LMFDB - Embedded newform 31.4.g.a.10.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,4,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, 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:	$1.82905921018$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	31.10
Dual form			31.4.g.a.28.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.25803 - 2.36710i) q^{2} +(0.539766 + 5.13553i) q^{3} +(2.53947 + 7.81570i) q^{4} +(4.24115 + 7.34588i) q^{5} +(10.3977 - 18.0094i) q^{6} +(22.3519 + 4.75104i) q^{7} +(0.271177 - 0.834598i) q^{8} +(0.327669 - 0.0696482i) q^{9} +(3.57063 - 33.9723i) q^{10} +(-35.7599 + 39.7153i) q^{11} +(-38.7670 + 17.2602i) q^{12} +(-18.5320 - 8.25098i) q^{13} +(-61.5769 - 68.3881i) q^{14} +(-35.4358 + 25.7456i) q^{15} +(50.3283 - 36.5657i) q^{16} +(9.22668 + 10.2473i) q^{17} +(-1.23242 - 0.548708i) q^{18} +(22.1427 - 9.85858i) q^{19} +(-46.6429 + 51.8022i) q^{20} +(-12.3343 + 117.353i) q^{21} +(210.517 - 44.7467i) q^{22} +(57.4773 - 176.897i) q^{23} +(4.43247 + 0.942152i) q^{24} +(26.5254 - 45.9433i) q^{25} +(40.8469 + 70.7490i) q^{26} +(43.6186 + 134.244i) q^{27} +(19.6293 + 186.761i) q^{28} +(-172.639 - 125.430i) q^{29} +176.393 q^{30} +(7.52917 + 172.436i) q^{31} -257.546 q^{32} +(-223.261 - 162.209i) q^{33} +(-5.80453 - 55.2264i) q^{34} +(59.8970 + 184.344i) q^{35} +(1.37645 + 2.38409i) q^{36} +(101.323 - 175.497i) q^{37} +(-95.4779 - 20.2945i) q^{38} +(32.3702 - 99.6252i) q^{39} +(7.28096 - 1.54762i) q^{40} +(-16.6474 + 158.389i) q^{41} +(317.972 - 353.144i) q^{42} +(172.989 - 77.0196i) q^{43} +(-401.214 - 178.632i) q^{44} +(1.90132 + 2.11163i) q^{45} +(-605.995 + 440.281i) q^{46} +(425.832 - 309.385i) q^{47} +(214.950 + 238.726i) q^{48} +(163.688 + 72.8785i) q^{49} +(-195.173 + 86.8964i) q^{50} +(-47.6449 + 52.9150i) q^{51} +(17.4256 - 165.794i) q^{52} +(-153.964 + 32.7260i) q^{53} +(175.659 - 540.622i) q^{54} +(-443.407 - 94.2490i) q^{55} +(10.0265 - 17.3665i) q^{56} +(62.5809 + 108.393i) q^{57} +(265.559 + 817.307i) q^{58} +(46.2494 + 440.033i) q^{59} +(-291.208 - 211.575i) q^{60} -770.292 q^{61} +(383.643 - 579.625i) q^{62} +7.65491 q^{63} +(436.466 + 317.111i) q^{64} +(-17.9862 - 171.127i) q^{65} +(343.428 + 1056.96i) q^{66} +(-375.894 - 651.067i) q^{67} +(-56.6586 + 98.1356i) q^{68} +(939.483 + 199.693i) q^{69} +(241.214 - 742.380i) q^{70} +(1111.92 - 236.347i) q^{71} +(0.0307281 - 0.292359i) q^{72} +(323.582 - 359.375i) q^{73} +(-745.532 + 331.932i) q^{74} +(250.260 + 111.423i) q^{75} +(133.283 + 148.025i) q^{76} +(-987.989 + 717.816i) q^{77} +(-341.286 + 247.959i) q^{78} +(151.060 + 167.769i) q^{79} +(482.057 + 214.626i) q^{80} +(-657.609 + 292.787i) q^{81} +(429.160 - 476.631i) q^{82} +(67.3300 - 640.602i) q^{83} +(-948.519 + 201.614i) q^{84} +(-36.1435 + 111.238i) q^{85} +(-745.916 - 158.549i) q^{86} +(550.963 - 954.295i) q^{87} +(23.4491 + 40.6150i) q^{88} +(-159.523 - 490.962i) q^{89} +(-1.19612 - 11.3804i) q^{90} +(-375.024 - 272.471i) q^{91} +1528.53 q^{92} +(-881.488 + 131.742i) q^{93} -2119.72 q^{94} +(166.331 + 120.846i) q^{95} +(-139.015 - 1322.64i) q^{96} +(155.553 + 478.743i) q^{97} +(-360.789 - 624.905i) q^{98} +(-8.95129 + 15.5041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−3.25803	−	2.36710i	−1.15189	−	0.836895i	−0.163157	−	0.986600i	$-0.552168\pi$
$2$	−3.25803	−	2.36710i	−1.15189	−	0.836895i	−0.988731	+	0.149705i	$0.952168\pi$
$3$	0.539766	+	5.13553i	0.103878	+	0.988333i	0.914999	+	0.403455i	$0.132191\pi$
$3$	0.539766	+	5.13553i	0.103878	+	0.988333i	−0.811121	+	0.584878i	$0.801142\pi$
$4$	2.53947	+	7.81570i	0.317434	+	0.976962i
$5$	4.24115	+	7.34588i	0.379340	+	0.657036i	0.990966	−	0.134111i	$-0.0428179\pi$
$5$	4.24115	+	7.34588i	0.379340	+	0.657036i	−0.611627	+	0.791147i	$0.709485\pi$
$6$	10.3977	−	18.0094i	0.707476	−	1.22538i
$7$	22.3519	+	4.75104i	1.20689	+	0.256532i	0.767075	−	0.641558i	$-0.221711\pi$
$7$	22.3519	+	4.75104i	1.20689	+	0.256532i	0.439813	+	0.898089i	$0.355045\pi$
$8$	0.271177	−	0.834598i	0.0119845	−	0.0368844i
$9$	0.327669	−	0.0696482i	0.0121359	−	0.00257956i
$10$	3.57063	−	33.9723i	0.112913	−	1.07430i
$11$	−35.7599	+	39.7153i	−0.980182	+	1.08860i	0.0158740	+	0.999874i	$0.494947\pi$
$11$	−35.7599	+	39.7153i	−0.980182	+	1.08860i	−0.996056	+	0.0887283i	$0.971720\pi$
$12$	−38.7670	+	17.2602i	−0.932589	+	0.415216i
$13$	−18.5320	−	8.25098i	−0.395373	−	0.176031i	0.199413	−	0.979916i	$-0.436097\pi$
$13$	−18.5320	−	8.25098i	−0.395373	−	0.176031i	−0.594786	+	0.803884i	$0.702763\pi$
$14$	−61.5769	−	68.3881i	−1.17551	−	1.30553i
$15$	−35.4358	+	25.7456i	−0.609965	+	0.443165i
$16$	50.3283	−	36.5657i	0.786380	−	0.571339i
$17$	9.22668	+	10.2473i	0.131635	+	0.146196i	0.805359	−	0.592788i	$-0.201973\pi$
$17$	9.22668	+	10.2473i	0.131635	+	0.146196i	−0.673723	+	0.738984i	$0.735306\pi$
$18$	−1.23242	−	0.548708i	−0.0161380	−	0.00718510i
$19$	22.1427	−	9.85858i	0.267363	−	0.119038i	−0.268677	−	0.963230i	$-0.586586\pi$
$19$	22.1427	−	9.85858i	0.267363	−	0.119038i	0.536040	+	0.844193i	$0.319920\pi$
$20$	−46.6429	+	51.8022i	−0.521483	+	0.579166i
$21$	−12.3343	+	117.353i	−0.128170	+	1.21946i
$22$	210.517	−	44.7467i	2.04011	−	0.433638i
$23$	57.4773	−	176.897i	0.521080	−	1.60372i	−0.250860	−	0.968023i	$-0.580713\pi$
$23$	57.4773	−	176.897i	0.521080	−	1.60372i	0.771940	−	0.635696i	$-0.219287\pi$
$24$	4.43247	+	0.942152i	0.0376990	+	0.00801316i
$25$	26.5254	−	45.9433i	0.212203	−	0.367546i
$26$	40.8469	+	70.7490i	0.308106	+	0.533654i
$27$	43.6186	+	134.244i	0.310904	+	0.956865i
$28$	19.6293	+	186.761i	0.132485	+	1.26052i
$29$	−172.639	−	125.430i	−1.10546	−	0.803162i	−0.123515	−	0.992343i	$-0.539417\pi$
$29$	−172.639	−	125.430i	−1.10546	−	0.803162i	−0.981942	+	0.189181i	$0.939417\pi$
$30$	176.393			1.07349
$31$	7.52917	+	172.436i	0.0436219	+	0.999048i
$31$	7.52917	+	172.436i	0.0436219	+	0.999048i
$32$	−257.546			−1.42275
$33$	−223.261	−	162.209i	−1.17772	−	0.855664i
$34$	−5.80453	−	55.2264i	−0.0292785	−	0.278566i
$35$	59.8970	+	184.344i	0.289270	+	0.890281i
$36$	1.37645	+	2.38409i	0.00637248	+	0.0110375i
$37$	101.323	−	175.497i	0.450201	−	0.779770i	−0.548198	−	0.836349i	$-0.684686\pi$
$37$	101.323	−	175.497i	0.450201	−	0.779770i	0.998398	+	0.0565787i	$0.0180192\pi$
$38$	−95.4779	−	20.2945i	−0.407594	−	0.0866367i
$39$	32.3702	−	99.6252i	0.132907	−	0.409046i
$40$	7.28096	−	1.54762i	0.0287805	−	0.00611749i
$41$	−16.6474	+	158.389i	−0.0634118	+	0.603323i	0.915962	+	0.401265i	$0.131429\pi$
$41$	−16.6474	+	158.389i	−0.0634118	+	0.603323i	−0.979374	+	0.202057i	$0.935237\pi$
$42$	317.972	−	353.144i	1.16819	−	1.29741i
$43$	172.989	−	77.0196i	0.613501	−	0.273148i	−0.0763710	−	0.997079i	$-0.524333\pi$
$43$	172.989	−	77.0196i	0.613501	−	0.273148i	0.689872	+	0.723931i	$0.257667\pi$
$44$	−401.214	−	178.632i	−1.37467	−	0.612041i
$45$	1.90132	+	2.11163i	0.00629848	+	0.00699518i
$46$	−605.995	+	440.281i	−1.94237	+	1.41121i
$47$	425.832	−	309.385i	1.32158	−	0.960181i	0.321664	−	0.946854i	$-0.395758\pi$
$47$	425.832	−	309.385i	1.32158	−	0.960181i	0.999911	−	0.0133269i	$-0.00424221\pi$
$48$	214.950	+	238.726i	0.646361	+	0.717856i
$49$	163.688	+	72.8785i	0.477224	+	0.212474i
$50$	−195.173	+	86.8964i	−0.552031	+	0.245780i
$51$	−47.6449	+	52.9150i	−0.130816	+	0.145286i
$52$	17.4256	−	165.794i	0.0464711	−	0.442143i
$53$	−153.964	+	32.7260i	−0.399029	+	0.0848163i	−0.403055	−	0.915176i	$-0.632052\pi$
$53$	−153.964	+	32.7260i	−0.399029	+	0.0848163i	0.00402614	+	0.999992i	$0.498718\pi$
$54$	175.659	−	540.622i	0.442669	−	1.36239i
$55$	−443.407	−	94.2490i	−1.08707	−	0.231064i
$56$	10.0265	−	17.3665i	0.0239259	−	0.0414409i
$57$	62.5809	+	108.393i	0.145422	+	0.251878i
$58$	265.559	+	817.307i	0.601200	+	1.85030i
$59$	46.2494	+	440.033i	0.102053	+	0.970974i	0.918999	+	0.394259i	$0.128999\pi$
$59$	46.2494	+	440.033i	0.102053	+	0.970974i	−0.816946	+	0.576715i	$0.804334\pi$
$60$	−291.208	−	211.575i	−0.626579	−	0.455237i
$61$	−770.292			−1.61682			−0.808408	−	0.588622i	$-0.799670\pi$
$61$	−770.292			−1.61682			−0.808408	+	0.588622i	$0.799670\pi$
$62$	383.643	−	579.625i	0.785851	−	1.18730i
$63$	7.65491			0.0153084
$64$	436.466	+	317.111i	0.852473	+	0.619358i
$65$	−17.9862	−	171.127i	−0.0343218	−	0.326550i
$66$	343.428	+	1056.96i	0.640501	+	1.97126i
$67$	−375.894	−	651.067i	−0.685414	−	1.18717i	−0.973307	−	0.229508i	$-0.926288\pi$
$67$	−375.894	−	651.067i	−0.685414	−	1.18717i	0.287893	−	0.957663i	$-0.407045\pi$
$68$	−56.6586	+	98.1356i	−0.101042	+	0.175010i
$69$	939.483	+	199.693i	1.63914	+	0.348409i
$70$	241.214	−	742.380i	0.411866	−	1.26759i
$71$	1111.92	−	236.347i	1.85861	−	0.395059i	0.864425	−	0.502762i	$-0.167683\pi$
$71$	1111.92	−	236.347i	1.85861	−	0.395059i	0.994183	+	0.107703i	$0.0343496\pi$
$72$	0.0307281	−	0.292359i	5.02965e−5	−	0.000478539i
$73$	323.582	−	359.375i	0.518801	−	0.576187i	−0.425630	−	0.904897i	$-0.639947\pi$
$73$	323.582	−	359.375i	0.518801	−	0.576187i	0.944431	+	0.328711i	$0.106614\pi$
$74$	−745.532	+	331.932i	−1.17117	+	0.521437i
$75$	250.260	+	111.423i	0.385301	+	0.171547i
$76$	133.283	+	148.025i	0.201165	+	0.223417i
$77$	−987.989	+	717.816i	−1.46223	+	1.06237i
$78$	−341.286	+	247.959i	−0.495423	+	0.359946i
$79$	151.060	+	167.769i	0.215133	+	0.238930i	0.841046	−	0.540963i	$-0.181940\pi$
$79$	151.060	+	167.769i	0.215133	+	0.238930i	−0.625913	+	0.779893i	$0.715273\pi$
$80$	482.057	+	214.626i	0.673695	+	0.299948i
$81$	−657.609	+	292.787i	−0.902070	+	0.401628i
$82$	429.160	−	476.631i	0.577961	−	0.641891i
$83$	67.3300	−	640.602i	0.0890413	−	0.847171i	−0.855284	−	0.518159i	$-0.826618\pi$
$83$	67.3300	−	640.602i	0.0890413	−	0.847171i	0.944326	−	0.329012i	$-0.106716\pi$
$84$	−948.519	+	201.614i	−1.23205	+	0.261880i
$85$	−36.1435	+	111.238i	−0.0461213	+	0.141947i
$86$	−745.916	−	158.549i	−0.935281	−	0.198800i
$87$	550.963	−	954.295i	0.678959	−	1.17599i
$88$	23.4491	+	40.6150i	0.0284055	+	0.0491997i
$89$	−159.523	−	490.962i	−0.189994	−	0.584741i	0.810005	−	0.586423i	$-0.199464\pi$
$89$	−159.523	−	490.962i	−0.189994	−	0.584741i	−0.999999	+	0.00168261i	$0.999464\pi$
$90$	−1.19612	−	11.3804i	−0.00140092	−	0.0133288i
$91$	−375.024	−	272.471i	−0.432013	−	0.313876i
$92$	1528.53			1.73218
$93$	−881.488	+	131.742i	−0.982861	+	0.146892i
$94$	−2119.72			−2.32588
$95$	166.331	+	120.846i	0.179633	+	0.130511i
$96$	−139.015	−	1322.64i	−0.147793	−	1.40616i
$97$	155.553	+	478.743i	0.162825	+	0.501123i	0.998869	−	0.0475382i	$-0.0151376\pi$
$97$	155.553	+	478.743i	0.162825	+	0.501123i	−0.836045	+	0.548661i	$0.815138\pi$
$98$	−360.789	−	624.905i	−0.371890	−	0.644132i
$99$	−8.95129	+	15.5041i	−0.00908725	+	0.0157396i
$100$	426.439	+	90.6424i	0.426439	+	0.0906424i
$101$	72.0725	−	221.816i	0.0710048	−	0.218530i	−0.909257	−	0.416236i	$-0.863349\pi$
$101$	72.0725	−	221.816i	0.0710048	−	0.218530i	0.980261	+	0.197706i	$0.0633490\pi$
$102$	280.484	−	59.6186i	0.272275	−	0.0578738i
$103$	−167.770	+	1596.23i	−0.160494	+	1.52700i	0.557045	+	0.830482i	$0.311935\pi$
$103$	−167.770	+	1596.23i	−0.160494	+	1.52700i	−0.717539	+	0.696518i	$0.754732\pi$
$104$	−11.9117	+	13.2293i	−0.0112311	+	0.0124734i
$105$	−914.374	+	407.105i	−0.849845	+	0.378375i
$106$	579.084	+	257.825i	0.530619	+	0.236247i
$107$	222.662	+	247.291i	0.201173	+	0.223425i	0.835287	−	0.549814i	$-0.185302\pi$
$107$	222.662	+	247.291i	0.201173	+	0.223425i	−0.634114	+	0.773240i	$0.718635\pi$
$108$	−938.445	+	681.820i	−0.836129	+	0.607483i
$109$	−510.583	+	370.961i	−0.448670	+	0.325978i	−0.789070	−	0.614303i	$-0.789437\pi$
$109$	−510.583	+	370.961i	−0.448670	+	0.325978i	0.340400	+	0.940281i	$0.389437\pi$
$110$	1221.54	+	1356.65i	1.05881	+	1.17593i
$111$	955.960	+	425.621i	0.817439	+	0.363947i
$112$	1298.66	−	578.200i	1.09564	−	0.487810i
$113$	−424.059	+	470.965i	−0.353027	+	0.392076i	−0.893335	−	0.449391i	$-0.851641\pi$
$113$	−424.059	+	470.965i	−0.353027	+	0.392076i	0.540308	+	0.841467i	$0.318308\pi$
$114$	52.6871	−	501.284i	0.0432859	−	0.411838i
$115$	1543.23	−	328.024i	1.25137	−	0.265986i
$116$	541.907	−	1667.82i	0.433748	−	1.33494i
$117$	−6.64702	−	1.41287i	−0.00525229	−	0.00111641i
$118$	890.920	−	1543.12i	0.695049	−	1.20386i
$119$	157.549	+	272.882i	0.121365	+	0.210211i
$120$	11.8778	+	36.5562i	0.00903578	+	0.0278093i
$121$	−159.414	−	1516.72i	−0.119770	−	1.13953i
$122$	2509.63	+	1823.36i	1.86239	+	1.35311i
$123$	−822.398			−0.602871
$124$	−1328.59	+	496.743i	−0.962185	+	0.359749i
$125$	1510.28			1.08067
$126$	−24.9399	−	18.1199i	−0.0176335	−	0.0128115i
$127$	87.3521	+	831.099i	0.0610334	+	0.580694i	0.981712	+	0.190372i	$0.0609695\pi$
$127$	87.3521	+	831.099i	0.0610334	+	0.580694i	−0.920679	+	0.390322i	$0.872364\pi$
$128$	−34.6978	−	106.789i	−0.0239600	−	0.0737414i
$129$	488.910	+	846.817i	0.333691	+	0.577970i
$130$	−346.476	+	600.113i	−0.233753	+	0.404873i
$131$	−2299.60	−	488.795i	−1.53372	−	0.326002i	−0.637793	−	0.770208i	$-0.720152\pi$
$131$	−2299.60	−	488.795i	−1.53372	−	0.326002i	−0.895925	+	0.444206i	$0.853486\pi$
$132$	700.808	−	2156.87i	0.462103	−	1.42221i
$133$	541.770	−	115.157i	0.353214	−	0.0750779i
$134$	−316.466	+	3010.97i	−0.204019	+	1.94111i
$135$	−801.150	+	889.767i	−0.510756	+	0.567252i
$136$	11.0544	−	4.92174i	0.00696992	−	0.00310321i
$137$	−1345.38	−	599.002i	−0.839005	−	0.373549i	−0.0581853	−	0.998306i	$-0.518531\pi$
$137$	−1345.38	−	599.002i	−0.839005	−	0.373549i	−0.780819	+	0.624757i	$0.785198\pi$
$138$	−2588.17	−	2874.45i	−1.59652	−	1.77311i
$139$	−591.092	+	429.453i	−0.360689	+	0.262056i	−0.753339	−	0.657632i	$-0.771558\pi$
$139$	−591.092	+	429.453i	−0.360689	+	0.262056i	0.392651	+	0.919688i	$0.371558\pi$
$140$	−1288.67	+	936.274i	−0.777946	+	0.565211i
$141$	1818.71	+	2019.88i	1.08626	+	1.20642i
$142$	−4182.14	−	1862.01i	−2.47153	−	1.10040i
$143$	990.392	−	440.951i	0.579166	−	0.257861i
$144$	13.9443	−	15.4867i	0.00806961	−	0.00896222i
$145$	189.203	−	1800.15i	0.108362	−	1.03100i
$146$	−1904.92	+	404.902i	−1.07981	+	0.229520i
$147$	−285.917	+	879.961i	−0.160422	+	0.493728i
$148$	1628.94	+	346.241i	0.904715	+	0.192303i
$149$	165.067	−	285.904i	0.0907570	−	0.157196i	−0.817073	−	0.576534i	$-0.804405\pi$
$149$	165.067	−	285.904i	0.0907570	−	0.157196i	0.907830	+	0.419339i	$0.137738\pi$
$150$	−551.607	−	955.411i	−0.300257	−	0.520060i
$151$	80.8113	+	248.712i	0.0435519	+	0.134039i	0.970468	−	0.241229i	$-0.0775506\pi$
$151$	80.8113	+	248.712i	0.0435519	+	0.134039i	−0.926916	+	0.375268i	$0.877551\pi$
$152$	−2.22334	−	21.1537i	−0.00118643	−	0.0112881i
$153$	3.73700	+	2.71509i	0.00197463	+	0.00143465i
$154$	4918.04			2.57342
$155$	−1234.76	+	786.636i	−0.639863	+	0.407640i
$156$	860.844			0.441812
$157$	1170.70	+	850.563i	0.595108	+	0.432371i	0.844139	−	0.536124i	$-0.180112\pi$
$157$	1170.70	+	850.563i	0.595108	+	0.432371i	−0.249031	+	0.968495i	$0.580112\pi$
$158$	−95.0319	−	904.168i	−0.0478502	−	0.455264i
$159$	−251.170	−	773.021i	−0.125277	−	0.385563i
$160$	−1092.29	−	1891.90i	−0.539707	−	0.934801i
$161$	2125.17	−	3680.90i	1.04029	−	1.80184i
$162$	2835.57	+	602.718i	1.37520	+	0.292309i
$163$	−660.411	+	2032.54i	−0.317346	+	0.976691i	0.657432	+	0.753514i	$0.271643\pi$
$163$	−660.411	+	2032.54i	−0.317346	+	0.976691i	−0.974778	+	0.223177i	$0.928357\pi$
$164$	−1280.20	+	272.114i	−0.609552	+	0.129564i
$165$	244.683	−	2328.00i	0.115446	−	1.09839i
$166$	−1735.73	+	1927.72i	−0.811559	+	0.901327i
$167$	788.393	−	351.015i	0.365315	−	0.162649i	−0.215866	−	0.976423i	$-0.569257\pi$
$167$	788.393	−	351.015i	0.365315	−	0.162649i	0.581181	+	0.813774i	$0.302591\pi$
$168$	94.5979	+	42.1177i	0.0434428	+	0.0193420i
$169$	−1194.72	−	1326.88i	−0.543798	−	0.603949i
$170$	381.069	−	276.862i	0.171921	−	0.124908i
$171$	6.56885	−	4.77255i	0.00293762	−	0.00213430i
$172$	1041.26	+	1156.44i	0.461602	+	0.512661i
$173$	1182.15	+	526.329i	0.519523	+	0.231307i	0.649709	−	0.760183i	$-0.274891\pi$
$173$	1182.15	+	526.329i	0.519523	+	0.231307i	−0.130186	+	0.991490i	$0.541557\pi$
$174$	−4053.96	+	1804.94i	−1.76626	+	0.786392i
$175$	811.170	−	900.895i	0.350392	−	0.389150i
$176$	−347.516	+	3306.39i	−0.148835	+	1.41607i
$177$	−2234.84	+	475.030i	−0.949045	+	0.201726i
$178$	−642.424	+	1977.18i	−0.270515	+	0.832560i
$179$	764.812	+	162.566i	0.319356	+	0.0678812i	0.364801	−	0.931086i	$-0.381137\pi$
$179$	764.812	+	162.566i	0.319356	+	0.0678812i	−0.0454447	+	0.998967i	$0.514470\pi$
$180$	−11.6755	+	20.2225i	−0.00483467	+	0.00837389i
$181$	−929.268	−	1609.54i	−0.381613	−	0.660973i	0.609680	−	0.792648i	$-0.291298\pi$
$181$	−929.268	−	1609.54i	−0.381613	−	0.660973i	−0.991293	+	0.131675i	$0.957965\pi$
$182$	576.875	+	1775.44i	0.234949	+	0.723100i
$183$	−415.777	−	3955.86i	−0.167952	−	1.59795i
$184$	−132.051	−	95.9408i	−0.0529073	−	0.0384394i
$185$	1718.90			0.683116
$186$	3183.76	+	1657.35i	1.25508	+	0.653349i
$187$	−736.919			−0.288176
$188$	3499.45	+	2542.50i	1.35757	+	0.986335i
$189$	337.158	+	3207.85i	0.129760	+	1.23458i
$190$	−255.855	−	787.441i	−0.0976931	−	0.300668i
$191$	−1012.19	−	1753.16i	−0.383452	−	0.664159i	0.608101	−	0.793860i	$-0.291932\pi$
$191$	−1012.19	−	1753.16i	−0.383452	−	0.664159i	−0.991553	+	0.129701i	$0.958598\pi$
$192$	−1392.95	+	2412.65i	−0.523579	+	0.906865i
$193$	−2936.81	−	624.238i	−1.09532	−	0.232817i	−0.375390	−	0.926867i	$-0.622491\pi$
$193$	−2936.81	−	624.238i	−1.09532	−	0.232817i	−0.719927	+	0.694050i	$0.755825\pi$
$194$	626.434	−	1927.97i	0.231832	−	0.713505i
$195$	869.122	−	184.738i	0.319175	−	0.0678427i
$196$	−153.915	+	1464.41i	−0.0560916	+	0.533676i
$197$	274.084	−	304.401i	0.0991251	−	0.110090i	−0.691541	−	0.722337i	$-0.743068\pi$
$197$	274.084	−	304.401i	0.0991251	−	0.110090i	0.790666	+	0.612248i	$0.209734\pi$
$198$	65.8632	−	29.3242i	0.0236399	−	0.0105252i
$199$	457.303	+	203.604i	0.162901	+	0.0725283i	0.486567	−	0.873643i	$-0.338249\pi$
$199$	457.303	+	203.604i	0.162901	+	0.0725283i	−0.323666	+	0.946171i	$0.604915\pi$
$200$	−31.1511	−	34.5968i	−0.0110136	−	0.0122318i
$201$	3140.68	−	2281.84i	1.10212	−	0.800738i
$202$	−759.876	+	552.082i	−0.264677	+	0.192299i
$203$	−3262.88	−	3623.80i	−1.12813	−	1.25291i
$204$	−534.561	−	238.002i	−0.183464	−	0.0816836i
$205$	−1234.11	+	549.462i	−0.420459	+	0.187200i
$206$	4325.03	−	4803.43i	1.46281	−	1.62462i
$207$	6.51297	−	61.9668i	0.00218687	−	0.0208067i
$208$	−1234.39	+	262.377i	−0.411487	+	0.0874643i
$209$	−400.284	+	1231.95i	−0.132480	+	0.407730i
$210$	3942.72	+	838.050i	1.29559	+	0.275385i
$211$	−206.508	+	357.682i	−0.0673771	+	0.116701i	−0.897746	−	0.440514i	$-0.854796\pi$
$211$	−206.508	+	357.682i	−0.0673771	+	0.116701i	0.830369	+	0.557214i	$0.188130\pi$
$212$	−646.763	−	1120.23i	−0.209528	−	0.362913i
$213$	1813.95	+	5582.75i	0.583519	+	1.79589i
$214$	−140.077	−	1332.74i	−0.0447452	−	0.425722i
$215$	1299.45	+	944.104i	0.412194	+	0.299476i
$216$	123.868			0.0390194
$217$	−650.961	+	3890.05i	−0.203641	+	1.21693i
$218$	2541.60			0.789627
$219$	2020.24	+	1467.79i	0.623356	+	0.452895i
$220$	−389.398	−	3704.88i	−0.119333	−	1.13538i
$221$	−86.4389	−	266.032i	−0.0263100	−	0.0809738i
$222$	−2107.06	−	3649.53i	−0.637012	−	1.10334i
$223$	−3118.91	+	5402.12i	−0.936583	+	1.62221i	−0.164796	+	0.986328i	$0.552697\pi$
$223$	−3118.91	+	5402.12i	−0.936583	+	1.62221i	−0.771787	+	0.635881i	$0.780637\pi$
$224$	−5756.64	−	1223.61i	−1.71711	−	0.364982i
$225$	5.49167	−	16.9016i	0.00162716	−	0.00500789i
$226$	2496.41	−	530.629i	0.734774	−	0.156181i
$227$	450.753	−	4288.62i	0.131795	−	1.25395i	−0.706098	−	0.708114i	$-0.749546\pi$
$227$	450.753	−	4288.62i	0.131795	−	1.25395i	0.837894	−	0.545834i	$-0.183787\pi$
$228$	−688.247	+	764.376i	−0.199913	+	0.222026i
$229$	2992.31	−	1332.26i	0.863483	−	0.384447i	0.0732937	−	0.997310i	$-0.476649\pi$
$229$	2992.31	−	1332.26i	0.863483	−	0.384447i	0.790189	+	0.612863i	$0.209982\pi$
$230$	−5804.36	−	2584.27i	−1.66404	−	0.740877i
$231$	−4219.65	−	4686.39i	−1.20187	−	1.33481i
$232$	−151.499	+	110.070i	−0.0428724	+	0.0311486i
$233$	2826.00	−	2053.21i	0.794581	−	0.577297i	−0.114739	−	0.993396i	$-0.536603\pi$
$233$	2826.00	−	2053.21i	0.794581	−	0.577297i	0.909319	+	0.416099i	$0.136603\pi$
$234$	18.3118	+	20.3373i	0.00511573	+	0.00568159i
$235$	4078.73	+	1815.97i	1.13220	+	0.504087i
$236$	−3321.72	+	1478.92i	−0.916209	+	0.407923i
$237$	−780.044	+	866.327i	−0.213795	+	0.237443i
$238$	132.641	−	1261.99i	0.0361252	−	0.343709i
$239$	−6334.28	+	1346.39i	−1.71435	+	0.364397i	−0.957331	−	0.288993i	$-0.906680\pi$
$239$	−6334.28	+	1346.39i	−1.71435	+	0.364397i	−0.757022	+	0.653390i	$0.773346\pi$
$240$	−842.018	+	2591.47i	−0.226467	+	0.696993i
$241$	−952.034	−	202.361i	−0.254464	−	0.0540880i	0.0789132	−	0.996881i	$-0.474855\pi$
$241$	−952.034	−	202.361i	−0.254464	−	0.0540880i	−0.333377	+	0.942793i	$0.608188\pi$
$242$	−3070.85	+	5318.87i	−0.815710	+	1.41285i
$243$	46.9949	+	81.3976i	0.0124063	+	0.0214883i
$244$	−1956.14	−	6020.37i	−0.513233	−	1.57957i
$245$	158.867	+	1511.52i	0.0414271	+	0.394153i
$246$	2679.40	+	1946.70i	0.694439	+	0.504540i
$247$	−491.692			−0.126662
$248$	145.957	+	40.4770i	0.0373720	+	0.0103641i
$249$	3326.17			0.846537
$250$	−4920.53	−	3574.98i	−1.24481	−	0.904405i
$251$	388.074	+	3692.28i	0.0975897	+	0.928504i	0.928308	+	0.371811i	$0.121263\pi$
$251$	388.074	+	3692.28i	0.0975897	+	0.928504i	−0.830719	+	0.556693i	$0.812070\pi$
$252$	19.4394	+	59.8285i	0.00485940	+	0.0149557i
$253$	4970.14	+	8608.53i	1.23506	+	2.13919i
$254$	1682.70	−	2914.52i	0.415676	−	0.719973i
$255$	−590.777	−	125.573i	−0.145082	−	0.0308381i
$256$	1193.99	−	3674.72i	0.291501	−	0.897149i
$257$	−3381.56	+	718.773i	−0.820762	+	0.174458i	−0.599109	−	0.800667i	$-0.704479\pi$
$257$	−3381.56	+	718.773i	−0.820762	+	0.174458i	−0.221653	+	0.975126i	$0.571145\pi$
$258$	411.615	−	3916.25i	0.0993256	−	0.945020i
$259$	3098.55	−	3441.29i	0.743377	−	0.825604i
$260$	1291.80	−	575.148i	0.308132	−	0.137189i
$261$	−65.3043	−	29.0754i	−0.0154875	−	0.00689548i
$262$	6335.14	+	7035.89i	1.49384	+	1.65908i
$263$	−4134.12	+	3003.61i	−0.969280	+	0.704223i	−0.955287	−	0.295679i	$-0.904454\pi$
$263$	−4134.12	+	3003.61i	−0.969280	+	0.704223i	−0.0139923	+	0.999902i	$0.504454\pi$
$264$	−195.923	+	142.346i	−0.0456750	+	0.0331848i
$265$	−893.384	−	992.203i	−0.207095	−	0.230002i
$266$	−2037.69	−	907.238i	−0.469695	−	0.209122i
$267$	2435.25	−	1084.24i	0.558182	−	0.248519i
$268$	4133.97	−	4591.24i	0.942247	−	1.04647i
$269$	495.683	−	4716.11i	0.112351	−	1.06895i	−0.782521	−	0.622624i	$-0.786067\pi$
$269$	495.683	−	4716.11i	0.112351	−	1.06895i	0.894872	−	0.446322i	$-0.147267\pi$
$270$	4716.34	−	1002.49i	1.06306	−	0.225961i
$271$	−489.061	+	1505.17i	−0.109625	+	0.337390i	−0.990788	−	0.135422i	$-0.956761\pi$
$271$	−489.061	+	1505.17i	−0.109625	+	0.337390i	0.881163	+	0.472812i	$0.156761\pi$
$272$	839.062	+	178.348i	0.187043	+	0.0397572i
$273$	1196.86	−	2073.02i	0.265337	−	0.459578i
$274$	2965.39	+	5136.21i	0.653818	+	1.13245i
$275$	876.110	+	2696.39i	0.192114	+	0.591267i
$276$	825.050	+	7849.83i	0.179936	+	1.71197i
$277$	4185.95	+	3041.27i	0.907975	+	0.659683i	0.940502	−	0.339788i	$-0.110355\pi$
$277$	4185.95	+	3041.27i	0.907975	+	0.659683i	−0.0325267	+	0.999471i	$0.510355\pi$
$278$	2942.35			0.634786
$279$	14.4770	+	55.9776i	0.00310650	+	0.0120118i
$280$	170.096			0.0363042
$281$	96.6295	+	70.2054i	0.0205140	+	0.0149043i	0.597995	−	0.801500i	$-0.295964\pi$
$281$	96.6295	+	70.2054i	0.0205140	+	0.0149043i	−0.577481	+	0.816404i	$0.695964\pi$
$282$	−1144.15	−	10885.9i	−0.241607	−	2.29874i
$283$	−284.801	−	876.527i	−0.0598221	−	0.184114i	0.916680	−	0.399623i	$-0.130859\pi$
$283$	−284.801	−	876.527i	−0.0598221	−	0.184114i	−0.976502	+	0.215509i	$0.930859\pi$
$284$	4670.92	+	8090.27i	0.975943	+	1.69038i
$285$	−530.830	+	919.424i	−0.110329	+	0.191095i
$286$	−4270.50	−	907.723i	−0.882937	−	0.187674i
$287$	−1124.61	+	3461.20i	−0.231302	+	0.711876i
$288$	−84.3898	+	17.9376i	−0.0172664	+	0.00367008i
$289$	493.673	−	4696.99i	0.100483	−	0.956033i
$290$	−4877.56	+	5417.08i	−0.987656	+	1.09690i
$291$	−2374.64	+	1057.26i	−0.478363	+	0.212981i
$292$	3630.49	+	1616.40i	0.727598	+	0.323947i
$293$	93.1636	+	103.469i	0.0185757	+	0.0206304i	0.752361	−	0.658751i	$-0.228915\pi$
$293$	93.1636	+	103.469i	0.0185757	+	0.0206304i	−0.733785	+	0.679381i	$0.762248\pi$
$294$	3014.48	−	2190.15i	0.597986	−	0.434462i
$295$	−3036.28	+	2205.99i	−0.599252	+	0.435382i
$296$	−118.993	−	132.155i	−0.0233659	−	0.0259505i
$297$	−6891.36	−	3068.23i	−1.34639	−	0.599450i
$298$	−1214.55	+	540.755i	−0.236098	+	0.105118i
$299$	−2524.74	+	2804.01i	−0.488326	+	0.542341i
$300$	−235.320	+	2238.92i	−0.0452873	+	0.430880i
$301$	4232.55	−	899.656i	0.810498	−	0.172277i
$302$	325.439	−	1001.60i	0.0620096	−	0.190846i
$303$	1178.05	+	250.402i	0.223357	+	0.0474759i
$304$	753.922	−	1305.83i	0.142238	−	0.246364i
$305$	−3266.92	−	5658.47i	−0.613322	−	1.06231i
$306$	−5.74838	−	17.6917i	−0.00107390	−	0.00330512i
$307$	−1030.25	−	9802.17i	−0.191529	−	1.82228i	−0.494387	−	0.869242i	$-0.664608\pi$
$307$	−1030.25	−	9802.17i	−0.191529	−	1.82228i	0.302858	−	0.953036i	$-0.402059\pi$
$308$	−8119.20	−	5898.94i	−1.50206	−	1.09131i
$309$	−8288.03			−1.52586
$310$	5884.95	+	359.924i	1.07820	+	0.0659429i
$311$	−5397.19			−0.984073			−0.492037	−	0.870575i	$-0.663747\pi$
$311$	−5397.19			−0.984073			−0.492037	+	0.870575i	$0.663747\pi$
$312$	−74.3689	−	54.0322i	−0.0134946	−	0.00980439i
$313$	51.7605	+	492.468i	0.00934721	+	0.0889327i	0.998201	−	0.0599576i	$-0.0190965\pi$
$313$	51.7605	+	492.468i	0.00934721	+	0.0889327i	−0.988854	+	0.148890i	$0.952430\pi$
$314$	−1800.81	−	5542.32i	−0.323648	−	0.996086i
$315$	32.4656	+	56.2321i	0.00580708	+	0.0100582i
$316$	−927.617	+	1606.68i	−0.165135	+	0.286022i
$317$	3614.26	+	768.235i	0.640370	+	0.136115i	0.516642	−	0.856201i	$-0.327182\pi$
$317$	3614.26	+	768.235i	0.640370	+	0.136115i	0.123728	+	0.992316i	$0.460515\pi$
$318$	−1011.50	+	3113.07i	−0.178371	+	0.548969i
$319$	11155.0	−	2371.07i	1.95787	−	0.416159i
$320$	−478.345	+	4551.14i	−0.0835634	+	0.795052i
$321$	−1149.78	+	1276.97i	−0.199921	+	0.222035i
$322$	−15636.9	+	6962.00i	−2.70624	+	1.20490i
$323$	305.328	+	135.941i	0.0525972	+	0.0234178i
$324$	−3958.31	−	4396.15i	−0.678723	−	0.753798i
$325$	−870.645	+	632.560i	−0.148599	+	0.107964i
$326$	6962.85	−	5058.81i	1.18294	−	0.859453i
$327$	−2180.67	−	2421.88i	−0.368782	−	0.409573i
$328$	127.677	+	56.8454i	0.0214932	+	0.00956940i
$329$	10988.1	−	4892.20i	1.84131	−	0.819804i
$330$	−6307.79	+	7005.51i	−1.05222	+	1.16861i
$331$	−799.203	+	7603.91i	−0.132713	+	1.26268i	0.702071	+	0.712107i	$0.252259\pi$
$331$	−799.203	+	7603.91i	−0.132713	+	1.26268i	−0.834784	+	0.550577i	$0.814408\pi$
$332$	5177.73	−	1100.56i	0.855918	−	0.181931i
$333$	20.9774	−	64.5618i	0.00345211	−	0.0106245i
$334$	−3399.49	−	722.585i	−0.556922	−	0.118377i
$335$	3188.44	−	5522.54i	0.520009	−	0.900682i
$336$	3670.33	+	6357.20i	0.595932	+	1.03218i
$337$	−1866.27	−	5743.79i	−0.301668	−	0.928439i	−0.980900	−	0.194515i	$-0.937687\pi$
$337$	−1866.27	−	5743.79i	−0.301668	−	0.928439i	0.679231	−	0.733924i	$-0.262313\pi$
$338$	751.603	+	7151.03i	0.120952	+	1.15078i
$339$	−2647.55	−	1923.55i	−0.424174	−	0.308180i
$340$	−961.190			−0.153317
$341$	−7117.61	−	5867.28i	−1.13032	−	0.931762i
$342$	−32.6986			−0.00517000
$343$	−3028.57	−	2200.39i	−0.476757	−	0.346384i
$344$	−17.3697	−	165.262i	−0.00272242	−	0.0259021i
$345$	2517.56	+	7748.26i	0.392872	+	1.20914i
$346$	−2605.62	−	4513.07i	−0.404853	−	0.701226i
$347$	440.627	−	763.189i	0.0681675	−	0.118070i	−0.829927	−	0.557872i	$-0.811618\pi$
$347$	440.627	−	763.189i	0.0681675	−	0.118070i	0.898095	+	0.439802i	$0.144951\pi$
$348$	8857.64	+	1882.75i	1.36442	+	0.290017i
$349$	−2381.97	+	7330.96i	−0.365341	+	1.12440i	0.584426	+	0.811447i	$0.301320\pi$
$349$	−2381.97	+	7330.96i	−0.365341	+	1.12440i	−0.949767	+	0.312957i	$0.898680\pi$
$350$	−4775.32	+	1015.03i	−0.729290	+	0.155015i
$351$	299.307	−	2847.71i	0.0455151	−	0.433047i
$352$	9209.81	−	10228.5i	1.39456	−	1.54881i
$353$	7392.43	−	3291.32i	1.11462	−	0.496259i	0.235025	−	0.971989i	$-0.424483\pi$
$353$	7392.43	−	3291.32i	1.11462	−	0.496259i	0.879591	+	0.475730i	$0.157816\pi$
$354$	8405.62	+	3742.42i	1.26202	+	0.561886i
$355$	6452.01	+	7165.68i	0.964612	+	1.07131i
$356$	3432.11	−	2493.57i	0.510959	−	0.371233i
$357$	−1316.35	+	956.387i	−0.195151	+	0.141785i
$358$	−2106.97	−	2340.03i	−0.311053	−	0.345459i
$359$	7568.92	+	3369.90i	1.11274	+	0.495422i	0.878973	−	0.476871i	$-0.158229\pi$
$359$	7568.92	+	3369.90i	1.11274	+	0.495422i	0.233763	+	0.972294i	$0.424896\pi$
$360$	2.27795	−	1.01421i	0.000333497	−	0.000148482i
$361$	−4196.46	+	4660.64i	−0.611818	+	0.679492i
$362$	−782.353	+	7443.59i	−0.113590	+	1.08074i
$363$	7703.12	−	1637.35i	1.11380	−	0.236745i
$364$	1177.19	−	3623.01i	0.169509	−	0.521696i
$365$	4012.28	+	852.837i	0.575377	+	0.122300i
$366$	−8009.28	+	13872.5i	−1.14386	+	1.98122i
$367$	−2000.43	−	3464.85i	−0.284528	−	0.492817i	0.687967	−	0.725742i	$-0.258503\pi$
$367$	−2000.43	−	3464.85i	−0.284528	−	0.492817i	−0.972495	+	0.232926i	$0.925170\pi$
$368$	−3575.62	−	11004.6i	−0.506500	−	1.55885i
$369$	5.57669	+	53.0586i	0.000786750	+	0.00748543i
$370$	−5600.24	−	4068.81i	−0.786872	−	0.571696i
$371$	−3596.86			−0.503341
$372$	−3268.17	−	6554.89i	−0.455502	−	0.913589i
$373$	−9456.86			−1.31275			−0.656377	−	0.754433i	$-0.727912\pi$
$373$	−9456.86			−1.31275			−0.656377	+	0.754433i	$0.727912\pi$
$374$	2400.90	+	1744.36i	0.331946	+	0.241173i
$375$	815.197	+	7756.08i	0.112258	+	1.06806i
$376$	−142.736	−	439.297i	−0.0195773	−	0.0602527i
$377$	2164.43	+	3748.90i	0.295686	+	0.512144i
$378$	6494.81	−	11249.3i	0.883749	−	1.53070i
$379$	8733.49	+	1856.36i	1.18367	+	0.251596i	0.757369	−	0.652988i	$-0.226485\pi$
$379$	8733.49	+	1856.36i	1.18367	+	0.251596i	0.426297	+	0.904583i	$0.359818\pi$
$380$	−522.105	+	1606.87i	−0.0704827	+	0.216924i
$381$	−4220.99	+	897.198i	−0.567579	+	0.120643i
$382$	−852.164	+	8107.80i	−0.114137	+	1.08595i
$383$	1772.86	−	1968.96i	0.236525	−	0.262688i	−0.613183	−	0.789941i	$-0.710111\pi$
$383$	1772.86	−	1968.96i	0.236525	−	0.262688i	0.849708	+	0.527253i	$0.176778\pi$
$384$	529.689	−	235.833i	0.0703921	−	0.0313406i
$385$	−9463.19	−	4213.29i	−1.25270	−	0.557737i
$386$	8090.58	+	8985.50i	1.06684	+	1.18484i
$387$	51.3188	−	37.2853i	0.00674078	−	0.00489746i
$388$	−3346.68	+	2431.51i	−0.437892	+	0.318147i
$389$	5553.01	+	6167.24i	0.723775	+	0.803834i	0.986969	−	0.160909i	$-0.0514426\pi$
$389$	5553.01	+	6167.24i	0.723775	+	0.803834i	−0.263194	+	0.964743i	$0.584776\pi$
$390$	−3268.92	−	1455.42i	−0.424431	−	0.188969i
$391$	2343.03	−	1043.19i	0.303049	−	0.134926i
$392$	105.213	−	116.851i	0.0135562	−	0.0150557i
$393$	1268.98	−	12073.5i	0.162879	−	1.54969i
$394$	−1613.52	+	342.964i	−0.206314	+	0.0438535i
$395$	−591.743	+	1821.20i	−0.0753768	+	0.231986i
$396$	−143.907	−	30.5883i	−0.0182616	−	0.00388162i
$397$	2393.38	−	4145.46i	0.302570	−	0.524067i	−0.674147	−	0.738597i	$-0.735489\pi$
$397$	2393.38	−	4145.46i	0.302570	−	0.524067i	0.976717	+	0.214530i	$0.0688219\pi$
$398$	−1007.95	−	1745.83i	−0.126945	−	0.219876i
$399$	883.820	+	2720.12i	0.110893	+	0.341294i
$400$	−344.970	−	3282.17i	−0.0431212	−	0.410271i
$401$	−8100.59	−	5885.42i	−1.00879	−	0.732928i	−0.0448339	−	0.998994i	$-0.514276\pi$
$401$	−8100.59	−	5885.42i	−1.00879	−	0.732928i	−0.963955	+	0.266067i	$0.914276\pi$
$402$	−15633.8			−1.93965
$403$	1283.24	−	3257.71i	0.158617	−	0.402676i
$404$	1916.68			0.236035
$405$	−4939.79	−	3588.97i	−0.606075	−	0.440339i
$406$	2052.69	+	19530.0i	0.250919	+	2.38734i
$407$	3346.61	+	10299.8i	0.407581	+	1.25441i
$408$	31.2426	+	54.1137i	0.00379102	+	0.00656624i
$409$	−1416.55	+	2453.54i	−0.171257	+	0.296625i	−0.938859	−	0.344301i	$-0.888116\pi$
$409$	−1416.55	+	2453.54i	−0.171257	+	0.296625i	0.767603	+	0.640926i	$0.221449\pi$
$410$	5321.40	+	1131.10i	0.640989	+	0.136246i
$411$	2350.00	−	7232.56i	0.282037	−	0.868020i
$412$	−12901.7	+	2742.34i	−1.54277	+	0.327925i
$413$	−1056.85	+	10055.3i	−0.125919	+	1.19804i
$414$	−167.901	+	186.473i	−0.0199321	+	0.0221368i
$415$	4991.34	−	2222.29i	0.590398	−	0.262862i
$416$	4772.84	+	2125.01i	0.562519	+	0.250450i
$417$	−2524.52	−	2803.76i	−0.296466	−	0.329259i
$418$	4220.28	−	3066.21i	0.493829	−	0.358788i
$419$	5398.27	−	3922.07i	0.629410	−	0.457293i	−0.226786	−	0.973945i	$-0.572822\pi$
$419$	5398.27	−	3922.07i	0.629410	−	0.457293i	0.856196	+	0.516652i	$0.172822\pi$
$420$	−5503.84	−	6112.63i	−0.639428	−	0.710157i
$421$	4516.91	+	2011.06i	0.522900	+	0.232810i	0.651174	−	0.758929i	$-0.274277\pi$
$421$	4516.91	+	2011.06i	0.522900	+	0.232810i	−0.128274	+	0.991739i	$0.540944\pi$
$422$	1519.47	−	676.514i	0.175277	−	0.0780383i
$423$	117.984	−	131.034i	0.0135616	−	0.0150617i
$424$	−14.4384	+	137.372i	−0.00165375	+	0.0157344i
$425$	715.534	−	152.091i	0.0816671	−	0.0173589i
$426$	7305.02	−	22482.5i	0.830820	−	2.55700i
$427$	−17217.5	−	3659.69i	−1.95132	−	0.414765i
$428$	−1367.31	+	2368.25i	−0.154419	+	0.267461i
$429$	2799.10	+	4848.18i	0.315015	+	0.545623i
$430$	−1998.85	−	6151.84i	−0.224170	−	0.689926i
$431$	932.671	+	8873.77i	0.104235	+	0.991727i	0.914204	+	0.405255i	$0.132817\pi$
$431$	932.671	+	8873.77i	0.104235	+	0.991727i	−0.809969	+	0.586473i	$0.800516\pi$
$432$	7103.99	+	5161.35i	0.791183	+	0.574828i
$433$	2178.39			0.241771			0.120886	−	0.992666i	$-0.461427\pi$
$433$	2178.39			0.241771			0.120886	+	0.992666i	$0.461427\pi$
$434$	11329.0	−	11133.0i	1.25301	−	1.23134i
$435$	9346.85			1.03022
$436$	−4195.93	−	3048.52i	−0.460891	−	0.334857i
$437$	−471.248	−	4483.62i	−0.0515855	−	0.490803i
$438$	−3107.60	−	9564.20i	−0.339011	−	1.04337i
$439$	−7933.89	−	13741.9i	−0.862560	−	1.49400i	−0.869450	−	0.494021i	$-0.835526\pi$
$439$	−7933.89	−	13741.9i	−0.862560	−	1.49400i	0.00688995	−	0.999976i	$-0.497807\pi$
$440$	−198.902	+	344.508i	−0.0215506	+	0.0373268i
$441$	58.7112	+	12.4795i	0.00633962	+	0.00134753i
$442$	−348.102	+	1071.35i	−0.0374605	+	0.115291i
$443$	−13660.6	+	2903.65i	−1.46509	+	0.311414i	−0.870322	−	0.492483i	$-0.836089\pi$
$443$	−13660.6	+	2903.65i	−1.46509	+	0.311414i	−0.594768	+	0.803898i	$0.702756\pi$
$444$	−898.887	+	8552.34i	−0.0960795	+	0.914136i
$445$	2929.99	−	3254.08i	0.312123	−	0.346648i
$446$	22948.9	−	10217.5i	2.43646	−	1.08478i
$447$	1557.37	+	693.384i	0.164789	+	0.0733690i
$448$	8249.23	+	9161.70i	0.869954	+	0.966182i
$449$	−8087.71	+	5876.07i	−0.850073	+	0.617614i	−0.925166	−	0.379562i	$-0.876075\pi$
$449$	−8087.71	+	5876.07i	−0.850073	+	0.617614i	0.0750933	+	0.997177i	$0.476075\pi$
$450$	−57.8998	+	42.0667i	−0.00606538	+	0.00440676i
$451$	−5695.17	−	6325.13i	−0.594623	−	0.660396i
$452$	−4757.80	−	2118.31i	−0.495107	−	0.220436i
$453$	−1233.65	+	549.255i	−0.127951	+	0.0569674i
$454$	−11620.2	+	12905.5i	−1.20124	+	1.33411i
$455$	411.007	−	3910.47i	0.0423479	−	0.402914i
$456$	107.435	−	22.8361i	0.0110332	−	0.00234517i
$457$	−2955.01	+	9094.59i	−0.302472	+	0.930913i	0.678137	+	0.734936i	$0.262788\pi$
$457$	−2955.01	+	9094.59i	−0.302472	+	0.930913i	−0.980609	+	0.195977i	$0.937212\pi$
$458$	−12902.6	−	2742.54i	−1.31638	−	0.279805i
$459$	−973.183	+	1685.60i	−0.0989636	+	0.171410i
$460$	6482.74	+	11228.4i	0.657085	+	1.13810i
$461$	4387.67	+	13503.9i	0.443284	+	1.36429i	0.884354	+	0.466816i	$0.154599\pi$
$461$	4387.67	+	13503.9i	0.443284	+	1.36429i	−0.441070	+	0.897473i	$0.645401\pi$
$462$	2654.59	+	25256.7i	0.267322	+	2.54340i
$463$	−5294.20	−	3846.46i	−0.531409	−	0.386091i	0.289475	−	0.957185i	$-0.406519\pi$
$463$	−5294.20	−	3846.46i	−0.531409	−	0.386091i	−0.820885	+	0.571094i	$0.806519\pi$
$464$	−13275.1			−1.32819
$465$	−4706.28	−	5916.57i	−0.469351	−	0.590053i
$466$	−14067.3			−1.39840
$467$	−2786.63	−	2024.61i	−0.276124	−	0.200616i	0.441101	−	0.897457i	$-0.354588\pi$
$467$	−2786.63	−	2024.61i	−0.276124	−	0.200616i	−0.717225	+	0.696842i	$0.754588\pi$
$468$	−5.83739	−	55.5390i	−0.000576567	−	0.00548567i
$469$	−5308.68	−	16338.4i	−0.522670	−	1.60861i
$470$	−8990.04	−	15571.2i	−0.882297	−	1.52818i
$471$	−3736.19	+	6471.26i	−0.365508	+	0.633079i
$472$	379.793	+	80.7274i	0.0370368	+	0.00787242i
$473$	−3127.20	+	9624.52i	−0.303993	+	0.935594i
$474$	4592.09	−	976.078i	0.444982	−	0.0945839i
$475$	134.409	−	1278.81i	0.0129833	−	0.123528i
$476$	−1732.67	+	1924.33i	−0.166842	+	0.185297i
$477$	−48.1698	+	21.4466i	−0.00462378	+	0.00205864i
$478$	23824.3	+	10607.3i	2.27970	+	1.01499i
$479$	5045.95	+	5604.10i	0.481327	+	0.534567i	0.934078	−	0.357069i	$-0.116224\pi$
$479$	5045.95	+	5604.10i	0.481327	+	0.534567i	−0.452751	+	0.891637i	$0.649557\pi$
$480$	9126.34	−	6630.68i	0.867831	−	0.630516i
$481$	−3325.74	+	2416.29i	−0.315261	+	0.229051i
$482$	2622.75	+	2912.85i	0.247848	+	0.275263i
$483$	20050.5	+	8927.04i	1.88888	+	0.840982i
$484$	11449.4	−	5097.60i	1.07526	−	0.478738i
$485$	−2857.06	+	3173.09i	−0.267490	+	0.297078i
$486$	39.5652	−	376.438i	0.00369283	−	0.0351349i
$487$	14960.9	−	3180.04i	1.39208	−	0.295896i	0.549964	−	0.835188i	$-0.314641\pi$
$487$	14960.9	−	3180.04i	1.39208	−	0.295896i	0.842119	+	0.539292i	$0.181308\pi$
$488$	−208.886	+	642.884i	−0.0193767	+	0.0596352i
$489$	−10794.6	−	2294.47i	−0.998261	−	0.212187i
$490$	3060.32	−	5300.63i	0.282145	−	0.488690i
$491$	−3515.46	−	6088.96i	−0.323117	−	0.559655i	0.658012	−	0.753007i	$-0.271397\pi$
$491$	−3515.46	−	6088.96i	−0.323117	−	0.559655i	−0.981129	+	0.193352i	$0.938064\pi$
$492$	−2088.46	−	6427.61i	−0.191372	−	0.588982i
$493$	−307.575	−	2926.38i	−0.0280983	−	0.267338i
$494$	1601.95	+	1163.88i	0.145901	+	0.106003i
$495$	−151.855			−0.0137886
$496$	6684.18	+	8403.13i	0.605098	+	0.760709i
$497$	25976.5			2.34448
$498$	−10836.8	−	7873.37i	−0.975115	−	0.708462i
$499$	320.621	+	3050.50i	0.0287634	+	0.273666i	0.999445	+	0.0332985i	$0.0106012\pi$
$499$	320.621	+	3050.50i	0.0287634	+	0.273666i	−0.970682	+	0.240367i	$0.922732\pi$
$500$	3835.31	+	11803.9i	0.343041	+	1.05577i
$501$	2228.20	+	3859.35i	0.198699	+	0.344158i
$502$	7475.62	−	12948.2i	0.664648	−	1.15120i
$503$	13832.0	+	2940.09i	1.22612	+	0.260620i	0.775069	−	0.631877i	$-0.217715\pi$
$503$	13832.0	+	2940.09i	1.22612	+	0.260620i	0.451053	+	0.892497i	$0.351048\pi$
$504$	2.07584	−	6.38877i	0.000183463	−	0.000564640i
$505$	1935.11	−	411.320i	0.170517	−	0.0362445i
$506$	4184.37	−	39811.7i	0.367625	−	3.49772i
$507$	6169.33	−	6851.74i	0.540414	−	0.600190i
$508$	−6273.79	+	2793.27i	−0.547942	+	0.243959i
$509$	397.558	+	177.004i	0.0346197	+	0.0154137i	0.423973	−	0.905675i	$-0.360635\pi$
$509$	397.558	+	177.004i	0.0346197	+	0.0154137i	−0.389354	+	0.921088i	$0.627302\pi$
$510$	1627.52	+	1807.55i	0.141310	+	0.156940i
$511$	8940.08	−	6495.35i	0.773945	−	0.562304i
$512$	−13315.2	+	9674.06i	−1.14932	+	0.835033i
$513$	2289.30	+	2542.52i	0.197027	+	0.218821i
$514$	12718.6	+	5662.70i	1.09143	+	0.485936i
$515$	−12437.2	+	5537.41i	−1.06418	+	0.473801i
$516$	−5376.89	+	5971.64i	−0.458729	+	0.509471i
$517$	−2940.36	+	27975.7i	−0.250129	+	2.37982i
$518$	−18241.1	+	3877.26i	−1.54723	+	0.328874i
$519$	−2064.89	+	6355.08i	−0.174641	+	0.537490i
$520$	−147.700	−	31.3946i	−0.0124559	−	0.00264759i
$521$	659.028	−	1141.47i	0.0554176	−	0.0959860i	−0.836986	−	0.547225i	$-0.815684\pi$
$521$	659.028	−	1141.47i	0.0554176	−	0.0959860i	0.892403	+	0.451239i	$0.149018\pi$
$522$	143.939	+	249.310i	0.0120691	+	0.0209042i
$523$	2854.72	+	8785.93i	0.238677	+	0.734573i	0.996612	+	0.0822430i	$0.0262084\pi$
$523$	2854.72	+	8785.93i	0.238677	+	0.734573i	−0.757935	+	0.652330i	$0.773792\pi$
$524$	−2019.50	−	19214.3i	−0.168363	−	1.60187i
$525$	5064.42	+	3679.51i	0.421008	+	0.305880i
$526$	20578.9			1.70586
$527$	−1697.53	+	1668.17i	−0.140314	+	0.137887i
$528$	−17167.6			−1.41501
$529$	−18145.5	−	13183.5i	−1.49137	−	1.08355i
$530$	562.030	+	5347.36i	0.0460623	+	0.438253i
$531$	45.8020	+	140.964i	0.00374320	+	0.0115204i
$532$	2275.84	+	3941.87i	0.185470	+	0.321244i
$533$	1615.37	−	2797.91i	0.131275	−	0.227375i
$534$	−10500.6	−	2231.97i	−0.850947	−	0.180874i
$535$	−872.229	+	2684.44i	−0.0704855	+	0.216932i
$536$	−645.313	+	137.165i	−0.0520024	+	0.0110534i
$537$	−422.042	+	4015.46i	−0.0339152	+	0.322681i
$538$	−12778.4	+	14191.9i	−1.02401	+	1.13728i
$539$	−8747.85	+	3894.79i	−0.699066	+	0.311244i
$540$	−8988.65	−	4002.00i	−0.716315	−	0.318924i
$541$	−14022.8	−	15573.8i	−1.11439	−	1.23766i	−0.968676	−	0.248330i	$-0.920118\pi$
$541$	−14022.8	−	15573.8i	−1.11439	−	1.23766i	−0.145715	−	0.989327i	$-0.546548\pi$
$542$	5156.27	−	3746.25i	0.408636	−	0.296891i
$543$	7764.25	−	5641.06i	0.613620	−	0.445821i
$544$	−2376.30	−	2639.15i	−0.187285	−	0.208001i
$545$	−4890.49	−	2177.39i	−0.384377	−	0.171136i
$546$	−8806.43	+	3920.88i	−0.690257	+	0.307322i
$547$	11091.9	−	12318.8i	0.867013	−	0.962915i	−0.132588	−	0.991171i	$-0.542329\pi$
$547$	11091.9	−	12318.8i	0.867013	−	0.962915i	0.999601	+	0.0282561i	$0.00899538\pi$
$548$	1265.06	−	12036.2i	0.0986143	−	0.938253i
$549$	−252.401	+	53.6494i	−0.0196215	+	0.00417068i
$550$	3528.22	−	10858.7i	0.273534	−	0.841852i
$551$	−5059.26	−	1075.38i	−0.391165	−	0.0831446i
$552$	421.430	−	729.938i	0.0324950	−	0.0562831i
$553$	2579.39	+	4467.64i	0.198349	+	0.343550i
$554$	−6438.96	−	19817.1i	−0.493800	−	1.51976i
$555$	927.806	+	8827.49i	0.0709607	+	0.675146i
$556$	−4857.54	−	3529.21i	−0.370513	−	0.269194i
$557$	−12015.4			−0.914019			−0.457009	−	0.889462i	$-0.651079\pi$
$557$	−12015.4			−0.914019			−0.457009	+	0.889462i	$0.651079\pi$
$558$	85.3382	−	216.645i	0.00647429	−	0.0164361i
$559$	−3841.32			−0.290645
$560$	9755.18	+	7087.55i	0.736128	+	0.534828i
$561$	−397.764	−	3784.47i	−0.0299351	−	0.284813i
$562$	−148.639	−	457.463i	−0.0111565	−	0.0343361i
$563$	3940.92	+	6825.87i	0.295009	+	0.510970i	0.974987	−	0.222262i	$-0.0713441\pi$
$563$	3940.92	+	6825.87i	0.295009	+	0.510970i	−0.679978	+	0.733232i	$0.738011\pi$
$564$	−11168.2	+	19343.9i	−0.833805	+	1.44419i
$565$	−5258.14	−	1117.65i	−0.391525	−	0.0832213i
$566$	−1146.93	+	3529.90i	−0.0851754	+	0.262143i
$567$	−16089.8	+	3420.00i	−1.19173	+	0.253310i
$568$	104.274	−	992.102i	0.00770289	−	0.0732881i
$569$	−12809.9	+	14226.8i	−0.943793	+	1.04819i	0.0549715	+	0.998488i	$0.482493\pi$
$569$	−12809.9	+	14226.8i	−0.943793	+	1.04819i	−0.998764	+	0.0497000i	$0.984173\pi$
$570$	3905.83	−	1738.99i	0.287012	−	0.127786i
$571$	1788.18	+	796.149i	0.131056	+	0.0583499i	0.471217	−	0.882017i	$-0.343815\pi$
$571$	1788.18	+	796.149i	0.131056	+	0.0583499i	−0.340161	+	0.940367i	$0.610482\pi$
$572$	5961.41	+	6620.82i	0.435768	+	0.483969i
$573$	8457.07	−	6144.42i	0.616578	−	0.447970i
$574$	11857.0	−	8614.63i	0.862200	−	0.626425i
$575$	−6602.61	−	7332.95i	−0.478866	−	0.531835i
$576$	165.103	+	73.5084i	0.0119432	+	0.00531745i
$577$	16132.5	−	7182.66i	1.16396	−	0.518229i	0.268461	−	0.963290i	$-0.413485\pi$
$577$	16132.5	−	7182.66i	1.16396	−	0.518229i	0.895500	+	0.445062i	$0.146818\pi$
$578$	−12726.6	+	14134.4i	−0.915845	+	1.01715i
$579$	1620.60	−	15419.0i	0.116321	−	1.10672i
$580$	14549.9	−	3092.68i	1.04164	−	0.221408i
$581$	4548.47	−	13998.8i	0.324789	−	0.999598i
$582$	10239.3	+	2176.42i	0.729263	+	0.155010i
$583$	4206.00	−	7285.00i	0.298790	−	0.517519i
$584$	−212.185	−	367.516i	−0.0150347	−	0.0260409i
$585$	−17.8122	−	54.8204i	−0.00125888	−	0.00387444i
$586$	−58.6094	−	557.632i	−0.00413163	−	0.0393098i
$587$	−5822.98	−	4230.64i	−0.409438	−	0.297474i	0.363936	−	0.931424i	$-0.381433\pi$
$587$	−5822.98	−	4230.64i	−0.409438	−	0.297474i	−0.773374	+	0.633950i	$0.781433\pi$
$588$	−7603.58			−0.533276
$589$	1866.69	+	3743.99i	0.130587	+	0.261916i
$590$	15114.1			1.05464
$591$	1711.20	+	1243.26i	0.119102	+	0.0865327i
$592$	−1317.74	−	12537.4i	−0.0914841	−	0.870413i
$593$	3293.67	+	10136.9i	0.228086	+	0.701975i	0.997964	+	0.0637843i	$0.0203170\pi$
$593$	3293.67	+	10136.9i	0.228086	+	0.701975i	−0.769878	+	0.638191i	$0.779683\pi$
$594$	15189.4	+	26308.9i	1.04921	+	1.81728i
$595$	−1336.37	+	2314.67i	−0.0920772	+	0.159482i
$596$	2653.72	+	564.066i	0.182384	+	0.0387668i
$597$	−798.780	+	2458.39i	−0.0547602	+	0.168535i
$598$	14863.0	−	3159.24i	1.01638	−	0.216038i
$599$	−1049.29	+	9983.30i	−0.0715738	+	0.680980i	0.898633	+	0.438701i	$0.144561\pi$
$599$	−1049.29	+	9983.30i	−0.0715738	+	0.680980i	−0.970207	+	0.242278i	$0.922105\pi$
$600$	160.859	−	178.651i	0.0109450	−	0.0121557i
$601$	−5419.16	+	2412.76i	−0.367807	+	0.163758i	−0.582313	−	0.812964i	$-0.697852\pi$
$601$	−5419.16	+	2412.76i	−0.367807	+	0.163758i	0.214506	+	0.976723i	$0.431186\pi$
$602$	−15919.3	−	7087.75i	−1.07778	−	0.479859i
$603$	−168.514	−	187.154i	−0.0113805	−	0.0126393i
$604$	−1738.64	+	1263.19i	−0.117126	+	0.0850970i
$605$	10465.6	−	7603.67i	0.703281	−	0.510964i
$606$	−3245.39	−	3604.37i	−0.217549	−	0.241613i
$607$	−3406.84	−	1516.82i	−0.227808	−	0.101427i	0.289659	−	0.957130i	$-0.406458\pi$
$607$	−3406.84	−	1516.82i	−0.227808	−	0.101427i	−0.517467	+	0.855703i	$0.673125\pi$
$608$	−5702.78	+	2539.04i	−0.380392	+	0.169361i
$609$	16848.9	−	18712.6i	1.12111	−	1.24511i
$610$	−2750.43	+	26168.6i	−0.182560	+	1.73694i
$611$	−10444.3	+	2220.00i	−0.691537	+	0.146991i
$612$	−11.7303	+	36.1021i	−0.000774786	+	0.00238455i
$613$	29096.5	+	6184.65i	1.91712	+	0.407497i	0.999960	+	0.00898661i	$0.00286057\pi$
$613$	29096.5	+	6184.65i	1.91712	+	0.407497i	0.917164	+	0.398511i	$0.130473\pi$
$614$	−19846.1	+	34374.4i	−1.30444	+	2.25935i
$615$	−3487.91	−	6041.24i	−0.228693	−	0.396108i
$616$	331.167	+	1019.23i	0.0216609	+	0.0666654i
$617$	−1845.68	−	17560.5i	−0.120428	−	1.14580i	−0.873147	−	0.487457i	$-0.837924\pi$
$617$	−1845.68	−	17560.5i	−0.120428	−	1.14580i	0.752718	−	0.658343i	$-0.228742\pi$
$618$	27002.7	+	19618.6i	1.75761	+	1.27698i
$619$	15519.3			1.00771			0.503855	−	0.863788i	$-0.331914\pi$
$619$	15519.3			1.00771			0.503855	+	0.863788i	$0.331914\pi$
$620$	−9283.76	−	7652.90i	−0.601363	−	0.495723i
$621$	26254.5			1.69655
$622$	17584.2	+	12775.7i	1.13354	+	0.823566i
$623$	−1233.07	−	11731.8i	−0.0792965	−	0.754456i
$624$	−2013.73	−	6197.61i	−0.129188	−	0.397601i
$625$	3089.64	+	5351.42i	0.197737	+	0.342491i
$626$	997.083	−	1727.00i	0.0636605	−	0.110263i
$627$	−6542.76	−	1390.71i	−0.416735	−	0.0885798i
$628$	−3674.78	+	11309.8i	−0.233503	+	0.718647i
$629$	2733.24	−	580.968i	0.173261	−	0.0368278i
$630$	27.3329	−	260.055i	0.00172852	−	0.0164458i
$631$	168.009	−	186.593i	0.0105996	−	0.0117720i	−0.737822	−	0.674996i	$-0.764145\pi$
$631$	168.009	−	186.593i	0.0105996	−	0.0117720i	0.748421	+	0.663224i	$0.230812\pi$
$632$	180.983	−	80.5790i	0.0113910	−	0.00507161i
$633$	−1948.35	−	867.461i	−0.122338	−	0.0544684i
$634$	−9956.89	−	11058.2i	−0.623720	−	0.692711i
$635$	−5734.68	+	4166.49i	−0.358384	+	0.260381i
$636$	5403.86	−	3926.13i	0.336913	−	0.244782i
$637$	−2432.14	−	2701.17i	−0.151279	−	0.168013i
$638$	−41956.0	−	18680.0i	−2.60353	−	1.15917i
$639$	347.882	−	154.887i	0.0215368	−	0.00958878i
$640$	637.300	−	707.793i	0.0393617	−	0.0437156i
$641$	−645.944	+	6145.75i	−0.0398023	+	0.378694i	0.956430	+	0.291963i	$0.0943085\pi$
$641$	−645.944	+	6145.75i	−0.0398023	+	0.378694i	−0.996232	+	0.0867303i	$0.972358\pi$
$642$	6768.73	−	1438.74i	0.416107	−	0.0884462i
$643$	−7734.08	+	23803.0i	−0.474342	+	1.45988i	0.372500	+	0.928032i	$0.378501\pi$
$643$	−7734.08	+	23803.0i	−0.474342	+	1.45988i	−0.846843	+	0.531844i	$0.821499\pi$
$644$	34165.6	+	7262.12i	2.09055	+	0.444360i
$645$	−4147.08	+	7182.95i	−0.253164	+	0.438494i
$646$	−672.982	−	1165.64i	−0.0409878	−	0.0709930i
$647$	−383.053	−	1178.92i	−0.0232757	−	0.0716352i	0.938744	−	0.344615i	$-0.111991\pi$
$647$	−383.053	−	1178.92i	−0.0232757	−	0.0716352i	−0.962020	+	0.272980i	$0.911991\pi$
$648$	66.0303	+	628.237i	0.00400296	+	0.0380856i
$649$	−19129.9	−	13898.7i	−1.15704	−	0.840636i
$650$	4333.92			0.261523
$651$	−20328.8	−	1243.31i	−1.22389	−	0.0748529i
$652$	−17562.8			−1.05493
$653$	9322.82	+	6773.42i	0.558698	+	0.405918i	0.830982	−	0.556299i	$-0.187779\pi$
$653$	9322.82	+	6773.42i	0.558698	+	0.405918i	−0.272284	+	0.962217i	$0.587779\pi$
$654$	1371.87	+	13052.4i	0.0820248	+	0.780414i
$655$	−6162.31	−	18965.6i	−0.367605	−	1.13137i
$656$	4953.77	+	8580.18i	0.294836	+	0.510671i
$657$	80.9981	−	140.293i	0.00480980	−	0.00833081i
$658$	−47379.7	−	10070.9i	−2.80707	−	0.596662i
$659$	−261.056	+	803.447i	−0.0154314	+	0.0474930i	−0.958476	−	0.285174i	$-0.907949\pi$
$659$	−261.056	+	803.447i	−0.0154314	+	0.0474930i	0.943044	+	0.332667i	$0.107949\pi$
$660$	18816.3	−	3999.53i	1.10973	−	0.235881i
$661$	1046.65	−	9958.18i	0.0615883	−	0.585974i	−0.919591	−	0.392876i	$-0.871480\pi$
$661$	1046.65	−	9958.18i	0.0615883	−	0.585974i	0.981180	−	0.193097i	$-0.0618533\pi$
$662$	20603.0	−	22882.0i	1.20961	−	1.34340i
$663$	1319.56	−	587.504i	0.0772961	−	0.0344144i
$664$	−516.387	−	229.910i	−0.0301803	−	0.0134371i
$665$	3143.65	+	3491.38i	0.183317	+	0.203594i
$666$	−221.169	+	160.689i	−0.0128681	+	0.00934919i
$667$	−32110.9	+	23329.9i	−1.86408	+	1.35433i
$668$	4745.53	+	5270.44i	0.274865	+	0.305269i
$669$	−29426.2	−	13101.4i	−1.70057	−	0.757144i
$670$	−23460.4	+	10445.2i	−1.35277	+	0.602291i
$671$	27545.5	−	30592.4i	1.58477	−	1.76007i
$672$	3176.65	−	30223.9i	0.182354	−	1.73499i
$673$	7449.86	−	1583.52i	0.426703	−	0.0906984i	0.0104456	−	0.999945i	$-0.496675\pi$
$673$	7449.86	−	1583.52i	0.426703	−	0.0906984i	0.416257	+	0.909247i	$0.363342\pi$
$674$	−7515.74	+	23131.1i	−0.429518	+	1.32192i
$675$	7324.63	+	1556.90i	0.417667	+	0.0887778i
$676$	7336.48	−	12707.2i	0.417415	−	0.722984i
$677$	−9108.30	−	15776.0i	−0.517076	−	0.895602i	−0.999803	−	0.0198311i	$-0.993687\pi$
$677$	−9108.30	−	15776.0i	−0.517076	−	0.895602i	0.482727	−	0.875771i	$-0.339646\pi$
$678$	4072.54	+	12534.0i	0.230686	+	0.709978i
$679$	1202.38	+	11439.8i	0.0679572	+	0.646569i
$680$	83.0380	+	60.3306i	0.00468288	+	0.00340231i
$681$	22267.7			1.25301
$682$	9300.98	+	35963.8i	0.522218	+	2.01925i
$683$	−21572.4			−1.20856			−0.604279	−	0.796773i	$-0.706539\pi$
$683$	−21572.4			−1.20856			−0.604279	+	0.796773i	$0.706539\pi$
$684$	53.9822	+	39.2204i	0.00301763	+	0.00219244i
$685$	−1305.76	−	12423.5i	−0.0728328	−	0.692958i
$686$	4658.65	+	14337.8i	0.259283	+	0.797991i
$687$	8457.03	+	14648.0i	0.469659	+	0.813473i
$688$	5889.97	−	10201.7i	0.326385	−	0.565316i
$689$	3123.28	+	663.873i	0.172696	+	0.0367076i
$690$	10138.6	−	31203.4i	0.559376	−	1.72158i
$691$	5165.08	−	1097.87i	0.284355	−	0.0604415i	−0.0635263	−	0.997980i	$-0.520235\pi$
$691$	5165.08	−	1097.87i	0.284355	−	0.0604415i	0.347881	+	0.937539i	$0.386901\pi$
$692$	−1111.58	+	10576.0i	−0.0610634	+	0.580979i
$693$	−273.739	+	304.017i	−0.0150050	+	0.0166647i
$694$	−3242.12	+	1443.48i	−0.177333	+	0.0789538i
$695$	−5661.62	−	2520.72i	−0.309004	−	0.137577i
$696$	−647.044	−	718.615i	−0.0352387	−	0.0391366i
$697$	−1776.66	+	1290.82i	−0.0965504	+	0.0701480i
$698$	25113.6	−	18246.1i	1.36184	−	0.989435i
$699$	12069.7	+	13404.7i	0.653101	+	0.725342i
$700$	9101.07	+	4052.06i	0.491411	+	0.218790i
$701$	8823.40	−	3928.43i	0.475400	−	0.211661i	−0.155027	−	0.987910i	$-0.549547\pi$
$701$	8823.40	−	3928.43i	0.475400	−	0.211661i	0.630427	+	0.776249i	$0.282880\pi$
$702$	−7715.96	+	8569.45i	−0.414844	+	0.460731i
$703$	513.422	−	4884.88i	0.0275449	−	0.262072i
$704$	−28202.2	+	5994.55i	−1.50981	+	0.320921i
$705$	−7124.39	+	21926.6i	−0.380596	+	1.17135i
$706$	−31875.6	−	6775.38i	−1.69923	−	0.361182i
$707$	2664.81	−	4615.59i	0.141755	−	0.245527i
$708$	−9388.01	−	16260.5i	−0.498337	−	0.863146i
$709$	−544.500	−	1675.80i	−0.0288422	−	0.0887672i	0.935599	−	0.353064i	$-0.114860\pi$
$709$	−544.500	−	1675.80i	−0.0288422	−	0.0887672i	−0.964441	+	0.264297i	$0.914860\pi$
$710$	−4058.97	−	38618.5i	−0.214550	−	2.04131i
$711$	61.1823	+	44.4515i	0.00322717	+	0.00234467i
$712$	−453.015			−0.0238448
$713$	30936.2	+	8579.29i	1.62492	+	0.450627i
$714$	6552.58			0.343451
$715$	7439.57	+	5405.16i	0.389125	+	0.282716i
$716$	671.654	+	6390.37i	0.0350571	+	0.333546i
$717$	−10333.5	−	31803.1i	−0.538229	−	1.65650i
$718$	−16682.9	−	28895.6i	−0.867131	−	1.50191i
$719$	−11068.5	+	19171.2i	−0.574110	+	0.994388i	0.422028	+	0.906583i	$0.361318\pi$
$719$	−11068.5	+	19171.2i	−0.574110	+	0.994388i	−0.996138	+	0.0878047i	$0.972015\pi$
$720$	172.903	+	36.7517i	0.00894962	+	0.00190230i
$721$	−11333.7	+	34881.6i	−0.585423	+	1.80175i
$722$	24704.4	−	5251.08i	1.27341	−	0.270671i
$723$	525.356	−	4998.42i	0.0270238	−	0.257114i
$724$	10219.8	−	11350.3i	0.524608	−	0.582637i
$725$	−10342.0	+	4604.54i	−0.529780	+	0.235873i
$726$	−28972.7	−	12899.5i	−1.48110	−	0.659429i
$727$	13720.4	+	15238.0i	0.699944	+	0.777367i	0.983367	−	0.181628i	$-0.0581366\pi$
$727$	13720.4	+	15238.0i	0.699944	+	0.777367i	−0.283423	+	0.958995i	$0.591470\pi$
$728$	−329.102	+	239.106i	−0.0167546	+	0.0121729i
$729$	−16116.5	+	11709.3i	−0.818804	+	0.594896i
$730$	−11053.4	−	12276.0i	−0.560417	−	0.622406i
$731$	2385.35	+	1062.03i	0.120692	+	0.0537353i
$732$	29861.9	−	13295.4i	1.50783	−	0.671327i
$733$	−2509.45	+	2787.03i	−0.126451	+	0.140438i	−0.803046	−	0.595918i	$-0.796788\pi$
$733$	−2509.45	+	2787.03i	−0.126451	+	0.140438i	0.676594	+	0.736356i	$0.263455\pi$
$734$	−1684.17	+	16023.8i	−0.0846919	+	0.805789i
$735$	−7676.70	+	1631.73i	−0.385251	+	0.0818876i
$736$	−14803.0	+	45559.1i	−0.741369	+	2.28170i
$737$	39299.2	+	8353.31i	1.96419	+	0.417501i
$738$	107.426	−	186.067i	0.00535827	−	0.00928080i
$739$	−4173.16	−	7228.13i	−0.207730	−	0.359798i	0.743269	−	0.668992i	$-0.233274\pi$
$739$	−4173.16	−	7228.13i	−0.207730	−	0.359798i	−0.950999	+	0.309194i	$0.899941\pi$
$740$	4365.11	+	13434.4i	0.216844	+	0.667378i
$741$	−265.399	−	2525.10i	−0.0131574	−	0.125185i
$742$	11718.7	+	8514.12i	0.579793	+	0.421244i
$743$	−27848.8			−1.37507			−0.687533	−	0.726153i	$-0.741306\pi$
$743$	−27848.8			−1.37507			−0.687533	+	0.726153i	$0.741306\pi$
$744$	−129.088	+	771.414i	−0.00636103	+	0.0380126i
$745$	2800.29			0.137711
$746$	30810.7	+	22385.3i	1.51215	+	1.09864i
$747$	−22.5548	−	214.595i	−0.00110474	−	0.0105109i
$748$	−1871.39	−	5759.53i	−0.0914768	−	0.281537i
$749$	3802.02	+	6585.29i	0.185478	+	0.321257i
$750$	15703.5	−	27199.2i	0.764546	−	1.32423i
$751$	20024.1	+	4256.25i	0.972955	+	0.206808i	0.666852	−	0.745190i	$-0.267641\pi$
$751$	20024.1	+	4256.25i	0.972955	+	0.206808i	0.306103	+	0.951998i	$0.400975\pi$
$752$	10118.6	−	31141.7i	0.490672	−	1.51013i
$753$	−18752.3	+	3985.93i	−0.907534	+	0.192902i
$754$	1822.24	−	17337.4i	0.0880133	−	0.837391i
$755$	−1484.27	+	1648.45i	−0.0715473	+	0.0794614i
$756$	−24215.4	+	10781.4i	−1.16495	+	0.518670i
$757$	12156.8	+	5412.55i	0.583680	+	0.259871i	0.677264	−	0.735740i	$-0.263166\pi$
$757$	12156.8	+	5412.55i	0.583680	+	0.259871i	−0.0935839	+	0.995611i	$0.529832\pi$
$758$	−24059.8	−	26721.1i	−1.15289	−	1.28041i
$759$	−41526.7	+	30170.9i	−1.98593	+	1.44286i
$760$	145.963	−	106.048i	0.00696663	−	0.00506155i
$761$	650.754	+	722.736i	0.0309985	+	0.0344273i	0.758445	−	0.651737i	$-0.225960\pi$
$761$	650.754	+	722.736i	0.0309985	+	0.0344273i	−0.727446	+	0.686165i	$0.759293\pi$
$762$	15875.9	+	7068.38i	0.754752	+	0.336037i
$763$	−13174.9	+	5865.86i	−0.625118	+	0.278320i
$764$	11131.8	−	12363.1i	0.527137	−	0.585445i
$765$	−4.09556	+	38.9666i	−0.000193562	+	0.00184162i
$766$	−10436.8	+	2218.40i	−0.492292	+	0.104640i
$767$	2773.61	−	8536.30i	0.130573	−	0.401862i
$768$	19516.1	+	4148.28i	0.916962	+	0.194906i
$769$	16040.1	−	27782.3i	0.752174	−	1.30280i	−0.194592	−	0.980884i	$-0.562338\pi$
$769$	16040.1	−	27782.3i	0.752174	−	1.30280i	0.946767	−	0.321920i	$-0.104328\pi$
$770$	20858.1	+	36127.3i	0.976200	+	1.69083i
$771$	−5516.53	−	16978.1i	−0.257682	−	0.793064i
$772$	−2579.09	−	24538.4i	−0.120238	−	1.14399i
$773$	10019.4	+	7279.55i	0.466202	+	0.338716i	0.795959	−	0.605350i	$-0.206967\pi$
$773$	10019.4	+	7279.55i	0.466202	+	0.338716i	−0.329757	+	0.944066i	$0.606967\pi$
$774$	−255.456			−0.0118633
$775$	8122.01	+	4228.02i	0.376453	+	0.195968i
$776$	441.740			0.0204350
$777$	19345.4	+	14055.2i	0.893193	+	0.648942i
$778$	−3493.41	−	33237.5i	−0.160983	−	1.53165i
$779$	1192.87	+	3671.29i	0.0548641	+	0.168854i
$780$	3650.96	+	6323.65i	0.167597	+	0.290286i
$781$	−30375.7	+	52612.2i	−1.39171	+	2.41051i
$782$	−10103.0	−	2147.46i	−0.461998	−	0.0982007i
$783$	9307.94	−	28646.9i	0.424826	−	1.30748i
$784$	10903.0	−	2317.50i	0.496674	−	0.105571i
$785$	−1283.03	+	12207.2i	−0.0583352	+	0.555023i
$786$	−32713.5	+	36332.0i	−1.48454	+	1.64875i
$787$	14931.2	−	6647.81i	0.676291	−	0.301104i	−0.0397021	−	0.999212i	$-0.512641\pi$
$787$	14931.2	−	6647.81i	0.676291	−	0.301104i	0.715993	+	0.698107i	$0.245974\pi$
$788$	3075.13	+	1369.14i	0.139019	+	0.0618953i
$789$	−17656.6	−	19609.6i	−0.796694	−	0.884818i
$790$	6238.87	−	4532.80i	0.280973	−	0.204139i
$791$	−11716.1	+	8512.23i	−0.526644	+	0.382629i
$792$	10.5123	+	11.6751i	0.000471639	+	0.000523808i
$793$	14275.0	+	6355.66i	0.639246	+	0.284611i
$794$	−17610.4	+	7840.66i	−0.787116	+	0.350447i
$795$	4613.27	−	5123.56i	0.205806	−	0.228571i
$796$	−430.001	+	4091.19i	−0.0191470	+	0.182171i
$797$	−4507.38	+	958.073i	−0.200326	+	0.0425805i	−0.306982	−	0.951715i	$-0.599319\pi$
$797$	−4507.38	+	958.073i	−0.200326	+	0.0425805i	0.106656	+	0.994296i	$0.465986\pi$
$798$	3559.27	−	10954.3i	0.157891	−	0.485938i
$799$	7099.38	+	1509.02i	0.314340	+	0.0668151i
$800$	−6831.50	+	11832.5i	−0.301913	+	0.522928i
$801$	−86.4654	−	149.763i	−0.00381412	−	0.00660624i
$802$	12460.6	+	38349.8i	0.548627	+	1.68850i
$803$	2701.43	+	25702.4i	0.118719	+	1.12954i
$804$	25809.8	+	18751.9i	1.13214	+	0.822549i
$805$	36052.6			1.57849
$806$	−11892.2	+	7576.18i	−0.519706	+	0.331091i
$807$	24487.3			1.06815
$808$	−165.583	−	120.303i	−0.00720940	−	0.00523793i
$809$	−134.198	−	1276.81i	−0.00583207	−	0.0554884i	0.991219	−	0.132232i	$-0.0422144\pi$
$809$	−134.198	−	1276.81i	−0.00583207	−	0.0554884i	−0.997051	+	0.0767436i	$0.975548\pi$
$810$	7598.55	+	23385.9i	0.329612	+	1.01444i
$811$	−18405.5	−	31879.3i	−0.796923	−	1.38031i	−0.921611	−	0.388115i	$-0.873126\pi$
$811$	−18405.5	−	31879.3i	−0.796923	−	1.38031i	0.124688	−	0.992196i	$-0.460207\pi$
$812$	20036.5	−	34704.3i	0.865940	−	1.49985i
$813$	−7993.84	−	1699.14i	−0.344842	−	0.0732984i
$814$	13477.3	−	41478.9i	0.580319	−	1.78604i
$815$	−17731.7	+	3768.98i	−0.762103	+	0.161990i
$816$	−463.015	+	4405.29i	−0.0198637	+	0.188990i
$817$	3071.14	−	3410.85i	0.131512	−	0.146059i
$818$	10422.9	−	4640.59i	0.445513	−	0.198355i
$819$	−141.861	−	63.1605i	−0.00605252	−	0.00269476i
$820$	−7428.42	−	8250.10i	−0.316356	−	0.351349i
$821$	18361.4	−	13340.4i	0.780534	−	0.567091i	−0.124605	−	0.992206i	$-0.539766\pi$
$821$	18361.4	−	13340.4i	0.780534	−	0.567091i	0.905139	+	0.425115i	$0.139766\pi$
$822$	−24776.6	+	18001.2i	−1.05132	+	0.763826i
$823$	−8256.92	−	9170.24i	−0.349718	−	0.388401i	0.542462	−	0.840080i	$-0.317492\pi$
$823$	−8256.92	−	9170.24i	−0.349718	−	0.388401i	−0.892181	+	0.451679i	$0.850825\pi$
$824$	1286.71	+	572.881i	0.0543990	+	0.0242200i
$825$	−13374.5	+	5954.71i	−0.564412	+	0.251292i
$826$	27245.1	−	30258.8i	1.14768	−	1.27462i
$827$	4398.48	−	41848.7i	0.184946	−	1.75964i	−0.371198	−	0.928554i	$-0.621053\pi$
$827$	4398.48	−	41848.7i	0.184946	−	1.75964i	0.556143	−	0.831086i	$-0.312281\pi$
$828$	500.853	−	106.460i	0.0210215	−	0.00446827i
$829$	10211.6	−	31428.0i	0.427820	−	1.31670i	−0.472447	−	0.881359i	$-0.656629\pi$
$829$	10211.6	−	31428.0i	0.427820	−	1.31670i	0.900268	−	0.435337i	$-0.143371\pi$
$830$	−21522.3	−	4574.71i	−0.900061	−	0.191314i
$831$	−13359.1	+	23138.6i	−0.557668	+	0.965909i
$832$	−5472.11	−	9477.98i	−0.228019	−	0.394940i
$833$	763.490	+	2349.78i	0.0317567	+	0.0977372i
$834$	1588.18	+	15110.5i	0.0659403	+	0.627380i
$835$	5922.20	+	4302.73i	0.245445	+	0.178326i
$836$	−10645.0			−0.440390
$837$	−22820.2	+	8532.19i	−0.942391	+	0.352348i
$838$	−26871.6			−1.10772
$839$	−11244.9	−	8169.92i	−0.462715	−	0.336182i	0.331880	−	0.943322i	$-0.392317\pi$
$839$	−11244.9	−	8169.92i	−0.462715	−	0.336182i	−0.794595	+	0.607139i	$0.792317\pi$
$840$	91.8119	+	873.532i	0.00377121	+	0.0358806i
$841$	6535.03	+	20112.8i	0.267950	+	0.824665i
$842$	−9955.86	−	17244.1i	−0.407484	−	0.705783i
$843$	−308.385	+	534.138i	−0.0125994	+	0.0218229i
$844$	−3319.95	−	705.677i	−0.135400	−	0.0287801i
$845$	4680.07	−	14403.8i	0.190532	−	0.586396i
$846$	−694.566	+	147.635i	−0.0282266	+	0.00599974i
$847$	3642.80	−	34658.9i	0.147778	−	1.40602i
$848$	−6552.09	+	7276.83i	−0.265330	+	0.294679i
$849$	4347.70	−	1935.72i	0.175751	−	0.0782495i
$850$	−2691.25	−	1198.22i	−0.108599	−	0.0483513i
$851$	−25221.1	−	28010.8i	−1.01594	−	1.12832i
$852$	−39026.6	+	28354.5i	−1.56928	+	1.14015i
$853$	5015.96	−	3644.31i	0.201340	−	0.146282i	−0.482547	−	0.875870i	$-0.660288\pi$
$853$	5015.96	−	3644.31i	0.201340	−	0.146282i	0.683887	+	0.729588i	$0.260288\pi$
$854$	47432.2	+	52678.8i	1.90058	+	2.11081i
$855$	62.9181	+	28.0129i	0.00251667	+	0.00112049i
$856$	266.769	−	118.773i	0.0106519	−	0.00474251i
$857$	−3697.40	+	4106.38i	−0.147376	+	0.163677i	−0.812313	−	0.583222i	$-0.801792\pi$
$857$	−3697.40	+	4106.38i	−0.147376	+	0.163677i	0.664937	+	0.746899i	$0.268458\pi$
$858$	2356.57	−	22421.2i	0.0937667	−	0.892131i
$859$	−17918.9	+	3808.78i	−0.711741	+	0.151285i	−0.549534	−	0.835472i	$-0.685195\pi$
$859$	−17918.9	+	3808.78i	−0.711741	+	0.151285i	−0.162207	+	0.986757i	$0.551861\pi$
$860$	−4078.92	+	12553.6i	−0.161732	+	0.497761i
$861$	−18382.1	−	3907.24i	−0.727597	−	0.154656i
$862$	17966.4	−	31118.7i	0.709905	−	1.22959i
$863$	8729.60	+	15120.1i	0.344333	+	0.596402i	0.985232	−	0.171223i	$-0.0547719\pi$
$863$	8729.60	+	15120.1i	0.344333	+	0.596402i	−0.640900	+	0.767625i	$0.721439\pi$
$864$	−11233.8	−	34574.1i	−0.442340	−	1.36138i
$865$	1147.34	+	10916.2i	0.0450991	+	0.429089i
$866$	−7097.27	−	5156.47i	−0.278493	−	0.202337i
$867$	24388.0			0.955317
$868$	−32056.5	+	4790.96i	−1.25354	+	0.187345i
$869$	−12064.9			−0.470969
$870$	−30452.3	−	22124.9i	−1.18670	−	0.862189i
$871$	1594.12	+	15167.1i	0.0620146	+	0.590030i
$872$	171.144	+	526.728i	0.00664642	+	0.0204556i
$873$	84.3134	+	146.035i	0.00326870	+	0.00566156i
$874$	−9077.84	+	15723.3i	−0.351330	+	0.608521i
$875$	33757.5	+	7175.39i	1.30424	+	0.277226i
$876$	−6341.45	+	19517.0i	−0.244586	+	0.752760i
$877$	−9860.15	+	2095.84i	−0.379650	+	0.0806972i	−0.393784	−	0.919203i	$-0.628834\pi$
$877$	−9860.15	+	2095.84i	−0.379650	+	0.0806972i	0.0141337	+	0.999900i	$0.495501\pi$
$878$	−6679.56	+	63551.8i	−0.256748	+	2.44279i
$879$	−481.080	+	534.294i	−0.0184601	+	0.0205020i
$880$	−25762.2	+	11470.1i	−0.986868	+	0.439382i
$881$	−1747.43	−	778.007i	−0.0668246	−	0.0297522i	0.373052	−	0.927810i	$-0.378311\pi$
$881$	−1747.43	−	778.007i	−0.0668246	−	0.0297522i	−0.439877	+	0.898058i	$0.644978\pi$
$882$	−161.743	−	179.634i	−0.00617479	−	0.00685780i
$883$	−4953.54	+	3598.96i	−0.188788	+	0.137163i	−0.678165	−	0.734910i	$-0.737224\pi$
$883$	−4953.54	+	3598.96i	−0.188788	+	0.137163i	0.489377	+	0.872073i	$0.337224\pi$
$884$	1859.71	−	1351.16i	0.0707567	−	0.0514077i
$885$	−12967.8	−	14402.2i	−0.492551	−	0.547034i
$886$	51379.9	+	22875.8i	1.94824	+	0.867412i
$887$	−16523.0	+	7356.53i	−0.625467	+	0.278476i	−0.694895	−	0.719111i	$-0.744549\pi$
$887$	−16523.0	+	7356.53i	−0.625467	+	0.278476i	0.0694282	+	0.997587i	$0.477883\pi$
$888$	614.457	−	682.423i	0.0232205	−	0.0257890i
$889$	−1996.10	+	18991.6i	−0.0753061	+	0.716489i
$890$	−17248.7	+	3666.33i	−0.649639	+	0.138085i
$891$	11887.9	−	36587.2i	0.446980	−	1.37566i
$892$	−50141.7	−	10658.0i	−1.88214	−	0.400061i
$893$	6379.00	−	11048.7i	0.239042	−	0.414034i
$894$	−3432.64	−	5945.50i	−0.128417	−	0.222424i
$895$	2049.49	+	6307.68i	0.0765440	+	0.235578i
$896$	−268.203	−	2551.78i	−0.0100000	−	0.0951441i
$897$	−15762.8	−	11452.4i	−0.586740	−	0.426292i
$898$	40259.2			1.49607
$899$	20328.8	−	30713.6i	0.754175	−	1.13944i
$900$	146.044			0.00540903
$901$	−1755.93	−	1275.76i	−0.0649261	−	0.0471716i
$902$	3582.84	+	34088.5i	0.132257	+	1.25834i
$903$	6904.80	+	21250.8i	0.254460	+	0.783147i
$904$	278.071	+	481.633i	0.0102307	+	0.0177200i
$905$	7882.32	−	13652.6i	0.289522	−	0.501467i
$906$	5319.40	+	1130.67i	0.195061	+	0.0414615i
$907$	2750.71	−	8465.81i	0.100701	−	0.309926i	−0.887996	−	0.459850i	$-0.847903\pi$
$907$	2750.71	−	8465.81i	0.100701	−	0.309926i	0.988697	+	0.149925i	$0.0479031\pi$
$908$	34663.3	−	7367.90i	1.26689	−	0.269287i
$909$	8.16681	−	77.7020i	0.000297994	−	0.00283522i
$910$	−10595.5	+	11767.5i	−0.385977	+	0.428671i
$911$	21881.1	−	9742.09i	0.795777	−	0.354303i	0.0317574	−	0.999496i	$-0.489890\pi$
$911$	21881.1	−	9742.09i	0.795777	−	0.354303i	0.764020	+	0.645193i	$0.223223\pi$
$912$	7113.07	+	3166.94i	0.258265	+	0.114987i
$913$	23034.0	+	25581.9i	0.834956	+	0.927312i
$914$	31155.3	−	22635.7i	1.12749	−	0.819169i
$915$	27295.9	−	19831.6i	0.986201	−	0.716517i
$916$	18011.5	+	20003.8i	0.649689	+	0.721553i
$917$	−49078.1	−	21851.0i	−1.76739	−	0.786895i
$918$	7160.64	−	3188.12i	0.257447	−	0.114623i
$919$	−32364.6	+	35944.5i	−1.16171	+	1.29021i	−0.211929	+	0.977285i	$0.567974\pi$
$919$	−32364.6	+	35944.5i	−1.16171	+	1.29021i	−0.949779	+	0.312922i	$0.898692\pi$
$920$	144.721	−	1376.93i	0.00518622	−	0.0493436i
$921$	49783.2	−	10581.7i	1.78112	−	0.378589i
$922$	17669.8	−	54382.0i	0.631153	−	1.94249i
$923$	−22556.3	−	4794.48i	−0.804387	−	0.170978i
$924$	25911.7	−	44880.4i	0.922547	−	1.59790i
$925$	−5375.26	−	9310.23i	−0.191068	−	0.330939i
$926$	8143.72	+	25063.8i	0.289006	+	0.889468i
$927$	56.2012	+	534.719i	0.00199125	+	0.0189455i
$928$	44462.5	+	32303.9i	1.57279	+	1.14270i
$929$	50830.5			1.79515			0.897574	−	0.440863i	$-0.145328\pi$
$929$	50830.5			1.79515			0.897574	+	0.440863i	$0.145328\pi$
$930$	1328.09	+	30416.6i	0.0468279	+	1.07247i
$931$	4342.97			0.152884
$932$	23223.8	+	16873.1i	0.816224	+	0.593021i
$933$	−2913.22	−	27717.4i	−0.102224	−	0.972592i
$934$	4286.49	+	13192.5i	0.150169	+	0.462174i
$935$	−3125.38	−	5413.32i	−0.109316	−	0.189342i
$936$	−2.98170	+	5.16445i	−0.000104124	+	0.000180348i
$937$	−53802.7	−	11436.1i	−1.87583	−	0.398721i	−0.878903	−	0.477001i	$-0.841724\pi$
$937$	−53802.7	−	11436.1i	−1.87583	−	0.398721i	−0.996931	+	0.0782797i	$0.975057\pi$
$938$	−21378.8	+	65797.3i	−0.744183	+	2.29036i
$939$	−2501.15	+	531.635i	−0.0869242	+	0.0184763i
$940$	−3835.22	+	36489.7i	−0.133076	+	1.26613i
$941$	6497.53	−	7216.24i	0.225094	−	0.249992i	−0.620010	−	0.784594i	$-0.712872\pi$
$941$	6497.53	−	7216.24i	0.225094	−	0.249992i	0.845104	+	0.534602i	$0.179538\pi$
$942$	27490.7	−	12239.7i	0.950845	−	0.423343i
$943$	27061.7	+	12048.6i	0.934517	+	0.416074i
$944$	18417.8	+	20455.0i	0.635008	+	0.705248i
$945$	−22134.5	+	16081.7i	−0.761943	+	0.553584i
$946$	32970.7	−	23954.6i	1.13316	−	0.823289i
$947$	16778.3	+	18634.2i	0.575735	+	0.639418i	0.958725	−	0.284334i	$-0.0917725\pi$
$947$	16778.3	+	18634.2i	0.575735	+	0.639418i	−0.382991	+	0.923752i	$0.625106\pi$
$948$	−8751.85	−	3896.57i	−0.299838	−	0.133497i
$949$	−8961.82	+	3990.06i	−0.306547	+	0.136483i
$950$	−3464.98	+	3848.25i	−0.118336	+	0.131425i
$951$	−1994.44	+	18975.8i	−0.0680064	+	0.647038i
$952$	270.470	−	57.4903i	0.00920798	−	0.00195722i
$953$	9475.44	−	29162.4i	0.322077	−	0.991252i	−0.650666	−	0.759364i	$-0.725510\pi$
$953$	9475.44	−	29162.4i	0.322077	−	0.991252i	0.972743	−	0.231887i	$-0.0744900\pi$
$954$	207.705	+	44.1490i	0.00704894	+	0.00149830i
$955$	8585.68	−	14870.8i	0.290917	−	0.503883i
$956$	−26608.7	−	46087.7i	−0.900196	−	1.55919i
$957$	18197.8	+	56007.1i	0.614683	+	1.89180i
$958$	−3174.42	−	30202.6i	−0.107057	−	1.01858i
$959$	−27225.9	−	19780.8i	−0.916757	−	0.666063i
$960$	−23630.7			−0.794457
$961$	−29677.6	+	2596.61i	−0.996194	+	0.0871608i
$962$	16555.0			0.554837
$963$	90.1827	+	65.5215i	0.00301775	+	0.00219253i
$964$	−836.072	−	7954.70i	−0.0279337	−	0.265771i
$965$	−7869.86	−	24220.9i	−0.262528	−	0.807978i
$966$	−44193.8	−	76545.9i	−1.47196	−	2.54951i
$967$	7454.47	−	12911.5i	0.247900	−	0.429376i	−0.715043	−	0.699081i	$-0.753593\pi$
$967$	7454.47	−	12911.5i	0.247900	−	0.429376i	0.962943	+	0.269705i	$0.0869262\pi$
$968$	−1309.08	−	278.254i	−0.0434664	−	0.00923907i
$969$	−533.322	+	1641.40i	−0.0176809	+	0.0544161i
$970$	16819.4	−	3575.08i	0.556741	−	0.118339i
$971$	−4584.83	+	43621.7i	−0.151529	+	1.44170i	0.609401	+	0.792863i	$0.291410\pi$
$971$	−4584.83	+	43621.7i	−0.151529	+	1.44170i	−0.760929	+	0.648835i	$0.775256\pi$
$972$	−516.837	+	574.005i	−0.0170551	+	0.0189416i
$973$	−15252.4	+	6790.79i	−0.502537	+	0.223744i
$974$	−56270.6	−	25053.3i	−1.85116	−	0.824188i
$975$	−3718.48	−	4129.79i	−0.122140	−	0.135650i
$976$	−38767.5	+	28166.3i	−1.27143	+	0.923750i
$977$	−45440.4	+	33014.4i	−1.48799	+	1.08109i	−0.513122	+	0.858316i	$0.671511\pi$
$977$	−45440.4	+	33014.4i	−1.48799	+	1.08109i	−0.974870	+	0.222773i	$0.928489\pi$
$978$	29738.0	+	33027.4i	0.972306	+	1.07986i
$979$	25203.3	+	11221.2i	0.822778	+	0.366325i
$980$	−11410.1	+	5080.12i	−0.371922	+	0.165590i
$981$	−141.466	+	157.113i	−0.00460412	+	0.00511340i
$982$	−2959.68	+	28159.4i	−0.0961783	+	0.915075i
$983$	−25000.8	+	5314.09i	−0.811193	+	0.172424i	−0.594791	−	0.803880i	$-0.702765\pi$
$983$	−25000.8	+	5314.09i	−0.811193	+	0.172424i	−0.216401	+	0.976304i	$0.569432\pi$
$984$	−223.016	+	686.371i	−0.00722508	+	0.0222365i
$985$	3398.52	+	722.378i	0.109935	+	0.0233674i
$986$	−5924.93	+	10262.3i	−0.191367	+	0.331458i
$987$	31055.0	+	53788.8i	1.00151	+	1.73467i
$988$	−1248.64	−	3842.92i	−0.0402070	−	0.123744i
$989$	−3681.60	−	35028.1i	−0.118370	−	1.12622i
$990$	494.748	+	359.455i	0.0158829	+	0.0115396i
$991$	7412.56			0.237606			0.118803	−	0.992918i	$-0.462094\pi$
$991$	7412.56			0.237606			0.118803	+	0.992918i	$0.462094\pi$
$992$	−1939.11	−	44410.3i	−0.0620633	−	1.42140i
$993$	−39481.5			−1.26174
$994$	−84632.2	−	61488.9i	−2.70057	−	1.96208i
$995$	443.835	+	4222.81i	0.0141412	+	0.134545i
$996$	8446.73	+	25996.3i	0.268720	+	0.827034i
$997$	10062.9	+	17429.5i	0.319655	+	0.553659i	0.980416	−	0.196937i	$-0.0630996\pi$
$997$	10062.9	+	17429.5i	0.319655	+	0.553659i	−0.660761	+	0.750596i	$0.729766\pi$
$998$	6176.24	−	10697.6i	0.195897	−	0.339304i
$999$	27979.0	+	5947.13i	0.886104	+	0.188347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.10.2	✓	56
31.11	odd	30		961.4.a.l.1.23		28
31.20	even	15		961.4.a.m.1.23		28
31.28	even	15	inner	31.4.g.a.28.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.10.2	✓	56	1.1	even	1	trivial
31.4.g.a.28.2	yes	56	31.28	even	15	inner
961.4.a.l.1.23		28	31.11	odd	30
961.4.a.m.1.23		28	31.20	even	15

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.25803 - 2.36710i) q^{2} +(0.539766 + 5.13553i) q^{3} +(2.53947 + 7.81570i) q^{4} +(4.24115 + 7.34588i) q^{5} +(10.3977 - 18.0094i) q^{6} +(22.3519 + 4.75104i) q^{7} +(0.271177 - 0.834598i) q^{8} +(0.327669 - 0.0696482i) q^{9} +(3.57063 - 33.9723i) q^{10} +(-35.7599 + 39.7153i) q^{11} +(-38.7670 + 17.2602i) q^{12} +(-18.5320 - 8.25098i) q^{13} +(-61.5769 - 68.3881i) q^{14} +(-35.4358 + 25.7456i) q^{15} +(50.3283 - 36.5657i) q^{16} +(9.22668 + 10.2473i) q^{17} +(-1.23242 - 0.548708i) q^{18} +(22.1427 - 9.85858i) q^{19} +(-46.6429 + 51.8022i) q^{20} +(-12.3343 + 117.353i) q^{21} +(210.517 - 44.7467i) q^{22} +(57.4773 - 176.897i) q^{23} +(4.43247 + 0.942152i) q^{24} +(26.5254 - 45.9433i) q^{25} +(40.8469 + 70.7490i) q^{26} +(43.6186 + 134.244i) q^{27} +(19.6293 + 186.761i) q^{28} +(-172.639 - 125.430i) q^{29} +176.393 q^{30} +(7.52917 + 172.436i) q^{31} -257.546 q^{32} +(-223.261 - 162.209i) q^{33} +(-5.80453 - 55.2264i) q^{34} +(59.8970 + 184.344i) q^{35} +(1.37645 + 2.38409i) q^{36} +(101.323 - 175.497i) q^{37} +(-95.4779 - 20.2945i) q^{38} +(32.3702 - 99.6252i) q^{39} +(7.28096 - 1.54762i) q^{40} +(-16.6474 + 158.389i) q^{41} +(317.972 - 353.144i) q^{42} +(172.989 - 77.0196i) q^{43} +(-401.214 - 178.632i) q^{44} +(1.90132 + 2.11163i) q^{45} +(-605.995 + 440.281i) q^{46} +(425.832 - 309.385i) q^{47} +(214.950 + 238.726i) q^{48} +(163.688 + 72.8785i) q^{49} +(-195.173 + 86.8964i) q^{50} +(-47.6449 + 52.9150i) q^{51} +(17.4256 - 165.794i) q^{52} +(-153.964 + 32.7260i) q^{53} +(175.659 - 540.622i) q^{54} +(-443.407 - 94.2490i) q^{55} +(10.0265 - 17.3665i) q^{56} +(62.5809 + 108.393i) q^{57} +(265.559 + 817.307i) q^{58} +(46.2494 + 440.033i) q^{59} +(-291.208 - 211.575i) q^{60} -770.292 q^{61} +(383.643 - 579.625i) q^{62} +7.65491 q^{63} +(436.466 + 317.111i) q^{64} +(-17.9862 - 171.127i) q^{65} +(343.428 + 1056.96i) q^{66} +(-375.894 - 651.067i) q^{67} +(-56.6586 + 98.1356i) q^{68} +(939.483 + 199.693i) q^{69} +(241.214 - 742.380i) q^{70} +(1111.92 - 236.347i) q^{71} +(0.0307281 - 0.292359i) q^{72} +(323.582 - 359.375i) q^{73} +(-745.532 + 331.932i) q^{74} +(250.260 + 111.423i) q^{75} +(133.283 + 148.025i) q^{76} +(-987.989 + 717.816i) q^{77} +(-341.286 + 247.959i) q^{78} +(151.060 + 167.769i) q^{79} +(482.057 + 214.626i) q^{80} +(-657.609 + 292.787i) q^{81} +(429.160 - 476.631i) q^{82} +(67.3300 - 640.602i) q^{83} +(-948.519 + 201.614i) q^{84} +(-36.1435 + 111.238i) q^{85} +(-745.916 - 158.549i) q^{86} +(550.963 - 954.295i) q^{87} +(23.4491 + 40.6150i) q^{88} +(-159.523 - 490.962i) q^{89} +(-1.19612 - 11.3804i) q^{90} +(-375.024 - 272.471i) q^{91} +1528.53 q^{92} +(-881.488 + 131.742i) q^{93} -2119.72 q^{94} +(166.331 + 120.846i) q^{95} +(-139.015 - 1322.64i) q^{96} +(155.553 + 478.743i) q^{97} +(-360.789 - 624.905i) q^{98} +(-8.95129 + 15.5041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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