$330$	17.3686	+	7.19432i	0.956111	+	0.396034i
$331$	7.79907	−	7.79907i	0.428676	−	0.428676i	−0.459501	−	0.888177i	$-0.651972\pi$
$331$	7.79907	−	7.79907i	0.428676	−	0.428676i	0.888177	+	0.459501i	$0.151972\pi$
$332$	−26.2135	+	26.2135i	−1.43865	+	1.43865i
$333$	0.0350306	+	0.0145101i	0.00191966	+	0.000795150i
$334$	6.71585	−	16.2135i	0.367475	−	0.887162i
$335$	23.7660	−	9.84421i	1.29848	−	0.537847i
$336$		0			0
$337$	−2.78427	−	6.72182i	−0.151669	−	0.366161i	0.829723	−	0.558175i	$-0.188498\pi$
$337$	−2.78427	−	6.72182i	−0.151669	−	0.366161i	−0.981392	+	0.192014i	$0.938498\pi$
$338$	4.63455	+	4.63455i	0.252086	+	0.252086i
$339$	−34.3907			−1.86785
$340$	16.8210	+	18.4963i	0.912246	+	1.00310i
$341$	−5.52758			−0.299335
$342$	−1.31990	−	1.31990i	−0.0713719	−	0.0713719i
$343$		0			0
$344$		−	27.0467i		−	1.45826i
$345$	−18.0205	+	7.46433i	−0.970190	+	0.401866i
$346$	−9.83235	+	23.7374i	−0.528591	+	1.27613i
$347$	1.22938	+	0.509226i	0.0659966	+	0.0273367i	0.415438	−	0.909622i	$-0.363628\pi$
$347$	1.22938	+	0.509226i	0.0659966	+	0.0273367i	−0.349441	+	0.936958i	$0.613628\pi$
$348$	−4.13102	+	4.13102i	−0.221446	+	0.221446i
$349$	−7.00576	+	7.00576i	−0.375010	+	0.375010i	−0.869298	−	0.494288i	$-0.835429\pi$
$349$	−7.00576	+	7.00576i	−0.375010	+	0.375010i	0.494288	+	0.869298i	$0.335429\pi$
$350$		0			0
$351$	7.71783	−	18.6325i	0.411947	−	0.994529i
$352$	−13.0898	+	5.42198i	−0.697689	+	0.288992i
$353$			3.00968i			0.160189i	0.996787	+	0.0800945i	$0.0255222\pi$
$353$			3.00968i			0.160189i	−0.996787	+	0.0800945i	$0.974478\pi$
$354$	−11.6087	−	28.0258i	−0.616994	−	1.48956i
$355$	15.3355	+	15.3355i	0.813921	+	0.813921i
$356$	−27.2511			−1.44430
$357$		0			0
$358$	−14.6370			−0.773588
$359$	4.21352	+	4.21352i	0.222381	+	0.222381i	0.809500	−	0.587119i	$-0.199738\pi$
$359$	4.21352	+	4.21352i	0.222381	+	0.222381i	−0.587119	+	0.809500i	$0.699738\pi$
$360$	0.291747	+	0.704339i	0.0153764	+	0.0371220i
$361$			12.5349i			0.659733i
$362$	−23.9528	+	9.92157i	−1.25893	+	0.521466i
$363$	3.35203	−	8.09251i	0.175936	−	0.424747i
$364$		0			0
$365$	−5.01711	+	5.01711i	−0.262608	+	0.262608i
$366$	40.5011	−	40.5011i	2.11703	−	2.11703i
$367$	28.4279	+	11.7752i	1.48392	+	0.614661i	0.969985	−	0.243165i	$-0.0781857\pi$
$367$	28.4279	+	11.7752i	1.48392	+	0.614661i	0.513939	+	0.857827i	$0.328186\pi$
$368$	0.192593	−	0.464960i	0.0100396	−	0.0242377i
$369$	1.01442	−	0.420187i	0.0528086	−	0.0218740i
$370$			1.12174i			0.0583166i
$371$		0			0
$372$	−9.05728	−	9.05728i	−0.469598	−	0.469598i
$373$	−22.2837			−1.15381			−0.576903	−	0.816813i	$-0.695739\pi$
$373$	−22.2837			−1.15381			−0.576903	+	0.816813i	$0.695739\pi$
$374$	−17.1524	+	15.5989i	−0.886931	+	0.806599i
$375$	21.5526			1.11297
$376$	−15.8222	−	15.8222i	−0.815967	−	0.815967i
$377$	−1.56113	−	3.76889i	−0.0804021	−	0.194108i
$378$		0			0
$379$	−3.56567	+	1.47695i	−0.183156	+	0.0758659i	−0.472377	−	0.881397i	$-0.656604\pi$
$379$	−3.56567	+	1.47695i	−0.183156	+	0.0758659i	0.289221	+	0.957262i	$0.406604\pi$
$380$	13.0308	−	31.4591i	0.668466	−	1.61382i
$381$	−0.0454480	−	0.0188252i	−0.00232837	−	0.000964443i
$382$	−15.2308	+	15.2308i	−0.779278	+	0.779278i
$383$	19.2005	−	19.2005i	0.981099	−	0.981099i	−0.0187259	−	0.999825i	$-0.505961\pi$
$383$	19.2005	−	19.2005i	0.981099	−	0.981099i	0.999825	+	0.0187259i	$0.00596099\pi$
$384$	−29.6870	−	12.2968i	−1.51496	−	0.627517i
$385$		0			0
$386$	30.4101	−	12.5963i	1.54783	−	0.641133i
$387$			1.41643i			0.0720014i
$388$	3.89294	+	9.39839i	0.197634	+	0.477131i
$389$	20.3594	+	20.3594i	1.03226	+	1.03226i	0.999462	+	0.0327981i	$0.0104418\pi$
$389$	20.3594	+	20.3594i	1.03226	+	1.03226i	0.0327981	+	0.999462i	$0.489558\pi$
$390$	−30.4196			−1.54036
$391$	1.13976	−	24.0278i	0.0576401	−	1.21514i
$392$		0			0
$393$	1.18225	+	1.18225i	0.0596367	+	0.0596367i
$394$	14.4833	+	34.9658i	0.729659	+	1.76155i
$395$			5.70002i			0.286799i
$396$	−1.06480	+	0.441053i	−0.0535080	+	0.0221637i
$397$	−11.4152	+	27.5587i	−0.572912	+	1.38313i	0.326154	+	0.945317i	$0.394247\pi$
$397$	−11.4152	+	27.5587i	−0.572912	+	1.38313i	−0.899066	+	0.437814i	$0.855753\pi$
$398$	37.2969	+	15.4489i	1.86952	+	0.774382i
$399$		0			0
$400$	−0.0882346	+	0.0882346i	−0.00441173	+	0.00441173i
$401$	10.8984	+	4.51425i	0.544238	+	0.225431i	0.637826	−	0.770180i	$-0.279834\pi$
$401$	10.8984	+	4.51425i	0.544238	+	0.225431i	−0.0935883	+	0.995611i	$0.529834\pi$
$402$	−21.1544	+	51.0712i	−1.05508	+	2.54720i
$403$	8.26331	−	3.42278i	0.411625	−	0.170501i
$404$			42.8366i			2.13120i
$405$	6.79211	+	16.3976i	0.337503	+	0.814804i
$406$		0			0
$407$	−0.641431			−0.0317945
$408$	−20.2985	−	0.962857i	−1.00492	−	0.0476685i
$409$	28.1122			1.39006			0.695030	−	0.718980i	$-0.255391\pi$
$409$	28.1122			1.39006			0.695030	+	0.718980i	$0.255391\pi$
$410$	22.9694	+	22.9694i	1.13438	+	1.13438i
$411$	−8.46452	−	20.4352i	−0.417524	−	1.00799i
$412$		−	37.4517i		−	1.84511i
$413$		0			0
$414$	0.742126	−	1.79165i	0.0364735	−	0.0880548i
$415$	20.0711	+	8.31371i	0.985250	+	0.408104i
$416$	16.2109	−	16.2109i	0.794804	−	0.794804i
$417$	−16.5906	+	16.5906i	−0.812447	+	0.812447i
$418$	29.1735	+	12.0841i	1.42692	+	0.591051i
$419$	3.52193	−	8.50269i	0.172058	−	0.415384i	−0.814203	−	0.580580i	$-0.802826\pi$
$419$	3.52193	−	8.50269i	0.172058	−	0.415384i	0.986261	+	0.165196i	$0.0528258\pi$
$420$		0			0
$421$		−	2.38966i		−	0.116465i	−0.998303	−	0.0582323i	$-0.981454\pi$
$421$		−	2.38966i		−	0.116465i	0.998303	−	0.0582323i	$-0.0185464\pi$
$422$	−8.02567	−	19.3757i	−0.390683	−	0.943193i
$423$	0.828607	+	0.828607i	0.0402883	+	0.0402883i
$424$	6.06177			0.294386
$425$	−2.54094	+	5.39592i	−0.123254	+	0.261740i
$426$	−46.6048			−2.25801
$427$		0			0
$428$	−6.04702	−	14.5988i	−0.292294	−	0.705660i
$429$		−	17.3944i		−	0.839811i
$430$	−38.7145	+	16.0361i	−1.86698	+	0.773327i
$431$	5.26155	−	12.7025i	0.253440	−	0.611858i	−0.745037	−	0.667023i	$-0.767568\pi$
$431$	5.26155	−	12.7025i	0.253440	−	0.611858i	0.998477	+	0.0551648i	$0.0175684\pi$
$432$	−0.403469	−	0.167122i	−0.0194119	−	0.00804067i
$433$	2.41708	−	2.41708i	0.116157	−	0.116157i	−0.646639	−	0.762796i	$-0.723826\pi$
$433$	2.41708	−	2.41708i	0.116157	−	0.116157i	0.762796	+	0.646639i	$0.223826\pi$
$434$		0			0
$435$	3.16303	+	1.31017i	0.151656	+	0.0628178i
$436$	21.4776	−	51.8514i	1.02859	−	2.48323i
$437$	−30.2684	+	12.5376i	−1.44793	+	0.599754i
$438$		−	15.2471i		−	0.728536i
$439$	−7.70996	−	18.6135i	−0.367976	−	0.888374i	−0.994082	−	0.108635i	$-0.965352\pi$
$439$	−7.70996	−	18.6135i	−0.367976	−	0.888374i	0.626105	−	0.779739i	$-0.284648\pi$
$440$	−9.11947	−	9.11947i	−0.434754	−	0.434754i
$441$		0			0
$442$	15.9825	−	33.9402i	0.760209	−	1.61437i
$443$	−19.8767			−0.944371			−0.472185	−	0.881499i	$-0.656535\pi$
$443$	−19.8767			−0.944371			−0.472185	+	0.881499i	$0.656535\pi$
$444$	−1.05102	−	1.05102i	−0.0498793	−	0.0498793i
$445$	6.11138	+	14.7542i	0.289707	+	0.699415i
$446$		−	53.8080i		−	2.54788i
$447$	16.7451	−	6.93604i	0.792015	−	0.328063i
$448$		0			0
$449$	36.1936	+	14.9919i	1.70808	+	0.707510i	0.999999	+	0.00137848i	$0.000438784\pi$
$449$	36.1936	+	14.9919i	1.70808	+	0.707510i	0.708081	+	0.706131i	$0.249561\pi$
$450$	−0.339998	+	0.339998i	−0.0160276	+	0.0160276i
$451$	−13.1343	+	13.1343i	−0.618468	+	0.618468i
$452$	57.6261	+	23.8695i	2.71051	+	1.12273i
$453$	−14.5326	+	35.0847i	−0.682799	+	1.64842i
$454$	−52.4536	+	21.7270i	−2.46177	+	1.01970i
$455$		0			0
$456$	10.5916	+	25.5704i	0.495998	+	1.19744i
$457$	−12.6945	−	12.6945i	−0.593824	−	0.593824i	0.344838	−	0.938662i	$-0.387934\pi$
$457$	−12.6945	−	12.6945i	−0.593824	−	0.593824i	−0.938662	+	0.344838i	$0.887934\pi$
$458$	12.0945			0.565137
$459$	−20.8501	−	0.989025i	−0.973200	−	0.0461637i
$460$	35.3764			1.64943
$461$	−13.6856	−	13.6856i	−0.637400	−	0.637400i	0.312514	−	0.949913i	$-0.398829\pi$
$461$	−13.6856	−	13.6856i	−0.637400	−	0.637400i	−0.949913	+	0.312514i	$0.898829\pi$
$462$		0			0
$463$		−	19.3890i		−	0.901082i	−0.892756	−	0.450541i	$-0.851231\pi$
$463$		−	19.3890i		−	0.901082i	0.892756	−	0.450541i	$-0.148769\pi$
$464$	−0.0816117	+	0.0338047i	−0.00378873	+	0.00156934i
$465$	−2.87255	+	6.93495i	−0.133211	+	0.321601i
$466$	−36.5755	−	15.1501i	−1.69433	−	0.701813i
$467$	15.2955	−	15.2955i	0.707792	−	0.707792i	−0.258279	−	0.966070i	$-0.583155\pi$
$467$	15.2955	−	15.2955i	0.707792	−	0.707792i	0.966070	+	0.258279i	$0.0831552\pi$
$468$	1.31868	−	1.31868i	0.0609561	−	0.0609561i
$469$		0			0
$470$	−13.2668	+	32.0288i	−0.611950	+	1.47738i
$471$	−13.9088	+	5.76119i	−0.640881	+	0.265462i
$472$			20.8103i			0.957871i
$473$	−9.16967	−	22.1375i	−0.421622	−	1.01789i
$474$	−8.66126	−	8.66126i	−0.397825	−	0.397825i
$475$	8.12320			0.372718
$476$		0			0
$477$	−0.317455			−0.0145352
$478$	7.64529	+	7.64529i	0.349688	+	0.349688i
$479$	1.08787	+	2.62635i	0.0497061	+	0.120001i	0.946782	−	0.321875i	$-0.104313\pi$
$479$	1.08787	+	2.62635i	0.0497061	+	0.120001i	−0.897076	+	0.441876i	$0.854313\pi$
$480$			19.2403i			0.878194i
$481$	0.958890	−	0.397185i	0.0437216	−	0.0181101i
$482$	−0.395184	+	0.954057i	−0.0180001	+	0.0434561i
$483$		0			0
$484$	−11.2335	+	11.2335i	−0.510614	+	0.510614i
$485$	4.21540	−	4.21540i	0.191411	−	0.191411i
$486$	−3.18867	−	1.32079i	−0.144641	−	0.0599122i
$487$	−1.29736	+	3.13210i	−0.0587890	+	0.141929i	−0.950545	−	0.310588i	$-0.899474\pi$
$487$	−1.29736	+	3.13210i	−0.0587890	+	0.141929i	0.891756	+	0.452517i	$0.149474\pi$
$488$	−36.3021	+	15.0368i	−1.64332	+	0.680686i
$489$		−	3.05788i		−	0.138282i
$490$		0			0
$491$	−18.9120	−	18.9120i	−0.853487	−	0.853487i	0.137074	−	0.990561i	$-0.456230\pi$
$491$	−18.9120	−	18.9120i	−0.853487	−	0.853487i	−0.990561	+	0.137074i	$0.956230\pi$
$492$	−43.0425			−1.94051
$493$	−3.12366	+	2.84074i	−0.140683	+	0.127940i
$494$	−51.0948			−2.29886
$495$	0.477586	+	0.477586i	0.0214659	+	0.0214659i
$496$	−0.0741169	−	0.178934i	−0.00332795	−	0.00803438i
$497$		0			0
$498$	−43.1310	+	17.8655i	−1.93275	+	0.800571i
$499$	−11.6401	+	28.1018i	−0.521085	+	1.25801i	0.416146	+	0.909298i	$0.363381\pi$
$499$	−11.6401	+	28.1018i	−0.521085	+	1.25801i	−0.937230	+	0.348711i	$0.886619\pi$
$500$	−36.1142	−	14.9590i	−1.61507	−	0.668986i
$501$	9.63597	−	9.63597i	0.430503	−	0.430503i
$502$	3.91715	−	3.91715i	0.174831	−	0.174831i
$503$	−4.39981	−	1.82246i	−0.196178	−	0.0812595i	0.282432	−	0.959287i	$-0.408859\pi$
$503$	−4.39981	−	1.82246i	−0.196178	−	0.0812595i	−0.478609	+	0.878028i	$0.658859\pi$
$504$		0			0
$505$	23.1924	−	9.60661i	1.03205	−	0.427488i
$506$			32.8062i			1.45841i
$507$	1.94765	+	4.70205i	0.0864983	+	0.208825i
$508$	0.0630881	+	0.0630881i	0.00279908	+	0.00279908i
$509$	30.7767			1.36416			0.682078	−	0.731280i	$-0.261077\pi$
$509$	30.7767			1.36416			0.682078	+	0.731280i	$0.261077\pi$
$510$	10.6568	+	29.6260i	0.471890	+	1.31186i
$511$		0			0
$512$	−0.690044	−	0.690044i	−0.0304959	−	0.0304959i
$513$	10.8795	+	26.2654i	0.480340	+	1.15964i
$514$			23.5696i			1.03961i
$515$	−20.2769	+	8.39898i	−0.893508	+	0.370103i
$516$	21.2486	−	51.2988i	0.935419	−	2.25830i
$517$	−18.3146	−	7.58615i	−0.805474	−	0.333638i
$518$		0			0
$519$	−14.1076	+	14.1076i	−0.619254	+	0.619254i
$520$	19.2799	+	7.98598i	0.845477	+	0.350208i
$521$	16.2428	−	39.2136i	0.711610	−	1.71798i	0.0156715	−	0.999877i	$-0.495011\pi$
$521$	16.2428	−	39.2136i	0.711610	−	1.71798i	0.695939	−	0.718101i	$-0.254989\pi$
$522$	−0.314478	+	0.130261i	−0.0137643	+	0.00570137i
$523$			26.6878i			1.16697i	0.812122	+	0.583487i	$0.198312\pi$
$523$			26.6878i			1.16697i	−0.812122	+	0.583487i	$0.801688\pi$
$524$	−1.16045	−	2.80158i	−0.0506946	−	0.122388i
$525$		0			0
$526$	3.00534			0.131039
$527$	−6.22833	−	6.84864i	−0.271310	−	0.298331i
$528$	−0.376659			−0.0163920
$529$	−7.80464	−	7.80464i	−0.339332	−	0.339332i
$530$	−3.59404	−	8.67678i	−0.156115	−	0.376895i
$531$		−	1.08983i		−	0.0472947i
$532$		0			0
$533$	11.5017	−	27.7677i	0.498196	−	1.20275i
$534$	−31.7055	−	13.1328i	−1.37203	−	0.568313i
$535$	−6.54790	+	6.54790i	−0.283091	+	0.283091i
$536$	26.8151	−	26.8151i	1.15824	−	1.15824i
$537$	−10.5006	−	4.34951i	−0.453136	−	0.187695i
$538$	−2.21871	+	5.35644i	−0.0956555	+	0.230933i
$539$		0			0
$540$		−	30.6978i		−	1.32102i
$541$	2.45087	+	5.91693i	0.105371	+	0.254389i	0.967768	−	0.251845i	$-0.0810373\pi$
$541$	2.45087	+	5.91693i	0.105371	+	0.254389i	−0.862396	+	0.506234i	$0.831037\pi$
$542$	−35.7098	−	35.7098i	−1.53387	−	1.53387i
$543$	−20.1321			−0.863953
$544$	−21.4670	−	10.1088i	−0.920392	−	0.433413i
$545$	−32.8898			−1.40884
$546$		0			0
$547$	11.1327	+	26.8767i	0.475999	+	1.14916i	0.961470	+	0.274910i	$0.0886482\pi$
$547$	11.1327	+	26.8767i	0.475999	+	1.14916i	−0.485471	+	0.874253i	$0.661352\pi$
$548$			40.1167i			1.71370i
$549$	1.90114	−	0.787478i	0.0811387	−	0.0336088i
$550$	3.11278	−	7.51492i	0.132729	−	0.320437i
$551$	5.31283	+	2.20065i	0.226334	+	0.0937508i
$552$	−20.3325	+	20.3325i	−0.865407	+	0.865407i
$553$		0			0
$554$	−32.1603	−	13.3212i	−1.36636	−	0.565965i
$555$	−0.333336	+	0.804745i	−0.0141493	+	0.0341595i
$556$	39.3148	−	16.2847i	1.66732	−	0.690627i
$557$		−	25.0065i		−	1.05956i	−0.848136	−	0.529779i	$-0.822275\pi$
$557$		−	25.0065i		−	1.05956i	0.848136	−	0.529779i	$-0.177725\pi$
$558$	−0.285598	−	0.689494i	−0.0120903	−	0.0291886i
$559$	27.4159	+	27.4159i	1.15957	+	1.15957i
$560$		0			0
$561$	−16.9406	+	6.09372i	−0.715233	+	0.257277i
$562$	−9.80247			−0.413492
$563$	−16.7767	−	16.7767i	−0.707055	−	0.707055i	0.258860	−	0.965915i	$-0.416653\pi$
$563$	−16.7767	−	16.7767i	−0.707055	−	0.707055i	−0.965915	+	0.258860i	$0.916653\pi$
$564$	−17.5792	−	42.4399i	−0.740217	−	1.78704i
$565$		−	36.5527i		−	1.53778i
$566$	26.4958	−	10.9749i	1.11370	−	0.461311i
$567$		0			0
$568$	29.5380	+	12.2350i	1.23939	+	0.513371i
$569$	−2.94427	+	2.94427i	−0.123430	+	0.123430i	−0.766124	−	0.642693i	$-0.777817\pi$
$569$	−2.94427	+	2.94427i	−0.123430	+	0.123430i	0.642693	+	0.766124i	$0.277817\pi$
$570$	30.3215	−	30.3215i	1.27003	−	1.27003i
$571$	14.5640	+	6.03259i	0.609483	+	0.252456i	0.666008	−	0.745945i	$-0.268002\pi$
$571$	14.5640	+	6.03259i	0.609483	+	0.252456i	−0.0565243	+	0.998401i	$0.518002\pi$
$572$	−12.0729	+	29.1466i	−0.504794	+	1.21868i
$573$	−15.4527	+	6.40071i	−0.645545	+	0.267393i
$574$		0			0
$575$	3.22961	+	7.79696i	0.134684	+	0.325156i
$576$	−1.33489	−	1.33489i	−0.0556203	−	0.0556203i
$577$	30.2286			1.25843			0.629217	−	0.777230i	$-0.283376\pi$
$577$	30.2286			1.25843			0.629217	+	0.777230i	$0.283376\pi$
$578$	−38.6538	−	3.67535i	−1.60779	−	0.152875i
$579$	25.5594			1.06221
$580$	−4.39072	−	4.39072i	−0.182315	−	0.182315i
$581$		0			0
$582$			12.8107i			0.531021i
$583$	4.96152	−	2.05513i	0.205485	−	0.0851148i
$584$	−4.00279	+	9.66358i	−0.165636	+	0.399882i
$585$	−1.00968	−	0.418225i	−0.0417453	−	0.0172915i
$586$	47.7177	−	47.7177i	1.97120	−	1.97120i
$587$	29.4702	−	29.4702i	1.21636	−	1.21636i	0.247468	−	0.968896i	$-0.420401\pi$
$587$	29.4702	−	29.4702i	1.21636	−	1.21636i	0.968896	−	0.247468i	$-0.0795986\pi$
$588$		0			0
$589$	−4.82493	+	11.6484i	−0.198808	+	0.479965i
$590$	29.7877	−	12.3385i	1.22634	−	0.507967i
$591$			29.3885i			1.20888i
$592$	−0.00860066	−	0.0207638i	−0.000353485	−	0.000853389i
$593$	27.3497	+	27.3497i	1.12312	+	1.12312i	0.991270	+	0.131850i	$0.0420917\pi$
$593$	27.3497	+	27.3497i	1.12312	+	1.12312i	0.131850	+	0.991270i	$0.457908\pi$
$594$	28.4675			1.16804
$595$		0			0
$596$	−32.8727			−1.34652
$597$	22.1662	+	22.1662i	0.907203	+	0.907203i
$598$	−20.3142	−	49.0427i	−0.830708	−	2.00551i
$599$			11.6262i			0.475034i	0.971383	+	0.237517i	$0.0763335\pi$
$599$			11.6262i			0.475034i	−0.971383	+	0.237517i	$0.923667\pi$
$600$	6.58678	−	2.72834i	0.268904	−	0.111384i
$601$	−16.4713	+	39.7652i	−0.671877	+	1.62205i	0.106541	+	0.994308i	$0.466023\pi$
$601$	−16.4713	+	39.7652i	−0.671877	+	1.62205i	−0.778418	+	0.627747i	$0.783977\pi$
$602$		0			0
$603$	−1.40431	+	1.40431i	−0.0571878	+	0.0571878i
$604$	48.7024	−	48.7024i	1.98167	−	1.98167i
$605$	8.60125	+	3.56276i	0.349691	+	0.144847i
$606$	−20.6438	+	49.8385i	−0.838596	+	2.02455i
$607$	−26.6289	+	11.0301i	−1.08083	+	0.447696i	−0.850802	−	0.525487i	$-0.823883\pi$
$607$	−26.6289	+	11.0301i	−1.08083	+	0.447696i	−0.230032	+	0.973183i	$0.573883\pi$
$608$			32.3172i			1.31064i
$609$		0			0
$610$	43.0473	+	43.0473i	1.74293	+	1.74293i
$611$	32.0764			1.29767
$612$	−1.74625	−	0.822309i	−0.0705878	−	0.0332399i
$613$	38.8872			1.57064			0.785320	−	0.619090i	$-0.212498\pi$
$613$	38.8872			1.57064			0.785320	+	0.619090i	$0.212498\pi$
$614$	−20.3222	−	20.3222i	−0.820138	−	0.820138i
$615$	9.65280	+	23.3039i	0.389238	+	0.939704i
$616$		0			0
$617$	41.0826	−	17.0170i	1.65392	−	0.685077i	0.656333	−	0.754472i	$-0.272107\pi$
$617$	41.0826	−	17.0170i	1.65392	−	0.685077i	0.997589	+	0.0693948i	$0.0221068\pi$
$618$	18.0487	−	43.5734i	0.726025	−	1.75278i
$619$	−2.72836	−	1.13012i	−0.109662	−	0.0454235i	0.327178	−	0.944963i	$-0.393902\pi$
$619$	−2.72836	−	1.13012i	−0.109662	−	0.0454235i	−0.436840	+	0.899539i	$0.643902\pi$
$620$	9.62667	−	9.62667i	0.386616	−	0.386616i
$621$	−20.8850	+	20.8850i	−0.838088	+	0.838088i
$622$	15.9863	+	6.62173i	0.640991	+	0.265507i
$623$		0			0
$624$	0.563077	−	0.233234i	0.0225411	−	0.00933684i
$625$			15.6748i			0.626992i
$626$	−12.0875	−	29.1819i	−0.483115	−	1.16634i
$627$	17.3383	+	17.3383i	0.692427	+	0.692427i
$628$	27.3046			1.08957
$629$	−0.722747	−	0.794728i	−0.0288178	−	0.0316879i
$630$		0			0
$631$	−22.8445	−	22.8445i	−0.909427	−	0.909427i	0.0867991	−	0.996226i	$-0.472336\pi$
$631$	−22.8445	−	22.8445i	−0.909427	−	0.909427i	−0.996226	+	0.0867991i	$0.972336\pi$
$632$	3.21566	+	7.76330i	0.127912	+	0.308807i
$633$		−	16.2851i		−	0.647275i
$634$	22.8077	−	9.44727i	0.905810	−	0.375199i
$635$	0.0200086	−	0.0483051i	0.000794018	−	0.00191693i
$636$	11.4972	+	4.76230i	0.455894	+	0.188837i
$637$		0			0
$638$	4.07172	−	4.07172i	0.161201	−	0.161201i
$639$	−1.54690	−	0.640748i	−0.0611946	−	0.0253476i
$640$	13.0698	−	31.5533i	0.516629	−	1.24725i
$641$	37.0737	−	15.3564i	1.46432	−	0.606542i	0.498766	−	0.866737i	$-0.333787\pi$
$641$	37.0737	−	15.3564i	1.46432	−	0.606542i	0.965556	+	0.260195i	$0.0837868\pi$
$642$		−	19.8993i		−	0.785361i
$643$	−2.75313	−	6.64664i	−0.108573	−	0.262118i	0.860250	−	0.509872i	$-0.170307\pi$
$643$	−2.75313	−	6.64664i	−0.108573	−	0.262118i	−0.968823	+	0.247754i	$0.920307\pi$
$644$		0			0
$645$	−32.5392			−1.28123
$646$	17.8998	+	49.7618i	0.704260	+	1.95785i
$647$	22.0001			0.864914			0.432457	−	0.901654i	$-0.357647\pi$
$647$	22.0001			0.864914			0.432457	+	0.901654i	$0.357647\pi$
$648$	18.5014	+	18.5014i	0.726803	+	0.726803i
$649$	7.05533	+	17.0331i	0.276946	+	0.668607i
$650$			13.1617i			0.516245i
$651$		0			0
$652$	−2.12238	+	5.12388i	−0.0831188	+	0.200667i
$653$	−21.1899	−	8.77714i	−0.829224	−	0.343476i	−0.0726286	−	0.997359i	$-0.523139\pi$
$653$	−21.1899	−	8.77714i	−0.829224	−	0.343476i	−0.756596	+	0.653883i	$0.773139\pi$
$654$	49.9764	−	49.9764i	1.95423	−	1.95423i
$655$	−1.25657	+	1.25657i	−0.0490984	+	0.0490984i
$656$	−0.601282	−	0.249059i	−0.0234761	−	0.00972413i
$657$	0.209626	−	0.506081i	0.00817828	−	0.0197441i
$658$		0			0
$659$			15.7505i			0.613551i	0.951782	+	0.306776i	$0.0992501\pi$
$659$			15.7505i			0.613551i	−0.951782	+	0.306776i	$0.900750\pi$
$660$	−10.1322	−	24.4612i	−0.394394	−	0.952150i
$661$	22.1588	+	22.1588i	0.861877	+	0.861877i	0.991556	−	0.129679i	$-0.0413947\pi$
$661$	22.1588	+	22.1588i	0.861877	+	0.861877i	−0.129679	+	0.991556i	$0.541395\pi$
$662$	−25.1916			−0.979099
$663$	21.5516	−	19.5996i	0.836994	−	0.761184i
$664$	32.0265			1.24287
$665$		0			0
$666$	−0.0331413	−	0.0800101i	−0.00128420	−	0.00310033i
$667$			5.97439i			0.231329i
$668$	−22.8343	+	9.45829i	−0.883487	+	0.365952i
$669$	15.9895	−	38.6021i	0.618191	−	1.49245i
$670$	−54.2818	−	22.4843i	−2.09709	−	0.868643i
$671$	−24.6151	+	24.6151i	−0.950256	+	0.950256i
$672$		0			0
$673$	31.3529	+	12.9868i	1.20857	+	0.500604i	0.893757	−	0.448551i	$-0.148060\pi$
$673$	31.3529	+	12.9868i	1.20857	+	0.500604i	0.314809	+	0.949155i	$0.398060\pi$
$674$	−6.35930	+	15.3527i	−0.244951	+	0.591364i
$675$	6.76580	−	2.80248i	0.260416	−	0.107868i
$676$		−	9.23070i		−	0.355027i
$677$	−1.18090	−	2.85094i	−0.0453857	−	0.109571i	0.899561	−	0.436795i	$-0.143887\pi$
$677$	−1.18090	−	2.85094i	−0.0453857	−	0.109571i	−0.944947	+	0.327225i	$0.893887\pi$
$678$	55.5423	+	55.5423i	2.13309	+	2.13309i
$679$		0			0
$680$	1.02339	−	21.5745i	0.0392451	−	0.827346i
$681$	−44.0868			−1.68941
$682$	8.92725	+	8.92725i	0.341842	+	0.341842i
$683$	16.1518	+	38.9938i	0.618030	+	1.49206i	0.853988	+	0.520293i	$0.174177\pi$
$683$	16.1518	+	38.9938i	0.618030	+	1.49206i	−0.235957	+	0.971763i	$0.575823\pi$
$684$			2.62886i			0.100517i
$685$	21.7198	−	8.99665i	0.829872	−	0.343744i
$686$		0			0
$687$	8.67663	+	3.59398i	0.331034	+	0.137119i
$688$	0.593665	−	0.593665i	0.0226333	−	0.0226333i
$689$	−6.14453	+	6.14453i	−0.234088	+	0.234088i
$690$	41.1589	+	17.0486i	1.56689	+	0.649029i
$691$	8.26814	−	19.9611i	0.314535	−	0.759354i	−0.684991	−	0.728552i	$-0.740194\pi$
$691$	8.26814	−	19.9611i	0.314535	−	0.759354i	0.999525	−	0.0308025i	$-0.00980630\pi$
$692$	33.4307	−	13.8474i	1.27084	−	0.526401i
$693$		0			0
$694$	−1.16308	−	2.80792i	−0.0441498	−	0.106587i
$695$	−17.6336	−	17.6336i	−0.668882	−	0.668882i
$696$	5.04710			0.191310
$697$	−31.0726	−	1.47393i	−1.17696	−	0.0558290i
$698$	22.6291			0.856525
$699$	−21.7375	−	21.7375i	−0.822187	−	0.822187i
$700$		0			0
$701$			37.2258i			1.40600i	0.711191	+	0.702999i	$0.248156\pi$
$701$			37.2258i			1.40600i	−0.711191	+	0.702999i	$0.751844\pi$
$702$	−42.5568	+	17.6276i	−1.60620	+	0.665310i
$703$	−0.559894	+	1.35170i	−0.0211168	+	0.0509804i
$704$	29.5048	+	12.2213i	1.11200	+	0.460607i
$705$	−19.0353	+	19.0353i	−0.716911	+	0.716911i
$706$	4.86074	−	4.86074i	0.182936	−	0.182936i
$707$		0			0
$708$	−16.3491	+	39.4703i	−0.614438	+	1.48339i
$709$	−28.6353	+	11.8611i	−1.07542	+	0.445454i	−0.848901	−	0.528552i	$-0.822735\pi$
$709$	−28.6353	+	11.8611i	−1.07542	+	0.445454i	−0.226521	+	0.974006i	$0.572735\pi$
$710$		−	49.5347i		−	1.85900i
$711$	−0.168404	−	0.406563i	−0.00631565	−	0.0152473i
$712$	16.6471	+	16.6471i	0.623876	+	0.623876i
$713$	−13.0989			−0.490557
$714$		0			0
$715$	18.4879			0.691410
$716$	14.5763	+	14.5763i	0.544743	+	0.544743i
$717$	3.21291	+	7.75664i	0.119988	+	0.289677i
$718$		−	13.6100i		−	0.507920i
$719$	16.5877	−	6.87085i	0.618617	−	0.256239i	−0.0512911	−	0.998684i	$-0.516334\pi$
$719$	16.5877	−	6.87085i	0.618617	−	0.256239i	0.669908	+	0.742444i	$0.266334\pi$
$720$	−0.00905626	+	0.0218638i	−0.000337507	+	0.000814814i
$721$		0			0
$722$	20.2444	−	20.2444i	0.753418	−	0.753418i
$723$	−0.567014	+	0.567014i	−0.0210875	+	0.0210875i
$724$	33.7340	+	13.9731i	1.25372	+	0.519306i
$725$	0.566874	−	1.36855i	0.0210532	−	0.0508268i
$726$	−18.4834	+	7.65606i	−0.685982	+	0.284143i
$727$		−	34.3650i		−	1.27453i	−0.770646	−	0.637264i	$-0.780066\pi$
$727$		−	34.3650i		−	1.27453i	0.770646	−	0.637264i	$-0.219934\pi$
$728$		0			0
$729$	18.0780	+	18.0780i	0.669557	+	0.669557i
$730$	16.2056			0.599798
$731$	17.0961	−	36.3052i	0.632323	−	1.34279i
$732$	−80.6667			−2.98153
$733$	−23.1874	−	23.1874i	−0.856445	−	0.856445i	0.134472	−	0.990917i	$-0.457066\pi$
$733$	−23.1874	−	23.1874i	−0.856445	−	0.856445i	−0.990917	+	0.134472i	$0.957066\pi$
$734$	−26.8947	−	64.9296i	−0.992702	−	2.39659i
$735$		0			0
$736$	−31.0193	+	12.8486i	−1.14339	+	0.473606i
$737$	12.8569	−	31.0392i	0.473588	−	1.14334i
$738$	−2.31694	−	0.959710i	−0.0852879	−	0.0353274i
$739$	−33.7180	+	33.7180i	−1.24034	+	1.24034i	−0.280475	+	0.959861i	$0.590492\pi$
$739$	−33.7180	+	33.7180i	−1.24034	+	1.24034i	−0.959861	+	0.280475i	$0.909508\pi$
$740$	1.11710	−	1.11710i	0.0410653	−	0.0410653i
$741$	−36.6557	−	15.1833i	−1.34658	−	0.557772i
$742$		0			0
$743$	30.0240	−	12.4364i	1.10147	−	0.456246i	0.243481	−	0.969906i	$-0.421711\pi$
$743$	30.0240	−	12.4364i	1.10147	−	0.456246i	0.857994	+	0.513660i	$0.171711\pi$
$744$			11.0658i			0.405691i
$745$	7.37208	+	17.7978i	0.270092	+	0.652060i
$746$	35.9890	+	35.9890i	1.31765	+	1.31765i
$747$	−1.67723			−0.0613665
$748$	32.6156	+	1.54712i	1.19255	+	0.0565684i
$749$		0			0
$750$	−34.8083	−	34.8083i	−1.27102	−	1.27102i
$751$	−14.0011	−	33.8016i	−0.510907	−	1.23344i	−0.943357	−	0.331780i	$-0.892351\pi$
$751$	−14.0011	−	33.8016i	−0.510907	−	1.23344i	0.432450	−	0.901658i	$-0.357649\pi$
$752$		−	0.694583i		−	0.0253288i
$753$	3.97421	−	1.64617i	0.144828	−	0.0599898i
$754$	−3.56563	+	8.60818i	−0.129852	+	0.313492i
$755$	−37.2903	−	15.4462i	−1.35713	−	0.562143i
$756$		0			0
$757$	−27.8575	+	27.8575i	−1.01250	+	1.01250i	−0.0125781	+	0.999921i	$0.504004\pi$
$757$	−27.8575	+	27.8575i	−1.01250	+	1.01250i	−0.999921	+	0.0125781i	$0.995996\pi$
$758$	8.14403	+	3.37337i	0.295805	+	0.122526i
$759$	−9.74865	+	23.5353i	−0.353854	+	0.854279i
$760$	−27.1779	+	11.2575i	−0.985847	+	0.408351i
$761$			11.4516i			0.415119i	0.978222	+	0.207560i	$0.0665521\pi$
$761$			11.4516i			0.415119i	−0.978222	+	0.207560i	$0.933448\pi$
$762$	0.0429969	+	0.103804i	0.00155761	+	0.00376041i
$763$		0			0
$764$	30.3355			1.09750
$765$	−0.0535947	+	1.12986i	−0.00193772	+	0.0408501i
$766$	−62.0190			−2.24084
$767$	−21.0944	−	21.0944i	−0.761674	−	0.761674i
$768$	10.4777	+	25.2954i	0.378082	+	0.912771i
$769$			18.8057i			0.678151i	0.940759	+	0.339075i	$0.110114\pi$
$769$			18.8057i			0.678151i	−0.940759	+	0.339075i	$0.889886\pi$
$770$		0			0
$771$	−7.00392	+	16.9090i	−0.252240	+	0.608961i
$772$	−42.8282	−	17.7400i	−1.54142	−	0.638477i
$773$	−4.96599	+	4.96599i	−0.178614	+	0.178614i	−0.790751	−	0.612137i	$-0.790310\pi$
$773$	−4.96599	+	4.96599i	−0.178614	+	0.178614i	0.612137	+	0.790751i	$0.290310\pi$
$774$	2.28759	−	2.28759i	0.0822259	−	0.0822259i
$775$	3.00056	+	1.24287i	0.107783	+	0.0446453i
$776$	3.36316	−	8.11938i	0.120730	−	0.291469i
$777$		0			0
$778$		−	65.7622i		−	2.35769i
$779$	16.2135	+	39.1428i	0.580908	+	1.40244i
$780$	30.2936	+	30.2936i	1.08468	+	1.08468i
$781$	28.3247			1.01354
$782$	−40.6466	+	36.9651i	−1.45352	+	1.32187i
$783$	5.18427			0.185271
$784$		0			0
$785$	−6.12338	−	14.7831i	−0.218553	−	0.527633i
$786$		−	3.81876i		−	0.136211i
$787$	1.07792	−	0.446489i	0.0384237	−	0.0159156i	−0.363389	−	0.931638i	$-0.618380\pi$
$787$	1.07792	−	0.446489i	0.0384237	−	0.0159156i	0.401813	+	0.915722i	$0.368380\pi$
$788$	20.3977	−	49.2443i	0.726636	−	1.75426i
$789$	2.15605	+	0.893064i	0.0767573	+	0.0317939i
$790$	9.20576	−	9.20576i	0.327526	−	0.327526i
$791$		0			0
$792$	0.919890	+	0.381031i	0.0326869	+	0.0135394i
$793$	21.5556	−	52.0398i	0.765462	−	1.84799i
$794$	62.9443	−	26.0724i	2.23381	−	0.925274i
$795$		−	7.29277i		−	0.258648i
$796$	−21.7575	−	52.5273i	−0.771175	−	1.86178i
$797$	−35.8663	−	35.8663i	−1.27045	−	1.27045i	−0.945852	−	0.324599i	$-0.894771\pi$
$797$	−35.8663	−	35.8663i	−1.27045	−	1.27045i	−0.324599	−	0.945852i	$-0.605229\pi$
$798$		0			0
$799$	−11.2372	−	31.2395i	−0.397543	−	1.10517i
$800$	8.32473			0.294323
$801$	−0.871807	−	0.871807i	−0.0308038	−	0.0308038i
$802$	−10.3106	−	24.8919i	−0.364079	−	0.878965i
$803$			9.26665i			0.327013i
$804$	71.9263	−	29.7929i	2.53665	−	1.05071i
$805$		0			0
$806$	−18.8735	−	7.81765i	−0.664790	−	0.275365i
$807$	−3.18343	+	3.18343i	−0.112062	+	0.112062i
$808$	26.1679	−	26.1679i	0.920585	−	0.920585i
$809$	17.2993	+	7.16560i	0.608211	+	0.251929i	0.665463	−	0.746431i	$-0.268234\pi$
$809$	17.2993	+	7.16560i	0.608211	+	0.251929i	−0.0572526	+	0.998360i	$0.518234\pi$
$810$	15.5132	−	37.4523i	0.545080	−	1.31594i
$811$	42.5947	−	17.6433i	1.49570	−	0.619540i	0.523153	−	0.852239i	$-0.324756\pi$
$811$	42.5947	−	17.6433i	1.49570	−	0.619540i	0.972549	+	0.232699i	$0.0747557\pi$
$812$		0			0
$813$	−15.0069	−	36.2299i	−0.526316	−	1.27064i
$814$	1.03593	+	1.03593i	0.0363095	+	0.0363095i
$815$	3.25012			0.113847
$816$	−0.424410	−	0.466679i	−0.0148573	−	0.0163370i
$817$	−54.6551			−1.91214
$818$	−45.4023	−	45.4023i	−1.58746	−	1.58746i
$819$		0			0
$820$		−	45.7484i		−	1.59760i
$821$	47.8961	−	19.8392i	1.67159	−	0.692394i	0.672715	−	0.739902i	$-0.265128\pi$
$821$	47.8961	−	19.8392i	1.67159	−	0.692394i	0.998871	+	0.0475081i	$0.0151280\pi$
$822$	−19.3330	+	46.6741i	−0.674317	+	1.62795i
$823$	−18.1724	−	7.52726i	−0.633451	−	0.262384i	0.0427676	−	0.999085i	$-0.486382\pi$
$823$	−18.1724	−	7.52726i	−0.633451	−	0.262384i	−0.676219	+	0.736701i	$0.736382\pi$
$824$	−22.8784	+	22.8784i	−0.797007	+	0.797007i
$825$	4.46625	−	4.46625i	0.155495	−	0.155495i
$826$		0			0
$827$	2.36013	−	5.69786i	0.0820698	−	0.198134i	−0.877518	−	0.479544i	$-0.840802\pi$
$827$	2.36013	−	5.69786i	0.0820698	−	0.198134i	0.959588	+	0.281410i	$0.0908021\pi$
$828$	−2.52328	+	1.04518i	−0.0876900	+	0.0363224i
$829$			22.0937i			0.767348i	0.923469	+	0.383674i	$0.125341\pi$
$829$			22.0937i			0.767348i	−0.923469	+	0.383674i	$0.874659\pi$
$830$	−18.9886	−	45.8425i	−0.659103	−	1.59122i
$831$	−19.1135	−	19.1135i	−0.663039	−	0.663039i
$832$	−51.6751			−1.79151
$833$		0			0
$834$	53.5890			1.85564
$835$	10.2417	+	10.2417i	0.354430	+	0.354430i
$836$	−17.0186	−	41.0866i	−0.588602	−	1.42101i
$837$			11.3665i			0.392885i
$838$	−19.4202	+	8.04412i	−0.670861	+	0.277880i
$839$	0.717533	−	1.73228i	0.0247720	−	0.0598049i	−0.911009	−	0.412385i	$-0.864696\pi$
$839$	0.717533	−	1.73228i	0.0247720	−	0.0598049i	0.935781	+	0.352580i	$0.114696\pi$
$840$		0			0
$841$	−19.7646	+	19.7646i	−0.681538	+	0.681538i
$842$	−3.85938	+	3.85938i	−0.133003	+	0.133003i
$843$	−7.03235	−	2.91289i	−0.242207	−	0.100325i
$844$	−11.3030	+	27.2878i	−0.389065	+	0.939286i
$845$	−4.99765	+	2.07009i	−0.171924	+	0.0712134i
$846$		−	2.67646i		−	0.0920187i
$847$		0			0
$848$	0.133054	+	0.133054i	0.00456909	+	0.00456909i
$849$	22.2695			0.764289
$850$	12.8183	−	4.61089i	0.439665	−	0.158152i
$851$	−1.52002			−0.0521055
$852$	46.4118	+	46.4118i	1.59004	+	1.59004i
$853$	−3.25322	−	7.85396i	−0.111388	−	0.268915i	0.858349	−	0.513066i	$-0.171491\pi$
$853$	−3.25322	−	7.85396i	−0.111388	−	0.268915i	−0.969737	+	0.244152i	$0.921491\pi$
$854$		0			0
$855$	1.42331	−	0.589553i	0.0486761	−	0.0201623i
$856$	−5.22409	+	12.6121i	−0.178556	+	0.431072i
$857$	30.0752	+	12.4575i	1.02735	+	0.425542i	0.831755	−	0.555143i	$-0.187337\pi$
$857$	30.0752	+	12.4575i	1.02735	+	0.425542i	0.195594	+	0.980685i	$0.437337\pi$
$858$	−28.0927	+	28.0927i	−0.959067	+	0.959067i
$859$	−30.4622	+	30.4622i	−1.03936	+	1.03936i	−0.0401650	+	0.999193i	$0.512788\pi$
$859$	−30.4622	+	30.4622i	−1.03936	+	1.03936i	−0.999193	+	0.0401650i	$0.987212\pi$
$860$	54.5237	+	22.5845i	1.85924	+	0.770124i
$861$		0			0
$862$	−29.0126	+	12.0174i	−0.988173	+	0.409315i
$863$			26.9501i			0.917393i	0.888593	+	0.458696i	$0.151683\pi$
$863$			26.9501i			0.917393i	−0.888593	+	0.458696i	$0.848317\pi$
$864$	11.1494	+	26.9170i	0.379309	+	0.915733i
$865$	−14.9945	−	14.9945i	−0.509827	−	0.509827i
$866$	−7.80735			−0.265304
$867$	−26.6383	−	14.1230i	−0.904684	−	0.479644i
$868$		0			0
$869$	5.26400	+	5.26400i	0.178569	+	0.178569i
$870$	−2.99244	−	7.22438i	−0.101453	−	0.244930i
$871$			54.3624i			1.84200i
$872$	−44.7951	+	18.5547i	−1.51695	+	0.628342i
$873$	−0.176128	+	0.425212i	−0.00596104	+	0.0143912i
$874$	69.1333	+	28.6360i	2.33847	+	0.968625i
$875$		0			0
$876$	−15.1840	+	15.1840i	−0.513019	+	0.513019i
$877$	−23.9890	−	9.93659i	−0.810052	−	0.335535i	−0.0610774	−	0.998133i	$-0.519454\pi$
$877$	−23.9890	−	9.93659i	−0.810052	−	0.335535i	−0.748975	+	0.662598i	$0.769454\pi$
$878$	−17.6096	+	42.5134i	−0.594296	+	1.43476i
$879$	48.4127	−	20.0532i	1.63292	−	0.676377i
$880$		−	0.400338i		−	0.0134954i
$881$	−19.8613	−	47.9494i	−0.669143	−	1.61545i	−0.783047	−	0.621963i	$-0.786335\pi$
$881$	−19.8613	−	47.9494i	−0.669143	−	1.61545i	0.113903	−	0.993492i	$-0.463665\pi$
$882$		0			0
$883$	−33.2783			−1.11990			−0.559951	−	0.828525i	$-0.689180\pi$
$883$	−33.2783			−1.11990			−0.559951	+	0.828525i	$0.689180\pi$
$884$	−49.7159	+	17.8834i	−1.67213	+	0.601482i
$885$	25.0363			0.841588
$886$	32.1016	+	32.1016i	1.07848	+	1.07848i
$887$	4.60001	+	11.1054i	0.154453	+	0.372883i	0.982098	−	0.188369i	$-0.0603200\pi$
$887$	4.60001	+	11.1054i	0.154453	+	0.372883i	−0.827645	+	0.561252i	$0.810320\pi$
$888$			1.28409i			0.0430914i
$889$		0			0
$890$	13.9584	−	33.6986i	0.467888	−	1.12958i
$891$	21.4158	+	8.87072i	0.717457	+	0.297180i
$892$	−53.5851	+	53.5851i	−1.79416	+	1.79416i
$893$	−31.9730	+	31.9730i	−1.06993	+	1.06993i
$894$	−38.2459	−	15.8420i	−1.27913	−	0.529835i
$895$	4.62295	−	11.1608i	0.154528	−	0.373064i
$896$		0			0
$897$		−	41.2201i		−	1.37630i
$898$	−34.2415	−	82.6664i	−1.14266	−	2.75861i
$899$	1.62576	+	1.62576i	0.0542220	+	0.0542220i
$900$	0.677178			0.0225726
$901$	8.13680	+	3.83163i	0.271076	+	0.127650i
$902$	42.4246			1.41259
$903$		0			0
$904$	−20.6212	−	49.7839i	−0.685850	−	1.65579i
$905$		−	21.3978i		−	0.711286i
$906$	80.1338	−	33.1925i	2.66227	−	1.10275i
$907$	1.51367	−	3.65433i	0.0502607	−	0.121340i	−0.896755	−	0.442527i	$-0.854082\pi$
$907$	1.51367	−	3.65433i	0.0502607	−	0.121340i	0.947016	+	0.321187i	$0.104082\pi$
$908$	73.8732	+	30.5993i	2.45157	+	1.01547i
$909$	−1.37041	+	1.37041i	−0.0454537	+	0.0454537i
$910$		0			0
$911$	23.3809	+	9.68468i	0.774644	+	0.320868i	0.734752	−	0.678336i	$-0.237299\pi$
$911$	23.3809	+	9.68468i	0.774644	+	0.320868i	0.0398919	+	0.999204i	$0.487299\pi$
$912$	−0.328780	+	0.793744i	−0.0108870	+	0.0262835i
$913$	26.2135	−	10.8580i	0.867540	−	0.359347i
$914$			41.0042i			1.35630i
$915$	18.0905	+	43.6742i	0.598052	+	1.44383i
$916$	−12.0444	−	12.0444i	−0.397957	−	0.397957i
$917$		0			0
$918$	32.0764	+	35.2710i	1.05868	+	1.16412i
$919$	18.6523			0.615284			0.307642	−	0.951502i	$-0.400460\pi$
$919$	18.6523			0.615284			0.307642	+	0.951502i	$0.400460\pi$
$920$	−21.6107	−	21.6107i	−0.712483	−	0.712483i
$921$	−8.54034	−	20.6182i	−0.281414	−	0.679393i
$922$			44.2054i			1.45583i
$923$	−42.3433	+	17.5392i	−1.39375	+	0.577309i
$924$		0			0
$925$	0.348190	+	0.144225i	0.0114484	+	0.00474210i
$926$	−31.3139	+	31.3139i	−1.02904	+	1.02904i
$927$	1.19814	−	1.19814i	0.0393521	−	0.0393521i
$928$	5.44464	+	2.25524i	0.178729	+	0.0740320i
$929$	−6.20422	+	14.9783i	−0.203554	+	0.491423i	−0.992383	−	0.123190i	$-0.960688\pi$
$929$	−6.20422	+	14.9783i	−0.203554	+	0.491423i	0.788829	+	0.614612i	$0.210688\pi$
$930$	15.8395	−	6.56093i	0.519398	−	0.215141i
$931$		0			0
$932$	21.3367	+	51.5113i	0.698906	+	1.68731i
$933$	9.50093	+	9.50093i	0.311046	+	0.311046i
$934$	−49.4057			−1.61660
$935$	−6.47680	−	18.0056i	−0.211814	−	0.588846i
$936$	−1.61111			−0.0526607
$937$	30.4579	+	30.4579i	0.995018	+	0.995018i	0.999988	−	0.00497011i	$-0.00158204\pi$
$937$	30.4579	+	30.4579i	0.995018	+	0.995018i	−0.00497011	+	0.999988i	$0.501582\pi$
$938$		0			0
$939$		−	24.5272i		−	0.800414i
$940$	45.1079	−	18.6843i	1.47126	−	0.609415i
$941$	−1.35319	+	3.26689i	−0.0441127	+	0.106497i	−0.944400	−	0.328799i	$-0.893356\pi$
$941$	−1.35319	+	3.26689i	−0.0441127	+	0.106497i	0.900287	+	0.435296i	$0.143356\pi$
$942$	31.7677	+	13.1586i	1.03505	+	0.428731i
$943$	−31.1246	+	31.1246i	−1.01356	+	1.01356i
$944$	−0.456778	+	0.456778i	−0.0148669	+	0.0148669i
$945$		0			0
$946$	−20.9436	+	50.5623i	−0.680935	+	1.64392i
$947$	−16.0014	+	6.62800i	−0.519976	+	0.215381i	−0.627206	−	0.778853i	$-0.715802\pi$
$947$	−16.0014	+	6.62800i	−0.519976	+	0.215381i	0.107230	+	0.994234i	$0.465802\pi$
$948$			17.2508i			0.560279i
$949$	−5.73807	−	13.8529i	−0.186266	−	0.449685i
$950$	−13.1193	−	13.1193i	−0.425646	−	0.425646i
$951$	19.1697			0.621621
$952$		0			0
$953$	−12.5597			−0.406849			−0.203425	−	0.979091i	$-0.565207\pi$
$953$	−12.5597			−0.406849			−0.203425	+	0.979091i	$0.565207\pi$
$954$	0.512701	+	0.512701i	0.0165993	+	0.0165993i
$955$	−6.80309	−	16.4241i	−0.220143	−	0.531472i
$956$		−	15.2272i		−	0.492484i
$957$	4.13102	−	1.71112i	0.133537	−	0.0553128i
$958$	2.48471	−	5.99861i	0.0802772	−	0.193806i
$959$		0			0
$960$	30.6659	−	30.6659i	0.989738	−	0.989738i
$961$	18.3558	−	18.3558i	0.592124	−	0.592124i
$962$	−2.19011	−	0.907174i	−0.0706121	−	0.0292485i
$963$	0.273586	−	0.660494i	0.00881617	−	0.0212841i
$964$	1.34365	−	0.556559i	0.0432761	−	0.0179255i
$965$			27.1663i			0.874513i
$966$		0			0
$967$	6.47092	+	6.47092i	0.208091	+	0.208091i	0.803456	−	0.595365i	$-0.202992\pi$
$967$	6.47092	+	6.47092i	0.208091	+	0.208091i	−0.595365	+	0.803456i	$0.702992\pi$
$968$	13.7246			0.441126
$969$	−1.94571	+	41.0185i	−0.0625052	+	1.31770i
$970$	−13.6161			−0.437185
$971$	0.723980	+	0.723980i	0.0232336	+	0.0232336i	0.718628	−	0.695395i	$-0.244770\pi$
$971$	0.723980	+	0.723980i	0.0232336	+	0.0232336i	−0.695395	+	0.718628i	$0.744770\pi$
$972$	1.86014	+	4.49078i	0.0596640	+	0.144042i
$973$		0			0
$974$	7.15375	−	2.96318i	0.229221	−	0.0949465i
$975$	−3.91112	+	9.44229i	−0.125256	+	0.302395i
$976$	−1.12687	−	0.466766i	−0.0360703	−	0.0149408i
$977$	−9.46628	+	9.46628i	−0.302853	+	0.302853i	−0.842129	−	0.539276i	$-0.818698\pi$
$977$	−9.46628	+	9.46628i	−0.302853	+	0.302853i	0.539276	+	0.842129i	$0.318698\pi$
$978$	−4.93860	+	4.93860i	−0.157919	+	0.157919i
$979$	19.2694	+	7.98166i	0.615853	+	0.255095i
$980$		0			0
$981$	2.34591	−	0.971710i	0.0748993	−	0.0310243i
$982$			61.0872i			1.94937i
$983$	−2.73573	−	6.60463i	−0.0872561	−	0.210655i	0.874228	−	0.485516i	$-0.161368\pi$
$983$	−2.73573	−	6.60463i	−0.0872561	−	0.210655i	−0.961484	+	0.274861i	$0.911368\pi$
$984$	26.2937	+	26.2937i	0.838214	+	0.838214i
$985$	−31.2361			−0.995263
$986$	9.63273	+	0.456928i	0.306769	+	0.0145516i
$987$		0			0
$988$	50.8832	+	50.8832i	1.61881	+	1.61881i
$989$	−21.7296	−	52.4600i	−0.690962	−	1.66813i
$990$		−	1.54264i		−	0.0490283i
$991$	5.74483	−	2.37959i	0.182491	−	0.0755901i	−0.289567	−	0.957158i	$-0.593511\pi$
$991$	5.74483	−	2.37959i	0.182491	−	0.0755901i	0.472058	+	0.881568i	$0.343511\pi$
$992$	−4.94463	+	11.9374i	−0.156992	+	0.379013i
$993$	−18.0726	−	7.48591i	−0.573516	−	0.237558i
$994$		0			0
$995$	−23.5597	+	23.5597i	−0.746893	+	0.746893i
$996$	60.7438	+	25.1609i	1.92474	+	0.797254i
$997$	10.6986	−	25.8287i	0.338828	−	0.818003i	−0.659001	−	0.752142i	$-0.729021\pi$
$997$	10.6986	−	25.8287i	0.338828	−	0.818003i	0.997829	−	0.0658608i	$-0.0209793\pi$
$998$	64.1848	−	26.5862i	2.03173	−	0.841571i
$999$			1.31899i			0.0417311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.l.b.491.1	yes	32
7.2	even	3		833.2.v.d.508.2		64
7.3	odd	6		833.2.v.d.814.8		64
7.4	even	3		833.2.v.d.814.7		64
7.5	odd	6		833.2.v.d.508.1		64
7.6	odd	2	inner	833.2.l.b.491.2	yes	32
17.8	even	8	inner	833.2.l.b.246.1	✓	32
119.25	even	24		833.2.v.d.569.2		64
119.59	odd	24		833.2.v.d.569.1		64
119.76	odd	8	inner	833.2.l.b.246.2	yes	32
119.93	even	24		833.2.v.d.263.7		64
119.110	odd	24		833.2.v.d.263.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.l.b.246.1	✓	32	17.8	even	8	inner
833.2.l.b.246.2	yes	32	119.76	odd	8	inner
833.2.l.b.491.1	yes	32	1.1	even	1	trivial
833.2.l.b.491.2	yes	32	7.6	odd	2	inner
833.2.v.d.263.7		64	119.93	even	24
833.2.v.d.263.8		64	119.110	odd	24
833.2.v.d.508.1		64	7.5	odd	6
833.2.v.d.508.2		64	7.2	even	3
833.2.v.d.569.1		64	119.59	odd	24
833.2.v.d.569.2		64	119.25	even	24
833.2.v.d.814.7		64	7.4	even	3
833.2.v.d.814.8		64	7.3	odd	6

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61504 - 1.61504i) q^{2} +(-0.678714 - 1.63856i) q^{3} +3.21670i q^{4} +(1.74157 - 0.721382i) q^{5} +(-1.55019 + 3.74249i) q^{6} +(1.96501 - 1.96501i) q^{8} +(-0.102907 + 0.102907i) q^{9} +O(q^{10})\)	\(q+(-1.61504 - 1.61504i) q^{2} +(-0.678714 - 1.63856i) q^{3} +3.21670i q^{4} +(1.74157 - 0.721382i) q^{5} +(-1.55019 + 3.74249i) q^{6} +(1.96501 - 1.96501i) q^{8} +(-0.102907 + 0.102907i) q^{9} +(-3.97776 - 1.64764i) q^{10} +(0.942148 - 2.27455i) q^{11} +(5.27075 - 2.18322i) q^{12} +3.98367i q^{13} +(-2.36406 - 2.36406i) q^{15} +0.0862625 q^{16} +(3.87974 - 1.39558i) q^{17} +0.332399 q^{18} +(-3.97083 - 3.97083i) q^{19} +(2.32047 + 5.60210i) q^{20} +(-5.19508 + 2.15187i) q^{22} +(2.23264 - 5.39006i) q^{23} +(-4.55346 - 1.88611i) q^{24} +(-1.02286 + 1.02286i) q^{25} +(6.43378 - 6.43378i) q^{26} +(-4.67722 - 1.93737i) q^{27} +(-0.946086 + 0.391882i) q^{29} +7.63608i q^{30} +(-0.859202 - 2.07430i) q^{31} +(-4.06934 - 4.06934i) q^{32} -4.36643 q^{33} +(-8.51984 - 4.01200i) q^{34} +(-0.331022 - 0.331022i) q^{36} +(-0.0997033 - 0.240705i) q^{37} +12.8261i q^{38} +(6.52748 - 2.70377i) q^{39} +(2.00468 - 4.83972i) q^{40} +(-6.97038 - 2.88722i) q^{41} +(6.88208 - 6.88208i) q^{43} +(7.31652 + 3.03060i) q^{44} +(-0.104985 + 0.253456i) q^{45} +(-12.3109 + 5.09936i) q^{46} -8.05197i q^{47} +(-0.0585476 - 0.141346i) q^{48} +3.30392 q^{50} +(-4.91998 - 5.40998i) q^{51} -12.8143 q^{52} +(1.54243 + 1.54243i) q^{53} +(4.42496 + 10.6828i) q^{54} -4.64093i q^{55} +(-3.81138 + 9.20149i) q^{57} +(2.16087 + 0.895061i) q^{58} +(-5.29521 + 5.29521i) q^{59} +(7.60445 - 7.60445i) q^{60} +(-13.0633 - 5.41099i) q^{61} +(-1.96242 + 4.73771i) q^{62} +12.9717i q^{64} +(2.87375 + 6.93784i) q^{65} +(7.05195 + 7.05195i) q^{66} +13.6463 q^{67} +(4.48917 + 12.4799i) q^{68} -10.3473 q^{69} +(4.40277 + 10.6292i) q^{71} +0.404428i q^{72} +(-3.47743 + 1.44040i) q^{73} +(-0.227723 + 0.549773i) q^{74} +(2.37025 + 0.981789i) q^{75} +(12.7729 - 12.7729i) q^{76} +(-14.9088 - 6.17544i) q^{78} +(-1.15715 + 2.79362i) q^{79} +(0.150232 - 0.0622282i) q^{80} +9.41542i q^{81} +(6.59444 + 15.9204i) q^{82} +(8.14920 + 8.14920i) q^{83} +(5.75008 - 5.22928i) q^{85} -22.2296 q^{86} +(1.28424 + 1.28424i) q^{87} +(-2.61818 - 6.32083i) q^{88} +8.47176i q^{89} +(0.578896 - 0.239786i) q^{90} +(17.3382 + 7.18171i) q^{92} +(-2.81571 + 2.81571i) q^{93} +(-13.0042 + 13.0042i) q^{94} +(-9.77995 - 4.05099i) q^{95} +(-3.90594 + 9.42977i) q^{96} +(2.92175 - 1.21023i) q^{97} +(0.137114 + 0.331022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 24 q^{9}+O(q^{10}) \) 32 * q + 24 * q^9	\( 32 q + 24 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 24 q^{18} + 8 q^{23} + 8 q^{25} - 16 q^{29} - 40 q^{32} - 8 q^{36} - 8 q^{37} + 8 q^{39} - 24 q^{43} + 64 q^{44} - 80 q^{46} + 16 q^{50} + 8 q^{51} + 32 q^{53} - 8 q^{57} - 104 q^{58} + 152 q^{60} - 64 q^{65} + 96 q^{67} - 48 q^{71} - 24 q^{74} - 136 q^{78} - 80 q^{79} + 72 q^{85} - 72 q^{86} + 56 q^{88} + 8 q^{92} - 48 q^{93} - 32 q^{95} + 8 q^{99}+O(q^{100}) \) 32 * q + 24 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 24 * q^18 + 8 * q^23 + 8 * q^25 - 16 * q^29 - 40 * q^32 - 8 * q^36 - 8 * q^37 + 8 * q^39 - 24 * q^43 + 64 * q^44 - 80 * q^46 + 16 * q^50 + 8 * q^51 + 32 * q^53 - 8 * q^57 - 104 * q^58 + 152 * q^60 - 64 * q^65 + 96 * q^67 - 48 * q^71 - 24 * q^74 - 136 * q^78 - 80 * q^79 + 72 * q^85 - 72 * q^86 + 56 * q^88 + 8 * q^92 - 48 * q^93 - 32 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more