LMFDB - Embedded newform 240.2.s.b.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.4
Root			$0.500000 - 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.b.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.874559 - 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 - 1.94392i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.40426 + 0.167452i) q^{6} -1.41421i q^{7} +(-2.57172 - 1.17740i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.874559 - 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 - 1.94392i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.40426 + 0.167452i) q^{6} -1.41421i q^{7} +(-2.57172 - 1.17740i) q^{8} +1.00000i q^{9} +(-0.167452 - 1.40426i) q^{10} +(-0.808530 + 0.808530i) q^{11} +(-1.04201 + 1.70711i) q^{12} +(-0.749118 - 0.749118i) q^{13} +(-1.57172 - 1.23681i) q^{14} -1.00000 q^{15} +(-3.55765 + 1.82843i) q^{16} +5.97186 q^{17} +(1.11137 + 0.874559i) q^{18} +(-1.88784 - 1.88784i) q^{19} +(-1.70711 - 1.04201i) q^{20} +(-1.00000 + 1.00000i) q^{21} +(0.191470 + 1.60568i) q^{22} -1.88118i q^{23} +(0.985930 + 2.65103i) q^{24} -1.00000i q^{25} +(-1.48770 + 0.177401i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.74912 + 0.665096i) q^{28} +(5.88784 + 5.88784i) q^{29} +(-0.874559 + 1.11137i) q^{30} +1.61040 q^{31} +(-1.07931 + 5.55294i) q^{32} +1.14343 q^{33} +(5.22274 - 6.63696i) q^{34} +(-1.00000 - 1.00000i) q^{35} +(1.94392 - 0.470294i) q^{36} +(3.69637 - 3.69637i) q^{37} +(-3.74912 + 0.447065i) q^{38} +1.05941i q^{39} +(-2.65103 + 0.985930i) q^{40} +8.77215i q^{41} +(0.236813 + 1.98593i) q^{42} +(-0.744406 + 0.744406i) q^{43} +(1.95196 + 1.19147i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-2.09069 - 1.64520i) q^{46} +13.5608 q^{47} +(3.80853 + 1.22274i) q^{48} +5.00000 q^{49} +(-1.11137 - 0.874559i) q^{50} +(-4.22274 - 4.22274i) q^{51} +(-1.10392 + 1.80853i) q^{52} +(0.863230 - 0.863230i) q^{53} +(-0.167452 - 1.40426i) q^{54} +1.14343i q^{55} +(-1.66510 + 3.63696i) q^{56} +2.66981i q^{57} +(11.6928 - 1.39432i) q^{58} +(-10.7523 + 10.7523i) q^{59} +(0.470294 + 1.94392i) q^{60} +(-9.05588 - 9.05588i) q^{61} +(1.40839 - 1.78975i) q^{62} +1.41421 q^{63} +(5.22746 + 6.05588i) q^{64} -1.05941 q^{65} +(1.00000 - 1.27078i) q^{66} +(-2.94725 - 2.94725i) q^{67} +(-2.80853 - 11.6088i) q^{68} +(-1.33019 + 1.33019i) q^{69} +(-1.98593 + 0.236813i) q^{70} -6.78863i q^{71} +(1.17740 - 2.57172i) q^{72} +2.32666i q^{73} +(-0.875348 - 7.34073i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-2.78197 + 4.55765i) q^{76} +(1.14343 + 1.14343i) q^{77} +(1.17740 + 0.926518i) q^{78} -4.27078 q^{79} +(-1.22274 + 3.80853i) q^{80} -1.00000 q^{81} +(9.74912 + 7.67176i) q^{82} +(-3.11529 - 3.11529i) q^{83} +(2.41421 + 1.47363i) q^{84} +(4.22274 - 4.22274i) q^{85} +(0.176285 + 1.47834i) q^{86} -8.32666i q^{87} +(3.03127 - 1.12735i) q^{88} +10.3172i q^{89} +(1.40426 - 0.167452i) q^{90} +(-1.05941 + 1.05941i) q^{91} +(-3.65685 + 0.884705i) q^{92} +(-1.13872 - 1.13872i) q^{93} +(11.8597 - 15.0711i) q^{94} -2.66981 q^{95} +(4.68971 - 3.16333i) q^{96} -3.72256 q^{97} +(4.37279 - 5.55686i) q^{98} +(-0.808530 - 0.808530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8	$ 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} + 8 q^{17} - 4 q^{18} + 8 q^{19} - 8 q^{20} - 8 q^{21} + 16 q^{22} - 12 q^{24} - 20 q^{26} - 8 q^{28} + 24 q^{29} + 8 q^{31} - 8 q^{33} + 16 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{37} - 16 q^{38} - 4 q^{40} - 4 q^{42} - 16 q^{44} + 24 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 16 q^{56} + 8 q^{59} + 4 q^{60} - 16 q^{61} + 28 q^{62} + 8 q^{64} - 8 q^{65} + 8 q^{66} - 8 q^{68} - 16 q^{69} + 4 q^{70} + 4 q^{72} - 36 q^{74} - 40 q^{76} - 8 q^{77} + 4 q^{78} - 40 q^{79} + 16 q^{80} - 8 q^{81} + 64 q^{82} + 32 q^{83} + 8 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{88} + 4 q^{90} - 8 q^{91} + 16 q^{92} + 32 q^{94} - 16 q^{95} + 24 q^{96} - 48 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 8 * q^15 + 8 * q^17 - 4 * q^18 + 8 * q^19 - 8 * q^20 - 8 * q^21 + 16 * q^22 - 12 * q^24 - 20 * q^26 - 8 * q^28 + 24 * q^29 + 8 * q^31 - 8 * q^33 + 16 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^37 - 16 * q^38 - 4 * q^40 - 4 * q^42 - 16 * q^44 + 24 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 16 * q^56 + 8 * q^59 + 4 * q^60 - 16 * q^61 + 28 * q^62 + 8 * q^64 - 8 * q^65 + 8 * q^66 - 8 * q^68 - 16 * q^69 + 4 * q^70 + 4 * q^72 - 36 * q^74 - 40 * q^76 - 8 * q^77 + 4 * q^78 - 40 * q^79 + 16 * q^80 - 8 * q^81 + 64 * q^82 + 32 * q^83 + 8 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^88 + 4 * q^90 - 8 * q^91 + 16 * q^92 + 32 * q^94 - 16 * q^95 + 24 * q^96 - 48 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.874559	−	1.11137i	0.618406	−	0.785858i
$2$	0.874559	−	1.11137i	0.618406	−	0.785858i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.470294	−	1.94392i	−0.235147	−	0.971960i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−1.40426	+	0.167452i	−0.573289	+	0.0683620i
$7$		−	1.41421i		−	0.534522i	−0.963624	−	0.267261i	$-0.913881\pi$
$7$		−	1.41421i		−	0.534522i	0.963624	−	0.267261i	$-0.0861187\pi$
$8$	−2.57172	−	1.17740i	−0.909239	−	0.416274i
$9$			1.00000i			0.333333i
$10$	−0.167452	−	1.40426i	−0.0529530	−	0.444068i
$11$	−0.808530	+	0.808530i	−0.243781	+	0.243781i	−0.818412	−	0.574631i	$-0.805145\pi$
$11$	−0.808530	+	0.808530i	−0.243781	+	0.243781i	0.574631	+	0.818412i	$0.305145\pi$
$12$	−1.04201	+	1.70711i	−0.300803	+	0.492799i
$13$	−0.749118	−	0.749118i	−0.207768	−	0.207768i	0.595550	−	0.803318i	$-0.296934\pi$
$13$	−0.749118	−	0.749118i	−0.207768	−	0.207768i	−0.803318	+	0.595550i	$0.796934\pi$
$14$	−1.57172	−	1.23681i	−0.420059	−	0.330552i
$15$	−1.00000			−0.258199
$16$	−3.55765	+	1.82843i	−0.889412	+	0.457107i
$17$	5.97186			1.44839			0.724195	−	0.689596i	$-0.242212\pi$
$17$	5.97186			1.44839			0.724195	+	0.689596i	$0.242212\pi$
$18$	1.11137	+	0.874559i	0.261953	+	0.206135i
$19$	−1.88784	−	1.88784i	−0.433100	−	0.433100i	0.456582	−	0.889682i	$-0.349074\pi$
$19$	−1.88784	−	1.88784i	−0.433100	−	0.433100i	−0.889682	+	0.456582i	$0.849074\pi$
$20$	−1.70711	−	1.04201i	−0.381721	−	0.233001i
$21$	−1.00000	+	1.00000i	−0.218218	+	0.218218i
$22$	0.191470	+	1.60568i	0.0408216	+	0.342333i
$23$		−	1.88118i		−	0.392252i	−0.980579	−	0.196126i	$-0.937164\pi$
$23$		−	1.88118i		−	0.392252i	0.980579	−	0.196126i	$-0.0628362\pi$
$24$	0.985930	+	2.65103i	0.201252	+	0.541139i
$25$		−	1.00000i		−	0.200000i
$26$	−1.48770	+	0.177401i	−0.291761	+	0.0347911i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.74912	+	0.665096i	−0.519534	+	0.125691i
$29$	5.88784	+	5.88784i	1.09334	+	1.09334i	0.995169	+	0.0981752i	$0.0313005\pi$
$29$	5.88784	+	5.88784i	1.09334	+	1.09334i	0.0981752	+	0.995169i	$0.468699\pi$
$30$	−0.874559	+	1.11137i	−0.159672	+	0.202908i
$31$	1.61040			0.289236			0.144618	−	0.989488i	$-0.453805\pi$
$31$	1.61040			0.289236			0.144618	+	0.989488i	$0.453805\pi$
$32$	−1.07931	+	5.55294i	−0.190797	+	0.981630i
$33$	1.14343			0.199046
$34$	5.22274	−	6.63696i	0.895693	−	1.13823i
$35$	−1.00000	−	1.00000i	−0.169031	−	0.169031i
$36$	1.94392	−	0.470294i	0.323987	−	0.0783823i
$37$	3.69637	−	3.69637i	0.607679	−	0.607679i	−0.334660	−	0.942339i	$-0.608621\pi$
$37$	3.69637	−	3.69637i	0.607679	−	0.607679i	0.942339	+	0.334660i	$0.108621\pi$
$38$	−3.74912	+	0.447065i	−0.608187	+	0.0725235i
$39$			1.05941i			0.169642i
$40$	−2.65103	+	0.985930i	−0.419164	+	0.155889i
$41$			8.77215i			1.36998i	0.728553	+	0.684990i	$0.240193\pi$
$41$			8.77215i			1.36998i	−0.728553	+	0.684990i	$0.759807\pi$
$42$	0.236813	+	1.98593i	0.0365410	+	0.306436i
$43$	−0.744406	+	0.744406i	−0.113521	+	0.113521i	−0.761585	−	0.648065i	$-0.775579\pi$
$43$	−0.744406	+	0.744406i	−0.113521	+	0.113521i	0.648065	+	0.761585i	$0.275579\pi$
$44$	1.95196	+	1.19147i	0.294270	+	0.179621i
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$	−2.09069	−	1.64520i	−0.308255	−	0.242571i
$47$	13.5608			1.97804			0.989022	−	0.147771i	$-0.0472098\pi$
$47$	13.5608			1.97804			0.989022	+	0.147771i	$0.0472098\pi$
$48$	3.80853	+	1.22274i	0.549714	+	0.176488i
$49$	5.00000			0.714286
$50$	−1.11137	−	0.874559i	−0.157172	−	0.123681i
$51$	−4.22274	−	4.22274i	−0.591302	−	0.591302i
$52$	−1.10392	+	1.80853i	−0.153086	+	0.250798i
$53$	0.863230	−	0.863230i	0.118574	−	0.118574i	−0.645330	−	0.763904i	$-0.723280\pi$
$53$	0.863230	−	0.863230i	0.118574	−	0.118574i	0.763904	+	0.645330i	$0.223280\pi$
$54$	−0.167452	−	1.40426i	−0.0227873	−	0.191096i
$55$			1.14343i			0.154181i
$56$	−1.66510	+	3.63696i	−0.222508	+	0.486009i
$57$			2.66981i			0.353625i
$58$	11.6928	−	1.39432i	1.53535	−	0.183083i
$59$	−10.7523	+	10.7523i	−1.39982	+	1.39982i	−0.599298	+	0.800526i	$0.704553\pi$
$59$	−10.7523	+	10.7523i	−1.39982	+	1.39982i	−0.800526	+	0.599298i	$0.795447\pi$
$60$	0.470294	+	1.94392i	0.0607147	+	0.250959i
$61$	−9.05588	−	9.05588i	−1.15949	−	1.15949i	−0.984586	−	0.174901i	$-0.944040\pi$
$61$	−9.05588	−	9.05588i	−1.15949	−	1.15949i	−0.174901	−	0.984586i	$-0.555960\pi$
$62$	1.40839	−	1.78975i	0.178865	−	0.227298i
$63$	1.41421			0.178174
$64$	5.22746	+	6.05588i	0.653432	+	0.756985i
$65$	−1.05941			−0.131404
$66$	1.00000	−	1.27078i	0.123091	−	0.156422i
$67$	−2.94725	−	2.94725i	−0.360064	−	0.360064i	0.503772	−	0.863836i	$-0.331945\pi$
$67$	−2.94725	−	2.94725i	−0.360064	−	0.360064i	−0.863836	+	0.503772i	$0.831945\pi$
$68$	−2.80853	−	11.6088i	−0.340584	−	1.40778i
$69$	−1.33019	+	1.33019i	−0.160136	+	0.160136i
$70$	−1.98593	+	0.236813i	−0.237364	+	0.0283046i
$71$		−	6.78863i		−	0.805662i	−0.915274	−	0.402831i	$-0.868026\pi$
$71$		−	6.78863i		−	0.805662i	0.915274	−	0.402831i	$-0.131974\pi$
$72$	1.17740	−	2.57172i	0.138758	−	0.303080i
$73$			2.32666i			0.272315i	0.990687	+	0.136158i	$0.0434754\pi$
$73$			2.32666i			0.272315i	−0.990687	+	0.136158i	$0.956525\pi$
$74$	−0.875348	−	7.34073i	−0.101757	−	0.853343i
$75$	−0.707107	+	0.707107i	−0.0816497	+	0.0816497i
$76$	−2.78197	+	4.55765i	−0.319114	+	0.522798i
$77$	1.14343	+	1.14343i	0.130306	+	0.130306i
$78$	1.17740	+	0.926518i	0.133314	+	0.104908i
$79$	−4.27078			−0.480500			−0.240250	−	0.970711i	$-0.577229\pi$
$79$	−4.27078			−0.480500			−0.240250	+	0.970711i	$0.577229\pi$
$80$	−1.22274	+	3.80853i	−0.136707	+	0.425807i
$81$	−1.00000			−0.111111
$82$	9.74912	+	7.67176i	1.07661	+	0.847204i
$83$	−3.11529	−	3.11529i	−0.341948	−	0.341948i	0.515151	−	0.857099i	$-0.327736\pi$
$83$	−3.11529	−	3.11529i	−0.341948	−	0.341948i	−0.857099	+	0.515151i	$0.827736\pi$
$84$	2.41421	+	1.47363i	0.263412	+	0.160786i
$85$	4.22274	−	4.22274i	0.458021	−	0.458021i
$86$	0.176285	+	1.47834i	0.0190093	+	0.159413i
$87$		−	8.32666i		−	0.892712i
$88$	3.03127	−	1.12735i	0.323135	−	0.120175i
$89$			10.3172i			1.09363i	0.837255	+	0.546813i	$0.184159\pi$
$89$			10.3172i			1.09363i	−0.837255	+	0.546813i	$0.815841\pi$
$90$	1.40426	−	0.167452i	0.148023	−	0.0176510i
$91$	−1.05941	+	1.05941i	−0.111057	+	0.111057i
$92$	−3.65685	+	0.884705i	−0.381253	+	0.0922369i
$93$	−1.13872	−	1.13872i	−0.118080	−	0.118080i
$94$	11.8597	−	15.0711i	1.22323	−	1.55446i
$95$	−2.66981			−0.273917
$96$	4.68971	−	3.16333i	0.478641	−	0.322856i
$97$	−3.72256			−0.377968			−0.188984	−	0.981980i	$-0.560519\pi$
$97$	−3.72256			−0.377968			−0.188984	+	0.981980i	$0.560519\pi$
$98$	4.37279	−	5.55686i	0.441719	−	0.561327i
$99$	−0.808530	−	0.808530i	−0.0812603	−	0.0812603i
$100$	−1.94392	+	0.470294i	−0.194392	+	0.0470294i
$101$	−5.29539	+	5.29539i	−0.526911	+	0.526911i	−0.919650	−	0.392739i	$-0.871528\pi$
$101$	−5.29539	+	5.29539i	−0.526911	+	0.526911i	0.392739	+	0.919650i	$0.371528\pi$
$102$	−8.38607	+	1.00000i	−0.830345	+	0.0990148i
$103$			15.8503i			1.56177i	0.624672	+	0.780887i	$0.285233\pi$
$103$			15.8503i			1.56177i	−0.624672	+	0.780887i	$0.714767\pi$
$104$	1.04451	+	2.80853i	0.102422	+	0.275399i
$105$			1.41421i			0.138013i
$106$	−0.204424	−	1.71431i	−0.0198554	−	0.166509i
$107$	−1.33962	+	1.33962i	−0.129506	+	0.129506i	−0.768888	−	0.639383i	$-0.779190\pi$
$107$	−1.33962	+	1.33962i	−0.129506	+	0.129506i	0.639383	+	0.768888i	$0.279190\pi$
$108$	−1.70711	−	1.04201i	−0.164266	−	0.100268i
$109$	−8.67294	−	8.67294i	−0.830717	−	0.830717i	0.156898	−	0.987615i	$-0.449851\pi$
$109$	−8.67294	−	8.67294i	−0.830717	−	0.830717i	−0.987615	+	0.156898i	$0.949851\pi$
$110$	1.27078	+	1.00000i	0.121164	+	0.0953463i
$111$	−5.22746			−0.496168
$112$	2.58579	+	5.03127i	0.244334	+	0.475411i
$113$	−15.3248			−1.44164			−0.720818	−	0.693124i	$-0.756234\pi$
$113$	−15.3248			−1.44164			−0.720818	+	0.693124i	$0.756234\pi$
$114$	2.96715	+	2.33490i	0.277899	+	0.218684i
$115$	−1.33019	−	1.33019i	−0.124041	−	0.124041i
$116$	8.67647	−	14.2145i	0.805590	−	1.31978i
$117$	0.749118	−	0.749118i	0.0692559	−	0.0692559i
$118$	2.54627	+	21.3532i	0.234403	+	1.96572i
$119$		−	8.44549i		−	0.774196i
$120$	2.57172	+	1.17740i	0.234765	+	0.107481i
$121$			9.69256i			0.881142i
$122$	−17.9844	+	2.14455i	−1.62823	+	0.194158i
$123$	6.20285	−	6.20285i	0.559292	−	0.559292i
$124$	−0.757359	−	3.13048i	−0.0680129	−	0.281125i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.23681	−	1.57172i	0.110184	−	0.140020i
$127$	4.18636			0.371480			0.185740	−	0.982599i	$-0.440532\pi$
$127$	4.18636			0.371480			0.185740	+	0.982599i	$0.440532\pi$
$128$	11.3021	−	0.513421i	0.998970	−	0.0453804i
$129$	1.05275			0.0926893
$130$	−0.926518	+	1.17740i	−0.0812610	+	0.103265i
$131$	4.29734	+	4.29734i	0.375460	+	0.375460i	0.869461	−	0.494001i	$-0.164466\pi$
$131$	4.29734	+	4.29734i	0.375460	+	0.375460i	−0.494001	+	0.869461i	$0.664466\pi$
$132$	−0.537750	−	2.22274i	−0.0468051	−	0.193465i
$133$	−2.66981	+	2.66981i	−0.231502	+	0.231502i
$134$	−5.85304	+	0.697947i	−0.505625	+	0.0602934i
$135$		−	1.00000i		−	0.0860663i
$136$	−15.3579	−	7.03127i	−1.31693	−	0.602927i
$137$		−	7.68499i		−	0.656573i	−0.944578	−	0.328287i	$-0.893529\pi$
$137$		−	7.68499i		−	0.656573i	0.944578	−	0.328287i	$-0.106471\pi$
$138$	0.315007	+	2.64167i	0.0268151	+	0.224874i
$139$	−10.8776	+	10.8776i	−0.922630	+	0.922630i	−0.997215	−	0.0745848i	$-0.976237\pi$
$139$	−10.8776	+	10.8776i	−0.922630	+	0.922630i	0.0745848	+	0.997215i	$0.476237\pi$
$140$	−1.47363	+	2.41421i	−0.124544	+	0.204038i
$141$	−9.58892	−	9.58892i	−0.807533	−	0.807533i
$142$	−7.54469	−	5.93706i	−0.633137	−	0.498227i
$143$	1.21137			0.101300
$144$	−1.82843	−	3.55765i	−0.152369	−	0.296471i
$145$	8.32666			0.691492
$146$	2.58579	+	2.03480i	0.214001	+	0.168401i
$147$	−3.53553	−	3.53553i	−0.291606	−	0.291606i
$148$	−8.92382	−	5.44706i	−0.733534	−	0.447746i
$149$	12.0559	−	12.0559i	0.987656	−	0.987656i	−0.0122684	−	0.999925i	$-0.503905\pi$
$149$	12.0559	−	12.0559i	0.987656	−	0.987656i	0.999925	+	0.0122684i	$0.00390524\pi$
$150$	0.167452	+	1.40426i	0.0136724	+	0.114658i
$151$		−	4.21450i		−	0.342971i	−0.985187	−	0.171486i	$-0.945143\pi$
$151$		−	4.21450i		−	0.342971i	0.985187	−	0.171486i	$-0.0548567\pi$
$152$	2.63224	+	7.07773i	0.213503	+	0.574080i
$153$			5.97186i			0.482796i
$154$	2.27078	−	0.270780i	0.182985	−	0.0218201i
$155$	1.13872	−	1.13872i	0.0914643	−	0.0914643i
$156$	2.05941	−	0.498235i	0.164885	−	0.0398907i
$157$	−9.53775	−	9.53775i	−0.761195	−	0.761195i	0.215343	−	0.976538i	$-0.430913\pi$
$157$	−9.53775	−	9.53775i	−0.761195	−	0.761195i	−0.976538	+	0.215343i	$0.930913\pi$
$158$	−3.73505	+	4.74642i	−0.297144	+	0.377605i
$159$	−1.22079			−0.0968151
$160$	3.16333	+	4.68971i	0.250083	+	0.370754i
$161$	−2.66038			−0.209668
$162$	−0.874559	+	1.11137i	−0.0687118	+	0.0873176i
$163$	11.0805	+	11.0805i	0.867891	+	0.867891i	0.992239	−	0.124348i	$-0.0396838\pi$
$163$	11.0805	+	11.0805i	0.867891	+	0.867891i	−0.124348	+	0.992239i	$0.539684\pi$
$164$	17.0524	−	4.12549i	1.33157	−	0.322146i
$165$	0.808530	−	0.808530i	0.0629440	−	0.0629440i
$166$	−6.18676	+	0.737742i	−0.480186	+	0.0572599i
$167$		−	11.7359i		−	0.908150i	−0.890963	−	0.454075i	$-0.849970\pi$
$167$		−	11.7359i		−	0.908150i	0.890963	−	0.454075i	$-0.150030\pi$
$168$	3.74912	−	1.39432i	0.289251	−	0.107574i
$169$		−	11.8776i		−	0.913665i
$170$	−1.00000	−	8.38607i	−0.0766965	−	0.643183i
$171$	1.88784	−	1.88784i	0.144367	−	0.144367i
$172$	1.79715	+	1.09698i	0.137032	+	0.0836436i
$173$	7.18766	+	7.18766i	0.546468	+	0.546468i	0.925417	−	0.378950i	$-0.123715\pi$
$173$	7.18766	+	7.18766i	0.546468	+	0.546468i	−0.378950	+	0.925417i	$0.623715\pi$
$174$	−9.25402	−	7.28216i	−0.701545	−	0.552059i
$175$	−1.41421			−0.106904
$176$	1.39813	−	4.35480i	0.105388	−	0.328256i
$177$	15.2060			1.14295
$178$	11.4663	+	9.02303i	0.859434	+	0.676305i
$179$	−6.84832	−	6.84832i	−0.511868	−	0.511868i	0.403231	−	0.915098i	$-0.367887\pi$
$179$	−6.84832	−	6.84832i	−0.511868	−	0.511868i	−0.915098	+	0.403231i	$0.867887\pi$
$180$	1.04201	−	1.70711i	0.0776669	−	0.127240i
$181$	8.26725	−	8.26725i	0.614500	−	0.614500i	−0.329615	−	0.944115i	$-0.606919\pi$
$181$	8.26725	−	8.26725i	0.614500	−	0.614500i	0.944115	+	0.329615i	$0.106919\pi$
$182$	0.250882	+	2.10392i	0.0185966	+	0.155953i
$183$			12.8070i			0.946717i
$184$	−2.21490	+	4.83785i	−0.163284	+	0.356651i
$185$		−	5.22746i		−	0.384330i
$186$	−2.26142	+	0.269664i	−0.165816	+	0.0197727i
$187$	−4.82843	+	4.82843i	−0.353090	+	0.353090i
$188$	−6.37755	−	26.3611i	−0.465131	−	1.92258i
$189$	−1.00000	−	1.00000i	−0.0727393	−	0.0727393i
$190$	−2.33490	+	2.96715i	−0.169392	+	0.215260i
$191$	17.2435			1.24770			0.623849	−	0.781545i	$-0.285568\pi$
$191$	17.2435			1.24770			0.623849	+	0.781545i	$0.285568\pi$
$192$	0.585786	−	7.97852i	0.0422755	−	0.575800i
$193$	−26.8347			−1.93160			−0.965802	−	0.259281i	$-0.916514\pi$
$193$	−26.8347			−1.93160			−0.965802	+	0.259281i	$0.916514\pi$
$194$	−3.25559	+	4.13714i	−0.233738	+	0.297030i
$195$	0.749118	+	0.749118i	0.0536454	+	0.0536454i
$196$	−2.35147	−	9.71960i	−0.167962	−	0.694257i
$197$	0.821763	−	0.821763i	0.0585482	−	0.0585482i	−0.677226	−	0.735775i	$-0.736818\pi$
$197$	0.821763	−	0.821763i	0.0585482	−	0.0585482i	0.735775	+	0.677226i	$0.236818\pi$
$198$	−1.60568	+	0.191470i	−0.114111	+	0.0136072i
$199$			20.3263i			1.44089i	0.693512	+	0.720445i	$0.256063\pi$
$199$			20.3263i			1.44089i	−0.693512	+	0.720445i	$0.743937\pi$
$200$	−1.17740	+	2.57172i	−0.0832548	+	0.181848i
$201$			4.16804i			0.293991i
$202$	1.25402	+	10.5163i	0.0882323	+	0.739922i
$203$	8.32666	−	8.32666i	0.584417	−	0.584417i
$204$	−6.22274	+	10.1946i	−0.435679	+	0.713765i
$205$	6.20285	+	6.20285i	0.433226	+	0.433226i
$206$	17.6155	+	13.8620i	1.22733	+	0.965811i
$207$	1.88118			0.130751
$208$	4.03480	+	1.29539i	0.279763	+	0.0898191i
$209$	3.05275			0.211163
$210$	1.57172	+	1.23681i	0.108459	+	0.0853482i
$211$	20.0625	+	20.0625i	1.38116	+	1.38116i	0.842560	+	0.538603i	$0.181048\pi$
$211$	20.0625	+	20.0625i	1.38116	+	1.38116i	0.538603	+	0.842560i	$0.318952\pi$
$212$	−2.08402	−	1.27208i	−0.143131	−	0.0873667i
$213$	−4.80029	+	4.80029i	−0.328910	+	0.328910i
$214$	0.317238	+	2.66038i	0.0216860	+	0.181860i
$215$			1.05275i			0.0717969i
$216$	−2.65103	+	0.985930i	−0.180380	+	0.0670841i
$217$		−	2.27744i		−	0.154603i
$218$	−17.2239	+	2.05386i	−1.16655	+	0.139105i
$219$	1.64520	−	1.64520i	0.111172	−	0.111172i
$220$	2.22274	−	0.537750i	0.149857	−	0.0362551i
$221$	−4.47363	−	4.47363i	−0.300929	−	0.300929i
$222$	−4.57172	+	5.80965i	−0.306834	+	0.389918i
$223$	10.6787			0.715099			0.357549	−	0.933894i	$-0.383612\pi$
$223$	10.6787			0.715099			0.357549	+	0.933894i	$0.383612\pi$
$224$	7.85304	+	1.52637i	0.524703	+	0.101985i
$225$	1.00000			0.0666667
$226$	−13.4024	+	17.0316i	−0.891517	+	1.13292i
$227$	17.5514	+	17.5514i	1.16492	+	1.16492i	0.983383	+	0.181541i	$0.0581086\pi$
$227$	17.5514	+	17.5514i	1.16492	+	1.16492i	0.181541	+	0.983383i	$0.441891\pi$
$228$	5.18989	−	1.25559i	0.343709	−	0.0831538i
$229$	−9.61077	+	9.61077i	−0.635098	+	0.635098i	−0.949342	−	0.314245i	$-0.898249\pi$
$229$	−9.61077	+	9.61077i	−0.635098	+	0.635098i	0.314245	+	0.949342i	$0.398249\pi$
$230$	−2.64167	+	0.315007i	−0.174186	+	0.0207709i
$231$		−	1.61706i		−	0.106395i
$232$	−8.20951	−	22.0742i	−0.538981	−	1.44924i
$233$		−	16.4268i		−	1.07615i	−0.842896	−	0.538077i	$-0.819151\pi$
$233$		−	16.4268i		−	1.07615i	0.842896	−	0.538077i	$-0.180849\pi$
$234$	−0.177401	−	1.48770i	−0.0115970	−	0.0972537i
$235$	9.58892	−	9.58892i	0.625512	−	0.625512i
$236$	25.9582	+	15.8448i	1.68974	+	1.03141i
$237$	3.01990	+	3.01990i	0.196163	+	0.196163i
$238$	−9.38607	−	7.38607i	−0.608409	−	0.478768i
$239$	−14.6439			−0.947235			−0.473618	−	0.880731i	$-0.657052\pi$
$239$	−14.6439			−0.947235			−0.473618	+	0.880731i	$0.657052\pi$
$240$	3.55765	−	1.82843i	0.229645	−	0.118024i
$241$	23.3529			1.50430			0.752148	−	0.658995i	$-0.229018\pi$
$241$	23.3529			1.50430			0.752148	+	0.658995i	$0.229018\pi$
$242$	10.7720	+	8.47671i	0.692453	+	0.544904i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−13.3450	+	21.8628i	−0.854325	+	1.39962i
$245$	3.53553	−	3.53553i	0.225877	−	0.225877i
$246$	−1.46891	−	12.3184i	−0.0936545	−	0.785394i
$247$			2.82843i			0.179969i
$248$	−4.14148	−	1.89608i	−0.262984	−	0.120401i
$249$			4.40569i			0.279199i
$250$	−1.40426	+	0.167452i	−0.0888135	+	0.0105906i
$251$	−12.8085	+	12.8085i	−0.808467	+	0.808467i	−0.984402	−	0.175935i	$-0.943705\pi$
$251$	−12.8085	+	12.8085i	−0.808467	+	0.808467i	0.175935	+	0.984402i	$0.443705\pi$
$252$	−0.665096	−	2.74912i	−0.0418971	−	0.173178i
$253$	1.52099	+	1.52099i	0.0956236	+	0.0956236i
$254$	3.66122	−	4.65260i	0.229725	−	0.291930i
$255$	−5.97186			−0.373972
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	−22.3024			−1.39119			−0.695594	−	0.718436i	$-0.744859\pi$
$257$	−22.3024			−1.39119			−0.695594	+	0.718436i	$0.744859\pi$
$258$	0.920690	−	1.16999i	0.0573197	−	0.0728407i
$259$	−5.22746	−	5.22746i	−0.324818	−	0.324818i
$260$	0.498235	+	2.05941i	0.0308992	+	0.127719i
$261$	−5.88784	+	5.88784i	−0.364448	+	0.364448i
$262$	8.53422	−	1.01767i	0.527246	−	0.0628716i
$263$		−	2.49471i		−	0.153830i	−0.997038	−	0.0769151i	$-0.975493\pi$
$263$		−	2.49471i		−	0.153830i	0.997038	−	0.0769151i	$-0.0245070\pi$
$264$	−2.94059	−	1.34628i	−0.180981	−	0.0828578i
$265$		−	1.22079i		−	0.0749926i
$266$	0.632245	+	5.30205i	0.0387654	+	0.325090i
$267$	7.29539	−	7.29539i	0.446471	−	0.446471i
$268$	−4.34315	+	7.11529i	−0.265300	+	0.434636i
$269$	19.0031	+	19.0031i	1.15864	+	1.15864i	0.984768	+	0.173874i	$0.0556284\pi$
$269$	19.0031	+	19.0031i	1.15864	+	1.15864i	0.173874	+	0.984768i	$0.444372\pi$
$270$	−1.11137	−	0.874559i	−0.0676359	−	0.0532240i
$271$	21.7918			1.32376			0.661878	−	0.749612i	$-0.269760\pi$
$271$	21.7918			1.32376			0.661878	+	0.749612i	$0.269760\pi$
$272$	−21.2458	+	10.9191i	−1.28821	+	0.662068i
$273$	1.49824			0.0906773
$274$	−8.54088	−	6.72098i	−0.515974	−	0.406029i
$275$	0.808530	+	0.808530i	0.0487562	+	0.0487562i
$276$	3.21137	+	1.96021i	0.193302	+	0.117990i
$277$	−11.6401	+	11.6401i	−0.699385	+	0.699385i	−0.964278	−	0.264893i	$-0.914663\pi$
$277$	−11.6401	+	11.6401i	−0.699385	+	0.699385i	0.264893	+	0.964278i	$0.414663\pi$
$278$	2.57597	+	21.6022i	0.154496	+	1.29562i
$279$			1.61040i			0.0964119i
$280$	1.39432	+	3.74912i	0.0833263	+	0.224053i
$281$		−	1.55136i		−	0.0925462i	−0.998929	−	0.0462731i	$-0.985266\pi$
$281$		−	1.55136i		−	0.0925462i	0.998929	−	0.0462731i	$-0.0147344\pi$
$282$	−19.0429	+	2.27078i	−1.13399	+	0.135223i
$283$	18.5737	−	18.5737i	1.10409	−	1.10409i	0.110183	−	0.993911i	$-0.464856\pi$
$283$	18.5737	−	18.5737i	1.10409	−	1.10409i	0.993911	−	0.110183i	$-0.0351436\pi$
$284$	−13.1966	+	3.19265i	−0.783072	+	0.189449i
$285$	1.88784	+	1.88784i	0.111826	+	0.111826i
$286$	1.05941	−	1.34628i	0.0626444	−	0.0796072i
$287$	12.4057			0.732285
$288$	−5.55294	−	1.07931i	−0.327210	−	0.0635989i
$289$	18.6631			1.09783
$290$	7.28216	−	9.25402i	0.427623	−	0.543415i
$291$	2.63224	+	2.63224i	0.154305	+	0.154305i
$292$	4.52284	−	1.09422i	0.264679	−	0.0640341i
$293$	−10.5671	+	10.5671i	−0.617335	+	0.617335i	−0.944847	−	0.327512i	$-0.893790\pi$
$293$	−10.5671	+	10.5671i	−0.617335	+	0.617335i	0.327512	+	0.944847i	$0.393790\pi$
$294$	−7.02132	+	0.837260i	−0.409492	+	0.0488300i
$295$			15.2060i			0.885326i
$296$	−13.8581	+	5.15391i	−0.805487	+	0.299565i
$297$			1.14343i			0.0663488i
$298$	−2.85499	−	23.9421i	−0.165385	−	1.38693i
$299$	−1.40922	+	1.40922i	−0.0814974	+	0.0814974i
$300$	1.70711	+	1.04201i	0.0985599	+	0.0601605i
$301$	1.05275	+	1.05275i	0.0606794	+	0.0606794i
$302$	−4.68388	−	3.68583i	−0.269527	−	0.212096i
$303$	7.48881			0.430221
$304$	10.1680	+	3.26449i	0.583177	+	0.187231i
$305$	−12.8070			−0.733324
$306$	6.63696	+	5.22274i	0.379410	+	0.298564i
$307$	−11.4584	−	11.4584i	−0.653968	−	0.653968i	0.299978	−	0.953946i	$-0.403021\pi$
$307$	−11.4584	−	11.4584i	−0.653968	−	0.653968i	−0.953946	+	0.299978i	$0.903021\pi$
$308$	1.68499	−	2.76049i	0.0960114	−	0.157294i
$309$	11.2078	−	11.2078i	0.637592	−	0.637592i
$310$	−0.269664	−	2.26142i	−0.0153159	−	0.128440i
$311$		−	6.80196i		−	0.385704i	−0.981228	−	0.192852i	$-0.938226\pi$
$311$		−	6.80196i		−	0.385704i	0.981228	−	0.192852i	$-0.0617737\pi$
$312$	1.24735	−	2.72451i	0.0706174	−	0.154245i
$313$		−	15.8382i		−	0.895229i	−0.894227	−	0.447615i	$-0.852274\pi$
$313$		−	15.8382i		−	0.895229i	0.894227	−	0.447615i	$-0.147726\pi$
$314$	−18.9413	+	2.25866i	−1.06892	+	0.127464i
$315$	1.00000	−	1.00000i	0.0563436	−	0.0563436i
$316$	2.00852	+	8.30205i	0.112988	+	0.467027i
$317$	−9.37665	−	9.37665i	−0.526645	−	0.526645i	0.392925	−	0.919570i	$-0.371463\pi$
$317$	−9.37665	−	9.37665i	−0.526645	−	0.526645i	−0.919570	+	0.392925i	$0.871463\pi$
$318$	−1.06765	+	1.35675i	−0.0598711	+	0.0760829i
$319$	−9.52099			−0.533073
$320$	7.97852	+	0.585786i	0.446013	+	0.0327465i
$321$	1.89450			0.105741
$322$	−2.32666	+	2.95668i	−0.129660	+	0.164769i
$323$	−11.2739	−	11.2739i	−0.627297	−	0.627297i
$324$	0.470294	+	1.94392i	0.0261274	+	0.107996i
$325$	−0.749118	+	0.749118i	−0.0415536	+	0.0415536i
$326$	22.0051	−	2.62400i	1.21875	−	0.145330i
$327$			12.2654i			0.678278i
$328$	10.3283	−	22.5595i	0.570287	−	1.24564i
$329$		−	19.1778i		−	1.05731i
$330$	−0.191470	−	1.60568i	−0.0105401	−	0.0883900i
$331$	9.26059	−	9.26059i	0.509008	−	0.509008i	−0.405214	−	0.914222i	$-0.632803\pi$
$331$	9.26059	−	9.26059i	0.509008	−	0.509008i	0.914222	+	0.405214i	$0.132803\pi$
$332$	−4.59078	+	7.52099i	−0.251952	+	0.412768i
$333$	3.69637	+	3.69637i	0.202560	+	0.202560i
$334$	−13.0429	−	10.2637i	−0.713677	−	0.561606i
$335$	−4.16804			−0.227725
$336$	1.72922	−	5.38607i	0.0943367	−	0.293834i
$337$	2.99411			0.163099			0.0815497	−	0.996669i	$-0.474013\pi$
$337$	2.99411			0.163099			0.0815497	+	0.996669i	$0.474013\pi$
$338$	−13.2005	−	10.3877i	−0.718011	−	0.565016i
$339$	10.8363	+	10.8363i	0.588546	+	0.588546i
$340$	−10.1946	−	6.22274i	−0.552880	−	0.337476i
$341$	−1.30205	+	1.30205i	−0.0705101	+	0.0705101i
$342$	−0.447065	−	3.74912i	−0.0241745	−	0.202729i
$343$		−	16.9706i		−	0.916324i
$344$	2.79086	−	1.03794i	0.150473	−	0.0559618i
$345$			1.88118i			0.101279i
$346$	14.2742	−	1.70213i	0.767385	−	0.0915071i
$347$	−14.4455	+	14.4455i	−0.775474	+	0.775474i	−0.979058	−	0.203583i	$-0.934741\pi$
$347$	−14.4455	+	14.4455i	−0.775474	+	0.775474i	0.203583	+	0.979058i	$0.434741\pi$
$348$	−16.1864	+	3.91598i	−0.867680	+	0.209918i
$349$	−5.63668	−	5.63668i	−0.301724	−	0.301724i	0.539964	−	0.841688i	$-0.318438\pi$
$349$	−5.63668	−	5.63668i	−0.301724	−	0.301724i	−0.841688	+	0.539964i	$0.818438\pi$
$350$	−1.23681	+	1.57172i	−0.0661104	+	0.0840118i
$351$	−1.05941			−0.0565472
$352$	−3.61706	−	5.36237i	−0.192790	−	0.285815i
$353$	−26.9058			−1.43205			−0.716025	−	0.698074i	$-0.754040\pi$
$353$	−26.9058			−1.43205			−0.716025	+	0.698074i	$0.754040\pi$
$354$	13.2985	−	16.8995i	0.706809	−	0.898198i
$355$	−4.80029	−	4.80029i	−0.254773	−	0.254773i
$356$	20.0559	−	4.85213i	1.06296	−	0.257163i
$357$	−5.97186	+	5.97186i	−0.316064	+	0.316064i
$358$	−13.6003	+	1.62177i	−0.718798	+	0.0857133i
$359$		−	14.7533i		−	0.778649i	−0.921101	−	0.389325i	$-0.872708\pi$
$359$		−	14.7533i		−	0.778649i	0.921101	−	0.389325i	$-0.127292\pi$
$360$	−0.985930	−	2.65103i	−0.0519631	−	0.139721i
$361$		−	11.8721i		−	0.624849i
$362$	−1.95779	−	16.4182i	−0.102899	−	0.862921i
$363$	6.85367	−	6.85367i	0.359725	−	0.359725i
$364$	2.55765	+	1.56118i	0.134057	+	0.0818279i
$365$	1.64520	+	1.64520i	0.0861136	+	0.0861136i
$366$	14.2333	+	11.2004i	0.743986	+	0.585456i
$367$	−34.6779			−1.81017			−0.905086	−	0.425228i	$-0.860194\pi$
$367$	−34.6779			−1.81017			−0.905086	+	0.425228i	$0.860194\pi$
$368$	3.43959	+	6.69256i	0.179301	+	0.348874i
$369$	−8.77215			−0.456660
$370$	−5.80965	−	4.57172i	−0.302029	−	0.237672i
$371$	−1.22079	−	1.22079i	−0.0633803	−	0.0633803i
$372$	−1.67805	+	2.74912i	−0.0870028	+	0.142535i
$373$	10.8679	−	10.8679i	0.562721	−	0.562721i	−0.367359	−	0.930079i	$-0.619738\pi$
$373$	10.8679	−	10.8679i	0.562721	−	0.562721i	0.930079	+	0.367359i	$0.119738\pi$
$374$	1.14343	+	9.58892i	0.0591256	+	0.495831i
$375$			1.00000i			0.0516398i
$376$	−34.8745	−	15.9665i	−1.79851	−	0.823408i
$377$		−	8.82137i		−	0.454324i
$378$	−1.98593	+	0.236813i	−0.102145	+	0.0121803i
$379$	12.9374	−	12.9374i	0.664551	−	0.664551i	−0.291898	−	0.956449i	$-0.594287\pi$
$379$	12.9374	−	12.9374i	0.664551	−	0.664551i	0.956449	+	0.291898i	$0.0942868\pi$
$380$	1.25559	+	5.18989i	0.0644106	+	0.266236i
$381$	−2.96021	−	2.96021i	−0.151656	−	0.151656i
$382$	15.0805	−	19.1640i	0.771585	−	0.980515i
$383$	−12.1814			−0.622439			−0.311219	−	0.950338i	$-0.600737\pi$
$383$	−12.1814			−0.622439			−0.311219	+	0.950338i	$0.600737\pi$
$384$	−8.35480	−	7.62872i	−0.426354	−	0.389301i
$385$	1.61706			0.0824130
$386$	−23.4685	+	29.8233i	−1.19452	+	1.51797i
$387$	−0.744406	−	0.744406i	−0.0378403	−	0.0378403i
$388$	1.75070	+	7.23635i	0.0888781	+	0.367370i
$389$	−2.57246	+	2.57246i	−0.130429	+	0.130429i	−0.769308	−	0.638879i	$-0.779399\pi$
$389$	−2.57246	+	2.57246i	−0.130429	+	0.130429i	0.638879	+	0.769308i	$0.279399\pi$
$390$	1.48770	−	0.177401i	0.0753324	−	0.00898303i
$391$		−	11.2341i		−	0.568134i
$392$	−12.8586	−	5.88700i	−0.649457	−	0.297339i
$393$		−	6.07736i		−	0.306562i
$394$	−0.194604	−	1.63196i	−0.00980402	−	0.0822172i
$395$	−3.01990	+	3.01990i	−0.151948	+	0.151948i
$396$	−1.19147	+	1.95196i	−0.0598736	+	0.0980899i
$397$	8.94753	+	8.94753i	0.449064	+	0.449064i	0.895043	−	0.445979i	$-0.147145\pi$
$397$	8.94753	+	8.94753i	0.449064	+	0.449064i	−0.445979	+	0.895043i	$0.647145\pi$
$398$	22.5900	+	17.7765i	1.13234	+	0.891056i
$399$	3.77568			0.189020
$400$	1.82843	+	3.55765i	0.0914214	+	0.177882i
$401$	14.3306			0.715634			0.357817	−	0.933792i	$-0.383521\pi$
$401$	14.3306			0.715634			0.357817	+	0.933792i	$0.383521\pi$
$402$	4.63224	+	3.64520i	0.231035	+	0.181806i
$403$	−1.20638	−	1.20638i	−0.0600939	−	0.0600939i
$404$	12.7842	+	7.80342i	0.636038	+	0.388235i
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$	−1.97186	−	16.5362i	−0.0978618	−	0.820676i
$407$			5.97725i			0.296281i
$408$	5.88784	+	15.8316i	0.291491	+	0.783779i
$409$			11.2019i			0.553900i	0.960884	+	0.276950i	$0.0893237\pi$
$409$			11.2019i			0.553900i	−0.960884	+	0.276950i	$0.910676\pi$
$410$	12.3184	−	1.46891i	0.608363	−	0.0725445i
$411$	−5.43411	+	5.43411i	−0.268045	+	0.268045i
$412$	30.8117	−	7.45429i	1.51798	−	0.367246i
$413$	15.2060	+	15.2060i	0.748237	+	0.748237i
$414$	1.64520	−	2.09069i	0.0808571	−	0.102752i
$415$	−4.40569			−0.216267
$416$	4.96833	−	3.35127i	0.243592	−	0.164310i
$417$	15.3833			0.753324
$418$	2.66981	−	3.39274i	0.130585	−	0.165944i
$419$	−12.6405	−	12.6405i	−0.617528	−	0.617528i	0.327369	−	0.944897i	$-0.393838\pi$
$419$	−12.6405	−	12.6405i	−0.617528	−	0.617528i	−0.944897	+	0.327369i	$0.893838\pi$
$420$	2.74912	−	0.665096i	0.134143	−	0.0324534i
$421$	−2.83862	+	2.83862i	−0.138346	+	0.138346i	−0.772888	−	0.634542i	$-0.781189\pi$
$421$	−2.83862	+	2.83862i	−0.138346	+	0.138346i	0.634542	+	0.772888i	$0.281189\pi$
$422$	39.8428	−	4.75107i	1.93952	−	0.231278i
$423$			13.5608i			0.659348i
$424$	−3.23635	+	1.20362i	−0.157171	+	0.0584527i
$425$		−	5.97186i		−	0.289678i
$426$	1.13677	+	9.53304i	0.0550767	+	0.461877i
$427$	−12.8070	+	12.8070i	−0.619772	+	0.619772i
$428$	3.23412	+	1.97409i	0.156327	+	0.0954214i
$429$	−0.856566	−	0.856566i	−0.0413554	−	0.0413554i
$430$	1.16999	+	0.920690i	0.0564222	+	0.0443996i
$431$	−29.9874			−1.44444			−0.722222	−	0.691662i	$-0.756879\pi$
$431$	−29.9874			−1.44444			−0.722222	+	0.691662i	$0.756879\pi$
$432$	−1.22274	+	3.80853i	−0.0588293	+	0.183238i
$433$	−23.2176			−1.11577			−0.557884	−	0.829919i	$-0.688387\pi$
$433$	−23.2176			−1.11577			−0.557884	+	0.829919i	$0.688387\pi$
$434$	−2.53109	−	1.99176i	−0.121496	−	0.0956075i
$435$	−5.88784	−	5.88784i	−0.282300	−	0.282300i
$436$	−12.7807	+	20.9383i	−0.612083	+	1.00276i
$437$	−3.55136	+	3.55136i	−0.169884	+	0.169884i
$438$	−0.389604	−	3.26725i	−0.0186160	−	0.156115i
$439$			11.2110i			0.535070i	0.963548	+	0.267535i	$0.0862092\pi$
$439$			11.2110i			0.535070i	−0.963548	+	0.267535i	$0.913791\pi$
$440$	1.34628	−	2.94059i	0.0641814	−	0.140187i
$441$			5.00000i			0.238095i
$442$	−8.88431	+	1.05941i	−0.422584	+	0.0503911i
$443$	21.0684	−	21.0684i	1.00099	−	1.00099i	0.000992295	−	1.00000i	$-0.499684\pi$
$443$	21.0684	−	21.0684i	1.00099	−	1.00099i	1.00000		0.000992295i	$-0.000315857\pi$
$444$	2.45844	+	10.1618i	0.116672	+	0.482255i
$445$	7.29539	+	7.29539i	0.345835	+	0.345835i
$446$	9.33915	−	11.8680i	0.442222	−	0.561966i
$447$	−17.0496			−0.806418
$448$	8.56431	−	7.39274i	0.404626	−	0.349274i
$449$	20.6970			0.976753			0.488376	−	0.872633i	$-0.337589\pi$
$449$	20.6970			0.976753			0.488376	+	0.872633i	$0.337589\pi$
$450$	0.874559	−	1.11137i	0.0412271	−	0.0523906i
$451$	−7.09254	−	7.09254i	−0.333975	−	0.333975i
$452$	7.20716	+	29.7902i	0.338996	+	1.40121i
$453$	−2.98010	+	2.98010i	−0.140017	+	0.140017i
$454$	34.8558	−	4.15639i	1.63586	−	0.195069i
$455$			1.49824i			0.0702383i
$456$	3.14343	−	6.86599i	0.147205	−	0.321529i
$457$			18.7986i			0.879362i	0.898154	+	0.439681i	$0.144909\pi$
$457$			18.7986i			0.879362i	−0.898154	+	0.439681i	$0.855091\pi$
$458$	2.27595	+	19.0863i	0.106348	+	0.891845i
$459$	4.22274	−	4.22274i	0.197101	−	0.197101i
$460$	−1.96021	+	3.21137i	−0.0913950	+	0.149731i
$461$	−1.68943	−	1.68943i	−0.0786844	−	0.0786844i	0.666669	−	0.745354i	$-0.267719\pi$
$461$	−1.68943	−	1.68943i	−0.0786844	−	0.0786844i	−0.745354	+	0.666669i	$0.767719\pi$
$462$	−1.79715	−	1.41421i	−0.0836112	−	0.0657952i
$463$	−38.0434			−1.76803			−0.884014	−	0.467460i	$-0.845169\pi$
$463$	−38.0434			−1.76803			−0.884014	+	0.467460i	$0.845169\pi$
$464$	−31.7123	−	10.1814i	−1.47221	−	0.472658i
$465$	−1.61040			−0.0746803
$466$	−18.2562	−	14.3662i	−0.845704	−	0.665500i
$467$	15.2247	+	15.2247i	0.704515	+	0.704515i	0.965376	−	0.260861i	$-0.0840066\pi$
$467$	15.2247	+	15.2247i	0.704515	+	0.704515i	−0.260861	+	0.965376i	$0.584007\pi$
$468$	−1.80853	−	1.10392i	−0.0835993	−	0.0510287i
$469$	−4.16804	+	4.16804i	−0.192462	+	0.192462i
$470$	−2.27078	−	19.0429i	−0.104743	−	0.878385i
$471$			13.4884i			0.621513i
$472$	40.3115	−	14.9920i	1.85549	−	0.690064i
$473$		−	1.20375i		−	0.0553484i
$474$	5.99731	−	0.715151i	0.275465	−	0.0328480i
$475$	−1.88784	+	1.88784i	−0.0866200	+	0.0866200i
$476$	−16.4173	+	3.97186i	−0.752488	+	0.182050i
$477$	0.863230	+	0.863230i	0.0395246	+	0.0395246i
$478$	−12.8070	+	16.2748i	−0.585776	+	0.744393i
$479$	−13.0004			−0.594002			−0.297001	−	0.954877i	$-0.595987\pi$
$479$	−13.0004			−0.594002			−0.297001	+	0.954877i	$0.595987\pi$
$480$	1.07931	−	5.55294i	0.0492635	−	0.253456i
$481$	−5.53803			−0.252512
$482$	20.4235	−	25.9538i	0.930266	−	1.18216i
$483$	1.88118	+	1.88118i	0.0855965	+	0.0855965i
$484$	18.8416	−	4.55835i	0.856434	−	0.207198i
$485$	−2.63224	+	2.63224i	−0.119524	+	0.119524i
$486$	1.40426	−	0.167452i	0.0636987	−	0.00759578i
$487$		−	16.1068i		−	0.729868i	−0.931033	−	0.364934i	$-0.881092\pi$
$487$		−	16.1068i		−	0.729868i	0.931033	−	0.364934i	$-0.118908\pi$
$488$	12.6268	+	33.9516i	0.571587	+	1.53692i
$489$		−	15.6702i		−	0.708630i
$490$	−0.837260	−	7.02132i	−0.0378235	−	0.317191i
$491$	−16.9993	+	16.9993i	−0.767169	+	0.767169i	−0.977607	−	0.210438i	$-0.932511\pi$
$491$	−16.9993	+	16.9993i	−0.767169	+	0.767169i	0.210438	+	0.977607i	$0.432511\pi$
$492$	−14.9750	−	9.14067i	−0.675125	−	0.412093i
$493$	35.1614	+	35.1614i	1.58359	+	1.58359i
$494$	3.14343	+	2.47363i	0.141430	+	0.111294i
$495$	−1.14343			−0.0513935
$496$	−5.72922	+	2.94449i	−0.257250	+	0.132212i
$497$	−9.60058			−0.430645
$498$	4.89636	+	3.85304i	0.219411	+	0.172659i
$499$	−3.60373	−	3.60373i	−0.161325	−	0.161325i	0.621828	−	0.783154i	$-0.286390\pi$
$499$	−3.60373	−	3.60373i	−0.161325	−	0.161325i	−0.783154	+	0.621828i	$0.786390\pi$
$500$	−1.04201	+	1.70711i	−0.0466001	+	0.0763441i
$501$	−8.29852	+	8.29852i	−0.370751	+	0.370751i
$502$	3.03322	+	25.4368i	0.135379	+	1.13530i
$503$			25.4482i			1.13468i	0.823484	+	0.567340i	$0.192028\pi$
$503$			25.4482i			1.13468i	−0.823484	+	0.567340i	$0.807972\pi$
$504$	−3.63696	−	1.66510i	−0.162003	−	0.0741693i
$505$			7.48881i			0.333248i
$506$	3.02057	−	0.360189i	0.134281	−	0.0160124i
$507$	−8.39876	+	8.39876i	−0.373002	+	0.373002i
$508$	−1.96882	−	8.13795i	−0.0873523	−	0.361063i
$509$	8.08087	+	8.08087i	0.358178	+	0.358178i	0.863141	−	0.504963i	$-0.168494\pi$
$509$	8.08087	+	8.08087i	0.358178	+	0.358178i	−0.504963	+	0.863141i	$0.668494\pi$
$510$	−5.22274	+	6.63696i	−0.231267	+	0.293889i
$511$	3.29040			0.145559
$512$	−6.31333	−	21.7288i	−0.279013	−	0.960287i
$513$	−2.66981			−0.117875
$514$	−19.5048	+	24.7863i	−0.860319	+	1.09328i
$515$	11.2078	+	11.2078i	0.493876	+	0.493876i
$516$	−0.495101	−	2.04646i	−0.0217956	−	0.0900903i
$517$	−10.9643	+	10.9643i	−0.482209	+	0.482209i
$518$	−10.3814	+	1.23793i	−0.456131	+	0.0543915i
$519$		−	10.1649i		−	0.446189i
$520$	2.72451	+	1.24735i	0.119478	+	0.0547000i
$521$		−	10.7981i		−	0.473071i	−0.971623	−	0.236536i	$-0.923988\pi$
$521$		−	10.7981i		−	0.473071i	0.971623	−	0.236536i	$-0.0760120\pi$
$522$	1.39432	+	11.6928i	0.0610276	+	0.511782i
$523$	17.9785	−	17.9785i	0.786146	−	0.786146i	−0.194714	−	0.980860i	$-0.562378\pi$
$523$	17.9785	−	17.9785i	0.786146	−	0.786146i	0.980860	+	0.194714i	$0.0623779\pi$
$524$	6.33267	−	10.3747i	0.276644	−	0.453221i
$525$	1.00000	+	1.00000i	0.0436436	+	0.0436436i
$526$	−2.77254	−	2.18177i	−0.120889	−	0.0951295i
$527$	9.61706			0.418926
$528$	−4.06793	+	2.09069i	−0.177034	+	0.0909854i
$529$	19.4612			0.846138
$530$	−1.35675	−	1.06765i	−0.0589336	−	0.0463759i
$531$	−10.7523	−	10.7523i	−0.466608	−	0.466608i
$532$	6.44549	+	3.93430i	0.279447	+	0.170573i
$533$	6.57137	−	6.57137i	0.284638	−	0.284638i
$534$	−1.72764	−	14.4881i	−0.0747624	−	0.626963i
$535$			1.89450i			0.0819065i
$536$	4.10940	+	11.0496i	0.177499	+	0.477270i
$537$			9.68499i			0.417938i
$538$	37.7389	−	4.50019i	1.62704	−	0.194017i
$539$	−4.04265	+	4.04265i	−0.174129	+	0.174129i
$540$	−1.94392	+	0.470294i	−0.0836530	+	0.0202382i
$541$	6.61666	+	6.61666i	0.284473	+	0.284473i	0.834890	−	0.550417i	$-0.185531\pi$
$541$	6.61666	+	6.61666i	0.284473	+	0.284473i	−0.550417	+	0.834890i	$0.685531\pi$
$542$	19.0582	−	24.2188i	0.818619	−	1.04028i
$543$	−11.6917			−0.501737
$544$	−6.44549	+	33.1614i	−0.276348	+	1.42178i
$545$	−12.2654			−0.525392
$546$	1.31029	−	1.66510i	0.0560754	−	0.0712595i
$547$	−9.62205	−	9.62205i	−0.411409	−	0.411409i	0.470820	−	0.882229i	$-0.343958\pi$
$547$	−9.62205	−	9.62205i	−0.411409	−	0.411409i	−0.882229	+	0.470820i	$0.843958\pi$
$548$	−14.9390	+	3.61421i	−0.638163	+	0.154391i
$549$	9.05588	−	9.05588i	0.386496	−	0.386496i
$550$	1.60568	−	0.191470i	0.0684666	−	0.00816432i
$551$		−	22.2306i		−	0.947055i
$552$	4.98705	−	1.85471i	0.212263	−	0.0789416i
$553$			6.03979i			0.256838i
$554$	2.75652	+	23.1164i	0.117113	+	0.982122i
$555$	−3.69637	+	3.69637i	−0.156902	+	0.156902i
$556$	26.2610	+	16.0296i	1.11371	+	0.679806i
$557$	−2.50137	−	2.50137i	−0.105986	−	0.105986i	0.652125	−	0.758111i	$-0.273878\pi$
$557$	−2.50137	−	2.50137i	−0.105986	−	0.105986i	−0.758111	+	0.652125i	$0.773878\pi$
$558$	1.78975	+	1.40839i	0.0757661	+	0.0596217i
$559$	1.11529			0.0471719
$560$	5.38607	+	1.72922i	0.227603	+	0.0730729i
$561$	6.82843			0.288296
$562$	−1.72413	−	1.35675i	−0.0727282	−	0.0572312i
$563$	−2.20547	−	2.20547i	−0.0929496	−	0.0929496i	0.659103	−	0.752053i	$-0.270936\pi$
$563$	−2.20547	−	2.20547i	−0.0929496	−	0.0929496i	−0.752053	+	0.659103i	$0.770936\pi$
$564$	−14.1305	+	23.1497i	−0.595001	+	0.974778i
$565$	−10.8363	+	10.8363i	−0.455885	+	0.455885i
$566$	−4.39850	−	36.8861i	−0.184883	−	1.55044i
$567$			1.41421i			0.0593914i
$568$	−7.99294	+	17.4584i	−0.335376	+	0.732540i
$569$			17.5569i			0.736023i	0.929821	+	0.368011i	$0.119961\pi$
$569$			17.5569i			0.736023i	−0.929821	+	0.368011i	$0.880039\pi$
$570$	3.74912	−	0.447065i	0.157033	−	0.0187255i
$571$	−5.36237	+	5.36237i	−0.224408	+	0.224408i	−0.810352	−	0.585944i	$-0.800724\pi$
$571$	−5.36237	+	5.36237i	−0.224408	+	0.224408i	0.585944	+	0.810352i	$0.300724\pi$
$572$	−0.569699	−	2.35480i	−0.0238203	−	0.0984592i
$573$	−12.1930	−	12.1930i	−0.509371	−	0.509371i
$574$	10.8495	−	13.7873i	0.452850	−	0.575472i
$575$	−1.88118			−0.0784504
$576$	−6.05588	+	5.22746i	−0.252328	+	0.217811i
$577$	13.7422			0.572093			0.286047	−	0.958216i	$-0.407659\pi$
$577$	13.7422			0.572093			0.286047	+	0.958216i	$0.407659\pi$
$578$	16.3220	−	20.7417i	0.678906	−	0.862740i
$579$	18.9750	+	18.9750i	0.788574	+	0.788574i
$580$	−3.91598	−	16.1864i	−0.162602	−	0.672102i
$581$	−4.40569	+	4.40569i	−0.182779	+	0.182779i
$582$	5.22746	−	0.623349i	0.216685	−	0.0258387i
$583$			1.39589i			0.0578120i
$584$	2.73941	−	5.98352i	0.113358	−	0.247600i
$585$		−	1.05941i		−	0.0438013i
$586$	2.50242	+	20.9855i	0.103374	+	0.866902i
$587$	17.5608	−	17.5608i	0.724811	−	0.724811i	−0.244770	−	0.969581i	$-0.578712\pi$
$587$	17.5608	−	17.5608i	0.724811	−	0.724811i	0.969581	+	0.244770i	$0.0787125\pi$
$588$	−5.21005	+	8.53553i	−0.214859	+	0.351999i
$589$	−3.04017	−	3.04017i	−0.125268	−	0.125268i
$590$	16.8995	+	13.2985i	0.695741	+	0.547492i
$591$	−1.16215			−0.0478044
$592$	−6.39184	+	19.9089i	−0.262703	+	0.818252i
$593$	41.3973			1.69998			0.849992	−	0.526795i	$-0.176606\pi$
$593$	41.3973			1.69998			0.849992	+	0.526795i	$0.176606\pi$
$594$	1.27078	+	1.00000i	0.0521407	+	0.0410305i
$595$	−5.97186	−	5.97186i	−0.244822	−	0.244822i
$596$	−29.1055	−	17.7659i	−1.19221	−	0.727718i
$597$	14.3728	−	14.3728i	0.588241	−	0.588241i
$598$	0.333722	+	2.79862i	0.0136469	+	0.114444i
$599$		−	36.7651i		−	1.50218i	−0.660199	−	0.751090i	$-0.729528\pi$
$599$		−	36.7651i		−	1.50218i	0.660199	−	0.751090i	$-0.270472\pi$
$600$	2.65103	−	0.985930i	0.108228	−	0.0402504i
$601$			13.3396i			0.544134i	0.962278	+	0.272067i	$0.0877073\pi$
$601$			13.3396i			0.544134i	−0.962278	+	0.272067i	$0.912293\pi$
$602$	2.09069	−	0.249304i	0.0852100	−	0.0101609i
$603$	2.94725	−	2.94725i	0.120021	−	0.120021i
$604$	−8.19265	+	1.98205i	−0.333354	+	0.0806486i
$605$	6.85367	+	6.85367i	0.278641	+	0.278641i
$606$	6.54941	−	8.32285i	0.266051	−	0.338093i
$607$	−17.5393			−0.711898			−0.355949	−	0.934505i	$-0.615842\pi$
$607$	−17.5393			−0.711898			−0.355949	+	0.934505i	$0.615842\pi$
$608$	12.5206	−	8.44549i	0.507778	−	0.342510i
$609$	−11.7757			−0.477175
$610$	−11.2004	+	14.2333i	−0.453492	+	0.576289i
$611$	−10.1586	−	10.1586i	−0.410974	−	0.410974i
$612$	11.6088	−	2.80853i	0.469259	−	0.113528i
$613$	14.9538	−	14.9538i	0.603978	−	0.603978i	−0.337388	−	0.941366i	$-0.609543\pi$
$613$	14.9538	−	14.9538i	0.603978	−	0.603978i	0.941366	+	0.337388i	$0.109543\pi$
$614$	−22.7557	+	2.71351i	−0.918344	+	0.109508i
$615$		−	8.77215i		−	0.353727i
$616$	−1.59431	−	4.28687i	−0.0642365	−	0.172723i
$617$		−	7.04165i		−	0.283486i	−0.989903	−	0.141743i	$-0.954729\pi$
$617$		−	7.04165i		−	0.283486i	0.989903	−	0.141743i	$-0.0452707\pi$
$618$	−2.65416	−	22.2580i	−0.106766	−	0.895348i
$619$	14.2931	−	14.2931i	0.574490	−	0.574490i	−0.358890	−	0.933380i	$-0.616845\pi$
$619$	14.2931	−	14.2931i	0.574490	−	0.574490i	0.933380	+	0.358890i	$0.116845\pi$
$620$	−2.74912	−	1.67805i	−0.110407	−	0.0673921i
$621$	−1.33019	−	1.33019i	−0.0533788	−	0.0533788i
$622$	−7.55951	−	5.94871i	−0.303109	−	0.238522i
$623$	14.5908			0.584567
$624$	−1.93706	−	3.76901i	−0.0775444	−	0.150881i
$625$	−1.00000			−0.0400000
$626$	−17.6022	−	13.8515i	−0.703524	−	0.553616i
$627$	−2.15862	−	2.15862i	−0.0862069	−	0.0862069i
$628$	−14.0551	+	23.0262i	−0.560859	+	0.918844i
$629$	22.0742	−	22.0742i	0.880156	−	0.880156i
$630$	−0.236813	−	1.98593i	−0.00943485	−	0.0791214i
$631$		−	41.3531i		−	1.64624i	−0.567867	−	0.823121i	$-0.692231\pi$
$631$		−	41.3531i		−	1.64624i	0.567867	−	0.823121i	$-0.307769\pi$
$632$	10.9832	+	5.02842i	0.436890	+	0.200020i
$633$		−	28.3727i		−	1.12771i
$634$	−18.6214	+	2.22051i	−0.739549	+	0.0881878i
$635$	2.96021	−	2.96021i	0.117472	−	0.117472i
$636$	0.574131	+	2.37312i	0.0227658	+	0.0941004i
$637$	−3.74559	−	3.74559i	−0.148406	−	0.148406i
$638$	−8.32666	+	10.5814i	−0.329656	+	0.418920i
$639$	6.78863			0.268554
$640$	7.62872	−	8.35480i	0.301551	−	0.330253i
$641$	−14.3228			−0.565715			−0.282857	−	0.959162i	$-0.591282\pi$
$641$	−14.3228			−0.565715			−0.282857	+	0.959162i	$0.591282\pi$
$642$	1.65685	−	2.10550i	0.0653908	−	0.0830973i
$643$	13.4370	+	13.4370i	0.529902	+	0.529902i	0.920543	−	0.390641i	$-0.127747\pi$
$643$	13.4370	+	13.4370i	0.529902	+	0.529902i	−0.390641	+	0.920543i	$0.627747\pi$
$644$	1.25116	+	5.17157i	0.0493027	+	0.203789i
$645$	0.744406	−	0.744406i	0.0293109	−	0.0293109i
$646$	−22.3892	+	2.66981i	−0.880892	+	0.105042i
$647$			17.3231i			0.681043i	0.940237	+	0.340521i	$0.110604\pi$
$647$			17.3231i			0.681043i	−0.940237	+	0.340521i	$0.889396\pi$
$648$	2.57172	+	1.17740i	0.101027	+	0.0462527i
$649$		−	17.3870i		−	0.682501i
$650$	0.177401	+	1.48770i	0.00695823	+	0.0583522i
$651$	−1.61040	+	1.61040i	−0.0631164	+	0.0631164i
$652$	16.3285	−	26.7507i	0.639473	−	1.04764i
$653$	31.0148	+	31.0148i	1.21370	+	1.21370i	0.969800	+	0.243903i	$0.0784278\pi$
$653$	31.0148	+	31.0148i	1.21370	+	1.21370i	0.243903	+	0.969800i	$0.421572\pi$
$654$	13.6314	+	10.7268i	0.533030	+	0.419451i
$655$	6.07736			0.237462
$656$	−16.0392	−	31.2082i	−0.626227	−	1.21848i
$657$	−2.32666			−0.0907717
$658$	−21.3137	−	16.7721i	−0.830895	−	0.653846i
$659$	29.8050	+	29.8050i	1.16104	+	1.16104i	0.984249	+	0.176789i	$0.0565711\pi$
$659$	29.8050	+	29.8050i	1.16104	+	1.16104i	0.176789	+	0.984249i	$0.443429\pi$
$660$	−1.95196	−	1.19147i	−0.0759801	−	0.0463779i
$661$	−3.86546	+	3.86546i	−0.150349	+	0.150349i	−0.778274	−	0.627925i	$-0.783904\pi$
$661$	−3.86546	+	3.86546i	−0.150349	+	0.150349i	0.627925	+	0.778274i	$0.283904\pi$
$662$	−2.19303	−	18.3909i	−0.0852344	−	0.714782i
$663$			6.32666i			0.245707i
$664$	4.34371	+	11.6796i	0.168568	+	0.453257i
$665$			3.77568i			0.146415i
$666$	7.34073	−	0.875348i	0.284448	−	0.0339190i
$667$	11.0761	−	11.0761i	0.428867	−	0.428867i
$668$	−22.8136	+	5.51931i	−0.882685	+	0.213549i
$669$	−7.55098	−	7.55098i	−0.291938	−	0.291938i
$670$	−3.64520	+	4.63224i	−0.140826	+	0.178959i
$671$	14.6439			0.565322
$672$	−4.47363	−	6.63224i	−0.172574	−	0.255844i
$673$	−24.2478			−0.934685			−0.467342	−	0.884076i	$-0.654788\pi$
$673$	−24.2478			−0.934685			−0.467342	+	0.884076i	$0.654788\pi$
$674$	2.61852	−	3.32756i	0.100862	−	0.128173i
$675$	−0.707107	−	0.707107i	−0.0272166	−	0.0272166i
$676$	−23.0892	+	5.58598i	−0.888046	+	0.214846i
$677$	−9.11030	+	9.11030i	−0.350137	+	0.350137i	−0.860161	−	0.510023i	$-0.829637\pi$
$677$	−9.11030	+	9.11030i	−0.350137	+	0.350137i	0.510023	+	0.860161i	$0.329637\pi$
$678$	21.5201	−	2.56617i	0.826474	−	0.0985531i
$679$			5.26449i			0.202033i
$680$	−15.8316	+	5.88784i	−0.607113	+	0.225788i
$681$		−	24.8214i		−	0.951157i
$682$	0.308343	+	2.58579i	0.0118071	+	0.0990149i
$683$	−6.43216	+	6.43216i	−0.246120	+	0.246120i	−0.819376	−	0.573256i	$-0.805680\pi$
$683$	−6.43216	+	6.43216i	−0.246120	+	0.246120i	0.573256	+	0.819376i	$0.305680\pi$
$684$	−4.55765	−	2.78197i	−0.174266	−	0.106371i
$685$	−5.43411	−	5.43411i	−0.207627	−	0.207627i
$686$	−18.8606	−	14.8418i	−0.720101	−	0.566661i
$687$	13.5917			0.518555
$688$	1.28724	−	4.00942i	0.0490756	−	0.152858i
$689$	−1.29332			−0.0492716
$690$	2.09069	+	1.64520i	0.0795910	+	0.0626316i
$691$	8.79586	+	8.79586i	0.334610	+	0.334610i	0.854334	−	0.519724i	$-0.173965\pi$
$691$	8.79586	+	8.79586i	0.334610	+	0.334610i	−0.519724	+	0.854334i	$0.673965\pi$
$692$	10.5919	−	17.3525i	0.402644	−	0.659645i
$693$	−1.14343	+	1.14343i	−0.0434355	+	0.0434355i
$694$	3.42088	+	28.6877i	0.129855	+	1.08897i
$695$			15.3833i			0.583522i
$696$	−9.80382	+	21.4138i	−0.371613	+	0.811689i
$697$			52.3861i			1.98426i
$698$	−11.1940	+	1.33484i	−0.423701	+	0.0505244i
$699$	−11.6155	+	11.6155i	−0.439338	+	0.439338i
$700$	0.665096	+	2.74912i	0.0251383	+	0.103907i
$701$	−27.7073	−	27.7073i	−1.04649	−	1.04649i	−0.998865	−	0.0476269i	$-0.984834\pi$
$701$	−27.7073	−	27.7073i	−1.04649	−	1.04649i	−0.0476269	−	0.998865i	$-0.515166\pi$
$702$	−0.926518	+	1.17740i	−0.0349692	+	0.0444381i
$703$	−13.9563			−0.526372
$704$	−9.12291	−	0.669808i	−0.343833	−	0.0252443i
$705$	−13.5608			−0.510729
$706$	−23.5307	+	29.9023i	−0.885589	+	1.12539i
$707$	7.48881	+	7.48881i	0.281646	+	0.281646i
$708$	−7.15128	−	29.5592i	−0.268762	−	1.11090i
$709$	−25.2865	+	25.2865i	−0.949653	+	0.949653i	−0.998792	−	0.0491386i	$-0.984352\pi$
$709$	−25.2865	+	25.2865i	−0.949653	+	0.949653i	0.0491386	+	0.998792i	$0.484352\pi$
$710$	−9.53304	+	1.13677i	−0.357769	+	0.0426622i
$711$		−	4.27078i		−	0.160167i
$712$	12.1475	−	26.5330i	0.455248	−	0.994367i
$713$		−	3.02944i		−	0.113453i
$714$	1.41421	+	11.8597i	0.0529256	+	0.443838i
$715$	0.856566	−	0.856566i	0.0320338	−	0.0320338i
$716$	−10.0919	+	16.5333i	−0.377151	+	0.617879i
$717$	10.3548	+	10.3548i	0.386707	+	0.386707i
$718$	−16.3964	−	12.9026i	−0.611908	−	0.481522i
$719$	9.43253			0.351774			0.175887	−	0.984410i	$-0.443721\pi$
$719$	9.43253			0.351774			0.175887	+	0.984410i	$0.443721\pi$
$720$	−3.80853	−	1.22274i	−0.141936	−	0.0455690i
$721$	22.4157			0.834803
$722$	−13.1943	−	10.3829i	−0.491043	−	0.386410i
$723$	−16.5130	−	16.5130i	−0.614126	−	0.614126i
$724$	−19.9589	−	12.1828i	−0.741767	−	0.452771i
$725$	5.88784	−	5.88784i	0.218669	−	0.218669i
$726$	−1.62304	−	13.6109i	−0.0602366	−	0.505149i
$727$		−	1.10144i		−	0.0408501i	−0.999791	−	0.0204250i	$-0.993498\pi$
$727$		−	1.10144i		−	0.0408501i	0.999791	−	0.0204250i	$-0.00650195\pi$
$728$	3.97186	−	1.47716i	0.147207	−	0.0547470i
$729$		−	1.00000i		−	0.0370370i
$730$	3.26725	−	0.389604i	0.120926	−	0.0144199i
$731$	−4.44549	+	4.44549i	−0.164422	+	0.164422i
$732$	24.8957	−	6.02303i	0.920171	−	0.222618i
$733$	−18.2214	−	18.2214i	−0.673024	−	0.673024i	0.285388	−	0.958412i	$-0.407878\pi$
$733$	−18.2214	−	18.2214i	−0.673024	−	0.673024i	−0.958412	+	0.285388i	$0.907878\pi$
$734$	−30.3279	+	38.5400i	−1.11942	+	1.42254i
$735$	−5.00000			−0.184428
$736$	10.4460	+	2.03037i	0.385046	+	0.0748405i
$737$	4.76588			0.175553
$738$	−7.67176	+	9.74912i	−0.282401	+	0.358870i
$739$	−22.0953	−	22.0953i	−0.812788	−	0.812788i	0.172263	−	0.985051i	$-0.444892\pi$
$739$	−22.0953	−	22.0953i	−0.812788	−	0.812788i	−0.985051	+	0.172263i	$0.944892\pi$
$740$	−10.1618	+	2.45844i	−0.373553	+	0.0903741i
$741$	2.00000	−	2.00000i	0.0734718	−	0.0734718i
$742$	−2.42441	+	0.289099i	−0.0890028	+	0.0106132i
$743$			47.3029i			1.73538i	0.497109	+	0.867688i	$0.334395\pi$
$743$			47.3029i			1.73538i	−0.497109	+	0.867688i	$0.665605\pi$
$744$	1.58774	+	4.26920i	0.0582093	+	0.156517i
$745$		−	17.0496i		−	0.624649i
$746$	−2.57367	−	21.5830i	−0.0942287	−	0.790209i
$747$	3.11529	−	3.11529i	0.113983	−	0.113983i
$748$	11.6569	+	7.11529i	0.426217	+	0.260161i
$749$	1.89450	+	1.89450i	0.0692236	+	0.0692236i
$750$	1.11137	+	0.874559i	0.0405816	+	0.0319344i
$751$	−4.81234			−0.175605			−0.0878024	−	0.996138i	$-0.527984\pi$
$751$	−4.81234			−0.175605			−0.0878024	+	0.996138i	$0.527984\pi$
$752$	−48.2445	+	24.7949i	−1.75930	+	0.904177i
$753$	18.1140			0.660111
$754$	−9.80382	−	7.71480i	−0.357034	−	0.280957i
$755$	−2.98010	−	2.98010i	−0.108457	−	0.108457i
$756$	−1.47363	+	2.41421i	−0.0535953	+	0.0878041i
$757$	19.5838	−	19.5838i	0.711786	−	0.711786i	−0.255123	−	0.966909i	$-0.582116\pi$
$757$	19.5838	−	19.5838i	0.711786	−	0.711786i	0.966909	+	0.255123i	$0.0821159\pi$
$758$	−3.06375	−	25.6928i	−0.111280	−	0.933206i
$759$		−	2.15100i		−	0.0780763i
$760$	6.86599	+	3.14343i	0.249056	+	0.114024i
$761$		−	0.278003i		−	0.0100776i	−0.999987	−	0.00503881i	$-0.998396\pi$
$761$		−	0.278003i		−	0.0100776i	0.999987	−	0.00503881i	$-0.00160391\pi$
$762$	−5.87876	+	0.701015i	−0.212965	+	0.0253951i
$763$	−12.2654	+	12.2654i	−0.444037	+	0.444037i
$764$	−8.10953	−	33.5201i	−0.293393	−	1.21271i
$765$	4.22274	+	4.22274i	0.152674	+	0.152674i
$766$	−10.6533	+	13.5380i	−0.384920	+	0.489149i
$767$	16.1094			0.581677
$768$	−15.7851	+	2.61353i	−0.569596	+	0.0943076i
$769$	−20.5808			−0.742162			−0.371081	−	0.928600i	$-0.621013\pi$
$769$	−20.5808			−0.742162			−0.371081	+	0.928600i	$0.621013\pi$
$770$	1.41421	−	1.79715i	0.0509647	−	0.0647649i
$771$	15.7702	+	15.7702i	0.567950	+	0.567950i
$772$	12.6202	+	52.1645i	0.454211	+	1.87744i
$773$	18.3427	−	18.3427i	0.659743	−	0.659743i	−0.295576	−	0.955319i	$-0.595512\pi$
$773$	18.3427	−	18.3427i	0.659743	−	0.659743i	0.955319	+	0.295576i	$0.0955117\pi$
$774$	−1.47834	+	0.176285i	−0.0531378	+	0.00633643i
$775$		−	1.61040i		−	0.0578471i
$776$	9.57336	+	4.38294i	0.343664	+	0.157338i
$777$			7.39274i			0.265213i
$778$	0.609191	+	5.10872i	0.0218406	+	0.183157i
$779$	16.5604	−	16.5604i	0.593338	−	0.593338i
$780$	1.10392	−	1.80853i	0.0395266	−	0.0647558i
$781$	5.48881	+	5.48881i	0.196405	+	0.196405i
$782$	−12.4853	−	9.82490i	−0.446473	−	0.351338i
$783$	8.32666			0.297571
$784$	−17.7882	+	9.14214i	−0.635294	+	0.326505i
$785$	−13.4884			−0.481422
$786$	−6.75420	−	5.31501i	−0.240914	−	0.189580i
$787$	21.0313	+	21.0313i	0.749684	+	0.749684i	0.974420	−	0.224736i	$-0.0721519\pi$
$787$	21.0313	+	21.0313i	0.749684	+	0.749684i	−0.224736	+	0.974420i	$0.572152\pi$
$788$	−1.98391	−	1.21097i	−0.0706740	−	0.0431391i
$789$	−1.76402	+	1.76402i	−0.0628009	+	0.0628009i
$790$	0.715151	+	5.99731i	0.0254439	+	0.213375i
$791$			21.6725i			0.770587i
$792$	1.12735	+	3.03127i	0.0400585	+	0.107712i
$793$			13.5678i			0.481808i
$794$	17.7692	−	2.11889i	0.630604	−	0.0751966i
$795$	−0.863230	+	0.863230i	−0.0306156	+	0.0306156i
$796$	39.5126	−	9.55932i	1.40049	−	0.338821i
$797$	−34.4451	−	34.4451i	−1.22011	−	1.22011i	−0.967593	−	0.252515i	$-0.918742\pi$
$797$	−34.4451	−	34.4451i	−1.22011	−	1.22011i	−0.252515	−	0.967593i	$-0.581258\pi$
$798$	3.30205	−	4.19618i	0.116891	−	0.148543i
$799$	80.9831			2.86498
$800$	5.55294	+	1.07931i	0.196326	+	0.0381594i
$801$	−10.3172			−0.364542
$802$	12.5329	−	15.9266i	0.442553	−	0.562387i
$803$	−1.88118	−	1.88118i	−0.0663852	−	0.0663852i
$804$	8.10234	−	1.96021i	0.285748	−	0.0691311i
$805$	−1.88118	+	1.88118i	−0.0663027	+	0.0663027i
$806$	−2.39578	+	0.285685i	−0.0843877	+	0.0100628i
$807$		−	26.8745i		−	0.946027i
$808$	19.8530	−	7.38345i	0.698427	−	0.259749i
$809$			4.84727i			0.170421i	0.996363	+	0.0852106i	$0.0271563\pi$
$809$			4.84727i			0.170421i	−0.996363	+	0.0852106i	$0.972844\pi$
$810$	0.167452	+	1.40426i	0.00588366	+	0.0493408i
$811$	−37.5774	+	37.5774i	−1.31952	+	1.31952i	−0.405369	+	0.914153i	$0.632857\pi$
$811$	−37.5774	+	37.5774i	−1.31952	+	1.31952i	−0.914153	+	0.405369i	$0.867143\pi$
$812$	−20.1023	−	12.2704i	−0.705454	−	0.430606i
$813$	−15.4091	−	15.4091i	−0.540421	−	0.540421i
$814$	6.64294	+	5.22746i	0.232835	+	0.183222i
$815$	15.6702			0.548903
$816$	22.7440	+	7.30205i	0.796200	+	0.255623i
$817$	2.81064			0.0983317
$818$	12.4495	+	9.79676i	0.435287	+	0.342536i
$819$	−1.05941	−	1.05941i	−0.0370189	−	0.0370189i
$820$	9.14067	−	14.9750i	0.319206	−	0.522950i
$821$	−6.23725	+	6.23725i	−0.217682	+	0.217682i	−0.807521	−	0.589839i	$-0.799191\pi$
$821$	−6.23725	+	6.23725i	−0.217682	+	0.217682i	0.589839	+	0.807521i	$0.299191\pi$
$822$	1.28687	+	10.7918i	0.0448847	+	0.376406i
$823$		−	20.6905i		−	0.721225i	−0.932716	−	0.360613i	$-0.882568\pi$
$823$		−	20.6905i		−	0.721225i	0.932716	−	0.360613i	$-0.117432\pi$
$824$	18.6621	−	40.7624i	0.650126	−	1.42003i
$825$		−	1.14343i		−	0.0398093i
$826$	30.1980	−	3.60097i	1.05072	−	0.125294i
$827$	−5.53413	+	5.53413i	−0.192440	+	0.192440i	−0.796750	−	0.604309i	$-0.793449\pi$
$827$	−5.53413	+	5.53413i	−0.192440	+	0.192440i	0.604309	+	0.796750i	$0.293449\pi$
$828$	−0.884705	−	3.65685i	−0.0307456	−	0.127084i
$829$	−21.2582	−	21.2582i	−0.738328	−	0.738328i	0.233926	−	0.972254i	$-0.424842\pi$
$829$	−21.2582	−	21.2582i	−0.738328	−	0.738328i	−0.972254	+	0.233926i	$0.924842\pi$
$830$	−3.85304	+	4.89636i	−0.133741	+	0.169955i
$831$	16.4616			0.571046
$832$	0.620589	−	8.45255i	0.0215151	−	0.293039i
$833$	29.8593			1.03456
$834$	13.4536	−	17.0966i	0.465860	−	0.592006i
$835$	−8.29852	−	8.29852i	−0.287182	−	0.287182i
$836$	−1.43569	−	5.93430i	−0.0496543	−	0.205242i
$837$	1.13872	−	1.13872i	0.0393600	−	0.0393600i
$838$	−25.1031	+	2.99343i	−0.867173	+	0.103406i
$839$		−	3.55688i		−	0.122797i	−0.998113	−	0.0613985i	$-0.980444\pi$
$839$		−	3.55688i		−	0.122797i	0.998113	−	0.0613985i	$-0.0195561\pi$
$840$	1.66510	−	3.63696i	0.0574513	−	0.125487i
$841$			40.3333i			1.39080i
$842$	0.672222	+	5.63730i	0.0231663	+	0.194274i
$843$	−1.09698	+	1.09698i	−0.0377818	+	0.0377818i
$844$	29.5647	−	48.4353i	1.01766	−	1.66721i
$845$	−8.39876	−	8.39876i	−0.288926	−	0.288926i
$846$	15.0711	+	11.8597i	0.518154	+	0.407745i
$847$	13.7073			0.470990
$848$	−1.49271	+	4.64942i	−0.0512600	+	0.159662i
$849$	−26.2672			−0.901489
$850$	−6.63696	−	5.22274i	−0.227646	−	0.179139i
$851$	−6.95352	−	6.95352i	−0.238364	−	0.238364i
$852$	11.5889	+	7.07383i	0.397030	+	0.242345i
$853$	7.41187	−	7.41187i	0.253777	−	0.253777i	−0.568740	−	0.822517i	$-0.692569\pi$
$853$	7.41187	−	7.41187i	0.253777	−	0.253777i	0.822517	+	0.568740i	$0.192569\pi$
$854$	3.03285	+	25.4337i	0.103782	+	0.870324i
$855$		−	2.66981i		−	0.0913055i
$856$	5.02238	−	1.86785i	0.171661	−	0.0638417i
$857$			31.1426i			1.06381i	0.846803	+	0.531906i	$0.178524\pi$
$857$			31.1426i			1.06381i	−0.846803	+	0.531906i	$0.821476\pi$
$858$	−1.70108	+	0.202846i	−0.0580739	+	0.00692505i
$859$	32.0035	−	32.0035i	1.09195	−	1.09195i	0.0966247	−	0.995321i	$-0.469195\pi$
$859$	32.0035	−	32.0035i	1.09195	−	1.09195i	0.995321	−	0.0966247i	$-0.0308047\pi$
$860$	2.04646	−	0.495101i	0.0697837	−	0.0168828i
$861$	−8.77215	−	8.77215i	−0.298954	−	0.298954i
$862$	−26.2258	+	33.3272i	−0.893253	+	1.13513i
$863$	−29.2347			−0.995160			−0.497580	−	0.867418i	$-0.665778\pi$
$863$	−29.2347			−0.995160			−0.497580	+	0.867418i	$0.665778\pi$
$864$	3.16333	+	4.68971i	0.107619	+	0.159547i
$865$	10.1649			0.345617
$866$	−20.3052	+	25.8034i	−0.689998	+	0.876836i
$867$	−13.1968	−	13.1968i	−0.448188	−	0.448188i
$868$	−4.42717	+	1.07107i	−0.150268	+	0.0363544i
$869$	3.45305	−	3.45305i	0.117137	−	0.117137i
$870$	−11.6928	+	1.39432i	−0.396424	+	0.0472717i
$871$			4.41568i			0.149619i
$872$	12.0928	+	32.5159i	0.409515	+	1.10113i
$873$		−	3.72256i		−	0.125989i
$874$	0.841007	+	7.05275i	0.0284475	+	0.238563i
$875$	−1.00000	+	1.00000i	−0.0338062	+	0.0338062i
$876$	−3.97186	−	2.42441i	−0.134197	−	0.0819131i
$877$	11.9832	+	11.9832i	0.404645	+	0.404645i	0.879866	−	0.475221i	$-0.157632\pi$
$877$	11.9832	+	11.9832i	0.404645	+	0.404645i	−0.475221	+	0.879866i	$0.657632\pi$
$878$	12.4596	+	9.80465i	0.420490	+	0.330891i
$879$	14.9441			0.504052
$880$	−2.09069	−	4.06793i	−0.0704770	−	0.137130i
$881$	31.6194			1.06529			0.532643	−	0.846340i	$-0.321199\pi$
$881$	31.6194			1.06529			0.532643	+	0.846340i	$0.321199\pi$
$882$	5.55686	+	4.37279i	0.187109	+	0.147240i
$883$	−9.32520	−	9.32520i	−0.313818	−	0.313818i	0.532569	−	0.846387i	$-0.321227\pi$
$883$	−9.32520	−	9.32520i	−0.313818	−	0.313818i	−0.846387	+	0.532569i	$0.821227\pi$
$884$	−6.59245	+	10.8003i	−0.221728	+	0.363253i
$885$	10.7523	−	10.7523i	0.361433	−	0.361433i
$886$	−4.98928	−	41.8405i	−0.167618	−	1.40566i
$887$			44.8049i			1.50440i	0.658934	+	0.752200i	$0.271007\pi$
$887$			44.8049i			1.50440i	−0.658934	+	0.752200i	$0.728993\pi$
$888$	13.4435	+	6.15481i	0.451135	+	0.206542i
$889$		−	5.92041i		−	0.198564i
$890$	14.4881	−	1.72764i	0.485643	−	0.0579107i
$891$	0.808530	−	0.808530i	0.0270868	−	0.0270868i
$892$	−5.02213	−	20.7585i	−0.168153	−	0.695047i
$893$	−25.6006	−	25.6006i	−0.856691	−	0.856691i
$894$	−14.9109	+	18.9484i	−0.498694	+	0.633730i
$895$	−9.68499			−0.323734
$896$	−0.726086	−	15.9835i	−0.0242568	−	0.533972i
$897$	1.99294			0.0665423
$898$	18.1008	−	23.0021i	0.604030	−	0.767589i
$899$	9.48175	+	9.48175i	0.316234	+	0.316234i
$900$	−0.470294	−	1.94392i	−0.0156765	−	0.0647973i
$901$	5.15509	−	5.15509i	0.171741	−	0.171741i
$902$	−14.0853	+	1.67961i	−0.468989	+	0.0559247i
$903$		−	1.48881i		−	0.0495445i
$904$	39.4111	+	18.0434i	1.31079	+	0.600116i
$905$		−	11.6917i		−	0.388644i
$906$	0.705727	+	5.91828i	0.0234462	+	0.196622i
$907$	−19.4040	+	19.4040i	−0.644299	+	0.644299i	−0.951609	−	0.307310i	$-0.900571\pi$
$907$	−19.4040	+	19.4040i	−0.644299	+	0.644299i	0.307310	+	0.951609i	$0.400571\pi$
$908$	25.8641	−	42.3727i	0.858331	−	1.40619i
$909$	−5.29539	−	5.29539i	−0.175637	−	0.175637i
$910$	1.66510	+	1.31029i	0.0551974	+	0.0434358i
$911$	44.4094			1.47135			0.735674	−	0.677336i	$-0.236866\pi$
$911$	44.4094			1.47135			0.735674	+	0.677336i	$0.236866\pi$
$912$	−4.88155	−	9.49824i	−0.161644	−	0.314518i
$913$	5.03762			0.166721
$914$	20.8922	+	16.4405i	0.691054	+	0.543803i
$915$	9.05588	+	9.05588i	0.299378	+	0.299378i
$916$	23.2025	+	14.1627i	0.766631	+	0.467948i
$917$	6.07736	−	6.07736i	0.200692	−	0.200692i
$918$	−1.00000	−	8.38607i	−0.0330049	−	0.276782i
$919$			26.3092i			0.867861i	0.900946	+	0.433931i	$0.142874\pi$
$919$			26.3092i			0.867861i	−0.900946	+	0.433931i	$0.857126\pi$
$920$	1.85471	+	4.98705i	0.0611479	+	0.164418i
$921$			16.2047i			0.533962i
$922$	−3.35508	+	0.400078i	−0.110494	+	0.0131759i
$923$	−5.08548	+	5.08548i	−0.167391	+	0.167391i
$924$	−3.14343	+	0.760493i	−0.103411	+	0.0250184i
$925$	−3.69637	−	3.69637i	−0.121536	−	0.121536i
$926$	−33.2712	+	42.2804i	−1.09336	+	1.38942i
$927$	−15.8503			−0.520591
$928$	−39.0496	+	26.3400i	−1.28187	+	0.864653i
$929$	−41.9008			−1.37472			−0.687360	−	0.726317i	$-0.741230\pi$
$929$	−41.9008			−1.37472			−0.687360	+	0.726317i	$0.741230\pi$
$930$	−1.40839	+	1.78975i	−0.0461828	+	0.0586882i
$931$	−9.43920	−	9.43920i	−0.309357	−	0.309357i
$932$	−31.9323	+	7.72541i	−1.04598	+	0.253054i
$933$	−4.80971	+	4.80971i	−0.157463	+	0.157463i
$934$	30.2352	−	3.60540i	0.989325	−	0.117972i
$935$			6.82843i			0.223313i
$936$	−2.80853	+	1.04451i	−0.0917997	+	0.0341408i
$937$		−	50.1251i		−	1.63752i	−0.574139	−	0.818758i	$-0.694663\pi$
$937$		−	50.1251i		−	1.63752i	0.574139	−	0.818758i	$-0.305337\pi$
$938$	0.987046	+	8.27744i	0.0322282	+	0.270268i
$939$	−11.1993	+	11.1993i	−0.365476	+	0.365476i
$940$	−23.1497	−	14.1305i	−0.755060	−	0.460885i
$941$	17.7315	+	17.7315i	0.578029	+	0.578029i	0.934360	−	0.356331i	$-0.115972\pi$
$941$	17.7315	+	17.7315i	0.578029	+	0.578029i	−0.356331	+	0.934360i	$0.615972\pi$
$942$	14.9906	+	11.7964i	0.488422	+	0.384348i
$943$	16.5020			0.537378
$944$	18.5930	−	57.9124i	0.605151	−	1.88489i
$945$	−1.41421			−0.0460044
$946$	−1.33781	−	1.05275i	−0.0434960	−	0.0342278i
$947$	−8.29393	−	8.29393i	−0.269516	−	0.269516i	0.559389	−	0.828905i	$-0.311036\pi$
$947$	−8.29393	−	8.29393i	−0.269516	−	0.269516i	−0.828905	+	0.559389i	$0.811036\pi$
$948$	4.45020	−	7.29068i	0.144536	−	0.236790i
$949$	1.74294	−	1.74294i	0.0565783	−	0.0565783i
$950$	0.447065	+	3.74912i	0.0145047	+	0.121637i
$951$			13.2606i			0.430004i
$952$	−9.94372	+	21.7194i	−0.322278	+	0.703930i
$953$			22.6285i			0.733010i	0.930416	+	0.366505i	$0.119446\pi$
$953$			22.6285i			0.733010i	−0.930416	+	0.366505i	$0.880554\pi$
$954$	1.71431	−	0.204424i	0.0555030	−	0.00661847i
$955$	12.1930	−	12.1930i	0.394557	−	0.394557i
$956$	6.88694	+	28.4666i	0.222739	+	0.920675i
$957$	6.73235	+	6.73235i	0.217626	+	0.217626i
$958$	−11.3696	+	14.4482i	−0.367335	+	0.466802i
$959$	−10.8682			−0.350953
$960$	−5.22746	−	6.05588i	−0.168715	−	0.195453i
$961$	−28.4066			−0.916343
$962$	−4.84333	+	6.15481i	−0.156155	+	0.198439i
$963$	−1.33962	−	1.33962i	−0.0431685	−	0.0431685i
$964$	−10.9827	−	45.3962i	−0.353730	−	1.46211i
$965$	−18.9750	+	18.9750i	−0.610827	+	0.610827i
$966$	3.73588	−	0.445487i	0.120200	−	0.0143333i
$967$		−	41.6144i		−	1.33823i	−0.743159	−	0.669115i	$-0.766673\pi$
$967$		−	41.6144i		−	1.33823i	0.743159	−	0.669115i	$-0.233327\pi$
$968$	11.4120	−	24.9265i	0.366796	−	0.801169i
$969$			15.9437i			0.512186i
$970$	0.623349	+	5.22746i	0.0200145	+	0.167843i
$971$	21.7691	−	21.7691i	0.698604	−	0.698604i	−0.265505	−	0.964109i	$-0.585539\pi$
$971$	21.7691	−	21.7691i	0.698604	−	0.698604i	0.964109	+	0.265505i	$0.0855388\pi$
$972$	1.04201	−	1.70711i	0.0334225	−	0.0547555i
$973$	15.3833	+	15.3833i	0.493166	+	0.493166i
$974$	−17.9006	−	14.0863i	−0.573573	−	0.451355i
$975$	1.05941			0.0339283
$976$	48.7757	+	15.6596i	1.56127	+	0.501252i
$977$	17.3840			0.556164			0.278082	−	0.960557i	$-0.410301\pi$
$977$	17.3840			0.556164			0.278082	+	0.960557i	$0.410301\pi$
$978$	−17.4154	−	13.7045i	−0.556883	−	0.438221i
$979$	−8.34179	−	8.34179i	−0.266605	−	0.266605i
$980$	−8.53553	−	5.21005i	−0.272658	−	0.166429i
$981$	8.67294	−	8.67294i	0.276906	−	0.276906i
$982$	4.02566	+	33.7595i	0.128464	+	1.07731i
$983$			4.91428i			0.156741i	0.996924	+	0.0783707i	$0.0249718\pi$
$983$			4.91428i			0.156741i	−0.996924	+	0.0783707i	$0.975028\pi$
$984$	−23.2552	+	8.64873i	−0.741349	+	0.275711i
$985$		−	1.16215i		−	0.0370291i
$986$	69.8280	−	8.32666i	2.22378	−	0.265175i
$987$	−13.5608	+	13.5608i	−0.431644	+	0.431644i
$988$	5.49824	−	1.33019i	0.174922	−	0.0423190i
$989$	1.40036	+	1.40036i	0.0445288	+	0.0445288i
$990$	−1.00000	+	1.27078i	−0.0317821	+	0.0403880i
$991$	23.5415			0.747822			0.373911	−	0.927465i	$-0.378017\pi$
$991$	23.5415			0.747822			0.373911	+	0.927465i	$0.378017\pi$
$992$	−1.73812	+	8.94242i	−0.0551852	+	0.283922i
$993$	−13.0964			−0.415603
$994$	−8.39627	+	10.6698i	−0.266313	+	0.338426i
$995$	14.3728	+	14.3728i	0.455650	+	0.455650i
$996$	8.56431	−	2.07197i	0.271371	−	0.0656529i
$997$	−19.6097	+	19.6097i	−0.621046	+	0.621046i	−0.945799	−	0.324753i	$-0.894719\pi$
$997$	−19.6097	+	19.6097i	−0.621046	+	0.621046i	0.324753	+	0.945799i	$0.394719\pi$
$998$	−7.15676	+	0.853410i	−0.226543	+	0.0270142i
$999$		−	5.22746i		−	0.165389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.b.61.4	✓	8
3.2	odd	2		720.2.t.b.541.1		8
4.3	odd	2		960.2.s.b.721.4		8
8.3	odd	2		1920.2.s.d.1441.1		8
8.5	even	2		1920.2.s.c.1441.4		8
12.11	even	2		2880.2.t.b.721.1		8
16.3	odd	4		1920.2.s.d.481.1		8
16.5	even	4	inner	240.2.s.b.181.4	yes	8
16.11	odd	4		960.2.s.b.241.4		8
16.13	even	4		1920.2.s.c.481.4		8
48.5	odd	4		720.2.t.b.181.1		8
48.11	even	4		2880.2.t.b.2161.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.b.61.4	✓	8	1.1	even	1	trivial
240.2.s.b.181.4	yes	8	16.5	even	4	inner
720.2.t.b.181.1		8	48.5	odd	4
720.2.t.b.541.1		8	3.2	odd	2
960.2.s.b.241.4		8	16.11	odd	4
960.2.s.b.721.4		8	4.3	odd	2
1920.2.s.c.481.4		8	16.13	even	4
1920.2.s.c.1441.4		8	8.5	even	2
1920.2.s.d.481.1		8	16.3	odd	4
1920.2.s.d.1441.1		8	8.3	odd	2
2880.2.t.b.721.1		8	12.11	even	2
2880.2.t.b.2161.1		8	48.11	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.874559 - 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 - 1.94392i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.40426 + 0.167452i) q^{6} -1.41421i q^{7} +(-2.57172 - 1.17740i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.874559 - 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 - 1.94392i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.40426 + 0.167452i) q^{6} -1.41421i q^{7} +(-2.57172 - 1.17740i) q^{8} +1.00000i q^{9} +(-0.167452 - 1.40426i) q^{10} +(-0.808530 + 0.808530i) q^{11} +(-1.04201 + 1.70711i) q^{12} +(-0.749118 - 0.749118i) q^{13} +(-1.57172 - 1.23681i) q^{14} -1.00000 q^{15} +(-3.55765 + 1.82843i) q^{16} +5.97186 q^{17} +(1.11137 + 0.874559i) q^{18} +(-1.88784 - 1.88784i) q^{19} +(-1.70711 - 1.04201i) q^{20} +(-1.00000 + 1.00000i) q^{21} +(0.191470 + 1.60568i) q^{22} -1.88118i q^{23} +(0.985930 + 2.65103i) q^{24} -1.00000i q^{25} +(-1.48770 + 0.177401i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.74912 + 0.665096i) q^{28} +(5.88784 + 5.88784i) q^{29} +(-0.874559 + 1.11137i) q^{30} +1.61040 q^{31} +(-1.07931 + 5.55294i) q^{32} +1.14343 q^{33} +(5.22274 - 6.63696i) q^{34} +(-1.00000 - 1.00000i) q^{35} +(1.94392 - 0.470294i) q^{36} +(3.69637 - 3.69637i) q^{37} +(-3.74912 + 0.447065i) q^{38} +1.05941i q^{39} +(-2.65103 + 0.985930i) q^{40} +8.77215i q^{41} +(0.236813 + 1.98593i) q^{42} +(-0.744406 + 0.744406i) q^{43} +(1.95196 + 1.19147i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-2.09069 - 1.64520i) q^{46} +13.5608 q^{47} +(3.80853 + 1.22274i) q^{48} +5.00000 q^{49} +(-1.11137 - 0.874559i) q^{50} +(-4.22274 - 4.22274i) q^{51} +(-1.10392 + 1.80853i) q^{52} +(0.863230 - 0.863230i) q^{53} +(-0.167452 - 1.40426i) q^{54} +1.14343i q^{55} +(-1.66510 + 3.63696i) q^{56} +2.66981i q^{57} +(11.6928 - 1.39432i) q^{58} +(-10.7523 + 10.7523i) q^{59} +(0.470294 + 1.94392i) q^{60} +(-9.05588 - 9.05588i) q^{61} +(1.40839 - 1.78975i) q^{62} +1.41421 q^{63} +(5.22746 + 6.05588i) q^{64} -1.05941 q^{65} +(1.00000 - 1.27078i) q^{66} +(-2.94725 - 2.94725i) q^{67} +(-2.80853 - 11.6088i) q^{68} +(-1.33019 + 1.33019i) q^{69} +(-1.98593 + 0.236813i) q^{70} -6.78863i q^{71} +(1.17740 - 2.57172i) q^{72} +2.32666i q^{73} +(-0.875348 - 7.34073i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(-2.78197 + 4.55765i) q^{76} +(1.14343 + 1.14343i) q^{77} +(1.17740 + 0.926518i) q^{78} -4.27078 q^{79} +(-1.22274 + 3.80853i) q^{80} -1.00000 q^{81} +(9.74912 + 7.67176i) q^{82} +(-3.11529 - 3.11529i) q^{83} +(2.41421 + 1.47363i) q^{84} +(4.22274 - 4.22274i) q^{85} +(0.176285 + 1.47834i) q^{86} -8.32666i q^{87} +(3.03127 - 1.12735i) q^{88} +10.3172i q^{89} +(1.40426 - 0.167452i) q^{90} +(-1.05941 + 1.05941i) q^{91} +(-3.65685 + 0.884705i) q^{92} +(-1.13872 - 1.13872i) q^{93} +(11.8597 - 15.0711i) q^{94} -2.66981 q^{95} +(4.68971 - 3.16333i) q^{96} -3.72256 q^{97} +(4.37279 - 5.55686i) q^{98} +(-0.808530 - 0.808530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8	\( 8 q - 4 q^{4} - 4 q^{6} - 12 q^{8} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} + 8 q^{17} - 4 q^{18} + 8 q^{19} - 8 q^{20} - 8 q^{21} + 16 q^{22} - 12 q^{24} - 20 q^{26} - 8 q^{28} + 24 q^{29} + 8 q^{31} - 8 q^{33} + 16 q^{34} - 8 q^{35} + 4 q^{36} - 8 q^{37} - 16 q^{38} - 4 q^{40} - 4 q^{42} - 16 q^{44} + 24 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 16 q^{56} + 8 q^{59} + 4 q^{60} - 16 q^{61} + 28 q^{62} + 8 q^{64} - 8 q^{65} + 8 q^{66} - 8 q^{68} - 16 q^{69} + 4 q^{70} + 4 q^{72} - 36 q^{74} - 40 q^{76} - 8 q^{77} + 4 q^{78} - 40 q^{79} + 16 q^{80} - 8 q^{81} + 64 q^{82} + 32 q^{83} + 8 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{88} + 4 q^{90} - 8 q^{91} + 16 q^{92} + 32 q^{94} - 16 q^{95} + 24 q^{96} - 48 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 4 * q^6 - 12 * q^8 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 8 * q^15 + 8 * q^17 - 4 * q^18 + 8 * q^19 - 8 * q^20 - 8 * q^21 + 16 * q^22 - 12 * q^24 - 20 * q^26 - 8 * q^28 + 24 * q^29 + 8 * q^31 - 8 * q^33 + 16 * q^34 - 8 * q^35 + 4 * q^36 - 8 * q^37 - 16 * q^38 - 4 * q^40 - 4 * q^42 - 16 * q^44 + 24 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 16 * q^56 + 8 * q^59 + 4 * q^60 - 16 * q^61 + 28 * q^62 + 8 * q^64 - 8 * q^65 + 8 * q^66 - 8 * q^68 - 16 * q^69 + 4 * q^70 + 4 * q^72 - 36 * q^74 - 40 * q^76 - 8 * q^77 + 4 * q^78 - 40 * q^79 + 16 * q^80 - 8 * q^81 + 64 * q^82 + 32 * q^83 + 8 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^88 + 4 * q^90 - 8 * q^91 + 16 * q^92 + 32 * q^94 - 16 * q^95 + 24 * q^96 - 48 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more