LMFDB - Embedded newform 330.2.m.f.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(31,330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("330.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.m (of order $5$, degree $4$, 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:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.2769390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 $ x^8 - x^7 - 2x^6 + 5x^5 + 21x^4 + 75x^3 - 198x^2 - 87x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$1.77873 - 1.10367i$ of defining polynomial
Character	$\chi$	$=$	330.31
Dual form			330.2.m.f.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.27873 - 0.929049i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.27873 - 0.929049i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.00000 q^{10} +(-2.99607 + 1.42251i) q^{11} +1.00000 q^{12} +(1.77873 - 5.47436i) q^{13} +(1.27873 - 0.929049i) q^{14} +(0.809017 + 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.21735 - 6.82429i) q^{17} +(0.809017 + 0.587785i) q^{18} +(1.06902 - 0.776691i) q^{19} +(-0.309017 + 0.951057i) q^{20} +1.58059 q^{21} +(-0.427051 - 3.28902i) q^{22} -0.358826 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(4.65677 + 3.38334i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.488430 + 1.50323i) q^{28} +(7.82381 + 5.68433i) q^{29} +(-0.809017 + 0.587785i) q^{30} +(2.22450 - 6.84630i) q^{31} -1.00000 q^{32} +(1.58774 - 2.91188i) q^{33} +7.17549 q^{34} +(-0.488430 + 1.50323i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-7.87411 - 5.72088i) q^{37} +(0.408331 + 1.25671i) q^{38} +(1.77873 + 5.47436i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-9.71342 + 7.05721i) q^{41} +(-0.488430 + 1.50323i) q^{42} +6.41156 q^{43} +(3.26001 + 0.610212i) q^{44} -1.00000 q^{45} +(0.110883 - 0.341264i) q^{46} +(-5.27480 + 3.83237i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-1.39111 - 4.28140i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(5.80509 + 4.21765i) q^{51} +(-4.65677 + 3.38334i) q^{52} +(0.724498 - 2.22978i) q^{53} -1.00000 q^{54} +(2.27873 + 2.40986i) q^{55} -1.58059 q^{56} +(-0.408331 + 1.25671i) q^{57} +(-7.82381 + 5.68433i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(-0.309017 - 0.951057i) q^{60} +(-1.74079 - 5.35761i) q^{61} +(5.82381 + 4.23125i) q^{62} +(-1.27873 + 0.929049i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.75608 q^{65} +(2.27873 + 2.40986i) q^{66} -5.07747 q^{67} +(-2.21735 + 6.82429i) q^{68} +(0.290297 - 0.210913i) q^{69} +(-1.27873 - 0.929049i) q^{70} +(2.81666 + 8.66879i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(5.61803 + 4.08174i) q^{73} +(7.87411 - 5.72088i) q^{74} +(0.309017 - 0.951057i) q^{75} -1.32139 q^{76} +(5.15274 + 0.964497i) q^{77} -5.75608 q^{78} +(-3.56187 + 10.9623i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.71020 - 11.4188i) q^{82} +(-2.47214 - 7.60845i) q^{83} +(-1.27873 - 0.929049i) q^{84} +(-5.80509 + 4.21765i) q^{85} +(-1.98128 + 6.09775i) q^{86} -9.67076 q^{87} +(-1.58774 + 2.91188i) q^{88} +7.16764 q^{89} +(0.309017 - 0.951057i) q^{90} +(-7.36045 + 5.34768i) q^{91} +(0.290297 + 0.210913i) q^{92} +(2.22450 + 6.84630i) q^{93} +(-2.01479 - 6.20090i) q^{94} +(-1.06902 - 0.776691i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.594894 + 1.83090i) q^{97} +4.50173 q^{98} +(0.427051 + 3.28902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20} - 2 q^{21} + 10 q^{22} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + 27 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 5 q^{33} + 22 q^{34} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 13 q^{38} + q^{39} - 2 q^{40} - 23 q^{41} + 2 q^{42} - 2 q^{43} + 10 q^{44} - 8 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} - 53 q^{49} + 2 q^{50} + 8 q^{51} + q^{52} - 18 q^{53} - 8 q^{54} + 5 q^{55} + 2 q^{56} + 13 q^{57} - 27 q^{58} - 40 q^{59} + 2 q^{60} - 20 q^{61} + 11 q^{62} + 3 q^{63} - 2 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 3 q^{68} - 5 q^{69} + 3 q^{70} - 10 q^{71} + 2 q^{72} + 36 q^{73} + 4 q^{74} - 2 q^{75} - 2 q^{76} + 50 q^{77} + 4 q^{78} - 11 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 16 q^{83} + 3 q^{84} - 8 q^{85} - 13 q^{86} - 18 q^{87} + 5 q^{88} - 46 q^{89} - 2 q^{90} - 39 q^{91} - 5 q^{92} - 6 q^{93} + 15 q^{94} + 12 q^{95} + 2 q^{96} + 16 q^{97} - 62 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.27873	−	0.929049i	−0.483313	−	0.351148i	0.319294	−	0.947656i	$-0.396554\pi$
$7$	−1.27873	−	0.929049i	−0.483313	−	0.351148i	−0.802607	+	0.596508i	$0.796554\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.00000			0.316228
$11$	−2.99607	+	1.42251i	−0.903350	+	0.428903i
$11$	−2.99607	+	1.42251i	−0.903350	+	0.428903i
$12$	1.00000			0.288675
$13$	1.77873	−	5.47436i	0.493330	−	1.51831i	−0.326213	−	0.945296i	$-0.605773\pi$
$13$	1.77873	−	5.47436i	0.493330	−	1.51831i	0.819543	−	0.573017i	$-0.194227\pi$
$14$	1.27873	−	0.929049i	0.341754	−	0.248299i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.21735	−	6.82429i	−0.537786	−	1.65513i	−0.737552	−	0.675291i	$-0.764018\pi$
$17$	−2.21735	−	6.82429i	−0.537786	−	1.65513i	0.199766	−	0.979844i	$-0.435982\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	1.06902	−	0.776691i	0.245251	−	0.178185i	−0.458369	−	0.888762i	$-0.651566\pi$
$19$	1.06902	−	0.776691i	0.245251	−	0.178185i	0.703619	+	0.710577i	$0.251566\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	1.58059			0.344914
$22$	−0.427051	−	3.28902i	−0.0910476	−	0.701221i
$23$	−0.358826			−0.0748205			−0.0374102	−	0.999300i	$-0.511911\pi$
$23$	−0.358826			−0.0748205			−0.0374102	+	0.999300i	$0.511911\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	4.65677	+	3.38334i	0.913267	+	0.663527i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.488430	+	1.50323i	0.0923046	+	0.284084i
$29$	7.82381	+	5.68433i	1.45285	+	1.05555i	0.985156	+	0.171661i	$0.0549134\pi$
$29$	7.82381	+	5.68433i	1.45285	+	1.05555i	0.467689	+	0.883893i	$0.345087\pi$
$30$	−0.809017	+	0.587785i	−0.147706	+	0.107314i
$31$	2.22450	−	6.84630i	0.399532	−	1.22963i	−0.525844	−	0.850581i	$-0.676250\pi$
$31$	2.22450	−	6.84630i	0.399532	−	1.22963i	0.925376	−	0.379051i	$-0.123750\pi$
$32$	−1.00000			−0.176777
$33$	1.58774	−	2.91188i	0.276391	−	0.506894i
$34$	7.17549			1.23059
$35$	−0.488430	+	1.50323i	−0.0825598	+	0.254093i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−7.87411	−	5.72088i	−1.29450	−	0.940507i	−0.294611	−	0.955617i	$-0.595190\pi$
$37$	−7.87411	−	5.72088i	−1.29450	−	0.940507i	−0.999886	+	0.0151107i	$0.995190\pi$
$38$	0.408331	+	1.25671i	0.0662400	+	0.203866i
$39$	1.77873	+	5.47436i	0.284824	+	0.876599i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	−9.71342	+	7.05721i	−1.51698	+	1.10215i	−0.554023	+	0.832501i	$0.686908\pi$
$41$	−9.71342	+	7.05721i	−1.51698	+	1.10215i	−0.962958	+	0.269651i	$0.913092\pi$
$42$	−0.488430	+	1.50323i	−0.0753664	+	0.231954i
$43$	6.41156			0.977753			0.488877	−	0.872353i	$-0.337407\pi$
$43$	6.41156			0.977753			0.488877	+	0.872353i	$0.337407\pi$
$44$	3.26001	+	0.610212i	0.491464	+	0.0919930i
$45$	−1.00000			−0.149071
$46$	0.110883	−	0.341264i	0.0163489	−	0.0503166i
$47$	−5.27480	+	3.83237i	−0.769409	+	0.559008i	−0.901782	−	0.432192i	$-0.857740\pi$
$47$	−5.27480	+	3.83237i	−0.769409	+	0.559008i	0.132373	+	0.991200i	$0.457740\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	−1.39111	−	4.28140i	−0.198730	−	0.611628i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	5.80509	+	4.21765i	0.812875	+	0.590589i
$52$	−4.65677	+	3.38334i	−0.645777	+	0.469185i
$53$	0.724498	−	2.22978i	0.0995175	−	0.306283i	−0.888887	−	0.458126i	$-0.848521\pi$
$53$	0.724498	−	2.22978i	0.0995175	−	0.306283i	0.988405	+	0.151843i	$0.0485208\pi$
$54$	−1.00000			−0.136083
$55$	2.27873	+	2.40986i	0.307263	+	0.324945i
$56$	−1.58059			−0.211216
$57$	−0.408331	+	1.25671i	−0.0540847	+	0.166456i
$58$	−7.82381	+	5.68433i	−1.02732	+	0.746389i
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.108617	−	0.994084i	$-0.534642\pi$
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.978994	+	0.203888i	$0.934642\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−1.74079	−	5.35761i	−0.222886	−	0.685971i	−0.998499	−	0.0547636i	$-0.982559\pi$
$61$	−1.74079	−	5.35761i	−0.222886	−	0.685971i	0.775614	−	0.631208i	$-0.217441\pi$
$62$	5.82381	+	4.23125i	0.739625	+	0.537369i
$63$	−1.27873	+	0.929049i	−0.161104	+	0.117049i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.75608			−0.713954
$66$	2.27873	+	2.40986i	0.280492	+	0.296633i
$67$	−5.07747			−0.620311			−0.310156	−	0.950686i	$-0.600381\pi$
$67$	−5.07747			−0.620311			−0.310156	+	0.950686i	$0.600381\pi$
$68$	−2.21735	+	6.82429i	−0.268893	+	0.827567i
$69$	0.290297	−	0.210913i	0.0349476	−	0.0253909i
$70$	−1.27873	−	0.929049i	−0.152837	−	0.111043i
$71$	2.81666	+	8.66879i	0.334276	+	1.02880i	0.967077	+	0.254482i	$0.0819050\pi$
$71$	2.81666	+	8.66879i	0.334276	+	1.02880i	−0.632801	+	0.774314i	$0.718095\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	5.61803	+	4.08174i	0.657541	+	0.477732i	0.865832	−	0.500335i	$-0.166790\pi$
$73$	5.61803	+	4.08174i	0.657541	+	0.477732i	−0.208291	+	0.978067i	$0.566790\pi$
$74$	7.87411	−	5.72088i	0.915347	−	0.665039i
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$	−1.32139			−0.151573
$77$	5.15274	+	0.964497i	0.587210	+	0.109915i
$78$	−5.75608			−0.651748
$79$	−3.56187	+	10.9623i	−0.400742	+	1.23336i	0.523657	+	0.851929i	$0.324567\pi$
$79$	−3.56187	+	10.9623i	−0.400742	+	1.23336i	−0.924399	+	0.381428i	$0.875433\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.71020	−	11.4188i	−0.409723	−	1.26100i
$83$	−2.47214	−	7.60845i	−0.271352	−	0.835136i	−0.990162	−	0.139929i	$-0.955313\pi$
$83$	−2.47214	−	7.60845i	−0.271352	−	0.835136i	0.718809	−	0.695207i	$-0.244687\pi$
$84$	−1.27873	−	0.929049i	−0.139521	−	0.101368i
$85$	−5.80509	+	4.21765i	−0.629651	+	0.457468i
$86$	−1.98128	+	6.09775i	−0.213647	+	0.657537i
$87$	−9.67076			−1.03681
$88$	−1.58774	+	2.91188i	−0.169254	+	0.310408i
$89$	7.16764			0.759768			0.379884	−	0.925034i	$-0.375964\pi$
$89$	7.16764			0.759768			0.379884	+	0.925034i	$0.375964\pi$
$90$	0.309017	−	0.951057i	0.0325733	−	0.100250i
$91$	−7.36045	+	5.34768i	−0.771585	+	0.560589i
$92$	0.290297	+	0.210913i	0.0302655	+	0.0219892i
$93$	2.22450	+	6.84630i	0.230670	+	0.709928i
$94$	−2.01479	−	6.20090i	−0.207810	−	0.639574i
$95$	−1.06902	−	0.776691i	−0.109679	−	0.0796868i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−0.594894	+	1.83090i	−0.0604024	+	0.185899i	−0.976705	−	0.214588i	$-0.931159\pi$
$97$	−0.594894	+	1.83090i	−0.0604024	+	0.185899i	0.916302	+	0.400487i	$0.131159\pi$
$98$	4.50173			0.454743
$99$	0.427051	+	3.28902i	0.0429202	+	0.330559i
$100$	1.00000			0.100000
$101$	2.54658	−	7.83758i	0.253395	−	0.779868i	−0.740747	−	0.671784i	$-0.765528\pi$
$101$	2.54658	−	7.83758i	0.253395	−	0.779868i	0.994142	−	0.108084i	$-0.0344717\pi$
$102$	−5.80509	+	4.21765i	−0.574790	+	0.417609i
$103$	3.97100	+	2.88510i	0.391274	+	0.284278i	0.765978	−	0.642867i	$-0.222255\pi$
$103$	3.97100	+	2.88510i	0.391274	+	0.284278i	−0.374703	+	0.927145i	$0.622255\pi$
$104$	−1.77873	−	5.47436i	−0.174419	−	0.536805i
$105$	−0.488430	−	1.50323i	−0.0476659	−	0.146701i
$106$	1.89676	+	1.37808i	0.184230	+	0.133851i
$107$	−1.33409	+	0.969273i	−0.128971	+	0.0937031i	−0.650401	−	0.759591i	$-0.725399\pi$
$107$	−1.33409	+	0.969273i	−0.128971	+	0.0937031i	0.521429	+	0.853294i	$0.325399\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$	−2.99607	+	1.42251i	−0.285664	+	0.135631i
$111$	9.73294			0.923810
$112$	0.488430	−	1.50323i	0.0461523	−	0.142042i
$113$	−0.0302903	+	0.0220072i	−0.00284947	+	0.00207026i	−0.589209	−	0.807981i	$-0.700561\pi$
$113$	−0.0302903	+	0.0220072i	−0.00284947	+	0.00207026i	0.586360	+	0.810051i	$0.300561\pi$
$114$	−1.06902	−	0.776691i	−0.100123	−	0.0727438i
$115$	0.110883	+	0.341264i	0.0103399	+	0.0318230i
$116$	−2.98843	−	9.19744i	−0.277469	−	0.853961i
$117$	−4.65677	−	3.38334i	−0.430518	−	0.312790i
$118$	8.35410	−	6.06961i	0.769057	−	0.558753i
$119$	−3.50472	+	10.7864i	−0.321278	+	0.988791i
$120$	1.00000			0.0912871
$121$	6.95292	−	8.52390i	0.632084	−	0.774900i
$122$	5.63332			0.510017
$123$	3.71020	−	11.4188i	0.334537	−	1.02960i
$124$	−5.82381	+	4.23125i	−0.522994	+	0.379977i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−0.488430	−	1.50323i	−0.0435128	−	0.133919i
$127$	5.11168	+	15.7321i	0.453588	+	1.39600i	0.872784	+	0.488106i	$0.162312\pi$
$127$	5.11168	+	15.7321i	0.453588	+	1.39600i	−0.419196	+	0.907896i	$0.637688\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−5.18706	+	3.76862i	−0.456695	+	0.331808i
$130$	1.77873	−	5.47436i	0.156005	−	0.480133i
$131$	12.5096			1.09297			0.546483	−	0.837470i	$-0.315966\pi$
$131$	12.5096			1.09297			0.546483	+	0.837470i	$0.315966\pi$
$132$	−2.99607	+	1.42251i	−0.260775	+	0.123814i
$133$	−2.08857			−0.181102
$134$	1.56902	−	4.82896i	0.135543	−	0.417158i
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$	−5.80509	−	4.21765i	−0.497782	−	0.361660i
$137$	−3.80509	−	11.7109i	−0.325091	−	1.00053i	−0.971400	−	0.237451i	$-0.923688\pi$
$137$	−3.80509	−	11.7109i	−0.325091	−	1.00053i	0.646309	−	0.763076i	$-0.276312\pi$
$138$	0.110883	+	0.341264i	0.00943902	+	0.0290503i
$139$	10.5148	+	7.63945i	0.891853	+	0.647969i	0.936361	−	0.351040i	$-0.114172\pi$
$139$	10.5148	+	7.63945i	0.891853	+	0.647969i	−0.0445073	+	0.999009i	$0.514172\pi$
$140$	1.27873	−	0.929049i	0.108072	−	0.0785190i
$141$	2.01479	−	6.20090i	0.169676	−	0.522210i
$142$	−9.11491			−0.764906
$143$	2.45814	+	18.9318i	0.205560	+	1.58316i
$144$	1.00000			0.0833333
$145$	2.98843	−	9.19744i	0.248176	−	0.763806i
$146$	−5.61803	+	4.08174i	−0.464952	+	0.337807i
$147$	3.64197	+	2.64605i	0.300385	+	0.218242i
$148$	3.00764	+	9.25658i	0.247227	+	0.760886i
$149$	0.509144	+	1.56698i	0.0417107	+	0.128372i	0.969743	−	0.244126i	$-0.0785012\pi$
$149$	0.509144	+	1.56698i	0.0417107	+	0.128372i	−0.928033	+	0.372499i	$0.878501\pi$
$150$	0.809017	+	0.587785i	0.0660560	+	0.0479925i
$151$	5.45943	−	3.96651i	0.444282	−	0.322790i	−0.343052	−	0.939316i	$-0.611461\pi$
$151$	5.45943	−	3.96651i	0.444282	−	0.322790i	0.787334	+	0.616526i	$0.211461\pi$
$152$	0.408331	−	1.25671i	0.0331200	−	0.101933i
$153$	−7.17549			−0.580104
$154$	−2.50958	+	4.60250i	−0.202227	+	0.370880i
$155$	−7.19863			−0.578208
$156$	1.77873	−	5.47436i	0.142412	−	0.438299i
$157$	−7.22370	+	5.24832i	−0.576514	+	0.418862i	−0.837466	−	0.546490i	$-0.815964\pi$
$157$	−7.22370	+	5.24832i	−0.576514	+	0.418862i	0.260952	+	0.965352i	$0.415964\pi$
$158$	−9.32510	−	6.77508i	−0.741865	−	0.538997i
$159$	0.724498	+	2.22978i	0.0574564	+	0.176833i
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	0.458841	+	0.333367i	0.0361617	+	0.0262730i
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	3.00442	−	9.24665i	0.235324	−	0.724254i	−0.761754	−	0.647866i	$-0.775661\pi$
$163$	3.00442	−	9.24665i	0.235324	−	0.724254i	0.997078	−	0.0763872i	$-0.0243385\pi$
$164$	12.0064			0.937546
$165$	−3.26001	−	0.610212i	−0.253791	−	0.0475050i
$166$	8.00000			0.620920
$167$	4.77873	−	14.7074i	0.369789	−	1.13809i	−0.577139	−	0.816646i	$-0.695831\pi$
$167$	4.77873	−	14.7074i	0.369789	−	1.13809i	0.946928	−	0.321447i	$-0.104169\pi$
$168$	1.27873	−	0.929049i	0.0986559	−	0.0716777i
$169$	−16.2875	−	11.8336i	−1.25288	−	0.910274i
$170$	−2.21735	−	6.82429i	−0.170063	−	0.523399i
$171$	−0.408331	−	1.25671i	−0.0312258	−	0.0961032i
$172$	−5.18706	−	3.76862i	−0.395509	−	0.287354i
$173$	14.8889	−	10.8174i	1.13198	−	0.822434i	0.146001	−	0.989284i	$-0.453360\pi$
$173$	14.8889	−	10.8174i	1.13198	−	0.822434i	0.985982	+	0.166851i	$0.0533598\pi$
$174$	2.98843	−	9.19744i	0.226552	−	0.697256i
$175$	1.58059			0.119482
$176$	−2.27873	−	2.40986i	−0.171765	−	0.181650i
$177$	10.3262			0.776168
$178$	−2.21492	+	6.81683i	−0.166015	+	0.510943i
$179$	15.0172	−	10.9106i	1.12244	−	0.815500i	0.137863	−	0.990451i	$-0.455977\pi$
$179$	15.0172	−	10.9106i	1.12244	−	0.815500i	0.984577	+	0.174951i	$0.0559767\pi$
$180$	0.809017	+	0.587785i	0.0603006	+	0.0438109i
$181$	2.94427	+	9.06154i	0.218846	+	0.673539i	0.998858	+	0.0477744i	$0.0152128\pi$
$181$	2.94427	+	9.06154i	0.218846	+	0.673539i	−0.780012	+	0.625764i	$0.784787\pi$
$182$	−2.81144	−	8.65273i	−0.208398	−	0.641383i
$183$	4.55745	+	3.31118i	0.336897	+	0.244770i
$184$	−0.290297	+	0.210913i	−0.0214009	+	0.0155487i
$185$	−3.00764	+	9.25658i	−0.221126	+	0.680557i
$186$	−7.19863			−0.527829
$187$	16.3510	+	17.2919i	1.19570	+	1.26451i
$188$	6.52001			0.475521
$189$	0.488430	−	1.50323i	0.0355281	−	0.109344i
$190$	1.06902	−	0.776691i	0.0775551	−	0.0563471i
$191$	−16.2051	−	11.7737i	−1.17256	−	0.851913i	−0.181245	−	0.983438i	$-0.558013\pi$
$191$	−16.2051	−	11.7737i	−1.17256	−	0.851913i	−0.991313	+	0.131525i	$0.958013\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	2.41941	+	7.44617i	0.174153	+	0.535987i	0.999594	−	0.0285014i	$-0.00907351\pi$
$193$	2.41941	+	7.44617i	0.174153	+	0.535987i	−0.825441	+	0.564488i	$0.809074\pi$
$194$	−1.55745	−	1.13156i	−0.111819	−	0.0812410i
$195$	4.65677	−	3.38334i	0.333478	−	0.242286i
$196$	−1.39111	+	4.28140i	−0.0993650	+	0.305814i
$197$	20.6798			1.47337			0.736687	−	0.676234i	$-0.236389\pi$
$197$	20.6798			1.47337			0.736687	+	0.676234i	$0.236389\pi$
$198$	−3.26001	−	0.610212i	−0.231679	−	0.0433659i
$199$	−3.12921			−0.221824			−0.110912	−	0.993830i	$-0.535377\pi$
$199$	−3.12921			−0.221824			−0.110912	+	0.993830i	$0.535377\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	4.10776	−	2.98446i	0.289739	−	0.210508i
$202$	6.66704	+	4.84389i	0.469092	+	0.340815i
$203$	−4.72349	−	14.5374i	−0.331524	−	1.02033i
$204$	−2.21735	−	6.82429i	−0.155245	−	0.477796i
$205$	9.71342	+	7.05721i	0.678415	+	0.492897i
$206$	−3.97100	+	2.88510i	−0.276673	+	0.201015i
$207$	−0.110883	+	0.341264i	−0.00770693	+	0.0237195i
$208$	5.75608			0.399112
$209$	−2.09802	+	3.84772i	−0.145123	+	0.266152i
$210$	1.58059			0.109071
$211$	4.42039	−	13.6046i	0.304312	−	0.936577i	−0.675620	−	0.737250i	$-0.736124\pi$
$211$	4.42039	−	13.6046i	0.304312	−	0.936577i	0.979933	−	0.199328i	$-0.0638759\pi$
$212$	−1.89676	+	1.37808i	−0.130270	+	0.0946467i
$213$	−7.37411	−	5.35761i	−0.505266	−	0.367097i
$214$	−0.509577	−	1.56832i	−0.0348340	−	0.107208i
$215$	−1.98128	−	6.09775i	−0.135122	−	0.415863i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−9.20508	+	6.68788i	−0.624881	+	0.454003i
$218$	−2.76393	+	8.50651i	−0.187197	+	0.576133i
$219$	−6.94427			−0.469250
$220$	−0.427051	−	3.28902i	−0.0287918	−	0.221745i
$221$	−41.3027			−2.77832
$222$	−3.00764	+	9.25658i	−0.201860	+	0.621261i
$223$	−4.51479	+	3.28019i	−0.302333	+	0.219658i	−0.728600	−	0.684940i	$-0.759829\pi$
$223$	−4.51479	+	3.28019i	−0.302333	+	0.219658i	0.426267	+	0.904598i	$0.359829\pi$
$224$	1.27873	+	0.929049i	0.0854385	+	0.0620747i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−0.0115699	−	0.0356084i	−0.000769616	−	0.00236863i
$227$	−3.79352	−	2.75615i	−0.251785	−	0.182932i	0.454733	−	0.890628i	$-0.349735\pi$
$227$	−3.79352	−	2.75615i	−0.251785	−	0.182932i	−0.706517	+	0.707696i	$0.749735\pi$
$228$	1.06902	−	0.776691i	0.0707978	−	0.0514376i
$229$	2.59489	−	7.98626i	0.171475	−	0.527747i	−0.827980	−	0.560758i	$-0.810510\pi$
$229$	2.59489	−	7.98626i	0.171475	−	0.527747i	0.999455	+	0.0330112i	$0.0105097\pi$
$230$	−0.358826			−0.0236603
$231$	−4.73557	+	2.24841i	−0.311578	+	0.147935i
$232$	9.67076			0.634917
$233$	2.24764	−	6.91752i	0.147248	−	0.453182i	−0.850046	−	0.526709i	$-0.823426\pi$
$233$	2.24764	−	6.91752i	0.147248	−	0.453182i	0.997293	+	0.0735275i	$0.0234257\pi$
$234$	4.65677	−	3.38334i	0.304422	−	0.221176i
$235$	5.27480	+	3.83237i	0.344090	+	0.249996i
$236$	3.19098	+	9.82084i	0.207715	+	0.639282i
$237$	−3.56187	−	10.9623i	−0.231368	−	0.712079i
$238$	−9.17549	−	6.66638i	−0.594759	−	0.432117i
$239$	−17.6271	+	12.8068i	−1.14020	+	0.828404i	−0.987147	−	0.159814i	$-0.948911\pi$
$239$	−17.6271	+	12.8068i	−1.14020	+	0.828404i	−0.153053	+	0.988218i	$0.548911\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	4.54057			0.292484			0.146242	−	0.989249i	$-0.453282\pi$
$241$	4.54057			0.292484			0.146242	+	0.989249i	$0.453282\pi$
$242$	5.95814	+	9.24665i	0.383004	+	0.594397i
$243$	1.00000			0.0641500
$244$	−1.74079	+	5.35761i	−0.111443	+	0.342986i
$245$	−3.64197	+	2.64605i	−0.232677	+	0.169050i
$246$	9.71342	+	7.05721i	0.619305	+	0.449952i
$247$	−2.35038	−	7.23374i	−0.149551	−	0.460272i
$248$	−2.22450	−	6.84630i	−0.141256	−	0.434741i
$249$	6.47214	+	4.70228i	0.410155	+	0.297995i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	1.30067	−	4.00306i	0.0820977	−	0.252671i	−0.901579	−	0.432614i	$-0.857591\pi$
$251$	1.30067	−	4.00306i	0.0820977	−	0.252671i	0.983677	+	0.179943i	$0.0575914\pi$
$252$	1.58059			0.0995680
$253$	1.07507	−	0.510435i	0.0675891	−	0.0320907i
$254$	−16.5418			−1.03792
$255$	2.21735	−	6.82429i	0.138856	−	0.427354i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.9690	+	8.69599i	0.746606	+	0.542441i	0.894773	−	0.446521i	$-0.147337\pi$
$257$	11.9690	+	8.69599i	0.746606	+	0.542441i	−0.148167	+	0.988962i	$0.547337\pi$
$258$	−1.98128	−	6.09775i	−0.123349	−	0.379629i
$259$	4.75386	+	14.6309i	0.295391	+	0.909119i
$260$	4.65677	+	3.38334i	0.288800	+	0.209826i
$261$	7.82381	−	5.68433i	0.484282	−	0.351851i
$262$	−3.86567	+	11.8973i	−0.238822	+	0.735019i
$263$	−7.90358			−0.487355			−0.243678	−	0.969856i	$-0.578354\pi$
$263$	−7.90358			−0.487355			−0.243678	+	0.969856i	$0.578354\pi$
$264$	−0.427051	−	3.28902i	−0.0262832	−	0.202425i
$265$	−2.34453			−0.144023
$266$	0.645404	−	1.98635i	0.0395723	−	0.121791i
$267$	−5.79874	+	4.21303i	−0.354877	+	0.257833i
$268$	4.10776	+	2.98446i	0.250921	+	0.182305i
$269$	5.54588	+	17.0685i	0.338138	+	1.04068i	0.965155	+	0.261678i	$0.0842757\pi$
$269$	5.54588	+	17.0685i	0.338138	+	1.04068i	−0.627017	+	0.779006i	$0.715724\pi$
$270$	0.309017	+	0.951057i	0.0188062	+	0.0578795i
$271$	4.74451	+	3.44709i	0.288208	+	0.209396i	0.722490	−	0.691382i	$-0.242998\pi$
$271$	4.74451	+	3.44709i	0.288208	+	0.209396i	−0.434281	+	0.900777i	$0.642998\pi$
$272$	5.80509	−	4.21765i	0.351985	−	0.255732i
$273$	2.81144	−	8.65273i	0.170156	−	0.523687i
$274$	12.3135			0.743888
$275$	1.58774	−	2.91188i	0.0957445	−	0.175593i
$276$	−0.358826			−0.0215988
$277$	2.60616	−	8.02093i	0.156589	−	0.481931i	−0.841729	−	0.539899i	$-0.818462\pi$
$277$	2.60616	−	8.02093i	0.156589	−	0.481931i	0.998318	+	0.0579683i	$0.0184622\pi$
$278$	−10.5148	+	7.63945i	−0.630635	+	0.458183i
$279$	−5.82381	−	4.23125i	−0.348662	−	0.253318i
$280$	0.488430	+	1.50323i	0.0291893	+	0.0898354i
$281$	1.80782	+	5.56391i	0.107846	+	0.331915i	0.990388	−	0.138319i	$-0.0441698\pi$
$281$	1.80782	+	5.56391i	0.107846	+	0.331915i	−0.882542	+	0.470233i	$0.844170\pi$
$282$	5.27480	+	3.83237i	0.314110	+	0.228214i
$283$	−8.92442	+	6.48397i	−0.530502	+	0.385432i	−0.820545	−	0.571581i	$-0.806330\pi$
$283$	−8.92442	+	6.48397i	−0.530502	+	0.385432i	0.290044	+	0.957013i	$0.406330\pi$
$284$	2.81666	−	8.66879i	0.167138	−	0.514398i
$285$	1.32139			0.0782721
$286$	−18.7649	−	3.51243i	−1.10959	−	0.207694i
$287$	18.9773			1.12020
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−27.9011	+	20.2713i	−1.64124	+	1.19243i
$290$	7.82381	+	5.68433i	0.459430	+	0.333795i
$291$	−0.594894	−	1.83090i	−0.0348733	−	0.107329i
$292$	−2.14590	−	6.60440i	−0.125579	−	0.386493i
$293$	−2.61282	−	1.89832i	−0.152642	−	0.110901i	0.508843	−	0.860860i	$-0.330073\pi$
$293$	−2.61282	−	1.89832i	−0.152642	−	0.110901i	−0.661485	+	0.749958i	$0.730073\pi$
$294$	−3.64197	+	2.64605i	−0.212404	+	0.154321i
$295$	−3.19098	+	9.82084i	−0.185786	+	0.571791i
$296$	−9.73294			−0.565716
$297$	−2.27873	−	2.40986i	−0.132225	−	0.139834i
$298$	−1.64762			−0.0954443
$299$	−0.638254	+	1.96434i	−0.0369112	+	0.113601i
$300$	−0.809017	+	0.587785i	−0.0467086	+	0.0339358i
$301$	−8.19863	−	5.95665i	−0.472561	−	0.343336i
$302$	2.08532	+	6.41795i	0.119997	+	0.369311i
$303$	2.54658	+	7.83758i	0.146297	+	0.450257i
$304$	1.06902	+	0.776691i	0.0613127	+	0.0445463i
$305$	−4.55745	+	3.31118i	−0.260959	+	0.189598i
$306$	2.21735	−	6.82429i	0.126757	−	0.390119i
$307$	−22.9531			−1.31000			−0.655002	−	0.755627i	$-0.727332\pi$
$307$	−22.9531			−1.31000			−0.655002	+	0.755627i	$0.727332\pi$
$308$	−3.60174	−	3.80900i	−0.205228	−	0.217038i
$309$	−4.90843			−0.279231
$310$	2.22450	−	6.84630i	0.126343	−	0.388844i
$311$	−3.39885	+	2.46941i	−0.192731	+	0.140027i	−0.679966	−	0.733244i	$-0.738006\pi$
$311$	−3.39885	+	2.46941i	−0.192731	+	0.140027i	0.487235	+	0.873271i	$0.338006\pi$
$312$	4.65677	+	3.38334i	0.263638	+	0.191544i
$313$	−5.68021	−	17.4819i	−0.321065	−	0.988135i	−0.973186	−	0.230020i	$-0.926121\pi$
$313$	−5.68021	−	17.4819i	−0.321065	−	0.988135i	0.652121	−	0.758115i	$-0.273879\pi$
$314$	−2.75921	−	8.49197i	−0.155711	−	0.479229i
$315$	1.27873	+	0.929049i	0.0720481	+	0.0523460i
$316$	9.32510	−	6.77508i	0.524578	−	0.381128i
$317$	−7.82774	+	24.0913i	−0.439650	+	1.35310i	0.448597	+	0.893734i	$0.351924\pi$
$317$	−7.82774	+	24.0913i	−0.439650	+	1.35310i	−0.888246	+	0.459368i	$0.848076\pi$
$318$	−2.34453			−0.131474
$319$	−31.5267	−	5.90122i	−1.76516	−	0.330405i
$320$	−1.00000			−0.0559017
$321$	0.509577	−	1.56832i	0.0284418	−	0.0875349i
$322$	−0.458841	+	0.333367i	−0.0255702	+	0.0185778i
$323$	−7.67076	−	5.57314i	−0.426813	−	0.310098i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	1.77873	+	5.47436i	0.0986660	+	0.303663i
$326$	7.86567	+	5.71475i	0.435639	+	0.316510i
$327$	−7.23607	+	5.25731i	−0.400155	+	0.290730i
$328$	−3.71020	+	11.4188i	−0.204861	+	0.630498i
$329$	10.3055			0.568160
$330$	1.58774	−	2.91188i	0.0874024	−	0.160294i
$331$	26.1159			1.43546			0.717730	−	0.696322i	$-0.245181\pi$
$331$	26.1159			1.43546			0.717730	+	0.696322i	$0.245181\pi$
$332$	−2.47214	+	7.60845i	−0.135676	+	0.417568i
$333$	−7.87411	+	5.72088i	−0.431499	+	0.313502i
$334$	12.5109	+	9.08968i	0.684564	+	0.497365i
$335$	1.56902	+	4.82896i	0.0857249	+	0.263834i
$336$	0.488430	+	1.50323i	0.0266460	+	0.0820081i
$337$	14.7251	+	10.6984i	0.802127	+	0.582779i	0.911537	−	0.411217i	$-0.134896\pi$
$337$	14.7251	+	10.6984i	0.802127	+	0.582779i	−0.109411	+	0.993997i	$0.534896\pi$
$338$	16.2875	−	11.8336i	0.885923	−	0.643661i
$339$	0.0115699	−	0.0356084i	0.000628388	−	0.00193398i
$340$	7.17549			0.389145
$341$	3.07418	+	23.6764i	0.166476	+	1.28215i
$342$	1.32139			0.0714523
$343$	−5.61779	+	17.2898i	−0.303332	+	0.933560i
$344$	5.18706	−	3.76862i	0.279667	−	0.203190i
$345$	−0.290297	−	0.210913i	−0.0156290	−	0.0113552i
$346$	5.68706	+	17.5030i	0.305738	+	0.940965i
$347$	−5.68021	−	17.4819i	−0.304930	−	0.938477i	−0.979703	−	0.200453i	$-0.935759\pi$
$347$	−5.68021	−	17.4819i	−0.304930	−	0.938477i	0.674774	−	0.738025i	$-0.264241\pi$
$348$	7.82381	+	5.68433i	0.419400	+	0.304712i
$349$	23.6398	−	17.1753i	1.26541	−	0.919373i	0.266398	−	0.963863i	$-0.414166\pi$
$349$	23.6398	−	17.1753i	1.26541	−	0.919373i	0.999010	+	0.0444904i	$0.0141664\pi$
$350$	−0.488430	+	1.50323i	−0.0261077	+	0.0803512i
$351$	5.75608			0.307237
$352$	2.99607	−	1.42251i	0.159691	−	0.0758201i
$353$	−4.41156			−0.234803			−0.117402	−	0.993085i	$-0.537457\pi$
$353$	−4.41156			−0.234803			−0.117402	+	0.993085i	$0.537457\pi$
$354$	−3.19098	+	9.82084i	−0.169599	+	0.521972i
$355$	7.37411	−	5.35761i	0.391377	−	0.284352i
$356$	−5.79874	−	4.21303i	−0.307333	−	0.223290i
$357$	−3.50472	−	10.7864i	−0.185490	−	0.570879i
$358$	5.73607	+	17.6538i	0.303161	+	0.933032i
$359$	−17.9443	−	13.0373i	−0.947062	−	0.688081i	0.00304782	−	0.999995i	$-0.499030\pi$
$359$	−17.9443	−	13.0373i	−0.947062	−	0.688081i	−0.950110	+	0.311914i	$0.899030\pi$
$360$	−0.809017	+	0.587785i	−0.0426389	+	0.0309790i
$361$	−5.33176	+	16.4095i	−0.280619	+	0.863656i
$362$	−9.52786			−0.500773
$363$	−0.614809	+	10.9828i	−0.0322691	+	0.576448i
$364$	9.09802			0.476866
$365$	2.14590	−	6.60440i	0.112321	−	0.345690i
$366$	−4.55745	+	3.31118i	−0.238222	+	0.173078i
$367$	6.06058	+	4.40327i	0.316360	+	0.229849i	0.734621	−	0.678478i	$-0.237360\pi$
$367$	6.06058	+	4.40327i	0.316360	+	0.229849i	−0.418261	+	0.908327i	$0.637360\pi$
$368$	−0.110883	−	0.341264i	−0.00578020	−	0.0177896i
$369$	3.71020	+	11.4188i	0.193145	+	0.594440i
$370$	−7.87411	−	5.72088i	−0.409356	−	0.297414i
$371$	−2.99801	+	2.17818i	−0.155649	+	0.113085i
$372$	2.22450	−	6.84630i	0.115335	−	0.354964i
$373$	−7.50173			−0.388425			−0.194212	−	0.980960i	$-0.562215\pi$
$373$	−7.50173			−0.388425			−0.194212	+	0.980960i	$0.562215\pi$
$374$	−21.4983	+	10.2072i	−1.11165	+	0.527802i
$375$	−1.00000			−0.0516398
$376$	−2.01479	+	6.20090i	−0.103905	+	0.319787i
$377$	45.0345	−	32.7195i	2.31939	−	1.68514i
$378$	1.27873	+	0.929049i	0.0657706	+	0.0477851i
$379$	−7.00199	−	21.5499i	−0.359668	−	1.10694i	−0.953253	−	0.302173i	$-0.902288\pi$
$379$	−7.00199	−	21.5499i	−0.359668	−	1.10694i	0.593585	−	0.804772i	$-0.297712\pi$
$380$	0.408331	+	1.25671i	0.0209469	+	0.0644680i
$381$	−13.3826	−	9.72300i	−0.685609	−	0.498124i
$382$	16.2051	−	11.7737i	0.829124	−	0.602394i
$383$	−2.00472	+	6.16991i	−0.102437	+	0.315268i	−0.989120	−	0.147109i	$-0.953003\pi$
$383$	−2.00472	+	6.16991i	−0.102437	+	0.315268i	0.886684	+	0.462377i	$0.153003\pi$
$384$	−1.00000			−0.0510310
$385$	−0.674994	−	5.19860i	−0.0344009	−	0.264945i
$386$	−7.82937			−0.398504
$387$	1.98128	−	6.09775i	0.100714	−	0.309966i
$388$	1.55745	−	1.13156i	0.0790677	−	0.0574461i
$389$	−17.4606	−	12.6858i	−0.885286	−	0.643198i	0.0493588	−	0.998781i	$-0.484282\pi$
$389$	−17.4606	−	12.6858i	−0.885286	−	0.643198i	−0.934645	+	0.355583i	$0.884282\pi$
$390$	1.77873	+	5.47436i	0.0900693	+	0.277205i
$391$	0.795643	+	2.44874i	0.0402374	+	0.123838i
$392$	−3.64197	−	2.64605i	−0.183947	−	0.133646i
$393$	−10.1205	+	7.35294i	−0.510510	+	0.370907i
$394$	−6.39041	+	19.6677i	−0.321944	+	0.990842i
$395$	11.5265			0.579959
$396$	1.58774	−	2.91188i	0.0797871	−	0.146328i
$397$	16.5235			0.829289			0.414644	−	0.909984i	$-0.363906\pi$
$397$	16.5235			0.829289			0.414644	+	0.909984i	$0.363906\pi$
$398$	0.966978	−	2.97605i	0.0484702	−	0.149176i
$399$	1.68969	−	1.22763i	0.0845903	−	0.0614585i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	4.50150	+	13.8542i	0.224794	+	0.691845i	0.998312	+	0.0580713i	$0.0184951\pi$
$401$	4.50150	+	13.8542i	0.224794	+	0.691845i	−0.773518	+	0.633774i	$0.781505\pi$
$402$	1.56902	+	4.82896i	0.0782558	+	0.240846i
$403$	−33.5223	−	24.3554i	−1.66987	−	1.21323i
$404$	−6.66704	+	4.84389i	−0.331698	+	0.240993i
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	15.2855			0.758609
$407$	31.7294	+	5.93916i	1.57277	+	0.294393i
$408$	7.17549			0.355240
$409$	6.99264	−	21.5211i	0.345764	−	1.06415i	−0.615410	−	0.788207i	$-0.711009\pi$
$409$	6.99264	−	21.5211i	0.345764	−	1.06415i	0.961174	−	0.275944i	$-0.0889906\pi$
$410$	−9.71342	+	7.05721i	−0.479712	+	0.348531i
$411$	9.96186	+	7.23771i	0.491382	+	0.357010i
$412$	−1.51679	−	4.66819i	−0.0747268	−	0.229985i
$413$	5.04365	+	15.5227i	0.248182	+	0.763824i
$414$	−0.290297	−	0.210913i	−0.0142673	−	0.0103658i
$415$	−6.47214	+	4.70228i	−0.317705	+	0.230826i
$416$	−1.77873	+	5.47436i	−0.0872093	+	0.268402i
$417$	−12.9970			−0.636466
$418$	−3.01108	−	3.18435i	−0.147277	−	0.155752i
$419$	5.41057			0.264324			0.132162	−	0.991228i	$-0.457808\pi$
$419$	5.41057			0.264324			0.132162	+	0.991228i	$0.457808\pi$
$420$	−0.488430	+	1.50323i	−0.0238330	+	0.0733503i
$421$	−2.81666	+	2.04642i	−0.137276	+	0.0997366i	−0.654304	−	0.756232i	$-0.727038\pi$
$421$	−2.81666	+	2.04642i	−0.137276	+	0.0997366i	0.517028	+	0.855968i	$0.327038\pi$
$422$	11.5727	+	8.40809i	0.563352	+	0.409299i
$423$	2.01479	+	6.20090i	0.0979627	+	0.301498i
$424$	−0.724498	−	2.22978i	−0.0351847	−	0.108287i
$425$	5.80509	+	4.21765i	0.281588	+	0.204586i
$426$	7.37411	−	5.35761i	0.357277	−	0.259577i
$427$	−2.75148	+	8.46820i	−0.133154	+	0.409805i
$428$	1.64903			0.0797086
$429$	−13.1165	−	13.8713i	−0.633272	−	0.669714i
$430$	6.41156			0.309193
$431$	3.77523	−	11.6190i	0.181847	−	0.559666i	−0.818033	−	0.575171i	$-0.804935\pi$
$431$	3.77523	−	11.6190i	0.181847	−	0.559666i	0.999880	+	0.0155047i	$0.00493549\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−7.67236	−	5.57430i	−0.368710	−	0.267884i	0.387966	−	0.921674i	$-0.373178\pi$
$433$	−7.67236	−	5.57430i	−0.368710	−	0.267884i	−0.756676	+	0.653790i	$0.773178\pi$
$434$	−3.51603	−	10.8212i	−0.168775	−	0.519435i
$435$	2.98843	+	9.19744i	0.143284	+	0.440984i
$436$	−7.23607	−	5.25731i	−0.346545	−	0.251780i
$437$	−0.383594	+	0.278697i	−0.0183498	+	0.0133319i
$438$	2.14590	−	6.60440i	0.102535	−	0.315570i
$439$	−7.54960			−0.360323			−0.180161	−	0.983637i	$-0.557662\pi$
$439$	−7.54960			−0.360323			−0.180161	+	0.983637i	$0.557662\pi$
$440$	3.26001	+	0.610212i	0.155415	+	0.0290907i
$441$	−4.50173			−0.214368
$442$	12.7632	−	39.2812i	0.607085	−	1.86842i
$443$	19.0696	−	13.8549i	0.906025	−	0.658265i	−0.0339816	−	0.999422i	$-0.510819\pi$
$443$	19.0696	−	13.8549i	0.906025	−	0.658265i	0.940006	+	0.341157i	$0.110819\pi$
$444$	−7.87411	−	5.72088i	−0.373689	−	0.271501i
$445$	−2.21492	−	6.81683i	−0.104997	−	0.323149i
$446$	−1.72450	−	5.30746i	−0.0816574	−	0.251315i
$447$	−1.33296	−	0.968449i	−0.0630466	−	0.0458061i
$448$	−1.27873	+	0.929049i	−0.0604142	+	0.0438935i
$449$	−0.614809	+	1.89219i	−0.0290146	+	0.0892979i	−0.964515	−	0.264027i	$-0.914949\pi$
$449$	−0.614809	+	1.89219i	−0.0290146	+	0.0892979i	0.935501	+	0.353325i	$0.114949\pi$
$450$	−1.00000			−0.0471405
$451$	19.0632	−	34.9614i	0.897649	−	1.64627i
$452$	0.0374409			0.00176107
$453$	−2.08532	+	6.41795i	−0.0979768	+	0.301541i
$454$	3.79352	−	2.75615i	0.178039	−	0.129353i
$455$	7.36045	+	5.34768i	0.345063	+	0.250703i
$456$	0.408331	+	1.25671i	0.0191218	+	0.0588509i
$457$	9.25921	+	28.4969i	0.433127	+	1.33303i	0.894993	+	0.446079i	$0.147180\pi$
$457$	9.25921	+	28.4969i	0.433127	+	1.33303i	−0.461866	+	0.886950i	$0.652820\pi$
$458$	6.79352	+	4.93578i	0.317440	+	0.230634i
$459$	5.80509	−	4.21765i	0.270958	−	0.196863i
$460$	0.110883	−	0.341264i	0.00516997	−	0.0159115i
$461$	12.0143			0.559562			0.279781	−	0.960064i	$-0.409738\pi$
$461$	12.0143			0.559562			0.279781	+	0.960064i	$0.409738\pi$
$462$	−0.674994	−	5.19860i	−0.0314036	−	0.241861i
$463$	4.85895			0.225815			0.112907	−	0.993606i	$-0.463984\pi$
$463$	4.85895			0.225815			0.112907	+	0.993606i	$0.463984\pi$
$464$	−2.98843	+	9.19744i	−0.138734	+	0.426981i
$465$	5.82381	−	4.23125i	0.270073	−	0.196219i
$466$	5.88439	+	4.27526i	0.272589	+	0.198048i
$467$	−4.75509	−	14.6347i	−0.220039	−	0.677212i	−0.998757	−	0.0498376i	$-0.984130\pi$
$467$	−4.75509	−	14.6347i	−0.220039	−	0.677212i	0.778718	−	0.627374i	$-0.215870\pi$
$468$	1.77873	+	5.47436i	0.0822217	+	0.253052i
$469$	6.49269	+	4.71722i	0.299805	+	0.217821i
$470$	−5.27480	+	3.83237i	−0.243308	+	0.176774i
$471$	2.75921	−	8.49197i	0.127138	−	0.391289i
$472$	−10.3262			−0.475304
$473$	−19.2095	+	9.12051i	−0.883254	+	0.419362i
$474$	11.5265			0.529428
$475$	−0.408331	+	1.25671i	−0.0187355	+	0.0576619i
$476$	9.17549	−	6.66638i	0.420558	−	0.305553i
$477$	−1.89676	−	1.37808i	−0.0868467	−	0.0630978i
$478$	−6.73294	−	20.7219i	−0.307958	−	0.947796i
$479$	−1.11976	−	3.44626i	−0.0511631	−	0.157464i	0.922211	−	0.386688i	$-0.126381\pi$
$479$	−1.11976	−	3.44626i	−0.0511631	−	0.157464i	−0.973374	+	0.229224i	$0.926381\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−45.3240	+	32.9298i	−2.06660	+	1.50147i
$482$	−1.40311	+	4.31834i	−0.0639100	+	0.196695i
$483$	−0.567158			−0.0258066
$484$	−10.6353	+	2.80916i	−0.483421	+	0.127689i
$485$	1.92512			0.0874151
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−2.64277	+	1.92009i	−0.119755	+	0.0870074i	−0.646051	−	0.763294i	$-0.723581\pi$
$487$	−2.64277	+	1.92009i	−0.119755	+	0.0870074i	0.526295	+	0.850302i	$0.323581\pi$
$488$	−4.55745	−	3.31118i	−0.206306	−	0.149890i
$489$	3.00442	+	9.24665i	0.135865	+	0.418148i
$490$	−1.39111	−	4.28140i	−0.0628439	−	0.193414i
$491$	−27.7286	−	20.1460i	−1.25138	−	0.909178i	−0.253075	−	0.967447i	$-0.581442\pi$
$491$	−27.7286	−	20.1460i	−1.25138	−	0.909178i	−0.998301	+	0.0582683i	$0.981442\pi$
$492$	−9.71342	+	7.05721i	−0.437915	+	0.318164i
$493$	21.4434	−	65.9961i	0.965764	−	2.97232i
$494$	7.60600			0.342210
$495$	2.99607	−	1.42251i	0.134664	−	0.0639371i
$496$	7.19863			0.323228
$497$	4.45200	−	13.7018i	0.199699	−	0.614611i
$498$	−6.47214	+	4.70228i	−0.290023	+	0.210714i
$499$	−30.9106	−	22.4579i	−1.38375	−	1.00535i	−0.996519	−	0.0833714i	$-0.973431\pi$
$499$	−30.9106	−	22.4579i	−1.38375	−	1.00535i	−0.387232	−	0.921982i	$-0.626569\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	4.77873	+	14.7074i	0.213498	+	0.657079i
$502$	3.40520	+	2.47403i	0.151982	+	0.110421i
$503$	16.9224	−	12.2949i	0.754534	−	0.548201i	−0.142695	−	0.989767i	$-0.545577\pi$
$503$	16.9224	−	12.2949i	0.754534	−	0.548201i	0.897229	+	0.441566i	$0.145577\pi$
$504$	−0.488430	+	1.50323i	−0.0217564	+	0.0669593i
$505$	−8.24092			−0.366716
$506$	0.153237	+	1.18019i	0.00681222	+	0.0524656i
$507$	20.1325			0.894114
$508$	5.11168	−	15.7321i	0.226794	−	0.698001i
$509$	28.0146	−	20.3538i	1.24172	−	0.902166i	0.244013	−	0.969772i	$-0.421536\pi$
$509$	28.0146	−	20.3538i	1.24172	−	0.902166i	0.997712	+	0.0676062i	$0.0215361\pi$
$510$	5.80509	+	4.21765i	0.257054	+	0.186760i
$511$	−3.39179	−	10.4389i	−0.150044	−	0.461788i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	1.06902	+	0.776691i	0.0471985	+	0.0342917i
$514$	−11.9690	+	8.69599i	−0.527930	+	0.383564i
$515$	1.51679	−	4.66819i	0.0668377	−	0.205705i
$516$	6.41156			0.282253
$517$	10.3521	−	18.9855i	0.455285	−	0.834982i
$518$	−15.3838			−0.675926
$519$	−5.68706	+	17.5030i	−0.249634	+	0.768295i
$520$	−4.65677	+	3.38334i	−0.204213	+	0.148369i
$521$	11.4942	+	8.35105i	0.503572	+	0.365866i	0.810380	−	0.585905i	$-0.199261\pi$
$521$	11.4942	+	8.35105i	0.503572	+	0.365866i	−0.306808	+	0.951771i	$0.599261\pi$
$522$	2.98843	+	9.19744i	0.130800	+	0.402561i
$523$	−0.476122	−	1.46535i	−0.0208194	−	0.0640754i	0.940107	−	0.340879i	$-0.110725\pi$
$523$	−0.476122	−	1.46535i	−0.0208194	−	0.0640754i	−0.960926	+	0.276804i	$0.910725\pi$
$524$	−10.1205	−	7.35294i	−0.442114	−	0.321215i
$525$	−1.27873	+	0.929049i	−0.0558082	+	0.0405470i
$526$	2.44234	−	7.51675i	0.106491	−	0.327746i
$527$	−51.6537			−2.25007
$528$	3.26001	+	0.610212i	0.141874	+	0.0265561i
$529$	−22.8712			−0.994402
$530$	0.724498	−	2.22978i	0.0314702	−	0.0968553i
$531$	−8.35410	+	6.06961i	−0.362537	+	0.263399i
$532$	1.68969	+	1.22763i	0.0732574	+	0.0532246i
$533$	21.3562	+	65.7276i	0.925039	+	2.84698i
$534$	−2.21492	−	6.81683i	−0.0958490	−	0.294993i
$535$	1.33409	+	0.969273i	0.0576777	+	0.0419053i
$536$	−4.10776	+	2.98446i	−0.177428	+	0.128909i
$537$	−5.73607	+	17.6538i	−0.247530	+	0.761818i
$538$	−17.9469			−0.773744
$539$	10.2582	+	10.8485i	0.441852	+	0.467278i
$540$	−1.00000			−0.0430331
$541$	−6.54015	+	20.1285i	−0.281183	+	0.865393i	0.706334	+	0.707879i	$0.250348\pi$
$541$	−6.54015	+	20.1285i	−0.281183	+	0.865393i	−0.987517	+	0.157514i	$0.949652\pi$
$542$	−4.74451	+	3.44709i	−0.203794	+	0.148065i
$543$	−7.70820	−	5.60034i	−0.330791	−	0.240334i
$544$	2.21735	+	6.82429i	0.0950680	+	0.292589i
$545$	−2.76393	−	8.50651i	−0.118394	−	0.364379i
$546$	7.36045	+	5.34768i	0.314998	+	0.228860i
$547$	20.9309	−	15.2072i	0.894939	−	0.650211i	−0.0422219	−	0.999108i	$-0.513444\pi$
$547$	20.9309	−	15.2072i	0.894939	−	0.650211i	0.937161	+	0.348897i	$0.113444\pi$
$548$	−3.80509	+	11.7109i	−0.162545	+	0.500263i
$549$	−5.63332			−0.240424
$550$	2.27873	+	2.40986i	0.0971652	+	0.102757i
$551$	12.7788			0.544395
$552$	0.110883	−	0.341264i	0.00471951	−	0.0145252i
$553$	14.7392	−	10.7087i	0.626774	−	0.455378i
$554$	6.82301	+	4.95721i	0.289882	+	0.210612i
$555$	−3.00764	−	9.25658i	−0.127667	−	0.392920i
$556$	−4.01629	−	12.3609i	−0.170329	−	0.524218i
$557$	7.90257	+	5.74155i	0.334843	+	0.243277i	0.742483	−	0.669865i	$-0.233648\pi$
$557$	7.90257	+	5.74155i	0.334843	+	0.243277i	−0.407640	+	0.913143i	$0.633648\pi$
$558$	5.82381	−	4.23125i	0.246542	−	0.179123i
$559$	11.4044	−	35.0991i	0.482355	−	1.48454i
$560$	−1.58059			−0.0667923
$561$	−23.3921	−	4.37857i	−0.987617	−	0.184863i
$562$	−5.85024			−0.246777
$563$	−6.77823	+	20.8613i	−0.285668	+	0.879197i	0.700529	+	0.713624i	$0.252947\pi$
$563$	−6.77823	+	20.8613i	−0.285668	+	0.879197i	−0.986197	+	0.165573i	$0.947053\pi$
$564$	−5.27480	+	3.83237i	−0.222109	+	0.161372i
$565$	0.0302903	+	0.0220072i	0.00127432	+	0.000925849i
$566$	−3.40882	−	10.4913i	−0.143284	−	0.440981i
$567$	0.488430	+	1.50323i	0.0205121	+	0.0631299i
$568$	7.37411	+	5.35761i	0.309411	+	0.224800i
$569$	33.7495	−	24.5204i	1.41485	−	1.02795i	0.422256	−	0.906477i	$-0.361238\pi$
$569$	33.7495	−	24.5204i	1.41485	−	1.02795i	0.992595	−	0.121473i	$-0.0387618\pi$
$570$	−0.408331	+	1.25671i	−0.0171031	+	0.0526379i
$571$	23.0928			0.966402			0.483201	−	0.875510i	$-0.339474\pi$
$571$	23.0928			0.966402			0.483201	+	0.875510i	$0.339474\pi$
$572$	9.13918	−	16.7610i	0.382128	−	0.700814i
$573$	20.0306			0.836789
$574$	−5.86431	+	18.0485i	−0.244772	+	0.753330i
$575$	0.290297	−	0.210913i	0.0121062	−	0.00879567i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−9.34938	−	28.7744i	−0.389220	−	1.19790i	−0.933373	−	0.358909i	$-0.883149\pi$
$577$	−9.34938	−	28.7744i	−0.389220	−	1.19790i	0.544153	−	0.838986i	$-0.316851\pi$
$578$	−10.6573	−	32.7997i	−0.443284	−	1.36429i
$579$	−6.33409	−	4.60199i	−0.263236	−	0.191252i
$580$	−7.82381	+	5.68433i	−0.324866	+	0.236029i
$581$	−3.90744	+	12.0259i	−0.162108	+	0.498917i
$582$	1.92512			0.0797987
$583$	1.00123	+	7.71118i	0.0414668	+	0.319364i
$584$	6.94427			0.287356
$585$	−1.77873	+	5.47436i	−0.0735413	+	0.226337i
$586$	2.61282	−	1.89832i	0.107934	−	0.0784190i
$587$	−4.37411	−	3.17798i	−0.180539	−	0.131169i	0.493845	−	0.869550i	$-0.335591\pi$
$587$	−4.37411	−	3.17798i	−0.180539	−	0.131169i	−0.674384	+	0.738380i	$0.735591\pi$
$588$	−1.39111	−	4.28140i	−0.0573684	−	0.176562i
$589$	−2.93942	−	9.04660i	−0.121117	−	0.372759i
$590$	−8.35410	−	6.06961i	−0.343933	−	0.249882i
$591$	−16.7303	+	12.1553i	−0.688193	+	0.500001i
$592$	3.00764	−	9.25658i	0.123613	−	0.380443i
$593$	33.4413			1.37327			0.686636	−	0.727002i	$-0.259087\pi$
$593$	33.4413			1.37327			0.686636	+	0.727002i	$0.259087\pi$
$594$	2.99607	−	1.42251i	0.122930	−	0.0583664i
$595$	11.3415			0.464957
$596$	0.509144	−	1.56698i	0.0208553	−	0.0641861i
$597$	2.53158	−	1.83930i	0.103611	−	0.0752776i
$598$	−1.67097	−	1.21403i	−0.0683311	−	0.0496454i
$599$	1.97041	+	6.06430i	0.0805088	+	0.247781i	0.983207	−	0.182494i	$-0.0584169\pi$
$599$	1.97041	+	6.06430i	0.0805088	+	0.247781i	−0.902698	+	0.430274i	$0.858417\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	−4.66232	−	3.38737i	−0.190180	−	0.138174i	0.488621	−	0.872496i	$-0.337500\pi$
$601$	−4.66232	−	3.38737i	−0.190180	−	0.138174i	−0.678801	+	0.734322i	$0.737500\pi$
$602$	8.19863	−	5.95665i	0.334151	−	0.242775i
$603$	−1.56902	+	4.82896i	−0.0638956	+	0.196650i
$604$	−6.74823			−0.274582
$605$	−10.2553	−	3.97859i	−0.416937	−	0.161753i
$606$	−8.24092			−0.334765
$607$	−14.0735	+	43.3137i	−0.571225	+	1.75805i	0.0774632	+	0.996995i	$0.475318\pi$
$607$	−14.0735	+	43.3137i	−0.571225	+	1.75805i	−0.648688	+	0.761054i	$0.724682\pi$
$608$	−1.06902	+	0.776691i	−0.0433546	+	0.0314990i
$609$	12.3663	+	8.98462i	0.501106	+	0.364075i
$610$	−1.74079	−	5.35761i	−0.0704826	−	0.216923i
$611$	11.5973	+	35.6929i	0.469177	+	1.44398i
$612$	5.80509	+	4.21765i	0.234657	+	0.170488i
$613$	−25.2051	+	18.3126i	−1.01802	+	0.739637i	−0.965877	−	0.259002i	$-0.916606\pi$
$613$	−25.2051	+	18.3126i	−1.01802	+	0.739637i	−0.0521467	+	0.998639i	$0.516606\pi$
$614$	7.09290	−	21.8297i	0.286246	−	0.880975i
$615$	−12.0064			−0.484147
$616$	4.73557	−	2.24841i	0.190802	−	0.0905911i
$617$	−30.2761			−1.21887			−0.609435	−	0.792836i	$-0.708604\pi$
$617$	−30.2761			−1.21887			−0.609435	+	0.792836i	$0.708604\pi$
$618$	1.51679	−	4.66819i	0.0610142	−	0.187782i
$619$	30.0328	−	21.8201i	1.20712	−	0.877023i	0.212153	−	0.977237i	$-0.431953\pi$
$619$	30.0328	−	21.8201i	1.20712	−	0.877023i	0.994966	+	0.100213i	$0.0319526\pi$
$620$	5.82381	+	4.23125i	0.233890	+	0.169931i
$621$	−0.110883	−	0.341264i	−0.00444960	−	0.0136945i
$622$	−1.29825	−	3.99559i	−0.0520549	−	0.160209i
$623$	−9.16545	−	6.65909i	−0.367206	−	0.266791i
$624$	−4.65677	+	3.38334i	−0.186420	+	0.135442i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	18.3816			0.734675
$627$	−0.564299	−	4.34606i	−0.0225359	−	0.173565i
$628$	8.92898			0.356305
$629$	−21.5813	+	66.4205i	−0.860503	+	2.64836i
$630$	−1.27873	+	0.929049i	−0.0509457	+	0.0370142i
$631$	28.3024	+	20.5629i	1.12670	+	0.818596i	0.985211	−	0.171344i	$-0.0548109\pi$
$631$	28.3024	+	20.5629i	1.12670	+	0.818596i	0.141489	+	0.989940i	$0.454811\pi$
$632$	3.56187	+	10.9623i	0.141684	+	0.436058i
$633$	4.42039	+	13.6046i	0.175695	+	0.540733i
$634$	−20.4933	−	14.8892i	−0.813892	−	0.591327i
$635$	13.3826	−	9.72300i	0.531071	−	0.385845i
$636$	0.724498	−	2.22978i	0.0287282	−	0.0884164i
$637$	−25.9123			−1.02668
$638$	15.3547	−	28.1601i	0.607898	−	1.11487i
$639$	9.11491			0.360580
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	−6.36985	+	4.62797i	−0.251594	+	0.182794i	−0.706433	−	0.707780i	$-0.749697\pi$
$641$	−6.36985	+	4.62797i	−0.251594	+	0.182794i	0.454839	+	0.890574i	$0.349697\pi$
$642$	1.33409	+	0.969273i	0.0526523	+	0.0382541i
$643$	14.1506	+	43.5511i	0.558045	+	1.71749i	0.687762	+	0.725936i	$0.258593\pi$
$643$	14.1506	+	43.5511i	0.558045	+	1.71749i	−0.129717	+	0.991551i	$0.541407\pi$
$644$	−0.175262	−	0.539400i	−0.00690627	−	0.0212553i
$645$	5.18706	+	3.76862i	0.204240	+	0.148389i
$646$	7.67076	−	5.57314i	0.301802	−	0.219272i
$647$	−9.59631	+	29.5344i	−0.377270	+	1.16112i	0.564664	+	0.825321i	$0.309006\pi$
$647$	−9.59631	+	29.5344i	−0.377270	+	1.16112i	−0.941934	+	0.335797i	$0.890994\pi$
$648$	−1.00000			−0.0392837
$649$	33.6636	+	6.30120i	1.32141	+	0.247344i
$650$	−5.75608			−0.225772
$651$	3.51603	−	10.8212i	0.137804	−	0.424117i
$652$	−7.86567	+	5.71475i	−0.308043	+	0.223807i
$653$	18.5333	+	13.4652i	0.725264	+	0.526935i	0.888062	−	0.459724i	$-0.152052\pi$
$653$	18.5333	+	13.4652i	0.725264	+	0.526935i	−0.162797	+	0.986660i	$0.552052\pi$
$654$	−2.76393	−	8.50651i	−0.108078	−	0.332631i
$655$	−3.86567	−	11.8973i	−0.151044	−	0.464867i
$656$	−9.71342	−	7.05721i	−0.379245	−	0.275538i
$657$	5.61803	−	4.08174i	0.219180	−	0.159244i
$658$	−3.18457	+	9.80110i	−0.124147	+	0.382087i
$659$	17.9907			0.700820			0.350410	−	0.936596i	$-0.386042\pi$
$659$	17.9907			0.700820			0.350410	+	0.936596i	$0.386042\pi$
$660$	2.27873	+	2.40986i	0.0886993	+	0.0938035i
$661$	−36.6576			−1.42582			−0.712909	−	0.701257i	$-0.752623\pi$
$661$	−36.6576			−1.42582			−0.712909	+	0.701257i	$0.752623\pi$
$662$	−8.07026	+	24.8377i	−0.313659	+	0.965344i
$663$	33.4146	−	24.2771i	1.29771	−	0.942845i
$664$	−6.47214	−	4.70228i	−0.251168	−	0.182484i
$665$	0.645404	+	1.98635i	0.0250277	+	0.0770274i
$666$	−3.00764	−	9.25658i	−0.116544	−	0.358685i
$667$	−2.80739	−	2.03969i	−0.108703	−	0.0789770i
$668$	−12.5109	+	9.08968i	−0.484060	+	0.351690i
$669$	1.72450	−	5.30746i	0.0666729	−	0.205198i
$670$	−5.07747			−0.196160
$671$	12.8368	+	13.5755i	0.495559	+	0.524076i
$672$	−1.58059			−0.0609727
$673$	0.473123	−	1.45612i	0.0182376	−	0.0561294i	−0.941524	−	0.336947i	$-0.890606\pi$
$673$	0.473123	−	1.45612i	0.0182376	−	0.0561294i	0.959761	+	0.280818i	$0.0906056\pi$
$674$	−14.7251	+	10.6984i	−0.567189	+	0.412087i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	6.22127	+	19.1471i	0.239280	+	0.736427i
$677$	−0.535716	−	1.64876i	−0.0205892	−	0.0633671i	0.940234	−	0.340529i	$-0.110606\pi$
$677$	−0.535716	−	1.64876i	−0.0205892	−	0.0633671i	−0.960823	+	0.277162i	$0.910606\pi$
$678$	0.0302903	+	0.0220072i	0.00116329	+	0.000845181i
$679$	2.46170	−	1.78853i	0.0944714	−	0.0686375i
$680$	−2.21735	+	6.82429i	−0.0850314	+	0.261700i
$681$	4.68905			0.179685
$682$	−23.4676	−	4.39269i	−0.898620	−	0.168205i
$683$	−15.3161			−0.586055			−0.293027	−	0.956104i	$-0.594663\pi$
$683$	−15.3161			−0.586055			−0.293027	+	0.956104i	$0.594663\pi$
$684$	−0.408331	+	1.25671i	−0.0156129	+	0.0480516i
$685$	−9.96186	+	7.23771i	−0.380623	+	0.276539i
$686$	−14.7076	−	10.6857i	−0.561537	−	0.407981i
$687$	2.59489	+	7.98626i	0.0990014	+	0.304695i
$688$	1.98128	+	6.09775i	0.0755356	+	0.232475i
$689$	−10.9179	−	7.93232i	−0.415939	−	0.302197i
$690$	0.290297	−	0.210913i	0.0110514	−	0.00802931i
$691$	7.77139	−	23.9179i	0.295638	−	0.909879i	−0.687369	−	0.726308i	$-0.741234\pi$
$691$	7.77139	−	23.9179i	0.295638	−	0.909879i	0.983007	−	0.183570i	$-0.0587655\pi$
$692$	−18.4037			−0.699604
$693$	2.50958	−	4.60250i	0.0953309	−	0.174835i
$694$	18.3816			0.697754
$695$	4.01629	−	12.3609i	0.152347	−	0.468875i
$696$	−7.82381	+	5.68433i	−0.296561	+	0.215464i
$697$	69.6985	+	50.6390i	2.64002	+	1.91809i
$698$	9.02959	+	27.7902i	0.341775	+	1.05188i
$699$	2.24764	+	6.91752i	0.0850135	+	0.261645i
$700$	−1.27873	−	0.929049i	−0.0483313	−	0.0351148i
$701$	17.8088	−	12.9389i	0.672629	−	0.488694i	−0.198275	−	0.980146i	$-0.563534\pi$
$701$	17.8088	−	12.9389i	0.672629	−	0.488694i	0.870904	+	0.491453i	$0.163534\pi$
$702$	−1.77873	+	5.47436i	−0.0671337	+	0.206616i
$703$	−12.8610			−0.485061
$704$	0.427051	+	3.28902i	0.0160951	+	0.123959i
$705$	−6.52001			−0.245558
$706$	1.36325	−	4.19564i	0.0513064	−	0.157905i
$707$	−10.5379	+	7.65622i	−0.396318	+	0.287942i
$708$	−8.35410	−	6.06961i	−0.313966	−	0.228110i
$709$	10.5106	+	32.3482i	0.394733	+	1.21486i	0.929170	+	0.369654i	$0.120524\pi$
$709$	10.5106	+	32.3482i	0.394733	+	1.21486i	−0.534437	+	0.845208i	$0.679476\pi$
$710$	2.81666	+	8.66879i	0.105707	+	0.325334i
$711$	9.32510	+	6.77508i	0.349719	+	0.254086i
$712$	5.79874	−	4.21303i	0.217317	−	0.157890i
$713$	−0.798208	+	2.45663i	−0.0298931	+	0.0920016i
$714$	11.3415			0.424446
$715$	17.2456	−	8.18809i	0.644951	−	0.306217i
$716$	−18.5623			−0.693706
$717$	6.73294	−	20.7219i	0.251446	−	0.773872i
$718$	17.9443	−	13.0373i	0.669674	−	0.486547i
$719$	−30.2936	−	22.0096i	−1.12976	−	0.820820i	−0.144102	−	0.989563i	$-0.546029\pi$
$719$	−30.2936	−	22.0096i	−1.12976	−	0.820820i	−0.985660	+	0.168742i	$0.946029\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	−2.39742	−	7.37851i	−0.0892847	−	0.274790i
$722$	−13.9587	−	10.1416i	−0.519490	−	0.377432i
$723$	−3.67340	+	2.66888i	−0.136615	+	0.0992567i
$724$	2.94427	−	9.06154i	0.109423	−	0.336769i
$725$	−9.67076			−0.359163
$726$	−10.2553	−	3.97859i	−0.380609	−	0.147659i
$727$	−36.1119			−1.33932			−0.669658	−	0.742669i	$-0.733559\pi$
$727$	−36.1119			−1.33932			−0.669658	+	0.742669i	$0.733559\pi$
$728$	−2.81144	+	8.65273i	−0.104199	+	0.320692i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	5.61803	+	4.08174i	0.207933	+	0.151072i
$731$	−14.2166	−	43.7543i	−0.525822	−	1.61831i
$732$	−1.74079	−	5.35761i	−0.0643415	−	0.198023i
$733$	14.4632	+	10.5081i	0.534209	+	0.388125i	0.821930	−	0.569589i	$-0.192898\pi$
$733$	14.4632	+	10.5081i	0.534209	+	0.388125i	−0.287721	+	0.957714i	$0.592898\pi$
$734$	−6.06058	+	4.40327i	−0.223700	+	0.162528i
$735$	1.39111	−	4.28140i	0.0513119	−	0.157922i
$736$	0.358826			0.0132265
$737$	15.2125	−	7.22275i	0.560358	−	0.266054i
$738$	−12.0064			−0.441964
$739$	−9.21977	+	28.3755i	−0.339155	+	1.04381i	0.625484	+	0.780237i	$0.284901\pi$
$739$	−9.21977	+	28.3755i	−0.339155	+	1.04381i	−0.964639	+	0.263574i	$0.915099\pi$
$740$	7.87411	−	5.72088i	0.289458	−	0.210304i
$741$	6.15338	+	4.47070i	0.226050	+	0.164235i
$742$	−1.14514	−	3.52437i	−0.0420393	−	0.129384i
$743$	−6.83808	−	21.0454i	−0.250865	−	0.772082i	−0.994616	−	0.103626i	$-0.966955\pi$
$743$	−6.83808	−	21.0454i	−0.250865	−	0.772082i	0.743752	−	0.668456i	$-0.233045\pi$
$744$	5.82381	+	4.23125i	0.213511	+	0.155125i
$745$	1.33296	−	0.968449i	0.0488357	−	0.0354812i
$746$	2.31816	−	7.13456i	0.0848739	−	0.261215i
$747$	−8.00000			−0.292705
$748$	−3.06430	−	23.6003i	−0.112042	−	0.862912i
$749$	2.60644			0.0952372
$750$	0.309017	−	0.951057i	0.0112837	−	0.0347277i
$751$	11.2724	−	8.18986i	0.411335	−	0.298852i	−0.362807	−	0.931864i	$-0.618182\pi$
$751$	11.2724	−	8.18986i	0.411335	−	0.298852i	0.774142	+	0.633012i	$0.218182\pi$
$752$	−5.27480	−	3.83237i	−0.192352	−	0.139752i
$753$	1.30067	+	4.00306i	0.0473991	+	0.145879i
$754$	17.2016	+	52.9412i	0.626447	+	1.92801i
$755$	−5.45943	−	3.96651i	−0.198689	−	0.144356i
$756$	−1.27873	+	0.929049i	−0.0465068	+	0.0337892i
$757$	−14.7822	+	45.4949i	−0.537267	+	1.65354i	0.201431	+	0.979503i	$0.435441\pi$
$757$	−14.7822	+	45.4949i	−0.537267	+	1.65354i	−0.738698	+	0.674036i	$0.764559\pi$
$758$	22.6589			0.823009
$759$	−0.569724	+	1.04486i	−0.0206797	+	0.0379260i
$760$	−1.32139			−0.0479317
$761$	9.48742	−	29.1993i	0.343919	−	1.05847i	−0.618241	−	0.785988i	$-0.712154\pi$
$761$	9.48742	−	29.1993i	0.343919	−	1.05847i	0.962160	−	0.272485i	$-0.0878455\pi$
$762$	13.3826	−	9.72300i	0.484799	−	0.352227i
$763$	−11.4373	−	8.30967i	−0.414057	−	0.300830i
$764$	6.18979	+	19.0502i	0.223939	+	0.689212i
$765$	2.21735	+	6.82429i	0.0801684	+	0.246733i
$766$	−5.24844	−	3.81321i	−0.189634	−	0.137777i
$767$	−48.0869	+	34.9372i	−1.73632	+	1.26151i
$768$	0.309017	−	0.951057i	0.0111507	−	0.0343183i
$769$	7.23993			0.261079			0.130539	−	0.991443i	$-0.458329\pi$
$769$	7.23993			0.261079			0.130539	+	0.991443i	$0.458329\pi$
$770$	5.15274	+	0.964497i	0.185692	+	0.0347581i
$771$	−14.7945			−0.532811
$772$	2.41941	−	7.44617i	0.0870764	−	0.267993i
$773$	−42.3727	+	30.7855i	−1.52404	+	1.10728i	−0.564599	+	0.825365i	$0.690969\pi$
$773$	−42.3727	+	30.7855i	−1.52404	+	1.10728i	−0.959440	+	0.281914i	$0.909031\pi$
$774$	5.18706	+	3.76862i	0.186445	+	0.135460i
$775$	2.22450	+	6.84630i	0.0799063	+	0.245926i
$776$	0.594894	+	1.83090i	0.0213555	+	0.0657253i
$777$	−12.4458	−	9.04238i	−0.446490	−	0.324394i
$778$	17.4606	−	12.6858i	0.625992	−	0.454810i
$779$	−4.90260	+	15.0887i	−0.175654	+	0.540607i
$780$	−5.75608			−0.206101
$781$	−20.7704	−	21.9656i	−0.743223	−	0.785991i
$782$	−2.57475			−0.0920730
$783$	−2.98843	+	9.19744i	−0.106798	+	0.328690i
$784$	3.64197	−	2.64605i	0.130070	−	0.0945017i
$785$	7.22370	+	5.24832i	0.257825	+	0.187321i
$786$	−3.86567	−	11.8973i	−0.137884	−	0.424363i
$787$	−12.4273	−	38.2472i	−0.442985	−	1.36337i	−0.884679	−	0.466201i	$-0.845622\pi$
$787$	−12.4273	−	38.2472i	−0.442985	−	1.36337i	0.441694	−	0.897166i	$-0.354378\pi$
$788$	−16.7303	−	12.1553i	−0.595993	−	0.433014i
$789$	6.39413	−	4.64561i	0.227637	−	0.165388i
$790$	−3.56187	+	10.9623i	−0.126726	+	0.390022i
$791$	0.0591788			0.00210415
$792$	2.27873	+	2.40986i	0.0809710	+	0.0856305i
$793$	−32.4259			−1.15148
$794$	−5.10603	+	15.7147i	−0.181206	+	0.557696i
$795$	1.89676	−	1.37808i	0.0672712	−	0.0488754i
$796$	2.53158	+	1.83930i	0.0897296	+	0.0651923i
$797$	2.54778	+	7.84126i	0.0902470	+	0.277752i	0.985986	−	0.166829i	$-0.0533528\pi$
$797$	2.54778	+	7.84126i	0.0902470	+	0.277752i	−0.895739	+	0.444581i	$0.853353\pi$
$798$	0.645404	+	1.98635i	0.0228471	+	0.0703161i
$799$	37.8493	+	27.4991i	1.33901	+	0.972848i
$800$	0.809017	−	0.587785i	0.0286031	−	0.0207813i
$801$	2.21492	−	6.81683i	0.0782604	−	0.240861i
$802$	−14.5672			−0.514384
$803$	−22.6384	−	4.23748i	−0.798891	−	0.149537i
$804$	−5.07747			−0.179068
$805$	0.175262	−	0.539400i	0.00617716	−	0.0190113i
$806$	33.5223	−	24.3554i	1.18077	−	0.857882i
$807$	−14.5193	−	10.5489i	−0.511104	−	0.371339i
$808$	−2.54658	−	7.83758i	−0.0895885	−	0.275725i
$809$	−0.134822	−	0.414939i	−0.00474008	−	0.0145885i	0.948659	−	0.316302i	$-0.102441\pi$
$809$	−0.134822	−	0.414939i	−0.00474008	−	0.0145885i	−0.953399	+	0.301714i	$0.902441\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−6.50209	+	4.72405i	−0.228319	+	0.165884i	−0.696064	−	0.717980i	$-0.745067\pi$
$811$	−6.50209	+	4.72405i	−0.228319	+	0.165884i	0.467744	+	0.883864i	$0.345067\pi$
$812$	−4.72349	+	14.5374i	−0.165762	+	0.510163i
$813$	−5.86454			−0.205678
$814$	−15.4534	+	28.3412i	−0.541642	+	0.993358i
$815$	−9.72251			−0.340564
$816$	−2.21735	+	6.82429i	−0.0776227	+	0.238898i
$817$	6.85410	−	4.97980i	0.239795	−	0.174221i
$818$	18.3070	+	13.3008i	0.640088	+	0.465051i
$819$	2.81144	+	8.65273i	0.0982398	+	0.302351i
$820$	−3.71020	−	11.4188i	−0.129566	−	0.398762i
$821$	−8.79611	−	6.39074i	−0.306986	−	0.223039i	0.423616	−	0.905842i	$-0.360761\pi$
$821$	−8.79611	−	6.39074i	−0.306986	−	0.223039i	−0.730602	+	0.682803i	$0.760761\pi$
$822$	−9.96186	+	7.23771i	−0.347460	+	0.252444i
$823$	2.12439	−	6.53819i	0.0740514	−	0.227907i	−0.907179	−	0.420744i	$-0.861769\pi$
$823$	2.12439	−	6.53819i	0.0740514	−	0.227907i	0.981231	+	0.192837i	$0.0617690\pi$
$824$	4.90843			0.170993
$825$	0.427051	+	3.28902i	0.0148680	+	0.114509i
$826$	−16.3216			−0.567900
$827$	2.28694	−	7.03849i	0.0795248	−	0.244752i	−0.903388	−	0.428824i	$-0.858928\pi$
$827$	2.28694	−	7.03849i	0.0795248	−	0.244752i	0.982913	+	0.184072i	$0.0589280\pi$
$828$	0.290297	−	0.210913i	0.0100885	−	0.00732973i
$829$	2.02959	+	1.47458i	0.0704906	+	0.0512144i	0.622472	−	0.782642i	$-0.286128\pi$
$829$	2.02959	+	1.47458i	0.0704906	+	0.0512144i	−0.551982	+	0.833856i	$0.686128\pi$
$830$	−2.47214	−	7.60845i	−0.0858091	−	0.264093i
$831$	2.60616	+	8.02093i	0.0904067	+	0.278243i
$832$	−4.65677	−	3.38334i	−0.161444	−	0.117296i
$833$	−26.1329	+	18.9867i	−0.905452	+	0.657850i
$834$	4.01629	−	12.3609i	0.139073	−	0.428022i
$835$	−15.4643			−0.535164
$836$	3.95897	−	1.87969i	0.136924	−	0.0650103i
$837$	7.19863			0.248821
$838$	−1.67196	+	5.14576i	−0.0577568	+	0.177757i
$839$	8.69292	−	6.31577i	0.300113	−	0.218045i	−0.427530	−	0.904001i	$-0.640616\pi$
$839$	8.69292	−	6.31577i	0.300113	−	0.218045i	0.727642	+	0.685957i	$0.240616\pi$
$840$	−1.27873	−	0.929049i	−0.0441203	−	0.0320552i
$841$	19.9389	+	61.3656i	0.687549	+	2.11606i
$842$	−1.07587	−	3.31118i	−0.0370769	−	0.114111i
$843$	−4.73294	−	3.43868i	−0.163011	−	0.118435i
$844$	−11.5727	+	8.40809i	−0.398350	+	0.289418i
$845$	−6.22127	+	19.1471i	−0.214018	+	0.658681i
$846$	−6.52001			−0.224163
$847$	−16.8100	+	4.44013i	−0.577599	+	0.152565i
$848$	2.34453			0.0805113
$849$	3.40882	−	10.4913i	0.116991	−	0.360060i
$850$	−5.80509	+	4.21765i	−0.199113	+	0.144664i
$851$	2.82544	+	2.05280i	0.0968548	+	0.0703691i
$852$	2.81666	+	8.66879i	0.0964972	+	0.296988i
$853$	2.37997	+	7.32480i	0.0814887	+	0.250796i	0.983498	−	0.180921i	$-0.0579078\pi$
$853$	2.37997	+	7.32480i	0.0814887	+	0.250796i	−0.902009	+	0.431717i	$0.857908\pi$
$854$	−7.20348	−	5.23363i	−0.246498	−	0.179091i
$855$	−1.06902	+	0.776691i	−0.0365598	+	0.0265623i
$856$	−0.509577	+	1.56832i	−0.0174170	+	0.0536039i
$857$	−7.18839			−0.245551			−0.122775	−	0.992434i	$-0.539179\pi$
$857$	−7.18839			−0.245551			−0.122775	+	0.992434i	$0.539179\pi$
$858$	17.2456	−	8.18809i	0.588757	−	0.279537i
$859$	40.4661			1.38068			0.690342	−	0.723483i	$-0.257460\pi$
$859$	40.4661			1.38068			0.690342	+	0.723483i	$0.257460\pi$
$860$	−1.98128	+	6.09775i	−0.0675611	+	0.207932i
$861$	−15.3530	+	11.1546i	−0.523228	+	0.380147i
$862$	9.88369	+	7.18092i	0.336640	+	0.244583i
$863$	−15.3403	−	47.2127i	−0.522191	−	1.60714i	−0.769805	−	0.638280i	$-0.779646\pi$
$863$	−15.3403	−	47.2127i	−0.522191	−	1.60714i	0.247614	−	0.968859i	$-0.420354\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−14.8889	−	10.8174i	−0.506238	−	0.367804i
$866$	7.67236	−	5.57430i	0.260717	−	0.189422i
$867$	10.6573	−	32.7997i	0.361940	−	1.11394i
$868$	11.3781			0.386198
$869$	−4.92239	−	37.9107i	−0.166981	−	1.28603i
$870$	−9.67076			−0.327870
$871$	−9.03142	+	27.7959i	−0.306018	+	0.941827i
$872$	7.23607	−	5.25731i	0.245044	−	0.178035i
$873$	1.55745	+	1.13156i	0.0527118	+	0.0382974i
$874$	−0.146520	−	0.450941i	−0.00495610	−	0.0152533i
$875$	−0.488430	−	1.50323i	−0.0165120	−	0.0508186i
$876$	5.61803	+	4.08174i	0.189816	+	0.137909i
$877$	−7.34625	+	5.33736i	−0.248065	+	0.180230i	−0.704869	−	0.709338i	$-0.748994\pi$
$877$	−7.34625	+	5.33736i	−0.248065	+	0.180230i	0.456804	+	0.889568i	$0.348994\pi$
$878$	2.33296	−	7.18010i	0.0787334	−	0.242317i
$879$	3.22962			0.108932
$880$	−1.58774	+	2.91188i	−0.0535228	+	0.0981596i
$881$	−9.85152			−0.331906			−0.165953	−	0.986134i	$-0.553070\pi$
$881$	−9.85152			−0.331906			−0.165953	+	0.986134i	$0.553070\pi$
$882$	1.39111	−	4.28140i	0.0468411	−	0.144162i
$883$	15.0037	−	10.9008i	0.504915	−	0.366842i	−0.305976	−	0.952039i	$-0.598983\pi$
$883$	15.0037	−	10.9008i	0.504915	−	0.366842i	0.810891	+	0.585197i	$0.198983\pi$
$884$	33.4146	+	24.2771i	1.12385	+	0.816528i
$885$	−3.19098	−	9.82084i	−0.107264	−	0.330124i
$886$	7.28394	+	22.4177i	0.244709	+	0.753137i
$887$	−18.2977	−	13.2941i	−0.614378	−	0.446372i	0.236575	−	0.971613i	$-0.423975\pi$
$887$	−18.2977	−	13.2941i	−0.614378	−	0.446372i	−0.850953	+	0.525242i	$0.823975\pi$
$888$	7.87411	−	5.72088i	0.264238	−	0.191980i
$889$	8.07949	−	24.8661i	0.270977	−	0.833983i
$890$	7.16764			0.240260
$891$	3.26001	+	0.610212i	0.109214	+	0.0204429i
$892$	5.58059			0.186852
$893$	−2.66232	+	8.19378i	−0.0890912	+	0.274194i
$894$	1.33296	−	0.968449i	0.0445807	−	0.0323898i
$895$	−15.0172	−	10.9106i	−0.501970	−	0.364703i
$896$	−0.488430	−	1.50323i	−0.0163173	−	0.0502195i
$897$	−0.638254	−	1.96434i	−0.0213107	−	0.0655875i
$898$	−1.60959	−	1.16944i	−0.0537128	−	0.0390246i
$899$	56.3207	−	40.9194i	1.87840	−	1.36474i
$900$	0.309017	−	0.951057i	0.0103006	−	0.0317019i
$901$	−16.8231			−0.560459
$902$	27.3594	+	28.9338i	0.910969	+	0.963391i
$903$	10.1341			0.337240
$904$	−0.0115699	+	0.0356084i	−0.000384808	+	0.00118432i
$905$	7.70820	−	5.60034i	0.256229	−	0.186162i
$906$	−5.45943	−	3.96651i	−0.181377	−	0.131778i
$907$	−10.6386	−	32.7423i	−0.353249	−	1.08719i	−0.957018	−	0.290029i	$-0.906335\pi$
$907$	−10.6386	−	32.7423i	−0.353249	−	1.08719i	0.603769	−	0.797160i	$-0.293665\pi$
$908$	1.44900	+	4.45955i	0.0480866	+	0.147995i
$909$	−6.66704	−	4.84389i	−0.221132	−	0.160662i
$910$	−7.36045	+	5.34768i	−0.243997	+	0.177274i
$911$	0.735940	−	2.26499i	0.0243828	−	0.0750425i	−0.938125	−	0.346298i	$-0.887439\pi$
$911$	0.735940	−	2.26499i	0.0243828	−	0.0750425i	0.962507	+	0.271255i	$0.0874387\pi$
$912$	−1.32139			−0.0437554
$913$	18.2298	+	19.2788i	0.603319	+	0.638037i
$914$	−29.9634			−0.991102
$915$	1.74079	−	5.35761i	0.0575488	−	0.177117i
$916$	−6.79352	+	4.93578i	−0.224464	+	0.163083i
$917$	−15.9963	−	11.6220i	−0.528245	−	0.383793i
$918$	2.21735	+	6.82429i	0.0731834	+	0.225235i
$919$	2.19819	+	6.76535i	0.0725117	+	0.223168i	0.980744	−	0.195299i	$-0.0625676\pi$
$919$	2.19819	+	6.76535i	0.0725117	+	0.223168i	−0.908232	+	0.418467i	$0.862568\pi$
$920$	0.290297	+	0.210913i	0.00957079	+	0.00695359i
$921$	18.5695	−	13.4915i	0.611884	−	0.444560i
$922$	−3.71262	+	11.4263i	−0.122269	+	0.376304i
$923$	52.4661			1.72694
$924$	5.15274	+	0.964497i	0.169513	+	0.0317296i
$925$	9.73294			0.320017
$926$	−1.50150	+	4.62114i	−0.0493423	+	0.151860i
$927$	3.97100	−	2.88510i	0.130425	−	0.0947592i
$928$	−7.82381	−	5.68433i	−0.256829	−	0.186597i
$929$	2.02115	+	6.22045i	0.0663117	+	0.204086i	0.978722	−	0.205190i	$-0.0657812\pi$
$929$	2.02115	+	6.22045i	0.0663117	+	0.204086i	−0.912410	+	0.409276i	$0.865781\pi$
$930$	2.22450	+	6.84630i	0.0729442	+	0.224499i
$931$	−4.81245	−	3.49645i	−0.157722	−	0.114591i
$932$	−5.88439	+	4.27526i	−0.192750	+	0.140041i
$933$	1.29825	−	3.99559i	0.0425027	−	0.130810i
$934$	15.3878			0.503504
$935$	11.3928	−	20.8942i	0.372586	−	0.683313i
$936$	−5.75608			−0.188143
$937$	11.3790	−	35.0209i	0.371735	−	1.14408i	−0.573921	−	0.818911i	$-0.694578\pi$
$937$	11.3790	−	35.0209i	0.371735	−	1.14408i	0.945655	−	0.325171i	$-0.105422\pi$
$938$	−6.49269	+	4.71722i	−0.211994	+	0.154023i
$939$	14.8710	+	10.8044i	0.485296	+	0.352588i
$940$	−2.01479	−	6.20090i	−0.0657154	−	0.202251i
$941$	−2.96628	−	9.12926i	−0.0966979	−	0.297605i	0.890995	−	0.454014i	$-0.150008\pi$
$941$	−2.96628	−	9.12926i	−0.0966979	−	0.297605i	−0.987692	+	0.156408i	$0.950008\pi$
$942$	7.22370	+	5.24832i	0.235361	+	0.171000i
$943$	3.48543	−	2.53231i	0.113501	−	0.0824635i
$944$	3.19098	−	9.82084i	0.103858	−	0.319641i
$945$	−1.58059			−0.0514167
$946$	−2.73806	−	21.0877i	−0.0890220	−	0.685621i
$947$	−35.5427			−1.15498			−0.577492	−	0.816396i	$-0.695968\pi$
$947$	−35.5427			−1.15498			−0.577492	+	0.816396i	$0.695968\pi$
$948$	−3.56187	+	10.9623i	−0.115684	+	0.356040i
$949$	32.3379	−	23.4948i	1.04973	−	0.762674i
$950$	−1.06902	−	0.776691i	−0.0346837	−	0.0251992i
$951$	−7.82774	−	24.0913i	−0.253832	−	0.781214i
$952$	3.50472	+	10.7864i	0.113589	+	0.349590i
$953$	−24.7135	−	17.9554i	−0.800549	−	0.581633i	0.110526	−	0.993873i	$-0.464747\pi$
$953$	−24.7135	−	17.9554i	−0.800549	−	0.581633i	−0.911075	+	0.412240i	$0.864747\pi$
$954$	1.89676	−	1.37808i	0.0614099	−	0.0446169i
$955$	−6.18979	+	19.0502i	−0.200297	+	0.616450i
$956$	21.7883			0.704683
$957$	28.9743	−	13.7568i	0.936607	−	0.444693i
$958$	3.62362			0.117074
$959$	−6.01430	+	18.5101i	−0.194212	+	0.597723i
$960$	0.809017	−	0.587785i	0.0261109	−	0.0189707i
$961$	−16.8439	−	12.2378i	−0.543352	−	0.394769i
$962$	−17.3122	−	53.2816i	−0.558169	−	1.71787i
$963$	0.509577	+	1.56832i	0.0164209	+	0.0505383i
$964$	−3.67340	−	2.66888i	−0.118312	−	0.0859588i
$965$	6.33409	−	4.60199i	0.203902	−	0.148143i
$966$	0.175262	−	0.539400i	0.00563895	−	0.0173549i
$967$	−22.9241			−0.737190			−0.368595	−	0.929590i	$-0.620161\pi$
$967$	−22.9241			−0.737190			−0.368595	+	0.929590i	$0.620161\pi$
$968$	0.614809	−	10.9828i	0.0197607	−	0.353001i
$969$	9.48158			0.304592
$970$	−0.594894	+	1.83090i	−0.0191009	+	0.0587865i
$971$	42.2115	−	30.6684i	1.35463	−	0.984197i	0.355865	−	0.934538i	$-0.384186\pi$
$971$	42.2115	−	30.6684i	1.35463	−	0.984197i	0.998766	−	0.0496593i	$-0.0158136\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−6.34813	−	19.5375i	−0.203512	−	0.626344i
$974$	−1.00945	−	3.10676i	−0.0323448	−	0.0995471i
$975$	−4.65677	−	3.38334i	−0.149136	−	0.108354i
$976$	4.55745	−	3.31118i	0.145881	−	0.105988i
$977$	2.31653	−	7.12956i	0.0741125	−	0.228095i	−0.907137	−	0.420834i	$-0.861737\pi$
$977$	2.31653	−	7.12956i	0.0741125	−	0.228095i	0.981250	+	0.192740i	$0.0617373\pi$
$978$	−9.72251			−0.310891
$979$	−21.4748	+	10.1960i	−0.686337	+	0.325867i
$980$	4.50173			0.143802
$981$	2.76393	−	8.50651i	0.0882456	−	0.271592i
$982$	27.7286	−	20.1460i	0.884857	−	0.642886i
$983$	46.8048	+	34.0057i	1.49284	+	1.08461i	0.973126	+	0.230272i	$0.0739615\pi$
$983$	46.8048	+	34.0057i	1.49284	+	1.08461i	0.519714	+	0.854340i	$0.326038\pi$
$984$	−3.71020	−	11.4188i	−0.118277	−	0.364018i
$985$	−6.39041	−	19.6677i	−0.203615	−	0.626664i
$986$	56.1397	+	40.7879i	1.78785	+	1.29895i
$987$	−8.33731	+	6.05741i	−0.265380	+	0.192810i
$988$	−2.35038	+	7.23374i	−0.0747757	+	0.230136i
$989$	−2.30063			−0.0731559
$990$	0.427051	+	3.28902i	0.0135726	+	0.104532i
$991$	15.1292			0.480595			0.240298	−	0.970699i	$-0.422755\pi$
$991$	15.1292			0.480595			0.240298	+	0.970699i	$0.422755\pi$
$992$	−2.22450	+	6.84630i	−0.0706279	+	0.217370i
$993$	−21.1282	+	15.3505i	−0.670483	+	0.487135i
$994$	11.6555	+	8.46820i	0.369689	+	0.268595i
$995$	0.966978	+	2.97605i	0.0306553	+	0.0943472i
$996$	−2.47214	−	7.60845i	−0.0783326	−	0.241083i
$997$	16.9301	+	12.3005i	0.536182	+	0.389559i	0.822665	−	0.568526i	$-0.192486\pi$
$997$	16.9301	+	12.3005i	0.536182	+	0.389559i	−0.286483	+	0.958085i	$0.592486\pi$
$998$	30.9106	−	22.4579i	0.978459	−	0.710892i
$999$	3.00764	−	9.25658i	0.0951576	−	0.292865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.m.f.31.1	✓	8
3.2	odd	2		990.2.n.i.361.1		8
11.4	even	5		3630.2.a.bq.1.3		4
11.5	even	5	inner	330.2.m.f.181.1	yes	8
11.7	odd	10		3630.2.a.bs.1.2		4
33.5	odd	10		990.2.n.i.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.31.1	✓	8	1.1	even	1	trivial
330.2.m.f.181.1	yes	8	11.5	even	5	inner
990.2.n.i.181.1		8	33.5	odd	10
990.2.n.i.361.1		8	3.2	odd	2
3630.2.a.bq.1.3		4	11.4	even	5
3630.2.a.bs.1.2		4	11.7	odd	10

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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.27873 - 0.929049i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.27873 - 0.929049i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.00000 q^{10} +(-2.99607 + 1.42251i) q^{11} +1.00000 q^{12} +(1.77873 - 5.47436i) q^{13} +(1.27873 - 0.929049i) q^{14} +(0.809017 + 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.21735 - 6.82429i) q^{17} +(0.809017 + 0.587785i) q^{18} +(1.06902 - 0.776691i) q^{19} +(-0.309017 + 0.951057i) q^{20} +1.58059 q^{21} +(-0.427051 - 3.28902i) q^{22} -0.358826 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(4.65677 + 3.38334i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.488430 + 1.50323i) q^{28} +(7.82381 + 5.68433i) q^{29} +(-0.809017 + 0.587785i) q^{30} +(2.22450 - 6.84630i) q^{31} -1.00000 q^{32} +(1.58774 - 2.91188i) q^{33} +7.17549 q^{34} +(-0.488430 + 1.50323i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-7.87411 - 5.72088i) q^{37} +(0.408331 + 1.25671i) q^{38} +(1.77873 + 5.47436i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-9.71342 + 7.05721i) q^{41} +(-0.488430 + 1.50323i) q^{42} +6.41156 q^{43} +(3.26001 + 0.610212i) q^{44} -1.00000 q^{45} +(0.110883 - 0.341264i) q^{46} +(-5.27480 + 3.83237i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(-1.39111 - 4.28140i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(5.80509 + 4.21765i) q^{51} +(-4.65677 + 3.38334i) q^{52} +(0.724498 - 2.22978i) q^{53} -1.00000 q^{54} +(2.27873 + 2.40986i) q^{55} -1.58059 q^{56} +(-0.408331 + 1.25671i) q^{57} +(-7.82381 + 5.68433i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(-0.309017 - 0.951057i) q^{60} +(-1.74079 - 5.35761i) q^{61} +(5.82381 + 4.23125i) q^{62} +(-1.27873 + 0.929049i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.75608 q^{65} +(2.27873 + 2.40986i) q^{66} -5.07747 q^{67} +(-2.21735 + 6.82429i) q^{68} +(0.290297 - 0.210913i) q^{69} +(-1.27873 - 0.929049i) q^{70} +(2.81666 + 8.66879i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(5.61803 + 4.08174i) q^{73} +(7.87411 - 5.72088i) q^{74} +(0.309017 - 0.951057i) q^{75} -1.32139 q^{76} +(5.15274 + 0.964497i) q^{77} -5.75608 q^{78} +(-3.56187 + 10.9623i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.71020 - 11.4188i) q^{82} +(-2.47214 - 7.60845i) q^{83} +(-1.27873 - 0.929049i) q^{84} +(-5.80509 + 4.21765i) q^{85} +(-1.98128 + 6.09775i) q^{86} -9.67076 q^{87} +(-1.58774 + 2.91188i) q^{88} +7.16764 q^{89} +(0.309017 - 0.951057i) q^{90} +(-7.36045 + 5.34768i) q^{91} +(0.290297 + 0.210913i) q^{92} +(2.22450 + 6.84630i) q^{93} +(-2.01479 - 6.20090i) q^{94} +(-1.06902 - 0.776691i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.594894 + 1.83090i) q^{97} +4.50173 q^{98} +(0.427051 + 3.28902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20} - 2 q^{21} + 10 q^{22} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + 27 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 5 q^{33} + 22 q^{34} + 2 q^{35} - 2 q^{36} - 4 q^{37} - 13 q^{38} + q^{39} - 2 q^{40} - 23 q^{41} + 2 q^{42} - 2 q^{43} + 10 q^{44} - 8 q^{45} - 5 q^{46} + 5 q^{47} - 2 q^{48} - 53 q^{49} + 2 q^{50} + 8 q^{51} + q^{52} - 18 q^{53} - 8 q^{54} + 5 q^{55} + 2 q^{56} + 13 q^{57} - 27 q^{58} - 40 q^{59} + 2 q^{60} - 20 q^{61} + 11 q^{62} + 3 q^{63} - 2 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 3 q^{68} - 5 q^{69} + 3 q^{70} - 10 q^{71} + 2 q^{72} + 36 q^{73} + 4 q^{74} - 2 q^{75} - 2 q^{76} + 50 q^{77} + 4 q^{78} - 11 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 16 q^{83} + 3 q^{84} - 8 q^{85} - 13 q^{86} - 18 q^{87} + 5 q^{88} - 46 q^{89} - 2 q^{90} - 39 q^{91} - 5 q^{92} - 6 q^{93} + 15 q^{94} + 12 q^{95} + 2 q^{96} + 16 q^{97} - 62 q^{98} - 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

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