LMFDB - Embedded newform 108.3.j.a.31.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(7,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			31.16
Character	$\chi$	$=$	108.31
Dual form			108.3.j.a.7.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.443343 - 1.95024i) q^{2} +(-2.60238 - 1.49253i) q^{3} +(-3.60689 + 1.72925i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-1.75705 + 5.73697i) q^{6} +(-0.0265129 - 0.0315969i) q^{7} +(4.97155 + 6.26767i) q^{8} +(4.54473 + 7.76823i) q^{9} +O(q^{10})$	\(q+(-0.443343 - 1.95024i) q^{2} +(-2.60238 - 1.49253i) q^{3} +(-3.60689 + 1.72925i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-1.75705 + 5.73697i) q^{6} +(-0.0265129 - 0.0315969i) q^{7} +(4.97155 + 6.26767i) q^{8} +(4.54473 + 7.76823i) q^{9} +(10.2450 - 0.502357i) q^{10} +(-4.18050 + 0.737135i) q^{11} +(11.9675 + 0.883222i) q^{12} +(-1.91152 + 0.695736i) q^{13} +(-0.0498672 + 0.0657149i) q^{14} +(9.85597 - 11.8147i) q^{15} +(10.0194 - 12.4745i) q^{16} +(-15.1353 + 26.2152i) q^{17} +(13.1351 - 12.3073i) q^{18} +(5.91027 - 3.41230i) q^{19} +(-5.52176 - 19.7575i) q^{20} +(0.0218374 + 0.121798i) q^{21} +(3.29099 + 7.82619i) q^{22} +(-25.3540 + 30.2157i) q^{23} +(-3.58319 - 23.7310i) q^{24} +(-1.22440 - 0.445645i) q^{25} +(2.20431 + 3.41948i) q^{26} +(-0.232786 - 26.9990i) q^{27} +(0.150268 + 0.0681190i) q^{28} +(-20.7044 - 7.53578i) q^{29} +(-27.4111 - 13.9836i) q^{30} +(-25.1859 + 30.0153i) q^{31} +(-28.7702 - 14.0097i) q^{32} +(11.9794 + 4.32121i) q^{33} +(57.8360 + 17.8953i) q^{34} +(0.183199 - 0.105770i) q^{35} +(-29.8256 - 20.1602i) q^{36} +(15.9508 - 27.6276i) q^{37} +(-9.27508 - 10.0136i) q^{38} +(6.01290 + 1.04243i) q^{39} +(-36.0838 + 19.5281i) q^{40} +(53.8833 - 19.6119i) q^{41} +(0.227855 - 0.0965866i) q^{42} +(-40.8395 + 7.20111i) q^{43} +(13.8039 - 9.88791i) q^{44} +(-43.2827 + 16.0359i) q^{45} +(70.1685 + 36.0505i) q^{46} +(-9.40005 - 11.2025i) q^{47} +(-44.6926 + 17.5091i) q^{48} +(8.50847 - 48.2539i) q^{49} +(-0.326287 + 2.58545i) q^{50} +(78.5146 - 45.6318i) q^{51} +(5.69155 - 5.81495i) q^{52} -43.0946 q^{53} +(-52.5514 + 12.4238i) q^{54} -21.7710i q^{55} +(0.0662283 - 0.323260i) q^{56} +(-20.4737 + 0.0588402i) q^{57} +(-5.51746 + 43.7195i) q^{58} +(40.5818 + 7.15567i) q^{59} +(-15.1189 + 59.6578i) q^{60} +(14.2464 - 11.9542i) q^{61} +(69.7032 + 35.8115i) q^{62} +(0.124958 - 0.349558i) q^{63} +(-14.5673 + 62.3201i) q^{64} +(-1.81161 - 10.2742i) q^{65} +(3.11641 - 25.2786i) q^{66} +(-16.7275 - 45.9585i) q^{67} +(9.25890 - 120.728i) q^{68} +(111.078 - 40.7912i) q^{69} +(-0.287497 - 0.310390i) q^{70} +(111.053 + 64.1166i) q^{71} +(-26.0944 + 67.1050i) q^{72} +(63.7153 + 110.358i) q^{73} +(-60.9523 - 18.8595i) q^{74} +(2.52121 + 2.98718i) q^{75} +(-15.4170 + 22.5281i) q^{76} +(0.134128 + 0.112547i) q^{77} +(-0.632789 - 12.1888i) q^{78} +(-1.11267 + 3.05705i) q^{79} +(54.0821 + 61.7146i) q^{80} +(-39.6909 + 70.6090i) q^{81} +(-62.1368 - 96.3907i) q^{82} +(-40.0201 + 109.954i) q^{83} +(-0.289385 - 0.401551i) q^{84} +(-118.926 - 99.7911i) q^{85} +(32.1498 + 76.4544i) q^{86} +(42.6332 + 50.5128i) q^{87} +(-25.4037 - 22.5373i) q^{88} +(-26.9272 - 46.6393i) q^{89} +(50.4630 + 77.3023i) q^{90} +(0.0726630 + 0.0419520i) q^{91} +(39.1986 - 152.828i) q^{92} +(110.342 - 40.5206i) q^{93} +(-17.6802 + 23.2989i) q^{94} +(11.9710 + 32.8901i) q^{95} +(53.9611 + 79.3990i) q^{96} +(-5.60171 - 31.7689i) q^{97} +(-97.8790 + 4.79945i) q^{98} +(-24.7255 - 29.1250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.443343	−	1.95024i	−0.221671	−	0.975121i
$2$	−0.443343	−	1.95024i	−0.221671	−	0.975121i
$3$	−2.60238	−	1.49253i	−0.867459	−	0.497509i
$3$	−2.60238	−	1.49253i	−0.867459	−	0.497509i
$4$	−3.60689	+	1.72925i	−0.901724	+	0.432313i
$5$	−0.890579	+	5.05073i	−0.178116	+	1.01015i	0.756370	+	0.654144i	$0.226971\pi$
$5$	−0.890579	+	5.05073i	−0.178116	+	1.01015i	−0.934486	+	0.356001i	$0.884140\pi$
$6$	−1.75705	+	5.73697i	−0.292841	+	0.956161i
$7$	−0.0265129	−	0.0315969i	−0.00378756	−	0.00451384i	0.764147	−	0.645042i	$-0.223160\pi$
$7$	−0.0265129	−	0.0315969i	−0.00378756	−	0.00451384i	−0.767935	+	0.640528i	$0.778716\pi$
$8$	4.97155	+	6.26767i	0.621444	+	0.783459i
$9$	4.54473	+	7.76823i	0.504970	+	0.863137i
$10$	10.2450	−	0.502357i	1.02450	−	0.0502357i
$11$	−4.18050	+	0.737135i	−0.380045	+	0.0670123i	−0.360408	−	0.932795i	$-0.617362\pi$
$11$	−4.18050	+	0.737135i	−0.380045	+	0.0670123i	−0.0196378	+	0.999807i	$0.506251\pi$
$12$	11.9675	+	0.883222i	0.997288	+	0.0736018i
$13$	−1.91152	+	0.695736i	−0.147040	+	0.0535182i	−0.414492	−	0.910053i	$-0.636041\pi$
$13$	−1.91152	+	0.695736i	−0.147040	+	0.0535182i	0.267452	+	0.963571i	$0.413818\pi$
$14$	−0.0498672	+	0.0657149i	−0.00356195	+	0.00469392i
$15$	9.85597	−	11.8147i	0.657065	−	0.787645i
$16$	10.0194	−	12.4745i	0.626211	−	0.779654i
$17$	−15.1353	+	26.2152i	−0.890313	+	1.54207i	−0.0508130	+	0.998708i	$0.516181\pi$
$17$	−15.1353	+	26.2152i	−0.890313	+	1.54207i	−0.839500	+	0.543359i	$0.817152\pi$
$18$	13.1351	−	12.3073i	0.729726	−	0.683739i
$19$	5.91027	−	3.41230i	0.311067	−	0.179595i	−0.336337	−	0.941742i	$-0.609188\pi$
$19$	5.91027	−	3.41230i	0.311067	−	0.179595i	0.647404	+	0.762147i	$0.275855\pi$
$20$	−5.52176	−	19.7575i	−0.276088	−	0.987874i
$21$	0.0218374	+	0.121798i	0.00103988	+	0.00579991i
$22$	3.29099	+	7.82619i	0.149590	+	0.355736i
$23$	−25.3540	+	30.2157i	−1.10235	+	1.31373i	−0.157024	+	0.987595i	$0.550190\pi$
$23$	−25.3540	+	30.2157i	−1.10235	+	1.31373i	−0.945324	+	0.326133i	$0.894254\pi$
$24$	−3.58319	−	23.7310i	−0.149299	−	0.988792i
$25$	−1.22440	−	0.445645i	−0.0489760	−	0.0178258i
$26$	2.20431	+	3.41948i	0.0847813	+	0.131518i
$27$	−0.232786	−	26.9990i	−0.00862169	−	0.999963i
$28$	0.150268	+	0.0681190i	0.00536672	+	0.00243282i
$29$	−20.7044	−	7.53578i	−0.713944	−	0.259854i	−0.0405915	−	0.999176i	$-0.512924\pi$
$29$	−20.7044	−	7.53578i	−0.713944	−	0.259854i	−0.673353	+	0.739321i	$0.735146\pi$
$30$	−27.4111	−	13.9836i	−0.913702	−	0.466119i
$31$	−25.1859	+	30.0153i	−0.812447	+	0.968237i	−0.999901	−	0.0140364i	$-0.995532\pi$
$31$	−25.1859	+	30.0153i	−0.812447	+	0.968237i	0.187454	+	0.982273i	$0.439976\pi$
$32$	−28.7702	−	14.0097i	−0.899070	−	0.437805i
$33$	11.9794	+	4.32121i	0.363013	+	0.130946i
$34$	57.8360	+	17.8953i	1.70106	+	0.526331i
$35$	0.183199	−	0.105770i	0.00523426	−	0.00302200i
$36$	−29.8256	−	20.1602i	−0.828488	−	0.560006i
$37$	15.9508	−	27.6276i	0.431103	−	0.746693i	−0.565865	−	0.824498i	$-0.691458\pi$
$37$	15.9508	−	27.6276i	0.431103	−	0.746693i	0.996969	+	0.0778047i	$0.0247911\pi$
$38$	−9.27508	−	10.0136i	−0.244081	−	0.263517i
$39$	6.01290	+	1.04243i	0.154177	+	0.0267289i
$40$	−36.0838	+	19.5281i	−0.902096	+	0.488203i
$41$	53.8833	−	19.6119i	1.31423	−	0.478340i	0.412623	−	0.910902i	$-0.364613\pi$
$41$	53.8833	−	19.6119i	1.31423	−	0.478340i	0.901604	+	0.432562i	$0.142390\pi$
$42$	0.227855	−	0.0965866i	0.00542511	−	0.00229968i
$43$	−40.8395	+	7.20111i	−0.949756	+	0.167468i	−0.627004	−	0.779016i	$-0.715719\pi$
$43$	−40.8395	+	7.20111i	−0.949756	+	0.167468i	−0.322752	+	0.946484i	$0.604608\pi$
$44$	13.8039	−	9.88791i	0.313726	−	0.224725i
$45$	−43.2827	+	16.0359i	−0.961837	+	0.356354i
$46$	70.1685	+	36.0505i	1.52540	+	0.783708i
$47$	−9.40005	−	11.2025i	−0.200001	−	0.238352i	0.656717	−	0.754137i	$-0.271945\pi$
$47$	−9.40005	−	11.2025i	−0.200001	−	0.238352i	−0.856718	+	0.515785i	$0.827500\pi$
$48$	−44.6926	+	17.5091i	−0.931097	+	0.364772i
$49$	8.50847	−	48.2539i	0.173642	−	0.984774i
$50$	−0.326287	+	2.58545i	−0.00652574	+	0.0517090i
$51$	78.5146	−	45.6318i	1.53950	−	0.894741i
$52$	5.69155	−	5.81495i	0.109453	−	0.111826i
$53$	−43.0946			−0.813105			−0.406553	−	0.913627i	$-0.633269\pi$
$53$	−43.0946			−0.813105			−0.406553	+	0.913627i	$0.633269\pi$
$54$	−52.5514	+	12.4238i	−0.973174	+	0.230070i
$55$		−	21.7710i		−	0.395837i
$56$	0.0662283	−	0.323260i	0.00118265	−	0.00577249i
$57$	−20.4737	+	0.0588402i	−0.359188	+	0.00103228i
$58$	−5.51746	+	43.7195i	−0.0951286	+	0.753785i
$59$	40.5818	+	7.15567i	0.687828	+	0.121283i	0.506629	−	0.862164i	$-0.330891\pi$
$59$	40.5818	+	7.15567i	0.687828	+	0.121283i	0.181199	+	0.983447i	$0.442002\pi$
$60$	−15.1189	+	59.6578i	−0.251981	+	0.994296i
$61$	14.2464	−	11.9542i	0.233548	−	0.195970i	−0.518501	−	0.855077i	$-0.673510\pi$
$61$	14.2464	−	11.9542i	0.233548	−	0.195970i	0.752050	+	0.659107i	$0.229065\pi$
$62$	69.7032	+	35.8115i	1.12424	+	0.577604i
$63$	0.124958	−	0.349558i	0.00198346	−	0.00554853i
$64$	−14.5673	+	62.3201i	−0.227614	+	0.973751i
$65$	−1.81161	−	10.2742i	−0.0278710	−	0.158064i
$66$	3.11641	−	25.2786i	0.0472183	−	0.383009i
$67$	−16.7275	−	45.9585i	−0.249664	−	0.685948i	−0.999699	−	0.0245484i	$-0.992185\pi$
$67$	−16.7275	−	45.9585i	−0.249664	−	0.685948i	0.750034	−	0.661399i	$-0.230037\pi$
$68$	9.25890	−	120.728i	0.136160	−	1.77541i
$69$	111.078	−	40.7912i	1.60983	−	0.591176i
$70$	−0.287497	−	0.310390i	−0.00410710	−	0.00443414i
$71$	111.053	+	64.1166i	1.56413	+	0.903051i	0.996832	+	0.0795386i	$0.0253447\pi$
$71$	111.053	+	64.1166i	1.56413	+	0.903051i	0.567298	+	0.823512i	$0.307989\pi$
$72$	−26.0944	+	67.1050i	−0.362422	+	0.932014i
$73$	63.7153	+	110.358i	0.872813	+	1.51176i	0.859075	+	0.511851i	$0.171040\pi$
$73$	63.7153	+	110.358i	0.872813	+	1.51176i	0.0137383	+	0.999906i	$0.495627\pi$
$74$	−60.9523	−	18.8595i	−0.823680	−	0.254858i
$75$	2.52121	+	2.98718i	0.0336161	+	0.0398291i
$76$	−15.4170	+	22.5281i	−0.202855	+	0.296423i
$77$	0.134128	+	0.112547i	0.00174193	+	0.00146165i
$78$	−0.632789	−	12.1888i	−0.00811268	−	0.156266i
$79$	−1.11267	+	3.05705i	−0.0140845	+	0.0386968i	−0.946536	−	0.322599i	$-0.895443\pi$
$79$	−1.11267	+	3.05705i	−0.0140845	+	0.0386968i	0.932451	+	0.361296i	$0.117666\pi$
$80$	54.0821	+	61.7146i	0.676026	+	0.771433i
$81$	−39.6909	+	70.6090i	−0.490012	+	0.871716i
$82$	−62.1368	−	96.3907i	−0.757766	−	1.17550i
$83$	−40.0201	+	109.954i	−0.482169	+	1.32475i	0.425460	+	0.904977i	$0.360112\pi$
$83$	−40.0201	+	109.954i	−0.482169	+	1.32475i	−0.907629	+	0.419772i	$0.862110\pi$
$84$	−0.289385	−	0.401551i	−0.00344506	−	0.00478037i
$85$	−118.926	−	99.7911i	−1.39913	−	1.17401i
$86$	32.1498	+	76.4544i	0.373835	+	0.889004i
$87$	42.6332	+	50.5128i	0.490037	+	0.580607i
$88$	−25.4037	−	22.5373i	−0.288678	−	0.256105i
$89$	−26.9272	−	46.6393i	−0.302553	−	0.524037i	0.674160	−	0.738585i	$-0.264506\pi$
$89$	−26.9272	−	46.6393i	−0.302553	−	0.524037i	−0.976714	+	0.214548i	$0.931172\pi$
$90$	50.4630	+	77.3023i	0.560700	+	0.858915i
$91$	0.0726630	+	0.0419520i	0.000798495	+	0.000461011i
$92$	39.1986	−	152.828i	0.426072	−	1.66118i
$93$	110.342	−	40.5206i	1.18647	−	0.435706i
$94$	−17.6802	+	23.2989i	−0.188088	+	0.247861i
$95$	11.9710	+	32.8901i	0.126011	+	0.346211i
$96$	53.9611	+	79.3990i	0.562095	+	0.827073i
$97$	−5.60171	−	31.7689i	−0.0577496	−	0.327514i	0.942222	−	0.334988i	$-0.108732\pi$
$97$	−5.60171	−	31.7689i	−0.0577496	−	0.327514i	−0.999972	+	0.00747351i	$0.997621\pi$
$98$	−97.8790	+	4.79945i	−0.998765	+	0.0489740i
$99$	−24.7255	−	29.1250i	−0.249752	−	0.294192i
$100$	5.18691	−	0.509901i	0.0518691	−	0.00509901i
$101$	−105.877	+	88.8411i	−1.04828	+	0.879615i	−0.992912	−	0.118851i	$-0.962079\pi$
$101$	−105.877	+	88.8411i	−1.04828	+	0.879615i	−0.0553723	+	0.998466i	$0.517635\pi$
$102$	−123.802	−	132.892i	−1.21375	−	1.30286i
$103$	70.1342	+	12.3665i	0.680914	+	0.120064i	0.503398	−	0.864054i	$-0.332083\pi$
$103$	70.1342	+	12.3665i	0.680914	+	0.120064i	0.177516	+	0.984118i	$0.443194\pi$
$104$	−13.8639	−	8.52188i	−0.133306	−	0.0819412i
$105$	−0.634617	+	0.00182385i	−0.00604397	+	1.73700e-5i
$106$	19.1057	+	84.0449i	0.180242	+	0.792876i
$107$		−	106.755i		−	0.997712i	−0.866685	−	0.498856i	$-0.833754\pi$
$107$		−	106.755i		−	0.997712i	0.866685	−	0.498856i	$-0.166246\pi$
$108$	47.5277	+	96.9800i	0.440071	+	0.897963i
$109$	53.1106			0.487253			0.243627	−	0.969869i	$-0.421663\pi$
$109$	53.1106			0.487253			0.243627	+	0.969869i	$0.421663\pi$
$110$	−42.4588	+	9.65203i	−0.385989	+	0.0877458i
$111$	−82.7451	+	48.0905i	−0.745451	+	0.433248i
$112$	−0.659797	+	0.0141536i	−0.00589104	+	0.000126371i
$113$	22.6559	−	128.488i	0.200494	−	1.13706i	−0.703880	−	0.710319i	$-0.748551\pi$
$113$	22.6559	−	128.488i	0.200494	−	1.13706i	0.904374	−	0.426740i	$-0.140338\pi$
$114$	9.19162	+	39.9026i	0.0806282	+	0.350023i
$115$	−130.032	−	154.966i	−1.13071	−	1.34753i
$116$	87.7098	−	8.62234i	0.756119	−	0.0743305i
$117$	−14.0920	−	11.6872i	−0.120444	−	0.0998906i
$118$	−4.03637	−	82.3169i	−0.0342065	−	0.697601i
$119$	1.22960	−	0.216811i	0.0103328	−	0.00182194i
$120$	123.050	+	3.03665i	1.02542	+	0.0253054i
$121$	−96.7696	+	35.2213i	−0.799749	+	0.291085i
$122$	−29.6296	−	22.4842i	−0.242866	−	0.184297i
$123$	−169.496	−	29.3847i	−1.37802	−	0.238900i
$124$	38.9386	−	151.815i	0.314021	−	1.22431i
$125$	−60.7668	+	105.251i	−0.486134	+	0.842009i
$126$	−0.737121	−	0.0887244i	−0.00585017	−	0.000704162i
$127$	−90.4208	+	52.2045i	−0.711975	+	0.411059i	−0.811792	−	0.583947i	$-0.801508\pi$
$127$	−90.4208	+	52.2045i	−0.711975	+	0.411059i	0.0998168	+	0.995006i	$0.468174\pi$
$128$	127.998	+	0.780665i	0.999981	+	0.00609894i
$129$	117.028	+	42.2141i	0.907191	+	0.327241i
$130$	−19.2340	+	8.08807i	−0.147954	+	0.0622159i
$131$	87.8938	−	104.748i	0.670945	−	0.799601i	−0.317968	−	0.948102i	$-0.603000\pi$
$131$	87.8938	−	104.748i	0.670945	−	0.799601i	0.988912	+	0.148501i	$0.0474448\pi$
$132$	−50.6810	+	5.12932i	−0.383947	+	0.0388585i
$133$	−0.264516	−	0.0962761i	−0.00198884	−	0.000723880i
$134$	−82.2142	+	52.9981i	−0.613539	+	0.395508i
$135$	136.572	+	22.8690i	1.01164	+	0.169400i
$136$	−239.554	+	35.4668i	−1.76143	+	0.260785i
$137$	100.206	+	36.4722i	0.731434	+	0.266220i	0.680772	−	0.732496i	$-0.261645\pi$
$137$	100.206	+	36.4722i	0.731434	+	0.266220i	0.0506624	+	0.998716i	$0.483867\pi$
$138$	−128.799	−	198.546i	−0.933323	−	1.43874i
$139$	55.0613	−	65.6195i	0.396124	−	0.472083i	−0.530710	−	0.847554i	$-0.678075\pi$
$139$	55.0613	−	65.6195i	0.396124	−	0.472083i	0.926834	+	0.375471i	$0.122519\pi$
$140$	−0.477876	+	0.698298i	−0.00341340	+	0.00498785i
$141$	7.74237	+	43.1831i	0.0549104	+	0.306263i
$142$	75.8083	−	245.006i	0.533861	−	1.72540i
$143$	7.47826	−	4.31757i	0.0522955	−	0.0301928i
$144$	142.440	+	21.1398i	0.989166	+	0.146804i
$145$	56.5001	−	97.8610i	0.389656	−	0.674903i
$146$	186.978	−	173.187i	1.28067	−	1.18621i
$147$	−94.1625	+	112.876i	−0.640561	+	0.767862i
$148$	−9.75778	+	127.233i	−0.0659310	+	0.859682i
$149$	147.356	−	53.6331i	0.988965	−	0.359954i	0.203646	−	0.979045i	$-0.434721\pi$
$149$	147.356	−	53.6331i	0.988965	−	0.359954i	0.785319	+	0.619091i	$0.212499\pi$
$150$	4.70797	−	6.24132i	0.0313865	−	0.0416088i
$151$	−24.6643	+	4.34897i	−0.163339	+	0.0288011i	−0.254720	−	0.967015i	$-0.581983\pi$
$151$	−24.6643	+	4.34897i	−0.163339	+	0.0288011i	0.0913803	+	0.995816i	$0.470872\pi$
$152$	50.7704	+	20.0792i	0.334015	+	0.132100i
$153$	−272.431	+	1.56592i	−1.78060	+	0.0102347i
$154$	0.160029	−	0.311480i	0.00103915	−	0.00202260i
$155$	−129.169	−	153.938i	−0.833350	−	0.993148i
$156$	−23.4905	+	6.63790i	−0.150580	+	0.0425506i
$157$	−19.7195	+	111.835i	−0.125602	+	0.712324i	0.855347	+	0.518056i	$0.173344\pi$
$157$	−19.7195	+	111.835i	−0.125602	+	0.712324i	−0.980949	+	0.194268i	$0.937767\pi$
$158$	6.45528	+	0.814665i	0.0408562	+	0.00515611i
$159$	112.148	+	64.3198i	0.705335	+	0.404527i
$160$	96.3816	−	132.834i	0.602385	−	0.830212i
$161$	1.62693			0.0101052
$162$	155.301	+	46.1030i	0.958650	+	0.284586i
$163$			228.549i			1.40214i	0.713091	+	0.701072i	$0.247295\pi$
$163$			228.549i			1.40214i	−0.713091	+	0.701072i	$0.752705\pi$
$164$	−160.437	+	163.916i	−0.978277	+	0.999488i
$165$	−32.4939	+	56.6564i	−0.196933	+	0.343372i
$166$	232.180	+	29.3014i	1.39867	+	0.176515i
$167$	15.9992	+	2.82109i	0.0958035	+	0.0168927i	0.221344	−	0.975196i	$-0.428956\pi$
$167$	15.9992	+	2.82109i	0.0958035	+	0.0168927i	−0.125541	+	0.992088i	$0.540067\pi$
$168$	−0.654825	+	0.742396i	−0.00389777	+	0.00441902i
$169$	−126.292	+	105.971i	−0.747288	+	0.627049i
$170$	−141.892	+	276.177i	−0.834657	+	1.62457i
$171$	53.3681	+	30.4044i	0.312094	+	0.177804i
$172$	134.851	−	96.5954i	0.784019	−	0.561601i
$173$	16.7323	+	94.8933i	0.0967182	+	0.548516i	0.994207	+	0.107480i	$0.0342781\pi$
$173$	16.7323	+	94.8933i	0.0967182	+	0.548516i	−0.897489	+	0.441037i	$0.854611\pi$
$174$	79.6110	−	105.540i	0.457535	−	0.606550i
$175$	0.0183814	+	0.0505025i	0.000105037	+	0.000288586i
$176$	−32.6906	+	59.5351i	−0.185742	+	0.338268i
$177$	−94.9292	−	79.1913i	−0.536323	−	0.447408i
$178$	−79.0200	+	73.1918i	−0.443933	+	0.411190i
$179$	−198.630	−	114.679i	−1.10967	−	0.640666i	−0.170923	−	0.985284i	$-0.554675\pi$
$179$	−198.630	−	114.679i	−1.10967	−	0.640666i	−0.938743	+	0.344619i	$0.888008\pi$
$180$	128.386	−	132.687i	0.713255	−	0.737148i
$181$	154.487	+	267.580i	0.853522	+	1.47834i	0.878010	+	0.478643i	$0.158871\pi$
$181$	154.487	+	267.580i	0.853522	+	1.47834i	−0.0244878	+	0.999700i	$0.507795\pi$
$182$	0.0496020	−	0.160310i	0.000272538	−	0.000880823i
$183$	−54.9165	+	9.84609i	−0.300090	+	0.0538037i
$184$	−315.431	−	8.69141i	−1.71430	−	0.0472359i
$185$	125.334	+	105.168i	0.677482	+	0.568475i
$186$	−127.944	−	197.229i	−0.687873	−	1.06037i
$187$	43.9491	−	120.749i	0.235022	−	0.645718i
$188$	53.2770	+	24.1513i	0.283388	+	0.128465i
$189$	−0.846912	+	0.723177i	−0.00448101	+	0.00382633i
$190$	58.8364	−	37.9280i	0.309665	−	0.199621i
$191$	−76.7399	+	210.841i	−0.401779	+	1.10388i	0.559626	+	0.828745i	$0.310945\pi$
$191$	−76.7399	+	210.841i	−0.401779	+	1.10388i	−0.961406	+	0.275135i	$0.911278\pi$
$192$	130.924	−	140.438i	0.681896	−	0.731449i
$193$	−130.384	−	109.405i	−0.675564	−	0.566865i	0.239142	−	0.970984i	$-0.423134\pi$
$193$	−130.384	−	109.405i	−0.675564	−	0.566865i	−0.914706	+	0.404119i	$0.867578\pi$
$194$	−59.4736	+	25.0092i	−0.306565	+	0.128913i
$195$	−10.6200	+	29.4412i	−0.0544615	+	0.150980i
$196$	52.7540	+	188.760i	0.269153	+	0.963061i
$197$	−100.143	−	173.453i	−0.508341	−	0.880473i	−0.999953	−	0.00965858i	$-0.996926\pi$
$197$	−100.143	−	173.453i	−0.508341	−	0.880473i	0.491612	−	0.870814i	$-0.336408\pi$
$198$	−45.8390	+	61.1330i	−0.231510	+	0.308753i
$199$	230.445	+	133.047i	1.15801	+	0.668579i	0.950827	−	0.309722i	$-0.100236\pi$
$199$	230.445	+	133.047i	1.15801	+	0.668579i	0.207186	+	0.978301i	$0.433569\pi$
$200$	−3.29401	−	9.88967i	−0.0164701	−	0.0494484i
$201$	−25.0630	+	144.568i	−0.124691	+	0.719242i
$202$	220.201	+	167.098i	1.09011	+	0.827219i
$203$	0.310826	+	0.853989i	0.00153117	+	0.00420684i
$204$	−204.285	+	300.361i	−1.00140	+	1.47236i
$205$	51.0671	+	289.616i	0.249108	+	1.41276i
$206$	−6.97571	−	142.261i	−0.0338627	−	0.690589i
$207$	−349.950	−	59.6337i	−1.69058	−	0.288085i
$208$	−10.4733	+	30.8160i	−0.0503524	+	0.148154i
$209$	−22.1926	+	18.6218i	−0.106184	+	0.0890994i
$210$	0.284910	+	1.23685i	0.00135671	+	0.00588976i
$211$	393.246	+	69.3398i	1.86372	+	0.328625i	0.988032	−	0.154247i	$-0.0492953\pi$
$211$	393.246	+	69.3398i	1.86372	+	0.328625i	0.875691	+	0.482872i	$0.160406\pi$
$212$	155.438	−	74.5214i	0.733196	−	0.351516i
$213$	−193.307	−	332.606i	−0.907542	−	1.56153i
$214$	−208.199	+	47.3292i	−0.972891	+	0.221164i
$215$		−	212.682i		−	0.989220i
$216$	168.063	−	135.686i	0.778072	−	0.628176i
$217$	1.61614			0.00744765
$218$	−23.5462	−	103.579i	−0.108010	−	0.475131i
$219$	−1.09868	−	382.290i	−0.00501680	−	1.74562i
$220$	37.6476	+	78.5258i	0.171126	+	0.356936i
$221$	10.6926	−	60.6410i	0.0483830	−	0.274394i
$222$	130.473	+	140.052i	0.587714	+	0.630867i
$223$	178.190	+	212.358i	0.799056	+	0.952278i	0.999625	−	0.0274016i	$-0.00872331\pi$
$223$	178.190	+	212.358i	0.799056	+	0.952278i	−0.200568	+	0.979680i	$0.564279\pi$
$224$	0.320119	+	1.28049i	0.00142910	+	0.00571647i
$225$	−2.10268	−	11.5368i	−0.00934526	−	0.0512745i
$226$	−260.627	+	12.7797i	−1.15321	+	0.0565473i
$227$	157.783	−	27.8214i	0.695079	−	0.122561i	0.185064	−	0.982727i	$-0.440751\pi$
$227$	157.783	−	27.8214i	0.695079	−	0.122561i	0.510015	+	0.860165i	$0.329640\pi$
$228$	73.7447	−	35.6164i	0.323442	−	0.156212i
$229$	391.957	−	142.661i	1.71160	−	0.622972i	0.714540	−	0.699594i	$-0.246636\pi$
$229$	391.957	−	142.661i	1.71160	−	0.622972i	0.997060	+	0.0766226i	$0.0244136\pi$
$230$	−244.572	+	322.296i	−1.06336	+	1.40129i
$231$	−0.181073	−	0.493080i	−0.000783866	−	0.00213455i
$232$	−55.7012	−	167.233i	−0.240091	−	0.720831i
$233$	113.470	−	196.537i	0.486998	−	0.843505i	−0.512890	−	0.858454i	$-0.671425\pi$
$233$	113.470	−	196.537i	0.486998	−	0.843505i	0.999888	+	0.0149492i	$0.00475865\pi$
$234$	−16.5453	+	32.6642i	−0.0707065	+	0.139591i
$235$	64.9525	−	37.5003i	0.276394	−	0.159576i
$236$	−158.748	+	44.3665i	−0.672663	+	0.187994i
$237$	7.45832	−	6.29489i	0.0314697	−	0.0265607i
$238$	−0.967968	−	2.30189i	−0.00406709	−	0.00967182i
$239$	−100.927	+	120.281i	−0.422290	+	0.503266i	−0.934682	−	0.355486i	$-0.884315\pi$
$239$	−100.927	+	120.281i	−0.422290	+	0.503266i	0.512391	+	0.858752i	$0.328760\pi$
$240$	−48.6311	−	241.324i	−0.202630	−	1.00551i
$241$	−113.715	−	41.3887i	−0.471845	−	0.171737i	0.0951430	−	0.995464i	$-0.469669\pi$
$241$	−113.715	−	41.3887i	−0.471845	−	0.171737i	−0.566988	+	0.823726i	$0.691891\pi$
$242$	111.592	+	173.109i	0.461124	+	0.715327i
$243$	208.677	−	124.511i	0.858751	−	0.512392i
$244$	−30.7136	+	67.7532i	−0.125875	+	0.277677i
$245$	236.140	+	85.9479i	0.963836	+	0.350808i
$246$	17.8375	+	343.586i	0.0725102	+	1.39669i
$247$	−8.92354	+	10.6347i	−0.0361277	+	0.0430553i
$248$	−313.339	−	8.63377i	−1.26346	−	0.0348136i
$249$	268.257	−	226.411i	1.07734	−	0.909282i
$250$	232.206	+	71.8476i	0.928823	+	0.287391i
$251$	−3.42052	+	1.97484i	−0.0136276	+	0.00786788i	−0.506798	−	0.862065i	$-0.669171\pi$
$251$	−3.42052	+	1.97484i	−0.0136276	+	0.00786788i	0.493171	+	0.869933i	$0.335838\pi$
$252$	0.153763	+	1.47690i	0.000610172	+	0.00586072i
$253$	83.7194	−	145.006i	0.330907	−	0.573147i
$254$	141.899	+	153.198i	0.558657	+	0.603142i
$255$	160.550	+	437.195i	0.629609	+	1.71449i
$256$	−55.2243	−	249.973i	−0.215720	−	0.976455i
$257$	70.1778	−	25.5426i	0.273065	−	0.0993876i	−0.201858	−	0.979415i	$-0.564698\pi$
$257$	70.1778	−	25.5426i	0.273065	−	0.0993876i	0.474923	+	0.880027i	$0.342476\pi$
$258$	30.4443	−	246.948i	0.118001	−	0.957161i
$259$	−1.29585	+	0.228493i	−0.00500328	+	0.000882213i
$260$	24.3009	+	33.9251i	0.0934652	+	0.130481i
$261$	−35.5560	−	195.085i	−0.136230	−	0.747450i
$262$	−243.251	−	124.975i	−0.928437	−	0.477004i
$263$	−258.741	−	308.356i	−0.983807	−	1.17246i	−0.985017	−	0.172456i	$-0.944830\pi$
$263$	−258.741	−	308.356i	−0.983807	−	1.17246i	0.00121067	−	0.999999i	$-0.499615\pi$
$264$	32.4725	+	96.5662i	0.123002	+	0.365781i
$265$	38.3791	−	217.659i	0.144827	−	0.821354i
$266$	−0.0704903	+	0.558554i	−0.000265001	+	0.00209983i
$267$	0.464321	+	161.563i	0.00173903	+	0.605104i
$268$	139.808	+	136.841i	0.521672	+	0.510602i
$269$	−256.494			−0.953508			−0.476754	−	0.879037i	$-0.658187\pi$
$269$	−256.494			−0.953508			−0.476754	+	0.879037i	$0.658187\pi$
$270$	−15.9480	−	276.487i	−0.0590668	−	1.02403i
$271$		−	98.1325i		−	0.362112i	−0.983473	−	0.181056i	$-0.942048\pi$
$271$		−	98.1325i		−	0.362112i	0.983473	−	0.181056i	$-0.0579516\pi$
$272$	175.373	+	451.464i	0.644755	+	1.65980i
$273$	−0.126482	−	0.217627i	−0.000463304	−	0.000797167i
$274$	26.7038	−	211.597i	0.0974591	−	0.772251i
$275$	5.44710	+	0.960471i	0.0198076	+	0.00349262i
$276$	−330.110	+	339.212i	−1.19605	+	1.22903i
$277$	−240.716	+	201.985i	−0.869011	+	0.729187i	−0.963890	−	0.266302i	$-0.914198\pi$
$277$	−240.716	+	201.985i	−0.869011	+	0.729187i	0.0948788	+	0.995489i	$0.469754\pi$
$278$	−152.385	−	78.2910i	−0.548147	−	0.281622i
$279$	−347.629	−	59.2382i	−1.24598	−	0.212323i
$280$	1.57371	+	0.622389i	0.00562041	+	0.00222282i
$281$	13.7932	+	78.2252i	0.0490862	+	0.278381i	0.999465	−	0.0327143i	$-0.0104151\pi$
$281$	13.7932	+	78.2252i	0.0490862	+	0.278381i	−0.950379	+	0.311096i	$0.899304\pi$
$282$	80.7849	−	34.2444i	0.286471	−	0.121434i
$283$	−49.7122	−	136.583i	−0.175661	−	0.482626i	0.820349	−	0.571863i	$-0.193779\pi$
$283$	−49.7122	−	136.583i	−0.175661	−	0.482626i	−0.996010	+	0.0892374i	$0.971557\pi$
$284$	−511.431	−	39.2228i	−1.80081	−	0.138108i
$285$	17.9363	−	103.459i	0.0629343	−	0.363016i
$286$	−11.7357	−	12.6703i	−0.0410341	−	0.0443016i
$287$	−2.04828	−	1.18257i	−0.00713686	−	0.00412047i
$288$	−21.9219	−	287.164i	−0.0761176	−	0.997099i
$289$	−313.656	−	543.268i	−1.08532	−	1.87982i
$290$	−215.902	−	66.8029i	−0.744488	−	0.230355i
$291$	−32.8382	+	91.0353i	−0.112846	+	0.312836i
$292$	−420.652	−	287.870i	−1.44059	−	0.985858i
$293$	−91.9061	−	77.1184i	−0.313673	−	0.263203i	0.472335	−	0.881419i	$-0.343411\pi$
$293$	−91.9061	−	77.1184i	−0.313673	−	0.263203i	−0.786008	+	0.618216i	$0.787856\pi$
$294$	261.881	+	133.597i	0.890753	+	0.454412i
$295$	−72.2827	+	198.595i	−0.245026	+	0.673204i
$296$	252.461	−	37.3778i	0.852910	−	0.126276i
$297$	20.8751	+	112.698i	0.0702864	+	0.379454i
$298$	−169.927	−	263.602i	−0.570224	−	0.884570i
$299$	27.4425	−	75.3977i	0.0917810	−	0.252166i
$300$	−14.2593	−	6.41465i	−0.0475311	−	0.0213822i
$301$	1.31031	+	1.09948i	0.00435318	+	0.00365275i
$302$	19.4163	+	46.1732i	0.0642923	+	0.152891i
$303$	408.129	−	73.1742i	1.34696	−	0.241499i
$304$	16.6506	−	107.916i	0.0547719	−	0.354988i
$305$	47.6897	+	82.6010i	0.156360	+	0.270823i
$306$	123.834	+	530.613i	0.404688	+	1.73403i
$307$	−177.597	−	102.536i	−0.578491	−	0.333992i	0.182042	−	0.983291i	$-0.441729\pi$
$307$	−177.597	−	102.536i	−0.578491	−	0.333992i	−0.760534	+	0.649299i	$0.775063\pi$
$308$	−0.678409	−	0.174004i	−0.00220263	−	0.000564947i
$309$	−164.058	−	136.860i	−0.530932	−	0.442911i
$310$	−242.950	+	320.159i	−0.783710	+	1.03277i
$311$	83.6144	+	229.729i	0.268857	+	0.738677i	0.998495	+	0.0548442i	$0.0174662\pi$
$311$	83.6144	+	229.729i	0.268857	+	0.738677i	−0.729638	+	0.683833i	$0.760312\pi$
$312$	23.3599	+	42.8693i	0.0748713	+	0.137402i
$313$	23.7303	+	134.581i	0.0758156	+	0.429971i	0.998963	+	0.0455257i	$0.0144963\pi$
$313$	23.7303	+	134.581i	0.0758156	+	0.429971i	−0.923148	+	0.384446i	$0.874393\pi$
$314$	226.848	−	11.1234i	0.722445	−	0.0354247i
$315$	1.65424	+	0.942437i	0.00525154	+	0.00299186i
$316$	−1.27311	−	12.9505i	−0.00402882	−	0.0409827i
$317$	−108.274	+	90.8524i	−0.341557	+	0.286601i	−0.797389	−	0.603465i	$-0.793786\pi$
$317$	−108.274	+	90.8524i	−0.341557	+	0.286601i	0.455832	+	0.890066i	$0.349342\pi$
$318$	75.7191	−	247.232i	0.238110	−	0.777460i
$319$	92.1095	+	16.2414i	0.288745	+	0.0509135i
$320$	−301.788	−	129.077i	−0.943089	−	0.403364i
$321$	−159.335	+	277.817i	−0.496371	+	0.865474i
$322$	−0.721288	−	3.17291i	−0.00224003	−	0.00985376i
$323$			206.585i			0.639581i
$324$	21.0603	−	323.315i	0.0650008	−	0.997885i
$325$	2.65051			0.00815543
$326$	445.727	−	101.326i	1.36726	−	0.310815i
$327$	−138.214	−	79.2690i	−0.422672	−	0.242413i
$328$	390.805	+	240.221i	1.19148	+	0.732381i
$329$	−0.104742	+	0.594024i	−0.000318366	+	0.00180554i
$330$	124.900	+	38.2527i	0.378484	+	0.115917i
$331$	−97.6833	−	116.414i	−0.295116	−	0.351705i	0.598029	−	0.801474i	$-0.295951\pi$
$331$	−97.6833	−	116.414i	−0.295116	−	0.351705i	−0.893145	+	0.449769i	$0.851506\pi$
$332$	−45.7905	−	465.798i	−0.137923	−	1.40301i
$333$	287.110	−	1.65029i	0.862193	−	0.00495582i
$334$	−1.59132	−	32.4530i	−0.00476442	−	0.0971647i
$335$	247.021	−	43.5565i	0.737376	−	0.130019i
$336$	1.73816	+	0.947931i	0.00517311	+	0.00282122i
$337$	119.675	−	43.5582i	0.355119	−	0.129253i	−0.158299	−	0.987391i	$-0.550601\pi$
$337$	119.675	−	43.5582i	0.355119	−	0.129253i	0.513418	+	0.858138i	$0.328379\pi$
$338$	262.660	+	199.318i	0.777101	+	0.589698i
$339$	−250.730	+	300.559i	−0.739618	+	0.886604i
$340$	601.519	+	154.282i	1.76917	+	0.453771i
$341$	83.1641	−	144.045i	0.243883	−	0.422418i
$342$	35.6356	−	117.560i	0.104198	−	0.343743i
$343$	−3.50057	+	2.02106i	−0.0102058	+	0.00589229i
$344$	−248.170	−	220.168i	−0.721424	−	0.640023i
$345$	107.101	+	597.355i	0.310437	+	1.73146i
$346$	177.647	−	74.7022i	0.513430	−	0.215902i
$347$	−19.4708	+	23.2044i	−0.0561119	+	0.0668715i	−0.793370	−	0.608739i	$-0.791676\pi$
$347$	−19.4708	+	23.2044i	−0.0561119	+	0.0668715i	0.737258	+	0.675611i	$0.236120\pi$
$348$	−241.123	−	108.471i	−0.692882	−	0.311697i
$349$	162.407	+	59.1115i	0.465351	+	0.169374i	0.564045	−	0.825744i	$-0.309244\pi$
$349$	162.407	+	59.1115i	0.465351	+	0.169374i	−0.0986944	+	0.995118i	$0.531467\pi$
$350$	0.0903429	−	0.0582381i	0.000258123	−	0.000166395i
$351$	19.2292	+	51.4472i	0.0547839	+	0.146573i
$352$	130.601	+	37.3602i	0.371026	+	0.106137i
$353$	364.507	+	132.670i	1.03260	+	0.375835i	0.802069	−	0.597231i	$-0.203733\pi$
$353$	364.507	+	132.670i	1.03260	+	0.375835i	0.230528	+	0.973066i	$0.425955\pi$
$354$	−112.356	+	220.244i	−0.317390	+	0.622158i
$355$	−422.737	+	503.799i	−1.19081	+	1.41915i
$356$	177.775	+	121.659i	0.499367	+	0.341739i
$357$	−3.52347	−	1.27098i	−0.00986967	−	0.00356018i
$358$	−135.591	+	438.219i	−0.378746	+	1.22408i
$359$	494.326	−	285.399i	1.37695	−	0.794983i	0.385160	−	0.922850i	$-0.374146\pi$
$359$	494.326	−	285.399i	1.37695	−	0.794983i	0.991791	+	0.127866i	$0.0408129\pi$
$360$	−315.690	−	191.558i	−0.876917	−	0.532105i
$361$	−157.212	+	272.300i	−0.435492	+	0.754294i
$362$	453.355	−	419.918i	1.25236	−	1.15999i
$363$	304.400	+	52.7723i	0.838566	+	0.145378i
$364$	−0.334634	−	0.0256638i	−0.000919323	−	7.05049e-5i
$365$	−614.133	+	223.526i	−1.68256	+	0.612400i
$366$	43.5491	+	102.735i	0.118987	+	0.280698i
$367$	77.7710	−	13.7131i	0.211910	−	0.0373655i	−0.0666852	−	0.997774i	$-0.521242\pi$
$367$	77.7710	−	13.7131i	0.211910	−	0.0373655i	0.278595	+	0.960409i	$0.410131\pi$
$368$	122.894	+	619.020i	0.333950	+	1.68212i
$369$	397.235	+	329.447i	1.07652	+	0.892811i
$370$	149.537	−	291.058i	0.404154	−	0.786642i
$371$	1.14256	+	1.36165i	0.00307968	+	0.00367022i
$372$	−327.921	+	336.962i	−0.881508	+	0.905813i
$373$	−102.883	+	583.480i	−0.275827	+	1.56429i	0.460498	+	0.887661i	$0.347671\pi$
$373$	−102.883	+	583.480i	−0.275827	+	1.56429i	−0.736324	+	0.676629i	$0.763440\pi$
$374$	−254.975	−	32.1782i	−0.681751	−	0.0860378i
$375$	315.228	−	183.207i	0.840609	−	0.488552i
$376$	23.4810	−	114.610i	0.0624494	−	0.304815i
$377$	44.8198			0.118885
$378$	1.78584	+	1.33107i	0.00472445	+	0.00352134i
$379$		−	93.1184i		−	0.245695i	−0.992426	−	0.122847i	$-0.960797\pi$
$379$		−	93.1184i		−	0.245695i	0.992426	−	0.122847i	$-0.0392026\pi$
$380$	−100.053	−	97.9301i	−0.263298	−	0.257711i
$381$	313.226	−	0.900192i	0.822115	−	0.00236271i
$382$	445.213	+	56.1865i	1.16548	+	0.147085i
$383$	−185.774	−	32.7570i	−0.485051	−	0.0855275i	−0.0742251	−	0.997242i	$-0.523648\pi$
$383$	−185.774	−	32.7570i	−0.485051	−	0.0855275i	−0.410825	+	0.911714i	$0.634759\pi$
$384$	−331.933	−	193.072i	−0.864408	−	0.502790i
$385$	−0.687896	+	0.577214i	−0.00178674	+	0.00149926i
$386$	−155.562	+	302.784i	−0.403009	+	0.784415i
$387$	−241.544	−	284.524i	−0.624145	−	0.735203i
$388$	75.1412	+	104.900i	0.193663	+	0.270361i
$389$	−27.7003	−	157.096i	−0.0712091	−	0.403847i	−0.999489	−	0.0319646i	$-0.989824\pi$
$389$	−27.7003	−	157.096i	−0.0712091	−	0.403847i	0.928280	−	0.371882i	$-0.121288\pi$
$390$	62.1257	+	7.65902i	0.159297	+	0.0196385i
$391$	−408.369	−	1121.98i	−1.04442	−	2.86952i
$392$	344.740	−	186.569i	0.879438	−	0.475940i
$393$	−385.071	+	141.409i	−0.979825	+	0.359820i
$394$	−293.878	+	272.203i	−0.745883	+	0.690870i
$395$	−14.4494	−	8.34236i	−0.0365807	−	0.0211199i
$396$	139.547	+	62.2943i	0.352391	+	0.157309i
$397$	58.9618	+	102.125i	0.148518	+	0.257241i	0.930680	−	0.365834i	$-0.119216\pi$
$397$	58.9618	+	102.125i	0.148518	+	0.257241i	−0.782162	+	0.623075i	$0.785883\pi$
$398$	157.309	−	508.409i	0.395248	−	1.27741i
$399$	0.544676	+	0.645344i	0.00136510	+	0.00161740i
$400$	−17.8269	+	10.8086i	−0.0445672	+	0.0270216i
$401$	−104.236	−	87.4644i	−0.259940	−	0.218116i	0.503498	−	0.863996i	$-0.332046\pi$
$401$	−104.236	−	87.4644i	−0.259940	−	0.218116i	−0.763439	+	0.645881i	$0.776490\pi$
$402$	293.053	−	15.2141i	0.728988	−	0.0378460i
$403$	27.2605	−	74.8977i	0.0676440	−	0.185850i
$404$	228.257	−	503.528i	0.564994	−	1.24636i
$405$	−321.279	−	263.351i	−0.793281	−	0.650249i
$406$	1.52768	−	0.984797i	0.00376277	−	0.00242561i
$407$	−46.3171	+	127.255i	−0.113801	+	0.312667i
$408$	676.345	+	265.243i	1.65771	+	0.650105i
$409$	−98.1152	−	82.3284i	−0.239890	−	0.201292i	0.514914	−	0.857242i	$-0.327824\pi$
$409$	−98.1152	−	82.3284i	−0.239890	−	0.201292i	−0.754804	+	0.655950i	$0.772268\pi$
$410$	542.181	−	227.992i	1.32239	−	0.556079i
$411$	−206.339	−	244.475i	−0.502042	−	0.594830i
$412$	−274.351	+	76.6748i	−0.665901	+	0.186104i
$413$	−0.849846	−	1.47198i	−0.00205774	−	0.00356411i
$414$	38.8476	+	708.925i	0.0938348	+	1.71238i
$415$	−519.708	−	300.053i	−1.25231	−	0.723020i
$416$	64.7420	+	6.76341i	0.155630	+	0.0162582i
$417$	−241.229	+	88.5861i	−0.578487	+	0.212437i
$418$	46.1559	+	35.0251i	0.110421	+	0.0837920i
$419$	139.827	+	384.171i	0.333716	+	0.916876i	0.987136	+	0.159881i	$0.0511112\pi$
$419$	139.827	+	384.171i	0.333716	+	0.916876i	−0.653421	+	0.756995i	$0.726667\pi$
$420$	2.28584	−	1.10399i	0.00544248	−	0.00262855i
$421$	−26.5187	−	150.395i	−0.0629897	−	0.357233i	−0.999969	−	0.00784813i	$-0.997502\pi$
$421$	−26.5187	−	150.395i	−0.0629897	−	0.357233i	0.936979	−	0.349384i	$-0.113609\pi$
$422$	−39.1131	−	797.666i	−0.0926852	−	1.89020i
$423$	44.3033	−	123.934i	0.104736	−	0.292989i
$424$	−214.247	−	270.102i	−0.505299	−	0.637034i
$425$	30.2143	−	25.3528i	0.0710925	−	0.0596537i
$426$	−562.961	+	524.453i	−1.32150	+	1.23111i
$427$	−0.755429	−	0.133203i	−0.00176916	−	0.000311950i
$428$	184.607	+	385.055i	0.431324	+	0.899661i
$429$	−25.9053	+	0.0744504i	−0.0603854	+	0.000173544i
$430$	−414.782	+	94.2912i	−0.964610	+	0.219282i
$431$			640.109i			1.48517i	0.669751	+	0.742585i	$0.266401\pi$
$431$			640.109i			1.48517i	−0.669751	+	0.742585i	$0.733599\pi$
$432$	−339.130	−	267.609i	−0.785024	−	0.619466i
$433$	343.700			0.793765			0.396883	−	0.917869i	$-0.370092\pi$
$433$	343.700			0.793765			0.396883	+	0.917869i	$0.370092\pi$
$434$	−0.716505	−	3.15187i	−0.00165093	−	0.00726237i
$435$	−293.095	+	170.343i	−0.673781	+	0.391594i
$436$	−191.564	+	91.8416i	−0.439368	+	0.210646i
$437$	−46.7440	+	265.099i	−0.106966	+	0.606633i
$438$	−745.072	+	171.628i	−1.70108	+	0.391846i
$439$	58.0596	+	69.1928i	0.132254	+	0.157615i	0.828107	−	0.560570i	$-0.189418\pi$
$439$	58.0596	+	69.1928i	0.132254	+	0.157615i	−0.695853	+	0.718184i	$0.744973\pi$
$440$	136.454	−	108.236i	0.310122	−	0.245991i
$441$	413.516	−	153.205i	0.937679	−	0.347404i
$442$	−123.005	+	6.03150i	−0.278292	+	0.0136459i
$443$	288.931	−	50.9464i	0.652215	−	0.115003i	0.162256	−	0.986749i	$-0.448123\pi$
$443$	288.931	−	50.9464i	0.652215	−	0.115003i	0.489959	+	0.871746i	$0.337012\pi$
$444$	215.292	−	316.544i	0.484892	−	0.712938i
$445$	259.543	−	94.4660i	0.583243	−	0.212283i
$446$	335.151	−	441.660i	0.751459	−	0.990270i
$447$	−463.524	−	80.3589i	−1.03697	−	0.179774i
$448$	2.35534	−	1.19201i	0.00525746	−	0.00266073i
$449$	63.8556	−	110.601i	0.142217	−	0.246328i	−0.786114	−	0.618082i	$-0.787910\pi$
$449$	63.8556	−	110.601i	0.142217	−	0.246328i	0.928331	+	0.371754i	$0.121243\pi$
$450$	−21.5673	+	9.21548i	−0.0479272	+	0.0204788i
$451$	−210.803	+	121.707i	−0.467411	+	0.269860i
$452$	140.470	+	502.619i	0.310775	+	1.11199i
$453$	70.6766	+	25.4944i	0.156019	+	0.0562790i
$454$	−124.210	−	295.381i	−0.273591	−	0.650618i
$455$	−0.276600	+	0.329640i	−0.000607913	+	0.000724483i
$456$	−102.155	−	128.030i	−0.224024	−	0.280767i
$457$	−394.951	−	143.750i	−0.864225	−	0.314552i	−0.128399	−	0.991723i	$-0.540984\pi$
$457$	−394.951	−	143.750i	−0.864225	−	0.314552i	−0.735826	+	0.677170i	$0.763206\pi$
$458$	−451.994	−	701.163i	−0.986886	−	1.53092i
$459$	711.306	+	402.536i	1.54969	+	0.876985i
$460$	736.985	+	334.087i	1.60214	+	0.726277i
$461$	−648.376	−	235.990i	−1.40646	−	0.511908i	−0.476368	−	0.879246i	$-0.658047\pi$
$461$	−648.376	−	235.990i	−1.40646	−	0.511908i	−0.930088	+	0.367338i	$0.880269\pi$
$462$	−0.881348	+	0.571740i	−0.00190768	+	0.00123753i
$463$	−354.216	+	422.138i	−0.765045	+	0.911745i	−0.998156	−	0.0607054i	$-0.980665\pi$
$463$	−354.216	+	422.138i	−0.765045	+	0.911745i	0.233111	+	0.972450i	$0.425109\pi$
$464$	−301.450	+	182.772i	−0.649676	+	0.393906i
$465$	106.391	+	593.393i	0.228797	+	1.27611i
$466$	−433.600	−	134.162i	−0.930473	−	0.287901i
$467$	−535.942	+	309.426i	−1.14763	+	0.662583i	−0.948308	−	0.317351i	$-0.897207\pi$
$467$	−535.942	+	309.426i	−1.14763	+	0.662583i	−0.199320	+	0.979934i	$0.563873\pi$
$468$	71.0384	+	17.7859i	0.151791	+	0.0380041i
$469$	−1.00865	+	1.74703i	−0.00215064	+	0.00372501i
$470$	−101.931	−	110.048i	−0.216874	−	0.234144i
$471$	218.234	−	261.604i	0.463342	−	0.555424i
$472$	156.905	+	289.928i	0.332427	+	0.614255i
$473$	165.421	−	60.2084i	0.349728	−	0.127291i
$474$	−15.5832	−	11.7547i	−0.0328759	−	0.0247990i
$475$	−8.75720	+	1.54413i	−0.0184362	+	0.00325080i
$476$	−4.06011	+	2.90830i	−0.00852964	+	0.00610987i
$477$	−195.853	−	334.769i	−0.410593	−	0.701821i
$478$	279.322	+	143.507i	0.584355	+	0.300225i
$479$	205.959	+	245.453i	0.429977	+	0.512427i	0.936916	−	0.349555i	$-0.113667\pi$
$479$	205.959	+	245.453i	0.429977	+	0.512427i	−0.506938	+	0.861982i	$0.669223\pi$
$480$	−449.079	+	201.832i	−0.935582	+	0.420482i
$481$	−11.2688	+	63.9084i	−0.0234278	+	0.132866i
$482$	−30.3035	+	240.120i	−0.0628704	+	0.498175i
$483$	−4.23389	−	2.42824i	−0.00876581	−	0.00502741i
$484$	288.131	−	294.378i	0.595313	−	0.608220i
$485$	165.445			0.341123
$486$	−335.343	−	351.769i	−0.690005	−	0.723804i
$487$			5.24750i			0.0107752i	0.999985	+	0.00538758i	$0.00171493\pi$
$487$			5.24750i			0.0107752i	−0.999985	+	0.00538758i	$0.998285\pi$
$488$	145.752	+	29.8611i	0.298672	+	0.0611908i
$489$	341.116	−	594.772i	0.697579	−	1.21630i
$490$	62.9283	−	498.634i	0.128425	−	1.01762i
$491$	593.831	+	104.708i	1.20943	+	0.213255i	0.741771	−	0.670653i	$-0.233986\pi$
$491$	593.831	+	104.708i	1.20943	+	0.213255i	0.467660	+	0.883908i	$0.345097\pi$
$492$	662.168	−	187.114i	1.34587	−	0.380313i
$493$	510.919	−	428.712i	1.03635	−	0.869598i
$494$	24.6964	+	12.6883i	0.0499926	+	0.0256848i
$495$	169.123	−	98.9434i	0.341662	−	0.199886i
$496$	122.079	+	614.915i	0.246126	+	1.23975i
$497$	−0.918461	−	5.20885i	−0.00184801	−	0.0104806i
$498$	−560.487	−	422.788i	−1.12548	−	0.848973i
$499$	1.99347	+	5.47702i	0.00399494	+	0.0109760i	0.941674	−	0.336526i	$-0.109252\pi$
$499$	1.99347	+	5.47702i	0.00399494	+	0.0109760i	−0.937679	+	0.347502i	$0.887030\pi$
$500$	37.1736	−	484.711i	0.0743471	−	0.969422i
$501$	−37.4254	−	31.2208i	−0.0747013	−	0.0623169i
$502$	5.36788	+	5.79532i	0.0106930	+	0.0115445i
$503$	−103.706	−	59.8746i	−0.206175	−	0.119035i	0.393358	−	0.919386i	$-0.371313\pi$
$503$	−103.706	−	59.8746i	−0.206175	−	0.119035i	−0.599532	+	0.800350i	$0.704647\pi$
$504$	2.81215	−	0.954649i	0.00557965	−	0.00189415i
$505$	−354.421	−	613.875i	−0.701823	−	1.21559i
$506$	−319.914	−	98.9856i	−0.632240	−	0.195624i
$507$	486.823	−	87.2834i	0.960204	−	0.172157i
$508$	235.864	−	344.657i	0.464299	−	0.678458i
$509$	−280.047	−	234.987i	−0.550190	−	0.461664i	0.324816	−	0.945777i	$-0.394698\pi$
$509$	−280.047	−	234.987i	−0.550190	−	0.461664i	−0.875005	+	0.484113i	$0.839142\pi$
$510$	781.457	−	506.939i	1.53227	−	0.993998i
$511$	1.79769	−	4.93912i	0.00351799	−	0.00966560i
$512$	−463.024	+	218.524i	−0.904343	+	0.426805i
$513$	−93.5044	−	158.777i	−0.182270	−	0.309507i
$514$	−80.9271	−	125.540i	−0.157446	−	0.244240i
$515$	−124.920	+	343.215i	−0.242563	+	0.666437i
$516$	−495.105	+	50.1085i	−0.959506	+	0.0971096i
$517$	47.5547	+	39.9031i	0.0919820	+	0.0771821i
$518$	1.02012	+	2.42592i	0.00196935	+	0.00468324i
$519$	98.0873	−	271.922i	0.188993	−	0.523934i
$520$	55.3886	−	62.4332i	0.106517	−	0.120064i
$521$	109.267	+	189.256i	0.209726	+	0.363255i	0.951628	−	0.307253i	$-0.0994096\pi$
$521$	109.267	+	189.256i	0.209726	+	0.363255i	−0.741903	+	0.670508i	$0.766076\pi$
$522$	−364.699	+	155.832i	−0.698657	+	0.298529i
$523$	696.524	+	402.138i	1.33179	+	0.768907i	0.985573	−	0.169250i	$-0.0541344\pi$
$523$	696.524	+	402.138i	1.33179	+	0.768907i	0.346212	+	0.938156i	$0.387468\pi$
$524$	−135.888	+	529.804i	−0.259329	+	1.01108i
$525$	0.0275410	−	0.158861i	5.24591e−5	−	0.000302593i
$526$	−486.657	+	641.315i	−0.925204	+	1.21923i
$527$	−405.661	−	1114.54i	−0.769754	−	2.11488i
$528$	173.931	−	106.141i	0.329415	−	0.201025i
$529$	−178.305	−	1011.22i	−0.337060	−	1.91156i
$530$	−441.503	+	21.6489i	−0.833024	+	0.0408469i
$531$	128.846	+	347.770i	0.242649	+	0.654934i
$532$	1.12057	−	0.110158i	0.00210633	−	0.000207064i
$533$	−89.3543	+	74.9772i	−0.167644	+	0.140670i
$534$	314.881	−	72.5332i	0.589664	−	0.135830i
$535$	539.192	+	95.0740i	1.00783	+	0.177708i
$536$	204.891	−	333.328i	0.382259	−	0.621880i
$537$	345.749	+	594.899i	0.643852	+	1.10782i
$538$	113.715	+	500.225i	0.211366	+	0.929787i
$539$			207.997i			0.385895i
$540$	−532.147	+	153.681i	−0.985457	+	0.284595i
$541$	−172.884			−0.319563			−0.159782	−	0.987152i	$-0.551079\pi$
$541$	−172.884			−0.319563			−0.159782	+	0.987152i	$0.551079\pi$
$542$	−191.382	+	43.5063i	−0.353104	+	0.0802700i
$543$	−2.66391	−	926.921i	−0.00490592	−	1.70704i
$544$	802.715	−	542.174i	1.47558	−	0.996644i
$545$	−47.2992	+	268.247i	−0.0867875	+	0.492197i
$546$	−0.368350	+	0.343154i	−0.000674633	+	0.000628487i
$547$	−164.443	−	195.975i	−0.300627	−	0.358273i	0.594491	−	0.804102i	$-0.297353\pi$
$547$	−164.443	−	195.975i	−0.300627	−	0.358273i	−0.895118	+	0.445829i	$0.852909\pi$
$548$	−424.504	+	41.7310i	−0.774642	+	0.0761515i
$549$	157.609	+	56.3412i	0.287084	+	0.102625i
$550$	−0.541782	−	11.0490i	−0.000985058	−	0.0200891i
$551$	−148.083	+	26.1110i	−0.268753	+	0.0473884i
$552$	807.898	+	493.408i	1.46358	+	0.893854i
$553$	0.126093	−	0.0458942i	0.000228017	−	8.29913e-5i
$554$	500.639	+	379.906i	0.903680	+	0.685751i
$555$	−169.201	−	460.751i	−0.304866	−	0.830182i
$556$	−85.1276	+	331.897i	−0.153107	+	0.596938i
$557$	−177.380	+	307.231i	−0.318456	+	0.551582i	−0.980166	−	0.198178i	$-0.936498\pi$
$557$	−177.380	+	307.231i	−0.318456	+	0.551582i	0.661710	+	0.749760i	$0.269831\pi$
$558$	38.5900	+	704.224i	0.0691577	+	1.26205i
$559$	73.0554	−	42.1786i	0.130690	−	0.0754536i
$560$	0.516115	−	3.34506i	0.000921635	−	0.00597332i
$561$	−294.594	+	248.640i	−0.525122	+	0.443208i
$562$	146.443	−	61.5807i	0.260575	−	0.109574i
$563$	7.92579	−	9.44559i	0.0140778	−	0.0167773i	−0.758960	−	0.651138i	$-0.774292\pi$
$563$	7.92579	−	9.44559i	0.0140778	−	0.0167773i	0.773037	+	0.634360i	$0.218736\pi$
$564$	−102.600	−	142.368i	−0.181915	−	0.252426i
$565$	628.780	+	228.857i	1.11288	+	0.405057i
$566$	−244.331	+	157.504i	−0.431680	+	0.278276i
$567$	3.28334	−	0.617941i	0.00579073	−	0.00108984i
$568$	150.245	+	1014.80i	0.264516	+	1.78663i
$569$	−168.484	−	61.3233i	−0.296106	−	0.107774i	0.189695	−	0.981843i	$-0.439250\pi$
$569$	−168.484	−	61.3233i	−0.296106	−	0.107774i	−0.485801	+	0.874069i	$0.661472\pi$
$570$	−209.723	+	10.8879i	−0.367935	+	0.0191016i
$571$	−254.026	+	302.737i	−0.444880	+	0.530187i	−0.941154	−	0.337979i	$-0.890257\pi$
$571$	−254.026	+	302.737i	−0.444880	+	0.530187i	0.496274	+	0.868166i	$0.334701\pi$
$572$	−19.5071	+	28.5048i	−0.0341033	+	0.0498336i
$573$	514.392	−	434.151i	0.897717	−	0.757681i
$574$	−1.39822	+	4.51893i	−0.00243592	+	0.00787269i
$575$	44.5089	−	25.6972i	0.0774068	−	0.0446908i
$576$	−550.322	+	170.065i	−0.955419	+	0.295252i
$577$	−344.513	+	596.713i	−0.597075	+	1.03417i	0.396175	+	0.918175i	$0.370337\pi$
$577$	−344.513	+	596.713i	−0.597075	+	1.03417i	−0.993250	+	0.115990i	$0.962996\pi$
$578$	−920.448	+	852.560i	−1.59247	+	1.47502i
$579$	176.018	+	479.314i	0.304003	+	0.827832i
$580$	−34.5634	+	450.677i	−0.0595921	+	0.777029i
$581$	4.53526	−	1.65070i	0.00780595	−	0.00284113i
$582$	192.100	+	23.6825i	0.330068	+	0.0406917i
$583$	180.157	−	31.7665i	0.309017	−	0.0544880i
$584$	−374.924	+	947.998i	−0.641994	+	1.62328i
$585$	71.5789	−	60.7664i	0.122357	−	0.103874i
$586$	−109.654	+	213.429i	−0.187122	+	0.364213i
$587$	207.235	+	246.973i	0.353040	+	0.420737i	0.913113	−	0.407706i	$-0.133671\pi$
$587$	207.235	+	246.973i	0.353040	+	0.420737i	−0.560073	+	0.828443i	$0.689227\pi$
$588$	144.444	−	569.961i	0.245652	−	0.969322i
$589$	−46.4340	+	263.340i	−0.0788353	+	0.447097i
$590$	419.355	+	52.9231i	0.710771	+	0.0897002i
$591$	1.72683	+	600.857i	0.00292187	+	1.01668i
$592$	−184.823	−	475.790i	−0.312200	−	0.803699i
$593$	469.564			0.791846			0.395923	−	0.918284i	$-0.370425\pi$
$593$	469.564			0.791846			0.395923	+	0.918284i	$0.370425\pi$
$594$	210.533	−	90.6752i	0.354433	−	0.152652i
$595$			6.40345i			0.0107621i
$596$	−438.752	+	448.264i	−0.736160	+	0.752121i
$597$	−401.127	−	690.184i	−0.671905	−	1.15609i
$598$	−159.210	−	20.0925i	−0.266238	−	0.0335996i
$599$	−527.632	−	93.0357i	−0.880854	−	0.155318i	−0.285112	−	0.958494i	$-0.592031\pi$
$599$	−527.632	−	93.0357i	−0.880854	−	0.155318i	−0.595742	+	0.803176i	$0.703142\pi$
$600$	−6.18835	+	30.6531i	−0.0103139	+	0.0510884i
$601$	647.757	−	543.533i	1.07780	−	0.904381i	0.0820627	−	0.996627i	$-0.473849\pi$
$601$	647.757	−	543.533i	1.07780	−	0.904381i	0.995736	+	0.0922465i	$0.0294048\pi$
$602$	1.56333	−	3.04286i	0.00259690	−	0.00505459i
$603$	280.994	−	338.812i	0.465994	−	0.561877i
$604$	81.4409	−	58.3370i	0.134836	−	0.0965844i
$605$	−91.7119	−	520.124i	−0.151590	−	0.859709i
$606$	−323.648	−	763.509i	−0.534073	−	1.25992i
$607$	138.471	+	380.445i	0.228123	+	0.626763i	0.999959	−	0.00905875i	$-0.00288353\pi$
$607$	138.471	+	380.445i	0.228123	+	0.626763i	−0.771836	+	0.635822i	$0.780661\pi$
$608$	−217.845	+	15.3712i	−0.358298	+	0.0252816i
$609$	0.465714	−	2.68632i	0.000764719	−	0.00441103i
$610$	139.949	−	129.627i	0.229425	−	0.212504i
$611$	25.7624	+	14.8739i	0.0421643	+	0.0243436i
$612$	979.923	−	476.751i	1.60118	−	0.779004i
$613$	62.6459	+	108.506i	0.102196	+	0.177008i	0.912589	−	0.408878i	$-0.134080\pi$
$613$	62.6459	+	108.506i	0.102196	+	0.177008i	−0.810393	+	0.585886i	$0.800747\pi$
$614$	−121.233	+	391.815i	−0.197448	+	0.638136i
$615$	299.364	−	829.909i	0.486770	−	1.34944i
$616$	−0.0385814	+	1.40021i	−6.26321e−5	+	0.00227306i
$617$	221.013	+	185.452i	0.358205	+	0.300570i	0.804075	−	0.594528i	$-0.202661\pi$
$617$	221.013	+	185.452i	0.358205	+	0.300570i	−0.445870	+	0.895098i	$0.647105\pi$
$618$	−194.175	+	380.629i	−0.314200	+	0.615904i
$619$	−122.807	+	337.411i	−0.198397	+	0.545090i	−0.998499	−	0.0547735i	$-0.982556\pi$
$619$	−122.807	+	337.411i	−0.198397	+	0.545090i	0.800102	+	0.599864i	$0.204779\pi$
$620$	732.098	+	331.872i	1.18080	+	0.535277i
$621$	821.696	+	677.499i	1.32318	+	1.09098i
$622$	410.957	−	264.917i	0.660702	−	0.425911i
$623$	−0.759737	+	2.08736i	−0.00121948	+	0.00335050i
$624$	73.2492	−	64.5632i	0.117387	−	0.103467i
$625$	−502.431	−	421.589i	−0.803889	−	0.674543i
$626$	251.945	−	105.945i	0.402468	−	0.169242i
$627$	85.5469	−	15.3379i	0.136438	−	0.0244623i
$628$	−122.265	−	437.476i	−0.194689	−	0.696619i
$629$	482.842	+	836.307i	0.767634	+	1.32958i
$630$	1.10459	−	3.64398i	0.00175331	−	0.00578410i
$631$	−874.059	−	504.638i	−1.38520	−	0.799743i	−0.392427	−	0.919783i	$-0.628364\pi$
$631$	−874.059	−	504.638i	−1.38520	−	0.799743i	−0.992769	+	0.120040i	$0.961698\pi$
$632$	−24.6923	+	8.22440i	−0.0390700	+	0.0130133i
$633$	−919.881	−	767.378i	−1.45321	−	1.21229i
$634$	225.187	+	170.881i	0.355184	+	0.269529i
$635$	−183.144	−	503.183i	−0.288415	−	0.792415i
$636$	−515.732	−	38.0621i	−0.810900	−	0.0598460i
$637$	17.3079	+	98.1580i	0.0271710	+	0.154094i
$638$	−9.16144	−	186.836i	−0.0143596	−	0.292847i
$639$	6.63357	+	1154.08i	0.0103812	+	1.80607i
$640$	−117.935	+	645.786i	−0.184273	+	1.00904i
$641$	610.695	−	512.434i	0.952722	−	0.799429i	−0.0270317	−	0.999635i	$-0.508606\pi$
$641$	610.695	−	512.434i	0.952722	−	0.799429i	0.979754	+	0.200206i	$0.0641611\pi$
$642$	612.451	+	187.574i	0.953974	+	0.292171i
$643$	696.625	+	122.834i	1.08340	+	0.191032i	0.686717	−	0.726925i	$-0.259051\pi$
$643$	696.625	+	122.834i	1.08340	+	0.191032i	0.396680	+	0.917957i	$0.370162\pi$
$644$	−5.86817	+	2.81337i	−0.00911206	+	0.00436859i
$645$	−317.434	+	553.479i	−0.492146	+	0.858108i
$646$	402.891	−	91.5879i	0.623670	−	0.141777i
$647$		−	595.093i		−	0.919774i	−0.887978	−	0.459887i	$-0.847890\pi$
$647$		−	595.093i		−	0.919774i	0.887978	−	0.459887i	$-0.152110\pi$
$648$	−639.879	+	102.267i	−0.987468	+	0.157819i
$649$	−174.927			−0.269533
$650$	−1.17509	−	5.16915i	−0.00180783	−	0.00795253i
$651$	−4.20581	−	2.41213i	−0.00646053	−	0.00370528i
$652$	−395.220	−	824.354i	−0.606165	−	1.26435i
$653$	−128.322	+	727.750i	−0.196511	+	1.11447i	0.713738	+	0.700412i	$0.247001\pi$
$653$	−128.322	+	727.750i	−0.196511	+	1.11447i	−0.910250	+	0.414060i	$0.864111\pi$
$654$	−93.3177	+	304.694i	−0.142688	+	0.465893i
$655$	450.776	+	537.214i	0.688207	+	0.820173i
$656$	295.229	−	868.664i	0.450044	−	1.32418i
$657$	−567.720	+	996.503i	−0.864109	+	1.51675i
$658$	1.20493	−	0.0590831i	0.00183120	−	8.97919e-5i
$659$	−225.185	+	39.7062i	−0.341707	+	0.0602522i	−0.341869	−	0.939748i	$-0.611060\pi$
$659$	−225.185	+	39.7062i	−0.341707	+	0.0602522i	0.000161354		1.00000i	$0.499949\pi$
$660$	19.2287	−	260.544i	0.0291343	−	0.394763i
$661$	247.564	−	90.1059i	0.374529	−	0.136318i	−0.147895	−	0.989003i	$-0.547250\pi$
$661$	247.564	−	90.1059i	0.374529	−	0.136318i	0.522425	+	0.852686i	$0.325028\pi$
$662$	−183.729	+	242.118i	−0.277537	+	0.365737i
$663$	−118.335	+	141.852i	−0.178484	+	0.213954i
$664$	−888.118	+	295.811i	−1.33753	+	0.445498i
$665$	0.721837	−	1.25026i	0.00108547	−	0.00188009i
$666$	−130.507	−	559.203i	−0.195956	−	0.839644i
$667$	752.638	−	434.536i	1.12839	−	0.651478i
$668$	−62.5858	+	17.4913i	−0.0936913	+	0.0261845i
$669$	−146.766	−	818.588i	−0.219381	−	1.22360i
$670$	−194.461	−	462.440i	−0.290240	−	0.690210i
$671$	−50.7454	+	60.4760i	−0.0756265	+	0.0901282i
$672$	1.07809	−	3.81010i	0.00160431	−	0.00566979i
$673$	262.025	+	95.3693i	0.389339	+	0.141708i	0.529270	−	0.848453i	$-0.322466\pi$
$673$	262.025	+	95.3693i	0.389339	+	0.141708i	−0.139931	+	0.990161i	$0.544688\pi$
$674$	−138.006	−	214.084i	−0.204757	−	0.317632i
$675$	−11.7469	+	33.1613i	−0.0174029	+	0.0491278i
$676$	272.270	−	600.617i	0.402766	−	0.888487i
$677$	−213.983	−	77.8835i	−0.316076	−	0.115042i	0.179111	−	0.983829i	$-0.442678\pi$
$677$	−213.983	−	77.8835i	−0.316076	−	0.115042i	−0.495186	+	0.868787i	$0.664900\pi$
$678$	697.322	+	355.735i	1.02850	+	0.524682i
$679$	−0.855279	+	1.01928i	−0.00125962	+	0.00150115i
$680$	34.2086	−	1241.51i	0.0503068	−	1.82575i
$681$	−452.135	−	163.094i	−0.663928	−	0.239491i
$682$	−317.792	−	98.3292i	−0.465971	−	0.144178i
$683$	−662.983	+	382.773i	−0.970692	+	0.560429i	−0.899447	−	0.437030i	$-0.856031\pi$
$683$	−662.983	+	382.773i	−0.970692	+	0.560429i	−0.0712449	+	0.997459i	$0.522697\pi$
$684$	−245.070	−	17.3786i	−0.358289	−	0.0254074i
$685$	−273.453	+	473.634i	−0.399201	+	0.691437i
$686$	5.49350	+	5.93095i	0.00800802	+	0.00864569i
$687$	−1232.94	−	213.749i	−1.79468	−	0.311135i
$688$	−319.356	+	581.601i	−0.464181	+	0.845351i
$689$	82.3761	−	29.9825i	0.119559	−	0.0435159i
$690$	1117.50	−	473.706i	1.61957	−	0.686530i
$691$	−460.568	+	81.2105i	−0.666523	+	0.117526i	−0.496665	−	0.867942i	$-0.665442\pi$
$691$	−460.568	+	81.2105i	−0.666523	+	0.117526i	−0.169858	+	0.985468i	$0.554331\pi$
$692$	−224.446	−	313.336i	−0.324344	−	0.452798i
$693$	−0.264715	+	1.55344i	−0.000381985	+	0.00224161i
$694$	53.8865	+	27.6853i	0.0776462	+	0.0398924i
$695$	282.390	+	336.539i	0.406316	+	0.484229i
$696$	−104.644	+	518.338i	−0.150351	+	0.744738i
$697$	−301.412	+	1709.39i	−0.432442	+	2.45250i
$698$	43.2795	−	342.941i	0.0620051	−	0.491319i
$699$	−588.629	+	342.105i	−0.842102	+	0.489420i
$700$	−0.153631	−	0.150371i	−0.000219473	−	0.000214816i
$701$	−88.4726			−0.126209			−0.0631046	−	0.998007i	$-0.520100\pi$
$701$	−88.4726			−0.126209			−0.0631046	+	0.998007i	$0.520100\pi$
$702$	91.8094	−	60.3103i	0.130783	−	0.0859121i
$703$		−	217.716i		−	0.309695i
$704$	14.9604	−	271.267i	0.0212506	−	0.385323i
$705$	−225.001	+	0.646640i	−0.319150	+	0.000917219i
$706$	97.1365	−	769.695i	0.137587	−	1.09022i
$707$	5.61420	+	0.989935i	0.00794088	+	0.00140019i
$708$	479.341	+	121.478i	0.677036	+	0.171579i
$709$	−0.313958	+	0.263442i	−0.000442819	+	0.000371569i	−0.643009	−	0.765859i	$-0.722314\pi$
$709$	−0.313958	+	0.263442i	−0.000442819	+	0.000371569i	0.642566	+	0.766230i	$0.277870\pi$
$710$	1169.95	+	601.085i	1.64781	+	0.846598i
$711$	−28.8047	+	5.24993i	−0.0405129	+	0.00738386i
$712$	158.450	−	400.641i	0.222542	−	0.562698i
$713$	−268.373	−	1522.02i	−0.376400	−	2.13467i
$714$	−0.916620	+	7.43511i	−0.00128378	+	0.0104133i
$715$	15.1469	+	41.6158i	0.0211845	+	0.0582039i
$716$	914.747	+	70.1540i	1.27758	+	0.0979804i
$717$	442.173	−	162.378i	0.616699	−	0.226469i
$718$	−775.753	−	837.525i	−1.08044	−	1.16647i
$719$	437.936	+	252.842i	0.609090	+	0.351658i	0.772609	−	0.634882i	$-0.218951\pi$
$719$	437.936	+	252.842i	0.609090	+	0.351658i	−0.163519	+	0.986540i	$0.552285\pi$
$720$	−233.626	+	700.598i	−0.324480	+	0.973053i
$721$	−1.46872	−	2.54389i	−0.00203706	−	0.00352828i
$722$	600.750	+	185.880i	0.832064	+	0.257452i
$723$	234.154	+	277.431i	0.323865	+	0.383722i
$724$	−1019.93	−	697.985i	−1.40875	−	0.964068i
$725$	21.9921	+	18.4536i	0.0303340	+	0.0254532i
$726$	−32.0346	−	617.049i	−0.0441248	−	0.849930i
$727$	317.879	−	873.365i	0.437247	−	1.20133i	−0.504028	−	0.863687i	$-0.668149\pi$
$727$	317.879	−	873.365i	0.437247	−	1.20133i	0.941275	−	0.337640i	$-0.109629\pi$
$728$	0.0983068	+	0.663995i	0.000135037	+	0.000912080i
$729$	−728.892	+	12.5700i	−0.999851	+	0.0172427i
$730$	708.201	+	1098.61i	0.970139	+	1.50494i
$731$	429.341	−	1179.60i	0.587334	−	1.61369i
$732$	181.052	−	130.478i	0.247339	−	0.178249i
$733$	465.367	+	390.489i	0.634880	+	0.532728i	0.902441	−	0.430813i	$-0.141773\pi$
$733$	465.367	+	390.489i	0.634880	+	0.532728i	−0.267561	+	0.963541i	$0.586218\pi$
$734$	−61.2231	−	145.593i	−0.0834103	−	0.198355i
$735$	−486.245	−	576.114i	−0.661558	−	0.783828i
$736$	1152.76	−	514.111i	1.56624	−	0.698520i
$737$	103.807	+	179.799i	0.140851	+	0.243961i
$738$	466.391	−	920.763i	0.631966	−	1.24765i
$739$	1027.02	+	592.950i	1.38974	+	0.802368i	0.993286	−	0.115685i	$-0.0369063\pi$
$739$	1027.02	+	592.950i	1.38974	+	0.802368i	0.396457	+	0.918053i	$0.370240\pi$
$740$	−633.929	−	162.595i	−0.856661	−	0.219723i
$741$	39.0949	−	14.3568i	0.0527597	−	0.0193749i
$742$	2.14901	−	2.83195i	0.00289624	−	0.00381665i
$743$	−66.6908	−	183.232i	−0.0897589	−	0.246610i	0.886688	−	0.462368i	$-0.153000\pi$
$743$	−66.6908	−	183.232i	−0.0897589	−	0.246610i	−0.976447	+	0.215758i	$0.930778\pi$
$744$	802.540	+	490.135i	1.07868	+	0.658784i
$745$	139.654	+	792.018i	0.187455	+	1.06311i
$746$	1183.54	−	58.0343i	1.58652	−	0.0777940i
$747$	−1036.03	+	188.827i	−1.38692	+	0.252780i
$748$	50.2860	+	511.529i	0.0672273	+	0.683862i
$749$	−3.37313	+	2.83039i	−0.00450351	+	0.00377889i
$750$	−497.052	−	533.548i	−0.662737	−	0.711397i
$751$	−352.727	−	62.1954i	−0.469677	−	0.0828167i	−0.0661997	−	0.997806i	$-0.521087\pi$
$751$	−352.727	−	62.1954i	−0.469677	−	0.0828167i	−0.403477	+	0.914990i	$0.632199\pi$
$752$	−233.928	+	5.01810i	−0.311075	+	0.00667300i
$753$	11.8490	−	0.0340533i	0.0157357	−	4.52235e-5i
$754$	−19.8705	−	87.4094i	−0.0263535	−	0.115928i
$755$		−	128.446i		−	0.170127i
$756$	1.80416	−	4.07295i	0.00238646	−	0.00538750i
$757$	−692.369			−0.914622			−0.457311	−	0.889307i	$-0.651187\pi$
$757$	−692.369			−0.914622			−0.457311	+	0.889307i	$0.651187\pi$
$758$	−181.603	+	41.2834i	−0.239582	+	0.0544636i
$759$	−434.295	+	252.407i	−0.572194	+	0.332552i
$760$	−146.630	+	238.545i	−0.192934	+	0.313875i
$761$	202.751	−	1149.86i	0.266427	−	1.51098i	−0.498514	−	0.866882i	$-0.666121\pi$
$761$	202.751	−	1149.86i	0.266427	−	1.51098i	0.764941	−	0.644100i	$-0.222768\pi$
$762$	−140.622	−	610.467i	−0.184543	−	0.801138i
$763$	−1.40812	−	1.67813i	−0.00184550	−	0.00219938i
$764$	−87.8048	−	893.184i	−0.114928	−	1.16909i
$765$	234.713	−	1377.37i	0.306814	−	1.80048i
$766$	18.4776	+	376.828i	0.0241221	+	0.491942i
$767$	−82.5515	+	14.5561i	−0.107629	+	0.0189779i
$768$	−229.376	+	732.946i	−0.298667	+	0.954357i
$769$	332.286	−	120.942i	0.432102	−	0.157272i	−0.116807	−	0.993155i	$-0.537266\pi$
$769$	332.286	−	120.942i	0.432102	−	0.157272i	0.548908	+	0.835882i	$0.315044\pi$
$770$	1.43068	+	1.08566i	0.00185803	+	0.00140995i
$771$	−220.752	−	38.2707i	−0.286319	−	0.0496378i
$772$	659.470	+	169.146i	0.854235	+	0.219101i
$773$	−530.607	+	919.038i	−0.686425	+	1.18892i	0.286561	+	0.958062i	$0.407488\pi$
$773$	−530.607	+	919.038i	−0.686425	+	1.18892i	−0.972987	+	0.230862i	$0.925845\pi$
$774$	−447.804	+	597.211i	−0.578558	+	0.771591i
$775$	44.2137	−	25.5268i	0.0570500	−	0.0329378i
$776$	171.268	−	193.050i	0.220706	−	0.248776i
$777$	3.71332	+	1.33947i	0.00477905	+	0.00172389i
$778$	−294.095	+	123.670i	−0.378015	+	0.158959i
$779$	251.543	−	299.778i	0.322905	−	0.384824i
$780$	−12.6060	−	124.556i	−0.0161616	−	0.159687i
$781$	−511.521	−	186.178i	−0.654956	−	0.238384i
$782$	−2007.09	+	1293.84i	−2.56662	+	1.65453i
$783$	−198.639	+	560.752i	−0.253689	+	0.716158i
$784$	−516.692	−	589.612i	−0.659046	−	0.752057i
$785$	−547.286	−	199.196i	−0.697179	−	0.253752i
$786$	446.501	+	688.290i	0.568067	+	0.875687i
$787$	−936.718	+	1116.34i	−1.19024	+	1.41847i	−0.305621	+	0.952153i	$0.598864\pi$
$787$	−936.718	+	1116.34i	−1.19024	+	1.41847i	−0.884617	+	0.466318i	$0.845580\pi$
$788$	661.150	+	452.454i	0.839023	+	0.574181i
$789$	213.113	+	1188.64i	0.270105	+	1.50651i
$790$	−9.86359	+	31.8783i	−0.0124856	+	0.0403523i
$791$	−4.66048	+	2.69073i	−0.00589188	+	0.00340168i
$792$	59.6221	−	299.768i	0.0752804	−	0.378494i
$793$	−18.9154	+	32.7624i	−0.0238530	+	0.0413145i
$794$	173.028	−	160.266i	0.217919	−	0.201846i
$795$	−424.739	+	509.149i	−0.534263	+	0.640438i
$796$	−1061.26	−	81.3906i	−1.33324	−	0.102249i
$797$	508.103	−	184.934i	0.637519	−	0.232038i	−0.00298155	−	0.999996i	$-0.500949\pi$
$797$	508.103	−	184.934i	0.637519	−	0.232038i	0.640501	+	0.767958i	$0.278727\pi$
$798$	1.01710	−	1.34836i	0.00127456	−	0.00168967i
$799$	435.949	−	76.8696i	0.545618	−	0.0962073i
$800$	28.9829	+	29.9748i	0.0362286	+	0.0374685i
$801$	239.928	−	421.140i	0.299536	−	0.525768i
$802$	−124.364	+	242.062i	−0.155068	+	0.301823i
$803$	−347.711	−	414.386i	−0.433015	−	0.516047i
$804$	−159.594	−	564.780i	−0.198500	−	0.702463i
$805$	−1.44891	+	8.21718i	−0.00179989	+	0.0102077i
$806$	−158.154	−	19.9593i	−0.196221	−	0.0247634i
$807$	667.493	+	382.824i	0.827129	+	0.474379i
$808$	−1083.20	−	221.922i	−1.34059	−	0.274656i
$809$	1070.62			1.32338			0.661692	−	0.749776i	$-0.269839\pi$
$809$	1070.62			1.32338			0.661692	+	0.749776i	$0.269839\pi$
$810$	−371.162	+	743.326i	−0.458224	+	0.917687i
$811$		−	1307.05i		−	1.61165i	−0.592153	−	0.805826i	$-0.701722\pi$
$811$		−	1307.05i		−	1.61165i	0.592153	−	0.805826i	$-0.298278\pi$
$812$	−2.59788	−	2.54275i	−0.00319936	−	0.00313147i
$813$	−146.465	+	255.378i	−0.180154	+	0.314118i
$814$	268.713	+	33.9119i	0.330114	+	0.0416609i
$815$	−1154.34	−	203.541i	−1.41637	−	0.249744i
$816$	217.435	−	1436.63i	0.266465	−	1.76058i
$817$	−216.800	+	181.917i	−0.265361	+	0.222665i
$818$	−117.062	+	227.848i	−0.143107	+	0.278543i
$819$	0.00434040	+	0.755124i	5.29963e−6	+	0.000922007i
$820$	−685.013	−	956.306i	−0.835381	−	1.16623i
$821$	113.123	+	641.554i	0.137787	+	0.781430i	0.972878	+	0.231318i	$0.0743038\pi$
$821$	113.123	+	641.554i	0.137787	+	0.781430i	−0.835091	+	0.550112i	$0.814585\pi$
$822$	−385.307	+	510.798i	−0.468743	+	0.621409i
$823$	−175.770	−	482.923i	−0.213572	−	0.586784i	0.785931	−	0.618314i	$-0.212184\pi$
$823$	−175.770	−	482.923i	−0.213572	−	0.586784i	−0.999503	+	0.0315306i	$0.989962\pi$
$824$	271.166	+	501.059i	0.329085	+	0.608081i
$825$	−12.7419	−	10.6295i	−0.0154447	−	0.0128842i
$826$	−2.49394	+	2.31000i	−0.00301930	+	0.00279661i
$827$	144.231	+	83.2717i	0.174402	+	0.100691i	0.584660	−	0.811278i	$-0.301228\pi$
$827$	144.231	+	83.2717i	0.174402	+	0.100691i	−0.410258	+	0.911970i	$0.634561\pi$
$828$	1365.35	−	390.059i	1.64898	−	0.471086i
$829$	569.032	+	985.592i	0.686407	+	1.18889i	0.972992	+	0.230838i	$0.0741466\pi$
$829$	569.032	+	985.592i	0.686407	+	1.18889i	−0.286585	+	0.958055i	$0.592520\pi$
$830$	−354.768	+	1146.58i	−0.427432	+	1.38142i
$831$	927.901	−	166.365i	1.11661	−	0.200199i
$832$	−15.5126	−	129.261i	−0.0186450	−	0.155362i
$833$	1136.20	+	953.389i	1.36399	+	1.14452i
$834$	279.712	+	431.181i	0.335386	+	0.517004i
$835$	−28.4971	+	78.2951i	−0.0341283	+	0.0937666i
$836$	47.8445	−	105.543i	0.0572302	−	0.126248i
$837$	816.247	+	673.006i	0.975206	+	0.804069i
$838$	687.236	−	443.016i	0.820091	−	0.528659i
$839$	254.878	−	700.272i	0.303788	−	0.834650i	−0.690045	−	0.723766i	$-0.742409\pi$
$839$	254.878	−	700.272i	0.303788	−	0.834650i	0.993833	−	0.110884i	$-0.0353683\pi$
$840$	−3.16646	−	3.96850i	−0.00376960	−	0.00472441i
$841$	−272.360	−	228.537i	−0.323853	−	0.271745i
$842$	−281.550	+	118.394i	−0.334382	+	0.140611i
$843$	80.8581	−	224.158i	0.0959171	−	0.265905i
$844$	−1538.30	+	429.919i	−1.82263	+	0.509383i
$845$	−422.759	−	732.241i	−0.500307	−	0.866557i
$846$	−261.344	−	31.4569i	−0.308917	−	0.0371831i
$847$	3.67852	+	2.12380i	0.00434300	+	0.00250743i
$848$	−431.781	+	537.582i	−0.509175	+	0.633941i
$849$	−74.4842	+	429.638i	−0.0877317	+	0.506051i
$850$	−62.8395	−	47.6853i	−0.0739288	−	0.0561003i
$851$	430.372	+	1182.44i	0.505725	+	1.38947i
$852$	1272.40	+	865.397i	1.49342	+	1.01572i
$853$	−202.360	−	1147.64i	−0.237233	−	1.34542i	−0.837859	−	0.545886i	$-0.816193\pi$
$853$	−202.360	−	1147.64i	−0.237233	−	1.34542i	0.600626	−	0.799530i	$-0.294918\pi$
$854$	0.0751368	+	1.53233i	8.79822e−5	+	0.00179429i
$855$	−201.093	+	242.470i	−0.235196	+	0.283591i
$856$	669.106	−	530.739i	0.781666	−	0.620022i
$857$	350.934	−	294.468i	0.409491	−	0.343604i	−0.414658	−	0.909978i	$-0.636099\pi$
$857$	350.934	−	294.468i	0.409491	−	0.343604i	0.824148	+	0.566374i	$0.191654\pi$
$858$	11.6301	+	50.4887i	0.0135549	+	0.0588446i
$859$	−1043.94	−	184.076i	−1.21530	−	0.214291i	−0.471000	−	0.882133i	$-0.656107\pi$
$859$	−1043.94	−	184.076i	−1.21530	−	0.214291i	−0.744302	+	0.667843i	$0.767218\pi$
$860$	367.781	+	767.123i	0.427653	+	0.892003i
$861$	3.56537	+	6.13461i	0.00414096	+	0.00712499i
$862$	1248.37	−	283.788i	1.44822	−	0.329220i
$863$		−	842.741i		−	0.976525i	−0.872697	−	0.488262i	$-0.837631\pi$
$863$		−	842.741i		−	0.976525i	0.872697	−	0.488262i	$-0.162369\pi$
$864$	−371.552	+	780.029i	−0.430037	+	0.902811i
$865$	−494.182			−0.571308
$866$	−152.377	−	670.299i	−0.175955	−	0.774017i
$867$	5.40855	+	1881.93i	0.00623824	+	2.17062i
$868$	−5.82925	+	2.79472i	−0.00671573	+	0.00321972i
$869$	2.39808	−	13.6002i	0.00275958	−	0.0156504i
$870$	462.152	+	496.085i	0.531209	+	0.570213i
$871$	63.9500	+	76.2126i	0.0734213	+	0.0875001i
$872$	264.042	+	332.880i	0.302801	+	0.381743i
$873$	221.330	−	187.896i	0.253528	−	0.215231i
$874$	537.730	−	26.3673i	0.615252	−	0.0301686i
$875$	4.93671	−	0.870475i	0.00564195	−	0.000994829i
$876$	665.039	+	1376.98i	0.759177	+	1.57190i
$877$	−919.491	+	334.667i	−1.04845	+	0.381605i	−0.808078	−	0.589076i	$-0.799492\pi$
$877$	−919.491	+	334.667i	−1.04845	+	0.381605i	−0.240373	+	0.970681i	$0.577270\pi$
$878$	109.202	−	143.906i	0.124376	−	0.163903i
$879$	124.073	+	337.863i	0.141152	+	0.384372i
$880$	−271.582	−	218.132i	−0.308616	−	0.247877i
$881$	22.0835	−	38.2497i	0.0250664	−	0.0434163i	−0.853220	−	0.521551i	$-0.825354\pi$
$881$	22.0835	−	38.2497i	0.0250664	−	0.0434163i	0.878286	+	0.478135i	$0.158687\pi$
$882$	−482.116	−	738.535i	−0.546617	−	0.837341i
$883$	445.575	−	257.253i	0.504615	−	0.291339i	−0.226002	−	0.974127i	$-0.572566\pi$
$883$	445.575	−	257.253i	0.504615	−	0.291339i	0.730617	+	0.682787i	$0.239232\pi$
$884$	66.2963	+	237.216i	0.0749959	+	0.268344i
$885$	484.516	−	408.935i	0.547475	−	0.462074i
$886$	−227.453	−	540.900i	−0.256719	−	0.610496i
$887$	918.503	−	1094.63i	1.03552	−	1.23408i	0.0637919	−	0.997963i	$-0.479681\pi$
$887$	918.503	−	1094.63i	1.03552	−	1.23408i	0.971725	−	0.236117i	$-0.0758749\pi$
$888$	−712.787	−	279.534i	−0.802688	−	0.314791i
$889$	4.04682	+	1.47292i	0.00455210	+	0.00165683i
$890$	−299.298	−	464.292i	−0.336290	−	0.521676i
$891$	113.880	−	324.438i	0.127811	−	0.364128i
$892$	−1009.93	−	457.818i	−1.13221	−	0.513249i
$893$	−93.7832	−	34.1343i	−0.105020	−	0.0382243i
$894$	48.7806	+	939.611i	0.0545645	+	1.05102i
$895$	756.109	−	901.096i	0.844814	−	1.00681i
$896$	−3.36892	−	4.06502i	−0.00375996	−	0.00453685i
$897$	−183.949	+	155.254i	−0.205071	+	0.173082i
$898$	−244.009	−	75.4998i	−0.271725	−	0.0840755i
$899$	747.647	−	431.654i	0.831643	−	0.480149i
$900$	27.5341	+	37.9758i	0.0305935	+	0.0421953i
$901$	652.250	−	1129.73i	0.723918	−	1.25386i
$902$	330.816	+	357.158i	0.366758	+	0.395963i
$903$	−1.76891	−	4.81692i	−0.00195893	−	0.00533435i
$904$	917.953	−	496.784i	1.01543	−	0.549540i
$905$	−1489.06	+	541.973i	−1.64537	+	0.598865i
$906$	18.3863	−	149.139i	0.0202939	−	0.164613i
$907$	1252.53	−	220.855i	1.38096	−	0.243501i	0.566663	−	0.823949i	$-0.308234\pi$
$907$	1252.53	−	220.855i	1.38096	−	0.243501i	0.814297	+	0.580449i	$0.197123\pi$
$908$	−520.996	+	373.195i	−0.573784	+	0.411008i
$909$	−1171.32	−	418.717i	−1.28858	−	0.460634i
$910$	0.765506	+	0.393295i	0.000841216	+	0.000432192i
$911$	985.284	+	1174.22i	1.08154	+	1.28893i	0.954882	+	0.296985i	$0.0959810\pi$
$911$	985.284	+	1174.22i	1.08154	+	1.28893i	0.126659	+	0.991946i	$0.459575\pi$
$912$	−204.400	+	255.988i	−0.224122	+	0.280688i
$913$	86.2528	−	489.164i	0.0944718	−	0.535776i
$914$	−105.249	+	833.981i	−0.115153	+	0.912452i
$915$	−0.822341	−	286.137i	−0.000898734	−	0.312718i
$916$	−1167.05	+	1192.35i	−1.27407	+	1.30170i
$917$	−5.64002			−0.00615051
$918$	469.691	−	1565.68i	0.511646	−	1.70553i
$919$			958.663i			1.04316i	0.853203	+	0.521580i	$0.174657\pi$
$919$			958.663i			1.04316i	−0.853203	+	0.521580i	$0.825343\pi$
$920$	324.814	−	1585.42i	0.353059	−	1.72328i
$921$	309.137	+	531.904i	0.335653	+	0.577529i
$922$	−172.784	+	1369.12i	−0.187401	+	1.48494i
$923$	−256.889	−	45.2964i	−0.278319	−	0.0490752i
$924$	1.50577	+	1.46537i	0.00162962	+	0.00158589i
$925$	−31.8423	+	26.7189i	−0.0344241	+	0.0288853i
$926$	980.310	+	503.655i	1.05865	+	0.543904i
$927$	222.674	+	601.021i	0.240210	+	0.648351i
$928$	490.096	+	506.869i	0.528120	+	0.546195i
$929$	249.626	+	1415.70i	0.268704	+	1.52389i	0.758277	+	0.651933i	$0.226042\pi$
$929$	249.626	+	1415.70i	0.268704	+	1.52389i	−0.489573	+	0.871962i	$0.662847\pi$
$930$	1110.09	−	470.564i	1.19365	−	0.505983i
$931$	−114.369	−	314.227i	−0.122846	−	0.337516i
$932$	−69.4146	+	905.106i	−0.0744792	+	0.971144i
$933$	125.280	−	722.637i	0.134277	−	0.774531i
$934$	841.063	+	908.036i	0.900495	+	0.972201i
$935$	570.731	+	329.512i	0.610408	+	0.352419i
$936$	3.19251	−	146.427i	0.00341081	−	0.156440i
$937$	151.138	+	261.779i	0.161300	+	0.279380i	0.935335	−	0.353763i	$-0.115098\pi$
$937$	151.138	+	261.779i	0.161300	+	0.279380i	−0.774035	+	0.633143i	$0.781765\pi$
$938$	3.85431	+	1.19258i	0.00410907	+	0.00127140i
$939$	139.111	−	385.649i	0.148148	−	0.410701i
$940$	−169.429	+	247.579i	−0.180244	+	0.263382i
$941$	−629.923	−	528.568i	−0.669419	−	0.561709i	0.243475	−	0.969907i	$-0.421713\pi$
$941$	−629.923	−	528.568i	−0.669419	−	0.561709i	−0.912893	+	0.408198i	$0.866157\pi$
$942$	−606.945	−	309.629i	−0.644315	−	0.328693i
$943$	−773.569	+	2125.36i	−0.820328	+	2.25383i
$944$	495.868	−	434.541i	0.525284	−	0.460319i
$945$	−2.89833	−	4.92157i	−0.00306702	−	0.00520801i
$946$	−190.759	−	295.919i	−0.201648	−	0.312811i
$947$	456.809	−	1255.07i	0.482375	−	1.32531i	−0.425076	−	0.905158i	$-0.639753\pi$
$947$	456.809	−	1255.07i	0.482375	−	1.32531i	0.907451	−	0.420157i	$-0.138025\pi$
$948$	−16.0159	+	35.6023i	−0.0168944	+	0.0375552i
$949$	−198.573	−	166.623i	−0.209245	−	0.175577i
$950$	6.89387	+	16.3941i	0.00725671	+	0.0172569i
$951$	417.369	−	74.8307i	0.438873	−	0.0786864i
$952$	7.47191	+	6.62882i	0.00784865	+	0.00696305i
$953$	−156.667	−	271.356i	−0.164394	−	0.284739i	0.772046	−	0.635567i	$-0.219233\pi$
$953$	−156.667	−	271.356i	−0.164394	−	0.284739i	−0.936440	+	0.350828i	$0.885900\pi$
$954$	−566.050	+	530.378i	−0.593344	+	0.555952i
$955$	−996.558	−	575.363i	−1.04352	−	0.602474i
$956$	156.039	−	608.368i	0.163221	−	0.636369i
$957$	−215.463	−	179.742i	−0.225144	−	0.187818i
$958$	387.382	−	510.490i	0.404365	−	0.532871i
$959$	−1.50436	−	4.13319i	−0.00156868	−	0.00430990i
$960$	592.717	+	786.333i	0.617413	+	0.819097i
$961$	−99.7172	−	565.524i	−0.103764	−	0.588475i
$962$	129.633	−	6.35648i	0.134753	−	0.00660757i
$963$	829.300	−	485.173i	0.861163	−	0.503814i
$964$	481.728	−	47.3565i	0.499718	−	0.0491250i
$965$	668.692	−	561.099i	0.692945	−	0.581450i
$966$	−2.85859	+	9.33365i	−0.00295920	+	0.00966216i
$967$	1793.17	+	316.184i	1.85437	+	0.326975i	0.985711	−	0.168444i	$-0.0538744\pi$
$967$	1793.17	+	316.184i	1.85437	+	0.326975i	0.868654	+	0.495419i	$0.164986\pi$
$968$	−701.850	−	431.415i	−0.725052	−	0.445677i
$969$	308.333	−	537.611i	0.318198	−	0.554811i
$970$	−73.3487	−	322.657i	−0.0756173	−	0.332637i
$971$			1200.07i			1.23592i	0.786211	+	0.617958i	$0.212040\pi$
$971$			1200.07i			1.23592i	−0.786211	+	0.617958i	$0.787960\pi$
$972$	−537.363	+	809.954i	−0.552842	+	0.833286i
$973$	−3.53321			−0.00363125
$974$	10.2339	−	2.32644i	0.0105071	−	0.00238854i
$975$	−6.89764	−	3.95597i	−0.00707450	−	0.00405740i
$976$	−6.38159	−	297.490i	−0.00653851	−	0.304805i
$977$	35.8447	−	203.285i	0.0366885	−	0.208071i	−0.960953	−	0.276712i	$-0.910755\pi$
$977$	35.8447	−	203.285i	0.0366885	−	0.208071i	0.997641	+	0.0686410i	$0.0218663\pi$
$978$	−1311.18	−	401.572i	−1.34068	−	0.410605i
$979$	146.949	+	175.127i	0.150101	+	0.178883i
$980$	−1000.36	+	98.3405i	−1.02077	+	0.100347i
$981$	241.373	+	412.576i	0.246048	+	0.420566i
$982$	−59.0638	−	1204.54i	−0.0601464	−	1.22661i
$983$	−1420.62	+	250.494i	−1.44519	+	0.254826i	−0.840575	−	0.541695i	$-0.817783\pi$
$983$	−1420.62	+	250.494i	−1.44519	+	0.254826i	−0.604612	+	0.796520i	$0.706672\pi$
$984$	−658.485	−	1208.43i	−0.669192	−	1.22808i
$985$	965.250	−	351.322i	0.979949	−	0.356672i
$986$	−1062.60	−	806.350i	−1.07769	−	0.817799i
$987$	1.15918	−	1.38954i	0.00117444	−	0.00140785i
$988$	13.7963	−	53.7892i	0.0139638	−	0.0544425i
$989$	817.858	−	1416.57i	0.826955	−	1.43233i
$990$	−267.943	−	285.964i	−0.270649	−	0.288853i
$991$	−814.600	+	470.309i	−0.821998	+	0.474581i	−0.851105	−	0.524996i	$-0.824067\pi$
$991$	−814.600	+	470.309i	−0.821998	+	0.474581i	0.0291073	+	0.999576i	$0.490734\pi$
$992$	1145.11	−	510.701i	1.15435	−	0.514820i
$993$	80.4571	+	448.749i	0.0810242	+	0.451913i
$994$	−9.75133	+	4.10053i	−0.00981019	+	0.00412528i
$995$	−877.215	+	1045.42i	−0.881623	+	1.05068i
$996$	−576.052	+	1280.53i	−0.578366	+	1.28567i
$997$	173.772	+	63.2477i	0.174294	+	0.0634380i	0.427693	−	0.903924i	$-0.359326\pi$
$997$	173.772	+	63.2477i	0.174294	+	0.0634380i	−0.253399	+	0.967362i	$0.581549\pi$
$998$	9.79773	−	6.31596i	0.00981737	−	0.00632861i
$999$	−749.632	−	424.225i	−0.750382	−	0.424650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.31.16	yes	204
3.2	odd	2		324.3.j.a.307.19		204
4.3	odd	2	inner	108.3.j.a.31.8	yes	204
12.11	even	2		324.3.j.a.307.27		204
27.7	even	9	inner	108.3.j.a.7.8	✓	204
27.20	odd	18		324.3.j.a.19.27		204
108.7	odd	18	inner	108.3.j.a.7.16	yes	204
108.47	even	18		324.3.j.a.19.19		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.8	✓	204	27.7	even	9	inner
108.3.j.a.7.16	yes	204	108.7	odd	18	inner
108.3.j.a.31.8	yes	204	4.3	odd	2	inner
108.3.j.a.31.16	yes	204	1.1	even	1	trivial
324.3.j.a.19.19		204	108.47	even	18
324.3.j.a.19.27		204	27.20	odd	18
324.3.j.a.307.19		204	3.2	odd	2
324.3.j.a.307.27		204	12.11	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.443343 - 1.95024i) q^{2} +(-2.60238 - 1.49253i) q^{3} +(-3.60689 + 1.72925i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-1.75705 + 5.73697i) q^{6} +(-0.0265129 - 0.0315969i) q^{7} +(4.97155 + 6.26767i) q^{8} +(4.54473 + 7.76823i) q^{9} +O(q^{10})\)	\(q+(-0.443343 - 1.95024i) q^{2} +(-2.60238 - 1.49253i) q^{3} +(-3.60689 + 1.72925i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-1.75705 + 5.73697i) q^{6} +(-0.0265129 - 0.0315969i) q^{7} +(4.97155 + 6.26767i) q^{8} +(4.54473 + 7.76823i) q^{9} +(10.2450 - 0.502357i) q^{10} +(-4.18050 + 0.737135i) q^{11} +(11.9675 + 0.883222i) q^{12} +(-1.91152 + 0.695736i) q^{13} +(-0.0498672 + 0.0657149i) q^{14} +(9.85597 - 11.8147i) q^{15} +(10.0194 - 12.4745i) q^{16} +(-15.1353 + 26.2152i) q^{17} +(13.1351 - 12.3073i) q^{18} +(5.91027 - 3.41230i) q^{19} +(-5.52176 - 19.7575i) q^{20} +(0.0218374 + 0.121798i) q^{21} +(3.29099 + 7.82619i) q^{22} +(-25.3540 + 30.2157i) q^{23} +(-3.58319 - 23.7310i) q^{24} +(-1.22440 - 0.445645i) q^{25} +(2.20431 + 3.41948i) q^{26} +(-0.232786 - 26.9990i) q^{27} +(0.150268 + 0.0681190i) q^{28} +(-20.7044 - 7.53578i) q^{29} +(-27.4111 - 13.9836i) q^{30} +(-25.1859 + 30.0153i) q^{31} +(-28.7702 - 14.0097i) q^{32} +(11.9794 + 4.32121i) q^{33} +(57.8360 + 17.8953i) q^{34} +(0.183199 - 0.105770i) q^{35} +(-29.8256 - 20.1602i) q^{36} +(15.9508 - 27.6276i) q^{37} +(-9.27508 - 10.0136i) q^{38} +(6.01290 + 1.04243i) q^{39} +(-36.0838 + 19.5281i) q^{40} +(53.8833 - 19.6119i) q^{41} +(0.227855 - 0.0965866i) q^{42} +(-40.8395 + 7.20111i) q^{43} +(13.8039 - 9.88791i) q^{44} +(-43.2827 + 16.0359i) q^{45} +(70.1685 + 36.0505i) q^{46} +(-9.40005 - 11.2025i) q^{47} +(-44.6926 + 17.5091i) q^{48} +(8.50847 - 48.2539i) q^{49} +(-0.326287 + 2.58545i) q^{50} +(78.5146 - 45.6318i) q^{51} +(5.69155 - 5.81495i) q^{52} -43.0946 q^{53} +(-52.5514 + 12.4238i) q^{54} -21.7710i q^{55} +(0.0662283 - 0.323260i) q^{56} +(-20.4737 + 0.0588402i) q^{57} +(-5.51746 + 43.7195i) q^{58} +(40.5818 + 7.15567i) q^{59} +(-15.1189 + 59.6578i) q^{60} +(14.2464 - 11.9542i) q^{61} +(69.7032 + 35.8115i) q^{62} +(0.124958 - 0.349558i) q^{63} +(-14.5673 + 62.3201i) q^{64} +(-1.81161 - 10.2742i) q^{65} +(3.11641 - 25.2786i) q^{66} +(-16.7275 - 45.9585i) q^{67} +(9.25890 - 120.728i) q^{68} +(111.078 - 40.7912i) q^{69} +(-0.287497 - 0.310390i) q^{70} +(111.053 + 64.1166i) q^{71} +(-26.0944 + 67.1050i) q^{72} +(63.7153 + 110.358i) q^{73} +(-60.9523 - 18.8595i) q^{74} +(2.52121 + 2.98718i) q^{75} +(-15.4170 + 22.5281i) q^{76} +(0.134128 + 0.112547i) q^{77} +(-0.632789 - 12.1888i) q^{78} +(-1.11267 + 3.05705i) q^{79} +(54.0821 + 61.7146i) q^{80} +(-39.6909 + 70.6090i) q^{81} +(-62.1368 - 96.3907i) q^{82} +(-40.0201 + 109.954i) q^{83} +(-0.289385 - 0.401551i) q^{84} +(-118.926 - 99.7911i) q^{85} +(32.1498 + 76.4544i) q^{86} +(42.6332 + 50.5128i) q^{87} +(-25.4037 - 22.5373i) q^{88} +(-26.9272 - 46.6393i) q^{89} +(50.4630 + 77.3023i) q^{90} +(0.0726630 + 0.0419520i) q^{91} +(39.1986 - 152.828i) q^{92} +(110.342 - 40.5206i) q^{93} +(-17.6802 + 23.2989i) q^{94} +(11.9710 + 32.8901i) q^{95} +(53.9611 + 79.3990i) q^{96} +(-5.60171 - 31.7689i) q^{97} +(-97.8790 + 4.79945i) q^{98} +(-24.7255 - 29.1250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more