LMFDB - Embedded newform 240.2.s.c.61.5

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.5
Root			$-0.491956 + 1.32589i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.491956 + 1.32589i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.51596 - 1.30456i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.28541 + 0.589679i) q^{6} +3.46600i q^{7} +(2.47548 - 1.36821i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.491956 + 1.32589i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.51596 - 1.30456i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.28541 + 0.589679i) q^{6} +3.46600i q^{7} +(2.47548 - 1.36821i) q^{8} +1.00000i q^{9} +(0.589679 + 1.28541i) q^{10} +(-2.79706 + 2.79706i) q^{11} +(-0.149484 - 1.99441i) q^{12} +(2.41254 + 2.41254i) q^{13} +(-4.59553 - 1.70512i) q^{14} +1.00000 q^{15} +(0.596265 + 3.95531i) q^{16} +0.598465 q^{17} +(-1.32589 - 0.491956i) q^{18} +(1.22261 + 1.22261i) q^{19} +(-1.99441 + 0.149484i) q^{20} +(-2.45083 + 2.45083i) q^{21} +(-2.33256 - 5.08463i) q^{22} -3.77119i q^{23} +(2.71790 + 0.782960i) q^{24} -1.00000i q^{25} +(-4.38562 + 2.01189i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.52159 - 5.25431i) q^{28} +(-7.33768 - 7.33768i) q^{29} +(-0.491956 + 1.32589i) q^{30} +6.08712 q^{31} +(-5.53763 - 1.15526i) q^{32} -3.95565 q^{33} +(-0.294418 + 0.793497i) q^{34} +(2.45083 + 2.45083i) q^{35} +(1.30456 - 1.51596i) q^{36} +(7.71609 - 7.71609i) q^{37} +(-2.22252 + 1.01958i) q^{38} +3.41184i q^{39} +(0.782960 - 2.71790i) q^{40} +6.67193i q^{41} +(-2.04383 - 4.45523i) q^{42} +(-5.43382 + 5.43382i) q^{43} +(7.88916 - 0.591307i) q^{44} +(0.707107 + 0.707107i) q^{45} +(5.00017 + 1.85526i) q^{46} +6.63070 q^{47} +(-2.37520 + 3.21845i) q^{48} -5.01315 q^{49} +(1.32589 + 0.491956i) q^{50} +(0.423179 + 0.423179i) q^{51} +(-0.510017 - 6.80460i) q^{52} +(6.76955 - 6.76955i) q^{53} +(-0.589679 - 1.28541i) q^{54} +3.95565i q^{55} +(4.74221 + 8.58001i) q^{56} +1.72903i q^{57} +(13.3388 - 6.11913i) q^{58} +(6.80686 - 6.80686i) q^{59} +(-1.51596 - 1.30456i) q^{60} +(-3.65199 - 3.65199i) q^{61} +(-2.99460 + 8.07085i) q^{62} -3.46600 q^{63} +(4.25601 - 6.77395i) q^{64} +3.41184 q^{65} +(1.94600 - 5.24474i) q^{66} +(1.30569 + 1.30569i) q^{67} +(-0.907248 - 0.780731i) q^{68} +(2.66663 - 2.66663i) q^{69} +(-4.45523 + 2.04383i) q^{70} +4.48691i q^{71} +(1.36821 + 2.47548i) q^{72} -4.50053i q^{73} +(6.43470 + 14.0266i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-0.258464 - 3.44840i) q^{76} +(-9.69462 - 9.69462i) q^{77} +(-4.52372 - 1.67848i) q^{78} +0.465344 q^{79} +(3.21845 + 2.37520i) q^{80} -1.00000 q^{81} +(-8.84623 - 3.28229i) q^{82} +(-9.66313 - 9.66313i) q^{83} +(6.91261 - 0.518113i) q^{84} +(0.423179 - 0.423179i) q^{85} +(-4.53144 - 9.87784i) q^{86} -10.3770i q^{87} +(-3.09711 + 10.7510i) q^{88} +4.19617i q^{89} +(-1.28541 + 0.589679i) q^{90} +(-8.36186 + 8.36186i) q^{91} +(-4.91973 + 5.71697i) q^{92} +(4.30425 + 4.30425i) q^{93} +(-3.26201 + 8.79156i) q^{94} +1.72903 q^{95} +(-3.09881 - 4.73259i) q^{96} +5.24318 q^{97} +(2.46625 - 6.64688i) q^{98} +(-2.79706 - 2.79706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 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 $

$2$	−0.491956	+	1.32589i	−0.347865	+	0.937545i
$2$	−0.491956	+	1.32589i	−0.347865	+	0.937545i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.51596	−	1.30456i	−0.757980	−	0.652278i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−1.28541	+	0.589679i	−0.524766	+	0.240736i
$7$			3.46600i			1.31002i	0.755618	+	0.655012i	$0.227337\pi$
$7$			3.46600i			1.31002i	−0.755618	+	0.655012i	$0.772663\pi$
$8$	2.47548	−	1.36821i	0.875215	−	0.483735i
$9$			1.00000i			0.333333i
$10$	0.589679	+	1.28541i	0.186473	+	0.406482i
$11$	−2.79706	+	2.79706i	−0.843346	+	0.843346i	−0.989293	−	0.145946i	$-0.953377\pi$
$11$	−2.79706	+	2.79706i	−0.843346	+	0.843346i	0.145946	+	0.989293i	$0.453377\pi$
$12$	−0.149484	−	1.99441i	−0.0431524	−	0.575735i
$13$	2.41254	+	2.41254i	0.669118	+	0.669118i	0.957512	−	0.288394i	$-0.0931213\pi$
$13$	2.41254	+	2.41254i	0.669118	+	0.669118i	−0.288394	+	0.957512i	$0.593121\pi$
$14$	−4.59553	−	1.70512i	−1.22821	−	0.455712i
$15$	1.00000			0.258199
$16$	0.596265	+	3.95531i	0.149066	+	0.988827i
$17$	0.598465			0.145149			0.0725745	−	0.997363i	$-0.476878\pi$
$17$	0.598465			0.145149			0.0725745	+	0.997363i	$0.476878\pi$
$18$	−1.32589	−	0.491956i	−0.312515	−	0.115955i
$19$	1.22261	+	1.22261i	0.280486	+	0.280486i	0.833303	−	0.552817i	$-0.186447\pi$
$19$	1.22261	+	1.22261i	0.280486	+	0.280486i	−0.552817	+	0.833303i	$0.686447\pi$
$20$	−1.99441	+	0.149484i	−0.445963	+	0.0334257i
$21$	−2.45083	+	2.45083i	−0.534815	+	0.534815i
$22$	−2.33256	−	5.08463i	−0.497304	−	1.08405i
$23$		−	3.77119i		−	0.786347i	−0.919464	−	0.393174i	$-0.871377\pi$
$23$		−	3.77119i		−	0.786347i	0.919464	−	0.393174i	$-0.128623\pi$
$24$	2.71790	+	0.782960i	0.554789	+	0.159821i
$25$		−	1.00000i		−	0.200000i
$26$	−4.38562	+	2.01189i	−0.860090	+	0.394565i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.52159	−	5.25431i	0.854501	−	0.992972i
$29$	−7.33768	−	7.33768i	−1.36257	−	1.36257i	−0.870624	−	0.491950i	$-0.836284\pi$
$29$	−7.33768	−	7.33768i	−1.36257	−	1.36257i	−0.491950	−	0.870624i	$-0.663716\pi$
$30$	−0.491956	+	1.32589i	−0.0898184	+	0.242073i
$31$	6.08712			1.09328			0.546640	−	0.837368i	$-0.315907\pi$
$31$	6.08712			1.09328			0.546640	+	0.837368i	$0.315907\pi$
$32$	−5.53763	−	1.15526i	−0.978925	−	0.204222i
$33$	−3.95565			−0.688589
$34$	−0.294418	+	0.793497i	−0.0504923	+	0.136084i
$35$	2.45083	+	2.45083i	0.414266	+	0.414266i
$36$	1.30456	−	1.51596i	0.217426	−	0.252660i
$37$	7.71609	−	7.71609i	1.26852	−	1.26852i	0.321664	−	0.946854i	$-0.395758\pi$
$37$	7.71609	−	7.71609i	1.26852	−	1.26852i	0.946854	−	0.321664i	$-0.104242\pi$
$38$	−2.22252	+	1.01958i	−0.360540	+	0.165397i
$39$			3.41184i			0.546332i
$40$	0.782960	−	2.71790i	0.123797	−	0.429738i
$41$			6.67193i			1.04198i	0.853563	+	0.520990i	$0.174437\pi$
$41$			6.67193i			1.04198i	−0.853563	+	0.520990i	$0.825563\pi$
$42$	−2.04383	−	4.45523i	−0.315370	−	0.687457i
$43$	−5.43382	+	5.43382i	−0.828650	+	0.828650i	−0.987330	−	0.158680i	$-0.949276\pi$
$43$	−5.43382	+	5.43382i	−0.828650	+	0.828650i	0.158680	+	0.987330i	$0.449276\pi$
$44$	7.88916	−	0.591307i	1.18934	−	0.0891429i
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$	5.00017	+	1.85526i	0.737236	+	0.273543i
$47$	6.63070			0.967187			0.483593	−	0.875293i	$-0.339331\pi$
$47$	6.63070			0.967187			0.483593	+	0.875293i	$0.339331\pi$
$48$	−2.37520	+	3.21845i	−0.342831	+	0.464543i
$49$	−5.01315			−0.716164
$50$	1.32589	+	0.491956i	0.187509	+	0.0695730i
$51$	0.423179	+	0.423179i	0.0592568	+	0.0592568i
$52$	−0.510017	−	6.80460i	−0.0707267	−	0.943629i
$53$	6.76955	−	6.76955i	0.929870	−	0.929870i	−0.0678275	−	0.997697i	$-0.521607\pi$
$53$	6.76955	−	6.76955i	0.929870	−	0.929870i	0.997697	+	0.0678275i	$0.0216068\pi$
$54$	−0.589679	−	1.28541i	−0.0802452	−	0.174922i
$55$			3.95565i			0.533379i
$56$	4.74221	+	8.58001i	0.633705	+	1.14655i
$57$			1.72903i			0.229016i
$58$	13.3388	−	6.11913i	1.75146	−	0.803481i
$59$	6.80686	−	6.80686i	0.886178	−	0.886178i	−0.107975	−	0.994154i	$-0.534437\pi$
$59$	6.80686	−	6.80686i	0.886178	−	0.886178i	0.994154	+	0.107975i	$0.0344368\pi$
$60$	−1.51596	−	1.30456i	−0.195710	−	0.168418i
$61$	−3.65199	−	3.65199i	−0.467590	−	0.467590i	0.433543	−	0.901133i	$-0.357263\pi$
$61$	−3.65199	−	3.65199i	−0.467590	−	0.467590i	−0.901133	+	0.433543i	$0.857263\pi$
$62$	−2.99460	+	8.07085i	−0.380314	+	1.02500i
$63$	−3.46600			−0.436675
$64$	4.25601	−	6.77395i	0.532001	−	0.846744i
$65$	3.41184			0.423187
$66$	1.94600	−	5.24474i	0.239536	−	0.645583i
$67$	1.30569	+	1.30569i	0.159516	+	0.159516i	0.782352	−	0.622836i	$-0.214020\pi$
$67$	1.30569	+	1.30569i	0.159516	+	0.159516i	−0.622836	+	0.782352i	$0.714020\pi$
$68$	−0.907248	−	0.780731i	−0.110020	−	0.0946776i
$69$	2.66663	−	2.66663i	0.321025	−	0.321025i
$70$	−4.45523	+	2.04383i	−0.532502	+	0.244284i
$71$			4.48691i			0.532498i	0.963904	+	0.266249i	$0.0857844\pi$
$71$			4.48691i			0.532498i	−0.963904	+	0.266249i	$0.914216\pi$
$72$	1.36821	+	2.47548i	0.161245	+	0.291738i
$73$		−	4.50053i		−	0.526747i	−0.964694	−	0.263374i	$-0.915165\pi$
$73$		−	4.50053i		−	0.526747i	0.964694	−	0.263374i	$-0.0848352\pi$
$74$	6.43470	+	14.0266i	0.748019	+	1.63056i
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$	−0.258464	−	3.44840i	−0.0296478	−	0.395558i
$77$	−9.69462	−	9.69462i	−1.10480	−	1.10480i
$78$	−4.52372	−	1.67848i	−0.512211	−	0.190050i
$79$	0.465344			0.0523553			0.0261776	−	0.999657i	$-0.491666\pi$
$79$	0.465344			0.0523553			0.0261776	+	0.999657i	$0.491666\pi$
$80$	3.21845	+	2.37520i	0.359834	+	0.265556i
$81$	−1.00000			−0.111111
$82$	−8.84623	−	3.28229i	−0.976903	−	0.362469i
$83$	−9.66313	−	9.66313i	−1.06067	−	1.06067i	−0.998037	−	0.0626300i	$-0.980051\pi$
$83$	−9.66313	−	9.66313i	−1.06067	−	1.06067i	−0.0626300	−	0.998037i	$-0.519949\pi$
$84$	6.91261	−	0.518113i	0.754227	−	0.0565307i
$85$	0.423179	−	0.423179i	0.0459002	−	0.0459002i
$86$	−4.53144	−	9.87784i	−0.488638	−	1.06515i
$87$		−	10.3770i		−	1.11254i
$88$	−3.09711	+	10.7510i	−0.330153	+	1.14607i
$89$			4.19617i			0.444793i	0.974956	+	0.222397i	$0.0713880\pi$
$89$			4.19617i			0.444793i	−0.974956	+	0.222397i	$0.928612\pi$
$90$	−1.28541	+	0.589679i	−0.135494	+	0.0621577i
$91$	−8.36186	+	8.36186i	−0.876561	+	0.876561i
$92$	−4.91973	+	5.71697i	−0.512917	+	0.596035i
$93$	4.30425	+	4.30425i	0.446330	+	0.446330i
$94$	−3.26201	+	8.79156i	−0.336451	+	0.906781i
$95$	1.72903			0.177395
$96$	−3.09881	−	4.73259i	−0.316271	−	0.483018i
$97$	5.24318			0.532364			0.266182	−	0.963923i	$-0.414238\pi$
$97$	5.24318			0.532364			0.266182	+	0.963923i	$0.414238\pi$
$98$	2.46625	−	6.64688i	0.249129	−	0.671436i
$99$	−2.79706	−	2.79706i	−0.281115	−	0.281115i
$100$	−1.30456	+	1.51596i	−0.130456	+	0.151596i
$101$	0.631292	−	0.631292i	0.0628159	−	0.0628159i	−0.675001	−	0.737817i	$-0.735857\pi$
$101$	0.631292	−	0.631292i	0.0628159	−	0.0628159i	0.737817	+	0.675001i	$0.235857\pi$
$102$	−0.769272	+	0.352902i	−0.0761693	+	0.0349425i
$103$			10.0778i			0.992999i	0.868037	+	0.496500i	$0.165382\pi$
$103$			10.0778i			0.992999i	−0.868037	+	0.496500i	$0.834618\pi$
$104$	9.27305	+	2.67134i	0.909297	+	0.261946i
$105$			3.46600i			0.338247i
$106$	5.64535	+	12.3060i	0.548325	+	1.19526i
$107$	4.84988	−	4.84988i	0.468855	−	0.468855i	−0.432688	−	0.901544i	$-0.642435\pi$
$107$	4.84988	−	4.84988i	0.468855	−	0.468855i	0.901544	+	0.432688i	$0.142435\pi$
$108$	1.99441	−	0.149484i	0.191912	−	0.0143841i
$109$	−13.2255	−	13.2255i	−1.26677	−	1.26677i	−0.947748	−	0.319021i	$-0.896646\pi$
$109$	−13.2255	−	13.2255i	−1.26677	−	1.26677i	−0.319021	−	0.947748i	$-0.603354\pi$
$110$	−5.24474	−	1.94600i	−0.500067	−	0.185544i
$111$	10.9122			1.03574
$112$	−13.7091	+	2.06665i	−1.29539	+	0.195280i
$113$	−3.38294			−0.318240			−0.159120	−	0.987259i	$-0.550866\pi$
$113$	−3.38294			−0.318240			−0.159120	+	0.987259i	$0.550866\pi$
$114$	−2.29251	−	0.850608i	−0.214713	−	0.0796667i
$115$	−2.66663	−	2.66663i	−0.248665	−	0.248665i
$116$	1.55121	+	20.6960i	0.144026	+	1.92158i
$117$	−2.41254	+	2.41254i	−0.223039	+	0.223039i
$118$	5.67647	+	12.3738i	0.522561	+	1.13910i
$119$			2.07428i			0.190149i
$120$	2.47548	−	1.36821i	0.225979	−	0.124900i
$121$		−	4.64713i		−	0.422466i
$122$	6.63875	−	3.04552i	0.601044	−	0.275728i
$123$	−4.71777	+	4.71777i	−0.425387	+	0.425387i
$124$	−9.22783	−	7.94100i	−0.828684	−	0.713123i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.70512	−	4.59553i	0.151904	−	0.409402i
$127$	7.70840			0.684010			0.342005	−	0.939698i	$-0.388894\pi$
$127$	7.70840			0.684010			0.342005	+	0.939698i	$0.388894\pi$
$128$	6.88773	+	8.97548i	0.608795	+	0.793327i
$129$	−7.68458			−0.676590
$130$	−1.67848	+	4.52372i	−0.147212	+	0.396757i
$131$	−9.88328	−	9.88328i	−0.863506	−	0.863506i	0.128237	−	0.991743i	$-0.459068\pi$
$131$	−9.88328	−	9.88328i	−0.863506	−	0.863506i	−0.991743	+	0.128237i	$0.959068\pi$
$132$	5.99660	+	5.16036i	0.521937	+	0.449152i
$133$	−4.23757	+	4.23757i	−0.367444	+	0.367444i
$134$	−2.37355	+	1.08886i	−0.205043	+	0.0940632i
$135$			1.00000i			0.0860663i
$136$	1.48149	−	0.818825i	0.127037	−	0.0702136i
$137$			13.5558i			1.15815i	0.815276	+	0.579073i	$0.196585\pi$
$137$			13.5558i			1.15815i	−0.815276	+	0.579073i	$0.803415\pi$
$138$	2.22379	+	4.84752i	0.189302	+	0.412649i
$139$	−16.5457	+	16.5457i	−1.40339	+	1.40339i	−0.614387	+	0.789004i	$0.710597\pi$
$139$	−16.5457	+	16.5457i	−1.40339	+	1.40339i	−0.789004	+	0.614387i	$0.789403\pi$
$140$	−0.518113	−	6.91261i	−0.0437885	−	0.584222i
$141$	4.68861	+	4.68861i	0.394852	+	0.394852i
$142$	−5.94914	−	2.20736i	−0.499241	−	0.185238i
$143$	−13.4960			−1.12860
$144$	−3.95531	+	0.596265i	−0.329609	+	0.0496888i
$145$	−10.3770			−0.861767
$146$	5.96720	+	2.21406i	0.493849	+	0.183237i
$147$	−3.54483	−	3.54483i	−0.292373	−	0.292373i
$148$	−21.7634	+	1.63120i	−1.78894	+	0.134084i
$149$	−11.1413	+	11.1413i	−0.912732	+	0.912732i	−0.996486	−	0.0837547i	$-0.973309\pi$
$149$	−11.1413	+	11.1413i	−0.912732	+	0.912732i	0.0837547	+	0.996486i	$0.473309\pi$
$150$	0.589679	+	1.28541i	0.0481471	+	0.104953i
$151$		−	19.1952i		−	1.56208i	−0.624481	−	0.781040i	$-0.714690\pi$
$151$		−	19.1952i		−	1.56208i	0.624481	−	0.781040i	$-0.285310\pi$
$152$	4.69934	+	1.35376i	0.381167	+	0.109805i
$153$			0.598465i			0.0483830i
$154$	17.6233	−	8.08466i	1.42013	−	0.651481i
$155$	4.30425	−	4.30425i	0.345725	−	0.345725i
$156$	4.45094	−	5.17222i	0.356361	−	0.414109i
$157$	14.8020	+	14.8020i	1.18133	+	1.18133i	0.979401	+	0.201926i	$0.0647201\pi$
$157$	14.8020	+	14.8020i	1.18133	+	1.18133i	0.201926	+	0.979401i	$0.435280\pi$
$158$	−0.228929	+	0.616994i	−0.0182126	+	0.0490854i
$159$	9.57359			0.759235
$160$	−4.73259	+	3.09881i	−0.374144	+	0.244982i
$161$	13.0709			1.03013
$162$	0.491956	−	1.32589i	0.0386517	−	0.104172i
$163$	−7.71881	−	7.71881i	−0.604584	−	0.604584i	0.336942	−	0.941525i	$-0.390607\pi$
$163$	−7.71881	−	7.71881i	−0.604584	−	0.604584i	−0.941525	+	0.336942i	$0.890607\pi$
$164$	8.70391	−	10.1144i	0.679661	−	0.789800i
$165$	−2.79706	+	2.79706i	−0.217751	+	0.217751i
$166$	17.5661	−	8.05840i	1.36339	−	0.625453i
$167$		−	4.34420i		−	0.336164i	−0.985773	−	0.168082i	$-0.946243\pi$
$167$		−	4.34420i		−	0.336164i	0.985773	−	0.168082i	$-0.0537574\pi$
$168$	−2.71374	+	9.42024i	−0.209369	+	0.726787i
$169$		−	1.35932i		−	0.104563i
$170$	0.352902	+	0.769272i	0.0270664	+	0.0590005i
$171$	−1.22261	+	1.22261i	−0.0934954	+	0.0934954i
$172$	15.3262	−	1.14873i	1.16861	−	0.0875895i
$173$	8.94328	+	8.94328i	0.679945	+	0.679945i	0.959988	−	0.280042i	$-0.0903486\pi$
$173$	8.94328	+	8.94328i	0.679945	+	0.679945i	−0.280042	+	0.959988i	$0.590349\pi$
$174$	13.7588	+	5.10505i	1.04305	+	0.387013i
$175$	3.46600			0.262005
$176$	−12.7310	−	9.39546i	−0.959638	−	0.708209i
$177$	9.62636			0.723562
$178$	−5.56365	−	2.06433i	−0.417014	−	0.154728i
$179$	0.416664	+	0.416664i	0.0311429	+	0.0311429i	0.722507	−	0.691364i	$-0.242990\pi$
$179$	0.416664	+	0.416664i	0.0311429	+	0.0311429i	−0.691364	+	0.722507i	$0.742990\pi$
$180$	−0.149484	−	1.99441i	−0.0111419	−	0.148654i
$181$	4.95211	−	4.95211i	0.368087	−	0.368087i	−0.498692	−	0.866779i	$-0.666186\pi$
$181$	4.95211	−	4.95211i	0.368087	−	0.368087i	0.866779	+	0.498692i	$0.166186\pi$
$182$	−6.97322	−	15.2005i	−0.516890	−	1.12674i
$183$		−	5.16470i		−	0.381785i
$184$	−5.15977	−	9.33551i	−0.380384	−	0.688223i
$185$		−	10.9122i		−	0.802281i
$186$	−7.82445	+	3.58945i	−0.573716	+	0.263191i
$187$	−1.67394	+	1.67394i	−0.122411	+	0.122411i
$188$	−10.0519	−	8.65012i	−0.733108	−	0.630875i
$189$	−2.45083	−	2.45083i	−0.178272	−	0.178272i
$190$	−0.850608	+	2.29251i	−0.0617096	+	0.166316i
$191$	6.75184			0.488546			0.244273	−	0.969706i	$-0.421451\pi$
$191$	6.75184			0.488546			0.244273	+	0.969706i	$0.421451\pi$
$192$	7.79936	−	1.78045i	0.562870	−	0.128493i
$193$	22.0415			1.58658			0.793292	−	0.608842i	$-0.208366\pi$
$193$	22.0415			1.58658			0.793292	+	0.608842i	$0.208366\pi$
$194$	−2.57941	+	6.95187i	−0.185191	+	0.499115i
$195$	2.41254	+	2.41254i	0.172765	+	0.172765i
$196$	7.59973	+	6.53994i	0.542838	+	0.467138i
$197$	1.97920	−	1.97920i	0.141012	−	0.141012i	−0.633077	−	0.774089i	$-0.718208\pi$
$197$	1.97920	−	1.97920i	0.141012	−	0.141012i	0.774089	+	0.633077i	$0.218208\pi$
$198$	5.08463	−	2.33256i	0.361349	−	0.165768i
$199$		−	1.39700i		−	0.0990305i	−0.998773	−	0.0495153i	$-0.984232\pi$
$199$		−	1.39700i		−	0.0990305i	0.998773	−	0.0495153i	$-0.0157676\pi$
$200$	−1.36821	−	2.47548i	−0.0967470	−	0.175043i
$201$			1.84653i			0.130244i
$202$	0.526455	+	1.14759i	0.0370413	+	0.0807442i
$203$	25.4324	−	25.4324i	1.78500	−	1.78500i
$204$	−0.0894611	−	1.19358i	−0.00626353	−	0.0835674i
$205$	4.71777	+	4.71777i	0.329503	+	0.329503i
$206$	−13.3621	−	4.95785i	−0.930981	−	0.345430i
$207$	3.77119			0.262116
$208$	−8.10382	+	10.9808i	−0.561899	+	0.761385i
$209$	−6.83944			−0.473094
$210$	−4.59553	−	1.70512i	−0.317122	−	0.117664i
$211$	−13.3519	−	13.3519i	−0.919182	−	0.919182i	0.0777879	−	0.996970i	$-0.475214\pi$
$211$	−13.3519	−	13.3519i	−0.919182	−	0.919182i	−0.996970	+	0.0777879i	$0.975214\pi$
$212$	−19.0936	+	1.43110i	−1.31136	+	0.0982885i
$213$	−3.17272	+	3.17272i	−0.217391	+	0.217391i
$214$	4.04447	+	8.81632i	0.276474	+	0.602671i
$215$			7.68458i			0.524084i
$216$	−0.782960	+	2.71790i	−0.0532737	+	0.184930i
$217$			21.0980i			1.43222i
$218$	24.0418	−	11.0291i	1.62832	−	0.746987i
$219$	3.18235	−	3.18235i	0.215044	−	0.215044i
$220$	5.16036	−	5.99660i	0.347912	−	0.404291i
$221$	1.44382	+	1.44382i	0.0971218	+	0.0971218i
$222$	−5.36832	+	14.4684i	−0.360298	+	0.971053i
$223$	−24.7211			−1.65545			−0.827725	−	0.561134i	$-0.810365\pi$
$223$	−24.7211			−1.65545			−0.827725	+	0.561134i	$0.810365\pi$
$224$	4.00412	−	19.1934i	0.267536	−	1.28242i
$225$	1.00000			0.0666667
$226$	1.66425	−	4.48540i	0.110705	−	0.298364i
$227$	16.3586	+	16.3586i	1.08576	+	1.08576i	0.995960	+	0.0898019i	$0.0286234\pi$
$227$	16.3586	+	16.3586i	1.08576	+	1.08576i	0.0898019	+	0.995960i	$0.471377\pi$
$228$	2.25562	−	2.62114i	0.149382	−	0.173590i
$229$	7.44978	−	7.44978i	0.492295	−	0.492295i	−0.416734	−	0.909029i	$-0.636825\pi$
$229$	7.44978	−	7.44978i	0.492295	−	0.492295i	0.909029	+	0.416734i	$0.136825\pi$
$230$	4.84752	−	2.22379i	0.319636	−	0.146633i
$231$		−	13.7103i		−	0.902069i
$232$	−28.2038	−	8.12481i	−1.85167	−	0.533420i
$233$			13.2661i			0.869090i	0.900650	+	0.434545i	$0.143091\pi$
$233$			13.2661i			0.869090i	−0.900650	+	0.434545i	$0.856909\pi$
$234$	−2.01189	−	4.38562i	−0.131522	−	0.286697i
$235$	4.68861	−	4.68861i	0.305851	−	0.305851i
$236$	−19.1989	+	1.43899i	−1.24974	+	0.0936703i
$237$	0.329048	+	0.329048i	0.0213740	+	0.0213740i
$238$	−2.75026	−	1.02045i	−0.178273	−	0.0661461i
$239$	−9.61938			−0.622226			−0.311113	−	0.950373i	$-0.600702\pi$
$239$	−9.61938			−0.622226			−0.311113	+	0.950373i	$0.600702\pi$
$240$	0.596265	+	3.95531i	0.0384887	+	0.255314i
$241$	1.80641			0.116361			0.0581805	−	0.998306i	$-0.481470\pi$
$241$	1.80641			0.116361			0.0581805	+	0.998306i	$0.481470\pi$
$242$	6.16158	+	2.28618i	0.396081	+	0.146961i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	0.772042	+	10.3005i	0.0494249	+	0.659422i
$245$	−3.54483	+	3.54483i	−0.226471	+	0.226471i
$246$	−3.93430	−	8.57616i	−0.250842	−	0.546796i
$247$			5.89919i			0.375357i
$248$	15.0686	−	8.32846i	0.956854	−	0.528858i
$249$		−	13.6657i		−	0.866031i
$250$	1.28541	−	0.589679i	0.0812965	−	0.0372946i
$251$	−8.81021	+	8.81021i	−0.556096	+	0.556096i	−0.928194	−	0.372098i	$-0.878639\pi$
$251$	−8.81021	+	8.81021i	−0.556096	+	0.556096i	0.372098	+	0.928194i	$0.378639\pi$
$252$	5.25431	+	4.52159i	0.330991	+	0.284834i
$253$	10.5483	+	10.5483i	0.663163	+	0.663163i
$254$	−3.79219	+	10.2205i	−0.237943	+	0.641289i
$255$	0.598465			0.0374773
$256$	−15.2889	+	4.71682i	−0.955559	+	0.294802i
$257$	14.4849			0.903544			0.451772	−	0.892133i	$-0.350792\pi$
$257$	14.4849			0.903544			0.451772	+	0.892133i	$0.350792\pi$
$258$	3.78047	−	10.1889i	0.235362	−	0.634333i
$259$	26.7440	+	26.7440i	1.66179	+	1.66179i
$260$	−5.17222	−	4.45094i	−0.320767	−	0.276036i
$261$	7.33768	−	7.33768i	0.454191	−	0.454191i
$262$	17.9663	−	8.24199i	1.10996	−	0.509192i
$263$			14.9147i			0.919679i	0.888002	+	0.459840i	$0.152093\pi$
$263$			14.9147i			0.919679i	−0.888002	+	0.459840i	$0.847907\pi$
$264$	−9.79212	+	5.41215i	−0.602664	+	0.333095i
$265$		−	9.57359i		−	0.588101i
$266$	−3.53385	−	7.70324i	−0.216674	−	0.472316i
$267$	−2.96714	+	2.96714i	−0.181586	+	0.181586i
$268$	−0.276027	−	3.68273i	−0.0168611	−	0.224959i
$269$	4.33647	+	4.33647i	0.264399	+	0.264399i	0.826838	−	0.562439i	$-0.190137\pi$
$269$	4.33647	+	4.33647i	0.264399	+	0.264399i	−0.562439	+	0.826838i	$0.690137\pi$
$270$	−1.32589	−	0.491956i	−0.0806910	−	0.0299395i
$271$	−16.0392			−0.974312			−0.487156	−	0.873315i	$-0.661966\pi$
$271$	−16.0392			−0.974312			−0.487156	+	0.873315i	$0.661966\pi$
$272$	0.356844	+	2.36711i	0.0216368	+	0.143527i
$273$	−11.8254			−0.715709
$274$	−17.9734	−	6.66883i	−1.08581	−	0.402879i
$275$	2.79706	+	2.79706i	0.168669	+	0.168669i
$276$	−7.52128	+	0.563734i	−0.452728	+	0.0339328i
$277$	−3.90837	+	3.90837i	−0.234831	+	0.234831i	−0.814706	−	0.579875i	$-0.803102\pi$
$277$	−3.90837	+	3.90837i	−0.234831	+	0.234831i	0.579875	+	0.814706i	$0.303102\pi$
$278$	−13.7980	−	30.0776i	−0.827551	−	1.80393i
$279$			6.08712i			0.364427i
$280$	9.42024	+	2.71374i	0.562967	+	0.162177i
$281$			28.9991i			1.72994i	0.501820	+	0.864972i	$0.332664\pi$
$281$			28.9991i			1.72994i	−0.501820	+	0.864972i	$0.667336\pi$
$282$	−8.52316	+	3.90999i	−0.507547	+	0.232836i
$283$	20.1981	−	20.1981i	1.20065	−	1.20065i	0.226684	−	0.973968i	$-0.427212\pi$
$283$	20.1981	−	20.1981i	1.20065	−	1.20065i	0.973968	−	0.226684i	$-0.0727884\pi$
$284$	5.85343	−	6.80197i	0.347337	−	0.403623i
$285$	1.22261	+	1.22261i	0.0724213	+	0.0724213i
$286$	6.63946	−	17.8942i	0.392599	−	1.05811i
$287$	−23.1249			−1.36502
$288$	1.15526	−	5.53763i	0.0680741	−	0.326308i
$289$	−16.6418			−0.978932
$290$	5.10505	−	13.7588i	0.299779	−	0.807945i
$291$	3.70749	+	3.70749i	0.217337	+	0.217337i
$292$	−5.87119	+	6.82262i	−0.343586	+	0.399264i
$293$	0.204952	−	0.204952i	0.0119734	−	0.0119734i	−0.701095	−	0.713068i	$-0.747305\pi$
$293$	0.204952	−	0.204952i	0.0119734	−	0.0119734i	0.713068	+	0.701095i	$0.247305\pi$
$294$	6.44395	−	2.95615i	0.375819	−	0.172406i
$295$		−	9.62636i		−	0.560468i
$296$	8.54381	−	29.6583i	0.496599	−	1.72385i
$297$		−	3.95565i		−	0.229530i
$298$	−9.29110	−	20.2532i	−0.538219	−	1.17323i
$299$	9.09814	−	9.09814i	0.526159	−	0.526159i
$300$	−1.99441	+	0.149484i	−0.115147	+	0.00863048i
$301$	−18.8336	−	18.8336i	−1.08555	−	1.08555i
$302$	25.4506	+	9.44317i	1.46452	+	0.543393i
$303$	0.892782			0.0512890
$304$	−4.10681	+	5.56481i	−0.235541	+	0.319164i
$305$	−5.16470			−0.295730
$306$	−0.793497	−	0.294418i	−0.0453612	−	0.0168308i
$307$	−3.29375	−	3.29375i	−0.187984	−	0.187984i	0.606840	−	0.794824i	$-0.292437\pi$
$307$	−3.29375	−	3.29375i	−0.187984	−	0.187984i	−0.794824	+	0.606840i	$0.792437\pi$
$308$	2.04947	+	27.3438i	0.116779	+	1.55806i
$309$	−7.12611	+	7.12611i	−0.405390	+	0.405390i
$310$	3.58945	+	7.82445i	0.203867	+	0.444399i
$311$		−	5.46620i		−	0.309960i	−0.987918	−	0.154980i	$-0.950469\pi$
$311$		−	5.46620i		−	0.309960i	0.987918	−	0.154980i	$-0.0495313\pi$
$312$	4.66811	+	8.44595i	0.264280	+	0.478158i
$313$		−	13.5625i		−	0.766595i	−0.923625	−	0.383298i	$-0.874788\pi$
$313$		−	13.5625i		−	0.766595i	0.923625	−	0.383298i	$-0.125212\pi$
$314$	−26.9077	+	12.3439i	−1.51849	+	0.696604i
$315$	−2.45083	+	2.45083i	−0.138089	+	0.138089i
$316$	−0.705443	−	0.607068i	−0.0396842	−	0.0341502i
$317$	−17.3680	−	17.3680i	−0.975482	−	0.975482i	0.0242242	−	0.999707i	$-0.492288\pi$
$317$	−17.3680	−	17.3680i	−0.975482	−	0.975482i	−0.999707	+	0.0242242i	$0.992288\pi$
$318$	−4.70978	+	12.6935i	−0.264112	+	0.711817i
$319$	41.0479			2.29824
$320$	−1.78045	−	7.79936i	−0.0995303	−	0.435997i
$321$	6.85876			0.382819
$322$	−6.43032	+	17.3306i	−0.358348	+	0.965797i
$323$	0.731690	+	0.731690i	0.0407123	+	0.0407123i
$324$	1.51596	+	1.30456i	0.0842200	+	0.0724754i
$325$	2.41254	−	2.41254i	0.133824	−	0.133824i
$326$	14.0316	−	6.43697i	0.777138	−	0.356511i
$327$		−	18.7036i		−	1.03431i
$328$	9.12859	+	16.5162i	0.504042	+	0.911956i
$329$			22.9820i			1.26704i
$330$	−2.33256	−	5.08463i	−0.128403	−	0.279899i
$331$	−2.19411	+	2.19411i	−0.120599	+	0.120599i	−0.764830	−	0.644232i	$-0.777177\pi$
$331$	−2.19411	+	2.19411i	−0.120599	+	0.120599i	0.644232	+	0.764830i	$0.277177\pi$
$332$	2.04281	+	27.2550i	0.112114	+	1.49581i
$333$	7.71609	+	7.71609i	0.422839	+	0.422839i
$334$	5.75993	+	2.13715i	0.315169	+	0.116940i
$335$	1.84653			0.100887
$336$	−11.1551	−	8.23245i	−0.608563	−	0.449117i
$337$	−4.22709			−0.230264			−0.115132	−	0.993350i	$-0.536729\pi$
$337$	−4.22709			−0.230264			−0.115132	+	0.993350i	$0.536729\pi$
$338$	1.80230	+	0.668724i	0.0980324	+	0.0363738i
$339$	−2.39210	−	2.39210i	−0.129921	−	0.129921i
$340$	−1.19358	+	0.0894611i	−0.0647311	+	0.00485171i
$341$	−17.0261	+	17.0261i	−0.922014	+	0.922014i
$342$	−1.01958	−	2.22252i	−0.0551323	−	0.120180i
$343$			6.88642i			0.371832i
$344$	−6.01672	+	20.8859i	−0.324400	+	1.12609i
$345$		−	3.77119i		−	0.203034i
$346$	−16.2575	+	7.45809i	−0.874008	+	0.400950i
$347$	−24.2376	+	24.2376i	−1.30114	+	1.30114i	−0.373522	+	0.927621i	$0.621850\pi$
$347$	−24.2376	+	24.2376i	−1.30114	+	1.30114i	−0.927621	+	0.373522i	$0.878150\pi$
$348$	−13.5374	+	15.7312i	−0.725683	+	0.843280i
$349$	25.5234	+	25.5234i	1.36624	+	1.36624i	0.865737	+	0.500499i	$0.166850\pi$
$349$	25.5234	+	25.5234i	1.36624	+	1.36624i	0.500499	+	0.865737i	$0.333150\pi$
$350$	−1.70512	+	4.59553i	−0.0911424	+	0.245641i
$351$	−3.41184			−0.182111
$352$	18.7204	−	12.2578i	0.997803	−	0.653342i
$353$	1.33952			0.0712953			0.0356476	−	0.999364i	$-0.488651\pi$
$353$	1.33952			0.0712953			0.0356476	+	0.999364i	$0.488651\pi$
$354$	−4.73574	+	12.7635i	−0.251702	+	0.678371i
$355$	3.17272	+	3.17272i	0.168391	+	0.168391i
$356$	5.47414	−	6.36123i	0.290129	−	0.337144i
$357$	−1.46674	+	1.46674i	−0.0776279	+	0.0776279i
$358$	−0.757430	+	0.347470i	−0.0400314	+	0.0183644i
$359$		−	1.58190i		−	0.0834893i	−0.999128	−	0.0417446i	$-0.986708\pi$
$359$		−	1.58190i		−	0.0834893i	0.999128	−	0.0417446i	$-0.0132916\pi$
$360$	2.71790	+	0.782960i	0.143246	+	0.0412656i
$361$		−	16.0104i		−	0.842655i
$362$	4.12972	+	9.00216i	0.217053	+	0.473143i
$363$	3.28602	−	3.28602i	0.172471	−	0.172471i
$364$	23.5847	−	1.76772i	1.23618	−	0.0926537i
$365$	−3.18235	−	3.18235i	−0.166572	−	0.166572i
$366$	6.84781	+	2.54080i	0.357941	+	0.132810i
$367$	−2.77759			−0.144989			−0.0724946	−	0.997369i	$-0.523096\pi$
$367$	−2.77759			−0.144989			−0.0724946	+	0.997369i	$0.523096\pi$
$368$	14.9162	−	2.24863i	0.777562	−	0.117218i
$369$	−6.67193			−0.347327
$370$	14.4684	+	5.36832i	0.752174	+	0.279086i
$371$	23.4633	+	23.4633i	1.21815	+	1.21815i
$372$	−0.909930	−	12.1402i	−0.0471777	−	0.629440i
$373$	−1.01960	+	1.01960i	−0.0527927	+	0.0527927i	−0.733010	−	0.680218i	$-0.761885\pi$
$373$	−1.01960	+	1.01960i	−0.0527927	+	0.0527927i	0.680218	+	0.733010i	$0.261885\pi$
$374$	−1.39596	−	3.04297i	−0.0721832	−	0.157348i
$375$		−	1.00000i		−	0.0516398i
$376$	16.4142	−	9.07218i	0.846496	−	0.467862i
$377$		−	35.4049i		−	1.82344i
$378$	4.45523	−	2.04383i	0.229152	−	0.105123i
$379$	0.0985440	−	0.0985440i	0.00506187	−	0.00506187i	−0.704571	−	0.709633i	$-0.748861\pi$
$379$	0.0985440	−	0.0985440i	0.00506187	−	0.00506187i	0.709633	+	0.704571i	$0.248861\pi$
$380$	−2.62114	−	2.25562i	−0.134462	−	0.115711i
$381$	5.45066	+	5.45066i	0.279246	+	0.279246i
$382$	−3.32161	+	8.95219i	−0.169948	+	0.458034i
$383$	−25.2940			−1.29246			−0.646232	−	0.763141i	$-0.723656\pi$
$383$	−25.2940			−1.29246			−0.646232	+	0.763141i	$0.723656\pi$
$384$	−1.47626	+	11.2170i	−0.0753350	+	0.572414i
$385$	−13.7103			−0.698740
$386$	−10.8434	+	29.2246i	−0.551917	+	1.48749i
$387$	−5.43382	−	5.43382i	−0.276217	−	0.276217i
$388$	−7.94845	−	6.84003i	−0.403521	−	0.347250i
$389$	1.32712	−	1.32712i	0.0672875	−	0.0672875i	−0.672662	−	0.739950i	$-0.734849\pi$
$389$	1.32712	−	1.32712i	0.0672875	−	0.0672875i	0.739950	+	0.672662i	$0.234849\pi$
$390$	−4.38562	+	2.01189i	−0.222074	+	0.101876i
$391$		−	2.25692i		−	0.114138i
$392$	−12.4100	+	6.85904i	−0.626798	+	0.346434i
$393$		−	13.9771i		−	0.705050i
$394$	1.65052	+	3.59788i	0.0831519	+	0.181258i
$395$	0.329048	−	0.329048i	0.0165562	−	0.0165562i
$396$	0.591307	+	7.88916i	0.0297143	+	0.396445i
$397$	2.31928	+	2.31928i	0.116401	+	0.116401i	0.762908	−	0.646507i	$-0.223771\pi$
$397$	2.31928	+	2.31928i	0.116401	+	0.116401i	−0.646507	+	0.762908i	$0.723771\pi$
$398$	1.85226	+	0.687261i	0.0928455	+	0.0344493i
$399$	−5.99283			−0.300017
$400$	3.95531	−	0.596265i	0.197765	−	0.0298133i
$401$	19.2547			0.961536			0.480768	−	0.876848i	$-0.340358\pi$
$401$	19.2547			0.961536			0.480768	+	0.876848i	$0.340358\pi$
$402$	−2.44829	−	0.908411i	−0.122110	−	0.0453074i
$403$	14.6854	+	14.6854i	0.731533	+	0.731533i
$404$	−1.78057	+	0.133457i	−0.0885866	+	0.00663973i
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$	21.2089	+	46.2321i	1.05258	+	2.29446i
$407$			43.1648i			2.13960i
$408$	1.62657	+	0.468574i	0.0805271	+	0.0231979i
$409$		−	36.9776i		−	1.82842i	−0.405236	−	0.914212i	$-0.632811\pi$
$409$		−	36.9776i		−	1.82842i	0.405236	−	0.914212i	$-0.367189\pi$
$410$	−8.57616	+	3.93430i	−0.423547	+	0.194301i
$411$	−9.58537	+	9.58537i	−0.472811	+	0.472811i
$412$	13.1471	−	15.2776i	0.647712	−	0.752673i
$413$	23.5926	+	23.5926i	1.16092	+	1.16092i
$414$	−1.85526	+	5.00017i	−0.0911809	+	0.245745i
$415$	−13.6657			−0.670825
$416$	−10.5727	−	16.1469i	−0.518367	−	0.791665i
$417$	−23.3992			−1.14586
$418$	3.36470	−	9.06834i	0.164573	−	0.443547i
$419$	−17.9125	−	17.9125i	−0.875083	−	0.875083i	0.117938	−	0.993021i	$-0.462372\pi$
$419$	−17.9125	−	17.9125i	−0.875083	−	0.875083i	−0.993021	+	0.117938i	$0.962372\pi$
$420$	4.52159	−	5.25431i	0.220631	−	0.256384i
$421$	−5.46938	+	5.46938i	−0.266561	+	0.266561i	−0.827713	−	0.561152i	$-0.810358\pi$
$421$	−5.46938	+	5.46938i	−0.266561	+	0.266561i	0.561152	+	0.827713i	$0.310358\pi$
$422$	24.2717	−	11.1346i	1.18153	−	0.542023i
$423$			6.63070i			0.322396i
$424$	7.49574	−	26.0201i	0.364025	−	1.26365i
$425$		−	0.598465i		−	0.0290298i
$426$	−2.64584	−	5.76752i	−0.128191	−	0.279437i
$427$	12.6578	−	12.6578i	0.612554	−	0.612554i
$428$	−13.6792	+	1.02528i	−0.661207	+	0.0495587i
$429$	−9.54315	−	9.54315i	−0.460747	−	0.460747i
$430$	−10.1889	−	3.78047i	−0.491352	−	0.182311i
$431$	−10.4721			−0.504422			−0.252211	−	0.967672i	$-0.581158\pi$
$431$	−10.4721			−0.504422			−0.252211	+	0.967672i	$0.581158\pi$
$432$	−3.21845	−	2.37520i	−0.154848	−	0.114277i
$433$	−40.3793			−1.94050			−0.970252	−	0.242096i	$-0.922165\pi$
$433$	−40.3793			−1.94050			−0.970252	+	0.242096i	$0.922165\pi$
$434$	−27.9735	−	10.3793i	−1.34277	−	0.498221i
$435$	−7.33768	−	7.33768i	−0.351815	−	0.351815i
$436$	2.79590	+	37.3026i	0.133899	+	1.78647i
$437$	4.61070	−	4.61070i	0.220560	−	0.220560i
$438$	2.65387	+	5.78502i	0.126807	+	0.276419i
$439$		−	30.6715i		−	1.46387i	−0.681375	−	0.731934i	$-0.738618\pi$
$439$		−	30.6715i		−	1.46387i	0.681375	−	0.731934i	$-0.261382\pi$
$440$	5.41215	+	9.79212i	0.258014	+	0.466821i
$441$		−	5.01315i		−	0.238721i
$442$	−2.62464	+	1.20405i	−0.124841	+	0.0572707i
$443$	4.24029	−	4.24029i	0.201462	−	0.201462i	−0.599164	−	0.800626i	$-0.704500\pi$
$443$	4.24029	−	4.24029i	0.201462	−	0.201462i	0.800626	+	0.599164i	$0.204500\pi$
$444$	−16.5425	−	14.2356i	−0.785070	−	0.675591i
$445$	2.96714	+	2.96714i	0.140656	+	0.140656i
$446$	12.1617	−	32.7775i	0.575874	−	1.55206i
$447$	−15.7562			−0.745242
$448$	23.4785	+	14.7513i	1.10925	+	0.696935i
$449$	24.0771			1.13627			0.568134	−	0.822936i	$-0.307666\pi$
$449$	24.0771			1.13627			0.568134	+	0.822936i	$0.307666\pi$
$450$	−0.491956	+	1.32589i	−0.0231910	+	0.0625030i
$451$	−18.6618	−	18.6618i	−0.878750	−	0.878750i
$452$	5.12839	+	4.41323i	0.241219	+	0.207581i
$453$	13.5730	−	13.5730i	0.637716	−	0.637716i
$454$	−29.7375	+	13.6420i	−1.39565	+	0.640251i
$455$			11.8254i			0.554386i
$456$	2.36568	+	4.28019i	0.110783	+	0.200438i
$457$		−	0.491242i		−	0.0229793i	−0.999934	−	0.0114897i	$-0.996343\pi$
$457$		−	0.491242i		−	0.0229793i	0.999934	−	0.0114897i	$-0.00365735\pi$
$458$	6.21261	+	13.5425i	0.290296	+	0.632801i
$459$	−0.423179	+	0.423179i	−0.0197523	+	0.0197523i
$460$	0.563734	+	7.52128i	0.0262842	+	0.350682i
$461$	−27.3136	−	27.3136i	−1.27212	−	1.27212i	−0.944973	−	0.327148i	$-0.893912\pi$
$461$	−27.3136	−	27.3136i	−1.27212	−	1.27212i	−0.327148	−	0.944973i	$-0.606088\pi$
$462$	18.1783	+	6.74484i	0.845730	+	0.313798i
$463$	−3.23138			−0.150175			−0.0750876	−	0.997177i	$-0.523924\pi$
$463$	−3.23138			−0.150175			−0.0750876	+	0.997177i	$0.523924\pi$
$464$	24.6476	−	33.3980i	1.14424	−	1.55046i
$465$	6.08712			0.282284
$466$	−17.5893	−	6.52632i	−0.814810	−	0.302326i
$467$	−10.1748	−	10.1748i	−0.470832	−	0.470832i	0.431352	−	0.902184i	$-0.358037\pi$
$467$	−10.1748	−	10.1748i	−0.470832	−	0.470832i	−0.902184	+	0.431352i	$0.858037\pi$
$468$	6.80460	−	0.510017i	0.314543	−	0.0235756i
$469$	−4.52553	+	4.52553i	−0.208970	+	0.208970i
$470$	3.90999	+	8.52316i	0.180354	+	0.393144i
$471$			20.9332i			0.964549i
$472$	7.53705	−	26.1635i	0.346921	−	1.20427i
$473$		−	30.3975i		−	1.39768i
$474$	−0.598158	+	0.274404i	−0.0274743	+	0.0126038i
$475$	1.22261	−	1.22261i	0.0560973	−	0.0560973i
$476$	2.70601	−	3.14452i	0.124030	−	0.144129i
$477$	6.76955	+	6.76955i	0.309957	+	0.309957i
$478$	4.73231	−	12.7542i	0.216451	−	0.583364i
$479$	9.52356			0.435143			0.217571	−	0.976044i	$-0.430187\pi$
$479$	9.52356			0.435143			0.217571	+	0.976044i	$0.430187\pi$
$480$	−5.53763	−	1.15526i	−0.252757	−	0.0527300i
$481$	37.2307			1.69758
$482$	−0.888673	+	2.39510i	−0.0404780	+	0.109094i
$483$	9.24255	+	9.24255i	0.420551	+	0.420551i
$484$	−6.06245	+	7.04486i	−0.275566	+	0.320221i
$485$	3.70749	−	3.70749i	0.168348	−	0.168348i
$486$	1.28541	−	0.589679i	0.0583074	−	0.0267484i
$487$		−	16.8290i		−	0.762595i	−0.924452	−	0.381297i	$-0.875477\pi$
$487$		−	16.8290i		−	0.762595i	0.924452	−	0.381297i	$-0.124523\pi$
$488$	−14.0371	−	4.04375i	−0.635431	−	0.183052i
$489$		−	10.9160i		−	0.493641i
$490$	−2.95615	−	6.44395i	−0.133545	−	0.291108i
$491$	8.17064	−	8.17064i	0.368736	−	0.368736i	−0.498280	−	0.867016i	$-0.666035\pi$
$491$	8.17064	−	8.17064i	0.368736	−	0.368736i	0.867016	+	0.498280i	$0.166035\pi$
$492$	13.3065	−	0.997349i	0.599905	−	0.0449640i
$493$	−4.39134	−	4.39134i	−0.197776	−	0.197776i
$494$	−7.82167	−	2.90214i	−0.351914	−	0.130574i
$495$	−3.95565			−0.177793
$496$	3.62954	+	24.0765i	0.162971	+	1.08106i
$497$	−15.5516			−0.697586
$498$	18.1192	+	6.72294i	0.811942	+	0.301262i
$499$	26.5417	+	26.5417i	1.18817	+	1.18817i	0.977573	+	0.210596i	$0.0675404\pi$
$499$	26.5417	+	26.5417i	1.18817	+	1.18817i	0.210596	+	0.977573i	$0.432460\pi$
$500$	0.149484	+	1.99441i	0.00668514	+	0.0891925i
$501$	3.07181	−	3.07181i	0.137239	−	0.137239i
$502$	−7.34713	−	16.0156i	−0.327918	−	0.714811i
$503$		−	20.8629i		−	0.930231i	−0.885250	−	0.465116i	$-0.846013\pi$
$503$		−	20.8629i		−	0.930231i	0.885250	−	0.465116i	$-0.153987\pi$
$504$	−8.58001	+	4.74221i	−0.382184	+	0.211235i
$505$		−	0.892782i		−	0.0397283i
$506$	−19.1751	+	8.79653i	−0.852436	+	0.391054i
$507$	0.961183	−	0.961183i	0.0426877	−	0.0426877i
$508$	−11.6856	−	10.0560i	−0.518465	−	0.446165i
$509$	−12.6455	−	12.6455i	−0.560504	−	0.560504i	0.368947	−	0.929451i	$-0.379718\pi$
$509$	−12.6455	−	12.6455i	−0.560504	−	0.560504i	−0.929451	+	0.368947i	$0.879718\pi$
$510$	−0.294418	+	0.793497i	−0.0130371	+	0.0351367i
$511$	15.5988			0.690052
$512$	1.26750	−	22.5919i	0.0560159	−	0.998430i
$513$	−1.72903			−0.0763387
$514$	−7.12594	+	19.2054i	−0.314312	+	0.847113i
$515$	7.12611	+	7.12611i	0.314014	+	0.314014i
$516$	11.6495	+	10.0250i	0.512841	+	0.441325i
$517$	−18.5465	+	18.5465i	−0.815673	+	0.815673i
$518$	−48.6164	+	22.3027i	−2.13608	+	0.979923i
$519$			12.6477i			0.555173i
$520$	8.44595	−	4.66811i	0.370380	−	0.204710i
$521$			0.506099i			0.0221726i	0.999939	+	0.0110863i	$0.00352895\pi$
$521$			0.506099i			0.0221726i	−0.999939	+	0.0110863i	$0.996471\pi$
$522$	6.11913	+	13.3388i	0.267827	+	0.583822i
$523$	5.87445	−	5.87445i	0.256872	−	0.256872i	−0.566909	−	0.823781i	$-0.691861\pi$
$523$	5.87445	−	5.87445i	0.256872	−	0.256872i	0.823781	+	0.566909i	$0.191861\pi$
$524$	2.08935	+	27.8759i	0.0912738	+	1.21777i
$525$	2.45083	+	2.45083i	0.106963	+	0.106963i
$526$	−19.7752	−	7.33737i	−0.862240	−	0.319924i
$527$	3.64293			0.158689
$528$	−2.35861	−	15.6458i	−0.102645	−	0.680896i
$529$	8.77813			0.381658
$530$	12.6935	+	4.70978i	0.551371	+	0.204580i
$531$	6.80686	+	6.80686i	0.295393	+	0.295393i
$532$	11.9521	−	0.895834i	0.518191	−	0.0388393i
$533$	−16.0963	+	16.0963i	−0.697207	+	0.697207i
$534$	−2.47440	−	5.39380i	−0.107078	−	0.233413i
$535$		−	6.85876i		−	0.296530i
$536$	5.01868	+	1.44576i	0.216774	+	0.0624472i
$537$			0.589252i			0.0254281i
$538$	−7.88302	+	3.61632i	−0.339861	+	0.155911i
$539$	14.0221	−	14.0221i	0.603975	−	0.603975i
$540$	1.30456	−	1.51596i	0.0561392	−	0.0652365i
$541$	−4.64109	−	4.64109i	−0.199536	−	0.199536i	0.600265	−	0.799801i	$-0.295062\pi$
$541$	−4.64109	−	4.64109i	−0.199536	−	0.199536i	−0.799801	+	0.600265i	$0.795062\pi$
$542$	7.89057	−	21.2662i	0.338929	−	0.913461i
$543$	7.00334			0.300542
$544$	−3.31408	−	0.691380i	−0.142090	−	0.0296427i
$545$	−18.7036			−0.801175
$546$	5.81760	−	15.6792i	0.248970	−	0.671009i
$547$	−8.83067	−	8.83067i	−0.377572	−	0.377572i	0.492653	−	0.870226i	$-0.336027\pi$
$547$	−8.83067	−	8.83067i	−0.377572	−	0.377572i	−0.870226	+	0.492653i	$0.836027\pi$
$548$	17.6843	−	20.5500i	0.755434	−	0.877851i
$549$	3.65199	−	3.65199i	0.155863	−	0.155863i
$550$	−5.08463	+	2.33256i	−0.216809	+	0.0994608i
$551$		−	17.9423i		−	0.764366i
$552$	2.95269	−	10.2497i	0.125675	−	0.436257i
$553$			1.61288i			0.0685867i
$554$	−3.25932	−	7.10481i	−0.138475	−	0.301854i
$555$	7.71609	−	7.71609i	0.327530	−	0.327530i
$556$	46.6675	−	3.49782i	1.97914	−	0.148341i
$557$	−23.1040	−	23.1040i	−0.978949	−	0.978949i	0.0208344	−	0.999783i	$-0.493368\pi$
$557$	−23.1040	−	23.1040i	−0.978949	−	0.978949i	−0.999783	+	0.0208344i	$0.993368\pi$
$558$	−8.07085	−	2.99460i	−0.341666	−	0.126771i
$559$	−26.2186			−1.10893
$560$	−8.23245	+	11.1551i	−0.347885	+	0.471391i
$561$	−2.36731			−0.0999481
$562$	−38.4496	−	14.2663i	−1.62190	−	0.601787i
$563$	18.0010	+	18.0010i	0.758651	+	0.758651i	0.976077	−	0.217426i	$-0.0697659\pi$
$563$	18.0010	+	18.0010i	0.758651	+	0.758651i	−0.217426	+	0.976077i	$0.569766\pi$
$564$	−0.991186	−	13.2243i	−0.0417364	−	0.556844i
$565$	−2.39210	+	2.39210i	−0.100636	+	0.100636i
$566$	16.8439	+	36.7170i	0.708000	+	1.54333i
$567$		−	3.46600i		−	0.145558i
$568$	6.13903	+	11.1073i	0.257588	+	0.466050i
$569$		−	22.1289i		−	0.927693i	−0.885916	−	0.463847i	$-0.846469\pi$
$569$		−	22.1289i		−	0.927693i	0.885916	−	0.463847i	$-0.153531\pi$
$570$	−2.22252	+	1.01958i	−0.0930910	+	0.0427053i
$571$	−1.89239	+	1.89239i	−0.0791940	+	0.0791940i	−0.745594	−	0.666400i	$-0.767834\pi$
$571$	−1.89239	+	1.89239i	−0.0791940	+	0.0791940i	0.666400	+	0.745594i	$0.267834\pi$
$572$	20.4595	+	17.6064i	0.855453	+	0.736159i
$573$	4.77427	+	4.77427i	0.199448	+	0.199448i
$574$	11.3764	−	30.6610i	0.474843	−	1.27977i
$575$	−3.77119			−0.157269
$576$	6.77395	+	4.25601i	0.282248	+	0.177334i
$577$	19.9145			0.829051			0.414525	−	0.910038i	$-0.363948\pi$
$577$	19.9145			0.829051			0.414525	+	0.910038i	$0.363948\pi$
$578$	8.18705	−	22.0652i	0.340536	−	0.917792i
$579$	15.5857	+	15.5857i	0.647720	+	0.647720i
$580$	15.7312	+	13.5374i	0.653202	+	0.562112i
$581$	33.4924	−	33.4924i	1.38950	−	1.38950i
$582$	−6.73964	+	3.09180i	−0.279367	+	0.128159i
$583$			37.8697i			1.56840i
$584$	−6.15766	−	11.1410i	−0.254806	−	0.461017i
$585$			3.41184i			0.141062i
$586$	0.170916	+	0.372570i	0.00706047	+	0.0153907i
$587$	0.596001	−	0.596001i	0.0245996	−	0.0245996i	−0.694700	−	0.719300i	$-0.744463\pi$
$587$	0.596001	−	0.596001i	0.0245996	−	0.0245996i	0.719300	+	0.694700i	$0.244463\pi$
$588$	0.749388	+	9.99826i	0.0309042	+	0.412321i
$589$	7.44219	+	7.44219i	0.306650	+	0.306650i
$590$	12.7635	+	4.73574i	0.525464	+	0.194967i
$591$	2.79901			0.115136
$592$	35.1204	+	25.9187i	1.44344	+	1.06525i
$593$	−6.53092			−0.268193			−0.134096	−	0.990968i	$-0.542813\pi$
$593$	−6.53092			−0.268193			−0.134096	+	0.990968i	$0.542813\pi$
$594$	5.24474	+	1.94600i	0.215194	+	0.0798454i
$595$	1.46674	+	1.46674i	0.0601303	+	0.0601303i
$596$	31.4242	−	2.35530i	1.28719	−	0.0964770i
$597$	0.987826	−	0.987826i	0.0404290	−	0.0404290i
$598$	7.58723	+	16.5390i	0.310265	+	0.676330i
$599$			23.8960i			0.976366i	0.872741	+	0.488183i	$0.162340\pi$
$599$			23.8960i			0.976366i	−0.872741	+	0.488183i	$0.837660\pi$
$600$	0.782960	−	2.71790i	0.0319642	−	0.110958i
$601$			13.0267i			0.531369i	0.964060	+	0.265684i	$0.0855979\pi$
$601$			13.0267i			0.531369i	−0.964060	+	0.265684i	$0.914402\pi$
$602$	34.2366	−	15.7060i	1.39538	−	0.640128i
$603$	−1.30569	+	1.30569i	−0.0531720	+	0.0531720i
$604$	−25.0412	+	29.0991i	−1.01891	+	1.18402i
$605$	−3.28602	−	3.28602i	−0.133596	−	0.133596i
$606$	−0.439209	+	1.18373i	−0.0178417	+	0.0480857i
$607$	10.9108			0.442855			0.221427	−	0.975177i	$-0.428928\pi$
$607$	10.9108			0.442855			0.221427	+	0.975177i	$0.428928\pi$
$608$	−5.35795	−	8.18280i	−0.217293	−	0.331857i
$609$	35.9668			1.45745
$610$	2.54080	−	6.84781i	0.102874	−	0.277260i
$611$	15.9968	+	15.9968i	0.647162	+	0.647162i
$612$	0.780731	−	0.907248i	0.0315592	−	0.0366733i
$613$	−17.0276	+	17.0276i	−0.687737	+	0.687737i	−0.961731	−	0.273994i	$-0.911655\pi$
$613$	−17.0276	+	17.0276i	−0.687737	+	0.687737i	0.273994	+	0.961731i	$0.411655\pi$
$614$	5.98752	−	2.74676i	0.241637	−	0.110850i
$615$			6.67193i			0.269038i
$616$	−37.2631	−	10.7346i	−1.50137	−	0.432509i
$617$		−	11.3001i		−	0.454926i	−0.973787	−	0.227463i	$-0.926957\pi$
$617$		−	11.3001i		−	0.454926i	0.973787	−	0.227463i	$-0.0730431\pi$
$618$	−5.94270	−	12.9542i	−0.239050	−	0.521093i
$619$	−0.281710	+	0.281710i	−0.0113229	+	0.0113229i	−0.712746	−	0.701423i	$-0.752549\pi$
$619$	−0.281710	+	0.281710i	−0.0113229	+	0.0113229i	0.701423	+	0.712746i	$0.252549\pi$
$620$	−12.1402	+	0.909930i	−0.487562	+	0.0365437i
$621$	2.66663	+	2.66663i	0.107008	+	0.107008i
$622$	7.24757	+	2.68913i	0.290601	+	0.107824i
$623$	−14.5439			−0.582690
$624$	−13.4949	+	2.03436i	−0.540228	+	0.0814397i
$625$	−1.00000			−0.0400000
$626$	17.9823	+	6.67212i	0.718717	+	0.266672i
$627$	−4.83622	−	4.83622i	−0.193140	−	0.193140i
$628$	−3.12918	−	41.7492i	−0.124868	−	1.66598i
$629$	4.61781	−	4.61781i	0.184124	−	0.184124i
$630$	−2.04383	−	4.45523i	−0.0814281	−	0.177501i
$631$			10.6722i			0.424853i	0.977177	+	0.212427i	$0.0681367\pi$
$631$			10.6722i			0.424853i	−0.977177	+	0.212427i	$0.931863\pi$
$632$	1.15195	−	0.636688i	0.0458221	−	0.0253261i
$633$		−	18.8824i		−	0.750509i
$634$	31.5723	−	14.4837i	1.25389	−	0.575222i
$635$	5.45066	−	5.45066i	0.216303	−	0.216303i
$636$	−14.5132	−	12.4893i	−0.575485	−	0.495233i
$637$	−12.0944	−	12.0944i	−0.479198	−	0.479198i
$638$	−20.1938	+	54.4250i	−0.799479	+	2.15470i
$639$	−4.48691			−0.177499
$640$	11.2170	+	1.47626i	0.443390	+	0.0583543i
$641$	−19.3577			−0.764584			−0.382292	−	0.924042i	$-0.624865\pi$
$641$	−19.3577			−0.764584			−0.382292	+	0.924042i	$0.624865\pi$
$642$	−3.37421	+	9.09395i	−0.133169	+	0.358910i
$643$	−28.1959	−	28.1959i	−1.11194	−	1.11194i	−0.992888	−	0.119051i	$-0.962015\pi$
$643$	−28.1959	−	28.1959i	−1.11194	−	1.11194i	−0.119051	−	0.992888i	$-0.537985\pi$
$644$	−19.8150	−	17.0518i	−0.780821	−	0.671934i
$645$	−5.43382	+	5.43382i	−0.213957	+	0.213957i
$646$	−1.33010	+	0.610180i	−0.0523320	+	0.0240072i
$647$		−	27.3560i		−	1.07548i	−0.843112	−	0.537738i	$-0.819279\pi$
$647$		−	27.3560i		−	1.07548i	0.843112	−	0.537738i	$-0.180721\pi$
$648$	−2.47548	+	1.36821i	−0.0972461	+	0.0537483i
$649$			38.0785i			1.49471i
$650$	2.01189	+	4.38562i	0.0789130	+	0.172018i
$651$	−14.9185	+	14.9185i	−0.584703	+	0.584703i
$652$	1.63178	+	21.7710i	0.0639054	+	0.852619i
$653$	9.97726	+	9.97726i	0.390440	+	0.390440i	0.874844	−	0.484404i	$-0.160964\pi$
$653$	9.97726	+	9.97726i	0.390440	+	0.390440i	−0.484404	+	0.874844i	$0.660964\pi$
$654$	24.7989	+	9.20135i	0.969714	+	0.359801i
$655$	−13.9771			−0.546129
$656$	−26.3895	+	3.97824i	−1.03034	+	0.155324i
$657$	4.50053			0.175582
$658$	−30.4716	−	11.3061i	−1.18790	−	0.440758i
$659$	−7.55194	−	7.55194i	−0.294182	−	0.294182i	0.544548	−	0.838730i	$-0.316701\pi$
$659$	−7.55194	−	7.55194i	−0.294182	−	0.294182i	−0.838730	+	0.544548i	$0.816701\pi$
$660$	7.88916	−	0.591307i	0.307085	−	0.0230166i
$661$	−21.3017	+	21.3017i	−0.828539	+	0.828539i	−0.987315	−	0.158776i	$-0.949245\pi$
$661$	−21.3017	+	21.3017i	−0.828539	+	0.828539i	0.158776	+	0.987315i	$0.449245\pi$
$662$	−1.82974	−	3.98854i	−0.0711147	−	0.155019i
$663$			2.04187i			0.0792996i
$664$	−37.1421	−	10.6997i	−1.44139	−	0.415230i
$665$			5.99283i			0.232392i
$666$	−14.0266	+	6.43470i	−0.543522	+	0.249340i
$667$	−27.6718	+	27.6718i	−1.07146	+	1.07146i
$668$	−5.66726	+	6.58563i	−0.219273	+	0.254806i
$669$	−17.4805	−	17.4805i	−0.675835	−	0.675835i
$670$	−0.908411	+	2.44829i	−0.0350950	+	0.0945858i
$671$	20.4297			0.788680
$672$	16.4031	−	10.7405i	0.632765	−	0.414323i
$673$	5.59770			0.215776			0.107888	−	0.994163i	$-0.465591\pi$
$673$	5.59770			0.215776			0.107888	+	0.994163i	$0.465591\pi$
$674$	2.07954	−	5.60465i	0.0801010	−	0.215883i
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$	−1.77331	+	2.06067i	−0.0682041	+	0.0792566i
$677$	3.03008	−	3.03008i	0.116455	−	0.116455i	−0.646478	−	0.762933i	$-0.723759\pi$
$677$	3.03008	−	3.03008i	0.116455	−	0.116455i	0.762933	+	0.646478i	$0.223759\pi$
$678$	4.34846	−	1.99485i	0.167002	−	0.0766117i
$679$			18.1729i			0.697410i
$680$	0.468574	−	1.62657i	0.0179690	−	0.0623760i
$681$			23.1346i			0.886521i
$682$	−14.1986	−	30.9507i	−0.543692	−	1.18517i
$683$	−18.6842	+	18.6842i	−0.714929	+	0.714929i	−0.967562	−	0.252633i	$-0.918703\pi$
$683$	−18.6842	+	18.6842i	−0.714929	+	0.714929i	0.252633	+	0.967562i	$0.418703\pi$
$684$	3.44840	−	0.258464i	0.131853	−	0.00988260i
$685$	9.58537	+	9.58537i	0.366238	+	0.366238i
$686$	−9.13062	−	3.38781i	−0.348609	−	0.129347i
$687$	10.5356			0.401957
$688$	−24.7324	−	18.2524i	−0.942916	−	0.695868i
$689$	32.6636			1.24438
$690$	5.00017	+	1.85526i	0.190353	+	0.0706285i
$691$	22.0112	+	22.0112i	0.837344	+	0.837344i	0.988509	−	0.151165i	$-0.0483024\pi$
$691$	22.0112	+	22.0112i	0.837344	+	0.837344i	−0.151165	+	0.988509i	$0.548302\pi$
$692$	−1.89064	−	25.2247i	−0.0718712	−	0.958898i
$693$	9.69462	−	9.69462i	0.368268	−	0.368268i
$694$	−20.2125	−	44.0602i	−0.767258	−	1.67250i
$695$			23.3992i			0.887583i
$696$	−14.1980	−	25.6882i	−0.538173	−	0.973708i
$697$			3.99291i			0.151242i
$698$	−46.3975	+	21.2848i	−1.75617	+	0.805641i
$699$	−9.38053	+	9.38053i	−0.354804	+	0.354804i
$700$	−5.25431	−	4.52159i	−0.198594	−	0.170900i
$701$	35.1644	+	35.1644i	1.32814	+	1.32814i	0.906992	+	0.421147i	$0.138373\pi$
$701$	35.1644	+	35.1644i	1.32814	+	1.32814i	0.421147	+	0.906992i	$0.361627\pi$
$702$	1.67848	−	4.52372i	0.0633500	−	0.170737i
$703$	18.8676			0.711604
$704$	7.04283	+	30.8515i	0.265437	+	1.16276i
$705$	6.63070			0.249726
$706$	−0.658983	+	1.77605i	−0.0248011	+	0.0668425i
$707$	2.18806	+	2.18806i	0.0822904	+	0.0822904i
$708$	−14.5932	−	12.5581i	−0.548445	−	0.471963i
$709$	18.7390	−	18.7390i	0.703759	−	0.703759i	−0.261456	−	0.965215i	$-0.584203\pi$
$709$	18.7390	−	18.7390i	0.703759	−	0.703759i	0.965215	+	0.261456i	$0.0842026\pi$
$710$	−5.76752	+	2.64584i	−0.216451	+	0.0992965i
$711$			0.465344i			0.0174518i
$712$	5.74124	+	10.3875i	0.215162	+	0.389290i
$713$		−	22.9557i		−	0.859698i
$714$	−1.22316	−	2.66630i	−0.0457756	−	0.0997837i
$715$	−9.54315	+	9.54315i	−0.356893	+	0.356893i
$716$	−0.0880840	−	1.17521i	−0.00329185	−	0.0439196i
$717$	−6.80193	−	6.80193i	−0.254023	−	0.254023i
$718$	2.09742	+	0.778222i	0.0782749	+	0.0290430i
$719$	1.26449			0.0471577			0.0235788	−	0.999722i	$-0.492494\pi$
$719$	1.26449			0.0471577			0.0235788	+	0.999722i	$0.492494\pi$
$720$	−2.37520	+	3.21845i	−0.0885186	+	0.119945i
$721$	−34.9298			−1.30085
$722$	21.2281	+	7.87643i	0.790026	+	0.293130i
$723$	1.27732	+	1.27732i	0.0475042	+	0.0475042i
$724$	−13.9675	+	1.04689i	−0.519098	+	0.0389073i
$725$	−7.33768	+	7.33768i	−0.272515	+	0.272515i
$726$	2.74032	+	5.97347i	0.101703	+	0.221696i
$727$		−	37.0184i		−	1.37294i	−0.727160	−	0.686468i	$-0.759160\pi$
$727$		−	37.0184i		−	1.37294i	0.727160	−	0.686468i	$-0.240840\pi$
$728$	−9.25885	+	32.1404i	−0.343156	+	1.19120i
$729$		−	1.00000i		−	0.0370370i
$730$	5.78502	−	2.65387i	0.214113	−	0.0982241i
$731$	−3.25195	+	3.25195i	−0.120278	+	0.120278i
$732$	−6.73764	+	7.82947i	−0.249030	+	0.289386i
$733$	22.6752	+	22.6752i	0.837528	+	0.837528i	0.988533	−	0.151005i	$-0.0482509\pi$
$733$	22.6752	+	22.6752i	0.837528	+	0.837528i	−0.151005	+	0.988533i	$0.548251\pi$
$734$	1.36645	−	3.68278i	0.0504367	−	0.135934i
$735$	−5.01315			−0.184913
$736$	−4.35669	+	20.8835i	−0.160590	+	0.769775i
$737$	−7.30422			−0.269054
$738$	3.28229	−	8.84623i	0.120823	−	0.325634i
$739$	−24.3479	−	24.3479i	−0.895650	−	0.895650i	0.0993974	−	0.995048i	$-0.468309\pi$
$739$	−24.3479	−	24.3479i	−0.895650	−	0.895650i	−0.995048	+	0.0993974i	$0.968309\pi$
$740$	−14.2356	+	16.5425i	−0.523310	+	0.608113i
$741$	−4.17136	+	4.17136i	−0.153239	+	0.153239i
$742$	−42.6526	+	19.5668i	−1.56582	+	0.718319i
$743$			8.30540i			0.304696i	0.988327	+	0.152348i	$0.0486834\pi$
$743$			8.30540i			0.304696i	−0.988327	+	0.152348i	$0.951317\pi$
$744$	16.5442	+	4.76597i	0.606539	+	0.174729i
$745$			15.7562i			0.577262i
$746$	−0.850275	−	1.85347i	−0.0311308	−	0.0678603i
$747$	9.66313	−	9.66313i	0.353556	−	0.353556i
$748$	4.72139	−	0.353877i	0.172631	−	0.0129390i
$749$	16.8097	+	16.8097i	0.614212	+	0.614212i
$750$	1.32589	+	0.491956i	0.0484146	+	0.0179637i
$751$	25.5429			0.932072			0.466036	−	0.884766i	$-0.345682\pi$
$751$	25.5429			0.932072			0.466036	+	0.884766i	$0.345682\pi$
$752$	3.95365	+	26.2265i	0.144175	+	0.956380i
$753$	−12.4595			−0.454050
$754$	46.9429	+	17.4176i	1.70956	+	0.634313i
$755$	−13.5730	−	13.5730i	−0.493973	−	0.493973i
$756$	0.518113	+	6.91261i	0.0188436	+	0.251409i
$757$	−33.5257	+	33.5257i	−1.21851	+	1.21851i	−0.250360	+	0.968153i	$0.580549\pi$
$757$	−33.5257	+	33.5257i	−1.21851	+	1.21851i	−0.968153	+	0.250360i	$0.919451\pi$
$758$	0.0821791	+	0.179138i	0.00298488	+	0.00650657i
$759$			14.9175i			0.541470i
$760$	4.28019	−	2.36568i	0.155259	−	0.0858122i
$761$			1.11780i			0.0405204i	0.999795	+	0.0202602i	$0.00644946\pi$
$761$			1.11780i			0.0405204i	−0.999795	+	0.0202602i	$0.993551\pi$
$762$	−9.90845	+	4.54548i	−0.358945	+	0.164665i
$763$	45.8394	−	45.8394i	1.65950	−	1.65950i
$764$	−10.2355	−	8.80816i	−0.370308	−	0.318668i
$765$	0.423179	+	0.423179i	0.0153001	+	0.0153001i
$766$	12.4435	−	33.5371i	0.449604	−	1.21174i
$767$	32.8436			1.18592
$768$	−14.1462	−	7.47561i	−0.510457	−	0.269753i
$769$	−45.1363			−1.62766			−0.813828	−	0.581105i	$-0.802621\pi$
$769$	−45.1363			−1.62766			−0.813828	+	0.581105i	$0.802621\pi$
$770$	6.74484	−	18.1783i	0.243067	−	0.655100i
$771$	10.2424	+	10.2424i	0.368870	+	0.368870i
$772$	−33.4140	−	28.7544i	−1.20260	−	1.03489i
$773$	8.92923	−	8.92923i	0.321162	−	0.321162i	−0.528051	−	0.849213i	$-0.677077\pi$
$773$	8.92923	−	8.92923i	0.321162	−	0.321162i	0.849213	+	0.528051i	$0.177077\pi$
$774$	9.87784	−	4.53144i	0.355052	−	0.162879i
$775$		−	6.08712i		−	0.218656i
$776$	12.9794	−	7.17377i	0.465933	−	0.257523i
$777$			37.8217i			1.35685i
$778$	1.10673	+	2.41249i	0.0396781	+	0.0864920i
$779$	−8.15718	+	8.15718i	−0.292261	+	0.292261i
$780$	−0.510017	−	6.80460i	−0.0182616	−	0.243644i
$781$	−12.5502	−	12.5502i	−0.449080	−	0.449080i
$782$	2.99243	+	1.11031i	0.107009	+	0.0397045i
$783$	10.3770			0.370845
$784$	−2.98917	−	19.8286i	−0.106756	−	0.708163i
$785$	20.9332			0.747137
$786$	18.5320	+	6.87610i	0.661016	+	0.245262i
$787$	−3.29068	−	3.29068i	−0.117300	−	0.117300i	0.646020	−	0.763320i	$-0.276432\pi$
$787$	−3.29068	−	3.29068i	−0.117300	−	0.117300i	−0.763320	+	0.646020i	$0.776432\pi$
$788$	−5.58236	+	0.418408i	−0.198863	+	0.0149052i
$789$	−10.5463	+	10.5463i	−0.375458	+	0.375458i
$790$	0.274404	+	0.598158i	0.00976285	+	0.0212815i
$791$		−	11.7253i		−	0.416902i
$792$	−10.7510	−	3.09711i	−0.382022	−	0.110051i
$793$		−	17.6211i		−	0.625745i
$794$	−4.21608	+	1.93412i	−0.149623	+	0.0686394i
$795$	6.76955	−	6.76955i	0.240091	−	0.240091i
$796$	−1.82246	+	2.11779i	−0.0645954	+	0.0750631i
$797$	11.8032	+	11.8032i	0.418090	+	0.418090i	0.884545	−	0.466455i	$-0.154469\pi$
$797$	11.8032	+	11.8032i	0.418090	+	0.418090i	−0.466455	+	0.884545i	$0.654469\pi$
$798$	2.94821	−	7.94582i	0.104365	−	0.281279i
$799$	3.96824			0.140386
$800$	−1.15526	+	5.53763i	−0.0408445	+	0.195785i
$801$	−4.19617			−0.148264
$802$	−9.47248	+	25.5296i	−0.334485	+	0.901483i
$803$	12.5883	+	12.5883i	0.444230	+	0.444230i
$804$	2.40890	−	2.79926i	0.0849554	−	0.0987224i
$805$	9.24255	−	9.24255i	0.325757	−	0.325757i
$806$	−26.6958	+	12.2467i	−0.940320	+	0.431370i
$807$			6.13269i			0.215881i
$808$	0.699012	−	2.42649i	0.0245912	−	0.0853637i
$809$			42.6601i			1.49985i	0.661524	+	0.749924i	$0.269910\pi$
$809$			42.6601i			1.49985i	−0.661524	+	0.749924i	$0.730090\pi$
$810$	−0.589679	−	1.28541i	−0.0207192	−	0.0451647i
$811$	4.50680	−	4.50680i	0.158255	−	0.158255i	−0.623538	−	0.781793i	$-0.714305\pi$
$811$	4.50680	−	4.50680i	0.158255	−	0.158255i	0.781793	+	0.623538i	$0.214305\pi$
$812$	−71.7325	+	5.37648i	−2.51732	+	0.188678i
$813$	−11.3414	−	11.3414i	−0.397761	−	0.397761i
$814$	−57.2317	−	21.2352i	−2.00597	−	0.744292i
$815$	−10.9160			−0.382372
$816$	−1.42148	+	1.92613i	−0.0497616	+	0.0674280i
$817$	−13.2869			−0.464850
$818$	49.0281	+	18.1913i	1.71423	+	0.636045i
$819$	−8.36186	−	8.36186i	−0.292187	−	0.292187i
$820$	−0.997349	−	13.3065i	−0.0348289	−	0.464684i
$821$	2.96883	−	2.96883i	0.103613	−	0.103613i	−0.653400	−	0.757013i	$-0.726658\pi$
$821$	2.96883	−	2.96883i	0.103613	−	0.103613i	0.757013	+	0.653400i	$0.226658\pi$
$822$	−7.99355	−	17.4247i	−0.278807	−	0.607756i
$823$			19.6410i			0.684641i	0.939583	+	0.342321i	$0.111213\pi$
$823$			19.6410i			0.684641i	−0.939583	+	0.342321i	$0.888787\pi$
$824$	13.7886	+	24.9475i	0.480348	+	0.869088i
$825$			3.95565i			0.137718i
$826$	−42.8876	+	19.6746i	−1.49225	+	0.684568i
$827$	3.67783	−	3.67783i	0.127891	−	0.127891i	−0.640264	−	0.768155i	$-0.721175\pi$
$827$	3.67783	−	3.67783i	0.127891	−	0.127891i	0.768155	+	0.640264i	$0.221175\pi$
$828$	−5.71697	−	4.91973i	−0.198678	−	0.170972i
$829$	2.44218	+	2.44218i	0.0848204	+	0.0848204i	0.748244	−	0.663424i	$-0.230897\pi$
$829$	2.44218	+	2.44218i	0.0848204	+	0.0848204i	−0.663424	+	0.748244i	$0.730897\pi$
$830$	6.72294	−	18.1192i	0.233357	−	0.628928i
$831$	−5.52727			−0.191739
$832$	26.6102	−	6.07462i	0.922543	−	0.210600i
$833$	−3.00019			−0.103951
$834$	11.5114	−	31.0248i	0.398606	−	1.07430i
$835$	−3.07181	−	3.07181i	−0.106305	−	0.106305i
$836$	10.3683	+	8.92244i	0.358596	+	0.308589i
$837$	−4.30425	+	4.30425i	−0.148777	+	0.148777i
$838$	32.5621	−	14.9378i	1.12484	−	0.516018i
$839$		−	38.9897i		−	1.34607i	−0.739610	−	0.673036i	$-0.764990\pi$
$839$		−	38.9897i		−	1.34607i	0.739610	−	0.673036i	$-0.235010\pi$
$840$	4.74221	+	8.58001i	0.163622	+	0.296039i
$841$			78.6831i			2.71321i
$842$	−4.56109	−	9.94248i	−0.157186	−	0.342640i
$843$	−20.5055	+	20.5055i	−0.706247	+	0.706247i
$844$	2.82263	+	37.6592i	0.0971588	+	1.29628i
$845$	−0.961183	−	0.961183i	−0.0330657	−	0.0330657i
$846$	−8.79156	−	3.26201i	−0.302260	−	0.112150i
$847$	16.1070			0.553441
$848$	30.8121	+	22.7392i	1.05809	+	0.780868i
$849$	28.5644			0.980328
$850$	0.793497	+	0.294418i	0.0272167	+	0.0100985i
$851$	−29.0988	−	29.0988i	−0.997495	−	0.997495i
$852$	8.94872	−	0.670723i	0.306578	−	0.0229786i
$853$	19.3876	−	19.3876i	0.663820	−	0.663820i	−0.292458	−	0.956278i	$-0.594473\pi$
$853$	19.3876	−	19.3876i	0.663820	−	0.663820i	0.956278	+	0.292458i	$0.0944732\pi$
$854$	10.5558	+	23.0099i	0.361211	+	0.787383i
$855$			1.72903i			0.0591317i
$856$	5.37013	−	18.6414i	0.183547	−	0.637151i
$857$		−	49.8844i		−	1.70402i	−0.523526	−	0.852009i	$-0.675384\pi$
$857$		−	49.8844i		−	1.70402i	0.523526	−	0.852009i	$-0.324616\pi$
$858$	17.3479	−	7.95834i	0.592249	−	0.271693i
$859$	1.36794	−	1.36794i	0.0466734	−	0.0466734i	−0.683385	−	0.730058i	$-0.739493\pi$
$859$	1.36794	−	1.36794i	0.0466734	−	0.0466734i	0.730058	+	0.683385i	$0.239493\pi$
$860$	10.0250	−	11.6495i	0.341849	−	0.397245i
$861$	−16.3518	−	16.3518i	−0.557267	−	0.557267i
$862$	5.15180	−	13.8848i	0.175471	−	0.472918i
$863$	23.2019			0.789801			0.394900	−	0.918724i	$-0.370779\pi$
$863$	23.2019			0.789801			0.394900	+	0.918724i	$0.370779\pi$
$864$	4.73259	−	3.09881i	0.161006	−	0.105424i
$865$	12.6477			0.430035
$866$	19.8648	−	53.5384i	0.675034	−	1.81931i
$867$	−11.7676	−	11.7676i	−0.399647	−	0.399647i
$868$	27.5235	−	31.9837i	0.934208	−	1.08560i
$869$	−1.30160	+	1.30160i	−0.0441537	+	0.0441537i
$870$	13.3388	−	6.11913i	0.452226	−	0.207458i
$871$			6.30007i			0.213470i
$872$	−50.8345	−	14.6442i	−1.72147	−	0.495914i
$873$			5.24318i			0.177455i
$874$	3.84501	+	8.38153i	0.130059	+	0.283510i
$875$	2.45083	−	2.45083i	0.0828532	−	0.0828532i
$876$	−8.97588	+	0.672759i	−0.303267	+	0.0227304i
$877$	5.54070	+	5.54070i	0.187096	+	0.187096i	0.794439	−	0.607343i	$-0.207765\pi$
$877$	5.54070	+	5.54070i	0.187096	+	0.187096i	−0.607343	+	0.794439i	$0.707765\pi$
$878$	40.6669	+	15.0890i	1.37244	+	0.509229i
$879$	0.289845			0.00977624
$880$	−15.6458	+	2.35861i	−0.527420	+	0.0795088i
$881$	−3.18531			−0.107316			−0.0536580	−	0.998559i	$-0.517088\pi$
$881$	−3.18531			−0.107316			−0.0536580	+	0.998559i	$0.517088\pi$
$882$	6.64688	+	2.46625i	0.223812	+	0.0830429i
$883$	−4.64476	−	4.64476i	−0.156309	−	0.156309i	0.624620	−	0.780929i	$-0.285254\pi$
$883$	−4.64476	−	4.64476i	−0.156309	−	0.156309i	−0.780929	+	0.624620i	$0.785254\pi$
$884$	−0.305227	−	4.07231i	−0.0102659	−	0.136967i
$885$	6.80686	−	6.80686i	0.228810	−	0.228810i
$886$	3.53612	+	7.70819i	0.118798	+	0.258962i
$887$			6.16778i			0.207094i	0.994625	+	0.103547i	$0.0330192\pi$
$887$			6.16778i			0.207094i	−0.994625	+	0.103547i	$0.966981\pi$
$888$	27.0129	−	14.9302i	0.906495	−	0.501024i
$889$			26.7173i			0.896069i
$890$	−5.39380	+	2.47440i	−0.180801	+	0.0829419i
$891$	2.79706	−	2.79706i	0.0937052	−	0.0937052i
$892$	37.4763	+	32.2501i	1.25480	+	1.07981i
$893$	8.10677	+	8.10677i	0.271283	+	0.271283i
$894$	7.75135	−	20.8910i	0.259244	−	0.698698i
$895$	0.589252			0.0196965
$896$	−31.1090	+	23.8729i	−1.03928	+	0.797537i
$897$	12.8667			0.429607
$898$	−11.8449	+	31.9235i	−0.395268	+	1.06530i
$899$	−44.6654	−	44.6654i	−1.48967	−	1.48967i
$900$	−1.51596	−	1.30456i	−0.0505320	−	0.0434852i
$901$	4.05134	−	4.05134i	0.134970	−	0.134970i
$902$	33.9243	−	15.5627i	1.12955	−	0.518181i
$903$		−	26.6348i		−	0.886349i
$904$	−8.37439	+	4.62856i	−0.278528	+	0.153944i
$905$		−	7.00334i		−	0.232799i
$906$	11.3190	+	24.6736i	0.376048	+	0.819727i
$907$	−14.7781	+	14.7781i	−0.490699	+	0.490699i	−0.908526	−	0.417827i	$-0.862792\pi$
$907$	−14.7781	+	14.7781i	−0.490699	+	0.490699i	0.417827	+	0.908526i	$0.362792\pi$
$908$	−3.45826	−	46.1398i	−0.114767	−	1.53120i
$909$	0.631292	+	0.631292i	0.0209386	+	0.0209386i
$910$	−15.6792	−	5.81760i	−0.519761	−	0.192851i
$911$	22.6301			0.749767			0.374884	−	0.927072i	$-0.377683\pi$
$911$	22.6301			0.749767			0.374884	+	0.927072i	$0.377683\pi$
$912$	−6.83886	+	1.03096i	−0.226457	+	0.0341386i
$913$	54.0568			1.78902
$914$	0.651331	+	0.241669i	0.0215441	+	0.00799370i
$915$	−3.65199	−	3.65199i	−0.120731	−	0.120731i
$916$	−21.0122	+	1.57490i	−0.694263	+	0.0520363i
$917$	34.2554	−	34.2554i	1.13121	−	1.13121i
$918$	−0.352902	−	0.769272i	−0.0116475	−	0.0253898i
$919$		−	43.5179i		−	1.43552i	−0.696289	−	0.717762i	$-0.745167\pi$
$919$		−	43.5179i		−	1.43552i	0.696289	−	0.717762i	$-0.254833\pi$
$920$	−10.2497	−	2.95269i	−0.337923	−	0.0973473i
$921$		−	4.65806i		−	0.153488i
$922$	49.6519	−	22.7777i	1.63520	−	0.750144i
$923$	−10.8248	+	10.8248i	−0.356304	+	0.356304i
$924$	−17.8858	+	20.7842i	−0.588400	+	0.683750i
$925$	−7.71609	−	7.71609i	−0.253704	−	0.253704i
$926$	1.58970	−	4.28445i	0.0522407	−	0.140796i
$927$	−10.0778			−0.331000
$928$	32.1565	+	49.1103i	1.05559	+	1.61212i
$929$	25.4107			0.833700			0.416850	−	0.908975i	$-0.363134\pi$
$929$	25.4107			0.833700			0.416850	+	0.908975i	$0.363134\pi$
$930$	−2.99460	+	8.07085i	−0.0981966	+	0.264653i
$931$	−6.12914	−	6.12914i	−0.200874	−	0.200874i
$932$	17.3063	−	20.1108i	0.566888	−	0.658752i
$933$	3.86519	−	3.86519i	0.126541	−	0.126541i
$934$	18.4961	−	8.48507i	0.605212	−	0.277640i
$935$			2.36731i			0.0774195i
$936$	−2.67134	+	9.27305i	−0.0873154	+	0.303099i
$937$			31.3262i			1.02338i	0.859169	+	0.511692i	$0.170981\pi$
$937$			31.3262i			1.02338i	−0.859169	+	0.511692i	$0.829019\pi$
$938$	−3.77399	−	8.22671i	−0.123225	−	0.268612i
$939$	9.59010	−	9.59010i	0.312961	−	0.312961i
$940$	−13.2243	+	0.991186i	−0.431329	+	0.0323289i
$941$	−27.7568	−	27.7568i	−0.904846	−	0.904846i	0.0910049	−	0.995850i	$-0.470992\pi$
$941$	−27.7568	−	27.7568i	−0.904846	−	0.904846i	−0.995850	+	0.0910049i	$0.970992\pi$
$942$	−27.7550	−	10.2982i	−0.904308	−	0.335533i
$943$	25.1611			0.819358
$944$	30.9819	+	22.8646i	1.00838	+	0.744178i
$945$	−3.46600			−0.112749
$946$	40.3037	+	14.9542i	1.31039	+	0.486204i
$947$	10.6786	+	10.6786i	0.347007	+	0.347007i	0.858994	−	0.511986i	$-0.171090\pi$
$947$	10.6786	+	10.6786i	0.347007	+	0.347007i	−0.511986	+	0.858994i	$0.671090\pi$
$948$	−0.0695617	−	0.928085i	−0.00225926	−	0.0301428i
$949$	10.8577	−	10.8577i	0.352456	−	0.352456i
$950$	1.01958	+	2.22252i	0.0330794	+	0.0721080i
$951$		−	24.5620i		−	0.796478i
$952$	2.83805	+	5.13484i	0.0919816	+	0.166421i
$953$			55.8599i			1.80948i	0.425964	+	0.904740i	$0.359935\pi$
$953$			55.8599i			1.80948i	−0.425964	+	0.904740i	$0.640065\pi$
$954$	−12.3060	+	5.64535i	−0.398421	+	0.182775i
$955$	4.77427	−	4.77427i	0.154492	−	0.154492i
$956$	14.5826	+	12.5490i	0.471634	+	0.405864i
$957$	29.0253	+	29.0253i	0.938254	+	0.938254i
$958$	−4.68517	+	12.6272i	−0.151371	+	0.407966i
$959$	−46.9842			−1.51720
$960$	4.25601	−	6.77395i	0.137362	−	0.218628i
$961$	6.05308			0.195261
$962$	−18.3159	+	49.3638i	−0.590527	+	1.59155i
$963$	4.84988	+	4.84988i	0.156285	+	0.156285i
$964$	−2.73844	−	2.35656i	−0.0881993	−	0.0758998i
$965$	15.5857	−	15.5857i	0.501722	−	0.501722i
$966$	−16.8015	+	7.70766i	−0.540580	+	0.247990i
$967$			11.9955i			0.385751i	0.981223	+	0.192875i	$0.0617813\pi$
$967$			11.9955i			0.385751i	−0.981223	+	0.192875i	$0.938219\pi$
$968$	−6.35825	−	11.5039i	−0.204362	−	0.369749i
$969$			1.03477i			0.0332415i
$970$	3.09180	+	6.73964i	0.0992716	+	0.216397i
$971$	−11.8724	+	11.8724i	−0.381003	+	0.381003i	−0.871463	−	0.490460i	$-0.836829\pi$
$971$	−11.8724	+	11.8724i	−0.381003	+	0.381003i	0.490460	+	0.871463i	$0.336829\pi$
$972$	0.149484	+	1.99441i	0.00479471	+	0.0639706i
$973$	−57.3475	−	57.3475i	−1.83848	−	1.83848i
$974$	22.3134	+	8.27912i	0.714967	+	0.265280i
$975$	3.41184			0.109266
$976$	12.2672	−	16.6223i	0.392664	−	0.532067i
$977$	−50.9567			−1.63025			−0.815124	−	0.579287i	$-0.803331\pi$
$977$	−50.9567			−1.63025			−0.815124	+	0.579287i	$0.803331\pi$
$978$	14.4735	+	5.37021i	0.462810	+	0.171720i
$979$	−11.7370	−	11.7370i	−0.375115	−	0.375115i
$980$	9.99826	−	0.749388i	0.319383	−	0.0239383i
$981$	13.2255	−	13.2255i	0.422256	−	0.422256i
$982$	6.81376	+	14.8529i	0.217436	+	0.473977i
$983$		−	21.6483i		−	0.690472i	−0.938516	−	0.345236i	$-0.887799\pi$
$983$		−	21.6483i		−	0.690472i	0.938516	−	0.345236i	$-0.112201\pi$
$984$	−5.22385	+	18.1336i	−0.166530	+	0.578079i
$985$		−	2.79901i		−	0.0891839i
$986$	7.98278	−	3.66208i	0.254223	−	0.116625i
$987$	−16.2507	+	16.2507i	−0.517266	+	0.517266i
$988$	7.69583	−	8.94294i	0.244837	−	0.284513i
$989$	20.4920	+	20.4920i	0.651607	+	0.651607i
$990$	1.94600	−	5.24474i	0.0618480	−	0.166689i
$991$	−19.1200			−0.607366			−0.303683	−	0.952773i	$-0.598216\pi$
$991$	−19.1200			−0.607366			−0.303683	+	0.952773i	$0.598216\pi$
$992$	−33.7083	−	7.03219i	−1.07024	−	0.223272i
$993$	−3.10293			−0.0984686
$994$	7.65071	−	20.6197i	0.242666	−	0.654018i
$995$	−0.987826	−	0.987826i	−0.0313162	−	0.0313162i
$996$	−17.8277	+	20.7167i	−0.564893	+	0.656434i
$997$	33.6653	−	33.6653i	1.06619	−	1.06619i	0.0685411	−	0.997648i	$-0.478166\pi$
$997$	33.6653	−	33.6653i	1.06619	−	1.06619i	0.997648	−	0.0685411i	$-0.0218344\pi$
$998$	−48.2486	+	22.1340i	−1.52728	+	0.700639i
$999$			10.9122i			0.345247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.5	✓	20
3.2	odd	2		720.2.t.d.541.6		20
4.3	odd	2		960.2.s.c.721.2		20
8.3	odd	2		1920.2.s.f.1441.7		20
8.5	even	2		1920.2.s.e.1441.4		20
12.11	even	2		2880.2.t.d.721.2		20
16.3	odd	4		1920.2.s.f.481.9		20
16.5	even	4	inner	240.2.s.c.181.5	yes	20
16.11	odd	4		960.2.s.c.241.4		20
16.13	even	4		1920.2.s.e.481.2		20
48.5	odd	4		720.2.t.d.181.6		20
48.11	even	4		2880.2.t.d.2161.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.5	✓	20	1.1	even	1	trivial
240.2.s.c.181.5	yes	20	16.5	even	4	inner
720.2.t.d.181.6		20	48.5	odd	4
720.2.t.d.541.6		20	3.2	odd	2
960.2.s.c.241.4		20	16.11	odd	4
960.2.s.c.721.2		20	4.3	odd	2
1920.2.s.e.481.2		20	16.13	even	4
1920.2.s.e.1441.4		20	8.5	even	2
1920.2.s.f.481.9		20	16.3	odd	4
1920.2.s.f.1441.7		20	8.3	odd	2
2880.2.t.d.721.2		20	12.11	even	2
2880.2.t.d.2161.4		20	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)

\(f(q)\)	\(=\)	\(q+(-0.491956 + 1.32589i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.51596 - 1.30456i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.28541 + 0.589679i) q^{6} +3.46600i q^{7} +(2.47548 - 1.36821i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.491956 + 1.32589i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.51596 - 1.30456i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.28541 + 0.589679i) q^{6} +3.46600i q^{7} +(2.47548 - 1.36821i) q^{8} +1.00000i q^{9} +(0.589679 + 1.28541i) q^{10} +(-2.79706 + 2.79706i) q^{11} +(-0.149484 - 1.99441i) q^{12} +(2.41254 + 2.41254i) q^{13} +(-4.59553 - 1.70512i) q^{14} +1.00000 q^{15} +(0.596265 + 3.95531i) q^{16} +0.598465 q^{17} +(-1.32589 - 0.491956i) q^{18} +(1.22261 + 1.22261i) q^{19} +(-1.99441 + 0.149484i) q^{20} +(-2.45083 + 2.45083i) q^{21} +(-2.33256 - 5.08463i) q^{22} -3.77119i q^{23} +(2.71790 + 0.782960i) q^{24} -1.00000i q^{25} +(-4.38562 + 2.01189i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.52159 - 5.25431i) q^{28} +(-7.33768 - 7.33768i) q^{29} +(-0.491956 + 1.32589i) q^{30} +6.08712 q^{31} +(-5.53763 - 1.15526i) q^{32} -3.95565 q^{33} +(-0.294418 + 0.793497i) q^{34} +(2.45083 + 2.45083i) q^{35} +(1.30456 - 1.51596i) q^{36} +(7.71609 - 7.71609i) q^{37} +(-2.22252 + 1.01958i) q^{38} +3.41184i q^{39} +(0.782960 - 2.71790i) q^{40} +6.67193i q^{41} +(-2.04383 - 4.45523i) q^{42} +(-5.43382 + 5.43382i) q^{43} +(7.88916 - 0.591307i) q^{44} +(0.707107 + 0.707107i) q^{45} +(5.00017 + 1.85526i) q^{46} +6.63070 q^{47} +(-2.37520 + 3.21845i) q^{48} -5.01315 q^{49} +(1.32589 + 0.491956i) q^{50} +(0.423179 + 0.423179i) q^{51} +(-0.510017 - 6.80460i) q^{52} +(6.76955 - 6.76955i) q^{53} +(-0.589679 - 1.28541i) q^{54} +3.95565i q^{55} +(4.74221 + 8.58001i) q^{56} +1.72903i q^{57} +(13.3388 - 6.11913i) q^{58} +(6.80686 - 6.80686i) q^{59} +(-1.51596 - 1.30456i) q^{60} +(-3.65199 - 3.65199i) q^{61} +(-2.99460 + 8.07085i) q^{62} -3.46600 q^{63} +(4.25601 - 6.77395i) q^{64} +3.41184 q^{65} +(1.94600 - 5.24474i) q^{66} +(1.30569 + 1.30569i) q^{67} +(-0.907248 - 0.780731i) q^{68} +(2.66663 - 2.66663i) q^{69} +(-4.45523 + 2.04383i) q^{70} +4.48691i q^{71} +(1.36821 + 2.47548i) q^{72} -4.50053i q^{73} +(6.43470 + 14.0266i) q^{74} +(0.707107 - 0.707107i) q^{75} +(-0.258464 - 3.44840i) q^{76} +(-9.69462 - 9.69462i) q^{77} +(-4.52372 - 1.67848i) q^{78} +0.465344 q^{79} +(3.21845 + 2.37520i) q^{80} -1.00000 q^{81} +(-8.84623 - 3.28229i) q^{82} +(-9.66313 - 9.66313i) q^{83} +(6.91261 - 0.518113i) q^{84} +(0.423179 - 0.423179i) q^{85} +(-4.53144 - 9.87784i) q^{86} -10.3770i q^{87} +(-3.09711 + 10.7510i) q^{88} +4.19617i q^{89} +(-1.28541 + 0.589679i) q^{90} +(-8.36186 + 8.36186i) q^{91} +(-4.91973 + 5.71697i) q^{92} +(4.30425 + 4.30425i) q^{93} +(-3.26201 + 8.79156i) q^{94} +1.72903 q^{95} +(-3.09881 - 4.73259i) q^{96} +5.24318 q^{97} +(2.46625 - 6.64688i) q^{98} +(-2.79706 - 2.79706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

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