LMFDB - Embedded newform 230.2.l.a.83.12

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			83.12
Character	$\chi$	$=$	230.83
Dual form			230.2.l.a.97.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.479249 - 0.877679i) q^{2} +(0.216786 - 3.03106i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.67624 + 1.47994i) q^{5} +(-2.55641 - 1.64290i) q^{6} +(3.64718 - 1.36033i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(-6.17089 - 0.887239i) q^{9} +O(q^{10})$	\(q+(0.479249 - 0.877679i) q^{2} +(0.216786 - 3.03106i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.67624 + 1.47994i) q^{5} +(-2.55641 - 1.64290i) q^{6} +(3.64718 - 1.36033i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(-6.17089 - 0.887239i) q^{9} +(2.10225 - 0.761935i) q^{10} +(-0.0570612 + 0.194333i) q^{11} +(-2.66710 + 1.45634i) q^{12} +(-2.31388 + 6.20374i) q^{13} +(0.553977 - 3.85299i) q^{14} +(4.84919 - 4.75995i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.680388 + 3.12769i) q^{17} +(-3.73610 + 4.99085i) q^{18} +(-4.00065 + 2.57106i) q^{19} +(0.338767 - 2.21026i) q^{20} +(-3.33259 - 11.3497i) q^{21} +(0.143215 + 0.143215i) q^{22} +(-3.15480 - 3.61210i) q^{23} +3.03881i q^{24} +(0.619531 + 4.96147i) q^{25} +(4.33597 + 5.00398i) q^{26} +(-2.08921 + 9.60393i) q^{27} +(-3.11620 - 2.33276i) q^{28} +(1.17472 - 1.82789i) q^{29} +(-1.85374 - 6.53723i) q^{30} +(1.41408 - 1.63193i) q^{31} +(0.599278 + 0.800541i) q^{32} +(0.576664 + 0.215085i) q^{33} +(3.07118 + 0.901781i) q^{34} +(8.12675 + 3.11740i) q^{35} +(2.58984 + 5.67096i) q^{36} +(1.84910 - 1.38422i) q^{37} +(0.339260 + 4.74347i) q^{38} +(18.3023 + 8.35839i) q^{39} +(-1.77754 - 1.35659i) q^{40} +(-1.09725 - 7.63155i) q^{41} +(-11.5586 - 2.51441i) q^{42} +(5.80518 + 0.415195i) q^{43} +(0.194333 - 0.0570612i) q^{44} +(-9.03079 - 10.6198i) q^{45} +(-4.68220 + 1.03781i) q^{46} +(-1.72572 + 1.72572i) q^{47} +(2.66710 + 1.45634i) q^{48} +(6.16120 - 5.33871i) q^{49} +(4.65149 + 1.83403i) q^{50} +(9.62773 - 1.38426i) q^{51} +(6.46990 - 1.40744i) q^{52} +(-2.18956 - 5.87044i) q^{53} +(7.42791 + 6.43632i) q^{54} +(-0.383249 + 0.241300i) q^{55} +(-3.54085 + 1.61705i) q^{56} +(6.92578 + 12.6836i) q^{57} +(-1.04132 - 1.90704i) q^{58} +(-2.26227 + 1.03315i) q^{59} +(-6.62599 - 1.50598i) q^{60} +(1.61532 + 1.39968i) q^{61} +(-0.754618 - 2.02321i) q^{62} +(-23.7133 + 5.15851i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-13.0598 + 6.97453i) q^{65} +(0.465141 - 0.403047i) q^{66} +(1.80383 + 0.984965i) q^{67} +(2.26334 - 2.26334i) q^{68} +(-11.6324 + 8.77935i) q^{69} +(6.63081 - 5.63867i) q^{70} +(-11.8058 + 3.46651i) q^{71} +(6.21846 + 0.444753i) q^{72} +(2.02950 + 0.441491i) q^{73} +(-0.328720 - 2.28630i) q^{74} +(15.1728 - 0.802260i) q^{75} +(4.32583 + 1.97554i) q^{76} +(0.0562436 + 0.786388i) q^{77} +(16.1074 - 12.0578i) q^{78} +(-5.83137 - 12.7689i) q^{79} +(-2.04254 + 0.909966i) q^{80} +(10.7118 + 3.14526i) q^{81} +(-7.22391 - 2.69438i) q^{82} +(3.77693 + 5.04539i) q^{83} +(-7.74628 + 8.93969i) q^{84} +(-3.48832 + 6.24968i) q^{85} +(3.14654 - 4.89611i) q^{86} +(-5.28580 - 3.95690i) q^{87} +(0.0430523 - 0.197908i) q^{88} +(-5.94416 - 6.85993i) q^{89} +(-13.6488 + 2.83661i) q^{90} +25.7738i q^{91} +(-1.33307 + 4.60683i) q^{92} +(-4.63994 - 4.63994i) q^{93} +(0.687577 + 2.34167i) q^{94} +(-10.5111 - 1.61104i) q^{95} +(2.55641 - 1.64290i) q^{96} +(-5.98166 + 7.99056i) q^{97} +(-1.73293 - 7.96613i) q^{98} +(0.524538 - 1.14858i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{21}{22}\right)$

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 $

$2$	0.479249	−	0.877679i	0.338880	−	0.620613i
$2$	0.479249	−	0.877679i	0.338880	−	0.620613i
$3$	0.216786	−	3.03106i	0.125161	−	1.74999i	−0.416271	−	0.909241i	$-0.636663\pi$
$3$	0.216786	−	3.03106i	0.125161	−	1.74999i	0.541432	−	0.840745i	$-0.317882\pi$
$4$	−0.540641	−	0.841254i	−0.270320	−	0.420627i
$5$	1.67624	+	1.47994i	0.749635	+	0.661851i
$5$	1.67624	+	1.47994i	0.749635	+	0.661851i
$6$	−2.55641	−	1.64290i	−1.04365	−	0.670712i
$7$	3.64718	−	1.36033i	1.37851	−	0.514156i	0.452533	−	0.891747i	$-0.350520\pi$
$7$	3.64718	−	1.36033i	1.37851	−	0.514156i	0.925972	+	0.377591i	$0.123248\pi$
$8$	−0.997452	+	0.0713392i	−0.352653	+	0.0252222i
$9$	−6.17089	−	0.887239i	−2.05696	−	0.295746i
$10$	2.10225	−	0.761935i	0.664790	−	0.240945i
$11$	−0.0570612	+	0.194333i	−0.0172046	+	0.0585935i	−0.967648	−	0.252304i	$-0.918812\pi$
$11$	−0.0570612	+	0.194333i	−0.0172046	+	0.0585935i	0.950443	+	0.310898i	$0.100630\pi$
$12$	−2.66710	+	1.45634i	−0.769924	+	0.420411i
$13$	−2.31388	+	6.20374i	−0.641754	+	1.72061i	0.0502716	+	0.998736i	$0.483991\pi$
$13$	−2.31388	+	6.20374i	−0.641754	+	1.72061i	−0.692025	+	0.721873i	$0.743281\pi$
$14$	0.553977	−	3.85299i	0.148057	−	1.02976i
$15$	4.84919	−	4.75995i	1.25206	−	1.22901i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	0.680388	+	3.12769i	0.165018	+	0.758577i	0.983040	+	0.183390i	$0.0587070\pi$
$17$	0.680388	+	3.12769i	0.165018	+	0.758577i	−0.818022	+	0.575187i	$0.804929\pi$
$18$	−3.73610	+	4.99085i	−0.880608	+	1.17635i
$19$	−4.00065	+	2.57106i	−0.917813	+	0.589843i	−0.912022	−	0.410141i	$-0.865480\pi$
$19$	−4.00065	+	2.57106i	−0.917813	+	0.589843i	−0.00579084	+	0.999983i	$0.501843\pi$
$20$	0.338767	−	2.21026i	0.0757506	−	0.494229i
$21$	−3.33259	−	11.3497i	−0.727230	−	2.47672i
$22$	0.143215	+	0.143215i	0.0305336	+	0.0305336i
$23$	−3.15480	−	3.61210i	−0.657821	−	0.753174i
$23$	−3.15480	−	3.61210i	−0.657821	−	0.753174i
$24$			3.03881i			0.620294i
$25$	0.619531	+	4.96147i	0.123906	+	0.992294i
$26$	4.33597	+	5.00398i	0.850354	+	0.981361i
$27$	−2.08921	+	9.60393i	−0.402068	+	1.84828i
$28$	−3.11620	−	2.33276i	−0.588906	−	0.440850i
$29$	1.17472	−	1.82789i	0.218139	−	0.339431i	−0.714887	−	0.699240i	$-0.753522\pi$
$29$	1.17472	−	1.82789i	0.218139	−	0.339431i	0.933026	+	0.359809i	$0.117158\pi$
$30$	−1.85374	−	6.53723i	−0.338444	−	1.19353i
$31$	1.41408	−	1.63193i	0.253976	−	0.293104i	−0.614416	−	0.788982i	$-0.710608\pi$
$31$	1.41408	−	1.63193i	0.253976	−	0.293104i	0.868392	+	0.495878i	$0.165154\pi$
$32$	0.599278	+	0.800541i	0.105938	+	0.141517i
$33$	0.576664	+	0.215085i	0.100384	+	0.0374414i
$34$	3.07118	+	0.901781i	0.526704	+	0.154654i
$35$	8.12675	+	3.11740i	1.37367	+	0.526936i
$36$	2.58984	+	5.67096i	0.431640	+	0.945160i
$37$	1.84910	−	1.38422i	0.303990	−	0.227564i	−0.436382	−	0.899762i	$-0.643740\pi$
$37$	1.84910	−	1.38422i	0.303990	−	0.227564i	0.740372	+	0.672197i	$0.234649\pi$
$38$	0.339260	+	4.74347i	0.0550352	+	0.769493i
$39$	18.3023	+	8.35839i	2.93072	+	1.33841i
$40$	−1.77754	−	1.35659i	−0.281054	−	0.214496i
$41$	−1.09725	−	7.63155i	−0.171362	−	1.19185i	−0.876010	−	0.482292i	$-0.839804\pi$
$41$	−1.09725	−	7.63155i	−0.171362	−	1.19185i	0.704649	−	0.709557i	$-0.251105\pi$
$42$	−11.5586	−	2.51441i	−1.78353	−	0.387982i
$43$	5.80518	+	0.415195i	0.885282	+	0.0633166i	0.506571	−	0.862198i	$-0.330913\pi$
$43$	5.80518	+	0.415195i	0.885282	+	0.0633166i	0.378711	+	0.925515i	$0.376367\pi$
$44$	0.194333	−	0.0570612i	0.0292967	−	0.00860230i
$45$	−9.03079	−	10.6198i	−1.34623	−	1.58310i
$46$	−4.68220	+	1.03781i	−0.690352	+	0.153016i
$47$	−1.72572	+	1.72572i	−0.251721	+	0.251721i	−0.821676	−	0.569955i	$-0.806961\pi$
$47$	−1.72572	+	1.72572i	−0.251721	+	0.251721i	0.569955	+	0.821676i	$0.306961\pi$
$48$	2.66710	+	1.45634i	0.384962	+	0.210205i
$49$	6.16120	−	5.33871i	0.880172	−	0.762673i
$50$	4.65149	+	1.83403i	0.657820	+	0.259371i
$51$	9.62773	−	1.38426i	1.34815	−	0.193835i
$52$	6.46990	−	1.40744i	0.897213	−	0.195177i
$53$	−2.18956	−	5.87044i	−0.300759	−	0.806367i	−0.996144	−	0.0877298i	$-0.972039\pi$
$53$	−2.18956	−	5.87044i	−0.300759	−	0.806367i	0.695385	−	0.718638i	$-0.255234\pi$
$54$	7.42791	+	6.43632i	1.01081	+	0.875873i
$55$	−0.383249	+	0.241300i	−0.0516773	+	0.0325369i
$56$	−3.54085	+	1.61705i	−0.473165	+	0.216087i
$57$	6.92578	+	12.6836i	0.917341	+	1.67999i
$58$	−1.04132	−	1.90704i	−0.136732	−	0.250407i
$59$	−2.26227	+	1.03315i	−0.294523	+	0.134504i	−0.557196	−	0.830381i	$-0.688123\pi$
$59$	−2.26227	+	1.03315i	−0.294523	+	0.134504i	0.262674	+	0.964885i	$0.415396\pi$
$60$	−6.62599	−	1.50598i	−0.855412	−	0.194421i
$61$	1.61532	+	1.39968i	0.206820	+	0.179211i	0.752112	−	0.659036i	$-0.229035\pi$
$61$	1.61532	+	1.39968i	0.206820	+	0.179211i	−0.545291	+	0.838247i	$0.683581\pi$
$62$	−0.754618	−	2.02321i	−0.0958365	−	0.256948i
$63$	−23.7133	+	5.15851i	−2.98759	+	0.649911i
$64$	0.989821	−	0.142315i	0.123728	−	0.0177894i
$65$	−13.0598	+	6.97453i	−1.61987	+	0.865083i
$66$	0.465141	−	0.403047i	0.0572549	−	0.0496117i
$67$	1.80383	+	0.984965i	0.220373	+	0.120333i	0.585644	−	0.810569i	$-0.300842\pi$
$67$	1.80383	+	0.984965i	0.220373	+	0.120333i	−0.365271	+	0.930901i	$0.619024\pi$
$68$	2.26334	−	2.26334i	0.274470	−	0.274470i
$69$	−11.6324	+	8.77935i	−1.40038	+	1.05691i
$70$	6.63081	−	5.63867i	0.792533	−	0.673950i
$71$	−11.8058	+	3.46651i	−1.40109	+	0.411398i	−0.893060	−	0.449938i	$-0.851446\pi$
$71$	−11.8058	+	3.46651i	−1.40109	+	0.411398i	−0.508035	+	0.861337i	$0.669628\pi$
$72$	6.21846	+	0.444753i	0.732852	+	0.0524146i
$73$	2.02950	+	0.441491i	0.237535	+	0.0516726i	0.329757	−	0.944066i	$-0.393033\pi$
$73$	2.02950	+	0.441491i	0.237535	+	0.0516726i	−0.0922216	+	0.995739i	$0.529397\pi$
$74$	−0.328720	−	2.28630i	−0.0382130	−	0.265777i
$75$	15.1728	−	0.802260i	1.75201	−	0.0926371i
$76$	4.32583	+	1.97554i	0.496207	+	0.226610i
$77$	0.0562436	+	0.786388i	0.00640955	+	0.0896173i
$78$	16.1074	−	12.0578i	1.82380	−	1.36528i
$79$	−5.83137	−	12.7689i	−0.656081	−	1.43662i	−0.886130	−	0.463438i	$-0.846616\pi$
$79$	−5.83137	−	12.7689i	−0.656081	−	1.43662i	0.230049	−	0.973179i	$-0.426111\pi$
$80$	−2.04254	+	0.909966i	−0.228363	+	0.101737i
$81$	10.7118	+	3.14526i	1.19020	+	0.349474i
$82$	−7.22391	−	2.69438i	−0.797748	−	0.297544i
$83$	3.77693	+	5.04539i	0.414572	+	0.553804i	0.958413	−	0.285385i	$-0.0921214\pi$
$83$	3.77693	+	5.04539i	0.414572	+	0.553804i	−0.543841	+	0.839188i	$0.683030\pi$
$84$	−7.74628	+	8.93969i	−0.845189	+	0.975400i
$85$	−3.48832	+	6.24968i	−0.378361	+	0.677873i
$86$	3.14654	−	4.89611i	0.339300	−	0.527961i
$87$	−5.28580	−	3.95690i	−0.566697	−	0.424224i
$88$	0.0430523	−	0.197908i	0.00458939	−	0.0210971i
$89$	−5.94416	−	6.85993i	−0.630080	−	0.727151i	0.347508	−	0.937677i	$-0.387028\pi$
$89$	−5.94416	−	6.85993i	−0.630080	−	0.727151i	−0.977588	+	0.210526i	$0.932482\pi$
$90$	−13.6488	+	2.83661i	−1.43871	+	0.299005i
$91$			25.7738i			2.70183i
$92$	−1.33307	+	4.60683i	−0.138983	+	0.480296i
$93$	−4.63994	−	4.63994i	−0.481139	−	0.481139i
$94$	0.687577	+	2.34167i	0.0709181	+	0.241525i
$95$	−10.5111	−	1.61104i	−1.07841	−	0.165289i
$96$	2.55641	−	1.64290i	0.260912	−	0.167678i
$97$	−5.98166	+	7.99056i	−0.607346	+	0.811319i	−0.993823	−	0.110980i	$-0.964601\pi$
$97$	−5.98166	+	7.99056i	−0.607346	+	0.811319i	0.386477	+	0.922299i	$0.373692\pi$
$98$	−1.73293	−	7.96613i	−0.175052	−	0.804701i
$99$	0.524538	−	1.14858i	0.0527180	−	0.115436i
$100$	3.83891	−	3.20356i	0.383891	−	0.320356i
$101$	0.762887	−	5.30599i	0.0759101	−	0.527966i	−0.916015	−	0.401143i	$-0.868613\pi$
$101$	0.762887	−	5.30599i	0.0759101	−	0.527966i	0.991925	−	0.126823i	$-0.0404780\pi$
$102$	3.39914	−	9.11346i	0.336565	−	0.902367i
$103$	11.1074	−	6.06509i	1.09444	−	0.597612i	0.172529	−	0.985004i	$-0.444806\pi$
$103$	11.1074	−	6.06509i	1.09444	−	0.597612i	0.921915	+	0.387393i	$0.126624\pi$
$104$	1.86541	−	6.35301i	0.182919	−	0.622964i
$105$	11.2108	−	23.9569i	1.09406	−	2.33795i
$106$	−6.20171	−	0.891671i	−0.602363	−	0.0866068i
$107$	−8.47442	+	0.606103i	−0.819253	+	0.0585942i	−0.474673	−	0.880162i	$-0.657434\pi$
$107$	−8.47442	+	0.606103i	−0.819253	+	0.0585942i	−0.344581	+	0.938757i	$0.611979\pi$
$108$	9.20885	−	3.43472i	0.886122	−	0.330506i
$109$	12.7993	+	8.22563i	1.22595	+	0.787872i	0.983256	−	0.182230i	$-0.0583315\pi$
$109$	12.7993	+	8.22563i	1.22595	+	0.787872i	0.242697	+	0.970102i	$0.421968\pi$
$110$	0.0281119	+	0.452013i	0.00268036	+	0.0430977i
$111$	−3.79479	−	5.90481i	−0.360186	−	0.560460i
$112$	−0.277696	+	3.88270i	−0.0262398	+	0.366880i
$113$	0.0610399	−	0.111786i	0.00574215	−	0.0105160i	−0.874792	−	0.484498i	$-0.839002\pi$
$113$	0.0610399	−	0.111786i	0.00574215	−	0.0105160i	0.880534	+	0.473982i	$0.157184\pi$
$114$	14.4513			1.35349
$115$	0.0575127	−	10.7237i	0.00536309	−	0.999986i
$116$	−2.17282			−0.201741
$117$	19.7829	−	36.2296i	1.82893	−	3.34943i
$118$	−0.177422	+	2.48068i	−0.0163330	+	0.228365i
$119$	6.73619	+	10.4817i	0.617505	+	0.960857i
$120$	−4.49726	+	5.09375i	−0.410542	+	0.464994i
$121$	9.21928	+	5.92487i	0.838116	+	0.538625i
$122$	2.00261	−	0.746936i	0.181308	−	0.0676244i
$123$	−23.3696	+	1.67143i	−2.10717	+	0.150707i
$124$	−2.13738	−	0.307308i	−0.191942	−	0.0275971i
$125$	−6.30422	+	9.23346i	−0.563866	+	0.825866i
$126$	−6.83705	+	23.2849i	−0.609093	+	2.07438i
$127$	−12.8028	+	6.99088i	−1.13607	+	0.620340i	−0.933375	−	0.358902i	$-0.883151\pi$
$127$	−12.8028	+	6.99088i	−1.13607	+	0.620340i	−0.202693	+	0.979242i	$0.564969\pi$
$128$	0.349464	−	0.936950i	0.0308886	−	0.0828154i
$129$	2.51696	−	17.5059i	0.221606	−	1.54131i
$130$	−0.137498	+	14.8048i	−0.0120594	+	1.29847i
$131$	8.08095	−	17.6948i	0.706035	−	1.54600i	−0.126461	−	0.991972i	$-0.540362\pi$
$131$	8.08095	−	17.6948i	0.706035	−	1.54600i	0.832496	−	0.554030i	$-0.186911\pi$
$132$	−0.130828	−	0.601404i	−0.0113871	−	0.0523455i
$133$	−11.0936	+	14.8194i	−0.961940	+	1.28500i
$134$	1.72897	−	1.11114i	0.149360	−	0.0959878i
$135$	−17.7153	+	13.0065i	−1.52469	+	1.11942i
$136$	−0.901781	−	3.07118i	−0.0773271	−	0.263352i
$137$	−6.44414	−	6.44414i	−0.550560	−	0.550560i	0.376042	−	0.926602i	$-0.377285\pi$
$137$	−6.44414	−	6.44414i	−0.550560	−	0.550560i	−0.926602	+	0.376042i	$0.877285\pi$
$138$	2.13063	+	14.4170i	0.181371	+	1.22726i
$139$			11.0649i			0.938511i	0.883062	+	0.469256i	$0.155478\pi$
$139$			11.0649i			0.938511i	−0.883062	+	0.469256i	$0.844522\pi$
$140$	−1.77113	−	8.52205i	−0.149688	−	0.720245i
$141$	4.85664	+	5.60486i	0.409003	+	0.472015i
$142$	−2.61545	+	12.0231i	−0.219484	+	1.00895i
$143$	−1.07356	−	0.803654i	−0.0897753	−	0.0672050i
$144$	3.37054	−	5.24466i	0.280878	−	0.437055i
$145$	4.67428	−	1.32547i	0.388178	−	0.110074i
$146$	1.36012	−	1.56967i	0.112565	−	0.129907i
$147$	−14.8463	−	19.8324i	−1.22450	−	1.63575i
$148$	−2.16418	−	0.807196i	−0.177894	−	0.0663511i
$149$	−1.32654	−	0.389507i	−0.108674	−	0.0319097i	0.226943	−	0.973908i	$-0.427127\pi$
$149$	−1.32654	−	0.389507i	−0.108674	−	0.0319097i	−0.335618	+	0.941998i	$0.608945\pi$
$150$	6.56744	−	13.7014i	0.536229	−	1.11871i
$151$	−2.57896	−	5.64713i	−0.209872	−	0.459557i	0.775196	−	0.631721i	$-0.217651\pi$
$151$	−2.57896	−	5.64713i	−0.209872	−	0.459557i	−0.985068	+	0.172165i	$0.944924\pi$
$152$	3.80704	−	2.84992i	0.308792	−	0.231159i
$153$	−1.42358	−	19.9043i	−0.115090	−	1.60917i
$154$	0.717151	+	0.327512i	0.0577897	+	0.0263917i
$155$	4.78550	−	0.642747i	0.384380	−	0.0516267i
$156$	−2.86346	−	19.9158i	−0.229260	−	1.59454i
$157$	1.37749	+	0.299655i	0.109936	+	0.0239151i	0.267197	−	0.963642i	$-0.413903\pi$
$157$	1.37749	+	0.299655i	0.109936	+	0.0239151i	−0.157261	+	0.987557i	$0.550266\pi$
$158$	−14.0017	−	1.00142i	−1.11392	−	0.0796688i
$159$	−18.2684	+	5.36407i	−1.44877	+	0.425399i
$160$	−0.180226	+	2.22879i	−0.0142481	+	0.176202i
$161$	−16.4198	−	8.88241i	−1.29406	−	0.700032i
$162$	7.89414	−	7.89414i	0.620222	−	0.620222i
$163$	12.4675	+	6.80776i	0.976529	+	0.533225i	0.886507	−	0.462715i	$-0.153125\pi$
$163$	12.4675	+	6.80776i	0.976529	+	0.533225i	0.0900217	+	0.995940i	$0.471306\pi$
$164$	−5.82685	+	5.04900i	−0.455001	+	0.394260i
$165$	0.648312	+	1.21396i	0.0504710	+	0.0945069i
$166$	6.23833	−	0.896936i	0.484188	−	0.0696157i
$167$	15.9268	−	3.46467i	1.23246	−	0.268104i	0.451261	−	0.892392i	$-0.350974\pi$
$167$	15.9268	−	3.46467i	1.23246	−	0.268104i	0.781195	+	0.624287i	$0.214611\pi$
$168$	4.13378	+	11.0831i	0.318928	+	0.855078i
$169$	−23.3077	−	20.1962i	−1.79290	−	1.55355i
$170$	3.81344	+	6.05678i	0.292478	+	0.464534i
$171$	26.9687	−	12.3162i	2.06235	−	0.941844i
$172$	−2.78924	−	5.10810i	−0.212677	−	0.389489i
$173$	4.23178	+	7.74993i	0.321737	+	0.589216i	0.987625	−	0.156835i	$-0.0501291\pi$
$173$	4.23178	+	7.74993i	0.321737	+	0.589216i	−0.665888	+	0.746051i	$0.731947\pi$
$174$	−6.00610	+	2.74290i	−0.455322	+	0.207938i
$175$	9.00877	+	17.2526i	0.680999	+	1.30418i
$176$	−0.153067	−	0.132633i	−0.0115379	−	0.00999761i
$177$	2.64110	+	7.08106i	0.198517	+	0.532245i
$178$	−8.86955	+	1.92945i	−0.664801	+	0.144619i
$179$	5.16903	−	0.743194i	0.386351	−	0.0555489i	0.0535973	−	0.998563i	$-0.482931\pi$
$179$	5.16903	−	0.743194i	0.386351	−	0.0555489i	0.332754	+	0.943014i	$0.392022\pi$
$180$	−4.05152	+	13.3387i	−0.301982	+	0.994206i
$181$	−11.6668	+	10.1093i	−0.867183	+	0.751418i	−0.969954	−	0.243287i	$-0.921774\pi$
$181$	−11.6668	+	10.1093i	−0.867183	+	0.751418i	0.102772	+	0.994705i	$0.467229\pi$
$182$	22.6211	+	12.3521i	1.67679	+	0.915597i
$183$	4.59270	−	4.59270i	0.339503	−	0.339503i
$184$	3.40445	+	3.37783i	0.250979	+	0.249017i
$185$	5.14809	+	0.416287i	0.378495	+	0.0306061i
$186$	−6.29606	+	1.84869i	−0.461650	+	0.135553i
$187$	−0.646636	−	0.0462483i	−0.0472867	−	0.00338201i
$188$	2.38476	+	0.518772i	0.173926	+	0.0378353i
$189$	5.44478	+	37.8693i	0.396050	+	2.75459i
$190$	−6.45139	+	8.45326i	−0.468033	+	0.613264i
$191$	−8.18223	−	3.73670i	−0.592046	−	0.270378i	0.0967794	−	0.995306i	$-0.469146\pi$
$191$	−8.18223	−	3.73670i	−0.592046	−	0.270378i	−0.688825	+	0.724928i	$0.741873\pi$
$192$	−0.216786	−	3.03106i	−0.0156452	−	0.218748i
$193$	0.00879024	−	0.00658029i	0.000632735	−	0.000473660i	−0.598961	−	0.800778i	$-0.704420\pi$
$193$	0.00879024	−	0.00658029i	0.000632735	−	0.000473660i	0.599594	+	0.800304i	$0.295329\pi$
$194$	4.14644	+	9.07945i	0.297697	+	0.651866i
$195$	18.3091	+	41.0970i	1.31114	+	2.94302i
$196$	−7.82221	−	2.29681i	−0.558729	−	0.164058i
$197$	19.5367	+	7.28680i	1.39193	+	0.519163i	0.929937	−	0.367720i	$-0.119861\pi$
$197$	19.5367	+	7.28680i	1.39193	+	0.519163i	0.461994	+	0.886883i	$0.347134\pi$
$198$	−0.756698	−	1.01083i	−0.0537762	−	0.0718366i
$199$	12.3511	−	14.2539i	0.875547	−	1.01043i	−0.124288	−	0.992246i	$-0.539665\pi$
$199$	12.3511	−	14.2539i	0.875547	−	1.01043i	0.999835	−	0.0181886i	$-0.00578993\pi$
$200$	−0.971900	−	4.90463i	−0.0687237	−	0.346810i
$201$	3.37654	−	5.25400i	0.238163	−	0.370588i
$202$	−4.29135	−	3.21246i	−0.301938	−	0.226028i
$203$	1.79787	−	8.26467i	0.126186	−	0.580066i
$204$	−6.36966	−	7.35097i	−0.445965	−	0.514671i
$205$	9.45502	−	14.4162i	0.660367	−	1.00687i
$206$		−	12.6554i		−	0.881744i
$207$	16.2631	+	25.0889i	1.13036	+	1.74380i
$208$	−4.68190	−	4.68190i	−0.324632	−	0.324632i
$209$	−0.271359	−	0.924165i	−0.0187703	−	0.0639259i
$210$	−15.6537	−	21.3208i	−1.08021	−	1.47127i
$211$	2.33135	−	1.49827i	0.160497	−	0.103145i	−0.457927	−	0.888990i	$-0.651408\pi$
$211$	2.33135	−	1.49827i	0.160497	−	0.103145i	0.618424	+	0.785845i	$0.287771\pi$
$212$	−3.75476	+	5.01578i	−0.257878	+	0.344485i
$213$	7.94786	+	36.5357i	0.544578	+	2.50339i
$214$	−3.52940	+	7.72830i	−0.241264	+	0.528296i
$215$	9.11639	+	9.28731i	0.621733	+	0.633389i
$216$	1.39875	−	9.72850i	0.0951727	−	0.661941i
$217$	2.93744	−	7.87557i	0.199406	−	0.534628i
$218$	13.3535	−	7.29158i	0.904415	−	0.493848i
$219$	1.77816	−	6.05584i	0.120157	−	0.409216i
$220$	0.410194	+	0.191953i	0.0276553	+	0.0129415i
$221$	−20.9777	−	3.01614i	−1.41111	−	0.202888i
$222$	−7.00118	+	0.500735i	−0.469889	+	0.0336071i
$223$	5.91565	−	2.20642i	0.396141	−	0.147753i	−0.143496	−	0.989651i	$-0.545834\pi$
$223$	5.91565	−	2.20642i	0.396141	−	0.147753i	0.539637	+	0.841898i	$0.318562\pi$
$224$	3.27468	+	2.10451i	0.218798	+	0.140613i
$225$	0.578957	−	31.1663i	0.0385972	−	2.07776i
$226$	−0.0688591	−	0.107147i	−0.00458044	−	0.00712730i
$227$	−1.17865	+	16.4797i	−0.0782298	+	1.09379i	0.795040	+	0.606557i	$0.207450\pi$
$227$	−1.17865	+	16.4797i	−0.0782298	+	1.09379i	−0.873269	+	0.487238i	$0.838005\pi$
$228$	6.92578	−	12.6836i	0.458671	−	0.839993i
$229$	0.454378			0.0300262			0.0150131	−	0.999887i	$-0.495221\pi$
$229$	0.454378			0.0300262			0.0150131	+	0.999887i	$0.495221\pi$
$230$	−9.38436	−	5.18978i	−0.618786	−	0.342204i
$231$	2.39579			0.157631
$232$	−1.04132	+	1.90704i	−0.0683662	+	0.125203i
$233$	−0.831666	+	11.6282i	−0.0544843	+	0.761790i	0.894620	+	0.446828i	$0.147446\pi$
$233$	−0.831666	+	11.6282i	−0.0544843	+	0.761790i	−0.949104	+	0.314962i	$0.898008\pi$
$234$	−22.3171	−	34.7260i	−1.45891	−	2.27011i
$235$	−5.44667	+	0.338743i	−0.355301	+	0.0220972i
$236$	2.09221	+	1.34458i	0.136191	+	0.0875250i
$237$	−39.9676	+	14.9071i	−2.59617	+	0.968323i
$238$	12.4279	−	0.888860i	0.805580	−	0.0576163i
$239$	−22.9899	−	3.30545i	−1.48709	−	0.213812i	−0.649607	−	0.760270i	$-0.725067\pi$
$239$	−22.9899	−	3.30545i	−1.48709	−	0.213812i	−0.837486	+	0.546458i	$0.815976\pi$
$240$	2.31537	+	6.38833i	0.149457	+	0.412365i
$241$	−2.87026	+	9.77522i	−0.184890	+	0.629677i	0.813923	+	0.580972i	$0.197328\pi$
$241$	−2.87026	+	9.77522i	−0.184890	+	0.629677i	−0.998813	+	0.0487048i	$0.984491\pi$
$242$	9.61847	−	5.25208i	0.618298	−	0.337616i
$243$	1.55148	−	4.15969i	0.0995277	−	0.266844i
$244$	0.304180	−	2.11562i	0.0194731	−	0.135439i
$245$	18.2286	+	0.169296i	1.16458	+	0.0108159i
$246$	−9.73288	+	21.3120i	−0.620546	+	1.35881i
$247$	−6.69320	−	30.7682i	−0.425878	−	1.95773i
$248$	−1.29405	+	1.72865i	−0.0821725	+	0.109770i
$249$	16.1117	−	10.3544i	1.02104	−	0.656181i
$250$	5.08273	+	9.95821i	0.321460	+	0.629812i
$251$	−1.93079	−	6.57566i	−0.121870	−	0.415052i	0.875846	−	0.482590i	$-0.160304\pi$
$251$	−1.93079	−	6.57566i	−0.121870	−	0.415052i	−0.997717	+	0.0675379i	$0.978486\pi$
$252$	17.1600	+	17.1600i	1.08098	+	1.08098i
$253$	0.881964	−	0.406970i	0.0554486	−	0.0255860i
$254$			14.5872i			0.915279i
$255$	18.1870	+	11.9282i	1.13891	+	0.746970i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−0.782738	+	3.59819i	−0.0488259	+	0.224449i	−0.995094	−	0.0989343i	$-0.968457\pi$
$257$	−0.782738	+	3.59819i	−0.0488259	+	0.224449i	0.946268	+	0.323383i	$0.104820\pi$
$258$	−14.1583	−	10.5988i	−0.881456	−	0.659850i
$259$	4.86101	−	7.56388i	0.302048	−	0.469997i
$260$	12.9280	+	7.21588i	0.801761	+	0.447510i
$261$	−8.87082	+	10.2375i	−0.549090	+	0.633684i
$262$	−11.6576	−	15.5727i	−0.720207	−	0.962084i
$263$	4.71092	+	1.75708i	0.290488	+	0.108346i	0.490484	−	0.871450i	$-0.336820\pi$
$263$	4.71092	+	1.75708i	0.290488	+	0.108346i	−0.199996	+	0.979797i	$0.564093\pi$
$264$	−0.590539	−	0.173398i	−0.0363452	−	0.0106719i
$265$	5.01771	−	13.0807i	0.308235	−	0.803539i
$266$	7.69002	+	16.8388i	0.471506	+	1.03245i
$267$	−22.0815	+	16.5300i	−1.35137	+	1.01162i
$268$	−0.146618	−	2.04999i	−0.00895613	−	0.125223i
$269$	−21.7694	−	9.94175i	−1.32730	−	0.606159i	−0.379553	−	0.925170i	$-0.623922\pi$
$269$	−21.7694	−	9.94175i	−1.32730	−	0.606159i	−0.947751	+	0.319011i	$0.896649\pi$
$270$	2.92553	+	21.7817i	0.178042	+	1.32559i
$271$	2.87903	+	20.0241i	0.174889	+	1.21638i	0.868375	+	0.495908i	$0.165165\pi$
$271$	2.87903	+	20.0241i	0.174889	+	1.21638i	−0.693487	+	0.720469i	$0.743926\pi$
$272$	−3.12769	−	0.680388i	−0.189644	−	0.0412546i
$273$	78.1221	+	5.58740i	4.72816	+	0.338165i
$274$	−8.74424	+	2.56754i	−0.528259	+	0.155111i
$275$	−0.999526	−	0.162712i	−0.0602737	−	0.00981192i
$276$	13.6746	+	5.03933i	0.823115	+	0.303332i
$277$	−5.72940	+	5.72940i	−0.344246	+	0.344246i	−0.857961	−	0.513715i	$-0.828269\pi$
$277$	−5.72940	+	5.72940i	−0.344246	+	0.344246i	0.513715	+	0.857961i	$0.328269\pi$
$278$	9.71142	+	5.30283i	0.582452	+	0.318043i
$279$	−10.1740	+	8.81584i	−0.609103	+	0.527791i
$280$	−8.32844	−	2.52970i	−0.497719	−	0.151178i
$281$	−16.8552	+	2.42341i	−1.00550	+	0.144568i	−0.625338	−	0.780354i	$-0.715039\pi$
$281$	−16.8552	+	2.42341i	−1.00550	+	0.144568i	−0.380157	+	0.924922i	$0.624130\pi$
$282$	7.24681	−	1.57645i	0.431541	−	0.0938761i
$283$	−3.22358	−	8.64275i	−0.191622	−	0.513758i	0.805237	−	0.592953i	$-0.202038\pi$
$283$	−3.22358	−	8.64275i	−0.191622	−	0.513758i	−0.996859	+	0.0791945i	$0.974765\pi$
$284$	9.29892	+	8.05756i	0.551790	+	0.478128i
$285$	−7.16180	+	31.5105i	−0.424229	+	1.86652i
$286$	−1.21985	+	0.557088i	−0.0721313	+	0.0329413i
$287$	−14.3833	−	26.3411i	−0.849020	−	1.55486i
$288$	−2.98780	−	5.47175i	−0.176058	−	0.322426i
$289$	6.14422	−	2.80597i	0.361425	−	0.165057i
$290$	1.07681	−	4.73775i	0.0632325	−	0.278210i
$291$	22.9232	+	19.8630i	1.34378	+	1.16439i
$292$	−0.725826	−	1.94601i	−0.0424757	−	0.113882i
$293$	10.4504	−	2.27334i	0.610519	−	0.132810i	0.103333	−	0.994647i	$-0.467049\pi$
$293$	10.4504	−	2.27334i	0.610519	−	0.132810i	0.507186	+	0.861837i	$0.330686\pi$
$294$	−24.5215	+	3.52566i	−1.43012	+	0.205621i
$295$	−5.32110	−	1.61624i	−0.309806	−	0.0941012i
$296$	−1.74564	+	1.51260i	−0.101463	+	0.0879183i
$297$	−1.74714	−	0.954012i	−0.101380	−	0.0553574i
$298$	−0.977605	+	0.977605i	−0.0566311	+	0.0566311i
$299$	29.7083	−	11.2136i	1.71808	−	0.648501i
$300$	−8.87796	−	12.3305i	−0.512569	−	0.711900i
$301$	21.7374	−	6.38267i	1.25292	−	0.367891i
$302$	−6.19233	−	0.442884i	−0.356328	−	0.0254851i
$303$	−15.9174	−	3.46262i	−0.914432	−	0.198922i
$304$	−0.676791	−	4.70718i	−0.0388166	−	0.269975i
$305$	0.636204	+	4.73678i	0.0364290	+	0.271227i
$306$	−18.1518	−	8.28966i	−1.03767	−	0.473888i
$307$	0.903841	+	12.6373i	0.0515849	+	0.721252i	0.955771	+	0.294112i	$0.0950240\pi$
$307$	0.903841	+	12.6373i	0.0515849	+	0.721252i	−0.904186	+	0.427139i	$0.859521\pi$
$308$	0.631144	−	0.472469i	0.0359628	−	0.0269214i
$309$	−15.9758	−	34.9820i	−0.908829	−	1.99006i
$310$	1.72932	−	4.50817i	0.0982187	−	0.256047i
$311$	1.11295	+	0.326791i	0.0631095	+	0.0185306i	0.313135	−	0.949709i	$-0.398621\pi$
$311$	1.11295	+	0.326791i	0.0631095	+	0.0185306i	−0.250025	+	0.968239i	$0.580439\pi$
$312$	−18.8520	−	7.03142i	−1.06728	−	0.398076i
$313$	−1.90498	−	2.54476i	−0.107676	−	0.143838i	0.743466	−	0.668773i	$-0.233180\pi$
$313$	−1.90498	−	2.54476i	−0.107676	−	0.143838i	−0.851142	+	0.524935i	$0.824089\pi$
$314$	0.923163	−	1.06539i	0.0520971	−	0.0601232i
$315$	−47.3834	−	26.4475i	−2.66975	−	1.49015i
$316$	−7.58923	+	11.8091i	−0.426927	+	0.664312i
$317$	9.43859	+	7.06564i	0.530124	+	0.396846i	0.830537	−	0.556963i	$-0.188034\pi$
$317$	9.43859	+	7.06564i	0.530124	+	0.396846i	−0.300413	+	0.953809i	$0.597124\pi$
$318$	−4.04716	+	18.6045i	−0.226953	+	1.04329i
$319$	0.288189	+	0.332587i	0.0161355	+	0.0186213i
$320$	1.86979	+	1.22633i	0.104525	+	0.0685538i
$321$			25.8179i			1.44102i
$322$	−15.6651	+	10.1544i	−0.872980	+	0.565883i
$323$	−10.7635	−	10.7635i	−0.598897	−	0.598897i
$324$	−3.14526	−	10.7118i	−0.174737	−	0.595099i
$325$	−32.2132	−	7.63682i	−1.78687	−	0.423614i
$326$	11.9501	−	7.67984i	0.661853	−	0.425347i
$327$	27.7071	−	37.0124i	1.53221	−	2.04679i
$328$	1.63889	+	7.53383i	0.0904923	+	0.415986i
$329$	−3.94646	+	8.64154i	−0.217575	+	0.476424i
$330$	1.37617	+	0.0127810i	0.0757558	+	0.000703573i
$331$	2.50422	−	17.4172i	0.137644	−	0.957338i	−0.797562	−	0.603236i	$-0.793878\pi$
$331$	2.50422	−	17.4172i	0.137644	−	0.957338i	0.935207	−	0.354102i	$-0.115213\pi$
$332$	2.20249	−	5.90510i	0.120877	−	0.324085i
$333$	−12.6387	+	6.90126i	−0.692597	+	0.378187i
$334$	4.59205	−	15.6391i	0.251266	−	0.855733i
$335$	1.56595	+	4.32060i	0.0855570	+	0.236060i
$336$	11.7085	+	1.68343i	0.638751	+	0.0918385i
$337$	5.44497	−	0.389432i	0.296607	−	0.0212137i	0.0777570	−	0.996972i	$-0.475224\pi$
$337$	5.44497	−	0.389432i	0.296607	−	0.0212137i	0.218850	+	0.975759i	$0.429770\pi$
$338$	−28.8960	+	10.7776i	−1.57173	+	0.586226i
$339$	−0.325599	−	0.209249i	−0.0176841	−	0.0113649i
$340$	7.14349	−	0.444273i	0.387410	−	0.0240941i
$341$	0.236449	+	0.367921i	0.0128044	+	0.0199241i
$342$	2.11506	−	29.5724i	0.114369	−	1.59909i
$343$	2.14992	−	3.93728i	0.116085	−	0.212593i
$344$	−5.82001			−0.313794
$345$	−32.4916	−	2.49906i	−1.74929	−	0.134545i
$346$	8.83003			0.474705
$347$	14.8735	−	27.2387i	0.798450	−	1.46225i	−0.0863426	−	0.996266i	$-0.527518\pi$
$347$	14.8735	−	27.2387i	0.798450	−	1.46225i	0.884792	−	0.465986i	$-0.154300\pi$
$348$	−0.471037	+	6.58596i	−0.0252502	+	0.353045i
$349$	−1.01133	−	1.57367i	−0.0541354	−	0.0842364i	0.813131	−	0.582081i	$-0.197761\pi$
$349$	−1.01133	−	1.57367i	−0.0541354	−	0.0842364i	−0.867266	+	0.497845i	$0.834125\pi$
$350$	19.4597	+	0.361491i	1.04017	+	0.0193225i
$351$	−54.7461	−	35.1832i	−2.92213	−	1.87794i
$352$	−0.189767	+	0.0707793i	−0.0101146	+	0.00377255i
$353$	27.6523	−	1.97773i	1.47178	−	0.105264i	0.687733	−	0.725963i	$-0.258606\pi$
$353$	27.6523	−	1.97773i	1.47178	−	0.105264i	0.784049	+	0.620699i	$0.213151\pi$
$354$	7.48064	+	1.07555i	0.397592	+	0.0571651i
$355$	−24.9196	−	11.6613i	−1.32259	−	0.618917i
$356$	−2.55728	+	8.70931i	−0.135536	+	0.461592i
$357$	33.2310	−	18.1455i	1.75877	−	0.960363i
$358$	1.82497	−	4.89292i	0.0964524	−	0.258599i
$359$	4.30795	−	29.9624i	0.227365	−	1.58136i	−0.481779	−	0.876293i	$-0.660009\pi$
$359$	4.30795	−	29.9624i	0.227365	−	1.58136i	0.709143	−	0.705064i	$-0.249082\pi$
$360$	9.76539	+	9.94848i	0.514681	+	0.524331i
$361$	1.50198	−	3.28888i	0.0790516	−	0.173099i
$362$	3.28144	+	15.0845i	0.172469	+	0.792826i
$363$	19.9573	−	26.6598i	1.04749	−	1.39928i
$364$	21.6823	−	13.9344i	1.13646	−	0.730360i
$365$	2.74854	+	3.74359i	0.143865	+	0.195949i
$366$	−1.82987	−	6.23197i	−0.0956489	−	0.325750i
$367$	10.9121	+	10.9121i	0.569606	+	0.569606i	0.932018	−	0.362412i	$-0.118047\pi$
$367$	10.9121	+	10.9121i	0.569606	+	0.569606i	−0.362412	+	0.932018i	$0.618047\pi$
$368$	4.59623	−	1.36919i	0.239595	−	0.0713739i
$369$			48.0670i			2.50227i
$370$	2.83258	−	4.31887i	0.147259	−	0.224527i
$371$	−15.9715	−	18.4321i	−0.829197	−	0.956945i
$372$	−1.39482	+	6.41191i	−0.0723183	+	0.332442i
$373$	−19.1618	−	14.3444i	−0.992162	−	0.742723i	−0.0257360	−	0.999669i	$-0.508193\pi$
$373$	−19.1618	−	14.3444i	−0.992162	−	0.742723i	−0.966426	+	0.256946i	$0.917284\pi$
$374$	−0.350491	+	0.545374i	−0.0181234	+	0.0282006i
$375$	26.6205	+	21.1102i	1.37468	+	1.09012i
$376$	1.59821	−	1.84443i	0.0824212	−	0.0951192i
$377$	8.62164	+	11.5172i	0.444037	+	0.593164i
$378$	35.8465	+	13.3700i	1.84374	+	0.687681i
$379$	−12.5360	−	3.68090i	−0.643931	−	0.189075i	−0.0565681	−	0.998399i	$-0.518016\pi$
$379$	−12.5360	−	3.68090i	−0.643931	−	0.189075i	−0.587363	+	0.809323i	$0.699834\pi$
$380$	4.32743	+	9.71347i	0.221992	+	0.498290i
$381$	18.4143	+	40.3217i	0.943394	+	2.06575i
$382$	−7.20095	+	5.39056i	−0.368433	+	0.275805i
$383$	−0.897012	−	12.5419i	−0.0458352	−	0.640860i	−0.967500	−	0.252872i	$-0.918625\pi$
$383$	−0.897012	−	12.5419i	−0.0458352	−	0.640860i	0.921665	−	0.387988i	$-0.126830\pi$
$384$	−2.76420	−	1.26237i	−0.141060	−	0.0644198i
$385$	−1.06953	+	1.40141i	−0.0545085	+	0.0714224i
$386$	−0.00156267	−	0.0108686i	−7.95378e−5	−	0.000553198i
$387$	−35.4547	−	7.71271i	−1.80227	−	0.392059i
$388$	9.95602	+	0.712068i	0.505440	+	0.0361498i
$389$	−27.1918	+	7.98422i	−1.37868	+	0.404816i	−0.885308	−	0.465004i	$-0.846053\pi$
$389$	−27.1918	+	7.98422i	−1.37868	+	0.404816i	−0.493369	+	0.869820i	$0.664235\pi$
$390$	44.8446	+	3.62625i	2.27080	+	0.183622i
$391$	9.15103	−	12.3249i	0.462788	−	0.623295i
$392$	−5.76465	+	5.76465i	−0.291159	+	0.291159i
$393$	−51.8822	−	28.3298i	−2.61711	−	1.42905i
$394$	15.7584	−	13.6547i	0.793897	−	0.687916i
$395$	9.12254	−	30.0338i	0.459005	−	1.51117i
$396$	−1.24983	+	0.179699i	−0.0628064	+	0.00903019i
$397$	−28.0394	+	6.09960i	−1.40726	+	0.306130i	−0.851125	−	0.524963i	$-0.824079\pi$
$397$	−28.0394	+	6.09960i	−1.40726	+	0.306130i	−0.556133	+	0.831093i	$0.687715\pi$
$398$	−6.59113	−	17.6715i	−0.330383	−	0.885792i
$399$	42.5135	+	36.8381i	2.12833	+	1.84421i
$400$	−4.77047	−	1.49752i	−0.238524	−	0.0748762i
$401$	−6.72407	+	3.07078i	−0.335784	+	0.153347i	−0.576170	−	0.817330i	$-0.695453\pi$
$401$	−6.72407	+	3.07078i	−0.335784	+	0.153347i	0.240386	+	0.970677i	$0.422726\pi$
$402$	−2.99312	−	5.48149i	−0.149283	−	0.273392i
$403$	6.85209	+	12.5487i	0.341327	+	0.625094i
$404$	−4.87613	+	2.22686i	−0.242597	+	0.110790i
$405$	13.3007	+	21.1250i	0.660915	+	1.04971i
$406$	−6.39210	−	5.53878i	−0.317234	−	0.274885i
$407$	0.163487	+	0.438325i	0.00810374	+	0.0217270i
$408$	−9.50445	+	2.06757i	−0.470540	+	0.102360i
$409$	23.8702	−	3.43202i	1.18031	−	0.169703i	0.475901	−	0.879499i	$-0.342122\pi$
$409$	23.8702	−	3.43202i	1.18031	−	0.169703i	0.704407	+	0.709796i	$0.251213\pi$
$410$	−8.12145	−	15.2074i	−0.401090	−	0.751040i
$411$	−20.9296	+	18.1356i	−1.03238	+	0.894563i
$412$	−11.1074	−	6.06509i	−0.547222	−	0.298806i
$413$	−6.84550	+	6.84550i	−0.336845	+	0.336845i
$414$	29.8141	−	2.24997i	1.46528	−	0.110580i
$415$	−1.13587	+	14.0469i	−0.0557576	+	0.689536i
$416$	−6.35301	+	1.86541i	−0.311482	+	0.0914593i
$417$	33.5384	+	2.39871i	1.64238	+	0.117465i
$418$	−0.941169	−	0.204739i	−0.0460341	−	0.0100141i
$419$	0.427346	+	2.97226i	0.0208772	+	0.145204i	0.997594	−	0.0693294i	$-0.0220859\pi$
$419$	0.427346	+	2.97226i	0.0208772	+	0.145204i	−0.976717	+	0.214534i	$0.931177\pi$
$420$	−26.2148	+	3.52095i	−1.27915	+	0.171805i
$421$	34.5783	+	15.7914i	1.68524	+	0.769625i	0.999111	+	0.0421474i	$0.0134199\pi$
$421$	34.5783	+	15.7914i	1.68524	+	0.769625i	0.686132	+	0.727477i	$0.259307\pi$
$422$	−0.197701	−	2.76423i	−0.00962395	−	0.134560i
$423$	12.1803	−	9.11807i	0.592227	−	0.443336i
$424$	2.60278	+	5.69928i	0.126402	+	0.276782i
$425$	−15.0964	+	5.31342i	−0.732284	+	0.257739i
$426$	35.8756	+	10.5340i	1.73818	+	0.510376i
$427$	7.79540	+	2.90753i	0.377246	+	0.140705i
$428$	5.09151	+	6.80145i	0.246107	+	0.328761i
$429$	−2.66866	+	3.07980i	−0.128844	+	0.148694i
$430$	12.5203	−	3.55033i	0.603782	−	0.171212i
$431$	−2.45773	+	3.82430i	−0.118385	+	0.184210i	−0.895389	−	0.445286i	$-0.853102\pi$
$431$	−2.45773	+	3.82430i	−0.118385	+	0.184210i	0.777004	+	0.629496i	$0.216738\pi$
$432$	−7.86815	−	5.89002i	−0.378557	−	0.283384i
$433$	6.93459	−	31.8778i	0.333255	−	1.53195i	−0.440084	−	0.897956i	$-0.645051\pi$
$433$	6.93459	−	31.8778i	0.333255	−	1.53195i	0.773339	−	0.633992i	$-0.218585\pi$
$434$	−5.50446	−	6.35248i	−0.264222	−	0.304929i
$435$	−3.00425	−	14.4554i	−0.144043	−	0.693083i
$436$		−	15.2146i		−	0.728647i
$437$	21.9082	+	6.33955i	1.04801	+	0.303262i
$438$	−4.46291	−	4.46291i	−0.213246	−	0.213246i
$439$	1.60846	+	5.47790i	0.0767674	+	0.261446i	0.988930	−	0.148383i	$-0.0474067\pi$
$439$	1.60846	+	5.47790i	0.0767674	+	0.261446i	−0.912163	+	0.409829i	$0.865589\pi$
$440$	0.365059	−	0.268026i	0.0174035	−	0.0127776i
$441$	−42.7568	+	27.4781i	−2.03604	+	1.30848i
$442$	−12.7008	+	16.9662i	−0.604113	+	0.807001i
$443$	3.68527	+	16.9409i	0.175092	+	0.804887i	0.977970	+	0.208743i	$0.0669373\pi$
$443$	3.68527	+	16.9409i	0.175092	+	0.804887i	−0.802878	+	0.596143i	$0.796699\pi$
$444$	−2.91583	+	6.38477i	−0.138379	+	0.303008i
$445$	0.188496	−	20.2959i	0.00893555	−	0.962117i
$446$	0.898537	−	6.24946i	0.0425470	−	0.295921i
$447$	−1.46820	+	3.93639i	−0.0694433	+	0.186185i
$448$	3.41647	−	1.86553i	0.161413	−	0.0881381i
$449$	−3.19615	+	10.8851i	−0.150836	+	0.513700i	−0.999893	−	0.0146007i	$-0.995352\pi$
$449$	−3.19615	+	10.8851i	−0.150836	+	0.513700i	0.849058	+	0.528300i	$0.177170\pi$
$450$	−27.0766	−	15.4446i	−1.27640	−	0.728064i
$451$	1.54567	+	0.222234i	0.0727828	+	0.0104646i
$452$	−0.127041	+	0.00908617i	−0.00597552	+	0.000427377i
$453$	−17.6759	+	6.59276i	−0.830485	+	0.309755i
$454$	13.8990	+	8.93235i	0.652313	+	0.419216i
$455$	−38.1438	+	43.2030i	−1.78821	+	2.02539i
$456$	−7.81297	−	12.1572i	−0.365876	−	0.569314i
$457$	1.15095	−	16.0924i	0.0538394	−	0.752773i	−0.896792	−	0.442452i	$-0.854109\pi$
$457$	1.15095	−	16.0924i	0.0538394	−	0.752773i	0.950632	−	0.310321i	$-0.100437\pi$
$458$	0.217760	−	0.398798i	0.0101753	−	0.0186346i
$459$	−31.4596			−1.46841
$460$	−9.05240	+	5.74926i	−0.422070	+	0.268061i
$461$	31.6954			1.47620			0.738101	−	0.674690i	$-0.235723\pi$
$461$	31.6954			1.47620			0.738101	+	0.674690i	$0.235723\pi$
$462$	1.14818	−	2.10273i	0.0534181	−	0.0978279i
$463$	−2.70196	+	37.7783i	−0.125571	+	1.75571i	0.410800	+	0.911725i	$0.365249\pi$
$463$	−2.70196	+	37.7783i	−0.125571	+	1.75571i	−0.536371	+	0.843982i	$0.680205\pi$
$464$	1.17472	+	1.82789i	0.0545348	+	0.0848578i
$465$	−0.910780	−	14.6445i	−0.0422364	−	0.679122i
$466$	9.80726	+	6.30275i	0.454313	+	0.291969i
$467$	10.0233	−	3.73849i	0.463822	−	0.172997i	−0.106679	−	0.994294i	$-0.534022\pi$
$467$	10.0233	−	3.73849i	0.463822	−	0.172997i	0.570501	+	0.821297i	$0.306749\pi$
$468$	−41.1737	+	2.94480i	−1.90326	+	0.136124i
$469$	7.91877	+	1.13855i	0.365655	+	0.0525733i
$470$	−2.31300	+	4.94277i	−0.106691	+	0.227993i
$471$	1.20689	−	4.11030i	0.0556108	−	0.189393i
$472$	2.18280	−	1.19190i	0.100472	−	0.0548617i
$473$	−0.411937	+	1.10444i	−0.0189409	+	0.0507824i
$474$	−6.07074	+	42.2230i	−0.278839	+	1.93936i
$475$	−15.2348	−	18.2563i	−0.699020	−	0.837655i
$476$	5.17592	−	11.3337i	0.237238	−	0.519479i
$477$	8.30305	+	38.1685i	0.380170	+	1.74762i
$478$	−13.9190	+	18.5936i	−0.636641	+	0.850453i
$479$	−1.64260	+	1.05563i	−0.0750522	+	0.0482331i	−0.577629	−	0.816300i	$-0.696022\pi$
$479$	−1.64260	+	1.05563i	−0.0750522	+	0.0482331i	0.502577	+	0.864533i	$0.332386\pi$
$480$	6.71654	+	1.02945i	0.306567	+	0.0469876i
$481$	4.30875	+	14.6742i	0.196462	+	0.669088i
$482$	7.20393	+	7.20393i	0.328130	+	0.328130i
$483$	−30.4827	+	47.8438i	−1.38701	+	2.17697i
$484$		−	10.9590i		−	0.498135i
$485$	−21.8523	+	4.54154i	−0.992260	+	0.206221i
$486$	−2.90732	−	3.35523i	−0.131879	−	0.152196i
$487$	6.14867	−	28.2650i	0.278623	−	1.28081i	−0.598725	−	0.800954i	$-0.704326\pi$
$487$	6.14867	−	28.2650i	0.278623	−	1.28081i	0.877348	−	0.479854i	$-0.159310\pi$
$488$	−1.71106	−	1.28088i	−0.0774559	−	0.0579827i
$489$	23.3375	−	36.3139i	1.05536	−	1.64217i
$490$	8.88464	−	15.9178i	0.401367	−	0.719091i
$491$	−11.3583	+	13.1081i	−0.512591	+	0.591562i	−0.951760	−	0.306843i	$-0.900727\pi$
$491$	−11.3583	+	13.1081i	−0.512591	+	0.591562i	0.439169	+	0.898404i	$0.355273\pi$
$492$	14.0407	+	18.7561i	0.633001	+	0.845591i
$493$	6.51635	+	2.43047i	0.293482	+	0.109463i
$494$	−30.2123	−	8.87113i	−1.35931	−	0.399131i
$495$	2.57908	−	1.14900i	0.115921	−	0.0516437i
$496$	0.897029	+	1.96422i	0.0402778	+	0.0881961i
$497$	−38.3425	+	28.7028i	−1.71989	+	1.28750i
$498$	−1.36629	−	19.1032i	−0.0612248	−	0.856035i
$499$	14.8132	+	6.76494i	0.663128	+	0.302841i	0.718399	−	0.695631i	$-0.244875\pi$
$499$	14.8132	+	6.76494i	0.663128	+	0.302841i	−0.0552712	+	0.998471i	$0.517602\pi$
$500$	11.1760	+	0.311459i	0.499806	+	0.0139289i
$501$	−7.04893	−	49.0264i	−0.314923	−	2.19034i
$502$	−6.69665	−	1.45677i	−0.298886	−	0.0650187i
$503$	−7.42010	−	0.530696i	−0.330846	−	0.0236626i	−0.0950716	−	0.995470i	$-0.530308\pi$
$503$	−7.42010	−	0.530696i	−0.330846	−	0.0236626i	−0.235774	+	0.971808i	$0.575763\pi$
$504$	23.2849	−	6.83705i	1.03719	−	0.304547i
$505$	9.13135	−	7.76506i	0.406340	−	0.345541i
$506$	0.0654917	−	0.969122i	0.00291146	−	0.0430827i
$507$	−66.2687	+	66.2687i	−2.94310	+	2.94310i
$508$	12.8028	+	6.99088i	0.568034	+	0.310170i
$509$	−21.4645	+	18.5991i	−0.951397	+	0.824390i	−0.984558	−	0.175060i	$-0.943988\pi$
$509$	−21.4645	+	18.5991i	−0.951397	+	0.824390i	0.0331609	+	0.999450i	$0.489443\pi$
$510$	19.1852	−	10.2458i	0.849534	−	0.453690i
$511$	8.00254	−	1.15059i	0.354012	−	0.0508992i
$512$	−0.977147	+	0.212565i	−0.0431842	+	0.00939415i
$513$	−16.3341	−	43.7935i	−0.721169	−	1.93353i
$514$	2.78293	+	2.41142i	0.122750	+	0.106363i
$515$	27.5946	+	6.27179i	1.21596	+	0.276368i
$516$	−16.0877	+	7.34698i	−0.708219	+	0.323433i
$517$	−0.236891	−	0.433834i	−0.0104185	−	0.0190800i
$518$	−4.30902	−	7.89139i	−0.189328	−	0.346728i
$519$	24.4079	−	11.1467i	1.07139	−	0.489287i
$520$	12.5290	−	7.88843i	0.549431	−	0.345931i
$521$	18.3768	+	15.9236i	0.805104	+	0.697627i	0.956783	−	0.290803i	$-0.0939225\pi$
$521$	18.3768	+	15.9236i	0.805104	+	0.697627i	−0.151679	+	0.988430i	$0.548468\pi$
$522$	4.73388	+	12.6920i	0.207196	+	0.555515i
$523$	33.8498	−	7.36358i	1.48015	−	0.321987i	0.601276	−	0.799041i	$-0.294659\pi$
$523$	33.8498	−	7.36358i	1.48015	−	0.321987i	0.878874	+	0.477054i	$0.158295\pi$
$524$	−19.2547	+	2.76841i	−0.841146	+	0.120938i
$525$	54.2468	−	23.5660i	2.36752	−	1.02851i
$526$	3.79986	−	3.29260i	0.165682	−	0.143564i
$527$	6.06630	+	3.31245i	0.264252	+	0.144293i
$528$	−0.435203	+	0.435203i	−0.0189398	+	0.0189398i
$529$	−3.09448	+	22.7909i	−0.134542	+	0.990908i
$530$	−9.07590	−	10.6728i	−0.394232	−	0.463598i
$531$	14.8769	−	4.36824i	0.645601	−	0.189566i
$532$	18.4645	+	1.32061i	0.800538	+	0.0572556i
$533$	49.8831	+	10.8514i	2.16068	+	0.470027i
$534$	3.92550	+	27.3025i	0.169873	+	1.18149i
$535$	−15.1021	−	11.5257i	−0.652922	−	0.498300i
$536$	−1.86950	−	0.853772i	−0.0807501	−	0.0368773i
$537$	−1.13210	−	15.8288i	−0.0488535	−	0.683062i
$538$	−19.1586	+	14.3420i	−0.825987	+	0.618326i
$539$	0.685920	+	1.50196i	0.0295447	+	0.0646938i
$540$	20.5194	+	7.87118i	0.883014	+	0.338721i
$541$	−31.4781	−	9.24282i	−1.35335	−	0.397380i	−0.476937	−	0.878938i	$-0.658253\pi$
$541$	−31.4781	−	9.24282i	−1.35335	−	0.397380i	−0.876414	+	0.481558i	$0.840071\pi$
$542$	18.9545	+	7.06966i	0.814165	+	0.303668i
$543$	28.1127	+	37.5542i	1.20643	+	1.61161i
$544$	−2.09610	+	2.41903i	−0.0898697	+	0.103715i
$545$	9.28122	+	32.7304i	0.397564	+	1.40202i
$546$	42.3439	−	65.8884i	1.81215	−	2.81976i
$547$	−10.7553	−	8.05132i	−0.459864	−	0.344250i	0.344095	−	0.938935i	$-0.388186\pi$
$547$	−10.7553	−	8.05132i	−0.459864	−	0.344250i	−0.803959	+	0.594685i	$0.797277\pi$
$548$	−1.93719	+	8.90512i	−0.0827527	+	0.380408i
$549$	−8.72610	−	10.0705i	−0.372421	−	0.429797i
$550$	−0.621831	+	0.799283i	−0.0265150	+	0.0340816i
$551$			10.3330i			0.440202i
$552$	10.9765	−	9.58683i	0.467189	−	0.408042i
$553$	−38.6380	−	38.6380i	−1.64306	−	1.64306i
$554$	2.28276	+	7.77438i	0.0969854	+	0.330302i
$555$	2.37783	−	15.5139i	0.100933	−	0.658530i
$556$	9.30837	−	5.98213i	0.394763	−	0.253699i
$557$	16.0599	−	21.4535i	0.680479	−	0.909014i	−0.318767	−	0.947833i	$-0.603269\pi$
$557$	16.0599	−	21.4535i	0.680479	−	0.909014i	0.999246	+	0.0388190i	$0.0123596\pi$
$558$	2.86159	+	13.1545i	0.121141	+	0.556875i
$559$	−16.0082	+	35.0532i	−0.677076	+	1.48259i
$560$	−6.21166	+	6.09734i	−0.262490	+	0.257660i
$561$	−0.280363	+	1.94997i	−0.0118369	+	0.0823277i
$562$	−5.95085	+	15.9548i	−0.251021	+	0.673015i
$563$	4.33089	−	2.36485i	0.182525	−	0.0996663i	−0.385388	−	0.922754i	$-0.625933\pi$
$563$	4.33089	−	2.36485i	0.182525	−	0.0996663i	0.567914	+	0.823088i	$0.307751\pi$
$564$	2.08941	−	7.11588i	0.0879801	−	0.299633i
$565$	0.267755	−	0.0970444i	0.0112645	−	0.00408269i
$566$	−9.13046	−	1.31276i	−0.383782	−	0.0551795i
$567$	43.3464	−	3.10020i	1.82038	−	0.130196i
$568$	11.5285	−	4.29989i	0.483723	−	0.180419i
$569$	16.2721	+	10.4574i	0.682160	+	0.438398i	0.835291	−	0.549808i	$-0.185299\pi$
$569$	16.2721	+	10.4574i	0.682160	+	0.438398i	−0.153131	+	0.988206i	$0.548936\pi$
$570$	24.2238	+	21.3871i	1.01462	+	0.895808i
$571$	−13.6444	−	21.2312i	−0.571002	−	0.888497i	0.428887	−	0.903358i	$-0.358906\pi$
$571$	−13.6444	−	21.2312i	−0.571002	−	0.888497i	−0.999890	+	0.0148610i	$0.995269\pi$
$572$	−0.0956686	+	1.33762i	−0.00400010	+	0.0559288i
$573$	−13.1000	+	23.9908i	−0.547259	+	1.00223i
$574$	−30.0122			−1.25268
$575$	15.9668	−	17.8902i	0.665862	−	0.746075i
$576$	−6.23434			−0.259764
$577$	−2.20504	+	4.03823i	−0.0917970	+	0.168114i	−0.919543	−	0.392989i	$-0.871441\pi$
$577$	−2.20504	+	4.03823i	−0.0917970	+	0.168114i	0.827746	+	0.561103i	$0.189623\pi$
$578$	0.481869	−	6.73741i	0.0200431	−	0.280239i
$579$	−0.0180397	−	0.0280703i	−0.000749704	−	0.00116656i
$580$	−3.64216	−	3.21565i	−0.151233	−	0.133523i
$581$	20.6386	+	13.2636i	0.856232	+	0.550267i
$582$	28.4193	−	10.5998i	1.17802	−	0.439377i
$583$	1.26576	−	0.0905287i	0.0524223	−	0.00374932i
$584$	−2.05583	−	0.295583i	−0.0850707	−	0.0122313i
$585$	86.7786	−	31.4518i	3.58785	−	1.30037i
$586$	3.01308	−	10.2616i	0.124469	−	0.423902i
$587$	4.67737	−	2.55404i	0.193056	−	0.105416i	−0.379814	−	0.925063i	$-0.624012\pi$
$587$	4.67737	−	2.55404i	0.193056	−	0.105416i	0.572870	+	0.819647i	$0.305830\pi$
$588$	−8.65752	+	23.2117i	−0.357030	+	0.957235i
$589$	−1.46143	+	10.1645i	−0.0602173	+	0.418820i
$590$	−3.96867	+	3.89563i	−0.163388	+	0.160381i
$591$	26.3220	−	57.6372i	1.08274	−	2.37088i
$592$	0.490986	+	2.25702i	0.0201794	+	0.0927631i
$593$	−12.0954	+	16.1576i	−0.496699	+	0.663512i	−0.976913	−	0.213640i	$-0.931468\pi$
$593$	−12.0954	+	16.1576i	−0.496699	+	0.663512i	0.480214	+	0.877152i	$0.340559\pi$
$594$	−1.67463	+	1.07622i	−0.0687110	+	0.0441579i
$595$	−4.22091	+	27.5390i	−0.173041	+	1.12899i
$596$	0.389507	+	1.32654i	0.0159548	+	0.0543372i
$597$	−40.5270	−	40.5270i	−1.65866	−	1.65866i
$598$	4.39573	−	31.4485i	0.179755	−	1.28602i
$599$		−	23.2906i		−	0.951630i	−0.879545	−	0.475815i	$-0.842153\pi$
$599$		−	23.2906i		−	0.951630i	0.879545	−	0.475815i	$-0.157847\pi$
$600$	−15.0769	+	1.88263i	−0.615514	+	0.0768582i
$601$	−22.4635	−	25.9243i	−0.916305	−	1.05747i	−0.998148	−	0.0608272i	$-0.980626\pi$
$601$	−22.4635	−	25.9243i	−0.916305	−	1.05747i	0.0818433	−	0.996645i	$-0.473919\pi$
$602$	4.81568	−	22.1373i	0.196272	−	0.902250i
$603$	−10.2573	−	7.67854i	−0.417711	−	0.312694i
$604$	−3.35638	+	5.22262i	−0.136569	+	0.212505i
$605$	6.68521	+	23.5755i	0.271792	+	0.958480i
$606$	−10.6675	+	12.3109i	−0.433337	+	0.500097i
$607$	−27.8001	−	37.1366i	−1.12837	−	1.50733i	−0.834104	−	0.551607i	$-0.814015\pi$
$607$	−27.8001	−	37.1366i	−1.12837	−	1.50733i	−0.294269	−	0.955723i	$-0.595076\pi$
$608$	−4.45575	−	1.66191i	−0.180704	−	0.0673993i
$609$	−24.6610	−	7.24112i	−0.999313	−	0.293425i
$610$	4.46227	+	1.71171i	0.180672	+	0.0693053i
$611$	−6.71280	−	14.6990i	−0.271571	−	0.594657i
$612$	−15.9749	+	11.9587i	−0.645747	+	0.483400i
$613$	−3.00227	−	41.9773i	−0.121261	−	1.69545i	−0.586251	−	0.810130i	$-0.699397\pi$
$613$	−3.00227	−	41.9773i	−0.121261	−	1.69545i	0.464990	−	0.885316i	$-0.346058\pi$
$614$	11.5247	+	5.26315i	0.465099	+	0.212404i
$615$	−41.6466	−	31.7840i	−1.67935	−	1.28165i
$616$	−0.112201	−	0.780372i	−0.00452069	−	0.0314421i
$617$	22.9668	+	4.99611i	0.924607	+	0.201136i	0.649574	−	0.760299i	$-0.274947\pi$
$617$	22.9668	+	4.99611i	0.924607	+	0.201136i	0.275034	+	0.961435i	$0.411311\pi$
$618$	−38.3594	−	2.74352i	−1.54304	−	0.110360i
$619$	17.4631	−	5.12762i	0.701900	−	0.206096i	0.0887395	−	0.996055i	$-0.471716\pi$
$619$	17.4631	−	5.12762i	0.701900	−	0.206096i	0.613160	+	0.789958i	$0.289898\pi$
$620$	−3.12795	−	3.67832i	−0.125621	−	0.147725i
$621$	41.2813	−	22.7521i	1.65656	−	0.913008i
$622$	0.820196	−	0.820196i	0.0328869	−	0.0328869i
$623$	−31.0112	−	16.9334i	−1.24244	−	0.678423i
$624$	−15.2061	+	13.1762i	−0.608732	+	0.527469i
$625$	−24.2324	+	6.14757i	−0.969295	+	0.245903i
$626$	−3.14644	+	0.452390i	−0.125757	+	0.0180811i
$627$	−2.86003	+	0.622162i	−0.114219	+	0.0248467i
$628$	−0.492643	−	1.32083i	−0.0196586	−	0.0527067i
$629$	5.58751	+	4.84161i	0.222789	+	0.193047i
$630$	−45.9208	+	28.9125i	−1.82953	+	1.15190i
$631$	−30.5341	+	13.9444i	−1.21554	+	0.555120i	−0.916851	−	0.399230i	$-0.869277\pi$
$631$	−30.5341	+	13.9444i	−1.21554	+	0.555120i	−0.298692	+	0.954350i	$0.596550\pi$
$632$	6.72744	+	12.3204i	0.267603	+	0.490079i
$633$	−4.03595	−	7.39129i	−0.160415	−	0.293777i
$634$	10.7248	−	4.89785i	0.425936	−	0.194519i
$635$	−31.8067	−	7.22913i	−1.26221	−	0.286879i
$636$	14.3892	+	12.4683i	0.570567	+	0.494399i
$637$	18.8637	+	50.5757i	0.747409	+	2.00388i
$638$	0.430019	−	0.0935449i	0.0170246	−	0.00370348i
$639$	75.9281	−	10.9168i	3.00367	−	0.431862i
$640$	1.97242	−	1.05336i	0.0779666	−	0.0416377i
$641$	4.51402	−	3.91142i	0.178293	−	0.154492i	−0.561142	−	0.827719i	$-0.689638\pi$
$641$	4.51402	−	3.91142i	0.178293	−	0.154492i	0.739435	+	0.673228i	$0.235093\pi$
$642$	22.6598	+	12.3732i	0.894312	+	0.488332i
$643$	−19.5288	+	19.5288i	−0.770142	+	0.770142i	−0.978131	−	0.207989i	$-0.933308\pi$
$643$	−19.5288	+	19.5288i	−0.770142	+	0.770142i	0.207989	+	0.978131i	$0.433308\pi$
$644$	1.40484	+	18.6154i	0.0553585	+	0.733549i
$645$	30.1267	−	25.6190i	1.18624	−	1.00875i
$646$	−14.6053	+	4.28850i	−0.574637	+	0.168729i
$647$	19.8626	+	1.42060i	0.780880	+	0.0558496i	0.456087	−	0.889935i	$-0.349251\pi$
$647$	19.8626	+	1.42060i	0.780880	+	0.0558496i	0.324793	+	0.945785i	$0.394705\pi$
$648$	−10.9089	−	2.37308i	−0.428541	−	0.0932233i
$649$	−0.0716858	−	0.498586i	−0.00281391	−	0.0195712i
$650$	−22.1408	+	24.6129i	−0.868434	+	0.965398i
$651$	−23.2346	−	10.6109i	−0.910634	−	0.415873i
$652$	−1.01338	−	14.1689i	−0.0396869	−	0.554896i
$653$	23.0758	−	17.2744i	0.903027	−	0.675998i	−0.0433504	−	0.999060i	$-0.513803\pi$
$653$	23.0758	−	17.2744i	0.903027	−	0.675998i	0.946378	+	0.323062i	$0.104712\pi$
$654$	−19.2064	−	42.0561i	−0.751029	−	1.64452i
$655$	39.7329	−	17.7013i	1.55249	−	0.691647i
$656$	7.39772	+	2.17217i	0.288832	+	0.0848089i
$657$	−12.1321	−	4.52505i	−0.473319	−	0.176539i
$658$	5.69316	+	7.60517i	0.221943	+	0.296481i
$659$	−20.7434	+	23.9392i	−0.808048	+	0.932537i	−0.998794	−	0.0491024i	$-0.984364\pi$
$659$	−20.7434	+	23.9392i	−0.808048	+	0.932537i	0.190746	+	0.981639i	$0.438909\pi$
$660$	0.670747	−	1.20171i	0.0261088	−	0.0467766i
$661$	−22.9990	+	35.7871i	−0.894557	+	1.39196i	0.0252897	+	0.999680i	$0.491949\pi$
$661$	−22.9990	+	35.7871i	−0.894557	+	1.39196i	−0.919847	+	0.392278i	$0.871687\pi$
$662$	−14.0866	−	10.5451i	−0.547491	−	0.409847i
$663$	−13.6898	+	62.9310i	−0.531667	+	2.44404i
$664$	−4.12724	−	4.76309i	−0.160168	−	0.184844i
$665$	−40.5273	+	8.42277i	−1.57158	+	0.326621i
$666$			14.4002i			0.557995i
$667$	−10.3085	+	1.52345i	−0.399148	+	0.0589883i
$668$	−11.5254	−	11.5254i	−0.445930	−	0.445930i
$669$	−5.40538	−	18.4090i	−0.208984	−	0.711734i
$670$	4.54258	+	0.696243i	0.175495	+	0.0268982i
$671$	−0.364176	+	0.234042i	−0.0140589	+	0.00903508i
$672$	7.08879	−	9.46952i	0.273456	−	0.365295i
$673$	−0.880464	−	4.04743i	−0.0339394	−	0.156017i	0.957058	−	0.289895i	$-0.0936205\pi$
$673$	−0.880464	−	4.04743i	−0.0339394	−	0.156017i	−0.990998	+	0.133878i	$0.957257\pi$
$674$	2.26770	−	4.96557i	0.0873486	−	0.191267i
$675$	−48.9439	−	4.41561i	−1.88385	−	0.169957i
$676$	−4.38905	+	30.5265i	−0.168810	+	1.17410i
$677$	−7.62729	+	20.4496i	−0.293141	+	0.785941i	0.703988	+	0.710212i	$0.251401\pi$
$677$	−7.62729	+	20.4496i	−0.293141	+	0.785941i	−0.997128	+	0.0757285i	$0.975872\pi$
$678$	−0.339697	+	0.185488i	−0.0130460	+	0.00712364i
$679$	−10.9464	+	37.2801i	−0.420085	+	1.43068i
$680$	3.03358	−	6.48261i	0.116333	−	0.248597i
$681$	49.6955	+	7.14513i	1.90433	+	0.273802i
$682$	0.436235	−	0.0312001i	0.0167043	−	0.00119471i
$683$	−43.9716	+	16.4005i	−1.68253	+	0.627550i	−0.995115	−	0.0987197i	$-0.968525\pi$
$683$	−43.9716	+	16.4005i	−1.68253	+	0.627550i	−0.687410	+	0.726269i	$0.741253\pi$
$684$	−24.9415	−	16.0289i	−0.953660	−	0.612880i
$685$	−1.26493	−	20.3389i	−0.0483305	−	0.777108i
$686$	−2.42532	−	3.77387i	−0.0925992	−	0.144087i
$687$	0.0985028	−	1.37725i	0.00375812	−	0.0525453i
$688$	−2.78924	+	5.10810i	−0.106339	+	0.194745i
$689$	41.4851			1.58046
$690$	−17.7649	+	27.3195i	−0.676300	+	1.04004i
$691$	11.8561			0.451027			0.225514	−	0.974240i	$-0.427594\pi$
$691$	11.8561			0.451027			0.225514	+	0.974240i	$0.427594\pi$
$692$	4.23178	−	7.74993i	0.160868	−	0.294608i
$693$	0.350642	−	4.90261i	0.0133198	−	0.186235i
$694$	−16.7788	−	26.1083i	−0.636913	−	0.991056i
$695$	−16.3754	+	18.5474i	−0.621155	+	0.703541i
$696$	5.55462	+	3.56973i	0.210547	+	0.135310i
$697$	23.1226	−	8.62428i	0.875831	−	0.326668i
$698$	−1.86585	+	0.133448i	−0.0706236	+	0.00505110i
$699$	35.0656	+	5.04167i	1.32630	+	0.190693i
$700$	9.64332	−	16.9061i	0.364483	−	0.638992i
$701$	12.8551	−	43.7804i	0.485530	−	1.65356i	−0.244123	−	0.969744i	$-0.578500\pi$
$701$	12.8551	−	43.7804i	0.485530	−	1.65356i	0.729653	−	0.683818i	$-0.239682\pi$
$702$	−57.1166	+	31.1880i	−2.15573	+	1.17712i
$703$	−3.83869	+	10.2919i	−0.144779	+	0.388168i
$704$	−0.0288240	+	0.200475i	−0.00108634	+	0.00755569i
$705$	−0.154009	+	16.5826i	−0.00580032	+	0.624538i
$706$	11.5165	−	25.2176i	0.433430	−	0.949079i
$707$	−4.43551	−	20.3897i	−0.166814	−	0.766834i
$708$	4.52908	−	6.05015i	0.170213	−	0.227378i
$709$	−39.6354	+	25.4721i	−1.48854	+	0.956625i	−0.492258	+	0.870449i	$0.663828\pi$
$709$	−39.6354	+	25.4721i	−1.48854	+	0.956625i	−0.996280	+	0.0861756i	$0.972535\pi$
$710$	−22.1776	+	16.2827i	−0.832309	+	0.611080i
$711$	24.6556	+	83.9694i	0.924659	+	3.14910i
$712$	6.41840	+	6.41840i	0.240540	+	0.240540i
$713$	−10.3558	+	0.0406365i	−0.387829	+	0.00152185i
$714$		−	37.8624i		−	1.41697i
$715$	−0.610170	−	2.93592i	−0.0228191	−	0.109797i
$716$	−3.41980	−	3.94666i	−0.127804	−	0.147494i
$717$	−15.0029	+	68.9673i	−0.560294	+	2.57563i
$718$	−24.2328	−	18.1405i	−0.904361	−	0.676996i
$719$	8.35016	−	12.9931i	0.311408	−	0.484561i	−0.649906	−	0.760015i	$-0.725192\pi$
$719$	8.35016	−	12.9931i	0.311408	−	0.484561i	0.961314	+	0.275454i	$0.0888281\pi$
$720$	13.4116	−	3.80308i	0.499822	−	0.141732i
$721$	32.2602	−	37.2302i	1.20143	−	1.38653i
$722$	−2.16676	−	2.89445i	−0.0806383	−	0.107720i
$723$	29.0071	+	10.8191i	1.07878	+	0.402366i
$724$	14.8120	+	4.34920i	0.550484	+	0.161637i
$725$	9.79681	+	4.69588i	0.363845	+	0.174401i
$726$	−13.8342	−	30.2928i	−0.513437	−	1.12427i
$727$	38.7481	−	29.0065i	1.43709	−	1.07579i	0.454341	−	0.890828i	$-0.349875\pi$
$727$	38.7481	−	29.0065i	1.43709	−	1.07579i	0.982746	−	0.184962i	$-0.0592163\pi$
$728$	−1.83868	−	25.7082i	−0.0681461	−	0.952808i
$729$	18.1934	+	8.30867i	0.673831	+	0.307728i
$730$	4.60291	−	0.618224i	0.170361	−	0.0228815i
$731$	2.65117	+	18.4393i	0.0980572	+	0.682003i
$732$	−6.34663	−	1.38063i	−0.234578	−	0.0510294i
$733$	−33.4499	−	2.39238i	−1.23550	−	0.0883647i	−0.561739	−	0.827314i	$-0.689868\pi$
$733$	−33.4499	−	2.39238i	−1.23550	−	0.0883647i	−0.673761	+	0.738950i	$0.735322\pi$
$734$	14.8069	−	4.34770i	0.546533	−	0.160476i
$735$	4.46486	−	55.2154i	0.164689	−	2.03665i
$736$	1.00103	−	4.69020i	0.0368985	−	0.172883i
$737$	−0.294340	+	0.294340i	−0.0108421	+	0.0108421i
$738$	42.1874	+	23.0361i	1.55294	+	0.847969i
$739$	0.355518	−	0.308058i	0.0130779	−	0.0113321i	−0.648297	−	0.761387i	$-0.724519\pi$
$739$	0.355518	−	0.308058i	0.0130779	−	0.0113321i	0.661375	+	0.750055i	$0.269973\pi$
$740$	−2.43306	−	4.55591i	−0.0894412	−	0.167479i
$741$	−94.7112	+	13.6174i	−3.47930	+	0.500248i
$742$	−23.8317	+	5.18428i	−0.874891	+	0.190321i
$743$	−9.08685	−	24.3628i	−0.333364	−	0.893784i	−0.990188	−	0.139740i	$-0.955373\pi$
$743$	−9.08685	−	24.3628i	−0.333364	−	0.893784i	0.656824	−	0.754044i	$-0.271899\pi$
$744$	4.95913	+	4.29711i	0.181810	+	0.157540i
$745$	−1.64714	−	2.61611i	−0.0603467	−	0.0958469i
$746$	−21.7730	+	9.94341i	−0.797167	+	0.364054i
$747$	−18.8306	−	34.4856i	−0.688974	−	1.26176i
$748$	0.310691	+	0.568988i	0.0113600	+	0.0208043i
$749$	−30.0833	+	13.7386i	−1.09922	+	0.501996i
$750$	31.2858	−	13.2473i	1.14240	−	0.483722i
$751$	−4.71080	−	4.08193i	−0.171899	−	0.148952i	0.564662	−	0.825322i	$-0.309006\pi$
$751$	−4.71080	−	4.08193i	−0.171899	−	0.148952i	−0.736562	+	0.676370i	$0.763552\pi$
$752$	−0.852878	−	2.28665i	−0.0311012	−	0.0833857i
$753$	−20.3498	+	4.42683i	−0.741588	+	0.161323i
$754$	14.2403	−	2.04744i	0.518600	−	0.0745635i
$755$	4.03449	−	13.2826i	0.146830	−	0.483404i
$756$	28.9140	−	25.0541i	1.05159	−	0.911210i
$757$	−3.02517	−	1.65187i	−0.109952	−	0.0600382i	0.423332	−	0.905975i	$-0.360860\pi$
$757$	−3.02517	−	1.65187i	−0.109952	−	0.0600382i	−0.533284	+	0.845936i	$0.679042\pi$
$758$	−9.23852	+	9.23852i	−0.335558	+	0.335558i
$759$	−1.04235	−	2.76152i	−0.0378350	−	0.100237i
$760$	10.5992	+	0.857080i	0.384474	+	0.0310895i
$761$	47.2952	−	13.8871i	1.71445	−	0.503407i	0.730660	−	0.682742i	$-0.239213\pi$
$761$	47.2952	−	13.8871i	1.71445	−	0.503407i	0.983788	+	0.179334i	$0.0573944\pi$
$762$	44.2146	+	3.16229i	1.60173	+	0.114558i
$763$	57.8710	+	12.5891i	2.09507	+	0.455755i
$764$	1.28014	+	8.90354i	0.0463137	+	0.322119i
$765$	27.0710	−	35.4711i	0.978753	−	1.28246i
$766$	−11.4376	−	5.22339i	−0.413258	−	0.188729i
$767$	−1.17475	−	16.4251i	−0.0424177	−	0.593077i
$768$	−2.43269	+	1.82109i	−0.0877821	+	0.0657129i
$769$	−12.2540	−	26.8324i	−0.441889	−	0.967602i	−0.991248	−	0.132015i	$-0.957855\pi$
$769$	−12.2540	−	26.8324i	−0.441889	−	0.967602i	0.549359	−	0.835587i	$-0.314872\pi$
$770$	0.717415	+	1.61033i	0.0258538	+	0.0580323i
$771$	10.7367	+	3.15257i	0.386671	+	0.113537i
$772$	−0.0102881	−	0.00383725i	−0.000370275	−	0.000138106i
$773$	−19.5286	−	26.0871i	−0.702394	−	0.938288i	0.297471	−	0.954731i	$-0.403857\pi$
$773$	−19.5286	−	26.0871i	−0.702394	−	0.938288i	−0.999865	+	0.0164428i	$0.994766\pi$
$774$	−23.7609	+	27.4216i	−0.854069	+	0.985648i
$775$	8.97285	+	6.00487i	0.322314	+	0.215701i
$776$	5.39638	−	8.39693i	0.193719	−	0.301432i
$777$	−21.8728	−	16.3738i	−0.784682	−	0.587406i
$778$	−6.02404	+	27.6921i	−0.215972	+	0.992809i
$779$	24.0109	+	27.7101i	0.860281	+	0.992818i
$780$	24.6744	−	37.6213i	0.883486	−	1.34706i
$781$		−	2.49206i		−	0.0891729i
$782$	−6.43165	−	13.9383i	−0.229995	−	0.498434i
$783$	15.1007	+	15.1007i	0.539656	+	0.539656i
$784$	2.29681	+	7.82221i	0.0820289	+	0.279365i
$785$	1.86553	+	2.54090i	0.0665836	+	0.0906887i
$786$	−49.7290	+	31.9589i	−1.77378	+	1.13994i
$787$	0.128462	−	0.171605i	0.00457918	−	0.00611707i	−0.798246	−	0.602332i	$-0.794238\pi$
$787$	0.128462	−	0.171605i	0.00457918	−	0.00611707i	0.802825	+	0.596215i	$0.203329\pi$
$788$	−4.43228	−	20.3748i	−0.157893	−	0.725824i
$789$	6.34709	−	13.8982i	0.225962	−	0.494789i
$790$	−21.9881	−	22.4004i	−0.782302	−	0.796969i
$791$	0.0705576	−	0.490739i	0.00250874	−	0.0174487i
$792$	−0.441263	+	1.18307i	−0.0156796	+	0.0420386i
$793$	−12.4209	+	6.78233i	−0.441080	+	0.240848i
$794$	−8.08437	+	27.5328i	−0.286903	+	0.977103i
$795$	−38.5606	−	18.0447i	−1.36760	−	0.639979i
$796$	−18.6687	−	2.68415i	−0.661694	−	0.0951372i
$797$	−28.7732	+	2.05790i	−1.01920	+	0.0728947i	−0.570926	−	0.821001i	$-0.693416\pi$
$797$	−28.7732	+	2.05790i	−1.01920	+	0.0728947i	−0.448274	+	0.893896i	$0.647961\pi$
$798$	52.7066	−	19.6585i	1.86579	−	0.695905i
$799$	−6.57166	−	4.22335i	−0.232489	−	0.149411i
$800$	−3.60059	+	3.46926i	−0.127300	+	0.122657i
$801$	30.5944	+	47.6057i	1.08100	+	1.68207i
$802$	−0.527345	+	7.37324i	−0.0186212	+	0.260358i
$803$	−0.201602	+	0.369206i	−0.00711438	+	0.0130290i
$804$	−6.24544			−0.220260
$805$	−14.3779	−	39.1894i	−0.506756	−	1.38124i
$806$	14.2976			0.503610
$807$	−34.8534	+	63.8292i	−1.22690	+	2.24689i
$808$	−0.382418	+	5.34690i	−0.0134534	+	0.188103i
$809$	9.36888	+	14.5783i	0.329392	+	0.512545i	0.965965	−	0.258672i	$-0.0832849\pi$
$809$	9.36888	+	14.5783i	0.329392	+	0.512545i	−0.636573	+	0.771217i	$0.719649\pi$
$810$	24.9153	−	1.54955i	0.875435	−	0.0544457i
$811$	15.0094	+	9.64595i	0.527051	+	0.338715i	0.776956	−	0.629555i	$-0.216763\pi$
$811$	15.0094	+	9.64595i	0.527051	+	0.338715i	−0.249905	+	0.968270i	$0.580399\pi$
$812$	−7.92468	+	2.95575i	−0.278102	+	0.103727i
$813$	61.3184	−	4.38558i	2.15053	−	0.153809i
$814$	0.463060	+	0.0665779i	0.0162302	+	0.00233356i
$815$	10.8233	+	29.8626i	0.379125	+	1.04604i
$816$	−2.74034	+	9.33273i	−0.0959310	+	0.326711i
$817$	−24.2920	+	13.2645i	−0.849871	+	0.464064i
$818$	8.42757	−	22.5952i	0.294663	−	0.790023i
$819$	22.8676	−	159.047i	0.799057	−	5.55756i
$820$	−17.2394	−	0.160109i	−0.602026	−	0.00559125i
$821$	−22.3503	+	48.9402i	−0.780030	+	1.70803i	−0.0768186	+	0.997045i	$0.524476\pi$
$821$	−22.3503	+	48.9402i	−0.780030	+	1.70803i	−0.703211	+	0.710981i	$0.748251\pi$
$822$	5.88675	+	27.0609i	0.205324	+	0.943859i
$823$	−3.38887	+	4.52700i	−0.118129	+	0.157801i	−0.855708	−	0.517459i	$-0.826878\pi$
$823$	−3.38887	+	4.52700i	−0.118129	+	0.157801i	0.737579	+	0.675261i	$0.235969\pi$
$824$	−10.6464	+	6.84203i	−0.370885	+	0.238354i
$825$	−0.709875	+	2.99435i	−0.0247147	+	0.104250i
$826$	2.72745	+	9.28886i	0.0949003	+	0.323201i
$827$	29.3438	+	29.3438i	1.02038	+	1.02038i	0.999788	+	0.0205953i	$0.00655616\pi$
$827$	29.3438	+	29.3438i	1.02038	+	1.02038i	0.0205953	+	0.999788i	$0.493444\pi$
$828$	12.3136	−	27.2455i	0.427928	−	0.946846i
$829$			9.58582i			0.332929i	0.986047	+	0.166465i	$0.0532352\pi$
$829$			9.58582i			0.332929i	−0.986047	+	0.166465i	$0.946765\pi$
$830$	11.7843	+	7.72890i	0.409040	+	0.268274i
$831$	16.1241	+	18.6082i	0.559339	+	0.645512i
$832$	−1.40744	+	6.46990i	−0.0487942	+	0.224303i
$833$	20.8899	+	15.6380i	0.723791	+	0.541823i
$834$	18.1785	−	28.2863i	0.629471	−	0.979476i
$835$	31.8247	+	17.7632i	1.10134	+	0.614722i
$836$	−0.630749	+	0.727924i	−0.0218149	+	0.0251758i
$837$	12.7187	+	16.9901i	0.439621	+	0.587265i
$838$	2.81349	+	1.04938i	0.0971904	+	0.0362502i
$839$	31.8393	+	9.34886i	1.09921	+	0.322759i	0.780540	−	0.625106i	$-0.214944\pi$
$839$	31.8393	+	9.34886i	1.09921	+	0.322759i	0.318675	+	0.947864i	$0.396762\pi$
$840$	−9.47316	+	24.6956i	−0.326855	+	0.852080i
$841$	10.0858	+	22.0848i	0.347786	+	0.761545i
$842$	30.4314	−	22.7806i	1.04873	−	0.785073i
$843$	3.69154	+	51.6145i	0.127143	+	1.77770i
$844$	−2.52085	−	1.15123i	−0.0867713	−	0.0396271i
$845$	−9.17987	−	68.3476i	−0.315797	−	2.35123i
$846$	−2.16533	−	15.0602i	−0.0744457	−	0.517781i
$847$	41.6842	+	9.06784i	1.43229	+	0.311575i
$848$	6.24952	+	0.446974i	0.214609	+	0.0153492i
$849$	−26.8956	+	7.89725i	−0.923053	+	0.271033i
$850$	−2.57147	+	15.7963i	−0.0882005	+	0.541807i
$851$	−10.8335	−	2.31219i	−0.371366	−	0.0792609i
$852$	26.4389	−	26.4389i	0.905781	−	0.905781i
$853$	37.6323	+	20.5488i	1.28851	+	0.703577i	0.969713	−	0.244248i	$-0.0785410\pi$
$853$	37.6323	+	20.5488i	1.28851	+	0.703577i	0.318792	+	0.947825i	$0.396723\pi$
$854$	6.28782	−	5.44842i	0.215165	−	0.186441i
$855$	63.4333	+	19.2674i	2.16937	+	0.658930i
$856$	8.40959	−	1.20912i	0.287434	−	0.0413268i
$857$	9.59289	−	2.08681i	0.327687	−	0.0712839i	−0.0457123	−	0.998955i	$-0.514556\pi$
$857$	9.59289	−	2.08681i	0.327687	−	0.0712839i	0.373399	+	0.927671i	$0.378192\pi$
$858$	1.42412	+	3.81822i	0.0486187	+	0.130352i
$859$	17.7898	+	15.4150i	0.606981	+	0.525952i	0.903229	−	0.429159i	$-0.141190\pi$
$859$	17.7898	+	15.4150i	0.606981	+	0.525952i	−0.296248	+	0.955111i	$0.595736\pi$
$860$	2.88429	−	12.6903i	0.0983535	−	0.432735i
$861$	−82.9595	+	37.8863i	−2.82725	+	1.29116i
$862$	2.17864	+	3.98989i	0.0742049	+	0.135896i
$863$	−24.3814	−	44.6512i	−0.829952	−	1.51994i	−0.854024	−	0.520233i	$-0.825845\pi$
$863$	−24.3814	−	44.6512i	−0.829952	−	1.51994i	0.0240722	−	0.999710i	$-0.492337\pi$
$864$	−8.94035	+	4.08292i	−0.304157	+	0.138904i
$865$	−4.37600	+	19.2535i	−0.148789	+	0.654639i
$866$	−24.6551	−	21.3637i	−0.837813	−	0.725969i
$867$	−7.17310	−	19.2318i	−0.243611	−	0.653147i
$868$	−8.21345	+	1.78673i	−0.278783	+	0.0606454i
$869$	2.81416	−	0.404616i	0.0954640	−	0.0137256i
$870$	−14.1270	−	4.29096i	−0.478949	−	0.145477i
$871$	−10.2843	+	8.91141i	−0.348471	+	0.301951i
$872$	−13.3535	−	7.29158i	−0.452207	−	0.246924i
$873$	44.0017	−	44.0017i	1.48923	−	1.48923i
$874$	16.0636	−	16.1901i	0.543359	−	0.547640i
$875$	−10.4321	+	42.2519i	−0.352669	+	1.42838i
$876$	−6.05584	+	1.77816i	−0.204608	+	0.0600783i
$877$	14.9185	+	1.06700i	0.503764	+	0.0360299i	0.320909	−	0.947110i	$-0.396012\pi$
$877$	14.9185	+	1.06700i	0.503764	+	0.0360299i	0.182855	+	0.983140i	$0.441466\pi$
$878$	5.57869	+	1.21357i	0.188272	+	0.0409560i
$879$	−4.62515	−	32.1686i	−0.156003	−	1.08502i
$880$	−0.0602865	−	0.448855i	−0.00203226	−	0.0151309i
$881$	−10.6700	−	4.87282i	−0.359481	−	0.164170i	0.227484	−	0.973782i	$-0.426950\pi$
$881$	−10.6700	−	4.87282i	−0.359481	−	0.164170i	−0.586965	+	0.809612i	$0.699677\pi$
$882$	3.62582	+	50.6956i	0.122088	+	1.70701i
$883$	−27.0663	+	20.2616i	−0.910854	+	0.681857i	−0.948278	−	0.317443i	$-0.897176\pi$
$883$	−27.0663	+	20.2616i	−0.910854	+	0.681857i	0.0374233	+	0.999300i	$0.488085\pi$
$884$	8.80407	+	19.2782i	0.296113	+	0.648397i
$885$	−6.05247	+	15.7782i	−0.203452	+	0.530379i
$886$	16.6348	+	4.88443i	0.558858	+	0.164096i
$887$	−9.57673	−	3.57193i	−0.321555	−	0.119934i	0.183503	−	0.983019i	$-0.441256\pi$
$887$	−9.57673	−	3.57193i	−0.321555	−	0.119934i	−0.505058	+	0.863085i	$0.668529\pi$
$888$	4.20637	+	5.61905i	0.141157	+	0.188563i
$889$	−37.1844	+	42.9131i	−1.24712	+	1.43926i
$890$	−17.7229	−	9.89222i	−0.594074	−	0.331588i
$891$	−1.22245	+	1.90217i	−0.0409537	+	0.0637253i
$892$	−5.05440	−	3.78368i	−0.169234	−	0.126687i
$893$	2.46707	−	11.3409i	0.0825572	−	0.379509i
$894$	2.75125	+	3.17511i	0.0920156	+	0.106192i
$895$	9.76439	+	6.40410i	0.326388	+	0.214066i
$896$		−	3.89261i		−	0.130043i
$897$	−27.5489	−	92.4788i	−0.919830	−	3.08778i
$898$	8.02187	+	8.02187i	0.267693	+	0.267693i
$899$	−1.32186	−	4.50184i	−0.0440865	−	0.150145i
$900$	−26.5318	+	16.3627i	−0.884393	+	0.545425i
$901$	16.8712	−	10.8425i	0.562061	−	0.361214i
$902$	0.935811	−	1.25010i	0.0311591	−	0.0416237i
$903$	−14.6339	−	67.2710i	−0.486986	−	2.23864i
$904$	−0.0529096	+	0.115856i	−0.00175975	+	0.00385331i
$905$	−34.5174	−	0.320577i	−1.14740	−	0.0106563i
$906$	−2.68482	+	18.6733i	−0.0891971	+	0.620380i
$907$	−11.4742	+	30.7634i	−0.380993	+	1.02148i	0.595008	+	0.803720i	$0.297149\pi$
$907$	−11.4742	+	30.7634i	−0.380993	+	1.02148i	−0.976002	+	0.217763i	$0.930124\pi$
$908$	14.5008	−	7.91805i	0.481227	−	0.262770i
$909$	−9.41537	+	32.0658i	−0.312288	+	1.06356i
$910$	19.6380	+	54.1830i	0.650993	+	1.79615i
$911$	−32.0598	−	4.60951i	−1.06219	−	0.152720i	−0.411000	−	0.911635i	$-0.634820\pi$
$911$	−32.0598	−	4.60951i	−1.06219	−	0.152720i	−0.651189	+	0.758915i	$0.725730\pi$
$912$	−14.4145	+	1.03094i	−0.477311	+	0.0341380i
$913$	−1.19600	+	0.446085i	−0.0395818	+	0.0147633i
$914$	−13.5724	−	8.72246i	−0.448935	−	0.288513i
$915$	14.4954	−	0.901508i	0.479203	−	0.0298029i
$916$	−0.245655	−	0.382247i	−0.00811668	−	0.0126298i
$917$	5.40194	−	75.5289i	0.178388	−	2.49419i
$918$	−15.0770	+	27.6114i	−0.497614	+	0.911313i
$919$	−47.0659			−1.55256			−0.776280	−	0.630388i	$-0.782896\pi$
$919$	−47.0659			−1.55256			−0.776280	+	0.630388i	$0.782896\pi$
$920$	0.707650	+	10.7004i	0.0233305	+	0.352783i
$921$	38.5005			1.26864
$922$	15.1900	−	27.8184i	0.500256	−	0.916150i
$923$	5.81193	−	81.2614i	0.191302	−	2.67475i
$924$	−1.29526	−	2.01546i	−0.0426109	−	0.0663039i
$925$	8.01333	+	8.31668i	0.263477	+	0.273451i
$926$	31.8623	+	20.4767i	1.04706	+	0.672905i
$927$	−73.9236	+	27.5721i	−2.42797	+	0.905586i
$928$	2.16729	−	0.155007i	0.0711446	−	0.00508837i
$929$	37.0416	+	5.32577i	1.21529	+	0.174733i	0.719989	−	0.693986i	$-0.244147\pi$
$929$	37.0416	+	5.32577i	1.21529	+	0.174733i	0.495306	+	0.868719i	$0.335056\pi$
$930$	−13.2896	−	6.21898i	−0.435785	−	0.203928i
$931$	−10.9227	+	37.1992i	−0.357976	+	1.21915i
$932$	10.2319	−	5.58704i	0.335157	−	0.183010i
$933$	1.23180	−	3.30257i	0.0403272	−	0.108121i
$934$	1.52245	−	10.5889i	0.0498162	−	0.346479i
$935$	−1.01547	−	1.03451i	−0.0332094	−	0.0338320i
$936$	−17.1479	+	37.5486i	−0.560496	+	1.22731i
$937$	−7.69780	−	35.3862i	−0.251476	−	1.15602i	−0.913597	−	0.406620i	$-0.866707\pi$
$937$	−7.69780	−	35.3862i	−0.251476	−	1.15602i	0.662121	−	0.749397i	$-0.269656\pi$
$938$	4.79434	−	6.40449i	0.156541	−	0.209114i
$939$	−8.12629	+	5.22245i	−0.265191	+	0.170428i
$940$	3.22966	+	4.39889i	0.105340	+	0.143476i
$941$	−5.81606	−	19.8077i	−0.189598	−	0.645712i	−0.998343	−	0.0575519i	$-0.981671\pi$
$941$	−5.81606	−	19.8077i	−0.189598	−	0.645712i	0.808744	−	0.588160i	$-0.200148\pi$
$942$	−3.02913	−	3.02913i	−0.0986942	−	0.0986942i
$943$	−24.1043	+	28.0394i	−0.784944	+	0.913089i
$944$		−	2.48702i		−	0.0809456i
$945$	−46.9177	+	71.5358i	−1.52623	+	2.32706i
$946$	0.771928	+	0.890852i	0.0250975	+	0.0289641i
$947$	−7.78801	+	35.8009i	−0.253076	+	1.16337i	0.658610	+	0.752485i	$0.271145\pi$
$947$	−7.78801	+	35.8009i	−0.253076	+	1.16337i	−0.911686	+	0.410888i	$0.865219\pi$
$948$	34.1488	+	25.5635i	1.10910	+	0.830263i
$949$	−7.43492	+	11.5690i	−0.241348	+	0.375544i
$950$	−23.3244	+	4.62195i	−0.756744	+	0.149956i
$951$	23.4626	−	27.0772i	0.760826	−	0.878040i
$952$	−7.46678	−	9.97445i	−0.242000	−	0.323274i
$953$	47.0046	+	17.5318i	1.52263	+	0.567911i	0.965016	−	0.262191i	$-0.0844452\pi$
$953$	47.0046	+	17.5318i	1.52263	+	0.567911i	0.557611	+	0.830102i	$0.311718\pi$
$954$	37.4789	+	11.0048i	1.21342	+	0.356294i
$955$	−8.18524	−	18.3728i	−0.264868	−	0.594531i
$956$	9.64856	+	21.1274i	0.312057	+	0.683309i
$957$	1.07057	−	0.801418i	0.0346066	−	0.0259062i
$958$	0.139294	+	1.94759i	0.00450039	+	0.0629236i
$959$	−32.2691	−	14.7368i	−1.04202	−	0.475877i
$960$	4.12242	−	5.40161i	0.133051	−	0.174336i
$961$	3.74817	+	26.0691i	0.120909	+	0.840939i
$962$	14.9442	+	3.25092i	0.481822	+	0.104814i
$963$	52.8325	+	3.77865i	1.70250	+	0.121765i
$964$	9.77522	−	2.87026i	0.314839	−	0.0924449i
$965$	0.0244730	+	0.00197895i	0.000787813	+	6.37045e-5i
$966$	27.3827	+	49.6831i	0.881023	+	1.59853i
$967$	17.4019	−	17.4019i	0.559609	−	0.559609i	−0.369587	−	0.929196i	$-0.620501\pi$
$967$	17.4019	−	17.4019i	0.559609	−	0.559609i	0.929196	+	0.369587i	$0.120501\pi$
$968$	−9.61847	−	5.25208i	−0.309149	−	0.168808i
$969$	−34.9582	+	30.2915i	−1.12302	+	0.973102i
$970$	−6.48666	+	21.3558i	−0.208274	+	0.685693i
$971$	30.0302	−	4.31769i	0.963716	−	0.138561i	0.357545	−	0.933896i	$-0.383614\pi$
$971$	30.0302	−	4.31769i	0.963716	−	0.138561i	0.606171	+	0.795335i	$0.292705\pi$
$972$	−4.33815	+	0.943706i	−0.139146	+	0.0302694i
$973$	15.0519	+	40.3557i	0.482541	+	1.29374i
$974$	−21.8608	−	18.9425i	−0.700466	−	0.606958i
$975$	−30.1310	+	95.9847i	−0.964966	+	3.07397i
$976$	−1.94422	+	0.887897i	−0.0622331	+	0.0284209i
$977$	0.608596	+	1.11456i	0.0194707	+	0.0356579i	0.887233	−	0.461321i	$-0.152624\pi$
$977$	0.608596	+	1.11456i	0.0194707	+	0.0356579i	−0.867763	+	0.496979i	$0.834443\pi$
$978$	−20.6875	−	37.8863i	−0.661512	−	1.21147i
$979$	1.67229	−	0.763709i	0.0534466	−	0.0244082i
$980$	−9.71272	−	15.4264i	−0.310261	−	0.492779i
$981$	−71.6851	−	62.1155i	−2.28873	−	1.98319i
$982$	6.06130	+	16.2510i	0.193424	+	0.518589i
$983$	10.2483	−	2.22938i	0.326870	−	0.0711063i	−0.0461358	−	0.998935i	$-0.514691\pi$
$983$	10.2483	−	2.22938i	0.326870	−	0.0711063i	0.373006	+	0.927829i	$0.378327\pi$
$984$	23.1908	−	3.33434i	0.739296	−	0.106295i
$985$	21.9640	+	41.1276i	0.699831	+	1.31043i
$986$	5.25613	−	4.55446i	0.167389	−	0.145044i
$987$	25.3375	+	13.8353i	0.806502	+	0.440383i
$988$	−22.2652	+	22.2652i	−0.708351	+	0.708351i
$989$	−16.8145	−	22.2787i	−0.534669	−	0.708423i
$990$	0.227568	−	2.81426i	0.00723259	−	0.0894430i
$991$	−16.4692	+	4.83578i	−0.523160	+	0.153614i	−0.532641	−	0.846341i	$-0.678800\pi$
$991$	−16.4692	+	4.83578i	−0.523160	+	0.153614i	0.00948076	+	0.999955i	$0.496982\pi$
$992$	2.15385	+	0.154047i	0.0683850	+	0.00489099i
$993$	−52.2499	−	11.3663i	−1.65810	−	0.360698i
$994$	6.81626	+	47.4081i	0.216199	+	1.50370i
$995$	41.7984	−	5.61401i	1.32510	−	0.177976i
$996$	−17.4213	−	7.95603i	−0.552014	−	0.252096i
$997$	1.42022	+	19.8573i	0.0449789	+	0.628887i	0.969081	+	0.246742i	$0.0793600\pi$
$997$	1.42022	+	19.8573i	0.0449789	+	0.628887i	−0.924102	+	0.382145i	$0.875185\pi$
$998$	13.0366	−	9.75911i	0.412668	−	0.308919i
$999$	9.43078	+	20.6505i	0.298377	+	0.653354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.83.12	yes	240
5.2	odd	4	inner	230.2.l.a.37.7	✓	240
23.5	odd	22	inner	230.2.l.a.143.7	yes	240
115.97	even	44	inner	230.2.l.a.97.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.37.7	✓	240	5.2	odd	4	inner
230.2.l.a.83.12	yes	240	1.1	even	1	trivial
230.2.l.a.97.12	yes	240	115.97	even	44	inner
230.2.l.a.143.7	yes	240	23.5	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.479249 - 0.877679i) q^{2} +(0.216786 - 3.03106i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.67624 + 1.47994i) q^{5} +(-2.55641 - 1.64290i) q^{6} +(3.64718 - 1.36033i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(-6.17089 - 0.887239i) q^{9} +O(q^{10})\)	\(q+(0.479249 - 0.877679i) q^{2} +(0.216786 - 3.03106i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(1.67624 + 1.47994i) q^{5} +(-2.55641 - 1.64290i) q^{6} +(3.64718 - 1.36033i) q^{7} +(-0.997452 + 0.0713392i) q^{8} +(-6.17089 - 0.887239i) q^{9} +(2.10225 - 0.761935i) q^{10} +(-0.0570612 + 0.194333i) q^{11} +(-2.66710 + 1.45634i) q^{12} +(-2.31388 + 6.20374i) q^{13} +(0.553977 - 3.85299i) q^{14} +(4.84919 - 4.75995i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.680388 + 3.12769i) q^{17} +(-3.73610 + 4.99085i) q^{18} +(-4.00065 + 2.57106i) q^{19} +(0.338767 - 2.21026i) q^{20} +(-3.33259 - 11.3497i) q^{21} +(0.143215 + 0.143215i) q^{22} +(-3.15480 - 3.61210i) q^{23} +3.03881i q^{24} +(0.619531 + 4.96147i) q^{25} +(4.33597 + 5.00398i) q^{26} +(-2.08921 + 9.60393i) q^{27} +(-3.11620 - 2.33276i) q^{28} +(1.17472 - 1.82789i) q^{29} +(-1.85374 - 6.53723i) q^{30} +(1.41408 - 1.63193i) q^{31} +(0.599278 + 0.800541i) q^{32} +(0.576664 + 0.215085i) q^{33} +(3.07118 + 0.901781i) q^{34} +(8.12675 + 3.11740i) q^{35} +(2.58984 + 5.67096i) q^{36} +(1.84910 - 1.38422i) q^{37} +(0.339260 + 4.74347i) q^{38} +(18.3023 + 8.35839i) q^{39} +(-1.77754 - 1.35659i) q^{40} +(-1.09725 - 7.63155i) q^{41} +(-11.5586 - 2.51441i) q^{42} +(5.80518 + 0.415195i) q^{43} +(0.194333 - 0.0570612i) q^{44} +(-9.03079 - 10.6198i) q^{45} +(-4.68220 + 1.03781i) q^{46} +(-1.72572 + 1.72572i) q^{47} +(2.66710 + 1.45634i) q^{48} +(6.16120 - 5.33871i) q^{49} +(4.65149 + 1.83403i) q^{50} +(9.62773 - 1.38426i) q^{51} +(6.46990 - 1.40744i) q^{52} +(-2.18956 - 5.87044i) q^{53} +(7.42791 + 6.43632i) q^{54} +(-0.383249 + 0.241300i) q^{55} +(-3.54085 + 1.61705i) q^{56} +(6.92578 + 12.6836i) q^{57} +(-1.04132 - 1.90704i) q^{58} +(-2.26227 + 1.03315i) q^{59} +(-6.62599 - 1.50598i) q^{60} +(1.61532 + 1.39968i) q^{61} +(-0.754618 - 2.02321i) q^{62} +(-23.7133 + 5.15851i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-13.0598 + 6.97453i) q^{65} +(0.465141 - 0.403047i) q^{66} +(1.80383 + 0.984965i) q^{67} +(2.26334 - 2.26334i) q^{68} +(-11.6324 + 8.77935i) q^{69} +(6.63081 - 5.63867i) q^{70} +(-11.8058 + 3.46651i) q^{71} +(6.21846 + 0.444753i) q^{72} +(2.02950 + 0.441491i) q^{73} +(-0.328720 - 2.28630i) q^{74} +(15.1728 - 0.802260i) q^{75} +(4.32583 + 1.97554i) q^{76} +(0.0562436 + 0.786388i) q^{77} +(16.1074 - 12.0578i) q^{78} +(-5.83137 - 12.7689i) q^{79} +(-2.04254 + 0.909966i) q^{80} +(10.7118 + 3.14526i) q^{81} +(-7.22391 - 2.69438i) q^{82} +(3.77693 + 5.04539i) q^{83} +(-7.74628 + 8.93969i) q^{84} +(-3.48832 + 6.24968i) q^{85} +(3.14654 - 4.89611i) q^{86} +(-5.28580 - 3.95690i) q^{87} +(0.0430523 - 0.197908i) q^{88} +(-5.94416 - 6.85993i) q^{89} +(-13.6488 + 2.83661i) q^{90} +25.7738i q^{91} +(-1.33307 + 4.60683i) q^{92} +(-4.63994 - 4.63994i) q^{93} +(0.687577 + 2.34167i) q^{94} +(-10.5111 - 1.61104i) q^{95} +(2.55641 - 1.64290i) q^{96} +(-5.98166 + 7.99056i) q^{97} +(-1.73293 - 7.96613i) q^{98} +(0.524538 - 1.14858i) 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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