LMFDB - Embedded newform 230.4.l.a.53.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			53.21
Character	$\chi$	$=$	230.53
Dual form			230.4.l.a.217.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.142678 + 1.99490i) q^{2} +(-7.79240 - 1.69513i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(5.05966 + 9.96995i) q^{5} +(2.26982 - 15.7870i) q^{6} +(11.3272 + 6.18513i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(33.2880 + 15.2021i) q^{9} +(-19.1672 + 11.5160i) q^{10} +(47.3150 - 40.9987i) q^{11} +(31.8173 + 2.27562i) q^{12} +(1.24808 + 2.28569i) q^{13} +(-10.7226 + 23.4792i) q^{14} +(-22.5265 - 86.2666i) q^{15} +(15.3519 - 4.50772i) q^{16} +(-34.3638 + 25.7244i) q^{17} +(-25.5773 + 68.5753i) q^{18} +(12.4909 + 86.8764i) q^{19} +(-25.7081 - 36.5936i) q^{20} +(-77.7817 - 67.3982i) q^{21} +(88.5393 + 88.5393i) q^{22} +(-35.9343 + 104.287i) q^{23} +63.7972i q^{24} +(-73.7996 + 100.889i) q^{25} +(-4.38165 + 2.81592i) q^{26} +(-61.2547 - 45.8547i) q^{27} +(-48.3687 - 18.0406i) q^{28} +(-166.667 - 23.9631i) q^{29} +(168.880 - 57.2466i) q^{30} +(67.0723 + 43.1048i) q^{31} +(11.1829 + 29.9824i) q^{32} +(-438.196 + 239.273i) q^{33} +(-56.2207 - 64.8822i) q^{34} +(-4.35351 + 144.227i) q^{35} +(-140.451 - 41.2400i) q^{36} +(-69.3509 + 25.8666i) q^{37} +(-171.528 + 37.3136i) q^{38} +(-5.85099 - 19.9266i) q^{39} +(69.3327 - 56.5064i) q^{40} +(67.9144 + 148.712i) q^{41} +(123.355 - 164.783i) q^{42} +(-25.7803 + 118.510i) q^{43} +(-163.995 + 189.260i) q^{44} +(16.8617 + 408.797i) q^{45} +(-213.169 - 56.8061i) q^{46} +(70.0685 - 70.0685i) q^{47} +(-127.269 + 9.10248i) q^{48} +(-95.3896 - 148.429i) q^{49} +(-211.794 - 132.829i) q^{50} +(311.383 - 142.204i) q^{51} +(-6.24265 - 8.33921i) q^{52} +(-66.3809 + 121.568i) q^{53} +(82.7360 - 128.740i) q^{54} +(648.153 + 264.289i) q^{55} +(29.0881 - 99.0649i) q^{56} +(49.9326 - 698.150i) q^{57} +(24.0243 - 335.904i) q^{58} +(-69.1230 + 235.411i) q^{59} +(138.297 + 328.731i) q^{60} +(356.042 - 554.011i) q^{61} +(-76.4201 + 139.953i) q^{62} +(283.033 + 378.088i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(-16.4733 + 24.0081i) q^{65} +(-539.848 - 840.020i) q^{66} +(-583.229 + 41.7134i) q^{67} +(121.412 - 121.412i) q^{68} +(456.795 - 751.731i) q^{69} +(-288.339 + 11.8932i) q^{70} +(-64.6606 + 74.6223i) q^{71} +(62.2306 - 286.069i) q^{72} +(-540.397 + 721.886i) q^{73} +(-61.4962 - 134.658i) q^{74} +(746.097 - 661.068i) q^{75} +(-98.9104 - 336.858i) q^{76} +(789.531 - 171.752i) q^{77} +(38.9169 - 14.5153i) q^{78} +(86.1370 + 25.2921i) q^{79} +(122.617 + 130.250i) q^{80} +(-247.453 - 285.576i) q^{81} +(-286.976 + 156.701i) q^{82} +(450.503 + 1207.85i) q^{83} +(346.327 + 222.571i) q^{84} +(-430.340 - 212.448i) q^{85} +(-240.095 - 34.5204i) q^{86} +(1258.12 + 469.253i) q^{87} +(-400.954 - 300.151i) q^{88} +(293.818 - 188.825i) q^{89} +(-813.105 + 91.9639i) q^{90} +33.6100i q^{91} +(82.9081 - 433.357i) q^{92} +(-449.586 - 449.586i) q^{93} +(149.777 + 129.783i) q^{94} +(-802.953 + 564.099i) q^{95} +(-36.3171 - 252.591i) q^{96} +(-288.234 + 772.785i) q^{97} +(282.492 - 211.471i) q^{98} +(2198.29 - 645.476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$3$	−7.79240	−	1.69513i	−1.49965	−	0.326228i	−0.613524	−	0.789676i	$-0.710249\pi$
$3$	−7.79240	−	1.69513i	−1.49965	−	0.326228i	−0.886124	+	0.463448i	$0.846612\pi$
$4$	−3.95929	+	0.569259i	−0.494911	+	0.0711574i
$5$	5.05966	+	9.96995i	0.452550	+	0.891739i
$5$	5.05966	+	9.96995i	0.452550	+	0.891739i
$6$	2.26982	−	15.7870i	0.154442	−	1.07417i
$7$	11.3272	+	6.18513i	0.611613	+	0.333966i	0.755024	−	0.655697i	$-0.227625\pi$
$7$	11.3272	+	6.18513i	0.611613	+	0.333966i	−0.143411	+	0.989663i	$0.545807\pi$
$8$	−1.70052	−	7.81717i	−0.0751532	−	0.345474i
$9$	33.2880	+	15.2021i	1.23289	+	0.563041i
$10$	−19.1672	+	11.5160i	−0.606120	+	0.364169i
$11$	47.3150	−	40.9987i	1.29691	−	1.12378i	0.312119	−	0.950043i	$-0.398961\pi$
$11$	47.3150	−	40.9987i	1.29691	−	1.12378i	0.984792	−	0.173737i	$-0.0555842\pi$
$12$	31.8173	+	2.27562i	0.765406	+	0.0547429i
$13$	1.24808	+	2.28569i	0.0266273	+	0.0487643i	0.890654	−	0.454682i	$-0.150247\pi$
$13$	1.24808	+	2.28569i	0.0266273	+	0.0487643i	−0.864027	+	0.503446i	$0.832065\pi$
$14$	−10.7226	+	23.4792i	−0.204695	+	0.448220i
$15$	−22.5265	−	86.2666i	−0.387755	−	1.48493i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	−34.3638	+	25.7244i	−0.490262	+	0.367005i	−0.815622	−	0.578585i	$-0.803605\pi$
$17$	−34.3638	+	25.7244i	−0.490262	+	0.367005i	0.325361	+	0.945590i	$0.394514\pi$
$18$	−25.5773	+	68.5753i	−0.334923	+	0.897964i
$19$	12.4909	+	86.8764i	0.150822	+	1.04899i	0.914846	+	0.403803i	$0.132312\pi$
$19$	12.4909	+	86.8764i	0.150822	+	1.04899i	−0.764024	+	0.645188i	$0.776779\pi$
$20$	−25.7081	−	36.5936i	−0.287426	−	0.409129i
$21$	−77.7817	−	67.3982i	−0.808255	−	0.700357i
$22$	88.5393	+	88.5393i	0.858030	+	0.858030i
$23$	−35.9343	+	104.287i	−0.325775	+	0.945447i
$23$	−35.9343	+	104.287i	−0.325775	+	0.945447i
$24$			63.7972i			0.542606i
$25$	−73.7996	+	100.889i	−0.590397	+	0.807113i
$26$	−4.38165	+	2.81592i	−0.0330505	+	0.0212403i
$27$	−61.2547	−	45.8547i	−0.436610	−	0.326842i
$28$	−48.3687	−	18.0406i	−0.326458	−	0.121762i
$29$	−166.667	−	23.9631i	−1.06722	−	0.153443i	−0.413745	−	0.910393i	$-0.635780\pi$
$29$	−166.667	−	23.9631i	−1.06722	−	0.153443i	−0.653473	+	0.756950i	$0.726689\pi$
$30$	168.880	−	57.2466i	1.02777	−	0.348392i
$31$	67.0723	+	43.1048i	0.388598	+	0.249737i	0.720322	−	0.693640i	$-0.243994\pi$
$31$	67.0723	+	43.1048i	0.388598	+	0.249737i	−0.331724	+	0.943376i	$0.607630\pi$
$32$	11.1829	+	29.9824i	0.0617771	+	0.165631i
$33$	−438.196	+	239.273i	−2.31152	+	1.26219i
$34$	−56.2207	−	64.8822i	−0.283582	−	0.327271i
$35$	−4.35351	+	144.227i	−0.0210251	+	0.696535i
$36$	−140.451	−	41.2400i	−0.650234	−	0.190926i
$37$	−69.3509	+	25.8666i	−0.308141	+	0.114931i	−0.498778	−	0.866730i	$-0.666218\pi$
$37$	−69.3509	+	25.8666i	−0.308141	+	0.114931i	0.190637	+	0.981661i	$0.438945\pi$
$38$	−171.528	+	37.3136i	−0.732250	+	0.159291i
$39$	−5.85099	−	19.9266i	−0.0240233	−	0.0818158i
$40$	69.3327	−	56.5064i	0.274062	−	0.223361i
$41$	67.9144	+	148.712i	0.258694	+	0.566461i	0.993761	−	0.111534i	$-0.0355764\pi$
$41$	67.9144	+	148.712i	0.258694	+	0.566461i	−0.735067	+	0.677995i	$0.762849\pi$
$42$	123.355	−	164.783i	0.453193	−	0.605395i
$43$	−25.7803	+	118.510i	−0.0914293	+	0.420294i	0.908567	+	0.417738i	$0.137177\pi$
$43$	−25.7803	+	118.510i	−0.0914293	+	0.420294i	−0.999997	+	0.00255544i	$0.999187\pi$
$44$	−163.995	+	189.260i	−0.561890	+	0.648456i
$45$	16.8617	+	408.797i	0.0558576	+	1.35422i
$46$	−213.169	−	56.8061i	−0.683262	−	0.182078i
$47$	70.0685	−	70.0685i	0.217458	−	0.217458i	−0.589968	−	0.807427i	$-0.700860\pi$
$47$	70.0685	−	70.0685i	0.217458	−	0.217458i	0.807427	+	0.589968i	$0.200860\pi$
$48$	−127.269	+	9.10248i	−0.382703	+	0.0273714i
$49$	−95.3896	−	148.429i	−0.278104	−	0.432738i
$50$	−211.794	−	132.829i	−0.599043	−	0.375696i
$51$	311.383	−	142.204i	0.854948	−	0.390442i
$52$	−6.24265	−	8.33921i	−0.0166481	−	0.0222392i
$53$	−66.3809	+	121.568i	−0.172040	+	0.315068i	−0.949445	−	0.313932i	$-0.898354\pi$
$53$	−66.3809	+	121.568i	−0.172040	+	0.315068i	0.777405	+	0.629000i	$0.216535\pi$
$54$	82.7360	−	128.740i	0.208499	−	0.324431i
$55$	648.153	+	264.289i	1.58904	+	0.647940i
$56$	29.0881	−	99.0649i	0.0694117	−	0.236395i
$57$	49.9326	−	698.150i	0.116031	−	1.62232i
$58$	24.0243	−	335.904i	0.0543888	−	0.760455i
$59$	−69.1230	+	235.411i	−0.152526	+	0.519456i	−0.999934	−	0.0114860i	$-0.996344\pi$
$59$	−69.1230	+	235.411i	−0.152526	+	0.519456i	0.847408	+	0.530942i	$0.178162\pi$
$60$	138.297	+	328.731i	0.297568	+	0.707316i
$61$	356.042	−	554.011i	0.747319	−	1.16285i	−0.234331	−	0.972157i	$-0.575290\pi$
$61$	356.042	−	554.011i	0.747319	−	1.16285i	0.981650	−	0.190694i	$-0.0610738\pi$
$62$	−76.4201	+	139.953i	−0.156538	+	0.286678i
$63$	283.033	+	378.088i	0.566013	+	0.756105i
$64$	−58.2164	+	26.5866i	−0.113704	+	0.0519269i
$65$	−16.4733	+	24.0081i	−0.0314348	+	0.0458129i
$66$	−539.848	−	840.020i	−1.00683	−	1.56666i
$67$	−583.229	+	41.7134i	−1.06347	+	0.0760612i	−0.592094	−	0.805869i	$-0.701699\pi$
$67$	−583.229	+	41.7134i	−1.06347	+	0.0760612i	−0.471380	+	0.881930i	$0.656244\pi$
$68$	121.412	−	121.412i	0.216521	−	0.216521i
$69$	456.795	−	751.731i	0.796980	−	1.31156i
$70$	−288.339	+	11.8932i	−0.492331	+	0.0203072i
$71$	−64.6606	+	74.6223i	−0.108082	+	0.124733i	−0.807213	−	0.590261i	$-0.799025\pi$
$71$	−64.6606	+	74.6223i	−0.108082	+	0.124733i	0.699131	+	0.714994i	$0.253570\pi$
$72$	62.2306	−	286.069i	0.101860	−	0.468244i
$73$	−540.397	+	721.886i	−0.866420	+	1.15740i	0.119937	+	0.992781i	$0.461731\pi$
$73$	−540.397	+	721.886i	−0.866420	+	1.15740i	−0.986357	+	0.164620i	$0.947360\pi$
$74$	−61.4962	−	134.658i	−0.0966052	−	0.211536i
$75$	746.097	−	661.068i	1.14869	−	1.01778i
$76$	−98.9104	−	336.858i	−0.149287	−	0.508424i
$77$	789.531	−	171.752i	1.16851	−	0.254194i
$78$	38.9169	−	14.5153i	0.0564933	−	0.0210709i
$79$	86.1370	+	25.2921i	0.122673	+	0.0360200i	0.342493	−	0.939520i	$-0.388729\pi$
$79$	86.1370	+	25.2921i	0.122673	+	0.0360200i	−0.219820	+	0.975540i	$0.570547\pi$
$80$	122.617	+	130.250i	0.171363	+	0.182030i
$81$	−247.453	−	285.576i	−0.339442	−	0.391737i
$82$	−286.976	+	156.701i	−0.386478	+	0.211033i
$83$	450.503	+	1207.85i	0.595773	+	1.59733i	0.787794	+	0.615938i	$0.211223\pi$
$83$	450.503	+	1207.85i	0.595773	+	1.59733i	−0.192022	+	0.981391i	$0.561504\pi$
$84$	346.327	+	222.571i	0.449850	+	0.289101i
$85$	−430.340	−	212.448i	−0.549141	−	0.271097i
$86$	−240.095	−	34.5204i	−0.301047	−	0.0432841i
$87$	1258.12	+	469.253i	1.55039	+	0.578267i
$88$	−400.954	−	300.151i	−0.485703	−	0.363593i
$89$	293.818	−	188.825i	0.349940	−	0.224892i	−0.353848	−	0.935303i	$-0.615127\pi$
$89$	293.818	−	188.825i	0.349940	−	0.224892i	0.703788	+	0.710410i	$0.251491\pi$
$90$	−813.105	+	91.9639i	−0.952319	+	0.107709i
$91$			33.6100i			0.0387175i
$92$	82.9081	−	433.357i	0.0939540	−	0.491093i
$93$	−449.586	−	449.586i	−0.501289	−	0.501289i
$94$	149.777	+	129.783i	0.164344	+	0.142405i
$95$	−802.953	+	564.099i	−0.867171	+	0.609214i
$96$	−36.3171	−	252.591i	−0.0386104	−	0.268542i
$97$	−288.234	+	772.785i	−0.301708	+	0.808911i	0.694303	+	0.719683i	$0.255713\pi$
$97$	−288.234	+	772.785i	−0.301708	+	0.808911i	−0.996011	+	0.0892284i	$0.971560\pi$
$98$	282.492	−	211.471i	0.291184	−	0.217977i
$99$	2198.29	−	645.476i	2.23168	−	0.655280i
$100$	234.762	−	441.460i	0.234762	−	0.441460i
$101$	−340.545	+	745.689i	−0.335500	+	0.734642i	−0.999919	−	0.0127180i	$-0.995952\pi$
$101$	−340.545	+	745.689i	−0.335500	+	0.734642i	0.664419	+	0.747360i	$0.268679\pi$
$102$	328.111	+	600.890i	0.318508	+	0.583303i
$103$	1313.60	+	93.9507i	1.25663	+	0.0898761i	0.683722	−	0.729743i	$-0.260360\pi$
$103$	1313.60	+	93.9507i	1.25663	+	0.0898761i	0.572910	+	0.819619i	$0.305815\pi$
$104$	15.7452	−	13.6433i	0.0148456	−	0.0128638i
$105$	278.408	−	1116.49i	0.258760	−	1.03770i
$106$	−251.987	−	115.079i	−0.230897	−	0.105447i
$107$	326.726	+	1501.93i	0.295194	+	1.35698i	0.850778	+	0.525525i	$0.176131\pi$
$107$	326.726	+	1501.93i	0.295194	+	1.35698i	−0.555584	+	0.831460i	$0.687505\pi$
$108$	268.628	+	146.682i	0.239340	+	0.130690i
$109$	−235.086	+	1635.06i	−0.206579	+	1.43679i	0.577633	+	0.816297i	$0.303977\pi$
$109$	−235.086	+	1635.06i	−0.206579	+	1.43679i	−0.784212	+	0.620493i	$0.786932\pi$
$110$	−434.753	+	1330.71i	−0.376837	+	1.15344i
$111$	584.257	−	84.0035i	0.499597	−	0.0718312i
$112$	201.775	+	43.8935i	0.170232	+	0.0370317i
$113$	78.3676	+	1095.72i	0.0652407	+	0.912185i	0.919689	+	0.392648i	$0.128441\pi$
$113$	78.3676	+	1095.72i	0.0652407	+	0.912185i	−0.854448	+	0.519537i	$0.826105\pi$
$114$	1399.87			1.15008
$115$	−1221.55	+	169.392i	−0.990522	+	0.137356i
$116$	673.524			0.539096
$117$	6.79878	+	95.0593i	0.00537220	+	0.0751131i
$118$	−479.485	−	104.306i	−0.374069	−	0.0813738i
$119$	−548.356	+	78.8417i	−0.422418	+	0.0607345i
$120$	−636.054	+	322.792i	−0.483863	+	0.245556i
$121$	368.397	−	2562.26i	0.276782	−	1.92506i
$122$	1156.00	+	631.223i	0.857863	+	0.468428i
$123$	−277.130	−	1273.95i	−0.203154	−	0.933885i
$124$	−290.096	−	132.483i	−0.210092	−	0.0959458i
$125$	−1379.26	−	225.314i	−0.986918	−	0.161221i
$126$	−713.867	+	618.569i	−0.504733	+	0.437354i
$127$	−2079.12	−	148.702i	−1.45270	−	0.103899i	−0.677455	−	0.735564i	$-0.736917\pi$
$127$	−2079.12	−	148.702i	−1.45270	−	0.103899i	−0.775241	+	0.631665i	$0.782372\pi$
$128$	−61.3439	−	112.343i	−0.0423600	−	0.0775766i
$129$	401.781	−	879.777i	0.274223	−	0.600466i
$130$	−50.2442	−	29.4372i	−0.0338978	−	0.0198601i
$131$	1847.97	−	542.614i	1.23251	−	0.361896i	0.400311	−	0.916379i	$-0.368902\pi$
$131$	1847.97	−	542.614i	1.23251	−	0.361896i	0.832195	+	0.554483i	$0.187084\pi$
$132$	1598.73	−	1196.80i	1.05418	−	0.789151i
$133$	−395.855	+	1061.33i	−0.258082	+	0.691945i
$134$	−166.428	−	1157.53i	−0.107293	−	0.746237i
$135$	147.241	−	842.715i	0.0938701	−	0.537255i
$136$	259.529	+	224.883i	0.163635	+	0.141791i
$137$	−1900.47	−	1900.47i	−1.18517	−	1.18517i	−0.978388	−	0.206779i	$-0.933702\pi$
$137$	−1900.47	−	1900.47i	−1.18517	−	1.18517i	−0.206779	−	0.978388i	$-0.566298\pi$
$138$	1564.81	+	804.006i	0.965254	+	0.495953i
$139$		−	3221.90i		−	1.96603i	−0.183521	−	0.983016i	$-0.558749\pi$
$139$		−	3221.90i		−	1.96603i	0.183521	−	0.983016i	$-0.441251\pi$
$140$	−64.8655	−	573.512i	−0.0391581	−	0.346219i
$141$	−664.778	+	427.227i	−0.397052	+	0.255170i
$142$	−158.090	−	118.345i	−0.0934270	−	0.0699385i
$143$	152.763	+	56.9777i	0.0893335	+	0.0333197i
$144$	579.560	+	83.3281i	0.335394	+	0.0482223i
$145$	−604.369	−	1782.91i	−0.346138	−	1.02112i
$146$	−1517.20	−	975.042i	−0.860027	−	0.552706i
$147$	491.707	+	1318.32i	0.275886	+	0.739680i
$148$	259.855	−	141.892i	0.144324	−	0.0788069i
$149$	1978.21	+	2282.98i	1.08766	+	1.25523i	0.964851	+	0.262797i	$0.0846450\pi$
$149$	1978.21	+	2282.98i	1.08766	+	1.25523i	0.122810	+	0.992430i	$0.460810\pi$
$150$	1425.22	+	1394.07i	0.775791	+	0.758837i
$151$	1073.15	+	315.104i	0.578353	+	0.169820i	0.557809	−	0.829969i	$-0.311642\pi$
$151$	1073.15	+	315.104i	0.578353	+	0.169820i	0.0205439	+	0.999789i	$0.493460\pi$
$152$	657.887	−	245.379i	0.351064	−	0.130940i
$153$	−1534.97	+	333.912i	−0.811077	+	0.176439i
$154$	455.278	+	1550.53i	0.238229	+	0.811335i
$155$	−90.3889	+	886.803i	−0.0468401	+	0.459547i
$156$	34.5092	+	75.5646i	0.0177112	+	0.0387821i
$157$	134.286	−	179.385i	0.0682624	−	0.0911880i	−0.765111	−	0.643899i	$-0.777316\pi$
$157$	134.286	−	179.385i	0.0682624	−	0.0911880i	0.833373	+	0.552711i	$0.186407\pi$
$158$	−38.1654	+	175.444i	−0.0192169	+	0.0883389i
$159$	723.340	−	834.779i	0.360784	−	0.416366i
$160$	−242.341	+	263.193i	−0.119742	+	0.130045i
$161$	−1052.06	+	959.021i	−0.514995	+	0.469450i
$162$	534.391	−	534.391i	0.259171	−	0.259171i
$163$	2814.48	−	201.295i	1.35243	−	0.0967280i	0.623775	−	0.781604i	$-0.285598\pi$
$163$	2814.48	−	201.295i	1.35243	−	0.0967280i	0.728659	+	0.684876i	$0.240144\pi$
$164$	−353.548	−	550.132i	−0.168338	−	0.261940i
$165$	−4602.66	−	3158.15i	−2.17162	−	1.49007i
$166$	−2345.26	+	1071.04i	−1.09655	+	0.500778i
$167$	−1472.50	−	1967.03i	−0.682309	−	0.911458i	0.317008	−	0.948423i	$-0.397322\pi$
$167$	−1472.50	−	1967.03i	−0.682309	−	0.911458i	−0.999317	+	0.0369651i	$0.988231\pi$
$168$	−394.594	+	722.645i	−0.181212	+	0.331865i
$169$	1184.12	−	1842.53i	0.538972	−	0.838657i
$170$	362.414	−	888.800i	0.163505	−	0.400987i
$171$	−904.906	+	3081.83i	−0.404678	+	1.37821i
$172$	34.6086	−	483.891i	0.0153423	−	0.214514i
$173$	213.239	−	2981.47i	0.0937126	−	1.31027i	−0.705279	−	0.708930i	$-0.749178\pi$
$173$	213.239	−	2981.47i	0.0937126	−	1.31027i	0.798991	−	0.601343i	$-0.205367\pi$
$174$	−756.609	+	2576.78i	−0.329646	+	1.12267i
$175$	−1459.96	+	686.333i	−0.630643	+	0.296468i
$176$	541.564	−	842.691i	0.231943	−	0.360910i
$177$	937.687	−	1717.25i	0.398197	−	0.729244i
$178$	418.610	+	559.197i	0.176270	+	0.235470i
$179$	−862.538	+	393.908i	−0.360163	+	0.164481i	−0.587274	−	0.809388i	$-0.699799\pi$
$179$	−862.538	+	393.908i	−0.360163	+	0.164481i	0.227112	+	0.973869i	$0.427072\pi$
$180$	−299.472	−	1608.94i	−0.124007	−	0.666242i
$181$	763.280	+	1187.69i	0.313448	+	0.487735i	0.961855	−	0.273559i	$-0.0882008\pi$
$181$	763.280	+	1187.69i	0.313448	+	0.487735i	−0.648407	+	0.761294i	$0.724564\pi$
$182$	−67.0488	+	4.79542i	−0.0273076	+	0.00195308i
$183$	−3713.54	+	3713.54i	−1.50007	+	1.50007i
$184$	876.335	+	103.563i	0.351110	+	0.0414933i
$185$	−608.780	−	560.549i	−0.241937	−	0.222770i
$186$	832.735	−	961.028i	0.328275	−	0.378849i
$187$	−571.257	+	2626.02i	−0.223393	+	1.02692i
$188$	−237.534	+	317.309i	−0.0921487	+	0.123096i
$189$	−410.229	−	898.275i	−0.157882	−	0.345714i
$190$	−1239.89	−	1521.33i	−0.473426	−	0.580889i
$191$	289.472	+	985.851i	0.109662	+	0.373475i	0.995977	−	0.0896080i	$-0.0285614\pi$
$191$	289.472	+	985.851i	0.109662	+	0.373475i	−0.886315	+	0.463083i	$0.846743\pi$
$192$	498.714	−	108.489i	0.187456	−	0.0407786i
$193$	−2911.72	+	1086.01i	−1.08596	+	0.405042i	−0.827779	−	0.561055i	$-0.810396\pi$
$193$	−2911.72	+	1086.01i	−1.08596	+	0.405042i	−0.258180	+	0.966097i	$0.583123\pi$
$194$	−1582.76	−	464.739i	−0.585749	−	0.171991i
$195$	169.064	−	159.156i	0.0620866	−	0.0584483i
$196$	462.169	+	533.372i	0.168429	+	0.194377i
$197$	3301.75	−	1802.89i	1.19411	−	0.652034i	0.245782	−	0.969325i	$-0.420955\pi$
$197$	3301.75	−	1802.89i	1.19411	−	0.652034i	0.948328	+	0.317291i	$0.102773\pi$
$198$	1601.31	+	4293.28i	0.574748	+	1.54096i
$199$	1476.77	+	949.059i	0.526056	+	0.338076i	0.776563	−	0.630039i	$-0.216961\pi$
$199$	1476.77	+	949.059i	0.526056	+	0.338076i	−0.250508	+	0.968115i	$0.580598\pi$
$200$	914.166	+	405.341i	0.323206	+	0.143310i
$201$	4615.46	+	663.604i	1.61965	+	0.232871i
$202$	−1536.17	−	572.961i	−0.535071	−	0.199571i
$203$	−1739.66	−	1302.29i	−0.601480	−	0.450262i
$204$	−1151.90	+	740.283i	−0.395340	+	0.254070i
$205$	−1139.03	+	1429.54i	−0.388063	+	0.487039i
$206$			2633.92i			0.890843i
$207$	−2781.56	+	2925.22i	−0.933970	+	0.982206i
$208$	29.4636	+	29.4636i	0.00982180	+	0.00982180i
$209$	4152.83	+	3598.45i	1.37444	+	1.19096i
$210$	2267.02	+	396.097i	0.744947	+	0.130159i
$211$	−39.2217	−	272.793i	−0.0127968	−	0.0890039i	0.982422	−	0.186673i	$-0.0597705\pi$
$211$	−39.2217	−	272.793i	−0.0127968	−	0.0890039i	−0.995219	+	0.0976690i	$0.968861\pi$
$212$	193.618	−	519.109i	0.0627250	−	0.168172i
$213$	630.356	−	471.879i	0.202776	−	0.151796i
$214$	−2949.60	+	866.080i	−0.942197	+	0.276654i
$215$	−1311.98	+	342.593i	−0.416169	+	0.108673i
$216$	−254.289	+	556.816i	−0.0801027	+	0.175400i
$217$	493.135	+	903.109i	0.154268	+	0.282521i
$218$	−3295.32	−	235.686i	−1.02380	−	0.0732233i
$219$	5434.68	−	4709.18i	1.67690	−	1.45304i
$220$	−2716.67	−	677.428i	−0.832536	−	0.207601i
$221$	−101.687	−	46.4388i	−0.0309511	−	0.0141349i
$222$	250.940	+	1153.55i	0.0758648	+	0.348745i
$223$	−4058.51	−	2216.11i	−1.21873	−	0.665479i	−0.264456	−	0.964398i	$-0.585192\pi$
$223$	−4058.51	−	2216.11i	−1.21873	−	0.665479i	−0.954279	+	0.298919i	$0.903374\pi$
$224$	−58.7744	+	408.785i	−0.0175314	+	0.121933i
$225$	−3990.37	+	2236.48i	−1.18233	+	0.662662i
$226$	−2174.68	+	312.672i	−0.640078	+	0.0920293i
$227$	4217.08	+	917.370i	1.23303	+	0.268229i	0.781430	−	0.623993i	$-0.214490\pi$
$227$	4217.08	+	917.370i	1.23303	+	0.268229i	0.451598	+	0.892221i	$0.350854\pi$
$228$	199.731	+	2792.60i	0.0580153	+	0.811159i
$229$	−4338.72			−1.25201			−0.626006	−	0.779818i	$-0.715312\pi$
$229$	−4338.72			−1.25201			−0.626006	+	0.779818i	$0.715312\pi$
$230$	−512.210	−	2412.70i	−0.146844	−	0.691691i
$231$	−6443.48			−1.83528
$232$	96.0973	+	1343.62i	0.0271944	+	0.380227i
$233$	14.5753	+	3.17067i	0.00409812	+	0.000891491i	0.214614	−	0.976699i	$-0.431151\pi$
$233$	14.5753	+	3.17067i	0.00409812	+	0.000891491i	−0.210516	+	0.977590i	$0.567514\pi$
$234$	−188.664	+	27.1258i	−0.0527067	+	0.00757808i
$235$	1053.10	+	344.056i	0.292327	+	0.0955054i
$236$	139.668	−	971.409i	0.0385237	−	0.267938i
$237$	−628.340	−	343.100i	−0.172216	−	0.0940368i
$238$	−235.520	−	1082.67i	−0.0641450	−	0.294870i
$239$	−4334.12	−	1979.32i	−1.17302	−	0.535698i	−0.268976	−	0.963147i	$-0.586685\pi$
$239$	−4334.12	−	1979.32i	−1.17302	−	0.535698i	−0.904040	+	0.427449i	$0.859412\pi$
$240$	−734.691	−	1222.81i	−0.197600	−	0.328884i
$241$	−4932.27	+	4273.83i	−1.31832	+	1.14233i	−0.338828	+	0.940848i	$0.610031\pi$
$241$	−4932.27	+	4273.83i	−1.31832	+	1.14233i	−0.979492	+	0.201483i	$0.935424\pi$
$242$	5164.02	+	369.338i	1.37172	+	0.0981073i
$243$	2434.27	+	4458.03i	0.642627	+	1.17688i
$244$	−1094.29	+	2396.17i	−0.287111	+	0.628685i
$245$	997.191	−	1702.03i	0.260033	−	0.443832i
$246$	2501.86	−	734.613i	0.648426	−	0.190395i
$247$	−182.983	+	136.979i	−0.0471373	+	0.0352865i
$248$	222.900	−	597.617i	0.0570731	−	0.153019i
$249$	−1463.04	−	10175.7i	−0.372356	−	2.58979i
$250$	252.689	−	2783.64i	0.0639258	−	0.704211i
$251$	4415.97	+	3826.46i	1.11049	+	0.962247i	0.999501	−	0.0315748i	$-0.0100522\pi$
$251$	4415.97	+	3826.46i	1.11049	+	0.962247i	0.110990	+	0.993821i	$0.464598\pi$
$252$	−1335.84	−	1335.84i	−0.333929	−	0.333929i
$253$	2575.39	+	6407.59i	0.639973	+	1.59226i
$254$		−	4168.87i		−	1.02984i
$255$	2993.26	+	2384.97i	0.735078	+	0.585696i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	1719.00	+	1286.82i	0.417230	+	0.312334i	0.787187	−	0.616715i	$-0.211537\pi$
$257$	1719.00	+	1286.82i	0.417230	+	0.312334i	−0.369957	+	0.929049i	$0.620628\pi$
$258$	1812.40	+	675.989i	0.437345	+	0.163121i
$259$	−945.542	−	135.948i	−0.226846	−	0.0326155i
$260$	51.5557	−	104.432i	0.0122975	−	0.0249101i
$261$	−5183.72	−	3331.38i	−1.22937	−	0.790065i
$262$	1346.13	+	3609.11i	0.317421	+	0.851037i
$263$	2859.91	−	1561.63i	0.670530	−	0.366137i	−0.107640	−	0.994190i	$-0.534330\pi$
$263$	2859.91	−	1561.63i	0.670530	−	0.366137i	0.778171	+	0.628053i	$0.216148\pi$
$264$	2615.60	+	3018.57i	0.609770	+	0.703712i
$265$	−1547.89	−	46.7234i	−0.358815	−	0.0108309i
$266$	−2173.73	−	638.263i	−0.501051	−	0.147122i
$267$	−2609.63	+	973.341i	−0.598153	+	0.223099i
$268$	2285.42	−	497.164i	0.520912	−	0.113318i
$269$	444.208	+	1512.83i	0.100683	+	0.342896i	0.994393	−	0.105750i	$-0.0337245\pi$
$269$	444.208	+	1512.83i	0.100683	+	0.342896i	−0.893709	+	0.448646i	$0.851906\pi$
$270$	1702.14	+	173.494i	0.383664	+	0.0391056i
$271$	−3168.67	−	6938.41i	−0.710269	−	1.55527i	−0.827059	−	0.562115i	$-0.809988\pi$
$271$	−3168.67	−	6938.41i	−0.710269	−	1.55527i	0.116791	−	0.993157i	$-0.462739\pi$
$272$	−411.591	+	549.821i	−0.0917513	+	0.122565i
$273$	56.9735	−	261.903i	0.0126307	−	0.0580626i
$274$	3520.09	−	4062.41i	0.776119	−	0.895689i
$275$	644.491	+	7799.26i	0.141325	+	1.71023i
$276$	−1380.65	+	3236.35i	−0.301107	+	0.705817i
$277$	−2437.89	+	2437.89i	−0.528803	+	0.528803i	−0.920215	−	0.391412i	$-0.871987\pi$
$277$	−2437.89	+	2437.89i	−0.528803	+	0.528803i	0.391412	+	0.920215i	$0.371987\pi$
$278$	6427.39	−	459.696i	1.38665	−	0.0991753i
$279$	1577.42	+	2454.51i	0.338486	+	0.526694i
$280$	1134.85	−	211.228i	0.242215	−	0.0450832i
$281$	7251.74	−	3311.76i	1.53951	−	0.703071i	0.548412	−	0.836208i	$-0.315232\pi$
$281$	7251.74	−	3311.76i	1.53951	−	0.703071i	0.991098	+	0.133137i	$0.0425051\pi$
$282$	−947.126	−	1265.21i	−0.200002	−	0.267171i
$283$	3984.15	−	7296.42i	0.836866	−	1.53261i	−0.00946988	−	0.999955i	$-0.503014\pi$
$283$	3984.15	−	7296.42i	0.836866	−	1.53261i	0.846336	−	0.532650i	$-0.178804\pi$
$284$	213.530	−	332.260i	0.0446151	−	0.0694225i
$285$	7213.16	−	3034.58i	1.49919	−	0.630711i
$286$	−91.8691	+	312.877i	−0.0189942	+	0.0646882i
$287$	−150.521	+	2104.55i	−0.0309580	+	0.432850i
$288$	−83.5410	+	1168.06i	−0.0170927	+	0.238987i
$289$	−865.027	+	2946.01i	−0.176069	+	0.599636i
$290$	3470.50	−	1460.04i	0.702741	−	0.295643i
$291$	3556.01	−	5533.25i	0.716346	−	1.11466i
$292$	1728.65	−	3165.78i	0.346443	−	0.634463i
$293$	3418.32	+	4566.34i	0.681571	+	0.910473i	0.999289	−	0.0377128i	$-0.0120072\pi$
$293$	3418.32	+	4566.34i	0.681571	+	0.910473i	−0.317717	+	0.948185i	$0.602916\pi$
$294$	−2559.76	+	1169.00i	−0.507783	+	0.231897i
$295$	−2696.78	+	501.949i	−0.532245	+	0.0990664i
$296$	320.136	+	498.142i	0.0628633	+	0.0978172i
$297$	−4778.25	+	341.747i	−0.933543	+	0.0667683i
$298$	−4272.08	+	4272.08i	−0.830452	+	0.830452i
$299$	−283.216	+	48.0235i	−0.0547786	+	0.00928853i
$300$	−2577.69	+	3042.08i	−0.496077	+	0.585449i
$301$	−1025.02	+	1182.94i	−0.196283	+	0.226523i
$302$	−475.488	+	2185.78i	−0.0906001	+	0.416482i
$303$	3917.70	−	5233.44i	0.742793	−	0.992255i
$304$	583.374	+	1277.41i	0.110062	+	0.241002i
$305$	7324.91	+	746.604i	1.37516	+	0.140165i
$306$	−885.128	−	3014.47i	−0.165358	−	0.563156i
$307$	8712.06	−	1895.19i	1.61962	−	0.352327i	0.690855	−	0.722994i	$-0.257234\pi$
$307$	8712.06	−	1895.19i	1.61962	−	0.352327i	0.928766	+	0.370667i	$0.120871\pi$
$308$	−3028.21	+	1129.46i	−0.560221	+	0.208952i
$309$	−10076.9	−	2958.83i	−1.85519	−	0.544732i
$310$	−1781.98	−	53.7896i	−0.326483	−	0.00985499i
$311$	−1986.72	−	2292.80i	−0.362240	−	0.418047i	0.545149	−	0.838339i	$-0.316473\pi$
$311$	−1986.72	−	2292.80i	−0.362240	−	0.418047i	−0.907389	+	0.420292i	$0.861928\pi$
$312$	−145.820	+	79.6239i	−0.0264598	+	0.0144481i
$313$	−3558.92	−	9541.82i	−0.642690	−	1.72312i	−0.689572	−	0.724217i	$-0.742201\pi$
$313$	−3558.92	−	9541.82i	−0.642690	−	1.72312i	0.0468825	−	0.998900i	$-0.485071\pi$
$314$	377.016	+	242.294i	0.0677588	+	0.0435459i
$315$	−2337.47	+	4734.83i	−0.418099	+	0.846912i
$316$	−355.439	−	51.1044i	−0.0632753	−	0.00909761i
$317$	6783.14	+	2529.98i	1.20183	+	0.448258i	0.869039	−	0.494744i	$-0.164738\pi$
$317$	6783.14	+	2529.98i	1.20183	+	0.448258i	0.332788	+	0.943002i	$0.392011\pi$
$318$	1768.51	+	1323.89i	0.311865	+	0.233459i
$319$	−8868.32	+	5699.32i	−1.55652	+	1.00032i
$320$	−559.622	−	445.896i	−0.0977620	−	0.0778948i
$321$		−	12257.5i		−	2.13130i
$322$	−2063.26	−	1961.94i	−0.357084	−	0.339548i
$323$	−2664.08	−	2664.08i	−0.458927	−	0.458927i
$324$	1142.31	+	989.813i	0.195869	+	0.169721i
$325$	−322.709	−	42.7653i	−0.0550789	−	0.00729905i
$326$	803.130	+	5585.89i	0.136445	+	0.948999i
$327$	4603.52	−	12342.5i	0.778518	−	2.08729i
$328$	1047.02	−	783.787i	0.176256	−	0.131943i
$329$	1227.07	−	360.299i	0.205624	−	0.0603767i
$330$	5643.51	−	9632.47i	0.941408	−	1.60682i
$331$	−1457.85	+	3192.25i	−0.242087	+	0.530096i	−0.991204	−	0.132341i	$-0.957751\pi$
$331$	−1457.85	+	3192.25i	−0.242087	+	0.530096i	0.749118	+	0.662437i	$0.230478\pi$
$332$	−2471.25	−	4525.75i	−0.408516	−	0.748142i
$333$	−2701.78	−	193.235i	−0.444614	−	0.0317994i
$334$	3713.95	−	3218.15i	0.608437	−	0.527214i
$335$	−3366.82	−	5603.71i	−0.549102	−	0.913920i
$336$	−1497.91	−	684.072i	−0.243207	−	0.111069i
$337$	500.168	+	2299.24i	0.0808484	+	0.371654i	0.999739	−	0.0228592i	$-0.00727693\pi$
$337$	500.168	+	2299.24i	0.0808484	+	0.371654i	−0.918890	+	0.394513i	$0.870913\pi$
$338$	3844.62	+	2099.32i	0.618697	+	0.337834i
$339$	1246.72	−	8671.15i	0.199742	−	1.38924i
$340$	1824.78	+	596.169i	0.291066	+	0.0950935i
$341$	4940.77	−	710.376i	0.784627	−	0.112812i
$342$	−6277.06	−	1365.49i	−0.992470	−	0.215899i
$343$	−478.244	−	6686.73i	−0.0752850	−	1.05262i
$344$	970.254			0.152072
$345$	9805.94	+	750.716i	1.53024	+	0.117151i
$346$	5978.18			0.928869
$347$	−236.442	−	3305.89i	−0.0365789	−	0.511440i	−0.982405	−	0.186765i	$-0.940200\pi$
$347$	−236.442	−	3305.89i	−0.0365789	−	0.511440i	0.945826	−	0.324675i	$-0.105255\pi$
$348$	−5248.37	−	1141.71i	−0.808455	−	0.175869i
$349$	−1411.35	+	202.921i	−0.216469	+	0.0311235i	−0.249696	−	0.968324i	$-0.580331\pi$
$349$	−1411.35	+	202.921i	−0.216469	+	0.0311235i	0.0332271	+	0.999448i	$0.489422\pi$
$350$	−1577.47	−	2814.55i	−0.240913	−	0.429840i
$351$	28.3587	−	197.239i	0.00431247	−	0.0299939i
$352$	1758.36	+	960.135i	0.266252	+	0.145385i
$353$	−1063.35	−	4888.14i	−0.160330	−	0.737024i	−0.985159	−	0.171642i	$-0.945093\pi$
$353$	−1063.35	−	4888.14i	−0.160330	−	0.737024i	0.824830	−	0.565381i	$-0.191271\pi$
$354$	3559.53	+	1625.58i	0.534426	+	0.244064i
$355$	−1071.14	−	267.099i	−0.160142	−	0.0399328i
$356$	−1055.82	+	914.871i	−0.157186	+	0.136203i
$357$	4406.66	+	315.170i	0.653291	+	0.0467243i
$358$	−908.875	−	1664.48i	−0.134177	−	0.245728i
$359$	−1244.00	+	2723.99i	−0.182886	+	0.400464i	−0.978763	−	0.204994i	$-0.934283\pi$
$359$	−1244.00	+	2723.99i	−0.182886	+	0.400464i	0.795878	+	0.605458i	$0.207010\pi$
$360$	3166.96	−	826.979i	0.463649	−	0.121071i
$361$	−810.325	+	237.933i	−0.118140	+	0.0346891i
$362$	−2260.42	+	1692.13i	−0.328190	+	0.245680i
$363$	−7214.07	+	19341.7i	−1.04309	+	2.79662i
$364$	−19.1328	−	133.072i	−0.00275503	−	0.0191617i
$365$	−9931.38	−	1735.23i	−1.42420	−	0.248839i
$366$	−7938.00	−	6878.32i	−1.13368	−	0.982337i
$367$	4396.12	+	4396.12i	0.625274	+	0.625274i	0.946875	−	0.321601i	$-0.104221\pi$
$367$	4396.12	+	4396.12i	0.625274	+	0.625274i	−0.321601	+	0.946875i	$0.604221\pi$
$368$	−81.5644	+	1762.98i	−0.0115539	+	0.249733i
$369$			5982.76i			0.844038i
$370$	1031.38	−	1294.44i	0.144916	−	0.181877i
$371$	−1503.82	+	966.449i	−0.210444	+	0.135244i
$372$	2035.97	+	1524.11i	0.283764	+	0.212423i
$373$	−8881.20	−	3312.52i	−1.23284	−	0.459827i	−0.353240	−	0.935533i	$-0.614920\pi$
$373$	−8881.20	−	3312.52i	−1.23284	−	0.459827i	−0.879605	+	0.475706i	$0.842193\pi$
$374$	−5320.17	−	764.925i	−0.735561	−	0.105758i
$375$	10365.8	+	4093.76i	1.42744	+	0.563736i
$376$	−666.891	−	428.585i	−0.0914689	−	0.0587835i
$377$	−153.242	−	410.857i	−0.0209346	−	0.0561279i
$378$	1733.44	−	946.531i	0.235869	−	0.128794i
$379$	5940.33	+	6855.51i	0.805104	+	0.929139i	0.998650	−	0.0519520i	$-0.0165443\pi$
$379$	5940.33	+	6855.51i	0.805104	+	0.929139i	−0.193546	+	0.981091i	$0.561999\pi$
$380$	2858.00	−	2690.52i	0.385822	−	0.363212i
$381$	15949.3	+	4683.14i	2.14464	+	0.629723i
$382$	−1925.38	+	718.129i	−0.257882	+	0.0961850i
$383$	11997.8	−	2609.96i	1.60068	−	0.348206i	0.678386	−	0.734705i	$-0.262680\pi$
$383$	11997.8	−	2609.96i	1.60068	−	0.348206i	0.922289	+	0.386500i	$0.126316\pi$
$384$	287.580	+	979.407i	0.0382174	+	0.130157i
$385$	5707.12	+	7002.57i	0.755485	+	0.926972i
$386$	−2581.93	−	5653.65i	−0.340459	−	0.745500i
$387$	−2659.78	+	3553.05i	−0.349365	+	0.466696i
$388$	701.285	−	3223.76i	0.0917586	−	0.421808i
$389$	−6759.36	+	7800.72i	−0.881011	+	1.01674i	0.118706	+	0.992930i	$0.462126\pi$
$389$	−6759.36	+	7800.72i	−0.881011	+	1.01674i	−0.999716	+	0.0238113i	$0.992420\pi$
$390$	341.623	+	314.557i	0.0443558	+	0.0408416i
$391$	−1447.88	−	4508.08i	−0.187269	−	0.583078i
$392$	−998.084	+	998.084i	−0.128599	+	0.128599i
$393$	−15320.0	+	1095.71i	−1.96639	+	0.140639i
$394$	4067.68	+	6329.44i	0.520119	+	0.809321i
$395$	183.663	+	986.750i	0.0233952	+	0.125693i
$396$	−8336.21	+	3807.02i	−1.05785	+	0.483106i
$397$	−7.27983	−	9.72471i	−0.000920313	−	0.00122939i	0.800081	−	0.599892i	$-0.204790\pi$
$397$	−7.27983	−	9.72471i	−0.000920313	−	0.00122939i	−0.801001	+	0.598663i	$0.795699\pi$
$398$	−1682.58	+	3081.42i	−0.211910	+	0.388084i
$399$	4883.75	−	7599.26i	0.612765	−	0.953481i
$400$	−678.184	+	1881.51i	−0.0847730	+	0.235188i
$401$	−2317.18	+	7891.60i	−0.288565	+	0.982762i	0.679836	+	0.733364i	$0.262051\pi$
$401$	−2317.18	+	7891.60i	−0.288565	+	0.982762i	−0.968401	+	0.249398i	$0.919767\pi$
$402$	−665.299	+	9302.09i	−0.0825425	+	1.15409i
$403$	−14.8124	+	207.105i	−0.00183091	+	0.0255995i
$404$	923.824	−	3146.25i	0.113767	−	0.387456i
$405$	1595.15	−	3912.02i	0.195713	−	0.479974i
$406$	2349.74	−	3656.27i	0.287231	−	0.446940i
$407$	−2220.85	+	4067.18i	−0.270475	+	0.495338i
$408$	−1641.15	−	2192.31i	−0.199139	−	0.266019i
$409$	4395.57	−	2007.39i	0.531411	−	0.242687i	−0.131592	−	0.991304i	$-0.542009\pi$
$409$	4395.57	−	2007.39i	0.531411	−	0.242687i	0.663003	+	0.748617i	$0.269282\pi$
$410$	−3014.30	−	2068.28i	−0.363087	−	0.249135i
$411$	11587.7	+	18030.7i	1.39070	+	2.16397i
$412$	−5254.41	+	375.803i	−0.628316	+	0.0449380i
$413$	−2239.02	+	2239.02i	−0.266768	+	0.266768i
$414$	−6232.39	−	5131.58i	−0.739868	−	0.609187i
$415$	−9762.76	+	10602.8i	−1.15478	+	1.25415i
$416$	−54.5733	+	62.9809i	−0.00643191	+	0.00742282i
$417$	−5461.56	+	25106.4i	−0.641376	+	2.94836i
$418$	−6586.04	+	8797.92i	−0.770655	+	1.02947i
$419$	−565.801	−	1238.93i	−0.0659695	−	0.144453i	0.873775	−	0.486330i	$-0.161665\pi$
$419$	−565.801	−	1238.93i	−0.0659695	−	0.144453i	−0.939745	+	0.341877i	$0.888937\pi$
$420$	−466.722	+	4578.99i	−0.0542231	+	0.531981i
$421$	−2875.62	−	9793.47i	−0.332896	−	1.13374i	−0.940583	−	0.339563i	$-0.889721\pi$
$421$	−2875.62	−	9793.47i	−0.332896	−	1.13374i	0.607687	−	0.794177i	$-0.292097\pi$
$422$	538.599	−	117.165i	0.0621294	−	0.0135154i
$423$	3397.63	−	1267.25i	0.390540	−	0.145664i
$424$	1063.20	+	312.183i	0.121777	+	0.0357569i
$425$	−59.2773	−	5365.39i	−0.00676558	−	0.612375i
$426$	1031.29	+	1190.17i	0.117292	+	0.135362i
$427$	7459.60	−	4073.25i	0.845422	−	0.461635i
$428$	−2148.59	−	5760.59i	−0.242654	−	0.650581i
$429$	−1093.81	−	702.947i	−0.123099	−	0.0791110i
$430$	−870.631	−	2568.39i	−0.0976408	−	0.288044i
$431$	4563.45	+	656.126i	0.510009	+	0.0733282i	0.392515	−	0.919745i	$-0.371605\pi$
$431$	4563.45	+	656.126i	0.510009	+	0.0733282i	0.117494	+	0.993074i	$0.462514\pi$
$432$	−1147.08	−	427.837i	−0.127752	−	0.0476489i
$433$	−6181.16	−	4627.16i	−0.686022	−	0.513550i	0.198469	−	0.980107i	$-0.436403\pi$
$433$	−6181.16	−	4627.16i	−0.686022	−	0.513550i	−0.884491	+	0.466557i	$0.845494\pi$
$434$	−1731.26	+	1112.61i	−0.191481	+	0.123058i
$435$	1687.22	+	14917.6i	0.185967	+	1.64424i
$436$		−	6607.48i		−	0.725782i
$437$	−9508.91	−	1819.21i	−1.04090	−	0.199141i
$438$	10169.8	+	10169.8i	1.10943	+	1.10943i
$439$	8616.85	+	7466.54i	0.936810	+	0.811751i	0.982319	−	0.187213i	$-0.0599455\pi$
$439$	8616.85	+	7466.54i	0.936810	+	0.811751i	−0.0455091	+	0.998964i	$0.514491\pi$
$440$	963.793	−	5516.16i	0.104425	−	0.597664i
$441$	−918.891	−	6391.03i	−0.0992216	−	0.690101i
$442$	78.1324	−	209.481i	0.00840810	−	0.0225430i
$443$	6252.02	−	4680.20i	0.670525	−	0.501949i	−0.208930	−	0.977931i	$-0.566998\pi$
$443$	6252.02	−	4680.20i	0.670525	−	0.501949i	0.879455	+	0.475982i	$0.157907\pi$
$444$	−2265.42	+	665.188i	−0.242145	+	0.0711000i
$445$	3369.20	+	1973.96i	0.358911	+	0.210280i
$446$	3841.87	−	8412.53i	0.407888	−	0.893149i
$447$	−11545.1	−	21143.2i	−1.22162	−	2.23723i
$448$	−823.872	−	58.9245i	−0.0868846	−	0.00621411i
$449$	9385.22	−	8132.34i	0.986450	−	0.854764i	−0.00294755	−	0.999996i	$-0.500938\pi$
$449$	9385.22	−	8132.34i	0.986450	−	0.854764i	0.989398	+	0.145232i	$0.0463928\pi$
$450$	−5030.91	−	7641.30i	−0.527021	−	0.800477i
$451$	9310.37	+	4251.90i	0.972080	+	0.443934i
$452$	−934.030	−	4293.67i	−0.0971970	−	0.446808i
$453$	−7828.24	−	4274.54i	−0.811926	−	0.443345i
$454$	−1228.38	+	8543.56i	−0.126984	+	0.883192i
$455$	−335.090	+	170.055i	−0.0345259	+	0.0175216i
$456$	−5542.47	+	796.887i	−0.569188	+	0.0818369i
$457$	4548.83	+	989.537i	0.465613	+	0.101288i	0.439251	−	0.898364i	$-0.355244\pi$
$457$	4548.83	+	989.537i	0.465613	+	0.101288i	0.0263625	+	0.999652i	$0.491608\pi$
$458$	−619.042	−	8655.34i	−0.0631571	−	0.883051i
$459$	3284.53			0.334006
$460$	4740.03	−	1366.05i	0.480446	−	0.138462i
$461$	6847.61			0.691812			0.345906	−	0.938269i	$-0.387572\pi$
$461$	6847.61			0.691812			0.345906	+	0.938269i	$0.387572\pi$
$462$	−919.346	−	12854.1i	−0.0925797	−	1.29443i
$463$	12681.9	+	2758.78i	1.27295	+	0.276914i	0.797764	−	0.602969i	$-0.206016\pi$
$463$	12681.9	+	2758.78i	1.27295	+	0.276914i	0.475189	+	0.879884i	$0.342380\pi$
$464$	−2666.68	+	383.410i	−0.266804	+	0.0383607i
$465$	2207.60	−	6757.10i	0.220161	−	0.673878i
$466$	−4.24559	+	29.5288i	−0.000422046	+	0.00293539i
$467$	2273.55	+	1241.45i	0.225284	+	0.123014i	0.587928	−	0.808914i	$-0.299944\pi$
$467$	2273.55	+	1241.45i	0.225284	+	0.123014i	−0.362644	+	0.931928i	$0.618126\pi$
$468$	−81.0317	−	372.497i	−0.00800361	−	0.0367920i
$469$	−6864.37	−	3134.85i	−0.675836	−	0.308644i
$470$	−536.105	+	2149.93i	−0.0526142	+	0.210997i
$471$	−1350.49	+	1170.21i	−0.132118	+	0.114481i
$472$	1957.80	+	140.024i	0.190921	+	0.0136550i
$473$	3638.97	+	6664.27i	0.353742	+	0.647830i
$474$	594.801	−	1302.43i	0.0576373	−	0.126208i
$475$	−9686.71	−	5151.25i	−0.935698	−	0.497591i
$476$	2126.22	−	624.313i	0.204737	−	0.0601163i
$477$	−4057.77	+	3037.61i	−0.389502	+	0.291578i
$478$	3330.18	−	8928.55i	0.318659	−	0.854357i
$479$	478.082	+	3325.13i	0.0456036	+	0.317180i	0.999836	+	0.0181136i	$0.00576606\pi$
$479$	478.082	+	3325.13i	0.0456036	+	0.317180i	−0.954232	+	0.299066i	$0.903325\pi$
$480$	2334.57	−	1640.11i	0.221996	−	0.155959i
$481$	−145.678	−	126.231i	−0.0138095	−	0.0119660i
$482$	−9229.61	−	9229.61i	−0.872194	−	0.872194i
$483$	9823.77	−	5689.69i	0.925460	−	0.536004i
$484$			10354.4i			0.972430i
$485$	−9162.99	+	1036.35i	−0.857876	+	0.0970276i
$486$	−8546.03	+	5492.20i	−0.797645	+	0.512616i
$487$	−9969.46	−	7463.05i	−0.927638	−	0.694421i	0.0246263	−	0.999697i	$-0.492160\pi$
$487$	−9969.46	−	7463.05i	−0.927638	−	0.694421i	−0.952264	+	0.305276i	$0.901251\pi$
$488$	−4936.26	−	1841.13i	−0.457898	−	0.170787i
$489$	−22272.7	−	3202.34i	−2.05973	−	0.296145i
$490$	3537.66	+	1746.46i	0.326154	+	0.161014i
$491$	1393.23	+	895.377i	0.128057	+	0.0822970i	0.603101	−	0.797665i	$-0.293932\pi$
$491$	1393.23	+	895.377i	0.128057	+	0.0822970i	−0.475044	+	0.879962i	$0.657568\pi$
$492$	1822.44	+	4886.16i	0.166996	+	0.447734i
$493$	6343.76	−	3463.95i	0.579530	−	0.316448i
$494$	−299.368	−	345.489i	−0.0272656	−	0.0314661i
$495$	17558.0	+	18650.9i	1.59429	+	1.69353i
$496$	1223.99	+	359.396i	0.110804	+	0.0325350i
$497$	−1193.97	+	445.330i	−0.107761	+	0.0401927i
$498$	20090.8	−	4370.48i	1.80781	−	0.393265i
$499$	−1609.36	−	5480.96i	−0.144378	−	0.491707i	0.855271	−	0.518180i	$-0.173390\pi$
$499$	−1609.36	−	5480.96i	−0.144378	−	0.491707i	−0.999650	+	0.0264736i	$0.991572\pi$
$500$	5589.15	+	106.925i	0.499909	+	0.00956364i
$501$	8139.94	+	17824.0i	0.725880	+	1.58945i
$502$	−7003.36	+	9355.39i	−0.622659	+	0.831776i
$503$	−1146.28	+	5269.37i	−0.101611	+	0.467096i	0.898021	+	0.439953i	$0.145005\pi$
$503$	−1146.28	+	5269.37i	−0.101611	+	0.467096i	−0.999632	+	0.0271436i	$0.991359\pi$
$504$	2474.28	−	2855.47i	0.218677	−	0.252366i
$505$	−9157.52	+	377.721i	−0.806939	+	0.0332839i
$506$	−12415.1	+	6051.88i	−1.09075	+	0.531697i
$507$	−12350.5	+	12350.5i	−1.08186	+	1.08186i
$508$	8316.50	−	594.808i	0.726348	−	0.0519494i
$509$	1047.53	+	1629.98i	0.0912197	+	0.141941i	0.883864	−	0.467743i	$-0.154933\pi$
$509$	1047.53	+	1629.98i	0.0912197	+	0.141941i	−0.792645	+	0.609684i	$0.791296\pi$
$510$	−4330.71	+	6311.54i	−0.376014	+	0.548000i
$511$	−10586.2	+	4834.54i	−0.916446	+	0.418527i
$512$	306.830	+	409.877i	0.0264846	+	0.0353793i
$513$	3218.56	−	5894.36i	0.277004	−	0.507295i
$514$	−2321.83	+	3612.83i	−0.199244	+	0.310030i
$515$	5709.70	+	13571.9i	0.488543	+	1.16126i
$516$	−1089.94	+	3712.01i	−0.0929886	+	0.316690i
$517$	442.576	−	6188.02i	0.0376489	−	0.526400i
$518$	136.296	−	1905.66i	0.0115608	−	0.161641i
$519$	−6715.64	+	22871.4i	−0.567984	+	1.93438i
$520$	215.689	+	87.9485i	0.0181896	+	0.00741692i
$521$	−1655.27	+	2575.65i	−0.139191	+	0.216586i	−0.903850	−	0.427850i	$-0.859271\pi$
$521$	−1655.27	+	2575.65i	−0.139191	+	0.216586i	0.764659	+	0.644436i	$0.222908\pi$
$522$	5906.17	−	10816.3i	0.495222	−	0.906932i
$523$	−13271.2	−	17728.2i	−1.10957	−	1.48222i	−0.857481	−	0.514515i	$-0.827972\pi$
$523$	−13271.2	−	17728.2i	−1.10957	−	1.48222i	−0.252093	−	0.967703i	$-0.581119\pi$
$524$	−7007.77	+	3200.34i	−0.584229	+	0.266808i
$525$	12540.0	−	2873.36i	1.04246	−	0.238864i
$526$	3523.35	+	5482.43i	0.292063	+	0.454459i
$527$	−3413.71	+	244.153i	−0.282170	+	0.0201812i
$528$	−5648.56	+	5648.56i	−0.465572	+	0.465572i
$529$	−9584.45	−	7494.95i	−0.787741	−	0.616006i
$530$	−127.641	−	3094.55i	−0.0104611	−	0.253620i
$531$	−5879.71	+	6785.55i	−0.480523	+	0.554553i
$532$	963.131	−	4427.44i	0.0784906	−	0.360816i
$533$	−255.146	+	340.835i	−0.0207347	+	0.0276983i
$534$	−2314.06	−	5067.09i	−0.187527	−	0.410626i
$535$	−13321.1	+	10856.7i	−1.07649	+	0.877339i
$536$	1317.87	+	4488.27i	0.106201	+	0.361686i
$537$	7388.97	−	1607.37i	0.593776	−	0.129168i
$538$	−2954.58	+	1102.00i	−0.236767	+	0.0883097i
$539$	−10598.8	−	3112.08i	−0.846978	−	0.248695i
$540$	−103.245	+	3420.37i	−0.00822768	+	0.272573i
$541$	8829.70	+	10190.0i	0.701698	+	0.809803i	0.988981	−	0.148043i	$-0.0472975\pi$
$541$	8829.70	+	10190.0i	0.701698	+	0.809803i	−0.287283	+	0.957846i	$0.592752\pi$
$542$	13389.4	−	7311.15i	1.06111	−	0.579411i
$543$	−3934.50	−	10548.8i	−0.310949	−	0.833687i
$544$	−1155.57	−	742.637i	−0.0910744	−	0.0585299i
$545$	−17490.9	+	5929.05i	−1.37473	+	0.466004i
$546$	530.600	+	76.2888i	0.0415890	+	0.00597959i
$547$	−12724.1	−	4745.85i	−0.994595	−	0.370965i	−0.201119	−	0.979567i	$-0.564458\pi$
$547$	−12724.1	−	4745.85i	−0.994595	−	0.370965i	−0.793476	+	0.608602i	$0.791731\pi$
$548$	8606.35	+	6442.63i	0.670885	+	0.502218i
$549$	20274.0	−	13029.3i	1.57609	−	1.01289i
$550$	−15466.8	+	2398.48i	−1.19911	+	0.185948i
$551$		−	14778.8i		−	1.14264i
$552$	−6653.20	−	2292.51i	−0.513005	−	0.176768i
$553$	819.258	+	819.258i	0.0629989	+	0.0629989i
$554$	−5211.18	−	4515.52i	−0.399643	−	0.346292i
$555$	3793.66	+	5399.98i	0.290147	+	0.413003i
$556$	1834.10	+	12756.4i	0.139898	+	0.973010i
$557$	1884.39	−	5052.26i	0.143347	−	0.384328i	−0.845358	−	0.534199i	$-0.820613\pi$
$557$	1884.39	−	5052.26i	0.143347	−	0.384328i	0.988706	+	0.149871i	$0.0478858\pi$
$558$	−4671.45	+	3497.00i	−0.354406	+	0.265305i
$559$	−303.053	+	88.9844i	−0.0229298	+	0.00673280i
$560$	583.298	+	2233.77i	0.0440158	+	0.168561i
$561$	8902.92	−	19494.7i	0.670021	−	1.46714i
$562$	7641.30	+	13994.0i	0.573539	+	1.05036i
$563$	14027.4	+	1003.26i	1.05006	+	0.0751020i	0.585688	−	0.810536i	$-0.300824\pi$
$563$	14027.4	+	1003.26i	1.05006	+	0.0751020i	0.464375	+	0.885638i	$0.346279\pi$
$564$	2388.84	−	2069.94i	0.178348	−	0.154540i
$565$	−10527.8	+	6325.30i	−0.783906	+	0.470987i
$566$	15124.1	+	6906.95i	1.12317	+	0.512934i
$567$	−1036.63	−	4765.32i	−0.0767803	−	0.352954i
$568$	693.293	+	378.567i	0.0512146	+	0.0279653i
$569$	199.558	−	1387.96i	0.0147029	−	0.102261i	−0.981149	−	0.193255i	$-0.938095\pi$
$569$	199.558	−	1387.96i	0.0147029	−	0.102261i	0.995851	+	0.0909945i	$0.0290046\pi$
$570$	7082.85	+	13956.6i	0.520470	+	1.02557i
$571$	10825.0	−	1556.40i	0.793368	−	0.114069i	0.266298	−	0.963891i	$-0.414200\pi$
$571$	10825.0	−	1556.40i	0.793368	−	0.114069i	0.527070	+	0.849822i	$0.323290\pi$
$572$	−637.268	−	138.629i	−0.0465831	−	0.0101335i
$573$	−584.533	−	8172.84i	−0.0426165	−	0.595856i
$574$	−4219.86			−0.306853
$575$	−7869.45	−	11321.7i	−0.570746	−	0.821127i
$576$	−2342.08			−0.169421
$577$	−1349.89	−	18873.9i	−0.0973944	−	1.36175i	−0.777613	−	0.628743i	$-0.783570\pi$
$577$	−1349.89	−	18873.9i	−0.0973944	−	1.36175i	0.680219	−	0.733009i	$-0.261885\pi$
$578$	−6000.43	−	1305.31i	−0.431808	−	0.0939340i
$579$	24530.2	−	3526.91i	1.76069	−	0.253149i
$580$	3407.81	+	6715.00i	0.243968	+	0.480733i
$581$	−2367.74	+	16468.0i	−0.169071	+	1.17591i
$582$	11545.7	+	6304.42i	0.822309	+	0.449015i
$583$	1843.30	+	8473.51i	0.130946	+	0.601950i
$584$	6562.06	+	2996.79i	0.464966	+	0.212343i
$585$	−913.337	+	548.751i	−0.0645501	+	0.0387830i
$586$	−8621.69	+	7470.74i	−0.607780	+	0.526644i
$587$	−10943.2	−	782.674i	−0.769463	−	0.0550331i	−0.318913	−	0.947784i	$-0.603318\pi$
$587$	−10943.2	−	782.674i	−0.769463	−	0.0550331i	−0.450550	+	0.892751i	$0.648772\pi$
$588$	−2697.27	−	4939.69i	−0.189173	−	0.346444i
$589$	−2906.99	+	6365.42i	−0.203362	+	0.445302i
$590$	−1386.11	−	5308.19i	−0.0967209	−	0.370398i
$591$	−28784.7	+	8451.94i	−2.00346	+	0.588268i
$592$	−948.068	+	709.715i	−0.0658199	+	0.0492721i
$593$	1745.72	−	4680.45i	0.120890	−	0.324120i	−0.862383	−	0.506257i	$-0.831029\pi$
$593$	1745.72	−	4680.45i	0.120890	−	0.324120i	0.983273	+	0.182137i	$0.0583015\pi$
$594$	−1363.51	−	9483.40i	−0.0941841	−	0.655065i
$595$	−3560.54	−	5068.17i	−0.245324	−	0.349201i
$596$	−9131.91	−	7912.85i	−0.627614	−	0.543830i
$597$	−9898.76	−	9898.76i	−0.678609	−	0.678609i
$598$	−136.211	−	558.136i	−0.00931452	−	0.0381670i
$599$			8338.39i			0.568777i	0.958709	+	0.284388i	$0.0917905\pi$
$599$			8338.39i			0.568777i	−0.958709	+	0.284388i	$0.908209\pi$
$600$	−6436.44	−	4708.21i	−0.437944	−	0.320353i
$601$	−14328.2	+	9208.19i	−0.972480	+	0.624975i	−0.927425	−	0.374010i	$-0.877983\pi$
$601$	−14328.2	+	9208.19i	−0.972480	+	0.624975i	−0.0450550	+	0.998985i	$0.514346\pi$
$602$	−2506.09	−	1876.04i	−0.169669	−	0.127013i
$603$	−20048.6	−	7477.76i	−1.35397	−	0.505005i
$604$	−4428.27	−	636.688i	−0.298317	−	0.0428915i
$605$	27409.6	−	9291.27i	1.84191	−	0.624370i
$606$	10999.2	+	7068.75i	0.737312	+	0.473842i
$607$	−1455.45	−	3902.23i	−0.0973231	−	0.260933i	0.879160	−	0.476526i	$-0.158104\pi$
$607$	−1455.45	−	3902.23i	−0.0973231	−	0.260933i	−0.976483	+	0.215593i	$0.930832\pi$
$608$	−2465.08	+	1346.03i	−0.164428	+	0.0897844i
$609$	11348.6	+	13097.0i	0.755119	+	0.871454i
$610$	−444.298	+	14719.0i	−0.0294903	+	0.976977i
$611$	247.606	+	72.7036i	0.0163945	+	0.00481387i
$612$	5887.29	−	2195.85i	0.388856	−	0.145036i
$613$	−17146.1	+	3729.90i	−1.12973	+	0.245757i	−0.738314	−	0.674457i	$-0.764378\pi$
$613$	−17146.1	+	3729.90i	−1.12973	+	0.245757i	−0.391414	+	0.920215i	$0.628014\pi$
$614$	5023.75	+	17109.3i	0.330199	+	1.12455i
$615$	11299.0	−	9208.71i	0.740845	−	0.603790i
$616$	−2685.23	−	5879.83i	−0.175635	−	0.384586i
$617$	460.899	−	615.689i	0.0300731	−	0.0401729i	−0.785253	−	0.619175i	$-0.787467\pi$
$617$	460.899	−	615.689i	0.0300731	−	0.0401729i	0.815326	+	0.579003i	$0.196558\pi$
$618$	4464.84	−	20524.5i	0.290618	−	1.33595i
$619$	9204.16	−	10622.2i	0.597652	−	0.689727i	−0.373652	−	0.927569i	$-0.621895\pi$
$619$	9204.16	−	10622.2i	0.597652	−	0.689727i	0.971304	+	0.237842i	$0.0764400\pi$
$620$	−146.945	−	3562.56i	−0.00951850	−	0.230768i
$621$	6983.18	−	4740.29i	0.451249	−	0.306315i
$622$	4290.45	−	4290.45i	0.276578	−	0.276578i
$623$	4496.05	−	321.564i	0.289134	−	0.0206793i
$624$	−179.648	−	279.537i	−0.0115251	−	0.0179334i
$625$	−4732.22	−	14891.2i	−0.302862	−	0.953034i
$626$	18527.2	−	8461.11i	1.18290	−	0.540214i
$627$	−26260.7	−	35080.2i	−1.67265	−	2.23440i
$628$	−429.561	+	786.681i	−0.0272951	+	0.0499873i
$629$	1717.76	−	2672.89i	0.108890	−	0.169436i
$630$	−9779.03	−	3987.47i	−0.618422	−	0.252166i
$631$	−5734.96	+	19531.5i	−0.361815	+	1.23223i	0.554640	+	0.832090i	$0.312856\pi$
$631$	−5734.96	+	19531.5i	−0.361815	+	1.23223i	−0.916455	+	0.400138i	$0.868962\pi$
$632$	51.2349	−	716.357i	0.00322471	−	0.0450873i
$633$	−156.789	+	2192.20i	−0.00984487	+	0.137649i
$634$	−4079.26	+	13892.7i	−0.255533	+	0.870267i
$635$	−9037.11	−	21481.1i	−0.564767	−	1.34245i
$636$	−2388.70	+	3716.90i	−0.148928	+	0.231737i
$637$	220.209	−	403.282i	0.0136970	−	0.0250842i
$638$	−12634.9	−	16878.3i	−0.784046	−	1.04736i
$639$	−3286.84	+	1501.05i	−0.203482	+	0.0929273i
$640$	809.674	−	1180.01i	0.0500081	−	0.0728814i
$641$	−2531.39	−	3938.92i	−0.155981	−	0.242711i	0.754464	−	0.656342i	$-0.227897\pi$
$641$	−2531.39	−	3938.92i	−0.155981	−	0.242711i	−0.910445	+	0.413630i	$0.864261\pi$
$642$	24452.6	−	1748.88i	1.50322	−	0.107512i
$643$	9477.31	−	9477.31i	0.581257	−	0.581257i	−0.353991	−	0.935249i	$-0.615176\pi$
$643$	9477.31	−	9477.31i	0.581257	−	0.581257i	0.935249	+	0.353991i	$0.115176\pi$
$644$	3619.49	−	4395.94i	0.221472	−	0.268982i
$645$	10804.2	−	445.642i	0.659559	−	0.0272049i
$646$	4934.48	−	5694.70i	0.300533	−	0.346834i
$647$	−1800.95	+	8278.83i	−0.109432	+	0.503052i	0.889504	+	0.456928i	$0.151050\pi$
$647$	−1800.95	+	8278.83i	−0.109432	+	0.503052i	−0.998936	+	0.0461235i	$0.985313\pi$
$648$	−1811.60	+	2420.02i	−0.109825	+	0.146709i
$649$	6381.00	+	13972.4i	0.385942	+	0.845095i
$650$	39.2690	−	649.875i	0.00236963	−	0.0392157i
$651$	−2311.81	−	7873.32i	−0.139181	−	0.474009i
$652$	−11028.7	+	2399.15i	−0.662451	+	0.144107i
$653$	7751.16	−	2891.03i	0.464512	−	0.173254i	−0.106301	−	0.994334i	$-0.533901\pi$
$653$	7751.16	−	2891.03i	0.464512	−	0.173254i	0.570813	+	0.821080i	$0.306628\pi$
$654$	25279.0	+	7422.58i	1.51145	+	0.443801i
$655$	14760.0	+	15678.8i	0.880488	+	0.935298i
$656$	1712.97	+	1976.87i	0.101951	+	0.117658i
$657$	−28962.9	+	15814.9i	−1.71986	+	0.939116i
$658$	893.838	+	2396.47i	0.0529566	+	0.141982i
$659$	−2914.32	−	1872.92i	−0.172270	−	0.110711i	0.451664	−	0.892188i	$-0.350830\pi$
$659$	−2914.32	−	1872.92i	−0.172270	−	0.110711i	−0.623934	+	0.781477i	$0.714467\pi$
$660$	20021.1	+	9883.91i	1.18079	+	0.582925i
$661$	24584.0	+	3534.65i	1.44661	+	0.207991i	0.820455	−	0.571711i	$-0.193720\pi$
$661$	24584.0	+	3534.65i	1.44661	+	0.207991i	0.626151	+	0.779701i	$0.284629\pi$
$662$	−6576.23	−	2452.81i	−0.386091	−	0.144005i
$663$	713.664	+	534.242i	0.0418045	+	0.0312945i
$664$	8675.85	−	5575.63i	0.507061	−	0.325868i
$665$	−12584.3	+	1423.31i	−0.733830	+	0.0829977i
$666$		−	5417.36i		−	0.315193i
$667$	8488.11	−	16520.1i	0.492745	−	0.959011i
$668$	6949.80	+	6949.80i	0.402539	+	0.402539i
$669$	27868.9	+	24148.5i	1.61057	+	1.39557i
$670$	10698.5	−	7516.02i	0.616893	−	0.433387i
$671$	−5867.64	−	40810.3i	−0.337582	−	2.34794i
$672$	1150.94	−	3085.78i	0.0660691	−	0.177138i
$673$	7756.10	−	5806.15i	0.444243	−	0.332556i	−0.353626	−	0.935387i	$-0.615051\pi$
$673$	7756.10	−	5806.15i	0.444243	−	0.332556i	0.797869	+	0.602831i	$0.205960\pi$
$674$	−4515.39	+	1325.84i	−0.258051	+	0.0757706i
$675$	9146.81	−	2795.87i	0.521572	−	0.159427i
$676$	−3639.40	+	7969.17i	−0.207066	+	0.453412i
$677$	13346.1	+	24441.5i	0.757654	+	1.38754i	0.916418	+	0.400223i	$0.131067\pi$
$677$	13346.1	+	24441.5i	0.757654	+	1.38754i	−0.158764	+	0.987317i	$0.550751\pi$
$678$	17476.0	+	1249.91i	0.989914	+	0.0708000i
$679$	−8044.67	+	6970.74i	−0.454677	+	0.393980i
$680$	−928.943	+	3725.32i	−0.0523873	+	0.210087i
$681$	−31306.1	−	14297.0i	−1.76160	−	0.804498i
$682$	2122.07	+	9755.01i	0.119147	+	0.547711i
$683$	−4307.42	−	2352.03i	−0.241316	−	0.131768i	0.354041	−	0.935230i	$-0.384807\pi$
$683$	−4307.42	−	2352.03i	−0.241316	−	0.131768i	−0.595357	+	0.803462i	$0.702989\pi$
$684$	1828.42	−	12717.0i	0.102210	−	0.710885i
$685$	9331.83	−	28563.3i	0.520513	−	1.59321i
$686$	13271.1	−	1908.10i	0.738622	−	0.106198i
$687$	33809.1	+	7354.71i	1.87758	+	0.408442i
$688$	138.434	+	1935.56i	0.00767116	+	0.107257i
$689$	−360.714			−0.0199450
$690$	−98.5101	+	19669.0i	−0.00543510	+	1.08520i
$691$	27971.2			1.53990			0.769952	−	0.638102i	$-0.220280\pi$
$691$	27971.2			1.53990			0.769952	+	0.638102i	$0.220280\pi$
$692$	852.957	+	11925.9i	0.0468563	+	0.655136i
$693$	28892.9	+	6285.26i	1.58377	+	0.344527i
$694$	6561.20	−	943.358i	0.358876	−	0.0515986i
$695$	32122.2	−	16301.7i	1.75319	−	0.889727i
$696$	1528.78	−	10632.9i	0.0832590	−	0.579079i
$697$	−6159.33	−	3363.25i	−0.334722	−	0.182772i
$698$	−606.176	−	2786.55i	−0.0328712	−	0.151107i
$699$	−108.202	−	49.4142i	−0.00585490	−	0.00267385i
$700$	5389.69	−	3548.48i	0.291016	−	0.191600i
$701$	−7360.93	+	6378.28i	−0.396603	+	0.343658i	−0.830217	−	0.557440i	$-0.811783\pi$
$701$	−7360.93	+	6378.28i	−0.396603	+	0.343658i	0.433614	+	0.901099i	$0.357238\pi$
$702$	397.520	+	28.4312i	0.0213724	+	0.00152858i
$703$	−3113.45	−	5701.86i	−0.167036	−	0.305903i
$704$	−1664.50	+	3644.74i	−0.0891096	+	0.195123i
$705$	−7622.98	−	4466.18i	−0.407231	−	0.238590i
$706$	9599.65	−	2818.71i	0.511739	−	0.150260i
$707$	−8469.62	+	6340.28i	−0.450541	+	0.337271i
$708$	−2735.01	+	7332.85i	−0.145181	+	0.389245i
$709$	−1569.40	−	10915.4i	−0.0831315	−	0.578192i	−0.988228	−	0.152987i	$-0.951111\pi$
$709$	−1569.40	−	10915.4i	−0.0831315	−	0.578192i	0.905097	−	0.425206i	$-0.139798\pi$
$710$	380.009	−	2174.93i	0.0200866	−	0.114963i
$711$	2482.83	+	2151.39i	0.130961	+	0.113479i
$712$	−1975.72	−	1975.72i	−0.103993	−	0.103993i
$713$	−6905.46	+	5445.81i	−0.362709	+	0.286041i
$714$			8835.82i			0.463127i
$715$	204.865	+	1811.33i	0.0107154	+	0.0947410i
$716$	3190.80	−	2050.60i	0.166544	−	0.107032i
$717$	30418.0	+	22770.6i	1.58435	+	1.18603i
$718$	−5611.58	−	2093.01i	−0.291675	−	0.108789i
$719$	−34703.3	−	4989.58i	−1.80002	−	0.258804i	−0.840776	−	0.541383i	$-0.817901\pi$
$719$	−34703.3	−	4989.58i	−1.80002	−	0.258804i	−0.959244	+	0.282579i	$0.908810\pi$
$720$	2101.60	+	6199.79i	0.108781	+	0.320907i
$721$	14298.4	+	9189.01i	0.738556	+	0.474641i
$722$	−590.269	−	1582.57i	−0.0304260	−	0.0815751i
$723$	45678.9	−	24942.6i	2.34968	−	1.28302i
$724$	−3698.15	−	4267.89i	−0.189835	−	0.219081i
$725$	14717.6	−	15046.4i	0.753928	−	0.770773i
$726$	−39614.1	−	11631.7i	−2.02509	−	0.594620i
$727$	10560.4	−	3938.83i	0.538740	−	0.200940i	−0.0653402	−	0.997863i	$-0.520813\pi$
$727$	10560.4	−	3938.83i	0.538740	−	0.200940i	0.604081	+	0.796923i	$0.293541\pi$
$728$	262.736	−	57.1546i	0.0133759	−	0.00290974i
$729$	−8537.46	−	29075.9i	−0.433748	−	1.47721i
$730$	2044.62	−	20059.7i	0.103664	−	1.01705i
$731$	−2162.70	−	4735.64i	−0.109426	−	0.239609i
$732$	12589.0	−	16816.9i	0.635660	−	0.849142i
$733$	−2031.97	+	9340.80i	−0.102391	+	0.470682i	0.897188	+	0.441649i	$0.145606\pi$
$733$	−2031.97	+	9340.80i	−0.102391	+	0.470682i	−0.999578	+	0.0290331i	$0.990757\pi$
$734$	−8142.61	+	9397.07i	−0.409467	+	0.472551i
$735$	−10655.7	+	11572.5i	−0.534749	+	0.580761i
$736$	−3528.61	+	88.8260i	−0.176721	+	0.00444860i
$737$	−25885.3	+	25885.3i	−1.29376	+	1.29376i
$738$	−11935.0	+	853.610i	−0.595304	+	0.0425770i
$739$	−12388.7	−	19277.2i	−0.616680	−	0.959572i	−0.999363	−	0.0356926i	$-0.988636\pi$
$739$	−12388.7	−	19277.2i	−0.616680	−	0.959572i	0.382683	−	0.923880i	$-0.375000\pi$
$740$	2729.43	+	1872.82i	0.135589	+	0.0930354i
$741$	1658.07	−	757.216i	0.0822008	−	0.0375398i
$742$	−2142.54	−	2862.09i	−0.106004	−	0.141605i
$743$	−8205.97	+	15028.1i	−0.405179	+	0.742029i	−0.997994	−	0.0633091i	$-0.979835\pi$
$743$	−8205.97	+	15028.1i	−0.405179	+	0.742029i	0.592815	+	0.805338i	$0.298016\pi$
$744$	−2749.96	+	4279.03i	−0.135509	+	0.210856i
$745$	−12752.1	+	31273.8i	−0.627115	+	1.53796i
$746$	5341.00	−	18189.8i	0.262128	−	0.892727i
$747$	−3365.46	+	47055.3i	−0.164841	+	2.30477i
$748$	766.879	−	10722.4i	0.0374865	−	0.524130i
$749$	−5588.76	+	19033.6i	−0.272642	+	0.928534i
$750$	−6687.69	+	21262.9i	−0.325600	+	1.03521i
$751$	−1172.03	+	1823.71i	−0.0569480	+	0.0886127i	−0.868560	−	0.495584i	$-0.834954\pi$
$751$	−1172.03	+	1823.71i	−0.0569480	+	0.0886127i	0.811612	+	0.584197i	$0.198590\pi$
$752$	759.835	−	1391.53i	0.0368462	−	0.0674787i
$753$	−27924.6	−	37303.0i	−1.35143	−	1.80531i
$754$	797.756	−	364.323i	0.0385312	−	0.0175966i
$755$	2288.18	+	12293.5i	0.110299	+	0.592592i
$756$	2135.56	+	3323.00i	0.102738	+	0.159863i
$757$	13405.3	−	958.765i	0.643624	−	0.0460329i	0.254288	−	0.967129i	$-0.418159\pi$
$757$	13405.3	−	958.765i	0.643624	−	0.0460329i	0.389336	+	0.921096i	$0.372704\pi$
$758$	−12828.5	+	12828.5i	−0.614714	+	0.614714i
$759$	−9206.73	−	54296.2i	−0.440294	−	2.59661i
$760$	5775.10	+	5317.56i	0.275638	+	0.253800i
$761$	−18889.5	+	21799.7i	−0.899797	+	1.03842i	0.0992627	+	0.995061i	$0.468352\pi$
$761$	−18889.5	+	21799.7i	−0.899797	+	1.03842i	−0.999060	+	0.0433596i	$0.986194\pi$
$762$	−7066.79	+	32485.5i	−0.335962	+	1.54439i
$763$	−12775.9	+	17066.6i	−0.606185	+	0.809769i
$764$	−1707.31	−	3738.48i	−0.0808485	−	0.177033i
$765$	−11095.5	−	13614.1i	−0.524390	−	0.643421i
$766$	6918.45	+	23562.1i	0.326336	+	1.11140i
$767$	−624.347	+	135.818i	−0.0293923	+	0.00639390i
$768$	−1912.79	+	713.434i	−0.0898723	+	0.0335206i
$769$	34410.1	+	10103.7i	1.61360	+	0.473796i	0.959289	−	0.282427i	$-0.0911396\pi$
$769$	34410.1	+	10103.7i	1.61360	+	0.473796i	0.654313	+	0.756224i	$0.272958\pi$
$770$	−13155.2	+	12384.3i	−0.615688	+	0.579608i
$771$	−11213.8	−	12941.4i	−0.523805	−	0.604504i
$772$	10910.1	−	5957.37i	0.508631	−	0.277734i
$773$	−13138.2	−	35224.9i	−0.611317	−	1.63900i	−0.759851	−	0.650098i	$-0.774728\pi$
$773$	−13138.2	−	35224.9i	−0.611317	−	1.63900i	0.148533	−	0.988907i	$-0.452545\pi$
$774$	−7467.48	−	4799.06i	−0.346787	−	0.222866i
$775$	−9298.72	+	3585.75i	−0.430993	+	0.166199i
$776$	6531.14	+	939.036i	0.302132	+	0.0434400i
$777$	7137.59	+	2662.18i	0.329549	+	0.122915i
$778$	−16526.1	−	12371.3i	−0.761555	−	0.570093i
$779$	−12071.2	+	7757.71i	−0.555195	+	0.356802i
$780$	−578.770	+	726.386i	−0.0265683	+	0.0333446i
$781$			6181.76i			0.283228i
$782$	8786.61	−	3531.58i	0.401801	−	0.161495i
$783$	9110.33	+	9110.33i	0.415807	+	0.415807i
$784$	−2133.49	−	1848.68i	−0.0971887	−	0.0842145i
$785$	2467.90	+	431.197i	0.112208	+	0.0196052i
$786$	−4371.66	−	30405.5i	−0.198386	−	1.37981i
$787$	153.091	−	410.454i	0.00693408	−	0.0185910i	−0.933437	−	0.358742i	$-0.883206\pi$
$787$	153.091	−	410.454i	0.00693408	−	0.0185910i	0.940371	+	0.340151i	$0.110478\pi$
$788$	−12046.2	+	9017.71i	−0.544581	+	0.407668i
$789$	−24932.7	+	7320.91i	−1.12500	+	0.330331i
$790$	−1942.27	+	507.178i	−0.0874719	+	0.0228413i
$791$	−5889.50	+	12896.2i	−0.264736	+	0.579692i
$792$	−8784.04	−	16086.8i	−0.394100	−	0.721740i
$793$	1710.66	+	122.349i	0.0766046	+	0.00547887i
$794$	18.3612	−	15.9101i	0.000820673	−	0.000711117i
$795$	11982.6	+	2987.96i	0.534563	+	0.133298i
$796$	−6387.20	−	2916.93i	−0.284407	−	0.129884i
$797$	5210.64	+	23952.9i	0.231581	+	1.06456i	0.935237	+	0.354021i	$0.115186\pi$
$797$	5210.64	+	23952.9i	0.231581	+	1.06456i	−0.703656	+	0.710541i	$0.748450\pi$
$798$	15856.6	+	8658.36i	0.703405	+	0.384088i
$799$	−605.349	+	4210.30i	−0.0268031	+	0.186420i
$800$	−3850.19	−	1084.46i	−0.170156	−	0.0479269i
$801$	12651.1	−	1818.96i	0.558060	−	0.0802369i
$802$	−16073.6	−	3496.60i	−0.707704	−	0.153952i
$803$	4027.49	+	56311.6i	0.176995	+	2.47471i
$804$	−18651.7			−0.818153
$805$	−14884.5	−	5636.70i	−0.651688	−	0.246792i
$806$	−415.267			−0.0181478
$807$	−896.992	−	12541.6i	−0.0391271	−	0.547069i
$808$	6408.29	+	1394.04i	0.279013	+	0.0606956i
$809$	4833.17	−	694.905i	0.210043	−	0.0301997i	−0.0364898	−	0.999334i	$-0.511618\pi$
$809$	4833.17	−	694.905i	0.210043	−	0.0301997i	0.246533	+	0.969134i	$0.420709\pi$
$810$	8031.69	+	2624.01i	0.348401	+	0.113825i
$811$	−1498.86	+	10424.8i	−0.0648978	+	0.451374i	0.931300	+	0.364253i	$0.118676\pi$
$811$	−1498.86	+	10424.8i	−0.0648978	+	0.451374i	−0.996198	+	0.0871210i	$0.972233\pi$
$812$	7629.16	+	4165.84i	0.329718	+	0.180040i
$813$	12930.0	+	59438.2i	0.557779	+	2.56407i
$814$	−8430.49	−	3850.08i	−0.363008	−	0.165780i
$815$	16247.2	+	27041.7i	0.698300	+	1.16224i
$816$	4139.30	−	3586.72i	0.177579	−	0.153873i
$817$	−10617.8	−	759.397i	−0.454673	−	0.0325189i
$818$	4631.71	+	8482.33i	0.197975	+	0.362565i
$819$	−510.943	+	1118.81i	−0.0217995	+	0.0477343i
$820$	3695.95	−	6308.34i	0.157400	−	0.268655i
$821$	16414.0	−	4819.60i	0.697752	−	0.204878i	0.0864268	−	0.996258i	$-0.472455\pi$
$821$	16414.0	−	4819.60i	0.697752	−	0.204878i	0.611325	+	0.791380i	$0.290637\pi$
$822$	−34316.3	+	25688.9i	−1.45611	+	1.09003i
$823$	2746.41	−	7363.40i	0.116323	−	0.311874i	−0.865721	−	0.500527i	$-0.833140\pi$
$823$	2746.41	−	7363.40i	0.116323	−	0.311874i	0.982044	+	0.188653i	$0.0604123\pi$
$824$	−1499.38	−	10428.4i	−0.0633901	−	0.440888i
$825$	8198.66	−	61867.5i	0.345989	−	2.61085i
$826$	−4786.09	−	4147.17i	−0.201610	−	0.174696i
$827$	−1295.11	−	1295.11i	−0.0544564	−	0.0544564i	0.679354	−	0.733811i	$-0.262260\pi$
$827$	−1295.11	−	1295.11i	−0.0544564	−	0.0544564i	−0.733811	+	0.679354i	$0.762260\pi$
$828$	9347.78	−	13165.2i	0.392340	−	0.552563i
$829$		−	5818.54i		−	0.243771i	−0.992544	−	0.121886i	$-0.961106\pi$
$829$		−	5818.54i		−	0.243771i	0.992544	−	0.121886i	$-0.0388941\pi$
$830$	−22544.5	−	17963.0i	−0.942807	−	0.751210i
$831$	23129.5	−	14864.4i	0.965529	−	0.620508i
$832$	−133.427	−	99.8824i	−0.00555981	−	0.00416202i
$833$	7096.20	+	2646.75i	0.295161	+	0.110089i
$834$	−50864.1	−	7313.15i	−2.11184	−	0.303637i
$835$	12160.8	−	24633.3i	0.504004	−	1.02092i
$836$	−18490.7	−	11883.2i	−0.764969	−	0.491616i
$837$	−2131.94	−	5715.95i	−0.0880414	−	0.236048i
$838$	2390.82	−	1305.49i	0.0985557	−	0.0538155i
$839$	753.952	+	870.106i	0.0310242	+	0.0358038i	0.771050	−	0.636775i	$-0.219732\pi$
$839$	753.952	+	870.106i	0.0310242	+	0.0358038i	−0.740025	+	0.672579i	$0.765187\pi$
$840$	−9201.25	−	277.742i	−0.377944	−	0.0114083i
$841$	3802.65	+	1116.56i	0.155917	+	0.0457812i
$842$	19126.7	−	7133.91i	0.782840	−	0.291984i
$843$	−62122.3	+	13513.9i	−2.53809	+	0.552127i
$844$	310.580	+	1057.74i	0.0126666	+	0.0431384i
$845$	24361.2	+	2483.05i	0.991775	+	0.101088i
$846$	3012.81	+	6597.14i	0.122438	+	0.268102i
$847$	20020.8	−	26744.7i	0.812189	−	1.08496i
$848$	−471.080	+	2165.52i	−0.0190766	+	0.0876936i
$849$	−43414.5	+	50103.0i	−1.75498	+	2.02536i
$850$	10695.0	−	883.777i	0.431570	−	0.0356627i
$851$	−205.459	−	8161.88i	−0.00827621	−	0.328773i
$852$	−2227.14	+	2227.14i	−0.0895546	+	0.0895546i
$853$	3551.53	−	254.010i	0.142558	−	0.0101959i	0.000122165	−	1.00000i	$-0.499961\pi$
$853$	3551.53	−	254.010i	0.142558	−	0.0101959i	0.142436	+	0.989804i	$0.454507\pi$
$854$	9190.07	+	14300.0i	0.368241	+	0.572994i
$855$	−35304.2	+	6571.14i	−1.41214	+	0.262840i
$856$	11185.3	−	5108.14i	0.446618	−	0.203963i
$857$	714.868	+	954.952i	0.0284941	+	0.0380637i	0.814562	−	0.580076i	$-0.196977\pi$
$857$	714.868	+	954.952i	0.0284941	+	0.0380637i	−0.786068	+	0.618140i	$0.787886\pi$
$858$	1246.25	−	2282.34i	0.0495877	−	0.0908131i
$859$	10973.2	−	17074.7i	0.435858	−	0.678208i	−0.551952	−	0.833876i	$-0.686117\pi$
$859$	10973.2	−	17074.7i	0.435858	−	0.678208i	0.987809	+	0.155668i	$0.0497531\pi$
$860$	4999.48	−	2103.28i	0.198233	−	0.0833968i
$861$	4740.41	−	16144.4i	0.187634	−	0.639023i
$862$	−657.802	+	9197.27i	−0.0259917	+	0.363411i
$863$	−1105.60	+	15458.3i	−0.0436096	+	0.609741i	0.927913	+	0.372796i	$0.121601\pi$
$863$	−1105.60	+	15458.3i	−0.0436096	+	0.609741i	−0.971523	+	0.236945i	$0.923854\pi$
$864$	689.831	−	2349.35i	0.0271626	−	0.0925075i
$865$	30804.0	−	12959.3i	1.21083	−	0.509397i
$866$	8348.82	−	12991.0i	0.327603	−	0.509761i
$867$	11734.5	−	21490.2i	0.459660	−	0.841804i
$868$	−2466.56	−	3294.95i	−0.0964524	−	0.128845i
$869$	5112.52	−	2334.81i	0.199575	−	0.0911426i
$870$	−29518.5	+	5494.25i	−1.15031	+	0.214107i
$871$	−823.260	−	1281.02i	−0.0320265	−	0.0498342i
$872$	13181.3	−	942.745i	0.511898	−	0.0366117i
$873$	−21342.7	+	21342.7i	−0.827423	+	0.827423i
$874$	2272.43	−	19228.9i	0.0879474	−	0.744197i
$875$	−14229.6	−	11083.1i	−0.549769	−	0.428202i
$876$	−18836.7	+	21738.7i	−0.726522	+	0.838451i
$877$	−4074.32	+	18729.4i	−0.156876	+	0.721147i	0.829749	+	0.558137i	$0.188484\pi$
$877$	−4074.32	+	18729.4i	−0.156876	+	0.721147i	−0.986625	+	0.163009i	$0.947880\pi$
$878$	−13665.6	+	18255.1i	−0.525275	+	0.701685i
$879$	−18896.4	−	41377.3i	−0.725095	−	1.58774i
$880$	11141.7	+	1135.64i	0.426804	+	0.0435027i
$881$	2189.01	+	7455.08i	0.0837113	+	0.285094i	0.990701	−	0.136059i	$-0.0434436\pi$
$881$	2189.01	+	7455.08i	0.0837113	+	0.285094i	−0.906989	+	0.421153i	$0.861625\pi$
$882$	12618.4	−	2744.96i	0.481727	−	0.104793i
$883$	−34842.7	+	12995.7i	−1.32792	+	0.495288i	−0.910531	−	0.413441i	$-0.864327\pi$
$883$	−34842.7	+	12995.7i	−1.32792	+	0.495288i	−0.417387	+	0.908729i	$0.637054\pi$
$884$	429.043	+	125.978i	0.0163238	+	0.00479311i
$885$	21865.2	+	660.008i	0.830499	+	0.0250688i
$886$	10228.6	+	11804.4i	0.387851	+	0.447604i
$887$	−20911.4	+	11418.5i	−0.791584	+	0.432238i	−0.823545	−	0.567251i	$-0.808007\pi$
$887$	−20911.4	+	11418.5i	−0.791584	+	0.432238i	0.0319603	+	0.999489i	$0.489825\pi$
$888$	−1650.21	−	4424.39i	−0.0623621	−	0.167199i
$889$	−22631.0	−	14544.0i	−0.853789	−	0.548697i
$890$	−3457.14	+	7002.86i	−0.130206	+	0.263749i
$891$	−23416.5	−	3366.79i	−0.880453	−	0.126590i
$892$	17330.3	+	6463.88i	0.650518	+	0.242631i
$893$	6962.53	+	5212.08i	0.260909	+	0.195314i
$894$	40531.5	−	26048.0i	1.51630	−	0.974469i
$895$	−8291.40	−	6606.42i	−0.309666	−	0.246736i
$896$		−	1651.95i		−	0.0615936i
$897$	2288.34	+	105.870i	0.0851787	+	0.00394080i
$898$	17562.3	+	17562.3i	0.652630	+	0.652630i
$899$	−10145.8	−	8791.41i	−0.376399	−	0.326151i
$900$	14525.9	−	11126.4i	0.537995	−	0.412090i
$901$	−846.155	−	5885.14i	−0.0312869	−	0.217605i
$902$	−7153.75	+	19180.0i	−0.264073	+	0.708007i
$903$	9992.60	−	7480.37i	0.368254	−	0.275671i
$904$	8432.19	−	2475.91i	0.310233	−	0.0910925i
$905$	−7979.24	+	13619.2i	−0.293082	+	0.500239i
$906$	7410.38	−	16226.5i	0.271737	−	0.595020i
$907$	−22103.0	−	40478.6i	−0.809170	−	1.48188i	−0.875037	−	0.484055i	$-0.839163\pi$
$907$	−22103.0	−	40478.6i	−0.809170	−	1.48188i	0.0658677	−	0.997828i	$-0.479018\pi$
$908$	−17218.8	−	1231.52i	−0.629325	−	0.0450102i
$909$	−22672.1	+	19645.5i	−0.827267	+	0.716831i
$910$	−387.054	−	644.210i	−0.0140997	−	0.0234674i
$911$	14156.3	+	6464.96i	0.514840	+	0.235119i	0.655853	−	0.754888i	$-0.272309\pi$
$911$	14156.3	+	6464.96i	0.514840	+	0.235119i	−0.141014	+	0.990008i	$0.545036\pi$
$912$	−2380.50	−	10943.0i	−0.0864324	−	0.397323i
$913$	70835.7	+	38679.2i	2.56771	+	1.40208i
$914$	−1325.01	+	9215.67i	−0.0479513	+	0.333509i
$915$	−55813.1	−	18234.5i	−2.01653	−	0.658815i
$916$	17178.2	−	2469.86i	0.619635	−	0.0890900i
$917$	24288.6	+	5283.66i	0.874678	+	0.190274i
$918$	468.632	+	6552.32i	0.0168487	+	0.235576i
$919$	3814.77			0.136929			0.0684645	−	0.997654i	$-0.478190\pi$
$919$	3814.77			0.136929			0.0684645	+	0.997654i	$0.478190\pi$
$920$	3401.44	+	9261.00i	0.121894	+	0.331876i
$921$	−71100.5			−2.54380
$922$	977.006	+	13660.3i	0.0348980	+	0.487938i
$923$	−251.265	−	54.6593i	−0.00896044	−	0.00194922i
$924$	25511.6	−	3668.01i	0.908301	−	0.130594i
$925$	2508.42	−	8905.69i	0.0891636	−	0.316559i
$926$	−3694.06	+	25692.8i	−0.131096	+	0.911790i
$927$	42298.9	+	23096.9i	1.49868	+	0.818342i
$928$	−1145.34	−	5265.06i	−0.0405148	−	0.186244i
$929$	37763.5	+	17246.0i	1.33367	+	0.609067i	0.949376	−	0.314143i	$-0.101717\pi$
$929$	37763.5	+	17246.0i	1.33367	+	0.609067i	0.384296	+	0.923210i	$0.374444\pi$
$930$	13794.8	+	3439.85i	0.486395	+	0.121287i
$931$	11703.5	−	10141.1i	0.411994	−	0.356995i
$932$	−59.5128	−	4.25644i	−0.00209164	−	0.000149597i
$933$	11594.7	+	21234.1i	0.406853	+	0.745096i
$934$	−2152.20	+	4712.65i	−0.0753983	+	0.165099i
$935$	−29071.7	+	7591.40i	−1.01684	+	0.265524i
$936$	731.534	−	214.798i	0.0255459	−	0.00750094i
$937$	14377.8	−	10763.1i	0.501284	−	0.375256i	−0.318506	−	0.947921i	$-0.603181\pi$
$937$	14377.8	−	10763.1i	0.501284	−	0.375256i	0.819790	+	0.572664i	$0.194090\pi$
$938$	5274.34	−	14141.0i	0.183596	−	0.492240i
$939$	11557.8	+	80386.5i	0.401678	+	2.79373i
$940$	−4365.39	−	762.729i	−0.151472	−	0.0264654i
$941$	−4433.13	−	3841.33i	−0.153577	−	0.133075i	0.574683	−	0.818376i	$-0.305125\pi$
$941$	−4433.13	−	3841.33i	−0.153577	−	0.133075i	−0.728260	+	0.685301i	$0.759671\pi$
$942$	−2527.14	−	2527.14i	−0.0874084	−	0.0874084i
$943$	−17949.1	+	1738.71i	−0.619835	+	0.0600427i
$944$			3925.59i			0.135347i
$945$	6880.14	−	8634.92i	0.236837	−	0.297242i
$946$	−12775.4	+	8210.24i	−0.439073	+	0.282175i
$947$	−14514.2	−	10865.2i	−0.498045	−	0.372832i	0.320524	−	0.947240i	$-0.396141\pi$
$947$	−14514.2	−	10865.2i	−0.498045	−	0.372832i	−0.818569	+	0.574409i	$0.805232\pi$
$948$	2683.09	+	1000.74i	0.0919227	+	0.0342854i
$949$	−2324.46	−	334.207i	−0.0795103	−	0.0114318i
$950$	8894.16	−	20059.0i	0.303752	−	0.685054i
$951$	−48568.3	−	31212.9i	−1.65608	−	1.06430i
$952$	1548.81	+	4152.52i	0.0527282	+	0.141370i
$953$	−8141.27	+	4445.47i	−0.276728	+	0.151105i	−0.611620	−	0.791152i	$-0.709482\pi$
$953$	−8141.27	+	4445.47i	−0.276728	+	0.151105i	0.334892	+	0.942256i	$0.391300\pi$
$954$	−6638.69	−	7661.46i	−0.225299	−	0.260009i
$955$	−8364.25	+	7874.10i	−0.283415	+	0.266806i
$956$	18286.8	+	5369.48i	0.618657	+	0.181654i
$957$	78766.6	−	29378.4i	2.66057	−	0.992341i
$958$	−6565.11	+	1428.15i	−0.221408	+	0.0481644i
$959$	−9772.38	−	33281.7i	−0.329058	−	1.12067i
$960$	3604.95	+	4423.23i	0.121197	+	0.148708i
$961$	−9734.95	−	21316.6i	−0.326775	−	0.715537i
$962$	231.034	−	308.625i	0.00774306	−	0.0103435i
$963$	−11956.5	+	54963.2i	−0.400097	+	1.83922i
$964$	17095.3	−	19729.1i	0.571166	−	0.659160i
$965$	−25559.8	−	23534.8i	−0.852642	−	0.785090i
$966$	12752.0	+	18785.7i	0.424730	+	0.625693i
$967$	−8029.87	+	8029.87i	−0.267035	+	0.267035i	−0.827904	−	0.560869i	$-0.810467\pi$
$967$	−8029.87	+	8029.87i	−0.267035	+	0.267035i	0.560869	+	0.827904i	$0.310467\pi$
$968$	−20656.1	+	1477.35i	−0.685860	+	0.0490537i
$969$	16243.6	+	25275.6i	0.538514	+	0.837945i
$970$	−3374.79	−	18131.4i	−0.111709	−	0.600170i
$971$	9538.21	−	4355.96i	0.315238	−	0.143964i	−0.251512	−	0.967854i	$-0.580928\pi$
$971$	9538.21	−	4355.96i	0.315238	−	0.143964i	0.566750	+	0.823890i	$0.308201\pi$
$972$	−12175.7	−	16264.9i	−0.401787	−	0.536725i
$973$	19927.9	−	36495.2i	0.656587	−	1.20245i
$974$	13465.6	−	20952.9i	0.442984	−	0.689297i
$975$	2442.18	+	880.278i	0.0802179	+	0.0289143i
$976$	2968.58	−	10110.1i	0.0973586	−	0.331573i
$977$	2959.72	−	41382.3i	0.0969191	−	1.35511i	−0.683547	−	0.729907i	$-0.739563\pi$
$977$	2959.72	−	41382.3i	0.0969191	−	1.35511i	0.780466	−	0.625199i	$-0.214982\pi$
$978$	3210.52	−	44888.9i	0.104970	−	1.46768i
$979$	6160.41	−	20980.4i	0.201111	−	0.684921i
$980$	−2979.27	+	7306.48i	−0.0971115	+	0.238160i
$981$	−32681.8	+	50853.9i	−1.06366	+	1.65509i
$982$	−1587.41	+	2907.12i	−0.0515847	+	0.0944704i
$983$	−2398.70	−	3204.29i	−0.0778297	−	0.103968i	0.759937	−	0.649997i	$-0.225230\pi$
$983$	−2398.70	−	3204.29i	−0.0778297	−	0.103968i	−0.837766	+	0.546029i	$0.816139\pi$
$984$	−9487.40	+	4332.75i	−0.307365	+	0.140369i
$985$	34680.4	+	23796.2i	1.12184	+	0.769757i
$986$	7815.37	+	12161.0i	0.252426	+	0.392783i
$987$	−10172.5	+	727.555i	−0.328060	+	0.0234633i
$988$	646.504	−	646.504i	0.0208178	−	0.0208178i
$989$	−11432.6	−	6947.13i	−0.367580	−	0.223363i
$990$	−34701.7	+	37687.5i	−1.11403	+	1.20989i
$991$	26277.2	−	30325.4i	0.842302	−	0.972068i	−0.157579	−	0.987506i	$-0.550369\pi$
$991$	26277.2	−	30325.4i	0.842302	−	0.972068i	0.999881	+	0.0154382i	$0.00491432\pi$
$992$	−542.324	+	2493.02i	−0.0173577	+	0.0797919i
$993$	16771.4	−	22404.0i	0.535977	−	0.715982i
$994$	−1058.74	−	2318.33i	−0.0337840	−	0.0739767i
$995$	−1990.14	+	19525.2i	−0.0634087	+	0.622101i
$996$	11585.2	+	39455.6i	0.368565	+	1.25522i
$997$	34023.3	−	7401.32i	1.08077	−	0.235108i	0.363284	−	0.931678i	$-0.381655\pi$
$997$	34023.3	−	7401.32i	1.08077	−	0.235108i	0.717488	+	0.696571i	$0.245292\pi$
$998$	10704.4	−	3992.53i	0.339520	−	0.126634i
$999$	5434.17	+	1595.62i	0.172102	+	0.0505336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.53.21	yes	720
5.2	odd	4	inner	230.4.l.a.7.3	✓	720
23.10	odd	22	inner	230.4.l.a.33.3	yes	720
115.102	even	44	inner	230.4.l.a.217.21	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.3	✓	720	5.2	odd	4	inner
230.4.l.a.33.3	yes	720	23.10	odd	22	inner
230.4.l.a.53.21	yes	720	1.1	even	1	trivial
230.4.l.a.217.21	yes	720	115.102	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142678 + 1.99490i) q^{2} +(-7.79240 - 1.69513i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(5.05966 + 9.96995i) q^{5} +(2.26982 - 15.7870i) q^{6} +(11.3272 + 6.18513i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(33.2880 + 15.2021i) q^{9} +(-19.1672 + 11.5160i) q^{10} +(47.3150 - 40.9987i) q^{11} +(31.8173 + 2.27562i) q^{12} +(1.24808 + 2.28569i) q^{13} +(-10.7226 + 23.4792i) q^{14} +(-22.5265 - 86.2666i) q^{15} +(15.3519 - 4.50772i) q^{16} +(-34.3638 + 25.7244i) q^{17} +(-25.5773 + 68.5753i) q^{18} +(12.4909 + 86.8764i) q^{19} +(-25.7081 - 36.5936i) q^{20} +(-77.7817 - 67.3982i) q^{21} +(88.5393 + 88.5393i) q^{22} +(-35.9343 + 104.287i) q^{23} +63.7972i q^{24} +(-73.7996 + 100.889i) q^{25} +(-4.38165 + 2.81592i) q^{26} +(-61.2547 - 45.8547i) q^{27} +(-48.3687 - 18.0406i) q^{28} +(-166.667 - 23.9631i) q^{29} +(168.880 - 57.2466i) q^{30} +(67.0723 + 43.1048i) q^{31} +(11.1829 + 29.9824i) q^{32} +(-438.196 + 239.273i) q^{33} +(-56.2207 - 64.8822i) q^{34} +(-4.35351 + 144.227i) q^{35} +(-140.451 - 41.2400i) q^{36} +(-69.3509 + 25.8666i) q^{37} +(-171.528 + 37.3136i) q^{38} +(-5.85099 - 19.9266i) q^{39} +(69.3327 - 56.5064i) q^{40} +(67.9144 + 148.712i) q^{41} +(123.355 - 164.783i) q^{42} +(-25.7803 + 118.510i) q^{43} +(-163.995 + 189.260i) q^{44} +(16.8617 + 408.797i) q^{45} +(-213.169 - 56.8061i) q^{46} +(70.0685 - 70.0685i) q^{47} +(-127.269 + 9.10248i) q^{48} +(-95.3896 - 148.429i) q^{49} +(-211.794 - 132.829i) q^{50} +(311.383 - 142.204i) q^{51} +(-6.24265 - 8.33921i) q^{52} +(-66.3809 + 121.568i) q^{53} +(82.7360 - 128.740i) q^{54} +(648.153 + 264.289i) q^{55} +(29.0881 - 99.0649i) q^{56} +(49.9326 - 698.150i) q^{57} +(24.0243 - 335.904i) q^{58} +(-69.1230 + 235.411i) q^{59} +(138.297 + 328.731i) q^{60} +(356.042 - 554.011i) q^{61} +(-76.4201 + 139.953i) q^{62} +(283.033 + 378.088i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(-16.4733 + 24.0081i) q^{65} +(-539.848 - 840.020i) q^{66} +(-583.229 + 41.7134i) q^{67} +(121.412 - 121.412i) q^{68} +(456.795 - 751.731i) q^{69} +(-288.339 + 11.8932i) q^{70} +(-64.6606 + 74.6223i) q^{71} +(62.2306 - 286.069i) q^{72} +(-540.397 + 721.886i) q^{73} +(-61.4962 - 134.658i) q^{74} +(746.097 - 661.068i) q^{75} +(-98.9104 - 336.858i) q^{76} +(789.531 - 171.752i) q^{77} +(38.9169 - 14.5153i) q^{78} +(86.1370 + 25.2921i) q^{79} +(122.617 + 130.250i) q^{80} +(-247.453 - 285.576i) q^{81} +(-286.976 + 156.701i) q^{82} +(450.503 + 1207.85i) q^{83} +(346.327 + 222.571i) q^{84} +(-430.340 - 212.448i) q^{85} +(-240.095 - 34.5204i) q^{86} +(1258.12 + 469.253i) q^{87} +(-400.954 - 300.151i) q^{88} +(293.818 - 188.825i) q^{89} +(-813.105 + 91.9639i) q^{90} +33.6100i q^{91} +(82.9081 - 433.357i) q^{92} +(-449.586 - 449.586i) q^{93} +(149.777 + 129.783i) q^{94} +(-802.953 + 564.099i) q^{95} +(-36.3171 - 252.591i) q^{96} +(-288.234 + 772.785i) q^{97} +(282.492 - 211.471i) q^{98} +(2198.29 - 645.476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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