LMFDB - Embedded newform 507.2.k.k.188.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.2
Character	$\chi$	$=$	507.188
Dual form			507.2.k.k.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49335 + 0.668092i) q^{2} +(0.116023 + 1.72816i) q^{3} +(4.03841 - 2.33158i) q^{4} +(-0.624703 - 0.624703i) q^{5} +(-1.44386 - 4.23140i) q^{6} +(0.435181 - 1.62412i) q^{7} +(-4.86096 + 4.86096i) q^{8} +(-2.97308 + 0.401012i) q^{9} +O(q^{10})$	\(q+(-2.49335 + 0.668092i) q^{2} +(0.116023 + 1.72816i) q^{3} +(4.03841 - 2.33158i) q^{4} +(-0.624703 - 0.624703i) q^{5} +(-1.44386 - 4.23140i) q^{6} +(0.435181 - 1.62412i) q^{7} +(-4.86096 + 4.86096i) q^{8} +(-2.97308 + 0.401012i) q^{9} +(1.97496 + 1.14025i) q^{10} +(0.0927163 + 0.346022i) q^{11} +(4.49789 + 6.70851i) q^{12} +4.34024i q^{14} +(1.00711 - 1.15207i) q^{15} +(4.20937 - 7.29084i) q^{16} +(-1.31381 - 2.27558i) q^{17} +(7.14502 - 2.98615i) q^{18} +(5.90581 + 1.58246i) q^{19} +(-3.97935 - 1.06626i) q^{20} +(2.85722 + 0.563628i) q^{21} +(-0.462349 - 0.800812i) q^{22} +(2.70887 - 4.69190i) q^{23} +(-8.96451 - 7.83654i) q^{24} -4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(-2.02932 - 7.57351i) q^{28} +(7.24949 + 4.18549i) q^{29} +(-1.74139 + 3.54535i) q^{30} +(-1.27341 + 1.27341i) q^{31} +(-2.06602 + 7.71050i) q^{32} +(-0.587225 + 0.200375i) q^{33} +(4.79608 + 4.79608i) q^{34} +(-1.28645 + 0.742731i) q^{35} +(-11.0715 + 8.55142i) q^{36} +(-3.33944 + 0.894800i) q^{37} -15.7825 q^{38} +6.07331 q^{40} +(6.68847 - 1.79217i) q^{41} +(-7.50063 + 0.503566i) q^{42} +(0.825277 - 0.476474i) q^{43} +(1.18121 + 1.18121i) q^{44} +(2.10780 + 1.60678i) q^{45} +(-3.61955 + 13.5083i) q^{46} +(5.33521 - 5.33521i) q^{47} +(13.0881 + 6.42856i) q^{48} +(3.61381 + 2.08643i) q^{49} +(2.81901 + 10.5207i) q^{50} +(3.78013 - 2.53449i) q^{51} +9.69778i q^{53} +(5.98954 + 12.0013i) q^{54} +(0.158241 - 0.274081i) q^{55} +(5.77937 + 10.0102i) q^{56} +(-2.04953 + 10.3898i) q^{57} +(-20.8718 - 5.59259i) q^{58} +(9.95670 + 2.66789i) q^{59} +(1.38098 - 7.00067i) q^{60} +(-2.43931 - 4.22500i) q^{61} +(2.32431 - 4.02583i) q^{62} +(-0.642536 + 5.00314i) q^{63} -3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(3.25877 + 12.1619i) q^{67} +(-10.6114 - 6.12649i) q^{68} +(8.42264 + 4.13699i) q^{69} +(2.71136 - 2.71136i) q^{70} +(0.832745 - 3.10785i) q^{71} +(12.5027 - 16.4013i) q^{72} +(-0.246530 - 0.246530i) q^{73} +(7.72860 - 4.46211i) q^{74} +(7.29196 - 0.489557i) q^{75} +(27.5397 - 7.37925i) q^{76} +0.602329 q^{77} -3.68180 q^{79} +(-7.18422 + 1.92500i) q^{80} +(8.67838 - 2.38448i) q^{81} +(-15.4794 + 8.93703i) q^{82} +(-8.47001 - 8.47001i) q^{83} +(12.8528 - 4.38568i) q^{84} +(-0.600822 + 2.24230i) q^{85} +(-1.73938 + 1.73938i) q^{86} +(-6.39210 + 13.0139i) q^{87} +(-2.13269 - 1.23131i) q^{88} +(-1.77317 - 6.61757i) q^{89} +(-6.32897 - 2.59806i) q^{90} -25.2638i q^{92} +(-2.34841 - 2.05292i) q^{93} +(-9.73816 + 16.8670i) q^{94} +(-2.70081 - 4.67794i) q^{95} +(-13.5647 - 2.67583i) q^{96} +(5.11027 + 1.36929i) q^{97} +(-10.4044 - 2.78786i) q^{98} +(-0.414412 - 0.991570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9}+O(q^{10}) $ 96 * q + 24 * q^9	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−2.49335	+	0.668092i	−1.76307	+	0.472412i	−0.987335	−	0.158650i	$-0.949286\pi$
$2$	−2.49335	+	0.668092i	−1.76307	+	0.472412i	−0.775732	+	0.631062i	$0.782619\pi$
$3$	0.116023	+	1.72816i	0.0669857	+	0.997754i
$3$	0.116023	+	1.72816i	0.0669857	+	0.997754i
$4$	4.03841	−	2.33158i	2.01921	−	1.16579i
$5$	−0.624703	−	0.624703i	−0.279376	−	0.279376i	0.553484	−	0.832860i	$-0.313298\pi$
$5$	−0.624703	−	0.624703i	−0.279376	−	0.279376i	−0.832860	+	0.553484i	$0.813298\pi$
$6$	−1.44386	−	4.23140i	−0.589452	−	1.72746i
$7$	0.435181	−	1.62412i	0.164483	−	0.613858i	−0.833623	−	0.552334i	$-0.813737\pi$
$7$	0.435181	−	1.62412i	0.164483	−	0.613858i	0.998106	−	0.0615241i	$-0.0195961\pi$
$8$	−4.86096	+	4.86096i	−1.71861	+	1.71861i
$9$	−2.97308	+	0.401012i	−0.991026	+	0.133671i
$10$	1.97496	+	1.14025i	0.624538	+	0.360577i
$11$	0.0927163	+	0.346022i	0.0279550	+	0.104330i	0.978494	−	0.206277i	$-0.0661347\pi$
$11$	0.0927163	+	0.346022i	0.0279550	+	0.104330i	−0.950539	+	0.310606i	$0.899468\pi$
$12$	4.49789	+	6.70851i	1.29843	+	1.93658i
$13$		0			0
$13$		0			0
$14$			4.34024i			1.15998i
$15$	1.00711	−	1.15207i	0.260034	−	0.297462i
$16$	4.20937	−	7.29084i	1.05234	−	1.82271i
$17$	−1.31381	−	2.27558i	−0.318645	−	0.551909i	0.661561	−	0.749892i	$-0.269894\pi$
$17$	−1.31381	−	2.27558i	−0.318645	−	0.551909i	−0.980206	+	0.197983i	$0.936561\pi$
$18$	7.14502	−	2.98615i	1.68410	−	0.703843i
$19$	5.90581	+	1.58246i	1.35488	+	0.363040i	0.861936	−	0.507018i	$-0.169252\pi$
$19$	5.90581	+	1.58246i	1.35488	+	0.363040i	0.492949	+	0.870058i	$0.335919\pi$
$20$	−3.97935	−	1.06626i	−0.889810	−	0.238424i
$21$	2.85722	+	0.563628i	0.623498	+	0.122994i
$22$	−0.462349	−	0.800812i	−0.0985732	−	0.170734i
$23$	2.70887	−	4.69190i	0.564838	−	0.978328i	−0.432227	−	0.901765i	$-0.642272\pi$
$23$	2.70887	−	4.69190i	0.564838	−	0.978328i	0.997065	−	0.0765633i	$-0.0243947\pi$
$24$	−8.96451	−	7.83654i	−1.82987	−	1.59963i
$25$		−	4.21949i		−	0.843899i
$26$		0			0
$27$	−1.03796	−	5.09143i	−0.199755	−	0.979846i
$28$	−2.02932	−	7.57351i	−0.383505	−	1.43126i
$29$	7.24949	+	4.18549i	1.34620	+	0.777227i	0.987708	−	0.156308i	$-0.0499592\pi$
$29$	7.24949	+	4.18549i	1.34620	+	0.777227i	0.358488	+	0.933535i	$0.383293\pi$
$30$	−1.74139	+	3.54535i	−0.317932	+	0.647289i
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	−0.812154	−	0.583443i	$-0.801705\pi$
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	0.583443	+	0.812154i	$0.301705\pi$
$32$	−2.06602	+	7.71050i	−0.365225	+	1.36304i
$33$	−0.587225	+	0.200375i	−0.102223	+	0.0348808i
$34$	4.79608	+	4.79608i	0.822521	+	0.822521i
$35$	−1.28645	+	0.742731i	−0.217449	+	0.125545i
$36$	−11.0715	+	8.55142i	−1.84526	+	1.42524i
$37$	−3.33944	+	0.894800i	−0.549001	+	0.147104i	−0.522648	−	0.852548i	$-0.675056\pi$
$37$	−3.33944	+	0.894800i	−0.549001	+	0.147104i	−0.0263524	+	0.999653i	$0.508389\pi$
$38$	−15.7825			−2.56026
$39$		0			0
$40$	6.07331			0.960275
$41$	6.68847	−	1.79217i	1.04456	−	0.279890i	0.304560	−	0.952493i	$-0.401490\pi$
$41$	6.68847	−	1.79217i	1.04456	−	0.279890i	0.740004	+	0.672603i	$0.234824\pi$
$42$	−7.50063	+	0.503566i	−1.15737	+	0.0777019i
$43$	0.825277	−	0.476474i	0.125854	−	0.0726616i	−0.435752	−	0.900067i	$-0.643517\pi$
$43$	0.825277	−	0.476474i	0.125854	−	0.0726616i	0.561605	+	0.827405i	$0.310184\pi$
$44$	1.18121	+	1.18121i	0.178073	+	0.178073i
$45$	2.10780	+	1.60678i	0.314213	+	0.239524i
$46$	−3.61955	+	13.5083i	−0.533673	+	1.99170i
$47$	5.33521	−	5.33521i	0.778220	−	0.778220i	−0.201308	−	0.979528i	$-0.564519\pi$
$47$	5.33521	−	5.33521i	0.778220	−	0.778220i	0.979528	+	0.201308i	$0.0645191\pi$
$48$	13.0881	+	6.42856i	1.88911	+	0.927883i
$49$	3.61381	+	2.08643i	0.516258	+	0.298062i
$50$	2.81901	+	10.5207i	0.398668	+	1.48785i
$51$	3.78013	−	2.53449i	0.529325	−	0.354899i
$52$		0			0
$53$			9.69778i			1.33209i	0.745911	+	0.666046i	$0.232015\pi$
$53$			9.69778i			1.33209i	−0.745911	+	0.666046i	$0.767985\pi$
$54$	5.98954	+	12.0013i	0.815073	+	1.63317i
$55$	0.158241	−	0.274081i	0.0213372	−	0.0369571i
$56$	5.77937	+	10.0102i	0.772301	+	1.33766i
$57$	−2.04953	+	10.3898i	−0.271467	+	1.37616i
$58$	−20.8718	−	5.59259i	−2.74061	−	0.734343i
$59$	9.95670	+	2.66789i	1.29625	+	0.347330i	0.840032	−	0.542538i	$-0.182536\pi$
$59$	9.95670	+	2.66789i	1.29625	+	0.347330i	0.456220	+	0.889867i	$0.349203\pi$
$60$	1.38098	−	7.00067i	0.178284	−	0.903783i
$61$	−2.43931	−	4.22500i	−0.312321	−	0.540956i	0.666543	−	0.745466i	$-0.267773\pi$
$61$	−2.43931	−	4.22500i	−0.312321	−	0.540956i	−0.978864	+	0.204510i	$0.934440\pi$
$62$	2.32431	−	4.02583i	0.295188	−	0.511281i
$63$	−0.642536	+	5.00314i	−0.0809520	+	0.630336i
$64$		−	3.76781i		−	0.470977i
$65$		0			0
$66$	1.33029	−	0.891926i	0.163747	−	0.109789i
$67$	3.25877	+	12.1619i	0.398122	+	1.48581i	0.816397	+	0.577491i	$0.195968\pi$
$67$	3.25877	+	12.1619i	0.398122	+	1.48581i	−0.418275	+	0.908320i	$0.637365\pi$
$68$	−10.6114	−	6.12649i	−1.28682	−	0.742946i
$69$	8.42264	+	4.13699i	1.01397	+	0.498035i
$70$	2.71136	−	2.71136i	0.324069	−	0.324069i
$71$	0.832745	−	3.10785i	0.0988287	−	0.368834i	−0.898743	−	0.438475i	$-0.855519\pi$
$71$	0.832745	−	3.10785i	0.0988287	−	0.368834i	0.997572	+	0.0696413i	$0.0221855\pi$
$72$	12.5027	−	16.4013i	1.47346	−	1.93291i
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	0.692532	−	0.721387i	$-0.256495\pi$
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	−0.721387	+	0.692532i	$0.756495\pi$
$74$	7.72860	−	4.46211i	0.898431	−	0.518709i
$75$	7.29196	−	0.489557i	0.842003	−	0.0565291i
$76$	27.5397	−	7.37925i	3.15902	−	0.846457i
$77$	0.602329			0.0686417
$78$		0			0
$79$	−3.68180			−0.414235			−0.207118	−	0.978316i	$-0.566408\pi$
$79$	−3.68180			−0.414235			−0.207118	+	0.978316i	$0.566408\pi$
$80$	−7.18422	+	1.92500i	−0.803220	+	0.215222i
$81$	8.67838	−	2.38448i	0.964264	−	0.264942i
$82$	−15.4794	+	8.93703i	−1.70941	+	0.986930i
$83$	−8.47001	−	8.47001i	−0.929705	−	0.929705i	0.0679819	−	0.997687i	$-0.478344\pi$
$83$	−8.47001	−	8.47001i	−0.929705	−	0.929705i	−0.997687	+	0.0679819i	$0.978344\pi$
$84$	12.8528	−	4.38568i	1.40236	−	0.478517i
$85$	−0.600822	+	2.24230i	−0.0651683	+	0.243211i
$86$	−1.73938	+	1.73938i	−0.187562	+	0.187562i
$87$	−6.39210	+	13.0139i	−0.685305	+	1.39524i
$88$	−2.13269	−	1.23131i	−0.227346	−	0.131258i
$89$	−1.77317	−	6.61757i	−0.187956	−	0.701461i	−0.993978	−	0.109576i	$-0.965051\pi$
$89$	−1.77317	−	6.61757i	−0.187956	−	0.701461i	0.806022	−	0.591885i	$-0.201616\pi$
$90$	−6.32897	−	2.59806i	−0.667132	−	0.273859i
$91$		0			0
$92$		−	25.2638i		−	2.63393i
$93$	−2.34841	−	2.05292i	−0.243519	−	0.212878i
$94$	−9.73816	+	16.8670i	−1.00441	+	1.73970i
$95$	−2.70081	−	4.67794i	−0.277097	−	0.479946i
$96$	−13.5647	−	2.67583i	−1.38444	−	0.273100i
$97$	5.11027	+	1.36929i	0.518870	+	0.139031i	0.508744	−	0.860918i	$-0.330110\pi$
$97$	5.11027	+	1.36929i	0.518870	+	0.139031i	0.0101260	+	0.999949i	$0.496777\pi$
$98$	−10.4044	−	2.78786i	−1.05101	−	0.281616i
$99$	−0.414412	−	0.991570i	−0.0416499	−	0.0996566i
$100$	−9.83809	−	17.0401i	−0.983809	−	1.70401i
$101$	−4.24104	+	7.34570i	−0.421999	+	0.730924i	−0.996135	−	0.0878358i	$-0.972005\pi$
$101$	−4.24104	+	7.34570i	−0.421999	+	0.730924i	0.574136	+	0.818760i	$0.305338\pi$
$102$	−7.73194	+	8.84485i	−0.765576	+	0.875770i
$103$		−	0.554855i		−	0.0546714i	−0.999626	−	0.0273357i	$-0.991298\pi$
$103$		−	0.554855i		−	0.0546714i	0.999626	−	0.0273357i	$-0.00870232\pi$
$104$		0			0
$105$	−1.43282	−	2.13702i	−0.139829	−	0.208551i
$106$	−6.47901	−	24.1800i	−0.629297	−	2.34857i
$107$	−2.87486	−	1.65980i	−0.277923	−	0.160459i	0.354560	−	0.935033i	$-0.384631\pi$
$107$	−2.87486	−	1.65980i	−0.277923	−	0.160459i	−0.632483	+	0.774574i	$0.717964\pi$
$108$	−16.0628	−	18.1412i	−1.54564	−	1.74564i
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	−0.607319	−	0.794458i	$-0.707755\pi$
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	0.794458	+	0.607319i	$0.207755\pi$
$110$	−0.211439	+	0.789101i	−0.0201599	+	0.0752378i
$111$	−1.93381	−	5.66727i	−0.183549	−	0.537914i
$112$	−10.0093	−	10.0093i	−0.945794	−	0.945794i
$113$	4.96947	−	2.86913i	0.467489	−	0.269905i	−0.247699	−	0.968837i	$-0.579674\pi$
$113$	4.96947	−	2.86913i	0.467489	−	0.269905i	0.715188	+	0.698932i	$0.246341\pi$
$114$	−1.83113	−	27.2747i	−0.171501	−	2.55451i
$115$	−4.62328	+	1.23880i	−0.431123	+	0.115519i
$116$	39.0352			3.62433
$117$		0			0
$118$	−26.6080			−2.44946
$119$	−4.26755	+	1.14349i	−0.391205	+	0.104823i
$120$	0.704642	+	10.4957i	0.0643247	+	0.958119i
$121$	9.41514	−	5.43584i	0.855922	−	0.494167i
$122$	8.90475	+	8.90475i	0.806198	+	0.806198i
$123$	3.87317	+	11.3508i	0.349232	+	1.02347i
$124$	−2.17351	+	8.11164i	−0.195187	+	0.728447i
$125$	−5.75944	+	5.75944i	−0.515140	+	0.515140i
$126$	−1.74049	−	12.9039i	−0.155055	−	1.14957i
$127$	−11.7986	−	6.81191i	−1.04695	−	0.604459i	−0.125159	−	0.992137i	$-0.539944\pi$
$127$	−11.7986	−	6.81191i	−1.04695	−	0.604459i	−0.921795	+	0.387678i	$0.873277\pi$
$128$	−1.61480	−	6.02651i	−0.142729	−	0.532673i
$129$	0.919175	+	1.37093i	0.0809288	+	0.120704i
$130$		0			0
$131$			6.35913i			0.555599i	0.960639	+	0.277800i	$0.0896052\pi$
$131$			6.35913i			0.555599i	−0.960639	+	0.277800i	$0.910395\pi$
$132$	−1.90427	+	2.17836i	−0.165745	+	0.189602i
$133$	5.14019	−	8.90306i	0.445711	−	0.771993i
$134$	−16.2505	−	28.1467i	−1.40383	−	2.43151i
$135$	−2.53222	+	3.82904i	−0.217938	+	0.329552i
$136$	17.4479	+	4.67514i	1.49614	+	0.400890i
$137$	1.97329	+	0.528741i	0.168589	+	0.0451734i	0.342126	−	0.939654i	$-0.388853\pi$
$137$	1.97329	+	0.528741i	0.168589	+	0.0451734i	−0.173537	+	0.984827i	$0.555520\pi$
$138$	−23.7645	−	4.68789i	−2.02297	−	0.399059i
$139$	2.55676	+	4.42843i	0.216861	+	0.375615i	0.953847	−	0.300294i	$-0.0970848\pi$
$139$	2.55676	+	4.42843i	0.216861	+	0.375615i	−0.736986	+	0.675908i	$0.763751\pi$
$140$	−3.46348	+	5.99892i	−0.292717	+	0.507001i
$141$	9.83911	+	8.60110i	0.828602	+	0.724343i
$142$			8.30531i			0.696966i
$143$		0			0
$144$	−9.59107	+	23.3642i	−0.799256	+	1.94702i
$145$	−1.91409	−	7.14346i	−0.158956	−	0.593232i
$146$	0.779393	+	0.449983i	0.0645030	+	0.0372408i
$147$	−3.18641	+	6.48731i	−0.262810	+	0.535064i
$148$	−11.3997	+	11.3997i	−0.937053	+	0.937053i
$149$	2.74363	−	10.2394i	0.224767	−	0.838841i	−0.757731	−	0.652567i	$-0.773692\pi$
$149$	2.74363	−	10.2394i	0.224767	−	0.838841i	0.982498	−	0.186274i	$-0.0596412\pi$
$150$	−17.8544	+	6.09234i	−1.45780	+	0.497437i
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	0.383925	−	0.923364i	$-0.374572\pi$
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	−0.923364	+	0.383925i	$0.874572\pi$
$152$	−36.4002	+	21.0156i	−2.95244	+	1.70459i
$153$	4.81858	+	6.23862i	0.389559	+	0.504362i
$154$	−1.50182	+	0.402411i	−0.121020	+	0.0324272i
$155$	1.59101			0.127793
$156$		0			0
$157$	21.9960			1.75547			0.877735	−	0.479147i	$-0.159054\pi$
$157$	21.9960			1.75547			0.877735	+	0.479147i	$0.159054\pi$
$158$	9.18004	−	2.45978i	0.730325	−	0.195690i
$159$	−16.7593	+	1.12516i	−1.32910	+	0.0892311i
$160$	6.10742	−	3.52612i	0.482834	−	0.278764i
$161$	−6.44134	−	6.44134i	−0.507649	−	0.507649i
$162$	−20.0452	+	11.7433i	−1.57490	+	0.922641i
$163$	5.32291	−	19.8654i	0.416923	−	1.55598i	−0.364030	−	0.931387i	$-0.618600\pi$
$163$	5.32291	−	19.8654i	0.416923	−	1.55598i	0.780953	−	0.624590i	$-0.214734\pi$
$164$	22.8322	−	22.8322i	1.78290	−	1.78290i
$165$	0.492016	+	0.241666i	0.0383034	+	0.0188137i
$166$	26.7775	+	15.4600i	2.07834	+	1.19993i
$167$	−2.59464	−	9.68331i	−0.200779	−	0.749317i	−0.990695	−	0.136102i	$-0.956542\pi$
$167$	−2.59464	−	9.68331i	−0.200779	−	0.749317i	0.789916	−	0.613215i	$-0.210124\pi$
$168$	−16.6286	+	11.1491i	−1.28293	+	0.860171i
$169$		0			0
$170$		−	5.99225i		−	0.459584i
$171$	−18.1930	−	2.33647i	−1.39125	−	0.178674i
$172$	2.22188	−	3.84840i	0.169416	−	0.293438i
$173$	5.88220	+	10.1883i	0.447215	+	0.774599i	0.998204	−	0.0599136i	$-0.0190825\pi$
$173$	5.88220	+	10.1883i	0.447215	+	0.774599i	−0.550988	+	0.834513i	$0.685749\pi$
$174$	7.24329	−	36.7187i	0.549112	−	2.78364i
$175$	−6.85295	−	1.83624i	−0.518034	−	0.138807i
$176$	2.91307	+	0.780555i	0.219581	+	0.0588365i
$177$	−3.45534	+	17.5163i	−0.259719	+	1.31661i
$178$	8.84230	+	15.3153i	0.662758	+	1.14793i
$179$	−5.90594	+	10.2294i	−0.441431	+	0.764580i	−0.997796	−	0.0663576i	$-0.978862\pi$
$179$	−5.90594	+	10.2294i	−0.441431	+	0.764580i	0.556365	+	0.830938i	$0.312196\pi$
$180$	12.2585	+	1.57432i	0.913695	+	0.117343i
$181$		−	20.0999i		−	1.49402i	−0.664815	−	0.747008i	$-0.731490\pi$
$181$		−	20.0999i		−	1.49402i	0.664815	−	0.747008i	$-0.268510\pi$
$182$		0			0
$183$	7.01847	−	4.70571i	0.518820	−	0.347856i
$184$	9.63943	+	35.9749i	0.710628	+	2.65210i
$185$	2.64514	+	1.52717i	0.194475	+	0.112280i
$186$	7.22695	+	3.54970i	0.529906	+	0.260277i
$187$	0.665589	−	0.665589i	0.0486727	−	0.0486727i
$188$	9.10632	−	33.9853i	0.664147	−	2.47863i
$189$	−8.72077	−	0.529929i	−0.634343	−	0.0385467i
$190$	9.85936	+	9.85936i	0.715274	+	0.715274i
$191$	14.6715	−	8.47057i	1.06159	−	0.612909i	0.135718	−	0.990748i	$-0.456666\pi$
$191$	14.6715	−	8.47057i	1.06159	−	0.612909i	0.925871	+	0.377839i	$0.123333\pi$
$192$	6.51139	−	0.437152i	0.469919	−	0.0315487i
$193$	16.1609	−	4.33031i	1.16329	−	0.311702i	0.375010	−	0.927021i	$-0.377639\pi$
$193$	16.1609	−	4.33031i	1.16329	−	0.311702i	0.788279	+	0.615318i	$0.210973\pi$
$194$	−13.6565			−0.980482
$195$		0			0
$196$	19.4587			1.38991
$197$	−14.1277	+	3.78551i	−1.00656	+	0.269706i	−0.724190	−	0.689600i	$-0.757786\pi$
$197$	−14.1277	+	3.78551i	−1.00656	+	0.269706i	−0.282367	+	0.959306i	$0.591120\pi$
$198$	1.69574	+	2.19547i	0.120511	+	0.156025i
$199$	−0.289508	+	0.167148i	−0.0205227	+	0.0118488i	−0.510226	−	0.860040i	$-0.670438\pi$
$199$	−0.289508	+	0.167148i	−0.0205227	+	0.0118488i	0.489704	+	0.871889i	$0.337105\pi$
$200$	20.5108	+	20.5108i	1.45033	+	1.45033i
$201$	−20.6396	+	7.04273i	−1.45581	+	0.496756i
$202$	5.66681	−	21.1488i	0.398716	−	1.48803i
$203$	9.95256	−	9.95256i	0.698533	−	0.698533i
$204$	9.35639	−	19.0490i	0.655078	−	1.33370i
$205$	−5.29788	−	3.05873i	−0.370020	−	0.213631i
$206$	0.370694	+	1.38345i	0.0258275	+	0.0963894i
$207$	−6.17217	+	15.0357i	−0.428996	+	1.04505i
$208$		0			0
$209$			2.19026i			0.151503i
$210$	5.00024	+	4.37108i	0.345049	+	0.301633i
$211$	1.34455	−	2.32883i	0.0925626	−	0.160323i	−0.816026	−	0.578015i	$-0.803828\pi$
$211$	1.34455	−	2.32883i	0.0925626	−	0.160323i	0.908589	+	0.417692i	$0.137161\pi$
$212$	22.6111	+	39.1636i	1.55294	+	2.68977i
$213$	5.46748	+	1.07854i	0.374625	+	0.0739001i
$214$	8.27694	+	2.21780i	0.565800	+	0.151606i
$215$	−0.813208	−	0.217898i	−0.0554603	−	0.0148605i
$216$	29.7947	+	19.7038i	2.02727	+	1.34067i
$217$	1.51401	+	2.62234i	0.102778	+	0.178016i
$218$	−3.56617	+	6.17679i	−0.241532	+	0.418345i
$219$	0.397441	−	0.454647i	0.0268566	−	0.0307222i
$220$		−	1.47580i		−	0.0994987i
$221$		0			0
$222$	8.60793	+	12.8386i	0.577726	+	0.861667i
$223$	2.00597	+	7.48636i	0.134329	+	0.501324i	1.00000		0.000709598i	$0.000225872\pi$
$223$	2.00597	+	7.48636i	0.134329	+	0.501324i	−0.865670	+	0.500614i	$0.833107\pi$
$224$	11.6237	+	6.71092i	0.776638	+	0.448392i
$225$	1.69207	+	12.5449i	0.112804	+	0.836325i
$226$	−10.4738	+	10.4738i	−0.696708	+	0.696708i
$227$	−4.85285	+	18.1111i	−0.322095	+	1.20207i	0.595105	+	0.803648i	$0.297110\pi$
$227$	−4.85285	+	18.1111i	−0.322095	+	1.20207i	−0.917200	+	0.398427i	$0.869556\pi$
$228$	15.9478	+	46.7369i	1.05617	+	3.09523i
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	0.386178	−	0.922424i	$-0.373795\pi$
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	−0.922424	+	0.386178i	$0.873795\pi$
$230$	10.6998	−	6.17755i	0.705526	−	0.407336i
$231$	0.0698838	+	1.04092i	0.00459801	+	0.0684875i
$232$	−55.5850	+	14.8940i	−3.64934	+	0.977837i
$233$	11.2799			0.738973			0.369486	−	0.929236i	$-0.379534\pi$
$233$	11.2799			0.738973			0.369486	+	0.929236i	$0.379534\pi$
$234$		0			0
$235$	−6.66584			−0.434832
$236$	46.4297	−	12.4408i	3.02231	−	0.809827i
$237$	−0.427173	−	6.36275i	−0.0277478	−	0.413305i
$238$	9.87655	−	5.70223i	0.640202	−	0.369621i
$239$	1.32193	+	1.32193i	0.0855084	+	0.0855084i	0.748567	−	0.663059i	$-0.230742\pi$
$239$	1.32193	+	1.32193i	0.0855084	+	0.0855084i	−0.663059	+	0.748567i	$0.730742\pi$
$240$	−4.16025	−	12.1921i	−0.268543	−	0.786999i
$241$	−6.02040	+	22.4684i	−0.387808	+	1.44732i	0.445885	+	0.895090i	$0.352889\pi$
$241$	−6.02040	+	22.4684i	−0.387808	+	1.44732i	−0.833693	+	0.552228i	$0.813778\pi$
$242$	−19.8436	+	19.8436i	−1.27560	+	1.27560i
$243$	5.12765	+	14.7210i	0.328939	+	0.944351i
$244$	−19.7019	−	11.3749i	−1.26128	−	0.728202i
$245$	−0.954155	−	3.56095i	−0.0609587	−	0.227501i
$246$	−17.2406	−	25.7140i	−1.09922	−	1.63946i
$247$		0			0
$248$		−	12.3800i		−	0.786133i
$249$	13.6548	−	15.6203i	0.865340	−	0.989893i
$250$	10.5125	−	18.2082i	0.664868	−	1.15159i
$251$	−5.39681	−	9.34756i	−0.340644	−	0.590013i	0.643909	−	0.765102i	$-0.277312\pi$
$251$	−5.39681	−	9.34756i	−0.340644	−	0.590013i	−0.984552	+	0.175090i	$0.943978\pi$
$252$	9.07038	+	21.7029i	0.571380	+	1.36715i
$253$	1.87466	+	0.502313i	0.117859	+	0.0315801i
$254$	33.9690	+	9.10196i	2.13140	+	0.571108i
$255$	−3.94476	−	0.778159i	−0.247030	−	0.0487302i
$256$	11.8203	+	20.4734i	0.738771	+	1.27959i
$257$	−2.12801	+	3.68582i	−0.132741	+	0.229915i	−0.924732	−	0.380618i	$-0.875711\pi$
$257$	−2.12801	+	3.68582i	−0.132741	+	0.229915i	0.791991	+	0.610533i	$0.209045\pi$
$258$	−3.20773	−	2.80412i	−0.199705	−	0.174577i
$259$			5.81304i			0.361205i
$260$		0			0
$261$	−23.2317	−	9.53667i	−1.43801	−	0.590305i
$262$	−4.24848	−	15.8555i	−0.262472	−	0.979559i
$263$	−21.9508	−	12.6733i	−1.35355	−	0.781470i	−0.364801	−	0.931085i	$-0.618863\pi$
$263$	−21.9508	−	12.6733i	−1.35355	−	0.781470i	−0.988744	+	0.149615i	$0.952196\pi$
$264$	1.88046	−	3.82849i	0.115734	−	0.235627i
$265$	6.05823	−	6.05823i	0.372154	−	0.372154i
$266$	−6.86823	+	25.6326i	−0.421118	+	1.57164i
$267$	11.2305	−	3.83212i	0.687295	−	0.234522i
$268$	41.5167	+	41.5167i	2.53604	+	2.53604i
$269$	19.6286	−	11.3326i	1.19677	−	0.690958i	0.236940	−	0.971524i	$-0.423855\pi$
$269$	19.6286	−	11.3326i	1.19677	−	0.690958i	0.959835	+	0.280566i	$0.0905222\pi$
$270$	3.75555	−	11.2389i	0.228556	−	0.683979i
$271$	−20.5887	+	5.51672i	−1.25067	+	0.335117i	−0.822597	−	0.568625i	$-0.807476\pi$
$271$	−20.5887	+	5.51672i	−1.25067	+	0.335117i	−0.428077	+	0.903742i	$0.640809\pi$
$272$	−22.1212			−1.34129
$273$		0			0
$274$	−5.27335			−0.318575
$275$	1.46004	−	0.391216i	0.0880436	−	0.0235912i
$276$	43.6599	−	2.93117i	2.62801	−	0.176436i
$277$	−9.25074	+	5.34092i	−0.555823	+	0.320905i	−0.751467	−	0.659770i	$-0.770654\pi$
$277$	−9.25074	+	5.34092i	−0.555823	+	0.320905i	0.195644	+	0.980675i	$0.437320\pi$
$278$	−9.33349	−	9.33349i	−0.559786	−	0.559786i
$279$	3.27530	−	4.29661i	0.196087	−	0.257231i
$280$	2.64299	−	9.86377i	0.157949	−	0.589473i
$281$	−9.84122	+	9.84122i	−0.587078	+	0.587078i	−0.936839	−	0.349761i	$-0.886263\pi$
$281$	−9.84122	+	9.84122i	−0.587078	+	0.587078i	0.349761	+	0.936839i	$0.386263\pi$
$282$	−30.2787	−	14.8721i	−1.80307	−	0.885623i
$283$	−14.1131	−	8.14822i	−0.838938	−	0.484361i	0.0179649	−	0.999839i	$-0.494281\pi$
$283$	−14.1131	−	8.14822i	−0.838938	−	0.484361i	−0.856903	+	0.515477i	$0.827615\pi$
$284$	−3.88322	−	14.4924i	−0.230427	−	0.859965i
$285$	7.77087	−	5.21018i	0.460307	−	0.308624i
$286$		0			0
$287$		−	11.6428i		−	0.687251i
$288$	3.05044	−	23.7524i	0.179749	−	1.39962i
$289$	5.04783	−	8.74310i	0.296931	−	0.514300i
$290$	9.54498	+	16.5324i	0.560501	+	0.970816i
$291$	−1.77345	+	8.99024i	−0.103962	+	0.527017i
$292$	−1.57040	−	0.420787i	−0.0919006	−	0.0246247i
$293$	−15.8895	−	4.25757i	−0.928272	−	0.248730i	−0.237154	−	0.971472i	$-0.576215\pi$
$293$	−15.8895	−	4.25757i	−0.928272	−	0.248730i	−0.691117	+	0.722742i	$0.742881\pi$
$294$	3.61072	−	18.3040i	0.210581	−	1.06751i
$295$	−4.55334	−	7.88661i	−0.265106	−	0.459176i
$296$	11.8833	−	20.5825i	0.690703	−	1.19633i
$297$	1.66551	−	0.831215i	0.0966428	−	0.0482320i
$298$			27.3633i			1.58512i
$299$		0			0
$300$	28.3065	−	18.9788i	1.63428	−	1.09574i
$301$	−0.414705	−	1.54770i	−0.0239032	−	0.0892079i
$302$	20.9564	+	12.0992i	1.20591	+	0.696231i
$303$	−13.1866	−	6.47693i	−0.757551	−	0.372090i
$304$	36.3972	−	36.3972i	2.08752	−	2.08752i
$305$	−1.11553	+	4.16321i	−0.0638750	+	0.238385i
$306$	−16.1824	−	12.3358i	−0.925086	−	0.705192i
$307$	−5.70702	−	5.70702i	−0.325717	−	0.325717i	0.525238	−	0.850955i	$-0.323976\pi$
$307$	−5.70702	−	5.70702i	−0.325717	−	0.325717i	−0.850955	+	0.525238i	$0.823976\pi$
$308$	2.43245	−	1.40438i	0.138602	−	0.0800218i
$309$	0.958878	−	0.0643757i	0.0545487	−	0.00366221i
$310$	−3.96695	+	1.06294i	−0.225308	+	0.0603710i
$311$	−25.3416			−1.43699			−0.718496	−	0.695531i	$-0.755169\pi$
$311$	−25.3416			−1.43699			−0.718496	+	0.695531i	$0.755169\pi$
$312$		0			0
$313$	−3.49487			−0.197542			−0.0987709	−	0.995110i	$-0.531491\pi$
$313$	−3.49487			−0.197542			−0.0987709	+	0.995110i	$0.531491\pi$
$314$	−54.8437	+	14.6953i	−3.09501	+	0.829306i
$315$	3.52687	−	2.72408i	0.198716	−	0.153484i
$316$	−14.8687	+	8.58442i	−0.836427	+	0.482911i
$317$	5.25697	+	5.25697i	0.295261	+	0.295261i	0.839154	−	0.543893i	$-0.183050\pi$
$317$	5.25697	+	5.25697i	0.295261	+	0.295261i	−0.543893	+	0.839154i	$0.683050\pi$
$318$	41.0352	−	14.0022i	2.30114	−	0.785204i
$319$	−0.776127	+	2.89655i	−0.0434548	+	0.162175i
$320$	−2.35376	+	2.35376i	−0.131579	+	0.131579i
$321$	2.53485	−	5.16080i	0.141482	−	0.288048i
$322$	20.3640	+	11.7571i	1.13484	+	0.655199i
$323$	−4.15808	−	15.5182i	−0.231362	−	0.863454i
$324$	29.4873	−	29.8638i	1.63818	−	1.65910i
$325$		0			0
$326$			53.0876i			2.94025i
$327$	3.60314	+	3.14977i	0.199254	+	0.174183i
$328$	−23.8007	+	41.2241i	−1.31418	+	2.27622i
$329$	−6.34322	−	10.9868i	−0.349713	−	0.605721i
$330$	−1.38822	−	0.273847i	−0.0764192	−	0.0150748i
$331$	−17.3691	−	4.65404i	−0.954693	−	0.255809i	−0.252341	−	0.967638i	$-0.581200\pi$
$331$	−17.3691	−	4.65404i	−0.954693	−	0.255809i	−0.702353	+	0.711829i	$0.747867\pi$
$332$	−53.9539	−	14.4569i	−2.96111	−	0.793426i
$333$	9.56959	−	3.99946i	0.524410	−	0.219169i
$334$	12.9387	+	22.4105i	0.707974	+	1.22625i
$335$	5.56180	−	9.63333i	0.303874	−	0.526325i
$336$	16.1364	−	18.4591i	0.880315	−	1.00702i
$337$			16.3852i			0.892558i	0.894894	+	0.446279i	$0.147251\pi$
$337$			16.3852i			0.892558i	−0.894894	+	0.446279i	$0.852749\pi$
$338$		0			0
$339$	5.53488	+	8.25516i	0.300614	+	0.448359i
$340$	2.80173	+	10.4562i	0.151945	+	0.567067i
$341$	−0.558696	−	0.322563i	−0.0302551	−	0.0174678i
$342$	46.9226	−	6.32896i	2.53728	−	0.342231i
$343$	13.2838	−	13.2838i	0.717259	−	0.717259i
$344$	−1.69552	+	6.32777i	−0.0914163	+	0.341170i
$345$	−2.67726	−	7.84604i	−0.144139	−	0.422417i
$346$	−21.4731	−	21.4731i	−1.15440	−	1.15440i
$347$	−20.8470	+	12.0360i	−1.11912	+	0.646126i	−0.941177	−	0.337914i	$-0.890279\pi$
$347$	−20.8470	+	12.0360i	−1.11912	+	0.646126i	−0.177946	+	0.984040i	$0.556945\pi$
$348$	4.52897	+	67.4592i	0.242778	+	3.61619i
$349$	16.7180	−	4.47957i	0.894894	−	0.239786i	0.218072	−	0.975933i	$-0.430023\pi$
$349$	16.7180	−	4.47957i	0.894894	−	0.239786i	0.676822	+	0.736147i	$0.263357\pi$
$350$	18.3136			0.978903
$351$		0			0
$352$	−2.85956			−0.152415
$353$	20.4711	−	5.48522i	1.08957	−	0.291949i	0.331058	−	0.943611i	$-0.392595\pi$
$353$	20.4711	−	5.48522i	1.08957	−	0.291949i	0.758510	+	0.651662i	$0.225928\pi$
$354$	−3.08713	−	45.9828i	−0.164079	−	2.44396i
$355$	−2.46170	+	1.42126i	−0.130653	+	0.0754328i
$356$	−22.5902	−	22.5902i	−1.19728	−	1.19728i
$357$	−2.47126	−	7.24234i	−0.130793	−	0.383305i
$358$	7.89142	−	29.4512i	0.417075	−	1.55654i
$359$	−18.7493	+	18.7493i	−0.989548	+	0.989548i	−0.999946	−	0.0103977i	$-0.996690\pi$
$359$	−18.7493	+	18.7493i	−0.989548	+	0.989548i	0.0103977	+	0.999946i	$0.496690\pi$
$360$	−18.0564	+	2.43547i	−0.951658	+	0.128361i
$361$	15.9199	+	9.19136i	0.837889	+	0.483756i
$362$	13.4286	+	50.1162i	0.705792	+	2.63405i
$363$	10.4864	+	15.6402i	0.550392	+	0.820898i
$364$		0			0
$365$			0.308016i			0.0161223i
$366$	−14.3557	+	16.4220i	−0.750383	+	0.858391i
$367$	−10.1653	+	17.6069i	−0.530626	+	0.919072i	0.468735	+	0.883339i	$0.344710\pi$
$367$	−10.1653	+	17.6069i	−0.530626	+	0.919072i	−0.999361	+	0.0357329i	$0.988623\pi$
$368$	−22.8053	−	39.4999i	−1.18881	−	2.05907i
$369$	−19.1667	+	8.01042i	−0.997777	+	0.417006i
$370$	−7.61557	−	2.04058i	−0.395914	−	0.106085i
$371$	15.7503	+	4.22028i	0.817716	+	0.219106i
$372$	−14.2704	−	2.81504i	−0.739885	−	0.145953i
$373$	−16.0055	−	27.7224i	−0.828735	−	1.43541i	−0.899031	−	0.437885i	$-0.855728\pi$
$373$	−16.0055	−	27.7224i	−0.828735	−	1.43541i	0.0702957	−	0.997526i	$-0.477606\pi$
$374$	−1.21487	+	2.10422i	−0.0628197	+	0.108807i
$375$	−10.6215	−	9.28502i	−0.548490	−	0.479476i
$376$			51.8685i			2.67492i
$377$		0			0
$378$	22.0980	−	4.50498i	1.13660	−	0.231711i
$379$	4.51091	+	16.8350i	0.231710	+	0.864754i	0.979604	+	0.200936i	$0.0643983\pi$
$379$	4.51091	+	16.8350i	0.231710	+	0.864754i	−0.747894	+	0.663818i	$0.768935\pi$
$380$	−21.8140	−	12.5943i	−1.11903	−	0.646074i
$381$	10.4032	−	21.1802i	0.532970	−	1.08509i
$382$	−30.9220	+	30.9220i	−1.58211	+	1.58211i
$383$	5.61681	−	20.9622i	0.287005	−	1.07112i	−0.660356	−	0.750953i	$-0.729595\pi$
$383$	5.61681	−	20.9622i	0.287005	−	1.07112i	0.947361	−	0.320166i	$-0.103739\pi$
$384$	10.2274	−	3.48984i	0.521916	−	0.178090i
$385$	−0.376276	−	0.376276i	−0.0191768	−	0.0191768i
$386$	−37.4019	+	21.5940i	−1.90370	+	1.09910i
$387$	−2.26254	+	1.74754i	−0.115011	+	0.0888325i
$388$	23.8300	−	6.38524i	1.20979	−	0.324161i
$389$	3.24468			0.164512			0.0822559	−	0.996611i	$-0.473788\pi$
$389$	3.24468			0.164512			0.0822559	+	0.996611i	$0.473788\pi$
$390$		0			0
$391$	−14.2357			−0.719931
$392$	−27.7086	+	7.42451i	−1.39950	+	0.374994i
$393$	−10.9896	+	0.737803i	−0.554351	+	0.0372172i
$394$	32.6963	−	18.8772i	1.64722	−	0.951020i
$395$	2.30003	+	2.30003i	0.115727	+	0.115727i
$396$	−3.98549	−	3.03814i	−0.200279	−	0.152672i
$397$	−8.23536	+	30.7348i	−0.413321	+	1.54253i	0.374855	+	0.927084i	$0.377693\pi$
$397$	−8.23536	+	30.7348i	−0.413321	+	1.54253i	−0.788175	+	0.615451i	$0.788974\pi$
$398$	0.610176	−	0.610176i	0.0305854	−	0.0305854i
$399$	15.9823	+	7.85011i	0.800116	+	0.392997i
$400$	−30.7637	−	17.7614i	−1.53818	−	0.888070i
$401$	9.78507	+	36.5184i	0.488643	+	1.82364i	0.563062	+	0.826414i	$0.309623\pi$
$401$	9.78507	+	36.5184i	0.488643	+	1.82364i	−0.0744193	+	0.997227i	$0.523710\pi$
$402$	46.7567	−	31.3492i	2.33201	−	1.56355i
$403$		0			0
$404$			39.5533i			1.96785i
$405$	−6.91100	−	3.93182i	−0.343410	−	0.195374i
$406$	−18.1660	+	31.4645i	−0.901565	+	1.56156i
$407$	−0.619241	−	1.07256i	−0.0306947	−	0.0531647i
$408$	−6.05505	+	30.6951i	−0.299770	+	1.51964i
$409$	2.93087	+	0.785323i	0.144922	+	0.0388317i	0.330551	−	0.943788i	$-0.392766\pi$
$409$	2.93087	+	0.785323i	0.144922	+	0.0388317i	−0.185629	+	0.982620i	$0.559432\pi$
$410$	15.2530	+	4.08703i	0.753292	+	0.201844i
$411$	−0.684803	+	3.47151i	−0.0337789	+	0.171237i
$412$	−1.29369	−	2.24073i	−0.0637354	−	0.110393i
$413$	8.66592	−	15.0098i	0.426422	−	0.738585i
$414$	5.34420	−	41.6128i	0.262653	−	2.04516i
$415$			10.5825i			0.519474i
$416$		0			0
$417$	−7.35640	+	4.93228i	−0.360244	+	0.241535i
$418$	−1.46329	−	5.46109i	−0.0715721	−	0.267111i
$419$	32.1726	+	18.5749i	1.57173	+	0.907442i	0.995957	+	0.0898356i	$0.0286342\pi$
$419$	32.1726	+	18.5749i	1.57173	+	0.907442i	0.575778	+	0.817606i	$0.304699\pi$
$420$	−10.7689	−	5.28943i	−0.525470	−	0.258098i
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	−0.0840970	−	0.996458i	$-0.526801\pi$
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	0.996458	+	0.0840970i	$0.0268006\pi$
$422$	−1.79657	+	6.70488i	−0.0874555	+	0.326388i
$423$	−13.7225	+	18.0015i	−0.667211	+	0.875262i
$424$	−47.1405	−	47.1405i	−2.28935	−	2.28935i
$425$	−9.60179	+	5.54359i	−0.465755	+	0.268904i
$426$	−14.3529	+	0.963604i	−0.695401	+	0.0466868i
$427$	−7.92344	+	2.12308i	−0.383442	+	0.102743i
$428$	−15.4798			−0.748246
$429$		0			0
$430$	2.17319			0.104801
$431$	−7.01461	+	1.87956i	−0.337882	+	0.0905352i	−0.423771	−	0.905770i	$-0.639294\pi$
$431$	−7.01461	+	1.87956i	−0.337882	+	0.0905352i	0.0858886	+	0.996305i	$0.472627\pi$
$432$	−41.4900	−	13.8641i	−1.99619	−	0.667038i
$433$	−5.89093	+	3.40113i	−0.283100	+	0.163448i	−0.634826	−	0.772655i	$-0.718928\pi$
$433$	−5.89093	+	3.40113i	−0.283100	+	0.163448i	0.351726	+	0.936103i	$0.385595\pi$
$434$	−5.52692	−	5.52692i	−0.265301	−	0.265301i
$435$	12.1230	−	4.13665i	0.581252	−	0.198337i
$436$	3.33479	−	12.4456i	0.159708	−	0.596037i
$437$	23.4228	−	23.4228i	1.12046	−	1.12046i
$438$	−0.687215	+	1.39912i	−0.0328364	+	0.0668527i
$439$	−14.0407	−	8.10639i	−0.670125	−	0.386897i	0.125999	−	0.992030i	$-0.459786\pi$
$439$	−14.0407	−	8.10639i	−0.670125	−	0.386897i	−0.796124	+	0.605134i	$0.793120\pi$
$440$	0.563096	+	2.10150i	0.0268445	+	0.100185i
$441$	−11.5808	−	4.75395i	−0.551467	−	0.226378i
$442$		0			0
$443$		−	6.09878i		−	0.289762i	−0.989449	−	0.144881i	$-0.953720\pi$
$443$		−	6.09878i		−	0.289762i	0.989449	−	0.144881i	$-0.0462799\pi$
$444$	−21.0232	−	18.3780i	−0.997718	−	0.872180i
$445$	−3.02631	+	5.24172i	−0.143461	+	0.248481i
$446$	−10.0032	−	17.3260i	−0.473663	−	0.820409i
$447$	18.0136	+	3.55343i	0.852013	+	0.168072i
$448$	−6.11937	−	1.63968i	−0.289113	−	0.0774676i
$449$	−25.8980	−	6.93935i	−1.22220	−	0.327488i	−0.410663	−	0.911787i	$-0.634703\pi$
$449$	−25.8980	−	6.93935i	−1.22220	−	0.327488i	−0.811538	+	0.584299i	$0.801370\pi$
$450$	−12.6001	−	30.1484i	−0.593972	−	1.42121i
$451$	1.24026	+	2.14820i	0.0584016	+	0.101155i
$452$	13.3792	−	23.1734i	0.629304	−	1.08999i
$453$	10.6865	−	12.2246i	0.502094	−	0.574363i
$454$		−	48.3995i		−	2.27150i
$455$		0			0
$456$	−40.5417	−	60.4670i	−1.89854	−	2.83163i
$457$	−4.95873	−	18.5062i	−0.231960	−	0.865686i	−0.979496	−	0.201464i	$-0.935430\pi$
$457$	−4.95873	−	18.5062i	−0.231960	−	0.865686i	0.747536	−	0.664221i	$-0.231237\pi$
$458$	25.6547	+	14.8118i	1.19877	+	0.692109i
$459$	−10.2223	+	9.05110i	−0.477135	+	0.422469i
$460$	−15.7823	+	15.7823i	−0.735856	+	0.735856i
$461$	−1.15751	+	4.31989i	−0.0539106	+	0.201197i	−0.987628	−	0.156813i	$-0.949878\pi$
$461$	−1.15751	+	4.31989i	−0.0539106	+	0.201197i	0.933718	+	0.358010i	$0.116545\pi$
$462$	−0.869676	−	2.54869i	−0.0404610	−	0.118576i
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.983134	+	0.182885i	$0.0585437\pi$
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.182885	+	0.983134i	$0.441456\pi$
$464$	61.0316	−	35.2366i	2.83332	−	1.63582i
$465$	0.184593	+	2.74952i	0.00856031	+	0.127506i
$466$	−28.1249	+	7.53603i	−1.30286	+	0.349100i
$467$	−10.0568			−0.465374			−0.232687	−	0.972552i	$-0.574752\pi$
$467$	−10.0568			−0.465374			−0.232687	+	0.972552i	$0.574752\pi$
$468$		0			0
$469$	21.1705			0.977562
$470$	16.6203	−	4.45340i	0.766637	−	0.205420i
$471$	2.55203	+	38.0126i	0.117591	+	1.75153i
$472$	−61.3676	+	35.4306i	−2.82467	+	1.63083i
$473$	0.241387	+	0.241387i	0.0110990	+	0.0110990i
$474$	5.31599	+	15.5792i	0.244172	+	0.715576i
$475$	6.67716	−	24.9195i	0.306369	−	1.14339i
$476$	−14.5680	+	14.5680i	−0.667723	+	0.667723i
$477$	−3.88892	−	28.8322i	−0.178061	−	1.32014i
$478$	−4.17920	−	2.41286i	−0.191152	−	0.110362i
$479$	1.53075	+	5.71284i	0.0699418	+	0.261026i	0.992039	−	0.125932i	$-0.0401923\pi$
$479$	1.53075	+	5.71284i	0.0699418	+	0.261026i	−0.922097	+	0.386959i	$0.873526\pi$
$480$	6.80230	+	10.1455i	0.310481	+	0.463076i
$481$		0			0
$482$		−	60.0439i		−	2.73493i
$483$	10.3843	−	11.8790i	0.472503	−	0.540514i
$484$	25.3482	−	43.9043i	1.15219	−	1.99565i
$485$	−2.33700	−	4.04780i	−0.106118	−	0.183801i
$486$	−22.6200	−	33.2789i	−1.02606	−	1.50956i
$487$	9.07613	+	2.43194i	0.411279	+	0.110202i	0.458525	−	0.888681i	$-0.348378\pi$
$487$	9.07613	+	2.43194i	0.411279	+	0.110202i	−0.0472463	+	0.998883i	$0.515045\pi$
$488$	32.3950	+	8.68021i	1.46645	+	0.392934i
$489$	34.9481	+	6.89401i	1.58041	+	0.311758i
$490$	4.75809	+	8.24126i	0.214949	+	0.372302i
$491$	12.1772	−	21.0915i	0.549548	−	0.951845i	−0.448758	−	0.893654i	$-0.648133\pi$
$491$	12.1772	−	21.0915i	0.549548	−	0.951845i	0.998305	−	0.0581914i	$-0.0185334\pi$
$492$	42.1068	+	36.8087i	1.89832	+	1.65947i
$493$		−	21.9957i		−	0.990637i
$494$		0			0
$495$	−0.360552	+	0.878321i	−0.0162056	+	0.0394776i
$496$	3.92399	+	14.6445i	0.176192	+	0.657559i
$497$	−4.68511	−	2.70495i	−0.210156	−	0.121334i
$498$	−23.6105	+	48.0695i	−1.05801	+	2.15405i
$499$	6.97195	−	6.97195i	0.312107	−	0.312107i	−0.533618	−	0.845725i	$-0.679168\pi$
$499$	6.97195	−	6.97195i	0.312107	−	0.312107i	0.845725	+	0.533618i	$0.179168\pi$
$500$	−9.83042	+	36.6876i	−0.439630	+	1.64072i
$501$	16.4333	−	5.60743i	0.734185	−	0.250522i
$502$	19.7012	+	19.7012i	0.879307	+	0.879307i
$503$	−11.3931	+	6.57779i	−0.507992	+	0.293289i	−0.732008	−	0.681296i	$-0.761417\pi$
$503$	−11.3931	+	6.57779i	−0.507992	+	0.293289i	0.224016	+	0.974586i	$0.428083\pi$
$504$	−21.1967	−	27.4434i	−0.944177	−	1.22243i
$505$	7.23827	−	1.93949i	0.322099	−	0.0863061i
$506$	−5.00977			−0.222712
$507$		0			0
$508$	−63.5300			−2.81869
$509$	19.2244	−	5.15115i	0.852105	−	0.228321i	0.193771	−	0.981047i	$-0.437928\pi$
$509$	19.2244	−	5.15115i	0.852105	−	0.228321i	0.658334	+	0.752726i	$0.271261\pi$
$510$	10.3556	−	0.695236i	0.458552	−	0.0307856i
$511$	−0.507679	+	0.293109i	−0.0224584	+	0.0129664i
$512$	−34.3270	−	34.3270i	−1.51705	−	1.51705i
$513$	1.92699	−	31.7115i	0.0850787	−	1.40010i
$514$	2.84341	−	10.6117i	0.125417	−	0.468064i
$515$	−0.346619	+	0.346619i	−0.0152739	+	0.0152739i
$516$	6.90844	+	3.39326i	0.304127	+	0.149380i
$517$	2.34076	+	1.35144i	0.102947	+	0.0594362i
$518$	−3.88365	−	14.4940i	−0.170638	−	0.636828i
$519$	−16.9245	+	11.3474i	−0.742902	+	0.498098i
$520$		0			0
$521$		−	12.9958i		−	0.569355i	−0.958623	−	0.284678i	$-0.908113\pi$
$521$		−	12.9958i		−	0.569355i	0.958623	−	0.284678i	$-0.0918865\pi$
$522$	64.2963	+	8.25736i	2.81417	+	0.361415i
$523$	−3.05976	+	5.29966i	−0.133794	+	0.231738i	−0.925136	−	0.379636i	$-0.876049\pi$
$523$	−3.05976	+	5.29966i	−0.133794	+	0.231738i	0.791342	+	0.611374i	$0.209383\pi$
$524$	14.8268	+	25.6808i	0.647712	+	1.12187i
$525$	2.37822	−	12.0560i	0.103794	−	0.526169i
$526$	63.1981	+	16.9339i	2.75557	+	0.738352i
$527$	4.57077	+	1.22473i	0.199106	+	0.0533503i
$528$	−1.01094	+	5.12482i	−0.0439956	+	0.223029i
$529$	−3.17594	−	5.50088i	−0.138084	−	0.239169i
$530$	−11.0578	+	19.1528i	−0.480322	+	0.831943i
$531$	−30.6719	−	3.93909i	−1.33105	−	0.170942i
$532$		−	47.9390i		−	2.07842i
$533$		0			0
$534$	−25.4414	+	17.0578i	−1.10096	+	0.738164i
$535$	0.759051	+	2.83282i	0.0328166	+	0.122473i
$536$	−74.9593	−	43.2778i	−3.23775	−	1.86931i
$537$	−18.3632	−	9.01957i	−0.792432	−	0.389223i
$538$	−41.3698	+	41.3698i	−1.78358	+	1.78358i
$539$	−0.386893	+	1.44390i	−0.0166646	+	0.0621933i
$540$	−1.29841	+	21.3673i	−0.0558748	+	0.919503i
$541$	−9.48746	−	9.48746i	−0.407898	−	0.407898i	0.473107	−	0.881005i	$-0.343132\pi$
$541$	−9.48746	−	9.48746i	−0.407898	−	0.407898i	−0.881005	+	0.473107i	$0.843132\pi$
$542$	47.6492	−	27.5103i	2.04671	−	1.18167i
$543$	34.7359	−	2.33205i	1.49066	−	0.100078i
$544$	20.2602	−	5.42870i	0.868649	−	0.232754i
$545$	−2.44107			−0.104564
$546$		0			0
$547$	8.20259			0.350717			0.175359	−	0.984505i	$-0.443892\pi$
$547$	8.20259			0.350717			0.175359	+	0.984505i	$0.443892\pi$
$548$	9.20176	−	2.46560i	0.393080	−	0.105325i
$549$	8.94652	+	11.5831i	0.381828	+	0.494354i
$550$	−3.37902	+	1.95088i	−0.144082	+	0.0831858i
$551$	36.1907	+	36.1907i	1.54178	+	1.54178i
$552$	−61.0519	+	20.8324i	−2.59854	+	0.886685i
$553$	−1.60225	+	5.97968i	−0.0681346	+	0.254282i
$554$	19.4971	−	19.4971i	0.828354	−	0.828354i
$555$	−2.33230	+	4.74842i	−0.0990008	+	0.201559i
$556$	20.6505	+	11.9226i	0.875775	+	0.505629i
$557$	5.70912	+	21.3067i	0.241903	+	0.902795i	0.974915	+	0.222579i	$0.0714474\pi$
$557$	5.70912	+	21.3067i	0.241903	+	0.902795i	−0.733012	+	0.680216i	$0.761886\pi$
$558$	−5.29596	+	12.9012i	−0.224196	+	0.546150i
$559$		0			0
$560$			12.5057i			0.528463i
$561$	1.22747	+	1.07302i	0.0518238	+	0.0453030i
$562$	17.9628	−	31.1125i	0.757715	−	1.31240i
$563$	19.7230	+	34.1613i	0.831227	+	1.43973i	0.897066	+	0.441897i	$0.145694\pi$
$563$	19.7230	+	34.1613i	0.831227	+	1.43973i	−0.0658393	+	0.997830i	$0.520972\pi$
$564$	59.7885	+	11.7941i	2.51755	+	0.496622i
$565$	−4.89679	−	1.31209i	−0.206010	−	0.0552001i
$566$	40.6328	+	10.8875i	1.70792	+	0.457637i
$567$	−0.0960047	−	15.1324i	−0.00403182	−	0.635500i
$568$	11.0592	+	19.1551i	0.464033	+	0.803729i
$569$	−7.67489	+	13.2933i	−0.321748	+	0.557284i	−0.980849	−	0.194771i	$-0.937604\pi$
$569$	−7.67489	+	13.2933i	−0.321748	+	0.557284i	0.659101	+	0.752055i	$0.270937\pi$
$570$	−15.8947	+	18.1825i	−0.665754	+	0.761580i
$571$		−	4.70947i		−	0.197085i	−0.995133	−	0.0985425i	$-0.968582\pi$
$571$		−	4.70947i		−	0.197085i	0.995133	−	0.0985425i	$-0.0314181\pi$
$572$		0			0
$573$	16.3407	+	24.3718i	0.682643	+	1.01815i
$574$	7.77845	+	29.0296i	0.324666	+	1.21167i
$575$	−19.7974	−	11.4301i	−0.825610	−	0.476666i
$576$	1.51094	+	11.2020i	0.0629557	+	0.466750i
$577$	−25.1056	+	25.1056i	−1.04516	+	1.04516i	−0.0462290	+	0.998931i	$0.514720\pi$
$577$	−25.1056	+	25.1056i	−1.04516	+	1.04516i	−0.998931	+	0.0462290i	$0.985280\pi$
$578$	−6.74483	+	25.1720i	−0.280548	+	1.04702i
$579$	9.35850	+	27.4263i	0.388926	+	1.13980i
$580$	−24.3854	−	24.3854i	−1.01255	−	1.01255i
$581$	−17.4423	+	10.0703i	−0.723627	+	0.417786i
$582$	−1.58447	−	23.6007i	−0.0656783	−	0.978280i
$583$	−3.35564	+	0.899142i	−0.138977	+	0.0372387i
$584$	2.39675			0.0991783
$585$		0			0
$586$	42.4625			1.75411
$587$	−16.7912	+	4.49920i	−0.693049	+	0.185702i	−0.588115	−	0.808777i	$-0.700130\pi$
$587$	−16.7912	+	4.49920i	−0.693049	+	0.185702i	−0.104934	+	0.994479i	$0.533463\pi$
$588$	2.25765	+	33.6278i	0.0931041	+	1.38679i
$589$	−9.53566	+	5.50541i	−0.392910	+	0.226847i
$590$	16.6221	+	16.6221i	0.684320	+	0.684320i
$591$	−8.18110	−	23.9757i	−0.336525	−	0.986230i
$592$	−7.53309	+	28.1139i	−0.309608	+	1.15547i
$593$	3.78428	−	3.78428i	0.155402	−	0.155402i	−0.625124	−	0.780526i	$-0.714952\pi$
$593$	3.78428	−	3.78428i	0.155402	−	0.155402i	0.780526	+	0.625124i	$0.214952\pi$
$594$	−3.59738	+	3.18523i	−0.147602	+	0.130691i
$595$	3.38029	+	1.95161i	0.138578	+	0.0800082i
$596$	−12.7940	−	47.7478i	−0.524062	−	1.95582i
$597$	−0.322448	−	0.480924i	−0.0131969	−	0.0196829i
$598$		0			0
$599$			6.35465i			0.259644i	0.991537	+	0.129822i	$0.0414406\pi$
$599$			6.35465i			0.259644i	−0.991537	+	0.129822i	$0.958559\pi$
$600$	−33.0662	+	37.8257i	−1.34992	+	1.54423i
$601$	−12.4761	+	21.6093i	−0.508912	+	0.881461i	0.491035	+	0.871140i	$0.336619\pi$
$601$	−12.4761	+	21.6093i	−0.508912	+	0.881461i	−0.999947	+	0.0103212i	$0.996715\pi$
$602$	2.06801	+	3.58190i	0.0842858	+	0.145987i
$603$	−14.5656	−	34.8514i	−0.593158	−	1.41926i
$604$	−42.2251	−	11.3142i	−1.71811	−	0.460367i
$605$	−9.27745	−	2.48588i	−0.377182	−	0.101066i
$606$	37.2061	+	7.33942i	1.51139	+	0.298143i
$607$	−2.11757	−	3.66773i	−0.0859494	−	0.148869i	0.819846	−	0.572584i	$-0.194059\pi$
$607$	−2.11757	−	3.66773i	−0.0859494	−	0.148869i	−0.905795	+	0.423715i	$0.860726\pi$
$608$	−24.4031	+	42.2673i	−0.989674	+	1.71417i
$609$	18.3544	+	16.0449i	0.743756	+	0.650172i
$610$		−	11.1256i		−	0.450464i
$611$		0			0
$612$	34.0053	+	13.9592i	1.37458	+	0.564268i
$613$	9.48855	+	35.4117i	0.383239	+	1.43027i	0.840924	+	0.541153i	$0.182012\pi$
$613$	9.48855	+	35.4117i	0.383239	+	1.43027i	−0.457686	+	0.889114i	$0.651321\pi$
$614$	18.0424	+	10.4168i	0.728134	+	0.420388i
$615$	4.67131	−	9.51047i	0.188365	−	0.383499i
$616$	−2.92790	+	2.92790i	−0.117968	+	0.117968i
$617$	7.90398	−	29.4981i	0.318202	−	1.18755i	−0.602769	−	0.797916i	$-0.705936\pi$
$617$	7.90398	−	29.4981i	0.318202	−	1.18755i	0.920971	−	0.389631i	$-0.127398\pi$
$618$	−2.34781	+	0.801130i	−0.0944429	+	0.0322262i
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	0.904042	−	0.427443i	$-0.140586\pi$
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	−0.427443	+	0.904042i	$0.640586\pi$
$620$	6.42516	−	3.70957i	0.258041	−	0.148980i
$621$	−26.7002	−	8.92202i	−1.07144	−	0.358028i
$622$	63.1857	−	16.9306i	2.53352	−	0.678853i
$623$	−11.5194			−0.461513
$624$		0			0
$625$	−13.9016			−0.556063
$626$	8.71395	−	2.33490i	0.348279	−	0.0933212i
$627$	−3.78512	+	0.254120i	−0.151163	+	0.0101486i
$628$	88.8289	−	51.2854i	3.54466	−	2.04651i
$629$	6.42356	+	6.42356i	0.256124	+	0.256124i
$630$	−6.97379	+	9.14836i	−0.277843	+	0.364480i
$631$	7.19263	−	26.8433i	0.286334	−	1.06861i	−0.661525	−	0.749923i	$-0.730090\pi$
$631$	7.19263	−	26.8433i	0.286334	−	1.06861i	0.947859	−	0.318690i	$-0.103243\pi$
$632$	17.8971	−	17.8971i	0.711909	−	0.711909i
$633$	4.18059	+	2.05340i	0.166163	+	0.0816154i
$634$	−16.6196	−	9.59535i	−0.660050	−	0.381080i
$635$	3.11518	+	11.6260i	0.123622	+	0.461364i
$636$	−65.0577	+	43.6195i	−2.57970	+	1.72963i
$637$		0			0
$638$		−	7.74064i		−	0.306455i
$639$	−1.22953	+	9.57381i	−0.0486396	+	0.378734i
$640$	−2.75601	+	4.77354i	−0.108941	+	0.188691i
$641$	4.28764	+	7.42640i	0.169351	+	0.293325i	0.938192	−	0.346115i	$-0.112499\pi$
$641$	4.28764	+	7.42640i	0.169351	+	0.293325i	−0.768841	+	0.639440i	$0.779166\pi$
$642$	−2.87240	+	14.5612i	−0.113365	+	0.574685i
$643$	2.17600	+	0.583059i	0.0858132	+	0.0229936i	0.301470	−	0.953476i	$-0.402523\pi$
$643$	2.17600	+	0.583059i	0.0858132	+	0.0229936i	−0.215657	+	0.976469i	$0.569189\pi$
$644$	−41.0313	−	10.9943i	−1.61686	−	0.433236i
$645$	0.282213	−	1.43063i	0.0111121	−	0.0563312i
$646$	20.7351	+	35.9143i	0.815813	+	1.41303i
$647$	−12.2169	+	21.1603i	−0.480296	+	0.831897i	−0.999744	−	0.0226045i	$-0.992804\pi$
$647$	−12.2169	+	21.1603i	−0.480296	+	0.831897i	0.519448	+	0.854502i	$0.326137\pi$
$648$	−30.5944	+	53.7761i	−1.20186	+	2.11253i
$649$			3.69259i			0.144947i
$650$		0			0
$651$	−4.35616	+	2.92070i	−0.170731	+	0.114471i
$652$	−24.8216	−	92.6355i	−0.972089	−	3.62788i
$653$	11.0765	+	6.39504i	0.433458	+	0.250257i	0.700819	−	0.713339i	$-0.252818\pi$
$653$	11.0765	+	6.39504i	0.433458	+	0.250257i	−0.267361	+	0.963597i	$0.586151\pi$
$654$	−11.0882	−	5.44627i	−0.433585	−	0.212966i
$655$	3.97256	−	3.97256i	0.155221	−	0.155221i
$656$	15.0878	−	56.3085i	0.589081	−	2.19848i
$657$	0.831816	+	0.634093i	0.0324522	+	0.0247383i
$658$	23.1561	+	23.1561i	0.902718	+	0.902718i
$659$	−26.1230	+	15.0821i	−1.01761	+	0.587515i	−0.913410	−	0.407041i	$-0.866561\pi$
$659$	−26.1230	+	15.0821i	−1.01761	+	0.587515i	−0.104197	+	0.994557i	$0.533227\pi$
$660$	2.55043	−	0.171227i	0.0992752	−	0.00666499i
$661$	−24.1859	+	6.48058i	−0.940721	+	0.252065i	−0.696420	−	0.717634i	$-0.745225\pi$
$661$	−24.1859	+	6.48058i	−0.940721	+	0.252065i	−0.244301	+	0.969700i	$0.578558\pi$
$662$	46.4167			1.80404
$663$		0			0
$664$	82.3448			3.19560
$665$	−8.77286	+	2.35068i	−0.340197	+	0.0911554i
$666$	−21.1884	+	16.3654i	−0.821032	+	0.634148i
$667$	39.2758	−	22.6759i	1.52077	−	0.878014i
$668$	−33.0556	−	33.0556i	−1.27896	−	1.27896i
$669$	−12.7049	+	4.33522i	−0.491200	+	0.167609i
$670$	−7.43160	+	27.7351i	−0.287108	+	1.07150i
$671$	1.23578	−	1.23578i	0.0477068	−	0.0477068i
$672$	−10.2489	+	20.8662i	−0.395361	+	0.804930i
$673$	36.1567	+	20.8751i	1.39374	+	0.804674i	0.993727	−	0.111836i	$-0.0356732\pi$
$673$	36.1567	+	20.8751i	1.39374	+	0.804674i	0.400010	+	0.916511i	$0.369007\pi$
$674$	−10.9468	−	40.8541i	−0.421656	−	1.57364i
$675$	−21.4832	+	4.37965i	−0.826891	+	0.168573i
$676$		0			0
$677$		−	23.6516i		−	0.909004i	−0.890746	−	0.454502i	$-0.849817\pi$
$677$		−	23.6516i		−	0.909004i	0.890746	−	0.454502i	$-0.150183\pi$
$678$	−19.3156	−	16.8852i	−0.741812	−	0.648473i
$679$	4.44779	−	7.70379i	0.170690	−	0.295644i
$680$	−7.97916	−	13.8203i	−0.305987	−	0.529984i
$681$	−31.8619	−	6.28521i	−1.22095	−	0.240850i
$682$	1.60853	+	0.431004i	0.0615937	+	0.0165040i
$683$	−7.89669	−	2.11591i	−0.302158	−	0.0809631i	0.104554	−	0.994519i	$-0.466658\pi$
$683$	−7.89669	−	2.11591i	−0.302158	−	0.0809631i	−0.406713	+	0.913556i	$0.633325\pi$
$684$	−78.9186	+	32.9828i	−3.01753	+	1.26113i
$685$	−0.902413	−	1.56302i	−0.0344794	−	0.0597201i
$686$	−24.2464	+	41.9961i	−0.925733	+	1.60342i
$687$	13.0823	−	14.9653i	0.499121	−	0.570963i
$688$		−	8.02262i		−	0.305860i
$689$		0			0
$690$	11.9172	+	17.7743i	0.453681	+	0.676656i
$691$	3.87934	+	14.4779i	0.147577	+	0.550764i	0.999627	+	0.0273044i	$0.00869235\pi$
$691$	3.87934	+	14.4779i	0.147577	+	0.550764i	−0.852050	+	0.523460i	$0.824641\pi$
$692$	47.5095	+	27.4296i	1.80604	+	1.04272i
$693$	−1.79077	+	0.241541i	−0.0680257	+	0.00917537i
$694$	43.9377	−	43.9377i	1.66785	−	1.66785i
$695$	1.16924	−	4.36366i	0.0443518	−	0.165523i
$696$	−32.1883	−	94.3318i	−1.22009	−	3.57564i
$697$	−12.8656	−	12.8656i	−0.487319	−	0.487319i
$698$	−38.6911	+	22.3383i	−1.46448	+	0.845518i
$699$	1.30873	+	19.4935i	0.0495006	+	0.737313i
$700$	−31.9564	+	8.56269i	−1.20784	+	0.323639i
$701$	38.5186			1.45483			0.727414	−	0.686199i	$-0.240722\pi$
$701$	38.5186			1.45483			0.727414	+	0.686199i	$0.240722\pi$
$702$		0			0
$703$	−21.1381			−0.797237
$704$	1.30375	−	0.349338i	0.0491368	−	0.0131662i
$705$	−0.773389	−	11.5196i	−0.0291275	−	0.433855i
$706$	−47.3771	+	27.3532i	−1.78306	+	1.02945i
$707$	10.0847	+	10.0847i	0.379272	+	0.379272i
$708$	26.8866	+	78.7945i	1.01046	+	2.96128i
$709$	−9.53453	+	35.5833i	−0.358077	+	1.33636i	0.518492	+	0.855083i	$0.326494\pi$
$709$	−9.53453	+	35.5833i	−0.358077	+	1.33636i	−0.876568	+	0.481278i	$0.840173\pi$
$710$	5.18835	−	5.18835i	0.194715	−	0.194715i
$711$	10.9463	−	1.47645i	0.410518	−	0.0553710i
$712$	40.7871	+	23.5484i	1.52856	+	0.882515i
$713$	2.52522	+	9.42424i	0.0945701	+	0.352940i
$714$	11.0003	+	16.4067i	0.411675	+	0.614004i
$715$		0			0
$716$			55.0807i			2.05846i
$717$	−2.13113	+	2.43788i	−0.0795885	+	0.0910442i
$718$	34.2223	−	59.2748i	1.27717	−	2.21212i
$719$	2.38818	+	4.13644i	0.0890640	+	0.154263i	0.907116	−	0.420881i	$-0.138279\pi$
$719$	2.38818	+	4.13644i	0.0890640	+	0.154263i	−0.818052	+	0.575145i	$0.804946\pi$
$720$	20.5873	−	8.60414i	0.767243	−	0.320657i
$721$	−0.901148	−	0.241462i	−0.0335605	−	0.00899251i
$722$	−45.8346	−	12.2813i	−1.70579	−	0.457064i
$723$	−39.5276	−	7.79737i	−1.47005	−	0.289987i
$724$	−46.8646	−	81.1718i	−1.74171	−	3.01673i
$725$	17.6607	−	30.5892i	0.655900	−	1.13605i
$726$	−36.5953	−	31.9907i	−1.35818	−	1.18729i
$727$			26.2267i			0.972694i	0.873766	+	0.486347i	$0.161671\pi$
$727$			26.2267i			0.972694i	−0.873766	+	0.486347i	$0.838329\pi$
$728$		0			0
$729$	−24.8453	+	10.5694i	−0.920196	+	0.391458i
$730$	−0.205783	−	0.767994i	−0.00761638	−	0.0284247i
$731$	−2.16851	−	1.25199i	−0.0802052	−	0.0463065i
$732$	17.3718	−	35.3677i	0.642078	−	1.30723i
$733$	9.54380	−	9.54380i	0.352508	−	0.352508i	−0.508534	−	0.861042i	$-0.669812\pi$
$733$	9.54380	−	9.54380i	0.352508	−	0.352508i	0.861042	+	0.508534i	$0.169812\pi$
$734$	13.5828	−	50.6916i	0.501349	−	1.87106i
$735$	6.04320	−	2.06208i	0.222907	−	0.0760611i
$736$	30.5803	+	30.5803i	1.12720	+	1.12720i
$737$	−3.90614	+	2.25521i	−0.143885	+	0.0830718i
$738$	42.4376	−	32.7779i	1.56215	−	1.20657i
$739$	11.6421	−	3.11949i	0.428261	−	0.114752i	−0.0382487	−	0.999268i	$-0.512178\pi$
$739$	11.6421	−	3.11949i	0.428261	−	0.114752i	0.466510	+	0.884516i	$0.345511\pi$
$740$	14.2429			0.523580
$741$		0			0
$742$	−42.0906			−1.54520
$743$	21.4713	−	5.75322i	0.787706	−	0.211065i	0.157526	−	0.987515i	$-0.449648\pi$
$743$	21.4713	−	5.75322i	0.787706	−	0.211065i	0.630179	+	0.776450i	$0.282981\pi$
$744$	21.3947	−	1.43636i	0.784367	−	0.0526597i
$745$	−8.11051	+	4.68260i	−0.297146	+	0.171557i
$746$	58.4286	+	58.4286i	2.13922	+	2.13922i
$747$	28.5786	+	21.7854i	1.04564	+	0.797087i
$748$	1.13605	−	4.23980i	0.0415381	−	0.155022i
$749$	−3.94679	+	3.94679i	−0.144213	+	0.144213i
$750$	32.6863	+	16.0547i	1.19354	+	0.586235i
$751$	−32.4803	−	18.7525i	−1.18522	−	0.684288i	−0.228005	−	0.973660i	$-0.573220\pi$
$751$	−32.4803	−	18.7525i	−1.18522	−	0.684288i	−0.957217	+	0.289372i	$0.906553\pi$
$752$	−16.4403	−	61.3561i	−0.599516	−	2.23743i
$753$	15.5279	−	10.4111i	0.565869	−	0.379401i
$754$		0			0
$755$			8.28200i			0.301413i
$756$	−36.4537	+	18.1931i	−1.32581	+	0.661677i
$757$	10.6958	−	18.5257i	0.388747	−	0.673329i	−0.603534	−	0.797337i	$-0.706241\pi$
$757$	10.6958	−	18.5257i	0.388747	−	0.673329i	0.992281	+	0.124008i	$0.0395747\pi$
$758$	−22.4946	−	38.9618i	−0.817041	−	1.41516i
$759$	−0.650574	+	3.29799i	−0.0236144	+	0.119709i
$760$	35.8678	+	9.61075i	1.30106	+	0.348619i
$761$	49.3165	+	13.2143i	1.78772	+	0.479018i	0.991955	−	0.126587i	$-0.0404024\pi$
$761$	49.3165	+	13.2143i	1.78772	+	0.479018i	0.795765	+	0.605606i	$0.207069\pi$
$762$	−11.7885	+	59.7599i	−0.427051	+	2.16487i
$763$	−2.32293	−	4.02343i	−0.0840956	−	0.145658i
$764$	39.4996	−	68.4153i	1.42905	−	2.47518i
$765$	0.887103	−	6.90746i	0.0320733	−	0.249740i
$766$			56.0187i			2.02404i
$767$		0			0
$768$	−34.0099	+	22.8028i	−1.22723	+	0.822826i
$769$	−11.7364	−	43.8009i	−0.423226	−	1.57950i	−0.767767	−	0.640729i	$-0.778632\pi$
$769$	−11.7364	−	43.8009i	−0.423226	−	1.57950i	0.344541	−	0.938771i	$-0.388035\pi$
$770$	1.18958	+	0.686803i	0.0428694	+	0.0247507i
$771$	−6.61658	−	3.24990i	−0.238290	−	0.117042i
$772$	55.1681	−	55.1681i	1.98554	−	1.98554i
$773$	−10.5635	+	39.4237i	−0.379944	+	1.41797i	0.466040	+	0.884763i	$0.345680\pi$
$773$	−10.5635	+	39.4237i	−0.379944	+	1.41797i	−0.845985	+	0.533207i	$0.820987\pi$
$774$	4.47380	−	5.86882i	0.160807	−	0.210950i
$775$	5.37316	+	5.37316i	0.193010	+	0.193010i
$776$	−31.4969	+	18.1848i	−1.13067	+	0.652795i
$777$	−10.0459	+	0.674444i	−0.360393	+	0.0241956i
$778$	−8.09013	+	2.16774i	−0.290045	+	0.0777174i
$779$	42.3369			1.51688
$780$		0			0
$781$	1.15259			0.0412430
$782$	35.4947	−	9.51076i	1.26929	−	0.340104i
$783$	13.7855	−	41.2546i	0.492653	−	1.47432i
$784$	30.4237	−	17.5651i	1.08656	−	0.627326i
$785$	−13.7409	−	13.7409i	−0.490435	−	0.490435i
$786$	26.9080	−	9.18166i	0.959777	−	0.327499i
$787$	−2.08283	+	7.77322i	−0.0742448	+	0.277086i	−0.993061	−	0.117600i	$-0.962480\pi$
$787$	−2.08283	+	7.77322i	−0.0742448	+	0.277086i	0.918816	+	0.394686i	$0.129147\pi$
$788$	−48.2273	+	48.2273i	−1.71803	+	1.71803i
$789$	19.3547	−	39.4049i	0.689046	−	1.40285i
$790$	−7.27143	−	4.19816i	−0.258706	−	0.149364i
$791$	−2.49718	−	9.31959i	−0.0887894	−	0.331366i
$792$	6.83443	+	2.80555i	0.242851	+	0.0996908i
$793$		0			0
$794$		−	82.1347i		−	2.91485i
$795$	11.1725	+	9.76670i	0.396247	+	0.346389i
$796$	−0.779436	+	1.35002i	−0.0276264	+	0.0478503i
$797$	−7.69611	−	13.3300i	−0.272610	−	0.472174i	0.696919	−	0.717150i	$-0.254554\pi$
$797$	−7.69611	−	13.3300i	−0.272610	−	0.472174i	−0.969529	+	0.244975i	$0.921220\pi$
$798$	−45.0941	−	8.89545i	−1.59631	−	0.314895i
$799$	−19.1501	−	5.13126i	−0.677483	−	0.181531i
$800$	32.5344	+	8.71757i	1.15026	+	0.308212i
$801$	7.92550	+	18.9635i	0.280034	+	0.670042i
$802$	−48.7953	−	84.5159i	−1.72302	−	2.98436i
$803$	0.0624476	−	0.108162i	0.00220373	−	0.00381697i
$804$	−66.9306	+	76.5644i	−2.36046	+	2.70022i
$805$			8.04785i			0.283649i
$806$		0			0
$807$	21.8618	+	32.6065i	0.769573	+	1.14780i
$808$	−15.0916	−	56.3227i	−0.530922	−	1.98143i
$809$	−34.8060	−	20.0952i	−1.22371	−	0.706511i	−0.258005	−	0.966143i	$-0.583065\pi$
$809$	−34.8060	−	20.0952i	−1.22371	−	0.706511i	−0.965707	+	0.259633i	$0.916399\pi$
$810$	19.8584	+	5.18623i	0.697752	+	0.182226i
$811$	−24.5095	+	24.5095i	−0.860644	+	0.860644i	−0.991413	−	0.130769i	$-0.958255\pi$
$811$	−24.5095	+	24.5095i	−0.860644	+	0.860644i	0.130769	+	0.991413i	$0.458255\pi$
$812$	16.9874	−	63.3978i	0.596140	−	2.22483i
$813$	−11.9225	−	34.9405i	−0.418142	−	1.22542i
$814$	2.26056	+	2.26056i	0.0792324	+	0.0792324i
$815$	−15.7352	+	9.08472i	−0.551180	+	0.318224i
$816$	−2.56656	−	38.2289i	−0.0898475	−	1.33828i
$817$	5.62793	−	1.50800i	0.196896	−	0.0527582i
$818$	−7.83235			−0.273852
$819$		0			0
$820$	−28.5267			−0.996197
$821$	−35.7677	+	9.58393i	−1.24830	+	0.334482i	−0.821680	−	0.569949i	$-0.806963\pi$
$821$	−35.7677	+	9.58393i	−1.24830	+	0.334482i	−0.426622	+	0.904430i	$0.640296\pi$
$822$	−0.611829	−	9.11320i	−0.0213400	−	0.317859i
$823$	−33.1584	+	19.1440i	−1.15583	+	0.667318i	−0.950301	−	0.311334i	$-0.899224\pi$
$823$	−33.1584	+	19.1440i	−1.15583	+	0.667318i	−0.205527	+	0.978651i	$0.565891\pi$
$824$	2.69713	+	2.69713i	0.0939589	+	0.0939589i
$825$	0.845481	+	2.47779i	0.0294359	+	0.0862656i
$826$	−11.5793	+	43.2144i	−0.402894	+	1.50362i
$827$	−10.8851	+	10.8851i	−0.378512	+	0.378512i	−0.870565	−	0.492053i	$-0.836246\pi$
$827$	−10.8851	+	10.8851i	−0.378512	+	0.378512i	0.492053	+	0.870565i	$0.336246\pi$
$828$	10.1311	+	75.1112i	0.352079	+	2.61029i
$829$	−4.66824	−	2.69521i	−0.162135	−	0.0936085i	0.416737	−	0.909027i	$-0.363174\pi$
$829$	−4.66824	−	2.69521i	−0.162135	−	0.0936085i	−0.578872	+	0.815419i	$0.696507\pi$
$830$	−7.07007	−	26.3859i	−0.245406	−	0.915867i
$831$	−10.3033	−	15.3671i	−0.357416	−	0.533079i
$832$		0			0
$833$		−	10.9647i		−	0.379903i
$834$	15.0469	−	17.2127i	0.521031	−	0.596026i
$835$	−4.42832	+	7.67007i	−0.153248	+	0.265434i
$836$	5.10676	+	8.84517i	0.176621	+	0.305917i
$837$	7.80524	+	5.16175i	0.269789	+	0.178416i
$838$	−92.6274	−	24.8194i	−3.19976	−	0.857373i
$839$	−52.3903	−	14.0379i	−1.80871	−	0.484643i	−0.813430	−	0.581663i	$-0.802402\pi$
$839$	−52.3903	−	14.0379i	−1.80871	−	0.484643i	−0.995282	+	0.0970197i	$0.969069\pi$
$840$	17.3528	+	3.42309i	0.598729	+	0.118108i
$841$	20.5367	+	35.5706i	0.708162	+	1.22657i
$842$	−34.1690	+	59.1825i	−1.17754	+	2.03956i
$843$	−18.1490	−	15.8654i	−0.625085	−	0.546433i
$844$		−	12.5397i		−	0.431634i
$845$		0			0
$846$	22.1884	−	54.0520i	0.762854	−	1.85834i
$847$	−4.73114	−	17.6569i	−0.162564	−	0.606697i
$848$	70.7050	+	40.8215i	2.42802	+	1.40182i
$849$	12.4440	−	25.3351i	0.427076	−	0.869499i
$850$	20.2370	−	20.2370i	0.694124	−	0.694124i
$851$	−4.84779	+	18.0922i	−0.166180	+	0.620193i
$852$	24.5946	−	8.39228i	0.842598	−	0.287515i
$853$	−26.8752	−	26.8752i	−0.920190	−	0.920190i	0.0768525	−	0.997042i	$-0.475513\pi$
$853$	−26.8752	−	26.8752i	−0.920190	−	0.920190i	−0.997042	+	0.0768525i	$0.975513\pi$
$854$	18.3375	−	10.5872i	0.627497	−	0.362286i
$855$	9.90562	+	12.8248i	0.338765	+	0.438599i
$856$	22.0428	−	5.90636i	0.753408	−	0.201875i
$857$	−26.9236			−0.919691			−0.459846	−	0.887999i	$-0.652095\pi$
$857$	−26.9236			−0.919691			−0.459846	+	0.887999i	$0.652095\pi$
$858$		0			0
$859$	2.86268			0.0976735			0.0488368	−	0.998807i	$-0.484449\pi$
$859$	2.86268			0.0976735			0.0488368	+	0.998807i	$0.484449\pi$
$860$	−3.79212	+	1.01609i	−0.129310	+	0.0346485i
$861$	20.1206	−	1.35083i	0.685708	−	0.0460360i
$862$	16.2342	−	9.37281i	0.552939	−	0.319239i
$863$	−12.8305	−	12.8305i	−0.436756	−	0.436756i	0.454163	−	0.890919i	$-0.349938\pi$
$863$	−12.8305	−	12.8305i	−0.436756	−	0.436756i	−0.890919	+	0.454163i	$0.849938\pi$
$864$	41.4019	+	2.51584i	1.40852	+	0.0855906i
$865$	2.69001	−	10.0393i	0.0914631	−	0.341345i
$866$	12.4159	−	12.4159i	0.421909	−	0.421909i
$867$	15.6951	+	7.70906i	0.533035	+	0.261813i
$868$	12.2284	+	7.06006i	0.415058	+	0.239634i
$869$	−0.341363	−	1.27399i	−0.0115800	−	0.0432170i
$870$	−27.4632	+	18.4134i	−0.931090	+	0.624273i
$871$		0			0
$872$			18.9946i			0.643237i
$873$	−15.7423	−	2.02174i	−0.532798	−	0.0684255i
$874$	−42.7527	+	74.0498i	−1.44613	+	2.50477i
$875$	6.84761	+	11.8604i	0.231491	+	0.400955i
$876$	0.544985	−	2.76272i	0.0184134	−	0.0933437i
$877$	24.8420	+	6.65640i	0.838856	+	0.224771i	0.652573	−	0.757726i	$-0.273689\pi$
$877$	24.8420	+	6.65640i	0.838856	+	0.224771i	0.186282	+	0.982496i	$0.440356\pi$
$878$	40.4242	+	10.8316i	1.36425	+	0.365550i
$879$	5.51422	−	27.9535i	0.185990	−	0.942848i
$880$	−1.33219	−	2.30742i	−0.0449081	−	0.0777830i
$881$	−25.2073	+	43.6603i	−0.849255	+	1.47095i	0.0326196	+	0.999468i	$0.489615\pi$
$881$	−25.2073	+	43.6603i	−0.849255	+	1.47095i	−0.881874	+	0.471485i	$0.843718\pi$
$882$	32.0511	+	4.11622i	1.07922	+	0.138600i
$883$		−	22.1092i		−	0.744035i	−0.928226	−	0.372018i	$-0.878666\pi$
$883$		−	22.1092i		−	0.744035i	0.928226	−	0.372018i	$-0.121334\pi$
$884$		0			0
$885$	13.1010	−	8.78392i	0.440387	−	0.295268i
$886$	4.07455	+	15.2064i	0.136887	+	0.510870i
$887$	18.4767	+	10.6675i	0.620388	+	0.358181i	0.777020	−	0.629476i	$-0.216730\pi$
$887$	18.4767	+	10.6675i	0.620388	+	0.358181i	−0.156632	+	0.987657i	$0.550064\pi$
$888$	36.9486	+	18.1482i	1.23991	+	0.609015i
$889$	−16.1978	+	16.1978i	−0.543258	+	0.543258i
$890$	4.04371	−	15.0913i	0.135545	−	0.505862i
$891$	1.62971	+	2.78183i	0.0545973	+	0.0931949i
$892$	25.5560	+	25.5560i	0.855677	+	0.855677i
$893$	39.9515	−	23.0660i	1.33692	−	0.771874i
$894$	−47.2882	+	3.17477i	−1.58156	+	0.106180i
$895$	10.0798	−	2.70087i	0.336930	−	0.0902801i
$896$	−10.4905			−0.350462
$897$		0			0
$898$	69.2090			2.30953
$899$	−14.5615	+	3.90173i	−0.485652	+	0.130130i
$900$	36.0827	+	46.7162i	1.20276	+	1.55721i
$901$	22.0680	−	12.7410i	0.735193	−	0.424464i
$902$	−4.52760	−	4.52760i	−0.150753	−	0.150753i
$903$	2.62656	−	0.896244i	0.0874063	−	0.0298251i
$904$	−10.2097	+	38.1031i	−0.339570	+	1.26729i
$905$	−12.5565	+	12.5565i	−0.417391	+	0.417391i
$906$	−18.4779	+	37.6199i	−0.613888	+	1.24984i
$907$	−9.85845	−	5.69178i	−0.327344	−	0.188992i	0.327317	−	0.944915i	$-0.393855\pi$
$907$	−9.85845	−	5.69178i	−0.327344	−	0.188992i	−0.654662	+	0.755922i	$0.727189\pi$
$908$	22.6296	+	84.4549i	0.750990	+	2.80273i
$909$	9.66324	−	23.5400i	0.320509	−	0.780774i
$910$		0			0
$911$		−	21.7806i		−	0.721625i	−0.932638	−	0.360812i	$-0.882499\pi$
$911$		−	21.7806i		−	0.721625i	0.932638	−	0.360812i	$-0.117501\pi$
$912$	67.1230	+	58.6772i	2.22267	+	1.94300i
$913$	2.14550	−	3.71612i	0.0710058	−	0.122986i
$914$	24.7278	+	42.8297i	0.817921	+	1.41668i
$915$	−7.32413	−	1.44479i	−0.242128	−	0.0477632i
$916$	−51.6917	−	13.8508i	−1.70794	−	0.457642i
$917$	10.3280	+	2.76737i	0.341059	+	0.0913866i
$918$	19.4408	−	29.3970i	0.641641	−	0.970246i
$919$	11.2307	+	19.4521i	0.370465	+	0.641665i	0.989637	−	0.143591i	$-0.0458649\pi$
$919$	11.2307	+	19.4521i	0.370465	+	0.641665i	−0.619172	+	0.785256i	$0.712532\pi$
$920$	16.4518	−	28.4954i	0.542400	−	0.939465i
$921$	9.20051	−	10.5248i	0.303167	−	0.346804i
$922$		−	11.5443i		−	0.380192i
$923$		0			0
$924$	2.70921	+	4.04073i	0.0891264	+	0.132930i
$925$	3.77560	+	14.0907i	0.124141	+	0.463301i
$926$	−79.3199	−	45.7954i	−2.60661	−	1.50493i
$927$	0.222503	+	1.64963i	0.00730796	+	0.0541808i
$928$	−47.2498	+	47.2498i	−1.55105	+	1.55105i
$929$	−7.03088	+	26.2396i	−0.230676	+	0.860893i	0.749375	+	0.662146i	$0.230354\pi$
$929$	−7.03088	+	26.2396i	−0.230676	+	0.860893i	−0.980051	+	0.198747i	$0.936313\pi$
$930$	−2.29719	−	6.73220i	−0.0753278	−	0.220758i
$931$	18.0408	+	18.0408i	0.591262	+	0.591262i
$932$	45.5530	−	26.3001i	1.49214	−	0.861487i
$933$	−2.94020	−	43.7944i	−0.0962580	−	1.43377i
$934$	25.0752	−	6.71888i	0.820486	−	0.219849i
$935$	−0.831591			−0.0271959
$936$		0			0
$937$	31.2647			1.02137			0.510687	−	0.859767i	$-0.329391\pi$
$937$	31.2647			1.02137			0.510687	+	0.859767i	$0.329391\pi$
$938$	−52.7855	+	14.1438i	−1.72351	+	0.461812i
$939$	−0.405484	−	6.03970i	−0.0132325	−	0.197098i
$940$	−26.9194	+	15.5419i	−0.878015	+	0.506922i
$941$	18.1003	+	18.1003i	0.590052	+	0.590052i	0.937645	−	0.347593i	$-0.113001\pi$
$941$	18.1003	+	18.1003i	0.590052	+	0.590052i	−0.347593	+	0.937645i	$0.613001\pi$
$942$	−31.7590	−	93.0738i	−1.03476	−	3.03251i
$943$	9.70951	−	36.2364i	0.316185	−	1.18002i
$944$	61.3626	−	61.3626i	1.99718	−	1.99718i
$945$	5.11684	+	5.77894i	0.166451	+	0.187989i
$946$	−0.763133	−	0.440595i	−0.0248116	−	0.0143250i
$947$	−7.28196	−	27.1767i	−0.236632	−	0.883123i	−0.977406	−	0.211369i	$-0.932208\pi$
$947$	−7.28196	−	27.1767i	−0.236632	−	0.883123i	0.740774	−	0.671754i	$-0.234459\pi$
$948$	−16.5604	−	24.6994i	−0.537855	−	0.802200i
$949$		0			0
$950$			66.5941i			2.16060i
$951$	−8.47497	+	9.69482i	−0.274820	+	0.314376i
$952$	15.1859	−	26.3028i	0.492179	−	0.852480i
$953$	26.5304	+	45.9519i	0.859403	+	1.48853i	0.872500	+	0.488615i	$0.162498\pi$
$953$	26.5304	+	45.9519i	0.859403	+	1.48853i	−0.0130968	+	0.999914i	$0.504169\pi$
$954$	28.9590	+	69.2908i	0.937584	+	2.24337i
$955$	−14.4569	−	3.87371i	−0.467814	−	0.125350i
$956$	8.42068	+	2.25631i	0.272344	+	0.0729744i
$957$	−5.09575	−	1.00521i	−0.164722	−	0.0324937i
$958$	−7.63340	−	13.2214i	−0.246624	−	0.427165i
$959$	1.71747	−	2.97475i	0.0554601	−	0.0960598i
$960$	−4.34077	−	3.79459i	−0.140098	−	0.122470i
$961$			27.7568i			0.895382i
$962$		0			0
$963$	9.21278	+	3.78187i	0.296878	+	0.121869i
$964$	28.0741	+	104.774i	0.904205	+	3.37454i
$965$	−12.8009	−	7.39062i	−0.412077	−	0.237912i
$966$	−17.9555	+	36.5563i	−0.577710	+	1.17618i
$967$	6.28251	−	6.28251i	0.202032	−	0.202032i	−0.598838	−	0.800870i	$-0.704371\pi$
$967$	6.28251	−	6.28251i	0.202032	−	0.202032i	0.800870	+	0.598838i	$0.204371\pi$
$968$	−19.3433	+	72.1901i	−0.621716	+	2.32028i
$969$	26.3354	−	8.98629i	0.846016	−	0.288681i
$970$	8.53128	+	8.53128i	0.273923	+	0.273923i
$971$	45.4442	−	26.2372i	1.45838	−	0.841993i	0.459444	−	0.888207i	$-0.348049\pi$
$971$	45.4442	−	26.2372i	1.45838	−	0.841993i	0.998932	+	0.0462136i	$0.0147155\pi$
$972$	55.0307	+	47.4939i	1.76511	+	1.52337i
$973$	8.30494	−	2.22530i	0.266244	−	0.0713399i
$974$	−24.2548			−0.777173
$975$		0			0
$976$	−41.0718			−1.31468
$977$	18.5228	−	4.96318i	0.592598	−	0.158786i	0.0499578	−	0.998751i	$-0.484091\pi$
$977$	18.5228	−	4.96318i	0.592598	−	0.158786i	0.542640	+	0.839965i	$0.317425\pi$
$978$	−91.7439	+	6.15937i	−2.93365	+	0.196955i
$979$	2.12542	−	1.22711i	0.0679288	−	0.0392187i
$980$	−12.1559	−	12.1559i	−0.388307	−	0.388307i
$981$	−5.02527	+	6.59225i	−0.160444	+	0.210474i
$982$	−16.2709	+	60.7240i	−0.519227	+	1.93778i
$983$	−11.5787	+	11.5787i	−0.369303	+	0.369303i	−0.867223	−	0.497920i	$-0.834097\pi$
$983$	−11.5787	+	11.5787i	−0.369303	+	0.369303i	0.497920	+	0.867223i	$0.334097\pi$
$984$	−74.0033	−	36.3486i	−2.35914	−	1.15875i
$985$	11.1904	+	6.46080i	0.356557	+	0.205858i
$986$	14.6952	+	54.8431i	0.467989	+	1.74656i
$987$	18.2510	−	12.2368i	0.580935	−	0.389502i
$988$		0			0
$989$		−	5.16282i		−	0.164168i
$990$	0.312186	−	2.43085i	0.00992191	−	0.0772574i
$991$	17.6883	−	30.6370i	0.561886	−	0.973215i	−0.435446	−	0.900215i	$-0.643409\pi$
$991$	17.6883	−	30.6370i	0.561886	−	0.973215i	0.997332	−	0.0730004i	$-0.0232574\pi$
$992$	−7.18776	−	12.4496i	−0.228211	−	0.395274i
$993$	6.02772	−	30.5566i	0.191284	−	0.969685i
$994$	13.4888	+	3.61431i	0.427839	+	0.114639i
$995$	0.285274	+	0.0764390i	0.00904380	+	0.00242328i
$996$	18.7240	−	94.9184i	0.593292	−	3.00760i
$997$	27.2807	+	47.2516i	0.863990	+	1.49647i	0.868047	+	0.496482i	$0.165375\pi$
$997$	27.2807	+	47.2516i	0.863990	+	1.49647i	−0.00405739	+	0.999992i	$0.501292\pi$
$998$	−12.7256	+	22.0414i	−0.402823	+	0.697709i
$999$	8.02201	+	16.0738i	0.253805	+	0.508551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.188.2		96
3.2	odd	2	inner	507.2.k.k.188.23		96
13.2	odd	12	inner	507.2.k.k.89.1		96
13.3	even	3	inner	507.2.k.k.80.23		96
13.4	even	6		507.2.f.g.239.1	✓	48
13.5	odd	4	inner	507.2.k.k.488.24		96
13.6	odd	12		507.2.f.g.437.23	yes	48
13.7	odd	12		507.2.f.g.437.1	yes	48
13.8	odd	4	inner	507.2.k.k.488.2		96
13.9	even	3		507.2.f.g.239.23	yes	48
13.10	even	6	inner	507.2.k.k.80.1		96
13.11	odd	12	inner	507.2.k.k.89.23		96
13.12	even	2	inner	507.2.k.k.188.24		96
39.2	even	12	inner	507.2.k.k.89.24		96
39.5	even	4	inner	507.2.k.k.488.1		96
39.8	even	4	inner	507.2.k.k.488.23		96
39.11	even	12	inner	507.2.k.k.89.2		96
39.17	odd	6		507.2.f.g.239.24	yes	48
39.20	even	12		507.2.f.g.437.24	yes	48
39.23	odd	6	inner	507.2.k.k.80.24		96
39.29	odd	6	inner	507.2.k.k.80.2		96
39.32	even	12		507.2.f.g.437.2	yes	48
39.35	odd	6		507.2.f.g.239.2	yes	48
39.38	odd	2	inner	507.2.k.k.188.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.1	✓	48	13.4	even	6
507.2.f.g.239.2	yes	48	39.35	odd	6
507.2.f.g.239.23	yes	48	13.9	even	3
507.2.f.g.239.24	yes	48	39.17	odd	6
507.2.f.g.437.1	yes	48	13.7	odd	12
507.2.f.g.437.2	yes	48	39.32	even	12
507.2.f.g.437.23	yes	48	13.6	odd	12
507.2.f.g.437.24	yes	48	39.20	even	12
507.2.k.k.80.1		96	13.10	even	6	inner
507.2.k.k.80.2		96	39.29	odd	6	inner
507.2.k.k.80.23		96	13.3	even	3	inner
507.2.k.k.80.24		96	39.23	odd	6	inner
507.2.k.k.89.1		96	13.2	odd	12	inner
507.2.k.k.89.2		96	39.11	even	12	inner
507.2.k.k.89.23		96	13.11	odd	12	inner
507.2.k.k.89.24		96	39.2	even	12	inner
507.2.k.k.188.1		96	39.38	odd	2	inner
507.2.k.k.188.2		96	1.1	even	1	trivial
507.2.k.k.188.23		96	3.2	odd	2	inner
507.2.k.k.188.24		96	13.12	even	2	inner
507.2.k.k.488.1		96	39.5	even	4	inner
507.2.k.k.488.2		96	13.8	odd	4	inner
507.2.k.k.488.23		96	39.8	even	4	inner
507.2.k.k.488.24		96	13.5	odd	4	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.49335 + 0.668092i) q^{2} +(0.116023 + 1.72816i) q^{3} +(4.03841 - 2.33158i) q^{4} +(-0.624703 - 0.624703i) q^{5} +(-1.44386 - 4.23140i) q^{6} +(0.435181 - 1.62412i) q^{7} +(-4.86096 + 4.86096i) q^{8} +(-2.97308 + 0.401012i) q^{9} +O(q^{10})\)	\(q+(-2.49335 + 0.668092i) q^{2} +(0.116023 + 1.72816i) q^{3} +(4.03841 - 2.33158i) q^{4} +(-0.624703 - 0.624703i) q^{5} +(-1.44386 - 4.23140i) q^{6} +(0.435181 - 1.62412i) q^{7} +(-4.86096 + 4.86096i) q^{8} +(-2.97308 + 0.401012i) q^{9} +(1.97496 + 1.14025i) q^{10} +(0.0927163 + 0.346022i) q^{11} +(4.49789 + 6.70851i) q^{12} +4.34024i q^{14} +(1.00711 - 1.15207i) q^{15} +(4.20937 - 7.29084i) q^{16} +(-1.31381 - 2.27558i) q^{17} +(7.14502 - 2.98615i) q^{18} +(5.90581 + 1.58246i) q^{19} +(-3.97935 - 1.06626i) q^{20} +(2.85722 + 0.563628i) q^{21} +(-0.462349 - 0.800812i) q^{22} +(2.70887 - 4.69190i) q^{23} +(-8.96451 - 7.83654i) q^{24} -4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(-2.02932 - 7.57351i) q^{28} +(7.24949 + 4.18549i) q^{29} +(-1.74139 + 3.54535i) q^{30} +(-1.27341 + 1.27341i) q^{31} +(-2.06602 + 7.71050i) q^{32} +(-0.587225 + 0.200375i) q^{33} +(4.79608 + 4.79608i) q^{34} +(-1.28645 + 0.742731i) q^{35} +(-11.0715 + 8.55142i) q^{36} +(-3.33944 + 0.894800i) q^{37} -15.7825 q^{38} +6.07331 q^{40} +(6.68847 - 1.79217i) q^{41} +(-7.50063 + 0.503566i) q^{42} +(0.825277 - 0.476474i) q^{43} +(1.18121 + 1.18121i) q^{44} +(2.10780 + 1.60678i) q^{45} +(-3.61955 + 13.5083i) q^{46} +(5.33521 - 5.33521i) q^{47} +(13.0881 + 6.42856i) q^{48} +(3.61381 + 2.08643i) q^{49} +(2.81901 + 10.5207i) q^{50} +(3.78013 - 2.53449i) q^{51} +9.69778i q^{53} +(5.98954 + 12.0013i) q^{54} +(0.158241 - 0.274081i) q^{55} +(5.77937 + 10.0102i) q^{56} +(-2.04953 + 10.3898i) q^{57} +(-20.8718 - 5.59259i) q^{58} +(9.95670 + 2.66789i) q^{59} +(1.38098 - 7.00067i) q^{60} +(-2.43931 - 4.22500i) q^{61} +(2.32431 - 4.02583i) q^{62} +(-0.642536 + 5.00314i) q^{63} -3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(3.25877 + 12.1619i) q^{67} +(-10.6114 - 6.12649i) q^{68} +(8.42264 + 4.13699i) q^{69} +(2.71136 - 2.71136i) q^{70} +(0.832745 - 3.10785i) q^{71} +(12.5027 - 16.4013i) q^{72} +(-0.246530 - 0.246530i) q^{73} +(7.72860 - 4.46211i) q^{74} +(7.29196 - 0.489557i) q^{75} +(27.5397 - 7.37925i) q^{76} +0.602329 q^{77} -3.68180 q^{79} +(-7.18422 + 1.92500i) q^{80} +(8.67838 - 2.38448i) q^{81} +(-15.4794 + 8.93703i) q^{82} +(-8.47001 - 8.47001i) q^{83} +(12.8528 - 4.38568i) q^{84} +(-0.600822 + 2.24230i) q^{85} +(-1.73938 + 1.73938i) q^{86} +(-6.39210 + 13.0139i) q^{87} +(-2.13269 - 1.23131i) q^{88} +(-1.77317 - 6.61757i) q^{89} +(-6.32897 - 2.59806i) q^{90} -25.2638i q^{92} +(-2.34841 - 2.05292i) q^{93} +(-9.73816 + 16.8670i) q^{94} +(-2.70081 - 4.67794i) q^{95} +(-13.5647 - 2.67583i) q^{96} +(5.11027 + 1.36929i) q^{97} +(-10.4044 - 2.78786i) q^{98} +(-0.414412 - 0.991570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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