LMFDB - Embedded newform 819.2.fk.a.187.96

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(31,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 2, 9]))

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

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

chi := DirichletCharacter("819.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fk (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$108$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.96
Character	$\chi$	$=$	819.187
Dual form			819.2.fk.a.346.96

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.19119 + 0.587129i) q^{2} +(-0.935526 - 1.45767i) q^{3} +(2.72456 + 1.57302i) q^{4} +(1.74171 + 1.74171i) q^{5} +(-1.19408 - 3.74330i) q^{6} +(0.988320 + 2.45423i) q^{7} +(1.83834 + 1.83834i) q^{8} +(-1.24958 + 2.72737i) q^{9} +O(q^{10})$	\(q+(2.19119 + 0.587129i) q^{2} +(-0.935526 - 1.45767i) q^{3} +(2.72456 + 1.57302i) q^{4} +(1.74171 + 1.74171i) q^{5} +(-1.19408 - 3.74330i) q^{6} +(0.988320 + 2.45423i) q^{7} +(1.83834 + 1.83834i) q^{8} +(-1.24958 + 2.72737i) q^{9} +(2.79381 + 4.83902i) q^{10} +(-0.148260 - 0.148260i) q^{11} +(-0.255952 - 5.44310i) q^{12} +(-0.522038 + 3.56756i) q^{13} +(0.724655 + 5.95795i) q^{14} +(0.909414 - 4.16824i) q^{15} +(-0.197235 - 0.341621i) q^{16} +(1.30624 + 2.26248i) q^{17} +(-4.33939 + 5.24253i) q^{18} +(0.461262 - 0.123595i) q^{19} +(2.00563 + 7.48513i) q^{20} +(2.65284 - 3.73663i) q^{21} +(-0.237819 - 0.411914i) q^{22} -3.31759i q^{23} +(0.959870 - 4.39950i) q^{24} +1.06708i q^{25} +(-3.23850 + 7.51071i) q^{26} +(5.14461 - 0.730055i) q^{27} +(-1.16782 + 8.24134i) q^{28} +(3.48198 - 6.03096i) q^{29} +(4.43999 - 8.59947i) q^{30} +(-6.61101 + 1.77141i) q^{31} +(-1.57736 - 5.88679i) q^{32} +(-0.0774125 + 0.354815i) q^{33} +(1.53386 + 5.72446i) q^{34} +(-2.55318 + 5.99590i) q^{35} +(-7.69478 + 5.46526i) q^{36} +(10.5072 - 2.81539i) q^{37} +1.08328 q^{38} +(5.68869 - 2.57659i) q^{39} +6.40369i q^{40} +(1.04149 - 3.88691i) q^{41} +(8.00678 - 6.63013i) q^{42} +(-6.49650 - 3.75075i) q^{43} +(-0.170727 - 0.637160i) q^{44} +(-6.92668 + 2.57387i) q^{45} +(1.94785 - 7.26949i) q^{46} +(0.917279 + 0.245784i) q^{47} +(-0.313451 + 0.607098i) q^{48} +(-5.04645 + 4.85112i) q^{49} +(-0.626514 + 2.33818i) q^{50} +(2.07591 - 4.02067i) q^{51} +(-7.03418 + 8.89885i) q^{52} +(4.32791 + 7.49617i) q^{53} +(11.7015 + 1.42086i) q^{54} -0.516451i q^{55} +(-2.69483 + 6.32857i) q^{56} +(-0.611682 - 0.556739i) q^{57} +(11.1706 - 11.1706i) q^{58} +(-0.590589 - 2.20411i) q^{59} +(9.03450 - 9.92608i) q^{60} +(10.1708 - 5.87212i) q^{61} -15.5260 q^{62} +(-7.92857 - 0.371239i) q^{63} -13.0363i q^{64} +(-7.12288 + 5.30440i) q^{65} +(-0.377948 + 0.732017i) q^{66} +(-1.26030 - 4.70352i) q^{67} +8.21901i q^{68} +(-4.83594 + 3.10370i) q^{69} +(-9.11487 + 11.6391i) q^{70} +(-2.65094 + 2.65094i) q^{71} +(-7.31098 + 2.71668i) q^{72} +(0.719141 + 0.192693i) q^{73} +24.6763 q^{74} +(1.55545 - 0.998283i) q^{75} +(1.45115 + 0.388835i) q^{76} +(0.217335 - 0.510392i) q^{77} +(13.9778 - 2.30581i) q^{78} +(-1.76612 - 3.05900i) q^{79} +(0.251478 - 0.938528i) q^{80} +(-5.87709 - 6.81614i) q^{81} +(4.56423 - 7.90548i) q^{82} +(-14.7136 + 3.94250i) q^{83} +(13.1056 - 6.00769i) q^{84} +(-1.66548 + 6.21566i) q^{85} +(-12.0329 - 12.0329i) q^{86} +(-12.0486 + 0.566563i) q^{87} -0.545105i q^{88} +(1.34867 + 5.03329i) q^{89} +(-16.6889 + 1.57301i) q^{90} +(-9.27153 + 2.24469i) q^{91} +(5.21866 - 9.03898i) q^{92} +(8.76690 + 7.97944i) q^{93} +(1.86563 + 1.07712i) q^{94} +(1.01865 + 0.588117i) q^{95} +(-7.10532 + 7.80652i) q^{96} +(-15.2302 + 4.08091i) q^{97} +(-13.9060 + 7.66683i) q^{98} +(0.589623 - 0.219097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 432 * q + 2 * q^2 - 12 * q^3 + 12 * q^6 - 8 * q^8 - 4 * q^9	$ 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9} - 12 q^{11} - 4 q^{14} - 14 q^{15} + 196 q^{16} + 14 q^{18} - 12 q^{19} - 60 q^{20} - 8 q^{22} - 24 q^{24} - 12 q^{26} - 36 q^{27} + 4 q^{28} - 24 q^{29} - 30 q^{31} + 10 q^{32} - 60 q^{33} - 12 q^{34} - 60 q^{35} - 2 q^{37} - 22 q^{39} - 100 q^{42} + 32 q^{44} - 6 q^{45} + 4 q^{46} + 30 q^{47} - 12 q^{48} + 22 q^{50} + 8 q^{53} + 30 q^{54} - 44 q^{57} + 12 q^{58} - 6 q^{59} - 64 q^{60} - 12 q^{61} + 14 q^{63} + 16 q^{65} - 12 q^{66} + 16 q^{67} + 32 q^{70} + 48 q^{71} + 34 q^{72} - 12 q^{73} + 104 q^{74} - 48 q^{76} + 2 q^{78} + 28 q^{79} - 6 q^{80} - 44 q^{81} + 84 q^{83} - 38 q^{84} - 6 q^{85} + 84 q^{86} + 24 q^{87} + 18 q^{89} + 52 q^{92} - 108 q^{93} - 12 q^{94} + 42 q^{96} + 6 q^{97} - 112 q^{98} - 50 q^{99}+O(q^{100}) $ 432 * q + 2 * q^2 - 12 * q^3 + 12 * q^6 - 8 * q^8 - 4 * q^9 - 12 * q^11 - 4 * q^14 - 14 * q^15 + 196 * q^16 + 14 * q^18 - 12 * q^19 - 60 * q^20 - 8 * q^22 - 24 * q^24 - 12 * q^26 - 36 * q^27 + 4 * q^28 - 24 * q^29 - 30 * q^31 + 10 * q^32 - 60 * q^33 - 12 * q^34 - 60 * q^35 - 2 * q^37 - 22 * q^39 - 100 * q^42 + 32 * q^44 - 6 * q^45 + 4 * q^46 + 30 * q^47 - 12 * q^48 + 22 * q^50 + 8 * q^53 + 30 * q^54 - 44 * q^57 + 12 * q^58 - 6 * q^59 - 64 * q^60 - 12 * q^61 + 14 * q^63 + 16 * q^65 - 12 * q^66 + 16 * q^67 + 32 * q^70 + 48 * q^71 + 34 * q^72 - 12 * q^73 + 104 * q^74 - 48 * q^76 + 2 * q^78 + 28 * q^79 - 6 * q^80 - 44 * q^81 + 84 * q^83 - 38 * q^84 - 6 * q^85 + 84 * q^86 + 24 * q^87 + 18 * q^89 + 52 * q^92 - 108 * q^93 - 12 * q^94 + 42 * q^96 + 6 * q^97 - 112 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.19119	+	0.587129i	1.54941	+	0.415163i	0.929291	−	0.369347i	$-0.120419\pi$
$2$	2.19119	+	0.587129i	1.54941	+	0.415163i	0.620116	+	0.784510i	$0.287085\pi$
$3$	−0.935526	−	1.45767i	−0.540126	−	0.841584i
$3$	−0.935526	−	1.45767i	−0.540126	−	0.841584i
$4$	2.72456	+	1.57302i	1.36228	+	0.786512i
$5$	1.74171	+	1.74171i	0.778915	+	0.778915i	0.979646	−	0.200732i	$-0.0643319\pi$
$5$	1.74171	+	1.74171i	0.778915	+	0.778915i	−0.200732	+	0.979646i	$0.564332\pi$
$6$	−1.19408	−	3.74330i	−0.487482	−	1.52820i
$7$	0.988320	+	2.45423i	0.373550	+	0.927610i
$7$	0.988320	+	2.45423i	0.373550	+	0.927610i
$8$	1.83834	+	1.83834i	0.649951	+	0.649951i
$9$	−1.24958	+	2.72737i	−0.416527	+	0.909123i
$10$	2.79381	+	4.83902i	0.883480	+	1.53023i
$11$	−0.148260	−	0.148260i	−0.0447021	−	0.0447021i	0.684402	−	0.729104i	$-0.260063\pi$
$11$	−0.148260	−	0.148260i	−0.0447021	−	0.0447021i	−0.729104	+	0.684402i	$0.760063\pi$
$12$	−0.255952	−	5.44310i	−0.0738869	−	1.57129i
$13$	−0.522038	+	3.56756i	−0.144787	+	0.989463i
$13$	−0.522038	+	3.56756i	−0.144787	+	0.989463i
$14$	0.724655	+	5.95795i	0.193672	+	1.59233i
$15$	0.909414	−	4.16824i	0.234810	−	1.07623i
$16$	−0.197235	−	0.341621i	−0.0493087	−	0.0854052i
$17$	1.30624	+	2.26248i	0.316810	+	0.548732i	0.979821	−	0.199879i	$-0.0640548\pi$
$17$	1.30624	+	2.26248i	0.316810	+	0.548732i	−0.663010	+	0.748610i	$0.730721\pi$
$18$	−4.33939	+	5.24253i	−1.02280	+	1.23568i
$19$	0.461262	−	0.123595i	0.105821	−	0.0283546i	−0.205520	−	0.978653i	$-0.565889\pi$
$19$	0.461262	−	0.123595i	0.105821	−	0.0283546i	0.311341	+	0.950298i	$0.399222\pi$
$20$	2.00563	+	7.48513i	0.448473	+	1.67373i
$21$	2.65284	−	3.73663i	0.578898	−	0.815400i
$22$	−0.237819	−	0.411914i	−0.0507032	−	0.0878205i
$23$		−	3.31759i		−	0.691766i	−0.938278	−	0.345883i	$-0.887579\pi$
$23$		−	3.31759i		−	0.691766i	0.938278	−	0.345883i	$-0.112421\pi$
$24$	0.959870	−	4.39950i	0.195933	−	0.898044i
$25$			1.06708i			0.213416i
$26$	−3.23850	+	7.51071i	−0.635122	+	1.47297i
$27$	5.14461	−	0.730055i	0.990081	−	0.140499i
$28$	−1.16782	+	8.24134i	−0.220698	+	1.55747i
$29$	3.48198	−	6.03096i	0.646587	−	1.11992i	−0.337346	−	0.941381i	$-0.609529\pi$
$29$	3.48198	−	6.03096i	0.646587	−	1.11992i	0.983933	−	0.178541i	$-0.0571376\pi$
$30$	4.43999	−	8.59947i	0.810628	−	1.57004i
$31$	−6.61101	+	1.77141i	−1.18737	+	0.318155i	−0.797847	−	0.602861i	$-0.794028\pi$
$31$	−6.61101	+	1.77141i	−1.18737	+	0.318155i	−0.389525	+	0.921016i	$0.627361\pi$
$32$	−1.57736	−	5.88679i	−0.278841	−	1.04065i
$33$	−0.0774125	+	0.354815i	−0.0134758	+	0.0617654i
$34$	1.53386	+	5.72446i	0.263056	+	0.981737i
$35$	−2.55318	+	5.99590i	−0.431566	+	1.01349i
$36$	−7.69478	+	5.46526i	−1.28246	+	0.910877i
$37$	10.5072	−	2.81539i	1.72737	−	0.462848i	0.747797	−	0.663928i	$-0.231112\pi$
$37$	10.5072	−	2.81539i	1.72737	−	0.462848i	0.979575	+	0.201080i	$0.0644452\pi$
$38$	1.08328			0.175731
$39$	5.68869	−	2.57659i	0.910919	−	0.412584i
$40$			6.40369i			1.01251i
$41$	1.04149	−	3.88691i	0.162654	−	0.607033i	−0.835674	−	0.549226i	$-0.814923\pi$
$41$	1.04149	−	3.88691i	0.162654	−	0.607033i	0.998328	−	0.0578070i	$-0.0184108\pi$
$42$	8.00678	−	6.63013i	1.23547	−	1.02305i
$43$	−6.49650	−	3.75075i	−0.990706	−	0.571985i	−0.0852209	−	0.996362i	$-0.527160\pi$
$43$	−6.49650	−	3.75075i	−0.990706	−	0.571985i	−0.905485	+	0.424378i	$0.860493\pi$
$44$	−0.170727	−	0.637160i	−0.0257380	−	0.0960555i
$45$	−6.92668	+	2.57387i	−1.03257	+	0.383691i
$46$	1.94785	−	7.26949i	0.287195	−	1.07183i
$47$	0.917279	+	0.245784i	0.133799	+	0.0358513i	0.325097	−	0.945681i	$-0.394603\pi$
$47$	0.917279	+	0.245784i	0.133799	+	0.0358513i	−0.191298	+	0.981532i	$0.561270\pi$
$48$	−0.313451	+	0.607098i	−0.0452427	+	0.0876270i
$49$	−5.04645	+	4.85112i	−0.720921	+	0.693017i
$50$	−0.626514	+	2.33818i	−0.0886025	+	0.330669i
$51$	2.07591	−	4.02067i	0.290686	−	0.563007i
$52$	−7.03418	+	8.89885i	−0.975466	+	1.23405i
$53$	4.32791	+	7.49617i	0.594485	+	1.02968i	0.993619	+	0.112785i	$0.0359773\pi$
$53$	4.32791	+	7.49617i	0.594485	+	1.02968i	−0.399135	+	0.916892i	$0.630689\pi$
$54$	11.7015	+	1.42086i	1.59237	+	0.193354i
$55$		−	0.516451i		−	0.0696383i
$56$	−2.69483	+	6.32857i	−0.360112	+	0.845690i
$57$	−0.611682	−	0.556739i	−0.0810193	−	0.0737419i
$58$	11.1706	−	11.1706i	1.46678	−	1.46678i
$59$	−0.590589	−	2.20411i	−0.0768881	−	0.286950i	0.916767	−	0.399423i	$-0.130790\pi$
$59$	−0.590589	−	2.20411i	−0.0768881	−	0.286950i	−0.993655	+	0.112473i	$0.964123\pi$
$60$	9.03450	−	9.92608i	1.16635	−	1.28145i
$61$	10.1708	−	5.87212i	1.30224	−	0.751849i	0.321452	−	0.946926i	$-0.395829\pi$
$61$	10.1708	−	5.87212i	1.30224	−	0.751849i	0.980788	+	0.195077i	$0.0624958\pi$
$62$	−15.5260			−1.97181
$63$	−7.92857	−	0.371239i	−0.998906	−	0.0467717i
$64$		−	13.0363i		−	1.62954i
$65$	−7.12288	+	5.30440i	−0.883484	+	0.657930i
$66$	−0.377948	+	0.732017i	−0.0465222	+	0.0901051i
$67$	−1.26030	−	4.70352i	−0.153971	−	0.574626i	−0.999191	−	0.0402086i	$-0.987198\pi$
$67$	−1.26030	−	4.70352i	−0.153971	−	0.574626i	0.845221	−	0.534417i	$-0.179469\pi$
$68$			8.21901i			0.996701i
$69$	−4.83594	+	3.10370i	−0.582179	+	0.373641i
$70$	−9.11487	+	11.6391i	−1.08944	+	1.39114i
$71$	−2.65094	+	2.65094i	−0.314609	+	0.314609i	−0.846692	−	0.532083i	$-0.821409\pi$
$71$	−2.65094	+	2.65094i	−0.314609	+	0.314609i	0.532083	+	0.846692i	$0.321409\pi$
$72$	−7.31098	+	2.71668i	−0.861608	+	0.320163i
$73$	0.719141	+	0.192693i	0.0841691	+	0.0225530i	0.300658	−	0.953732i	$-0.402794\pi$
$73$	0.719141	+	0.192693i	0.0841691	+	0.0225530i	−0.216489	+	0.976285i	$0.569460\pi$
$74$	24.6763			2.86856
$75$	1.55545	−	0.998283i	0.179608	−	0.115272i
$76$	1.45115	+	0.388835i	0.166459	+	0.0446024i
$77$	0.217335	−	0.510392i	0.0247677	−	0.0581646i
$78$	13.9778	−	2.30581i	1.58268	−	0.261082i
$79$	−1.76612	−	3.05900i	−0.198704	−	0.344165i	0.749405	−	0.662112i	$-0.230340\pi$
$79$	−1.76612	−	3.05900i	−0.198704	−	0.344165i	−0.948108	+	0.317947i	$0.897006\pi$
$80$	0.251478	−	0.938528i	0.0281161	−	0.104931i
$81$	−5.87709	−	6.81614i	−0.653011	−	0.757349i
$82$	4.56423	−	7.90548i	0.504035	−	0.873014i
$83$	−14.7136	+	3.94250i	−1.61503	+	0.432746i	−0.949536	−	0.313657i	$-0.898446\pi$
$83$	−14.7136	+	3.94250i	−1.61503	+	0.432746i	−0.665494	+	0.746403i	$0.731779\pi$
$84$	13.1056	−	6.00769i	1.42994	−	0.655493i
$85$	−1.66548	+	6.21566i	−0.180647	+	0.674183i
$86$	−12.0329	−	12.0329i	−1.29754	−	1.29754i
$87$	−12.0486	+	0.566563i	−1.29175	+	0.0607419i
$88$		−	0.545105i		−	0.0581084i
$89$	1.34867	+	5.03329i	0.142958	+	0.533528i	0.999838	+	0.0180108i	$0.00573334\pi$
$89$	1.34867	+	5.03329i	0.142958	+	0.533528i	−0.856880	+	0.515517i	$0.827600\pi$
$90$	−16.6889	+	1.57301i	−1.75916	+	0.165809i
$91$	−9.27153	+	2.24469i	−0.971921	+	0.235308i
$92$	5.21866	−	9.03898i	0.544083	−	0.942379i
$93$	8.76690	+	7.97944i	0.909085	+	0.827429i
$94$	1.86563	+	1.07712i	0.192425	+	0.111097i
$95$	1.01865	+	0.588117i	0.104511	+	0.0603395i
$96$	−7.10532	+	7.80652i	−0.725183	+	0.796749i
$97$	−15.2302	+	4.08091i	−1.54639	+	0.414354i	−0.928324	−	0.371772i	$-0.878750\pi$
$97$	−15.2302	+	4.08091i	−1.54639	+	0.414354i	−0.618066	+	0.786126i	$0.712084\pi$
$98$	−13.9060	+	7.66683i	−1.40472	+	0.774467i
$99$	0.589623	−	0.219097i	0.0592594	−	0.0220201i
$100$	−1.67855	+	2.90733i	−0.167855	+	0.290733i
$101$	3.24237			0.322628			0.161314	−	0.986903i	$-0.448427\pi$
$101$	3.24237			0.322628			0.161314	+	0.986903i	$0.448427\pi$
$102$	6.90938	−	7.59125i	0.684131	−	0.751645i
$103$	6.17190			0.608135			0.304068	−	0.952650i	$-0.401655\pi$
$103$	6.17190			0.608135			0.304068	+	0.952650i	$0.401655\pi$
$104$	−7.51806	+	5.59870i	−0.737207	+	0.548998i
$105$	11.1286	−	1.88765i	1.08604	−	0.184215i
$106$	5.08208	+	18.9666i	0.493616	+	1.84220i
$107$	1.23525	−	2.13951i	0.119416	−	0.206834i	−0.800120	−	0.599839i	$-0.795231\pi$
$107$	1.23525	−	2.13951i	0.119416	−	0.206834i	0.919536	+	0.393005i	$0.128565\pi$
$108$	15.1652	+	6.10352i	1.45927	+	0.587312i
$109$	−3.33734	−	0.894237i	−0.319659	−	0.0856524i	0.0954217	−	0.995437i	$-0.469580\pi$
$109$	−3.33734	−	0.894237i	−0.319659	−	0.0856524i	−0.415081	+	0.909785i	$0.636247\pi$
$110$	0.303223	−	1.13164i	0.0289112	−	0.107898i
$111$	−13.9337	−	12.6821i	−1.32252	−	1.20373i
$112$	0.643483	−	0.821689i	0.0608034	−	0.0776423i
$113$	4.96518	+	8.59995i	0.467085	+	0.809015i	0.999293	−	0.0375988i	$-0.0119709\pi$
$113$	4.96518	+	8.59995i	0.467085	+	0.809015i	−0.532208	+	0.846614i	$0.678638\pi$
$114$	−1.01344	−	1.57906i	−0.0949170	−	0.147893i
$115$	5.77827	−	5.77827i	0.538827	−	0.538827i
$116$	18.9737	−	10.9545i	1.76166	−	1.01710i
$117$	−9.07772	−	5.88174i	−0.839236	−	0.543767i
$118$		−	5.17638i		−	0.476524i
$119$	−4.26165	+	5.44187i	−0.390665	+	0.498855i
$120$	9.33445	−	5.99082i	0.852114	−	0.546885i
$121$		−	10.9560i		−	0.996003i
$122$	25.7339	−	6.89538i	2.32984	−	0.624279i
$123$	−6.64016	+	2.11816i	−0.598723	+	0.190988i
$124$	−20.7986	−	5.57296i	−1.86777	−	0.500466i
$125$	6.84999	−	6.84999i	0.612682	−	0.612682i
$126$	−17.1551	−	5.46855i	−1.52829	−	0.487177i
$127$		−	12.2283i		−	1.08508i	−0.840029	−	0.542542i	$-0.817462\pi$
$127$		−	12.2283i		−	1.08508i	0.840029	−	0.542542i	$-0.182538\pi$
$128$	4.49925	−	16.7914i	0.397681	−	1.48417i
$129$	0.610296	+	12.9786i	0.0537336	+	1.14271i
$130$	−18.7220	+	7.44093i	−1.64203	+	0.652613i
$131$		−	11.2286i		−	0.981044i	−0.871429	−	0.490522i	$-0.836806\pi$
$131$		−	11.2286i		−	0.981044i	0.871429	−	0.490522i	$-0.163194\pi$
$132$	−0.769048	+	0.844943i	−0.0669370	+	0.0735428i
$133$	0.759203	+	1.00989i	0.0658313	+	0.0875685i
$134$		−	11.0463i		−	0.954253i
$135$	10.2319	+	7.68886i	0.880625	+	0.661752i
$136$	−1.75789	+	6.56052i	−0.150737	+	0.562560i
$137$	−9.87595	−	9.87595i	−0.843759	−	0.843759i	0.145587	−	0.989346i	$-0.453493\pi$
$137$	−9.87595	−	9.87595i	−0.843759	−	0.843759i	−0.989346	+	0.145587i	$0.953493\pi$
$138$	−12.4188	+	3.96148i	−1.05715	+	0.337223i
$139$	−9.34183	+	5.39351i	−0.792364	+	0.457471i	−0.840794	−	0.541355i	$-0.817911\pi$
$139$	−9.34183	+	5.39351i	−0.792364	+	0.457471i	0.0484303	+	0.998827i	$0.484578\pi$
$140$	−16.3880	+	12.3200i	−1.38504	+	1.04123i
$141$	−0.499868	−	1.56702i	−0.0420964	−	0.131967i
$142$	−7.36517	+	4.25228i	−0.618071	+	0.356844i
$143$	0.606324	−	0.451529i	0.0507034	−	0.0377588i
$144$	1.17819	−	0.111050i	0.0981822	−	0.00925413i
$145$	16.5687	−	4.43958i	1.37596	−	0.368687i
$146$	1.46264	+	0.844456i	0.121049	+	0.0698877i
$147$	11.7924	+	2.81768i	0.972621	+	0.232399i
$148$	33.0561	+	8.85737i	2.71720	+	0.728071i
$149$	−13.5404	+	13.5404i	−1.10927	+	1.10927i	−0.116024	+	0.993246i	$0.537015\pi$
$149$	−13.5404	+	13.5404i	−1.10927	+	1.10927i	−0.993246	+	0.116024i	$0.962985\pi$
$150$	3.99441	−	1.27418i	0.326142	−	0.104037i
$151$	12.8339	+	12.8339i	1.04441	+	1.04441i	0.998967	+	0.0454379i	$0.0144683\pi$
$151$	12.8339	+	12.8339i	1.04441	+	1.04441i	0.0454379	+	0.998967i	$0.485532\pi$
$152$	1.07516	+	0.620746i	0.0872073	+	0.0503492i
$153$	−7.80287	+	0.735457i	−0.630825	+	0.0594581i
$154$	0.775890	−	0.990765i	0.0625230	−	0.0798381i
$155$	−14.5997	−	8.42915i	−1.17268	−	0.677046i
$156$	19.5522	+	1.92838i	1.56543	+	0.154394i
$157$	−10.5118	−	6.06899i	−0.838933	−	0.484358i	0.0179682	−	0.999839i	$-0.494280\pi$
$157$	−10.5118	−	6.06899i	−0.838933	−	0.484358i	−0.856901	+	0.515480i	$0.827614\pi$
$158$	−2.07388	−	7.73981i	−0.164989	−	0.615746i
$159$	6.87803	−	13.3215i	0.545463	−	1.05646i
$160$	7.50577	−	13.0004i	0.593383	−	1.02777i
$161$	8.14212	−	3.27884i	0.641689	−	0.258409i
$162$	−8.87590	−	18.3861i	−0.697357	−	1.44455i
$163$	10.7077	−	2.86911i	0.838690	−	0.224726i	0.186189	−	0.982514i	$-0.440386\pi$
$163$	10.7077	−	2.86911i	0.838690	−	0.224726i	0.652501	+	0.757788i	$0.273720\pi$
$164$	8.95182	−	8.95182i	0.699020	−	0.699020i
$165$	−0.752813	+	0.483154i	−0.0586064	+	0.0376135i
$166$	−34.5552			−2.68200
$167$	8.19443	+	2.19569i	0.634104	+	0.169908i	0.561531	−	0.827455i	$-0.310212\pi$
$167$	8.19443	+	2.19569i	0.634104	+	0.169908i	0.0725728	+	0.997363i	$0.476879\pi$
$168$	11.7460	−	1.99238i	0.906225	−	0.153715i
$169$	−12.4550	−	3.72480i	−0.958073	−	0.286523i
$170$	−7.29879	+	12.6419i	−0.559791	+	0.969587i
$171$	−0.239295	+	1.41247i	−0.0182994	+	0.108014i
$172$	−11.8001	−	20.4383i	−0.899746	−	1.55841i
$173$	9.07831	+	15.7241i	0.690211	+	1.19548i	0.971769	+	0.235936i	$0.0758157\pi$
$173$	9.07831	+	15.7241i	0.690211	+	1.19548i	−0.281557	+	0.959544i	$0.590851\pi$
$174$	−26.7335	−	5.83263i	−2.02666	−	0.442171i
$175$	−2.61886	+	1.05462i	−0.197967	+	0.0797217i
$176$	−0.0214067	+	0.0798908i	−0.00161359	+	0.00602199i
$177$	−2.66034	+	2.92288i	−0.199964	+	0.219697i
$178$			11.8208i			0.886003i
$179$	−1.35594	+	0.782854i	−0.101348	+	0.0585133i	−0.549817	−	0.835285i	$-0.685303\pi$
$179$	−1.35594	+	0.782854i	−0.101348	+	0.0585133i	0.448469	+	0.893798i	$0.351969\pi$
$180$	−22.9209	−	3.88317i	−1.70842	−	0.289434i
$181$	−7.63912			−0.567811			−0.283906	−	0.958852i	$-0.591630\pi$
$181$	−7.63912			−0.567811			−0.283906	+	0.958852i	$0.591630\pi$
$182$	−21.6337	−	0.525029i	−1.60359	−	0.0389178i
$183$	−18.0747	−	9.33213i	−1.33612	−	0.689851i
$184$	6.09886	−	6.09886i	0.449614	−	0.449614i
$185$	23.2040	+	13.3969i	1.70599	+	0.984956i
$186$	14.5250	+	22.6318i	1.06503	+	1.65944i
$187$	0.141772	−	0.529099i	0.0103674	−	0.0386916i
$188$	2.11256	+	2.11256i	0.154074	+	0.154074i
$189$	6.87624	+	11.9045i	0.500173	+	0.865926i
$190$	1.88676	+	1.88676i	0.136880	+	0.136880i
$191$	−0.316906	−	0.548897i	−0.0229305	−	0.0397168i	0.854332	−	0.519727i	$-0.173966\pi$
$191$	−0.316906	−	0.548897i	−0.0229305	−	0.0397168i	−0.877263	+	0.480010i	$0.840633\pi$
$192$	−19.0025	+	12.1958i	−1.37139	+	0.880155i
$193$	−20.1430	+	5.39730i	−1.44992	+	0.388506i	−0.895997	−	0.444059i	$-0.853538\pi$
$193$	−20.1430	+	5.39730i	−1.44992	+	0.388506i	−0.553927	+	0.832565i	$0.686871\pi$
$194$	−35.7683			−2.56801
$195$	14.3957	+	5.42037i	1.03090	+	0.388161i
$196$	−21.3803	+	5.27898i	−1.52716	+	0.377070i
$197$	−9.75420	+	9.75420i	−0.694958	+	0.694958i	−0.963319	−	0.268361i	$-0.913518\pi$
$197$	−9.75420	+	9.75420i	−0.694958	+	0.694958i	0.268361	+	0.963319i	$0.413518\pi$
$198$	1.42062	−	0.133900i	0.100959	−	0.00951584i
$199$	−6.29110	−	10.8965i	−0.445965	−	0.772433i	0.552154	−	0.833742i	$-0.313806\pi$
$199$	−6.29110	−	10.8965i	−0.445965	−	0.772433i	−0.998119	+	0.0613086i	$0.980473\pi$
$200$	−1.96166	+	1.96166i	−0.138710	+	0.138710i
$201$	−5.67711	+	6.23736i	−0.400432	+	0.439950i
$202$	7.10466	+	1.90369i	0.499882	+	0.133943i
$203$	18.2426	+	2.58504i	1.28038	+	0.181434i
$204$	11.9806	−	7.68910i	0.838808	−	0.538345i
$205$	8.58383	−	4.95588i	0.599521	−	0.346134i
$206$	13.5238	+	3.62370i	0.942249	+	0.252475i
$207$	9.04830	+	4.14560i	0.628901	+	0.288139i
$208$	1.32172	−	0.525308i	0.0916445	−	0.0364235i
$209$	−0.0867109	−	0.0500626i	−0.00599792	−	0.00346290i
$210$	25.4932	+	2.39772i	1.75920	+	0.165458i
$211$	−10.4851	−	18.1608i	−0.721826	−	1.25024i	−0.960267	−	0.279082i	$-0.909970\pi$
$211$	−10.4851	−	18.1608i	−0.721826	−	1.25024i	0.238441	−	0.971157i	$-0.423364\pi$
$212$			27.2317i			1.87028i
$213$	6.34421	+	1.38416i	0.434698	+	0.0948412i
$214$	3.96283	−	3.96283i	0.270894	−	0.270894i
$215$	−4.78228	−	17.8477i	−0.326149	−	1.21720i
$216$	10.7996	+	8.11545i	0.734821	+	0.552186i
$217$	−10.8812	−	14.4742i	−0.738667	−	0.982571i
$218$	−6.78773	−	3.91890i	−0.459723	−	0.265421i
$219$	−0.391893	−	1.22854i	−0.0264817	−	0.0830168i
$220$	0.812391	−	1.40710i	0.0547714	−	0.0948668i
$221$	−8.75343	+	3.47900i	−0.588820	+	0.234023i
$222$	−23.0853	−	35.9698i	−1.54938	−	2.41413i
$223$	15.8221	−	4.23951i	1.05952	−	0.283899i	0.313342	−	0.949640i	$-0.398551\pi$
$223$	15.8221	−	4.23951i	1.05952	−	0.283899i	0.746182	+	0.665742i	$0.231885\pi$
$224$	12.8886	−	9.68924i	0.861155	−	0.647389i
$225$	−2.91033	−	1.33341i	−0.194022	−	0.0888937i
$226$	5.83040	+	21.7593i	0.387832	+	1.44741i
$227$	12.2804	+	12.2804i	0.815079	+	0.815079i	0.985390	−	0.170311i	$-0.0544772\pi$
$227$	12.2804	+	12.2804i	0.815079	+	0.815079i	−0.170311	+	0.985390i	$0.554477\pi$
$228$	−0.790799	−	2.47906i	−0.0523720	−	0.164180i
$229$	−13.1695	+	13.1695i	−0.870267	+	0.870267i	−0.992501	−	0.122235i	$-0.960994\pi$
$229$	−13.1695	+	13.1695i	−0.870267	+	0.870267i	0.122235	+	0.992501i	$0.460994\pi$
$230$	16.0539	−	9.26873i	1.05856	−	0.611162i
$231$	−0.947304	+	0.160683i	−0.0623281	+	0.0105722i
$232$	17.4880	−	4.68590i	1.14814	−	0.307644i
$233$	18.9197	+	10.9233i	1.23947	+	0.715608i	0.968986	−	0.247117i	$-0.0794833\pi$
$233$	18.9197	+	10.9233i	1.23947	+	0.715608i	0.270483	+	0.962725i	$0.412817\pi$
$234$	−16.4377	−	18.2178i	−1.07457	−	1.19094i
$235$	1.16955	+	2.02572i	0.0762928	+	0.132143i
$236$	1.85802	−	6.93423i	0.120947	−	0.451380i
$237$	−2.80676	+	5.43619i	−0.182319	+	0.353118i
$238$	−12.5332	+	9.42205i	−0.812405	+	0.610741i
$239$	28.6743	+	7.68327i	1.85479	+	0.496989i	0.999767	−	0.0216018i	$-0.00687660\pi$
$239$	28.6743	+	7.68327i	1.85479	+	0.496989i	0.855022	+	0.518591i	$0.173543\pi$
$240$	−1.60332	+	0.511447i	−0.103494	+	0.0330138i
$241$	−3.91954	+	3.91954i	−0.252480	+	0.252480i	−0.821987	−	0.569507i	$-0.807134\pi$
$241$	−3.91954	+	3.91954i	−0.252480	+	0.252480i	0.569507	+	0.821987i	$0.307134\pi$
$242$	6.43260	−	24.0068i	0.413503	−	1.54322i
$243$	−4.43748	+	14.9435i	−0.284664	+	0.958627i
$244$	36.9480			2.36535
$245$	−17.2387	−	0.340201i	−1.10134	−	0.0217346i
$246$	−15.7935	+	0.742660i	−1.00696	+	0.0473503i
$247$	0.200135	+	1.71010i	0.0127343	+	0.108811i
$248$	−15.4097	−	8.89681i	−0.978519	−	0.564948i
$249$	19.5118	+	17.7592i	1.23651	+	1.12545i
$250$	19.0315	−	10.9878i	1.20366	−	0.694931i
$251$	8.28887			0.523189			0.261594	−	0.965178i	$-0.415752\pi$
$251$	8.28887			0.523189			0.261594	+	0.965178i	$0.415752\pi$
$252$	−21.0179	−	13.4833i	−1.32400	−	0.849368i
$253$	−0.491867	+	0.491867i	−0.0309234	+	0.0309234i
$254$	7.17957	−	26.7945i	0.450487	−	1.68124i
$255$	10.6185	−	3.38720i	0.664954	−	0.212115i
$256$	6.68118	−	11.5721i	0.417573	−	0.723259i
$257$	−7.72143			−0.481650			−0.240825	−	0.970569i	$-0.577418\pi$
$257$	−7.72143			−0.481650			−0.240825	+	0.970569i	$0.577418\pi$
$258$	−6.28286	+	28.7971i	−0.391154	+	1.79283i
$259$	17.2941	+	23.0045i	1.07460	+	1.42943i
$260$	−27.7507	+	3.24770i	−1.72102	+	0.201414i
$261$	12.0977	+	17.0328i	0.748826	+	1.05430i
$262$	6.59261	−	24.6039i	0.407293	−	1.52004i
$263$	3.41269			0.210435			0.105218	−	0.994449i	$-0.466446\pi$
$263$	3.41269			0.210435			0.105218	+	0.994449i	$0.466446\pi$
$264$	−0.794581	+	0.509960i	−0.0489031	+	0.0313859i
$265$	−5.51817	+	20.5941i	−0.338978	+	1.26508i
$266$	1.07063	+	2.65861i	0.0656444	+	0.163010i
$267$	6.07514	−	6.67468i	0.371793	−	0.408484i
$268$	3.96498	−	14.7975i	0.242200	−	0.903901i
$269$	21.0264	−	12.1396i	1.28200	−	0.740164i	0.304788	−	0.952420i	$-0.401414\pi$
$269$	21.0264	−	12.1396i	1.28200	−	0.740164i	0.977214	+	0.212256i	$0.0680811\pi$
$270$	17.9058	+	22.8552i	1.08971	+	1.39093i
$271$	4.99722	+	18.6499i	0.303560	+	1.13290i	0.934178	+	0.356807i	$0.116135\pi$
$271$	4.99722	+	18.6499i	0.303560	+	1.13290i	−0.630618	+	0.776093i	$0.717199\pi$
$272$	0.515273	−	0.892479i	0.0312430	−	0.0541145i
$273$	11.9458	+	11.4148i	0.722991	+	0.690857i
$274$	−15.8417	−	27.4386i	−0.957030	−	1.65762i
$275$	0.158206	−	0.158206i	0.00954016	−	0.00954016i
$276$	−18.0580	+	0.849143i	−1.08696	+	0.0511124i
$277$			8.69403i			0.522374i	0.965288	+	0.261187i	$0.0841139\pi$
$277$			8.69403i			0.522374i	−0.965288	+	0.261187i	$0.915886\pi$
$278$	−23.6364	+	6.33337i	−1.41762	+	0.379850i
$279$	3.42969	−	20.2442i	0.205330	−	1.21199i
$280$	−15.7161	+	6.32890i	−0.939217	+	0.378224i
$281$	21.4074	−	5.73611i	1.27706	−	0.342187i	0.444329	−	0.895864i	$-0.353442\pi$
$281$	21.4074	−	5.73611i	1.27706	−	0.342187i	0.832732	+	0.553676i	$0.186776\pi$
$282$	−0.175262	−	3.72714i	−0.0104367	−	0.221948i
$283$	−1.12579	+	1.94993i	−0.0669213	+	0.115911i	−0.897545	−	0.440924i	$-0.854651\pi$
$283$	−1.12579	+	1.94993i	−0.0669213	+	0.115911i	0.830623	+	0.556835i	$0.187984\pi$
$284$	−11.3926	+	3.05265i	−0.676029	+	0.181141i
$285$	−0.0956942	−	2.03505i	−0.00566844	−	0.120546i
$286$	1.59368	−	0.633398i	0.0942362	−	0.0374536i
$287$	10.5687	−	1.28545i	0.623850	−	0.0758776i
$288$	18.0265	+	3.05398i	1.06222	+	0.179957i
$289$	5.08746	−	8.81174i	0.299262	−	0.518338i
$290$	38.9119			2.28499
$291$	20.1968	+	18.3827i	1.18396	+	1.07761i
$292$	1.65623	+	1.65623i	0.0969236	+	0.0969236i
$293$	4.31819	+	1.15706i	0.252271	+	0.0675959i	0.382738	−	0.923857i	$-0.374981\pi$
$293$	4.31819	+	1.15706i	0.252271	+	0.0675959i	−0.130467	+	0.991453i	$0.541648\pi$
$294$	24.1851	+	13.0977i	1.41050	+	0.763876i
$295$	2.81028	−	4.86754i	0.163621	−	0.283399i
$296$	24.4914	+	14.1401i	1.42353	+	0.821878i
$297$	−0.870979	−	0.654503i	−0.0505393	−	0.0379781i
$298$	−37.6195	+	21.7196i	−2.17924	+	1.25818i
$299$	11.8357	+	1.73191i	0.684477	+	0.100159i
$300$	5.80824	−	0.273121i	0.335339	−	0.0157687i
$301$	2.78458	−	19.6508i	0.160500	−	1.13265i
$302$	20.5864	+	35.6566i	1.18461	+	2.05181i
$303$	−3.03332	−	4.72629i	−0.174260	−	0.271518i
$304$	−0.133199	−	0.133199i	−0.00763951	−	0.00763951i
$305$	27.9421	+	7.48706i	1.59996	+	0.428708i
$306$	−17.5294	−	2.96976i	−1.00209	−	0.169770i
$307$	8.59086	−	8.59086i	0.490306	−	0.490306i	−0.418096	−	0.908403i	$-0.637303\pi$
$307$	8.59086	−	8.59086i	0.490306	−	0.490306i	0.908403	+	0.418096i	$0.137303\pi$
$308$	1.39500	−	1.04872i	0.0794877	−	0.0597564i
$309$	−5.77397	−	8.99657i	−0.328470	−	0.511797i
$310$	−27.0418	−	27.0418i	−1.53587	−	1.53587i
$311$	−1.03544	+	1.79344i	−0.0587145	+	0.101697i	−0.893889	−	0.448289i	$-0.852034\pi$
$311$	−1.03544	+	1.79344i	−0.0587145	+	0.101697i	0.835174	+	0.549986i	$0.185367\pi$
$312$	15.1944	+	5.72110i	0.860212	+	0.323893i
$313$	−22.0356	+	12.7222i	−1.24552	+	0.719104i	−0.970214	−	0.242251i	$-0.922114\pi$
$313$	−22.0356	+	12.7222i	−1.24552	+	0.719104i	−0.275311	+	0.961355i	$0.588781\pi$
$314$	−19.4701	−	19.4701i	−1.09876	−	1.09876i
$315$	−13.1626	−	14.4558i	−0.741631	−	0.814494i
$316$		−	11.1126i		−	0.625132i
$317$	24.7478	+	6.63114i	1.38997	+	0.372442i	0.874733	−	0.484605i	$-0.161036\pi$
$317$	24.7478	+	6.63114i	1.38997	+	0.372442i	0.515239	+	0.857047i	$0.327703\pi$
$318$	22.8925	−	25.1517i	1.28375	−	1.41044i
$319$	−1.41039	+	0.377913i	−0.0789667	+	0.0211591i
$320$	22.7054	−	22.7054i	1.26927	−	1.26927i
$321$	−4.27430	+	0.200991i	−0.238568	+	0.0112182i
$322$	19.7661	−	2.40411i	1.10152	−	0.133976i
$323$	0.882150	+	0.882150i	0.0490841	+	0.0490841i
$324$	−5.29053	−	27.8158i	−0.293919	−	1.54532i
$325$	−3.80688	−	0.557057i	−0.211168	−	0.0309000i
$326$	25.1471			1.39277
$327$	1.81867	+	5.70131i	0.100573	+	0.315283i
$328$	9.06008	−	5.23084i	0.500259	−	0.288825i
$329$	0.303356	+	2.49412i	0.0167245	+	0.137506i
$330$	−1.93323	+	0.616685i	−0.106421	+	0.0339474i
$331$	−16.4710	−	4.41339i	−0.905328	−	0.242582i	−0.224025	−	0.974583i	$-0.571920\pi$
$331$	−16.4710	−	4.41339i	−0.905328	−	0.242582i	−0.681303	+	0.732001i	$0.738586\pi$
$332$	−46.2898	−	12.4033i	−2.54048	−	0.680720i
$333$	−5.45097	+	32.1751i	−0.298711	+	1.76318i
$334$	16.6664	+	9.62237i	0.911947	+	0.526513i
$335$	5.99707	−	10.3872i	0.327655	−	0.567515i
$336$	−1.79974	−	0.169272i	−0.0981841	−	0.00923452i
$337$	17.6057	−	10.1647i	0.959045	−	0.553705i	0.0631658	−	0.998003i	$-0.479880\pi$
$337$	17.6057	−	10.1647i	0.959045	−	0.553705i	0.895879	+	0.444298i	$0.146547\pi$
$338$	−25.1043	−	15.4744i	−1.36549	−	0.841697i
$339$	7.89079	−	15.2831i	0.428569	−	0.830061i
$340$	−14.3151	+	14.3151i	−0.776345	+	0.776345i
$341$	1.24278	+	0.717519i	0.0673002	+	0.0388558i
$342$	−1.35365	+	2.95450i	−0.0731968	+	0.159761i
$343$	−16.8932	−	7.59066i	−0.912150	−	0.409857i
$344$	−5.04760	−	18.8379i	−0.272149	−	1.01567i
$345$	−13.8285	−	3.01707i	−0.744502	−	0.162433i
$346$	10.6603	+	39.7847i	0.573100	+	2.13884i
$347$	−1.23911	+	2.14620i	−0.0665190	+	0.115214i	−0.897367	−	0.441285i	$-0.854523\pi$
$347$	−1.23911	+	2.14620i	−0.0665190	+	0.115214i	0.830848	+	0.556500i	$0.187856\pi$
$348$	−33.7184	−	17.4091i	−1.80749	−	0.933227i
$349$	7.18182	+	26.8029i	0.384434	+	1.43473i	0.839057	+	0.544043i	$0.183107\pi$
$349$	7.18182	+	26.8029i	0.384434	+	1.43473i	−0.454624	+	0.890684i	$0.650226\pi$
$350$	−6.35763	+	0.773266i	−0.339829	+	0.0413328i
$351$	−0.0811683	+	18.7348i	−0.00433244	+	0.999991i
$352$	−0.638917	+	1.10664i	−0.0340544	+	0.0589839i
$353$	3.25539	+	3.25539i	0.173267	+	0.173267i	0.788413	−	0.615146i	$-0.210903\pi$
$353$	3.25539	+	3.25539i	0.173267	+	0.173267i	−0.615146	+	0.788413i	$0.710903\pi$
$354$	−7.54543	+	4.84264i	−0.401035	+	0.257383i
$355$	−9.23432			−0.490107
$356$	−4.24297	+	15.8350i	−0.224877	+	0.839252i
$357$	11.9193	+	1.12105i	0.630837	+	0.0593322i
$358$	−3.43077	+	0.919272i	−0.181322	+	0.0485850i
$359$	−28.5057	+	7.63807i	−1.50447	+	0.403122i	−0.914595	−	0.404371i	$-0.867490\pi$
$359$	−28.5057	+	7.63807i	−1.50447	+	0.403122i	−0.589877	+	0.807493i	$0.700824\pi$
$360$	−17.4652	−	8.00193i	−0.920499	−	0.421739i
$361$	−16.2570	+	9.38598i	−0.855631	+	0.493999i
$362$	−16.7388	−	4.48514i	−0.879771	−	0.235734i
$363$	−15.9702	+	10.2497i	−0.838220	+	0.537968i
$364$	−28.7918	−	8.46856i	−1.50910	−	0.443873i
$365$	0.916917	+	1.58815i	0.0479936	+	0.0831274i
$366$	−34.1259	−	31.0607i	−1.78379	−	1.62357i
$367$		−	25.0310i		−	1.30661i	−0.757097	−	0.653303i	$-0.773383\pi$
$367$		−	25.0310i		−	1.30661i	0.757097	−	0.653303i	$-0.226617\pi$
$368$	−1.13336	+	0.654345i	−0.0590804	+	0.0341101i
$369$	9.29961	+	7.69755i	0.484118	+	0.400718i
$370$	42.9788	+	42.9788i	2.23436	+	2.23436i
$371$	−14.1199	+	18.0303i	−0.733070	+	0.936086i
$372$	11.3341	+	35.5310i	0.587645	+	1.84220i
$373$	−10.8410			−0.561327			−0.280664	−	0.959806i	$-0.590555\pi$
$373$	−10.8410			−0.561327			−0.280664	+	0.959806i	$0.590555\pi$
$374$	0.621298	−	1.07612i	0.0321266	−	0.0556449i
$375$	−16.3933	−	3.57665i	−0.846548	−	0.184697i
$376$	1.23444	+	2.13810i	0.0636611	+	0.110264i
$377$	19.6981	+	15.5706i	1.01450	+	0.801924i
$378$	8.07770	+	30.1223i	0.415472	+	1.54933i
$379$	−15.8038	+	15.8038i	−0.811789	+	0.811789i	−0.984902	−	0.173113i	$-0.944617\pi$
$379$	−15.8038	+	15.8038i	−0.811789	+	0.811789i	0.173113	+	0.984902i	$0.444617\pi$
$380$	1.85024	+	3.20472i	0.0949155	+	0.164399i
$381$	−17.8248	+	11.4399i	−0.913190	+	0.586083i
$382$	−0.372129	−	1.38880i	−0.0190398	−	0.0710573i
$383$	6.82095	+	6.82095i	0.348534	+	0.348534i	0.859563	−	0.511029i	$-0.170736\pi$
$383$	6.82095	+	6.82095i	0.348534	+	0.348534i	−0.511029	+	0.859563i	$0.670736\pi$
$384$	−28.6855	+	9.15042i	−1.46385	+	0.466955i
$385$	1.26749	−	0.510419i	0.0645972	−	0.0260134i
$386$	−47.3061			−2.40782
$387$	18.3476	−	13.0315i	0.932660	−	0.662427i
$388$	−47.9149	−	12.8388i	−2.43251	−	0.651789i
$389$		−	22.8527i		−	1.15868i	−0.815086	−	0.579339i	$-0.803311\pi$
$389$		−	22.8527i		−	1.15868i	0.815086	−	0.579339i	$-0.196689\pi$
$390$	28.3613	+	20.3292i	1.43613	+	1.02941i
$391$	7.50598	−	4.33358i	0.379594	−	0.219159i
$392$	−18.1951	−	0.359076i	−0.918990	−	0.0181361i
$393$	−16.3675	+	10.5046i	−0.825631	+	0.529888i
$394$	−27.1003	+	15.6464i	−1.36529	+	0.788253i
$395$	2.25183	−	8.40395i	0.113302	−	0.422848i
$396$	1.95111	+	0.330549i	0.0980469	+	0.0166107i
$397$	−4.72794	−	17.6449i	−0.237289	−	0.885573i	−0.977104	−	0.212763i	$-0.931754\pi$
$397$	−4.72794	−	17.6449i	−0.237289	−	0.885573i	0.739815	−	0.672810i	$-0.234913\pi$
$398$	−7.38738	−	27.5701i	−0.370296	−	1.38196i
$399$	0.761826	−	2.05144i	0.0381390	−	0.102701i
$400$	0.364537	−	0.210466i	0.0182269	−	0.0105233i
$401$	7.32440	+	7.32440i	0.365763	+	0.365763i	0.865929	−	0.500166i	$-0.166728\pi$
$401$	7.32440	+	7.32440i	0.365763	+	0.365763i	−0.500166	+	0.865929i	$0.666728\pi$
$402$	−16.1018	+	10.3341i	−0.803084	+	0.515417i
$403$	−2.86843	−	24.5099i	−0.142887	−	1.22093i
$404$	8.83403	+	5.10033i	0.439509	+	0.253751i
$405$	1.63554	−	22.1079i	0.0812706	−	1.09855i
$406$	38.4554	+	16.3751i	1.90851	+	0.812683i
$407$	−1.97521	−	1.14039i	−0.0979074	−	0.0565269i
$408$	11.2076	−	3.57513i	0.554859	−	0.176995i
$409$	19.1181	−	5.12268i	0.945330	−	0.253300i	0.246951	−	0.969028i	$-0.420571\pi$
$409$	19.1181	−	5.12268i	0.945330	−	0.253300i	0.698380	+	0.715728i	$0.253905\pi$
$410$	21.7186	−	5.81948i	1.07260	−	0.287403i
$411$	−5.15662	+	23.6350i	−0.254358	+	1.16583i
$412$	16.8157	+	9.70855i	0.828450	+	0.478306i
$413$	4.82569	−	3.62780i	0.237457	−	0.178512i
$414$	17.3926	+	14.3963i	0.854799	+	0.707541i
$415$	−32.4935	−	18.7601i	−1.59504	−	0.920899i
$416$	21.8249	−	2.55420i	1.07006	−	0.125230i
$417$	16.6015	+	8.57150i	0.812977	+	0.419748i
$418$	−0.160607	−	0.160607i	−0.00785555	−	0.00785555i
$419$	−26.1346	+	15.0888i	−1.27676	+	0.737138i	−0.976251	−	0.216641i	$-0.930490\pi$
$419$	−26.1346	+	15.0888i	−1.27676	+	0.737138i	−0.300509	+	0.953779i	$0.597157\pi$
$420$	33.2898	+	12.3625i	1.62438	+	0.603231i
$421$	−1.98760	−	7.41783i	−0.0968698	−	0.361523i	0.900426	−	0.435008i	$-0.143255\pi$
$421$	−1.98760	−	7.41783i	−0.0968698	−	0.361523i	−0.997296	+	0.0734851i	$0.976588\pi$
$422$	−12.3122	−	45.9499i	−0.599350	−	2.23681i
$423$	−1.81656	+	2.19463i	−0.0883241	+	0.106707i
$424$	−5.82432	+	21.7367i	−0.282854	+	1.05563i
$425$	−2.41425	+	1.39387i	−0.117108	+	0.0676125i
$426$	13.0887	+	6.75784i	0.634151	+	0.327418i
$427$	24.4635	+	19.1579i	1.18387	+	0.927118i
$428$	6.73101	−	3.88615i	0.325355	−	0.187844i
$429$	−1.22541	−	0.461401i	−0.0591634	−	0.0222766i
$430$		−	41.9156i		−	2.02135i
$431$	−35.0078	−	9.38030i	−1.68627	−	0.451833i	−0.716843	−	0.697234i	$-0.754414\pi$
$431$	−35.0078	−	9.38030i	−1.68627	−	0.451833i	−0.969422	+	0.245401i	$0.921080\pi$
$432$	−1.26410	−	1.61351i	−0.0608189	−	0.0776302i
$433$	−32.4764			−1.56072			−0.780358	−	0.625333i	$-0.784963\pi$
$433$	−32.4764			−1.56072			−0.780358	+	0.625333i	$0.784963\pi$
$434$	−15.3447	−	38.1044i	−0.736569	−	1.82907i
$435$	−21.9719	−	19.9984i	−1.05347	−	0.958848i
$436$	−7.68612	−	7.68612i	−0.368098	−	0.368098i
$437$	−0.410037	−	1.53028i	−0.0196147	−	0.0732031i
$438$	−0.137404	−	2.92205i	−0.00656542	−	0.139621i
$439$	−17.1158	−	29.6454i	−0.816892	−	1.41490i	−0.907961	−	0.419054i	$-0.862362\pi$
$439$	−17.1158	−	29.6454i	−0.816892	−	1.41490i	0.0910689	−	0.995845i	$-0.470972\pi$
$440$	0.949412	−	0.949412i	0.0452615	−	0.0452615i
$441$	−6.92486	−	19.8254i	−0.329755	−	0.944067i
$442$	−21.2231	+	2.48377i	−1.00948	+	0.118141i
$443$	18.9842	+	32.8816i	0.901965	+	1.56225i	0.824940	+	0.565221i	$0.191209\pi$
$443$	18.9842	+	32.8816i	0.901965	+	1.56225i	0.0770254	+	0.997029i	$0.475458\pi$
$444$	−18.0138	−	56.4711i	−0.854898	−	2.68000i
$445$	−6.41753	+	11.1155i	−0.304220	+	0.526925i
$446$	37.1584			1.75950
$447$	32.4047	+	7.06996i	1.53269	+	0.334398i
$448$	31.9940	−	12.8840i	1.51157	−	0.608713i
$449$	2.15888	+	2.15888i	0.101884	+	0.101884i	0.756211	−	0.654327i	$-0.227048\pi$
$449$	2.15888	+	2.15888i	0.101884	+	0.101884i	−0.654327	+	0.756211i	$0.727048\pi$
$450$	−5.59421	−	4.63049i	−0.263714	−	0.218283i
$451$	−0.730686	+	0.421862i	−0.0344066	+	0.0198647i
$452$			31.2414i			1.46947i
$453$	6.70107	−	30.7139i	0.314844	−	1.44307i
$454$	19.6986	+	34.1189i	0.924500	+	1.60128i
$455$	−20.0579	−	12.2387i	−0.940328	−	0.573759i
$456$	−0.101004	−	2.14795i	−0.00472992	−	0.100587i
$457$	11.8069	+	3.16365i	0.552303	+	0.147989i	0.524168	−	0.851615i	$-0.324376\pi$
$457$	11.8069	+	3.16365i	0.552303	+	0.147989i	0.0281353	+	0.999604i	$0.491043\pi$
$458$	−36.5892	+	21.1248i	−1.70970	+	0.987096i
$459$	8.37184	+	10.6859i	0.390764	+	0.498777i
$460$	24.8326	−	6.65388i	1.15783	−	0.310239i
$461$	−33.6672	+	9.02109i	−1.56804	+	0.420154i	−0.935197	−	0.354129i	$-0.884777\pi$
$461$	−33.6672	+	9.02109i	−1.56804	+	0.420154i	−0.632840	+	0.774283i	$0.718111\pi$
$462$	−2.17007	−	0.204102i	−0.100961	−	0.00949568i
$463$	7.52337	−	28.0776i	0.349641	−	1.30488i	−0.537455	−	0.843292i	$-0.680614\pi$
$463$	7.52337	−	28.0776i	0.349641	−	1.30488i	0.887096	−	0.461585i	$-0.152719\pi$
$464$	−2.74707			−0.127529
$465$	1.37153	+	29.1672i	0.0636033	+	1.35260i
$466$	35.0433	+	35.0433i	1.62335	+	1.62335i
$467$	11.8083	−	20.4526i	0.546423	−	0.946432i	−0.452093	−	0.891971i	$-0.649323\pi$
$467$	11.8083	−	20.4526i	0.546423	−	0.946432i	0.998516	−	0.0544613i	$-0.0173442\pi$
$468$	−15.4807	−	30.3046i	−0.715594	−	1.40083i
$469$	10.2979	−	7.74165i	0.475513	−	0.357476i
$470$	1.37335	+	5.12541i	0.0633479	+	0.236417i
$471$	0.987504	+	21.0004i	0.0455018	+	0.967647i
$472$	2.96619	−	5.13760i	0.136530	−	0.236477i
$473$	0.407084	+	1.51926i	0.0187177	+	0.0698556i
$474$	−9.34189	+	10.2638i	−0.429087	+	0.471433i
$475$	0.131886	+	0.492204i	0.00605133	+	0.0225839i
$476$	−20.1713	+	8.12301i	−0.924550	+	0.372318i
$477$	−25.8529	+	2.43676i	−1.18372	+	0.111571i
$478$	58.3200	+	33.6711i	2.66749	+	1.54008i
$479$	3.93894	−	3.93894i	0.179975	−	0.179975i	−0.611370	−	0.791345i	$-0.709381\pi$
$479$	3.93894	−	3.93894i	0.179975	−	0.179975i	0.791345	+	0.611370i	$0.209381\pi$
$480$	−25.9720	+	1.22129i	−1.18546	+	0.0557438i
$481$	4.55893	+	38.9548i	0.207869	+	1.77618i
$482$	−10.8897	+	6.28720i	−0.496014	+	0.286374i
$483$	−12.3966	−	8.80105i	−0.564066	−	0.400462i
$484$	17.2341	−	29.8504i	0.783369	−	1.35684i
$485$	−33.6343	−	19.4187i	−1.52725	−	0.881760i
$486$	−18.4971	+	30.1388i	−0.839047	+	1.36712i
$487$	−18.2954	−	4.90225i	−0.829046	−	0.222142i	−0.180748	−	0.983529i	$-0.557852\pi$
$487$	−18.2954	−	4.90225i	−0.829046	−	0.222142i	−0.648297	+	0.761387i	$0.724519\pi$
$488$	29.4924	+	7.90246i	1.33506	+	0.357727i
$489$	−14.1995	−	12.9241i	−0.642124	−	0.584447i
$490$	−37.5735	−	10.8668i	−1.69740	−	0.490910i
$491$	−8.74371	+	5.04818i	−0.394598	+	0.227821i	−0.684151	−	0.729341i	$-0.739827\pi$
$491$	−8.74371	+	5.04818i	−0.394598	+	0.227821i	0.289552	+	0.957162i	$0.406494\pi$
$492$	−21.4234	−	4.67410i	−0.965843	−	0.210725i
$493$	18.1932			0.819382
$494$	−0.565513	+	3.86466i	−0.0254436	+	0.173879i
$495$	1.40855	+	0.645348i	0.0633098	+	0.0290062i
$496$	1.90907	+	1.90907i	0.0857199	+	0.0857199i
$497$	−9.12599	−	3.88603i	−0.409357	−	0.174312i
$498$	32.3273	+	50.3699i	1.44862	+	2.25713i
$499$	−10.2554	+	10.2554i	−0.459095	+	0.459095i	−0.898358	−	0.439264i	$-0.855239\pi$
$499$	−10.2554	+	10.2554i	−0.459095	+	0.459095i	0.439264	+	0.898358i	$0.355239\pi$
$500$	29.4384	−	7.88800i	1.31653	−	0.352762i
$501$	−4.46552	−	13.9989i	−0.199505	−	0.625424i
$502$	18.1625	+	4.86663i	0.810632	+	0.217208i
$503$		−	40.4517i		−	1.80365i	−0.432099	−	0.901826i	$-0.642227\pi$
$503$		−	40.4517i		−	1.80365i	0.432099	−	0.901826i	$-0.357773\pi$
$504$	−13.8929	−	15.2579i	−0.618840	−	0.679639i
$505$	5.64726	+	5.64726i	0.251300	+	0.251300i
$506$	−1.36656	+	0.788986i	−0.0607512	+	0.0350747i
$507$	6.22242	+	21.6398i	0.276347	+	0.961058i
$508$	19.2354	−	33.3167i	0.853433	−	1.47819i
$509$	−4.32857	−	4.32857i	−0.191860	−	0.191860i	0.604639	−	0.796499i	$-0.293317\pi$
$509$	−4.32857	−	4.32857i	−0.191860	−	0.191860i	−0.796499	+	0.604639i	$0.793317\pi$
$510$	25.2558	−	1.18761i	1.11835	−	0.0525882i
$511$	0.237829	+	1.95538i	0.0105209	+	0.0865008i
$512$	−3.15028	+	3.15028i	−0.139224	+	0.139224i
$513$	2.28278	−	0.972593i	0.100787	−	0.0429410i
$514$	−16.9192	−	4.53347i	−0.746272	−	0.199963i
$515$	10.7496	+	10.7496i	0.473685	+	0.473685i
$516$	−18.7530	+	36.3211i	−0.825553	+	1.59895i
$517$	−0.0995559	−	0.172436i	−0.00437847	−	0.00758372i
$518$	24.3881	+	60.5612i	1.07155	+	2.66091i
$519$	14.4275	−	27.9434i	0.633296	−	1.22658i
$520$	−22.8456	−	3.34297i	−1.00184	−	0.146599i
$521$	11.9848	−	6.91942i	0.525063	−	0.303145i	−0.213941	−	0.976847i	$-0.568630\pi$
$521$	11.9848	−	6.91942i	0.525063	−	0.303145i	0.739004	+	0.673701i	$0.235297\pi$
$522$	16.5078	+	44.4251i	0.722529	+	1.94443i
$523$	−2.08274	−	1.20247i	−0.0910718	−	0.0525804i	0.453772	−	0.891118i	$-0.350078\pi$
$523$	−2.08274	−	1.20247i	−0.0910718	−	0.0525804i	−0.544844	+	0.838537i	$0.683411\pi$
$524$	17.6628	−	30.5929i	0.771603	−	1.33646i
$525$	3.98729	+	2.83080i	0.174020	+	0.123546i
$526$	7.47786	+	2.00369i	0.326050	+	0.0873648i
$527$	−12.6434	−	12.6434i	−0.550754	−	0.550754i
$528$	0.136481	−	0.0435362i	0.00593956	−	0.00189467i
$529$	11.9936			0.521460
$530$	−24.1827	+	41.8857i	−1.05043	+	1.81940i
$531$	6.74941	+	1.14346i	0.292899	+	0.0496218i
$532$	0.479914	+	3.94575i	0.0208069	+	0.171070i
$533$	13.3231	+	5.74471i	0.577087	+	0.248831i
$534$	17.2307	−	11.0586i	0.745646	−	0.478553i
$535$	5.87784	−	1.57496i	0.254121	−	0.0680915i
$536$	6.32979	−	10.9635i	0.273405	−	0.473552i
$537$	2.40966	+	1.24413i	0.103985	+	0.0536882i
$538$	53.2004	−	14.2550i	2.29363	−	0.614577i
$539$	1.46741	+	0.0289591i	0.0632060	+	0.00124736i
$540$	15.7828	+	37.0439i	0.679182	+	1.59411i
$541$	20.3605	−	5.45558i	0.875366	−	0.234554i	0.206959	−	0.978350i	$-0.433643\pi$
$541$	20.3605	−	5.45558i	0.875366	−	0.234554i	0.668407	+	0.743796i	$0.266977\pi$
$542$			43.7996i			1.88135i
$543$	7.14660	+	11.1353i	0.306690	+	0.477861i
$544$	11.2583	−	11.2583i	0.482697	−	0.482697i
$545$	−4.25517	−	7.37016i	−0.182271	−	0.315703i
$546$	19.4735	+	32.0258i	0.833390	+	1.37058i
$547$	1.38303	−	2.39548i	0.0591341	−	0.102423i	−0.834943	−	0.550337i	$-0.814499\pi$
$547$	1.38303	−	2.39548i	0.0591341	−	0.102423i	0.894077	+	0.447913i	$0.147833\pi$
$548$	−11.3725	−	42.4427i	−0.485809	−	1.81306i
$549$	3.30620	+	35.0773i	0.141105	+	1.49706i
$550$	0.439547	−	0.253772i	0.0187423	−	0.0108209i
$551$	0.860708	−	3.21221i	0.0366674	−	0.136845i
$552$	−14.5957	−	3.18446i	−0.621236	−	0.135540i
$553$	5.76200	−	7.35773i	0.245025	−	0.312882i
$554$	−5.10451	+	19.0503i	−0.216870	+	0.809370i
$555$	−2.17984	−	46.3568i	−0.0925291	−	1.96774i
$556$	−33.9365			−1.43923
$557$	−8.33340	+	31.1007i	−0.353098	+	1.31778i	0.529764	+	0.848145i	$0.322281\pi$
$557$	−8.33340	+	31.1007i	−0.353098	+	1.31778i	−0.882862	+	0.469633i	$0.844386\pi$
$558$	19.4010	−	42.3453i	0.821312	−	1.79262i
$559$	16.7724	−	21.2186i	0.709399	−	0.897451i
$560$	2.55190	−	0.310383i	0.107837	−	0.0131161i
$561$	−0.903881	+	0.288330i	−0.0381619	+	0.0121733i
$562$	50.2757			2.12075
$563$	−3.58943	+	6.21708i	−0.151276	+	0.262019i	−0.931697	−	0.363236i	$-0.881672\pi$
$563$	−3.58943	+	6.21708i	−0.151276	+	0.262019i	0.780421	+	0.625255i	$0.215005\pi$
$564$	1.10305	−	5.05576i	0.0464468	−	0.212886i
$565$	−6.33069	+	23.6265i	−0.266334	+	0.993973i
$566$	−3.61168	+	3.61168i	−0.151810	+	0.151810i
$567$	10.9199	−	21.1602i	0.458592	−	0.888647i
$568$	−9.74666			−0.408961
$569$	−22.2400	+	12.8403i	−0.932349	+	0.538292i	−0.887554	−	0.460704i	$-0.847597\pi$
$569$	−22.2400	+	12.8403i	−0.932349	+	0.538292i	−0.0447951	+	0.998996i	$0.514263\pi$
$570$	0.985150	−	4.51537i	0.0412634	−	0.189128i
$571$	21.2124	+	12.2470i	0.887711	+	0.512520i	0.873193	−	0.487374i	$-0.162045\pi$
$571$	21.2124	+	12.2470i	0.887711	+	0.512520i	0.0145180	+	0.999895i	$0.495379\pi$
$572$	2.36223	−	0.276455i	0.0987699	−	0.0115592i
$573$	−0.503634	+	0.975450i	−0.0210396	+	0.0407500i
$574$	23.9128	+	3.38851i	0.998099	+	0.141434i
$575$	3.54014			0.147634
$576$	35.5548	+	16.2899i	1.48145	+	0.678745i
$577$	6.72289	−	25.0902i	0.279878	−	1.04452i	−0.672624	−	0.739984i	$-0.734833\pi$
$577$	6.72289	−	25.0902i	0.279878	−	1.04452i	0.952502	−	0.304533i	$-0.0985005\pi$
$578$	16.3212	−	16.3212i	0.678874	−	0.678874i
$579$	26.7118	+	24.3124i	1.11010	+	1.01039i
$580$	52.1261	+	13.9671i	2.16442	+	0.579954i
$581$	−24.2176	−	32.2141i	−1.00471	−	1.33647i
$582$	33.4622	+	52.1382i	1.38705	+	2.16120i
$583$	0.469726	−	1.75304i	0.0194540	−	0.0726035i
$584$	0.967789	+	1.67626i	0.0400474	+	0.0693641i
$585$	−5.56646	−	26.0550i	−0.230145	−	1.07724i
$586$	8.78265	+	5.07066i	0.362808	+	0.209467i
$587$	−15.3675	+	4.11772i	−0.634286	+	0.169956i	−0.561614	−	0.827400i	$-0.689819\pi$
$587$	−15.3675	+	4.11772i	−0.634286	+	0.169956i	−0.0726721	+	0.997356i	$0.523153\pi$
$588$	27.6968	+	26.2267i	1.14220	+	1.08157i
$589$	−2.83047	+	1.63417i	−0.116627	+	0.0673348i
$590$	9.01573	−	9.01573i	0.371172	−	0.371172i
$591$	23.3437	+	5.09306i	0.960231	+	0.209500i
$592$	−3.03418	−	3.03418i	−0.124704	−	0.124704i
$593$	−11.3567	−	42.3837i	−0.466363	−	1.74049i	−0.652330	−	0.757935i	$-0.726208\pi$
$593$	−11.3567	−	42.3837i	−0.466363	−	1.74049i	0.185966	−	0.982556i	$-0.440458\pi$
$594$	−1.52421	−	1.94552i	−0.0625389	−	0.0798256i
$595$	−16.9007	+	2.05560i	−0.692860	+	0.0842712i
$596$	−58.1909	+	15.5922i	−2.38359	+	0.638681i
$597$	−9.99798	+	19.3643i	−0.409190	+	0.792528i
$598$	24.9175	+	10.7440i	1.01895	+	0.439356i
$599$	−15.9003	+	27.5402i	−0.649670	+	1.12526i	0.333531	+	0.942739i	$0.391760\pi$
$599$	−15.9003	+	27.5402i	−0.649670	+	1.12526i	−0.983202	+	0.182523i	$0.941574\pi$
$600$	4.69463	+	1.02426i	0.191657	+	0.0418152i
$601$	5.58164	+	3.22256i	0.227680	+	0.131451i	0.609501	−	0.792785i	$-0.291370\pi$
$601$	5.58164	+	3.22256i	0.227680	+	0.131451i	−0.381821	+	0.924236i	$0.624703\pi$
$602$	17.6391	−	41.4238i	0.718916	−	1.68831i
$603$	14.4031	+	2.44011i	0.586539	+	0.0993690i
$604$	14.7786	+	55.1546i	0.601334	+	2.24421i
$605$	19.0822	−	19.0822i	0.775802	−	0.775802i
$606$	−3.87166	−	12.1372i	−0.157275	−	0.493039i
$607$		−	16.3251i		−	0.662613i	−0.943523	−	0.331307i	$-0.892511\pi$
$607$		−	16.3251i		−	0.662613i	0.943523	−	0.331307i	$-0.107489\pi$
$608$	−1.45515	−	2.52040i	−0.0590142	−	0.102216i
$609$	−13.2984	−	29.0101i	−0.538877	−	1.17555i
$610$	56.8307	+	32.8112i	2.30101	+	1.32849i
$611$	−1.35570	+	3.14414i	−0.0548459	+	0.127198i
$612$	−22.4163	−	10.2703i	−0.906124	−	0.415153i
$613$	−16.3029	−	4.36834i	−0.658467	−	0.176436i	−0.0859127	−	0.996303i	$-0.527381\pi$
$613$	−16.3029	−	4.36834i	−0.658467	−	0.176436i	−0.572554	+	0.819867i	$0.694047\pi$
$614$	23.8682	−	13.7803i	0.963241	−	0.556128i
$615$	−15.2544	−	7.87601i	−0.615117	−	0.317591i
$616$	1.33781	−	0.538738i	0.0539019	−	0.0217064i
$617$	2.86991	+	0.768991i	0.115538	+	0.0309584i	0.316125	−	0.948718i	$-0.397618\pi$
$617$	2.86991	+	0.768991i	0.115538	+	0.0309584i	−0.200587	+	0.979676i	$0.564285\pi$
$618$	−7.36975	−	23.1033i	−0.296455	−	0.929350i
$619$	−9.15802	+	9.15802i	−0.368092	+	0.368092i	−0.866781	−	0.498689i	$-0.833815\pi$
$619$	−9.15802	+	9.15802i	−0.368092	+	0.368092i	0.498689	+	0.866781i	$0.333815\pi$
$620$	−26.5185	−	45.9314i	−1.06501	−	1.84465i
$621$	−2.42202	−	17.0677i	−0.0971925	−	0.684904i
$622$	−3.32183	+	3.32183i	−0.133193	+	0.133193i
$623$	−11.0199	+	8.28443i	−0.441504	+	0.331909i
$624$	−2.00222	−	1.43518i	−0.0801531	−	0.0574532i
$625$	29.1967			1.16787
$626$	−55.7538	+	14.9392i	−2.22837	+	0.597090i
$627$	0.00814583	+	0.173230i	0.000325313	+	0.00691815i
$628$	−19.0934	−	33.0707i	−0.761908	−	1.31966i
$629$	20.0947	+	20.0947i	0.801228	+	0.801228i
$630$	−20.3545	−	39.4037i	−0.810942	−	1.56988i
$631$	12.7439	+	12.7439i	0.507327	+	0.507327i	0.913705	−	0.406378i	$-0.133208\pi$
$631$	12.7439	+	12.7439i	0.507327	+	0.507327i	−0.406378	+	0.913705i	$0.633208\pi$
$632$	2.37677	−	8.87021i	0.0945427	−	0.352838i
$633$	−16.6632	+	32.2737i	−0.662304	+	1.28276i
$634$	50.3338	+	29.0602i	1.99901	+	1.15413i
$635$	21.2981	−	21.2981i	0.845188	−	0.845188i
$636$	39.6947	−	25.4759i	1.57400	−	1.01019i
$637$	−14.6722	−	20.5360i	−0.581335	−	0.813665i
$638$	−3.31232			−0.131136
$639$	−3.91753	−	10.5427i	−0.154975	−	0.417061i
$640$	37.0821	−	21.4094i	1.46580	−	0.846280i
$641$			28.0964i			1.10974i	0.831937	+	0.554871i	$0.187232\pi$
$641$			28.0964i			1.10974i	−0.831937	+	0.554871i	$0.812768\pi$
$642$	−9.48382	−	2.06915i	−0.374297	−	0.0816629i
$643$	−10.4078	+	38.8423i	−0.410442	+	1.53179i	0.383351	+	0.923603i	$0.374770\pi$
$643$	−10.4078	+	38.8423i	−0.410442	+	1.53179i	−0.793793	+	0.608188i	$0.791897\pi$
$644$	27.3414	+	3.87436i	1.07740	+	0.152671i
$645$	−21.5420	+	23.6680i	−0.848217	+	0.931925i
$646$	1.41503	+	2.45090i	0.0556734	+	0.0964292i
$647$	1.20123	+	2.08058i	0.0472251	+	0.0817962i	0.888672	−	0.458544i	$-0.151629\pi$
$647$	1.20123	+	2.08058i	0.0472251	+	0.0817962i	−0.841447	+	0.540340i	$0.818296\pi$
$648$	1.72628	−	23.3345i	0.0678148	−	0.916664i
$649$	−0.239220	+	0.414342i	−0.00939023	+	0.0162643i
$650$	−8.01454	−	3.45575i	−0.314356	−	0.135546i
$651$	−10.9188	+	29.4022i	−0.427943	+	1.15236i
$652$	33.6869	+	9.02637i	1.31928	+	0.353500i
$653$	23.3953			0.915531			0.457765	−	0.889073i	$-0.348650\pi$
$653$	23.3953			0.915531			0.457765	+	0.889073i	$0.348650\pi$
$654$	0.637655	+	13.5605i	0.0249343	+	0.530256i
$655$	19.5568	−	19.5568i	0.764149	−	0.764149i
$656$	−1.53327	+	0.410838i	−0.0598640	+	0.0160405i
$657$	−1.42417	+	1.72058i	−0.0555622	+	0.0671261i
$658$	−0.799661	+	5.64322i	−0.0311740	+	0.219996i
$659$	10.0679	−	17.4382i	0.392191	−	0.679295i	−0.600547	−	0.799589i	$-0.705050\pi$
$659$	10.0679	−	17.4382i	0.392191	−	0.679295i	0.992738	+	0.120294i	$0.0383838\pi$
$660$	−2.81110	+	0.132187i	−0.109422	+	0.00514535i
$661$	4.63189	+	17.2864i	0.180160	+	0.672365i	0.995615	+	0.0935448i	$0.0298198\pi$
$661$	4.63189	+	17.2864i	0.180160	+	0.672365i	−0.815456	+	0.578820i	$0.803513\pi$
$662$	−33.4999	−	19.3412i	−1.30201	−	0.751717i
$663$	13.2603	+	9.50489i	0.514987	+	0.369139i
$664$	−34.2963	−	19.8010i	−1.33095	−	0.768427i
$665$	−0.436621	+	3.08124i	−0.0169314	+	0.119485i
$666$	−30.8350	+	67.3014i	−1.19483	+	2.60787i
$667$	−20.0083	−	11.5518i	−0.774724	−	0.447287i
$668$	18.8723	+	18.8723i	0.730193	+	0.730193i
$669$	−20.9818	−	19.0971i	−0.811201	−	0.738337i
$670$	19.2394	−	19.2394i	0.743282	−	0.743282i
$671$	−2.37853	−	0.637325i	−0.0918221	−	0.0246037i
$672$	−26.1813	−	9.72271i	−1.00996	−	0.375062i
$673$	0.0858892	+	0.0495882i	0.00331079	+	0.00191148i	0.501654	−	0.865068i	$-0.332725\pi$
$673$	0.0858892	+	0.0495882i	0.00331079	+	0.00191148i	−0.498344	+	0.866980i	$0.666058\pi$
$674$	44.5455	−	11.9359i	1.71583	−	0.459755i
$675$	0.779028	+	5.48972i	0.0299848	+	0.211299i
$676$	−28.0751	−	29.7404i	−1.07981	−	1.14386i
$677$	−20.3047	+	11.7229i	−0.780372	+	0.450548i	−0.836562	−	0.547872i	$-0.815438\pi$
$677$	−20.3047	+	11.7229i	−0.780372	+	0.450548i	0.0561902	+	0.998420i	$0.482105\pi$
$678$	26.2634	−	28.8552i	1.00864	−	1.10818i
$679$	−25.0678	−	33.3451i	−0.962013	−	1.27967i
$680$	−14.4882	+	8.36478i	−0.555598	+	0.320774i
$681$	6.41209	−	29.3894i	0.245712	−	1.12620i
$682$	2.30189	+	2.30189i	0.0881440	+	0.0881440i
$683$	4.12287	−	15.3868i	0.157757	−	0.588758i	−0.841096	−	0.540886i	$-0.818089\pi$
$683$	4.12287	−	15.3868i	0.157757	−	0.588758i	0.998853	−	0.0478726i	$-0.0152441\pi$
$684$	−2.87383	+	3.47195i	−0.109884	+	0.132753i
$685$		−	34.4020i		−	1.31443i
$686$	−32.5597	−	26.5511i	−1.24313	−	1.01373i
$687$	31.5172	+	6.87633i	1.20246	+	0.262348i
$688$			2.95912i			0.112815i
$689$	−29.0024	+	11.5268i	−1.10490	+	0.439136i
$690$	−28.5296	−	14.7301i	−1.08610	−	0.560765i
$691$	−9.24980	+	34.5207i	−0.351879	+	1.31323i	0.532488	+	0.846437i	$0.321257\pi$
$691$	−9.24980	+	34.5207i	−0.351879	+	1.31323i	−0.884367	+	0.466792i	$0.845410\pi$
$692$			57.1216i			2.17144i
$693$	1.12045	+	1.23053i	0.0425624	+	0.0467440i
$694$	−3.97523	+	3.97523i	−0.150898	+	0.150898i
$695$	−25.6646	−	6.87682i	−0.973515	−	0.260853i
$696$	−23.1910	−	21.1079i	−0.879051	−	0.800093i
$697$	10.1545	−	2.72089i	0.384629	−	0.103061i
$698$			62.9470i			2.38258i
$699$	−1.77736	−	37.7976i	−0.0672259	−	1.42964i
$700$	−8.79418	−	1.24616i	−0.332389	−	0.0471005i
$701$		−	7.71012i		−	0.291207i	−0.989343	−	0.145604i	$-0.953488\pi$
$701$		−	7.71012i		−	0.291207i	0.989343	−	0.145604i	$-0.0465124\pi$
$702$	−11.1776	+	41.0040i	−0.421871	+	1.54759i
$703$	4.49860	−	2.59727i	0.169668	−	0.0979577i
$704$	−1.93276	+	1.93276i	−0.0728437	+	0.0728437i
$705$	1.85867	−	3.59992i	0.0700017	−	0.135581i
$706$	5.22185	+	9.04451i	0.196527	+	0.340395i
$707$	3.20450	+	7.95751i	0.120518	+	0.299273i
$708$	−11.8460	+	3.77878i	−0.445201	+	0.142015i
$709$	−13.3439	+	49.8002i	−0.501142	+	1.87029i	−0.00866148	+	0.999962i	$0.502757\pi$
$709$	−13.3439	+	49.8002i	−0.501142	+	1.87029i	−0.492480	+	0.870324i	$0.663910\pi$
$710$	−20.2342	−	5.42174i	−0.759376	−	0.203474i
$711$	10.5499	−	0.994381i	0.395654	−	0.0372922i
$712$	−6.77359	+	11.7322i	−0.253851	+	0.439683i
$713$	5.87683	+	21.9326i	0.220089	+	0.821383i
$714$	25.4593	+	9.45460i	0.952791	+	0.353830i
$715$	1.84247	+	0.269607i	0.0689045	+	0.0100827i
$716$	−4.92580			−0.184086
$717$	−15.6260	−	48.9855i	−0.583562	−	1.82940i
$718$	−66.9460			−2.49840
$719$	−9.43607	+	16.3437i	−0.351906	+	0.609519i	−0.986583	−	0.163258i	$-0.947800\pi$
$719$	−9.43607	+	16.3437i	−0.351906	+	0.609519i	0.634678	+	0.772777i	$0.281133\pi$
$720$	2.24547	+	1.85864i	0.0836838	+	0.0692674i
$721$	6.09981	+	15.1472i	0.227169	+	0.564112i
$722$	−41.1330	+	11.0216i	−1.53081	+	0.410180i
$723$	9.38022	+	2.04655i	0.348854	+	0.0761119i
$724$	−20.8132	−	12.0165i	−0.773518	−	0.446591i
$725$	6.43553	+	3.71556i	0.239010	+	0.137992i
$726$	−41.0118	+	13.0824i	−1.52209	+	0.485534i
$727$	12.6171	−	21.8534i	0.467941	−	0.810498i	−0.531388	−	0.847129i	$-0.678329\pi$
$727$	12.6171	−	21.8534i	0.467941	−	0.810498i	0.999329	+	0.0366309i	$0.0116626\pi$
$728$	−21.1707	−	12.9177i	−0.784639	−	0.478763i
$729$	25.9340	−	7.51169i	0.960520	−	0.278211i
$730$	1.07670	+	4.01829i	0.0398503	+	0.148723i
$731$		−	19.5976i		−	0.724842i
$732$	−34.5658	−	53.8578i	−1.27759	−	1.99064i
$733$	−29.3573	−	29.3573i	−1.08434	−	1.08434i	−0.996100	−	0.0882371i	$-0.971877\pi$
$733$	−29.3573	−	29.3573i	−1.08434	−	1.08434i	−0.0882371	−	0.996100i	$-0.528123\pi$
$734$	14.6964	−	54.8477i	0.542454	−	2.02446i
$735$	15.6313	+	25.4465i	0.576570	+	0.938607i
$736$	−19.5300	+	5.23304i	−0.719885	+	0.192893i
$737$	−0.510491	+	0.884197i	−0.0188042	+	0.0325698i
$738$	15.8578	+	22.3269i	0.583733	+	0.821864i
$739$	−4.45407	+	16.6228i	−0.163846	+	0.611481i	0.834339	+	0.551252i	$0.185850\pi$
$739$	−4.45407	+	16.6228i	−0.163846	+	0.611481i	−0.998185	+	0.0602287i	$0.980817\pi$
$740$	42.1472	+	73.0010i	1.54936	+	2.68357i
$741$	2.30552	−	1.89157i	0.0846955	−	0.0694887i
$742$	−41.5256	+	31.2177i	−1.52445	+	1.14604i
$743$	−40.8022	−	10.9329i	−1.49689	−	0.401089i	−0.584831	−	0.811156i	$-0.698839\pi$
$743$	−40.8022	−	10.9329i	−1.49689	−	0.401089i	−0.912056	+	0.410066i	$0.865506\pi$
$744$	1.44763	+	30.7854i	0.0530726	+	1.12865i
$745$	−47.1667			−1.72805
$746$	−23.7548	−	6.36508i	−0.869725	−	0.233042i
$747$	7.63320	−	45.0560i	0.279284	−	1.64851i
$748$	1.21855	−	1.21855i	0.0445546	−	0.0445546i
$749$	6.47166	+	0.917054i	0.236469	+	0.0335084i
$750$	−33.8210	−	17.4621i	−1.23497	−	0.637627i
$751$		−	3.34004i		−	0.121880i	−0.998141	−	0.0609398i	$-0.980590\pi$
$751$		−	3.34004i		−	0.121880i	0.998141	−	0.0609398i	$-0.0194098\pi$
$752$	−0.0969544	−	0.361839i	−0.00353556	−	0.0131949i
$753$	−7.75445	−	12.0824i	−0.282588	−	0.440307i
$754$	34.0204	+	45.6834i	1.23895	+	1.66369i
$755$			44.7056i			1.62701i
$756$	0.00863650	+	43.2510i	0.000314106	+	1.57302i
$757$	51.0120			1.85406			0.927032	−	0.374983i	$-0.122351\pi$
$757$	51.0120			1.85406			0.927032	+	0.374983i	$0.122351\pi$
$758$	−43.9082	+	25.3504i	−1.59482	+	0.920768i
$759$	1.17713	+	0.256823i	0.0427272	+	0.00932209i
$760$	0.791462	+	2.95378i	0.0287094	+	0.107145i
$761$	−0.557170	+	0.557170i	−0.0201974	+	0.0201974i	−0.717133	−	0.696936i	$-0.754546\pi$
$761$	−0.557170	+	0.557170i	−0.0201974	+	0.0201974i	0.696936	+	0.717133i	$0.254546\pi$
$762$	−45.7742	+	14.6016i	−1.65822	+	0.528959i
$763$	−1.10370	−	9.07438i	−0.0399566	−	0.328515i
$764$		−	1.99400i		−	0.0721404i
$765$	−14.8713	−	12.3094i	−0.537672	−	0.445046i
$766$	10.9412	+	18.9508i	0.395323	+	0.684720i
$767$	8.17159	−	0.956333i	0.295059	−	0.0345312i
$768$	−23.1187	+	1.08711i	−0.834225	+	0.0392279i
$769$	5.69867	−	21.2677i	0.205499	−	0.766934i	−0.783798	−	0.621016i	$-0.786720\pi$
$769$	5.69867	−	21.2677i	0.205499	−	0.766934i	0.989297	−	0.145917i	$-0.0466133\pi$
$770$	3.07699	−	0.374249i	0.110887	−	0.0134870i
$771$	7.22360	+	11.2553i	0.260152	+	0.405349i
$772$	−63.3708	−	16.9802i	−2.28077	−	0.611130i
$773$	4.99149	−	18.6285i	0.179532	−	0.670021i	−0.816204	−	0.577764i	$-0.803925\pi$
$773$	4.99149	−	18.6285i	0.179532	−	0.670021i	0.995735	−	0.0922566i	$-0.0294080\pi$
$774$	47.8543	−	17.7821i	1.72009	−	0.639164i
$775$	−1.89024	−	7.05449i	−0.0678996	−	0.253405i
$776$	−35.5003	−	20.4961i	−1.27439	−	0.735768i
$777$	17.3538	−	46.7303i	0.622565	−	1.67644i
$778$	13.4175	−	50.0747i	0.481040	−	1.79527i
$779$		−	1.92161i		−	0.0688487i
$780$	30.6955	+	37.4129i	1.09908	+	1.33960i
$781$	0.786058			0.0281274
$782$	18.9914	−	5.08874i	0.679132	−	0.181973i
$783$	13.5105	−	33.5690i	0.482825	−	1.19966i
$784$	2.65258	+	0.767161i	0.0947349	+	0.0273986i
$785$	−7.73807	−	28.8789i	−0.276184	−	1.03073i
$786$	−42.0319	+	13.4078i	−1.49923	+	0.478241i
$787$	−12.0815	−	45.0889i	−0.430660	−	1.60724i	−0.751244	−	0.660025i	$-0.770546\pi$
$787$	−12.0815	−	45.0889i	−0.430660	−	1.60724i	0.320584	−	0.947220i	$-0.396121\pi$
$788$	−41.9195	+	11.2323i	−1.49332	+	0.400134i
$789$	−3.19266	−	4.97456i	−0.113662	−	0.177099i
$790$	9.86839	−	17.0926i	0.351102	−	0.608126i
$791$	−16.1990	+	20.6852i	−0.575971	+	0.735480i
$792$	1.48670	+	0.681152i	0.0528277	+	0.0242037i
$793$	15.6396	+	39.3505i	0.555378	+	1.39738i
$794$		−	41.4393i		−	1.47063i
$795$	35.1817	−	11.2227i	1.24777	−	0.398027i
$796$		−	39.5843i		−	1.40303i
$797$	−11.1403	−	19.2956i	−0.394610	−	0.683485i	0.598441	−	0.801167i	$-0.295787\pi$
$797$	−11.1403	−	19.2956i	−0.394610	−	0.683485i	−0.993051	+	0.117682i	$0.962454\pi$
$798$	2.87377	−	4.04782i	0.101730	−	0.143291i
$799$	0.642108	+	2.39638i	0.0227161	+	0.0847778i
$800$	6.28169	−	1.68317i	0.222091	−	0.0595092i
$801$	−15.4129	−	2.61119i	−0.544588	−	0.0922619i
$802$	11.7488	+	20.3496i	0.414865	+	0.718568i
$803$	−0.0780512	−	0.135189i	−0.00275437	−	0.00477070i
$804$	−25.2791	+	8.06383i	−0.891527	+	0.284389i
$805$	19.8920	+	8.47040i	0.701100	+	0.298542i
$806$	8.10518	−	55.3901i	0.285493	−	1.95103i
$807$	−37.3662	−	19.2926i	−1.31535	−	0.679130i
$808$	5.96058	+	5.96058i	0.209692	+	0.209692i
$809$	−11.3644	−	19.6837i	−0.399550	−	0.692042i	0.594120	−	0.804376i	$-0.297500\pi$
$809$	−11.3644	−	19.6837i	−0.399550	−	0.692042i	−0.993670	+	0.112335i	$0.964167\pi$
$810$	16.5640	−	47.4824i	0.581998	−	1.66836i
$811$	5.88698	+	5.88698i	0.206720	+	0.206720i	0.802872	−	0.596152i	$-0.203304\pi$
$811$	5.88698	+	5.88698i	0.206720	+	0.206720i	−0.596152	+	0.802872i	$0.703304\pi$
$812$	45.6369	+	35.7392i	1.60154	+	1.25420i
$813$	22.5103	−	24.7318i	0.789470	−	0.867381i
$814$	−3.65851	−	3.65851i	−0.128231	−	0.128231i
$815$	23.6468	+	13.6525i	0.828310	+	0.478225i
$816$	−1.78299	+	0.0838416i	−0.0624170	+	0.00293504i
$817$	−3.46016	−	0.927146i	−0.121056	−	0.0324367i
$818$	44.8992			1.56986
$819$	5.46343	−	28.0918i	0.190908	−	0.981608i
$820$	31.1829			1.08895
$821$	12.3097	+	3.29837i	0.429611	+	0.115114i	0.467143	−	0.884182i	$-0.345283\pi$
$821$	12.3097	+	3.29837i	0.429611	+	0.115114i	−0.0375328	+	0.999295i	$0.511950\pi$
$822$	−25.1760	+	48.7613i	−0.878113	+	1.70075i
$823$	−7.52394	−	4.34395i	−0.262268	−	0.151421i	0.363101	−	0.931750i	$-0.381718\pi$
$823$	−7.52394	−	4.34395i	−0.262268	−	0.151421i	−0.625369	+	0.780329i	$0.715051\pi$
$824$	11.3460	+	11.3460i	0.395258	+	0.395258i
$825$	−0.378617	−	0.0826055i	−0.0131817	−	0.00287595i
$826$	12.7040	−	5.11592i	0.442029	−	0.178006i
$827$	29.4938	+	29.4938i	1.02560	+	1.02560i	0.999664	+	0.0259373i	$0.00825702\pi$
$827$	29.4938	+	29.4938i	1.02560	+	1.02560i	0.0259373	+	0.999664i	$0.491743\pi$
$828$	18.1315	+	25.5281i	0.630113	+	0.887164i
$829$	4.40225	+	7.62492i	0.152897	+	0.264825i	0.932291	−	0.361709i	$-0.117807\pi$
$829$	4.40225	+	7.62492i	0.152897	+	0.264825i	−0.779395	+	0.626533i	$0.784473\pi$
$830$	−60.1849	−	60.1849i	−2.08905	−	2.08905i
$831$	12.6730	−	8.13349i	0.439621	−	0.282148i
$832$	46.5077	+	6.80543i	1.61236	+	0.235936i
$833$	−17.5674	−	5.08074i	−0.608676	−	0.176037i
$834$	31.3444	+	28.5290i	1.08537	+	0.987879i
$835$	10.4480	+	18.0965i	0.361569	+	0.626257i
$836$	−0.157499	−	0.272797i	−0.00544723	−	0.00943487i
$837$	−32.7178	+	13.9396i	−1.13089	+	0.481824i
$838$	−66.1251	+	17.7182i	−2.28425	+	0.612064i
$839$	4.36682	+	16.2972i	0.150759	+	0.562642i	0.999431	+	0.0337222i	$0.0107361\pi$
$839$	4.36682	+	16.2972i	0.150759	+	0.562642i	−0.848672	+	0.528920i	$0.822597\pi$
$840$	23.9283	+	16.9880i	0.825603	+	0.586141i
$841$	−9.74834	−	16.8846i	−0.336149	−	0.582228i
$842$		−	17.4209i		−	0.600364i
$843$	−28.3885	−	25.8386i	−0.977754	−	0.889929i
$844$		−	65.9735i		−	2.27090i
$845$	−15.2054	−	28.1804i	−0.523080	−	0.969435i
$846$	−5.26897	+	3.74231i	−0.181151	+	0.128663i
$847$	26.8886	−	10.8281i	0.923903	−	0.372057i
$848$	1.70723	−	2.95701i	0.0586265	−	0.101544i
$849$	3.89555	−	0.183181i	0.133695	−	0.00628675i
$850$	−6.10847	+	1.63676i	−0.209519	+	0.0561404i
$851$	−9.34033	−	34.8586i	−0.320182	−	1.19494i
$852$	15.1079	+	13.7508i	0.517587	+	0.471096i
$853$	0.467603	+	1.74512i	0.0160104	+	0.0597516i	0.973469	−	0.228819i	$-0.0734865\pi$
$853$	0.467603	+	1.74512i	0.0160104	+	0.0597516i	−0.957458	+	0.288571i	$0.906820\pi$
$854$	42.3562	+	56.3420i	1.44940	+	1.92798i
$855$	−2.87690	+	2.04333i	−0.0983877	+	0.0698804i
$856$	6.20395	−	1.66234i	0.212047	−	0.0568177i
$857$	8.07968			0.275997			0.137998	−	0.990432i	$-0.455933\pi$
$857$	8.07968			0.275997			0.137998	+	0.990432i	$0.455933\pi$
$858$	−2.41421	−	1.73049i	−0.0824198	−	0.0590780i
$859$			24.6063i			0.839557i	0.907627	+	0.419778i	$0.137892\pi$
$859$			24.6063i			0.839557i	−0.907627	+	0.419778i	$0.862108\pi$
$860$	15.0453	−	56.1498i	0.513040	−	1.91469i
$861$	−11.7610	−	14.2030i	−0.400815	−	0.484038i
$862$	−71.2014	−	41.1081i	−2.42513	−	1.40015i
$863$	5.01568	+	18.7188i	0.170736	+	0.637195i	0.997239	+	0.0742623i	$0.0236602\pi$
$863$	5.01568	+	18.7188i	0.170736	+	0.637195i	−0.826503	+	0.562932i	$0.809673\pi$
$864$	−12.4126	−	29.1337i	−0.422285	−	0.991149i
$865$	−11.5750	+	43.1985i	−0.393562	+	1.46879i
$866$	−71.1621	−	19.0678i	−2.41819	−	0.647951i
$867$	−17.6040	+	0.827796i	−0.597864	+	0.0281134i
$868$	−6.87834	−	56.5522i	−0.233466	−	1.91951i
$869$	−0.191684	+	0.715373i	−0.00650242	+	0.0242674i
$870$	−36.4031	−	56.7206i	−1.23418	−	1.92301i
$871$	17.4380	−	2.04079i	0.590864	−	0.0691496i
$872$	−4.49125	−	7.77907i	−0.152093	−	0.263433i
$873$	7.90118	−	46.6378i	0.267414	−	1.57845i
$874$		−	3.59388i		−	0.121565i
$875$	23.5814	+	10.0414i	0.797197	+	0.339462i
$876$	0.864784	−	3.96368i	0.0292183	−	0.133920i
$877$	12.8512	−	12.8512i	0.433953	−	0.433953i	−0.456018	−	0.889971i	$-0.650725\pi$
$877$	12.8512	−	12.8512i	0.433953	−	0.433953i	0.889971	+	0.456018i	$0.150725\pi$
$878$	−20.0983	−	75.0080i	−0.678286	−	2.53140i
$879$	−2.35318	−	7.37693i	−0.0793708	−	0.248818i
$880$	−0.176430	+	0.101862i	−0.00594747	+	0.00343377i
$881$	16.2485			0.547425			0.273712	−	0.961812i	$-0.411748\pi$
$881$	16.2485			0.547425			0.273712	+	0.961812i	$0.411748\pi$
$882$	−3.53365	−	47.5071i	−0.118984	−	1.59965i
$883$		−	21.6065i		−	0.727117i	−0.931571	−	0.363558i	$-0.881562\pi$
$883$		−	21.6065i		−	0.727117i	0.931571	−	0.363558i	$-0.118438\pi$
$884$	−29.3218	−	4.29063i	−0.986199	−	0.144310i
$885$	−9.72434	+	0.457268i	−0.326880	+	0.0153709i
$886$	22.2923	+	83.1960i	0.748925	+	2.79502i
$887$			48.4650i			1.62730i	0.581358	+	0.813648i	$0.302522\pi$
$887$			48.4650i			1.62730i	−0.581358	+	0.813648i	$0.697478\pi$
$888$	−2.30078	−	48.9288i	−0.0772092	−	1.64194i
$889$	30.0110	−	12.0855i	1.00654	−	0.405333i
$890$	−20.5883	+	20.5883i	−0.690121	+	0.690121i
$891$	−0.139223	+	1.88190i	−0.00466414	+	0.0630460i
$892$	49.7770	+	13.3377i	1.66666	+	0.446580i
$893$	0.453483			0.0151752
$894$	66.8540	+	34.5174i	2.23593	+	1.15443i
$895$	−3.72516	−	0.998153i	−0.124518	−	0.0333646i
$896$	45.6567	−	5.55313i	1.52528	−	0.185517i
$897$	−8.54807	−	18.8728i	−0.285412	−	0.630143i
$898$	3.46299	+	5.99807i	0.115561	+	0.200158i
$899$	−12.3360	+	46.0388i	−0.411430	+	1.53548i
$900$	−5.83188	−	8.21096i	−0.194396	−	0.273699i
$901$	−11.3066	+	19.5836i	−0.376678	+	0.652425i
$902$	−1.84876	+	0.495374i	−0.0615570	+	0.0164942i
$903$	−31.2494	+	14.3249i	−1.03991	+	0.476702i
$904$	−6.68193	+	24.9373i	−0.222238	+	0.829402i
$905$	−13.3051	−	13.3051i	−0.442276	−	0.442276i
$906$	32.7164	−	63.3657i	1.08693	−	2.10519i
$907$			30.0184i			0.996745i	0.866963	+	0.498373i	$0.166069\pi$
$907$			30.0184i			0.996745i	−0.866963	+	0.498373i	$0.833931\pi$
$908$	14.1413	+	52.7761i	0.469296	+	1.75144i
$909$	−4.05160	+	8.84314i	−0.134383	+	0.293309i
$910$	−36.7650	−	38.5939i	−1.21875	−	1.27938i
$911$	−23.6741	+	41.0047i	−0.784356	+	1.35854i	0.145027	+	0.989428i	$0.453673\pi$
$911$	−23.6741	+	41.0047i	−0.784356	+	1.35854i	−0.929383	+	0.369117i	$0.879660\pi$
$912$	−0.0695487	+	0.318772i	−0.00230299	+	0.0105556i
$913$	2.76596	+	1.59693i	0.0915399	+	0.0528506i
$914$	24.0137	+	13.8643i	0.794304	+	0.458591i
$915$	−15.2269	−	47.7346i	−0.503387	−	1.57806i
$916$	−56.5971	+	15.1652i	−1.87002	+	0.501071i
$917$	27.5574	−	11.0974i	0.910026	−	0.366469i
$918$	12.0703	+	28.3303i	0.398379	+	0.935040i
$919$	−10.3721	+	17.9650i	−0.342144	+	0.592610i	−0.984831	−	0.173519i	$-0.944486\pi$
$919$	−10.3721	+	17.9650i	−0.342144	+	0.592610i	0.642687	+	0.766129i	$0.277820\pi$
$920$	21.2448			0.700422
$921$	−20.5596	−	4.48563i	−0.677461	−	0.147806i
$922$	−79.0678			−2.60396
$923$	−8.07350	−	10.8413i	−0.265742	−	0.356845i
$924$	−2.83375	−	1.05234i	−0.0932234	−	0.0346195i
$925$	3.00426	+	11.2120i	0.0987793	+	0.368649i
$926$	32.9703	−	57.1063i	1.08347	−	1.87663i
$927$	−7.71229	+	16.8330i	−0.253305	+	0.552870i
$928$	−40.9954	−	10.9847i	−1.34574	−	0.360590i
$929$	−11.1310	+	41.5414i	−0.365195	+	1.36293i	0.501960	+	0.864891i	$0.332612\pi$
$929$	−11.1310	+	41.5414i	−0.365195	+	1.36293i	−0.867156	+	0.498037i	$0.834054\pi$
$930$	−14.1196	+	64.7163i	−0.463000	+	2.12213i
$931$	−1.72816	+	2.86135i	−0.0566381	+	0.0937770i
$932$	34.3652	+	59.5222i	1.12567	+	1.94971i
$933$	3.58292	−	0.168480i	0.117299	−	0.00551578i
$934$	37.8826	−	37.8826i	1.23956	−	1.23956i
$935$	1.16846	−	0.674611i	0.0382127	−	0.0220621i
$936$	−5.87530	−	27.5006i	−0.192040	−	0.898884i
$937$		−	7.89287i		−	0.257849i	−0.991654	−	0.128924i	$-0.958848\pi$
$937$		−	7.89287i		−	0.257849i	0.991654	−	0.128924i	$-0.0411525\pi$
$938$	27.1100	−	10.9173i	0.885174	−	0.356461i
$939$	39.1597	+	20.2185i	1.27793	+	0.659807i
$940$			7.35891i			0.240021i
$941$	−4.68271	+	1.25473i	−0.152652	+	0.0409030i	−0.334336	−	0.942454i	$-0.608512\pi$
$941$	−4.68271	+	1.25473i	−0.152652	+	0.0409030i	0.181684	+	0.983357i	$0.441845\pi$
$942$	−10.1661	+	46.5957i	−0.331230	+	1.51817i
$943$	−12.8952	−	3.45525i	−0.419925	−	0.112519i
$944$	−0.636484	+	0.636484i	−0.0207158	+	0.0207158i
$945$	−8.75777	+	32.7105i	−0.284890	+	1.06407i
$946$			3.56800i			0.116006i
$947$	−8.16405	+	30.4686i	−0.265296	+	0.990098i	0.696773	+	0.717292i	$0.254618\pi$
$947$	−8.16405	+	30.4686i	−0.265296	+	0.990098i	−0.962069	+	0.272806i	$0.912048\pi$
$948$	−16.1984	+	10.3961i	−0.526101	+	0.337650i
$949$	−1.06286	+	2.46498i	−0.0345020	+	0.0800168i
$950$			1.15595i			0.0375039i
$951$	−13.4862	−	42.2776i	−0.437320	−	1.37094i
$952$	−17.8383	+	2.16964i	−0.578144	+	0.0703186i
$953$		−	24.7311i		−	0.801119i	−0.916271	−	0.400560i	$-0.868816\pi$
$953$		−	24.7311i		−	0.801119i	0.916271	−	0.400560i	$-0.131184\pi$
$954$	−58.0794	−	9.83957i	−1.88039	−	0.318568i
$955$	0.404060	−	1.50797i	0.0130751	−	0.0487969i
$956$	66.0390	+	66.0390i	2.13585	+	2.13585i
$957$	1.87033	+	1.70233i	0.0604591	+	0.0550285i
$958$	10.9436	−	6.31831i	0.353573	−	0.204135i
$959$	14.4772	−	33.9984i	0.467493	−	1.09787i
$960$	−54.3383	−	11.8554i	−1.75376	−	0.382631i
$961$	13.7207	−	7.92166i	0.442604	−	0.255537i
$962$	−12.8820	+	88.0341i	−0.415331	+	2.83833i
$963$	4.29170	+	6.04247i	0.138298	+	0.194716i
$964$	−16.8446	+	4.51349i	−0.542527	+	0.145370i
$965$	−44.4837	−	25.6827i	−1.43198	−	0.826754i
$966$	−21.9961	−	26.5632i	−0.707712	−	0.854658i
$967$	−14.3067	−	3.83347i	−0.460072	−	0.123276i	0.0213361	−	0.999772i	$-0.493208\pi$
$967$	−14.3067	−	3.83347i	−0.460072	−	0.123276i	−0.481409	+	0.876496i	$0.659875\pi$
$968$	20.1409	−	20.1409i	0.647353	−	0.647353i
$969$	0.460606	−	2.11115i	0.0147968	−	0.0678201i
$970$	−62.2979	−	62.2979i	−2.00026	−	2.00026i
$971$	13.8617	+	8.00306i	0.444843	+	0.256830i	0.705650	−	0.708561i	$-0.250655\pi$
$971$	13.8617	+	8.00306i	0.444843	+	0.256830i	−0.260807	+	0.965391i	$0.583988\pi$
$972$	−35.5967	+	33.7342i	−1.14176	+	1.08203i
$973$	−22.4696	−	17.5964i	−0.720342	−	0.564116i
$974$	−37.2106	−	21.4836i	−1.19230	−	0.688378i
$975$	2.74943	+	6.07030i	0.0880523	+	0.194405i
$976$	−4.01208	−	2.31637i	−0.128424	−	0.0741453i
$977$	0.320618	+	1.19656i	0.0102575	+	0.0382815i	0.970865	−	0.239627i	$-0.0770253\pi$
$977$	0.320618	+	1.19656i	0.0102575	+	0.0382815i	−0.960607	+	0.277909i	$0.910359\pi$
$978$	−23.5258	−	36.6561i	−0.752272	−	1.17213i
$979$	0.546283	−	0.946189i	0.0174593	−	0.0302403i
$980$	−46.4326	−	28.0437i	−1.48323	−	0.895824i
$981$	6.60919	−	7.98474i	0.211015	−	0.254933i
$982$	−22.1231	+	5.92787i	−0.705976	+	0.189166i
$983$	16.5436	−	16.5436i	0.527658	−	0.527658i	−0.392216	−	0.919873i	$-0.628291\pi$
$983$	16.5436	−	16.5436i	0.527658	−	0.527658i	0.919873	+	0.392216i	$0.128291\pi$
$984$	−16.1008	−	8.31298i	−0.513273	−	0.265008i
$985$	−33.9779			−1.08263
$986$	39.8649	+	10.6818i	1.26956	+	0.340177i
$987$	3.35180	−	2.77551i	0.106689	−	0.0883454i
$988$	−2.14475	+	4.97408i	−0.0682335	+	0.158247i
$989$	−12.4435	+	21.5527i	−0.395679	+	0.685337i
$990$	2.70751	+	2.24108i	0.0860504	+	0.0712263i
$991$	18.5363	+	32.1058i	0.588825	+	1.01987i	0.994387	+	0.105807i	$0.0337426\pi$
$991$	18.5363	+	32.1058i	0.588825	+	1.01987i	−0.405562	+	0.914068i	$0.632924\pi$
$992$	20.8559	+	36.1235i	0.662175	+	1.14692i
$993$	8.97580	+	28.1381i	0.284839	+	0.892934i
$994$	−17.7152	−	13.8732i	−0.561892	−	0.440030i
$995$	8.02127	−	29.9358i	0.254291	−	0.949028i
$996$	25.2254	+	79.0787i	0.799298	+	2.50570i
$997$			50.6361i			1.60366i	0.597551	+	0.801831i	$0.296140\pi$
$997$			50.6361i			1.60366i	−0.597551	+	0.801831i	$0.703860\pi$
$998$	−28.4928	+	16.4503i	−0.901924	+	0.520726i
$999$	52.0000	−	22.1549i	1.64521	−	0.700951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fk.a.187.96	yes	432
7.3	odd	6		819.2.ep.a.304.13	yes	432
9.4	even	3		819.2.ep.a.733.13	yes	432
13.8	odd	4	inner	819.2.fk.a.502.13	yes	432
63.31	odd	6	inner	819.2.fk.a.31.13	yes	432
91.73	even	12		819.2.ep.a.619.13	yes	432
117.112	odd	12		819.2.ep.a.229.13	✓	432
819.346	even	12	inner	819.2.fk.a.346.96	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ep.a.229.13	✓	432	117.112	odd	12
819.2.ep.a.304.13	yes	432	7.3	odd	6
819.2.ep.a.619.13	yes	432	91.73	even	12
819.2.ep.a.733.13	yes	432	9.4	even	3
819.2.fk.a.31.13	yes	432	63.31	odd	6	inner
819.2.fk.a.187.96	yes	432	1.1	even	1	trivial
819.2.fk.a.346.96	yes	432	819.346	even	12	inner
819.2.fk.a.502.13	yes	432	13.8	odd	4	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.19119 + 0.587129i) q^{2} +(-0.935526 - 1.45767i) q^{3} +(2.72456 + 1.57302i) q^{4} +(1.74171 + 1.74171i) q^{5} +(-1.19408 - 3.74330i) q^{6} +(0.988320 + 2.45423i) q^{7} +(1.83834 + 1.83834i) q^{8} +(-1.24958 + 2.72737i) q^{9} +O(q^{10})\)	\(q+(2.19119 + 0.587129i) q^{2} +(-0.935526 - 1.45767i) q^{3} +(2.72456 + 1.57302i) q^{4} +(1.74171 + 1.74171i) q^{5} +(-1.19408 - 3.74330i) q^{6} +(0.988320 + 2.45423i) q^{7} +(1.83834 + 1.83834i) q^{8} +(-1.24958 + 2.72737i) q^{9} +(2.79381 + 4.83902i) q^{10} +(-0.148260 - 0.148260i) q^{11} +(-0.255952 - 5.44310i) q^{12} +(-0.522038 + 3.56756i) q^{13} +(0.724655 + 5.95795i) q^{14} +(0.909414 - 4.16824i) q^{15} +(-0.197235 - 0.341621i) q^{16} +(1.30624 + 2.26248i) q^{17} +(-4.33939 + 5.24253i) q^{18} +(0.461262 - 0.123595i) q^{19} +(2.00563 + 7.48513i) q^{20} +(2.65284 - 3.73663i) q^{21} +(-0.237819 - 0.411914i) q^{22} -3.31759i q^{23} +(0.959870 - 4.39950i) q^{24} +1.06708i q^{25} +(-3.23850 + 7.51071i) q^{26} +(5.14461 - 0.730055i) q^{27} +(-1.16782 + 8.24134i) q^{28} +(3.48198 - 6.03096i) q^{29} +(4.43999 - 8.59947i) q^{30} +(-6.61101 + 1.77141i) q^{31} +(-1.57736 - 5.88679i) q^{32} +(-0.0774125 + 0.354815i) q^{33} +(1.53386 + 5.72446i) q^{34} +(-2.55318 + 5.99590i) q^{35} +(-7.69478 + 5.46526i) q^{36} +(10.5072 - 2.81539i) q^{37} +1.08328 q^{38} +(5.68869 - 2.57659i) q^{39} +6.40369i q^{40} +(1.04149 - 3.88691i) q^{41} +(8.00678 - 6.63013i) q^{42} +(-6.49650 - 3.75075i) q^{43} +(-0.170727 - 0.637160i) q^{44} +(-6.92668 + 2.57387i) q^{45} +(1.94785 - 7.26949i) q^{46} +(0.917279 + 0.245784i) q^{47} +(-0.313451 + 0.607098i) q^{48} +(-5.04645 + 4.85112i) q^{49} +(-0.626514 + 2.33818i) q^{50} +(2.07591 - 4.02067i) q^{51} +(-7.03418 + 8.89885i) q^{52} +(4.32791 + 7.49617i) q^{53} +(11.7015 + 1.42086i) q^{54} -0.516451i q^{55} +(-2.69483 + 6.32857i) q^{56} +(-0.611682 - 0.556739i) q^{57} +(11.1706 - 11.1706i) q^{58} +(-0.590589 - 2.20411i) q^{59} +(9.03450 - 9.92608i) q^{60} +(10.1708 - 5.87212i) q^{61} -15.5260 q^{62} +(-7.92857 - 0.371239i) q^{63} -13.0363i q^{64} +(-7.12288 + 5.30440i) q^{65} +(-0.377948 + 0.732017i) q^{66} +(-1.26030 - 4.70352i) q^{67} +8.21901i q^{68} +(-4.83594 + 3.10370i) q^{69} +(-9.11487 + 11.6391i) q^{70} +(-2.65094 + 2.65094i) q^{71} +(-7.31098 + 2.71668i) q^{72} +(0.719141 + 0.192693i) q^{73} +24.6763 q^{74} +(1.55545 - 0.998283i) q^{75} +(1.45115 + 0.388835i) q^{76} +(0.217335 - 0.510392i) q^{77} +(13.9778 - 2.30581i) q^{78} +(-1.76612 - 3.05900i) q^{79} +(0.251478 - 0.938528i) q^{80} +(-5.87709 - 6.81614i) q^{81} +(4.56423 - 7.90548i) q^{82} +(-14.7136 + 3.94250i) q^{83} +(13.1056 - 6.00769i) q^{84} +(-1.66548 + 6.21566i) q^{85} +(-12.0329 - 12.0329i) q^{86} +(-12.0486 + 0.566563i) q^{87} -0.545105i q^{88} +(1.34867 + 5.03329i) q^{89} +(-16.6889 + 1.57301i) q^{90} +(-9.27153 + 2.24469i) q^{91} +(5.21866 - 9.03898i) q^{92} +(8.76690 + 7.97944i) q^{93} +(1.86563 + 1.07712i) q^{94} +(1.01865 + 0.588117i) q^{95} +(-7.10532 + 7.80652i) q^{96} +(-15.2302 + 4.08091i) q^{97} +(-13.9060 + 7.66683i) q^{98} +(0.589623 - 0.219097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 432 * q + 2 * q^2 - 12 * q^3 + 12 * q^6 - 8 * q^8 - 4 * q^9	\( 432 q + 2 q^{2} - 12 q^{3} + 12 q^{6} - 8 q^{8} - 4 q^{9} - 12 q^{11} - 4 q^{14} - 14 q^{15} + 196 q^{16} + 14 q^{18} - 12 q^{19} - 60 q^{20} - 8 q^{22} - 24 q^{24} - 12 q^{26} - 36 q^{27} + 4 q^{28} - 24 q^{29} - 30 q^{31} + 10 q^{32} - 60 q^{33} - 12 q^{34} - 60 q^{35} - 2 q^{37} - 22 q^{39} - 100 q^{42} + 32 q^{44} - 6 q^{45} + 4 q^{46} + 30 q^{47} - 12 q^{48} + 22 q^{50} + 8 q^{53} + 30 q^{54} - 44 q^{57} + 12 q^{58} - 6 q^{59} - 64 q^{60} - 12 q^{61} + 14 q^{63} + 16 q^{65} - 12 q^{66} + 16 q^{67} + 32 q^{70} + 48 q^{71} + 34 q^{72} - 12 q^{73} + 104 q^{74} - 48 q^{76} + 2 q^{78} + 28 q^{79} - 6 q^{80} - 44 q^{81} + 84 q^{83} - 38 q^{84} - 6 q^{85} + 84 q^{86} + 24 q^{87} + 18 q^{89} + 52 q^{92} - 108 q^{93} - 12 q^{94} + 42 q^{96} + 6 q^{97} - 112 q^{98} - 50 q^{99}+O(q^{100}) \) 432 * q + 2 * q^2 - 12 * q^3 + 12 * q^6 - 8 * q^8 - 4 * q^9 - 12 * q^11 - 4 * q^14 - 14 * q^15 + 196 * q^16 + 14 * q^18 - 12 * q^19 - 60 * q^20 - 8 * q^22 - 24 * q^24 - 12 * q^26 - 36 * q^27 + 4 * q^28 - 24 * q^29 - 30 * q^31 + 10 * q^32 - 60 * q^33 - 12 * q^34 - 60 * q^35 - 2 * q^37 - 22 * q^39 - 100 * q^42 + 32 * q^44 - 6 * q^45 + 4 * q^46 + 30 * q^47 - 12 * q^48 + 22 * q^50 + 8 * q^53 + 30 * q^54 - 44 * q^57 + 12 * q^58 - 6 * q^59 - 64 * q^60 - 12 * q^61 + 14 * q^63 + 16 * q^65 - 12 * q^66 + 16 * q^67 + 32 * q^70 + 48 * q^71 + 34 * q^72 - 12 * q^73 + 104 * q^74 - 48 * q^76 + 2 * q^78 + 28 * q^79 - 6 * q^80 - 44 * q^81 + 84 * q^83 - 38 * q^84 - 6 * q^85 + 84 * q^86 + 24 * q^87 + 18 * q^89 + 52 * q^92 - 108 * q^93 - 12 * q^94 + 42 * q^96 + 6 * q^97 - 112 * q^98 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more