LMFDB - Embedded newform 380.2.bb.a.319.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.51
Character	$\chi$	$=$	380.319
Dual form			380.2.bb.a.299.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37332 - 0.337626i) q^{2} +(2.10992 - 0.372036i) q^{3} +(1.77202 - 0.927337i) q^{4} +(0.960929 - 2.01906i) q^{5} +(2.77199 - 1.22329i) q^{6} +(-2.30925 + 3.99973i) q^{7} +(2.12045 - 1.87181i) q^{8} +(1.49427 - 0.543869i) q^{9} +O(q^{10})$	\(q+(1.37332 - 0.337626i) q^{2} +(2.10992 - 0.372036i) q^{3} +(1.77202 - 0.927337i) q^{4} +(0.960929 - 2.01906i) q^{5} +(2.77199 - 1.22329i) q^{6} +(-2.30925 + 3.99973i) q^{7} +(2.12045 - 1.87181i) q^{8} +(1.49427 - 0.543869i) q^{9} +(0.637976 - 3.09725i) q^{10} +(-4.04114 + 2.33315i) q^{11} +(3.39381 - 2.61586i) q^{12} +(0.00737135 - 0.0418050i) q^{13} +(-1.82092 + 6.27258i) q^{14} +(1.27632 - 4.61756i) q^{15} +(2.28009 - 3.28652i) q^{16} +(-0.769892 + 2.11526i) q^{17} +(1.86848 - 1.25141i) q^{18} +(-3.38609 - 2.74489i) q^{19} +(-0.169568 - 4.46892i) q^{20} +(-3.38428 + 9.29823i) q^{21} +(-4.76205 + 4.56856i) q^{22} +(0.563436 + 0.472779i) q^{23} +(3.77761 - 4.73825i) q^{24} +(-3.15323 - 3.88035i) q^{25} +(-0.00399123 - 0.0599004i) q^{26} +(-2.61585 + 1.51026i) q^{27} +(-0.382925 + 9.22905i) q^{28} +(-1.79272 - 4.92545i) q^{29} +(0.193788 - 6.77231i) q^{30} +(1.55132 - 2.68696i) q^{31} +(2.02168 - 5.28326i) q^{32} +(-7.65846 + 6.42621i) q^{33} +(-0.343141 + 3.16486i) q^{34} +(5.85669 + 8.50597i) q^{35} +(2.14352 - 2.34944i) q^{36} +7.27599 q^{37} +(-5.57693 - 2.62638i) q^{38} -0.0909476i q^{39} +(-1.74169 - 6.08001i) q^{40} +(5.80377 - 1.02336i) q^{41} +(-1.50838 + 13.9121i) q^{42} +(-2.14439 + 1.79936i) q^{43} +(-4.99735 + 7.88189i) q^{44} +(0.337780 - 3.53964i) q^{45} +(0.933401 + 0.459046i) q^{46} +(3.42681 - 1.24726i) q^{47} +(3.58811 - 7.78255i) q^{48} +(-7.16524 - 12.4106i) q^{49} +(-5.64050 - 4.26436i) q^{50} +(-0.837457 + 4.74945i) q^{51} +(-0.0257052 - 0.0809149i) q^{52} +(9.67237 + 8.11608i) q^{53} +(-3.08249 + 2.95725i) q^{54} +(0.827533 + 10.4013i) q^{55} +(2.59009 + 12.8037i) q^{56} +(-8.16556 - 4.53175i) q^{57} +(-4.12493 - 6.15895i) q^{58} +(13.1583 + 4.78922i) q^{59} +(-2.02037 - 9.36597i) q^{60} +(-0.805551 - 0.675937i) q^{61} +(1.22327 - 4.21383i) q^{62} +(-1.27530 + 7.23260i) q^{63} +(0.992655 - 7.93818i) q^{64} +(-0.0773236 - 0.0550549i) q^{65} +(-8.34787 + 11.4109i) q^{66} +(-0.319592 - 0.878072i) q^{67} +(0.597298 + 4.46223i) q^{68} +(1.36470 + 0.787907i) q^{69} +(10.9149 + 9.70406i) q^{70} +(4.43036 - 3.71751i) q^{71} +(2.15051 - 3.95024i) q^{72} +(-9.74523 + 1.71835i) q^{73} +(9.99227 - 2.45656i) q^{74} +(-8.09669 - 7.01412i) q^{75} +(-8.54564 - 1.72395i) q^{76} -21.5513i q^{77} +(-0.0307063 - 0.124900i) q^{78} +(-1.90947 - 10.8291i) q^{79} +(-4.44467 - 7.76176i) q^{80} +(-8.61177 + 7.22613i) q^{81} +(7.62492 - 3.36490i) q^{82} +(-4.20812 + 7.28867i) q^{83} +(2.62559 + 19.6150i) q^{84} +(3.53103 + 3.58707i) q^{85} +(-2.33743 + 3.19510i) q^{86} +(-5.61493 - 9.72534i) q^{87} +(-4.20184 + 12.5116i) q^{88} +(-11.6628 - 2.05646i) q^{89} +(-0.731194 - 4.97510i) q^{90} +(0.150187 + 0.126022i) q^{91} +(1.43684 + 0.315278i) q^{92} +(2.27351 - 6.24642i) q^{93} +(4.28500 - 2.86986i) q^{94} +(-8.79590 + 4.19907i) q^{95} +(2.30003 - 11.8994i) q^{96} +(3.39769 + 1.23666i) q^{97} +(-14.0303 - 14.6245i) q^{98} +(-4.76962 + 5.68421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$-1$

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 $

$2$	1.37332	−	0.337626i	0.971084	−	0.238738i
$2$	1.37332	−	0.337626i	0.971084	−	0.238738i
$3$	2.10992	−	0.372036i	1.21816	−	0.214795i	0.472628	−	0.881262i	$-0.343306\pi$
$3$	2.10992	−	0.372036i	1.21816	−	0.214795i	0.745534	+	0.666467i	$0.232194\pi$
$4$	1.77202	−	0.927337i	0.886009	−	0.463669i
$5$	0.960929	−	2.01906i	0.429741	−	0.902952i
$5$	0.960929	−	2.01906i	0.429741	−	0.902952i
$6$	2.77199	−	1.22329i	1.13166	−	0.499405i
$7$	−2.30925	+	3.99973i	−0.872813	+	1.51176i	−0.0137389	+	0.999906i	$0.504373\pi$
$7$	−2.30925	+	3.99973i	−0.872813	+	1.51176i	−0.859074	+	0.511851i	$0.828960\pi$
$8$	2.12045	−	1.87181i	0.749694	−	0.661785i
$9$	1.49427	−	0.543869i	0.498089	−	0.181290i
$10$	0.637976	−	3.09725i	0.201746	−	0.979438i
$11$	−4.04114	+	2.33315i	−1.21845	+	0.703472i	−0.964586	−	0.263768i	$-0.915035\pi$
$11$	−4.04114	+	2.33315i	−1.21845	+	0.703472i	−0.253864	+	0.967240i	$0.581701\pi$
$12$	3.39381	−	2.61586i	0.979709	−	0.755134i
$13$	0.00737135	−	0.0418050i	0.00204445	−	0.0115946i	−0.983768	−	0.179442i	$-0.942571\pi$
$13$	0.00737135	−	0.0418050i	0.00204445	−	0.0115946i	0.985813	+	0.167848i	$0.0536817\pi$
$14$	−1.82092	+	6.27258i	−0.486662	+	1.67642i
$15$	1.27632	−	4.61756i	0.329544	−	1.19225i
$16$	2.28009	−	3.28652i	0.570023	−	0.821629i
$17$	−0.769892	+	2.11526i	−0.186726	+	0.513026i	−0.997367	−	0.0725176i	$-0.976897\pi$
$17$	−0.769892	+	2.11526i	−0.186726	+	0.513026i	0.810641	+	0.585544i	$0.199119\pi$
$18$	1.86848	−	1.25141i	0.440406	−	0.294960i
$19$	−3.38609	−	2.74489i	−0.776821	−	0.629721i
$19$	−3.38609	−	2.74489i	−0.776821	−	0.629721i
$20$	−0.169568	−	4.46892i	−0.0379166	−	0.999281i
$21$	−3.38428	+	9.29823i	−0.738510	+	2.02904i
$22$	−4.76205	+	4.56856i	−1.01527	+	0.974021i
$23$	0.563436	+	0.472779i	0.117485	+	0.0985813i	0.699637	−	0.714498i	$-0.253345\pi$
$23$	0.563436	+	0.472779i	0.117485	+	0.0985813i	−0.582153	+	0.813079i	$0.697789\pi$
$24$	3.77761	−	4.73825i	0.771101	−	0.967191i
$25$	−3.15323	−	3.88035i	−0.630646	−	0.776071i
$26$	−0.00399123	−	0.0599004i	−0.000782744	−	0.0117474i
$27$	−2.61585	+	1.51026i	−0.503420	+	0.290650i
$28$	−0.382925	+	9.22905i	−0.0723660	+	1.74413i
$29$	−1.79272	−	4.92545i	−0.332899	−	0.914633i	−0.987354	−	0.158532i	$-0.949324\pi$
$29$	−1.79272	−	4.92545i	−0.332899	−	0.914633i	0.654455	−	0.756101i	$-0.272898\pi$
$30$	0.193788	−	6.77231i	0.0353808	−	1.23645i
$31$	1.55132	−	2.68696i	0.278625	−	0.482593i	−0.692418	−	0.721496i	$-0.743455\pi$
$31$	1.55132	−	2.68696i	0.278625	−	0.482593i	0.971043	+	0.238904i	$0.0767880\pi$
$32$	2.02168	−	5.28326i	0.357387	−	0.933957i
$33$	−7.65846	+	6.42621i	−1.33317	+	1.11866i
$34$	−0.343141	+	3.16486i	−0.0588482	+	0.542770i
$35$	5.85669	+	8.50597i	0.989961	+	1.43777i
$36$	2.14352	−	2.34944i	0.357253	−	0.391573i
$37$	7.27599			1.19617			0.598083	−	0.801434i	$-0.295929\pi$
$37$	7.27599			1.19617			0.598083	+	0.801434i	$0.295929\pi$
$38$	−5.57693	−	2.62638i	−0.904697	−	0.426056i
$39$		−	0.0909476i		−	0.0145633i
$40$	−1.74169	−	6.08001i	−0.275386	−	0.961334i
$41$	5.80377	−	1.02336i	0.906396	−	0.159822i	0.299030	−	0.954244i	$-0.403337\pi$
$41$	5.80377	−	1.02336i	0.906396	−	0.159822i	0.607366	+	0.794422i	$0.292226\pi$
$42$	−1.50838	+	13.9121i	−0.232747	+	2.14668i
$43$	−2.14439	+	1.79936i	−0.327017	+	0.274400i	−0.791483	−	0.611191i	$-0.790691\pi$
$43$	−2.14439	+	1.79936i	−0.327017	+	0.274400i	0.464466	+	0.885591i	$0.346246\pi$
$44$	−4.99735	+	7.88189i	−0.753379	+	1.18824i
$45$	0.337780	−	3.53964i	0.0503533	−	0.527659i
$46$	0.933401	+	0.459046i	0.137622	+	0.0676827i
$47$	3.42681	−	1.24726i	0.499851	−	0.181931i	−0.0797760	−	0.996813i	$-0.525420\pi$
$47$	3.42681	−	1.24726i	0.499851	−	0.181931i	0.579627	+	0.814882i	$0.303198\pi$
$48$	3.58811	−	7.78255i	0.517899	−	1.12331i
$49$	−7.16524	−	12.4106i	−1.02361	−	1.77294i
$50$	−5.64050	−	4.26436i	−0.797687	−	0.603071i
$51$	−0.837457	+	4.74945i	−0.117267	+	0.665056i
$52$	−0.0257052	−	0.0809149i	−0.00356467	−	0.0112209i
$53$	9.67237	+	8.11608i	1.32860	+	1.11483i	0.984402	+	0.175934i	$0.0562944\pi$
$53$	9.67237	+	8.11608i	1.32860	+	1.11483i	0.344200	+	0.938896i	$0.388150\pi$
$54$	−3.08249	+	2.95725i	−0.419474	+	0.402431i
$55$	0.827533	+	10.4013i	0.111585	+	1.40251i
$56$	2.59009	+	12.8037i	0.346115	+	1.71097i
$57$	−8.16556	−	4.53175i	−1.08156	−	0.600245i
$58$	−4.12493	−	6.15895i	−0.541630	−	0.808710i
$59$	13.1583	+	4.78922i	1.71306	+	0.623504i	0.997203	−	0.0747412i	$-0.0238131\pi$
$59$	13.1583	+	4.78922i	1.71306	+	0.623504i	0.715859	+	0.698245i	$0.246035\pi$
$60$	−2.02037	−	9.36597i	−0.260829	−	1.20914i
$61$	−0.805551	−	0.675937i	−0.103140	−	0.0865449i	0.589759	−	0.807579i	$-0.299223\pi$
$61$	−0.805551	−	0.675937i	−0.103140	−	0.0865449i	−0.692900	+	0.721034i	$0.743667\pi$
$62$	1.22327	−	4.21383i	0.155355	−	0.535156i
$63$	−1.27530	+	7.23260i	−0.160673	+	0.911222i
$64$	0.992655	−	7.93818i	0.124082	−	0.992272i
$65$	−0.0773236	−	0.0550549i	−0.00959081	−	0.00682872i
$66$	−8.34787	+	11.4109i	−1.02755	+	1.40459i
$67$	−0.319592	−	0.878072i	−0.0390444	−	0.107274i	0.918638	−	0.395099i	$-0.129290\pi$
$67$	−0.319592	−	0.878072i	−0.0390444	−	0.107274i	−0.957683	+	0.287826i	$0.907068\pi$
$68$	0.597298	+	4.46223i	0.0724330	+	0.541124i
$69$	1.36470	+	0.787907i	0.164290	+	0.0948529i
$70$	10.9149	+	9.70406i	1.30459	+	1.15986i
$71$	4.43036	−	3.71751i	0.525786	−	0.441187i	−0.340857	−	0.940115i	$-0.610717\pi$
$71$	4.43036	−	3.71751i	0.525786	−	0.441187i	0.866643	+	0.498928i	$0.166273\pi$
$72$	2.15051	−	3.95024i	0.253440	−	0.465540i
$73$	−9.74523	+	1.71835i	−1.14059	+	0.201117i	−0.711865	−	0.702316i	$-0.752149\pi$
$73$	−9.74523	+	1.71835i	−1.14059	+	0.201117i	−0.428728	+	0.903434i	$0.641038\pi$
$74$	9.99227	−	2.45656i	1.16158	−	0.285570i
$75$	−8.09669	−	7.01412i	−0.934925	−	0.809920i
$76$	−8.54564	−	1.72395i	−0.980252	−	0.197751i
$77$		−	21.5513i		−	2.45600i
$78$	−0.0307063	−	0.124900i	−0.00347680	−	0.0141422i
$79$	−1.90947	−	10.8291i	−0.214832	−	1.21837i	−0.881198	−	0.472748i	$-0.843262\pi$
$79$	−1.90947	−	10.8291i	−0.214832	−	1.21837i	0.666366	−	0.745625i	$-0.267849\pi$
$80$	−4.44467	−	7.76176i	−0.496930	−	0.867791i
$81$	−8.61177	+	7.22613i	−0.956864	+	0.802904i
$82$	7.62492	−	3.36490i	0.842031	−	0.371591i
$83$	−4.20812	+	7.28867i	−0.461901	+	0.800036i	−0.999056	−	0.0434480i	$-0.986166\pi$
$83$	−4.20812	+	7.28867i	−0.461901	+	0.800036i	0.537155	+	0.843484i	$0.319499\pi$
$84$	2.62559	+	19.6150i	0.286476	+	2.14017i
$85$	3.53103	+	3.58707i	0.382994	+	0.389073i
$86$	−2.33743	+	3.19510i	−0.252051	+	0.344536i
$87$	−5.61493	−	9.72534i	−0.601983	−	1.04267i
$88$	−4.20184	+	12.5116i	−0.447917	+	1.33374i
$89$	−11.6628	−	2.05646i	−1.23625	−	0.217984i	−0.482942	−	0.875652i	$-0.660432\pi$
$89$	−11.6628	−	2.05646i	−1.23625	−	0.217984i	−0.753308	+	0.657668i	$0.771543\pi$
$90$	−0.731194	−	4.97510i	−0.0770746	−	0.524422i
$91$	0.150187	+	0.126022i	0.0157438	+	0.0132106i
$92$	1.43684	+	0.315278i	0.149801	+	0.0328700i
$93$	2.27351	−	6.24642i	0.235752	−	0.647723i
$94$	4.28500	−	2.86986i	0.441964	−	0.296003i
$95$	−8.79590	+	4.19907i	−0.902440	+	0.430816i
$96$	2.30003	−	11.8994i	0.234746	−	1.21448i
$97$	3.39769	+	1.23666i	0.344983	+	0.125563i	0.508700	−	0.860944i	$-0.330126\pi$
$97$	3.39769	+	1.23666i	0.344983	+	0.125563i	−0.163717	+	0.986507i	$0.552348\pi$
$98$	−14.0303	−	14.6245i	−1.41727	−	1.47730i
$99$	−4.76962	+	5.68421i	−0.479365	+	0.571285i
$100$	−9.18597	−	3.95195i	−0.918597	−	0.395195i
$101$	−2.72180	+	15.4361i	−0.270829	+	1.53595i	0.481078	+	0.876678i	$0.340245\pi$
$101$	−2.72180	+	15.4361i	−0.270829	+	1.53595i	−0.751907	+	0.659269i	$0.770866\pi$
$102$	0.453442	+	6.80527i	0.0448975	+	0.673822i
$103$	8.83597	−	5.10145i	0.870634	−	0.502661i	0.00307530	−	0.999995i	$-0.499021\pi$
$103$	8.83597	−	5.10145i	0.870634	−	0.502661i	0.867559	+	0.497334i	$0.165688\pi$
$104$	−0.0626204	−	0.102443i	−0.00614044	−	0.0100454i
$105$	15.5217	+	15.7680i	1.51476	+	1.53880i
$106$	16.0235	+	7.88034i	1.55634	+	0.765406i
$107$	−0.887465	−	0.512378i	−0.0857945	−	0.0495335i	0.456489	−	0.889729i	$-0.349107\pi$
$107$	−0.887465	−	0.512378i	−0.0857945	−	0.0495335i	−0.542283	+	0.840196i	$0.682440\pi$
$108$	−3.23481	+	5.10198i	−0.311270	+	0.490938i
$109$	7.25036	+	8.64064i	0.694459	+	0.827624i	0.991887	−	0.127121i	$-0.0405735\pi$
$109$	7.25036	+	8.64064i	0.694459	+	0.827624i	−0.297429	+	0.954744i	$0.596129\pi$
$110$	4.64822	+	14.0049i	0.443190	+	1.33532i
$111$	15.3518	−	2.70693i	1.45712	−	0.256930i
$112$	7.87989	+	16.7091i	0.744579	+	1.57886i
$113$	−3.94355			−0.370978			−0.185489	−	0.982646i	$-0.559387\pi$
$113$	−3.94355			−0.370978			−0.185489	+	0.982646i	$0.559387\pi$
$114$	−12.7440	−	3.46664i	−1.19358	−	0.324681i
$115$	1.49599	−	0.683306i	0.139502	−	0.0637186i
$116$	−7.74427	−	7.06553i	−0.719038	−	0.656018i
$117$	−0.0117217	−	0.0664770i	−0.00108367	−	0.00614580i
$118$	19.6875	+	2.13456i	1.81238	+	0.196502i
$119$	−6.68260	−	7.96402i	−0.612593	−	0.730060i
$120$	−5.93681	−	12.1804i	−0.541954	−	1.11191i
$121$	5.38721	−	9.33093i	0.489747	−	0.848266i
$122$	−1.33449	−	0.656304i	−0.120819	−	0.0594189i
$123$	11.8647	−	4.31841i	1.06981	−	0.389378i
$124$	0.257244	−	6.19994i	0.0231011	−	0.556771i
$125$	−10.8647	+	2.63782i	−0.971769	+	0.235934i
$126$	0.690514	+	10.3633i	0.0615159	+	0.923232i
$127$	−15.7041	−	2.76906i	−1.39351	−	0.245714i	−0.574038	−	0.818828i	$-0.694624\pi$
$127$	−15.7041	−	2.76906i	−1.39351	−	0.245714i	−0.819475	+	0.573114i	$0.805735\pi$
$128$	−1.31690	−	11.2368i	−0.116399	−	0.993203i
$129$	−3.85507	+	4.59429i	−0.339420	+	0.404505i
$130$	−0.124778	−	0.0495015i	−0.0109438	−	0.00434157i
$131$	−3.97678	+	10.9261i	−0.347453	+	0.954619i	0.635716	+	0.771923i	$0.280705\pi$
$131$	−3.97678	+	10.9261i	−0.347453	+	0.954619i	−0.983169	+	0.182697i	$0.941517\pi$
$132$	−7.61166	+	18.4893i	−0.662510	+	1.60929i
$133$	18.7981	−	7.20480i	1.63000	−	0.624736i
$134$	−0.735362	−	1.09797i	−0.0635256	−	0.0948503i
$135$	0.535666	+	6.73282i	0.0461028	+	0.579469i
$136$	2.32684	+	5.92640i	0.199525	+	0.508185i
$137$	−1.08681	+	1.29521i	−0.0928526	+	0.110657i	−0.810470	−	0.585780i	$-0.800788\pi$
$137$	−1.08681	+	1.29521i	−0.0928526	+	0.110657i	0.717617	+	0.696438i	$0.245233\pi$
$138$	2.14018	+	0.621292i	0.182184	+	0.0528879i
$139$	−3.72321	−	0.656503i	−0.315799	−	0.0556838i	0.0135023	−	0.999909i	$-0.495702\pi$
$139$	−3.72321	−	0.656503i	−0.315799	−	0.0556838i	−0.329301	+	0.944225i	$0.606813\pi$
$140$	18.2661	+	9.64161i	1.54376	+	0.814865i
$141$	6.76626	−	3.90650i	0.569822	−	0.328987i
$142$	4.82917	−	6.60113i	0.405255	−	0.553955i
$143$	0.0677489	+	0.186138i	0.00566544	+	0.0155657i
$144$	1.61963	−	6.15101i	0.134970	−	0.512584i
$145$	−11.6675	−	1.11340i	−0.968930	−	0.0924629i
$146$	−12.8032	+	5.65008i	−1.05960	+	0.467604i
$147$	−19.7352	−	23.5195i	−1.62774	−	1.93986i
$148$	12.8932	−	6.74730i	1.05981	−	0.554625i
$149$	0.145078	+	0.822777i	0.0118852	+	0.0674045i	0.990174	−	0.139844i	$-0.0446602\pi$
$149$	0.145078	+	0.822777i	0.0118852	+	0.0674045i	−0.978288	+	0.207249i	$0.933549\pi$
$150$	−13.4875	−	6.89898i	−1.10125	−	0.563299i
$151$	5.19281			0.422585			0.211292	−	0.977423i	$-0.432233\pi$
$151$	5.19281			0.422585			0.211292	+	0.977423i	$0.432233\pi$
$152$	−12.3180	+	0.517691i	−0.999118	+	0.0419903i
$153$			3.57949i			0.289384i
$154$	−7.27628	−	29.5969i	−0.586339	−	2.38498i
$155$	−3.93444	−	5.71419i	−0.316022	−	0.458975i
$156$	−0.0843391	−	0.161161i	−0.00675253	−	0.0129032i
$157$	7.49193	+	8.92854i	0.597921	+	0.712575i	0.977108	−	0.212746i	$-0.0682406\pi$
$157$	7.49193	+	8.92854i	0.597921	+	0.712575i	−0.379186	+	0.925320i	$0.623796\pi$
$158$	−6.27851	−	14.2272i	−0.499491	−	1.13185i
$159$	23.4274	+	13.5258i	1.85791	+	1.07267i
$160$	−8.72453	−	9.15874i	−0.689735	−	0.724062i
$161$	−3.19210	+	1.16183i	−0.251573	+	0.0915651i
$162$	−9.38699	+	12.8314i	−0.737512	+	1.00813i
$163$	−8.59894	−	14.8938i	−0.673521	−	1.16657i	−0.976899	−	0.213702i	$-0.931448\pi$
$163$	−8.59894	−	14.8938i	−0.673521	−	1.16657i	0.303378	−	0.952870i	$-0.401886\pi$
$164$	9.33537	−	7.19546i	0.728970	−	0.561871i
$165$	5.61569	+	21.6381i	0.437181	+	1.68452i
$166$	−3.31825	+	11.4304i	−0.257546	+	0.887175i
$167$	12.2118	−	14.5534i	0.944977	−	1.12618i	−0.0468902	−	0.998900i	$-0.514931\pi$
$167$	12.2118	−	14.5534i	0.944977	−	1.12618i	0.991867	−	0.127279i	$-0.0406245\pi$
$168$	10.2283	+	26.0512i	0.789131	+	2.00989i
$169$	12.2143	+	4.44565i	0.939562	+	0.341973i
$170$	6.06033	+	3.73404i	0.464806	+	0.286387i
$171$	−6.55258	−	2.26002i	−0.501088	−	0.172828i
$172$	−2.13129	+	5.17707i	−0.162509	+	0.394748i
$173$	−18.8980	−	6.87831i	−1.43679	−	0.522948i	−0.497920	−	0.867223i	$-0.665903\pi$
$173$	−18.8980	−	6.87831i	−1.43679	−	0.522948i	−0.938869	+	0.344275i	$0.888125\pi$
$174$	−10.9946	−	11.4603i	−0.833500	−	0.868800i
$175$	22.8020	−	3.65138i	1.72367	−	0.276018i
$176$	−1.54623	+	18.6011i	−0.116551	+	1.40211i
$177$	29.5447	+	5.20952i	2.22071	+	0.391572i
$178$	−16.7110	+	1.11347i	−1.25254	+	0.0834583i
$179$	−4.40574	−	7.63096i	−0.329300	−	0.570365i	0.653073	−	0.757295i	$-0.273480\pi$
$179$	−4.40574	−	7.63096i	−0.329300	−	0.570365i	−0.982373	+	0.186930i	$0.940146\pi$
$180$	−2.68389	−	6.58554i	−0.200045	−	0.490857i
$181$	−0.746136	−	2.04999i	−0.0554599	−	0.152375i	0.908869	−	0.417082i	$-0.136947\pi$
$181$	−0.746136	−	2.04999i	−0.0554599	−	0.152375i	−0.964329	+	0.264707i	$0.914725\pi$
$182$	0.248802	+	0.122361i	0.0184425	+	0.00907000i
$183$	−1.95112	−	1.12648i	−0.144231	−	0.0832717i
$184$	2.07969	−	0.0521388i	0.153317	−	0.00384373i
$185$	6.99172	−	14.6907i	0.514041	−	1.08008i
$186$	1.01331	−	9.34593i	0.0742991	−	0.685277i
$187$	−1.82399	−	10.3443i	−0.133383	−	0.756453i
$188$	4.91573	−	5.38796i	0.358517	−	0.392958i
$189$		−	13.9503i		−	1.01473i
$190$	−10.6619	+	8.73639i	−0.773493	+	0.633805i
$191$			19.5994i			1.41817i	0.705125	+	0.709083i	$0.250891\pi$
$191$			19.5994i			1.41817i	−0.705125	+	0.709083i	$0.749109\pi$
$192$	−0.858862	−	17.1182i	−0.0619830	−	1.23540i
$193$	−0.572281	−	3.24557i	−0.0411937	−	0.233621i	0.957259	−	0.289233i	$-0.0934002\pi$
$193$	−0.572281	−	3.24557i	−0.0411937	−	0.233621i	−0.998452	+	0.0556118i	$0.982289\pi$
$194$	5.08364	+	0.551179i	0.364984	+	0.0395723i
$195$	−0.183629	−	0.0873942i	−0.0131499	−	0.00625843i
$196$	−24.2057	−	15.3471i	−1.72898	−	1.09622i
$197$	−10.1822	−	5.87872i	−0.725455	−	0.418842i	0.0913021	−	0.995823i	$-0.470897\pi$
$197$	−10.1822	−	5.87872i	−0.725455	−	0.418842i	−0.816757	+	0.576982i	$0.804230\pi$
$198$	−4.63108	+	9.41659i	−0.329116	+	0.669208i
$199$	−3.67530	−	10.0978i	−0.260535	−	0.715814i	−0.999132	−	0.0416666i	$-0.986733\pi$
$199$	−3.67530	−	10.0978i	−0.260535	−	0.715814i	0.738596	−	0.674148i	$-0.235489\pi$
$200$	−13.9496	−	2.32587i	−0.986383	−	0.164464i
$201$	−1.00099	−	1.73376i	−0.0706042	−	0.122290i
$202$	1.47372	+	22.1176i	0.103691	+	1.55619i
$203$	23.8403	+	4.20369i	1.67326	+	0.295041i
$204$	2.92036	+	9.19272i	0.204466	+	0.643619i
$205$	3.51078	−	12.7015i	0.245204	−	0.887114i
$206$	10.4122	−	9.98918i	0.725455	−	0.695979i
$207$	1.09905	+	0.400023i	0.0763896	+	0.0278035i
$208$	−0.120585	−	0.119545i	−0.00836110	−	0.00828898i
$209$	20.0879	+	3.19223i	1.38951	+	0.220811i
$210$	26.6399	+	16.4140i	1.83833	+	1.13268i
$211$	10.1136	+	3.68107i	0.696252	+	0.253415i	0.665810	−	0.746122i	$-0.268086\pi$
$211$	10.1136	+	3.68107i	0.696252	+	0.253415i	0.0304422	+	0.999537i	$0.490308\pi$
$212$	24.6660	+	5.41229i	1.69406	+	0.371718i
$213$	7.96464	−	9.49189i	0.545728	−	0.650374i
$214$	−1.39177	−	0.404028i	−0.0951391	−	0.0276188i
$215$	1.57241	+	6.05872i	0.107237	+	0.413201i
$216$	−2.71987	+	8.09881i	−0.185063	+	0.551054i
$217$	7.16475	+	12.4097i	0.486375	+	0.842426i
$218$	12.8744	+	9.41846i	0.871963	+	0.637899i
$219$	−19.9224	+	7.25114i	−1.34623	+	0.489987i
$220$	11.1119	+	17.6639i	0.749166	+	1.19090i
$221$	0.0827533	+	0.0477777i	0.00556659	+	0.00321387i
$222$	20.1689	−	8.90063i	1.35365	−	0.597371i
$223$	−3.54568	−	4.22558i	−0.237436	−	0.282966i	0.634147	−	0.773212i	$-0.281351\pi$
$223$	−3.54568	−	4.22558i	−0.237436	−	0.282966i	−0.871584	+	0.490246i	$0.836907\pi$
$224$	16.4630	+	20.2865i	1.09998	+	1.35545i
$225$	−6.82217	−	4.08335i	−0.454812	−	0.272223i
$226$	−5.41575	+	1.33144i	−0.360251	+	0.0885663i
$227$			10.7122i			0.710994i	0.934677	+	0.355497i	$0.115688\pi$
$227$			10.7122i			0.710994i	−0.934677	+	0.355497i	$0.884312\pi$
$228$	−18.6720	−	0.458116i	−1.23658	−	0.0303395i
$229$	12.2667			0.810609			0.405305	−	0.914182i	$-0.367165\pi$
$229$	12.2667			0.810609			0.405305	+	0.914182i	$0.367165\pi$
$230$	1.82378	−	1.44348i	0.120256	−	0.0951805i
$231$	−8.01785	−	45.4715i	−0.527536	−	2.99181i
$232$	−13.0209	−	7.08856i	−0.854862	−	0.465387i
$233$	6.61144	+	7.87921i	0.433130	+	0.516184i	0.937823	−	0.347115i	$-0.112839\pi$
$233$	6.61144	+	7.87921i	0.433130	+	0.516184i	−0.504693	+	0.863299i	$0.668394\pi$
$234$	−0.0385420	−	0.0873366i	−0.00251957	−	0.00570937i
$235$	0.774632	−	8.11746i	0.0505314	−	0.529525i
$236$	27.7579	−	3.71558i	1.80689	−	0.241863i
$237$	−8.05764	−	22.1382i	−0.523400	−	1.43803i
$238$	−11.8662	−	8.68093i	−0.769172	−	0.562701i
$239$	9.95951	−	5.75013i	0.644227	−	0.371945i	−0.142014	−	0.989865i	$-0.545358\pi$
$239$	9.95951	−	5.75013i	0.644227	−	0.371945i	0.786241	+	0.617920i	$0.212024\pi$
$240$	−12.2655	−	14.7231i	−0.791738	−	0.950372i
$241$	0.529759	+	0.0934108i	0.0341248	+	0.00601712i	0.190684	−	0.981651i	$-0.438929\pi$
$241$	0.529759	+	0.0934108i	0.0341248	+	0.00601712i	−0.156560	+	0.987668i	$0.550040\pi$
$242$	4.24801	−	14.6332i	0.273072	−	0.940659i
$243$	−9.65710	+	11.5089i	−0.619503	+	0.738295i
$244$	−2.05427	−	0.450756i	−0.131511	−	0.0288567i
$245$	−31.9430	+	2.54140i	−2.04076	+	0.162364i
$246$	14.8361	−	9.93641i	0.945915	−	0.633523i
$247$	−0.139710	+	0.121322i	−0.00888955	+	0.00771952i
$248$	−1.73998	−	8.60135i	−0.110489	−	0.546187i
$249$	−6.16714	+	16.9441i	−0.390826	+	1.07379i
$250$	−14.0301	+	7.29078i	−0.887343	+	0.461110i
$251$	1.67157	−	1.99210i	0.105509	−	0.125741i	−0.710706	−	0.703489i	$-0.751624\pi$
$251$	1.67157	−	1.99210i	0.105509	−	0.125741i	0.816215	+	0.577749i	$0.196069\pi$
$252$	4.44720	+	13.9989i	0.280147	+	0.881850i
$253$	−3.37999	−	0.595984i	−0.212498	−	0.0374692i
$254$	−22.5017	+	1.49931i	−1.41188	+	0.0940751i
$255$	8.78471	+	6.25477i	0.550120	+	0.391689i
$256$	−5.60236	−	14.9871i	−0.350148	−	0.936695i
$257$	−12.5253	+	4.55884i	−0.781308	+	0.284373i	−0.701718	−	0.712455i	$-0.747583\pi$
$257$	−12.5253	+	4.55884i	−0.781308	+	0.284373i	−0.0795899	+	0.996828i	$0.525361\pi$
$258$	−3.74309	+	7.61100i	−0.233035	+	0.473840i
$259$	−16.8021	+	29.1020i	−1.04403	+	1.80831i
$260$	−0.188073	−	0.0258532i	−0.0116638	−	0.00160335i
$261$	−5.35760	−	6.38494i	−0.331627	−	0.395218i
$262$	−1.77245	+	16.3477i	−0.109503	+	1.00997i
$263$	0.423618	+	2.40246i	0.0261214	+	0.148142i	0.995079	−	0.0990853i	$-0.0315917\pi$
$263$	0.423618	+	2.40246i	0.0261214	+	0.148142i	−0.968958	+	0.247227i	$0.920481\pi$
$264$	−4.21077	+	27.9617i	−0.259155	+	1.72092i
$265$	25.6814	−	11.7301i	1.57759	−	0.720577i
$266$	23.3833	−	16.2412i	1.43372	−	0.995814i
$267$	−25.3725			−1.55277
$268$	−1.38059	−	1.25959i	−0.0843330	−	0.0769417i
$269$	−14.4823	+	2.55362i	−0.883001	+	0.155697i	−0.596721	−	0.802449i	$-0.703530\pi$
$269$	−14.4823	+	2.55362i	−0.883001	+	0.155697i	−0.286280	+	0.958146i	$0.592419\pi$
$270$	3.00881	+	9.06546i	0.183111	+	0.551706i
$271$	−10.3857	−	12.3772i	−0.630885	−	0.751860i	0.352016	−	0.935994i	$-0.385496\pi$
$271$	−10.3857	−	12.3772i	−0.630885	−	0.751860i	−0.982901	+	0.184134i	$0.941052\pi$
$272$	5.19641	+	7.35325i	0.315079	+	0.445856i
$273$	0.363766	+	0.210020i	0.0220161	+	0.0127110i
$274$	−1.05524	+	2.14568i	−0.0637496	+	0.129625i
$275$	21.7961	+	8.32409i	1.31435	+	0.501961i
$276$	3.14892	+	0.130653i	0.189543	+	0.00786437i
$277$	18.0877	−	10.4430i	1.08679	−	0.627457i	0.154068	−	0.988060i	$-0.450763\pi$
$277$	18.0877	−	10.4430i	1.08679	−	0.627457i	0.932719	+	0.360604i	$0.117429\pi$
$278$	−5.33482	+	0.355464i	−0.319961	+	0.0213193i
$279$	0.856730	−	4.85876i	0.0512911	−	0.290886i
$280$	28.3404	+	7.07393i	1.69366	+	0.422748i
$281$	5.83031	−	6.94829i	0.347807	−	0.414500i	−0.563573	−	0.826066i	$-0.690574\pi$
$281$	5.83031	−	6.94829i	0.347807	−	0.414500i	0.911380	+	0.411566i	$0.135018\pi$
$282$	7.97330	−	7.64934i	0.474803	−	0.455512i
$283$	−31.1684	−	11.3444i	−1.85277	−	0.674352i	−0.983743	−	0.179582i	$-0.942525\pi$
$283$	−31.1684	−	11.3444i	−1.85277	−	0.674352i	−0.869024	−	0.494770i	$-0.835252\pi$
$284$	4.40328	−	10.6959i	0.261287	−	0.634686i
$285$	−16.9964	+	12.1321i	−1.00678	+	0.718643i
$286$	0.155886	+	0.232754i	0.00921774	+	0.0137630i
$287$	−9.30916	+	25.5767i	−0.549502	+	1.50974i
$288$	0.147538	−	8.99413i	0.00869375	−	0.529984i
$289$	9.14116	+	7.67035i	0.537716	+	0.451197i
$290$	−16.3991	+	2.41018i	−0.962987	+	0.141531i
$291$	7.62892	+	1.34518i	0.447215	+	0.0788561i
$292$	−15.6752	+	12.0821i	−0.917323	+	0.707049i
$293$	9.82898	+	17.0243i	0.574215	+	0.994569i	0.996126	+	0.0879324i	$0.0280260\pi$
$293$	9.82898	+	17.0243i	0.574215	+	0.994569i	−0.421911	+	0.906637i	$0.638641\pi$
$294$	−35.0436	−	25.6367i	−2.04378	−	1.49516i
$295$	22.3139	−	21.9653i	1.29917	−	1.27887i
$296$	15.4284	−	13.6193i	0.896758	−	0.791604i
$297$	7.04734	−	12.2064i	0.408928	−	0.708284i
$298$	0.477029	+	1.08095i	0.0276335	+	0.0626180i
$299$	0.0239178	−	0.0200694i	0.00138320	−	0.00116065i
$300$	−20.8519	−	4.92078i	−1.20389	−	0.284101i
$301$	−2.24502	−	12.7322i	−0.129401	−	0.733869i
$302$	7.13139	−	1.75323i	0.410365	−	0.100887i
$303$			33.5815i			1.92921i
$304$	−16.7417	+	4.86982i	−0.960203	+	0.279303i
$305$	−2.13884	+	0.976930i	−0.122469	+	0.0559388i
$306$	1.20853	+	4.91578i	0.0690869	+	0.281016i
$307$	6.53060	−	1.15152i	0.372721	−	0.0657208i	0.0158499	−	0.999874i	$-0.494955\pi$
$307$	6.53060	−	1.15152i	0.372721	−	0.0657208i	0.356871	+	0.934154i	$0.383843\pi$
$308$	−19.9853	−	38.1893i	−1.13877	−	2.17604i
$309$	16.7453	−	14.0509i	0.952605	−	0.799330i
$310$	−7.33250	−	6.51905i	−0.416458	−	0.370257i
$311$	−9.49031	−	5.47923i	−0.538146	−	0.310699i	0.206181	−	0.978514i	$-0.433896\pi$
$311$	−9.49031	−	5.47923i	−0.538146	−	0.310699i	−0.744327	+	0.667815i	$0.767230\pi$
$312$	−0.170237	−	0.192850i	−0.00963775	−	0.0109180i
$313$	−10.7665	−	29.5806i	−0.608556	−	1.67199i	−0.733383	−	0.679816i	$-0.762060\pi$
$313$	−10.7665	−	29.5806i	−0.608556	−	1.67199i	0.124826	−	0.992179i	$-0.460163\pi$
$314$	13.3033	+	9.73227i	0.750750	+	0.549224i
$315$	13.3776	+	9.52494i	0.753742	+	0.536669i
$316$	−13.4259	−	17.4187i	−0.755264	−	0.979878i
$317$	−1.15237	+	6.53540i	−0.0647234	+	0.367065i	0.935193	+	0.354138i	$0.115226\pi$
$317$	−1.15237	+	6.53540i	−0.0647234	+	0.367065i	−0.999916	+	0.0129263i	$0.995885\pi$
$318$	36.7400	+	10.6656i	2.06028	+	0.598096i
$319$	18.7364	+	15.7217i	1.04904	+	0.880249i
$320$	−15.0738	−	9.63226i	−0.842651	−	0.538460i
$321$	−2.06310	−	0.750908i	−0.115151	−	0.0419116i
$322$	−3.99152	+	2.67330i	−0.222438	+	0.148977i
$323$	8.41308	−	5.04918i	0.468116	−	0.280944i
$324$	−8.55915	+	20.7909i	−0.475508	+	1.15505i
$325$	−0.185462	+	0.103217i	−0.0102876	+	0.00572547i
$326$	−16.8376	−	17.5507i	−0.932550	−	0.972045i
$327$	18.5123	+	15.5337i	1.02373	+	0.859013i
$328$	10.3911	−	13.0335i	0.573752	−	0.719657i
$329$	−2.92465	+	16.5865i	−0.161241	+	0.914445i
$330$	15.0177	+	27.8200i	0.826697	+	1.53144i
$331$	12.0559	+	20.8814i	0.662651	+	1.14775i	0.979916	+	0.199408i	$0.0639020\pi$
$331$	12.0559	+	20.8814i	0.662651	+	1.14775i	−0.317265	+	0.948337i	$0.602765\pi$
$332$	−0.697800	+	16.8180i	−0.0382968	+	0.923007i
$333$	10.8723	−	3.95719i	0.595798	−	0.216853i
$334$	11.8571	−	24.1096i	0.648791	−	1.31922i
$335$	−2.07999	−	0.198489i	−0.113642	−	0.0108446i
$336$	22.8423	+	32.3233i	1.24615	+	1.76338i
$337$	−10.4997	+	8.81031i	−0.571956	+	0.479928i	−0.882294	−	0.470698i	$-0.844002\pi$
$337$	−10.4997	+	8.81031i	−0.571956	+	0.479928i	0.310338	+	0.950626i	$0.399558\pi$
$338$	18.2751	+	1.98143i	0.994036	+	0.107775i
$339$	−8.32056	+	1.46714i	−0.451911	+	0.0796841i
$340$	9.58348	+	3.08190i	0.519737	+	0.167140i
$341$			14.4779i			0.784020i
$342$	−9.76183	−	0.891405i	−0.527859	−	0.0482016i
$343$	33.8558			1.82804
$344$	−1.17903	+	7.82935i	−0.0635690	+	0.422130i
$345$	2.90221	−	1.99828i	0.156250	−	0.107584i
$346$	−28.2753	−	3.06567i	−1.52009	−	0.164811i
$347$	4.47175	−	3.75224i	0.240056	−	0.201431i	−0.514820	−	0.857298i	$-0.672141\pi$
$347$	4.47175	−	3.75224i	0.240056	−	0.201431i	0.754876	+	0.655867i	$0.227697\pi$
$348$	−18.9684	−	12.0265i	−1.01681	−	0.644690i
$349$	−14.8319	+	25.6897i	−0.793936	+	1.37514i	0.129577	+	0.991569i	$0.458638\pi$
$349$	−14.8319	+	25.6897i	−0.793936	+	1.37514i	−0.923513	+	0.383567i	$0.874695\pi$
$350$	30.0816	−	12.7130i	1.60793	−	0.679541i
$351$	0.0438541	+	0.120488i	0.00234076	+	0.00643119i
$352$	4.15674	+	26.0673i	0.221555	+	1.38939i
$353$	−10.6549	+	6.15163i	−0.567105	+	0.327418i	−0.755992	−	0.654580i	$-0.772845\pi$
$353$	−10.6549	+	6.15163i	−0.567105	+	0.327418i	0.188887	+	0.981999i	$0.439512\pi$
$354$	42.3331	−	2.82070i	2.24998	−	0.149919i
$355$	−3.24863	−	12.5174i	−0.172419	−	0.664356i
$356$	−22.5736	+	7.17122i	−1.19640	+	0.380074i
$357$	−17.0626	−	14.3173i	−0.903051	−	0.757750i
$358$	−8.62690	−	8.99226i	−0.455946	−	0.475256i
$359$	−10.9856	+	30.1826i	−0.579796	+	1.59298i	0.208729	+	0.977973i	$0.433067\pi$
$359$	−10.9856	+	30.1826i	−0.579796	+	1.59298i	−0.788525	+	0.615003i	$0.789155\pi$
$360$	−5.90929	−	8.13791i	−0.311447	−	0.428905i
$361$	3.93115	+	18.5889i	0.206902	+	0.978362i
$362$	−1.71681	−	2.56338i	−0.0902338	−	0.134728i
$363$	7.89515	−	21.6917i	0.414388	−	1.13852i
$364$	0.382998	+	0.0840387i	0.0200745	+	0.00440483i
$365$	−5.89503	+	21.3274i	−0.308560	+	1.11633i
$366$	−3.05984	−	0.888268i	−0.159940	−	0.0464305i
$367$	1.55323	−	8.80881i	0.0810780	−	0.459816i	−0.917056	−	0.398758i	$-0.869441\pi$
$367$	1.55323	−	8.80881i	0.0810780	−	0.459816i	0.998134	−	0.0610582i	$-0.0194475\pi$
$368$	2.83848	−	0.773762i	0.147966	−	0.0403351i
$369$	8.11581	−	4.68566i	0.422492	−	0.243926i
$370$	4.64191	−	22.5356i	0.241321	−	1.17157i
$371$	−54.7981	+	19.9449i	−2.84497	+	1.03549i
$372$	−1.76384	−	13.1771i	−0.0914506	−	0.683199i
$373$	−1.06463	+	1.84399i	−0.0551243	+	0.0954781i	−0.892271	−	0.451501i	$-0.850889\pi$
$373$	−1.06463	+	1.84399i	−0.0551243	+	0.0954781i	0.837146	+	0.546979i	$0.184222\pi$
$374$	−5.99743	−	13.5903i	−0.310120	−	0.702736i
$375$	−21.9423	+	9.60765i	−1.13309	+	0.496137i
$376$	4.93176	−	9.05908i	0.254336	−	0.467186i
$377$	−0.219123	+	0.0386373i	−0.0112854	+	0.00198992i
$378$	−4.70997	−	19.1582i	−0.242255	−	0.985390i
$379$	−14.0550			−0.721958			−0.360979	−	0.932574i	$-0.617557\pi$
$379$	−14.0550			−0.721958			−0.360979	+	0.932574i	$0.617557\pi$
$380$	−11.6925	+	15.5976i	−0.599814	+	0.800140i
$381$	−34.1646			−1.75030
$382$	6.61728	+	26.9163i	0.338569	+	1.37716i
$383$	10.5836	−	1.86618i	0.540798	−	0.0953573i	0.103425	−	0.994637i	$-0.467020\pi$
$383$	10.5836	−	1.86618i	0.540798	−	0.0953573i	0.437373	+	0.899280i	$0.355909\pi$
$384$	−6.95904	−	23.2188i	−0.355127	−	1.18488i
$385$	−43.5134	−	20.7093i	−2.21765	−	1.05544i
$386$	−1.88171	−	4.26399i	−0.0957767	−	0.217031i
$387$	−2.22568	+	3.85499i	−0.113138	+	0.195960i
$388$	7.16756	−	0.959423i	0.363878	−	0.0487073i
$389$	−24.5523	+	8.93632i	−1.24485	+	0.453089i	−0.878659	−	0.477449i	$-0.841561\pi$
$389$	−24.5523	+	8.93632i	−1.24485	+	0.453089i	−0.366194	+	0.930539i	$0.619339\pi$
$390$	−0.281688	−	0.0580224i	−0.0142638	−	0.00293808i
$391$	−1.43384	+	0.827825i	−0.0725122	+	0.0418649i
$392$	−38.4238	−	12.9041i	−1.94069	−	0.651753i
$393$	−4.32578	+	24.5327i	−0.218207	+	1.23751i
$394$	−15.9683	−	4.63558i	−0.804471	−	0.233537i
$395$	−23.6996	−	6.55069i	−1.19245	−	0.329601i
$396$	−3.18067	+	14.4956i	−0.159835	+	0.728429i
$397$	−2.28870	+	6.28816i	−0.114867	+	0.315594i	−0.983782	−	0.179367i	$-0.942595\pi$
$397$	−2.28870	+	6.28816i	−0.114867	+	0.315594i	0.868916	+	0.494960i	$0.164817\pi$
$398$	−8.45665	−	12.6266i	−0.423893	−	0.632917i
$399$	36.9821	−	22.1951i	1.85142	−	1.11115i
$400$	−19.9425	+	1.51557i	−0.997125	+	0.0757786i
$401$	10.5046	−	28.8612i	0.524575	−	1.44126i	−0.340802	−	0.940135i	$-0.610699\pi$
$401$	10.5046	−	28.8612i	0.524575	−	1.44126i	0.865377	−	0.501122i	$-0.167079\pi$
$402$	−1.96004	−	2.04305i	−0.0977578	−	0.101898i
$403$	−0.100893	−	0.0846594i	−0.00502585	−	0.00421719i
$404$	9.49138	+	29.8770i	0.472214	+	1.48644i
$405$	6.31471	+	24.3315i	0.313781	+	1.20904i
$406$	34.1596	−	2.27609i	1.69531	−	0.112961i
$407$	−29.4033	+	16.9760i	−1.45747	+	0.841470i
$408$	7.11428	+	11.6386i	0.352210	+	0.576195i
$409$	−2.25645	−	6.19954i	−0.111574	−	0.306548i	0.871321	−	0.490714i	$-0.163264\pi$
$409$	−2.25645	−	6.19954i	−0.111574	−	0.306548i	−0.982895	+	0.184166i	$0.941042\pi$
$410$	0.533055	−	18.6286i	0.0263257	−	0.920002i
$411$	−1.81122	+	3.13713i	−0.0893409	+	0.154743i
$412$	10.9267	−	17.2338i	0.538321	−	0.849048i
$413$	−49.5413	+	41.5701i	−2.43777	+	2.04553i
$414$	1.64441	+	0.178291i	0.0808185	+	0.00876251i
$415$	10.6726	+	15.5003i	0.523896	+	0.760882i
$416$	−0.205964	−	0.123461i	−0.0100982	−	0.00605319i
$417$	−8.09992			−0.396655
$418$	28.6649	−	2.39824i	1.40205	−	0.117302i
$419$		−	31.3002i		−	1.52912i	−0.644554	−	0.764559i	$-0.722957\pi$
$419$		−	31.3002i		−	1.52912i	0.644554	−	0.764559i	$-0.277043\pi$
$420$	42.1269	+	13.5474i	2.05558	+	0.661045i
$421$	10.1971	−	1.79802i	0.496975	−	0.0876301i	0.0804580	−	0.996758i	$-0.474362\pi$
$421$	10.1971	−	1.79802i	0.496975	−	0.0876301i	0.416517	+	0.909128i	$0.363251\pi$
$422$	15.1321	+	1.64065i	0.736619	+	0.0798658i
$423$	4.44222	−	3.72747i	0.215988	−	0.181236i
$424$	35.7016	−	0.895055i	1.73382	−	0.0434677i
$425$	10.6356	−	3.68245i	0.515902	−	0.178625i
$426$	7.73330	−	15.7245i	0.374680	−	0.761854i
$427$	4.56378	−	1.66108i	0.220857	−	0.0803854i
$428$	−2.04775	−	0.0849638i	−0.0989818	−	0.00410688i
$429$	0.212195	+	0.367532i	0.0102449	+	0.0177446i
$430$	4.20500	+	7.78968i	0.202783	+	0.375652i
$431$	3.81828	−	21.6545i	0.183920	−	1.04306i	−0.743415	−	0.668830i	$-0.766795\pi$
$431$	3.81828	−	21.6545i	0.183920	−	1.04306i	0.927335	−	0.374232i	$-0.122094\pi$
$432$	−1.00088	+	12.0406i	−0.0481548	+	0.579302i
$433$	−24.8994	−	20.8931i	−1.19659	−	1.00406i	−0.999721	−	0.0236291i	$-0.992478\pi$
$433$	−24.8994	−	20.8931i	−1.19659	−	1.00406i	−0.196870	−	0.980430i	$-0.563078\pi$
$434$	14.0293	+	14.6235i	0.673430	+	0.701951i
$435$	−25.0316	+	1.99153i	−1.20017	+	0.0954864i
$436$	20.8606	+	8.58784i	0.999039	+	0.411283i
$437$	−0.610116	−	3.14744i	−0.0291858	−	0.150563i
$438$	−24.9116	+	16.6844i	−1.19032	+	0.797214i
$439$	−13.0271	−	4.74149i	−0.621751	−	0.226299i	0.0118858	−	0.999929i	$-0.496217\pi$
$439$	−13.0271	−	4.74149i	−0.621751	−	0.226299i	−0.633637	+	0.773630i	$0.718439\pi$
$440$	21.2240	+	20.5065i	1.01182	+	0.977610i
$441$	−17.4565	−	14.6477i	−0.831262	−	0.697512i
$442$	0.129778	+	0.0376744i	0.00617290	+	0.00179199i
$443$	−6.72351	+	38.1309i	−0.319444	+	1.81166i	0.226701	+	0.973964i	$0.427206\pi$
$443$	−6.72351	+	38.1309i	−0.319444	+	1.81166i	−0.546145	+	0.837691i	$0.683905\pi$
$444$	24.6933	−	19.0330i	1.17189	−	0.903265i
$445$	−15.3592	+	21.5717i	−0.728096	+	1.02260i
$446$	−6.29602	−	4.60596i	−0.298125	−	0.218099i
$447$	0.612204	+	1.68202i	0.0289563	+	0.0795567i
$448$	29.4583	+	22.3016i	1.39177	+	1.05365i
$449$	6.08984	+	3.51597i	0.287397	+	0.165929i	0.636768	−	0.771056i	$-0.280271\pi$
$449$	6.08984	+	3.51597i	0.287397	+	0.165929i	−0.349370	+	0.936985i	$0.613604\pi$
$450$	−10.7477	−	3.30440i	−0.506650	−	0.155771i
$451$	−21.0662	+	17.6766i	−0.991968	+	0.832360i
$452$	−6.98803	+	3.65700i	−0.328689	+	0.172011i
$453$	10.9564	−	1.93191i	0.514777	−	0.0907690i
$454$	3.61672	+	14.7113i	0.169741	+	0.690435i
$455$	0.398764	−	0.182138i	0.0186943	−	0.00853878i
$456$	−25.7973	+	5.67500i	−1.20807	+	0.265756i
$457$			0.882966i			0.0413034i	0.999787	+	0.0206517i	$0.00657411\pi$
$457$			0.882966i			0.0413034i	−0.999787	+	0.0206517i	$0.993426\pi$
$458$	16.8462	−	4.14157i	0.787170	−	0.193523i
$459$	−1.18067	−	6.69594i	−0.0551091	−	0.312540i
$460$	2.01727	−	2.59812i	0.0940558	−	0.121138i
$461$	30.5136	−	25.6039i	1.42116	−	1.19249i	0.470444	−	0.882430i	$-0.344094\pi$
$461$	30.5136	−	25.6039i	1.42116	−	1.19249i	0.950716	−	0.310064i	$-0.100351\pi$
$462$	−26.3634	−	59.7399i	−1.22654	−	2.77935i
$463$	−4.93813	+	8.55310i	−0.229495	+	0.397496i	−0.957658	−	0.287907i	$-0.907041\pi$
$463$	−4.93813	+	8.55310i	−0.229495	+	0.397496i	0.728164	+	0.685403i	$0.240374\pi$
$464$	−20.2751	−	5.33868i	−0.941249	−	0.247842i
$465$	−10.4272	−	10.5927i	−0.483551	−	0.491226i
$466$	11.7399	+	8.58849i	0.543838	+	0.397854i
$467$	2.15701	+	3.73605i	0.0998145	+	0.172884i	0.911608	−	0.411061i	$-0.134842\pi$
$467$	2.15701	+	3.73605i	0.0998145	+	0.172884i	−0.811793	+	0.583945i	$0.801508\pi$
$468$	−0.0824176	−	0.106928i	−0.00380975	−	0.00494277i
$469$	4.25007	+	0.749402i	0.196250	+	0.0346042i
$470$	−1.67685	−	11.4094i	−0.0773472	−	0.526277i
$471$	19.1291	+	16.0512i	0.881422	+	0.739601i
$472$	36.8660	−	14.4745i	1.69690	−	0.666241i
$473$	4.46761	−	12.2747i	0.205421	−	0.564390i
$474$	−18.5402	−	27.6824i	−0.851577	−	1.27149i
$475$	0.0259551	+	21.7945i	0.00119090	+	0.999999i
$476$	−19.2270	−	7.91535i	−0.881269	−	0.362799i
$477$	18.8672	+	6.86710i	0.863870	+	0.314423i
$478$	11.7362	−	11.2594i	0.536802	−	0.514991i
$479$	0.367149	−	0.437551i	0.0167755	−	0.0199922i	−0.757591	−	0.652729i	$-0.773624\pi$
$479$	0.367149	−	0.437551i	0.0167755	−	0.0199922i	0.774367	+	0.632737i	$0.218068\pi$
$480$	−21.8154	−	16.0784i	−0.995733	−	0.733874i
$481$	0.0536339	−	0.304173i	0.00244550	−	0.0138691i
$482$	0.759067	−	0.0505774i	0.0345745	−	0.00230374i
$483$	−6.30284	+	3.63894i	−0.286789	+	0.165578i
$484$	0.893322	−	21.5303i	0.0406055	−	0.978652i
$485$	5.76183	−	5.67180i	0.261631	−	0.257543i
$486$	−9.37659	+	19.0659i	−0.425331	+	0.864845i
$487$	13.2185	+	7.63171i	0.598988	+	0.345826i	0.768643	−	0.639678i	$-0.220932\pi$
$487$	13.2185	+	7.63171i	0.598988	+	0.345826i	−0.169655	+	0.985503i	$0.554265\pi$
$488$	−2.97336	+	0.0745435i	−0.134598	+	0.00337442i
$489$	−23.6841	−	28.2256i	−1.07103	−	1.27641i
$490$	−43.0099	+	14.2749i	−1.94299	+	0.644876i
$491$	19.9841	−	3.52374i	0.901870	−	0.159024i	0.296560	−	0.955014i	$-0.404160\pi$
$491$	19.9841	−	3.52374i	0.901870	−	0.159024i	0.605310	+	0.795990i	$0.293049\pi$
$492$	17.0199	−	18.6549i	0.767317	−	0.841029i
$493$	11.7988			0.531391
$494$	−0.150906	+	0.213783i	−0.00678956	+	0.00961857i
$495$	6.89351	+	15.0923i	0.309840	+	0.678348i
$496$	−5.29359	−	11.2250i	−0.237689	−	0.504015i
$497$	4.63826	+	26.3049i	0.208054	+	1.17994i
$498$	−2.74870	+	25.3518i	−0.123172	+	1.13604i
$499$	−1.05639	−	1.25895i	−0.0472903	−	0.0563584i	0.741881	−	0.670532i	$-0.233934\pi$
$499$	−1.05639	−	1.25895i	−0.0472903	−	0.0563584i	−0.789171	+	0.614173i	$0.789490\pi$
$500$	−16.8063	+	14.7495i	−0.751601	+	0.659618i
$501$	20.3515	−	35.2498i	0.909237	−	1.57485i
$502$	1.62302	−	3.30016i	0.0724389	−	0.147294i
$503$	−13.1602	+	4.78990i	−0.586782	+	0.213571i	−0.618314	−	0.785932i	$-0.712184\pi$
$503$	−13.1602	+	4.78990i	−0.586782	+	0.213571i	0.0315314	+	0.999503i	$0.489962\pi$
$504$	10.8338	+	17.7235i	0.482577	+	0.789469i
$505$	28.5510	+	20.3285i	1.27050	+	0.904605i
$506$	−4.84303	+	0.322696i	−0.215299	+	0.0143456i
$507$	27.4251	+	4.83579i	1.21799	+	0.214765i
$508$	−30.3958	+	9.65618i	−1.34860	+	0.428424i
$509$	14.3274	−	17.0748i	0.635053	−	0.756827i	−0.348527	−	0.937299i	$-0.613318\pi$
$509$	14.3274	−	17.0748i	0.635053	−	0.756827i	0.983580	+	0.180472i	$0.0577625\pi$
$510$	14.1760	+	5.62385i	0.627723	+	0.249028i
$511$	15.6312	−	42.9464i	0.691484	−	1.89984i
$512$	−12.7539	−	18.6906i	−0.563647	−	0.826016i
$513$	13.0030	+	2.06635i	0.574096	+	0.0912314i
$514$	−15.6621	+	10.4896i	−0.690825	+	0.462677i
$515$	−1.80940	−	22.7425i	−0.0797319	−	1.00216i
$516$	−2.57079	+	11.7161i	−0.113173	+	0.515773i
$517$	−10.9382	+	13.0356i	−0.481060	+	0.573305i
$518$	−13.2490	+	45.6392i	−0.582128	+	2.00527i
$519$	−42.4322	−	7.48195i	−1.86257	−	0.328421i
$520$	−0.267013	+	0.0279937i	−0.0117093	+	0.00122760i
$521$	−14.0423	+	8.10735i	−0.615206	+	0.355189i	−0.775000	−	0.631961i	$-0.782250\pi$
$521$	−14.0423	+	8.10735i	−0.615206	+	0.355189i	0.159794	+	0.987150i	$0.448917\pi$
$522$	−9.51342	−	6.95970i	−0.416391	−	0.304618i
$523$	−1.16768	−	3.20818i	−0.0510592	−	0.140284i	0.911542	−	0.411208i	$-0.134893\pi$
$523$	−1.16768	−	3.20818i	−0.0510592	−	0.140284i	−0.962601	+	0.270924i	$0.912671\pi$
$524$	3.08527	+	23.0491i	0.134781	+	1.00690i
$525$	46.7518	−	16.1873i	2.04042	−	0.706470i
$526$	1.39290	+	3.15632i	0.0607331	+	0.137622i
$527$	4.48928	+	5.35011i	0.195556	+	0.233055i
$528$	3.65785	+	39.8220i	0.159187	+	1.73303i
$529$	−3.89997	−	22.1178i	−0.169564	−	0.961644i
$530$	31.3083	−	24.7799i	1.35995	−	1.07637i
$531$	22.2667			0.966293
$532$	26.6293	−	30.1992i	1.15453	−	1.30930i
$533$		−	0.250170i		−	0.0108361i
$534$	−34.8446	+	8.56643i	−1.50787	+	0.370706i
$535$	−1.88731	+	1.29949i	−0.0815957	+	0.0561818i
$536$	−2.32126	−	1.26370i	−0.100263	−	0.0545834i
$537$	−12.1347	−	14.4616i	−0.523653	−	0.624065i
$538$	−19.0267	+	8.39653i	−0.820297	+	0.362000i
$539$	57.9115	+	33.4352i	2.49442	+	1.44016i
$540$	7.19280	+	11.4339i	0.309529	+	0.492038i
$541$	32.4830	−	11.8228i	1.39655	−	0.508303i	0.469399	−	0.882986i	$-0.344471\pi$
$541$	32.4830	−	11.8228i	1.39655	−	0.508303i	0.927153	+	0.374683i	$0.122248\pi$
$542$	−18.4417	−	13.4913i	−0.792140	−	0.579503i
$543$	−2.33696	−	4.04773i	−0.100288	−	0.173705i
$544$	9.61898	+	8.34392i	0.412410	+	0.357743i
$545$	24.4131	−	6.33588i	1.04574	−	0.271399i
$546$	0.570476	+	0.165608i	0.0244141	+	0.00708739i
$547$	−7.91061	+	9.42750i	−0.338233	+	0.403091i	−0.908173	−	0.418596i	$-0.862522\pi$
$547$	−7.91061	+	9.42750i	−0.338233	+	0.403091i	0.569939	+	0.821687i	$0.306967\pi$
$548$	−0.724752	+	3.30298i	−0.0309599	+	0.141096i
$549$	−1.57133	−	0.571918i	−0.0670627	−	0.0244088i
$550$	32.7435	+	4.07271i	1.39619	+	0.173661i
$551$	−7.44953	+	21.5988i	−0.317360	+	0.920140i
$552$	4.36859	−	0.883729i	0.185939	−	0.0376140i
$553$	47.7231	+	17.3698i	2.02939	+	0.738638i
$554$	21.3144	−	20.4484i	0.905564	−	0.868770i
$555$	9.28649	−	33.5973i	0.394190	−	1.42613i
$556$	−7.20640	+	2.28934i	−0.305619	+	0.0970896i
$557$	3.05230	+	0.538203i	0.129330	+	0.0228044i	0.237938	−	0.971280i	$-0.423528\pi$
$557$	3.05230	+	0.538203i	0.129330	+	0.0228044i	−0.108608	+	0.994085i	$0.534639\pi$
$558$	−0.463878	−	6.96188i	−0.0196375	−	0.294720i
$559$	0.0594152	+	0.102910i	0.00251299	+	0.00435263i
$560$	41.3088	+	0.146310i	1.74562	+	0.00618273i
$561$	−7.69692	−	21.1471i	−0.324964	−	0.892832i
$562$	5.66096	−	11.5107i	0.238793	−	0.485549i
$563$	−3.00681	−	1.73598i	−0.126722	−	0.0731629i	0.435299	−	0.900286i	$-0.356643\pi$
$563$	−3.00681	−	1.73598i	−0.126722	−	0.0731629i	−0.562021	+	0.827123i	$0.689976\pi$
$564$	8.36729	−	13.1970i	0.352326	−	0.555694i
$565$	−3.78947	+	7.96227i	−0.159424	+	0.334975i
$566$	−46.6343	−	5.05619i	−1.96019	−	0.212527i
$567$	−9.01590	−	51.1317i	−0.378632	−	2.14733i
$568$	2.43590	−	16.1756i	0.102208	−	0.678713i
$569$			13.7076i			0.574654i	0.957833	+	0.287327i	$0.0927667\pi$
$569$			13.7076i			0.574654i	−0.957833	+	0.287327i	$0.907233\pi$
$570$	−19.2454	+	22.3997i	−0.806102	+	0.938219i
$571$			15.0381i			0.629326i	0.949203	+	0.314663i	$0.101892\pi$
$571$			15.0381i			0.629326i	−0.949203	+	0.314663i	$0.898108\pi$
$572$	0.292665	+	0.267015i	0.0122369	+	0.0111644i
$573$	7.29169	+	41.3532i	0.304615	+	1.72756i
$574$	−4.14910	+	38.2680i	−0.173180	+	1.59728i
$575$	0.0579067	−	3.67711i	0.00241488	−	0.153346i
$576$	−2.83404	−	12.4016i	−0.118085	−	0.516735i
$577$	−3.18751	−	1.84031i	−0.132698	−	0.0766130i	0.432182	−	0.901787i	$-0.357744\pi$
$577$	−3.18751	−	1.84031i	−0.132698	−	0.0766130i	−0.564879	+	0.825174i	$0.691077\pi$
$578$	15.1435	+	7.44755i	0.629885	+	0.309777i
$579$	−2.41493	−	6.63497i	−0.100361	−	0.275740i
$580$	−21.7074	+	8.84670i	−0.901353	+	0.367339i
$581$	−19.4352	−	33.6627i	−0.806306	−	1.39656i
$582$	10.9311	−	0.728352i	0.453110	−	0.0301912i
$583$	−58.0235	−	10.2311i	−2.40309	−	0.423729i
$584$	−17.4479	+	21.8849i	−0.721999	+	0.905603i
$585$	−0.145485	−	0.0402129i	−0.00601506	−	0.00166260i
$586$	19.2462	+	20.0613i	0.795052	+	0.828724i
$587$	24.0208	+	8.74285i	0.991443	+	0.360856i	0.786279	−	0.617872i	$-0.212005\pi$
$587$	24.0208	+	8.74285i	0.991443	+	0.360856i	0.205164	+	0.978728i	$0.434227\pi$
$588$	−56.7817	−	23.3758i	−2.34164	−	0.964003i
$589$	−12.6283	+	4.84008i	−0.520341	+	0.199432i
$590$	23.2281	−	37.6991i	0.956286	−	1.55205i
$591$	−23.6708	−	8.61547i	−0.973687	−	0.354393i
$592$	16.5899	−	23.9127i	0.681842	−	0.982804i
$593$	26.4990	−	31.5803i	1.08818	−	1.29685i	0.136204	−	0.990681i	$-0.456510\pi$
$593$	26.4990	−	31.5803i	1.08818	−	1.29685i	0.951979	−	0.306165i	$-0.0990458\pi$
$594$	5.55708	−	19.1426i	0.228010	−	0.785430i
$595$	−22.5014	+	5.83974i	−0.922466	+	0.239406i
$596$	1.02007	+	1.32344i	0.0417838	+	0.0542102i
$597$	−11.5113	−	19.9382i	−0.471127	−	0.816016i
$598$	0.0260709	−	0.0356370i	0.00106612	−	0.00145731i
$599$	−3.33236	+	1.21288i	−0.136157	+	0.0495570i	−0.409200	−	0.912445i	$-0.634192\pi$
$599$	−3.33236	+	1.21288i	−0.136157	+	0.0495570i	0.273043	+	0.962002i	$0.411970\pi$
$600$	−30.2978	+	0.282341i	−1.23690	+	0.0115265i
$601$	21.3318	+	12.3159i	0.870144	+	0.502378i	0.867396	−	0.497618i	$-0.165792\pi$
$601$	21.3318	+	12.3159i	0.870144	+	0.502378i	0.00274801	+	0.999996i	$0.499125\pi$
$602$	−7.38184	−	16.7274i	−0.300861	−	0.681756i
$603$	−0.955113	−	1.13826i	−0.0388952	−	0.0463535i
$604$	9.20175	−	4.81548i	0.374414	−	0.195939i
$605$	−13.6630	−	19.8435i	−0.555480	−	0.806753i
$606$	11.3380	+	46.1181i	0.460574	+	1.87342i
$607$			3.62563i			0.147160i	0.997289	+	0.0735798i	$0.0234424\pi$
$607$			3.62563i			0.147160i	−0.997289	+	0.0735798i	$0.976558\pi$
$608$	−21.3476	+	12.3403i	−0.865758	+	0.500463i
$609$	51.8650			2.10168
$610$	−2.60747	+	2.06376i	−0.105573	+	0.0835594i
$611$	−0.0268813	−	0.152452i	−0.00108750	−	0.00616753i
$612$	3.31939	+	6.34291i	0.134178	+	0.256397i
$613$	6.51979	+	7.76998i	0.263332	+	0.313826i	0.881467	−	0.472245i	$-0.156556\pi$
$613$	6.51979	+	7.76998i	0.263332	+	0.313826i	−0.618136	+	0.786071i	$0.712112\pi$
$614$	8.57983	−	3.78631i	0.346254	−	0.152803i
$615$	2.68203	−	28.1054i	0.108150	−	1.13332i
$616$	−40.3400	−	45.6986i	−1.62534	−	1.84125i
$617$	6.40098	+	17.5866i	0.257694	+	0.708008i	0.999309	+	0.0371820i	$0.0118381\pi$
$617$	6.40098	+	17.5866i	0.257694	+	0.708008i	−0.741615	+	0.670826i	$0.765940\pi$
$618$	18.2526	−	24.9501i	0.734229	−	1.00364i
$619$	34.2815	−	19.7924i	1.37789	−	0.795526i	0.385986	−	0.922505i	$-0.373861\pi$
$619$	34.2815	−	19.7924i	1.37789	−	0.795526i	0.991905	+	0.126979i	$0.0405281\pi$
$620$	−12.2709	−	6.47709i	−0.492810	−	0.260126i
$621$	−2.18788	−	0.385783i	−0.0877967	−	0.0154809i
$622$	−14.8832	−	4.32057i	−0.596760	−	0.173239i
$623$	35.1575	−	41.8990i	1.40855	−	1.67865i
$624$	−0.298901	−	0.207369i	−0.0119656	−	0.00830140i
$625$	−5.11429	+	24.4713i	−0.204572	+	0.978852i
$626$	−24.7730	−	36.9886i	−0.990127	−	1.47836i
$627$	43.5715	−	0.738061i	1.74008	−	0.0294753i
$628$	21.5556	+	8.87398i	0.860162	+	0.354110i
$629$	−5.60173	+	15.3906i	−0.223355	+	0.613664i
$630$	21.5876	+	8.56416i	0.860070	+	0.341204i
$631$	9.16168	−	10.9185i	0.364721	−	0.434657i	−0.552209	−	0.833706i	$-0.686215\pi$
$631$	9.16168	−	10.9185i	0.364721	−	0.434657i	0.916930	+	0.399048i	$0.130659\pi$
$632$	−24.3190	−	19.3885i	−0.967358	−	0.771234i
$633$	22.7085	+	4.00411i	0.902580	+	0.159149i
$634$	0.623951	+	9.36426i	0.0247803	+	0.371902i
$635$	−20.6814	+	29.0467i	−0.820718	+	1.15268i
$636$	54.0567	+	2.24288i	2.14349	+	0.0889361i
$637$	−0.571641	+	0.208060i	−0.0226492	+	0.00824365i
$638$	31.0392	+	15.2651i	1.22885	+	0.604350i
$639$	4.59830	−	7.96449i	0.181906	−	0.315070i
$640$	−23.9533	−	8.13887i	−0.946836	−	0.321717i
$641$	20.4313	+	24.3491i	0.806988	+	0.961731i	0.999810	−	0.0195029i	$-0.00620836\pi$
$641$	20.4313	+	24.3491i	0.806988	+	0.961731i	−0.192822	+	0.981234i	$0.561764\pi$
$642$	−3.08683	−	0.334680i	−0.121827	−	0.0132088i
$643$	−0.732122	−	4.15207i	−0.0288721	−	0.163742i	0.966963	−	0.254918i	$-0.0820484\pi$
$643$	−0.732122	−	4.15207i	−0.0288721	−	0.163742i	−0.995835	+	0.0911763i	$0.970937\pi$
$644$	−4.57905	+	5.01894i	−0.180440	+	0.197774i
$645$	5.57171	+	12.1984i	0.219386	+	0.480312i
$646$	9.84911	−	9.77462i	0.387508	−	0.384577i
$647$	29.8369			1.17301			0.586505	−	0.809946i	$-0.300504\pi$
$647$	29.8369			1.17301			0.586505	+	0.809946i	$0.300504\pi$
$648$	−4.73492	+	31.4423i	−0.186005	+	1.23517i
$649$	−64.3485	+	11.3464i	−2.52590	+	0.445384i
$650$	−0.219850	+	0.204367i	−0.00862321	+	0.00801594i
$651$	19.7339	+	23.5179i	0.773433	+	0.921741i
$652$	−29.0491	−	18.4180i	−1.13765	−	0.721303i
$653$	−13.5122	−	7.80128i	−0.528774	−	0.305288i	0.211743	−	0.977325i	$-0.432086\pi$
$653$	−13.5122	−	7.80128i	−0.528774	−	0.305288i	−0.740517	+	0.672038i	$0.765419\pi$
$654$	30.6679	+	15.0825i	1.19921	+	0.589771i
$655$	18.2391	+	18.5286i	0.712661	+	0.723972i
$656$	9.86983	−	21.4075i	0.385352	−	0.835823i
$657$	−13.6274	+	7.86780i	−0.531657	+	0.306952i
$658$	1.58356	+	23.7661i	0.0617335	+	0.926497i
$659$	4.07326	−	23.1006i	0.158672	−	0.899873i	−0.796680	−	0.604402i	$-0.793412\pi$
$659$	4.07326	−	23.1006i	0.158672	−	0.899873i	0.955352	−	0.295471i	$-0.0954766\pi$
$660$	30.0169	+	33.1354i	1.16840	+	1.28979i
$661$	−26.4772	+	31.5542i	−1.02984	+	1.22732i	−0.0563942	+	0.998409i	$0.517960\pi$
$661$	−26.4772	+	31.5542i	−1.02984	+	1.22732i	−0.973448	+	0.228909i	$0.926484\pi$
$662$	23.6067	+	24.6065i	0.917500	+	0.956357i
$663$	0.192378	+	0.0700198i	0.00747133	+	0.00271934i
$664$	4.71989	+	23.3321i	0.183167	+	0.905461i
$665$	3.51673	−	44.8779i	0.136373	−	1.74029i
$666$	13.5951	−	9.10525i	0.526799	−	0.352821i
$667$	1.31857	−	3.62273i	0.0510551	−	0.140273i
$668$	8.14356	−	37.1134i	0.315084	−	1.43596i
$669$	−9.05317	−	7.59651i	−0.350016	−	0.293698i
$670$	−2.92350	+	0.429669i	−0.112945	+	0.0165996i
$671$	4.83241	+	0.852084i	0.186553	+	0.0328944i
$672$	42.2830	+	36.6781i	1.63110	+	1.41489i
$673$	−12.8578	−	22.2704i	−0.495634	−	0.858463i	0.504354	−	0.863497i	$-0.331731\pi$
$673$	−12.8578	−	22.2704i	−0.495634	−	0.858463i	−0.999987	+	0.00503462i	$0.998397\pi$
$674$	−11.4449	+	15.6444i	−0.440841	+	0.602598i
$675$	14.1087	+	5.38822i	0.543045	+	0.207393i
$676$	25.7666	−	3.44902i	0.991022	−	0.132655i
$677$	11.9938	−	20.7739i	0.460959	−	0.798405i	−0.538050	−	0.842913i	$-0.680839\pi$
$677$	11.9938	−	20.7739i	0.460959	−	0.798405i	0.999009	+	0.0445081i	$0.0141720\pi$
$678$	−10.9315	+	4.82409i	−0.419820	+	0.185268i
$679$	−12.7924	+	10.7341i	−0.490927	+	0.411937i
$680$	14.2017	+	0.996811i	0.544611	+	0.0382260i
$681$	3.98532	+	22.6019i	0.152718	+	0.866106i
$682$	4.88810	+	19.8827i	0.187175	+	0.761349i
$683$			6.35030i			0.242988i	0.992592	+	0.121494i	$0.0387685\pi$
$683$			6.35030i			0.242988i	−0.992592	+	0.121494i	$0.961232\pi$
$684$	−13.7071	+	2.07166i	−0.524103	+	0.0792120i
$685$	1.57077	+	3.43895i	0.0600159	+	0.131396i
$686$	46.4948	−	11.4306i	1.77518	−	0.436422i
$687$	25.8818	−	4.56367i	0.987454	−	0.174115i
$688$	1.02421	+	11.1503i	0.0390476	+	0.425101i
$689$	0.410591	−	0.344527i	0.0156423	−	0.0131254i
$690$	3.31099	−	3.72414i	0.126047	−	0.141776i
$691$	−37.9275	−	21.8975i	−1.44283	−	0.833019i	−0.444793	−	0.895633i	$-0.646723\pi$
$691$	−37.9275	−	21.8975i	−1.44283	−	0.833019i	−0.998038	+	0.0626143i	$0.980056\pi$
$692$	−39.8661	+	5.33633i	−1.51548	+	0.202857i
$693$	−11.7211	−	32.2034i	−0.445248	−	1.22331i
$694$	4.87429	−	6.66281i	0.185025	−	0.252917i
$695$	−4.90326	+	6.88655i	−0.185991	+	0.261222i
$696$	−30.1102	−	10.1121i	−1.14132	−	0.383297i
$697$	−2.30360	+	13.0644i	−0.0872550	+	0.494848i
$698$	−11.6955	+	40.2878i	−0.442681	+	1.52492i
$699$	16.8810	+	14.1648i	0.638496	+	0.535762i
$700$	37.0194	−	27.6154i	1.39920	−	1.04376i
$701$	27.8137	+	10.1233i	1.05051	+	0.382353i	0.808854	−	0.588009i	$-0.200088\pi$
$701$	27.8137	+	10.1233i	1.05051	+	0.382353i	0.241653	+	0.970363i	$0.422310\pi$
$702$	0.100906	+	0.150663i	0.00380844	+	0.00568640i
$703$	−24.6371	−	19.9718i	−0.929207	−	0.753251i
$704$	14.5095	+	34.3953i	0.546848	+	1.29632i
$705$	−1.38557	−	17.4154i	−0.0521837	−	0.655901i
$706$	−12.5557	+	12.0455i	−0.472540	+	0.453340i
$707$	−55.4549	−	46.5322i	−2.08560	−	1.75002i
$708$	57.1846	−	18.1665i	2.14913	−	0.682739i
$709$	5.32799	−	30.2165i	0.200097	−	1.13481i	−0.704874	−	0.709332i	$-0.748997\pi$
$709$	5.32799	−	30.2165i	0.200097	−	1.13481i	0.904971	−	0.425473i	$-0.139892\pi$
$710$	−8.68761	−	16.0936i	−0.326040	−	0.603983i
$711$	−8.74289	−	15.1431i	−0.327884	−	0.567912i
$712$	−28.5796	+	17.4698i	−1.07107	+	0.654710i
$713$	2.14441	−	0.780501i	0.0803087	−	0.0292300i
$714$	−28.2664	−	13.9014i	−1.05784	−	0.520247i
$715$	0.440927	+	0.0420767i	0.0164897	+	0.00157358i
$716$	−14.8835	−	9.43659i	−0.556223	−	0.352662i
$717$	18.8745	−	15.8376i	0.704882	−	0.591466i
$718$	−4.89627	+	45.1594i	−0.182727	+	1.68533i
$719$	−21.1740	+	3.73354i	−0.789655	+	0.139238i	−0.553909	−	0.832577i	$-0.686865\pi$
$719$	−21.1740	+	3.73354i	−0.789655	+	0.139238i	−0.235746	+	0.971815i	$0.575753\pi$
$720$	−10.8629	−	9.18083i	−0.404837	−	0.342149i
$721$			47.1220i			1.75492i
$722$	11.6748	+	24.2012i	0.434491	+	0.900676i
$723$	1.15250			0.0428619
$724$	−3.22320	−	2.94070i	−0.119789	−	0.109290i
$725$	−13.4596	+	22.4874i	−0.499878	+	0.835162i
$726$	3.51887	−	32.4553i	0.130598	−	1.20453i
$727$	10.2359	−	8.58898i	0.379630	−	0.318548i	−0.432927	−	0.901429i	$-0.642519\pi$
$727$	10.2359	−	8.58898i	0.379630	−	0.318548i	0.812557	+	0.582881i	$0.198075\pi$
$728$	0.554352	−	0.0138979i	0.0205457	−	0.000515089i
$729$	0.768828	−	1.33165i	0.0284751	−	0.0493203i
$730$	−0.895065	+	31.2797i	−0.0331278	+	1.15771i
$731$	−2.15516	−	5.92126i	−0.0797115	−	0.219006i
$732$	−4.50204	−	0.186796i	−0.166400	−	0.00690417i
$733$	−29.7311	+	17.1653i	−1.09814	+	0.634013i	−0.935733	−	0.352710i	$-0.885260\pi$
$733$	−29.7311	+	17.1653i	−1.09814	+	0.634013i	−0.162410	+	0.986723i	$0.551927\pi$
$734$	−0.840999	−	12.6217i	−0.0310418	−	0.465877i
$735$	−66.4516	+	17.2461i	−2.45110	+	0.636131i
$736$	3.63690	−	2.02097i	0.134058	−	0.0744939i
$737$	3.34019	+	2.80276i	0.123038	+	0.103241i
$738$	9.56360	−	9.17503i	0.352041	−	0.337737i
$739$	10.9118	−	29.9798i	0.401396	−	1.10283i	−0.560200	−	0.828357i	$-0.689276\pi$
$739$	10.9118	−	29.9798i	0.401396	−	1.10283i	0.961596	−	0.274469i	$-0.0885021\pi$
$740$	−1.23378	−	32.5158i	−0.0453545	−	1.19531i
$741$	−0.249641	+	0.307956i	−0.00917080	+	0.0113131i
$742$	−68.5214	+	45.8919i	−2.51550	+	1.68475i
$743$	0.882098	−	2.42355i	0.0323611	−	0.0889113i	−0.922460	−	0.386093i	$-0.873824\pi$
$743$	0.882098	−	2.42355i	0.0323611	−	0.0889113i	0.954821	+	0.297182i	$0.0960467\pi$
$744$	−6.87123	−	17.5008i	−0.251912	−	0.641611i
$745$	1.80065	+	0.497709i	0.0659706	+	0.0182347i
$746$	−0.839496	+	2.89183i	−0.0307361	+	0.105878i
$747$	−2.32397	+	13.1799i	−0.0850296	+	0.482227i
$748$	−12.8248	−	16.6389i	−0.468922	−	0.608378i
$749$	4.09875	−	2.36641i	0.149765	−	0.0864669i
$750$	−26.8900	+	20.6027i	−0.981884	+	0.752303i
$751$	8.22496	−	2.99364i	0.300133	−	0.109240i	−0.187564	−	0.982252i	$-0.560059\pi$
$751$	8.22496	−	2.99364i	0.300133	−	0.109240i	0.487697	+	0.873013i	$0.337837\pi$
$752$	3.71431	−	14.1061i	0.135447	−	0.514397i
$753$	2.78575	−	4.82506i	0.101518	−	0.175835i
$754$	−0.287881	+	0.127043i	−0.0104840	+	0.00462664i
$755$	4.98992	−	10.4846i	0.181602	−	0.381574i
$756$	−12.9366	−	24.7201i	−0.470499	−	0.899061i
$757$	−41.3717	+	7.29494i	−1.50368	+	0.265139i	−0.863996	−	0.503499i	$-0.832046\pi$
$757$	−41.3717	+	7.29494i	−1.50368	+	0.265139i	−0.639684	+	0.768638i	$0.720935\pi$
$758$	−19.3020	+	4.74534i	−0.701082	+	0.172358i
$759$	−7.35323			−0.266906
$760$	−10.7914	+	25.3682i	−0.391446	+	0.920201i
$761$	−29.8172			−1.08087			−0.540436	−	0.841385i	$-0.681741\pi$
$761$	−29.8172			−1.08087			−0.540436	+	0.841385i	$0.681741\pi$
$762$	−46.9189	+	11.5348i	−1.69969	+	0.417863i
$763$	−51.3031	+	9.04613i	−1.85730	+	0.327492i
$764$	18.1753	+	34.7305i	0.657559	+	1.25651i
$765$	7.22721	+	3.43963i	0.261300	+	0.124360i
$766$	13.9046	−	6.13617i	0.502395	−	0.221709i
$767$	0.297208	−	0.514779i	0.0107316	−	0.0185876i
$768$	−17.3963	−	29.5373i	−0.627734	−	1.06584i
$769$	18.4990	−	6.73309i	0.667092	−	0.242802i	0.0137966	−	0.999905i	$-0.495608\pi$
$769$	18.4990	−	6.73309i	0.667092	−	0.242802i	0.653295	+	0.757103i	$0.273386\pi$
$770$	−66.7499	−	13.7492i	−2.40550	−	0.495487i
$771$	−24.7313	+	14.2786i	−0.890678	+	0.514233i
$772$	−4.02383	−	5.22050i	−0.144821	−	0.187890i
$773$	−1.79313	+	10.1694i	−0.0644945	+	0.365767i	0.935430	+	0.353511i	$0.115012\pi$
$773$	−1.79313	+	10.1694i	−0.0644945	+	0.365767i	−0.999925	+	0.0122556i	$0.996099\pi$
$774$	−1.75503	+	6.04559i	−0.0630832	+	0.217304i
$775$	−15.3180	+	2.45294i	−0.550240	+	0.0881123i
$776$	9.51943	−	3.73755i	0.341728	−	0.134170i
$777$	−24.6240	+	67.6539i	−0.883381	+	2.42707i
$778$	−30.7011	+	20.5619i	−1.10069	+	0.737181i
$779$	−22.4611	−	12.4655i	−0.804751	−	0.446624i
$780$	−0.406437	+	0.0154218i	−0.0145528	+	0.000552189i
$781$	−9.23017	+	25.3597i	−0.330281	+	0.907441i
$782$	−1.68962	+	1.62097i	−0.0604207	+	0.0579657i
$783$	12.1282	+	10.1768i	0.433426	+	0.363688i
$784$	−57.1249	−	4.74855i	−2.04017	−	0.169591i
$785$	25.2265	−	6.54699i	0.900372	−	0.233672i
$786$	2.34220	+	35.1518i	0.0835435	+	1.25382i
$787$	−5.14937	+	2.97299i	−0.183555	+	0.105976i	−0.588962	−	0.808161i	$-0.700463\pi$
$787$	−5.14937	+	2.97299i	−0.183555	+	0.105976i	0.405407	+	0.914136i	$0.367130\pi$
$788$	−23.4947	−	0.974825i	−0.836963	−	0.0347267i
$789$	1.78760	+	4.91139i	0.0636403	+	0.174850i
$790$	−34.7588	−	0.994617i	−1.23666	−	0.0353869i
$791$	9.10662	−	15.7731i	0.323794	−	0.560828i
$792$	0.526001	+	20.9809i	0.0186906	+	0.745525i
$793$	−0.0341956	+	0.0286935i	−0.00121432	+	0.00101894i
$794$	−1.02008	+	9.40839i	−0.0362012	+	0.333891i
$795$	49.8215	−	34.3040i	1.76699	−	1.21664i
$796$	−15.8768	−	14.4852i	−0.562737	−	0.513416i
$797$	39.4183			1.39627			0.698134	−	0.715967i	$-0.254014\pi$
$797$	39.4183			1.39627			0.698134	+	0.715967i	$0.254014\pi$
$798$	43.2946	−	42.9671i	1.53261	−	1.52102i
$799$			8.20884i			0.290408i
$800$	−26.8757	+	8.81447i	−0.950201	+	0.311639i
$801$	−18.5457	+	3.27011i	−0.655281	+	0.115544i
$802$	4.68191	−	43.1822i	0.165324	−	1.52482i
$803$	35.3727	−	29.6812i	1.24827	−	1.04743i
$804$	−3.38155	−	2.14400i	−0.119258	−	0.0756131i
$805$	−0.721577	+	7.56149i	−0.0254322	+	0.266508i
$806$	−0.167142	−	0.0822004i	−0.00588732	−	0.00289538i
$807$	−29.6064	+	10.7759i	−1.04220	+	0.379328i
$808$	23.1220	+	37.8262i	0.813428	+	1.33072i
$809$	21.8002	+	37.7591i	0.766454	+	1.32754i	0.939474	+	0.342620i	$0.111314\pi$
$809$	21.8002	+	37.7591i	0.766454	+	1.32754i	−0.173020	+	0.984918i	$0.555352\pi$
$810$	16.8871	+	31.2830i	0.593351	+	1.09917i
$811$	−9.55817	+	54.2070i	−0.335633	+	1.90347i	0.0852642	+	0.996358i	$0.472827\pi$
$811$	−9.55817	+	54.2070i	−0.335633	+	1.90347i	−0.420897	+	0.907109i	$0.638285\pi$
$812$	46.1437	−	14.6590i	1.61932	−	0.514429i
$813$	−26.5177	−	22.2510i	−0.930016	−	0.780376i
$814$	−34.6486	+	33.2408i	−1.21443	+	1.16509i
$815$	−38.3345	+	3.04991i	−1.34280	+	0.106834i
$816$	13.6997	+	13.5815i	0.479584	+	0.475448i
$817$	12.2001	−	0.206659i	0.426829	−	0.00723009i
$818$	−5.19195	−	7.75212i	−0.181532	−	0.271047i
$819$	0.292958	+	0.106628i	0.0102368	+	0.00372589i
$820$	−5.55745	−	25.7630i	−0.194075	−	0.899684i
$821$	10.7563	+	9.02562i	0.375398	+	0.314996i	0.810893	−	0.585195i	$-0.198982\pi$
$821$	10.7563	+	9.02562i	0.375398	+	0.314996i	−0.435495	+	0.900191i	$0.643426\pi$
$822$	−1.42821	+	4.91979i	−0.0498146	+	0.171598i
$823$	−2.22380	+	12.6118i	−0.0775167	+	0.439619i	0.921205	+	0.389077i	$0.127206\pi$
$823$	−2.22380	+	12.6118i	−0.0775167	+	0.439619i	−0.998722	+	0.0505421i	$0.983905\pi$
$824$	9.18733	−	27.3567i	0.320056	−	0.953014i
$825$	49.0849	+	9.45422i	1.70892	+	0.329154i
$826$	−54.0010	+	73.8155i	−1.87893	+	2.56837i
$827$	16.2695	+	44.7002i	0.565747	+	1.55438i	0.811078	+	0.584938i	$0.198881\pi$
$827$	16.2695	+	44.7002i	0.565747	+	1.55438i	−0.245331	+	0.969439i	$0.578897\pi$
$828$	2.31850	−	0.310346i	0.0805735	−	0.0107853i
$829$	−45.4549	−	26.2434i	−1.57872	−	0.911472i	−0.995039	−	0.0994855i	$-0.968280\pi$
$829$	−45.4549	−	26.2434i	−1.57872	−	0.911472i	−0.583676	−	0.811986i	$-0.698386\pi$
$830$	19.8902	+	17.6836i	0.690399	+	0.613807i
$831$	34.2785	−	28.7631i	1.18911	−	0.997780i
$832$	−0.324538	−	0.100013i	−0.0112513	−	0.00346733i
$833$	31.7680	−	5.60156i	1.10070	−	0.194082i
$834$	−11.1238	+	2.73474i	−0.385185	+	0.0946964i
$835$	−17.6497	−	38.6412i	−0.610791	−	1.33723i
$836$	38.5564	−	12.9716i	1.33350	−	0.448631i
$837$			9.37158i			0.323929i
$838$	−10.5678	−	42.9853i	−0.365058	−	1.48490i
$839$	7.92515	+	44.9458i	0.273607	+	1.55170i	0.743353	+	0.668899i	$0.233234\pi$
$839$	7.92515	+	44.9458i	0.273607	+	1.55170i	−0.469746	+	0.882801i	$0.655655\pi$
$840$	62.4277	+	4.38177i	2.15396	+	0.151185i
$841$	1.16909	−	0.980982i	0.0403134	−	0.0338270i
$842$	13.3968	−	5.91206i	0.461684	−	0.203743i
$843$	9.71647	−	16.8294i	0.334653	−	0.579636i
$844$	21.3351	−	2.85585i	0.734386	−	0.0983022i
$845$	20.7131	−	20.3895i	0.712553	−	0.701420i
$846$	4.84211	−	6.61882i	0.166475	−	0.227560i
$847$	24.8808	+	43.0948i	0.854915	+	1.48076i
$848$	48.7275	−	13.2830i	1.67331	−	0.456139i
$849$	−69.9832	−	12.3399i	−2.40182	−	0.423505i
$850$	13.3628	−	8.64803i	0.458340	−	0.296625i
$851$	4.09956	+	3.43994i	0.140531	+	0.117920i
$852$	5.31130	−	24.2057i	0.181962	−	0.829274i
$853$	12.6265	−	34.6910i	0.432322	−	1.18780i	−0.512061	−	0.858949i	$-0.671118\pi$
$853$	12.6265	−	34.6910i	0.432322	−	1.18780i	0.944383	−	0.328847i	$-0.106660\pi$
$854$	5.70671	−	3.82205i	0.195280	−	0.130788i
$855$	−10.8597	+	11.0584i	−0.371393	+	0.378188i
$856$	−2.84090	+	0.574691i	−0.0971001	+	0.0196425i
$857$	−41.5768	−	15.1327i	−1.42024	−	0.516924i	−0.486120	−	0.873892i	$-0.661588\pi$
$857$	−41.5768	−	15.1327i	−1.42024	−	0.516924i	−0.934116	+	0.356969i	$0.883810\pi$
$858$	0.415500	+	0.433097i	0.0141849	+	0.0147857i
$859$	−2.99749	+	3.57227i	−0.102273	+	0.121884i	−0.814753	−	0.579808i	$-0.803127\pi$
$859$	−2.99749	+	3.57227i	−0.102273	+	0.121884i	0.712480	+	0.701692i	$0.247572\pi$
$860$	8.40481	+	9.27800i	0.286602	+	0.316377i
$861$	−10.1261	+	57.4281i	−0.345097	+	1.95714i
$862$	−2.06741	−	31.0278i	−0.0704164	−	1.05681i
$863$	0.999058	−	0.576806i	0.0340083	−	0.0196347i	−0.482899	−	0.875676i	$-0.660416\pi$
$863$	0.999058	−	0.576806i	0.0340083	−	0.0196347i	0.516908	+	0.856041i	$0.327083\pi$
$864$	2.69068	+	16.8735i	0.0915387	+	0.574047i
$865$	−32.0474	+	31.5467i	−1.08964	+	1.07262i
$866$	−41.2490	−	20.2862i	−1.40170	−	0.689354i
$867$	22.1408	+	12.7830i	0.751939	+	0.434132i
$868$	24.2041	+	15.3461i	0.821539	+	0.520880i
$869$	32.9825	+	39.3070i	1.11885	+	1.33340i
$870$	−33.7040	+	11.1863i	−1.14267	+	0.379252i
$871$	−0.0390636	+	0.00688797i	−0.00132362	+	0.000233390i
$872$	31.5477	+	4.75079i	1.06834	+	0.160882i
$873$	5.74964			0.194596
$874$	−1.90054	−	4.11645i	−0.0642868	−	0.139241i
$875$	14.5387	−	49.5473i	0.491498	−	1.67500i
$876$	−28.5785	+	31.3239i	−0.965578	+	1.05834i
$877$	−0.465040	−	2.63737i	−0.0157033	−	0.0890577i	0.975949	−	0.217999i	$-0.0699531\pi$
$877$	−0.465040	−	2.63737i	−0.0157033	−	0.0890577i	−0.991652	+	0.128942i	$0.958842\pi$
$878$	−19.4913	−	2.11329i	−0.657799	−	0.0713199i
$879$	27.0720	+	32.2631i	0.913115	+	1.08821i
$880$	36.0709	+	20.9963i	1.21595	+	0.707784i
$881$	−13.0069	+	22.5286i	−0.438213	+	0.759007i	−0.997552	−	0.0699321i	$-0.977722\pi$
$881$	−13.0069	+	22.5286i	−0.438213	+	0.759007i	0.559339	+	0.828939i	$0.311055\pi$
$882$	−28.9188	−	14.2223i	−0.973748	−	0.478889i
$883$	35.7463	−	13.0106i	1.20296	−	0.437841i	0.338703	−	0.940893i	$-0.390012\pi$
$883$	35.7463	−	13.0106i	1.20296	−	0.437841i	0.864256	+	0.503052i	$0.167790\pi$
$884$	0.190946	+	0.00792261i	0.00642222	+	0.000266466i
$885$	38.9087	−	54.6465i	1.30790	−	1.83692i
$886$	3.64045	+	54.6360i	0.122303	+	1.83553i
$887$	−11.0221	−	1.94349i	−0.370086	−	0.0652562i	−0.0144878	−	0.999895i	$-0.504612\pi$
$887$	−11.0221	−	1.94349i	−0.370086	−	0.0652562i	−0.355598	+	0.934639i	$0.615723\pi$
$888$	27.4858	−	34.4755i	0.922365	−	1.15692i
$889$	47.3401	−	56.4178i	1.58774	−	1.89219i
$890$	−13.8099	+	34.8105i	−0.462910	+	1.16685i
$891$	17.9417	−	49.2944i	0.601070	−	1.65143i
$892$	−10.2015	−	4.19976i	−0.341573	−	0.140618i
$893$	−15.0270	−	5.18290i	−0.502861	−	0.173439i
$894$	1.40865	+	2.10325i	0.0471121	+	0.0703433i
$895$	−19.6410	+	1.56265i	−0.656526	+	0.0522335i
$896$	47.9853	+	20.6813i	1.60307	+	0.690914i
$897$	0.0429981	−	0.0512432i	0.00143567	−	0.00171096i
$898$	9.55039	+	2.77247i	0.318701	+	0.0925184i
$899$	−16.0156	−	2.82398i	−0.534149	−	0.0941849i
$900$	−15.8757	−	0.909303i	−0.529188	−	0.0303101i
$901$	−24.6143	+	14.2111i	−0.820021	+	0.473440i
$902$	−22.9625	+	31.3882i	−0.764569	+	1.04511i
$903$	−9.47363	−	26.0286i	−0.315263	−	0.866177i
$904$	−8.36211	+	7.38157i	−0.278120	+	0.245507i
$905$	−4.85605	−	0.463402i	−0.161420	−	0.0154040i
$906$	14.3944	−	6.35230i	0.478222	−	0.211041i
$907$	−1.77559	−	2.11607i	−0.0589575	−	0.0702628i	0.735760	−	0.677243i	$-0.236825\pi$
$907$	−1.77559	−	2.11607i	−0.0589575	−	0.0702628i	−0.794717	+	0.606980i	$0.792381\pi$
$908$	9.93382	+	18.9822i	0.329665	+	0.629947i
$909$	4.32811	+	24.5459i	0.143554	+	0.814138i
$910$	0.486136	−	0.384767i	0.0161153	−	0.0127549i
$911$	10.4193			0.345207			0.172604	−	0.984991i	$-0.444782\pi$
$911$	10.4193			0.345207			0.172604	+	0.984991i	$0.444782\pi$
$912$	−33.5119	+	16.5034i	−1.10969	+	0.546483i
$913$		−	39.2727i		−	1.29974i
$914$	0.298112	+	1.21260i	0.00986068	+	0.0401091i
$915$	−4.14932	+	2.85697i	−0.137172	+	0.0944484i
$916$	21.7369	−	11.3754i	0.718207	−	0.375854i
$917$	−34.5182	−	41.1372i	−1.13989	−	1.35847i
$918$	−3.88217	−	8.79704i	−0.128131	−	0.290346i
$919$	31.4170	+	18.1386i	1.03635	+	0.598337i	0.918797	−	0.394729i	$-0.129162\pi$
$919$	31.4170	+	18.1386i	1.03635	+	0.598337i	0.117553	+	0.993067i	$0.462495\pi$
$920$	1.89317	−	4.24913i	0.0624159	−	0.140090i
$921$	13.3506	−	4.85923i	0.439918	−	0.160117i
$922$	33.2604	−	45.4646i	1.09537	−	1.49730i
$923$	−0.122753	−	0.212614i	−0.00404046	−	0.00699828i
$924$	−56.3752	−	73.1411i	−1.85461	−	2.40616i
$925$	−22.9429	−	28.2334i	−0.754357	−	0.928309i
$926$	−3.89389	+	13.4134i	−0.127961	+	0.440791i
$927$	10.4288	−	12.4285i	0.342526	−	0.408207i
$928$	−29.6467	−	0.486318i	−0.973201	−	0.0159642i
$929$	−40.6669	−	14.8015i	−1.33424	−	0.485623i	−0.426244	−	0.904608i	$-0.640164\pi$
$929$	−40.6669	−	14.8015i	−1.33424	−	0.485623i	−0.907993	+	0.418985i	$0.862386\pi$
$930$	−17.8963	−	11.0267i	−0.586843	−	0.361580i
$931$	−9.80352	+	61.6910i	−0.321297	+	2.02184i
$932$	19.0223	+	7.83107i	0.623096	+	0.256515i
$933$	−22.0622	−	8.03000i	−0.722285	−	0.262890i
$934$	4.22365	+	4.40253i	0.138202	+	0.144055i
$935$	−22.6386	−	6.25744i	−0.740361	−	0.204640i
$936$	−0.149288	−	0.119021i	−0.00487961	−	0.00389031i
$937$	19.1598	+	3.37839i	0.625923	+	0.110367i	0.477608	−	0.878573i	$-0.341504\pi$
$937$	19.1598	+	3.37839i	0.625923	+	0.110367i	0.148315	+	0.988940i	$0.452615\pi$
$938$	6.08972	−	0.405765i	0.198837	−	0.0132487i
$939$	−33.7214	−	58.4072i	−1.10046	−	1.90605i
$940$	−6.15496	−	15.1026i	−0.200753	−	0.492593i
$941$	−7.54167	−	20.7206i	−0.245851	−	0.675471i	−0.999828	−	0.0185696i	$-0.994089\pi$
$941$	−7.54167	−	20.7206i	−0.245851	−	0.675471i	0.753976	−	0.656902i	$-0.228133\pi$
$942$	31.6897	+	15.5850i	1.03251	+	0.507786i
$943$	3.75388	+	2.16730i	0.122243	+	0.0705770i
$944$	45.7419	−	32.3250i	1.48877	−	1.05209i
$945$	−28.1664	−	13.4052i	−0.916254	−	0.436072i
$946$	1.99122	−	18.3654i	0.0647401	−	0.597111i
$947$	5.00750	+	28.3990i	0.162722	+	0.922842i	0.951382	+	0.308013i	$0.0996640\pi$
$947$	5.00750	+	28.3990i	0.162722	+	0.922842i	−0.788660	+	0.614829i	$0.789225\pi$
$948$	−34.8079	−	31.7571i	−1.13051	−	1.03142i
$949$			0.420066i			0.0136359i
$950$	7.39403	+	29.9220i	0.239894	+	0.970799i
$951$			14.2179i			0.461046i
$952$	−29.0773	−	4.37877i	−0.942400	−	0.141917i
$953$	−5.94793	−	33.7324i	−0.192672	−	1.09270i	−0.915695	−	0.401875i	$-0.868359\pi$
$953$	−5.94793	−	33.7324i	−0.192672	−	1.09270i	0.723022	−	0.690825i	$-0.242752\pi$
$954$	28.2292	+	3.06067i	0.913955	+	0.0990929i
$955$	39.5725	+	18.8337i	1.28054	+	0.609443i
$956$	12.3161	−	19.4252i	0.398332	−	0.628254i
$957$	45.3814	+	26.2010i	1.46697	+	0.846957i
$958$	0.356485	−	0.724857i	0.0115175	−	0.0234191i
$959$	−2.67079	−	7.33792i	−0.0862442	−	0.236954i
$960$	−35.3880	−	14.7153i	−1.14214	−	0.474934i
$961$	10.6868	+	18.5101i	0.344736	+	0.597101i
$962$	−0.0290402	−	0.435835i	−0.000936292	−	0.0140519i
$963$	−1.60478	−	0.282966i	−0.0517132	−	0.00911844i
$964$	1.02537	−	0.325740i	0.0330248	−	0.0104914i
$965$	−7.10293	−	1.96329i	−0.228651	−	0.0632005i
$966$	−7.42721	+	7.12544i	−0.238967	+	0.229257i
$967$	42.4214	+	15.4401i	1.36418	+	0.496521i	0.917344	−	0.398095i	$-0.130329\pi$
$967$	42.4214	+	15.4401i	1.36418	+	0.496521i	0.446836	+	0.894616i	$0.352551\pi$
$968$	−6.04238	−	29.8697i	−0.194210	−	0.960047i
$969$	15.8724	−	13.7833i	0.509896	−	0.442784i
$970$	5.99788	−	9.73454i	0.192580	−	0.312557i
$971$	23.1763	+	8.43549i	0.743763	+	0.270708i	0.685979	−	0.727621i	$-0.259374\pi$
$971$	23.1763	+	8.43549i	0.743763	+	0.270708i	0.0577844	+	0.998329i	$0.481596\pi$
$972$	−6.43993	+	29.3493i	−0.206561	+	0.941380i
$973$	11.2236	−	13.3758i	0.359814	−	0.428809i
$974$	20.7299	+	6.01787i	0.664229	+	0.192825i
$975$	−0.352909	+	0.286779i	−0.0113021	+	0.00918426i
$976$	−4.05821	+	1.10626i	−0.129900	+	0.0354104i
$977$	17.3362	+	30.0272i	0.554634	+	0.960654i	0.997932	+	0.0642797i	$0.0204750\pi$
$977$	17.3362	+	30.0272i	0.554634	+	0.960654i	−0.443298	+	0.896374i	$0.646192\pi$
$978$	−42.0555	−	30.7664i	−1.34479	−	0.983802i
$979$	51.9289	−	18.9006i	1.65965	−	0.604065i
$980$	−54.2468	+	34.1253i	−1.73285	+	1.09009i
$981$	15.5334	+	8.96819i	0.495942	+	0.286332i
$982$	26.2549	−	11.5864i	0.837826	−	0.369736i
$983$	−0.409133	−	0.487585i	−0.0130493	−	0.0155516i	0.759480	−	0.650530i	$-0.225453\pi$
$983$	−0.409133	−	0.487585i	−0.0130493	−	0.0155516i	−0.772530	+	0.634979i	$0.781009\pi$
$984$	17.0754	−	31.3656i	0.544344	−	0.999897i
$985$	−21.6539	+	14.9096i	−0.689952	+	0.475058i
$986$	16.2035	−	3.98358i	0.516025	−	0.126863i
$987$			36.0843i			1.14858i
$988$	−0.135063	+	0.344543i	−0.00429692	+	0.0109614i
$989$	−2.05893			−0.0654701
$990$	14.5625	+	18.3991i	0.462828	+	0.584762i
$991$	5.37116	+	30.4613i	0.170620	+	0.967636i	0.943078	+	0.332570i	$0.107916\pi$
$991$	5.37116	+	30.4613i	0.170620	+	0.967636i	−0.772458	+	0.635066i	$0.780973\pi$
$992$	−11.0596	−	13.6282i	−0.351144	−	0.432696i
$993$	33.2055	+	39.5728i	1.05375	+	1.25581i
$994$	15.2510	+	34.5590i	0.483733	+	1.09615i
$995$	−23.9198	−	2.28262i	−0.758309	−	0.0723638i
$996$	4.78459	+	35.7442i	0.151606	+	1.13260i
$997$	1.00081	+	2.74970i	0.0316959	+	0.0870838i	0.954531	−	0.298111i	$-0.0963565\pi$
$997$	1.00081	+	2.74970i	0.0316959	+	0.0870838i	−0.922835	+	0.385195i	$0.874134\pi$
$998$	−1.87581	−	1.37228i	−0.0593778	−	0.0434388i
$999$	−19.0329	+	10.9886i	−0.602174	+	0.347665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.319.51	yes	336
4.3	odd	2	inner	380.2.bb.a.319.40	yes	336
5.4	even	2	inner	380.2.bb.a.319.6	yes	336
19.14	odd	18	inner	380.2.bb.a.299.17	yes	336
20.19	odd	2	inner	380.2.bb.a.319.17	yes	336
76.71	even	18	inner	380.2.bb.a.299.6	✓	336
95.14	odd	18	inner	380.2.bb.a.299.40	yes	336
380.299	even	18	inner	380.2.bb.a.299.51	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.299.6	✓	336	76.71	even	18	inner
380.2.bb.a.299.17	yes	336	19.14	odd	18	inner
380.2.bb.a.299.40	yes	336	95.14	odd	18	inner
380.2.bb.a.299.51	yes	336	380.299	even	18	inner
380.2.bb.a.319.6	yes	336	5.4	even	2	inner
380.2.bb.a.319.17	yes	336	20.19	odd	2	inner
380.2.bb.a.319.40	yes	336	4.3	odd	2	inner
380.2.bb.a.319.51	yes	336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37332 - 0.337626i) q^{2} +(2.10992 - 0.372036i) q^{3} +(1.77202 - 0.927337i) q^{4} +(0.960929 - 2.01906i) q^{5} +(2.77199 - 1.22329i) q^{6} +(-2.30925 + 3.99973i) q^{7} +(2.12045 - 1.87181i) q^{8} +(1.49427 - 0.543869i) q^{9} +O(q^{10})\)	\(q+(1.37332 - 0.337626i) q^{2} +(2.10992 - 0.372036i) q^{3} +(1.77202 - 0.927337i) q^{4} +(0.960929 - 2.01906i) q^{5} +(2.77199 - 1.22329i) q^{6} +(-2.30925 + 3.99973i) q^{7} +(2.12045 - 1.87181i) q^{8} +(1.49427 - 0.543869i) q^{9} +(0.637976 - 3.09725i) q^{10} +(-4.04114 + 2.33315i) q^{11} +(3.39381 - 2.61586i) q^{12} +(0.00737135 - 0.0418050i) q^{13} +(-1.82092 + 6.27258i) q^{14} +(1.27632 - 4.61756i) q^{15} +(2.28009 - 3.28652i) q^{16} +(-0.769892 + 2.11526i) q^{17} +(1.86848 - 1.25141i) q^{18} +(-3.38609 - 2.74489i) q^{19} +(-0.169568 - 4.46892i) q^{20} +(-3.38428 + 9.29823i) q^{21} +(-4.76205 + 4.56856i) q^{22} +(0.563436 + 0.472779i) q^{23} +(3.77761 - 4.73825i) q^{24} +(-3.15323 - 3.88035i) q^{25} +(-0.00399123 - 0.0599004i) q^{26} +(-2.61585 + 1.51026i) q^{27} +(-0.382925 + 9.22905i) q^{28} +(-1.79272 - 4.92545i) q^{29} +(0.193788 - 6.77231i) q^{30} +(1.55132 - 2.68696i) q^{31} +(2.02168 - 5.28326i) q^{32} +(-7.65846 + 6.42621i) q^{33} +(-0.343141 + 3.16486i) q^{34} +(5.85669 + 8.50597i) q^{35} +(2.14352 - 2.34944i) q^{36} +7.27599 q^{37} +(-5.57693 - 2.62638i) q^{38} -0.0909476i q^{39} +(-1.74169 - 6.08001i) q^{40} +(5.80377 - 1.02336i) q^{41} +(-1.50838 + 13.9121i) q^{42} +(-2.14439 + 1.79936i) q^{43} +(-4.99735 + 7.88189i) q^{44} +(0.337780 - 3.53964i) q^{45} +(0.933401 + 0.459046i) q^{46} +(3.42681 - 1.24726i) q^{47} +(3.58811 - 7.78255i) q^{48} +(-7.16524 - 12.4106i) q^{49} +(-5.64050 - 4.26436i) q^{50} +(-0.837457 + 4.74945i) q^{51} +(-0.0257052 - 0.0809149i) q^{52} +(9.67237 + 8.11608i) q^{53} +(-3.08249 + 2.95725i) q^{54} +(0.827533 + 10.4013i) q^{55} +(2.59009 + 12.8037i) q^{56} +(-8.16556 - 4.53175i) q^{57} +(-4.12493 - 6.15895i) q^{58} +(13.1583 + 4.78922i) q^{59} +(-2.02037 - 9.36597i) q^{60} +(-0.805551 - 0.675937i) q^{61} +(1.22327 - 4.21383i) q^{62} +(-1.27530 + 7.23260i) q^{63} +(0.992655 - 7.93818i) q^{64} +(-0.0773236 - 0.0550549i) q^{65} +(-8.34787 + 11.4109i) q^{66} +(-0.319592 - 0.878072i) q^{67} +(0.597298 + 4.46223i) q^{68} +(1.36470 + 0.787907i) q^{69} +(10.9149 + 9.70406i) q^{70} +(4.43036 - 3.71751i) q^{71} +(2.15051 - 3.95024i) q^{72} +(-9.74523 + 1.71835i) q^{73} +(9.99227 - 2.45656i) q^{74} +(-8.09669 - 7.01412i) q^{75} +(-8.54564 - 1.72395i) q^{76} -21.5513i q^{77} +(-0.0307063 - 0.124900i) q^{78} +(-1.90947 - 10.8291i) q^{79} +(-4.44467 - 7.76176i) q^{80} +(-8.61177 + 7.22613i) q^{81} +(7.62492 - 3.36490i) q^{82} +(-4.20812 + 7.28867i) q^{83} +(2.62559 + 19.6150i) q^{84} +(3.53103 + 3.58707i) q^{85} +(-2.33743 + 3.19510i) q^{86} +(-5.61493 - 9.72534i) q^{87} +(-4.20184 + 12.5116i) q^{88} +(-11.6628 - 2.05646i) q^{89} +(-0.731194 - 4.97510i) q^{90} +(0.150187 + 0.126022i) q^{91} +(1.43684 + 0.315278i) q^{92} +(2.27351 - 6.24642i) q^{93} +(4.28500 - 2.86986i) q^{94} +(-8.79590 + 4.19907i) q^{95} +(2.30003 - 11.8994i) q^{96} +(3.39769 + 1.23666i) q^{97} +(-14.0303 - 14.6245i) q^{98} +(-4.76962 + 5.68421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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