LMFDB - Embedded newform 31.4.g.a.10.5

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			10.5
Character	$\chi$	$=$	31.10
Dual form			31.4.g.a.28.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24677 + 0.905833i) q^{2} +(0.665097 + 6.32798i) q^{3} +(-1.73823 - 5.34972i) q^{4} +(6.49781 + 11.2545i) q^{5} +(-4.90287 + 8.49201i) q^{6} +(-5.97991 - 1.27107i) q^{7} +(6.48857 - 19.9698i) q^{8} +(-13.1909 + 2.80382i) q^{9} +(-2.09344 + 19.9178i) q^{10} +(34.9280 - 38.7915i) q^{11} +(32.6968 - 14.5575i) q^{12} +(-35.4607 - 15.7881i) q^{13} +(-6.30421 - 7.00153i) q^{14} +(-66.8967 + 48.6033i) q^{15} +(-10.2269 + 7.43026i) q^{16} +(-34.8654 - 38.7220i) q^{17} +(-18.9859 - 8.45306i) q^{18} +(45.0886 - 20.0747i) q^{19} +(48.9139 - 54.3244i) q^{20} +(4.06607 - 38.6861i) q^{21} +(78.6860 - 16.7252i) q^{22} +(-63.3209 + 194.882i) q^{23} +(130.684 + 27.7777i) q^{24} +(-21.9430 + 38.0064i) q^{25} +(-29.9100 - 51.8057i) q^{26} +(26.5723 + 81.7810i) q^{27} +(3.59459 + 34.2002i) q^{28} +(-106.319 - 77.2456i) q^{29} -127.431 q^{30} +(97.3959 + 142.496i) q^{31} -187.461 q^{32} +(268.702 + 195.224i) q^{33} +(-8.39360 - 79.8598i) q^{34} +(-24.5510 - 75.5602i) q^{35} +(37.9285 + 65.6941i) q^{36} +(46.4194 - 80.4008i) q^{37} +(74.3995 + 15.8141i) q^{38} +(76.3221 - 234.895i) q^{39} +(266.912 - 56.7339i) q^{40} +(31.7580 - 302.157i) q^{41} +(40.1126 - 44.5496i) q^{42} +(-484.870 + 215.878i) q^{43} +(-268.237 - 119.427i) q^{44} +(-117.268 - 130.239i) q^{45} +(-255.477 + 185.615i) q^{46} +(157.678 - 114.560i) q^{47} +(-53.8204 - 59.7736i) q^{48} +(-279.202 - 124.309i) q^{49} +(-61.7853 + 27.5086i) q^{50} +(221.843 - 246.382i) q^{51} +(-22.8232 + 217.148i) q^{52} +(-147.695 + 31.3936i) q^{53} +(-40.9504 + 126.032i) q^{54} +(663.536 + 141.039i) q^{55} +(-64.1840 + 111.170i) q^{56} +(157.021 + 271.968i) q^{57} +(-62.5845 - 192.615i) q^{58} +(-17.7944 - 169.302i) q^{59} +(376.296 + 273.395i) q^{60} +457.365 q^{61} +(-7.64685 + 265.884i) q^{62} +82.4444 q^{63} +(-151.906 - 110.366i) q^{64} +(-52.7289 - 501.682i) q^{65} +(158.171 + 486.799i) q^{66} +(370.980 + 642.556i) q^{67} +(-146.548 + 253.828i) q^{68} +(-1275.32 - 271.078i) q^{69} +(37.8354 - 116.445i) q^{70} +(543.379 - 115.499i) q^{71} +(-29.5987 + 281.613i) q^{72} +(-52.6392 + 58.4617i) q^{73} +(130.704 - 58.1933i) q^{74} +(-255.098 - 113.577i) q^{75} +(-185.768 - 206.317i) q^{76} +(-258.173 + 187.574i) q^{77} +(307.932 - 223.726i) q^{78} +(462.291 + 513.426i) q^{79} +(-150.076 - 66.8183i) q^{80} +(-832.468 + 370.639i) q^{81} +(313.298 - 347.953i) q^{82} +(83.4608 - 794.077i) q^{83} +(-214.027 + 45.4929i) q^{84} +(209.249 - 644.002i) q^{85} +(-800.072 - 170.061i) q^{86} +(418.095 - 724.162i) q^{87} +(-548.025 - 949.207i) q^{88} +(393.217 + 1210.20i) q^{89} +(-28.2314 - 268.604i) q^{90} +(191.984 + 139.485i) q^{91} +1152.63 q^{92} +(-836.932 + 711.092i) q^{93} +300.360 q^{94} +(518.908 + 377.009i) q^{95} +(-124.680 - 1186.25i) q^{96} +(-86.9834 - 267.707i) q^{97} +(-235.499 - 407.896i) q^{98} +(-351.969 + 609.629i) 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 $

$2$	1.24677	+	0.905833i	0.440801	+	0.320260i	0.785953	−	0.618286i	$-0.212173\pi$
$2$	1.24677	+	0.905833i	0.440801	+	0.320260i	−0.345152	+	0.938547i	$0.612173\pi$
$3$	0.665097	+	6.32798i	0.127998	+	1.21782i	0.850321	+	0.526264i	$0.176408\pi$
$3$	0.665097	+	6.32798i	0.127998	+	1.21782i	−0.722323	+	0.691556i	$0.756926\pi$
$4$	−1.73823	−	5.34972i	−0.217279	−	0.668715i
$5$	6.49781	+	11.2545i	0.581181	+	1.00664i	0.995340	+	0.0964310i	$0.0307427\pi$
$5$	6.49781	+	11.2545i	0.581181	+	1.00664i	−0.414158	+	0.910205i	$0.635924\pi$
$6$	−4.90287	+	8.49201i	−0.333598	+	0.577808i
$7$	−5.97991	−	1.27107i	−0.322885	−	0.0686312i	0.0436180	−	0.999048i	$-0.486112\pi$
$7$	−5.97991	−	1.27107i	−0.322885	−	0.0686312i	−0.366503	+	0.930417i	$0.619445\pi$
$8$	6.48857	−	19.9698i	0.286757	−	0.882548i
$9$	−13.1909	+	2.80382i	−0.488553	+	0.103845i
$10$	−2.09344	+	19.9178i	−0.0662004	+	0.629855i
$11$	34.9280	−	38.7915i	0.957382	−	1.06328i	−0.0405612	−	0.999177i	$-0.512915\pi$
$11$	34.9280	−	38.7915i	0.957382	−	1.06328i	0.997943	−	0.0641034i	$-0.0204188\pi$
$12$	32.6968	−	14.5575i	0.786563	−	0.350200i
$13$	−35.4607	−	15.7881i	−0.756541	−	0.336834i	−0.00804021	−	0.999968i	$-0.502559\pi$
$13$	−35.4607	−	15.7881i	−0.756541	−	0.336834i	−0.748501	+	0.663134i	$0.769226\pi$
$14$	−6.30421	−	7.00153i	−0.120348	−	0.133660i
$15$	−66.8967	+	48.6033i	−1.15151	+	0.836622i
$16$	−10.2269	+	7.43026i	−0.159795	+	0.116098i
$17$	−34.8654	−	38.7220i	−0.497418	−	0.552439i	0.441194	−	0.897412i	$-0.354555\pi$
$17$	−34.8654	−	38.7220i	−0.497418	−	0.552439i	−0.938613	+	0.344972i	$0.887888\pi$
$18$	−18.9859	−	8.45306i	−0.248612	−	0.110689i
$19$	45.0886	−	20.0747i	0.544422	−	0.242392i	−0.116049	−	0.993243i	$-0.537023\pi$
$19$	45.0886	−	20.0747i	0.544422	−	0.242392i	0.660472	+	0.750851i	$0.270356\pi$
$20$	48.9139	−	54.3244i	0.546874	−	0.607365i
$21$	4.06607	−	38.6861i	0.0422519	−	0.402000i
$22$	78.6860	−	16.7252i	0.762541	−	0.162083i
$23$	−63.3209	+	194.882i	−0.574057	+	1.76677i	0.0653101	+	0.997865i	$0.479196\pi$
$23$	−63.3209	+	194.882i	−0.574057	+	1.76677i	−0.639367	+	0.768901i	$0.720804\pi$
$24$	130.684	+	27.7777i	1.11149	+	0.236254i
$25$	−21.9430	+	38.0064i	−0.175544	+	0.304051i
$26$	−29.9100	−	51.8057i	−0.225609	−	0.390767i
$27$	26.5723	+	81.7810i	0.189401	+	0.582917i
$28$	3.59459	+	34.2002i	0.0242612	+	0.230830i
$29$	−106.319	−	77.2456i	−0.680794	−	0.494626i	0.192827	−	0.981233i	$-0.438234\pi$
$29$	−106.319	−	77.2456i	−0.680794	−	0.494626i	−0.873621	+	0.486607i	$0.838234\pi$
$30$	−127.431			−0.775523
$31$	97.3959	+	142.496i	0.564285	+	0.825580i
$31$	97.3959	+	142.496i	0.564285	+	0.825580i
$32$	−187.461			−1.03558
$33$	268.702	+	195.224i	1.41743	+	1.02982i
$34$	−8.39360	−	79.8598i	−0.0423380	−	0.402819i
$35$	−24.5510	−	75.5602i	−0.118568	−	0.364914i
$36$	37.9285	+	65.6941i	0.175595	+	0.304139i
$37$	46.4194	−	80.4008i	0.206252	−	0.357238i	−0.744279	−	0.667869i	$-0.767207\pi$
$37$	46.4194	−	80.4008i	0.206252	−	0.357238i	0.950531	+	0.310630i	$0.100540\pi$
$38$	74.3995	+	15.8141i	0.317610	+	0.0675102i
$39$	76.3221	−	234.895i	0.313367	−	0.964444i
$40$	266.912	−	56.7339i	1.05506	−	0.224260i
$41$	31.7580	−	302.157i	0.120970	−	1.15095i	−0.750627	−	0.660726i	$-0.770248\pi$
$41$	31.7580	−	302.157i	0.120970	−	1.15095i	0.871597	−	0.490224i	$-0.163085\pi$
$42$	40.1126	−	44.5496i	0.147369	−	0.163670i
$43$	−484.870	+	215.878i	−1.71958	+	0.765607i	−0.722327	+	0.691551i	$0.756928\pi$
$43$	−484.870	+	215.878i	−1.71958	+	0.765607i	−0.997254	+	0.0740558i	$0.976406\pi$
$44$	−268.237	−	119.427i	−0.919050	−	0.409187i
$45$	−117.268	−	130.239i	−0.388472	−	0.431442i
$46$	−255.477	+	185.615i	−0.818870	+	0.594944i
$47$	157.678	−	114.560i	0.489355	−	0.355537i	−0.315581	−	0.948899i	$-0.602199\pi$
$47$	157.678	−	114.560i	0.489355	−	0.355537i	0.804936	+	0.593361i	$0.202199\pi$
$48$	−53.8204	−	59.7736i	−0.161840	−	0.179741i
$49$	−279.202	−	124.309i	−0.814001	−	0.362417i
$50$	−61.7853	+	27.5086i	−0.174755	+	0.0778061i
$51$	221.843	−	246.382i	0.609103	−	0.676477i
$52$	−22.8232	+	217.148i	−0.0608655	+	0.579097i
$53$	−147.695	+	31.3936i	−0.382784	+	0.0813632i	−0.395285	−	0.918559i	$-0.629354\pi$
$53$	−147.695	+	31.3936i	−0.382784	+	0.0813632i	0.0125010	+	0.999922i	$0.496021\pi$
$54$	−40.9504	+	126.032i	−0.103197	+	0.317608i
$55$	663.536	+	141.039i	1.62675	+	0.345776i
$56$	−64.1840	+	111.170i	−0.153160	+	0.265281i
$57$	157.021	+	271.968i	0.364875	+	0.631982i
$58$	−62.5845	−	192.615i	−0.141685	−	0.436063i
$59$	−17.7944	−	169.302i	−0.0392649	−	0.373580i	−0.996455	−	0.0841219i	$-0.973191\pi$
$59$	−17.7944	−	169.302i	−0.0392649	−	0.373580i	0.957191	−	0.289458i	$-0.0934752\pi$
$60$	376.296	+	273.395i	0.809660	+	0.588252i
$61$	457.365			0.959993			0.479997	−	0.877270i	$-0.340638\pi$
$61$	457.365			0.959993			0.479997	+	0.877270i	$0.340638\pi$
$62$	−7.64685	+	265.884i	−0.0156637	+	0.544634i
$63$	82.4444			0.164873
$64$	−151.906	−	110.366i	−0.296691	−	0.215559i
$65$	−52.7289	−	501.682i	−0.100619	−	0.957323i
$66$	158.171	+	486.799i	0.294992	+	0.907891i
$67$	370.980	+	642.556i	0.676454	+	1.17165i	0.976042	+	0.217583i	$0.0698174\pi$
$67$	370.980	+	642.556i	0.676454	+	1.17165i	−0.299588	+	0.954069i	$0.596849\pi$
$68$	−146.548	+	253.828i	−0.261346	+	0.452664i
$69$	−1275.32	−	271.078i	−2.22508	−	0.472956i
$70$	37.8354	−	116.445i	0.0646028	−	0.198827i
$71$	543.379	−	115.499i	0.908270	−	0.193059i	0.269990	−	0.962863i	$-0.412980\pi$
$71$	543.379	−	115.499i	0.908270	−	0.193059i	0.638280	+	0.769804i	$0.279646\pi$
$72$	−29.5987	+	281.613i	−0.0484478	+	0.460950i
$73$	−52.6392	+	58.4617i	−0.0843966	+	0.0937319i	−0.783864	−	0.620933i	$-0.786754\pi$
$73$	−52.6392	+	58.4617i	−0.0843966	+	0.0937319i	0.699467	+	0.714665i	$0.253421\pi$
$74$	130.704	−	58.1933i	0.205325	−	0.0914166i
$75$	−255.098	−	113.577i	−0.392748	−	0.174863i
$76$	−185.768	−	206.317i	−0.280383	−	0.311397i
$77$	−258.173	+	187.574i	−0.382098	+	0.277611i
$78$	307.932	−	223.726i	0.447006	−	0.324769i
$79$	462.291	+	513.426i	0.658377	+	0.731202i	0.976182	−	0.216954i	$-0.0696122\pi$
$79$	462.291	+	513.426i	0.658377	+	0.731202i	−0.317804	+	0.948156i	$0.602946\pi$
$80$	−150.076	−	66.8183i	−0.209738	−	0.0933814i
$81$	−832.468	+	370.639i	−1.14193	+	0.508421i
$82$	313.298	−	347.953i	0.421927	−	0.468598i
$83$	83.4608	−	794.077i	0.110374	−	1.05014i	−0.789430	−	0.613841i	$-0.789624\pi$
$83$	83.4608	−	794.077i	0.110374	−	1.05014i	0.899804	−	0.436295i	$-0.143710\pi$
$84$	−214.027	+	45.4929i	−0.278004	+	0.0590915i
$85$	209.249	−	644.002i	0.267015	−	0.821787i
$86$	−800.072	−	170.061i	−1.00319	−	0.213234i
$87$	418.095	−	724.162i	0.515225	−	0.892395i
$88$	−548.025	−	949.207i	−0.663860	−	1.14984i
$89$	393.217	+	1210.20i	0.468325	+	1.44135i	0.854753	+	0.519035i	$0.173709\pi$
$89$	393.217	+	1210.20i	0.468325	+	1.44135i	−0.386428	+	0.922320i	$0.626291\pi$
$90$	−28.2314	−	268.604i	−0.0330650	−	0.314592i
$91$	191.984	+	139.485i	0.221158	+	0.160681i
$92$	1152.63			1.30619
$93$	−836.932	+	711.092i	−0.933181	+	0.792869i
$94$	300.360			0.329573
$95$	518.908	+	377.009i	0.560409	+	0.407161i
$96$	−124.680	−	1186.25i	−0.132553	−	1.26116i
$97$	−86.9834	−	267.707i	−0.0910497	−	0.280222i	0.895154	−	0.445756i	$-0.147065\pi$
$97$	−86.9834	−	267.707i	−0.0910497	−	0.280222i	−0.986204	+	0.165534i	$0.947065\pi$
$98$	−235.499	−	407.896i	−0.242744	−	0.420446i
$99$	−351.969	+	609.629i	−0.357316	+	0.618889i
$100$	241.465	+	51.3250i	0.241465	+	0.0513250i
$101$	−136.588	+	420.374i	−0.134564	+	0.414146i	−0.995522	−	0.0945304i	$-0.969865\pi$
$101$	−136.588	+	420.374i	−0.134564	+	0.414146i	0.860958	+	0.508676i	$0.169865\pi$
$102$	499.768	−	106.229i	0.485141	−	0.103120i
$103$	21.0105	−	199.902i	0.0200993	−	0.191232i	−0.979865	−	0.199660i	$-0.936016\pi$
$103$	21.0105	−	199.902i	0.0200993	−	0.191232i	0.999964	+	0.00842813i	$0.00268279\pi$
$104$	−545.375	+	605.700i	−0.514215	+	0.571094i
$105$	461.814	−	205.613i	0.429223	−	0.191103i
$106$	−212.580	−	94.6467i	−0.194789	−	0.0867255i
$107$	−782.141	−	868.655i	−0.706658	−	0.784823i	0.277763	−	0.960650i	$-0.410407\pi$
$107$	−782.141	−	868.655i	−0.706658	−	0.784823i	−0.984421	+	0.175827i	$0.943740\pi$
$108$	391.317	−	284.308i	0.348652	−	0.253311i
$109$	−1281.47	+	931.044i	−1.12608	+	0.818146i	−0.985120	−	0.171870i	$-0.945019\pi$
$109$	−1281.47	+	931.044i	−1.12608	+	0.818146i	−0.140961	+	0.990015i	$0.545019\pi$
$110$	699.521	+	776.896i	0.606333	+	0.673402i
$111$	539.648	+	240.267i	0.461451	+	0.205451i
$112$	70.6001	−	31.4332i	0.0595633	−	0.0265193i
$113$	416.143	−	462.173i	0.346437	−	0.384758i	−0.544594	−	0.838700i	$-0.683316\pi$
$113$	416.143	−	462.173i	0.346437	−	0.384758i	0.891031	+	0.453942i	$0.149983\pi$
$114$	−50.5884	+	481.316i	−0.0415617	+	0.395433i
$115$	−2604.75	+	553.656i	−2.11212	+	0.448945i
$116$	−228.435	+	703.049i	−0.182842	+	0.562728i
$117$	512.027	+	108.835i	0.404589	+	0.0859981i
$118$	131.174	−	227.200i	0.102335	−	0.177249i
$119$	159.274	+	275.870i	0.122694	+	0.212513i
$120$	536.533	+	1651.28i	0.408154	+	1.25617i
$121$	−145.687	−	1386.12i	−0.109457	−	1.04141i
$122$	570.230	+	414.296i	0.423165	+	0.307448i
$123$	1933.16			1.41713
$124$	593.016	−	768.731i	0.429471	−	0.556726i
$125$	1054.13			0.754272
$126$	102.789	+	74.6809i	0.0726763	+	0.0528024i
$127$	185.060	+	1760.73i	0.129302	+	1.23023i	0.846129	+	0.532978i	$0.178927\pi$
$127$	185.060	+	1760.73i	0.129302	+	1.23023i	−0.716827	+	0.697251i	$0.754406\pi$
$128$	374.010	+	1151.08i	0.258267	+	0.794863i
$129$	−1688.56	−	2924.67i	−1.15247	−	1.99614i
$130$	388.699	−	673.247i	0.262240	−	0.454213i
$131$	1576.83	+	335.165i	1.05166	+	0.223538i	0.701146	−	0.713018i	$-0.252672\pi$
$131$	1576.83	+	335.165i	1.05166	+	0.223538i	0.350518	+	0.936556i	$0.386005\pi$
$132$	577.325	−	1776.83i	0.380680	−	1.17161i
$133$	−295.142	+	62.7343i	−0.192421	+	0.0409004i
$134$	−119.521	+	1137.17i	−0.0770526	+	0.733106i
$135$	−747.746	+	830.456i	−0.476709	+	0.529439i
$136$	−999.497	+	445.005i	−0.630192	+	0.280580i
$137$	504.047	+	224.416i	0.314333	+	0.139950i	0.557839	−	0.829949i	$-0.311631\pi$
$137$	504.047	+	224.416i	0.314333	+	0.139950i	−0.243505	+	0.969900i	$0.578297\pi$
$138$	−1344.48	−	1493.20i	−0.829348	−	0.921084i
$139$	−2232.70	+	1622.15i	−1.36241	+	0.989847i	−0.364120	+	0.931352i	$0.618630\pi$
$139$	−2232.70	+	1622.15i	−1.36241	+	0.989847i	−0.998288	+	0.0584956i	$0.981370\pi$
$140$	−361.550	+	262.682i	−0.218261	+	0.158576i
$141$	829.802	+	921.589i	0.495617	+	0.550438i
$142$	782.092	+	348.210i	0.462195	+	0.205783i
$143$	−1851.02	+	824.127i	−1.08245	+	0.481937i
$144$	114.069	−	126.686i	0.0660121	−	0.0733139i
$145$	178.520	−	1698.50i	0.102243	−	0.972779i
$146$	−118.586	+	25.2061i	−0.0672206	+	0.0142882i
$147$	600.927	−	1849.46i	0.337168	−	1.03770i
$148$	−510.809	−	108.576i	−0.283704	−	0.0603033i
$149$	1428.40	−	2474.05i	0.785360	−	1.36028i	−0.143423	−	0.989661i	$-0.545811\pi$
$149$	1428.40	−	2474.05i	0.785360	−	1.36028i	0.928784	−	0.370622i	$-0.120856\pi$
$150$	−215.167	−	372.680i	−0.117122	−	0.202861i
$151$	−643.111	−	1979.29i	−0.346593	−	1.06670i	−0.960725	−	0.277501i	$-0.910494\pi$
$151$	−643.111	−	1979.29i	−0.346593	−	1.06670i	0.614132	−	0.789203i	$-0.289506\pi$
$152$	−108.327	−	1030.66i	−0.0578059	−	0.549986i
$153$	568.477	+	413.023i	0.300384	+	0.218241i
$154$	−491.794			−0.257337
$155$	−970.863	+	2022.06i	−0.503107	+	1.04784i
$156$	−1389.29			−0.713026
$157$	2886.11	+	2096.88i	1.46711	+	1.06592i	0.981439	+	0.191777i	$0.0614250\pi$
$157$	2886.11	+	2096.88i	1.46711	+	1.06592i	0.485672	+	0.874141i	$0.338575\pi$
$158$	111.293	+	1058.88i	0.0560381	+	0.533167i
$159$	−296.890	−	913.734i	−0.148081	−	0.455747i
$160$	−1218.08	−	2109.78i	−0.601863	−	1.04246i
$161$	626.361	−	1084.89i	0.306610	−	0.531063i
$162$	−1373.63	−	291.975i	−0.666191	−	0.141603i
$163$	927.562	−	2854.74i	0.445719	−	1.37178i	−0.435974	−	0.899959i	$-0.643596\pi$
$163$	927.562	−	2854.74i	0.445719	−	1.37178i	0.881693	−	0.471823i	$-0.156404\pi$
$164$	−1671.66	+	355.321i	−0.795941	+	0.169183i
$165$	−451.175	+	4292.65i	−0.212872	+	2.02535i
$166$	823.358	−	914.431i	0.384970	−	0.427552i
$167$	1660.41	−	739.261i	0.769379	−	0.342549i	0.0157724	−	0.999876i	$-0.494979\pi$
$167$	1660.41	−	739.261i	0.769379	−	0.342549i	0.753606	+	0.657326i	$0.228313\pi$
$168$	−746.169	−	332.216i	−0.342668	−	0.152566i
$169$	−461.883	−	512.973i	−0.210233	−	0.233488i
$170$	844.244	−	613.380i	0.380886	−	0.276730i
$171$	−538.475	+	391.225i	−0.240808	+	0.174957i
$172$	1997.70	+	2218.67i	0.885601	+	0.983559i
$173$	−1411.45	−	628.416i	−0.620290	−	0.276171i	0.0724343	−	0.997373i	$-0.476923\pi$
$173$	−1411.45	−	628.416i	−0.620290	−	0.276171i	−0.692725	+	0.721202i	$0.743590\pi$
$174$	1177.24	−	524.141i	0.512910	−	0.228362i
$175$	179.526	−	199.383i	0.0775478	−	0.0861256i
$176$	−68.9737	+	656.241i	−0.0295403	+	0.281057i
$177$	1059.50	−	225.204i	0.449928	−	0.0956351i
$178$	−605.984	+	1865.03i	−0.255171	+	0.785336i
$179$	−321.887	−	68.4192i	−0.134408	−	0.0285692i	0.140217	−	0.990121i	$-0.455220\pi$
$179$	−321.887	−	68.4192i	−0.134408	−	0.0285692i	−0.274624	+	0.961552i	$0.588553\pi$
$180$	−492.904	+	853.735i	−0.204105	+	0.353520i
$181$	353.990	+	613.129i	0.145370	+	0.251788i	0.929511	−	0.368795i	$-0.120230\pi$
$181$	353.990	+	613.129i	0.145370	+	0.251788i	−0.784141	+	0.620582i	$0.786896\pi$
$182$	113.011	+	347.811i	0.0460269	+	0.141656i
$183$	304.192	+	2894.19i	0.122877	+	1.16910i
$184$	3480.88	+	2529.01i	1.39464	+	1.01327i
$185$	1206.50			0.479478
$186$	−1687.59	+	128.450i	−0.665271	+	0.0506365i
$187$	−2719.87			−1.06362
$188$	−886.942	−	644.401i	−0.344079	−	0.249988i
$189$	−54.9504	−	522.818i	−0.0211484	−	0.201214i
$190$	305.453	+	940.089i	0.116631	+	0.358954i
$191$	−438.419	−	759.364i	−0.166088	−	0.287673i	0.770953	−	0.636892i	$-0.219780\pi$
$191$	−438.419	−	759.364i	−0.166088	−	0.287673i	−0.937041	+	0.349219i	$0.886447\pi$
$192$	597.362	−	1034.66i	0.224536	−	0.388908i
$193$	302.013	+	64.1949i	0.112639	+	0.0239422i	0.263886	−	0.964554i	$-0.414996\pi$
$193$	302.013	+	64.1949i	0.112639	+	0.0239422i	−0.151247	+	0.988496i	$0.548329\pi$
$194$	134.050	−	412.562i	0.0496093	−	0.152682i
$195$	3139.56	−	667.334i	1.15297	−	0.245071i
$196$	−179.700	+	1709.73i	−0.0654883	+	0.623080i
$197$	−139.142	+	154.533i	−0.0503221	+	0.0558884i	−0.767780	−	0.640713i	$-0.778639\pi$
$197$	−139.142	+	154.533i	−0.0503221	+	0.0558884i	0.717458	+	0.696602i	$0.245305\pi$
$198$	−991.047	+	441.243i	−0.355710	+	0.158372i
$199$	1131.39	+	503.728i	0.403026	+	0.179439i	0.598231	−	0.801324i	$-0.295871\pi$
$199$	1131.39	+	503.728i	0.403026	+	0.179439i	−0.195205	+	0.980762i	$0.562537\pi$
$200$	616.600	+	684.803i	0.218001	+	0.242115i
$201$	−3819.34	+	2774.91i	−1.34028	+	0.973768i
$202$	−551.082	+	400.385i	−0.191951	+	0.139460i
$203$	537.596	+	597.061i	0.185871	+	0.206431i
$204$	−1703.69	−	758.530i	−0.584715	−	0.260332i
$205$	3606.99	−	1605.94i	1.22889	−	0.547138i
$206$	207.273	−	230.200i	0.0701039	−	0.0778583i
$207$	288.849	−	2748.21i	0.0969873	−	0.922773i
$208$	479.962	−	102.019i	0.159997	−	0.0340084i
$209$	796.126	−	2450.23i	0.263489	−	0.810936i
$210$	762.028	+	161.974i	0.250405	+	0.0532251i
$211$	753.440	−	1305.00i	0.245824	−	0.425780i	−0.716539	−	0.697547i	$-0.754275\pi$
$211$	753.440	−	1305.00i	0.245824	−	0.425780i	0.962363	+	0.271767i	$0.0876080\pi$
$212$	424.676	+	735.560i	0.137579	+	0.238295i
$213$	1092.27	+	3361.67i	0.351368	+	1.08140i
$214$	−188.295	−	1791.50i	−0.0601475	−	0.572265i
$215$	−5580.20	−	4054.25i	−1.77008	−	1.28604i
$216$	1805.56			0.568764
$217$	−401.297	−	975.908i	−0.125538	−	0.305295i
$218$	−2441.07			−0.758397
$219$	−404.954	−	294.217i	−0.124951	−	0.0907823i
$220$	−398.859	−	3794.89i	−0.122232	−	1.16296i
$221$	625.006	+	1923.57i	0.190237	+	0.585490i
$222$	455.177	+	788.389i	0.137610	+	0.238348i
$223$	−63.2107	+	109.484i	−0.0189816	+	0.0328771i	−0.875360	−	0.483471i	$-0.839376\pi$
$223$	−63.2107	+	109.484i	−0.0189816	+	0.0328771i	0.856379	+	0.516348i	$0.172709\pi$
$224$	1121.00	+	238.276i	0.334374	+	0.0710735i
$225$	182.886	−	562.864i	0.0541883	−	0.166774i
$226$	937.487	−	199.269i	0.275932	−	0.0586512i
$227$	82.3436	−	783.447i	0.0240764	−	0.229071i	−0.975866	−	0.218369i	$-0.929926\pi$
$227$	82.3436	−	783.447i	0.0240764	−	0.229071i	0.999943	−	0.0107027i	$-0.00340684\pi$
$228$	1182.01	−	1312.76i	0.343336	−	0.381314i
$229$	−4178.85	+	1860.54i	−1.20588	+	0.536892i	−0.908507	−	0.417870i	$-0.862777\pi$
$229$	−4178.85	+	1860.54i	−1.20588	+	0.536892i	−0.297372	+	0.954762i	$0.596110\pi$
$230$	−3749.05	−	1669.18i	−1.07480	−	0.478534i
$231$	−1358.67	−	1508.96i	−0.386987	−	0.429793i
$232$	−2232.44	+	1621.96i	−0.631753	+	0.458996i
$233$	−1319.35	+	958.566i	−0.370960	+	0.269518i	−0.757609	−	0.652709i	$-0.773633\pi$
$233$	−1319.35	+	958.566i	−0.370960	+	0.269518i	0.386649	+	0.922227i	$0.373633\pi$
$234$	539.795	+	599.503i	0.150801	+	0.167482i
$235$	2313.88	+	1030.20i	0.642301	+	0.285971i
$236$	−874.787	+	389.480i	−0.241287	+	0.107428i
$237$	−2941.48	+	3266.85i	−0.806201	+	0.895377i
$238$	−51.3143	+	488.223i	−0.0139757	+	0.132970i
$239$	403.143	−	85.6907i	0.109109	−	0.0231919i	−0.153033	−	0.988221i	$-0.548904\pi$
$239$	403.143	−	85.6907i	0.109109	−	0.0231919i	0.262143	+	0.965029i	$0.415571\pi$
$240$	323.009	−	994.120i	0.0868757	−	0.267376i
$241$	−638.070	−	135.626i	−0.170546	−	0.0362508i	0.121847	−	0.992549i	$-0.461118\pi$
$241$	−638.070	−	135.626i	−0.170546	−	0.0362508i	−0.292393	+	0.956298i	$0.594452\pi$
$242$	1073.95	−	1860.14i	0.285274	−	0.494108i
$243$	−1738.20	−	3010.66i	−0.458872	−	0.794789i
$244$	−795.005	−	2446.77i	−0.208586	−	0.641961i
$245$	−415.165	−	3950.03i	−0.108261	−	1.03003i
$246$	2410.21	+	1751.12i	0.624673	+	0.453852i
$247$	−1915.81			−0.493524
$248$	3477.57	−	1020.38i	0.890427	−	0.261267i
$249$	5080.41			1.29300
$250$	1314.26	+	954.863i	0.332483	+	0.241563i
$251$	−257.832	−	2453.11i	−0.0648374	−	0.616887i	−0.977901	−	0.209069i	$-0.932957\pi$
$251$	−257.832	−	2453.11i	−0.0648374	−	0.616887i	0.913063	−	0.407818i	$-0.133710\pi$
$252$	−143.307	−	441.054i	−0.0358234	−	0.110253i
$253$	5348.08	+	9263.15i	1.32898	+	2.30185i
$254$	−1364.20	+	2362.86i	−0.336997	+	0.583696i
$255$	4214.40	+	895.799i	1.03497	+	0.219989i
$256$	−1040.57	+	3202.54i	−0.254045	+	0.781870i
$257$	4325.88	−	919.495i	1.04997	−	0.223177i	0.349554	−	0.936916i	$-0.386333\pi$
$257$	4325.88	−	919.495i	1.04997	−	0.223177i	0.700412	+	0.713739i	$0.253000\pi$
$258$	544.014	−	5175.94i	0.131274	−	1.24899i
$259$	−379.779	+	421.787i	−0.0911132	+	0.101191i
$260$	−2592.20	+	1154.12i	−0.618314	+	0.275291i
$261$	1619.04	+	720.841i	0.383969	+	0.170954i
$262$	1662.34	+	1846.22i	0.391984	+	0.435342i
$263$	−1218.57	+	885.341i	−0.285704	+	0.207576i	−0.721401	−	0.692517i	$-0.756502\pi$
$263$	−1218.57	+	885.341i	−0.285704	+	0.207576i	0.435698	+	0.900093i	$0.356502\pi$
$264$	5642.07	−	4099.20i	1.31532	−	0.955638i
$265$	−1313.02	−	1458.25i	−0.304370	−	0.338037i
$266$	−424.801	−	189.134i	−0.0979182	−	0.0435960i
$267$	−7396.57	+	3293.16i	−1.69537	+	0.754825i
$268$	2792.64	−	3101.55i	0.636522	−	0.706929i
$269$	−321.248	+	3056.47i	−0.0728136	+	0.692775i	0.895843	+	0.444371i	$0.146573\pi$
$269$	−321.248	+	3056.47i	−0.0728136	+	0.692775i	−0.968656	+	0.248404i	$0.920094\pi$
$270$	−1684.52	+	358.056i	−0.379692	+	0.0807060i
$271$	−662.549	+	2039.12i	−0.148513	+	0.457076i	−0.997446	−	0.0714245i	$-0.977245\pi$
$271$	−662.549	+	2039.12i	−0.148513	+	0.457076i	0.848933	+	0.528500i	$0.177245\pi$
$272$	644.279	+	136.946i	0.143622	+	0.0305278i
$273$	−754.967	+	1307.64i	−0.167372	+	0.289897i
$274$	425.149	+	736.379i	0.0937378	+	0.162359i
$275$	707.899	+	2178.69i	0.155229	+	0.477745i
$276$	766.609	+	7293.80i	0.167190	+	1.59071i
$277$	−7101.76	−	5159.73i	−1.54045	−	1.11920i	−0.950055	−	0.312082i	$-0.898974\pi$
$277$	−7101.76	−	5159.73i	−1.54045	−	1.11920i	−0.590391	−	0.807117i	$-0.701026\pi$
$278$	−4253.06			−0.917559
$279$	−1684.28	−	1606.57i	−0.361416	−	0.344742i
$280$	−1668.22			−0.356055
$281$	−2163.29	−	1571.72i	−0.459257	−	0.333669i	0.333983	−	0.942579i	$-0.391607\pi$
$281$	−2163.29	−	1571.72i	−0.459257	−	0.333669i	−0.793240	+	0.608910i	$0.791607\pi$
$282$	199.769	+	1900.67i	0.0421846	+	0.401360i
$283$	1815.00	+	5585.98i	0.381238	+	1.17333i	0.939173	+	0.343445i	$0.111594\pi$
$283$	1815.00	+	5585.98i	0.381238	+	1.17333i	−0.557935	+	0.829884i	$0.688406\pi$
$284$	−1562.40	−	2706.16i	−0.326449	−	0.565426i
$285$	−2040.58	+	3534.39i	−0.424117	+	0.734593i
$286$	−3054.32	−	649.216i	−0.631489	−	0.134227i
$287$	−573.971	+	1766.50i	−0.118050	+	0.363322i
$288$	2472.78	−	525.607i	0.505938	−	0.107541i
$289$	229.754	−	2185.97i	0.0467646	−	0.444935i
$290$	1761.13	−	1955.94i	0.356611	−	0.396057i
$291$	1636.19	−	728.480i	0.329606	−	0.146750i
$292$	404.253	+	179.985i	0.0810174	+	0.0360713i
$293$	320.236	+	355.658i	0.0638511	+	0.0709138i	0.774224	−	0.632912i	$-0.218140\pi$
$293$	320.236	+	355.658i	0.0638511	+	0.0709138i	−0.710373	+	0.703825i	$0.751474\pi$
$294$	2424.52	−	1761.52i	0.480956	−	0.349435i
$295$	1789.79	−	1300.36i	0.353239	−	0.256643i
$296$	−1304.39	−	1448.67i	−0.256136	−	0.284467i
$297$	4100.53	+	1825.67i	0.801134	+	0.356688i
$298$	4021.96	−	1790.69i	0.781832	−	0.348094i
$299$	5322.22	−	5910.92i	1.02940	−	1.14327i
$300$	−164.186	+	1562.12i	−0.0315975	+	0.300631i
$301$	3173.87	−	674.628i	0.607771	−	0.129186i
$302$	991.095	−	3050.28i	0.188845	−	0.581204i
$303$	−2750.96	−	584.734i	−0.521579	−	0.110865i
$304$	−311.955	+	540.322i	−0.0588547	+	0.101939i
$305$	2971.87	+	5147.43i	0.557930	+	0.966363i
$306$	334.632	+	1029.89i	0.0625152	+	0.192402i
$307$	376.297	+	3580.23i	0.0699558	+	0.665585i	0.972167	+	0.234290i	$0.0752765\pi$
$307$	376.297	+	3580.23i	0.0699558	+	0.665585i	−0.902211	+	0.431295i	$0.858057\pi$
$308$	1452.23	+	1055.11i	0.268664	+	0.195196i
$309$	1278.95			0.235459
$310$	−3042.09	+	1641.60i	−0.557352	+	0.300764i
$311$	−1764.49			−0.321721			−0.160860	−	0.986977i	$-0.551427\pi$
$311$	−1764.49			−0.321721			−0.160860	+	0.986977i	$0.551427\pi$
$312$	−4195.58	−	3048.27i	−0.761308	−	0.553123i
$313$	−905.742	−	8617.56i	−0.163564	−	1.55621i	−0.701159	−	0.713005i	$-0.747334\pi$
$313$	−905.742	−	8617.56i	−0.163564	−	1.55621i	0.537595	−	0.843203i	$-0.319333\pi$
$314$	1698.89	+	5228.66i	0.305332	+	0.939715i
$315$	535.708	+	927.873i	0.0958213	+	0.165967i
$316$	1943.12	−	3365.58i	0.345914	−	0.599141i
$317$	−7895.52	−	1678.24i	−1.39892	−	0.297349i	−0.554120	−	0.832437i	$-0.686945\pi$
$317$	−7895.52	−	1678.24i	−1.39892	−	0.297349i	−0.844796	+	0.535088i	$0.820278\pi$
$318$	457.536	−	1408.15i	0.0806834	−	0.248318i
$319$	−6710.00	+	1426.26i	−1.17771	+	0.250329i
$320$	255.064	−	2426.77i	0.0445578	−	0.423939i
$321$	4976.63	−	5527.11i	0.865322	−	0.961037i
$322$	1763.66	−	785.231i	0.305232	−	0.135898i
$323$	−2349.37	−	1046.01i	−0.404713	−	0.180190i
$324$	3429.83	+	3809.21i	0.588106	+	0.653157i
$325$	1378.16	−	1001.29i	0.235221	−	0.170898i
$326$	3742.38	−	2719.00i	0.635801	−	0.461936i
$327$	−6743.93	−	7489.89i	−1.14049	−	1.26664i
$328$	−5827.94	−	2594.76i	−0.981079	−	0.436805i
$329$	−1088.51	+	484.637i	−0.182406	+	0.0812125i
$330$	−4450.93	+	4943.26i	−0.742472	+	0.824599i
$331$	448.899	−	4270.99i	0.0745430	−	0.709229i	−0.891880	−	0.452272i	$-0.850614\pi$
$331$	448.899	−	4270.99i	0.0745430	−	0.709229i	0.966423	−	0.256957i	$-0.0827198\pi$
$332$	−4393.16	+	933.795i	−0.726223	+	0.154363i
$333$	−386.886	+	1190.71i	−0.0636674	+	0.195948i
$334$	2739.80	+	582.362i	0.448847	+	0.0954055i
$335$	−4821.11	+	8350.41i	−0.786285	+	1.36189i
$336$	245.865	+	425.850i	0.0399197	+	0.0691429i
$337$	−599.051	−	1843.69i	−0.0968320	−	0.298018i	0.890895	−	0.454210i	$-0.150078\pi$
$337$	−599.051	−	1843.69i	−0.0968320	−	0.298018i	−0.987727	+	0.156191i	$0.950078\pi$
$338$	−111.195	−	1057.95i	−0.0178941	−	0.170251i
$339$	3201.40	+	2325.95i	0.512909	+	0.372650i
$340$	−3808.95			−0.607557
$341$	8929.48	+	1198.96i	1.41806	+	0.190403i
$342$	−1025.74			−0.162180
$343$	3208.05	+	2330.79i	0.505010	+	0.366911i
$344$	1164.92	+	11083.5i	0.182582	+	1.73716i
$345$	−5235.93	−	16114.5i	−0.817082	−	2.51472i
$346$	−1190.51	−	2062.03i	−0.184978	−	0.320391i
$347$	−515.876	+	893.524i	−0.0798089	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$347$	−515.876	+	893.524i	−0.0798089	+	0.138233i	0.823358	+	0.567522i	$0.192098\pi$
$348$	−4600.81	−	977.932i	−0.708705	−	0.150640i
$349$	−1354.63	+	4169.12i	−0.207770	+	0.639449i	0.791819	+	0.610756i	$0.209134\pi$
$349$	−1354.63	+	4169.12i	−0.207770	+	0.639449i	−0.999588	+	0.0286929i	$0.990866\pi$
$350$	404.436	−	85.9655i	0.0617657	−	0.0131287i
$351$	348.898	−	3319.54i	0.0530564	−	0.504798i
$352$	−6547.64	+	7271.89i	−0.991450	+	1.10112i
$353$	10890.6	−	4848.80i	1.64206	−	0.731093i	0.642675	−	0.766139i	$-0.277824\pi$
$353$	10890.6	−	4848.80i	1.64206	−	0.731093i	0.999386	+	0.0350459i	$0.0111578\pi$
$354$	1524.96	+	678.955i	0.228956	+	0.101938i
$355$	4830.65	+	5364.98i	0.722210	+	0.802095i
$356$	5790.71	−	4207.20i	0.862098	−	0.626351i
$357$	−1639.77	+	1191.36i	−0.243097	+	0.176621i
$358$	−339.343	−	376.879i	−0.0500974	−	0.0556387i
$359$	3727.26	+	1659.48i	0.547959	+	0.243967i	0.661993	−	0.749510i	$-0.269711\pi$
$359$	3727.26	+	1659.48i	0.547959	+	0.243967i	−0.114035	+	0.993477i	$0.536377\pi$
$360$	−3361.75	+	1496.75i	−0.492166	+	0.219126i
$361$	−2959.58	+	3286.95i	−0.431489	+	0.479217i
$362$	−114.047	+	1085.09i	−0.0165586	+	0.157544i
$363$	8674.41	−	1843.80i	1.25424	−	0.266597i
$364$	412.491	−	1269.52i	0.0593967	−	0.182804i
$365$	−999.998	−	212.556i	−0.143404	−	0.0304814i
$366$	−2242.40	+	3883.95i	−0.320251	+	0.554692i
$367$	−1243.15	−	2153.20i	−0.176818	−	0.306257i	0.763971	−	0.645250i	$-0.223247\pi$
$367$	−1243.15	−	2153.20i	−0.176818	−	0.306257i	−0.940789	+	0.338993i	$0.889914\pi$
$368$	−800.447	−	2463.52i	−0.113386	−	0.348967i
$369$	428.276	+	4074.77i	0.0604205	+	0.574863i
$370$	1504.23	+	1092.89i	0.211354	+	0.153558i
$371$	923.109			0.129179
$372$	5258.92	+	3241.31i	0.732963	+	0.451758i
$373$	5220.33			0.724661			0.362330	−	0.932050i	$-0.381981\pi$
$373$	5220.33			0.724661			0.362330	+	0.932050i	$0.381981\pi$
$374$	−3391.06	−	2463.75i	−0.468843	−	0.340634i
$375$	701.097	+	6670.49i	0.0965452	+	0.918567i
$376$	−1264.63	−	3892.12i	−0.173453	−	0.533832i
$377$	2550.60	+	4417.77i	0.348442	+	0.603519i
$378$	405.075	−	701.611i	0.0551186	−	0.0954682i
$379$	9274.08	+	1971.27i	1.25693	+	0.267169i	0.787785	−	0.615950i	$-0.211228\pi$
$379$	9274.08	+	1971.27i	1.25693	+	0.267169i	0.469148	+	0.883120i	$0.344561\pi$
$380$	1114.91	−	3431.34i	0.150510	−	0.463221i
$381$	−11018.7	+	2342.11i	−1.48165	+	0.314934i
$382$	141.248	−	1343.89i	0.0189186	−	0.179998i
$383$	−1084.86	+	1204.86i	−0.144735	+	0.160745i	−0.811154	−	0.584833i	$-0.801160\pi$
$383$	−1084.86	+	1204.86i	−0.144735	+	0.160745i	0.666418	+	0.745578i	$0.267827\pi$
$384$	−7035.28	+	3132.31i	−0.934942	+	0.416263i
$385$	−3788.61	−	1686.80i	−0.501521	−	0.223292i
$386$	318.392	+	353.610i	0.0419837	+	0.0466276i
$387$	5790.61	−	4207.12i	0.760603	−	0.552610i
$388$	−1280.96	+	930.673i	−0.167606	+	0.121773i
$389$	1802.46	+	2001.84i	0.234932	+	0.260918i	0.849070	−	0.528280i	$-0.177163\pi$
$389$	1802.46	+	2001.84i	0.234932	+	0.260918i	−0.614138	+	0.789199i	$0.710496\pi$
$390$	4518.81	+	2011.90i	0.586715	+	0.261222i
$391$	9753.92	−	4342.72i	1.26158	−	0.561690i
$392$	−4294.05	+	4769.02i	−0.553271	+	0.614469i
$393$	−1072.17	+	10201.0i	−0.137618	+	1.30935i
$394$	−313.459	+	66.6278i	−0.0400808	+	0.00851945i
$395$	−2774.49	+	8539.01i	−0.353418	+	1.08771i
$396$	3873.14	+	823.262i	0.491497	+	0.104471i
$397$	852.173	−	1476.01i	0.107731	−	0.186596i	−0.807120	−	0.590388i	$-0.798975\pi$
$397$	852.173	−	1476.01i	0.107731	−	0.186596i	0.914851	+	0.403792i	$0.132308\pi$
$398$	954.294	+	1652.89i	0.120187	+	0.208170i
$399$	−593.279	−	1825.93i	−0.0744389	−	0.229099i
$400$	−57.9890	−	551.728i	−0.00724863	−	0.0689661i
$401$	−2628.53	−	1909.74i	−0.327338	−	0.237825i	0.411962	−	0.911201i	$-0.364844\pi$
$401$	−2628.53	−	1909.74i	−0.327338	−	0.237825i	−0.739300	+	0.673376i	$0.764844\pi$
$402$	−7275.46			−0.902654
$403$	−1203.99	−	6590.70i	−0.148821	−	0.814655i
$404$	2486.30			0.306183
$405$	−9580.58	−	6960.70i	−1.17546	−	0.854025i
$406$	129.422	+	1231.37i	0.0158205	+	0.150522i
$407$	−1497.53	−	4608.92i	−0.182383	−	0.561317i
$408$	−3480.74	−	6028.82i	−0.422359	−	0.731547i
$409$	1776.45	−	3076.90i	0.214767	−	0.371987i	−0.738434	−	0.674326i	$-0.764434\pi$
$409$	1776.45	−	3076.90i	0.214767	−	0.371987i	0.953200	+	0.302339i	$0.0977675\pi$
$410$	5951.80	+	1265.09i	0.716923	+	0.152387i
$411$	−1084.86	+	3338.86i	−0.130200	+	0.400715i
$412$	−1105.94	+	235.075i	−0.132247	+	0.0281100i
$413$	−108.786	+	1035.03i	−0.0129613	+	0.123318i
$414$	2849.55	−	3164.75i	0.338280	−	0.375697i
$415$	9479.28	−	4220.45i	1.12125	−	0.499213i
$416$	6647.50	+	2959.66i	0.783462	+	0.348820i
$417$	−11749.9	−	13049.6i	−1.37984	−	1.53247i
$418$	3212.08	−	2333.71i	0.375857	−	0.273076i
$419$	−9847.98	+	7154.97i	−1.14822	+	0.834232i	−0.988244	−	0.152888i	$-0.951143\pi$
$419$	−9847.98	+	7154.97i	−1.14822	+	0.834232i	−0.159979	+	0.987120i	$0.551143\pi$
$420$	−1902.71	−	2113.17i	−0.221054	−	0.245506i
$421$	−9549.14	−	4251.55i	−1.10546	−	0.492180i	−0.228885	−	0.973454i	$-0.573508\pi$
$421$	−9549.14	−	4251.55i	−1.10546	−	0.492180i	−0.876571	+	0.481273i	$0.840175\pi$
$422$	2121.48	−	944.542i	0.244720	−	0.108956i
$423$	−1758.71	+	1953.25i	−0.202155	+	0.224516i
$424$	−331.409	+	3153.14i	−0.0379591	+	0.361156i
$425$	2236.73	−	475.433i	0.255288	−	0.0542632i
$426$	−1683.30	+	5180.65i	−0.191446	+	0.589210i
$427$	−2735.00	−	581.342i	−0.309967	−	0.0658855i
$428$	−3287.52	+	5694.15i	−0.371281	+	0.643078i
$429$	−6446.16	−	11165.1i	−0.725463	−	1.25654i
$430$	−3284.76	−	10109.5i	−0.368384	−	1.13377i
$431$	−1201.59	−	11432.4i	−0.134289	−	1.27768i	−0.829351	−	0.558728i	$-0.811290\pi$
$431$	−1201.59	−	11432.4i	−0.134289	−	1.27768i	0.695061	−	0.718950i	$-0.255377\pi$
$432$	−879.406	−	638.926i	−0.0979408	−	0.0711582i
$433$	−463.686			−0.0514627			−0.0257313	−	0.999669i	$-0.508191\pi$
$433$	−463.686			−0.0514627			−0.0257313	+	0.999669i	$0.508191\pi$
$434$	383.684	−	1580.24i	0.0424365	−	0.174779i
$435$	10866.8			1.19776
$436$	7208.32	+	5237.15i	0.791779	+	0.575261i
$437$	1057.15	+	10058.1i	0.115721	+	1.10101i
$438$	−238.375	−	733.642i	−0.0260045	−	0.0800338i
$439$	568.461	+	984.603i	0.0618022	+	0.107045i	0.895271	−	0.445522i	$-0.146982\pi$
$439$	568.461	+	984.603i	0.0618022	+	0.107045i	−0.833469	+	0.552566i	$0.813649\pi$
$440$	7121.92	−	12335.5i	0.771646	−	1.33653i
$441$	4031.48	+	856.918i	0.435318	+	0.0925297i
$442$	−963.193	+	2964.40i	−0.103653	+	0.319010i
$443$	−12552.2	+	2668.05i	−1.34621	+	0.286146i	−0.823961	−	0.566646i	$-0.808241\pi$
$443$	−12552.2	+	2668.05i	−1.34621	+	0.286146i	−0.522250	+	0.852792i	$0.674907\pi$
$444$	347.328	−	3304.60i	0.0371249	−	0.353220i
$445$	−11065.1	+	12289.1i	−1.17874	+	1.30912i
$446$	−177.984	+	79.2435i	−0.0188964	+	0.00841320i
$447$	16605.8	+	7393.36i	1.75710	+	0.782313i
$448$	768.101	+	853.062i	0.0810030	+	0.0899629i
$449$	11748.8	−	8535.98i	1.23488	−	0.897189i	0.237629	−	0.971356i	$-0.423630\pi$
$449$	11748.8	−	8535.98i	1.23488	−	0.897189i	0.997246	+	0.0741665i	$0.0236296\pi$
$450$	737.877	−	536.099i	0.0772975	−	0.0561599i
$451$	−10611.9	−	11785.7i	−1.10797	−	1.23052i
$452$	−3195.85	−	1422.88i	−0.332566	−	0.148068i
$453$	12097.2	−	5386.01i	1.25469	−	0.558624i
$454$	812.336	−	902.190i	0.0839753	−	0.0932640i
$455$	−322.358	+	3067.03i	−0.0332140	+	0.316010i
$456$	6449.97	−	1370.98i	0.662385	−	0.140794i
$457$	−3119.68	+	9601.37i	−0.319327	+	0.982786i	0.654610	+	0.755967i	$0.272833\pi$
$457$	−3119.68	+	9601.37i	−0.319327	+	0.982786i	−0.973937	+	0.226820i	$0.927167\pi$
$458$	−6895.42	−	1465.67i	−0.703497	−	0.149533i
$459$	2240.27	−	3880.26i	0.227815	−	0.394586i
$460$	7489.55	+	12972.3i	0.759135	+	1.31486i
$461$	−772.813	−	2378.47i	−0.0780769	−	0.240296i	0.904398	−	0.426689i	$-0.140320\pi$
$461$	−772.813	−	2378.47i	−0.0780769	−	0.240296i	−0.982475	+	0.186393i	$0.940320\pi$
$462$	−327.090	−	3112.06i	−0.0329386	−	0.313390i
$463$	321.406	+	233.515i	0.0322614	+	0.0234393i	0.603799	−	0.797137i	$-0.293653\pi$
$463$	321.406	+	233.515i	0.0322614	+	0.0234393i	−0.571538	+	0.820576i	$0.693653\pi$
$464$	1661.27			0.166212
$465$	−13441.2	−	4798.74i	−1.34048	−	0.478572i
$466$	−2513.23			−0.249835
$467$	4576.86	+	3325.28i	0.453516	+	0.329499i	0.790982	−	0.611839i	$-0.209570\pi$
$467$	4576.86	+	3325.28i	0.453516	+	0.329499i	−0.337466	+	0.941338i	$0.609570\pi$
$468$	−307.785	−	2928.38i	−0.0304004	−	0.289240i
$469$	−1401.69	−	4313.96i	−0.138005	−	0.424734i
$470$	1951.68	+	3380.42i	0.191541	+	0.331760i
$471$	−11349.5	+	19657.8i	−1.11031	+	1.92311i
$472$	−3496.38	−	743.179i	−0.340962	−	0.0724737i
$473$	−8561.33	+	26349.1i	−0.832241	+	2.56138i
$474$	−6626.57	+	1408.52i	−0.642128	+	0.136488i
$475$	−226.410	+	2154.15i	−0.0218704	+	0.208083i
$476$	1198.97	−	1331.60i	0.115451	−	0.128222i
$477$	1860.22	−	828.223i	0.178561	−	0.0795005i
$478$	580.249	+	258.343i	0.0555229	+	0.0247204i
$479$	11101.5	+	12329.4i	1.05895	+	1.17609i	0.983865	+	0.178911i	$0.0572573\pi$
$479$	11101.5	+	12329.4i	1.05895	+	1.17609i	0.0750888	+	0.997177i	$0.476076\pi$
$480$	12540.5	−	9111.22i	1.19249	−	0.866392i
$481$	−2915.45	+	2118.19i	−0.276368	+	0.200793i
$482$	−672.673	−	747.079i	−0.0635673	−	0.0705986i
$483$	7281.74	+	3242.04i	0.685985	+	0.305420i
$484$	−7162.09	+	3188.77i	−0.672623	+	0.299471i
$485$	2447.72	−	2718.47i	0.229165	−	0.254514i
$486$	560.009	−	5328.13i	0.0522686	−	0.497302i
$487$	142.858	−	30.3654i	0.0132926	−	0.00282544i	−0.201261	−	0.979538i	$-0.564504\pi$
$487$	142.858	−	30.3654i	0.0132926	−	0.00282544i	0.214553	+	0.976712i	$0.431170\pi$
$488$	2967.65	−	9133.47i	0.275285	−	0.847240i
$489$	18681.7	+	3970.91i	1.72763	+	0.367220i
$490$	3060.45	−	5300.85i	0.282157	−	0.488711i
$491$	−5319.12	−	9212.99i	−0.488898	−	0.846795i	0.511021	−	0.859568i	$-0.329267\pi$
$491$	−5319.12	−	9212.99i	−0.488898	−	0.846795i	−0.999918	+	0.0127729i	$0.995934\pi$
$492$	−3360.28	−	10341.9i	−0.307913	−	0.947658i
$493$	715.771	+	6810.10i	0.0653888	+	0.622133i
$494$	−2388.58	−	1735.41i	−0.217546	−	0.158056i
$495$	−9148.11			−0.830661
$496$	−2054.84	−	733.610i	−0.186018	−	0.0664114i
$497$	−3396.16			−0.306516
$498$	6334.11	+	4602.00i	0.569957	+	0.414098i
$499$	1236.33	+	11762.9i	0.110913	+	1.05527i	0.898472	+	0.439030i	$0.144678\pi$
$499$	1236.33	+	11762.9i	0.110913	+	1.05527i	−0.787559	+	0.616239i	$0.788655\pi$
$500$	−1832.31	−	5639.28i	−0.163887	−	0.504392i
$501$	5782.36	+	10015.3i	0.515642	+	0.893119i
$502$	1900.65	−	3292.02i	0.168984	−	0.292689i
$503$	4035.59	+	857.790i	0.357729	+	0.0760377i	0.383271	−	0.923636i	$-0.374798\pi$
$503$	4035.59	+	857.790i	0.357729	+	0.0760377i	−0.0255413	+	0.999674i	$0.508131\pi$
$504$	534.947	−	1646.40i	0.0472786	−	0.145509i
$505$	−5618.63	+	1194.28i	−0.495101	+	0.105237i
$506$	−1723.03	+	16393.5i	−0.151379	+	1.44028i
$507$	2938.88	−	3263.96i	0.257437	−	0.285912i
$508$	9097.71	−	4050.56i	0.794578	−	0.353769i
$509$	−4675.01	−	2081.45i	−0.407104	−	0.181255i	0.192959	−	0.981207i	$-0.438191\pi$
$509$	−4675.01	−	2081.45i	−0.407104	−	0.181255i	−0.600064	+	0.799952i	$0.704858\pi$
$510$	4442.96	+	4934.40i	0.385760	+	0.428429i
$511$	389.086	−	282.688i	0.0336833	−	0.0244723i
$512$	3635.05	−	2641.02i	0.313765	−	0.227964i
$513$	2839.84	+	3153.96i	0.244409	+	0.271444i
$514$	6226.30	+	2772.13i	0.534300	+	0.237886i
$515$	2386.32	−	1062.46i	0.204183	−	0.0909079i
$516$	−12711.0	+	14117.0i	−1.08444	+	1.20440i
$517$	1063.44	−	10117.9i	0.0904639	−	0.860707i
$518$	−855.566	+	181.856i	−0.0725703	+	0.0154253i
$519$	3037.85	−	9349.55i	0.256931	−	0.790751i
$520$	−10360.6	−	2202.22i	−0.873736	−	0.185718i
$521$	3650.01	−	6322.00i	0.306928	−	0.531616i	−0.670760	−	0.741674i	$-0.734032\pi$
$521$	3650.01	−	6322.00i	0.306928	−	0.531616i	0.977689	+	0.210058i	$0.0673654\pi$
$522$	1365.61	+	2365.30i	0.114504	+	0.198326i
$523$	−132.300	−	407.178i	−0.0110614	−	0.0340433i	0.945374	−	0.325989i	$-0.105697\pi$
$523$	−132.300	−	407.178i	−0.0110614	−	0.0340433i	−0.956435	+	0.291946i	$0.905697\pi$
$524$	−947.848	−	9018.17i	−0.0790209	−	0.751833i
$525$	1381.10	+	1003.42i	0.114811	+	0.0834153i
$526$	−2321.25			−0.192417
$527$	2121.97	−	8739.54i	0.175397	−	0.722392i
$528$	−4198.55			−0.346058
$529$	−24126.0	−	17528.6i	−1.98290	−	1.44066i
$530$	−316.099	−	3007.48i	−0.0259066	−	0.246484i
$531$	709.417	+	2183.36i	0.0579775	+	0.178436i
$532$	848.635	+	1469.88i	0.0691597	+	0.119788i
$533$	−5896.65	+	10213.3i	−0.479197	+	0.829994i
$534$	−12204.9	−	2594.23i	−0.989059	−	0.210231i
$535$	4694.11	−	14447.0i	0.379335	−	1.16747i
$536$	15238.8	−	3239.11i	1.22802	−	0.261023i
$537$	218.869	−	2082.40i	0.0175882	−	0.167341i
$538$	−3169.18	+	3519.73i	−0.253965	+	0.282056i
$539$	−14574.1	+	6488.82i	−1.16466	+	0.518540i
$540$	5742.46	+	2556.71i	0.457622	+	0.203747i
$541$	12187.0	+	13535.0i	0.968503	+	1.07563i	0.997105	+	0.0760402i	$0.0242277\pi$
$541$	12187.0	+	13535.0i	0.968503	+	1.07563i	−0.0286022	+	0.999591i	$0.509106\pi$
$542$	−2673.15	+	1942.16i	−0.211848	+	0.153916i
$543$	−3644.43	+	2647.83i	−0.288025	+	0.209262i
$544$	6535.91	+	7258.86i	0.515119	+	0.572097i
$545$	−18805.2	−	8372.63i	−1.47803	−	0.658062i
$546$	−2125.78	+	946.456i	−0.166621	+	0.0741842i
$547$	9024.81	−	10023.1i	0.705435	−	0.783465i	−0.278797	−	0.960350i	$-0.589936\pi$
$547$	9024.81	−	10023.1i	0.705435	−	0.783465i	0.984231	+	0.176885i	$0.0566022\pi$
$548$	324.415	−	3086.60i	0.0252889	−	0.240608i
$549$	−6033.07	+	1282.37i	−0.469008	+	0.0996907i
$550$	−1090.94	+	3357.57i	−0.0845779	+	0.260304i
$551$	−6344.47	−	1348.56i	−0.490533	−	0.104266i
$552$	−13688.4	+	23709.0i	−1.05546	+	1.82812i
$553$	−2111.86	−	3657.85i	−0.162397	−	0.281279i
$554$	−4180.42	−	12866.0i	−0.320594	−	0.986688i
$555$	802.438	+	7634.69i	0.0613723	+	0.583918i
$556$	12559.0	+	9124.62i	0.957948	+	0.695990i
$557$	8568.26			0.651793			0.325896	−	0.945405i	$-0.394334\pi$
$557$	8568.26			0.651793			0.325896	+	0.945405i	$0.394334\pi$
$558$	−644.622	−	3528.70i	−0.0489051	−	0.267709i
$559$	20602.2			1.55882
$560$	812.512	+	590.325i	0.0613123	+	0.0445460i
$561$	−1808.98	−	17211.3i	−0.136141	−	1.29529i
$562$	−1273.41	−	3919.16i	−0.0955795	−	0.294163i
$563$	−8821.33	−	15279.0i	−0.660346	−	1.14375i	−0.980525	−	0.196396i	$-0.937076\pi$
$563$	−8821.33	−	15279.0i	−0.660346	−	1.14375i	0.320179	−	0.947357i	$-0.396257\pi$
$564$	3487.85	−	6041.14i	0.260399	−	0.451025i
$565$	7905.56	+	1680.38i	0.588654	+	0.125122i
$566$	−2797.08	+	8608.53i	−0.207721	+	0.639299i
$567$	5449.19	−	1158.26i	0.403606	−	0.0857890i
$568$	1219.27	−	11600.6i	0.0900694	−	0.856953i
$569$	15697.1	−	17433.4i	1.15651	−	1.28444i	0.204331	−	0.978902i	$-0.434498\pi$
$569$	15697.1	−	17433.4i	1.15651	−	1.28444i	0.952181	−	0.305535i	$-0.0988352\pi$
$570$	−5745.70	+	2558.15i	−0.422212	+	0.187981i
$571$	−5903.10	−	2628.23i	−0.432640	−	0.192624i	0.178849	−	0.983876i	$-0.442762\pi$
$571$	−5903.10	−	2628.23i	−0.432640	−	0.192624i	−0.611489	+	0.791253i	$0.709429\pi$
$572$	7626.34	+	8469.91i	0.557471	+	0.619134i
$573$	4513.64	−	3279.35i	0.329075	−	0.239087i
$574$	−2315.77	+	1682.50i	−0.168394	+	0.122346i
$575$	−6017.29	−	6682.88i	−0.436415	−	0.484688i
$576$	2313.23	+	1029.92i	0.167334	+	0.0745020i
$577$	6726.53	−	2994.85i	0.485319	−	0.216078i	−0.149466	−	0.988767i	$-0.547755\pi$
$577$	6726.53	−	2994.85i	0.485319	−	0.216078i	0.634785	+	0.772689i	$0.281089\pi$
$578$	2266.57	−	2517.28i	0.163109	−	0.181151i
$579$	−205.356	+	1953.83i	−0.0147397	+	0.140239i
$580$	−9396.81	+	1997.35i	−0.672727	+	0.142992i
$581$	−1508.41	+	4642.42i	−0.107710	+	0.331498i
$582$	2699.84	+	573.869i	0.192289	+	0.0408722i
$583$	−3940.91	+	6825.85i	−0.279958	+	0.484902i
$584$	825.914	+	1430.53i	0.0585215	+	0.101362i
$585$	2102.17	+	6469.81i	0.148571	+	0.457254i
$586$	77.0944	+	733.504i	0.00543471	+	0.0517078i
$587$	−8753.57	−	6359.84i	−0.615500	−	0.447187i	0.235847	−	0.971790i	$-0.424214\pi$
$587$	−8753.57	−	6359.84i	−0.615500	−	0.447187i	−0.851347	+	0.524603i	$0.824214\pi$
$588$	−10938.7			−0.767181
$589$	7252.00	+	4469.73i	0.507324	+	0.312686i
$590$	3409.37			0.237901
$591$	−1070.42	−	777.708i	−0.0745031	−	0.0541297i
$592$	122.673	+	1167.16i	0.00851662	+	0.0810302i
$593$	3112.86	+	9580.38i	0.215564	+	0.663439i	0.999113	+	0.0421085i	$0.0134075\pi$
$593$	3112.86	+	9580.38i	0.215564	+	0.663439i	−0.783549	+	0.621330i	$0.786592\pi$
$594$	3458.67	+	5990.59i	0.238907	+	0.413800i
$595$	−2069.86	+	3585.10i	−0.142615	+	0.247017i
$596$	−15718.4	−	3341.04i	−1.08028	−	0.229621i
$597$	−2435.09	+	7494.44i	−0.166937	+	0.513781i
$598$	11989.9	−	2548.53i	0.819906	−	0.174276i
$599$	1248.37	−	11877.4i	0.0851533	−	0.810180i	−0.865705	−	0.500554i	$-0.833130\pi$
$599$	1248.37	−	11877.4i	0.0851533	−	0.810180i	0.950859	−	0.309626i	$-0.100204\pi$
$600$	−3923.32	+	4357.29i	−0.266948	+	0.296476i
$601$	−2992.59	+	1332.39i	−0.203112	+	0.0904312i	−0.505772	−	0.862667i	$-0.668792\pi$
$601$	−2992.59	+	1332.39i	−0.203112	+	0.0904312i	0.302660	+	0.953099i	$0.402125\pi$
$602$	4568.20	+	2033.89i	0.309279	+	0.137700i
$603$	−6695.18	−	7435.75i	−0.452154	−	0.502168i
$604$	−9470.77	+	6880.92i	−0.638014	+	0.463544i
$605$	14653.4	−	10646.3i	0.984706	−	0.715431i
$606$	−2900.15	−	3220.94i	−0.194407	−	0.215910i
$607$	24887.4	+	11080.6i	1.66416	+	0.740933i	0.999978	−	0.00663552i	$-0.00211217\pi$
$607$	24887.4	+	11080.6i	1.66416	+	0.740933i	0.664185	+	0.747568i	$0.268779\pi$
$608$	−8452.34	+	3763.22i	−0.563796	+	0.251018i
$609$	−3420.63	+	3799.00i	−0.227604	+	0.252780i
$610$	−957.467	+	9109.69i	−0.0635520	+	0.604656i
$611$	−7400.06	+	1572.93i	−0.489974	+	0.104147i
$612$	1221.41	−	3759.12i	0.0806743	−	0.248290i
$613$	−12476.4	−	2651.94i	−0.822049	−	0.174732i	−0.222360	−	0.974965i	$-0.571376\pi$
$613$	−12476.4	−	2651.94i	−0.822049	−	0.174732i	−0.599690	+	0.800233i	$0.704709\pi$
$614$	−2773.93	+	4804.59i	−0.182324	+	0.315794i
$615$	12561.3	+	21756.8i	0.823612	+	1.42654i
$616$	2070.63	+	6372.74i	0.135435	+	0.416827i
$617$	342.023	+	3254.13i	0.0223166	+	0.212328i	0.999998	+	0.00223281i	$0.000710726\pi$
$617$	342.023	+	3254.13i	0.0223166	+	0.212328i	−0.977681	+	0.210095i	$0.932623\pi$
$618$	1594.56	+	1158.51i	0.103790	+	0.0754082i
$619$	−14020.0			−0.910359			−0.455179	−	0.890400i	$-0.650425\pi$
$619$	−14020.0			−0.910359			−0.455179	+	0.890400i	$0.650425\pi$
$620$	12505.0	+	1679.05i	0.810021	+	0.108762i
$621$	−17620.2			−1.13861
$622$	−2199.92	−	1598.34i	−0.141815	−	0.103034i
$623$	−813.157	−	7736.67i	−0.0522928	−	0.497533i
$624$	964.796	+	2969.34i	0.0618954	+	0.190495i
$625$	9592.38	+	16614.5i	0.613913	+	1.06333i
$626$	6676.82	−	11564.6i	0.426293	−	0.738361i
$627$	16034.5	+	3408.23i	1.02130	+	0.217084i
$628$	6201.00	−	19084.7i	0.394023	−	1.21268i
$629$	−4731.72	+	1005.76i	−0.299946	+	0.0637554i
$630$	−172.593	+	1642.11i	−0.0109147	+	0.103846i
$631$	−4392.03	+	4877.85i	−0.277091	+	0.307740i	−0.865586	−	0.500760i	$-0.833054\pi$
$631$	−4392.03	+	4877.85i	−0.277091	+	0.307740i	0.588495	+	0.808501i	$0.299720\pi$
$632$	13252.6	−	5900.45i	0.834115	−	0.371372i
$633$	8759.10	+	3899.80i	0.549989	+	0.244871i
$634$	−8323.70	−	9244.41i	−0.521414	−	0.579089i
$635$	−18613.7	+	13523.6i	−1.16325	+	0.845147i
$636$	−4372.15	+	3176.56i	−0.272590	+	0.198048i
$637$	7938.11	+	8816.17i	0.493751	+	0.548366i
$638$	−9657.80	−	4299.93i	−0.599304	−	0.266827i
$639$	−6843.84	+	3047.07i	−0.423690	+	0.188639i
$640$	−10524.7	+	11688.8i	−0.650038	+	0.721940i
$641$	−97.4612	+	927.282i	−0.00600544	+	0.0571380i	−0.997114	−	0.0759163i	$-0.975812\pi$
$641$	−97.4612	+	927.282i	−0.00600544	+	0.0571380i	0.991109	+	0.133054i	$0.0424785\pi$
$642$	11211.4	−	2383.05i	0.689217	−	0.146498i
$643$	1342.88	−	4132.97i	0.0823610	−	0.253481i	−0.901393	−	0.433001i	$-0.857455\pi$
$643$	1342.88	−	4132.97i	0.0823610	−	0.253481i	0.983754	+	0.179520i	$0.0574545\pi$
$644$	−6892.61	−	1465.07i	−0.421750	−	0.0896456i
$645$	21943.8	−	38007.8i	1.33959	−	2.32024i
$646$	−1981.62	−	3432.26i	−0.120690	−	0.209041i
$647$	7475.79	+	23008.1i	0.454256	+	1.39806i	0.872006	+	0.489494i	$0.162819\pi$
$647$	7475.79	+	23008.1i	0.454256	+	1.39806i	−0.417750	+	0.908562i	$0.637181\pi$
$648$	2000.04	+	19029.1i	0.121248	+	1.15360i
$649$	−7189.00	−	5223.12i	−0.434812	−	0.315910i
$650$	2625.26			0.158417
$651$	5908.62	−	3188.47i	0.355725	−	0.191960i
$652$	−16884.4			−1.01418
$653$	22207.8	+	16134.9i	1.33087	+	0.966935i	0.999727	+	0.0233553i	$0.00743491\pi$
$653$	22207.8	+	16134.9i	1.33087	+	0.966935i	0.331145	+	0.943580i	$0.392565\pi$
$654$	−1623.55	−	15447.1i	−0.0970732	−	0.923590i
$655$	6473.79	+	19924.3i	0.386186	+	1.18856i
$656$	1920.32	+	3326.09i	0.114292	+	0.197960i
$657$	530.444	−	918.756i	0.0314986	−	0.0545572i
$658$	−1796.13	−	381.779i	−0.106414	−	0.0226190i
$659$	−356.586	+	1097.46i	−0.0210783	+	0.0648724i	−0.961042	−	0.276401i	$-0.910858\pi$
$659$	−356.586	+	1097.46i	−0.0210783	+	0.0648724i	0.939964	+	0.341273i	$0.110858\pi$
$660$	23748.7	−	5047.94i	1.40063	−	0.297713i
$661$	1723.10	−	16394.2i	0.101393	−	0.964691i	−0.819026	−	0.573757i	$-0.805485\pi$
$661$	1723.10	−	16394.2i	0.101393	−	0.964691i	0.920419	−	0.390934i	$-0.127848\pi$
$662$	4428.48	−	4918.32i	0.259997	−	0.288755i
$663$	−11756.6	+	5234.38i	−0.688671	+	0.306616i
$664$	−15316.0	−	6819.12i	−0.895144	−	0.398544i
$665$	−2623.82	−	2914.05i	−0.153004	−	0.169928i
$666$	−1560.95	+	1134.09i	−0.0908190	+	0.0659839i
$667$	21786.0	−	15828.4i	1.26470	−	0.918860i
$668$	−6841.01	−	7597.71i	−0.396237	−	0.440066i
$669$	−734.854	−	327.178i	−0.0424680	−	0.0189080i
$670$	−13574.9	+	6043.94i	−0.782753	+	0.348504i
$671$	15974.9	−	17741.9i	0.919080	−	1.02074i
$672$	−762.229	+	7252.13i	−0.0437554	+	0.416305i
$673$	21076.4	−	4479.93i	1.20718	−	0.256595i	0.439986	−	0.898005i	$-0.354983\pi$
$673$	21076.4	−	4479.93i	1.20718	−	0.256595i	0.767199	+	0.641410i	$0.221650\pi$
$674$	923.195	−	2841.30i	0.0527599	−	0.162378i
$675$	−3691.27	−	784.604i	−0.210485	−	0.0447399i
$676$	−1941.40	+	3362.61i	−0.110457	+	0.191318i
$677$	−6785.33	−	11752.5i	−0.385202	−	0.667189i	0.606596	−	0.795011i	$-0.292535\pi$
$677$	−6785.33	−	11752.5i	−0.385202	−	0.667189i	−0.991797	+	0.127822i	$0.959201\pi$
$678$	1884.49	+	5799.86i	0.106745	+	0.328529i
$679$	179.878	+	1711.43i	0.0101666	+	0.0967283i
$680$	−11502.9	−	8357.31i	−0.648697	−	0.471306i
$681$	5012.40			0.282049
$682$	10047.0	+	9583.45i	0.564103	+	0.538078i
$683$	−24506.3			−1.37293			−0.686463	−	0.727165i	$-0.740837\pi$
$683$	−24506.3			−1.37293			−0.686463	+	0.727165i	$0.740837\pi$
$684$	3028.93	+	2200.65i	0.169319	+	0.123017i
$685$	749.502	+	7131.03i	0.0418058	+	0.397756i
$686$	1888.41	+	5811.92i	0.105102	+	0.323470i
$687$	−14552.8	−	25206.2i	−0.808188	−	1.39982i
$688$	3354.68	−	5810.47i	0.185895	−	0.321980i
$689$	5733.03	+	1218.59i	0.316997	+	0.0673799i
$690$	8069.07	−	24834.1i	0.445195	−	1.37017i
$691$	−28250.2	+	6004.76i	−1.55526	+	0.330581i	−0.903752	−	0.428057i	$-0.859198\pi$
$691$	−28250.2	+	6004.76i	−1.55526	+	0.330581i	−0.651512	+	0.758639i	$0.725865\pi$
$692$	−908.433	+	8643.17i	−0.0499038	+	0.474803i
$693$	2879.62	−	3198.15i	0.157847	−	0.175307i
$694$	−1452.56	+	646.723i	−0.0794504	+	0.0353736i
$695$	−32764.1	−	14587.5i	−1.78822	−	0.796168i
$696$	−11748.5	−	13048.1i	−0.639837	−	0.710611i
$697$	−12807.4	+	9305.10i	−0.696002	+	0.505675i
$698$	−5465.44	+	3970.87i	−0.296375	+	0.215329i
$699$	−6943.28	−	7711.30i	−0.375707	−	0.417265i
$700$	−1378.70	−	613.838i	−0.0744429	−	0.0331441i
$701$	−2262.29	+	1007.24i	−0.121891	+	0.0542694i	−0.466776	−	0.884376i	$-0.654585\pi$
$701$	−2262.29	+	1007.24i	−0.121891	+	0.0542694i	0.344885	+	0.938645i	$0.387918\pi$
$702$	3441.94	−	3822.67i	0.185054	−	0.205523i
$703$	478.962	−	4557.02i	0.0256961	−	0.244482i
$704$	−9587.05	+	2037.79i	−0.513247	+	0.109094i
$705$	−4980.16	+	15327.3i	−0.266048	+	0.818810i
$706$	17970.3	+	3819.70i	0.957961	+	0.203621i
$707$	1351.11	−	2340.18i	0.0718721	−	0.124486i
$708$	−3046.44	−	5276.59i	−0.161712	−	0.280094i
$709$	4541.71	+	13978.0i	0.240575	+	0.740414i	0.996333	+	0.0855625i	$0.0272687\pi$
$709$	4541.71	+	13978.0i	0.240575	+	0.740414i	−0.755758	+	0.654851i	$0.772731\pi$
$710$	1162.94	+	11064.7i	0.0614712	+	0.584859i
$711$	−7537.61	−	5476.39i	−0.397584	−	0.288862i
$712$	26718.8			1.40636
$713$	−33937.0	+	9957.72i	−1.78254	+	0.523029i
$714$	−3123.59			−0.163722
$715$	−21302.7	−	15477.3i	−1.11423	−	0.809538i
$716$	193.490	+	1840.93i	0.0100992	+	0.0960878i
$717$	810.378	+	2494.09i	0.0422094	+	0.129907i
$718$	3143.83	+	5445.27i	0.163408	+	0.283030i
$719$	−7053.88	+	12217.7i	−0.365877	+	0.633717i	−0.988916	−	0.148473i	$-0.952564\pi$
$719$	−7053.88	+	12217.7i	−0.365877	+	0.633717i	0.623040	+	0.782190i	$0.285898\pi$
$720$	2166.99	+	460.609i	0.112165	+	0.0238415i
$721$	−379.730	+	1168.69i	−0.0196143	+	0.0603665i
$722$	−6667.35	+	1417.19i	−0.343675	+	0.0730503i
$723$	433.859	−	4127.89i	0.0223173	−	0.212335i
$724$	2664.75	−	2959.51i	0.136788	−	0.151919i
$725$	5268.79	−	2345.82i	0.269901	−	0.120167i
$726$	12485.2	+	5558.77i	0.638249	+	0.284167i
$727$	−19949.2	−	22155.8i	−1.01771	−	1.13028i	−0.991432	−	0.130624i	$-0.958302\pi$
$727$	−19949.2	−	22155.8i	−1.01771	−	1.13028i	−0.0262759	−	0.999655i	$-0.508365\pi$
$728$	4031.18	−	2928.82i	0.205227	−	0.149106i
$729$	−2009.55	+	1460.02i	−0.102096	+	0.0741769i
$730$	−1054.23	−	1170.84i	−0.0534504	−	0.0593627i
$731$	25264.4	+	11248.5i	1.27830	+	0.569137i
$732$	14954.4	−	6658.11i	0.755095	−	0.336190i
$733$	4210.41	−	4676.14i	0.212163	−	0.235630i	−0.627665	−	0.778483i	$-0.715989\pi$
$733$	4210.41	−	4676.14i	0.212163	−	0.235630i	0.839828	+	0.542853i	$0.182656\pi$
$734$	400.515	−	3810.65i	0.0201407	−	0.191626i
$735$	24719.6	−	5254.30i	1.24054	−	0.263684i
$736$	11870.2	−	36532.7i	0.594485	−	1.82964i
$737$	37883.3	+	8052.35i	1.89342	+	0.402459i
$738$	−3157.10	+	5468.26i	−0.157472	+	0.272750i
$739$	11273.3	+	19525.9i	0.561156	+	0.971951i	0.997396	+	0.0721204i	$0.0229766\pi$
$739$	11273.3	+	19525.9i	0.561156	+	0.971951i	−0.436240	+	0.899830i	$0.643690\pi$
$740$	−2097.17	−	6454.42i	−0.104180	−	0.320634i
$741$	−1274.20	−	12123.2i	−0.0631701	−	0.601023i
$742$	1150.91	+	836.182i	0.0569422	+	0.0413709i
$743$	3115.32			0.153823			0.0769113	−	0.997038i	$-0.475494\pi$
$743$	3115.32			0.153823			0.0769113	+	0.997038i	$0.475494\pi$
$744$	8769.86	+	21327.3i	0.432149	+	1.05094i
$745$	37125.7			1.82575
$746$	6508.56	+	4728.75i	0.319431	+	0.232080i
$747$	1125.52	+	10708.6i	0.0551281	+	0.524509i
$748$	4727.75	+	14550.5i	0.231101	+	0.711256i
$749$	3573.01	+	6188.63i	0.174306	+	0.301906i
$750$	−5168.24	+	8951.66i	−0.251623	+	0.435824i
$751$	−12907.9	−	2743.67i	−0.627187	−	0.133313i	−0.116657	−	0.993172i	$-0.537218\pi$
$751$	−12907.9	−	2743.67i	−0.627187	−	0.133313i	−0.510531	+	0.859860i	$0.670551\pi$
$752$	−761.344	+	2343.18i	−0.0369194	+	0.113626i
$753$	15351.7	−	3263.11i	0.742958	−	0.157921i
$754$	−821.744	+	7818.37i	−0.0396898	+	0.377624i
$755$	18097.2	−	20099.0i	0.872350	−	0.968842i
$756$	−2701.41	+	1202.75i	−0.129960	+	0.0578617i
$757$	−28202.2	−	12556.4i	−1.35407	−	0.602869i	−0.403954	−	0.914779i	$-0.632364\pi$
$757$	−28202.2	−	12556.4i	−1.35407	−	0.602869i	−0.950111	+	0.311911i	$0.899031\pi$
$758$	9777.03	+	10858.5i	0.468493	+	0.520314i
$759$	−55060.0	+	40003.4i	−2.63314	+	1.91309i
$760$	10895.8	−	7916.23i	0.520040	−	0.377831i
$761$	27140.0	+	30142.0i	1.29280	+	1.43580i	0.838447	+	0.544984i	$0.183464\pi$
$761$	27140.0	+	30142.0i	1.29280	+	1.43580i	0.454356	+	0.890820i	$0.349869\pi$
$762$	−15859.4	−	7061.07i	−0.753972	−	0.335690i
$763$	8846.51	−	3938.72i	0.419744	−	0.186882i
$764$	−3300.31	+	3665.36i	−0.156284	+	0.173571i
$765$	−954.524	+	9081.69i	−0.0451123	+	0.429215i
$766$	−2443.97	+	519.482i	−0.115280	+	0.0245035i
$767$	−2041.96	+	6284.51i	−0.0961290	+	0.295855i
$768$	−20957.7	−	4454.69i	−0.984694	−	0.209303i
$769$	−13431.8	+	23264.6i	−0.629861	+	1.09095i	0.357718	+	0.933830i	$0.383555\pi$
$769$	−13431.8	+	23264.6i	−0.629861	+	1.09095i	−0.987579	+	0.157122i	$0.949778\pi$
$770$	−3195.58	−	5534.91i	−0.149559	−	0.259044i
$771$	8695.67	+	26762.5i	0.406183	+	1.25010i
$772$	−181.543	−	1727.27i	−0.00846359	−	0.0805257i
$773$	−20119.8	−	14617.9i	−0.936169	−	0.680166i	0.0113266	−	0.999936i	$-0.496395\pi$
$773$	−20119.8	−	14617.9i	−0.936169	−	0.680166i	−0.947495	+	0.319769i	$0.896395\pi$
$774$	11030.5			0.512253
$775$	−7552.90	+	574.882i	−0.350075	+	0.0266456i
$776$	−5910.45			−0.273419
$777$	−2921.65	−	2122.70i	−0.134895	−	0.0980071i
$778$	433.930	+	4128.57i	0.0199963	+	0.190252i
$779$	−4633.79	−	14261.3i	−0.213123	−	0.655925i
$780$	−9027.32	−	15635.8i	−0.414398	−	0.717758i
$781$	14498.8	−	25112.6i	0.664286	−	1.15058i
$782$	16094.7	+	3421.03i	0.735991	+	0.156440i
$783$	3492.07	−	10747.5i	0.159383	−	0.490529i
$784$	3779.02	−	803.255i	0.172149	−	0.0365914i
$785$	−4846.03	+	46106.9i	−0.220334	+	2.09634i
$786$	−10577.2	+	11747.2i	−0.479995	+	0.533088i
$787$	−1800.72	+	801.731i	−0.0815612	+	0.0363134i	−0.447112	−	0.894478i	$-0.647547\pi$
$787$	−1800.72	+	801.731i	−0.0815612	+	0.0363134i	0.365551	+	0.930791i	$0.380881\pi$
$788$	1068.57	+	475.757i	0.0483073	+	0.0215078i
$789$	−6412.88	−	7122.22i	−0.289359	−	0.321366i
$790$	−11194.1	+	8132.98i	−0.504136	+	0.366276i
$791$	−3075.95	+	2234.81i	−0.138266	+	0.100456i
$792$	9890.37	+	10984.4i	0.443736	+	0.492819i
$793$	−16218.5	−	7220.94i	−0.726274	−	0.323358i
$794$	2399.48	−	1068.32i	0.107247	−	0.0477496i
$795$	8354.51	−	9278.62i	0.372709	−	0.413936i
$796$	728.185	−	6928.22i	0.0324244	−	0.308498i
$797$	−6497.50	+	1381.09i	−0.288774	+	0.0613809i	−0.350021	−	0.936742i	$-0.613826\pi$
$797$	−6497.50	+	1381.09i	−0.288774	+	0.0613809i	0.0612469	+	0.998123i	$0.480492\pi$
$798$	914.300	−	2813.92i	0.0405587	−	0.124827i
$799$	−9933.49	−	2111.43i	−0.439827	−	0.0934881i
$800$	4113.45	−	7124.71i	0.181791	−	0.314870i
$801$	−8580.07	−	14861.1i	−0.378479	−	0.655545i
$802$	−1547.28	−	4762.02i	−0.0681249	−	0.209667i
$803$	429.236	+	4083.91i	0.0188635	+	0.179474i
$804$	21483.9	+	15609.0i	0.942386	+	0.684683i
$805$	16279.9			0.712783
$806$	4468.98	−	9307.71i	0.195301	−	0.406762i
$807$	−19555.0			−0.852995
$808$	7508.51	+	5455.25i	0.326916	+	0.237519i
$809$	1137.55	+	10823.0i	0.0494363	+	0.470355i	0.991034	+	0.133614i	$0.0426581\pi$
$809$	1137.55	+	10823.0i	0.0494363	+	0.470355i	−0.941597	+	0.336741i	$0.890675\pi$
$810$	−5639.57	−	17356.8i	−0.244635	−	0.752909i
$811$	−3973.43	−	6882.19i	−0.172042	−	0.297986i	0.767092	−	0.641538i	$-0.221703\pi$
$811$	−3973.43	−	6882.19i	−0.172042	−	0.297986i	−0.939134	+	0.343552i	$0.888370\pi$
$812$	2259.64	−	3913.81i	0.0976575	−	0.169148i
$813$	−13344.1	−	2836.39i	−0.575645	−	0.122357i
$814$	2307.84	−	7102.79i	0.0993730	−	0.305839i
$815$	38155.9	−	8110.28i	1.63993	−	0.348578i
$816$	−438.081	+	4168.07i	−0.0187940	+	0.178813i
$817$	−17528.4	+	19467.3i	−0.750601	+	0.833627i
$818$	5001.98	−	2227.02i	0.213802	−	0.0951908i
$819$	−2923.54	−	1301.64i	−0.124733	−	0.0555349i
$820$	−14861.1	−	16504.9i	−0.632892	−	0.702897i
$821$	3991.82	−	2900.23i	0.169690	−	0.123287i	−0.499699	−	0.866199i	$-0.666556\pi$
$821$	3991.82	−	2900.23i	0.169690	−	0.123287i	0.669389	+	0.742912i	$0.266556\pi$
$822$	−4377.02	+	3180.09i	−0.185725	+	0.134937i
$823$	18441.9	+	20481.8i	0.781099	+	0.867499i	0.993978	−	0.109580i	$-0.0349506\pi$
$823$	18441.9	+	20481.8i	0.781099	+	0.867499i	−0.212879	+	0.977079i	$0.568284\pi$
$824$	−3855.67	−	1716.65i	−0.163008	−	0.0725758i
$825$	−13315.9	+	5928.61i	−0.561938	+	0.250191i
$826$	−1073.19	+	1191.90i	−0.0452072	+	0.0502077i
$827$	1961.67	−	18664.1i	0.0824837	−	0.784780i	−0.872598	−	0.488439i	$-0.837567\pi$
$827$	1961.67	−	18664.1i	0.0824837	−	0.784780i	0.955082	−	0.296342i	$-0.0957667\pi$
$828$	−15204.2	+	3231.76i	−0.638145	+	0.135642i
$829$	14110.6	−	43428.0i	0.591172	−	1.81944i	0.0182448	−	0.999834i	$-0.494192\pi$
$829$	14110.6	−	43428.0i	0.591172	−	1.81944i	0.572927	−	0.819606i	$-0.305808\pi$
$830$	15641.5	+	3324.71i	0.654126	+	0.139039i
$831$	27927.3	−	48371.5i	1.16581	−	2.01924i
$832$	3644.22	+	6311.97i	0.151852	+	0.263015i
$833$	4921.03	+	15145.4i	0.204686	+	0.629959i
$834$	−2828.70	−	26913.2i	−0.117446	−	1.11742i
$835$	19109.0	+	13883.5i	0.791971	+	0.575401i
$836$	−14491.9			−0.599535
$837$	−9065.42	+	11751.6i	−0.374369	+	0.485297i
$838$	−18759.4			−0.773309
$839$	25039.0	+	18191.9i	1.03032	+	0.748574i	0.968374	−	0.249505i	$-0.0802679\pi$
$839$	25039.0	+	18191.9i	1.03032	+	0.748574i	0.0619507	+	0.998079i	$0.480268\pi$
$840$	−1109.53	−	10556.5i	−0.0455743	−	0.433610i
$841$	−2199.68	−	6769.91i	−0.0901913	−	0.277580i
$842$	−8054.41	−	13950.6i	−0.329659	−	0.570987i
$843$	8507.02	−	14734.6i	0.347565	−	0.602001i
$844$	−8291.01	−	1762.31i	−0.338138	−	0.0718734i
$845$	2772.04	−	8531.47i	0.112853	−	0.347327i
$846$	−3962.04	+	842.157i	−0.161014	+	0.0342245i
$847$	−890.656	+	8474.02i	−0.0361314	+	0.343767i
$848$	1277.20	−	1418.47i	0.0517208	−	0.0574418i
$849$	−34140.8	+	15200.5i	−1.38011	+	0.614462i
$850$	3219.36	+	1433.35i	0.129910	+	0.0578395i
$851$	12729.3	+	14137.3i	0.512756	+	0.569474i
$852$	16085.4	−	11686.7i	0.646802	−	0.469929i
$853$	−20081.2	+	14589.9i	−0.806059	+	0.585636i	−0.912685	−	0.408663i	$-0.865995\pi$
$853$	−20081.2	+	14589.9i	−0.806059	+	0.585636i	0.106627	+	0.994299i	$0.465995\pi$
$854$	−2883.32	−	3202.25i	−0.115533	−	0.128313i
$855$	−7901.95	−	3518.18i	−0.316071	−	0.140724i
$856$	−22421.8	+	9982.84i	−0.895283	+	0.398606i
$857$	−4255.81	+	4726.56i	−0.169633	+	0.188397i	−0.821967	−	0.569535i	$-0.807123\pi$
$857$	−4255.81	+	4726.56i	−0.169633	+	0.188397i	0.652334	+	0.757932i	$0.273790\pi$
$858$	2076.80	−	19759.5i	0.0826351	−	0.786220i
$859$	−31002.0	+	6589.69i	−1.23140	+	0.261743i	−0.777257	−	0.629184i	$-0.783389\pi$
$859$	−31002.0	+	6589.69i	−1.23140	+	0.261743i	−0.454147	+	0.890927i	$0.650056\pi$
$860$	−11989.4	+	36899.7i	−0.475391	+	1.46310i
$861$	−11560.1	−	2457.18i	−0.457571	−	0.0972596i
$862$	8857.73	−	15342.0i	0.349995	−	0.606209i
$863$	−17179.2	−	29755.3i	−0.677622	−	1.17368i	−0.975695	−	0.219133i	$-0.929677\pi$
$863$	−17179.2	−	29755.3i	−0.677622	−	1.17368i	0.298073	−	0.954543i	$-0.403656\pi$
$864$	−4981.26	−	15330.7i	−0.196141	−	0.603660i
$865$	−2098.77	−	19968.5i	−0.0824976	−	0.784912i
$866$	−578.111	−	420.022i	−0.0226848	−	0.0164815i
$867$	13985.6			0.547836
$868$	−4523.29	+	3843.17i	−0.176878	+	0.150283i
$869$	36063.5			1.40779
$870$	13548.4	+	9843.52i	0.527971	+	0.383594i
$871$	−3010.46	−	28642.6i	−0.117113	−	1.11426i
$872$	10277.8	+	31631.9i	0.399141	+	1.22843i
$873$	1898.00	+	3287.42i	0.0735824	+	0.127448i
$874$	−7792.92	+	13497.7i	−0.301601	+	0.522389i
$875$	−6303.58	−	1339.87i	−0.243543	−	0.0517666i
$876$	−870.072	+	2677.81i	−0.0335582	+	0.103282i
$877$	−21747.6	+	4622.60i	−0.837361	+	0.177987i	−0.606583	−	0.795020i	$-0.707460\pi$
$877$	−21747.6	+	4622.60i	−0.837361	+	0.177987i	−0.230778	+	0.973007i	$0.574127\pi$
$878$	−183.145	+	1742.51i	−0.00703968	+	0.0669781i
$879$	−2037.61	+	2262.99i	−0.0781874	+	0.0868359i
$880$	−7833.86	+	3487.86i	−0.300090	+	0.133609i
$881$	27681.5	+	12324.6i	1.05858	+	0.471312i	0.860805	−	0.508935i	$-0.169960\pi$
$881$	27681.5	+	12324.6i	1.05858	+	0.471312i	0.197779	+	0.980247i	$0.436627\pi$
$882$	4250.11	+	4720.23i	0.162255	+	0.180202i
$883$	31557.9	−	22928.2i	1.20273	−	0.873833i	0.208177	−	0.978091i	$-0.433247\pi$
$883$	31557.9	−	22928.2i	1.20273	−	0.873833i	0.994550	+	0.104258i	$0.0332469\pi$
$884$	9204.15	−	6687.21i	0.350191	−	0.254429i
$885$	9419.02	+	10460.9i	0.357759	+	0.397332i
$886$	−18066.5	−	8043.73i	−0.685052	−	0.305005i
$887$	−6051.57	+	2694.33i	−0.229078	+	0.101992i	−0.518066	−	0.855341i	$-0.673348\pi$
$887$	−6051.57	+	2694.33i	−0.229078	+	0.101992i	0.288988	+	0.957333i	$0.406681\pi$
$888$	8299.62	−	9217.66i	0.313645	−	0.348338i
$889$	1131.36	−	10764.2i	0.0426824	−	0.406096i
$890$	−24927.6	+	5298.52i	−0.938848	+	0.199558i
$891$	−14698.8	+	45238.4i	−0.552671	+	1.70095i
$892$	695.584	+	147.851i	0.0261097	+	0.00554979i
$893$	4809.72	−	8330.67i	0.180236	−	0.312178i
$894$	14006.5	+	24259.9i	0.523989	+	0.907575i
$895$	−1321.53	−	4067.26i	−0.0493564	−	0.151903i
$896$	−773.438	−	7358.77i	−0.0288379	−	0.274374i
$897$	40944.0	+	29747.5i	1.52406	+	1.10729i
$898$	22380.2			0.831668
$899$	652.091	−	22673.5i	0.0241918	−	0.841160i
$900$	−3329.06			−0.123298
$901$	6365.09	+	4624.51i	0.235352	+	0.170993i
$902$	−2554.73	−	24306.7i	−0.0943052	−	0.897254i
$903$	6379.96	+	19635.5i	0.235118	+	0.723620i
$904$	−6529.32	−	11309.1i	−0.240224	−	0.416079i
$905$	−4600.32	+	7967.99i	−0.168972	+	0.292669i
$906$	19961.2	+	4242.89i	0.731974	+	0.155586i
$907$	−1171.09	+	3604.26i	−0.0428727	+	0.131949i	−0.970202	−	0.242298i	$-0.922099\pi$
$907$	−1171.09	+	3604.26i	−0.0428727	+	0.131949i	0.927329	+	0.374247i	$0.122099\pi$
$908$	−4334.35	+	921.295i	−0.158415	+	0.0336721i
$909$	623.068	−	5928.09i	0.0227347	−	0.216306i
$910$	−3180.13	+	3531.89i	−0.115846	+	0.128660i
$911$	34252.5	−	15250.2i	1.24570	−	0.554623i	0.325307	−	0.945608i	$-0.394532\pi$
$911$	34252.5	−	15250.2i	1.24570	−	0.554623i	0.920397	+	0.390985i	$0.127866\pi$
$912$	−3626.62	−	1614.68i	−0.131677	−	0.0586264i
$913$	−27888.3	−	30973.1i	−1.01092	−	1.12274i
$914$	−12586.8	+	9144.82i	−0.455507	+	0.330945i
$915$	−30596.2	+	22229.5i	−1.10544	+	0.803151i
$916$	17217.2	+	19121.6i	0.621039	+	0.689734i
$917$	−9003.26	−	4008.51i	−0.324224	−	0.144354i
$918$	6307.98	−	2808.49i	0.226791	−	0.100974i
$919$	−4851.53	+	5388.17i	−0.174143	+	0.193405i	−0.823898	−	0.566739i	$-0.808205\pi$
$919$	−4851.53	+	5388.17i	−0.174143	+	0.193405i	0.649755	+	0.760144i	$0.274872\pi$
$920$	−5844.71	+	55608.7i	−0.209450	+	1.99279i
$921$	−22405.3	+	4762.40i	−0.801608	+	0.170387i
$922$	1190.98	−	3665.45i	0.0425410	−	0.130928i
$923$	−21092.1	−	4483.27i	−0.752172	−	0.159879i
$924$	−5710.82	+	9891.43i	−0.203325	+	0.352169i
$925$	2037.16	+	3528.47i	0.0724124	+	0.125422i
$926$	189.195	+	582.281i	0.00671417	+	0.0206641i
$927$	283.340	+	2695.80i	0.0100390	+	0.0955143i
$928$	19930.7	+	14480.5i	0.705020	+	0.512227i
$929$	18748.9			0.662144			0.331072	−	0.943606i	$-0.392590\pi$
$929$	18748.9			0.662144			0.331072	+	0.943606i	$0.392590\pi$
$930$	−12411.3	−	18158.4i	−0.437616	−	0.640257i
$931$	−15084.3			−0.531008
$932$	7421.40	+	5391.96i	0.260833	+	0.189506i
$933$	−1173.56	−	11165.7i	−0.0411796	−	0.391798i
$934$	2694.15	+	8291.75i	0.0943847	+	0.290486i
$935$	−17673.2	−	30610.8i	−0.618155	−	1.07068i
$936$	5495.73	−	9518.88i	0.191916	−	0.332409i
$937$	−557.651	−	118.532i	−0.0194425	−	0.00413264i	0.198180	−	0.980166i	$-0.436497\pi$
$937$	−557.651	−	118.532i	−0.0194425	−	0.00413264i	−0.217623	+	0.976033i	$0.569830\pi$
$938$	2160.14	−	6648.23i	0.0751931	−	0.231420i
$939$	53929.3	−	11463.0i	1.87425	−	0.398383i
$940$	1489.26	−	14169.3i	0.0516746	−	0.491651i
$941$	−4542.24	+	5044.67i	−0.157357	+	0.174762i	−0.816668	−	0.577108i	$-0.804181\pi$
$941$	−4542.24	+	5044.67i	−0.157357	+	0.174762i	0.659311	+	0.751870i	$0.270848\pi$
$942$	−31956.9	+	14228.1i	−1.10532	+	0.492121i
$943$	56873.9	+	25321.9i	1.96402	+	0.874436i
$944$	1439.94	+	1599.21i	0.0496462	+	0.0551377i
$945$	5527.02	−	4015.61i	0.190258	−	0.138231i
$946$	−34541.9	+	25096.1i	−1.18716	+	0.862522i
$947$	−2546.70	−	2828.40i	−0.0873884	−	0.0970546i	0.697865	−	0.716230i	$-0.254134\pi$
$947$	−2546.70	−	2828.40i	−0.0873884	−	0.0970546i	−0.785253	+	0.619175i	$0.787467\pi$
$948$	22589.7	+	10057.6i	0.773922	+	0.344572i
$949$	2789.62	−	1242.02i	0.0954215	−	0.0424844i
$950$	−2233.58	+	2480.65i	−0.0762811	+	0.0847187i
$951$	5368.60	−	51078.8i	0.183059	−	1.74169i
$952$	6542.53	−	1390.66i	0.222736	−	0.0473440i
$953$	345.167	−	1062.31i	0.0117325	−	0.0361089i	−0.945019	−	0.327016i	$-0.893957\pi$
$953$	345.167	−	1062.31i	0.0117325	−	0.0361089i	0.956751	+	0.290907i	$0.0939570\pi$
$954$	3069.50	+	652.443i	0.104171	+	0.0221422i
$955$	5697.52	−	9868.40i	0.193055	−	0.334381i
$956$	−1159.18	−	2007.75i	−0.0392159	−	0.0679240i
$957$	−13488.1	−	41512.1i	−0.455600	−	1.40219i
$958$	2672.60	+	25428.1i	0.0901333	+	0.857561i
$959$	−2728.91	−	1982.67i	−0.0918885	−	0.0667609i
$960$	15526.2			0.521984
$961$	−10819.1	+	27757.0i	−0.363166	+	0.931724i
$962$	−5553.63			−0.186129
$963$	12752.7	+	9265.39i	0.426740	+	0.310045i
$964$	383.551	+	3649.24i	0.0128147	+	0.121923i
$965$	1239.94	+	3816.14i	0.0413628	+	0.127302i
$966$	6141.93	+	10638.1i	0.204569	+	0.354323i
$967$	−20963.2	+	36309.4i	−0.697137	+	1.20748i	0.272318	+	0.962207i	$0.412210\pi$
$967$	−20963.2	+	36309.4i	−0.697137	+	1.20748i	−0.969455	+	0.245269i	$0.921124\pi$
$968$	−28625.7	−	6084.58i	−0.950481	−	0.202031i
$969$	5056.54	−	15562.4i	0.167636	−	0.515931i
$970$	5514.23	−	1172.08i	0.182527	−	0.0387973i
$971$	−5330.19	+	50713.4i	−0.176163	+	1.67608i	0.447423	+	0.894322i	$0.352342\pi$
$971$	−5330.19	+	50713.4i	−0.176163	+	1.67608i	−0.623586	+	0.781755i	$0.714325\pi$
$972$	−13084.8	+	14532.1i	−0.431784	+	0.479545i
$973$	15413.2	−	6862.39i	0.507835	−	0.226103i
$974$	205.617	+	91.5467i	0.00676427	+	0.00301165i
$975$	7252.78	+	8055.03i	0.238231	+	0.264582i
$976$	−4677.42	+	3398.34i	−0.153402	+	0.111453i
$977$	467.413	−	339.595i	0.0153059	−	0.0111204i	−0.580106	−	0.814541i	$-0.696989\pi$
$977$	467.413	−	339.595i	0.0153059	−	0.0111204i	0.595412	+	0.803421i	$0.296989\pi$
$978$	19694.8	+	21873.3i	0.643936	+	0.715164i
$979$	60679.7	+	27016.3i	1.98093	+	0.881967i
$980$	−20409.9	+	9087.06i	−0.665275	+	0.296200i
$981$	14293.3	−	15874.4i	0.465190	−	0.516646i
$982$	1713.70	−	16304.7i	0.0556887	−	0.529842i
$983$	−58900.1	+	12519.6i	−1.91111	+	0.406219i	−0.999983	−	0.00590426i	$-0.998121\pi$
$983$	−58900.1	+	12519.6i	−1.91111	+	0.406219i	−0.911128	+	0.412123i	$0.864787\pi$
$984$	12543.5	−	38604.8i	0.406373	−	1.25069i
$985$	−2643.31	−	561.853i	−0.0855055	−	0.0181748i
$986$	−5276.41	+	9139.01i	−0.170421	+	0.295178i
$987$	−3790.74	−	6565.75i	−0.122250	−	0.211743i
$988$	3330.12	+	10249.1i	0.107232	+	0.330027i
$989$	−11368.3	−	108162.i	−0.365511	−	3.47760i
$990$	−11405.6	−	8286.66i	−0.366156	−	0.266028i
$991$	−36644.2			−1.17461			−0.587307	−	0.809364i	$-0.699812\pi$
$991$	−36644.2			−1.17461			−0.587307	+	0.809364i	$0.699812\pi$
$992$	−18257.9	−	26712.4i	−0.584364	−	0.854958i
$993$	27325.3			0.873254
$994$	−4234.24	−	3076.35i	−0.135113	−	0.0981650i
$995$	1682.34	+	16006.4i	0.0536018	+	0.509987i
$996$	−8830.91	−	27178.8i	−0.280942	−	0.864650i
$997$	6778.62	+	11740.9i	0.215327	+	0.372957i	0.953374	−	0.301792i	$-0.0975849\pi$
$997$	6778.62	+	11740.9i	0.215327	+	0.372957i	−0.738047	+	0.674750i	$0.764252\pi$
$998$	−9113.80	+	15785.6i	−0.289070	+	0.500684i
$999$	7808.73	+	1659.80i	0.247305	+	0.0525662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.10.5	✓	56
31.11	odd	30		961.4.a.l.1.11		28
31.20	even	15		961.4.a.m.1.11		28
31.28	even	15	inner	31.4.g.a.28.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.10.5	✓	56	1.1	even	1	trivial
31.4.g.a.28.5	yes	56	31.28	even	15	inner
961.4.a.l.1.11		28	31.11	odd	30
961.4.a.m.1.11		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+(1.24677 + 0.905833i) q^{2} +(0.665097 + 6.32798i) q^{3} +(-1.73823 - 5.34972i) q^{4} +(6.49781 + 11.2545i) q^{5} +(-4.90287 + 8.49201i) q^{6} +(-5.97991 - 1.27107i) q^{7} +(6.48857 - 19.9698i) q^{8} +(-13.1909 + 2.80382i) q^{9} +(-2.09344 + 19.9178i) q^{10} +(34.9280 - 38.7915i) q^{11} +(32.6968 - 14.5575i) q^{12} +(-35.4607 - 15.7881i) q^{13} +(-6.30421 - 7.00153i) q^{14} +(-66.8967 + 48.6033i) q^{15} +(-10.2269 + 7.43026i) q^{16} +(-34.8654 - 38.7220i) q^{17} +(-18.9859 - 8.45306i) q^{18} +(45.0886 - 20.0747i) q^{19} +(48.9139 - 54.3244i) q^{20} +(4.06607 - 38.6861i) q^{21} +(78.6860 - 16.7252i) q^{22} +(-63.3209 + 194.882i) q^{23} +(130.684 + 27.7777i) q^{24} +(-21.9430 + 38.0064i) q^{25} +(-29.9100 - 51.8057i) q^{26} +(26.5723 + 81.7810i) q^{27} +(3.59459 + 34.2002i) q^{28} +(-106.319 - 77.2456i) q^{29} -127.431 q^{30} +(97.3959 + 142.496i) q^{31} -187.461 q^{32} +(268.702 + 195.224i) q^{33} +(-8.39360 - 79.8598i) q^{34} +(-24.5510 - 75.5602i) q^{35} +(37.9285 + 65.6941i) q^{36} +(46.4194 - 80.4008i) q^{37} +(74.3995 + 15.8141i) q^{38} +(76.3221 - 234.895i) q^{39} +(266.912 - 56.7339i) q^{40} +(31.7580 - 302.157i) q^{41} +(40.1126 - 44.5496i) q^{42} +(-484.870 + 215.878i) q^{43} +(-268.237 - 119.427i) q^{44} +(-117.268 - 130.239i) q^{45} +(-255.477 + 185.615i) q^{46} +(157.678 - 114.560i) q^{47} +(-53.8204 - 59.7736i) q^{48} +(-279.202 - 124.309i) q^{49} +(-61.7853 + 27.5086i) q^{50} +(221.843 - 246.382i) q^{51} +(-22.8232 + 217.148i) q^{52} +(-147.695 + 31.3936i) q^{53} +(-40.9504 + 126.032i) q^{54} +(663.536 + 141.039i) q^{55} +(-64.1840 + 111.170i) q^{56} +(157.021 + 271.968i) q^{57} +(-62.5845 - 192.615i) q^{58} +(-17.7944 - 169.302i) q^{59} +(376.296 + 273.395i) q^{60} +457.365 q^{61} +(-7.64685 + 265.884i) q^{62} +82.4444 q^{63} +(-151.906 - 110.366i) q^{64} +(-52.7289 - 501.682i) q^{65} +(158.171 + 486.799i) q^{66} +(370.980 + 642.556i) q^{67} +(-146.548 + 253.828i) q^{68} +(-1275.32 - 271.078i) q^{69} +(37.8354 - 116.445i) q^{70} +(543.379 - 115.499i) q^{71} +(-29.5987 + 281.613i) q^{72} +(-52.6392 + 58.4617i) q^{73} +(130.704 - 58.1933i) q^{74} +(-255.098 - 113.577i) q^{75} +(-185.768 - 206.317i) q^{76} +(-258.173 + 187.574i) q^{77} +(307.932 - 223.726i) q^{78} +(462.291 + 513.426i) q^{79} +(-150.076 - 66.8183i) q^{80} +(-832.468 + 370.639i) q^{81} +(313.298 - 347.953i) q^{82} +(83.4608 - 794.077i) q^{83} +(-214.027 + 45.4929i) q^{84} +(209.249 - 644.002i) q^{85} +(-800.072 - 170.061i) q^{86} +(418.095 - 724.162i) q^{87} +(-548.025 - 949.207i) q^{88} +(393.217 + 1210.20i) q^{89} +(-28.2314 - 268.604i) q^{90} +(191.984 + 139.485i) q^{91} +1152.63 q^{92} +(-836.932 + 711.092i) q^{93} +300.360 q^{94} +(518.908 + 377.009i) q^{95} +(-124.680 - 1186.25i) q^{96} +(-86.9834 - 267.707i) q^{97} +(-235.499 - 407.896i) q^{98} +(-351.969 + 609.629i) 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

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