LMFDB - Embedded newform 230.2.l.a.203.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			203.10
Character	$\chi$	$=$	230.203
Dual form			230.2.l.a.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.936950 + 0.349464i) q^{2} +(0.783134 + 0.427624i) q^{3} +(0.755750 + 0.654861i) q^{4} +(2.12759 + 0.688005i) q^{5} +(0.584318 + 0.674339i) q^{6} +(-2.40639 + 3.21457i) q^{7} +(0.479249 + 0.877679i) q^{8} +(-1.19149 - 1.85399i) q^{9} +O(q^{10})$	\(q+(0.936950 + 0.349464i) q^{2} +(0.783134 + 0.427624i) q^{3} +(0.755750 + 0.654861i) q^{4} +(2.12759 + 0.688005i) q^{5} +(0.584318 + 0.674339i) q^{6} +(-2.40639 + 3.21457i) q^{7} +(0.479249 + 0.877679i) q^{8} +(-1.19149 - 1.85399i) q^{9} +(1.75301 + 1.38814i) q^{10} +(-3.79945 - 1.73515i) q^{11} +(0.311819 + 0.836020i) q^{12} +(3.70372 - 2.77257i) q^{13} +(-3.37805 + 2.17094i) q^{14} +(1.37198 + 1.44861i) q^{15} +(0.142315 + 0.989821i) q^{16} +(0.315585 - 4.41246i) q^{17} +(-0.468460 - 2.15347i) q^{18} +(0.989230 - 1.14163i) q^{19} +(1.15738 + 1.91324i) q^{20} +(-3.25915 + 1.48841i) q^{21} +(-2.95352 - 2.95352i) q^{22} +(2.75594 + 3.92489i) q^{23} +0.892278i q^{24} +(4.05330 + 2.92759i) q^{25} +(4.43911 - 1.30344i) q^{26} +(-0.331247 - 4.63144i) q^{27} +(-3.92373 + 0.853554i) q^{28} +(-2.10514 + 1.82412i) q^{29} +(0.779242 + 1.83673i) q^{30} +(-0.937468 - 0.275265i) q^{31} +(-0.212565 + 0.977147i) q^{32} +(-2.23349 - 2.98359i) q^{33} +(1.83768 - 4.02397i) q^{34} +(-7.33146 + 5.18368i) q^{35} +(0.313639 - 2.18141i) q^{36} +(-7.21355 - 1.56921i) q^{37} +(1.32582 - 0.723952i) q^{38} +(4.08612 - 0.587495i) q^{39} +(0.415799 + 2.19707i) q^{40} +(0.452129 + 0.290566i) q^{41} +(-3.57381 + 0.255604i) q^{42} +(2.15845 - 3.95291i) q^{43} +(-1.73515 - 3.79945i) q^{44} +(-1.25944 - 4.76428i) q^{45} +(1.21057 + 4.64053i) q^{46} +(2.48109 - 2.48109i) q^{47} +(-0.311819 + 0.836020i) q^{48} +(-2.57058 - 8.75459i) q^{49} +(2.77465 + 4.15948i) q^{50} +(2.13402 - 3.32059i) q^{51} +(4.61473 + 0.330052i) q^{52} +(-0.196980 - 0.147457i) q^{53} +(1.30816 - 4.45519i) q^{54} +(-6.88990 - 6.30574i) q^{55} +(-3.97462 - 0.571464i) q^{56} +(1.26289 - 0.471033i) q^{57} +(-2.60987 + 0.973433i) q^{58} +(-4.24460 - 0.610282i) q^{59} +(0.0882389 + 1.99324i) q^{60} +(-3.98577 + 13.5743i) q^{61} +(-0.782165 - 0.585521i) q^{62} +(8.82695 + 0.631316i) q^{63} +(-0.540641 + 0.841254i) q^{64} +(9.78754 - 3.35072i) q^{65} +(-1.05001 - 3.57600i) q^{66} +(-5.65963 + 15.1741i) q^{67} +(3.12805 - 3.12805i) q^{68} +(0.479894 + 4.25222i) q^{69} +(-8.68072 + 2.29476i) q^{70} +(-1.92905 - 4.22404i) q^{71} +(1.05619 - 1.93426i) q^{72} +(0.431145 - 0.0308361i) q^{73} +(-6.21035 - 3.99115i) q^{74} +(1.92237 + 4.02598i) q^{75} +(1.49522 - 0.214980i) q^{76} +(14.7208 - 8.03814i) q^{77} +(4.03380 + 0.877499i) q^{78} +(-1.61270 + 11.2166i) q^{79} +(-0.378214 + 2.20385i) q^{80} +(-1.02542 + 2.24536i) q^{81} +(0.322080 + 0.430249i) q^{82} +(1.74548 - 8.02384i) q^{83} +(-3.43780 - 1.00943i) q^{84} +(3.70723 - 9.17079i) q^{85} +(3.40376 - 2.94937i) q^{86} +(-2.42864 + 0.528319i) q^{87} +(-0.297978 - 4.16627i) q^{88} +(-16.8404 + 4.94480i) q^{89} +(0.484909 - 4.90402i) q^{90} +18.5777i q^{91} +(-0.487458 + 4.77099i) q^{92} +(-0.616453 - 0.616453i) q^{93} +(3.19171 - 1.45760i) q^{94} +(2.89013 - 1.74833i) q^{95} +(-0.584318 + 0.674339i) q^{96} +(-0.489792 - 2.25154i) q^{97} +(0.650911 - 9.10093i) q^{98} +(1.31004 + 9.11155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	0.936950	+	0.349464i	0.662524	+	0.247108i
$2$	0.936950	+	0.349464i	0.662524	+	0.247108i
$3$	0.783134	+	0.427624i	0.452143	+	0.246889i	0.689149	−	0.724620i	$-0.257984\pi$
$3$	0.783134	+	0.427624i	0.452143	+	0.246889i	−0.237007	+	0.971508i	$0.576166\pi$
$4$	0.755750	+	0.654861i	0.377875	+	0.327430i
$5$	2.12759	+	0.688005i	0.951488	+	0.307685i
$5$	2.12759	+	0.688005i	0.951488	+	0.307685i
$6$	0.584318	+	0.674339i	0.238547	+	0.275298i
$7$	−2.40639	+	3.21457i	−0.909532	+	1.21499i	0.0665927	+	0.997780i	$0.478787\pi$
$7$	−2.40639	+	3.21457i	−0.909532	+	1.21499i	−0.976124	+	0.217212i	$0.930304\pi$
$8$	0.479249	+	0.877679i	0.169440	+	0.310306i
$9$	−1.19149	−	1.85399i	−0.397162	−	0.617996i
$10$	1.75301	+	1.38814i	0.554352	+	0.438969i
$11$	−3.79945	−	1.73515i	−1.14558	−	0.523168i	−0.250077	−	0.968226i	$-0.580456\pi$
$11$	−3.79945	−	1.73515i	−1.14558	−	0.523168i	−0.895502	+	0.445058i	$0.853183\pi$
$12$	0.311819	+	0.836020i	0.0900145	+	0.241338i
$13$	3.70372	−	2.77257i	1.02723	−	0.768972i	0.0539344	−	0.998544i	$-0.482824\pi$
$13$	3.70372	−	2.77257i	1.02723	−	0.768972i	0.973291	+	0.229573i	$0.0737329\pi$
$14$	−3.37805	+	2.17094i	−0.902821	+	0.580208i
$15$	1.37198	+	1.44861i	0.354244	+	0.374029i
$16$	0.142315	+	0.989821i	0.0355787	+	0.247455i
$17$	0.315585	−	4.41246i	0.0765407	−	1.07018i	−0.803508	−	0.595294i	$-0.797035\pi$
$17$	0.315585	−	4.41246i	0.0765407	−	1.07018i	0.880048	−	0.474884i	$-0.157510\pi$
$18$	−0.468460	−	2.15347i	−0.110417	−	0.507579i
$19$	0.989230	−	1.14163i	0.226945	−	0.261908i	−0.630845	−	0.775909i	$-0.717292\pi$
$19$	0.989230	−	1.14163i	0.226945	−	0.261908i	0.857790	+	0.514000i	$0.171837\pi$
$20$	1.15738	+	1.91324i	0.258798	+	0.427813i
$21$	−3.25915	+	1.48841i	−0.711206	+	0.324797i
$22$	−2.95352	−	2.95352i	−0.629694	−	0.629694i
$23$	2.75594	+	3.92489i	0.574653	+	0.818397i
$23$	2.75594	+	3.92489i	0.574653	+	0.818397i
$24$			0.892278i			0.182136i
$25$	4.05330	+	2.92759i	0.810660	+	0.585517i
$26$	4.43911	−	1.30344i	0.870581	−	0.255626i
$27$	−0.331247	−	4.63144i	−0.0637486	−	0.891322i
$28$	−3.92373	+	0.853554i	−0.741514	+	0.161307i
$29$	−2.10514	+	1.82412i	−0.390915	+	0.338730i	−0.828038	−	0.560672i	$-0.810543\pi$
$29$	−2.10514	+	1.82412i	−0.390915	+	0.338730i	0.437123	+	0.899402i	$0.355997\pi$
$30$	0.779242	+	1.83673i	0.142270	+	0.335340i
$31$	−0.937468	−	0.275265i	−0.168374	−	0.0494391i	0.196459	−	0.980512i	$-0.437056\pi$
$31$	−0.937468	−	0.275265i	−0.168374	−	0.0494391i	−0.364833	+	0.931073i	$0.618874\pi$
$32$	−0.212565	+	0.977147i	−0.0375766	+	0.172737i
$33$	−2.23349	−	2.98359i	−0.388801	−	0.519377i
$34$	1.83768	−	4.02397i	0.315160	−	0.690104i
$35$	−7.33146	+	5.18368i	−1.23924	+	0.876202i
$36$	0.313639	−	2.18141i	0.0522732	−	0.363568i
$37$	−7.21355	−	1.56921i	−1.18590	−	0.257977i	−0.423995	−	0.905665i	$-0.639373\pi$
$37$	−7.21355	−	1.56921i	−1.18590	−	0.257977i	−0.761906	+	0.647688i	$0.775736\pi$
$38$	1.32582	−	0.723952i	0.215076	−	0.117440i
$39$	4.08612	−	0.587495i	0.654303	−	0.0940746i
$40$	0.415799	+	2.19707i	0.0657437	+	0.347387i
$41$	0.452129	+	0.290566i	0.0706108	+	0.0453788i	0.575470	−	0.817823i	$-0.304819\pi$
$41$	0.452129	+	0.290566i	0.0706108	+	0.0453788i	−0.504859	+	0.863202i	$0.668456\pi$
$42$	−3.57381	+	0.255604i	−0.551451	+	0.0394405i
$43$	2.15845	−	3.95291i	0.329161	−	0.602813i	−0.659722	−	0.751510i	$-0.729326\pi$
$43$	2.15845	−	3.95291i	0.329161	−	0.602813i	0.988883	+	0.148697i	$0.0475079\pi$
$44$	−1.73515	−	3.79945i	−0.261584	−	0.572789i
$45$	−1.25944	−	4.76428i	−0.187747	−	0.710217i
$46$	1.21057	+	4.64053i	0.178488	+	0.684209i
$47$	2.48109	−	2.48109i	0.361904	−	0.361904i	−0.502610	−	0.864514i	$-0.667627\pi$
$47$	2.48109	−	2.48109i	0.361904	−	0.361904i	0.864514	+	0.502610i	$0.167627\pi$
$48$	−0.311819	+	0.836020i	−0.0450072	+	0.120669i
$49$	−2.57058	−	8.75459i	−0.367225	−	1.25066i
$50$	2.77465	+	4.15948i	0.392395	+	0.588240i
$51$	2.13402	−	3.32059i	0.298822	−	0.464976i
$52$	4.61473	+	0.330052i	0.639947	+	0.0457699i
$53$	−0.196980	−	0.147457i	−0.0270572	−	0.0202548i	0.585663	−	0.810554i	$-0.300834\pi$
$53$	−0.196980	−	0.147457i	−0.0270572	−	0.0202548i	−0.612721	+	0.790300i	$0.709925\pi$
$54$	1.30816	−	4.45519i	0.178018	−	0.606274i
$55$	−6.88990	−	6.30574i	−0.929034	−	0.850266i
$56$	−3.97462	−	0.571464i	−0.531131	−	0.0763651i
$57$	1.26289	−	0.471033i	0.167274	−	0.0623899i
$58$	−2.60987	+	0.973433i	−0.342693	+	0.127818i
$59$	−4.24460	−	0.610282i	−0.552600	−	0.0794519i	−0.139642	−	0.990202i	$-0.544595\pi$
$59$	−4.24460	−	0.610282i	−0.552600	−	0.0794519i	−0.412958	+	0.910750i	$0.635504\pi$
$60$	0.0882389	+	1.99324i	0.0113916	+	0.257327i
$61$	−3.98577	+	13.5743i	−0.510326	+	1.73801i	0.151602	+	0.988442i	$0.451557\pi$
$61$	−3.98577	+	13.5743i	−0.510326	+	1.73801i	−0.661928	+	0.749568i	$0.730261\pi$
$62$	−0.782165	−	0.585521i	−0.0993350	−	0.0743613i
$63$	8.82695	+	0.631316i	1.11209	+	0.0795384i
$64$	−0.540641	+	0.841254i	−0.0675801	+	0.105157i
$65$	9.78754	−	3.35072i	1.21399	−	0.415606i
$66$	−1.05001	−	3.57600i	−0.129247	−	0.440175i
$67$	−5.65963	+	15.1741i	−0.691434	+	1.85381i	−0.208881	+	0.977941i	$0.566982\pi$
$67$	−5.65963	+	15.1741i	−0.691434	+	1.85381i	−0.482554	+	0.875866i	$0.660291\pi$
$68$	3.12805	−	3.12805i	0.379332	−	0.379332i
$69$	0.479894	+	4.25222i	0.0577724	+	0.511907i
$70$	−8.68072	+	2.29476i	−1.03754	+	0.274276i
$71$	−1.92905	−	4.22404i	−0.228937	−	0.501301i	0.759948	−	0.649983i	$-0.225224\pi$
$71$	−1.92905	−	4.22404i	−0.228937	−	0.501301i	−0.988885	+	0.148682i	$0.952497\pi$
$72$	1.05619	−	1.93426i	0.124473	−	0.227955i
$73$	0.431145	−	0.0308361i	0.0504617	−	0.00360909i	−0.0460855	−	0.998937i	$-0.514675\pi$
$73$	0.431145	−	0.0308361i	0.0504617	−	0.00360909i	0.0965472	+	0.995328i	$0.469220\pi$
$74$	−6.21035	−	3.99115i	−0.721939	−	0.463962i
$75$	1.92237	+	4.02598i	0.221976	+	0.464880i
$76$	1.49522	−	0.214980i	0.171514	−	0.0246599i
$77$	14.7208	−	8.03814i	1.67759	−	0.916031i
$78$	4.03380	+	0.877499i	0.456738	+	0.0993572i
$79$	−1.61270	+	11.2166i	−0.181443	+	1.26196i	0.671911	+	0.740632i	$0.265474\pi$
$79$	−1.61270	+	11.2166i	−0.181443	+	1.26196i	−0.853354	+	0.521332i	$0.825435\pi$
$80$	−0.378214	+	2.20385i	−0.0422856	+	0.246398i
$81$	−1.02542	+	2.24536i	−0.113936	+	0.249484i
$82$	0.322080	+	0.430249i	0.0355678	+	0.0475130i
$83$	1.74548	−	8.02384i	0.191591	−	0.880731i	−0.776497	−	0.630121i	$-0.783005\pi$
$83$	1.74548	−	8.02384i	0.191591	−	0.880731i	0.968088	−	0.250610i	$-0.0806311\pi$
$84$	−3.43780	−	1.00943i	−0.375095	−	0.110138i
$85$	3.70723	−	9.17079i	0.402105	−	0.994712i
$86$	3.40376	−	2.94937i	0.367037	−	0.318039i
$87$	−2.42864	+	0.528319i	−0.260378	+	0.0566417i
$88$	−0.297978	−	4.16627i	−0.0317645	−	0.444126i
$89$	−16.8404	+	4.94480i	−1.78508	+	0.524148i	−0.995937	−	0.0900563i	$-0.971295\pi$
$89$	−16.8404	+	4.94480i	−1.78508	+	0.524148i	−0.789147	+	0.614204i	$0.789477\pi$
$90$	0.484909	−	4.90402i	0.0511139	−	0.516929i
$91$			18.5777i			1.94748i
$92$	−0.487458	+	4.77099i	−0.0508210	+	0.497411i
$93$	−0.616453	−	0.616453i	−0.0639232	−	0.0639232i
$94$	3.19171	−	1.45760i	0.329199	−	0.150340i
$95$	2.89013	−	1.74833i	0.296521	−	0.179375i
$96$	−0.584318	+	0.674339i	−0.0596367	+	0.0688244i
$97$	−0.489792	−	2.25154i	−0.0497308	−	0.228609i	0.945573	−	0.325410i	$-0.105502\pi$
$97$	−0.489792	−	2.25154i	−0.0497308	−	0.228609i	−0.995304	+	0.0968014i	$0.969139\pi$
$98$	0.650911	−	9.10093i	0.0657520	−	0.919333i
$99$	1.31004	+	9.11155i	0.131664	+	0.915745i
$100$	1.14612	+	4.86687i	0.114612	+	0.486687i
$101$	7.75976	−	4.98689i	0.772125	−	0.496215i	−0.0942867	−	0.995545i	$-0.530057\pi$
$101$	7.75976	−	4.98689i	0.772125	−	0.496215i	0.866412	+	0.499331i	$0.166421\pi$
$102$	3.15989	−	2.36547i	0.312876	−	0.234216i
$103$	1.99253	+	5.34218i	0.196330	+	0.526381i	0.997390	−	0.0722033i	$-0.0230031\pi$
$103$	1.99253	+	5.34218i	0.196330	+	0.526381i	−0.801060	+	0.598584i	$0.795730\pi$
$104$	4.20843	+	1.92192i	0.412670	+	0.188460i
$105$	−7.95818	+	0.924408i	−0.776639	+	0.0902130i
$106$	−0.133029	−	0.206997i	−0.0129209	−	0.0201053i
$107$	−7.84829	−	14.3731i	−0.758722	−	1.38950i	−0.915687	−	0.401892i	$-0.868353\pi$
$107$	−7.84829	−	14.3731i	−0.758722	−	1.38950i	0.156965	−	0.987604i	$-0.449829\pi$
$108$	2.78261	−	3.71713i	0.267757	−	0.357681i
$109$	−2.03973	−	2.35397i	−0.195370	−	0.225469i	0.649609	−	0.760269i	$-0.274933\pi$
$109$	−2.03973	−	2.35397i	−0.195370	−	0.225469i	−0.844979	+	0.534799i	$0.820387\pi$
$110$	−4.25186	−	8.31593i	−0.405399	−	0.792893i
$111$	−4.97815	−	4.31359i	−0.472505	−	0.409428i
$112$	−3.52431	−	1.92442i	−0.333016	−	0.181841i
$113$	17.2369	+	6.42904i	1.62151	+	0.604793i	0.985918	−	0.167229i	$-0.0534819\pi$
$113$	17.2369	+	6.42904i	1.62151	+	0.604793i	0.635596	+	0.772022i	$0.280755\pi$
$114$	1.34787			0.126240
$115$	3.16317	+	10.2467i	0.294967	+	0.955507i
$116$	−2.78550			−0.258627
$117$	−9.55323	−	3.56317i	−0.883196	−	0.329415i
$118$	−3.76371	−	2.05514i	−0.346477	−	0.189191i
$119$	13.4247	+	11.6326i	1.23064	+	1.06636i
$120$	−0.613892	+	1.89840i	−0.0560404	+	0.173300i
$121$	4.22163	+	4.87202i	0.383785	+	0.442911i
$122$	−8.47819	+	11.3255i	−0.767580	+	1.02537i
$123$	0.229825	+	0.420893i	0.0207226	+	0.0379507i
$124$	−0.528230	−	0.821943i	−0.0474365	−	0.0738126i
$125$	6.60958	+	9.01740i	0.591178	+	0.806541i
$126$	8.04979	+	3.67622i	0.717132	+	0.327503i
$127$	2.07162	+	5.55422i	0.183826	+	0.492858i	0.995875	−	0.0907316i	$-0.0289205\pi$
$127$	2.07162	+	5.55422i	0.183826	+	0.492858i	−0.812049	+	0.583589i	$0.801648\pi$
$128$	−0.800541	+	0.599278i	−0.0707585	+	0.0529692i
$129$	3.38071	−	2.17265i	0.297655	−	0.191291i
$130$	10.3414	+	0.280938i	0.907000	+	0.0246399i
$131$	0.984884	+	6.85002i	0.0860497	+	0.598489i	0.986529	+	0.163589i	$0.0523071\pi$
$131$	0.984884	+	6.85002i	0.0860497	+	0.598489i	−0.900479	+	0.434900i	$0.856784\pi$
$132$	0.265879	−	3.71747i	0.0231418	−	0.323565i
$133$	1.28938	+	5.92717i	0.111803	+	0.513950i
$134$	−10.6056	+	12.2395i	−0.916183	+	1.05733i
$135$	2.48169	−	10.0817i	0.213590	−	0.867697i
$136$	4.02397	−	1.83768i	0.345052	−	0.157580i
$137$	7.94223	+	7.94223i	0.678550	+	0.678550i	0.959672	−	0.281122i	$-0.0907065\pi$
$137$	7.94223	+	7.94223i	0.678550	+	0.678550i	−0.281122	+	0.959672i	$0.590707\pi$
$138$	−1.03636	+	4.15182i	−0.0882211	+	0.353427i
$139$			12.8162i			1.08706i	0.839391	+	0.543528i	$0.182912\pi$
$139$			12.8162i			1.08706i	−0.839391	+	0.543528i	$0.817088\pi$
$140$	−8.93534	−	0.883526i	−0.755174	−	0.0746715i
$141$	3.00400	−	0.882053i	0.252982	−	0.0742823i
$142$	−0.331276	−	4.63185i	−0.0278001	−	0.388696i
$143$	−18.8829	+	4.10773i	−1.57907	+	0.343506i
$144$	1.66555	−	1.44321i	0.138796	−	0.120267i
$145$	−5.73388	+	2.43263i	−0.476173	+	0.202019i
$146$	0.414737	+	0.121778i	0.0343239	+	0.0100784i
$147$	1.73056	−	7.95525i	0.142734	−	0.656138i
$148$	−4.42402	−	5.90981i	−0.363653	−	0.485783i
$149$	7.74279	−	16.9543i	0.634314	−	1.38895i	−0.270322	−	0.962770i	$-0.587130\pi$
$149$	7.74279	−	16.9543i	0.634314	−	1.38895i	0.904636	−	0.426184i	$-0.140142\pi$
$150$	0.394230	+	4.44394i	0.0321888	+	0.362846i
$151$	2.89000	−	20.1004i	0.235185	−	1.63575i	−0.439927	−	0.898033i	$-0.644996\pi$
$151$	2.89000	−	20.1004i	0.235185	−	1.63575i	0.675113	−	0.737715i	$-0.264095\pi$
$152$	1.47607	+	0.321100i	0.119725	+	0.0260447i
$153$	−8.55666	+	4.67229i	−0.691765	+	0.377732i
$154$	16.6016	−	2.38696i	1.33780	−	0.192346i
$155$	−1.80517	−	1.23063i	−0.144994	−	0.0988470i
$156$	3.47281	+	2.23184i	0.278047	+	0.178690i
$157$	22.1257	−	1.58246i	1.76583	−	0.126294i	0.849721	−	0.527232i	$-0.176770\pi$
$157$	22.1257	−	1.58246i	1.76583	−	0.126294i	0.916105	+	0.400938i	$0.131316\pi$
$158$	−5.43081	+	9.94579i	−0.432052	+	0.791245i
$159$	−0.0912053	−	0.199712i	−0.00723305	−	0.0158382i
$160$	−1.12453	+	1.93272i	−0.0889022	+	0.152795i
$161$	−19.2487	−	0.585690i	−1.51701	−	0.0461588i
$162$	−1.74544	+	1.74544i	−0.137135	+	0.137135i
$163$	−0.240670	+	0.645260i	−0.0188507	+	0.0505407i	−0.946034	−	0.324067i	$-0.894950\pi$
$163$	−0.240670	+	0.645260i	−0.0188507	+	0.0505407i	0.927184	+	0.374607i	$0.122222\pi$
$164$	0.151416	+	0.515677i	0.0118236	+	0.0402676i
$165$	−2.69923	−	7.88452i	−0.210135	−	0.613809i
$166$	4.43947	−	6.90795i	0.344570	−	0.536161i
$167$	20.7694	+	1.48546i	1.60719	+	0.114948i	0.845854	−	0.533415i	$-0.179091\pi$
$167$	20.7694	+	1.48546i	1.60719	+	0.114948i	0.761332	+	0.648363i	$0.224546\pi$
$168$	−2.86829	−	2.14717i	−0.221293	−	0.165658i
$169$	2.36786	−	8.06419i	0.182143	−	0.620322i
$170$	6.67835	−	7.29702i	0.512206	−	0.559656i
$171$	−3.29523	−	0.473782i	−0.251992	−	0.0362310i
$172$	4.21985	−	1.57392i	0.321761	−	0.120011i
$173$	20.0156	−	7.46544i	1.52176	−	0.567587i	0.556952	−	0.830544i	$-0.311971\pi$
$173$	20.0156	−	7.46544i	1.52176	−	0.567587i	0.964807	+	0.262957i	$0.0846979\pi$
$174$	−2.46014	−	0.353715i	−0.186503	−	0.0268151i
$175$	−19.1648	+	5.98467i	−1.44872	+	0.452399i
$176$	1.17677	−	4.00772i	0.0887026	−	0.302093i
$177$	−3.06312	−	2.29302i	−0.230238	−	0.172354i
$178$	−17.5067	−	1.25210i	−1.31218	−	0.0938491i
$179$	0.373996	−	0.581949i	0.0279537	−	0.0434969i	−0.826995	−	0.562209i	$-0.809952\pi$
$179$	0.373996	−	0.581949i	0.0279537	−	0.0434969i	0.854949	+	0.518712i	$0.173588\pi$
$180$	2.16811	−	4.42536i	0.161602	−	0.329847i
$181$	−1.05494	−	3.59280i	−0.0784131	−	0.267050i	0.910950	−	0.412516i	$-0.135350\pi$
$181$	−1.05494	−	3.59280i	−0.0784131	−	0.267050i	−0.989363	+	0.145466i	$0.953532\pi$
$182$	−6.49225	+	17.4064i	−0.481238	+	1.29025i
$183$	−8.92608	+	8.92608i	−0.659835	+	0.659835i
$184$	−2.12402	+	4.29983i	−0.156584	+	0.316988i
$185$	−14.2679	−	8.30160i	−1.04900	−	0.610346i
$186$	−0.362157	−	0.793014i	−0.0265547	−	0.0581466i
$187$	−8.85534	+	16.2173i	−0.647567	+	1.18593i
$188$	3.49985	−	0.250314i	0.255253	−	0.0182560i
$189$	15.6852	+	10.0803i	1.14093	+	0.733231i
$190$	3.31888	−	0.628105i	0.240777	−	0.0455675i
$191$	−5.29798	+	0.761734i	−0.383348	+	0.0551172i	−0.331295	−	0.943527i	$-0.607486\pi$
$191$	−5.29798	+	0.761734i	−0.383348	+	0.0551172i	−0.0520531	+	0.998644i	$0.516577\pi$
$192$	−0.783134	+	0.427624i	−0.0565178	+	0.0308611i
$193$	−12.2408	−	2.66282i	−0.881110	−	0.191674i	−0.250820	−	0.968034i	$-0.580700\pi$
$193$	−12.2408	−	2.66282i	−0.881110	−	0.191674i	−0.630290	+	0.776360i	$0.717064\pi$
$194$	0.327921	−	2.28074i	0.0235434	−	0.163748i
$195$	9.09780	+	1.56132i	0.651507	+	0.111808i
$196$	3.79032	−	8.29965i	0.270737	−	0.592832i
$197$	−5.04664	−	6.74152i	−0.359558	−	0.480314i	0.583890	−	0.811833i	$-0.301530\pi$
$197$	−5.04664	−	6.74152i	−0.359558	−	0.480314i	−0.943449	+	0.331519i	$0.892439\pi$
$198$	−1.95672	+	8.99488i	−0.139058	+	0.639238i
$199$	2.56764	+	0.753926i	0.182015	+	0.0534444i	0.371470	−	0.928445i	$-0.378854\pi$
$199$	2.56764	+	0.753926i	0.182015	+	0.0534444i	−0.189455	+	0.981889i	$0.560672\pi$
$200$	−0.626942	+	4.96054i	−0.0443315	+	0.350763i
$201$	−10.9210	+	9.46314i	−0.770311	+	0.667478i
$202$	9.01324	−	1.96071i	0.634170	−	0.137955i
$203$	−0.797940	−	11.1567i	−0.0560044	−	0.783044i
$204$	3.78731	−	1.11205i	0.265165	−	0.0778594i
$205$	0.762036	+	0.929273i	0.0532229	+	0.0649032i
$206$			5.70167i			0.397254i
$207$	3.99304	−	9.78593i	0.277536	−	0.680169i
$208$	3.27144	+	3.27144i	0.226834	+	0.226834i
$209$	−5.73944	+	2.62112i	−0.397006	+	0.181306i
$210$	−7.77946	−	1.91498i	−0.536834	−	0.132146i
$211$	1.71134	−	1.97500i	0.117814	−	0.135964i	−0.693779	−	0.720188i	$-0.744055\pi$
$211$	1.71134	−	1.97500i	0.117814	−	0.135964i	0.811593	+	0.584224i	$0.198601\pi$
$212$	−0.0523034	−	0.240435i	−0.00359221	−	0.0165131i
$213$	0.295591	−	4.13290i	0.0202535	−	0.283182i
$214$	−2.33058	−	16.2095i	−0.159315	−	1.10806i
$215$	7.31192	−	6.92515i	0.498669	−	0.472291i
$216$	3.90617	−	2.51034i	0.265781	−	0.170807i
$217$	3.14078	−	2.35116i	0.213210	−	0.159607i
$218$	−1.08849	−	2.91836i	−0.0737221	−	0.197657i
$219$	0.350830	+	0.160219i	0.0237069	+	0.0108266i
$220$	−1.07766	−	9.27748i	−0.0726555	−	0.625488i
$221$	−11.0650	−	17.2175i	−0.744312	−	1.15817i
$222$	−3.15683	−	5.78130i	−0.211872	−	0.388015i
$223$	−11.3723	+	15.1917i	−0.761548	+	1.01731i	0.237398	+	0.971412i	$0.423705\pi$
$223$	−11.3723	+	15.1917i	−0.761548	+	1.01731i	−0.998946	+	0.0458965i	$0.985386\pi$
$224$	−2.62959	−	3.03471i	−0.175697	−	0.202765i
$225$	0.598262	−	11.0029i	0.0398841	−	0.733530i
$226$	13.9034	+	12.0474i	0.924841	+	0.801380i
$227$	1.20173	+	0.656192i	0.0797613	+	0.0435530i	0.518635	−	0.854996i	$-0.326440\pi$
$227$	1.20173	+	0.656192i	0.0797613	+	0.0435530i	−0.438873	+	0.898549i	$0.644622\pi$
$228$	1.26289	+	0.471033i	0.0836369	+	0.0311949i
$229$	−26.7915			−1.77043			−0.885215	−	0.465182i	$-0.845989\pi$
$229$	−26.7915			−1.77043			−0.885215	+	0.465182i	$0.845989\pi$
$230$	−0.617112	+	10.7060i	−0.0406911	+	0.705935i
$231$	14.9656			0.984666
$232$	−2.60987	−	0.973433i	−0.171347	−	0.0639090i
$233$	1.66231	+	0.907687i	0.108901	+	0.0594646i	0.532776	−	0.846256i	$-0.321149\pi$
$233$	1.66231	+	0.907687i	0.108901	+	0.0594646i	−0.423875	+	0.905721i	$0.639330\pi$
$234$	−7.70569	−	6.67702i	−0.503737	−	0.436491i
$235$	6.98574	−	3.57174i	0.455700	−	0.232995i
$236$	−2.80821	−	3.24084i	−0.182799	−	0.210961i
$237$	−6.05944	+	8.09446i	−0.393603	+	0.525792i
$238$	8.51312	+	15.5906i	0.551823	+	1.01059i
$239$	−12.4151	−	19.3182i	−0.803063	−	1.24959i	−0.964860	−	0.262766i	$-0.915365\pi$
$239$	−12.4151	−	19.3182i	−0.803063	−	1.24959i	0.161797	−	0.986824i	$-0.448271\pi$
$240$	−1.23861	+	1.56418i	−0.0799519	+	0.100967i
$241$	−4.48437	−	2.04795i	−0.288864	−	0.131920i	0.265713	−	0.964052i	$-0.414393\pi$
$241$	−4.48437	−	2.04795i	−0.288864	−	0.131920i	−0.554577	+	0.832132i	$0.687120\pi$
$242$	2.25286	+	6.04015i	0.144819	+	0.388276i
$243$	−12.9146	+	9.66775i	−0.828472	+	0.620187i
$244$	−11.9015	+	7.64864i	−0.761916	+	0.489654i
$245$	0.554052	−	20.3948i	0.0353971	−	1.30297i
$246$	0.0682474	+	0.474671i	0.00435130	+	0.0302639i
$247$	0.498575	−	6.97099i	0.0317236	−	0.443553i
$248$	−0.207686	−	0.954716i	−0.0131881	−	0.0606246i
$249$	4.79813	−	5.53733i	0.304069	−	0.350914i
$250$	3.04158	+	10.7587i	0.192367	+	0.680437i
$251$	10.1667	−	4.64300i	0.641720	−	0.293064i	−0.0678536	−	0.997695i	$-0.521615\pi$
$251$	10.1667	−	4.64300i	0.641720	−	0.293064i	0.709573	+	0.704632i	$0.248888\pi$
$252$	6.25754	+	6.25754i	0.394188	+	0.394188i
$253$	−3.66078	−	19.6944i	−0.230151	−	1.23818i
$254$			5.92799i			0.371955i
$255$	6.82490	−	5.59666i	0.427392	−	0.350476i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	1.25891	+	17.6019i	0.0785289	+	1.09798i	0.872044	+	0.489427i	$0.162794\pi$
$257$	1.25891	+	17.6019i	0.0785289	+	1.09798i	−0.793516	+	0.608550i	$0.791751\pi$
$258$	3.92682	−	0.854227i	0.244473	−	0.0531819i
$259$	22.4030	−	19.4123i	1.39205	−	1.20622i
$260$	9.59118	+	3.87717i	0.594820	+	0.240452i
$261$	5.89013	+	1.72950i	0.364590	+	0.107053i
$262$	−1.47105	+	6.76230i	−0.0908817	+	0.417776i
$263$	−11.3873	−	15.2117i	−0.702172	−	0.937991i	0.297689	−	0.954663i	$-0.403784\pi$
$263$	−11.3873	−	15.2117i	−0.702172	−	0.937991i	−0.999861	+	0.0166713i	$0.994693\pi$
$264$	1.54824	−	3.39017i	0.0952875	−	0.208651i
$265$	−0.317641	−	0.449252i	−0.0195125	−	0.0275973i
$266$	−0.863252	+	6.00405i	−0.0529294	+	0.368132i
$267$	−15.3028	−	3.32893i	−0.936519	−	0.203727i
$268$	−14.2142	+	7.76152i	−0.868269	+	0.474110i
$269$	6.44256	−	0.926300i	0.392810	−	0.0564775i	0.0569199	−	0.998379i	$-0.481872\pi$
$269$	6.44256	−	0.926300i	0.392810	−	0.0564775i	0.335890	+	0.941901i	$0.390963\pi$
$270$	5.84842	−	8.57880i	0.355924	−	0.522089i
$271$	−12.7493	−	8.19347i	−0.774464	−	0.497718i	0.0927281	−	0.995691i	$-0.470441\pi$
$271$	−12.7493	−	8.19347i	−0.774464	−	0.497718i	−0.867192	+	0.497974i	$0.834078\pi$
$272$	4.41246	−	0.315585i	0.267545	−	0.0191352i
$273$	−7.94428	+	14.5489i	−0.480809	+	0.880537i
$274$	4.66594	+	10.2170i	0.281880	+	0.617231i
$275$	−10.3205	−	18.1563i	−0.622351	−	1.09487i
$276$	−2.42193	+	3.52788i	−0.145783	+	0.212353i
$277$	−20.9447	+	20.9447i	−1.25844	+	1.25844i	−0.306607	+	0.951836i	$0.599194\pi$
$277$	−20.9447	+	20.9447i	−1.25844	+	1.25844i	−0.951836	+	0.306607i	$0.900806\pi$
$278$	−4.47880	+	12.0081i	−0.268621	+	0.720200i
$279$	0.606641	+	2.06603i	0.0363186	+	0.123690i
$280$	−8.06320	−	3.95040i	−0.481869	−	0.236082i
$281$	6.26349	−	9.74617i	0.373648	−	0.581408i	−0.602605	−	0.798039i	$-0.705871\pi$
$281$	6.26349	−	9.74617i	0.373648	−	0.581408i	0.976253	+	0.216631i	$0.0695070\pi$
$282$	3.12284	+	0.223350i	0.185962	+	0.0133003i
$283$	−1.38898	−	1.03978i	−0.0825665	−	0.0618085i	0.557197	−	0.830380i	$-0.311877\pi$
$283$	−1.38898	−	1.03978i	−0.0825665	−	0.0618085i	−0.639764	+	0.768572i	$0.720968\pi$
$284$	1.30828	−	4.45558i	0.0776319	−	0.264390i
$285$	3.01099	−	0.133293i	0.178355	−	0.00789562i
$286$	−19.1279	−	2.75017i	−1.13105	−	0.162621i
$287$	−2.02205	+	0.754184i	−0.119358	+	0.0445181i
$288$	2.06489	−	0.770163i	0.121675	−	0.0453823i
$289$	−2.54323	−	0.365661i	−0.149602	−	0.0215095i
$290$	−6.22248	+	0.275463i	−0.365396	+	0.0161757i
$291$	0.579238	−	1.97270i	0.0339555	−	0.115642i
$292$	0.346031	+	0.259036i	0.0202499	+	0.0151589i
$293$	6.21656	+	0.444617i	0.363175	+	0.0259748i	0.251735	−	0.967796i	$-0.418999\pi$
$293$	6.21656	+	0.444617i	0.363175	+	0.0259748i	0.111441	+	0.993771i	$0.464453\pi$
$294$	4.40152	−	6.84890i	0.256702	−	0.399436i
$295$	−8.61091	−	4.21874i	−0.501346	−	0.245624i
$296$	−2.07982	−	7.08323i	−0.120887	−	0.411704i
$297$	−6.77770	+	18.1717i	−0.393282	+	1.05443i
$298$	13.1795	−	13.1795i	0.763470	−	0.763470i
$299$	21.0892	+	6.89566i	1.21962	+	0.398786i
$300$	−1.18362	+	4.30152i	−0.0683366	+	0.248348i
$301$	7.51280	+	16.4507i	0.433031	+	0.948205i
$302$	9.73216	−	17.8231i	0.560023	−	1.02561i
$303$	8.20944	−	0.587151i	0.471620	−	0.0337309i
$304$	1.27079	+	0.816690i	0.0728851	+	0.0468404i
$305$	−17.8193	+	26.1383i	−1.02033	+	1.49668i
$306$	−9.64996	+	1.38745i	−0.551651	+	0.0793155i
$307$	18.1045	−	9.88579i	1.03328	−	0.564212i	0.129216	−	0.991616i	$-0.458754\pi$
$307$	18.1045	−	9.88579i	1.03328	−	0.564212i	0.904060	+	0.427405i	$0.140572\pi$
$308$	16.3891	+	3.56522i	0.933854	+	0.203147i
$309$	−0.724024	+	5.03569i	−0.0411883	+	0.286471i
$310$	−1.26129	−	1.78388i	−0.0716363	−	0.101318i
$311$	−5.50088	+	12.0452i	−0.311926	+	0.683023i	−0.999053	−	0.0435146i	$-0.986145\pi$
$311$	−5.50088	+	12.0452i	−0.311926	+	0.683023i	0.687127	+	0.726538i	$0.258872\pi$
$312$	2.47390	+	3.30475i	0.140057	+	0.187094i
$313$	−5.61749	+	25.8232i	−0.317519	+	1.45961i	0.491009	+	0.871155i	$0.336628\pi$
$313$	−5.61749	+	25.8232i	−0.317519	+	1.45961i	−0.808528	+	0.588458i	$0.799735\pi$
$314$	21.2837	+	6.24947i	1.20111	+	0.352678i
$315$	18.3458	+	7.41617i	1.03367	+	0.417854i
$316$	−8.56410	+	7.42083i	−0.481768	+	0.417454i
$317$	11.2197	−	2.44069i	0.630160	−	0.137083i	0.113869	−	0.993496i	$-0.463676\pi$
$317$	11.2197	−	2.44069i	0.630160	−	0.137083i	0.516292	+	0.856413i	$0.327312\pi$
$318$	−0.0156627	−	0.218993i	−0.000878320	−	0.0122805i
$319$	11.1635	−	3.27790i	0.625037	−	0.183527i
$320$	−1.72905	+	1.41788i	−0.0966568	+	0.0792620i
$321$		−	14.6121i		−	0.815570i
$322$	−17.8304	−	7.27550i	−0.993649	−	0.405448i
$323$	−4.72522	−	4.72522i	−0.262918	−	0.262918i
$324$	−2.24536	+	1.02542i	−0.124742	+	0.0569678i
$325$	23.1292	−	0.395095i	1.28298	−	0.0219159i
$326$	−0.450991	+	0.520471i	−0.0249781	+	0.0288262i
$327$	−0.590766	−	2.71571i	−0.0326695	−	0.150179i
$328$	−0.0383410	+	0.536078i	−0.00211703	+	0.0296000i
$329$	2.00515	+	13.9461i	0.110547	+	0.768874i
$330$	0.226315	−	8.33069i	0.0124582	−	0.458589i
$331$	24.5853	−	15.8000i	1.35133	−	0.868448i	0.353575	−	0.935406i	$-0.384966\pi$
$331$	24.5853	−	15.8000i	1.35133	−	0.868448i	0.997756	+	0.0669582i	$0.0213294\pi$
$332$	6.57364	−	4.92097i	0.360775	−	0.270073i
$333$	5.68554	+	15.2435i	0.311566	+	0.835340i
$334$	18.9408	+	8.64997i	1.03639	+	0.473305i
$335$	−22.4812	+	28.3904i	−1.22828	+	1.55113i
$336$	−1.93708	−	3.01416i	−0.105676	−	0.164436i
$337$	8.96798	+	16.4236i	0.488517	+	0.894652i	0.999388	+	0.0349944i	$0.0111413\pi$
$337$	8.96798	+	16.4236i	0.488517	+	0.894652i	−0.510871	+	0.859658i	$0.670677\pi$
$338$	5.03671	−	6.72826i	0.273961	−	0.365969i
$339$	10.7496	+	12.4057i	0.583839	+	0.673786i
$340$	8.80733	−	4.50310i	0.477644	−	0.244215i
$341$	3.08424	+	2.67251i	0.167021	+	0.144724i
$342$	−2.92189	−	1.59547i	−0.157998	−	0.0862733i
$343$	7.99183	+	2.98080i	0.431518	+	0.160948i
$344$	4.50382			0.242830
$345$	−1.90453	+	9.37717i	−0.102536	+	0.504850i
$346$	21.3625			1.14846
$347$	−7.56424	−	2.82132i	−0.406070	−	0.151456i	0.138126	−	0.990415i	$-0.455892\pi$
$347$	−7.56424	−	2.82132i	−0.406070	−	0.151456i	−0.544195	+	0.838959i	$0.683165\pi$
$348$	−2.18142	−	1.19115i	−0.116936	−	0.0638521i
$349$	1.16317	+	1.00789i	0.0622629	+	0.0539511i	0.685436	−	0.728133i	$-0.259611\pi$
$349$	1.16317	+	1.00789i	0.0622629	+	0.0539511i	−0.623173	+	0.782084i	$0.714157\pi$
$350$	−20.0478	−	1.09006i	−1.07160	−	0.0582661i
$351$	−14.0678	−	16.2351i	−0.750885	−	0.866568i
$352$	2.50313	−	3.34379i	0.133417	−	0.178225i
$353$	−7.58364	−	13.8884i	−0.403637	−	0.739205i	0.594243	−	0.804285i	$-0.297452\pi$
$353$	−7.58364	−	13.8884i	−0.403637	−	0.739205i	−0.997880	+	0.0650800i	$0.979270\pi$
$354$	−2.06866	−	3.21890i	−0.109948	−	0.171083i
$355$	−1.19808	−	10.3142i	−0.0635877	−	0.547423i
$356$	−15.9653	−	7.29112i	−0.846160	−	0.386428i
$357$	5.53899	+	14.8506i	0.293154	+	0.785977i
$358$	0.553785	−	0.414558i	0.0292685	−	0.0219101i
$359$	17.2757	−	11.1024i	0.911779	−	0.585965i	0.00151742	−	0.999999i	$-0.499517\pi$
$359$	17.2757	−	11.1024i	0.911779	−	0.585965i	0.910261	+	0.414034i	$0.135881\pi$
$360$	3.57792	−	3.38866i	0.188573	−	0.178598i
$361$	2.37923	+	16.5479i	0.125223	+	0.870944i
$362$	0.267128	−	3.73493i	0.0140399	−	0.196304i
$363$	1.22271	+	5.62072i	0.0641758	+	0.295011i
$364$	−12.1658	+	14.0401i	−0.637663	+	0.735902i
$365$	0.938516	+	0.231023i	0.0491242	+	0.0120923i
$366$	−11.4826	+	5.24394i	−0.600207	+	0.274105i
$367$	−16.4956	−	16.4956i	−0.861064	−	0.861064i	0.130398	−	0.991462i	$-0.458375\pi$
$367$	−16.4956	−	16.4956i	−0.861064	−	0.861064i	−0.991462	+	0.130398i	$0.958375\pi$
$368$	−3.49273	+	3.28646i	−0.182071	+	0.171319i
$369$		−	1.18445i		−	0.0616599i
$370$	−10.4672	−	12.7643i	−0.544162	−	0.663584i
$371$	0.948022	−	0.278364i	0.0492188	−	0.0144520i
$372$	−0.0621932	−	0.869575i	−0.00322457	−	0.0450854i
$373$	24.7138	−	5.37617i	1.27963	−	0.278367i	0.479156	−	0.877730i	$-0.340943\pi$
$373$	24.7138	−	5.37617i	1.27963	−	0.278367i	0.800478	+	0.599362i	$0.204579\pi$
$374$	−13.9644	+	12.1002i	−0.722081	+	0.625687i
$375$	1.32013	+	9.88824i	0.0681713	+	0.510627i
$376$	3.36666	+	0.988540i	0.173622	+	0.0509801i
$377$	−2.73936	+	12.5927i	−0.141084	+	0.648555i
$378$	11.1735	+	14.9261i	0.574705	+	0.767716i
$379$	8.93244	−	19.5593i	0.458829	−	1.00470i	−0.528924	−	0.848669i	$-0.677404\pi$
$379$	8.93244	−	19.5593i	0.458829	−	1.00470i	0.987753	−	0.156026i	$-0.0498683\pi$
$380$	3.32913	+	0.571328i	0.170781	+	0.0293085i
$381$	−0.752762	+	5.23557i	−0.0385652	+	0.268227i
$382$	−5.23014	−	1.13775i	−0.267597	−	0.0582122i
$383$	−15.0829	+	8.23588i	−0.770700	+	0.420834i	−0.815936	−	0.578142i	$-0.803778\pi$
$383$	−15.0829	+	8.23588i	−0.770700	+	0.420834i	0.0452360	+	0.998976i	$0.485596\pi$
$384$	−0.883196	+	0.126984i	−0.0450704	+	0.00648015i
$385$	36.8500	−	6.97394i	1.87805	−	0.355425i
$386$	−10.5384	−	6.77263i	−0.536392	−	0.344718i
$387$	−9.90040	+	0.708091i	−0.503266	+	0.0359943i
$388$	1.10428	−	2.02234i	0.0560615	−	0.102669i
$389$	10.6200	+	23.2545i	0.538453	+	1.17905i	0.961969	+	0.273159i	$0.0880685\pi$
$389$	10.6200	+	23.2545i	0.538453	+	1.17905i	−0.423516	+	0.905889i	$0.639204\pi$
$390$	7.97855	+	4.64223i	0.404010	+	0.235069i
$391$	18.1882	−	10.9218i	0.919815	−	0.552341i
$392$	6.45177	−	6.45177i	0.325864	−	0.325864i
$393$	−2.15793	+	5.78564i	−0.108853	+	0.291847i
$394$	−2.37253	−	8.08009i	−0.119526	−	0.407069i
$395$	−11.1482	+	22.7548i	−0.560928	+	1.14492i
$396$	−4.97673	+	7.74395i	−0.250090	+	0.389148i
$397$	−1.09012	−	0.0779671i	−0.0547117	−	0.00391306i	0.0439565	−	0.999033i	$-0.486004\pi$
$397$	−1.09012	−	0.0779671i	−0.0547117	−	0.00391306i	−0.0986682	+	0.995120i	$0.531458\pi$
$398$	2.14228	+	1.60369i	0.107383	+	0.0803856i
$399$	−1.52484	+	5.19313i	−0.0763375	+	0.259982i
$400$	−2.32094	+	4.42868i	−0.116047	+	0.221434i
$401$	11.8188	+	1.69929i	0.590205	+	0.0848586i	0.430945	−	0.902378i	$-0.358180\pi$
$401$	11.8188	+	1.69929i	0.590205	+	0.0848586i	0.159260	+	0.987237i	$0.449089\pi$
$402$	−13.5395	+	5.04997i	−0.675289	+	0.251870i
$403$	−4.23531	+	1.57969i	−0.210976	+	0.0786898i
$404$	9.13016	+	1.31272i	0.454242	+	0.0653102i
$405$	−3.72650	+	4.07171i	−0.185171	+	0.202325i
$406$	3.15122	−	10.7321i	0.156393	−	0.532624i
$407$	24.6847	+	18.4788i	1.22358	+	0.915959i
$408$	3.93714	+	0.281590i	0.194918	+	0.0139408i
$409$	−14.0043	+	21.7911i	−0.692466	+	1.07750i	0.299876	+	0.953978i	$0.403055\pi$
$409$	−14.0043	+	21.7911i	−0.692466	+	1.07750i	−0.992342	+	0.123521i	$0.960582\pi$
$410$	0.389242	+	1.13699i	0.0192233	+	0.0561518i
$411$	2.82354	+	9.61611i	0.139275	+	0.474328i
$412$	−1.99253	+	5.34218i	−0.0981649	+	0.263190i
$413$	12.1760	−	12.1760i	0.599141	−	0.599141i
$414$	7.16111	−	7.77350i	0.351949	−	0.382047i
$415$	9.23411	−	15.8706i	0.453284	−	0.779055i
$416$	1.92192	+	4.20843i	0.0942301	+	0.206335i
$417$	−5.48051	+	10.0368i	−0.268382	+	0.491504i
$418$	−6.29356	+	0.450124i	−0.307828	+	0.0220163i
$419$	−15.5349	−	9.98366i	−0.758929	−	0.487734i	0.103051	−	0.994676i	$-0.467139\pi$
$419$	−15.5349	−	9.98366i	−0.758929	−	0.487734i	−0.861980	+	0.506942i	$0.830776\pi$
$420$	−6.61975	−	4.51288i	−0.323011	−	0.220206i
$421$	11.6975	−	1.68185i	0.570102	−	0.0819682i	0.148765	−	0.988873i	$-0.452470\pi$
$421$	11.6975	−	1.68185i	0.570102	−	0.0819682i	0.421337	+	0.906904i	$0.361561\pi$
$422$	2.29363	−	1.25242i	0.111652	−	0.0609668i
$423$	−7.55609	−	1.64373i	−0.367390	−	0.0799207i
$424$	0.0350177	−	0.243554i	0.00170061	−	0.0118280i
$425$	14.1970	−	16.9611i	0.688656	−	0.822735i
$426$	1.72125	−	3.76902i	0.0833950	−	0.182610i
$427$	−34.0441	−	45.4776i	−1.64751	−	2.20082i
$428$	3.48102	−	16.0020i	0.168261	−	0.773484i
$429$	−16.5444	−	4.85788i	−0.798772	−	0.234541i
$430$	9.27099	−	3.93326i	0.447087	−	0.189679i
$431$	−7.77407	+	6.73627i	−0.374464	+	0.324475i	−0.821678	−	0.569952i	$-0.806962\pi$
$431$	−7.77407	+	6.73627i	−0.374464	+	0.324475i	0.447214	+	0.894427i	$0.352416\pi$
$432$	4.53716	−	0.986999i	0.218294	−	0.0474870i
$433$	−1.18097	−	16.5121i	−0.0567537	−	0.793520i	−0.943523	−	0.331308i	$-0.892510\pi$
$433$	−1.18097	−	16.5121i	−0.0567537	−	0.793520i	0.886769	−	0.462213i	$-0.152944\pi$
$434$	3.76439	−	1.10533i	0.180697	−	0.0530574i
$435$	−5.53065	−	0.546870i	−0.265174	−	0.0262204i
$436$		−	3.11475i		−	0.149169i
$437$	7.20705	+	0.736353i	0.344760	+	0.0352245i
$438$	0.272720	+	0.272720i	0.0130311	+	0.0130311i
$439$	6.93139	−	3.16546i	0.330817	−	0.151079i	−0.243081	−	0.970006i	$-0.578158\pi$
$439$	6.93139	−	3.16546i	0.330817	−	0.151079i	0.573898	+	0.818927i	$0.305431\pi$
$440$	2.23244	−	9.06914i	0.106427	−	0.432354i
$441$	−13.1681	+	15.1968i	−0.627052	+	0.723656i
$442$	−4.35046	−	19.9987i	−0.206930	−	0.951242i
$443$	−0.582938	+	8.15054i	−0.0276962	+	0.387244i	0.964631	+	0.263604i	$0.0849113\pi$
$443$	−0.582938	+	8.15054i	−0.0276962	+	0.387244i	−0.992327	+	0.123640i	$0.960543\pi$
$444$	−0.937432	−	6.51999i	−0.0444886	−	0.309425i
$445$	−39.2317	−	1.06578i	−1.85976	−	0.0505229i
$446$	−15.9642	+	10.2596i	−0.755929	+	0.485806i
$447$	13.3137	−	9.96652i	0.629717	−	0.471400i
$448$	−1.40327	−	3.76231i	−0.0662983	−	0.177753i
$449$	−35.4436	−	16.1865i	−1.67269	−	0.763890i	−0.999706	−	0.0242294i	$-0.992287\pi$
$449$	−35.4436	−	16.1865i	−1.67269	−	0.763890i	−0.672980	−	0.739661i	$-0.734986\pi$
$450$	4.40568	−	10.1001i	0.207686	−	0.476125i
$451$	−1.21367	−	1.88851i	−0.0571494	−	0.0889263i
$452$	8.81667	+	16.1465i	0.414701	+	0.759469i
$453$	10.8587	−	14.5055i	0.510185	−	0.681527i
$454$	0.896641	+	1.03478i	0.0420815	+	0.0485646i
$455$	−12.7816	+	39.5258i	−0.599209	+	1.85300i
$456$	1.01865	+	0.882669i	0.0477028	+	0.0413348i
$457$	−21.2504	−	11.6036i	−0.994051	−	0.542793i	−0.102027	−	0.994782i	$-0.532533\pi$
$457$	−21.2504	−	11.6036i	−0.994051	−	0.542793i	−0.892024	+	0.451989i	$0.850715\pi$
$458$	−25.1023	−	9.36266i	−1.17295	−	0.437488i
$459$	−20.5406			−0.958752
$460$	−4.31958	+	9.81536i	−0.201401	+	0.457643i
$461$	8.94789			0.416745			0.208372	−	0.978050i	$-0.433183\pi$
$461$	8.94789			0.416745			0.208372	+	0.978050i	$0.433183\pi$
$462$	14.0220	+	5.22995i	0.652364	+	0.243319i
$463$	18.6810	+	10.2006i	0.868182	+	0.474063i	0.850619	−	0.525783i	$-0.176227\pi$
$463$	18.6810	+	10.2006i	0.868182	+	0.474063i	0.0175628	+	0.999846i	$0.494409\pi$
$464$	−2.10514	−	1.82412i	−0.0977287	−	0.0846824i
$465$	−0.887438	−	1.73568i	−0.0411540	−	0.0804904i
$466$	1.24029	+	1.43137i	0.0574554	+	0.0663071i
$467$	19.5275	−	26.0857i	0.903625	−	1.20710i	−0.0741083	−	0.997250i	$-0.523611\pi$
$467$	19.5275	−	26.0857i	0.903625	−	1.20710i	0.977733	−	0.209851i	$-0.0672980\pi$
$468$	−4.88647	−	8.94890i	−0.225877	−	0.413663i
$469$	−35.1587	−	54.7081i	−1.62348	−	2.52618i
$470$	7.79349	−	0.905278i	0.359487	−	0.0417573i
$471$	18.0041	+	8.22221i	0.829586	+	0.378859i
$472$	−1.49859	−	4.01787i	−0.0689782	−	0.184938i
$473$	−15.0598	+	11.2736i	−0.692452	+	0.518363i
$474$	−8.50611	+	5.46654i	−0.390699	+	0.251087i
$475$	7.35187	−	1.73132i	0.337327	−	0.0794385i
$476$	2.52800	+	17.5826i	0.115871	+	0.805899i
$477$	−0.0386853	+	0.540891i	−0.00177128	+	0.0247657i
$478$	−4.88126	−	22.4388i	−0.223264	−	1.02633i
$479$	0.320114	−	0.369431i	0.0146264	−	0.0168798i	−0.748389	−	0.663260i	$-0.769172\pi$
$479$	0.320114	−	0.369431i	0.0146264	−	0.0168798i	0.763016	+	0.646380i	$0.223718\pi$
$480$	−1.70714	+	1.03271i	−0.0779199	+	0.0471363i
$481$	−31.0677	+	14.1881i	−1.41657	+	0.646924i
$482$	−3.48595	−	3.48595i	−0.158781	−	0.158781i
$483$	−14.8239	−	8.68988i	−0.674509	−	0.395403i
$484$			6.44661i			0.293028i
$485$	0.506990	−	5.12733i	0.0230212	−	0.232820i
$486$	−15.4789	+	4.54501i	−0.702136	+	0.206166i
$487$	0.391602	+	5.47531i	0.0177452	+	0.248110i	0.998580	+	0.0532697i	$0.0169643\pi$
$487$	0.391602	+	5.47531i	0.0177452	+	0.248110i	−0.980835	+	0.194840i	$0.937581\pi$
$488$	−13.8240	+	3.00724i	−0.625785	+	0.136131i
$489$	−0.464405	+	0.402409i	−0.0210011	+	0.0181976i
$490$	7.64636	−	18.9152i	0.345427	−	0.854504i
$491$	−6.06351	−	1.78041i	−0.273642	−	0.0803487i	0.142032	−	0.989862i	$-0.454636\pi$
$491$	−6.06351	−	1.78041i	−0.273642	−	0.0803487i	−0.415675	+	0.909513i	$0.636455\pi$
$492$	−0.101936	+	0.468593i	−0.00459564	+	0.0211258i
$493$	7.38448	+	9.86451i	0.332580	+	0.444275i
$494$	2.90325	−	6.35723i	0.130623	−	0.286025i
$495$	−3.48155	+	20.2870i	−0.156484	+	0.911832i
$496$	0.139048	−	0.967100i	0.00624344	−	0.0434241i
$497$	18.2205	+	3.96363i	0.817303	+	0.177793i
$498$	6.43070	−	3.51143i	0.288167	−	0.157351i
$499$	−13.4654	+	1.93603i	−0.602795	+	0.0866688i	−0.436954	−	0.899484i	$-0.643943\pi$
$499$	−13.4654	+	1.93603i	−0.602795	+	0.0866688i	−0.165841	+	0.986153i	$0.553034\pi$
$500$	−0.909957	+	11.1432i	−0.0406945	+	0.498341i
$501$	15.6300	+	10.0448i	0.698298	+	0.448769i
$502$	11.1483	−	0.797342i	0.497573	−	0.0355871i
$503$	3.43792	−	6.29609i	0.153289	−	0.280729i	−0.789738	−	0.613445i	$-0.789783\pi$
$503$	3.43792	−	6.29609i	0.153289	−	0.280729i	0.943027	+	0.332716i	$0.107965\pi$
$504$	3.67622	+	8.04979i	0.163752	+	0.358566i
$505$	19.9406	−	5.27133i	0.887346	−	0.234571i
$506$	3.45253	−	19.7320i	0.153484	−	0.877195i
$507$	5.30279	−	5.30279i	0.235505	−	0.235505i
$508$	−2.07162	+	5.55422i	−0.0919132	+	0.246429i
$509$	−1.45006	−	4.93847i	−0.0642730	−	0.218894i	0.921094	−	0.389341i	$-0.127297\pi$
$509$	−1.45006	−	4.93847i	−0.0642730	−	0.218894i	−0.985367	+	0.170447i	$0.945479\pi$
$510$	8.35042	−	2.85873i	0.369763	−	0.126587i
$511$	−0.938380	+	1.46015i	−0.0415115	+	0.0645931i
$512$	−0.997452	−	0.0713392i	−0.0440816	−	0.00315278i
$513$	−5.61509	−	4.20340i	−0.247912	−	0.185585i
$514$	−4.97170	+	16.9320i	−0.219292	+	0.746841i
$515$	0.563848	+	12.7368i	0.0248461	+	0.561253i
$516$	3.97776	+	0.571915i	0.175111	+	0.0251771i
$517$	−13.7319	+	5.12172i	−0.603926	+	0.225253i
$518$	27.7744	−	10.3593i	1.22034	−	0.455162i
$519$	18.8673	+	2.71271i	0.828183	+	0.119075i
$520$	7.63152	+	6.98449i	0.334664	+	0.306290i
$521$	1.06618	−	3.63107i	0.0467101	−	0.159080i	−0.932835	−	0.360303i	$-0.882673\pi$
$521$	1.06618	−	3.63107i	0.0467101	−	0.159080i	0.979545	+	0.201223i	$0.0644916\pi$
$522$	4.91436	+	3.67884i	0.215096	+	0.161019i
$523$	1.81787	+	0.130017i	0.0794900	+	0.00568524i	0.111028	−	0.993817i	$-0.464586\pi$
$523$	1.81787	+	0.130017i	0.0794900	+	0.00568524i	−0.0315375	+	0.999503i	$0.510040\pi$
$524$	−3.74148	+	5.82186i	−0.163447	+	0.254329i
$525$	−17.5678	−	3.50850i	−0.766720	−	0.153124i
$526$	−5.35340	−	18.2320i	−0.233420	−	0.794954i
$527$	−1.51045	+	4.04967i	−0.0657961	+	0.176406i
$528$	2.63537	−	2.63537i	0.114690	−	0.114690i
$529$	−7.80959	+	21.6335i	−0.339547	+	0.940589i
$530$	−0.140617	−	0.531930i	−0.00610799	−	0.0231056i
$531$	3.92593	+	8.59658i	0.170371	+	0.373060i
$532$	−2.90702	+	5.32381i	−0.126035	+	0.230817i
$533$	2.48017	−	0.177385i	0.107428	−	0.00768342i
$534$	−13.1746	−	8.46683i	−0.570123	−	0.366396i
$535$	−6.80922	−	35.9797i	−0.294388	−	1.55554i
$536$	−16.0303	+	2.30481i	−0.692405	+	0.0995528i
$537$	0.541744	−	0.295814i	0.0233780	−	0.0127653i
$538$	6.36006	+	1.38355i	0.274202	+	0.0596490i
$539$	−5.42375	+	37.7230i	−0.233617	+	1.62484i
$540$	8.47766	−	5.99409i	0.364821	−	0.257945i
$541$	12.5379	−	27.4541i	0.539045	−	1.18034i	−0.422668	−	0.906285i	$-0.638906\pi$
$541$	12.5379	−	27.4541i	0.539045	−	1.18034i	0.961713	−	0.274059i	$-0.0883664\pi$
$542$	−9.08212	−	12.1323i	−0.390110	−	0.521126i
$543$	0.710205	−	3.26476i	0.0304778	−	0.140104i
$544$	4.24454	+	1.24631i	0.181983	+	0.0534350i
$545$	−2.72017	−	6.41163i	−0.116519	−	0.274644i
$546$	−12.5277	+	10.8553i	−0.536136	+	0.464564i
$547$	27.9985	−	6.09070i	1.19713	−	0.260420i	0.430549	−	0.902567i	$-0.358320\pi$
$547$	27.9985	−	6.09070i	1.19713	−	0.260420i	0.766581	+	0.642148i	$0.221956\pi$
$548$	0.801282	+	11.2034i	0.0342291	+	0.478585i
$549$	29.9155	−	8.78400i	1.27676	−	0.374892i
$550$	−3.32482	−	20.6182i	−0.141771	−	0.879164i
$551$			4.20777i			0.179257i
$552$	−3.50210	+	2.45907i	−0.149059	+	0.104665i
$553$	−32.1757	−	32.1757i	−1.36825	−	1.36825i
$554$	−26.9435	+	12.3047i	−1.14472	+	0.522776i
$555$	−7.62370	−	12.6025i	−0.323608	−	0.534948i
$556$	−8.39282	+	9.68583i	−0.355935	+	0.410771i
$557$	4.14243	+	19.0424i	0.175520	+	0.806854i	0.977739	+	0.209824i	$0.0672891\pi$
$557$	4.14243	+	19.0424i	0.175520	+	0.806854i	−0.802219	+	0.597030i	$0.796347\pi$
$558$	−0.153611	+	2.14776i	−0.00650288	+	0.0909221i
$559$	−2.96541	−	20.6249i	−0.125424	−	0.872340i
$560$	−6.17429	−	6.51913i	−0.260911	−	0.275483i
$561$	−13.8698	+	8.91360i	−0.585585	+	0.376333i
$562$	9.27451	−	6.94281i	0.391222	−	0.292865i
$563$	0.376446	+	1.00929i	0.0158653	+	0.0425365i	0.944641	−	0.328106i	$-0.106410\pi$
$563$	0.376446	+	1.00929i	0.0158653	+	0.0425365i	−0.928776	+	0.370642i	$0.879138\pi$
$564$	2.84789	+	1.30059i	0.119918	+	0.0547646i
$565$	32.2499	+	25.5375i	1.35677	+	1.07437i
$566$	−0.938041	−	1.45962i	−0.0394288	−	0.0613524i
$567$	−4.75029	−	8.69951i	−0.199493	−	0.365345i
$568$	2.78285	−	3.71746i	0.116766	−	0.155981i
$569$	−17.5656	−	20.2718i	−0.736388	−	0.849837i	0.256787	−	0.966468i	$-0.417336\pi$
$569$	−17.5656	−	20.2718i	−0.736388	−	0.849837i	−0.993175	+	0.116631i	$0.962791\pi$
$570$	2.86772	+	0.927342i	0.120116	+	0.0388421i
$571$	16.5037	+	14.3006i	0.690659	+	0.598460i	0.927828	−	0.373009i	$-0.121674\pi$
$571$	16.5037	+	14.3006i	0.690659	+	0.598460i	−0.237168	+	0.971469i	$0.576219\pi$
$572$	−16.9608	−	9.26127i	−0.709165	−	0.387233i
$573$	−4.47476	−	1.66900i	−0.186936	−	0.0697235i
$574$	−2.15812			−0.0900780
$575$	−0.319816	+	23.9770i	−0.0133373	+	0.999911i
$576$	2.20384			0.0918266
$577$	0.171440	+	0.0639438i	0.00713714	+	0.00266201i	0.353030	−	0.935612i	$-0.385151\pi$
$577$	0.171440	+	0.0639438i	0.00713714	+	0.00266201i	−0.345893	+	0.938274i	$0.612424\pi$
$578$	−2.25509	−	1.23137i	−0.0937994	−	0.0512183i
$579$	−8.44748	−	7.31978i	−0.351065	−	0.304200i
$580$	−5.92641	−	1.91644i	−0.246081	−	0.0795757i
$581$	21.5929	+	24.9195i	0.895823	+	1.03383i
$582$	1.23211	−	1.64590i	0.0510724	−	0.0682247i
$583$	0.492555	+	0.902046i	0.0203995	+	0.0373589i
$584$	0.233690	+	0.363629i	0.00967016	+	0.0150471i
$585$	−17.8739	−	14.1536i	−0.738995	−	0.585181i
$586$	5.66923	+	2.58905i	0.234194	+	0.106953i
$587$	−5.10232	−	13.6798i	−0.210595	−	0.564628i	0.788108	−	0.615537i	$-0.211061\pi$
$587$	−5.10232	−	13.6798i	−0.210595	−	0.564628i	−0.998703	+	0.0509093i	$0.983788\pi$
$588$	6.51745	−	4.87890i	0.268775	−	0.201203i
$589$	−1.24162	+	0.797943i	−0.0511602	+	0.0328787i
$590$	−6.59369	−	6.96195i	−0.271458	−	0.286619i
$591$	−1.06936	−	7.43758i	−0.0439877	−	0.305941i
$592$	0.526645	−	7.36345i	0.0216450	−	0.302636i
$593$	3.96850	+	18.2429i	0.162967	+	0.749145i	0.983986	+	0.178245i	$0.0570420\pi$
$593$	3.96850	+	18.2429i	0.162967	+	0.749145i	−0.821019	+	0.570900i	$0.806594\pi$
$594$	−12.7007	+	14.6574i	−0.521117	+	0.601401i
$595$	20.5591	+	33.9857i	0.842839	+	1.39328i
$596$	16.9543	−	7.74279i	0.694477	−	0.317157i
$597$	1.68841	+	1.68841i	0.0691019	+	0.0691019i
$598$	17.3498	+	13.8308i	0.709485	+	0.565585i
$599$			19.9012i			0.813142i	0.913619	+	0.406571i	$0.133276\pi$
$599$			19.9012i			0.813142i	−0.913619	+	0.406571i	$0.866724\pi$
$600$	−2.61222	+	3.61667i	−0.106644	+	0.147650i
$601$	16.1548	−	4.74348i	0.658968	−	0.193491i	0.0648833	−	0.997893i	$-0.479332\pi$
$601$	16.1548	−	4.74348i	0.658968	−	0.193491i	0.594085	+	0.804402i	$0.297514\pi$
$602$	1.29017	+	18.0390i	0.0525835	+	0.735213i
$603$	34.8759	−	7.58679i	1.42026	−	0.308958i
$604$	15.3471	−	13.2983i	0.624464	−	0.541101i
$605$	5.62994	+	13.2702i	0.228890	+	0.539510i
$606$	7.89702	+	2.31878i	0.320795	+	0.0941938i
$607$	−2.84386	+	13.0730i	−0.115429	+	0.530618i	0.882726	+	0.469889i	$0.155706\pi$
$607$	−2.84386	+	13.0730i	−0.115429	+	0.530618i	−0.998154	+	0.0607286i	$0.980658\pi$
$608$	0.905267	+	1.20929i	0.0367134	+	0.0490434i
$609$	4.14596	−	9.07838i	0.168003	−	0.367874i
$610$	−25.8302	+	18.2631i	−1.04583	+	0.739451i
$611$	2.31026	−	16.0682i	0.0934632	−	0.650051i
$612$	−9.52639	−	2.07234i	−0.385081	−	0.0837693i
$613$	22.9960	−	12.5568i	0.928801	−	0.507164i	0.0577365	−	0.998332i	$-0.481612\pi$
$613$	22.9960	−	12.5568i	0.928801	−	0.507164i	0.871065	+	0.491168i	$0.163430\pi$
$614$	20.4177	−	2.93562i	0.823992	−	0.118472i
$615$	0.199398	+	1.05361i	0.00804049	+	0.0424857i
$616$	14.1098	+	9.06783i	0.568501	+	0.365353i
$617$	17.1404	−	1.22591i	0.690047	−	0.0493531i	0.278088	−	0.960556i	$-0.410299\pi$
$617$	17.1404	−	1.22591i	0.690047	−	0.0493531i	0.411959	+	0.911203i	$0.364845\pi$
$618$	−2.43817	+	4.46517i	−0.0980775	+	0.179616i
$619$	−12.9673	−	28.3944i	−0.521200	−	1.14127i	−0.968983	−	0.247126i	$-0.920514\pi$
$619$	−12.9673	−	28.3944i	−0.521200	−	1.14127i	0.447783	−	0.894142i	$-0.352214\pi$
$620$	−0.558359	−	2.11218i	−0.0224242	−	0.0848273i
$621$	17.2650	−	14.0641i	0.692822	−	0.564373i
$622$	−9.36343	+	9.36343i	−0.375439	+	0.375439i
$623$	24.6294	−	66.0339i	0.986755	−	2.64559i
$624$	1.16303	+	3.96092i	0.0465585	+	0.158564i
$625$	7.85847	+	23.7328i	0.314339	+	0.949311i
$626$	−14.2876	+	22.2319i	−0.571047	+	0.888566i
$627$	−5.61560	−	0.401636i	−0.224266	−	0.0160398i
$628$	17.7578	+	13.2933i	0.708614	+	0.530462i
$629$	−9.20058	+	31.3343i	−0.366851	+	1.24938i
$630$	14.5974	+	13.3598i	0.581575	+	0.532266i
$631$	21.3596	+	3.07104i	0.850311	+	0.122256i	0.553673	−	0.832734i	$-0.313226\pi$
$631$	21.3596	+	3.07104i	0.850311	+	0.122256i	0.296637	+	0.954990i	$0.404135\pi$
$632$	−10.6174	+	3.96010i	−0.422339	+	0.157524i
$633$	2.18477	−	0.814876i	0.0868367	−	0.0323884i
$634$	11.3652	+	1.63407i	0.451370	+	0.0648973i
$635$	0.586228	+	13.2424i	0.0232638	+	0.525509i
$636$	0.0618550	−	0.210659i	0.00245271	−	0.00835317i
$637$	−33.7934	−	25.2974i	−1.33894	−	1.00232i
$638$	11.6052	+	0.830017i	0.459453	+	0.0328607i
$639$	−5.53288	+	8.60933i	−0.218877	+	0.340580i
$640$	−2.11553	+	0.724243i	−0.0836237	+	0.0286282i
$641$	−5.96264	−	20.3069i	−0.235510	−	0.802074i	−0.989418	−	0.145094i	$-0.953652\pi$
$641$	−5.96264	−	20.3069i	−0.235510	−	0.802074i	0.753908	−	0.656980i	$-0.228167\pi$
$642$	5.10642	−	13.6908i	0.201534	−	0.540335i
$643$	−9.83652	+	9.83652i	−0.387915	+	0.387915i	−0.873943	−	0.486028i	$-0.838445\pi$
$643$	−9.83652	+	9.83652i	−0.387915	+	0.387915i	0.486028	+	0.873943i	$0.338445\pi$
$644$	−14.1637	−	13.0479i	−0.558127	−	0.514158i
$645$	8.68757	−	2.29657i	0.342073	−	0.0904274i
$646$	−2.77600	−	6.07859i	−0.109220	−	0.239159i
$647$	−18.3009	+	33.5155i	−0.719481	+	1.31763i	0.220159	+	0.975464i	$0.429343\pi$
$647$	−18.3009	+	33.5155i	−0.719481	+	1.31763i	−0.939639	+	0.342167i	$0.888839\pi$
$648$	−2.46214	+	0.176095i	−0.0967218	+	0.00691768i
$649$	15.0682	+	9.68377i	0.591480	+	0.380121i
$650$	21.8090	+	7.71264i	0.855418	+	0.302515i
$651$	3.46506	−	0.498200i	0.135806	−	0.0195260i
$652$	−0.604441	+	0.330050i	−0.0236717	+	0.0129258i
$653$	0.681417	+	0.148233i	0.0266659	+	0.00580081i	0.225878	−	0.974155i	$-0.427475\pi$
$653$	0.681417	+	0.148233i	0.0266659	+	0.00580081i	−0.199213	+	0.979956i	$0.563838\pi$
$654$	0.395525	−	2.75093i	0.0154662	−	0.107570i
$655$	−2.61741	+	15.2516i	−0.102271	+	0.595931i
$656$	−0.223264	+	0.488879i	−0.00871698	+	0.0190875i
$657$	−0.570873	−	0.762597i	−0.0222719	−	0.0297517i
$658$	−2.99494	+	13.7675i	−0.116755	+	0.536714i
$659$	−13.3916	−	3.93212i	−0.521662	−	0.153174i	0.0102921	−	0.999947i	$-0.496724\pi$
$659$	−13.3916	−	3.93212i	−0.521662	−	0.153174i	−0.531954	+	0.846773i	$0.678542\pi$
$660$	3.12332	−	7.72634i	0.121575	−	0.300748i
$661$	−32.4020	+	28.0765i	−1.26029	+	1.09205i	−0.268623	+	0.963245i	$0.586568\pi$
$661$	−32.4020	+	28.0765i	−1.26029	+	1.09205i	−0.991670	+	0.128804i	$0.958886\pi$
$662$	28.5567	−	6.21214i	1.10989	−	0.241442i
$663$	−1.30278	−	18.2152i	−0.0505958	−	0.707421i
$664$	7.87887	−	2.31345i	0.305760	−	0.0897791i
$665$	−1.33465	+	13.4977i	−0.0517555	+	0.523418i
$666$			16.2693i			0.630423i
$667$	−12.9611	−	3.23530i	−0.501856	−	0.125271i
$668$	14.7237	+	14.7237i	0.569677	+	0.569677i
$669$	−15.4024	+	7.03403i	−0.595490	+	0.271951i
$670$	−30.9852	+	18.7440i	−1.19706	+	0.724143i
$671$	38.6972	−	44.6590i	1.49389	−	1.72404i
$672$	−0.761608	−	3.50106i	−0.0293797	−	0.135056i
$673$	0.793064	−	11.0885i	0.0305704	−	0.427429i	−0.959003	−	0.283397i	$-0.908539\pi$
$673$	0.793064	−	11.0885i	0.0305704	−	0.427429i	0.989573	−	0.144032i	$-0.0460069\pi$
$674$	2.66308	+	18.5221i	0.102578	+	0.713445i
$675$	12.2163	−	19.7424i	0.470206	−	0.759885i
$676$	7.07043	−	4.54389i	0.271940	−	0.174765i
$677$	−30.8300	+	23.0791i	−1.18489	+	0.887000i	−0.995487	−	0.0948982i	$-0.969747\pi$
$677$	−30.8300	+	23.0791i	−1.18489	+	0.887000i	−0.189407	+	0.981899i	$0.560657\pi$
$678$	5.73649	+	15.3801i	0.220309	+	0.590671i
$679$	8.41635	+	3.84362i	0.322990	+	0.147505i
$680$	9.82569	−	1.14133i	0.376798	−	0.0437682i
$681$	0.660509	+	1.02777i	0.0253108	+	0.0393843i
$682$	1.95583	+	3.58184i	0.0748926	+	0.137156i
$683$	−11.1253	+	14.8616i	−0.425697	+	0.568664i	−0.961194	−	0.275873i	$-0.911033\pi$
$683$	−11.1253	+	14.8616i	−0.425697	+	0.568664i	0.535497	+	0.844537i	$0.320124\pi$
$684$	−2.18010	−	2.51597i	−0.0833584	−	0.0962007i
$685$	11.4335	+	22.3621i	0.436853	+	0.854412i
$686$	6.44626	+	5.58572i	0.246119	+	0.213264i
$687$	−20.9813	−	11.4567i	−0.800487	−	0.437099i
$688$	4.21985	+	1.57392i	0.160880	+	0.0600053i
$689$	−1.13839			−0.0433693
$690$	−5.06143	+	8.12037i	−0.192685	+	0.309137i
$691$	−34.3181			−1.30552			−0.652760	−	0.757565i	$-0.726389\pi$
$691$	−34.3181			−1.30552			−0.652760	+	0.757565i	$0.726389\pi$
$692$	20.0156	+	7.46544i	0.760880	+	0.283794i
$693$	−32.4422	−	17.7148i	−1.23238	−	0.672928i
$694$	−6.10136	−	5.28686i	−0.231605	−	0.200687i
$695$	−8.81760	+	27.2676i	−0.334471	+	1.03432i
$696$	−1.62762	−	1.87837i	−0.0616947	−	0.0711995i
$697$	1.42480	−	1.90330i	0.0539680	−	0.0720928i
$698$	0.737608	+	1.35083i	0.0279189	+	0.0511296i
$699$	0.913659	+	1.42168i	0.0345578	+	0.0537729i
$700$	−18.4029	−	8.02734i	−0.695564	−	0.303405i
$701$	−18.3603	−	8.38485i	−0.693458	−	0.316691i	0.0373237	−	0.999303i	$-0.488117\pi$
$701$	−18.3603	−	8.38485i	−0.693458	−	0.316691i	−0.730781	+	0.682612i	$0.760844\pi$
$702$	−7.50725	−	20.1277i	−0.283343	−	0.759672i
$703$	−8.92733	+	6.68292i	−0.336701	+	0.252051i
$704$	3.51384	−	2.25821i	0.132433	−	0.0851095i
$705$	6.99814	+	0.190114i	0.263565	+	0.00716011i
$706$	−2.25199	−	15.6629i	−0.0847548	−	0.589483i
$707$	−2.64234	+	36.9447i	−0.0993753	+	1.38945i
$708$	−0.813341	−	3.73887i	−0.0305672	−	0.140515i
$709$	13.4210	−	15.4887i	0.504038	−	0.581691i	−0.445524	−	0.895270i	$-0.646983\pi$
$709$	13.4210	−	15.4887i	0.504038	−	0.581691i	0.949562	+	0.313579i	$0.101528\pi$
$710$	2.48191	−	10.0826i	0.0931445	−	0.378394i
$711$	22.7169	−	10.3745i	0.851951	−	0.389073i
$712$	−12.4107	−	12.4107i	−0.465111	−	0.465111i
$713$	−1.50322	−	4.43808i	−0.0562960	−	0.166207i
$714$			15.8499i			0.593169i
$715$	−43.0013	−	4.25197i	−1.60816	−	0.159015i
$716$	0.663742	−	0.194892i	0.0248052	−	0.00728347i
$717$	−1.46173	−	20.4377i	−0.0545894	−	0.763260i
$718$	20.0664	−	4.36518i	0.748872	−	0.162907i
$719$	−34.7670	+	30.1257i	−1.29659	+	1.12350i	−0.311725	+	0.950172i	$0.600907\pi$
$719$	−34.7670	+	30.1257i	−1.29659	+	1.12350i	−0.984864	+	0.173328i	$0.944548\pi$
$720$	4.53655	−	1.92465i	0.169067	−	0.0717275i
$721$	−21.9676	−	6.45027i	−0.818116	−	0.240221i
$722$	−3.55369	+	16.3360i	−0.132255	+	0.607964i
$723$	−2.63612	−	3.52144i	−0.0980382	−	0.130964i
$724$	1.55551	−	3.40609i	0.0578101	−	0.126586i
$725$	−13.8730	+	1.23070i	−0.515231	+	0.0457071i
$726$	−0.818620	+	5.69362i	−0.0303818	+	0.211310i
$727$	16.2497	+	3.53490i	0.602667	+	0.131102i	0.503539	−	0.863973i	$-0.332031\pi$
$727$	16.2497	+	3.53490i	0.602667	+	0.131102i	0.0991279	+	0.995075i	$0.468395\pi$
$728$	−16.3053	+	8.90336i	−0.604314	+	0.329980i
$729$	−6.91812	+	0.994676i	−0.256227	+	0.0368398i
$730$	0.798608	+	0.544435i	0.0295578	+	0.0201504i
$731$	−16.7609	−	10.7715i	−0.619923	−	0.398400i
$732$	−12.5912	+	0.900541i	−0.465385	+	0.0332850i
$733$	9.71383	−	17.7896i	0.358789	−	0.657072i	−0.634476	−	0.772943i	$-0.718784\pi$
$733$	9.71383	−	17.7896i	0.358789	−	0.657072i	0.993264	+	0.115870i	$0.0369658\pi$
$734$	−9.69093	−	21.2202i	−0.357699	−	0.783251i
$735$	9.15518	−	15.7349i	0.337694	−	0.580391i
$736$	−4.42102	+	1.85866i	−0.162961	+	0.0685112i
$737$	47.8329	−	47.8329i	1.76195	−	1.76195i
$738$	0.413922	−	1.10977i	0.0152367	−	0.0408511i
$739$	10.2360	+	34.8606i	0.376537	+	1.28237i	0.902069	+	0.431592i	$0.142048\pi$
$739$	10.2360	+	34.8606i	0.376537	+	1.28237i	−0.525532	+	0.850774i	$0.676134\pi$
$740$	−5.34655	−	15.6174i	−0.196543	−	0.574107i
$741$	3.37141	−	5.24602i	0.123852	−	0.192717i
$742$	0.985527	+	0.0704863i	0.0361798	+	0.00258763i
$743$	19.8334	+	14.8471i	0.727615	+	0.544686i	0.897627	−	0.440756i	$-0.145290\pi$
$743$	19.8334	+	14.8471i	0.727615	+	0.544686i	−0.170012	+	0.985442i	$0.554380\pi$
$744$	0.245613	−	0.836482i	0.00900462	−	0.0306669i
$745$	28.1382	−	30.7449i	1.03090	−	1.12640i
$746$	25.0344	+	3.59940i	0.916575	+	0.131784i
$747$	−16.9558	+	6.32419i	−0.620381	+	0.231390i
$748$	−17.3125	+	6.45724i	−0.633009	+	0.236100i
$749$	65.0892	+	9.35842i	2.37831	+	0.341949i
$750$	−2.21869	+	9.72612i	−0.0810151	+	0.355148i
$751$	1.07129	−	3.64846i	0.0390918	−	0.133134i	−0.937635	−	0.347621i	$-0.886990\pi$
$751$	1.07129	−	3.64846i	0.0390918	−	0.133134i	0.976727	+	0.214487i	$0.0688078\pi$
$752$	2.80893	+	2.10274i	0.102431	+	0.0766790i
$753$	9.94738	+	0.711451i	0.362503	+	0.0259267i
$754$	−6.96733	+	10.8414i	−0.253735	+	0.394819i
$755$	19.9779	−	40.7771i	0.727071	−	1.48403i
$756$	5.25291	+	17.8898i	0.191047	+	0.650645i
$757$	10.3360	−	27.7119i	0.375669	−	1.00721i	−0.602266	−	0.798296i	$-0.705735\pi$
$757$	10.3360	−	27.7119i	0.375669	−	1.00721i	0.977935	−	0.208911i	$-0.0669920\pi$
$758$	15.2045	−	15.2045i	0.552254	−	0.552254i
$759$	5.55492	−	16.9888i	0.201631	−	0.616655i
$760$	2.91957	+	1.69872i	0.105904	+	0.0616189i
$761$	−16.8360	−	36.8656i	−0.610304	−	1.33638i	−0.922366	−	0.386317i	$-0.873747\pi$
$761$	−16.8360	−	36.8656i	−0.610304	−	1.33638i	0.312063	−	0.950062i	$-0.398980\pi$
$762$	−2.53495	+	4.64241i	−0.0918314	+	0.168177i
$763$	12.4754	−	0.892257i	0.451639	−	0.0323019i
$764$	−4.50278	−	2.89376i	−0.162905	−	0.104692i
$765$	−21.4196	+	4.05371i	−0.774429	+	0.146562i
$766$	−17.0101	+	2.44568i	−0.614598	+	0.0883659i
$767$	−17.4128	+	9.50813i	−0.628741	+	0.343319i
$768$	−0.871887	−	0.189667i	−0.0314615	−	0.00684403i
$769$	2.50634	−	17.4320i	0.0903810	−	0.628614i	−0.893403	−	0.449256i	$-0.851689\pi$
$769$	2.50634	−	17.4320i	0.0903810	−	0.628614i	0.983784	−	0.179357i	$-0.0574018\pi$
$770$	36.9638	+	6.34354i	1.33208	+	0.228605i
$771$	−6.54109	+	14.3230i	−0.235572	+	0.515830i
$772$	−7.50718	−	10.0284i	−0.270189	−	0.360931i
$773$	−3.08411	+	14.1774i	−0.110928	+	0.509926i	0.887833	+	0.460165i	$0.152210\pi$
$773$	−3.08411	+	14.1774i	−0.110928	+	0.509926i	−0.998761	+	0.0497614i	$0.984154\pi$
$774$	−9.52363	−	2.79639i	−0.342320	−	0.100514i
$775$	−2.99397	−	3.86025i	−0.107547	−	0.138664i
$776$	1.74139	−	1.50893i	0.0625124	−	0.0541673i
$777$	25.8457	−	5.62239i	0.927210	−	0.201702i
$778$	1.82376	+	25.4995i	0.0653851	+	0.914203i
$779$	0.778980	−	0.228729i	0.0279098	−	0.00819507i
$780$	5.85321	+	7.13776i	0.209579	+	0.255573i
$781$			19.3963i			0.694053i
$782$	20.8582	−	3.87710i	0.745887	−	0.138645i
$783$	9.14561	+	9.14561i	0.326837	+	0.326837i
$784$	8.29965	−	3.79032i	0.296416	−	0.135369i
$785$	48.1633	+	11.8558i	1.71902	+	0.423151i
$786$	−4.04375	+	4.66673i	−0.144236	+	0.166457i
$787$	10.4444	+	48.0121i	0.372302	+	1.71145i	0.657907	+	0.753099i	$0.271442\pi$
$787$	10.4444	+	48.0121i	0.372302	+	1.71145i	−0.285605	+	0.958347i	$0.592194\pi$
$788$	0.600762	−	8.39975i	0.0214013	−	0.299229i
$789$	−2.41292	−	16.7823i	−0.0859024	−	0.597464i
$790$	−18.3973	+	17.4242i	−0.654547	+	0.619924i
$791$	−62.1454	+	39.9384i	−2.20964	+	1.42005i
$792$	−7.36918	+	5.51650i	−0.261852	+	0.196020i
$793$	22.8735	+	61.3261i	0.812260	+	2.17775i
$794$	−0.994143	−	0.454010i	−0.0352808	−	0.0161122i
$795$	−0.0566451	−	0.487655i	−0.00200900	−	0.0172953i
$796$	1.44677	+	2.25122i	0.0512795	+	0.0797925i
$797$	−8.49990	−	15.5664i	−0.301082	−	0.551390i	0.682713	−	0.730686i	$-0.260800\pi$
$797$	−8.49990	−	15.5664i	−0.301082	−	0.551390i	−0.983795	+	0.179296i	$0.942618\pi$
$798$	−3.24351	+	4.33283i	−0.114819	+	0.153380i
$799$	−10.1647	−	11.7307i	−0.359601	−	0.415002i
$800$	−3.72227	+	3.33837i	−0.131602	+	0.118029i
$801$	29.2327	+	25.3303i	1.03289	+	0.895003i
$802$	10.4798	+	5.72241i	0.370055	+	0.202065i
$803$	−1.69162	−	0.630942i	−0.0596960	−	0.0222655i
$804$	−14.4506			−0.509634
$805$	−40.5505	−	14.4893i	−1.42922	−	0.510681i
$806$	−4.52031			−0.159221
$807$	5.44150	+	2.02957i	0.191550	+	0.0714444i
$808$	8.09575	+	4.42061i	0.284807	+	0.155517i
$809$	−20.4161	−	17.6907i	−0.717792	−	0.621970i	0.217412	−	0.976080i	$-0.430239\pi$
$809$	−20.4161	−	17.6907i	−0.717792	−	0.621970i	−0.935204	+	0.354110i	$0.884784\pi$
$810$	−4.91446	+	2.51271i	−0.172676	+	0.0882878i
$811$	−5.47193	−	6.31495i	−0.192146	−	0.221748i	0.651500	−	0.758649i	$-0.274140\pi$
$811$	−5.47193	−	6.31495i	−0.192146	−	0.221748i	−0.843645	+	0.536901i	$0.819595\pi$
$812$	6.70302	−	8.95418i	0.235230	−	0.314230i
$813$	−6.48068	−	11.8685i	−0.227287	−	0.416246i
$814$	16.6707	+	25.9401i	0.584308	+	0.909201i
$815$	−0.955989	+	1.20727i	−0.0334868	+	0.0422888i
$816$	3.59050	+	1.63973i	0.125693	+	0.0574019i
$817$	−2.37756	−	6.37449i	−0.0831804	−	0.223015i
$818$	−20.7365	+	15.5231i	−0.725034	+	0.542754i
$819$	34.4429	−	22.1351i	1.20353	−	0.773463i
$820$	−0.0326357	+	1.20133i	−0.00113969	+	0.0419521i
$821$	4.59259	+	31.9421i	0.160282	+	1.11479i	0.898101	+	0.439789i	$0.144947\pi$
$821$	4.59259	+	31.9421i	0.160282	+	1.11479i	−0.737819	+	0.674999i	$0.764144\pi$
$822$	−0.714967	+	9.99654i	−0.0249373	+	0.348669i
$823$	−8.39439	−	38.5884i	−0.292610	−	1.34511i	−0.855169	−	0.518349i	$-0.826547\pi$
$823$	−8.39439	−	38.5884i	−0.292610	−	1.34511i	0.562559	−	0.826757i	$-0.309817\pi$
$824$	−3.73380	+	4.30904i	−0.130073	+	0.150112i
$825$	−0.318276	−	18.6321i	−0.0110809	−	0.648688i
$826$	15.6633	−	7.15321i	0.544998	−	0.248892i
$827$	7.28553	+	7.28553i	0.253343	+	0.253343i	0.822340	−	0.568997i	$-0.192668\pi$
$827$	7.28553	+	7.28553i	0.253343	+	0.253343i	−0.568997	+	0.822340i	$0.692668\pi$
$828$	9.42616	−	4.78083i	0.327582	−	0.166145i
$829$			36.7854i			1.27761i	0.769369	+	0.638804i	$0.220571\pi$
$829$			36.7854i			1.27761i	−0.769369	+	0.638804i	$0.779429\pi$
$830$	14.1981	−	11.6429i	0.492823	−	0.404132i
$831$	−25.3589	+	7.44605i	−0.879691	+	0.258301i
$832$	0.330052	+	4.61473i	0.0114425	+	0.159987i
$833$	−39.4405	+	8.57975i	−1.36653	+	0.297271i
$834$	−8.64246	+	7.48873i	−0.299264	+	0.259314i
$835$	43.1668	+	17.4499i	1.49385	+	0.603879i
$836$	−6.05405	−	1.77763i	−0.209384	−	0.0614806i
$837$	−0.964342	+	4.43301i	−0.0333325	+	0.153227i
$838$	−11.0665	−	14.7831i	−0.382285	−	0.510673i
$839$	10.4288	−	22.8360i	0.360043	−	0.788385i	−0.639760	−	0.768574i	$-0.720966\pi$
$839$	10.4288	−	22.8360i	0.360043	−	0.788385i	0.999804	−	0.0198105i	$-0.00630628\pi$
$840$	−4.62528	−	6.54171i	−0.159587	−	0.225710i
$841$	−3.02291	+	21.0248i	−0.104238	+	0.724992i
$842$	11.5477	+	2.51205i	0.397961	+	0.0865711i
$843$	9.07284	−	4.95415i	0.312485	−	0.170630i
$844$	2.58669	−	0.371911i	0.0890377	−	0.0128017i
$845$	10.5860	−	15.5282i	0.364171	−	0.534187i
$846$	−6.50525	−	4.18067i	−0.223655	−	0.143734i
$847$	−25.8204	+	1.84671i	−0.887198	+	0.0634537i
$848$	0.117923	−	0.215960i	0.00404950	−	0.00741610i
$849$	−0.643125	−	1.40825i	−0.0220720	−	0.0483310i
$850$	19.2292	−	10.9304i	0.659556	−	0.374908i
$851$	−13.7211	−	32.6371i	−0.470354	−	1.11879i
$852$	2.92987	−	2.92987i	0.100376	−	0.100376i
$853$	−0.478761	+	1.28361i	−0.0163925	+	0.0439499i	−0.944888	−	0.327393i	$-0.893830\pi$
$853$	−0.478761	+	1.28361i	−0.0163925	+	0.0439499i	0.928496	+	0.371343i	$0.121103\pi$
$854$	−16.0048	−	54.5074i	−0.547674	−	1.86521i
$855$	−6.68493	−	3.27515i	−0.228620	−	0.112008i
$856$	8.85365	−	13.7766i	0.302612	−	0.470873i
$857$	−5.84835	−	0.418282i	−0.199776	−	0.0142883i	−0.0289074	−	0.999582i	$-0.509203\pi$
$857$	−5.84835	−	0.418282i	−0.199776	−	0.0142883i	−0.170868	+	0.985294i	$0.554657\pi$
$858$	−13.8036	−	10.3333i	−0.471248	−	0.352772i
$859$	3.33502	−	11.3580i	0.113789	−	0.387531i	−0.882830	−	0.469694i	$-0.844364\pi$
$859$	3.33502	−	11.3580i	0.113789	−	0.387531i	0.996619	+	0.0821623i	$0.0261826\pi$
$860$	10.0610	−	0.445390i	0.343077	−	0.0151877i
$861$	−1.90604	−	0.274047i	−0.0649577	−	0.00933950i
$862$	−9.63800	+	3.59479i	−0.328272	+	0.122439i
$863$	7.21891	−	2.69251i	0.245735	−	0.0916542i	−0.223579	−	0.974686i	$-0.571774\pi$
$863$	7.21891	−	2.69251i	0.245735	−	0.0916542i	0.469314	+	0.883032i	$0.344501\pi$
$864$	4.59601	+	0.660807i	0.156359	+	0.0224811i
$865$	47.7214	−	2.11258i	1.62257	−	0.0718298i
$866$	4.66388	−	15.8837i	0.158485	−	0.539750i
$867$	−1.83532	−	1.37391i	−0.0623308	−	0.0466603i
$868$	3.91332	+	0.279886i	0.132827	+	0.00949996i
$869$	25.5899	−	39.8186i	0.868077	−	1.35075i
$870$	−4.99083	−	2.44515i	−0.169205	−	0.0828984i
$871$	21.1094	+	71.8921i	0.715266	+	2.43597i
$872$	1.08849	−	2.91836i	0.0368610	−	0.0988283i
$873$	−3.59074	+	3.59074i	−0.121528	+	0.121528i
$874$	6.49531	+	3.20853i	0.219707	+	0.108530i
$875$	−44.8923	−	0.452497i	−1.51764	−	0.0152972i
$876$	0.160219	+	0.350830i	0.00541330	+	0.0118535i
$877$	−0.532691	+	0.975550i	−0.0179877	+	0.0329420i	−0.886518	−	0.462694i	$-0.846883\pi$
$877$	−0.532691	+	0.975550i	−0.0179877	+	0.0329420i	0.868531	+	0.495636i	$0.165065\pi$
$878$	7.60057	−	0.543604i	0.256507	−	0.0183457i
$879$	4.67827	+	3.00654i	0.157794	+	0.101408i
$880$	5.26102	−	7.71717i	0.177349	−	0.260146i
$881$	−10.1476	+	1.45900i	−0.341881	+	0.0491551i	−0.311117	−	0.950372i	$-0.600703\pi$
$881$	−10.1476	+	1.45900i	−0.341881	+	0.0491551i	−0.0307640	+	0.999527i	$0.509794\pi$
$882$	−17.6486	+	9.63685i	−0.594258	+	0.324489i
$883$	27.3178	+	5.94263i	0.919317	+	0.199985i	0.647237	−	0.762289i	$-0.275925\pi$
$883$	27.3178	+	5.94263i	0.919317	+	0.199985i	0.272081	+	0.962274i	$0.412288\pi$
$884$	2.91268	−	20.2581i	0.0979640	−	0.681355i
$885$	−4.93946	−	6.98606i	−0.166038	−	0.234834i
$886$	−3.39451	+	7.43293i	−0.114041	+	0.249714i
$887$	−12.3478	−	16.4948i	−0.414600	−	0.553841i	0.543820	−	0.839202i	$-0.316977\pi$
$887$	−12.3478	−	16.4948i	−0.414600	−	0.553841i	−0.958420	+	0.285361i	$0.907886\pi$
$888$	1.40017	−	6.43650i	0.0469868	−	0.215995i
$889$	−22.8396	−	6.70630i	−0.766014	−	0.224922i
$890$	−36.3856	−	14.7086i	−1.21965	−	0.493035i
$891$	7.79208	−	6.75188i	0.261045	−	0.226196i
$892$	−18.5431	+	4.03380i	−0.620868	+	0.135061i
$893$	−0.378124	−	5.28686i	−0.0126534	−	0.176918i
$894$	15.9572	−	4.68546i	0.533690	−	0.156705i
$895$	1.19609	−	0.980839i	0.0399810	−	0.0327858i
$896$		−	4.01549i		−	0.134148i
$897$	13.5670	+	14.4185i	0.452988	+	0.481419i
$898$	−27.5522	−	27.5522i	−0.919430	−	0.919430i
$899$	2.47562	−	1.13058i	0.0825665	−	0.0377069i
$900$	7.65753	−	7.92369i	0.255251	−	0.264123i
$901$	−0.712812	+	0.822629i	−0.0237472	+	0.0274057i
$902$	−0.477182	−	2.19357i	−0.0158884	−	0.0730379i
$903$	−1.15119	+	16.0958i	−0.0383093	+	0.535634i
$904$	2.61815	+	18.2096i	0.0870782	+	0.605642i
$905$	0.227377	−	8.36981i	0.00755828	−	0.278222i
$906$	15.2432	−	9.79619i	0.506420	−	0.325457i
$907$	31.6755	−	23.7120i	1.05177	−	0.787344i	0.0740475	−	0.997255i	$-0.476408\pi$
$907$	31.6755	−	23.7120i	1.05177	−	0.787344i	0.977720	+	0.209911i	$0.0673174\pi$
$908$	0.478489	+	1.28288i	0.0158792	+	0.0425739i
$909$	−18.4913	−	8.44468i	−0.613317	−	0.280093i
$910$	−25.7886	+	32.5670i	−0.854882	+	1.07959i
$911$	−12.2185	−	19.0124i	−0.404818	−	0.629909i	0.577662	−	0.816276i	$-0.303965\pi$
$911$	−12.2185	−	19.0124i	−0.404818	−	0.629909i	−0.982480	+	0.186367i	$0.940329\pi$
$912$	0.645967	+	1.18300i	0.0213901	+	0.0391730i
$913$	−20.5545	+	27.4575i	−0.680253	+	0.908712i
$914$	−15.8555	−	18.2982i	−0.524453	−	0.605251i
$915$	−25.1322	+	12.8499i	−0.830846	+	0.424804i
$916$	−20.2476	−	17.5447i	−0.669001	−	0.579693i
$917$	−24.3899	−	13.3179i	−0.805424	−	0.439795i
$918$	−19.2455	−	7.17820i	−0.635196	−	0.236916i
$919$	3.92312			0.129412			0.0647059	−	0.997904i	$-0.479389\pi$
$919$	3.92312			0.129412			0.0647059	+	0.997904i	$0.479389\pi$
$920$	−7.47734	+	7.68696i	−0.246521	+	0.253432i
$921$	18.4056			0.606486
$922$	8.38372	+	3.12697i	0.276103	+	0.102981i
$923$	−18.8561	−	10.2962i	−0.620656	−	0.338904i
$924$	11.3103	+	9.80040i	0.372080	+	0.322409i
$925$	−24.6447	−	27.4788i	−0.810312	−	0.903497i
$926$	13.9384	+	16.0858i	0.458046	+	0.528613i
$927$	7.53026	−	10.0593i	0.247326	−	0.330389i
$928$	−1.33495	−	2.44478i	−0.0438218	−	0.0802537i
$929$	21.2611	+	33.0829i	0.697553	+	1.08541i	0.991565	+	0.129612i	$0.0413733\pi$
$929$	21.2611	+	33.0829i	0.697553	+	1.08541i	−0.294011	+	0.955802i	$0.594990\pi$
$930$	−0.224926	−	1.93638i	−0.00737561	−	0.0634963i
$931$	−12.5374	−	5.72565i	−0.410897	−	0.187650i
$932$	0.661878	+	1.77456i	0.0216805	+	0.0581277i
$933$	−9.45875	+	7.08074i	−0.309666	+	0.231813i
$934$	27.4123	−	17.6168i	0.896958	−	0.576440i
$935$	−29.9982	+	28.4114i	−0.981045	+	0.929152i
$936$	−1.45106	−	10.0923i	−0.0474292	−	0.329878i
$937$	0.140069	−	1.95842i	0.00457585	−	0.0639787i	−0.994651	−	0.103292i	$-0.967062\pi$
$937$	0.140069	−	1.95842i	0.00457585	−	0.0639787i	0.999227	+	0.0393131i	$0.0125170\pi$
$938$	−13.8235	−	63.5454i	−0.451352	−	2.07483i
$939$	−15.4418	+	17.8208i	−0.503926	+	0.581561i
$940$	7.61847	+	1.87535i	0.248487	+	0.0611670i
$941$	2.10446	−	0.961074i	0.0686034	−	0.0313301i	−0.380818	−	0.924650i	$-0.624358\pi$
$941$	2.10446	−	0.961074i	0.0686034	−	0.0313301i	0.449421	+	0.893320i	$0.351630\pi$
$942$	13.9956	+	13.9956i	0.456001	+	0.456001i
$943$	0.105601	+	2.57534i	0.00343885	+	0.0838647i
$944$		−	4.28825i		−	0.139571i
$945$	26.4364	+	32.2382i	0.859977	+	1.04871i
$946$	−18.0500	+	5.29997i	−0.586857	+	0.172317i
$947$	−1.61481	−	22.5781i	−0.0524744	−	0.733688i	−0.953780	−	0.300505i	$-0.902845\pi$
$947$	−1.61481	−	22.5781i	−0.0524744	−	0.733688i	0.901306	−	0.433183i	$-0.142610\pi$
$948$	−9.88016	+	2.14930i	−0.320893	+	0.0698059i
$949$	1.51134	−	1.30959i	0.0490603	−	0.0425110i
$950$	7.49337	+	0.947056i	0.243117	+	0.0307265i
$951$	9.83022	+	2.88641i	0.318767	+	0.0935983i
$952$	−3.77589	+	17.3575i	−0.122377	+	0.562560i
$953$	−4.55215	−	6.08095i	−0.147458	−	0.196981i	0.720730	−	0.693216i	$-0.243807\pi$
$953$	−4.55215	−	6.08095i	−0.147458	−	0.196981i	−0.868189	+	0.496234i	$0.834716\pi$
$954$	−0.225268	+	0.493268i	−0.00729332	+	0.0159702i
$955$	−11.7960	−	2.02437i	−0.381710	−	0.0655072i
$956$	3.26806	−	22.7299i	0.105697	−	0.735136i
$957$	10.1442	+	2.20674i	0.327916	+	0.0713339i
$958$	0.429034	−	0.234270i	0.0138615	−	0.00756893i
$959$	−44.6430	+	6.41869i	−1.44160	+	0.207270i
$960$	−1.96040	+	0.371009i	−0.0632715	+	0.0119743i
$961$	−25.2758	−	16.2438i	−0.815348	−	0.523992i
$962$	−34.0671	+	2.43653i	−1.09837	+	0.0785568i
$963$	−17.2964	+	31.6759i	−0.557367	+	1.02074i
$964$	−2.04795	−	4.48437i	−0.0659599	−	0.144432i
$965$	−24.2113	−	14.0871i	−0.779390	−	0.453480i
$966$	−10.8524	−	13.3224i	−0.349171	−	0.428641i
$967$	26.8776	−	26.8776i	0.864325	−	0.864325i	−0.127512	−	0.991837i	$-0.540699\pi$
$967$	26.8776	−	26.8776i	0.864325	−	0.864325i	0.991837	+	0.127512i	$0.0406992\pi$
$968$	−2.25286	+	6.04015i	−0.0724097	+	0.194138i
$969$	−1.67986	−	5.72109i	−0.0539650	−	0.183788i
$970$	2.26684	−	4.62688i	0.0727840	−	0.148560i
$971$	28.1611	−	43.8196i	0.903734	−	1.40624i	−0.0100108	−	0.999950i	$-0.503187\pi$
$971$	28.1611	−	43.8196i	0.903734	−	1.40624i	0.913745	−	0.406288i	$-0.133177\pi$
$972$	−16.0912	−	1.15087i	−0.516127	−	0.0369141i
$973$	−41.1985	−	30.8408i	−1.32076	−	0.988712i
$974$	−1.54651	+	5.26694i	−0.0495535	+	0.168764i
$975$	18.2822	+	9.58118i	0.585499	+	0.306843i
$976$	−14.0034	−	2.01338i	−0.448236	−	0.0644467i
$977$	−51.4111	+	19.1753i	−1.64479	+	0.613474i	−0.989838	−	0.142200i	$-0.954582\pi$
$977$	−51.4111	+	19.1753i	−1.64479	+	0.613474i	−0.654948	+	0.755674i	$0.727310\pi$
$978$	−0.575752	+	0.214744i	−0.0184105	+	0.00686676i
$979$	72.5645	+	10.4332i	2.31917	+	0.333447i
$980$	13.7745	−	15.0505i	0.440009	−	0.480771i
$981$	−1.93393	+	6.58635i	−0.0617455	+	0.210286i
$982$	−5.05902	−	3.78713i	−0.161440	−	0.120852i
$983$	−36.6824	−	2.62357i	−1.16999	−	0.0836790i	−0.527211	−	0.849734i	$-0.676762\pi$
$983$	−36.6824	−	2.62357i	−1.16999	−	0.0836790i	−0.642775	+	0.766055i	$0.722217\pi$
$984$	−0.259266	+	0.403425i	−0.00826509	+	0.0128607i
$985$	−6.09900	−	17.8153i	−0.194330	−	0.567644i
$986$	3.47159	+	11.8232i	0.110558	+	0.376526i
$987$	−4.39338	+	11.7791i	−0.139843	+	0.374933i
$988$	4.94183	−	4.94183i	0.157220	−	0.157220i
$989$	21.4633	−	2.42229i	0.682493	−	0.0770242i
$990$	−10.3516	+	17.7912i	−0.328996	+	0.565442i
$991$	15.9106	+	34.8393i	0.505416	+	1.10671i	0.974671	+	0.223644i	$0.0717952\pi$
$991$	15.9106	+	34.8393i	0.505416	+	1.10671i	−0.469255	+	0.883063i	$0.655478\pi$
$992$	0.468248	−	0.857532i	0.0148669	−	0.0272267i
$993$	26.0101	−	1.86028i	0.825404	−	0.0590341i
$994$	15.6866	+	10.0811i	0.497548	+	0.319755i
$995$	4.94418	+	3.37059i	0.156741	+	0.106855i
$996$	7.25236	−	1.04273i	0.229800	−	0.0330402i
$997$	−10.0063	+	5.46385i	−0.316902	+	0.173042i	−0.629826	−	0.776737i	$-0.716874\pi$
$997$	−10.0063	+	5.46385i	−0.316902	+	0.173042i	0.312923	+	0.949778i	$0.398692\pi$
$998$	−13.2930	−	2.89171i	−0.420782	−	0.0915356i
$999$	−4.87825	+	33.9290i	−0.154341	+	1.07346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.203.10	yes	240
5.2	odd	4	inner	230.2.l.a.157.4	yes	240
23.17	odd	22	inner	230.2.l.a.63.4	yes	240
115.17	even	44	inner	230.2.l.a.17.10	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.10	✓	240	115.17	even	44	inner
230.2.l.a.63.4	yes	240	23.17	odd	22	inner
230.2.l.a.157.4	yes	240	5.2	odd	4	inner
230.2.l.a.203.10	yes	240	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.936950 + 0.349464i) q^{2} +(0.783134 + 0.427624i) q^{3} +(0.755750 + 0.654861i) q^{4} +(2.12759 + 0.688005i) q^{5} +(0.584318 + 0.674339i) q^{6} +(-2.40639 + 3.21457i) q^{7} +(0.479249 + 0.877679i) q^{8} +(-1.19149 - 1.85399i) q^{9} +O(q^{10})\)	\(q+(0.936950 + 0.349464i) q^{2} +(0.783134 + 0.427624i) q^{3} +(0.755750 + 0.654861i) q^{4} +(2.12759 + 0.688005i) q^{5} +(0.584318 + 0.674339i) q^{6} +(-2.40639 + 3.21457i) q^{7} +(0.479249 + 0.877679i) q^{8} +(-1.19149 - 1.85399i) q^{9} +(1.75301 + 1.38814i) q^{10} +(-3.79945 - 1.73515i) q^{11} +(0.311819 + 0.836020i) q^{12} +(3.70372 - 2.77257i) q^{13} +(-3.37805 + 2.17094i) q^{14} +(1.37198 + 1.44861i) q^{15} +(0.142315 + 0.989821i) q^{16} +(0.315585 - 4.41246i) q^{17} +(-0.468460 - 2.15347i) q^{18} +(0.989230 - 1.14163i) q^{19} +(1.15738 + 1.91324i) q^{20} +(-3.25915 + 1.48841i) q^{21} +(-2.95352 - 2.95352i) q^{22} +(2.75594 + 3.92489i) q^{23} +0.892278i q^{24} +(4.05330 + 2.92759i) q^{25} +(4.43911 - 1.30344i) q^{26} +(-0.331247 - 4.63144i) q^{27} +(-3.92373 + 0.853554i) q^{28} +(-2.10514 + 1.82412i) q^{29} +(0.779242 + 1.83673i) q^{30} +(-0.937468 - 0.275265i) q^{31} +(-0.212565 + 0.977147i) q^{32} +(-2.23349 - 2.98359i) q^{33} +(1.83768 - 4.02397i) q^{34} +(-7.33146 + 5.18368i) q^{35} +(0.313639 - 2.18141i) q^{36} +(-7.21355 - 1.56921i) q^{37} +(1.32582 - 0.723952i) q^{38} +(4.08612 - 0.587495i) q^{39} +(0.415799 + 2.19707i) q^{40} +(0.452129 + 0.290566i) q^{41} +(-3.57381 + 0.255604i) q^{42} +(2.15845 - 3.95291i) q^{43} +(-1.73515 - 3.79945i) q^{44} +(-1.25944 - 4.76428i) q^{45} +(1.21057 + 4.64053i) q^{46} +(2.48109 - 2.48109i) q^{47} +(-0.311819 + 0.836020i) q^{48} +(-2.57058 - 8.75459i) q^{49} +(2.77465 + 4.15948i) q^{50} +(2.13402 - 3.32059i) q^{51} +(4.61473 + 0.330052i) q^{52} +(-0.196980 - 0.147457i) q^{53} +(1.30816 - 4.45519i) q^{54} +(-6.88990 - 6.30574i) q^{55} +(-3.97462 - 0.571464i) q^{56} +(1.26289 - 0.471033i) q^{57} +(-2.60987 + 0.973433i) q^{58} +(-4.24460 - 0.610282i) q^{59} +(0.0882389 + 1.99324i) q^{60} +(-3.98577 + 13.5743i) q^{61} +(-0.782165 - 0.585521i) q^{62} +(8.82695 + 0.631316i) q^{63} +(-0.540641 + 0.841254i) q^{64} +(9.78754 - 3.35072i) q^{65} +(-1.05001 - 3.57600i) q^{66} +(-5.65963 + 15.1741i) q^{67} +(3.12805 - 3.12805i) q^{68} +(0.479894 + 4.25222i) q^{69} +(-8.68072 + 2.29476i) q^{70} +(-1.92905 - 4.22404i) q^{71} +(1.05619 - 1.93426i) q^{72} +(0.431145 - 0.0308361i) q^{73} +(-6.21035 - 3.99115i) q^{74} +(1.92237 + 4.02598i) q^{75} +(1.49522 - 0.214980i) q^{76} +(14.7208 - 8.03814i) q^{77} +(4.03380 + 0.877499i) q^{78} +(-1.61270 + 11.2166i) q^{79} +(-0.378214 + 2.20385i) q^{80} +(-1.02542 + 2.24536i) q^{81} +(0.322080 + 0.430249i) q^{82} +(1.74548 - 8.02384i) q^{83} +(-3.43780 - 1.00943i) q^{84} +(3.70723 - 9.17079i) q^{85} +(3.40376 - 2.94937i) q^{86} +(-2.42864 + 0.528319i) q^{87} +(-0.297978 - 4.16627i) q^{88} +(-16.8404 + 4.94480i) q^{89} +(0.484909 - 4.90402i) q^{90} +18.5777i q^{91} +(-0.487458 + 4.77099i) q^{92} +(-0.616453 - 0.616453i) q^{93} +(3.19171 - 1.45760i) q^{94} +(2.89013 - 1.74833i) q^{95} +(-0.584318 + 0.674339i) q^{96} +(-0.489792 - 2.25154i) q^{97} +(0.650911 - 9.10093i) q^{98} +(1.31004 + 9.11155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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