LMFDB - Embedded newform 348.2.t.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41321 - 0.0532282i) q^{2} +(-1.71646 + 0.231871i) q^{3} +(1.99433 + 0.150445i) q^{4} +(2.31270 + 1.84432i) q^{5} +(2.43806 - 0.236318i) q^{6} +(1.11294 + 0.254022i) q^{7} +(-2.81041 - 0.318766i) q^{8} +(2.89247 - 0.795994i) q^{9} +O(q^{10})$	\(q+(-1.41321 - 0.0532282i) q^{2} +(-1.71646 + 0.231871i) q^{3} +(1.99433 + 0.150445i) q^{4} +(2.31270 + 1.84432i) q^{5} +(2.43806 - 0.236318i) q^{6} +(1.11294 + 0.254022i) q^{7} +(-2.81041 - 0.318766i) q^{8} +(2.89247 - 0.795994i) q^{9} +(-3.17016 - 2.72951i) q^{10} +(-0.377036 - 0.782923i) q^{11} +(-3.45808 + 0.204194i) q^{12} +(-1.24344 + 0.598808i) q^{13} +(-1.55930 - 0.418227i) q^{14} +(-4.39730 - 2.62945i) q^{15} +(3.95473 + 0.600077i) q^{16} -0.276589 q^{17} +(-4.13004 + 0.970946i) q^{18} +(-0.203928 - 0.893468i) q^{19} +(4.33482 + 4.02611i) q^{20} +(-1.96922 - 0.177960i) q^{21} +(0.491158 + 1.12650i) q^{22} +(5.89480 + 7.39185i) q^{23} +(4.89786 - 0.104502i) q^{24} +(0.834469 + 3.65605i) q^{25} +(1.78911 - 0.780056i) q^{26} +(-4.78025 + 2.03697i) q^{27} +(2.18136 + 0.674042i) q^{28} +(5.21345 + 1.34907i) q^{29} +(6.07435 + 3.95002i) q^{30} +(0.294598 - 0.369414i) q^{31} +(-5.55693 - 1.05854i) q^{32} +(0.828704 + 1.25643i) q^{33} +(0.390879 + 0.0147223i) q^{34} +(2.10541 + 2.64009i) q^{35} +(5.88831 - 1.15232i) q^{36} +(-4.09463 + 8.50259i) q^{37} +(0.240636 + 1.27351i) q^{38} +(1.99546 - 1.31615i) q^{39} +(-5.91172 - 5.92049i) q^{40} +7.95625 q^{41} +(2.77346 + 0.356313i) q^{42} +(3.06359 + 3.84162i) q^{43} +(-0.634148 - 1.61813i) q^{44} +(8.15748 + 3.49374i) q^{45} +(-7.93714 - 10.7600i) q^{46} +(3.32933 + 6.91342i) q^{47} +(-6.92728 - 0.113021i) q^{48} +(-5.13267 - 2.47176i) q^{49} +(-0.984677 - 5.21119i) q^{50} +(0.474754 - 0.0641328i) q^{51} +(-2.56992 + 1.00715i) q^{52} +(-6.65105 - 5.30404i) q^{53} +(6.86392 - 2.62423i) q^{54} +(0.571987 - 2.50604i) q^{55} +(-3.04685 - 1.06867i) q^{56} +(0.557204 + 1.48632i) q^{57} +(-7.29589 - 2.18402i) q^{58} -5.99393 q^{59} +(-8.37409 - 5.90555i) q^{60} +(-1.77364 - 0.404822i) q^{61} +(-0.435993 + 0.506380i) q^{62} +(3.42136 - 0.151144i) q^{63} +(7.79678 + 1.79172i) q^{64} +(-3.98008 - 0.908428i) q^{65} +(-1.10426 - 1.81972i) q^{66} +(1.51455 - 3.14499i) q^{67} +(-0.551610 - 0.0416115i) q^{68} +(-11.8321 - 11.3210i) q^{69} +(-2.83486 - 3.84308i) q^{70} +(-10.1405 + 4.88340i) q^{71} +(-8.38276 + 1.31504i) q^{72} +(9.74375 - 7.77038i) q^{73} +(6.23916 - 11.7980i) q^{74} +(-2.28006 - 6.08197i) q^{75} +(-0.272283 - 1.81255i) q^{76} +(-0.220740 - 0.967124i) q^{77} +(-2.89007 + 1.75378i) q^{78} +(10.1702 + 4.89772i) q^{79} +(8.03937 + 8.68157i) q^{80} +(7.73279 - 4.60478i) q^{81} +(-11.2439 - 0.423497i) q^{82} +(-1.58856 - 6.95992i) q^{83} +(-3.90051 - 0.651172i) q^{84} +(-0.639666 - 0.510117i) q^{85} +(-4.12502 - 5.59209i) q^{86} +(-9.26148 - 1.10678i) q^{87} +(0.810055 + 2.32052i) q^{88} +(4.40529 - 5.52406i) q^{89} +(-11.3423 - 5.37160i) q^{90} +(-1.53599 + 0.350579i) q^{91} +(10.6441 + 15.6287i) q^{92} +(-0.420010 + 0.702394i) q^{93} +(-4.33706 - 9.94734i) q^{94} +(1.17621 - 2.44243i) q^{95} +(9.78370 + 0.528450i) q^{96} +(-5.00469 + 1.14229i) q^{97} +(7.12198 + 3.76632i) q^{98} +(-1.71377 - 1.96446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41321	−	0.0532282i	−0.999291	−	0.0376380i
$2$	−1.41321	−	0.0532282i	−0.999291	−	0.0376380i
$3$	−1.71646	+	0.231871i	−0.990999	+	0.133871i
$3$	−1.71646	+	0.231871i	−0.990999	+	0.133871i
$4$	1.99433	+	0.150445i	0.997167	+	0.0752227i
$5$	2.31270	+	1.84432i	1.03427	+	0.824803i	0.984751	−	0.173970i	$-0.0556597\pi$
$5$	2.31270	+	1.84432i	1.03427	+	0.824803i	0.0495191	+	0.998773i	$0.484231\pi$
$6$	2.43806	−	0.236318i	0.995335	−	0.0964765i
$7$	1.11294	+	0.254022i	0.420653	+	0.0960113i	0.427608	−	0.903965i	$-0.359357\pi$
$7$	1.11294	+	0.254022i	0.420653	+	0.0960113i	−0.00695445	+	0.999976i	$0.502214\pi$
$8$	−2.81041	−	0.318766i	−0.993629	−	0.112701i
$9$	2.89247	−	0.795994i	0.964157	−	0.265331i
$10$	−3.17016	−	2.72951i	−1.00249	−	0.863146i
$11$	−0.377036	−	0.782923i	−0.113681	−	0.236060i	0.836364	−	0.548175i	$-0.184677\pi$
$11$	−0.377036	−	0.782923i	−0.113681	−	0.236060i	−0.950045	+	0.312114i	$0.898963\pi$
$12$	−3.45808	+	0.204194i	−0.998261	+	0.0589457i
$13$	−1.24344	+	0.598808i	−0.344867	+	0.166079i	−0.598297	−	0.801274i	$-0.704156\pi$
$13$	−1.24344	+	0.598808i	−0.344867	+	0.166079i	0.253430	+	0.967354i	$0.418441\pi$
$14$	−1.55930	−	0.418227i	−0.416741	−	0.111776i
$15$	−4.39730	−	2.62945i	−1.13538	−	0.678920i
$16$	3.95473	+	0.600077i	0.988683	+	0.150019i
$17$	−0.276589			−0.0670826			−0.0335413	−	0.999437i	$-0.510679\pi$
$17$	−0.276589			−0.0670826			−0.0335413	+	0.999437i	$0.510679\pi$
$18$	−4.13004	+	0.970946i	−0.973461	+	0.228854i
$19$	−0.203928	−	0.893468i	−0.0467844	−	0.204976i	0.946134	−	0.323776i	$-0.104952\pi$
$19$	−0.203928	−	0.893468i	−0.0467844	−	0.204976i	−0.992918	+	0.118800i	$0.962095\pi$
$20$	4.33482	+	4.02611i	0.969296	+	0.900267i
$21$	−1.96922	−	0.177960i	−0.429720	−	0.0388340i
$22$	0.491158	+	1.12650i	0.104715	+	0.240172i
$23$	5.89480	+	7.39185i	1.22915	+	1.54131i	0.746311	+	0.665598i	$0.231823\pi$
$23$	5.89480	+	7.39185i	1.22915	+	1.54131i	0.482840	+	0.875709i	$0.339605\pi$
$24$	4.89786	−	0.104502i	0.999772	−	0.0213313i
$25$	0.834469	+	3.65605i	0.166894	+	0.731210i
$26$	1.78911	−	0.780056i	0.350874	−	0.152982i
$27$	−4.78025	+	2.03697i	−0.919959	+	0.392015i
$28$	2.18136	+	0.674042i	0.412239	+	0.127382i
$29$	5.21345	+	1.34907i	0.968112	+	0.250516i
$29$	5.21345	+	1.34907i	0.968112	+	0.250516i
$30$	6.07435	+	3.95002i	1.10902	+	0.721173i
$31$	0.294598	−	0.369414i	0.0529114	−	0.0663488i	−0.754672	−	0.656103i	$-0.772204\pi$
$31$	0.294598	−	0.369414i	0.0529114	−	0.0663488i	0.807583	+	0.589754i	$0.200775\pi$
$32$	−5.55693	−	1.05854i	−0.982336	−	0.187125i
$33$	0.828704	+	1.25643i	0.144259	+	0.218717i
$34$	0.390879	+	0.0147223i	0.0670351	+	0.00252486i
$35$	2.10541	+	2.64009i	0.355878	+	0.446257i
$36$	5.88831	−	1.15232i	0.981385	−	0.192053i
$37$	−4.09463	+	8.50259i	−0.673153	+	1.39782i	0.231994	+	0.972717i	$0.425475\pi$
$37$	−4.09463	+	8.50259i	−0.673153	+	1.39782i	−0.905147	+	0.425099i	$0.860239\pi$
$38$	0.240636	+	1.27351i	0.0390363	+	0.206591i
$39$	1.99546	−	1.31615i	0.319530	−	0.210752i
$40$	−5.91172	−	5.92049i	−0.934725	−	0.936111i
$41$	7.95625			1.24256			0.621279	−	0.783589i	$-0.286613\pi$
$41$	7.95625			1.24256			0.621279	+	0.783589i	$0.286613\pi$
$42$	2.77346	+	0.356313i	0.427954	+	0.0549803i
$43$	3.06359	+	3.84162i	0.467193	+	0.585841i	0.958481	−	0.285156i	$-0.0920453\pi$
$43$	3.06359	+	3.84162i	0.467193	+	0.585841i	−0.491288	+	0.870997i	$0.663474\pi$
$44$	−0.634148	−	1.61813i	−0.0956014	−	0.243943i
$45$	8.15748	+	3.49374i	1.21604	+	0.520816i
$46$	−7.93714	−	10.7600i	−1.17027	−	1.58648i
$47$	3.32933	+	6.91342i	0.485632	+	1.00843i	0.989485	+	0.144636i	$0.0462012\pi$
$47$	3.32933	+	6.91342i	0.485632	+	1.00843i	−0.503852	+	0.863790i	$0.668084\pi$
$48$	−6.92728	−	0.113021i	−0.999867	−	0.0163132i
$49$	−5.13267	−	2.47176i	−0.733238	−	0.353109i
$50$	−0.984677	−	5.21119i	−0.139254	−	0.736973i
$51$	0.474754	−	0.0641328i	0.0664788	−	0.00898039i
$52$	−2.56992	+	1.00715i	−0.356383	+	0.139667i
$53$	−6.65105	−	5.30404i	−0.913592	−	0.728566i	0.0492053	−	0.998789i	$-0.484331\pi$
$53$	−6.65105	−	5.30404i	−0.913592	−	0.728566i	−0.962798	+	0.270223i	$0.912903\pi$
$54$	6.86392	−	2.62423i	0.934062	−	0.357112i
$55$	0.571987	−	2.50604i	0.0771267	−	0.337914i
$56$	−3.04685	−	1.06867i	−0.407153	−	0.142808i
$57$	0.557204	+	1.48632i	0.0738035	+	0.196868i
$58$	−7.29589	−	2.18402i	−0.957998	−	0.286776i
$59$	−5.99393			−0.780343			−0.390172	−	0.920742i	$-0.627584\pi$
$59$	−5.99393			−0.780343			−0.390172	+	0.920742i	$0.627584\pi$
$60$	−8.37409	−	5.90555i	−1.08109	−	0.762403i
$61$	−1.77364	−	0.404822i	−0.227092	−	0.0518322i	0.107461	−	0.994209i	$-0.465728\pi$
$61$	−1.77364	−	0.404822i	−0.227092	−	0.0518322i	−0.334552	+	0.942377i	$0.608585\pi$
$62$	−0.435993	+	0.506380i	−0.0553711	+	0.0643103i
$63$	3.42136	−	0.151144i	0.431051	−	0.0190424i
$64$	7.79678	+	1.79172i	0.974597	+	0.223966i
$65$	−3.98008	−	0.908428i	−0.493669	−	0.112677i
$66$	−1.10426	−	1.81972i	−0.135925	−	0.223991i
$67$	1.51455	−	3.14499i	0.185031	−	0.384222i	−0.787733	−	0.616016i	$-0.788745\pi$
$67$	1.51455	−	3.14499i	0.185031	−	0.384222i	0.972765	+	0.231795i	$0.0744597\pi$
$68$	−0.551610	−	0.0416115i	−0.0668926	−	0.00504614i
$69$	−11.8321	−	11.3210i	−1.42442	−	1.36289i
$70$	−2.83486	−	3.84308i	−0.338830	−	0.459336i
$71$	−10.1405	+	4.88340i	−1.20345	+	0.579553i	−0.924658	−	0.380798i	$-0.875649\pi$
$71$	−10.1405	+	4.88340i	−1.20345	+	0.579553i	−0.278796	+	0.960350i	$0.589935\pi$
$72$	−8.38276	+	1.31504i	−0.987918	+	0.154979i
$73$	9.74375	−	7.77038i	1.14042	−	0.909454i	0.143639	−	0.989630i	$-0.454120\pi$
$73$	9.74375	−	7.77038i	1.14042	−	0.909454i	0.996781	+	0.0801759i	$0.0255482\pi$
$74$	6.23916	−	11.7980i	0.725287	−	1.37149i
$75$	−2.28006	−	6.08197i	−0.263279	−	0.702286i
$76$	−0.272283	−	1.81255i	−0.0312330	−	0.207914i
$77$	−0.220740	−	0.967124i	−0.0251556	−	0.110214i
$78$	−2.89007	+	1.75378i	−0.327236	+	0.198576i
$79$	10.1702	+	4.89772i	1.14424	+	0.551036i	0.907298	−	0.420488i	$-0.138141\pi$
$79$	10.1702	+	4.89772i	1.14424	+	0.551036i	0.236941	+	0.971524i	$0.423855\pi$
$80$	8.03937	+	8.68157i	0.898829	+	0.970629i
$81$	7.73279	−	4.60478i	0.859199	−	0.511642i
$82$	−11.2439	−	0.423497i	−1.24168	−	0.0467674i
$83$	−1.58856	−	6.95992i	−0.174367	−	0.763950i	−0.984167	−	0.177245i	$-0.943282\pi$
$83$	−1.58856	−	6.95992i	−0.174367	−	0.763950i	0.809800	−	0.586706i	$-0.199576\pi$
$84$	−3.90051	−	0.651172i	−0.425581	−	0.0710487i
$85$	−0.639666	−	0.510117i	−0.0693816	−	0.0553300i
$86$	−4.12502	−	5.59209i	−0.444812	−	0.603010i
$87$	−9.26148	−	1.10678i	−0.992935	−	0.118659i
$88$	0.810055	+	2.32052i	0.0863521	+	0.247368i
$89$	4.40529	−	5.52406i	0.466960	−	0.585549i	−0.491464	−	0.870898i	$-0.663538\pi$
$89$	4.40529	−	5.52406i	0.466960	−	0.585549i	0.958424	+	0.285349i	$0.0921095\pi$
$90$	−11.3423	−	5.37160i	−1.19558	−	0.566216i
$91$	−1.53599	+	0.350579i	−0.161015	+	0.0367506i
$92$	10.6441	+	15.6287i	1.10973	+	1.62940i
$93$	−0.420010	+	0.702394i	−0.0435530	+	0.0728348i
$94$	−4.33706	−	9.94734i	−0.447333	−	1.02599i
$95$	1.17621	−	2.44243i	0.120677	−	0.250588i
$96$	9.78370	+	0.528450i	0.998544	+	0.0539347i
$97$	−5.00469	+	1.14229i	−0.508149	+	0.115982i	−0.468906	−	0.883248i	$-0.655352\pi$
$97$	−5.00469	+	1.14229i	−0.508149	+	0.115982i	−0.0392430	+	0.999230i	$0.512495\pi$
$98$	7.12198	+	3.76632i	0.719428	+	0.380456i
$99$	−1.71377	−	1.96446i	−0.172240	−	0.197436i
$100$	1.11417	+	7.41692i	0.111417	+	0.741692i
$101$	4.07862	+	5.11443i	0.405838	+	0.508905i	0.942185	−	0.335092i	$-0.108768\pi$
$101$	4.07862	+	5.11443i	0.405838	+	0.508905i	−0.536347	+	0.843998i	$0.680196\pi$
$102$	−0.674341	+	0.0653630i	−0.0667697	+	0.00647190i
$103$	−3.71483	−	7.71393i	−0.366034	−	0.760076i	0.633877	−	0.773434i	$-0.281462\pi$
$103$	−3.71483	−	7.71393i	−0.366034	−	0.760076i	−0.999911	+	0.0133572i	$0.995748\pi$
$104$	3.68544	−	1.28653i	0.361387	−	0.126154i
$105$	−4.22600	−	4.04344i	−0.412416	−	0.394599i
$106$	9.11702	+	7.84975i	0.885523	+	0.762435i
$107$	−5.37482	−	2.58838i	−0.519604	−	0.250228i	0.155652	−	0.987812i	$-0.450252\pi$
$107$	−5.37482	−	2.58838i	−0.519604	−	0.250228i	−0.675255	+	0.737584i	$0.735967\pi$
$108$	−9.83986	+	3.34323i	−0.946841	+	0.321703i
$109$	−2.74200	+	12.0135i	−0.262636	+	1.15068i	0.655744	+	0.754984i	$0.272355\pi$
$109$	−2.74200	+	12.0135i	−0.262636	+	1.15068i	−0.918380	+	0.395700i	$0.870502\pi$
$110$	−0.941730	+	3.51111i	−0.0897904	+	0.334772i
$111$	5.05677	−	15.5438i	0.479967	−	1.47535i
$112$	4.24896	+	1.67244i	0.401489	+	0.158031i
$113$	0.0872893	−	0.382439i	0.00821149	−	0.0359769i	−0.970656	−	0.240471i	$-0.922698\pi$
$113$	0.0872893	−	0.382439i	0.00821149	−	0.0359769i	0.978868	+	0.204495i	$0.0655551\pi$
$114$	−0.708333	−	2.13014i	−0.0663415	−	0.199506i
$115$			27.9670i			2.60793i
$116$	10.1944	+	3.47483i	0.946525	+	0.322630i
$117$	−3.11996	+	2.72180i	−0.288440	+	0.251631i
$118$	8.47069	+	0.319046i	0.779790	+	0.0293706i
$119$	−0.307828	−	0.0702597i	−0.0282185	−	0.00644069i
$120$	11.5200	+	8.79152i	1.05163	+	0.802553i
$121$	6.38758	−	8.00977i	0.580689	−	0.728161i
$122$	2.48498	+	0.666507i	0.224980	+	0.0603427i
$123$	−13.6566	+	1.84482i	−1.23137	+	0.166342i
$124$	0.643104	−	0.692414i	0.0577524	−	0.0621806i
$125$	1.60422	−	3.33120i	0.143486	−	0.297952i
$126$	−4.84315	+	0.0314859i	−0.431462	+	0.00280499i
$127$	0.0368348	−	0.0177387i	0.00326856	−	0.00157405i	−0.432249	−	0.901754i	$-0.642280\pi$
$127$	0.0368348	−	0.0177387i	0.00326856	−	0.00157405i	0.435517	+	0.900180i	$0.356565\pi$
$128$	−10.9231	−	2.94709i	−0.965477	−	0.260489i
$129$	−6.14929	−	5.88363i	−0.541414	−	0.518025i
$130$	5.57635	+	1.49565i	0.489078	+	0.131178i
$131$	14.3970	−	11.4812i	1.25787	−	1.00312i	0.258563	−	0.965994i	$-0.416751\pi$
$131$	14.3970	−	11.4812i	1.25787	−	1.00312i	0.999311	−	0.0371261i	$-0.0118203\pi$
$132$	1.46369	+	2.63042i	0.127398	+	0.228949i
$133$		−	1.04618i		−	0.0907155i
$134$	−2.30778	+	4.36392i	−0.199362	+	0.376985i
$135$	−14.8121	−	4.10538i	−1.27482	−	0.353335i
$136$	0.777327	+	0.0881671i	0.0666553	+	0.00756027i
$137$	−19.4940	−	9.38783i	−1.66549	−	0.802057i	−0.998368	−	0.0571060i	$-0.981813\pi$
$137$	−19.4940	−	9.38783i	−1.66549	−	0.802057i	−0.667120	−	0.744951i	$-0.732473\pi$
$138$	16.1187	+	16.6287i	1.37212	+	1.41553i
$139$	9.82088	−	7.83189i	0.832996	−	0.664292i	−0.111156	−	0.993803i	$-0.535455\pi$
$139$	9.82088	−	7.83189i	0.832996	−	0.664292i	0.944152	+	0.329511i	$0.106884\pi$
$140$	3.80169	+	5.58198i	0.321301	+	0.471763i
$141$	−7.31768	−	11.0946i	−0.616260	−	0.934337i
$142$	14.5906	−	6.36152i	1.22441	−	0.533847i
$143$	0.937640	+	0.747743i	0.0784094	+	0.0625294i
$144$	11.9166	−	1.41224i	0.993051	−	0.117686i
$145$	9.56902	+	12.7352i	0.794664	+	1.05760i
$146$	−14.1836	+	10.4625i	−1.17384	+	0.865887i
$147$	9.38315	+	3.05257i	0.773909	+	0.251771i
$148$	−9.44523	+	16.3410i	−0.776393	+	1.34322i
$149$	−19.5284	+	4.45723i	−1.59983	+	0.365151i	−0.927122	−	0.374759i	$-0.877725\pi$
$149$	−19.5284	+	4.45723i	−1.59983	+	0.365151i	−0.672707	+	0.739909i	$0.734868\pi$
$150$	2.89848	+	8.71648i	0.236660	+	0.711697i
$151$	13.0663	−	10.4200i	1.06332	−	0.847969i	0.0745205	−	0.997219i	$-0.476257\pi$
$151$	13.0663	−	10.4200i	1.06332	−	0.847969i	0.988799	+	0.149250i	$0.0476859\pi$
$152$	0.288314	+	2.57602i	0.0233854	+	0.208942i
$153$	−0.800025	+	0.220163i	−0.0646782	+	0.0177991i
$154$	0.260474	+	1.37850i	0.0209896	+	0.111083i
$155$	1.36263	−	0.311012i	0.109449	−	0.0249811i
$156$	4.17763	−	2.32463i	0.334478	−	0.186119i
$157$		−	3.75459i		−	0.299649i	−0.988713	−	0.149824i	$-0.952129\pi$
$157$		−	3.75459i		−	0.299649i	0.988713	−	0.149824i	$-0.0478708\pi$
$158$	−14.1120	−	7.46286i	−1.12269	−	0.593713i
$159$	12.6461	+	7.56199i	1.00290	+	0.599705i
$160$	−10.8992	−	12.6968i	−0.861660	−	1.00377i
$161$	4.68289	+	9.72411i	0.369063	+	0.766368i
$162$	−11.1732	+	6.09592i	−0.877847	+	0.478941i
$163$	−8.40774	+	4.04895i	−0.658545	+	0.317138i	−0.733142	−	0.680075i	$-0.761947\pi$
$163$	−8.40774	+	4.04895i	−0.658545	+	0.317138i	0.0745975	+	0.997214i	$0.476233\pi$
$164$	15.8674	+	1.19698i	1.23904	+	0.0934686i
$165$	−0.400716	+	4.43414i	−0.0311957	+	0.345197i
$166$	1.87450	+	9.92039i	0.145490	+	0.769972i
$167$	4.78347	−	20.9578i	0.370156	−	1.62176i	−0.356178	−	0.934418i	$-0.615920\pi$
$167$	4.78347	−	20.9578i	0.370156	−	1.62176i	0.726334	−	0.687342i	$-0.241223\pi$
$168$	5.47759	+	1.12786i	0.422605	+	0.0870164i
$169$	−6.91780	+	8.67465i	−0.532139	+	0.667281i
$170$	0.876831	+	0.754951i	0.0672499	+	0.0579021i
$171$	−1.30105	−	2.42201i	−0.0994939	−	0.185215i
$172$	5.53186	+	8.12237i	0.421801	+	0.619325i
$173$			17.2487i			1.31140i	0.755023	+	0.655698i	$0.227626\pi$
$173$			17.2487i			1.31140i	−0.755023	+	0.655698i	$0.772374\pi$
$174$	13.0295	+	2.05708i	0.987765	+	0.155947i
$175$			4.28095i			0.323609i
$176$	−1.02126	−	3.32250i	−0.0769805	−	0.250443i
$177$	10.2883	−	1.38982i	0.773319	−	0.104465i
$178$	−6.51964	+	7.57218i	−0.488668	+	0.567559i
$179$	−7.42367	+	9.30898i	−0.554871	+	0.695786i	−0.977600	−	0.210470i	$-0.932501\pi$
$179$	−7.42367	+	9.30898i	−0.554871	+	0.695786i	0.422729	+	0.906256i	$0.361072\pi$
$180$	15.7431	+	8.19493i	1.17342	+	0.610814i
$181$	2.09489	−	9.17833i	0.155712	−	0.682220i	−0.835450	−	0.549566i	$-0.814793\pi$
$181$	2.09489	−	9.17833i	0.155712	−	0.682220i	0.991162	−	0.132654i	$-0.0423498\pi$
$182$	2.18933	−	0.413684i	0.162284	−	0.0306643i
$183$	3.13825	+	0.283606i	0.231986	+	0.0209647i
$184$	−14.2105	−	22.6532i	−1.04761	−	1.67001i
$185$	−25.1511	+	12.1121i	−1.84915	+	0.890501i
$186$	0.630950	−	0.970274i	0.0462635	−	0.0711440i
$187$	0.104284	+	0.216548i	0.00762599	+	0.0158355i
$188$	5.59970	+	14.2885i	0.408400	+	1.04210i
$189$	−5.83758	+	1.05275i	−0.424621	+	0.0765760i
$190$	−1.79224	+	3.38906i	−0.130023	+	0.245868i
$191$		−	22.1200i		−	1.60055i	−0.599635	−	0.800274i	$-0.704688\pi$
$191$		−	22.1200i		−	1.60055i	0.599635	−	0.800274i	$-0.295312\pi$
$192$	−13.7983	−	1.26758i	−0.995807	−	0.0914797i
$193$	−6.42858	+	1.46728i	−0.462739	+	0.105617i	−0.447534	−	0.894267i	$-0.647698\pi$
$193$	−6.42858	+	1.46728i	−0.462739	+	0.105617i	−0.0152059	+	0.999884i	$0.504840\pi$
$194$	7.13349	−	1.34790i	0.512155	−	0.0967738i
$195$	7.04229	+	0.636416i	0.504309	+	0.0455747i
$196$	−9.86438	−	5.70170i	−0.704599	−	0.407265i
$197$	20.8217	−	16.6047i	1.48348	−	1.18304i	0.544650	−	0.838664i	$-0.316663\pi$
$197$	20.8217	−	16.6047i	1.48348	−	1.18304i	0.938833	−	0.344374i	$-0.111909\pi$
$198$	2.31735	+	2.86742i	0.164687	+	0.203779i
$199$	9.86234	−	2.25101i	0.699122	−	0.159570i	0.141836	−	0.989890i	$-0.454700\pi$
$199$	9.86234	−	2.25101i	0.699122	−	0.159570i	0.557287	+	0.830320i	$0.311842\pi$
$200$	−1.17977	−	10.5410i	−0.0834226	−	0.745360i
$201$	−1.87043	+	5.74943i	−0.131930	+	0.405534i
$202$	−5.49173	−	7.44487i	−0.386397	−	0.523820i
$203$	5.45958	+	2.82577i	0.383187	+	0.198330i
$204$	0.956466	−	0.0564777i	0.0669660	−	0.00395423i
$205$	18.4004	+	14.6738i	1.28514	+	1.02487i
$206$	4.83925	+	11.0992i	0.337166	+	0.773315i
$207$	22.9344	+	16.6885i	1.59405	+	1.15993i
$208$	−5.27679	+	1.62197i	−0.365880	+	0.112463i
$209$	−0.622629	+	0.496530i	−0.0430681	+	0.0343457i
$210$	5.75701	+	5.93917i	0.397272	+	0.409842i
$211$	−12.2212	−	5.88540i	−0.841339	−	0.405168i	−0.0369838	−	0.999316i	$-0.511775\pi$
$211$	−12.2212	−	5.88540i	−0.841339	−	0.405168i	−0.804356	+	0.594148i	$0.797489\pi$
$212$	−12.4665	−	11.5786i	−0.856199	−	0.795224i
$213$	16.2734	−	10.7334i	1.11504	−	0.735443i
$214$	7.45798	+	3.94402i	0.509817	+	0.269607i
$215$			14.5347i			0.991260i
$216$	14.0838	−	4.20094i	0.958278	−	0.285838i
$217$	0.421710	−	0.336303i	0.0286276	−	0.0228297i
$218$	4.51449	−	16.8317i	0.305760	−	1.13998i
$219$	−14.9230	+	15.5968i	−1.00841	+	1.05394i
$220$	1.51775	−	4.91182i	0.102327	−	0.331155i
$221$	0.343921	−	0.165623i	0.0231346	−	0.0111410i
$222$	−7.97365	+	21.6975i	−0.535157	+	1.45624i
$223$	12.6337	−	26.2341i	0.846015	−	1.75677i	0.222543	−	0.974923i	$-0.428564\pi$
$223$	12.6337	−	26.2341i	0.846015	−	1.75677i	0.623472	−	0.781845i	$-0.285721\pi$
$224$	−5.91566	−	2.58968i	−0.395257	−	0.173030i
$225$	5.32387	+	9.91079i	0.354925	+	0.660719i
$226$	−0.143715	+	0.535822i	−0.00955977	+	0.0356423i
$227$	1.09775	−	1.37654i	0.0728605	−	0.0913642i	−0.744065	−	0.668107i	$-0.767105\pi$
$227$	1.09775	−	1.37654i	0.0728605	−	0.0913642i	0.816926	+	0.576742i	$0.195676\pi$
$228$	0.887641	+	3.04804i	0.0587854	+	0.201862i
$229$	−8.15263	−	1.86079i	−0.538741	−	0.122964i	−0.0555119	−	0.998458i	$-0.517679\pi$
$229$	−8.15263	−	1.86079i	−0.538741	−	0.122964i	−0.483229	+	0.875494i	$0.660536\pi$
$230$	1.48863	−	39.5232i	0.0981575	−	2.60609i
$231$	0.603139	+	1.60885i	0.0396836	+	0.105854i
$232$	−14.2219	−	5.45330i	−0.933711	−	0.358027i
$233$			9.99952i			0.655090i	0.944836	+	0.327545i	$0.106221\pi$
$233$			9.99952i			0.655090i	−0.944836	+	0.327545i	$0.893779\pi$
$234$	4.55404	−	3.68041i	0.297707	−	0.240596i
$235$	−5.05080	+	22.1290i	−0.329478	+	1.44354i
$236$	−11.9539	−	0.901759i	−0.778132	−	0.0586995i
$237$	−18.5924	−	6.04856i	−1.20771	−	0.392896i
$238$	0.431286	+	0.115677i	0.0279561	+	0.00749822i
$239$	0.739901	−	3.24172i	0.0478602	−	0.209689i	−0.945344	−	0.326075i	$-0.894274\pi$
$239$	0.739901	−	3.24172i	0.0478602	−	0.209689i	0.993204	+	0.116386i	$0.0371309\pi$
$240$	−15.8123	−	13.0375i	−1.02068	−	0.841565i
$241$	8.39885	+	4.04468i	0.541018	+	0.260540i	0.684375	−	0.729131i	$-0.260075\pi$
$241$	8.39885	+	4.04468i	0.541018	+	0.260540i	−0.143357	+	0.989671i	$0.545790\pi$
$242$	−9.45334	+	10.9795i	−0.607684	+	0.705789i
$243$	−12.2053	+	9.69693i	−0.782971	+	0.622058i
$244$	−3.47633	−	1.07419i	−0.222549	−	0.0687678i
$245$	−7.31160	−	15.1827i	−0.467121	−	0.969987i
$246$	19.3979	−	1.88021i	1.23676	−	0.119878i
$247$	0.788588	+	0.988858i	0.0501766	+	0.0629195i
$248$	−0.945697	+	0.944297i	−0.0600518	+	0.0599629i
$249$	4.34049	+	11.5781i	0.275068	+	0.733731i
$250$	−2.44442	+	4.62230i	−0.154599	+	0.292340i
$251$	−14.2946	+	3.26265i	−0.902267	+	0.205937i	−0.648397	−	0.761302i	$-0.724560\pi$
$251$	−14.2946	+	3.26265i	−0.902267	+	0.205937i	−0.253869	+	0.967239i	$0.581703\pi$
$252$	6.84607	+	0.213296i	0.431262	+	0.0134364i
$253$	3.56469	−	7.40216i	0.224110	−	0.465370i
$254$	−0.0529995	+	0.0231079i	−0.00332548	+	0.00144992i
$255$	1.21624	+	0.727276i	0.0761641	+	0.0455438i
$256$	15.2798	+	4.74629i	0.954988	+	0.296643i
$257$	14.6057	−	3.33366i	0.911079	−	0.207948i	0.258804	−	0.965930i	$-0.416672\pi$
$257$	14.6057	−	3.33366i	0.911079	−	0.207948i	0.652275	+	0.757982i	$0.273815\pi$
$258$	8.37707	+	8.64213i	0.521533	+	0.538035i
$259$	−6.71694	+	8.42277i	−0.417370	+	0.523366i
$260$	−7.80095	−	2.41049i	−0.483794	−	0.149493i
$261$	16.1536	−	0.247724i	0.999882	−	0.0153337i
$262$	−20.9572	+	15.4591i	−1.29474	+	0.955066i
$263$	−6.43858	−	5.13460i	−0.397020	−	0.316613i	0.404548	−	0.914517i	$-0.367429\pi$
$263$	−6.43858	−	5.13460i	−0.397020	−	0.316613i	−0.801568	+	0.597904i	$0.796000\pi$
$264$	−1.92849	−	3.79525i	−0.118690	−	0.233581i
$265$	−5.59956	−	24.5333i	−0.343978	−	1.50707i
$266$	−0.0556864	+	1.47848i	−0.00341435	+	0.0906512i
$267$	−6.28064	+	10.5033i	−0.384369	+	0.642790i
$268$	3.49366	−	6.04430i	0.213409	−	0.369215i
$269$	2.89457	+	1.39395i	0.176485	+	0.0849908i	0.520040	−	0.854142i	$-0.325917\pi$
$269$	2.89457	+	1.39395i	0.176485	+	0.0849908i	−0.343555	+	0.939133i	$0.611631\pi$
$270$	20.7141	+	6.59019i	1.26062	+	0.401066i
$271$	−1.34721	−	5.90251i	−0.0818372	−	0.358552i	0.917384	−	0.398002i	$-0.130296\pi$
$271$	−1.34721	−	5.90251i	−0.0818372	−	0.358552i	−0.999222	+	0.0394504i	$0.987439\pi$
$272$	−1.09383	−	0.165975i	−0.0663235	−	0.0100637i
$273$	2.55517	−	0.957904i	0.154646	−	0.0579750i
$274$	27.0495	+	14.3046i	1.63412	+	0.864174i
$275$	2.54778	−	2.03179i	0.153637	−	0.122521i
$276$	−21.8940	−	24.3579i	−1.31787	−	1.46617i
$277$	−14.6833	+	7.07109i	−0.882233	+	0.424861i	−0.819439	−	0.573166i	$-0.805715\pi$
$277$	−14.6833	+	7.07109i	−0.882233	+	0.424861i	−0.0627932	+	0.998027i	$0.520001\pi$
$278$	−14.2959	+	10.5454i	−0.857409	+	0.632469i
$279$	0.558065	−	1.30302i	0.0334105	−	0.0780097i
$280$	−5.07547	−	8.09087i	−0.303318	−	0.483522i
$281$	−2.42579	+	5.03721i	−0.144711	+	0.300495i	−0.960708	−	0.277561i	$-0.910474\pi$
$281$	−2.42579	+	5.03721i	−0.144711	+	0.300495i	0.815997	+	0.578056i	$0.196188\pi$
$282$	9.75088	+	16.0686i	0.580656	+	0.956870i
$283$	15.5922	+	3.55881i	0.926858	+	0.211549i	0.659202	−	0.751966i	$-0.270894\pi$
$283$	15.5922	+	3.55881i	0.926858	+	0.211549i	0.267655	+	0.963515i	$0.413751\pi$
$284$	−20.9582	+	8.21354i	−1.24364	+	0.487384i
$285$	−1.45259	+	4.46506i	−0.0860442	+	0.264488i
$286$	−1.28528	−	1.10663i	−0.0760004	−	0.0654363i
$287$	8.85486	+	2.02106i	0.522686	+	0.119300i
$288$	−16.9159	+	1.36149i	−0.996777	+	0.0802265i
$289$	−16.9235			−0.995500
$290$	−12.8452	−	18.5069i	−0.754294	−	1.08676i
$291$	8.32549	−	3.12113i	0.488049	−	0.182964i
$292$	20.6013	−	14.0308i	1.20560	−	0.821092i
$293$	0.602679	−	2.64051i	0.0352089	−	0.154260i	−0.954268	−	0.298954i	$-0.903362\pi$
$293$	0.602679	−	2.64051i	0.0352089	−	0.154260i	0.989477	+	0.144693i	$0.0462196\pi$
$294$	−13.0979	−	4.81337i	−0.763884	−	0.280721i
$295$	−13.8622	−	11.0547i	−0.807086	−	0.643629i
$296$	14.2179	−	22.5905i	0.826399	−	1.31305i
$297$	3.39712	+	2.97455i	0.197121	+	0.172601i
$298$	27.8350	−	5.25955i	1.61244	−	0.304677i
$299$	−11.7561	−	5.66144i	−0.679873	−	0.327410i
$300$	−3.63220	−	12.4725i	−0.209705	−	0.720101i
$301$	2.43374	+	5.05372i	0.140279	+	0.291292i
$302$	−19.0201	+	14.0302i	−1.09448	+	0.807347i
$303$	−8.18669	−	7.83301i	−0.470313	−	0.449995i
$304$	−0.270332	−	3.65580i	−0.0155046	−	0.209675i
$305$	−3.35528	−	4.20739i	−0.192123	−	0.240914i
$306$	1.14232	−	0.268553i	0.0653023	−	0.0153521i
$307$	−5.55741			−0.317178			−0.158589	−	0.987345i	$-0.550695\pi$
$307$	−5.55741			−0.317178			−0.158589	+	0.987345i	$0.550695\pi$
$308$	−0.294729	−	1.96198i	−0.0167938	−	0.111794i
$309$	8.16500	+	12.3793i	0.464491	+	0.704234i
$310$	−1.94224	+	0.366995i	−0.110312	+	0.0208439i
$311$	−3.83618	+	7.96590i	−0.217530	+	0.451705i	−0.980966	−	0.194178i	$-0.937796\pi$
$311$	−3.83618	+	7.96590i	−0.217530	+	0.451705i	0.763437	+	0.645883i	$0.223510\pi$
$312$	−6.02761	+	3.06282i	−0.341246	+	0.173398i
$313$	−12.1825	−	15.2763i	−0.688594	−	0.863469i	0.307520	−	0.951541i	$-0.400501\pi$
$313$	−12.1825	−	15.2763i	−0.688594	−	0.863469i	−0.996114	+	0.0880724i	$0.971929\pi$
$314$	−0.199850	+	5.30602i	−0.0112782	+	0.299436i
$315$	8.19132	+	5.96051i	0.461529	+	0.335837i
$316$	19.5460	+	11.2977i	1.09955	+	0.635548i
$317$	15.2694	−	19.1472i	0.857613	−	1.07541i	−0.138760	−	0.990326i	$-0.544312\pi$
$317$	15.2694	−	19.1472i	0.857613	−	1.07541i	0.996374	−	0.0850869i	$-0.0271168\pi$
$318$	−17.4691	−	11.3598i	−0.979620	−	0.637027i
$319$	−0.909438	−	4.59037i	−0.0509188	−	0.257012i
$320$	14.7271	+	18.5234i	0.823269	+	1.03549i
$321$	9.82584	+	3.19658i	0.548425	+	0.178416i
$322$	−6.10031	−	13.9915i	−0.339957	−	0.779715i
$323$	0.0564043	+	0.247123i	0.00313842	+	0.0137503i
$324$	16.1145	−	8.02010i	0.895251	−	0.445561i
$325$	−3.22688	−	4.04638i	−0.178995	−	0.224453i
$326$	12.0974	−	5.27450i	0.670015	−	0.292127i
$327$	1.92096	−	21.2565i	0.106229	−	1.17549i
$328$	−22.3603	−	2.53618i	−1.23464	−	0.140037i
$329$	1.94919	+	8.53997i	0.107462	+	0.470824i
$330$	0.802318	−	6.24505i	0.0441661	−	0.343779i
$331$	−8.38814			−0.461054			−0.230527	−	0.973066i	$-0.574045\pi$
$331$	−8.38814			−0.461054			−0.230527	+	0.973066i	$0.574045\pi$
$332$	−2.12102	−	14.1194i	−0.116406	−	0.774902i
$333$	−5.07560	+	27.8528i	−0.278141	+	1.52632i
$334$	−7.87560	+	29.3631i	−0.430934	+	1.60668i
$335$	9.30305	−	4.48011i	0.508280	−	0.244775i
$336$	−7.68096	−	1.88547i	−0.419031	−	0.102861i
$337$	−9.57619	−	19.8852i	−0.521648	−	1.08321i	−0.980829	−	0.194871i	$-0.937571\pi$
$337$	−9.57619	−	19.8852i	−0.521648	−	1.08321i	0.459181	−	0.888343i	$-0.348143\pi$
$338$	10.2381	−	11.8909i	0.556877	−	0.646779i
$339$	−0.0611521	+	0.676682i	−0.00332133	+	0.0367523i
$340$	−1.19896	−	1.11358i	−0.0650229	−	0.0603923i
$341$	−0.400297	−	0.0913652i	−0.0216773	−	0.00494770i
$342$	1.70974	+	3.49206i	0.0924523	+	0.188829i
$343$	−11.3321	−	9.03702i	−0.611874	−	0.487953i
$344$	−7.38535	−	11.7731i	−0.398192	−	0.634762i
$345$	−6.48472	−	48.0042i	−0.349126	−	2.58446i
$346$	0.918119	−	24.3761i	0.0493584	−	1.31047i
$347$	−13.5469			−0.727233			−0.363617	−	0.931549i	$-0.618458\pi$
$347$	−13.5469			−0.727233			−0.363617	+	0.931549i	$0.618458\pi$
$348$	−18.3040	−	3.60063i	−0.981196	−	0.193014i
$349$	−24.3192			−1.30178			−0.650888	−	0.759174i	$-0.725603\pi$
$349$	−24.3192			−1.30178			−0.650888	+	0.759174i	$0.725603\pi$
$350$	0.227867	−	6.04989i	0.0121800	−	0.323380i
$351$	4.72418	−	5.39529i	0.252158	−	0.287979i
$352$	1.26641	+	4.74976i	0.0674998	+	0.253163i
$353$	14.7230	+	11.7412i	0.783625	+	0.624920i	0.931357	−	0.364108i	$-0.118626\pi$
$353$	14.7230	+	11.7412i	0.783625	+	0.624920i	−0.147732	+	0.989027i	$0.547197\pi$
$354$	−14.6136	+	1.41647i	−0.776703	+	0.0752848i
$355$	−32.4584	−	7.40842i	−1.72271	−	0.393198i
$356$	9.61668	−	10.3541i	0.509683	−	0.548764i
$357$	0.544665	+	0.0492217i	0.0288267	+	0.00260509i
$358$	10.9867	−	12.7604i	0.580666	−	0.674409i
$359$	−2.01244	−	4.17888i	−0.106213	−	0.220553i	0.841088	−	0.540898i	$-0.181915\pi$
$359$	−2.01244	−	4.17888i	−0.106213	−	0.220553i	−0.947301	+	0.320345i	$0.896201\pi$
$360$	−21.8121	−	12.4191i	−1.14960	−	0.654547i
$361$	16.3617	−	7.87938i	0.861143	−	0.414704i
$362$	−3.44907	+	12.8594i	−0.181279	+	0.675876i
$363$	−9.10679	+	15.2295i	−0.477983	+	0.799343i
$364$	−3.11601	+	0.468089i	−0.163323	+	0.0245345i
$365$	36.8654			1.92962
$366$	−4.41992	−	0.567839i	−0.231033	−	0.0296814i
$367$	5.95358	+	26.0843i	0.310774	+	1.36159i	0.853243	+	0.521514i	$0.174633\pi$
$367$	5.95358	+	26.0843i	0.310774	+	1.36159i	−0.542469	+	0.840076i	$0.682510\pi$
$368$	18.8767	+	32.7701i	0.984015	+	1.70826i
$369$	23.0132	−	6.33313i	1.19802	−	0.329689i
$370$	36.1885	−	15.7783i	1.88135	−	0.820272i
$371$	−6.05490	−	7.59261i	−0.314355	−	0.394189i
$372$	−0.943311	+	1.33762i	−0.0489084	+	0.0693523i
$373$	0.543252	+	2.38014i	0.0281285	+	0.123239i	0.987043	−	0.160456i	$-0.0512966\pi$
$373$	0.543252	+	2.38014i	0.0281285	+	0.123239i	−0.958914	+	0.283696i	$0.908439\pi$
$374$	−0.135849	−	0.311579i	−0.00702457	−	0.0161113i
$375$	−1.98118	+	6.08985i	−0.102308	+	0.314478i
$376$	−7.15300	−	20.4908i	−0.368888	−	1.05673i
$377$	−7.29042	+	1.44437i	−0.375476	+	0.0743888i
$378$	8.30577	−	1.17703i	0.427203	−	0.0605398i
$379$	−7.70476	+	9.66147i	−0.395767	+	0.496276i	−0.939293	−	0.343116i	$-0.888518\pi$
$379$	−7.70476	+	9.66147i	−0.395767	+	0.496276i	0.543526	+	0.839392i	$0.317089\pi$
$380$	2.71321	−	4.69406i	0.139185	−	0.240800i
$381$	−0.0591123	+	0.0389886i	−0.00302842	+	0.00199745i
$382$	−1.17741	+	31.2602i	−0.0602414	+	1.59941i
$383$	11.4232	+	14.3243i	0.583700	+	0.731937i	0.982739	−	0.184997i	$-0.0592276\pi$
$383$	11.4232	+	14.3243i	0.583700	+	0.731937i	−0.399039	+	0.916934i	$0.630656\pi$
$384$	19.4325	+	2.52582i	0.991658	+	0.128895i
$385$	1.27318	−	2.64378i	0.0648871	−	0.134740i
$386$	9.16305	−	1.73140i	0.466387	−	0.0881258i
$387$	11.9192	+	8.67318i	0.605889	+	0.440882i
$388$	−10.1529	+	1.52517i	−0.515434	+	0.0774288i
$389$	−6.08137			−0.308338			−0.154169	−	0.988045i	$-0.549270\pi$
$389$	−6.08137			−0.308338			−0.154169	+	0.988045i	$0.549270\pi$
$390$	−9.91838	−	1.27424i	−0.502236	−	0.0645236i
$391$	−1.63044	−	2.04450i	−0.0824547	−	0.103395i
$392$	13.6370	+	8.58278i	0.688771	+	0.433496i
$393$	−22.0497	+	23.0453i	−1.11226	+	1.16248i
$394$	−30.3093	+	22.3577i	−1.52696	+	1.12636i
$395$	14.4877	+	30.0840i	0.728956	+	1.51369i
$396$	−3.12228	−	4.17563i	−0.156900	−	0.209833i
$397$	29.2669	+	14.0942i	1.46886	+	0.707366i	0.985754	−	0.168194i	$-0.0537936\pi$
$397$	29.2669	+	14.0942i	1.46886	+	0.707366i	0.483108	+	0.875561i	$0.339508\pi$
$398$	−14.0574	+	2.65620i	−0.704633	+	0.133143i
$399$	0.242579	+	1.79573i	0.0121441	+	0.0898989i
$400$	1.10619	+	14.9594i	0.0553096	+	0.747972i
$401$	4.02222	+	3.20762i	0.200860	+	0.160181i	0.718755	−	0.695264i	$-0.244713\pi$
$401$	4.02222	+	3.20762i	0.200860	+	0.160181i	−0.517894	+	0.855445i	$0.673284\pi$
$402$	2.94935	−	8.02560i	0.147100	−	0.400281i
$403$	−0.145106	+	0.635751i	−0.00722824	+	0.0316690i
$404$	7.36470	+	10.8135i	0.366407	+	0.537992i
$405$	26.3763	+	3.61224i	1.31065	+	0.179493i
$406$	−7.56513	−	4.28401i	−0.375451	−	0.212612i
$407$	8.20069			0.406493
$408$	−1.35469	+	0.0289040i	−0.0670674	+	0.00143096i
$409$	21.9164	+	5.00227i	1.08369	+	0.247346i	0.726835	−	0.686812i	$-0.240990\pi$
$409$	21.9164	+	5.00227i	1.08369	+	0.247346i	0.356859	+	0.934158i	$0.383848\pi$
$410$	−25.2226	−	21.7167i	−1.24566	−	1.07251i
$411$	35.6375	+	11.5937i	1.75787	+	0.571877i
$412$	−6.24809	−	15.9430i	−0.307821	−	0.785457i
$413$	−6.67090	−	1.52259i	−0.328254	−	0.0749218i
$414$	−31.5229	−	24.8051i	−1.54926	−	1.21910i
$415$	9.16243	−	19.0260i	0.449766	−	0.933949i
$416$	7.54356	−	2.01131i	0.369853	−	0.0986125i
$417$	−15.0412	+	15.7203i	−0.736569	+	0.769827i
$418$	0.906335	−	0.668560i	0.0443303	−	0.0327003i
$419$	−15.6898	+	7.55581i	−0.766497	+	0.369125i	−0.775921	−	0.630830i	$-0.782714\pi$
$419$	−15.6898	+	7.55581i	−0.766497	+	0.369125i	0.00942419	+	0.999956i	$0.497000\pi$
$420$	−7.81975	−	8.69974i	−0.381565	−	0.424504i
$421$	14.5343	−	11.5907i	0.708360	−	0.564899i	−0.201663	−	0.979455i	$-0.564635\pi$
$421$	14.5343	−	11.5907i	0.708360	−	0.564899i	0.910024	+	0.414556i	$0.136063\pi$
$422$	16.9578	+	8.96783i	0.825494	+	0.436547i
$423$	15.1330	+	17.3468i	0.735793	+	0.843428i
$424$	17.0014	+	17.0266i	0.825662	+	0.826887i
$425$	−0.230805	−	1.01122i	−0.0111957	−	0.0490515i
$426$	−23.5691	+	14.3024i	−1.14193	+	0.692955i
$427$	−1.87113	−	0.901089i	−0.0905503	−	0.0436067i
$428$	−10.3298	−	5.97071i	−0.499309	−	0.288605i
$429$	−1.78280	−	1.06606i	−0.0860745	−	0.0514699i
$430$	0.773657	−	20.5406i	0.0373091	−	0.990558i
$431$	5.15163	+	22.5708i	0.248145	+	1.08720i	0.933385	+	0.358878i	$0.116840\pi$
$431$	5.15163	+	22.5708i	0.248145	+	1.08720i	−0.685239	+	0.728318i	$0.740302\pi$
$432$	−20.1269	+	5.18716i	−0.968357	+	0.249567i
$433$	−5.14472	−	4.10278i	−0.247240	−	0.197167i	0.492027	−	0.870580i	$-0.336256\pi$
$433$	−5.14472	−	4.10278i	−0.247240	−	0.197167i	−0.739266	+	0.673413i	$0.764828\pi$
$434$	−0.613867	+	0.452820i	−0.0294665	+	0.0217361i
$435$	−19.3778	−	19.6407i	−0.929093	−	0.941701i
$436$	−7.27584	+	23.5464i	−0.348450	+	1.12767i
$437$	5.40226	−	6.77422i	0.258425	−	0.324055i
$438$	21.9196	−	21.2473i	1.04736	−	1.01524i
$439$	−33.5905	+	7.66681i	−1.60319	+	0.365917i	−0.928250	−	0.371958i	$-0.878686\pi$
$439$	−33.5905	+	7.66681i	−1.60319	+	0.365917i	−0.674937	+	0.737875i	$0.735829\pi$
$440$	−2.40635	+	6.86066i	−0.114718	+	0.327069i
$441$	−16.8136	−	3.06393i	−0.800648	−	0.145902i
$442$	−0.494849	+	0.215755i	−0.0235375	+	0.0102624i
$443$	−4.02671	+	8.36155i	−0.191315	+	0.397269i	−0.974457	−	0.224573i	$-0.927901\pi$
$443$	−4.02671	+	8.36155i	−0.191315	+	0.397269i	0.783142	+	0.621842i	$0.213616\pi$
$444$	12.4234	−	30.2387i	0.589587	−	1.43507i
$445$	20.3762	−	4.65074i	0.965925	−	0.220466i
$446$	−19.2505	+	36.4019i	−0.911537	+	1.72368i
$447$	32.4862	−	12.1787i	1.53655	−	0.576034i
$448$	8.22223	+	3.97464i	0.388464	+	0.187784i
$449$	16.9521	+	21.2572i	0.800017	+	1.00319i	0.999728	+	0.0233345i	$0.00742827\pi$
$449$	16.9521	+	21.2572i	0.800017	+	1.00319i	−0.199711	+	0.979855i	$0.564000\pi$
$450$	−6.99622	−	14.2894i	−0.329805	−	0.673610i
$451$	−2.99979	−	6.22913i	−0.141255	−	0.293318i
$452$	0.231620	−	0.749580i	0.0108945	−	0.0352573i
$453$	−20.0117	+	20.9152i	−0.940231	+	0.982684i
$454$	−1.62463	+	1.88691i	−0.0762477	+	0.0885572i
$455$	−4.19885	−	2.02206i	−0.196845	−	0.0947956i
$456$	−1.09218	−	4.35478i	−0.0511461	−	0.203931i
$457$	−4.61486	+	20.2190i	−0.215874	+	0.945807i	0.744616	+	0.667493i	$0.232633\pi$
$457$	−4.61486	+	20.2190i	−0.215874	+	0.945807i	−0.960490	+	0.278314i	$0.910225\pi$
$458$	11.4223	+	3.06363i	0.533731	+	0.143154i
$459$	1.32216	−	0.563403i	0.0617133	−	0.0262974i
$460$	−4.20750	+	55.7755i	−0.196176	+	2.60054i
$461$	5.81131	−	25.4610i	0.270660	−	1.18584i	−0.638577	−	0.769558i	$-0.720476\pi$
$461$	5.81131	−	25.4610i	0.270660	−	1.18584i	0.909236	−	0.416280i	$-0.136666\pi$
$462$	−0.766727	−	2.30575i	−0.0356714	−	0.107273i
$463$			25.5462i			1.18723i	0.804749	+	0.593615i	$0.202300\pi$
$463$			25.5462i			1.18723i	−0.804749	+	0.593615i	$0.797700\pi$
$464$	19.8082	+	8.46368i	0.919574	+	0.392916i
$465$	−2.26679	+	0.849794i	−0.105120	+	0.0394083i
$466$	0.532257	−	14.1314i	0.0246563	−	0.654626i
$467$	4.31865	+	0.985703i	0.199843	+	0.0456129i	0.321271	−	0.946987i	$-0.395890\pi$
$467$	4.31865	+	0.985703i	0.199843	+	0.0456129i	−0.121428	+	0.992600i	$0.538747\pi$
$468$	−6.63172	+	4.95880i	−0.306551	+	0.229220i
$469$	2.48450	−	3.11547i	0.114724	−	0.143859i
$470$	8.31573	−	31.0041i	0.383576	−	1.43011i
$471$	0.870578	+	6.44460i	0.0401141	+	0.296951i
$472$	16.8454	+	1.91066i	0.775372	+	0.0879453i
$473$	1.85261	−	3.84698i	0.0851830	−	0.176884i
$474$	25.9531	+	9.53754i	1.19206	+	0.438074i
$475$	3.09639	−	1.49114i	0.142072	−	0.0684184i
$476$	−0.603341	−	0.186432i	−0.0276541	−	0.00854512i
$477$	−23.4600	−	10.0476i	−1.07416	−	0.460047i
$478$	−1.21819	+	4.54185i	−0.0557186	+	0.207740i
$479$	−20.4698	+	16.3241i	−0.935288	+	0.745867i	−0.967304	−	0.253620i	$-0.918379\pi$
$479$	−20.4698	+	16.3241i	−0.935288	+	0.745867i	0.0320159	+	0.999487i	$0.489807\pi$
$480$	21.6521	+	19.2664i	0.988279	+	0.879385i
$481$		−	13.0243i		−	0.593858i
$482$	−11.6541	−	6.16304i	−0.530828	−	0.280719i
$483$	−10.2927	−	15.6052i	−0.468335	−	0.710063i
$484$	13.9440	−	15.0132i	0.633818	−	0.682417i
$485$	−13.6811	−	6.58846i	−0.621226	−	0.299166i
$486$	17.7648	−	13.0541i	0.805829	−	0.592148i
$487$	4.46671	−	3.56208i	0.202406	−	0.161413i	−0.517041	−	0.855960i	$-0.672967\pi$
$487$	4.46671	−	3.56208i	0.202406	−	0.161413i	0.719447	+	0.694547i	$0.244395\pi$
$488$	4.85561	+	1.70309i	0.219803	+	0.0770954i
$489$	13.4927	−	8.89938i	0.610162	−	0.402444i
$490$	9.52469	+	21.8455i	0.430282	+	0.986881i
$491$	20.0948	+	16.0250i	0.906864	+	0.723200i	0.961354	−	0.275315i	$-0.0887820\pi$
$491$	20.0948	+	16.0250i	0.906864	+	0.723200i	−0.0544904	+	0.998514i	$0.517353\pi$
$492$	−27.5133	+	1.62462i	−1.24040	+	0.0732434i
$493$	−1.44198	−	0.373137i	−0.0649435	−	0.0168053i
$494$	−1.06181	−	1.43944i	−0.0477729	−	0.0647635i
$495$	−0.340334	−	7.70394i	−0.0152969	−	0.346266i
$496$	1.38673	−	1.28415i	0.0622662	−	0.0576602i
$497$	−12.5263	+	2.85904i	−0.561880	+	0.128246i
$498$	−5.51776	−	16.5933i	−0.247257	−	0.743564i
$499$	−5.72228	+	4.56336i	−0.256164	+	0.204284i	−0.743148	−	0.669127i	$-0.766668\pi$
$499$	−5.72228	+	4.56336i	−0.256164	+	0.204284i	0.486984	+	0.873411i	$0.338097\pi$
$500$	3.70052	−	6.40218i	0.165492	−	0.286314i
$501$	−3.35115	+	37.0823i	−0.149718	+	1.65672i
$502$	20.3750	−	3.84994i	0.909379	−	0.171831i
$503$	7.68374	−	1.75376i	0.342601	−	0.0781964i	−0.0477586	−	0.998859i	$-0.515208\pi$
$503$	7.68374	−	1.75376i	0.342601	−	0.0781964i	0.390360	+	0.920662i	$0.372351\pi$
$504$	−9.66359	−	0.665836i	−0.430450	−	0.0296587i
$505$			19.3504i			0.861082i
$506$	−5.43167	+	10.2711i	−0.241467	+	0.456605i
$507$	9.86274	−	16.4937i	0.438020	−	0.732512i
$508$	0.0761295	−	0.0298352i	0.00337770	−	0.00132372i
$509$	−7.85459	−	16.3102i	−0.348149	−	0.722938i	0.651204	−	0.758902i	$-0.274264\pi$
$509$	−7.85459	−	16.3102i	−0.348149	−	0.722938i	−0.999353	+	0.0359642i	$0.988550\pi$
$510$	−1.68010	−	1.09253i	−0.0743960	−	0.0483782i
$511$	12.8181	−	6.17287i	0.567039	−	0.273072i
$512$	−21.3410	−	7.52082i	−0.943147	−	0.332377i
$513$	2.79480	+	3.85560i	0.123393	+	0.170229i
$514$	−20.8184	+	3.93373i	−0.918260	+	0.173509i
$515$	5.63563	−	24.6913i	0.248336	−	1.08803i
$516$	−11.3786	−	12.6590i	−0.500913	−	0.557284i
$517$	4.15740	−	5.21321i	0.182842	−	0.229277i
$518$	9.94078	−	11.5456i	0.436773	−	0.507286i
$519$	−3.99947	−	29.6067i	−0.175557	−	1.29959i
$520$	10.8961	+	3.82177i	0.477825	+	0.167596i
$521$			22.1448i			0.970182i	0.874464	+	0.485091i	$0.161213\pi$
$521$			22.1448i			0.970182i	−0.874464	+	0.485091i	$0.838787\pi$
$522$	−22.8416	−	0.509740i	−0.999751	−	0.0223107i
$523$		−	29.0663i		−	1.27098i	−0.772109	−	0.635491i	$-0.780798\pi$
$523$		−	29.0663i		−	1.27098i	0.772109	−	0.635491i	$-0.219202\pi$
$524$	30.4398	−	20.7315i	1.32977	−	0.905658i
$525$	−0.992626	−	7.34808i	−0.0433218	−	0.320696i
$526$	8.82578	+	7.59899i	0.384822	+	0.331332i
$527$	−0.0814825	+	0.102176i	−0.00354944	+	0.00445085i
$528$	2.52335	+	5.46614i	0.109815	+	0.237883i
$529$	−14.7727	+	64.7236i	−0.642293	+	2.81407i
$530$	6.60750	+	34.9688i	0.287012	+	1.51895i
$531$	−17.3373	+	4.77113i	−0.752374	+	0.207049i
$532$	0.157393	−	2.08644i	0.00682386	−	0.0904585i
$533$	−9.89310	+	4.76426i	−0.428518	+	0.206363i
$534$	9.43494	−	14.5091i	0.408290	−	0.627868i
$535$	−7.65655	−	15.8990i	−0.331022	−	0.687374i
$536$	−5.25901	+	8.35592i	−0.227155	+	0.360921i
$537$	10.5839	−	17.6998i	0.456731	−	0.763804i
$538$	−4.01645	−	2.12402i	−0.173161	−	0.0915731i
$539$			4.95043i			0.213230i
$540$	−28.9226	−	10.4159i	−1.24463	−	0.448229i
$541$	19.4453	−	4.43825i	0.836017	−	0.190815i	0.216979	−	0.976176i	$-0.430380\pi$
$541$	19.4453	−	4.43825i	0.836017	−	0.190815i	0.619038	+	0.785361i	$0.287523\pi$
$542$	1.58971	+	8.41321i	0.0682840	+	0.361378i
$543$	−1.46762	+	16.2400i	−0.0629815	+	0.696924i
$544$	1.53699	+	0.292780i	0.0658977	+	0.0125528i
$545$	−28.4981	+	22.7265i	−1.22072	+	0.973495i
$546$	−3.66198	+	1.21771i	−0.156718	+	0.0521134i
$547$	26.6253	−	6.07705i	1.13842	−	0.259836i	0.388551	−	0.921427i	$-0.372976\pi$
$547$	26.6253	−	6.07705i	1.13842	−	0.259836i	0.749865	+	0.661591i	$0.230119\pi$
$548$	−37.4652	−	21.6553i	−1.60044	−	0.925067i
$549$	−5.45245	+	0.240871i	−0.232705	+	0.0102801i
$550$	−3.70870	+	2.73573i	−0.158139	+	0.116652i
$551$	0.142182	−	4.93316i	0.00605714	−	0.210160i
$552$	29.6444	+	35.5882i	1.26175	+	1.51474i
$553$	10.0747	+	8.03434i	0.428422	+	0.341655i
$554$	21.1270	−	9.21139i	0.897598	−	0.391354i
$555$	40.3624	−	26.6218i	1.71329	−	1.13003i
$556$	20.7644	−	14.1419i	0.880606	−	0.599750i
$557$	4.01907	−	3.20510i	0.170294	−	0.135805i	−0.534634	−	0.845083i	$-0.679551\pi$
$557$	4.01907	−	3.20510i	0.170294	−	0.135805i	0.704928	+	0.709279i	$0.250979\pi$
$558$	−0.858022	+	1.81174i	−0.0363230	+	0.0766969i
$559$	−6.10977	−	2.94231i	−0.258416	−	0.124446i
$560$	6.74205	+	11.7043i	0.284904	+	0.494596i
$561$	−0.229210	−	0.347515i	−0.00967726	−	0.0146721i
$562$	3.69628	−	6.98952i	0.155918	−	0.294835i
$563$		−	34.8824i		−	1.47012i	−0.678004	−	0.735058i	$-0.737155\pi$
$563$		−	34.8824i		−	1.47012i	0.678004	−	0.735058i	$-0.262845\pi$
$564$	−12.9248	−	23.2273i	−0.544230	−	0.978047i
$565$	0.907213	−	0.723478i	0.0381667	−	0.0304369i
$566$	−21.8456	−	5.85929i	−0.918239	−	0.246284i
$567$	9.77587	−	3.16056i	0.410548	−	0.132731i
$568$	30.0556	−	10.4919i	1.26110	−	0.440230i
$569$	−20.6651	+	9.95180i	−0.866327	+	0.417201i	−0.813612	−	0.581408i	$-0.802502\pi$
$569$	−20.6651	+	9.95180i	−0.866327	+	0.417201i	−0.0527154	+	0.998610i	$0.516788\pi$
$570$	2.29049	−	6.23276i	0.0959381	−	0.261062i
$571$	5.03453	−	10.4543i	0.210688	−	0.437499i	−0.768666	−	0.639651i	$-0.779079\pi$
$571$	5.03453	−	10.4543i	0.210688	−	0.437499i	0.979354	+	0.202152i	$0.0647934\pi$
$572$	1.75747	+	1.63231i	0.0734836	+	0.0682504i
$573$	5.12898	+	37.9681i	0.214266	+	1.58614i
$574$	−12.4062	−	3.32752i	−0.517825	−	0.138888i
$575$	−22.1059	+	27.7199i	−0.921880	+	1.15600i
$576$	23.9782	−	1.02367i	0.999090	−	0.0426530i
$577$	−24.6320	−	5.62209i	−1.02544	−	0.234051i	−0.323458	−	0.946243i	$-0.604845\pi$
$577$	−24.6320	−	5.62209i	−1.02544	−	0.234051i	−0.701985	+	0.712192i	$0.747703\pi$
$578$	23.9165	+	0.900807i	0.994795	+	0.0374687i
$579$	10.6942	−	4.00913i	0.444435	−	0.166614i
$580$	17.1679	+	26.8379i	0.712856	+	1.11438i
$581$		−	8.14952i		−	0.338099i
$582$	−11.9318	+	3.96767i	−0.494589	+	0.164465i
$583$	−1.64497	+	7.20708i	−0.0681276	+	0.298487i
$584$	−29.8608	+	18.7320i	−1.23565	+	0.775134i
$585$	−12.2354	+	0.540518i	−0.505871	+	0.0223477i
$586$	−0.992262	+	3.69952i	−0.0409900	+	0.152826i
$587$	4.86802	−	21.3282i	0.200925	−	0.880309i	−0.769451	−	0.638706i	$-0.779470\pi$
$587$	4.86802	−	21.3282i	0.200925	−	0.880309i	0.970375	−	0.241602i	$-0.0776730\pi$
$588$	18.2539	+	7.49949i	0.752777	+	0.309274i
$589$	−0.390137	−	0.187880i	−0.0160753	−	0.00774146i
$590$	19.0017	+	16.3605i	0.782289	+	0.673550i
$591$	−31.8894	+	33.3293i	−1.31176	+	1.37098i
$592$	−21.2954	+	31.1684i	−0.875234	+	1.28101i
$593$	−14.7453	−	30.6190i	−0.605517	−	1.25737i	−0.948127	−	0.317892i	$-0.897025\pi$
$593$	−14.7453	−	30.6190i	−0.605517	−	1.25737i	0.342609	−	0.939478i	$-0.388689\pi$
$594$	−4.64251	−	4.38450i	−0.190485	−	0.179898i
$595$	−0.582332	−	0.730221i	−0.0238733	−	0.0299361i
$596$	−39.6167	+	5.95124i	−1.62276	+	0.243772i
$597$	−16.4064	+	6.15056i	−0.671468	+	0.251726i
$598$	16.3125	+	8.62657i	0.667068	+	0.352767i
$599$	14.9237	−	3.40624i	0.609767	−	0.139175i	0.0935232	−	0.995617i	$-0.470187\pi$
$599$	14.9237	−	3.40624i	0.609767	−	0.139175i	0.516244	+	0.856442i	$0.327330\pi$
$600$	4.46918	+	17.8196i	0.182454	+	0.727483i
$601$	14.2818	−	29.6565i	0.582568	−	1.20971i	−0.376468	−	0.926430i	$-0.622861\pi$
$601$	14.2818	−	29.6565i	0.582568	−	1.20971i	0.959036	−	0.283285i	$-0.0914243\pi$
$602$	−3.17039	−	7.27152i	−0.129216	−	0.296365i
$603$	1.87739	−	10.3024i	0.0764534	−	0.419545i
$604$	27.6262	−	18.8152i	1.12409	−	0.765581i
$605$	29.5451	−	6.74347i	1.20118	−	0.274161i
$606$	11.1526	+	11.5055i	0.453043	+	0.467377i
$607$	−3.98441	+	4.99629i	−0.161722	+	0.202793i	−0.856090	−	0.516828i	$-0.827113\pi$
$607$	−3.98441	+	4.99629i	−0.161722	+	0.202793i	0.694367	+	0.719621i	$0.255684\pi$
$608$	0.187445	+	5.18081i	0.00760190	+	0.210110i
$609$	−10.0264	−	3.58440i	−0.406289	−	0.145247i
$610$	4.51777	+	6.12452i	0.182919	+	0.247975i
$611$	−8.27962	−	6.60278i	−0.334958	−	0.267120i
$612$	−1.62864	+	0.318718i	−0.0658339	+	0.0128834i
$613$	−7.78724	−	34.1181i	−0.314524	−	1.37802i	−0.847009	−	0.531579i	$-0.821599\pi$
$613$	−7.78724	−	34.1181i	−0.314524	−	1.37802i	0.532485	−	0.846440i	$-0.321258\pi$
$614$	7.85380	+	0.295811i	0.316954	+	0.0119380i
$615$	−34.9860	−	20.9205i	−1.41077	−	0.843598i
$616$	0.312082	+	2.78838i	0.0125742	+	0.112347i
$617$	−28.8515	−	13.8942i	−1.16152	−	0.559358i	−0.249044	−	0.968492i	$-0.580117\pi$
$617$	−28.8515	−	13.8942i	−1.16152	−	0.559358i	−0.912474	+	0.409134i	$0.865831\pi$
$618$	−10.8799	−	17.9292i	−0.437656	−	0.721217i
$619$	6.65688	+	29.1657i	0.267563	+	1.17227i	0.912839	+	0.408319i	$0.133885\pi$
$619$	6.65688	+	29.1657i	0.267563	+	1.17227i	−0.645277	+	0.763949i	$0.723258\pi$
$620$	2.76433	−	0.415260i	0.111018	−	0.0166772i
$621$	−43.2356	−	23.3273i	−1.73498	−	0.936092i
$622$	5.84534	−	11.0533i	0.234377	−	0.443198i
$623$	6.30607	−	5.02892i	0.252647	−	0.201480i
$624$	8.68131	−	4.00757i	0.347531	−	0.160431i
$625$	26.7474	−	12.8808i	1.06989	−	0.515234i
$626$	16.4033	+	22.2371i	0.655606	+	0.888775i
$627$	0.953587	−	0.996643i	0.0380826	−	0.0398021i
$628$	0.564860	−	7.48790i	0.0225404	−	0.298800i
$629$	1.13253	−	2.35172i	0.0451569	−	0.0937692i
$630$	−11.2588	−	8.85947i	−0.448562	−	0.352970i
$631$	−42.4516	−	9.68931i	−1.68997	−	0.385725i	−0.733993	−	0.679157i	$-0.762345\pi$
$631$	−42.4516	−	9.68931i	−1.68997	−	0.385725i	−0.955980	+	0.293432i	$0.905203\pi$
$632$	−27.0212	−	17.0065i	−1.07485	−	0.676482i
$633$	22.3418	+	7.26833i	0.888006	+	0.288890i
$634$	−22.5980	+	26.2463i	−0.897482	+	1.04237i
$635$	0.117903	+	0.0269107i	0.00467885	+	0.00106792i
$636$	24.0829	+	16.9837i	0.954950	+	0.673447i
$637$	7.86226			0.311514
$638$	1.04089	+	6.53558i	0.0412093	+	0.258746i
$639$	−25.4439	+	22.1969i	−1.00655	+	0.878094i
$640$	−19.8265	−	26.9614i	−0.783712	−	1.06574i
$641$	−3.10462	+	13.6022i	−0.122625	+	0.537256i	0.875877	+	0.482535i	$0.160284\pi$
$641$	−3.10462	+	13.6022i	−0.122625	+	0.537256i	−0.998502	+	0.0547205i	$0.982573\pi$
$642$	−13.7158	−	5.04046i	−0.541321	−	0.198931i
$643$	−23.1033	−	18.4242i	−0.911104	−	0.726581i	0.0511623	−	0.998690i	$-0.483707\pi$
$643$	−23.1033	−	18.4242i	−0.911104	−	0.726581i	−0.962266	+	0.272109i	$0.912279\pi$
$644$	7.87629	+	20.0976i	0.310369	+	0.791958i
$645$	−3.37018	−	24.9483i	−0.132701	−	0.982337i
$646$	−0.0665573	−	0.352240i	−0.00261866	−	0.0138587i
$647$	16.6808	+	8.03306i	0.655790	+	0.315812i	0.732025	−	0.681278i	$-0.238575\pi$
$647$	16.6808	+	8.03306i	0.655790	+	0.315812i	−0.0762345	+	0.997090i	$0.524290\pi$
$648$	−23.2001	+	10.4764i	−0.911387	+	0.411550i
$649$	2.25993	+	4.69279i	0.0887099	+	0.184208i
$650$	4.34488	+	5.89015i	0.170420	+	0.231031i
$651$	−0.645870	+	0.675033i	−0.0253137	+	0.0264566i
$652$	−17.3770	+	6.81006i	−0.680535	+	0.266702i
$653$	13.9893	+	17.5420i	0.547442	+	0.686471i	0.976181	−	0.216958i	$-0.0696133\pi$
$653$	13.9893	+	17.5420i	0.547442	+	0.686471i	−0.428739	+	0.903429i	$0.641042\pi$
$654$	−3.84617	+	29.9376i	−0.150397	+	1.17065i
$655$	54.4710			2.12836
$656$	31.4649	+	4.77436i	1.22850	+	0.186408i
$657$	21.9983	−	30.2316i	0.858237	−	1.17945i
$658$	−2.30005	−	12.1725i	−0.0896654	−	0.474535i
$659$	−9.01713	+	18.7243i	−0.351257	+	0.729394i	−0.999486	−	0.0320520i	$-0.989796\pi$
$659$	−9.01713	+	18.7243i	−0.351257	+	0.729394i	0.648229	+	0.761446i	$0.275510\pi$
$660$	−1.46626	+	8.78287i	−0.0570740	+	0.341873i
$661$	−13.7996	−	17.3042i	−0.536743	−	0.673054i	0.437327	−	0.899303i	$-0.355925\pi$
$661$	−13.7996	−	17.3042i	−0.536743	−	0.673054i	−0.974070	+	0.226249i	$0.927354\pi$
$662$	11.8542	+	0.446486i	0.460727	+	0.0173532i
$663$	−0.551923	+	0.364031i	−0.0214349	+	0.0141378i
$664$	2.24590	+	20.0666i	0.0871580	+	0.778735i
$665$	1.92949	−	2.41950i	0.0748224	−	0.0938243i
$666$	8.65545	−	39.0917i	0.335392	−	1.51477i
$667$	20.7601	+	46.4895i	0.803834	+	1.80008i
$668$	12.6928	−	41.0771i	0.491101	−	1.58932i
$669$	−15.6023	+	47.9593i	−0.603220	+	1.85421i
$670$	−13.3856	+	5.83616i	−0.517132	+	0.225471i
$671$	0.351782	+	1.54126i	0.0135804	+	0.0594996i
$672$	10.7545	+	3.07341i	0.414862	+	0.118559i
$673$	7.35463	+	9.22241i	0.283500	+	0.355498i	0.903108	−	0.429414i	$-0.141280\pi$
$673$	7.35463	+	9.22241i	0.283500	+	0.355498i	−0.619608	+	0.784912i	$0.712708\pi$
$674$	12.4747	+	28.6117i	0.480509	+	1.10208i
$675$	−11.4362	−	15.7770i	−0.440181	−	0.607258i
$676$	−15.1015	+	16.2594i	−0.580826	+	0.625361i
$677$	−1.20665	−	5.28666i	−0.0463752	−	0.203183i	0.946433	−	0.322901i	$-0.104658\pi$
$677$	−1.20665	−	5.28666i	−0.0463752	−	0.203183i	−0.992808	+	0.119718i	$0.961801\pi$
$678$	0.122439	−	0.953040i	0.00470226	−	0.0366013i
$679$	−5.86010			−0.224890
$680$	1.63512	+	1.63754i	0.0627038	+	0.0627968i
$681$	−1.56507	+	2.61731i	−0.0599737	+	0.100296i
$682$	0.560841	+	0.150425i	0.0214757	+	0.00576009i
$683$	26.4832	−	12.7536i	1.01335	−	0.488005i	0.147903	−	0.989002i	$-0.452748\pi$
$683$	26.4832	−	12.7536i	1.01335	−	0.488005i	0.865449	+	0.500997i	$0.167033\pi$
$684$	−2.23035	−	5.02603i	−0.0852796	−	0.192175i
$685$	−27.7697	−	57.6644i	−1.06103	−	2.20324i
$686$	15.5336	+	13.3744i	0.593075	+	0.510637i
$687$	14.4251	+	1.30361i	0.550353	+	0.0497357i
$688$	9.81041	+	17.0310i	0.374018	+	0.649299i
$689$	11.4463	+	2.61253i	0.436068	+	0.0995297i
$690$	6.60911	+	68.1853i	0.251604	+	2.59577i
$691$	17.0217	+	13.5744i	0.647537	+	0.516394i	0.891284	−	0.453445i	$-0.149805\pi$
$691$	17.0217	+	13.5744i	0.647537	+	0.516394i	−0.243747	+	0.969839i	$0.578377\pi$
$692$	−2.59499	+	34.3997i	−0.0986468	+	1.30768i
$693$	−1.40831	−	2.62167i	−0.0534972	−	0.0995891i
$694$	19.1446	+	0.721075i	0.726718	+	0.0273716i
$695$	37.1572			1.40945
$696$	25.6757	+	6.06274i	0.973236	+	0.229808i
$697$	−2.20061			−0.0833541
$698$	34.3682	+	1.29447i	1.30085	+	0.0489963i
$699$	−2.31860	−	17.1638i	−0.0876973	−	0.649194i
$700$	−0.644049	+	8.53764i	−0.0243428	+	0.322692i
$701$	40.5943	+	32.3729i	1.53323	+	1.22271i	0.889034	+	0.457842i	$0.151377\pi$
$701$	40.5943	+	32.3729i	1.53323	+	1.22271i	0.644191	+	0.764864i	$0.277194\pi$
$702$	−6.96345	+	7.37323i	−0.262818	+	0.278285i
$703$	8.43180	+	1.92450i	0.318011	+	0.0725840i
$704$	−1.53688	−	6.77982i	−0.0579234	−	0.255524i
$705$	3.53843	−	39.1547i	0.133265	−	1.47465i
$706$	−20.1817	−	17.3764i	−0.759549	−	0.653971i
$707$	3.24010	+	6.72814i	0.121856	+	0.253038i
$708$	20.7275	−	1.22392i	0.778986	−	0.0459979i
$709$	−21.3247	+	10.2694i	−0.800865	+	0.385676i	−0.789108	−	0.614255i	$-0.789457\pi$
$709$	−21.3247	+	10.2694i	−0.800865	+	0.385676i	−0.0117571	+	0.999931i	$0.503742\pi$
$710$	45.4763	+	12.1974i	1.70669	+	0.457759i
$711$	33.3156	+	6.07109i	1.24943	+	0.227684i
$712$	−14.1415	+	14.1206i	−0.529976	+	0.529192i
$713$	4.46725			0.167300
$714$	−0.767107	−	0.0985522i	−0.0287083	−	0.00368822i
$715$	0.789405	+	3.45861i	0.0295221	+	0.129345i
$716$	−16.2058	+	17.4484i	−0.605638	+	0.652076i
$717$	−0.518352	+	5.73585i	−0.0193582	+	0.214209i
$718$	2.62157	+	6.01275i	0.0978361	+	0.224394i
$719$	−14.8133	−	18.5753i	−0.552443	−	0.692742i	0.424697	−	0.905335i	$-0.360381\pi$
$719$	−14.8133	−	18.5753i	−0.552443	−	0.692742i	−0.977141	+	0.212593i	$0.931809\pi$
$720$	30.1641	+	18.7119i	1.12415	+	0.697352i
$721$	−2.17489	−	9.52882i	−0.0809972	−	0.354872i
$722$	−23.5420	+	10.2643i	−0.876141	+	0.381999i
$723$	−15.3541	−	4.99508i	−0.571027	−	0.185769i
$724$	5.55876	−	17.9895i	0.206590	−	0.668574i
$725$	−0.581803	+	20.1864i	−0.0216076	+	0.749703i
$726$	13.6805	−	21.0378i	0.507730	−	0.780787i
$727$	−29.6937	+	37.2348i	−1.10128	+	1.38096i	−0.183901	+	0.982945i	$0.558872\pi$
$727$	−29.6937	+	37.2348i	−1.10128	+	1.38096i	−0.917379	+	0.398016i	$0.869699\pi$
$728$	4.42850	−	0.495649i	0.164131	−	0.0183700i
$729$	18.7015	−	19.4744i	0.692648	−	0.721276i
$730$	−52.0986	−	1.96228i	−1.92825	−	0.0726272i
$731$	−0.847354	−	1.06255i	−0.0313405	−	0.0392998i
$732$	6.21606	+	1.03774i	0.229752	+	0.0383560i
$733$	−0.229032	+	0.475590i	−0.00845949	+	0.0175663i	−0.905156	−	0.425080i	$-0.860246\pi$
$733$	−0.229032	+	0.475590i	−0.00845949	+	0.0175663i	0.896696	+	0.442646i	$0.145960\pi$
$734$	−7.02524	−	37.1796i	−0.259306	−	1.37232i
$735$	16.0705	+	24.3651i	0.592769	+	0.898722i
$736$	−24.9324	−	47.3159i	−0.919022	−	1.74409i
$737$	−3.03332			−0.111734
$738$	−32.8597	+	7.72509i	−1.20958	+	0.284365i
$739$	−25.8313	−	32.3914i	−0.950219	−	1.19154i	−0.981391	−	0.192023i	$-0.938495\pi$
$739$	−25.8313	−	32.3914i	−0.950219	−	1.19154i	0.0311718	−	0.999514i	$-0.490076\pi$
$740$	−51.9819	+	20.3718i	−1.91089	+	0.748881i
$741$	−1.58287	−	1.51448i	−0.0581480	−	0.0556360i
$742$	8.15272	+	11.0523i	0.299296	+	0.405741i
$743$	−21.2405	−	44.1063i	−0.779238	−	1.61810i	−0.786077	−	0.618128i	$-0.787891\pi$
$743$	−21.2405	−	44.1063i	−0.779238	−	1.61810i	0.00683891	−	0.999977i	$-0.497823\pi$
$744$	1.40430	−	1.84013i	0.0514840	−	0.0674623i
$745$	−53.3838	−	25.7083i	−1.95583	−	0.941879i
$746$	−0.641040	−	3.39256i	−0.0234701	−	0.124211i
$747$	−10.1349	−	18.8669i	−0.370817	−	0.690303i
$748$	0.175398	+	0.447557i	0.00641320	+	0.0163643i
$749$	−5.32437	−	4.24604i	−0.194548	−	0.155147i
$750$	3.12397	−	8.50079i	0.114071	−	0.310405i
$751$	9.01170	−	39.4828i	0.328841	−	1.44075i	−0.492500	−	0.870312i	$-0.663917\pi$
$751$	9.01170	−	39.4828i	0.328841	−	1.44075i	0.821342	−	0.570436i	$-0.193226\pi$
$752$	9.01802	+	29.3386i	0.328853	+	1.06987i
$753$	23.7796	−	8.91470i	0.866577	−	0.324870i
$754$	10.3798	−	1.65314i	0.378010	−	0.0602039i
$755$	49.4362			1.79917
$756$	−11.8005	+	1.22129i	−0.429179	+	0.0444178i
$757$	0.718330	+	0.163954i	0.0261082	+	0.00595902i	0.235555	−	0.971861i	$-0.424309\pi$
$757$	0.718330	+	0.163954i	0.0261082	+	0.00595902i	−0.209447	+	0.977820i	$0.567166\pi$
$758$	11.4027	−	13.2436i	0.414165	−	0.481029i
$759$	−4.40231	+	13.5321i	−0.159794	+	0.491183i
$760$	−4.08420	+	6.48929i	−0.148149	+	0.235391i
$761$	−41.5996	−	9.49483i	−1.50798	−	0.344187i	−0.612927	−	0.790140i	$-0.710008\pi$
$761$	−41.5996	−	9.49483i	−1.50798	−	0.344187i	−0.895057	+	0.445952i	$0.852865\pi$
$762$	0.0856135	−	0.0519528i	0.00310145	−	0.00188205i
$763$	−6.10339	+	12.6738i	−0.220957	+	0.458823i
$764$	3.32785	−	44.1147i	0.120398	−	1.59601i
$765$	−2.25627	−	0.966329i	−0.0815755	−	0.0349377i
$766$	−15.3810	−	20.8513i	−0.555738	−	0.753387i
$767$	7.45307	−	3.58921i	0.269115	−	0.129599i
$768$	−27.3277	−	4.60387i	−0.986104	−	0.166128i
$769$	2.38549	−	1.90237i	0.0860231	−	0.0686011i	−0.579534	−	0.814948i	$-0.696765\pi$
$769$	2.38549	−	1.90237i	0.0860231	−	0.0686011i	0.665557	+	0.746347i	$0.268194\pi$
$770$	−1.93999	+	3.66845i	−0.0699125	+	0.132202i
$771$	−24.2971	+	9.10872i	−0.875040	+	0.328043i
$772$	−13.0415	+	1.95910i	−0.469373	+	0.0705095i
$773$	−4.74891	−	20.8063i	−0.170806	−	0.748352i	−0.985668	−	0.168696i	$-0.946044\pi$
$773$	−4.74891	−	20.8063i	−0.170806	−	0.748352i	0.814862	−	0.579656i	$-0.196813\pi$
$774$	−16.3828	−	12.8915i	−0.588866	−	0.463374i
$775$	1.59643	+	0.768800i	0.0573454	+	0.0276161i
$776$	14.4293	−	1.61497i	0.517983	−	0.0579740i
$777$	9.57636	−	16.0148i	0.343550	−	0.574528i
$778$	8.59427	+	0.323701i	0.308119	+	0.0116052i
$779$	−1.62251	−	7.10866i	−0.0581323	−	0.254694i
$780$	13.9489	+	2.32871i	0.499452	+	0.0833811i
$781$	7.64665	+	6.09800i	0.273619	+	0.218204i
$782$	2.19533	+	2.97610i	0.0785047	+	0.106425i
$783$	−27.6696	+	4.17075i	−0.988830	+	0.149051i
$784$	−18.8151	−	12.8551i	−0.671967	−	0.459112i
$785$	6.92464	−	8.68322i	0.247151	−	0.309917i
$786$	32.3876	−	31.3943i	1.15523	−	1.11980i
$787$	−39.6184	+	9.04263i	−1.41224	+	0.322335i	−0.859550	−	0.511051i	$-0.829256\pi$
$787$	−39.6184	+	9.04263i	−1.41224	+	0.322335i	−0.552692	+	0.833386i	$0.686399\pi$
$788$	44.0235	−	29.9828i	1.56827	−	1.06809i
$789$	12.2421	+	7.32042i	0.435832	+	0.260614i
$790$	−18.8729	−	43.2863i	−0.671467	−	1.54006i
$791$	0.194296	−	0.403460i	0.00690838	−	0.0143454i
$792$	4.19018	+	6.06724i	0.148892	+	0.215590i
$793$	2.44782	−	0.558700i	0.0869247	−	0.0198400i
$794$	−40.6101	−	21.4759i	−1.44120	−	0.762150i
$795$	15.3000	+	40.8120i	0.542634	+	1.44745i
$796$	20.0074	−	3.00553i	0.709145	−	0.106528i
$797$	−12.3504	−	15.4869i	−0.437475	−	0.548576i	0.513401	−	0.858149i	$-0.328385\pi$
$797$	−12.3504	−	15.4869i	−0.437475	−	0.548576i	−0.950876	+	0.309573i	$0.899814\pi$
$798$	−0.247232	−	2.55066i	−0.00875191	−	0.0902923i
$799$	−0.920855	−	1.91217i	−0.0325775	−	0.0676479i
$800$	−0.767020	−	21.1997i	−0.0271183	−	0.749524i
$801$	8.34506	−	19.4848i	0.294858	−	0.688460i
$802$	−5.51352	−	4.74714i	−0.194689	−	0.167627i
$803$	−9.75735	−	4.69889i	−0.344329	−	0.165820i
$804$	−4.59524	+	11.1849i	−0.162062	+	0.394461i
$805$	−7.10423	+	31.1257i	−0.250391	+	1.09704i
$806$	0.238905	−	0.890727i	0.00841508	−	0.0313745i
$807$	−5.29164	−	1.72150i	−0.186274	−	0.0605996i
$808$	−9.83229	−	15.6738i	−0.345899	−	0.551401i
$809$	−6.44040	+	28.2172i	−0.226432	+	0.992065i	0.726091	+	0.687599i	$0.241335\pi$
$809$	−6.44040	+	28.2172i	−0.226432	+	0.992065i	−0.952523	+	0.304466i	$0.901522\pi$
$810$	−37.0830	−	6.50882i	−1.30296	−	0.228696i
$811$		−	13.4058i		−	0.470741i	−0.971906	−	0.235370i	$-0.924370\pi$
$811$		−	13.4058i		−	0.470741i	0.971906	−	0.235370i	$-0.0756303\pi$
$812$	10.4631	+	6.45689i	0.367183	+	0.226592i
$813$	3.68105	+	9.81905i	0.129100	+	0.344369i
$814$	−11.5893	−	0.436508i	−0.406205	−	0.0152996i
$815$	−26.9121	−	6.14251i	−0.942690	−	0.215163i
$816$	1.91601	+	0.0312604i	0.0670737	+	0.00109433i
$817$	2.80761	−	3.52063i	0.0982259	−	0.123171i
$818$	−30.7062	−	8.23583i	−1.07362	−	0.287959i
$819$	−4.16374	+	2.23667i	−0.145493	+	0.0781557i
$820$	34.4889	+	32.0328i	1.20441	+	1.11863i
$821$	−1.67911	+	3.48671i	−0.0586013	+	0.121687i	−0.928213	−	0.372050i	$-0.878655\pi$
$821$	−1.67911	+	3.48671i	−0.0586013	+	0.121687i	0.869611	+	0.493737i	$0.164369\pi$
$822$	−49.7462	−	18.2813i	−1.73510	−	0.637635i
$823$	−1.65017	+	0.794678i	−0.0575212	+	0.0277007i	−0.462423	−	0.886659i	$-0.653020\pi$
$823$	−1.65017	+	0.794678i	−0.0575212	+	0.0277007i	0.404902	+	0.914360i	$0.367306\pi$
$824$	7.98126	+	22.8635i	0.278040	+	0.796486i
$825$	−3.90205	+	4.07824i	−0.135852	+	0.141986i
$826$	9.34635	+	2.50682i	0.325201	+	0.0872235i
$827$	−13.6419	+	10.8790i	−0.474374	+	0.378301i	−0.831293	−	0.555835i	$-0.812399\pi$
$827$	−13.6419	+	10.8790i	−0.474374	+	0.378301i	0.356919	+	0.934136i	$0.383827\pi$
$828$	43.2281	+	36.7328i	1.50228	+	1.27655i
$829$		−	14.8810i		−	0.516838i	−0.966033	−	0.258419i	$-0.916798\pi$
$829$		−	14.8810i		−	0.516838i	0.966033	−	0.258419i	$-0.0832016\pi$
$830$	−13.9612	+	26.4000i	−0.484599	+	0.916359i
$831$	23.5637	−	15.5419i	0.817415	−	0.539142i
$832$	−10.7677	+	2.44087i	−0.373303	+	0.0846220i
$833$	1.41964	+	0.683662i	0.0491875	+	0.0236875i
$834$	22.0931	−	21.4155i	0.765022	−	0.741558i
$835$	49.7154	−	39.6467i	1.72047	−	1.37203i
$836$	−1.31643	+	0.896574i	−0.0455297	+	0.0310087i
$837$	−0.655765	+	2.36598i	−0.0226666	+	0.0817802i
$838$	22.5752	−	9.84281i	0.779847	−	0.340014i
$839$	−19.9404	−	15.9020i	−0.688420	−	0.548997i	0.215603	−	0.976481i	$-0.430828\pi$
$839$	−19.9404	−	15.9020i	−0.688420	−	0.548997i	−0.904023	+	0.427484i	$0.859400\pi$
$840$	10.5879	+	12.7108i	0.365317	+	0.438565i
$841$	25.3600	+	14.0666i	0.874484	+	0.485055i
$842$	−21.1571	+	15.6065i	−0.729120	+	0.537837i
$843$	2.99580	−	9.20864i	0.103181	−	0.317162i
$844$	−23.4876	−	13.5761i	−0.808478	−	0.467308i
$845$	−31.9976	+	7.30324i	−1.10075	+	0.251239i
$846$	−20.4628	−	25.3201i	−0.703527	−	0.870524i
$847$	9.14367	−	7.29183i	0.314180	−	0.250550i
$848$	−23.1203	−	24.9672i	−0.793955	−	0.857377i
$849$	−27.5885	−	2.49319i	−0.946835	−	0.0855660i
$850$	0.272351	+	1.44136i	0.00934155	+	0.0494381i
$851$	−86.9868	+	19.8542i	−2.98187	+	0.680592i
$852$	34.0694	−	18.9578i	1.16720	−	0.649484i
$853$		−	9.92051i		−	0.339672i	−0.985472	−	0.169836i	$-0.945676\pi$
$853$		−	9.92051i		−	0.339672i	0.985472	−	0.169836i	$-0.0543237\pi$
$854$	2.59634	+	1.37303i	0.0888449	+	0.0469840i
$855$	1.45800	−	8.00092i	0.0498626	−	0.273626i
$856$	14.2803	+	8.98770i	0.488092	+	0.307193i
$857$	−8.78417	−	18.2405i	−0.300061	−	0.623084i	0.695361	−	0.718661i	$-0.255245\pi$
$857$	−8.78417	−	18.2405i	−0.300061	−	0.623084i	−0.995422	+	0.0955770i	$0.969530\pi$
$858$	2.46273	+	1.60146i	0.0840763	+	0.0546731i
$859$	37.6348	−	18.1240i	1.28408	−	0.618381i	0.337646	−	0.941273i	$-0.390369\pi$
$859$	37.6348	−	18.1240i	1.28408	−	0.618381i	0.946436	+	0.322892i	$0.104655\pi$
$860$	−2.18668	+	28.9871i	−0.0745653	+	0.988451i
$861$	−15.6676	−	1.41589i	−0.533952	−	0.0482535i
$862$	−6.07894	−	32.1715i	−0.207050	−	1.09576i
$863$	−3.93636	+	17.2463i	−0.133995	+	0.587072i	0.862691	+	0.505731i	$0.168777\pi$
$863$	−3.93636	+	17.2463i	−0.133995	+	0.587072i	−0.996686	+	0.0813406i	$0.974080\pi$
$864$	28.7197	−	6.25923i	0.977065	−	0.212943i
$865$	−31.8121	+	39.8911i	−1.08164	+	1.35634i
$866$	7.05220	+	6.07194i	0.239643	+	0.206333i
$867$	29.0485	−	3.92406i	0.986539	−	0.133268i
$868$	0.891626	−	0.607256i	0.0302638	−	0.0206116i
$869$		−	9.80911i		−	0.332751i
$870$	26.3394	+	28.7880i	0.892990	+	0.976003i
$871$			4.81752i			0.163235i
$872$	11.5356	−	32.8888i	0.390646	−	1.11375i
$873$	−13.5667	+	7.28774i	−0.459162	+	0.246653i
$874$	−7.99512	+	9.28586i	−0.270439	+	0.314099i
$875$	2.63161	−	3.29993i	0.0889646	−	0.111558i
$876$	−32.1080	+	28.8602i	−1.08483	+	0.975096i
$877$	−6.75471	+	29.5943i	−0.228090	+	0.999328i	0.723105	+	0.690738i	$0.242714\pi$
$877$	−6.75471	+	29.5943i	−0.228090	+	0.999328i	−0.951195	+	0.308590i	$0.900143\pi$
$878$	47.8786	−	9.04686i	1.61582	−	0.305317i
$879$	−0.422218	+	4.67207i	−0.0142410	+	0.157585i
$880$	3.76587	−	9.56747i	0.126947	−	0.322519i
$881$	24.7825	−	11.9346i	0.834944	−	0.402088i	0.0329771	−	0.999456i	$-0.489501\pi$
$881$	24.7825	−	11.9346i	0.834944	−	0.402088i	0.801967	+	0.597368i	$0.203787\pi$
$882$	23.5981	+	5.22494i	0.794589	+	0.175933i
$883$	0.471123	+	0.978297i	0.0158545	+	0.0329223i	0.908746	−	0.417350i	$-0.137041\pi$
$883$	0.471123	+	0.978297i	0.0158545	+	0.0329223i	−0.892891	+	0.450272i	$0.851327\pi$
$884$	0.710810	−	0.278567i	0.0239071	−	0.00936923i
$885$	26.3571	+	15.7607i	0.885984	+	0.529791i
$886$	6.13566	−	11.6023i	0.206132	−	0.389787i
$887$			7.91116i			0.265631i	0.991141	+	0.132815i	$0.0424017\pi$
$887$			7.91116i			0.265631i	−0.991141	+	0.132815i	$0.957598\pi$
$888$	−19.1664	+	42.0724i	−0.643183	+	1.41186i
$889$	0.0455010	−	0.0103853i	0.00152606	−	0.000348312i
$890$	−29.0434	+	5.48788i	−0.973538	+	0.183954i
$891$	−6.52073	−	4.31801i	−0.218453	−	0.144659i
$892$	29.1426	−	50.4190i	0.975767	−	1.68815i
$893$	5.49798	−	4.38449i	0.183983	−	0.146721i
$894$	−46.5582	+	15.4819i	−1.55714	+	0.517793i
$895$	−34.3374	+	7.83729i	−1.14777	+	0.261972i
$896$	−11.4082	−	6.05466i	−0.381121	−	0.202272i
$897$	21.4916	+	6.99174i	0.717584	+	0.233448i
$898$	−22.8254	−	30.9432i	−0.761692	−	1.03259i
$899$	2.03424	−	1.52849i	0.0678456	−	0.0509779i
$900$	9.12654	+	20.5664i	0.304218	+	0.685545i
$901$	1.83961	+	1.46704i	0.0612862	+	0.0488741i
$902$	3.90778	+	8.96276i	0.130115	+	0.298427i
$903$	−5.34924	−	8.11020i	−0.178011	−	0.269891i
$904$	−0.367227	+	1.04699i	−0.0122138	+	0.0348222i
$905$	21.7726	−	17.3631i	0.723745	−	0.577168i
$906$	29.3940	−	28.4925i	0.976551	−	0.946599i
$907$	24.3110	+	11.7076i	0.807234	+	0.388743i	0.791528	−	0.611133i	$-0.209286\pi$
$907$	24.3110	+	11.7076i	0.807234	+	0.388743i	0.0157060	+	0.999877i	$0.495000\pi$
$908$	2.39638	−	2.58013i	0.0795268	−	0.0856246i
$909$	15.8684	+	11.5468i	0.526320	+	0.382983i
$910$	5.82623	+	3.08109i	0.193138	+	0.102137i
$911$			19.2692i			0.638416i	0.947685	+	0.319208i	$0.103417\pi$
$911$			19.2692i			0.638416i	−0.947685	+	0.319208i	$0.896583\pi$
$912$	1.31169	+	6.21235i	0.0434343	+	0.205712i
$913$	−4.85014	+	3.86786i	−0.160516	+	0.128007i
$914$	7.59800	−	28.3281i	0.251320	−	0.937011i
$915$	6.73477	+	6.44382i	0.222645	+	0.213026i
$916$	−15.9791	−	4.93755i	−0.527965	−	0.163141i
$917$	18.9396	−	9.12081i	0.625439	−	0.301196i
$918$	−1.89848	+	0.725832i	−0.0626593	+	0.0239560i
$919$	−8.23667	+	17.1036i	−0.271703	+	0.564197i	−0.991518	−	0.129969i	$-0.958512\pi$
$919$	−8.23667	+	17.1036i	−0.271703	+	0.564197i	0.719815	+	0.694166i	$0.244226\pi$
$920$	8.91492	−	78.5986i	0.293916	−	2.59132i
$921$	9.53908	−	1.28860i	0.314323	−	0.0424609i
$922$	−9.56786	+	35.6725i	−0.315101	+	1.17481i
$923$	9.68483	−	12.1444i	0.318780	−	0.399738i
$924$	0.960816	+	3.29932i	0.0316085	+	0.108540i
$925$	−34.5027	−	7.87502i	−1.13444	−	0.258929i
$926$	1.35978	−	36.1021i	0.0446850	−	1.18639i
$927$	−16.8853	−	19.3554i	−0.554586	−	0.635713i
$928$	−27.5427	−	13.0153i	−0.904134	−	0.427249i
$929$			38.4796i			1.26247i	0.775590	+	0.631237i	$0.217452\pi$
$929$			38.4796i			1.26247i	−0.775590	+	0.631237i	$0.782548\pi$
$930$	3.24869	−	1.08028i	0.106529	−	0.0354238i
$931$	−1.16174	+	5.08994i	−0.0380746	+	0.166816i
$932$	−1.50438	+	19.9424i	−0.0492777	+	0.653234i
$933$	4.73759	−	14.5627i	0.155102	−	0.476760i
$934$	−6.05070	−	1.62288i	−0.197985	−	0.0531023i
$935$	−0.158205	+	0.693142i	−0.00517386	+	0.0226682i
$936$	9.63597	−	6.65484i	0.314962	−	0.217520i
$937$	7.94256	+	3.82494i	0.259472	+	0.124955i	0.559098	−	0.829102i	$-0.311148\pi$
$937$	7.94256	+	3.82494i	0.259472	+	0.124955i	−0.299626	+	0.954057i	$0.596862\pi$
$938$	−3.67696	+	4.27057i	−0.120057	+	0.139439i
$939$	24.4528	+	23.3965i	0.797989	+	0.763514i
$940$	−13.4022	+	43.3727i	−0.437131	+	1.41466i
$941$	−11.5561	−	23.9965i	−0.376718	−	0.782262i	−1.00000		0.000265363i	$-0.999916\pi$
$941$	−11.5561	−	23.9965i	−0.376718	−	0.782262i	0.623282	−	0.781997i	$-0.285799\pi$
$942$	−0.887277	−	9.15392i	−0.0289090	−	0.298251i
$943$	46.9005	+	58.8114i	1.52729	+	1.91516i
$944$	−23.7044	−	3.59682i	−0.771512	−	0.117066i
$945$	−15.4422	−	8.33165i	−0.502333	−	0.271029i
$946$	−2.82290	+	5.33799i	−0.0917802	+	0.173553i
$947$	16.3928	−	3.74154i	0.532693	−	0.121584i	0.0522908	−	0.998632i	$-0.483348\pi$
$947$	16.3928	−	3.74154i	0.532693	−	0.121584i	0.480403	+	0.877048i	$0.340491\pi$
$948$	−36.1695	−	14.8600i	−1.17473	−	0.482630i
$949$	−7.46277	+	15.4966i	−0.242252	+	0.503041i
$950$	−4.45523	+	1.94249i	−0.144547	+	0.0630226i
$951$	−21.7696	+	36.4059i	−0.705927	+	1.18054i
$952$	0.842725	+	0.295583i	0.0273129	+	0.00957991i
$953$	20.2715	−	4.62683i	0.656658	−	0.149878i	0.118806	−	0.992917i	$-0.462093\pi$
$953$	20.2715	−	4.62683i	0.656658	−	0.149878i	0.537851	+	0.843040i	$0.319236\pi$
$954$	32.6191	+	15.4481i	1.05608	+	0.500151i
$955$	40.7963	−	51.1569i	1.32014	−	1.65540i
$956$	1.96331	−	6.35376i	0.0634981	−	0.205495i
$957$	2.62539	+	7.66832i	0.0848667	+	0.247882i
$958$	29.7970	−	21.9798i	0.962698	−	0.710136i
$959$	−19.3110	−	15.4000i	−0.623586	−	0.497293i
$960$	−29.5735	−	28.3800i	−0.954481	−	0.915959i
$961$	6.84847	+	30.0051i	0.220918	+	0.967907i
$962$	−0.693262	+	18.4061i	−0.0223516	+	0.593437i
$963$	−17.6069	−	3.20849i	−0.567373	−	0.103392i
$964$	16.1416	+	9.33000i	0.519886	+	0.300499i
$965$	−17.5735	−	8.46295i	−0.565711	−	0.272432i
$966$	13.7152	+	22.6014i	0.441278	+	0.727187i
$967$	−1.26052	−	5.52268i	−0.0405355	−	0.177597i	0.950608	−	0.310395i	$-0.100461\pi$
$967$	−1.26052	−	5.52268i	−0.0405355	−	0.177597i	−0.991143	+	0.132797i	$0.957604\pi$
$968$	−20.5049	+	20.4746i	−0.659053	+	0.658077i
$969$	−0.154116	−	0.411099i	−0.00495093	−	0.0132064i
$970$	18.9836	+	10.0391i	0.609525	+	0.322336i
$971$	−22.4540	+	17.9065i	−0.720585	+	0.574647i	−0.913632	−	0.406542i	$-0.866734\pi$
$971$	−22.4540	+	17.9065i	−0.720585	+	0.574647i	0.193047	+	0.981189i	$0.438163\pi$
$972$	−25.8003	+	17.5027i	−0.827546	+	0.561398i
$973$	12.9196	−	6.22173i	0.414182	−	0.199460i
$974$	−6.50201	+	4.79622i	−0.208338	+	0.153681i
$975$	6.47705	+	6.19723i	0.207432	+	0.198470i
$976$	−6.77136	−	2.66529i	−0.216746	−	0.0853137i
$977$	11.8758	−	24.6603i	0.379940	−	0.788953i	−0.620051	−	0.784562i	$-0.712888\pi$
$977$	11.8758	−	24.6603i	0.379940	−	0.788953i	0.999990	−	0.00439105i	$-0.00139772\pi$
$978$	−19.5418	+	11.8585i	−0.624876	+	0.379193i
$979$	−5.98586	−	1.36623i	−0.191309	−	0.0436650i
$980$	−12.2976	−	31.3794i	−0.392832	−	1.00238i
$981$	1.63150	+	36.9313i	0.0520898	+	1.17913i
$982$	−27.5452	−	23.7164i	−0.879001	−	0.756820i
$983$	16.1976	+	3.69699i	0.516622	+	0.117916i	0.472879	−	0.881127i	$-0.343215\pi$
$983$	16.1976	+	3.69699i	0.516622	+	0.117916i	0.0437426	+	0.999043i	$0.486072\pi$
$984$	38.9687	−	0.831443i	1.24228	−	0.0265054i
$985$	78.7786			2.51009
$986$	2.01796	+	0.604076i	0.0642650	+	0.0192377i
$987$	−5.32588	−	14.2066i	−0.169525	−	0.452200i
$988$	1.42394	+	2.09075i	0.0453015	+	0.0665157i
$989$	−10.3374	+	45.2911i	−0.328710	+	1.44017i
$990$	0.0708975	+	10.9054i	0.00225327	+	0.346597i
$991$	9.33144	+	7.44158i	0.296423	+	0.236390i	0.760396	−	0.649460i	$-0.225005\pi$
$991$	9.33144	+	7.44158i	0.296423	+	0.236390i	−0.463973	+	0.885850i	$0.653576\pi$
$992$	−2.02810	+	1.74097i	−0.0643923	+	0.0552758i
$993$	14.3979	−	1.94496i	0.456904	−	0.0617216i
$994$	17.8545	−	3.37368i	0.566309	−	0.107007i
$995$	26.9602	+	12.9833i	0.854695	+	0.411600i
$996$	6.91452	+	23.7436i	0.219095	+	0.752344i
$997$	13.4734	+	27.9777i	0.426705	+	0.886063i	0.997870	+	0.0652275i	$0.0207773\pi$
$997$	13.4734	+	27.9777i	0.426705	+	0.886063i	−0.571165	+	0.820835i	$0.693508\pi$
$998$	8.32969	−	6.14441i	0.263672	−	0.194498i
$999$	2.25382	−	48.9851i	0.0713076	−	1.54982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.1	✓	336
3.2	odd	2	inner	348.2.t.a.35.56	yes	336
4.3	odd	2	inner	348.2.t.a.35.33	yes	336
12.11	even	2	inner	348.2.t.a.35.24	yes	336
29.5	even	14	inner	348.2.t.a.179.24	yes	336
87.5	odd	14	inner	348.2.t.a.179.33	yes	336
116.63	odd	14	inner	348.2.t.a.179.56	yes	336
348.179	even	14	inner	348.2.t.a.179.1	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.1	✓	336	1.1	even	1	trivial
348.2.t.a.35.24	yes	336	12.11	even	2	inner
348.2.t.a.35.33	yes	336	4.3	odd	2	inner
348.2.t.a.35.56	yes	336	3.2	odd	2	inner
348.2.t.a.179.1	yes	336	348.179	even	14	inner
348.2.t.a.179.24	yes	336	29.5	even	14	inner
348.2.t.a.179.33	yes	336	87.5	odd	14	inner
348.2.t.a.179.56	yes	336	116.63	odd	14	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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41321 - 0.0532282i) q^{2} +(-1.71646 + 0.231871i) q^{3} +(1.99433 + 0.150445i) q^{4} +(2.31270 + 1.84432i) q^{5} +(2.43806 - 0.236318i) q^{6} +(1.11294 + 0.254022i) q^{7} +(-2.81041 - 0.318766i) q^{8} +(2.89247 - 0.795994i) q^{9} +O(q^{10})\)	\(q+(-1.41321 - 0.0532282i) q^{2} +(-1.71646 + 0.231871i) q^{3} +(1.99433 + 0.150445i) q^{4} +(2.31270 + 1.84432i) q^{5} +(2.43806 - 0.236318i) q^{6} +(1.11294 + 0.254022i) q^{7} +(-2.81041 - 0.318766i) q^{8} +(2.89247 - 0.795994i) q^{9} +(-3.17016 - 2.72951i) q^{10} +(-0.377036 - 0.782923i) q^{11} +(-3.45808 + 0.204194i) q^{12} +(-1.24344 + 0.598808i) q^{13} +(-1.55930 - 0.418227i) q^{14} +(-4.39730 - 2.62945i) q^{15} +(3.95473 + 0.600077i) q^{16} -0.276589 q^{17} +(-4.13004 + 0.970946i) q^{18} +(-0.203928 - 0.893468i) q^{19} +(4.33482 + 4.02611i) q^{20} +(-1.96922 - 0.177960i) q^{21} +(0.491158 + 1.12650i) q^{22} +(5.89480 + 7.39185i) q^{23} +(4.89786 - 0.104502i) q^{24} +(0.834469 + 3.65605i) q^{25} +(1.78911 - 0.780056i) q^{26} +(-4.78025 + 2.03697i) q^{27} +(2.18136 + 0.674042i) q^{28} +(5.21345 + 1.34907i) q^{29} +(6.07435 + 3.95002i) q^{30} +(0.294598 - 0.369414i) q^{31} +(-5.55693 - 1.05854i) q^{32} +(0.828704 + 1.25643i) q^{33} +(0.390879 + 0.0147223i) q^{34} +(2.10541 + 2.64009i) q^{35} +(5.88831 - 1.15232i) q^{36} +(-4.09463 + 8.50259i) q^{37} +(0.240636 + 1.27351i) q^{38} +(1.99546 - 1.31615i) q^{39} +(-5.91172 - 5.92049i) q^{40} +7.95625 q^{41} +(2.77346 + 0.356313i) q^{42} +(3.06359 + 3.84162i) q^{43} +(-0.634148 - 1.61813i) q^{44} +(8.15748 + 3.49374i) q^{45} +(-7.93714 - 10.7600i) q^{46} +(3.32933 + 6.91342i) q^{47} +(-6.92728 - 0.113021i) q^{48} +(-5.13267 - 2.47176i) q^{49} +(-0.984677 - 5.21119i) q^{50} +(0.474754 - 0.0641328i) q^{51} +(-2.56992 + 1.00715i) q^{52} +(-6.65105 - 5.30404i) q^{53} +(6.86392 - 2.62423i) q^{54} +(0.571987 - 2.50604i) q^{55} +(-3.04685 - 1.06867i) q^{56} +(0.557204 + 1.48632i) q^{57} +(-7.29589 - 2.18402i) q^{58} -5.99393 q^{59} +(-8.37409 - 5.90555i) q^{60} +(-1.77364 - 0.404822i) q^{61} +(-0.435993 + 0.506380i) q^{62} +(3.42136 - 0.151144i) q^{63} +(7.79678 + 1.79172i) q^{64} +(-3.98008 - 0.908428i) q^{65} +(-1.10426 - 1.81972i) q^{66} +(1.51455 - 3.14499i) q^{67} +(-0.551610 - 0.0416115i) q^{68} +(-11.8321 - 11.3210i) q^{69} +(-2.83486 - 3.84308i) q^{70} +(-10.1405 + 4.88340i) q^{71} +(-8.38276 + 1.31504i) q^{72} +(9.74375 - 7.77038i) q^{73} +(6.23916 - 11.7980i) q^{74} +(-2.28006 - 6.08197i) q^{75} +(-0.272283 - 1.81255i) q^{76} +(-0.220740 - 0.967124i) q^{77} +(-2.89007 + 1.75378i) q^{78} +(10.1702 + 4.89772i) q^{79} +(8.03937 + 8.68157i) q^{80} +(7.73279 - 4.60478i) q^{81} +(-11.2439 - 0.423497i) q^{82} +(-1.58856 - 6.95992i) q^{83} +(-3.90051 - 0.651172i) q^{84} +(-0.639666 - 0.510117i) q^{85} +(-4.12502 - 5.59209i) q^{86} +(-9.26148 - 1.10678i) q^{87} +(0.810055 + 2.32052i) q^{88} +(4.40529 - 5.52406i) q^{89} +(-11.3423 - 5.37160i) q^{90} +(-1.53599 + 0.350579i) q^{91} +(10.6441 + 15.6287i) q^{92} +(-0.420010 + 0.702394i) q^{93} +(-4.33706 - 9.94734i) q^{94} +(1.17621 - 2.44243i) q^{95} +(9.78370 + 0.528450i) q^{96} +(-5.00469 + 1.14229i) q^{97} +(7.12198 + 3.76632i) q^{98} +(-1.71377 - 1.96446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more