LMFDB - Embedded newform 446.2.g.a.101.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [446,2,Mod(9,446)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(446, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("446.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 446 = 2 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	446.g (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [648,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.56132793015$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$9$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	446.101
Dual form			446.2.g.a.53.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.911228 - 0.411901i) q^{2} +(0.591281 - 1.26024i) q^{3} +(0.660675 + 0.750672i) q^{4} +(1.89116 - 0.435670i) q^{5} +(-1.05788 + 0.904814i) q^{6} +(0.489184 + 0.794485i) q^{7} +(-0.292823 - 0.956167i) q^{8} +(0.678917 + 0.816897i) q^{9} +(-1.90274 - 0.381978i) q^{10} +(0.284401 + 1.52845i) q^{11} +(1.33667 - 0.388749i) q^{12} +(4.40585 + 0.374993i) q^{13} +(-0.118509 - 0.925452i) q^{14} +(0.569161 - 2.64092i) q^{15} +(-0.127018 + 0.991900i) q^{16} +(5.05372 + 1.78559i) q^{17} +(-0.282168 - 1.02403i) q^{18} +(-5.64845 - 0.320074i) q^{19} +(1.57649 + 1.13181i) q^{20} +(1.29048 - 0.146724i) q^{21} +(0.370417 - 1.50991i) q^{22} +(-3.42496 - 3.67630i) q^{23} +(-1.37814 - 0.196337i) q^{24} +(-1.10934 + 0.539768i) q^{25} +(-3.86027 - 2.15648i) q^{26} +(5.47232 - 1.42488i) q^{27} +(-0.273206 + 0.892113i) q^{28} +(-0.106704 + 0.0446411i) q^{29} +(-1.60643 + 2.17204i) q^{30} +(1.18948 + 7.57947i) q^{31} +(0.524307 - 0.851529i) q^{32} +(2.09437 + 0.545332i) q^{33} +(-3.86961 - 3.70872i) q^{34} +(1.27126 + 1.28938i) q^{35} +(-0.164678 + 1.04935i) q^{36} +(-6.56894 - 5.61845i) q^{37} +(5.01519 + 2.61826i) q^{38} +(3.07767 - 5.33068i) q^{39} +(-0.970349 - 1.68069i) q^{40} +(-0.442258 - 10.4111i) q^{41} +(-1.23636 - 0.397853i) q^{42} +(-0.497070 - 7.01335i) q^{43} +(-0.959471 + 1.22330i) q^{44} +(1.63984 + 1.24910i) q^{45} +(1.60665 + 4.76069i) q^{46} +(4.50069 - 0.255035i) q^{47} +(1.17493 + 0.746564i) q^{48} +(2.75952 - 5.47318i) q^{49} +(1.23320 - 0.0349120i) q^{50} +(5.23844 - 5.31310i) q^{51} +(2.62934 + 3.55510i) q^{52} +(1.31868 + 0.786429i) q^{53} +(-5.57344 - 0.955663i) q^{54} +(1.20375 + 2.76665i) q^{55} +(0.616416 - 0.700384i) q^{56} +(-3.74319 + 6.92913i) q^{57} +(0.115619 + 0.00327321i) q^{58} +(-2.65452 + 2.54415i) q^{59} +(2.35849 - 1.31753i) q^{60} +(-5.06743 + 7.27349i) q^{61} +(2.03811 - 7.39658i) q^{62} +(-0.316897 + 0.939002i) q^{63} +(-0.828510 + 0.559975i) q^{64} +(8.49555 - 1.21032i) q^{65} +(-1.68383 - 1.35960i) q^{66} +(-7.33888 + 1.47329i) q^{67} +(1.99847 + 4.97339i) q^{68} +(-6.65812 + 2.14254i) q^{69} +(-0.627312 - 1.69855i) q^{70} +(-2.41187 - 9.83137i) q^{71} +(0.582287 - 0.888364i) q^{72} +(1.92227 - 4.41807i) q^{73} +(3.67156 + 7.82545i) q^{74} +(0.0243021 + 1.71719i) q^{75} +(-3.49152 - 4.45160i) q^{76} +(-1.07521 + 0.973646i) q^{77} +(-5.00018 + 3.58977i) q^{78} +(-7.44358 + 4.72975i) q^{79} +(0.191930 + 1.93118i) q^{80} +(0.857065 - 4.60612i) q^{81} +(-3.88534 + 9.66905i) q^{82} +(-1.03562 + 14.6119i) q^{83} +(0.962731 + 0.871794i) q^{84} +(10.3353 + 1.17509i) q^{85} +(-2.43586 + 6.59550i) q^{86} +(-0.00683357 + 0.160868i) q^{87} +(1.37818 - 0.719500i) q^{88} +(7.03153 + 1.61986i) q^{89} +(-0.979763 - 1.81367i) q^{90} +(1.85734 + 3.68382i) q^{91} +(0.496909 - 4.99986i) q^{92} +(10.2552 + 2.98257i) q^{93} +(-4.20621 - 1.62145i) q^{94} +(-10.8216 + 1.85555i) q^{95} +(-0.763115 - 1.16424i) q^{96} +(-11.0170 + 11.8255i) q^{97} +(-4.76897 + 3.85067i) q^{98} +(-1.05550 + 1.27002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 18 q^{2} + 2 q^{3} - 18 q^{4} + 3 q^{5} + 2 q^{6} + 4 q^{7} - 18 q^{8} + 13 q^{9} + 3 q^{10} - 33 q^{11} + 2 q^{12} - 10 q^{13} + 78 q^{14} + 2 q^{15} - 18 q^{16} + 10 q^{17} + 13 q^{18} - 3 q^{19}+ \cdots - 323 q^{99}+O(q^{100}) $ 648 * q - 18 * q^2 + 2 * q^3 - 18 * q^4 + 3 * q^5 + 2 * q^6 + 4 * q^7 - 18 * q^8 + 13 * q^9 + 3 * q^10 - 33 * q^11 + 2 * q^12 - 10 * q^13 + 78 * q^14 + 2 * q^15 - 18 * q^16 + 10 * q^17 + 13 * q^18 - 3 * q^19 + 3 * q^20 + 15 * q^21 + 4 * q^22 - 5 * q^23 - 35 * q^24 + 22 * q^25 - 10 * q^26 - 22 * q^27 + 4 * q^28 + 258 * q^29 - 109 * q^30 + 11 * q^31 - 18 * q^32 - 2 * q^33 + 10 * q^34 - 9 * q^35 + 13 * q^36 - 27 * q^37 - 3 * q^38 - 9 * q^39 - 71 * q^40 - 63 * q^41 + 15 * q^42 - 26 * q^43 + 4 * q^44 + 9 * q^45 - 42 * q^46 - 102 * q^47 + 2 * q^48 + 2 * q^49 + 22 * q^50 - 85 * q^51 - 10 * q^52 - 8 * q^53 - 22 * q^54 - 6 * q^55 + 4 * q^56 - 105 * q^57 - 75 * q^58 + 156 * q^59 + 2 * q^60 - 15 * q^61 - 211 * q^62 - 24 * q^63 - 18 * q^64 + 7 * q^65 - 113 * q^66 - 71 * q^67 + 10 * q^68 - 215 * q^69 - 83 * q^70 + 16 * q^71 + 87 * q^72 - 11 * q^73 + 158 * q^74 - 101 * q^75 - 3 * q^76 + 33 * q^77 - 9 * q^78 - 216 * q^79 + 3 * q^80 - 229 * q^81 - 26 * q^82 - 140 * q^83 + 15 * q^84 - 77 * q^85 + 11 * q^86 + 128 * q^87 + 4 * q^88 + 162 * q^89 + 9 * q^90 + 20 * q^91 - 79 * q^92 - 26 * q^93 - 28 * q^94 - 204 * q^95 + 2 * q^96 + 8 * q^97 - 35 * q^98 - 323 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/446\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{71}{111}\right)$

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 $

$2$	−0.911228	−	0.411901i	−0.644336	−	0.291258i
$2$	−0.911228	−	0.411901i	−0.644336	−	0.291258i
$3$	0.591281	−	1.26024i	0.341376	−	0.727598i	−0.658308	−	0.752749i	$-0.728727\pi$
$3$	0.591281	−	1.26024i	0.341376	−	0.727598i	0.999684	+	0.0251510i	$0.00800667\pi$
$4$	0.660675	+	0.750672i	0.330337	+	0.375336i
$5$	1.89116	−	0.435670i	0.845754	−	0.194838i	0.220625	−	0.975359i	$-0.429190\pi$
$5$	1.89116	−	0.435670i	0.845754	−	0.194838i	0.625129	+	0.780521i	$0.285046\pi$
$6$	−1.05788	+	0.904814i	−0.431880	+	0.369389i
$7$	0.489184	+	0.794485i	0.184894	+	0.300287i	0.930635	−	0.365949i	$-0.119256\pi$
$7$	0.489184	+	0.794485i	0.184894	+	0.300287i	−0.745741	+	0.666236i	$0.767904\pi$
$8$	−0.292823	−	0.956167i	−0.103528	−	0.338056i
$9$	0.678917	+	0.816897i	0.226306	+	0.272299i
$10$	−1.90274	−	0.381978i	−0.601698	−	0.120792i
$11$	0.284401	+	1.52845i	0.0857500	+	0.460846i	0.998616	+	0.0525871i	$0.0167467\pi$
$11$	0.284401	+	1.52845i	0.0857500	+	0.460846i	−0.912866	+	0.408259i	$0.866136\pi$
$12$	1.33667	−	0.388749i	0.385863	−	0.112222i
$13$	4.40585	+	0.374993i	1.22196	+	0.104004i	0.677972	−	0.735087i	$-0.262859\pi$
$13$	4.40585	+	0.374993i	1.22196	+	0.104004i	0.543990	+	0.839092i	$0.316913\pi$
$14$	−0.118509	−	0.925452i	−0.0316728	−	0.247338i
$15$	0.569161	−	2.64092i	0.146957	−	0.681882i
$16$	−0.127018	+	0.991900i	−0.0317545	+	0.247975i
$17$	5.05372	+	1.78559i	1.22571	+	0.433070i	0.866023	−	0.500004i	$-0.166668\pi$
$17$	5.05372	+	1.78559i	1.22571	+	0.433070i	0.359684	+	0.933074i	$0.382884\pi$
$18$	−0.282168	−	1.02403i	−0.0665076	−	0.241365i
$19$	−5.64845	−	0.320074i	−1.29584	−	0.0734300i	−0.604878	−	0.796318i	$-0.706778\pi$
$19$	−5.64845	−	0.320074i	−1.29584	−	0.0734300i	−0.690965	+	0.722888i	$0.742814\pi$
$20$	1.57649	+	1.13181i	0.352514	+	0.253080i
$21$	1.29048	−	0.146724i	0.281607	−	0.0320177i
$22$	0.370417	−	1.50991i	0.0789733	−	0.321915i
$23$	−3.42496	−	3.67630i	−0.714154	−	0.766561i	0.266177	−	0.963924i	$-0.414240\pi$
$23$	−3.42496	−	3.67630i	−0.714154	−	0.766561i	−0.980330	+	0.197364i	$0.936762\pi$
$24$	−1.37814	−	0.196337i	−0.281311	−	0.0400771i
$25$	−1.10934	+	0.539768i	−0.221869	+	0.107954i
$26$	−3.86027	−	2.15648i	−0.757062	−	0.422920i
$27$	5.47232	−	1.42488i	1.05315	−	0.274218i
$28$	−0.273206	+	0.892113i	−0.0516312	+	0.168593i
$29$	−0.106704	+	0.0446411i	−0.0198144	+	0.00828965i	−0.395835	−	0.918322i	$-0.629545\pi$
$29$	−0.106704	+	0.0446411i	−0.0198144	+	0.00828965i	0.376020	+	0.926612i	$0.377292\pi$
$30$	−1.60643	+	2.17204i	−0.293293	+	0.396559i
$31$	1.18948	+	7.57947i	0.213637	+	1.36131i	0.822828	+	0.568290i	$0.192395\pi$
$31$	1.18948	+	7.57947i	0.213637	+	1.36131i	−0.609191	+	0.793023i	$0.708506\pi$
$32$	0.524307	−	0.851529i	0.0926853	−	0.150531i
$33$	2.09437	+	0.545332i	0.364583	+	0.0949302i
$34$	−3.86961	−	3.70872i	−0.663632	−	0.636040i
$35$	1.27126	+	1.28938i	0.214882	+	0.217945i
$36$	−0.164678	+	1.04935i	−0.0274464	+	0.174891i
$37$	−6.56894	−	5.61845i	−1.07993	−	0.923667i	−0.0825893	−	0.996584i	$-0.526319\pi$
$37$	−6.56894	−	5.61845i	−1.07993	−	0.923667i	−0.997338	+	0.0729162i	$0.976769\pi$
$38$	5.01519	+	2.61826i	0.813571	+	0.424739i
$39$	3.07767	−	5.33068i	0.492822	−	0.853593i
$40$	−0.970349	−	1.68069i	−0.153426	−	0.265741i
$41$	−0.442258	−	10.4111i	−0.0690691	−	1.62594i	−0.615292	−	0.788299i	$-0.710962\pi$
$41$	−0.442258	−	10.4111i	−0.0690691	−	1.62594i	0.546223	−	0.837640i	$-0.316065\pi$
$42$	−1.23636	−	0.397853i	−0.190775	−	0.0613900i
$43$	−0.497070	−	7.01335i	−0.0758025	−	1.06953i	−0.879941	−	0.475083i	$-0.842418\pi$
$43$	−0.497070	−	7.01335i	−0.0758025	−	1.06953i	0.804138	−	0.594442i	$-0.202627\pi$
$44$	−0.959471	+	1.22330i	−0.144646	+	0.184420i
$45$	1.63984	+	1.24910i	0.244453	+	0.186205i
$46$	1.60665	+	4.76069i	0.236888	+	0.701926i
$47$	4.50069	−	0.255035i	0.656494	−	0.0372007i	0.274817	−	0.961497i	$-0.411383\pi$
$47$	4.50069	−	0.255035i	0.656494	−	0.0372007i	0.381677	+	0.924296i	$0.375347\pi$
$48$	1.17493	+	0.746564i	0.169586	+	0.107757i
$49$	2.75952	−	5.47318i	0.394217	−	0.781883i
$50$	1.23320	−	0.0349120i	0.174400	−	0.00493731i
$51$	5.23844	−	5.31310i	0.733528	−	0.743983i
$52$	2.62934	+	3.55510i	0.364623	+	0.493003i
$53$	1.31868	+	0.786429i	0.181135	+	0.108024i	0.599917	−	0.800063i	$-0.295200\pi$
$53$	1.31868	+	0.786429i	0.181135	+	0.108024i	−0.418782	+	0.908087i	$0.637543\pi$
$54$	−5.57344	−	0.955663i	−0.758449	−	0.130049i
$55$	1.20375	+	2.76665i	0.162314	+	0.373055i
$56$	0.616416	−	0.700384i	0.0823720	−	0.0935928i
$57$	−3.74319	+	6.92913i	−0.495797	+	0.917786i
$58$	0.115619	+	0.00327321i	0.0151816	+	0.000429793i
$59$	−2.65452	+	2.54415i	−0.345589	+	0.331221i	−0.844623	−	0.535362i	$-0.820175\pi$
$59$	−2.65452	+	2.54415i	−0.345589	+	0.331221i	0.499033	+	0.866583i	$0.333689\pi$
$60$	2.35849	−	1.31753i	0.304480	−	0.170093i
$61$	−5.06743	+	7.27349i	−0.648818	+	0.931275i	−0.999987	−	0.00503671i	$-0.998397\pi$
$61$	−5.06743	+	7.27349i	−0.648818	+	0.931275i	0.351169	+	0.936312i	$0.385784\pi$
$62$	2.03811	−	7.39658i	0.258840	−	0.939367i
$63$	−0.316897	+	0.939002i	−0.0399253	+	0.118303i
$64$	−0.828510	+	0.559975i	−0.103564	+	0.0699968i
$65$	8.49555	−	1.21032i	1.05374	−	0.150122i
$66$	−1.68383	−	1.35960i	−0.207265	−	0.167355i
$67$	−7.33888	+	1.47329i	−0.896587	+	0.179992i	−0.623339	−	0.781952i	$-0.714224\pi$
$67$	−7.33888	+	1.47329i	−0.896587	+	0.179992i	−0.273248	+	0.961944i	$0.588098\pi$
$68$	1.99847	+	4.97339i	0.242350	+	0.603112i
$69$	−6.65812	+	2.14254i	−0.801543	+	0.257931i
$70$	−0.627312	−	1.69855i	−0.0749781	−	0.203016i
$71$	−2.41187	−	9.83137i	−0.286236	−	1.16677i	−0.919581	−	0.392900i	$-0.871472\pi$
$71$	−2.41187	−	9.83137i	−0.286236	−	1.16677i	0.633345	−	0.773869i	$-0.281681\pi$
$72$	0.582287	−	0.888364i	0.0686232	−	0.104695i
$73$	1.92227	−	4.41807i	0.224985	−	0.517096i	−0.767269	−	0.641326i	$-0.778385\pi$
$73$	1.92227	−	4.41807i	0.224985	−	0.517096i	0.992253	+	0.124230i	$0.0396461\pi$
$74$	3.67156	+	7.82545i	0.426810	+	0.909690i
$75$	0.0243021	+	1.71719i	0.00280617	+	0.198284i
$76$	−3.49152	−	4.45160i	−0.400504	−	0.510633i
$77$	−1.07521	+	0.973646i	−0.122531	+	0.110957i
$78$	−5.00018	+	3.58977i	−0.566159	+	0.406462i
$79$	−7.44358	+	4.72975i	−0.837468	+	0.532139i	−0.884384	−	0.466760i	$-0.845421\pi$
$79$	−7.44358	+	4.72975i	−0.837468	+	0.532139i	0.0469158	+	0.998899i	$0.485061\pi$
$80$	0.191930	+	1.93118i	0.0214584	+	0.215913i
$81$	0.857065	−	4.60612i	0.0952295	−	0.511791i
$82$	−3.88534	+	9.66905i	−0.429064	+	1.06777i
$83$	−1.03562	+	14.6119i	−0.113674	+	1.60386i	0.536382	+	0.843976i	$0.319791\pi$
$83$	−1.03562	+	14.6119i	−0.113674	+	1.60386i	−0.650055	+	0.759887i	$0.725254\pi$
$84$	0.962731	+	0.871794i	0.105043	+	0.0951205i
$85$	10.3353	+	1.17509i	1.12103	+	0.127457i
$86$	−2.43586	+	6.59550i	−0.262666	+	0.711212i
$87$	−0.00683357	+	0.160868i	−0.000732636	+	0.0172468i
$88$	1.37818	−	0.719500i	0.146914	−	0.0766990i
$89$	7.03153	+	1.61986i	0.745341	+	0.171705i	0.580097	−	0.814547i	$-0.303015\pi$
$89$	7.03153	+	1.61986i	0.745341	+	0.171705i	0.165244	+	0.986253i	$0.447159\pi$
$90$	−0.979763	−	1.81367i	−0.103276	−	0.191178i
$91$	1.85734	+	3.68382i	0.194702	+	0.386169i
$92$	0.496909	−	4.99986i	0.0518063	−	0.521271i
$93$	10.2552	+	2.98257i	1.06342	+	0.309278i
$94$	−4.20621	−	1.62145i	−0.433837	−	0.167239i
$95$	−10.8216	+	1.85555i	−1.11027	+	0.190375i
$96$	−0.763115	−	1.16424i	−0.0778851	−	0.118825i
$97$	−11.0170	+	11.8255i	−1.11861	+	1.20070i	−0.141060	+	0.990001i	$0.545051\pi$
$97$	−11.0170	+	11.8255i	−1.11861	+	1.20070i	−0.977551	+	0.210698i	$0.932426\pi$
$98$	−4.76897	+	3.85067i	−0.481738	+	0.388976i
$99$	−1.05550	+	1.27002i	−0.106082	+	0.127642i
$100$	−1.13810	−	0.476142i	−0.113810	−	0.0476142i
$101$	13.4428	−	8.01697i	1.33761	−	0.797719i	0.347457	−	0.937696i	$-0.387045\pi$
$101$	13.4428	−	8.01697i	1.33761	−	0.797719i	0.990155	+	0.139977i	$0.0447030\pi$
$102$	−6.96189	+	2.68373i	−0.689329	+	0.265729i
$103$	−6.93617	+	0.590355i	−0.683441	+	0.0581694i	−0.421383	−	0.906883i	$-0.638455\pi$
$103$	−6.93617	+	0.590355i	−0.683441	+	0.0581694i	−0.262058	+	0.965052i	$0.584401\pi$
$104$	−0.931577	−	4.32253i	−0.0913486	−	0.423859i
$105$	2.37659	−	0.839704i	0.231932	−	0.0819467i
$106$	−0.877689	−	1.25978i	−0.0852487	−	0.122361i
$107$	−1.85380	−	0.901996i	−0.179214	−	0.0871992i	0.345738	−	0.938331i	$-0.387629\pi$
$107$	−1.85380	−	0.901996i	−0.179214	−	0.0871992i	−0.524952	+	0.851132i	$0.675917\pi$
$108$	4.68504	+	3.16654i	0.450818	+	0.304700i
$109$	−10.2882	+	7.83673i	−0.985430	+	0.750623i	−0.968444	−	0.249233i	$-0.919822\pi$
$109$	−10.2882	+	7.83673i	−0.985430	+	0.750623i	−0.0169864	+	0.999856i	$0.505407\pi$
$110$	0.0426956	−	3.01688i	0.00407087	−	0.287648i
$111$	−10.9647	+	4.95634i	−1.04072	+	0.470435i
$112$	−0.850185	+	0.384308i	−0.0803349	+	0.0363137i
$113$	−0.0758372	+	5.35866i	−0.00713416	+	0.504100i	0.964044	+	0.265744i	$0.0856176\pi$
$113$	−0.0758372	+	5.35866i	−0.00713416	+	0.504100i	−0.971178	+	0.238356i	$0.923391\pi$
$114$	6.26502	−	4.77220i	0.586773	−	0.446957i
$115$	−8.07881	−	5.46033i	−0.753353	−	0.509178i
$116$	−0.104007	−	0.0506064i	−0.00965685	−	0.00469869i
$117$	2.68488	+	3.85371i	0.248217	+	0.356276i
$118$	3.46682	−	1.22490i	0.319146	−	0.112762i
$119$	1.05357	+	4.88859i	0.0965807	+	0.448136i
$120$	−2.69182	+	0.229108i	−0.245729	+	0.0209146i
$121$	8.00851	−	3.08719i	0.728047	−	0.280654i
$122$	7.61355	−	4.54053i	0.689298	−	0.411080i
$123$	−13.3819	−	5.59853i	−1.20661	−	0.504802i
$124$	−4.90384	+	5.90047i	−0.440378	+	0.529878i
$125$	−9.41245	+	7.60002i	−0.841875	+	0.679767i
$126$	0.675542	−	0.725115i	0.0601820	−	0.0645984i
$127$	3.40182	+	5.18997i	0.301862	+	0.460535i	0.954958	−	0.296740i	$-0.0958995\pi$
$127$	3.40182	+	5.18997i	0.301862	+	0.460535i	−0.653096	+	0.757275i	$0.726530\pi$
$128$	0.985616	−	0.169001i	0.0871170	−	0.0149377i
$129$	−9.13238	−	3.52043i	−0.804062	−	0.309957i
$130$	−8.23992	−	2.39645i	−0.722689	−	0.210182i
$131$	−0.140490	+	1.41360i	−0.0122747	+	0.123507i	−0.999317	−	0.0369533i	$-0.988235\pi$
$131$	−0.140490	+	1.41360i	−0.0122747	+	0.123507i	0.987042	+	0.160460i	$0.0512978\pi$
$132$	0.974333	+	1.93247i	0.0848048	+	0.168200i
$133$	−2.50884	−	4.64418i	−0.217544	−	0.402702i
$134$	7.29425	+	1.68039i	0.630127	+	0.145163i
$135$	9.72827	−	5.07881i	0.837276	−	0.437114i
$136$	0.227480	−	5.35506i	0.0195063	−	0.459193i
$137$	−7.71832	+	20.8986i	−0.659421	+	1.78549i	−0.0416518	+	0.999132i	$0.513262\pi$
$137$	−7.71832	+	20.8986i	−0.659421	+	1.78549i	−0.617769	+	0.786360i	$0.711963\pi$
$138$	6.94958	+	0.790144i	0.591587	+	0.0672615i
$139$	−10.4284	−	9.44332i	−0.884522	−	0.800972i	0.0964061	−	0.995342i	$-0.469265\pi$
$139$	−10.4284	−	9.44332i	−0.884522	−	0.800972i	−0.980928	+	0.194370i	$0.937734\pi$
$140$	−0.128011	+	1.80616i	−0.0108189	+	0.152648i
$141$	2.33977	−	5.82274i	0.197044	−	0.490363i
$142$	−1.85179	+	9.95208i	−0.155399	+	0.835160i
$143$	0.679867	+	6.84078i	0.0568534	+	0.572055i
$144$	−0.896515	+	0.569658i	−0.0747096	+	0.0474715i
$145$	−0.182346	+	0.130911i	−0.0151430	+	0.0108716i
$146$	−3.57143	+	3.23408i	−0.295574	+	0.267655i
$147$	−5.26585	−	6.71384i	−0.434320	−	0.553748i
$148$	−0.122319	−	8.64309i	−0.0100546	−	0.710458i
$149$	−3.38093	−	7.20601i	−0.276977	−	0.590339i	0.717349	−	0.696714i	$-0.245355\pi$
$149$	−3.38093	−	7.20601i	−0.276977	−	0.590339i	−0.994326	+	0.106374i	$0.966076\pi$
$150$	0.685168	−	1.57476i	0.0559437	−	0.128579i
$151$	7.87313	−	12.0116i	0.640706	−	0.977491i	−0.358330	−	0.933595i	$-0.616654\pi$
$151$	7.87313	−	12.0116i	0.640706	−	0.977491i	0.999036	−	0.0438958i	$-0.0139770\pi$
$152$	1.34795	+	5.49458i	0.109333	+	0.445670i
$153$	1.97241	+	5.34064i	0.159460	+	0.431765i
$154$	1.38081	−	0.444334i	0.111269	−	0.0358055i
$155$	5.55165	+	13.8158i	0.445919	+	1.10971i
$156$	6.03494	−	1.21153i	0.483182	−	0.0969997i
$157$	2.64880	+	2.13876i	0.211397	+	0.170692i	0.728094	−	0.685477i	$-0.240406\pi$
$157$	2.64880	+	2.13876i	0.211397	+	0.170692i	−0.516697	+	0.856168i	$0.672839\pi$
$158$	8.73099	−	1.24386i	0.694600	−	0.0989566i
$159$	1.77080	−	1.19685i	0.140433	−	0.0949164i
$160$	0.620565	−	1.83881i	0.0490600	−	0.145370i
$161$	1.24533	−	4.51946i	0.0981454	−	0.356184i
$162$	−2.67825	+	3.84420i	−0.210423	+	0.302029i
$163$	−8.75455	+	4.89058i	−0.685709	+	0.383060i	−0.791366	−	0.611343i	$-0.790630\pi$
$163$	−8.75455	+	4.89058i	−0.685709	+	0.383060i	0.105657	+	0.994403i	$0.466305\pi$
$164$	7.52313	−	7.21034i	0.587458	−	0.563033i
$165$	4.19839	+	0.118857i	0.326844	+	0.00925302i
$166$	6.96234	−	12.8882i	0.540382	−	1.00032i
$167$	10.5577	−	11.9959i	0.816979	−	0.928268i	−0.181501	−	0.983391i	$-0.558096\pi$
$167$	10.5577	−	11.9959i	0.816979	−	0.928268i	0.998480	+	0.0551227i	$0.0175550\pi$
$168$	−0.518175	−	1.19095i	−0.0399781	−	0.0918840i
$169$	6.45787	+	1.10731i	0.496759	+	0.0851779i
$170$	−8.93384	−	5.32792i	−0.685194	−	0.408633i
$171$	−3.57336	−	4.83150i	−0.273262	−	0.369474i
$172$	4.93632	−	5.00668i	0.376391	−	0.381756i
$173$	0.603574	−	0.0170873i	0.0458888	−	0.00129912i	−0.00534698	−	0.999986i	$-0.501702\pi$
$173$	0.603574	−	0.0170873i	0.0458888	−	0.00129912i	0.0512358	+	0.998687i	$0.483684\pi$
$174$	0.0724885	−	0.143772i	0.00549534	−	0.0108994i
$175$	−0.971510	−	0.617310i	−0.0734392	−	0.0466643i
$176$	−1.55220	+	0.0879565i	−0.117001	+	0.00662997i
$177$	1.63667	+	4.84964i	0.123020	+	0.364521i
$178$	−5.74011	−	4.37236i	−0.430239	−	0.327723i
$179$	−1.21347	+	1.54714i	−0.0906986	+	0.115639i	−0.830070	−	0.557660i	$-0.811699\pi$
$179$	−1.21347	+	1.54714i	−0.0906986	+	0.115639i	0.739371	+	0.673298i	$0.235123\pi$
$180$	0.145735	+	2.05623i	0.0108625	+	0.153263i
$181$	−12.6223	−	4.06177i	−0.938207	−	0.301909i	−0.202557	−	0.979271i	$-0.564925\pi$
$181$	−12.6223	−	4.06177i	−0.938207	−	0.301909i	−0.735650	+	0.677362i	$0.763123\pi$
$182$	−0.175094	−	4.12184i	−0.0129788	−	0.305531i
$183$	6.17005	+	10.6868i	0.456103	+	0.789994i
$184$	−2.51225	+	4.35134i	−0.185205	+	0.320785i
$185$	−14.8707	−	7.76352i	−1.09332	−	0.570785i
$186$	−8.11635	−	6.94195i	−0.595119	−	0.509009i
$187$	−1.29191	+	8.23220i	−0.0944740	+	0.601998i
$188$	3.16494	+	3.21005i	0.230827	+	0.234117i
$189$	3.80901	+	3.65064i	0.277065	+	0.265545i
$190$	10.6252	+	2.76660i	0.770836	+	0.200710i
$191$	9.66108	−	15.6906i	0.699051	−	1.13533i	−0.285185	−	0.958472i	$-0.592055\pi$
$191$	9.66108	−	15.6906i	0.699051	−	1.13533i	0.984236	−	0.176859i	$-0.0565936\pi$
$192$	0.215819	+	1.37522i	0.0155754	+	0.0992480i
$193$	4.17210	−	5.64106i	0.300315	−	0.406052i	−0.627783	−	0.778388i	$-0.716038\pi$
$193$	4.17210	−	5.64106i	0.300315	−	0.406052i	0.928098	+	0.372336i	$0.121443\pi$
$194$	14.9100	−	6.23781i	1.07047	−	0.447849i
$195$	3.49796	−	11.4220i	0.250494	−	0.817950i
$196$	5.93171	−	1.54450i	0.423694	−	0.110321i
$197$	11.7282	+	6.55174i	0.835597	+	0.466792i	0.846019	−	0.533153i	$-0.178993\pi$
$197$	11.7282	+	6.55174i	0.835597	+	0.466792i	−0.0104219	+	0.999946i	$0.503317\pi$
$198$	1.48493	−	0.722514i	0.105529	−	0.0513468i
$199$	9.00952	+	1.28355i	0.638668	+	0.0909881i	0.452837	−	0.891593i	$-0.350412\pi$
$199$	9.00952	+	1.28355i	0.638668	+	0.0909881i	0.185831	+	0.982582i	$0.440502\pi$
$200$	0.840949	+	0.902661i	0.0594641	+	0.0638277i
$201$	−2.48264	+	10.1199i	−0.175112	+	0.713800i
$202$	−15.5517	+	1.76818i	−1.09421	+	0.124408i
$203$	−0.0876645	−	0.0629369i	−0.00615284	−	0.00441730i
$204$	7.44930	+	0.422121i	0.521555	+	0.0295544i
$205$	−5.37218	−	19.4964i	−0.375210	−	1.36169i
$206$	6.56360	+	2.31907i	0.457308	+	0.161577i
$207$	0.677890	−	5.29374i	0.0471166	−	0.367940i
$208$	−0.931577	+	4.32253i	−0.0645932	+	0.299714i
$209$	−1.11721	−	8.72442i	−0.0772787	−	0.603481i
$210$	−2.51149	−	0.213760i	−0.173310	−	0.0147508i
$211$	−22.9373	+	6.67093i	−1.57907	+	0.459246i	−0.948471	−	0.316865i	$-0.897370\pi$
$211$	−22.9373	+	6.67093i	−1.57907	+	0.459246i	−0.630596	+	0.776111i	$0.717190\pi$
$212$	0.280869	+	1.50947i	0.0192902	+	0.103671i
$213$	−13.8159	−	2.77358i	−0.946653	−	0.190042i
$214$	1.31770	+	1.58551i	0.0900764	+	0.108383i
$215$	−3.99555	−	13.0468i	−0.272494	−	0.889786i
$216$	−2.96484	−	4.81521i	−0.201732	−	0.327634i
$217$	−5.43990	+	4.65278i	−0.369285	+	0.315851i
$218$	12.6029	−	2.90334i	0.853573	−	0.196639i
$219$	−4.43121	−	5.03483i	−0.299433	−	0.340222i
$220$	−1.28156	+	2.73148i	−0.0864028	+	0.184156i
$221$	21.5963	+	9.76216i	1.45273	+	0.656674i
$222$	12.0328			0.807591
$223$	12.3714	−	8.36348i	0.828452	−	0.560060i
$223$	12.3714	−	8.36348i	0.828452	−	0.560060i
$224$	0.933009			0.0623393
$225$	−1.19409	−	0.539761i	−0.0796058	−	0.0359841i
$226$	2.27634	−	4.85173i	0.151420	−	0.322732i
$227$	8.85064	+	10.0563i	0.587438	+	0.667459i	0.966128	−	0.258065i	$-0.0830848\pi$
$227$	8.85064	+	10.0563i	0.587438	+	0.667459i	−0.378690	+	0.925524i	$0.623625\pi$
$228$	−7.67454	+	1.76799i	−0.508259	+	0.117088i
$229$	−10.1675	+	8.69630i	−0.671886	+	0.574667i	−0.918970	−	0.394327i	$-0.870978\pi$
$229$	−10.1675	+	8.69630i	−0.671886	+	0.574667i	0.247085	+	0.968994i	$0.420527\pi$
$230$	5.11253	+	8.30328i	0.337110	+	0.547502i
$231$	0.591275	+	1.93071i	0.0389030	+	0.127032i
$232$	0.0739297	+	0.0889548i	0.00485372	+	0.00584017i
$233$	22.9303	+	4.60330i	1.50221	+	0.301572i	0.877612	−	0.479371i	$-0.159135\pi$
$233$	22.9303	+	4.60330i	1.50221	+	0.301572i	0.624601	+	0.780944i	$0.285261\pi$
$234$	−0.859186	−	4.61752i	−0.0561667	−	0.301856i
$235$	8.40044	−	2.44313i	0.547984	−	0.159372i
$236$	−3.66360	−	0.311818i	−0.238480	−	0.0202977i
$237$	1.55936	+	12.1773i	0.101291	+	0.790999i
$238$	1.05357	−	4.88859i	0.0682929	−	0.316880i
$239$	0.506333	−	3.95403i	0.0327520	−	0.255765i	−0.967246	−	0.253840i	$-0.918306\pi$
$239$	0.506333	−	3.95403i	0.0327520	−	0.255765i	0.999998	−	0.00192472i	$-0.000612659\pi$
$240$	2.54723	+	0.899995i	0.164423	+	0.0580944i
$241$	−1.42786	−	5.18191i	−0.0919767	−	0.333796i	0.903526	−	0.428534i	$-0.140970\pi$
$241$	−1.42786	−	5.18191i	−0.0919767	−	0.333796i	−0.995502	+	0.0947380i	$0.969799\pi$
$242$	−8.56920	−	0.485581i	−0.550849	−	0.0312143i
$243$	8.48263	+	6.08993i	0.544161	+	0.390669i
$244$	−8.80793	+	1.00143i	−0.563870	+	0.0641102i
$245$	2.83420	−	11.5529i	0.181071	−	0.738090i
$246$	9.88796	+	10.6136i	0.630433	+	0.676697i
$247$	−24.7662	−	3.52833i	−1.57583	−	0.224502i
$248$	6.89893	−	3.35678i	0.438083	−	0.213156i
$249$	17.8021	+	9.94484i	1.12816	+	0.630229i
$250$	11.7074	−	3.04836i	0.740438	−	0.192795i
$251$	−2.86111	+	9.34252i	−0.180592	+	0.589694i	0.819275	+	0.573400i	$0.194376\pi$
$251$	−2.86111	+	9.34252i	−0.180592	+	0.589694i	−0.999867	+	0.0162941i	$0.994813\pi$
$252$	−0.914248	+	0.382489i	−0.0575922	+	0.0240945i
$253$	4.64498	−	6.28043i	0.292028	−	0.394847i
$254$	−0.962078	−	6.13046i	−0.0603662	−	0.384659i
$255$	7.59199	−	12.3302i	0.475429	−	0.772145i
$256$	−0.967733	−	0.251978i	−0.0604833	−	0.0157486i
$257$	−0.222580	−	0.213326i	−0.0138842	−	0.0133069i	0.684965	−	0.728576i	$-0.259818\pi$
$257$	−0.222580	−	0.213326i	−0.0138842	−	0.0133069i	−0.698849	+	0.715269i	$0.746304\pi$
$258$	6.87162	+	6.96956i	0.427808	+	0.433906i
$259$	1.25035	−	7.96738i	0.0776932	−	0.495069i
$260$	6.52135	+	5.57775i	0.404437	+	0.345917i
$261$	−0.108910	−	0.0568585i	−0.00674138	−	0.00351945i
$262$	0.710281	−	1.23024i	0.0438813	−	0.0760047i
$263$	−6.84082	−	11.8486i	−0.421823	−	0.730619i	0.574295	−	0.818648i	$-0.305276\pi$
$263$	−6.84082	−	11.8486i	−0.421823	−	0.730619i	−0.996118	+	0.0880299i	$0.971943\pi$
$264$	−0.0918515	−	2.16226i	−0.00565307	−	0.133078i
$265$	2.83647	+	0.912757i	0.174243	+	0.0560702i
$266$	0.373178	+	5.26530i	0.0228810	+	0.322836i
$267$	6.19902	−	7.90360i	0.379374	−	0.483693i
$268$	−5.95457	−	4.53573i	−0.363733	−	0.277064i
$269$	−8.83513	−	26.1795i	−0.538687	−	1.59619i	−0.780023	−	0.625751i	$-0.784793\pi$
$269$	−8.83513	−	26.1795i	−0.538687	−	1.59619i	0.241336	−	0.970442i	$-0.422415\pi$
$270$	−10.9566	+	0.620867i	−0.666800	+	0.0377848i
$271$	−2.44707	−	1.55490i	−0.148649	−	0.0944534i	0.459897	−	0.887972i	$-0.347886\pi$
$271$	−2.44707	−	1.55490i	−0.148649	−	0.0944534i	−0.608546	+	0.793519i	$0.708247\pi$
$272$	−2.41304	+	4.78599i	−0.146312	+	0.290193i
$273$	5.74069	−	0.162520i	0.347443	−	0.00983617i
$274$	15.6413	−	15.8643i	0.944927	−	0.958395i
$275$	−1.14051	−	1.54207i	−0.0687752	−	0.0929902i
$276$	−6.00719	−	3.58254i	−0.361591	−	0.215644i
$277$	28.0611	+	4.81156i	1.68603	+	0.289098i	0.930574	−	0.366104i	$-0.119309\pi$
$277$	28.0611	+	4.81156i	1.68603	+	0.289098i	0.755453	+	0.655203i	$0.227417\pi$
$278$	5.61291	+	12.9005i	0.336640	+	0.773719i
$279$	−5.38409	+	6.11752i	−0.322337	+	0.366246i
$280$	0.860607	−	1.59310i	0.0514311	−	0.0952057i
$281$	−10.8113	−	0.306071i	−0.644951	−	0.0182587i	−0.295689	−	0.955284i	$-0.595549\pi$
$281$	−10.8113	−	0.306071i	−0.644951	−	0.0182587i	−0.349261	+	0.937025i	$0.613567\pi$
$282$	−4.53046	+	4.34209i	−0.269785	+	0.258568i
$283$	10.4187	−	5.82024i	0.619328	−	0.345977i	−0.146320	−	0.989237i	$-0.546743\pi$
$283$	10.4187	−	5.82024i	0.619328	−	0.345977i	0.765648	+	0.643260i	$0.222419\pi$
$284$	5.78668	−	8.30586i	0.343376	−	0.492862i
$285$	−4.06017	+	14.7349i	−0.240504	+	0.872821i
$286$	2.19821	−	6.51355i	0.129983	−	0.385154i
$287$	8.05511	−	5.44430i	0.475478	−	0.321367i
$288$	1.05157	−	0.149813i	0.0619645	−	0.00882780i
$289$	9.12515	+	7.36804i	0.536774	+	0.433414i
$290$	0.220081	−	0.0441817i	0.0129236	−	0.00259444i
$291$	8.38878	+	20.8763i	0.491759	+	1.22379i
$292$	4.58651	−	1.47591i	0.268405	−	0.0863711i
$293$	−4.89757	−	13.2610i	−0.286119	−	0.774716i	−0.997417	−	0.0718251i	$-0.977118\pi$
$293$	−4.89757	−	13.2610i	−0.286119	−	0.774716i	0.711298	−	0.702890i	$-0.248108\pi$
$294$	2.03296	+	8.28685i	0.118565	+	0.483299i
$295$	−3.91173	+	5.96791i	−0.227750	+	0.347465i
$296$	−3.44864	+	7.92621i	−0.200448	+	0.460702i
$297$	3.73419	+	7.95894i	0.216680	+	0.461825i
$298$	0.112637	+	7.95893i	0.00652488	+	0.461049i
$299$	−13.7113	−	17.4815i	−0.792943	−	1.01098i
$300$	−1.27299	+	1.15275i	−0.0734961	+	0.0665538i
$301$	5.32884	−	3.82573i	0.307149	−	0.220511i
$302$	−12.1218	+	7.70237i	−0.697532	+	0.443221i
$303$	−2.15480	−	21.6814i	−0.123790	−	1.24557i
$304$	1.03494	−	5.56204i	0.0593576	−	0.319005i
$305$	−6.41450	+	15.9631i	−0.367293	+	0.914044i
$306$	0.402497	−	5.67898i	0.0230092	−	0.324646i
$307$	−8.66143	−	7.84329i	−0.494334	−	0.447640i	0.385649	−	0.922646i	$-0.373978\pi$
$307$	−8.66143	−	7.84329i	−0.494334	−	0.447640i	−0.879983	+	0.475005i	$0.842446\pi$
$308$	−1.44125	−	0.163866i	−0.0821229	−	0.00933711i
$309$	−3.35723	+	9.09028i	−0.190986	+	0.517128i
$310$	0.631928	−	14.8761i	0.0358911	−	0.844905i
$311$	−11.2795	+	5.88865i	−0.639601	+	0.333915i	−0.751430	−	0.659813i	$-0.770635\pi$
$311$	−11.2795	+	5.88865i	−0.639601	+	0.333915i	0.111829	+	0.993727i	$0.464329\pi$
$312$	−5.99824	−	1.38182i	−0.339583	−	0.0782303i
$313$	14.1720	+	26.2343i	0.801051	+	1.48285i	0.874220	+	0.485530i	$0.161374\pi$
$313$	14.1720	+	26.2343i	0.801051	+	1.48285i	−0.0731687	+	0.997320i	$0.523311\pi$
$314$	−1.53271	−	3.03994i	−0.0864957	−	0.171554i
$315$	−0.190209	+	1.91387i	−0.0107171	+	0.107834i
$316$	−8.46828	−	2.46286i	−0.476378	−	0.138547i
$317$	−24.1403	−	9.30582i	−1.35586	−	0.522667i	−0.430782	−	0.902456i	$-0.641762\pi$
$317$	−24.1403	−	9.30582i	−1.35586	−	0.522667i	−0.925073	+	0.379789i	$0.875997\pi$
$318$	−2.10659	+	0.361210i	−0.118131	+	0.0202557i
$319$	−0.0985785	−	0.150396i	−0.00551934	−	0.00842055i
$320$	−1.32288	+	1.41996i	−0.0739514	+	0.0793782i
$321$	−2.23285	+	1.80290i	−0.124625	+	0.100628i
$322$	−2.99635	+	3.60531i	−0.166980	+	0.200916i
$323$	−27.9742	−	11.7034i	−1.55652	−	0.651195i
$324$	4.02393	−	2.39977i	0.223552	−	0.133321i
$325$	−5.09001	+	1.96214i	−0.282343	+	0.108840i
$326$	9.99183	−	0.850430i	0.553396	−	0.0471010i
$327$	3.79293	+	17.5993i	0.209750	+	0.973242i
$328$	−9.82524	+	3.47148i	−0.542508	+	0.191680i
$329$	2.40429	+	3.45097i	0.132553	+	0.190258i
$330$	−3.77673	−	1.83763i	−0.207902	−	0.101158i
$331$	−3.87738	−	2.62065i	−0.213120	−	0.144044i	0.448764	−	0.893650i	$-0.351864\pi$
$331$	−3.87738	−	2.62065i	−0.213120	−	0.144044i	−0.661884	+	0.749606i	$0.730243\pi$
$332$	−11.6529	+	8.87629i	−0.639538	+	0.487150i
$333$	0.129926	−	9.18061i	0.00711992	−	0.503094i
$334$	−14.5616	+	6.58225i	−0.796774	+	0.360165i
$335$	−13.2372	+	5.98357i	−0.723223	+	0.326917i
$336$	−0.0183791	+	1.29867i	−0.00100266	+	0.0708481i
$337$	−20.1341	+	15.3366i	−1.09677	+	0.835437i	−0.987350	−	0.158558i	$-0.949315\pi$
$337$	−20.1341	+	15.3366i	−1.09677	+	0.835437i	−0.109425	+	0.993995i	$0.534901\pi$
$338$	−5.42849	−	3.66902i	−0.295271	−	0.199568i
$339$	6.70834	+	3.26404i	0.364347	+	0.177279i
$340$	5.94619	+	8.53481i	0.322477	+	0.462865i
$341$	−11.2466	+	3.97367i	−0.609036	+	0.215186i
$342$	1.26605	+	5.87448i	0.0684600	+	0.317655i
$343$	12.2058	−	1.03887i	0.659052	−	0.0560936i
$344$	−6.56037	+	2.52895i	−0.353712	+	0.136352i
$345$	−11.6581	+	6.95263i	−0.627654	+	0.374317i
$346$	−0.557032	−	0.233042i	−0.0299462	−	0.0125284i
$347$	−10.7207	+	12.8995i	−0.575515	+	0.692480i	−0.974477	−	0.224488i	$-0.927929\pi$
$347$	−10.7207	+	12.8995i	−0.575515	+	0.692480i	0.398962	+	0.916968i	$0.369371\pi$
$348$	−0.125274	+	0.101151i	−0.00671537	+	0.00542228i
$349$	3.35129	−	3.59722i	0.179391	−	0.192555i	−0.635618	−	0.772004i	$-0.719255\pi$
$349$	3.35129	−	3.59722i	0.179391	−	0.192555i	0.815009	+	0.579449i	$0.196732\pi$
$350$	0.630996	+	0.962677i	0.0337282	+	0.0514572i
$351$	24.6445	−	4.22573i	1.31543	−	0.225553i
$352$	1.45064	+	0.559203i	0.0773191	+	0.0298056i
$353$	−14.3972	−	4.18720i	−0.766286	−	0.222862i	−0.127075	−	0.991893i	$-0.540559\pi$
$353$	−14.3972	−	4.18720i	−0.766286	−	0.222862i	−0.639211	+	0.769031i	$0.720739\pi$
$354$	0.506192	−	5.09327i	0.0269038	−	0.270704i
$355$	−8.84447	−	17.5420i	−0.469416	−	0.931031i
$356$	3.42957	+	6.34858i	0.181767	+	0.336474i
$357$	6.78373	+	1.56278i	0.359033	+	0.0827110i
$358$	1.74301	−	0.909969i	0.0921211	−	0.0480933i
$359$	0.0567968	−	1.33704i	0.00299762	−	0.0705664i	−0.996977	−	0.0776979i	$-0.975243\pi$
$359$	0.0567968	−	1.33704i	0.00299762	−	0.0705664i	0.999975	+	0.00713154i	$0.00227006\pi$
$360$	0.714167	−	1.93373i	0.0376399	−	0.101916i
$361$	12.9242	+	1.46943i	0.680219	+	0.0773387i
$362$	9.82874	+	8.90033i	0.516587	+	0.467791i
$363$	0.844688	−	11.9180i	0.0443346	−	0.625534i
$364$	−1.53824	+	3.82806i	−0.0806258	+	0.200645i
$365$	1.71051	−	9.19276i	0.0895320	−	0.481171i
$366$	−1.22040	−	12.2796i	−0.0637914	−	0.641865i
$367$	−24.6993	+	15.6943i	−1.28930	+	0.819236i	−0.990821	−	0.135182i	$-0.956838\pi$
$367$	−24.6993	+	15.6943i	−1.28930	+	0.819236i	−0.298475	+	0.954418i	$0.596478\pi$
$368$	4.08155	−	2.93026i	0.212766	−	0.152751i
$369$	8.20453	−	7.42955i	0.427111	−	0.386767i
$370$	10.3528	+	13.1996i	0.538218	+	0.686215i
$371$	0.0202714	+	1.43238i	0.00105244	+	0.0743655i
$372$	4.53645	+	9.66884i	0.235204	+	0.501306i
$373$	11.2150	−	25.7761i	0.580691	−	1.33464i	−0.338552	−	0.940948i	$-0.609937\pi$
$373$	11.2150	−	25.7761i	0.580691	−	1.33464i	0.919243	−	0.393689i	$-0.128801\pi$
$374$	4.56808	−	6.96927i	0.236210	−	0.360373i
$375$	4.01243	+	16.3557i	0.207201	+	0.844603i
$376$	−1.56176	−	4.22873i	−0.0805417	−	0.218080i
$377$	−0.486861	+	0.156669i	−0.0250746	+	0.00806885i
$378$	−1.96718	−	4.89551i	−0.101181	−	0.251798i
$379$	7.77457	−	1.56076i	0.399353	−	0.0801708i	0.00697653	−	0.999976i	$-0.497779\pi$
$379$	7.77457	−	1.56076i	0.399353	−	0.0801708i	0.392376	+	0.919805i	$0.371653\pi$
$380$	−8.54246	−	6.89756i	−0.438219	−	0.353837i
$381$	8.55202	−	1.21837i	0.438133	−	0.0624188i
$382$	−15.2664	+	10.3183i	−0.781098	+	0.527930i
$383$	2.46561	−	7.30588i	0.125987	−	0.373313i	−0.865936	−	0.500154i	$-0.833277\pi$
$383$	2.46561	−	7.30588i	0.125987	−	0.373313i	0.991923	+	0.126841i	$0.0404839\pi$
$384$	0.369795	−	1.34204i	0.0188710	−	0.0684855i
$385$	−1.60921	+	2.30976i	−0.0820127	+	0.117716i
$386$	−6.12530	+	3.42180i	−0.311770	+	0.174165i
$387$	5.39171	−	5.16754i	0.274076	−	0.262681i
$388$	−16.1558	−	0.457373i	−0.820185	−	0.0232196i
$389$	−10.2641	+	19.0002i	−0.520410	+	0.963347i	0.476061	+	0.879412i	$0.342064\pi$
$389$	−10.2641	+	19.0002i	−0.520410	+	0.963347i	−0.996471	+	0.0839346i	$0.973251\pi$
$390$	−7.89220	+	8.96728i	−0.399637	+	0.454076i
$391$	−10.7444	−	24.6946i	−0.543369	−	1.24886i
$392$	−6.04133	−	1.03589i	−0.305133	−	0.0523203i
$393$	1.69840	+	1.01288i	0.0856730	+	0.0510932i
$394$	−7.98836	−	10.8010i	−0.402448	−	0.544145i
$395$	−12.0164	+	12.1877i	−0.604612	+	0.613229i
$396$	−1.65071	+	0.0467320i	−0.0829514	+	0.00234837i
$397$	−4.71287	+	9.34742i	−0.236532	+	0.469133i	−0.979831	−	0.199826i	$-0.935962\pi$
$397$	−4.71287	+	9.34742i	−0.236532	+	0.469133i	0.743299	+	0.668959i	$0.233260\pi$
$398$	−7.68104	−	4.88064i	−0.385016	−	0.244644i
$399$	−7.33619	+	0.415711i	−0.367269	+	0.0208116i
$400$	−0.394490	−	1.16892i	−0.0197245	−	0.0584459i
$401$	0.461125	+	0.351249i	0.0230275	+	0.0175405i	0.617401	−	0.786648i	$-0.288186\pi$
$401$	0.461125	+	0.351249i	0.0230275	+	0.0175405i	−0.594374	+	0.804189i	$0.702600\pi$
$402$	6.43063	−	8.19890i	0.320731	−	0.408924i
$403$	2.39841	+	33.8401i	0.119473	+	1.68569i
$404$	14.8995	+	4.79455i	0.741276	+	0.238538i
$405$	−0.385897	−	9.08433i	−0.0191754	−	0.451404i
$406$	0.0539586	+	0.0934590i	0.00267792	+	0.00463829i
$407$	6.71932	−	11.6382i	0.333064	−	0.576885i
$408$	−6.61414	−	3.45302i	−0.327449	−	0.170950i
$409$	15.3923	+	13.1651i	0.761100	+	0.650972i	0.943169	−	0.332313i	$-0.107829\pi$
$409$	15.3923	+	13.1651i	0.761100	+	0.650972i	−0.182069	+	0.983286i	$0.558280\pi$
$410$	−3.13531	+	19.9785i	−0.154842	+	0.986667i
$411$	21.7735	+	22.0839i	1.07401	+	1.08932i
$412$	−5.02571	−	4.81676i	−0.247599	−	0.237304i
$413$	−3.31984	−	0.864419i	−0.163359	−	0.0425353i
$414$	−2.79821	+	4.54458i	−0.137525	+	0.223354i
$415$	4.40744	+	28.0847i	0.216353	+	1.37862i
$416$	2.62934	−	3.55510i	0.128914	−	0.174303i
$417$	−18.0669	+	7.55855i	−0.884740	+	0.370144i
$418$	−2.57557	+	8.41012i	−0.125975	+	0.411352i
$419$	−22.3434	+	5.81777i	−1.09155	+	0.284217i	−0.753856	−	0.657040i	$-0.771808\pi$
$419$	−22.3434	+	5.81777i	−1.09155	+	0.284217i	−0.337692	+	0.941257i	$0.609646\pi$
$420$	2.20050	+	1.22927i	0.107373	+	0.0599823i
$421$	−9.79146	+	4.76419i	−0.477207	+	0.232192i	−0.660442	−	0.750877i	$-0.729631\pi$
$421$	−9.79146	+	4.76419i	−0.477207	+	0.232192i	0.183236	+	0.983069i	$0.441343\pi$
$422$	23.6489	+	3.36915i	1.15121	+	0.164007i
$423$	3.26394	+	3.50345i	0.158698	+	0.170344i
$424$	0.365818	−	1.49116i	0.0177657	−	0.0724173i
$425$	−6.57012	+	0.747001i	−0.318697	+	0.0362349i
$426$	11.4470	+	8.21817i	0.554611	+	0.398172i
$427$	−8.25758	−	0.467923i	−0.399612	−	0.0226444i
$428$	−0.547657	−	1.98752i	−0.0264720	−	0.0960706i
$429$	9.02299	+	3.18803i	0.435634	+	0.153919i
$430$	−1.73315	+	13.5344i	−0.0835799	+	0.652687i
$431$	1.83742	−	8.52566i	0.0885054	−	0.410666i	−0.911494	−	0.411312i	$-0.865071\pi$
$431$	1.83742	−	8.52566i	0.0885054	−	0.410666i	1.00000		0.000646040i	$0.000205641\pi$
$432$	0.718258	+	5.60898i	0.0345572	+	0.269862i
$433$	4.32396	+	0.368023i	0.207796	+	0.0176861i	0.188242	−	0.982123i	$-0.439721\pi$
$433$	4.32396	+	0.368023i	0.207796	+	0.0176861i	0.0195545	+	0.999809i	$0.493775\pi$
$434$	6.87348	−	1.99904i	0.329938	−	0.0959570i
$435$	0.0571618	+	0.307204i	0.00274070	+	0.0147293i
$436$	−12.6800	−	2.54553i	−0.607260	−	0.121909i
$437$	18.1690	+	21.8616i	0.869143	+	1.04578i
$438$	1.96399	+	6.41310i	0.0938431	+	0.306430i
$439$	15.1102	+	24.5405i	0.721169	+	1.17125i	0.978762	+	0.205000i	$0.0657193\pi$
$439$	15.1102	+	24.5405i	0.721169	+	1.17125i	−0.257593	+	0.966254i	$0.582929\pi$
$440$	2.29289	−	1.96112i	0.109309	−	0.0934929i
$441$	6.34451	−	1.46159i	0.302120	−	0.0695997i
$442$	−15.6582	−	17.7911i	−0.744783	−	0.846237i
$443$	10.3176	−	21.9906i	0.490204	−	1.04480i	−0.494276	−	0.869305i	$-0.664567\pi$
$443$	10.3176	−	21.9906i	0.490204	−	1.04480i	0.984480	−	0.175500i	$-0.0561541\pi$
$444$	−10.9647	−	4.95634i	−0.520360	−	0.235218i
$445$	14.0035			0.663830
$446$	−14.7181	+	2.52523i	−0.696923	+	0.119573i
$447$	−11.0804			−0.524083
$448$	−0.850185	−	0.384308i	−0.0401675	−	0.0181568i
$449$	2.69025	−	5.73391i	0.126961	−	0.270600i	−0.831661	−	0.555284i	$-0.812609\pi$
$449$	2.69025	−	5.73391i	0.126961	−	0.270600i	0.958621	+	0.284684i	$0.0918888\pi$
$450$	0.865758	+	0.983692i	0.0408122	+	0.0463717i
$451$	15.7871	−	3.63689i	0.743385	−	0.171255i
$452$	−4.07270	+	3.48340i	−0.191564	+	0.163845i
$453$	−10.4822	−	17.0242i	−0.492499	−	0.799869i
$454$	−3.92276	−	12.8092i	−0.184104	−	0.601164i
$455$	5.11747	+	6.15752i	0.239911	+	0.288669i
$456$	7.72149	+	1.55010i	0.361592	+	0.0725903i
$457$	2.74115	+	14.7318i	0.128226	+	0.689123i	0.984881	+	0.173233i	$0.0554214\pi$
$457$	2.74115	+	14.7318i	0.128226	+	0.689123i	−0.856655	+	0.515890i	$0.827461\pi$
$458$	12.8469	−	3.73632i	0.600297	−	0.174587i
$459$	30.1998	+	2.57038i	1.40961	+	0.119975i
$460$	−1.23855	−	9.67204i	−0.0577479	−	0.450961i
$461$	6.63394	−	30.7816i	0.308974	−	1.43364i	−0.510180	−	0.860068i	$-0.670421\pi$
$461$	6.63394	−	30.7816i	0.308974	−	1.43364i	0.819153	−	0.573574i	$-0.194444\pi$
$462$	0.256477	−	2.00287i	0.0119324	−	0.0931819i
$463$	2.99368	+	1.05773i	0.139128	+	0.0491570i	0.401796	−	0.915729i	$-0.368386\pi$
$463$	2.99368	+	1.05773i	0.139128	+	0.0491570i	−0.262668	+	0.964886i	$0.584602\pi$
$464$	−0.0307263	−	0.111510i	−0.00142643	−	0.00517672i
$465$	20.6938	+	1.17263i	0.959651	+	0.0543794i
$466$	−18.9986	−	13.6397i	−0.880095	−	0.631846i
$467$	31.6584	−	3.59945i	1.46497	−	0.166563i	0.656158	−	0.754624i	$-0.272181\pi$
$467$	31.6584	−	3.59945i	1.46497	−	0.166563i	0.808817	+	0.588061i	$0.200108\pi$
$468$	−1.11905	+	4.56151i	−0.0517279	+	0.210856i
$469$	−4.76057	−	5.10992i	−0.219823	−	0.235954i
$470$	−8.66105	−	1.23390i	−0.399504	−	0.0569156i
$471$	4.26153	−	2.07351i	0.196361	−	0.0955424i
$472$	3.20994	+	1.79318i	0.147749	+	0.0825378i
$473$	10.5782	−	2.75435i	0.486386	−	0.126645i
$474$	3.59490	−	11.7386i	0.165119	−	0.539171i
$475$	6.43883	−	2.69378i	0.295434	−	0.123599i
$476$	−2.97366	+	4.02065i	−0.136297	+	0.184286i
$477$	0.252844	+	1.61115i	0.0115769	+	0.0737694i
$478$	−2.09006	+	3.39447i	−0.0955969	+	0.155259i
$479$	−20.3063	−	5.28735i	−0.927820	−	0.241585i	−0.242772	−	0.970083i	$-0.578057\pi$
$479$	−20.3063	−	5.28735i	−0.927820	−	0.241585i	−0.685048	+	0.728498i	$0.740219\pi$
$480$	−1.95040	−	1.86931i	−0.0890233	−	0.0853219i
$481$	−26.8349	−	27.2173i	−1.22357	−	1.24100i
$482$	−0.833327	+	5.31004i	−0.0379570	+	0.241866i
$483$	−4.95926	−	4.24168i	−0.225654	−	0.193003i
$484$	7.60849	+	3.97214i	0.345840	+	0.180552i
$485$	−15.6830	+	27.1638i	−0.712129	+	1.23344i
$486$	−5.22117	−	9.04332i	−0.236837	−	0.410214i
$487$	0.705650	+	16.6116i	0.0319761	+	0.752742i	0.941485	+	0.337056i	$0.109431\pi$
$487$	0.705650	+	16.6116i	0.0319761	+	0.752742i	−0.909508	+	0.415685i	$0.863542\pi$
$488$	8.43853	+	2.71546i	0.381994	+	0.122923i
$489$	0.986898	+	13.9245i	0.0446291	+	0.629688i
$490$	−7.34127	+	9.35994i	−0.331645	+	0.422839i
$491$	−9.42716	−	7.18087i	−0.425442	−	0.324068i	0.371164	−	0.928567i	$-0.378959\pi$
$491$	−9.42716	−	7.18087i	−0.425442	−	0.324068i	−0.796606	+	0.604499i	$0.793373\pi$
$492$	−4.63845	−	13.7443i	−0.209117	−	0.619639i
$493$	−0.618963	+	0.0350740i	−0.0278767	+	0.00157965i
$494$	21.1143	+	13.4163i	0.949979	+	0.603629i
$495$	−1.44282	+	2.86167i	−0.0648500	+	0.128622i
$496$	−7.66917	+	0.217116i	−0.344356	+	0.00974878i
$497$	6.63103	−	6.72554i	0.297442	−	0.301682i
$498$	−12.1255	−	16.3947i	−0.543356	−	0.734665i
$499$	3.86850	+	2.30708i	0.173178	+	0.103279i	0.596184	−	0.802848i	$-0.296683\pi$
$499$	3.86850	+	2.30708i	0.173178	+	0.103279i	−0.423006	+	0.906127i	$0.639025\pi$
$500$	−11.9237	−	2.04452i	−0.533244	−	0.0914339i
$501$	−8.87507	−	20.3981i	−0.396509	−	0.911320i
$502$	6.45532	−	7.33467i	0.288115	−	0.327362i
$503$	11.6692	−	21.6013i	0.520305	−	0.963153i	−0.476177	−	0.879350i	$-0.657978\pi$
$503$	11.6692	−	21.6013i	0.520305	−	0.963153i	0.996482	−	0.0838038i	$-0.0267069\pi$
$504$	0.990637	+	0.0280451i	0.0441265	+	0.00124923i
$505$	21.9298	−	21.0180i	0.975865	−	0.935291i
$506$	−6.81956	+	3.80963i	−0.303166	+	0.169359i
$507$	5.21389	−	7.48371i	0.231557	−	0.332363i
$508$	−1.64847	+	5.98253i	−0.0731391	+	0.265432i
$509$	2.92097	−	8.65518i	0.129470	−	0.383634i	−0.863143	−	0.504960i	$-0.831507\pi$
$509$	2.92097	−	8.65518i	0.129470	−	0.383634i	0.992613	+	0.121326i	$0.0387145\pi$
$510$	−11.9968	+	8.10845i	−0.531229	+	0.359048i
$511$	4.45043	−	0.634032i	0.196875	−	0.0280479i
$512$	0.778036	+	0.628220i	0.0343846	+	0.0277637i
$513$	−31.3662	+	6.29682i	−1.38485	+	0.278011i
$514$	0.114952	+	0.286070i	0.00507033	+	0.0126180i
$515$	−12.8602	+	4.13834i	−0.566689	+	0.182357i
$516$	−3.39085	−	9.18129i	−0.149274	−	0.404184i
$517$	1.66981	+	6.80656i	0.0734382	+	0.299352i
$518$	−4.42113	+	6.74508i	−0.194253	+	0.296362i
$519$	0.335347	−	0.770749i	0.0147201	−	0.0338321i
$520$	−3.64496	−	7.76876i	−0.159842	−	0.340682i
$521$	0.325294	+	22.9853i	0.0142514	+	1.00700i	0.871004	+	0.491276i	$0.163469\pi$
$521$	0.325294	+	22.9853i	0.0142514	+	1.00700i	−0.856752	+	0.515728i	$0.827522\pi$
$522$	0.0758221	+	0.0966713i	0.00331864	+	0.00423119i
$523$	28.4109	−	25.7273i	1.24232	−	1.12497i	0.254883	−	0.966972i	$-0.417963\pi$
$523$	28.4109	−	25.7273i	1.24232	−	1.12497i	0.987439	−	0.158002i	$-0.0505054\pi$
$524$	−1.15397	+	0.828467i	−0.0504113	+	0.0361918i
$525$	−1.35239	+	0.859328i	−0.0590232	+	0.0375042i
$526$	1.35308	+	13.6146i	0.0589969	+	0.593623i
$527$	−7.52257	+	40.4285i	−0.327688	+	1.76109i
$528$	−0.806938	+	2.00814i	−0.0351175	+	0.0873932i
$529$	−0.158752	+	2.23989i	−0.00690226	+	0.0973865i
$530$	−2.20870	−	2.00007i	−0.0959400	−	0.0868777i
$531$	−3.88051	−	0.441201i	−0.168400	−	0.0191465i
$532$	1.82873	−	4.95161i	0.0792857	−	0.214679i
$533$	1.95557	−	46.0355i	0.0847049	−	1.99402i
$534$	−8.90423	+	4.64860i	−0.385324	+	0.201165i
$535$	−3.89882	−	0.898176i	−0.168561	−	0.0388315i
$536$	3.55771	+	6.58578i	0.153669	+	0.284462i
$537$	1.23226	+	2.44405i	0.0531760	+	0.105468i
$538$	−2.73255	+	27.4947i	−0.117809	+	1.18538i
$539$	9.15031	+	2.66122i	0.394132	+	0.114627i
$540$	10.2397	+	3.94730i	0.440648	+	0.169865i
$541$	36.9753	−	6.34004i	1.58969	−	0.272580i	0.694914	−	0.719093i	$-0.255443\pi$
$541$	36.9753	−	6.34004i	1.58969	−	0.272580i	0.894777	+	0.446514i	$0.147335\pi$
$542$	1.58937	+	2.42482i	0.0682694	+	0.104155i
$543$	−12.5821	+	13.5054i	−0.539950	+	0.579573i
$544$	4.17019	−	3.36719i	0.178795	−	0.144367i
$545$	−16.0424	+	19.3028i	−0.687182	+	0.826841i
$546$	−5.29803	−	2.21651i	−0.226735	−	0.0948577i
$547$	−16.3858	+	9.77209i	−0.700606	+	0.417824i	−0.817967	−	0.575265i	$-0.804899\pi$
$547$	−16.3858	+	9.77209i	−0.700606	+	0.417824i	0.117361	+	0.993089i	$0.462557\pi$
$548$	−20.7873	+	8.01328i	−0.887991	+	0.342310i
$549$	−9.38206	+	0.798531i	−0.400417	+	0.0340805i
$550$	0.404083	+	1.87495i	0.0172302	+	0.0799482i
$551$	0.617000	−	0.218000i	0.0262851	−	0.00928711i
$552$	3.99827	+	5.73888i	0.170178	+	0.244263i
$553$	−7.39899	−	3.60009i	−0.314637	−	0.153092i
$554$	−23.5882	−	15.9428i	−1.00217	−	0.677346i
$555$	−18.5767	+	14.1502i	−0.788535	+	0.600644i
$556$	0.199083	−	14.0672i	0.00844302	−	0.596584i
$557$	10.2675	−	4.64120i	0.435047	−	0.196654i	−0.182469	−	0.983212i	$-0.558409\pi$
$557$	10.2675	−	4.64120i	0.435047	−	0.196654i	0.617517	+	0.786558i	$0.288139\pi$
$558$	7.42595	−	3.35674i	0.314366	−	0.142102i
$559$	0.439939	−	31.0861i	0.0186074	−	1.31480i
$560$	−1.44041	+	1.09719i	−0.0608683	+	0.0463647i
$561$	9.61063	+	6.49566i	0.405761	+	0.274247i
$562$	9.72553	+	4.73211i	0.410247	+	0.199612i
$563$	−15.2444	−	21.8809i	−0.642473	−	0.922168i	0.357458	−	0.933929i	$-0.383644\pi$
$563$	−15.2444	−	21.8809i	−0.642473	−	0.922168i	−0.999931	+	0.0117612i	$0.996256\pi$
$564$	5.91679	−	2.09054i	0.249142	−	0.0880274i
$565$	2.19119	+	10.1671i	0.0921839	+	0.427735i
$566$	−11.8912	+	1.01209i	−0.499824	+	0.0425413i
$567$	4.07875	−	1.57231i	0.171292	−	0.0660309i
$568$	−8.69418	+	5.18500i	−0.364800	+	0.217558i
$569$	1.10890	+	0.463924i	0.0464875	+	0.0194487i	0.409071	−	0.912503i	$-0.365853\pi$
$569$	1.10890	+	0.463924i	0.0464875	+	0.0194487i	−0.362583	+	0.931951i	$0.618105\pi$
$570$	9.76907	−	11.7545i	0.409181	−	0.492341i
$571$	29.4003	−	23.7391i	1.23036	−	0.993450i	0.230573	−	0.973055i	$-0.425940\pi$
$571$	29.4003	−	23.7391i	1.23036	−	0.993450i	0.999792	−	0.0203948i	$-0.00649232\pi$
$572$	−4.68601	+	5.02989i	−0.195932	+	0.210310i
$573$	−14.0614	−	21.4528i	−0.587425	−	0.896203i
$574$	−9.58256	+	1.64309i	−0.399968	+	0.0685814i
$575$	5.78380	+	2.22959i	0.241201	+	0.0929803i
$576$	−1.01993	−	0.296630i	−0.0424971	−	0.0123596i
$577$	−1.34441	+	13.5273i	−0.0559685	+	0.563151i	0.926445	+	0.376431i	$0.122849\pi$
$577$	−1.34441	+	13.5273i	−0.0559685	+	0.563151i	−0.982413	+	0.186720i	$0.940214\pi$
$578$	−5.28019	−	10.4726i	−0.219627	−	0.435604i
$579$	−4.64218	−	8.59329i	−0.192923	−	0.357125i
$580$	−0.218743	−	0.0503921i	−0.00908280	−	0.00209242i
$581$	−12.1155	+	6.32511i	−0.502637	+	0.262410i
$582$	0.954871	−	22.4784i	0.0395807	−	0.931760i
$583$	−0.826986	+	2.23920i	−0.0342503	+	0.0927384i
$584$	−4.78729	−	0.544299i	−0.198100	−	0.0225233i
$585$	6.75649	+	6.11828i	0.279346	+	0.252960i
$586$	−0.999415	+	14.1011i	−0.0412855	+	0.582512i
$587$	−8.78614	+	21.8652i	−0.362643	+	0.902472i	0.629459	+	0.777034i	$0.283277\pi$
$587$	−8.78614	+	21.8652i	−0.362643	+	0.902472i	−0.992102	+	0.125438i	$0.959966\pi$
$588$	1.56087	−	8.38859i	0.0643694	−	0.345940i
$589$	−4.29272	−	43.1930i	−0.176878	−	1.77974i
$590$	6.02267	−	3.82688i	0.247949	−	0.157550i
$591$	15.1914	−	10.9063i	0.624890	−	0.448627i
$592$	6.40732	−	5.80209i	0.263339	−	0.238465i
$593$	0.703969	+	0.897544i	0.0289086	+	0.0368577i	0.801086	−	0.598549i	$-0.204256\pi$
$593$	0.703969	+	0.897544i	0.0289086	+	0.0368577i	−0.772178	+	0.635407i	$0.780832\pi$
$594$	−0.124406	−	8.79053i	−0.00510444	−	0.360680i
$595$	4.12229	+	8.78611i	0.168997	+	0.360195i
$596$	3.17566	−	7.29880i	0.130080	−	0.298971i
$597$	6.94473	−	10.5952i	0.284229	−	0.433632i
$598$	5.29343	+	21.5774i	0.216465	+	0.882364i
$599$	11.4281	+	30.9434i	0.466938	+	1.26431i	0.926543	+	0.376190i	$0.122766\pi$
$599$	11.4281	+	30.9434i	0.466938	+	1.26431i	−0.459605	+	0.888124i	$0.652009\pi$
$600$	1.63480	−	0.526069i	0.0667405	−	0.0214767i
$601$	−5.28094	−	13.1421i	−0.215414	−	0.536079i	0.780625	−	0.625000i	$-0.214901\pi$
$601$	−5.28094	−	13.1421i	−0.215414	−	0.536079i	−0.996039	+	0.0889217i	$0.971658\pi$
$602$	−6.43161	+	1.29116i	−0.262133	+	0.0526237i
$603$	−6.18602	−	4.99486i	−0.251914	−	0.203407i
$604$	14.2184	−	2.02563i	0.578537	−	0.0824215i
$605$	13.8004	−	9.32745i	0.561067	−	0.379215i
$606$	−6.96709	+	20.6443i	−0.283019	+	0.838617i
$607$	−0.370553	+	1.34479i	−0.0150403	+	0.0545833i	−0.971204	−	0.238249i	$-0.923427\pi$
$607$	−0.370553	+	1.34479i	−0.0150403	+	0.0545833i	0.956164	+	0.292832i	$0.0945978\pi$
$608$	−3.23408	+	4.64200i	−0.131159	+	0.188258i
$609$	−0.131150	+	0.0732646i	−0.00531445	+	0.00296883i
$610$	12.4203	−	11.9039i	0.502883	−	0.481974i
$611$	19.9250	+	0.564081i	0.806079	+	0.0228203i
$612$	−2.70595	+	5.00906i	−0.109381	+	0.202479i
$613$	1.80187	−	2.04732i	0.0727767	−	0.0826904i	−0.713145	−	0.701017i	$-0.752730\pi$
$613$	1.80187	−	2.04732i	0.0727767	−	0.0826904i	0.785921	+	0.618327i	$0.212189\pi$
$614$	4.66188	+	10.7147i	0.188138	+	0.432410i
$615$	−27.7466	−	4.75762i	−1.11885	−	0.191846i
$616$	1.24581	+	0.742972i	0.0501952	+	0.0299352i
$617$	−10.3255	−	13.9610i	−0.415688	−	0.562047i	0.545440	−	0.838150i	$-0.316362\pi$
$617$	−10.3255	−	13.9610i	−0.415688	−	0.562047i	−0.961128	+	0.276103i	$0.910957\pi$
$618$	6.80350	−	6.90047i	0.273677	−	0.277578i
$619$	31.2681	−	0.885205i	1.25677	−	0.0355794i	0.606377	−	0.795177i	$-0.292622\pi$
$619$	31.2681	−	0.885205i	1.25677	−	0.0355794i	0.650393	+	0.759598i	$0.274604\pi$
$620$	−6.70331	+	13.2952i	−0.269211	+	0.533949i
$621$	−23.9808	−	15.2377i	−0.962315	−	0.611468i
$622$	12.7037	−	0.719867i	0.509373	−	0.0288640i
$623$	2.15275	+	6.37886i	0.0862483	+	0.255564i
$624$	4.89659	+	3.72984i	0.196020	+	0.149313i
$625$	−10.6825	+	13.6200i	−0.427302	+	0.544799i
$626$	−2.10803	−	29.7429i	−0.0842537	−	1.18877i
$627$	−11.6554	−	3.75064i	−0.465472	−	0.149786i
$628$	0.144490	+	3.40141i	0.00576578	+	0.135731i
$629$	−23.1653	−	40.1235i	−0.923662	−	1.59983i
$630$	0.961649	−	1.66562i	0.0383130	−	0.0663601i
$631$	4.04372	+	2.11109i	0.160978	+	0.0840413i	0.541372	−	0.840783i	$-0.317905\pi$
$631$	4.04372	+	2.11109i	0.160978	+	0.0840413i	−0.380394	+	0.924825i	$0.624211\pi$
$632$	6.70208	+	5.73232i	0.266594	+	0.228020i
$633$	−5.15541	+	32.8508i	−0.204909	+	1.30570i
$634$	18.1643	+	18.4232i	0.721395	+	0.731677i
$635$	8.69451	+	8.33301i	0.345031	+	0.330685i
$636$	2.06836	+	0.538560i	0.0820160	+	0.0213553i
$637$	14.2104	−	23.0792i	0.563038	−	0.914432i
$638$	0.0278793	+	0.177650i	0.00110375	+	0.00703322i
$639$	6.39376	−	8.64493i	0.252933	−	0.341988i
$640$	1.79033	−	0.749012i	0.0707691	−	0.0296073i
$641$	−11.7880	+	38.4917i	−0.465596	+	1.52033i	0.347204	+	0.937789i	$0.387131\pi$
$641$	−11.7880	+	38.4917i	−0.465596	+	1.52033i	−0.812801	+	0.582542i	$0.802058\pi$
$642$	2.77725	−	0.723139i	0.109609	−	0.0285400i
$643$	30.4756	+	17.0247i	1.20184	+	0.671387i	0.954693	−	0.297591i	$-0.0961832\pi$
$643$	30.4756	+	17.0247i	1.20184	+	0.671387i	0.247145	+	0.968978i	$0.420508\pi$
$644$	4.21539	−	2.05106i	0.166110	−	0.0808232i
$645$	−18.8046	−	2.67900i	−0.740430	−	0.105486i
$646$	20.6702	+	22.1871i	0.813259	+	0.872938i
$647$	−8.78378	+	35.8049i	−0.345326	+	1.40764i	0.496570	+	0.867997i	$0.334593\pi$
$647$	−8.78378	+	35.8049i	−0.345326	+	1.40764i	−0.841896	+	0.539640i	$0.818561\pi$
$648$	−4.65519	+	0.529279i	−0.182873	+	0.0207921i
$649$	−4.64357	−	3.33375i	−0.182276	−	0.130861i
$650$	5.44637	+	0.308623i	0.213624	+	0.0121052i
$651$	2.64709	+	9.60666i	0.103748	+	0.376515i
$652$	−9.45513	−	3.34071i	−0.370292	−	0.130832i
$653$	2.57588	−	20.1154i	0.100802	−	0.787176i	−0.860069	−	0.510178i	$-0.829579\pi$
$653$	2.57588	−	20.1154i	0.100802	−	0.787176i	0.960871	−	0.276998i	$-0.0893394\pi$
$654$	3.79293	−	17.5993i	0.148315	−	0.688186i
$655$	0.350173	+	2.73455i	0.0136824	+	0.106848i
$656$	10.3829	+	0.883719i	0.405386	+	0.0345034i
$657$	4.91417	−	1.42921i	0.191720	−	0.0557586i
$658$	−0.769395	−	4.13495i	−0.0299941	−	0.161197i
$659$	−5.53245	−	1.11065i	−0.215514	−	0.0432648i	0.0878757	−	0.996131i	$-0.471992\pi$
$659$	−5.53245	−	1.11065i	−0.215514	−	0.0432648i	−0.303389	+	0.952867i	$0.598118\pi$
$660$	2.68455	+	3.23014i	0.104496	+	0.125733i
$661$	5.84114	+	19.0733i	0.227194	+	0.741866i	0.994882	+	0.101042i	$0.0322178\pi$
$661$	5.84114	+	19.0733i	0.227194	+	0.741866i	−0.767688	+	0.640824i	$0.778593\pi$
$662$	2.45373	+	3.98511i	0.0953670	+	0.154886i
$663$	25.0721	−	21.4443i	0.973721	−	0.832829i
$664$	14.2746	−	3.28847i	0.553964	−	0.127617i
$665$	−6.76795	−	7.68988i	−0.262450	−	0.298201i
$666$	−3.89990	+	8.31212i	−0.151118	+	0.322088i
$667$	0.529571	+	0.239381i	0.0205051	+	0.00926887i
$668$	15.9802			0.618291
$669$	−3.22498	−	20.5361i	−0.124685	−	0.793971i
$670$	14.5267			0.561216
$671$	−12.5584	−	5.67674i	−0.484810	−	0.219148i
$672$	0.551670	−	1.17581i	0.0212811	−	0.0453580i
$673$	−10.1205	−	11.4991i	−0.390115	−	0.443257i	0.522152	−	0.852852i	$-0.325129\pi$
$673$	−10.1205	−	11.4991i	−0.390115	−	0.443257i	−0.912267	+	0.409595i	$0.865670\pi$
$674$	24.6639	−	5.68186i	0.950019	−	0.218857i
$675$	−5.30157	+	4.53446i	−0.204058	+	0.174532i
$676$	3.43532	+	5.57932i	0.132128	+	0.214589i
$677$	−11.1344	−	36.3577i	−0.427930	−	1.39734i	−0.866741	−	0.498759i	$-0.833789\pi$
$677$	−11.1344	−	36.3577i	−0.427930	−	1.39734i	0.438811	−	0.898580i	$-0.355400\pi$
$678$	−4.76837	−	5.73746i	−0.183128	−	0.220346i
$679$	−14.7845	−	2.96803i	−0.567379	−	0.113902i
$680$	−1.90284	−	10.2264i	−0.0729705	−	0.392165i
$681$	17.9065	−	5.20782i	0.686179	−	0.199564i
$682$	11.8850	+	1.01156i	0.455099	+	0.0387346i
$683$	6.28774	+	49.1019i	0.240594	+	1.87883i	0.438675	+	0.898646i	$0.355448\pi$
$683$	6.28774	+	49.1019i	0.240594	+	1.87883i	−0.198082	+	0.980186i	$0.563471\pi$
$684$	1.26605	−	5.87448i	0.0484085	−	0.224616i
$685$	−5.49169	+	42.8854i	−0.209827	+	1.63857i
$686$	−11.5502	−	4.08094i	−0.440988	−	0.155811i
$687$	4.94756	+	17.9554i	0.188761	+	0.685040i
$688$	7.01968	+	0.397776i	0.267623	+	0.0151651i
$689$	5.51501	+	3.95938i	0.210105	+	0.150841i
$690$	13.4870	−	1.53343i	0.513443	−	0.0583767i
$691$	−11.3311	+	46.1886i	−0.431057	+	1.75710i	0.198459	+	0.980109i	$0.436406\pi$
$691$	−11.3311	+	46.1886i	−0.431057	+	1.75710i	−0.629516	+	0.776987i	$0.716747\pi$
$692$	0.411593	+	0.441797i	0.0156464	+	0.0167946i
$693$	−1.52535	−	0.217309i	−0.0579431	−	0.00825489i
$694$	15.0823	−	7.33851i	0.572516	−	0.278566i
$695$	−23.8359	−	13.3155i	−0.904148	−	0.505087i
$696$	0.155817	−	0.0405717i	0.00590624	−	0.00153786i
$697$	16.3549	−	53.4045i	0.619487	−	2.02284i
$698$	−4.53549	+	1.89749i	−0.171671	+	0.0718210i
$699$	19.3595	−	26.1758i	0.732243	−	0.990058i
$700$	−0.178454	−	1.13713i	−0.00674493	−	0.0429794i
$701$	8.20555	−	13.3267i	0.309919	−	0.503341i	−0.658529	−	0.752555i	$-0.728821\pi$
$701$	8.20555	−	13.3267i	0.309919	−	0.503341i	0.968448	+	0.249214i	$0.0801724\pi$
$702$	−24.1974	−	6.30051i	−0.913271	−	0.237797i
$703$	35.3060	+	33.8381i	1.33159	+	1.27623i
$704$	−1.09152	−	1.10708i	−0.0411383	−	0.0417247i
$705$	1.88809	−	12.0311i	0.0711097	−	0.453118i
$706$	11.3944	+	9.74572i	0.428835	+	0.366785i
$707$	12.9454	+	6.75835i	0.486861	+	0.254174i
$708$	−2.55918	+	4.43263i	−0.0961800	+	0.166589i
$709$	−10.4087	−	18.0283i	−0.390906	−	0.677068i	0.601664	−	0.798750i	$-0.294505\pi$
$709$	−10.4087	−	18.0283i	−0.390906	−	0.677068i	−0.992569	+	0.121681i	$0.961171\pi$
$710$	0.833778	+	19.6278i	0.0312911	+	0.736618i
$711$	−8.91729	−	2.86953i	−0.334425	−	0.107616i
$712$	−0.510133	−	7.19765i	−0.0191180	−	0.269743i
$713$	23.7905	−	30.3323i	0.890960	−	1.13595i
$714$	−5.53782	−	4.21828i	−0.207248	−	0.157865i
$715$	4.26606	+	12.6408i	0.159542	+	0.472740i
$716$	−1.96310	+	0.111241i	−0.0733645	+	0.00415726i
$717$	−4.68363	−	2.97604i	−0.174913	−	0.111142i
$718$	−0.602484	+	1.19496i	−0.0224845	+	0.0445954i
$719$	26.1891	−	0.741418i	0.976688	−	0.0276502i	0.463652	−	0.886017i	$-0.346539\pi$
$719$	26.1891	−	0.741418i	0.976688	−	0.0276502i	0.513036	+	0.858367i	$0.328521\pi$
$720$	−1.44727	+	1.46790i	−0.0539367	+	0.0547054i
$721$	−3.86209	−	5.22189i	−0.143832	−	0.194473i
$722$	−11.1716	−	6.66247i	−0.415764	−	0.247951i
$723$	−7.37470	−	1.26452i	−0.274268	−	0.0470280i
$724$	−5.29017	−	12.1587i	−0.196607	−	0.451875i
$725$	0.0942754	−	0.107118i	0.00350130	−	0.00397825i
$726$	−5.67875	+	10.5121i	−0.210758	+	0.390141i
$727$	43.0346	+	1.21832i	1.59607	+	0.0451849i	0.815074	−	0.579357i	$-0.196696\pi$
$727$	43.0346	+	1.21832i	1.59607	+	0.0451849i	0.780992	+	0.624542i	$0.214714\pi$
$728$	2.97847	−	2.85463i	0.110390	−	0.105800i
$729$	24.9611	−	13.9441i	0.924483	−	0.516447i
$730$	−5.34517	+	7.67215i	−0.197834	+	0.283959i
$731$	10.0109	−	36.3311i	0.370268	−	1.34375i
$732$	−3.94592	+	11.6922i	−0.145845	+	0.432156i
$733$	−24.5219	+	16.5739i	−0.905737	+	0.612171i	−0.921786	−	0.387700i	$-0.873270\pi$
$733$	−24.5219	+	16.5739i	−0.905737	+	0.612171i	0.0160487	+	0.999871i	$0.494891\pi$
$734$	28.9713	−	4.12740i	1.06935	−	0.152345i
$735$	−12.8836	−	10.4028i	−0.475219	−	0.383713i
$736$	−4.92620	+	0.988945i	−0.181582	+	0.0364530i
$737$	−4.33904	−	10.7981i	−0.159831	−	0.397754i
$738$	−10.5364	+	3.39056i	−0.387852	+	0.124808i
$739$	6.86271	+	18.5819i	0.252449	+	0.683548i	0.999817	+	0.0191374i	$0.00609199\pi$
$739$	6.86271	+	18.5819i	0.252449	+	0.683548i	−0.747368	+	0.664410i	$0.768683\pi$
$740$	−3.99686	−	16.2922i	−0.146928	−	0.598914i
$741$	−19.0903	+	29.1250i	−0.701299	+	1.06993i
$742$	0.571528	−	1.31358i	0.0209814	−	0.0482229i
$743$	8.48995	+	18.0952i	0.311466	+	0.663849i	0.997998	−	0.0632510i	$-0.0201469\pi$
$743$	8.48995	+	18.0952i	0.311466	+	0.663849i	−0.686531	+	0.727100i	$0.740868\pi$
$744$	−0.151133	−	10.6791i	−0.00554082	−	0.391514i
$745$	−9.53334	−	12.1548i	−0.349275	−	0.445317i
$746$	−20.8366	+	18.8685i	−0.762884	+	0.690823i
$747$	−12.6395	+	9.07427i	−0.462455	+	0.332010i
$748$	−7.03322	+	4.46900i	−0.257160	+	0.163403i
$749$	−0.190228	−	1.91406i	−0.00695078	−	0.0699382i
$750$	3.08068	−	16.5565i	0.112491	−	0.604557i
$751$	13.9987	−	34.8370i	0.510818	−	1.27122i	−0.420593	−	0.907250i	$-0.638178\pi$
$751$	13.9987	−	34.8370i	0.510818	−	1.27122i	0.931411	−	0.363970i	$-0.118579\pi$
$752$	−0.318699	+	4.49663i	−0.0116217	+	0.163975i
$753$	10.0821	+	9.12973i	0.367411	+	0.332706i
$754$	0.508174	+	0.0577777i	0.0185066	+	0.00210414i
$755$	9.65628	−	26.1460i	0.351428	−	0.951551i
$756$	−0.223918	+	5.27121i	−0.00814383	+	0.191712i
$757$	−32.4386	+	16.9351i	−1.17900	+	0.615517i	−0.935135	−	0.354292i	$-0.884722\pi$
$757$	−32.4386	+	16.9351i	−1.17900	+	0.615517i	−0.243866	+	0.969809i	$0.578416\pi$
$758$	−7.72729	−	1.78015i	−0.280668	−	0.0646578i
$759$	−5.16834	−	9.56727i	−0.187599	−	0.347270i
$760$	4.94302	+	9.80390i	0.179302	+	0.355625i
$761$	−2.50666	+	25.2219i	−0.0908665	+	0.914292i	0.838443	+	0.544990i	$0.183466\pi$
$761$	−2.50666	+	25.2219i	−0.0908665	+	0.914292i	−0.929309	+	0.369302i	$0.879597\pi$
$762$	−8.29469	−	2.41238i	−0.300485	−	0.0873911i
$763$	−11.2590	−	4.34021i	−0.407602	−	0.157126i
$764$	18.1613	−	3.11407i	0.657054	−	0.112663i
$765$	6.05691	+	9.24070i	0.218988	+	0.334098i
$766$	−5.25603	+	5.64174i	−0.189908	+	0.203844i
$767$	−12.6495	+	10.2137i	−0.456746	+	0.368796i
$768$	−0.889754	+	1.07058i	−0.0321062	+	0.0386313i
$769$	−25.0488	−	10.4795i	−0.903281	−	0.377901i	−0.115107	−	0.993353i	$-0.536721\pi$
$769$	−25.0488	−	10.4795i	−0.903281	−	0.377901i	−0.788174	+	0.615452i	$0.788973\pi$
$770$	2.41775	−	1.44189i	0.0871296	−	0.0519619i
$771$	−0.400449	+	0.154368i	−0.0144218	+	0.00555944i
$772$	6.99099	−	0.595021i	0.251611	−	0.0214153i
$773$	2.87885	+	13.3579i	0.103545	+	0.480451i	0.999352	+	0.0360063i	$0.0114637\pi$
$773$	2.87885	+	13.3579i	0.103545	+	0.480451i	−0.895807	+	0.444444i	$0.853401\pi$
$774$	−7.04160	+	2.48795i	−0.253105	+	0.0894277i
$775$	−5.41069	−	7.76619i	−0.194358	−	0.278970i
$776$	14.5332	+	7.07135i	0.521712	+	0.253847i
$777$	−9.30147	−	6.28670i	−0.333688	−	0.225534i
$778$	17.1791	−	13.0857i	0.615901	−	0.469145i
$779$	−0.834249	+	58.9481i	−0.0298901	+	2.11203i
$780$	10.8852	−	4.92044i	0.389754	−	0.176180i
$781$	14.3408	−	6.48247i	0.513156	−	0.231961i
$782$	−0.381093	+	26.9280i	−0.0136278	+	0.962945i
$783$	−0.520309	+	0.396331i	−0.0185943	+	0.0141637i
$784$	5.07834	+	3.43236i	0.181369	+	0.122584i
$785$	5.94111	+	2.89074i	0.212047	+	0.103175i
$786$	−1.13042	−	1.62254i	−0.0403208	−	0.0578742i
$787$	−18.7958	+	6.64098i	−0.669998	+	0.236725i	−0.646403	−	0.762996i	$-0.723728\pi$
$787$	−18.7958	+	6.64098i	−0.669998	+	0.236725i	−0.0235953	+	0.999722i	$0.507511\pi$
$788$	2.83029	+	13.1326i	0.100825	+	0.467829i
$789$	−18.9769	+	1.61518i	−0.675597	+	0.0575018i
$790$	15.9698	−	6.15618i	0.568181	−	0.219027i
$791$	−4.29447	+	2.56112i	−0.152694	+	0.0910628i
$792$	1.52343	+	0.637347i	0.0541326	+	0.0226471i
$793$	−25.0538	+	30.1456i	−0.889688	+	1.07050i
$794$	8.14471	−	6.57640i	0.289045	−	0.233388i
$795$	2.82744	−	3.03493i	0.100279	−	0.107638i
$796$	4.98884	+	7.61121i	0.176825	+	0.269772i
$797$	−4.76825	+	0.817599i	−0.168900	+	0.0289608i	−0.252829	−	0.967511i	$-0.581361\pi$
$797$	−4.76825	+	0.817599i	−0.168900	+	0.0289608i	0.0839293	+	0.996472i	$0.473253\pi$
$798$	6.85618	+	2.64298i	0.242706	+	0.0935605i
$799$	23.2006	+	6.74753i	0.820780	+	0.238710i
$800$	−0.122009	+	1.22764i	−0.00431366	+	0.0434037i
$801$	3.45057	+	6.84379i	0.121920	+	0.241814i
$802$	−0.275511	−	0.510006i	−0.00972862	−	0.0180089i
$803$	7.29950	+	1.68160i	0.257594	+	0.0593422i
$804$	−9.23691	+	4.82229i	−0.325761	+	0.170069i
$805$	0.386121	−	9.08960i	0.0136090	−	0.320366i
$806$	11.7533	−	31.8239i	0.413991	−	1.12095i
$807$	−38.2164	−	4.34508i	−1.34528	−	0.152954i
$808$	−11.6019	−	10.5060i	−0.408154	−	0.369601i
$809$	−0.525165	+	7.40975i	−0.0184638	+	0.260513i	0.979725	+	0.200349i	$0.0642075\pi$
$809$	−0.525165	+	7.40975i	−0.0184638	+	0.260513i	−0.998188	+	0.0601643i	$0.980838\pi$
$810$	−3.39020	+	8.43685i	−0.119120	+	0.296441i
$811$	2.77529	−	14.9152i	0.0974535	−	0.523744i	−0.898880	−	0.438194i	$-0.855618\pi$
$811$	2.77529	−	14.9152i	0.0974535	−	0.523744i	0.996334	−	0.0855497i	$-0.0272646\pi$
$812$	−0.0106727	−	0.107388i	−0.000374539	−	0.00376858i
$813$	−3.40644	+	2.16450i	−0.119469	+	0.0759124i
$814$	−10.9166	+	7.83737i	−0.382628	+	0.274700i
$815$	−14.4256	+	13.0630i	−0.505307	+	0.457577i
$816$	4.60469	+	5.87087i	0.161196	+	0.205521i
$817$	0.562887	+	39.7736i	0.0196929	+	1.39150i
$818$	−8.60317	−	18.3365i	−0.300803	−	0.641121i
$819$	−1.74832	+	4.01827i	−0.0610912	+	0.140410i
$820$	11.0861	−	16.9135i	0.387145	−	0.590646i
$821$	−4.71942	−	19.2376i	−0.164709	−	0.671395i	−0.993694	−	0.112125i	$-0.964234\pi$
$821$	−4.71942	−	19.2376i	−0.164709	−	0.671395i	0.828985	−	0.559271i	$-0.188919\pi$
$822$	−10.7443	−	29.0920i	−0.374751	−	1.01470i
$823$	−14.5690	+	4.68821i	−0.507844	+	0.163421i	−0.549147	−	0.835726i	$-0.685047\pi$
$823$	−14.5690	+	4.68821i	−0.507844	+	0.163421i	0.0413030	+	0.999147i	$0.486849\pi$
$824$	2.59554	+	6.45926i	0.0904201	+	0.225019i
$825$	−2.61773	+	0.525514i	−0.0911377	+	0.0182961i
$826$	2.66908	+	2.15513i	0.0928691	+	0.0749866i
$827$	−28.8730	+	4.11340i	−1.00401	+	0.143037i	−0.623569	−	0.781768i	$-0.714318\pi$
$827$	−28.8730	+	4.11340i	−1.00401	+	0.143037i	−0.380442	+	0.924805i	$0.624228\pi$
$828$	4.42173	−	2.98857i	0.153666	−	0.103860i
$829$	−1.21405	+	3.59738i	−0.0421658	+	0.124942i	−0.966518	−	0.256597i	$-0.917399\pi$
$829$	−1.21405	+	3.59738i	−0.0421658	+	0.124942i	0.924353	+	0.381539i	$0.124606\pi$
$830$	7.55192	−	27.4070i	0.262131	−	0.951310i
$831$	22.6557	−	32.5186i	0.785917	−	1.12806i
$832$	−3.86027	+	2.15648i	−0.133831	+	0.0747624i
$833$	23.7187	−	22.7326i	0.821805	−	0.787637i
$834$	19.5765	+	0.554213i	0.677877	+	0.0191908i
$835$	14.7401	−	27.2858i	0.510102	−	0.944265i
$836$	5.81107	−	6.60266i	0.200980	−	0.228358i
$837$	17.3090	+	39.7824i	0.598288	+	1.37508i
$838$	22.7563	+	3.90196i	0.786103	+	0.134791i
$839$	−13.3159	−	7.94130i	−0.459717	−	0.274164i	0.263662	−	0.964615i	$-0.415070\pi$
$839$	−13.3159	−	7.94130i	−0.459717	−	0.274164i	−0.723379	+	0.690451i	$0.757412\pi$
$840$	−1.49882	−	2.02653i	−0.0517141	−	0.0699221i
$841$	−20.3511	+	20.6411i	−0.701762	+	0.711764i
$842$	10.8846	−	0.308146i	0.375109	−	0.0106194i
$843$	−6.77826	+	13.4439i	−0.233456	+	0.463032i
$844$	−20.1618	−	12.8111i	−0.693996	−	0.440975i
$845$	12.6953	−	0.719390i	0.436732	−	0.0247478i
$846$	−1.53111	−	4.53687i	−0.0526408	−	0.155981i
$847$	6.37036	+	4.85244i	0.218888	+	0.166732i
$848$	−0.947556	+	1.20811i	−0.0325392	+	0.0414867i
$849$	−1.17450	−	16.5714i	−0.0403087	−	0.568730i
$850$	6.29457	+	2.02555i	0.215902	+	0.0694758i
$851$	1.84328	+	43.3923i	0.0631870	+	1.48747i
$852$	−7.04580	−	12.2037i	−0.241385	−	0.418091i
$853$	20.3857	−	35.3091i	0.697994	−	1.20896i	−0.271167	−	0.962532i	$-0.587409\pi$
$853$	20.3857	−	35.3091i	0.697994	−	1.20896i	0.969161	−	0.246429i	$-0.0792572\pi$
$854$	7.33181	+	3.82769i	0.250889	+	0.130981i
$855$	−8.86276	−	7.58036i	−0.303100	−	0.259243i
$856$	−0.319623	+	2.03667i	−0.0109245	+	0.0696119i
$857$	−25.8151	−	26.1830i	−0.881825	−	0.894394i	0.113245	−	0.993567i	$-0.463876\pi$
$857$	−25.8151	−	26.1830i	−0.881825	−	0.894394i	−0.995070	+	0.0991736i	$0.968380\pi$
$858$	−6.90885	−	6.62160i	−0.235864	−	0.226058i
$859$	−12.0367	−	3.13411i	−0.410686	−	0.106934i	0.0408970	−	0.999163i	$-0.486978\pi$
$859$	−12.0367	−	3.13411i	−0.410686	−	0.106934i	−0.451583	+	0.892229i	$0.649141\pi$
$860$	7.15414	−	11.6191i	0.243954	−	0.396207i
$861$	−2.09828	−	13.3705i	−0.0715092	−	0.455664i
$862$	−5.18604	+	7.01199i	−0.176637	+	0.238829i
$863$	22.6245	−	9.46531i	0.770148	−	0.322203i	0.0343558	−	0.999410i	$-0.489062\pi$
$863$	22.6245	−	9.46531i	0.770148	−	0.322203i	0.735793	+	0.677207i	$0.236810\pi$
$864$	1.65585	−	5.40691i	0.0563331	−	0.183947i
$865$	1.13401	−	0.295274i	0.0385576	−	0.0100396i
$866$	−3.78853	−	2.11640i	−0.128739	−	0.0719181i
$867$	14.6810	−	7.14327i	0.498593	−	0.242598i
$868$	−7.08672	−	1.00961i	−0.240539	−	0.0342685i
$869$	−9.34616	−	10.0320i	−0.317047	−	0.340313i
$870$	0.0744503	−	0.303478i	0.00252410	−	0.0102889i
$871$	−32.8865	+	3.73908i	−1.11432	+	0.126694i
$872$	10.5058	+	7.54245i	0.355773	+	0.255420i
$873$	−17.1399	−	0.971245i	−0.580097	−	0.0328717i
$874$	−7.55131	−	27.4048i	−0.255427	−	0.926980i
$875$	−10.6425	−	3.76024i	−0.359783	−	0.127119i
$876$	0.851921	−	6.65277i	0.0287837	−	0.224776i
$877$	1.70364	−	7.90490i	0.0575277	−	0.266929i	−0.939638	−	0.342171i	$-0.888838\pi$
$877$	1.70364	−	7.90490i	0.0575277	−	0.266929i	0.997165	+	0.0752418i	$0.0239729\pi$
$878$	−3.66057	−	28.5859i	−0.123538	−	0.964727i
$879$	−19.6078	−	1.66887i	−0.661356	−	0.0562897i
$880$	−2.89714	+	0.842586i	−0.0976625	+	0.0284036i
$881$	4.37683	+	23.5224i	0.147459	+	0.792489i	0.973466	+	0.228830i	$0.0734899\pi$
$881$	4.37683	+	23.5224i	0.147459	+	0.792489i	−0.826007	+	0.563660i	$0.809393\pi$
$882$	−6.38333	−	1.28147i	−0.214938	−	0.0431492i
$883$	−6.75178	−	8.12398i	−0.227216	−	0.273394i	0.643214	−	0.765686i	$-0.277600\pi$
$883$	−6.75178	−	8.12398i	−0.227216	−	0.273394i	−0.870430	+	0.492293i	$0.836159\pi$
$884$	6.93997	+	22.6614i	0.233417	+	0.762185i
$885$	5.20805	+	8.45841i	0.175067	+	0.284326i
$886$	−18.4596	+	15.7886i	−0.620164	+	0.530429i
$887$	57.7062	−	13.2938i	1.93758	−	0.446364i	0.944579	−	0.328284i	$-0.106470\pi$
$887$	57.7062	−	13.2938i	1.93758	−	0.446364i	0.993004	−	0.118079i	$-0.0376737\pi$
$888$	7.94979	+	9.03272i	0.266778	+	0.303118i
$889$	−2.45924	+	5.24154i	−0.0824802	+	0.175796i
$890$	−12.7604	−	5.76806i	−0.427730	−	0.193346i
$891$	7.28399			0.244023
$892$	14.4517	+	3.76135i	0.483879	+	0.125939i
$893$	−25.5036			−0.853444
$894$	10.0967	+	4.56401i	0.337685	+	0.152643i
$895$	−1.62082	+	3.45456i	−0.0541780	+	0.115473i
$896$	0.616416	+	0.700384i	0.0205930	+	0.0233982i
$897$	−30.1381	+	6.94295i	−1.00628	+	0.231818i
$898$	−4.81323	+	4.11678i	−0.160620	+	0.137379i
$899$	−0.465278	−	0.755660i	−0.0155179	−	0.0252027i
$900$	−0.383719	−	1.25297i	−0.0127906	−	0.0417658i
$901$	5.26001	+	6.32903i	0.175236	+	0.210850i
$902$	−15.8837	−	3.18868i	−0.528869	−	0.106171i
$903$	−1.67049	−	8.97768i	−0.0555903	−	0.298758i
$904$	5.14598	−	1.49662i	0.171153	−	0.0497770i
$905$	−25.6404	−	2.18232i	−0.852316	−	0.0725428i
$906$	2.53941	+	19.8306i	0.0843663	+	0.658828i
$907$	10.4764	−	48.6108i	0.347864	−	1.61410i	−0.377691	−	0.925932i	$-0.623282\pi$
$907$	10.4764	−	48.6108i	0.347864	−	1.61410i	0.725555	−	0.688164i	$-0.241583\pi$
$908$	−1.70158	+	13.2879i	−0.0564688	+	0.440973i
$909$	15.6756	+	5.53854i	0.519927	+	0.183702i
$910$	−2.12689	−	7.71880i	−0.0705059	−	0.255876i
$911$	28.0715	+	1.59069i	0.930050	+	0.0527021i	0.515089	−	0.857137i	$-0.327759\pi$
$911$	28.0715	+	1.59069i	0.930050	+	0.0527021i	0.414962	+	0.909839i	$0.363795\pi$
$912$	−6.39756	−	4.59299i	−0.211844	−	0.152089i
$913$	−22.6281	+	2.57274i	−0.748881	+	0.0851453i
$914$	3.57021	−	14.5531i	0.118092	−	0.481373i
$915$	16.3245	+	17.5225i	0.539672	+	0.579275i
$916$	−13.2455	−	1.88702i	−0.437642	−	0.0623489i
$917$	−1.19181	+	0.579892i	−0.0393570	+	0.0191497i
$918$	−26.4602	−	14.7816i	−0.873317	−	0.487864i
$919$	12.9803	−	3.37980i	0.428180	−	0.111489i	−0.0316445	−	0.999499i	$-0.510074\pi$
$919$	12.9803	−	3.37980i	0.428180	−	0.111489i	0.459825	+	0.888010i	$0.347912\pi$
$920$	−2.85532	+	9.32360i	−0.0941371	+	0.307390i
$921$	−15.0057	+	6.27787i	−0.494456	+	0.206863i
$922$	−18.7240	+	25.3165i	−0.616643	+	0.833756i
$923$	−6.93962	−	44.2200i	−0.228420	−	1.45552i
$924$	−1.05869	+	1.71943i	−0.0348285	+	0.0565650i
$925$	10.3199	+	2.68708i	0.339315	+	0.0883508i
$926$	−2.29224	−	2.19693i	−0.0753277	−	0.0721958i
$927$	−5.19134	−	5.26533i	−0.170506	−	0.172936i
$928$	−0.0179324	+	0.114267i	−0.000588660	+	0.00375100i
$929$	−4.69167	−	4.01281i	−0.153929	−	0.131656i	0.569680	−	0.821867i	$-0.307067\pi$
$929$	−4.69167	−	4.01281i	−0.153929	−	0.131656i	−0.723608	+	0.690211i	$0.757518\pi$
$930$	−18.3737	−	9.59232i	−0.602499	−	0.314545i
$931$	−17.3388	+	30.0317i	−0.568257	+	0.984251i
$932$	11.6939	+	20.2544i	0.383046	+	0.663456i
$933$	0.751745	+	17.6967i	0.0246110	+	0.579363i
$934$	−30.3306	−	9.76020i	−0.992448	−	0.319363i
$935$	1.14330	+	16.1313i	0.0373900	+	0.527549i
$936$	2.89860	−	3.69564i	0.0947437	−	0.120796i
$937$	47.5152	+	36.1933i	1.55225	+	1.18238i	0.909049	+	0.416689i	$0.136809\pi$
$937$	47.5152	+	36.1933i	1.55225	+	1.18238i	0.643203	+	0.765695i	$0.277605\pi$
$938$	2.23319	+	6.61719i	0.0729161	+	0.216059i
$939$	41.4411	−	2.34829i	1.35238	−	0.0766336i
$940$	7.38395	+	4.69186i	0.240838	+	0.153032i
$941$	12.9132	−	25.6118i	0.420959	−	0.834922i	−0.578851	−	0.815433i	$-0.696499\pi$
$941$	12.9132	−	25.6118i	0.420959	−	0.834922i	0.999810	−	0.0194891i	$-0.00620396\pi$
$942$	−4.73731	+	0.134114i	−0.154350	+	0.00436967i
$943$	−36.7595	+	37.2835i	−1.19706	+	1.21412i
$944$	−2.18638	−	2.95618i	−0.0711605	−	0.0962153i
$945$	8.79395	+	5.24449i	0.286067	+	0.170603i
$946$	−10.7737	−	1.84733i	−0.350282	−	0.0600620i
$947$	−6.73146	−	15.4713i	−0.218743	−	0.502750i	0.772466	−	0.635056i	$-0.219023\pi$
$947$	−6.73146	−	15.4713i	−0.218743	−	0.502750i	−0.991209	+	0.132306i	$0.957762\pi$
$948$	−8.11092	+	9.21579i	−0.263430	+	0.299315i
$949$	10.1260	−	18.7445i	0.328703	−	0.608472i
$950$	−6.97682	−	0.197515i	−0.226358	−	0.00640824i
$951$	−26.0012	+	24.9202i	−0.843148	+	0.808092i
$952$	4.36580	−	2.43888i	0.141496	−	0.0790445i
$953$	−5.81867	+	8.35177i	−0.188485	+	0.270540i	−0.903518	−	0.428551i	$-0.859024\pi$
$953$	−5.81867	+	8.35177i	−0.188485	+	0.270540i	0.715033	+	0.699091i	$0.246412\pi$
$954$	0.433235	−	1.57227i	0.0140265	−	0.0509041i
$955$	11.4348	−	33.8825i	0.370020	−	1.09641i
$956$	3.30270	−	2.23224i	0.106817	−	0.0721957i
$957$	−0.247822	+	0.0353061i	−0.00801095	+	0.00114128i
$958$	16.3258	+	13.1822i	0.527464	+	0.425897i
$959$	−20.3793	+	4.09119i	−0.658083	+	0.132111i
$960$	1.00729	+	2.50674i	0.0325102	+	0.0809047i
$961$	−26.5238	+	8.53519i	−0.855607	+	0.275329i
$962$	13.2418	+	35.8545i	0.426934	+	1.15600i
$963$	−0.521741	−	2.12675i	−0.0168129	−	0.0685334i
$964$	2.94656	−	4.49541i	0.0949025	−	0.144788i
$965$	5.43249	−	12.4858i	0.174878	−	0.401933i
$966$	2.77186	+	5.90786i	0.0891832	+	0.190082i
$967$	−0.416546	−	29.4332i	−0.0133952	−	0.946506i	−0.887510	−	0.460788i	$-0.847567\pi$
$967$	−0.416546	−	29.4332i	−0.0133952	−	0.946506i	0.874115	−	0.485719i	$-0.161442\pi$
$968$	−5.29694	−	6.75347i	−0.170250	−	0.217065i
$969$	−31.2896	+	28.3341i	−1.00517	+	0.910222i
$970$	25.4796	−	18.2926i	0.818101	−	0.587339i
$971$	23.4921	−	14.9272i	0.753897	−	0.479037i	−0.102899	−	0.994692i	$-0.532812\pi$
$971$	23.4921	−	14.9272i	0.753897	−	0.479037i	0.856796	+	0.515655i	$0.172451\pi$
$972$	1.03272	+	10.3911i	0.0331245	+	0.333296i
$973$	2.40119	−	12.9047i	0.0769786	−	0.413705i
$974$	6.19931	−	15.4276i	0.198639	−	0.494332i
$975$	−0.536862	+	7.57479i	−0.0171934	+	0.242587i
$976$	−6.57093	−	5.95025i	−0.210330	−	0.190463i
$977$	20.0481	+	2.27941i	0.641396	+	0.0729247i	0.427621	−	0.903958i	$-0.359352\pi$
$977$	20.0481	+	2.27941i	0.641396	+	0.0729247i	0.213776	+	0.976883i	$0.431424\pi$
$978$	4.83623	−	13.0949i	0.154646	−	0.418729i
$979$	−0.476112	+	11.2081i	−0.0152166	+	0.358211i
$980$	10.5450	−	5.50517i	0.336846	−	0.175856i
$981$	−13.3866	−	3.08390i	−0.427402	−	0.0984613i
$982$	5.63249	+	10.4265i	0.179740	+	0.332722i
$983$	2.44445	+	4.84828i	0.0779659	+	0.154636i	0.928555	−	0.371195i	$-0.121052\pi$
$983$	2.44445	+	4.84828i	0.0779659	+	0.154636i	−0.850589	+	0.525831i	$0.823754\pi$
$984$	−1.43459	+	14.4347i	−0.0457331	+	0.460163i
$985$	25.0343	+	7.28081i	0.797658	+	0.231986i
$986$	0.578463	+	0.222991i	0.0184220	+	0.00710148i
$987$	5.77065	−	0.989477i	0.183682	−	0.0314954i
$988$	−13.7138	−	20.9224i	−0.436293	−	0.665629i
$989$	−24.0807	+	25.8478i	−0.765721	+	0.821913i
$990$	2.49346	−	2.01333i	0.0792475	−	0.0639879i
$991$	11.2789	−	13.5712i	0.358286	−	0.431102i	−0.559101	−	0.829100i	$-0.688853\pi$
$991$	11.2789	−	13.5712i	0.358286	−	0.431102i	0.917386	+	0.397998i	$0.130295\pi$
$992$	7.07779	+	2.96110i	0.224720	+	0.0940150i
$993$	−5.59527	+	3.33688i	−0.177560	+	0.105893i
$994$	−8.81264	+	3.39717i	−0.279520	+	0.107752i
$995$	17.5977	−	1.49778i	0.557884	−	0.0474829i
$996$	4.29607	+	19.9338i	0.136126	+	0.631628i
$997$	−8.01082	+	2.83040i	−0.253705	+	0.0896398i	−0.456964	−	0.889485i	$-0.651063\pi$
$997$	−8.01082	+	2.83040i	−0.253705	+	0.0896398i	0.203258	+	0.979125i	$0.434847\pi$
$998$	−2.57480	−	3.69572i	−0.0815039	−	0.116986i
$999$	−43.9530	−	21.3860i	−1.39061	−	0.676623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	446.2.g.a.101.6	yes	648
223.53	even	111	inner	446.2.g.a.53.6	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
446.2.g.a.53.6	✓	648	223.53	even	111	inner
446.2.g.a.101.6	yes	648	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.g (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.911228 - 0.411901i) q^{2} +(0.591281 - 1.26024i) q^{3} +(0.660675 + 0.750672i) q^{4} +(1.89116 - 0.435670i) q^{5} +(-1.05788 + 0.904814i) q^{6} +(0.489184 + 0.794485i) q^{7} +(-0.292823 - 0.956167i) q^{8} +(0.678917 + 0.816897i) q^{9} +(-1.90274 - 0.381978i) q^{10} +(0.284401 + 1.52845i) q^{11} +(1.33667 - 0.388749i) q^{12} +(4.40585 + 0.374993i) q^{13} +(-0.118509 - 0.925452i) q^{14} +(0.569161 - 2.64092i) q^{15} +(-0.127018 + 0.991900i) q^{16} +(5.05372 + 1.78559i) q^{17} +(-0.282168 - 1.02403i) q^{18} +(-5.64845 - 0.320074i) q^{19} +(1.57649 + 1.13181i) q^{20} +(1.29048 - 0.146724i) q^{21} +(0.370417 - 1.50991i) q^{22} +(-3.42496 - 3.67630i) q^{23} +(-1.37814 - 0.196337i) q^{24} +(-1.10934 + 0.539768i) q^{25} +(-3.86027 - 2.15648i) q^{26} +(5.47232 - 1.42488i) q^{27} +(-0.273206 + 0.892113i) q^{28} +(-0.106704 + 0.0446411i) q^{29} +(-1.60643 + 2.17204i) q^{30} +(1.18948 + 7.57947i) q^{31} +(0.524307 - 0.851529i) q^{32} +(2.09437 + 0.545332i) q^{33} +(-3.86961 - 3.70872i) q^{34} +(1.27126 + 1.28938i) q^{35} +(-0.164678 + 1.04935i) q^{36} +(-6.56894 - 5.61845i) q^{37} +(5.01519 + 2.61826i) q^{38} +(3.07767 - 5.33068i) q^{39} +(-0.970349 - 1.68069i) q^{40} +(-0.442258 - 10.4111i) q^{41} +(-1.23636 - 0.397853i) q^{42} +(-0.497070 - 7.01335i) q^{43} +(-0.959471 + 1.22330i) q^{44} +(1.63984 + 1.24910i) q^{45} +(1.60665 + 4.76069i) q^{46} +(4.50069 - 0.255035i) q^{47} +(1.17493 + 0.746564i) q^{48} +(2.75952 - 5.47318i) q^{49} +(1.23320 - 0.0349120i) q^{50} +(5.23844 - 5.31310i) q^{51} +(2.62934 + 3.55510i) q^{52} +(1.31868 + 0.786429i) q^{53} +(-5.57344 - 0.955663i) q^{54} +(1.20375 + 2.76665i) q^{55} +(0.616416 - 0.700384i) q^{56} +(-3.74319 + 6.92913i) q^{57} +(0.115619 + 0.00327321i) q^{58} +(-2.65452 + 2.54415i) q^{59} +(2.35849 - 1.31753i) q^{60} +(-5.06743 + 7.27349i) q^{61} +(2.03811 - 7.39658i) q^{62} +(-0.316897 + 0.939002i) q^{63} +(-0.828510 + 0.559975i) q^{64} +(8.49555 - 1.21032i) q^{65} +(-1.68383 - 1.35960i) q^{66} +(-7.33888 + 1.47329i) q^{67} +(1.99847 + 4.97339i) q^{68} +(-6.65812 + 2.14254i) q^{69} +(-0.627312 - 1.69855i) q^{70} +(-2.41187 - 9.83137i) q^{71} +(0.582287 - 0.888364i) q^{72} +(1.92227 - 4.41807i) q^{73} +(3.67156 + 7.82545i) q^{74} +(0.0243021 + 1.71719i) q^{75} +(-3.49152 - 4.45160i) q^{76} +(-1.07521 + 0.973646i) q^{77} +(-5.00018 + 3.58977i) q^{78} +(-7.44358 + 4.72975i) q^{79} +(0.191930 + 1.93118i) q^{80} +(0.857065 - 4.60612i) q^{81} +(-3.88534 + 9.66905i) q^{82} +(-1.03562 + 14.6119i) q^{83} +(0.962731 + 0.871794i) q^{84} +(10.3353 + 1.17509i) q^{85} +(-2.43586 + 6.59550i) q^{86} +(-0.00683357 + 0.160868i) q^{87} +(1.37818 - 0.719500i) q^{88} +(7.03153 + 1.61986i) q^{89} +(-0.979763 - 1.81367i) q^{90} +(1.85734 + 3.68382i) q^{91} +(0.496909 - 4.99986i) q^{92} +(10.2552 + 2.98257i) q^{93} +(-4.20621 - 1.62145i) q^{94} +(-10.8216 + 1.85555i) q^{95} +(-0.763115 - 1.16424i) q^{96} +(-11.0170 + 11.8255i) q^{97} +(-4.76897 + 3.85067i) q^{98} +(-1.05550 + 1.27002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 18 q^{2} + 2 q^{3} - 18 q^{4} + 3 q^{5} + 2 q^{6} + 4 q^{7} - 18 q^{8} + 13 q^{9} + 3 q^{10} - 33 q^{11} + 2 q^{12} - 10 q^{13} + 78 q^{14} + 2 q^{15} - 18 q^{16} + 10 q^{17} + 13 q^{18} - 3 q^{19}+ \cdots - 323 q^{99}+O(q^{100}) \) 648 * q - 18 * q^2 + 2 * q^3 - 18 * q^4 + 3 * q^5 + 2 * q^6 + 4 * q^7 - 18 * q^8 + 13 * q^9 + 3 * q^10 - 33 * q^11 + 2 * q^12 - 10 * q^13 + 78 * q^14 + 2 * q^15 - 18 * q^16 + 10 * q^17 + 13 * q^18 - 3 * q^19 + 3 * q^20 + 15 * q^21 + 4 * q^22 - 5 * q^23 - 35 * q^24 + 22 * q^25 - 10 * q^26 - 22 * q^27 + 4 * q^28 + 258 * q^29 - 109 * q^30 + 11 * q^31 - 18 * q^32 - 2 * q^33 + 10 * q^34 - 9 * q^35 + 13 * q^36 - 27 * q^37 - 3 * q^38 - 9 * q^39 - 71 * q^40 - 63 * q^41 + 15 * q^42 - 26 * q^43 + 4 * q^44 + 9 * q^45 - 42 * q^46 - 102 * q^47 + 2 * q^48 + 2 * q^49 + 22 * q^50 - 85 * q^51 - 10 * q^52 - 8 * q^53 - 22 * q^54 - 6 * q^55 + 4 * q^56 - 105 * q^57 - 75 * q^58 + 156 * q^59 + 2 * q^60 - 15 * q^61 - 211 * q^62 - 24 * q^63 - 18 * q^64 + 7 * q^65 - 113 * q^66 - 71 * q^67 + 10 * q^68 - 215 * q^69 - 83 * q^70 + 16 * q^71 + 87 * q^72 - 11 * q^73 + 158 * q^74 - 101 * q^75 - 3 * q^76 + 33 * q^77 - 9 * q^78 - 216 * q^79 + 3 * q^80 - 229 * q^81 - 26 * q^82 - 140 * q^83 + 15 * q^84 - 77 * q^85 + 11 * q^86 + 128 * q^87 + 4 * q^88 + 162 * q^89 + 9 * q^90 + 20 * q^91 - 79 * q^92 - 26 * q^93 - 28 * q^94 - 204 * q^95 + 2 * q^96 + 8 * q^97 - 35 * q^98 - 323 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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