LMFDB - Embedded newform 507.2.t.b.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	507.4
Dual form			507.2.t.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60202 - 0.104858i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.76600 + 0.384751i) q^{4} +(-0.705070 - 0.267398i) q^{5} +(0.824645 - 2.47011i) q^{6} +(0.861409 + 2.02180i) q^{7} +(-7.19059 - 0.873096i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(-2.60202 - 0.104858i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.76600 + 0.384751i) q^{4} +(-0.705070 - 0.267398i) q^{5} +(0.824645 - 2.47011i) q^{6} +(0.861409 + 2.02180i) q^{7} +(-7.19059 - 0.873096i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.80657 + 0.769706i) q^{10} +(-2.17645 - 3.44179i) q^{11} +(-1.69554 + 4.47078i) q^{12} +(0.939825 - 3.48091i) q^{13} +(-2.02940 - 5.35109i) q^{14} +(0.453003 - 0.602838i) q^{15} +(9.17934 + 1.49179i) q^{16} +(3.69987 - 1.57637i) q^{17} +(2.14316 + 1.47932i) q^{18} +(-6.05425 + 3.49542i) q^{19} +(-3.25748 - 1.54569i) q^{20} +(-2.18164 + 0.264899i) q^{21} +(5.30228 + 9.18382i) q^{22} +(0.272907 - 0.472689i) q^{23} +(2.83917 - 6.66378i) q^{24} +(-3.31693 - 2.93855i) q^{25} +(-2.81044 + 8.95885i) q^{26} +(0.748511 - 0.663123i) q^{27} +(3.32758 + 9.96733i) q^{28} +(-0.236814 + 5.87648i) q^{29} +(-1.24194 + 1.52109i) q^{30} +(-4.18685 - 4.72598i) q^{31} +(-9.53437 - 1.94646i) q^{32} +(3.91143 - 1.13296i) q^{33} +(-9.79244 + 3.71378i) q^{34} +(-0.0667285 - 1.65585i) q^{35} +(-3.82254 - 2.87245i) q^{36} +(9.47866 - 1.93508i) q^{37} +(16.1198 - 8.46033i) q^{38} +(3.08200 + 1.87117i) q^{39} +(4.83641 + 2.53834i) q^{40} +(-1.15890 - 0.335681i) q^{41} +(5.70444 - 0.460510i) q^{42} +(2.26922 - 11.1154i) q^{43} +(-9.04875 - 17.2409i) q^{44} +(0.453003 + 0.602838i) q^{45} +(-0.759674 + 1.20133i) q^{46} +(-1.43072 + 0.987558i) q^{47} +(-3.98674 + 8.40188i) q^{48} +(1.50342 - 1.56522i) q^{49} +(8.32259 + 7.99396i) q^{50} +(0.484761 + 3.99237i) q^{51} +(5.81849 - 16.2284i) q^{52} +(0.291156 - 2.39789i) q^{53} +(-2.01717 + 1.64697i) q^{54} +(0.614226 + 3.00868i) q^{55} +(-4.42881 - 15.2900i) q^{56} +(-1.67302 - 6.78771i) q^{57} +(1.23239 - 15.2659i) q^{58} +(-2.22927 - 13.7173i) q^{59} +(2.39095 - 2.69883i) q^{60} +(6.88255 - 5.17190i) q^{61} +(10.3987 + 12.7361i) q^{62} +(0.352529 - 2.16920i) q^{63} +(6.54545 + 1.61331i) q^{64} +(-1.59343 + 2.20298i) q^{65} +(-10.2964 + 2.53784i) q^{66} +(0.0808096 + 1.00101i) q^{67} +(18.2401 - 6.08944i) q^{68} +(0.378098 + 0.393642i) q^{69} +4.31555i q^{70} +(-1.91691 + 1.84121i) q^{71} +(5.61078 + 4.58106i) q^{72} +(0.0218612 - 0.0416530i) q^{73} +(-24.8666 + 4.04121i) q^{74} +(3.74535 - 2.36842i) q^{75} +(-30.1994 + 14.3298i) q^{76} +(5.08379 - 7.36514i) q^{77} +(-7.82322 - 5.19199i) q^{78} +(-0.892723 - 1.29333i) q^{79} +(-6.07318 - 3.50635i) q^{80} +(0.428693 + 0.903450i) q^{81} +(2.98029 + 0.994968i) q^{82} +(3.76641 - 15.2809i) q^{83} +(-10.4996 + 0.423119i) q^{84} +(-3.03019 + 0.122112i) q^{85} +(-7.07008 + 28.6844i) q^{86} +(-5.57858 - 1.86240i) q^{87} +(12.6450 + 26.6487i) q^{88} +(3.51336 + 2.02844i) q^{89} +(-1.11551 - 1.61610i) q^{90} +(7.84728 - 1.09835i) q^{91} +(1.48254 - 2.14783i) q^{92} +(5.70424 - 2.70670i) q^{93} +(3.82633 - 2.41962i) q^{94} +(5.20334 - 0.845625i) q^{95} +(4.52223 - 8.61640i) q^{96} +(0.831809 + 0.679151i) q^{97} +(-4.07605 + 3.91509i) q^{98} +4.07220i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	−2.60202	−	0.104858i	−1.83991	−	0.0741457i	−0.904238	−	0.427028i	$-0.859561\pi$
$2$	−2.60202	−	0.104858i	−1.83991	−	0.0741457i	−0.935668	+	0.352882i	$0.885202\pi$
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$3$	−0.278217	+	0.960518i	−0.160629	+	0.554555i
$4$	4.76600	+	0.384751i	2.38300	+	0.192376i
$5$	−0.705070	−	0.267398i	−0.315317	−	0.119584i	0.191869	−	0.981421i	$-0.438545\pi$
$5$	−0.705070	−	0.267398i	−0.315317	−	0.119584i	−0.507186	+	0.861837i	$0.669314\pi$
$6$	0.824645	−	2.47011i	0.336660	−	1.00842i
$7$	0.861409	+	2.02180i	0.325582	+	0.764169i	0.999674	+	0.0255218i	$0.00812474\pi$
$7$	0.861409	+	2.02180i	0.325582	+	0.764169i	−0.674092	+	0.738647i	$0.735465\pi$
$8$	−7.19059	−	0.873096i	−2.54226	−	0.308686i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	1.80657	+	0.769706i	0.571287	+	0.243403i
$11$	−2.17645	−	3.44179i	−0.656226	−	1.03774i	−0.995287	−	0.0969736i	$-0.969084\pi$
$11$	−2.17645	−	3.44179i	−0.656226	−	1.03774i	0.339061	−	0.940764i	$-0.389891\pi$
$12$	−1.69554	+	4.47078i	−0.489462	+	1.29060i
$13$	0.939825	−	3.48091i	0.260661	−	0.965431i
$13$	0.939825	−	3.48091i	0.260661	−	0.965431i
$14$	−2.02940	−	5.35109i	−0.542380	−	1.43014i
$15$	0.453003	−	0.602838i	0.116965	−	0.155652i
$16$	9.17934	+	1.49179i	2.29484	+	0.372947i
$17$	3.69987	−	1.57637i	0.897351	−	0.382326i	0.106485	−	0.994314i	$-0.466040\pi$
$17$	3.69987	−	1.57637i	0.897351	−	0.382326i	0.790866	+	0.611989i	$0.209630\pi$
$18$	2.14316	+	1.47932i	0.505147	+	0.348678i
$19$	−6.05425	+	3.49542i	−1.38894	+	0.801905i	−0.993196	−	0.116455i	$-0.962847\pi$
$19$	−6.05425	+	3.49542i	−1.38894	+	0.801905i	−0.395745	+	0.918361i	$0.629513\pi$
$20$	−3.25748	−	1.54569i	−0.728395	−	0.345628i
$21$	−2.18164	+	0.264899i	−0.476072	+	0.0578056i
$22$	5.30228	+	9.18382i	1.13045	+	1.95800i
$23$	0.272907	−	0.472689i	0.0569050	−	0.0985624i	−0.836170	−	0.548471i	$-0.815210\pi$
$23$	0.272907	−	0.472689i	0.0569050	−	0.0985624i	0.893075	+	0.449909i	$0.148543\pi$
$24$	2.83917	−	6.66378i	0.579544	−	1.36024i
$25$	−3.31693	−	2.93855i	−0.663386	−	0.587709i
$26$	−2.81044	+	8.95885i	−0.551173	+	1.75697i
$27$	0.748511	−	0.663123i	0.144051	−	0.127618i
$28$	3.32758	+	9.96733i	0.628854	+	1.88365i
$29$	−0.236814	+	5.87648i	−0.0439752	+	1.09123i	0.815079	+	0.579350i	$0.196693\pi$
$29$	−0.236814	+	5.87648i	−0.0439752	+	1.09123i	−0.859054	+	0.511884i	$0.828948\pi$
$30$	−1.24194	+	1.52109i	−0.226745	+	0.277713i
$31$	−4.18685	−	4.72598i	−0.751981	−	0.848811i	0.240571	−	0.970631i	$-0.422665\pi$
$31$	−4.18685	−	4.72598i	−0.751981	−	0.848811i	−0.992552	+	0.121820i	$0.961127\pi$
$32$	−9.53437	−	1.94646i	−1.68545	−	0.344088i
$33$	3.91143	−	1.13296i	0.680892	−	0.197223i
$34$	−9.79244	+	3.71378i	−1.67939	+	0.636909i
$35$	−0.0667285	−	1.65585i	−0.0112792	−	0.279890i
$36$	−3.82254	−	2.87245i	−0.637090	−	0.478742i
$37$	9.47866	−	1.93508i	1.55828	−	0.318126i	0.657860	−	0.753141i	$-0.271462\pi$
$37$	9.47866	−	1.93508i	1.55828	−	0.318126i	0.900423	+	0.435015i	$0.143257\pi$
$38$	16.1198	−	8.46033i	2.61498	−	1.37245i
$39$	3.08200	+	1.87117i	0.493515	+	0.299627i
$40$	4.83641	+	2.53834i	0.764703	+	0.401347i
$41$	−1.15890	−	0.335681i	−0.180990	−	0.0524245i	0.186485	−	0.982458i	$-0.440291\pi$
$41$	−1.15890	−	0.335681i	−0.180990	−	0.0524245i	−0.367475	+	0.930033i	$0.619778\pi$
$42$	5.70444	−	0.460510i	0.880214	−	0.0710582i
$43$	2.26922	−	11.1154i	0.346052	−	1.69508i	−0.318572	−	0.947899i	$-0.603203\pi$
$43$	2.26922	−	11.1154i	0.346052	−	1.69508i	0.664624	−	0.747178i	$-0.268592\pi$
$44$	−9.04875	−	17.2409i	−1.36415	−	2.59917i
$45$	0.453003	+	0.602838i	0.0675297	+	0.0898657i
$46$	−0.759674	+	1.20133i	−0.112008	+	0.177126i
$47$	−1.43072	+	0.987558i	−0.208693	+	0.144050i	−0.667827	−	0.744317i	$-0.732775\pi$
$47$	−1.43072	+	0.987558i	−0.208693	+	0.144050i	0.459134	+	0.888367i	$0.348160\pi$
$48$	−3.98674	+	8.40188i	−0.575437	+	1.21271i
$49$	1.50342	−	1.56522i	0.214774	−	0.223603i
$50$	8.32259	+	7.99396i	1.17699	+	1.13052i
$51$	0.484761	+	3.99237i	0.0678802	+	0.559043i
$52$	5.81849	−	16.2284i	0.806879	−	2.25048i
$53$	0.291156	−	2.39789i	0.0399934	−	0.329375i	−0.958956	−	0.283554i	$-0.908487\pi$
$53$	0.291156	−	2.39789i	0.0399934	−	0.329375i	0.998950	−	0.0458210i	$-0.0145904\pi$
$54$	−2.01717	+	1.64697i	−0.274503	+	0.224124i
$55$	0.614226	+	3.00868i	0.0828222	+	0.405690i
$56$	−4.42881	−	15.2900i	−0.591825	−	2.04322i
$57$	−1.67302	−	6.78771i	−0.221597	−	0.899054i
$58$	1.23239	−	15.2659i	0.161821	−	2.00451i
$59$	−2.22927	−	13.7173i	−0.290226	−	1.78584i	−0.565787	−	0.824551i	$-0.691428\pi$
$59$	−2.22927	−	13.7173i	−0.290226	−	1.78584i	0.275560	−	0.961284i	$-0.411137\pi$
$60$	2.39095	−	2.69883i	0.308671	−	0.348417i
$61$	6.88255	−	5.17190i	0.881221	−	0.662194i	−0.0606539	−	0.998159i	$-0.519319\pi$
$61$	6.88255	−	5.17190i	0.881221	−	0.662194i	0.941875	+	0.335964i	$0.109062\pi$
$62$	10.3987	+	12.7361i	1.32064	+	1.61749i
$63$	0.352529	−	2.16920i	0.0444145	−	0.273293i
$64$	6.54545	+	1.61331i	0.818181	+	0.201664i
$65$	−1.59343	+	2.20298i	−0.197641	+	0.273246i
$66$	−10.2964	+	2.53784i	−1.26740	+	0.312386i
$67$	0.0808096	+	1.00101i	0.00987246	+	0.122292i	0.999816	−	0.0191688i	$-0.00610201\pi$
$67$	0.0808096	+	1.00101i	0.00987246	+	0.122292i	−0.989944	+	0.141461i	$0.954820\pi$
$68$	18.2401	−	6.08944i	2.21194	−	0.738453i
$69$	0.378098	+	0.393642i	0.0455177	+	0.0473890i
$70$			4.31555i			0.515807i
$71$	−1.91691	+	1.84121i	−0.227495	+	0.218512i	−0.797802	−	0.602920i	$-0.794004\pi$
$71$	−1.91691	+	1.84121i	−0.227495	+	0.218512i	0.570307	+	0.821432i	$0.306824\pi$
$72$	5.61078	+	4.58106i	0.661236	+	0.539883i
$73$	0.0218612	−	0.0416530i	0.00255866	−	0.00487511i	−0.884173	−	0.467159i	$-0.845278\pi$
$73$	0.0218612	−	0.0416530i	0.00255866	−	0.00487511i	0.886732	+	0.462284i	$0.152970\pi$
$74$	−24.8666	+	4.04121i	−2.89068	+	0.469781i
$75$	3.74535	−	2.36842i	0.432476	−	0.273481i
$76$	−30.1994	+	14.3298i	−3.46411	+	1.64374i
$77$	5.08379	−	7.36514i	0.579352	−	0.839336i
$78$	−7.82322	−	5.19199i	−0.885805	−	0.587877i
$79$	−0.892723	−	1.29333i	−0.100439	−	0.145511i	0.769542	−	0.638596i	$-0.220485\pi$
$79$	−0.892723	−	1.29333i	−0.100439	−	0.145511i	−0.869981	+	0.493085i	$0.835869\pi$
$80$	−6.07318	−	3.50635i	−0.679002	−	0.392022i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	2.98029	+	0.994968i	0.329118	+	0.109876i
$83$	3.76641	−	15.2809i	0.413417	−	1.67730i	−0.282571	−	0.959246i	$-0.591187\pi$
$83$	3.76641	−	15.2809i	0.413417	−	1.67730i	0.695988	−	0.718053i	$-0.254967\pi$
$84$	−10.4996	+	0.423119i	−1.14560	+	0.0461661i
$85$	−3.03019	+	0.122112i	−0.328670	+	0.0132449i
$86$	−7.07008	+	28.6844i	−0.762387	+	3.09312i
$87$	−5.57858	−	1.86240i	−0.598086	−	0.199670i
$88$	12.6450	+	26.6487i	1.34796	+	2.84077i
$89$	3.51336	+	2.02844i	0.372415	+	0.215014i	0.674513	−	0.738263i	$-0.264354\pi$
$89$	3.51336	+	2.02844i	0.372415	+	0.215014i	−0.302098	+	0.953277i	$0.597687\pi$
$90$	−1.11551	−	1.61610i	−0.117585	−	0.170352i
$91$	7.84728	−	1.09835i	0.822618	−	0.115138i
$92$	1.48254	−	2.14783i	0.154566	−	0.223927i
$93$	5.70424	−	2.70670i	0.591503	−	0.280671i
$94$	3.82633	−	2.41962i	0.394655	−	0.249565i
$95$	5.20334	−	0.845625i	0.533851	−	0.0867593i
$96$	4.52223	−	8.61640i	0.461549	−	0.879407i
$97$	0.831809	+	0.679151i	0.0844574	+	0.0689573i	0.673734	−	0.738974i	$-0.264690\pi$
$97$	0.831809	+	0.679151i	0.0844574	+	0.0689573i	−0.589276	+	0.807932i	$0.700587\pi$
$98$	−4.07605	+	3.91509i	−0.411743	+	0.395484i
$99$			4.07220i			0.409272i
$100$	−14.6779	−	15.2813i	−1.46779	−	1.52813i
$101$	−4.43996	+	1.48227i	−0.441792	+	0.147492i	−0.528857	−	0.848711i	$-0.677379\pi$
$101$	−4.43996	+	1.48227i	−0.441792	+	0.147492i	0.0870653	+	0.996203i	$0.472251\pi$
$102$	−0.842728	−	10.4391i	−0.0834425	−	1.03362i
$103$	−13.3840	+	3.29886i	−1.31877	+	0.325047i	−0.835048	−	0.550177i	$-0.814560\pi$
$103$	−13.3840	+	3.29886i	−1.31877	+	0.325047i	−0.483718	+	0.875224i	$0.660714\pi$
$104$	−9.79706	+	24.2092i	−0.960681	+	2.37391i
$105$	1.60904	+	0.396592i	0.157026	+	0.0387035i
$106$	−1.00903	+	6.20882i	−0.0980057	+	0.603054i
$107$	8.58131	+	10.5102i	0.829586	+	1.01606i	0.999532	+	0.0306054i	$0.00974352\pi$
$107$	8.58131	+	10.5102i	0.829586	+	1.01606i	−0.169945	+	0.985454i	$0.554359\pi$
$108$	3.82254	−	2.87245i	0.367824	−	0.276402i
$109$	5.52397	−	6.23528i	0.529101	−	0.597231i	−0.421815	−	0.906682i	$-0.638607\pi$
$109$	5.52397	−	6.23528i	0.529101	−	0.597231i	0.950915	+	0.309451i	$0.100145\pi$
$110$	−1.28275	−	7.89305i	−0.122305	−	0.752573i
$111$	−0.778447	+	9.64280i	−0.0738870	+	0.915254i
$112$	4.89107	+	19.8438i	0.462163	+	1.87507i
$113$	1.72759	+	5.96433i	0.162518	+	0.561077i	0.999896	+	0.0144524i	$0.00460050\pi$
$113$	1.72759	+	5.96433i	0.162518	+	0.561077i	−0.837378	+	0.546625i	$0.815912\pi$
$114$	3.64149	+	17.8372i	0.341056	+	1.67060i
$115$	−0.318814	+	0.260304i	−0.0297296	+	0.0242735i
$116$	−3.38964	+	27.9162i	−0.314720	+	2.59195i
$117$	−2.65476	+	2.43973i	−0.245432	+	0.225553i
$118$	4.36225	+	35.9263i	0.401577	+	3.30729i
$119$	6.37421	+	6.12251i	0.584323	+	0.561250i
$120$	−3.78370	+	3.93924i	−0.345403	+	0.359602i
$121$	−2.39333	+	5.04383i	−0.217575	+	0.458530i
$122$	−18.4509	+	12.7357i	−1.67046	+	1.15304i
$123$	0.644855	−	1.01976i	0.0581446	−	0.0919483i
$124$	−18.1362	−	24.1349i	−1.62868	−	2.16738i
$125$	3.30508	+	6.29731i	0.295616	+	0.563248i
$126$	−1.14475	+	5.60734i	−0.101982	+	0.499541i
$127$	5.78607	−	0.467100i	0.513431	−	0.0414484i	0.178963	−	0.983856i	$-0.442726\pi$
$127$	5.78607	−	0.467100i	0.513431	−	0.0414484i	0.334467	+	0.942407i	$0.391444\pi$
$128$	1.83144	+	0.530482i	0.161878	+	0.0468885i
$129$	10.0452	+	5.27211i	0.884428	+	0.464184i
$130$	4.37713	−	5.56511i	0.383900	−	0.488092i
$131$	7.06568	−	3.70835i	0.617331	−	0.324000i	−0.126907	−	0.991915i	$-0.540505\pi$
$131$	7.06568	−	3.70835i	0.617331	−	0.324000i	0.744238	+	0.667914i	$0.232813\pi$
$132$	19.0778	−	3.89475i	1.66051	−	0.338995i
$133$	−12.2822	−	9.22950i	−1.06501	−	0.800299i
$134$	−0.105305	−	2.61311i	−0.00909695	−	0.225738i
$135$	−0.705070	+	0.267398i	−0.0606827	+	0.0230139i
$136$	−27.9806	+	8.10468i	−2.39932	+	0.694971i
$137$	−17.0576	−	3.48232i	−1.45733	−	0.297515i	−0.594941	−	0.803769i	$-0.702825\pi$
$137$	−17.0576	−	3.48232i	−1.45733	−	0.297515i	−0.862384	+	0.506254i	$0.831030\pi$
$138$	−0.942543	−	1.06391i	−0.0802346	−	0.0905662i
$139$	−4.29925	+	5.26563i	−0.364658	+	0.446625i	−0.924046	−	0.382281i	$-0.875139\pi$
$139$	−4.29925	+	5.26563i	−0.364658	+	0.446625i	0.559388	+	0.828906i	$0.311036\pi$
$140$	0.319062	−	7.91745i	0.0269657	−	0.669147i
$141$	−0.550515	−	1.64899i	−0.0463617	−	0.138870i
$142$	5.18089	−	4.58987i	0.434771	−	0.385174i
$143$	−14.0260	+	4.34136i	−1.17292	+	0.363043i
$144$	−6.96098	−	6.16689i	−0.580082	−	0.513908i
$145$	1.73833	−	4.08000i	0.144360	−	0.338826i
$146$	−0.0612508	+	0.106090i	−0.00506915	+	0.00878003i
$147$	1.08515	+	1.87953i	0.0895015	+	0.155021i
$148$	45.9198	−	5.57568i	3.77459	−	0.458318i
$149$	8.13907	+	3.86204i	0.666779	+	0.316390i	0.731826	−	0.681492i	$-0.238668\pi$
$149$	8.13907	+	3.86204i	0.666779	+	0.316390i	−0.0650471	+	0.997882i	$0.520720\pi$
$150$	−9.99383	+	5.76994i	−0.815993	+	0.471114i
$151$	−16.9546	−	11.7029i	−1.37975	−	0.952372i	−0.999624	−	0.0274367i	$-0.991266\pi$
$151$	−16.9546	−	11.7029i	−1.37975	−	0.952372i	−0.380125	−	0.924935i	$-0.624119\pi$
$152$	46.5855	−	19.8482i	3.77858	−	1.60990i
$153$	−3.96961	−	0.645125i	−0.320924	−	0.0521552i
$154$	−14.0004	+	18.6312i	−1.12819	+	1.50134i
$155$	1.68831	+	4.45170i	0.135608	+	0.357569i
$156$	13.9689	+	10.1038i	1.11841	+	0.808951i
$157$	2.02074	−	5.32825i	0.161272	−	0.425241i	−0.829884	−	0.557935i	$-0.811594\pi$
$157$	2.02074	−	5.32825i	0.161272	−	0.425241i	0.991157	+	0.132695i	$0.0423630\pi$
$158$	2.18727	+	3.45889i	0.174010	+	0.275174i
$159$	2.22221	+	0.946794i	0.176233	+	0.0750857i
$160$	6.20192	+	3.92186i	0.490305	+	0.310050i
$161$	1.19077	+	0.144585i	0.0938456	+	0.0113949i
$162$	−1.02073	−	2.39575i	−0.0801963	−	0.188228i
$163$	−6.27883	+	18.8074i	−0.491796	+	1.47311i	0.351771	+	0.936086i	$0.385580\pi$
$163$	−6.27883	+	18.8074i	−0.491796	+	1.47311i	−0.843567	+	0.537024i	$0.819549\pi$
$164$	−5.39418	−	2.04574i	−0.421215	−	0.159746i
$165$	−3.06078	−	0.247092i	−0.238281	−	0.0192361i
$166$	−11.4026	+	39.3663i	−0.885014	+	3.05542i
$167$	13.3475	+	0.537887i	1.03286	+	0.0416229i	0.550902	−	0.834570i	$-0.314284\pi$
$167$	13.3475	+	0.537887i	1.03286	+	0.0416229i	0.481961	+	0.876193i	$0.339925\pi$
$168$	15.9185			1.22814
$169$	−11.2335	−	6.54289i	−0.864112	−	0.503299i
$170$	7.89741			0.605704
$171$	6.98518	+	0.281493i	0.534170	+	0.0215263i
$172$	15.0917	−	52.1027i	1.15073	−	3.97280i
$173$	0.173951	+	0.0140427i	0.0132252	+	0.00106765i	0.0870774	−	0.996202i	$-0.472247\pi$
$173$	0.173951	+	0.0140427i	0.0132252	+	0.00106765i	−0.0738522	+	0.997269i	$0.523529\pi$
$174$	14.3203	+	5.43096i	1.08562	+	0.411720i
$175$	3.08392	−	9.23747i	0.233122	−	0.698287i
$176$	−14.8440	−	34.8402i	−1.11891	−	2.62618i
$177$	13.7959	+	1.67513i	1.03696	+	0.125910i
$178$	−8.92913	−	5.64644i	−0.669267	−	0.423219i
$179$	−18.1213	−	7.72078i	−1.35445	−	0.577078i	−0.411929	−	0.911216i	$-0.635145\pi$
$179$	−18.1213	−	7.72078i	−1.35445	−	0.577078i	−0.942524	+	0.334138i	$0.891555\pi$
$180$	1.92707	+	3.04742i	0.143635	+	0.227141i
$181$	2.70448	−	7.13114i	0.201023	−	0.530053i	−0.796158	−	0.605089i	$-0.793138\pi$
$181$	2.70448	−	7.13114i	0.201023	−	0.530053i	0.997181	+	0.0750352i	$0.0239069\pi$
$182$	−20.5339	+	2.03507i	−1.52208	+	0.150850i
$183$	3.05286	+	8.04973i	0.225674	+	0.595053i
$184$	−2.37506	+	3.16064i	−0.175092	+	0.233005i
$185$	−7.20056	−	1.17020i	−0.529395	−	0.0860351i
$186$	−15.1264	+	6.44475i	−1.10912	+	0.472552i
$187$	−13.4781	−	9.30328i	−0.985619	−	0.680323i
$188$	−7.19879	+	4.15623i	−0.525026	+	0.303124i
$189$	1.98548	+	0.942120i	0.144422	+	0.0685291i
$190$	−13.6279	+	1.65472i	−0.988669	+	0.120046i
$191$	3.20330	+	5.54828i	0.231783	+	0.401460i	0.958333	−	0.285654i	$-0.0922108\pi$
$191$	3.20330	+	5.54828i	0.231783	+	0.401460i	−0.726550	+	0.687114i	$0.758877\pi$
$192$	−3.37067	+	5.83817i	−0.243257	+	0.421334i
$193$	−7.37891	+	17.3189i	−0.531145	+	1.24664i	0.411060	+	0.911608i	$0.365159\pi$
$193$	−7.37891	+	17.3189i	−0.531145	+	1.24664i	−0.942205	+	0.335036i	$0.891252\pi$
$194$	−2.09317	−	1.85439i	−0.150281	−	0.133137i
$195$	−1.67268	−	2.14342i	−0.119783	−	0.153494i
$196$	7.76750	−	6.88141i	0.554822	−	0.491529i
$197$	−6.72905	−	20.1560i	−0.479425	−	1.43605i	−0.859518	−	0.511105i	$-0.829236\pi$
$197$	−6.72905	−	20.1560i	−0.479425	−	1.43605i	0.380093	−	0.924948i	$-0.375892\pi$
$198$	0.427003	−	10.5960i	0.0303457	−	0.753022i
$199$	−0.372910	+	0.456731i	−0.0264349	+	0.0323768i	−0.787653	−	0.616119i	$-0.788704\pi$
$199$	−0.372910	+	0.456731i	−0.0264349	+	0.0323768i	0.761218	+	0.648496i	$0.224602\pi$
$200$	21.2851	+	24.0259i	1.50508	+	1.69889i
$201$	−0.983967	−	0.200878i	−0.0694037	−	0.0141689i
$202$	11.7083	−	3.39134i	0.823792	−	0.238614i
$203$	−12.0851	+	4.58326i	−0.848205	+	0.321682i
$204$	0.774303	+	19.2141i	0.0542121	+	1.34526i
$205$	0.727348	+	0.546567i	0.0508002	+	0.0381739i
$206$	35.1714	−	7.18029i	2.45051	−	0.500275i
$207$	−0.483294	+	0.253652i	−0.0335913	+	0.0176301i
$208$	13.8198	−	30.5504i	0.958228	−	2.11829i
$209$	25.2073	+	13.2298i	1.74363	+	0.915125i
$210$	−4.14517	−	1.20066i	−0.286044	−	0.0828535i
$211$	−8.09058	+	0.653140i	−0.556979	+	0.0449640i	−0.355751	−	0.934581i	$-0.615775\pi$
$211$	−8.09058	+	0.653140i	−0.556979	+	0.0449640i	−0.201227	+	0.979545i	$0.564493\pi$
$212$	2.31024	−	11.3163i	0.158668	−	0.777206i
$213$	−1.23520	−	2.35348i	−0.0846347	−	0.161258i
$214$	−21.2267	−	28.2476i	−1.45102	−	1.93096i
$215$	−4.57218	+	7.23032i	−0.311820	+	0.493104i
$216$	−5.96120	+	4.11472i	−0.405609	+	0.279971i
$217$	5.94840	−	12.5360i	0.403804	−	0.850998i
$218$	−15.0273	+	15.6451i	−1.01778	+	1.05962i
$219$	0.0339263	+	0.0325866i	0.00229253	+	0.00220200i
$220$	1.76981	+	14.5757i	0.119320	+	0.982693i
$221$	−2.00996	−	14.3604i	−0.135205	−	0.965987i
$222$	3.03666	−	25.0091i	0.203807	−	1.67850i
$223$	−7.47300	+	6.10152i	−0.500429	+	0.408588i	−0.848756	−	0.528785i	$-0.822648\pi$
$223$	−7.47300	+	6.10152i	−0.500429	+	0.408588i	0.348326	+	0.937373i	$0.386750\pi$
$224$	−4.27765	−	20.9533i	−0.285812	−	1.40000i
$225$	1.23289	+	4.25642i	0.0821924	+	0.283761i
$226$	−3.86982	−	15.7005i	−0.257416	−	1.04438i
$227$	1.77389	−	21.9736i	0.117737	−	1.45844i	−0.620665	−	0.784076i	$-0.713137\pi$
$227$	1.77389	−	21.9736i	0.117737	−	1.45844i	0.738402	−	0.674361i	$-0.235581\pi$
$228$	−5.36203	−	32.9939i	−0.355109	−	2.18507i
$229$	0.805499	−	0.909221i	0.0532289	−	0.0600830i	−0.721293	−	0.692630i	$-0.756452\pi$
$229$	0.805499	−	0.909221i	0.0532289	−	0.0600830i	0.774522	+	0.632547i	$0.217990\pi$
$230$	0.856856	−	0.643886i	0.0564994	−	0.0424566i
$231$	5.65995	+	6.93219i	0.372398	+	0.456104i
$232$	6.83356	−	42.0486i	0.448645	−	2.76062i
$233$	4.73551	+	1.16720i	0.310234	+	0.0764658i	0.391359	−	0.920238i	$-0.372005\pi$
$233$	4.73551	+	1.16720i	0.310234	+	0.0764658i	−0.0811250	+	0.996704i	$0.525851\pi$
$234$	7.16356	−	6.06984i	0.468296	−	0.396798i
$235$	1.27283	−	0.313725i	0.0830304	−	0.0204651i
$236$	−5.34697	−	66.2342i	−0.348058	−	4.31148i
$237$	1.49064	−	0.497649i	0.0968275	−	0.0323258i
$238$	−15.9438	−	16.5993i	−1.03348	−	1.07597i
$239$			3.75000i			0.242568i	0.992618	+	0.121284i	$0.0387011\pi$
$239$			3.75000i			0.242568i	−0.992618	+	0.121284i	$0.961299\pi$
$240$	5.05758	−	4.85787i	0.326465	−	0.313574i
$241$	21.5136	+	17.5653i	1.38581	+	1.13148i	0.975616	+	0.219486i	$0.0704379\pi$
$241$	21.5136	+	17.5653i	1.38581	+	1.13148i	0.410198	+	0.911996i	$0.365460\pi$
$242$	6.75637	−	12.8732i	0.434316	−	0.827520i
$243$	−0.987050	+	0.160411i	−0.0633193	+	0.0102904i
$244$	34.7921	−	22.0012i	2.22734	−	1.40848i
$245$	−1.47855	+	0.701581i	−0.0944611	+	0.0448224i
$246$	−1.78485	+	2.58581i	−0.113798	+	0.164865i
$247$	6.47732	+	24.3594i	0.412142	+	1.54995i
$248$	25.9797	+	37.6381i	1.64971	+	2.39002i
$249$	13.6297	+	7.86913i	0.863749	+	0.498686i
$250$	−7.93957	−	16.7323i	−0.502142	−	1.05824i
$251$	−9.36793	−	3.12748i	−0.591299	−	0.197405i	0.00524341	−	0.999986i	$-0.498331\pi$
$251$	−9.36793	−	3.12748i	−0.591299	−	0.197405i	−0.596542	+	0.802582i	$0.703459\pi$
$252$	2.51476	−	10.2028i	0.158415	−	0.642714i
$253$	−2.22086	+	0.0894977i	−0.139624	+	0.00562667i
$254$	−15.1045	+	0.608689i	−0.947738	+	0.0381925i
$255$	0.725760	−	2.94452i	0.0454488	−	0.184393i
$256$	−17.4986	−	5.84190i	−1.09366	−	0.365119i
$257$	−2.81665	−	5.93597i	−0.175698	−	0.370276i	0.796428	−	0.604733i	$-0.206720\pi$
$257$	−2.81665	−	5.93597i	−0.175698	−	0.370276i	−0.972127	+	0.234457i	$0.924669\pi$
$258$	−25.5849	−	14.7715i	−1.59285	−	0.919631i
$259$	12.0774	+	17.4971i	0.750451	+	1.08722i
$260$	−8.44188	+	9.88631i	−0.523543	+	0.613123i
$261$	3.34093	−	4.84017i	0.206798	−	0.299599i
$262$	−18.7739	+	8.90832i	−1.15985	+	0.550358i
$263$	−14.8681	+	9.40203i	−0.916808	+	0.579754i	−0.907431	−	0.420202i	$-0.861959\pi$
$263$	−14.8681	+	9.40203i	−0.916808	+	0.579754i	−0.00937708	+	0.999956i	$0.502985\pi$
$264$	−29.1147	+	4.73159i	−1.79188	+	0.291209i
$265$	−0.846474	+	1.61282i	−0.0519985	+	0.0990749i
$266$	30.9908	+	25.3032i	1.90017	+	1.55144i
$267$	−2.92583	+	2.81030i	−0.179058	+	0.171987i
$268$			4.80189i			0.293322i
$269$	−3.07679	−	3.20327i	−0.187595	−	0.195307i	0.620763	−	0.783998i	$-0.286823\pi$
$269$	−3.07679	−	3.20327i	−0.187595	−	0.195307i	−0.808358	+	0.588691i	$0.799643\pi$
$270$	1.86264	−	0.621842i	0.113357	−	0.0378441i
$271$	1.49591	+	18.5302i	0.0908703	+	1.12563i	0.868092	+	0.496404i	$0.165346\pi$
$271$	1.49591	+	18.5302i	0.0908703	+	1.12563i	−0.777221	+	0.629227i	$0.783371\pi$
$272$	36.3140	−	8.95060i	2.20186	−	0.542710i
$273$	−1.12827	+	7.84303i	−0.0682859	+	0.474682i
$274$	44.0190	+	10.8497i	2.65928	+	0.655454i
$275$	−2.89470	+	17.8118i	−0.174557	+	1.07409i
$276$	1.65056	+	2.02157i	0.0993522	+	0.121684i
$277$	−14.0085	+	10.5267i	−0.841690	+	0.632489i	−0.931610	−	0.363460i	$-0.881595\pi$
$277$	−14.0085	+	10.5267i	−0.841690	+	0.632489i	0.0899194	+	0.995949i	$0.471339\pi$
$278$	11.7389	−	13.2505i	0.704052	−	0.794710i
$279$	1.01281	+	6.23208i	0.0606355	+	0.373105i
$280$	−0.965898	+	11.9648i	−0.0577235	+	0.715034i
$281$	−6.36711	−	25.8324i	−0.379830	−	1.54103i	−0.780706	−	0.624898i	$-0.785140\pi$
$281$	−6.36711	−	25.8324i	−0.379830	−	1.54103i	0.400876	−	0.916132i	$-0.368706\pi$
$282$	1.25954	+	4.34844i	0.0750045	+	0.258946i
$283$	0.675244	+	3.30757i	0.0401391	+	0.196614i	0.994916	−	0.100709i	$-0.0321111\pi$
$283$	0.675244	+	3.30757i	0.0401391	+	0.196614i	−0.954777	+	0.297324i	$0.903906\pi$
$284$	−9.84438	+	8.03769i	−0.584157	+	0.476949i
$285$	−0.635422	+	5.23317i	−0.0376391	+	0.309986i
$286$	36.9512	−	9.82557i	2.18497	−	0.580998i
$287$	−0.319611	−	2.63223i	−0.0188660	−	0.155376i
$288$	7.01804	+	6.74092i	0.413542	+	0.397213i
$289$	−0.572187	+	0.595710i	−0.0336581	+	0.0350418i
$290$	−4.95098	+	10.4340i	−0.290732	+	0.612704i
$291$	−0.883760	+	0.610016i	−0.0518069	+	0.0357598i
$292$	0.120216	−	0.190107i	0.00703513	−	0.0111252i
$293$	17.0939	+	22.7479i	0.998637	+	1.32894i	0.943824	+	0.330448i	$0.107200\pi$
$293$	17.0939	+	22.7479i	0.998637	+	1.32894i	0.0548132	+	0.998497i	$0.482544\pi$
$294$	−2.62649	−	5.00436i	−0.153180	−	0.291860i
$295$	−2.09617	+	10.2677i	−0.122044	+	0.597810i
$296$	−69.8467	+	5.63861i	−4.05976	+	0.327738i
$297$	−3.91143	−	1.13296i	−0.226964	−	0.0657409i
$298$	−20.7731	−	10.9025i	−1.20335	−	0.631567i
$299$	−1.38890	−	1.39421i	−0.0803222	−	0.0806292i
$300$	18.7616	−	9.84685i	1.08320	−	0.568508i
$301$	24.4278	−	4.98697i	1.40799	−	0.287444i
$302$	42.8892	+	32.2291i	2.46799	+	1.85458i
$303$	−0.188479	−	4.67705i	−0.0108278	−	0.268690i
$304$	−60.7885	+	23.0540i	−3.48646	+	1.32224i
$305$	−6.23564	+	1.80617i	−0.357052	+	0.103421i
$306$	10.2614	+	2.09487i	0.586603	+	0.119756i
$307$	19.4755	+	21.9833i	1.11153	+	1.25465i	0.964088	+	0.265582i	$0.0855641\pi$
$307$	19.4755	+	21.9833i	1.11153	+	1.25465i	0.147438	+	0.989071i	$0.452897\pi$
$308$	27.0631	−	33.1463i	1.54206	−	1.88868i
$309$	0.555049	−	13.7734i	0.0315756	−	0.783541i
$310$	−3.92621	−	11.7604i	−0.222994	−	0.667949i
$311$	−20.6299	+	18.2765i	−1.16981	+	1.03636i	−0.171120	+	0.985250i	$0.554739\pi$
$311$	−20.6299	+	18.2765i	−1.16981	+	1.03636i	−0.998693	+	0.0511134i	$0.983723\pi$
$312$	−20.5277	−	16.1457i	−1.16215	−	0.914070i
$313$	−18.5662	−	16.4482i	−1.04942	−	0.929707i	−0.0518021	−	0.998657i	$-0.516496\pi$
$313$	−18.5662	−	16.4482i	−1.04942	−	0.929707i	−0.997620	+	0.0689505i	$0.978035\pi$
$314$	−5.81671	+	13.6523i	−0.328256	+	0.770445i
$315$	−0.828597	+	1.43517i	−0.0466861	+	0.0808628i
$316$	−3.75711	−	6.50750i	−0.211354	−	0.366075i
$317$	7.81791	−	0.949266i	0.439097	−	0.0533161i	0.101997	−	0.994785i	$-0.467477\pi$
$317$	7.81791	−	0.949266i	0.439097	−	0.0533161i	0.337101	+	0.941469i	$0.390554\pi$
$318$	−5.68295	−	2.69659i	−0.318684	−	0.151217i
$319$	20.7410	−	11.9748i	1.16127	−	0.670461i
$320$	−4.18360	−	2.88773i	−0.233871	−	0.161429i
$321$	−12.4827	+	5.31838i	−0.696717	+	0.296843i
$322$	−3.08324	−	0.501075i	−0.171822	−	0.0279238i
$323$	−16.8899	+	22.4764i	−0.939779	+	1.25062i
$324$	1.69554	+	4.47078i	0.0941969	+	0.248377i
$325$	−13.3461	+	8.78422i	−0.740311	+	0.487261i
$326$	18.3098	−	48.2789i	1.01408	−	2.67392i
$327$	4.45223	+	7.04064i	0.246209	+	0.389348i
$328$	8.04012	+	3.42558i	0.443942	+	0.189146i
$329$	−3.22908	−	2.04195i	−0.178025	−	0.112576i
$330$	7.93830	+	0.963884i	0.436989	+	0.0530601i
$331$	0.126404	+	0.296681i	0.00694779	+	0.0163071i	0.923417	−	0.383798i	$-0.125384\pi$
$331$	0.126404	+	0.296681i	0.00694779	+	0.0163071i	−0.916469	+	0.400105i	$0.868974\pi$
$332$	23.8301	−	71.3798i	1.30784	−	3.91747i
$333$	−9.04551	−	3.43051i	−0.495691	−	0.187991i
$334$	−34.6741	−	2.79919i	−1.89728	−	0.153165i
$335$	0.210690	−	0.727387i	0.0115112	−	0.0397414i
$336$	−20.4212	−	0.822944i	−1.11407	−	0.0448953i
$337$	−10.0331			−0.546540			−0.273270	−	0.961937i	$-0.588105\pi$
$337$	−10.0331			−0.546540			−0.273270	+	0.961937i	$0.588105\pi$
$338$	28.5436	+	18.2026i	1.55257	+	0.990094i
$339$	−6.20950			−0.337254
$340$	−14.4889	−	0.583881i	−0.785768	−	0.0316654i
$341$	−7.15332	+	24.6961i	−0.387374	+	1.33737i
$342$	−18.1461	−	1.46490i	−0.981226	−	0.0792128i
$343$	18.8436	+	7.14642i	1.01746	+	0.385870i
$344$	−26.0218	+	77.9448i	−1.40300	+	4.20250i
$345$	−0.161327	−	0.378648i	−0.00868554	−	0.0203857i
$346$	−0.451151	−	0.0547796i	−0.0242540	−	0.00294497i
$347$	5.23035	+	3.30747i	0.280780	+	0.177554i	0.667431	−	0.744672i	$-0.267394\pi$
$347$	5.23035	+	3.30747i	0.280780	+	0.177554i	−0.386651	+	0.922226i	$0.626368\pi$
$348$	−25.8709	−	11.0226i	−1.38683	−	0.590872i
$349$	−3.13105	−	4.95135i	−0.167601	−	0.265040i	0.750936	−	0.660375i	$-0.229603\pi$
$349$	−3.13105	−	4.95135i	−0.167601	−	0.265040i	−0.918537	+	0.395335i	$0.870628\pi$
$350$	−8.99304	+	23.7127i	−0.480698	+	1.26750i
$351$	−1.60480	−	3.22872i	−0.0856579	−	0.172336i
$352$	14.0518	+	37.0516i	0.748965	+	1.97486i
$353$	19.9243	−	26.5145i	1.06047	−	1.41122i	0.154440	−	0.988002i	$-0.450643\pi$
$353$	19.9243	−	26.5145i	1.06047	−	1.41122i	0.906026	−	0.423222i	$-0.139101\pi$
$354$	−35.7216	−	5.80532i	−1.89858	−	0.308549i
$355$	1.84389	−	0.785608i	0.0978635	−	0.0416957i
$356$	15.9642	+	11.0193i	0.846102	+	0.584022i
$357$	−7.65420	+	4.41915i	−0.405103	+	0.233886i
$358$	46.3425	+	21.9898i	2.44928	+	1.16220i
$359$	−20.1741	+	2.44958i	−1.06475	+	0.129284i	−0.634113	−	0.773241i	$-0.718634\pi$
$359$	−20.1741	+	2.44958i	−1.06475	+	0.129284i	−0.430638	+	0.902525i	$0.641711\pi$
$360$	−2.73103	−	4.73027i	−0.143938	−	0.249307i
$361$	14.9360	−	25.8699i	0.786104	−	1.36157i
$362$	−7.78488	+	18.2718i	−0.409164	+	0.960343i
$363$	−4.17882	−	3.70212i	−0.219331	−	0.194311i
$364$	37.8227	−	2.21547i	1.98245	−	0.116122i
$365$	−0.0265516	+	0.0235226i	−0.00138977	+	0.00123123i
$366$	−7.09953	−	21.2657i	−0.371098	−	1.11157i
$367$	0.845652	−	20.9846i	0.0441427	−	1.09539i	−0.813638	−	0.581372i	$-0.802516\pi$
$367$	0.845652	−	20.9846i	0.0441427	−	1.09539i	0.857780	−	0.514016i	$-0.171843\pi$
$368$	3.21026	−	3.93185i	0.167346	−	0.204962i
$369$	0.800084	+	0.903108i	0.0416507	+	0.0470139i
$370$	18.6133	+	3.79993i	0.967659	+	0.197549i
$371$	5.09885	−	1.47690i	0.264719	−	0.0766768i
$372$	28.2278	−	10.7054i	1.46354	−	0.555049i
$373$	−0.944226	−	23.4307i	−0.0488902	−	1.21320i	−0.818433	−	0.574602i	$-0.805157\pi$
$373$	−0.944226	−	23.4307i	−0.0488902	−	1.21320i	0.769543	−	0.638595i	$-0.220484\pi$
$374$	34.0948	+	25.6206i	1.76300	+	1.32481i
$375$	−6.96821	+	1.42257i	−0.359837	+	0.0734612i
$376$	11.1500	−	5.85196i	0.575017	−	0.301792i
$377$	20.2329	+	6.34719i	1.04205	+	0.326897i
$378$	−5.06746	−	2.65961i	−0.260642	−	0.136795i
$379$	−16.2738	−	4.71377i	−0.835929	−	0.242130i	−0.167469	−	0.985877i	$-0.553559\pi$
$379$	−16.2738	−	4.71377i	−0.835929	−	0.242130i	−0.668461	+	0.743748i	$0.733046\pi$
$380$	25.1245	−	2.02826i	1.28886	−	0.104047i
$381$	−1.16113	+	5.68758i	−0.0594864	+	0.291384i
$382$	−7.75328	−	14.7726i	−0.396692	−	0.755834i
$383$	22.9530	+	30.5449i	1.17285	+	1.56077i	0.759931	+	0.650004i	$0.225233\pi$
$383$	22.9530	+	30.5449i	1.17285	+	1.56077i	0.412915	+	0.910770i	$0.364511\pi$
$384$	−1.01908	+	1.61154i	−0.0520045	+	0.0822385i
$385$	−5.55385	+	3.83355i	−0.283050	+	0.195376i
$386$	21.0161	−	44.2905i	1.06969	−	2.25433i
$387$	−7.85870	+	8.18177i	−0.399480	+	0.415903i
$388$	3.70310	+	3.55687i	0.187996	+	0.180573i
$389$	−4.42636	−	36.4544i	−0.224426	−	1.84831i	−0.474715	−	0.880140i	$-0.657449\pi$
$389$	−4.42636	−	36.4544i	−0.224426	−	1.84831i	0.250289	−	0.968171i	$-0.419474\pi$
$390$	4.12759	+	5.75263i	0.209009	+	0.291296i
$391$	0.264589	−	2.17909i	0.0133809	−	0.110201i
$392$	−12.1770	+	9.94225i	−0.615033	+	0.502159i
$393$	1.59615	+	7.81844i	0.0805149	+	0.394388i
$394$	15.3956	+	53.1518i	0.775620	+	2.67775i
$395$	0.283598	+	1.15060i	0.0142694	+	0.0578931i
$396$	−1.56679	+	19.4081i	−0.0787339	+	0.975295i
$397$	−4.42977	−	27.2575i	−0.222324	−	1.36801i	−0.822782	−	0.568358i	$-0.807579\pi$
$397$	−4.42977	−	27.2575i	−0.222324	−	1.36801i	0.600458	−	0.799657i	$-0.294985\pi$
$398$	1.01821	−	1.14932i	0.0510383	−	0.0576103i
$399$	12.2822	−	9.22950i	0.614881	−	0.462053i
$400$	−26.0636	−	31.9221i	−1.30318	−	1.59610i
$401$	0.883496	−	5.43637i	0.0441197	−	0.271479i	−0.955612	−	0.294627i	$-0.904805\pi$
$401$	0.883496	−	5.43637i	0.0441197	−	0.271479i	0.999732	+	0.0231475i	$0.00736873\pi$
$402$	2.53924	+	0.625866i	0.126646	+	0.0312154i
$403$	−20.3856	+	10.1325i	−1.01548	+	0.504734i
$404$	−21.7311	+	5.35624i	−1.08116	+	0.266483i
$405$	−0.0606776	−	0.751627i	−0.00301509	−	0.0373486i
$406$	31.9262	−	10.6585i	1.58447	−	0.528973i
$407$	−27.2900	−	28.4119i	−1.35272	−	1.40833i
$408$		−	29.1307i		−	1.44219i
$409$	−20.5198	+	19.7096i	−1.01464	+	0.974575i	−0.999680	−	0.0253131i	$-0.991942\pi$
$409$	−20.5198	+	19.7096i	−1.01464	+	0.974575i	−0.0149605	+	0.999888i	$0.504762\pi$
$410$	−1.83526	−	1.49845i	−0.0906371	−	0.0740029i
$411$	8.09055	−	15.4152i	0.399077	−	0.760378i
$412$	−65.0575	+	10.5729i	−3.20515	+	0.520888i
$413$	25.8133	−	16.3233i	1.27019	−	0.803218i
$414$	1.28414	−	0.609331i	0.0631120	−	0.0299470i
$415$	−6.74167	+	9.76699i	−0.330935	+	0.479443i
$416$	−15.7361	+	31.3590i	−0.771525	+	1.53750i
$417$	−3.86161	−	5.59450i	−0.189104	−	0.273964i
$418$	−64.2027	−	37.0674i	−3.14025	−	1.81303i
$419$	−3.07962	−	6.49015i	−0.150449	−	0.317065i	0.814208	−	0.580573i	$-0.197172\pi$
$419$	−3.07962	−	6.49015i	−0.150449	−	0.317065i	−0.964657	+	0.263509i	$0.915120\pi$
$420$	7.51609	+	2.50924i	0.366748	+	0.122438i
$421$	−1.48065	+	6.00721i	−0.0721622	+	0.292774i	−0.995924	−	0.0901933i	$-0.971252\pi$
$421$	−1.48065	+	6.00721i	−0.0721622	+	0.292774i	0.923762	+	0.382967i	$0.125098\pi$
$422$	21.1204	−	0.851121i	1.02812	−	0.0414319i
$423$	1.73705	−	0.0700007i	0.0844583	−	0.00340355i
$424$	−4.18717	+	16.9880i	−0.203347	+	0.825011i
$425$	−16.9045	−	5.64354i	−0.819987	−	0.273752i
$426$	2.96724	+	6.25333i	0.143763	+	0.302975i
$427$	16.3853	+	9.46003i	0.792938	+	0.457803i
$428$	36.8547	+	53.3933i	1.78144	+	2.58086i
$429$	−0.267670	−	14.6801i	−0.0129232	−	0.708762i
$430$	12.6551	−	18.3340i	0.610281	−	0.884145i
$431$	22.3380	−	10.5995i	1.07598	−	0.510560i	0.193595	−	0.981082i	$-0.437985\pi$
$431$	22.3380	−	10.5995i	1.07598	−	0.510560i	0.882389	+	0.470521i	$0.155934\pi$
$432$	7.86008	−	4.97041i	0.378168	−	0.239139i
$433$	−26.3504	+	4.28236i	−1.26632	+	0.205797i	−0.756220	−	0.654317i	$-0.772956\pi$
$433$	−26.3504	+	4.28236i	−1.26632	+	0.205797i	−0.510101	+	0.860114i	$0.670392\pi$
$434$	−16.7923	+	31.9951i	−0.806059	+	1.53582i
$435$	3.43528	+	2.80482i	0.164709	+	0.134481i
$436$	28.7263	−	27.5920i	1.37574	−	1.32142i
$437$			3.81570i			0.182530i
$438$	−0.0848599	−	0.0883485i	−0.00405476	−	0.00422145i
$439$	29.0148	−	9.68657i	1.38480	−	0.462315i	0.475965	−	0.879464i	$-0.342099\pi$
$439$	29.0148	−	9.68657i	1.38480	−	0.462315i	0.908838	+	0.417150i	$0.136971\pi$
$440$	−1.78978	−	22.1705i	−0.0853246	−	1.05694i
$441$	−2.10723	+	0.519386i	−0.100344	+	0.0247326i
$442$	3.72416	+	37.5769i	0.177140	+	1.78735i
$443$	−10.3463	−	2.55014i	−0.491569	−	0.121161i	−0.0142635	−	0.999898i	$-0.504540\pi$
$443$	−10.3463	−	2.55014i	−0.491569	−	0.121161i	−0.477306	+	0.878737i	$0.658387\pi$
$444$	−7.42016	+	45.6581i	−0.352145	+	2.16684i
$445$	−1.93476	−	2.36966i	−0.0917166	−	0.112332i
$446$	20.0847	−	15.0927i	0.951038	−	0.714659i
$447$	−5.97399	+	6.74324i	−0.282560	+	0.318944i
$448$	2.37652	+	14.6233i	0.112280	+	0.690887i
$449$	−1.41130	+	17.4821i	−0.0666034	+	0.825031i	0.874088	+	0.485768i	$0.161460\pi$
$449$	−1.41130	+	17.4821i	−0.0666034	+	0.825031i	−0.940691	+	0.339263i	$0.889822\pi$
$450$	−2.76168	−	11.2046i	−0.130187	−	0.528188i
$451$	1.36696	+	4.71929i	0.0643676	+	0.222223i
$452$	5.93891	+	29.0907i	0.279343	+	1.36831i
$453$	15.9580	−	13.0293i	0.749770	−	0.612169i
$454$	−6.91980	+	56.9897i	−0.324762	+	2.67466i
$455$	−5.82658	−	1.32393i	−0.273154	−	0.0620669i
$456$	6.10368	+	50.2683i	0.285831	+	2.35403i
$457$	30.4537	+	29.2512i	1.42456	+	1.36831i	0.820899	+	0.571074i	$0.193473\pi$
$457$	30.4537	+	29.2512i	1.42456	+	1.36831i	0.603665	+	0.797238i	$0.293706\pi$
$458$	−2.19126	+	2.28135i	−0.102391	+	0.106600i
$459$	1.72407	−	3.63340i	0.0804727	−	0.169593i
$460$	−1.61962	+	1.11794i	−0.0755152	+	0.0521244i
$461$	−5.11863	+	8.09446i	−0.238398	+	0.376997i	−0.943101	−	0.332506i	$-0.892106\pi$
$461$	−5.11863	+	8.09446i	−0.238398	+	0.376997i	0.704703	+	0.709502i	$0.251080\pi$
$462$	−14.0004	−	18.6312i	−0.651359	−	0.866801i
$463$	−2.30290	−	4.38782i	−0.107025	−	0.203919i	0.826054	−	0.563591i	$-0.190581\pi$
$463$	−2.30290	−	4.38782i	−0.107025	−	0.203919i	−0.933079	+	0.359672i	$0.882888\pi$
$464$	−10.9403	+	53.5889i	−0.507889	+	2.48780i
$465$	−4.74566	+	0.383109i	−0.220075	+	0.0177663i
$466$	−12.1995	−	3.53363i	−0.565132	−	0.163692i
$467$	−3.73610	−	1.96085i	−0.172886	−	0.0907375i	0.376060	−	0.926595i	$-0.377279\pi$
$467$	−3.73610	−	1.96085i	−0.172886	−	0.0907375i	−0.548946	+	0.835858i	$0.684971\pi$
$468$	−13.5913	+	10.6063i	−0.628256	+	0.490277i
$469$	−1.95422	+	1.02566i	−0.0902377	+	0.0473604i
$470$	−3.34483	+	0.682852i	−0.154285	+	0.0314976i
$471$	4.55568	+	3.42337i	0.209914	+	0.157740i
$472$	4.05330	+	100.582i	0.186568	+	4.62964i
$473$	−43.1956	+	16.3819i	−1.98613	+	0.753241i
$474$	−3.93086	+	1.13859i	−0.180550	+	0.0522971i
$475$	30.3530	+	6.19661i	1.39269	+	0.284320i
$476$	28.0238	+	31.6324i	1.28447	+	1.44987i
$477$	−1.52767	+	1.87106i	−0.0699472	+	0.0856698i
$478$	0.393217	−	9.75759i	0.0179853	−	0.446302i
$479$	−5.37105	−	16.0883i	−0.245409	−	0.735091i	−0.997137	−	0.0756172i	$-0.975907\pi$
$479$	−5.37105	−	16.0883i	−0.245409	−	0.735091i	0.751727	−	0.659474i	$-0.229221\pi$
$480$	−5.49250	+	4.86593i	−0.250697	+	0.222098i
$481$	2.17244	−	34.8130i	0.0990546	−	1.58734i
$482$	−54.1370	−	47.9612i	−2.46587	−	2.18457i
$483$	−0.470169	+	1.10353i	−0.0213934	+	0.0502122i
$484$	−13.3472	+	23.1181i	−0.606692	+	1.05082i
$485$	−0.404880	−	0.701272i	−0.0183846	−	0.0318431i
$486$	2.58515	−	0.313893i	0.117265	−	0.0142385i
$487$	36.6665	+	17.3985i	1.66152	+	0.788400i	0.999233	+	0.0391479i	$0.0124643\pi$
$487$	36.6665	+	17.3985i	1.66152	+	0.788400i	0.662285	+	0.749252i	$0.269587\pi$
$488$	−54.0052	+	31.1799i	−2.44470	+	1.41145i
$489$	−16.3180	−	11.2635i	−0.737924	−	0.509352i
$490$	3.92078	−	1.67049i	0.177123	−	0.0754650i
$491$	6.21228	+	1.00959i	0.280356	+	0.0455623i	0.298963	−	0.954265i	$-0.403359\pi$
$491$	6.21228	+	1.00959i	0.280356	+	0.0455623i	−0.0186073	+	0.999827i	$0.505923\pi$
$492$	3.46573	−	4.61205i	0.156247	−	0.207927i
$493$	8.38731	+	22.1155i	0.377746	+	0.996033i
$494$	−14.2998	−	64.0628i	−0.643380	−	2.88232i
$495$	1.08890	−	2.87119i	0.0489423	−	0.129050i
$496$	−31.3824	−	49.6273i	−1.40911	−	2.22833i
$497$	−5.37381	−	2.28957i	−0.241048	−	0.102701i
$498$	−34.6397	−	21.9048i	−1.55224	−	0.981578i
$499$	−32.0625	−	3.89309i	−1.43531	−	0.174279i	−0.634376	−	0.773025i	$-0.718743\pi$
$499$	−32.0625	−	3.89309i	−1.43531	−	0.174279i	−0.800939	+	0.598746i	$0.795666\pi$
$500$	13.3291	+	31.2846i	0.596097	+	1.39909i
$501$	−4.23017	+	12.6709i	−0.188990	+	0.566094i
$502$	24.0476	+	9.12006i	1.07330	+	0.407048i
$503$	−33.7710	−	2.72628i	−1.50577	−	0.121559i	−0.700155	−	0.713991i	$-0.746886\pi$
$503$	−33.7710	−	2.72628i	−1.50577	−	0.121559i	−0.805620	+	0.592432i	$0.798168\pi$
$504$	−4.42881	+	15.2900i	−0.197275	+	0.681072i
$505$	3.52684	+	0.142127i	0.156942	+	0.00632455i
$506$	5.78811			0.257313
$507$	9.40991	−	8.96959i	0.417909	−	0.398354i
$508$	27.7561			1.23148
$509$	−26.8974	−	1.08393i	−1.19221	−	0.0480443i	−0.563788	−	0.825919i	$-0.690657\pi$
$509$	−26.8974	−	1.08393i	−1.19221	−	0.0480443i	−0.628419	+	0.777875i	$0.716298\pi$
$510$	−2.19720	+	7.58561i	−0.0972936	+	0.335896i
$511$	0.103045	+	0.00831869i	0.00455846	+	0.000367997i
$512$	41.3536	+	15.6833i	1.82759	+	0.693112i
$513$	−2.21378	+	6.63107i	−0.0977407	+	0.292769i
$514$	6.70656	+	15.7409i	0.295814	+	0.694300i
$515$	10.3188	+	1.25293i	0.454700	+	0.0552105i
$516$	45.8468	+	28.9918i	2.01829	+	1.27629i
$517$	6.51287	+	2.77487i	0.286436	+	0.122039i
$518$	−29.5908	−	46.7941i	−1.30015	−	2.05602i
$519$	−0.0618844	+	0.163176i	−0.00271642	+	0.00716262i
$520$	13.3811	−	14.4495i	0.586800	−	0.633652i
$521$	4.32352	+	11.4002i	0.189417	+	0.499451i	0.995759	−	0.0919978i	$-0.0293253\pi$
$521$	4.32352	+	11.4002i	0.189417	+	0.499451i	−0.806342	+	0.591449i	$0.798556\pi$
$522$	−9.20069	+	12.2439i	−0.402703	+	0.535901i
$523$	15.2955	+	2.48577i	0.668827	+	0.108695i	0.485338	−	0.874327i	$-0.338697\pi$
$523$	15.2955	+	2.48577i	0.668827	+	0.108695i	0.183489	+	0.983022i	$0.441261\pi$
$524$	35.1018	−	14.9555i	1.53343	−	0.653333i
$525$	8.01475	+	5.53218i	0.349792	+	0.241444i
$526$	39.6730	−	22.9052i	1.72983	−	0.998716i
$527$	−22.9407	−	10.8855i	−0.999313	−	0.474180i
$528$	37.5945	−	4.56479i	1.63609	−	0.198657i
$529$	11.3510	+	19.6606i	0.493524	+	0.854808i
$530$	2.37166	−	4.10784i	0.103018	−	0.178433i
$531$	−5.44725	+	12.7852i	−0.236390	+	0.554829i
$532$	−54.9861	−	48.7134i	−2.38395	−	2.11199i
$533$	−2.25764	+	3.71856i	−0.0977893	+	0.161069i
$534$	7.90775	−	7.00566i	0.342202	−	0.303164i
$535$	−3.24002	−	9.70504i	−0.140078	−	0.419586i
$536$	0.292906	−	7.26838i	0.0126516	−	0.313946i
$537$	12.4576	−	15.2578i	0.537586	−	0.658424i
$538$	7.66997	+	8.65761i	0.330676	+	0.373256i
$539$	−8.65928	−	1.76780i	−0.372982	−	0.0761447i
$540$	−3.46324	+	1.00314i	−0.149034	+	0.0431683i
$541$	0.856623	−	0.324874i	0.0368291	−	0.0139674i	−0.336122	−	0.941819i	$-0.609115\pi$
$541$	0.856623	−	0.324874i	0.0368291	−	0.0139674i	0.372951	+	0.927851i	$0.378346\pi$
$542$	−1.94936	−	48.3729i	−0.0837322	−	2.07779i
$543$	6.09715	+	4.58171i	0.261654	+	0.196620i
$544$	−38.3443	+	7.82805i	−1.64400	+	0.335625i
$545$	−5.56209	+	2.91921i	−0.238254	+	0.125045i
$546$	3.75818	−	20.2894i	0.160835	−	0.868307i
$547$	14.2814	+	7.49544i	0.610627	+	0.320482i	0.741537	−	0.670912i	$-0.234097\pi$
$547$	14.2814	+	7.49544i	0.610627	+	0.320482i	−0.130909	+	0.991394i	$0.541790\pi$
$548$	−79.9565	−	23.1597i	−3.41557	−	0.989332i
$549$	−8.58127	+	0.692752i	−0.366240	+	0.0295659i
$550$	9.39976	−	46.0431i	0.400807	−	1.96328i
$551$	−19.1070	−	36.4054i	−0.813987	−	1.55092i
$552$	−2.37506	−	3.16064i	−0.101089	−	0.134526i
$553$	1.84586	−	2.91900i	0.0784940	−	0.124128i
$554$	37.5543	−	25.9218i	1.59553	−	1.10131i
$555$	3.12732	−	6.59069i	0.132747	−	0.279759i
$556$	−22.5162	+	23.4418i	−0.954900	+	0.994156i
$557$	4.12160	+	3.95885i	0.174638	+	0.167742i	0.774947	−	0.632026i	$-0.217776\pi$
$557$	4.12160	+	3.95885i	0.174638	+	0.167742i	−0.600309	+	0.799768i	$0.704956\pi$
$558$	−1.98187	−	16.3222i	−0.0838994	−	0.690974i
$559$	−36.5589	−	18.3454i	−1.54628	−	0.775929i
$560$	1.85765	−	15.2992i	0.0785002	−	0.646507i
$561$	12.6858	−	10.3577i	0.535596	−	0.437300i
$562$	13.8586	+	67.8840i	0.584591	+	2.86351i
$563$	6.78858	+	23.4369i	0.286105	+	0.987748i	0.966875	+	0.255251i	$0.0821580\pi$
$563$	6.78858	+	23.4369i	0.286105	+	0.987748i	−0.680770	+	0.732497i	$0.738355\pi$
$564$	−1.98930	−	8.07091i	−0.0837646	−	0.339847i
$565$	0.376777	−	4.66723i	0.0158511	−	0.196352i
$566$	−1.41018	−	8.67716i	−0.0592741	−	0.364728i
$567$	−1.45732	+	1.64497i	−0.0612016	+	0.0690823i
$568$	15.3912	−	11.5658i	0.645802	−	0.485289i
$569$	3.83169	+	4.69296i	0.160633	+	0.196739i	0.848650	−	0.528955i	$-0.177416\pi$
$569$	3.83169	+	4.69296i	0.160633	+	0.196739i	−0.688017	+	0.725694i	$0.741519\pi$
$570$	2.20212	−	13.5502i	0.0922366	−	0.567555i
$571$	23.2559	+	5.73206i	0.973228	+	0.239879i	0.693704	−	0.720260i	$-0.255977\pi$
$571$	23.2559	+	5.73206i	0.973228	+	0.239879i	0.279523	+	0.960139i	$0.409824\pi$
$572$	−68.5184	+	15.2944i	−2.86490	+	0.639491i
$573$	−6.22044	+	1.53320i	−0.259863	+	0.0640504i
$574$	0.555624	+	6.88263i	0.0231913	+	0.287276i
$575$	−2.29423	+	0.765927i	−0.0956760	+	0.0319413i
$576$	−4.66989	−	4.86187i	−0.194579	−	0.202578i
$577$		−	30.8395i		−	1.28386i	−0.766762	−	0.641932i	$-0.778133\pi$
$577$		−	30.8395i		−	1.28386i	0.766762	−	0.641932i	$-0.221867\pi$
$578$	1.55131	−	1.49005i	0.0645259	−	0.0619780i
$579$	−14.5822	−	11.9060i	−0.606016	−	0.494797i
$580$	9.85465	−	18.7765i	0.409192	−	0.779650i
$581$	34.1394	−	5.54820i	1.41634	−	0.230178i
$582$	2.36353	−	1.49460i	0.0979714	−	0.0619533i
$583$	−8.88670	+	4.21679i	−0.368049	+	0.174642i
$584$	−0.193562	+	0.280423i	−0.00800964	+	0.0116040i
$585$	2.52417	−	1.01030i	0.104361	−	0.0417708i
$586$	−42.0934	−	60.9829i	−1.73886	−	2.51918i
$587$	17.3978	+	10.0446i	0.718084	+	0.414586i	0.814047	−	0.580799i	$-0.197260\pi$
$587$	17.3978	+	10.0446i	0.718084	+	0.414586i	−0.0959634	+	0.995385i	$0.530593\pi$
$588$	4.44866	+	9.37535i	0.183460	+	0.386633i
$589$	41.8676	+	13.9774i	1.72512	+	0.575931i
$590$	6.53093	−	26.4970i	0.268874	−	1.09087i
$591$	21.2323	−	0.855633i	0.873381	−	0.0351960i
$592$	89.8946	−	3.62263i	3.69465	−	0.148889i
$593$	2.66753	−	10.8226i	0.109542	−	0.444431i	−0.890400	−	0.455179i	$-0.849575\pi$
$593$	2.66753	−	10.8226i	0.109542	−	0.444431i	0.999942	+	0.0107481i	$0.00342129\pi$
$594$	10.0588	+	3.35812i	0.412718	+	0.137786i
$595$	−2.85712	−	6.02125i	−0.117130	−	0.246847i
$596$	37.3049	+	21.5380i	1.52807	+	0.882230i
$597$	−0.334949	−	0.485257i	−0.0137085	−	0.0198603i
$598$	3.46776	+	3.77340i	0.141807	+	0.154306i
$599$	18.9986	−	27.5243i	0.776264	−	1.12461i	−0.212796	−	0.977097i	$-0.568257\pi$
$599$	18.9986	−	27.5243i	0.776264	−	1.12461i	0.989060	−	0.147515i	$-0.0471276\pi$
$600$	−28.9992	+	13.7603i	−1.18389	+	0.561761i
$601$	−6.52216	+	4.12436i	−0.266044	+	0.168236i	−0.660827	−	0.750538i	$-0.729794\pi$
$601$	−6.52216	+	4.12436i	−0.266044	+	0.168236i	0.394783	+	0.918775i	$0.370820\pi$
$602$	−64.0845	+	10.4147i	−2.61189	+	0.424473i
$603$	0.466704	−	0.889230i	0.0190057	−	0.0362123i
$604$	−76.3031	−	62.2995i	−3.10473	−	2.53493i
$605$	3.03617	−	2.91628i	0.123438	−	0.118564i
$606$			12.1895i			0.495166i
$607$	−12.6748	−	13.1959i	−0.514454	−	0.535604i	0.412411	−	0.910998i	$-0.364687\pi$
$607$	−12.6748	−	13.1959i	−0.514454	−	0.535604i	−0.926865	+	0.375394i	$0.877507\pi$
$608$	64.5272	−	21.5423i	2.61692	−	0.873657i
$609$	−1.04003	−	12.8831i	−0.0421441	−	0.522048i
$610$	16.4146	−	4.04585i	0.664610	−	0.163812i
$611$	2.09297	+	5.90835i	0.0846724	+	0.239026i
$612$	−18.6710	−	4.60198i	−0.754729	−	0.186024i
$613$	2.05952	−	12.6727i	0.0831833	−	0.511847i	−0.911703	−	0.410849i	$-0.865232\pi$
$613$	2.05952	−	12.6727i	0.0831833	−	0.511847i	0.994887	−	0.100998i	$-0.0322036\pi$
$614$	−48.3705	−	59.2432i	−1.95208	−	2.39086i
$615$	−0.727348	+	0.546567i	−0.0293295	+	0.0220397i
$616$	−42.9859	+	48.5211i	−1.73195	+	1.95497i
$617$	−3.62832	−	22.3260i	−0.146071	−	0.898809i	−0.951843	−	0.306584i	$-0.900814\pi$
$617$	−3.62832	−	22.3260i	−0.146071	−	0.898809i	0.805773	−	0.592225i	$-0.201750\pi$
$618$	−2.88850	+	35.7804i	−0.116192	+	1.43930i
$619$	4.39536	+	17.8327i	0.176665	+	0.716756i	0.990714	+	0.135961i	$0.0434122\pi$
$619$	4.39536	+	17.8327i	0.176665	+	0.716756i	−0.814050	+	0.580795i	$0.802742\pi$
$620$	6.33367	+	21.8664i	0.254366	+	0.878175i
$621$	−0.109177	−	0.534783i	−0.00438111	−	0.0214601i
$622$	55.5958	−	45.3925i	2.22919	−	1.82008i
$623$	−1.07466	+	8.85063i	−0.0430554	+	0.354593i
$624$	25.4994	+	21.7738i	1.02079	+	0.871649i
$625$	2.02429	+	16.6715i	0.0809715	+	0.666860i
$626$	46.5848	+	44.7453i	1.86190	+	1.78838i
$627$	−19.7206	+	20.5313i	−0.787564	+	0.819941i
$628$	11.6809	−	24.6170i	0.466118	−	0.982323i
$629$	32.0195	−	22.1014i	1.27670	−	0.881242i
$630$	2.30651	−	3.64746i	0.0918937	−	0.145318i
$631$	17.9869	+	23.9363i	0.716049	+	0.952888i	0.999982	−	0.00595622i	$-0.00189593\pi$
$631$	17.9869	+	23.9363i	0.716049	+	0.952888i	−0.283934	+	0.958844i	$0.591640\pi$
$632$	5.29000	+	10.0793i	0.210425	+	0.400932i
$633$	1.62359	−	7.95287i	0.0645319	−	0.316098i
$634$	−20.4419	+	1.65024i	−0.811851	+	0.0655394i
$635$	−4.20449	−	1.21784i	−0.166850	−	0.0483287i
$636$	10.2268	+	5.36742i	0.405517	+	0.212832i
$637$	−4.03545	−	6.70429i	−0.159890	−	0.265634i
$638$	−55.2241	+	28.9839i	−2.18634	+	1.14748i
$639$	2.60422	−	0.531654i	0.103021	−	0.0210319i
$640$	−1.14944	−	0.863749i	−0.0454357	−	0.0341427i
$641$	1.83693	+	45.5830i	0.0725545	+	1.80042i	0.469866	+	0.882738i	$0.344302\pi$
$641$	1.83693	+	45.5830i	0.0725545	+	1.80042i	−0.397311	+	0.917684i	$0.630057\pi$
$642$	33.0379	−	12.5296i	1.30390	−	0.494505i
$643$	42.1222	−	12.2009i	1.66114	−	0.481155i	0.690829	−	0.723018i	$-0.257246\pi$
$643$	42.1222	−	12.2009i	1.66114	−	0.481155i	0.970310	+	0.241864i	$0.0777587\pi$
$644$	5.61956	+	1.14724i	0.221442	+	0.0452077i
$645$	−5.67280	−	6.40326i	−0.223366	−	0.252128i
$646$	46.3047	−	56.7129i	1.82183	−	2.23134i
$647$	1.63618	−	40.6014i	0.0643249	−	1.59621i	−0.569012	−	0.822330i	$-0.692674\pi$
$647$	1.63618	−	40.6014i	0.0643249	−	1.59621i	0.633336	−	0.773877i	$-0.281685\pi$
$648$	−2.29375	−	6.87063i	−0.0901072	−	0.269904i
$649$	−42.3600	+	37.5277i	−1.66277	+	1.47309i
$650$	35.6480	−	21.4573i	1.39823	−	0.841623i
$651$	10.3861	+	9.20127i	0.407063	+	0.360626i
$652$	−37.1611	+	87.2203i	−1.45534	+	3.41581i
$653$	−0.199676	+	0.345849i	−0.00781393	+	0.0135341i	−0.869906	−	0.493218i	$-0.835821\pi$
$653$	−0.199676	+	0.345849i	−0.00781393	+	0.0135341i	0.862092	+	0.506752i	$0.169154\pi$
$654$	−10.8465	−	18.7867i	−0.424133	−	0.734620i
$655$	−5.97340	+	0.725302i	−0.233400	+	0.0283399i
$656$	−10.1372	−	4.81017i	−0.395792	−	0.187805i
$657$	−0.0407389	+	0.0235206i	−0.00158938	+	0.000917627i
$658$	8.18803	+	5.65179i	0.319203	+	0.220330i
$659$	−8.66269	+	3.69083i	−0.337450	+	0.143774i	−0.554043	−	0.832488i	$-0.686916\pi$
$659$	−8.66269	+	3.69083i	−0.337450	+	0.143774i	0.216593	+	0.976262i	$0.430506\pi$
$660$	−14.4926	−	2.35528i	−0.564124	−	0.0916790i
$661$	9.99535	−	13.3014i	0.388774	−	0.517364i	−0.562047	−	0.827105i	$-0.689986\pi$
$661$	9.99535	−	13.3014i	0.388774	−	0.517364i	0.950821	+	0.309741i	$0.100242\pi$
$662$	−0.297796	−	0.785224i	−0.0115742	−	0.0305186i
$663$	14.3527	+	2.06472i	0.557411	+	0.0801870i
$664$	−40.4244	+	106.590i	−1.56877	+	4.13651i
$665$	6.19189	+	9.79169i	0.240111	+	0.379705i
$666$	23.1769	+	9.87475i	0.898086	+	0.382639i
$667$	2.71311	+	1.71567i	0.105052	+	0.0664310i
$668$	63.4074	+	7.69905i	2.45330	+	0.297885i
$669$	−3.78150	−	8.87550i	−0.146201	−	0.343147i
$670$	−0.624493	+	1.87058i	−0.0241263	+	0.0722670i
$671$	−32.7802	−	12.4319i	−1.26546	−	0.479927i
$672$	21.3161	+	1.72082i	0.822288	+	0.0663819i
$673$	−3.79979	+	13.1184i	−0.146471	+	0.505678i	−0.999879	−	0.0155667i	$-0.995045\pi$
$673$	−3.79979	+	13.1184i	−0.146471	+	0.505678i	0.853408	+	0.521244i	$0.174532\pi$
$674$	26.1064	+	1.05205i	1.00558	+	0.0405236i
$675$	−4.43137			−0.170564
$676$	−51.0213	−	35.5055i	−1.96236	−	1.36560i
$677$	41.4768			1.59408			0.797041	−	0.603926i	$-0.206398\pi$
$677$	41.4768			1.59408			0.797041	+	0.603926i	$0.206398\pi$
$678$	16.1572	+	0.651114i	0.620515	+	0.0250059i
$679$	−0.656580	+	2.26678i	−0.0251972	+	0.0869910i
$680$	21.8955	+	1.76758i	0.839652	+	0.0677837i
$681$	20.6125	+	7.81729i	0.789872	+	0.299559i
$682$	21.2027	−	63.5098i	0.811892	−	2.43191i
$683$	12.8642	+	30.1934i	0.492235	+	1.15532i	0.962129	+	0.272595i	$0.0878820\pi$
$683$	12.8642	+	30.1934i	0.492235	+	1.15532i	−0.469894	+	0.882723i	$0.655708\pi$
$684$	33.1830	+	4.02915i	1.26879	+	0.154058i
$685$	11.0956	+	7.01643i	0.423941	+	0.268084i
$686$	−48.2819	−	20.5710i	−1.84341	−	0.785405i
$687$	0.649219	+	1.02666i	0.0247693	+	0.0391694i
$688$	37.4117	−	98.6465i	1.42631	−	3.76086i
$689$	−8.07319	−	3.26708i	−0.307564	−	0.124466i
$690$	0.380071	+	1.00217i	0.0144691	+	0.0381518i
$691$	−5.90378	+	7.85650i	−0.224590	+	0.298875i	−0.897647	−	0.440716i	$-0.854725\pi$
$691$	−5.90378	+	7.85650i	−0.224590	+	0.298875i	0.673056	+	0.739591i	$0.264981\pi$
$692$	0.823646	+	0.133855i	0.0313103	+	0.00508842i
$693$	−8.23319	+	3.50783i	−0.312753	+	0.133252i
$694$	−13.2627	−	9.15455i	−0.503443	−	0.347502i
$695$	4.43929	−	2.56303i	0.168392	−	0.0972211i
$696$	38.4872	+	18.2624i	1.45885	+	0.692235i
$697$	−4.81695	+	0.584884i	−0.182455	+	0.0221541i
$698$	7.62786	+	13.2118i	0.288719	+	0.500076i
$699$	−2.43862	+	4.22381i	−0.0922370	+	0.159759i
$700$	18.2521	−	42.8392i	0.689864	−	1.61917i
$701$	−11.9240	−	10.5638i	−0.450364	−	0.398988i	0.407221	−	0.913330i	$-0.366498\pi$
$701$	−11.9240	−	10.5638i	−0.450364	−	0.398988i	−0.857585	+	0.514342i	$0.828036\pi$
$702$	3.83717	+	8.56946i	0.144825	+	0.323434i
$703$	−50.6223	+	44.8474i	−1.90926	+	1.69145i
$704$	−8.69321	−	26.0393i	−0.327638	−	0.981394i
$705$	−0.0527856	+	1.30986i	−0.00198802	+	0.0493322i
$706$	−54.6238	+	66.9020i	−2.05579	+	2.51789i
$707$	−6.82148	−	7.69986i	−0.256548	−	0.289583i
$708$	65.1067	+	13.2916i	2.44686	+	0.499530i
$709$	13.1509	−	3.80920i	0.493891	−	0.143057i	−0.0219198	−	0.999760i	$-0.506978\pi$
$709$	13.1509	−	3.80920i	0.493891	−	0.143057i	0.515811	+	0.856702i	$0.327491\pi$
$710$	−4.88021	+	1.85082i	−0.183151	+	0.0694601i
$711$	0.0632786	+	1.57024i	0.00237313	+	0.0588887i
$712$	−23.4921	−	17.6532i	−0.880404	−	0.661581i
$713$	−3.37654	+	0.689325i	−0.126452	+	0.0258154i
$714$	20.3798	−	10.6961i	0.762693	−	0.400292i
$715$	11.0502	+	0.689566i	0.413254	+	0.0257883i
$716$	−83.3957	−	43.7695i	−3.11664	−	1.63574i
$717$	−3.60195	−	1.04332i	−0.134517	−	0.0389634i
$718$	52.7504	−	4.25845i	1.96863	−	0.158924i
$719$	0.254895	−	1.24856i	0.00950598	−	0.0465634i	−0.974761	−	0.223251i	$-0.928333\pi$
$719$	0.254895	−	1.24856i	0.00950598	−	0.0465634i	0.984267	+	0.176688i	$0.0565382\pi$
$720$	3.25896	+	6.20944i	0.121454	+	0.231412i
$721$	−18.1988	−	24.2182i	−0.677757	−	0.901931i
$722$	−41.5764	+	65.7477i	−1.54731	+	2.44688i
$723$	−22.8573	+	15.7772i	−0.850071	+	0.586762i
$724$	15.6333	−	32.9464i	0.581006	−	1.22445i
$725$	18.0538	−	18.7960i	0.670501	−	0.698065i
$726$	10.4852	+	10.0712i	0.389142	+	0.373776i
$727$	−3.78694	−	31.1883i	−0.140450	−	1.15671i	−0.877057	−	0.480387i	$-0.840496\pi$
$727$	−3.78694	−	31.1883i	−0.140450	−	1.15671i	0.736607	−	0.676321i	$-0.236427\pi$
$728$	−57.3855	+	1.04634i	−2.12685	+	0.0387799i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	0.0715542	−	0.0584222i	0.00264834	−	0.00216230i
$731$	−9.12609	−	44.7026i	−0.337541	−	1.65338i
$732$	11.4528	+	39.5396i	0.423307	+	1.46143i
$733$	−11.0168	−	44.6969i	−0.406914	−	1.65092i	−0.714678	−	0.699453i	$-0.753427\pi$
$733$	−11.0168	−	44.6969i	−0.406914	−	1.65092i	0.307764	−	0.951463i	$-0.400419\pi$
$734$	−4.40081	+	54.5138i	−0.162437	+	2.01214i
$735$	−0.262523	−	1.61537i	−0.00968329	−	0.0595837i
$736$	−3.52206	+	3.97559i	−0.129825	+	0.146542i
$737$	3.26937	−	2.45677i	0.120429	−	0.0904964i
$738$	−1.98714	−	2.43380i	−0.0731475	−	0.0895895i
$739$	0.227471	−	1.39969i	0.00836766	−	0.0514883i	−0.982531	−	0.186101i	$-0.940415\pi$
$739$	0.227471	−	1.39969i	0.00836766	−	0.0514883i	0.990898	+	0.134613i	$0.0429790\pi$
$740$	−33.8676	−	8.34762i	−1.24500	−	0.306864i
$741$	−25.1997	−	0.555627i	−0.925735	−	0.0204115i
$742$	−13.4222	+	3.30827i	−0.492744	+	0.121450i
$743$	3.61596	+	44.7917i	0.132657	+	1.64325i	0.630650	+	0.776067i	$0.282788\pi$
$743$	3.61596	+	44.7917i	0.132657	+	1.64325i	−0.497994	+	0.867181i	$0.665930\pi$
$744$	−43.3801	+	14.4824i	−1.59039	+	0.530951i
$745$	−4.70591	−	4.89937i	−0.172411	−	0.179499i
$746$			61.0662i			2.23579i
$747$	−11.3505	+	10.9023i	−0.415292	+	0.398893i
$748$	−60.6573	−	49.5252i	−2.21785	−	1.81082i
$749$	−13.8575	+	26.4033i	−0.506342	+	0.964755i
$750$	18.2806	−	2.97089i	0.667513	−	0.108481i
$751$	0.196934	−	0.124533i	0.00718622	−	0.00454429i	−0.530868	−	0.847455i	$-0.678134\pi$
$751$	0.196934	−	0.124533i	0.00718622	−	0.00454429i	0.538054	+	0.842910i	$0.319160\pi$
$752$	−14.6063	+	6.93079i	−0.532638	+	0.252740i
$753$	5.61032	−	8.12795i	0.204451	−	0.296199i
$754$	−51.9809	−	18.6371i	−1.89303	−	0.678723i
$755$	8.82486	+	12.7850i	0.321170	+	0.465295i
$756$	9.10029	+	5.25406i	0.330975	+	0.191088i
$757$	18.0565	+	38.0533i	0.656274	+	1.38307i	0.909517	+	0.415666i	$0.136452\pi$
$757$	18.0565	+	38.0533i	0.656274	+	1.38307i	−0.253243	+	0.967403i	$0.581497\pi$
$758$	41.8505	+	13.9717i	1.52008	+	0.507477i
$759$	0.531919	−	2.15808i	0.0193074	−	0.0783333i
$760$	−38.1534	+	1.53753i	−1.38397	+	0.0557720i
$761$	−2.66265	+	0.107301i	−0.0965210	+	0.00388966i	−0.0884794	−	0.996078i	$-0.528201\pi$
$761$	−2.66265	+	0.107301i	−0.0965210	+	0.00388966i	−0.00804154	+	0.999968i	$0.502560\pi$
$762$	3.61767	−	14.6774i	0.131054	−	0.531708i
$763$	17.3649	+	5.79725i	0.628651	+	0.209875i
$764$	13.1322	+	27.6756i	0.475107	+	1.00127i
$765$	2.62635	+	1.51632i	0.0949558	+	0.0548228i
$766$	−56.5214	−	81.8854i	−2.04220	−	2.95864i
$767$	−49.8437	−	5.13193i	−1.79975	−	0.185303i
$768$	10.4797	−	15.1824i	0.378153	−	0.547849i
$769$	12.6014	−	5.97942i	0.454416	−	0.215623i	−0.187706	−	0.982225i	$-0.560105\pi$
$769$	12.6014	−	5.97942i	0.454416	−	0.215623i	0.642123	+	0.766602i	$0.278054\pi$
$770$	14.8532	−	9.39260i	0.535272	−	0.338486i
$771$	6.48525	−	1.05396i	0.233561	−	0.0379573i
$772$	−41.8313	+	79.7030i	−1.50554	+	2.86857i
$773$	14.7070	+	12.0079i	0.528975	+	0.431895i	0.858923	−	0.512104i	$-0.171134\pi$
$773$	14.7070	+	12.0079i	0.528975	+	0.431895i	−0.329948	+	0.943999i	$0.607031\pi$
$774$	21.3064	−	20.4651i	0.765843	−	0.735603i
$775$			27.9790i			1.00504i
$776$	−5.38823	−	5.60974i	−0.193426	−	0.201378i
$777$	−20.1664	+	6.73253i	−0.723465	+	0.241528i
$778$	7.69496	+	95.3192i	0.275878	+	3.41736i
$779$	8.18964	−	2.01857i	0.293424	−	0.0723226i
$780$	−7.14730	−	10.8591i	−0.255915	−	0.388819i
$781$	10.5091	+	2.59027i	0.376046	+	0.0926870i
$782$	−0.916962	+	5.64229i	−0.0327905	+	0.201768i
$783$	3.71957	+	4.55564i	0.132926	+	0.162805i
$784$	16.1354	−	12.1249i	0.576263	−	0.433033i
$785$	−2.84952	+	3.21645i	−0.101704	+	0.114800i
$786$	−3.33338	−	20.5111i	−0.118898	−	0.731607i
$787$	0.362557	−	4.49107i	0.0129237	−	0.160089i	−0.987076	−	0.160251i	$-0.948770\pi$
$787$	0.362557	−	4.49107i	0.0129237	−	0.160089i	1.00000		0.000162039i	$5.15786e-5\pi$
$788$	−24.3156	−	98.6524i	−0.866208	−	3.51435i
$789$	−4.89425	−	16.8969i	−0.174240	−	0.601546i
$790$	−0.617278	−	3.02363i	−0.0219618	−	0.107576i
$791$	−10.5705	+	8.63058i	−0.375845	+	0.306868i
$792$	3.55543	−	29.2816i	0.126337	−	1.04047i
$793$	−11.5345	−	28.8182i	−0.409603	−	1.02337i
$794$	8.66820	+	71.3890i	0.307623	+	2.53350i
$795$	−1.31364	−	1.26177i	−0.0465900	−	0.0447503i
$796$	−1.95301	+	2.03330i	−0.0692228	+	0.0720685i
$797$	2.99582	−	6.31355i	0.106117	−	0.223638i	−0.843445	−	0.537215i	$-0.819476\pi$
$797$	2.99582	−	6.31355i	0.106117	−	0.223638i	0.949563	+	0.313578i	$0.101528\pi$
$798$	−32.9264	+	22.7275i	−1.16558	+	0.804543i
$799$	−3.73674	+	5.90919i	−0.132197	+	0.209052i
$800$	25.9051	+	34.4734i	0.915884	+	1.21882i
$801$	−1.88532	−	3.59219i	−0.0666147	−	0.126924i
$802$	−2.86892	+	14.0529i	−0.101305	+	0.496225i
$803$	−0.190940	+	0.0154143i	−0.00673814	+	0.000543959i
$804$	−4.61230	−	1.33597i	−0.162663	−	0.0471160i
$805$	−0.800912	−	0.420351i	−0.0282284	−	0.0148154i
$806$	54.1063	−	24.2273i	1.90581	−	0.853369i
$807$	3.93282	−	2.06410i	0.138442	−	0.0726598i
$808$	33.2201	−	6.78193i	1.16868	−	0.238587i
$809$	44.9772	+	33.7982i	1.58131	+	1.18828i	0.879475	+	0.475946i	$0.157894\pi$
$809$	44.9772	+	33.7982i	1.58131	+	1.18828i	0.701840	+	0.712335i	$0.252362\pi$
$810$	0.0790704	+	1.96211i	0.00277825	+	0.0689416i
$811$	13.3439	−	5.06068i	0.468568	−	0.177704i	−0.109009	−	0.994041i	$-0.534768\pi$
$811$	13.3439	−	5.06068i	0.468568	−	0.177704i	0.577577	+	0.816336i	$0.303998\pi$
$812$	−59.3608	+	17.1941i	−2.08316	+	0.603393i
$813$	−18.2148	−	3.71858i	−0.638821	−	0.130416i
$814$	68.0300	+	76.7900i	2.38445	+	2.69149i
$815$	9.45607	−	11.5816i	0.331232	−	0.405685i
$816$	−1.50598	+	37.3705i	−0.0527198	+	1.30823i
$817$	25.1145	+	75.2271i	0.878645	+	2.63186i
$818$	55.4597	−	49.1330i	1.93910	−	1.71790i
$819$	−7.21947	−	3.26579i	−0.252269	−	0.114116i
$820$	3.25625	+	2.88478i	0.113713	+	0.100741i
$821$	11.0180	−	25.8602i	0.384531	−	0.902527i	−0.609435	−	0.792836i	$-0.708604\pi$
$821$	11.0180	−	25.8602i	0.384531	−	0.902527i	0.993966	−	0.109691i	$-0.0349861\pi$
$822$	−22.6682	+	39.2624i	−0.790643	+	1.36943i
$823$	−13.5657	−	23.4965i	−0.472872	−	0.819038i	0.526646	−	0.850085i	$-0.323449\pi$
$823$	−13.5657	−	23.4965i	−0.472872	−	0.819038i	−0.999518	+	0.0310466i	$0.990116\pi$
$824$	99.1192	−	12.0353i	3.45298	−	0.419268i
$825$	−16.3032	−	7.73596i	−0.567604	−	0.269331i
$826$	−68.8782	+	39.7669i	−2.39658	+	1.38367i
$827$	24.2347	+	16.7280i	0.842721	+	0.581689i	0.909323	−	0.416091i	$-0.136600\pi$
$827$	24.2347	+	16.7280i	0.842721	+	0.581689i	−0.0666015	+	0.997780i	$0.521216\pi$
$828$	−2.40097	+	1.02296i	−0.0834396	+	0.0355503i
$829$	15.1093	+	2.45550i	0.524769	+	0.0852832i	0.417024	−	0.908895i	$-0.363073\pi$
$829$	15.1093	+	2.45550i	0.524769	+	0.0852832i	0.107744	+	0.994179i	$0.465637\pi$
$830$	18.5661	−	24.7070i	0.644439	−	0.857592i
$831$	−6.21369	−	16.3842i	−0.215551	−	0.568360i
$832$	11.7674	−	21.2679i	0.407960	−	0.737331i
$833$	3.09508	−	8.16106i	0.107238	−	0.282764i
$834$	9.46135	+	14.9619i	0.327620	+	0.518089i
$835$	−9.26711	−	3.94835i	−0.320702	−	0.136638i
$836$	115.048	+	72.7518i	3.97901	+	2.51617i
$837$	−6.26781	−	0.761050i	−0.216647	−	0.0263057i
$838$	7.33268	+	17.2104i	0.253303	+	0.594524i
$839$	9.09660	−	27.2477i	0.314050	−	0.940693i	−0.666684	−	0.745341i	$-0.732287\pi$
$839$	9.09660	−	27.2477i	0.314050	−	0.940693i	0.980733	−	0.195352i	$-0.0625851\pi$
$840$	−11.2237	−	4.25658i	−0.387254	−	0.146866i
$841$	−5.57092	−	0.449731i	−0.192101	−	0.0155080i
$842$	4.48257	−	15.4756i	0.154480	−	0.533325i
$843$	26.5839	+	1.07129i	0.915598	+	0.0368974i
$844$	−38.8110			−1.33593
$845$	6.17082	+	7.61700i	0.212283	+	0.262033i
$846$	−4.52718			−0.155648
$847$	−12.2593	−	0.494031i	−0.421233	−	0.0169751i
$848$	6.24976	−	21.5767i	0.214618	−	0.740946i
$849$	−3.36484	−	0.271638i	−0.115481	−	0.00932260i
$850$	43.3940	+	16.4572i	1.48840	+	0.564476i
$851$	1.67210	−	5.00855i	0.0573189	−	0.171691i
$852$	−4.98147	−	11.6919i	−0.170662	−	0.400559i
$853$	−29.5813	−	3.59182i	−1.01285	−	0.122982i	−0.402750	−	0.915310i	$-0.631946\pi$
$853$	−29.5813	−	3.59182i	−1.01285	−	0.122982i	−0.610095	+	0.792328i	$0.708869\pi$
$854$	−41.6428	−	26.3333i	−1.42499	−	0.901107i
$855$	−4.84977	−	2.06629i	−0.165859	−	0.0706657i
$856$	−52.5283	−	83.0668i	−1.79538	−	2.83917i
$857$	−6.82281	+	17.9903i	−0.233063	+	0.614536i	−0.999618	−	0.0276427i	$-0.991200\pi$
$857$	−6.82281	+	17.9903i	−0.233063	+	0.614536i	0.766555	+	0.642178i	$0.221969\pi$
$858$	−0.842842	+	38.2260i	−0.0287742	+	1.30501i
$859$	−15.5808	−	41.0833i	−0.531611	−	1.40174i	−0.884703	−	0.466155i	$-0.845639\pi$
$859$	−15.5808	−	41.0833i	−0.531611	−	1.40174i	0.353091	−	0.935589i	$-0.385130\pi$
$860$	−24.5729	+	32.7006i	−0.837928	+	1.11508i
$861$	2.61723	+	0.425341i	0.0891949	+	0.0144956i
$862$	−59.2353	+	25.2378i	−2.01756	+	0.859604i
$863$	31.5903	+	21.8052i	1.07535	+	0.742257i	0.967744	−	0.251937i	$-0.0810675\pi$
$863$	31.5903	+	21.8052i	1.07535	+	0.742257i	0.107602	+	0.994194i	$0.465683\pi$
$864$	−8.42732	+	4.86551i	−0.286703	+	0.165528i
$865$	−0.118892	−	0.0564151i	−0.00404246	−	0.00191817i
$866$	69.0134	−	8.37975i	2.34517	−	0.284755i
$867$	−0.412998	−	0.715333i	−0.0140261	−	0.0242940i
$868$	33.1733	−	57.4578i	1.12598	−	1.95025i
$869$	−2.50841	+	5.88744i	−0.0850918	+	0.199718i
$870$	−8.64457	−	7.65842i	−0.293078	−	0.259645i
$871$	3.56036	+	0.659480i	0.120638	+	0.0223456i
$872$	−45.1646	+	40.0124i	−1.52947	+	1.35499i
$873$	−0.340054	−	1.01858i	−0.0115091	−	0.0344739i
$874$	0.400106	−	9.92853i	0.0135338	−	0.335838i
$875$	−9.88488	+	12.1068i	−0.334170	+	0.409284i
$876$	0.149155	+	0.168361i	0.00503948	+	0.00568839i
$877$	18.9533	+	3.86934i	0.640006	+	0.130658i	0.509060	−	0.860731i	$-0.329993\pi$
$877$	18.9533	+	3.86934i	0.640006	+	0.130658i	0.130947	+	0.991389i	$0.458198\pi$
$878$	−76.5129	+	22.1622i	−2.58219	+	0.747939i
$879$	−26.6056	+	10.0902i	−0.897384	+	0.340333i
$880$	1.14988	+	28.5340i	0.0387625	+	0.961881i
$881$	14.4325	+	10.8453i	0.486244	+	0.365389i	0.815411	−	0.578883i	$-0.196511\pi$
$881$	14.4325	+	10.8453i	0.486244	+	0.365389i	−0.329166	+	0.944272i	$0.606768\pi$
$882$	5.53752	−	1.13049i	0.186458	−	0.0380657i
$883$	45.9056	−	24.0931i	1.54485	−	0.810798i	0.545225	−	0.838290i	$-0.316444\pi$
$883$	45.9056	−	24.0931i	1.54485	−	0.810798i	0.999622	+	0.0274911i	$0.00875179\pi$
$884$	−4.05429	−	69.2152i	−0.136360	−	2.32796i
$885$	−9.27915	−	4.87007i	−0.311915	−	0.163706i
$886$	26.6540	+	7.72041i	0.895457	+	0.259372i
$887$	−11.1998	+	0.904143i	−0.376053	+	0.0303582i	−0.267049	−	0.963683i	$-0.586048\pi$
$887$	−11.1998	+	0.904143i	−0.376053	+	0.0303582i	−0.109005	+	0.994041i	$0.534766\pi$
$888$	14.0166	−	68.6578i	0.470366	−	2.30400i
$889$	5.92856	+	11.2959i	0.198837	+	0.378853i
$890$	4.78582	+	6.36877i	0.160421	+	0.213482i
$891$	2.17645	−	3.44179i	0.0729140	−	0.115304i
$892$	−37.9639	+	26.2046i	−1.27113	+	0.877394i
$893$	5.21003	−	10.9799i	0.174347	−	0.367429i
$894$	16.2515	−	16.9196i	0.543532	−	0.565877i
$895$	10.7123	+	10.2893i	0.358072	+	0.343933i
$896$	0.505087	+	4.15977i	0.0168738	+	0.138968i
$897$	1.72558	−	0.946172i	0.0576154	−	0.0315918i
$898$	5.50537	−	45.3408i	0.183716	−	1.51304i
$899$	28.7636	−	23.4848i	0.959320	−	0.783261i
$900$	4.23827	+	20.7604i	0.141276	+	0.692014i
$901$	−2.70271	−	9.33084i	−0.0900404	−	0.310855i
$902$	−3.06200	−	12.4230i	−0.101954	−	0.413642i
$903$	−2.00616	+	24.8508i	−0.0667609	+	0.826982i
$904$	−7.21496	−	44.3954i	−0.239966	−	1.47657i
$905$	−3.81370	+	4.30478i	−0.126772	+	0.143096i
$906$	−42.8892	+	32.2291i	−1.42490	+	1.07074i
$907$	18.4672	+	22.6183i	0.613195	+	0.751027i	0.984095	−	0.177646i	$-0.0568481\pi$
$907$	18.4672	+	22.6183i	0.613195	+	0.751027i	−0.370900	+	0.928673i	$0.620951\pi$
$908$	16.9087	−	104.044i	0.561135	−	3.45281i
$909$	4.54483	+	1.12020i	0.150743	+	0.0371547i
$910$	15.0220	+	4.05586i	0.497976	+	0.134451i
$911$	−25.5328	+	6.29328i	−0.845940	+	0.208506i	−0.638384	−	0.769718i	$-0.720397\pi$
$911$	−25.5328	+	6.29328i	−0.845940	+	0.208506i	−0.207556	+	0.978223i	$0.566551\pi$
$912$	−5.23140	−	64.8025i	−0.173229	−	2.14582i
$913$	−60.7911	+	20.2951i	−2.01189	+	0.671668i
$914$	−76.1739	−	79.3054i	−2.51961	−	2.62319i
$915$		−	6.49195i		−	0.214617i
$916$	4.18883	−	4.02343i	0.138403	−	0.132938i
$917$	13.5840	+	11.0910i	0.448583	+	0.366257i
$918$	−4.86705	+	9.27340i	−0.160637	+	0.306068i
$919$	51.5917	−	8.38447i	1.70185	−	0.276578i	0.769637	−	0.638481i	$-0.220437\pi$
$919$	51.5917	−	8.38447i	1.70185	−	0.276578i	0.932216	+	0.361903i	$0.117873\pi$
$920$	2.51973	−	1.59338i	0.0830731	−	0.0525323i
$921$	−26.5338	+	12.5904i	−0.874318	+	0.414869i
$922$	14.1675	−	20.5252i	0.466583	−	0.675962i
$923$	4.60754	+	8.40300i	0.151659	+	0.276588i
$924$	24.3082	+	35.2165i	0.799680	+	1.15854i
$925$	−37.1264	−	21.4349i	−1.22071	−	0.704777i
$926$	5.53211	+	11.6587i	0.181796	+	0.383128i
$927$	13.0752	+	4.36513i	0.429445	+	0.143370i
$928$	13.6962	−	55.5676i	0.449599	−	1.82409i
$929$	−37.9838	+	1.53070i	−1.24621	+	0.0502205i	−0.654582	−	0.755991i	$-0.727155\pi$
$929$	−37.9838	+	1.53070i	−1.24621	+	0.0502205i	−0.591627	+	0.806212i	$0.701514\pi$
$930$	12.3885	−	0.499238i	0.406234	−	0.0163707i
$931$	−3.63095	+	14.7313i	−0.118999	+	0.482800i
$932$	22.1204	+	7.38487i	0.724577	+	0.241899i
$933$	−11.8153	−	24.9002i	−0.386815	−	0.815196i
$934$	9.51579	+	5.49394i	0.311366	+	0.179767i
$935$	7.01535	+	10.1635i	0.229426	+	0.332382i
$936$	21.2194	−	15.2252i	0.693578	−	0.497652i
$937$	−10.7181	+	15.5279i	−0.350147	+	0.507275i	−0.957998	−	0.286776i	$-0.907416\pi$
$937$	−10.7181	+	15.5279i	−0.350147	+	0.507275i	0.607851	+	0.794051i	$0.292032\pi$
$938$	5.19248	−	2.46386i	0.169541	−	0.0804480i
$939$	20.9642	−	13.2570i	0.684142	−	0.432625i
$940$	6.18702	−	1.00549i	0.201798	−	0.0327954i
$941$	0.262209	−	0.499598i	0.00854777	−	0.0162864i	−0.881145	−	0.472847i	$-0.843226\pi$
$941$	0.262209	−	0.499598i	0.00854777	−	0.0162864i	0.889692	+	0.456560i	$0.150919\pi$
$942$	−11.4950	−	9.38537i	−0.374527	−	0.305792i
$943$	−0.474945	+	0.456191i	−0.0154663	+	0.0148556i
$944$		−	129.241i		−	4.20644i
$945$	−1.14798	−	1.19517i	−0.0373437	−	0.0388790i
$946$	114.113	−	38.0967i	3.71015	−	1.23863i
$947$	1.09829	+	13.6048i	0.0356897	+	0.442096i	0.989783	+	0.142585i	$0.0455414\pi$
$947$	1.09829	+	13.6048i	0.0356897	+	0.442096i	−0.954093	+	0.299511i	$0.903177\pi$
$948$	7.29586	−	1.79827i	0.236959	−	0.0584051i
$949$	−0.124445	−	0.115243i	−0.00403964	−	0.00374095i
$950$	−78.3294	−	19.3065i	−2.54134	−	0.626384i
$951$	−1.26329	+	7.77334i	−0.0409650	+	0.252068i
$952$	−40.4888	−	49.5898i	−1.31225	−	1.60721i
$953$	−14.7404	+	11.0767i	−0.477490	+	0.358810i	−0.812073	−	0.583556i	$-0.801661\pi$
$953$	−14.7404	+	11.0767i	−0.477490	+	0.358810i	0.334583	+	0.942366i	$0.391405\pi$
$954$	4.17122	−	4.70834i	0.135048	−	0.152438i
$955$	−0.774954	−	4.76848i	−0.0250769	−	0.154304i
$956$	−1.44282	+	17.8725i	−0.0466641	+	0.578039i
$957$	5.73152	+	23.2537i	0.185274	+	0.751685i
$958$	12.2886	+	42.4252i	0.397027	+	1.37069i
$959$	−7.65296	−	37.4867i	−0.247127	−	1.21051i
$960$	3.93767	−	3.21501i	0.127088	−	0.103764i
$961$	−1.06851	+	8.79999i	−0.0344681	+	0.283871i
$962$	−9.30314	+	90.3564i	−0.299945	+	2.91321i
$963$	−1.63550	−	13.4695i	−0.0527032	−	0.434050i
$964$	95.7756	+	91.9937i	3.08472	+	2.96292i
$965$	9.83369	−	10.2380i	0.316558	−	0.329571i
$966$	1.33910	−	2.82210i	0.0430849	−	0.0907995i
$967$	−18.9202	+	13.0597i	−0.608433	+	0.419971i	−0.832046	−	0.554707i	$-0.812830\pi$
$967$	−18.9202	+	13.0597i	−0.608433	+	0.419971i	0.223613	+	0.974678i	$0.428215\pi$
$968$	21.6132	−	34.1785i	0.694674	−	1.09854i
$969$	−16.8899	−	22.4764i	−0.542581	−	0.722045i
$970$	0.979972	+	1.86718i	0.0314650	+	0.0599515i
$971$	−4.93008	+	24.1491i	−0.158214	+	0.774982i	0.820805	+	0.571209i	$0.193525\pi$
$971$	−4.93008	+	24.1491i	−0.158214	+	0.774982i	−0.979018	+	0.203773i	$0.934680\pi$
$972$	−4.76600	+	0.384751i	−0.152869	+	0.0123409i
$973$	−14.3495	−	4.15638i	−0.460023	−	0.133247i
$974$	−93.5826	−	49.1160i	−2.99858	−	1.57378i
$975$	−4.72427	−	15.2631i	−0.151298	−	0.488812i
$976$	70.8927	−	37.2074i	2.26922	−	1.19098i
$977$	−13.4152	+	2.73872i	−0.429189	+	0.0876195i	−0.409764	−	0.912192i	$-0.634389\pi$
$977$	−13.4152	+	2.73872i	−0.429189	+	0.0876195i	−0.0194253	+	0.999811i	$0.506184\pi$
$978$	41.2786	+	31.0189i	1.31995	+	0.991874i
$979$	−0.665211	−	16.5070i	−0.0212602	−	0.527567i
$980$	−7.31670	+	2.77486i	−0.233724	+	0.0886396i
$981$	−8.00135	+	2.31762i	−0.255463	+	0.0739959i
$982$	−16.0586	−	3.27839i	−0.512451	−	0.104618i
$983$	−28.5879	−	32.2691i	−0.911812	−	1.02922i	−0.999453	−	0.0330708i	$-0.989471\pi$
$983$	−28.5879	−	32.2691i	−0.911812	−	1.02922i	0.0876410	−	0.996152i	$-0.472067\pi$
$984$	−5.52723	+	6.76963i	−0.176202	+	0.215808i
$985$	−0.645209	+	16.0107i	−0.0205581	+	0.510143i
$986$	−19.5050	−	58.4245i	−0.621165	−	1.86062i
$987$	2.85972	−	2.53349i	0.0910258	−	0.0806418i
$988$	21.4986	+	118.589i	0.683961	+	3.77282i
$989$	−4.63482	−	4.10609i	−0.147379	−	0.130566i
$990$	−3.13440	+	7.35671i	−0.0996178	+	0.233812i
$991$	1.31817	−	2.28314i	0.0418731	−	0.0725264i	−0.844329	−	0.535825i	$-0.820001\pi$
$991$	1.31817	−	2.28314i	0.0418731	−	0.0725264i	0.886202	+	0.463298i	$0.153334\pi$
$992$	30.7201	+	53.2088i	0.975364	+	1.68938i
$993$	−0.320135	+	0.0388715i	−0.0101592	+	0.00123355i
$994$	13.7427	+	6.52098i	0.435891	+	0.206833i
$995$	0.385056	−	0.222312i	0.0122071	−	0.00704777i
$996$	61.9316	+	42.7483i	1.96238	+	1.35453i
$997$	35.9991	−	15.3378i	1.14010	−	0.485753i	0.262402	−	0.964959i	$-0.415485\pi$
$997$	35.9991	−	15.3378i	1.14010	−	0.485753i	0.877703	+	0.479206i	$0.159075\pi$
$998$	83.0190	+	13.4919i	2.62792	+	0.427079i
$999$	5.81168	−	7.73395i	0.183874	−	0.244691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.4.1	✓	360
169.127	even	78	inner	507.2.t.b.127.1	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.1	✓	360	1.1	even	1	trivial
507.2.t.b.127.1	yes	360	169.127	even	78	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60202 - 0.104858i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.76600 + 0.384751i) q^{4} +(-0.705070 - 0.267398i) q^{5} +(0.824645 - 2.47011i) q^{6} +(0.861409 + 2.02180i) q^{7} +(-7.19059 - 0.873096i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(-2.60202 - 0.104858i) q^{2} +(-0.278217 + 0.960518i) q^{3} +(4.76600 + 0.384751i) q^{4} +(-0.705070 - 0.267398i) q^{5} +(0.824645 - 2.47011i) q^{6} +(0.861409 + 2.02180i) q^{7} +(-7.19059 - 0.873096i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(1.80657 + 0.769706i) q^{10} +(-2.17645 - 3.44179i) q^{11} +(-1.69554 + 4.47078i) q^{12} +(0.939825 - 3.48091i) q^{13} +(-2.02940 - 5.35109i) q^{14} +(0.453003 - 0.602838i) q^{15} +(9.17934 + 1.49179i) q^{16} +(3.69987 - 1.57637i) q^{17} +(2.14316 + 1.47932i) q^{18} +(-6.05425 + 3.49542i) q^{19} +(-3.25748 - 1.54569i) q^{20} +(-2.18164 + 0.264899i) q^{21} +(5.30228 + 9.18382i) q^{22} +(0.272907 - 0.472689i) q^{23} +(2.83917 - 6.66378i) q^{24} +(-3.31693 - 2.93855i) q^{25} +(-2.81044 + 8.95885i) q^{26} +(0.748511 - 0.663123i) q^{27} +(3.32758 + 9.96733i) q^{28} +(-0.236814 + 5.87648i) q^{29} +(-1.24194 + 1.52109i) q^{30} +(-4.18685 - 4.72598i) q^{31} +(-9.53437 - 1.94646i) q^{32} +(3.91143 - 1.13296i) q^{33} +(-9.79244 + 3.71378i) q^{34} +(-0.0667285 - 1.65585i) q^{35} +(-3.82254 - 2.87245i) q^{36} +(9.47866 - 1.93508i) q^{37} +(16.1198 - 8.46033i) q^{38} +(3.08200 + 1.87117i) q^{39} +(4.83641 + 2.53834i) q^{40} +(-1.15890 - 0.335681i) q^{41} +(5.70444 - 0.460510i) q^{42} +(2.26922 - 11.1154i) q^{43} +(-9.04875 - 17.2409i) q^{44} +(0.453003 + 0.602838i) q^{45} +(-0.759674 + 1.20133i) q^{46} +(-1.43072 + 0.987558i) q^{47} +(-3.98674 + 8.40188i) q^{48} +(1.50342 - 1.56522i) q^{49} +(8.32259 + 7.99396i) q^{50} +(0.484761 + 3.99237i) q^{51} +(5.81849 - 16.2284i) q^{52} +(0.291156 - 2.39789i) q^{53} +(-2.01717 + 1.64697i) q^{54} +(0.614226 + 3.00868i) q^{55} +(-4.42881 - 15.2900i) q^{56} +(-1.67302 - 6.78771i) q^{57} +(1.23239 - 15.2659i) q^{58} +(-2.22927 - 13.7173i) q^{59} +(2.39095 - 2.69883i) q^{60} +(6.88255 - 5.17190i) q^{61} +(10.3987 + 12.7361i) q^{62} +(0.352529 - 2.16920i) q^{63} +(6.54545 + 1.61331i) q^{64} +(-1.59343 + 2.20298i) q^{65} +(-10.2964 + 2.53784i) q^{66} +(0.0808096 + 1.00101i) q^{67} +(18.2401 - 6.08944i) q^{68} +(0.378098 + 0.393642i) q^{69} +4.31555i q^{70} +(-1.91691 + 1.84121i) q^{71} +(5.61078 + 4.58106i) q^{72} +(0.0218612 - 0.0416530i) q^{73} +(-24.8666 + 4.04121i) q^{74} +(3.74535 - 2.36842i) q^{75} +(-30.1994 + 14.3298i) q^{76} +(5.08379 - 7.36514i) q^{77} +(-7.82322 - 5.19199i) q^{78} +(-0.892723 - 1.29333i) q^{79} +(-6.07318 - 3.50635i) q^{80} +(0.428693 + 0.903450i) q^{81} +(2.98029 + 0.994968i) q^{82} +(3.76641 - 15.2809i) q^{83} +(-10.4996 + 0.423119i) q^{84} +(-3.03019 + 0.122112i) q^{85} +(-7.07008 + 28.6844i) q^{86} +(-5.57858 - 1.86240i) q^{87} +(12.6450 + 26.6487i) q^{88} +(3.51336 + 2.02844i) q^{89} +(-1.11551 - 1.61610i) q^{90} +(7.84728 - 1.09835i) q^{91} +(1.48254 - 2.14783i) q^{92} +(5.70424 - 2.70670i) q^{93} +(3.82633 - 2.41962i) q^{94} +(5.20334 - 0.845625i) q^{95} +(4.52223 - 8.61640i) q^{96} +(0.831809 + 0.679151i) q^{97} +(-4.07605 + 3.91509i) q^{98} +4.07220i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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