LMFDB - Embedded newform 756.2.ci.a.95.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.14
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35369 + 0.409293i) q^{2} +(-1.06364 + 1.36699i) q^{3} +(1.66496 - 1.10811i) q^{4} +(4.32435 + 0.762500i) q^{5} +(0.880342 - 2.28583i) q^{6} +(-0.0657043 + 2.64494i) q^{7} +(-1.80029 + 2.18150i) q^{8} +(-0.737329 - 2.90798i) q^{9} +O(q^{10})$	\(q+(-1.35369 + 0.409293i) q^{2} +(-1.06364 + 1.36699i) q^{3} +(1.66496 - 1.10811i) q^{4} +(4.32435 + 0.762500i) q^{5} +(0.880342 - 2.28583i) q^{6} +(-0.0657043 + 2.64494i) q^{7} +(-1.80029 + 2.18150i) q^{8} +(-0.737329 - 2.90798i) q^{9} +(-6.16592 + 0.737740i) q^{10} +(0.136172 + 0.772270i) q^{11} +(-0.256138 + 3.45462i) q^{12} +(-0.717990 + 4.07192i) q^{13} +(-0.993611 - 3.60732i) q^{14} +(-5.64190 + 5.10032i) q^{15} +(1.54417 - 3.68992i) q^{16} +(-3.91513 + 2.26040i) q^{17} +(2.18833 + 3.63472i) q^{18} +(-2.74447 - 1.58452i) q^{19} +(8.04480 - 3.52234i) q^{20} +(-3.54572 - 2.90308i) q^{21} +(-0.500420 - 0.989680i) q^{22} +(-1.15585 - 0.969872i) q^{23} +(-1.06722 - 4.78132i) q^{24} +(13.4202 + 4.88454i) q^{25} +(-0.694675 - 5.80599i) q^{26} +(4.75944 + 2.08513i) q^{27} +(2.82149 + 4.47651i) q^{28} +(-0.739473 + 0.130389i) q^{29} +(5.54985 - 9.21345i) q^{30} +(3.60690 + 0.635994i) q^{31} +(-0.580064 + 5.62704i) q^{32} +(-1.20052 - 0.635273i) q^{33} +(4.37470 - 4.66232i) q^{34} +(-2.30089 + 11.3875i) q^{35} +(-4.44999 - 4.02462i) q^{36} +8.87259 q^{37} +(4.36370 + 1.02166i) q^{38} +(-4.80260 - 5.31256i) q^{39} +(-9.44850 + 8.06085i) q^{40} +(-8.42798 - 1.48608i) q^{41} +(5.98802 + 2.47864i) q^{42} +(3.14209 + 3.74460i) q^{43} +(1.08248 + 1.13490i) q^{44} +(-0.971138 - 13.1373i) q^{45} +(1.96162 + 0.839826i) q^{46} +(-1.69271 - 9.59986i) q^{47} +(3.40165 + 6.03562i) q^{48} +(-6.99137 - 0.347567i) q^{49} +(-20.1660 - 1.11937i) q^{50} +(1.07435 - 7.75620i) q^{51} +(3.31673 + 7.57519i) q^{52} +(2.86627 + 1.65484i) q^{53} +(-7.29624 - 0.874612i) q^{54} +3.44340i q^{55} +(-5.65164 - 4.90500i) q^{56} +(5.08516 - 2.06630i) q^{57} +(0.947650 - 0.479168i) q^{58} +(-6.61842 + 2.40891i) q^{59} +(-3.74178 + 14.7437i) q^{60} +(0.495742 + 2.81149i) q^{61} +(-5.14294 + 0.615342i) q^{62} +(7.73986 - 1.75912i) q^{63} +(-1.51788 - 7.85468i) q^{64} +(-6.20968 + 17.0610i) q^{65} +(1.88515 + 0.368596i) q^{66} +(2.94761 - 3.51283i) q^{67} +(-4.01374 + 8.10187i) q^{68} +(2.55522 - 0.548438i) q^{69} +(-1.54615 - 16.3569i) q^{70} +(-0.788950 + 1.36650i) q^{71} +(7.67117 + 3.62674i) q^{72} -14.2202 q^{73} +(-12.0107 + 3.63149i) q^{74} +(-20.9514 + 13.1498i) q^{75} +(-6.32526 + 0.403025i) q^{76} +(-2.05155 + 0.309425i) q^{77} +(8.67563 + 5.22589i) q^{78} +(8.87571 + 10.5777i) q^{79} +(9.49110 - 14.7791i) q^{80} +(-7.91269 + 4.28828i) q^{81} +(12.0171 - 1.43782i) q^{82} +(0.0158260 + 0.0897540i) q^{83} +(-9.12041 - 0.904452i) q^{84} +(-18.6539 + 6.78948i) q^{85} +(-5.78607 - 3.78300i) q^{86} +(0.608294 - 1.14954i) q^{87} +(-1.92986 - 1.09325i) q^{88} +(6.00926 + 3.46945i) q^{89} +(6.69165 + 17.3864i) q^{90} +(-10.7228 - 2.16658i) q^{91} +(-2.99917 - 0.333985i) q^{92} +(-4.70585 + 4.25413i) q^{93} +(6.22057 + 12.3024i) q^{94} +(-10.6599 - 8.94469i) q^{95} +(-7.07513 - 6.77810i) q^{96} +(-0.776264 + 0.651363i) q^{97} +(9.60640 - 2.39102i) q^{98} +(2.14534 - 0.965402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.35369	+	0.409293i	−0.957204	+	0.289414i
$2$	−1.35369	+	0.409293i	−0.957204	+	0.289414i
$3$	−1.06364	+	1.36699i	−0.614094	+	0.789233i
$3$	−1.06364	+	1.36699i	−0.614094	+	0.789233i
$4$	1.66496	−	1.10811i	0.832479	−	0.554057i
$5$	4.32435	+	0.762500i	1.93391	+	0.341000i	0.999869	−	0.0161680i	$-0.00514664\pi$
$5$	4.32435	+	0.762500i	1.93391	+	0.341000i	0.934040	+	0.357168i	$0.116258\pi$
$6$	0.880342	−	2.28583i	0.359398	−	0.933184i
$7$	−0.0657043	+	2.64494i	−0.0248339	+	0.999692i
$7$	−0.0657043	+	2.64494i	−0.0248339	+	0.999692i
$8$	−1.80029	+	2.18150i	−0.636500	+	0.771277i
$9$	−0.737329	−	2.90798i	−0.245776	−	0.969327i
$10$	−6.16592	+	0.737740i	−1.94984	+	0.233294i
$11$	0.136172	+	0.772270i	0.0410574	+	0.232848i	0.998430	−	0.0560064i	$-0.0178367\pi$
$11$	0.136172	+	0.772270i	0.0410574	+	0.232848i	−0.957373	+	0.288854i	$0.906726\pi$
$12$	−0.256138	+	3.45462i	−0.0739407	+	0.997263i
$13$	−0.717990	+	4.07192i	−0.199135	+	1.12935i	0.707272	+	0.706942i	$0.249926\pi$
$13$	−0.717990	+	4.07192i	−0.199135	+	1.12935i	−0.906406	+	0.422407i	$0.861185\pi$
$14$	−0.993611	−	3.60732i	−0.265554	−	0.964096i
$15$	−5.64190	+	5.10032i	−1.45673	+	1.31690i
$16$	1.54417	−	3.68992i	0.386042	−	0.922481i
$17$	−3.91513	+	2.26040i	−0.949558	+	0.548227i	−0.892944	−	0.450169i	$-0.851364\pi$
$17$	−3.91513	+	2.26040i	−0.949558	+	0.548227i	−0.0566142	+	0.998396i	$0.518030\pi$
$18$	2.18833	+	3.63472i	0.515795	+	0.856712i
$19$	−2.74447	−	1.58452i	−0.629625	−	0.363514i	0.150982	−	0.988537i	$-0.451756\pi$
$19$	−2.74447	−	1.58452i	−0.629625	−	0.363514i	−0.780607	+	0.625022i	$0.785090\pi$
$20$	8.04480	−	3.52234i	1.79887	−	0.787620i
$21$	−3.54572	−	2.90308i	−0.773739	−	0.633505i
$22$	−0.500420	−	0.989680i	−0.106690	−	0.211000i
$23$	−1.15585	−	0.969872i	−0.241011	−	0.202232i	0.514279	−	0.857623i	$-0.328060\pi$
$23$	−1.15585	−	0.969872i	−0.241011	−	0.202232i	−0.755290	+	0.655391i	$0.772504\pi$
$24$	−1.06722	−	4.78132i	−0.217846	−	0.975983i
$25$	13.4202	+	4.88454i	2.68403	+	0.976908i
$26$	−0.694675	−	5.80599i	−0.136237	−	1.13865i
$27$	4.75944	+	2.08513i	0.915954	+	0.401283i
$28$	2.82149	+	4.47651i	0.533212	+	0.845981i
$29$	−0.739473	+	0.130389i	−0.137317	+	0.0242126i	−0.241884	−	0.970305i	$-0.577765\pi$
$29$	−0.739473	+	0.130389i	−0.137317	+	0.0242126i	0.104567	+	0.994518i	$0.466654\pi$
$30$	5.54985	−	9.21345i	1.01326	−	1.68214i
$31$	3.60690	+	0.635994i	0.647819	+	0.114228i	0.487896	−	0.872902i	$-0.337764\pi$
$31$	3.60690	+	0.635994i	0.647819	+	0.114228i	0.159922	+	0.987130i	$0.448876\pi$
$32$	−0.580064	+	5.62704i	−0.102542	+	0.994729i
$33$	−1.20052	−	0.635273i	−0.208984	−	0.110587i
$34$	4.37470	−	4.66232i	0.750256	−	0.799581i
$35$	−2.30089	+	11.3875i	−0.388922	+	1.92484i
$36$	−4.44999	−	4.02462i	−0.741666	−	0.670770i
$37$	8.87259			1.45865			0.729323	−	0.684170i	$-0.239835\pi$
$37$	8.87259			1.45865			0.729323	+	0.684170i	$0.239835\pi$
$38$	4.36370	+	1.02166i	0.707886	+	0.165735i
$39$	−4.80260	−	5.31256i	−0.769031	−	0.850690i
$40$	−9.44850	+	8.06085i	−1.49394	+	1.27453i
$41$	−8.42798	−	1.48608i	−1.31623	−	0.232087i	−0.528934	−	0.848663i	$-0.677408\pi$
$41$	−8.42798	−	1.48608i	−1.31623	−	0.232087i	−0.787296	+	0.616576i	$0.788519\pi$
$42$	5.98802	+	2.47864i	0.923971	+	0.382462i
$43$	3.14209	+	3.74460i	0.479165	+	0.571047i	0.950427	−	0.310946i	$-0.100646\pi$
$43$	3.14209	+	3.74460i	0.479165	+	0.571047i	−0.471263	+	0.881993i	$0.656202\pi$
$44$	1.08248	+	1.13490i	0.163190	+	0.171093i
$45$	−0.971138	−	13.1373i	−0.144769	−	1.95840i
$46$	1.96162	+	0.839826i	0.289226	+	0.123826i
$47$	−1.69271	−	9.59986i	−0.246908	−	1.40028i	−0.816020	−	0.578023i	$-0.803824\pi$
$47$	−1.69271	−	9.59986i	−0.246908	−	1.40028i	0.569113	−	0.822260i	$-0.307287\pi$
$48$	3.40165	+	6.03562i	0.490986	+	0.871167i
$49$	−6.99137	−	0.347567i	−0.998767	−	0.0496525i
$50$	−20.1660	−	1.11937i	−2.85190	−	0.158303i
$51$	1.07435	−	7.75620i	0.150439	−	1.08609i
$52$	3.31673	+	7.57519i	0.459948	+	1.05049i
$53$	2.86627	+	1.65484i	0.393713	+	0.227310i	0.683768	−	0.729700i	$-0.260340\pi$
$53$	2.86627	+	1.65484i	0.393713	+	0.227310i	−0.290055	+	0.957010i	$0.593674\pi$
$54$	−7.29624	−	0.874612i	−0.992892	−	0.119020i
$55$			3.44340i			0.464308i
$56$	−5.65164	−	4.90500i	−0.755232	−	0.655458i
$57$	5.08516	−	2.06630i	0.673546	−	0.273689i
$58$	0.947650	−	0.479168i	0.124433	−	0.0629178i
$59$	−6.61842	+	2.40891i	−0.861645	+	0.313613i	−0.734779	−	0.678307i	$-0.762714\pi$
$59$	−6.61842	+	2.40891i	−0.861645	+	0.313613i	−0.126866	+	0.991920i	$0.540492\pi$
$60$	−3.74178	+	14.7437i	−0.483062	+	1.90340i
$61$	0.495742	+	2.81149i	0.0634732	+	0.359975i	0.999957	+	0.00926389i	$0.00294883\pi$
$61$	0.495742	+	2.81149i	0.0634732	+	0.359975i	−0.936484	+	0.350711i	$0.885940\pi$
$62$	−5.14294	+	0.615342i	−0.653154	+	0.0781485i
$63$	7.73986	−	1.75912i	0.975131	−	0.221629i
$64$	−1.51788	−	7.85468i	−0.189735	−	0.981835i
$65$	−6.20968	+	17.0610i	−0.770216	+	2.11615i
$66$	1.88515	+	0.368596i	0.232046	+	0.0453711i
$67$	2.94761	−	3.51283i	0.360108	−	0.429161i	−0.555323	−	0.831635i	$-0.687405\pi$
$67$	2.94761	−	3.51283i	0.360108	−	0.429161i	0.915431	+	0.402474i	$0.131850\pi$
$68$	−4.01374	+	8.10187i	−0.486738	+	0.982497i
$69$	2.55522	−	0.548438i	0.307612	−	0.0660242i
$70$	−1.54615	−	16.3569i	−0.184800	−	1.95503i
$71$	−0.788950	+	1.36650i	−0.0936312	+	0.162174i	−0.909037	−	0.416716i	$-0.863181\pi$
$71$	−0.788950	+	1.36650i	−0.0936312	+	0.162174i	0.815405	+	0.578890i	$0.196514\pi$
$72$	7.67117	+	3.62674i	0.904056	+	0.427415i
$73$	−14.2202			−1.66435			−0.832177	−	0.554510i	$-0.812906\pi$
$73$	−14.2202			−1.66435			−0.832177	+	0.554510i	$0.812906\pi$
$74$	−12.0107	+	3.63149i	−1.39622	+	0.422153i
$75$	−20.9514	+	13.1498i	−2.41926	+	1.51841i
$76$	−6.32526	+	0.403025i	−0.725557	+	0.0462302i
$77$	−2.05155	+	0.309425i	−0.233796	+	0.0352622i
$78$	8.67563	+	5.22589i	0.982321	+	0.591715i
$79$	8.87571	+	10.5777i	0.998595	+	1.19008i	0.981741	+	0.190221i	$0.0609205\pi$
$79$	8.87571	+	10.5777i	0.998595	+	1.19008i	0.0168536	+	0.999858i	$0.494635\pi$
$80$	9.49110	−	14.7791i	1.06114	−	1.65235i
$81$	−7.91269	+	4.28828i	−0.879188	+	0.476475i
$82$	12.0171	−	1.43782i	1.32707	−	0.158781i
$83$	0.0158260	+	0.0897540i	0.00173713	+	0.00985178i	0.985664	−	0.168720i	$-0.0539634\pi$
$83$	0.0158260	+	0.0897540i	0.00173713	+	0.00985178i	−0.983927	+	0.178572i	$0.942852\pi$
$84$	−9.12041	−	0.904452i	−0.995119	−	0.0986838i
$85$	−18.6539	+	6.78948i	−2.02330	+	0.736423i
$86$	−5.78607	−	3.78300i	−0.623928	−	0.407931i
$87$	0.608294	−	1.14954i	0.0652160	−	0.123244i
$88$	−1.92986	−	1.09325i	−0.205723	−	0.116541i
$89$	6.00926	+	3.46945i	0.636981	+	0.367761i	0.783451	−	0.621454i	$-0.213458\pi$
$89$	6.00926	+	3.46945i	0.636981	+	0.367761i	−0.146470	+	0.989215i	$0.546791\pi$
$90$	6.69165	+	17.3864i	0.705362	+	1.83269i
$91$	−10.7228	−	2.16658i	−1.12405	−	0.227119i
$92$	−2.99917	−	0.333985i	−0.312685	−	0.0348203i
$93$	−4.70585	+	4.25413i	−0.487974	+	0.441133i
$94$	6.22057	+	12.3024i	0.641603	+	1.26890i
$95$	−10.6599	−	8.94469i	−1.09368	−	0.917706i
$96$	−7.07513	−	6.77810i	−0.722102	−	0.691787i
$97$	−0.776264	+	0.651363i	−0.0788177	+	0.0661359i	−0.681345	−	0.731962i	$-0.738605\pi$
$97$	−0.776264	+	0.651363i	−0.0788177	+	0.0661359i	0.602528	+	0.798098i	$0.294160\pi$
$98$	9.60640	−	2.39102i	0.970393	−	0.241530i
$99$	2.14534	−	0.965402i	0.215615	−	0.0970266i
$100$	27.7566	−	6.73851i	2.77566	−	0.673851i
$101$	0.767733	+	0.914948i	0.0763922	+	0.0910407i	0.802887	−	0.596131i	$-0.203296\pi$
$101$	0.767733	+	0.914948i	0.0763922	+	0.0910407i	−0.726495	+	0.687172i	$0.758852\pi$
$102$	1.72023	+	10.9392i	0.170328	+	1.08314i
$103$	10.4679	+	1.84577i	1.03143	+	0.181869i	0.663651	−	0.748043i	$-0.269006\pi$
$103$	10.4679	+	1.84577i	1.03143	+	0.181869i	0.367782	+	0.929912i	$0.380117\pi$
$104$	−7.59031	−	8.89695i	−0.744291	−	0.872418i
$105$	−13.1193	−	15.2576i	−1.28032	−	1.48899i
$106$	−4.55736	−	1.06700i	−0.442650	−	0.103636i
$107$	−2.31381	−	4.00764i	−0.223685	−	0.387433i	0.732239	−	0.681048i	$-0.238475\pi$
$107$	−2.31381	−	4.00764i	−0.223685	−	0.387433i	−0.955924	+	0.293614i	$0.905142\pi$
$108$	10.2348	−	1.80235i	0.984846	−	0.173431i
$109$	8.53683	−	14.7862i	0.817680	−	1.41626i	−0.0897068	−	0.995968i	$-0.528593\pi$
$109$	8.53683	−	14.7862i	0.817680	−	1.41626i	0.907387	−	0.420296i	$-0.138074\pi$
$110$	−1.40936	−	4.66129i	−0.134377	−	0.444437i
$111$	−9.43727	+	12.1288i	−0.895746	+	1.15121i
$112$	9.65815	+	4.32667i	0.912610	+	0.408832i
$113$	−4.79273	+	5.71175i	−0.450862	+	0.537316i	−0.942820	−	0.333303i	$-0.891837\pi$
$113$	−4.79273	+	5.71175i	−0.450862	+	0.537316i	0.491958	+	0.870619i	$0.336281\pi$
$114$	−6.03801	+	4.87846i	−0.565512	+	0.456910i
$115$	−4.25877	−	5.07541i	−0.397132	−	0.473284i
$116$	−1.08671	+	1.03651i	−0.100898	+	0.0962378i
$117$	12.3705	−	0.914449i	1.14365	−	0.0845408i
$118$	7.97334	−	5.96979i	0.734006	−	0.549564i
$119$	−5.72137	−	10.5038i	−0.524477	−	0.962879i
$120$	−0.969283	−	21.4899i	−0.0884830	−	1.96175i
$121$	9.75876	−	3.55190i	0.887160	−	0.322900i
$122$	−1.82181	−	3.60299i	−0.164939	−	0.326199i
$123$	10.9958	−	9.94032i	0.991460	−	0.896288i
$124$	6.71009	−	2.93795i	0.602584	−	0.263836i
$125$	35.2952	+	20.3777i	3.15690	+	1.82263i
$126$	−9.75739	+	5.54918i	−0.869257	+	0.494361i
$127$	−16.6572	+	9.61705i	−1.47809	+	0.853375i	−0.999693	−	0.0247698i	$-0.992115\pi$
$127$	−16.6572	+	9.61705i	−1.47809	+	0.853375i	−0.478395	+	0.878145i	$0.658781\pi$
$128$	5.26961	+	10.0116i	0.465772	+	0.884905i
$129$	−8.46090	+	0.312297i	−0.744941	+	0.0274962i
$130$	1.42305	−	25.6369i	0.124810	−	2.24850i
$131$	−0.694516	−	0.582768i	−0.0606802	−	0.0509167i	0.611943	−	0.790902i	$-0.290388\pi$
$131$	−0.694516	−	0.582768i	−0.0606802	−	0.0509167i	−0.672623	+	0.739985i	$0.734833\pi$
$132$	−2.70278	+	0.272615i	−0.235246	+	0.0237281i
$133$	4.37128	−	7.15484i	0.379038	−	0.620403i
$134$	−2.55238	+	5.96173i	−0.220492	+	0.515015i
$135$	18.9916	+	12.6459i	1.63453	+	1.08839i
$136$	2.11732	−	12.6102i	0.181559	−	1.08132i
$137$	3.52672	−	9.68958i	0.301308	−	0.827837i	−0.692966	−	0.720971i	$-0.743696\pi$
$137$	3.52672	−	9.68958i	0.301308	−	0.827837i	0.994273	−	0.106866i	$-0.0340816\pi$
$138$	−3.23450	+	1.78825i	−0.275339	+	0.152226i
$139$	−1.61895	−	4.44803i	−0.137317	−	0.377277i	0.851905	−	0.523696i	$-0.175447\pi$
$139$	−1.61895	−	4.44803i	−0.137317	−	0.377277i	−0.989223	+	0.146420i	$0.953225\pi$
$140$	8.78779	+	21.5094i	0.742704	+	1.81788i
$141$	14.9234	+	7.89689i	1.25677	+	0.665038i
$142$	0.508694	−	2.17273i	0.0426887	−	0.182332i
$143$	−3.24239			−0.271142
$144$	−11.8688	−	1.76972i	−0.989066	−	0.147477i
$145$	−3.29716			−0.273815
$146$	19.2498	−	5.82025i	1.59313	−	0.481688i
$147$	7.91143	−	9.18745i	0.652524	−	0.757768i
$148$	14.7725	−	9.83184i	1.21429	−	0.808172i
$149$	−0.581779	−	1.59843i	−0.0476612	−	0.130948i	0.913578	−	0.406663i	$-0.133308\pi$
$149$	−0.581779	−	1.59843i	−0.0476612	−	0.130948i	−0.961239	+	0.275715i	$0.911085\pi$
$150$	22.9795	−	26.3761i	1.87627	−	2.15360i
$151$	16.8084	−	2.96377i	1.36785	−	0.241188i	0.558981	−	0.829181i	$-0.311192\pi$
$151$	16.8084	−	2.96377i	1.36785	−	0.241188i	0.808867	+	0.587992i	$0.200081\pi$
$152$	8.39749	−	3.13446i	0.681126	−	0.254238i
$153$	9.45993	+	9.71845i	0.764790	+	0.785690i
$154$	2.65052	−	1.25855i	0.213585	−	0.101417i
$155$	15.1126	+	5.50052i	1.21387	+	0.441813i
$156$	−13.8830	−	3.52336i	−1.11153	−	0.282094i
$157$	1.02096	−	0.371599i	0.0814814	−	0.0296568i	−0.300958	−	0.953637i	$-0.597306\pi$
$157$	1.02096	−	0.371599i	0.0814814	−	0.0296568i	0.382439	+	0.923981i	$0.375084\pi$
$158$	−16.3443	−	10.6861i	−1.30028	−	0.850141i
$159$	−5.31084	+	2.15801i	−0.421177	+	0.171141i
$160$	−6.79902	+	23.8910i	−0.537510	+	1.88875i
$161$	2.64119	−	2.99342i	0.208155	−	0.235915i
$162$	8.95617	−	9.04362i	0.703663	−	0.710534i
$163$	−6.53622	+	3.77369i	−0.511956	+	0.295578i	−0.733637	−	0.679541i	$-0.762179\pi$
$163$	−6.53622	+	3.77369i	−0.511956	+	0.295578i	0.221681	+	0.975119i	$0.428846\pi$
$164$	−15.6790	+	6.86490i	−1.22432	+	0.536059i
$165$	−4.70709	−	3.66254i	−0.366447	−	0.285129i
$166$	−0.0581593	−	0.115022i	−0.00451404	−	0.00892741i
$167$	−7.65897	−	6.42664i	−0.592669	−	0.497308i	0.296411	−	0.955061i	$-0.404210\pi$
$167$	−7.65897	−	6.42664i	−0.592669	−	0.497308i	−0.889080	+	0.457752i	$0.848655\pi$
$168$	12.7164	−	2.50858i	0.981092	−	0.193541i
$169$	−3.84904	−	1.40094i	−0.296080	−	0.107764i
$170$	22.4728	−	16.8258i	1.72358	−	1.29048i
$171$	−2.58418	+	9.14918i	−0.197617	+	0.699655i
$172$	9.38090	+	2.75281i	0.715287	+	0.209900i
$173$	2.74469	−	7.54097i	0.208675	−	0.573329i	−0.790562	−	0.612382i	$-0.790212\pi$
$173$	2.74469	−	7.54097i	0.208675	−	0.573329i	0.999237	+	0.0390522i	$0.0124339\pi$
$174$	−0.352943	+	1.80509i	−0.0267565	+	0.136844i
$175$	−13.8010	+	35.1745i	−1.04326	+	2.65894i
$176$	3.05989	+	0.690050i	0.230648	+	0.0520145i
$177$	3.74668	−	11.6095i	0.281617	−	0.872626i
$178$	−9.55471	−	2.23701i	−0.716156	−	0.167671i
$179$	4.28031	+	7.41372i	0.319926	+	0.554127i	0.980472	−	0.196658i	$-0.0630088\pi$
$179$	4.28031	+	7.41372i	0.319926	+	0.554127i	−0.660547	+	0.750785i	$0.729675\pi$
$180$	−16.1746	−	20.7970i	−1.20558	−	1.55012i
$181$	3.58892	+	6.21619i	0.266762	+	0.462045i	0.968024	−	0.250858i	$-0.0807129\pi$
$181$	3.58892	+	6.21619i	0.266762	+	0.462045i	−0.701262	+	0.712904i	$0.747380\pi$
$182$	15.4021	−	1.45589i	1.14168	−	0.107918i
$183$	−4.37058	−	2.31275i	−0.323082	−	0.170963i
$184$	4.19664	−	0.775428i	0.309381	−	0.0571653i
$185$	38.3682	+	6.76535i	2.82089	+	0.497399i
$186$	4.62908	−	7.68485i	0.339421	−	0.563481i
$187$	−2.27877	−	2.71573i	−0.166640	−	0.198594i
$188$	−13.4560	−	14.1076i	−0.981382	−	1.02891i
$189$	−5.82774	+	12.4514i	−0.423906	+	0.905706i
$190$	18.0912	+	7.74533i	1.31247	+	0.561905i
$191$	−0.699928	+	0.587309i	−0.0506450	+	0.0424962i	−0.667759	−	0.744378i	$-0.732746\pi$
$191$	−0.699928	+	0.587309i	−0.0506450	+	0.0424962i	0.617114	+	0.786874i	$0.288302\pi$
$192$	12.3518	+	6.27964i	0.891412	+	0.453194i
$193$	−1.75594	+	9.95843i	−0.126395	+	0.716823i	0.854074	+	0.520151i	$0.174124\pi$
$193$	−1.75594	+	9.95843i	−0.126395	+	0.716823i	−0.980469	+	0.196672i	$0.936987\pi$
$194$	0.784223	−	1.19946i	0.0563039	−	0.0861165i
$195$	−16.7173	−	26.6353i	−1.19715	−	1.90740i
$196$	−12.0255	+	7.16854i	−0.858962	+	0.512039i
$197$	7.22705	−	4.17254i	0.514906	−	0.297281i	−0.219942	−	0.975513i	$-0.570587\pi$
$197$	7.22705	−	4.17254i	0.514906	−	0.297281i	0.734848	+	0.678232i	$0.237253\pi$
$198$	−2.50899	+	2.18493i	−0.178306	+	0.155276i
$199$	8.74686	−	5.05000i	0.620049	−	0.357985i	−0.156839	−	0.987624i	$-0.550130\pi$
$199$	8.74686	−	5.05000i	0.620049	−	0.357985i	0.776888	+	0.629639i	$0.216797\pi$
$200$	−34.8158	+	20.4825i	−2.46185	+	1.44833i
$201$	1.66680	+	7.76576i	0.117567	+	0.547754i
$202$	−1.41375	−	0.924329i	−0.0994714	−	0.0650356i
$203$	−0.296284	−	1.96443i	−0.0207951	−	0.137876i
$204$	−6.80601	−	14.1042i	−0.476516	−	0.987495i
$205$	−35.3124	−	12.8527i	−2.46633	−	0.897670i
$206$	−14.9258	+	1.78584i	−1.03993	+	0.124425i
$207$	−1.96813	+	4.07630i	−0.136794	+	0.283322i
$208$	13.9164	+	8.93706i	0.964928	+	0.619674i
$209$	0.849958	−	2.33524i	0.0587928	−	0.161532i
$210$	24.0043	+	15.2844i	1.65646	+	1.05472i
$211$	8.23902	−	9.81888i	0.567197	−	0.675960i	−0.403856	−	0.914823i	$-0.632330\pi$
$211$	8.23902	−	9.81888i	0.567197	−	0.675960i	0.971053	+	0.238863i	$0.0767747\pi$
$212$	6.60597	−	0.420912i	0.453700	−	0.0289083i
$213$	−1.02884	−	2.53196i	−0.0704946	−	0.173487i
$214$	4.77249	+	4.47808i	0.326241	+	0.306115i
$215$	10.7323	+	18.5888i	0.731934	+	1.26775i
$216$	−13.1171	+	6.62887i	−0.892505	+	0.451037i
$217$	−1.91915	+	9.49823i	−0.130281	+	0.644782i
$218$	−5.50433	+	23.5101i	−0.372800	+	1.59230i
$219$	15.1253	−	19.4390i	1.02207	−	1.31356i
$220$	3.81568	+	5.73311i	0.257253	+	0.386526i
$221$	−6.39315	−	17.5650i	−0.430050	−	1.18155i
$222$	7.81092	−	20.2812i	0.524235	−	1.36118i
$223$	−8.84562	+	24.3031i	−0.592346	+	1.62746i	0.173792	+	0.984782i	$0.444398\pi$
$223$	−8.84562	+	24.3031i	−0.592346	+	1.62746i	−0.766138	+	0.642676i	$0.777824\pi$
$224$	−14.8450	−	1.90395i	−0.991875	−	0.127213i
$225$	4.30906	−	42.6271i	0.287271	−	2.84180i
$226$	4.15009	−	9.69358i	0.276060	−	0.644807i
$227$	1.90722	+	10.8164i	0.126587	+	0.717910i	0.980353	+	0.197253i	$0.0632020\pi$
$227$	1.90722	+	10.8164i	0.126587	+	0.717910i	−0.853766	+	0.520657i	$0.825687\pi$
$228$	6.17688	−	9.07525i	0.409074	−	0.601023i
$229$	−19.4571	+	7.08182i	−1.28576	+	0.467980i	−0.892334	−	0.451375i	$-0.850934\pi$
$229$	−19.4571	+	7.08182i	−1.28576	+	0.467980i	−0.393429	+	0.919355i	$0.628711\pi$
$230$	7.84239	+	5.12744i	0.517112	+	0.338094i
$231$	1.75914	−	3.13357i	0.115743	−	0.206174i
$232$	1.04683	−	1.84790i	0.0687275	−	0.121320i
$233$		−	12.3832i		−	0.811249i	−0.914040	−	0.405624i	$-0.867054\pi$
$233$		−	12.3832i		−	0.811249i	0.914040	−	0.405624i	$-0.132946\pi$
$234$	−16.3715	+	6.30103i	−1.07024	+	0.411911i
$235$		−	42.8039i		−	2.79222i
$236$	−8.35004	+	11.3447i	−0.543541	+	0.738476i
$237$	−23.9001	+	0.882169i	−1.55248	+	0.0573030i
$238$	12.0441	+	11.8771i	0.780703	+	0.769881i
$239$	23.3669	−	8.50484i	1.51148	−	0.550133i	0.552474	−	0.833530i	$-0.313684\pi$
$239$	23.3669	−	8.50484i	1.51148	−	0.550133i	0.959003	+	0.283397i	$0.0914616\pi$
$240$	10.1078	+	28.6939i	0.652454	+	1.85219i
$241$	5.58396	+	2.03240i	0.359695	+	0.130918i	0.515545	−	0.856863i	$-0.327590\pi$
$241$	5.58396	+	2.03240i	0.359695	+	0.130918i	−0.155850	+	0.987781i	$0.549812\pi$
$242$	−11.7566	+	8.80237i	−0.755741	+	0.565838i
$243$	2.55424	−	15.3778i	0.163854	−	0.986485i
$244$	3.94084	+	4.13168i	0.252286	+	0.264503i
$245$	−29.9681	−	6.83392i	−1.91459	−	0.436603i
$246$	−10.8164	+	17.9566i	−0.689631	+	1.14487i
$247$	8.42255	−	10.0376i	0.535914	−	0.638678i
$248$	−7.88090	+	6.72348i	−0.500438	+	0.426941i
$249$	−0.139526	−	0.0738321i	−0.00884211	−	0.00467892i
$250$	−56.1192	−	13.1390i	−3.54929	−	0.830983i
$251$	−12.5200	−	21.6852i	−0.790253	−	1.36876i	−0.925810	−	0.377989i	$-0.876616\pi$
$251$	−12.5200	−	21.6852i	−0.790253	−	1.36876i	0.135557	−	0.990770i	$-0.456718\pi$
$252$	10.9372	−	11.5055i	0.688981	−	0.724779i
$253$	0.591609	−	1.02470i	0.0371941	−	0.0644221i
$254$	18.6125	−	19.8362i	1.16785	−	1.24463i
$255$	10.5600	−	32.7214i	0.661291	−	2.04909i
$256$	−11.2311	−	11.3957i	−0.701943	−	0.712233i
$257$	5.09066	+	13.9865i	0.317547	+	0.872452i	0.991077	+	0.133292i	$0.0425549\pi$
$257$	5.09066	+	13.9865i	0.317547	+	0.872452i	−0.673530	+	0.739160i	$0.735223\pi$
$258$	11.3256	−	3.88575i	0.705103	−	0.241916i
$259$	−0.582968	+	23.4674i	−0.0362238	+	1.45820i
$260$	8.56663	+	35.2868i	0.531280	+	2.18840i
$261$	0.924404	+	2.05423i	0.0572192	+	0.127154i
$262$	1.17868	+	0.504627i	0.0728193	+	0.0311760i
$263$	8.72993	−	7.32528i	0.538311	−	0.451696i	−0.332649	−	0.943051i	$-0.607942\pi$
$263$	8.72993	−	7.32528i	0.538311	−	0.451696i	0.870960	+	0.491355i	$0.163498\pi$
$264$	3.54714	−	1.47526i	0.218312	−	0.0907962i
$265$	11.1330	+	9.34166i	0.683892	+	0.573853i
$266$	−2.98893	+	11.4746i	−0.183263	+	0.703552i
$267$	−11.1344	+	4.52436i	−0.681415	+	0.276886i
$268$	1.01504	−	9.11501i	0.0620033	−	0.556788i
$269$	3.59609	+	2.07621i	0.219258	+	0.126589i	0.605607	−	0.795764i	$-0.292931\pi$
$269$	3.59609	+	2.07621i	0.219258	+	0.126589i	−0.386349	+	0.922353i	$0.626264\pi$
$270$	−30.8846	−	9.34551i	−1.87958	−	0.568750i
$271$	18.8299	−	10.8715i	1.14384	−	0.660395i	0.196460	−	0.980512i	$-0.437056\pi$
$271$	18.8299	−	10.8715i	1.14384	−	0.660395i	0.947378	+	0.320117i	$0.103722\pi$
$272$	2.29509	+	17.9370i	0.139160	+	1.08759i
$273$	14.3669	−	12.3535i	0.869525	−	0.747668i
$274$	−0.808205	+	14.5602i	−0.0488254	+	0.879611i
$275$	−1.94473	+	11.0291i	−0.117272	+	0.665081i
$276$	3.64660	−	3.74460i	0.219499	−	0.225398i
$277$	−3.56877	+	2.99455i	−0.214427	+	0.179925i	−0.743674	−	0.668542i	$-0.766919\pi$
$277$	−3.56877	+	2.99455i	−0.214427	+	0.179925i	0.529248	+	0.848467i	$0.322474\pi$
$278$	4.01210	+	5.35863i	0.240630	+	0.321389i
$279$	−0.810017	−	10.9577i	−0.0484944	−	0.656022i
$280$	−20.6996	−	25.5203i	−1.23704	−	1.52513i
$281$	11.9622	+	14.2560i	0.713604	+	0.850440i	0.993993	−	0.109446i	$-0.0349077\pi$
$281$	11.9622	+	14.2560i	0.713604	+	0.850440i	−0.280388	+	0.959887i	$0.590463\pi$
$282$	−23.4338	−	4.58191i	−1.39546	−	0.272849i
$283$	−9.61377	+	11.4572i	−0.571480	+	0.681063i	−0.971934	−	0.235254i	$-0.924408\pi$
$283$	−9.61377	+	11.4572i	−0.571480	+	0.681063i	0.400454	+	0.916317i	$0.368852\pi$
$284$	0.200671	+	3.14942i	0.0119076	+	0.186883i
$285$	23.5656	−	5.05799i	1.39591	−	0.299609i
$286$	4.38920	−	1.32709i	0.259539	−	0.0784725i
$287$	4.48434	−	22.1938i	0.264702	−	1.31006i
$288$	16.7910	−	2.46216i	0.989419	−	0.145084i
$289$	1.71881	−	2.97707i	0.101107	−	0.175122i
$290$	4.46334	−	1.34951i	0.262096	−	0.0792458i
$291$	−0.0647399	−	1.75396i	−0.00379512	−	0.102819i
$292$	−23.6761	+	15.7577i	−1.38554	+	0.922147i
$293$	4.77975	+	13.1323i	0.279236	+	0.767195i	0.997450	+	0.0713720i	$0.0227378\pi$
$293$	4.77975	+	13.1323i	0.279236	+	0.767195i	−0.718214	+	0.695822i	$0.755040\pi$
$294$	−6.94927	+	15.6751i	−0.405290	+	0.914188i
$295$	−30.4572	+	5.37042i	−1.77328	+	0.312678i
$296$	−15.9733	+	19.3556i	−0.928428	+	1.12502i
$297$	−0.962179	+	3.95950i	−0.0558313	+	0.229754i
$298$	1.44177	+	1.92566i	0.0835197	+	0.111550i
$299$	4.77913	−	4.01017i	0.276384	−	0.231914i
$300$	−20.3116	+	45.1104i	−1.17269	+	2.60445i
$301$	−10.1107	+	8.06460i	−0.582770	+	0.464836i
$302$	−21.5403	+	10.8916i	−1.23951	+	0.626741i
$303$	−2.06732	+	0.0763060i	−0.118764	+	0.00438367i
$304$	−10.0847	+	7.68013i	−0.578397	+	0.440485i
$305$			12.5359i			0.717803i
$306$	−16.7835	−	9.28389i	−0.959450	−	0.530724i
$307$	17.0927	+	9.86850i	0.975534	+	0.563225i	0.900919	−	0.433987i	$-0.142894\pi$
$307$	17.0927	+	9.86850i	0.975534	+	0.563225i	0.0746153	+	0.997212i	$0.476227\pi$
$308$	−3.07287	+	2.78853i	−0.175093	+	0.158891i
$309$	−13.6573	+	12.3463i	−0.776934	+	0.702355i
$310$	−22.7091	−	1.26053i	−1.28979	−	0.0715935i
$311$	6.98498	+	5.86109i	0.396082	+	0.332352i	0.818977	−	0.573827i	$-0.194542\pi$
$311$	6.98498	+	5.86109i	0.396082	+	0.332352i	−0.422895	+	0.906179i	$0.638986\pi$
$312$	20.2354	−	0.912702i	1.14561	−	0.0516716i
$313$	2.75408	+	1.00240i	0.155670	+	0.0566592i	0.418680	−	0.908134i	$-0.362493\pi$
$313$	2.75408	+	1.00240i	0.155670	+	0.0566592i	−0.263010	+	0.964793i	$0.584715\pi$
$314$	−1.22997	+	0.920902i	−0.0694112	+	0.0519695i
$315$	34.8112	−	1.70542i	1.96139	−	0.0960894i
$316$	26.4989	+	7.77606i	1.49068	+	0.437437i
$317$	12.0794	−	2.12992i	0.678446	−	0.119628i	0.176202	−	0.984354i	$-0.443619\pi$
$317$	12.0794	−	2.12992i	0.678446	−	0.119628i	0.502244	+	0.864726i	$0.332508\pi$
$318$	6.30598	−	5.09497i	0.353622	−	0.285712i
$319$	−0.201391	−	0.553317i	−0.0112757	−	0.0309798i
$320$	−0.574658	−	35.1238i	−0.0321243	−	1.96348i
$321$	7.93948	+	1.09974i	0.443139	+	0.0613813i
$322$	−2.35017	+	5.13319i	−0.130970	+	0.286062i
$323$	14.3266			0.797154
$324$	−8.42240	+	15.9080i	−0.467911	+	0.883776i
$325$	−29.5250	+	51.1388i	−1.63775	+	2.83667i
$326$	7.30347	−	7.78364i	0.404502	−	0.431096i
$327$	11.1325	+	27.3970i	0.615629	+	1.51506i
$328$	18.4147	−	15.7103i	1.01678	−	0.867454i
$329$	25.5022	−	3.84637i	1.40598	−	0.212057i
$330$	7.87100	+	3.03137i	0.433285	+	0.166871i
$331$	−5.92510	+	1.04475i	−0.325673	+	0.0574249i	−0.334094	−	0.942540i	$-0.608430\pi$
$331$	−5.92510	+	1.04475i	−0.325673	+	0.0574249i	0.00842155	+	0.999965i	$0.497319\pi$
$332$	0.125807	+	0.131900i	0.00690457	+	0.00723893i
$333$	−6.54202	−	25.8013i	−0.358501	−	1.41390i
$334$	12.9983	+	5.56492i	0.711233	+	0.304499i
$335$	15.4251	−	12.9432i	0.842761	−	0.707160i
$336$	−16.1873	+	8.60058i	−0.883092	+	0.469200i
$337$	2.26279	−	12.8329i	0.123262	−	0.699054i	−0.859063	−	0.511870i	$-0.828953\pi$
$337$	2.26279	−	12.8329i	0.123262	−	0.699054i	0.982325	−	0.187184i	$-0.0599360\pi$
$338$	5.78381	+	0.321047i	0.314598	+	0.0174627i
$339$	−2.71016	−	12.6269i	−0.147196	−	0.685798i
$340$	−23.5345	+	31.9749i	−1.27634	+	1.73408i
$341$			2.87210i			0.155533i
$342$	−0.246525	−	13.4428i	−0.0133305	−	0.726906i
$343$	1.37866	−	18.4689i	0.0744404	−	0.997225i
$344$	−13.8255	+	0.113092i	−0.745423	+	0.00609750i
$345$	11.4678	−	0.423285i	0.617408	−	0.0227889i
$346$	−0.628990	+	11.3315i	−0.0338147	+	0.609187i
$347$	4.45741	−	25.2792i	0.239286	−	1.35706i	−0.594110	−	0.804384i	$-0.702496\pi$
$347$	4.45741	−	25.2792i	0.239286	−	1.35706i	0.833396	−	0.552676i	$-0.186393\pi$
$348$	−0.261037	−	2.58800i	−0.0139931	−	0.138731i
$349$	−5.00839	−	28.4040i	−0.268093	−	1.52043i	−0.760081	−	0.649828i	$-0.774841\pi$
$349$	−5.00839	−	28.4040i	−0.268093	−	1.52043i	0.491989	−	0.870602i	$-0.336270\pi$
$350$	4.28565	−	53.2641i	0.229078	−	2.84709i
$351$	−11.9077	+	17.8830i	−0.635586	+	0.954522i
$352$	−4.42458	+	0.318278i	−0.235831	+	0.0169643i
$353$	6.59979	−	18.1328i	0.351271	−	0.965110i	−0.630691	−	0.776034i	$-0.717229\pi$
$353$	6.59979	−	18.1328i	0.351271	−	0.965110i	0.981962	−	0.189076i	$-0.0605492\pi$
$354$	−0.320134	+	17.2492i	−0.0170149	+	0.916785i
$355$	−4.45366	+	5.30766i	−0.236376	+	0.281701i
$356$	13.8497	−	0.882460i	0.734033	−	0.0467703i
$357$	20.4441	+	3.35120i	1.08201	+	0.177364i
$358$	−8.82861	−	8.28398i	−0.466606	−	0.437822i
$359$	15.1515	−	26.2431i	0.799663	−	1.38506i	−0.120172	−	0.992753i	$-0.538345\pi$
$359$	15.1515	−	26.2431i	0.799663	−	1.38506i	0.919836	−	0.392304i	$-0.128322\pi$
$360$	30.4074	+	21.5325i	1.60261	+	1.13486i
$361$	−4.47858	−	7.75713i	−0.235715	−	0.408270i
$362$	−7.40253	−	6.94587i	−0.389068	−	0.365067i
$363$	−5.52442	+	17.1181i	−0.289957	+	0.898467i
$364$	−20.2538	+	8.27482i	−1.06159	+	0.433718i
$365$	−61.4934	−	10.8429i	−3.21871	−	0.567545i
$366$	6.86300	+	1.34190i	0.358735	+	0.0701420i
$367$	32.3216	−	5.69916i	1.68717	−	0.297494i	0.753987	−	0.656890i	$-0.228128\pi$
$367$	32.3216	−	5.69916i	1.68717	−	0.297494i	0.933185	+	0.359396i	$0.117017\pi$
$368$	−5.36358	+	2.76735i	−0.279596	+	0.144258i
$369$	1.89271	+	25.6041i	0.0985304	+	1.33290i
$370$	−54.7077	+	6.54567i	−2.84412	+	0.340293i
$371$	−4.56528	+	7.47237i	−0.237017	+	0.387946i
$372$	−3.12098	+	12.2976i	−0.161815	+	0.637599i
$373$	4.21742	−	23.9182i	0.218370	−	1.23844i	−0.656593	−	0.754245i	$-0.728003\pi$
$373$	4.21742	−	23.9182i	0.218370	−	1.23844i	0.874963	−	0.484191i	$-0.160886\pi$
$374$	4.19628	+	2.74357i	0.216984	+	0.141867i
$375$	−65.3975	+	26.5736i	−3.37711	+	1.37226i
$376$	23.9895	+	13.5899i	1.23716	+	0.700846i
$377$		−	3.10470i		−	0.159900i
$378$	2.79269	−	19.2406i	0.143640	−	0.989630i
$379$		−	6.49511i		−	0.333631i	−0.985988	−	0.166816i	$-0.946652\pi$
$379$		−	6.49511i		−	0.333631i	0.985988	−	0.166816i	$-0.0533485\pi$
$380$	−27.6600	−	3.08019i	−1.41893	−	0.158010i
$381$	4.57090	−	32.9994i	0.234174	−	1.69061i
$382$	0.707104	−	1.08151i	0.0361786	−	0.0553349i
$383$	0.725963	−	4.11714i	0.0370950	−	0.210376i	−0.960627	−	0.277843i	$-0.910381\pi$
$383$	0.725963	−	4.11714i	0.0370950	−	0.210376i	0.997722	+	0.0674668i	$0.0214917\pi$
$384$	−19.2907	−	3.44520i	−0.984424	−	0.175812i
$385$	−9.10756	−	0.226246i	−0.464164	−	0.0115306i
$386$	−1.69892	−	14.1993i	−0.0864728	−	0.722727i
$387$	8.57247	−	11.8982i	0.435763	−	0.604817i
$388$	−0.570663	+	1.94468i	−0.0289710	+	0.0987262i
$389$	−19.4542	+	3.43031i	−0.986370	+	0.173924i	−0.643489	−	0.765455i	$-0.722514\pi$
$389$	−19.4542	+	3.43031i	−0.986370	+	0.173924i	−0.342881	+	0.939379i	$0.611403\pi$
$390$	33.5317	+	29.2137i	1.69795	+	1.47930i
$391$	6.71759	+	1.18449i	0.339723	+	0.0599024i
$392$	13.3447	−	14.6259i	0.674011	−	0.738721i
$393$	1.53536	−	0.329540i	0.0774485	−	0.0166231i
$394$	−8.07540	+	8.60632i	−0.406833	+	0.433580i
$395$	30.3162	+	52.5092i	1.52537	+	2.64203i
$396$	2.50213	−	3.98464i	0.125737	−	0.200235i
$397$	9.02442	−	15.6307i	0.452922	−	0.784485i	−0.545644	−	0.838017i	$-0.683715\pi$
$397$	9.02442	−	15.6307i	0.452922	−	0.784485i	0.998566	+	0.0535326i	$0.0170481\pi$
$398$	−9.77361	+	10.4162i	−0.489907	+	0.522116i
$399$	5.13112	+	13.5857i	0.256877	+	0.680135i
$400$	38.7466	−	41.9768i	1.93733	−	2.09884i
$401$	−13.1112	+	15.6253i	−0.654742	+	0.780292i	−0.986621	−	0.163030i	$-0.947873\pi$
$401$	−13.1112	+	15.6253i	−0.654742	+	0.780292i	0.331879	+	0.943322i	$0.392318\pi$
$402$	−5.43481	−	9.83023i	−0.271064	−	0.490287i
$403$	−5.17944	+	14.2304i	−0.258006	+	0.708866i
$404$	2.29211	+	0.672615i	0.114037	+	0.0334638i
$405$	−37.4871	+	12.5106i	−1.86275	+	0.621657i
$406$	1.20510	+	2.53796i	0.0598083	+	0.125957i
$407$	1.20820	+	6.85203i	0.0598882	+	0.339643i
$408$	14.9860	+	16.3071i	0.741918	+	0.807323i
$409$	5.51686	−	31.2877i	0.272791	−	1.54707i	−0.473101	−	0.881008i	$-0.656865\pi$
$409$	5.51686	−	31.2877i	0.272791	−	1.54707i	0.745892	−	0.666067i	$-0.232023\pi$
$410$	53.0626	+	2.94540i	2.62058	+	0.145463i
$411$	9.49440	+	15.1272i	0.468324	+	0.746172i
$412$	19.4739	−	8.52649i	0.959412	−	0.420070i
$413$	−5.93654	−	17.6636i	−0.292118	−	0.869167i
$414$	0.995833	−	6.32359i	0.0489425	−	0.310788i
$415$			0.400195i			0.0196448i
$416$	−22.4964	−	6.40213i	−1.10298	−	0.313890i
$417$	7.80239	+	2.51802i	0.382085	+	0.123308i
$418$	−0.194782	+	3.50907i	−0.00952708	+	0.171634i
$419$	−1.50255	+	8.52141i	−0.0734046	+	0.416298i	0.925857	+	0.377874i	$0.123345\pi$
$419$	−1.50255	+	8.52141i	−0.0734046	+	0.416298i	−0.999262	+	0.0384239i	$0.987766\pi$
$420$	−38.7502	−	10.8655i	−1.89082	−	0.530181i
$421$	−19.9891	+	16.7728i	−0.974209	+	0.817458i	−0.983206	−	0.182501i	$-0.941581\pi$
$421$	−19.9891	+	16.7728i	−0.974209	+	0.817458i	0.00899697	+	0.999960i	$0.497136\pi$
$422$	−7.13428	+	16.6639i	−0.347291	+	0.811186i
$423$	−26.6681	+	12.0006i	−1.29665	+	0.583491i
$424$	−8.77017	+	3.27357i	−0.425917	+	0.158978i
$425$	−63.5826	+	11.2113i	−3.08421	+	0.543829i
$426$	2.42904	+	3.00639i	0.117687	+	0.145660i
$427$	−7.46878	+	1.12648i	−0.361440	+	0.0545141i
$428$	−8.29333	−	4.10859i	−0.400873	−	0.198596i
$429$	3.44875	−	4.43232i	0.166507	−	0.213994i
$430$	−22.1365	−	20.7709i	−1.06751	−	1.00166i
$431$	−15.8834	+	27.5108i	−0.765075	+	1.32515i	0.175132	+	0.984545i	$0.443965\pi$
$431$	−15.8834	+	27.5108i	−0.765075	+	1.32515i	−0.940207	+	0.340604i	$0.889369\pi$
$432$	15.0433	−	14.3422i	0.723773	−	0.690038i
$433$	7.64583			0.367435			0.183718	−	0.982979i	$-0.441187\pi$
$433$	7.64583			0.367435			0.183718	+	0.982979i	$0.441187\pi$
$434$	−1.28963	−	13.6432i	−0.0619040	−	0.654893i
$435$	3.50700	−	4.50719i	0.168148	−	0.216103i
$436$	−2.17136	−	34.0782i	−0.103989	−	1.63205i
$437$	1.63541	+	4.49325i	0.0782323	+	0.214942i
$438$	−12.5187	+	32.5050i	−0.598166	+	1.55315i
$439$	34.6418	−	6.10829i	1.65336	−	0.291533i	0.732311	−	0.680970i	$-0.238442\pi$
$439$	34.6418	−	6.10829i	1.65336	−	0.291533i	0.921053	+	0.389437i	$0.127330\pi$
$440$	−7.51177	−	6.19913i	−0.358110	−	0.295532i
$441$	4.14422	+	20.5870i	0.197344	+	0.980334i
$442$	15.8436	+	21.1610i	0.753603	+	1.00652i
$443$	−0.530499	−	0.193086i	−0.0252048	−	0.00917378i	0.329387	−	0.944195i	$-0.393158\pi$
$443$	−0.530499	−	0.193086i	−0.0252048	−	0.00917378i	−0.354592	+	0.935021i	$0.615380\pi$
$444$	−2.27261	+	30.6514i	−0.107853	+	1.45465i
$445$	23.3407	+	19.5852i	1.10646	+	0.928427i
$446$	2.02712	−	36.5194i	0.0959868	−	1.72924i
$447$	2.80384	+	0.904866i	0.132617	+	0.0427987i
$448$	20.8749	−	3.49861i	0.986244	−	0.165294i
$449$	2.33580	+	1.34857i	0.110233	+	0.0636432i	0.554103	−	0.832448i	$-0.313061\pi$
$449$	2.33580	+	1.34857i	0.110233	+	0.0636432i	−0.443870	+	0.896091i	$0.646395\pi$
$450$	11.6138	+	59.4675i	0.547482	+	2.80333i
$451$		−	6.71104i		−	0.316010i
$452$	−1.65042	+	14.8207i	−0.0776292	+	0.697108i
$453$	−13.8267	+	26.1293i	−0.649634	+	1.22766i
$454$	−7.00888	−	13.8615i	−0.328943	−	0.650551i
$455$	−44.7171	−	17.5452i	−2.09637	−	0.822531i
$456$	−4.64715	+	14.8132i	−0.217623	+	0.693693i
$457$	15.5859	−	13.0782i	0.729080	−	0.611771i	−0.200801	−	0.979632i	$-0.564354\pi$
$457$	15.5859	−	13.0782i	0.729080	−	0.611771i	0.929881	+	0.367862i	$0.119910\pi$
$458$	23.4404	−	17.5503i	1.09530	−	0.820070i
$459$	−23.3470	+	2.59469i	−1.08975	+	0.121110i
$460$	−12.7148	−	3.73113i	−0.592831	−	0.173965i
$461$	13.1119	−	2.31198i	0.610683	−	0.107680i	0.140251	−	0.990116i	$-0.455209\pi$
$461$	13.1119	−	2.31198i	0.610683	−	0.107680i	0.470432	+	0.882436i	$0.344098\pi$
$462$	−1.09878	+	4.96188i	−0.0511197	+	0.230848i
$463$	10.4304	+	28.6573i	0.484742	+	1.33182i	0.905385	+	0.424592i	$0.139582\pi$
$463$	10.4304	+	28.6573i	0.484742	+	1.33182i	−0.420643	+	0.907226i	$0.638195\pi$
$464$	−0.660745	+	2.92994i	−0.0306743	+	0.136019i
$465$	−23.5935	+	14.8082i	−1.09412	+	0.686712i
$466$	5.06835	+	16.7630i	0.234787	+	0.776531i
$467$	7.77388	−	13.4648i	0.359732	−	0.623074i	−0.628184	−	0.778065i	$-0.716201\pi$
$467$	7.77388	−	13.4648i	0.359732	−	0.623074i	0.987916	+	0.154991i	$0.0495347\pi$
$468$	19.5830	−	15.2304i	0.905224	−	0.704025i
$469$	9.09754	+	8.02706i	0.420085	+	0.370655i
$470$	17.5193	+	57.9432i	0.808107	+	2.67272i
$471$	−0.577963	+	1.79089i	−0.0266311	+	0.0825199i
$472$	6.66007	−	18.7748i	0.306555	−	0.864181i
$473$	−2.46398	+	2.93645i	−0.113294	+	0.135018i
$474$	31.9923	−	10.9764i	1.46946	−	0.504161i
$475$	−29.0916	−	34.6700i	−1.33481	−	1.59077i
$476$	−21.1652	−	11.1484i	−0.970106	−	0.510987i
$477$	2.69886	−	9.55522i	0.123572	−	0.437504i
$478$	−28.1505	+	21.0768i	−1.28758	+	0.964032i
$479$	−1.87235	+	1.57109i	−0.0855500	+	0.0717849i	−0.684560	−	0.728957i	$-0.740006\pi$
$479$	−1.87235	+	1.57109i	−0.0855500	+	0.0717849i	0.599010	+	0.800742i	$0.295561\pi$
$480$	−25.4270	−	34.7057i	−1.16058	−	1.58409i
$481$	−6.37043	+	36.1285i	−0.290467	+	1.64732i
$482$	−8.39080	−	0.465756i	−0.382191	−	0.0212146i
$483$	1.28269	+	6.79442i	0.0583646	+	0.309157i
$484$	12.3120	−	16.7276i	0.559637	−	0.760344i
$485$	−3.85350	+	2.22482i	−0.174979	+	0.101024i
$486$	2.83638	+	21.8622i	0.128661	+	0.991689i
$487$	13.0516	+	7.53536i	0.591426	+	0.341460i	0.765661	−	0.643244i	$-0.222412\pi$
$487$	13.0516	+	7.53536i	0.591426	+	0.341460i	−0.174235	+	0.984704i	$0.555745\pi$
$488$	−7.02575	−	3.98005i	−0.318041	−	0.180168i
$489$	1.79360	−	12.9488i	0.0811095	−	0.585565i
$490$	43.3646	−	3.01474i	1.95901	−	0.136192i
$491$	−21.9831	−	18.4460i	−0.992084	−	0.832458i	−0.00621626	−	0.999981i	$-0.501979\pi$
$491$	−21.9831	−	18.4460i	−0.992084	−	0.832458i	−0.985868	+	0.167523i	$0.946423\pi$
$492$	7.29257	−	28.7348i	0.328775	−	1.29547i
$493$	2.60040	−	2.18199i	0.117116	−	0.0982721i
$494$	−7.29320	+	17.0351i	−0.328137	+	0.766446i
$495$	10.0133	−	2.53892i	0.450066	−	0.114116i
$496$	7.91643	−	12.3271i	0.355458	−	0.553504i
$497$	−3.56247	−	2.17651i	−0.159799	−	0.0976297i
$498$	0.219094	+	0.0428387i	0.00981785	+	0.00191965i
$499$	13.0745	+	35.9218i	0.585294	+	1.60808i	0.779001	+	0.627023i	$0.215727\pi$
$499$	13.0745	+	35.9218i	0.585294	+	1.60808i	−0.193707	+	0.981059i	$0.562051\pi$
$500$	81.3457	−	5.18309i	3.63789	−	0.231795i
$501$	16.9316	−	3.63410i	0.756447	−	0.162360i
$502$	25.8238	+	24.2307i	1.15257	+	1.08147i
$503$	−14.0707	+	24.3712i	−0.627381	+	1.08666i	0.360694	+	0.932684i	$0.382540\pi$
$503$	−14.0707	+	24.3712i	−0.627381	+	1.08666i	−0.988075	+	0.153972i	$0.950793\pi$
$504$	−10.0965	+	20.0514i	−0.449734	+	0.893162i
$505$	2.62230	+	4.54195i	0.116691	+	0.202114i
$506$	−0.381454	+	1.62926i	−0.0169577	+	0.0724296i
$507$	6.00907	−	3.77151i	0.266872	−	0.167499i
$508$	−17.0768	+	34.4701i	−0.757659	+	1.52936i
$509$	−12.1906	+	14.5282i	−0.540339	+	0.643950i	−0.965264	−	0.261278i	$-0.915856\pi$
$509$	−12.1906	+	14.5282i	−0.540339	+	0.643950i	0.424925	+	0.905229i	$0.360300\pi$
$510$	−0.902293	+	48.6167i	−0.0399542	+	2.15278i
$511$	0.934331	−	37.6116i	0.0413324	−	1.66384i
$512$	19.8676	+	10.8295i	0.878033	+	0.478600i
$513$	−9.75821	−	13.2640i	−0.430836	−	0.585620i
$514$	−12.6157	−	16.8498i	−0.556457	−	0.743212i
$515$	43.8595	+	15.9635i	1.93268	+	0.703438i
$516$	−13.7410	+	9.89560i	−0.604913	+	0.435630i
$517$	7.18318	−	2.61446i	0.315916	−	0.114984i
$518$	−8.81591	−	32.0063i	−0.387349	−	1.40627i
$519$	7.38907	+	11.7729i	0.324344	+	0.516771i
$520$	−26.0392	−	44.2612i	−1.14190	−	1.94098i
$521$			32.2374i			1.41235i	0.708039	+	0.706174i	$0.249580\pi$
$521$			32.2374i			1.41235i	−0.708039	+	0.706174i	$0.750420\pi$
$522$	−2.09214	−	2.40244i	−0.0915705	−	0.105152i
$523$		−	20.2272i		−	0.884474i	−0.896898	−	0.442237i	$-0.854185\pi$
$523$		−	20.2272i		−	0.884474i	0.896898	−	0.442237i	$-0.145815\pi$
$524$	−1.80211	−	0.200682i	−0.0787257	−	0.00876682i
$525$	−33.4039	−	56.2790i	−1.45786	−	2.45622i
$526$	−8.81944	+	13.4893i	−0.384546	+	0.588160i
$527$	−15.5591	+	5.66304i	−0.677764	+	0.246686i
$528$	−4.19792	+	3.44887i	−0.182691	+	0.150093i
$529$	−3.59857	−	20.4085i	−0.156460	−	0.887327i
$530$	−18.8941	−	8.08907i	−0.820705	−	0.351367i
$531$	11.8850	+	17.4701i	0.515765	+	0.758136i
$532$	−0.650379	−	16.7564i	−0.0281975	−	0.726481i
$533$	12.1024	−	33.2511i	0.524214	−	1.44027i
$534$	13.2208	−	10.6818i	0.572119	−	0.462248i
$535$	−6.94992	−	19.0947i	−0.300471	−	0.825538i
$536$	2.35666	+	12.7543i	0.101792	+	0.550904i
$537$	−14.6872	−	2.03440i	−0.633800	−	0.0877907i
$538$	−5.71778	−	1.33868i	−0.246511	−	0.0577147i
$539$	−0.683612	−	5.44655i	−0.0294453	−	0.234599i
$540$	45.6333	+	0.0100628i	1.96374	+	0.000433032i
$541$	−12.4206	−	21.5131i	−0.534003	−	0.924920i	−0.999211	−	0.0397186i	$-0.987354\pi$
$541$	−12.4206	−	21.5131i	−0.534003	−	0.924920i	0.465208	−	0.885201i	$-0.345979\pi$
$542$	−21.0403	+	22.4236i	−0.903758	+	0.963176i
$543$	−12.3148	−	1.70578i	−0.528478	−	0.0732021i
$544$	−10.4483	−	23.3417i	−0.447968	−	1.00077i
$545$	48.1908	−	57.4315i	2.06427	−	2.46010i
$546$	−14.3922	+	22.6031i	−0.615927	+	0.967324i
$547$	8.35086	−	22.9438i	0.357057	−	0.981007i	−0.622988	−	0.782231i	$-0.714081\pi$
$547$	8.35086	−	22.9438i	0.357057	−	0.981007i	0.980045	−	0.198775i	$-0.0636963\pi$
$548$	−4.86532	−	20.0407i	−0.207836	−	0.856098i
$549$	7.81023	−	3.51460i	0.333333	−	0.150000i
$550$	−1.88158	−	15.7260i	−0.0802309	−	0.670558i
$551$	2.23607	+	0.813862i	0.0952597	+	0.0346717i
$552$	−3.40373	+	6.56155i	−0.144872	+	0.279278i
$553$	−28.5604	+	22.7807i	−1.21451	+	0.968733i
$554$	3.60536	−	5.51437i	0.153177	−	0.234283i
$555$	−50.0583	+	45.2531i	−2.12485	+	1.92089i
$556$	−7.62440	−	5.61180i	−0.323347	−	0.237993i
$557$	24.8635	−	14.3549i	1.05350	−	0.608238i	0.129872	−	0.991531i	$-0.458543\pi$
$557$	24.8635	−	14.3549i	1.05350	−	0.608238i	0.923627	+	0.383293i	$0.125210\pi$
$558$	5.58144	+	14.5018i	0.236281	+	0.613912i
$559$	−17.5037	+	10.1058i	−0.740329	+	0.427429i
$560$	38.4662	+	26.0744i	1.62549	+	1.10184i
$561$	6.13617	−	0.226490i	0.259069	−	0.00956241i
$562$	−22.0280	−	14.4021i	−0.929194	−	0.607518i
$563$	−1.73159	+	9.82035i	−0.0729779	+	0.413878i	0.926331	+	0.376710i	$0.122945\pi$
$563$	−1.73159	+	9.82035i	−0.0729779	+	0.413878i	−0.999309	+	0.0371680i	$0.988166\pi$
$564$	33.5974	−	3.38879i	1.41471	−	0.142694i
$565$	−25.0807	+	21.0452i	−1.05515	+	0.885377i
$566$	8.32470	−	19.4444i	0.349913	−	0.817310i
$567$	−10.8223	−	21.2103i	−0.454495	−	0.890749i
$568$	−1.56068	−	4.18120i	−0.0654847	−	0.175439i
$569$	9.59084	+	11.4299i	0.402069	+	0.479167i	0.928650	−	0.370958i	$-0.120971\pi$
$569$	9.59084	+	11.4299i	0.402069	+	0.479167i	−0.526581	+	0.850125i	$0.676526\pi$
$570$	−29.8303	+	16.4922i	−1.24945	+	0.690782i
$571$	−2.77996	−	0.490182i	−0.116338	−	0.0205135i	0.115176	−	0.993345i	$-0.463257\pi$
$571$	−2.77996	−	0.490182i	−0.116338	−	0.0205135i	−0.231514	+	0.972832i	$0.574368\pi$
$572$	−5.39845	+	3.59294i	−0.225720	+	0.150228i
$573$	−0.0583735	−	1.58148i	−0.00243859	−	0.0660674i
$574$	3.01338	+	31.8790i	0.125776	+	1.33060i
$575$	−10.7743	−	18.6616i	−0.449319	−	0.778244i
$576$	−21.7221	+	10.2055i	−0.905087	+	0.425227i
$577$	10.4072	+	18.0258i	0.433258	+	0.750425i	0.997152	−	0.0754222i	$-0.0240305\pi$
$577$	10.4072	+	18.0258i	0.433258	+	0.750425i	−0.563893	+	0.825848i	$0.690697\pi$
$578$	−1.10824	+	4.73353i	−0.0460969	+	0.196889i
$579$	−11.7454	−	12.9926i	−0.488122	−	0.539952i
$580$	−5.48964	+	3.65363i	−0.227945	+	0.151709i
$581$	−0.238433	+	0.0359617i	−0.00989188	+	0.00149194i
$582$	0.805524	+	2.34783i	0.0333900	+	0.0973206i
$583$	−0.887679	+	2.43888i	−0.0367639	+	0.101008i
$584$	25.6006	−	31.0215i	1.05936	−	1.28368i
$585$	54.1915	+	5.47808i	2.24054	+	0.226491i
$586$	−11.8452	−	15.8207i	−0.489323	−	0.653547i
$587$	28.4953	+	10.3714i	1.17613	+	0.428075i	0.854832	−	0.518905i	$-0.173660\pi$
$587$	28.4953	+	10.3714i	1.17613	+	0.428075i	0.321294	+	0.946980i	$0.395882\pi$
$588$	2.99147	−	24.0635i	0.123366	−	0.992361i
$589$	−8.89129	−	7.46068i	−0.366359	−	0.307412i
$590$	39.0315	−	19.7358i	1.60690	−	0.812510i
$591$	−1.98317	+	14.3174i	−0.0815769	+	0.588939i
$592$	13.7008	−	32.7392i	0.563099	−	1.34557i
$593$	5.22332	−	3.01569i	0.214496	−	0.123839i	−0.388903	−	0.921279i	$-0.627146\pi$
$593$	5.22332	−	3.01569i	0.214496	−	0.123839i	0.603399	+	0.797439i	$0.293813\pi$
$594$	−0.318107	−	5.75376i	−0.0130521	−	0.236080i
$595$	−16.7321	−	49.7846i	−0.685949	−	2.04097i
$596$	−2.73987	−	2.01663i	−0.112230	−	0.0826045i
$597$	−2.40022	+	17.3283i	−0.0982346	+	0.709199i
$598$	−4.82813	+	7.38460i	−0.197437	+	0.301979i
$599$	9.91368	−	3.60828i	0.405062	−	0.147430i	−0.131451	−	0.991323i	$-0.541964\pi$
$599$	9.91368	−	3.60828i	0.405062	−	0.147430i	0.536513	+	0.843892i	$0.319741\pi$
$600$	9.03227	−	69.3790i	0.368741	−	2.83238i
$601$	6.15356	+	2.23971i	0.251009	+	0.0913598i	0.464460	−	0.885594i	$-0.346248\pi$
$601$	6.15356	+	2.23971i	0.251009	+	0.0913598i	−0.213451	+	0.976954i	$0.568470\pi$
$602$	10.3859	−	15.0552i	0.423300	−	0.613605i
$603$	−12.3886	−	5.98149i	−0.504503	−	0.243585i
$604$	24.7011	−	23.5602i	1.00507	−	0.958650i
$605$	44.9086	−	7.91861i	1.82580	−	0.321937i
$606$	2.76728	−	0.949435i	0.112413	−	0.0385682i
$607$	−0.718566	−	1.97424i	−0.0291657	−	0.0801321i	0.924255	−	0.381775i	$-0.124687\pi$
$607$	−0.718566	−	1.97424i	−0.0291657	−	0.0801321i	−0.953421	+	0.301643i	$0.902465\pi$
$608$	10.5081	−	14.5241i	0.426161	−	0.589031i
$609$	3.00049	+	1.68443i	0.121586	+	0.0682565i
$610$	−5.13086	−	16.9697i	−0.207742	−	0.687083i
$611$	40.3052			1.63058
$612$	26.5195	+	5.69813i	1.07199	+	0.230333i
$613$	−16.2623			−0.656827			−0.328414	−	0.944534i	$-0.606514\pi$
$613$	−16.2623			−0.656827			−0.328414	+	0.944534i	$0.606514\pi$
$614$	−27.1774	−	6.36295i	−1.09679	−	0.256788i
$615$	55.1293	−	34.6011i	2.22303	−	1.39525i
$616$	3.01838	−	5.03251i	0.121614	−	0.202766i
$617$	−1.86823	−	5.13293i	−0.0752122	−	0.206644i	0.896389	−	0.443268i	$-0.146181\pi$
$617$	−1.86823	−	5.13293i	−0.0752122	−	0.206644i	−0.971601	+	0.236624i	$0.923959\pi$
$618$	13.4344	−	22.3029i	0.540413	−	0.897153i
$619$	13.3888	−	36.7855i	0.538142	−	1.47853i	−0.311022	−	0.950403i	$-0.600671\pi$
$619$	13.3888	−	36.7855i	0.538142	−	1.47853i	0.849164	−	0.528130i	$-0.177107\pi$
$620$	31.2570	−	7.58830i	1.25531	−	0.304753i
$621$	−3.47888	−	7.02614i	−0.139603	−	0.281949i
$622$	−11.8544	−	5.07520i	−0.475319	−	0.203497i
$623$	−9.57131	+	15.6662i	−0.383466	+	0.627651i
$624$	−27.0190	+	9.51774i	−1.08162	+	0.381015i
$625$	82.3897	+	69.1332i	3.29559	+	2.76533i
$626$	−4.13845	−	0.229717i	−0.165406	−	0.00918135i
$627$	2.28820	+	3.64574i	0.0913819	+	0.145597i
$628$	1.28808	−	1.75004i	0.0514000	−	0.0698340i
$629$	−34.7373	+	20.0556i	−1.38507	+	0.799669i
$630$	−46.4256	+	16.5566i	−1.84964	+	0.659631i
$631$	−1.20648	−	0.696560i	−0.0480291	−	0.0277296i	0.475793	−	0.879557i	$-0.342161\pi$
$631$	−1.20648	−	0.696560i	−0.0480291	−	0.0277296i	−0.523822	+	0.851828i	$0.675494\pi$
$632$	−39.0540	+	0.319459i	−1.55349	+	0.0127074i
$633$	4.65895	+	21.7064i	0.185177	+	0.862754i
$634$	−15.4800	+	7.82727i	−0.614789	+	0.310861i
$635$	−79.3647	+	28.8864i	−3.14949	+	1.14632i
$636$	−6.45101	+	9.47801i	−0.255799	+	0.375827i
$637$	6.43500	−	28.2188i	0.254964	−	1.11807i
$638$	0.499090	+	0.666592i	0.0197592	+	0.0263906i
$639$	4.55548	+	1.28669i	0.180212	+	0.0509006i
$640$	15.1539	+	47.3116i	0.599009	+	1.87015i
$641$	13.7592	+	16.3976i	0.543457	+	0.647667i	0.965959	−	0.258695i	$-0.0832926\pi$
$641$	13.7592	+	16.3976i	0.543457	+	0.647667i	−0.422502	+	0.906362i	$0.638848\pi$
$642$	−11.1977	+	1.76088i	−0.441939	+	0.0694962i
$643$	−15.0017	+	17.8784i	−0.591611	+	0.705055i	−0.975915	−	0.218152i	$-0.929997\pi$
$643$	−15.0017	+	17.8784i	−0.591611	+	0.705055i	0.384304	+	0.923207i	$0.374442\pi$
$644$	1.08043	−	7.91066i	0.0425747	−	0.311724i
$645$	−36.8261	−	5.10096i	−1.45002	−	0.200850i
$646$	−19.3938	+	5.86379i	−0.763039	+	0.230708i
$647$	−6.23943	+	10.8070i	−0.245297	+	0.424867i	−0.962215	−	0.272290i	$-0.912219\pi$
$647$	−6.23943	+	10.8070i	−0.245297	+	0.424867i	0.716918	+	0.697158i	$0.245552\pi$
$648$	4.89029	−	24.9817i	0.192109	−	0.981374i
$649$	−2.76157	−	4.78318i	−0.108401	−	0.187756i
$650$	19.0369	−	81.3105i	0.746690	−	3.18926i
$651$	−10.9427	−	12.7262i	−0.428879	−	0.498779i
$652$	−6.70085	+	13.5259i	−0.262426	+	0.529715i
$653$	−37.7833	−	6.66222i	−1.47858	−	0.260713i	−0.624567	−	0.780971i	$-0.714725\pi$
$653$	−37.7833	−	6.66222i	−1.47858	−	0.260713i	−0.854009	+	0.520258i	$0.825836\pi$
$654$	−26.2834	−	32.5307i	−1.02776	−	1.27205i
$655$	−2.55897	−	3.04967i	−0.0999873	−	0.119160i
$656$	−18.4978	+	28.8039i	−0.722216	+	1.12460i
$657$	10.4850	+	41.3522i	0.409059	+	1.61330i
$658$	−32.9478	+	15.6447i	−1.28444	+	0.609893i
$659$	24.0222	−	20.1570i	0.935773	−	0.785207i	−0.0410719	−	0.999156i	$-0.513077\pi$
$659$	24.0222	−	20.1570i	0.935773	−	0.785207i	0.976845	+	0.213950i	$0.0686328\pi$
$660$	−11.8956	−	0.881985i	−0.463037	−	0.0343312i
$661$	−13.6613	−	11.4632i	−0.531361	−	0.445865i	0.337210	−	0.941429i	$-0.390517\pi$
$661$	−13.6613	−	11.4632i	−0.531361	−	0.445865i	−0.868571	+	0.495565i	$0.834961\pi$
$662$	7.59314	−	3.83938i	0.295116	−	0.149222i
$663$	30.8113	+	9.94354i	1.19661	+	0.386175i
$664$	−0.224290	−	0.127059i	−0.00870413	−	0.00493085i
$665$	24.3585	−	27.6070i	0.944583	−	1.07055i
$666$	19.4162	+	32.2494i	0.752362	+	1.24964i
$667$	0.981180	+	0.566484i	0.0379914	+	0.0219344i
$668$	−19.8733	−	2.21307i	−0.768921	−	0.0856264i
$669$	−23.8136	−	37.9417i	−0.920687	−	1.46691i
$670$	−15.5832	+	23.8344i	−0.602032	+	0.920804i
$671$	−2.10372	+	0.765693i	−0.0812133	+	0.0295592i
$672$	18.3925	−	18.2679i	0.709506	−	0.704700i
$673$	−0.798285	−	4.52730i	−0.0307716	−	0.174515i	0.965549	−	0.260223i	$-0.0837959\pi$
$673$	−0.798285	−	4.52730i	−0.0307716	−	0.174515i	−0.996320	+	0.0857079i	$0.972685\pi$
$674$	2.18931	+	18.2980i	0.0843292	+	0.704811i
$675$	53.6875	+	51.2304i	2.06643	+	1.97186i
$676$	−7.96089	+	1.93268i	−0.306188	+	0.0743337i
$677$	1.72055	+	2.05047i	0.0661259	+	0.0788058i	0.798093	−	0.602534i	$-0.205842\pi$
$677$	1.72055	+	2.05047i	0.0661259	+	0.0788058i	−0.731967	+	0.681340i	$0.761398\pi$
$678$	8.83682	+	15.9836i	0.339376	+	0.613848i
$679$	−1.67181	−	2.09597i	−0.0641581	−	0.0804358i
$680$	18.7713	−	52.9166i	0.719848	−	2.02926i
$681$	−16.8145	−	8.89763i	−0.644335	−	0.340958i
$682$	−1.17553	−	3.88794i	−0.0450135	−	0.148877i
$683$	−3.93500			−0.150569			−0.0752843	−	0.997162i	$-0.523986\pi$
$683$	−3.93500			−0.150569			−0.0752843	+	0.997162i	$0.523986\pi$
$684$	5.83579	+	18.0966i	0.223137	+	0.691939i
$685$	22.6391	−	39.2120i	0.864995	−	1.49821i
$686$	5.69292	+	25.5654i	0.217357	+	0.976092i
$687$	11.0147	−	34.1303i	0.420235	−	1.30215i
$688$	18.6692	−	5.81180i	0.711757	−	0.221573i
$689$	−8.79635	+	10.4831i	−0.335114	+	0.399373i
$690$	−15.3507	+	5.26671i	−0.584390	+	0.200500i
$691$	3.13223	−	8.60572i	0.119156	−	0.327377i	−0.865748	−	0.500480i	$-0.833157\pi$
$691$	3.13223	−	8.60572i	0.119156	−	0.327377i	0.984904	+	0.173103i	$0.0553792\pi$
$692$	−3.78646	−	15.5968i	−0.143940	−	0.592902i
$693$	2.41247	+	5.73772i	0.0916421	+	0.217958i
$694$	4.31267	+	36.0446i	0.163707	+	1.36824i
$695$	−3.60929	−	20.4693i	−0.136908	−	0.776444i
$696$	1.41261	+	3.39650i	0.0535450	+	0.128744i
$697$	36.3558	−	13.2324i	1.37707	−	0.501213i
$698$	18.4054	+	36.4003i	0.696653	+	1.37777i
$699$	16.9277	+	13.1713i	0.640264	+	0.498183i
$700$	15.9992	+	73.8572i	0.604713	+	2.79154i
$701$		−	47.5482i		−	1.79587i	−0.440128	−	0.897935i	$-0.645067\pi$
$701$		−	47.5482i		−	1.79587i	0.440128	−	0.897935i	$-0.354933\pi$
$702$	8.79997	−	29.0817i	0.332134	−	1.09762i
$703$	−24.3506	−	14.0588i	−0.918400	−	0.530238i
$704$	5.85924	−	2.24180i	0.220828	−	0.0844910i
$705$	58.5125	+	45.5280i	2.20371	+	1.71468i
$706$	−1.51245	+	27.2474i	−0.0569217	+	1.02547i
$707$	−2.47042	+	1.97049i	−0.0929098	+	0.0741078i
$708$	−6.62663	−	23.4811i	−0.249044	−	0.882475i
$709$	3.04205	+	17.2523i	0.114247	+	0.647925i	0.987120	+	0.159979i	$0.0511426\pi$
$709$	3.04205	+	17.2523i	0.114247	+	0.647925i	−0.872874	+	0.487946i	$0.837746\pi$
$710$	3.85648	−	9.00779i	0.144731	−	0.338056i
$711$	24.2153	−	33.6096i	0.908144	−	1.26046i
$712$	−18.3870	+	6.86318i	−0.689084	+	0.257208i
$713$	−3.55220	−	4.23335i	−0.133031	−	0.158540i
$714$	−29.0466	+	3.83113i	−1.08704	+	0.143377i
$715$	−14.0212	−	2.47232i	−0.524365	−	0.0924597i
$716$	15.3418	+	7.60046i	0.573349	+	0.284042i
$717$	−13.2279	+	40.9884i	−0.494007	+	1.53074i
$718$	−9.76926	+	41.7264i	−0.364586	+	1.55722i
$719$	−24.8847			−0.928044			−0.464022	−	0.885824i	$-0.653594\pi$
$719$	−24.8847			−0.928044			−0.464022	+	0.885824i	$0.653594\pi$
$720$	−49.9754	−	16.7028i	−1.86247	−	0.622478i
$721$	−5.56974	+	27.5656i	−0.207428	+	1.02660i
$722$	9.23756	+	8.66771i	0.343786	+	0.322579i
$723$	−8.71761	+	5.47148i	−0.324211	+	0.203487i
$724$	12.8636	+	6.37276i	0.478073	+	0.236842i
$725$	−10.5607	−	1.86214i	−0.392216	−	0.0691582i
$726$	0.472032	−	25.4337i	0.0175188	−	0.943934i
$727$	−13.8884	+	2.44891i	−0.515094	+	0.0908249i	−0.425152	−	0.905122i	$-0.639779\pi$
$727$	−13.8884	+	2.44891i	−0.515094	+	0.0908249i	−0.0899419	+	0.995947i	$0.528668\pi$
$728$	24.0306	−	19.4913i	0.890633	−	0.722396i
$729$	18.3045	+	19.8481i	0.677944	+	0.735114i
$730$	87.6810	−	10.4908i	3.24522	−	0.388284i
$731$	−20.7660	−	7.55820i	−0.768058	−	0.279550i
$732$	−9.83961	+	0.992469i	−0.363682	+	0.0366827i
$733$	−9.29239	−	7.79724i	−0.343222	−	0.287998i	0.454839	−	0.890573i	$-0.349697\pi$
$733$	−9.29239	−	7.79724i	−0.343222	−	0.287998i	−0.798062	+	0.602576i	$0.794141\pi$
$734$	−41.4208	+	20.9439i	−1.52887	+	0.773054i
$735$	41.2173	−	33.6973i	1.52032	−	1.24294i
$736$	6.12797	−	5.94141i	0.225880	−	0.219003i
$737$	3.11423	+	1.79800i	0.114714	+	0.0662303i
$738$	−13.0417	−	33.8854i	−0.480073	−	1.24734i
$739$	−2.53944	+	1.46615i	−0.0934149	+	0.0539331i	−0.545980	−	0.837798i	$-0.683842\pi$
$739$	−2.53944	+	1.46615i	−0.0934149	+	0.0539331i	0.452565	+	0.891732i	$0.350509\pi$
$740$	71.3783	−	31.2523i	2.62392	−	1.14886i
$741$	4.76274	+	22.1900i	0.174963	+	0.815169i
$742$	3.12158	−	11.9838i	0.114597	−	0.439940i
$743$	−4.57662	+	25.9553i	−0.167900	+	0.952208i	0.778124	+	0.628111i	$0.216172\pi$
$743$	−4.57662	+	25.9553i	−0.167900	+	0.952208i	−0.946024	+	0.324097i	$0.894940\pi$
$744$	−0.808469	−	17.9245i	−0.0296399	−	0.657144i
$745$	−1.29702	−	7.35576i	−0.0475191	−	0.269494i
$746$	4.08047	+	34.1040i	0.149397	+	1.24863i
$747$	0.249334	−	0.112200i	0.00912264	−	0.00410519i
$748$	−6.80339	−	1.99644i	−0.248757	−	0.0729971i
$749$	10.7520	−	5.85657i	0.392869	−	0.213994i
$750$	77.6516	−	62.7393i	2.83544	−	2.29091i
$751$	−43.5164	−	7.67312i	−1.58794	−	0.279996i	−0.691235	−	0.722630i	$-0.742933\pi$
$751$	−43.5164	−	7.67312i	−1.58794	−	0.279996i	−0.896702	+	0.442634i	$0.854044\pi$
$752$	−38.0366	−	8.57781i	−1.38705	−	0.312800i
$753$	42.9603	+	5.95063i	1.56556	+	0.216853i
$754$	1.27073	+	4.20280i	0.0462773	+	0.153057i
$755$	74.9453			2.72754
$756$	4.09462	+	27.1889i	0.148920	+	0.988849i
$757$	25.6651			0.932815			0.466407	−	0.884570i	$-0.345548\pi$
$757$	25.6651			0.932815			0.466407	+	0.884570i	$0.345548\pi$
$758$	2.65841	+	8.79237i	0.0965576	+	0.319353i
$759$	0.771491	+	1.89863i	0.0280033	+	0.0689161i
$760$	38.7037	−	7.15142i	1.40393	−	0.259409i
$761$	15.7631	+	2.77945i	0.571411	+	0.100755i	0.451885	−	0.892076i	$-0.350752\pi$
$761$	15.7631	+	2.77945i	0.571411	+	0.100755i	0.119525	+	0.992831i	$0.461863\pi$
$762$	7.31883	+	46.5418i	0.265133	+	1.68603i
$763$	38.5477	+	23.5509i	1.39552	+	0.852600i
$764$	−0.514545	+	1.75344i	−0.0186156	+	0.0634374i
$765$	33.4978	+	49.2392i	1.21111	+	1.78025i
$766$	0.702389	+	5.87046i	0.0253783	+	0.212109i
$767$	−5.05693	−	28.6793i	−0.182595	−	1.03555i
$768$	27.5237	−	3.23182i	0.993177	−	0.116618i
$769$	0.516261	−	2.92786i	0.0186168	−	0.105581i	−0.974083	−	0.226189i	$-0.927373\pi$
$769$	0.516261	−	2.92786i	0.0186168	−	0.105581i	0.992700	+	0.120608i	$0.0384844\pi$
$770$	12.4214	−	3.42140i	0.447637	−	0.123299i
$771$	−24.5340	−	7.91772i	−0.883571	−	0.285150i
$772$	8.11150	+	18.5261i	0.291939	+	0.666770i
$773$	−46.2183	+	26.6841i	−1.66236	+	0.959761i	−0.690769	+	0.723075i	$0.742728\pi$
$773$	−46.2183	+	26.6841i	−1.66236	+	0.959761i	−0.971586	+	0.236686i	$0.923939\pi$
$774$	−6.73464	+	19.6151i	−0.242071	+	0.705049i
$775$	45.2986	+	26.1532i	1.62718	+	0.939450i
$776$	−0.0234442	−	2.86607i	−0.000841596	−	0.102886i
$777$	−31.4597	−	25.7579i	−1.12861	−	0.924059i
$778$	24.9310	−	12.6061i	0.893821	−	0.451950i
$779$	20.7756	+	17.4328i	0.744364	+	0.624596i
$780$	−57.3486	−	25.8221i	−2.05341	−	0.924578i
$781$	−1.16274	−	0.423203i	−0.0416061	−	0.0151434i
$782$	−9.57835	+	1.14603i	−0.342521	+	0.0409820i
$783$	−3.79135	−	0.921317i	−0.135492	−	0.0329252i
$784$	−12.0783	+	25.2609i	−0.431369	+	0.902175i
$785$	4.69833	−	0.828443i	0.167691	−	0.0295684i
$786$	−1.94352	+	1.07451i	−0.0693230	+	0.0383264i
$787$	−49.6296	−	8.75104i	−1.76910	−	0.311941i	−0.808218	−	0.588884i	$-0.799568\pi$
$787$	−49.6296	−	8.75104i	−1.76910	−	0.311941i	−0.960886	+	0.276943i	$0.910679\pi$
$788$	7.40909	−	14.9555i	0.263938	−	0.532768i
$789$	0.728070	+	19.7252i	0.0259200	+	0.702236i
$790$	−62.5305	−	58.6730i	−2.22473	−	2.08749i
$791$	−14.7923	−	13.0517i	−0.525954	−	0.464067i
$792$	−1.75622	+	6.41807i	−0.0624045	+	0.228056i
$793$	−11.8041			−0.419176
$794$	−5.81871	+	24.8528i	−0.206498	+	0.881994i
$795$	−24.6114	+	5.28246i	−0.872878	+	0.187350i
$796$	8.96718	−	18.1006i	0.317833	−	0.641557i
$797$	18.5692	+	3.27426i	0.657756	+	0.115980i	0.492557	−	0.870280i	$-0.336062\pi$
$797$	18.5692	+	3.27426i	0.657756	+	0.115980i	0.165199	+	0.986260i	$0.447173\pi$
$798$	−12.5065	−	16.2907i	−0.442725	−	0.576684i
$799$	28.3267	+	33.7584i	1.00213	+	1.19429i
$800$	−35.2700	+	72.6823i	−1.24698	+	2.56971i
$801$	5.65828	−	20.0329i	0.199926	−	0.707829i
$802$	11.3532	−	26.5182i	0.400895	−	0.936390i
$803$	−1.93640	−	10.9819i	−0.0683340	−	0.387542i
$804$	11.3805	+	11.0827i	0.401359	+	0.390855i
$805$	13.7039	−	10.9307i	0.483000	−	0.385256i
$806$	1.18695	−	21.3835i	0.0418086	−	0.753200i
$807$	−6.66311	+	2.70749i	−0.234553	+	0.0953081i
$808$	−3.37810	+	0.0276326i	−0.118841	+	0.000972111i
$809$	28.4991	+	16.4540i	1.00198	+	0.578491i	0.908832	−	0.417162i	$-0.136975\pi$
$809$	28.4991	+	16.4540i	1.00198	+	0.578491i	0.0931436	+	0.995653i	$0.470308\pi$
$810$	45.6254	−	32.2787i	1.60311	−	1.13416i
$811$		−	9.92289i		−	0.348440i	−0.984707	−	0.174220i	$-0.944260\pi$
$811$		−	9.92289i		−	0.348440i	0.984707	−	0.174220i	$-0.0557404\pi$
$812$	−2.67011	−	2.94237i	−0.0937024	−	0.103257i
$813$	−5.16712	+	37.3037i	−0.181219	+	1.30830i
$814$	−4.44002	−	8.78103i	−0.155623	−	0.307775i
$815$	−31.1423	+	11.3349i	−1.09087	+	0.397044i
$816$	−26.9608	−	15.9411i	−0.943817	−	0.558052i
$817$	−2.68999	−	15.2557i	−0.0941107	−	0.533728i
$818$	5.33771	+	44.6118i	0.186629	+	1.55982i
$819$	1.60587	+	32.7792i	0.0561135	+	1.14540i
$820$	−73.0359	+	17.7310i	−2.55053	+	0.619195i
$821$	7.30350	−	20.0662i	0.254894	−	0.700315i	−0.744569	−	0.667545i	$-0.767345\pi$
$821$	7.30350	−	20.0662i	0.254894	−	0.700315i	0.999463	−	0.0327697i	$-0.0104328\pi$
$822$	−19.0440	−	16.5916i	−0.664235	−	0.578699i
$823$	−29.8722	+	35.6003i	−1.04128	+	1.24095i	−0.0713787	+	0.997449i	$0.522740\pi$
$823$	−29.8722	+	35.6003i	−1.04128	+	1.24095i	−0.969901	+	0.243500i	$0.921705\pi$
$824$	−22.8718	+	19.5128i	−0.796779	+	0.679760i
$825$	−13.0082	−	14.3895i	−0.452888	−	0.500977i
$826$	15.2658	+	21.4812i	0.531166	+	0.747427i
$827$	−8.02969	+	13.9078i	−0.279220	+	0.483623i	−0.971191	−	0.238302i	$-0.923409\pi$
$827$	−8.02969	+	13.9078i	−0.279220	+	0.483623i	0.691971	+	0.721925i	$0.256742\pi$
$828$	1.24016	+	8.96778i	0.0430984	+	0.311652i
$829$	−41.8356			−1.45301			−0.726506	−	0.687160i	$-0.758857\pi$
$829$	−41.8356			−1.45301			−0.726506	+	0.687160i	$0.758857\pi$
$830$	−0.163797	−	0.541741i	−0.00568549	−	0.0188041i
$831$	−0.297633	−	8.06361i	−0.0103248	−	0.279724i
$832$	33.0735	−	0.541113i	1.14662	−	0.0187597i
$833$	28.1577	−	14.4425i	0.975607	−	0.500403i
$834$	−11.5926	−	0.215152i	−0.401420	−	0.00745009i
$835$	−28.2198	−	33.6310i	−0.976586	−	1.16385i
$836$	−1.17257	−	4.82992i	−0.0405541	−	0.167046i
$837$	15.8407	+	10.5478i	0.547534	+	0.364586i
$838$	−1.45376	−	12.1503i	−0.0502194	−	0.419727i
$839$	−1.35841	−	7.70393i	−0.0468975	−	0.265969i	0.952339	−	0.305042i	$-0.0986706\pi$
$839$	−1.35841	−	7.70393i	−0.0468975	−	0.265969i	−0.999236	+	0.0390731i	$0.987559\pi$
$840$	56.9030	−	1.15171i	1.96334	−	0.0397379i
$841$	−26.7213	+	9.72575i	−0.921423	+	0.335371i
$842$	20.1940	−	30.8866i	0.695932	−	1.06442i
$843$	−32.2113	+	1.18894i	−1.10942	+	0.0409492i
$844$	2.83718	−	25.4778i	0.0976598	−	0.876982i
$845$	−15.5764	−	8.99304i	−0.535845	−	0.309370i
$846$	31.1886	−	27.1602i	1.07229	−	0.933788i
$847$	8.75335	+	26.0447i	0.300769	+	0.894905i
$848$	10.5323	−	8.02097i	0.361679	−	0.275441i
$849$	−5.43634	−	25.3284i	−0.186575	−	0.869267i
$850$	81.4825	−	41.2006i	2.79483	−	1.41317i
$851$	−10.2554	−	8.60528i	−0.351550	−	0.294985i
$852$	−4.51866	−	3.07554i	−0.154807	−	0.105366i
$853$	−28.9885	+	24.3242i	−0.992546	+	0.832845i	−0.985934	−	0.167133i	$-0.946549\pi$
$853$	−28.9885	+	24.3242i	−0.992546	+	0.832845i	−0.00661182	+	0.999978i	$0.502105\pi$
$854$	9.64937	−	4.58183i	0.330194	−	0.156787i
$855$	−18.1511	+	37.5939i	−0.620756	+	1.28568i
$856$	12.9082	+	2.16735i	0.441194	+	0.0740786i
$857$	−13.8171	−	16.4665i	−0.471982	−	0.562486i	0.476558	−	0.879143i	$-0.341884\pi$
$857$	−13.8171	−	16.4665i	−0.471982	−	0.562486i	−0.948540	+	0.316657i	$0.897440\pi$
$858$	−2.85442	+	7.41154i	−0.0974481	+	0.253026i
$859$	2.42549	+	0.427679i	0.0827565	+	0.0145922i	0.214873	−	0.976642i	$-0.431066\pi$
$859$	2.42549	+	0.427679i	0.0827565	+	0.0145922i	−0.132117	+	0.991234i	$0.542177\pi$
$860$	38.4673	+	19.0570i	1.31172	+	0.649840i
$861$	25.5690	+	29.7364i	0.871390	+	1.01341i
$862$	10.2412	−	43.7421i	0.348816	−	1.48986i
$863$	−17.4524	−	30.2285i	−0.594087	−	1.02899i	−0.993675	−	0.112294i	$-0.964180\pi$
$863$	−17.4524	−	30.2285i	−0.594087	−	1.02899i	0.399588	−	0.916695i	$-0.369153\pi$
$864$	−14.4939	+	25.5720i	−0.493091	+	0.869978i
$865$	17.6190	−	30.5170i	0.599064	−	1.03761i
$866$	−10.3501	+	3.12939i	−0.351710	+	0.106341i
$867$	2.24143	+	5.51614i	0.0761228	+	0.187338i
$868$	7.32981	+	17.9408i	0.248790	+	0.608950i
$869$	−6.96018	+	8.29482i	−0.236108	+	0.281382i
$870$	−2.90263	+	7.53674i	−0.0984085	+	0.255519i
$871$	12.1876	+	14.5246i	0.412962	+	0.492149i
$872$	16.8873	+	45.2427i	0.571878	+	1.53211i
$873$	2.46651	+	1.77709i	0.0834788	+	0.0601454i
$874$	−4.05290	−	5.41311i	−0.137091	−	0.183101i
$875$	−56.2167	+	92.0145i	−1.90047	+	3.11066i
$876$	3.64235	−	49.1255i	0.123064	−	1.65980i
$877$	−11.3592	+	4.13440i	−0.383572	+	0.139609i	−0.526607	−	0.850109i	$-0.676536\pi$
$877$	−11.3592	+	4.13440i	−0.383572	+	0.139609i	0.143035	+	0.989718i	$0.454314\pi$
$878$	−44.3943	+	22.4474i	−1.49823	+	0.757564i
$879$	−23.0356	−	7.43415i	−0.776972	−	0.250748i
$880$	12.7059	+	5.31718i	0.428315	+	0.179242i
$881$	−11.1944	−	6.46309i	−0.377149	−	0.217747i	0.299428	−	0.954119i	$-0.403204\pi$
$881$	−11.1944	−	6.46309i	−0.377149	−	0.217747i	−0.676577	+	0.736372i	$0.736537\pi$
$882$	−14.0361	−	26.1723i	−0.472621	−	0.881266i
$883$	−19.0632	+	11.0062i	−0.641528	+	0.370387i	−0.785203	−	0.619238i	$-0.787441\pi$
$883$	−19.0632	+	11.0062i	−0.641528	+	0.370387i	0.143675	+	0.989625i	$0.454108\pi$
$884$	−30.1084	−	22.1607i	−1.01265	−	0.745345i
$885$	25.0542	−	47.3469i	0.842188	−	1.59155i
$886$	0.797160	+	0.0442487i	0.0267811	+	0.00148657i
$887$	−30.9068	−	25.9338i	−1.03775	−	0.870773i	−0.0459950	−	0.998942i	$-0.514646\pi$
$887$	−30.9068	−	25.9338i	−1.03775	−	0.870773i	−0.991752	+	0.128168i	$0.959090\pi$
$888$	−9.46902	−	42.4227i	−0.317760	−	1.42361i
$889$	−24.3420	−	44.6891i	−0.816405	−	1.49883i
$890$	−39.6122	−	16.9591i	−1.32780	−	0.568470i
$891$	−4.38919	−	5.52679i	−0.147044	−	0.185154i
$892$	12.2031	+	50.2656i	0.408588	+	1.68302i
$893$	−10.5656	+	29.0287i	−0.353563	+	0.971408i
$894$	−4.16589	−	0.0773160i	−0.139328	−	0.00258583i
$895$	12.8566	+	35.3233i	0.429749	+	1.18073i
$896$	−26.8261	+	13.2800i	−0.896199	+	0.443653i
$897$	0.398576	+	10.7984i	0.0133081	+	0.360549i
$898$	−3.71391	−	0.869526i	−0.123935	−	0.0290164i
$899$	−2.75013			−0.0917221
$900$	−40.0612	−	75.7472i	−1.33537	−	2.52491i
$901$	−14.9624			−0.498471
$902$	2.74678	+	9.08467i	0.0914579	+	0.302486i
$903$	−0.270088	−	22.3991i	−0.00898797	−	0.745394i
$904$	−3.83186	−	20.7382i	−0.127446	−	0.689741i
$905$	10.7799	+	29.6175i	0.358336	+	0.984520i
$906$	8.02247	−	41.0302i	0.266529	−	1.36314i
$907$	13.2545	−	2.33713i	0.440108	−	0.0776030i	0.0507965	−	0.998709i	$-0.483824\pi$
$907$	13.2545	−	2.33713i	0.440108	−	0.0776030i	0.389312	+	0.921106i	$0.372713\pi$
$908$	15.1613	+	15.8954i	0.503144	+	0.527509i
$909$	2.09458	−	2.90717i	0.0694728	−	0.0964247i
$910$	67.7143	+	5.44833i	2.24471	+	0.180610i
$911$	−5.19154	−	1.88957i	−0.172003	−	0.0626042i	0.254583	−	0.967051i	$-0.418062\pi$
$911$	−5.19154	−	1.88957i	−0.172003	−	0.0626042i	−0.426586	+	0.904447i	$0.640284\pi$
$912$	0.227841	−	21.9546i	0.00754457	−	0.726989i
$913$	−0.0671592	+	0.0244440i	−0.00222265	+	0.000808977i
$914$	−15.7457	+	24.0830i	−0.520823	+	0.796595i
$915$	−17.1364	−	13.3337i	−0.566513	−	0.440798i
$916$	−24.5479	+	33.3516i	−0.811084	+	1.10197i
$917$	1.58702	−	1.79866i	0.0524079	−	0.0593970i
$918$	30.5427	−	13.0682i	1.00806	−	0.431315i
$919$	−29.1931	+	16.8546i	−0.962991	+	0.555983i	−0.897092	−	0.441843i	$-0.854325\pi$
$919$	−29.1931	+	16.8546i	−0.962991	+	0.555983i	−0.0658987	+	0.997826i	$0.520991\pi$
$920$	18.7390	−	0.153284i	0.617808	−	0.00505361i
$921$	−31.6707	+	12.8691i	−1.04359	+	0.424050i
$922$	−16.8032	+	8.49633i	−0.553384	+	0.279812i
$923$	−4.99783	−	4.19368i	−0.164506	−	0.138037i
$924$	−0.543464	−	7.16658i	−0.0178786	−	0.235763i
$925$	119.072	+	43.3385i	3.91505	+	1.42496i
$926$	−25.8488	−	34.5240i	−0.849444	−	1.13453i
$927$	−2.35082	−	31.8014i	−0.0772111	−	1.04449i
$928$	−0.304762	−	4.23667i	−0.0100043	−	0.139076i
$929$	6.03352	−	16.5770i	0.197954	−	0.543873i	−0.800508	−	0.599322i	$-0.795437\pi$
$929$	6.03352	−	16.5770i	0.197954	−	0.543873i	0.998462	+	0.0554493i	$0.0176591\pi$
$930$	25.8775	−	29.7023i	0.848556	−	0.973978i
$931$	18.6369	+	12.0319i	0.610799	+	0.394328i
$932$	−13.7220	−	20.6175i	−0.449478	−	0.675348i
$933$	−15.4416	+	3.31430i	−0.505535	+	0.108505i
$934$	−5.01239	+	21.4089i	−0.164011	+	0.700521i
$935$	−7.78345	−	13.4813i	−0.254546	−	0.440887i
$936$	−20.2756	+	28.6324i	−0.662729	+	0.935881i
$937$	7.33945	+	12.7123i	0.239769	+	0.415293i	0.960648	−	0.277769i	$-0.0895949\pi$
$937$	7.33945	+	12.7123i	0.239769	+	0.415293i	−0.720879	+	0.693061i	$0.756262\pi$
$938$	−15.6007	−	7.14259i	−0.509380	−	0.233214i
$939$	−4.29964	+	2.69861i	−0.140313	+	0.0880657i
$940$	−47.4315	−	71.2666i	−1.54705	−	2.32446i
$941$	−8.10725	−	1.42953i	−0.264289	−	0.0466013i	0.0399333	−	0.999202i	$-0.487285\pi$
$941$	−8.10725	−	1.42953i	−0.264289	−	0.0466013i	−0.304222	+	0.952601i	$0.598397\pi$
$942$	0.0493839	−	2.66087i	0.00160902	−	0.0866958i
$943$	8.30017	+	9.89175i	0.270291	+	0.322120i
$944$	−1.33126	+	28.1412i	−0.0433290	+	0.915919i
$945$	−34.6954	+	49.4006i	−1.12864	+	1.60700i
$946$	2.13359	−	4.98354i	0.0693691	−	0.162029i
$947$	13.6528	−	11.4561i	0.443656	−	0.372272i	−0.393419	−	0.919359i	$-0.628708\pi$
$947$	13.6528	−	11.4561i	0.443656	−	0.372272i	0.837076	+	0.547087i	$0.184263\pi$
$948$	−38.8152	+	27.9528i	−1.26066	+	0.907866i
$949$	10.2100	−	57.9038i	0.331430	−	1.87964i
$950$	53.5712	+	35.0255i	1.73808	+	1.13638i
$951$	−9.93656	+	18.7779i	−0.322215	+	0.608915i
$952$	33.2141	+	6.42872i	1.07648	+	0.208356i
$953$	−38.9204	+	22.4707i	−1.26076	+	0.727898i	−0.973221	−	0.229872i	$-0.926169\pi$
$953$	−38.9204	+	22.4707i	−1.26076	+	0.727898i	−0.287535	+	0.957770i	$0.592836\pi$
$954$	0.257466	+	14.0394i	0.00833576	+	0.454544i
$955$	−3.47456	+	2.00604i	−0.112434	+	0.0649138i
$956$	29.4805	−	40.0533i	0.953468	−	1.29542i
$957$	0.970588	+	0.313232i	0.0313746	+	0.0101254i
$958$	1.89155	−	2.89311i	0.0611132	−	0.0934722i
$959$	25.3966	+	9.96459i	0.820099	+	0.321773i
$960$	48.6252	+	36.5736i	1.56937	+	1.18041i
$961$	−16.5252	−	6.01469i	−0.533072	−	0.194022i
$962$	−6.16357	−	51.5142i	−0.198722	−	1.66089i
$963$	−9.94810	+	9.68348i	−0.320573	+	0.312046i
$964$	11.5492	−	2.80381i	0.371974	−	0.0903047i
$965$	−15.1866	+	41.7248i	−0.488874	+	1.34317i
$966$	−4.51728	−	8.67254i	−0.145341	−	0.279035i
$967$	13.3155	−	15.8687i	0.428196	−	0.510304i	−0.508205	−	0.861236i	$-0.669691\pi$
$967$	13.3155	−	15.8687i	0.428196	−	0.510304i	0.936401	+	0.350932i	$0.114135\pi$
$968$	−9.82018	+	27.6832i	−0.315632	+	0.889772i
$969$	−15.2384	+	19.5843i	−0.489527	+	0.629140i
$970$	4.30585	−	4.58894i	0.138252	−	0.147342i
$971$	−26.5669	−	46.0152i	−0.852572	−	1.47670i	−0.878880	−	0.477044i	$-0.841708\pi$
$971$	−26.5669	−	46.0152i	−0.852572	−	1.47670i	0.0263078	−	0.999654i	$-0.491625\pi$
$972$	−12.7876	−	28.4337i	−0.410163	−	0.912012i
$973$	11.8711	−	3.98976i	0.380570	−	0.127906i
$974$	−20.7521	−	4.85860i	−0.664939	−	0.155680i
$975$	−38.5022	−	94.7538i	−1.23306	−	3.03455i
$976$	11.1397	+	2.51217i	0.356573	+	0.0804125i
$977$	1.67458	+	4.60087i	0.0535746	+	0.147195i	0.963593	−	0.267372i	$-0.0861553\pi$
$977$	1.67458	+	4.60087i	0.0535746	+	0.147195i	−0.910019	+	0.414567i	$0.863933\pi$
$978$	2.87188	+	18.2628i	0.0918326	+	0.583980i
$979$	−1.86106	+	5.11321i	−0.0594797	+	0.163419i
$980$	−57.4684	+	21.8299i	−1.83576	+	0.697330i
$981$	−49.2925	−	13.9226i	−1.57379	−	0.444515i
$982$	37.3082	+	15.9727i	1.19055	+	0.509708i
$983$	0.747192	+	4.23754i	0.0238317	+	0.135156i	0.994402	−	0.105661i	$-0.0336957\pi$
$983$	0.747192	+	4.23754i	0.0238317	+	0.135156i	−0.970571	+	0.240817i	$0.922585\pi$
$984$	1.88909	+	41.8829i	0.0602220	+	1.33518i
$985$	34.4339	−	12.5329i	1.09715	−	0.399332i
$986$	−2.62706	+	4.01807i	−0.0836627	+	0.127961i
$987$	−21.8673	+	38.9525i	−0.696044	+	1.23987i
$988$	2.90038	−	26.0453i	0.0922735	−	0.828612i
$989$		−	7.37563i		−	0.234531i
$990$	−12.5158	+	7.53530i	−0.397778	+	0.239488i
$991$		−	24.2742i		−	0.771096i	−0.922688	−	0.385548i	$-0.874012\pi$
$991$		−	24.2742i		−	0.771096i	0.922688	−	0.385548i	$-0.125988\pi$
$992$	−5.67099	+	19.9272i	−0.180054	+	0.632691i
$993$	4.87401	−	9.21080i	0.154672	−	0.292296i
$994$	5.71332	+	1.48822i	0.181215	+	0.0472035i
$995$	41.6751	−	15.1685i	1.32119	−	0.480874i
$996$	−0.314119	+	0.0316836i	−0.00995326	+	0.00100393i
$997$	51.1880	+	18.6309i	1.62114	+	0.590046i	0.983599	−	0.180371i	$-0.0577297\pi$
$997$	51.1880	+	18.6309i	1.62114	+	0.590046i	0.637540	+	0.770417i	$0.279952\pi$
$998$	−32.4014	−	43.2758i	−1.02565	−	1.36987i
$999$	42.2286	+	18.5005i	1.33605	+	0.585330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.14	yes	840
4.3	odd	2	inner	756.2.ci.a.95.92	yes	840
7.2	even	3		756.2.bs.a.527.107	yes	840
27.2	odd	18		756.2.bs.a.515.3	✓	840
28.23	odd	6		756.2.bs.a.527.3	yes	840
108.83	even	18		756.2.bs.a.515.107	yes	840
189.2	odd	18	inner	756.2.ci.a.191.92	yes	840
756.191	even	18	inner	756.2.ci.a.191.14	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.3	✓	840	27.2	odd	18
756.2.bs.a.515.107	yes	840	108.83	even	18
756.2.bs.a.527.3	yes	840	28.23	odd	6
756.2.bs.a.527.107	yes	840	7.2	even	3
756.2.ci.a.95.14	yes	840	1.1	even	1	trivial
756.2.ci.a.95.92	yes	840	4.3	odd	2	inner
756.2.ci.a.191.14	yes	840	756.191	even	18	inner
756.2.ci.a.191.92	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35369 + 0.409293i) q^{2} +(-1.06364 + 1.36699i) q^{3} +(1.66496 - 1.10811i) q^{4} +(4.32435 + 0.762500i) q^{5} +(0.880342 - 2.28583i) q^{6} +(-0.0657043 + 2.64494i) q^{7} +(-1.80029 + 2.18150i) q^{8} +(-0.737329 - 2.90798i) q^{9} +O(q^{10})\)	\(q+(-1.35369 + 0.409293i) q^{2} +(-1.06364 + 1.36699i) q^{3} +(1.66496 - 1.10811i) q^{4} +(4.32435 + 0.762500i) q^{5} +(0.880342 - 2.28583i) q^{6} +(-0.0657043 + 2.64494i) q^{7} +(-1.80029 + 2.18150i) q^{8} +(-0.737329 - 2.90798i) q^{9} +(-6.16592 + 0.737740i) q^{10} +(0.136172 + 0.772270i) q^{11} +(-0.256138 + 3.45462i) q^{12} +(-0.717990 + 4.07192i) q^{13} +(-0.993611 - 3.60732i) q^{14} +(-5.64190 + 5.10032i) q^{15} +(1.54417 - 3.68992i) q^{16} +(-3.91513 + 2.26040i) q^{17} +(2.18833 + 3.63472i) q^{18} +(-2.74447 - 1.58452i) q^{19} +(8.04480 - 3.52234i) q^{20} +(-3.54572 - 2.90308i) q^{21} +(-0.500420 - 0.989680i) q^{22} +(-1.15585 - 0.969872i) q^{23} +(-1.06722 - 4.78132i) q^{24} +(13.4202 + 4.88454i) q^{25} +(-0.694675 - 5.80599i) q^{26} +(4.75944 + 2.08513i) q^{27} +(2.82149 + 4.47651i) q^{28} +(-0.739473 + 0.130389i) q^{29} +(5.54985 - 9.21345i) q^{30} +(3.60690 + 0.635994i) q^{31} +(-0.580064 + 5.62704i) q^{32} +(-1.20052 - 0.635273i) q^{33} +(4.37470 - 4.66232i) q^{34} +(-2.30089 + 11.3875i) q^{35} +(-4.44999 - 4.02462i) q^{36} +8.87259 q^{37} +(4.36370 + 1.02166i) q^{38} +(-4.80260 - 5.31256i) q^{39} +(-9.44850 + 8.06085i) q^{40} +(-8.42798 - 1.48608i) q^{41} +(5.98802 + 2.47864i) q^{42} +(3.14209 + 3.74460i) q^{43} +(1.08248 + 1.13490i) q^{44} +(-0.971138 - 13.1373i) q^{45} +(1.96162 + 0.839826i) q^{46} +(-1.69271 - 9.59986i) q^{47} +(3.40165 + 6.03562i) q^{48} +(-6.99137 - 0.347567i) q^{49} +(-20.1660 - 1.11937i) q^{50} +(1.07435 - 7.75620i) q^{51} +(3.31673 + 7.57519i) q^{52} +(2.86627 + 1.65484i) q^{53} +(-7.29624 - 0.874612i) q^{54} +3.44340i q^{55} +(-5.65164 - 4.90500i) q^{56} +(5.08516 - 2.06630i) q^{57} +(0.947650 - 0.479168i) q^{58} +(-6.61842 + 2.40891i) q^{59} +(-3.74178 + 14.7437i) q^{60} +(0.495742 + 2.81149i) q^{61} +(-5.14294 + 0.615342i) q^{62} +(7.73986 - 1.75912i) q^{63} +(-1.51788 - 7.85468i) q^{64} +(-6.20968 + 17.0610i) q^{65} +(1.88515 + 0.368596i) q^{66} +(2.94761 - 3.51283i) q^{67} +(-4.01374 + 8.10187i) q^{68} +(2.55522 - 0.548438i) q^{69} +(-1.54615 - 16.3569i) q^{70} +(-0.788950 + 1.36650i) q^{71} +(7.67117 + 3.62674i) q^{72} -14.2202 q^{73} +(-12.0107 + 3.63149i) q^{74} +(-20.9514 + 13.1498i) q^{75} +(-6.32526 + 0.403025i) q^{76} +(-2.05155 + 0.309425i) q^{77} +(8.67563 + 5.22589i) q^{78} +(8.87571 + 10.5777i) q^{79} +(9.49110 - 14.7791i) q^{80} +(-7.91269 + 4.28828i) q^{81} +(12.0171 - 1.43782i) q^{82} +(0.0158260 + 0.0897540i) q^{83} +(-9.12041 - 0.904452i) q^{84} +(-18.6539 + 6.78948i) q^{85} +(-5.78607 - 3.78300i) q^{86} +(0.608294 - 1.14954i) q^{87} +(-1.92986 - 1.09325i) q^{88} +(6.00926 + 3.46945i) q^{89} +(6.69165 + 17.3864i) q^{90} +(-10.7228 - 2.16658i) q^{91} +(-2.99917 - 0.333985i) q^{92} +(-4.70585 + 4.25413i) q^{93} +(6.22057 + 12.3024i) q^{94} +(-10.6599 - 8.94469i) q^{95} +(-7.07513 - 6.77810i) q^{96} +(-0.776264 + 0.651363i) q^{97} +(9.60640 - 2.39102i) q^{98} +(2.14534 - 0.965402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more