LMFDB - Embedded newform 152.4.v.b.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,4,Mod(3,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("152.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$152 = 2^{3} \cdot 19$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	152.v (of order $18$ , degree $6$ , 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:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	152.3
Dual form			152.4.v.b.51.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59925 - 1.11530i) q^{2} +(0.142296 + 0.390954i) q^{3} +(5.51222 + 5.79788i) q^{4} +(-20.2800 - 3.57591i) q^{5} +(0.0661683 - 1.17489i) q^{6} +(-16.1140 + 9.30340i) q^{7} +(-7.86127 - 21.2179i) q^{8} +(20.5506 - 17.2440i) q^{9} +(48.7246 + 31.9129i) q^{10} +(4.07367 - 7.05581i) q^{11} +(-1.48234 + 2.98004i) q^{12} +(26.9604 + 9.81279i) q^{13} +(52.2603 - 6.21000i) q^{14} +(-1.48774 - 8.43738i) q^{15} +(-3.23090 + 63.9184i) q^{16} +(32.2805 + 27.0866i) q^{17} +(-72.6484 + 21.9014i) q^{18} +(-57.1414 + 59.9488i) q^{19} +(-91.0550 - 137.292i) q^{20} +(-5.93015 - 4.97598i) q^{21} +(-18.4578 + 13.7965i) q^{22} +(179.881 - 31.7178i) q^{23} +(7.17661 - 6.09261i) q^{24} +(281.029 + 102.286i) q^{25} +(-59.1327 - 55.5748i) q^{26} +(19.3941 + 11.1972i) q^{27} +(-142.764 - 42.1445i) q^{28} +(15.3848 - 12.9094i) q^{29} +(-5.54319 + 23.5901i) q^{30} +(8.46371 + 14.6596i) q^{31} +(79.6860 - 162.537i) q^{32} +(3.33816 + 0.588608i) q^{33} +(-53.6956 - 106.407i) q^{34} +(360.059 - 131.051i) q^{35} +(213.258 + 24.0973i) q^{36} +235.284 q^{37} +(215.386 - 92.0923i) q^{38} +11.9366i q^{39} +(83.5531 + 458.411i) q^{40} +(-110.560 - 303.760i) q^{41} +(9.86424 + 19.5477i) q^{42} +(12.2311 - 69.3658i) q^{43} +(63.3637 - 15.2745i) q^{44} +(-478.429 + 276.221i) q^{45} +(-502.930 - 118.178i) q^{46} +(338.396 + 403.285i) q^{47} +(-25.4489 + 7.83217i) q^{48} +(1.60643 - 2.78241i) q^{49} +(-616.386 - 579.300i) q^{50} +(-5.99623 + 16.4745i) q^{51} +(91.7183 + 210.404i) q^{52} +(-82.4925 - 467.838i) q^{53} +(-37.9220 - 50.7346i) q^{54} +(-107.845 + 128.525i) q^{55} +(324.075 + 268.768i) q^{56} +(-31.5682 - 13.8092i) q^{57} +(-54.3868 + 16.3961i) q^{58} +(-45.7959 + 54.5774i) q^{59} +(40.7182 - 55.1344i) q^{60} +(-709.749 + 125.148i) q^{61} +(-5.64951 - 47.5435i) q^{62} +(-170.724 + 469.060i) q^{63} +(-388.401 + 333.600i) q^{64} +(-511.668 - 295.411i) q^{65} +(-8.02025 - 5.25299i) q^{66} +(430.735 + 513.329i) q^{67} +(20.8925 + 336.466i) q^{68} +(37.9964 + 65.8117i) q^{69} +(-1082.04 - 60.9394i) q^{70} +(-127.744 + 724.470i) q^{71} +(-527.436 - 300.481i) q^{72} +(407.728 - 148.401i) q^{73} +(-611.563 - 262.412i) q^{74} +124.424i q^{75} +(-662.552 - 0.848360i) q^{76} +151.596i q^{77} +(13.3129 - 31.0262i) q^{78} +(955.479 - 347.766i) q^{79} +(294.089 - 1284.71i) q^{80} +(124.160 - 704.147i) q^{81} +(-51.4109 + 912.856i) q^{82} +(-122.127 - 211.531i) q^{83} +(-3.83809 - 61.8110i) q^{84} +(-557.790 - 664.748i) q^{85} +(-109.155 + 166.658i) q^{86} +(7.23616 + 4.17780i) q^{87} +(-181.734 - 30.9673i) q^{88} +(-327.400 + 899.525i) q^{89} +(1551.63 - 184.377i) q^{90} +(-525.731 + 92.7006i) q^{91} +(1175.44 + 868.091i) q^{92} +(-4.52687 + 5.39492i) q^{93} +(-429.793 - 1425.65i) q^{94} +(1373.20 - 1011.43i) q^{95} +(74.8833 + 8.02532i) q^{96} +(741.907 - 884.170i) q^{97} +(-7.27872 + 5.44054i) q^{98} +(-37.9540 - 215.248i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$336 q - 6 q^{2} - 42 q^{3} + 12 q^{4} + 36 q^{6} - 9 q^{8} + 126 q^{9} - 105 q^{10} - 6 q^{11} - 9 q^{12} - 129 q^{14} + 192 q^{16} - 12 q^{17} - 12 q^{19} - 582 q^{20} + 1218 q^{22} - 300 q^{24} - 12 q^{25}+ \cdots - 5580 q^{99}+O(q^{100})$ 336 * q - 6 * q^2 - 42 * q^3 + 12 * q^4 + 36 * q^6 - 9 * q^8 + 126 * q^9 - 105 * q^10 - 6 * q^11 - 9 * q^12 - 129 * q^14 + 192 * q^16 - 12 * q^17 - 12 * q^19 - 582 * q^20 + 1218 * q^22 - 300 * q^24 - 12 * q^25 - 411 * q^26 + 1692 * q^27 - 1152 * q^28 + 516 * q^30 - 51 * q^32 + 120 * q^33 - 1548 * q^34 - 762 * q^35 + 261 * q^36 - 3222 * q^38 + 1056 * q^40 + 1614 * q^41 - 3027 * q^42 - 12 * q^43 - 255 * q^44 + 1566 * q^46 - 7089 * q^48 + 8814 * q^49 + 3204 * q^50 - 498 * q^51 + 207 * q^52 - 999 * q^54 - 12 * q^57 + 4092 * q^58 - 2550 * q^59 + 4476 * q^60 + 3336 * q^62 - 2697 * q^64 - 18 * q^65 + 6228 * q^66 + 198 * q^67 + 2532 * q^68 - 5031 * q^70 - 14034 * q^72 - 3240 * q^73 + 2343 * q^74 - 6558 * q^76 - 6639 * q^78 - 6885 * q^80 + 10632 * q^81 - 2451 * q^82 - 6 * q^83 - 333 * q^84 + 3792 * q^86 + 5823 * q^88 - 12 * q^89 + 1866 * q^90 - 2070 * q^91 + 7656 * q^92 + 18942 * q^96 - 5742 * q^97 - 13749 * q^98 - 5580 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$ .

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−2.59925	−	1.11530i	−0.918974	−	0.394318i
$2$	−2.59925	−	1.11530i	−0.918974	−	0.394318i
$3$	0.142296	+	0.390954i	0.0273848	+	0.0752391i	0.952632	−	0.304126i	$-0.0983645\pi$
$3$	0.142296	+	0.390954i	0.0273848	+	0.0752391i	−0.925247	+	0.379366i	$0.876142\pi$
$4$	5.51222	+	5.79788i	0.689027	+	0.724735i
$5$	−20.2800	−	3.57591i	−1.81390	−	0.319839i	−0.839277	−	0.543704i	$-0.817022\pi$
$5$	−20.2800	−	3.57591i	−1.81390	−	0.319839i	−0.974620	+	0.223864i	$0.928133\pi$
$6$	0.0661683	−	1.17489i	0.00450218	−	0.0799411i
$7$	−16.1140	+	9.30340i	−0.870072	+	0.502336i	−0.867372	−	0.497660i	$-0.834193\pi$
$7$	−16.1140	+	9.30340i	−0.870072	+	0.502336i	−0.00269980	+	0.999996i	$0.500859\pi$
$8$	−7.86127	−	21.2179i	−0.347422	−	0.937709i
$9$	20.5506	−	17.2440i	0.761133	−	0.638667i
$10$	48.7246	+	31.9129i	1.54081	+	1.00918i
$11$	4.07367	−	7.05581i	0.111660	−	0.193401i	−0.804780	−	0.593574i	$-0.797717\pi$
$11$	4.07367	−	7.05581i	0.111660	−	0.193401i	0.916440	+	0.400173i	$0.131050\pi$
$12$	−1.48234	+	2.98004i	−0.0356596	+	0.0716886i
$13$	26.9604	+	9.81279i	0.575191	+	0.209352i	0.613203	−	0.789925i	$-0.289881\pi$
$13$	26.9604	+	9.81279i	0.575191	+	0.209352i	−0.0380129	+	0.999277i	$0.512103\pi$
$14$	52.2603	−	6.21000i	0.997654	−	0.118549i
$15$	−1.48774	−	8.43738i	−0.0256088	−	0.145235i
$16$	−3.23090	+	63.9184i	−0.0504828	+	0.998725i
$17$	32.2805	+	27.0866i	0.460540	+	0.386439i	0.843330	−	0.537397i	$-0.180592\pi$
$17$	32.2805	+	27.0866i	0.460540	+	0.386439i	−0.382790	+	0.923835i	$0.625037\pi$
$18$	−72.6484	+	21.9014i	−0.951300	+	0.286790i
$19$	−57.1414	+	59.9488i	−0.689955	+	0.723853i
$19$	−57.1414	+	59.9488i	−0.689955	+	0.723853i
$20$	−91.0550	−	137.292i	−1.01803	−	1.53497i
$21$	−5.93015	−	4.97598i	−0.0616221	−	0.0517071i
$22$	−18.4578	+	13.7965i	−0.178874	+	0.133701i
$23$	179.881	−	31.7178i	1.63077	−	0.287549i	0.718006	−	0.696037i	$-0.245055\pi$
$23$	179.881	−	31.7178i	1.63077	−	0.287549i	0.912764	+	0.408488i	$0.133944\pi$
$24$	7.17661	−	6.09261i	0.0610383	−	0.0518187i
$25$	281.029	+	102.286i	2.24823	+	0.818291i
$26$	−59.1327	−	55.5748i	−0.446034	−	0.419197i
$27$	19.3941	+	11.1972i	0.138237	+	0.0798112i
$28$	−142.764	−	42.1445i	−0.963564	−	0.284449i
$29$	15.3848	−	12.9094i	0.0985133	−	0.0826624i	−0.592201	−	0.805790i	$-0.701741\pi$
$29$	15.3848	−	12.9094i	0.0985133	−	0.0826624i	0.690714	+	0.723128i	$0.257296\pi$
$30$	−5.54319	+	23.5901i	−0.0337348	+	0.143565i
$31$	8.46371	+	14.6596i	0.0490364	+	0.0849335i	0.889502	−	0.456932i	$-0.151052\pi$
$31$	8.46371	+	14.6596i	0.0490364	+	0.0849335i	−0.840465	+	0.541865i	$0.817718\pi$
$32$	79.6860	−	162.537i	0.440207	−	0.897896i
$33$	3.33816	+	0.588608i	0.0176091	+	0.00310496i
$34$	−53.6956	−	106.407i	−0.270845	−	0.536726i
$35$	360.059	−	131.051i	1.73889	−	0.632904i
$36$	213.258	+	24.0973i	0.987306	+	0.111562i
$37$	235.284			1.04542			0.522710	−	0.852511i	$-0.324921\pi$
$37$	235.284			1.04542			0.522710	+	0.852511i	$0.324921\pi$
$38$	215.386	−	92.0923i	0.919478	−	0.393141i
$39$			11.9366i			0.0490099i
$40$	83.5531	+	458.411i	0.330273	+	1.81203i
$41$	−110.560	−	303.760i	−0.421134	−	1.15706i	−0.951058	−	0.309012i	$-0.900002\pi$
$41$	−110.560	−	303.760i	−0.421134	−	1.15706i	0.529924	−	0.848045i	$-0.322221\pi$
$42$	9.86424	+	19.5477i	0.0362401	+	0.0718161i
$43$	12.2311	−	69.3658i	0.0433772	−	0.246004i	−0.955407	−	0.295291i	$-0.904584\pi$
$43$	12.2311	−	69.3658i	0.0433772	−	0.246004i	0.998785	+	0.0492862i	$0.0156946\pi$
$44$	63.3637	−	15.2745i	0.217101	−	0.0523344i
$45$	−478.429	+	276.221i	−1.58489	+	0.915036i
$46$	−502.930	−	118.178i	−1.61202	−	0.378791i
$47$	338.396	+	403.285i	1.05022	+	1.25160i	0.966922	+	0.255073i	$0.0820994\pi$
$47$	338.396	+	403.285i	1.05022	+	1.25160i	0.0832934	+	0.996525i	$0.473456\pi$
$48$	−25.4489	+	7.83217i	−0.0765257	+	0.0235516i
$49$	1.60643	−	2.78241i	0.00468346	−	0.00811198i
$50$	−616.386	−	579.300i	−1.74340	−	1.63851i
$51$	−5.99623	+	16.4745i	−0.0164635	+	0.0452332i
$52$	91.7183	+	210.404i	0.244597	+	0.561110i
$53$	−82.4925	−	467.838i	−0.213796	−	1.21250i	−0.882983	−	0.469405i	$-0.844468\pi$
$53$	−82.4925	−	467.838i	−0.213796	−	1.21250i	0.669186	−	0.743095i	$-0.266643\pi$
$54$	−37.9220	−	50.7346i	−0.0955653	−	0.127854i
$55$	−107.845	+	128.525i	−0.264397	+	0.315096i
$56$	324.075	+	268.768i	0.773328	+	0.641351i
$57$	−31.5682	−	13.8092i	−0.0733563	−	0.0320890i
$58$	−54.3868	+	16.3961i	−0.123126	+	0.0371191i
$59$	−45.7959	+	54.5774i	−0.101053	+	0.120430i	−0.814201	−	0.580584i	$-0.802824\pi$
$59$	−45.7959	+	54.5774i	−0.101053	+	0.120430i	0.713148	+	0.701014i	$0.247269\pi$
$60$	40.7182	−	55.1344i	0.0876116	−	0.118630i
$61$	−709.749	+	125.148i	−1.48974	+	0.262681i	−0.858462	−	0.512877i	$-0.828580\pi$
$61$	−709.749	+	125.148i	−1.48974	+	0.262681i	−0.631276	+	0.775558i	$0.717469\pi$
$62$	−5.64951	−	47.5435i	−0.0115724	−	0.0973876i
$63$	−170.724	+	469.060i	−0.341415	+	0.938031i
$64$	−388.401	+	333.600i	−0.758595	+	0.651562i
$65$	−511.668	−	295.411i	−0.976378	−	0.563712i
$66$	−8.02025	−	5.25299i	−0.0149580	−	0.00979694i
$67$	430.735	+	513.329i	0.785412	+	0.936018i	0.999164	−	0.0408703i	$-0.0130130\pi$
$67$	430.735	+	513.329i	0.785412	+	0.936018i	−0.213752	+	0.976888i	$0.568569\pi$
$68$	20.8925	+	336.466i	0.0372586	+	0.600036i
$69$	37.9964	+	65.8117i	0.0662932	+	0.114823i
$70$	−1082.04	−	60.9394i	−1.84756	−	0.104052i
$71$	−127.744	+	724.470i	−0.213527	+	1.21097i	0.669919	+	0.742434i	$0.266329\pi$
$71$	−127.744	+	724.470i	−0.213527	+	1.21097i	−0.883445	+	0.468535i	$0.844782\pi$
$72$	−527.436	−	300.481i	−0.863318	−	0.491834i
$73$	407.728	−	148.401i	0.653712	−	0.237932i	0.00619250	−	0.999981i	$-0.498029\pi$
$73$	407.728	−	148.401i	0.653712	−	0.237932i	0.647519	+	0.762049i	$0.275807\pi$
$74$	−611.563	−	262.412i	−0.960713	−	0.412227i
$75$			124.424i			0.191564i
$76$	−662.552	−	0.848360i	−0.999999	−	0.00128044i
$77$			151.596i			0.224363i
$78$	13.3129	−	31.0262i	0.0193255	−	0.0450388i
$79$	955.479	−	347.766i	1.36076	−	0.495275i	0.444469	−	0.895794i	$-0.353392\pi$
$79$	955.479	−	347.766i	1.36076	−	0.495275i	0.916288	+	0.400519i	$0.131170\pi$
$80$	294.089	−	1284.71i	0.411002	−	1.79544i
$81$	124.160	−	704.147i	0.170316	−	0.965908i
$82$	−51.4109	+	912.856i	−0.0692364	+	1.22937i
$83$	−122.127	−	211.531i	−0.161509	−	0.279741i	0.773901	−	0.633306i	$-0.218303\pi$
$83$	−122.127	−	211.531i	−0.161509	−	0.279741i	−0.935410	+	0.353565i	$0.884969\pi$
$84$	−3.83809	−	61.8110i	−0.00498536	−	0.0802873i
$85$	−557.790	−	664.748i	−0.711774	−	0.848259i
$86$	−109.155	+	166.658i	−0.136866	+	0.208967i
$87$	7.23616	+	4.17780i	0.00891722	+	0.00514836i
$88$	−181.734	−	30.9673i	−0.220147	−	0.0375128i
$89$	−327.400	+	899.525i	−0.389937	+	1.07134i	0.577093	+	0.816678i	$0.304187\pi$
$89$	−327.400	+	899.525i	−0.389937	+	1.07134i	−0.967030	+	0.254664i	$0.918035\pi$
$90$	1551.63	−	184.377i	1.81729	−	0.215945i
$91$	−525.731	+	92.7006i	−0.605622	+	0.106788i
$92$	1175.44	+	868.091i	1.33204	+	0.983747i
$93$	−4.52687	+	5.39492i	−0.00504747	+	0.00601534i
$94$	−429.793	−	1425.65i	−0.471594	−	1.56430i
$95$	1373.20	−	1011.43i	1.48302	−	1.09232i
$96$	74.8833	+	8.02532i	0.0796119	+	0.00853210i
$97$	741.907	−	884.170i	0.776590	−	0.925504i	−0.222184	−	0.975005i	$-0.571319\pi$
$97$	741.907	−	884.170i	0.776590	−	0.925504i	0.998774	+	0.0495006i	$0.0157630\pi$
$98$	−7.27872	+	5.44054i	−0.00750267	+	0.00560793i
$99$	−37.9540	−	215.248i	−0.0385305	−	0.218517i
$100$	956.051	+	2193.20i	0.956051	+	2.19320i
$101$	200.494	−	550.853i	0.197524	−	0.542692i	−0.800901	−	0.598797i	$-0.795646\pi$
$101$	200.494	−	550.853i	0.197524	−	0.542692i	0.998425	+	0.0561046i	$0.0178680\pi$
$102$	33.9597	−	36.1338i	0.0329658	−	0.0350763i
$103$	100.127	−	173.426i	0.0957848	−	0.165904i	−0.814151	−	0.580653i	$-0.802797\pi$
$103$	100.127	−	173.426i	0.0957848	−	0.165904i	0.909936	+	0.414749i	$0.136131\pi$
$104$	−3.73612	−	649.185i	−0.00352266	−	0.612095i
$105$	102.470	+	122.119i	0.0952382	+	0.113500i
$106$	−307.360	+	1308.03i	−0.281637	+	1.19856i
$107$	142.603	−	82.3318i	0.128840	−	0.0743861i	−0.434195	−	0.900819i	$-0.642967\pi$
$107$	142.603	−	82.3318i	0.128840	−	0.0743861i	0.563035	+	0.826433i	$0.309634\pi$
$108$	41.9845	+	174.166i	0.0374071	+	0.155177i
$109$	−266.634	+	1512.15i	−0.234302	+	1.32879i	0.609778	+	0.792572i	$0.291259\pi$
$109$	−266.634	+	1512.15i	−0.234302	+	1.32879i	−0.844080	+	0.536218i	$0.819853\pi$
$110$	423.660	−	213.789i	0.367222	−	0.185309i
$111$	33.4799	+	91.9854i	0.0286286	+	0.0786564i
$112$	−542.596	−	1060.04i	−0.457772	−	0.894322i
$113$			1307.30i			1.08833i	0.838980	+	0.544163i	$0.183153\pi$
$113$			1307.30i			1.08833i	−0.838980	+	0.544163i	$0.816847\pi$
$114$	66.6523	+	71.1016i	0.0547593	+	0.0584147i
$115$	−3761.40			−3.05002
$116$	159.651	+	18.0399i	0.127787	+	0.0144394i
$117$	723.265	−	263.247i	0.571503	−	0.208010i
$118$	179.905	−	90.7843i	0.140353	−	0.0708252i
$119$	−772.164	−	136.153i	−0.594825	−	0.104884i
$120$	−167.328	+	97.8952i	−0.127291	+	0.0744714i
$121$	632.310	+	1095.19i	0.475064	+	0.822835i
$122$	1984.39	+	466.291i	1.47261	+	0.346033i
$123$	103.024	−	86.4475i	0.0755233	−	0.0633716i
$124$	−38.3407	+	129.878i	−0.0277669	+	0.0940599i
$125$	−3104.27	−	1792.25i	−2.22123	−	1.28243i
$126$	966.895	−	1028.80i	0.683634	−	0.727400i
$127$	1442.27	+	524.943i	1.00772	+	0.366781i	0.792558	−	0.609797i	$-0.208749\pi$
$127$	1442.27	+	524.943i	1.00772	+	0.366781i	0.215165	+	0.976578i	$0.430971\pi$
$128$	1381.61	−	433.927i	0.954052	−	0.299641i
$129$	28.8593	−	5.08867i	0.0196970	−	0.00347312i
$130$	1000.48	+	1338.51i	0.674984	+	0.903040i
$131$	998.135	+	837.535i	0.665706	+	0.558593i	0.911791	−	0.410655i	$-0.134700\pi$
$131$	998.135	+	837.535i	0.665706	+	0.558593i	−0.246085	+	0.969248i	$0.579144\pi$
$132$	14.9880	+	22.5988i	0.00988287	+	0.0149013i
$133$	363.047	−	1497.62i	0.236693	−	0.976393i
$134$	−547.072	−	1814.67i	−0.352685	−	1.16988i
$135$	−353.272	−	296.431i	−0.225221	−	0.188983i
$136$	320.955	−	897.861i	0.202365	−	0.566110i
$137$	−376.572	−	2135.64i	−0.234837	−	1.33183i	−0.842956	−	0.537982i	$-0.819187\pi$
$137$	−376.572	−	2135.64i	−0.234837	−	1.33183i	0.608119	−	0.793846i	$-0.291924\pi$
$138$	−25.3625	−	213.439i	−0.0156449	−	0.131660i
$139$	507.149	+	184.587i	0.309466	+	0.112637i	0.492085	−	0.870547i	$-0.336235\pi$
$139$	507.149	+	184.587i	0.309466	+	0.112637i	−0.182618	+	0.983184i	$0.558457\pi$
$140$	2744.54	+	1365.20i	1.65683	+	0.824146i
$141$	−109.513	+	189.683i	−0.0654092	+	0.113292i
$142$	1140.04	−	1740.61i	0.673732	−	1.02865i
$143$	179.065	−	150.254i	0.104715	−	0.0878660i
$144$	1035.81	+	1369.28i	0.599428	+	0.792405i
$145$	−358.166	+	206.787i	−0.205132	+	0.118433i
$146$	−1225.30	−	69.0073i	−0.694565	−	0.0391170i
$147$	1.31638	+	0.232114i	0.000738594	+	0.000130234i
$148$	1296.94	+	1364.15i	0.720322	+	0.757652i
$149$	−65.3946	−	179.670i	−0.0359553	−	0.0987863i	0.920416	−	0.390940i	$-0.127850\pi$
$149$	−65.3946	−	179.670i	−0.0359553	−	0.0987863i	−0.956371	+	0.292154i	$0.905628\pi$
$150$	138.770	−	323.410i	0.0755370	−	0.176042i
$151$	1548.53			0.834554			0.417277	−	0.908779i	$-0.362984\pi$
$151$	1548.53			0.834554			0.417277	+	0.908779i	$0.362984\pi$
$152$	1721.19	+	741.148i	0.918469	+	0.395494i
$153$	1130.47			0.597338
$154$	169.075	−	394.036i	0.0884704	−	0.206184i
$155$	−119.223	−	327.562i	−0.0617819	−	0.169744i
$156$	−69.2070	+	65.7972i	−0.0355192	+	0.0337692i
$157$	−121.046	−	21.3437i	−0.0615321	−	0.0108498i	0.142797	−	0.989752i	$-0.454390\pi$
$157$	−121.046	−	21.3437i	−0.0615321	−	0.0108498i	−0.204329	+	0.978902i	$0.565501\pi$
$158$	−2871.39	−	161.713i	−1.44580	−	0.0814254i
$159$	171.165	−	98.8221i	0.0853727	−	0.0492899i
$160$	−2197.25	+	3011.29i	−1.08567	+	1.48790i
$161$	−2603.51	+	2184.60i	−1.27444	+	1.06938i
$162$	−1108.06	+	1691.78i	−0.537390	+	0.820486i
$163$	232.657	−	402.973i	0.111798	−	0.193640i	−0.804697	−	0.593685i	$-0.797672\pi$
$163$	232.657	−	402.973i	0.111798	−	0.193640i	0.916495	+	0.400046i	$0.131006\pi$
$164$	1151.74	−	2315.40i	0.548387	−	1.10246i
$165$	−65.5931	−	23.8739i	−0.0309480	−	0.0112641i
$166$	81.5197	+	686.030i	0.0381154	+	0.320761i
$167$	−151.390	−	858.578i	−0.0701493	−	0.397837i	−0.999584	−	0.0288494i	$-0.990816\pi$
$167$	−151.390	−	858.578i	−0.0701493	−	0.397837i	0.929434	−	0.368987i	$-0.120295\pi$
$168$	−58.9616	+	164.943i	−0.0270773	+	0.0757478i
$169$	−1052.43	−	883.090i	−0.479029	−	0.401953i
$170$	708.443	+	2349.95i	0.319618	+	1.06019i
$171$	−140.533	+	2217.33i	−0.0628470	+	0.991600i
$172$	469.595	−	311.445i	0.208176	−	0.138067i
$173$	−426.014	−	357.469i	−0.187221	−	0.157097i	0.544360	−	0.838852i	$-0.316773\pi$
$173$	−426.014	−	357.469i	−0.187221	−	0.157097i	−0.731581	+	0.681755i	$0.761217\pi$
$174$	−14.1491	−	18.9296i	−0.00616460	−	0.00824742i
$175$	−5480.11	+	966.290i	−2.36718	+	0.417398i
$176$	437.834	+	283.179i	0.187517	+	0.121281i
$177$	−27.8538	−	10.1380i	−0.0118284	−	0.00430517i
$178$	1854.23	−	1972.94i	0.780791	−	0.830777i
$179$	3394.68	+	1959.92i	1.41749	+	0.818386i	0.996078	−	0.0884849i	$-0.0282025\pi$
$179$	3394.68	+	1959.92i	1.41749	+	0.818386i	0.421409	+	0.906871i	$0.361536\pi$
$180$	−4238.70	−	1251.28i	−1.75519	−	0.518140i
$181$	3440.05	−	2886.55i	1.41269	−	1.18539i	0.457571	−	0.889173i	$-0.348720\pi$
$181$	3440.05	−	2886.55i	1.41269	−	1.18539i	0.955121	−	0.296216i	$-0.0957247\pi$
$182$	1469.90	+	345.395i	0.598660	+	0.140673i
$183$	−149.921	−	259.671i	−0.0605601	−	0.104893i
$184$	−2087.08	−	3567.35i	−0.836203	−	1.42929i
$185$	−4771.57	−	841.356i	−1.89628	−	0.334366i
$186$	17.7834	−	8.97393i	0.00701045	−	0.00353764i
$187$	322.618	−	117.423i	0.126161	−	0.0459190i
$188$	−472.885	+	4184.97i	−0.183450	+	1.62351i
$189$	−416.688			−0.160368
$190$	−4697.33	+	1097.43i	−1.79358	+	0.419032i
$191$			395.690i			0.149901i	0.997187	+	0.0749506i	$0.0238799\pi$
$191$			395.690i			0.149901i	−0.997187	+	0.0749506i	$0.976120\pi$
$192$	−185.690	−	104.377i	−0.0697969	−	0.0392332i
$193$	−344.664	−	946.956i	−0.128546	−	0.353178i	0.858678	−	0.512516i	$-0.171286\pi$
$193$	−344.664	−	946.956i	−0.128546	−	0.353178i	−0.987224	+	0.159338i	$0.949064\pi$
$194$	−2914.52	+	1470.73i	−1.07861	+	0.544291i
$195$	42.6842	−	242.074i	0.0156753	−	0.0888990i
$196$	24.9871	−	6.02339i	0.00910607	−	0.00219511i
$197$	1270.70	−	733.637i	0.459560	−	0.265327i	−0.252299	−	0.967649i	$-0.581187\pi$
$197$	1270.70	−	733.637i	0.459560	−	0.265327i	0.711859	+	0.702322i	$0.247853\pi$
$198$	−141.413	+	601.813i	−0.0507566	+	0.216005i
$199$	297.043	+	354.002i	0.105813	+	0.126103i	0.816352	−	0.577555i	$-0.195993\pi$
$199$	297.043	+	354.002i	0.105813	+	0.126103i	−0.710539	+	0.703658i	$0.751549\pi$
$200$	−38.9445	−	6766.96i	−0.0137689	−	2.39248i
$201$	−139.397	+	241.442i	−0.0489168	+	0.0847264i
$202$	−1135.50	+	1208.19i	−0.395512	+	0.420833i
$203$	−127.809	+	351.152i	−0.0441893	+	0.121409i
$204$	−128.570	+	56.0456i	−0.0441259	+	0.0192352i
$205$	1155.93	+	6555.60i	0.393823	+	2.23348i
$206$	−453.677	+	339.105i	−0.153443	+	0.114692i
$207$	3149.71	−	3753.68i	1.05759	−	1.26038i
$208$	−714.324	+	1691.56i	−0.238123	+	0.563888i
$209$	190.212	+	647.391i	0.0629533	+	0.214263i
$210$	−130.146	−	431.701i	−0.0427662	−	0.141858i
$211$	12.3252	−	14.6886i	0.00402132	−	0.00479243i	−0.764030	−	0.645181i	$-0.776782\pi$
$211$	12.3252	−	14.6886i	0.00402132	−	0.00479243i	0.768051	+	0.640388i	$0.221227\pi$
$212$	2257.75	−	3057.11i	0.731430	−	0.990391i
$213$	−301.412	+	53.1471i	−0.0969596	+	0.0170966i
$214$	−462.485	+	54.9563i	−0.147733	+	0.0175548i
$215$	−496.092	+	1363.00i	−0.157364	+	0.432353i
$216$	85.1189	−	499.527i	0.0268130	−	0.157354i
$217$	−272.768	−	157.483i	−0.0853304	−	0.0492655i
$218$	2379.55	−	3633.09i	0.739282	−	1.12873i
$219$	116.036	+	138.286i	0.0358035	+	0.0426690i
$220$	−1339.64	+	83.1833i	−0.410538	+	0.0254919i
$221$	604.502	+	1047.03i	0.183996	+	0.318691i
$222$	15.5684	−	276.433i	0.00470667	−	0.0835720i
$223$	−818.884	+	4644.12i	−0.245904	+	1.39459i	0.572481	+	0.819918i	$0.305981\pi$
$223$	−818.884	+	4644.12i	−0.245904	+	1.39459i	−0.818385	+	0.574671i	$0.805130\pi$
$224$	228.085	+	3360.46i	0.0680339	+	1.00237i
$225$	7539.15	−	2744.03i	2.23382	−	0.813045i
$226$	1458.03	−	3398.01i	0.429146	−	1.00014i
$227$		−	5875.99i		−	1.71808i	−0.511911	−	0.859038i	$-0.671062\pi$
$227$		−	5875.99i		−	1.71808i	0.511911	−	0.859038i	$-0.328938\pi$
$228$	−93.9466	−	259.148i	−0.0272884	−	0.0752741i
$229$			6219.11i			1.79463i	0.441390	+	0.897315i	$0.354486\pi$
$229$			6219.11i			1.79463i	−0.441390	+	0.897315i	$0.645514\pi$
$230$	9776.82	+	4195.08i	2.80289	+	1.20268i
$231$	−59.2671	+	21.5715i	−0.0168809	+	0.00614414i
$232$	−394.854	−	224.949i	−0.111739	−	0.0636580i
$233$	−484.962	+	2750.36i	−0.136356	+	0.773313i	0.837550	+	0.546361i	$0.183987\pi$
$233$	−484.962	+	2750.36i	−0.136356	+	0.773313i	−0.973906	+	0.226952i	$0.927124\pi$
$234$	−2173.55	−	122.411i	−0.607219	−	0.0341978i
$235$	−5420.56	−	9388.68i	−1.50467	−	2.60617i
$236$	−568.870	+	35.3234i	−0.156908	+	0.00974304i
$237$	271.921	+	324.063i	0.0745282	+	0.0888192i
$238$	1855.20	+	1215.09i	0.505271	+	0.330935i
$239$	−4410.53	−	2546.42i	−1.19370	−	0.689181i	−0.234553	−	0.972103i	$-0.575363\pi$
$239$	−4410.53	−	2546.42i	−1.19370	−	0.689181i	−0.959143	+	0.282923i	$0.908696\pi$
$240$	544.111	−	67.8335i	0.146342	−	0.0182443i
$241$	2065.76	−	5675.63i	0.552147	−	1.51701i	−0.278626	−	0.960400i	$-0.589879\pi$
$241$	2065.76	−	5675.63i	0.552147	−	1.51701i	0.830773	−	0.556611i	$-0.187899\pi$
$242$	−422.066	−	3551.90i	−0.112113	−	0.943490i
$243$	888.419	−	156.652i	0.234535	−	0.0413549i
$244$	−4637.88	−	3425.20i	−1.21684	−	0.898672i
$245$	−42.5279	+	50.6828i	−0.0110898	+	0.0132164i
$246$	−364.200	+	109.796i	−0.0943925	+	0.0284567i
$247$	−2128.82	+	1055.53i	−0.548396	+	0.271910i
$248$	244.510	−	294.825i	0.0626066	−	0.0754896i
$249$	65.3206	−	77.8460i	0.0166246	−	0.0198124i
$250$	6069.88	+	8120.69i	1.53557	+	2.05439i
$251$	400.351	+	2270.50i	0.100677	+	0.570968i	0.992859	+	0.119292i	$0.0380625\pi$
$251$	400.351	+	2270.50i	0.100677	+	0.570968i	−0.892182	+	0.451676i	$0.850826\pi$
$252$	−3660.62	+	1595.72i	−0.915069	+	0.398893i
$253$	508.980	−	1398.41i	0.126479	−	0.347499i
$254$	−3163.35	−	2973.02i	−0.781443	−	0.734425i
$255$	180.515	−	312.661i	0.0443305	−	0.0767827i
$256$	−4075.12	−	413.028i	−0.994903	−	0.100837i
$257$	3040.95	+	3624.06i	0.738090	+	0.879622i	0.996254	−	0.0864797i	$-0.0275618\pi$
$257$	3040.95	+	3624.06i	0.738090	+	0.879622i	−0.258163	+	0.966101i	$0.583117\pi$
$258$	−80.6879	−	18.9600i	−0.0194706	−	0.00457518i
$259$	−3791.36	+	2188.94i	−0.909590	+	0.525152i
$260$	−1107.66	−	4594.96i	−0.264209	−	1.09603i
$261$	93.5575	−	530.591i	0.0221880	−	0.125834i
$262$	−1660.30	−	3290.18i	−0.391503	−	0.775833i
$263$	−1128.63	−	3100.90i	−0.264618	−	0.727033i	−0.998841	−	0.0481243i	$-0.984676\pi$
$263$	−1128.63	−	3100.90i	−0.264618	−	0.727033i	0.734223	−	0.678908i	$-0.237547\pi$
$264$	−13.7532	−	75.4561i	−0.00320624	−	0.0175909i
$265$			9782.74i			2.26773i
$266$	−2613.95	+	3487.79i	−0.602524	+	0.803948i
$267$	−398.261			−0.0912852
$268$	−601.921	+	5326.93i	−0.137195	+	1.21416i
$269$	1571.17	−	571.859i	0.356119	−	0.129617i	−0.157764	−	0.987477i	$-0.550429\pi$
$269$	1571.17	−	571.859i	0.356119	−	0.129617i	0.513883	+	0.857860i	$0.328206\pi$
$270$	587.635	+	1164.50i	0.132453	+	0.262479i
$271$	−5698.56	−	1004.81i	−1.27735	−	0.225232i	−0.506497	−	0.862242i	$-0.669060\pi$
$271$	−5698.56	−	1004.81i	−1.27735	−	0.225232i	−0.770856	+	0.637010i	$0.780171\pi$
$272$	−1835.63	+	1975.81i	−0.409195	+	0.440444i
$273$	−111.051	−	192.346i	−0.0246195	−	0.0426421i
$274$	−1403.08	+	5971.07i	−0.309354	+	1.31652i
$275$	1866.53	−	1566.21i	0.409296	−	0.343440i
$276$	−172.124	+	583.067i	−0.0375386	+	0.127161i
$277$	2169.25	+	1252.42i	0.470533	+	0.271662i	0.716463	−	0.697625i	$-0.245760\pi$
$277$	2169.25	+	1252.42i	0.470533	+	0.271662i	−0.245930	+	0.969288i	$0.579093\pi$
$278$	−1112.34	−	1045.41i	−0.239977	−	0.225538i
$279$	426.724	+	155.315i	0.0915674	+	0.0333278i
$280$	−5611.15	−	6609.48i	−1.19761	−	1.41069i
$281$	1633.79	−	288.082i	0.346847	−	0.0611584i	0.00248890	−	0.999997i	$-0.499208\pi$
$281$	1633.79	−	288.082i	0.346847	−	0.0611584i	0.344358	+	0.938838i	$0.388097\pi$
$282$	496.206	−	370.893i	0.104782	−	0.0783205i
$283$	3541.29	+	2971.49i	0.743844	+	0.624159i	0.933867	−	0.357621i	$-0.116412\pi$
$283$	3541.29	+	2971.49i	0.743844	+	0.624159i	−0.190023	+	0.981780i	$0.560856\pi$
$284$	−4904.54	+	3252.80i	−1.02476	+	0.679640i
$285$	590.822	+	392.936i	0.122798	+	0.0816684i
$286$	−633.013	+	190.836i	−0.130877	+	0.0394558i
$287$	4607.55	+	3866.20i	0.947649	+	0.795172i
$288$	−1165.19	−	4714.33i	−0.238400	−	0.964565i
$289$	−544.784	−	3089.62i	−0.110886	−	0.628867i
$290$	1161.59	−	138.030i	0.235211	−	0.0279497i
$291$	451.240	+	164.238i	0.0909009	+	0.0330852i
$292$	3107.90	+	1545.94i	0.622862	+	0.309827i
$293$	−305.895	+	529.826i	−0.0609918	+	0.105641i	−0.894909	−	0.446249i	$-0.852760\pi$
$293$	−305.895	+	529.826i	−0.0609918	+	0.105641i	0.833917	+	0.551890i	$0.186093\pi$
$294$	−3.16273	−	2.07148i	−0.000627395	−	0.000410922i
$295$	1123.90	−	943.067i	0.221818	−	0.186127i
$296$	−1849.63	−	4992.25i	−0.363202	−	0.980299i
$297$	158.011	−	91.2275i	0.0308711	−	0.0178234i
$298$	−30.4089	+	539.943i	−0.00591121	+	0.104960i
$299$	5160.90	+	910.006i	0.998202	+	0.176010i
$300$	−721.398	+	685.855i	−0.138833	+	0.131993i
$301$	448.247	+	1231.55i	0.0858356	+	0.235831i
$302$	−4025.02	−	1727.07i	−0.766934	−	0.329079i
$303$	243.887			0.0462408
$304$	−3647.21	−	3846.08i	−0.688099	−	0.725617i
$305$	14841.2			2.78625
$306$	−2938.36	−	1260.81i	−0.548938	−	0.235541i
$307$	3054.62	+	8392.50i	0.567871	+	1.56021i	0.807822	+	0.589427i	$0.200646\pi$
$307$	3054.62	+	8392.50i	0.567871	+	1.56021i	−0.239951	+	0.970785i	$0.577131\pi$
$308$	−878.936	+	835.630i	−0.162604	+	0.154592i
$309$	82.0491	+	14.4675i	0.0151055	+	0.00266351i
$310$	−55.4393	+	984.384i	−0.0101572	+	0.180352i
$311$	1418.51	−	818.974i	0.258637	−	0.149324i	−0.365076	−	0.930978i	$-0.618957\pi$
$311$	1418.51	−	818.974i	0.258637	−	0.149324i	0.623713	+	0.781654i	$0.285624\pi$
$312$	253.270	−	93.8369i	0.0459570	−	0.0170271i
$313$	−6179.09	+	5184.87i	−1.11586	+	0.936314i	−0.998388	−	0.0567628i	$-0.981922\pi$
$313$	−6179.09	+	5184.87i	−1.11586	+	0.936314i	−0.117468	+	0.993077i	$0.537478\pi$
$314$	290.825	+	190.481i	0.0522682	+	0.0342339i
$315$	5139.59	−	8902.03i	0.919311	−	1.59229i
$316$	7283.12	+	3622.80i	1.29654	+	0.644931i
$317$	4965.40	+	1807.26i	0.879763	+	0.320207i	0.742114	−	0.670274i	$-0.233823\pi$
$317$	4965.40	+	1807.26i	0.879763	+	0.320207i	0.137649	+	0.990481i	$0.456045\pi$
$318$	−555.117	+	65.9635i	−0.0978912	+	0.0116322i
$319$	−28.4135	−	161.141i	−0.00498699	−	0.0282826i
$320$	9069.69	−	5376.51i	1.58441	−	0.939238i
$321$	52.4797	+	44.0357i	0.00912502	+	0.00765680i
$322$	9203.65	−	2774.64i	1.59285	−	0.480201i
$323$	−3468.36	+	387.414i	−0.597476	+	0.0667377i
$324$	4766.96	−	3161.55i	0.817380	−	0.542103i
$325$	6572.96	+	5515.37i	1.12185	+	0.941346i
$326$	−1054.17	+	787.947i	−0.179095	+	0.133866i
$327$	−629.124	+	110.931i	−0.106393	+	0.0187600i
$328$	−5576.02	+	4733.79i	−0.938671	+	0.796889i
$329$	−9204.81	−	3350.28i	−1.54249	−	0.561419i
$330$	143.866	+	135.210i	0.0239987	+	0.0225548i
$331$	6002.40	+	3465.49i	0.996742	+	0.575469i	0.907283	−	0.420521i	$-0.138153\pi$
$331$	6002.40	+	3465.49i	0.996742	+	0.575469i	0.0894595	+	0.995990i	$0.471486\pi$
$332$	553.238	−	1874.08i	0.0914544	−	0.309800i
$333$	4835.24	−	4057.24i	0.795704	−	0.667675i
$334$	−564.069	+	2400.50i	−0.0924086	+	0.393263i
$335$	−6899.67	−	11950.6i	−1.12528	−	1.94905i
$336$	337.217	−	362.969i	0.0547520	−	0.0589332i
$337$	−4722.76	−	832.749i	−0.763397	−	0.134608i	−0.221624	−	0.975132i	$-0.571136\pi$
$337$	−4722.76	−	832.749i	−0.763397	−	0.134608i	−0.541773	+	0.840525i	$0.682247\pi$
$338$	1750.61	+	3469.14i	0.281718	+	0.558274i
$339$	−511.095	+	186.024i	−0.0818847	+	0.0298036i
$340$	779.472	−	6898.23i	0.124332	−	1.10032i
$341$	137.914			0.0219016
$342$	2838.27	−	5606.66i	0.448760	−	0.886473i
$343$		−	6322.35i		−	0.995262i
$344$	−1567.95	+	285.786i	−0.245751	+	0.0447923i
$345$	−535.230	−	1470.53i	−0.0835242	−	0.229481i
$346$	708.634	+	1404.28i	0.110105	+	0.218193i
$347$	−1664.68	+	9440.86i	−0.257535	+	1.46055i	0.531946	+	0.846778i	$0.321461\pi$
$347$	−1664.68	+	9440.86i	−0.257535	+	1.46055i	−0.789481	+	0.613775i	$0.789650\pi$
$348$	15.6649	+	64.9834i	0.00241301	+	0.0100100i
$349$	3207.36	−	1851.77i	0.491937	−	0.284020i	−0.233440	−	0.972371i	$-0.574998\pi$
$349$	3207.36	−	1851.77i	0.491937	−	0.284020i	0.725378	+	0.688351i	$0.241665\pi$
$350$	15321.9	+	3600.32i	2.33997	+	0.549844i
$351$	412.998	+	492.192i	0.0628040	+	0.0748468i
$352$	−822.212	−	1224.37i	−0.124500	−	0.185395i
$353$	−2258.51	+	3911.86i	−0.340534	+	0.589822i	−0.984532	−	0.175205i	$-0.943941\pi$
$353$	−2258.51	+	3911.86i	−0.340534	+	0.589822i	0.643998	+	0.765027i	$0.277274\pi$
$354$	61.0922	+	57.4164i	0.00917235	+	0.00862047i
$355$	5181.28	−	14235.5i	0.774630	−	2.12828i
$356$	−7020.04	+	3060.15i	−1.04512	+	0.455583i
$357$	−56.6459	−	321.255i	−0.00839781	−	0.0476263i
$358$	−6637.72	−	8880.40i	−0.979929	−	1.31102i
$359$	−7295.00	+	8693.84i	−1.07247	+	1.27812i	−0.113824	+	0.993501i	$0.536310\pi$
$359$	−7295.00	+	8693.84i	−1.07247	+	1.27812i	−0.958642	+	0.284615i	$0.908134\pi$
$360$	9621.90	+	7979.82i	1.40866	+	1.16826i
$361$	−328.718	−	6851.12i	−0.0479250	−	0.998851i
$362$	−12160.9	+	3666.18i	−1.76565	+	0.532293i
$363$	−338.195	+	403.046i	−0.0488999	+	0.0582766i
$364$	−3435.41	−	2537.14i	−0.494683	−	0.365336i
$365$	−8799.39	+	1551.57i	−1.26187	+	0.222501i
$366$	100.072	+	842.158i	0.0142919	+	0.120274i
$367$	−3084.41	+	8474.35i	−0.438706	+	1.20533i	0.501629	+	0.865083i	$0.332734\pi$
$367$	−3084.41	+	8474.35i	−0.438706	+	1.20533i	−0.940335	+	0.340251i	$0.889488\pi$
$368$	1446.17	+	11600.2i	0.204856	+	1.64321i
$369$	−7510.11	−	4335.96i	−1.05951	−	0.611710i
$370$	11464.1	+	7508.61i	1.61079	+	1.05501i
$371$	5681.76	+	6771.26i	0.795101	+	0.947564i
$372$	−56.2322	+	3.49168i	−0.00783738	+	0.000486654i
$373$	−2804.25	−	4857.10i	−0.389272	−	0.674239i	0.603080	−	0.797681i	$-0.293940\pi$
$373$	−2804.25	−	4857.10i	−0.389272	−	0.674239i	−0.992352	+	0.123442i	$0.960607\pi$
$374$	−969.528	−	54.6026i	−0.134046	−	0.00754928i
$375$	258.963	−	1468.65i	0.0356608	−	0.202243i
$376$	5896.64	−	10350.4i	0.808766	−	1.41963i
$377$	541.458	−	197.074i	0.0739695	−	0.0269227i
$378$	1083.08	+	464.731i	0.147374	+	0.0632360i
$379$		−	4240.28i		−	0.574692i	−0.957827	−	0.287346i	$-0.907227\pi$
$379$		−	4240.28i		−	0.574692i	0.957827	−	0.287346i	$-0.0927730\pi$
$380$	13433.5	+	2386.43i	1.81349	+	0.322161i
$381$			638.558i			0.0858644i
$382$	441.313	−	1028.50i	0.0591087	−	0.137755i
$383$	3516.60	−	1279.94i	0.469165	−	0.170762i	−0.0966092	−	0.995322i	$-0.530800\pi$
$383$	3516.60	−	1279.94i	0.469165	−	0.170762i	0.565774	+	0.824560i	$0.308577\pi$
$384$	366.243	+	478.402i	0.0486713	+	0.0635764i
$385$	542.094	−	3074.37i	0.0717601	−	0.406972i
$386$	−160.271	+	2845.78i	−0.0211336	+	0.375250i
$387$	−944.789	−	1636.42i	−0.124099	−	0.214946i
$388$	9215.87	−	572.250i	1.20584	−	0.0748752i
$389$	−9696.70	−	11556.1i	−1.26386	−	1.50621i	−0.772131	−	0.635464i	$-0.780809\pi$
$389$	−9696.70	−	11556.1i	−1.26386	−	1.50621i	−0.491730	−	0.870748i	$-0.663635\pi$
$390$	−380.932	+	581.606i	−0.0494596	+	0.0755148i
$391$	6665.77	+	3848.48i	0.862154	+	0.497765i
$392$	−71.6655	−	12.2117i	−0.00923381	−	0.00157343i
$393$	−185.407	+	509.402i	−0.0237979	+	0.0653841i
$394$	−4121.08	+	489.701i	−0.526947	+	0.0626162i
$395$	−20620.7	+	3635.98i	−2.62668	+	0.463155i
$396$	1038.77	−	1406.54i	0.131819	−	0.178489i
$397$	5665.65	−	6752.06i	0.716249	−	0.853592i	−0.278012	−	0.960578i	$-0.589675\pi$
$397$	5665.65	−	6752.06i	0.716249	−	0.853592i	0.994261	+	0.106986i	$0.0341199\pi$
$398$	−377.271	−	1251.43i	−0.0475148	−	0.157610i
$399$	637.161	−	71.1704i	0.0799448	−	0.00892977i
$400$	−7445.96	+	17632.5i	−0.930744	+	2.20406i
$401$	−5855.49	+	6978.30i	−0.729200	+	0.869026i	−0.995490	−	0.0948666i	$-0.969758\pi$
$401$	−5855.49	+	6978.30i	−0.729200	+	0.869026i	0.266290	+	0.963893i	$0.414202\pi$
$402$	631.607	−	472.100i	0.0783624	−	0.0585726i
$403$	84.3339	+	478.281i	0.0104242	+	0.0591188i
$404$	4298.95	−	1873.98i	0.529407	−	0.230777i
$405$	−5035.93	+	13836.1i	−0.617870	+	1.69758i
$406$	723.847	−	770.187i	0.0884825	−	0.0941472i
$407$	958.472	−	1660.12i	0.116731	−	0.202185i
$408$	396.693	−	2.28300i	0.0481353	−	0.000277023i
$409$	−1799.59	−	2144.67i	−0.217565	−	0.259283i	0.646212	−	0.763158i	$-0.276352\pi$
$409$	−1799.59	−	2144.67i	−0.217565	−	0.259283i	−0.863777	+	0.503874i	$0.831908\pi$
$410$	4306.90	−	18328.9i	0.518787	−	2.20780i
$411$	781.354	−	451.115i	0.0937746	−	0.0541408i
$412$	1557.42	−	375.433i	0.186235	−	0.0448939i
$413$	230.198	−	1305.51i	0.0274268	−	0.155545i
$414$	−12373.4	+	6243.89i	−1.46888	+	0.741233i
$415$	1720.33	+	4726.56i	0.203488	+	0.559078i
$416$	3743.31	−	3600.11i	0.441180	−	0.424303i
$417$			224.538i			0.0263685i
$418$	227.626	−	1894.87i	0.0266352	−	0.221726i
$419$	−14131.7			−1.64768			−0.823840	−	0.566823i	$-0.808172\pi$
$419$	−14131.7			−1.64768			−0.823840	+	0.566823i	$0.808172\pi$
$420$	−143.194	+	1267.25i	−0.0166361	+	0.147227i
$421$	3022.64	−	1100.15i	0.349915	−	0.127359i	−0.161082	−	0.986941i	$-0.551498\pi$
$421$	3022.64	−	1100.15i	0.349915	−	0.127359i	0.510997	+	0.859582i	$0.329276\pi$
$422$	−48.4183	+	24.4330i	−0.00558523	+	0.00281844i
$423$	13908.5	+	2452.44i	1.59871	+	0.281895i
$424$	−9278.06	+	5428.12i	−1.06269	+	0.621728i
$425$	6301.19	+	10914.0i	0.719183	+	1.24566i
$426$	842.720	+	198.022i	0.0958449	+	0.0225216i
$427$	10272.6	−	8619.70i	1.16423	−	0.976901i
$428$	1263.41	+	372.964i	0.142685	+	0.0421212i
$429$	84.2224	+	48.6258i	0.00947855	+	0.00547244i
$430$	2809.62	−	2989.49i	0.315098	−	0.335270i
$431$	−11210.0	−	4080.09i	−1.25282	−	0.455989i	−0.371465	−	0.928447i	$-0.621145\pi$
$431$	−11210.0	−	4080.09i	−1.25282	−	0.455989i	−0.881353	+	0.472458i	$0.843367\pi$
$432$	−778.367	+	1203.46i	−0.0866880	+	0.134032i
$433$	7709.93	−	1359.47i	0.855694	−	0.150882i	0.271442	−	0.962455i	$-0.412499\pi$
$433$	7709.93	−	1359.47i	0.855694	−	0.150882i	0.584251	+	0.811573i	$0.301388\pi$
$434$	533.352	+	713.554i	0.0589901	+	0.0789210i
$435$	−131.810	−	110.602i	−0.0145283	−	0.0121907i
$436$	−10237.0	+	6789.42i	−1.12446	+	0.745766i
$437$	−8377.19	+	12596.0i	−0.917014	+	1.37883i
$438$	−147.376	−	488.855i	−0.0160774	−	0.0533297i
$439$	−10267.3	−	8615.30i	−1.11625	−	0.936642i	−0.117838	−	0.993033i	$-0.537596\pi$
$439$	−10267.3	−	8615.30i	−1.11625	−	0.936642i	−0.998409	+	0.0563904i	$0.982041\pi$
$440$	3574.83	+	1277.88i	0.387325	+	0.138456i
$441$	−14.9669	−	84.8814i	−0.00161612	−	0.00916547i
$442$	−403.504	−	3395.69i	−0.0434224	−	0.365422i
$443$	−10632.0	−	3869.72i	−1.14027	−	0.415024i	−0.298259	−	0.954485i	$-0.596406\pi$
$443$	−10632.0	−	3869.72i	−1.14027	−	0.415024i	−0.842011	+	0.539460i	$0.818628\pi$
$444$	−348.772	+	701.156i	−0.0372792	+	0.0749446i
$445$	9856.30	−	17071.6i	1.04996	−	1.81859i
$446$	7308.07	−	11157.9i	0.775890	−	1.18463i
$447$	60.9374	−	51.1326i	0.00644797	−	0.00541049i
$448$	3155.06	−	8989.06i	0.332729	−	0.947976i
$449$	−2566.52	+	1481.78i	−0.269758	+	0.155745i	−0.628778	−	0.777585i	$-0.716444\pi$
$449$	−2566.52	+	1481.78i	−0.269758	+	0.155745i	0.359019	+	0.933330i	$0.383111\pi$
$450$	−22656.6	−	1275.99i	−2.37342	−	0.133668i
$451$	−2593.66	−	457.332i	−0.270799	−	0.0477493i
$452$	−7579.59	+	7206.14i	−0.788748	+	0.749886i
$453$	220.349	+	605.404i	0.0228541	+	0.0627911i
$454$	−6553.49	+	15273.2i	−0.677468	+	1.57887i
$455$	10993.3			1.13269
$456$	−44.8367	+	778.370i	−0.00460454	+	0.0799353i
$457$	−559.157			−0.0572347			−0.0286174	−	0.999590i	$-0.509110\pi$
$457$	−559.157			−0.0572347			−0.0286174	+	0.999590i	$0.509110\pi$
$458$	6936.17	−	16165.0i	0.707654	−	1.64922i
$459$	322.758	+	886.772i	0.0328215	+	0.0901764i
$460$	−20733.6	−	21808.1i	−2.10155	−	2.21046i
$461$	2616.39	+	461.341i	0.264333	+	0.0466091i	0.304244	−	0.952594i	$-0.401596\pi$
$461$	2616.39	+	461.341i	0.264333	+	0.0466091i	−0.0399107	+	0.999203i	$0.512707\pi$
$462$	178.109	+	10.0309i	0.0179359	+	0.00101012i
$463$	6042.91	−	3488.88i	0.606561	−	0.350198i	−0.165057	−	0.986284i	$-0.552781\pi$
$463$	6042.91	−	3488.88i	0.606561	−	0.350198i	0.771618	+	0.636086i	$0.219448\pi$
$464$	775.440	+	1025.08i	0.0775838	+	0.102561i
$465$	111.097	−	93.2212i	0.0110795	−	0.00929684i
$466$	4328.01	−	6608.00i	0.430239	−	0.656887i
$467$	−7970.43	+	13805.2i	−0.789781	+	1.36794i	0.136320	+	0.990665i	$0.456472\pi$
$467$	−7970.43	+	13805.2i	−0.789781	+	1.36794i	−0.926101	+	0.377276i	$0.876861\pi$
$468$	5513.07	+	2742.33i	0.544533	+	0.270864i
$469$	−11716.5	−	4264.47i	−1.15356	−	0.419862i
$470$	3618.21	+	30449.1i	0.355097	+	2.98832i
$471$	−8.87994	−	50.3607i	−0.000868718	−	0.00492674i
$472$	1518.03	+	542.646i	0.148036	+	0.0529180i
$473$	−439.607	−	368.874i	−0.0427339	−	0.0358580i
$474$	−345.364	−	1145.59i	−0.0334665	−	0.111010i
$475$	−22190.4	+	11002.6i	−2.14350	+	1.06281i
$476$	−3466.94	−	5227.43i	−0.333838	−	0.503359i
$477$	−9762.67	−	8191.85i	−0.937111	−	0.786330i
$478$	8624.05	+	11537.8i	0.825220	+	1.10403i
$479$	6020.99	−	1061.66i	0.574335	−	0.101271i	0.121066	−	0.992644i	$-0.461369\pi$
$479$	6020.99	−	1061.66i	0.574335	−	0.101271i	0.453269	+	0.891374i	$0.350258\pi$
$480$	−1489.93	−	430.529i	−0.141679	−	0.0409394i
$481$	6343.37	+	2308.80i	0.601315	+	0.218861i
$482$	−11699.5	+	12448.5i	−1.10559	+	1.17637i
$483$	−1224.55	−	706.992i	−0.115360	−	0.0666030i
$484$	−2864.37	+	9703.01i	−0.269006	+	0.911252i
$485$	−18207.6	+	15278.0i	−1.70467	+	1.43039i
$486$	−2483.94	−	583.674i	−0.231839	−	0.0544773i
$487$	51.3714	+	88.9779i	0.00478000	+	0.00827920i	0.868406	−	0.495855i	$-0.165145\pi$
$487$	51.3714	+	88.9779i	0.00478000	+	0.00827920i	−0.863626	+	0.504134i	$0.831812\pi$
$488$	8234.91	+	14075.6i	0.763887	+	1.30568i
$489$	190.650	+	33.6168i	0.0176309	+	0.00310880i
$490$	167.067	−	84.3061i	0.0154027	−	0.00777257i
$491$	9529.50	−	3468.46i	0.875887	−	0.318797i	0.135338	−	0.990799i	$-0.456788\pi$
$491$	9529.50	−	3468.46i	0.875887	−	0.318797i	0.740549	+	0.672003i	$0.234566\pi$
$492$	1069.10	+	120.804i	0.0979653	+	0.0110697i
$493$	846.300			0.0773133
$494$	6710.57	−	369.312i	0.611180	−	0.0336359i
$495$			4500.94i			0.408691i
$496$	−964.362	+	493.623i	−0.0873007	+	0.0446862i
$497$	−4681.58	−	12862.5i	−0.422530	−	1.16089i
$498$	−256.606	+	129.490i	−0.0230900	+	0.0116517i
$499$	2091.84	−	11863.4i	0.187662	−	1.06428i	−0.734825	−	0.678257i	$-0.762736\pi$
$499$	2091.84	−	11863.4i	0.187662	−	1.06428i	0.922487	−	0.386028i	$-0.126153\pi$
$500$	−6720.14	−	27877.4i	−0.601068	−	2.49343i
$501$	314.122	−	181.358i	0.0280119	−	0.0161727i
$502$	1491.68	−	6348.12i	0.132623	−	0.564403i
$503$	−1301.65	−	1551.24i	−0.115383	−	0.137508i	0.705261	−	0.708947i	$-0.250830\pi$
$503$	−1301.65	−	1551.24i	−0.115383	−	0.137508i	−0.820644	+	0.571439i	$0.806385\pi$
$504$	11294.6	−	65.0013i	0.998215	−	0.00574482i
$505$	−6035.82	+	10454.3i	−0.531862	+	0.921212i
$506$	−2882.61	+	3067.16i	−0.253257	+	0.269470i
$507$	195.492	−	537.110i	0.0171245	−	0.0470491i
$508$	4906.55	+	11255.7i	0.428529	+	0.983054i
$509$	−498.412	−	2826.64i	−0.0434022	−	0.246146i	0.955386	−	0.295360i	$-0.0954396\pi$
$509$	−498.412	−	2826.64i	−0.0434022	−	0.246146i	−0.998788	+	0.0492137i	$0.984328\pi$
$510$	−817.914	+	611.356i	−0.0710153	+	0.0530810i
$511$	−5189.48	+	6184.58i	−0.449254	+	0.535401i
$512$	10131.6	+	5618.54i	0.874528	+	0.484974i
$513$	−1779.47	+	522.830i	−0.153149	+	0.0449971i
$514$	−3862.28	−	12811.4i	−0.331436	−	1.09939i
$515$	−2650.74	+	3159.02i	−0.226807	+	0.270297i
$516$	188.582	+	139.273i	0.0160889	+	0.0118821i
$517$	4224.01	−	744.808i	0.359327	−	0.0633590i
$518$	12296.0	−	1461.12i	1.04297	−	0.123934i
$519$	79.1338	−	217.418i	0.00669285	−	0.0183884i
$520$	−2245.66	+	13178.8i	−0.189382	+	1.11140i
$521$	−7435.50	−	4292.89i	−0.625250	−	0.360988i	0.153660	−	0.988124i	$-0.450894\pi$
$521$	−7435.50	−	4292.89i	−0.625250	−	0.360988i	−0.778910	+	0.627136i	$0.784227\pi$
$522$	−834.947	+	1274.79i	−0.0700089	+	0.106889i
$523$	4683.29	+	5581.33i	0.391560	+	0.466644i	0.925427	−	0.378925i	$-0.123706\pi$
$523$	4683.29	+	5581.33i	0.391560	+	0.466644i	−0.533867	+	0.845568i	$0.679262\pi$
$524$	646.010	+	10403.7i	0.0538570	+	0.867347i
$525$	−1157.57	−	2004.97i	−0.0962295	−	0.166674i
$526$	−524.822	+	9318.78i	−0.0435044	+	0.772468i
$527$	−123.865	+	702.472i	−0.0102384	+	0.0580648i
$528$	−48.4082	+	211.468i	−0.00398995	+	0.0174299i
$529$	19917.8	−	7249.48i	1.63703	−	0.595831i
$530$	10910.7	−	25427.8i	0.894206	−	2.08399i
$531$			1911.30i			0.156202i
$532$	10684.2	−	6150.32i	0.870714	−	0.501222i
$533$		−	9274.40i		−	0.753694i
$534$	1035.18	+	444.179i	0.0838888	+	0.0359954i
$535$	−3186.39	+	1159.75i	−0.257495	+	0.0937205i
$536$	7505.67	−	13174.7i	0.604842	−	1.06168i
$537$	−283.190	+	1606.05i	−0.0227571	+	0.129062i
$538$	−4721.66	−	265.918i	−0.378374	−	0.0213096i
$539$	−13.0881	−	22.6693i	−0.00104591	−	0.00181157i
$540$	−228.644	−	3682.22i	−0.0182208	−	0.293440i
$541$	3903.73	+	4652.28i	0.310230	+	0.369718i	0.898520	−	0.438932i	$-0.144643\pi$
$541$	3903.73	+	4652.28i	0.310230	+	0.369718i	−0.588290	+	0.808650i	$0.700199\pi$
$542$	13691.3	+	8967.34i	1.08504	+	0.710665i
$543$	1618.01	+	934.160i	0.127874	+	0.0738280i
$544$	6974.87	−	3088.35i	0.549715	−	0.243404i
$545$	10814.7	−	29713.0i	0.849998	−	2.33535i
$546$	74.1263	+	623.810i	0.00581010	+	0.0488949i
$547$	20945.7	−	3693.30i	1.63725	−	0.288691i	0.722094	−	0.691795i	$-0.243180\pi$
$547$	20945.7	−	3693.30i	1.63725	−	0.288691i	0.915154	+	0.403103i	$0.132069\pi$
$548$	10306.5	−	13955.5i	0.803413	−	1.08786i
$549$	−12427.7	+	14810.8i	−0.966124	+	1.15138i
$550$	−6598.38	+	1989.23i	−0.511556	+	0.154220i
$551$	−105.207	+	1659.96i	−0.00813427	+	0.128342i
$552$	1097.69	−	1323.57i	0.0846390	−	0.102056i
$553$	−12161.1	+	14493.1i	−0.935162	+	1.11448i
$554$	−4241.61	−	5674.71i	−0.325286	−	0.435190i
$555$	−350.041	−	1985.18i	−0.0267720	−	0.151831i
$556$	1725.30	+	3957.87i	0.131599	+	0.301891i
$557$	−144.481	+	396.959i	−0.0109908	+	0.0301969i	−0.945067	−	0.326878i	$-0.894004\pi$
$557$	−144.481	+	396.959i	−0.0109908	+	0.0301969i	0.934076	+	0.357074i	$0.116226\pi$
$558$	−935.941	−	879.628i	−0.0710064	−	0.0667341i
$559$	1010.43	−	1750.11i	0.0764517	−	0.132418i
$560$	7213.24	+	23437.8i	0.544313	+	1.76862i
$561$	91.8143	+	109.420i	0.00690981	+	0.00823479i
$562$	−4567.94	−	1073.37i	−0.342859	−	0.0805648i
$563$	−9980.40	+	5762.19i	−0.747111	+	0.431345i	−0.824649	−	0.565644i	$-0.808627\pi$
$563$	−9980.40	+	5762.19i	−0.747111	+	0.431345i	0.0775379	+	0.996989i	$0.475294\pi$
$564$	−1703.42	+	410.627i	−0.127175	+	0.0306570i
$565$	4674.80	−	26512.1i	0.348089	−	1.97411i
$566$	−5890.60	−	11673.3i	−0.437456	−	0.866897i
$567$	4550.25	+	12501.7i	0.337024	+	0.925965i
$568$	16376.0	−	2984.80i	1.20972	−	0.220492i
$569$			3394.11i			0.250068i	0.992152	+	0.125034i	$0.0399039\pi$
$569$			3394.11i			0.250068i	−0.992152	+	0.125034i	$0.960096\pi$
$570$	−1097.46	−	1680.28i	−0.0806445	−	0.123472i
$571$	19146.6			1.40326			0.701628	−	0.712543i	$-0.252457\pi$
$571$	19146.6			1.40326			0.701628	+	0.712543i	$0.252457\pi$
$572$	1858.20	+	209.969i	0.135831	+	0.0153483i
$573$	−154.697	+	56.3050i	−0.0112784	+	0.00410502i
$574$	−7664.23	−	15188.0i	−0.557315	−	1.10442i
$575$	53796.0	+	9485.69i	3.90165	+	0.687966i
$576$	−2229.28	+	13553.3i	−0.161261	+	0.980415i
$577$	−2922.71	−	5062.28i	−0.210874	−	0.365244i	0.741115	−	0.671379i	$-0.234298\pi$
$577$	−2922.71	−	5062.28i	−0.210874	−	0.365244i	−0.951988	+	0.306135i	$0.900964\pi$
$578$	−2029.82	+	8638.30i	−0.146072	+	0.621637i
$579$	321.172	−	269.495i	0.0230526	−	0.0193434i
$580$	−3173.22	−	936.749i	−0.227174	−	0.0670627i
$581$	3935.91	+	2272.40i	0.281048	+	0.162263i
$582$	−989.712	−	930.163i	−0.0704895	−	0.0662483i
$583$	−3637.02	−	1323.77i	−0.258371	−	0.0940393i
$584$	−6354.02	−	7484.52i	−0.450225	−	0.530328i
$585$	−15609.2	+	2752.31i	−1.10318	+	0.194520i
$586$	1386.01	−	1035.99i	0.0977059	−	0.0730311i
$587$	10277.2	+	8623.56i	0.722630	+	0.606358i	0.928111	−	0.372303i	$-0.121432\pi$
$587$	10277.2	+	8623.56i	0.722630	+	0.606358i	−0.205482	+	0.978661i	$0.565876\pi$
$588$	5.91042	+	8.91169i	0.000414526	+	0.000625020i
$589$	−1362.45	−	330.280i	−0.0953122	−	0.0231052i
$590$	−3973.11	+	1197.78i	−0.277238	+	0.0835794i
$591$	467.633	+	392.391i	0.0325480	+	0.0273110i
$592$	−760.180	+	15039.0i	−0.0527757	+	1.04409i
$593$	−2085.44	−	11827.1i	−0.144416	−	0.819024i	−0.967834	−	0.251589i	$-0.919047\pi$
$593$	−2085.44	−	11827.1i	−0.144416	−	0.819024i	0.823418	−	0.567435i	$-0.192064\pi$
$594$	−512.455	+	60.8941i	−0.0353978	+	0.00420626i
$595$	15172.6	+	5522.38i	1.04541	+	0.380497i
$596$	681.238	−	1369.53i	0.0468198	−	0.0941245i
$597$	−96.1306	+	166.503i	−0.00659022	+	0.0114146i
$598$	−12399.5	−	8121.28i	−0.847918	−	0.555357i
$599$	−11777.8	+	9882.74i	−0.803385	+	0.674120i	−0.949019	−	0.315219i	$-0.897922\pi$
$599$	−11777.8	+	9882.74i	−0.803385	+	0.674120i	0.145634	+	0.989339i	$0.453478\pi$
$600$	2640.03	−	978.134i	0.179631	−	0.0665536i
$601$	8517.40	−	4917.52i	0.578090	−	0.333760i	−0.182284	−	0.983246i	$-0.558349\pi$
$601$	8517.40	−	4917.52i	0.578090	−	0.333760i	0.760374	+	0.649486i	$0.225016\pi$
$602$	208.438	−	3701.03i	0.0141118	−	0.250570i
$603$	17703.7	+	3121.64i	1.19561	+	0.210818i
$604$	8535.84	+	8978.20i	0.575031	+	0.604831i
$605$	−8906.94	−	24471.6i	−0.598543	−	1.64448i
$606$	−633.925	−	272.007i	−0.0424941	−	0.0182336i
$607$	16042.6			1.07273			0.536366	−	0.843985i	$-0.319797\pi$
$607$	16042.6			1.07273			0.536366	+	0.843985i	$0.319797\pi$
$608$	5190.50	+	14064.7i	0.346221	+	0.938153i
$609$	−155.471			−0.0103448
$610$	−38576.1	−	16552.4i	−2.56049	−	1.09867i
$611$	5165.95	+	14193.3i	0.342049	+	0.939772i
$612$	6231.37	+	6554.31i	0.411582	+	0.432912i
$613$	−1433.01	−	252.679i	−0.0944189	−	0.0166486i	0.126239	−	0.992000i	$-0.459709\pi$
$613$	−1433.01	−	252.679i	−0.0944189	−	0.0166486i	−0.220658	+	0.975351i	$0.570820\pi$
$614$	1420.42	−	25221.0i	0.0933605	−	1.65772i
$615$	−2398.46	+	1384.75i	−0.157260	+	0.0907943i
$616$	3216.55	−	1191.74i	0.210387	−	0.0779488i
$617$	−5519.02	+	4631.01i	−0.360109	+	0.302167i	−0.804834	−	0.593500i	$-0.797746\pi$
$617$	−5519.02	+	4631.01i	−0.360109	+	0.302167i	0.444725	+	0.895667i	$0.353301\pi$
$618$	−197.131	−	129.114i	−0.0128313	−	0.00840408i
$619$	−1548.18	+	2681.52i	−0.100527	+	0.174119i	−0.911902	−	0.410408i	$-0.865386\pi$
$619$	−1548.18	+	2681.52i	−0.100527	+	0.174119i	0.811375	+	0.584526i	$0.198720\pi$
$620$	1241.98	−	2496.83i	0.0804504	−	0.161734i
$621$	3843.77	+	1399.02i	0.248382	+	0.0904037i
$622$	−4600.45	+	546.664i	−0.296562	+	0.0352399i
$623$	−3092.92	−	17540.8i	−0.198901	−	1.12802i
$624$	−762.969	−	38.5660i	−0.0489474	−	0.00247416i
$625$	27908.4	+	23417.9i	1.78614	+	1.49875i
$626$	21843.7	−	6585.26i	1.39465	−	0.420447i
$627$	−226.034	+	166.485i	−0.0143970	+	0.0106041i
$628$	−543.485	−	819.464i	−0.0345341	−	0.0520703i
$629$	7595.10	+	6373.05i	0.481457	+	0.403991i
$630$	−23287.5	+	17406.4i	−1.47269	+	1.10078i
$631$	4204.39	−	741.348i	0.265252	−	0.0467712i	−0.0394401	−	0.999222i	$-0.512557\pi$
$631$	4204.39	−	741.348i	0.265252	−	0.0467712i	0.304692	+	0.952451i	$0.401446\pi$
$632$	−14890.2	−	17539.4i	−0.937181	−	1.10392i
$633$	7.49637	+	2.72846i	0.000470701	+	0.000171321i
$634$	−10890.7	−	10235.4i	−0.682216	−	0.641168i
$635$	−27372.1	−	15803.3i	−1.71059	−	0.987612i
$636$	1516.46	+	447.665i	0.0945463	+	0.0279105i
$637$	70.6131	−	59.2514i	0.00439214	−	0.00368544i
$638$	−105.866	+	450.535i	−0.00656942	+	0.0279574i
$639$	9867.56	+	17091.1i	0.610884	+	1.05808i
$640$	−29570.8	+	3859.50i	−1.82639	+	0.238375i
$641$	29173.3	+	5144.04i	1.79762	+	0.316969i	0.969778	−	0.243988i	$-0.0784558\pi$
$641$	29173.3	+	5144.04i	1.79762	+	0.316969i	0.827845	+	0.560957i	$0.189567\pi$
$642$	−87.2950	−	172.990i	−0.00536645	−	0.0106346i
$643$	730.278	−	265.799i	0.0447890	−	0.0163019i	−0.319528	−	0.947577i	$-0.603525\pi$
$643$	730.278	−	265.799i	0.0447890	−	0.0163019i	0.364318	+	0.931275i	$0.381302\pi$
$644$	−27017.1	−	3052.83i	−1.65314	−	0.186798i
$645$	−603.463			−0.0368392
$646$	9447.23	+	2861.27i	0.575381	+	0.174265i
$647$			3714.38i			0.225699i	0.993612	+	0.112850i	$0.0359978\pi$
$647$			3714.38i			0.225699i	−0.993612	+	0.112850i	$0.964002\pi$
$648$	−15916.6	+	2901.07i	−0.964912	+	0.175872i
$649$	198.530	+	545.457i	0.0120077	+	0.0329909i
$650$	−10933.5	−	21666.6i	−0.659764	−	1.30744i
$651$	22.7548	−	129.049i	0.00136994	−	0.00776931i
$652$	3618.85	−	872.360i	0.217370	−	0.0523992i
$653$	2742.49	−	1583.37i	0.164352	−	0.0948886i	−0.415568	−	0.909562i	$-0.636417\pi$
$653$	2742.49	−	1583.37i	0.164352	−	0.0948886i	0.579920	+	0.814674i	$0.303084\pi$
$654$	1758.97	+	413.322i	0.105170	+	0.0247128i
$655$	−17247.2	−	20554.4i	−1.02886	−	1.22615i
$656$	19773.1	−	6085.38i	1.17684	−	0.362186i
$657$	5820.03	−	10080.6i	0.345603	−	0.598601i
$658$	20189.1	+	18974.3i	1.19613	+	1.12416i
$659$	9483.82	−	26056.6i	0.560602	−	1.54024i	−0.258155	−	0.966103i	$-0.583115\pi$
$659$	9483.82	−	26056.6i	0.560602	−	1.54024i	0.818758	−	0.574139i	$-0.194663\pi$
$660$	−223.145	−	511.900i	−0.0131605	−	0.0301904i
$661$	2517.25	+	14276.0i	0.148123	+	0.840050i	0.964806	+	0.262963i	$0.0846996\pi$
$661$	2517.25	+	14276.0i	0.148123	+	0.840050i	−0.816683	+	0.577087i	$0.804189\pi$
$662$	−11736.7	−	15702.1i	−0.689063	−	0.921875i
$663$	−323.322	+	385.320i	−0.0189393	+	0.0225710i
$664$	−3528.17	+	4254.19i	−0.206204	+	0.248636i
$665$	−12717.9	+	29073.5i	−0.741625	+	1.69537i
$666$	−17093.0	+	5153.07i	−0.994507	+	0.299816i
$667$	2357.97	−	2810.12i	0.136883	−	0.163131i
$668$	4143.44	−	5610.41i	0.239992	−	0.324960i
$669$	−1932.16	+	340.692i	−0.111662	+	0.0196890i
$670$	4605.52	+	38757.8i	0.265562	+	2.23484i
$671$	−2008.27	+	5517.66i	−0.115541	+	0.317447i
$672$	−1281.33	+	567.349i	−0.0735541	+	0.0325684i
$673$	−7762.13	−	4481.47i	−0.444589	−	0.256683i	0.260953	−	0.965351i	$-0.415963\pi$
$673$	−7762.13	−	4481.47i	−0.444589	−	0.256683i	−0.705542	+	0.708668i	$0.749296\pi$
$674$	11346.9	+	7431.81i	0.648464	+	0.424722i
$675$	4304.99	+	5130.49i	0.245480	+	0.292552i
$676$	−681.148	−	10969.6i	−0.0387544	−	0.624125i
$677$	−7583.65	−	13135.3i	−0.430522	−	0.745686i	0.566396	−	0.824133i	$-0.308337\pi$
$677$	−7583.65	−	13135.3i	−0.430522	−	0.745686i	−0.996918	+	0.0784471i	$0.975004\pi$
$678$	1535.94	+	86.5021i	0.0870020	+	0.00489984i
$679$	−3729.27	+	21149.7i	−0.210775	+	1.19536i
$680$	−9719.64	+	17060.9i	−0.548134	+	0.962141i
$681$	2297.24	−	836.128i	0.129267	−	0.0470492i
$682$	−358.472	−	153.815i	−0.0201270	−	0.00863618i
$683$			14049.3i			0.787088i	0.919306	+	0.393544i	$0.128751\pi$
$683$			14049.3i			0.787088i	−0.919306	+	0.393544i	$0.871249\pi$
$684$	−13630.5	+	11407.6i	−0.761951	+	0.637692i
$685$			44657.4i			2.49091i
$686$	−7051.31	+	16433.4i	−0.392449	+	0.914620i
$687$	−2431.39	+	884.952i	−0.135026	+	0.0491456i
$688$	4394.24	+	1005.90i	0.243501	+	0.0557409i
$689$	2366.77	−	13422.6i	0.130866	−	0.742177i
$690$	−248.885	+	4419.23i	−0.0137317	+	0.243822i
$691$	−11681.0	−	20232.1i	−0.643077	−	1.11384i	−0.984742	−	0.174021i	$-0.944324\pi$
$691$	−11681.0	−	20232.1i	−0.643077	−	1.11384i	0.341665	−	0.939822i	$-0.389009\pi$
$692$	−275.724	−	4440.43i	−0.0151466	−	0.243930i
$693$	2614.12	+	3115.39i	0.143293	+	0.170770i
$694$	14856.3	−	22682.6i	0.812590	−	1.24066i
$695$	−9624.91	−	5556.94i	−0.525315	−	0.303290i
$696$	31.7588	−	186.379i	0.00172962	−	0.0101504i
$697$	4658.90	−	12800.2i	0.253183	−	0.695614i
$698$	−10402.0	+	1236.05i	−0.564072	+	0.0670277i
$699$	−1144.27	+	201.766i	−0.0619175	+	0.0109177i
$700$	−35810.0	−	26446.6i	−1.93356	−	1.42798i
$701$	−19171.4	+	22847.6i	−1.03294	+	1.23101i	−0.0604296	+	0.998172i	$0.519247\pi$
$701$	−19171.4	+	22847.6i	−1.03294	+	1.23101i	−0.972514	+	0.232842i	$0.925197\pi$
$702$	−524.545	−	1739.95i	−0.0282018	−	0.0935470i
$703$	−13444.5	+	14105.0i	−0.721292	+	0.756729i
$704$	771.598	+	4099.46i	0.0413078	+	0.219466i
$705$	2899.22	−	3455.16i	0.154881	−	0.184580i
$706$	10233.3	−	7648.98i	0.545519	−	0.407753i
$707$	1894.05	+	10741.7i	0.100754	+	0.571404i
$708$	−94.7576	−	217.376i	−0.00502995	−	0.0115388i
$709$	177.859	−	488.663i	0.00942119	−	0.0258845i	−0.934893	−	0.354930i	$-0.884505\pi$
$709$	177.859	−	488.663i	0.00942119	−	0.0258845i	0.944314	+	0.329045i	$0.106727\pi$
$710$	−29344.2	+	31222.8i	−1.55108	+	1.65038i
$711$	13638.8	−	23623.1i	0.719402	−	1.24604i
$712$	21659.8	−	124.654i	1.14008	−	0.00656126i
$713$	1987.43	+	2368.52i	0.104390	+	0.124407i
$714$	−211.058	+	898.199i	−0.0110625	+	0.0470788i
$715$	−4168.73	+	2406.82i	−0.218044	+	0.125888i
$716$	7348.82	+	30485.4i	0.383573	+	1.59119i
$717$	367.934	−	2086.66i	0.0191642	−	0.108686i
$718$	28657.8	−	14461.4i	1.48955	−	0.751663i
$719$	−4601.88	−	12643.6i	−0.238694	−	0.655808i	−0.999973	−	0.00738239i	$-0.997650\pi$
$719$	−4601.88	−	12643.6i	−0.238694	−	0.655808i	0.761278	−	0.648425i	$-0.224572\pi$
$720$	−16109.9	−	31472.9i	−0.833860	−	1.62906i
$721$			3726.10i			0.192465i
$722$	−6786.62	+	18174.4i	−0.349823	+	0.936816i
$723$	2512.86			0.129259
$724$	35698.2	+	4033.75i	1.83248	+	0.207062i
$725$	5644.03	−	2054.26i	0.289123	−	0.105232i
$726$	1328.57	−	670.428i	0.0679172	−	0.0342726i
$727$	−27539.1	−	4855.88i	−1.40491	−	0.247723i	−0.580750	−	0.814082i	$-0.697240\pi$
$727$	−27539.1	−	4855.88i	−1.40491	−	0.247723i	−0.824159	+	0.566359i	$0.808352\pi$
$728$	6099.83	+	10426.2i	0.310542	+	0.530797i
$729$	−9464.97	−	16393.8i	−0.480870	−	0.832891i
$730$	24602.3	+	5781.02i	1.24736	+	0.293103i
$731$	2273.71	−	1907.87i	0.115043	−	0.0965322i
$732$	679.145	−	2300.59i	0.0342922	−	0.116164i
$733$	4000.85	+	2309.89i	0.201603	+	0.116395i	0.597403	−	0.801941i	$-0.296199\pi$
$733$	4000.85	+	2309.89i	0.201603	+	0.116395i	−0.395800	+	0.918337i	$0.629533\pi$
$734$	17468.6	−	18586.9i	0.878443	−	0.934681i
$735$	−25.8662	−	9.41452i	−0.00129808	−	0.000472462i
$736$	9178.66	−	31764.6i	0.459688	−	1.59084i
$737$	5376.63	−	948.045i	0.268725	−	0.0473835i
$738$	14684.8	+	19646.3i	0.732458	+	0.979931i
$739$	−9796.45	−	8220.20i	−0.487643	−	0.409181i	0.365538	−	0.930797i	$-0.380885\pi$
$739$	−9796.45	−	8220.20i	−0.487643	−	0.409181i	−0.853181	+	0.521615i	$0.825330\pi$
$740$	−21423.8	−	32302.7i	−1.06426	−	1.60469i
$741$	−715.585	−	682.074i	−0.0354759	−	0.0338146i
$742$	−7216.35	−	23937.1i	−0.357036	−	1.18431i
$743$	4494.58	+	3771.40i	0.221925	+	0.186217i	0.746971	−	0.664857i	$-0.231507\pi$
$743$	4494.58	+	3771.40i	0.221925	+	0.186217i	−0.525046	+	0.851074i	$0.675952\pi$
$744$	150.056	+	53.6400i	0.00739424	+	0.00264319i
$745$	683.718	+	3877.56i	0.0336235	+	0.190688i
$746$	1871.83	+	15752.4i	0.0918667	+	0.773105i
$747$	−6157.43	−	2241.12i	−0.301591	−	0.109770i
$748$	2459.15	+	1223.24i	0.120208	+	0.0597942i
$749$	−1531.93	+	2653.38i	−0.0747337	+	0.129443i
$750$	−2311.10	+	3528.58i	−0.112519	+	0.171794i
$751$	−7469.59	+	6267.73i	−0.362942	+	0.304544i	−0.805962	−	0.591967i	$-0.798351\pi$
$751$	−7469.59	+	6267.73i	−0.362942	+	0.304544i	0.443020	+	0.896512i	$0.353907\pi$
$752$	−26870.6	+	20326.8i	−1.30302	+	0.985692i
$753$	−830.694	+	479.602i	−0.0402021	+	0.0232107i
$754$	−1627.18	−	91.6408i	−0.0785921	−	0.00442621i
$755$	−31404.2	−	5537.41i	−1.51380	−	0.266923i
$756$	−2296.87	−	2415.91i	−0.110498	−	0.116224i
$757$	−3424.17	−	9407.82i	−0.164404	−	0.451695i	0.829947	−	0.557842i	$-0.188371\pi$
$757$	−3424.17	−	9407.82i	−0.164404	−	0.451695i	−0.994350	+	0.106147i	$0.966148\pi$
$758$	−4729.18	+	11021.5i	−0.226611	+	0.528127i
$759$	619.140			0.0296092
$760$	−32255.5	−	21185.3i	−1.53951	−	1.01115i
$761$	−25618.4			−1.22032			−0.610161	−	0.792278i	$-0.708895\pi$
$761$	−25618.4			−1.22032			−0.610161	+	0.792278i	$0.708895\pi$
$762$	712.183	−	1659.77i	0.0338578	−	0.0789072i
$763$	−9771.65	−	26847.4i	−0.463640	−	1.27384i
$764$	−2294.17	+	2181.13i	−0.108639	+	0.103286i
$765$	−22925.8	−	4042.44i	−1.08351	−	0.191052i
$766$	−10568.1	−	595.179i	−0.498485	−	0.0280740i
$767$	−1770.23	+	1022.04i	−0.0833369	+	0.0481146i
$768$	−418.397	−	1651.96i	−0.0196583	−	0.0776170i
$769$	15571.9	−	13066.4i	0.730220	−	0.612727i	−0.199972	−	0.979802i	$-0.564085\pi$
$769$	15571.9	−	13066.4i	0.730220	−	0.612727i	0.930191	+	0.367075i	$0.119641\pi$
$770$	−4837.87	+	7386.46i	−0.226422	+	0.345701i
$771$	−984.128	+	1704.56i	−0.0459695	+	0.0796215i
$772$	3590.48	−	7218.15i	0.167389	−	0.336511i
$773$	32306.5	+	11758.6i	1.50321	+	0.547125i	0.956890	−	0.290450i	$-0.0938050\pi$
$773$	32306.5	+	11758.6i	1.50321	+	0.547125i	0.546323	+	0.837575i	$0.316027\pi$
$774$	630.645	+	5307.19i	0.0292869	+	0.246464i
$775$	879.077	+	4985.50i	0.0407450	+	0.231076i
$776$	−24592.6	−	8791.03i	−1.13766	−	0.406675i
$777$	−1395.27	−	1170.77i	−0.0644209	−	0.0540556i
$778$	12315.7	+	40851.9i	0.567530	+	1.88253i
$779$	24527.6	+	10729.4i	1.12810	+	0.493478i
$780$	1638.80	−	1086.89i	0.0752289	−	0.0498934i
$781$	4591.34	+	3852.59i	0.210360	+	0.176513i
$782$	−13033.8	−	17437.5i	−0.596020	−	0.797396i
$783$	442.923	−	78.0993i	0.0202156	−	0.00356455i
$784$	172.657	+	111.670i	0.00786521	+	0.00508700i
$785$	2378.49	+	865.701i	0.108143	+	0.0393608i
$786$	1050.06	−	1117.28i	0.0476517	−	0.0507024i
$787$	−17514.3	−	10111.9i	−0.793289	−	0.458005i	0.0478303	−	0.998855i	$-0.484769\pi$
$787$	−17514.3	−	10111.9i	−0.793289	−	0.458005i	−0.841119	+	0.540850i	$0.818103\pi$
$788$	11257.9	+	3323.38i	0.508942	+	0.150242i
$789$	1051.71	−	882.488i	0.0474548	−	0.0398193i
$790$	57653.6	+	13547.4i	2.59648	+	0.610120i
$791$	−12162.4	−	21065.8i	−0.546705	−	0.946921i
$792$	−4268.74	+	2497.42i	−0.191519	+	0.112048i
$793$	−20363.2	−	3590.58i	−0.911876	−	0.160788i
$794$	−22257.0	+	11231.4i	−0.994800	+	0.501999i
$795$	−3824.60	+	1392.04i	−0.170622	+	0.0621014i
$796$	−415.097	+	3673.56i	−0.0184833	+	0.163575i
$797$	4284.17			0.190405			0.0952027	−	0.995458i	$-0.469650\pi$
$797$	4284.17			0.190405			0.0952027	+	0.995458i	$0.469650\pi$
$798$	−1735.52	−	525.635i	−0.0769883	−	0.0233174i
$799$			22184.2i			0.982255i
$800$	39019.4	−	37526.8i	1.72443	−	1.65846i
$801$	8783.14	+	24131.5i	0.387437	+	1.06447i
$802$	23002.8	−	11607.7i	1.01279	−	0.511077i
$803$	613.863	−	3481.39i	0.0269773	−	0.152996i
$804$	−2168.24	+	522.676i	−0.0951092	+	0.0229271i
$805$	60611.0	−	34993.8i	2.65374	−	1.53213i
$806$	314.221	−	1337.23i	0.0137320	−	0.0584391i
$807$	447.141	+	532.882i	0.0195045	+	0.0232445i
$808$	−13264.1	+	76.3360i	−0.577511	+	0.00332363i
$809$	−2127.10	+	3684.25i	−0.0924412	+	0.160113i	−0.908538	−	0.417803i	$-0.862800\pi$
$809$	−2127.10	+	3684.25i	−0.0924412	+	0.160113i	0.816097	+	0.577916i	$0.196134\pi$
$810$	28521.0	−	30347.0i	1.23719	−	1.31640i
$811$	−6134.11	+	16853.3i	−0.265595	+	0.729717i	0.733170	+	0.680045i	$0.238040\pi$
$811$	−6134.11	+	16853.3i	−0.265595	+	0.729717i	−0.998766	+	0.0496721i	$0.984182\pi$
$812$	−2740.45	+	1194.61i	−0.118437	+	0.0516286i
$813$	−418.045	−	2370.85i	−0.0180338	−	0.102275i
$814$	−4342.84	+	3246.09i	−0.186998	+	0.139773i
$815$	−6159.27	+	7340.34i	−0.264724	+	0.315486i
$816$	−1033.65	−	436.497i	−0.0443444	−	0.0187260i
$817$	3459.50	+	4696.90i	0.148143	+	0.201131i
$818$	2285.64	+	7581.61i	0.0976963	+	0.324064i
$819$	−9205.57	+	10970.8i	−0.392758	+	0.468070i
$820$	−31636.9	+	42837.9i	−1.34733	+	1.82435i
$821$	−2683.90	+	473.244i	−0.114091	+	0.0201174i	−0.230402	−	0.973095i	$-0.574004\pi$
$821$	−2683.90	+	473.244i	−0.114091	+	0.0201174i	0.116311	+	0.993213i	$0.462893\pi$
$822$	−2534.06	+	301.118i	−0.107525	+	0.0127770i
$823$	2527.73	−	6944.87i	0.107061	−	0.294147i	−0.874581	−	0.484879i	$-0.838864\pi$
$823$	2527.73	−	6944.87i	0.107061	−	0.294147i	0.981642	+	0.190732i	$0.0610860\pi$
$824$	−4466.86	−	761.148i	−0.188848	−	0.0321794i
$825$	877.915	+	506.865i	0.0370486	+	0.0213900i
$826$	−2054.38	+	3136.62i	−0.0865388	+	0.132127i
$827$	−3123.28	−	3722.18i	−0.131327	−	0.156509i	0.696374	−	0.717679i	$-0.254796\pi$
$827$	−3123.28	−	3722.18i	−0.131327	−	0.156509i	−0.827700	+	0.561170i	$0.810351\pi$
$828$	39125.3	−	2429.45i	1.64215	−	0.101967i
$829$	8176.54	+	14162.2i	0.342561	+	0.593333i	0.984907	−	0.173082i	$-0.0553724\pi$
$829$	8176.54	+	14162.2i	0.342561	+	0.593333i	−0.642347	+	0.766414i	$0.722039\pi$
$830$	799.962	−	14204.2i	0.0334543	−	0.594018i
$831$	−180.963	+	1026.29i	−0.00755419	+	0.0428419i
$832$	−13745.0	+	5182.70i	−0.572743	+	0.215959i
$833$	127.222	−	46.3051i	0.00529170	−	0.00192602i
$834$	250.427	−	583.630i	0.0103976	−	0.0242320i
$835$			17953.3i			0.744071i
$836$	−2705.01	+	4671.39i	−0.111907	+	0.193257i
$837$			379.079i			0.0156546i
$838$	36731.8	+	15761.0i	1.51417	+	0.649709i
$839$	13382.4	−	4870.78i	0.550668	−	0.200427i	−0.0516754	−	0.998664i	$-0.516456\pi$
$839$	13382.4	−	4870.78i	0.550668	−	0.200427i	0.602343	+	0.798237i	$0.294234\pi$
$840$	1785.56	−	3134.20i	0.0733425	−	0.128738i
$841$	−4165.07	+	23621.3i	−0.170776	+	0.968521i
$842$	−9083.60	−	511.577i	−0.371783	−	0.0209384i
$843$	345.108	+	597.745i	0.0140998	+	0.0244216i
$844$	153.102	−	9.50668i	0.00624405	−	0.000387717i
$845$	18185.3	+	21672.4i	0.740349	+	0.882313i
$846$	−33416.4	−	21886.6i	−1.35802	−	0.889453i
$847$	−20378.0	−	11765.3i	−0.826680	−	0.477284i
$848$	30170.0	−	3761.25i	1.22175	−	0.152313i
$849$	−657.808	+	1807.31i	−0.0265912	+	0.0730586i
$850$	−4206.03	−	35395.9i	−0.169724	−	1.42832i
$851$	42323.1	−	7462.70i	1.70484	−	0.300609i
$852$	−1969.59	−	1454.59i	−0.0791984	−	0.0584901i
$853$	27017.2	−	32197.8i	1.08447	−	1.29242i	0.130848	−	0.991402i	$-0.458230\pi$
$853$	27017.2	−	32197.8i	1.08447	−	1.29242i	0.953619	−	0.301015i	$-0.0973255\pi$
$854$	−36314.5	+	10947.8i	−1.45510	+	0.438672i
$855$	10779.0	−	44464.9i	0.431150	−	1.77856i
$856$	−2867.95	−	2378.50i	−0.114515	−	0.0949715i
$857$	−11555.9	+	13771.8i	−0.460608	+	0.548932i	−0.945491	−	0.325647i	$-0.894418\pi$
$857$	−11555.9	+	13771.8i	−0.460608	+	0.548932i	0.484883	+	0.874579i	$0.338862\pi$
$858$	−164.683	−	220.324i	−0.00655266	−	0.00876659i
$859$	−1389.81	−	7881.98i	−0.0552032	−	0.313073i	0.944686	−	0.327977i	$-0.106367\pi$
$859$	−1389.81	−	7881.98i	−0.0552032	−	0.313073i	−0.999889	+	0.0149040i	$0.995256\pi$
$860$	−10637.1	+	4636.88i	−0.421769	+	0.183856i
$861$	−855.870	+	2351.48i	−0.0338769	+	0.0930759i
$862$	24587.0	+	23107.6i	0.971504	+	0.913050i
$863$	8349.94	−	14462.5i	0.329357	−	0.570464i	−0.653027	−	0.757334i	$-0.726501\pi$
$863$	8349.94	−	14462.5i	0.329357	−	0.570464i	0.982384	+	0.186871i	$0.0598346\pi$
$864$	3365.39	−	2259.99i	0.132515	−	0.0889890i
$865$	7361.29	+	8772.85i	0.289354	+	0.344839i
$866$	−21556.2	−	5065.27i	−0.845856	−	0.198759i
$867$	1130.38	−	652.625i	0.0442788	−	0.0255644i
$868$	−590.490	−	2449.55i	−0.0230905	−	0.0957872i
$869$	1438.54	−	8158.37i	0.0561555	−	0.318474i
$870$	219.253	+	434.489i	0.00854411	+	0.0169317i
$871$	6575.59	+	18066.3i	0.255804	+	0.702816i
$872$	34180.9	−	6230.04i	1.32742	−	0.241945i
$873$		−	30963.7i		−	1.20041i
$874$	35822.7	−	23397.2i	1.38641	−	0.905516i
$875$	66696.0			2.57684
$876$	−162.152	+	1435.02i	−0.00625411	+	0.0553482i
$877$	−41220.2	+	15002.9i	−1.58712	+	0.577665i	−0.976737	−	0.214439i	$-0.931208\pi$
$877$	−41220.2	+	15002.9i	−1.58712	+	0.577665i	−0.610385	+	0.792105i	$0.708985\pi$
$878$	17078.7	+	33844.5i	0.656468	+	1.30091i
$879$	−250.665	−	44.1990i	−0.00961857	−	0.00169601i
$880$	−7866.66	−	7308.53i	−0.301346	−	0.279967i
$881$	−11492.7	−	19905.9i	−0.439498	−	0.761232i	0.558153	−	0.829738i	$-0.311510\pi$
$881$	−11492.7	−	19905.9i	−0.439498	−	0.761232i	−0.997651	+	0.0685057i	$0.978177\pi$
$882$	−55.7654	+	237.321i	−0.00212893	+	0.00906009i
$883$	−22121.8	+	18562.4i	−0.843099	+	0.707444i	−0.958259	−	0.285903i	$-0.907706\pi$
$883$	−22121.8	+	18562.4i	−0.843099	+	0.707444i	0.115160	+	0.993347i	$0.463262\pi$
$884$	−2738.40	+	9276.28i	−0.104188	+	0.352935i
$885$	528.622	+	305.200i	0.0200785	+	0.0115923i
$886$	23319.3	+	21916.2i	0.884228	+	0.831025i
$887$	14396.3	+	5239.81i	0.544959	+	0.198349i	0.599806	−	0.800146i	$-0.295245\pi$
$887$	14396.3	+	5239.81i	0.544959	+	0.198349i	−0.0548461	+	0.998495i	$0.517467\pi$
$888$	1688.54	−	1433.50i	0.0638106	−	0.0541723i
$889$	−28124.4	+	4959.10i	−1.06104	+	0.187090i
$890$	−44658.9	+	33380.7i	−1.68199	+	1.25722i
$891$	−4462.54	−	3744.51i	−0.167790	−	0.140792i
$892$	−31439.9	+	20851.6i	−1.18014	+	0.782695i
$893$	−43512.8	−	2757.82i	−1.63057	−	0.103345i
$894$	−215.420	+	64.9430i	−0.00805897	+	0.00242955i
$895$	−61835.5	−	51886.2i	−2.30942	−	1.93784i
$896$	−18226.3	+	19846.0i	−0.679573	+	0.739964i
$897$	378.603	+	2147.16i	0.0140927	+	0.0799239i
$898$	8323.65	−	989.085i	0.309314	−	0.0367552i
$899$	319.459	+	116.273i	0.0118515	+	0.00431361i
$900$	57467.0	+	28585.4i	2.12841	+	1.05872i
$901$	10009.2	−	17336.5i	0.370095	−	0.641024i
$902$	6231.51	+	4081.42i	0.230029	+	0.150661i
$903$	−417.695	+	350.488i	−0.0153932	+	0.0129164i
$904$	27738.3	−	10277.1i	1.02053	−	0.378109i
$905$	−80086.3	+	46237.8i	−2.94161	+	1.69834i
$906$	102.464	−	1819.35i	0.00375732	−	0.0667152i
$907$	−47602.0	−	8393.52i	−1.74267	−	0.307279i	−0.790410	−	0.612578i	$-0.790133\pi$
$907$	−47602.0	−	8393.52i	−1.74267	−	0.307279i	−0.952257	+	0.305298i	$0.901244\pi$
$908$	34068.3	−	32389.8i	1.24515	−	1.18380i
$909$	−5378.63	−	14777.7i	−0.196257	−	0.539213i
$910$	−28574.4	−	12260.8i	−1.04091	−	0.446640i
$911$	−22422.4			−0.815463			−0.407731	−	0.913102i	$-0.633680\pi$
$911$	−22422.4			−0.815463			−0.407731	+	0.913102i	$0.633680\pi$
$912$	984.656	−	1973.17i	0.0357513	−	0.0716428i
$913$	−1990.03			−0.0721361
$914$	1453.39	+	623.627i	0.0525972	+	0.0225687i
$915$	2111.84	+	5802.23i	0.0763009	+	0.209635i
$916$	−36057.7	+	34281.1i	−1.30063	+	1.23655i
$917$	−23875.8	−	4209.95i	−0.859814	−	0.151608i
$918$	150.085	−	2664.91i	0.00539600	−	0.0958119i
$919$	−30935.7	+	17860.7i	−1.11042	+	0.641100i	−0.938938	−	0.344087i	$-0.888188\pi$
$919$	−30935.7	+	17860.7i	−1.11042	+	0.641100i	−0.171481	+	0.985188i	$0.554855\pi$
$920$	29569.4	+	79809.0i	1.05964	+	2.86003i
$921$	−2846.42	+	2388.43i	−0.101838	+	0.0854522i
$922$	−6286.13	−	4117.20i	−0.224537	−	0.147064i
$923$	−10553.1	+	18278.5i	−0.376337	+	0.651836i
$924$	−451.762	−	224.717i	−0.0160843	−	0.00800070i
$925$	66121.8	+	24066.4i	2.35035	+	0.855457i
$926$	−19598.2	+	2328.82i	−0.695504	+	0.0826455i
$927$	−932.875	−	5290.60i	−0.0330525	−	0.187450i
$928$	−872.293	−	3529.29i	−0.0308560	−	0.124843i
$929$	−2906.33	−	2438.70i	−0.102641	−	0.0861261i	0.590023	−	0.807386i	$-0.299119\pi$
$929$	−2906.33	−	2438.70i	−0.102641	−	0.0861261i	−0.692664	+	0.721260i	$0.743563\pi$
$930$	−392.738	+	118.399i	−0.0138477	+	0.00417470i
$931$	75.0087	+	255.294i	0.00264051	+	0.00898703i
$932$	−18619.5	+	12348.8i	−0.654401	+	0.434012i
$933$	522.028	+	438.034i	0.0183177	+	0.0153704i
$934$	36114.1	−	26993.8i	1.26519	−	0.945678i
$935$	−6962.59	+	1227.69i	−0.243530	+	0.0429410i
$936$	−11271.3	−	13276.7i	−0.393606	−	0.463636i
$937$	31264.1	+	11379.2i	1.09002	+	0.396737i	0.823630	−	0.567127i	$-0.191945\pi$
$937$	31264.1	+	11379.2i	1.09002	+	0.396737i	0.266395	+	0.963864i	$0.414168\pi$
$938$	25698.1	+	24151.9i	0.894534	+	0.840711i
$939$	−2906.30	−	1677.96i	−0.101005	−	0.0583152i
$940$	24555.2	−	83180.2i	0.852023	−	2.88621i
$941$	18321.9	−	15373.9i	0.634725	−	0.532598i	−0.267668	−	0.963511i	$-0.586253\pi$
$941$	18321.9	−	15373.9i	0.634725	−	0.532598i	0.902393	+	0.430914i	$0.141809\pi$
$942$	−33.0860	+	140.804i	−0.00114437	+	0.00487010i
$943$	−29522.1	−	51133.8i	−1.01948	−	1.76580i
$944$	−3340.54	−	3103.53i	−0.115175	−	0.107004i
$945$	8450.43	+	1490.04i	0.290891	+	0.0512920i
$946$	731.244	+	1449.09i	0.0251319	+	0.0498033i
$947$	38564.0	−	14036.2i	1.32330	−	0.481641i	0.418784	−	0.908086i	$-0.362456\pi$
$947$	38564.0	−	14036.2i	1.32330	−	0.481641i	0.904513	+	0.426445i	$0.140234\pi$
$948$	−379.991	+	3362.87i	−0.0130185	+	0.115212i
$949$	12448.7			0.425820
$950$	69949.5	−	3849.62i	2.38891	−	0.131472i
$951$			2198.41i			0.0749614i
$952$	3181.30	+	17454.1i	0.108305	+	0.594212i
$953$	2398.13	+	6588.81i	0.0815143	+	0.223959i	0.973754	−	0.227604i	$-0.0730891\pi$
$953$	2398.13	+	6588.81i	0.0815143	+	0.223959i	−0.892240	+	0.451562i	$0.850867\pi$
$954$	16239.3	+	32181.0i	0.551117	+	1.09214i
$955$	1414.95	−	8024.60i	0.0479443	−	0.271906i
$956$	−9547.95	−	39608.1i	−0.323015	−	1.33998i
$957$	58.9555	−	34.0380i	0.00199139	−	0.00114973i
$958$	−16834.2	−	3955.68i	−0.567732	−	0.133405i
$959$	25936.8	+	30910.3i	0.873351	+	1.04082i
$960$	3392.55	+	2780.78i	0.114056	+	0.0934887i
$961$	14752.2	−	25551.6i	0.495191	−	0.857696i
$962$	−13913.0	−	13075.9i	−0.466293	−	0.438237i
$963$	1510.84	−	4151.01i	0.0505569	−	0.138904i
$964$	44293.6	−	19308.3i	1.47988	−	0.645101i
$965$	3603.55	+	20436.7i	0.120210	+	0.681743i
$966$	2394.40	+	3203.38i	0.0797499	+	0.106695i
$967$	−8832.33	+	10526.0i	−0.293721	+	0.350043i	−0.892643	−	0.450764i	$-0.851152\pi$
$967$	−8832.33	+	10526.0i	−0.293721	+	0.350043i	0.598922	+	0.800807i	$0.295596\pi$
$968$	18267.0	−	22025.9i	0.606532	−	0.731343i
$969$	−644.994	−	1300.84i	−0.0213831	−	0.0431260i
$970$	64365.6	−	19404.4i	2.13057	−	0.642307i
$971$	24302.2	−	28962.3i	0.803188	−	0.957202i	−0.196541	−	0.980496i	$-0.562971\pi$
$971$	24302.2	−	28962.3i	0.803188	−	0.957202i	0.999729	+	0.0232935i	$0.00741523\pi$
$972$	5805.41	+	4287.45i	0.191573	+	0.141481i
$973$	−9889.46	+	1743.78i	−0.325839	+	0.0574543i
$974$	−34.2903	−	288.570i	−0.00112806	−	0.00949321i
$975$	−1220.95	+	3354.54i	−0.0401043	+	0.110186i
$976$	−5706.12	−	45770.3i	−0.187140	−	1.50110i
$977$	34224.9	+	19759.7i	1.12073	+	0.647052i	0.941586	−	0.336772i	$-0.109335\pi$
$977$	34224.9	+	19759.7i	1.12073	+	0.647052i	0.179140	+	0.983824i	$0.442668\pi$
$978$	−458.055	−	300.010i	−0.0149765	−	0.00980907i
$979$	5013.16	+	5974.45i	0.163658	+	0.195040i
$980$	−528.276	+	32.8028i	−0.0172196	+	0.00106923i
$981$	20596.1	+	35673.5i	0.670319	+	1.16103i
$982$	−28637.9	−	1612.85i	−0.930625	−	0.0524116i
$983$	2872.03	−	16288.1i	0.0931878	−	0.528494i	−0.902100	−	0.431528i	$-0.857975\pi$
$983$	2872.03	−	16288.1i	0.0931878	−	0.528494i	0.995288	−	0.0969669i	$-0.0309141\pi$
$984$	−2644.14	−	1506.37i	−0.0856626	−	0.0488022i
$985$	−28393.1	+	10334.3i	−0.918457	+	0.334291i
$986$	−2199.75	−	943.877i	−0.0710489	−	0.0304860i
$987$		−	4075.39i		−	0.131430i
$988$	−17854.4	−	6524.36i	−0.574922	−	0.210089i
$989$		−	12865.5i		−	0.413650i
$990$	5019.89	−	11699.1i	0.161154	−	0.375577i
$991$	−172.945	+	62.9467i	−0.00554366	+	0.00201773i	−0.344790	−	0.938680i	$-0.612050\pi$
$991$	−172.945	+	62.9467i	−0.00554366	+	0.00201773i	0.339247	+	0.940697i	$0.389828\pi$
$992$	3057.16	−	207.499i	0.0978476	−	0.00664124i
$993$	−500.731	+	2839.79i	−0.0160022	+	0.0907531i
$994$	−2176.96	+	38654.3i	−0.0694658	+	1.23344i
$995$	−4758.15	−	8241.36i	−0.151601	−	0.262581i
$996$	811.404	−	50.3833i	0.0258136	−	0.00160287i
$997$	−15986.2	−	19051.6i	−0.507811	−	0.605185i	0.449843	−	0.893108i	$-0.351480\pi$
$997$	−15986.2	−	19051.6i	−0.507811	−	0.605185i	−0.957654	+	0.287923i	$0.907035\pi$
$998$	−18668.4	+	28502.9i	−0.592123	+	0.904052i
$999$	4563.13	+	2634.53i	0.144516	+	0.0834361i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.v.b.3.7	✓	336
8.3	odd	2	inner	152.4.v.b.3.39	yes	336
19.13	odd	18	inner	152.4.v.b.51.39	yes	336
152.51	even	18	inner	152.4.v.b.51.7	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.v.b.3.7	✓	336	1.1	even	1	trivial
152.4.v.b.3.39	yes	336	8.3	odd	2	inner
152.4.v.b.51.7	yes	336	152.51	even	18	inner
152.4.v.b.51.39	yes	336	19.13	odd	18	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	152.4.v.b.3.7

Level	$152$
Weight	$4$
Character	152.3
Analytic conductor	$8.968$
Analytic rank	$0$
Dimension	$336$
Inner twists	$4$