LMFDB - Embedded newform 153.4.r.a.25.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,4,Mod(25,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.25"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([16, 15])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.r (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	153.25
Dual form			153.4.r.a.49.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04078 - 3.88424i) q^{2} +(5.17689 - 0.447034i) q^{3} +(-7.07588 + 4.08526i) q^{4} +(-2.37395 - 18.0319i) q^{5} +(-7.12438 - 19.6430i) q^{6} +(0.696851 - 5.29311i) q^{7} +(0.484882 + 0.484882i) q^{8} +(26.6003 - 4.62849i) q^{9} +(-67.5695 + 27.9882i) q^{10} +(56.3769 + 7.42216i) q^{11} +(-34.8048 + 24.3121i) q^{12} +(-24.3765 + 14.0738i) q^{13} +(-21.2850 + 2.80222i) q^{14} +(-20.3505 - 92.2879i) q^{15} +(-31.3034 + 54.2190i) q^{16} +(-65.8768 + 23.9427i) q^{17} +(-45.6632 - 98.5047i) q^{18} +(31.0949 - 31.0949i) q^{19} +(90.4629 + 117.893i) q^{20} +(1.24132 - 27.7133i) q^{21} +(-29.8464 - 226.706i) q^{22} +(38.9314 - 50.7364i) q^{23} +(2.72694 + 2.29342i) q^{24} +(-198.773 + 53.2612i) q^{25} +(80.0363 + 80.0363i) q^{26} +(135.638 - 35.8524i) q^{27} +(16.6929 + 40.3002i) q^{28} +(-27.7946 + 21.3276i) q^{29} +(-337.288 + 175.098i) q^{30} +(-194.110 + 25.5550i) q^{31} +(248.478 + 66.5796i) q^{32} +(295.175 + 13.2213i) q^{33} +(161.562 + 230.962i) q^{34} -97.0991 q^{35} +(-169.312 + 141.420i) q^{36} +(-76.4350 + 184.531i) q^{37} +(-153.143 - 88.4170i) q^{38} +(-119.903 + 83.7554i) q^{39} +(7.59226 - 9.89443i) q^{40} +(184.070 + 141.242i) q^{41} +(-108.937 + 24.0219i) q^{42} +(266.697 - 71.4612i) q^{43} +(-429.238 + 177.796i) q^{44} +(-146.608 - 468.667i) q^{45} +(-237.591 - 98.4135i) q^{46} +(-3.53544 - 2.04119i) q^{47} +(-137.816 + 294.679i) q^{48} +(303.781 + 81.3979i) q^{49} +(413.758 + 716.650i) q^{50} +(-330.333 + 153.398i) q^{51} +(114.990 - 199.168i) q^{52} +(225.134 - 225.134i) q^{53} +(-280.428 - 489.535i) q^{54} -1034.20i q^{55} +(2.90442 - 2.22864i) q^{56} +(147.074 - 174.875i) q^{57} +(111.769 + 85.7637i) q^{58} +(132.494 - 494.473i) q^{59} +(521.018 + 569.881i) q^{60} +(114.317 - 868.323i) q^{61} +(301.287 + 727.371i) q^{62} +(-5.96266 - 144.024i) q^{63} -533.590i q^{64} +(311.645 + 406.144i) q^{65} +(-255.857 - 1160.29i) q^{66} +(-61.2517 - 106.091i) q^{67} +(368.324 - 438.540i) q^{68} +(178.863 - 280.060i) q^{69} +(101.059 + 377.156i) q^{70} +(-263.024 + 634.995i) q^{71} +(15.1423 + 10.6537i) q^{72} +(175.501 + 72.6949i) q^{73} +(796.312 + 104.837i) q^{74} +(-1005.22 + 364.586i) q^{75} +(-92.9929 + 347.054i) q^{76} +(78.5726 - 293.237i) q^{77} +(450.118 + 378.560i) q^{78} +(951.766 + 125.302i) q^{79} +(1051.98 + 435.746i) q^{80} +(686.154 - 246.239i) q^{81} +(357.041 - 861.973i) q^{82} +(-298.927 - 1115.61i) q^{83} +(104.433 + 201.167i) q^{84} +(588.121 + 1131.04i) q^{85} +(-555.144 - 961.538i) q^{86} +(-134.356 + 122.836i) q^{87} +(23.7373 + 30.9350i) q^{88} +1408.05i q^{89} +(-1667.83 + 1057.24i) q^{90} +(57.5072 + 138.835i) q^{91} +(-68.2026 + 518.050i) q^{92} +(-993.460 + 219.069i) q^{93} +(-4.24884 + 15.8569i) q^{94} +(-634.517 - 486.882i) q^{95} +(1316.11 + 233.597i) q^{96} +(-1298.33 + 996.246i) q^{97} -1264.68i q^{98} +(1534.00 - 63.5083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 80 q^{8} + 52 q^{9} - 16 q^{10} + 96 q^{11} - 212 q^{12} - 4 q^{14} - 256 q^{15} + 2936 q^{16} - 16 q^{17} - 240 q^{18} - 16 q^{19} - 516 q^{20}+ \cdots - 18916 q^{99}+O(q^{100}) $ 416 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 80 * q^8 + 52 * q^9 - 16 * q^10 + 96 * q^11 - 212 * q^12 - 4 * q^14 - 256 * q^15 + 2936 * q^16 - 16 * q^17 - 240 * q^18 - 16 * q^19 - 516 * q^20 - 4 * q^22 - 172 * q^23 + 1216 * q^24 - 4 * q^25 - 80 * q^26 + 544 * q^27 - 528 * q^28 - 4 * q^29 - 4 * q^31 + 316 * q^32 - 512 * q^33 - 796 * q^34 - 4512 * q^35 + 328 * q^36 - 16 * q^37 + 1148 * q^39 + 252 * q^40 + 956 * q^41 + 3648 * q^42 - 688 * q^43 - 1040 * q^44 - 1240 * q^45 + 128 * q^46 + 528 * q^48 - 4 * q^49 - 5288 * q^50 - 352 * q^51 - 1032 * q^52 - 1424 * q^53 + 1708 * q^54 + 284 * q^56 + 4372 * q^57 - 4 * q^58 + 56 * q^59 - 3248 * q^60 - 4 * q^61 + 5168 * q^62 + 1008 * q^63 - 2284 * q^65 - 7516 * q^66 - 8 * q^67 + 252 * q^68 + 6224 * q^69 - 36 * q^70 + 624 * q^71 - 16 * q^73 - 3644 * q^74 - 508 * q^75 + 188 * q^76 + 1772 * q^77 - 10080 * q^78 - 4 * q^79 + 472 * q^80 + 3296 * q^82 + 4364 * q^83 + 8632 * q^84 + 3308 * q^85 + 1312 * q^86 + 4376 * q^87 - 1380 * q^88 - 15160 * q^90 - 4776 * q^91 - 1748 * q^92 - 1720 * q^93 - 68 * q^94 + 4436 * q^95 - 2196 * q^96 + 104 * q^97 - 18916 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.04078	−	3.88424i	−0.367971	−	1.37329i	−0.863349	−	0.504608i	$-0.831637\pi$
$2$	−1.04078	−	3.88424i	−0.367971	−	1.37329i	0.495378	−	0.868678i	$-0.335030\pi$
$3$	5.17689	−	0.447034i	0.996292	−	0.0860318i
$3$	5.17689	−	0.447034i	0.996292	−	0.0860318i
$4$	−7.07588	+	4.08526i	−0.884485	+	0.510658i
$5$	−2.37395	−	18.0319i	−0.212332	−	1.61282i	−0.682936	−	0.730478i	$-0.739297\pi$
$5$	−2.37395	−	18.0319i	−0.212332	−	1.61282i	0.470604	−	0.882345i	$-0.344036\pi$
$6$	−7.12438	−	19.6430i	−0.484753	−	1.33654i
$7$	0.696851	−	5.29311i	0.0376264	−	0.285801i	−0.962279	−	0.272064i	$-0.912294\pi$
$7$	0.696851	−	5.29311i	0.0376264	−	0.285801i	0.999906	−	0.0137372i	$-0.00437283\pi$
$8$	0.484882	+	0.484882i	0.0214289	+	0.0214289i
$9$	26.6003	−	4.62849i	0.985197	−	0.171426i
$10$	−67.5695	+	27.9882i	−2.13673	+	0.885064i
$11$	56.3769	+	7.42216i	1.54530	+	0.203442i	0.854441	−	0.519548i	$-0.173900\pi$
$11$	56.3769	+	7.42216i	1.54530	+	0.203442i	0.690858	+	0.722991i	$0.257233\pi$
$12$	−34.8048	+	24.3121i	−0.837273	+	0.584858i
$13$	−24.3765	+	14.0738i	−0.520063	+	0.300258i	−0.736960	−	0.675936i	$-0.763740\pi$
$13$	−24.3765	+	14.0738i	−0.520063	+	0.300258i	0.216898	+	0.976194i	$0.430406\pi$
$14$	−21.2850	+	2.80222i	−0.406332	+	0.0534946i
$15$	−20.3505	−	92.2879i	−0.350299	−	1.58858i
$16$	−31.3034	+	54.2190i	−0.489115	+	0.847172i
$17$	−65.8768	+	23.9427i	−0.939851	+	0.341586i
$17$	−65.8768	+	23.9427i	−0.939851	+	0.341586i
$18$	−45.6632	−	98.5047i	−0.597940	−	1.28988i
$19$	31.0949	−	31.0949i	0.375455	−	0.375455i	−0.494004	−	0.869459i	$-0.664467\pi$
$19$	31.0949	−	31.0949i	0.375455	−	0.375455i	0.869459	+	0.494004i	$0.164467\pi$
$20$	90.4629	+	117.893i	1.01141	+	1.31809i
$21$	1.24132	−	27.7133i	0.0128989	−	0.287978i
$22$	−29.8464	−	226.706i	−0.289240	−	2.19700i
$23$	38.9314	−	50.7364i	0.352946	−	0.459968i	−0.582814	−	0.812606i	$-0.698048\pi$
$23$	38.9314	−	50.7364i	0.352946	−	0.459968i	0.935760	+	0.352637i	$0.114715\pi$
$24$	2.72694	+	2.29342i	0.0231931	+	0.0195059i
$25$	−198.773	+	53.2612i	−1.59019	+	0.426089i
$26$	80.0363	+	80.0363i	0.603708	+	0.603708i
$27$	135.638	−	35.8524i	0.966796	−	0.255548i
$28$	16.6929	+	40.3002i	0.112666	+	0.272001i
$29$	−27.7946	+	21.3276i	−0.177977	+	0.136567i	−0.693908	−	0.720063i	$-0.744113\pi$
$29$	−27.7946	+	21.3276i	−0.177977	+	0.136567i	0.515931	+	0.856630i	$0.327446\pi$
$30$	−337.288	+	175.098i	−2.05267	+	1.06561i
$31$	−194.110	+	25.5550i	−1.12462	+	0.148059i	−0.669811	−	0.742532i	$-0.733625\pi$
$31$	−194.110	+	25.5550i	−1.12462	+	0.148059i	−0.454806	+	0.890590i	$0.650292\pi$
$32$	248.478	+	66.5796i	1.37266	+	0.367804i
$33$	295.175	+	13.2213i	1.55707	+	0.0697433i
$34$	161.562	+	230.962i	0.814933	+	1.16499i
$35$	−97.0991			−0.468936
$36$	−169.312	+	141.420i	−0.783852	+	0.654722i
$37$	−76.4350	+	184.531i	−0.339617	+	0.819909i	0.658135	+	0.752900i	$0.271346\pi$
$37$	−76.4350	+	184.531i	−0.339617	+	0.819909i	−0.997752	+	0.0670089i	$0.978654\pi$
$38$	−153.143	−	88.4170i	−0.653764	−	0.377451i
$39$	−119.903	+	83.7554i	−0.492303	+	0.343887i
$40$	7.59226	−	9.89443i	0.0300110	−	0.0391112i
$41$	184.070	+	141.242i	0.701144	+	0.538007i	0.896674	−	0.442691i	$-0.145976\pi$
$41$	184.070	+	141.242i	0.701144	+	0.538007i	−0.195530	+	0.980698i	$0.562643\pi$
$42$	−108.937	+	24.0219i	−0.400223	+	0.0882537i
$43$	266.697	−	71.4612i	0.945834	−	0.253435i	0.247241	−	0.968954i	$-0.420476\pi$
$43$	266.697	−	71.4612i	0.945834	−	0.253435i	0.698594	+	0.715519i	$0.253810\pi$
$44$	−429.238	+	177.796i	−1.47068	+	0.609177i
$45$	−146.608	−	468.667i	−0.485668	−	1.55255i
$46$	−237.591	−	98.4135i	−0.761542	−	0.315441i
$47$	−3.53544	−	2.04119i	−0.0109723	−	0.00633484i	0.494504	−	0.869175i	$-0.335350\pi$
$47$	−3.53544	−	2.04119i	−0.0109723	−	0.00633484i	−0.505476	+	0.862841i	$0.668683\pi$
$48$	−137.816	+	294.679i	−0.414418	+	0.886110i
$49$	303.781	+	81.3979i	0.885659	+	0.237312i
$50$	413.758	+	716.650i	1.17029	+	2.02699i
$51$	−330.333	+	153.398i	−0.906979	+	0.421177i
$52$	114.990	−	199.168i	0.306658	−	0.531148i
$53$	225.134	−	225.134i	0.583483	−	0.583483i	−0.352376	−	0.935859i	$-0.614626\pi$
$53$	225.134	−	225.134i	0.583483	−	0.583483i	0.935859	+	0.352376i	$0.114626\pi$
$54$	−280.428	−	489.535i	−0.706694	−	1.23365i
$55$		−	1034.20i		−	2.53549i
$56$	2.90442	−	2.22864i	0.00693071	−	0.00531812i
$57$	147.074	−	174.875i	0.341762	−	0.406364i
$58$	111.769	+	85.7637i	0.253035	+	0.194161i
$59$	132.494	−	494.473i	0.292360	−	1.09110i	−0.650932	−	0.759136i	$-0.725622\pi$
$59$	132.494	−	494.473i	0.292360	−	1.09110i	0.943292	−	0.331965i	$-0.107712\pi$
$60$	521.018	+	569.881i	1.12105	+	1.22619i
$61$	114.317	−	868.323i	0.239947	−	1.82258i	−0.270557	−	0.962704i	$-0.587208\pi$
$61$	114.317	−	868.323i	0.239947	−	1.82258i	0.510504	−	0.859875i	$-0.329459\pi$
$62$	301.287	+	727.371i	0.617153	+	1.48994i
$63$	−5.96266	−	144.024i	−0.0119242	−	0.288020i
$64$		−	533.590i		−	1.04217i
$65$	311.645	+	406.144i	0.594690	+	0.775015i
$66$	−255.857	−	1160.29i	−0.477179	−	2.16397i
$67$	−61.2517	−	106.091i	−0.111688	−	0.193449i	0.804763	−	0.593596i	$-0.202292\pi$
$67$	−61.2517	−	106.091i	−0.111688	−	0.193449i	−0.916451	+	0.400147i	$0.868959\pi$
$68$	368.324	−	438.540i	0.656850	−	0.782070i
$69$	178.863	−	280.060i	0.312066	−	0.488628i
$70$	101.059	+	377.156i	0.172555	+	0.643983i
$71$	−263.024	+	634.995i	−0.439650	+	1.06141i	0.536419	+	0.843952i	$0.319777\pi$
$71$	−263.024	+	634.995i	−0.439650	+	1.06141i	−0.976070	+	0.217458i	$0.930223\pi$
$72$	15.1423	+	10.6537i	0.0247852	+	0.0174383i
$73$	175.501	+	72.6949i	0.281382	+	0.116552i	0.518911	−	0.854828i	$-0.326338\pi$
$73$	175.501	+	72.6949i	0.281382	+	0.116552i	−0.237529	+	0.971380i	$0.576338\pi$
$74$	796.312	+	104.837i	1.25094	+	0.164689i
$75$	−1005.22	+	364.586i	−1.54763	+	0.561316i
$76$	−92.9929	+	347.054i	−0.140355	+	0.523814i
$77$	78.5726	−	293.237i	0.116288	−	0.433993i
$78$	450.118	+	378.560i	0.653408	+	0.549532i
$79$	951.766	+	125.302i	1.35547	+	0.178451i	0.773002	−	0.634404i	$-0.218754\pi$
$79$	951.766	+	125.302i	1.35547	+	0.178451i	0.582467	+	0.812855i	$0.302088\pi$
$80$	1051.98	+	435.746i	1.47019	+	0.608974i
$81$	686.154	−	246.239i	0.941226	−	0.337776i
$82$	357.041	−	861.973i	0.480836	−	1.16084i
$83$	−298.927	−	1115.61i	−0.395319	−	1.47535i	−0.821236	−	0.570589i	$-0.806715\pi$
$83$	−298.927	−	1115.61i	−0.395319	−	1.47535i	0.425917	−	0.904762i	$-0.359952\pi$
$84$	104.433	+	201.167i	0.135650	+	0.261300i
$85$	588.121	+	1131.04i	0.750478	+	1.44328i
$86$	−555.144	−	961.538i	−0.696079	−	1.20564i
$87$	−134.356	+	122.836i	−0.165568	+	0.151372i
$88$	23.7373	+	30.9350i	0.0287546	+	0.0374737i
$89$			1408.05i			1.67700i	0.544903	+	0.838499i	$0.316567\pi$
$89$			1408.05i			1.67700i	−0.544903	+	0.838499i	$0.683433\pi$
$90$	−1667.83	+	1057.24i	−1.95338	+	1.23825i
$91$	57.5072	+	138.835i	0.0662460	+	0.159932i
$92$	−68.2026	+	518.050i	−0.0772892	+	0.587070i
$93$	−993.460	+	219.069i	−1.10771	+	0.244263i
$94$	−4.24884	+	15.8569i	−0.00466207	+	0.0173991i
$95$	−634.517	−	486.882i	−0.685264	−	0.525822i
$96$	1316.11	+	233.597i	1.39922	+	0.248347i
$97$	−1298.33	+	996.246i	−1.35903	+	1.04282i	−0.365312	+	0.930885i	$0.619038\pi$
$97$	−1298.33	+	996.246i	−1.35903	+	1.04282i	−0.993716	+	0.111934i	$0.964296\pi$
$98$		−	1264.68i		−	1.30359i
$99$	1534.00	−	63.5083i	1.55730	−	0.0644730i
$100$	1188.91	−	1188.91i	1.18891	−	1.18891i
$101$	525.573	−	910.320i	0.517787	−	0.896834i	−0.481999	−	0.876172i	$-0.660089\pi$
$101$	525.573	−	910.320i	0.517787	−	0.896834i	0.999787	−	0.0206621i	$-0.00657742\pi$
$102$	939.638	+	1123.44i	0.912137	+	1.09056i
$103$	−210.548	−	364.679i	−0.201416	−	0.348863i	0.747569	−	0.664184i	$-0.231221\pi$
$103$	−210.548	−	364.679i	−0.201416	−	0.348863i	−0.948985	+	0.315321i	$0.897888\pi$
$104$	−18.6438	−	4.99559i	−0.0175786	−	0.00471017i
$105$	−502.671	+	43.4067i	−0.467197	+	0.0403434i
$106$	−1108.79	−	640.161i	−1.01599	−	0.586584i
$107$	210.418	+	87.1580i	0.190111	+	0.0787466i	0.475708	−	0.879603i	$-0.342192\pi$
$107$	210.418	+	87.1580i	0.190111	+	0.0787466i	−0.285597	+	0.958350i	$0.592192\pi$
$108$	−813.290	+	807.804i	−0.724619	+	0.719731i
$109$	−1229.05	+	509.091i	−1.08002	+	0.447359i	−0.850516	−	0.525949i	$-0.823710\pi$
$109$	−1229.05	+	509.091i	−1.08002	+	0.447359i	−0.229503	+	0.973308i	$0.573710\pi$
$110$	−4017.09	+	1076.38i	−3.48195	+	0.932986i
$111$	−313.204	+	989.463i	−0.267820	+	0.846087i
$112$	265.173	+	203.475i	0.223719	+	0.171666i
$113$	883.199	−	1151.01i	0.735260	−	0.958209i	−0.264722	−	0.964325i	$-0.585280\pi$
$113$	883.199	−	1151.01i	0.735260	−	0.958209i	0.999981	+	0.00611574i	$0.00194671\pi$
$114$	−832.328	−	389.265i	−0.683813	−	0.319807i
$115$	−1007.30	−	581.562i	−0.816789	−	0.471574i
$116$	109.543	−	264.460i	0.0876793	−	0.211677i
$117$	−583.281	+	487.193i	−0.460892	+	0.384966i
$118$	−2058.55			−1.60597
$119$	80.8251	+	365.377i	0.0622624	+	0.281463i
$120$	34.8811	−	54.6163i	0.0265350	−	0.0415480i
$121$	1837.62	+	492.390i	1.38063	+	0.369940i
$122$	−3491.75	+	459.698i	−2.59121	+	0.341140i
$123$	1016.05	+	648.908i	0.744830	+	0.475691i
$124$	1269.10	−	973.814i	0.919100	−	0.705250i
$125$	562.271	+	1357.44i	0.402329	+	0.971307i
$126$	−553.217	+	173.057i	−0.391146	+	0.122358i
$127$	908.585	+	908.585i	0.634834	+	0.634834i	0.949276	−	0.314443i	$-0.101818\pi$
$127$	908.585	+	908.585i	0.634834	+	0.634834i	−0.314443	+	0.949276i	$0.601818\pi$
$128$	−84.7629	+	22.7122i	−0.0585317	+	0.0156835i
$129$	1348.71	−	489.169i	0.920524	−	0.333868i
$130$	1253.21	−	1633.21i	0.845488	−	1.10186i
$131$	32.3070	+	245.396i	0.0215471	+	0.163667i	0.998835	−	0.0482474i	$-0.0153636\pi$
$131$	32.3070	+	245.396i	0.0215471	+	0.163667i	−0.977288	+	0.211914i	$0.932030\pi$
$132$	−2142.64	+	1112.32i	−1.41282	+	0.733444i
$133$	−142.920	−	186.257i	−0.0931784	−	0.121433i
$134$	−348.333	+	348.333i	−0.224563	+	0.224563i
$135$	−968.485	−	2360.70i	−0.617436	−	1.50501i
$136$	−43.5518	−	20.3330i	−0.0274598	−	0.0128202i
$137$	133.747	−	231.656i	0.0834069	−	0.144465i	−0.821304	−	0.570490i	$-0.806753\pi$
$137$	133.747	−	231.656i	0.0834069	−	0.144465i	0.904711	+	0.426025i	$0.140087\pi$
$138$	−1273.98	−	403.264i	−0.785856	−	0.248755i
$139$	2393.24	−	315.076i	1.46037	−	0.192262i	0.641892	−	0.766795i	$-0.278150\pi$
$139$	2393.24	−	315.076i	1.46037	−	0.192262i	0.818481	+	0.574533i	$0.194816\pi$
$140$	687.062	−	396.675i	0.414767	−	0.239466i
$141$	−19.2150	−	8.98653i	−0.0114766	−	0.00536739i
$142$	2740.22	+	360.757i	1.61940	+	0.213198i
$143$	−1478.73	+	612.509i	−0.864737	+	0.358186i
$144$	−581.727	+	1587.13i	−0.336648	+	0.918478i
$145$	450.560	+	450.560i	0.258048	+	0.258048i
$146$	99.7067	−	757.348i	0.0565191	−	0.429305i
$147$	1609.03	+	285.587i	0.902792	+	0.160237i
$148$	−213.010	−	1617.97i	−0.118306	−	0.898626i
$149$	1577.22	−	910.609i	0.867187	−	0.500671i	0.000774845	−	1.00000i	$-0.499753\pi$
$149$	1577.22	−	910.609i	0.867187	−	0.500671i	0.866413	+	0.499329i	$0.166420\pi$
$150$	2462.35	+	3525.05i	1.34033	+	1.91880i
$151$	326.555	+	1218.72i	0.175991	+	0.656809i	0.996381	+	0.0850033i	$0.0270901\pi$
$151$	326.555	+	1218.72i	0.175991	+	0.656809i	−0.820389	+	0.571805i	$0.806243\pi$
$152$	30.1547			0.0160912
$153$	−1641.52	+	941.794i	−0.867381	+	0.497644i
$154$	−1220.78			−0.638787
$155$	921.612	+	3439.50i	0.477585	+	1.78237i
$156$	506.255	−	1082.48i	0.259826	−	0.555561i
$157$	−3082.87	+	1779.89i	−1.56713	+	0.904783i	−0.570629	+	0.821208i	$0.693300\pi$
$157$	−3082.87	+	1779.89i	−1.56713	+	0.904783i	−0.996502	+	0.0835746i	$0.973366\pi$
$158$	−503.873	−	3827.30i	−0.253709	−	1.92711i
$159$	1064.85	−	1266.14i	0.531121	−	0.631518i
$160$	610.683	−	4638.59i	0.301742	−	2.29196i
$161$	−241.424	−	241.424i	−0.118179	−	0.118179i
$162$	−1670.58	−	2408.91i	−0.810207	−	1.16828i
$163$	−1181.15	+	489.248i	−0.567575	+	0.235097i	−0.647970	−	0.761666i	$-0.724382\pi$
$163$	−1181.15	+	489.248i	−0.567575	+	0.235097i	0.0803952	+	0.996763i	$0.474382\pi$
$164$	−1879.47	−	247.437i	−0.894889	−	0.117814i
$165$	−462.325	−	5353.96i	−0.218133	−	2.52609i
$166$	−4022.18	+	2322.21i	−1.88061	+	1.08577i
$167$	1304.81	−	171.782i	0.604608	−	0.0795981i	0.177993	−	0.984032i	$-0.443039\pi$
$167$	1304.81	−	171.782i	0.604608	−	0.0795981i	0.426614	+	0.904434i	$0.359706\pi$
$168$	14.0396	−	12.8358i	0.00644748	−	0.00589466i
$169$	−702.359	+	1216.52i	−0.319690	+	0.553719i
$170$	3781.14	−	3461.57i	1.70589	−	1.56171i
$171$	683.211	−	971.056i	0.305535	−	0.434260i
$172$	−1595.18	+	1595.18i	−0.707158	+	0.707158i
$173$	−2241.07	−	2920.62i	−0.984888	−	1.28353i	−0.958863	−	0.283869i	$-0.908382\pi$
$173$	−2241.07	−	2920.62i	−0.984888	−	1.28353i	−0.0260248	−	0.999661i	$-0.508285\pi$
$174$	616.957	+	394.024i	0.268801	+	0.171672i
$175$	143.402	+	1089.24i	0.0619437	+	0.470509i
$176$	−2167.21	+	2824.36i	−0.928180	+	1.20963i
$177$	464.858	−	2619.06i	0.197406	−	1.11221i
$178$	5469.20	−	1465.47i	2.30300	−	0.617086i
$179$	1112.14	+	1112.14i	0.464387	+	0.464387i	0.900090	−	0.435703i	$-0.143500\pi$
$179$	1112.14	+	1112.14i	0.464387	+	0.464387i	−0.435703	+	0.900090i	$0.643500\pi$
$180$	2952.01	+	2717.30i	1.22239	+	1.12520i
$181$	926.043	+	2235.66i	0.380288	+	0.918098i	0.991910	+	0.126947i	$0.0405177\pi$
$181$	926.043	+	2235.66i	0.380288	+	0.918098i	−0.611621	+	0.791151i	$0.709482\pi$
$182$	479.414	−	367.867i	0.195256	−	0.149825i
$183$	203.635	−	4546.31i	0.0822577	−	1.83646i
$184$	43.4783	−	5.72402i	0.0174199	−	0.00229337i
$185$	3508.89	+	940.204i	1.39448	+	0.373650i
$186$	1884.89	+	3630.83i	0.743047	+	1.43132i
$187$	−3891.64	+	860.869i	−1.52184	+	0.336647i
$188$	33.3551			0.0129397
$189$	−95.2516	−	742.929i	−0.0366589	−	0.285927i
$190$	−1230.77	+	2971.35i	−0.469946	+	1.13455i
$191$	−2532.31	−	1462.03i	−0.959327	−	0.553868i	−0.0633614	−	0.997991i	$-0.520182\pi$
$191$	−2532.31	−	1462.03i	−0.959327	−	0.553868i	−0.895966	+	0.444123i	$0.853515\pi$
$192$	−238.533	−	2762.33i	−0.0896595	−	1.03830i
$193$	−2411.43	+	3142.64i	−0.899371	+	1.17208i	0.0850711	+	0.996375i	$0.472888\pi$
$193$	−2411.43	+	3142.64i	−0.899371	+	1.17208i	−0.984442	+	0.175708i	$0.943778\pi$
$194$	5220.93	+	4006.16i	1.93217	+	1.48261i
$195$	1794.91	+	1963.24i	0.659161	+	0.720979i
$196$	−2482.05	+	665.064i	−0.904538	+	0.242370i
$197$	−2699.46	+	1118.16i	−0.976289	+	0.404392i	−0.813050	−	0.582194i	$-0.802194\pi$
$197$	−2699.46	+	1118.16i	−0.976289	+	0.404392i	−0.163239	+	0.986587i	$0.552194\pi$
$198$	−1843.23	−	5892.32i	−0.661580	−	2.11489i
$199$	−3770.25	−	1561.69i	−1.34305	−	0.556308i	−0.408698	−	0.912670i	$-0.634017\pi$
$199$	−3770.25	−	1561.69i	−1.34305	−	0.556308i	−0.934348	+	0.356362i	$0.884017\pi$
$200$	−122.207	−	70.5562i	−0.0432067	−	0.0249454i
$201$	−364.520	−	521.840i	−0.127917	−	0.183123i
$202$	−4082.90	−	1094.01i	−1.42214	−	0.381061i
$203$	93.5204	+	161.982i	0.0323342	+	0.0560045i
$204$	1710.73	−	2434.92i	0.587132	−	0.835680i
$205$	2109.89	−	3654.43i	0.718834	−	1.24506i
$206$	−1197.37	+	1197.37i	−0.404974	+	0.404974i
$207$	800.755	−	1529.80i	0.268871	−	0.513664i
$208$		−	1762.22i		−	0.587443i
$209$	1983.82	−	1522.24i	0.656574	−	0.503807i
$210$	691.771	+	1907.32i	0.227318	+	0.626750i
$211$	2108.35	+	1617.80i	0.687891	+	0.527837i	0.892523	−	0.451002i	$-0.148933\pi$
$211$	2108.35	+	1617.80i	0.687891	+	0.527837i	−0.204632	+	0.978839i	$0.565600\pi$
$212$	−673.291	+	2512.76i	−0.218122	+	0.814042i
$213$	−1077.78	+	3404.88i	−0.346705	+	1.09530i
$214$	119.544	−	908.026i	0.0381862	−	0.290053i
$215$	−1921.71	−	4639.41i	−0.609578	−	1.47165i
$216$	83.1525	+	48.3841i	0.0261936	+	0.0152413i
$217$			1045.25i			0.326988i
$218$	3256.61	+	4244.09i	1.01177	+	1.31856i
$219$	941.047	+	297.878i	0.290365	+	0.0919122i
$220$	4224.99	+	7317.90i	1.29477	+	2.24260i
$221$	1268.88	−	1510.77i	0.386217	−	0.459844i
$222$	4169.28	+	186.748i	1.26047	+	0.0564581i
$223$	1322.46	+	4935.48i	0.397123	+	1.48208i	0.818134	+	0.575027i	$0.195008\pi$
$223$	1322.46	+	4935.48i	0.397123	+	1.48208i	−0.421012	+	0.907055i	$0.638325\pi$
$224$	525.565	−	1268.83i	0.156767	−	0.378469i
$225$	−5040.92	+	2336.79i	−1.49361	+	0.692381i
$226$	−5390.00	−	2232.61i	−1.58645	−	0.657129i
$227$	1154.09	+	151.939i	0.337443	+	0.0444253i	0.297344	−	0.954770i	$-0.403899\pi$
$227$	1154.09	+	151.939i	0.337443	+	0.0444253i	0.0400995	+	0.999196i	$0.487233\pi$
$228$	−326.269	+	1838.23i	−0.0947705	+	0.533947i
$229$	−687.684	+	2566.47i	−0.198443	+	0.740600i	0.792906	+	0.609345i	$0.208567\pi$
$229$	−687.684	+	2566.47i	−0.198443	+	0.740600i	−0.991349	+	0.131255i	$0.958099\pi$
$230$	−1210.56	+	4517.85i	−0.347051	+	1.29521i
$231$	275.675	−	1553.18i	0.0785197	−	0.442388i
$232$	−23.8185	−	3.13576i	−0.00674034	−	0.000887382i
$233$	2507.38	+	1038.59i	0.704995	+	0.292018i	0.706232	−	0.707981i	$-0.250394\pi$
$233$	2507.38	+	1038.59i	0.704995	+	0.292018i	−0.00123698	+	0.999999i	$0.500394\pi$
$234$	2499.44	+	1758.54i	0.698263	+	0.491280i
$235$	−28.4135	+	68.5964i	−0.00788721	+	0.0190414i
$236$	1082.54	+	4040.11i	0.298591	+	1.11436i
$237$	4983.20	+	223.204i	1.36580	+	0.0611758i
$238$	1335.09	−	694.221i	0.363618	−	0.189074i
$239$	595.784	+	1031.93i	0.161247	+	0.279288i	0.935316	−	0.353813i	$-0.115115\pi$
$239$	595.784	+	1031.93i	0.161247	+	0.279288i	−0.774069	+	0.633101i	$0.781782\pi$
$240$	5640.80	+	1785.54i	1.51713	+	0.480233i
$241$	1781.33	+	2321.48i	0.476123	+	0.620496i	0.968237	−	0.250035i	$-0.0804422\pi$
$241$	1781.33	+	2321.48i	0.476123	+	0.620496i	−0.492114	+	0.870531i	$0.663776\pi$
$242$		−	7650.23i		−	2.03213i
$243$	3442.07	−	1581.48i	0.908677	−	0.417499i
$244$	2738.43	+	6611.16i	0.718485	+	1.73458i
$245$	746.600	−	5670.99i	0.194688	−	1.47880i
$246$	1463.03	−	4621.95i	0.379184	−	1.19791i
$247$	−320.361	+	1195.60i	−0.0825267	+	0.307994i
$248$	−106.511	−	81.7291i	−0.0272721	−	0.0209266i
$249$	−2046.23	−	5641.76i	−0.520780	−	1.43587i
$250$	4687.43	−	3596.79i	1.18584	−	0.909924i
$251$			6458.99i			1.62426i	0.583480	+	0.812128i	$0.301691\pi$
$251$			6458.99i			1.62426i	−0.583480	+	0.812128i	$0.698309\pi$
$252$	630.566	+	994.736i	0.157627	+	0.248661i
$253$	2571.41	−	2571.41i	0.638984	−	0.638984i
$254$	2583.52	−	4474.80i	0.638208	−	1.10541i
$255$	3550.25	+	5592.38i	0.871864	+	1.37337i
$256$	−1957.92	−	3391.22i	−0.478008	−	0.827934i
$257$	−3917.79	−	1049.77i	−0.950915	−	0.254797i	−0.250164	−	0.968203i	$-0.580485\pi$
$257$	−3917.79	−	1049.77i	−0.950915	−	0.254797i	−0.700750	+	0.713407i	$0.747151\pi$
$258$	−3303.76	−	4729.61i	−0.797221	−	1.14129i
$259$	923.476	+	533.169i	0.221552	+	0.127913i
$260$	−3864.37	−	1600.67i	−0.921761	−	0.381806i
$261$	−640.632	+	695.968i	−0.151931	+	0.165055i
$262$	919.552	−	380.891i	0.216833	−	0.0898150i
$263$	−4627.41	+	1239.91i	−1.08494	+	0.290708i	−0.756617	−	0.653858i	$-0.773149\pi$
$263$	−4627.41	+	1239.91i	−1.08494	+	0.290708i	−0.328321	+	0.944566i	$0.606483\pi$
$264$	136.714	+	149.536i	0.0318719	+	0.0348609i
$265$	−4594.06	−	3525.15i	−1.06495	−	0.817162i
$266$	−574.718	+	748.987i	−0.132475	+	0.172644i
$267$	629.446	+	7289.31i	0.144275	+	1.67078i
$268$	866.820	+	500.459i	0.197573	+	0.114069i
$269$	3113.26	−	7516.08i	0.705647	−	1.70358i	−0.00495585	−	0.999988i	$-0.501578\pi$
$269$	3113.26	−	7516.08i	0.705647	−	1.70358i	0.710602	−	0.703594i	$-0.248422\pi$
$270$	−8161.53	+	6218.79i	−1.83961	+	1.40172i
$271$	−687.662			−0.154142			−0.0770711	−	0.997026i	$-0.524557\pi$
$271$	−687.662			−0.154142			−0.0770711	+	0.997026i	$0.524557\pi$
$272$	764.013	−	4321.26i	0.170313	−	0.963290i
$273$	359.772	+	693.023i	0.0797596	+	0.153640i
$274$	−1039.01	−	278.401i	−0.229083	−	0.0613826i
$275$	−11601.6	+	1527.37i	−2.54400	+	0.334924i
$276$	−121.491	+	2712.37i	−0.0264960	+	0.591543i
$277$	−388.694	+	298.255i	−0.0843117	+	0.0646946i	−0.650057	−	0.759885i	$-0.725255\pi$
$277$	−388.694	+	298.255i	−0.0843117	+	0.0646946i	0.565746	+	0.824580i	$0.308588\pi$
$278$	−3714.66	−	8967.98i	−0.801405	−	1.93476i
$279$	−5045.10	+	1578.21i	−1.08259	+	0.338655i
$280$	−47.0816	−	47.0816i	−0.0100488	−	0.0100488i
$281$	−1848.10	+	495.198i	−0.392344	+	0.105128i	−0.449597	−	0.893232i	$-0.648432\pi$
$281$	−1848.10	+	495.198i	−0.392344	+	0.105128i	0.0572533	+	0.998360i	$0.481766\pi$
$282$	−14.9072	+	83.9888i	−0.00314791	+	0.0177357i
$283$	1061.58	−	1383.48i	0.222983	−	0.290598i	−0.668443	−	0.743764i	$-0.733039\pi$
$283$	1061.58	−	1383.48i	0.222983	−	0.290598i	0.891426	+	0.453166i	$0.149705\pi$
$284$	−732.998	−	5567.67i	−0.153153	−	1.16331i
$285$	−3502.48	−	2236.88i	−0.727961	−	0.464918i
$286$	3918.16	+	5106.25i	0.810090	+	1.05573i
$287$	875.878	−	875.878i	0.180144	−	0.180144i
$288$	6917.77	+	620.957i	1.41539	+	0.127050i
$289$	3766.49	−	3154.54i	0.766638	−	0.642080i
$290$	1281.15	−	2219.02i	0.259420	−	0.449328i
$291$	−6275.97	+	5737.85i	−1.26427	+	1.15587i
$292$	−1538.80	+	202.587i	−0.308396	+	0.0406011i
$293$	565.290	−	326.370i	0.112712	−	0.0650742i	−0.442584	−	0.896727i	$-0.645938\pi$
$293$	565.290	−	326.370i	0.112712	−	0.0650742i	0.555296	+	0.831653i	$0.312605\pi$
$294$	−565.353	−	6547.08i	−0.112150	−	1.29875i
$295$	−9230.83	−	1215.26i	−1.82183	−	0.239848i
$296$	−126.537	+	52.4135i	−0.0248474	+	0.0102921i
$297$	7912.94	−	1014.53i	1.54598	−	0.198211i
$298$	−5178.56	−	5178.56i	−1.00666	−	1.00666i
$299$	−234.958	+	1784.69i	−0.0454448	+	0.345187i
$300$	5623.38	−	6686.35i	1.08222	−	1.28679i
$301$	−192.404	−	1461.45i	−0.0368438	−	0.279856i
$302$	4393.93	−	2536.84i	0.837226	−	0.483373i
$303$	2313.89	−	4947.57i	0.438711	−	0.938055i
$304$	712.559	+	2659.31i	0.134434	+	0.501716i
$305$	−15928.9			−2.99045
$306$	5366.61	+	5395.87i	1.00258	+	1.00804i
$307$	2901.01			0.539313			0.269657	−	0.962957i	$-0.413090\pi$
$307$	2901.01			0.539313			0.269657	+	0.962957i	$0.413090\pi$
$308$	641.980	+	2395.90i	0.118767	+	0.443244i
$309$	−1253.01	−	1793.78i	−0.230683	−	0.330242i
$310$	12400.7	−	7159.52i	2.27197	−	1.31172i
$311$	1246.50	+	9468.08i	0.227274	+	1.72632i	0.601406	+	0.798944i	$0.294608\pi$
$311$	1246.50	+	9468.08i	0.227274	+	1.72632i	−0.374131	+	0.927376i	$0.622059\pi$
$312$	−98.7501	−	17.5272i	−0.0179187	−	0.00318039i
$313$	1048.90	−	7967.19i	0.189417	−	1.43876i	−0.587534	−	0.809200i	$-0.699901\pi$
$313$	1048.90	−	7967.19i	0.189417	−	1.43876i	0.776950	−	0.629562i	$-0.216766\pi$
$314$	10122.1	+	10122.1i	1.81918	+	1.81918i
$315$	−2582.87	+	449.423i	−0.461994	+	0.0803876i
$316$	−7246.47	+	3001.59i	−1.29002	+	0.534343i
$317$	4363.85	+	574.511i	0.773180	+	0.101791i	0.506785	−	0.862073i	$-0.330834\pi$
$317$	4363.85	+	574.511i	0.773180	+	0.101791i	0.266395	+	0.963864i	$0.414167\pi$
$318$	−6026.26	−	2818.37i	−1.06269	−	0.497001i
$319$	−1725.27	+	996.087i	−0.302811	+	0.174828i
$320$	−9621.64	+	1266.71i	−1.68083	+	0.221286i
$321$	1128.27	+	357.143i	0.196181	+	0.0620990i
$322$	−686.479	+	1189.02i	−0.118807	+	0.205780i
$323$	−1303.93	+	2792.92i	−0.224622	+	0.481122i
$324$	−3849.20	+	4545.48i	−0.660013	+	0.779403i
$325$	4095.81	−	4095.81i	0.699060	−	0.699060i
$326$	3129.67	+	4078.66i	0.531706	+	0.692933i
$327$	−6135.10	+	3184.94i	−1.03753	+	0.538616i
$328$	20.7666	+	157.738i	0.00349586	+	0.0265537i
$329$	−13.2679	+	17.2910i	−0.00222335	+	0.00289753i
$330$	−20314.9	+	7368.06i	−3.38878	+	1.22909i
$331$	5040.55	−	1350.61i	0.837020	−	0.224279i	0.185246	−	0.982692i	$-0.440692\pi$
$331$	5040.55	−	1350.61i	0.837020	−	0.224279i	0.651774	+	0.758413i	$0.274025\pi$
$332$	6672.73	+	6672.73i	1.10305	+	1.10305i
$333$	−1179.10	+	5262.35i	−0.194037	+	0.865991i
$334$	−2025.26	−	4889.42i	−0.331789	−	0.801009i
$335$	−1767.62	+	1356.34i	−0.288284	+	0.221208i
$336$	1463.73	+	934.824i	0.237658	+	0.151782i
$337$	890.897	−	117.289i	0.144007	−	0.0189588i	−0.0581782	−	0.998306i	$-0.518529\pi$
$337$	890.897	−	117.289i	0.144007	−	0.0189588i	0.202185	+	0.979347i	$0.435196\pi$
$338$	5456.26	+	1462.00i	0.878051	+	0.235273i
$339$	4057.68	−	6353.45i	0.650097	−	1.01791i
$340$	−8782.09	−	5600.51i	−1.40081	−	0.893325i
$341$	−11133.0			−1.76799
$342$	−4482.88	−	1643.10i	−0.708791	−	0.259791i
$343$	1343.31	−	3243.03i	0.211463	−	0.510517i
$344$	163.967	+	94.6661i	0.0256991	+	0.0148374i
$345$	−5474.63	−	2560.39i	−0.854331	−	0.399555i
$346$	−9011.93	+	11744.6i	−1.40024	+	1.82483i
$347$	−4884.43	−	3747.95i	−0.755648	−	0.579829i	0.157470	−	0.987524i	$-0.449666\pi$
$347$	−4884.43	−	3747.95i	−0.755648	−	0.579829i	−0.913118	+	0.407694i	$0.866333\pi$
$348$	448.868	−	1418.05i	0.0691433	−	0.218435i
$349$	2640.95	−	707.641i	0.405063	−	0.108536i	−0.0505345	−	0.998722i	$-0.516092\pi$
$349$	2640.95	−	707.641i	0.405063	−	0.108536i	0.455597	+	0.890186i	$0.349426\pi$
$350$	4081.64	−	1690.67i	0.623350	−	0.258200i
$351$	−2801.79	+	2782.89i	−0.426064	+	0.423190i
$352$	13514.3	+	5597.80i	2.04635	+	0.847624i
$353$	5543.88	+	3200.76i	0.835895	+	0.482604i	0.855867	−	0.517196i	$-0.173024\pi$
$353$	5543.88	+	3200.76i	0.835895	+	0.482604i	−0.0199715	+	0.999801i	$0.506358\pi$
$354$	−10656.9	+	920.242i	−1.60002	+	0.138165i
$355$	12074.6	+	3235.37i	1.80522	+	0.483707i
$356$	−5752.25	−	9963.19i	−0.856373	−	1.48328i
$357$	581.759	+	1855.39i	0.0862463	+	0.275063i
$358$	3162.33	−	5477.31i	0.466855	−	0.808617i
$359$	−5145.67	+	5145.67i	−0.756485	+	0.756485i	−0.975681	−	0.219196i	$-0.929657\pi$
$359$	−5145.67	+	5145.67i	−0.756485	+	0.756485i	0.219196	+	0.975681i	$0.429657\pi$
$360$	156.160	−	298.336i	0.0228621	−	0.0436769i
$361$			4925.22i			0.718067i
$362$	7720.05	−	5923.80i	1.12088	−	0.860078i
$363$	9733.28	+	1727.56i	1.40734	+	0.249790i
$364$	−974.089	−	747.445i	−0.140264	−	0.107628i
$365$	894.199	−	3337.19i	0.128231	−	0.478566i
$366$	−17870.9	+	3940.74i	−2.55226	+	0.562802i
$367$	−462.910	+	3516.15i	−0.0658411	+	0.500113i	0.926472	+	0.376363i	$0.122825\pi$
$367$	−462.910	+	3516.15i	−0.0658411	+	0.500113i	−0.992313	+	0.123750i	$0.960508\pi$
$368$	1532.19	+	3699.04i	0.217041	+	0.523984i
$369$	5550.06	+	2905.11i	0.782993	+	0.409849i
$370$		−	14607.9i		−	2.05251i
$371$	−1034.78	−	1348.55i	−0.144806	−	0.188714i
$372$	6134.65	−	5608.65i	0.855019	−	0.781708i
$373$	2478.91	+	4293.60i	0.344110	+	0.596017i	0.985192	−	0.171456i	$-0.0548472\pi$
$373$	2478.91	+	4293.60i	0.344110	+	0.596017i	−0.641081	+	0.767473i	$0.721514\pi$
$374$	7394.15	+	14220.1i	1.02231	+	1.96605i
$375$	3517.64	+	6775.97i	0.484400	+	0.933093i
$376$	−0.724535	−	2.70400i	−9.93751e−5	−	0.000370873i
$377$	377.376	−	911.066i	0.0515540	−	0.124462i
$378$	−2786.58	+	1143.20i	−0.379170	+	0.155556i
$379$	−4155.22	−	1721.15i	−0.563164	−	0.233270i	0.0828939	−	0.996558i	$-0.473584\pi$
$379$	−4155.22	−	1721.15i	−0.563164	−	0.233270i	−0.646058	+	0.763288i	$0.723584\pi$
$380$	6478.81	+	852.952i	0.874621	+	0.115146i
$381$	5109.81	+	4297.47i	0.687096	+	0.577864i
$382$	−3043.30	+	11357.7i	−0.407614	+	1.52124i
$383$	1409.22	−	5259.27i	0.188009	−	0.701661i	−0.805957	−	0.591974i	$-0.798349\pi$
$383$	1409.22	−	5259.27i	0.188009	−	0.701661i	0.993966	−	0.109686i	$-0.0349847\pi$
$384$	−428.655	+	155.470i	−0.0569654	+	0.0206609i
$385$	−5474.15	−	720.686i	−0.724646	−	0.0954014i
$386$	14716.5	+	6095.78i	1.94055	+	0.803801i
$387$	6763.46	−	3135.29i	0.888388	−	0.411824i
$388$	5116.92	−	12353.3i	0.669517	−	1.61636i
$389$	−2147.29	−	8013.81i	−0.279877	−	1.04452i	−0.952502	−	0.304532i	$-0.901500\pi$
$389$	−2147.29	−	8013.81i	−0.279877	−	1.04452i	0.672625	−	0.739983i	$-0.265167\pi$
$390$	5757.60	−	9015.17i	0.747558	−	1.17051i
$391$	−1349.91	+	4274.47i	−0.174598	+	0.552863i
$392$	107.830	+	186.766i	0.0138934	+	0.0240641i
$393$	276.950	+	1255.95i	0.0355478	+	0.161206i
$394$	7152.73	+	9321.61i	0.914592	+	1.19192i
$395$		−	17459.6i		−	2.22402i
$396$	−10594.9	+	6716.16i	−1.34448	+	0.852272i
$397$	−428.660	−	1034.88i	−0.0541911	−	0.130829i	0.894465	−	0.447137i	$-0.147556\pi$
$397$	−428.660	−	1034.88i	−0.0541911	−	0.130829i	−0.948656	+	0.316309i	$0.897556\pi$
$398$	−2141.98	+	16269.9i	−0.269768	+	2.04909i
$399$	−823.144	−	900.341i	−0.103280	−	0.112966i
$400$	3334.51	−	12444.6i	0.416814	−	1.55557i
$401$	6030.63	+	4627.46i	0.751010	+	0.576271i	0.911759	−	0.410725i	$-0.134724\pi$
$401$	6030.63	+	4627.46i	0.751010	+	0.576271i	−0.160749	+	0.986995i	$0.551391\pi$
$402$	−1647.57	+	1959.00i	−0.204411	+	0.243050i
$403$	4372.05	−	3354.79i	0.540416	−	0.414676i
$404$			8588.42i			1.05765i
$405$	−6069.05	−	11788.1i	−0.744626	−	1.44631i
$406$	531.843	−	531.843i	0.0650122	−	0.0650122i
$407$	−5678.79	+	9835.95i	−0.691615	+	1.19791i
$408$	−234.552	−	85.7927i	−0.0284610	−	0.0104102i
$409$	−1954.79	−	3385.80i	−0.236328	−	0.409333i	0.723330	−	0.690503i	$-0.242611\pi$
$409$	−1954.79	−	3385.80i	−0.236328	−	0.409333i	−0.959658	+	0.281170i	$0.909277\pi$
$410$	−16390.6	−	4391.85i	−1.97433	−	0.529020i
$411$	588.833	−	1259.05i	0.0706691	−	0.151105i
$412$	2979.62	+	1720.28i	0.356299	+	0.205710i
$413$	−2524.97	−	1045.88i	−0.300837	−	0.124611i
$414$	−6775.51	−	1518.14i	−0.804343	−	0.180224i
$415$	−19406.9	+	8038.62i	−2.29554	+	0.950844i
$416$	−6994.05	+	1874.05i	−0.824306	+	0.220872i
$417$	12248.7	−	2700.97i	1.43842	−	0.317187i
$418$	−7977.47	−	6121.33i	−0.933471	−	0.716277i
$419$	−8279.79	+	10790.4i	−0.965380	+	1.25811i	0.000735535		1.00000i	$0.499766\pi$
$419$	−8279.79	+	10790.4i	−0.965380	+	1.25811i	−0.966116	+	0.258109i	$0.916901\pi$
$420$	3379.52	−	2360.68i	0.392627	−	0.274261i
$421$	4165.44	+	2404.92i	0.482211	+	0.278405i	0.721337	−	0.692584i	$-0.243528\pi$
$421$	4165.44	+	2404.92i	0.482211	+	0.278405i	−0.239126	+	0.970988i	$0.576861\pi$
$422$	4089.58	−	9873.11i	0.471748	−	1.13890i
$423$	−103.491	−	37.9324i	−0.0118958	−	0.00436014i
$424$	218.327			0.0250068
$425$	11819.3	−	8267.85i	1.34899	−	0.943646i
$426$	14347.1	+	642.625i	1.63173	+	0.0730875i
$427$	−4516.46	−	1210.18i	−0.511866	−	0.137154i
$428$	−1844.96	+	242.893i	−0.208363	+	0.0274315i
$429$	−7381.40	+	3831.93i	−0.830716	+	0.431253i
$430$	−16020.5	+	12293.0i	−1.79669	+	1.37865i
$431$	−635.847	−	1535.07i	−0.0710619	−	0.171559i	0.884358	−	0.466810i	$-0.154597\pi$
$431$	−635.847	−	1535.07i	−0.0710619	−	0.171559i	−0.955420	+	0.295251i	$0.904597\pi$
$432$	−2302.03	+	8476.45i	−0.256381	+	0.944035i
$433$	−215.879	−	215.879i	−0.0239596	−	0.0239596i	0.695026	−	0.718985i	$-0.255393\pi$
$433$	−215.879	−	215.879i	−0.0239596	−	0.0239596i	−0.718985	+	0.695026i	$0.755393\pi$
$434$	4060.01	−	1087.88i	0.449047	−	0.120322i
$435$	2533.91	+	2131.08i	0.279292	+	0.234891i
$436$	6616.88	−	8623.28i	0.726814	−	0.947203i
$437$	−367.075	−	2788.21i	−0.0401821	−	0.305213i
$438$	177.610	−	3965.27i	0.0193756	−	0.432576i
$439$	−1290.93	−	1682.38i	−0.140348	−	0.182905i	0.717891	−	0.696156i	$-0.245108\pi$
$439$	−1290.93	−	1682.38i	−0.140348	−	0.182905i	−0.858239	+	0.513251i	$0.828441\pi$
$440$	501.466	−	501.466i	0.0543329	−	0.0543329i
$441$	8457.43	+	759.162i	0.913230	+	0.0819741i
$442$	−7188.82	−	3356.25i	−0.773614	−	0.361177i
$443$	1200.63	−	2079.55i	0.128767	−	0.223031i	−0.794432	−	0.607353i	$-0.792231\pi$
$443$	1200.63	−	2079.55i	0.128767	−	0.223031i	0.923199	+	0.384322i	$0.125565\pi$
$444$	−1826.02	−	8280.84i	−0.195178	−	0.885116i
$445$	25389.8	−	3342.63i	2.70470	−	0.356081i
$446$	17794.2	−	10273.5i	1.88919	−	1.09073i
$447$	7758.02	−	5419.19i	0.820899	−	0.573420i
$448$	−2824.35	−	371.832i	−0.297852	−	0.0392130i
$449$	−6459.63	+	2675.67i	−0.678950	+	0.281230i	−0.695388	−	0.718634i	$-0.744767\pi$
$449$	−6459.63	+	2675.67i	−0.678950	+	0.281230i	0.0164377	+	0.999865i	$0.494767\pi$
$450$	14323.1	+	17148.1i	1.50044	+	1.79637i
$451$	9328.98	+	9328.98i	0.974024	+	0.974024i
$452$	−1547.24	+	11752.5i	−0.161009	+	1.22299i
$453$	2235.35	+	6163.20i	0.231845	+	0.639233i
$454$	−610.986	−	4640.90i	−0.0631607	−	0.479753i
$455$	2366.93	−	1366.55i	0.243876	−	0.140802i
$456$	156.107	−	13.4802i	0.0160316	−	0.00138436i
$457$	−2268.02	−	8464.38i	−0.232152	−	0.866405i	−0.979412	−	0.201872i	$-0.935297\pi$
$457$	−2268.02	−	8464.38i	−0.232152	−	0.866405i	0.747259	−	0.664533i	$-0.231369\pi$
$458$	10684.5			1.09008
$459$	−8076.97	+	5609.38i	−0.821352	+	0.570421i
$460$	9503.34			0.963251
$461$	1048.52	+	3913.15i	0.105932	+	0.395344i	0.998449	−	0.0556697i	$-0.0177294\pi$
$461$	1048.52	+	3913.15i	0.105932	+	0.395344i	−0.892517	+	0.451013i	$0.851063\pi$
$462$	−6319.84	+	545.730i	−0.636419	+	0.0549560i
$463$	8779.57	−	5068.89i	0.881255	−	0.508793i	0.0101831	−	0.999948i	$-0.496759\pi$
$463$	8779.57	−	5068.89i	0.881255	−	0.508793i	0.871072	+	0.491155i	$0.163425\pi$
$464$	−286.294	−	2174.62i	−0.0286442	−	0.217574i
$465$	6308.66	+	17393.9i	0.629155	+	1.73468i
$466$	1424.51	−	10820.2i	0.141607	−	1.07561i
$467$	−7002.83	−	7002.83i	−0.693902	−	0.693902i	0.269186	−	0.963088i	$-0.413245\pi$
$467$	−7002.83	−	7002.83i	−0.693902	−	0.693902i	−0.963088	+	0.269186i	$0.913245\pi$
$468$	2136.92	−	5830.18i	0.211067	−	0.575855i
$469$	−604.235	+	250.282i	−0.0594903	+	0.0246417i
$470$	296.017	+	38.9713i	0.0290516	+	0.00382471i
$471$	−15164.0	+	10592.5i	−1.48348	+	1.03625i
$472$	304.005	−	175.517i	0.0296461	−	0.0171162i
$473$	15565.9	−	2049.29i	1.51316	−	0.199211i
$474$	−4319.43	−	19588.2i	−0.418561	−	1.89814i
$475$	−4524.68	+	7836.98i	−0.437067	+	0.757022i
$476$	−2064.57	−	2255.17i	−0.198801	−	0.217155i
$477$	4946.61	−	7030.68i	0.474822	−	0.674870i
$478$	3388.18	−	3388.18i	0.324208	−	0.324208i
$479$	3653.76	+	4761.68i	0.348528	+	0.454210i	0.934417	−	0.356181i	$-0.115921\pi$
$479$	3653.76	+	4761.68i	0.348528	+	0.454210i	−0.585889	+	0.810391i	$0.699255\pi$
$480$	1087.82	−	24286.5i	0.103442	−	2.30942i
$481$	−733.822	−	5573.93i	−0.0695621	−	0.528377i
$482$	7163.20	−	9335.26i	0.676919	−	0.882177i
$483$	−1357.75	−	1141.90i	−0.127908	−	0.107574i
$484$	−15014.3	+	4023.08i	−1.41006	+	0.377825i
$485$	21046.4	+	21046.4i	1.97045	+	1.97045i
$486$	−9725.29	−	11723.8i	−0.907712	−	1.09425i
$487$	4400.99	+	10624.9i	0.409503	+	0.988628i	0.985269	+	0.171013i	$0.0547042\pi$
$487$	4400.99	+	10624.9i	0.409503	+	0.988628i	−0.575765	+	0.817615i	$0.695296\pi$
$488$	476.464	−	365.604i	0.0441978	−	0.0339141i
$489$	−5895.96	+	3060.79i	−0.545245	+	0.283055i
$490$	−22804.5	+	3002.27i	−2.10246	+	0.276793i
$491$	−1295.31	−	347.078i	−0.119056	−	0.0319011i	0.198799	−	0.980040i	$-0.436296\pi$
$491$	−1295.31	−	347.078i	−0.119056	−	0.0319011i	−0.317855	+	0.948139i	$0.602963\pi$
$492$	−9840.41	−	440.765i	−0.901707	−	0.0403886i
$493$	1320.38	−	2070.47i	0.120623	−	0.189147i
$494$	4977.44			0.453331
$495$	−4786.80	−	27510.1i	−0.434648	−	2.49796i
$496$	4690.72	−	11324.4i	0.424636	−	1.02516i
$497$	3177.81	+	1834.71i	0.286809	+	0.165589i
$498$	−19784.3	+	13819.8i	−1.78023	+	1.24354i
$499$	10347.7	−	13485.4i	0.928313	−	1.20980i	−0.0491703	−	0.998790i	$-0.515658\pi$
$499$	10347.7	−	13485.4i	0.928313	−	1.20980i	0.977484	−	0.211011i	$-0.0676756\pi$
$500$	−9524.07	−	7308.08i	−0.851859	−	0.653655i
$501$	6678.08	−	1472.59i	0.595518	−	0.131319i
$502$	25088.3	−	6722.38i	2.23057	−	0.597678i
$503$	3254.28	−	1347.96i	0.288471	−	0.119489i	−0.233756	−	0.972295i	$-0.575102\pi$
$503$	3254.28	−	1347.96i	0.288471	−	0.119489i	0.522227	+	0.852807i	$0.325102\pi$
$504$	66.9433	−	72.7257i	0.00591645	−	0.00642750i
$505$	−17662.5	−	7316.04i	−1.55638	−	0.644672i
$506$	−12664.2	−	7311.69i	−1.11264	−	0.642380i
$507$	−3092.21	+	6611.77i	−0.270867	+	0.579170i
$508$	−10140.8	−	2717.23i	−0.885684	−	0.237318i
$509$	9587.32	+	16605.7i	0.834873	+	1.44604i	0.894134	+	0.447800i	$0.147792\pi$
$509$	9587.32	+	16605.7i	0.834873	+	1.44604i	−0.0592608	+	0.998243i	$0.518874\pi$
$510$	18027.1	−	19610.5i	1.56520	−	1.70268i
$511$	507.080	−	878.289i	0.0438981	−	0.0760337i
$512$	−11630.9	+	11630.9i	−1.00394	+	1.00394i
$513$	3102.81	−	5332.46i	0.267042	−	0.458936i
$514$			16310.2i			1.39964i
$515$	−6076.03	+	4662.31i	−0.519888	+	0.398924i
$516$	−7544.95	+	8971.15i	−0.643698	+	0.765374i
$517$	−184.167	−	141.316i	−0.0156667	−	0.0120214i
$518$	1109.82	−	4141.91i	0.0941366	−	0.351323i
$519$	−12907.4	−	14117.9i	−1.09166	−	1.19404i
$520$	−45.8207	+	348.043i	−0.00386417	+	0.0293513i
$521$	−8249.51	−	19916.1i	−0.693700	−	1.67474i	−0.737189	−	0.675686i	$-0.763847\pi$
$521$	−8249.51	−	19916.1i	−0.693700	−	1.67474i	0.0434891	−	0.999054i	$-0.486153\pi$
$522$	3370.06	+	1764.02i	0.282574	+	0.147910i
$523$			19394.5i			1.62153i	0.585368	+	0.810767i	$0.300950\pi$
$523$			19394.5i			1.62153i	−0.585368	+	0.810767i	$0.699050\pi$
$524$	−1231.11	−	1604.41i	−0.102636	−	0.133758i
$525$	1229.30	+	5574.79i	0.102193	+	0.463436i
$526$	9632.23	+	16683.5i	0.798451	+	1.38296i
$527$	12175.5	−	6331.00i	1.00640	−	0.523307i
$528$	−9956.81	+	15590.2i	−0.820672	+	1.28500i
$529$	2090.52	+	7801.94i	0.171819	+	0.641238i
$530$	−8911.11	+	21513.3i	−0.730328	+	1.76317i
$531$	1235.71	−	13766.4i	0.100989	−	1.12507i
$532$	1772.19	+	734.066i	0.144425	+	0.0598230i
$533$	−6474.78	−	852.421i	−0.526180	−	0.0692729i
$534$	27658.3	−	10031.5i	2.24137	−	0.812930i
$535$	1072.10	−	4001.15i	0.0866376	−	0.323336i
$536$	21.7418	−	81.1414i	0.00175206	−	0.00653876i
$537$	6254.59	+	5260.26i	0.502617	+	0.422713i
$538$	−32434.5	−	4270.08i	−2.59916	−	0.342186i
$539$	16522.1	+	6843.68i	1.32033	+	0.546898i
$540$	16496.9	+	12747.5i	1.31466	+	1.01586i
$541$	1208.09	−	2916.60i	0.0960075	−	0.231782i	−0.868578	−	0.495552i	$-0.834966\pi$
$541$	1208.09	−	2916.60i	0.0960075	−	0.231782i	0.964586	+	0.263769i	$0.0849658\pi$
$542$	715.704	+	2671.04i	0.0567198	+	0.211681i
$543$	5793.44	+	11159.8i	0.457864	+	0.881977i
$544$	−17963.0	+	1563.20i	−1.41573	+	0.123202i
$545$	12097.6	+	20953.7i	0.950833	+	1.64689i
$546$	2317.42	−	2118.72i	0.181642	−	0.166068i
$547$	4690.09	+	6112.24i	0.366606	+	0.477771i	0.939837	−	0.341623i	$-0.110977\pi$
$547$	4690.09	+	6112.24i	0.366606	+	0.477771i	−0.573231	+	0.819394i	$0.694310\pi$
$548$			2185.56i			0.170370i
$549$	−978.161	−	23626.8i	−0.0760417	−	1.83673i
$550$	18007.3	+	43473.5i	1.39606	+	3.37040i
$551$	−201.092	+	1527.45i	−0.0155478	+	0.118097i
$552$	222.523	−	49.0689i	0.0171580	−	0.00378354i
$553$	1326.48	−	4950.48i	0.102003	−	0.380680i
$554$	1563.04	+	1199.36i	0.119868	+	0.0919783i
$555$	18585.4	+	3298.74i	1.42146	+	0.252295i
$556$	−15647.1	+	12006.4i	−1.19350	+	0.915804i
$557$		−	12494.4i		−	0.950460i	−0.879862	−	0.475230i	$-0.842365\pi$
$557$		−	12494.4i		−	0.950460i	0.879862	−	0.475230i	$-0.157635\pi$
$558$	11381.0	+	17953.8i	0.863431	+	1.36209i
$559$	−5495.40	+	5495.40i	−0.415797	+	0.415797i
$560$	3039.53	−	5264.62i	0.229363	−	0.397269i
$561$	−19761.7	+	6196.32i	−1.48724	+	0.466326i
$562$	3846.93	+	6663.08i	0.288742	+	0.500116i
$563$	−19467.2	−	5216.22i	−1.45727	−	0.390475i	−0.558726	−	0.829352i	$-0.688710\pi$
$563$	−19467.2	−	5216.22i	−1.45727	−	0.390475i	−0.898547	+	0.438877i	$0.855376\pi$
$564$	172.676	−	14.9109i	0.0128918	−	0.00111323i
$565$	−22851.5	−	13193.3i	−1.70154	−	0.982385i
$566$	−6478.62	−	2683.53i	−0.481125	−	0.199289i
$567$	−825.221	−	3803.48i	−0.0611218	−	0.281713i
$568$	−435.433	+	180.362i	−0.0321661	+	0.0133236i
$569$	6963.09	−	1865.76i	0.513020	−	0.137463i	0.00698369	−	0.999976i	$-0.497777\pi$
$569$	6963.09	−	1865.76i	0.513020	−	0.137463i	0.506036	+	0.862512i	$0.331110\pi$
$570$	−5043.28	+	15932.6i	−0.370596	+	1.17077i
$571$	−10948.8	−	8401.33i	−0.802442	−	0.615735i	0.123954	−	0.992288i	$-0.460443\pi$
$571$	−10948.8	−	8401.33i	−0.802442	−	0.615735i	−0.926395	+	0.376553i	$0.877109\pi$
$572$	7961.04	−	10375.0i	0.581937	−	0.758395i
$573$	−13763.1	−	6436.73i	−1.00342	−	0.469282i
$574$	−4313.71	−	2490.52i	−0.313678	−	0.181102i
$575$	−5036.25	+	12158.6i	−0.365263	+	0.881823i
$576$	−2469.72	−	14193.7i	−0.178654	−	1.02674i
$577$	−15990.2			−1.15369			−0.576845	−	0.816854i	$-0.695716\pi$
$577$	−15990.2			−1.15369			−0.576845	+	0.816854i	$0.695716\pi$
$578$	−16173.1	−	11346.8i	−1.16386	−	0.816546i
$579$	−11078.8	+	17347.1i	−0.795200	+	1.24511i
$580$	−5028.76	−	1347.45i	−0.360014	−	0.0964654i
$581$	−6113.35	+	804.838i	−0.436531	+	0.0574704i
$582$	28819.1	+	18405.5i	2.05256	+	1.31088i
$583$	14363.4	−	11021.4i	1.02036	−	0.782950i
$584$	49.8488	+	120.346i	0.00353212	+	0.00852730i
$585$	10169.7	+	9361.11i	0.718744	+	0.661597i
$586$	−1856.04	−	1856.04i	−0.130840	−	0.130840i
$587$	−5061.24	+	1356.16i	−0.355877	+	0.0953570i	−0.432328	−	0.901716i	$-0.642308\pi$
$587$	−5061.24	+	1356.16i	−0.355877	+	0.0953570i	0.0764511	+	0.997073i	$0.475641\pi$
$588$	−12552.0	+	4552.52i	−0.880333	+	0.319291i
$589$	−5241.19	+	6830.45i	−0.366654	+	0.477833i
$590$	4886.88	+	37119.6i	0.341000	+	2.59015i
$591$	−13475.0	+	6995.32i	−0.937879	+	0.486885i
$592$	−7612.39	−	9920.66i	−0.528492	−	0.688744i
$593$	−10969.6	+	10969.6i	−0.759640	+	0.759640i	−0.976257	−	0.216617i	$-0.930498\pi$
$593$	−10969.6	+	10969.6i	−0.759640	+	0.759640i	0.216617	+	0.976257i	$0.430498\pi$
$594$	−12176.3	−	29679.9i	−0.841075	−	2.05013i
$595$	6396.58	−	2324.82i	0.440729	−	0.160182i
$596$	−7440.15	+	12886.7i	−0.511343	+	0.885672i
$597$	−20216.3	−	6399.26i	−1.38593	−	0.438701i
$598$	7176.68	−	944.828i	0.490763	−	0.0646102i
$599$	−2737.49	+	1580.49i	−0.186729	+	0.107808i	−0.590451	−	0.807074i	$-0.701050\pi$
$599$	−2737.49	+	1580.49i	−0.186729	+	0.107808i	0.403721	+	0.914882i	$0.367717\pi$
$600$	−664.193	−	310.631i	−0.0451926	−	0.0211358i
$601$	2791.51	+	367.510i	0.189465	+	0.0249435i	0.224661	−	0.974437i	$-0.427872\pi$
$601$	2791.51	+	367.510i	0.189465	+	0.0249435i	−0.0351967	+	0.999380i	$0.511206\pi$
$602$	−5476.38	+	2268.39i	−0.370765	+	0.153576i
$603$	−2120.36	−	2538.55i	−0.143197	−	0.171439i
$604$	−7289.46	−	7289.46i	−0.491066	−	0.491066i
$605$	4516.31	−	34304.8i	0.303494	−	2.30527i
$606$	−21625.8	−	3838.37i	−1.44965	−	0.257299i
$607$	−439.452	−	3337.97i	−0.0293852	−	0.223203i	0.970451	−	0.241298i	$-0.0775731\pi$
$607$	−439.452	−	3337.97i	−0.0293852	−	0.223203i	−0.999836	+	0.0180952i	$0.994240\pi$
$608$	9796.68	−	5656.12i	0.653467	−	0.377279i
$609$	556.556	+	796.757i	0.0370325	+	0.0530151i
$610$	16578.5	+	61871.6i	1.10040	+	4.10674i
$611$	114.909			0.00760835
$612$	7767.75	−	13370.1i	0.513060	−	0.883094i
$613$	16196.8			1.06718			0.533591	−	0.845742i	$-0.320842\pi$
$613$	16196.8			1.06718			0.533591	+	0.845742i	$0.320842\pi$
$614$	−3019.31	−	11268.2i	−0.198452	−	0.740631i
$615$	9289.00	−	19861.8i	0.609055	−	1.30228i
$616$	180.284	−	104.087i	0.0117919	−	0.00680808i
$617$	1084.07	+	8234.29i	0.0707339	+	0.537277i	0.989723	+	0.142995i	$0.0456734\pi$
$617$	1084.07	+	8234.29i	0.0707339	+	0.537277i	−0.918989	+	0.394282i	$0.870993\pi$
$618$	−5663.37	+	6733.90i	−0.368631	+	0.438313i
$619$	−940.486	+	7143.70i	−0.0610684	+	0.463860i	0.933401	+	0.358835i	$0.116826\pi$
$619$	−940.486	+	7143.70i	−0.0610684	+	0.463860i	−0.994470	+	0.105026i	$0.966508\pi$
$620$	−20572.5	−	20572.5i	−1.33260	−	1.33260i
$621$	3461.55	−	8277.56i	0.223683	−	0.534891i
$622$	35478.9	−	14695.9i	2.28710	−	0.947348i
$623$	7452.96	+	981.200i	0.479288	+	0.0630994i
$624$	−787.774	−	9122.83i	−0.0505388	−	0.585265i
$625$	865.559	−	499.731i	0.0553958	−	0.0319828i
$626$	−32038.1	+	4217.90i	−2.04553	+	0.269299i
$627$	9589.54	−	8767.31i	0.610796	−	0.558425i
$628$	14542.7	−	25188.6i	0.924069	−	1.60053i
$629$	617.131	−	13986.3i	0.0391202	−	0.886600i
$630$	4433.86	+	9564.73i	0.280395	+	0.604869i
$631$	−1040.96	+	1040.96i	−0.0656737	+	0.0656737i	−0.739181	−	0.673507i	$-0.764787\pi$
$631$	−1040.96	+	1040.96i	−0.0656737	+	0.0656737i	0.673507	+	0.739181i	$0.264787\pi$
$632$	400.737	+	522.250i	0.0252222	+	0.0328703i
$633$	11637.9	+	7432.64i	0.730752	+	0.466700i
$634$	−2310.26	−	17548.2i	−0.144719	−	1.09925i
$635$	14226.6	−	18540.5i	0.889079	−	1.15867i
$636$	−2362.26	+	13309.2i	−0.147280	+	0.829789i
$637$	−8550.68	+	2291.15i	−0.531853	+	0.142510i
$638$	5664.67	+	5664.67i	0.351515	+	0.351515i
$639$	−4057.44	+	18108.5i	−0.251189	+	1.12106i
$640$	610.766	+	1474.52i	0.0377229	+	0.0910711i
$641$	−8608.83	+	6605.79i	−0.530465	+	0.407040i	−0.838966	−	0.544184i	$-0.816839\pi$
$641$	−8608.83	+	6605.79i	−0.530465	+	0.407040i	0.308501	+	0.951224i	$0.400173\pi$
$642$	212.946	−	4754.19i	0.0130908	−	0.292263i
$643$	−15151.0	+	1994.66i	−0.929231	+	0.122336i	−0.579922	−	0.814672i	$-0.696917\pi$
$643$	−15151.0	+	1994.66i	−0.929231	+	0.122336i	−0.349309	+	0.937008i	$0.613584\pi$
$644$	2694.57	+	722.007i	0.164877	+	0.0441787i
$645$	−12022.4	−	23158.6i	−0.733926	−	1.41375i
$646$	12205.5	+	2157.97i	0.743372	+	0.131431i
$647$	5004.68			0.304103			0.152051	−	0.988373i	$-0.451412\pi$
$647$	5004.68			0.304103			0.152051	+	0.988373i	$0.451412\pi$
$648$	452.100	+	213.307i	0.0274077	+	0.0129313i
$649$	11139.7	−	26893.5i	0.673759	−	1.62660i
$650$	−20171.9	−	11646.3i	−1.21724	−	0.702776i
$651$	467.264	+	5411.15i	0.0281313	+	0.325775i
$652$	6358.96	−	8287.16i	0.381957	−	0.497776i
$653$	−14417.4	−	11062.9i	−0.864008	−	0.662977i	0.0785895	−	0.996907i	$-0.474958\pi$
$653$	−14417.4	−	11062.9i	−0.864008	−	0.662977i	−0.942598	+	0.333930i	$0.891625\pi$
$654$	18756.3	+	20515.4i	1.12145	+	1.22663i
$655$	4348.26	−	1165.11i	0.259390	−	0.0695035i
$656$	−13420.0	+	5558.75i	−0.798724	+	0.330842i
$657$	5004.85	+	1121.40i	0.297196	+	0.0665907i
$658$	80.9715	+	33.5395i	0.00479726	+	0.00198709i
$659$	1186.99	+	685.309i	0.0701647	+	0.0405096i	0.534672	−	0.845060i	$-0.320435\pi$
$659$	1186.99	+	685.309i	0.0701647	+	0.0405096i	−0.464507	+	0.885569i	$0.653769\pi$
$660$	25143.7	+	35995.2i	1.48290	+	2.12290i
$661$	−177.061	−	47.4433i	−0.0104189	−	0.00279172i	0.253606	−	0.967308i	$-0.418383\pi$
$661$	−177.061	−	47.4433i	−0.0104189	−	0.00279172i	−0.264025	+	0.964516i	$0.585050\pi$
$662$	−10492.2	−	18173.0i	−0.615998	−	1.06694i
$663$	5893.47	−	8388.33i	0.345224	−	0.491366i
$664$	395.995	−	685.883i	0.0231439	−	0.0400865i
$665$	−3019.28	+	3019.28i	−0.176064	+	0.176064i
$666$	21667.4	−	897.042i	1.26065	−	0.0521917i
$667$			2240.51i			0.130064i
$668$	−8530.93	+	6546.01i	−0.494119	+	0.379151i
$669$	9052.55	+	24959.3i	0.523157	+	1.44242i
$670$	7108.04	+	5454.19i	0.409862	+	0.314498i
$671$	12889.7	−	48104.9i	0.741580	−	2.76761i
$672$	2153.58	−	6803.52i	0.123625	−	0.390553i
$673$	4080.97	−	30998.1i	0.233744	−	1.77546i	−0.324596	−	0.945853i	$-0.605228\pi$
$673$	4080.97	−	30998.1i	0.233744	−	1.77546i	0.558341	−	0.829612i	$-0.311438\pi$
$674$	−1382.80	−	3338.39i	−0.0790262	−	0.190786i
$675$	−25051.6	+	14350.7i	−1.42850	+	0.818312i
$676$		−	11477.3i		−	0.653009i
$677$	−16045.5	−	20910.9i	−0.910897	−	1.18710i	−0.981857	−	0.189625i	$-0.939273\pi$
$677$	−16045.5	−	20910.9i	−0.910897	−	1.18710i	0.0709594	−	0.997479i	$-0.477394\pi$
$678$	−28901.5	−	9148.46i	−1.63710	−	0.518207i
$679$	4368.49	+	7566.45i	0.246903	+	0.427649i
$680$	−263.254	+	833.592i	−0.0148461	+	0.0470100i
$681$	6042.52	+	270.652i	0.340014	+	0.0152297i
$682$	11587.0	+	43243.2i	0.650569	+	2.42796i
$683$	−8415.96	+	20317.9i	−0.471490	+	1.13828i	0.492015	+	0.870587i	$0.336261\pi$
$683$	−8415.96	+	20317.9i	−0.471490	+	1.13828i	−0.963505	+	0.267691i	$0.913739\pi$
$684$	−867.303	+	9662.17i	−0.0484827	+	0.540120i
$685$	−4494.71	−	1861.77i	−0.250706	−	0.103846i
$686$	−13994.8	−	1842.45i	−0.778898	−	0.102544i
$687$	−2412.76	+	13593.8i	−0.133992	+	0.754926i
$688$	−4473.95	+	16697.0i	−0.247918	+	0.925243i
$689$	−2319.49	+	8656.47i	−0.128252	+	0.478643i
$690$	−4247.27	+	23929.6i	−0.234335	+	1.32027i
$691$	−19233.1	−	2532.08i	−1.05884	−	0.139399i	−0.419063	−	0.907957i	$-0.637641\pi$
$691$	−19233.1	−	2532.08i	−1.05884	−	0.139399i	−0.639780	+	0.768558i	$0.720975\pi$
$692$	27789.1	+	11510.6i	1.52656	+	0.632323i
$693$	732.812	−	8163.87i	0.0401691	−	0.447503i
$694$	−9474.34	+	22873.1i	−0.518215	+	1.25108i
$695$	−11362.8	−	42406.7i	−0.620168	−	2.31450i
$696$	−124.707	−	5.58580i	−0.00679169	−	0.000304209i
$697$	−15507.6	−	4897.42i	−0.842746	−	0.266145i
$698$	−5497.29	−	9521.58i	−0.298102	−	0.516328i
$699$	13444.7	+	4255.78i	0.727504	+	0.230284i
$700$	−5464.54	−	7121.53i	−0.295058	−	0.384527i
$701$			6639.62i			0.357739i	0.983873	+	0.178869i	$0.0572440\pi$
$701$			6639.62i			0.357739i	−0.983873	+	0.178869i	$0.942756\pi$
$702$	13725.4	+	7986.45i	0.737939	+	0.429386i
$703$	3361.21	+	8114.69i	0.180328	+	0.435350i
$704$	3960.39	−	30082.1i	0.212021	−	1.61046i
$705$	−116.429	+	367.817i	−0.00621980	+	0.0196494i
$706$	6662.57	−	24865.0i	0.355169	−	1.32551i
$707$	−4452.17	−	3416.27i	−0.236833	−	0.181729i
$708$	7410.27	+	20431.2i	0.393355	+	1.08454i
$709$	−14666.9	+	11254.3i	−0.776905	+	0.596140i	−0.919249	−	0.393677i	$-0.871203\pi$
$709$	−14666.9	+	11254.3i	−0.776905	+	0.596140i	0.142344	+	0.989817i	$0.454536\pi$
$710$		−	50267.9i		−	2.65707i
$711$	25897.2	−	1072.16i	1.36599	−	0.0565529i
$712$	−682.737	+	682.737i	−0.0359363	+	0.0359363i
$713$	−6260.40	+	10843.3i	−0.328827	+	0.569545i
$714$	6601.28	−	4190.73i	0.346004	−	0.219656i
$715$	14555.1	+	25210.2i	0.761302	+	1.31861i
$716$	−12412.8	−	3325.99i	−0.647887	−	0.173601i
$717$	3545.62	+	5075.84i	0.184677	+	0.264381i
$718$	25342.5	+	14631.5i	1.31723	+	0.760506i
$719$	18950.8	+	7849.69i	0.982958	+	0.407155i	0.815521	−	0.578728i	$-0.196451\pi$
$719$	18950.8	+	7849.69i	0.982958	+	0.407155i	0.167438	+	0.985883i	$0.446451\pi$
$720$	30000.0	+	6721.89i	1.55282	+	0.347931i
$721$	−2077.01	+	860.324i	−0.107284	+	0.0444385i
$722$	19130.7	−	5126.06i	0.986111	−	0.264228i
$723$	10259.5	+	11221.7i	0.527740	+	0.577234i
$724$	−15685.8	−	12036.2i	−0.805193	−	0.617847i
$725$	4388.90	−	5719.73i	0.224827	−	0.293001i
$726$	−3419.92	−	39604.4i	−0.174828	−	2.02460i
$727$	30225.0	+	17450.4i	1.54193	+	0.890232i	0.998717	+	0.0506359i	$0.0161248\pi$
$727$	30225.0	+	17450.4i	1.54193	+	0.890232i	0.543211	+	0.839596i	$0.317209\pi$
$728$	−39.4342	+	95.2025i	−0.00200759	+	0.00484676i
$729$	17112.2	−	9725.89i	0.869390	−	0.494126i
$730$	−13893.1			−0.704394
$731$	−15858.1	+	11093.1i	−0.802373	+	0.561275i
$732$	17132.0	+	33001.1i	0.865049	+	1.66633i
$733$	20273.4	+	5432.23i	1.02157	+	0.273730i	0.730458	−	0.682958i	$-0.239307\pi$
$733$	20273.4	+	5432.23i	1.02157	+	0.273730i	0.291116	+	0.956688i	$0.405973\pi$
$734$	14139.3	−	1861.48i	0.711026	−	0.0936083i
$735$	1329.94	−	29691.8i	0.0667421	−	1.49007i
$736$	13051.6	−	10014.9i	0.653654	−	0.501566i
$737$	−2665.76	−	6435.71i	−0.133235	−	0.321659i
$738$	5507.77	−	24581.3i	0.274721	−	1.22609i
$739$	25055.7	+	25055.7i	1.24721	+	1.24721i	0.956947	+	0.290262i	$0.0937424\pi$
$739$	25055.7	+	25055.7i	1.24721	+	1.24721i	0.290262	+	0.956947i	$0.406258\pi$
$740$	−28669.5	+	7681.96i	−1.42420	+	0.381614i
$741$	−1124.00	+	6332.72i	−0.0557234	+	0.313952i
$742$	−4161.10	+	5422.85i	−0.205874	+	0.268301i
$743$	3158.36	+	23990.2i	0.155948	+	1.18454i	0.873071	+	0.487594i	$0.162125\pi$
$743$	3158.36	+	23990.2i	0.155948	+	1.18454i	−0.717123	+	0.696947i	$0.754541\pi$
$744$	−587.933	−	375.488i	−0.0289714	−	0.0185028i
$745$	−20164.2	−	26278.6i	−0.991625	−	1.29231i
$746$	14097.4	−	14097.4i	0.691878	−	0.691878i
$747$	−13115.1	−	28292.0i	−0.642380	−	1.38574i
$748$	24019.9	−	21989.8i	1.17414	−	1.07490i
$749$	607.967	−	1053.03i	0.0296590	−	0.0513710i
$750$	22658.4	−	20715.6i	1.10316	−	1.00857i
$751$	−18553.5	+	2442.62i	−0.901502	+	0.118685i	−0.567007	−	0.823713i	$-0.691899\pi$
$751$	−18553.5	+	2442.62i	−0.901502	+	0.118685i	−0.334495	+	0.942398i	$0.608566\pi$
$752$	221.342	−	127.792i	0.0107334	−	0.00619693i
$753$	2887.39	+	33437.5i	0.139738	+	1.61823i
$754$	−3931.56	−	517.600i	−0.189893	−	0.0249998i
$755$	21200.6	−	8781.59i	1.02195	−	0.423304i
$756$	3709.05	+	4867.75i	0.178435	+	0.234178i
$757$	−6495.85	−	6495.85i	−0.311883	−	0.311883i	0.533756	−	0.845639i	$-0.320780\pi$
$757$	−6495.85	−	6495.85i	−0.311883	−	0.311883i	−0.845639	+	0.533756i	$0.820780\pi$
$758$	−2360.69	+	17931.2i	−0.113119	+	0.859222i
$759$	12162.4	−	14461.4i	0.581642	−	0.691588i
$760$	−71.5855	−	543.746i	−0.00341668	−	0.0259523i
$761$	−31508.2	+	18191.3i	−1.50088	+	0.866535i	−0.500882	+	0.865515i	$0.666991\pi$
$761$	−31508.2	+	18191.3i	−1.50088	+	0.866535i	−0.999999	+	0.00101922i	$0.999676\pi$
$762$	11374.2	−	24320.4i	0.540741	−	1.15622i
$763$	1838.21	+	6860.28i	0.0872183	+	0.325503i
$764$	23891.1			1.13135
$765$	20879.2	+	27364.0i	0.986785	+	1.29327i
$766$	−21894.9			−1.03276
$767$	3729.37	+	13918.2i	0.175567	+	0.655224i
$768$	−11651.9	−	16680.7i	−0.547464	−	0.783740i
$769$	−104.671	+	60.4317i	−0.00490836	+	0.00283384i	−0.502452	−	0.864605i	$-0.667569\pi$
$769$	−104.671	+	60.4317i	−0.00490836	+	0.00283384i	0.497544	+	0.867439i	$0.334235\pi$
$770$	2898.06	+	22013.0i	0.135635	+	1.03025i
$771$	−20751.2	−	3683.15i	−0.969310	−	0.172043i
$772$	4224.50	−	32088.3i	0.196947	−	1.49596i
$773$	17375.3	+	17375.3i	0.808467	+	0.808467i	0.984402	−	0.175935i	$-0.0562947\pi$
$773$	17375.3	+	17375.3i	0.808467	+	0.808467i	−0.175935	+	0.984402i	$0.556295\pi$
$774$	−19217.5	−	23007.7i	−0.892453	−	1.06847i
$775$	37222.8	−	15418.2i	1.72527	−	0.714629i
$776$	−1112.60	−	146.476i	−0.0514690	−	0.00677603i
$777$	5019.08	+	2347.33i	0.231735	+	0.108378i
$778$	−28892.7	+	16681.2i	−1.33143	+	0.768702i
$779$	10115.5	−	1331.73i	0.465246	−	0.0612508i
$780$	−20721.0	−	6559.00i	−0.951191	−	0.301090i
$781$	−19541.5	+	33846.9i	−0.895327	+	1.55075i
$782$	18008.0	+	794.583i	0.823486	+	0.0363353i
$783$	−3005.36	+	3889.33i	−0.137168	+	0.177514i
$784$	−13922.7	+	13922.7i	−0.634233	+	0.634233i
$785$	39413.4	+	51364.6i	1.79201	+	2.33539i
$786$	4590.15	−	2382.90i	0.208302	−	0.108136i
$787$	−2392.95	−	18176.3i	−0.108386	−	0.823270i	−0.956146	−	0.292891i	$-0.905383\pi$
$787$	−2392.95	−	18176.3i	−0.108386	−	0.823270i	0.847760	−	0.530380i	$-0.177951\pi$
$788$	14533.1	−	18940.0i	0.657007	−	0.856228i
$789$	−23401.3	+	8487.50i	−1.05591	+	0.382970i
$790$	−67817.3	+	18171.6i	−3.05422	+	0.818375i
$791$	−5476.95	−	5476.95i	−0.246192	−	0.246192i
$792$	774.602	+	713.014i	0.0347529	+	0.0319897i
$793$	9433.92	+	22775.5i	0.422457	+	1.01990i
$794$	−3573.57	+	2742.10i	−0.159725	+	0.122561i
$795$	−25358.8	−	16195.6i	−1.13130	−	0.722513i
$796$	33057.8	−	4352.14i	1.47199	−	0.193791i
$797$	−6574.70	−	1761.68i	−0.292205	−	0.0782962i	0.109739	−	0.993960i	$-0.464999\pi$
$797$	−6574.70	−	1761.68i	−0.292205	−	0.0782962i	−0.401944	+	0.915664i	$0.631665\pi$
$798$	−2640.43	+	4134.34i	−0.117131	+	0.183401i
$799$	281.775	+	49.8187i	0.0124762	+	0.00220583i
$800$	−52937.0			−2.33951
$801$	6517.14	+	37454.6i	0.287481	+	1.65217i
$802$	11697.6	−	28240.6i	0.515034	−	1.24340i
$803$	9354.66	+	5400.92i	0.411107	+	0.237353i
$804$	4711.15	+	2203.32i	0.206654	+	0.0966481i
$805$	−3780.21	+	4926.46i	−0.165509	+	0.215696i
$806$	−17581.2	−	13490.5i	−0.768325	−	0.589557i
$807$	12757.1	−	40301.6i	0.556468	−	1.75797i
$808$	696.238	−	186.556i	0.0303138	−	0.00812257i
$809$	19058.2	−	7894.18i	0.828247	−	0.343071i	0.0720387	−	0.997402i	$-0.477049\pi$
$809$	19058.2	−	7894.18i	0.828247	−	0.343071i	0.756209	+	0.654331i	$0.227049\pi$
$810$	−39471.3	+	35842.4i	−1.71220	+	1.55478i
$811$	−5530.37	−	2290.75i	−0.239454	−	0.0991853i	0.259729	−	0.965681i	$-0.416367\pi$
$811$	−5530.37	−	2290.75i	−0.239454	−	0.0991853i	−0.499184	+	0.866496i	$0.666367\pi$
$812$	−1323.48	−	764.111i	−0.0571983	−	0.0330235i
$813$	−3559.95	+	307.409i	−0.153571	+	0.0132611i
$814$	44115.5	+	11820.7i	1.89957	+	0.508988i
$815$	11626.1	+	20136.9i	0.499685	+	0.865479i
$816$	2023.46	−	22712.2i	0.0868079	−	0.974371i
$817$	6070.82	−	10515.0i	0.259965	−	0.450272i
$818$	−11116.8	+	11116.8i	−0.475169	+	0.475169i
$819$	2172.30	+	3426.87i	0.0926818	+	0.146208i
$820$			34477.8i			1.46831i
$821$	4731.53	−	3630.63i	0.201135	−	0.154336i	−0.503283	−	0.864122i	$-0.667875\pi$
$821$	4731.53	−	3630.63i	0.201135	−	0.154336i	0.704418	+	0.709785i	$0.251208\pi$
$822$	−5503.28	−	976.780i	−0.233514	−	0.0414466i
$823$	−17229.5	−	13220.6i	−0.729747	−	0.559955i	0.175685	−	0.984446i	$-0.443786\pi$
$823$	−17229.5	−	13220.6i	−0.729747	−	0.559955i	−0.905432	+	0.424492i	$0.860453\pi$
$824$	74.7356	−	278.917i	0.00315963	−	0.0117919i
$825$	−59377.1	+	13093.3i	−2.50575	+	0.552547i
$826$	−1434.50	+	10896.1i	−0.0604270	+	0.458989i
$827$	8091.47	+	19534.5i	0.340227	+	0.821382i	0.997692	+	0.0678965i	$0.0216288\pi$
$827$	8091.47	+	19534.5i	0.340227	+	0.821382i	−0.657465	+	0.753485i	$0.728371\pi$
$828$	583.580	+	14096.0i	0.0244937	+	0.591629i
$829$		−	28330.9i		−	1.18694i	−0.804856	−	0.593470i	$-0.797757\pi$
$829$		−	28330.9i		−	1.18694i	0.804856	−	0.593470i	$-0.202243\pi$
$830$	51422.2	+	67014.8i	2.15047	+	2.80255i
$831$	−1878.89	+	1717.79i	−0.0784333	+	0.0717083i
$832$	7509.61	+	13007.0i	0.312919	+	0.541992i
$833$	−21961.0	+	1911.12i	−0.913450	+	0.0794913i
$834$	−23239.4	−	44765.7i	−0.964885	−	1.85864i
$835$	−6195.11	−	23120.5i	−0.256755	−	0.958224i
$836$	−7818.55	+	18875.6i	−0.323457	+	0.780895i
$837$	−25412.4	+	10425.5i	−1.04944	+	0.430537i
$838$	50530.1	+	20930.2i	2.08297	+	0.862796i
$839$	−9740.55	−	1282.37i	−0.400812	−	0.0527679i	−0.0725740	−	0.997363i	$-0.523121\pi$
$839$	−9740.55	−	1282.37i	−0.400812	−	0.0527679i	−0.328238	+	0.944595i	$0.606455\pi$
$840$	−264.783	−	222.689i	−0.0108761	−	0.00914702i
$841$	−5994.66	+	22372.4i	−0.245794	+	0.917314i
$842$	5005.97	−	18682.5i	0.204890	−	0.764658i
$843$	−9346.05	+	3389.75i	−0.381845	+	0.138492i
$844$	−21527.6	−	2834.16i	−0.877974	−	0.115587i
$845$	23603.6	+	9776.91i	0.960932	+	0.398031i
$846$	−39.6271	+	441.464i	−0.00161041	+	0.0179407i
$847$	3886.82	−	9383.62i	0.157677	−	0.380667i
$848$	5159.10	+	19254.0i	0.208920	+	0.779701i
$849$	4877.21	−	7636.67i	0.197156	−	0.308704i
$850$	−44415.6	−	37304.1i	−1.79229	−	1.50532i
$851$	6386.69	+	11062.1i	0.257266	+	0.445597i
$852$	−6283.59	−	28495.5i	−0.252667	−	1.14582i
$853$	−8764.28	−	11421.8i	−0.351797	−	0.458471i	0.583615	−	0.812031i	$-0.301638\pi$
$853$	−8764.28	−	11421.8i	−0.351797	−	0.458471i	−0.935412	+	0.353559i	$0.884971\pi$
$854$			18802.6i			0.753408i
$855$	−19131.9	−	10014.4i	−0.765260	−	0.400566i
$856$	59.7665	+	144.289i	0.00238642	+	0.00576133i
$857$	849.047	−	6449.15i	0.0338423	−	0.257058i	−0.966157	−	0.257954i	$-0.916952\pi$
$857$	849.047	−	6449.15i	0.0338423	−	0.257058i	1.00000		0.000895675i	$0.000285102\pi$
$858$	22566.5	+	24682.9i	0.897912	+	0.982122i
$859$	87.2982	−	325.801i	0.00346749	−	0.0129409i	−0.964170	−	0.265284i	$-0.914534\pi$
$859$	87.2982	−	325.801i	0.00346749	−	0.0129409i	0.967638	+	0.252343i	$0.0812011\pi$
$860$	32551.0	+	24977.2i	1.29067	+	0.990368i
$861$	4142.77	−	4925.87i	0.163978	−	0.194975i
$862$	−5300.80	+	4067.45i	−0.209450	+	0.160717i
$863$		−	40227.4i		−	1.58674i	−0.608739	−	0.793371i	$-0.708324\pi$
$863$		−	40227.4i		−	1.58674i	0.608739	−	0.793371i	$-0.291676\pi$
$864$	36090.1	+	122.148i	1.42108	+	0.00480967i
$865$	−47344.2	+	47344.2i	−1.86098	+	1.86098i
$866$	−613.844	+	1063.21i	−0.0240869	+	0.0417197i
$867$	18088.5	−	18014.4i	0.708556	−	0.705654i
$868$	−4270.13	−	7396.08i	−0.166979	−	0.289216i
$869$	52727.6	+	14128.3i	2.05830	+	0.551520i
$870$	5640.39	−	12060.3i	0.219801	−	0.469980i
$871$	2986.20	+	1724.08i	0.116169	+	0.0670704i
$872$	−842.795	−	349.097i	−0.0327301	−	0.0135573i
$873$	−29924.9	+	32509.8i	−1.16014	+	1.26035i
$874$	−10448.0	+	4327.71i	−0.404359	+	0.167491i
$875$	7576.91	−	2030.23i	0.292739	−	0.0784391i
$876$	−7875.65	+	1736.67i	−0.303760	+	0.0669825i
$877$	−22437.2	−	17216.7i	−0.863912	−	0.662903i	0.0786619	−	0.996901i	$-0.474935\pi$
$877$	−22437.2	−	17216.7i	−0.863912	−	0.662903i	−0.942574	+	0.333999i	$0.891602\pi$
$878$	−5191.17	+	6765.27i	−0.199537	+	0.260042i
$879$	2780.54	−	1942.29i	0.106696	−	0.0745298i
$880$	56073.5	+	32374.1i	2.14800	+	1.24015i
$881$	−6126.47	+	14790.6i	−0.234286	+	0.565616i	−0.996673	−	0.0815051i	$-0.974027\pi$
$881$	−6126.47	+	14790.6i	−0.234286	+	0.565616i	0.762387	+	0.647121i	$0.224027\pi$
$882$	−5853.54	−	33640.8i	−0.223468	−	1.28429i
$883$	13232.8			0.504326			0.252163	−	0.967685i	$-0.418858\pi$
$883$	13232.8			0.504326			0.252163	+	0.967685i	$0.418858\pi$
$884$	−2806.53	+	15873.7i	−0.106780	+	0.603950i
$885$	−48330.2	−	2164.78i	−1.83571	−	0.0822239i
$886$	−9327.07	−	2499.18i	−0.353667	−	0.0947649i
$887$	−42870.5	+	5644.00i	−1.62283	+	0.213650i	−0.886418	−	0.462885i	$-0.846814\pi$
$887$	−42870.5	+	5644.00i	−1.62283	+	0.213650i	−0.736411	+	0.676535i	$0.763481\pi$
$888$	−631.639	+	327.905i	−0.0238698	+	0.0123917i
$889$	5442.39	−	4176.09i	0.205323	−	0.157550i
$890$	−39408.7	−	95141.1i	−1.48425	−	3.58330i
$891$	40510.9	−	8789.44i	1.52319	−	0.330480i
$892$	−29520.3	−	29520.3i	−1.10809	−	1.10809i
$893$	−173.404	+	46.4635i	−0.00649804	+	0.00174115i
$894$	−29123.8	−	24493.8i	−1.08954	−	0.916326i
$895$	17413.9	−	22694.2i	0.650370	−	0.847579i
$896$	61.1508	+	464.486i	0.00228003	+	0.0173185i
$897$	−418.537	+	9344.15i	−0.0155792	+	0.347817i
$898$	17116.0	+	22306.0i	0.636044	+	0.828908i
$899$	4850.18	−	4850.18i	0.179936	−	0.179936i
$900$	26122.6	−	37128.3i	0.967502	−	1.37512i
$901$	−9440.79	+	20221.5i	−0.349077	+	0.747696i
$902$	26526.6	−	45945.4i	0.979200	−	1.69602i
$903$	−1649.37	−	7479.76i	−0.0607837	−	0.275649i
$904$	986.349	−	129.855i	0.0362893	−	0.00477757i
$905$	38114.9	−	22005.7i	1.39998	−	0.808280i
$906$	21612.8	−	15097.2i	0.792537	−	0.553609i
$907$	−9983.58	−	1314.36i	−0.365490	−	0.0481177i	−0.0544552	−	0.998516i	$-0.517342\pi$
$907$	−9983.58	−	1314.36i	−0.365490	−	0.0481177i	−0.311035	+	0.950399i	$0.600676\pi$
$908$	−8786.92	+	3639.66i	−0.321150	+	0.133025i
$909$	9767.01	−	26647.4i	0.356382	−	0.972320i
$910$	−7771.46	−	7771.46i	−0.283100	−	0.283100i
$911$	1635.19	−	12420.5i	0.0594689	−	0.451711i	−0.935642	−	0.352950i	$-0.885179\pi$
$911$	1635.19	−	12420.5i	0.0594689	−	0.451711i	0.995111	−	0.0987613i	$-0.0314880\pi$
$912$	4877.64	+	13448.4i	0.177099	+	0.488290i
$913$	−8572.34	−	65113.4i	−0.310737	−	2.36028i
$914$	−30517.2	+	17619.1i	−1.10440	+	0.637623i
$915$	−82462.1	+	7120.77i	−2.97936	+	0.257273i
$916$	−5618.74	−	20969.4i	−0.202673	−	0.756386i
$917$	1321.42			0.0475869
$918$	30194.5	+	25534.8i	1.08558	+	0.918053i
$919$	−21936.6			−0.787403			−0.393701	−	0.919238i	$-0.628806\pi$
$919$	−21936.6			−0.787403			−0.393701	+	0.919238i	$0.628806\pi$
$920$	−206.430	−	770.408i	−0.00739761	−	0.0276083i
$921$	15018.2	−	1296.85i	0.537314	−	0.0463981i
$922$	14108.3	−	8145.44i	0.503940	−	0.290950i
$923$	−2525.18	−	19180.7i	−0.0900514	−	0.684008i
$924$	4394.51	+	12116.3i	0.156460	+	0.431383i
$925$	5364.94	−	40750.8i	0.190701	−	1.44852i
$926$	−28826.3	−	28826.3i	−1.02299	−	1.02299i
$927$	−7288.55	−	8726.07i	−0.258239	−	0.309171i
$928$	−8326.34	+	3448.88i	−0.294532	+	0.121999i
$929$	−4212.32	−	554.562i	−0.148764	−	0.0195851i	0.0557764	−	0.998443i	$-0.482237\pi$
$929$	−4212.32	−	554.562i	−0.148764	−	0.0195851i	−0.204540	+	0.978858i	$0.565570\pi$
$930$	60996.2	−	42607.6i	2.15069	−	1.50232i
$931$	11977.1	−	6914.98i	0.421625	−	0.243426i
$932$	−21984.8	+	2894.36i	−0.772679	+	0.101725i
$933$	10685.5	+	48457.9i	0.374950	+	1.70037i
$934$	−19912.3	+	34489.1i	−0.697590	+	1.20826i
$935$	24761.6	+	68130.0i	0.866088	+	2.38298i
$936$	−519.053	−	46.5916i	−0.0181258	−	0.00162703i
$937$	8659.85	−	8659.85i	0.301926	−	0.301926i	−0.539841	−	0.841767i	$-0.681516\pi$
$937$	8659.85	−	8659.85i	0.301926	−	0.301926i	0.841767	+	0.539841i	$0.181516\pi$
$938$	1601.03	+	2086.50i	0.0557308	+	0.0726298i
$939$	1868.43	−	41714.1i	0.0649350	−	1.44972i
$940$	−79.1832	−	601.456i	−0.00274752	−	0.0208695i
$941$	21157.6	−	27573.1i	0.732963	−	0.955216i	−0.267001	−	0.963696i	$-0.586033\pi$
$941$	21157.6	−	27573.1i	0.732963	−	0.955216i	0.999964	+	0.00848007i	$0.00269932\pi$
$942$	56925.9	+	47876.1i	1.96895	+	1.65593i
$943$	14332.2	−	3840.30i	0.494932	−	0.132617i
$944$	22662.4	+	22662.4i	0.781353	+	0.781353i
$945$	−13170.3	+	3481.24i	−0.453365	+	0.119836i
$946$	−24160.6	−	58329.0i	−0.830370	−	2.00469i
$947$	−6301.93	+	4835.64i	−0.216246	+	0.165932i	−0.711205	−	0.702985i	$-0.751850\pi$
$947$	−6301.93	+	4835.64i	−0.216246	+	0.165932i	0.494958	+	0.868917i	$0.335183\pi$
$948$	−36172.4	+	18778.3i	−1.23927	+	0.643345i
$949$	−5301.19	+	697.915i	−0.181332	+	0.0238728i
$950$	35149.9	+	9418.39i	1.20043	+	0.321656i
$951$	22848.0	+	1023.39i	0.779071	+	0.0348956i
$952$	−137.974	+	216.355i	−0.00469723	+	0.00736567i
$953$	−21625.8			−0.735077			−0.367538	−	0.930008i	$-0.619799\pi$
$953$	−21625.8			−0.735077			−0.367538	+	0.930008i	$0.619799\pi$
$954$	−32457.2	−	11896.4i	−1.10151	−	0.403733i
$955$	−20351.6	+	49133.2i	−0.689595	+	1.66483i
$956$	−8431.40	−	4867.87i	−0.285242	−	0.164684i
$957$	−8486.26	+	5927.89i	−0.286648	+	0.200231i
$958$	14692.7	−	19147.9i	0.495512	−	0.645764i
$959$	−1132.98	−	869.365i	−0.0381499	−	0.0292735i
$960$	−49243.9	+	10858.8i	−1.65556	+	0.365070i
$961$	8249.65	−	2210.49i	0.276917	−	0.0741998i
$962$	−20886.7	+	8651.56i	−0.700016	+	0.289956i
$963$	6000.60	+	1344.51i	0.200796	+	0.0449910i
$964$	−22088.3	−	9149.29i	−0.737985	−	0.305683i
$965$	62392.4	+	36022.3i	2.08133	+	1.20166i
$966$	−3022.29	+	6462.28i	−0.100663	+	0.215239i
$967$	−27850.5	−	7462.52i	−0.926175	−	0.248168i	−0.235952	−	0.971765i	$-0.575821\pi$
$967$	−27850.5	−	7462.52i	−0.926175	−	0.248168i	−0.690223	+	0.723597i	$0.742488\pi$
$968$	652.279	+	1129.78i	0.0216581	+	0.0375129i
$969$	−5501.78	+	15041.6i	−0.182397	+	0.498663i
$970$	59844.5	−	103654.i	1.98092	−	3.43105i
$971$	−24014.0	+	24014.0i	−0.793661	+	0.793661i	−0.982087	−	0.188426i	$-0.939661\pi$
$971$	−24014.0	+	24014.0i	−0.793661	+	0.793661i	0.188426	+	0.982087i	$0.439661\pi$
$972$	−17894.9	+	25252.1i	−0.590512	+	0.833295i
$973$		−	12887.2i		−	0.424610i
$974$	36689.3	−	28152.7i	1.20698	−	0.926151i
$975$	19372.6	−	23034.5i	0.636327	−	0.756610i
$976$	43501.1	+	33379.6i	1.42668	+	1.09473i
$977$	−3784.07	+	14122.3i	−0.123913	+	0.462450i	−0.999799	−	0.0200688i	$-0.993611\pi$
$977$	−3784.07	+	14122.3i	−0.123913	+	0.462450i	0.875885	+	0.482519i	$0.160278\pi$
$978$	18025.2	+	19715.7i	0.589349	+	0.644621i
$979$	−10450.8	+	79381.5i	−0.341173	+	2.59146i
$980$	17884.6	+	43177.3i	0.582963	+	1.40740i
$981$	−30336.9	+	19230.7i	−0.987343	+	0.625880i
$982$			5392.54i			0.175237i
$983$	−17949.8	−	23392.6i	−0.582411	−	0.759013i	0.405490	−	0.914099i	$-0.367101\pi$
$983$	−17949.8	−	23392.6i	−0.582411	−	0.759013i	−0.987901	+	0.155087i	$0.950434\pi$
$984$	178.020	+	807.307i	0.00576736	+	0.0261545i
$985$	26570.9	+	46022.1i	0.859511	+	1.48872i
$986$	−9416.42	−	2973.77i	−0.304138	−	0.0960488i
$987$	−60.9567	+	95.4450i	−0.00196583	+	0.00307806i
$988$	−2617.52	−	9768.71i	−0.0842858	−	0.314559i
$989$	6757.20	−	16313.3i	0.217256	−	0.524503i
$990$	−101874.	+	47225.1i	−3.27047	+	1.51607i
$991$	−30560.2	−	12658.5i	−0.979594	−	0.405761i	−0.165319	−	0.986240i	$-0.552865\pi$
$991$	−30560.2	−	12658.5i	−0.979594	−	0.405761i	−0.814275	+	0.580479i	$0.802865\pi$
$992$	−49933.5	−	6573.87i	−1.59818	−	0.210404i
$993$	25490.6	−	9245.26i	0.814622	−	0.295458i
$994$	3819.05	−	14252.9i	0.121864	−	0.454803i
$995$	−19209.9	+	71692.2i	−0.612054	+	2.28422i
$996$	37526.9	+	31561.0i	1.19386	+	1.00407i
$997$	19072.0	+	2510.87i	0.605833	+	0.0797594i	0.427201	−	0.904157i	$-0.359500\pi$
$997$	19072.0	+	2510.87i	0.605833	+	0.0797594i	0.178632	+	0.983916i	$0.442833\pi$
$998$	−63150.3	−	26157.7i	−2.00300	−	0.829668i
$999$	−3751.61	+	27769.7i	−0.118814	+	0.879474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.r.a.25.9	✓	416
9.4	even	3	inner	153.4.r.a.76.44	yes	416
17.15	even	8	inner	153.4.r.a.151.44	yes	416
153.49	even	24	inner	153.4.r.a.49.9	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.r.a.25.9	✓	416	1.1	even	1	trivial
153.4.r.a.49.9	yes	416	153.49	even	24	inner
153.4.r.a.76.44	yes	416	9.4	even	3	inner
153.4.r.a.151.44	yes	416	17.15	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.r (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04078 - 3.88424i) q^{2} +(5.17689 - 0.447034i) q^{3} +(-7.07588 + 4.08526i) q^{4} +(-2.37395 - 18.0319i) q^{5} +(-7.12438 - 19.6430i) q^{6} +(0.696851 - 5.29311i) q^{7} +(0.484882 + 0.484882i) q^{8} +(26.6003 - 4.62849i) q^{9} +(-67.5695 + 27.9882i) q^{10} +(56.3769 + 7.42216i) q^{11} +(-34.8048 + 24.3121i) q^{12} +(-24.3765 + 14.0738i) q^{13} +(-21.2850 + 2.80222i) q^{14} +(-20.3505 - 92.2879i) q^{15} +(-31.3034 + 54.2190i) q^{16} +(-65.8768 + 23.9427i) q^{17} +(-45.6632 - 98.5047i) q^{18} +(31.0949 - 31.0949i) q^{19} +(90.4629 + 117.893i) q^{20} +(1.24132 - 27.7133i) q^{21} +(-29.8464 - 226.706i) q^{22} +(38.9314 - 50.7364i) q^{23} +(2.72694 + 2.29342i) q^{24} +(-198.773 + 53.2612i) q^{25} +(80.0363 + 80.0363i) q^{26} +(135.638 - 35.8524i) q^{27} +(16.6929 + 40.3002i) q^{28} +(-27.7946 + 21.3276i) q^{29} +(-337.288 + 175.098i) q^{30} +(-194.110 + 25.5550i) q^{31} +(248.478 + 66.5796i) q^{32} +(295.175 + 13.2213i) q^{33} +(161.562 + 230.962i) q^{34} -97.0991 q^{35} +(-169.312 + 141.420i) q^{36} +(-76.4350 + 184.531i) q^{37} +(-153.143 - 88.4170i) q^{38} +(-119.903 + 83.7554i) q^{39} +(7.59226 - 9.89443i) q^{40} +(184.070 + 141.242i) q^{41} +(-108.937 + 24.0219i) q^{42} +(266.697 - 71.4612i) q^{43} +(-429.238 + 177.796i) q^{44} +(-146.608 - 468.667i) q^{45} +(-237.591 - 98.4135i) q^{46} +(-3.53544 - 2.04119i) q^{47} +(-137.816 + 294.679i) q^{48} +(303.781 + 81.3979i) q^{49} +(413.758 + 716.650i) q^{50} +(-330.333 + 153.398i) q^{51} +(114.990 - 199.168i) q^{52} +(225.134 - 225.134i) q^{53} +(-280.428 - 489.535i) q^{54} -1034.20i q^{55} +(2.90442 - 2.22864i) q^{56} +(147.074 - 174.875i) q^{57} +(111.769 + 85.7637i) q^{58} +(132.494 - 494.473i) q^{59} +(521.018 + 569.881i) q^{60} +(114.317 - 868.323i) q^{61} +(301.287 + 727.371i) q^{62} +(-5.96266 - 144.024i) q^{63} -533.590i q^{64} +(311.645 + 406.144i) q^{65} +(-255.857 - 1160.29i) q^{66} +(-61.2517 - 106.091i) q^{67} +(368.324 - 438.540i) q^{68} +(178.863 - 280.060i) q^{69} +(101.059 + 377.156i) q^{70} +(-263.024 + 634.995i) q^{71} +(15.1423 + 10.6537i) q^{72} +(175.501 + 72.6949i) q^{73} +(796.312 + 104.837i) q^{74} +(-1005.22 + 364.586i) q^{75} +(-92.9929 + 347.054i) q^{76} +(78.5726 - 293.237i) q^{77} +(450.118 + 378.560i) q^{78} +(951.766 + 125.302i) q^{79} +(1051.98 + 435.746i) q^{80} +(686.154 - 246.239i) q^{81} +(357.041 - 861.973i) q^{82} +(-298.927 - 1115.61i) q^{83} +(104.433 + 201.167i) q^{84} +(588.121 + 1131.04i) q^{85} +(-555.144 - 961.538i) q^{86} +(-134.356 + 122.836i) q^{87} +(23.7373 + 30.9350i) q^{88} +1408.05i q^{89} +(-1667.83 + 1057.24i) q^{90} +(57.5072 + 138.835i) q^{91} +(-68.2026 + 518.050i) q^{92} +(-993.460 + 219.069i) q^{93} +(-4.24884 + 15.8569i) q^{94} +(-634.517 - 486.882i) q^{95} +(1316.11 + 233.597i) q^{96} +(-1298.33 + 996.246i) q^{97} -1264.68i q^{98} +(1534.00 - 63.5083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 80 q^{8} + 52 q^{9} - 16 q^{10} + 96 q^{11} - 212 q^{12} - 4 q^{14} - 256 q^{15} + 2936 q^{16} - 16 q^{17} - 240 q^{18} - 16 q^{19} - 516 q^{20}+ \cdots - 18916 q^{99}+O(q^{100}) \) 416 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 80 * q^8 + 52 * q^9 - 16 * q^10 + 96 * q^11 - 212 * q^12 - 4 * q^14 - 256 * q^15 + 2936 * q^16 - 16 * q^17 - 240 * q^18 - 16 * q^19 - 516 * q^20 - 4 * q^22 - 172 * q^23 + 1216 * q^24 - 4 * q^25 - 80 * q^26 + 544 * q^27 - 528 * q^28 - 4 * q^29 - 4 * q^31 + 316 * q^32 - 512 * q^33 - 796 * q^34 - 4512 * q^35 + 328 * q^36 - 16 * q^37 + 1148 * q^39 + 252 * q^40 + 956 * q^41 + 3648 * q^42 - 688 * q^43 - 1040 * q^44 - 1240 * q^45 + 128 * q^46 + 528 * q^48 - 4 * q^49 - 5288 * q^50 - 352 * q^51 - 1032 * q^52 - 1424 * q^53 + 1708 * q^54 + 284 * q^56 + 4372 * q^57 - 4 * q^58 + 56 * q^59 - 3248 * q^60 - 4 * q^61 + 5168 * q^62 + 1008 * q^63 - 2284 * q^65 - 7516 * q^66 - 8 * q^67 + 252 * q^68 + 6224 * q^69 - 36 * q^70 + 624 * q^71 - 16 * q^73 - 3644 * q^74 - 508 * q^75 + 188 * q^76 + 1772 * q^77 - 10080 * q^78 - 4 * q^79 + 472 * q^80 + 3296 * q^82 + 4364 * q^83 + 8632 * q^84 + 3308 * q^85 + 1312 * q^86 + 4376 * q^87 - 1380 * q^88 - 15160 * q^90 - 4776 * q^91 - 1748 * q^92 - 1720 * q^93 - 68 * q^94 + 4436 * q^95 - 2196 * q^96 + 104 * q^97 - 18916 * q^99

Introduction

L-functions

Modular forms

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Database

Properties

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