LMFDB - Embedded newform 195.2.k.a.148.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(112,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.112"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			148.3
Character	$\chi$	$=$	195.148
Dual form			195.2.k.a.112.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.97160i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.88719 q^{4} +(0.644677 - 2.14112i) q^{5} +(-1.39413 + 1.39413i) q^{6} -0.616758 q^{7} -0.222418i q^{8} +1.00000i q^{9} +(-4.22142 - 1.27104i) q^{10} +(1.14213 + 1.14213i) q^{11} +(1.33444 + 1.33444i) q^{12} +(-3.56264 - 0.554621i) q^{13} +1.21600i q^{14} +(-1.96986 + 1.05814i) q^{15} -4.21290 q^{16} +(0.816014 + 0.816014i) q^{17} +1.97160 q^{18} +(4.26977 + 4.26977i) q^{19} +(-1.21663 + 4.04070i) q^{20} +(0.436114 + 0.436114i) q^{21} +(2.25182 - 2.25182i) q^{22} +(5.27080 - 5.27080i) q^{23} +(-0.157273 + 0.157273i) q^{24} +(-4.16878 - 2.76066i) q^{25} +(-1.09349 + 7.02408i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.16394 q^{28} -2.25597i q^{29} +(2.08623 + 3.88376i) q^{30} +(4.04241 - 4.04241i) q^{31} +7.86129i q^{32} -1.61522i q^{33} +(1.60885 - 1.60885i) q^{34} +(-0.397610 + 1.32055i) q^{35} -1.88719i q^{36} +3.21038 q^{37} +(8.41825 - 8.41825i) q^{38} +(2.12699 + 2.91134i) q^{39} +(-0.476223 - 0.143388i) q^{40} +(-1.89994 + 1.89994i) q^{41} +(0.859840 - 0.859840i) q^{42} +(0.687115 - 0.687115i) q^{43} +(-2.15542 - 2.15542i) q^{44} +(2.14112 + 0.644677i) q^{45} +(-10.3919 - 10.3919i) q^{46} +9.07993 q^{47} +(2.97897 + 2.97897i) q^{48} -6.61961 q^{49} +(-5.44291 + 8.21915i) q^{50} -1.15402i q^{51} +(6.72337 + 1.04667i) q^{52} +(-2.76736 - 2.76736i) q^{53} +(-1.39413 - 1.39413i) q^{54} +(3.18175 - 1.70913i) q^{55} +0.137178i q^{56} -6.03836i q^{57} -4.44785 q^{58} +(4.05498 - 4.05498i) q^{59} +(3.71749 - 1.99692i) q^{60} +12.5604 q^{61} +(-7.97000 - 7.97000i) q^{62} -0.616758i q^{63} +7.07349 q^{64} +(-3.48426 + 7.27048i) q^{65} -3.18456 q^{66} -1.67100i q^{67} +(-1.53997 - 1.53997i) q^{68} -7.45404 q^{69} +(2.60360 + 0.783926i) q^{70} +(-2.76337 + 2.76337i) q^{71} +0.222418 q^{72} +15.5003i q^{73} -6.32956i q^{74} +(0.995692 + 4.89986i) q^{75} +(-8.05786 - 8.05786i) q^{76} +(-0.704419 - 0.704419i) q^{77} +(5.73999 - 4.19356i) q^{78} +15.4528i q^{79} +(-2.71596 + 9.02031i) q^{80} -1.00000 q^{81} +(3.74591 + 3.74591i) q^{82} -4.88302 q^{83} +(-0.823029 - 0.823029i) q^{84} +(2.27325 - 1.22112i) q^{85} +(-1.35471 - 1.35471i) q^{86} +(-1.59521 + 1.59521i) q^{87} +(0.254031 - 0.254031i) q^{88} +(-7.34335 + 7.34335i) q^{89} +(1.27104 - 4.22142i) q^{90} +(2.19729 + 0.342067i) q^{91} +(-9.94700 + 9.94700i) q^{92} -5.71683 q^{93} -17.9019i q^{94} +(11.8947 - 6.38946i) q^{95} +(5.55877 - 5.55877i) q^{96} +13.3663i q^{97} +13.0512i q^{98} +(-1.14213 + 1.14213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40}+ \cdots + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.97160i		−	1.39413i	−0.717009	−	0.697064i	$-0.754489\pi$
$2$		−	1.97160i		−	1.39413i	0.717009	−	0.697064i	$-0.245511\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.88719			−0.943594
$5$	0.644677	−	2.14112i	0.288308	−	0.957538i
$5$	0.644677	−	2.14112i	0.288308	−	0.957538i
$6$	−1.39413	+	1.39413i	−0.569151	+	0.569151i
$7$	−0.616758			−0.233113			−0.116556	−	0.993184i	$-0.537186\pi$
$7$	−0.616758			−0.233113			−0.116556	+	0.993184i	$0.537186\pi$
$8$		−	0.222418i		−	0.0786366i
$9$			1.00000i			0.333333i
$10$	−4.22142	−	1.27104i	−1.33493	−	0.401939i
$11$	1.14213	+	1.14213i	0.344366	+	0.344366i	0.858006	−	0.513640i	$-0.171703\pi$
$11$	1.14213	+	1.14213i	0.344366	+	0.344366i	−0.513640	+	0.858006i	$0.671703\pi$
$12$	1.33444	+	1.33444i	0.385221	+	0.385221i
$13$	−3.56264	−	0.554621i	−0.988098	−	0.153824i
$13$	−3.56264	−	0.554621i	−0.988098	−	0.153824i
$14$			1.21600i			0.324989i
$15$	−1.96986	+	1.05814i	−0.508615	+	0.273212i
$16$	−4.21290			−1.05322
$17$	0.816014	+	0.816014i	0.197912	+	0.197912i	0.799105	−	0.601192i	$-0.205307\pi$
$17$	0.816014	+	0.816014i	0.197912	+	0.197912i	−0.601192	+	0.799105i	$0.705307\pi$
$18$	1.97160			0.464710
$19$	4.26977	+	4.26977i	0.979552	+	0.979552i	0.999795	−	0.0202433i	$-0.00644408\pi$
$19$	4.26977	+	4.26977i	0.979552	+	0.979552i	−0.0202433	+	0.999795i	$0.506444\pi$
$20$	−1.21663	+	4.04070i	−0.272046	+	0.903527i
$21$	0.436114	+	0.436114i	0.0951678	+	0.0951678i
$22$	2.25182	−	2.25182i	0.480090	−	0.480090i
$23$	5.27080	−	5.27080i	1.09904	−	1.09904i	0.104516	−	0.994523i	$-0.466671\pi$
$23$	5.27080	−	5.27080i	1.09904	−	1.09904i	0.994523	−	0.104516i	$-0.0333292\pi$
$24$	−0.157273	+	0.157273i	−0.0321033	+	0.0321033i
$25$	−4.16878	−	2.76066i	−0.833757	−	0.552132i
$26$	−1.09349	+	7.02408i	−0.214451	+	1.37754i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.16394			0.219964
$29$		−	2.25597i		−	0.418923i	−0.977817	−	0.209461i	$-0.932829\pi$
$29$		−	2.25597i		−	0.418923i	0.977817	−	0.209461i	$-0.0671710\pi$
$30$	2.08623	+	3.88376i	0.380892	+	0.709074i
$31$	4.04241	−	4.04241i	0.726038	−	0.726038i	−0.243790	−	0.969828i	$-0.578391\pi$
$31$	4.04241	−	4.04241i	0.726038	−	0.726038i	0.969828	+	0.243790i	$0.0783907\pi$
$32$			7.86129i			1.38969i
$33$		−	1.61522i		−	0.281173i
$34$	1.60885	−	1.60885i	0.275915	−	0.275915i
$35$	−0.397610	+	1.32055i	−0.0672083	+	0.223214i
$36$		−	1.88719i		−	0.314531i
$37$	3.21038			0.527783			0.263891	−	0.964552i	$-0.414994\pi$
$37$	3.21038			0.527783			0.263891	+	0.964552i	$0.414994\pi$
$38$	8.41825	−	8.41825i	1.36562	−	1.36562i
$39$	2.12699	+	2.91134i	0.340591	+	0.466188i
$40$	−0.476223	−	0.143388i	−0.0752975	−	0.0226716i
$41$	−1.89994	+	1.89994i	−0.296721	+	0.296721i	−0.839728	−	0.543007i	$-0.817286\pi$
$41$	−1.89994	+	1.89994i	−0.296721	+	0.296721i	0.543007	+	0.839728i	$0.317286\pi$
$42$	0.859840	−	0.859840i	0.132676	−	0.132676i
$43$	0.687115	−	0.687115i	0.104784	−	0.104784i	−0.652771	−	0.757555i	$-0.726394\pi$
$43$	0.687115	−	0.687115i	0.104784	−	0.104784i	0.757555	+	0.652771i	$0.226394\pi$
$44$	−2.15542	−	2.15542i	−0.324941	−	0.324941i
$45$	2.14112	+	0.644677i	0.319179	+	0.0961028i
$46$	−10.3919	−	10.3919i	−1.53220	−	1.53220i
$47$	9.07993			1.32444			0.662222	−	0.749308i	$-0.269614\pi$
$47$	9.07993			1.32444			0.662222	+	0.749308i	$0.269614\pi$
$48$	2.97897	+	2.97897i	0.429977	+	0.429977i
$49$	−6.61961			−0.945659
$50$	−5.44291	+	8.21915i	−0.769743	+	1.16236i
$51$		−	1.15402i		−	0.161595i
$52$	6.72337	+	1.04667i	0.932364	+	0.145148i
$53$	−2.76736	−	2.76736i	−0.380127	−	0.380127i	0.491021	−	0.871148i	$-0.336624\pi$
$53$	−2.76736	−	2.76736i	−0.380127	−	0.380127i	−0.871148	+	0.491021i	$0.836624\pi$
$54$	−1.39413	−	1.39413i	−0.189717	−	0.189717i
$55$	3.18175	−	1.70913i	0.429026	−	0.230460i
$56$			0.137178i			0.0183312i
$57$		−	6.03836i		−	0.799801i
$58$	−4.44785			−0.584032
$59$	4.05498	−	4.05498i	0.527913	−	0.527913i	−0.392037	−	0.919950i	$-0.628229\pi$
$59$	4.05498	−	4.05498i	0.527913	−	0.527913i	0.919950	+	0.392037i	$0.128229\pi$
$60$	3.71749	−	1.99692i	0.479926	−	0.257801i
$61$	12.5604			1.60819			0.804094	−	0.594502i	$-0.202651\pi$
$61$	12.5604			1.60819			0.804094	+	0.594502i	$0.202651\pi$
$62$	−7.97000	−	7.97000i	−1.01219	−	1.01219i
$63$		−	0.616758i		−	0.0777042i
$64$	7.07349			0.884187
$65$	−3.48426	+	7.27048i	−0.432169	+	0.901792i
$66$	−3.18456			−0.391992
$67$		−	1.67100i		−	0.204145i	−0.994777	−	0.102073i	$-0.967453\pi$
$67$		−	1.67100i		−	0.204145i	0.994777	−	0.102073i	$-0.0325474\pi$
$68$	−1.53997	−	1.53997i	−0.186749	−	0.186749i
$69$	−7.45404			−0.897361
$70$	2.60360	+	0.783926i	0.311189	+	0.0936970i
$71$	−2.76337	+	2.76337i	−0.327952	+	0.327952i	−0.851807	−	0.523856i	$-0.824493\pi$
$71$	−2.76337	+	2.76337i	−0.327952	+	0.327952i	0.523856	+	0.851807i	$0.324493\pi$
$72$	0.222418			0.0262122
$73$			15.5003i			1.81417i	0.420945	+	0.907086i	$0.361699\pi$
$73$			15.5003i			1.81417i	−0.420945	+	0.907086i	$0.638301\pi$
$74$		−	6.32956i		−	0.735797i
$75$	0.995692	+	4.89986i	0.114973	+	0.565787i
$76$	−8.05786	−	8.05786i	−0.924300	−	0.924300i
$77$	−0.704419	−	0.704419i	−0.0802760	−	0.0802760i
$78$	5.73999	−	4.19356i	0.649926	−	0.474828i
$79$			15.4528i			1.73858i	0.494306	+	0.869288i	$0.335422\pi$
$79$			15.4528i			1.73858i	−0.494306	+	0.869288i	$0.664578\pi$
$80$	−2.71596	+	9.02031i	−0.303653	+	1.00850i
$81$	−1.00000			−0.111111
$82$	3.74591	+	3.74591i	0.413667	+	0.413667i
$83$	−4.88302			−0.535981			−0.267990	−	0.963422i	$-0.586360\pi$
$83$	−4.88302			−0.535981			−0.267990	+	0.963422i	$0.586360\pi$
$84$	−0.823029	−	0.823029i	−0.0897998	−	0.0897998i
$85$	2.27325	−	1.22112i	0.246568	−	0.132449i
$86$	−1.35471	−	1.35471i	−0.146082	−	0.146082i
$87$	−1.59521	+	1.59521i	−0.171024	+	0.171024i
$88$	0.254031	−	0.254031i	0.0270798	−	0.0270798i
$89$	−7.34335	+	7.34335i	−0.778394	+	0.778394i	−0.979558	−	0.201164i	$-0.935528\pi$
$89$	−7.34335	+	7.34335i	−0.778394	+	0.778394i	0.201164	+	0.979558i	$0.435528\pi$
$90$	1.27104	−	4.22142i	0.133980	−	0.444977i
$91$	2.19729	+	0.342067i	0.230338	+	0.0358583i
$92$	−9.94700	+	9.94700i	−1.03705	+	1.03705i
$93$	−5.71683			−0.592808
$94$		−	17.9019i		−	1.84644i
$95$	11.8947	−	6.38946i	1.22037	−	0.655545i
$96$	5.55877	−	5.55877i	0.567340	−	0.567340i
$97$			13.3663i			1.35715i	0.734533	+	0.678573i	$0.237401\pi$
$97$			13.3663i			1.35715i	−0.734533	+	0.678573i	$0.762599\pi$
$98$			13.0512i			1.31837i
$99$	−1.14213	+	1.14213i	−0.114789	+	0.114789i
$100$	7.86728	+	5.20989i	0.786728	+	0.520989i
$101$		−	7.85108i		−	0.781212i	−0.920558	−	0.390606i	$-0.872266\pi$
$101$		−	7.85108i		−	0.781212i	0.920558	−	0.390606i	$-0.127734\pi$
$102$	−2.27526			−0.225284
$103$	−11.7628	+	11.7628i	−1.15902	+	1.15902i	−0.174337	+	0.984686i	$0.555778\pi$
$103$	−11.7628	+	11.7628i	−1.15902	+	1.15902i	−0.984686	+	0.174337i	$0.944222\pi$
$104$	−0.123358	+	0.792395i	−0.0120962	+	0.0777007i
$105$	1.21492	−	0.652619i	0.118564	−	0.0636891i
$106$	−5.45612	+	5.45612i	−0.529945	+	0.529945i
$107$	−1.18744	+	1.18744i	−0.114794	+	0.114794i	−0.762171	−	0.647376i	$-0.775866\pi$
$107$	−1.18744	+	1.18744i	−0.114794	+	0.114794i	0.647376	+	0.762171i	$0.275866\pi$
$108$	−1.33444	+	1.33444i	−0.128407	+	0.128407i
$109$	4.90378	+	4.90378i	0.469697	+	0.469697i	0.901816	−	0.432120i	$-0.142234\pi$
$109$	4.90378	+	4.90378i	0.469697	+	0.469697i	−0.432120	+	0.901816i	$0.642234\pi$
$110$	−3.36972	−	6.27312i	−0.321290	−	0.598118i
$111$	−2.27008	−	2.27008i	−0.215466	−	0.215466i
$112$	2.59834			0.245520
$113$	−12.0427	−	12.0427i	−1.13288	−	1.13288i	−0.989695	−	0.143189i	$-0.954264\pi$
$113$	−12.0427	−	12.0427i	−1.13288	−	1.13288i	−0.143189	−	0.989695i	$-0.545736\pi$
$114$	−11.9052			−1.11502
$115$	−7.88745	−	14.6834i	−0.735509	−	1.36923i
$116$			4.25744i			0.395293i
$117$	0.554621	−	3.56264i	0.0512747	−	0.329366i
$118$	−7.99478	−	7.99478i	−0.735979	−	0.735979i
$119$	−0.503283	−	0.503283i	−0.0461359	−	0.0461359i
$120$	0.235350	+	0.438131i	0.0214844	+	0.0399957i
$121$		−	8.39107i		−	0.762825i
$122$		−	24.7639i		−	2.24202i
$123$	2.68692			0.242271
$124$	−7.62879	+	7.62879i	−0.685086	+	0.685086i
$125$	−8.59842	+	7.14613i	−0.769066	+	0.639169i
$126$	−1.21600			−0.108330
$127$	4.87707	+	4.87707i	0.432770	+	0.432770i	0.889569	−	0.456800i	$-0.151004\pi$
$127$	4.87707	+	4.87707i	0.432770	+	0.432770i	−0.456800	+	0.889569i	$0.651004\pi$
$128$			1.77651i			0.157023i
$129$	−0.971727			−0.0855558
$130$	14.3345	+	6.86955i	1.25721	+	0.602500i
$131$	22.3622			1.95380			0.976898	−	0.213705i	$-0.0685532\pi$
$131$	22.3622			1.95380			0.976898	+	0.213705i	$0.0685532\pi$
$132$			3.04822i			0.265314i
$133$	−2.63341	−	2.63341i	−0.228346	−	0.228346i
$134$	−3.29454			−0.284605
$135$	−1.05814	−	1.96986i	−0.0910706	−	0.169538i
$136$	0.181496	−	0.181496i	0.0155632	−	0.0155632i
$137$	0.867850			0.0741455			0.0370727	−	0.999313i	$-0.488197\pi$
$137$	0.867850			0.0741455			0.0370727	+	0.999313i	$0.488197\pi$
$138$			14.6964i			1.25104i
$139$		−	12.2315i		−	1.03746i	−0.854937	−	0.518732i	$-0.826404\pi$
$139$		−	12.2315i		−	1.03746i	0.854937	−	0.518732i	$-0.173596\pi$
$140$	0.750365	−	2.49213i	0.0634174	−	0.210624i
$141$	−6.42048	−	6.42048i	−0.540702	−	0.540702i
$142$	5.44825	+	5.44825i	0.457207	+	0.457207i
$143$	−3.43555	−	4.70245i	−0.287295	−	0.393239i
$144$		−	4.21290i		−	0.351075i
$145$	−4.83029	−	1.45437i	−0.401134	−	0.120779i
$146$	30.5603			2.52919
$147$	4.68077	+	4.68077i	0.386063	+	0.386063i
$148$	−6.05859			−0.498013
$149$	−0.122919	−	0.122919i	−0.0100699	−	0.0100699i	0.702054	−	0.712124i	$-0.252267\pi$
$149$	−0.122919	−	0.122919i	−0.0100699	−	0.0100699i	−0.712124	+	0.702054i	$0.752267\pi$
$150$	9.66054	−	1.96310i	0.788779	−	0.160287i
$151$	−3.40378	−	3.40378i	−0.276996	−	0.276996i	0.554913	−	0.831908i	$-0.312752\pi$
$151$	−3.40378	−	3.40378i	−0.276996	−	0.276996i	−0.831908	+	0.554913i	$0.812752\pi$
$152$	0.949673	−	0.949673i	0.0770287	−	0.0770287i
$153$	−0.816014	+	0.816014i	−0.0659708	+	0.0659708i
$154$	−1.38883	+	1.38883i	−0.111915	+	0.111915i
$155$	−6.04923	−	11.2613i	−0.485886	−	0.904532i
$156$	−4.01403	−	5.49425i	−0.321380	−	0.439892i
$157$	−4.75071	+	4.75071i	−0.379148	+	0.379148i	−0.870795	−	0.491647i	$-0.836395\pi$
$157$	−4.75071	+	4.75071i	−0.379148	+	0.379148i	0.491647	+	0.870795i	$0.336395\pi$
$158$	30.4667			2.42380
$159$			3.91364i			0.310372i
$160$	16.8320	+	5.06799i	1.33068	+	0.400660i
$161$	−3.25081	+	3.25081i	−0.256200	+	0.256200i
$162$			1.97160i			0.154903i
$163$		−	0.624871i		−	0.0489437i	−0.999701	−	0.0244719i	$-0.992210\pi$
$163$		−	0.624871i		−	0.0489437i	0.999701	−	0.0244719i	$-0.00779041\pi$
$164$	3.58554	−	3.58554i	0.279984	−	0.279984i
$165$	−3.45837	−	1.04129i	−0.269234	−	0.0810646i
$166$			9.62734i			0.747226i
$167$	−15.2581			−1.18070			−0.590352	−	0.807146i	$-0.701011\pi$
$167$	−15.2581			−1.18070			−0.590352	+	0.807146i	$0.701011\pi$
$168$	0.0969996	−	0.0969996i	0.00748368	−	0.00748368i
$169$	12.3848	+	3.95183i	0.952676	+	0.303987i
$170$	−2.40755	−	4.48193i	−0.184651	−	0.343748i
$171$	−4.26977	+	4.26977i	−0.326517	+	0.326517i
$172$	−1.29672	+	1.29672i	−0.0988736	+	0.0988736i
$173$	6.24191	−	6.24191i	0.474564	−	0.474564i	−0.428824	−	0.903388i	$-0.641072\pi$
$173$	6.24191	−	6.24191i	0.474564	−	0.474564i	0.903388	+	0.428824i	$0.141072\pi$
$174$	3.14511	+	3.14511i	0.238430	+	0.238430i
$175$	2.57113	+	1.70266i	0.194359	+	0.128709i
$176$	−4.81168	−	4.81168i	−0.362694	−	0.362694i
$177$	−5.73460			−0.431039
$178$	14.4781	+	14.4781i	1.08518	+	1.08518i
$179$	9.48145			0.708677			0.354338	−	0.935117i	$-0.384706\pi$
$179$	9.48145			0.708677			0.354338	+	0.935117i	$0.384706\pi$
$180$	−4.04070	−	1.21663i	−0.301176	−	0.0906821i
$181$			13.2402i			0.984134i	0.870557	+	0.492067i	$0.163759\pi$
$181$			13.2402i			0.984134i	−0.870557	+	0.492067i	$0.836241\pi$
$182$	0.674417	−	4.33216i	0.0499911	−	0.321121i
$183$	−8.88151	−	8.88151i	−0.656540	−	0.656540i
$184$	−1.17232	−	1.17232i	−0.0864247	−	0.0864247i
$185$	2.06966	−	6.87380i	0.152164	−	0.505372i
$186$			11.2713i			0.826450i
$187$			1.86399i			0.136308i
$188$	−17.1355			−1.24974
$189$	−0.436114	+	0.436114i	−0.0317226	+	0.0317226i
$190$	−12.5974	−	23.4515i	−0.913914	−	1.70135i
$191$	−16.7819			−1.21430			−0.607149	−	0.794588i	$-0.707687\pi$
$191$	−16.7819			−1.21430			−0.607149	+	0.794588i	$0.707687\pi$
$192$	−5.00172	−	5.00172i	−0.360968	−	0.360968i
$193$		−	9.58754i		−	0.690126i	−0.938580	−	0.345063i	$-0.887858\pi$
$193$		−	9.58754i		−	0.690126i	0.938580	−	0.345063i	$-0.112142\pi$
$194$	26.3530			1.89204
$195$	7.60475	−	2.67726i	0.544588	−	0.191723i
$196$	12.4925			0.892318
$197$		−	12.3175i		−	0.877588i	−0.898588	−	0.438794i	$-0.855406\pi$
$197$		−	12.3175i		−	0.877588i	0.898588	−	0.438794i	$-0.144594\pi$
$198$	2.25182	+	2.25182i	0.160030	+	0.160030i
$199$	−1.71900			−0.121856			−0.0609282	−	0.998142i	$-0.519406\pi$
$199$	−1.71900			−0.121856			−0.0609282	+	0.998142i	$0.519406\pi$
$200$	−0.614021	+	0.927212i	−0.0434178	+	0.0655638i
$201$	−1.18158	+	1.18158i	−0.0833419	+	0.0833419i
$202$	−15.4792			−1.08911
$203$			1.39139i			0.0976561i
$204$			2.17785i			0.152480i
$205$	2.84315	+	5.29284i	0.198574	+	0.369668i
$206$	23.1915	+	23.1915i	1.61583	+	1.61583i
$207$	5.27080	+	5.27080i	0.366346	+	0.366346i
$208$	15.0090	+	2.33656i	1.04069	+	0.162011i
$209$			9.75327i			0.674648i
$210$	−1.28670	−	2.39534i	−0.0887908	−	0.165294i
$211$	1.43543			0.0988190			0.0494095	−	0.998779i	$-0.484266\pi$
$211$	1.43543			0.0988190			0.0494095	+	0.998779i	$0.484266\pi$
$212$	5.22254	+	5.22254i	0.358685	+	0.358685i
$213$	3.90799			0.267771
$214$	2.34115	+	2.34115i	0.160038	+	0.160038i
$215$	−1.02823	−	1.91416i	−0.0701245	−	0.130545i
$216$	−0.157273	−	0.157273i	−0.0107011	−	0.0107011i
$217$	−2.49319	+	2.49319i	−0.169249	+	0.169249i
$218$	9.66826	−	9.66826i	0.654818	−	0.654818i
$219$	10.9604	−	10.9604i	0.740633	−	0.740633i
$220$	−6.00455	+	3.22546i	−0.404827	+	0.217460i
$221$	−2.45458	−	3.35974i	−0.165113	−	0.226001i
$222$	−4.47568	+	4.47568i	−0.300388	+	0.300388i
$223$	22.6123			1.51423			0.757115	−	0.653281i	$-0.226608\pi$
$223$	22.6123			1.51423			0.757115	+	0.653281i	$0.226608\pi$
$224$		−	4.84851i		−	0.323955i
$225$	2.76066	−	4.16878i	0.184044	−	0.277919i
$226$	−23.7434	+	23.7434i	−1.57939	+	1.57939i
$227$			24.6499i			1.63607i	0.575166	+	0.818037i	$0.304938\pi$
$227$			24.6499i			1.63607i	−0.575166	+	0.818037i	$0.695062\pi$
$228$			11.3955i			0.754687i
$229$	0.422937	−	0.422937i	0.0279485	−	0.0279485i	−0.692994	−	0.720943i	$-0.743709\pi$
$229$	0.422937	−	0.422937i	0.0279485	−	0.0279485i	0.720943	+	0.692994i	$0.243709\pi$
$230$	−28.9497	+	15.5509i	−1.90889	+	1.02539i
$231$			0.996199i			0.0655450i
$232$	−0.501768			−0.0329427
$233$	−12.1713	+	12.1713i	−0.797370	+	0.797370i	−0.982680	−	0.185310i	$-0.940671\pi$
$233$	−12.1713	+	12.1713i	−0.797370	+	0.797370i	0.185310	+	0.982680i	$0.440671\pi$
$234$	−7.02408	−	1.09349i	−0.459179	−	0.0714835i
$235$	5.85362	−	19.4412i	0.381848	−	1.26820i
$236$	−7.65251	+	7.65251i	−0.498136	+	0.498136i
$237$	10.9268	−	10.9268i	0.709771	−	0.709771i
$238$	−0.992271	+	0.992271i	−0.0643193	+	0.0643193i
$239$	8.24673	+	8.24673i	0.533437	+	0.533437i	0.921593	−	0.388157i	$-0.126888\pi$
$239$	8.24673	+	8.24673i	0.533437	+	0.533437i	−0.388157	+	0.921593i	$0.626888\pi$
$240$	8.29880	−	4.45785i	0.535685	−	0.287753i
$241$	−3.53345	−	3.53345i	−0.227610	−	0.227610i	0.584084	−	0.811693i	$-0.301454\pi$
$241$	−3.53345	−	3.53345i	−0.227610	−	0.227610i	−0.811693	+	0.584084i	$0.801454\pi$
$242$	−16.5438			−1.06348
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−23.7038			−1.51748
$245$	−4.26751	+	14.1734i	−0.272641	+	0.905504i
$246$		−	5.29752i		−	0.337757i
$247$	−12.8435	−	17.5797i	−0.817215	−	1.11857i
$248$	−0.899105	−	0.899105i	−0.0570932	−	0.0570932i
$249$	3.45281	+	3.45281i	0.218813	+	0.218813i
$250$	14.0893	+	16.9526i	0.891084	+	1.07218i
$251$			29.1666i			1.84098i	0.390769	+	0.920489i	$0.372209\pi$
$251$			29.1666i			1.84098i	−0.390769	+	0.920489i	$0.627791\pi$
$252$			1.16394i			0.0733213i
$253$	12.0399			0.756942
$254$	9.61560	−	9.61560i	0.603336	−	0.603336i
$255$	−2.47089	−	0.743969i	−0.154733	−	0.0465891i
$256$	17.6496			1.10310
$257$	−4.74387	−	4.74387i	−0.295914	−	0.295914i	0.543497	−	0.839411i	$-0.317100\pi$
$257$	−4.74387	−	4.74387i	−0.295914	−	0.295914i	−0.839411	+	0.543497i	$0.817100\pi$
$258$			1.91585i			0.119276i
$259$	−1.98003			−0.123033
$260$	6.57546	−	13.7208i	0.407793	−	0.850926i
$261$	2.25597			0.139641
$262$		−	44.0893i		−	2.72384i
$263$	−1.87371	−	1.87371i	−0.115538	−	0.115538i	0.646974	−	0.762512i	$-0.276034\pi$
$263$	−1.87371	−	1.87371i	−0.115538	−	0.115538i	−0.762512	+	0.646974i	$0.776034\pi$
$264$	−0.359254			−0.0221105
$265$	−7.70931	+	4.14120i	−0.473579	+	0.254392i
$266$	−5.19203	+	5.19203i	−0.318344	+	0.318344i
$267$	10.3851			0.635556
$268$			3.15349i			0.192630i
$269$		−	22.0866i		−	1.34664i	−0.739350	−	0.673321i	$-0.764867\pi$
$269$		−	22.0866i		−	1.34664i	0.739350	−	0.673321i	$-0.235133\pi$
$270$	−3.88376	+	2.08623i	−0.236358	+	0.126964i
$271$	9.96038	+	9.96038i	0.605050	+	0.605050i	0.941648	−	0.336598i	$-0.109276\pi$
$271$	9.96038	+	9.96038i	0.605050	+	0.605050i	−0.336598	+	0.941648i	$0.609276\pi$
$272$	−3.43778	−	3.43778i	−0.208446	−	0.208446i
$273$	−1.31184	−	1.79559i	−0.0793961	−	0.108674i
$274$		−	1.71105i		−	0.103368i
$275$	−1.60826	−	7.91434i	−0.0969817	−	0.477252i
$276$	14.0672			0.846745
$277$	−22.8459	−	22.8459i	−1.37268	−	1.37268i	−0.856452	−	0.516226i	$-0.827336\pi$
$277$	−22.8459	−	22.8459i	−1.37268	−	1.37268i	−0.516226	−	0.856452i	$-0.672664\pi$
$278$	−24.1156			−1.44636
$279$	4.04241	+	4.04241i	0.242013	+	0.242013i
$280$	0.293715	+	0.0884356i	0.0175528	+	0.00528504i
$281$	−20.0201	−	20.0201i	−1.19430	−	1.19430i	−0.975847	−	0.218454i	$-0.929899\pi$
$281$	−20.0201	−	20.0201i	−1.19430	−	1.19430i	−0.218454	−	0.975847i	$-0.570101\pi$
$282$	−12.6586	+	12.6586i	−0.753808	+	0.753808i
$283$	3.65399	−	3.65399i	0.217207	−	0.217207i	−0.590113	−	0.807321i	$-0.700917\pi$
$283$	3.65399	−	3.65399i	0.217207	−	0.217207i	0.807321	+	0.590113i	$0.200917\pi$
$284$	5.21500	−	5.21500i	0.309453	−	0.309453i
$285$	−12.9289	−	3.89279i	−0.765839	−	0.230589i
$286$	−9.27133	+	6.77352i	−0.548225	+	0.400527i
$287$	1.17180	−	1.17180i	0.0691693	−	0.0691693i
$288$	−7.86129			−0.463231
$289$		−	15.6682i		−	0.921661i
$290$	−2.86743	+	9.52339i	−0.168381	+	0.559232i
$291$	9.45143	−	9.45143i	0.554053	−	0.554053i
$292$		−	29.2520i		−	1.71184i
$293$			23.4969i			1.37270i	0.727271	+	0.686351i	$0.240788\pi$
$293$			23.4969i			1.37270i	−0.727271	+	0.686351i	$0.759212\pi$
$294$	9.22859	−	9.22859i	0.538222	−	0.538222i
$295$	−6.06804	−	11.2963i	−0.353295	−	0.657698i
$296$		−	0.714046i		−	0.0415031i
$297$	1.61522			0.0937244
$298$	−0.242346	+	0.242346i	−0.0140387	+	0.0140387i
$299$	−21.7013	+	15.8547i	−1.25502	+	0.916900i
$300$	−1.87906	−	9.24696i	−0.108488	−	0.533873i
$301$	−0.423784	+	0.423784i	−0.0244265	+	0.0244265i
$302$	−6.71087	+	6.71087i	−0.386167	+	0.386167i
$303$	−5.55155	+	5.55155i	−0.318928	+	0.318928i
$304$	−17.9881	−	17.9881i	−1.03169	−	1.03169i
$305$	8.09738	−	26.8932i	0.463654	−	1.53990i
$306$	1.60885	+	1.60885i	0.0919718	+	0.0919718i
$307$	−23.1262			−1.31988			−0.659940	−	0.751318i	$-0.729418\pi$
$307$	−23.1262			−1.31988			−0.659940	+	0.751318i	$0.729418\pi$
$308$	1.32937	+	1.32937i	0.0757480	+	0.0757480i
$309$	16.6351			0.946339
$310$	−22.2028	+	11.9266i	−1.26103	+	0.677388i
$311$			22.4967i			1.27567i	0.770174	+	0.637834i	$0.220169\pi$
$311$			22.4967i			1.27567i	−0.770174	+	0.637834i	$0.779831\pi$
$312$	0.647535	−	0.473081i	0.0366594	−	0.0267829i
$313$	−18.8706	−	18.8706i	−1.06663	−	1.06663i	−0.997616	−	0.0690156i	$-0.978014\pi$
$313$	−18.8706	−	18.8706i	−1.06663	−	1.06663i	−0.0690156	−	0.997616i	$-0.521986\pi$
$314$	9.36647	+	9.36647i	0.528581	+	0.528581i
$315$	−1.32055	−	0.397610i	−0.0744047	−	0.0224028i
$316$		−	29.1624i		−	1.64051i
$317$			23.3062i			1.30901i	0.756059	+	0.654504i	$0.227123\pi$
$317$			23.3062i			1.30901i	−0.756059	+	0.654504i	$0.772877\pi$
$318$	7.71612			0.432699
$319$	2.57661	−	2.57661i	0.144262	−	0.144262i
$320$	4.56012	−	15.1452i	0.254918	−	0.846642i
$321$	1.67930			0.0937291
$322$	6.40928	+	6.40928i	0.357175	+	0.357175i
$323$			6.96838i			0.387731i
$324$	1.88719			0.104844
$325$	13.3207	+	12.1473i	0.738902	+	0.673813i
$326$	−1.23199			−0.0682338
$327$		−	6.93499i		−	0.383506i
$328$	0.422581	+	0.422581i	0.0233331	+	0.0233331i
$329$	−5.60012			−0.308745
$330$	−2.05301	+	6.81851i	−0.113015	+	0.375347i
$331$	13.4530	−	13.4530i	0.739445	−	0.739445i	−0.233026	−	0.972471i	$-0.574863\pi$
$331$	13.4530	−	13.4530i	0.739445	−	0.739445i	0.972471	+	0.233026i	$0.0748627\pi$
$332$	9.21518			0.505748
$333$			3.21038i			0.175928i
$334$			30.0827i			1.64605i
$335$	−3.57781	−	1.07726i	−0.195477	−	0.0588567i
$336$	−1.83730	−	1.83730i	−0.100233	−	0.100233i
$337$	14.7923	+	14.7923i	0.805788	+	0.805788i	0.983993	−	0.178205i	$-0.0570291\pi$
$337$	14.7923	+	14.7923i	0.805788	+	0.805788i	−0.178205	+	0.983993i	$0.557029\pi$
$338$	7.79140	−	24.4178i	0.423796	−	1.32815i
$339$			17.0310i			0.924996i
$340$	−4.29005	+	2.30448i	−0.232661	+	0.124978i
$341$	9.23393			0.500045
$342$	8.41825	+	8.41825i	0.455207	+	0.455207i
$343$	8.40000			0.453558
$344$	−0.152827	−	0.152827i	−0.00823987	−	0.00823987i
$345$	−4.80545	+	15.9600i	−0.258717	+	0.859257i
$346$	−12.3065	−	12.3065i	−0.661603	−	0.661603i
$347$	−0.845469	+	0.845469i	−0.0453872	+	0.0453872i	−0.729436	−	0.684049i	$-0.760217\pi$
$347$	−0.845469	+	0.845469i	−0.0453872	+	0.0453872i	0.684049	+	0.729436i	$0.260217\pi$
$348$	3.01046	−	3.01046i	0.161378	−	0.161378i
$349$	1.75292	−	1.75292i	0.0938316	−	0.0938316i	−0.658633	−	0.752464i	$-0.728865\pi$
$349$	1.75292	−	1.75292i	0.0938316	−	0.0938316i	0.752464	+	0.658633i	$0.228865\pi$
$350$	3.35696	−	5.06923i	0.179437	−	0.270962i
$351$	−2.91134	+	2.12699i	−0.155396	+	0.113530i
$352$	−8.97863	+	8.97863i	−0.478562	+	0.478562i
$353$	26.6289			1.41731			0.708655	−	0.705555i	$-0.249302\pi$
$353$	26.6289			1.41731			0.708655	+	0.705555i	$0.249302\pi$
$354$			11.3063i			0.600924i
$355$	4.13522	+	7.69818i	0.219475	+	0.408577i
$356$	13.8583	−	13.8583i	0.734488	−	0.734488i
$357$			0.711750i			0.0376698i
$358$		−	18.6936i		−	0.987987i
$359$	14.9162	−	14.9162i	0.787249	−	0.787249i	−0.193793	−	0.981042i	$-0.562079\pi$
$359$	14.9162	−	14.9162i	0.787249	−	0.787249i	0.981042	+	0.193793i	$0.0620791\pi$
$360$	0.143388	−	0.476223i	0.00755720	−	0.0250992i
$361$			17.4618i			0.919043i
$362$	26.1043			1.37201
$363$	−5.93338	+	5.93338i	−0.311422	+	0.311422i
$364$	−4.14669	−	0.645544i	−0.217346	−	0.0338357i
$365$	33.1880	+	9.99269i	1.73714	+	0.523041i
$366$	−17.5108	+	17.5108i	−0.915302	+	0.915302i
$367$	−18.8082	+	18.8082i	−0.981780	+	0.981780i	−0.999837	−	0.0180574i	$-0.994252\pi$
$367$	−18.8082	+	18.8082i	−0.981780	+	0.981780i	0.0180574	+	0.999837i	$0.494252\pi$
$368$	−22.2054	+	22.2054i	−1.15753	+	1.15753i
$369$	−1.89994	−	1.89994i	−0.0989069	−	0.0989069i
$370$	−13.5524	−	4.08053i	−0.704553	−	0.212136i
$371$	1.70679	+	1.70679i	0.0886123	+	0.0886123i
$372$	10.7887			0.559370
$373$	4.68051	+	4.68051i	0.242348	+	0.242348i	0.817821	−	0.575473i	$-0.195182\pi$
$373$	4.68051	+	4.68051i	0.242348	+	0.242348i	−0.575473	+	0.817821i	$0.695182\pi$
$374$	3.67503			0.190032
$375$	11.1331	+	1.02693i	0.574910	+	0.0530304i
$376$		−	2.01954i		−	0.104150i
$377$	−1.25121	+	8.03719i	−0.0644404	+	0.413937i
$378$	0.859840	+	0.859840i	0.0442254	+	0.0442254i
$379$	−0.473536	−	0.473536i	−0.0243239	−	0.0243239i	0.694840	−	0.719164i	$-0.255475\pi$
$379$	−0.473536	−	0.473536i	−0.0243239	−	0.0243239i	−0.719164	+	0.694840i	$0.755475\pi$
$380$	−22.4475	+	12.0581i	−1.15153	+	0.618568i
$381$		−	6.89721i		−	0.353355i
$382$			33.0872i			1.69289i
$383$	−4.42380			−0.226045			−0.113023	−	0.993592i	$-0.536053\pi$
$383$	−4.42380			−0.226045			−0.113023	+	0.993592i	$0.536053\pi$
$384$	1.25618	−	1.25618i	0.0641044	−	0.0641044i
$385$	−1.96237	+	1.05412i	−0.100011	+	0.0537230i
$386$	−18.9027			−0.962125
$387$	0.687115	+	0.687115i	0.0349280	+	0.0349280i
$388$		−	25.2248i		−	1.28060i
$389$	−24.4667			−1.24051			−0.620255	−	0.784400i	$-0.712971\pi$
$389$	−24.4667			−1.24051			−0.620255	+	0.784400i	$0.712971\pi$
$390$	−5.27848	−	14.9935i	−0.267286	−	0.759225i
$391$	8.60210			0.435027
$392$			1.47232i			0.0743634i
$393$	−15.8125	−	15.8125i	−0.797634	−	0.797634i
$394$	−24.2852			−1.22347
$395$	33.0863	+	9.96207i	1.66475	+	0.501246i
$396$	2.15542	−	2.15542i	0.108314	−	0.108314i
$397$	35.5142			1.78241			0.891204	−	0.453603i	$-0.149862\pi$
$397$	35.5142			1.78241			0.891204	+	0.453603i	$0.149862\pi$
$398$			3.38916i			0.169883i
$399$			3.72421i			0.186444i
$400$	17.5626	+	11.6304i	0.878132	+	0.581519i
$401$	−19.7141	−	19.7141i	−0.984476	−	0.984476i	0.0154049	−	0.999881i	$-0.495096\pi$
$401$	−19.7141	−	19.7141i	−0.984476	−	0.984476i	−0.999881	+	0.0154049i	$0.995096\pi$
$402$	2.32959	+	2.32959i	0.116189	+	0.116189i
$403$	−16.6437	+	12.1596i	−0.829079	+	0.605715i
$404$			14.8165i			0.737147i
$405$	−0.644677	+	2.14112i	−0.0320343	+	0.106393i
$406$	2.74325			0.136145
$407$	3.66667	+	3.66667i	0.181750	+	0.181750i
$408$	−0.256674			−0.0127073
$409$	18.5865	+	18.5865i	0.919045	+	0.919045i	0.996960	−	0.0779148i	$-0.0248262\pi$
$409$	18.5865	+	18.5865i	0.919045	+	0.919045i	−0.0779148	+	0.996960i	$0.524826\pi$
$410$	10.4353	−	5.60554i	0.515365	−	0.276838i
$411$	−0.613663	−	0.613663i	−0.0302698	−	0.0302698i
$412$	22.1986	−	22.1986i	1.09365	−	1.09365i
$413$	−2.50094	+	2.50094i	−0.123063	+	0.123063i
$414$	10.3919	−	10.3919i	0.510734	−	0.510734i
$415$	−3.14797	+	10.4551i	−0.154528	+	0.513222i
$416$	4.36003	−	28.0069i	0.213768	−	1.37315i
$417$	−8.64899	+	8.64899i	−0.423543	+	0.423543i
$418$	19.2295			0.940546
$419$		−	14.9331i		−	0.729531i	−0.931099	−	0.364766i	$-0.881149\pi$
$419$		−	14.9331i		−	0.729531i	0.931099	−	0.364766i	$-0.118851\pi$
$420$	−2.29279	+	1.23162i	−0.111877	+	0.0600967i
$421$	3.10901	−	3.10901i	0.151524	−	0.151524i	−0.627274	−	0.778798i	$-0.715830\pi$
$421$	3.10901	−	3.10901i	0.151524	−	0.151524i	0.778798	+	0.627274i	$0.215830\pi$
$422$		−	2.83008i		−	0.137766i
$423$			9.07993i			0.441481i
$424$	−0.615511	+	0.615511i	−0.0298919	+	0.0298919i
$425$	−1.14905	−	5.65452i	−0.0557369	−	0.274285i
$426$		−	7.70498i		−	0.373308i
$427$	−7.74670			−0.374889
$428$	2.24093	−	2.24093i	0.108319	−	0.108319i
$429$	−0.895833	+	5.75444i	−0.0432512	+	0.277827i
$430$	−3.77395	+	2.02725i	−0.181996	+	0.0977626i
$431$	−4.51912	+	4.51912i	−0.217678	+	0.217678i	−0.807519	−	0.589841i	$-0.799190\pi$
$431$	−4.51912	+	4.51912i	−0.217678	+	0.217678i	0.589841	+	0.807519i	$0.299190\pi$
$432$	−2.97897	+	2.97897i	−0.143326	+	0.143326i
$433$	−1.03908	+	1.03908i	−0.0499352	+	0.0499352i	−0.731633	−	0.681698i	$-0.761242\pi$
$433$	−1.03908	+	1.03908i	−0.0499352	+	0.0499352i	0.681698	+	0.731633i	$0.261242\pi$
$434$	4.91556	+	4.91556i	0.235954	+	0.235954i
$435$	2.38714	+	4.44393i	0.114455	+	0.213070i
$436$	−9.25435	−	9.25435i	−0.443203	−	0.443203i
$437$	45.0102			2.15313
$438$	−21.6094	−	21.6094i	−1.03254	−	1.03254i
$439$	−29.7565			−1.42020			−0.710101	−	0.704100i	$-0.751351\pi$
$439$	−29.7565			−1.42020			−0.710101	+	0.704100i	$0.751351\pi$
$440$	−0.380142	−	0.707678i	−0.0181226	−	0.0337372i
$441$		−	6.61961i		−	0.315220i
$442$	−6.62405	+	4.83945i	−0.315074	+	0.230189i
$443$	−2.16107	−	2.16107i	−0.102675	−	0.102675i	0.653903	−	0.756578i	$-0.273130\pi$
$443$	−2.16107	−	2.16107i	−0.102675	−	0.102675i	−0.756578	+	0.653903i	$0.773130\pi$
$444$	4.28407	+	4.28407i	0.203313	+	0.203313i
$445$	10.9889	+	20.4571i	0.520924	+	0.969759i
$446$		−	44.5823i		−	2.11103i
$447$			0.173833i			0.00822202i
$448$	−4.36263			−0.206115
$449$	−7.74049	+	7.74049i	−0.365296	+	0.365296i	−0.865758	−	0.500462i	$-0.833163\pi$
$449$	−7.74049	+	7.74049i	−0.365296	+	0.365296i	0.500462	+	0.865758i	$0.333163\pi$
$450$	−8.21915	−	5.44291i	−0.387455	−	0.256581i
$451$	−4.33996			−0.204361
$452$	22.7269	+	22.7269i	1.06898	+	1.06898i
$453$			4.81367i			0.226166i
$454$	48.5997			2.28090
$455$	2.14895	−	4.48413i	0.100744	−	0.210219i
$456$	−1.34304			−0.0628936
$457$			1.41670i			0.0662706i	0.999451	+	0.0331353i	$0.0105492\pi$
$457$			1.41670i			0.0662706i	−0.999451	+	0.0331353i	$0.989451\pi$
$458$	−0.833862	−	0.833862i	−0.0389638	−	0.0389638i
$459$	1.15402			0.0538649
$460$	14.8851	+	27.7103i	0.694022	+	1.29200i
$461$	17.4196	−	17.4196i	0.811313	−	0.811313i	−0.173517	−	0.984831i	$-0.555513\pi$
$461$	17.4196	−	17.4196i	0.811313	−	0.811313i	0.984831	+	0.173517i	$0.0555133\pi$
$462$	1.96410			0.0913782
$463$			9.40194i			0.436945i	0.975843	+	0.218473i	$0.0701074\pi$
$463$			9.40194i			0.436945i	−0.975843	+	0.218473i	$0.929893\pi$
$464$			9.50415i			0.441219i
$465$	−3.68551	+	12.2404i	−0.170911	+	0.567636i
$466$	23.9969	+	23.9969i	1.11164	+	1.11164i
$467$	−21.8639	−	21.8639i	−1.01174	−	1.01174i	−0.999930	−	0.0118107i	$-0.996240\pi$
$467$	−21.8639	−	21.8639i	−1.01174	−	1.01174i	−0.0118107	−	0.999930i	$-0.503760\pi$
$468$	−1.04667	+	6.72337i	−0.0483825	+	0.310788i
$469$			1.03060i			0.0475888i
$470$	−38.3302	−	11.5410i	−1.76804	−	0.532346i
$471$	6.71851			0.309573
$472$	−0.901900	−	0.901900i	−0.0415133	−	0.0415133i
$473$	1.56955			0.0721680
$474$	−21.5432	−	21.5432i	−0.989512	−	0.989512i
$475$	−6.01235	−	29.5871i	−0.275866	−	1.35755i
$476$	0.949790	+	0.949790i	0.0435336	+	0.0435336i
$477$	2.76736	−	2.76736i	0.126709	−	0.126709i
$478$	16.2592	−	16.2592i	0.743679	−	0.743679i
$479$	23.2067	−	23.2067i	1.06034	−	1.06034i	0.0622831	−	0.998059i	$-0.480162\pi$
$479$	23.2067	−	23.2067i	1.06034	−	1.06034i	0.998059	−	0.0622831i	$-0.0198382\pi$
$480$	−8.31838	−	15.4856i	−0.379680	−	0.706818i
$481$	−11.4374	−	1.78054i	−0.521501	−	0.0811857i
$482$	−6.96654	+	6.96654i	−0.317317	+	0.317317i
$483$	4.59734			0.209186
$484$			15.8355i			0.719797i
$485$	28.6189	+	8.61698i	1.29952	+	0.391277i
$486$	1.39413	−	1.39413i	0.0632390	−	0.0632390i
$487$		−	28.9645i		−	1.31251i	−0.754541	−	0.656253i	$-0.772141\pi$
$487$		−	28.9645i		−	1.31251i	0.754541	−	0.656253i	$-0.227859\pi$
$488$		−	2.79365i		−	0.126463i
$489$	−0.441851	+	0.441851i	−0.0199812	+	0.0199812i
$490$	27.9442	+	8.41381i	1.26239	+	0.380097i
$491$		−	1.65587i		−	0.0747282i	−0.999302	−	0.0373641i	$-0.988104\pi$
$491$		−	1.65587i		−	0.0747282i	0.999302	−	0.0373641i	$-0.0118961\pi$
$492$	−5.07072			−0.228606
$493$	1.84090	−	1.84090i	0.0829100	−	0.0829100i
$494$	−34.6601	+	25.3223i	−1.55943	+	1.13930i
$495$	1.70913	+	3.18175i	0.0768198	+	0.143009i
$496$	−17.0303	+	17.0303i	−0.764681	+	0.764681i
$497$	1.70433	−	1.70433i	0.0764497	−	0.0764497i
$498$	6.80755	−	6.80755i	0.305054	−	0.305054i
$499$	−19.9334	−	19.9334i	−0.892342	−	0.892342i	0.102401	−	0.994743i	$-0.467347\pi$
$499$	−19.9334	−	19.9334i	−0.892342	−	0.892342i	−0.994743	+	0.102401i	$0.967347\pi$
$500$	16.2268	−	13.4861i	0.725687	−	0.603116i
$501$	10.7891	+	10.7891i	0.482021	+	0.482021i
$502$	57.5047			2.56656
$503$	20.4695	+	20.4695i	0.912692	+	0.912692i	0.996483	−	0.0837917i	$-0.0267030\pi$
$503$	20.4695	+	20.4695i	0.912692	+	0.912692i	−0.0837917	+	0.996483i	$0.526703\pi$
$504$	−0.137178			−0.00611040
$505$	−16.8101	−	5.06141i	−0.748039	−	0.225230i
$506$		−	23.7378i		−	1.05527i
$507$	−5.96301	−	11.5517i	−0.264826	−	0.513030i
$508$	−9.20394	−	9.20394i	−0.408359	−	0.408359i
$509$	−16.0097	−	16.0097i	−0.709618	−	0.709618i	0.256837	−	0.966455i	$-0.417320\pi$
$509$	−16.0097	−	16.0097i	−0.709618	−	0.709618i	−0.966455	+	0.256837i	$0.917320\pi$
$510$	−1.46681	+	4.87159i	−0.0649513	+	0.215718i
$511$		−	9.55993i		−	0.422906i
$512$		−	31.2448i		−	1.38084i
$513$	6.03836			0.266600
$514$	−9.35299	+	9.35299i	−0.412543	+	0.412543i
$515$	17.6024	+	32.7688i	0.775652	+	1.44396i
$516$	1.83383			0.0807300
$517$	10.3705	+	10.3705i	0.456093	+	0.456093i
$518$			3.90381i			0.171524i
$519$	−8.82739			−0.387480
$520$	1.61709	+	0.774962i	0.0709139	+	0.0339843i
$521$	−30.6396			−1.34235			−0.671174	−	0.741300i	$-0.734209\pi$
$521$	−30.6396			−1.34235			−0.671174	+	0.741300i	$0.734209\pi$
$522$		−	4.44785i		−	0.194677i
$523$	−5.29306	−	5.29306i	−0.231449	−	0.231449i	0.581848	−	0.813297i	$-0.302330\pi$
$523$	−5.29306	−	5.29306i	−0.231449	−	0.231449i	−0.813297	+	0.581848i	$0.802330\pi$
$524$	−42.2017			−1.84359
$525$	−0.614101	−	3.02203i	−0.0268016	−	0.131892i
$526$	−3.69420	+	3.69420i	−0.161075	+	0.161075i
$527$	6.59733			0.287384
$528$			6.80474i			0.296138i
$529$		−	32.5628i		−	1.41577i
$530$	8.16477	+	15.1996i	0.354655	+	0.660230i
$531$	4.05498	+	4.05498i	0.175971	+	0.175971i
$532$	4.96975	+	4.96975i	0.215466	+	0.215466i
$533$	7.82254	−	5.71505i	0.338832	−	0.247546i
$534$		−	20.4752i		−	0.886046i
$535$	1.77694	+	3.30797i	0.0768237	+	0.143016i
$536$	−0.371660			−0.0160533
$537$	−6.70440	−	6.70440i	−0.289316	−	0.289316i
$538$	−43.5458			−1.87739
$539$	−7.56046	−	7.56046i	−0.325652	−	0.325652i
$540$	1.99692	+	3.71749i	0.0859337	+	0.159975i
$541$	−6.80449	−	6.80449i	−0.292548	−	0.292548i	0.545538	−	0.838086i	$-0.316325\pi$
$541$	−6.80449	−	6.80449i	−0.292548	−	0.292548i	−0.838086	+	0.545538i	$0.816325\pi$
$542$	19.6378	−	19.6378i	0.843517	−	0.843517i
$543$	9.36222	−	9.36222i	0.401771	−	0.401771i
$544$	−6.41492	+	6.41492i	−0.275038	+	0.275038i
$545$	13.6609	−	7.33822i	0.585170	−	0.314335i
$546$	−3.54018	+	2.58641i	−0.151506	+	0.110688i
$547$	11.7879	−	11.7879i	0.504014	−	0.504014i	−0.408669	−	0.912683i	$-0.634007\pi$
$547$	11.7879	−	11.7879i	0.504014	−	0.504014i	0.912683	+	0.408669i	$0.134007\pi$
$548$	−1.63780			−0.0699632
$549$			12.5604i			0.536063i
$550$	−15.6039	+	3.17084i	−0.665351	+	0.135205i
$551$	9.63245	−	9.63245i	0.410356	−	0.410356i
$552$			1.65791i			0.0705655i
$553$		−	9.53064i		−	0.405284i
$554$	−45.0429	+	45.0429i	−1.91369	+	1.91369i
$555$	−6.32398	+	3.39704i	−0.268438	+	0.144196i
$556$			23.0832i			0.978945i
$557$	2.73586			0.115922			0.0579611	−	0.998319i	$-0.481540\pi$
$557$	2.73586			0.115922			0.0579611	+	0.998319i	$0.481540\pi$
$558$	7.97000	−	7.97000i	0.337397	−	0.337397i
$559$	−2.82903	+	2.06685i	−0.119655	+	0.0874186i
$560$	1.67509	−	5.56335i	0.0707854	−	0.235094i
$561$	1.31804	−	1.31804i	0.0556477	−	0.0556477i
$562$	−39.4716	+	39.4716i	−1.66501	+	1.66501i
$563$	10.7281	−	10.7281i	0.452135	−	0.452135i	−0.443927	−	0.896063i	$-0.646415\pi$
$563$	10.7281	−	10.7281i	0.452135	−	0.452135i	0.896063	+	0.443927i	$0.146415\pi$
$564$	12.1167	+	12.1167i	0.510203	+	0.510203i
$565$	−33.5486	+	18.0212i	−1.41140	+	0.758159i
$566$	−7.20419	−	7.20419i	−0.302815	−	0.302815i
$567$	0.616758			0.0259014
$568$	0.614623	+	0.614623i	0.0257890	+	0.0257890i
$569$	−1.39618			−0.0585311			−0.0292656	−	0.999572i	$-0.509317\pi$
$569$	−1.39618			−0.0585311			−0.0292656	+	0.999572i	$0.509317\pi$
$570$	−7.67502	+	25.4905i	−0.321471	+	1.06768i
$571$		−	27.2780i		−	1.14155i	−0.821106	−	0.570775i	$-0.806643\pi$
$571$		−	27.2780i		−	1.14155i	0.821106	−	0.570775i	$-0.193357\pi$
$572$	6.48354	+	8.87441i	0.271090	+	0.371058i
$573$	11.8666	+	11.8666i	0.495735	+	0.495735i
$574$	−2.31032	−	2.31032i	−0.0964309	−	0.0964309i
$575$	−36.5237	+	7.42193i	−1.52315	+	0.309516i
$576$			7.07349i			0.294729i
$577$			31.6220i			1.31644i	0.752824	+	0.658221i	$0.228691\pi$
$577$			31.6220i			1.31644i	−0.752824	+	0.658221i	$0.771309\pi$
$578$	−30.8914			−1.28491
$579$	−6.77941	+	6.77941i	−0.281743	+	0.281743i
$580$	9.11568	+	2.74467i	0.378508	+	0.113966i
$581$	3.01164			0.124944
$582$	−18.6344	−	18.6344i	−0.772421	−	0.772421i
$583$		−	6.32139i		−	0.261805i
$584$	3.44754			0.142660
$585$	−7.27048	−	3.48426i	−0.300597	−	0.144056i
$586$	46.3263			1.91372
$587$			23.9243i			0.987460i	0.869615	+	0.493730i	$0.164367\pi$
$587$			23.9243i			0.987460i	−0.869615	+	0.493730i	$0.835633\pi$
$588$	−8.83350	−	8.83350i	−0.364287	−	0.364287i
$589$	34.5203			1.42238
$590$	−22.2718	+	11.9637i	−0.916916	+	0.492538i
$591$	−8.70981	+	8.70981i	−0.358274	+	0.358274i
$592$	−13.5250			−0.555873
$593$		−	4.28180i		−	0.175832i	−0.996128	−	0.0879162i	$-0.971979\pi$
$593$		−	4.28180i		−	0.175832i	0.996128	−	0.0879162i	$-0.0280208\pi$
$594$		−	3.18456i		−	0.130664i
$595$	−1.40204	+	0.753134i	−0.0574782	+	0.0308755i
$596$	0.231971	+	0.231971i	0.00950189	+	0.00950189i
$597$	1.21551	+	1.21551i	0.0497477	+	0.0497477i
$598$	31.2590	+	42.7861i	1.27828	+	1.74965i
$599$		−	28.9336i		−	1.18219i	−0.806600	−	0.591097i	$-0.798695\pi$
$599$		−	28.9336i		−	1.18219i	0.806600	−	0.591097i	$-0.201305\pi$
$600$	1.08982	−	0.221460i	0.0444916	−	0.00904106i
$601$	−42.3729			−1.72843			−0.864214	−	0.503124i	$-0.832184\pi$
$601$	−42.3729			−1.72843			−0.864214	+	0.503124i	$0.832184\pi$
$602$	0.835530	+	0.835530i	0.0340537	+	0.0340537i
$603$	1.67100			0.0680484
$604$	6.42357	+	6.42357i	0.261371	+	0.261371i
$605$	−17.9663	−	5.40953i	−0.730433	−	0.219929i
$606$	10.9454	+	10.9454i	0.444627	+	0.444627i
$607$	−17.6337	+	17.6337i	−0.715728	+	0.715728i	−0.967727	−	0.251999i	$-0.918912\pi$
$607$	−17.6337	+	17.6337i	−0.715728	+	0.715728i	0.251999	+	0.967727i	$0.418912\pi$
$608$	−33.5659	+	33.5659i	−1.36128	+	1.36128i
$609$	0.983858	−	0.983858i	0.0398679	−	0.0398679i
$610$	−53.0226	−	15.9647i	−2.14682	−	0.646394i
$611$	−32.3485	−	5.03592i	−1.30868	−	0.203731i
$612$	1.53997	−	1.53997i	0.0622497	−	0.0622497i
$613$	9.49560			0.383524			0.191762	−	0.981441i	$-0.438580\pi$
$613$	9.49560			0.383524			0.191762	+	0.981441i	$0.438580\pi$
$614$			45.5955i			1.84008i
$615$	1.73220	−	5.75301i	0.0698489	−	0.231984i
$616$	−0.156675	+	0.156675i	−0.00631263	+	0.00631263i
$617$			18.3651i			0.739350i	0.929161	+	0.369675i	$0.120531\pi$
$617$			18.3651i			0.739350i	−0.929161	+	0.369675i	$0.879469\pi$
$618$		−	32.7977i		−	1.31932i
$619$	7.70916	−	7.70916i	0.309857	−	0.309857i	−0.534997	−	0.844854i	$-0.679687\pi$
$619$	7.70916	−	7.70916i	0.309857	−	0.309857i	0.844854	+	0.534997i	$0.179687\pi$
$620$	11.4160	+	21.2523i	0.458479	+	0.853511i
$621$		−	7.45404i		−	0.299120i
$622$	44.3543			1.77845
$623$	4.52907	−	4.52907i	0.181453	−	0.181453i
$624$	−8.96079	−	12.2652i	−0.358719	−	0.491000i
$625$	9.75750	+	23.0172i	0.390300	+	0.920688i
$626$	−37.2053	+	37.2053i	−1.48702	+	1.48702i
$627$	6.89660	−	6.89660i	0.275424	−	0.275424i
$628$	8.96548	−	8.96548i	0.357762	−	0.357762i
$629$	2.61971	+	2.61971i	0.104455	+	0.104455i
$630$	−0.783926	+	2.60360i	−0.0312323	+	0.103730i
$631$	6.10664	+	6.10664i	0.243101	+	0.243101i	0.818132	−	0.575031i	$-0.195010\pi$
$631$	6.10664	+	6.10664i	0.243101	+	0.243101i	−0.575031	+	0.818132i	$0.695010\pi$
$632$	3.43698			0.136716
$633$	−1.01500	−	1.01500i	−0.0403427	−	0.0403427i
$634$	45.9504			1.82493
$635$	13.5865	−	7.29824i	0.539164	−	0.289622i
$636$		−	7.38578i		−	0.292865i
$637$	23.5833	+	3.67137i	0.934404	+	0.145465i
$638$	−5.08003	−	5.08003i	−0.201120	−	0.201120i
$639$	−2.76337	−	2.76337i	−0.109317	−	0.109317i
$640$	3.80373	+	1.14528i	0.150356	+	0.0452711i
$641$		−	4.53786i		−	0.179235i	−0.995976	−	0.0896174i	$-0.971436\pi$
$641$		−	4.53786i		−	0.179235i	0.995976	−	0.0896174i	$-0.0285644\pi$
$642$		−	3.31089i		−	0.130670i
$643$	−34.3287			−1.35379			−0.676896	−	0.736078i	$-0.736675\pi$
$643$	−34.3287			−1.35379			−0.676896	+	0.736078i	$0.736675\pi$
$644$	6.13489	−	6.13489i	0.241749	−	0.241749i
$645$	−0.626450	+	2.08058i	−0.0246665	+	0.0819229i
$646$	13.7388			0.540547
$647$	−21.2739	−	21.2739i	−0.836365	−	0.836365i	0.152014	−	0.988378i	$-0.451424\pi$
$647$	−21.2739	−	21.2739i	−0.836365	−	0.836365i	−0.988378	+	0.152014i	$0.951424\pi$
$648$			0.222418i			0.00873740i
$649$	9.26263			0.363590
$650$	23.9496	−	26.2631i	0.939382	−	1.03012i
$651$	3.52590			0.138191
$652$			1.17925i			0.0461830i
$653$	−5.83160	−	5.83160i	−0.228208	−	0.228208i	0.583736	−	0.811944i	$-0.301590\pi$
$653$	−5.83160	−	5.83160i	−0.228208	−	0.228208i	−0.811944	+	0.583736i	$0.801590\pi$
$654$	−13.6730			−0.534656
$655$	14.4164	−	47.8802i	0.563296	−	1.87083i
$656$	8.00425	−	8.00425i	0.312513	−	0.312513i
$657$	−15.5003			−0.604724
$658$			11.0412i			0.430430i
$659$			15.9399i			0.620932i	0.950585	+	0.310466i	$0.100485\pi$
$659$			15.9399i			0.620932i	−0.950585	+	0.310466i	$0.899515\pi$
$660$	6.52660	+	1.96512i	0.254048	+	0.0764921i
$661$	17.8217	+	17.8217i	0.693184	+	0.693184i	0.962931	−	0.269747i	$-0.0869401\pi$
$661$	17.8217	+	17.8217i	0.693184	+	0.693184i	−0.269747	+	0.962931i	$0.586940\pi$
$662$	−26.5239	−	26.5239i	−1.03088	−	1.03088i
$663$	−0.640042	+	4.11135i	−0.0248572	+	0.159672i
$664$			1.08607i			0.0421477i
$665$	−7.33615	+	3.94075i	−0.284484	+	0.152816i
$666$	6.32956			0.245266
$667$	−11.8908	−	11.8908i	−0.460412	−	0.460412i
$668$	28.7948			1.11411
$669$	−15.9893	−	15.9893i	−0.618182	−	0.618182i
$670$	−2.12391	+	7.05399i	−0.0820539	+	0.272520i
$671$	14.3456	+	14.3456i	0.553805	+	0.553805i
$672$	−3.42842	+	3.42842i	−0.132254	+	0.132254i
$673$	15.5332	−	15.5332i	0.598760	−	0.598760i	−0.341223	−	0.939982i	$-0.610841\pi$
$673$	15.5332	−	15.5332i	0.598760	−	0.598760i	0.939982	+	0.341223i	$0.110841\pi$
$674$	29.1644	−	29.1644i	1.12337	−	1.12337i
$675$	−4.89986	+	0.995692i	−0.188596	+	0.0383242i
$676$	−23.3724	−	7.45784i	−0.898940	−	0.286840i
$677$	15.6149	−	15.6149i	0.600128	−	0.600128i	−0.340219	−	0.940346i	$-0.610501\pi$
$677$	15.6149	−	15.6149i	0.600128	−	0.600128i	0.940346	+	0.340219i	$0.110501\pi$
$678$	33.5782			1.28956
$679$		−	8.24380i		−	0.316368i
$680$	−0.271598	−	0.505611i	−0.0104153	−	0.0193893i
$681$	17.4301	−	17.4301i	0.667924	−	0.667924i
$682$		−	18.2056i		−	0.697127i
$683$			18.7071i			0.715807i	0.933759	+	0.357904i	$0.116508\pi$
$683$			18.7071i			0.715807i	−0.933759	+	0.357904i	$0.883492\pi$
$684$	8.05786	−	8.05786i	0.308100	−	0.308100i
$685$	0.559483	−	1.85817i	0.0213768	−	0.0709971i
$686$		−	16.5614i		−	0.632318i
$687$	−0.598124			−0.0228198
$688$	−2.89474	+	2.89474i	−0.110361	+	0.110361i
$689$	8.32428	+	11.3940i	0.317130	+	0.434075i
$690$	31.4667	+	9.47441i	1.19792	+	0.360685i
$691$	−14.7577	+	14.7577i	−0.561410	+	0.561410i	−0.929708	−	0.368298i	$-0.879941\pi$
$691$	−14.7577	+	14.7577i	−0.561410	+	0.561410i	0.368298	+	0.929708i	$0.379941\pi$
$692$	−11.7797	+	11.7797i	−0.447796	+	0.447796i
$693$	0.704419	−	0.704419i	0.0267587	−	0.0267587i
$694$	1.66692	+	1.66692i	0.0632755	+	0.0632755i
$695$	−26.1891	−	7.88538i	−0.993410	−	0.299109i
$696$	0.354803	+	0.354803i	0.0134488	+	0.0134488i
$697$	−3.10075			−0.117449
$698$	−3.45605	−	3.45605i	−0.130813	−	0.130813i
$699$	17.2129			0.651050
$700$	−4.85221	−	3.21324i	−0.183396	−	0.121449i
$701$			31.8379i			1.20250i	0.799060	+	0.601251i	$0.205331\pi$
$701$			31.8379i			1.20250i	−0.799060	+	0.601251i	$0.794669\pi$
$702$	4.19356	+	5.73999i	0.158276	+	0.216642i
$703$	13.7076	+	13.7076i	0.516990	+	0.516990i
$704$	8.07886	+	8.07886i	0.304483	+	0.304483i
$705$	−17.8861	+	9.60788i	−0.673631	+	0.361854i
$706$		−	52.5013i		−	1.97591i
$707$			4.84222i			0.182110i
$708$	10.8223			0.406726
$709$	−23.4261	+	23.4261i	−0.879785	+	0.879785i	−0.993512	−	0.113727i	$-0.963721\pi$
$709$	−23.4261	+	23.4261i	−0.879785	+	0.879785i	0.113727	+	0.993512i	$0.463721\pi$
$710$	15.1777	−	8.15298i	0.569609	−	0.305976i
$711$	−15.4528			−0.579525
$712$	1.63329	+	1.63329i	0.0612103	+	0.0612103i
$713$		−	42.6135i		−	1.59589i
$714$	1.40328			0.0525165
$715$	−12.2833	+	4.32436i	−0.459371	+	0.161722i
$716$	−17.8933			−0.668704
$717$		−	11.6626i		−	0.435549i
$718$	−29.4088	−	29.4088i	−1.09753	−	1.09753i
$719$	3.34392			0.124707			0.0623537	−	0.998054i	$-0.480139\pi$
$719$	3.34392			0.124707			0.0623537	+	0.998054i	$0.480139\pi$
$720$	−9.02031	−	2.71596i	−0.336167	−	0.101218i
$721$	7.25480	−	7.25480i	0.270183	−	0.270183i
$722$	34.4277			1.28126
$723$			4.99706i			0.185843i
$724$		−	24.9867i		−	0.928624i
$725$	−6.22796	+	9.40464i	−0.231301	+	0.349279i
$726$	11.6982	+	11.6982i	0.434162	+	0.434162i
$727$	−25.9092	−	25.9092i	−0.960918	−	0.960918i	0.0383469	−	0.999264i	$-0.487791\pi$
$727$	−25.9092	−	25.9092i	−0.960918	−	0.960918i	−0.999264	+	0.0383469i	$0.987791\pi$
$728$	0.0760818	−	0.488716i	0.00281978	−	0.0181130i
$729$		−	1.00000i		−	0.0370370i
$730$	19.7015	−	65.4333i	0.729187	−	2.42179i
$731$	1.12139			0.0414761
$732$	16.7611	+	16.7611i	0.619508	+	0.619508i
$733$	36.2969			1.34066			0.670329	−	0.742064i	$-0.266153\pi$
$733$	36.2969			1.34066			0.670329	+	0.742064i	$0.266153\pi$
$734$	37.0821	+	37.0821i	1.36873	+	1.36873i
$735$	13.0397	−	7.00450i	0.480976	−	0.258365i
$736$	41.4353	+	41.4353i	1.52733	+	1.52733i
$737$	1.90850	−	1.90850i	0.0703005	−	0.0703005i
$738$	−3.74591	+	3.74591i	−0.137889	+	0.137889i
$739$	15.9043	−	15.9043i	0.585049	−	0.585049i	−0.351238	−	0.936286i	$-0.614239\pi$
$739$	15.9043	−	15.9043i	0.585049	−	0.585049i	0.936286	+	0.351238i	$0.114239\pi$
$740$	−3.90583	+	12.9722i	−0.143581	+	0.476866i
$741$	−3.34900	+	21.5125i	−0.123029	+	0.790282i
$742$	3.36511	−	3.36511i	0.123537	−	0.123537i
$743$	−16.7508			−0.614527			−0.307263	−	0.951625i	$-0.599413\pi$
$743$	−16.7508			−0.614527			−0.307263	+	0.951625i	$0.599413\pi$
$744$			1.27153i			0.0466164i
$745$	−0.342426	+	0.183941i	−0.0125455	+	0.00673906i
$746$	9.22807	−	9.22807i	0.337864	−	0.337864i
$747$		−	4.88302i		−	0.178660i
$748$		−	3.51770i		−	0.128620i
$749$	0.732364	−	0.732364i	0.0267600	−	0.0267600i
$750$	2.02469	−	21.9499i	0.0739313	−	0.801498i
$751$			10.3303i			0.376958i	0.982077	+	0.188479i	$0.0603558\pi$
$751$			10.3303i			0.376958i	−0.982077	+	0.188479i	$0.939644\pi$
$752$	−38.2528			−1.39494
$753$	20.6239	−	20.6239i	0.751576	−	0.751576i
$754$	15.8461	+	2.46687i	0.577081	+	0.0898381i
$755$	−9.48223	+	5.09356i	−0.345094	+	0.185373i
$756$	0.823029	−	0.823029i	0.0299333	−	0.0299333i
$757$	−0.186517	+	0.186517i	−0.00677908	+	0.00677908i	−0.710488	−	0.703709i	$-0.751526\pi$
$757$	−0.186517	+	0.186517i	−0.00677908	+	0.00677908i	0.703709	+	0.710488i	$0.251526\pi$
$758$	−0.933621	+	0.933621i	−0.0339106	+	0.0339106i
$759$	−8.51350	−	8.51350i	−0.309020	−	0.309020i
$760$	−1.42113	−	2.64560i	−0.0515498	−	0.0959658i
$761$	−5.78721	−	5.78721i	−0.209786	−	0.209786i	0.594390	−	0.804177i	$-0.297393\pi$
$761$	−5.78721	−	5.78721i	−0.209786	−	0.209786i	−0.804177	+	0.594390i	$0.797393\pi$
$762$	−13.5985			−0.492622
$763$	−3.02444	−	3.02444i	−0.109492	−	0.109492i
$764$	31.6707			1.14580
$765$	1.22112	+	2.27325i	0.0441496	+	0.0821895i
$766$			8.72194i			0.315136i
$767$	−16.6954	+	12.1974i	−0.602836	+	0.440424i
$768$	−12.4801	−	12.4801i	−0.450337	−	0.450337i
$769$	29.1513	+	29.1513i	1.05122	+	1.05122i	0.998615	+	0.0526059i	$0.0167527\pi$
$769$	29.1513	+	29.1513i	1.05122	+	1.05122i	0.0526059	+	0.998615i	$0.483247\pi$
$770$	2.07830	+	3.86899i	0.0748968	+	0.139429i
$771$			6.70884i			0.241613i
$772$			18.0935i			0.651199i
$773$	40.4990			1.45665			0.728325	−	0.685232i	$-0.240299\pi$
$773$	40.4990			1.45665			0.728325	+	0.685232i	$0.240299\pi$
$774$	1.35471	−	1.35471i	0.0486941	−	0.0486941i
$775$	−28.0117	+	5.69220i	−1.00621	+	0.204470i
$776$	2.97292			0.106721
$777$	1.40009	+	1.40009i	0.0502279	+	0.0502279i
$778$			48.2384i			1.72943i
$779$	−16.2246			−0.581306
$780$	−14.3516	+	5.05250i	−0.513870	+	0.180909i
$781$	−6.31226			−0.225870
$782$		−	16.9599i		−	0.606483i
$783$	−1.59521	−	1.59521i	−0.0570081	−	0.0570081i
$784$	27.8877			0.995990
$785$	7.10916	+	13.2345i	0.253737	+	0.472360i
$786$	−31.1758	+	31.1758i	−1.11200	+	1.11200i
$787$	6.05284			0.215761			0.107880	−	0.994164i	$-0.465594\pi$
$787$	6.05284			0.215761			0.107880	+	0.994164i	$0.465594\pi$
$788$			23.2455i			0.828087i
$789$			2.64983i			0.0943363i
$790$	19.6412	−	65.2328i	0.698802	−	2.32088i
$791$	7.42745	+	7.42745i	0.264090	+	0.264090i
$792$	0.254031	+	0.254031i	0.00902658	+	0.00902658i
$793$	−44.7480	−	6.96623i	−1.58905	−	0.247378i
$794$		−	70.0197i		−	2.48491i
$795$	8.37958	+	2.52304i	0.297193	+	0.0894829i
$796$	3.24407			0.114983
$797$	−16.7482	−	16.7482i	−0.593253	−	0.593253i	0.345256	−	0.938509i	$-0.387792\pi$
$797$	−16.7482	−	16.7482i	−0.593253	−	0.593253i	−0.938509	+	0.345256i	$0.887792\pi$
$798$	7.34263			0.259926
$799$	7.40935	+	7.40935i	0.262124	+	0.262124i
$800$	21.7024	−	32.7720i	0.767294	−	1.15867i
$801$	−7.34335	−	7.34335i	−0.259465	−	0.259465i
$802$	−38.8683	+	38.8683i	−1.37249	+	1.37249i
$803$	−17.7034	+	17.7034i	−0.624739	+	0.624739i
$804$	2.22986	−	2.22986i	0.0786409	−	0.0786409i
$805$	4.86465	+	9.05610i	0.171456	+	0.319186i
$806$	23.9739	+	32.8146i	0.844445	+	1.15584i
$807$	−15.6176	+	15.6176i	−0.549764	+	0.549764i
$808$	−1.74622			−0.0614318
$809$			18.1580i			0.638401i	0.947687	+	0.319200i	$0.103414\pi$
$809$			18.1580i			0.638401i	−0.947687	+	0.319200i	$0.896586\pi$
$810$	4.22142	+	1.27104i	0.148326	+	0.0446599i
$811$	−13.0477	+	13.0477i	−0.458168	+	0.458168i	−0.898054	−	0.439885i	$-0.855019\pi$
$811$	−13.0477	+	13.0477i	−0.458168	+	0.458168i	0.439885	+	0.898054i	$0.355019\pi$
$812$		−	2.62581i		−	0.0921478i
$813$		−	14.0861i		−	0.494021i
$814$	7.22919	−	7.22919i	0.253383	−	0.253383i
$815$	−1.33792	−	0.402840i	−0.0468654	−	0.0141109i
$816$			4.86176i			0.170196i
$817$	5.86764			0.205283
$818$	36.6451	−	36.6451i	1.28127	−	1.28127i
$819$	−0.342067	+	2.19729i	−0.0119528	+	0.0767794i
$820$	−5.36556	−	9.98859i	−0.187373	−	0.348817i
$821$	−5.41615	+	5.41615i	−0.189025	+	0.189025i	−0.795274	−	0.606250i	$-0.792673\pi$
$821$	−5.41615	+	5.41615i	−0.189025	+	0.189025i	0.606250	+	0.795274i	$0.292673\pi$
$822$	−1.20989	+	1.20989i	−0.0421999	+	0.0421999i
$823$	−27.4743	+	27.4743i	−0.957694	+	0.957694i	−0.999141	−	0.0414467i	$-0.986803\pi$
$823$	−27.4743	+	27.4743i	−0.957694	+	0.957694i	0.0414467	+	0.999141i	$0.486803\pi$
$824$	2.61626	+	2.61626i	0.0911417	+	0.0911417i
$825$	−4.45907	+	6.73349i	−0.155245	+	0.234430i
$826$	4.93084	+	4.93084i	0.171566	+	0.171566i
$827$	4.15065			0.144332			0.0721661	−	0.997393i	$-0.477009\pi$
$827$	4.15065			0.144332			0.0721661	+	0.997393i	$0.477009\pi$
$828$	−9.94700	−	9.94700i	−0.345682	−	0.345682i
$829$	−20.2410			−0.702998			−0.351499	−	0.936188i	$-0.614328\pi$
$829$	−20.2410			−0.702998			−0.351499	+	0.936188i	$0.614328\pi$
$830$	20.6133	+	6.20652i	0.715497	+	0.215432i
$831$			32.3090i			1.12079i
$832$	−25.2003	−	3.92310i	−0.873663	−	0.136009i
$833$	−5.40169	−	5.40169i	−0.187158	−	0.187158i
$834$	17.0523	+	17.0523i	0.590473	+	0.590473i
$835$	−9.83652	+	32.6693i	−0.340407	+	1.13057i
$836$		−	18.4063i		−	0.636594i
$837$		−	5.71683i		−	0.197603i
$838$	−29.4421			−1.01706
$839$	−10.7010	+	10.7010i	−0.369441	+	0.369441i	−0.867273	−	0.497833i	$-0.834129\pi$
$839$	−10.7010	+	10.7010i	−0.369441	+	0.369441i	0.497833	+	0.867273i	$0.334129\pi$
$840$	−0.145154	−	0.270221i	−0.00500830	−	0.00932351i
$841$	23.9106			0.824504
$842$	−6.12971	−	6.12971i	−0.211244	−	0.211244i
$843$			28.3127i			0.975143i
$844$	−2.70892			−0.0932450
$845$	16.4455	−	23.9697i	0.565743	−	0.824582i
$846$	17.9019			0.615482
$847$			5.17526i			0.177824i
$848$	11.6586	+	11.6586i	0.400358	+	0.400358i
$849$	−5.16753			−0.177349
$850$	−11.1484	+	2.26545i	−0.382388	+	0.0777045i
$851$	16.9213	−	16.9213i	0.580054	−	0.580054i
$852$	−7.37512			−0.252668
$853$		−	20.6709i		−	0.707757i	−0.935291	−	0.353879i	$-0.884863\pi$
$853$		−	20.6709i		−	0.707757i	0.935291	−	0.353879i	$-0.115137\pi$
$854$			15.2734i			0.522644i
$855$	6.38946	+	11.8947i	0.218515	+	0.406790i
$856$	0.264108	+	0.264108i	0.00902703	+	0.00902703i
$857$	20.4633	+	20.4633i	0.699013	+	0.699013i	0.964198	−	0.265185i	$-0.0854330\pi$
$857$	20.4633	+	20.4633i	0.699013	+	0.699013i	−0.265185	+	0.964198i	$0.585433\pi$
$858$	11.3454	+	1.76622i	0.387326	+	0.0602978i
$859$			22.8410i			0.779325i	0.920958	+	0.389663i	$0.127408\pi$
$859$			22.8410i			0.779325i	−0.920958	+	0.389663i	$0.872592\pi$
$860$	1.94046	+	3.61239i	0.0661691	+	0.123181i
$861$	−1.65718			−0.0564765
$862$	8.90988	+	8.90988i	0.303472	+	0.303472i
$863$	20.7883			0.707644			0.353822	−	0.935313i	$-0.384882\pi$
$863$	20.7883			0.707644			0.353822	+	0.935313i	$0.384882\pi$
$864$	5.55877	+	5.55877i	0.189113	+	0.189113i
$865$	−9.34066	−	17.3887i	−0.317592	−	0.591233i
$866$	2.04865	+	2.04865i	0.0696161	+	0.0696161i
$867$	−11.0791	+	11.0791i	−0.376267	+	0.376267i
$868$	4.70512	−	4.70512i	0.159702	−	0.159702i
$869$	−17.6491	+	17.6491i	−0.598706	+	0.598706i
$870$	8.76163	−	4.70647i	0.297047	−	0.159564i
$871$	−0.926771	+	5.95317i	−0.0314024	+	0.201715i
$872$	1.09069	−	1.09069i	0.0369354	−	0.0369354i
$873$	−13.3663			−0.452382
$874$		−	88.7419i		−	3.00174i
$875$	5.30315	−	4.40743i	0.179279	−	0.148998i
$876$	−20.6843	+	20.6843i	−0.698857	+	0.698857i
$877$		−	30.0306i		−	1.01406i	−0.861928	−	0.507031i	$-0.830743\pi$
$877$		−	30.0306i		−	1.01406i	0.861928	−	0.507031i	$-0.169257\pi$
$878$			58.6678i			1.97994i
$879$	16.6148	−	16.6148i	0.560403	−	0.560403i
$880$	−13.4044	+	7.20040i	−0.451861	+	0.242725i
$881$		−	10.2712i		−	0.346047i	−0.984918	−	0.173023i	$-0.944646\pi$
$881$		−	10.2712i		−	0.346047i	0.984918	−	0.173023i	$-0.0553536\pi$
$882$	−13.0512			−0.439457
$883$	−8.61028	+	8.61028i	−0.289759	+	0.289759i	−0.836985	−	0.547226i	$-0.815684\pi$
$883$	−8.61028	+	8.61028i	−0.289759	+	0.289759i	0.547226	+	0.836985i	$0.315684\pi$
$884$	4.63226	+	6.34046i	0.155800	+	0.213253i
$885$	−3.69697	+	12.2785i	−0.124272	+	0.412736i
$886$	−4.26075	+	4.26075i	−0.143143	+	0.143143i
$887$	30.1903	−	30.1903i	1.01369	−	1.01369i	0.0137874	−	0.999905i	$-0.495611\pi$
$887$	30.1903	−	30.1903i	1.01369	−	1.01369i	0.999905	−	0.0137874i	$-0.00438882\pi$
$888$	−0.504906	+	0.504906i	−0.0169436	+	0.0169436i
$889$	−3.00797	−	3.00797i	−0.100884	−	0.100884i
$890$	40.3331	−	21.6657i	1.35197	−	0.726235i
$891$	−1.14213	−	1.14213i	−0.0382628	−	0.0382628i
$892$	−42.6737			−1.42882
$893$	38.7692	+	38.7692i	1.29736	+	1.29736i
$894$	0.342729			0.0114626
$895$	6.11247	−	20.3009i	0.204317	−	0.678585i
$896$		−	1.09568i		−	0.0366041i
$897$	26.5561	+	4.13417i	0.886681	+	0.138036i
$898$	15.2611	+	15.2611i	0.509270	+	0.509270i
$899$	−9.11954	−	9.11954i	−0.304154	−	0.304154i
$900$	−5.20989	+	7.86728i	−0.173663	+	0.262243i
$901$		−	4.51641i		−	0.150464i
$902$			8.55665i			0.284905i
$903$	0.599321			0.0199441
$904$	−2.67852	+	2.67852i	−0.0890862	+	0.0890862i
$905$	28.3488	+	8.53564i	0.942346	+	0.283734i
$906$	9.49061			0.315304
$907$	2.97313	+	2.97313i	0.0987211	+	0.0987211i	0.754742	−	0.656021i	$-0.227762\pi$
$907$	2.97313	+	2.97313i	0.0987211	+	0.0987211i	−0.656021	+	0.754742i	$0.727762\pi$
$908$		−	46.5191i		−	1.54379i
$909$	7.85108			0.260404
$910$	−8.84089	−	4.23685i	−0.293073	−	0.140450i
$911$	−3.49551			−0.115811			−0.0579057	−	0.998322i	$-0.518442\pi$
$911$	−3.49551			−0.115811			−0.0579057	+	0.998322i	$0.518442\pi$
$912$			25.4390i			0.842369i
$913$	−5.57705	−	5.57705i	−0.184573	−	0.184573i
$914$	2.79317			0.0923898
$915$	−24.7421	+	13.2907i	−0.817948	+	0.439376i
$916$	−0.798163	+	0.798163i	−0.0263720	+	0.0263720i
$917$	−13.7921			−0.455455
$918$		−	2.27526i		−	0.0750946i
$919$			16.6055i			0.547766i	0.961763	+	0.273883i	$0.0883081\pi$
$919$			16.6055i			0.547766i	−0.961763	+	0.273883i	$0.911692\pi$
$920$	−3.26585	+	1.75431i	−0.107672	+	0.0578379i
$921$	16.3527	+	16.3527i	0.538839	+	0.538839i
$922$	−34.3445	−	34.3445i	−1.13108	−	1.13108i
$923$	11.3775	−	8.31227i	0.374495	−	0.273602i
$924$		−	1.88001i		−	0.0618479i
$925$	−13.3834	−	8.86276i	−0.440042	−	0.291406i
$926$	18.5368			0.609158
$927$	−11.7628	−	11.7628i	−0.386341	−	0.386341i
$928$	17.7348			0.582174
$929$	−21.1479	−	21.1479i	−0.693841	−	0.693841i	0.269234	−	0.963075i	$-0.413230\pi$
$929$	−21.1479	−	21.1479i	−0.693841	−	0.693841i	−0.963075	+	0.269234i	$0.913230\pi$
$930$	24.1332	+	7.26634i	0.791357	+	0.238273i
$931$	−28.2642	−	28.2642i	−0.926321	−	0.926321i
$932$	22.9696	−	22.9696i	0.752394	−	0.752394i
$933$	15.9075	−	15.9075i	0.520789	−	0.520789i
$934$	−43.1068	+	43.1068i	−1.41050	+	1.41050i
$935$	3.99102	+	1.20167i	0.130520	+	0.0392989i
$936$	−0.792395	−	0.123358i	−0.0259002	−	0.00403207i
$937$	8.85950	−	8.85950i	0.289427	−	0.289427i	−0.547427	−	0.836854i	$-0.684392\pi$
$937$	8.85950	−	8.85950i	0.289427	−	0.289427i	0.836854	+	0.547427i	$0.184392\pi$
$938$	2.03193			0.0663449
$939$			26.6871i			0.870901i
$940$	−11.0469	+	36.6892i	−0.360310	+	1.19667i
$941$	−19.6731	+	19.6731i	−0.641323	+	0.641323i	−0.950881	−	0.309557i	$-0.899819\pi$
$941$	−19.6731	+	19.6731i	−0.641323	+	0.641323i	0.309557	+	0.950881i	$0.399819\pi$
$942$		−	13.2462i		−	0.431584i
$943$			20.0284i			0.652215i
$944$	−17.0832	+	17.0832i	−0.556011	+	0.556011i
$945$	0.652619	+	1.21492i	0.0212297	+	0.0395215i
$946$		−	3.09452i		−	0.100612i
$947$	−40.3886			−1.31245			−0.656227	−	0.754564i	$-0.727849\pi$
$947$	−40.3886			−1.31245			−0.656227	+	0.754564i	$0.727849\pi$
$948$	−20.6209	+	20.6209i	−0.669736	+	0.669736i
$949$	8.59678	−	55.2220i	0.279063	−	1.79258i
$950$	−58.3338	+	11.8539i	−1.89260	+	0.384592i
$951$	16.4800	−	16.4800i	0.534400	−	0.534400i
$952$	−0.111939	+	0.111939i	−0.00362797	+	0.00362797i
$953$	−37.7716	+	37.7716i	−1.22354	+	1.22354i	−0.257176	+	0.966365i	$0.582792\pi$
$953$	−37.7716	+	37.7716i	−1.22354	+	1.22354i	−0.966365	+	0.257176i	$0.917208\pi$
$954$	−5.45612	−	5.45612i	−0.176648	−	0.176648i
$955$	−10.8189	+	35.9321i	−0.350092	+	1.16274i
$956$	−15.5631	−	15.5631i	−0.503348	−	0.503348i
$957$	−3.64388			−0.117790
$958$	−45.7542	−	45.7542i	−1.47825	−	1.47825i
$959$	−0.535254			−0.0172842
$960$	−13.9338	+	7.48478i	−0.449710	+	0.241570i
$961$		−	1.68217i		−	0.0542634i
$962$	−3.51051	+	22.5500i	−0.113183	+	0.727040i
$963$	−1.18744	−	1.18744i	−0.0382648	−	0.0382648i
$964$	6.66830	+	6.66830i	0.214771	+	0.214771i
$965$	−20.5281	−	6.18087i	−0.660822	−	0.198969i
$966$		−	9.06410i		−	0.291633i
$967$			2.41199i			0.0775644i	0.999248	+	0.0387822i	$0.0123479\pi$
$967$			2.41199i			0.0775644i	−0.999248	+	0.0387822i	$0.987652\pi$
$968$	−1.86633			−0.0599860
$969$	4.92739	−	4.92739i	0.158290	−	0.158290i
$970$	16.9892	−	56.4250i	0.545490	−	1.81170i
$971$	43.9182			1.40940			0.704701	−	0.709505i	$-0.251081\pi$
$971$	43.9182			1.40940			0.704701	+	0.709505i	$0.251081\pi$
$972$	−1.33444	−	1.33444i	−0.0428023	−	0.0428023i
$973$			7.54389i			0.241846i
$974$	−57.1062			−1.82980
$975$	−0.829731	−	18.0087i	−0.0265726	−	0.576738i
$976$	−52.9155			−1.69378
$977$			0.655019i			0.0209559i	0.999945	+	0.0104780i	$0.00333530\pi$
$977$			0.655019i			0.0209559i	−0.999945	+	0.0104780i	$0.996665\pi$
$978$	0.871151	+	0.871151i	0.0278563	+	0.0278563i
$979$	−16.7741			−0.536104
$980$	8.05360	−	26.7478i	0.257263	−	0.854428i
$981$	−4.90378	+	4.90378i	−0.156566	+	0.156566i
$982$	−3.26470			−0.104181
$983$		−	21.4040i		−	0.682681i	−0.939940	−	0.341340i	$-0.889119\pi$
$983$		−	21.4040i		−	0.682681i	0.939940	−	0.341340i	$-0.110881\pi$
$984$		−	0.597619i		−	0.0190514i
$985$	−26.3733	−	7.94083i	−0.840323	−	0.253016i
$986$	−3.62951	−	3.62951i	−0.115587	−	0.115587i
$987$	3.95988	+	3.95988i	0.126044	+	0.126044i
$988$	24.2382	+	33.1763i	0.771119	+	1.05548i
$989$		−	7.24330i		−	0.230323i
$990$	6.27312	−	3.36972i	0.199373	−	0.107097i
$991$	43.0224			1.36665			0.683326	−	0.730113i	$-0.260533\pi$
$991$	43.0224			1.36665			0.683326	+	0.730113i	$0.260533\pi$
$992$	31.7786	+	31.7786i	1.00897	+	1.00897i
$993$	−19.0254			−0.603754
$994$	−3.36025	−	3.36025i	−0.106581	−	0.106581i
$995$	−1.10820	+	3.68058i	−0.0351322	+	0.116682i
$996$	−6.51611	−	6.51611i	−0.206471	−	0.206471i
$997$	25.7164	−	25.7164i	0.814448	−	0.814448i	−0.170849	−	0.985297i	$-0.554651\pi$
$997$	25.7164	−	25.7164i	0.814448	−	0.814448i	0.985297	+	0.170849i	$0.0546511\pi$
$998$	−39.3006	+	39.3006i	−1.24404	+	1.24404i
$999$	2.27008	−	2.27008i	0.0718221	−	0.0718221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.k.a.148.3	yes	28
3.2	odd	2		585.2.n.g.343.12		28
5.2	odd	4		195.2.t.a.187.12	yes	28
5.3	odd	4		975.2.t.d.382.3		28
5.4	even	2		975.2.k.d.343.12		28
13.8	odd	4		195.2.t.a.73.12	yes	28
15.2	even	4		585.2.w.g.577.3		28
39.8	even	4		585.2.w.g.73.3		28
65.8	even	4		975.2.k.d.307.3		28
65.34	odd	4		975.2.t.d.268.3		28
65.47	even	4	inner	195.2.k.a.112.12	✓	28
195.47	odd	4		585.2.n.g.307.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.12	✓	28	65.47	even	4	inner
195.2.k.a.148.3	yes	28	1.1	even	1	trivial
195.2.t.a.73.12	yes	28	13.8	odd	4
195.2.t.a.187.12	yes	28	5.2	odd	4
585.2.n.g.307.3		28	195.47	odd	4
585.2.n.g.343.12		28	3.2	odd	2
585.2.w.g.73.3		28	39.8	even	4
585.2.w.g.577.3		28	15.2	even	4
975.2.k.d.307.3		28	65.8	even	4
975.2.k.d.343.12		28	5.4	even	2
975.2.t.d.268.3		28	65.34	odd	4
975.2.t.d.382.3		28	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.97160i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.88719 q^{4} +(0.644677 - 2.14112i) q^{5} +(-1.39413 + 1.39413i) q^{6} -0.616758 q^{7} -0.222418i q^{8} +1.00000i q^{9} +(-4.22142 - 1.27104i) q^{10} +(1.14213 + 1.14213i) q^{11} +(1.33444 + 1.33444i) q^{12} +(-3.56264 - 0.554621i) q^{13} +1.21600i q^{14} +(-1.96986 + 1.05814i) q^{15} -4.21290 q^{16} +(0.816014 + 0.816014i) q^{17} +1.97160 q^{18} +(4.26977 + 4.26977i) q^{19} +(-1.21663 + 4.04070i) q^{20} +(0.436114 + 0.436114i) q^{21} +(2.25182 - 2.25182i) q^{22} +(5.27080 - 5.27080i) q^{23} +(-0.157273 + 0.157273i) q^{24} +(-4.16878 - 2.76066i) q^{25} +(-1.09349 + 7.02408i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.16394 q^{28} -2.25597i q^{29} +(2.08623 + 3.88376i) q^{30} +(4.04241 - 4.04241i) q^{31} +7.86129i q^{32} -1.61522i q^{33} +(1.60885 - 1.60885i) q^{34} +(-0.397610 + 1.32055i) q^{35} -1.88719i q^{36} +3.21038 q^{37} +(8.41825 - 8.41825i) q^{38} +(2.12699 + 2.91134i) q^{39} +(-0.476223 - 0.143388i) q^{40} +(-1.89994 + 1.89994i) q^{41} +(0.859840 - 0.859840i) q^{42} +(0.687115 - 0.687115i) q^{43} +(-2.15542 - 2.15542i) q^{44} +(2.14112 + 0.644677i) q^{45} +(-10.3919 - 10.3919i) q^{46} +9.07993 q^{47} +(2.97897 + 2.97897i) q^{48} -6.61961 q^{49} +(-5.44291 + 8.21915i) q^{50} -1.15402i q^{51} +(6.72337 + 1.04667i) q^{52} +(-2.76736 - 2.76736i) q^{53} +(-1.39413 - 1.39413i) q^{54} +(3.18175 - 1.70913i) q^{55} +0.137178i q^{56} -6.03836i q^{57} -4.44785 q^{58} +(4.05498 - 4.05498i) q^{59} +(3.71749 - 1.99692i) q^{60} +12.5604 q^{61} +(-7.97000 - 7.97000i) q^{62} -0.616758i q^{63} +7.07349 q^{64} +(-3.48426 + 7.27048i) q^{65} -3.18456 q^{66} -1.67100i q^{67} +(-1.53997 - 1.53997i) q^{68} -7.45404 q^{69} +(2.60360 + 0.783926i) q^{70} +(-2.76337 + 2.76337i) q^{71} +0.222418 q^{72} +15.5003i q^{73} -6.32956i q^{74} +(0.995692 + 4.89986i) q^{75} +(-8.05786 - 8.05786i) q^{76} +(-0.704419 - 0.704419i) q^{77} +(5.73999 - 4.19356i) q^{78} +15.4528i q^{79} +(-2.71596 + 9.02031i) q^{80} -1.00000 q^{81} +(3.74591 + 3.74591i) q^{82} -4.88302 q^{83} +(-0.823029 - 0.823029i) q^{84} +(2.27325 - 1.22112i) q^{85} +(-1.35471 - 1.35471i) q^{86} +(-1.59521 + 1.59521i) q^{87} +(0.254031 - 0.254031i) q^{88} +(-7.34335 + 7.34335i) q^{89} +(1.27104 - 4.22142i) q^{90} +(2.19729 + 0.342067i) q^{91} +(-9.94700 + 9.94700i) q^{92} -5.71683 q^{93} -17.9019i q^{94} +(11.8947 - 6.38946i) q^{95} +(5.55877 - 5.55877i) q^{96} +13.3663i q^{97} +13.0512i q^{98} +(-1.14213 + 1.14213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40}+ \cdots + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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