LMFDB - Embedded newform 798.2.p.d.179.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(107,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("798.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.11
Character	$\chi$	$=$	798.179
Dual form			798.2.p.d.107.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.544247 + 1.64432i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(-0.544247 + 1.64432i) q^{6} +(-1.01122 + 2.44488i) q^{7} +1.00000 q^{8} +(-2.40759 - 1.78984i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.544247 + 1.64432i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(-0.544247 + 1.64432i) q^{6} +(-1.01122 + 2.44488i) q^{7} +1.00000 q^{8} +(-2.40759 - 1.78984i) q^{9} +4.07740i q^{10} +(0.930342 + 0.537133i) q^{11} +(-0.544247 + 1.64432i) q^{12} +(5.50387 - 3.17766i) q^{13} +(-1.01122 + 2.44488i) q^{14} +(-6.70456 - 2.21912i) q^{15} +1.00000 q^{16} +(-2.61890 + 1.51203i) q^{17} +(-2.40759 - 1.78984i) q^{18} +(4.34265 - 0.375980i) q^{19} +4.07740i q^{20} +(-3.46981 - 2.99339i) q^{21} +(0.930342 + 0.537133i) q^{22} +(-5.87482 - 3.39183i) q^{23} +(-0.544247 + 1.64432i) q^{24} -11.6252 q^{25} +(5.50387 - 3.17766i) q^{26} +(4.25339 - 2.98474i) q^{27} +(-1.01122 + 2.44488i) q^{28} +(2.84891 + 4.93446i) q^{29} +(-6.70456 - 2.21912i) q^{30} +(-4.45649 - 2.57296i) q^{31} +1.00000 q^{32} +(-1.38956 + 1.23745i) q^{33} +(-2.61890 + 1.51203i) q^{34} +(-9.96876 - 4.12315i) q^{35} +(-2.40759 - 1.78984i) q^{36} +(3.66771 - 2.11756i) q^{37} +(4.34265 - 0.375980i) q^{38} +(2.22963 + 10.7796i) q^{39} +4.07740i q^{40} +(1.99215 - 3.45051i) q^{41} +(-3.46981 - 2.99339i) q^{42} +(-3.14519 + 5.44764i) q^{43} +(0.930342 + 0.537133i) q^{44} +(7.29788 - 9.81671i) q^{45} +(-5.87482 - 3.39183i) q^{46} +(3.44099 + 1.98666i) q^{47} +(-0.544247 + 1.64432i) q^{48} +(-4.95487 - 4.94462i) q^{49} -11.6252 q^{50} +(-1.06092 - 5.12924i) q^{51} +(5.50387 - 3.17766i) q^{52} +4.73673 q^{53} +(4.25339 - 2.98474i) q^{54} +(-2.19011 + 3.79338i) q^{55} +(-1.01122 + 2.44488i) q^{56} +(-1.74525 + 7.34535i) q^{57} +(2.84891 + 4.93446i) q^{58} +(4.16467 + 7.21341i) q^{59} +(-6.70456 - 2.21912i) q^{60} +(3.84448 - 6.65884i) q^{61} +(-4.45649 - 2.57296i) q^{62} +(6.81053 - 4.07635i) q^{63} +1.00000 q^{64} +(12.9566 + 22.4415i) q^{65} +(-1.38956 + 1.23745i) q^{66} -7.59056i q^{67} +(-2.61890 + 1.51203i) q^{68} +(8.77462 - 7.81411i) q^{69} +(-9.96876 - 4.12315i) q^{70} +(-4.36350 + 7.55780i) q^{71} +(-2.40759 - 1.78984i) q^{72} +(4.19824 + 7.27157i) q^{73} +(3.66771 - 2.11756i) q^{74} +(6.32699 - 19.1156i) q^{75} +(4.34265 - 0.375980i) q^{76} +(-2.25401 + 1.73141i) q^{77} +(2.22963 + 10.7796i) q^{78} -6.87993i q^{79} +4.07740i q^{80} +(2.59298 + 8.61838i) q^{81} +(1.99215 - 3.45051i) q^{82} -0.0397535i q^{83} +(-3.46981 - 2.99339i) q^{84} +(-6.16514 - 10.6783i) q^{85} +(-3.14519 + 5.44764i) q^{86} +(-9.66435 + 1.99896i) q^{87} +(0.930342 + 0.537133i) q^{88} +(-0.110424 + 0.191260i) q^{89} +(7.29788 - 9.81671i) q^{90} +(2.20337 + 16.6696i) q^{91} +(-5.87482 - 3.39183i) q^{92} +(6.65621 - 5.92759i) q^{93} +(3.44099 + 1.98666i) q^{94} +(1.53302 + 17.7067i) q^{95} +(-0.544247 + 1.64432i) q^{96} +(12.0392 + 6.95084i) q^{97} +(-4.95487 - 4.94462i) q^{98} +(-1.27850 - 2.95836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.544247	+	1.64432i	−0.314221	+	0.949350i
$3$	−0.544247	+	1.64432i	−0.314221	+	0.949350i
$4$	1.00000			0.500000
$5$			4.07740i			1.82347i	0.410779	+	0.911735i	$0.365257\pi$
$5$			4.07740i			1.82347i	−0.410779	+	0.911735i	$0.634743\pi$
$6$	−0.544247	+	1.64432i	−0.222188	+	0.671292i
$7$	−1.01122	+	2.44488i	−0.382205	+	0.924077i
$7$	−1.01122	+	2.44488i	−0.382205	+	0.924077i
$8$	1.00000			0.353553
$9$	−2.40759	−	1.78984i	−0.802530	−	0.596612i
$10$			4.07740i			1.28939i
$11$	0.930342	+	0.537133i	0.280509	+	0.161952i	0.633654	−	0.773617i	$-0.281554\pi$
$11$	0.930342	+	0.537133i	0.280509	+	0.161952i	−0.353145	+	0.935569i	$0.614888\pi$
$12$	−0.544247	+	1.64432i	−0.157111	+	0.474675i
$13$	5.50387	−	3.17766i	1.52650	−	0.881324i	0.526993	−	0.849870i	$-0.323319\pi$
$13$	5.50387	−	3.17766i	1.52650	−	0.881324i	0.999505	−	0.0314543i	$-0.0100139\pi$
$14$	−1.01122	+	2.44488i	−0.270260	+	0.653421i
$15$	−6.70456	−	2.21912i	−1.73111	−	0.572973i
$16$	1.00000			0.250000
$17$	−2.61890	+	1.51203i	−0.635178	+	0.366720i	−0.782755	−	0.622331i	$-0.786186\pi$
$17$	−2.61890	+	1.51203i	−0.635178	+	0.366720i	0.147577	+	0.989051i	$0.452853\pi$
$18$	−2.40759	−	1.78984i	−0.567474	−	0.421868i
$19$	4.34265	−	0.375980i	0.996273	−	0.0862557i
$19$	4.34265	−	0.375980i	0.996273	−	0.0862557i
$20$			4.07740i			0.911735i
$21$	−3.46981	−	2.99339i	−0.757176	−	0.653211i
$22$	0.930342	+	0.537133i	0.198350	+	0.114517i
$23$	−5.87482	−	3.39183i	−1.22499	−	0.707246i	−0.259009	−	0.965875i	$-0.583396\pi$
$23$	−5.87482	−	3.39183i	−1.22499	−	0.707246i	−0.965977	+	0.258629i	$0.916729\pi$
$24$	−0.544247	+	1.64432i	−0.111094	+	0.335646i
$25$	−11.6252			−2.32504
$26$	5.50387	−	3.17766i	1.07940	−	0.623190i
$27$	4.25339	−	2.98474i	0.818565	−	0.574413i
$28$	−1.01122	+	2.44488i	−0.191103	+	0.462039i
$29$	2.84891	+	4.93446i	0.529029	+	0.916306i	0.999427	+	0.0338512i	$0.0107772\pi$
$29$	2.84891	+	4.93446i	0.529029	+	0.916306i	−0.470397	+	0.882455i	$0.655889\pi$
$30$	−6.70456	−	2.21912i	−1.22408	−	0.405153i
$31$	−4.45649	−	2.57296i	−0.800410	−	0.462117i	0.0432045	−	0.999066i	$-0.486243\pi$
$31$	−4.45649	−	2.57296i	−0.800410	−	0.462117i	−0.843615	+	0.536949i	$0.819577\pi$
$32$	1.00000			0.176777
$33$	−1.38956	+	1.23745i	−0.241891	+	0.215412i
$34$	−2.61890	+	1.51203i	−0.449138	+	0.259310i
$35$	−9.96876	−	4.12315i	−1.68503	−	0.696940i
$36$	−2.40759	−	1.78984i	−0.401265	−	0.298306i
$37$	3.66771	−	2.11756i	0.602968	−	0.348124i	−0.167240	−	0.985916i	$-0.553486\pi$
$37$	3.66771	−	2.11756i	0.602968	−	0.348124i	0.770208	+	0.637792i	$0.220152\pi$
$38$	4.34265	−	0.375980i	0.704471	−	0.0609920i
$39$	2.22963	+	10.7796i	0.357027	+	1.72611i
$40$			4.07740i			0.644694i
$41$	1.99215	−	3.45051i	0.311122	−	0.538880i	−0.667483	−	0.744625i	$-0.732628\pi$
$41$	1.99215	−	3.45051i	0.311122	−	0.538880i	0.978606	+	0.205745i	$0.0659618\pi$
$42$	−3.46981	−	2.99339i	−0.535404	−	0.461890i
$43$	−3.14519	+	5.44764i	−0.479638	+	0.830757i	−0.999727	−	0.0233549i	$-0.992565\pi$
$43$	−3.14519	+	5.44764i	−0.479638	+	0.830757i	0.520090	+	0.854112i	$0.325899\pi$
$44$	0.930342	+	0.537133i	0.140254	+	0.0809759i
$45$	7.29788	−	9.81671i	1.08790	−	1.46339i
$46$	−5.87482	−	3.39183i	−0.866196	−	0.500098i
$47$	3.44099	+	1.98666i	0.501920	+	0.289784i	0.729506	−	0.683974i	$-0.239750\pi$
$47$	3.44099	+	1.98666i	0.501920	+	0.289784i	−0.227586	+	0.973758i	$0.573083\pi$
$48$	−0.544247	+	1.64432i	−0.0785553	+	0.237337i
$49$	−4.95487	−	4.94462i	−0.707838	−	0.706375i
$50$	−11.6252			−1.64405
$51$	−1.06092	−	5.12924i	−0.148559	−	0.718237i
$52$	5.50387	−	3.17766i	0.763249	−	0.440662i
$53$	4.73673			0.650640			0.325320	−	0.945604i	$-0.394528\pi$
$53$	4.73673			0.650640			0.325320	+	0.945604i	$0.394528\pi$
$54$	4.25339	−	2.98474i	0.578813	−	0.406172i
$55$	−2.19011	+	3.79338i	−0.295314	+	0.511499i
$56$	−1.01122	+	2.44488i	−0.135130	+	0.326711i
$57$	−1.74525	+	7.34535i	−0.231163	+	0.972915i
$58$	2.84891	+	4.93446i	0.374080	+	0.647926i
$59$	4.16467	+	7.21341i	0.542193	+	0.939106i	0.998778	+	0.0494264i	$0.0157393\pi$
$59$	4.16467	+	7.21341i	0.542193	+	0.939106i	−0.456584	+	0.889680i	$0.650927\pi$
$60$	−6.70456	−	2.21912i	−0.865555	−	0.286487i
$61$	3.84448	−	6.65884i	0.492236	−	0.852577i	−0.507724	−	0.861520i	$-0.669513\pi$
$61$	3.84448	−	6.65884i	0.492236	−	0.852577i	0.999960	+	0.00894224i	$0.00284644\pi$
$62$	−4.45649	−	2.57296i	−0.565975	−	0.326766i
$63$	6.81053	−	4.07635i	0.858047	−	0.513572i
$64$	1.00000			0.125000
$65$	12.9566	+	22.4415i	1.60707	+	2.78352i
$66$	−1.38956	+	1.23745i	−0.171043	+	0.152319i
$67$		−	7.59056i		−	0.927334i	−0.886010	−	0.463667i	$-0.846533\pi$
$67$		−	7.59056i		−	0.927334i	0.886010	−	0.463667i	$-0.153467\pi$
$68$	−2.61890	+	1.51203i	−0.317589	+	0.183360i
$69$	8.77462	−	7.81411i	1.05634	−	0.940708i
$70$	−9.96876	−	4.12315i	−1.19149	−	0.492811i
$71$	−4.36350	+	7.55780i	−0.517852	+	0.896946i	0.481933	+	0.876208i	$0.339935\pi$
$71$	−4.36350	+	7.55780i	−0.517852	+	0.896946i	−0.999785	+	0.0207377i	$0.993399\pi$
$72$	−2.40759	−	1.78984i	−0.283737	−	0.210934i
$73$	4.19824	+	7.27157i	0.491367	+	0.851073i	0.999951	−	0.00993997i	$-0.00316404\pi$
$73$	4.19824	+	7.27157i	0.491367	+	0.851073i	−0.508584	+	0.861013i	$0.669831\pi$
$74$	3.66771	−	2.11756i	0.426363	−	0.246161i
$75$	6.32699	−	19.1156i	0.730578	−	2.20728i
$76$	4.34265	−	0.375980i	0.498137	−	0.0431278i
$77$	−2.25401	+	1.73141i	−0.256868	+	0.197313i
$78$	2.22963	+	10.7796i	0.252456	+	1.22055i
$79$		−	6.87993i		−	0.774052i	−0.922069	−	0.387026i	$-0.873502\pi$
$79$		−	6.87993i		−	0.774052i	0.922069	−	0.387026i	$-0.126498\pi$
$80$			4.07740i			0.455867i
$81$	2.59298	+	8.61838i	0.288109	+	0.957598i
$82$	1.99215	−	3.45051i	0.219997	−	0.381045i
$83$		−	0.0397535i		−	0.00436352i	−0.999998	−	0.00218176i	$-0.999306\pi$
$83$		−	0.0397535i		−	0.00436352i	0.999998	−	0.00218176i	$-0.000694476\pi$
$84$	−3.46981	−	2.99339i	−0.378588	−	0.326606i
$85$	−6.16514	−	10.6783i	−0.668703	−	1.15823i
$86$	−3.14519	+	5.44764i	−0.339155	+	0.587434i
$87$	−9.66435	+	1.99896i	−1.03613	+	0.214311i
$88$	0.930342	+	0.537133i	0.0991748	+	0.0572586i
$89$	−0.110424	+	0.191260i	−0.0117049	+	0.0202735i	−0.871819	−	0.489829i	$-0.837059\pi$
$89$	−0.110424	+	0.191260i	−0.0117049	+	0.0202735i	0.860114	+	0.510102i	$0.170393\pi$
$90$	7.29788	−	9.81671i	0.769264	−	1.03477i
$91$	2.20337	+	16.6696i	0.230976	+	1.74745i
$92$	−5.87482	−	3.39183i	−0.612493	−	0.353623i
$93$	6.65621	−	5.92759i	0.690217	−	0.614662i
$94$	3.44099	+	1.98666i	0.354911	+	0.204908i
$95$	1.53302	+	17.7067i	0.157285	+	1.81667i
$96$	−0.544247	+	1.64432i	−0.0555470	+	0.167823i
$97$	12.0392	+	6.95084i	1.22240	+	0.705751i	0.965428	−	0.260669i	$-0.0839430\pi$
$97$	12.0392	+	6.95084i	1.22240	+	0.705751i	0.256968	+	0.966420i	$0.417276\pi$
$98$	−4.95487	−	4.94462i	−0.500517	−	0.499482i
$99$	−1.27850	−	2.95836i	−0.128494	−	0.297326i
$100$	−11.6252			−1.16252
$101$			8.79633i			0.875267i	0.899153	+	0.437634i	$0.144183\pi$
$101$			8.79633i			0.875267i	−0.899153	+	0.437634i	$0.855817\pi$
$102$	−1.06092	−	5.12924i	−0.105047	−	0.507870i
$103$	−11.3862	+	6.57382i	−1.12192	+	0.647738i	−0.941889	−	0.335924i	$-0.890952\pi$
$103$	−11.3862	+	6.57382i	−1.12192	+	0.647738i	−0.180026	+	0.983662i	$0.557618\pi$
$104$	5.50387	−	3.17766i	0.539699	−	0.311595i
$105$	12.2053	−	14.1478i	1.19111	−	1.38069i
$106$	4.73673			0.460072
$107$	1.67647	+	2.90374i	0.162071	+	0.280715i	0.935611	−	0.353032i	$-0.114849\pi$
$107$	1.67647	+	2.90374i	0.162071	+	0.280715i	−0.773540	+	0.633747i	$0.781516\pi$
$108$	4.25339	−	2.98474i	0.409283	−	0.287207i
$109$	−8.50939	+	4.91290i	−0.815052	+	0.470570i	−0.848707	−	0.528863i	$-0.822618\pi$
$109$	−8.50939	+	4.91290i	−0.815052	+	0.470570i	0.0336554	+	0.999433i	$0.489285\pi$
$110$	−2.19011	+	3.79338i	−0.208819	+	0.361685i
$111$	1.48580	+	7.18338i	0.141026	+	0.681816i
$112$	−1.01122	+	2.44488i	−0.0955513	+	0.231019i
$113$	11.3167			1.06458			0.532292	−	0.846561i	$-0.321331\pi$
$113$	11.3167			1.06458			0.532292	+	0.846561i	$0.321331\pi$
$114$	−1.74525	+	7.34535i	−0.163457	+	0.687955i
$115$	13.8299	−	23.9540i	1.28964	−	2.23372i
$116$	2.84891	+	4.93446i	0.264515	+	0.458153i
$117$	−18.9385	−	2.20052i	−1.75087	−	0.203438i
$118$	4.16467	+	7.21341i	0.383389	+	0.664049i
$119$	−1.04843	−	7.93190i	−0.0961094	−	0.727116i
$120$	−6.70456	−	2.21912i	−0.612040	−	0.202577i
$121$	−4.92298	−	8.52684i	−0.447543	−	0.775168i
$122$	3.84448	−	6.65884i	0.348063	−	0.602863i
$123$	4.58953	+	5.15368i	0.413824	+	0.464691i
$124$	−4.45649	−	2.57296i	−0.400205	−	0.231058i
$125$		−	27.0137i		−	2.41617i
$126$	6.81053	−	4.07635i	0.606731	−	0.363150i
$127$	10.5158	−	6.07128i	0.933123	−	0.538739i	0.0453251	−	0.998972i	$-0.485568\pi$
$127$	10.5158	−	6.07128i	0.933123	−	0.538739i	0.887798	+	0.460233i	$0.152234\pi$
$128$	1.00000			0.0883883
$129$	−7.24591	−	8.13657i	−0.637966	−	0.716385i
$130$	12.9566	+	22.4415i	1.13637	+	1.96825i
$131$			12.7980i			1.11817i	0.829111	+	0.559084i	$0.188847\pi$
$131$			12.7980i			1.11817i	−0.829111	+	0.559084i	$0.811153\pi$
$132$	−1.38956	+	1.23745i	−0.120945	+	0.107706i
$133$	−3.47215	+	10.9975i	−0.301074	+	0.953601i
$134$		−	7.59056i		−	0.655724i
$135$	12.1700	+	17.3428i	1.04743	+	1.49263i
$136$	−2.61890	+	1.51203i	−0.224569	+	0.129655i
$137$		−	17.3126i		−	1.47911i	−0.673095	−	0.739556i	$-0.735035\pi$
$137$		−	17.3126i		−	1.47911i	0.673095	−	0.739556i	$-0.264965\pi$
$138$	8.77462	−	7.81411i	0.746945	−	0.665181i
$139$	0.616575	+	1.06794i	0.0522972	+	0.0905815i	0.890989	−	0.454025i	$-0.150012\pi$
$139$	0.616575	+	1.06794i	0.0522972	+	0.0905815i	−0.838692	+	0.544607i	$0.816679\pi$
$140$	−9.96876	−	4.12315i	−0.842514	−	0.348470i
$141$	−5.13945	+	4.57686i	−0.432820	+	0.385441i
$142$	−4.36350	+	7.55780i	−0.366177	+	0.634236i
$143$	6.82731			0.570928
$144$	−2.40759	−	1.78984i	−0.200632	−	0.149153i
$145$	−20.1198	+	11.6162i	−1.67086	+	0.964669i
$146$	4.19824	+	7.27157i	0.347449	+	0.601799i
$147$	10.8272	−	5.45630i	0.893014	−	0.450028i
$148$	3.66771	−	2.11756i	0.301484	−	0.174062i
$149$		−	17.8685i		−	1.46385i	−0.681387	−	0.731923i	$-0.738623\pi$
$149$		−	17.8685i		−	1.46385i	0.681387	−	0.731923i	$-0.261377\pi$
$150$	6.32699	−	19.1156i	0.516597	−	1.56078i
$151$	−17.6780	−	10.2064i	−1.43862	−	0.830586i	−0.440863	−	0.897575i	$-0.645327\pi$
$151$	−17.6780	−	10.2064i	−1.43862	−	0.830586i	−0.997754	+	0.0669889i	$0.978661\pi$
$152$	4.34265	−	0.375980i	0.352236	−	0.0304960i
$153$	9.01153	+	1.04707i	0.728539	+	0.0846507i
$154$	−2.25401	+	1.73141i	−0.181633	+	0.139521i
$155$	10.4910	−	18.1709i	0.842656	−	1.45952i
$156$	2.22963	+	10.7796i	0.178513	+	0.863056i
$157$	7.34628	+	12.7241i	0.586297	+	1.01550i	0.994712	+	0.102700i	$0.0327482\pi$
$157$	7.34628	+	12.7241i	0.586297	+	1.01550i	−0.408415	+	0.912796i	$0.633918\pi$
$158$		−	6.87993i		−	0.547338i
$159$	−2.57795	+	7.78871i	−0.204445	+	0.617685i
$160$			4.07740i			0.322347i
$161$	14.2334	−	10.9333i	1.12175	−	0.861669i
$162$	2.59298	+	8.61838i	0.203724	+	0.677124i
$163$	7.80445	+	13.5177i	0.611292	+	1.05879i	0.991023	+	0.133691i	$0.0426831\pi$
$163$	7.80445	+	13.5177i	0.611292	+	1.05879i	−0.379731	+	0.925097i	$0.623984\pi$
$164$	1.99215	−	3.45051i	0.155561	−	0.269440i
$165$	−5.04558	−	5.66578i	−0.392798	−	0.441080i
$166$		−	0.0397535i		−	0.00308547i
$167$	−3.87830	−	6.71742i	−0.300112	−	0.519809i	0.676049	−	0.736857i	$-0.263691\pi$
$167$	−3.87830	−	6.71742i	−0.300112	−	0.519809i	−0.976161	+	0.217047i	$0.930357\pi$
$168$	−3.46981	−	2.99339i	−0.267702	−	0.230945i
$169$	13.6950	−	23.7205i	1.05346	−	1.82465i
$170$	−6.16514	−	10.6783i	−0.472844	−	0.818990i
$171$	−11.1283	−	6.86743i	−0.851000	−	0.525166i
$172$	−3.14519	+	5.44764i	−0.239819	+	0.415378i
$173$	−0.882084			−0.0670636			−0.0335318	−	0.999438i	$-0.510676\pi$
$173$	−0.882084			−0.0670636			−0.0335318	+	0.999438i	$0.510676\pi$
$174$	−9.66435	+	1.99896i	−0.732652	+	0.151541i
$175$	11.7556	−	28.4222i	0.888643	−	2.14852i
$176$	0.930342	+	0.537133i	0.0701272	+	0.0404880i
$177$	−14.1278	+	2.92217i	−1.06191	+	0.219644i
$178$	−0.110424	+	0.191260i	−0.00827662	+	0.0143355i
$179$	3.25659	−	5.64058i	0.243409	−	0.421597i	−0.718274	−	0.695760i	$-0.755068\pi$
$179$	3.25659	−	5.64058i	0.243409	−	0.421597i	0.961683	+	0.274164i	$0.0884009\pi$
$180$	7.29788	−	9.81671i	0.543952	−	0.731695i
$181$	16.7223	−	9.65465i	1.24296	−	0.717625i	0.273266	−	0.961938i	$-0.411896\pi$
$181$	16.7223	−	9.65465i	1.24296	−	0.717625i	0.969696	+	0.244314i	$0.0785627\pi$
$182$	2.20337	+	16.6696i	0.163325	+	1.23563i
$183$	8.85693	+	9.94563i	0.654723	+	0.735202i
$184$	−5.87482	−	3.39183i	−0.433098	−	0.250049i
$185$	8.63413	+	14.9547i	0.634794	+	1.09949i
$186$	6.65621	−	5.92759i	0.488057	−	0.434632i
$187$	−3.24864			−0.237564
$188$	3.44099	+	1.98666i	0.250960	+	0.144892i
$189$	2.99621	+	13.4173i	0.217943	+	0.975962i
$190$	1.53302	+	17.7067i	0.111217	+	1.28458i
$191$	−7.77719	+	4.49016i	−0.562737	+	0.324897i	−0.754244	−	0.656595i	$-0.771996\pi$
$191$	−7.77719	+	4.49016i	−0.562737	+	0.324897i	0.191506	+	0.981491i	$0.438663\pi$
$192$	−0.544247	+	1.64432i	−0.0392777	+	0.118669i
$193$	0.0705418	−	0.0407273i	0.00507771	−	0.00293162i	−0.497459	−	0.867487i	$-0.665734\pi$
$193$	0.0705418	−	0.0407273i	0.00507771	−	0.00293162i	0.502537	+	0.864556i	$0.332400\pi$
$194$	12.0392	+	6.95084i	0.864365	+	0.499041i
$195$	−43.9526	+	9.09110i	−3.14751	+	0.651027i
$196$	−4.95487	−	4.94462i	−0.353919	−	0.353187i
$197$			22.2690i			1.58660i	0.608830	+	0.793301i	$0.291639\pi$
$197$			22.2690i			1.58660i	−0.608830	+	0.793301i	$0.708361\pi$
$198$	−1.27850	−	2.95836i	−0.0908592	−	0.210241i
$199$	3.50713			0.248614			0.124307	−	0.992244i	$-0.460329\pi$
$199$	3.50713			0.248614			0.124307	+	0.992244i	$0.460329\pi$
$200$	−11.6252			−0.822027
$201$	12.4813	+	4.13114i	0.880364	+	0.291388i
$202$			8.79633i			0.618907i
$203$	−14.9450	+	1.97542i	−1.04894	+	0.138647i
$204$	−1.06092	−	5.12924i	−0.0742796	−	0.359119i
$205$	14.0691	+	8.12282i	0.982631	+	0.567322i
$206$	−11.3862	+	6.57382i	−0.793314	+	0.458020i
$207$	8.07335	+	18.6811i	0.561136	+	1.29843i
$208$	5.50387	−	3.17766i	0.381625	−	0.220331i
$209$	4.24211	+	1.98279i	0.293433	+	0.137153i
$210$	12.2053	−	14.1478i	0.842243	−	0.976293i
$211$	4.52926	+	2.61497i	0.311807	+	0.180022i	0.647735	−	0.761866i	$-0.275716\pi$
$211$	4.52926	+	2.61497i	0.311807	+	0.180022i	−0.335928	+	0.941888i	$0.609050\pi$
$212$	4.73673			0.325320
$213$	−10.0526	−	11.2883i	−0.688795	−	0.773462i
$214$	1.67647	+	2.90374i	0.114601	+	0.198495i
$215$	−22.2122	−	12.8242i	−1.51486	−	0.874605i
$216$	4.25339	−	2.98474i	0.289407	−	0.203086i
$217$	10.7971	−	8.29376i	0.732953	−	0.563017i
$218$	−8.50939	+	4.91290i	−0.576329	+	0.332743i
$219$	−14.2417	+	2.94573i	−0.962364	+	0.199054i
$220$	−2.19011	+	3.79338i	−0.147657	+	0.255750i
$221$	−9.60940	+	16.6440i	−0.646398	+	1.11959i
$222$	1.48580	+	7.18338i	0.0997204	+	0.482117i
$223$	−6.31674	−	3.64697i	−0.423000	−	0.244219i	0.273360	−	0.961912i	$-0.411865\pi$
$223$	−6.31674	−	3.64697i	−0.423000	−	0.244219i	−0.696360	+	0.717693i	$0.745198\pi$
$224$	−1.01122	+	2.44488i	−0.0675650	+	0.163355i
$225$	27.9887	+	20.8072i	1.86592	+	1.38715i
$226$	11.3167			0.752775
$227$	−0.329401	+	0.570539i	−0.0218631	+	0.0378680i	−0.876750	−	0.480946i	$-0.840293\pi$
$227$	−0.329401	+	0.570539i	−0.0218631	+	0.0378680i	0.854887	+	0.518814i	$0.173626\pi$
$228$	−1.74525	+	7.34535i	−0.115582	+	0.486457i
$229$	−0.556790	−	0.964389i	−0.0367937	−	0.0637286i	0.847042	−	0.531526i	$-0.178381\pi$
$229$	−0.556790	−	0.964389i	−0.0367937	−	0.0637286i	−0.883836	+	0.467797i	$0.845048\pi$
$230$	13.8299	−	23.9540i	0.911914	−	1.57948i
$231$	−1.62027	−	4.64863i	−0.106606	−	0.305857i
$232$	2.84891	+	4.93446i	0.187040	+	0.323963i
$233$			18.5403i			1.21461i	0.794468	+	0.607307i	$0.207750\pi$
$233$			18.5403i			1.21461i	−0.794468	+	0.607307i	$0.792250\pi$
$234$	−18.9385	−	2.20052i	−1.23805	−	0.143852i
$235$	−8.10039	+	14.0303i	−0.528411	+	0.915236i
$236$	4.16467	+	7.21341i	0.271097	+	0.469553i
$237$	11.3128	+	3.74438i	0.734847	+	0.243224i
$238$	−1.04843	−	7.93190i	−0.0679596	−	0.514148i
$239$		−	16.5866i		−	1.07290i	−0.843933	−	0.536448i	$-0.819766\pi$
$239$		−	16.5866i		−	1.07290i	0.843933	−	0.536448i	$-0.180234\pi$
$240$	−6.70456	−	2.21912i	−0.432778	−	0.143243i
$241$		−	19.1897i		−	1.23612i	−0.786131	−	0.618059i	$-0.787919\pi$
$241$		−	19.1897i		−	1.23612i	0.786131	−	0.618059i	$-0.212081\pi$
$242$	−4.92298	−	8.52684i	−0.316461	−	0.548126i
$243$	−15.5826	−	0.426839i	−0.999625	−	0.0273818i
$244$	3.84448	−	6.65884i	0.246118	−	0.426289i
$245$	20.1612	−	20.2030i	1.28805	−	1.29072i
$246$	4.58953	+	5.15368i	0.292618	+	0.328586i
$247$	22.7067	−	15.8688i	1.44479	−	1.00971i
$248$	−4.45649	−	2.57296i	−0.282988	−	0.163383i
$249$	0.0653676	+	0.0216357i	0.00414250	+	0.00137111i
$250$		−	27.0137i		−	1.70849i
$251$	−2.51541	+	1.45227i	−0.158771	+	0.0916666i	−0.577280	−	0.816546i	$-0.695886\pi$
$251$	−2.51541	+	1.45227i	−0.158771	+	0.0916666i	0.418509	+	0.908213i	$0.362553\pi$
$252$	6.81053	−	4.07635i	0.429023	−	0.256786i
$253$	−3.64373	−	6.31113i	−0.229079	−	0.396777i
$254$	10.5158	−	6.07128i	0.659818	−	0.380946i
$255$	20.9140	−	4.32582i	1.30968	−	0.270893i
$256$	1.00000			0.0625000
$257$	10.6628	−	18.4686i	0.665130	−	1.15204i	−0.314120	−	0.949383i	$-0.601709\pi$
$257$	10.6628	−	18.4686i	0.665130	−	1.15204i	0.979250	−	0.202656i	$-0.0649572\pi$
$258$	−7.24591	−	8.13657i	−0.451110	−	0.506561i
$259$	1.46830	+	11.1084i	0.0912358	+	0.690244i
$260$	12.9566	+	22.4415i	0.803534	+	1.39176i
$261$	1.97286	−	16.9792i	0.122117	−	1.05099i
$262$			12.7980i			0.790665i
$263$	−24.8822	+	14.3657i	−1.53430	+	0.885830i	−0.535146	+	0.844760i	$0.679743\pi$
$263$	−24.8822	+	14.3657i	−1.53430	+	0.885830i	−0.999156	+	0.0410697i	$0.986923\pi$
$264$	−1.38956	+	1.23745i	−0.0855213	+	0.0761597i
$265$			19.3136i			1.18642i
$266$	−3.47215	+	10.9975i	−0.212891	+	0.674298i
$267$	−0.254395	−	0.285665i	−0.0155687	−	0.0174824i
$268$		−	7.59056i		−	0.463667i
$269$	3.16236	+	5.47737i	0.192812	+	0.333961i	0.946181	−	0.323637i	$-0.104906\pi$
$269$	3.16236	+	5.47737i	0.192812	+	0.333961i	−0.753369	+	0.657598i	$0.771572\pi$
$270$	12.1700	+	17.3428i	0.740642	+	1.05545i
$271$	−11.2321			−0.682301			−0.341150	−	0.940009i	$-0.610817\pi$
$271$	−11.2321			−0.682301			−0.341150	+	0.940009i	$0.610817\pi$
$272$	−2.61890	+	1.51203i	−0.158794	+	0.0916800i
$273$	−28.6094	−	5.44933i	−1.73152	−	0.329809i
$274$		−	17.3126i		−	1.04589i
$275$	−10.8154	−	6.24429i	−0.652195	−	0.376545i
$276$	8.77462	−	7.81411i	0.528170	−	0.470354i
$277$	6.94047	−	12.0212i	0.417012	−	0.722287i	−0.578625	−	0.815594i	$-0.696410\pi$
$277$	6.94047	−	12.0212i	0.417012	−	0.722287i	0.995637	+	0.0933070i	$0.0297438\pi$
$278$	0.616575	+	1.06794i	0.0369797	+	0.0640508i
$279$	6.12424	+	14.1710i	0.366649	+	0.848397i
$280$	−9.96876	−	4.12315i	−0.595747	−	0.246405i
$281$	−4.96581	−	8.60104i	−0.296235	−	0.513095i	0.679036	−	0.734105i	$-0.262398\pi$
$281$	−4.96581	−	8.60104i	−0.296235	−	0.513095i	−0.975272	+	0.221010i	$0.929065\pi$
$282$	−5.13945	+	4.57686i	−0.306050	+	0.272548i
$283$	2.44319	+	4.23173i	0.145233	+	0.251550i	0.929460	−	0.368924i	$-0.120274\pi$
$283$	2.44319	+	4.23173i	0.145233	+	0.251550i	−0.784227	+	0.620474i	$0.786940\pi$
$284$	−4.36350	+	7.55780i	−0.258926	+	0.448473i
$285$	−29.9499	−	7.11607i	−1.77408	−	0.421520i
$286$	6.82731			0.403707
$287$	6.42158	+	8.35980i	0.379054	+	0.493464i
$288$	−2.40759	−	1.78984i	−0.141869	−	0.105467i
$289$	−3.92756	+	6.80273i	−0.231033	+	0.400161i
$290$	−20.1198	+	11.6162i	−1.18147	+	0.682124i
$291$	−17.9817	+	16.0134i	−1.05411	+	0.938720i
$292$	4.19824	+	7.27157i	0.245684	+	0.425536i
$293$	5.22364			0.305168			0.152584	−	0.988290i	$-0.451241\pi$
$293$	5.22364			0.305168			0.152584	+	0.988290i	$0.451241\pi$
$294$	10.8272	−	5.45630i	0.631457	−	0.318218i
$295$	−29.4120	+	16.9810i	−1.71243	+	0.988673i
$296$	3.66771	−	2.11756i	0.213182	−	0.123080i
$297$	5.56031	−	0.492192i	0.322642	−	0.0285599i
$298$		−	17.8685i		−	1.03510i
$299$	−43.1123			−2.49325
$300$	6.32699	−	19.1156i	0.365289	−	1.10364i
$301$	−10.1383	−	13.1984i	−0.584364	−	0.760742i
$302$	−17.6780	−	10.2064i	−1.01726	−	0.587313i
$303$	−14.4640	−	4.78738i	−0.830935	−	0.275028i
$304$	4.34265	−	0.375980i	0.249068	−	0.0215639i
$305$	27.1508	+	15.6755i	1.55465	+	0.897577i
$306$	9.01153	+	1.04707i	0.515155	+	0.0598571i
$307$	−5.40797	−	3.12229i	−0.308649	−	0.178199i	0.337673	−	0.941264i	$-0.390360\pi$
$307$	−5.40797	−	3.12229i	−0.308649	−	0.178199i	−0.646322	+	0.763065i	$0.723694\pi$
$308$	−2.25401	+	1.73141i	−0.128434	+	0.0986565i
$309$	−4.61258	−	22.3004i	−0.262400	−	1.26862i
$310$	10.4910	−	18.1709i	0.595848	−	1.03204i
$311$	−13.4139	−	7.74450i	−0.760631	−	0.439151i	0.0688913	−	0.997624i	$-0.478054\pi$
$311$	−13.4139	−	7.74450i	−0.760631	−	0.439151i	−0.829522	+	0.558474i	$0.811387\pi$
$312$	2.22963	+	10.7796i	0.126228	+	0.610273i
$313$	2.62607	−	4.54849i	0.148434	−	0.257096i	−0.782215	−	0.623009i	$-0.785910\pi$
$313$	2.62607	−	4.54849i	0.148434	−	0.257096i	0.930649	+	0.365913i	$0.119243\pi$
$314$	7.34628	+	12.7241i	0.414575	+	0.718064i
$315$	16.6209	+	27.7693i	0.936482	+	1.56462i
$316$		−	6.87993i		−	0.387026i
$317$	4.04167	−	7.00037i	0.227003	−	0.393180i	−0.729916	−	0.683537i	$-0.760441\pi$
$317$	4.04167	−	7.00037i	0.227003	−	0.393180i	0.956918	+	0.290357i	$0.0937741\pi$
$318$	−2.57795	+	7.78871i	−0.144564	+	0.436769i
$319$			6.12098i			0.342709i
$320$			4.07740i			0.227934i
$321$	−5.68709	+	1.17631i	−0.317423	+	0.0656553i
$322$	14.2334	−	10.9333i	0.793194	−	0.609292i
$323$	−10.8045	+	7.55086i	−0.601179	+	0.420141i
$324$	2.59298	+	8.61838i	0.144054	+	0.478799i
$325$	−63.9836	+	36.9410i	−3.54917	+	2.04912i
$326$	7.80445	+	13.5177i	0.432248	+	0.748676i
$327$	−3.44718	−	16.6660i	−0.190629	−	0.921632i
$328$	1.99215	−	3.45051i	0.109998	−	0.190523i
$329$	−8.33673	+	6.40385i	−0.459619	+	0.353056i
$330$	−5.04558	−	5.66578i	−0.277750	−	0.311891i
$331$	−21.1450	+	12.2081i	−1.16223	+	0.671016i	−0.951838	−	0.306600i	$-0.900809\pi$
$331$	−21.1450	+	12.2081i	−1.16223	+	0.671016i	−0.210396	+	0.977616i	$0.567475\pi$
$332$		−	0.0397535i		−	0.00218176i
$333$	−12.6204	−	1.46640i	−0.691595	−	0.0803582i
$334$	−3.87830	−	6.71742i	−0.212211	−	0.367561i
$335$	30.9497			1.69097
$336$	−3.46981	−	2.99339i	−0.189294	−	0.163303i
$337$	7.76773	+	4.48470i	0.423135	+	0.244297i	0.696418	−	0.717637i	$-0.254776\pi$
$337$	7.76773	+	4.48470i	0.423135	+	0.244297i	−0.273283	+	0.961934i	$0.588109\pi$
$338$	13.6950	−	23.7205i	0.744912	−	1.29022i
$339$	−6.15907	+	18.6083i	−0.334515	+	1.01066i
$340$	−6.16514	−	10.6783i	−0.334351	−	0.579114i
$341$	−2.76404	−	4.78746i	−0.149681	−	0.259256i
$342$	−11.1283	−	6.86743i	−0.601748	−	0.371348i
$343$	17.0995	−	7.11395i	0.923284	−	0.384117i
$344$	−3.14519	+	5.44764i	−0.169578	+	0.293717i
$345$	31.8613	+	35.7777i	1.71535	+	1.92620i
$346$	−0.882084			−0.0474211
$347$	15.1730	−	8.76013i	0.814529	−	0.470268i	−0.0339974	−	0.999422i	$-0.510824\pi$
$347$	15.1730	−	8.76013i	0.814529	−	0.470268i	0.848526	+	0.529154i	$0.177490\pi$
$348$	−9.66435	+	1.99896i	−0.518064	+	0.107156i
$349$	−7.55071			−0.404180			−0.202090	−	0.979367i	$-0.564773\pi$
$349$	−7.55071			−0.404180			−0.202090	+	0.979367i	$0.564773\pi$
$350$	11.7556	−	28.4222i	0.628366	−	1.51923i
$351$	13.9256	−	29.9434i	0.743294	−	1.59826i
$352$	0.930342	+	0.537133i	0.0495874	+	0.0286293i
$353$	18.3795	+	10.6114i	0.978243	+	0.564789i	0.901739	−	0.432280i	$-0.142291\pi$
$353$	18.3795	+	10.6114i	0.978243	+	0.564789i	0.0765039	+	0.997069i	$0.475624\pi$
$354$	−14.1278	+	2.92217i	−0.750883	+	0.155312i
$355$	−30.8162	−	17.7917i	−1.63555	−	0.944287i
$356$	−0.110424	+	0.191260i	−0.00585245	+	0.0101367i
$357$	13.6132	+	2.59296i	0.720487	+	0.137234i
$358$	3.25659	−	5.64058i	0.172116	−	0.298114i
$359$		−	14.7462i		−	0.778272i	−0.921180	−	0.389136i	$-0.872774\pi$
$359$		−	14.7462i		−	0.778272i	0.921180	−	0.389136i	$-0.127226\pi$
$360$	7.29788	−	9.81671i	0.384632	−	0.517386i
$361$	18.7173	−	3.26550i	0.985120	−	0.171868i
$362$	16.7223	−	9.65465i	0.878907	−	0.507437i
$363$	16.7002	−	3.45425i	0.876533	−	0.181301i
$364$	2.20337	+	16.6696i	0.115488	+	0.873725i
$365$	−29.6491	+	17.1179i	−1.55191	+	0.895993i
$366$	8.85693	+	9.94563i	0.462959	+	0.519866i
$367$	24.9894			1.30443			0.652217	−	0.758033i	$-0.273839\pi$
$367$	24.9894			1.30443			0.652217	+	0.758033i	$0.273839\pi$
$368$	−5.87482	−	3.39183i	−0.306246	−	0.176811i
$369$	−10.9721	+	4.74179i	−0.571187	+	0.246848i
$370$	8.63413	+	14.9547i	0.448867	+	0.777460i
$371$	−4.78988	+	11.5807i	−0.248678	+	0.601242i
$372$	6.65621	−	5.92759i	0.345108	−	0.307331i
$373$	−4.75225	+	2.74372i	−0.246062	+	0.142064i	−0.617960	−	0.786210i	$-0.712041\pi$
$373$	−4.75225	+	2.74372i	−0.246062	+	0.142064i	0.371898	+	0.928274i	$0.378707\pi$
$374$	−3.24864			−0.167983
$375$	44.4191	+	14.7021i	2.29379	+	0.759214i
$376$	3.44099	+	1.98666i	0.177455	+	0.102454i
$377$	31.3600	+	18.1057i	1.61512	+	0.932493i
$378$	2.99621	+	13.4173i	0.154109	+	0.690109i
$379$		−	20.9015i		−	1.07364i	−0.843697	−	0.536820i	$-0.819626\pi$
$379$		−	20.9015i		−	1.07364i	0.843697	−	0.536820i	$-0.180374\pi$
$380$	1.53302	+	17.7067i	0.0786423	+	0.908337i
$381$	4.25996	+	20.5956i	0.218244	+	1.05514i
$382$	−7.77719	+	4.49016i	−0.397915	+	0.229737i
$383$	−19.1265			−0.977318			−0.488659	−	0.872475i	$-0.662514\pi$
$383$	−19.1265			−0.977318			−0.488659	+	0.872475i	$0.662514\pi$
$384$	−0.544247	+	1.64432i	−0.0277735	+	0.0839115i
$385$	−7.05967	−	9.19049i	−0.359794	−	0.468391i
$386$	0.0705418	−	0.0407273i	0.00359048	−	0.00207297i
$387$	17.3227	−	7.48629i	0.880563	−	0.380550i
$388$	12.0392	+	6.95084i	0.611198	+	0.352876i
$389$		−	30.6695i		−	1.55500i	−0.628880	−	0.777502i	$-0.716487\pi$
$389$		−	30.6695i		−	1.55500i	0.628880	−	0.777502i	$-0.283513\pi$
$390$	−43.9526	+	9.09110i	−2.22563	+	0.460346i
$391$	20.5141			1.03744
$392$	−4.95487	−	4.94462i	−0.250259	−	0.249741i
$393$	−21.0441	−	6.96529i	−1.06153	−	0.351352i
$394$			22.2690i			1.12190i
$395$	28.0522			1.41146
$396$	−1.27850	−	2.95836i	−0.0642472	−	0.148663i
$397$	13.3341			0.669221			0.334610	−	0.942357i	$-0.391395\pi$
$397$	13.3341			0.669221			0.334610	+	0.942357i	$0.391395\pi$
$398$	3.50713			0.175796
$399$	−16.1937	−	11.6947i	−0.810697	−	0.585466i
$400$	−11.6252			−0.581261
$401$	2.19502			0.109614			0.0548070	−	0.998497i	$-0.482546\pi$
$401$	2.19502			0.109614			0.0548070	+	0.998497i	$0.482546\pi$
$402$	12.4813	+	4.13114i	0.622512	+	0.206042i
$403$	−32.7039			−1.62910
$404$			8.79633i			0.437634i
$405$	−35.1406	+	10.5726i	−1.74615	+	0.525357i
$406$	−14.9450	+	1.97542i	−0.741709	+	0.0980384i
$407$	4.54964			0.225517
$408$	−1.06092	−	5.12924i	−0.0525236	−	0.253935i
$409$		−	3.79885i		−	0.187841i	−0.995580	−	0.0939204i	$-0.970060\pi$
$409$		−	3.79885i		−	0.187841i	0.995580	−	0.0939204i	$-0.0299399\pi$
$410$	14.0691	+	8.12282i	0.694825	+	0.401157i
$411$	28.4674	+	9.42232i	1.40420	+	0.464769i
$412$	−11.3862	+	6.57382i	−0.560958	+	0.323869i
$413$	−21.8473	+	2.88776i	−1.07504	+	0.142097i
$414$	8.07335	+	18.6811i	0.396783	+	0.918126i
$415$	0.162091			0.00795674
$416$	5.50387	−	3.17766i	0.269849	−	0.155798i
$417$	−2.09161	+	0.432625i	−0.102426	+	0.0211857i
$418$	4.24211	+	1.98279i	0.207488	+	0.0969816i
$419$		−	16.5211i		−	0.807108i	−0.914956	−	0.403554i	$-0.867775\pi$
$419$		−	16.5211i		−	0.807108i	0.914956	−	0.403554i	$-0.132225\pi$
$420$	12.2053	−	14.1478i	0.595556	−	0.690343i
$421$	7.50592	+	4.33355i	0.365816	+	0.211204i	0.671629	−	0.740888i	$-0.265595\pi$
$421$	7.50592	+	4.33355i	0.365816	+	0.211204i	−0.305813	+	0.952092i	$0.598928\pi$
$422$	4.52926	+	2.61497i	0.220481	+	0.127295i
$423$	−4.72870	−	10.9419i	−0.229917	−	0.532011i
$424$	4.73673			0.230036
$425$	30.4453	−	17.5776i	1.47681	−	0.852640i
$426$	−10.0526	−	11.2883i	−0.487052	−	0.546920i
$427$	12.3924	+	16.1329i	0.599712	+	0.780724i
$428$	1.67647	+	2.90374i	0.0810354	+	0.140357i
$429$	−3.71574	+	11.2263i	−0.179398	+	0.542010i
$430$	−22.2122	−	12.8242i	−1.07117	−	0.618439i
$431$	4.88374			0.235241			0.117621	−	0.993059i	$-0.462473\pi$
$431$	4.88374			0.235241			0.117621	+	0.993059i	$0.462473\pi$
$432$	4.25339	−	2.98474i	0.204641	−	0.143603i
$433$	9.13958	−	5.27674i	0.439220	−	0.253584i	−0.264047	−	0.964510i	$-0.585057\pi$
$433$	9.13958	−	5.27674i	0.439220	−	0.253584i	0.703267	+	0.710926i	$0.251724\pi$
$434$	10.7971	−	8.29376i	0.518276	−	0.398113i
$435$	−8.15057	−	39.4054i	−0.390790	−	1.88935i
$436$	−8.50939	+	4.91290i	−0.407526	+	0.235285i
$437$	−26.7876	−	12.5207i	−1.28142	−	0.598948i
$438$	−14.2417	+	2.94573i	−0.680494	+	0.140752i
$439$			9.52603i			0.454652i	0.973819	+	0.227326i	$0.0729984\pi$
$439$			9.52603i			0.454652i	−0.973819	+	0.227326i	$0.927002\pi$
$440$	−2.19011	+	3.79338i	−0.104409	+	0.180842i
$441$	3.07923	+	20.7730i	0.146630	+	0.989191i
$442$	−9.60940	+	16.6440i	−0.457073	+	0.791673i
$443$	25.2198	+	14.5607i	1.19823	+	0.691798i	0.960160	−	0.279450i	$-0.0901522\pi$
$443$	25.2198	+	14.5607i	1.19823	+	0.691798i	0.238069	+	0.971248i	$0.423486\pi$
$444$	1.48580	+	7.18338i	0.0705129	+	0.340908i
$445$	−0.779843	−	0.450242i	−0.0369681	−	0.0213435i
$446$	−6.31674	−	3.64697i	−0.299106	−	0.172689i
$447$	29.3816	+	9.72489i	1.38970	+	0.459972i
$448$	−1.01122	+	2.44488i	−0.0477757	+	0.115510i
$449$	−37.7884			−1.78335			−0.891674	−	0.452679i	$-0.850468\pi$
$449$	−37.7884			−1.78335			−0.891674	+	0.452679i	$0.850468\pi$
$450$	27.9887	+	20.8072i	1.31940	+	0.980862i
$451$	3.70677	−	2.14011i	0.174545	−	0.100774i
$452$	11.3167			0.532292
$453$	26.4038	−	23.5135i	1.24056	−	1.10476i
$454$	−0.329401	+	0.570539i	−0.0154595	+	0.0267767i
$455$	−67.9687	+	8.98403i	−3.18642	+	0.421178i
$456$	−1.74525	+	7.34535i	−0.0817286	+	0.343977i
$457$	−2.19166	−	3.79607i	−0.102522	−	0.177572i	0.810201	−	0.586152i	$-0.199358\pi$
$457$	−2.19166	−	3.79607i	−0.102522	−	0.177572i	−0.912723	+	0.408579i	$0.866024\pi$
$458$	−0.556790	−	0.964389i	−0.0260171	−	0.0450629i
$459$	−6.62622	+	14.2480i	−0.309286	+	0.665039i
$460$	13.8299	−	23.9540i	0.644821	−	1.11686i
$461$	11.0809	+	6.39758i	0.516091	+	0.297965i	0.735334	−	0.677705i	$-0.237025\pi$
$461$	11.0809	+	6.39758i	0.516091	+	0.297965i	−0.219243	+	0.975670i	$0.570359\pi$
$462$	−1.62027	−	4.64863i	−0.0753816	−	0.216274i
$463$	1.81932			0.0845510			0.0422755	−	0.999106i	$-0.486539\pi$
$463$	1.81932			0.0845510			0.0422755	+	0.999106i	$0.486539\pi$
$464$	2.84891	+	4.93446i	0.132257	+	0.229076i
$465$	24.1692	+	27.1400i	1.12082	+	1.25859i
$466$			18.5403i			0.858861i
$467$	15.3869	−	8.88363i	0.712021	−	0.411085i	−0.0997880	−	0.995009i	$-0.531816\pi$
$467$	15.3869	−	8.88363i	0.712021	−	0.411085i	0.811809	+	0.583923i	$0.198483\pi$
$468$	−18.9385	−	2.20052i	−0.875434	−	0.101719i
$469$	18.5580	+	7.67572i	0.856928	+	0.354432i
$470$	−8.10039	+	14.0303i	−0.373643	+	0.647169i
$471$	−24.9208	+	5.15458i	−1.14829	+	0.237510i
$472$	4.16467	+	7.21341i	0.191694	+	0.332024i
$473$	−5.85222	+	3.37878i	−0.269085	+	0.155356i
$474$	11.3128	+	3.74438i	0.519615	+	0.171985i
$475$	−50.4843	+	4.37084i	−2.31638	+	0.200548i
$476$	−1.04843	−	7.93190i	−0.0480547	−	0.363558i
$477$	−11.4041	−	8.47797i	−0.522158	−	0.388180i
$478$		−	16.5866i		−	0.758652i
$479$			14.5072i			0.662849i	0.943482	+	0.331425i	$0.107529\pi$
$479$			14.5072i			0.662849i	−0.943482	+	0.331425i	$0.892471\pi$
$480$	−6.70456	−	2.21912i	−0.306020	−	0.101288i
$481$	13.4577	−	23.3095i	0.613620	−	1.06282i
$482$		−	19.1897i		−	0.874068i
$483$	10.2315	+	29.3547i	0.465548	+	1.33568i
$484$	−4.92298	−	8.52684i	−0.223772	−	0.387584i
$485$	−28.3414	+	49.0887i	−1.28692	+	2.22900i
$486$	−15.5826	−	0.426839i	−0.706842	−	0.0193618i
$487$	2.57977	+	1.48943i	0.116900	+	0.0674925i	0.557310	−	0.830304i	$-0.311833\pi$
$487$	2.57977	+	1.48943i	0.116900	+	0.0674925i	−0.440410	+	0.897797i	$0.645167\pi$
$488$	3.84448	−	6.65884i	0.174032	−	0.301432i
$489$	−26.4750	+	5.47605i	−1.19724	+	0.247636i
$490$	20.1612	−	20.2030i	0.910791	−	0.912678i
$491$	−21.7386	−	12.5508i	−0.981048	−	0.566409i	−0.0784619	−	0.996917i	$-0.525001\pi$
$491$	−21.7386	−	12.5508i	−0.981048	−	0.566409i	−0.902586	+	0.430509i	$0.858334\pi$
$492$	4.58953	+	5.15368i	0.206912	+	0.232346i
$493$	−14.9221	−	8.61525i	−0.672055	−	0.388011i
$494$	22.7067	−	15.8688i	1.02162	−	0.713972i
$495$	12.0624	−	5.21297i	0.542165	−	0.234306i
$496$	−4.45649	−	2.57296i	−0.200103	−	0.115529i
$497$	−14.0654	−	18.3108i	−0.630922	−	0.821353i
$498$	0.0653676	+	0.0216357i	0.00292919	+	0.000969521i
$499$	−20.7249			−0.927773			−0.463887	−	0.885895i	$-0.653546\pi$
$499$	−20.7249			−0.927773			−0.463887	+	0.885895i	$0.653546\pi$
$500$		−	27.0137i		−	1.20809i
$501$	13.1564	−	2.72124i	0.587782	−	0.121576i
$502$	−2.51541	+	1.45227i	−0.112268	+	0.0648181i
$503$	−19.8551	+	11.4633i	−0.885294	+	0.511125i	−0.872400	−	0.488792i	$-0.837438\pi$
$503$	−19.8551	+	11.4633i	−0.885294	+	0.511125i	−0.0128938	+	0.999917i	$0.504104\pi$
$504$	6.81053	−	4.07635i	0.303365	−	0.181575i
$505$	−35.8662			−1.59602
$506$	−3.64373	−	6.31113i	−0.161984	−	0.280564i
$507$	31.5506	+	35.4289i	1.40121	+	1.57345i
$508$	10.5158	−	6.07128i	0.466562	−	0.269369i
$509$	−14.5868	+	25.2651i	−0.646549	+	1.11986i	0.337392	+	0.941364i	$0.390455\pi$
$509$	−14.5868	+	25.2651i	−0.646549	+	1.11986i	−0.983941	+	0.178492i	$0.942878\pi$
$510$	20.9140	−	4.32582i	0.926086	−	0.191550i
$511$	−22.0235	+	2.91104i	−0.974260	+	0.128777i
$512$	1.00000			0.0441942
$513$	17.3488	−	14.5609i	0.765968	−	0.642879i
$514$	10.6628	−	18.4686i	0.470318	−	0.814614i
$515$	−26.8041	−	46.4261i	−1.18113	−	2.04578i
$516$	−7.24591	−	8.13657i	−0.318983	−	0.358193i
$517$	2.13420	+	3.69654i	0.0938619	+	0.162574i
$518$	1.46830	+	11.1084i	0.0645135	+	0.488076i
$519$	0.480072	−	1.45043i	0.0210728	−	0.0636668i
$520$	12.9566	+	22.4415i	0.568184	+	0.984124i
$521$	−5.56777	+	9.64365i	−0.243928	+	0.422496i	−0.961830	−	0.273649i	$-0.911769\pi$
$521$	−5.56777	+	9.64365i	−0.243928	+	0.422496i	0.717902	+	0.696145i	$0.245103\pi$
$522$	1.97286	−	16.9792i	0.0863497	−	0.743161i
$523$	10.3965	+	6.00242i	0.454607	+	0.262467i	0.709774	−	0.704430i	$-0.248797\pi$
$523$	10.3965	+	6.00242i	0.454607	+	0.262467i	−0.255167	+	0.966897i	$0.582130\pi$
$524$			12.7980i			0.559084i
$525$	40.3373	+	34.7988i	1.76047	+	1.51874i
$526$	−24.8822	+	14.3657i	−1.08492	+	0.626376i
$527$	15.5615			0.677870
$528$	−1.38956	+	1.23745i	−0.0604727	+	0.0538531i
$529$	11.5090	+	19.9342i	0.500393	+	0.866706i
$530$			19.3136i			0.838927i
$531$	2.88402	−	24.8210i	0.125156	−	1.07714i
$532$	−3.47215	+	10.9975i	−0.150537	+	0.476800i
$533$		−	25.3216i		−	1.09680i
$534$	−0.254395	−	0.285665i	−0.0110087	−	0.0123619i
$535$	−11.8397	+	6.83565i	−0.511875	+	0.295531i
$536$		−	7.59056i		−	0.327862i
$537$	7.50254	+	8.42475i	0.323758	+	0.363555i
$538$	3.16236	+	5.47737i	0.136339	+	0.236146i
$539$	−1.95380	−	7.26162i	−0.0841562	−	0.312780i
$540$	12.1700	+	17.3428i	0.523713	+	0.746315i
$541$	0.439116	−	0.760571i	0.0188791	−	0.0326995i	−0.856432	−	0.516261i	$-0.827324\pi$
$541$	0.439116	−	0.760571i	0.0188791	−	0.0326995i	0.875311	+	0.483561i	$0.160657\pi$
$542$	−11.2321			−0.482459
$543$	6.77426	+	32.7514i	0.290712	+	1.40550i
$544$	−2.61890	+	1.51203i	−0.112285	+	0.0648276i
$545$	−20.0319	−	34.6962i	−0.858071	−	1.48622i
$546$	−28.6094	−	5.44933i	−1.22437	−	0.233210i
$547$	24.5555	−	14.1771i	1.04992	−	0.606171i	0.127292	−	0.991865i	$-0.459372\pi$
$547$	24.5555	−	14.1771i	1.04992	−	0.606171i	0.922626	+	0.385695i	$0.126038\pi$
$548$		−	17.3126i		−	0.739556i
$549$	−21.1742	+	9.15077i	−0.903692	+	0.390545i
$550$	−10.8154	−	6.24429i	−0.461171	−	0.266257i
$551$	14.2271	+	20.3575i	0.606094	+	0.867259i
$552$	8.77462	−	7.81411i	0.373473	−	0.332591i
$553$	16.8206	+	6.95712i	0.715284	+	0.295847i
$554$	6.94047	−	12.0212i	0.294872	−	0.510734i
$555$	−29.2895	+	6.05820i	−1.24327	+	0.257156i
$556$	0.616575	+	1.06794i	0.0261486	+	0.0452907i
$557$		−	20.4332i		−	0.865783i	−0.901446	−	0.432891i	$-0.857493\pi$
$557$		−	20.4332i		−	0.865783i	0.901446	−	0.432891i	$-0.142507\pi$
$558$	6.12424	+	14.1710i	0.259260	+	0.599907i
$559$			39.9774i			1.69087i
$560$	−9.96876	−	4.12315i	−0.421257	−	0.174235i
$561$	1.76806	−	5.34181i	0.0746476	−	0.225531i
$562$	−4.96581	−	8.60104i	−0.209470	−	0.362813i
$563$	−5.63759	+	9.76458i	−0.237596	+	0.411528i	−0.960024	−	0.279918i	$-0.909693\pi$
$563$	−5.63759	+	9.76458i	−0.237596	+	0.411528i	0.722428	+	0.691446i	$0.243026\pi$
$564$	−5.13945	+	4.57686i	−0.216410	+	0.192721i
$565$			46.1427i			1.94124i
$566$	2.44319	+	4.23173i	0.102695	+	0.177873i
$567$	−23.6930	−	2.37556i	−0.995011	−	0.0997642i
$568$	−4.36350	+	7.55780i	−0.183088	+	0.317118i
$569$	−10.4034	−	18.0192i	−0.436133	−	0.755404i	0.561254	−	0.827643i	$-0.310319\pi$
$569$	−10.4034	−	18.0192i	−0.436133	−	0.755404i	−0.997387	+	0.0722389i	$0.976986\pi$
$570$	−29.9499	−	7.11607i	−1.25446	−	0.298059i
$571$	−4.73612	+	8.20320i	−0.198201	+	0.343293i	−0.947945	−	0.318434i	$-0.896843\pi$
$571$	−4.73612	+	8.20320i	−0.198201	+	0.343293i	0.749744	+	0.661727i	$0.230176\pi$
$572$	6.82731			0.285464
$573$	−3.15056	−	15.2320i	−0.131616	−	0.636324i
$574$	6.42158	+	8.35980i	0.268032	+	0.348931i
$575$	68.2961	+	39.4308i	2.84814	+	1.64438i
$576$	−2.40759	−	1.78984i	−0.100316	−	0.0745765i
$577$	13.2596	−	22.9664i	0.552006	−	0.956102i	−0.446124	−	0.894971i	$-0.647196\pi$
$577$	13.2596	−	22.9664i	0.552006	−	0.956102i	0.998130	−	0.0611311i	$-0.0194708\pi$
$578$	−3.92756	+	6.80273i	−0.163365	+	0.282956i
$579$	0.0285767	+	0.138159i	0.00118761	+	0.00574170i
$580$	−20.1198	+	11.6162i	−0.835428	+	0.482335i
$581$	0.0971925	+	0.0401996i	0.00403223	+	0.00166776i
$582$	−17.9817	+	16.0134i	−0.745367	+	0.663775i
$583$	4.40678	+	2.54426i	0.182510	+	0.105372i
$584$	4.19824	+	7.27157i	0.173724	+	0.300900i
$585$	8.97239	−	77.2201i	0.370963	−	3.19266i
$586$	5.22364			0.215786
$587$	1.60097	+	0.924319i	0.0660790	+	0.0381507i	0.532675	−	0.846320i	$-0.321187\pi$
$587$	1.60097	+	0.924319i	0.0660790	+	0.0381507i	−0.466597	+	0.884470i	$0.654520\pi$
$588$	10.8272	−	5.45630i	0.446507	−	0.225014i
$589$	−20.3204	−	9.49792i	−0.837287	−	0.391355i
$590$	−29.4120	+	16.9810i	−1.21087	+	0.699098i
$591$	−36.6174	−	12.1199i	−1.50624	−	0.498544i
$592$	3.66771	−	2.11756i	0.150742	−	0.0870310i
$593$	−14.9410	−	8.62619i	−0.613553	−	0.354235i	0.160802	−	0.986987i	$-0.448592\pi$
$593$	−14.9410	−	8.62619i	−0.613553	−	0.354235i	−0.774355	+	0.632752i	$0.781925\pi$
$594$	5.56031	−	0.492192i	0.228142	−	0.0201949i
$595$	32.3415	−	4.27487i	1.32587	−	0.175253i
$596$		−	17.8685i		−	0.731923i
$597$	−1.90874	+	5.76685i	−0.0781197	+	0.236021i
$598$	−43.1123			−1.76299
$599$	37.2669			1.52268			0.761341	−	0.648351i	$-0.224541\pi$
$599$	37.2669			1.52268			0.761341	+	0.648351i	$0.224541\pi$
$600$	6.32699	−	19.1156i	0.258298	−	0.780391i
$601$		−	40.1070i		−	1.63600i	−0.575219	−	0.817999i	$-0.695083\pi$
$601$		−	40.1070i		−	1.63600i	0.575219	−	0.817999i	$-0.304917\pi$
$602$	−10.1383	−	13.1984i	−0.413207	−	0.537926i
$603$	−13.5858	+	18.2749i	−0.553258	+	0.744213i
$604$	−17.6780	−	10.2064i	−0.719308	−	0.415293i
$605$	34.7674	−	20.0730i	1.41349	−	0.816082i
$606$	−14.4640	−	4.78738i	−0.587560	−	0.194474i
$607$	10.0993	−	5.83086i	0.409920	−	0.236667i	−0.280836	−	0.959756i	$-0.590612\pi$
$607$	10.0993	−	5.83086i	0.409920	−	0.236667i	0.690755	+	0.723089i	$0.257278\pi$
$608$	4.34265	−	0.375980i	0.176118	−	0.0152480i
$609$	4.88557	−	25.6496i	0.197973	−	1.03937i
$610$	27.1508	+	15.6755i	1.09930	+	0.634683i
$611$	25.2517			1.02157
$612$	9.01153	+	1.04707i	0.364269	+	0.0423254i
$613$	−16.8208	−	29.1346i	−0.679388	−	1.17673i	−0.975166	−	0.221477i	$-0.928912\pi$
$613$	−16.8208	−	29.1346i	−0.679388	−	1.17673i	0.295778	−	0.955257i	$-0.404421\pi$
$614$	−5.40797	−	3.12229i	−0.218248	−	0.126006i
$615$	−21.0136	+	18.7134i	−0.847351	+	0.754595i
$616$	−2.25401	+	1.73141i	−0.0908165	+	0.0697607i
$617$	2.35772	−	1.36123i	0.0949181	−	0.0548010i	−0.451790	−	0.892125i	$-0.649214\pi$
$617$	2.35772	−	1.36123i	0.0949181	−	0.0548010i	0.546708	+	0.837324i	$0.315881\pi$
$618$	−4.61258	−	22.3004i	−0.185545	−	0.897052i
$619$	2.21738	−	3.84062i	0.0891240	−	0.154367i	−0.818017	−	0.575194i	$-0.804927\pi$
$619$	2.21738	−	3.84062i	0.0891240	−	0.154367i	0.907141	+	0.420827i	$0.138260\pi$
$620$	10.4910	−	18.1709i	0.421328	−	0.729762i
$621$	−35.1117	+	3.10804i	−1.40898	+	0.124721i
$622$	−13.4139	−	7.74450i	−0.537847	−	0.310526i
$623$	−0.355944	−	0.463379i	−0.0142606	−	0.0185649i
$624$	2.22963	+	10.7796i	0.0892566	+	0.431528i
$625$	52.0195			2.08078
$626$	2.62607	−	4.54849i	0.104959	−	0.181794i
$627$	−5.56911	+	5.89626i	−0.222409	+	0.235474i
$628$	7.34628	+	12.7241i	0.293149	+	0.507748i
$629$	−6.40359	+	11.0914i	−0.255328	+	0.442241i
$630$	16.6209	+	27.7693i	0.662193	+	1.10636i
$631$	20.1135	+	34.8376i	0.800706	+	1.38686i	0.919152	+	0.393902i	$0.128875\pi$
$631$	20.1135	+	34.8376i	0.800706	+	1.38686i	−0.118447	+	0.992960i	$0.537791\pi$
$632$		−	6.87993i		−	0.273669i
$633$	−6.76489	+	6.02437i	−0.268880	+	0.239447i
$634$	4.04167	−	7.00037i	0.160515	−	0.278020i
$635$	24.7550	+	42.8770i	0.982374	+	1.70152i
$636$	−2.57795	+	7.78871i	−0.102222	+	0.308842i
$637$	−42.9833	−	11.4697i	−1.70306	−	0.454444i
$638$			6.12098i			0.242332i
$639$	24.0327	−	10.3861i	0.950720	−	0.410869i
$640$			4.07740i			0.161173i
$641$	−15.2398	−	26.3961i	−0.601937	−	1.04258i	−0.992528	−	0.122020i	$-0.961063\pi$
$641$	−15.2398	−	26.3961i	−0.601937	−	1.04258i	0.390591	−	0.920564i	$-0.372271\pi$
$642$	−5.68709	+	1.17631i	−0.224452	+	0.0464253i
$643$	18.1504	−	31.4373i	0.715780	−	1.23977i	−0.246877	−	0.969047i	$-0.579405\pi$
$643$	18.1504	−	31.4373i	0.715780	−	1.23977i	0.962658	−	0.270721i	$-0.0872621\pi$
$644$	14.2334	−	10.9333i	0.560873	−	0.430834i
$645$	33.1761	−	29.5445i	1.30631	−	1.16331i
$646$	−10.8045	+	7.55086i	−0.425098	+	0.297085i
$647$	4.72685	+	2.72905i	0.185832	+	0.107290i	0.590030	−	0.807382i	$-0.299116\pi$
$647$	4.72685	+	2.72905i	0.185832	+	0.107290i	−0.404198	+	0.914671i	$0.632449\pi$
$648$	2.59298	+	8.61838i	0.101862	+	0.338562i
$649$			8.94793i			0.351237i
$650$	−63.9836	+	36.9410i	−2.50964	+	1.44894i
$651$	7.76134	+	22.2677i	0.304191	+	0.872741i
$652$	7.80445	+	13.5177i	0.305646	+	0.529394i
$653$	−11.0711	+	6.39190i	−0.433245	+	0.250134i	−0.700728	−	0.713428i	$-0.747141\pi$
$653$	−11.0711	+	6.39190i	−0.433245	+	0.250134i	0.267483	+	0.963563i	$0.413808\pi$
$654$	−3.44718	−	16.6660i	−0.134795	−	0.651693i
$655$	−52.1827			−2.03895
$656$	1.99215	−	3.45051i	0.0777806	−	0.134720i
$657$	2.90727	−	25.0211i	0.113423	−	0.976167i
$658$	−8.33673	+	6.40385i	−0.325000	+	0.249648i
$659$	−13.2530	−	22.9548i	−0.516262	−	0.894192i	−0.999822	−	0.0188808i	$-0.993990\pi$
$659$	−13.2530	−	22.9548i	−0.516262	−	0.894192i	0.483560	−	0.875311i	$-0.339344\pi$
$660$	−5.04558	−	5.66578i	−0.196399	−	0.220540i
$661$			27.5646i			1.07214i	0.844174	+	0.536069i	$0.180091\pi$
$661$			27.5646i			1.07214i	−0.844174	+	0.536069i	$0.819909\pi$
$662$	−21.1450	+	12.2081i	−0.821824	+	0.474480i
$663$	−22.1382	−	24.8594i	−0.859775	−	0.965459i
$664$		−	0.0397535i		−	0.00154274i
$665$	−44.8411	−	14.1574i	−1.73886	−	0.548999i
$666$	−12.6204	−	1.46640i	−0.489032	−	0.0568218i
$667$		−	38.6521i		−	1.49662i
$668$	−3.87830	−	6.71742i	−0.150056	−	0.259905i
$669$	9.43466	−	8.40190i	0.364765	−	0.324836i
$670$	30.9497			1.19569
$671$	7.15337	−	4.13000i	0.276153	−	0.159437i
$672$	−3.46981	−	2.99339i	−0.133851	−	0.115473i
$673$			32.6278i			1.25771i	0.777523	+	0.628854i	$0.216476\pi$
$673$			32.6278i			1.25771i	−0.777523	+	0.628854i	$0.783524\pi$
$674$	7.76773	+	4.48470i	0.299202	+	0.172744i
$675$	−49.4466	+	34.6982i	−1.90320	+	1.33554i
$676$	13.6950	−	23.7205i	0.526732	−	0.912327i
$677$	−10.8406	−	18.7764i	−0.416637	−	0.721637i	0.578961	−	0.815355i	$-0.303458\pi$
$677$	−10.8406	−	18.7764i	−0.416637	−	0.721637i	−0.995599	+	0.0937179i	$0.970125\pi$
$678$	−6.15907	+	18.6083i	−0.236538	+	0.714646i
$679$	−29.1683	+	22.4056i	−1.11938	+	0.859848i
$680$	−6.16514	−	10.6783i	−0.236422	−	0.409495i
$681$	−0.758874	−	0.852155i	−0.0290801	−	0.0326546i
$682$	−2.76404	−	4.78746i	−0.105841	−	0.183321i
$683$	20.9807	−	36.3396i	0.802804	−	1.39050i	−0.114960	−	0.993370i	$-0.536674\pi$
$683$	20.9807	−	36.3396i	0.802804	−	1.39050i	0.917764	−	0.397127i	$-0.129993\pi$
$684$	−11.1283	−	6.86743i	−0.425500	−	0.262583i
$685$	70.5903			2.69712
$686$	17.0995	−	7.11395i	0.652861	−	0.271612i
$687$	1.88880	−	0.390676i	0.0720621	−	0.0149052i
$688$	−3.14519	+	5.44764i	−0.119909	+	0.207689i
$689$	26.0703	−	15.0517i	0.993201	−	0.573425i
$690$	31.8613	+	35.7777i	1.21294	+	1.36203i
$691$	−0.748218	−	1.29595i	−0.0284635	−	0.0493003i	0.851443	−	0.524448i	$-0.175728\pi$
$691$	−0.748218	−	1.29595i	−0.0284635	−	0.0493003i	−0.879906	+	0.475147i	$0.842395\pi$
$692$	−0.882084			−0.0335318
$693$	8.52567	−	0.134234i	0.323864	−	0.00509912i
$694$	15.1730	−	8.76013i	0.575959	−	0.332530i
$695$	−4.35442	+	2.51403i	−0.165173	+	0.0953624i
$696$	−9.66435	+	1.99896i	−0.366326	+	0.0757704i
$697$			12.0488i			0.456379i
$698$	−7.55071			−0.285799
$699$	−30.4862	−	10.0905i	−1.15309	−	0.381657i
$700$	11.7556	−	28.4222i	0.444322	−	1.07426i
$701$	16.6203	+	9.59573i	0.627740	+	0.362426i	0.779876	−	0.625934i	$-0.215282\pi$
$701$	16.6203	+	9.59573i	0.627740	+	0.362426i	−0.152136	+	0.988359i	$0.548615\pi$
$702$	13.9256	−	29.9434i	0.525588	−	1.13014i
$703$	15.1315	−	10.5748i	0.570693	−	0.398836i
$704$	0.930342	+	0.537133i	0.0350636	+	0.0202440i
$705$	−18.6617	−	20.9556i	−0.702840	−	0.789234i
$706$	18.3795	+	10.6114i	0.691722	+	0.399366i
$707$	−21.5060	−	8.89502i	−0.808815	−	0.334532i
$708$	−14.1278	+	2.92217i	−0.530955	+	0.109822i
$709$	11.0038	−	19.0591i	0.413255	−	0.715778i	−0.581989	−	0.813197i	$-0.697725\pi$
$709$	11.0038	−	19.0591i	0.413255	−	0.715778i	0.995243	+	0.0974188i	$0.0310586\pi$
$710$	−30.8162	−	17.7917i	−1.15651	−	0.667712i
$711$	−12.3139	+	16.5640i	−0.461809	+	0.621200i
$712$	−0.110424	+	0.191260i	−0.00413831	+	0.00716776i
$713$	17.4541	+	30.2314i	0.653661	+	1.13217i
$714$	13.6132	+	2.59296i	0.509461	+	0.0970389i
$715$			27.8377i			1.04107i
$716$	3.25659	−	5.64058i	0.121704	−	0.210798i
$717$	27.2737	+	9.02719i	1.01855	+	0.337127i
$718$		−	14.7462i		−	0.550322i
$719$		−	3.79925i		−	0.141688i	−0.997487	−	0.0708441i	$-0.977431\pi$
$719$		−	3.79925i		−	0.141688i	0.997487	−	0.0708441i	$-0.0225693\pi$
$720$	7.29788	−	9.81671i	0.271976	−	0.365847i
$721$	−4.55825	−	34.4855i	−0.169758	−	1.28431i
$722$	18.7173	−	3.26550i	0.696585	−	0.121529i
$723$	31.5541	+	10.4440i	1.17351	+	0.388415i
$724$	16.7223	−	9.65465i	0.621481	−	0.358812i
$725$	−33.1192	−	57.3641i	−1.23002	−	2.13045i
$726$	16.7002	−	3.45425i	0.619802	−	0.128199i
$727$	11.8028	−	20.4431i	0.437742	−	0.758191i	−0.559773	−	0.828646i	$-0.689112\pi$
$727$	11.8028	−	20.4431i	0.437742	−	0.758191i	0.997515	+	0.0704549i	$0.0224451\pi$
$728$	2.20337	+	16.6696i	0.0816624	+	0.617817i
$729$	9.18266	−	25.3905i	0.340098	−	0.940390i
$730$	−29.6491	+	17.1179i	−1.09736	+	0.633563i
$731$		−	19.0225i		−	0.703571i
$732$	8.85693	+	9.94563i	0.327362	+	0.367601i
$733$	10.2965	+	17.8340i	0.380310	+	0.658716i	0.991106	−	0.133072i	$-0.0424841\pi$
$733$	10.2965	+	17.8340i	0.380310	+	0.658716i	−0.610797	+	0.791787i	$0.709151\pi$
$734$	24.9894			0.922374
$735$	22.2475	+	44.1469i	0.820613	+	1.62838i
$736$	−5.87482	−	3.39183i	−0.216549	−	0.125025i
$737$	4.07714	−	7.06182i	0.150183	−	0.260125i
$738$	−10.9721	+	4.74179i	−0.403890	+	0.174548i
$739$	14.2365	+	24.6583i	0.523698	+	0.907072i	0.999619	+	0.0275839i	$0.00878135\pi$
$739$	14.2365	+	24.6583i	0.523698	+	0.907072i	−0.475921	+	0.879488i	$0.657885\pi$
$740$	8.63413	+	14.9547i	0.317397	+	0.549747i
$741$	13.7354	+	45.9736i	0.504583	+	1.68888i
$742$	−4.78988	+	11.5807i	−0.175842	+	0.425142i
$743$	22.0790	−	38.2419i	0.809998	−	1.40296i	−0.102866	−	0.994695i	$-0.532801\pi$
$743$	22.0790	−	38.2419i	0.809998	−	1.40296i	0.912864	−	0.408263i	$-0.133865\pi$
$744$	6.65621	−	5.92759i	0.244028	−	0.217316i
$745$	72.8571			2.66928
$746$	−4.75225	+	2.74372i	−0.173992	+	0.100455i
$747$	−0.0711523	+	0.0957102i	−0.00260332	+	0.00350185i
$748$	−3.24864			−0.118782
$749$	−8.79457	+	1.16246i	−0.321346	+	0.0424752i
$750$	44.4191	+	14.7021i	1.62196	+	0.536845i
$751$	−20.3837	−	11.7685i	−0.743811	−	0.429440i	0.0796421	−	0.996824i	$-0.474622\pi$
$751$	−20.3837	−	11.7685i	−0.743811	−	0.429440i	−0.823453	+	0.567384i	$0.807956\pi$
$752$	3.44099	+	1.98666i	0.125480	+	0.0724459i
$753$	−1.01900	−	4.92654i	−0.0371344	−	0.179533i
$754$	31.3600	+	18.1057i	1.14207	+	0.659372i
$755$	41.6156	−	72.0804i	1.51455	−	2.62327i
$756$	2.99621	+	13.4173i	0.108971	+	0.487981i
$757$	−16.0174	+	27.7430i	−0.582163	+	1.00834i	0.413060	+	0.910704i	$0.364460\pi$
$757$	−16.0174	+	27.7430i	−0.582163	+	1.00834i	−0.995223	+	0.0976315i	$0.968873\pi$
$758$		−	20.9015i		−	0.759178i
$759$	12.3606	−	2.55665i	0.448662	−	0.0928007i
$760$	1.53302	+	17.7067i	0.0556085	+	0.642291i
$761$	26.4000	−	15.2420i	0.956999	−	0.552524i	0.0617510	−	0.998092i	$-0.480332\pi$
$761$	26.4000	−	15.2420i	0.956999	−	0.552524i	0.895248	+	0.445568i	$0.146998\pi$
$762$	4.25996	+	20.5956i	0.154322	+	0.746099i
$763$	−3.40658	−	25.7725i	−0.123326	−	0.933025i
$764$	−7.77719	+	4.49016i	−0.281369	+	0.162448i
$765$	−4.26933	+	36.7436i	−0.154358	+	1.32847i
$766$	−19.1265			−0.691068
$767$	45.8435	+	26.4678i	1.65531	+	0.955696i
$768$	−0.544247	+	1.64432i	−0.0196388	+	0.0593344i
$769$	24.0254	+	41.6132i	0.866377	+	1.50061i	0.865673	+	0.500610i	$0.166891\pi$
$769$	24.0254	+	41.6132i	0.866377	+	1.50061i	0.000704420		1.00000i	$0.499776\pi$
$770$	−7.05967	−	9.19049i	−0.254413	−	0.331202i
$771$	24.5651	+	27.5846i	0.884690	+	0.993436i
$772$	0.0705418	−	0.0407273i	0.00253886	−	0.00146581i
$773$	−32.6930			−1.17589			−0.587943	−	0.808903i	$-0.700062\pi$
$773$	−32.6930			−1.17589			−0.587943	+	0.808903i	$0.700062\pi$
$774$	17.3227	−	7.48629i	0.622652	−	0.269089i
$775$	51.8077	+	29.9112i	1.86099	+	1.07444i
$776$	12.0392	+	6.95084i	0.432183	+	0.249521i
$777$	−19.0650	−	3.63137i	−0.683951	−	0.130275i
$778$		−	30.6695i		−	1.09955i
$779$	7.35391	−	15.7334i	0.263481	−	0.563707i
$780$	−43.9526	+	9.09110i	−1.57376	+	0.325514i
$781$	−8.11909	+	4.68756i	−0.290524	+	0.167734i
$782$	20.5141			0.733584
$783$	26.8456	+	12.4849i	0.959384	+	0.446175i
$784$	−4.95487	−	4.94462i	−0.176960	−	0.176594i
$785$	−51.8814	+	29.9538i	−1.85173	+	1.06910i
$786$	−21.0441	−	6.96529i	−0.750617	−	0.248444i
$787$	−11.3817	−	6.57120i	−0.405712	−	0.234238i	0.283234	−	0.959051i	$-0.408593\pi$
$787$	−11.3817	−	6.57120i	−0.405712	−	0.234238i	−0.688946	+	0.724813i	$0.741926\pi$
$788$			22.2690i			0.793301i
$789$	−10.0798	−	48.7329i	−0.358852	−	1.73494i
$790$	28.0522			0.998054
$791$	−11.4437	+	27.6679i	−0.406890	+	0.983758i
$792$	−1.27850	−	2.95836i	−0.0454296	−	0.105121i
$793$		−	48.8658i		−	1.73528i
$794$	13.3341			0.473211
$795$	−31.7577	−	10.5114i	−1.12633	−	0.372799i
$796$	3.50713			0.124307
$797$	−25.4281			−0.900709			−0.450354	−	0.892850i	$-0.648702\pi$
$797$	−25.4281			−0.900709			−0.450354	+	0.892850i	$0.648702\pi$
$798$	−16.1937	−	11.6947i	−0.573249	−	0.413987i
$799$	−12.0155			−0.425078
$800$	−11.6252			−0.411013
$801$	0.608179	−	0.262834i	0.0214889	−	0.00928680i
$802$	2.19502			0.0775088
$803$			9.02006i			0.318311i
$804$	12.4813	+	4.13114i	0.440182	+	0.145694i
$805$	44.5797	+	58.0351i	1.57123	+	2.04547i
$806$	−32.7039			−1.15195
$807$	−10.7277	+	2.21890i	−0.377632	+	0.0781088i
$808$			8.79633i			0.309454i
$809$	9.16404	+	5.29086i	0.322191	+	0.186017i	0.652369	−	0.757902i	$-0.273775\pi$
$809$	9.16404	+	5.29086i	0.322191	+	0.186017i	−0.330178	+	0.943919i	$0.607109\pi$
$810$	−35.1406	+	10.5726i	−1.23471	+	0.371484i
$811$	−12.0831	+	6.97618i	−0.424295	+	0.244967i	−0.696913	−	0.717156i	$-0.745444\pi$
$811$	−12.0831	+	6.97618i	−0.424295	+	0.244967i	0.272618	+	0.962122i	$0.412110\pi$
$812$	−14.9450	+	1.97542i	−0.524468	+	0.0693236i
$813$	6.11303	−	18.4692i	0.214393	−	0.647742i
$814$	4.54964			0.159465
$815$	−55.1171	+	31.8219i	−1.93067	+	1.11467i
$816$	−1.06092	−	5.12924i	−0.0371398	−	0.179559i
$817$	−11.6103	+	24.8397i	−0.406193	+	0.869032i
$818$		−	3.79885i		−	0.132824i
$819$	24.5310	−	44.0772i	0.857184	−	1.54018i
$820$	14.0691	+	8.12282i	0.491315	+	0.283661i
$821$	9.80498	+	5.66091i	0.342196	+	0.197567i	0.661243	−	0.750172i	$-0.270029\pi$
$821$	9.80498	+	5.66091i	0.342196	+	0.197567i	−0.319047	+	0.947739i	$0.603363\pi$
$822$	28.4674	+	9.42232i	0.992916	+	0.328641i
$823$	22.1713			0.772843			0.386422	−	0.922322i	$-0.373711\pi$
$823$	22.1713			0.772843			0.386422	+	0.922322i	$0.373711\pi$
$824$	−11.3862	+	6.57382i	−0.396657	+	0.229010i
$825$	16.1539	−	14.3856i	0.562406	−	0.500843i
$826$	−21.8473	+	2.88776i	−0.760165	+	0.100478i
$827$	20.8618	+	36.1336i	0.725434	+	1.25649i	0.958795	+	0.284099i	$0.0916943\pi$
$827$	20.8618	+	36.1336i	0.725434	+	1.25649i	−0.233361	+	0.972390i	$0.574972\pi$
$828$	8.07335	+	18.6811i	0.280568	+	0.649213i
$829$	30.2594	+	17.4703i	1.05095	+	0.606769i	0.922916	−	0.385001i	$-0.125799\pi$
$829$	30.2594	+	17.4703i	1.05095	+	0.606769i	0.128038	+	0.991769i	$0.459132\pi$
$830$	0.162091			0.00562626
$831$	15.9895	+	17.9549i	0.554669	+	0.622849i
$832$	5.50387	−	3.17766i	0.190812	−	0.110166i
$833$	20.4527	+	5.45761i	0.708645	+	0.189095i
$834$	−2.09161	+	0.432625i	−0.0724264	+	0.0149806i
$835$	27.3896	−	15.8134i	0.947857	−	0.547245i
$836$	4.24211	+	1.98279i	0.146716	+	0.0685764i
$837$	−26.6348	+	2.35768i	−0.920634	+	0.0814934i
$838$		−	16.5211i		−	0.570711i
$839$	2.18245	−	3.78011i	0.0753465	−	0.130504i	−0.825890	−	0.563831i	$-0.809327\pi$
$839$	2.18245	−	3.78011i	0.0753465	−	0.130504i	0.901237	+	0.433327i	$0.142660\pi$
$840$	12.2053	−	14.1478i	0.421121	−	0.488147i
$841$	−1.73258	+	3.00092i	−0.0597442	+	0.103480i
$842$	7.50592	+	4.33355i	0.258671	+	0.149344i
$843$	16.8455	−	3.48430i	0.580190	−	0.120006i
$844$	4.52926	+	2.61497i	0.155904	+	0.0900110i
$845$	96.7180	+	55.8402i	3.32720	+	1.92096i
$846$	−4.72870	−	10.9419i	−0.162576	−	0.376189i
$847$	25.8253	−	3.41356i	0.887368	−	0.117291i
$848$	4.73673			0.162660
$849$	−8.28803	+	1.71429i	−0.284444	+	0.0588341i
$850$	30.4453	−	17.5776i	1.04427	−	0.602907i
$851$	−28.7296			−0.984837
$852$	−10.0526	−	11.2883i	−0.344398	−	0.386731i
$853$	−13.8221	+	23.9406i	−0.473260	+	0.819710i	−0.999532	−	0.0306066i	$-0.990256\pi$
$853$	−13.8221	+	23.9406i	−0.473260	+	0.819710i	0.526272	+	0.850316i	$0.323589\pi$
$854$	12.3924	+	16.1329i	0.424061	+	0.552055i
$855$	28.0013	−	45.3744i	0.957624	−	1.55177i
$856$	1.67647	+	2.90374i	0.0573007	+	0.0992476i
$857$	−6.56082	−	11.3637i	−0.224113	−	0.388176i	0.731940	−	0.681369i	$-0.238615\pi$
$857$	−6.56082	−	11.3637i	−0.224113	−	0.388176i	−0.956053	+	0.293194i	$0.905282\pi$
$858$	−3.71574	+	11.2263i	−0.126853	+	0.383259i
$859$	19.0279	−	32.9574i	0.649225	−	1.12449i	−0.334083	−	0.942544i	$-0.608427\pi$
$859$	19.0279	−	32.9574i	0.649225	−	1.12449i	0.983308	−	0.181947i	$-0.0582399\pi$
$860$	−22.2122	−	12.8242i	−0.757430	−	0.437302i
$861$	−17.2411	+	6.00934i	−0.587576	+	0.204798i
$862$	4.88374			0.166341
$863$	−22.1882	−	38.4312i	−0.755297	−	1.30821i	−0.945227	−	0.326415i	$-0.894159\pi$
$863$	−22.1882	−	38.4312i	−0.755297	−	1.30821i	0.189930	−	0.981798i	$-0.439174\pi$
$864$	4.25339	−	2.98474i	0.144703	−	0.101543i
$865$		−	3.59661i		−	0.122288i
$866$	9.13958	−	5.27674i	0.310576	−	0.179311i
$867$	−9.04832	−	10.1605i	−0.307297	−	0.345070i
$868$	10.7971	−	8.29376i	0.366476	−	0.281509i
$869$	3.69544	−	6.40069i	0.125359	−	0.217129i
$870$	−8.15057	−	39.4054i	−0.276330	−	1.33597i
$871$	−24.1202	−	41.7774i	−0.817282	−	1.41557i
$872$	−8.50939	+	4.91290i	−0.288164	+	0.166372i
$873$	−16.5446	−	38.2830i	−0.559951	−	1.29568i
$874$	−26.7876	−	12.5207i	−0.906104	−	0.423520i
$875$	66.0451	+	27.3167i	2.23273	+	0.923475i
$876$	−14.2417	+	2.94573i	−0.481182	+	0.0995270i
$877$			9.22011i			0.311341i	0.987809	+	0.155671i	$0.0497538\pi$
$877$			9.22011i			0.311341i	−0.987809	+	0.155671i	$0.950246\pi$
$878$			9.52603i			0.321488i
$879$	−2.84295	+	8.58934i	−0.0958903	+	0.289711i
$880$	−2.19011	+	3.79338i	−0.0738286	+	0.127875i
$881$		−	7.14044i		−	0.240568i	−0.992740	−	0.120284i	$-0.961620\pi$
$881$		−	7.14044i		−	0.240568i	0.992740	−	0.120284i	$-0.0383804\pi$
$882$	3.07923	+	20.7730i	0.103683	+	0.699464i
$883$	−21.5312	−	37.2932i	−0.724583	−	1.25501i	−0.959145	−	0.282914i	$-0.908699\pi$
$883$	−21.5312	−	37.2932i	−0.724583	−	1.25501i	0.234562	−	0.972101i	$-0.424634\pi$
$884$	−9.60940	+	16.6440i	−0.323199	+	0.559797i
$885$	−11.9149	−	57.6047i	−0.400514	−	1.93636i
$886$	25.2198	+	14.5607i	0.847276	+	0.489175i
$887$	−6.56550	+	11.3718i	−0.220448	+	0.381827i	−0.954944	−	0.296786i	$-0.904085\pi$
$887$	−6.56550	+	11.3718i	−0.220448	+	0.381827i	0.734496	+	0.678613i	$0.237419\pi$
$888$	1.48580	+	7.18338i	0.0498602	+	0.241058i
$889$	4.20979	+	31.8492i	0.141192	+	1.06819i
$890$	−0.779843	−	0.450242i	−0.0261404	−	0.0150922i
$891$	−2.21686	+	9.41082i	−0.0742677	+	0.315274i
$892$	−6.31674	−	3.64697i	−0.211500	−	0.122110i
$893$	15.6900	+	7.33362i	0.525045	+	0.245410i
$894$	29.3816	+	9.72489i	0.982668	+	0.325249i
$895$	22.9989	+	13.2784i	0.768769	+	0.443849i
$896$	−1.01122	+	2.44488i	−0.0337825	+	0.0816777i
$897$	23.4638	−	70.8906i	0.783433	−	2.36697i
$898$	−37.7884			−1.26102
$899$		−	29.3205i		−	0.977894i
$900$	27.9887	+	20.8072i	0.932958	+	0.693574i
$901$	−12.4050	+	7.16206i	−0.413272	+	0.238603i
$902$	3.70677	−	2.14011i	0.123422	−	0.0712577i
$903$	27.2201	−	9.48750i	0.905830	−	0.315724i
$904$	11.3167			0.376387
$905$	39.3659	+	68.1837i	1.30857	+	2.26650i
$906$	26.4038	−	23.5135i	0.877209	−	0.781185i
$907$	22.6413	−	13.0719i	0.751791	−	0.434047i	−0.0745496	−	0.997217i	$-0.523752\pi$
$907$	22.6413	−	13.0719i	0.751791	−	0.434047i	0.826341	+	0.563170i	$0.190419\pi$
$908$	−0.329401	+	0.570539i	−0.0109315	+	0.0189340i
$909$	15.7440	−	21.1779i	0.522195	−	0.702428i
$910$	−67.9687	+	8.98403i	−2.25314	+	0.297818i
$911$	−32.7316			−1.08445			−0.542224	−	0.840234i	$-0.682417\pi$
$911$	−32.7316			−1.08445			−0.542224	+	0.840234i	$0.682417\pi$
$912$	−1.74525	+	7.34535i	−0.0577909	+	0.243229i
$913$	0.0213529	−	0.0369844i	0.000706679	−	0.00122400i
$914$	−2.19166	−	3.79607i	−0.0724937	−	0.125563i
$915$	−40.5523	+	36.1133i	−1.34062	+	1.19387i
$916$	−0.556790	−	0.964389i	−0.0183969	−	0.0318643i
$917$	−31.2896	−	12.9416i	−1.03327	−	0.427370i
$918$	−6.62622	+	14.2480i	−0.218698	+	0.470254i
$919$	−19.0561	−	33.0061i	−0.628603	−	1.08877i	−0.987832	−	0.155522i	$-0.950294\pi$
$919$	−19.0561	−	33.0061i	−0.628603	−	1.08877i	0.359230	−	0.933249i	$-0.383039\pi$
$920$	13.8299	−	23.9540i	0.455957	−	0.789741i
$921$	8.07733	−	7.19315i	0.266157	−	0.237022i
$922$	11.0809	+	6.39758i	0.364931	+	0.210693i
$923$			55.4628i			1.82558i
$924$	−1.62027	−	4.64863i	−0.0533028	−	0.152929i
$925$	−42.6379	+	24.6170i	−1.40193	+	0.809403i
$926$	1.81932			0.0597866
$927$	39.1794	+	4.55235i	1.28682	+	0.149519i
$928$	2.84891	+	4.93446i	0.0935201	+	0.161982i
$929$		−	36.0008i		−	1.18115i	−0.806983	−	0.590574i	$-0.798901\pi$
$929$		−	36.0008i		−	1.18115i	0.806983	−	0.590574i	$-0.201099\pi$
$930$	24.1692	+	27.1400i	0.792538	+	0.889957i
$931$	−23.3764	−	19.6098i	−0.766129	−	0.642687i
$932$			18.5403i			0.607307i
$933$	20.0349	−	17.8418i	0.655914	−	0.584114i
$934$	15.3869	−	8.88363i	0.503475	−	0.290681i
$935$		−	13.2460i		−	0.433191i
$936$	−18.9385	−	2.20052i	−0.619026	−	0.0719261i
$937$	−24.8204	−	42.9901i	−0.810846	−	1.40443i	−0.912273	−	0.409583i	$-0.865674\pi$
$937$	−24.8204	−	42.9901i	−0.810846	−	1.40443i	0.101427	−	0.994843i	$-0.467659\pi$
$938$	18.5580	+	7.67572i	0.605940	+	0.250621i
$939$	6.04995	+	6.79361i	0.197433	+	0.221701i
$940$	−8.10039	+	14.0303i	−0.264206	+	0.457618i
$941$	−3.92865			−0.128070			−0.0640351	−	0.997948i	$-0.520397\pi$
$941$	−3.92865			−0.128070			−0.0640351	+	0.997948i	$0.520397\pi$
$942$	−24.9208	+	5.15458i	−0.811963	+	0.167945i
$943$	−23.4071	+	13.5141i	−0.762241	+	0.440080i
$944$	4.16467	+	7.21341i	0.135548	+	0.234777i
$945$	−54.7075	+	12.2168i	−1.77964	+	0.397412i
$946$	−5.85222	+	3.37878i	−0.190272	+	0.109854i
$947$			3.69623i			0.120111i	0.998195	+	0.0600556i	$0.0191278\pi$
$947$			3.69623i			0.120111i	−0.998195	+	0.0600556i	$0.980872\pi$
$948$	11.3128	+	3.74438i	0.367423	+	0.121612i
$949$	46.2131	+	26.6812i	1.50014	+	0.866107i
$950$	−50.4843	+	4.37084i	−1.63793	+	0.141809i
$951$	9.31120	+	10.4557i	0.301936	+	0.339051i
$952$	−1.04843	−	7.93190i	−0.0339798	−	0.257074i
$953$	−8.58734	+	14.8737i	−0.278171	+	0.481806i	−0.970930	−	0.239363i	$-0.923062\pi$
$953$	−8.58734	+	14.8737i	−0.278171	+	0.481806i	0.692759	+	0.721169i	$0.256395\pi$
$954$	−11.4041	−	8.47797i	−0.369222	−	0.274484i
$955$	−18.3082	−	31.7107i	−0.592439	−	1.02613i
$956$		−	16.5866i		−	0.536448i
$957$	−10.0649	−	3.33133i	−0.325351	−	0.107687i
$958$			14.5072i			0.468705i
$959$	42.3271	+	17.5068i	1.36681	+	0.565325i
$960$	−6.70456	−	2.21912i	−0.216389	−	0.0716216i
$961$	−2.25977	−	3.91404i	−0.0728958	−	0.126259i
$962$	13.4577	−	23.3095i	0.433895	−	0.751528i
$963$	1.16095	−	9.99161i	0.0374111	−	0.321975i
$964$		−	19.1897i		−	0.618059i
$965$	0.166062	+	0.287627i	0.00534572	+	0.00925905i
$966$	10.2315	+	29.3547i	0.329192	+	0.944471i
$967$	9.14064	−	15.8321i	0.293943	−	0.509125i	−0.680795	−	0.732474i	$-0.738366\pi$
$967$	9.14064	−	15.8321i	0.293943	−	0.509125i	0.974739	+	0.223349i	$0.0716990\pi$
$968$	−4.92298	−	8.52684i	−0.158230	−	0.274063i
$969$	−6.53572	−	21.8756i	−0.209958	−	0.702746i
$970$	−28.3414	+	49.0887i	−0.909987	+	1.57614i
$971$	6.83298			0.219281			0.109640	−	0.993971i	$-0.465030\pi$
$971$	6.83298			0.219281			0.109640	+	0.993971i	$0.465030\pi$
$972$	−15.5826	−	0.426839i	−0.499813	−	0.0136909i
$973$	−3.23448	+	0.427530i	−0.103693	+	0.0137060i
$974$	2.57977	+	1.48943i	0.0826611	+	0.0477244i
$975$	−25.9199	−	125.315i	−0.830102	−	4.01328i
$976$	3.84448	−	6.65884i	0.123059	−	0.213144i
$977$	10.4175	−	18.0437i	0.333286	−	0.577268i	−0.649868	−	0.760047i	$-0.725176\pi$
$977$	10.4175	−	18.0437i	0.333286	−	0.577268i	0.983154	+	0.182779i	$0.0585092\pi$
$978$	−26.4750	+	5.47605i	−0.846577	+	0.175105i
$979$	−0.205464	+	0.118625i	−0.00656666	+	0.00379126i
$980$	20.1612	−	20.2030i	0.644026	−	0.645361i
$981$	29.2804	+	3.40216i	0.934851	+	0.108623i
$982$	−21.7386	−	12.5508i	−0.693706	−	0.400511i
$983$	−9.33445	−	16.1677i	−0.297723	−	0.515671i	0.677892	−	0.735162i	$-0.262894\pi$
$983$	−9.33445	−	16.1677i	−0.297723	−	0.515671i	−0.975615	+	0.219491i	$0.929560\pi$
$984$	4.58953	+	5.15368i	0.146309	+	0.164293i
$985$	−90.7998			−2.89312
$986$	−14.9221	−	8.61525i	−0.475215	−	0.274365i
$987$	−5.99276	−	17.1935i	−0.190752	−	0.547277i
$988$	22.7067	−	15.8688i	0.722395	−	0.504854i
$989$	36.9549	−	21.3359i	1.17510	−	0.678444i
$990$	12.0624	−	5.21297i	0.383369	−	0.165679i
$991$	35.6196	−	20.5650i	1.13149	−	0.653269i	0.187184	−	0.982325i	$-0.440064\pi$
$991$	35.6196	−	20.5650i	1.13149	−	0.653269i	0.944310	+	0.329056i	$0.106731\pi$
$992$	−4.45649	−	2.57296i	−0.141494	−	0.0816915i
$993$	−8.56589	−	41.4134i	−0.271830	−	1.31421i
$994$	−14.0654	−	18.3108i	−0.446129	−	0.580784i
$995$			14.3000i			0.453340i
$996$	0.0653676	+	0.0216357i	0.00207125	+	0.000685555i
$997$	−37.6834			−1.19344			−0.596722	−	0.802448i	$-0.703531\pi$
$997$	−37.6834			−1.19344			−0.596722	+	0.802448i	$0.703531\pi$
$998$	−20.7249			−0.656035
$999$	9.27986	−	19.9540i	0.293602	−	0.631315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.p.d.179.11	yes	50
3.2	odd	2		798.2.p.c.179.3	yes	50
7.2	even	3		798.2.bh.c.65.7	yes	50
19.12	odd	6		798.2.bh.d.221.19	yes	50
21.2	odd	6		798.2.bh.d.65.19	yes	50
57.50	even	6		798.2.bh.c.221.7	yes	50
133.107	odd	6		798.2.p.c.107.3	✓	50
399.107	even	6	inner	798.2.p.d.107.11	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.p.c.107.3	✓	50	133.107	odd	6
798.2.p.c.179.3	yes	50	3.2	odd	2
798.2.p.d.107.11	yes	50	399.107	even	6	inner
798.2.p.d.179.11	yes	50	1.1	even	1	trivial
798.2.bh.c.65.7	yes	50	7.2	even	3
798.2.bh.c.221.7	yes	50	57.50	even	6
798.2.bh.d.65.19	yes	50	21.2	odd	6
798.2.bh.d.221.19	yes	50	19.12	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.544247 + 1.64432i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(-0.544247 + 1.64432i) q^{6} +(-1.01122 + 2.44488i) q^{7} +1.00000 q^{8} +(-2.40759 - 1.78984i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.544247 + 1.64432i) q^{3} +1.00000 q^{4} +4.07740i q^{5} +(-0.544247 + 1.64432i) q^{6} +(-1.01122 + 2.44488i) q^{7} +1.00000 q^{8} +(-2.40759 - 1.78984i) q^{9} +4.07740i q^{10} +(0.930342 + 0.537133i) q^{11} +(-0.544247 + 1.64432i) q^{12} +(5.50387 - 3.17766i) q^{13} +(-1.01122 + 2.44488i) q^{14} +(-6.70456 - 2.21912i) q^{15} +1.00000 q^{16} +(-2.61890 + 1.51203i) q^{17} +(-2.40759 - 1.78984i) q^{18} +(4.34265 - 0.375980i) q^{19} +4.07740i q^{20} +(-3.46981 - 2.99339i) q^{21} +(0.930342 + 0.537133i) q^{22} +(-5.87482 - 3.39183i) q^{23} +(-0.544247 + 1.64432i) q^{24} -11.6252 q^{25} +(5.50387 - 3.17766i) q^{26} +(4.25339 - 2.98474i) q^{27} +(-1.01122 + 2.44488i) q^{28} +(2.84891 + 4.93446i) q^{29} +(-6.70456 - 2.21912i) q^{30} +(-4.45649 - 2.57296i) q^{31} +1.00000 q^{32} +(-1.38956 + 1.23745i) q^{33} +(-2.61890 + 1.51203i) q^{34} +(-9.96876 - 4.12315i) q^{35} +(-2.40759 - 1.78984i) q^{36} +(3.66771 - 2.11756i) q^{37} +(4.34265 - 0.375980i) q^{38} +(2.22963 + 10.7796i) q^{39} +4.07740i q^{40} +(1.99215 - 3.45051i) q^{41} +(-3.46981 - 2.99339i) q^{42} +(-3.14519 + 5.44764i) q^{43} +(0.930342 + 0.537133i) q^{44} +(7.29788 - 9.81671i) q^{45} +(-5.87482 - 3.39183i) q^{46} +(3.44099 + 1.98666i) q^{47} +(-0.544247 + 1.64432i) q^{48} +(-4.95487 - 4.94462i) q^{49} -11.6252 q^{50} +(-1.06092 - 5.12924i) q^{51} +(5.50387 - 3.17766i) q^{52} +4.73673 q^{53} +(4.25339 - 2.98474i) q^{54} +(-2.19011 + 3.79338i) q^{55} +(-1.01122 + 2.44488i) q^{56} +(-1.74525 + 7.34535i) q^{57} +(2.84891 + 4.93446i) q^{58} +(4.16467 + 7.21341i) q^{59} +(-6.70456 - 2.21912i) q^{60} +(3.84448 - 6.65884i) q^{61} +(-4.45649 - 2.57296i) q^{62} +(6.81053 - 4.07635i) q^{63} +1.00000 q^{64} +(12.9566 + 22.4415i) q^{65} +(-1.38956 + 1.23745i) q^{66} -7.59056i q^{67} +(-2.61890 + 1.51203i) q^{68} +(8.77462 - 7.81411i) q^{69} +(-9.96876 - 4.12315i) q^{70} +(-4.36350 + 7.55780i) q^{71} +(-2.40759 - 1.78984i) q^{72} +(4.19824 + 7.27157i) q^{73} +(3.66771 - 2.11756i) q^{74} +(6.32699 - 19.1156i) q^{75} +(4.34265 - 0.375980i) q^{76} +(-2.25401 + 1.73141i) q^{77} +(2.22963 + 10.7796i) q^{78} -6.87993i q^{79} +4.07740i q^{80} +(2.59298 + 8.61838i) q^{81} +(1.99215 - 3.45051i) q^{82} -0.0397535i q^{83} +(-3.46981 - 2.99339i) q^{84} +(-6.16514 - 10.6783i) q^{85} +(-3.14519 + 5.44764i) q^{86} +(-9.66435 + 1.99896i) q^{87} +(0.930342 + 0.537133i) q^{88} +(-0.110424 + 0.191260i) q^{89} +(7.29788 - 9.81671i) q^{90} +(2.20337 + 16.6696i) q^{91} +(-5.87482 - 3.39183i) q^{92} +(6.65621 - 5.92759i) q^{93} +(3.44099 + 1.98666i) q^{94} +(1.53302 + 17.7067i) q^{95} +(-0.544247 + 1.64432i) q^{96} +(12.0392 + 6.95084i) q^{97} +(-4.95487 - 4.94462i) q^{98} +(-1.27850 - 2.95836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

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