LMFDB - Embedded newform 95.2.b.b.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(39,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("95.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.2
Root			$-2.68667i$ of defining polynomial
Character	$\chi$	$=$	95.39
Dual form			95.2.b.b.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82254i q^{2} +2.31446i q^{3} -1.32164 q^{4} +(1.94827 + 1.09737i) q^{5} +4.21819 q^{6} -1.45033i q^{7} -1.23634i q^{8} -2.35673 q^{9} +O(q^{10})$	\(q-1.82254i q^{2} +2.31446i q^{3} -1.32164 q^{4} +(1.94827 + 1.09737i) q^{5} +4.21819 q^{6} -1.45033i q^{7} -1.23634i q^{8} -2.35673 q^{9} +(2.00000 - 3.55080i) q^{10} -3.89655 q^{11} -3.05888i q^{12} +3.05888i q^{13} -2.64327 q^{14} +(-2.53982 + 4.50920i) q^{15} -4.89655 q^{16} -3.92301i q^{17} +4.29522i q^{18} +1.00000 q^{19} +(-2.57491 - 1.45033i) q^{20} +3.35673 q^{21} +7.10160i q^{22} -5.37334i q^{23} +2.86146 q^{24} +(2.59155 + 4.27596i) q^{25} +5.57491 q^{26} +1.48883i q^{27} +1.91681i q^{28} -6.00000 q^{29} +(8.21819 + 4.62892i) q^{30} -8.43637 q^{31} +6.45146i q^{32} -9.01841i q^{33} -7.14982 q^{34} +(1.59155 - 2.82564i) q^{35} +3.11474 q^{36} +5.95953i q^{37} -1.82254i q^{38} -7.07965 q^{39} +(1.35673 - 2.40873i) q^{40} +10.4364 q^{41} -6.11775i q^{42} -1.45033i q^{43} +5.14982 q^{44} +(-4.59155 - 2.58620i) q^{45} -9.79310 q^{46} -4.90686i q^{47} -11.3329i q^{48} +4.89655 q^{49} +(7.79310 - 4.72319i) q^{50} +9.07965 q^{51} -4.04272i q^{52} -4.23127i q^{53} +2.71345 q^{54} +(-7.59155 - 4.27596i) q^{55} -1.79310 q^{56} +2.31446i q^{57} +10.9352i q^{58} -3.35673 q^{59} +(3.35673 - 5.95953i) q^{60} +10.3329 q^{61} +15.3756i q^{62} +3.41802i q^{63} +1.96491 q^{64} +(-3.35673 + 5.95953i) q^{65} -16.4364 q^{66} +9.84404i q^{67} +5.18479i q^{68} +12.4364 q^{69} +(-5.14982 - 2.90066i) q^{70} +8.64327 q^{71} +2.91372i q^{72} -2.43418i q^{73} +10.8615 q^{74} +(-9.89655 + 5.99804i) q^{75} -1.32164 q^{76} +5.65127i q^{77} +12.9029i q^{78} +12.4364 q^{79} +(-9.53982 - 5.37334i) q^{80} -10.5160 q^{81} -19.0207i q^{82} +12.6635i q^{83} -4.43637 q^{84} +(4.30500 - 7.64310i) q^{85} -2.64327 q^{86} -13.8868i q^{87} +4.81746i q^{88} -12.3662 q^{89} +(-4.71345 + 8.36826i) q^{90} +4.43637 q^{91} +7.10160i q^{92} -19.5256i q^{93} -8.94292 q^{94} +(1.94827 + 1.09737i) q^{95} -14.9316 q^{96} -3.05888i q^{97} -8.92414i q^{98} +9.18310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{4} - q^{5} - 14 q^{9}+O(q^{10}) $ 6 * q - 8 * q^4 - q^5 - 14 * q^9	$ 6 q - 8 q^{4} - q^{5} - 14 q^{9} + 12 q^{10} + 2 q^{11} - 16 q^{14} + 10 q^{15} - 4 q^{16} + 6 q^{19} + 10 q^{20} + 20 q^{21} - 8 q^{24} + 3 q^{25} + 8 q^{26} - 36 q^{29} + 24 q^{30} + 8 q^{34} - 3 q^{35} - 32 q^{36} + 8 q^{39} + 8 q^{40} + 12 q^{41} - 20 q^{44} - 15 q^{45} - 8 q^{46} + 4 q^{49} - 4 q^{50} + 4 q^{51} + 16 q^{54} - 33 q^{55} + 40 q^{56} - 20 q^{59} + 20 q^{60} - 14 q^{61} + 12 q^{64} - 20 q^{65} - 48 q^{66} + 24 q^{69} + 20 q^{70} + 52 q^{71} + 40 q^{74} - 34 q^{75} - 8 q^{76} + 24 q^{79} - 32 q^{80} + 38 q^{81} + 24 q^{84} + 13 q^{85} - 16 q^{86} - 24 q^{89} - 28 q^{90} - 24 q^{91} + 48 q^{94} - q^{95} - 64 q^{96} + 30 q^{99}+O(q^{100}) $ 6 * q - 8 * q^4 - q^5 - 14 * q^9 + 12 * q^10 + 2 * q^11 - 16 * q^14 + 10 * q^15 - 4 * q^16 + 6 * q^19 + 10 * q^20 + 20 * q^21 - 8 * q^24 + 3 * q^25 + 8 * q^26 - 36 * q^29 + 24 * q^30 + 8 * q^34 - 3 * q^35 - 32 * q^36 + 8 * q^39 + 8 * q^40 + 12 * q^41 - 20 * q^44 - 15 * q^45 - 8 * q^46 + 4 * q^49 - 4 * q^50 + 4 * q^51 + 16 * q^54 - 33 * q^55 + 40 * q^56 - 20 * q^59 + 20 * q^60 - 14 * q^61 + 12 * q^64 - 20 * q^65 - 48 * q^66 + 24 * q^69 + 20 * q^70 + 52 * q^71 + 40 * q^74 - 34 * q^75 - 8 * q^76 + 24 * q^79 - 32 * q^80 + 38 * q^81 + 24 * q^84 + 13 * q^85 - 16 * q^86 - 24 * q^89 - 28 * q^90 - 24 * q^91 + 48 * q^94 - q^95 - 64 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.82254i		−	1.28873i	−0.764719	−	0.644364i	$-0.777122\pi$
$2$		−	1.82254i		−	1.28873i	0.764719	−	0.644364i	$-0.222878\pi$
$3$			2.31446i			1.33625i	0.744047	+	0.668127i	$0.232904\pi$
$3$			2.31446i			1.33625i	−0.744047	+	0.668127i	$0.767096\pi$
$4$	−1.32164			−0.660819
$5$	1.94827	+	1.09737i	0.871295	+	0.490760i
$5$	1.94827	+	1.09737i	0.871295	+	0.490760i
$6$	4.21819			1.72207
$7$		−	1.45033i		−	0.548172i	−0.961705	−	0.274086i	$-0.911625\pi$
$7$		−	1.45033i		−	0.548172i	0.961705	−	0.274086i	$-0.0883754\pi$
$8$		−	1.23634i		−	0.437112i
$9$	−2.35673			−0.785575
$10$	2.00000	−	3.55080i	0.632456	−	1.12286i
$11$	−3.89655			−1.17485			−0.587427	−	0.809277i	$-0.699859\pi$
$11$	−3.89655			−1.17485			−0.587427	+	0.809277i	$0.699859\pi$
$12$		−	3.05888i		−	0.883022i
$13$			3.05888i			0.848380i	0.905573	+	0.424190i	$0.139441\pi$
$13$			3.05888i			0.848380i	−0.905573	+	0.424190i	$0.860559\pi$
$14$	−2.64327			−0.706445
$15$	−2.53982	+	4.50920i	−0.655780	+	1.16427i
$16$	−4.89655			−1.22414
$17$		−	3.92301i		−	0.951469i	−0.879589	−	0.475735i	$-0.842182\pi$
$17$		−	3.92301i		−	0.951469i	0.879589	−	0.475735i	$-0.157818\pi$
$18$			4.29522i			1.01239i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−2.57491	−	1.45033i	−0.575768	−	0.324303i
$21$	3.35673			0.732498
$22$			7.10160i			1.51407i
$23$		−	5.37334i		−	1.12042i	−0.828351	−	0.560209i	$-0.810721\pi$
$23$		−	5.37334i		−	1.12042i	0.828351	−	0.560209i	$-0.189279\pi$
$24$	2.86146			0.584093
$25$	2.59155	+	4.27596i	0.518310	+	0.855193i
$26$	5.57491			1.09333
$27$			1.48883i			0.286526i
$28$			1.91681i			0.362242i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	8.21819	+	4.62892i	1.50043	+	0.845121i
$31$	−8.43637			−1.51522			−0.757609	−	0.652709i	$-0.773632\pi$
$31$	−8.43637			−1.51522			−0.757609	+	0.652709i	$0.773632\pi$
$32$			6.45146i			1.14047i
$33$		−	9.01841i		−	1.56990i
$34$	−7.14982			−1.22618
$35$	1.59155	−	2.82564i	0.269021	−	0.477620i
$36$	3.11474			0.519123
$37$			5.95953i			0.979741i	0.871795	+	0.489871i	$0.162956\pi$
$37$			5.95953i			0.979741i	−0.871795	+	0.489871i	$0.837044\pi$
$38$		−	1.82254i		−	0.295654i
$39$	−7.07965			−1.13365
$40$	1.35673	−	2.40873i	0.214517	−	0.380854i
$41$	10.4364			1.62989			0.814944	−	0.579540i	$-0.196768\pi$
$41$	10.4364			1.62989			0.814944	+	0.579540i	$0.196768\pi$
$42$		−	6.11775i		−	0.943990i
$43$		−	1.45033i		−	0.221173i	−0.993867	−	0.110586i	$-0.964727\pi$
$43$		−	1.45033i		−	0.221173i	0.993867	−	0.110586i	$-0.0352729\pi$
$44$	5.14982			0.776365
$45$	−4.59155	−	2.58620i	−0.684468	−	0.385529i
$46$	−9.79310			−1.44391
$47$		−	4.90686i		−	0.715739i	−0.933772	−	0.357869i	$-0.883503\pi$
$47$		−	4.90686i		−	0.715739i	0.933772	−	0.357869i	$-0.116497\pi$
$48$		−	11.3329i		−	1.63576i
$49$	4.89655			0.699507
$50$	7.79310	−	4.72319i	1.10211	−	0.667960i
$51$	9.07965			1.27140
$52$		−	4.04272i		−	0.560625i
$53$		−	4.23127i		−	0.581209i	−0.956843	−	0.290605i	$-0.906144\pi$
$53$		−	4.23127i		−	0.581209i	0.956843	−	0.290605i	$-0.0938564\pi$
$54$	2.71345			0.369254
$55$	−7.59155	−	4.27596i	−1.02364	−	0.576571i
$56$	−1.79310			−0.239613
$57$			2.31446i			0.306558i
$58$			10.9352i			1.43586i
$59$	−3.35673			−0.437008			−0.218504	−	0.975836i	$-0.570118\pi$
$59$	−3.35673			−0.437008			−0.218504	+	0.975836i	$0.570118\pi$
$60$	3.35673	−	5.95953i	0.433351	−	0.769372i
$61$	10.3329			1.32300			0.661498	−	0.749947i	$-0.269921\pi$
$61$	10.3329			1.32300			0.661498	+	0.749947i	$0.269921\pi$
$62$			15.3756i			1.95270i
$63$			3.41802i			0.430631i
$64$	1.96491			0.245614
$65$	−3.35673	+	5.95953i	−0.416351	+	0.739189i
$66$	−16.4364			−2.02318
$67$			9.84404i			1.20264i	0.799008	+	0.601320i	$0.205358\pi$
$67$			9.84404i			1.20264i	−0.799008	+	0.601320i	$0.794642\pi$
$68$			5.18479i			0.628749i
$69$	12.4364			1.49716
$70$	−5.14982	−	2.90066i	−0.615522	−	0.346695i
$71$	8.64327			1.02577			0.512884	−	0.858458i	$-0.328577\pi$
$71$	8.64327			1.02577			0.512884	+	0.858458i	$0.328577\pi$
$72$			2.91372i			0.343385i
$73$		−	2.43418i		−	0.284899i	−0.989802	−	0.142449i	$-0.954502\pi$
$73$		−	2.43418i		−	0.284899i	0.989802	−	0.142449i	$-0.0454978\pi$
$74$	10.8615			1.26262
$75$	−9.89655	+	5.99804i	−1.14276	+	0.692594i
$76$	−1.32164			−0.151602
$77$			5.65127i			0.644022i
$78$			12.9029i			1.46097i
$79$	12.4364			1.39920			0.699601	−	0.714534i	$-0.253361\pi$
$79$	12.4364			1.39920			0.699601	+	0.714534i	$0.253361\pi$
$80$	−9.53982	−	5.37334i	−1.06658	−	0.600757i
$81$	−10.5160			−1.16845
$82$		−	19.0207i		−	2.10048i
$83$			12.6635i			1.39000i	0.719011	+	0.694999i	$0.244595\pi$
$83$			12.6635i			1.39000i	−0.719011	+	0.694999i	$0.755405\pi$
$84$	−4.43637			−0.484048
$85$	4.30500	−	7.64310i	0.466943	−	0.829011i
$86$	−2.64327			−0.285032
$87$		−	13.8868i		−	1.48882i
$88$			4.81746i			0.513543i
$89$	−12.3662			−1.31081			−0.655407	−	0.755276i	$-0.727503\pi$
$89$	−12.3662			−1.31081			−0.655407	+	0.755276i	$0.727503\pi$
$90$	−4.71345	+	8.36826i	−0.496841	+	0.882092i
$91$	4.43637			0.465058
$92$			7.10160i			0.740393i
$93$		−	19.5256i		−	2.02472i
$94$	−8.94292			−0.922392
$95$	1.94827	+	1.09737i	0.199889	+	0.112588i
$96$	−14.9316			−1.52395
$97$		−	3.05888i		−	0.310582i	−0.987869	−	0.155291i	$-0.950369\pi$
$97$		−	3.05888i		−	0.310582i	0.987869	−	0.155291i	$-0.0496315\pi$
$98$		−	8.92414i		−	0.901474i
$99$	9.18310			0.922936
$100$	−3.42509	−	5.65127i	−0.342509	−	0.565127i
$101$	3.35673			0.334007			0.167003	−	0.985956i	$-0.446591\pi$
$101$	3.35673			0.334007			0.167003	+	0.985956i	$0.446591\pi$
$102$		−	16.5480i		−	1.63849i
$103$			13.0611i			1.28695i	0.765466	+	0.643476i	$0.222508\pi$
$103$			13.0611i			1.28695i	−0.765466	+	0.643476i	$0.777492\pi$
$104$	3.78181			0.370837
$105$	6.53982	+	3.68358i	0.638221	+	0.359480i
$106$	−7.71164			−0.749020
$107$			5.77099i			0.557903i	0.960305	+	0.278951i	$0.0899868\pi$
$107$			5.77099i			0.557903i	−0.960305	+	0.278951i	$0.910013\pi$
$108$		−	1.96770i		−	0.189342i
$109$	−6.64327			−0.636310			−0.318155	−	0.948039i	$-0.603063\pi$
$109$	−6.64327			−0.636310			−0.318155	+	0.948039i	$0.603063\pi$
$110$	−7.79310	+	13.8359i	−0.743043	+	1.31920i
$111$	−13.7931			−1.30918
$112$			7.10160i			0.671038i
$113$		−	9.41606i		−	0.885789i	−0.896574	−	0.442894i	$-0.853952\pi$
$113$		−	9.41606i		−	0.885789i	0.896574	−	0.442894i	$-0.146048\pi$
$114$	4.21819			0.395069
$115$	5.89655	−	10.4687i	0.549856	−	0.976215i
$116$	7.92982			0.736266
$117$		−	7.20893i		−	0.666466i
$118$			6.11775i			0.563185i
$119$	−5.68965			−0.521569
$120$	5.57491	+	3.14009i	0.508918	+	0.286649i
$121$	4.18310			0.380282
$122$		−	18.8321i		−	1.70498i
$123$			24.1546i			2.17794i
$124$	11.1498			1.00128
$125$	0.356726	+	11.1746i	0.0319065	+	0.999491i
$126$	6.22947			0.554966
$127$		−	11.0934i		−	0.984383i	−0.870487	−	0.492192i	$-0.836196\pi$
$127$		−	11.0934i		−	0.984383i	0.870487	−	0.492192i	$-0.163804\pi$
$128$			9.32179i			0.823938i
$129$	3.35673			0.295543
$130$	10.8615	+	6.11775i	0.952613	+	0.536562i
$131$	4.61000			0.402778			0.201389	−	0.979511i	$-0.435455\pi$
$131$	4.61000			0.402778			0.201389	+	0.979511i	$0.435455\pi$
$132$			11.9191i			1.03742i
$133$		−	1.45033i		−	0.125759i
$134$	17.9411			1.54988
$135$	−1.63380	+	2.90066i	−0.140615	+	0.249649i
$136$	−4.85018			−0.415899
$137$			13.1808i			1.12612i	0.826417	+	0.563058i	$0.190375\pi$
$137$			13.1808i			1.12612i	−0.826417	+	0.563058i	$0.809625\pi$
$138$		−	22.6657i		−	1.92944i
$139$	−1.18310			−0.100349			−0.0501745	−	0.998740i	$-0.515978\pi$
$139$	−1.18310			−0.100349			−0.0501745	+	0.998740i	$0.515978\pi$
$140$	−2.10345	+	3.73447i	−0.177774	+	0.315620i
$141$	11.3567			0.956409
$142$		−	15.7527i		−	1.32194i
$143$		−	11.9191i		−	0.996722i
$144$	11.5398			0.961652
$145$	−11.6896	−	6.58423i	−0.970772	−	0.546791i
$146$	−4.43637			−0.367157
$147$			11.3329i			0.934719i
$148$		−	7.87634i		−	0.647431i
$149$	−5.46018			−0.447315			−0.223658	−	0.974668i	$-0.571800\pi$
$149$	−5.46018			−0.447315			−0.223658	+	0.974668i	$0.571800\pi$
$150$	10.9316	+	18.0368i	0.892565	+	1.47270i
$151$	−5.07965			−0.413376			−0.206688	−	0.978407i	$-0.566268\pi$
$151$	−5.07965			−0.413376			−0.206688	+	0.978407i	$0.566268\pi$
$152$		−	1.23634i		−	0.100280i
$153$			9.24546i			0.747451i
$154$	10.2996			0.829969
$155$	−16.4364	−	9.25784i	−1.32020	−	0.743608i
$156$	9.35673			0.749138
$157$		−	6.11775i		−	0.488250i	−0.969744	−	0.244125i	$-0.921499\pi$
$157$		−	6.11775i		−	0.488250i	0.969744	−	0.244125i	$-0.0785007\pi$
$158$		−	22.6657i		−	1.80319i
$159$	9.79310			0.776643
$160$	−7.07965	+	12.5692i	−0.559695	+	0.993683i
$161$	−7.79310			−0.614182
$162$			19.1658i			1.50581i
$163$		−	16.4365i		−	1.28740i	−0.765277	−	0.643701i	$-0.777398\pi$
$163$		−	16.4365i		−	1.28740i	0.765277	−	0.643701i	$-0.222602\pi$
$164$	−13.7931			−1.07706
$165$	9.89655	−	17.5703i	0.770445	−	1.36785i
$166$	23.0796			1.79133
$167$			3.80329i			0.294308i	0.989114	+	0.147154i	$0.0470112\pi$
$167$			3.80329i			0.294308i	−0.989114	+	0.147154i	$0.952989\pi$
$168$		−	4.15006i		−	0.320184i
$169$	3.64327			0.280252
$170$	−13.9298	−	7.84602i	−1.06837	−	0.601762i
$171$	−2.35673			−0.180223
$172$			1.91681i			0.146155i
$173$		−	11.3838i		−	0.865491i	−0.901516	−	0.432746i	$-0.857545\pi$
$173$		−	11.3838i		−	0.865491i	0.901516	−	0.432746i	$-0.142455\pi$
$174$	−25.3091			−1.91868
$175$	6.20155	−	3.75860i	0.468793	−	0.284123i
$176$	19.0796			1.43818
$177$		−	7.76901i		−	0.583954i
$178$			22.5378i			1.68928i
$179$	−10.0702			−0.752680			−0.376340	−	0.926482i	$-0.622818\pi$
$179$	−10.0702			−0.752680			−0.376340	+	0.926482i	$0.622818\pi$
$180$	6.06836	+	3.41802i	0.452309	+	0.254765i
$181$	0.573097			0.0425980			0.0212990	−	0.999773i	$-0.493220\pi$
$181$	0.573097			0.0425980			0.0212990	+	0.999773i	$0.493220\pi$
$182$		−	8.08545i		−	0.599333i
$183$			23.9151i			1.76786i
$184$	−6.64327			−0.489749
$185$	−6.53982	+	11.6108i	−0.480817	+	0.853643i
$186$	−35.5862			−2.60931
$187$			15.2862i			1.11784i
$188$			6.48509i			0.472973i
$189$	2.15930			0.157066
$190$	2.00000	−	3.55080i	0.145095	−	0.257602i
$191$	−3.18310			−0.230321			−0.115160	−	0.993347i	$-0.536738\pi$
$191$	−3.18310			−0.230321			−0.115160	+	0.993347i	$0.536738\pi$
$192$			4.54771i			0.328203i
$193$			3.05888i			0.220183i	0.993921	+	0.110091i	$0.0351143\pi$
$193$			3.05888i			0.220183i	−0.993921	+	0.110091i	$0.964886\pi$
$194$	−5.57491			−0.400255
$195$	−13.7931	−	7.76901i	−0.987744	−	0.556350i
$196$	−6.47146			−0.462247
$197$		−	21.4933i		−	1.53134i	−0.643235	−	0.765669i	$-0.722408\pi$
$197$		−	21.4933i		−	1.53134i	0.643235	−	0.765669i	$-0.277592\pi$
$198$		−	16.7365i		−	1.18941i
$199$	4.81690			0.341461			0.170731	−	0.985318i	$-0.445387\pi$
$199$	4.81690			0.341461			0.170731	+	0.985318i	$0.445387\pi$
$200$	5.28655	−	3.20404i	0.373815	−	0.226560i
$201$	−22.7836			−1.60703
$202$		−	6.11775i		−	0.430444i
$203$			8.70197i			0.610758i
$204$	−12.0000			−0.840168
$205$	20.3329	+	11.4526i	1.42011	+	0.799883i
$206$	23.8044			1.65853
$207$			12.6635i			0.880173i
$208$		−	14.9779i		−	1.03853i
$209$	−3.89655			−0.269530
$210$	6.71345	−	11.9191i	0.463272	−	0.822494i
$211$	10.5066			0.723301			0.361650	−	0.932314i	$-0.382213\pi$
$211$	10.5066			0.723301			0.361650	+	0.932314i	$0.382213\pi$
$212$			5.59220i			0.384074i
$213$			20.0045i			1.37069i
$214$	10.5178			0.718984
$215$	1.59155	−	2.82564i	0.108543	−	0.192707i
$216$	1.84070			0.125244
$217$			12.2355i			0.830600i
$218$			12.1076i			0.820031i
$219$	5.63380			0.380697
$220$	10.0333	+	5.65127i	0.676443	+	0.381009i
$221$	12.0000			0.807207
$222$			25.1384i			1.68718i
$223$		−	16.8947i		−	1.13136i	−0.824626	−	0.565678i	$-0.808615\pi$
$223$		−	16.8947i		−	1.13136i	0.824626	−	0.565678i	$-0.191385\pi$
$224$	9.35673			0.625173
$225$	−6.10757	−	10.0773i	−0.407171	−	0.671818i
$226$	−17.1611			−1.14154
$227$		−	17.1342i		−	1.13724i	−0.822602	−	0.568618i	$-0.807478\pi$
$227$		−	17.1342i		−	1.13724i	0.822602	−	0.568618i	$-0.192522\pi$
$228$		−	3.05888i		−	0.202579i
$229$	−25.0464			−1.65511			−0.827555	−	0.561384i	$-0.810269\pi$
$229$	−25.0464			−1.65511			−0.827555	+	0.561384i	$0.810269\pi$
$230$	−19.0796	−	10.7467i	−1.25807	−	0.708615i
$231$	−13.0796			−0.860578
$232$			7.41804i			0.487018i
$233$			19.2986i			1.26429i	0.774849	+	0.632147i	$0.217826\pi$
$233$			19.2986i			1.26429i	−0.774849	+	0.632147i	$0.782174\pi$
$234$	−13.1385			−0.858893
$235$	5.38465	−	9.55991i	0.351256	−	0.623620i
$236$	4.43637			0.288783
$237$			28.7835i			1.86969i
$238$			10.3696i			0.672161i
$239$	−18.7693			−1.21408			−0.607042	−	0.794669i	$-0.707644\pi$
$239$	−18.7693			−1.21408			−0.607042	+	0.794669i	$0.707644\pi$
$240$	12.4364	−	22.0795i	0.802764	−	1.42523i
$241$	−14.4364			−0.929929			−0.464964	−	0.885329i	$-0.653933\pi$
$241$	−14.4364			−0.929929			−0.464964	+	0.885329i	$0.653933\pi$
$242$		−	7.62385i		−	0.490079i
$243$		−	19.8724i		−	1.27482i
$244$	−13.6564			−0.874260
$245$	9.53982	+	5.37334i	0.609477	+	0.343290i
$246$	44.0226			2.80678
$247$			3.05888i			0.194632i
$248$			10.4302i			0.662320i
$249$	−29.3091			−1.85739
$250$	20.3662	−	0.650145i	1.28807	−	0.0411188i
$251$	−10.9762			−0.692811			−0.346406	−	0.938085i	$-0.612598\pi$
$251$	−10.9762			−0.692811			−0.346406	+	0.938085i	$0.612598\pi$
$252$		−	4.51739i		−	0.284569i
$253$			20.9375i			1.31633i
$254$	−20.2182			−1.26860
$255$	17.6896	+	9.96375i	1.10777	+	0.623954i
$256$	20.9191			1.30745
$257$			17.6392i			1.10030i	0.835066	+	0.550150i	$0.185430\pi$
$257$			17.6392i			1.10030i	−0.835066	+	0.550150i	$0.814570\pi$
$258$		−	6.11775i		−	0.380875i
$259$	8.64327			0.537067
$260$	4.43637	−	7.87634i	0.275132	−	0.488470i
$261$	14.1404			0.875266
$262$		−	8.40189i		−	0.519071i
$263$		−	1.68976i		−	0.104195i	−0.998642	−	0.0520975i	$-0.983409\pi$
$263$		−	1.68976i		−	0.104195i	0.998642	−	0.0520975i	$-0.0165907\pi$
$264$	−11.1498			−0.686224
$265$	4.64327	−	8.24367i	0.285234	−	0.506405i
$266$	−2.64327			−0.162070
$267$		−	28.6211i		−	1.75158i
$268$		−	13.0102i		−	0.794727i
$269$	27.1022			1.65245			0.826226	−	0.563339i	$-0.190484\pi$
$269$	27.1022			1.65245			0.826226	+	0.563339i	$0.190484\pi$
$270$	5.28655	+	2.97767i	0.321729	+	0.181215i
$271$	23.9524			1.45500			0.727502	−	0.686105i	$-0.240681\pi$
$271$	23.9524			1.45500			0.727502	+	0.686105i	$0.240681\pi$
$272$			19.2092i			1.16473i
$273$			10.2678i			0.621436i
$274$	24.0226			1.45126
$275$	−10.0981	−	16.6615i	−0.608938	−	1.00473i
$276$	−16.4364			−0.989353
$277$		−	8.23549i		−	0.494822i	−0.968911	−	0.247411i	$-0.920420\pi$
$277$		−	8.23549i		−	0.494822i	0.968911	−	0.247411i	$-0.0795799\pi$
$278$			2.15624i			0.129323i
$279$	19.8822			1.19032
$280$	−3.49345	−	1.96770i	−0.208774	−	0.117592i
$281$	−10.4364			−0.622582			−0.311291	−	0.950315i	$-0.600761\pi$
$281$	−10.4364			−0.622582			−0.311291	+	0.950315i	$0.600761\pi$
$282$		−	20.6980i		−	1.23255i
$283$		−	10.4687i		−	0.622302i	−0.950361	−	0.311151i	$-0.899286\pi$
$283$		−	10.4687i		−	0.622302i	0.950361	−	0.311151i	$-0.100714\pi$
$284$	−11.4233			−0.677847
$285$	−2.53982	+	4.50920i	−0.150446	+	0.267102i
$286$	−21.7229			−1.28450
$287$		−	15.1362i		−	0.893459i
$288$		−	15.2043i		−	0.895923i
$289$	1.61000			0.0947059
$290$	−12.0000	+	21.3048i	−0.704664	+	1.25106i
$291$	7.07965			0.415016
$292$			3.21710i			0.188266i
$293$		−	16.4668i		−	0.961999i	−0.876721	−	0.481000i	$-0.840274\pi$
$293$		−	16.4668i		−	0.961999i	0.876721	−	0.481000i	$-0.159726\pi$
$294$	20.6546			1.20460
$295$	−6.53982	−	3.68358i	−0.380763	−	0.214466i
$296$	7.36801			0.428257
$297$		−	5.80131i		−	0.336626i
$298$			9.95137i			0.576467i
$299$	16.4364			0.950540
$300$	13.0796	−	7.92723i	0.755154	−	0.457679i
$301$	−2.10345			−0.121241
$302$			9.25784i			0.532729i
$303$			7.76901i			0.446318i
$304$	−4.89655			−0.280836
$305$	20.1314	+	11.3391i	1.15272	+	0.649273i
$306$	16.8502			0.963260
$307$		−	7.87634i		−	0.449526i	−0.974413	−	0.224763i	$-0.927839\pi$
$307$		−	7.87634i		−	0.449526i	0.974413	−	0.224763i	$-0.0721609\pi$
$308$		−	7.46893i		−	0.425582i
$309$	−30.2295			−1.71969
$310$	−16.8727	+	29.9559i	−0.958308	+	1.70138i
$311$	3.89655			0.220953			0.110477	−	0.993879i	$-0.464762\pi$
$311$	3.89655			0.220953			0.110477	+	0.993879i	$0.464762\pi$
$312$			8.75286i			0.495533i
$313$			7.76901i			0.439130i	0.975598	+	0.219565i	$0.0704638\pi$
$313$			7.76901i			0.439130i	−0.975598	+	0.219565i	$0.929536\pi$
$314$	−11.1498			−0.629221
$315$	−3.75084	+	6.65925i	−0.211336	+	0.375206i
$316$	−16.4364			−0.924618
$317$		−	19.0510i		−	1.07001i	−0.844849	−	0.535005i	$-0.820310\pi$
$317$		−	19.0510i		−	1.07001i	0.844849	−	0.535005i	$-0.179690\pi$
$318$		−	17.8483i		−	1.00088i
$319$	23.3793			1.30899
$320$	3.82819	+	2.15624i	0.214002	+	0.120537i
$321$	−13.3567			−0.745500
$322$			14.2032i			0.791514i
$323$		−	3.92301i		−	0.218282i
$324$	13.8984			0.772131
$325$	−13.0796	+	7.92723i	−0.725528	+	0.439724i
$326$	−29.9560			−1.65911
$327$		−	15.3756i		−	0.850272i
$328$		−	12.9029i		−	0.712444i
$329$	−7.11655			−0.392348
$330$	−32.0226	−	18.0368i	−1.76278	−	0.992894i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	16.7365i		−	0.918536i
$333$		−	14.0450i		−	0.769660i
$334$	6.93164			0.379282
$335$	−10.8026	+	19.1789i	−0.590207	+	1.04785i
$336$	−16.4364			−0.896678
$337$			6.89249i			0.375458i	0.982221	+	0.187729i	$0.0601127\pi$
$337$			6.89249i			0.375458i	−0.982221	+	0.187729i	$0.939887\pi$
$338$		−	6.64000i		−	0.361168i
$339$	21.7931			1.18364
$340$	−5.68965	+	10.1014i	−0.308565	+	0.547826i
$341$	32.8727			1.78016
$342$			4.29522i			0.232259i
$343$		−	17.2539i		−	0.931623i
$344$	−1.79310			−0.0966774
$345$	24.2295	+	13.6473i	1.30447	+	0.734747i
$346$	−20.7473			−1.11538
$347$			30.5503i			1.64002i	0.572346	+	0.820012i	$0.306033\pi$
$347$			30.5503i			1.64002i	−0.572346	+	0.820012i	$0.693967\pi$
$348$			18.3533i			0.983838i
$349$	−16.7693			−0.897640			−0.448820	−	0.893622i	$-0.648156\pi$
$349$	−16.7693			−0.897640			−0.448820	+	0.893622i	$0.648156\pi$
$350$	−6.85018	−	11.3025i	−0.366157	−	0.604147i
$351$	−4.55416			−0.243083
$352$		−	25.1384i		−	1.33988i
$353$			29.0999i			1.54883i	0.632676	+	0.774417i	$0.281956\pi$
$353$			29.0999i			1.54883i	−0.632676	+	0.774417i	$0.718044\pi$
$354$	−14.1593			−0.752558
$355$	16.8395	+	9.48489i	0.893746	+	0.503406i
$356$	16.3436			0.866210
$357$		−	13.1685i		−	0.696949i
$358$			18.3533i			0.970000i
$359$	11.6896			0.616956			0.308478	−	0.951231i	$-0.400180\pi$
$359$	11.6896			0.616956			0.308478	+	0.951231i	$0.400180\pi$
$360$	−3.19743	+	5.67672i	−0.168519	+	0.299189i
$361$	1.00000			0.0526316
$362$		−	1.04449i		−	0.0548972i
$363$			9.68161i			0.508153i
$364$	−5.86328			−0.307319
$365$	2.67120	−	4.74244i	0.139817	−	0.248231i
$366$	43.5862			2.27829
$367$			4.20095i			0.219288i	0.993971	+	0.109644i	$0.0349710\pi$
$367$			4.20095i			0.219288i	−0.993971	+	0.109644i	$0.965029\pi$
$368$			26.3108i			1.37155i
$369$	−24.5957			−1.28040
$370$	21.1611	+	11.9191i	1.10011	+	0.619643i
$371$	−6.13672			−0.318603
$372$			25.8058i			1.33797i
$373$		−	16.9456i		−	0.877412i	−0.898631	−	0.438706i	$-0.855437\pi$
$373$		−	16.9456i		−	0.877412i	0.898631	−	0.438706i	$-0.144563\pi$
$374$	27.8596			1.44059
$375$	−25.8633	+	0.825627i	−1.33557	+	0.0426352i
$376$	−6.06655			−0.312858
$377$		−	18.3533i		−	0.945241i
$378$		−	3.93539i		−	0.202415i
$379$	−10.3662			−0.532476			−0.266238	−	0.963907i	$-0.585781\pi$
$379$	−10.3662			−0.532476			−0.266238	+	0.963907i	$0.585781\pi$
$380$	−2.57491	−	1.45033i	−0.132090	−	0.0744002i
$381$	25.6753			1.31539
$382$			5.80131i			0.296821i
$383$			20.5907i			1.05214i	0.850442	+	0.526068i	$0.176334\pi$
$383$			20.5907i			1.05214i	−0.850442	+	0.526068i	$0.823666\pi$
$384$	−21.5749			−1.10099
$385$	−6.20155	+	11.0102i	−0.316060	+	0.561133i
$386$	5.57491			0.283756
$387$			3.41802i			0.173748i
$388$			4.04272i			0.205238i
$389$	−8.10345			−0.410861			−0.205431	−	0.978672i	$-0.565859\pi$
$389$	−8.10345			−0.410861			−0.205431	+	0.978672i	$0.565859\pi$
$390$	−14.1593	+	25.1384i	−0.716984	+	1.27293i
$391$	−21.0796			−1.06604
$392$		−	6.05380i		−	0.305763i
$393$			10.6697i			0.538213i
$394$	−39.1724			−1.97348
$395$	24.2295	+	13.6473i	1.21912	+	0.686672i
$396$	−12.1367			−0.609893
$397$		−	3.46891i		−	0.174100i	−0.996204	−	0.0870499i	$-0.972256\pi$
$397$		−	3.46891i		−	0.174100i	0.996204	−	0.0870499i	$-0.0277440\pi$
$398$		−	8.77898i		−	0.440050i
$399$	3.35673			0.168046
$400$	−12.6896	−	20.9375i	−0.634482	−	1.04687i
$401$	−15.9524			−0.796625			−0.398312	−	0.917250i	$-0.630404\pi$
$401$	−15.9524			−0.796625			−0.398312	+	0.917250i	$0.630404\pi$
$402$			41.5240i			2.07103i
$403$		−	25.8058i		−	1.28548i
$404$	−4.43637			−0.220718
$405$	−20.4881	−	11.5400i	−1.01806	−	0.573427i
$406$	15.8596			0.787101
$407$		−	23.2216i		−	1.15105i
$408$		−	11.2255i		−	0.555747i
$409$	3.92982			0.194317			0.0971586	−	0.995269i	$-0.469025\pi$
$409$	3.92982			0.194317			0.0971586	+	0.995269i	$0.469025\pi$
$410$	20.8727	−	37.0575i	1.03083	−	1.83014i
$411$	−30.5066			−1.50478
$412$		−	17.2621i		−	0.850442i
$413$			4.86835i			0.239556i
$414$	23.0796			1.13430
$415$	−13.8965	+	24.6719i	−0.682155	+	1.21110i
$416$	−19.7342			−0.967549
$417$		−	2.73823i		−	0.134092i
$418$			7.10160i			0.347351i
$419$	34.2996			1.67565			0.837824	−	0.545941i	$-0.183828\pi$
$419$	34.2996			1.67565			0.837824	+	0.545941i	$0.183828\pi$
$420$	−8.64327	−	4.86835i	−0.421749	−	0.237551i
$421$	−26.0891			−1.27151			−0.635753	−	0.771893i	$-0.719310\pi$
$421$	−26.0891			−1.27151			−0.635753	+	0.771893i	$0.719310\pi$
$422$		−	19.1486i		−	0.932138i
$423$			11.5641i			0.562267i
$424$	−5.23129			−0.254054
$425$	16.7746	−	10.1667i	0.813690	−	0.493156i
$426$	36.4589			1.76644
$427$		−	14.9861i		−	0.725229i
$428$		−	7.62715i		−	0.368672i
$429$	27.5862			1.33187
$430$	−5.14982	−	2.90066i	−0.248347	−	0.139882i
$431$	10.2996			0.496117			0.248058	−	0.968745i	$-0.420208\pi$
$431$	10.2996			0.496117			0.248058	+	0.968745i	$0.420208\pi$
$432$		−	7.29014i		−	0.350747i
$433$		−	36.2319i		−	1.74119i	−0.491999	−	0.870596i	$-0.663734\pi$
$433$		−	36.2319i		−	1.74119i	0.491999	−	0.870596i	$-0.336266\pi$
$434$	22.2996			1.07042
$435$	15.2389	−	27.0552i	0.730651	−	1.29720i
$436$	8.78000			0.420486
$437$		−	5.37334i		−	0.257042i
$438$		−	10.2678i		−	0.490615i
$439$	24.0891			1.14971			0.574855	−	0.818255i	$-0.305058\pi$
$439$	24.0891			1.14971			0.574855	+	0.818255i	$0.305058\pi$
$440$	−5.28655	+	9.38574i	−0.252026	+	0.447448i
$441$	−11.5398			−0.549515
$442$		−	21.8704i		−	1.04027i
$443$		−	5.52337i		−	0.262423i	−0.991354	−	0.131212i	$-0.958113\pi$
$443$		−	5.52337i		−	0.262423i	0.991354	−	0.131212i	$-0.0418868\pi$
$444$	18.2295			0.865132
$445$	−24.0927	−	13.5703i	−1.14211	−	0.643295i
$446$	−30.7913			−1.45801
$447$		−	12.6374i		−	0.597727i
$448$		−	2.84977i		−	0.134639i
$449$	−7.92982			−0.374231			−0.187116	−	0.982338i	$-0.559914\pi$
$449$	−7.92982			−0.374231			−0.187116	+	0.982338i	$0.559914\pi$
$450$	−18.3662	+	11.1313i	−0.865791	+	0.524733i
$451$	−40.6658			−1.91488
$452$			12.4446i			0.585346i
$453$		−	11.7566i		−	0.552375i
$454$	−31.2277			−1.46559
$455$	8.64327	+	4.86835i	0.405203	+	0.228232i
$456$	2.86146			0.134000
$457$			22.6534i			1.05968i	0.848098	+	0.529840i	$0.177748\pi$
$457$			22.6534i			1.05968i	−0.848098	+	0.529840i	$0.822252\pi$
$458$			45.6479i			2.13299i
$459$	5.84070			0.272621
$460$	−7.79310	+	13.8359i	−0.363355	+	0.645101i
$461$	13.3900			0.623634			0.311817	−	0.950142i	$-0.399062\pi$
$461$	13.3900			0.623634			0.311817	+	0.950142i	$0.399062\pi$
$462$			23.8381i			1.10905i
$463$		−	16.9029i		−	0.785546i	−0.919635	−	0.392773i	$-0.871516\pi$
$463$		−	16.9029i		−	0.785546i	0.919635	−	0.392773i	$-0.128484\pi$
$464$	29.3793			1.36390
$465$	21.4269	−	38.0413i	0.993649	−	1.76412i
$466$	35.1724			1.62933
$467$			22.2501i			1.02961i	0.857306	+	0.514807i	$0.172136\pi$
$467$			22.2501i			1.02961i	−0.857306	+	0.514807i	$0.827864\pi$
$468$			9.52759i			0.440413i
$469$	14.2771			0.659254
$470$	−17.4233	−	9.81371i	−0.803676	−	0.452673i
$471$	14.1593			0.652426
$472$			4.15006i			0.191022i
$473$			5.65127i			0.259846i
$474$	52.4589			2.40952
$475$	2.59155	+	4.27596i	0.118908	+	0.196195i
$476$	7.51965			0.344663
$477$			9.97194i			0.456584i
$478$			34.2077i			1.56462i
$479$	−0.366196			−0.0167319			−0.00836597	−	0.999965i	$-0.502663\pi$
$479$	−0.366196			−0.0167319			−0.00836597	+	0.999965i	$0.502663\pi$
$480$	−29.0909	−	16.3856i	−1.32781	−	0.747895i
$481$	−18.2295			−0.831192
$482$			26.3108i			1.19842i
$483$		−	18.0368i		−	0.820704i
$484$	−5.52854			−0.251297
$485$	3.35673	−	5.95953i	0.152421	−	0.270608i
$486$	−36.2182			−1.64289
$487$			26.8461i			1.21651i	0.793740	+	0.608257i	$0.208131\pi$
$487$			26.8461i			1.21651i	−0.793740	+	0.608257i	$0.791869\pi$
$488$		−	12.7750i		−	0.578298i
$489$	38.0415			1.72030
$490$	9.79310	−	17.3867i	0.442407	−	0.785450i
$491$	−23.7266			−1.07076			−0.535382	−	0.844610i	$-0.679832\pi$
$491$	−23.7266			−1.07076			−0.535382	+	0.844610i	$0.679832\pi$
$492$		−	31.9236i		−	1.43923i
$493$			23.5381i			1.06010i
$494$	5.57491			0.250827
$495$	17.8912	+	10.0773i	0.804150	+	0.452940i
$496$	41.3091			1.85483
$497$		−	12.5356i		−	0.562298i
$498$			53.4169i			2.39367i
$499$	−6.81690			−0.305166			−0.152583	−	0.988291i	$-0.548759\pi$
$499$	−6.81690			−0.305166			−0.152583	+	0.988291i	$0.548759\pi$
$500$	−0.471462	−	14.7688i	−0.0210844	−	0.660482i
$501$	−8.80257			−0.393270
$502$			20.0045i			0.892845i
$503$		−	23.4102i		−	1.04381i	−0.853004	−	0.521904i	$-0.825222\pi$
$503$		−	23.4102i		−	1.04381i	0.853004	−	0.521904i	$-0.174778\pi$
$504$	4.22584			0.188234
$505$	6.53982	+	3.68358i	0.291018	+	0.163917i
$506$	38.1593			1.69639
$507$			8.43221i			0.374488i
$508$			14.6615i			0.650499i
$509$	−16.9204			−0.749981			−0.374991	−	0.927029i	$-0.622354\pi$
$509$	−16.9204			−0.749981			−0.374991	+	0.927029i	$0.622354\pi$
$510$	18.1593	−	32.2400i	0.804107	−	1.42761i
$511$	−3.53035			−0.156174
$512$		−	19.4823i		−	0.861003i
$513$			1.48883i			0.0657336i
$514$	32.1480			1.41799
$515$	−14.3329	+	25.4467i	−0.631584	+	1.12131i
$516$	−4.43637			−0.195300
$517$			19.1198i			0.840888i
$518$		−	15.7527i		−	0.692133i
$519$	26.3473			1.15652
$520$	7.36801	+	4.15006i	0.323109	+	0.181992i
$521$	−3.49345			−0.153051			−0.0765254	−	0.997068i	$-0.524383\pi$
$521$	−3.49345			−0.153051			−0.0765254	+	0.997068i	$0.524383\pi$
$522$		−	25.7713i		−	1.12798i
$523$		−	14.9271i		−	0.652714i	−0.945247	−	0.326357i	$-0.894179\pi$
$523$		−	14.9271i		−	0.652714i	0.945247	−	0.326357i	$-0.105821\pi$
$524$	−6.09275			−0.266163
$525$	8.69912	+	14.3532i	0.379661	+	0.626427i
$526$	−3.07965			−0.134279
$527$			33.0960i			1.44168i
$528$			44.1591i			1.92178i
$529$	−5.87275			−0.255337
$530$	−15.0244	−	8.46253i	−0.652618	−	0.367589i
$531$	7.91088			0.343303
$532$			1.91681i			0.0831041i
$533$			31.9236i			1.38276i
$534$	−52.1629			−2.25731
$535$	−6.33292	+	11.2435i	−0.273796	+	0.486098i
$536$	12.1706			0.525689
$537$		−	23.3070i		−	1.00577i
$538$		−	49.3948i		−	2.12956i
$539$	−19.0796			−0.821819
$540$	2.15930	−	3.83361i	0.0929213	−	0.164972i
$541$	−12.6991			−0.545978			−0.272989	−	0.962017i	$-0.588012\pi$
$541$	−12.6991			−0.545978			−0.272989	+	0.962017i	$0.588012\pi$
$542$		−	43.6541i		−	1.87510i
$543$			1.32641i			0.0569217i
$544$	25.3091			1.08512
$545$	−12.9429	−	7.29014i	−0.554414	−	0.312275i
$546$	18.7135			0.800862
$547$			31.8162i			1.36036i	0.733043	+	0.680182i	$0.238099\pi$
$547$			31.8162i			1.36036i	−0.733043	+	0.680182i	$0.761901\pi$
$548$		−	17.4203i		−	0.744158i
$549$	−24.3519			−1.03931
$550$	−30.3662	+	18.4041i	−1.29482	+	0.784756i
$551$	−6.00000			−0.255609
$552$		−	15.3756i		−	0.654429i
$553$		−	18.0368i		−	0.767003i
$554$	−15.0095			−0.637691
$555$	−26.8727	−	15.1362i	−1.14068	−	0.642494i
$556$	1.56363			0.0663125
$557$			9.64731i			0.408770i	0.978891	+	0.204385i	$0.0655194\pi$
$557$			9.64731i			0.408770i	−0.978891	+	0.204385i	$0.934481\pi$
$558$		−	36.2361i		−	1.53399i
$559$	4.43637			0.187639
$560$	−7.79310	+	13.8359i	−0.329319	+	0.584672i
$561$	−35.3793			−1.49372
$562$			19.0207i			0.802338i
$563$		−	4.28216i		−	0.180471i	−0.995920	−	0.0902357i	$-0.971238\pi$
$563$		−	4.28216i		−	0.180471i	0.995920	−	0.0902357i	$-0.0287620\pi$
$564$	−15.0095			−0.632013
$565$	10.3329	−	18.3451i	0.434709	−	0.771783i
$566$	−19.0796			−0.801977
$567$			15.2517i			0.640510i
$568$		−	10.6860i		−	0.448376i
$569$	−42.2295			−1.77035			−0.885176	−	0.465257i	$-0.845962\pi$
$569$	−42.2295			−1.77035			−0.885176	+	0.465257i	$0.845962\pi$
$570$	8.21819	+	4.62892i	0.344222	+	0.193884i
$571$	−19.2200			−0.804332			−0.402166	−	0.915567i	$-0.631743\pi$
$571$	−19.2200			−0.804332			−0.402166	+	0.915567i	$0.631743\pi$
$572$			15.7527i			0.658653i
$573$		−	7.36715i		−	0.307767i
$574$	−27.5862			−1.15143
$575$	22.9762	−	13.9253i	0.958174	−	0.580724i
$576$	−4.63076			−0.192948
$577$			40.7919i			1.69819i	0.528239	+	0.849096i	$0.322852\pi$
$577$			40.7919i			1.69819i	−0.528239	+	0.849096i	$0.677148\pi$
$578$		−	2.93428i		−	0.122050i
$579$	−7.07965			−0.294220
$580$	15.4495	+	8.70197i	0.641504	+	0.361329i
$581$	18.3662			0.761958
$582$		−	12.9029i		−	0.534843i
$583$			16.4873i			0.682836i
$584$	−3.00947			−0.124533
$585$	7.91088	−	14.0450i	0.327075	−	0.580689i
$586$	−30.0113			−1.23975
$587$			31.8851i			1.31604i	0.753001	+	0.658019i	$0.228605\pi$
$587$			31.8851i			1.31604i	−0.753001	+	0.658019i	$0.771395\pi$
$588$		−	14.9779i		−	0.617680i
$589$	−8.43637			−0.347615
$590$	−6.71345	+	11.9191i	−0.276388	+	0.490700i
$591$	49.7455			2.04626
$592$		−	29.1811i		−	1.19934i
$593$		−	38.8973i		−	1.59732i	−0.601783	−	0.798660i	$-0.705543\pi$
$593$		−	38.8973i		−	1.59732i	0.601783	−	0.798660i	$-0.294457\pi$
$594$	−10.5731			−0.433819
$595$	−11.0850	−	6.24366i	−0.454441	−	0.255965i
$596$	7.21637			0.295594
$597$			11.1485i			0.456279i
$598$		−	29.9559i		−	1.22499i
$599$	−28.1629			−1.15071			−0.575353	−	0.817905i	$-0.695135\pi$
$599$	−28.1629			−1.15071			−0.575353	+	0.817905i	$0.695135\pi$
$600$	7.41562	+	12.2355i	0.302741	+	0.499512i
$601$	−5.56363			−0.226945			−0.113473	−	0.993541i	$-0.536197\pi$
$601$	−5.56363			−0.226945			−0.113473	+	0.993541i	$0.536197\pi$
$602$			3.83361i			0.156246i
$603$		−	23.1997i		−	0.944764i
$604$	6.71345			0.273166
$605$	8.14982	+	4.59042i	0.331337	+	0.186627i
$606$	14.1593			0.575182
$607$		−	33.9986i		−	1.37996i	−0.723828	−	0.689980i	$-0.757619\pi$
$607$		−	33.9986i		−	1.37996i	0.723828	−	0.689980i	$-0.242381\pi$
$608$			6.45146i			0.261641i
$609$	−20.1404			−0.816128
$610$	20.6658	−	36.6902i	0.836736	−	1.48554i
$611$	15.0095			0.607218
$612$		−	12.2191i		−	0.493929i
$613$			17.5703i			0.709659i	0.934931	+	0.354830i	$0.115461\pi$
$613$			17.5703i			0.709659i	−0.934931	+	0.354830i	$0.884539\pi$
$614$	−14.3549			−0.579317
$615$	−26.5066	+	47.0597i	−1.06885	+	1.89763i
$616$	6.98690			0.281510
$617$			13.0791i			0.526544i	0.964722	+	0.263272i	$0.0848016\pi$
$617$			13.0791i			0.526544i	−0.964722	+	0.263272i	$0.915198\pi$
$618$			55.0943i			2.21622i
$619$	18.9393			0.761234			0.380617	−	0.924733i	$-0.375712\pi$
$619$	18.9393			0.761234			0.380617	+	0.924733i	$0.375712\pi$
$620$	21.7229	+	12.2355i	0.872414	+	0.491390i
$621$	8.00000			0.321029
$622$		−	7.10160i		−	0.284748i
$623$			17.9350i			0.718552i
$624$	34.6658			1.38774
$625$	−11.5677	+	22.1627i	−0.462710	+	0.886510i
$626$	14.1593			0.565919
$627$		−	9.01841i		−	0.360161i
$628$			8.08545i			0.322645i
$629$	23.3793			0.932194
$630$	12.1367	+	6.83605i	0.483539	+	0.272355i
$631$	31.6896			1.26154			0.630772	−	0.775968i	$-0.282738\pi$
$631$	31.6896			1.26154			0.630772	+	0.775968i	$0.282738\pi$
$632$		−	15.3756i		−	0.611608i
$633$			24.3170i			0.966514i
$634$	−34.7211			−1.37895
$635$	12.1736	−	21.6131i	0.483096	−	0.857688i
$636$	−12.9429			−0.513220
$637$			14.9779i			0.593448i
$638$		−	42.6096i		−	1.68693i
$639$	−20.3698			−0.805818
$640$	−10.2295	+	18.1614i	−0.404355	+	0.717893i
$641$	47.9750			1.89490			0.947449	−	0.319908i	$-0.103652\pi$
$641$	47.9750			1.89490			0.947449	+	0.319908i	$0.103652\pi$
$642$			24.3431i			0.960746i
$643$		−	0.200927i		−	0.00792378i	−0.999992	−	0.00396189i	$-0.998739\pi$
$643$		−	0.200927i		−	0.00792378i	0.999992	−	0.00396189i	$-0.00126111\pi$
$644$	10.2996			0.405863
$645$	6.53982	+	3.68358i	0.257505	+	0.145041i
$646$	−7.14982			−0.281306
$647$		−	1.58798i		−	0.0624299i	−0.999513	−	0.0312150i	$-0.990062\pi$
$647$		−	1.58798i		−	0.0624299i	0.999513	−	0.0312150i	$-0.00993765\pi$
$648$			13.0014i			0.510743i
$649$	13.0796			0.513421
$650$	14.4477	+	23.8381i	0.566684	+	0.935008i
$651$	−28.3186			−1.10989
$652$			21.7230i			0.850739i
$653$		−	33.5624i		−	1.31340i	−0.754152	−	0.656700i	$-0.771952\pi$
$653$		−	33.5624i		−	1.31340i	0.754152	−	0.656700i	$-0.228048\pi$
$654$	−28.0226			−1.09577
$655$	8.98155	+	5.05889i	0.350938	+	0.197667i
$656$	−51.1022			−1.99521
$657$			5.73669i			0.223809i
$658$			12.9702i			0.505630i
$659$	−15.3567			−0.598213			−0.299107	−	0.954220i	$-0.596689\pi$
$659$	−15.3567			−0.598213			−0.299107	+	0.954220i	$0.596689\pi$
$660$	−13.0796	+	23.2216i	−0.509125	+	0.903900i
$661$	12.8026			0.497962			0.248981	−	0.968508i	$-0.419904\pi$
$661$	12.8026			0.497962			0.248981	+	0.968508i	$0.419904\pi$
$662$		−	14.5803i		−	0.566679i
$663$			27.7735i			1.07863i
$664$	15.6564			0.607585
$665$	1.59155	−	2.82564i	0.0617176	−	0.109573i
$666$	−25.5975			−0.991882
$667$			32.2400i			1.24834i
$668$		−	5.02657i		−	0.194484i
$669$	39.1022			1.51178
$670$	34.9542	+	19.6881i	1.35040	+	0.760617i
$671$	−40.2627			−1.55433
$672$			21.6558i			0.835389i
$673$			7.82545i			0.301649i	0.988561	+	0.150824i	$0.0481928\pi$
$673$			7.82545i			0.301649i	−0.988561	+	0.150824i	$0.951807\pi$
$674$	12.5618			0.483863
$675$	−6.36620	+	3.85838i	−0.245035	+	0.148509i
$676$	−4.81509			−0.185196
$677$		−	21.6516i		−	0.832137i	−0.909333	−	0.416069i	$-0.863408\pi$
$677$		−	21.6516i		−	0.832137i	0.909333	−	0.416069i	$-0.136592\pi$
$678$		−	39.7187i		−	1.52539i
$679$	−4.43637			−0.170252
$680$	−9.44947	−	5.32245i	−0.362371	−	0.204107i
$681$	39.6564			1.51964
$682$		−	59.9118i		−	2.29414i
$683$			6.38751i			0.244411i	0.992505	+	0.122206i	$0.0389967\pi$
$683$			6.38751i			0.244411i	−0.992505	+	0.122206i	$0.961003\pi$
$684$	3.11474			0.119095
$685$	−14.4643	+	25.6799i	−0.552652	+	0.981179i
$686$	−31.4458			−1.20061
$687$		−	57.9688i		−	2.21165i
$688$			7.10160i			0.270746i
$689$	12.9429			0.493086
$690$	24.8727	−	44.1591i	0.946889	−	1.68111i
$691$	44.4958			1.69270			0.846351	−	0.532626i	$-0.178795\pi$
$691$	44.4958			1.69270			0.846351	+	0.532626i	$0.178795\pi$
$692$			15.0452i			0.571933i
$693$		−	13.3185i		−	0.505928i
$694$	55.6789			2.11354
$695$	−2.30500	−	1.29830i	−0.0874336	−	0.0492473i
$696$	−17.1688			−0.650780
$697$		−	40.9420i		−	1.55079i
$698$			30.5626i			1.15681i
$699$	−44.6658			−1.68942
$700$	−8.19620	+	4.96750i	−0.309787	+	0.187754i
$701$	17.5160			0.661571			0.330785	−	0.943706i	$-0.392686\pi$
$701$	17.5160			0.661571			0.330785	+	0.943706i	$0.392686\pi$
$702$			8.30011i			0.313268i
$703$			5.95953i			0.224768i
$704$	−7.65638			−0.288560
$705$	22.1260	+	12.4626i	0.833314	+	0.469367i
$706$	53.0357			1.99602
$707$		−	4.86835i		−	0.183093i
$708$			10.2678i			0.385888i
$709$	−11.4269			−0.429146			−0.214573	−	0.976708i	$-0.568836\pi$
$709$	−11.4269			−0.429146			−0.214573	+	0.976708i	$0.568836\pi$
$710$	17.2865	−	30.6905i	0.648753	−	1.15180i
$711$	−29.3091			−1.09918
$712$			15.2888i			0.572973i
$713$			45.3315i			1.69768i
$714$	−24.0000			−0.898177
$715$	13.0796	−	23.2216i	0.489151	−	0.868439i
$716$	13.3091			0.497385
$717$		−	43.4408i		−	1.62233i
$718$		−	21.3048i		−	0.795088i
$719$	−15.8965			−0.592841			−0.296421	−	0.955057i	$-0.595793\pi$
$719$	−15.8965			−0.592841			−0.296421	+	0.955057i	$0.595793\pi$
$720$	22.4827	+	12.6635i	0.837883	+	0.471940i
$721$	18.9429			0.705471
$722$		−	1.82254i		−	0.0678278i
$723$		−	33.4124i		−	1.24262i
$724$	−0.757427			−0.0281495
$725$	−15.5493	−	25.6558i	−0.577486	−	0.952832i
$726$	17.6451			0.654871
$727$		−	41.9905i		−	1.55734i	−0.627434	−	0.778670i	$-0.715895\pi$
$727$		−	41.9905i		−	1.55734i	0.627434	−	0.778670i	$-0.284105\pi$
$728$		−	5.48487i		−	0.203283i
$729$	14.4458			0.535031
$730$	−8.64327	−	4.86835i	−0.319902	−	0.180186i
$731$	−5.68965			−0.210439
$732$		−	31.6071i		−	1.16823i
$733$		−	0.632884i		−	0.0233761i	−0.999932	−	0.0116881i	$-0.996279\pi$
$733$		−	0.632884i		−	0.0233761i	0.999932	−	0.0116881i	$-0.00372051\pi$
$734$	7.65638			0.282602
$735$	−12.4364	+	22.0795i	−0.458723	+	0.814416i
$736$	34.6658			1.27780
$737$		−	38.3578i		−	1.41293i
$738$			44.8265i			1.65009i
$739$	29.5493			1.08699			0.543494	−	0.839413i	$-0.317101\pi$
$739$	29.5493			1.08699			0.543494	+	0.839413i	$0.317101\pi$
$740$	8.64327	−	15.3453i	0.317733	−	0.564103i
$741$	−7.07965			−0.260077
$742$			11.1844i			0.410592i
$743$		−	31.3374i		−	1.14966i	−0.818274	−	0.574829i	$-0.805069\pi$
$743$		−	31.3374i		−	1.14966i	0.818274	−	0.574829i	$-0.194931\pi$
$744$	−24.1404			−0.885028
$745$	−10.6379	−	5.99184i	−0.389743	−	0.219524i
$746$	−30.8840			−1.13074
$747$		−	29.8443i		−	1.09195i
$748$		−	20.2028i		−	0.738688i
$749$	8.36983			0.305827
$750$	1.50474	+	47.1367i	0.0549452	+	1.72119i
$751$	25.0131			0.912741			0.456371	−	0.889790i	$-0.349149\pi$
$751$	25.0131			0.912741			0.456371	+	0.889790i	$0.349149\pi$
$752$			24.0267i			0.876163i
$753$		−	25.4040i		−	0.925772i
$754$	−33.4495			−1.21816
$755$	−9.89655	−	5.57426i	−0.360172	−	0.202868i
$756$	−2.85381			−0.103792
$757$			32.0900i			1.16633i	0.812354	+	0.583165i	$0.198186\pi$
$757$			32.0900i			1.16633i	−0.812354	+	0.583165i	$0.801814\pi$
$758$			18.8928i			0.686216i
$759$	−48.4589			−1.75895
$760$	1.35673	−	2.40873i	0.0492136	−	0.0873739i
$761$	−40.4922			−1.46784			−0.733921	−	0.679235i	$-0.762312\pi$
$761$	−40.4922			−1.46784			−0.733921	+	0.679235i	$0.762312\pi$
$762$		−	46.7942i		−	1.69517i
$763$			9.63492i			0.348808i
$764$	4.20690			0.152200
$765$	−10.1457	+	18.0127i	−0.366819	+	0.651250i
$766$	37.5273			1.35592
$767$		−	10.2678i		−	0.370749i
$768$			48.4165i			1.74708i
$769$	−3.09398			−0.111572			−0.0557859	−	0.998443i	$-0.517766\pi$
$769$	−3.09398			−0.111572			−0.0557859	+	0.998443i	$0.517766\pi$
$770$	20.0665	+	11.3025i	0.723148	+	0.407316i
$771$	−40.8251			−1.47028
$772$		−	4.04272i		−	0.145501i
$773$		−	1.96350i		−	0.0706220i	−0.999376	−	0.0353110i	$-0.988758\pi$
$773$		−	1.96350i		−	0.0706220i	0.999376	−	0.0353110i	$-0.0112422\pi$
$774$	6.22947			0.223914
$775$	−21.8633	−	36.0736i	−0.785352	−	1.29580i
$776$	−3.78181			−0.135759
$777$			20.0045i			0.717658i
$778$			14.7688i			0.529488i
$779$	10.4364			0.373922
$780$	18.2295	+	10.2678i	0.652720	+	0.367647i
$781$	−33.6789			−1.20513
$782$			38.4184i			1.37384i
$783$		−	8.93300i		−	0.319239i
$784$	−23.9762			−0.856293
$785$	6.71345	−	11.9191i	0.239613	−	0.425410i
$786$	19.4458			0.693610
$787$			0.107331i			0.00382595i	0.999998	+	0.00191297i	$0.000608919\pi$
$787$			0.107331i			0.00382595i	−0.999998	+	0.00191297i	$0.999391\pi$
$788$			28.4064i			1.01194i
$789$	3.91088			0.139231
$790$	24.8727	−	44.1591i	0.884933	−	1.57111i
$791$	−13.6564			−0.485565
$792$		−	11.3534i		−	0.403427i
$793$			31.6071i			1.12240i
$794$	−6.32222			−0.224367
$795$	19.0796	+	10.7467i	0.676685	+	0.381145i
$796$	−6.36620			−0.225644
$797$			8.32068i			0.294734i	0.989082	+	0.147367i	$0.0470798\pi$
$797$			8.32068i			0.294734i	−0.989082	+	0.147367i	$0.952920\pi$
$798$		−	6.11775i		−	0.216566i
$799$	−19.2496			−0.681003
$800$	−27.5862	+	16.7193i	−0.975319	+	0.591115i
$801$	29.1437			1.02974
$802$			29.0738i			1.02663i
$803$			9.48489i			0.334714i
$804$	30.1117			1.06196
$805$	−15.1831	−	8.55193i	−0.535134	−	0.301416i
$806$	−47.0320			−1.65663
$807$			62.7270i			2.20810i
$808$		−	4.15006i		−	0.145998i
$809$	27.6231			0.971177			0.485588	−	0.874188i	$-0.338605\pi$
$809$	27.6231			0.971177			0.485588	+	0.874188i	$0.338605\pi$
$810$	−21.0320	+	37.3403i	−0.738991	+	1.31200i
$811$	23.0095			0.807972			0.403986	−	0.914765i	$-0.367624\pi$
$811$	23.0095			0.807972			0.403986	+	0.914765i	$0.367624\pi$
$812$		−	11.5008i		−	0.403600i
$813$			55.4369i			1.94426i
$814$	−42.3222			−1.48339
$815$	18.0369	−	32.0227i	0.631805	−	1.12171i
$816$	−44.4589			−1.55637
$817$		−	1.45033i		−	0.0507405i
$818$		−	7.16224i		−	0.250422i
$819$	−10.4553			−0.365338
$820$	−26.8727	−	15.1362i	−0.938437	−	0.528578i
$821$	31.1355			1.08664			0.543318	−	0.839527i	$-0.317168\pi$
$821$	31.1355			1.08664			0.543318	+	0.839527i	$0.317168\pi$
$822$			55.5993i			1.93925i
$823$			20.4201i			0.711800i	0.934524	+	0.355900i	$0.115826\pi$
$823$			20.4201i			0.711800i	−0.934524	+	0.355900i	$0.884174\pi$
$824$	16.1480			0.562543
$825$	38.5624	−	23.3716i	1.34257	−	0.813696i
$826$	8.87275			0.308722
$827$			0.902638i			0.0313878i	0.999877	+	0.0156939i	$0.00499573\pi$
$827$			0.902638i			0.0313878i	−0.999877	+	0.0156939i	$0.995004\pi$
$828$		−	16.7365i		−	0.581634i
$829$	13.4971			0.468773			0.234386	−	0.972143i	$-0.424692\pi$
$829$	13.4971			0.468773			0.234386	+	0.972143i	$0.424692\pi$
$830$	44.9655	+	25.3270i	1.56078	+	0.879112i
$831$	19.0607			0.661209
$832$			6.01042i			0.208374i
$833$		−	19.2092i		−	0.665560i
$834$	−4.99053			−0.172808
$835$	−4.17363	+	7.40986i	−0.144434	+	0.256429i
$836$	5.14982			0.178110
$837$		−	12.5603i		−	0.434149i
$838$		−	62.5123i		−	2.15945i
$839$	−33.1022			−1.14282			−0.571408	−	0.820666i	$-0.693603\pi$
$839$	−33.1022			−1.14282			−0.571408	+	0.820666i	$0.693603\pi$
$840$	4.55416	−	8.08545i	0.157133	−	0.278975i
$841$	7.00000			0.241379
$842$			47.5484i			1.63862i
$843$		−	24.1546i		−	0.831928i
$844$	−13.8858			−0.477971
$845$	7.09810	+	3.99803i	0.244182	+	0.137536i
$846$	21.0760			0.724608
$847$		−	6.06686i		−	0.208460i
$848$			20.7186i			0.711480i
$849$	24.2295			0.831553
$850$	−18.5291	−	30.5724i	−0.635544	−	1.04862i
$851$	32.0226			1.09772
$852$		−	26.4387i		−	0.905775i
$853$			50.9097i			1.74312i	0.490293	+	0.871558i	$0.336890\pi$
$853$			50.9097i			1.74312i	−0.490293	+	0.871558i	$0.663110\pi$
$854$	−27.3128			−0.934623
$855$	−4.59155	−	2.58620i	−0.157028	−	0.0884463i
$856$	7.13491			0.243866
$857$		−	21.2333i		−	0.725317i	−0.931922	−	0.362659i	$-0.881869\pi$
$857$		−	21.2333i		−	0.725317i	0.931922	−	0.362659i	$-0.118131\pi$
$858$		−	50.2768i		−	1.71642i
$859$	−29.4827			−1.00594			−0.502969	−	0.864304i	$-0.667759\pi$
$859$	−29.4827			−1.00594			−0.502969	+	0.864304i	$0.667759\pi$
$860$	−2.10345	+	3.73447i	−0.0717271	+	0.127344i
$861$	35.0320			1.19389
$862$		−	18.7715i		−	0.639359i
$863$			25.7755i			0.877408i	0.898632	+	0.438704i	$0.144562\pi$
$863$			25.7755i			0.877408i	−0.898632	+	0.438704i	$0.855438\pi$
$864$	−9.60514			−0.326773
$865$	12.4922	−	22.1787i	0.424748	−	0.754098i
$866$	−66.0339			−2.24392
$867$			3.72628i			0.126551i
$868$		−	16.1709i		−	0.548876i
$869$	−48.4589			−1.64386
$870$	−49.3091	−	27.7735i	−1.67174	−	0.941611i
$871$	−30.1117			−1.02030
$872$			8.21335i			0.278139i
$873$			7.20893i			0.243985i
$874$	−9.79310			−0.331257
$875$	16.2069	−	0.517369i	0.547893	−	0.0174903i
$876$	−7.44584			−0.251572
$877$		−	54.2687i		−	1.83252i	−0.400581	−	0.916261i	$-0.631192\pi$
$877$		−	54.2687i		−	1.83252i	0.400581	−	0.916261i	$-0.368808\pi$
$878$		−	43.9033i		−	1.48166i
$879$	38.1117			1.28548
$880$	37.1724	+	20.9375i	1.25308	+	0.705802i
$881$	−28.4922			−0.959927			−0.479964	−	0.877288i	$-0.659350\pi$
$881$	−28.4922			−0.959927			−0.479964	+	0.877288i	$0.659350\pi$
$882$			21.0317i			0.708176i
$883$			40.5264i			1.36382i	0.731435	+	0.681911i	$0.238851\pi$
$883$			40.5264i			1.36382i	−0.731435	+	0.681911i	$0.761149\pi$
$884$	−15.8596			−0.533418
$885$	8.52549	−	15.1362i	0.286581	−	0.508797i
$886$	−10.0665			−0.338192
$887$			11.4705i			0.385142i	0.981283	+	0.192571i	$0.0616826\pi$
$887$			11.4705i			0.385142i	−0.981283	+	0.192571i	$0.938317\pi$
$888$			17.0530i			0.572260i
$889$	−16.0891			−0.539612
$890$	−24.7324	+	43.9099i	−0.829032	+	1.47186i
$891$	40.9762			1.37275
$892$			22.3287i			0.747621i
$893$		−	4.90686i		−	0.164202i
$894$	−23.0320			−0.770307
$895$	−19.6195	−	11.0507i	−0.655807	−	0.369385i
$896$	13.5197			0.451660
$897$			38.0413i			1.27016i
$898$			14.4524i			0.482282i
$899$	50.6182			1.68821
$900$	8.07199	+	13.3185i	0.269066	+	0.443950i
$901$	−16.5993			−0.553003
$902$			74.1150i			2.46776i
$903$		−	4.86835i		−	0.162009i
$904$	−11.6415			−0.387189
$905$	1.11655	+	0.628901i	0.0371154	+	0.0209054i
$906$	−21.4269			−0.711861
$907$			48.1000i			1.59714i	0.601905	+	0.798568i	$0.294409\pi$
$907$			48.1000i			1.59714i	−0.601905	+	0.798568i	$0.705591\pi$
$908$			22.6452i			0.751506i
$909$	−7.91088			−0.262387
$910$	8.87275	−	15.7527i	0.294129	−	0.522196i
$911$	−12.8062			−0.424288			−0.212144	−	0.977238i	$-0.568045\pi$
$911$	−12.8062			−0.424288			−0.212144	+	0.977238i	$0.568045\pi$
$912$		−	11.3329i		−	0.375269i
$913$		−	49.3439i		−	1.63304i
$914$	41.2865			1.36564
$915$	−26.2438	+	46.5933i	−0.867593	+	1.54033i
$916$	33.1022			1.09373
$917$		−	6.68601i		−	0.220792i
$918$		−	10.6449i		−	0.351334i
$919$	38.7135			1.27704			0.638519	−	0.769606i	$-0.279547\pi$
$919$	38.7135			1.27704			0.638519	+	0.769606i	$0.279547\pi$
$920$	−12.9429	−	7.29014i	−0.426716	−	0.240349i
$921$	18.2295			0.600682
$922$		−	24.4038i		−	0.803695i
$923$			26.4387i			0.870241i
$924$	17.2865			0.568686
$925$	−25.4827	+	15.4444i	−0.837868	+	0.507809i
$926$	−30.8062			−1.01235
$927$		−	30.7815i		−	1.01100i
$928$		−	38.7087i		−	1.27068i
$929$	36.0189			1.18174			0.590872	−	0.806766i	$-0.298784\pi$
$929$	36.0189			1.18174			0.590872	+	0.806766i	$0.298784\pi$
$930$	−69.3317	−	39.0513i	−2.27348	−	1.28054i
$931$	4.89655			0.160478
$932$		−	25.5058i		−	0.835469i
$933$			9.01841i			0.295249i
$934$	40.5517			1.32689
$935$	−16.7746	+	29.7817i	−0.548590	+	0.973966i
$936$	−8.91270			−0.291321
$937$		−	45.2421i		−	1.47799i	−0.673709	−	0.738997i	$-0.735300\pi$
$937$		−	45.2421i		−	1.47799i	0.673709	−	0.738997i	$-0.264700\pi$
$938$		−	26.0205i		−	0.849599i
$939$	−17.9811			−0.586790
$940$	−7.11655	+	12.6347i	−0.232116	+	0.412099i
$941$	−11.7455			−0.382892			−0.191446	−	0.981503i	$-0.561318\pi$
$941$	−11.7455			−0.382892			−0.191446	+	0.981503i	$0.561318\pi$
$942$		−	25.8058i		−	0.840799i
$943$		−	56.0781i		−	1.82616i
$944$	16.4364			0.534958
$945$	4.20690	+	2.36955i	0.136850	+	0.0770815i
$946$	10.2996			0.334870
$947$		−	13.7752i		−	0.447635i	−0.974631	−	0.223817i	$-0.928148\pi$
$947$		−	13.7752i		−	0.447635i	0.974631	−	0.223817i	$-0.0718519\pi$
$948$		−	38.0413i		−	1.23552i
$949$	7.44584			0.241702
$950$	7.79310	−	4.72319i	0.252842	−	0.153241i
$951$	44.0927			1.42981
$952$			7.03434i			0.227984i
$953$		−	9.01421i		−	0.291999i	−0.989285	−	0.145999i	$-0.953360\pi$
$953$		−	9.01421i		−	0.291999i	0.989285	−	0.145999i	$-0.0466398\pi$
$954$	18.1742			0.588412
$955$	−6.20155	−	3.49304i	−0.200677	−	0.113032i
$956$	24.8062			0.802290
$957$			54.1105i			1.74914i
$958$			0.667406i			0.0215629i
$959$	19.1166			0.617306
$960$	−4.99053	+	8.86019i	−0.161069	+	0.285961i
$961$	40.1724			1.29588
$962$			33.2239i			1.07118i
$963$		−	13.6006i		−	0.438274i
$964$	19.0796			0.614514
$965$	−3.35673	+	5.95953i	−0.108057	+	0.191844i
$966$	−32.8727			−1.05766
$967$			30.3232i			0.975129i	0.873087	+	0.487564i	$0.162115\pi$
$967$			30.3232i			0.975129i	−0.873087	+	0.487564i	$0.837885\pi$
$968$		−	5.17173i		−	0.166226i
$969$	9.07965			0.291680
$970$	−10.8615	−	6.11775i	−0.348740	−	0.196429i
$971$	−31.5636			−1.01292			−0.506462	−	0.862262i	$-0.669047\pi$
$971$	−31.5636			−1.01292			−0.506462	+	0.862262i	$0.669047\pi$
$972$			26.2641i			0.842422i
$973$			1.71588i			0.0550086i
$974$	48.9280			1.56775
$975$	−18.3473	−	30.2723i	−0.587582	−	0.969490i
$976$	−50.5957			−1.61953
$977$			43.1285i			1.37980i	0.723903	+	0.689902i	$0.242346\pi$
$977$			43.1285i			1.37980i	−0.723903	+	0.689902i	$0.757654\pi$
$978$		−	69.3320i		−	2.21699i
$979$	48.1855			1.54002
$980$	−12.6082	−	7.10160i	−0.402754	−	0.226852i
$981$	15.6564			0.499870
$982$			43.2425i			1.37992i
$983$		−	7.81570i		−	0.249282i	−0.992202	−	0.124641i	$-0.960222\pi$
$983$		−	7.81570i		−	0.249282i	0.992202	−	0.124641i	$-0.0397779\pi$
$984$	29.8633			0.952006
$985$	23.5862	−	41.8749i	0.751519	−	1.33425i
$986$	42.8989			1.36618
$987$		−	16.4710i		−	0.524277i
$988$		−	4.04272i		−	0.128616i
$989$	−7.79310			−0.247806
$990$	18.3662	−	32.6074i	0.583716	−	1.03633i
$991$	−23.5197			−0.747126			−0.373563	−	0.927605i	$-0.621864\pi$
$991$	−23.5197			−0.747126			−0.373563	+	0.927605i	$0.621864\pi$
$992$		−	54.4269i		−	1.72806i
$993$			18.5157i			0.587577i
$994$	−22.8465			−0.724648
$995$	9.38465	+	5.28593i	0.297513	+	0.167575i
$996$	38.7360			1.22740
$997$		−	33.6395i		−	1.06537i	−0.846313	−	0.532686i	$-0.821183\pi$
$997$		−	33.6395i		−	1.06537i	0.846313	−	0.532686i	$-0.178817\pi$
$998$			12.4240i			0.393276i
$999$	−8.87275			−0.280721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.b.b.39.2	✓	6
3.2	odd	2		855.2.c.d.514.5		6
4.3	odd	2		1520.2.d.h.609.2		6
5.2	odd	4		475.2.a.j.1.5		6
5.3	odd	4		475.2.a.j.1.2		6
5.4	even	2	inner	95.2.b.b.39.5	yes	6
15.2	even	4		4275.2.a.br.1.2		6
15.8	even	4		4275.2.a.br.1.5		6
15.14	odd	2		855.2.c.d.514.2		6
19.18	odd	2		1805.2.b.e.1084.5		6
20.3	even	4		7600.2.a.ck.1.5		6
20.7	even	4		7600.2.a.ck.1.2		6
20.19	odd	2		1520.2.d.h.609.5		6
95.18	even	4		9025.2.a.bx.1.5		6
95.37	even	4		9025.2.a.bx.1.2		6
95.94	odd	2		1805.2.b.e.1084.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.2	✓	6	1.1	even	1	trivial
95.2.b.b.39.5	yes	6	5.4	even	2	inner
475.2.a.j.1.2		6	5.3	odd	4
475.2.a.j.1.5		6	5.2	odd	4
855.2.c.d.514.2		6	15.14	odd	2
855.2.c.d.514.5		6	3.2	odd	2
1520.2.d.h.609.2		6	4.3	odd	2
1520.2.d.h.609.5		6	20.19	odd	2
1805.2.b.e.1084.2		6	95.94	odd	2
1805.2.b.e.1084.5		6	19.18	odd	2
4275.2.a.br.1.2		6	15.2	even	4
4275.2.a.br.1.5		6	15.8	even	4
7600.2.a.ck.1.2		6	20.7	even	4
7600.2.a.ck.1.5		6	20.3	even	4
9025.2.a.bx.1.2		6	95.37	even	4
9025.2.a.bx.1.5		6	95.18	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.82254i q^{2} +2.31446i q^{3} -1.32164 q^{4} +(1.94827 + 1.09737i) q^{5} +4.21819 q^{6} -1.45033i q^{7} -1.23634i q^{8} -2.35673 q^{9} +O(q^{10})\)	\(q-1.82254i q^{2} +2.31446i q^{3} -1.32164 q^{4} +(1.94827 + 1.09737i) q^{5} +4.21819 q^{6} -1.45033i q^{7} -1.23634i q^{8} -2.35673 q^{9} +(2.00000 - 3.55080i) q^{10} -3.89655 q^{11} -3.05888i q^{12} +3.05888i q^{13} -2.64327 q^{14} +(-2.53982 + 4.50920i) q^{15} -4.89655 q^{16} -3.92301i q^{17} +4.29522i q^{18} +1.00000 q^{19} +(-2.57491 - 1.45033i) q^{20} +3.35673 q^{21} +7.10160i q^{22} -5.37334i q^{23} +2.86146 q^{24} +(2.59155 + 4.27596i) q^{25} +5.57491 q^{26} +1.48883i q^{27} +1.91681i q^{28} -6.00000 q^{29} +(8.21819 + 4.62892i) q^{30} -8.43637 q^{31} +6.45146i q^{32} -9.01841i q^{33} -7.14982 q^{34} +(1.59155 - 2.82564i) q^{35} +3.11474 q^{36} +5.95953i q^{37} -1.82254i q^{38} -7.07965 q^{39} +(1.35673 - 2.40873i) q^{40} +10.4364 q^{41} -6.11775i q^{42} -1.45033i q^{43} +5.14982 q^{44} +(-4.59155 - 2.58620i) q^{45} -9.79310 q^{46} -4.90686i q^{47} -11.3329i q^{48} +4.89655 q^{49} +(7.79310 - 4.72319i) q^{50} +9.07965 q^{51} -4.04272i q^{52} -4.23127i q^{53} +2.71345 q^{54} +(-7.59155 - 4.27596i) q^{55} -1.79310 q^{56} +2.31446i q^{57} +10.9352i q^{58} -3.35673 q^{59} +(3.35673 - 5.95953i) q^{60} +10.3329 q^{61} +15.3756i q^{62} +3.41802i q^{63} +1.96491 q^{64} +(-3.35673 + 5.95953i) q^{65} -16.4364 q^{66} +9.84404i q^{67} +5.18479i q^{68} +12.4364 q^{69} +(-5.14982 - 2.90066i) q^{70} +8.64327 q^{71} +2.91372i q^{72} -2.43418i q^{73} +10.8615 q^{74} +(-9.89655 + 5.99804i) q^{75} -1.32164 q^{76} +5.65127i q^{77} +12.9029i q^{78} +12.4364 q^{79} +(-9.53982 - 5.37334i) q^{80} -10.5160 q^{81} -19.0207i q^{82} +12.6635i q^{83} -4.43637 q^{84} +(4.30500 - 7.64310i) q^{85} -2.64327 q^{86} -13.8868i q^{87} +4.81746i q^{88} -12.3662 q^{89} +(-4.71345 + 8.36826i) q^{90} +4.43637 q^{91} +7.10160i q^{92} -19.5256i q^{93} -8.94292 q^{94} +(1.94827 + 1.09737i) q^{95} -14.9316 q^{96} -3.05888i q^{97} -8.92414i q^{98} +9.18310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{4} - q^{5} - 14 q^{9}+O(q^{10}) \) 6 * q - 8 * q^4 - q^5 - 14 * q^9	\( 6 q - 8 q^{4} - q^{5} - 14 q^{9} + 12 q^{10} + 2 q^{11} - 16 q^{14} + 10 q^{15} - 4 q^{16} + 6 q^{19} + 10 q^{20} + 20 q^{21} - 8 q^{24} + 3 q^{25} + 8 q^{26} - 36 q^{29} + 24 q^{30} + 8 q^{34} - 3 q^{35} - 32 q^{36} + 8 q^{39} + 8 q^{40} + 12 q^{41} - 20 q^{44} - 15 q^{45} - 8 q^{46} + 4 q^{49} - 4 q^{50} + 4 q^{51} + 16 q^{54} - 33 q^{55} + 40 q^{56} - 20 q^{59} + 20 q^{60} - 14 q^{61} + 12 q^{64} - 20 q^{65} - 48 q^{66} + 24 q^{69} + 20 q^{70} + 52 q^{71} + 40 q^{74} - 34 q^{75} - 8 q^{76} + 24 q^{79} - 32 q^{80} + 38 q^{81} + 24 q^{84} + 13 q^{85} - 16 q^{86} - 24 q^{89} - 28 q^{90} - 24 q^{91} + 48 q^{94} - q^{95} - 64 q^{96} + 30 q^{99}+O(q^{100}) \) 6 * q - 8 * q^4 - q^5 - 14 * q^9 + 12 * q^10 + 2 * q^11 - 16 * q^14 + 10 * q^15 - 4 * q^16 + 6 * q^19 + 10 * q^20 + 20 * q^21 - 8 * q^24 + 3 * q^25 + 8 * q^26 - 36 * q^29 + 24 * q^30 + 8 * q^34 - 3 * q^35 - 32 * q^36 + 8 * q^39 + 8 * q^40 + 12 * q^41 - 20 * q^44 - 15 * q^45 - 8 * q^46 + 4 * q^49 - 4 * q^50 + 4 * q^51 + 16 * q^54 - 33 * q^55 + 40 * q^56 - 20 * q^59 + 20 * q^60 - 14 * q^61 + 12 * q^64 - 20 * q^65 - 48 * q^66 + 24 * q^69 + 20 * q^70 + 52 * q^71 + 40 * q^74 - 34 * q^75 - 8 * q^76 + 24 * q^79 - 32 * q^80 + 38 * q^81 + 24 * q^84 + 13 * q^85 - 16 * q^86 - 24 * q^89 - 28 * q^90 - 24 * q^91 + 48 * q^94 - q^95 - 64 * q^96 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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