LMFDB - Embedded newform 112.2.w.c.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(37,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("112.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	112.37
Dual form			112.2.w.c.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36184 - 0.381311i) q^{2} +(-1.60845 - 0.430984i) q^{3} +(1.70920 + 1.03857i) q^{4} +(1.94900 - 0.522232i) q^{5} +(2.02612 + 1.20025i) q^{6} +(-1.89075 - 1.85069i) q^{7} +(-1.93164 - 2.06610i) q^{8} +(-0.196696 - 0.113563i) q^{9} +(-2.85335 - 0.0319777i) q^{10} +(1.63411 - 6.09856i) q^{11} +(-2.30157 - 2.40713i) q^{12} +(1.13388 - 1.13388i) q^{13} +(1.86921 + 3.24130i) q^{14} -3.35995 q^{15} +(1.84276 + 3.55024i) q^{16} +(-0.960789 - 1.66414i) q^{17} +(0.224566 + 0.229656i) q^{18} +(1.63324 + 6.09532i) q^{19} +(3.87361 + 1.13156i) q^{20} +(2.24357 + 3.79164i) q^{21} +(-4.55083 + 7.68215i) q^{22} +(-0.924606 - 0.533821i) q^{23} +(2.21651 + 4.15573i) q^{24} +(-0.804265 + 0.464342i) q^{25} +(-1.97651 + 1.11180i) q^{26} +(3.79985 + 3.79985i) q^{27} +(-1.30962 - 5.12688i) q^{28} +(5.08936 - 5.08936i) q^{29} +(4.57570 + 1.28118i) q^{30} +(-0.198293 - 0.343454i) q^{31} +(-1.15579 - 5.53752i) q^{32} +(-5.25677 + 9.10499i) q^{33} +(0.673887 + 2.63264i) q^{34} +(-4.65156 - 2.61958i) q^{35} +(-0.218252 - 0.398384i) q^{36} +(0.327303 - 0.0877006i) q^{37} +(0.100007 - 8.92360i) q^{38} +(-2.31247 + 1.33510i) q^{39} +(-4.84375 - 3.01805i) q^{40} +7.26189i q^{41} +(-1.60959 - 6.01909i) q^{42} +(1.75565 + 1.75565i) q^{43} +(9.12678 - 8.72657i) q^{44} +(-0.442666 - 0.118612i) q^{45} +(1.05561 + 1.07954i) q^{46} +(-1.08118 + 1.87265i) q^{47} +(-1.43390 - 6.50461i) q^{48} +(0.149895 + 6.99839i) q^{49} +(1.27234 - 0.325684i) q^{50} +(0.828170 + 3.09077i) q^{51} +(3.11563 - 0.760420i) q^{52} +(0.111394 - 0.415727i) q^{53} +(-3.72585 - 6.62369i) q^{54} -12.7395i q^{55} +(-0.171444 + 7.48135i) q^{56} -10.5079i q^{57} +(-8.87151 + 4.99025i) q^{58} +(-2.32453 + 8.67527i) q^{59} +(-5.74284 - 3.48953i) q^{60} +(-2.72673 - 10.1763i) q^{61} +(0.139080 + 0.543339i) q^{62} +(0.161735 + 0.578743i) q^{63} +(-0.537512 + 7.98192i) q^{64} +(1.61777 - 2.80206i) q^{65} +(10.6307 - 10.3951i) q^{66} +(7.87441 + 2.10994i) q^{67} +(0.0861303 - 3.84219i) q^{68} +(1.25712 + 1.25712i) q^{69} +(5.33580 + 5.34113i) q^{70} -2.78982i q^{71} +(0.145316 + 0.625756i) q^{72} +(2.05730 - 1.18779i) q^{73} +(-0.479175 - 0.00537015i) q^{74} +(1.49375 - 0.400248i) q^{75} +(-3.53886 + 12.1144i) q^{76} +(-14.3762 + 8.50666i) q^{77} +(3.65830 - 0.936427i) q^{78} +(5.10829 - 8.84782i) q^{79} +(5.44558 + 5.95707i) q^{80} +(-4.13352 - 7.15947i) q^{81} +(2.76904 - 9.88952i) q^{82} +(1.17951 - 1.17951i) q^{83} +(-0.103140 + 8.81078i) q^{84} +(-2.74164 - 2.74164i) q^{85} +(-1.72147 - 3.06036i) q^{86} +(-10.3794 + 5.99257i) q^{87} +(-15.7567 + 8.40403i) q^{88} +(11.0470 + 6.37800i) q^{89} +(0.557612 + 0.330324i) q^{90} +(-4.24233 + 0.0454269i) q^{91} +(-1.02593 - 1.87267i) q^{92} +(0.170922 + 0.637891i) q^{93} +(2.18645 - 2.13799i) q^{94} +(6.36634 + 11.0268i) q^{95} +(-0.527542 + 9.40498i) q^{96} -2.21148 q^{97} +(2.46443 - 9.58784i) q^{98} +(-1.01399 + 1.01399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.36184	−	0.381311i	−0.962965	−	0.269627i
$2$	−1.36184	−	0.381311i	−0.962965	−	0.269627i
$3$	−1.60845	−	0.430984i	−0.928642	−	0.248829i	−0.237366	−	0.971420i	$-0.576284\pi$
$3$	−1.60845	−	0.430984i	−0.928642	−	0.248829i	−0.691275	+	0.722591i	$0.742951\pi$
$4$	1.70920	+	1.03857i	0.854602	+	0.519283i
$5$	1.94900	−	0.522232i	0.871618	−	0.233549i	0.204831	−	0.978797i	$-0.434336\pi$
$5$	1.94900	−	0.522232i	0.871618	−	0.233549i	0.666787	+	0.745248i	$0.267669\pi$
$6$	2.02612	+	1.20025i	0.827158	+	0.490001i
$7$	−1.89075	−	1.85069i	−0.714638	−	0.699495i
$7$	−1.89075	−	1.85069i	−0.714638	−	0.699495i
$8$	−1.93164	−	2.06610i	−0.682939	−	0.730476i
$9$	−0.196696	−	0.113563i	−0.0655654	−	0.0378542i
$10$	−2.85335	−	0.0319777i	−0.902309	−	0.0101122i
$11$	1.63411	−	6.09856i	0.492701	−	1.83879i	−0.0498403	−	0.998757i	$-0.515871\pi$
$11$	1.63411	−	6.09856i	0.492701	−	1.83879i	0.542542	−	0.840029i	$-0.317462\pi$
$12$	−2.30157	−	2.40713i	−0.664407	−	0.694878i
$13$	1.13388	−	1.13388i	0.314480	−	0.314480i	−0.532162	−	0.846642i	$-0.678620\pi$
$13$	1.13388	−	1.13388i	0.314480	−	0.314480i	0.846642	+	0.532162i	$0.178620\pi$
$14$	1.86921	+	3.24130i	0.499568	+	0.866275i
$15$	−3.35995			−0.867535
$16$	1.84276	+	3.55024i	0.460690	+	0.887561i
$17$	−0.960789	−	1.66414i	−0.233026	−	0.403612i	0.725671	−	0.688041i	$-0.241529\pi$
$17$	−0.960789	−	1.66414i	−0.233026	−	0.403612i	−0.958697	+	0.284429i	$0.908196\pi$
$18$	0.224566	+	0.229656i	0.0529307	+	0.0541305i
$19$	1.63324	+	6.09532i	0.374690	+	1.39836i	0.853797	+	0.520605i	$0.174294\pi$
$19$	1.63324	+	6.09532i	0.374690	+	1.39836i	−0.479107	+	0.877756i	$0.659040\pi$
$20$	3.87361	+	1.13156i	0.866165	+	0.253025i
$21$	2.24357	+	3.79164i	0.489588	+	0.827403i
$22$	−4.55083	+	7.68215i	−0.970241	+	1.63784i
$23$	−0.924606	−	0.533821i	−0.192794	−	0.111309i	0.400496	−	0.916298i	$-0.368838\pi$
$23$	−0.924606	−	0.533821i	−0.192794	−	0.111309i	−0.593290	+	0.804989i	$0.702171\pi$
$24$	2.21651	+	4.15573i	0.452442	+	0.848285i
$25$	−0.804265	+	0.464342i	−0.160853	+	0.0928685i
$26$	−1.97651	+	1.11180i	−0.387626	+	0.218041i
$27$	3.79985	+	3.79985i	0.731281	+	0.731281i
$28$	−1.30962	−	5.12688i	−0.247495	−	0.968889i
$29$	5.08936	−	5.08936i	0.945070	−	0.945070i	−0.0534979	−	0.998568i	$-0.517037\pi$
$29$	5.08936	−	5.08936i	0.945070	−	0.945070i	0.998568	+	0.0534979i	$0.0170370\pi$
$30$	4.57570	+	1.28118i	0.835405	+	0.233911i
$31$	−0.198293	−	0.343454i	−0.0356145	−	0.0616861i	0.847669	−	0.530526i	$-0.178006\pi$
$31$	−0.198293	−	0.343454i	−0.0356145	−	0.0616861i	−0.883283	+	0.468840i	$0.844672\pi$
$32$	−1.15579	−	5.53752i	−0.204317	−	0.978905i
$33$	−5.25677	+	9.10499i	−0.915086	+	1.58498i
$34$	0.673887	+	2.63264i	0.115571	+	0.451494i
$35$	−4.65156	−	2.61958i	−0.786257	−	0.442789i
$36$	−0.218252	−	0.398384i	−0.0363753	−	0.0663973i
$37$	0.327303	−	0.0877006i	0.0538083	−	0.0144179i	−0.231814	−	0.972760i	$-0.574466\pi$
$37$	0.327303	−	0.0877006i	0.0538083	−	0.0144179i	0.285623	+	0.958342i	$0.407800\pi$
$38$	0.100007	−	8.92360i	0.0162234	−	1.44760i
$39$	−2.31247	+	1.33510i	−0.370291	+	0.213788i
$40$	−4.84375	−	3.01805i	−0.765864	−	0.477196i
$41$			7.26189i			1.13412i	0.823678	+	0.567058i	$0.191919\pi$
$41$			7.26189i			1.13412i	−0.823678	+	0.567058i	$0.808081\pi$
$42$	−1.60959	−	6.01909i	−0.248365	−	0.928766i
$43$	1.75565	+	1.75565i	0.267734	+	0.267734i	0.828187	−	0.560452i	$-0.189373\pi$
$43$	1.75565	+	1.75565i	0.267734	+	0.267734i	−0.560452	+	0.828187i	$0.689373\pi$
$44$	9.12678	−	8.72657i	1.37591	−	1.31558i
$45$	−0.442666	−	0.118612i	−0.0659888	−	0.0176816i
$46$	1.05561	+	1.07954i	0.155641	+	0.159170i
$47$	−1.08118	+	1.87265i	−0.157706	+	0.273155i	−0.934041	−	0.357166i	$-0.883743\pi$
$47$	−1.08118	+	1.87265i	−0.157706	+	0.273155i	0.776335	+	0.630320i	$0.217076\pi$
$48$	−1.43390	−	6.50461i	−0.206965	−	0.938859i
$49$	0.149895	+	6.99839i	0.0214136	+	0.999771i
$50$	1.27234	−	0.325684i	0.179936	−	0.0460587i
$51$	0.828170	+	3.09077i	0.115967	+	0.432795i
$52$	3.11563	−	0.760420i	0.432060	−	0.105451i
$53$	0.111394	−	0.415727i	0.0153011	−	0.0571045i	−0.957853	−	0.287258i	$-0.907256\pi$
$53$	0.111394	−	0.415727i	0.0153011	−	0.0571045i	0.973154	+	0.230154i	$0.0739229\pi$
$54$	−3.72585	−	6.62369i	−0.507024	−	0.901371i
$55$		−	12.7395i		−	1.71779i
$56$	−0.171444	+	7.48135i	−0.0229102	+	0.999738i
$57$		−	10.5079i		−	1.39181i
$58$	−8.87151	+	4.99025i	−1.16489	+	0.655252i
$59$	−2.32453	+	8.67527i	−0.302628	+	1.12942i	0.632340	+	0.774691i	$0.282095\pi$
$59$	−2.32453	+	8.67527i	−0.302628	+	1.12942i	−0.934968	+	0.354732i	$0.884572\pi$
$60$	−5.74284	−	3.48953i	−0.741397	−	0.450496i
$61$	−2.72673	−	10.1763i	−0.349122	−	1.30294i	−0.887722	−	0.460379i	$-0.847713\pi$
$61$	−2.72673	−	10.1763i	−0.349122	−	1.30294i	0.538601	−	0.842561i	$-0.318953\pi$
$62$	0.139080	+	0.543339i	0.0176632	+	0.0690042i
$63$	0.161735	+	0.578743i	0.0203767	+	0.0729147i
$64$	−0.537512	+	7.98192i	−0.0671890	+	0.997740i
$65$	1.61777	−	2.80206i	0.200660	−	0.347553i
$66$	10.6307	−	10.3951i	1.30855	−	1.27954i
$67$	7.87441	+	2.10994i	0.962012	+	0.257770i	0.705452	−	0.708758i	$-0.250744\pi$
$67$	7.87441	+	2.10994i	0.962012	+	0.257770i	0.256560	+	0.966528i	$0.417411\pi$
$68$	0.0861303	−	3.84219i	0.0104448	−	0.465934i
$69$	1.25712	+	1.25712i	0.151339	+	0.151339i
$70$	5.33580	+	5.34113i	0.637750	+	0.638387i
$71$		−	2.78982i		−	0.331090i	−0.986202	−	0.165545i	$-0.947062\pi$
$71$		−	2.78982i		−	0.331090i	0.986202	−	0.165545i	$-0.0529384\pi$
$72$	0.145316	+	0.625756i	0.0171256	+	0.0737460i
$73$	2.05730	−	1.18779i	0.240789	−	0.139020i	−0.374750	−	0.927126i	$-0.622272\pi$
$73$	2.05730	−	1.18779i	0.240789	−	0.139020i	0.615539	+	0.788106i	$0.288938\pi$
$74$	−0.479175	−	0.00537015i	−0.0557030	−	0.000624267i
$75$	1.49375	−	0.400248i	0.172483	−	0.0462167i
$76$	−3.53886	+	12.1144i	−0.405935	+	1.38961i
$77$	−14.3762	+	8.50666i	−1.63832	+	0.969424i
$78$	3.65830	−	0.936427i	0.414221	−	0.106029i
$79$	5.10829	−	8.84782i	0.574727	−	0.995457i	−0.421344	−	0.906901i	$-0.638441\pi$
$79$	5.10829	−	8.84782i	0.574727	−	0.995457i	0.996071	−	0.0885562i	$-0.0282253\pi$
$80$	5.44558	+	5.95707i	0.608835	+	0.666020i
$81$	−4.13352	−	7.15947i	−0.459280	−	0.795496i
$82$	2.76904	−	9.88952i	0.305789	−	1.09211i
$83$	1.17951	−	1.17951i	0.129468	−	0.129468i	−0.639404	−	0.768871i	$-0.720819\pi$
$83$	1.17951	−	1.17951i	0.129468	−	0.129468i	0.768871	+	0.639404i	$0.220819\pi$
$84$	−0.103140	+	8.81078i	−0.0112535	+	0.961335i
$85$	−2.74164	−	2.74164i	−0.297373	−	0.297373i
$86$	−1.72147	−	3.06036i	−0.185630	−	0.330007i
$87$	−10.3794	+	5.99257i	−1.11279	+	0.642471i
$88$	−15.7567	+	8.40403i	−1.67967	+	0.895872i
$89$	11.0470	+	6.37800i	1.17098	+	0.676066i	0.953911	−	0.300089i	$-0.0970165\pi$
$89$	11.0470	+	6.37800i	1.17098	+	0.676066i	0.217070	+	0.976156i	$0.430350\pi$
$90$	0.557612	+	0.330324i	0.0587774	+	0.0348192i
$91$	−4.24233	+	0.0454269i	−0.444717	+	0.00476204i
$92$	−1.02593	−	1.87267i	−0.106961	−	0.195240i
$93$	0.170922	+	0.637891i	0.0177238	+	0.0661462i
$94$	2.18645	−	2.13799i	0.225515	−	0.220517i
$95$	6.36634	+	11.0268i	0.653173	+	1.13133i
$96$	−0.527542	+	9.40498i	−0.0538420	+	0.959892i
$97$	−2.21148			−0.224542			−0.112271	−	0.993678i	$-0.535813\pi$
$97$	−2.21148			−0.224542			−0.112271	+	0.993678i	$0.535813\pi$
$98$	2.46443	−	9.58784i	0.248945	−	0.968518i
$99$	−1.01399	+	1.01399i	−0.101910	+	0.101910i
$100$	−1.85690	−	0.0416261i	−0.185690	−	0.00416261i
$101$	1.86231	−	6.95024i	0.185307	−	0.691575i	−0.809258	−	0.587454i	$-0.800130\pi$
$101$	1.86231	−	6.95024i	0.185307	−	0.691575i	0.994565	−	0.104121i	$-0.0332030\pi$
$102$	0.0507111	−	4.52492i	0.00502115	−	0.448034i
$103$	15.1457	+	8.74438i	1.49235	+	0.861609i	0.999962	−	0.00876536i	$-0.00279014\pi$
$103$	15.1457	+	8.74438i	1.49235	+	0.861609i	0.492390	+	0.870375i	$0.336123\pi$
$104$	−4.53294	−	0.152454i	−0.444491	−	0.0149493i
$105$	6.35283	+	6.21822i	0.619973	+	0.606836i
$106$	−0.310221	+	0.523677i	−0.0301314	+	0.0508640i
$107$	2.90855	−	0.779344i	0.281180	−	0.0753420i	−0.115473	−	0.993311i	$-0.536838\pi$
$107$	2.90855	−	0.779344i	0.281180	−	0.0753420i	0.396653	+	0.917969i	$0.370172\pi$
$108$	2.54832	+	10.4411i	0.245212	+	1.00470i
$109$	6.86536	+	1.83957i	0.657583	+	0.176199i	0.572155	−	0.820146i	$-0.306108\pi$
$109$	6.86536	+	1.83957i	0.657583	+	0.176199i	0.0854277	+	0.996344i	$0.472774\pi$
$110$	−4.85769	+	17.3491i	−0.463163	+	1.65417i
$111$	−0.564250			−0.0535562
$112$	3.08620	−	10.1230i	0.291618	−	0.956535i
$113$	−5.96535			−0.561173			−0.280586	−	0.959829i	$-0.590529\pi$
$113$	−5.96535			−0.561173			−0.280586	+	0.959829i	$0.590529\pi$
$114$	−4.00679	+	14.3101i	−0.375270	+	1.34026i
$115$	−2.08083	−	0.557557i	−0.194039	−	0.0519925i
$116$	13.9844	−	3.41312i	1.29842	−	0.316900i
$117$	−0.351795	+	0.0942631i	−0.0325234	+	0.00871463i
$118$	6.47360	−	10.9279i	0.595944	−	1.00600i
$119$	−1.26318	+	4.92459i	−0.115796	+	0.451437i
$120$	6.49022	+	6.94198i	0.592473	+	0.633713i
$121$	−24.9959	−	14.4314i	−2.27235	−	1.31194i
$122$	−0.166965	+	14.8982i	−0.0151163	+	1.34882i
$123$	3.12976	−	11.6804i	0.282201	−	1.05319i
$124$	0.0177760	−	0.792973i	0.00159634	−	0.0712111i
$125$	−8.45884	+	8.45884i	−0.756582	+	0.756582i
$126$	0.000424062	−	0.849825i	3.77785e−5	−	0.0757084i
$127$	6.41296			0.569058			0.284529	−	0.958667i	$-0.408163\pi$
$127$	6.41296			0.569058			0.284529	+	0.958667i	$0.408163\pi$
$128$	3.77560	−	10.6651i	0.333719	−	0.942673i
$129$	−2.06723	−	3.58055i	−0.182009	−	0.315250i
$130$	−3.27160	+	3.19908i	−0.286938	+	0.280578i
$131$	−3.87298	−	14.4542i	−0.338384	−	1.26287i	−0.900154	−	0.435573i	$-0.856546\pi$
$131$	−3.87298	−	14.4542i	−0.338384	−	1.26287i	0.561769	−	0.827294i	$-0.310121\pi$
$132$	−18.4410	+	10.1028i	−1.60509	+	0.879335i
$133$	8.19250	−	14.5474i	0.710380	−	1.26142i
$134$	−9.91913	−	5.87600i	−0.856882	−	0.507609i
$135$	9.39029	+	5.42149i	0.808187	+	0.466607i
$136$	−1.58236	+	5.19960i	−0.135687	+	0.445862i
$137$	1.50928	−	0.871382i	0.128946	−	0.0744472i	−0.434139	−	0.900846i	$-0.642947\pi$
$137$	1.50928	−	0.871382i	0.128946	−	0.0744472i	0.563086	+	0.826399i	$0.309614\pi$
$138$	−1.23264	−	2.19134i	−0.104929	−	0.186540i
$139$	2.84436	+	2.84436i	0.241256	+	0.241256i	0.817370	−	0.576114i	$-0.195431\pi$
$139$	2.84436	+	2.84436i	0.241256	+	0.241256i	−0.576114	+	0.817370i	$0.695431\pi$
$140$	−5.22987	−	9.30835i	−0.442004	−	0.786699i
$141$	2.54611	−	2.54611i	0.214421	−	0.214421i
$142$	−1.06379	+	3.79928i	−0.0892710	+	0.318828i
$143$	−5.06214	−	8.76788i	−0.423317	−	0.733207i
$144$	0.0407112	−	0.907588i	0.00339260	−	0.0756324i
$145$	7.26132	−	12.5770i	0.603020	−	1.04446i
$146$	−3.25463	+	0.833099i	−0.269355	+	0.0689478i
$147$	2.77510	−	11.3212i	0.228886	−	0.933757i
$148$	0.650511	+	0.190028i	0.0534717	+	0.0156202i
$149$	−17.7848	+	4.76543i	−1.45699	+	0.390399i	−0.898449	−	0.439077i	$-0.855305\pi$
$149$	−17.7848	+	4.76543i	−1.45699	+	0.390399i	−0.558541	+	0.829477i	$0.688639\pi$
$150$	−2.18686	−	0.0245083i	−0.178556	−	0.00200110i
$151$	−5.52437	+	3.18949i	−0.449567	+	0.259557i	−0.707647	−	0.706566i	$-0.750243\pi$
$151$	−5.52437	+	3.18949i	−0.449567	+	0.259557i	0.258081	+	0.966123i	$0.416910\pi$
$152$	9.43869	−	15.1484i	0.765579	−	1.22870i
$153$			0.436439i			0.0352840i
$154$	22.8218	−	6.10287i	1.83903	−	0.491784i
$155$	−0.565835	−	0.565835i	−0.0454490	−	0.0454490i
$156$	−5.33908	−	0.119686i	−0.427468	−	0.00958254i
$157$	17.6177	+	4.72065i	1.40605	+	0.376749i	0.880512	−	0.474024i	$-0.157199\pi$
$157$	17.6177	+	4.72065i	1.40605	+	0.376749i	0.525534	+	0.850773i	$0.323866\pi$
$158$	−10.3304	+	10.1014i	−0.821845	+	0.803628i
$159$	−0.358344	+	0.620669i	−0.0284185	+	0.0492223i
$160$	−5.14451	−	10.1890i	−0.406709	−	0.805513i
$161$	0.760264	+	2.72048i	0.0599172	+	0.214404i
$162$	2.89920	+	11.3262i	0.227783	+	0.889869i
$163$	2.97338	+	11.0968i	0.232893	+	0.869170i	0.979087	+	0.203441i	$0.0652125\pi$
$163$	2.97338	+	11.0968i	0.232893	+	0.869170i	−0.746194	+	0.665729i	$0.768121\pi$
$164$	−7.54196	+	12.4121i	−0.588928	+	0.969219i
$165$	−5.49051	+	20.4909i	−0.427435	+	1.59521i
$166$	−2.05605	+	1.15654i	−0.159581	+	0.0897647i
$167$		−	21.6693i		−	1.67682i	−0.545040	−	0.838410i	$-0.683486\pi$
$167$		−	21.6693i		−	1.67682i	0.545040	−	0.838410i	$-0.316514\pi$
$168$	3.50010	−	11.9595i	0.270039	−	0.922697i
$169$			10.4287i			0.802204i
$170$	2.68825	+	4.77909i	0.206180	+	0.366539i
$171$	0.370949	−	1.38440i	0.0283672	−	0.105868i
$172$	1.17741	+	4.82413i	0.0897765	+	0.367837i
$173$	3.31175	+	12.3596i	0.251788	+	0.939684i	0.969849	+	0.243705i	$0.0783629\pi$
$173$	3.31175	+	12.3596i	0.251788	+	0.939684i	−0.718062	+	0.695979i	$0.754970\pi$
$174$	16.4201	−	4.20312i	1.24481	−	0.318638i
$175$	2.38002	+	0.610487i	0.179913	+	0.0461485i
$176$	24.6627	−	5.43671i	1.85902	−	0.409808i
$177$	7.47780	−	12.9519i	0.562066	−	0.973527i
$178$	−12.6122	−	12.8981i	−0.945328	−	0.966757i
$179$	3.05939	+	0.819762i	0.228670	+	0.0612719i	0.371334	−	0.928499i	$-0.378900\pi$
$179$	3.05939	+	0.819762i	0.228670	+	0.0612719i	−0.142665	+	0.989771i	$0.545567\pi$
$180$	−0.633421	−	0.662471i	−0.0472124	−	0.0493777i
$181$	−14.3765	−	14.3765i	−1.06860	−	1.06860i	−0.997467	−	0.0711279i	$-0.977340\pi$
$181$	−14.3765	−	14.3765i	−1.06860	−	1.06860i	−0.0711279	−	0.997467i	$-0.522660\pi$
$182$	5.79469	+	1.55578i	0.429531	+	0.115322i
$183$			17.5433i			1.29684i
$184$	0.683082	+	2.94148i	0.0503574	+	0.216849i
$185$	0.592113	−	0.341857i	0.0435330	−	0.0251338i
$186$	0.0104660	−	0.933878i	0.000767408	−	0.0684753i
$187$	−11.7189	+	3.14006i	−0.856969	+	0.229624i
$188$	−3.79283	+	2.07787i	−0.276620	+	0.151545i
$189$	−0.152235	−	14.2169i	−0.0110735	−	1.03413i
$190$	−4.46528	−	17.4443i	−0.323945	−	1.26554i
$191$	−6.12089	+	10.6017i	−0.442892	+	0.767111i	−0.997903	−	0.0647319i	$-0.979381\pi$
$191$	−6.12089	+	10.6017i	−0.442892	+	0.767111i	0.555011	+	0.831843i	$0.312714\pi$
$192$	4.30465	−	12.6069i	0.310661	−	0.909825i
$193$	1.08900	+	1.88620i	0.0783877	+	0.135771i	0.902554	−	0.430576i	$-0.141689\pi$
$193$	1.08900	+	1.88620i	0.0783877	+	0.135771i	−0.824167	+	0.566347i	$0.808356\pi$
$194$	3.01168	+	0.843263i	0.216226	+	0.0605427i
$195$	−3.80976	+	3.80976i	−0.272823	+	0.272823i
$196$	−7.01210	+	12.1174i	−0.500864	+	0.865526i
$197$	9.97878	+	9.97878i	0.710959	+	0.710959i	0.966736	−	0.255777i	$-0.0823313\pi$
$197$	9.97878	+	9.97878i	0.710959	+	0.710959i	−0.255777	+	0.966736i	$0.582331\pi$
$198$	1.76754	−	0.994246i	0.125613	−	0.0706580i
$199$	−9.14271	+	5.27854i	−0.648109	+	0.374186i	−0.787731	−	0.616019i	$-0.788745\pi$
$199$	−9.14271	+	5.27854i	−0.648109	+	0.374186i	0.139622	+	0.990205i	$0.455411\pi$
$200$	2.51293	+	0.764745i	0.177691	+	0.0540756i
$201$	−11.7563	−	6.78749i	−0.829224	−	0.478753i
$202$	−5.18637	+	8.75499i	−0.364912	+	0.615999i
$203$	−19.0415	+	0.203897i	−1.33645	+	0.0143108i
$204$	−1.79446	+	6.14287i	−0.125637	+	0.430087i
$205$	3.79239	+	14.1534i	0.264872	+	0.988516i
$206$	−17.2917	−	17.6836i	−1.20477	−	1.23208i
$207$	0.121244	+	0.210001i	0.00842706	+	0.0145961i
$208$	6.11499	+	1.93607i	0.423998	+	0.134243i
$209$	39.8416			2.75590
$210$	−6.28045	−	10.8906i	−0.433392	−	0.751523i
$211$	5.20378	−	5.20378i	0.358243	−	0.358243i	−0.504922	−	0.863165i	$-0.668479\pi$
$211$	5.20378	−	5.20378i	0.358243	−	0.358243i	0.863165	+	0.504922i	$0.168479\pi$
$212$	0.622155	−	0.594873i	0.0427298	−	0.0408560i
$213$	−1.20237	+	4.48730i	−0.0823849	+	0.307464i
$214$	−4.25815	−	0.0477214i	−0.291081	−	0.00326217i
$215$	4.33862	+	2.50490i	0.295891	+	0.170833i
$216$	0.510904	−	15.1908i	0.0347626	−	1.03360i
$217$	−0.260703	+	1.01636i	−0.0176977	+	0.0689953i
$218$	−8.64806	−	5.12303i	−0.585721	−	0.346975i
$219$	−3.82100	+	1.02383i	−0.258199	+	0.0691843i
$220$	13.2308	−	21.7743i	0.892019	−	1.46803i
$221$	−2.97634	−	0.797507i	−0.200210	−	0.0536461i
$222$	0.768417	+	0.215155i	0.0515728	+	0.0144402i
$223$	−22.3888			−1.49926			−0.749632	−	0.661855i	$-0.769770\pi$
$223$	−22.3888			−1.49926			−0.749632	+	0.661855i	$0.769770\pi$
$224$	−8.06291	+	12.6091i	−0.538726	+	0.842481i
$225$	0.210928			0.0140619
$226$	8.12384	+	2.27465i	0.540390	+	0.151307i
$227$	−17.9753	−	4.81647i	−1.19306	−	0.319680i	−0.392967	−	0.919552i	$-0.628552\pi$
$227$	−17.9753	−	4.81647i	−1.19306	−	0.319680i	−0.800096	+	0.599872i	$0.795218\pi$
$228$	10.9132	−	17.9602i	0.722744	−	1.18944i
$229$	8.12426	−	2.17689i	0.536866	−	0.143853i	0.0198093	−	0.999804i	$-0.493694\pi$
$229$	8.12426	−	2.17689i	0.536866	−	0.143853i	0.517057	+	0.855951i	$0.327027\pi$
$230$	2.62115	+	1.55275i	0.172834	+	0.102385i
$231$	26.7898	−	7.48664i	1.76264	−	0.492585i
$232$	−20.3459	−	0.684284i	−1.33578	−	0.0449255i
$233$	14.9278	+	8.61859i	0.977955	+	0.564623i	0.901652	−	0.432462i	$-0.142355\pi$
$233$	14.9278	+	8.61859i	0.977955	+	0.564623i	0.0763032	+	0.997085i	$0.475688\pi$
$234$	0.515031	+	0.00577199i	0.0336686	+	0.000377327i
$235$	−1.12925	+	4.21442i	−0.0736642	+	0.274919i
$236$	−12.9829	+	12.4136i	−0.845117	+	0.808058i
$237$	−12.0297	+	12.0297i	−0.781414	+	0.781414i
$238$	3.59805	−	6.22483i	0.233227	−	0.403496i
$239$	−0.572679			−0.0370435			−0.0185218	−	0.999828i	$-0.505896\pi$
$239$	−0.572679			−0.0370435			−0.0185218	+	0.999828i	$0.505896\pi$
$240$	−6.19158	−	11.9286i	−0.399664	−	0.769990i
$241$	5.89318	+	10.2073i	0.379613	+	0.657510i	0.991006	−	0.133818i	$-0.0427237\pi$
$241$	5.89318	+	10.2073i	0.379613	+	0.657510i	−0.611393	+	0.791327i	$0.709390\pi$
$242$	28.5375	+	29.1844i	1.83446	+	1.87605i
$243$	−0.609557	−	2.27490i	−0.0391031	−	0.145935i
$244$	5.90822	−	20.2252i	0.378235	−	1.29479i
$245$	3.94693	+	13.5616i	0.252160	+	0.866417i
$246$	−8.71610	+	14.7134i	−0.555718	+	0.938094i
$247$	8.76321	+	5.05944i	0.557590	+	0.321925i
$248$	−0.326577	+	1.07312i	−0.0207377	+	0.0681433i
$249$	−2.40553	+	1.38883i	−0.152444	+	0.0880137i
$250$	14.7450	−	8.29412i	0.932556	−	0.524566i
$251$	−5.57539	−	5.57539i	−0.351916	−	0.351916i	0.508906	−	0.860822i	$-0.330050\pi$
$251$	−5.57539	−	5.57539i	−0.351916	−	0.351916i	−0.860822	+	0.508906i	$0.830050\pi$
$252$	−0.324625	+	1.15716i	−0.0204494	+	0.0728943i
$253$	−4.76645	+	4.76645i	−0.299664	+	0.299664i
$254$	−8.73341	−	2.44533i	−0.547983	−	0.153434i
$255$	3.22820	+	5.59141i	0.202158	+	0.350148i
$256$	−9.20847	+	13.0845i	−0.575530	+	0.817781i
$257$	−14.5328	+	25.1715i	−0.906528	+	1.57015i	−0.0876753	+	0.996149i	$0.527944\pi$
$257$	−14.5328	+	25.1715i	−0.906528	+	1.57015i	−0.818853	+	0.574004i	$0.805390\pi$
$258$	1.44993	+	5.66438i	0.0902688	+	0.352649i
$259$	−0.781156	−	0.439916i	−0.0485387	−	0.0273351i
$260$	5.67523	−	3.10914i	0.351963	−	0.192820i
$261$	−1.57902	+	0.423097i	−0.0977388	+	0.0261890i
$262$	−0.237153	+	21.1610i	−0.0146514	+	1.30733i
$263$	−15.3142	+	8.84163i	−0.944311	+	0.545198i	−0.891309	−	0.453396i	$-0.850212\pi$
$263$	−15.3142	+	8.84163i	−0.944311	+	0.545198i	−0.0530021	+	0.998594i	$0.516879\pi$
$264$	28.9660	−	6.72660i	1.78273	−	0.413993i
$265$		−	0.868424i		−	0.0533469i
$266$	−16.7039	+	16.6872i	−1.02418	+	1.02316i
$267$	−15.0198	−	15.0198i	−0.919198	−	0.919198i
$268$	11.2677	+	11.7844i	0.688282	+	0.719848i
$269$	14.4268	+	3.86566i	0.879620	+	0.235693i	0.670243	−	0.742142i	$-0.266190\pi$
$269$	14.4268	+	3.86566i	0.879620	+	0.235693i	0.209377	+	0.977835i	$0.432856\pi$
$270$	−10.7208	−	10.9638i	−0.652446	−	0.667236i
$271$	6.93172	−	12.0061i	0.421072	−	0.729319i	−0.574972	−	0.818173i	$-0.694987\pi$
$271$	6.93172	−	12.0061i	0.421072	−	0.729319i	0.996045	+	0.0888543i	$0.0283205\pi$
$272$	4.13759	−	6.47764i	0.250878	−	0.392765i
$273$	6.84317	+	1.75531i	0.414168	+	0.106236i
$274$	−2.38766	+	0.611177i	−0.144244	+	0.0369226i
$275$	1.51757	+	5.66364i	0.0915128	+	0.341531i
$276$	0.843071	+	3.45427i	0.0507469	+	0.207923i
$277$	−0.597472	+	2.22980i	−0.0358986	+	0.133975i	−0.981550	−	0.191208i	$-0.938759\pi$
$277$	−0.597472	+	2.22980i	−0.0358986	+	0.133975i	0.945651	+	0.325184i	$0.105426\pi$
$278$	−2.78898	−	4.95815i	−0.167272	−	0.297370i
$279$			0.0900747i			0.00539263i
$280$	3.57286	+	14.6707i	0.213519	+	0.876740i
$281$		−	0.680351i		−	0.0405863i	−0.999794	−	0.0202932i	$-0.993540\pi$
$281$		−	0.680351i		−	0.0405863i	0.999794	−	0.0202932i	$-0.00645996\pi$
$282$	−4.43825	+	2.49653i	−0.264294	+	0.148666i
$283$	0.0985120	−	0.367652i	0.00585593	−	0.0218546i	−0.962936	−	0.269730i	$-0.913066\pi$
$283$	0.0985120	−	0.367652i	0.00585593	−	0.0218546i	0.968792	+	0.247875i	$0.0797323\pi$
$284$	2.89741	−	4.76837i	0.171930	−	0.282951i
$285$	−5.48759	−	20.4799i	−0.325056	−	1.21313i
$286$	3.55053	+	13.8707i	0.209947	+	0.820190i
$287$	13.4395	−	13.7304i	0.793309	−	0.810482i
$288$	−0.401515	+	1.22046i	−0.0236595	+	0.0719166i
$289$	6.65377	−	11.5247i	0.391398	−	0.677921i
$290$	−14.6845	+	14.3590i	−0.862302	+	0.843188i
$291$	3.55707	+	0.953115i	0.208519	+	0.0558726i
$292$	4.74995	+	0.106479i	0.277970	+	0.00623124i
$293$	7.49220	+	7.49220i	0.437699	+	0.437699i	0.891237	−	0.453538i	$-0.149838\pi$
$293$	7.49220	+	7.49220i	0.437699	+	0.437699i	−0.453538	+	0.891237i	$0.649838\pi$
$294$	−8.09613	+	14.3595i	−0.472176	+	0.837461i
$295$			18.1220i			1.05510i
$296$	−0.813431	−	0.506834i	−0.0472797	−	0.0294591i
$297$	29.3829	−	16.9643i	1.70497	−	0.984366i
$298$	26.0372	+	0.291801i	1.50829	+	0.0169036i
$299$	−1.65367	+	0.443101i	−0.0956345	+	0.0256252i
$300$	2.96880	+	0.867250i	0.171404	+	0.0500707i
$301$	−0.0703375	−	6.56867i	−0.00405418	−	0.378612i
$302$	8.73948	−	2.23707i	0.502901	−	0.128729i
$303$	−5.99089	+	10.3765i	−0.344168	+	0.596116i
$304$	−18.6302	+	17.0306i	−1.06852	+	0.976771i
$305$	−10.6288	−	18.4096i	−0.608602	−	1.05413i
$306$	0.166419	−	0.594359i	0.00951353	−	0.0339773i
$307$	−6.27988	+	6.27988i	−0.358412	+	0.358412i	−0.863227	−	0.504816i	$-0.831561\pi$
$307$	−6.27988	+	6.27988i	−0.358412	+	0.358412i	0.504816	+	0.863227i	$0.331561\pi$
$308$	−33.4067	−	0.391063i	−1.90352	−	0.0222829i
$309$	−20.5925	−	20.5925i	−1.17147	−	1.17147i
$310$	0.554817	+	0.986334i	0.0315115	+	0.0560200i
$311$	8.55685	−	4.94030i	0.485215	−	0.280139i	−0.237372	−	0.971419i	$-0.576286\pi$
$311$	8.55685	−	4.94030i	0.485215	−	0.280139i	0.722587	+	0.691280i	$0.242953\pi$
$312$	7.22532	+	2.19884i	0.409053	+	0.124485i
$313$	−14.8734	−	8.58714i	−0.840692	−	0.485374i	0.0168075	−	0.999859i	$-0.494650\pi$
$313$	−14.8734	−	8.58714i	−0.840692	−	0.485374i	−0.857499	+	0.514485i	$0.827983\pi$
$314$	−22.1924	−	13.1466i	−1.25239	−	0.741904i
$315$	0.617459	+	1.04350i	0.0347899	+	0.0587948i
$316$	17.9202	−	9.81743i	1.00809	−	0.552274i
$317$	−5.49870	−	20.5214i	−0.308838	−	1.15260i	−0.929591	−	0.368592i	$-0.879840\pi$
$317$	−5.49870	−	20.5214i	−0.308838	−	1.15260i	0.620754	−	0.784006i	$-0.286827\pi$
$318$	0.724674	−	0.708611i	0.0406377	−	0.0397369i
$319$	−22.7212	−	39.3543i	−1.27214	−	2.20342i
$320$	3.12081	+	15.8374i	0.174458	+	0.885340i
$321$	−5.01416			−0.279863
$322$	0.00199338	−	3.99475i	0.000111087	−	0.222619i
$323$	8.57424	−	8.57424i	0.477084	−	0.477084i
$324$	0.370551	−	16.5299i	0.0205862	−	0.918329i
$325$	−0.385429	+	1.43844i	−0.0213798	+	0.0797904i
$326$	0.182068	−	16.2458i	0.0100838	−	0.899774i
$327$	−10.2498	−	5.91773i	−0.566815	−	0.327251i
$328$	15.0038	−	14.0274i	0.828445	−	0.774532i
$329$	5.50994	−	1.53980i	0.303773	−	0.0848921i
$330$	15.2906	−	25.8116i	0.841718	−	1.42088i
$331$	23.3748	−	6.26326i	1.28479	−	0.344260i	0.449113	−	0.893475i	$-0.351740\pi$
$331$	23.3748	−	6.26326i	1.28479	−	0.344260i	0.835681	+	0.549215i	$0.185073\pi$
$332$	3.24101	−	0.791021i	0.177874	−	0.0434129i
$333$	−0.0743388	−	0.0199190i	−0.00407374	−	0.00109156i
$334$	−8.26273	+	29.5101i	−0.452116	+	1.61472i
$335$	16.4491			0.898709
$336$	−9.32687	+	14.9523i	−0.508822	+	0.815715i
$337$	−4.26739			−0.232460			−0.116230	−	0.993222i	$-0.537081\pi$
$337$	−4.26739			−0.232460			−0.116230	+	0.993222i	$0.537081\pi$
$338$	3.97656	−	14.2021i	0.216296	−	0.772494i
$339$	9.59499	+	2.57097i	0.521128	+	0.139636i
$340$	−1.83865	−	7.53340i	−0.0997147	−	0.408556i
$341$	−2.41861	+	0.648063i	−0.130975	+	0.0350946i
$342$	−1.03306	+	1.74388i	−0.0558614	+	0.0942983i
$343$	12.6684	−	13.5096i	0.684032	−	0.729452i
$344$	0.236054	−	7.01864i	0.0127272	−	0.378420i
$345$	3.10663	+	1.79361i	0.167255	+	0.0965648i
$346$	0.202788	−	18.0946i	0.0109019	−	0.972772i
$347$	−0.0139833	+	0.0521865i	−0.000750664	+	0.00280152i	−0.966300	−	0.257418i	$-0.917128\pi$
$347$	−0.0139833	+	0.0521865i	−0.000750664	+	0.00280152i	0.965549	+	0.260220i	$0.0837949\pi$
$348$	−23.9643	−	0.537206i	−1.28462	−	0.0287973i
$349$	−15.4928	+	15.4928i	−0.829309	+	0.829309i	−0.987421	−	0.158112i	$-0.949459\pi$
$349$	−15.4928	+	15.4928i	−0.829309	+	0.829309i	0.158112	+	0.987421i	$0.449459\pi$
$350$	−3.00842	−	1.73891i	−0.160807	−	0.0929487i
$351$	8.61710			0.459947
$352$	−35.6596	−	2.00021i	−1.90066	−	0.106612i
$353$	−8.38161	−	14.5174i	−0.446108	−	0.772682i	0.552020	−	0.833831i	$-0.313857\pi$
$353$	−8.38161	−	14.5174i	−0.446108	−	0.772682i	−0.998129	+	0.0611484i	$0.980524\pi$
$354$	−15.1223	+	14.7871i	−0.803740	+	0.785924i
$355$	−1.45693	−	5.43735i	−0.0773259	−	0.288584i
$356$	12.2576	+	22.3744i	0.649653	+	1.18584i
$357$	4.15420	−	7.37657i	0.219863	−	0.390410i
$358$	−3.85381	−	2.28296i	−0.203680	−	0.120658i
$359$	−29.8777	−	17.2499i	−1.57689	−	0.910415i	−0.995291	−	0.0969365i	$-0.969096\pi$
$359$	−29.8777	−	17.2499i	−1.57689	−	0.910415i	−0.581595	−	0.813479i	$-0.697571\pi$
$360$	0.610009	+	1.14371i	0.0321503	+	0.0602787i
$361$	−18.0310	+	10.4102i	−0.948998	+	0.547904i
$362$	14.0965	+	25.0603i	0.740897	+	1.31714i
$363$	33.9851	+	33.9851i	1.78375	+	1.78375i
$364$	−7.29819	−	4.32830i	−0.382529	−	0.226864i
$365$	3.38938	−	3.38938i	0.177408	−	0.177408i
$366$	6.68944	−	23.8911i	0.349663	−	1.24881i
$367$	10.2644	+	17.7785i	0.535799	+	0.928032i	0.999124	+	0.0418433i	$0.0133230\pi$
$367$	10.2644	+	17.7785i	0.535799	+	0.928032i	−0.463325	+	0.886189i	$0.653344\pi$
$368$	0.191370	−	4.26628i	0.00997587	−	0.222395i
$369$	0.824679	−	1.42839i	0.0429311	−	0.0743588i
$370$	−0.936715	+	0.239774i	−0.0486975	+	0.0124653i
$371$	−0.980000	+	0.579882i	−0.0508791	+	0.0301060i
$372$	−0.370351	+	1.26780i	−0.0192018	+	0.0657324i
$373$	15.2773	−	4.09353i	0.791027	−	0.211955i	0.159386	−	0.987216i	$-0.449049\pi$
$373$	15.2773	−	4.09353i	0.791027	−	0.211955i	0.631641	+	0.775261i	$0.282382\pi$
$374$	17.1565	+	0.192275i	0.887144	+	0.00994228i
$375$	17.2513	−	9.96003i	0.890853	−	0.514334i
$376$	5.95753	−	1.38348i	0.307236	−	0.0713476i
$377$		−	11.5414i		−	0.594412i
$378$	−5.21374	+	19.4192i	−0.268166	+	0.998814i
$379$	11.2717	+	11.2717i	0.578987	+	0.578987i	0.934624	−	0.355637i	$-0.115736\pi$
$379$	11.2717	+	11.2717i	0.578987	+	0.578987i	−0.355637	+	0.934624i	$0.615736\pi$
$380$	−0.570713	+	25.4590i	−0.0292770	+	1.30602i
$381$	−10.3150	−	2.76388i	−0.528451	−	0.141598i
$382$	12.3782	−	12.1038i	0.633323	−	0.619285i
$383$	−5.14594	+	8.91303i	−0.262945	+	0.455434i	−0.967023	−	0.254688i	$-0.918027\pi$
$383$	−5.14594	+	8.91303i	−0.262945	+	0.455434i	0.704078	+	0.710123i	$0.251360\pi$
$384$	−10.6694	+	15.5272i	−0.544469	+	0.792367i
$385$	−23.5768	+	24.0872i	−1.20158	+	1.22760i
$386$	−0.763809	−	2.98394i	−0.0388769	−	0.151879i
$387$	−0.145954	−	0.544707i	−0.00741925	−	0.0276890i
$388$	−3.77988	−	2.29677i	−0.191894	−	0.116601i
$389$	5.30513	−	19.7990i	0.268981	−	1.00385i	−0.690788	−	0.723058i	$-0.742736\pi$
$389$	5.30513	−	19.7990i	0.268981	−	1.00385i	0.959769	−	0.280792i	$-0.0905972\pi$
$390$	6.64098	−	3.73557i	0.336279	−	0.189158i
$391$			2.05156i			0.103752i
$392$	14.1698	−	13.8281i	0.715684	−	0.698424i
$393$			24.9181i			1.25695i
$394$	−9.78447	−	17.3945i	−0.492934	−	0.876322i
$395$	5.33543	−	19.9121i	0.268454	−	1.00189i
$396$	−2.78622	+	0.680021i	−0.140013	+	0.0341723i
$397$	−2.02632	−	7.56231i	−0.101698	−	0.379542i	0.896252	−	0.443546i	$-0.146280\pi$
$397$	−2.02632	−	7.56231i	−0.101698	−	0.379542i	−0.997950	+	0.0640041i	$0.979613\pi$
$398$	14.4636	−	3.70231i	0.724997	−	0.185580i
$399$	−19.4469	+	19.8679i	−0.973565	+	0.994640i
$400$	−3.13060	−	1.99966i	−0.156530	−	0.0999832i
$401$	−7.09985	+	12.2973i	−0.354549	+	0.614098i	−0.987041	−	0.160470i	$-0.948699\pi$
$401$	−7.09985	+	12.2973i	−0.354549	+	0.614098i	0.632491	+	0.774567i	$0.282032\pi$
$402$	13.4220	+	13.7263i	0.669429	+	0.684604i
$403$	−0.614273	−	0.164594i	−0.0305991	−	0.00819901i
$404$	10.4014	−	9.94525i	0.517487	−	0.494795i
$405$	−11.7951	−	11.7951i	−0.586104	−	0.586104i
$406$	26.0092	+	6.98307i	1.29082	+	0.346564i
$407$		−	2.13939i		−	0.106046i
$408$	4.78611	−	7.68135i	0.236948	−	0.380283i
$409$	−22.8759	+	13.2074i	−1.13114	+	0.653065i	−0.944222	−	0.329310i	$-0.893184\pi$
$409$	−22.8759	+	13.2074i	−1.13114	+	0.653065i	−0.186920	+	0.982375i	$0.559851\pi$
$410$	0.232219	−	20.7207i	0.0114685	−	1.02332i
$411$	−2.80316	+	0.751104i	−0.138270	+	0.0370492i
$412$	16.8055	+	30.6758i	0.827947	+	1.51129i
$413$	20.4503	−	12.1008i	1.00630	−	0.595442i
$414$	−0.0850394	−	0.332220i	−0.00417946	−	0.0163277i
$415$	1.68288	−	2.91483i	0.0826092	−	0.143083i
$416$	−7.58938	−	4.96833i	−0.372100	−	0.243592i
$417$	−3.34915	−	5.80091i	−0.164009	−	0.284072i
$418$	−54.2577	−	15.1920i	−2.65383	−	0.743065i
$419$	−15.6893	+	15.6893i	−0.766471	+	0.766471i	−0.977483	−	0.211012i	$-0.932324\pi$
$419$	−15.6893	+	15.6893i	−0.766471	+	0.766471i	0.211012	+	0.977483i	$0.432324\pi$
$420$	4.40025	+	17.2260i	0.214710	+	0.840545i
$421$	25.7068	+	25.7068i	1.25287	+	1.25287i	0.954427	+	0.298444i	$0.0964675\pi$
$421$	25.7068	+	25.7068i	1.25287	+	1.25287i	0.298444	+	0.954427i	$0.403532\pi$
$422$	−9.07096	+	5.10245i	−0.441568	+	0.248383i
$423$	0.425327	−	0.245563i	0.0206801	−	0.0119397i
$424$	−1.07411	+	0.572886i	−0.0521632	+	0.0278218i
$425$	1.54546	+	0.892270i	0.0749657	+	0.0432815i
$426$	3.34848	−	5.65249i	0.162235	−	0.273864i
$427$	−13.6776	+	24.2872i	−0.661905	+	1.17534i
$428$	5.78071	+	1.68867i	0.279421	+	0.0816247i
$429$	4.36340	+	16.2844i	0.210667	+	0.786220i
$430$	−4.95335	−	5.06563i	−0.238872	−	0.244287i
$431$	12.3981	+	21.4741i	0.597194	+	1.03437i	0.993233	+	0.116137i	$0.0370510\pi$
$431$	12.3981	+	21.4741i	0.597194	+	1.03437i	−0.396039	+	0.918234i	$0.629616\pi$
$432$	−6.48818	+	20.4926i	−0.312163	+	0.985950i
$433$	5.22863			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$433$	5.22863			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$434$	0.742586	−	1.28472i	0.0356453	−	0.0616683i
$435$	−17.1000	+	17.1000i	−0.819881	+	0.819881i
$436$	9.82380	+	10.2743i	0.470474	+	0.492051i
$437$	1.74371	−	6.50762i	0.0834131	−	0.311302i
$438$	5.59398	+	0.0626921i	0.267291	+	0.00299555i
$439$	−19.1771	−	11.0719i	−0.915273	−	0.528433i	−0.0331491	−	0.999450i	$-0.510554\pi$
$439$	−19.1771	−	11.0719i	−0.915273	−	0.528433i	−0.882124	+	0.471017i	$0.843887\pi$
$440$	−26.3210	+	24.6081i	−1.25480	+	1.17314i
$441$	0.765272	−	1.39358i	0.0364415	−	0.0663610i
$442$	3.74919	+	2.22098i	0.178331	+	0.105641i
$443$	21.8067	−	5.84309i	1.03607	−	0.277614i	0.299585	−	0.954070i	$-0.403152\pi$
$443$	21.8067	−	5.84309i	1.03607	−	0.277614i	0.736483	+	0.676456i	$0.236485\pi$
$444$	−0.964419	−	0.586011i	−0.0457693	−	0.0278109i
$445$	24.8614	+	6.66159i	1.17854	+	0.315790i
$446$	30.4899	+	8.53708i	1.44374	+	0.404243i
$447$	30.6599			1.45017
$448$	15.7884	−	14.0971i	0.745930	−	0.666024i
$449$	−36.3678			−1.71630			−0.858152	−	0.513396i	$-0.828387\pi$
$449$	−36.3678			−1.71630			−0.858152	+	0.513396i	$0.828387\pi$
$450$	−0.287249	−	0.0804290i	−0.0135411	−	0.00379146i
$451$	44.2871	+	11.8667i	2.08540	+	0.558781i
$452$	−10.1960	−	6.19541i	−0.479579	−	0.291408i
$453$	10.2603	−	2.74924i	0.482072	−	0.129171i
$454$	22.6429	+	13.4134i	1.06268	+	0.629523i
$455$	−8.24456	+	2.30402i	−0.386511	+	0.108014i
$456$	−21.7104	+	20.2976i	−1.01668	+	0.950522i
$457$	21.5807	+	12.4596i	1.00950	+	0.582837i	0.911046	−	0.412304i	$-0.135276\pi$
$457$	21.5807	+	12.4596i	1.00950	+	0.582837i	0.0984570	+	0.995141i	$0.468609\pi$
$458$	−11.8940	−	0.133297i	−0.555770	−	0.00622856i
$459$	2.67261	−	9.97431i	0.124747	−	0.465561i
$460$	−2.97751	−	3.11406i	−0.138827	−	0.145194i
$461$	−1.60588	+	1.60588i	−0.0747933	+	0.0747933i	−0.743514	−	0.668721i	$-0.766842\pi$
$461$	−1.60588	+	1.60588i	−0.0747933	+	0.0747933i	0.668721	+	0.743514i	$0.266842\pi$
$462$	−39.3381	−	0.0196297i	−1.83017	−	0.000913256i
$463$	−14.8176			−0.688634			−0.344317	−	0.938853i	$-0.611890\pi$
$463$	−14.8176			−0.688634			−0.344317	+	0.938853i	$0.611890\pi$
$464$	27.4469	+	8.69000i	1.27419	+	0.403423i
$465$	0.666254	+	1.15399i	0.0308968	+	0.0535148i
$466$	−17.0429	−	17.4293i	−0.789499	−	0.807395i
$467$	−3.21315	−	11.9916i	−0.148687	−	0.554907i	−0.999564	−	0.0295414i	$-0.990595\pi$
$467$	−3.21315	−	11.9916i	−0.148687	−	0.554907i	0.850877	−	0.525365i	$-0.176071\pi$
$468$	−0.699188	−	0.204247i	−0.0323200	−	0.00944133i
$469$	−10.9837	−	18.5625i	−0.507181	−	0.857135i
$470$	3.14486	−	5.30876i	0.145062	−	0.244875i
$471$	−26.3028	−	15.1859i	−1.21197	−	0.699730i
$472$	22.4141	−	11.9548i	1.03169	−	0.550265i
$473$	13.5759	−	7.83804i	0.624220	−	0.360393i
$474$	20.9696	−	11.7955i	0.963165	−	0.541784i
$475$	−4.14387	−	4.14387i	−0.190134	−	0.190134i
$476$	−7.27356	+	7.10524i	−0.333383	+	0.325668i
$477$	−0.0691218	+	0.0691218i	−0.00316487	+	0.00316487i
$478$	0.779896	+	0.218369i	0.0356716	+	0.00998795i
$479$	1.02709	+	1.77897i	0.0469288	+	0.0812831i	0.888536	−	0.458808i	$-0.151723\pi$
$479$	1.02709	+	1.77897i	0.0469288	+	0.0812831i	−0.841607	+	0.540091i	$0.818390\pi$
$480$	3.88341	+	18.6058i	0.177252	+	0.849234i
$481$	0.271679	−	0.470563i	0.0123875	−	0.0214558i
$482$	−4.13341	−	16.1478i	−0.188272	−	0.735513i
$483$	−0.0503645	−	4.70344i	−0.00229166	−	0.214014i
$484$	−27.7351	−	50.6261i	−1.26069	−	2.30119i
$485$	−4.31018	+	1.15491i	−0.195715	+	0.0524417i
$486$	−0.0373249	+	3.33047i	−0.00169309	+	0.151073i
$487$	−35.4045	+	20.4408i	−1.60433	+	0.926261i	−0.613724	+	0.789521i	$0.710329\pi$
$487$	−35.4045	+	20.4408i	−1.60433	+	0.926261i	−0.990607	+	0.136740i	$0.956338\pi$
$488$	−15.7581	+	25.2906i	−0.713337	+	1.14485i
$489$		−	19.1302i		−	0.865098i
$490$	−0.203910	−	19.9737i	−0.00921173	−	0.902318i
$491$	−0.278015	−	0.278015i	−0.0125466	−	0.0125466i	0.700806	−	0.713352i	$-0.252824\pi$
$491$	−0.278015	−	0.278015i	−0.0125466	−	0.0125466i	−0.713352	+	0.700806i	$0.752824\pi$
$492$	17.4803	−	16.7138i	0.788073	−	0.753515i
$493$	−13.3592	−	3.57958i	−0.601667	−	0.161216i
$494$	−10.0049	−	10.2316i	−0.450140	−	0.460344i
$495$	−1.44673	+	2.50580i	−0.0650255	+	0.112628i
$496$	0.853938	−	1.33689i	0.0383429	−	0.0600282i
$497$	−5.16309	+	5.27486i	−0.231596	+	0.236610i
$498$	3.80552	−	0.974112i	0.170529	−	0.0436510i
$499$	−3.19039	−	11.9067i	−0.142822	−	0.533018i	−0.999843	−	0.0177363i	$-0.994354\pi$
$499$	−3.19039	−	11.9067i	−0.142822	−	0.533018i	0.857021	−	0.515281i	$-0.172313\pi$
$500$	−23.2429	+	5.67282i	−1.03946	+	0.253696i
$501$	−9.33912	+	34.8541i	−0.417241	+	1.55717i
$502$	5.46682	+	9.71874i	0.243996	+	0.433768i
$503$		−	0.367839i		−	0.0164011i	−0.999966	−	0.00820057i	$-0.997390\pi$
$503$		−	0.367839i		−	0.0164011i	0.999966	−	0.00820057i	$-0.00261035\pi$
$504$	0.883324	−	1.45208i	0.0393464	−	0.0646810i
$505$		−	14.5186i		−	0.646068i
$506$	8.30862	−	4.67363i	0.369363	−	0.207768i
$507$	4.49459	−	16.7740i	0.199612	−	0.744960i
$508$	10.9611	+	6.66028i	0.486318	+	0.295502i
$509$	−2.09820	−	7.83060i	−0.0930012	−	0.347085i	0.903708	−	0.428150i	$-0.140835\pi$
$509$	−2.09820	−	7.83060i	−0.0930012	−	0.347085i	−0.996709	+	0.0810649i	$0.974168\pi$
$510$	−2.26422	−	8.84554i	−0.100262	−	0.391687i
$511$	−6.08808	−	1.56162i	−0.269321	−	0.0690822i
$512$	17.5297	−	14.3077i	0.774711	−	0.632316i
$513$	−16.9552	+	29.3673i	−0.748591	+	1.29660i
$514$	29.3894	−	28.7380i	1.29631	−	1.26758i
$515$	34.0855	+	9.13319i	1.50199	+	0.402457i
$516$	0.185317	−	8.26684i	0.00815815	−	0.363927i
$517$	9.65374	+	9.65374i	0.424571	+	0.424571i
$518$	0.896063	+	0.896958i	0.0393708	+	0.0394101i
$519$		−	21.3072i		−	0.935282i
$520$	−8.91430	+	2.07011i	−0.390918	+	0.0907805i
$521$	−11.5215	+	6.65193i	−0.504766	+	0.291427i	−0.730679	−	0.682721i	$-0.760797\pi$
$521$	−11.5215	+	6.65193i	−0.504766	+	0.291427i	0.225914	+	0.974147i	$0.427463\pi$
$522$	2.31170	+	0.0259074i	0.101180	+	0.00113394i
$523$	−27.4536	+	7.35616i	−1.20046	+	0.321663i	−0.803013	−	0.595962i	$-0.796771\pi$
$523$	−27.4536	+	7.35616i	−1.20046	+	0.321663i	−0.397448	+	0.917625i	$0.630104\pi$
$524$	8.39189	−	28.7275i	0.366602	−	1.25497i
$525$	−3.56504	−	2.00769i	−0.155591	−	0.0876229i
$526$	24.2268	−	6.20142i	1.05634	−	0.270395i
$527$	−0.381036	+	0.659973i	−0.0165982	+	0.0287489i
$528$	−42.0119	−	1.88451i	−1.82833	−	0.0820126i
$529$	−10.9301	−	18.9314i	−0.475220	−	0.823106i
$530$	−0.331139	+	1.18265i	−0.0143838	+	0.0513712i
$531$	1.44241	−	1.44241i	0.0625954	−	0.0625954i
$532$	29.1110	−	16.3559i	1.26212	−	0.709120i
$533$	8.23408	+	8.23408i	0.356657	+	0.356657i
$534$	14.7273	+	26.1818i	0.637314	+	1.13300i
$535$	5.26176	−	3.03788i	0.227486	−	0.131339i
$536$	−10.8512	−	20.3449i	−0.468701	−	0.878768i
$537$	−4.56759	−	2.63710i	−0.197106	−	0.113799i
$538$	−18.1730	−	10.7655i	−0.783494	−	0.464134i
$539$	42.9251	+	10.5220i	1.84892	+	0.453213i
$540$	10.4194	+	19.0189i	0.448377	+	0.818442i
$541$	−4.75802	−	17.7572i	−0.204563	−	0.763441i	−0.989582	−	0.143969i	$-0.954013\pi$
$541$	−4.75802	−	17.7572i	−0.204563	−	0.763441i	0.785019	−	0.619472i	$-0.212653\pi$
$542$	−14.0179	+	13.7072i	−0.602122	+	0.588775i
$543$	16.9279	+	29.3199i	0.726445	+	1.25824i
$544$	−8.10471	+	7.24379i	−0.347487	+	0.310575i
$545$	14.3413			0.614312
$546$	−8.64997	−	4.99982i	−0.370185	−	0.213973i
$547$	−22.9801	+	22.9801i	−0.982558	+	0.982558i	−0.999850	−	0.0172930i	$-0.994495\pi$
$547$	−22.9801	+	22.9801i	−0.982558	+	0.982558i	0.0172930	+	0.999850i	$0.494495\pi$
$548$	3.48465	+	0.0781153i	0.148857	+	0.00333692i
$549$	−0.619309	+	2.31129i	−0.0264315	+	0.0986436i
$550$	0.0929249	−	8.29163i	0.00396233	−	0.353556i
$551$	39.3334	+	22.7091i	1.67566	+	0.967442i
$552$	0.169024	−	5.02563i	0.00719416	−	0.213905i
$553$	−26.0331	+	7.27518i	−1.10704	+	0.309372i
$554$	1.66390	−	2.80880i	0.0706925	−	0.119334i
$555$	−1.09972	+	0.294670i	−0.0466806	+	0.0125080i
$556$	1.90754	+	7.81566i	0.0808976	+	0.331458i
$557$	4.50327	+	1.20665i	0.190810	+	0.0511273i	0.352958	−	0.935639i	$-0.385176\pi$
$557$	4.50327	+	1.20665i	0.190810	+	0.0511273i	−0.162149	+	0.986766i	$0.551842\pi$
$558$	0.0343464	−	0.122667i	0.00145400	−	0.00519291i
$559$	3.98138			0.168394
$560$	0.728427	−	21.3414i	0.0307817	−	0.901840i
$561$	20.2026			0.852954
$562$	−0.259425	+	0.926527i	−0.0109432	+	0.0390832i
$563$	−4.04301	−	1.08332i	−0.170393	−	0.0456566i	0.172614	−	0.984990i	$-0.444779\pi$
$563$	−4.04301	−	1.08332i	−0.170393	−	0.0456566i	−0.343007	+	0.939333i	$0.611445\pi$
$564$	6.99613	−	1.70752i	0.294590	−	0.0718995i
$565$	−11.6264	+	3.11530i	−0.489128	+	0.131061i
$566$	−0.274347	+	0.463118i	−0.0115317	+	0.0194663i
$567$	−5.43448	+	21.1866i	−0.228227	+	0.889755i
$568$	−5.76403	+	5.38893i	−0.241853	+	0.226115i
$569$	3.88173	+	2.24111i	0.162730	+	0.0939524i	0.579154	−	0.815218i	$-0.303383\pi$
$569$	3.88173	+	2.24111i	0.162730	+	0.0939524i	−0.416423	+	0.909171i	$0.636717\pi$
$570$	−0.336020	+	29.9828i	−0.0140743	+	1.25584i
$571$	−0.126176	+	0.470896i	−0.00528031	+	0.0197064i	−0.968516	−	0.248952i	$-0.919914\pi$
$571$	−0.126176	+	0.470896i	−0.00528031	+	0.0197064i	0.963235	+	0.268659i	$0.0865804\pi$
$572$	0.453797	−	20.2435i	0.0189742	−	0.846422i
$573$	14.4143	−	14.4143i	0.602167	−	0.602167i
$574$	−23.5380	+	13.5740i	−0.982457	+	0.566568i
$575$	0.991504			0.0413486
$576$	1.01217	−	1.50897i	0.0421739	−	0.0628739i
$577$	5.31982	+	9.21420i	0.221467	+	0.383592i	0.955254	−	0.295788i	$-0.0955821\pi$
$577$	5.31982	+	9.21420i	0.221467	+	0.383592i	−0.733787	+	0.679380i	$0.762249\pi$
$578$	−13.4558	+	13.1576i	−0.559689	+	0.547283i
$579$	−0.938680	−	3.50320i	−0.0390102	−	0.145588i
$580$	25.4731	−	13.9553i	1.05771	−	0.579460i
$581$	−4.41305	+	0.0472550i	−0.183084	+	0.00196047i
$582$	−4.48072	−	2.65434i	−0.185732	−	0.110026i
$583$	−2.35331	−	1.35868i	−0.0974641	−	0.0562709i
$584$	−6.42806	−	1.95621i	−0.265995	−	0.0809487i
$585$	−0.636420	+	0.367437i	−0.0263127	+	0.0151917i
$586$	−7.34631	−	13.0600i	−0.303473	−	0.539505i
$587$	−13.2861	−	13.2861i	−0.548376	−	0.548376i	0.377595	−	0.925971i	$-0.376751\pi$
$587$	−13.2861	−	13.2861i	−0.548376	−	0.548376i	−0.925971	+	0.377595i	$0.876751\pi$
$588$	16.5010	−	16.4681i	0.680491	−	0.679134i
$589$	1.76960	−	1.76960i	0.0729151	−	0.0729151i
$590$	6.91011	−	24.6792i	0.284485	−	1.01603i
$591$	−11.7497	−	20.3511i	−0.483319	−	0.837133i
$592$	0.914500	+	1.00040i	0.0375857	+	0.0411160i
$593$	0.198497	−	0.343806i	0.00815128	−	0.0141184i	−0.861921	−	0.507043i	$-0.830739\pi$
$593$	0.198497	−	0.343806i	0.00815128	−	0.0141184i	0.870072	+	0.492924i	$0.164072\pi$
$594$	−46.4835	+	11.8985i	−1.90724	+	0.488203i
$595$	0.109840	+	10.2577i	0.00450298	+	0.420524i
$596$	−35.3471	−	10.3256i	−1.44788	−	0.422954i
$597$	16.9806	−	4.54994i	0.694970	−	0.186217i
$598$	2.42100	+	0.0271323i	0.0990019	+	0.00110952i
$599$	11.9718	−	6.91190i	0.489153	−	0.282412i	−0.235070	−	0.971978i	$-0.575532\pi$
$599$	11.9718	−	6.91190i	0.489153	−	0.282412i	0.724223	+	0.689566i	$0.242199\pi$
$600$	−3.71234	−	2.31309i	−0.151556	−	0.0944315i
$601$			8.73396i			0.356266i	0.984006	+	0.178133i	$0.0570057\pi$
$601$			8.73396i			0.356266i	−0.984006	+	0.178133i	$0.942994\pi$
$602$	−2.40892	+	8.97229i	−0.0981801	+	0.365683i
$603$	−1.30926	−	1.30926i	−0.0533170	−	0.0533170i
$604$	−12.7548	−	0.285923i	−0.518984	−	0.0116341i
$605$	−56.2535	−	15.0731i	−2.28703	−	0.612807i
$606$	12.1153	−	11.8468i	0.492150	−	0.481242i
$607$	14.3937	−	24.9305i	0.584220	−	1.01190i	−0.410752	−	0.911747i	$-0.634734\pi$
$607$	14.3937	−	24.9305i	0.584220	−	1.01190i	0.994972	−	0.100152i	$-0.0319330\pi$
$608$	31.8653	−	16.0890i	1.29231	−	0.652495i
$609$	30.7153	+	7.87864i	1.24465	+	0.319259i
$610$	7.45490	+	29.1237i	0.301840	+	1.17918i
$611$	0.897436	+	3.34928i	0.0363064	+	0.135497i
$612$	−0.453271	+	0.745964i	−0.0183224	+	0.0301538i
$613$	9.13486	−	34.0918i	0.368954	−	1.37695i	−0.493028	−	0.870014i	$-0.664110\pi$
$613$	9.13486	−	34.0918i	0.368954	−	1.37695i	0.861981	−	0.506940i	$-0.169223\pi$
$614$	10.9468	−	6.15759i	0.441775	−	0.248500i
$615$		−	24.3996i		−	0.983886i
$616$	45.3453	+	13.2709i	1.82702	+	0.534699i
$617$		−	33.4612i		−	1.34710i	−0.739143	−	0.673548i	$-0.764769\pi$
$617$		−	33.4612i		−	1.34710i	0.739143	−	0.673548i	$-0.235231\pi$
$618$	20.1915	+	35.8958i	0.812222	+	1.44394i
$619$	−2.41362	+	9.00777i	−0.0970118	+	0.362053i	−0.997317	−	0.0732067i	$-0.976677\pi$
$619$	−2.41362	+	9.00777i	−0.0970118	+	0.362053i	0.900305	+	0.435260i	$0.143343\pi$
$620$	−0.379470	−	1.55478i	−0.0152399	−	0.0624417i
$621$	−1.48492	−	5.54180i	−0.0595878	−	0.222385i
$622$	−13.5368	+	3.46507i	−0.542778	+	0.138937i
$623$	−9.08349	−	32.5038i	−0.363922	−	1.30224i
$624$	−9.00127	−	5.74955i	−0.360339	−	0.230166i
$625$	−9.74706	+	16.8824i	−0.389882	+	0.675296i
$626$	16.9807	+	17.3657i	0.678687	+	0.694071i
$627$	−64.0834	−	17.1711i	−2.55924	−	0.685747i
$628$	25.2096	+	26.3657i	1.00597	+	1.05211i
$629$	−0.460415	−	0.460415i	−0.0183580	−	0.0183580i
$630$	−0.442979	−	1.65653i	−0.0176487	−	0.0659976i
$631$		−	22.2587i		−	0.886105i	−0.896496	−	0.443053i	$-0.853896\pi$
$631$		−	22.2587i		−	0.886105i	0.896496	−	0.443053i	$-0.146104\pi$
$632$	−28.1478	+	6.53660i	−1.11966	+	0.260012i
$633$	−10.6128	+	6.12730i	−0.421821	+	0.243538i
$634$	−0.336700	+	30.0436i	−0.0133721	+	1.19318i
$635$	12.4988	−	3.34905i	0.496001	−	0.132903i
$636$	−1.25709	+	0.688687i	−0.0498468	+	0.0273082i
$637$	8.10527	+	7.76534i	0.321142	+	0.307674i
$638$	15.9364	+	62.2580i	0.630928	+	2.46482i
$639$	−0.316819	+	0.548747i	−0.0125332	+	0.0217081i
$640$	1.78895	−	22.7580i	0.0707146	−	0.899590i
$641$	4.13758	+	7.16649i	0.163424	+	0.283059i	0.936095	−	0.351748i	$-0.114413\pi$
$641$	4.13758	+	7.16649i	0.163424	+	0.283059i	−0.772670	+	0.634808i	$0.781079\pi$
$642$	6.82847	+	1.91195i	0.269498	+	0.0754587i
$643$	4.19175	−	4.19175i	0.165307	−	0.165307i	−0.619606	−	0.784913i	$-0.712708\pi$
$643$	4.19175	−	4.19175i	0.165307	−	0.165307i	0.784913	+	0.619606i	$0.212708\pi$
$644$	−1.52596	+	5.43945i	−0.0601311	+	0.214344i
$645$	−5.89890	−	5.89890i	−0.232269	−	0.232269i
$646$	−14.9462	+	8.40728i	−0.588049	+	0.330780i
$647$	18.2428	−	10.5325i	0.717199	−	0.414075i	−0.0965221	−	0.995331i	$-0.530772\pi$
$647$	18.2428	−	10.5325i	0.717199	−	0.414075i	0.813721	+	0.581256i	$0.197439\pi$
$648$	−6.80767	+	22.3698i	−0.267430	+	0.878768i
$649$	49.1081	+	28.3526i	1.92766	+	1.11294i
$650$	1.07339	−	1.81196i	0.0421016	−	0.0710708i
$651$	0.857366	−	1.52242i	0.0336028	−	0.0596683i
$652$	−6.44266	+	22.0548i	−0.252314	+	0.863732i
$653$	4.43173	+	16.5394i	0.173427	+	0.647239i	0.996814	+	0.0797585i	$0.0254149\pi$
$653$	4.43173	+	16.5394i	0.173427	+	0.647239i	−0.823387	+	0.567480i	$0.807918\pi$
$654$	11.7021	+	11.9673i	0.457587	+	0.467960i
$655$	−15.0969	−	26.1485i	−0.589883	−	1.02171i
$656$	−25.7815	+	13.3819i	−1.00660	+	0.522476i
$657$	−0.539552			−0.0210499
$658$	−8.09079	−	0.00403730i	−0.315412	−	0.000157390i
$659$	19.9513	−	19.9513i	0.777192	−	0.777192i	−0.202161	−	0.979352i	$-0.564796\pi$
$659$	19.9513	−	19.9513i	0.777192	−	0.777192i	0.979352	+	0.202161i	$0.0647964\pi$
$660$	−30.6655	+	29.3208i	−1.19365	+	1.14131i
$661$	−5.55822	+	20.7436i	−0.216190	+	0.806831i	0.769555	+	0.638581i	$0.220478\pi$
$661$	−5.55822	+	20.7436i	−0.216190	+	0.806831i	−0.985744	+	0.168250i	$0.946188\pi$
$662$	−34.2209	−	0.383516i	−1.33003	−	0.0149058i
$663$	4.44359	+	2.56551i	0.172575	+	0.0996361i
$664$	−4.71536	−	0.158589i	−0.182991	−	0.00615445i
$665$	8.37005	−	32.6311i	0.324577	−	1.26538i
$666$	0.0936421	+	0.0554727i	0.00362856	+	0.00214952i
$667$	−7.42246	+	1.98884i	−0.287399	+	0.0770083i
$668$	22.5050	−	37.0372i	0.870744	−	1.43301i
$669$	36.0114	+	9.64922i	1.39228	+	0.373060i
$670$	−22.4010	−	6.27221i	−0.865425	−	0.242317i
$671$	−66.5165			−2.56784
$672$	18.4032	−	16.8062i	0.709917	−	0.648313i
$673$	21.0339			0.810796			0.405398	−	0.914140i	$-0.367133\pi$
$673$	21.0339			0.810796			0.405398	+	0.914140i	$0.367133\pi$
$674$	5.81150	+	1.62720i	0.223851	+	0.0626775i
$675$	−4.82051	−	1.29165i	−0.185542	−	0.0497157i
$676$	−10.8309	+	17.8247i	−0.416571	+	0.685566i
$677$	6.02033	−	1.61314i	0.231380	−	0.0619982i	−0.141266	−	0.989972i	$-0.545117\pi$
$677$	6.02033	−	1.61314i	0.231380	−	0.0619982i	0.372646	+	0.927974i	$0.378451\pi$
$678$	−12.0865	−	7.15992i	−0.464179	−	0.274975i
$679$	4.18137	+	4.09277i	0.160466	+	0.157066i
$680$	−0.368624	+	10.9604i	−0.0141361	+	0.420311i
$681$	26.8367	+	15.4942i	1.02838	+	0.593737i
$682$	3.54086	+	0.0396827i	0.135587	+	0.00151953i
$683$	−5.78001	+	21.5713i	−0.221166	+	0.825402i	0.762739	+	0.646707i	$0.223854\pi$
$683$	−5.78001	+	21.5713i	−0.221166	+	0.825402i	−0.983904	+	0.178695i	$0.942812\pi$
$684$	2.07182	−	1.98097i	0.0792180	−	0.0757442i
$685$	2.48651	−	2.48651i	0.0950048	−	0.0950048i
$686$	−22.4037	+	13.5673i	−0.855379	+	0.518003i
$687$	−14.0057			−0.534351
$688$	−2.99775	+	9.46824i	−0.114288	+	0.360973i
$689$	−0.345076	−	0.597689i	−0.0131463	−	0.0227701i
$690$	−3.54680	−	3.62720i	−0.135024	−	0.138085i
$691$	9.94413	+	37.1120i	0.378292	+	1.41181i	0.848474	+	0.529237i	$0.177522\pi$
$691$	9.94413	+	37.1120i	0.378292	+	1.41181i	−0.470182	+	0.882570i	$0.655812\pi$
$692$	−7.17583	+	24.5646i	−0.272784	+	0.933805i
$693$	3.79379	−	0.0406240i	0.144114	−	0.00154318i
$694$	0.0389423	−	0.0657375i	0.00147823	−	0.00249536i
$695$	7.02907	+	4.05824i	0.266628	+	0.153938i
$696$	32.4306	+	9.86941i	1.22928	+	0.374099i
$697$	12.0848	−	6.97715i	0.457743	−	0.264278i
$698$	27.0062	−	15.1911i	1.02220	−	0.574991i
$699$	−20.2963	−	20.2963i	−0.767676	−	0.767676i
$700$	3.43391	+	3.51526i	0.129790	+	0.132864i
$701$	1.40129	−	1.40129i	0.0529259	−	0.0529259i	−0.680148	−	0.733074i	$-0.738085\pi$
$701$	1.40129	−	1.40129i	0.0529259	−	0.0529259i	0.733074	+	0.680148i	$0.238085\pi$
$702$	−11.7351	−	3.28579i	−0.442913	−	0.124014i
$703$	1.06913	+	1.85178i	0.0403229	+	0.0698413i
$704$	47.7999	+	16.3214i	1.80153	+	0.615134i
$705$	3.63270	−	6.29202i	0.136815	−	0.236971i
$706$	5.87877	+	22.9663i	0.221250	+	0.864349i
$707$	−16.3839	+	9.69463i	−0.616181	+	0.364604i
$708$	26.2325	−	14.3713i	0.985879	−	0.540107i
$709$	−8.42034	+	2.25622i	−0.316232	+	0.0847342i	−0.413444	−	0.910530i	$-0.635674\pi$
$709$	−8.42034	+	2.25622i	−0.316232	+	0.0847342i	0.0972117	+	0.995264i	$0.469008\pi$
$710$	−0.0892120	+	7.96033i	−0.00334807	+	0.298746i
$711$	−2.00956	+	1.16022i	−0.0753645	+	0.0435117i
$712$	−8.16133	−	35.1442i	−0.305859	−	1.31709i
$713$			0.423412i			0.0158569i
$714$	−8.47011	+	8.46166i	−0.316986	+	0.316670i
$715$	−14.4450	−	14.4450i	−0.540211	−	0.540211i
$716$	4.37775	+	4.57852i	0.163604	+	0.171107i
$717$	0.921129	+	0.246816i	0.0344002	+	0.00921750i
$718$	34.1110	+	34.8843i	1.27301	+	1.30187i
$719$	−13.3330	+	23.0934i	−0.497236	+	0.861239i	−0.999995	−	0.00318810i	$-0.998985\pi$
$719$	−13.3330	+	23.0934i	−0.497236	+	0.861239i	0.502758	+	0.864427i	$0.332319\pi$
$720$	−0.394626	−	1.79015i	−0.0147068	−	0.0667149i
$721$	−12.4537	−	44.5635i	−0.463799	−	1.65963i
$722$	28.5247	−	7.30158i	1.06158	−	0.271737i
$723$	−5.07974	−	18.9578i	−0.188917	−	0.705050i
$724$	−9.64141	−	39.5033i	−0.358320	−	1.46813i
$725$	−1.72999	+	6.45640i	−0.0642501	+	0.239785i
$726$	−33.3233	−	59.2410i	−1.23674	−	2.19864i
$727$			37.7224i			1.39905i	0.714610	+	0.699523i	$0.246604\pi$
$727$			37.7224i			1.39905i	−0.714610	+	0.699523i	$0.753396\pi$
$728$	8.28852	+	8.67731i	0.307193	+	0.321603i
$729$			28.7229i			1.06381i
$730$	−5.90819	+	3.32338i	−0.218672	+	0.123004i
$731$	1.23483	−	4.60846i	0.0456719	−	0.170450i
$732$	−18.2199	+	29.9851i	−0.673425	+	1.10828i
$733$	5.88050	+	21.9463i	0.217201	+	0.810606i	0.985380	+	0.170371i	$0.0544965\pi$
$733$	5.88050	+	21.9463i	0.217201	+	0.810606i	−0.768179	+	0.640235i	$0.778837\pi$
$734$	−7.19936	−	28.1254i	−0.265733	−	1.03813i
$735$	−0.503639	−	23.5142i	−0.0185770	−	0.867336i
$736$	−1.88739	+	5.73701i	−0.0695703	+	0.211469i
$737$	25.7352	−	44.5747i	0.947969	−	1.64193i
$738$	−1.66774	+	1.63077i	−0.0613903	+	0.0600295i
$739$	25.3304	+	6.78727i	0.931795	+	0.249674i	0.692620	−	0.721303i	$-0.256456\pi$
$739$	25.3304	+	6.78727i	0.931795	+	0.249674i	0.239175	+	0.970977i	$0.423123\pi$
$740$	1.36708	+	0.0306458i	0.0502550	+	0.00112656i
$741$	−11.9147	−	11.9147i	−0.437697	−	0.437697i
$742$	1.55572	−	0.416021i	0.0571121	−	0.0152726i
$743$			20.7110i			0.759812i	0.925025	+	0.379906i	$0.124044\pi$
$743$			20.7110i			0.759812i	−0.925025	+	0.379906i	$0.875956\pi$
$744$	0.987783	−	1.58532i	0.0362139	−	0.0581206i
$745$	−32.1739	+	18.5756i	−1.17876	+	0.680558i
$746$	−22.3661	−	0.250658i	−0.818880	−	0.00917724i
$747$	−0.365952	+	0.0980566i	−0.0133895	+	0.00358770i
$748$	−23.2911	−	6.80382i	−0.851607	−	0.248772i
$749$	−6.94168	−	3.90928i	−0.253643	−	0.142842i
$750$	−27.2913	+	6.98585i	−0.996538	+	0.255087i
$751$	7.73865	−	13.4037i	0.282387	−	0.489109i	−0.689585	−	0.724205i	$-0.742207\pi$
$751$	7.73865	−	13.4037i	0.282387	−	0.489109i	0.971972	+	0.235096i	$0.0755403\pi$
$752$	−8.64073	−	0.387593i	−0.315095	−	0.0141341i
$753$	6.56486	+	11.3707i	0.239237	+	0.414370i
$754$	−4.40086	+	15.7175i	−0.160270	+	0.572398i
$755$	−9.10132	+	9.10132i	−0.331231	+	0.331231i
$756$	14.5050	−	24.4577i	0.527542	−	0.889518i
$757$	18.4631	+	18.4631i	0.671051	+	0.671051i	0.957958	−	0.286907i	$-0.0926272\pi$
$757$	18.4631	+	18.4631i	0.671051	+	0.671051i	−0.286907	+	0.957958i	$0.592627\pi$
$758$	−11.0522	−	19.6482i	−0.401434	−	0.713655i
$759$	9.72088	−	5.61235i	0.352846	−	0.203715i
$760$	10.4850	−	34.4534i	0.380331	−	1.24976i
$761$	−11.1420	−	6.43283i	−0.403897	−	0.233190i	0.284267	−	0.958745i	$-0.408250\pi$
$761$	−11.1420	−	6.43283i	−0.403897	−	0.233190i	−0.688164	+	0.725555i	$0.741583\pi$
$762$	12.9934	+	7.69716i	0.470701	+	0.278839i
$763$	−9.57624	−	16.1838i	−0.346683	−	0.585894i
$764$	−21.4724	+	11.7635i	−0.776844	+	0.425589i
$765$	0.227923	+	0.850618i	0.00824056	+	0.0307542i
$766$	10.4066	−	10.1759i	0.376004	−	0.367670i
$767$	7.20094	+	12.4724i	0.260011	+	0.450352i
$768$	20.4506	−	17.0771i	0.737948	−	0.616217i
$769$	−16.5676			−0.597443			−0.298722	−	0.954340i	$-0.596560\pi$
$769$	−16.5676			−0.597443			−0.298722	+	0.954340i	$0.596560\pi$
$770$	41.2925	−	23.8128i	1.48808	−	0.858152i
$771$	34.2238	−	34.2238i	1.23254	−	1.23254i
$772$	−0.0976234	+	4.35489i	−0.00351354	+	0.156736i
$773$	−12.6807	+	47.3250i	−0.456093	+	1.70216i	0.228763	+	0.973482i	$0.426532\pi$
$773$	−12.6807	+	47.3250i	−0.456093	+	1.70216i	−0.684856	+	0.728679i	$0.740135\pi$
$774$	−0.00893715	+	0.797456i	−0.000321239	+	0.0286640i
$775$	0.318960	+	0.184152i	0.0114574	+	0.00661492i
$776$	4.27180	+	4.56914i	0.153349	+	0.164023i
$777$	1.06686	+	1.04425i	0.0382733	+	0.0374623i
$778$	−14.7743	+	24.9401i	−0.529684	+	0.894147i
$779$	−44.2635	+	11.8604i	−1.58591	+	0.424942i
$780$	−10.4683	+	2.55497i	−0.374827	+	0.0914826i
$781$	−17.0139	−	4.55886i	−0.608805	−	0.163129i
$782$	0.782282	−	2.79389i	0.0279743	−	0.0999094i
$783$	38.6776			1.38222
$784$	−24.5698	+	13.4285i	−0.877493	+	0.479590i
$785$	36.8021			1.31352
$786$	9.50153	−	33.9344i	0.338908	−	1.21040i
$787$	−5.05999	−	1.35582i	−0.180369	−	0.0483298i	0.167504	−	0.985871i	$-0.446429\pi$
$787$	−5.05999	−	1.35582i	−0.180369	−	0.0483298i	−0.347873	+	0.937542i	$0.613096\pi$
$788$	6.69215	+	27.4194i	0.238398	+	0.976776i
$789$	28.4427	−	7.62121i	1.01259	−	0.271322i
$790$	−14.8587	+	25.0826i	−0.528648	+	0.892398i
$791$	11.2790	+	11.0400i	0.401035	+	0.392537i
$792$	4.05367	+	0.136335i	0.144041	+	0.00484446i
$793$	−14.6304	−	8.44687i	−0.519541	−	0.299957i
$794$	−0.124077	+	11.0713i	−0.00440332	+	0.392906i
$795$	−0.374277	+	1.39682i	−0.0132742	+	0.0495401i
$796$	−21.1089	−	0.473197i	−0.748184	−	0.0167720i
$797$	20.4204	−	20.4204i	0.723329	−	0.723329i	−0.245953	−	0.969282i	$-0.579101\pi$
$797$	20.4204	−	20.4204i	0.723329	−	0.723329i	0.969282	+	0.245953i	$0.0791009\pi$
$798$	34.0594	−	19.6416i	1.20569	−	0.695304i
$799$	4.15514			0.146998
$800$	3.50087	+	3.91695i	0.123774	+	0.138485i
$801$	−1.44860	−	2.50906i	−0.0511839	−	0.0886532i
$802$	14.3579	−	14.0397i	0.506996	−	0.495758i
$803$	−3.88193	−	14.4876i	−0.136990	−	0.511255i
$804$	−13.0446	−	23.8109i	−0.460049	−	0.839746i
$805$	2.90248	+	4.90518i	0.102299	+	0.172885i
$806$	0.773779	+	0.458379i	0.0272552	+	0.0161457i
$807$	−21.5389	−	12.4355i	−0.758205	−	0.437750i
$808$	−17.9572	+	9.57767i	−0.631732	+	0.336941i
$809$	−33.6734	+	19.4413i	−1.18389	+	0.683521i	−0.956912	−	0.290378i	$-0.906219\pi$
$809$	−33.6734	+	19.4413i	−1.18389	+	0.683521i	−0.226981	+	0.973899i	$0.572886\pi$
$810$	11.5654	+	20.5606i	0.406368	+	0.722427i
$811$	12.4718	+	12.4718i	0.437945	+	0.437945i	0.891320	−	0.453375i	$-0.149780\pi$
$811$	12.4718	+	12.4718i	0.437945	+	0.437945i	−0.453375	+	0.891320i	$0.649780\pi$
$812$	−32.7577	−	19.4274i	−1.14957	−	0.681768i
$813$	−16.3238	+	16.3238i	−0.572501	+	0.572501i
$814$	−0.815773	+	2.91350i	−0.0285928	+	0.102118i
$815$	11.5902	+	20.0749i	0.405988	+	0.703192i
$816$	−9.44688	+	8.63576i	−0.330707	+	0.302312i
$817$	−7.83387	+	13.5687i	−0.274072	+	0.474707i
$818$	36.1894	−	9.26354i	1.26533	−	0.323892i
$819$	0.839609	+	0.472835i	0.0293383	+	0.0165222i
$820$	−8.21727	+	28.1297i	−0.286960	+	0.982332i
$821$	−18.4979	+	4.95650i	−0.645581	+	0.172983i	−0.566730	−	0.823903i	$-0.691792\pi$
$821$	−18.4979	+	4.95650i	−0.645581	+	0.172983i	−0.0788511	+	0.996886i	$0.525125\pi$
$822$	4.10385	+	0.0459921i	0.143138	+	0.00160416i
$823$	8.96748	−	5.17738i	0.312587	−	0.180472i	−0.335497	−	0.942041i	$-0.608904\pi$
$823$	8.96748	−	5.17738i	0.312587	−	0.180472i	0.648083	+	0.761569i	$0.275571\pi$
$824$	−11.1894	−	48.1835i	−0.389800	−	1.67855i
$825$		−	9.76376i		−	0.339931i
$826$	−32.4642	+	8.68140i	−1.12957	+	0.302064i
$827$	−9.65786	−	9.65786i	−0.335837	−	0.335837i	0.518961	−	0.854798i	$-0.326319\pi$
$827$	−9.65786	−	9.65786i	−0.335837	−	0.335837i	−0.854798	+	0.518961i	$0.826319\pi$
$828$	−0.0108690	+	0.484856i	−0.000377723	+	0.0168499i
$829$	25.6983	+	6.88583i	0.892538	+	0.239155i	0.675809	−	0.737077i	$-0.263795\pi$
$829$	25.6983	+	6.88583i	0.892538	+	0.239155i	0.216729	+	0.976232i	$0.430461\pi$
$830$	−3.40326	+	3.32783i	−0.118129	+	0.115511i
$831$	1.92201	−	3.32902i	0.0666739	−	0.115483i
$832$	8.44103	+	9.65997i	0.292640	+	0.334899i
$833$	11.5023	−	6.97343i	0.398530	−	0.241615i
$834$	2.34906	+	9.17696i	0.0813412	+	0.317772i
$835$	−11.3164	−	42.2334i	−0.391620	−	1.46155i
$836$	68.0974	+	41.3781i	2.35520	+	1.43109i
$837$	0.551588	−	2.05855i	0.0190657	−	0.0711540i
$838$	27.3487	−	15.3838i	0.944747	−	0.531423i
$839$			46.4429i			1.60339i	0.597736	+	0.801693i	$0.296067\pi$
$839$			46.4429i			1.60339i	−0.597736	+	0.801693i	$0.703933\pi$
$840$	0.576044	−	25.1369i	0.0198754	−	0.867307i
$841$		−	22.8031i		−	0.786315i
$842$	−25.2062	−	44.8107i	−0.868662	−	1.54428i
$843$	−0.293220	+	1.09431i	−0.0100990	+	0.0376902i
$844$	14.2988	−	3.48985i	0.492185	−	0.120126i
$845$	5.44618	+	20.3254i	0.187354	+	0.699216i
$846$	−0.672862	+	0.172235i	−0.0231335	+	0.00592156i
$847$	20.5531	+	73.5459i	0.706211	+	2.52707i
$848$	1.68120	−	0.370610i	0.0577328	−	0.0127268i
$849$	−0.316904	+	0.548894i	−0.0108761	+	0.0188380i
$850$	−1.76443	−	1.80443i	−0.0605195	−	0.0618913i
$851$	−0.349443	−	0.0936330i	−0.0119788	−	0.00320970i
$852$	−6.71545	+	6.42097i	−0.230067	+	0.219979i
$853$	−31.3013	−	31.3013i	−1.07174	−	1.07174i	−0.997220	−	0.0745177i	$-0.976258\pi$
$853$	−31.3013	−	31.3013i	−1.07174	−	1.07174i	−0.0745177	−	0.997220i	$-0.523742\pi$
$854$	27.8876	−	27.8598i	0.954294	−	0.953342i
$855$		−	2.89191i		−	0.0989014i
$856$	−7.22848	−	4.50393i	−0.247064	−	0.153941i
$857$	22.8393	−	13.1863i	0.780175	−	0.450434i	−0.0563171	−	0.998413i	$-0.517936\pi$
$857$	22.8393	−	13.1863i	0.780175	−	0.450434i	0.836492	+	0.547979i	$0.184602\pi$
$858$	0.267183	−	23.8406i	0.00912148	−	0.813904i
$859$	−2.91867	+	0.782055i	−0.0995837	+	0.0266834i	−0.308267	−	0.951300i	$-0.599749\pi$
$859$	−2.91867	+	0.782055i	−0.0995837	+	0.0266834i	0.208683	+	0.977983i	$0.433082\pi$
$860$	4.81408	+	8.78734i	0.164159	+	0.299646i
$861$	−27.5344	+	16.2926i	−0.938371	+	0.555250i
$862$	−8.69586	−	33.9717i	−0.296182	−	1.15708i
$863$	−3.50456	+	6.07008i	−0.119297	+	0.206628i	−0.919489	−	0.393115i	$-0.871397\pi$
$863$	−3.50456	+	6.07008i	−0.119297	+	0.206628i	0.800192	+	0.599743i	$0.204731\pi$
$864$	16.6499	−	25.4336i	0.566441	−	0.865267i
$865$	12.9092	+	22.3594i	0.438925	+	0.760241i
$866$	−7.12055	−	1.99373i	−0.241966	−	0.0677498i
$867$	−15.6692	+	15.6692i	−0.532155	+	0.532155i
$868$	−1.50116	+	1.46642i	−0.0509526	+	0.0497735i
$869$	−45.6115	−	45.6115i	−1.54726	−	1.54726i
$870$	29.8078	−	16.7670i	1.01058	−	0.568454i
$871$	11.3210	−	6.53619i	0.383598	−	0.221470i
$872$	−9.46070	−	17.7379i	−0.320380	−	0.600681i
$873$	0.434991	+	0.251142i	0.0147222	+	0.00849987i
$874$	−4.85608	+	8.19743i	−0.164259	+	0.277282i
$875$	31.6483	−	0.338890i	1.06991	−	0.0114566i
$876$	−7.59419	−	2.21842i	−0.256584	−	0.0749535i
$877$	10.6267	+	39.6594i	0.358838	+	1.33920i	0.875585	+	0.483063i	$0.160476\pi$
$877$	10.6267	+	39.6594i	0.358838	+	1.33920i	−0.516748	+	0.856138i	$0.672857\pi$
$878$	21.8943	+	22.3906i	0.738896	+	0.755645i
$879$	−8.82185	−	15.2799i	−0.297554	−	0.515378i
$880$	45.2282	−	23.4758i	1.52464	−	0.791368i
$881$	−13.6166			−0.458755			−0.229377	−	0.973338i	$-0.573669\pi$
$881$	−13.6166			−0.458755			−0.229377	+	0.973338i	$0.573669\pi$
$882$	−1.57356	+	1.60602i	−0.0529846	+	0.0540776i
$883$	35.2238	−	35.2238i	1.18537	−	1.18537i	0.207042	−	0.978332i	$-0.433616\pi$
$883$	35.2238	−	35.2238i	1.18537	−	1.18537i	0.978332	−	0.207042i	$-0.0663836\pi$
$884$	−4.25890	−	4.45423i	−0.143242	−	0.149812i
$885$	7.81030	−	29.1484i	0.262540	−	0.979814i
$886$	−31.9252	−	0.357789i	−1.07255	−	0.0120201i
$887$	−5.44911	−	3.14604i	−0.182963	−	0.105634i	0.405721	−	0.913997i	$-0.367020\pi$
$887$	−5.44911	−	3.14604i	−0.182963	−	0.105634i	−0.588684	+	0.808363i	$0.700354\pi$
$888$	1.08993	+	1.16580i	0.0365756	+	0.0391215i
$889$	−12.1253	−	11.8684i	−0.406670	−	0.398053i
$890$	−31.3171	−	18.5519i	−1.04975	−	0.621862i
$891$	−50.4171	+	13.5092i	−1.68904	+	0.452576i
$892$	−38.2670	−	23.2522i	−1.28127	−	0.778543i
$893$	−13.1802	−	3.53163i	−0.441060	−	0.118182i
$894$	−41.7539	−	11.6910i	−1.39646	−	0.391004i
$895$	6.39085			0.213623
$896$	−26.8766	+	13.1777i	−0.897883	+	0.440235i
$897$	2.85083			0.0951864
$898$	49.5271	+	13.8674i	1.65274	+	0.462762i
$899$	−2.75714	−	0.738774i	−0.0919559	−	0.0246395i
$900$	0.360519	+	0.219062i	0.0120173	+	0.00730208i
$901$	−0.798852	+	0.214052i	−0.0266136	+	0.00713110i
$902$	−55.7870	−	33.0477i	−1.85750	−	1.10037i
$903$	−2.71786	+	10.5957i	−0.0904447	+	0.352604i
$904$	11.5229	+	12.3250i	0.383247	+	0.409923i
$905$	−35.5276	−	20.5118i	−1.18098	−	0.681837i
$906$	−15.0212	−	0.168344i	−0.499046	−	0.00559285i
$907$	11.6035	−	43.3049i	0.385289	−	1.43792i	−0.452423	−	0.891804i	$-0.649440\pi$
$907$	11.6035	−	43.3049i	0.385289	−	1.43792i	0.837711	−	0.546113i	$-0.183893\pi$
$908$	−25.7213	−	26.9009i	−0.853590	−	0.892737i
$909$	−1.15560	+	1.15560i	−0.0383288	+	0.0383288i
$910$	12.1063	+	0.00604104i	0.401320	+	0.000200259i
$911$	42.8973			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$911$	42.8973			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$912$	37.3058	−	19.3636i	1.23532	−	0.641193i
$913$	−5.26585	−	9.12073i	−0.174274	−	0.301852i
$914$	−24.6384	−	25.1970i	−0.814967	−	0.833441i
$915$	9.16166	+	34.1918i	0.302875	+	1.13035i
$916$	16.1469	+	4.71684i	0.533508	+	0.155849i
$917$	−19.4273	+	34.4970i	−0.641547	+	1.13919i
$918$	−7.44297	+	12.5643i	−0.245655	+	0.414684i
$919$	26.2242	+	15.1405i	0.865056	+	0.499440i	0.865702	−	0.500560i	$-0.166872\pi$
$919$	26.2242	+	15.1405i	0.865056	+	0.499440i	−0.000646343		1.00000i	$0.500206\pi$
$920$	2.86746	+	5.37620i	0.0945373	+	0.177248i
$921$	12.8074	−	7.39438i	0.422019	−	0.243653i
$922$	2.79929	−	1.57461i	0.0921896	−	0.0518570i
$923$	−3.16330	−	3.16330i	−0.104121	−	0.104121i
$924$	53.5646	+	15.0267i	1.76214	+	0.494344i
$925$	−0.222515	+	0.222515i	−0.00731626	+	0.00731626i
$926$	20.1792	+	5.65012i	0.663130	+	0.185675i
$927$	−1.98607	−	3.43997i	−0.0652311	−	0.112984i
$928$	−34.0647	−	22.3002i	−1.11823	−	0.732039i
$929$	6.93334	−	12.0089i	0.227475	−	0.393999i	−0.729584	−	0.683891i	$-0.760286\pi$
$929$	6.93334	−	12.0089i	0.227475	−	0.393999i	0.957059	+	0.289892i	$0.0936195\pi$
$930$	−0.467303	−	1.82559i	−0.0153235	−	0.0598635i
$931$	−42.4126	+	12.3437i	−1.39002	+	0.404548i
$932$	16.5638	+	30.2345i	0.542564	+	0.990364i
$933$	−15.8925	+	4.25838i	−0.520297	+	0.139413i
$934$	−0.196750	+	17.5559i	−0.00643786	+	0.574446i
$935$	−21.2002	+	12.2399i	−0.693321	+	0.400289i
$936$	0.874299	+	0.544759i	0.0285773	+	0.0178060i
$937$		−	46.7544i		−	1.52740i	−0.645572	−	0.763699i	$-0.723381\pi$
$937$		−	46.7544i		−	1.52740i	0.645572	−	0.763699i	$-0.276619\pi$
$938$	7.87998	+	29.4673i	0.257290	+	0.962141i
$939$	20.2222	+	20.2222i	0.659927	+	0.659927i
$940$	−6.30708	+	6.03051i	−0.205714	+	0.196693i
$941$	8.04407	+	2.15540i	0.262229	+	0.0702641i	0.387538	−	0.921854i	$-0.373326\pi$
$941$	8.04407	+	2.15540i	0.262229	+	0.0702641i	−0.125309	+	0.992118i	$0.539992\pi$
$942$	30.0295	+	30.7103i	0.978416	+	1.00059i
$943$	3.87655	−	6.71439i	0.126238	−	0.218651i
$944$	−35.0829	+	7.73378i	−1.14185	+	0.251713i
$945$	−7.72123	−	27.6292i	−0.251172	−	0.898778i
$946$	−21.4769	+	5.49751i	−0.698273	+	0.178739i
$947$	1.89988	+	7.09044i	0.0617378	+	0.230408i	0.989900	−	0.141767i	$-0.0452785\pi$
$947$	1.89988	+	7.09044i	0.0617378	+	0.230408i	−0.928162	+	0.372176i	$0.878612\pi$
$948$	−33.0549	+	8.06759i	−1.07357	+	0.262023i
$949$	0.985926	−	3.67953i	0.0320045	−	0.119442i
$950$	4.06317	+	7.22338i	0.131827	+	0.234357i
$951$			35.3776i			1.14720i
$952$	12.6147	−	6.90270i	0.408845	−	0.223718i
$953$			41.3553i			1.33963i	0.742528	+	0.669815i	$0.233627\pi$
$953$			41.3553i			1.33963i	−0.742528	+	0.669815i	$0.766373\pi$
$954$	0.120490	−	0.0677758i	0.00390099	−	0.00219432i
$955$	−6.39305	+	23.8592i	−0.206874	+	0.772065i
$956$	−0.978826	−	0.594765i	−0.0316575	−	0.0192361i
$957$	19.5850	+	73.0921i	0.633093	+	2.36273i
$958$	−0.720387	−	2.81430i	−0.0232746	−	0.0909260i
$959$	−4.46633	−	1.14564i	−0.144225	−	0.0369945i
$960$	1.80601	−	26.8188i	0.0582888	−	0.865574i
$961$	15.4214	−	26.7106i	0.497463	−	0.861632i
$962$	−0.549414	+	0.537236i	−0.0177138	+	0.0173212i
$963$	−0.660606	−	0.177009i	−0.0212877	−	0.00570403i
$964$	−0.528296	+	23.5668i	−0.0170153	+	0.759036i
$965$	3.10748	+	3.10748i	0.100033	+	0.100033i
$966$	−1.72488	+	6.42452i	−0.0554972	+	0.206706i
$967$		−	40.5984i		−	1.30556i	−0.757549	−	0.652778i	$-0.773603\pi$
$967$		−	40.5984i		−	1.30556i	0.757549	−	0.652778i	$-0.226397\pi$
$968$	18.4665	+	79.5202i	0.593536	+	2.55588i
$969$	−17.4866	+	10.0959i	−0.561752	+	0.324328i
$970$	6.31014	+	0.0707182i	0.202606	+	0.00227062i
$971$	31.4132	−	8.41714i	1.00810	−	0.270119i	0.283263	−	0.959042i	$-0.408583\pi$
$971$	31.4132	−	8.41714i	1.00810	−	0.270119i	0.724834	+	0.688924i	$0.241916\pi$
$972$	1.32077	−	4.52133i	0.0423639	−	0.145022i
$973$	−0.113955	−	10.6420i	−0.00365323	−	0.341168i
$974$	56.0095	−	14.3369i	1.79466	−	0.459385i
$975$	1.23989	−	2.14755i	0.0397083	−	0.0687768i
$976$	31.1036	−	28.4330i	0.995602	−	0.910118i
$977$	8.34286	+	14.4503i	0.266912	+	0.462305i	0.968063	−	0.250708i	$-0.0806635\pi$
$977$	8.34286	+	14.4503i	0.266912	+	0.462305i	−0.701151	+	0.713013i	$0.747330\pi$
$978$	−7.29455	+	26.0522i	−0.233254	+	0.833059i
$979$	56.9486	−	56.9486i	1.82009	−	1.82009i
$980$	−7.33848	+	27.2786i	−0.234419	+	0.871384i
$981$	−1.14148	−	1.14148i	−0.0364448	−	0.0364448i
$982$	0.272601	+	0.484621i	0.00869904	+	0.0154649i
$983$	−10.1999	+	5.88892i	−0.325326	+	0.187827i	−0.653764	−	0.756698i	$-0.726811\pi$
$983$	−10.1999	+	5.88892i	−0.325326	+	0.187827i	0.328438	+	0.944526i	$0.393478\pi$
$984$	−30.1785	+	16.0960i	−0.962054	+	0.513122i
$985$	24.6599	+	14.2374i	0.785728	+	0.453640i
$986$	16.8281	+	9.96881i	0.535916	+	0.317472i
$987$	−9.52612	+	0.102006i	−0.303220	+	0.00324688i
$988$	9.72355	+	17.7488i	0.309347	+	0.564665i
$989$	−0.686082	−	2.56049i	−0.0218161	−	0.0814189i
$990$	2.92570	−	2.86085i	0.0929848	−	0.0909237i
$991$	15.8872	+	27.5175i	0.504675	+	0.874122i	0.999985	+	0.00540613i	$0.00172083\pi$
$991$	15.8872	+	27.5175i	0.504675	+	0.874122i	−0.495311	+	0.868716i	$0.664946\pi$
$992$	−1.67270	+	1.49501i	−0.0531081	+	0.0474667i
$993$	−40.2967			−1.27878
$994$	9.04265	−	5.21476i	0.286815	−	0.165402i
$995$	−15.0625	+	15.0625i	−0.477513	+	0.477513i
$996$	−5.55394	−	0.124502i	−0.175983	−	0.00394501i
$997$	−0.309461	+	1.15492i	−0.00980073	+	0.0365768i	−0.970653	−	0.240484i	$-0.922694\pi$
$997$	−0.309461	+	1.15492i	−0.00980073	+	0.0365768i	0.960852	+	0.277061i	$0.0893604\pi$
$998$	−0.195357	+	17.4315i	−0.00618391	+	0.551786i
$999$	1.57695	+	0.910453i	0.0498925	+	0.0288055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.c.37.2	✓	48
4.3	odd	2		448.2.ba.c.177.9		48
7.2	even	3		784.2.m.j.197.6		24
7.3	odd	6		784.2.x.o.165.10		48
7.4	even	3	inner	112.2.w.c.53.10	yes	48
7.5	odd	6		784.2.m.k.197.6		24
7.6	odd	2		784.2.x.o.373.2		48
8.3	odd	2		896.2.ba.e.737.4		48
8.5	even	2		896.2.ba.f.737.9		48
16.3	odd	4		448.2.ba.c.401.4		48
16.5	even	4		896.2.ba.f.289.4		48
16.11	odd	4		896.2.ba.e.289.9		48
16.13	even	4	inner	112.2.w.c.93.10	yes	48
28.11	odd	6		448.2.ba.c.305.4		48
56.11	odd	6		896.2.ba.e.865.9		48
56.53	even	6		896.2.ba.f.865.4		48
112.11	odd	12		896.2.ba.e.417.4		48
112.13	odd	4		784.2.x.o.765.10		48
112.45	odd	12		784.2.x.o.557.2		48
112.53	even	12		896.2.ba.f.417.9		48
112.61	odd	12		784.2.m.k.589.6		24
112.67	odd	12		448.2.ba.c.81.9		48
112.93	even	12		784.2.m.j.589.6		24
112.109	even	12	inner	112.2.w.c.109.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.2	✓	48	1.1	even	1	trivial
112.2.w.c.53.10	yes	48	7.4	even	3	inner
112.2.w.c.93.10	yes	48	16.13	even	4	inner
112.2.w.c.109.2	yes	48	112.109	even	12	inner
448.2.ba.c.81.9		48	112.67	odd	12
448.2.ba.c.177.9		48	4.3	odd	2
448.2.ba.c.305.4		48	28.11	odd	6
448.2.ba.c.401.4		48	16.3	odd	4
784.2.m.j.197.6		24	7.2	even	3
784.2.m.j.589.6		24	112.93	even	12
784.2.m.k.197.6		24	7.5	odd	6
784.2.m.k.589.6		24	112.61	odd	12
784.2.x.o.165.10		48	7.3	odd	6
784.2.x.o.373.2		48	7.6	odd	2
784.2.x.o.557.2		48	112.45	odd	12
784.2.x.o.765.10		48	112.13	odd	4
896.2.ba.e.289.9		48	16.11	odd	4
896.2.ba.e.417.4		48	112.11	odd	12
896.2.ba.e.737.4		48	8.3	odd	2
896.2.ba.e.865.9		48	56.11	odd	6
896.2.ba.f.289.4		48	16.5	even	4
896.2.ba.f.417.9		48	112.53	even	12
896.2.ba.f.737.9		48	8.5	even	2
896.2.ba.f.865.4		48	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36184 - 0.381311i) q^{2} +(-1.60845 - 0.430984i) q^{3} +(1.70920 + 1.03857i) q^{4} +(1.94900 - 0.522232i) q^{5} +(2.02612 + 1.20025i) q^{6} +(-1.89075 - 1.85069i) q^{7} +(-1.93164 - 2.06610i) q^{8} +(-0.196696 - 0.113563i) q^{9} +(-2.85335 - 0.0319777i) q^{10} +(1.63411 - 6.09856i) q^{11} +(-2.30157 - 2.40713i) q^{12} +(1.13388 - 1.13388i) q^{13} +(1.86921 + 3.24130i) q^{14} -3.35995 q^{15} +(1.84276 + 3.55024i) q^{16} +(-0.960789 - 1.66414i) q^{17} +(0.224566 + 0.229656i) q^{18} +(1.63324 + 6.09532i) q^{19} +(3.87361 + 1.13156i) q^{20} +(2.24357 + 3.79164i) q^{21} +(-4.55083 + 7.68215i) q^{22} +(-0.924606 - 0.533821i) q^{23} +(2.21651 + 4.15573i) q^{24} +(-0.804265 + 0.464342i) q^{25} +(-1.97651 + 1.11180i) q^{26} +(3.79985 + 3.79985i) q^{27} +(-1.30962 - 5.12688i) q^{28} +(5.08936 - 5.08936i) q^{29} +(4.57570 + 1.28118i) q^{30} +(-0.198293 - 0.343454i) q^{31} +(-1.15579 - 5.53752i) q^{32} +(-5.25677 + 9.10499i) q^{33} +(0.673887 + 2.63264i) q^{34} +(-4.65156 - 2.61958i) q^{35} +(-0.218252 - 0.398384i) q^{36} +(0.327303 - 0.0877006i) q^{37} +(0.100007 - 8.92360i) q^{38} +(-2.31247 + 1.33510i) q^{39} +(-4.84375 - 3.01805i) q^{40} +7.26189i q^{41} +(-1.60959 - 6.01909i) q^{42} +(1.75565 + 1.75565i) q^{43} +(9.12678 - 8.72657i) q^{44} +(-0.442666 - 0.118612i) q^{45} +(1.05561 + 1.07954i) q^{46} +(-1.08118 + 1.87265i) q^{47} +(-1.43390 - 6.50461i) q^{48} +(0.149895 + 6.99839i) q^{49} +(1.27234 - 0.325684i) q^{50} +(0.828170 + 3.09077i) q^{51} +(3.11563 - 0.760420i) q^{52} +(0.111394 - 0.415727i) q^{53} +(-3.72585 - 6.62369i) q^{54} -12.7395i q^{55} +(-0.171444 + 7.48135i) q^{56} -10.5079i q^{57} +(-8.87151 + 4.99025i) q^{58} +(-2.32453 + 8.67527i) q^{59} +(-5.74284 - 3.48953i) q^{60} +(-2.72673 - 10.1763i) q^{61} +(0.139080 + 0.543339i) q^{62} +(0.161735 + 0.578743i) q^{63} +(-0.537512 + 7.98192i) q^{64} +(1.61777 - 2.80206i) q^{65} +(10.6307 - 10.3951i) q^{66} +(7.87441 + 2.10994i) q^{67} +(0.0861303 - 3.84219i) q^{68} +(1.25712 + 1.25712i) q^{69} +(5.33580 + 5.34113i) q^{70} -2.78982i q^{71} +(0.145316 + 0.625756i) q^{72} +(2.05730 - 1.18779i) q^{73} +(-0.479175 - 0.00537015i) q^{74} +(1.49375 - 0.400248i) q^{75} +(-3.53886 + 12.1144i) q^{76} +(-14.3762 + 8.50666i) q^{77} +(3.65830 - 0.936427i) q^{78} +(5.10829 - 8.84782i) q^{79} +(5.44558 + 5.95707i) q^{80} +(-4.13352 - 7.15947i) q^{81} +(2.76904 - 9.88952i) q^{82} +(1.17951 - 1.17951i) q^{83} +(-0.103140 + 8.81078i) q^{84} +(-2.74164 - 2.74164i) q^{85} +(-1.72147 - 3.06036i) q^{86} +(-10.3794 + 5.99257i) q^{87} +(-15.7567 + 8.40403i) q^{88} +(11.0470 + 6.37800i) q^{89} +(0.557612 + 0.330324i) q^{90} +(-4.24233 + 0.0454269i) q^{91} +(-1.02593 - 1.87267i) q^{92} +(0.170922 + 0.637891i) q^{93} +(2.18645 - 2.13799i) q^{94} +(6.36634 + 11.0268i) q^{95} +(-0.527542 + 9.40498i) q^{96} -2.21148 q^{97} +(2.46443 - 9.58784i) q^{98} +(-1.01399 + 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 24 q^{13} - 34 q^{14} - 40 q^{15} + 16 q^{16} + 8 q^{17} + 18 q^{18} - 4 q^{19} - 16 q^{20} - 8 q^{21} + 18 q^{24}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 24 * q^13 - 34 * q^14 - 40 * q^15 + 16 * q^16 + 8 * q^17 + 18 * q^18 - 4 * q^19 - 16 * q^20 - 8 * q^21 + 18 * q^24 - 10 * q^26 - 24 * q^27 - 10 * q^28 + 24 * q^29 - 4 * q^30 + 28 * q^31 + 16 * q^32 + 16 * q^33 - 44 * q^34 + 28 * q^35 - 72 * q^36 - 24 * q^37 + 20 * q^38 + 26 * q^40 + 6 * q^42 - 40 * q^43 + 6 * q^44 - 28 * q^45 - 14 * q^46 - 20 * q^47 + 56 * q^48 + 56 * q^50 + 24 * q^51 - 16 * q^52 - 16 * q^53 + 64 * q^54 + 40 * q^56 - 6 * q^58 - 20 * q^59 + 46 * q^60 + 8 * q^61 + 24 * q^62 - 16 * q^63 + 80 * q^64 + 8 * q^65 - 20 * q^66 + 48 * q^67 - 40 * q^69 + 82 * q^70 - 32 * q^72 - 8 * q^74 - 4 * q^75 - 36 * q^76 - 20 * q^77 + 116 * q^78 - 36 * q^79 - 28 * q^80 + 2 * q^82 - 8 * q^83 + 28 * q^84 - 20 * q^86 - 42 * q^88 - 20 * q^90 + 64 * q^91 + 76 * q^92 + 8 * q^93 - 72 * q^94 - 4 * q^95 - 120 * q^96 - 48 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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