LMFDB - Embedded newform 348.2.t.a.35.6

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			35.6
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31443 - 0.521790i) q^{2} +(-0.468526 + 1.66748i) q^{3} +(1.45547 + 1.37172i) q^{4} +(-0.227131 - 0.181131i) q^{5} +(1.48592 - 1.94732i) q^{6} +(-2.72634 - 0.622270i) q^{7} +(-1.19737 - 2.56248i) q^{8} +(-2.56097 - 1.56251i) q^{9} +O(q^{10})$	\(q+(-1.31443 - 0.521790i) q^{2} +(-0.468526 + 1.66748i) q^{3} +(1.45547 + 1.37172i) q^{4} +(-0.227131 - 0.181131i) q^{5} +(1.48592 - 1.94732i) q^{6} +(-2.72634 - 0.622270i) q^{7} +(-1.19737 - 2.56248i) q^{8} +(-2.56097 - 1.56251i) q^{9} +(0.204036 + 0.356598i) q^{10} +(-2.44077 - 5.06830i) q^{11} +(-2.96923 + 1.78428i) q^{12} +(4.69132 - 2.25922i) q^{13} +(3.25890 + 2.24051i) q^{14} +(0.408448 - 0.293871i) q^{15} +(0.236794 + 3.99298i) q^{16} +4.28762 q^{17} +(2.55092 + 3.39011i) q^{18} +(0.385765 + 1.69015i) q^{19} +(-0.0821224 - 0.575189i) q^{20} +(2.31499 - 4.25457i) q^{21} +(0.563638 + 7.93552i) q^{22} +(2.27067 + 2.84733i) q^{23} +(4.83388 - 0.796007i) q^{24} +(-1.09382 - 4.79236i) q^{25} +(-7.34526 + 0.521714i) q^{26} +(3.80534 - 3.53828i) q^{27} +(-3.11454 - 4.64546i) q^{28} +(-5.37233 + 0.371628i) q^{29} +(-0.690216 + 0.173150i) q^{30} +(5.36303 - 6.72503i) q^{31} +(1.77225 - 5.37207i) q^{32} +(9.59485 - 1.69529i) q^{33} +(-5.63579 - 2.23723i) q^{34} +(0.506524 + 0.635161i) q^{35} +(-1.58409 - 5.78711i) q^{36} +(-0.0232466 + 0.0482721i) q^{37} +(0.374839 - 2.42288i) q^{38} +(1.56919 + 8.88117i) q^{39} +(-0.192183 + 0.798898i) q^{40} -7.63789 q^{41} +(-5.26288 + 4.38441i) q^{42} +(0.385030 + 0.482812i) q^{43} +(3.39980 - 10.7248i) q^{44} +(0.298655 + 0.818764i) q^{45} +(-1.49894 - 4.92744i) q^{46} +(-3.68384 - 7.64958i) q^{47} +(-6.76916 - 1.47597i) q^{48} +(0.738951 + 0.355860i) q^{49} +(-1.06284 + 6.86998i) q^{50} +(-2.00886 + 7.14951i) q^{51} +(9.92708 + 3.14692i) q^{52} +(-4.19455 - 3.34505i) q^{53} +(-6.84810 + 2.66525i) q^{54} +(-0.363652 + 1.59326i) q^{55} +(1.66990 + 7.73129i) q^{56} +(-2.99903 - 0.148623i) q^{57} +(7.25548 + 2.31474i) q^{58} +6.71215 q^{59} +(0.997591 + 0.132554i) q^{60} +(-7.16798 - 1.63604i) q^{61} +(-10.5584 + 6.04123i) q^{62} +(6.00977 + 5.85356i) q^{63} +(-5.13259 + 6.13649i) q^{64} +(-1.47476 - 0.336603i) q^{65} +(-13.4964 - 2.77814i) q^{66} +(0.705540 - 1.46507i) q^{67} +(6.24050 + 5.88139i) q^{68} +(-5.81173 + 2.45225i) q^{69} +(-0.334372 - 1.09918i) q^{70} +(-3.98478 + 1.91897i) q^{71} +(-0.937474 + 8.43334i) q^{72} +(10.1816 - 8.11959i) q^{73} +(0.0557441 - 0.0513207i) q^{74} +(8.50364 + 0.421416i) q^{75} +(-1.75693 + 2.98912i) q^{76} +(3.50052 + 15.3368i) q^{77} +(2.57150 - 12.4925i) q^{78} +(-8.78958 - 4.23284i) q^{79} +(0.669468 - 0.949819i) q^{80} +(4.11710 + 8.00309i) q^{81} +(10.0395 + 3.98537i) q^{82} +(2.41305 + 10.5723i) q^{83} +(9.20545 - 3.01690i) q^{84} +(-0.973849 - 0.776618i) q^{85} +(-0.254170 - 0.835529i) q^{86} +(1.89739 - 9.13235i) q^{87} +(-10.0649 + 12.3231i) q^{88} +(2.74726 - 3.44495i) q^{89} +(0.0346606 - 1.23205i) q^{90} +(-14.1960 + 3.24014i) q^{91} +(-0.600832 + 7.25893i) q^{92} +(8.70112 + 12.0936i) q^{93} +(0.850697 + 11.9771i) q^{94} +(0.218518 - 0.453758i) q^{95} +(8.12747 + 5.47214i) q^{96} +(-0.166069 + 0.0379042i) q^{97} +(-0.785618 - 0.853331i) q^{98} +(-1.66857 + 16.7935i) 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 $

$2$	−1.31443	−	0.521790i	−0.929445	−	0.368961i
$2$	−1.31443	−	0.521790i	−0.929445	−	0.368961i
$3$	−0.468526	+	1.66748i	−0.270504	+	0.962719i
$3$	−0.468526	+	1.66748i	−0.270504	+	0.962719i
$4$	1.45547	+	1.37172i	0.727736	+	0.685858i
$5$	−0.227131	−	0.181131i	−0.101576	−	0.0810040i	0.571385	−	0.820682i	$-0.306406\pi$
$5$	−0.227131	−	0.181131i	−0.101576	−	0.0810040i	−0.672961	+	0.739678i	$0.734978\pi$
$6$	1.48592	−	1.94732i	0.606624	−	0.794989i
$7$	−2.72634	−	0.622270i	−1.03046	−	0.235196i	−0.326323	−	0.945258i	$-0.605810\pi$
$7$	−2.72634	−	0.622270i	−1.03046	−	0.235196i	−0.704139	+	0.710062i	$0.748667\pi$
$8$	−1.19737	−	2.56248i	−0.423336	−	0.905973i
$9$	−2.56097	−	1.56251i	−0.853656	−	0.520838i
$10$	0.204036	+	0.356598i	0.0645218	+	0.112766i
$11$	−2.44077	−	5.06830i	−0.735919	−	1.52815i	−0.845383	−	0.534161i	$-0.820628\pi$
$11$	−2.44077	−	5.06830i	−0.735919	−	1.52815i	0.109464	−	0.993991i	$-0.465086\pi$
$12$	−2.96923	+	1.78428i	−0.857143	+	0.515078i
$13$	4.69132	−	2.25922i	1.30114	−	0.626595i	0.350402	−	0.936599i	$-0.386045\pi$
$13$	4.69132	−	2.25922i	1.30114	−	0.626595i	0.950735	+	0.310005i	$0.100331\pi$
$14$	3.25890	+	2.24051i	0.870979	+	0.598802i
$15$	0.408448	−	0.293871i	0.105461	−	0.0758771i
$16$	0.236794	+	3.99298i	0.0591985	+	0.998246i
$17$	4.28762			1.03990			0.519950	−	0.854197i	$-0.325951\pi$
$17$	4.28762			1.03990			0.519950	+	0.854197i	$0.325951\pi$
$18$	2.55092	+	3.39011i	0.601257	+	0.799056i
$19$	0.385765	+	1.69015i	0.0885007	+	0.387747i	0.999707	−	0.0242034i	$-0.00770493\pi$
$19$	0.385765	+	1.69015i	0.0885007	+	0.387747i	−0.911206	+	0.411950i	$0.864848\pi$
$20$	−0.0821224	−	0.575189i	−0.0183631	−	0.128616i
$21$	2.31499	−	4.25457i	0.505171	−	0.928423i
$22$	0.563638	+	7.93552i	0.120168	+	1.69186i
$23$	2.27067	+	2.84733i	0.473468	+	0.593710i	0.960016	−	0.279944i	$-0.0903158\pi$
$23$	2.27067	+	2.84733i	0.473468	+	0.593710i	−0.486549	+	0.873654i	$0.661744\pi$
$24$	4.83388	−	0.796007i	0.986711	−	0.162484i
$25$	−1.09382	−	4.79236i	−0.218765	−	0.958472i
$26$	−7.34526	+	0.521714i	−1.44052	+	0.102316i
$27$	3.80534	−	3.53828i	0.732337	−	0.680942i
$28$	−3.11454	−	4.64546i	−0.588592	−	0.877910i
$29$	−5.37233	+	0.371628i	−0.997616	+	0.0690096i
$29$	−5.37233	+	0.371628i	−0.997616	+	0.0690096i
$30$	−0.690216	+	0.173150i	−0.126016	+	0.0316127i
$31$	5.36303	−	6.72503i	0.963229	−	1.20785i	−0.0149076	−	0.999889i	$-0.504745\pi$
$31$	5.36303	−	6.72503i	0.963229	−	1.20785i	0.978137	−	0.207962i	$-0.0666832\pi$
$32$	1.77225	−	5.37207i	0.313292	−	0.949657i
$33$	9.59485	−	1.69529i	1.67025	−	0.295113i
$34$	−5.63579	−	2.23723i	−0.966530	−	0.383682i
$35$	0.506524	+	0.635161i	0.0856182	+	0.107362i
$36$	−1.58409	−	5.78711i	−0.264015	−	0.964519i
$37$	−0.0232466	+	0.0482721i	−0.00382172	+	0.00793589i	−0.902871	−	0.429912i	$-0.858545\pi$
$37$	−0.0232466	+	0.0482721i	−0.00382172	+	0.00793589i	0.899049	+	0.437847i	$0.144259\pi$
$38$	0.374839	−	2.42288i	0.0608069	−	0.393043i
$39$	1.56919	+	8.88117i	0.251272	+	1.42213i
$40$	−0.192183	+	0.798898i	−0.0303868	+	0.126317i
$41$	−7.63789			−1.19284			−0.596419	−	0.802673i	$-0.703410\pi$
$41$	−7.63789			−1.19284			−0.596419	+	0.802673i	$0.703410\pi$
$42$	−5.26288	+	4.38441i	−0.812081	+	0.676530i
$43$	0.385030	+	0.482812i	0.0587165	+	0.0736281i	0.810323	−	0.585984i	$-0.199292\pi$
$43$	0.385030	+	0.482812i	0.0587165	+	0.0736281i	−0.751606	+	0.659612i	$0.770720\pi$
$44$	3.39980	−	10.7248i	0.512540	−	1.61683i
$45$	0.298655	+	0.818764i	0.0445208	+	0.122054i
$46$	−1.49894	−	4.92744i	−0.221007	−	0.726512i
$47$	−3.68384	−	7.64958i	−0.537344	−	1.11581i	−0.976124	−	0.217212i	$-0.930304\pi$
$47$	−3.68384	−	7.64958i	−0.537344	−	1.11581i	0.438781	−	0.898594i	$-0.355411\pi$
$48$	−6.76916	−	1.47597i	−0.977044	−	0.213038i
$49$	0.738951	+	0.355860i	0.105564	+	0.0508371i
$50$	−1.06284	+	6.86998i	−0.150309	+	0.971562i
$51$	−2.00886	+	7.14951i	−0.281297	+	1.00113i
$52$	9.92708	+	3.14692i	1.37664	+	0.436400i
$53$	−4.19455	−	3.34505i	−0.576166	−	0.459477i	0.291537	−	0.956560i	$-0.405833\pi$
$53$	−4.19455	−	3.34505i	−0.576166	−	0.459477i	−0.867703	+	0.497082i	$0.834405\pi$
$54$	−6.84810	+	2.66525i	−0.931908	+	0.362694i
$55$	−0.363652	+	1.59326i	−0.0490348	+	0.214836i
$56$	1.66990	+	7.73129i	0.223150	+	1.03314i
$57$	−2.99903	−	0.148623i	−0.397231	−	0.0196856i
$58$	7.25548	+	2.31474i	0.952691	+	0.303941i
$59$	6.71215			0.873848			0.436924	−	0.899498i	$-0.356068\pi$
$59$	6.71215			0.873848			0.436924	+	0.899498i	$0.356068\pi$
$60$	0.997591	+	0.132554i	0.128788	+	0.0171126i
$61$	−7.16798	−	1.63604i	−0.917766	−	0.209474i	−0.262552	−	0.964918i	$-0.584564\pi$
$61$	−7.16798	−	1.63604i	−0.917766	−	0.209474i	−0.655214	+	0.755444i	$0.727421\pi$
$62$	−10.5584	+	6.04123i	−1.34092	+	0.767237i
$63$	6.00977	+	5.85356i	0.757160	+	0.737480i
$64$	−5.13259	+	6.13649i	−0.641574	+	0.767061i
$65$	−1.47476	−	0.336603i	−0.182921	−	0.0417505i
$66$	−13.4964	−	2.77814i	−1.66129	−	0.341966i
$67$	0.705540	−	1.46507i	0.0861955	−	0.178987i	−0.853415	−	0.521231i	$-0.825473\pi$
$67$	0.705540	−	1.46507i	0.0861955	−	0.178987i	0.939611	+	0.342245i	$0.111187\pi$
$68$	6.24050	+	5.88139i	0.756772	+	0.713223i
$69$	−5.81173	+	2.45225i	−0.699651	+	0.295216i
$70$	−0.334372	−	1.09918i	−0.0399651	−	0.131377i
$71$	−3.98478	+	1.91897i	−0.472907	+	0.227740i	−0.655128	−	0.755518i	$-0.727385\pi$
$71$	−3.98478	+	1.91897i	−0.472907	+	0.227740i	0.182222	+	0.983257i	$0.441671\pi$
$72$	−0.937474	+	8.43334i	−0.110482	+	0.993878i
$73$	10.1816	−	8.11959i	1.19167	−	0.950327i	0.192154	−	0.981365i	$-0.438453\pi$
$73$	10.1816	−	8.11959i	1.19167	−	0.950327i	0.999518	+	0.0310381i	$0.00988134\pi$
$74$	0.0557441	−	0.0513207i	0.00648012	−	0.00596591i
$75$	8.50364	+	0.421416i	0.981916	+	0.0486610i
$76$	−1.75693	+	2.98912i	−0.201534	+	0.342876i
$77$	3.50052	+	15.3368i	0.398921	+	1.74779i
$78$	2.57150	−	12.4925i	0.291165	−	1.41450i
$79$	−8.78958	−	4.23284i	−0.988905	−	0.476232i	−0.131746	−	0.991283i	$-0.542058\pi$
$79$	−8.78958	−	4.23284i	−0.988905	−	0.476232i	−0.857159	+	0.515052i	$0.827773\pi$
$80$	0.669468	−	0.949819i	0.0748488	−	0.106193i
$81$	4.11710	+	8.00309i	0.457456	+	0.889232i
$82$	10.0395	+	3.98537i	1.10868	+	0.440111i
$83$	2.41305	+	10.5723i	0.264867	+	1.16046i	0.915899	+	0.401408i	$0.131479\pi$
$83$	2.41305	+	10.5723i	0.264867	+	1.16046i	−0.651032	+	0.759050i	$0.725664\pi$
$84$	9.20545	−	3.01690i	1.00440	−	0.329171i
$85$	−0.973849	−	0.776618i	−0.105629	−	0.0842361i
$86$	−0.254170	−	0.835529i	−0.0274078	−	0.0900974i
$87$	1.89739	−	9.13235i	0.203422	−	0.979091i
$88$	−10.0649	+	12.3231i	−1.07292	+	1.31364i
$89$	2.74726	−	3.44495i	0.291209	−	0.365164i	−0.614609	−	0.788832i	$-0.710686\pi$
$89$	2.74726	−	3.44495i	0.291209	−	0.365164i	0.905818	+	0.423668i	$0.139258\pi$
$90$	0.0346606	−	1.23205i	0.00365355	−	0.129869i
$91$	−14.1960	+	3.24014i	−1.48814	+	0.339659i
$92$	−0.600832	+	7.25893i	−0.0626411	+	0.756796i
$93$	8.70112	+	12.0936i	0.902264	+	1.25405i
$94$	0.850697	+	11.9771i	0.0877427	+	1.23534i
$95$	0.218518	−	0.453758i	0.0224195	−	0.0465546i
$96$	8.12747	+	5.47214i	0.829506	+	0.558498i
$97$	−0.166069	+	0.0379042i	−0.0168618	+	0.00384859i	−0.230944	−	0.972967i	$-0.574181\pi$
$97$	−0.166069	+	0.0379042i	−0.0168618	+	0.00384859i	0.214082	+	0.976816i	$0.431324\pi$
$98$	−0.785618	−	0.853331i	−0.0793594	−	0.0861994i
$99$	−1.66857	+	16.7935i	−0.167698	+	1.68781i
$100$	4.98172	−	8.47556i	0.498172	−	0.847556i
$101$	−3.38493	−	4.24456i	−0.336813	−	0.422350i	0.584365	−	0.811491i	$-0.301343\pi$
$101$	−3.38493	−	4.24456i	−0.336813	−	0.422350i	−0.921178	+	0.389141i	$0.872772\pi$
$102$	6.37105	−	8.34935i	0.630828	−	0.826709i
$103$	−4.99966	−	10.3819i	−0.492631	−	1.02296i	−0.988025	−	0.154291i	$-0.950691\pi$
$103$	−4.99966	−	10.3819i	−0.492631	−	1.02296i	0.495394	−	0.868668i	$-0.335024\pi$
$104$	−11.4065	−	9.31627i	−1.11850	−	0.913535i
$105$	−1.29644	+	0.547028i	−0.126519	+	0.0533845i
$106$	3.76805	+	6.58552i	0.365986	+	0.639642i
$107$	17.4998	+	8.42746i	1.69177	+	0.814713i	0.995269	+	0.0971569i	$0.0309749\pi$
$107$	17.4998	+	8.42746i	1.69177	+	0.814713i	0.696500	+	0.717556i	$0.254739\pi$
$108$	10.3921	+	0.0699779i	0.999977	+	0.00673362i
$109$	−1.53997	+	6.74703i	−0.147502	+	0.646248i	0.846072	+	0.533068i	$0.178961\pi$
$109$	−1.53997	+	6.74703i	−0.147502	+	0.646248i	−0.993574	+	0.113180i	$0.963896\pi$
$110$	1.30935	−	1.90449i	0.124841	−	0.181586i
$111$	−0.0696011	−	0.0613800i	−0.00660624	−	0.00582593i
$112$	1.83913	−	11.0336i	0.173782	−	1.04258i
$113$	3.43811	−	15.0633i	0.323430	−	1.41704i	−0.507975	−	0.861372i	$-0.669606\pi$
$113$	3.43811	−	15.0633i	0.323430	−	1.41704i	0.831405	−	0.555667i	$-0.187537\pi$
$114$	3.86447	+	1.76022i	0.361941	+	0.164859i
$115$		−	1.05800i		−	0.0986594i
$116$	−8.32904	−	6.82841i	−0.773331	−	0.634002i
$117$	−15.5444	−	1.54446i	−1.43708	−	0.142786i
$118$	−8.82268	−	3.50233i	−0.812194	−	0.322416i
$119$	−11.6895	−	2.66806i	−1.07158	−	0.244580i
$120$	−1.24210	−	0.694765i	−0.113388	−	0.0634231i
$121$	−12.8720	+	16.1410i	−1.17018	+	1.46736i
$122$	8.56816	+	5.89065i	0.775725	+	0.533314i
$123$	3.57855	−	12.7360i	0.322667	−	1.14837i
$124$	17.0306	−	2.43153i	1.52939	−	0.218358i
$125$	−1.24984	+	2.59532i	−0.111789	+	0.232133i
$126$	−4.84512	−	10.8300i	−0.431637	−	0.964809i
$127$	−15.0978	+	7.27069i	−1.33971	+	0.645170i	−0.960017	−	0.279943i	$-0.909684\pi$
$127$	−15.0978	+	7.27069i	−1.33971	+	0.645170i	−0.379692	+	0.925113i	$0.623970\pi$
$128$	9.94841	−	5.38787i	0.879323	−	0.476225i
$129$	−0.985475	+	0.415819i	−0.0867662	+	0.0366108i
$130$	1.76283	+	1.21195i	0.154611	+	0.106295i
$131$	−1.66568	+	1.32833i	−0.145531	+	0.116057i	−0.693549	−	0.720409i	$-0.743954\pi$
$131$	−1.66568	+	1.32833i	−0.145531	+	0.116057i	0.548018	+	0.836466i	$0.315382\pi$
$132$	16.2905	+	10.6940i	1.41790	+	0.930789i
$133$		−	4.84798i		−	0.420373i
$134$	−1.69184	+	1.55759i	−0.146153	+	0.134556i
$135$	−1.50520	+	0.114388i	−0.129547	+	0.00984495i
$136$	−5.13388	−	10.9869i	−0.440227	−	0.942121i
$137$	12.7582	+	6.14404i	1.09001	+	0.524921i	0.890504	−	0.454976i	$-0.150352\pi$
$137$	12.7582	+	6.14404i	1.09001	+	0.524921i	0.199505	+	0.979897i	$0.436066\pi$
$138$	8.91870	−	0.190813i	0.759210	−	0.0162431i
$139$	−3.94646	+	3.14719i	−0.334734	+	0.266942i	−0.776403	−	0.630236i	$-0.782958\pi$
$139$	−3.94646	+	3.14719i	−0.334734	+	0.266942i	0.441669	+	0.897178i	$0.354387\pi$
$140$	−0.134029	+	1.61926i	−0.0113275	+	0.136853i
$141$	14.4815	−	2.55870i	1.21956	−	0.215482i
$142$	6.23903	−	0.443141i	0.523568	−	0.0371876i
$143$	−22.9008	−	18.2628i	−1.91506	−	1.52721i
$144$	5.63267	−	10.5959i	0.469389	−	0.882991i
$145$	1.28753	+	0.888684i	0.106924	+	0.0738012i
$146$	−17.6198	+	5.35999i	−1.45823	+	0.443596i
$147$	−0.939606	+	1.06545i	−0.0774974	+	0.0878772i
$148$	−0.100050	+	0.0383710i	−0.00822410	+	0.00315407i
$149$	−2.27324	+	0.518852i	−0.186231	+	0.0425060i	−0.314619	−	0.949218i	$-0.601877\pi$
$149$	−2.27324	+	0.518852i	−0.186231	+	0.0425060i	0.128388	+	0.991724i	$0.459020\pi$
$150$	−10.9576	−	4.99103i	−0.894683	−	0.407516i
$151$	3.41895	−	2.72652i	0.278231	−	0.221881i	−0.474425	−	0.880296i	$-0.657344\pi$
$151$	3.41895	−	2.72652i	0.278231	−	0.221881i	0.752656	+	0.658414i	$0.228773\pi$
$152$	3.86906	−	3.01226i	0.313823	−	0.244326i
$153$	−10.9804	−	6.69946i	−0.887716	−	0.541619i
$154$	3.40137	−	21.9857i	0.274090	−	1.77166i
$155$	−2.43622	+	0.556051i	−0.195682	+	0.0446631i
$156$	−9.89852	+	15.0788i	−0.792516	+	1.20727i
$157$			5.71216i			0.455880i	0.973675	+	0.227940i	$0.0731990\pi$
$157$			5.71216i			0.455880i	−0.973675	+	0.227940i	$0.926801\pi$
$158$	9.34467	+	10.1501i	0.743422	+	0.807498i
$159$	7.54305	−	5.42709i	0.598203	−	0.430396i
$160$	−1.37558	+	0.899153i	−0.108749	+	0.0710843i
$161$	−4.41882	−	9.17578i	−0.348252	−	0.723153i
$162$	−1.23573	−	12.6678i	−0.0970878	−	0.995276i
$163$	9.08769	−	4.37640i	0.711803	−	0.342786i	−0.0426955	−	0.999088i	$-0.513595\pi$
$163$	9.08769	−	4.37640i	0.711803	−	0.342786i	0.754498	+	0.656302i	$0.227880\pi$
$164$	−11.1167	−	10.4770i	−0.868071	−	0.818118i
$165$	−2.48635	−	1.35287i	−0.193562	−	0.105321i
$166$	2.34470	−	15.1557i	0.181984	−	1.17631i
$167$	−0.937402	+	4.10703i	−0.0725384	+	0.317811i	−0.998160	−	0.0606396i	$-0.980686\pi$
$167$	−0.937402	+	4.10703i	−0.0725384	+	0.317811i	0.925621	+	0.378451i	$0.123543\pi$
$168$	−13.6741	−	0.837790i	−1.05498	−	0.0646369i
$169$	8.79902	−	11.0336i	0.676848	−	0.848740i
$170$	0.874828	+	1.52896i	0.0670963	+	0.117266i
$171$	1.65295	−	4.93118i	0.126404	−	0.377097i
$172$	−0.101881	+	1.23087i	−0.00776835	+	0.0938530i
$173$			24.1140i			1.83335i	0.399631	+	0.916676i	$0.369138\pi$
$173$			24.1140i			1.83335i	−0.399631	+	0.916676i	$0.630862\pi$
$174$	−7.25916	+	11.0138i	−0.550316	+	0.834957i
$175$			13.7463i			1.03912i
$176$	19.6597	−	10.9461i	1.48191	−	0.825092i
$177$	−3.14482	+	11.1924i	−0.236379	+	0.841270i
$178$	−5.40863	+	3.09467i	−0.405394	+	0.231955i
$179$	9.08167	−	11.3881i	0.678796	−	0.851183i	−0.316447	−	0.948610i	$-0.602490\pi$
$179$	9.08167	−	11.3881i	0.678796	−	0.851183i	0.995243	+	0.0974272i	$0.0310613\pi$
$180$	−0.688428	+	1.60136i	−0.0513124	+	0.119358i
$181$	−2.27274	+	9.95752i	−0.168931	+	0.740137i	0.817495	+	0.575935i	$0.195362\pi$
$181$	−2.27274	+	9.95752i	−0.168931	+	0.740137i	−0.986427	+	0.164202i	$0.947495\pi$
$182$	20.3504	+	3.14837i	1.50847	+	0.233373i
$183$	6.08645	−	11.1859i	0.449924	−	0.826887i
$184$	4.57739	−	9.22787i	0.337449	−	0.680288i
$185$	0.0140236	−	0.00675340i	0.00103103	−	0.000496520i
$186$	−5.12674	−	20.4364i	−0.375911	−	1.49847i
$187$	−10.4651	−	21.7309i	−0.765282	−	1.58912i
$188$	5.13132	−	16.1869i	0.374240	−	1.18055i
$189$	−12.5764	+	7.27861i	−0.914800	+	0.529441i
$190$	−0.523994	+	0.482414i	−0.0380145	+	0.0349980i
$191$			4.60547i			0.333240i	0.986021	+	0.166620i	$0.0532853\pi$
$191$			4.60547i			0.333240i	−0.986021	+	0.166620i	$0.946715\pi$
$192$	−7.82771	−	11.4336i	−0.564916	−	0.825148i
$193$	−9.52013	+	2.17291i	−0.685274	+	0.156409i	−0.550963	−	0.834530i	$-0.685739\pi$
$193$	−9.52013	+	2.17291i	−0.685274	+	0.156409i	−0.134311	+	0.990939i	$0.542882\pi$
$194$	0.238065	+	0.0368306i	0.0170921	+	0.00264428i
$195$	1.25224	−	2.30141i	0.0896747	−	0.164808i
$196$	0.587383	+	1.53157i	0.0419559	+	0.109398i
$197$	3.69639	−	2.94777i	0.263357	−	0.210020i	−0.482905	−	0.875673i	$-0.660418\pi$
$197$	3.69639	−	2.94777i	0.263357	−	0.210020i	0.746262	+	0.665653i	$0.231847\pi$
$198$	10.9559	−	21.2033i	0.778602	−	1.50685i
$199$	11.2171	−	2.56023i	0.795160	−	0.181490i	0.194403	−	0.980922i	$-0.437723\pi$
$199$	11.2171	−	2.56023i	0.795160	−	0.181490i	0.600757	+	0.799432i	$0.294866\pi$
$200$	−10.9706	+	8.54115i	−0.775739	+	0.603950i
$201$	2.11241	+	1.86290i	0.148998	+	0.131399i
$202$	2.23449	+	7.34542i	0.157218	+	0.516822i
$203$	14.8781	+	2.32985i	1.04424	+	0.163524i
$204$	−12.7309	+	7.65032i	−0.891343	+	0.535630i
$205$	1.73480	+	1.38346i	0.121164	+	0.0966247i
$206$	1.15455	+	16.2551i	0.0804416	+	1.13255i
$207$	−1.36612	−	10.8399i	−0.0949518	−	0.753424i
$208$	10.1319	+	18.1974i	0.702521	+	1.26176i
$209$	7.62463	−	6.08044i	0.527406	−	0.420593i
$210$	1.98951	−	0.0425651i	0.137289	−	0.00293727i
$211$	5.98198	+	2.88077i	0.411816	+	0.198320i	0.628309	−	0.777964i	$-0.283747\pi$
$211$	5.98198	+	2.88077i	0.411816	+	0.198320i	−0.216493	+	0.976284i	$0.569462\pi$
$212$	−1.51660	−	10.6224i	−0.104161	−	0.729546i
$213$	−1.33287	−	7.54363i	−0.0913265	−	0.516881i
$214$	−18.6050	−	20.2085i	−1.27181	−	1.38143i
$215$		−	0.179402i		−	0.0122351i
$216$	−13.6232	−	5.51445i	−0.926939	−	0.375211i
$217$	−18.8063	+	14.9975i	−1.27665	+	1.01810i
$218$	5.54471	−	8.06499i	0.375535	−	0.546230i
$219$	8.76888	+	20.7819i	0.592546	+	1.40431i
$220$	−2.71479	+	1.82012i	−0.183031	+	0.122713i
$221$	20.1146	−	9.68667i	1.35305	−	0.651596i
$222$	0.0594586	+	0.116997i	0.00399060	+	0.00785233i
$223$	0.0566980	−	0.117735i	0.00379678	−	0.00788409i	−0.899062	−	0.437822i	$-0.855750\pi$
$223$	0.0566980	−	0.117735i	0.00379678	−	0.00788409i	0.902859	+	0.429938i	$0.141464\pi$
$224$	−8.17464	+	13.5433i	−0.546191	+	0.904899i
$225$	−4.68688	+	13.9822i	−0.312459	+	0.932146i
$226$	−12.3791	+	18.0058i	−0.823442	+	1.19773i
$227$	−7.69206	+	9.64554i	−0.510540	+	0.640197i	−0.968570	−	0.248740i	$-0.919984\pi$
$227$	−7.69206	+	9.64554i	−0.510540	+	0.640197i	0.458030	+	0.888937i	$0.348555\pi$
$228$	−4.16113	−	4.33013i	−0.275578	−	0.286770i
$229$	19.6728	+	4.49020i	1.30002	+	0.296721i	0.815855	−	0.578257i	$-0.196267\pi$
$229$	19.6728	+	4.49020i	1.30002	+	0.296721i	0.484164	+	0.874978i	$0.339124\pi$
$230$	−0.552056	+	1.39068i	−0.0364015	+	0.0916985i
$231$	−27.2138	−	1.34864i	−1.79054	−	0.0887339i
$232$	7.38497	+	13.3215i	0.484847	+	0.874599i
$233$			10.3827i			0.680196i	0.940390	+	0.340098i	$0.110460\pi$
$233$			10.3827i			0.680196i	−0.940390	+	0.340098i	$0.889540\pi$
$234$	19.6262	+	10.1410i	1.28300	+	0.662937i
$235$	−0.548859	+	2.40471i	−0.0358036	+	0.156866i
$236$	9.76935	+	9.20717i	0.635930	+	0.599335i
$237$	11.1763	−	12.6732i	0.725980	−	0.823215i
$238$	13.9729	+	9.60645i	0.905731	+	0.622694i
$239$	3.11810	−	13.6613i	0.201693	−	0.883676i	−0.768212	−	0.640195i	$-0.778853\pi$
$239$	3.11810	−	13.6613i	0.201693	−	0.883676i	0.969906	−	0.243481i	$-0.0782894\pi$
$240$	1.27014	+	1.56134i	0.0819872	+	0.100784i
$241$	10.1826	+	4.90369i	0.655920	+	0.315874i	0.732077	−	0.681221i	$-0.238551\pi$
$241$	10.1826	+	4.90369i	0.655920	+	0.315874i	−0.0761576	+	0.997096i	$0.524265\pi$
$242$	25.3415	−	14.4997i	1.62902	−	0.932079i
$243$	−15.2739	+	3.11552i	−0.979824	+	0.199861i
$244$	−8.18860	−	12.2136i	−0.524222	−	0.781899i
$245$	−0.103381	−	0.214673i	−0.00660478	−	0.0137150i
$246$	−11.3493	+	14.8734i	−0.723604	+	0.948294i
$247$	5.62817	+	7.05750i	0.358112	+	0.449058i
$248$	−23.6543	−	5.69028i	−1.50205	−	0.361333i
$249$	−18.7596	−	0.929673i	−1.18884	−	0.0589156i
$250$	2.99705	−	2.75922i	0.189550	−	0.174509i
$251$	6.11811	−	1.39642i	0.386172	−	0.0881412i	−0.0250273	−	0.999687i	$-0.507967\pi$
$251$	6.11811	−	1.39642i	0.386172	−	0.0881412i	0.411199	+	0.911546i	$0.365110\pi$
$252$	0.717626	+	16.7634i	0.0452062	+	1.05599i
$253$	8.88897	−	18.4581i	0.558845	−	1.16045i
$254$	23.6388	−	1.67900i	1.48323	−	0.105350i
$255$	1.75127	−	1.26001i	0.109669	−	0.0789046i
$256$	−15.8879	+	1.89103i	−0.992991	+	0.118189i
$257$	12.6654	−	2.89080i	0.790047	−	0.180323i	0.191587	−	0.981476i	$-0.438637\pi$
$257$	12.6654	−	2.89080i	0.790047	−	0.180323i	0.598460	+	0.801152i	$0.295779\pi$
$258$	1.51231	−	0.0323555i	0.0941524	−	0.00201437i
$259$	0.0934167	−	0.117141i	0.00580463	−	0.00727877i
$260$	−1.68474	−	2.51286i	−0.104483	−	0.155841i
$261$	14.3390	+	7.44261i	0.887563	+	0.460686i
$262$	2.88253	−	0.876873i	0.178083	−	0.0541734i
$263$	9.61927	+	7.67111i	0.593150	+	0.473021i	0.873465	−	0.486887i	$-0.161868\pi$
$263$	9.61927	+	7.67111i	0.593150	+	0.473021i	−0.280315	+	0.959908i	$0.590439\pi$
$264$	−15.8328	−	22.5567i	−0.974440	−	1.38827i
$265$	0.346821	+	1.51952i	0.0213051	+	0.0933436i
$266$	−2.52962	+	6.37235i	−0.155101	+	0.390714i
$267$	4.45722	+	6.19504i	0.272777	+	0.379130i
$268$	3.03655	−	1.16457i	0.185487	−	0.0711372i
$269$	−17.9062	−	8.62319i	−1.09176	−	0.525765i	−0.200704	−	0.979652i	$-0.564323\pi$
$269$	−17.9062	−	8.62319i	−1.09176	−	0.525765i	−0.891059	+	0.453887i	$0.850037\pi$
$270$	2.03817	+	0.635041i	0.124039	+	0.0386474i
$271$	−3.57449	−	15.6609i	−0.217135	−	0.951330i	−0.959583	−	0.281426i	$-0.909193\pi$
$271$	−3.57449	−	15.6609i	−0.217135	−	0.951330i	0.742448	−	0.669904i	$-0.233665\pi$
$272$	1.01528	+	17.1204i	0.0615605	+	1.03808i
$273$	1.24832	−	25.1896i	0.0755521	−	1.52454i
$274$	−13.5639	−	14.7330i	−0.819428	−	0.890056i
$275$	−21.6194	+	17.2409i	−1.30370	+	1.03966i
$276$	−11.8226	−	4.40287i	−0.711637	−	0.265022i
$277$	−2.42652	+	1.16855i	−0.145795	+	0.0702113i	−0.505359	−	0.862909i	$-0.668640\pi$
$277$	−2.42652	+	1.16855i	−0.145795	+	0.0702113i	0.359564	+	0.933121i	$0.382926\pi$
$278$	6.82953	−	2.07756i	0.409608	−	0.124604i
$279$	−24.2425	+	8.84277i	−1.45136	+	0.529403i
$280$	1.02109	−	2.05848i	0.0610217	−	0.123018i
$281$	7.12552	−	14.7963i	0.425073	−	0.882672i	−0.572936	−	0.819600i	$-0.694196\pi$
$281$	7.12552	−	14.7963i	0.425073	−	0.882672i	0.998009	−	0.0630726i	$-0.0200900\pi$
$282$	−20.3701	−	4.19304i	−1.21302	−	0.249692i
$283$	25.2535	+	5.76394i	1.50116	+	0.342631i	0.892591	−	0.450867i	$-0.148885\pi$
$283$	25.2535	+	5.76394i	1.50116	+	0.342631i	0.608573	+	0.793498i	$0.291742\pi$
$284$	−8.43202	−	2.67298i	−0.500348	−	0.158612i
$285$	0.654250	+	0.576972i	0.0387545	+	0.0341769i
$286$	20.5723	+	35.9546i	1.21646	+	2.12604i
$287$	20.8235	+	4.75283i	1.22917	+	0.280551i
$288$	−12.9326	+	10.9885i	−0.762061	+	0.647505i
$289$	1.38366			0.0813919
$290$	−1.22867	−	1.83994i	−0.0721500	−	0.108045i
$291$	0.0146033	−	0.294676i	0.000856061	−	0.0172742i
$292$	25.9569	+	2.14849i	1.51901	+	0.125731i
$293$	0.366891	−	1.60745i	0.0214340	−	0.0939084i	−0.963080	−	0.269217i	$-0.913235\pi$
$293$	0.366891	−	1.60745i	0.0214340	−	0.0939084i	0.984514	+	0.175309i	$0.0560923\pi$
$294$	1.79099	−	0.910193i	0.104453	−	0.0530835i
$295$	−1.52454	−	1.21578i	−0.0887619	−	0.0707852i
$296$	0.151531	+	0.00176922i	0.00880757	+	0.000102834i
$297$	−27.2210	−	10.6505i	−1.57952	−	0.618005i
$298$	3.25875	+	0.504156i	0.188774	+	0.0292050i
$299$	17.0852	+	8.22780i	0.988062	+	0.475826i
$300$	11.7987	+	12.2779i	0.681201	+	0.708867i
$301$	−0.749284	−	1.55590i	−0.0431880	−	0.0896808i
$302$	−5.91666	+	1.79986i	−0.340466	+	0.103570i
$303$	8.66365	−	3.65560i	0.497713	−	0.210009i
$304$	−6.65739	+	1.94057i	−0.381828	+	0.111299i
$305$	1.33173	+	1.66994i	0.0762546	+	0.0956203i
$306$	10.9374	+	14.5355i	0.625247	+	0.830938i
$307$	−3.71065			−0.211778			−0.105889	−	0.994378i	$-0.533769\pi$
$307$	−3.71065			−0.211778			−0.105889	+	0.994378i	$0.533769\pi$
$308$	−15.9428	+	27.1239i	−0.908424	+	1.54553i
$309$	19.6541	−	3.47263i	1.11808	−	0.197551i
$310$	3.49239	+	0.540301i	0.198354	+	0.0306870i
$311$	−7.75590	+	16.1053i	−0.439797	+	0.913247i	0.556787	+	0.830655i	$0.312034\pi$
$311$	−7.75590	+	16.1053i	−0.439797	+	0.913247i	−0.996583	+	0.0825918i	$0.973680\pi$
$312$	20.8789	−	14.6551i	1.18204	−	0.829682i
$313$	1.57908	+	1.98010i	0.0892547	+	0.111922i	0.824454	−	0.565930i	$-0.191483\pi$
$313$	1.57908	+	1.98010i	0.0892547	+	0.111922i	−0.735199	+	0.677852i	$0.762911\pi$
$314$	2.98054	−	7.50825i	0.168202	−	0.423715i
$315$	−0.304743	−	2.41808i	−0.0171703	−	0.136243i
$316$	−6.98673	−	18.2176i	−0.393034	−	1.02482i
$317$	1.19091	−	1.49335i	0.0668881	−	0.0838751i	−0.747262	−	0.664530i	$-0.768632\pi$
$317$	1.19091	−	1.49335i	0.0668881	−	0.0838751i	0.814150	+	0.580655i	$0.197203\pi$
$318$	−12.7466	+	3.19766i	−0.714796	+	0.179316i
$319$	14.9961	+	26.3215i	0.839621	+	1.47372i
$320$	2.27727	−	0.464115i	0.127303	−	0.0259448i
$321$	−22.2517	+	25.2320i	−1.24197	+	1.40832i
$322$	1.02042	+	14.3667i	0.0568660	+	0.800622i
$323$	1.65401	+	7.24671i	0.0920318	+	0.403218i
$324$	−4.98564	+	17.2958i	−0.276980	+	0.960876i
$325$	−15.9585	−	20.0113i	−0.885217	−	1.11003i
$326$	−14.2287	+	1.01063i	−0.788056	+	0.0559734i
$327$	−10.5290	−	5.72902i	−0.582256	−	0.316815i
$328$	9.14541	+	19.5719i	0.504971	+	1.08068i
$329$	5.28332	+	23.1477i	0.291279	+	1.27618i
$330$	2.56223	+	3.07561i	0.141046	+	0.169307i
$331$	−15.8514			−0.871269			−0.435635	−	0.900124i	$-0.643476\pi$
$331$	−15.8514			−0.871269			−0.435635	+	0.900124i	$0.643476\pi$
$332$	−10.9900	+	18.6977i	−0.603156	+	1.02617i
$333$	0.134960	−	0.0873002i	0.00739575	−	0.00478402i
$334$	3.37516	−	4.90929i	0.184680	−	0.268624i
$335$	−0.425619	+	0.204967i	−0.0232540	+	0.0111985i
$336$	17.5366	+	8.23625i	0.956700	+	0.449324i
$337$	−14.0166	−	29.1058i	−0.763534	−	1.58550i	−0.809898	−	0.586570i	$-0.800478\pi$
$337$	−14.0166	−	29.1058i	−0.763534	−	1.58550i	0.0463641	−	0.998925i	$-0.485237\pi$
$338$	−17.3230	+	9.91173i	−0.942245	+	0.539127i
$339$	23.5069	+	12.7905i	1.27672	+	0.694686i
$340$	−0.352109	−	2.46619i	−0.0190958	−	0.133748i
$341$	−47.1744	−	10.7673i	−2.55464	−	0.583079i
$342$	−4.74573	+	5.61922i	−0.256620	+	0.303852i
$343$	13.5113	+	10.7749i	0.729542	+	0.581791i
$344$	0.776171	−	1.56474i	0.0418483	−	0.0843650i
$345$	1.76420	+	0.495703i	0.0949813	+	0.0266877i
$346$	12.5824	−	31.6962i	0.676435	−	1.70400i
$347$	−27.8089			−1.49286			−0.746429	−	0.665465i	$-0.768233\pi$
$347$	−27.8089			−1.49286			−0.746429	+	0.665465i	$0.768233\pi$
$348$	15.2886	−	10.6892i	0.819555	−	0.573001i
$349$	6.25044			0.334578			0.167289	−	0.985908i	$-0.446499\pi$
$349$	6.25044			0.334578			0.167289	+	0.985908i	$0.446499\pi$
$350$	7.17266	−	18.0686i	0.383395	−	0.965805i
$351$	9.85830	−	25.1963i	0.526197	−	1.34488i
$352$	−31.5529	+	4.12968i	−1.68178	+	0.220113i
$353$	26.2348	+	20.9216i	1.39634	+	1.11354i	0.978785	+	0.204891i	$0.0656839\pi$
$353$	26.2348	+	20.9216i	1.39634	+	1.11354i	0.417554	+	0.908652i	$0.362888\pi$
$354$	9.97372	−	13.0707i	0.530097	−	0.694700i
$355$	1.25265	+	0.285909i	0.0664838	+	0.0151745i
$356$	8.72405	−	1.24557i	0.462374	−	0.0660153i
$357$	9.92577	−	18.2420i	0.525328	−	0.965467i
$358$	−17.8794	+	10.2301i	−0.944957	+	0.540679i
$359$	−10.9577	−	22.7539i	−0.578324	−	1.20090i	−0.960879	−	0.276970i	$-0.910670\pi$
$359$	−10.9577	−	22.7539i	−0.578324	−	1.20090i	0.382554	−	0.923933i	$-0.375044\pi$
$360$	1.74046	−	1.74566i	0.0917305	−	0.0920045i
$361$	14.4106	−	6.93979i	0.758454	−	0.365252i
$362$	8.18310	−	11.9026i	0.430094	−	0.625587i
$363$	−20.8838	−	29.0262i	−1.09612	−	1.52348i
$364$	−25.1064	−	14.7569i	−1.31593	−	0.773473i
$365$	−3.78327			−0.198025
$366$	−13.8369	+	11.5273i	−0.723268	+	0.602542i
$367$	−1.58827	−	6.95867i	−0.0829070	−	0.363239i	0.916408	−	0.400245i	$-0.131075\pi$
$367$	−1.58827	−	6.95867i	−0.0829070	−	0.363239i	−0.999315	+	0.0370059i	$0.988218\pi$
$368$	−10.8317	+	9.74099i	−0.564640	+	0.507784i
$369$	19.5604	+	11.9343i	1.01827	+	0.621276i
$370$	−0.0219569	+	0.00155954i	−0.00114149	+	8.10766e-5i
$371$	9.35428	+	11.7299i	0.485650	+	0.608986i
$372$	−3.92473	+	29.5373i	−0.203488	+	1.53144i
$373$	3.18505	+	13.9546i	0.164916	+	0.722543i	0.987978	+	0.154593i	$0.0494065\pi$
$373$	3.18505	+	13.9546i	0.164916	+	0.722543i	−0.823062	+	0.567951i	$0.807736\pi$
$374$	2.41666	+	34.0245i	0.124963	+	1.75936i
$375$	−3.74206	−	3.30006i	−0.193239	−	0.170414i
$376$	−15.1909	+	18.5992i	−0.783413	+	0.959179i
$377$	−24.3637	+	13.8807i	−1.25479	+	0.714892i
$378$	20.3288	−	3.00501i	1.04560	−	0.154561i
$379$	−5.92732	+	7.43263i	−0.304466	+	0.381789i	−0.910402	−	0.413725i	$-0.864227\pi$
$379$	−5.92732	+	7.43263i	−0.304466	+	0.381789i	0.605936	+	0.795514i	$0.292799\pi$
$380$	0.940475	−	0.360687i	0.0482453	−	0.0185029i
$381$	−5.05003	−	28.5817i	−0.258721	−	1.46428i
$382$	2.40309	−	6.05359i	0.122953	−	0.309728i
$383$	−13.4453	−	16.8598i	−0.687021	−	0.861498i	0.308958	−	0.951076i	$-0.400020\pi$
$383$	−13.4453	−	16.8598i	−0.687021	−	0.861498i	−0.995980	+	0.0895780i	$0.971448\pi$
$384$	4.32307	+	19.1131i	0.220611	+	0.975362i
$385$	1.98288	−	4.11750i	0.101057	−	0.209847i
$386$	13.6474	+	2.11136i	0.694633	+	0.107465i
$387$	−0.231648	−	1.83808i	−0.0117753	−	0.0934348i
$388$	−0.293703	−	0.172631i	−0.0149105	−	0.00876403i
$389$	17.6671			0.895757			0.447879	−	0.894094i	$-0.352180\pi$
$389$	17.6671			0.895757			0.447879	+	0.894094i	$0.352180\pi$
$390$	−2.84684	+	2.37165i	−0.144155	+	0.120093i
$391$	9.73577	+	12.2083i	0.492359	+	0.617399i
$392$	0.0270832	−	2.31964i	0.00136791	−	0.117160i
$393$	−1.43455	−	3.39984i	−0.0723637	−	0.171499i
$394$	−6.39677	+	1.94591i	−0.322265	+	0.0980337i
$395$	1.22969	+	2.55347i	0.0618722	+	0.128479i
$396$	−25.4644	+	22.1536i	−1.27964	+	1.11326i
$397$	−15.9125	−	7.66306i	−0.798626	−	0.384598i	−0.0103706	−	0.999946i	$-0.503301\pi$
$397$	−15.9125	−	7.66306i	−0.798626	−	0.384598i	−0.788255	+	0.615348i	$0.789015\pi$
$398$	−16.0800	−	2.48772i	−0.806020	−	0.124698i
$399$	8.08390	+	2.27140i	0.404701	+	0.113712i
$400$	18.8768	−	5.50243i	0.943840	−	0.275121i
$401$	−10.3154	−	8.22623i	−0.515125	−	0.410798i	0.331123	−	0.943588i	$-0.392572\pi$
$401$	−10.3154	−	8.22623i	−0.515125	−	0.410798i	−0.846248	+	0.532789i	$0.821144\pi$
$402$	−1.80458	−	3.55089i	−0.0900042	−	0.177102i
$403$	9.96637	−	43.6655i	0.496460	−	2.17513i
$404$	0.895670	−	10.8210i	0.0445612	−	0.538365i
$405$	0.514485	−	2.56348i	0.0255650	−	0.127380i
$406$	−18.3405	−	10.8257i	−0.910225	−	0.537268i
$407$	0.301398			0.0149397
$408$	20.7258	−	3.41297i	1.02608	−	0.168967i
$409$	25.3261	+	5.78051i	1.25229	+	0.285828i	0.796708	−	0.604364i	$-0.206573\pi$
$409$	25.3261	+	5.78051i	1.25229	+	0.285828i	0.455586	+	0.890192i	$0.349430\pi$
$410$	−1.55840	−	2.72366i	−0.0769641	−	0.134512i
$411$	−16.2226	+	18.3954i	−0.800203	+	0.907379i
$412$	6.96416	−	21.9687i	0.343099	−	1.08232i
$413$	−18.2996	−	4.17677i	−0.900467	−	0.205526i
$414$	−3.86046	+	14.9611i	−0.189731	+	0.735299i
$415$	1.36688	−	2.83836i	0.0670977	−	0.139330i
$416$	−3.82251	−	29.2060i	−0.187414	−	1.43194i
$417$	−3.39886	−	8.05517i	−0.166443	−	0.394463i
$418$	−13.1948	+	4.01388i	−0.645377	+	0.196325i
$419$	7.04633	−	3.39333i	0.344236	−	0.165775i	−0.253775	−	0.967263i	$-0.581672\pi$
$419$	7.04633	−	3.39333i	0.344236	−	0.165775i	0.598011	+	0.801488i	$0.295958\pi$
$420$	−2.63729	−	0.982158i	−0.128687	−	0.0479244i
$421$	11.6027	−	9.25281i	0.565479	−	0.450954i	−0.298552	−	0.954393i	$-0.596504\pi$
$421$	11.6027	−	9.25281i	0.565479	−	0.450954i	0.864031	+	0.503439i	$0.167932\pi$
$422$	−6.35976	−	6.90791i	−0.309588	−	0.336272i
$423$	−2.51837	+	25.3464i	−0.122448	+	1.23238i
$424$	−3.54916	+	14.7537i	−0.172362	+	0.716504i
$425$	−4.68990	−	20.5478i	−0.227494	−	0.996715i
$426$	−2.18422	+	10.6111i	−0.105826	+	0.514108i
$427$	18.5243	+	8.92084i	0.896455	+	0.431710i
$428$	13.9104	+	36.2707i	0.672384	+	1.75321i
$429$	41.1824	−	29.6300i	1.98831	−	1.43055i
$430$	−0.0936101	+	0.235812i	−0.00451428	+	0.0113719i
$431$	−5.03642	−	22.0660i	−0.242596	−	1.06288i	−0.938644	−	0.344886i	$-0.887917\pi$
$431$	−5.03642	−	22.0660i	−0.242596	−	1.06288i	0.696049	−	0.717995i	$-0.254940\pi$
$432$	15.0294	+	14.3568i	0.723101	+	0.690742i
$433$	1.06219	+	0.847065i	0.0510454	+	0.0407073i	0.648680	−	0.761061i	$-0.275321\pi$
$433$	1.06219	+	0.847065i	0.0510454	+	0.0407073i	−0.597635	+	0.801768i	$0.703893\pi$
$434$	32.5451	−	9.90030i	1.56222	−	0.475230i
$435$	−2.08510	+	1.73056i	−0.0999731	+	0.0829740i
$436$	−11.4964	+	7.70772i	−0.550577	+	0.369133i
$437$	−3.93647	+	4.93618i	−0.188307	+	0.236129i
$438$	−0.682321	−	31.8920i	−0.0326025	−	1.52386i
$439$	−9.75887	+	2.22740i	−0.465765	+	0.106308i	−0.448962	−	0.893551i	$-0.648206\pi$
$439$	−9.75887	+	2.22740i	−0.465765	+	0.106308i	−0.0168034	+	0.999859i	$0.505349\pi$
$440$	4.51813	−	0.975882i	0.215393	−	0.0465233i
$441$	−1.33639	−	2.06597i	−0.0636377	−	0.0983793i
$442$	−31.4937	+	2.23691i	−1.49800	+	0.106399i
$443$	3.17957	−	6.60244i	0.151066	−	0.313692i	−0.811679	−	0.584104i	$-0.801446\pi$
$443$	3.17957	−	6.60244i	0.151066	−	0.313692i	0.962744	+	0.270413i	$0.0871602\pi$
$444$	−0.0171065	−	0.184810i	−0.000811837	−	0.00877068i
$445$	−1.24797	+	0.284841i	−0.0591595	+	0.0135028i
$446$	−0.135958	+	0.125170i	−0.00643781	+	0.00592696i
$447$	0.199897	−	4.03367i	0.00945481	−	0.190786i
$448$	17.8118	−	13.5363i	0.841527	−	0.639531i
$449$	11.9970	+	15.0437i	0.566172	+	0.709957i	0.979685	−	0.200541i	$-0.0642700\pi$
$449$	11.9970	+	15.0437i	0.566172	+	0.709957i	−0.413514	+	0.910498i	$0.635699\pi$
$450$	13.4564	−	15.9331i	0.634338	−	0.751093i
$451$	18.6423	+	38.7112i	0.877832	+	1.82284i
$452$	25.6667	−	17.2081i	1.20726	−	0.809403i
$453$	2.94455	+	6.97848i	0.138347	+	0.327878i
$454$	15.1436	−	8.66478i	0.710726	−	0.406658i
$455$	3.81123	+	1.83539i	0.178673	+	0.0860445i
$456$	3.21011	+	7.86290i	0.150327	+	0.368214i
$457$	2.46198	−	10.7867i	0.115167	−	0.504579i	−0.884136	−	0.467230i	$-0.845252\pi$
$457$	2.46198	−	10.7867i	0.115167	−	0.504579i	0.999302	−	0.0373481i	$-0.0118910\pi$
$458$	−23.5157	−	16.1672i	−1.09882	−	0.755441i
$459$	16.3158	−	15.1708i	0.761558	−	0.708111i
$460$	1.45128	−	1.53989i	0.0676663	−	0.0717980i
$461$	4.12711	−	18.0821i	0.192219	−	0.842165i	−0.783194	−	0.621778i	$-0.786411\pi$
$461$	4.12711	−	18.0821i	0.192219	−	0.842165i	0.975412	−	0.220387i	$-0.0707321\pi$
$462$	35.0670	+	15.9726i	1.63147	+	0.743111i
$463$			14.8614i			0.690669i	0.938480	+	0.345335i	$0.112235\pi$
$463$			14.8614i			0.690669i	−0.938480	+	0.345335i	$0.887765\pi$
$464$	−2.75604	−	21.3636i	−0.127946	−	0.991781i
$465$	0.214229	−	4.32286i	0.00993462	−	0.200468i
$466$	5.41761	−	13.6474i	0.250966	−	0.632205i
$467$	16.1272	+	3.68093i	0.746278	+	0.170333i	0.578717	−	0.815529i	$-0.303554\pi$
$467$	16.1272	+	3.68093i	0.746278	+	0.170333i	0.167561	+	0.985862i	$0.446411\pi$
$468$	−20.5058	−	23.5704i	−0.947882	−	1.08954i
$469$	−2.83522	+	3.55525i	−0.130918	+	0.164166i
$470$	1.97619	−	2.87444i	0.0911549	−	0.132588i
$471$	−9.52490	−	2.67629i	−0.438884	−	0.123317i
$472$	−8.03696	−	17.1998i	−0.369931	−	0.791683i
$473$	1.50727	−	3.12988i	0.0693044	−	0.143912i
$474$	−21.3033	+	10.8264i	−0.978492	+	0.497275i
$475$	7.67784	−	3.69745i	0.352283	−	0.169651i
$476$	−13.3539	−	19.9180i	−0.612077	−	0.912939i
$477$	5.51543	+	15.1206i	0.252534	+	0.692325i
$478$	−11.2269	+	16.3299i	−0.513505	+	0.746911i
$479$	−2.83844	+	2.26358i	−0.129691	+	0.103425i	−0.686187	−	0.727425i	$-0.740717\pi$
$479$	−2.83844	+	2.26358i	−0.129691	+	0.103425i	0.556496	+	0.830850i	$0.312146\pi$
$480$	−0.854824	−	2.71502i	−0.0390172	−	0.123923i
$481$			0.278979i			0.0127204i
$482$	−10.8257	−	11.7588i	−0.493096	−	0.535597i
$483$	17.3707	−	3.06920i	0.790396	−	0.139653i
$484$	−40.8756	+	5.83600i	−1.85798	+	0.265273i
$485$	0.0445850	+	0.0214710i	0.00202450	+	0.000974948i
$486$	21.7022	+	3.87464i	0.984434	+	0.175757i
$487$	24.6637	−	19.6687i	1.11762	−	0.891272i	0.122750	−	0.992438i	$-0.460829\pi$
$487$	24.6637	−	19.6687i	1.11762	−	0.891272i	0.994870	+	0.101166i	$0.0322572\pi$
$488$	4.39042	+	20.3268i	0.198745	+	0.920149i
$489$	3.03973	+	17.2040i	0.137461	+	0.777991i
$490$	0.0238734	+	0.336117i	0.00107849	+	0.0151842i
$491$	3.05910	+	2.43955i	0.138055	+	0.110095i	0.690083	−	0.723731i	$-0.257574\pi$
$491$	3.05910	+	2.43955i	0.138055	+	0.110095i	−0.552027	+	0.833826i	$0.686146\pi$
$492$	22.6787	−	13.6282i	1.02243	−	0.614405i
$493$	−23.0345	+	1.59340i	−1.03742	+	0.0717630i
$494$	−3.71532	−	12.2133i	−0.167160	−	0.549504i
$495$	3.42080	−	3.51208i	0.153753	−	0.157856i
$496$	28.1229	+	19.8221i	1.26275	+	0.890037i
$497$	12.0580	−	2.75216i	0.540876	−	0.123451i
$498$	24.1732	+	11.0106i	1.08323	+	0.493395i
$499$	−13.2741	+	10.5858i	−0.594232	+	0.473884i	−0.873829	−	0.486233i	$-0.838371\pi$
$499$	−13.2741	+	10.5858i	−0.594232	+	0.473884i	0.279597	+	0.960117i	$0.409799\pi$
$500$	−5.37915	+	2.06299i	−0.240563	+	0.0922597i
$501$	−6.40918	−	3.48735i	−0.286341	−	0.155803i
$502$	−8.77049	−	1.35687i	−0.391446	−	0.0605599i
$503$	−23.9600	+	5.46872i	−1.06832	+	0.243838i	−0.720311	−	0.693651i	$-0.756001\pi$
$503$	−23.9600	+	5.46872i	−1.06832	+	0.243838i	−0.348014	+	0.937489i	$0.613144\pi$
$504$	7.80369	−	22.4088i	0.347604	−	0.998168i
$505$			1.57718i			0.0701838i
$506$	−21.3152	+	19.6238i	−0.947577	+	0.872385i
$507$	14.2758	+	19.8417i	0.634009	+	0.881202i
$508$	−31.9477	−	10.1275i	−1.41745	−	0.449336i
$509$	14.4265	+	29.9570i	0.639445	+	1.32782i	0.928794	+	0.370598i	$0.120847\pi$
$509$	14.4265	+	29.9570i	0.639445	+	1.32782i	−0.289348	+	0.957224i	$0.593439\pi$
$510$	−2.95938	+	0.742400i	−0.131044	+	0.0328740i
$511$	−32.8113	+	15.8011i	−1.45148	+	0.698998i
$512$	21.8703	+	5.80449i	0.966538	+	0.256524i
$513$	7.44818	+	5.06664i	0.328845	+	0.223698i
$514$	−18.1562	−	2.80892i	−0.800838	−	0.123896i
$515$	−0.744904	+	3.26364i	−0.0328244	+	0.143813i
$516$	−2.00472	−	0.746579i	−0.0882527	−	0.0328663i
$517$	−29.7790	+	37.3417i	−1.30968	+	1.64229i
$518$	−0.183913	+	0.105230i	−0.00808067	+	0.00462354i
$519$	−40.2095	−	11.2980i	−1.76500	−	0.495928i
$520$	0.903294	+	4.18207i	0.0396121	+	0.183396i
$521$			4.44026i			0.194531i	0.995258	+	0.0972656i	$0.0310096\pi$
$521$			4.44026i			0.194531i	−0.995258	+	0.0972656i	$0.968990\pi$
$522$	−14.9642	−	17.2648i	−0.654966	−	0.755658i
$523$			26.8481i			1.17399i	0.809592	+	0.586993i	$0.199688\pi$
$523$			26.8481i			1.17399i	−0.809592	+	0.586993i	$0.800312\pi$
$524$	−4.24644	−	0.351484i	−0.185507	−	0.0153547i
$525$	−22.9216	−	6.44049i	−1.00038	−	0.281086i
$526$	−8.64118	−	15.1024i	−0.376774	−	0.658496i
$527$	22.9946	−	28.8344i	1.00166	−	1.25604i
$528$	9.04128	+	37.9107i	0.393471	+	1.64985i
$529$	2.16663	−	9.49262i	0.0942013	−	0.412723i
$530$	0.336998	−	2.17828i	0.0146383	−	0.0946185i
$531$	−17.1896	−	10.4878i	−0.745965	−	0.455133i
$532$	6.65005	−	7.05609i	0.288316	−	0.305920i
$533$	−35.8318	+	17.2557i	−1.55205	+	0.747426i
$534$	−2.62621	−	10.4687i	−0.113647	−	0.453025i
$535$	−2.44827	−	5.08388i	−0.105848	−	0.219795i
$536$	−4.59900	−	0.0536961i	−0.198647	−	0.00231932i
$537$	14.7343	+	20.4791i	0.635833	+	0.883738i
$538$	19.0371	+	20.6779i	0.820747	+	0.891488i
$539$		−	4.61380i		−	0.198730i
$540$	−2.34768	−	1.89822i	−0.101028	−	0.0816862i
$541$	8.58334	−	1.95909i	0.369027	−	0.0842280i	−0.0339860	−	0.999422i	$-0.510820\pi$
$541$	8.58334	−	1.95909i	0.369027	−	0.0842280i	0.403013	+	0.915194i	$0.367963\pi$
$542$	−3.47325	+	22.4503i	−0.149189	+	0.964323i
$543$	−15.5391	−	8.45510i	−0.666847	−	0.362843i
$544$	7.59872	−	23.0334i	0.325792	−	0.987548i
$545$	1.57187	−	1.25352i	0.0673314	−	0.0536950i
$546$	−14.7845	+	32.4587i	−0.632719	+	1.38910i
$547$	14.2220	−	3.24608i	0.608090	−	0.138792i	0.0926217	−	0.995701i	$-0.470475\pi$
$547$	14.2220	−	3.24608i	0.608090	−	0.138792i	0.515468	+	0.856909i	$0.327618\pi$
$548$	10.1414	+	26.4431i	0.433218	+	1.12959i
$549$	15.8006	+	15.3899i	0.674354	+	0.656826i
$550$	37.4133	−	11.3812i	1.59531	−	0.485297i
$551$	−2.70056	−	8.93667i	−0.115048	−	0.380715i
$552$	13.2426	+	11.9562i	0.563645	+	0.508889i
$553$	21.3295	+	17.0097i	0.907021	+	0.723325i
$554$	3.79923	−	0.269849i	0.161414	−	0.0114648i
$555$	0.00469074	+	0.0265482i	0.000199111	+	0.00112691i
$556$	−10.0610	−	0.832764i	−0.426682	−	0.0353171i
$557$	14.3218	−	11.4213i	0.606834	−	0.483934i	−0.271206	−	0.962521i	$-0.587422\pi$
$557$	14.3218	−	11.4213i	0.606834	−	0.483934i	0.878040	+	0.478587i	$0.158851\pi$
$558$	36.4792	+	1.02625i	1.54429	+	0.0434448i
$559$	2.89708	+	1.39516i	0.122533	+	0.0590089i
$560$	−2.41625	+	2.17294i	−0.102105	+	0.0918237i
$561$	41.1390	−	7.26877i	1.73689	−	0.306888i
$562$	−17.0866	+	15.7307i	−0.720753	+	0.663560i
$563$		−	3.59603i		−	0.151554i	−0.997125	−	0.0757772i	$-0.975856\pi$
$563$		−	3.59603i		−	0.151554i	0.997125	−	0.0757772i	$-0.0241438\pi$
$564$	24.5872	+	16.1404i	1.03531	+	0.679632i
$565$	−3.50933	+	2.79860i	−0.147639	+	0.117738i
$566$	−30.1865	−	20.7533i	−1.26883	−	0.872328i
$567$	−6.24455	−	24.3811i	−0.262246	−	1.02391i
$568$	9.68860	+	7.91320i	0.406524	+	0.332030i
$569$	28.1294	−	13.5464i	1.17925	−	0.567896i	0.261556	−	0.965188i	$-0.415765\pi$
$569$	28.1294	−	13.5464i	1.17925	−	0.567896i	0.917692	+	0.397293i	$0.130050\pi$
$570$	−0.558911	−	1.09977i	−0.0234102	−	0.0460644i
$571$	−1.23182	+	2.55791i	−0.0515503	+	0.107045i	−0.925153	−	0.379595i	$-0.876063\pi$
$571$	−1.23182	+	2.55791i	−0.0515503	+	0.107045i	0.873603	+	0.486640i	$0.161778\pi$
$572$	−8.28013	−	57.9944i	−0.346210	−	2.42487i
$573$	−7.67952	−	2.15778i	−0.320817	−	0.0901427i
$574$	−24.8912	−	17.1128i	−1.03894	−	0.714274i
$575$	11.1617	−	13.9964i	0.465476	−	0.583689i
$576$	22.7327	−	7.69560i	0.947198	−	0.320650i
$577$	−15.6547	−	3.57309i	−0.651714	−	0.148750i	−0.116134	−	0.993234i	$-0.537050\pi$
$577$	−15.6547	−	3.57309i	−0.651714	−	0.148750i	−0.535581	+	0.844484i	$0.679907\pi$
$578$	−1.81873	−	0.721980i	−0.0756493	−	0.0300304i
$579$	0.837153	−	16.8927i	0.0347909	−	0.702036i
$580$	0.654945	+	3.05958i	0.0271951	+	0.127042i
$581$		−	30.3252i		−	1.25810i
$582$	−0.172954	+	0.379712i	−0.00716917	+	0.0157396i
$583$	−6.71578	+	29.4238i	−0.278139	+	1.21861i
$584$	−32.9975	−	16.3681i	−1.36545	−	0.677316i
$585$	3.25085	+	3.16635i	0.134406	+	0.130913i
$586$	−1.32101	+	1.92145i	−0.0545702	+	0.0793744i
$587$	2.90943	−	12.7470i	0.120085	−	0.526126i	−0.878724	−	0.477330i	$-0.841605\pi$
$587$	2.90943	−	12.7470i	0.120085	−	0.526126i	0.998809	−	0.0487958i	$-0.0155384\pi$
$588$	−2.82907	+	0.261866i	−0.116669	+	0.0107992i
$589$	13.4352	+	6.47004i	0.553587	+	0.266593i
$590$	1.36952	+	2.39354i	0.0563823	+	0.0985406i
$591$	3.18349	+	7.54476i	0.130951	+	0.310350i
$592$	−0.198255	−	0.0813929i	−0.00814821	−	0.00334523i
$593$	−17.7934	−	36.9484i	−0.730689	−	1.51729i	−0.851351	−	0.524597i	$-0.824216\pi$
$593$	−17.7934	−	36.9484i	−0.730689	−	1.51729i	0.120662	−	0.992694i	$-0.461498\pi$
$594$	30.2229	+	28.2030i	1.24006	+	1.15718i
$595$	2.17178	+	2.72333i	0.0890343	+	0.111645i
$596$	−4.02035	−	2.36306i	−0.164680	−	0.0967948i
$597$	−0.986377	+	19.9038i	−0.0403697	+	0.814609i
$598$	−18.1642	−	19.7298i	−0.742788	−	0.806810i
$599$	1.30236	−	0.297255i	0.0532130	−	0.0121455i	−0.195832	−	0.980638i	$-0.562741\pi$
$599$	1.30236	−	0.297255i	0.0532130	−	0.0121455i	0.249045	+	0.968492i	$0.419883\pi$
$600$	−9.10216	−	22.2950i	−0.371594	−	0.910189i
$601$	−20.5880	+	42.7515i	−0.839803	+	1.74387i	−0.193018	+	0.981195i	$0.561828\pi$
$601$	−20.5880	+	42.7515i	−0.839803	+	1.74387i	−0.646784	+	0.762673i	$0.723887\pi$
$602$	0.173030	+	2.43610i	0.00705216	+	0.0992881i
$603$	−4.09606	+	2.64958i	−0.166804	+	0.107899i
$604$	8.71621	+	0.721453i	0.354657	+	0.0293555i
$605$	5.84724	−	1.33459i	0.237724	−	0.0542590i
$606$	−13.2952	+	0.284448i	−0.540082	+	0.0115549i
$607$	26.0382	−	32.6509i	1.05686	−	1.32526i	0.113480	−	0.993540i	$-0.463800\pi$
$607$	26.0382	−	32.6509i	1.05686	−	1.32526i	0.943378	−	0.331719i	$-0.107628\pi$
$608$	9.76327	+	0.923004i	0.395953	+	0.0374328i
$609$	−10.8557	+	23.7173i	−0.439897	+	0.961071i
$610$	−0.879115	−	2.88990i	−0.0355943	−	0.117009i
$611$	−34.5642	−	27.5640i	−1.39832	−	1.11512i
$612$	−6.79197	−	24.8129i	−0.274549	−	1.00300i
$613$	3.92936	+	17.2156i	0.158705	+	0.695333i	0.990183	+	0.139775i	$0.0446381\pi$
$613$	3.92936	+	17.2156i	0.158705	+	0.695333i	−0.831478	+	0.555558i	$0.812505\pi$
$614$	4.87741	+	1.93618i	0.196836	+	0.0781378i
$615$	−3.11968	+	2.24455i	−0.125798	+	0.0905092i
$616$	35.1087	−	27.3338i	1.41457	−	1.10131i
$617$	−38.0513	−	18.3246i	−1.53189	−	0.737719i	−0.537476	−	0.843279i	$-0.680622\pi$
$617$	−38.0513	−	18.3246i	−1.53189	−	0.737719i	−0.994413	+	0.105561i	$0.966336\pi$
$618$	−27.6460	−	5.69074i	−1.11208	−	0.228915i
$619$	−5.40266	−	23.6706i	−0.217151	−	0.951402i	−0.959571	−	0.281467i	$-0.909179\pi$
$619$	−5.40266	−	23.6706i	−0.217151	−	0.951402i	0.742420	−	0.669935i	$-0.233678\pi$
$620$	−4.30859	−	2.53248i	−0.173037	−	0.101707i
$621$	18.7153	+	2.80079i	0.751020	+	0.112392i
$622$	18.5982	−	17.1224i	0.745719	−	0.686545i
$623$	−9.63366	+	7.68259i	−0.385964	+	0.307796i
$624$	−35.0908	+	8.36878i	−1.40476	+	0.335019i
$625$	−21.3901	+	10.3009i	−0.855602	+	0.412036i
$626$	−1.04240	−	3.42665i	−0.0416625	−	0.136957i
$627$	6.56666	+	15.5627i	0.262247	+	0.621516i
$628$	−7.83545	+	8.31388i	−0.312669	+	0.331760i
$629$	−0.0996727	+	0.206972i	−0.00397421	+	0.00825253i
$630$	−0.861162	+	3.33741i	−0.0343095	+	0.132966i
$631$	−3.26807	−	0.745915i	−0.130100	−	0.0296944i	0.156975	−	0.987603i	$-0.449826\pi$
$631$	−3.26807	−	0.745915i	−0.130100	−	0.0296944i	−0.287075	+	0.957908i	$0.592683\pi$
$632$	−0.322146	+	27.5914i	−0.0128143	+	1.09753i
$633$	−7.60633	+	8.62510i	−0.302324	+	0.342817i
$634$	−2.34459	+	1.34151i	−0.0931155	+	0.0532781i
$635$	4.74610	+	1.08327i	0.188343	+	0.0429882i
$636$	18.4231	+	2.44795i	0.730524	+	0.0970674i
$637$	4.27062			0.169208
$638$	−5.97710	−	42.4227i	−0.236636	−	1.67953i
$639$	13.2033	+	1.31186i	0.522315	+	0.0518964i
$640$	−3.23550	−	0.578210i	−0.127894	−	0.0228557i
$641$	−9.56849	+	41.9223i	−0.377933	+	1.65583i	0.325854	+	0.945420i	$0.394348\pi$
$641$	−9.56849	+	41.9223i	−0.377933	+	1.65583i	−0.703787	+	0.710411i	$0.748509\pi$
$642$	42.4142	−	21.5551i	1.67396	−	0.850714i
$643$	−10.2505	−	8.17450i	−0.404240	−	0.322371i	0.400175	−	0.916439i	$-0.368949\pi$
$643$	−10.2505	−	8.17450i	−0.404240	−	0.322371i	−0.804415	+	0.594068i	$0.797521\pi$
$644$	6.15509	−	19.4165i	0.242545	−	0.765116i
$645$	0.299149	+	0.0840545i	0.0117790	+	0.00330964i
$646$	1.60717	−	10.3884i	0.0632331	−	0.408725i
$647$	1.53179	+	0.737671i	0.0602208	+	0.0290008i	0.463752	−	0.885965i	$-0.346503\pi$
$647$	1.53179	+	0.737671i	0.0602208	+	0.0290008i	−0.403531	+	0.914966i	$0.632217\pi$
$648$	15.5780	−	20.1327i	0.611963	−	0.790886i
$649$	−16.3828	−	34.0192i	−0.643081	−	1.33537i
$650$	10.5347	+	34.6305i	0.413204	+	1.35832i
$651$	−16.1968	−	38.3857i	−0.634801	−	1.50446i
$652$	19.2300	+	6.09600i	0.753107	+	0.238738i
$653$	21.6258	+	27.1180i	0.846285	+	1.06121i	0.997355	+	0.0726845i	$0.0231566\pi$
$653$	21.6258	+	27.1180i	0.846285	+	1.06121i	−0.151070	+	0.988523i	$0.548272\pi$
$654$	10.8503	+	13.0243i	0.424282	+	0.509292i
$655$	0.618928			0.0241835
$656$	−1.80861	−	30.4980i	−0.0706142	−	1.19075i
$657$	−38.7618	+	4.88504i	−1.51224	+	0.190584i
$658$	5.13367	−	33.1829i	0.200131	−	1.29361i
$659$	−19.5031	+	40.4985i	−0.759731	+	1.57760i	0.0554979	+	0.998459i	$0.482325\pi$
$659$	−19.5031	+	40.4985i	−0.759731	+	1.57760i	−0.815229	+	0.579139i	$0.803389\pi$
$660$	−1.76307	−	5.37963i	−0.0686272	−	0.209402i
$661$	−29.2717	−	36.7055i	−1.13854	−	1.42768i	−0.888162	−	0.459531i	$-0.848018\pi$
$661$	−29.2717	−	36.7055i	−1.13854	−	1.42768i	−0.250375	−	0.968149i	$-0.580554\pi$
$662$	20.8355	+	8.27107i	0.809797	+	0.321464i
$663$	6.72811	+	38.0791i	0.261298	+	1.47887i
$664$	24.2019	−	18.8424i	0.939216	−	0.731225i
$665$	−0.878117	+	1.10112i	−0.0340519	+	0.0426997i
$666$	−0.222948	+	0.0443297i	−0.00863906	+	0.00171774i
$667$	−13.2569	−	14.4530i	−0.513311	−	0.559621i
$668$	−6.99803	+	4.69181i	−0.270762	+	0.181532i
$669$	0.169755	+	0.149704i	0.00656312	+	0.00578790i
$670$	0.666397	−	0.0473323i	0.0257452	−	0.00182861i
$671$	9.20340	+	40.3227i	0.355293	+	1.55664i
$672$	−18.7531	−	19.9764i	−0.723417	−	0.770607i
$673$	19.4076	+	24.3364i	0.748109	+	0.938099i	0.999557	−	0.0297718i	$-0.00947804\pi$
$673$	19.4076	+	24.3364i	0.748109	+	0.938099i	−0.251448	+	0.967871i	$0.580907\pi$
$674$	3.23681	+	45.5714i	0.124677	+	1.75534i
$675$	−21.1191	−	14.3663i	−0.812873	−	0.552959i
$676$	27.9417	−	3.98937i	1.07468	−	0.153437i
$677$	6.60700	+	28.9472i	0.253928	+	1.11253i	0.927622	+	0.373520i	$0.121849\pi$
$677$	6.60700	+	28.9472i	0.253928	+	1.11253i	−0.673694	+	0.739010i	$0.735294\pi$
$678$	−24.2243	−	29.0780i	−0.930330	−	1.11673i
$679$	0.476349			0.0182806
$680$	−0.824007	+	3.42537i	−0.0315992	+	0.131357i
$681$	−12.4798	−	17.3455i	−0.478227	−	0.664682i
$682$	56.3894	+	38.7680i	2.15926	+	1.48450i
$683$	29.1471	−	14.0365i	1.11528	−	0.537091i	0.216850	−	0.976205i	$-0.430422\pi$
$683$	29.1471	−	14.0365i	1.11528	−	0.537091i	0.898431	+	0.439114i	$0.144708\pi$
$684$	9.16999	−	4.90981i	0.350623	−	0.187731i
$685$	−1.78491	−	3.70640i	−0.0681979	−	0.141614i
$686$	−12.1375	−	21.2130i	−0.463411	−	0.809915i
$687$	−16.7045	+	30.7003i	−0.637318	+	1.17129i
$688$	−1.83669	+	1.65174i	−0.0700231	+	0.0629722i
$689$	−27.2352	−	6.21625i	−1.03758	−	0.236820i
$690$	−2.06027	−	1.57211i	−0.0784331	−	0.0598492i
$691$	−18.1927	−	14.5082i	−0.692082	−	0.551917i	0.213053	−	0.977041i	$-0.431659\pi$
$691$	−18.1927	−	14.5082i	−0.692082	−	0.551917i	−0.905135	+	0.425124i	$0.860231\pi$
$692$	−33.0775	+	35.0972i	−1.25742	+	1.33420i
$693$	14.9992	−	44.7465i	0.569772	−	1.69978i
$694$	36.5529	+	14.5104i	1.38753	+	0.550806i
$695$	1.46641			0.0556242
$696$	−25.6734	+	6.07281i	−0.973146	+	0.230189i
$697$	−32.7484			−1.24043
$698$	−8.21579	−	3.26141i	−0.310972	−	0.123446i
$699$	−17.3130	−	4.86459i	−0.654838	−	0.183996i
$700$	−18.8560	+	20.0073i	−0.712689	+	0.756205i
$701$	−21.8797	−	17.4485i	−0.826386	−	0.659021i	0.116111	−	0.993236i	$-0.462957\pi$
$701$	−21.8797	−	17.4485i	−0.826386	−	0.659021i	−0.942497	+	0.334216i	$0.891529\pi$
$702$	−26.1052	+	27.9749i	−0.985279	+	1.05584i
$703$	−0.0905549	−	0.0206686i	−0.00341534	−	0.000779529i
$704$	43.6291	+	11.0358i	1.64433	+	0.415927i
$705$	−3.75265	−	2.04188i	−0.141333	−	0.0769017i
$706$	−23.5673	−	41.1891i	−0.886966	−	1.55017i
$707$	6.58721	+	13.6785i	0.247738	+	0.514432i
$708$	−19.9299	+	11.9764i	−0.749013	+	0.450100i
$709$	25.0455	−	12.0613i	0.940602	−	0.452970i	0.100221	−	0.994965i	$-0.468045\pi$
$709$	25.0455	−	12.0613i	0.940602	−	0.452970i	0.840382	+	0.541995i	$0.182331\pi$
$710$	−1.49734	−	1.02943i	−0.0561942	−	0.0386338i
$711$	15.8960	+	24.5740i	0.596145	+	0.921597i
$712$	−12.1171	−	2.91489i	−0.454108	−	0.109240i
$713$	31.3261			1.17317
$714$	−22.5652	+	18.7987i	−0.844483	+	0.703523i
$715$	1.89353	+	8.29608i	0.0708138	+	0.310256i
$716$	28.8393	−	4.11752i	1.07777	−	0.153879i
$717$	21.3190	+	11.6000i	0.796173	+	0.433212i
$718$	2.53042	+	35.6260i	0.0944344	+	1.32955i
$719$	7.40678	+	9.28781i	0.276226	+	0.346377i	0.900521	−	0.434812i	$-0.143185\pi$
$719$	7.40678	+	9.28781i	0.276226	+	0.346377i	−0.624295	+	0.781189i	$0.714614\pi$
$720$	−3.19859	+	1.38640i	−0.119204	+	0.0516682i
$721$	7.17045	+	31.4158i	0.267042	+	1.16999i
$722$	−22.5629	+	1.60258i	−0.839705	+	0.0596419i
$723$	−12.9476	+	14.6818i	−0.481527	+	0.546021i
$724$	−16.9668	+	11.3753i	−0.630566	+	0.422761i
$725$	7.65736	+	25.3396i	0.284387	+	0.941090i
$726$	12.3048	+	49.0500i	0.456675	+	1.82042i
$727$	17.3518	−	21.7585i	0.643544	−	0.806978i	−0.347898	−	0.937533i	$-0.613104\pi$
$727$	17.3518	−	21.7585i	0.643544	−	0.806978i	0.991441	+	0.130554i	$0.0416757\pi$
$728$	25.3007	+	32.4973i	0.937706	+	1.20443i
$729$	1.96118	−	26.9287i	0.0726364	−	0.997358i
$730$	4.97286	+	1.97407i	0.184054	+	0.0730636i
$731$	1.65086	+	2.07011i	0.0610593	+	0.0765659i
$732$	24.2026	−	7.93191i	0.894552	−	0.293172i
$733$	3.27593	−	6.80255i	0.120999	−	0.251258i	−0.831667	−	0.555274i	$-0.812613\pi$
$733$	3.27593	−	6.80255i	0.120999	−	0.251258i	0.952667	+	0.304016i	$0.0983277\pi$
$734$	−1.54328	+	9.97545i	−0.0569636	+	0.368201i
$735$	0.406400	−	0.0718058i	0.0149903	−	0.00264860i
$736$	19.3203	−	7.15203i	0.712154	−	0.263627i
$737$	−9.14748			−0.336952
$738$	−19.4836	−	25.8933i	−0.717203	−	0.953145i
$739$	19.5646	+	24.5332i	0.719694	+	0.902468i	0.998321	−	0.0579319i	$-0.0184506\pi$
$739$	19.5646	+	24.5332i	0.719694	+	0.902468i	−0.278627	+	0.960400i	$0.589879\pi$
$740$	0.0296747	+	0.00940698i	0.00109086	+	0.000345807i
$741$	−14.4052	+	6.07822i	−0.529187	+	0.223289i
$742$	−6.17504	−	20.2991i	−0.226693	−	0.745204i
$743$	4.75266	+	9.86900i	0.174358	+	0.362058i	0.969774	−	0.244006i	$-0.0784617\pi$
$743$	4.75266	+	9.86900i	0.174358	+	0.362058i	−0.795416	+	0.606064i	$0.792747\pi$
$744$	20.5711	−	36.7770i	0.754172	−	1.34831i
$745$	0.610302	+	0.293906i	0.0223597	+	0.0107679i
$746$	3.09484	−	20.0044i	0.113310	−	0.732412i
$747$	10.3396	−	30.8457i	0.378305	−	1.12858i
$748$	14.5771	−	45.9839i	0.532990	−	1.68134i
$749$	−42.4663	−	33.8658i	−1.55169	−	1.23743i
$750$	3.19675	+	6.29028i	0.116729	+	0.229688i
$751$	−5.59760	+	24.5247i	−0.204259	+	0.894919i	0.764048	+	0.645159i	$0.223209\pi$
$751$	−5.59760	+	24.5247i	−0.204259	+	0.894919i	−0.968308	+	0.249760i	$0.919648\pi$
$752$	29.6723	−	16.5209i	1.08204	−	0.602455i
$753$	−0.537996	+	10.8561i	−0.0196057	+	0.395617i
$754$	39.2673	−	5.53252i	1.43003	−	0.201482i
$755$	−1.27041			−0.0462348
$756$	−28.2888	−	6.65746i	−1.02885	−	0.242129i
$757$	35.2435	+	8.04410i	1.28095	+	0.292368i	0.808240	−	0.588853i	$-0.200420\pi$
$757$	35.2435	+	8.04410i	1.28095	+	0.292368i	0.472706	+	0.881220i	$0.343277\pi$
$758$	11.6693	−	6.67688i	0.423850	−	0.242515i
$759$	26.6138	+	23.4703i	0.966021	+	0.851917i
$760$	−1.42439	−	0.0166306i	−0.0516682	−	0.000603257i
$761$	19.2272	+	4.38849i	0.696987	+	0.159083i	0.556312	−	0.830973i	$-0.312216\pi$
$761$	19.2272	+	4.38849i	0.696987	+	0.159083i	0.140674	+	0.990056i	$0.455073\pi$
$762$	−8.27569	+	40.2038i	−0.299797	+	1.45643i
$763$	8.39695	−	17.4365i	0.303990	−	0.631242i
$764$	−6.31740	+	6.70313i	−0.228555	+	0.242511i
$765$	1.28052	+	3.51055i	0.0462972	+	0.126924i
$766$	8.87563	+	29.1767i	0.320690	+	1.05420i
$767$	31.4888	−	15.1642i	1.13700	−	0.547549i
$768$	4.29063	−	27.3787i	0.154825	−	0.987942i
$769$	−8.97562	+	7.15782i	−0.323669	+	0.258118i	−0.771821	−	0.635840i	$-0.780654\pi$
$769$	−8.97562	+	7.15782i	−0.323669	+	0.258118i	0.448152	+	0.893957i	$0.352082\pi$
$770$	−4.75483	+	4.37753i	−0.171352	+	0.157755i
$771$	−1.11373	+	22.4737i	−0.0401102	+	0.809372i
$772$	−16.8369	−	9.89630i	−0.605973	−	0.356176i
$773$	10.7306	+	47.0140i	0.385955	+	1.69098i	0.678398	+	0.734695i	$0.262675\pi$
$773$	10.7306	+	47.0140i	0.385955	+	1.69098i	−0.292443	+	0.956283i	$0.594468\pi$
$774$	−0.654605	+	2.53691i	−0.0235293	+	0.0911872i
$775$	−38.0950	−	18.3456i	−1.36841	−	0.658993i
$776$	0.295976	+	0.380163i	0.0106249	+	0.0136471i
$777$	0.151562	+	0.210654i	0.00543724	+	0.00755716i
$778$	−23.2222	−	9.21851i	−0.832557	−	0.330499i
$779$	−2.94644	−	12.9092i	−0.105567	−	0.462519i
$780$	4.97948	−	1.63193i	0.178294	−	0.0584323i
$781$	19.4519	+	15.5123i	0.696042	+	0.555075i
$782$	−6.42688	−	21.1270i	−0.229825	−	0.755500i
$783$	−19.1286	+	20.4230i	−0.683600	+	0.729857i
$784$	−1.24596	+	3.03488i	−0.0444987	+	0.108389i
$785$	1.03465	−	1.29741i	0.0369281	−	0.0463064i
$786$	0.111625	+	5.21740i	0.00398153	+	0.186098i
$787$	−32.2697	+	7.36535i	−1.15029	+	0.262546i	−0.754820	−	0.655932i	$-0.772276\pi$
$787$	−32.2697	+	7.36535i	−1.15029	+	0.262546i	−0.395471	+	0.918479i	$0.629419\pi$
$788$	9.42349	+	0.779996i	0.335698	+	0.0277862i
$789$	−17.2983	+	12.4458i	−0.615835	+	0.443082i
$790$	−0.283967	−	3.99800i	−0.0101031	−	0.142243i
$791$	−18.7469	+	38.9284i	−0.666564	+	1.38413i
$792$	45.0309	−	15.8324i	1.60010	−	0.562580i
$793$	−37.3235	+	8.51884i	−1.32539	+	0.302513i
$794$	16.9174	+	18.3756i	0.600377	+	0.652124i
$795$	−2.69627	−	0.133619i	−0.0956268	−	0.00473899i
$796$	19.8381	+	11.6603i	0.703142	+	0.413290i
$797$	−5.26380	−	6.60060i	−0.186454	−	0.233805i	0.679815	−	0.733383i	$-0.262060\pi$
$797$	−5.26380	−	6.60060i	−0.186454	−	0.233805i	−0.866269	+	0.499578i	$0.833488\pi$
$798$	−9.44055	−	7.20370i	−0.334192	−	0.255008i
$799$	−15.7949	−	32.7985i	−0.558784	−	1.16033i
$800$	−27.6834	−	2.61715i	−0.978757	−	0.0925301i
$801$	−12.4184	+	4.52978i	−0.438783	+	0.160052i
$802$	9.26650	+	16.1953i	0.327212	+	0.571875i
$803$	−66.0036	−	31.7857i	−2.32922	−	1.12169i
$804$	0.519185	+	5.60901i	0.0183102	+	0.197815i
$805$	−0.658365	+	2.88448i	−0.0232043	+	0.101665i
$806$	−35.8843	+	52.1951i	−1.26397	+	1.83849i
$807$	22.7685	−	25.8181i	0.801490	−	0.908839i
$808$	−6.82358	+	13.7561i	−0.240053	+	0.483939i
$809$	5.48900	−	24.0489i	0.192983	−	0.845514i	−0.782008	−	0.623269i	$-0.785804\pi$
$809$	5.48900	−	24.0489i	0.192983	−	0.845514i	0.974991	−	0.222245i	$-0.0713386\pi$
$810$	−2.01385	+	3.10107i	−0.0707596	+	0.108960i
$811$			13.2080i			0.463795i	0.972740	+	0.231898i	$0.0744935\pi$
$811$			13.2080i			0.463795i	−0.972740	+	0.231898i	$0.925507\pi$
$812$	18.4587	+	23.7995i	0.647773	+	0.835199i
$813$	27.7889	+	1.37714i	0.974599	+	0.0482984i
$814$	−0.396167	−	0.157266i	−0.0138856	−	0.00551217i
$815$	−2.85679	−	0.652044i	−0.100069	−	0.0228401i
$816$	−29.0236	−	6.32839i	−1.01603	−	0.221538i
$817$	−0.667493	+	0.837010i	−0.0233526	+	0.0292833i
$818$	−30.2732	−	20.8130i	−1.05848	−	0.727709i
$819$	41.4182	+	13.8835i	1.44727	+	0.485130i
$820$	0.627242	+	4.39323i	0.0219042	+	0.153418i
$821$	−16.0005	+	33.2253i	−0.558420	+	1.15957i	0.410422	+	0.911896i	$0.365381\pi$
$821$	−16.0005	+	33.2253i	−0.558420	+	1.15957i	−0.968843	+	0.247676i	$0.920333\pi$
$822$	30.9221	−	15.7148i	1.07853	−	0.548116i
$823$	−28.3036	+	13.6303i	−0.986601	+	0.475122i	−0.856370	−	0.516362i	$-0.827286\pi$
$823$	−28.3036	+	13.6303i	−0.986601	+	0.475122i	−0.130230	+	0.991484i	$0.541572\pi$
$824$	−20.6169	+	25.2426i	−0.718225	+	0.879366i
$825$	−18.6195	−	44.1276i	−0.648249	−	1.53633i
$826$	21.8743	+	15.0387i	0.761103	+	0.523262i
$827$	12.6336	−	10.0750i	0.439314	−	0.350341i	−0.378720	−	0.925511i	$-0.623636\pi$
$827$	12.6336	−	10.0750i	0.439314	−	0.350341i	0.818034	+	0.575170i	$0.195064\pi$
$828$	12.8809	−	17.6511i	0.447642	−	0.613417i
$829$			43.4071i			1.50759i	0.657109	+	0.753796i	$0.271779\pi$
$829$			43.4071i			1.50759i	−0.657109	+	0.753796i	$0.728221\pi$
$830$	−3.27771	+	3.01761i	−0.113771	+	0.104743i
$831$	−0.811644	−	4.59366i	−0.0281556	−	0.159352i
$832$	−10.2149	+	40.3839i	−0.354140	+	1.40006i
$833$	3.16834	+	1.52579i	0.109776	+	0.0528655i
$834$	0.264471	+	12.3615i	0.00915787	+	0.428043i
$835$	0.956821	−	0.763039i	0.0331121	−	0.0264061i
$836$	19.4381	+	1.60892i	0.672279	+	0.0556455i
$837$	−3.38688	−	44.5669i	−0.117068	−	1.54046i
$838$	−11.0325	+	0.783611i	−0.381113	+	0.0270694i
$839$	35.6940	+	28.4650i	1.23229	+	0.982722i	0.999949	+	0.0100882i	$0.00321123\pi$
$839$	35.6940	+	28.4650i	1.23229	+	0.982722i	0.232345	+	0.972633i	$0.425360\pi$
$840$	2.95407	+	2.66709i	0.101925	+	0.0920235i
$841$	28.7238	−	3.99301i	0.990475	−	0.137690i
$842$	−20.0789	+	6.10806i	−0.691966	+	0.210498i
$843$	21.3340	+	18.8141i	0.734782	+	0.647992i
$844$	4.75500	+	12.3984i	0.163674	+	0.426772i
$845$	−3.99705	+	0.912301i	−0.137503	+	0.0313841i
$846$	16.5357	−	32.0021i	0.568509	−	1.10025i
$847$	45.1375	−	35.9959i	1.55094	−	1.23684i
$848$	12.3635	−	17.5409i	0.424563	−	0.602356i
$849$	−21.4432	+	39.4091i	−0.735928	+	1.35252i
$850$	−4.55706	+	29.4559i	−0.156306	+	1.01033i
$851$	−0.190232	+	0.0434193i	−0.00652108	+	0.00148839i
$852$	8.40776	−	12.8078i	0.288045	−	0.438790i
$853$			14.9124i			0.510591i	0.966863	+	0.255295i	$0.0821727\pi$
$853$			14.9124i			0.510591i	−0.966863	+	0.255295i	$0.917827\pi$
$854$	−19.6942	−	21.3917i	−0.673921	−	0.732007i
$855$	−1.26862	+	0.820622i	−0.0433860	+	0.0280647i
$856$	0.641383	−	54.9337i	0.0219220	−	1.87759i
$857$	−19.5171	−	40.5277i	−0.666692	−	1.38440i	−0.910065	−	0.414466i	$-0.863968\pi$
$857$	−19.5171	−	40.5277i	−0.666692	−	1.38440i	0.243373	−	0.969933i	$-0.421746\pi$
$858$	−69.5922	+	17.4581i	−2.37584	+	0.596011i
$859$	6.25626	−	3.01286i	0.213461	−	0.102797i	−0.324098	−	0.946023i	$-0.605061\pi$
$859$	6.25626	−	3.01286i	0.213461	−	0.102797i	0.537559	+	0.843226i	$0.319347\pi$
$860$	0.246088	−	0.261114i	0.00839155	−	0.00890393i
$861$	−17.6816	+	32.4960i	−0.602588	+	1.10746i
$862$	−4.89376	+	31.6322i	−0.166682	+	1.07740i
$863$	−1.80222	+	7.89603i	−0.0613482	+	0.268784i	−0.996295	−	0.0860046i	$-0.972590\pi$
$863$	−1.80222	+	7.89603i	−0.0613482	+	0.268784i	0.934947	+	0.354789i	$0.115447\pi$
$864$	−12.2639	−	26.7132i	−0.417225	−	0.908803i
$865$	4.36778	−	5.47702i	0.148509	−	0.186224i
$866$	−0.954183	−	1.66765i	−0.0324245	−	0.0566690i
$867$	−0.648282	+	2.30723i	−0.0220168	+	0.0783575i
$868$	−47.9443	−	3.96842i	−1.62733	−	0.134697i
$869$			54.8796i			1.86166i
$870$	3.64372	−	1.18672i	0.123534	−	0.0402336i
$871$		−	8.46708i		−	0.286896i
$872$	19.1330	−	4.13259i	0.647926	−	0.139947i
$873$	0.484524	+	0.162414i	0.0163986	+	0.00549688i
$874$	7.74987	−	4.43427i	0.262143	−	0.149991i
$875$	5.02249	−	6.29800i	0.169791	−	0.212911i
$876$	−15.7440	+	42.2759i	−0.531941	+	1.42837i
$877$	−1.62927	+	7.13829i	−0.0550165	+	0.241043i	−0.994958	−	0.100293i	$-0.968022\pi$
$877$	−1.62927	+	7.13829i	−0.0550165	+	0.241043i	0.939941	+	0.341336i	$0.110879\pi$
$878$	13.9896	+	2.16431i	0.472127	+	0.0730419i
$879$	2.50849	+	1.36492i	0.0846094	+	0.0460375i
$880$	−6.44799	−	1.07478i	−0.217362	−	0.0362309i
$881$	42.9878	−	20.7018i	1.44829	−	0.697462i	0.465997	−	0.884786i	$-0.345696\pi$
$881$	42.9878	−	20.7018i	1.44829	−	0.697462i	0.982298	+	0.187324i	$0.0599815\pi$
$882$	0.678599	+	3.41289i	0.0228496	+	0.114918i
$883$	15.3550	+	31.8851i	0.516739	+	1.07302i	0.982180	+	0.187940i	$0.0601811\pi$
$883$	15.3550	+	31.8851i	0.516739	+	1.07302i	−0.465442	+	0.885078i	$0.654105\pi$
$884$	42.5635	+	13.4928i	1.43157	+	0.453812i
$885$	2.74156	−	1.97251i	0.0921567	−	0.0663051i
$886$	−7.62442	+	7.01941i	−0.256147	+	0.235822i
$887$		−	22.9648i		−	0.771082i	−0.922691	−	0.385541i	$-0.874015\pi$
$887$		−	22.9648i		−	0.771082i	0.922691	−	0.385541i	$-0.125985\pi$
$888$	−0.0739465	+	0.251846i	−0.00248148	+	0.00845140i
$889$	45.6860	−	10.4275i	1.53226	−	0.349728i
$890$	1.78900	+	0.276774i	0.0599675	+	0.00927747i
$891$	30.5132	−	40.4004i	1.02223	−	1.35346i
$892$	0.244021	−	0.0935858i	0.00817041	−	0.00313348i
$893$	11.5078	−	9.17719i	0.385095	−	0.307103i
$894$	−2.36748	+	5.19769i	−0.0791803	+	0.173837i
$895$	−4.12545	+	0.941607i	−0.137899	+	0.0314744i
$896$	−30.4755	+	8.49860i	−1.01811	+	0.283918i
$897$	−21.7245	+	24.6343i	−0.725361	+	0.822514i
$898$	−7.91956	−	26.0339i	−0.264279	−	0.868761i
$899$	−26.3128	+	38.1221i	−0.877580	+	1.27144i
$900$	−26.0012	+	13.9216i	−0.866707	+	0.464054i
$901$	−17.9846	−	14.3423i	−0.599155	−	0.477810i
$902$	−4.30500	−	60.6106i	−0.143341	−	2.01811i
$903$	2.94550	−	0.520433i	0.0980200	−	0.0173189i
$904$	−42.7162	+	9.22636i	−1.42072	+	0.306864i
$905$	2.31982	−	1.85000i	0.0771134	−	0.0614959i
$906$	−0.229120	−	10.7092i	−0.00761201	−	0.355789i
$907$	24.9411	+	12.0110i	0.828154	+	0.398818i	0.799423	−	0.600769i	$-0.205139\pi$
$907$	24.9411	+	12.0110i	0.828154	+	0.398818i	0.0287317	+	0.999587i	$0.490853\pi$
$908$	−24.4265	+	3.48749i	−0.810622	+	0.115736i
$909$	2.03650	+	16.1592i	0.0675463	+	0.535966i
$910$	−4.05192	−	4.40116i	−0.134320	−	0.145897i
$911$			0.736204i			0.0243915i	0.999926	+	0.0121958i	$0.00388213\pi$
$911$			0.736204i			0.0243915i	−0.999926	+	0.0121958i	$0.996118\pi$
$912$	−0.116701	−	12.0103i	−0.00386434	−	0.397700i
$913$	47.6938	−	38.0345i	1.57843	−	1.25876i
$914$	−8.86448	+	12.8937i	−0.293211	+	0.426486i
$915$	−3.40853	+	1.43822i	−0.112683	+	0.0475461i
$916$	22.4740	+	33.5209i	0.742562	+	1.10756i
$917$	5.36779	−	2.58499i	0.177260	−	0.0853640i
$918$	−29.3620	+	11.4276i	−0.969091	+	0.377165i
$919$	4.32881	−	8.98888i	0.142794	−	0.296516i	−0.817290	−	0.576227i	$-0.804524\pi$
$919$	4.32881	−	8.98888i	0.142794	−	0.296516i	0.960084	+	0.279711i	$0.0902387\pi$
$920$	−2.71111	+	1.26683i	−0.0893828	+	0.0417660i
$921$	1.73854	−	6.18743i	0.0572867	−	0.203883i
$922$	−14.8598	+	21.6142i	−0.489383	+	0.711825i
$923$	−14.3585	+	18.0050i	−0.472616	+	0.592642i
$924$	−37.7589	−	39.2925i	−1.24218	−	1.29263i
$925$	0.256765	+	0.0586050i	0.00844239	+	0.00192692i
$926$	7.75454	−	19.5344i	0.254830	−	0.641939i
$927$	−3.41790	+	34.3998i	−0.112259	+	1.12984i
$928$	−7.52468	+	29.5191i	−0.247010	+	0.969013i
$929$		−	39.4347i		−	1.29381i	−0.762570	−	0.646905i	$-0.776063\pi$
$929$		−	39.4347i		−	1.29381i	0.762570	−	0.646905i	$-0.223937\pi$
$930$	−2.53721	+	5.57033i	−0.0831985	+	0.182658i
$931$	−0.316395	+	1.38622i	−0.0103694	+	0.0454314i
$932$	−14.2422	+	15.1118i	−0.466518	+	0.495003i
$933$	−23.2214	−	20.4785i	−0.760234	−	0.670437i
$934$	−19.2775	−	13.2533i	−0.630778	−	0.433663i
$935$	−1.55920	+	6.83131i	−0.0509913	+	0.223408i
$936$	14.6548	+	41.6814i	0.479006	+	1.36240i
$937$	−21.0921	−	10.1574i	−0.689049	−	0.331829i	0.0563838	−	0.998409i	$-0.482043\pi$
$937$	−21.0921	−	10.1574i	−0.689049	−	0.331829i	−0.745433	+	0.666581i	$0.767757\pi$
$938$	5.58179	−	3.19375i	0.182252	−	0.104280i
$939$	−4.04161	+	1.70535i	−0.131893	+	0.0556519i
$940$	−4.09743	+	2.74711i	−0.133643	+	0.0896008i
$941$	−15.9804	−	33.1836i	−0.520945	−	1.08175i	−0.981026	−	0.193877i	$-0.937894\pi$
$941$	−15.9804	−	33.1836i	−0.520945	−	1.08175i	0.460081	−	0.887877i	$-0.347820\pi$
$942$	11.1234	+	8.48780i	0.362419	+	0.276548i
$943$	−17.3432	−	21.7476i	−0.564771	−	0.708200i
$944$	1.58940	+	26.8015i	0.0517305	+	0.872316i
$945$	4.17487	+	0.624779i	0.135809	+	0.0203241i
$946$	−3.61435	+	3.32754i	−0.117513	+	0.108188i
$947$	−21.3095	+	4.86375i	−0.692466	+	0.158051i	−0.554249	−	0.832351i	$-0.686994\pi$
$947$	−21.3095	+	4.86375i	−0.692466	+	0.158051i	−0.138217	+	0.990402i	$0.544137\pi$
$948$	33.6509	−	3.11481i	1.09293	−	0.101164i
$949$	29.4214	−	61.0942i	0.955059	−	1.98320i
$950$	−12.0213	+	0.853840i	−0.390023	+	0.0277022i
$951$	1.93216	+	2.68549i	0.0626546	+	0.0870830i
$952$	7.15989	+	33.1488i	0.232053	+	1.07436i
$953$	50.5987	−	11.5488i	1.63905	−	0.374103i	0.698997	−	0.715125i	$-0.253630\pi$
$953$	50.5987	−	11.5488i	1.63905	−	0.374103i	0.940055	+	0.341022i	$0.110773\pi$
$954$	0.640098	−	22.7529i	0.0207239	−	0.736653i
$955$	0.834192	−	1.04604i	0.0269938	−	0.0338492i
$956$	23.2777	−	15.6065i	0.752856	−	0.504750i
$957$	−50.9166	+	12.6734i	−1.64590	+	0.409672i
$958$	4.91205	−	1.49426i	0.158701	−	0.0482772i
$959$	−30.9601	−	24.6898i	−0.999753	−	0.797276i
$960$	−0.293061	+	4.01475i	−0.00945850	+	0.129576i
$961$	−9.56577	−	41.9104i	−0.308573	−	1.35195i
$962$	0.145568	−	0.366700i	0.00469331	−	0.0118229i
$963$	−31.6484	−	48.9261i	−1.01985	−	1.57662i
$964$	8.09404	+	21.1048i	0.260691	+	0.679741i
$965$	2.55589	+	1.23085i	0.0822771	+	0.0396226i
$966$	−24.4342	−	5.02962i	−0.786157	−	0.161825i
$967$	6.59879	+	28.9112i	0.212203	+	0.929721i	0.963066	+	0.269264i	$0.0867804\pi$
$967$	6.59879	+	28.9112i	0.212203	+	0.929721i	−0.750864	+	0.660457i	$0.770363\pi$
$968$	56.7734	+	13.6574i	1.82477	+	0.438966i
$969$	−12.8587	−	0.637240i	−0.413080	−	0.0204711i
$970$	−0.0474007	−	0.0514862i	−0.00152194	−	0.00165312i
$971$	43.2436	−	34.4856i	1.38775	−	1.10670i	0.406570	−	0.913620i	$-0.366725\pi$
$971$	43.2436	−	34.4856i	1.38775	−	1.10670i	0.981184	−	0.193077i	$-0.0618467\pi$
$972$	−26.5044	−	16.4170i	−0.850129	−	0.526574i
$973$	12.7178	−	6.12457i	0.407714	−	0.196345i
$974$	−42.6817	+	12.9839i	−1.36761	+	0.416030i
$975$	40.8453	−	17.2346i	1.30810	−	0.551949i
$976$	4.83537	−	29.0090i	0.154776	−	0.928557i
$977$	17.3523	−	36.0325i	0.555151	−	1.15278i	−0.414897	−	0.909868i	$-0.636182\pi$
$977$	17.3523	−	36.0325i	0.555151	−	1.15278i	0.970048	−	0.242914i	$-0.0781033\pi$
$978$	4.98133	−	24.1996i	0.159285	−	0.773818i
$979$	−24.1655	−	5.51561i	−0.772332	−	0.176280i
$980$	0.144002	−	0.454260i	0.00459998	−	0.0145108i
$981$	14.4861	−	14.8727i	0.462507	−	0.474849i
$982$	−2.74805	−	4.80283i	−0.0876939	−	0.153265i
$983$	48.1263	+	10.9845i	1.53499	+	0.350351i	0.904714	−	0.426020i	$-0.140085\pi$
$983$	48.1263	+	10.9845i	1.53499	+	0.350351i	0.630276	+	0.776371i	$0.282942\pi$
$984$	−36.9206	+	6.07981i	−1.17699	+	0.193817i
$985$	−1.37349			−0.0437632
$986$	31.1087	+	9.92473i	0.990703	+	0.316068i
$987$	−41.0737	−	2.03550i	−1.30739	−	0.0647906i
$988$	−1.48924	+	17.9922i	−0.0473791	+	0.572409i
$989$	−0.500450	+	2.19262i	−0.0159134	+	0.0697211i
$990$	−6.32898	+	2.83147i	−0.201148	+	0.0899899i
$991$	48.8365	+	38.9458i	1.55134	+	1.23715i	0.853785	+	0.520626i	$0.174301\pi$
$991$	48.8365	+	38.9458i	1.55134	+	1.23715i	0.697558	+	0.716529i	$0.254270\pi$
$992$	−26.6227	−	40.7290i	−0.845272	−	1.29315i
$993$	7.42677	−	26.4318i	0.235681	−	0.838787i
$994$	−17.2855	−	2.67421i	−0.548263	−	0.0848208i
$995$	−3.01148	−	1.45025i	−0.0954705	−	0.0459762i
$996$	−26.0288	−	27.0860i	−0.824755	−	0.858252i
$997$	−4.66349	−	9.68384i	−0.147694	−	0.306690i	0.813976	−	0.580898i	$-0.197299\pi$
$997$	−4.66349	−	9.68384i	−0.147694	−	0.306690i	−0.961670	+	0.274208i	$0.911584\pi$
$998$	22.9715	−	6.98799i	0.727151	−	0.221201i
$999$	0.0823389	+	0.265945i	0.00260509	+	0.00841412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.6	✓	336
3.2	odd	2	inner	348.2.t.a.35.51	yes	336
4.3	odd	2	inner	348.2.t.a.35.38	yes	336
12.11	even	2	inner	348.2.t.a.35.19	yes	336
29.5	even	14	inner	348.2.t.a.179.19	yes	336
87.5	odd	14	inner	348.2.t.a.179.38	yes	336
116.63	odd	14	inner	348.2.t.a.179.51	yes	336
348.179	even	14	inner	348.2.t.a.179.6	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.6	✓	336	1.1	even	1	trivial
348.2.t.a.35.19	yes	336	12.11	even	2	inner
348.2.t.a.35.38	yes	336	4.3	odd	2	inner
348.2.t.a.35.51	yes	336	3.2	odd	2	inner
348.2.t.a.179.6	yes	336	348.179	even	14	inner
348.2.t.a.179.19	yes	336	29.5	even	14	inner
348.2.t.a.179.38	yes	336	87.5	odd	14	inner
348.2.t.a.179.51	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)

\(f(q)\)	\(=\)	\(q+(-1.31443 - 0.521790i) q^{2} +(-0.468526 + 1.66748i) q^{3} +(1.45547 + 1.37172i) q^{4} +(-0.227131 - 0.181131i) q^{5} +(1.48592 - 1.94732i) q^{6} +(-2.72634 - 0.622270i) q^{7} +(-1.19737 - 2.56248i) q^{8} +(-2.56097 - 1.56251i) q^{9} +O(q^{10})\)	\(q+(-1.31443 - 0.521790i) q^{2} +(-0.468526 + 1.66748i) q^{3} +(1.45547 + 1.37172i) q^{4} +(-0.227131 - 0.181131i) q^{5} +(1.48592 - 1.94732i) q^{6} +(-2.72634 - 0.622270i) q^{7} +(-1.19737 - 2.56248i) q^{8} +(-2.56097 - 1.56251i) q^{9} +(0.204036 + 0.356598i) q^{10} +(-2.44077 - 5.06830i) q^{11} +(-2.96923 + 1.78428i) q^{12} +(4.69132 - 2.25922i) q^{13} +(3.25890 + 2.24051i) q^{14} +(0.408448 - 0.293871i) q^{15} +(0.236794 + 3.99298i) q^{16} +4.28762 q^{17} +(2.55092 + 3.39011i) q^{18} +(0.385765 + 1.69015i) q^{19} +(-0.0821224 - 0.575189i) q^{20} +(2.31499 - 4.25457i) q^{21} +(0.563638 + 7.93552i) q^{22} +(2.27067 + 2.84733i) q^{23} +(4.83388 - 0.796007i) q^{24} +(-1.09382 - 4.79236i) q^{25} +(-7.34526 + 0.521714i) q^{26} +(3.80534 - 3.53828i) q^{27} +(-3.11454 - 4.64546i) q^{28} +(-5.37233 + 0.371628i) q^{29} +(-0.690216 + 0.173150i) q^{30} +(5.36303 - 6.72503i) q^{31} +(1.77225 - 5.37207i) q^{32} +(9.59485 - 1.69529i) q^{33} +(-5.63579 - 2.23723i) q^{34} +(0.506524 + 0.635161i) q^{35} +(-1.58409 - 5.78711i) q^{36} +(-0.0232466 + 0.0482721i) q^{37} +(0.374839 - 2.42288i) q^{38} +(1.56919 + 8.88117i) q^{39} +(-0.192183 + 0.798898i) q^{40} -7.63789 q^{41} +(-5.26288 + 4.38441i) q^{42} +(0.385030 + 0.482812i) q^{43} +(3.39980 - 10.7248i) q^{44} +(0.298655 + 0.818764i) q^{45} +(-1.49894 - 4.92744i) q^{46} +(-3.68384 - 7.64958i) q^{47} +(-6.76916 - 1.47597i) q^{48} +(0.738951 + 0.355860i) q^{49} +(-1.06284 + 6.86998i) q^{50} +(-2.00886 + 7.14951i) q^{51} +(9.92708 + 3.14692i) q^{52} +(-4.19455 - 3.34505i) q^{53} +(-6.84810 + 2.66525i) q^{54} +(-0.363652 + 1.59326i) q^{55} +(1.66990 + 7.73129i) q^{56} +(-2.99903 - 0.148623i) q^{57} +(7.25548 + 2.31474i) q^{58} +6.71215 q^{59} +(0.997591 + 0.132554i) q^{60} +(-7.16798 - 1.63604i) q^{61} +(-10.5584 + 6.04123i) q^{62} +(6.00977 + 5.85356i) q^{63} +(-5.13259 + 6.13649i) q^{64} +(-1.47476 - 0.336603i) q^{65} +(-13.4964 - 2.77814i) q^{66} +(0.705540 - 1.46507i) q^{67} +(6.24050 + 5.88139i) q^{68} +(-5.81173 + 2.45225i) q^{69} +(-0.334372 - 1.09918i) q^{70} +(-3.98478 + 1.91897i) q^{71} +(-0.937474 + 8.43334i) q^{72} +(10.1816 - 8.11959i) q^{73} +(0.0557441 - 0.0513207i) q^{74} +(8.50364 + 0.421416i) q^{75} +(-1.75693 + 2.98912i) q^{76} +(3.50052 + 15.3368i) q^{77} +(2.57150 - 12.4925i) q^{78} +(-8.78958 - 4.23284i) q^{79} +(0.669468 - 0.949819i) q^{80} +(4.11710 + 8.00309i) q^{81} +(10.0395 + 3.98537i) q^{82} +(2.41305 + 10.5723i) q^{83} +(9.20545 - 3.01690i) q^{84} +(-0.973849 - 0.776618i) q^{85} +(-0.254170 - 0.835529i) q^{86} +(1.89739 - 9.13235i) q^{87} +(-10.0649 + 12.3231i) q^{88} +(2.74726 - 3.44495i) q^{89} +(0.0346606 - 1.23205i) q^{90} +(-14.1960 + 3.24014i) q^{91} +(-0.600832 + 7.25893i) q^{92} +(8.70112 + 12.0936i) q^{93} +(0.850697 + 11.9771i) q^{94} +(0.218518 - 0.453758i) q^{95} +(8.12747 + 5.47214i) q^{96} +(-0.166069 + 0.0379042i) q^{97} +(-0.785618 - 0.853331i) q^{98} +(-1.66857 + 16.7935i) 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

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Database

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