LMFDB - Embedded newform 185.2.n.a.84.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(84,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("185.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.n (of order $6$, degree $2$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			84.5
Character	$\chi$	$=$	185.84
Dual form			185.2.n.a.174.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58456 - 0.914845i) q^{2} +(-1.14999 + 0.663947i) q^{3} +(0.673882 + 1.16720i) q^{4} +(2.12799 - 0.686767i) q^{5} +2.42963 q^{6} +(-2.49908 + 1.44285i) q^{7} +1.19339i q^{8} +(-0.618348 + 1.07101i) q^{9} +O(q^{10})$	\(q+(-1.58456 - 0.914845i) q^{2} +(-1.14999 + 0.663947i) q^{3} +(0.673882 + 1.16720i) q^{4} +(2.12799 - 0.686767i) q^{5} +2.42963 q^{6} +(-2.49908 + 1.44285i) q^{7} +1.19339i q^{8} +(-0.618348 + 1.07101i) q^{9} +(-4.00021 - 0.858562i) q^{10} +1.49279 q^{11} +(-1.54992 - 0.894844i) q^{12} +(5.01190 - 2.89362i) q^{13} +5.27992 q^{14} +(-1.99119 + 2.20265i) q^{15} +(2.43953 - 4.22539i) q^{16} +(5.81727 + 3.35860i) q^{17} +(1.95962 - 1.13139i) q^{18} +(1.90807 + 3.30487i) q^{19} +(2.23561 + 2.02099i) q^{20} +(1.91595 - 3.31852i) q^{21} +(-2.36541 - 1.36567i) q^{22} +6.31522i q^{23} +(-0.792348 - 1.37239i) q^{24} +(4.05670 - 2.92287i) q^{25} -10.5889 q^{26} -5.62589i q^{27} +(-3.36817 - 1.94462i) q^{28} -6.15987 q^{29} +(5.17024 - 1.66859i) q^{30} +2.38247 q^{31} +(-5.66414 + 3.27019i) q^{32} +(-1.71669 + 0.991134i) q^{33} +(-6.14520 - 10.6438i) q^{34} +(-4.32713 + 4.78665i) q^{35} -1.66677 q^{36} +(-5.74855 - 1.98851i) q^{37} -6.98235i q^{38} +(-3.84242 + 6.65527i) q^{39} +(0.819580 + 2.53952i) q^{40} +(3.78277 + 6.55195i) q^{41} +(-6.07186 + 3.50559i) q^{42} -6.09393i q^{43} +(1.00596 + 1.74238i) q^{44} +(-0.580306 + 2.70376i) q^{45} +(5.77745 - 10.0068i) q^{46} +7.76674i q^{47} +6.47888i q^{48} +(0.663613 - 1.14941i) q^{49} +(-9.10205 + 0.920199i) q^{50} -8.91974 q^{51} +(6.75485 + 3.89992i) q^{52} +(0.317686 + 0.183416i) q^{53} +(-5.14681 + 8.91454i) q^{54} +(3.17665 - 1.02520i) q^{55} +(-1.72188 - 2.98238i) q^{56} +(-4.38852 - 2.53371i) q^{57} +(9.76067 + 5.63532i) q^{58} +(4.43904 - 7.68865i) q^{59} +(-3.91276 - 0.839791i) q^{60} +(3.97285 + 6.88118i) q^{61} +(-3.77516 - 2.17959i) q^{62} -3.56873i q^{63} +2.20876 q^{64} +(8.67804 - 9.59960i) q^{65} +3.62694 q^{66} +(-7.10312 + 4.10099i) q^{67} +9.05321i q^{68} +(-4.19297 - 7.26244i) q^{69} +(11.2356 - 3.62607i) q^{70} +(1.44131 + 2.49642i) q^{71} +(-1.27813 - 0.737931i) q^{72} -10.1976i q^{73} +(7.28974 + 8.40993i) q^{74} +(-2.72454 + 6.05471i) q^{75} +(-2.57163 + 4.45419i) q^{76} +(-3.73061 + 2.15387i) q^{77} +(12.1771 - 7.03044i) q^{78} +(-4.49978 - 7.79385i) q^{79} +(2.28945 - 10.6670i) q^{80} +(1.88025 + 3.25668i) q^{81} -13.8426i q^{82} +(-7.13420 - 4.11893i) q^{83} +5.16449 q^{84} +(14.6857 + 3.15197i) q^{85} +(-5.57500 + 9.65618i) q^{86} +(7.08379 - 4.08983i) q^{87} +1.78148i q^{88} +(-2.35419 + 4.07757i) q^{89} +(3.39305 - 3.75338i) q^{90} +(-8.35010 + 14.4628i) q^{91} +(-7.37111 + 4.25571i) q^{92} +(-2.73982 + 1.58183i) q^{93} +(7.10536 - 12.3068i) q^{94} +(6.33003 + 5.72235i) q^{95} +(4.34247 - 7.52138i) q^{96} -6.47879i q^{97} +(-2.10307 + 1.21421i) q^{98} +(-0.923065 + 1.59879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 16 q^{4} - 2 q^{5} - 16 q^{6} + 14 q^{9}+O(q^{10}) $ 36 * q + 16 * q^4 - 2 * q^5 - 16 * q^6 + 14 * q^9	$ 36 q + 16 q^{4} - 2 q^{5} - 16 q^{6} + 14 q^{9} - 12 q^{10} + 12 q^{11} - 8 q^{14} - 10 q^{15} - 16 q^{16} - 8 q^{19} + 22 q^{20} - 26 q^{21} - 42 q^{24} + 12 q^{26} - 16 q^{29} + 18 q^{34} - 16 q^{35} + 32 q^{36} - 2 q^{39} - 42 q^{40} + 2 q^{41} - 10 q^{44} - 56 q^{45} + 52 q^{46} + 10 q^{49} + 34 q^{50} - 28 q^{51} - 42 q^{54} + 4 q^{55} + 18 q^{56} - 28 q^{59} + 44 q^{60} + 20 q^{61} + 36 q^{64} + 10 q^{65} - 148 q^{66} + 70 q^{69} - 10 q^{70} - 46 q^{71} + 56 q^{74} + 32 q^{75} + 24 q^{76} + 2 q^{79} + 132 q^{80} - 2 q^{81} - 168 q^{84} - 28 q^{85} - 22 q^{86} + 8 q^{89} - 28 q^{90} - 48 q^{91} + 32 q^{94} - 10 q^{95} + 106 q^{96} + 64 q^{99}+O(q^{100}) $ 36 * q + 16 * q^4 - 2 * q^5 - 16 * q^6 + 14 * q^9 - 12 * q^10 + 12 * q^11 - 8 * q^14 - 10 * q^15 - 16 * q^16 - 8 * q^19 + 22 * q^20 - 26 * q^21 - 42 * q^24 + 12 * q^26 - 16 * q^29 + 18 * q^34 - 16 * q^35 + 32 * q^36 - 2 * q^39 - 42 * q^40 + 2 * q^41 - 10 * q^44 - 56 * q^45 + 52 * q^46 + 10 * q^49 + 34 * q^50 - 28 * q^51 - 42 * q^54 + 4 * q^55 + 18 * q^56 - 28 * q^59 + 44 * q^60 + 20 * q^61 + 36 * q^64 + 10 * q^65 - 148 * q^66 + 70 * q^69 - 10 * q^70 - 46 * q^71 + 56 * q^74 + 32 * q^75 + 24 * q^76 + 2 * q^79 + 132 * q^80 - 2 * q^81 - 168 * q^84 - 28 * q^85 - 22 * q^86 + 8 * q^89 - 28 * q^90 - 48 * q^91 + 32 * q^94 - 10 * q^95 + 106 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.58456	−	0.914845i	−1.12045	−	0.646893i	−0.178935	−	0.983861i	$-0.557265\pi$
$2$	−1.58456	−	0.914845i	−1.12045	−	0.646893i	−0.941516	+	0.336968i	$0.890599\pi$
$3$	−1.14999	+	0.663947i	−0.663947	+	0.383330i	−0.793779	−	0.608206i	$-0.791889\pi$
$3$	−1.14999	+	0.663947i	−0.663947	+	0.383330i	0.129832	+	0.991536i	$0.458556\pi$
$4$	0.673882	+	1.16720i	0.336941	+	0.583599i
$5$	2.12799	−	0.686767i	0.951667	−	0.307131i
$5$	2.12799	−	0.686767i	0.951667	−	0.307131i
$6$	2.42963			0.991894
$7$	−2.49908	+	1.44285i	−0.944565	+	0.545345i	−0.891388	−	0.453240i	$-0.850268\pi$
$7$	−2.49908	+	1.44285i	−0.944565	+	0.545345i	−0.0531765	+	0.998585i	$0.516935\pi$
$8$			1.19339i			0.421927i
$9$	−0.618348	+	1.07101i	−0.206116	+	0.357004i
$10$	−4.00021	−	0.858562i	−1.26498	−	0.271501i
$11$	1.49279			0.450093			0.225047	−	0.974348i	$-0.427747\pi$
$11$	1.49279			0.450093			0.225047	+	0.974348i	$0.427747\pi$
$12$	−1.54992	−	0.894844i	−0.447422	−	0.258319i
$13$	5.01190	−	2.89362i	1.39005	−	0.802546i	0.396730	−	0.917935i	$-0.370145\pi$
$13$	5.01190	−	2.89362i	1.39005	−	0.802546i	0.993320	+	0.115390i	$0.0368117\pi$
$14$	5.27992			1.41112
$15$	−1.99119	+	2.20265i	−0.514124	+	0.568722i
$16$	2.43953	−	4.22539i	0.609883	−	1.05635i
$17$	5.81727	+	3.35860i	1.41090	+	0.814581i	0.995473	−	0.0950479i	$-0.0303004\pi$
$17$	5.81727	+	3.35860i	1.41090	+	0.814581i	0.415422	+	0.909629i	$0.363634\pi$
$18$	1.95962	−	1.13139i	0.461886	−	0.266670i
$19$	1.90807	+	3.30487i	0.437741	+	0.758190i	0.997515	−	0.0704555i	$-0.0224453\pi$
$19$	1.90807	+	3.30487i	0.437741	+	0.758190i	−0.559774	+	0.828646i	$0.689112\pi$
$20$	2.23561	+	2.02099i	0.499897	+	0.451907i
$21$	1.91595	−	3.31852i	0.418094	−	0.724160i
$22$	−2.36541	−	1.36567i	−0.504308	−	0.291162i
$23$			6.31522i			1.31681i	0.752662	+	0.658407i	$0.228770\pi$
$23$			6.31522i			1.31681i	−0.752662	+	0.658407i	$0.771230\pi$
$24$	−0.792348	−	1.37239i	−0.161737	−	0.280137i
$25$	4.05670	−	2.92287i	0.811341	−	0.584574i
$26$	−10.5889			−2.07664
$27$		−	5.62589i		−	1.08270i
$28$	−3.36817	−	1.94462i	−0.636525	−	0.367498i
$29$	−6.15987			−1.14386			−0.571929	−	0.820303i	$-0.693805\pi$
$29$	−6.15987			−1.14386			−0.571929	+	0.820303i	$0.693805\pi$
$30$	5.17024	−	1.66859i	0.943953	−	0.304642i
$31$	2.38247			0.427904			0.213952	−	0.976844i	$-0.431366\pi$
$31$	2.38247			0.427904			0.213952	+	0.976844i	$0.431366\pi$
$32$	−5.66414	+	3.27019i	−1.00129	+	0.578094i
$33$	−1.71669	+	0.991134i	−0.298838	+	0.172534i
$34$	−6.14520	−	10.6438i	−1.05389	−	1.82540i
$35$	−4.32713	+	4.78665i	−0.731419	+	0.809092i
$36$	−1.66677			−0.277796
$37$	−5.74855	−	1.98851i	−0.945056	−	0.326908i
$37$	−5.74855	−	1.98851i	−0.945056	−	0.326908i
$38$		−	6.98235i		−	1.13269i
$39$	−3.84242	+	6.65527i	−0.615280	+	1.06570i
$40$	0.819580	+	2.53952i	0.129587	+	0.401534i
$41$	3.78277	+	6.55195i	0.590769	+	1.02324i	0.994129	+	0.108201i	$0.0345089\pi$
$41$	3.78277	+	6.55195i	0.590769	+	1.02324i	−0.403360	+	0.915041i	$0.632158\pi$
$42$	−6.07186	+	3.50559i	−0.936908	+	0.540924i
$43$		−	6.09393i		−	0.929315i	−0.885490	−	0.464658i	$-0.846177\pi$
$43$		−	6.09393i		−	0.929315i	0.885490	−	0.464658i	$-0.153823\pi$
$44$	1.00596	+	1.74238i	0.151655	+	0.262674i
$45$	−0.580306	+	2.70376i	−0.0865069	+	0.403053i
$46$	5.77745	−	10.0068i	0.851838	−	1.47543i
$47$			7.76674i			1.13290i	0.824098	+	0.566448i	$0.191683\pi$
$47$			7.76674i			1.13290i	−0.824098	+	0.566448i	$0.808317\pi$
$48$			6.47888i			0.935145i
$49$	0.663613	−	1.14941i	0.0948018	−	0.164202i
$50$	−9.10205	+	0.920199i	−1.28722	+	0.130136i
$51$	−8.91974			−1.24901
$52$	6.75485	+	3.89992i	0.936730	+	0.540821i
$53$	0.317686	+	0.183416i	0.0436376	+	0.0251942i	0.521660	−	0.853153i	$-0.325313\pi$
$53$	0.317686	+	0.183416i	0.0436376	+	0.0251942i	−0.478022	+	0.878348i	$0.658646\pi$
$54$	−5.14681	+	8.91454i	−0.700392	+	1.21312i
$55$	3.17665	−	1.02520i	0.428339	−	0.138238i
$56$	−1.72188	−	2.98238i	−0.230096	−	0.398537i
$57$	−4.38852	−	2.53371i	−0.581274	−	0.335599i
$58$	9.76067	+	5.63532i	1.28164	+	0.739954i
$59$	4.43904	−	7.68865i	0.577914	−	1.00098i	−0.417804	−	0.908537i	$-0.637200\pi$
$59$	4.43904	−	7.68865i	0.577914	−	1.00098i	0.995718	−	0.0924394i	$-0.0294665\pi$
$60$	−3.91276	−	0.839791i	−0.505135	−	0.108417i
$61$	3.97285	+	6.88118i	0.508671	+	0.881044i	0.999950	+	0.0100417i	$0.00319641\pi$
$61$	3.97285	+	6.88118i	0.508671	+	0.881044i	−0.491278	+	0.871003i	$0.663470\pi$
$62$	−3.77516	−	2.17959i	−0.479446	−	0.276808i
$63$		−	3.56873i		−	0.449617i
$64$	2.20876			0.276094
$65$	8.67804	−	9.59960i	1.07638	−	1.19068i
$66$	3.62694			0.446445
$67$	−7.10312	+	4.10099i	−0.867784	+	0.501015i	−0.866611	−	0.498984i	$-0.833707\pi$
$67$	−7.10312	+	4.10099i	−0.867784	+	0.501015i	−0.00117289	+	0.999999i	$0.500373\pi$
$68$			9.05321i			1.09786i
$69$	−4.19297	−	7.26244i	−0.504775	−	0.874295i
$70$	11.2356	−	3.62607i	1.34292	−	0.433399i
$71$	1.44131	+	2.49642i	0.171052	+	0.296270i	0.938788	−	0.344496i	$-0.111950\pi$
$71$	1.44131	+	2.49642i	0.171052	+	0.296270i	−0.767736	+	0.640766i	$0.778617\pi$
$72$	−1.27813	−	0.737931i	−0.150629	−	0.0869659i
$73$		−	10.1976i		−	1.19354i	−0.802411	−	0.596772i	$-0.796450\pi$
$73$		−	10.1976i		−	1.19354i	0.802411	−	0.596772i	$-0.203550\pi$
$74$	7.28974	+	8.40993i	0.847415	+	0.977635i
$75$	−2.72454	+	6.05471i	−0.314603	+	0.699137i
$76$	−2.57163	+	4.45419i	−0.294986	+	0.510930i
$77$	−3.73061	+	2.15387i	−0.425142	+	0.245456i
$78$	12.1771	−	7.03044i	1.37878	−	0.796040i
$79$	−4.49978	−	7.79385i	−0.506265	−	0.876877i	−0.999974	−	0.00724950i	$-0.997692\pi$
$79$	−4.49978	−	7.79385i	−0.506265	−	0.876877i	0.493709	−	0.869627i	$-0.335641\pi$
$80$	2.28945	−	10.6670i	0.255968	−	1.19261i
$81$	1.88025	+	3.25668i	0.208916	+	0.361854i
$82$		−	13.8426i		−	1.52866i
$83$	−7.13420	−	4.11893i	−0.783080	−	0.452112i	0.0544406	−	0.998517i	$-0.482662\pi$
$83$	−7.13420	−	4.11893i	−0.783080	−	0.452112i	−0.837521	+	0.546405i	$0.815996\pi$
$84$	5.16449			0.563492
$85$	14.6857	+	3.15197i	1.59289	+	0.341880i
$86$	−5.57500	+	9.65618i	−0.601167	+	1.04125i
$87$	7.08379	−	4.08983i	0.759462	−	0.438475i
$88$			1.78148i			0.189907i
$89$	−2.35419	+	4.07757i	−0.249543	+	0.432221i	−0.963399	−	0.268071i	$-0.913614\pi$
$89$	−2.35419	+	4.07757i	−0.249543	+	0.432221i	0.713856	+	0.700293i	$0.246947\pi$
$90$	3.39305	−	3.75338i	0.357659	−	0.395641i
$91$	−8.35010	+	14.4628i	−0.875328	+	1.51611i
$92$	−7.37111	+	4.25571i	−0.768491	+	0.443689i
$93$	−2.73982	+	1.58183i	−0.284106	+	0.164029i
$94$	7.10536	−	12.3068i	0.732862	−	1.26935i
$95$	6.33003	+	5.72235i	0.649448	+	0.587100i
$96$	4.34247	−	7.52138i	0.443202	−	0.767648i
$97$		−	6.47879i		−	0.657822i	−0.944361	−	0.328911i	$-0.893318\pi$
$97$		−	6.47879i		−	0.657822i	0.944361	−	0.328911i	$-0.106682\pi$
$98$	−2.10307	+	1.21421i	−0.212442	+	0.122653i
$99$	−0.923065	+	1.59879i	−0.0927715	+	0.160685i
$100$	6.14530	+	2.76531i	0.614530	+	0.276531i
$101$	0.551737			0.0548998			0.0274499	−	0.999623i	$-0.491261\pi$
$101$	0.551737			0.0548998			0.0274499	+	0.999623i	$0.491261\pi$
$102$	14.1338	+	8.16018i	1.39946	+	0.807978i
$103$			8.23105i			0.811029i	0.914089	+	0.405515i	$0.132908\pi$
$103$			8.23105i			0.811029i	−0.914089	+	0.405515i	$0.867092\pi$
$104$	3.45322	+	5.98115i	0.338616	+	0.586500i
$105$	1.79807	−	8.37759i	0.175474	−	0.817569i
$106$	−0.335595	−	0.581268i	−0.0325959	−	0.0564577i
$107$	12.4057	−	7.16241i	1.19930	−	0.692416i	0.238901	−	0.971044i	$-0.423213\pi$
$107$	12.4057	−	7.16241i	1.19930	−	0.692416i	0.960399	+	0.278627i	$0.0898795\pi$
$108$	6.56652	−	3.79118i	0.631864	−	0.364807i
$109$	5.28838	−	9.15975i	0.506535	−	0.877345i	−0.493436	−	0.869782i	$-0.664259\pi$
$109$	5.28838	−	9.15975i	0.506535	−	0.877345i	0.999971	−	0.00756274i	$-0.00240732\pi$
$110$	−5.97148	−	1.28165i	−0.569358	−	0.122201i
$111$	7.93104	−	1.52997i	0.752781	−	0.145218i
$112$			14.0795i			1.33039i
$113$	−0.555385	−	0.320652i	−0.0522462	−	0.0301644i	0.473649	−	0.880714i	$-0.342936\pi$
$113$	−0.555385	−	0.320652i	−0.0522462	−	0.0301644i	−0.525896	+	0.850549i	$0.676270\pi$
$114$	4.63591	+	8.02963i	0.434193	+	0.752044i
$115$	4.33708	+	13.4387i	0.404435	+	1.25317i
$116$	−4.15102	−	7.18978i	−0.385413	−	0.667555i
$117$			7.15706i			0.661670i
$118$	−14.0678	+	8.12207i	−1.29505	+	0.747697i
$119$	−19.3838			−1.77691
$120$	−2.62862	−	2.37627i	−0.239959	−	0.216923i
$121$	−8.77158			−0.797416
$122$		−	14.5382i		−	1.31622i
$123$	−8.70029	−	5.02312i	−0.784479	−	0.452919i
$124$	1.60550	+	2.78081i	0.144178	+	0.249724i
$125$	6.62531	−	9.00585i	0.592585	−	0.805508i
$126$	−3.26483	+	5.65485i	−0.290854	+	0.503774i
$127$	−2.57079	−	1.48425i	−0.228121	−	0.131706i	0.381584	−	0.924334i	$-0.375379\pi$
$127$	−2.57079	−	1.48425i	−0.228121	−	0.131706i	−0.609705	+	0.792629i	$0.708712\pi$
$128$	7.82838	+	4.51972i	0.691938	+	0.399490i
$129$	4.04605	+	7.00796i	0.356234	+	0.617016i
$130$	−22.5330	+	7.27207i	−1.97627	+	0.637803i
$131$	4.97710	−	8.62060i	0.434852	−	0.753185i	−0.562432	−	0.826844i	$-0.690134\pi$
$131$	4.97710	−	8.62060i	0.434852	−	0.753185i	0.997284	+	0.0736585i	$0.0234675\pi$
$132$	−2.31370	−	1.33581i	−0.201382	−	0.116268i
$133$	−9.53685	−	5.50610i	−0.826950	−	0.477440i
$134$	15.0071			1.29641
$135$	−3.86367	−	11.9718i	−0.332532	−	1.03037i
$136$	−4.00812	+	6.94227i	−0.343694	+	0.595295i
$137$			4.05771i			0.346674i	0.984863	+	0.173337i	$0.0554550\pi$
$137$			4.05771i			0.346674i	−0.984863	+	0.173337i	$0.944545\pi$
$138$			15.3437i			1.30614i
$139$	6.20529	−	10.7479i	0.526326	−	0.911623i	−0.473204	−	0.880953i	$-0.656903\pi$
$139$	6.20529	−	10.7479i	0.526326	−	0.911623i	0.999530	−	0.0306698i	$-0.00976404\pi$
$140$	−8.50295	−	1.82498i	−0.718630	−	0.154239i
$141$	−5.15671	−	8.93168i	−0.434273	−	0.752183i
$142$		−	5.27429i		−	0.442608i
$143$	7.48171	−	4.31957i	0.625652	−	0.361221i
$144$	3.01696	+	5.22553i	0.251413	+	0.435460i
$145$	−13.1082	+	4.23039i	−1.08857	+	0.351315i
$146$	−9.32926	+	16.1587i	−0.772095	+	1.33731i
$147$			1.76242i			0.145362i
$148$	−1.55286	−	8.04971i	−0.127645	−	0.661682i
$149$	−4.34618			−0.356053			−0.178026	−	0.984026i	$-0.556971\pi$
$149$	−4.34618			−0.356053			−0.178026	+	0.984026i	$0.556971\pi$
$150$	9.85631	−	7.10150i	0.804764	−	0.579835i
$151$	1.99735	+	3.45951i	0.162542	+	0.281531i	0.935780	−	0.352585i	$-0.114697\pi$
$151$	1.99735	+	3.45951i	0.162542	+	0.281531i	−0.773238	+	0.634116i	$0.781364\pi$
$152$	−3.94400	+	2.27707i	−0.319901	+	0.184695i
$153$	−7.19420	+	4.15357i	−0.581616	+	0.335796i
$154$	7.88182			0.635135
$155$	5.06988	−	1.63620i	0.407222	−	0.131423i
$156$	−10.3574			−0.829252
$157$	8.14426	+	4.70209i	0.649983	+	0.375268i	0.788450	−	0.615099i	$-0.210884\pi$
$157$	8.14426	+	4.70209i	0.649983	+	0.375268i	−0.138467	+	0.990367i	$0.544217\pi$
$158$			16.4664i			1.31000i
$159$	−0.487115			−0.0386307
$160$	−9.80739	+	10.8489i	−0.775342	+	0.857680i
$161$	−9.11189	−	15.7823i	−0.718118	−	1.24382i
$162$		−	6.88053i		−	0.540586i
$163$	−0.440311	−	0.254214i	−0.0344878	−	0.0199115i	0.482657	−	0.875809i	$-0.339672\pi$
$163$	−0.440311	−	0.254214i	−0.0344878	−	0.0199115i	−0.517145	+	0.855898i	$0.673005\pi$
$164$	−5.09828	+	8.83048i	−0.398109	+	0.689544i
$165$	−2.97244	+	3.28809i	−0.231404	+	0.255978i
$166$	7.53637	+	13.0534i	0.584936	+	1.01314i
$167$	13.7896	−	7.96143i	1.06707	−	0.616074i	0.139692	−	0.990195i	$-0.455389\pi$
$167$	13.7896	−	7.96143i	1.06707	−	0.616074i	0.927380	+	0.374121i	$0.122056\pi$
$168$	3.96029	+	2.28647i	0.305543	+	0.176405i
$169$	10.2461	−	17.7467i	0.788160	−	1.36513i
$170$	−20.3867	−	18.4296i	−1.56359	−	1.41349i
$171$	−4.71941			−0.360902
$172$	7.11282	−	4.10659i	0.542347	−	0.313124i
$173$	−7.37799	−	4.25969i	−0.560938	−	0.323858i	0.192584	−	0.981281i	$-0.438313\pi$
$173$	−7.37799	−	4.25969i	−0.560938	−	0.323858i	−0.753522	+	0.657423i	$0.771647\pi$
$174$	−14.9662			−1.13459
$175$	−5.92079	+	13.1577i	−0.447570	+	0.994628i
$176$	3.64171	−	6.30762i	0.274504	−	0.475455i
$177$			11.7892i			0.886127i
$178$	7.46069	−	4.30743i	0.559202	−	0.322855i
$179$	−2.00743			−0.150042			−0.0750211	−	0.997182i	$-0.523902\pi$
$179$	−2.00743			−0.150042			−0.0750211	+	0.997182i	$0.523902\pi$
$180$	−3.54688	+	1.14469i	−0.264369	+	0.0853198i
$181$	−6.83450	−	11.8377i	−0.508004	−	0.879889i	−0.999957	−	0.00926718i	$-0.997050\pi$
$181$	−6.83450	−	11.8377i	−0.508004	−	0.879889i	0.491953	−	0.870622i	$-0.336283\pi$
$182$	26.4624	−	15.2781i	1.96153	−	1.13249i
$183$	−9.13747	−	5.27552i	−0.675462	−	0.389978i
$184$	−7.53652			−0.555600
$185$	−13.5985	−	0.283613i	−0.999783	−	0.0208517i
$186$	5.78853			0.424436
$187$	8.68397	+	5.01369i	0.635035	+	0.366637i
$188$	−9.06532	+	5.23387i	−0.661157	+	0.381719i
$189$	8.11729	+	14.0596i	0.590446	+	1.02268i
$190$	−4.79524	−	14.8584i	−0.347884	−	1.07794i
$191$	−8.45931			−0.612095			−0.306047	−	0.952016i	$-0.599007\pi$
$191$	−8.45931			−0.612095			−0.306047	+	0.952016i	$0.599007\pi$
$192$	−2.54005	+	1.46650i	−0.183312	+	0.105835i
$193$			0.629762i			0.0453313i	0.999743	+	0.0226656i	$0.00721532\pi$
$193$			0.629762i			0.0453313i	−0.999743	+	0.0226656i	$0.992785\pi$
$194$	−5.92709	+	10.2660i	−0.425540	+	0.737057i
$195$	−3.60603	+	16.8012i	−0.258233	+	1.20316i
$196$	1.78879			0.127770
$197$	13.9931	+	8.07891i	0.996966	+	0.575599i	0.907349	−	0.420378i	$-0.138102\pi$
$197$	13.9931	+	8.07891i	0.996966	+	0.575599i	0.0896170	+	0.995976i	$0.471436\pi$
$198$	2.92530	−	1.68892i	0.207892	−	0.120026i
$199$	−18.5216			−1.31296			−0.656480	−	0.754343i	$-0.727955\pi$
$199$	−18.5216			−1.31296			−0.656480	+	0.754343i	$0.727955\pi$
$200$	3.48812	+	4.84123i	0.246647	+	0.342327i
$201$	5.44568	−	9.43219i	0.384109	−	0.665296i
$202$	−0.874258	−	0.504753i	−0.0615126	−	0.0355143i
$203$	15.3940	−	8.88775i	1.08045	−	0.623797i
$204$	−6.01085	−	10.4111i	−0.420844	−	0.728923i
$205$	12.5494	+	11.3446i	0.876485	+	0.792342i
$206$	7.53013	−	13.0426i	0.524649	−	0.908719i
$207$	−6.76367	−	3.90501i	−0.470107	−	0.271417i
$208$		−	28.2363i		−	1.95783i
$209$	2.84835	+	4.93348i	0.197024	+	0.341256i
$210$	−10.5133	+	11.6298i	−0.725490	+	0.802534i
$211$	21.8255			1.50253			0.751265	−	0.660001i	$-0.229444\pi$
$211$	21.8255			1.50253			0.751265	+	0.660001i	$0.229444\pi$
$212$			0.494404i			0.0339558i
$213$	−3.31498	−	1.91390i	−0.227139	−	0.131139i
$214$	−26.2100			−1.79168
$215$	−4.18511	−	12.9678i	−0.285422	−	0.884399i
$216$	6.71387			0.456821
$217$	−5.95399	+	3.43754i	−0.404183	+	0.233355i
$218$	−16.7595	+	9.67610i	−1.13510	+	0.655348i
$219$	6.77069	+	11.7272i	0.457521	+	0.792450i
$220$	3.33729	+	3.01691i	0.225000	+	0.203400i
$221$	38.8741			2.61495
$222$	−13.9669	−	4.83134i	−0.937395	−	0.324259i
$223$			3.35885i			0.224925i	0.993656	+	0.112463i	$0.0358738\pi$
$223$			3.35885i			0.224925i	−0.993656	+	0.112463i	$0.964126\pi$
$224$	9.43677	−	16.3450i	0.630521	−	1.09209i
$225$	0.621967	+	6.15212i	0.0414645	+	0.410142i
$226$	0.586693	+	1.01618i	0.0390262	+	0.0675954i
$227$	−5.85230	+	3.37883i	−0.388431	+	0.224261i	−0.681480	−	0.731837i	$-0.738663\pi$
$227$	−5.85230	+	3.37883i	−0.388431	+	0.224261i	0.293049	+	0.956097i	$0.405330\pi$
$228$		−	6.82970i		−	0.452308i
$229$	−1.74224	−	3.01765i	−0.115131	−	0.199412i	0.802701	−	0.596381i	$-0.203395\pi$
$229$	−1.74224	−	3.01765i	−0.115131	−	0.199412i	−0.917832	+	0.396969i	$0.870062\pi$
$230$	5.42201	−	25.2622i	0.357516	−	1.66574i
$231$	2.86011	−	4.95385i	0.188181	−	0.325940i
$232$		−	7.35112i		−	0.482625i
$233$		−	4.77515i		−	0.312831i	−0.987691	−	0.156415i	$-0.950006\pi$
$233$		−	4.77515i		−	0.312831i	0.987691	−	0.156415i	$-0.0499938\pi$
$234$	6.54760	−	11.3408i	0.428030	−	0.741370i
$235$	5.33394	+	16.5276i	0.347948	+	1.07814i
$236$	11.9656			0.778892
$237$	10.3494	+	5.97524i	0.672267	+	0.388133i
$238$	30.7147	+	17.7332i	1.99094	+	1.14947i
$239$	−0.357056	+	0.618439i	−0.0230960	+	0.0400035i	−0.877342	−	0.479865i	$-0.840686\pi$
$239$	−0.357056	+	0.618439i	−0.0230960	+	0.0400035i	0.854246	+	0.519868i	$0.174019\pi$
$240$	4.44948	+	13.7870i	0.287212	+	0.889947i
$241$	−4.26376	−	7.38505i	−0.274653	−	0.475713i	0.695394	−	0.718628i	$-0.255230\pi$
$241$	−4.26376	−	7.38505i	−0.274653	−	0.475713i	−0.970048	+	0.242915i	$0.921896\pi$
$242$	13.8991	+	8.02463i	0.893466	+	0.515843i
$243$	10.2920	+	5.94206i	0.660229	+	0.381183i
$244$	−5.35446	+	9.27420i	−0.342784	+	0.593720i
$245$	0.622786	−	2.90169i	0.0397883	−	0.185382i
$246$	9.19074	+	15.9188i	0.585980	+	1.01495i
$247$	19.1261	+	11.0425i	1.21696	+	0.702615i
$248$			2.84322i			0.180544i
$249$	10.9390			0.693232
$250$	−18.7371	+	8.20916i	−1.18504	+	0.519193i
$251$	−26.7145			−1.68620			−0.843102	−	0.537754i	$-0.819273\pi$
$251$	−26.7145			−1.68620			−0.843102	+	0.537754i	$0.819273\pi$
$252$	4.16541	−	2.40490i	0.262396	−	0.151494i
$253$			9.42730i			0.592689i
$254$	2.71571	+	4.70375i	0.170399	+	0.295139i
$255$	−18.9811	+	6.12578i	−1.18864	+	0.383611i
$256$	−10.4784	−	18.1492i	−0.654902	−	1.13432i
$257$	−21.3880	−	12.3484i	−1.33415	−	0.770270i	−0.348215	−	0.937415i	$-0.613212\pi$
$257$	−21.3880	−	12.3484i	−1.33415	−	0.770270i	−0.985932	+	0.167144i	$0.946545\pi$
$258$		−	14.8060i		−	0.921782i
$259$	17.2352	−	3.32483i	1.07094	−	0.206595i
$260$	17.0526	+	3.65999i	1.05756	+	0.226983i
$261$	3.80894	−	6.59728i	0.235768	−	0.408362i
$262$	−15.7730	+	9.10656i	−0.974460	+	0.562605i
$263$	−21.3360	+	12.3183i	−1.31563	+	0.759580i	−0.983023	−	0.183485i	$-0.941262\pi$
$263$	−21.3360	+	12.3183i	−1.31563	+	0.759580i	−0.332609	+	0.943065i	$0.607929\pi$
$264$	−1.18281	−	2.04869i	−0.0727969	−	0.126088i
$265$	0.801999	+	0.172132i	0.0492664	+	0.0105740i
$266$	10.0745	+	17.4495i	0.617705	+	1.06990i
$267$		−	6.25222i		−	0.382630i
$268$	−9.57333	−	5.52716i	−0.584784	−	0.337625i
$269$	−25.6522			−1.56404			−0.782021	−	0.623252i	$-0.785811\pi$
$269$	−25.6522			−1.56404			−0.782021	+	0.623252i	$0.785811\pi$
$270$	−4.83017	+	22.5047i	−0.293955	+	1.36959i
$271$	−4.22786	+	7.32287i	−0.256824	+	0.444832i	−0.965389	−	0.260813i	$-0.916009\pi$
$271$	−4.22786	+	7.32287i	−0.256824	+	0.444832i	0.708565	+	0.705645i	$0.249343\pi$
$272$	28.3828	−	16.3868i	1.72096	−	0.993597i
$273$		−	22.1761i		−	1.34216i
$274$	3.71218	−	6.42968i	0.224261	−	0.388431i
$275$	6.05581	−	4.36323i	0.365179	−	0.263113i
$276$	5.65114	−	9.78806i	0.340158	−	0.589172i
$277$	−24.2277	+	13.9879i	−1.45570	+	0.840451i	−0.998796	−	0.0490635i	$-0.984376\pi$
$277$	−24.2277	+	13.9879i	−1.45570	+	0.840451i	−0.456908	+	0.889514i	$0.651043\pi$
$278$	−19.6653	+	11.3537i	−1.17944	+	0.680953i
$279$	−1.47320	+	2.55165i	−0.0881979	+	0.152763i
$280$	−5.71234	−	5.16396i	−0.341378	−	0.308605i
$281$	−0.0257871	+	0.0446645i	−0.00153833	+	0.00266446i	−0.866794	−	0.498667i	$-0.833823\pi$
$281$	−0.0257871	+	0.0446645i	−0.00153833	+	0.00266446i	0.865255	+	0.501332i	$0.167156\pi$
$282$			18.8703i			1.12371i
$283$	−10.4255	+	6.01917i	−0.619732	+	0.357802i	−0.776765	−	0.629791i	$-0.783140\pi$
$283$	−10.4255	+	6.01917i	−0.619732	+	0.357802i	0.157033	+	0.987593i	$0.449807\pi$
$284$	−1.94254	+	3.36458i	−0.115269	+	0.199651i
$285$	−11.0788	−	2.37784i	−0.656252	−	0.140851i
$286$	−15.8069			−0.934684
$287$	−18.9069	−	10.9159i	−1.11604	−	0.644346i
$288$		−	8.08847i		−	0.476618i
$289$	14.0604	+	24.3534i	0.827083	+	1.43255i
$290$	24.6408	+	5.28863i	1.44696	+	0.310559i
$291$	4.30158	+	7.45055i	0.252163	+	0.436759i
$292$	11.9027	−	6.87201i	0.696551	−	0.402154i
$293$	18.5355	−	10.7015i	1.08285	−	0.625186i	0.151189	−	0.988505i	$-0.451690\pi$
$293$	18.5355	−	10.7015i	1.08285	−	0.625186i	0.931665	+	0.363319i	$0.118357\pi$
$294$	1.61234	−	2.79265i	0.0940334	−	0.162871i
$295$	4.16594	−	19.4100i	0.242551	−	1.13009i
$296$	2.37306	−	6.86026i	0.137931	−	0.398745i
$297$		−	8.39827i		−	0.487317i
$298$	6.88677	+	3.97608i	0.398940	+	0.230328i
$299$	18.2738	+	31.6512i	1.05680	+	1.83044i
$300$	−8.90306	+	0.900081i	−0.514018	+	0.0519662i
$301$	8.79260	+	15.2292i	0.506797	+	0.877799i
$302$		−	7.30906i		−	0.420589i
$303$	−0.634492	+	0.366324i	−0.0364506	+	0.0210448i
$304$	18.6192			1.06788
$305$	13.1800	+	11.9147i	0.754682	+	0.682232i
$306$	15.1995			0.868897
$307$		−	23.1222i		−	1.31965i	−0.751418	−	0.659826i	$-0.770630\pi$
$307$		−	23.1222i		−	1.31965i	0.751418	−	0.659826i	$-0.229370\pi$
$308$	−5.02798	−	2.90291i	−0.286496	−	0.165408i
$309$	−5.46498	−	9.46562i	−0.310892	−	0.538481i
$310$	−9.53038	−	2.04550i	−0.541289	−	0.116176i
$311$	3.26865	−	5.66147i	0.185348	−	0.321033i	−0.758346	−	0.651853i	$-0.773992\pi$
$311$	3.26865	−	5.66147i	0.185348	−	0.321033i	0.943694	+	0.330820i	$0.107325\pi$
$312$	−7.94233	−	4.58551i	−0.449646	−	0.259603i
$313$	7.26260	+	4.19306i	0.410506	+	0.237006i	0.691007	−	0.722848i	$-0.257167\pi$
$313$	7.26260	+	4.19306i	0.410506	+	0.237006i	−0.280501	+	0.959854i	$0.590501\pi$
$314$	−8.60337	−	14.9015i	−0.485516	−	0.840939i
$315$	−2.45088	−	7.59422i	−0.138092	−	0.427886i
$316$	6.06464	−	10.5043i	0.341163	−	0.590911i
$317$	3.25102	+	1.87698i	0.182596	+	0.105422i	0.588512	−	0.808489i	$-0.299714\pi$
$317$	3.25102	+	1.87698i	0.182596	+	0.105422i	−0.405916	+	0.913910i	$0.633047\pi$
$318$	0.771862	+	0.445635i	0.0432839	+	0.0249900i
$319$	−9.19539			−0.514843
$320$	4.70021	−	1.51690i	0.262750	−	0.0847972i
$321$	−9.51093	+	16.4734i	−0.530848	+	0.919456i
$322$			33.3439i			1.85818i
$323$			25.6338i			1.42630i
$324$	−2.53413	+	4.38924i	−0.140785	+	0.243847i
$325$	11.8741	−	26.3877i	0.658657	−	1.46372i
$326$	0.465132	+	0.805632i	0.0257613	+	0.0446198i
$327$			14.0448i			0.776681i
$328$	−7.81903	+	4.51432i	−0.431733	+	0.249261i
$329$	−11.2062	−	19.4097i	−0.617819	−	1.07009i
$330$	7.71809	−	2.49086i	0.424867	−	0.137117i
$331$	1.88192	−	3.25958i	0.103439	−	0.179162i	−0.809660	−	0.586899i	$-0.800349\pi$
$331$	1.88192	−	3.25958i	0.103439	−	0.179162i	0.913100	+	0.407737i	$0.133682\pi$
$332$		−	11.1027i		−	0.609340i
$333$	5.68432	−	4.92717i	0.311499	−	0.270007i
$334$	−29.1339			−1.59414
$335$	−12.2990	+	13.6051i	−0.671964	+	0.743324i
$336$	−9.34803	−	16.1913i	−0.509977	−	0.883305i
$337$	26.3577	−	15.2176i	1.43579	−	0.828956i	0.438240	−	0.898858i	$-0.355602\pi$
$337$	26.3577	−	15.2176i	1.43579	−	0.828956i	0.997554	+	0.0699021i	$0.0222687\pi$
$338$	−32.4710	+	18.7471i	−1.76619	+	1.01971i
$339$	0.851583			0.0462516
$340$	6.21744	+	19.2652i	0.337188	+	1.04480i
$341$	3.55653			0.192597
$342$	7.47817	+	4.31752i	0.404373	+	0.233465i
$343$		−	16.3699i		−	0.883891i
$344$	7.27243			0.392103
$345$	−13.9102	−	12.5748i	−0.748901	−	0.677006i
$346$	7.79390	+	13.4994i	0.419003	+	0.725734i
$347$		−	26.3541i		−	1.41476i	−0.706833	−	0.707380i	$-0.749877\pi$
$347$		−	26.3541i		−	1.41476i	0.706833	−	0.707380i	$-0.250123\pi$
$348$	9.54727	+	5.51212i	0.511788	+	0.295481i
$349$	−3.13889	+	5.43671i	−0.168021	+	0.291021i	−0.937724	−	0.347381i	$-0.887071\pi$
$349$	−3.13889	+	5.43671i	−0.168021	+	0.291021i	0.769703	+	0.638402i	$0.220404\pi$
$350$	21.4191	−	15.4325i	1.14490	−	0.824903i
$351$	−16.2792	−	28.1964i	−0.868918	−	1.50501i
$352$	−8.45538	+	4.88171i	−0.450673	+	0.260196i
$353$	−4.82553	−	2.78602i	−0.256837	−	0.148285i	0.366054	−	0.930594i	$-0.380709\pi$
$353$	−4.82553	−	2.78602i	−0.256837	−	0.148285i	−0.622891	+	0.782309i	$0.714042\pi$
$354$	10.7852	−	18.6806i	0.573230	−	0.992863i
$355$	4.78155	+	4.32251i	0.253778	+	0.229415i
$356$	−6.34577			−0.336325
$357$	22.2912	−	12.8698i	1.17977	−	0.681143i
$358$	3.18088	+	1.83648i	0.168115	+	0.0970612i
$359$	15.4499			0.815414			0.407707	−	0.913113i	$-0.366328\pi$
$359$	15.4499			0.815414			0.407707	+	0.913113i	$0.366328\pi$
$360$	−3.22664	−	0.692531i	−0.170059	−	0.0364996i
$361$	2.21854	−	3.84263i	0.116765	−	0.202243i
$362$			25.0100i			1.31450i
$363$	10.0872	−	5.82386i	0.529442	−	0.305674i
$364$	−22.5079			−1.17974
$365$	−7.00340	−	21.7005i	−0.366575	−	1.13586i
$366$	9.65257	+	16.7187i	0.504548	+	0.873903i
$367$	25.6099	−	14.7859i	1.33683	−	0.771817i	0.350491	−	0.936566i	$-0.386015\pi$
$367$	25.6099	−	14.7859i	1.33683	−	0.771817i	0.986335	+	0.164749i	$0.0526815\pi$
$368$	26.6843	+	15.4062i	1.39101	+	0.803102i
$369$	−9.35627			−0.487068
$370$	21.2882	+	12.8899i	1.10672	+	0.670116i
$371$	−1.05857			−0.0549581
$372$	−3.69263	−	2.13194i	−0.191454	−	0.110536i
$373$	−6.59101	+	3.80532i	−0.341270	+	0.197032i	−0.660833	−	0.750533i	$-0.729797\pi$
$373$	−6.59101	+	3.80532i	−0.341270	+	0.197032i	0.319564	+	0.947565i	$0.396464\pi$
$374$	−9.17350	−	15.8890i	−0.474350	−	0.821599i
$375$	−1.63963	+	14.7555i	−0.0846701	+	0.761970i
$376$	−9.26875			−0.477999
$377$	−30.8726	+	17.8243i	−1.59002	+	0.917999i
$378$		−	29.7042i		−	1.52782i
$379$	−0.214164	+	0.370943i	−0.0110009	+	0.0190541i	−0.871473	−	0.490443i	$-0.836835\pi$
$379$	−0.214164	+	0.370943i	−0.0110009	+	0.0190541i	0.860473	+	0.509497i	$0.170168\pi$
$380$	−2.41342	+	11.2446i	−0.123806	+	0.576835i
$381$	3.94185			0.201947
$382$	13.4043	+	7.73896i	0.685822	+	0.395960i
$383$	−12.0268	+	6.94365i	−0.614538	+	0.354804i	−0.774740	−	0.632280i	$-0.782119\pi$
$383$	−12.0268	+	6.94365i	−0.614538	+	0.354804i	0.160201	+	0.987084i	$0.448786\pi$
$384$	−12.0034			−0.612547
$385$	−6.45950	+	7.14547i	−0.329207	+	0.364167i
$386$	0.576135	−	0.997895i	0.0293245	−	0.0507915i
$387$	6.52666	+	3.76817i	0.331769	+	0.191547i
$388$	7.56203	−	4.36594i	0.383904	−	0.221647i
$389$	8.80176	+	15.2451i	0.446267	+	0.772957i	0.998139	−	0.0609716i	$-0.0194199\pi$
$389$	8.80176	+	15.2451i	0.446267	+	0.772957i	−0.551873	+	0.833928i	$0.686087\pi$
$390$	21.0845	−	23.3235i	1.06765	−	1.18103i
$391$	−21.2103	+	36.7373i	−1.07265	+	1.85789i
$392$	1.37170	+	0.791949i	0.0692811	+	0.0399995i
$393$			13.2181i			0.666767i
$394$	−14.7819	−	25.6030i	−0.744702	−	1.28986i
$395$	−14.9281	−	13.4950i	−0.751112	−	0.679005i
$396$	−2.48815			−0.125034
$397$			35.5112i			1.78226i	0.453750	+	0.891129i	$0.350086\pi$
$397$			35.5112i			1.78226i	−0.453750	+	0.891129i	$0.649914\pi$
$398$	29.3485	+	16.9444i	1.47111	+	0.849345i
$399$	14.6230			0.732068
$400$	−2.45381	−	24.2716i	−0.122690	−	1.21358i
$401$	1.15347			0.0576014			0.0288007	−	0.999585i	$-0.490831\pi$
$401$	1.15347			0.0576014			0.0288007	+	0.999585i	$0.490831\pi$
$402$	−17.2580	+	9.96390i	−0.860750	+	0.496954i
$403$	11.9407	−	6.89396i	0.594808	−	0.343413i
$404$	0.371805	+	0.643986i	0.0184980	+	0.0320395i
$405$	6.23773	+	5.63890i	0.309955	+	0.280199i
$406$	−32.5236			−1.61412
$407$	−8.58138	−	2.96842i	−0.425363	−	0.147139i
$408$		−	10.6447i		−	0.526992i
$409$	1.77430	−	3.07318i	0.0877335	−	0.151959i	−0.818819	−	0.574051i	$-0.805371\pi$
$409$	1.77430	−	3.07318i	0.0877335	−	0.151959i	0.906553	+	0.422093i	$0.138704\pi$
$410$	−9.50662	−	29.4569i	−0.469499	−	1.45477i
$411$	−2.69411	−	4.66633i	−0.132891	−	0.230173i
$412$	−9.60726	+	5.54675i	−0.473316	+	0.273269i
$413$			25.6194i			1.26065i
$414$	7.14495	+	12.3754i	0.351155	+	0.608218i
$415$	−18.0103	−	3.86553i	−0.884089	−	0.189751i
$416$	−18.9254	+	32.7797i	−0.927894	+	1.60716i
$417$			16.4799i			0.807026i
$418$		−	10.4232i		−	0.509815i
$419$	7.78517	−	13.4843i	0.380330	−	0.658751i	−0.610779	−	0.791801i	$-0.709144\pi$
$419$	7.78517	−	13.4843i	0.380330	−	0.658751i	0.991109	+	0.133050i	$0.0424770\pi$
$420$	10.9900	−	3.54680i	0.536257	−	0.173066i
$421$	−18.5709			−0.905092			−0.452546	−	0.891741i	$-0.649484\pi$
$421$	−18.5709			−0.905092			−0.452546	+	0.891741i	$0.649484\pi$
$422$	−34.5838	−	19.9669i	−1.68351	−	0.971976i
$423$	−8.31826	−	4.80255i	−0.404448	−	0.233508i
$424$	−0.218887	+	0.379124i	−0.0106301	+	0.0184119i
$425$	33.4157	−	3.37826i	1.62090	−	0.163870i
$426$	3.50185	+	6.06538i	0.169665	+	0.293869i
$427$	−19.8570	−	11.4644i	−0.960946	−	0.554802i
$428$	16.7199	+	9.65324i	0.808187	+	0.466607i
$429$	−5.73593	+	9.93493i	−0.276933	+	0.479663i
$430$	−5.23201	+	24.3770i	−0.252310	+	1.17556i
$431$	−10.5142	−	18.2111i	−0.506452	−	0.877200i	−0.999972	−	0.00746576i	$-0.997624\pi$
$431$	−10.5142	−	18.2111i	−0.506452	−	0.877200i	0.493521	−	0.869734i	$-0.335710\pi$
$432$	−23.7716	−	13.7245i	−1.14371	−	0.660321i
$433$		−	28.6971i		−	1.37909i	−0.724241	−	0.689547i	$-0.757810\pi$
$433$		−	28.6971i		−	1.37909i	0.724241	−	0.689547i	$-0.242190\pi$
$434$	12.5793			0.603824
$435$	12.2655	−	13.5680i	0.588085	−	0.650537i
$436$	14.2550			0.682690
$437$	−20.8710	+	12.0499i	−0.998396	+	0.576424i
$438$		−	24.7765i		−	1.18387i
$439$	7.49973	+	12.9899i	0.357942	+	0.619974i	0.987617	−	0.156885i	$-0.0501451\pi$
$439$	7.49973	+	12.9899i	0.357942	+	0.619974i	−0.629675	+	0.776859i	$0.716812\pi$
$440$	1.22346	+	3.79098i	0.0583263	+	0.180728i
$441$	0.820688	+	1.42147i	0.0390804	+	0.0676892i
$442$	−61.5982	−	35.5637i	−2.92993	−	1.69159i
$443$			2.90134i			0.137847i	0.997622	+	0.0689235i	$0.0219564\pi$
$443$			2.90134i			0.137847i	−0.997622	+	0.0689235i	$0.978044\pi$
$444$	7.13036	+	8.22607i	0.338392	+	0.390392i
$445$	−2.20935	+	10.2938i	−0.104733	+	0.487973i
$446$	3.07282	−	5.32229i	0.145502	−	0.252018i
$447$	4.99806	−	2.88563i	0.236400	−	0.136486i
$448$	−5.51986	+	3.18690i	−0.260789	+	0.150567i
$449$	20.3693	+	35.2807i	0.961286	+	1.66500i	0.719277	+	0.694723i	$0.244473\pi$
$449$	20.3693	+	35.2807i	0.961286	+	1.66500i	0.242009	+	0.970274i	$0.422194\pi$
$450$	4.64269	−	10.3174i	0.218859	−	0.486367i
$451$	5.64688	+	9.78068i	0.265901	+	0.460554i
$452$		−	0.864325i		−	0.0406544i
$453$	−4.59387	−	2.65227i	−0.215839	−	0.124614i
$454$	12.3644			0.580291
$455$	−7.83638	+	36.5113i	−0.367375	+	1.71168i
$456$	3.02371	−	5.23722i	0.141598	−	0.245255i
$457$	−18.3118	+	10.5723i	−0.856591	+	0.494553i	−0.862869	−	0.505427i	$-0.831335\pi$
$457$	−18.3118	+	10.5723i	−0.856591	+	0.494553i	0.00627810	+	0.999980i	$0.498002\pi$
$458$			6.37552i			0.297909i
$459$	18.8951	−	32.7273i	0.881948	−	1.52758i
$460$	−12.7630	+	14.1184i	−0.595077	+	0.658272i
$461$	−13.3588	+	23.1381i	−0.622180	+	1.07765i	0.366899	+	0.930261i	$0.380420\pi$
$461$	−13.3588	+	23.1381i	−0.622180	+	1.07765i	−0.989079	+	0.147387i	$0.952914\pi$
$462$	−9.06402	+	5.23311i	−0.421696	+	0.243466i
$463$	−10.1355	+	5.85173i	−0.471036	+	0.271953i	−0.716673	−	0.697409i	$-0.754336\pi$
$463$	−10.1355	+	5.85173i	−0.471036	+	0.271953i	0.245637	+	0.969362i	$0.421003\pi$
$464$	−15.0272	+	26.0278i	−0.697620	+	1.20831i
$465$	−4.74396	+	5.24775i	−0.219996	+	0.243358i
$466$	−4.36852	+	7.56650i	−0.202368	+	0.350511i
$467$		−	3.26099i		−	0.150901i	−0.997150	−	0.0754504i	$-0.975961\pi$
$467$		−	3.26099i		−	0.150901i	0.997150	−	0.0754504i	$-0.0240394\pi$
$468$	−8.35370	+	4.82301i	−0.386150	+	0.222944i
$469$	11.8342	−	20.4974i	0.546452	−	0.946483i
$470$	6.66822	−	31.0686i	0.307582	−	1.43309i
$471$	−12.4878			−0.575406
$472$	9.17555	+	5.29751i	0.422339	+	0.243838i
$473$		−	9.09696i		−	0.418279i
$474$	−10.9328	−	18.9362i	−0.502161	−	0.869769i
$475$	17.4002	+	7.82986i	0.798375	+	0.359258i
$476$	−13.0624	−	22.6247i	−0.598714	−	1.03700i
$477$	−0.392882	+	0.226830i	−0.0179888	+	0.0103859i
$478$	1.13155	−	0.653302i	0.0517560	−	0.0298813i
$479$	13.6313	−	23.6102i	0.622832	−	1.07878i	−0.366124	−	0.930566i	$-0.619315\pi$
$479$	13.6313	−	23.6102i	0.622832	−	1.07878i	0.988956	−	0.148210i	$-0.0473512\pi$
$480$	4.07531	−	18.9877i	0.186012	−	0.866666i
$481$	−34.5651	+	6.66794i	−1.57603	+	0.304032i
$482$			15.6027i			0.710685i
$483$	20.9572	+	12.0996i	0.953585	+	0.550552i
$484$	−5.91101	−	10.2382i	−0.268682	−	0.465371i
$485$	−4.44942	−	13.7868i	−0.202038	−	0.626027i
$486$	−10.8721	−	18.8311i	−0.493170	−	0.854195i
$487$		−	16.3720i		−	0.741887i	−0.928655	−	0.370943i	$-0.879034\pi$
$487$		−	16.3720i		−	0.741887i	0.928655	−	0.370943i	$-0.120966\pi$
$488$	−8.21192	+	4.74116i	−0.371736	+	0.214622i
$489$	0.675138			0.0305308
$490$	−3.64143	+	4.02814i	−0.164503	+	0.181973i
$491$	26.0754			1.17677			0.588383	−	0.808582i	$-0.299765\pi$
$491$	26.0754			1.17677			0.588383	+	0.808582i	$0.299765\pi$
$492$		−	13.5399i		−	0.610428i
$493$	−35.8336	−	20.6885i	−1.61386	−	0.931765i
$494$	−20.2043	−	34.9948i	−0.909033	−	1.57449i
$495$	−0.866276	+	4.03615i	−0.0389362	+	0.181412i
$496$	5.81211	−	10.0669i	0.260971	−	0.452016i
$497$	−7.20389	−	4.15917i	−0.323139	−	0.186564i
$498$	−17.3335	−	10.0075i	−0.776733	−	0.448447i
$499$	16.7452	+	29.0035i	0.749616	+	1.29837i	0.948007	+	0.318251i	$0.103095\pi$
$499$	16.7452	+	29.0035i	0.749616	+	1.29837i	−0.198390	+	0.980123i	$0.563571\pi$
$500$	14.9763	+	1.66416i	0.669760	+	0.0744236i
$501$	−10.5719	+	18.3111i	−0.472319	+	0.818081i
$502$	42.3306	+	24.4396i	1.88931	+	1.09079i
$503$	0.464139	+	0.267971i	0.0206949	+	0.0119482i	0.510312	−	0.859989i	$-0.329530\pi$
$503$	0.464139	+	0.267971i	0.0206949	+	0.0119482i	−0.489617	+	0.871938i	$0.662863\pi$
$504$	4.25888			0.189706
$505$	1.17409	−	0.378914i	0.0522464	−	0.0168615i
$506$	8.62452	−	14.9381i	0.383407	−	0.664080i
$507$			27.2114i			1.20850i
$508$		−	4.00083i		−	0.177508i
$509$	−8.53147	+	14.7769i	−0.378151	+	0.654976i	−0.990793	−	0.135384i	$-0.956773\pi$
$509$	−8.53147	+	14.7769i	−0.378151	+	0.654976i	0.612642	+	0.790360i	$0.290107\pi$
$510$	35.6808	+	7.65814i	1.57997	+	0.339108i
$511$	14.7136	+	25.4848i	0.650893	+	1.12738i
$512$			20.2657i			0.895626i
$513$	18.5928	−	10.7346i	0.820894	−	0.473943i
$514$	22.5937	+	39.1334i	0.996565	+	1.72610i
$515$	5.65281	+	17.5156i	0.249092	+	0.771830i
$516$	−5.45311	+	9.44507i	−0.240060	+	0.415796i
$517$			11.5941i			0.509909i
$518$	−30.3519	−	10.4992i	−1.33359	−	0.461307i
$519$	11.3128			0.496578
$520$	11.4561	+	10.3563i	0.502382	+	0.454153i
$521$	−5.87471	−	10.1753i	−0.257376	−	0.445788i	0.708162	−	0.706049i	$-0.249524\pi$
$521$	−5.87471	−	10.1753i	−0.257376	−	0.445788i	−0.965538	+	0.260262i	$0.916191\pi$
$522$	−12.0710	+	6.96918i	−0.528333	+	0.305033i
$523$	25.1834	−	14.5396i	1.10119	−	0.635774i	0.164658	−	0.986351i	$-0.447348\pi$
$523$	25.1834	−	14.5396i	1.10119	−	0.635774i	0.936534	+	0.350577i	$0.114014\pi$
$524$	13.4159			0.586077
$525$	−1.92716	−	19.0623i	−0.0841082	−	0.831947i
$526$	45.0774			1.96547
$527$	13.8595	+	8.00177i	0.603728	+	0.348563i
$528$			9.67161i			0.420903i
$529$	−16.8820			−0.734001
$530$	−1.11334	−	1.00646i	−0.0483603	−	0.0437177i
$531$	5.48975	+	9.50852i	0.238235	+	0.412635i
$532$		−	14.8419i		−	0.643476i
$533$	37.9177	+	21.8918i	1.64240	+	0.948238i
$534$	−5.71981	+	9.90700i	−0.247520	+	0.428718i
$535$	21.4802	−	23.7613i	0.928672	−	1.02729i
$536$	−4.89408	−	8.47679i	−0.211392	−	0.366142i
$537$	2.30852	−	1.33283i	0.0996200	−	0.0575157i
$538$	40.6474	+	23.4678i	1.75243	+	1.01177i
$539$	0.990635	−	1.71583i	0.0426697	−	0.0739061i
$540$	11.3698	−	12.5773i	0.489280	−	0.541240i
$541$	21.0758			0.906121			0.453060	−	0.891480i	$-0.350332\pi$
$541$	21.0758			0.906121			0.453060	+	0.891480i	$0.350332\pi$
$542$	13.3986	−	7.73567i	0.575518	−	0.332275i
$543$	15.7192	+	9.07549i	0.674576	+	0.389467i
$544$	−43.9331			−1.88362
$545$	4.96303	−	23.1238i	0.212593	−	0.990513i
$546$	−20.2877	+	35.1393i	−0.868233	+	1.50382i
$547$		−	21.8448i		−	0.934015i	−0.884253	−	0.467007i	$-0.845332\pi$
$547$		−	21.8448i		−	0.934015i	0.884253	−	0.467007i	$-0.154668\pi$
$548$	−4.73615	+	2.73442i	−0.202318	+	0.116809i
$549$	−9.82642			−0.419381
$550$	−13.5875	+	1.37366i	−0.579371	+	0.0585733i
$551$	−11.7535	−	20.3576i	−0.500714	−	0.867262i
$552$	8.66692	−	5.00385i	0.368889	−	0.212978i
$553$	22.4907	+	12.9850i	0.956400	+	0.552178i
$554$	51.1870			2.17473
$555$	15.8265	−	8.70254i	0.671796	−	0.369402i
$556$	16.7265			0.709363
$557$	−21.2624	−	12.2759i	−0.900917	−	0.520145i	−0.0234192	−	0.999726i	$-0.507455\pi$
$557$	−21.2624	−	12.2759i	−0.900917	−	0.520145i	−0.877497	+	0.479581i	$0.840789\pi$
$558$	4.66873	−	2.69549i	0.197643	−	0.114109i
$559$	−17.6335	−	30.5421i	−0.745818	−	1.29179i
$560$	9.66931	+	29.9610i	0.408603	+	1.26608i
$561$	−13.3153			−0.562173
$562$	0.0817222	−	0.0471824i	0.00344724	−	0.00199027i
$563$			4.18160i			0.176233i	0.996110	+	0.0881166i	$0.0280848\pi$
$563$			4.18160i			0.176233i	−0.996110	+	0.0881166i	$0.971915\pi$
$564$	6.95002	−	12.0378i	0.292649	−	0.506882i
$565$	−1.40207	−	0.300924i	−0.0589854	−	0.0126600i
$566$	22.0264			0.925839
$567$	−9.39778	−	5.42581i	−0.394670	−	0.227863i
$568$	−2.97920	+	1.72004i	−0.125004	+	0.0721713i
$569$	17.1123			0.717385			0.358692	−	0.933456i	$-0.383223\pi$
$569$	17.1123			0.717385			0.358692	+	0.933456i	$0.383223\pi$
$570$	15.3797	+	13.9032i	0.644183	+	0.582341i
$571$	11.1387	−	19.2928i	0.466141	−	0.807380i	−0.533111	−	0.846045i	$-0.678977\pi$
$571$	11.1387	−	19.2928i	0.466141	−	0.807380i	0.999252	+	0.0386650i	$0.0123105\pi$
$572$	10.0836	+	5.82176i	0.421616	+	0.243420i
$573$	9.72813	−	5.61654i	0.406398	−	0.234634i
$574$	19.9727	+	34.5938i	0.833645	+	1.44392i
$575$	18.4586	+	25.6190i	0.769775	+	1.06839i
$576$	−1.36578	+	2.36560i	−0.0569075	+	0.0985667i
$577$	11.7727	+	6.79700i	0.490106	+	0.282963i	0.724618	−	0.689150i	$-0.242016\pi$
$577$	11.7727	+	6.79700i	0.490106	+	0.282963i	−0.234513	+	0.972113i	$0.575349\pi$
$578$		−	51.4524i		−	2.14014i
$579$	−0.418129	−	0.724221i	−0.0173768	−	0.0300976i
$580$	−13.7710	−	12.4490i	−0.571812	−	0.516917i
$581$	23.7720			0.986227
$582$		−	15.7411i		−	0.652489i
$583$	0.474239	+	0.273802i	0.0196410	+	0.0113397i
$584$	12.1698			0.503588
$585$	4.91523	+	15.2302i	0.203220	+	0.629690i
$586$	−39.1607			−1.61771
$587$	−27.1337	+	15.6656i	−1.11993	+	0.646590i	−0.941382	−	0.337342i	$-0.890472\pi$
$587$	−27.1337	+	15.6656i	−1.11993	+	0.646590i	−0.178544	+	0.983932i	$0.557139\pi$
$588$	−2.05709	+	1.18766i	−0.0848329	+	0.0489783i
$589$	4.54592	+	7.87376i	0.187311	+	0.324433i
$590$	−24.3583	+	26.9450i	−1.00281	+	1.10931i
$591$	−21.4559			−0.882577
$592$	−22.4260	+	19.4389i	−0.921702	+	0.798932i
$593$			21.6238i			0.887984i	0.896031	+	0.443992i	$0.146438\pi$
$593$			21.6238i			0.887984i	−0.896031	+	0.443992i	$0.853562\pi$
$594$	−7.68311	+	13.3075i	−0.315242	+	0.546015i
$595$	−41.2486	+	13.3121i	−1.69103	+	0.545745i
$596$	−2.92881	−	5.07285i	−0.119969	−	0.207792i
$597$	21.2996	−	12.2974i	0.871736	−	0.503297i
$598$		−	66.8709i		−	2.73456i
$599$	−20.8325	−	36.0829i	−0.851193	−	1.47431i	−0.880133	−	0.474728i	$-0.842547\pi$
$599$	−20.8325	−	36.0829i	−0.851193	−	1.47431i	0.0289402	−	0.999581i	$-0.490787\pi$
$600$	−7.22562	−	3.25144i	−0.294985	−	0.132739i
$601$	19.4254	−	33.6457i	0.792377	−	1.37244i	−0.132114	−	0.991234i	$-0.542177\pi$
$601$	19.4254	−	33.6457i	0.792377	−	1.37244i	0.924491	−	0.381203i	$-0.124490\pi$
$602$		−	32.1755i		−	1.31137i
$603$		−	10.1434i		−	0.413069i
$604$	−2.69196	+	4.66260i	−0.109534	+	0.189719i
$605$	−18.6658	+	6.02402i	−0.758875	+	0.244911i
$606$	1.34052			0.0544548
$607$	−4.25176	−	2.45475i	−0.172573	−	0.0996353i	0.411225	−	0.911534i	$-0.365101\pi$
$607$	−4.25176	−	2.45475i	−0.172573	−	0.0996353i	−0.583799	+	0.811898i	$0.698434\pi$
$608$	−21.6151	−	12.4795i	−0.876610	−	0.506111i
$609$	−11.8020	+	20.4416i	−0.478241	+	0.828337i
$610$	−9.98432	−	30.9371i	−0.404253	−	1.25261i
$611$	22.4740	+	38.9261i	0.909201	+	1.57478i
$612$	−9.69608	−	5.59803i	−0.391941	−	0.226287i
$613$	−5.95511	−	3.43818i	−0.240525	−	0.138867i	0.374893	−	0.927068i	$-0.377679\pi$
$613$	−5.95511	−	3.43818i	−0.240525	−	0.138867i	−0.615418	+	0.788201i	$0.711013\pi$
$614$	−21.1532	+	36.6384i	−0.853674	+	1.47861i
$615$	−21.9639	−	4.71408i	−0.885668	−	0.190090i
$616$	−2.57040	−	4.45207i	−0.103565	−	0.179379i
$617$	39.3144	+	22.6982i	1.58274	+	0.913795i	0.994457	+	0.105140i	$0.0335291\pi$
$617$	39.3144	+	22.6982i	1.58274	+	0.913795i	0.588283	+	0.808655i	$0.299804\pi$
$618$			19.9984i			0.804455i
$619$	−9.07960			−0.364940			−0.182470	−	0.983211i	$-0.558409\pi$
$619$	−9.07960			−0.364940			−0.182470	+	0.983211i	$0.558409\pi$
$620$	5.32627	+	4.81494i	0.213908	+	0.193373i
$621$	35.5287			1.42572
$622$	−10.3587	+	5.98062i	−0.415348	+	0.239801i
$623$		−	13.5869i		−	0.544348i
$624$	18.7474	+	32.4715i	0.750497	+	1.29990i
$625$	7.91368	−	23.7144i	0.316547	−	0.948577i
$626$	−7.67200	−	13.2883i	−0.306635	−	0.531107i
$627$	−6.55115	−	3.78231i	−0.261628	−	0.151051i
$628$			12.6746i			0.505772i
$629$	−26.7623	−	30.8748i	−1.06708	−	1.23106i
$630$	−3.06397	+	14.2757i	−0.122072	+	0.568756i
$631$	12.8980	−	22.3399i	0.513460	−	0.889339i	−0.486418	−	0.873726i	$-0.661697\pi$
$631$	12.8980	−	22.3399i	0.513460	−	0.889339i	0.999878	−	0.0156127i	$-0.00496988\pi$
$632$	9.30110	−	5.36999i	0.369978	−	0.213607i
$633$	−25.0991	+	14.4910i	−0.997600	+	0.575965i
$634$	−3.43429	−	5.94836i	−0.136393	−	0.236240i
$635$	−6.48995	−	1.39293i	−0.257546	−	0.0552768i
$636$	−0.328258	−	0.568560i	−0.0130163	−	0.0225449i
$637$		−	7.68097i		−	0.304331i
$638$	14.5706	+	8.41236i	0.576857	+	0.333048i
$639$	−3.56492			−0.141026
$640$	19.7627	+	4.24166i	0.781190	+	0.167666i
$641$	−5.34634	+	9.26013i	−0.211168	+	0.365753i	−0.952080	−	0.305848i	$-0.901060\pi$
$641$	−5.34634	+	9.26013i	−0.211168	+	0.365753i	0.740913	+	0.671601i	$0.234393\pi$
$642$	30.1412	−	17.4020i	1.18958	−	0.686804i
$643$			32.3539i			1.27591i	0.770072	+	0.637956i	$0.220220\pi$
$643$			32.3539i			1.27591i	−0.770072	+	0.637956i	$0.779780\pi$
$644$	12.2807	−	21.2708i	0.483927	−	0.838186i
$645$	13.4228	+	12.1342i	0.528522	+	0.477783i
$646$	23.4509	−	40.6182i	0.922665	−	1.59810i
$647$	−22.2647	+	12.8545i	−0.875317	+	0.505364i	−0.869111	−	0.494616i	$-0.835309\pi$
$647$	−22.2647	+	12.8545i	−0.875317	+	0.505364i	−0.00620547	+	0.999981i	$0.501975\pi$
$648$	−3.88649	+	2.24387i	−0.152676	+	0.0881474i
$649$	6.62656	−	11.4775i	0.260115	−	0.450533i
$650$	−42.9558	+	30.9498i	−1.68487	+	1.21395i
$651$	4.56469	−	7.90627i	0.178904	−	0.309871i
$652$		−	0.685240i		−	0.0268361i
$653$	−1.92524	+	1.11154i	−0.0753405	+	0.0434979i	−0.537197	−	0.843457i	$-0.680517\pi$
$653$	−1.92524	+	1.11154i	−0.0753405	+	0.0434979i	0.461856	+	0.886955i	$0.347184\pi$
$654$	12.8488	−	22.2548i	0.502429	−	0.870233i
$655$	4.67090	−	21.7627i	0.182507	−	0.850338i
$656$	36.9127			1.44120
$657$	10.9218	+	6.30569i	0.426099	+	0.246009i
$658$			41.0078i			1.59865i
$659$	−7.59218	−	13.1500i	−0.295749	−	0.512253i	0.679410	−	0.733759i	$-0.262236\pi$
$659$	−7.59218	−	13.1500i	−0.295749	−	0.512253i	−0.975159	+	0.221506i	$0.928903\pi$
$660$	−5.84093	−	1.25363i	−0.227358	−	0.0487976i
$661$	2.37464	+	4.11300i	0.0923630	+	0.159977i	0.908505	−	0.417874i	$-0.137225\pi$
$661$	2.37464	+	4.11300i	0.0923630	+	0.159977i	−0.816142	+	0.577851i	$0.803891\pi$
$662$	−5.96401	+	3.44332i	−0.231798	+	0.133829i
$663$	−44.7048	+	25.8103i	−1.73619	+	1.00239i
$664$	4.91549	−	8.51388i	0.190758	−	0.330403i
$665$	−24.0758	−	5.16736i	−0.933618	−	0.200381i
$666$	−13.5147	+	2.60712i	−0.523685	+	0.101024i
$667$		−	38.9009i		−	1.50625i
$668$	18.5851	+	10.7301i	0.719080	+	0.415161i
$669$	−2.23010	−	3.86264i	−0.0862205	−	0.149338i
$670$	31.9349	−	10.3064i	1.23375	−	0.398169i
$671$	5.93063	+	10.2722i	0.228949	+	0.396552i
$672$			25.0621i			0.966791i
$673$	−24.1769	+	13.9585i	−0.931952	+	0.538063i	−0.887428	−	0.460946i	$-0.847510\pi$
$673$	−24.1769	+	13.9585i	−0.931952	+	0.538063i	−0.0445234	+	0.999008i	$0.514177\pi$
$674$	−55.6870			−2.14498
$675$	−16.4437	−	22.8225i	−0.632919	−	0.878440i
$676$	27.6186			1.06225
$677$		−	32.6132i		−	1.25343i	−0.779249	−	0.626714i	$-0.784399\pi$
$677$		−	32.6132i		−	1.25343i	0.779249	−	0.626714i	$-0.215601\pi$
$678$	−1.34938	−	0.779066i	−0.0518227	−	0.0299199i
$679$	9.34790	+	16.1910i	0.358740	+	0.621355i
$680$	−3.76153	+	17.5257i	−0.144248	+	0.672082i
$681$	4.48673	−	7.77124i	0.171932	−	0.297795i
$682$	−5.63553	−	3.25367i	−0.215795	−	0.124590i
$683$	−21.3812	−	12.3445i	−0.818130	−	0.472348i	0.0316412	−	0.999499i	$-0.489927\pi$
$683$	−21.3812	−	12.3445i	−0.818130	−	0.472348i	−0.849771	+	0.527152i	$0.823260\pi$
$684$	−3.18032	−	5.50848i	−0.121603	−	0.210622i
$685$	2.78670	+	8.63478i	0.106474	+	0.329918i
$686$	−14.9759	+	25.9390i	−0.571783	+	0.990357i
$687$	4.00712	+	2.31351i	0.152881	+	0.0882660i
$688$	−25.7492	−	14.8663i	−0.981680	−	0.566773i
$689$	2.12295			0.0808779
$690$	10.5375	+	32.6512i	0.401157	+	1.24301i
$691$	2.79475	−	4.84065i	0.106317	−	0.184147i	−0.807958	−	0.589240i	$-0.799427\pi$
$691$	2.79475	−	4.84065i	0.106317	−	0.184147i	0.914276	+	0.405093i	$0.132761\pi$
$692$		−	11.4821i		−	0.436484i
$693$		−	5.32736i		−	0.202370i
$694$	−24.1099	+	41.7595i	−0.915199	+	1.58517i
$695$	5.82352	−	27.1330i	0.220899	−	1.02921i
$696$	4.88076	+	8.45372i	0.185005	+	0.320437i
$697$			50.8192i			1.92492i
$698$	9.94749	−	5.74319i	0.376518	−	0.217383i
$699$	3.17045	+	5.49138i	0.119917	+	0.207703i
$700$	−19.3475	+	1.95600i	−0.731268	+	0.0739298i
$701$	−4.02911	+	6.97863i	−0.152178	+	0.263579i	−0.932028	−	0.362387i	$-0.881962\pi$
$701$	−4.02911	+	6.97863i	−0.152178	+	0.263579i	0.779850	+	0.625966i	$0.215295\pi$
$702$			59.5717i			2.24839i
$703$	−4.39687	−	22.7924i	−0.165831	−	0.859633i
$704$	3.29721			0.124268
$705$	−17.1074	−	15.4651i	−0.644302	−	0.582449i
$706$	5.09756	+	8.82923i	0.191849	+	0.332292i
$707$	−1.37884	+	0.796071i	−0.0518565	+	0.0299393i
$708$	−13.7603	+	7.94450i	−0.517143	+	0.298573i
$709$	−34.5858			−1.29890			−0.649449	−	0.760405i	$-0.725000\pi$
$709$	−34.5858			−1.29890			−0.649449	+	0.760405i	$0.725000\pi$
$710$	−3.62221	−	11.2236i	−0.135939	−	0.421216i
$711$	11.1297			0.417398
$712$	−4.86613	−	2.80946i	−0.182366	−	0.105289i
$713$			15.0458i			0.563471i
$714$	−47.0955			−1.76251
$715$	12.9545	−	14.3302i	0.484471	−	0.535919i
$716$	−1.35277	−	2.34306i	−0.0505553	−	0.0875644i
$717$		−	0.948266i		−	0.0354136i
$718$	−24.4813	−	14.1343i	−0.913632	−	0.527486i
$719$	12.0291	−	20.8350i	0.448610	−	0.777015i	−0.549686	−	0.835371i	$-0.685253\pi$
$719$	12.0291	−	20.8350i	0.448610	−	0.777015i	0.998296	+	0.0583564i	$0.0185860\pi$
$720$	10.0088	+	9.04793i	0.373005	+	0.337197i
$721$	−11.8761	−	20.5701i	−0.442291	−	0.766070i
$722$	−7.03081	+	4.05924i	−0.261660	+	0.151069i
$723$	9.80657	+	5.66183i	0.364710	+	0.210566i
$724$	9.21129	−	15.9544i	0.342335	−	0.592941i
$725$	−24.9888	+	18.0045i	−0.928059	+	0.668670i
$726$	−21.3117			−0.790952
$727$	14.9873	−	8.65294i	0.555849	−	0.320920i	−0.195628	−	0.980678i	$-0.562675\pi$
$727$	14.9873	−	8.65294i	0.555849	−	0.320920i	0.751478	+	0.659758i	$0.229341\pi$
$728$	−17.2598	−	9.96492i	−0.639689	−	0.369325i
$729$	−27.0623			−1.00231
$730$	−8.75530	+	40.7927i	−0.324048	+	1.50981i
$731$	20.4671	−	35.4500i	0.757002	−	1.31117i
$732$		−	14.2203i		−	0.525598i
$733$	21.6240	−	12.4846i	0.798702	−	0.461131i	−0.0443152	−	0.999018i	$-0.514111\pi$
$733$	21.6240	−	12.4846i	0.798702	−	0.461131i	0.843017	+	0.537887i	$0.180777\pi$
$734$	−54.1072			−1.99713
$735$	1.21037	+	3.75041i	0.0446451	+	0.138336i
$736$	−20.6520	−	35.7703i	−0.761242	−	1.31851i
$737$	−10.6035	+	6.12192i	−0.390584	+	0.225504i
$738$	14.8256	+	8.55954i	0.545736	+	0.315081i
$739$	−3.54421			−0.130376			−0.0651880	−	0.997873i	$-0.520765\pi$
$739$	−3.54421			−0.130376			−0.0651880	+	0.997873i	$0.520765\pi$
$740$	−8.83276	−	16.0633i	−0.324699	−	0.590498i
$741$	−29.3264			−1.07733
$742$	1.67736	+	0.968424i	0.0615778	+	0.0355520i
$743$	−13.8296	+	7.98451i	−0.507358	+	0.292923i	−0.731747	−	0.681576i	$-0.761295\pi$
$743$	−13.8296	+	7.98451i	−0.507358	+	0.292923i	0.224389	+	0.974500i	$0.427961\pi$
$744$	−1.88774	−	3.26967i	−0.0692081	−	0.119872i
$745$	−9.24864	+	2.98481i	−0.338844	+	0.109355i
$746$	13.9251			0.509835
$747$	8.82284	−	5.09387i	0.322811	−	0.186375i
$748$			13.5145i			0.494141i
$749$	−20.6685	+	35.7989i	−0.755211	+	1.30806i
$750$	16.0971	−	21.8809i	0.587782	−	0.798978i
$751$	−52.5468			−1.91746			−0.958731	−	0.284316i	$-0.908233\pi$
$751$	−52.5468			−1.91746			−0.958731	+	0.284316i	$0.908233\pi$
$752$	32.8175	+	18.9472i	1.19673	+	0.690933i
$753$	30.7214	−	17.7370i	1.11955	−	0.646372i
$754$	65.2259			2.37539
$755$	6.62622	+	5.99010i	0.241153	+	0.218002i
$756$	−10.9402	+	18.9490i	−0.397891	+	0.689167i
$757$	−17.6368	−	10.1826i	−0.641019	−	0.370093i	0.143988	−	0.989579i	$-0.454007\pi$
$757$	−17.6368	−	10.1826i	−0.641019	−	0.370093i	−0.785007	+	0.619487i	$0.787341\pi$
$758$	0.678711	−	0.391854i	0.0246519	−	0.0142328i
$759$	−6.25923	−	10.8413i	−0.227196	−	0.393515i
$760$	−6.82899	+	7.55420i	−0.247714	+	0.274020i
$761$	−16.2834	+	28.2037i	−0.590272	+	1.02238i	0.403923	+	0.914793i	$0.367646\pi$
$761$	−16.2834	+	28.2037i	−0.590272	+	1.02238i	−0.994195	+	0.107589i	$0.965687\pi$
$762$	−6.24608	−	3.60618i	−0.226272	−	0.130638i
$763$			30.5213i			1.10495i
$764$	−5.70058	−	9.87369i	−0.206240	−	0.357218i
$765$	−12.4567	+	13.7795i	−0.450372	+	0.498199i
$766$	25.4094			0.918081
$767$		−	51.3796i		−	1.85521i
$768$	24.1002	+	13.9143i	0.869641	+	0.502087i
$769$	27.4265			0.989025			0.494512	−	0.869171i	$-0.335347\pi$
$769$	27.4265			0.989025			0.494512	+	0.869171i	$0.335347\pi$
$770$	16.7725	−	5.41297i	0.604437	−	0.195070i
$771$	32.7947			1.18107
$772$	−0.735057	+	0.424385i	−0.0264553	+	0.0152740i
$773$	32.1441	−	18.5584i	1.15614	−	0.667500i	0.205767	−	0.978601i	$-0.434031\pi$
$773$	32.1441	−	18.5584i	1.15614	−	0.667500i	0.950377	+	0.311101i	$0.100698\pi$
$774$	−6.89458	−	11.9418i	−0.247821	−	0.429238i
$775$	9.66497	−	6.96365i	0.347176	−	0.250142i
$776$	7.73172			0.277553
$777$	−17.6128	+	15.2668i	−0.631856	+	0.547694i
$778$		−	32.2090i		−	1.15475i
$779$	−14.4356	+	25.0031i	−0.517208	+	0.895830i
$780$	−22.0404	+	7.11308i	−0.789172	+	0.254689i
$781$	2.15157	+	3.72663i	0.0769892	+	0.133349i
$782$	67.2179	−	38.8083i	2.40371	−	1.38778i
$783$			34.6547i			1.23846i
$784$	−3.23781	−	5.60805i	−0.115636	−	0.200287i
$785$	20.5602	+	4.41281i	0.733824	+	0.157500i
$786$	12.0925	−	20.9449i	0.431327	−	0.747080i
$787$			52.3565i			1.86631i	0.359478	+	0.933154i	$0.382955\pi$
$787$			52.3565i			1.86631i	−0.359478	+	0.933154i	$0.617045\pi$
$788$			21.7769i			0.775771i
$789$	16.3574	−	28.3319i	0.582340	−	1.00864i
$790$	11.3086	+	35.0404i	0.402341	+	1.24668i
$791$	1.85060			0.0657999
$792$	−1.90799	−	1.10158i	−0.0677973	−	0.0391428i
$793$	39.8230	+	22.9918i	1.41416	+	0.816464i
$794$	32.4873	−	56.2696i	1.15293	−	1.99693i
$795$	−1.03658	+	0.334534i	−0.0367636	+	0.0118647i
$796$	−12.4814	−	21.6184i	−0.442390	−	0.766242i
$797$	−45.4022	−	26.2130i	−1.60823	−	0.928511i	−0.989767	−	0.142696i	$-0.954423\pi$
$797$	−45.4022	−	26.2130i	−1.60823	−	0.928511i	−0.618462	−	0.785815i	$-0.712244\pi$
$798$	−23.1711	−	13.3778i	−0.820247	−	0.473570i
$799$	−26.0854	+	45.1812i	−0.922835	+	1.59840i
$800$	−13.4194	+	29.8217i	−0.474447	+	1.05436i
$801$	−2.91141	−	5.04272i	−0.102870	−	0.178176i
$802$	−1.82774	−	1.05524i	−0.0645396	−	0.0372620i
$803$		−	15.2229i		−	0.537206i
$804$	14.6790			0.517688
$805$	−30.2288	−	27.3268i	−1.06542	−	0.963143i
$806$	−25.2276			−0.888605
$807$	29.4998	−	17.0317i	1.03844	−	0.599545i
$808$			0.658437i			0.0231637i
$809$	10.5457	+	18.2657i	0.370767	+	0.642187i	0.989684	−	0.143269i	$-0.0457615\pi$
$809$	10.5457	+	18.2657i	0.370767	+	0.642187i	−0.618917	+	0.785457i	$0.712428\pi$
$810$	−4.72532	−	14.6417i	−0.166031	−	0.514458i
$811$	7.21021	+	12.4884i	0.253185	+	0.438529i	0.964401	−	0.264445i	$-0.0851887\pi$
$811$	7.21021	+	12.4884i	0.253185	+	0.438529i	−0.711216	+	0.702973i	$0.751855\pi$
$812$	20.7475	+	11.9786i	0.728095	+	0.420366i
$813$		−	11.2283i		−	0.393794i
$814$	10.8821	+	12.5543i	0.381416	+	0.440027i
$815$	−1.11156	−	0.238574i	−0.0389364	−	0.00835688i
$816$	−21.7600	+	37.6894i	−0.761751	+	1.31939i
$817$	20.1397	−	11.6276i	0.704598	−	0.406800i
$818$	−5.62296	+	3.24642i	−0.196602	+	0.113508i
$819$	−10.3265	−	17.8861i	−0.360839	−	0.624991i
$820$	−4.78462	+	22.2925i	−0.167086	+	0.778488i
$821$	−17.3462	−	30.0444i	−0.605385	−	1.04856i	−0.991991	−	0.126312i	$-0.959686\pi$
$821$	−17.3462	−	30.0444i	−0.605385	−	1.04856i	0.386606	−	0.922245i	$-0.373647\pi$
$822$			9.85876i			0.343864i
$823$	5.60347	+	3.23516i	0.195325	+	0.112771i	0.594473	−	0.804116i	$-0.297361\pi$
$823$	5.60347	+	3.23516i	0.195325	+	0.112771i	−0.399148	+	0.916886i	$0.630694\pi$
$824$	−9.82285			−0.342195
$825$	−4.06717	+	9.03841i	−0.141601	+	0.314677i
$826$	23.4378	−	40.5955i	0.815505	−	1.41250i
$827$	25.0641	−	14.4708i	0.871564	−	0.503198i	0.00369635	−	0.999993i	$-0.498823\pi$
$827$	25.0641	−	14.4708i	0.871564	−	0.503198i	0.867868	+	0.496795i	$0.165490\pi$
$828$		−	10.5261i		−	0.365806i
$829$	−14.7762	+	25.5931i	−0.513198	+	0.888885i	0.486685	+	0.873577i	$0.338206\pi$
$829$	−14.7762	+	25.5931i	−0.513198	+	0.888885i	−0.999883	+	0.0153071i	$0.995127\pi$
$830$	25.0020	+	22.6017i	0.867830	+	0.784518i
$831$	18.5744	−	32.1719i	0.644340	−	1.11603i
$832$	11.0701	−	6.39130i	0.383785	−	0.221578i
$833$	7.72083	−	4.45762i	0.267511	−	0.154448i
$834$	15.0766	−	26.1134i	0.522059	−	0.904233i
$835$	23.8765	−	26.4121i	0.826281	−	0.914029i
$836$	−3.83890	+	6.64917i	−0.132771	+	0.229966i
$837$		−	13.4035i		−	0.463293i
$838$	−24.6721	+	14.2444i	−0.852283	+	0.492066i
$839$	19.3359	−	33.4907i	0.667549	−	1.15623i	−0.311039	−	0.950397i	$-0.600677\pi$
$839$	19.3359	−	33.4907i	0.667549	−	1.15623i	0.978588	−	0.205831i	$-0.0659897\pi$
$840$	9.99773	+	2.14580i	0.344955	+	0.0740373i
$841$	8.94398			0.308413
$842$	29.4267	+	16.9895i	1.01411	+	0.585498i
$843$		−	0.0684850i		−	0.00235875i
$844$	14.7078	+	25.4747i	0.506264	+	0.876874i
$845$	9.61571	−	44.8016i	0.330791	−	1.54122i
$846$	8.78718	+	15.2198i	0.302109	+	0.523269i
$847$	21.9209	−	12.6560i	0.753211	−	0.434867i
$848$	1.55001	−	0.894900i	0.0532276	−	0.0307310i
$849$	7.99282	−	13.8440i	0.274313	−	0.475124i
$850$	−56.0397	−	25.2171i	−1.92214	−	0.864940i
$851$	12.5579	−	36.3034i	0.430478	−	1.24446i
$852$		−	5.15898i		−	0.176744i
$853$	−16.2600	−	9.38772i	−0.556732	−	0.321429i	0.195101	−	0.980783i	$-0.437497\pi$
$853$	−16.2600	−	9.38772i	−0.556732	−	0.321429i	−0.751833	+	0.659354i	$0.770830\pi$
$854$	20.9763	+	36.3321i	0.717795	+	1.24326i
$855$	−10.0429	+	3.24113i	−0.343459	+	0.110844i
$856$	8.54755	+	14.8048i	0.292149	+	0.506017i
$857$			16.4805i			0.562963i	0.959567	+	0.281481i	$0.0908258\pi$
$857$			16.4805i			0.562963i	−0.959567	+	0.281481i	$0.909174\pi$
$858$	18.1778	−	10.4950i	0.620581	−	0.358293i
$859$	40.3314			1.37609			0.688045	−	0.725668i	$-0.258469\pi$
$859$	40.3314			1.37609			0.688045	+	0.725668i	$0.258469\pi$
$860$	12.3158	−	13.6236i	0.419964	−	0.464562i
$861$	28.9903			0.987988
$862$			38.4755i			1.31048i
$863$	−22.7798	−	13.1519i	−0.775432	−	0.447696i	0.0593771	−	0.998236i	$-0.481089\pi$
$863$	−22.7798	−	13.1519i	−0.775432	−	0.447696i	−0.834809	+	0.550540i	$0.814422\pi$
$864$	18.3977	+	31.8658i	0.625904	+	1.08410i
$865$	−18.6257	−	3.99762i	−0.633294	−	0.135923i
$866$	−26.2534	+	45.4722i	−0.892126	+	1.54521i
$867$	−32.3387	−	18.6708i	−1.09828	−	0.634092i
$868$	−8.02457	−	4.63299i	−0.272372	−	0.157254i
$869$	−6.71723	−	11.6346i	−0.227867	−	0.394676i
$870$	−31.8480	+	10.2783i	−1.07975	+	0.348467i
$871$	−23.7334	+	41.1075i	−0.804176	+	1.39287i
$872$	10.9311	+	6.31110i	0.370175	+	0.213721i
$873$	6.93885	+	4.00615i	0.234845	+	0.135588i
$874$	44.0951			1.49154
$875$	−3.56313	+	32.0657i	−0.120456	+	1.08402i
$876$	−9.12530	+	15.8055i	−0.308315	+	0.534018i
$877$			14.1525i			0.477894i	0.971033	+	0.238947i	$0.0768023\pi$
$877$			14.1525i			0.477894i	−0.971033	+	0.238947i	$0.923198\pi$
$878$		−	27.4443i		−	0.926202i
$879$	−14.2104	+	24.6131i	−0.479305	+	0.830180i
$880$	3.41766	−	15.9236i	0.115209	−	0.536784i
$881$	−17.1877	−	29.7700i	−0.579069	−	1.00298i	−0.995586	−	0.0938492i	$-0.970083\pi$
$881$	−17.1877	−	29.7700i	−0.579069	−	1.00298i	0.416517	−	0.909128i	$-0.363251\pi$
$882$		−	3.00321i		−	0.101123i
$883$	50.1865	−	28.9752i	1.68891	−	0.975093i	0.733556	−	0.679629i	$-0.237859\pi$
$883$	50.1865	−	28.9752i	1.68891	−	0.975093i	0.955354	−	0.295463i	$-0.0954740\pi$
$884$	26.1965	+	45.3737i	0.881085	+	1.52608i
$885$	8.09640	+	25.0872i	0.272157	+	0.843298i
$886$	2.65428	−	4.59735i	0.0891723	−	0.154451i
$887$			5.60416i			0.188169i	0.995564	+	0.0940847i	$0.0299924\pi$
$887$			5.60416i			0.188169i	−0.995564	+	0.0940847i	$0.970008\pi$
$888$	1.82585	+	9.46482i	0.0612716	+	0.317619i
$889$	8.56616			0.287300
$890$	12.9181	−	14.2899i	0.433015	−	0.478999i
$891$	2.80681	+	4.86154i	0.0940318	+	0.162868i
$892$	−3.92044	+	2.26347i	−0.131266	+	0.0757865i
$893$	−25.6681	+	14.8195i	−0.858950	+	0.495915i
$894$	−10.5596			−0.353167
$895$	−4.27179	+	1.37863i	−0.142790	+	0.0460826i
$896$	−26.0850			−0.871440
$897$	−42.0295	−	24.2657i	−1.40332	−	0.810210i
$898$		−	74.5390i		−	2.48740i
$899$	−14.6757			−0.489462
$900$	−6.76161	+	4.87176i	−0.225387	+	0.162392i
$901$	1.23205	+	2.13397i	0.0410454	+	0.0710927i
$902$		−	20.6641i		−	0.688039i
$903$	−20.2228	−	11.6756i	−0.672973	−	0.388541i
$904$	0.382662	−	0.662791i	0.0127272	−	0.0220441i
$905$	−22.6735	−	20.4968i	−0.753692	−	0.681337i
$906$	4.85283	+	8.40535i	0.161224	+	0.279249i
$907$	38.9701	−	22.4994i	1.29398	−	0.747079i	0.314622	−	0.949217i	$-0.398122\pi$
$907$	38.9701	−	22.4994i	1.29398	−	0.747079i	0.979357	+	0.202138i	$0.0647888\pi$
$908$	−7.88752	−	4.55386i	−0.261757	−	0.151125i
$909$	−0.341165	+	0.590916i	−0.0113157	+	0.0195994i
$910$	45.8194	−	50.6852i	1.51890	−	1.68020i
$911$	−17.7187			−0.587046			−0.293523	−	0.955952i	$-0.594828\pi$
$911$	−17.7187			−0.587046			−0.293523	+	0.955952i	$0.594828\pi$
$912$	−21.4119	+	12.3621i	−0.709018	+	0.409352i
$913$	−10.6499	−	6.14870i	−0.352459	−	0.203492i
$914$	38.6882			1.27969
$915$	−23.0675	−	4.95096i	−0.762589	−	0.163674i
$916$	2.34813	−	4.06708i	0.0775844	−	0.134380i
$917$			28.7248i			0.948576i
$918$	−59.8808	+	34.5722i	−1.97636	+	1.14105i
$919$	15.4190			0.508626			0.254313	−	0.967122i	$-0.418151\pi$
$919$	15.4190			0.508626			0.254313	+	0.967122i	$0.418151\pi$
$920$	−16.0377	+	5.17583i	−0.528746	+	0.170642i
$921$	15.3519	+	26.5903i	0.505863	+	0.876180i
$922$	42.3355	−	24.4424i	1.39425	−	0.804968i
$923$	14.4474	+	8.34119i	0.475541	+	0.274554i
$924$	7.70950			0.253624
$925$	−29.1323	+	8.73548i	−0.957864	+	0.287221i
$926$	21.4137			0.703698
$927$	−8.81554	−	5.08965i	−0.289540	−	0.167166i
$928$	34.8904	−	20.1440i	1.14533	−	0.661258i
$929$	11.9368	+	20.6751i	0.391632	+	0.678327i	0.992665	−	0.120897i	$-0.0385771\pi$
$929$	11.9368	+	20.6751i	0.391632	+	0.678327i	−0.601033	+	0.799225i	$0.705244\pi$
$930$	12.3180	−	3.97537i	0.403921	−	0.130358i
$931$	5.06488			0.165995
$932$	5.57355	−	3.21789i	0.182568	−	0.105405i
$933$			8.68085i			0.284198i
$934$	−2.98330	+	5.16723i	−0.0976166	+	0.169077i
$935$	21.9227	+	4.70524i	0.716947	+	0.153878i
$936$	−8.54116			−0.279177
$937$	42.5045	+	24.5400i	1.38856	+	0.801687i	0.993153	−	0.116818i	$-0.0372695\pi$
$937$	42.5045	+	24.5400i	1.38856	+	0.801687i	0.395409	+	0.918505i	$0.370603\pi$
$938$	−37.5039	+	21.6529i	−1.22455	+	0.706992i
$939$	−11.1359			−0.363406
$940$	−15.6965	+	17.3634i	−0.511963	+	0.566331i
$941$	−29.3488	+	50.8336i	−0.956743	+	1.65713i	−0.226416	+	0.974031i	$0.572701\pi$
$941$	−29.3488	+	50.8336i	−0.956743	+	1.65713i	−0.730328	+	0.683097i	$0.760633\pi$
$942$	19.7876	+	11.4244i	0.644714	+	0.372226i
$943$	−41.3770	+	23.8890i	−1.34742	+	0.777933i
$944$	−21.6584	−	37.5134i	−0.704919	−	1.22096i
$945$	26.9292	+	24.3440i	0.876006	+	0.791909i
$946$	−8.32231	+	14.4147i	−0.270581	+	0.468661i
$947$	26.6354	+	15.3780i	0.865535	+	0.499717i	0.865862	−	0.500283i	$-0.166771\pi$
$947$	26.6354	+	15.3780i	0.865535	+	0.499717i	−0.000327165		1.00000i	$0.500104\pi$
$948$			16.1064i			0.523112i
$949$	−29.5081	−	51.1095i	−0.957873	−	1.65909i
$950$	−20.4085	−	28.3253i	−0.662139	−	0.918995i
$951$	−4.98486			−0.161645
$952$		−	23.1324i		−	0.749726i
$953$	−34.7007	−	20.0345i	−1.12407	−	0.648980i	−0.181631	−	0.983367i	$-0.558138\pi$
$953$	−34.7007	−	20.0345i	−1.12407	−	0.648980i	−0.942436	+	0.334386i	$0.891471\pi$
$954$	0.830058			0.0268741
$955$	−18.0014	+	5.80957i	−0.582510	+	0.187993i
$956$	−0.962455			−0.0311280
$957$	10.5746	−	6.10526i	0.341829	−	0.197355i
$958$	−43.1993	+	24.9411i	−1.39571	+	0.805811i
$959$	−5.85466	−	10.1406i	−0.189057	−	0.327456i
$960$	−4.39806	+	4.86511i	−0.141947	+	0.157021i
$961$	−25.3238			−0.816898
$962$	60.8706	+	21.0560i	1.96255	+	0.678873i
$963$			17.7155i			0.570873i
$964$	5.74654	−	9.95331i	0.185084	−	0.320574i
$965$	0.432500	+	1.34013i	0.0139227	+	0.0431403i
$966$	−22.1386	−	38.3451i	−0.712297	−	1.23373i
$967$	−14.4874	+	8.36429i	−0.465882	+	0.268977i	−0.714514	−	0.699621i	$-0.753352\pi$
$967$	−14.4874	+	8.36429i	−0.465882	+	0.268977i	0.248632	+	0.968598i	$0.420019\pi$
$968$		−	10.4679i		−	0.336451i
$969$	−17.0195	−	29.4786i	−0.546745	−	0.946989i
$970$	−5.56244	+	25.9165i	−0.178599	+	0.832130i
$971$	1.13592	−	1.96747i	0.0364534	−	0.0631392i	−0.847223	−	0.531237i	$-0.821727\pi$
$971$	1.13592	−	1.96747i	0.0364534	−	0.0631392i	0.883677	+	0.468098i	$0.155061\pi$
$972$			16.0170i			0.513745i
$973$			35.8131i			1.14812i
$974$	−14.9779	+	25.9424i	−0.479921	+	0.831248i
$975$	3.86491	+	38.2293i	0.123776	+	1.22432i
$976$	38.7675			1.24092
$977$	0.210332	+	0.121435i	0.00672912	+	0.00388506i	0.503361	−	0.864076i	$-0.332097\pi$
$977$	0.210332	+	0.121435i	0.00672912	+	0.00388506i	−0.496632	+	0.867961i	$0.665430\pi$
$978$	−1.06979	−	0.617646i	−0.0342083	−	0.0197501i
$979$	−3.51431	+	6.08696i	−0.112318	+	0.194540i
$980$	3.80653	−	1.22848i	0.121595	−	0.0392423i
$981$	6.54013	+	11.3278i	0.208810	+	0.361670i
$982$	−41.3180	−	23.8549i	−1.31851	−	0.761242i
$983$	39.2916	+	22.6850i	1.25321	+	0.723539i	0.971745	−	0.236034i	$-0.0758476\pi$
$983$	39.2916	+	22.6850i	1.25321	+	0.723539i	0.281461	+	0.959573i	$0.409181\pi$
$984$	5.99454	−	10.3828i	0.191099	−	0.330993i
$985$	35.3255	+	7.58188i	1.12556	+	0.241579i
$986$	37.8536	+	65.5644i	1.20550	+	2.08800i
$987$	25.7741	+	14.8807i	0.820398	+	0.473657i
$988$			29.7652i			0.946959i
$989$	38.4845			1.22374
$990$	5.06512	−	5.60301i	0.160980	−	0.178075i
$991$	47.9120			1.52198			0.760988	−	0.648766i	$-0.224715\pi$
$991$	47.9120			1.52198			0.760988	+	0.648766i	$0.224715\pi$
$992$	−13.4946	+	7.79114i	−0.428455	+	0.247369i
$993$			4.99797i			0.158606i
$994$	7.60999	+	13.1809i	0.241374	+	0.418072i
$995$	−39.4138	+	12.7200i	−1.24950	+	0.403251i
$996$	7.37160	+	12.7680i	0.233578	+	0.404569i
$997$	−20.9970	−	12.1226i	−0.664983	−	0.383928i	0.129190	−	0.991620i	$-0.458762\pi$
$997$	−20.9970	−	12.1226i	−0.664983	−	0.383928i	−0.794173	+	0.607692i	$0.792096\pi$
$998$		−	61.2769i		−	1.93969i
$999$	−11.1871	+	32.3407i	−0.353944	+	1.02321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.n.a.84.5	✓	36
5.2	odd	4		925.2.e.f.676.14		36
5.3	odd	4		925.2.e.f.676.5		36
5.4	even	2	inner	185.2.n.a.84.14	yes	36
37.26	even	3	inner	185.2.n.a.174.14	yes	36
185.63	odd	12		925.2.e.f.26.5		36
185.137	odd	12		925.2.e.f.26.14		36
185.174	even	6	inner	185.2.n.a.174.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.n.a.84.5	✓	36	1.1	even	1	trivial
185.2.n.a.84.14	yes	36	5.4	even	2	inner
185.2.n.a.174.5	yes	36	185.174	even	6	inner
185.2.n.a.174.14	yes	36	37.26	even	3	inner
925.2.e.f.26.5		36	185.63	odd	12
925.2.e.f.26.14		36	185.137	odd	12
925.2.e.f.676.5		36	5.3	odd	4
925.2.e.f.676.14		36	5.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58456 - 0.914845i) q^{2} +(-1.14999 + 0.663947i) q^{3} +(0.673882 + 1.16720i) q^{4} +(2.12799 - 0.686767i) q^{5} +2.42963 q^{6} +(-2.49908 + 1.44285i) q^{7} +1.19339i q^{8} +(-0.618348 + 1.07101i) q^{9} +O(q^{10})\)	\(q+(-1.58456 - 0.914845i) q^{2} +(-1.14999 + 0.663947i) q^{3} +(0.673882 + 1.16720i) q^{4} +(2.12799 - 0.686767i) q^{5} +2.42963 q^{6} +(-2.49908 + 1.44285i) q^{7} +1.19339i q^{8} +(-0.618348 + 1.07101i) q^{9} +(-4.00021 - 0.858562i) q^{10} +1.49279 q^{11} +(-1.54992 - 0.894844i) q^{12} +(5.01190 - 2.89362i) q^{13} +5.27992 q^{14} +(-1.99119 + 2.20265i) q^{15} +(2.43953 - 4.22539i) q^{16} +(5.81727 + 3.35860i) q^{17} +(1.95962 - 1.13139i) q^{18} +(1.90807 + 3.30487i) q^{19} +(2.23561 + 2.02099i) q^{20} +(1.91595 - 3.31852i) q^{21} +(-2.36541 - 1.36567i) q^{22} +6.31522i q^{23} +(-0.792348 - 1.37239i) q^{24} +(4.05670 - 2.92287i) q^{25} -10.5889 q^{26} -5.62589i q^{27} +(-3.36817 - 1.94462i) q^{28} -6.15987 q^{29} +(5.17024 - 1.66859i) q^{30} +2.38247 q^{31} +(-5.66414 + 3.27019i) q^{32} +(-1.71669 + 0.991134i) q^{33} +(-6.14520 - 10.6438i) q^{34} +(-4.32713 + 4.78665i) q^{35} -1.66677 q^{36} +(-5.74855 - 1.98851i) q^{37} -6.98235i q^{38} +(-3.84242 + 6.65527i) q^{39} +(0.819580 + 2.53952i) q^{40} +(3.78277 + 6.55195i) q^{41} +(-6.07186 + 3.50559i) q^{42} -6.09393i q^{43} +(1.00596 + 1.74238i) q^{44} +(-0.580306 + 2.70376i) q^{45} +(5.77745 - 10.0068i) q^{46} +7.76674i q^{47} +6.47888i q^{48} +(0.663613 - 1.14941i) q^{49} +(-9.10205 + 0.920199i) q^{50} -8.91974 q^{51} +(6.75485 + 3.89992i) q^{52} +(0.317686 + 0.183416i) q^{53} +(-5.14681 + 8.91454i) q^{54} +(3.17665 - 1.02520i) q^{55} +(-1.72188 - 2.98238i) q^{56} +(-4.38852 - 2.53371i) q^{57} +(9.76067 + 5.63532i) q^{58} +(4.43904 - 7.68865i) q^{59} +(-3.91276 - 0.839791i) q^{60} +(3.97285 + 6.88118i) q^{61} +(-3.77516 - 2.17959i) q^{62} -3.56873i q^{63} +2.20876 q^{64} +(8.67804 - 9.59960i) q^{65} +3.62694 q^{66} +(-7.10312 + 4.10099i) q^{67} +9.05321i q^{68} +(-4.19297 - 7.26244i) q^{69} +(11.2356 - 3.62607i) q^{70} +(1.44131 + 2.49642i) q^{71} +(-1.27813 - 0.737931i) q^{72} -10.1976i q^{73} +(7.28974 + 8.40993i) q^{74} +(-2.72454 + 6.05471i) q^{75} +(-2.57163 + 4.45419i) q^{76} +(-3.73061 + 2.15387i) q^{77} +(12.1771 - 7.03044i) q^{78} +(-4.49978 - 7.79385i) q^{79} +(2.28945 - 10.6670i) q^{80} +(1.88025 + 3.25668i) q^{81} -13.8426i q^{82} +(-7.13420 - 4.11893i) q^{83} +5.16449 q^{84} +(14.6857 + 3.15197i) q^{85} +(-5.57500 + 9.65618i) q^{86} +(7.08379 - 4.08983i) q^{87} +1.78148i q^{88} +(-2.35419 + 4.07757i) q^{89} +(3.39305 - 3.75338i) q^{90} +(-8.35010 + 14.4628i) q^{91} +(-7.37111 + 4.25571i) q^{92} +(-2.73982 + 1.58183i) q^{93} +(7.10536 - 12.3068i) q^{94} +(6.33003 + 5.72235i) q^{95} +(4.34247 - 7.52138i) q^{96} -6.47879i q^{97} +(-2.10307 + 1.21421i) q^{98} +(-0.923065 + 1.59879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 16 q^{4} - 2 q^{5} - 16 q^{6} + 14 q^{9}+O(q^{10}) \) 36 * q + 16 * q^4 - 2 * q^5 - 16 * q^6 + 14 * q^9	\( 36 q + 16 q^{4} - 2 q^{5} - 16 q^{6} + 14 q^{9} - 12 q^{10} + 12 q^{11} - 8 q^{14} - 10 q^{15} - 16 q^{16} - 8 q^{19} + 22 q^{20} - 26 q^{21} - 42 q^{24} + 12 q^{26} - 16 q^{29} + 18 q^{34} - 16 q^{35} + 32 q^{36} - 2 q^{39} - 42 q^{40} + 2 q^{41} - 10 q^{44} - 56 q^{45} + 52 q^{46} + 10 q^{49} + 34 q^{50} - 28 q^{51} - 42 q^{54} + 4 q^{55} + 18 q^{56} - 28 q^{59} + 44 q^{60} + 20 q^{61} + 36 q^{64} + 10 q^{65} - 148 q^{66} + 70 q^{69} - 10 q^{70} - 46 q^{71} + 56 q^{74} + 32 q^{75} + 24 q^{76} + 2 q^{79} + 132 q^{80} - 2 q^{81} - 168 q^{84} - 28 q^{85} - 22 q^{86} + 8 q^{89} - 28 q^{90} - 48 q^{91} + 32 q^{94} - 10 q^{95} + 106 q^{96} + 64 q^{99}+O(q^{100}) \) 36 * q + 16 * q^4 - 2 * q^5 - 16 * q^6 + 14 * q^9 - 12 * q^10 + 12 * q^11 - 8 * q^14 - 10 * q^15 - 16 * q^16 - 8 * q^19 + 22 * q^20 - 26 * q^21 - 42 * q^24 + 12 * q^26 - 16 * q^29 + 18 * q^34 - 16 * q^35 + 32 * q^36 - 2 * q^39 - 42 * q^40 + 2 * q^41 - 10 * q^44 - 56 * q^45 + 52 * q^46 + 10 * q^49 + 34 * q^50 - 28 * q^51 - 42 * q^54 + 4 * q^55 + 18 * q^56 - 28 * q^59 + 44 * q^60 + 20 * q^61 + 36 * q^64 + 10 * q^65 - 148 * q^66 + 70 * q^69 - 10 * q^70 - 46 * q^71 + 56 * q^74 + 32 * q^75 + 24 * q^76 + 2 * q^79 + 132 * q^80 - 2 * q^81 - 168 * q^84 - 28 * q^85 - 22 * q^86 + 8 * q^89 - 28 * q^90 - 48 * q^91 + 32 * q^94 - 10 * q^95 + 106 * q^96 + 64 * q^99

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