LMFDB - Embedded newform 230.4.l.a.217.21

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			217.21
Character	$\chi$	$=$	230.217
Dual form			230.4.l.a.53.21

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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	−0.886124	−	0.463448i	$-0.846612\pi$
$3$	−7.79240	+	1.69513i	−1.49965	+	0.326228i	−0.613524	+	0.789676i	$0.710249\pi$
$4$	−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	−0.143411	−	0.989663i	$-0.545807\pi$
$7$	11.3272	−	6.18513i	0.611613	−	0.333966i	0.755024	+	0.655697i	$0.227625\pi$
$8$	−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	0.984792	+	0.173737i	$0.0555842\pi$
$11$	47.3150	+	40.9987i	1.29691	+	1.12378i	0.312119	+	0.950043i	$0.398961\pi$
$12$	31.8173	−	2.27562i	0.765406	−	0.0547429i
$13$	1.24808	−	2.28569i	0.0266273	−	0.0487643i	−0.864027	−	0.503446i	$-0.832065\pi$
$13$	1.24808	−	2.28569i	0.0266273	−	0.0487643i	0.890654	+	0.454682i	$0.150247\pi$
$14$	−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	0.325361	−	0.945590i	$-0.394514\pi$
$17$	−34.3638	−	25.7244i	−0.490262	−	0.367005i	−0.815622	+	0.578585i	$0.803605\pi$
$18$	−25.5773	−	68.5753i	−0.334923	−	0.897964i
$19$	12.4909	−	86.8764i	0.150822	−	1.04899i	−0.764024	−	0.645188i	$-0.776779\pi$
$19$	12.4909	−	86.8764i	0.150822	−	1.04899i	0.914846	−	0.403803i	$-0.132312\pi$
$20$	−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	−0.653473	−	0.756950i	$-0.726689\pi$
$29$	−166.667	+	23.9631i	−1.06722	+	0.153443i	−0.413745	+	0.910393i	$0.635780\pi$
$30$	168.880	+	57.2466i	1.02777	+	0.348392i
$31$	67.0723	−	43.1048i	0.388598	−	0.249737i	−0.331724	−	0.943376i	$-0.607630\pi$
$31$	67.0723	−	43.1048i	0.388598	−	0.249737i	0.720322	+	0.693640i	$0.243994\pi$
$32$	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	0.190637	−	0.981661i	$-0.438945\pi$
$37$	−69.3509	−	25.8666i	−0.308141	−	0.114931i	−0.498778	+	0.866730i	$0.666218\pi$
$38$	−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	−0.735067	−	0.677995i	$-0.762849\pi$
$41$	67.9144	−	148.712i	0.258694	−	0.566461i	0.993761	+	0.111534i	$0.0355764\pi$
$42$	123.355	+	164.783i	0.453193	+	0.605395i
$43$	−25.7803	−	118.510i	−0.0914293	−	0.420294i	−0.999997	−	0.00255544i	$-0.999187\pi$
$43$	−25.7803	−	118.510i	−0.0914293	−	0.420294i	0.908567	−	0.417738i	$-0.137177\pi$
$44$	−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	0.807427	−	0.589968i	$-0.200860\pi$
$47$	70.0685	+	70.0685i	0.217458	+	0.217458i	−0.589968	+	0.807427i	$0.700860\pi$
$48$	−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	0.777405	−	0.629000i	$-0.216535\pi$
$53$	−66.3809	−	121.568i	−0.172040	−	0.315068i	−0.949445	+	0.313932i	$0.898354\pi$
$54$	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	0.847408	−	0.530942i	$-0.178162\pi$
$59$	−69.1230	−	235.411i	−0.152526	−	0.519456i	−0.999934	+	0.0114860i	$0.996344\pi$
$60$	138.297	−	328.731i	0.297568	−	0.707316i
$61$	356.042	+	554.011i	0.747319	+	1.16285i	0.981650	+	0.190694i	$0.0610738\pi$
$61$	356.042	+	554.011i	0.747319	+	1.16285i	−0.234331	+	0.972157i	$0.575290\pi$
$62$	−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	−0.471380	−	0.881930i	$-0.656244\pi$
$67$	−583.229	−	41.7134i	−1.06347	−	0.0760612i	−0.592094	+	0.805869i	$0.701699\pi$
$68$	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	0.699131	−	0.714994i	$-0.253570\pi$
$71$	−64.6606	−	74.6223i	−0.108082	−	0.124733i	−0.807213	+	0.590261i	$0.799025\pi$
$72$	62.2306	+	286.069i	0.101860	+	0.468244i
$73$	−540.397	−	721.886i	−0.866420	−	1.15740i	−0.986357	−	0.164620i	$-0.947360\pi$
$73$	−540.397	−	721.886i	−0.866420	−	1.15740i	0.119937	−	0.992781i	$-0.461731\pi$
$74$	−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	−0.219820	−	0.975540i	$-0.570547\pi$
$79$	86.1370	−	25.2921i	0.122673	−	0.0360200i	0.342493	+	0.939520i	$0.388729\pi$
$80$	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	−0.192022	−	0.981391i	$-0.561504\pi$
$83$	450.503	−	1207.85i	0.595773	−	1.59733i	0.787794	−	0.615938i	$-0.211223\pi$
$84$	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	0.703788	−	0.710410i	$-0.251491\pi$
$89$	293.818	+	188.825i	0.349940	+	0.224892i	−0.353848	+	0.935303i	$0.615127\pi$
$90$	−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	−0.996011	−	0.0892284i	$-0.971560\pi$
$97$	−288.234	−	772.785i	−0.301708	−	0.808911i	0.694303	−	0.719683i	$-0.255713\pi$
$98$	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	0.664419	−	0.747360i	$-0.268679\pi$
$101$	−340.545	−	745.689i	−0.335500	−	0.734642i	−0.999919	+	0.0127180i	$0.995952\pi$
$102$	328.111	−	600.890i	0.318508	−	0.583303i
$103$	1313.60	−	93.9507i	1.25663	−	0.0898761i	0.572910	−	0.819619i	$-0.305815\pi$
$103$	1313.60	−	93.9507i	1.25663	−	0.0898761i	0.683722	+	0.729743i	$0.260360\pi$
$104$	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	−0.555584	−	0.831460i	$-0.687505\pi$
$107$	326.726	−	1501.93i	0.295194	−	1.35698i	0.850778	−	0.525525i	$-0.176131\pi$
$108$	268.628	−	146.682i	0.239340	−	0.130690i
$109$	−235.086	−	1635.06i	−0.206579	−	1.43679i	−0.784212	−	0.620493i	$-0.786932\pi$
$109$	−235.086	−	1635.06i	−0.206579	−	1.43679i	0.577633	−	0.816297i	$-0.303977\pi$
$110$	−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	−0.854448	−	0.519537i	$-0.826105\pi$
$113$	78.3676	−	1095.72i	0.0652407	−	0.912185i	0.919689	−	0.392648i	$-0.128441\pi$
$114$	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	−0.775241	−	0.631665i	$-0.782372\pi$
$127$	−2079.12	+	148.702i	−1.45270	+	0.103899i	−0.677455	+	0.735564i	$0.736917\pi$
$128$	−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	0.832195	−	0.554483i	$-0.187084\pi$
$131$	1847.97	+	542.614i	1.23251	+	0.361896i	0.400311	+	0.916379i	$0.368902\pi$
$132$	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	−0.206779	+	0.978388i	$0.566298\pi$
$137$	−1900.47	+	1900.47i	−1.18517	+	1.18517i	−0.978388	+	0.206779i	$0.933702\pi$
$138$	1564.81	−	804.006i	0.965254	−	0.495953i
$139$			3221.90i			1.96603i	0.183521	+	0.983016i	$0.441251\pi$
$139$			3221.90i			1.96603i	−0.183521	+	0.983016i	$0.558749\pi$
$140$	−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	0.122810	−	0.992430i	$-0.460810\pi$
$149$	1978.21	−	2282.98i	1.08766	−	1.25523i	0.964851	−	0.262797i	$-0.0846450\pi$
$150$	1425.22	−	1394.07i	0.775791	−	0.758837i
$151$	1073.15	−	315.104i	0.578353	−	0.169820i	0.0205439	−	0.999789i	$-0.493460\pi$
$151$	1073.15	−	315.104i	0.578353	−	0.169820i	0.557809	+	0.829969i	$0.311642\pi$
$152$	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	0.833373	−	0.552711i	$-0.186407\pi$
$157$	134.286	+	179.385i	0.0682624	+	0.0911880i	−0.765111	+	0.643899i	$0.777316\pi$
$158$	−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	0.728659	−	0.684876i	$-0.240144\pi$
$163$	2814.48	+	201.295i	1.35243	+	0.0967280i	0.623775	+	0.781604i	$0.285598\pi$
$164$	−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	−0.999317	−	0.0369651i	$-0.988231\pi$
$167$	−1472.50	+	1967.03i	−0.682309	+	0.911458i	0.317008	+	0.948423i	$0.397322\pi$
$168$	−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	0.798991	+	0.601343i	$0.205367\pi$
$173$	213.239	+	2981.47i	0.0937126	+	1.31027i	−0.705279	+	0.708930i	$0.749178\pi$
$174$	−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	0.227112	−	0.973869i	$-0.427072\pi$
$179$	−862.538	−	393.908i	−0.360163	−	0.164481i	−0.587274	+	0.809388i	$0.699799\pi$
$180$	−299.472	+	1608.94i	−0.124007	+	0.666242i
$181$	763.280	−	1187.69i	0.313448	−	0.487735i	−0.648407	−	0.761294i	$-0.724564\pi$
$181$	763.280	−	1187.69i	0.313448	−	0.487735i	0.961855	+	0.273559i	$0.0882008\pi$
$182$	−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	−0.886315	−	0.463083i	$-0.846743\pi$
$191$	289.472	−	985.851i	0.109662	−	0.373475i	0.995977	+	0.0896080i	$0.0285614\pi$
$192$	498.714	+	108.489i	0.187456	+	0.0407786i
$193$	−2911.72	−	1086.01i	−1.08596	−	0.405042i	−0.258180	−	0.966097i	$-0.583123\pi$
$193$	−2911.72	−	1086.01i	−1.08596	−	0.405042i	−0.827779	+	0.561055i	$0.810396\pi$
$194$	−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	0.948328	−	0.317291i	$-0.102773\pi$
$197$	3301.75	+	1802.89i	1.19411	+	0.652034i	0.245782	+	0.969325i	$0.420955\pi$
$198$	1601.31	−	4293.28i	0.574748	−	1.54096i
$199$	1476.77	−	949.059i	0.526056	−	0.338076i	−0.250508	−	0.968115i	$-0.580598\pi$
$199$	1476.77	−	949.059i	0.526056	−	0.338076i	0.776563	+	0.630039i	$0.216961\pi$
$200$	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	−0.995219	−	0.0976690i	$-0.968861\pi$
$211$	−39.2217	+	272.793i	−0.0127968	+	0.0890039i	0.982422	+	0.186673i	$0.0597705\pi$
$212$	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	−0.954279	−	0.298919i	$-0.903374\pi$
$223$	−4058.51	+	2216.11i	−1.21873	+	0.665479i	−0.264456	+	0.964398i	$0.585192\pi$
$224$	−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	0.451598	−	0.892221i	$-0.350854\pi$
$227$	4217.08	−	917.370i	1.23303	−	0.268229i	0.781430	+	0.623993i	$0.214490\pi$
$228$	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	−0.210516	−	0.977590i	$-0.567514\pi$
$233$	14.5753	−	3.17067i	0.00409812	−	0.000891491i	0.214614	+	0.976699i	$0.431151\pi$
$234$	−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	−0.904040	−	0.427449i	$-0.859412\pi$
$239$	−4334.12	+	1979.32i	−1.17302	+	0.535698i	−0.268976	+	0.963147i	$0.586685\pi$
$240$	−734.691	+	1222.81i	−0.197600	+	0.328884i
$241$	−4932.27	−	4273.83i	−1.31832	−	1.14233i	−0.979492	−	0.201483i	$-0.935424\pi$
$241$	−4932.27	−	4273.83i	−1.31832	−	1.14233i	−0.338828	−	0.940848i	$-0.610031\pi$
$242$	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	0.110990	−	0.993821i	$-0.464598\pi$
$251$	4415.97	−	3826.46i	1.11049	−	0.962247i	0.999501	+	0.0315748i	$0.0100522\pi$
$252$	−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	−0.369957	−	0.929049i	$-0.620628\pi$
$257$	1719.00	−	1286.82i	0.417230	−	0.312334i	0.787187	+	0.616715i	$0.211537\pi$
$258$	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	0.778171	−	0.628053i	$-0.216148\pi$
$263$	2859.91	+	1561.63i	0.670530	+	0.366137i	−0.107640	+	0.994190i	$0.534330\pi$
$264$	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	−0.893709	−	0.448646i	$-0.851906\pi$
$269$	444.208	−	1512.83i	0.100683	−	0.342896i	0.994393	+	0.105750i	$0.0337245\pi$
$270$	1702.14	−	173.494i	0.383664	−	0.0391056i
$271$	−3168.67	+	6938.41i	−0.710269	+	1.55527i	0.116791	+	0.993157i	$0.462739\pi$
$271$	−3168.67	+	6938.41i	−0.710269	+	1.55527i	−0.827059	+	0.562115i	$0.809988\pi$
$272$	−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	0.391412	−	0.920215i	$-0.371987\pi$
$277$	−2437.89	−	2437.89i	−0.528803	−	0.528803i	−0.920215	+	0.391412i	$0.871987\pi$
$278$	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	0.991098	−	0.133137i	$-0.0425051\pi$
$281$	7251.74	+	3311.76i	1.53951	+	0.703071i	0.548412	+	0.836208i	$0.315232\pi$
$282$	−947.126	+	1265.21i	−0.200002	+	0.267171i
$283$	3984.15	+	7296.42i	0.836866	+	1.53261i	0.846336	+	0.532650i	$0.178804\pi$
$283$	3984.15	+	7296.42i	0.836866	+	1.53261i	−0.00946988	+	0.999955i	$0.503014\pi$
$284$	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	−0.317717	−	0.948185i	$-0.602916\pi$
$293$	3418.32	−	4566.34i	0.681571	−	0.910473i	0.999289	+	0.0377128i	$0.0120072\pi$
$294$	−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	0.928766	−	0.370667i	$-0.120871\pi$
$307$	8712.06	+	1895.19i	1.61962	+	0.352327i	0.690855	+	0.722994i	$0.257234\pi$
$308$	−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	−0.907389	−	0.420292i	$-0.861928\pi$
$311$	−1986.72	+	2292.80i	−0.362240	+	0.418047i	0.545149	+	0.838339i	$0.316473\pi$
$312$	−145.820	−	79.6239i	−0.0264598	−	0.0144481i
$313$	−3558.92	+	9541.82i	−0.642690	+	1.72312i	0.0468825	+	0.998900i	$0.485071\pi$
$313$	−3558.92	+	9541.82i	−0.642690	+	1.72312i	−0.689572	+	0.724217i	$0.742201\pi$
$314$	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	0.332788	−	0.943002i	$-0.392011\pi$
$317$	6783.14	−	2529.98i	1.20183	−	0.448258i	0.869039	+	0.494744i	$0.164738\pi$
$318$	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	0.749118	−	0.662437i	$-0.230478\pi$
$331$	−1457.85	−	3192.25i	−0.242087	−	0.530096i	−0.991204	+	0.132341i	$0.957751\pi$
$332$	−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	−0.918890	−	0.394513i	$-0.870913\pi$
$337$	500.168	−	2299.24i	0.0808484	−	0.371654i	0.999739	+	0.0228592i	$0.00727693\pi$
$338$	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	0.945826	+	0.324675i	$0.105255\pi$
$347$	−236.442	+	3305.89i	−0.0365789	+	0.511440i	−0.982405	+	0.186765i	$0.940200\pi$
$348$	−5248.37	+	1141.71i	−0.808455	+	0.175869i
$349$	−1411.35	−	202.921i	−0.216469	−	0.0311235i	0.0332271	−	0.999448i	$-0.489422\pi$
$349$	−1411.35	−	202.921i	−0.216469	−	0.0311235i	−0.249696	+	0.968324i	$0.580331\pi$
$350$	−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	0.824830	+	0.565381i	$0.191271\pi$
$353$	−1063.35	+	4888.14i	−0.160330	+	0.737024i	−0.985159	+	0.171642i	$0.945093\pi$
$354$	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	0.795878	−	0.605458i	$-0.207010\pi$
$359$	−1244.00	−	2723.99i	−0.182886	−	0.400464i	−0.978763	+	0.204994i	$0.934283\pi$
$360$	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	−0.321601	−	0.946875i	$-0.604221\pi$
$367$	4396.12	−	4396.12i	0.625274	−	0.625274i	0.946875	+	0.321601i	$0.104221\pi$
$368$	−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	−0.879605	−	0.475706i	$-0.842193\pi$
$373$	−8881.20	+	3312.52i	−1.23284	+	0.459827i	−0.353240	+	0.935533i	$0.614920\pi$
$374$	−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	−0.193546	−	0.981091i	$-0.561999\pi$
$379$	5940.33	−	6855.51i	0.805104	−	0.929139i	0.998650	+	0.0519520i	$0.0165443\pi$
$380$	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	0.922289	−	0.386500i	$-0.126316\pi$
$383$	11997.8	+	2609.96i	1.60068	+	0.348206i	0.678386	+	0.734705i	$0.262680\pi$
$384$	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	−0.999716	−	0.0238113i	$-0.992420\pi$
$389$	−6759.36	−	7800.72i	−0.881011	−	1.01674i	0.118706	−	0.992930i	$-0.462126\pi$
$390$	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	−0.801001	−	0.598663i	$-0.795699\pi$
$397$	−7.27983	+	9.72471i	−0.000920313	+	0.00122939i	0.800081	+	0.599892i	$0.204790\pi$
$398$	−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	−0.968401	−	0.249398i	$-0.919767\pi$
$401$	−2317.18	−	7891.60i	−0.288565	−	0.982762i	0.679836	−	0.733364i	$-0.262051\pi$
$402$	−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	0.663003	−	0.748617i	$-0.269282\pi$
$409$	4395.57	+	2007.39i	0.531411	+	0.242687i	−0.131592	+	0.991304i	$0.542009\pi$
$410$	−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	−0.939745	−	0.341877i	$-0.888937\pi$
$419$	−565.801	+	1238.93i	−0.0659695	+	0.144453i	0.873775	+	0.486330i	$0.161665\pi$
$420$	−466.722	−	4578.99i	−0.0542231	−	0.531981i
$421$	−2875.62	+	9793.47i	−0.332896	+	1.13374i	0.607687	+	0.794177i	$0.292097\pi$
$421$	−2875.62	+	9793.47i	−0.332896	+	1.13374i	−0.940583	+	0.339563i	$0.889721\pi$
$422$	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	0.117494	−	0.993074i	$-0.462514\pi$
$431$	4563.45	−	656.126i	0.510009	−	0.0733282i	0.392515	+	0.919745i	$0.371605\pi$
$432$	−1147.08	+	427.837i	−0.127752	+	0.0476489i
$433$	−6181.16	+	4627.16i	−0.686022	+	0.513550i	−0.884491	−	0.466557i	$-0.845494\pi$
$433$	−6181.16	+	4627.16i	−0.686022	+	0.513550i	0.198469	+	0.980107i	$0.436403\pi$
$434$	−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	−0.0455091	−	0.998964i	$-0.514491\pi$
$439$	8616.85	−	7466.54i	0.936810	−	0.811751i	0.982319	+	0.187213i	$0.0599455\pi$
$440$	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	0.879455	−	0.475982i	$-0.157907\pi$
$443$	6252.02	+	4680.20i	0.670525	+	0.501949i	−0.208930	+	0.977931i	$0.566998\pi$
$444$	−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	0.989398	−	0.145232i	$-0.0463928\pi$
$449$	9385.22	+	8132.34i	0.986450	+	0.854764i	−0.00294755	+	0.999996i	$0.500938\pi$
$450$	−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	0.0263625	−	0.999652i	$-0.491608\pi$
$457$	4548.83	−	989.537i	0.465613	−	0.101288i	0.439251	+	0.898364i	$0.355244\pi$
$458$	−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	0.475189	−	0.879884i	$-0.342380\pi$
$463$	12681.9	−	2758.78i	1.27295	−	0.276914i	0.797764	+	0.602969i	$0.206016\pi$
$464$	−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	−0.362644	−	0.931928i	$-0.618126\pi$
$467$	2273.55	−	1241.45i	0.225284	−	0.123014i	0.587928	+	0.808914i	$0.299944\pi$
$468$	−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	−0.954232	−	0.299066i	$-0.903325\pi$
$479$	478.082	−	3325.13i	0.0456036	−	0.317180i	0.999836	−	0.0181136i	$-0.00576606\pi$
$480$	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	−0.952264	−	0.305276i	$-0.901251\pi$
$487$	−9969.46	+	7463.05i	−0.927638	+	0.694421i	0.0246263	+	0.999697i	$0.492160\pi$
$488$	−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	−0.475044	−	0.879962i	$-0.657568\pi$
$491$	1393.23	−	895.377i	0.128057	−	0.0822970i	0.603101	+	0.797665i	$0.293932\pi$
$492$	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	−0.999650	−	0.0264736i	$-0.991572\pi$
$499$	−1609.36	+	5480.96i	−0.144378	+	0.491707i	0.855271	+	0.518180i	$0.173390\pi$
$500$	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	−0.999632	−	0.0271436i	$-0.991359\pi$
$503$	−1146.28	−	5269.37i	−0.101611	−	0.467096i	0.898021	−	0.439953i	$-0.145005\pi$
$504$	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	−0.792645	−	0.609684i	$-0.791296\pi$
$509$	1047.53	−	1629.98i	0.0912197	−	0.141941i	0.883864	+	0.467743i	$0.154933\pi$
$510$	−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	0.764659	−	0.644436i	$-0.222908\pi$
$521$	−1655.27	−	2575.65i	−0.139191	−	0.216586i	−0.903850	+	0.427850i	$0.859271\pi$
$522$	5906.17	+	10816.3i	0.495222	+	0.906932i
$523$	−13271.2	+	17728.2i	−1.10957	+	1.48222i	−0.252093	+	0.967703i	$0.581119\pi$
$523$	−13271.2	+	17728.2i	−1.10957	+	1.48222i	−0.857481	+	0.514515i	$0.827972\pi$
$524$	−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	−0.287283	−	0.957846i	$-0.592752\pi$
$541$	8829.70	−	10190.0i	0.701698	−	0.809803i	0.988981	+	0.148043i	$0.0472975\pi$
$542$	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	−0.793476	−	0.608602i	$-0.791731\pi$
$547$	−12724.1	+	4745.85i	−0.994595	+	0.370965i	−0.201119	+	0.979567i	$0.564458\pi$
$548$	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	0.988706	−	0.149871i	$-0.0478858\pi$
$557$	1884.39	+	5052.26i	0.143347	+	0.384328i	−0.845358	+	0.534199i	$0.820613\pi$
$558$	−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	0.464375	−	0.885638i	$-0.346279\pi$
$563$	14027.4	−	1003.26i	1.05006	−	0.0751020i	0.585688	+	0.810536i	$0.300824\pi$
$564$	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	0.995851	−	0.0909945i	$-0.0290046\pi$
$569$	199.558	+	1387.96i	0.0147029	+	0.102261i	−0.981149	+	0.193255i	$0.938095\pi$
$570$	7082.85	−	13956.6i	0.520470	−	1.02557i
$571$	10825.0	+	1556.40i	0.793368	+	0.114069i	0.527070	−	0.849822i	$-0.323290\pi$
$571$	10825.0	+	1556.40i	0.793368	+	0.114069i	0.266298	+	0.963891i	$0.414200\pi$
$572$	−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	0.680219	+	0.733009i	$0.261885\pi$
$577$	−1349.89	+	18873.9i	−0.0973944	+	1.36175i	−0.777613	+	0.628743i	$0.783570\pi$
$578$	−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	−0.450550	−	0.892751i	$-0.648772\pi$
$587$	−10943.2	+	782.674i	−0.769463	+	0.0550331i	−0.318913	+	0.947784i	$0.603318\pi$
$588$	−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	0.983273	−	0.182137i	$-0.0583015\pi$
$593$	1745.72	+	4680.45i	0.120890	+	0.324120i	−0.862383	+	0.506257i	$0.831029\pi$
$594$	−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	$-0.908209\pi$
$599$		−	8338.39i		−	0.568777i	0.958709	−	0.284388i	$-0.0917905\pi$
$600$	−6436.44	+	4708.21i	−0.437944	+	0.320353i
$601$	−14328.2	−	9208.19i	−0.972480	−	0.624975i	−0.0450550	−	0.998985i	$-0.514346\pi$
$601$	−14328.2	−	9208.19i	−0.972480	−	0.624975i	−0.927425	+	0.374010i	$0.877983\pi$
$602$	−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	−0.976483	−	0.215593i	$-0.930832\pi$
$607$	−1455.45	+	3902.23i	−0.0973231	+	0.260933i	0.879160	+	0.476526i	$0.158104\pi$
$608$	−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	−0.391414	−	0.920215i	$-0.628014\pi$
$613$	−17146.1	−	3729.90i	−1.12973	−	0.245757i	−0.738314	+	0.674457i	$0.764378\pi$
$614$	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	0.815326	−	0.579003i	$-0.196558\pi$
$617$	460.899	+	615.689i	0.0300731	+	0.0401729i	−0.785253	+	0.619175i	$0.787467\pi$
$618$	4464.84	+	20524.5i	0.290618	+	1.33595i
$619$	9204.16	+	10622.2i	0.597652	+	0.689727i	0.971304	−	0.237842i	$-0.0764400\pi$
$619$	9204.16	+	10622.2i	0.597652	+	0.689727i	−0.373652	+	0.927569i	$0.621895\pi$
$620$	−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	−0.916455	−	0.400138i	$-0.868962\pi$
$631$	−5734.96	−	19531.5i	−0.361815	−	1.23223i	0.554640	−	0.832090i	$-0.312856\pi$
$632$	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	−0.910445	−	0.413630i	$-0.864261\pi$
$641$	−2531.39	+	3938.92i	−0.155981	+	0.242711i	0.754464	+	0.656342i	$0.227897\pi$
$642$	24452.6	+	1748.88i	1.50322	+	0.107512i
$643$	9477.31	+	9477.31i	0.581257	+	0.581257i	0.935249	−	0.353991i	$-0.115176\pi$
$643$	9477.31	+	9477.31i	0.581257	+	0.581257i	−0.353991	+	0.935249i	$0.615176\pi$
$644$	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	−0.998936	−	0.0461235i	$-0.985313\pi$
$647$	−1800.95	−	8278.83i	−0.109432	−	0.503052i	0.889504	−	0.456928i	$-0.151050\pi$
$648$	−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	0.570813	−	0.821080i	$-0.306628\pi$
$653$	7751.16	+	2891.03i	0.464512	+	0.173254i	−0.106301	+	0.994334i	$0.533901\pi$
$654$	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	−0.623934	−	0.781477i	$-0.714467\pi$
$659$	−2914.32	+	1872.92i	−0.172270	+	0.110711i	0.451664	+	0.892188i	$0.350830\pi$
$660$	20021.1	−	9883.91i	1.18079	−	0.582925i
$661$	24584.0	−	3534.65i	1.44661	−	0.207991i	0.626151	−	0.779701i	$-0.284629\pi$
$661$	24584.0	−	3534.65i	1.44661	−	0.207991i	0.820455	+	0.571711i	$0.193720\pi$
$662$	−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	0.797869	−	0.602831i	$-0.205960\pi$
$673$	7756.10	+	5806.15i	0.444243	+	0.332556i	−0.353626	+	0.935387i	$0.615051\pi$
$674$	−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	−0.158764	−	0.987317i	$-0.550751\pi$
$677$	13346.1	−	24441.5i	0.757654	−	1.38754i	0.916418	−	0.400223i	$-0.131067\pi$
$678$	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	−0.595357	−	0.803462i	$-0.702989\pi$
$683$	−4307.42	+	2352.03i	−0.241316	+	0.131768i	0.354041	+	0.935230i	$0.384807\pi$
$684$	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	0.433614	−	0.901099i	$-0.357238\pi$
$701$	−7360.93	−	6378.28i	−0.396603	−	0.343658i	−0.830217	+	0.557440i	$0.811783\pi$
$702$	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	0.905097	+	0.425206i	$0.139798\pi$
$709$	−1569.40	+	10915.4i	−0.0831315	+	0.578192i	−0.988228	+	0.152987i	$0.951111\pi$
$710$	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	−0.959244	−	0.282579i	$-0.908810\pi$
$719$	−34703.3	+	4989.58i	−1.80002	+	0.258804i	−0.840776	+	0.541383i	$0.817901\pi$
$720$	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	0.604081	−	0.796923i	$-0.293541\pi$
$727$	10560.4	+	3938.83i	0.538740	+	0.200940i	−0.0653402	+	0.997863i	$0.520813\pi$
$728$	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	−0.999578	−	0.0290331i	$-0.990757\pi$
$733$	−2031.97	−	9340.80i	−0.102391	−	0.470682i	0.897188	−	0.441649i	$-0.145606\pi$
$734$	−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	0.382683	+	0.923880i	$0.375000\pi$
$739$	−12388.7	+	19277.2i	−0.616680	+	0.959572i	−0.999363	+	0.0356926i	$0.988636\pi$
$740$	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	0.592815	−	0.805338i	$-0.298016\pi$
$743$	−8205.97	−	15028.1i	−0.405179	−	0.742029i	−0.997994	+	0.0633091i	$0.979835\pi$
$744$	−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	0.811612	−	0.584197i	$-0.198590\pi$
$751$	−1172.03	−	1823.71i	−0.0569480	−	0.0886127i	−0.868560	+	0.495584i	$0.834954\pi$
$752$	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	0.389336	−	0.921096i	$-0.372704\pi$
$757$	13405.3	+	958.765i	0.643624	+	0.0460329i	0.254288	+	0.967129i	$0.418159\pi$
$758$	−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	−0.999060	−	0.0433596i	$-0.986194\pi$
$761$	−18889.5	−	21799.7i	−0.899797	−	1.03842i	0.0992627	−	0.995061i	$-0.468352\pi$
$762$	−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	0.654313	−	0.756224i	$-0.272958\pi$
$769$	34410.1	−	10103.7i	1.61360	−	0.473796i	0.959289	+	0.282427i	$0.0911396\pi$
$770$	−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	0.148533	+	0.988907i	$0.452545\pi$
$773$	−13138.2	+	35224.9i	−0.611317	+	1.63900i	−0.759851	+	0.650098i	$0.774728\pi$
$774$	−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	0.940371	−	0.340151i	$-0.110478\pi$
$787$	153.091	+	410.454i	0.00693408	+	0.0185910i	−0.933437	+	0.358742i	$0.883206\pi$
$788$	−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	−0.703656	−	0.710541i	$-0.748450\pi$
$797$	5210.64	−	23952.9i	0.231581	−	1.06456i	0.935237	−	0.354021i	$-0.115186\pi$
$798$	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	0.246533	−	0.969134i	$-0.420709\pi$
$809$	4833.17	+	694.905i	0.210043	+	0.0301997i	−0.0364898	+	0.999334i	$0.511618\pi$
$810$	8031.69	−	2624.01i	0.348401	−	0.113825i
$811$	−1498.86	−	10424.8i	−0.0648978	−	0.451374i	−0.996198	−	0.0871210i	$-0.972233\pi$
$811$	−1498.86	−	10424.8i	−0.0648978	−	0.451374i	0.931300	−	0.364253i	$-0.118676\pi$
$812$	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	0.611325	−	0.791380i	$-0.290637\pi$
$821$	16414.0	+	4819.60i	0.697752	+	0.204878i	0.0864268	+	0.996258i	$0.472455\pi$
$822$	−34316.3	−	25688.9i	−1.45611	−	1.09003i
$823$	2746.41	+	7363.40i	0.116323	+	0.311874i	0.982044	−	0.188653i	$-0.0604123\pi$
$823$	2746.41	+	7363.40i	0.116323	+	0.311874i	−0.865721	+	0.500527i	$0.833140\pi$
$824$	−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	−0.733811	−	0.679354i	$-0.762260\pi$
$827$	−1295.11	+	1295.11i	−0.0544564	+	0.0544564i	0.679354	+	0.733811i	$0.262260\pi$
$828$	9347.78	+	13165.2i	0.392340	+	0.552563i
$829$			5818.54i			0.243771i	0.992544	+	0.121886i	$0.0388941\pi$
$829$			5818.54i			0.243771i	−0.992544	+	0.121886i	$0.961106\pi$
$830$	−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	−0.740025	−	0.672579i	$-0.765187\pi$
$839$	753.952	−	870.106i	0.0310242	−	0.0358038i	0.771050	+	0.636775i	$0.219732\pi$
$840$	−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	0.142436	−	0.989804i	$-0.454507\pi$
$853$	3551.53	+	254.010i	0.142558	+	0.0101959i	0.000122165		1.00000i	$0.499961\pi$
$854$	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	−0.786068	−	0.618140i	$-0.787886\pi$
$857$	714.868	−	954.952i	0.0284941	−	0.0380637i	0.814562	+	0.580076i	$0.196977\pi$
$858$	1246.25	+	2282.34i	0.0495877	+	0.0908131i
$859$	10973.2	+	17074.7i	0.435858	+	0.678208i	0.987809	−	0.155668i	$-0.0497531\pi$
$859$	10973.2	+	17074.7i	0.435858	+	0.678208i	−0.551952	+	0.833876i	$0.686117\pi$
$860$	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	−0.971523	−	0.236945i	$-0.923854\pi$
$863$	−1105.60	−	15458.3i	−0.0436096	−	0.609741i	0.927913	−	0.372796i	$-0.121601\pi$
$864$	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	−0.986625	−	0.163009i	$-0.947880\pi$
$877$	−4074.32	−	18729.4i	−0.156876	−	0.721147i	0.829749	−	0.558137i	$-0.188484\pi$
$878$	−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	−0.906989	−	0.421153i	$-0.861625\pi$
$881$	2189.01	−	7455.08i	0.0837113	−	0.285094i	0.990701	+	0.136059i	$0.0434436\pi$
$882$	12618.4	+	2744.96i	0.481727	+	0.104793i
$883$	−34842.7	−	12995.7i	−1.32792	−	0.495288i	−0.417387	−	0.908729i	$-0.637054\pi$
$883$	−34842.7	−	12995.7i	−1.32792	−	0.495288i	−0.910531	+	0.413441i	$0.864327\pi$
$884$	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	0.0319603	−	0.999489i	$-0.489825\pi$
$887$	−20911.4	−	11418.5i	−0.791584	−	0.432238i	−0.823545	+	0.567251i	$0.808007\pi$
$888$	−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	0.0658677	+	0.997828i	$0.479018\pi$
$907$	−22103.0	+	40478.6i	−0.809170	+	1.48188i	−0.875037	+	0.484055i	$0.839163\pi$
$908$	−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	−0.141014	−	0.990008i	$-0.545036\pi$
$911$	14156.3	−	6464.96i	0.514840	−	0.235119i	0.655853	+	0.754888i	$0.272309\pi$
$912$	−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	0.384296	−	0.923210i	$-0.374444\pi$
$929$	37763.5	−	17246.0i	1.33367	−	0.609067i	0.949376	+	0.314143i	$0.101717\pi$
$930$	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	0.819790	−	0.572664i	$-0.194090\pi$
$937$	14377.8	+	10763.1i	0.501284	+	0.375256i	−0.318506	+	0.947921i	$0.603181\pi$
$938$	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	−0.728260	−	0.685301i	$-0.759671\pi$
$941$	−4433.13	+	3841.33i	−0.153577	+	0.133075i	0.574683	+	0.818376i	$0.305125\pi$
$942$	−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	−0.818569	−	0.574409i	$-0.805232\pi$
$947$	−14514.2	+	10865.2i	−0.498045	+	0.372832i	0.320524	+	0.947240i	$0.396141\pi$
$948$	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	0.334892	−	0.942256i	$-0.391300\pi$
$953$	−8141.27	−	4445.47i	−0.276728	−	0.151105i	−0.611620	+	0.791152i	$0.709482\pi$
$954$	−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	0.560869	−	0.827904i	$-0.310467\pi$
$967$	−8029.87	−	8029.87i	−0.267035	−	0.267035i	−0.827904	+	0.560869i	$0.810467\pi$
$968$	−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	0.566750	−	0.823890i	$-0.308201\pi$
$971$	9538.21	+	4355.96i	0.315238	+	0.143964i	−0.251512	+	0.967854i	$0.580928\pi$
$972$	−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	0.780466	+	0.625199i	$0.214982\pi$
$977$	2959.72	+	41382.3i	0.0969191	+	1.35511i	−0.683547	+	0.729907i	$0.739563\pi$
$978$	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	−0.837766	−	0.546029i	$-0.816139\pi$
$983$	−2398.70	+	3204.29i	−0.0778297	+	0.103968i	0.759937	+	0.649997i	$0.225230\pi$
$984$	−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	0.999881	−	0.0154382i	$-0.00491432\pi$
$991$	26277.2	+	30325.4i	0.842302	+	0.972068i	−0.157579	+	0.987506i	$0.550369\pi$
$992$	−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	0.717488	−	0.696571i	$-0.245292\pi$
$997$	34023.3	+	7401.32i	1.08077	+	0.235108i	0.363284	+	0.931678i	$0.381655\pi$
$998$	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.217.21	yes	720
5.3	odd	4	inner	230.4.l.a.33.3	yes	720
23.7	odd	22	inner	230.4.l.a.7.3	✓	720
115.53	even	44	inner	230.4.l.a.53.21	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.3	✓	720	23.7	odd	22	inner
230.4.l.a.33.3	yes	720	5.3	odd	4	inner
230.4.l.a.53.21	yes	720	115.53	even	44	inner
230.4.l.a.217.21	yes	720	1.1	even	1	trivial

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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