LMFDB - Embedded newform 507.2.k.k.89.2

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			89.2
Character	$\chi$	$=$	507.89
Dual form			507.2.k.k.188.2

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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	−0.775732	−	0.631062i	$-0.782619\pi$
$2$	−2.49335	−	0.668092i	−1.76307	−	0.472412i	−0.987335	+	0.158650i	$0.949286\pi$
$3$	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	−0.832860	−	0.553484i	$-0.813298\pi$
$5$	−0.624703	+	0.624703i	−0.279376	+	0.279376i	0.553484	+	0.832860i	$0.313298\pi$
$6$	−1.44386	+	4.23140i	−0.589452	+	1.72746i
$7$	0.435181	+	1.62412i	0.164483	+	0.613858i	0.998106	+	0.0615241i	$0.0195961\pi$
$7$	0.435181	+	1.62412i	0.164483	+	0.613858i	−0.833623	+	0.552334i	$0.813737\pi$
$8$	−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	−0.950539	−	0.310606i	$-0.899468\pi$
$11$	0.0927163	−	0.346022i	0.0279550	−	0.104330i	0.978494	+	0.206277i	$0.0661347\pi$
$12$	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	−0.980206	−	0.197983i	$-0.936561\pi$
$17$	−1.31381	+	2.27558i	−0.318645	+	0.551909i	0.661561	+	0.749892i	$0.269894\pi$
$18$	7.14502	+	2.98615i	1.68410	+	0.703843i
$19$	5.90581	−	1.58246i	1.35488	−	0.363040i	0.492949	−	0.870058i	$-0.335919\pi$
$19$	5.90581	−	1.58246i	1.35488	−	0.363040i	0.861936	+	0.507018i	$0.169252\pi$
$20$	−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	0.997065	+	0.0765633i	$0.0243947\pi$
$23$	2.70887	+	4.69190i	0.564838	+	0.978328i	−0.432227	+	0.901765i	$0.642272\pi$
$24$	−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	0.358488	−	0.933535i	$-0.383293\pi$
$29$	7.24949	−	4.18549i	1.34620	−	0.777227i	0.987708	+	0.156308i	$0.0499592\pi$
$30$	−1.74139	−	3.54535i	−0.317932	−	0.647289i
$31$	−1.27341	−	1.27341i	−0.228712	−	0.228712i	0.583443	−	0.812154i	$-0.301705\pi$
$31$	−1.27341	−	1.27341i	−0.228712	−	0.228712i	−0.812154	+	0.583443i	$0.801705\pi$
$32$	−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	−0.0263524	−	0.999653i	$-0.508389\pi$
$37$	−3.33944	−	0.894800i	−0.549001	−	0.147104i	−0.522648	+	0.852548i	$0.675056\pi$
$38$	−15.7825			−2.56026
$39$		0			0
$40$	6.07331			0.960275
$41$	6.68847	+	1.79217i	1.04456	+	0.279890i	0.740004	−	0.672603i	$-0.234824\pi$
$41$	6.68847	+	1.79217i	1.04456	+	0.279890i	0.304560	+	0.952493i	$0.401490\pi$
$42$	−7.50063	−	0.503566i	−1.15737	−	0.0777019i
$43$	0.825277	+	0.476474i	0.125854	+	0.0726616i	0.561605	−	0.827405i	$-0.310184\pi$
$43$	0.825277	+	0.476474i	0.125854	+	0.0726616i	−0.435752	+	0.900067i	$0.643517\pi$
$44$	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	0.979528	−	0.201308i	$-0.0645191\pi$
$47$	5.33521	+	5.33521i	0.778220	+	0.778220i	−0.201308	+	0.979528i	$0.564519\pi$
$48$	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	$-0.767985\pi$
$53$		−	9.69778i		−	1.33209i	0.745911	−	0.666046i	$-0.232015\pi$
$54$	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	0.456220	−	0.889867i	$-0.349203\pi$
$59$	9.95670	−	2.66789i	1.29625	−	0.347330i	0.840032	+	0.542538i	$0.182536\pi$
$60$	1.38098	+	7.00067i	0.178284	+	0.903783i
$61$	−2.43931	+	4.22500i	−0.312321	+	0.540956i	−0.978864	−	0.204510i	$-0.934440\pi$
$61$	−2.43931	+	4.22500i	−0.312321	+	0.540956i	0.666543	+	0.745466i	$0.267773\pi$
$62$	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	−0.418275	−	0.908320i	$-0.637365\pi$
$67$	3.25877	−	12.1619i	0.398122	−	1.48581i	0.816397	−	0.577491i	$-0.195968\pi$
$68$	−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	0.997572	−	0.0696413i	$-0.0221855\pi$
$71$	0.832745	+	3.10785i	0.0988287	+	0.368834i	−0.898743	+	0.438475i	$0.855519\pi$
$72$	12.5027	+	16.4013i	1.47346	+	1.93291i
$73$	−0.246530	+	0.246530i	−0.0288542	+	0.0288542i	−0.721387	−	0.692532i	$-0.756495\pi$
$73$	−0.246530	+	0.246530i	−0.0288542	+	0.0288542i	0.692532	+	0.721387i	$0.256495\pi$
$74$	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	−0.997687	−	0.0679819i	$-0.978344\pi$
$83$	−8.47001	+	8.47001i	−0.929705	+	0.929705i	0.0679819	+	0.997687i	$0.478344\pi$
$84$	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	0.806022	+	0.591885i	$0.201616\pi$
$89$	−1.77317	+	6.61757i	−0.187956	+	0.701461i	−0.993978	+	0.109576i	$0.965051\pi$
$90$	−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	0.0101260	−	0.999949i	$-0.496777\pi$
$97$	5.11027	−	1.36929i	0.518870	−	0.139031i	0.508744	+	0.860918i	$0.330110\pi$
$98$	−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	0.574136	−	0.818760i	$-0.305338\pi$
$101$	−4.24104	−	7.34570i	−0.421999	−	0.730924i	−0.996135	+	0.0878358i	$0.972005\pi$
$102$	−7.73194	−	8.84485i	−0.765576	−	0.875770i
$103$			0.554855i			0.0546714i	0.999626	+	0.0273357i	$0.00870232\pi$
$103$			0.554855i			0.0546714i	−0.999626	+	0.0273357i	$0.991298\pi$
$104$		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	−0.632483	−	0.774574i	$-0.717964\pi$
$107$	−2.87486	+	1.65980i	−0.277923	+	0.160459i	0.354560	+	0.935033i	$0.384631\pi$
$108$	−16.0628	+	18.1412i	−1.54564	+	1.74564i
$109$	1.95379	+	1.95379i	0.187139	+	0.187139i	0.794458	−	0.607319i	$-0.207755\pi$
$109$	1.95379	+	1.95379i	0.187139	+	0.187139i	−0.607319	+	0.794458i	$0.707755\pi$
$110$	−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	0.715188	−	0.698932i	$-0.246341\pi$
$113$	4.96947	+	2.86913i	0.467489	+	0.269905i	−0.247699	+	0.968837i	$0.579674\pi$
$114$	−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	−0.921795	−	0.387678i	$-0.873277\pi$
$127$	−11.7986	+	6.81191i	−1.04695	+	0.604459i	−0.125159	+	0.992137i	$0.539944\pi$
$128$	−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	$-0.910395\pi$
$131$		−	6.35913i		−	0.555599i	0.960639	−	0.277800i	$-0.0896052\pi$
$132$	−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	−0.173537	−	0.984827i	$-0.555520\pi$
$137$	1.97329	−	0.528741i	0.168589	−	0.0451734i	0.342126	+	0.939654i	$0.388853\pi$
$138$	−23.7645	+	4.68789i	−2.02297	+	0.399059i
$139$	2.55676	−	4.42843i	0.216861	−	0.375615i	−0.736986	−	0.675908i	$-0.763751\pi$
$139$	2.55676	−	4.42843i	0.216861	−	0.375615i	0.953847	+	0.300294i	$0.0970848\pi$
$140$	−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	0.982498	+	0.186274i	$0.0596412\pi$
$149$	2.74363	+	10.2394i	0.224767	+	0.838841i	−0.757731	+	0.652567i	$0.773692\pi$
$150$	−17.8544	−	6.09234i	−1.45780	−	0.497437i
$151$	−6.62875	+	6.62875i	−0.539440	+	0.539440i	−0.923364	−	0.383925i	$-0.874572\pi$
$151$	−6.62875	+	6.62875i	−0.539440	+	0.539440i	0.383925	+	0.923364i	$0.374572\pi$
$152$	−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	0.780953	+	0.624590i	$0.214734\pi$
$163$	5.32291	+	19.8654i	0.416923	+	1.55598i	−0.364030	+	0.931387i	$0.618600\pi$
$164$	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	0.789916	+	0.613215i	$0.210124\pi$
$167$	−2.59464	+	9.68331i	−0.200779	+	0.749317i	−0.990695	+	0.136102i	$0.956542\pi$
$168$	−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	−0.550988	−	0.834513i	$-0.685749\pi$
$173$	5.88220	−	10.1883i	0.447215	−	0.774599i	0.998204	+	0.0599136i	$0.0190825\pi$
$174$	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	0.556365	−	0.830938i	$-0.312196\pi$
$179$	−5.90594	−	10.2294i	−0.441431	−	0.764580i	−0.997796	+	0.0663576i	$0.978862\pi$
$180$	12.2585	−	1.57432i	0.913695	−	0.117343i
$181$			20.0999i			1.49402i	0.664815	+	0.747008i	$0.268510\pi$
$181$			20.0999i			1.49402i	−0.664815	+	0.747008i	$0.731490\pi$
$182$		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	0.925871	−	0.377839i	$-0.123333\pi$
$191$	14.6715	+	8.47057i	1.06159	+	0.612909i	0.135718	+	0.990748i	$0.456666\pi$
$192$	6.51139	+	0.437152i	0.469919	+	0.0315487i
$193$	16.1609	+	4.33031i	1.16329	+	0.311702i	0.788279	−	0.615318i	$-0.210973\pi$
$193$	16.1609	+	4.33031i	1.16329	+	0.311702i	0.375010	+	0.927021i	$0.377639\pi$
$194$	−13.6565			−0.980482
$195$		0			0
$196$	19.4587			1.38991
$197$	−14.1277	−	3.78551i	−1.00656	−	0.269706i	−0.282367	−	0.959306i	$-0.591120\pi$
$197$	−14.1277	−	3.78551i	−1.00656	−	0.269706i	−0.724190	+	0.689600i	$0.757786\pi$
$198$	1.69574	−	2.19547i	0.120511	−	0.156025i
$199$	−0.289508	−	0.167148i	−0.0205227	−	0.0118488i	0.489704	−	0.871889i	$-0.337105\pi$
$199$	−0.289508	−	0.167148i	−0.0205227	−	0.0118488i	−0.510226	+	0.860040i	$0.670438\pi$
$200$	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	0.908589	−	0.417692i	$-0.137161\pi$
$211$	1.34455	+	2.32883i	0.0925626	+	0.160323i	−0.816026	+	0.578015i	$0.803828\pi$
$212$	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	−0.865670	−	0.500614i	$-0.833107\pi$
$223$	2.00597	−	7.48636i	0.134329	−	0.501324i	1.00000		0.000709598i	$-0.000225872\pi$
$224$	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	−0.917200	−	0.398427i	$-0.869556\pi$
$227$	−4.85285	−	18.1111i	−0.322095	−	1.20207i	0.595105	−	0.803648i	$-0.297110\pi$
$228$	15.9478	−	46.7369i	1.05617	−	3.09523i
$229$	−8.11488	+	8.11488i	−0.536246	+	0.536246i	−0.922424	−	0.386178i	$-0.873795\pi$
$229$	−8.11488	+	8.11488i	−0.536246	+	0.536246i	0.386178	+	0.922424i	$0.373795\pi$
$230$	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	−0.663059	−	0.748567i	$-0.730742\pi$
$239$	1.32193	−	1.32193i	0.0855084	−	0.0855084i	0.748567	+	0.663059i	$0.230742\pi$
$240$	−4.16025	+	12.1921i	−0.268543	+	0.786999i
$241$	−6.02040	−	22.4684i	−0.387808	−	1.44732i	−0.833693	−	0.552228i	$-0.813778\pi$
$241$	−6.02040	−	22.4684i	−0.387808	−	1.44732i	0.445885	−	0.895090i	$-0.352889\pi$
$242$	−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	−0.984552	−	0.175090i	$-0.943978\pi$
$251$	−5.39681	+	9.34756i	−0.340644	+	0.590013i	0.643909	+	0.765102i	$0.277312\pi$
$252$	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	0.791991	−	0.610533i	$-0.209045\pi$
$257$	−2.12801	−	3.68582i	−0.132741	−	0.229915i	−0.924732	+	0.380618i	$0.875711\pi$
$258$	−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	−0.988744	−	0.149615i	$-0.952196\pi$
$263$	−21.9508	+	12.6733i	−1.35355	+	0.781470i	−0.364801	+	0.931085i	$0.618863\pi$
$264$	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	0.959835	−	0.280566i	$-0.0905222\pi$
$269$	19.6286	+	11.3326i	1.19677	+	0.690958i	0.236940	+	0.971524i	$0.423855\pi$
$270$	3.75555	+	11.2389i	0.228556	+	0.683979i
$271$	−20.5887	−	5.51672i	−1.25067	−	0.335117i	−0.428077	−	0.903742i	$-0.640809\pi$
$271$	−20.5887	−	5.51672i	−1.25067	−	0.335117i	−0.822597	+	0.568625i	$0.807476\pi$
$272$	−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	0.195644	−	0.980675i	$-0.437320\pi$
$277$	−9.25074	−	5.34092i	−0.555823	−	0.320905i	−0.751467	+	0.659770i	$0.770654\pi$
$278$	−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	0.349761	−	0.936839i	$-0.386263\pi$
$281$	−9.84122	−	9.84122i	−0.587078	−	0.587078i	−0.936839	+	0.349761i	$0.886263\pi$
$282$	−30.2787	+	14.8721i	−1.80307	+	0.885623i
$283$	−14.1131	+	8.14822i	−0.838938	+	0.484361i	−0.856903	−	0.515477i	$-0.827615\pi$
$283$	−14.1131	+	8.14822i	−0.838938	+	0.484361i	0.0179649	+	0.999839i	$0.494281\pi$
$284$	−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	−0.691117	−	0.722742i	$-0.742881\pi$
$293$	−15.8895	+	4.25757i	−0.928272	+	0.248730i	−0.237154	+	0.971472i	$0.576215\pi$
$294$	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	−0.850955	−	0.525238i	$-0.823976\pi$
$307$	−5.70702	+	5.70702i	−0.325717	+	0.325717i	0.525238	+	0.850955i	$0.323976\pi$
$308$	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	−0.543893	−	0.839154i	$-0.683050\pi$
$317$	5.25697	−	5.25697i	0.295261	−	0.295261i	0.839154	+	0.543893i	$0.183050\pi$
$318$	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	−0.702353	−	0.711829i	$-0.747867\pi$
$331$	−17.3691	+	4.65404i	−0.954693	+	0.255809i	−0.252341	+	0.967638i	$0.581200\pi$
$332$	−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	$-0.852749\pi$
$337$		−	16.3852i		−	0.892558i	0.894894	−	0.446279i	$-0.147251\pi$
$338$		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	−0.177946	−	0.984040i	$-0.556945\pi$
$347$	−20.8470	−	12.0360i	−1.11912	−	0.646126i	−0.941177	+	0.337914i	$0.890279\pi$
$348$	4.52897	−	67.4592i	0.242778	−	3.61619i
$349$	16.7180	+	4.47957i	0.894894	+	0.239786i	0.676822	−	0.736147i	$-0.263357\pi$
$349$	16.7180	+	4.47957i	0.894894	+	0.239786i	0.218072	+	0.975933i	$0.430023\pi$
$350$	18.3136			0.978903
$351$		0			0
$352$	−2.85956			−0.152415
$353$	20.4711	+	5.48522i	1.08957	+	0.291949i	0.758510	−	0.651662i	$-0.225928\pi$
$353$	20.4711	+	5.48522i	1.08957	+	0.291949i	0.331058	+	0.943611i	$0.392595\pi$
$354$	−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	0.0103977	−	0.999946i	$-0.496690\pi$
$359$	−18.7493	−	18.7493i	−0.989548	−	0.989548i	−0.999946	+	0.0103977i	$0.996690\pi$
$360$	−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	−0.999361	−	0.0357329i	$-0.988623\pi$
$367$	−10.1653	−	17.6069i	−0.530626	−	0.919072i	0.468735	−	0.883339i	$-0.344710\pi$
$368$	−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	0.0702957	+	0.997526i	$0.477606\pi$
$373$	−16.0055	+	27.7224i	−0.828735	+	1.43541i	−0.899031	+	0.437885i	$0.855728\pi$
$374$	−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	−0.747894	−	0.663818i	$-0.768935\pi$
$379$	4.51091	−	16.8350i	0.231710	−	0.864754i	0.979604	−	0.200936i	$-0.0643983\pi$
$380$	−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	0.947361	+	0.320166i	$0.103739\pi$
$383$	5.61681	+	20.9622i	0.287005	+	1.07112i	−0.660356	+	0.750953i	$0.729595\pi$
$384$	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	−0.788175	−	0.615451i	$-0.788974\pi$
$397$	−8.23536	−	30.7348i	−0.413321	−	1.54253i	0.374855	−	0.927084i	$-0.377693\pi$
$398$	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	−0.0744193	−	0.997227i	$-0.523710\pi$
$401$	9.78507	−	36.5184i	0.488643	−	1.82364i	0.563062	−	0.826414i	$-0.309623\pi$
$402$	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	−0.185629	−	0.982620i	$-0.559432\pi$
$409$	2.93087	−	0.785323i	0.144922	−	0.0388317i	0.330551	+	0.943788i	$0.392766\pi$
$410$	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	0.575778	−	0.817606i	$-0.304699\pi$
$419$	32.1726	−	18.5749i	1.57173	−	0.907442i	0.995957	−	0.0898356i	$-0.0286342\pi$
$420$	−10.7689	+	5.28943i	−0.525470	+	0.258098i
$421$	18.7201	+	18.7201i	0.912361	+	0.912361i	0.996458	−	0.0840970i	$-0.0268006\pi$
$421$	18.7201	+	18.7201i	0.912361	+	0.912361i	−0.0840970	+	0.996458i	$0.526801\pi$
$422$	−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	0.0858886	−	0.996305i	$-0.472627\pi$
$431$	−7.01461	−	1.87956i	−0.337882	−	0.0905352i	−0.423771	+	0.905770i	$0.639294\pi$
$432$	−41.4900	+	13.8641i	−1.99619	+	0.667038i
$433$	−5.89093	−	3.40113i	−0.283100	−	0.163448i	0.351726	−	0.936103i	$-0.385595\pi$
$433$	−5.89093	−	3.40113i	−0.283100	−	0.163448i	−0.634826	+	0.772655i	$0.718928\pi$
$434$	−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	−0.796124	−	0.605134i	$-0.793120\pi$
$439$	−14.0407	+	8.10639i	−0.670125	+	0.386897i	0.125999	+	0.992030i	$0.459786\pi$
$440$	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	$0.0462799\pi$
$443$			6.09878i			0.289762i	−0.989449	+	0.144881i	$0.953720\pi$
$444$	−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	−0.811538	−	0.584299i	$-0.801370\pi$
$449$	−25.8980	+	6.93935i	−1.22220	+	0.327488i	−0.410663	+	0.911787i	$0.634703\pi$
$450$	−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	0.747536	+	0.664221i	$0.231237\pi$
$457$	−4.95873	+	18.5062i	−0.231960	+	0.865686i	−0.979496	+	0.201464i	$0.935430\pi$
$458$	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	0.933718	−	0.358010i	$-0.116545\pi$
$461$	−1.15751	−	4.31989i	−0.0539106	−	0.201197i	−0.987628	+	0.156813i	$0.949878\pi$
$462$	−0.869676	+	2.54869i	−0.0404610	+	0.118576i
$463$	25.0898	−	25.0898i	1.16602	−	1.16602i	0.182885	−	0.983134i	$-0.441456\pi$
$463$	25.0898	−	25.0898i	1.16602	−	1.16602i	0.983134	−	0.182885i	$-0.0585437\pi$
$464$	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	−0.922097	−	0.386959i	$-0.873526\pi$
$479$	1.53075	−	5.71284i	0.0699418	−	0.261026i	0.992039	+	0.125932i	$0.0401923\pi$
$480$	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	−0.0472463	−	0.998883i	$-0.515045\pi$
$487$	9.07613	−	2.43194i	0.411279	−	0.110202i	0.458525	+	0.888681i	$0.348378\pi$
$488$	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	0.998305	+	0.0581914i	$0.0185334\pi$
$491$	12.1772	+	21.0915i	0.549548	+	0.951845i	−0.448758	+	0.893654i	$0.648133\pi$
$492$	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	0.845725	−	0.533618i	$-0.179168\pi$
$499$	6.97195	+	6.97195i	0.312107	+	0.312107i	−0.533618	+	0.845725i	$0.679168\pi$
$500$	−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	0.224016	−	0.974586i	$-0.428083\pi$
$503$	−11.3931	−	6.57779i	−0.507992	−	0.293289i	−0.732008	+	0.681296i	$0.761417\pi$
$504$	−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	0.658334	−	0.752726i	$-0.271261\pi$
$509$	19.2244	+	5.15115i	0.852105	+	0.228321i	0.193771	+	0.981047i	$0.437928\pi$
$510$	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	$0.0918865\pi$
$521$			12.9958i			0.569355i	−0.958623	+	0.284678i	$0.908113\pi$
$522$	64.2963	−	8.25736i	2.81417	−	0.361415i
$523$	−3.05976	−	5.29966i	−0.133794	−	0.231738i	0.791342	−	0.611374i	$-0.209383\pi$
$523$	−3.05976	−	5.29966i	−0.133794	−	0.231738i	−0.925136	+	0.379636i	$0.876049\pi$
$524$	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	−0.881005	−	0.473107i	$-0.843132\pi$
$541$	−9.48746	+	9.48746i	−0.407898	+	0.407898i	0.473107	+	0.881005i	$0.343132\pi$
$542$	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	−0.733012	−	0.680216i	$-0.761886\pi$
$557$	5.70912	−	21.3067i	0.241903	−	0.902795i	0.974915	−	0.222579i	$-0.0714474\pi$
$558$	−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	−0.0658393	−	0.997830i	$-0.520972\pi$
$563$	19.7230	−	34.1613i	0.831227	−	1.43973i	0.897066	−	0.441897i	$-0.145694\pi$
$564$	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	0.659101	−	0.752055i	$-0.270937\pi$
$569$	−7.67489	−	13.2933i	−0.321748	−	0.557284i	−0.980849	+	0.194771i	$0.937604\pi$
$570$	−15.8947	−	18.1825i	−0.665754	−	0.761580i
$571$			4.70947i			0.197085i	0.995133	+	0.0985425i	$0.0314181\pi$
$571$			4.70947i			0.197085i	−0.995133	+	0.0985425i	$0.968582\pi$
$572$		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	−0.998931	−	0.0462290i	$-0.985280\pi$
$577$	−25.1056	−	25.1056i	−1.04516	−	1.04516i	−0.0462290	−	0.998931i	$-0.514720\pi$
$578$	−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	−0.104934	−	0.994479i	$-0.533463\pi$
$587$	−16.7912	−	4.49920i	−0.693049	−	0.185702i	−0.588115	+	0.808777i	$0.700130\pi$
$588$	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	0.780526	−	0.625124i	$-0.214952\pi$
$593$	3.78428	+	3.78428i	0.155402	+	0.155402i	−0.625124	+	0.780526i	$0.714952\pi$
$594$	−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	$-0.958559\pi$
$599$		−	6.35465i		−	0.259644i	0.991537	−	0.129822i	$-0.0414406\pi$
$600$	−33.0662	−	37.8257i	−1.34992	−	1.54423i
$601$	−12.4761	−	21.6093i	−0.508912	−	0.881461i	−0.999947	−	0.0103212i	$-0.996715\pi$
$601$	−12.4761	−	21.6093i	−0.508912	−	0.881461i	0.491035	−	0.871140i	$-0.336619\pi$
$602$	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	−0.905795	−	0.423715i	$-0.860726\pi$
$607$	−2.11757	+	3.66773i	−0.0859494	+	0.148869i	0.819846	+	0.572584i	$0.194059\pi$
$608$	−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	−0.457686	−	0.889114i	$-0.651321\pi$
$613$	9.48855	−	35.4117i	0.383239	−	1.43027i	0.840924	−	0.541153i	$-0.182012\pi$
$614$	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	0.920971	+	0.389631i	$0.127398\pi$
$617$	7.90398	+	29.4981i	0.318202	+	1.18755i	−0.602769	+	0.797916i	$0.705936\pi$
$618$	−2.34781	−	0.801130i	−0.0944429	−	0.0322262i
$619$	11.8576	−	11.8576i	0.476599	−	0.476599i	−0.427443	−	0.904042i	$-0.640586\pi$
$619$	11.8576	−	11.8576i	0.476599	−	0.476599i	0.904042	+	0.427443i	$0.140586\pi$
$620$	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	0.947859	+	0.318690i	$0.103243\pi$
$631$	7.19263	+	26.8433i	0.286334	+	1.06861i	−0.661525	+	0.749923i	$0.730090\pi$
$632$	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	−0.768841	−	0.639440i	$-0.779166\pi$
$641$	4.28764	−	7.42640i	0.169351	−	0.293325i	0.938192	+	0.346115i	$0.112499\pi$
$642$	−2.87240	−	14.5612i	−0.113365	−	0.574685i
$643$	2.17600	−	0.583059i	0.0858132	−	0.0229936i	−0.215657	−	0.976469i	$-0.569189\pi$
$643$	2.17600	−	0.583059i	0.0858132	−	0.0229936i	0.301470	+	0.953476i	$0.402523\pi$
$644$	−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	0.519448	−	0.854502i	$-0.326137\pi$
$647$	−12.2169	−	21.1603i	−0.480296	−	0.831897i	−0.999744	+	0.0226045i	$0.992804\pi$
$648$	−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	−0.267361	−	0.963597i	$-0.586151\pi$
$653$	11.0765	−	6.39504i	0.433458	−	0.250257i	0.700819	+	0.713339i	$0.252818\pi$
$654$	−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	−0.104197	−	0.994557i	$-0.533227\pi$
$659$	−26.1230	−	15.0821i	−1.01761	−	0.587515i	−0.913410	+	0.407041i	$0.866561\pi$
$660$	2.55043	+	0.171227i	0.0992752	+	0.00666499i
$661$	−24.1859	−	6.48058i	−0.940721	−	0.252065i	−0.244301	−	0.969700i	$-0.578558\pi$
$661$	−24.1859	−	6.48058i	−0.940721	−	0.252065i	−0.696420	+	0.717634i	$0.745225\pi$
$662$	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	0.400010	−	0.916511i	$-0.369007\pi$
$673$	36.1567	−	20.8751i	1.39374	−	0.804674i	0.993727	+	0.111836i	$0.0356732\pi$
$674$	−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	$0.150183\pi$
$677$			23.6516i			0.909004i	−0.890746	+	0.454502i	$0.849817\pi$
$678$	−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	−0.406713	−	0.913556i	$-0.633325\pi$
$683$	−7.89669	+	2.11591i	−0.302158	+	0.0809631i	0.104554	+	0.994519i	$0.466658\pi$
$684$	−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	−0.852050	−	0.523460i	$-0.824641\pi$
$691$	3.87934	−	14.4779i	0.147577	−	0.550764i	0.999627	−	0.0273044i	$-0.00869235\pi$
$692$	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	−0.876568	−	0.481278i	$-0.840173\pi$
$709$	−9.53453	−	35.5833i	−0.358077	−	1.33636i	0.518492	−	0.855083i	$-0.326494\pi$
$710$	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	−0.818052	−	0.575145i	$-0.804946\pi$
$719$	2.38818	−	4.13644i	0.0890640	−	0.154263i	0.907116	+	0.420881i	$0.138279\pi$
$720$	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	$-0.838329\pi$
$727$		−	26.2267i		−	0.972694i	0.873766	−	0.486347i	$-0.161671\pi$
$728$		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	0.861042	−	0.508534i	$-0.169812\pi$
$733$	9.54380	+	9.54380i	0.352508	+	0.352508i	−0.508534	+	0.861042i	$0.669812\pi$
$734$	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	0.466510	−	0.884516i	$-0.345511\pi$
$739$	11.6421	+	3.11949i	0.428261	+	0.114752i	−0.0382487	+	0.999268i	$0.512178\pi$
$740$	14.2429			0.523580
$741$		0			0
$742$	−42.0906			−1.54520
$743$	21.4713	+	5.75322i	0.787706	+	0.211065i	0.630179	−	0.776450i	$-0.282981\pi$
$743$	21.4713	+	5.75322i	0.787706	+	0.211065i	0.157526	+	0.987515i	$0.449648\pi$
$744$	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	−0.957217	−	0.289372i	$-0.906553\pi$
$751$	−32.4803	+	18.7525i	−1.18522	+	0.684288i	−0.228005	+	0.973660i	$0.573220\pi$
$752$	−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	0.992281	−	0.124008i	$-0.0395747\pi$
$757$	10.6958	+	18.5257i	0.388747	+	0.673329i	−0.603534	+	0.797337i	$0.706241\pi$
$758$	−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	0.795765	−	0.605606i	$-0.207069\pi$
$761$	49.3165	−	13.2143i	1.78772	−	0.479018i	0.991955	+	0.126587i	$0.0404024\pi$
$762$	−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	0.344541	+	0.938771i	$0.388035\pi$
$769$	−11.7364	+	43.8009i	−0.423226	+	1.57950i	−0.767767	+	0.640729i	$0.778632\pi$
$770$	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	−0.845985	−	0.533207i	$-0.820987\pi$
$773$	−10.5635	−	39.4237i	−0.379944	−	1.41797i	0.466040	−	0.884763i	$-0.345680\pi$
$774$	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	0.918816	−	0.394686i	$-0.129147\pi$
$787$	−2.08283	−	7.77322i	−0.0742448	−	0.277086i	−0.993061	+	0.117600i	$0.962480\pi$
$788$	−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	−0.969529	−	0.244975i	$-0.921220\pi$
$797$	−7.69611	+	13.3300i	−0.272610	+	0.472174i	0.696919	+	0.717150i	$0.254554\pi$
$798$	−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	−0.965707	−	0.259633i	$-0.916399\pi$
$809$	−34.8060	+	20.0952i	−1.22371	+	0.706511i	−0.258005	+	0.966143i	$0.583065\pi$
$810$	19.8584	−	5.18623i	0.697752	−	0.182226i
$811$	−24.5095	−	24.5095i	−0.860644	−	0.860644i	0.130769	−	0.991413i	$-0.458255\pi$
$811$	−24.5095	−	24.5095i	−0.860644	−	0.860644i	−0.991413	+	0.130769i	$0.958255\pi$
$812$	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	−0.426622	−	0.904430i	$-0.640296\pi$
$821$	−35.7677	−	9.58393i	−1.24830	−	0.334482i	−0.821680	+	0.569949i	$0.806963\pi$
$822$	−0.611829	+	9.11320i	−0.0213400	+	0.317859i
$823$	−33.1584	−	19.1440i	−1.15583	−	0.667318i	−0.205527	−	0.978651i	$-0.565891\pi$
$823$	−33.1584	−	19.1440i	−1.15583	−	0.667318i	−0.950301	+	0.311334i	$0.899224\pi$
$824$	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	0.492053	−	0.870565i	$-0.336246\pi$
$827$	−10.8851	−	10.8851i	−0.378512	−	0.378512i	−0.870565	+	0.492053i	$0.836246\pi$
$828$	10.1311	−	75.1112i	0.352079	−	2.61029i
$829$	−4.66824	+	2.69521i	−0.162135	+	0.0936085i	−0.578872	−	0.815419i	$-0.696507\pi$
$829$	−4.66824	+	2.69521i	−0.162135	+	0.0936085i	0.416737	+	0.909027i	$0.363174\pi$
$830$	−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	−0.995282	−	0.0970197i	$-0.969069\pi$
$839$	−52.3903	+	14.0379i	−1.80871	+	0.484643i	−0.813430	+	0.581663i	$0.802402\pi$
$840$	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	−0.997042	−	0.0768525i	$-0.975513\pi$
$853$	−26.8752	+	26.8752i	−0.920190	+	0.920190i	0.0768525	+	0.997042i	$0.475513\pi$
$854$	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	−0.890919	−	0.454163i	$-0.849938\pi$
$863$	−12.8305	+	12.8305i	−0.436756	+	0.436756i	0.454163	+	0.890919i	$0.349938\pi$
$864$	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	0.186282	−	0.982496i	$-0.440356\pi$
$877$	24.8420	−	6.65640i	0.838856	−	0.224771i	0.652573	+	0.757726i	$0.273689\pi$
$878$	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	−0.881874	−	0.471485i	$-0.843718\pi$
$881$	−25.2073	−	43.6603i	−0.849255	−	1.47095i	0.0326196	−	0.999468i	$-0.489615\pi$
$882$	32.0511	−	4.11622i	1.07922	−	0.138600i
$883$			22.1092i			0.744035i	0.928226	+	0.372018i	$0.121334\pi$
$883$			22.1092i			0.744035i	−0.928226	+	0.372018i	$0.878666\pi$
$884$		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	−0.156632	−	0.987657i	$-0.550064\pi$
$887$	18.4767	−	10.6675i	0.620388	−	0.358181i	0.777020	+	0.629476i	$0.216730\pi$
$888$	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	−0.654662	−	0.755922i	$-0.727189\pi$
$907$	−9.85845	+	5.69178i	−0.327344	+	0.188992i	0.327317	+	0.944915i	$0.393855\pi$
$908$	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	$0.117501\pi$
$911$			21.7806i			0.721625i	−0.932638	+	0.360812i	$0.882499\pi$
$912$	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	−0.619172	−	0.785256i	$-0.712532\pi$
$919$	11.2307	−	19.4521i	0.370465	−	0.641665i	0.989637	+	0.143591i	$0.0458649\pi$
$920$	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	−0.980051	−	0.198747i	$-0.936313\pi$
$929$	−7.03088	−	26.2396i	−0.230676	−	0.860893i	0.749375	−	0.662146i	$-0.230354\pi$
$930$	−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	−0.347593	−	0.937645i	$-0.613001\pi$
$941$	18.1003	−	18.1003i	0.590052	−	0.590052i	0.937645	+	0.347593i	$0.113001\pi$
$942$	−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	0.740774	+	0.671754i	$0.234459\pi$
$947$	−7.28196	+	27.1767i	−0.236632	+	0.883123i	−0.977406	+	0.211369i	$0.932208\pi$
$948$	−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	−0.0130968	−	0.999914i	$-0.504169\pi$
$953$	26.5304	−	45.9519i	0.859403	−	1.48853i	0.872500	−	0.488615i	$-0.162498\pi$
$954$	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	0.800870	−	0.598838i	$-0.204371\pi$
$967$	6.28251	+	6.28251i	0.202032	+	0.202032i	−0.598838	+	0.800870i	$0.704371\pi$
$968$	−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	0.998932	−	0.0462136i	$-0.0147155\pi$
$971$	45.4442	+	26.2372i	1.45838	+	0.841993i	0.459444	+	0.888207i	$0.348049\pi$
$972$	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	0.542640	−	0.839965i	$-0.317425\pi$
$977$	18.5228	+	4.96318i	0.592598	+	0.158786i	0.0499578	+	0.998751i	$0.484091\pi$
$978$	−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	0.497920	−	0.867223i	$-0.334097\pi$
$983$	−11.5787	−	11.5787i	−0.369303	−	0.369303i	−0.867223	+	0.497920i	$0.834097\pi$
$984$	−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	0.997332	+	0.0730004i	$0.0232574\pi$
$991$	17.6883	+	30.6370i	0.561886	+	0.973215i	−0.435446	+	0.900215i	$0.643409\pi$
$992$	−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	−0.00405739	−	0.999992i	$-0.501292\pi$
$997$	27.2807	−	47.2516i	0.863990	−	1.49647i	0.868047	−	0.496482i	$-0.165375\pi$
$998$	−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.89.2		96
3.2	odd	2	inner	507.2.k.k.89.23		96
13.2	odd	12		507.2.f.g.239.2	yes	48
13.3	even	3		507.2.f.g.437.24	yes	48
13.4	even	6	inner	507.2.k.k.488.1		96
13.5	odd	4	inner	507.2.k.k.80.2		96
13.6	odd	12	inner	507.2.k.k.188.23		96
13.7	odd	12	inner	507.2.k.k.188.1		96
13.8	odd	4	inner	507.2.k.k.80.24		96
13.9	even	3	inner	507.2.k.k.488.23		96
13.10	even	6		507.2.f.g.437.2	yes	48
13.11	odd	12		507.2.f.g.239.24	yes	48
13.12	even	2	inner	507.2.k.k.89.24		96
39.2	even	12		507.2.f.g.239.23	yes	48
39.5	even	4	inner	507.2.k.k.80.23		96
39.8	even	4	inner	507.2.k.k.80.1		96
39.11	even	12		507.2.f.g.239.1	✓	48
39.17	odd	6	inner	507.2.k.k.488.24		96
39.20	even	12	inner	507.2.k.k.188.24		96
39.23	odd	6		507.2.f.g.437.23	yes	48
39.29	odd	6		507.2.f.g.437.1	yes	48
39.32	even	12	inner	507.2.k.k.188.2		96
39.35	odd	6	inner	507.2.k.k.488.2		96
39.38	odd	2	inner	507.2.k.k.89.1		96

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

Introduction

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