LMFDB - Embedded newform 31.4.g.a.9.2

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			9.2
Character	$\chi$	$=$	31.9
Dual form			31.4.g.a.7.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00392 + 3.08973i) q^{2} +(6.59870 + 1.40260i) q^{3} +(-2.06647 - 1.50138i) q^{4} +(-2.34783 - 4.06657i) q^{5} +(-10.9582 + 18.9801i) q^{6} +(-2.01209 + 0.895840i) q^{7} +(-14.3129 + 10.3989i) q^{8} +(16.9098 + 7.52874i) q^{9} +(14.9216 - 3.17169i) q^{10} +(2.75160 - 26.1797i) q^{11} +(-11.5302 - 12.8056i) q^{12} +(34.2207 - 38.0059i) q^{13} +(-0.747939 - 7.11617i) q^{14} +(-9.78889 - 30.1271i) q^{15} +(-24.0755 - 74.0968i) q^{16} +(-4.09024 - 38.9160i) q^{17} +(-40.2379 + 44.6887i) q^{18} +(82.2821 + 91.3835i) q^{19} +(-1.25373 + 11.9284i) q^{20} +(-14.5337 + 3.08923i) q^{21} +(78.1259 + 34.7839i) q^{22} +(-168.870 + 122.692i) q^{23} +(-109.032 + 48.5440i) q^{24} +(51.4754 - 89.1579i) q^{25} +(83.0734 + 143.887i) q^{26} +(-46.3354 - 33.6647i) q^{27} +(5.50292 + 1.16968i) q^{28} +(-18.9622 + 58.3596i) q^{29} +102.912 q^{30} +(14.6998 - 171.974i) q^{31} +111.576 q^{32} +(54.8765 - 168.893i) q^{33} +(124.346 + 26.4307i) q^{34} +(8.36704 + 6.07901i) q^{35} +(-23.6402 - 40.9460i) q^{36} +(-156.803 + 271.591i) q^{37} +(-364.955 + 162.488i) q^{38} +(279.119 - 202.792i) q^{39} +(75.8920 + 33.7893i) q^{40} +(-78.0154 + 16.5827i) q^{41} +(5.04569 - 48.0065i) q^{42} +(-12.5140 - 13.8982i) q^{43} +(-44.9917 + 49.9684i) q^{44} +(-9.08534 - 86.4412i) q^{45} +(-209.553 - 644.937i) q^{46} +(85.2535 + 262.383i) q^{47} +(-54.9391 - 522.710i) q^{48} +(-226.266 + 251.294i) q^{49} +(223.797 + 248.552i) q^{50} +(27.5932 - 262.532i) q^{51} +(-127.777 + 27.1599i) q^{52} +(-293.837 - 130.825i) q^{53} +(150.532 - 109.368i) q^{54} +(-112.922 + 50.2760i) q^{55} +(19.4830 - 33.7455i) q^{56} +(414.781 + 718.421i) q^{57} +(-161.279 - 117.176i) q^{58} +(622.479 + 132.312i) q^{59} +(-25.0037 + 76.9536i) q^{60} +27.1475 q^{61} +(516.595 + 218.065i) q^{62} -40.7687 q^{63} +(80.5915 - 248.035i) q^{64} +(-234.898 - 49.9291i) q^{65} +(466.742 + 339.108i) q^{66} +(342.496 + 593.220i) q^{67} +(-49.9753 + 86.5598i) q^{68} +(-1286.41 + 572.748i) q^{69} +(-27.1823 + 19.7491i) q^{70} +(-234.620 - 104.460i) q^{71} +(-320.319 + 68.0858i) q^{72} +(-19.9538 + 189.848i) q^{73} +(-681.727 - 757.135i) q^{74} +(464.723 - 516.127i) q^{75} +(-32.8322 - 312.378i) q^{76} +(17.9164 + 55.1409i) q^{77} +(346.361 + 1065.99i) q^{78} +(-93.2871 - 887.568i) q^{79} +(-244.794 + 271.871i) q^{80} +(-592.949 - 658.537i) q^{81} +(27.0848 - 257.694i) q^{82} +(1278.80 - 271.818i) q^{83} +(34.6715 + 15.4367i) q^{84} +(-148.651 + 108.002i) q^{85} +(55.5048 - 24.7123i) q^{86} +(-206.981 + 358.501i) q^{87} +(232.857 + 403.320i) q^{88} +(-325.646 - 236.596i) q^{89} +(276.201 + 58.7084i) q^{90} +(-34.8078 + 107.128i) q^{91} +533.172 q^{92} +(338.209 - 1114.18i) q^{93} -896.281 q^{94} +(178.433 - 549.159i) q^{95} +(736.254 + 156.496i) q^{96} +(299.871 + 217.869i) q^{97} +(-549.279 - 951.379i) q^{98} +(243.629 - 421.978i) 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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−1.00392	+	3.08973i	−0.354938	+	1.09239i	0.601108	+	0.799168i	$0.294726\pi$
$2$	−1.00392	+	3.08973i	−0.354938	+	1.09239i	−0.956046	+	0.293218i	$0.905274\pi$
$3$	6.59870	+	1.40260i	1.26992	+	0.269930i	0.793111	−	0.609077i	$-0.208460\pi$
$3$	6.59870	+	1.40260i	1.26992	+	0.269930i	0.476809	+	0.879007i	$0.341793\pi$
$4$	−2.06647	−	1.50138i	−0.258309	−	0.187672i
$5$	−2.34783	−	4.06657i	−0.209997	−	0.363725i	0.741717	−	0.670713i	$-0.234012\pi$
$5$	−2.34783	−	4.06657i	−0.209997	−	0.363725i	−0.951713	+	0.306989i	$0.900679\pi$
$6$	−10.9582	+	18.9801i	−0.745610	+	1.29143i
$7$	−2.01209	+	0.895840i	−0.108643	+	0.0483708i	−0.460338	−	0.887744i	$-0.652272\pi$
$7$	−2.01209	+	0.895840i	−0.108643	+	0.0483708i	0.351696	+	0.936114i	$0.385605\pi$
$8$	−14.3129	+	10.3989i	−0.632545	+	0.459571i
$9$	16.9098	+	7.52874i	0.626290	+	0.278842i
$10$	14.9216	−	3.17169i	0.471863	−	0.100298i
$11$	2.75160	−	26.1797i	0.0754216	−	0.717589i	−0.889835	−	0.456283i	$-0.849180\pi$
$11$	2.75160	−	26.1797i	0.0754216	−	0.717589i	0.965256	−	0.261305i	$-0.0841530\pi$
$12$	−11.5302	−	12.8056i	−0.277373	−	0.308054i
$13$	34.2207	−	38.0059i	0.730085	−	0.810842i	−0.257772	−	0.966206i	$-0.582988\pi$
$13$	34.2207	−	38.0059i	0.730085	−	0.810842i	0.987857	+	0.155364i	$0.0496551\pi$
$14$	−0.747939	−	7.11617i	−0.0142782	−	0.135848i
$15$	−9.78889	−	30.1271i	−0.168499	−	0.518586i
$16$	−24.0755	−	74.0968i	−0.376180	−	1.15776i
$17$	−4.09024	−	38.9160i	−0.0583547	−	0.555207i	−0.984169	−	0.177230i	$-0.943286\pi$
$17$	−4.09024	−	38.9160i	−0.0583547	−	0.555207i	0.925815	−	0.377977i	$-0.123380\pi$
$18$	−40.2379	+	44.6887i	−0.526897	+	0.585179i
$19$	82.2821	+	91.3835i	0.993516	+	1.10341i	0.994639	+	0.103412i	$0.0329760\pi$
$19$	82.2821	+	91.3835i	0.993516	+	1.10341i	−0.00112249	+	0.999999i	$0.500357\pi$
$20$	−1.25373	+	11.9284i	−0.0140171	+	0.133364i
$21$	−14.5337	+	3.08923i	−0.151024	+	0.0321012i
$22$	78.1259	+	34.7839i	0.757114	+	0.337089i
$23$	−168.870	+	122.692i	−1.53095	+	1.11230i	−0.575247	+	0.817980i	$0.695094\pi$
$23$	−168.870	+	122.692i	−1.53095	+	1.11230i	−0.955706	+	0.294323i	$0.904906\pi$
$24$	−109.032	+	48.5440i	−0.927333	+	0.412875i
$25$	51.4754	−	89.1579i	0.411803	−	0.713263i
$26$	83.0734	+	143.887i	0.626617	+	1.08533i
$27$	−46.3354	−	33.6647i	−0.330269	−	0.239954i
$28$	5.50292	+	1.16968i	0.0371412	+	0.00789460i
$29$	−18.9622	+	58.3596i	−0.121420	+	0.373694i	−0.993232	−	0.116148i	$-0.962945\pi$
$29$	−18.9622	+	58.3596i	−0.121420	+	0.373694i	0.871812	+	0.489841i	$0.162945\pi$
$30$	102.912			0.626302
$31$	14.6998	−	171.974i	0.0851664	−	0.996367i
$31$	14.6998	−	171.974i	0.0851664	−	0.996367i
$32$	111.576			0.616374
$33$	54.8765	−	168.893i	0.289478	−	0.890922i
$34$	124.346	+	26.4307i	0.627213	+	0.133318i
$35$	8.36704	+	6.07901i	0.0404082	+	0.0293583i
$36$	−23.6402	−	40.9460i	−0.109445	−	0.189565i
$37$	−156.803	+	271.591i	−0.696711	+	1.20674i	0.272890	+	0.962045i	$0.412020\pi$
$37$	−156.803	+	271.591i	−0.696711	+	1.20674i	−0.969601	+	0.244693i	$0.921313\pi$
$38$	−364.955	+	162.488i	−1.55799	+	0.693661i
$39$	279.119	−	202.792i	1.14602	−	0.832632i
$40$	75.8920	+	33.7893i	0.299989	+	0.133564i
$41$	−78.0154	+	16.5827i	−0.297170	+	0.0631653i	−0.354084	−	0.935214i	$-0.615207\pi$
$41$	−78.0154	+	16.5827i	−0.297170	+	0.0631653i	0.0569141	+	0.998379i	$0.481874\pi$
$42$	5.04569	−	48.0065i	0.0185373	−	0.176371i
$43$	−12.5140	−	13.8982i	−0.0443807	−	0.0492897i	0.720546	−	0.693407i	$-0.243891\pi$
$43$	−12.5140	−	13.8982i	−0.0443807	−	0.0492897i	−0.764926	+	0.644118i	$0.777225\pi$
$44$	−44.9917	+	49.9684i	−0.154154	+	0.171205i
$45$	−9.08534	−	86.4412i	−0.0300969	−	0.286353i
$46$	−209.553	−	644.937i	−0.671670	−	2.06719i
$47$	85.2535	+	262.383i	0.264585	+	0.814309i	0.991789	+	0.127887i	$0.0408196\pi$
$47$	85.2535	+	262.383i	0.264585	+	0.814309i	−0.727204	+	0.686422i	$0.759180\pi$
$48$	−54.9391	−	522.710i	−0.165204	−	1.57181i
$49$	−226.266	+	251.294i	−0.659667	+	0.732635i
$50$	223.797	+	248.552i	0.632994	+	0.703012i
$51$	27.5932	−	262.532i	0.0757613	−	0.720821i
$52$	−127.777	+	27.1599i	−0.340760	+	0.0724307i
$53$	−293.837	−	130.825i	−0.761539	−	0.339059i	−0.0110475	−	0.999939i	$-0.503517\pi$
$53$	−293.837	−	130.825i	−0.761539	−	0.339059i	−0.750492	+	0.660880i	$0.770183\pi$
$54$	150.532	−	109.368i	0.379347	−	0.275612i
$55$	−112.922	+	50.2760i	−0.276843	+	0.123258i
$56$	19.4830	−	33.7455i	0.0464915	−	0.0805257i
$57$	414.781	+	718.421i	0.963843	+	1.66942i
$58$	−161.279	−	117.176i	−0.365121	−	0.265276i
$59$	622.479	+	132.312i	1.37356	+	0.291959i	0.834824	−	0.550517i	$-0.185569\pi$
$59$	622.479	+	132.312i	1.37356	+	0.291959i	0.538734	+	0.842476i	$0.318903\pi$
$60$	−25.0037	+	76.9536i	−0.0537995	+	0.165578i
$61$	27.1475			0.0569817			0.0284909	−	0.999594i	$-0.490930\pi$
$61$	27.1475			0.0569817			0.0284909	+	0.999594i	$0.490930\pi$
$62$	516.595	+	218.065i	1.05819	+	0.446683i
$63$	−40.7687			−0.0815297
$64$	80.5915	−	248.035i	0.157405	−	0.484443i
$65$	−234.898	−	49.9291i	−0.448238	−	0.0952760i
$66$	466.742	+	339.108i	0.870484	+	0.632443i
$67$	342.496	+	593.220i	0.624515	+	1.08169i	0.988634	+	0.150339i	$0.0480366\pi$
$67$	342.496	+	593.220i	0.624515	+	1.08169i	−0.364120	+	0.931352i	$0.618630\pi$
$68$	−49.9753	+	86.5598i	−0.0891235	+	0.154366i
$69$	−1286.41	+	572.748i	−2.24443	+	0.999286i
$70$	−27.1823	+	19.7491i	−0.0464130	+	0.0337210i
$71$	−234.620	−	104.460i	−0.392173	−	0.174607i	0.201170	−	0.979556i	$-0.435526\pi$
$71$	−234.620	−	104.460i	−0.392173	−	0.174607i	−0.593343	+	0.804950i	$0.702192\pi$
$72$	−320.319	+	68.0858i	−0.524304	+	0.111444i
$73$	−19.9538	+	189.848i	−0.0319921	+	0.304384i	0.966812	+	0.255489i	$0.0822366\pi$
$73$	−19.9538	+	189.848i	−0.0319921	+	0.304384i	−0.998804	+	0.0488948i	$0.984430\pi$
$74$	−681.727	−	757.135i	−1.07093	−	1.18939i
$75$	464.723	−	516.127i	0.715488	−	0.794630i
$76$	−32.8322	−	312.378i	−0.0495541	−	0.471476i
$77$	17.9164	+	55.1409i	0.0265164	+	0.0816089i
$78$	346.361	+	1065.99i	0.502790	+	1.54743i
$79$	−93.2871	−	887.568i	−0.132856	−	1.26404i	−0.834298	−	0.551314i	$-0.814127\pi$
$79$	−93.2871	−	887.568i	−0.132856	−	1.26404i	0.701442	−	0.712727i	$-0.252540\pi$
$80$	−244.794	+	271.871i	−0.342110	+	0.379952i
$81$	−592.949	−	658.537i	−0.813373	−	0.903343i
$82$	27.0848	−	257.694i	0.0364757	−	0.347044i
$83$	1278.80	−	271.818i	1.69116	−	0.359468i	0.741069	−	0.671429i	$-0.234319\pi$
$83$	1278.80	−	271.818i	1.69116	−	0.359468i	0.950095	+	0.311961i	$0.100986\pi$
$84$	34.6715	+	15.4367i	0.0450354	+	0.0200510i
$85$	−148.651	+	108.002i	−0.189688	+	0.137817i
$86$	55.5048	−	24.7123i	0.0695958	−	0.0309860i
$87$	−206.981	+	358.501i	−0.255065	+	0.441786i
$88$	232.857	+	403.320i	0.282075	+	0.488569i
$89$	−325.646	−	236.596i	−0.387847	−	0.281787i	0.376726	−	0.926325i	$-0.377050\pi$
$89$	−325.646	−	236.596i	−0.387847	−	0.281787i	−0.764573	+	0.644538i	$0.777050\pi$
$90$	276.201	+	58.7084i	0.323491	+	0.0687601i
$91$	−34.8078	+	107.128i	−0.0400973	+	0.123407i
$92$	533.172			0.604207
$93$	338.209	−	1114.18i	0.377104	−	1.24232i
$94$	−896.281			−0.983451
$95$	178.433	−	549.159i	0.192703	−	0.593079i
$96$	736.254	+	156.496i	0.782746	+	0.166378i
$97$	299.871	+	217.869i	0.313890	+	0.228054i	0.733564	−	0.679621i	$-0.237856\pi$
$97$	299.871	+	217.869i	0.313890	+	0.228054i	−0.419674	+	0.907675i	$0.637856\pi$
$98$	−549.279	−	951.379i	−0.566179	−	0.980650i
$99$	243.629	−	421.978i	0.247330	−	0.428388i
$100$	−240.232	+	106.958i	−0.240232	+	0.106958i
$101$	−387.055	+	281.212i	−0.381321	+	0.277046i	−0.761890	−	0.647707i	$-0.775728\pi$
$101$	−387.055	+	281.212i	−0.381321	+	0.277046i	0.380569	+	0.924752i	$0.375728\pi$
$102$	783.453	+	348.816i	0.760524	+	0.338607i
$103$	−363.615	+	77.2887i	−0.347845	+	0.0739367i	−0.378521	−	0.925593i	$-0.623567\pi$
$103$	−363.615	+	77.2887i	−0.347845	+	0.0739367i	0.0306762	+	0.999529i	$0.490234\pi$
$104$	−94.5760	+	899.830i	−0.0891725	+	0.848419i
$105$	46.6852	+	51.8492i	0.0433906	+	0.0481901i
$106$	699.200	−	776.540i	0.640682	−	0.711550i
$107$	−157.428	−	1497.83i	−0.142235	−	1.35328i	−0.799975	−	0.600033i	$-0.795154\pi$
$107$	−157.428	−	1497.83i	−0.142235	−	1.35328i	0.657740	−	0.753245i	$-0.271513\pi$
$108$	45.2074	+	139.134i	0.0402785	+	0.123965i
$109$	86.9676	+	267.659i	0.0764218	+	0.235202i	0.981969	−	0.189044i	$-0.0605390\pi$
$109$	86.9676	+	267.659i	0.0764218	+	0.235202i	−0.905547	+	0.424247i	$0.860539\pi$
$110$	−41.9756	−	399.371i	−0.0363838	−	0.346168i
$111$	−1415.63	+	1572.22i	−1.21050	+	1.34440i
$112$	114.821	+	127.522i	0.0968710	+	0.107586i
$113$	−124.282	+	1182.47i	−0.103465	+	0.984400i	0.812451	+	0.583029i	$0.198133\pi$
$113$	−124.282	+	1182.47i	−0.103465	+	0.984400i	−0.915916	+	0.401371i	$0.868534\pi$
$114$	−2636.13	+	560.328i	−2.16576	+	0.460346i
$115$	895.413	+	398.664i	0.726067	+	0.323266i
$116$	126.805	−	92.1290i	0.101496	−	0.0737410i
$117$	864.803	−	385.035i	0.683342	−	0.304244i
$118$	−1033.73	+	1790.47i	−0.806459	+	1.39683i
$119$	43.0925	+	74.6384i	0.0331956	+	0.0574965i
$120$	453.396	+	329.411i	0.344910	+	0.250592i
$121$	624.109	+	132.658i	0.468902	+	0.0996683i
$122$	−27.2538	+	83.8786i	−0.0202250	+	0.0622460i
$123$	−538.059			−0.394432
$124$	−288.574	+	333.308i	−0.208990	+	0.241387i
$125$	−1070.38			−0.765902
$126$	40.9283	−	125.964i	0.0289379	−	0.0890618i
$127$	2245.72	+	477.343i	1.56910	+	0.333522i	0.908718	−	0.417410i	$-0.137062\pi$
$127$	2245.72	+	477.343i	1.56910	+	0.333522i	0.660380	+	0.750932i	$0.270395\pi$
$128$	1407.59	+	1022.67i	0.971987	+	0.706190i
$129$	−63.0826	−	109.262i	−0.0430552	−	0.0745737i
$130$	390.085	−	675.647i	0.263175	−	0.455832i
$131$	1731.94	−	771.110i	1.15512	−	0.514291i	0.262422	−	0.964953i	$-0.415479\pi$
$131$	1731.94	−	771.110i	1.15512	−	0.514291i	0.892695	+	0.450662i	$0.148812\pi$
$132$	−366.972	+	266.621i	−0.241976	+	0.175806i
$133$	−247.424	−	110.160i	−0.161311	−	0.0718203i
$134$	−2176.73	+	462.678i	−1.40329	+	0.298278i
$135$	−28.1117	+	267.465i	−0.0179220	+	0.170517i
$136$	463.227	+	514.466i	0.292069	+	0.324375i
$137$	1374.43	−	1526.45i	0.857117	−	0.951925i	−0.142164	−	0.989843i	$-0.545406\pi$
$137$	1374.43	−	1526.45i	0.857117	−	0.951925i	0.999281	+	0.0379181i	$0.0120726\pi$
$138$	−478.189	−	4549.66i	−0.294972	−	2.80647i
$139$	252.937	+	778.459i	0.154344	+	0.475022i	0.998094	−	0.0617146i	$-0.0196569\pi$
$139$	252.937	+	778.459i	0.154344	+	0.475022i	−0.843750	+	0.536737i	$0.819657\pi$
$140$	−8.16334	−	25.1242i	−0.00492806	−	0.0151670i
$141$	194.544	+	1850.96i	0.116196	+	1.10553i
$142$	558.291	−	620.045i	0.329935	−	0.366430i
$143$	−900.821	−	1000.46i	−0.526787	−	0.585056i
$144$	150.743	−	1434.22i	0.0872354	−	0.829990i
$145$	281.843	−	59.9077i	0.161419	−	0.0343108i
$146$	−566.548	−	252.243i	−0.321150	−	0.142985i
$147$	−1845.52	+	1340.85i	−1.03548	+	0.752324i
$148$	731.790	−	325.814i	0.406438	−	0.180958i
$149$	1467.65	−	2542.04i	0.806942	−	1.39767i	−0.108030	−	0.994148i	$-0.534454\pi$
$149$	1467.65	−	2542.04i	0.806942	−	1.39767i	0.914972	−	0.403518i	$-0.132213\pi$
$150$	1128.15	+	1954.02i	0.614089	+	1.06363i
$151$	−1613.03	−	1171.94i	−0.869316	−	0.631595i	0.0610874	−	0.998132i	$-0.480543\pi$
$151$	−1613.03	−	1171.94i	−0.869316	−	0.631595i	−0.930403	+	0.366537i	$0.880543\pi$
$152$	−2127.98	−	452.316i	−1.13554	−	0.241366i
$153$	223.824	−	688.858i	0.118268	−	0.363993i
$154$	−188.357			−0.0985601
$155$	−733.855	+	343.988i	−0.380288	+	0.178256i
$156$	−881.258			−0.452289
$157$	−81.2326	+	250.008i	−0.0412934	+	0.127088i	−0.969578	−	0.244782i	$-0.921283\pi$
$157$	−81.2326	+	250.008i	−0.0412934	+	0.127088i	0.928285	+	0.371870i	$0.121283\pi$
$158$	2836.00	+	602.810i	1.42798	+	0.303525i
$159$	−1755.45	−	1275.41i	−0.875572	−	0.636140i
$160$	−261.961	−	453.730i	−0.129436	−	0.224191i
$161$	229.870	−	398.147i	0.112524	−	0.194897i
$162$	2629.97	−	1170.94i	1.27550	−	0.567887i
$163$	−2815.83	+	2045.82i	−1.35308	+	0.983073i	−0.354233	+	0.935157i	$0.615258\pi$
$163$	−2815.83	+	2045.82i	−1.35308	+	0.983073i	−0.998851	+	0.0479162i	$0.984742\pi$
$164$	186.113	+	82.8629i	0.0886159	+	0.0394543i
$165$	−815.654	+	173.373i	−0.384840	+	0.0818002i
$166$	−443.964	+	4224.03i	−0.207580	+	1.97499i
$167$	681.992	+	757.429i	0.316013	+	0.350968i	0.880135	−	0.474724i	$-0.157452\pi$
$167$	681.992	+	757.429i	0.316013	+	0.350968i	−0.564122	+	0.825691i	$0.690785\pi$
$168$	175.894	−	195.350i	0.0807768	−	0.0897118i
$169$	−43.7454	−	416.210i	−0.0199114	−	0.189445i
$170$	−184.463	−	567.718i	−0.0832214	−	0.256129i
$171$	703.374	+	2164.76i	0.314552	+	0.968090i
$172$	4.99335	+	47.5085i	0.00221360	+	0.0210610i
$173$	−909.677	+	1010.30i	−0.399777	+	0.443998i	−0.909100	−	0.416578i	$-0.863229\pi$
$173$	−909.677	+	1010.30i	−0.399777	+	0.443998i	0.509323	+	0.860576i	$0.329896\pi$
$174$	−899.882	−	999.421i	−0.392068	−	0.435436i
$175$	−23.7018	+	225.507i	−0.0102382	+	0.0974101i
$176$	−2006.08	+	426.405i	−0.859169	+	0.182622i
$177$	3921.97	+	1746.18i	1.66550	+	0.741529i
$178$	1057.94	−	768.637i	0.445482	−	0.323662i
$179$	1152.25	−	513.013i	0.481133	−	0.214214i	−0.151814	−	0.988409i	$-0.548512\pi$
$179$	1152.25	−	513.013i	0.481133	−	0.214214i	0.632948	+	0.774195i	$0.281845\pi$
$180$	−111.006	+	192.269i	−0.0459662	+	0.0796159i
$181$	−2220.65	−	3846.28i	−0.911932	−	1.57951i	−0.811332	−	0.584585i	$-0.801257\pi$
$181$	−2220.65	−	3846.28i	−0.911932	−	1.57951i	−0.100599	−	0.994927i	$-0.532076\pi$
$182$	−296.051	−	215.094i	−0.120576	−	0.0876034i
$183$	179.138	+	38.0770i	0.0723622	+	0.0153811i
$184$	1141.16	−	3512.13i	0.457215	−	1.40716i
$185$	1472.59			0.585227
$186$	3103.00	+	2163.52i	1.22324	+	0.852888i
$187$	−1030.06			−0.402812
$188$	217.763	−	670.205i	0.0844786	−	0.259998i
$189$	123.389	+	26.2272i	0.0474881	+	0.0100939i
$190$	1517.62	+	1102.62i	0.579473	+	0.421012i
$191$	116.111	+	201.110i	0.0439868	+	0.0761873i	0.887181	−	0.461422i	$-0.152661\pi$
$191$	116.111	+	201.110i	0.0439868	+	0.0761873i	−0.843194	+	0.537610i	$0.819327\pi$
$192$	879.692	−	1523.67i	0.330658	−	0.572716i
$193$	−2482.88	+	1105.45i	−0.926018	+	0.412290i	−0.813636	−	0.581375i	$-0.802515\pi$
$193$	−2482.88	+	1105.45i	−0.926018	+	0.412290i	−0.112382	+	0.993665i	$0.535848\pi$
$194$	−974.203	+	707.800i	−0.360534	+	0.261944i
$195$	−1479.99	−	658.934i	−0.543509	−	0.241986i
$196$	844.858	−	179.580i	0.307893	−	0.0654447i
$197$	−411.688	+	3916.95i	−0.148891	+	1.41661i	0.623681	+	0.781679i	$0.285636\pi$
$197$	−411.688	+	3916.95i	−0.148891	+	1.41661i	−0.772572	+	0.634927i	$0.781030\pi$
$198$	1059.22	+	1176.38i	0.380178	+	0.422231i
$199$	−966.459	+	1073.36i	−0.344274	+	0.382355i	−0.890270	−	0.455433i	$-0.849485\pi$
$199$	−966.459	+	1073.36i	−0.344274	+	0.382355i	0.545996	+	0.837788i	$0.316151\pi$
$200$	190.385	+	1811.39i	0.0673112	+	0.640424i
$201$	1427.98	+	4394.86i	0.501103	+	1.54224i
$202$	−480.299	−	1478.21i	−0.167296	−	0.514883i
$203$	−14.1273	−	134.412i	−0.00488443	−	0.0464723i
$204$	−451.181	+	501.087i	−0.154848	+	0.171976i
$205$	250.602	+	278.321i	0.0853794	+	0.0948234i
$206$	126.237	−	1201.06i	0.0426958	−	0.406224i
$207$	−3779.28	+	803.312i	−1.26898	+	0.269730i
$208$	−3639.99	−	1620.63i	−1.21340	−	0.540242i
$209$	2618.80	−	1902.67i	0.866728	−	0.629715i
$210$	−207.068	+	92.1927i	−0.0680431	+	0.0302948i
$211$	227.145	−	393.428i	0.0741106	−	0.128363i	−0.826589	−	0.562807i	$-0.809722\pi$
$211$	227.145	−	393.428i	0.0741106	−	0.128363i	0.900699	+	0.434443i	$0.143055\pi$
$212$	410.788	+	711.505i	0.133080	+	0.230502i
$213$	−1401.67	−	1018.38i	−0.450897	−	0.327596i
$214$	4785.94	+	1017.28i	1.52879	+	0.324954i
$215$	−27.1372	+	83.5198i	−0.00860811	+	0.0264930i
$216$	1013.27			0.319186
$217$	124.484	+	359.195i	0.0389424	+	0.112367i
$218$	−914.302			−0.284057
$219$	−397.950	+	1224.76i	−0.122790	+	0.377908i
$220$	308.833	+	65.6444i	0.0946432	+	0.0201170i
$221$	−1619.01	−	1176.28i	−0.492789	−	0.358032i
$222$	−3436.56	−	5952.29i	−1.03895	−	1.79951i
$223$	631.146	−	1093.18i	0.189528	−	0.328272i	−0.755565	−	0.655074i	$-0.772638\pi$
$223$	631.146	−	1093.18i	0.189528	−	0.328272i	0.945093	+	0.326802i	$0.105971\pi$
$224$	−224.500	+	99.9540i	−0.0669645	+	0.0298145i
$225$	1541.69	−	1120.10i	0.456796	−	0.331882i
$226$	−3528.74	−	1571.10i	−1.03862	−	0.462424i
$227$	3185.29	−	677.053i	0.931343	−	0.197963i	0.282833	−	0.959169i	$-0.408726\pi$
$227$	3185.29	−	677.053i	0.931343	−	0.197963i	0.648510	+	0.761206i	$0.275392\pi$
$228$	221.490	−	2107.34i	0.0643357	−	0.612113i
$229$	−3935.51	−	4370.83i	−1.13566	−	1.26128i	−0.960969	−	0.276655i	$-0.910774\pi$
$229$	−3935.51	−	4370.83i	−1.13566	−	1.26128i	−0.174690	−	0.984623i	$-0.555892\pi$
$230$	−2130.68	+	2366.36i	−0.610839	+	0.678406i
$231$	40.8843	+	388.988i	0.0116450	+	0.110794i
$232$	−335.473	−	1032.48i	−0.0949348	−	0.292179i
$233$	283.318	+	871.964i	0.0796601	+	0.245168i	0.982953	−	0.183855i	$-0.0588577\pi$
$233$	283.318	+	871.964i	0.0796601	+	0.245168i	−0.903293	+	0.429024i	$0.858858\pi$
$234$	321.467	+	3058.55i	0.0898074	+	0.854461i
$235$	866.838	−	962.721i	0.240622	−	0.267238i
$236$	−1087.68	−	1208.00i	−0.300009	−	0.333194i
$237$	629.326	−	5987.64i	0.172486	−	1.64109i
$238$	−273.874	+	58.2137i	−0.0745908	+	0.0158548i
$239$	5980.27	+	2662.59i	1.61854	+	0.720621i	0.997980	−	0.0635364i	$-0.0202379\pi$
$239$	5980.27	+	2662.59i	1.61854	+	0.720621i	0.620562	+	0.784157i	$0.286905\pi$
$240$	−1996.65	+	1450.65i	−0.537013	+	0.390163i
$241$	1851.12	−	824.173i	0.494777	−	0.220289i	−0.144151	−	0.989556i	$-0.546045\pi$
$241$	1851.12	−	824.173i	0.494777	−	0.220289i	0.638928	+	0.769267i	$0.279378\pi$
$242$	−1036.43	+	1795.15i	−0.275307	+	0.476846i
$243$	−2215.84	−	3837.94i	−0.584963	−	1.01319i
$244$	−56.0995	−	40.7587i	−0.0147189	−	0.0106939i
$245$	1553.14	+	330.129i	0.405005	+	0.0860865i
$246$	540.165	−	1662.46i	0.139999	−	0.430872i
$247$	6288.86			1.62004
$248$	1577.94	+	2614.29i	0.404029	+	0.669387i
$249$	8819.67			2.24468
$250$	1074.57	−	3307.19i	0.271847	−	0.836660i
$251$	−2662.87	−	566.011i	−0.669638	−	0.142336i	−0.139467	−	0.990227i	$-0.544539\pi$
$251$	−2662.87	−	566.011i	−0.669638	−	0.142336i	−0.530171	+	0.847891i	$0.677872\pi$
$252$	84.2472	+	61.2092i	0.0210598	+	0.0153009i
$253$	2747.36	+	4758.57i	0.682709	+	1.18249i
$254$	−3729.37	+	6459.47i	−0.921267	+	1.59568i
$255$	−1132.39	+	504.172i	−0.278090	+	0.123814i
$256$	−2884.95	+	2096.04i	−0.704335	+	0.511729i
$257$	−5012.83	−	2231.86i	−1.21670	−	0.541710i	−0.304916	−	0.952379i	$-0.598628\pi$
$257$	−5012.83	−	2231.86i	−1.21670	−	0.541710i	−0.911784	+	0.410670i	$0.865295\pi$
$258$	400.921	−	85.2184i	0.0967452	−	0.0205638i
$259$	72.1999	−	686.936i	0.0173216	−	0.164804i
$260$	410.447	+	455.847i	0.0979032	+	0.108733i
$261$	−760.022	+	844.090i	−0.180246	+	0.200183i
$262$	643.802	+	6125.36i	0.151810	+	1.44437i
$263$	−160.411	−	493.693i	−0.0376097	−	0.115751i	0.930489	−	0.366320i	$-0.119382\pi$
$263$	−160.411	−	493.693i	−0.0376097	−	0.115751i	−0.968099	+	0.250569i	$0.919382\pi$
$264$	970.857	+	2987.99i	0.226334	+	0.696584i
$265$	157.873	+	1502.06i	0.0365964	+	0.348192i
$266$	588.758	−	653.883i	0.135711	−	0.150722i
$267$	−1816.99	−	2017.97i	−0.416472	−	0.462539i
$268$	182.890	−	1740.09i	0.0416858	−	0.396614i
$269$	−2858.20	+	607.529i	−0.647834	+	0.137701i	−0.520098	−	0.854107i	$-0.674104\pi$
$269$	−2858.20	+	607.529i	−0.647834	+	0.137701i	−0.127736	+	0.991808i	$0.540771\pi$
$270$	−798.174	−	355.370i	−0.179909	−	0.0801005i
$271$	−2977.77	+	2163.47i	−0.667477	+	0.484951i	−0.869180	−	0.494496i	$-0.835353\pi$
$271$	−2977.77	+	2163.47i	−0.667477	+	0.484951i	0.201702	+	0.979447i	$0.435353\pi$
$272$	−2785.08	+	1240.00i	−0.620846	+	0.276419i
$273$	−379.943	+	658.081i	−0.0842315	+	0.145893i
$274$	3336.53	+	5779.04i	0.735646	+	1.27418i
$275$	−2192.49	−	1592.94i	−0.480771	−	0.349301i
$276$	3518.24	+	747.825i	0.767294	+	0.163093i
$277$	−199.723	+	614.686i	−0.0433221	+	0.133332i	−0.970378	−	0.241591i	$-0.922331\pi$
$277$	−199.723	+	614.686i	−0.0433221	+	0.133332i	0.927056	+	0.374923i	$0.122331\pi$
$278$	−2659.16			−0.573690
$279$	1543.32	−	2797.37i	0.331168	−	0.600267i
$280$	−182.971			−0.0390522
$281$	−659.723	+	2030.42i	−0.140056	+	0.431049i	−0.996342	−	0.0854534i	$-0.972766\pi$
$281$	−659.723	+	2030.42i	−0.140056	+	0.431049i	0.856286	+	0.516502i	$0.172766\pi$
$282$	−5914.29	−	1257.12i	−1.24890	−	0.265463i
$283$	−4183.41	−	3039.43i	−0.878721	−	0.638428i	0.0541919	−	0.998531i	$-0.482742\pi$
$283$	−4183.41	−	3039.43i	−0.878721	−	0.638428i	−0.932913	+	0.360102i	$0.882742\pi$
$284$	328.002	+	568.116i	0.0685329	+	0.118702i
$285$	1947.67	−	3373.47i	0.404807	−	0.701147i
$286$	3995.51	−	1778.92i	0.826083	−	0.367796i
$287$	142.118	−	103.255i	0.0292299	−	0.0212368i
$288$	1886.73	+	840.025i	0.386029	+	0.171871i
$289$	3307.91	−	703.118i	0.673298	−	0.143114i
$290$	−97.8482	+	930.963i	−0.0198132	+	0.188510i
$291$	1673.18	+	1858.25i	0.337056	+	0.374339i
$292$	326.268	−	362.357i	0.0653883	−	0.0726210i
$293$	358.955	+	3415.23i	0.0715713	+	0.680955i	0.970210	+	0.242266i	$0.0778906\pi$
$293$	358.955	+	3415.23i	0.0715713	+	0.680955i	−0.898639	+	0.438690i	$0.855443\pi$
$294$	−2290.12	−	7048.28i	−0.454295	−	1.39818i
$295$	−923.422	−	2842.00i	−0.182250	−	0.560907i
$296$	−579.947	−	5517.83i	−0.113881	−	1.08350i
$297$	−1008.83	+	1120.42i	−0.197098	+	0.218899i
$298$	6380.83	+	7086.63i	1.24038	+	1.37758i
$299$	−1115.86	+	10616.7i	−0.215825	+	2.05344i
$300$	−1735.24	+	368.836i	−0.333947	+	0.0709826i
$301$	37.6299	+	16.7539i	0.00720582	+	0.00320824i
$302$	5240.32	−	3807.31i	0.998498	−	0.725451i
$303$	−2948.48	+	1312.75i	−0.559030	+	0.248896i
$304$	4790.24	−	8296.94i	0.903747	−	1.56534i
$305$	−63.7379	−	110.397i	−0.0119660	−	0.0207257i
$306$	1903.69	+	1383.11i	0.355643	+	0.258389i
$307$	−10076.5	−	2141.82i	−1.87327	−	0.398176i	−0.876709	−	0.481022i	$-0.840266\pi$
$307$	−10076.5	−	2141.82i	−1.87327	−	0.398176i	−0.996562	+	0.0828459i	$0.973599\pi$
$308$	45.7637	−	140.846i	0.00846633	−	0.0260567i
$309$	−2507.79			−0.461693
$310$	−326.102	−	2612.75i	−0.0597464	−	0.478691i
$311$	7233.59			1.31891			0.659453	−	0.751746i	$-0.270788\pi$
$311$	7233.59			1.31891			0.659453	+	0.751746i	$0.270788\pi$
$312$	−1886.18	+	5805.06i	−0.342256	+	1.05335i
$313$	6661.11	+	1415.86i	1.20290	+	0.255685i	0.765413	−	0.643539i	$-0.222535\pi$
$313$	6661.11	+	1415.86i	1.20290	+	0.255685i	0.437489	+	0.899224i	$0.355868\pi$
$314$	−690.908	−	501.974i	−0.124173	−	0.0902166i
$315$	95.7180	+	165.788i	0.0171209	+	0.0296544i
$316$	−1139.80	+	1974.19i	−0.202907	+	0.351446i
$317$	−2936.09	+	1307.23i	−0.520212	+	0.231613i	−0.650008	−	0.759927i	$-0.725234\pi$
$317$	−2936.09	+	1307.23i	−0.520212	+	0.231613i	0.129796	+	0.991541i	$0.458568\pi$
$318$	5702.98	−	4143.46i	1.00568	−	0.730672i
$319$	1475.66	+	657.007i	0.259001	+	0.115314i
$320$	−1197.87	+	254.614i	−0.209259	+	0.0444793i
$321$	1062.03	−	10104.5i	0.184663	−	1.75695i
$322$	999.399	+	1109.94i	0.172964	+	0.192096i
$323$	3219.73	−	3575.87i	0.554646	−	0.615997i
$324$	236.599	+	2251.09i	0.0405691	+	0.385989i
$325$	−1627.01	−	5007.41i	−0.277693	−	0.854650i
$326$	−3494.18	−	10754.0i	−0.593635	−	1.82702i
$327$	198.456	+	1888.18i	0.0335615	+	0.319317i
$328$	944.181	−	1048.62i	0.158944	−	0.176525i
$329$	−406.591	−	451.565i	−0.0681340	−	0.0756705i
$330$	283.172	−	2694.20i	0.0472367	−	0.449427i
$331$	1774.74	−	377.232i	0.294708	−	0.0626421i	−0.0581850	−	0.998306i	$-0.518531\pi$
$331$	1774.74	−	377.232i	0.294708	−	0.0626421i	0.352893	+	0.935664i	$0.385198\pi$
$332$	−3050.70	−	1358.26i	−0.504305	−	0.224531i
$333$	−4696.26	+	3412.03i	−0.772833	+	0.561496i
$334$	−3024.92	+	1346.78i	−0.495557	+	0.220636i
$335$	1608.24	−	2785.56i	0.262292	−	0.454303i
$336$	578.807	+	1002.52i	0.0939778	+	0.162774i
$337$	−1057.71	−	768.468i	−0.170970	−	0.124217i	0.499010	−	0.866596i	$-0.333697\pi$
$337$	−1057.71	−	768.468i	−0.170970	−	0.124217i	−0.669980	+	0.742379i	$0.733697\pi$
$338$	1329.89	+	282.678i	0.214014	+	0.0454900i
$339$	−2478.63	+	7628.43i	−0.397111	+	1.22218i
$340$	469.335			0.0748625
$341$	−4461.77	−	858.038i	−0.708558	−	0.136262i
$342$	−7394.66			−1.16917
$343$	463.598	−	1426.81i	0.0729794	−	0.224608i
$344$	323.637	+	68.7913i	0.0507249	+	0.0107819i
$345$	5349.40	+	3886.56i	0.834788	+	0.606509i
$346$	−2208.32	−	3824.91i	−0.343121	−	0.594303i
$347$	−2816.95	+	4879.10i	−0.435797	+	0.754823i	−0.997360	−	0.0726109i	$-0.976867\pi$
$347$	−2816.95	+	4879.10i	−0.435797	+	0.754823i	0.561563	+	0.827434i	$0.310200\pi$
$348$	965.966	−	430.076i	0.148797	−	0.0662485i
$349$	760.808	−	552.760i	0.116691	−	0.0847809i	−0.527909	−	0.849301i	$-0.677024\pi$
$349$	760.808	−	552.760i	0.116691	−	0.0847809i	0.644600	+	0.764520i	$0.277024\pi$
$350$	−672.963	−	299.623i	−0.102775	−	0.0457586i
$351$	−2865.08	+	608.993i	−0.435689	+	0.0926086i
$352$	307.011	−	2921.02i	0.0464879	−	0.442303i
$353$	−3655.89	−	4060.28i	−0.551228	−	0.612200i	0.401562	−	0.915832i	$-0.368467\pi$
$353$	−3655.89	−	4060.28i	−0.551228	−	0.612200i	−0.952790	+	0.303632i	$0.901801\pi$
$354$	−9332.55	+	10364.8i	−1.40118	+	1.55617i
$355$	126.057	+	1199.35i	0.0188462	+	0.179310i
$356$	317.718	+	977.835i	0.0473006	+	0.145576i
$357$	179.667	+	552.958i	0.0266358	+	0.0819765i
$358$	428.316	+	4075.15i	0.0632324	+	0.601616i
$359$	2646.79	−	2939.55i	0.389114	−	0.432155i	−0.516481	−	0.856299i	$-0.672758\pi$
$359$	2646.79	−	2939.55i	0.389114	−	0.432155i	0.905595	+	0.424144i	$0.139425\pi$
$360$	1028.93	+	1142.74i	0.150637	+	0.167300i
$361$	−863.644	+	8217.03i	−0.125914	+	1.19799i
$362$	14113.3	−	2999.88i	2.04912	−	0.435553i
$363$	3932.24	+	1750.75i	0.568565	+	0.253142i
$364$	232.768	−	169.116i	0.0335175	−	0.0243519i
$365$	818.878	−	364.588i	0.117430	−	0.0522833i
$366$	−297.488	+	515.264i	−0.0424861	+	0.0735881i
$367$	2100.17	+	3637.60i	0.298714	+	0.517387i	0.975842	−	0.218478i	$-0.0701092\pi$
$367$	2100.17	+	3637.60i	0.298714	+	0.517387i	−0.677128	+	0.735865i	$0.736776\pi$
$368$	13156.7	+	9558.89i	1.86369	+	1.35405i
$369$	−1444.07	−	306.947i	−0.203728	−	0.0433036i
$370$	−1478.36	+	4549.91i	−0.207719	+	0.639294i
$371$	708.424			0.0991362
$372$	−2371.71	+	1794.65i	−0.330558	+	0.250129i
$373$	−5359.52			−0.743982			−0.371991	−	0.928236i	$-0.621325\pi$
$373$	−5359.52			−0.743982			−0.371991	+	0.928236i	$0.621325\pi$
$374$	1034.10	−	3182.63i	0.142973	−	0.440026i
$375$	−7063.12	−	1501.31i	−0.972635	−	0.206740i
$376$	−3948.72	−	2868.91i	−0.541595	−	0.393491i
$377$	1569.11	+	2717.78i	0.214359	+	0.371281i
$378$	−204.907	+	354.910i	−0.0278817	+	0.0482926i
$379$	1773.23	−	789.493i	0.240329	−	0.107001i	−0.283038	−	0.959109i	$-0.591342\pi$
$379$	1773.23	−	789.493i	0.240329	−	0.107001i	0.523367	+	0.852107i	$0.324676\pi$
$380$	−1193.22	+	866.925i	−0.161081	+	0.117032i
$381$	14149.3	+	6299.68i	1.90260	+	0.847093i
$382$	−737.940	+	156.854i	−0.0988385	+	0.0210088i
$383$	208.217	−	1981.05i	0.0277790	−	0.264300i	−0.971813	−	0.235752i	$-0.924245\pi$
$383$	208.217	−	1981.05i	0.0277790	−	0.264300i	0.999592	−	0.0285485i	$-0.00908849\pi$
$384$	7853.85	+	8722.59i	1.04372	+	1.15917i
$385$	182.169	−	202.320i	0.0241148	−	0.0267823i
$386$	−922.942	−	8781.21i	−0.121701	−	1.15791i
$387$	−106.974	−	329.231i	−0.0140511	−	0.0432449i
$388$	−292.571	−	900.440i	−0.0382810	−	0.117817i
$389$	−1216.42	−	11573.5i	−0.158548	−	1.50848i	−0.727497	−	0.686110i	$-0.759317\pi$
$389$	−1216.42	−	11573.5i	−0.158548	−	1.50848i	0.568949	−	0.822373i	$-0.307350\pi$
$390$	3521.72	−	3911.26i	0.457254	−	0.507832i
$391$	5465.39	+	6069.93i	0.706897	+	0.785088i
$392$	625.333	−	5949.64i	0.0805716	−	0.766588i
$393$	12510.1	−	2659.11i	1.60573	−	0.341308i
$394$	−11689.0	−	5204.30i	−1.49463	−	0.665453i
$395$	−3390.33	+	2463.22i	−0.431863	+	0.313767i
$396$	−1137.00	+	506.226i	−0.144284	+	0.0642394i
$397$	−7566.47	+	13105.5i	−0.956550	+	1.65679i	−0.225768	+	0.974181i	$0.572489\pi$
$397$	−7566.47	+	13105.5i	−0.956550	+	1.65679i	−0.730782	+	0.682611i	$0.760844\pi$
$398$	−2346.16	−	4063.67i	−0.295483	−	0.511792i
$399$	−1478.17	−	1073.95i	−0.185466	−	0.134749i
$400$	−7845.61	−	1667.64i	−0.980701	−	0.208454i
$401$	−64.2286	+	197.675i	−0.00799856	+	0.0246170i	−0.954976	−	0.296683i	$-0.904120\pi$
$401$	−64.2286	+	197.675i	−0.00799856	+	0.0246170i	0.946978	+	0.321300i	$0.104120\pi$
$402$	−15012.5			−1.86258
$403$	−6032.98	−	6443.73i	−0.745717	−	0.796489i
$404$	1222.04			0.150492
$405$	−1285.84	+	3957.40i	−0.157762	+	0.485543i
$406$	429.480	+	91.2887i	0.0524993	+	0.0111591i
$407$	6678.72	+	4852.37i	0.813395	+	0.590966i
$408$	2335.11	+	4044.53i	0.283346	+	0.490769i
$409$	3302.52	−	5720.14i	0.399265	−	0.691547i	−0.594371	−	0.804191i	$-0.702599\pi$
$409$	3302.52	−	5720.14i	0.399265	−	0.691547i	0.993635	+	0.112645i	$0.0359322\pi$
$410$	−1111.52	+	494.881i	−0.133888	+	0.0596108i
$411$	11210.4	−	8144.85i	1.34542	−	0.977508i
$412$	867.438	+	386.208i	0.103727	+	0.0461823i
$413$	−1371.02	+	291.418i	−0.163349	+	0.0347210i
$414$	1312.06	−	12483.4i	0.155759	−	1.48195i
$415$	−4107.77	−	4562.15i	−0.485886	−	0.539631i
$416$	3818.19	−	4240.53i	0.450006	−	0.499782i
$417$	577.189	+	5491.59i	0.0677820	+	0.644902i
$418$	3249.69	+	10001.5i	0.380257	+	1.17031i
$419$	−1428.83	−	4397.48i	−0.166594	−	0.512723i	0.832557	−	0.553940i	$-0.186876\pi$
$419$	−1428.83	−	4397.48i	−0.166594	−	0.512723i	−0.999150	+	0.0412176i	$0.986876\pi$
$420$	−18.6283	−	177.237i	−0.00216421	−	0.0205911i
$421$	−2018.69	+	2241.98i	−0.233693	+	0.259542i	−0.848573	−	0.529078i	$-0.822538\pi$
$421$	−2018.69	+	2241.98i	−0.233693	+	0.259542i	0.614880	+	0.788621i	$0.289204\pi$
$422$	987.551	+	1096.79i	0.113918	+	0.126518i
$423$	−533.794	+	5078.71i	−0.0613568	+	0.583771i
$424$	5566.07	−	1183.11i	0.637529	−	0.135511i
$425$	−3680.22	−	1638.54i	−0.420040	−	0.187014i
$426$	4553.67	−	3308.43i	0.517901	−	0.376277i
$427$	−54.6233	+	24.3198i	−0.00619064	+	0.00275625i
$428$	−1923.49	+	3331.58i	−0.217232	+	0.376257i
$429$	−4541.00	−	7865.25i	−0.511053	−	0.885170i
$430$	−230.810	−	167.694i	−0.0258853	−	0.0188067i
$431$	−3899.32	−	828.826i	−0.435786	−	0.0926291i	−0.0152052	−	0.999884i	$-0.504840\pi$
$431$	−3899.32	−	828.826i	−0.435786	−	0.0926291i	−0.420580	+	0.907255i	$0.638173\pi$
$432$	−1378.89	+	4243.80i	−0.153570	+	0.472638i
$433$	−12101.2			−1.34306			−0.671532	−	0.740975i	$-0.734364\pi$
$433$	−12101.2			−1.34306			−0.671532	+	0.740975i	$0.734364\pi$
$434$	−1234.79	+	24.0198i	−0.136571	+	0.00265665i
$435$	1943.83			0.214251
$436$	222.141	−	683.679i	0.0244005	−	0.0750970i
$437$	−25107.0	−	5336.66i	−2.74835	−	0.584181i
$438$	−3384.68	−	2459.12i	−0.369239	−	0.268267i
$439$	6765.53	+	11718.2i	0.735538	+	1.27399i	0.954487	+	0.298253i	$0.0964039\pi$
$439$	6765.53	+	11718.2i	0.735538	+	1.27399i	−0.218949	+	0.975736i	$0.570263\pi$
$440$	1093.42	−	1893.86i	0.118470	−	0.205195i
$441$	−5718.04	+	2545.84i	−0.617433	+	0.274899i
$442$	5259.74	−	3821.42i	0.566019	−	0.411237i
$443$	3996.17	+	1779.21i	0.428587	+	0.190819i	0.609681	−	0.792647i	$-0.291297\pi$
$443$	3996.17	+	1779.21i	0.428587	+	0.190819i	−0.181095	+	0.983466i	$0.557964\pi$
$444$	5285.85	−	1123.54i	0.564989	−	0.120092i
$445$	−197.569	+	1879.75i	−0.0210465	+	0.200244i
$446$	2744.01	+	3047.53i	0.291329	+	0.323553i
$447$	13250.0	−	14715.6i	1.40202	−	1.55711i
$448$	60.0425	+	571.266i	0.00633201	+	0.0602450i
$449$	5034.72	+	15495.3i	0.529183	+	1.62866i	0.755892	+	0.654696i	$0.227204\pi$
$449$	5034.72	+	15495.3i	0.529183	+	1.62866i	−0.226708	+	0.973963i	$0.572796\pi$
$450$	1913.09	+	5887.89i	0.200409	+	0.616795i
$451$	219.463	+	2088.05i	0.0229137	+	0.218010i
$452$	2032.16	−	2256.94i	0.211470	−	0.234862i
$453$	−9000.16	−	9995.69i	−0.933476	−	1.03673i
$454$	−1105.84	+	10521.4i	−0.114317	+	1.08765i
$455$	517.364	−	109.969i	0.0533064	−	0.0113306i
$456$	−13407.5	−	5969.40i	−1.37689	−	0.613032i
$457$	14527.8	−	10555.1i	1.48705	−	1.08041i	0.511854	−	0.859072i	$-0.328959\pi$
$457$	14527.8	−	10555.1i	1.48705	−	1.08041i	0.975198	−	0.221334i	$-0.0710411\pi$
$458$	17455.6	−	7771.75i	1.78089	−	0.792904i
$459$	−1120.57	+	1940.89i	−0.113952	+	0.197370i
$460$	−1251.80	−	2168.18i	−0.126881	−	0.219765i
$461$	4204.18	+	3054.51i	0.424746	+	0.308596i	0.779545	−	0.626347i	$-0.215451\pi$
$461$	4204.18	+	3054.51i	0.424746	+	0.308596i	−0.354798	+	0.934943i	$0.615451\pi$
$462$	−1242.91	−	264.189i	−0.125163	−	0.0266043i
$463$	4817.29	−	14826.1i	0.483539	−	1.48818i	−0.350547	−	0.936545i	$-0.614004\pi$
$463$	4817.29	−	14826.1i	0.483539	−	1.48818i	0.834086	−	0.551635i	$-0.185996\pi$
$464$	4780.78			0.478324
$465$	−5324.96	+	1240.57i	−0.531052	+	0.123720i
$466$	−2978.56			−0.296093
$467$	3254.13	−	10015.2i	0.322447	−	0.992391i	−0.650132	−	0.759821i	$-0.725286\pi$
$467$	3254.13	−	10015.2i	0.322447	−	0.992391i	0.972580	−	0.232570i	$-0.0747135\pi$
$468$	−2365.17	−	502.733i	−0.233611	−	0.0496556i
$469$	−1220.56	−	886.790i	−0.120171	−	0.0873095i
$470$	2104.32	+	3644.79i	0.206521	+	0.357705i
$471$	−886.690	+	1535.79i	−0.0867442	+	0.150245i
$472$	−10285.4	+	4579.34i	−1.00301	+	0.446570i
$473$	−398.285	+	289.371i	−0.0387170	+	0.0281296i
$474$	17868.4	+	7955.53i	1.73148	+	0.770906i
$475$	12383.1	−	2632.10i	1.19616	−	0.254251i
$476$	23.0111	−	218.936i	0.00221578	−	0.0210818i
$477$	−3983.79	−	4424.44i	−0.382401	−	0.424699i
$478$	−14230.4	+	15804.4i	−1.36168	+	1.51230i
$479$	−55.1312	−	524.538i	−0.00525889	−	0.0500350i	0.991578	−	0.129513i	$-0.0413414\pi$
$479$	−55.1312	−	524.538i	−0.00525889	−	0.0500350i	−0.996837	+	0.0794779i	$0.974675\pi$
$480$	−1092.20	−	3361.45i	−0.103858	−	0.319643i
$481$	4956.16	+	15253.5i	0.469815	+	1.44594i
$482$	688.104	+	6546.87i	0.0650255	+	0.618676i
$483$	2075.29	−	2304.84i	0.195505	−	0.217130i
$484$	−1090.53	−	1211.16i	−0.102417	−	0.113745i
$485$	181.932	−	1730.97i	0.0170332	−	0.162060i
$486$	14082.7	−	2993.38i	1.31441	−	0.279387i
$487$	−6942.26	−	3090.89i	−0.645963	−	0.287601i	0.0574867	−	0.998346i	$-0.481691\pi$
$487$	−6942.26	−	3090.89i	−0.645963	−	0.287601i	−0.703450	+	0.710745i	$0.748358\pi$
$488$	−388.559	+	282.304i	−0.0360435	+	0.0261871i
$489$	−21450.3	+	9550.28i	−1.98367	+	0.883187i
$490$	−2579.23	+	4467.36i	−0.237791	+	0.411866i
$491$	−3418.66	−	5921.30i	−0.314220	−	0.544245i	0.665051	−	0.746798i	$-0.268410\pi$
$491$	−3418.66	−	5921.30i	−0.314220	−	0.544245i	−0.979271	+	0.202552i	$0.935076\pi$
$492$	1111.88	+	807.830i	0.101885	+	0.0740239i
$493$	2348.69	+	499.229i	0.214563	+	0.0456067i
$494$	−6313.48	+	19430.9i	−0.575014	+	1.76971i
$495$	−2288.00			−0.207754
$496$	−13096.6	+	3051.14i	−1.18559	+	0.276211i
$497$	565.656			0.0510526
$498$	−8854.20	+	27250.4i	−0.796720	+	2.45205i
$499$	10042.6	+	2134.61i	0.900936	+	0.191500i	0.635019	−	0.772496i	$-0.280992\pi$
$499$	10042.6	+	2134.61i	0.900936	+	0.191500i	0.265916	+	0.963996i	$0.414325\pi$
$500$	2211.91	+	1607.05i	0.197839	+	0.143739i
$501$	3437.89	+	5954.61i	0.306574	+	0.531002i
$502$	4422.12	−	7659.34i	0.393165	−	0.680982i
$503$	11590.6	−	5160.46i	1.02743	−	0.457442i	0.177381	−	0.984142i	$-0.443238\pi$
$503$	11590.6	−	5160.46i	1.02743	−	0.457442i	0.850051	+	0.526700i	$0.176571\pi$
$504$	583.516	−	423.949i	0.0515712	−	0.0374686i
$505$	2052.31	+	913.745i	0.180844	+	0.0805171i
$506$	−17460.8	+	3711.42i	−1.53405	+	0.326072i
$507$	295.112	−	2807.80i	0.0258508	−	0.245954i
$508$	−3924.04	−	4358.09i	−0.342719	−	0.380628i
$509$	−498.952	+	554.142i	−0.0434492	+	0.0482552i	−0.764478	−	0.644650i	$-0.777003\pi$
$509$	−498.952	+	554.142i	−0.0434492	+	0.0482552i	0.721028	+	0.692905i	$0.243670\pi$
$510$	−420.935	−	4004.93i	−0.0365477	−	0.347728i
$511$	−129.925	−	399.867i	−0.0112476	−	0.0346166i
$512$	721.245	+	2219.76i	0.0622555	+	0.191603i
$513$	−736.181	−	7004.29i	−0.0633590	−	0.602821i
$514$	11928.3	−	13247.7i	1.02361	−	1.13683i
$515$	1168.01	+	1297.20i	0.0999388	+	0.110993i
$516$	−33.6857	+	320.498i	−0.00287390	+	0.0273433i
$517$	7103.70	−	1509.94i	0.604295	−	0.128447i
$518$	2049.97	+	912.704i	0.173881	+	0.0774169i
$519$	−7419.73	+	5390.75i	−0.627534	+	0.455930i
$520$	3881.27	−	1728.05i	0.327317	−	0.145731i
$521$	−6242.74	+	10812.7i	−0.524951	+	0.909241i	0.474627	+	0.880187i	$0.342583\pi$
$521$	−6242.74	+	10812.7i	−0.524951	+	0.909241i	−0.999578	+	0.0290542i	$0.990750\pi$
$522$	−1845.02	−	3195.66i	−0.154701	−	0.267951i
$523$	8497.73	+	6173.96i	0.710478	+	0.516192i	0.883328	−	0.468756i	$-0.155298\pi$
$523$	8497.73	+	6173.96i	0.710478	+	0.516192i	−0.172850	+	0.984948i	$0.555298\pi$
$524$	−4736.73	−	1006.82i	−0.394895	−	0.0839375i
$525$	−472.697	+	1454.81i	−0.0392956	+	0.120939i
$526$	1686.42			0.139793
$527$	−6752.66	+	131.356i	−0.558160	+	0.0108576i
$528$	−13835.6			−1.14037
$529$	9704.20	−	29866.5i	0.797583	−	2.45471i
$530$	−4799.46	−	1020.16i	−0.393349	−	0.0836090i
$531$	9529.88	+	6923.86i	0.778836	+	0.565857i
$532$	345.902	+	599.120i	0.0281894	+	0.0488254i
$533$	−2039.50	+	3532.51i	−0.165742	+	0.287074i
$534$	8059.10	−	3588.14i	0.653093	−	0.290776i
$535$	−5721.41	+	4156.85i	−0.462352	+	0.335918i
$536$	−11070.9	−	4929.09i	−0.892147	−	0.397210i
$537$	8322.87	−	1769.08i	0.668824	−	0.142163i
$538$	992.286	−	9440.97i	0.0795177	−	0.756560i
$539$	5956.20	+	6615.03i	0.475977	+	0.528626i
$540$	459.658	−	510.502i	0.0366306	−	0.0406824i
$541$	1611.84	+	15335.6i	0.128093	+	1.21873i	0.850018	+	0.526754i	$0.176591\pi$
$541$	1611.84	+	15335.6i	0.128093	+	1.21873i	−0.721924	+	0.691972i	$0.756742\pi$
$542$	−3695.13	−	11372.4i	−0.292840	−	0.901270i
$543$	−9258.63	−	28495.1i	−0.731723	−	2.25201i
$544$	−456.371	−	4342.08i	−0.0359683	−	0.342216i
$545$	884.266	−	982.077i	0.0695006	−	0.0771882i
$546$	−1651.86	−	1834.58i	−0.129475	−	0.143796i
$547$	935.310	−	8898.88i	0.0731096	−	0.695592i	−0.895170	−	0.445724i	$-0.852946\pi$
$547$	935.310	−	8898.88i	0.0731096	−	0.695592i	0.968280	−	0.249868i	$-0.0803871\pi$
$548$	−5131.99	+	1090.84i	−0.400051	+	0.0850334i
$549$	459.060	+	204.387i	0.0356871	+	0.0158889i
$550$	7122.82	−	5175.03i	0.552215	−	0.401207i
$551$	−6893.36	+	3069.12i	−0.532971	+	0.237294i
$552$	12456.3	−	21574.9i	0.960462	−	1.66357i
$553$	982.821	+	1702.30i	0.0755765	+	0.130902i
$554$	−1698.71	−	1234.18i	−0.130273	−	0.0946489i
$555$	9717.19	+	2065.45i	0.743192	+	0.157970i
$556$	646.076	−	1988.42i	0.0492800	−	0.151668i
$557$	177.645			0.0135136			0.00675678	−	0.999977i	$-0.497849\pi$
$557$	177.645			0.0135136			0.00675678	+	0.999977i	$0.497849\pi$
$558$	7093.78	+	7576.76i	0.538179	+	0.574821i
$559$	−956.452			−0.0723678
$560$	248.994	−	766.326i	0.0187892	−	0.0578271i
$561$	−6797.09	−	1444.77i	−0.511539	−	0.108731i
$562$	−5611.15	−	4076.74i	−0.421160	−	0.305991i
$563$	−7306.27	−	12654.8i	−0.546932	−	0.947314i	−0.998483	−	0.0550683i	$-0.982462\pi$
$563$	−7306.27	−	12654.8i	−0.546932	−	0.947314i	0.451551	−	0.892245i	$-0.350871\pi$
$564$	2376.98	−	4117.05i	0.177462	−	0.307374i
$565$	5100.38	−	2270.83i	0.379778	−	0.169088i
$566$	13590.8	−	9874.30i	1.00930	−	0.733300i
$567$	1783.01	+	793.848i	0.132062	+	0.0587980i
$568$	4444.35	−	944.676i	0.328311	−	0.0697847i
$569$	−516.832	+	4917.33i	−0.0380786	+	0.362294i	0.958846	+	0.283927i	$0.0916372\pi$
$569$	−516.832	+	4917.33i	−0.0380786	+	0.362294i	−0.996925	+	0.0783669i	$0.975029\pi$
$570$	8467.81	+	9404.46i	0.622241	+	0.691069i
$571$	914.896	−	1016.10i	0.0670529	−	0.0744698i	−0.708685	−	0.705525i	$-0.750711\pi$
$571$	914.896	−	1016.10i	0.0670529	−	0.0744698i	0.775738	+	0.631055i	$0.217378\pi$
$572$	359.446	+	3419.90i	0.0262748	+	0.249988i
$573$	484.104	+	1489.92i	0.0352945	+	0.108625i
$574$	176.356	+	542.768i	0.0128240	+	0.0394681i
$575$	2246.26	+	21371.7i	0.162914	+	1.55002i
$576$	3230.18	−	3587.48i	0.233665	−	0.259511i
$577$	9469.45	+	10516.9i	0.683221	+	0.758794i	0.980611	−	0.195962i	$-0.0627830\pi$
$577$	9469.45	+	10516.9i	0.683221	+	0.758794i	−0.297390	+	0.954756i	$0.596116\pi$
$578$	−1148.41	+	10926.4i	−0.0826432	+	0.786297i
$579$	−17934.3	+	3812.05i	−1.28726	+	0.273615i
$580$	−672.365	−	299.356i	−0.0481352	−	0.0214312i
$581$	−2329.56	+	1692.52i	−0.166345	+	0.120857i
$582$	−7421.23	+	3304.14i	−0.528556	+	0.235329i
$583$	−4233.47	+	7332.58i	−0.300742	+	0.520900i
$584$	−1688.61	−	2924.77i	−0.119650	−	0.207239i
$585$	−3596.18	−	2612.78i	−0.254160	−	0.184658i
$586$	−10912.5	−	2319.53i	−0.769269	−	0.163513i
$587$	−2407.32	+	7408.96i	−0.169268	+	0.520955i	−0.999325	−	0.0367238i	$-0.988308\pi$
$587$	−2407.32	+	7408.96i	−0.169268	+	0.520955i	0.830057	+	0.557679i	$0.188308\pi$
$588$	5826.84			0.408665
$589$	16925.1	−	12807.0i	1.18402	−	0.895933i
$590$	9708.06			0.677414
$591$	−8210.52	+	25269.4i	−0.571464	+	1.75879i
$592$	23899.1	+	5079.92i	1.65920	+	0.352675i
$593$	−10348.8	−	7518.82i	−0.716649	−	0.520676i	0.168663	−	0.985674i	$-0.446055\pi$
$593$	−10348.8	−	7518.82i	−0.716649	−	0.520676i	−0.885312	+	0.464998i	$0.846055\pi$
$594$	−2449.01	−	4241.81i	−0.169165	−	0.293003i
$595$	202.348	−	350.477i	0.0139419	−	0.0241482i
$596$	−6849.41	+	3049.56i	−0.470743	+	0.209588i
$597$	−7882.87	+	5727.24i	−0.540409	+	0.392630i
$598$	−31682.4	−	14105.9i	−2.16654	−	0.964605i
$599$	−15593.9	+	3314.58i	−1.06369	+	0.226094i	−0.706336	−	0.707877i	$-0.749653\pi$
$599$	−15593.9	+	3314.58i	−1.06369	+	0.226094i	−0.357351	+	0.933970i	$0.616320\pi$
$600$	−1284.36	+	12219.9i	−0.0873896	+	0.831456i
$601$	−4300.47	−	4776.16i	−0.291880	−	0.324166i	0.579314	−	0.815105i	$-0.303321\pi$
$601$	−4300.47	−	4776.16i	−0.291880	−	0.324166i	−0.871194	+	0.490939i	$0.836654\pi$
$602$	−89.5423	+	99.4469i	−0.00606225	+	0.00673281i
$603$	1325.34	+	12609.8i	0.0895061	+	0.851594i
$604$	1573.76	+	4843.54i	0.106019	+	0.326293i
$605$	−925.840	−	2849.44i	−0.0622161	−	0.191481i
$606$	−1096.02	−	10427.9i	−0.0734698	−	0.699018i
$607$	−13311.0	+	14783.4i	−0.890079	+	0.988533i	−0.999985	−	0.00540908i	$-0.998278\pi$
$607$	−13311.0	+	14783.4i	−0.890079	+	0.988533i	0.109906	+	0.993942i	$0.464945\pi$
$608$	9180.68	+	10196.2i	0.612378	+	0.680114i
$609$	95.3042	−	906.759i	0.00634141	−	0.0603345i
$610$	405.085	−	86.1035i	0.0268876	−	0.00571513i
$611$	12889.5	+	5738.79i	0.853445	+	0.379978i
$612$	−1496.76	+	1087.46i	−0.0988611	+	0.0718268i
$613$	11937.2	−	5314.79i	0.786525	−	0.350183i	0.0261417	−	0.999658i	$-0.491678\pi$
$613$	11937.2	−	5314.79i	0.786525	−	0.350183i	0.760383	+	0.649475i	$0.225011\pi$
$614$	16733.6	−	28983.4i	1.09986	−	1.90501i
$615$	1263.27	+	2188.05i	0.0828294	+	0.143465i
$616$	−829.839	−	602.913i	−0.0542779	−	0.0394352i
$617$	−8220.37	−	1747.29i	−0.536369	−	0.114009i	−0.0682400	−	0.997669i	$-0.521738\pi$
$617$	−8220.37	−	1747.29i	−0.536369	−	0.114009i	−0.468129	+	0.883660i	$0.655072\pi$
$618$	2517.61	−	7748.40i	0.163872	−	0.504347i
$619$	−10445.4			−0.678246			−0.339123	−	0.940742i	$-0.610130\pi$
$619$	−10445.4			−0.678246			−0.339123	+	0.940742i	$0.610130\pi$
$620$	2032.94	+	390.953i	0.131685	+	0.0253243i
$621$	11955.1			0.772528
$622$	−7261.91	+	22349.9i	−0.468129	+	1.44075i
$623$	867.180	+	184.325i	0.0557670	+	0.0118536i
$624$	−21746.1	−	15799.5i	−1.39510	−	1.01360i
$625$	−3921.35	−	6791.97i	−0.250966	−	0.434686i
$626$	−11061.8	+	19159.7i	−0.706262	+	1.22328i
$627$	19949.4	−	8882.03i	1.27065	−	0.565732i
$628$	543.221	−	394.673i	0.0345173	−	0.0250783i
$629$	11210.6	+	4991.29i	0.710646	+	0.316400i
$630$	−608.335	+	129.306i	−0.0384709	+	0.00817723i
$631$	1383.39	−	13162.1i	0.0872774	−	0.830389i	−0.860069	−	0.510178i	$-0.829580\pi$
$631$	1383.39	−	13162.1i	0.0872774	−	0.830389i	0.947346	−	0.320211i	$-0.103754\pi$
$632$	10564.9	+	11733.5i	0.664953	+	0.738505i
$633$	2050.69	−	2277.52i	0.128764	−	0.143007i
$634$	−1091.41	−	10384.1i	−0.0683682	−	0.650480i
$635$	−3331.43	−	10253.1i	−0.208195	−	0.640758i
$636$	1712.71	+	5271.18i	0.106782	+	0.328641i
$637$	1807.67	+	17198.9i	0.112437	+	1.06977i
$638$	−3511.41	+	3899.82i	−0.217897	+	0.241999i
$639$	−3180.94	−	3532.79i	−0.196926	−	0.218709i
$640$	853.984	−	8125.11i	0.0527448	−	0.501833i
$641$	−15756.7	+	3349.19i	−0.970909	+	0.206373i	−0.665953	−	0.745993i	$-0.731975\pi$
$641$	−15756.7	+	3349.19i	−0.970909	+	0.206373i	−0.304956	+	0.952367i	$0.598642\pi$
$642$	30154.2	+	13425.5i	1.85372	+	0.825331i
$643$	−24130.9	+	17532.1i	−1.47998	+	1.07527i	−0.502421	+	0.864623i	$0.667557\pi$
$643$	−24130.9	+	17532.1i	−1.47998	+	1.07527i	−0.977562	+	0.210647i	$0.932443\pi$
$644$	−1072.79	+	477.637i	−0.0656426	+	0.0292260i
$645$	−296.215	+	513.059i	−0.0180829	+	0.0313205i
$646$	7816.16	+	13538.0i	0.476041	+	0.824528i
$647$	13013.0	+	9454.48i	0.790716	+	0.574489i	0.908176	−	0.418589i	$-0.137475\pi$
$647$	13013.0	+	9454.48i	0.790716	+	0.574489i	−0.117460	+	0.993078i	$0.537475\pi$
$648$	15334.9	+	3259.52i	0.929645	+	0.197602i
$649$	5176.70	−	15932.3i	0.313102	−	0.963630i
$650$	17104.9			1.03217
$651$	317.624	+	2544.82i	0.0191224	+	0.153209i
$652$	8890.37			0.534009
$653$	7284.62	−	22419.7i	0.436553	−	1.34357i	−0.454934	−	0.890525i	$-0.650337\pi$
$653$	7284.62	−	22419.7i	0.436553	−	1.34357i	0.891487	−	0.453047i	$-0.149663\pi$
$654$	−6033.20	−	1282.40i	−0.360729	−	0.0766754i
$655$	−7202.08	−	5232.61i	−0.429631	−	0.312145i
$656$	3106.98	+	5381.45i	0.184920	+	0.320290i
$657$	−1766.73	+	3060.07i	−0.104912	+	0.181712i
$658$	1803.40	−	802.925i	0.106845	−	0.0475703i
$659$	−21866.5	+	15886.9i	−1.29256	+	0.939100i	−0.999854	−	0.0171030i	$-0.994556\pi$
$659$	−21866.5	+	15886.9i	−1.29256	+	0.939100i	−0.292706	+	0.956203i	$0.594556\pi$
$660$	1945.82	+	866.336i	0.114759	+	0.0510940i
$661$	23966.2	−	5094.17i	1.41025	−	0.299758i	0.561030	−	0.827795i	$-0.310405\pi$
$661$	23966.2	−	5094.17i	1.41025	−	0.299758i	0.849221	+	0.528037i	$0.177072\pi$
$662$	−616.139	+	5862.17i	−0.0361736	+	0.344169i
$663$	−9033.51	−	10032.7i	−0.529159	−	0.587691i
$664$	−15476.7	+	17188.6i	−0.904536	+	1.00459i
$665$	132.936	+	1264.80i	0.00775195	+	0.0737549i
$666$	−5827.62	−	17935.6i	−0.339063	−	1.04353i
$667$	−3958.08	−	12181.7i	−0.229771	−	0.707163i
$668$	−272.129	−	2589.13i	−0.0157619	−	0.149965i
$669$	5698.03	−	6328.31i	0.329295	−	0.365720i
$670$	6992.10	+	7765.52i	0.403177	+	0.447773i
$671$	74.6990	−	710.714i	0.00429765	−	0.0408894i
$672$	−1621.61	+	344.683i	−0.0930875	+	0.0197864i
$673$	3413.74	+	1519.90i	0.195528	+	0.0870545i	0.502165	−	0.864772i	$-0.332537\pi$
$673$	3413.74	+	1519.90i	0.195528	+	0.0870545i	−0.306637	+	0.951827i	$0.599204\pi$
$674$	3436.21	−	2496.55i	0.196376	−	0.142676i
$675$	−5386.60	+	2398.27i	−0.307156	+	0.136755i
$676$	−534.490	+	925.763i	−0.0304102	+	0.0526720i
$677$	1160.74	+	2010.46i	0.0658948	+	0.114133i	0.897091	−	0.441847i	$-0.145676\pi$
$677$	1160.74	+	2010.46i	0.0658948	+	0.114133i	−0.831196	+	0.555980i	$0.812343\pi$
$678$	−21081.5	−	15316.6i	−1.19414	−	0.867596i
$679$	−798.544	−	169.736i	−0.0451330	−	0.00959331i
$680$	1004.53	−	3091.62i	0.0566499	−	0.174350i
$681$	21968.4			1.23617
$682$	7130.34	−	12924.3i	0.400345	−	0.725654i
$683$	33655.9			1.88551			0.942757	−	0.333481i	$-0.108223\pi$
$683$	33655.9			1.88551			0.942757	+	0.333481i	$0.108223\pi$
$684$	1796.62	−	5529.44i	0.100432	−	0.309099i
$685$	−9434.35	−	2005.33i	−0.526230	−	0.111854i
$686$	3943.04	+	2864.79i	0.219455	+	0.159443i
$687$	−19838.8	−	34361.7i	−1.10174	−	1.90827i
$688$	−728.532	+	1261.85i	−0.0403707	+	0.0699241i
$689$	−15027.4	+	6690.63i	−0.830912	+	0.369946i
$690$	−17378.8	+	12626.4i	−0.958839	+	0.696638i
$691$	−22185.1	−	9877.46i	−1.22136	−	0.543786i	−0.308178	−	0.951329i	$-0.599719\pi$
$691$	−22185.1	−	9877.46i	−1.22136	−	0.543786i	−0.913186	+	0.407543i	$0.866386\pi$
$692$	3396.66	−	721.983i	0.186592	−	0.0396614i
$693$	−112.179	+	1067.31i	−0.00614910	+	0.0585048i
$694$	−12247.1	−	13601.8i	−0.669877	−	0.743974i
$695$	2571.80	−	2856.28i	0.140366	−	0.155892i
$696$	−765.532	−	7283.55i	−0.0416917	−	0.396670i
$697$	964.434	+	2968.22i	0.0524111	+	0.161305i
$698$	944.092	+	2905.62i	0.0511955	+	0.157563i
$699$	646.518	+	6151.21i	0.0349836	+	0.332847i
$700$	387.551	−	430.419i	0.0209258	−	0.0232404i
$701$	−18502.1	−	20548.7i	−0.996885	−	1.10715i	−0.994242	−	0.107156i	$-0.965825\pi$
$701$	−18502.1	−	20548.7i	−0.996885	−	1.10715i	−0.00264264	−	0.999997i	$-0.500841\pi$
$702$	994.677	−	9463.72i	0.0534782	−	0.508811i
$703$	−37721.1	+	8017.86i	−2.02372	+	0.430155i
$704$	−6271.73	−	2792.35i	−0.335759	−	0.149490i
$705$	7070.31	−	5136.88i	0.377707	−	0.274420i
$706$	16215.4	−	7219.55i	0.864410	−	0.384860i
$707$	526.868	−	912.562i	0.0280267	−	0.0485437i
$708$	−5482.97	−	9496.78i	−0.291049	−	0.504112i
$709$	−16470.7	−	11966.6i	−0.872453	−	0.633874i	0.0587910	−	0.998270i	$-0.481275\pi$
$709$	−16470.7	−	11966.6i	−0.872453	−	0.633874i	−0.931244	+	0.364396i	$0.881275\pi$
$710$	−3832.23	−	814.565i	−0.202565	−	0.0430565i
$711$	5104.80	−	15711.0i	0.269262	−	0.828702i
$712$	7121.25			0.374832
$713$	18617.4	+	30844.8i	0.977876	+	1.62012i
$714$	−1888.86			−0.0990040
$715$	−1953.47	+	6012.17i	−0.102176	+	0.314465i
$716$	−3151.31	−	669.831i	−0.164483	−	0.0349619i
$717$	35727.5	+	25957.5i	1.86090	+	1.35202i
$718$	6425.29	+	11128.9i	0.333969	+	0.578451i
$719$	−2979.08	+	5159.92i	−0.154522	+	0.267639i	−0.932885	−	0.360175i	$-0.882717\pi$
$719$	−2979.08	+	5159.92i	−0.154522	+	0.267639i	0.778363	+	0.627814i	$0.216050\pi$
$720$	−6186.28	+	2754.31i	−0.320207	+	0.142565i
$721$	662.387	−	481.252i	0.0342144	−	0.0248582i
$722$	−24521.4	−	10917.6i	−1.26398	−	0.562759i
$723$	13371.0	−	2842.09i	0.687790	−	0.146194i
$724$	−1185.81	+	11282.3i	−0.0608707	+	0.579146i
$725$	4227.14	+	4694.71i	0.216541	+	0.240493i
$726$	−9356.98	+	10392.0i	−0.478333	+	0.531243i
$727$	2059.67	+	19596.4i	0.105074	+	0.999712i	0.912315	+	0.409490i	$0.134293\pi$
$727$	2059.67	+	19596.4i	0.105074	+	0.999712i	−0.807241	+	0.590222i	$0.799040\pi$
$728$	−615.809	−	1895.26i	−0.0313508	−	0.0964879i
$729$	−1845.01	−	5678.36i	−0.0937363	−	0.288491i
$730$	304.396	+	2896.13i	0.0154331	+	0.146836i
$731$	−489.678	+	543.843i	−0.0247762	+	0.0275168i
$732$	−313.016	−	347.639i	−0.0158052	−	0.0175534i
$733$	2074.81	−	19740.5i	0.104550	−	0.994723i	−0.808948	−	0.587880i	$-0.799963\pi$
$733$	2074.81	−	19740.5i	0.104550	−	0.994723i	0.913498	−	0.406843i	$-0.133370\pi$
$734$	−13347.6	+	2837.12i	−0.671211	+	0.142670i
$735$	9785.64	+	4356.85i	0.491087	+	0.218646i
$736$	−18841.8	+	13689.4i	−0.943640	+	0.685595i
$737$	16472.7	−	7334.13i	0.823311	−	0.366562i
$738$	2398.11	−	4153.65i	0.119615	−	0.207179i
$739$	9286.11	+	16084.0i	0.462240	+	0.800623i	0.999072	−	0.0430662i	$-0.0137126\pi$
$739$	9286.11	+	16084.0i	0.462240	+	0.800623i	−0.536833	+	0.843689i	$0.680379\pi$
$740$	−3043.06	−	2210.92i	−0.151169	−	0.109831i
$741$	41498.3	+	8820.74i	2.05733	+	0.437298i
$742$	−711.197	+	2188.84i	−0.0351872	+	0.108295i
$743$	4473.99			0.220908			0.110454	−	0.993881i	$-0.464769\pi$
$743$	4473.99			0.220908			0.110454	+	0.993881i	$0.464769\pi$
$744$	6745.55	+	19464.2i	0.332398	+	0.959127i
$745$	−13783.2			−0.677821
$746$	5380.50	−	16559.5i	0.264067	−	0.812715i
$747$	23670.8	+	5031.37i	1.15939	+	0.246437i
$748$	2128.60	+	1546.52i	0.104050	+	0.0755966i
$749$	1658.58	+	2872.74i	0.0809120	+	0.140144i
$750$	11729.4	−	20316.0i	0.571064	−	0.989112i
$751$	23967.1	−	10670.8i	1.16454	−	0.518488i	0.268860	−	0.963179i	$-0.413353\pi$
$751$	23967.1	−	10670.8i	1.16454	−	0.518488i	0.895684	+	0.444691i	$0.146687\pi$
$752$	17389.2	−	12634.0i	0.843245	−	0.612653i
$753$	−16777.6	−	7469.88i	−0.811966	−	0.361511i
$754$	−9972.47	+	2119.71i	−0.481666	+	0.102381i
$755$	−978.627	+	9311.01i	−0.0471734	+	0.448825i
$756$	−215.603	−	239.451i	−0.0103722	−	0.0115195i
$757$	−3255.32	+	3615.40i	−0.156297	+	0.173585i	−0.816208	−	0.577759i	$-0.803927\pi$
$757$	−3255.32	+	3615.40i	−0.156297	+	0.173585i	0.659911	+	0.751344i	$0.270594\pi$
$758$	659.150	+	6271.39i	0.0315850	+	0.300511i
$759$	11454.7	+	35253.9i	0.547797	+	1.68595i
$760$	3156.77	+	9715.53i	0.150668	+	0.463710i
$761$	−2358.20	−	22436.8i	−0.112332	−	1.06877i	−0.894919	−	0.446228i	$-0.852767\pi$
$761$	−2358.20	−	22436.8i	−0.112332	−	1.06877i	0.782587	−	0.622541i	$-0.213900\pi$
$762$	−33669.0	+	37393.3i	−1.60066	+	1.77771i
$763$	−414.766	−	460.644i	−0.0196796	−	0.0218564i
$764$	62.0023	−	589.913i	0.00293608	−	0.0279349i
$765$	−3326.79	+	707.131i	−0.157229	+	0.0334201i
$766$	5911.88	+	2632.14i	0.278858	+	0.124155i
$767$	26330.3	−	19130.1i	1.23955	−	0.900583i
$768$	−21976.9	+	9784.72i	−1.03258	+	0.459734i
$769$	−11614.3	+	20116.6i	−0.544634	+	0.943334i	0.453996	+	0.891004i	$0.349998\pi$
$769$	−11614.3	+	20116.6i	−0.544634	+	0.943334i	−0.998630	+	0.0523301i	$0.983335\pi$
$770$	442.231	+	765.967i	0.0206973	+	0.0358487i
$771$	−29947.8	−	21758.3i	−1.39889	−	1.01635i
$772$	6790.49	+	1443.36i	0.316574	+	0.0672898i
$773$	976.423	−	3005.12i	0.0454327	−	0.139828i	−0.925767	−	0.378095i	$-0.876579\pi$
$773$	976.423	−	3005.12i	0.0454327	−	0.139828i	0.971200	+	0.238267i	$0.0765794\pi$
$774$	1124.63			0.0522274
$775$	−14576.1	−	10163.0i	−0.675600	−	0.471053i
$776$	−6557.61			−0.303356
$777$	1439.92	−	4431.62i	0.0664825	−	0.204612i
$778$	36980.2	+	7860.39i	1.70412	+	0.362222i
$779$	−7934.65	−	5764.86i	−0.364940	−	0.265145i
$780$	2069.05	+	3583.69i	0.0949791	+	0.164509i
$781$	−3380.30	+	5854.85i	−0.154874	+	0.268250i
$782$	−24241.3	+	10792.9i	−1.10852	+	0.493547i
$783$	2843.28	−	2065.76i	0.129771	−	0.0942840i
$784$	24067.5	+	10715.5i	1.09637	+	0.488135i
$785$	1207.40	−	256.640i	0.0548965	−	0.0116686i
$786$	−4343.16	+	41322.4i	−0.197093	+	1.87522i
$787$	−11044.1	−	12265.7i	−0.500226	−	0.555557i	0.439164	−	0.898407i	$-0.355275\pi$
$787$	−11044.1	−	12265.7i	−0.500226	−	0.555557i	−0.939390	+	0.342849i	$0.888608\pi$
$788$	6731.57	−	7476.16i	0.304318	−	0.337979i
$789$	−366.049	−	3482.73i	−0.0165167	−	0.157146i
$790$	−4207.09	−	12948.1i	−0.189470	−	0.583129i
$791$	−809.235	−	2490.57i	−0.0363756	−	0.111952i
$792$	901.079	+	8573.19i	0.0404273	+	0.384640i
$793$	929.006	−	1031.77i	0.0416015	−	0.0462031i
$794$	−32896.4	−	36535.2i	−1.47034	−	1.63298i
$795$	−1065.03	+	10133.1i	−0.0475128	+	0.452055i
$796$	3608.68	−	767.049i	0.160686	−	0.0341549i
$797$	11178.3	+	4976.91i	0.496808	+	0.221193i	0.639816	−	0.768528i	$-0.279011\pi$
$797$	11178.3	+	4976.91i	0.496808	+	0.221193i	−0.143007	+	0.989722i	$0.545677\pi$
$798$	4802.17	−	3488.98i	0.213026	−	0.154773i
$799$	9862.21	−	4390.94i	0.436671	−	0.194418i
$800$	5743.40	−	9947.86i	0.253825	−	0.439637i
$801$	−3725.35	−	6452.50i	−0.164331	−	0.284629i
$802$	−546.284	−	396.899i	−0.0240523	−	0.0174750i
$803$	4915.26	+	1044.77i	0.216010	+	0.0459143i
$804$	3647.48	−	11225.8i	0.159996	−	0.492416i
$805$	−2158.79			−0.0945185
$806$	25966.0	−	12171.3i	1.13476	−	0.531907i
$807$	−19712.5			−0.859867
$808$	2615.57	−	8049.88i	0.113880	−	0.350487i
$809$	−23962.4	−	5093.37i	−1.04138	−	0.221351i	−0.344682	−	0.938719i	$-0.612013\pi$
$809$	−23962.4	−	5093.37i	−1.04138	−	0.221351i	−0.696694	+	0.717368i	$0.745347\pi$
$810$	−10936.4	−	7945.79i	−0.474404	−	0.344675i
$811$	1347.25	+	2333.50i	0.0583333	+	0.101036i	0.893717	−	0.448631i	$-0.148088\pi$
$811$	1347.25	+	2333.50i	0.0583333	+	0.101036i	−0.835384	+	0.549667i	$0.814755\pi$
$812$	−172.610	+	298.968i	−0.00745986	+	0.0129209i
$813$	−22683.9	+	10099.5i	−0.978546	+	0.435677i
$814$	−21697.4	+	15764.1i	−0.934267	+	0.678785i
$815$	14930.6	+	6647.51i	0.641711	+	0.285708i
$816$	−20117.1	+	4276.02i	−0.863039	+	0.183445i
$817$	240.389	−	2287.15i	0.0102939	−	0.0979403i
$818$	14358.2	+	15946.4i	0.613721	+	0.681607i
$819$	−1395.13	+	1549.45i	−0.0595236	+	0.0661076i
$820$	−99.9951	−	951.390i	−0.00425851	−	0.0405171i
$821$	−730.143	−	2247.15i	−0.0310380	−	0.0955250i	0.934337	−	0.356390i	$-0.115992\pi$
$821$	−730.143	−	2247.15i	−0.0310380	−	0.0955250i	−0.965375	+	0.260865i	$0.915992\pi$
$822$	13911.1	+	42813.9i	0.590274	+	1.81668i
$823$	−430.412	−	4095.10i	−0.0182299	−	0.173446i	0.981619	−	0.190853i	$-0.0611255\pi$
$823$	−430.412	−	4095.10i	−0.0182299	−	0.173446i	−0.999848	+	0.0174073i	$0.994459\pi$
$824$	4400.65	−	4887.41i	0.186048	−	0.206628i
$825$	−12233.3	−	13586.5i	−0.516254	−	0.573358i
$826$	475.978	−	4528.63i	0.0200501	−	0.190764i
$827$	−9894.16	+	2103.07i	−0.416026	+	0.0884291i	−0.411169	−	0.911559i	$-0.634879\pi$
$827$	−9894.16	+	2103.07i	−0.416026	+	0.0884291i	−0.00485708	+	0.999988i	$0.501546\pi$
$828$	9015.85	+	4014.12i	0.378409	+	0.168478i
$829$	14052.9	−	10210.1i	0.588756	−	0.427756i	−0.253114	−	0.967436i	$-0.581455\pi$
$829$	14052.9	−	10210.1i	0.588756	−	0.427756i	0.841870	+	0.539680i	$0.181455\pi$
$830$	18219.7	−	8111.92i	0.761945	−	0.339240i
$831$	−2180.07	+	3775.99i	−0.0910058	+	0.157627i
$832$	−6668.90	−	11550.9i	−0.277888	−	0.481316i
$833$	10704.8	+	7777.52i	0.445259	+	0.323499i
$834$	−17547.0	−	3729.73i	−0.728540	−	0.154856i
$835$	1478.93	−	4551.68i	0.0612940	−	0.188644i
$836$	−8268.30			−0.342063
$837$	−6470.55	+	7473.61i	−0.267210	+	0.308633i
$838$	15021.4			0.619221
$839$	1867.17	−	5746.55i	0.0768316	−	0.236463i	−0.905263	−	0.424852i	$-0.860326\pi$
$839$	1867.17	−	5746.55i	0.0768316	−	0.236463i	0.982095	+	0.188388i	$0.0603263\pi$
$840$	−1207.37	−	256.635i	−0.0495932	−	0.0105414i
$841$	16684.8	+	12122.2i	0.684113	+	0.497037i
$842$	−4900.52	−	8487.96i	−0.200574	−	0.347404i
$843$	−7201.17	+	12472.8i	−0.294213	+	0.509592i
$844$	−1060.07	+	471.975i	−0.0432337	+	0.0192489i
$845$	−1589.84	+	1155.08i	−0.0647244	+	0.0470250i
$846$	−15156.0	−	6747.87i	−0.615926	−	0.274228i
$847$	−1374.60	+	292.181i	−0.0557638	+	0.0118530i
$848$	−2619.41	+	24922.0i	−0.106074	+	1.00923i
$849$	−23342.0	−	25923.9i	−0.943575	−	1.04795i
$850$	8757.28	−	9725.94i	0.353379	−	0.392467i
$851$	−6842.51	−	65102.2i	−0.275627	−	2.62241i
$852$	1367.55	+	4208.88i	0.0549900	+	0.169242i
$853$	11227.9	+	34556.0i	0.450688	+	1.38707i	0.876124	+	0.482086i	$0.160121\pi$
$853$	11227.9	+	34556.0i	0.450688	+	1.38707i	−0.425436	+	0.904988i	$0.639879\pi$
$854$	−20.3047	−	193.186i	−0.000813598	−	0.00774087i
$855$	7151.74	−	7942.81i	0.286064	−	0.317706i
$856$	17829.0	+	19801.2i	0.711897	+	0.790642i
$857$	2681.41	−	25511.9i	0.106879	−	1.01689i	−0.801288	−	0.598279i	$-0.795852\pi$
$857$	2681.41	−	25511.9i	0.106879	−	1.01689i	0.908167	−	0.418608i	$-0.137482\pi$
$858$	28860.3	−	6134.45i	1.14834	−	0.244087i
$859$	−3217.94	−	1432.72i	−0.127817	−	0.0569077i	0.341832	−	0.939761i	$-0.388953\pi$
$859$	−3217.94	−	1432.72i	−0.127817	−	0.0569077i	−0.469649	+	0.882853i	$0.655619\pi$
$860$	181.473	−	131.848i	0.00719555	−	0.00522788i
$861$	1082.62	−	482.015i	0.0428521	−	0.0190790i
$862$	6475.44	−	11215.8i	0.255863	−	0.443168i
$863$	−11636.2	−	20154.4i	−0.458979	−	0.794976i	0.539928	−	0.841711i	$-0.318452\pi$
$863$	−11636.2	−	20154.4i	−0.458979	−	0.794976i	−0.998907	+	0.0467356i	$0.985118\pi$
$864$	−5169.91	−	3756.16i	−0.203569	−	0.147902i
$865$	6244.22	+	1327.25i	0.245445	+	0.0521709i
$866$	12148.6	−	37389.5i	0.476704	−	1.46714i
$867$	22814.1			0.893665
$868$	282.046	−	929.162i	0.0110291	−	0.0363339i
$869$	−23492.9			−0.917081
$870$	−1951.44	+	6005.90i	−0.0760459	+	0.234045i
$871$	34266.3	+	7283.52i	1.33303	+	0.283344i
$872$	−4028.11	−	2926.59i	−0.156432	−	0.113655i
$873$	3430.49	+	5941.79i	0.132995	+	0.230354i
$874$	41694.1	−	72216.4i	1.61364	−	2.79491i
$875$	2153.70	−	958.890i	0.0832096	−	0.0370473i
$876$	2661.18	−	1933.46i	0.102640	−	0.0745727i
$877$	8961.65	+	3989.98i	0.345055	+	0.153628i	0.571945	−	0.820292i	$-0.306189\pi$
$877$	8961.65	+	3989.98i	0.345055	+	0.153628i	−0.226890	+	0.973920i	$0.572856\pi$
$878$	−42998.3	+	9139.56i	−1.65276	+	0.351304i
$879$	−2421.56	+	23039.6i	−0.0929204	+	0.884079i
$880$	6443.94	+	7156.72i	0.246847	+	0.274151i
$881$	11014.1	−	12232.4i	0.421199	−	0.467788i	−0.494778	−	0.869019i	$-0.664751\pi$
$881$	11014.1	−	12232.4i	0.421199	−	0.467788i	0.915977	+	0.401231i	$0.131417\pi$
$882$	−2125.53	−	20223.0i	−0.0811454	−	0.772046i
$883$	−8212.05	−	25274.1i	−0.312976	−	0.963240i	−0.976580	−	0.215156i	$-0.930974\pi$
$883$	−8212.05	−	25274.1i	−0.312976	−	0.963240i	0.663604	−	0.748084i	$-0.269026\pi$
$884$	1579.59	+	4861.49i	0.0600990	+	0.184966i
$885$	−2107.20	−	20048.7i	−0.0800371	−	0.761502i
$886$	−9509.10	+	10560.9i	−0.360570	+	0.400453i
$887$	21270.5	+	23623.3i	0.805179	+	0.894242i	0.996178	−	0.0873479i	$-0.0278392\pi$
$887$	21270.5	+	23623.3i	0.805179	+	0.894242i	−0.190998	+	0.981590i	$0.561173\pi$
$888$	3912.39	−	37223.9i	0.147850	−	1.40670i
$889$	−4946.21	+	1051.35i	−0.186604	+	0.0396638i
$890$	−5609.57	−	2497.54i	−0.211273	−	0.0940650i
$891$	−18871.9	+	13711.2i	−0.709574	+	0.515536i
$892$	−2945.52	+	1311.43i	−0.110564	+	0.0492263i
$893$	−16962.7	+	29380.2i	−0.635648	+	1.10098i
$894$	32165.5	+	55712.3i	1.20333	+	2.08423i
$895$	−4791.48	−	3481.21i	−0.178951	−	0.130016i
$896$	−3748.34	−	796.735i	−0.139758	−	0.0297065i
$897$	−22254.1	+	68491.1i	−0.828364	+	2.54944i
$898$	−52930.7			−1.96695
$899$	9757.58	+	4118.87i	0.361995	+	0.152805i
$900$	−4867.54			−0.180279
$901$	−3889.31	+	11970.1i	−0.143809	+	0.442598i
$902$	−6671.83	−	1418.14i	−0.246283	−	0.0523492i
$903$	224.809	+	163.334i	0.00828482	+	0.00601927i
$904$	−10517.5	−	18216.9i	−0.386955	−	0.670226i
$905$	−10427.4	+	18060.8i	−0.383005	+	0.663384i
$906$	39919.4	−	17773.3i	1.46383	−	0.651741i
$907$	−36005.5	+	26159.5i	−1.31813	+	0.957676i	−0.318175	+	0.948032i	$0.603070\pi$
$907$	−36005.5	+	26159.5i	−1.31813	+	0.957676i	−0.999953	+	0.00964394i	$0.996930\pi$
$908$	−7598.81	−	3383.21i	−0.277726	−	0.123652i
$909$	−8662.20	+	1841.21i	−0.316069	+	0.0671826i
$910$	−179.614	+	1708.92i	−0.00654303	+	0.0622528i
$911$	19370.1	+	21512.7i	0.704459	+	0.782380i	0.984079	−	0.177730i	$-0.0568754\pi$
$911$	19370.1	+	21512.7i	0.704459	+	0.782380i	−0.279621	+	0.960111i	$0.590209\pi$
$912$	43246.6	−	48030.2i	1.57022	−	1.74390i
$913$	−3597.36	−	34226.6i	−0.130400	−	1.24067i
$914$	18027.7	+	55483.5i	0.652410	+	2.00791i
$915$	−265.744	−	817.877i	−0.00960135	−	0.0295499i
$916$	1570.35	+	14940.9i	0.0566439	+	0.538931i
$917$	−2794.03	+	3103.08i	−0.100618	+	0.111748i
$918$	−4871.87	−	5410.76i	−0.175159	−	0.194533i
$919$	−4679.59	+	44523.3i	−0.167971	+	1.59814i	0.508099	+	0.861299i	$0.330348\pi$
$919$	−4679.59	+	44523.3i	−0.167971	+	1.59814i	−0.676070	+	0.736838i	$0.736318\pi$
$920$	−16961.6	+	3605.29i	−0.607833	+	0.129199i
$921$	−63487.5	−	28266.4i	−2.27143	−	1.01130i
$922$	−13658.3	+	9923.31i	−0.487864	+	0.354454i
$923$	−11998.9	+	5342.27i	−0.427898	+	0.190512i
$924$	499.531	−	865.214i	0.0177850	−	0.0308046i
$925$	16143.0	+	27960.5i	0.573815	+	0.993877i
$926$	40972.5	+	29768.3i	1.45404	+	1.05642i
$927$	−6730.55	−	1430.62i	−0.238469	−	0.0506881i
$928$	−2115.72	+	6511.52i	−0.0748404	+	0.230335i
$929$	29103.5			1.02783			0.513915	−	0.857841i	$-0.328195\pi$
$929$	29103.5			1.02783			0.513915	+	0.857841i	$0.328195\pi$
$930$	1512.78	−	17698.1i	0.0533399	−	0.624027i
$931$	−41581.7			−1.46379
$932$	723.679	−	2227.25i	0.0254344	−	0.0782791i
$933$	47732.3	+	10145.8i	1.67490	+	0.356012i
$934$	27677.3	+	20108.8i	0.969625	+	0.704474i
$935$	2418.42	+	4188.83i	0.0845891	+	0.146513i
$936$	−8373.86	+	14503.9i	−0.292423	+	0.506492i
$937$	−23503.7	+	10464.5i	−0.819458	+	0.364846i	−0.773262	−	0.634086i	$-0.781376\pi$
$937$	−23503.7	+	10464.5i	−0.819458	+	0.364846i	−0.0461955	+	0.998932i	$0.514710\pi$
$938$	3965.29	−	2880.95i	0.138029	−	0.100284i
$939$	41968.8	+	18685.7i	1.45857	+	0.649399i
$940$	−3236.70	+	687.982i	−0.112308	+	0.0238718i
$941$	4262.94	−	40559.1i	0.147681	−	1.40509i	−0.630080	−	0.776530i	$-0.716978\pi$
$941$	4262.94	−	40559.1i	0.147681	−	1.40509i	0.777761	−	0.628560i	$-0.216355\pi$
$942$	−3855.03	−	4281.44i	−0.133337	−	0.148086i
$943$	11139.9	−	12372.2i	0.384694	−	0.427246i
$944$	−5182.60	−	49309.2i	−0.178686	−	1.70008i
$945$	−183.043	−	563.347i	−0.00630093	−	0.0193923i
$946$	−494.234	−	1521.10i	−0.0169862	−	0.0522782i
$947$	3315.64	+	31546.3i	0.113774	+	1.08249i	0.891231	+	0.453551i	$0.149843\pi$
$947$	3315.64	+	31546.3i	0.113774	+	1.08249i	−0.777457	+	0.628937i	$0.783490\pi$
$948$	−10290.2	+	11428.4i	−0.352542	+	0.391538i
$949$	6532.51	+	7255.09i	0.223450	+	0.248167i
$950$	−4299.06	+	40902.8i	−0.146821	+	1.39691i
$951$	−21207.9	+	4507.88i	−0.723147	+	0.153710i
$952$	−1392.93	−	620.174i	−0.0474215	−	0.0211134i
$953$	−18882.6	+	13719.0i	−0.641834	+	0.466319i	−0.860480	−	0.509485i	$-0.829836\pi$
$953$	−18882.6	+	13719.0i	−0.641834	+	0.466319i	0.218646	+	0.975804i	$0.429836\pi$
$954$	17669.7	−	7867.07i	0.599663	−	0.266987i
$955$	545.217	−	944.343i	0.0184741	−	0.0319981i
$956$	−8360.49	−	14480.8i	−0.282843	−	0.489898i
$957$	8815.93	+	6405.15i	0.297783	+	0.216352i
$958$	1676.03	+	356.251i	0.0565240	+	0.0120146i
$959$	−1398.01	+	4302.63i	−0.0470741	+	0.144879i
$960$	−8261.48			−0.277748
$961$	−29358.8	−	5055.95i	−0.985493	−	0.169714i
$962$	−52104.7			−1.74628
$963$	8614.70	−	26513.3i	0.288271	−	0.887207i
$964$	−5062.68	−	1076.11i	−0.169147	−	0.0359534i
$965$	10324.8	+	7501.38i	0.344421	+	0.250236i
$966$	5037.93	+	8725.94i	0.167798	+	0.290634i
$967$	7114.69	−	12323.0i	0.236601	−	0.409805i	−0.723136	−	0.690706i	$-0.757300\pi$
$967$	7114.69	−	12323.0i	0.236601	−	0.409805i	0.959737	+	0.280901i	$0.0906333\pi$
$968$	−10312.3	+	4591.33i	−0.342406	+	0.152449i
$969$	26261.5	−	19080.1i	0.870632	−	0.632551i
$970$	5165.58	+	2299.86i	0.170986	+	0.0761280i
$971$	−159.856	+	33.9785i	−0.00528324	+	0.00112299i	−0.210553	−	0.977583i	$-0.567526\pi$
$971$	−159.856	+	33.9785i	−0.00528324	+	0.00112299i	0.205269	+	0.978706i	$0.434193\pi$
$972$	−1183.24	+	11257.8i	−0.0390458	+	0.371496i
$973$	−1206.31	−	1339.74i	−0.0397455	−	0.0441419i
$974$	16519.5	−	18346.7i	0.543448	−	0.603560i
$975$	−3712.75	−	35324.4i	−0.121952	−	1.16029i
$976$	−653.590	−	2011.54i	−0.0214354	−	0.0659712i
$977$	−3695.95	−	11375.0i	−0.121028	−	0.372485i	0.872129	−	0.489276i	$-0.162739\pi$
$977$	−3695.95	−	11375.0i	−0.121028	−	0.372485i	−0.993156	+	0.116792i	$0.962739\pi$
$978$	−7973.55	−	75863.3i	−0.260702	−	2.48041i
$979$	−7090.05	+	7874.29i	−0.231459	+	0.257062i
$980$	−2713.86	−	3014.05i	−0.0884603	−	0.0982451i
$981$	−544.526	+	5180.82i	−0.0177221	+	0.168615i
$982$	21727.3	−	4618.28i	0.706055	−	0.150077i
$983$	34032.9	+	15152.4i	1.10425	+	0.491646i	0.876173	−	0.481996i	$-0.160088\pi$
$983$	34032.9	+	15152.4i	1.10425	+	0.491646i	0.228081	+	0.973642i	$0.426755\pi$
$984$	7701.16	−	5595.22i	0.249496	−	0.181269i
$985$	16895.1	−	7522.19i	0.546521	−	0.243327i
$986$	−3900.36	+	6755.63i	−0.125977	+	0.218198i
$987$	−2049.61	−	3550.03i	−0.0660991	−	0.114487i
$988$	−12995.7	−	9441.96i	−0.418471	−	0.304037i
$989$	3818.44	+	811.635i	0.122770	+	0.0260955i
$990$	2296.96	−	7069.32i	0.0737396	−	0.226947i
$991$	29534.4			0.946712			0.473356	−	0.880871i	$-0.343042\pi$
$991$	29534.4			0.946712			0.473356	+	0.880871i	$0.343042\pi$
$992$	1640.14	−	19188.1i	0.0524944	−	0.614135i
$993$	12240.1			0.391164
$994$	−567.871	+	1747.73i	−0.0181205	+	0.0557691i
$995$	6633.98	+	1410.10i	0.211368	+	0.0449277i
$996$	−18225.6	−	13241.7i	−0.579819	−	0.421263i
$997$	2957.15	+	5121.93i	0.0939357	+	0.162701i	0.909164	−	0.416438i	$-0.136722\pi$
$997$	2957.15	+	5121.93i	0.0939357	+	0.162701i	−0.815228	+	0.579140i	$0.803389\pi$
$998$	−16677.3	+	28885.9i	−0.528968	+	0.916199i
$999$	16408.6	−	7305.57i	0.519664	−	0.231369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.9.2	yes	56
31.7	even	15	inner	31.4.g.a.7.2	✓	56
31.10	even	15		961.4.a.m.1.6		28
31.21	odd	30		961.4.a.l.1.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.7.2	✓	56	31.7	even	15	inner
31.4.g.a.9.2	yes	56	1.1	even	1	trivial
961.4.a.l.1.6		28	31.21	odd	30
961.4.a.m.1.6		28	31.10	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+(-1.00392 + 3.08973i) q^{2} +(6.59870 + 1.40260i) q^{3} +(-2.06647 - 1.50138i) q^{4} +(-2.34783 - 4.06657i) q^{5} +(-10.9582 + 18.9801i) q^{6} +(-2.01209 + 0.895840i) q^{7} +(-14.3129 + 10.3989i) q^{8} +(16.9098 + 7.52874i) q^{9} +(14.9216 - 3.17169i) q^{10} +(2.75160 - 26.1797i) q^{11} +(-11.5302 - 12.8056i) q^{12} +(34.2207 - 38.0059i) q^{13} +(-0.747939 - 7.11617i) q^{14} +(-9.78889 - 30.1271i) q^{15} +(-24.0755 - 74.0968i) q^{16} +(-4.09024 - 38.9160i) q^{17} +(-40.2379 + 44.6887i) q^{18} +(82.2821 + 91.3835i) q^{19} +(-1.25373 + 11.9284i) q^{20} +(-14.5337 + 3.08923i) q^{21} +(78.1259 + 34.7839i) q^{22} +(-168.870 + 122.692i) q^{23} +(-109.032 + 48.5440i) q^{24} +(51.4754 - 89.1579i) q^{25} +(83.0734 + 143.887i) q^{26} +(-46.3354 - 33.6647i) q^{27} +(5.50292 + 1.16968i) q^{28} +(-18.9622 + 58.3596i) q^{29} +102.912 q^{30} +(14.6998 - 171.974i) q^{31} +111.576 q^{32} +(54.8765 - 168.893i) q^{33} +(124.346 + 26.4307i) q^{34} +(8.36704 + 6.07901i) q^{35} +(-23.6402 - 40.9460i) q^{36} +(-156.803 + 271.591i) q^{37} +(-364.955 + 162.488i) q^{38} +(279.119 - 202.792i) q^{39} +(75.8920 + 33.7893i) q^{40} +(-78.0154 + 16.5827i) q^{41} +(5.04569 - 48.0065i) q^{42} +(-12.5140 - 13.8982i) q^{43} +(-44.9917 + 49.9684i) q^{44} +(-9.08534 - 86.4412i) q^{45} +(-209.553 - 644.937i) q^{46} +(85.2535 + 262.383i) q^{47} +(-54.9391 - 522.710i) q^{48} +(-226.266 + 251.294i) q^{49} +(223.797 + 248.552i) q^{50} +(27.5932 - 262.532i) q^{51} +(-127.777 + 27.1599i) q^{52} +(-293.837 - 130.825i) q^{53} +(150.532 - 109.368i) q^{54} +(-112.922 + 50.2760i) q^{55} +(19.4830 - 33.7455i) q^{56} +(414.781 + 718.421i) q^{57} +(-161.279 - 117.176i) q^{58} +(622.479 + 132.312i) q^{59} +(-25.0037 + 76.9536i) q^{60} +27.1475 q^{61} +(516.595 + 218.065i) q^{62} -40.7687 q^{63} +(80.5915 - 248.035i) q^{64} +(-234.898 - 49.9291i) q^{65} +(466.742 + 339.108i) q^{66} +(342.496 + 593.220i) q^{67} +(-49.9753 + 86.5598i) q^{68} +(-1286.41 + 572.748i) q^{69} +(-27.1823 + 19.7491i) q^{70} +(-234.620 - 104.460i) q^{71} +(-320.319 + 68.0858i) q^{72} +(-19.9538 + 189.848i) q^{73} +(-681.727 - 757.135i) q^{74} +(464.723 - 516.127i) q^{75} +(-32.8322 - 312.378i) q^{76} +(17.9164 + 55.1409i) q^{77} +(346.361 + 1065.99i) q^{78} +(-93.2871 - 887.568i) q^{79} +(-244.794 + 271.871i) q^{80} +(-592.949 - 658.537i) q^{81} +(27.0848 - 257.694i) q^{82} +(1278.80 - 271.818i) q^{83} +(34.6715 + 15.4367i) q^{84} +(-148.651 + 108.002i) q^{85} +(55.5048 - 24.7123i) q^{86} +(-206.981 + 358.501i) q^{87} +(232.857 + 403.320i) q^{88} +(-325.646 - 236.596i) q^{89} +(276.201 + 58.7084i) q^{90} +(-34.8078 + 107.128i) q^{91} +533.172 q^{92} +(338.209 - 1114.18i) q^{93} -896.281 q^{94} +(178.433 - 549.159i) q^{95} +(736.254 + 156.496i) q^{96} +(299.871 + 217.869i) q^{97} +(-549.279 - 951.379i) q^{98} +(243.629 - 421.978i) 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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