LMFDB - Embedded newform 97.3.l.a.7.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,3,Mod(5,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(96)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	97.l (of order $96$, degree $32$, 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:	$2.64305856429$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$15$ over $\Q(\zeta_{96})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{96}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	97.7
Dual form			97.3.l.a.14.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.75983 + 0.115345i) q^{2} +(0.716397 - 2.11044i) q^{3} +(-0.882081 + 0.116128i) q^{4} +(3.67912 + 5.91650i) q^{5} +(-1.01731 + 3.79665i) q^{6} +(-3.93366 - 0.128775i) q^{7} +(8.45779 - 1.68236i) q^{8} +(3.19945 + 2.45503i) q^{9} +(-7.15707 - 9.98768i) q^{10} +(10.9169 - 9.57385i) q^{11} +(-0.386839 + 1.94477i) q^{12} +(15.5379 + 3.62294i) q^{13} +(6.93744 - 0.227108i) q^{14} +(15.1221 - 3.52599i) q^{15} +(-11.2527 + 3.01516i) q^{16} +(-14.8818 + 15.8892i) q^{17} +(-5.91367 - 3.95139i) q^{18} +(16.8292 + 8.99537i) q^{19} +(-3.93235 - 4.79158i) q^{20} +(-3.08984 + 8.20950i) q^{21} +(-18.1076 + 18.1076i) q^{22} +(8.58669 - 3.89058i) q^{23} +(2.50862 - 19.0549i) q^{24} +(-10.4119 + 21.1132i) q^{25} +(-27.7620 - 4.58353i) q^{26} +(24.1513 - 16.1374i) q^{27} +(3.48476 - 0.343219i) q^{28} +(-30.5346 - 21.8808i) q^{29} +(-26.2057 + 7.94941i) q^{30} +(-24.8536 + 12.2564i) q^{31} +(-13.2083 + 4.48360i) q^{32} +(-12.3842 - 29.8981i) q^{33} +(24.3568 - 29.6788i) q^{34} +(-13.7105 - 23.7473i) q^{35} +(-3.10727 - 1.79398i) q^{36} +(13.2099 + 35.0979i) q^{37} +(-30.6540 - 13.8892i) q^{38} +(18.7773 - 30.1964i) q^{39} +(41.0709 + 43.8510i) q^{40} +(-5.78758 - 35.0549i) q^{41} +(4.49066 - 14.8037i) q^{42} +(10.8456 + 14.1342i) q^{43} +(-8.51778 + 9.71267i) q^{44} +(-2.75401 + 27.9619i) q^{45} +(-14.6624 + 7.83719i) q^{46} +(-69.7330 - 28.8844i) q^{47} +(-1.69812 + 25.9082i) q^{48} +(-33.4380 - 2.19164i) q^{49} +(15.8879 - 38.3567i) q^{50} +(22.8718 + 42.7901i) q^{51} +(-14.1264 - 1.39133i) q^{52} +(66.8519 + 58.6275i) q^{53} +(-40.6407 + 31.1847i) q^{54} +(96.8083 + 29.3665i) q^{55} +(-33.4868 + 5.52869i) q^{56} +(31.0406 - 29.0727i) q^{57} +(56.2596 + 34.9844i) q^{58} +(16.7129 - 36.8862i) q^{59} +(-12.9295 + 4.86631i) q^{60} +(43.1302 - 74.7038i) q^{61} +(42.3244 - 24.4360i) q^{62} +(-12.2694 - 10.0693i) q^{63} +(65.7788 - 27.2465i) q^{64} +(35.7308 + 105.260i) q^{65} +(25.2427 + 51.1871i) q^{66} +(-8.56757 - 28.2435i) q^{67} +(11.2818 - 15.7437i) q^{68} +(-2.05934 - 20.9089i) q^{69} +(26.8673 + 40.2098i) q^{70} +(-0.933784 + 5.65585i) q^{71} +(31.1906 + 15.3815i) q^{72} +(-34.4364 - 4.53363i) q^{73} +(-27.2956 - 60.2426i) q^{74} +(37.0991 + 37.0991i) q^{75} +(-15.8893 - 5.98031i) q^{76} +(-44.1762 + 36.2545i) q^{77} +(-29.5619 + 55.3064i) q^{78} +(-5.75615 + 8.61469i) q^{79} +(-59.2393 - 55.4837i) q^{80} +(-7.36106 - 27.4718i) q^{81} +(14.2286 + 61.0230i) q^{82} +(-3.07473 - 93.9232i) q^{83} +(1.77213 - 7.60026i) q^{84} +(-148.760 - 29.5903i) q^{85} +(-20.7167 - 23.6229i) q^{86} +(-68.0530 + 48.7661i) q^{87} +(76.2261 - 99.3398i) q^{88} +(-25.3195 - 127.290i) q^{89} +(1.62131 - 49.5259i) q^{90} +(-60.6545 - 16.2523i) q^{91} +(-7.12234 + 4.42896i) q^{92} +(8.06142 + 61.2325i) q^{93} +(126.050 + 42.7882i) q^{94} +(8.69531 + 132.665i) q^{95} +31.0873i q^{96} +(-74.1601 + 62.5243i) q^{97} +59.0979 q^{98} +(58.4321 - 3.82984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) $ 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{31}{96}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.75983	+	0.115345i	−0.879915	+	0.0576727i	−0.498661	−	0.866797i	$-0.666175\pi$
$2$	−1.75983	+	0.115345i	−0.879915	+	0.0576727i	−0.381255	+	0.924470i	$0.624508\pi$
$3$	0.716397	−	2.11044i	0.238799	−	0.703480i	−0.759779	−	0.650181i	$-0.774693\pi$
$3$	0.716397	−	2.11044i	0.238799	−	0.703480i	0.998579	−	0.0532988i	$-0.0169736\pi$
$4$	−0.882081	+	0.116128i	−0.220520	+	0.0290320i
$5$	3.67912	+	5.91650i	0.735824	+	1.18330i	0.977087	+	0.212841i	$0.0682717\pi$
$5$	3.67912	+	5.91650i	0.735824	+	1.18330i	−0.241263	+	0.970460i	$0.577562\pi$
$6$	−1.01731	+	3.79665i	−0.169551	+	0.632775i
$7$	−3.93366	−	0.128775i	−0.561952	−	0.0183964i	−0.249576	−	0.968355i	$-0.580291\pi$
$7$	−3.93366	−	0.128775i	−0.561952	−	0.0183964i	−0.312376	+	0.949959i	$0.601125\pi$
$8$	8.45779	−	1.68236i	1.05722	−	0.210295i
$9$	3.19945	+	2.45503i	0.355495	+	0.272781i
$10$	−7.15707	−	9.98768i	−0.715707	−	0.998768i
$11$	10.9169	−	9.57385i	0.992444	−	0.870350i	0.000884473	−	1.00000i	$-0.499718\pi$
$11$	10.9169	−	9.57385i	0.992444	−	0.870350i	0.991560	+	0.129649i	$0.0413851\pi$
$12$	−0.386839	+	1.94477i	−0.0322366	+	0.162064i
$13$	15.5379	+	3.62294i	1.19523	+	0.278688i	0.776909	−	0.629613i	$-0.216787\pi$
$13$	15.5379	+	3.62294i	1.19523	+	0.278688i	0.418317	+	0.908301i	$0.362620\pi$
$14$	6.93744	−	0.227108i	0.495531	−	0.0162220i
$15$	15.1221	−	3.52599i	1.00814	−	0.235066i
$16$	−11.2527	+	3.01516i	−0.703295	+	0.188447i
$17$	−14.8818	+	15.8892i	−0.875402	+	0.934657i	−0.998331	−	0.0577587i	$-0.981605\pi$
$17$	−14.8818	+	15.8892i	−0.875402	+	0.934657i	0.122929	+	0.992415i	$0.460771\pi$
$18$	−5.91367	−	3.95139i	−0.328537	−	0.219522i
$19$	16.8292	+	8.99537i	0.885745	+	0.473441i	0.850522	−	0.525939i	$-0.176286\pi$
$19$	16.8292	+	8.99537i	0.885745	+	0.473441i	0.0352228	+	0.999379i	$0.488786\pi$
$20$	−3.93235	−	4.79158i	−0.196618	−	0.239579i
$21$	−3.08984	+	8.20950i	−0.147135	+	0.390929i
$22$	−18.1076	+	18.1076i	−0.823072	+	0.823072i
$23$	8.58669	−	3.89058i	0.373334	−	0.169156i	−0.217281	−	0.976109i	$-0.569719\pi$
$23$	8.58669	−	3.89058i	0.373334	−	0.169156i	0.590615	+	0.806954i	$0.298885\pi$
$24$	2.50862	−	19.0549i	0.104526	−	0.793954i
$25$	−10.4119	+	21.1132i	−0.416476	+	0.844529i
$26$	−27.7620	−	4.58353i	−1.06777	−	0.176290i
$27$	24.1513	−	16.1374i	0.894491	−	0.597680i
$28$	3.48476	−	0.343219i	0.124456	−	0.0122578i
$29$	−30.5346	−	21.8808i	−1.05292	−	0.754510i	−0.0826579	−	0.996578i	$-0.526341\pi$
$29$	−30.5346	−	21.8808i	−1.05292	−	0.754510i	−0.970259	+	0.242068i	$0.922174\pi$
$30$	−26.2057	+	7.94941i	−0.873523	+	0.264980i
$31$	−24.8536	+	12.2564i	−0.801730	+	0.395369i	−0.796516	−	0.604617i	$-0.793326\pi$
$31$	−24.8536	+	12.2564i	−0.801730	+	0.395369i	−0.00521344	+	0.999986i	$0.501659\pi$
$32$	−13.2083	+	4.48360i	−0.412759	+	0.140113i
$33$	−12.3842	−	29.8981i	−0.375279	−	0.906003i
$34$	24.3568	−	29.6788i	0.716375	−	0.872905i
$35$	−13.7105	−	23.7473i	−0.391729	−	0.678495i
$36$	−3.10727	−	1.79398i	−0.0863131	−	0.0498329i
$37$	13.2099	+	35.0979i	0.357025	+	0.948592i	0.985335	+	0.170629i	$0.0545800\pi$
$37$	13.2099	+	35.0979i	0.357025	+	0.948592i	−0.628311	+	0.777962i	$0.716253\pi$
$38$	−30.6540	−	13.8892i	−0.806685	−	0.365504i
$39$	18.7773	−	30.1964i	0.481470	−	0.774267i
$40$	41.0709	+	43.8510i	1.02677	+	1.09627i
$41$	−5.78758	−	35.0549i	−0.141160	−	0.854997i	−0.959799	−	0.280688i	$-0.909438\pi$
$41$	−5.78758	−	35.0549i	−0.141160	−	0.854997i	0.818639	−	0.574309i	$-0.194729\pi$
$42$	4.49066	−	14.8037i	0.106921	−	0.352470i
$43$	10.8456	+	14.1342i	0.252223	+	0.328703i	0.902255	−	0.431204i	$-0.141911\pi$
$43$	10.8456	+	14.1342i	0.252223	+	0.328703i	−0.650032	+	0.759907i	$0.725244\pi$
$44$	−8.51778	+	9.71267i	−0.193586	+	0.220742i
$45$	−2.75401	+	27.9619i	−0.0612002	+	0.621376i
$46$	−14.6624	+	7.83719i	−0.318747	+	0.170374i
$47$	−69.7330	−	28.8844i	−1.48368	−	0.614561i	−0.513750	−	0.857940i	$-0.671744\pi$
$47$	−69.7330	−	28.8844i	−1.48368	−	0.614561i	−0.969931	+	0.243379i	$0.921744\pi$
$48$	−1.69812	+	25.9082i	−0.0353774	+	0.539755i
$49$	−33.4380	−	2.19164i	−0.682407	−	0.0447273i
$50$	15.8879	−	38.3567i	0.317757	−	0.767134i
$51$	22.8718	+	42.7901i	0.448467	+	0.839022i
$52$	−14.1264	−	1.39133i	−0.271662	−	0.0267564i
$53$	66.8519	+	58.6275i	1.26136	+	1.10618i	0.989605	+	0.143812i	$0.0459361\pi$
$53$	66.8519	+	58.6275i	1.26136	+	1.10618i	0.271751	+	0.962368i	$0.412397\pi$
$54$	−40.6407	+	31.1847i	−0.752606	+	0.577495i
$55$	96.8083	+	29.3665i	1.76015	+	0.533936i
$56$	−33.4868	+	5.52869i	−0.597978	+	0.0987266i
$57$	31.0406	−	29.0727i	0.544571	−	0.510047i
$58$	56.2596	+	34.9844i	0.969992	+	0.603180i
$59$	16.7129	−	36.8862i	0.283270	−	0.625189i	−0.713910	−	0.700237i	$-0.753078\pi$
$59$	16.7129	−	36.8862i	0.283270	−	0.625189i	0.997180	+	0.0750478i	$0.0239109\pi$
$60$	−12.9295	+	4.86631i	−0.215491	+	0.0811052i
$61$	43.1302	−	74.7038i	0.707053	−	1.22465i	−0.258892	−	0.965906i	$-0.583357\pi$
$61$	43.1302	−	74.7038i	0.707053	−	1.22465i	0.965945	−	0.258746i	$-0.0833092\pi$
$62$	42.3244	−	24.4360i	0.682652	−	0.394129i
$63$	−12.2694	−	10.0693i	−0.194753	−	0.159830i
$64$	65.7788	−	27.2465i	1.02779	−	0.425726i
$65$	35.7308	+	105.260i	0.549705	+	1.61938i
$66$	25.2427	+	51.1871i	0.382465	+	0.775563i
$67$	−8.56757	−	28.2435i	−0.127874	−	0.421545i	0.869503	−	0.493928i	$-0.164439\pi$
$67$	−8.56757	−	28.2435i	−0.127874	−	0.421545i	−0.997377	+	0.0723834i	$0.976939\pi$
$68$	11.2818	−	15.7437i	0.165909	−	0.231525i
$69$	−2.05934	−	20.9089i	−0.0298456	−	0.303027i
$70$	26.8673	+	40.2098i	0.383819	+	0.574426i
$71$	−0.933784	+	5.65585i	−0.0131519	+	0.0796598i	−0.992415	−	0.122933i	$-0.960770\pi$
$71$	−0.933784	+	5.65585i	−0.0131519	+	0.0796598i	0.979263	+	0.202593i	$0.0649367\pi$
$72$	31.1906	+	15.3815i	0.433202	+	0.213632i
$73$	−34.4364	−	4.53363i	−0.471731	−	0.0621046i	−0.109087	−	0.994032i	$-0.534793\pi$
$73$	−34.4364	−	4.53363i	−0.471731	−	0.0621046i	−0.362644	+	0.931928i	$0.618126\pi$
$74$	−27.2956	−	60.2426i	−0.368859	−	0.814090i
$75$	37.0991	+	37.0991i	0.494655	+	0.494655i
$76$	−15.8893	−	5.98031i	−0.209070	−	0.0786882i
$77$	−44.1762	+	36.2545i	−0.573717	+	0.470838i
$78$	−29.5619	+	55.3064i	−0.378999	+	0.709057i
$79$	−5.75615	+	8.61469i	−0.0728627	+	0.109047i	−0.866111	−	0.499851i	$-0.833388\pi$
$79$	−5.75615	+	8.61469i	−0.0728627	+	0.109047i	0.793249	+	0.608898i	$0.208388\pi$
$80$	−59.2393	−	55.4837i	−0.740492	−	0.693546i
$81$	−7.36106	−	27.4718i	−0.0908773	−	0.339159i
$82$	14.2286	+	61.0230i	0.173519	+	0.744183i
$83$	−3.07473	−	93.9232i	−0.0370449	−	1.13160i	−0.842414	−	0.538831i	$-0.818866\pi$
$83$	−3.07473	−	93.9232i	−0.0370449	−	1.13160i	0.805369	−	0.592774i	$-0.201967\pi$
$84$	1.77213	−	7.60026i	0.0210968	−	0.0904793i
$85$	−148.760	−	29.5903i	−1.75012	−	0.348121i
$86$	−20.7167	−	23.6229i	−0.240892	−	0.274685i
$87$	−68.0530	+	48.7661i	−0.782218	+	0.560529i
$88$	76.2261	−	99.3398i	0.866206	−	1.12886i
$89$	−25.3195	−	127.290i	−0.284488	−	1.43022i	−0.813480	−	0.581593i	$-0.802430\pi$
$89$	−25.3195	−	127.290i	−0.284488	−	1.43022i	0.528992	−	0.848627i	$-0.322570\pi$
$90$	1.62131	−	49.5259i	0.0180146	−	0.550288i
$91$	−60.6545	−	16.2523i	−0.666533	−	0.178597i
$92$	−7.12234	+	4.42896i	−0.0774168	+	0.0481408i
$93$	8.06142	+	61.2325i	0.0866819	+	0.658414i
$94$	126.050	+	42.7882i	1.34096	+	0.455194i
$95$	8.69531	+	132.665i	0.0915296	+	1.39647i
$96$			31.0873i			0.323826i
$97$	−74.1601	+	62.5243i	−0.764537	+	0.644580i
$97$	−74.1601	+	62.5243i	−0.764537	+	0.644580i
$98$	59.0979			0.603040
$99$	58.4321	−	3.82984i	0.590224	−	0.0386853i
$100$	6.73229	−	19.8327i	0.0673229	−	0.198327i
$101$	84.3378	−	11.1033i	0.835027	−	0.109933i	0.299125	−	0.954214i	$-0.403305\pi$
$101$	84.3378	−	11.1033i	0.835027	−	0.109933i	0.535902	+	0.844280i	$0.319972\pi$
$102$	−45.1862	−	72.6652i	−0.443001	−	0.712404i
$103$	−45.7948	+	170.909i	−0.444610	+	1.65931i	0.272354	+	0.962197i	$0.412198\pi$
$103$	−45.7948	+	170.909i	−0.444610	+	1.65931i	−0.716964	+	0.697110i	$0.754469\pi$
$104$	137.512	+	4.50167i	1.32223	+	0.0432853i
$105$	−59.9395	+	11.9227i	−0.570852	+	0.113550i
$106$	−124.410	−	95.4635i	−1.17368	−	0.900599i
$107$	−87.8693	−	122.622i	−0.821209	−	1.14600i	−0.987140	−	0.159858i	$-0.948896\pi$
$107$	−87.8693	−	122.622i	−0.821209	−	1.14600i	0.165931	−	0.986137i	$-0.446937\pi$
$108$	−19.4294	+	17.0391i	−0.179901	+	0.157769i
$109$	5.93641	−	29.8444i	0.0544625	−	0.273801i	−0.943953	−	0.330081i	$-0.892924\pi$
$109$	5.93641	−	29.8444i	0.0544625	−	0.273801i	0.998415	+	0.0562797i	$0.0179239\pi$
$110$	−173.753	−	40.5136i	−1.57958	−	0.368306i
$111$	83.5355	−	2.73467i	0.752572	−	0.0246367i
$112$	44.6527	−	10.4116i	0.398685	−	0.0929603i
$113$	−133.490	+	35.7685i	−1.18133	+	0.316535i	−0.795452	−	0.606016i	$-0.792767\pi$
$113$	−133.490	+	35.7685i	−1.18133	+	0.316535i	−0.385874	+	0.922552i	$0.626100\pi$
$114$	−51.2727	+	54.7433i	−0.449761	+	0.480205i
$115$	54.6101	+	36.4893i	0.474870	+	0.317298i
$116$	29.4749	+	15.7547i	0.254094	+	0.135816i
$117$	40.8185	+	49.7375i	0.348876	+	0.425107i
$118$	−25.1572	+	66.8412i	−0.213197	+	0.566451i
$119$	60.5862	−	60.5862i	0.509128	−	0.509128i
$120$	121.968	−	55.2629i	1.01640	−	0.460525i
$121$	11.7261	−	89.0686i	0.0969099	−	0.736104i
$122$	−67.2852	+	136.441i	−0.551518	+	1.11837i
$123$	−78.1273	−	12.8989i	−0.635182	−	0.104869i
$124$	20.4996	−	13.6974i	0.165319	−	0.110463i
$125$	10.1165	−	0.996385i	0.0809317	−	0.00797108i
$126$	22.7536	+	16.3050i	0.180584	+	0.129405i
$127$	10.4174	−	3.16008i	0.0820266	−	0.0248825i	−0.249005	−	0.968502i	$-0.580103\pi$
$127$	10.4174	−	3.16008i	0.0820266	−	0.0248825i	0.331031	+	0.943620i	$0.392603\pi$
$128$	−62.5765	+	30.8593i	−0.488879	+	0.241089i
$129$	37.5992	−	12.7632i	0.291467	−	0.0989396i
$130$	−75.0213	−	181.118i	−0.577087	−	1.39321i
$131$	20.8815	−	25.4442i	0.159401	−	0.194230i	−0.687185	−	0.726482i	$-0.741154\pi$
$131$	20.8815	−	25.4442i	0.159401	−	0.194230i	0.846586	+	0.532252i	$0.178654\pi$
$132$	14.3959	+	24.9344i	0.109060	+	0.188897i
$133$	−65.0419	−	37.5520i	−0.489037	−	0.282345i
$134$	18.3352	+	48.7156i	0.136830	+	0.363549i
$135$	184.332	+	83.5198i	1.36542	+	0.618665i
$136$	−99.1361	+	159.424i	−0.728942	+	1.17223i
$137$	−75.7106	−	80.8354i	−0.552632	−	0.590039i	0.391265	−	0.920278i	$-0.372037\pi$
$137$	−75.7106	−	80.8354i	−0.552632	−	0.590039i	−0.943897	+	0.330239i	$0.892871\pi$
$138$	6.03584	+	36.5585i	0.0437380	+	0.264917i
$139$	2.41685	−	7.96729i	0.0173874	−	0.0573187i	−0.947817	−	0.318814i	$-0.896716\pi$
$139$	2.41685	−	7.96729i	0.0173874	−	0.0573187i	0.965205	+	0.261495i	$0.0842155\pi$
$140$	14.8515	+	19.3549i	0.106082	+	0.138249i
$141$	−110.915	+	126.475i	−0.786633	+	0.896983i
$142$	0.990926	−	10.0610i	0.00697835	−	0.0708524i
$143$	204.311	−	109.207i	1.42875	−	0.763684i
$144$	−43.4049	−	17.9789i	−0.301423	−	0.124853i
$145$	17.1173	−	261.160i	0.118051	−	1.80110i
$146$	61.1251	+	4.00635i	0.418665	+	0.0274408i
$147$	−28.5802	+	68.9987i	−0.194423	+	0.469379i
$148$	−15.7281	−	29.4251i	−0.106271	−	0.198818i
$149$	31.7108	+	3.12324i	0.212824	+	0.0209613i	0.203867	−	0.978999i	$-0.434649\pi$
$149$	31.7108	+	3.12324i	0.212824	+	0.0209613i	0.00895676	+	0.999960i	$0.497149\pi$
$150$	−69.5674	−	61.0090i	−0.463783	−	0.406727i
$151$	−117.490	+	90.1533i	−0.778080	+	0.597042i	−0.919583	−	0.392896i	$-0.871473\pi$
$151$	−117.490	+	90.1533i	−0.778080	+	0.597042i	0.141503	+	0.989938i	$0.454807\pi$
$152$	157.471	+	47.7683i	1.03599	+	0.314265i
$153$	−86.6220	+	14.3014i	−0.566157	+	0.0934729i
$154$	73.5609	−	68.8973i	0.477668	−	0.447385i
$155$	−163.955	−	101.954i	−1.05777	−	0.657765i
$156$	−13.0565	+	28.8162i	−0.0836953	+	0.184720i
$157$	33.8169	−	12.7278i	0.215394	−	0.0810687i	−0.242213	−	0.970223i	$-0.577873\pi$
$157$	33.8169	−	12.7278i	0.215394	−	0.0810687i	0.457607	+	0.889154i	$0.348707\pi$
$158$	9.13619	−	15.8243i	0.0578240	−	0.100154i
$159$	171.622	−	99.0862i	1.07939	−	0.623184i
$160$	−75.1221	−	61.6511i	−0.469513	−	0.385319i
$161$	−34.2781	+	14.1985i	−0.212908	+	0.0881893i
$162$	16.1230	+	47.4967i	0.0995245	+	0.293190i
$163$	26.0145	+	52.7522i	0.159598	+	0.323633i	0.961953	−	0.273214i	$-0.0880866\pi$
$163$	26.0145	+	52.7522i	0.159598	+	0.323633i	−0.802355	+	0.596847i	$0.796420\pi$
$164$	9.17597	+	30.2491i	0.0559510	+	0.184446i
$165$	131.329	−	183.270i	0.795936	−	1.11073i
$166$	16.2446	+	164.934i	0.0978590	+	0.993580i
$167$	82.7739	+	123.880i	0.495652	+	0.741795i	0.991988	−	0.126335i	$-0.0403215\pi$
$167$	82.7739	+	123.880i	0.495652	+	0.741795i	−0.496336	+	0.868131i	$0.665322\pi$
$168$	−12.3219	+	74.6325i	−0.0733445	+	0.444241i
$169$	76.7304	+	37.8393i	0.454026	+	0.223901i
$170$	265.206	+	34.9150i	1.56004	+	0.205383i
$171$	31.7602	+	70.0963i	0.185732	+	0.409920i
$172$	−11.2081	−	11.2081i	−0.0651632	−	0.0651632i
$173$	−256.052	−	96.3711i	−1.48007	−	0.557058i	−0.524392	−	0.851477i	$-0.675707\pi$
$173$	−256.052	−	96.3711i	−1.48007	−	0.557058i	−0.955676	+	0.294419i	$0.904874\pi$
$174$	114.137	−	93.6696i	0.655958	−	0.538331i
$175$	43.6758	−	81.7116i	0.249576	−	0.466923i
$176$	−93.9781	+	140.648i	−0.533966	+	0.799137i
$177$	−65.8729	−	61.6967i	−0.372163	−	0.348569i
$178$	59.2402	+	221.088i	0.332810	+	1.24206i
$179$	24.1533	+	103.588i	0.134935	+	0.578704i	0.997366	+	0.0725300i	$0.0231073\pi$
$179$	24.1533	+	103.588i	0.134935	+	0.578704i	−0.862431	+	0.506174i	$0.831059\pi$
$180$	−0.817907	−	24.9845i	−0.00454393	−	0.138803i
$181$	−10.1592	+	43.5703i	−0.0561280	+	0.240720i	−0.994475	−	0.104975i	$-0.966524\pi$
$181$	−10.1592	+	43.5703i	−0.0561280	+	0.240720i	0.938347	+	0.345695i	$0.112357\pi$
$182$	108.616	+	21.6051i	0.596793	+	0.118709i
$183$	−126.759	−	144.541i	−0.692674	−	0.789843i
$184$	66.0791	−	47.3516i	0.359125	−	0.257346i
$185$	−159.056	+	207.286i	−0.859762	+	1.12046i
$186$	−21.2496	−	106.829i	−0.114245	−	0.574350i
$187$	−10.3427	+	315.937i	−0.0553085	+	1.68950i
$188$	64.8644	+	17.3804i	0.345024	+	0.0924488i
$189$	−97.0810	+	60.3689i	−0.513656	+	0.319412i
$190$	−30.6046	−	232.465i	−0.161077	−	1.22350i
$191$	116.321	+	39.4858i	0.609013	+	0.206732i	0.608873	−	0.793268i	$-0.291622\pi$
$191$	116.321	+	39.4858i	0.609013	+	0.206732i	0.000140222		1.00000i	$0.499955\pi$
$192$	−10.3782	−	158.341i	−0.0540533	−	0.824695i
$193$			84.6309i			0.438502i	0.975668	+	0.219251i	$0.0703613\pi$
$193$			84.6309i			0.438502i	−0.975668	+	0.219251i	$0.929639\pi$
$194$	123.297	−	118.586i	0.635553	−	0.611269i
$195$	247.741			1.27047
$196$	29.7495	−	1.94988i	0.151783	−	0.00994839i
$197$	−110.187	+	324.602i	−0.559327	+	1.64772i	0.187165	+	0.982329i	$0.440070\pi$
$197$	−110.187	+	324.602i	−0.559327	+	1.64772i	−0.746492	+	0.665395i	$0.768263\pi$
$198$	−102.389	+	13.4798i	−0.517116	+	0.0680796i
$199$	−188.543	−	303.202i	−0.947453	−	1.52363i	−0.848938	−	0.528493i	$-0.822757\pi$
$199$	−188.543	−	303.202i	−0.947453	−	1.52363i	−0.0985151	−	0.995136i	$-0.531409\pi$
$200$	−52.5416	+	196.088i	−0.262708	+	0.980440i
$201$	−65.7440	−	2.15224i	−0.327085	−	0.0107076i
$202$	−147.139	+	29.2679i	−0.728413	+	0.144890i
$203$	117.295	+	90.0037i	0.577809	+	0.443368i
$204$	−25.1439	−	35.0883i	−0.123254	−	0.172001i
$205$	186.109	−	163.213i	0.907849	−	0.796162i
$206$	60.8776	−	306.052i	0.295522	−	1.48569i
$207$	37.0242	+	8.63282i	0.178861	+	0.0417045i
$208$	−185.768	+	6.08141i	−0.893115	+	0.0292376i
$209$	269.842	−	62.9184i	1.29111	−	0.301045i
$210$	104.108	−	27.8957i	0.495753	−	0.132837i
$211$	151.197	−	161.431i	0.716574	−	0.765078i	−0.263296	−	0.964715i	$-0.584810\pi$
$211$	151.197	−	161.431i	0.716574	−	0.765078i	0.979870	+	0.199637i	$0.0639764\pi$
$212$	−65.7770	−	43.9508i	−0.310269	−	0.207315i
$213$	11.2674	+	6.02253i	0.0528984	+	0.0282748i
$214$	168.779	+	205.658i	0.788687	+	0.961017i
$215$	−43.7231	+	116.170i	−0.203363	+	0.540323i
$216$	177.118	−	177.118i	0.819989	−	0.819989i
$217$	99.3441	−	45.0122i	0.457807	−	0.207430i
$218$	−7.00467	+	53.2058i	−0.0321315	+	0.244063i
$219$	−34.2381	+	69.4280i	−0.156338	+	0.317023i
$220$	−88.8030	−	14.6614i	−0.403650	−	0.0666429i
$221$	−288.798	+	192.969i	−1.30678	+	0.873163i
$222$	−146.693	+	14.4480i	−0.660779	+	0.0650810i
$223$	198.568	+	142.292i	0.890439	+	0.638080i	0.932553	−	0.361033i	$-0.117576\pi$
$223$	198.568	+	142.292i	0.890439	+	0.638080i	−0.0421140	+	0.999113i	$0.513409\pi$
$224$	52.5343	−	15.9361i	0.234528	−	0.0711433i
$225$	−85.1459	+	41.9893i	−0.378426	+	0.186619i
$226$	230.794	−	78.3439i	1.02121	−	0.346655i
$227$	−140.846	−	340.032i	−0.620466	−	1.49794i	−0.851157	−	0.524911i	$-0.824099\pi$
$227$	−140.846	−	340.032i	−0.620466	−	1.49794i	0.230691	−	0.973027i	$-0.425901\pi$
$228$	−24.0041	+	29.2491i	−0.105281	+	0.128286i
$229$	63.0847	+	109.266i	0.275479	+	0.477144i	0.970256	−	0.242082i	$-0.0778302\pi$
$229$	63.0847	+	109.266i	0.275479	+	0.477144i	−0.694777	+	0.719225i	$0.744497\pi$
$230$	−100.313	−	57.9159i	−0.436145	−	0.251808i
$231$	44.8652	+	119.204i	0.194222	+	0.516034i
$232$	−295.067	−	133.693i	−1.27184	−	0.576263i
$233$	−27.3578	+	43.9948i	−0.117415	+	0.188819i	−0.902646	−	0.430385i	$-0.858378\pi$
$233$	−27.3578	+	43.9948i	−0.117415	+	0.188819i	0.785230	+	0.619204i	$0.212545\pi$
$234$	−77.5706	−	82.8213i	−0.331498	−	0.353937i
$235$	−85.6616	−	518.845i	−0.364518	−	2.20785i
$236$	−10.4586	+	34.4774i	−0.0443161	+	0.146091i
$237$	14.0571	+	18.3195i	0.0593126	+	0.0772977i
$238$	−99.6332	+	113.610i	−0.418627	+	0.477352i
$239$	14.2835	−	145.023i	0.0597635	−	0.606789i	−0.917929	−	0.396746i	$-0.870139\pi$
$239$	14.2835	−	145.023i	0.0597635	−	0.606789i	0.977692	−	0.210043i	$-0.0673605\pi$
$240$	−159.534	+	85.2726i	−0.664724	+	0.355303i
$241$	−146.975	−	60.8791i	−0.609855	−	0.252610i	0.0563115	−	0.998413i	$-0.482066\pi$
$241$	−146.975	−	60.8791i	−0.609855	−	0.252610i	−0.666167	+	0.745803i	$0.732066\pi$
$242$	−10.3623	+	158.098i	−0.0428194	+	0.653298i
$243$	197.607	+	12.9519i	0.813199	+	0.0532999i
$244$	−29.3691	+	70.9034i	−0.120365	+	0.290588i
$245$	−110.055	−	205.899i	−0.449206	−	0.840405i
$246$	138.979	+	13.6882i	0.564954	+	0.0556431i
$247$	228.901	+	200.741i	0.926724	+	0.812715i
$248$	−189.587	+	145.475i	−0.764464	+	0.586594i
$249$	−200.422	−	60.7973i	−0.804907	−	0.244166i
$250$	−17.6883	+	2.92036i	−0.0707533	+	0.0116814i
$251$	−228.449	+	213.966i	−0.910156	+	0.852454i	−0.989521	−	0.144392i	$-0.953878\pi$
$251$	−228.449	+	213.966i	−0.910156	+	0.852454i	0.0793647	+	0.996846i	$0.474711\pi$
$252$	11.9919	+	7.45707i	0.0475871	+	0.0295916i
$253$	56.4921	−	124.681i	0.223289	−	0.492809i
$254$	−17.9683	+	6.76280i	−0.0707414	+	0.0266252i
$255$	−169.020	+	292.751i	−0.662823	+	1.14804i
$256$	−140.074	+	80.8717i	−0.547164	+	0.315905i
$257$	244.124	+	200.347i	0.949898	+	0.779561i	0.975475	−	0.220112i	$-0.0706423\pi$
$257$	244.124	+	200.347i	0.949898	+	0.779561i	−0.0255769	+	0.999673i	$0.508142\pi$
$258$	−64.6961	+	26.7980i	−0.250760	+	0.103868i
$259$	−47.4436	−	139.764i	−0.183180	−	0.539631i
$260$	−43.7410	−	88.6980i	−0.168235	−	0.341146i
$261$	−43.9761	−	144.970i	−0.168491	−	0.555440i
$262$	−33.8130	+	47.1860i	−0.129057	+	0.180099i
$263$	−31.0592	−	315.349i	−0.118096	−	1.19905i	−0.853381	−	0.521288i	$-0.825452\pi$
$263$	−31.0592	−	315.349i	−0.118096	−	1.19905i	0.735285	−	0.677758i	$-0.237048\pi$
$264$	−155.042	−	232.037i	−0.587282	−	0.878930i
$265$	−100.914	+	611.227i	−0.380808	+	2.30652i
$266$	118.794	+	58.5828i	0.446595	+	0.220236i
$267$	−286.776	−	37.7547i	−1.07407	−	0.141403i
$268$	10.8372	+	23.9181i	0.0404371	+	0.0892467i
$269$	−322.925	−	322.925i	−1.20047	−	1.20047i	−0.974025	−	0.226441i	$-0.927291\pi$
$269$	−322.925	−	322.925i	−1.20047	−	1.20047i	−0.226441	−	0.974025i	$-0.572709\pi$
$270$	−334.027	−	125.719i	−1.23714	−	0.465625i
$271$	112.205	−	92.0842i	0.414041	−	0.339794i	−0.404200	−	0.914671i	$-0.632450\pi$
$271$	112.205	−	92.0842i	0.414041	−	0.339794i	0.818240	+	0.574877i	$0.194950\pi$
$272$	119.553	−	223.668i	0.439532	−	0.822307i
$273$	−77.7523	+	116.364i	−0.284807	+	0.426244i
$274$	142.562	+	133.524i	0.520299	+	0.487313i
$275$	88.4695	+	330.173i	0.321707	+	1.20063i
$276$	4.24462	+	18.2042i	0.0153790	+	0.0659571i
$277$	4.65748	+	142.271i	0.0168140	+	0.513614i	0.974316	+	0.225187i	$0.0722992\pi$
$277$	4.65748	+	142.271i	0.0168140	+	0.513614i	−0.957502	+	0.288428i	$0.906867\pi$
$278$	−3.33426	+	14.2999i	−0.0119937	+	0.0514383i
$279$	−109.608	−	21.8024i	−0.392860	−	0.0781447i
$280$	−155.912	−	177.784i	−0.556830	−	0.634943i
$281$	415.153	−	297.494i	1.47741	−	1.05870i	0.495664	−	0.868514i	$-0.334925\pi$
$281$	415.153	−	297.494i	1.47741	−	1.05870i	0.981748	−	0.190184i	$-0.0609086\pi$
$282$	180.604	−	235.367i	0.640439	−	0.834636i
$283$	−29.1355	−	146.474i	−0.102952	−	0.517577i	−0.997504	−	0.0706117i	$-0.977505\pi$
$283$	−29.1355	−	146.474i	−0.102952	−	0.517577i	0.894551	−	0.446965i	$-0.147495\pi$
$284$	0.166870	−	5.09735i	0.000587570	−	0.0179484i
$285$	286.210	+	76.6898i	1.00425	+	0.269087i
$286$	−346.957	+	215.752i	−1.21314	+	0.754377i
$287$	18.2522	+	138.639i	0.0635966	+	0.483064i
$288$	−53.2666	−	18.0816i	−0.184954	−	0.0627833i
$289$	−12.0953	−	184.538i	−0.0418522	−	0.638541i
$290$			461.572i			1.59163i
$291$	78.8255	+	201.303i	0.270878	+	0.691761i
$292$	30.9021			0.105829
$293$	121.314	−	7.95131i	0.414040	−	0.0271376i	0.143040	−	0.989717i	$-0.454312\pi$
$293$	121.314	−	7.95131i	0.414040	−	0.0271376i	0.271000	+	0.962579i	$0.412646\pi$
$294$	42.3376	−	124.723i	0.144005	−	0.424226i
$295$	279.726	−	36.8266i	0.948224	−	0.124836i
$296$	170.774	+	274.627i	0.576939	+	0.927794i
$297$	109.160	−	407.390i	0.367542	−	1.37168i
$298$	−56.1658	−	1.83868i	−0.188476	−	0.00617006i
$299$	147.515	−	29.3425i	0.493360	−	0.0981355i
$300$	−37.0327	−	28.4162i	−0.123442	−	0.0947206i
$301$	−40.8428	−	56.9960i	−0.135690	−	0.189355i
$302$	196.364	−	172.206i	0.650211	−	0.570220i
$303$	36.9866	−	185.944i	0.122068	−	0.613677i
$304$	−216.496	−	50.4799i	−0.712159	−	0.166052i
$305$	600.667	−	19.6638i	1.96940	−	0.0644714i
$306$	150.790	−	35.1594i	0.492779	−	0.114900i
$307$	−182.145	+	48.8057i	−0.593307	+	0.158976i	−0.542964	−	0.839756i	$-0.682698\pi$
$307$	−182.145	+	48.8057i	−0.593307	+	0.158976i	−0.0503430	+	0.998732i	$0.516031\pi$
$308$	34.7568	−	37.1095i	0.112847	−	0.120485i
$309$	327.885	+	219.086i	1.06112	+	0.709015i
$310$	300.293	+	160.510i	0.968686	+	0.517773i
$311$	−178.822	−	217.895i	−0.574989	−	0.700626i	0.401581	−	0.915823i	$-0.368461\pi$
$311$	−178.822	−	217.895i	−0.574989	−	0.700626i	−0.976571	+	0.215197i	$0.930961\pi$
$312$	108.014	−	286.985i	0.346197	−	0.919825i
$313$	178.847	−	178.847i	0.571396	−	0.571396i	−0.361122	−	0.932518i	$-0.617606\pi$
$313$	178.847	−	178.847i	0.571396	−	0.571396i	0.932518	+	0.361122i	$0.117606\pi$
$314$	−58.0439	+	26.2994i	−0.184853	+	0.0837560i
$315$	14.4341	−	109.638i	0.0458227	−	0.348058i
$316$	4.07698	−	8.26730i	0.0129018	−	0.0261623i
$317$	367.946	+	60.7481i	1.16071	+	0.191634i	0.712091	−	0.702088i	$-0.247748\pi$
$317$	367.946	+	60.7481i	1.16071	+	0.191634i	0.448621	+	0.893722i	$0.351915\pi$
$318$	−290.597	+	194.171i	−0.913827	+	0.610600i
$319$	−542.826	+	53.4637i	−1.70165	+	0.167598i
$320$	403.212	+	288.937i	1.26004	+	0.902929i
$321$	−321.735	+	97.5971i	−1.00229	+	0.304041i
$322$	58.6860	−	28.9407i	0.182255	−	0.0898781i
$323$	−393.378	+	133.534i	−1.21789	+	0.413417i
$324$	9.68330	+	23.3776i	0.0298867	+	0.0721529i
$325$	−238.271	+	290.335i	−0.733143	+	0.893337i
$326$	−51.8658	−	89.8343i	−0.159098	−	0.275565i
$327$	−58.7319	−	33.9089i	−0.179608	−	0.103697i
$328$	−107.925	−	286.750i	−0.329040	−	0.874238i
$329$	270.587	+	122.601i	0.822452	+	0.372648i
$330$	−209.978	+	337.672i	−0.636297	+	1.02325i
$331$	184.769	+	197.276i	0.558214	+	0.595999i	0.945364	−	0.326018i	$-0.105707\pi$
$331$	184.769	+	197.276i	0.558214	+	0.595999i	−0.387149	+	0.922017i	$0.626540\pi$
$332$	13.6193	+	82.4907i	0.0410219	+	0.248466i
$333$	−43.9018	+	144.725i	−0.131837	+	0.434609i
$334$	−159.957	−	208.460i	−0.478913	−	0.624132i
$335$	135.582	−	154.601i	0.404722	−	0.461497i
$336$	10.0161	−	101.696i	0.0298100	−	0.302666i
$337$	345.282	−	184.557i	1.02457	−	0.547646i	0.128574	−	0.991700i	$-0.458960\pi$
$337$	345.282	−	184.557i	1.02457	−	0.547646i	0.896000	+	0.444053i	$0.146460\pi$
$338$	−139.397	−	57.7402i	−0.412418	−	0.170829i
$339$	−20.1446	+	307.347i	−0.0594235	+	0.906627i
$340$	134.655	+	8.82575i	0.396044	+	0.0259581i
$341$	−153.983	+	371.747i	−0.451562	+	1.09017i
$342$	−63.9779	−	119.694i	−0.187070	−	0.349983i
$343$	323.176	+	31.8300i	0.942203	+	0.0927989i
$344$	115.509	+	101.298i	0.335781	+	0.294472i
$345$	116.131	−	89.1104i	0.336611	−	0.258291i
$346$	461.724	+	140.062i	1.33446	+	0.404804i
$347$	322.665	−	53.2721i	0.929869	−	0.153522i	0.321259	−	0.946991i	$-0.395894\pi$
$347$	322.665	−	53.2721i	0.929869	−	0.153522i	0.608610	+	0.793469i	$0.291727\pi$
$348$	54.3651	−	50.9185i	0.156221	−	0.146317i
$349$	456.742	+	284.021i	1.30872	+	0.813813i	0.990934	−	0.134351i	$-0.0428949\pi$
$349$	456.742	+	284.021i	1.30872	+	0.813813i	0.317783	+	0.948163i	$0.397062\pi$
$350$	−67.4369	+	148.836i	−0.192677	+	0.425247i
$351$	433.725	−	163.243i	1.23569	−	0.465079i
$352$	−101.268	+	175.401i	−0.287693	+	0.498299i
$353$	−414.466	+	239.292i	−1.17412	+	0.677881i	−0.954648	−	0.297737i	$-0.903768\pi$
$353$	−414.466	+	239.292i	−1.17412	+	0.677881i	−0.219476	+	0.975618i	$0.570435\pi$
$354$	123.042	+	100.978i	0.347575	+	0.285248i
$355$	−36.8983	+	15.2838i	−0.103939	+	0.0430529i
$356$	37.1157	+	109.339i	0.104258	+	0.307133i
$357$	−84.4597	−	171.267i	−0.236582	−	0.479741i
$358$	−54.4542	−	179.511i	−0.152107	−	0.501428i
$359$	261.138	−	364.417i	0.727403	−	1.01509i	−0.271214	−	0.962519i	$-0.587425\pi$
$359$	261.138	−	364.417i	0.727403	−	1.01509i	0.998617	−	0.0525712i	$-0.0167416\pi$
$360$	23.7492	+	241.129i	0.0659699	+	0.669804i
$361$	1.74302	+	2.60861i	0.00482830	+	0.00722606i
$362$	12.8528	−	77.8482i	0.0355049	−	0.215050i
$363$	−179.573	−	88.5557i	−0.494692	−	0.243955i
$364$	55.3895	+	7.29217i	0.152169	+	0.0200334i
$365$	−99.8722	−	220.423i	−0.273623	−	0.603898i
$366$	239.747	+	239.747i	0.655047	+	0.655047i
$367$	270.022	+	101.629i	0.735755	+	0.276919i	0.691774	−	0.722114i	$-0.256829\pi$
$367$	270.022	+	101.629i	0.735755	+	0.276919i	0.0439807	+	0.999032i	$0.485996\pi$
$368$	−84.8929	+	69.6698i	−0.230687	+	0.189320i
$369$	67.5435	−	126.365i	0.183045	−	0.342453i
$370$	256.002	−	383.134i	0.691898	−	1.03550i
$371$	−255.423	−	239.230i	−0.688472	−	0.644824i
$372$	−14.2216	−	53.0759i	−0.0382302	−	0.142677i
$373$	89.3799	+	383.330i	0.239625	+	1.02769i	0.947096	+	0.320951i	$0.104003\pi$
$373$	89.3799	+	383.330i	0.239625	+	1.02769i	−0.707471	+	0.706742i	$0.750164\pi$
$374$	−18.2404	−	557.188i	−0.0487712	−	1.48981i
$375$	5.14460	−	22.0640i	0.0137189	−	0.0588373i
$376$	−638.382	−	126.982i	−1.69782	−	0.337718i
$377$	−395.172	−	450.607i	−1.04820	−	1.19524i
$378$	163.883	−	117.437i	0.433553	−	0.310679i
$379$	−428.665	+	558.647i	−1.13104	+	1.47400i	−0.271856	+	0.962338i	$0.587638\pi$
$379$	−428.665	+	558.647i	−1.13104	+	1.47400i	−0.859185	+	0.511665i	$0.829029\pi$
$380$	−23.0761	−	116.011i	−0.0607265	−	0.305293i
$381$	0.793834	−	24.2491i	0.00208355	−	0.0636460i
$382$	−209.261	−	56.0712i	−0.547803	−	0.146783i
$383$	−436.057	+	271.158i	−1.13853	+	0.707984i	−0.961114	−	0.276152i	$-0.910941\pi$
$383$	−436.057	+	271.158i	−1.13853	+	0.707984i	−0.177417	+	0.984136i	$0.556774\pi$
$384$	20.2971	+	154.172i	0.0528569	+	0.401488i
$385$	−377.030	−	127.984i	−0.979298	−	0.332427i
$386$	−9.76178	−	148.936i	−0.0252896	−	0.385845i
$387$			71.8480i			0.185654i
$388$	58.1543	−	63.7635i	0.149882	−	0.164339i
$389$	−26.9053			−0.0691653			−0.0345827	−	0.999402i	$-0.511010\pi$
$389$	−26.9053			−0.0691653			−0.0345827	+	0.999402i	$0.511010\pi$
$390$	−435.983	+	28.5758i	−1.11790	+	0.0732713i
$391$	−65.9676	+	194.334i	−0.168715	+	0.497018i
$392$	−286.498	+	37.7182i	−0.730863	+	0.0962200i
$393$	−38.7389	−	62.2973i	−0.0985724	−	0.158517i
$394$	156.470	−	583.953i	0.397131	−	1.48211i
$395$	−72.1464	−	2.36183i	−0.182649	−	0.00597931i
$396$	−51.0971	+	10.1638i	−0.129033	+	0.0256663i
$397$	−233.096	−	178.860i	−0.587142	−	0.450530i	0.271978	−	0.962303i	$-0.412322\pi$
$397$	−233.096	−	178.860i	−0.587142	−	0.450530i	−0.859121	+	0.511773i	$0.828989\pi$
$398$	366.777	+	511.837i	0.921550	+	1.28602i
$399$	−125.847	+	110.365i	−0.315406	+	0.276604i
$400$	53.5025	−	268.975i	0.133756	−	0.672437i
$401$	109.873	+	25.6187i	0.273996	+	0.0638870i	0.361816	−	0.932249i	$-0.382157\pi$
$401$	109.873	+	25.6187i	0.273996	+	0.0638870i	−0.0878201	+	0.996136i	$0.527990\pi$
$402$	115.947	−	3.79570i	0.288424	−	0.00944203i
$403$	−430.578	+	100.397i	−1.06843	+	0.249124i
$404$	−73.1033	+	19.5880i	−0.180949	+	0.0484851i
$405$	135.455	−	144.624i	0.334457	−	0.357096i
$406$	−216.801	−	144.862i	−0.533993	−	0.356803i
$407$	480.233	+	256.690i	1.17993	+	0.630688i
$408$	265.433	+	323.432i	0.650572	+	0.792725i
$409$	63.2667	−	168.096i	0.154686	−	0.410992i	−0.835724	−	0.549150i	$-0.814952\pi$
$409$	63.2667	−	168.096i	0.154686	−	0.410992i	0.990410	+	0.138158i	$0.0441183\pi$
$410$	−308.694	+	308.694i	−0.752913	+	0.752913i
$411$	−224.837	+	101.872i	−0.547049	+	0.247865i
$412$	20.5474	−	156.073i	0.0498724	−	0.378819i
$413$	−70.4930	+	142.946i	−0.170685	+	0.346115i
$414$	−66.1520	−	10.9217i	−0.159787	−	0.0263810i
$415$	544.385	−	363.746i	1.31177	−	0.876497i
$416$	−221.473	+	21.8132i	−0.532387	+	0.0524356i
$417$	−15.0831	−	10.8084i	−0.0361704	−	0.0259193i
$418$	−467.620	+	141.851i	−1.11871	+	0.339356i
$419$	−309.180	+	152.471i	−0.737901	+	0.363892i	−0.772082	−	0.635523i	$-0.780784\pi$
$419$	−309.180	+	152.471i	−0.737901	+	0.363892i	0.0341810	+	0.999416i	$0.489118\pi$
$420$	51.4869	−	17.4774i	0.122588	−	0.0416129i
$421$	−58.0324	−	140.102i	−0.137844	−	0.332785i	0.839850	−	0.542818i	$-0.182643\pi$
$421$	−58.0324	−	140.102i	−0.137844	−	0.332785i	−0.977694	+	0.210033i	$0.932643\pi$
$422$	−247.461	+	301.532i	−0.586400	+	0.714530i
$423$	−152.196	−	263.611i	−0.359801	−	0.623193i
$424$	664.052	+	383.391i	1.56616	+	0.904223i
$425$	−180.524	−	479.640i	−0.424761	−	1.12856i
$426$	−20.5233	−	9.29899i	−0.0481768	−	0.0218286i
$427$	−179.280	+	288.306i	−0.419859	+	0.675189i
$428$	91.7476	+	97.9579i	0.214364	+	0.228874i
$429$	−84.1060	−	509.422i	−0.196051	−	1.18746i
$430$	63.5456	−	209.482i	0.147781	−	0.487167i
$431$	17.8009	+	23.1986i	0.0413014	+	0.0538250i	0.813547	−	0.581499i	$-0.197533\pi$
$431$	17.8009	+	23.1986i	0.0413014	+	0.0538250i	−0.772246	+	0.635324i	$0.780867\pi$
$432$	−223.111	+	254.409i	−0.516460	+	0.588910i
$433$	−17.0805	+	173.421i	−0.0394468	+	0.400510i	0.955105	+	0.296267i	$0.0957419\pi$
$433$	−17.0805	+	173.421i	−0.0394468	+	0.400510i	−0.994552	+	0.104243i	$0.966758\pi$
$434$	−169.637	+	90.6728i	−0.390868	+	0.208924i
$435$	−538.900	−	223.220i	−1.23885	−	0.513148i
$436$	−1.77062	+	27.0145i	−0.00406107	+	0.0619599i
$437$	179.504	+	11.7653i	0.410764	+	0.0269229i
$438$	52.2450	−	126.131i	0.119281	−	0.287970i
$439$	−158.605	−	296.729i	−0.361286	−	0.675919i	0.633954	−	0.773371i	$-0.281431\pi$
$439$	−158.605	−	296.729i	−0.361286	−	0.675919i	−0.995240	+	0.0974516i	$0.968931\pi$
$440$	868.190	+	85.5092i	1.97316	+	0.194339i
$441$	−101.603	−	89.1031i	−0.230391	−	0.202048i
$442$	485.978	−	372.904i	1.09950	−	0.843675i
$443$	−166.198	−	50.4156i	−0.375165	−	0.113805i	0.0970707	−	0.995277i	$-0.469053\pi$
$443$	−166.198	−	50.4156i	−0.375165	−	0.113805i	−0.472235	+	0.881473i	$0.656553\pi$
$444$	−73.3675	+	12.1130i	−0.165242	+	0.0272816i
$445$	659.956	−	618.116i	1.48305	−	1.38902i
$446$	−365.859	−	227.505i	−0.820311	−	0.510102i
$447$	29.3089	−	64.6861i	0.0655680	−	0.144712i
$448$	−262.260	+	98.7078i	−0.585402	+	0.220330i
$449$	−284.947	+	493.543i	−0.634626	+	1.09920i	0.351968	+	0.936012i	$0.385513\pi$
$449$	−284.947	+	493.543i	−0.634626	+	1.09920i	−0.986594	+	0.163193i	$0.947821\pi$
$450$	144.999	−	83.7153i	0.322220	−	0.186034i
$451$	−398.792	−	327.281i	−0.884240	−	0.725677i
$452$	113.595	−	47.0526i	0.251317	−	0.104099i
$453$	106.093	+	312.541i	0.234202	+	0.689936i
$454$	287.086	+	582.153i	0.632348	+	1.28227i
$455$	−126.998	−	418.657i	−0.279117	−	0.920125i
$456$	213.624	−	298.112i	0.468474	−	0.653754i
$457$	38.8554	+	394.505i	0.0850227	+	0.863250i	0.939223	+	0.343307i	$0.111547\pi$
$457$	38.8554	+	394.505i	0.0850227	+	0.863250i	−0.854201	+	0.519944i	$0.825953\pi$
$458$	−123.622	−	185.013i	−0.269916	−	0.403959i
$459$	−103.006	+	623.897i	−0.224413	+	1.35925i
$460$	−52.4079	−	25.8447i	−0.113930	−	0.0561842i
$461$	481.150	+	63.3446i	1.04371	+	0.137407i	0.632836	−	0.774286i	$-0.281891\pi$
$461$	481.150	+	63.3446i	1.04371	+	0.137407i	0.410873	+	0.911693i	$0.365224\pi$
$462$	−92.7047	−	204.604i	−0.200660	−	0.442865i
$463$	−444.818	−	444.818i	−0.960729	−	0.960729i	0.0385280	−	0.999258i	$-0.487733\pi$
$463$	−444.818	−	444.818i	−0.960729	−	0.960729i	−0.999258	+	0.0385280i	$0.987733\pi$
$464$	409.572	+	154.152i	0.882697	+	0.332224i
$465$	−332.624	+	272.977i	−0.715320	+	0.587048i
$466$	43.0704	−	80.5791i	0.0924258	−	0.172916i
$467$	484.656	−	725.339i	1.03781	−	1.55319i	0.221847	−	0.975082i	$-0.428792\pi$
$467$	484.656	−	725.339i	1.03781	−	1.55319i	0.815961	−	0.578107i	$-0.196208\pi$
$468$	−41.7811	−	39.1323i	−0.0892759	−	0.0836160i
$469$	30.0649	+	112.204i	0.0641043	+	0.239240i
$470$	210.596	+	903.198i	0.448077	+	1.92170i
$471$	−2.63486	−	80.4867i	−0.00559419	−	0.170885i
$472$	79.2985	−	340.093i	0.168005	−	0.720535i
$473$	253.719	+	50.4679i	0.536404	+	0.106697i
$474$	−26.8512	−	30.6179i	−0.0566480	−	0.0645947i
$475$	−365.145	+	261.659i	−0.768726	+	0.550861i
$476$	−46.4062	+	60.4777i	−0.0974920	+	0.127054i
$477$	69.9573	+	351.699i	0.146661	+	0.737315i
$478$	−8.40882	+	256.863i	−0.0175917	+	0.537370i
$479$	226.698	+	60.7434i	0.473273	+	0.126813i	0.487568	−	0.873085i	$-0.337884\pi$
$479$	226.698	+	60.7434i	0.473273	+	0.126813i	−0.0142958	+	0.999898i	$0.504551\pi$
$480$	−183.928	+	114.374i	−0.383184	+	0.238279i
$481$	78.0973	+	593.208i	0.162364	+	1.23328i
$482$	265.673	+	90.1839i	0.551190	+	0.187104i
$483$	5.40823	+	82.5137i	0.0111972	+	0.170836i
$484$			79.9274i			0.165139i
$485$	−642.769	−	208.734i	−1.32530	−	0.430380i
$486$	−349.249			−0.718620
$487$	−77.5402	+	5.08225i	−0.159220	+	0.0104358i	−0.144805	−	0.989460i	$-0.546255\pi$
$487$	−77.5402	+	5.08225i	−0.159220	+	0.0104358i	−0.0144154	+	0.999896i	$0.504589\pi$
$488$	239.108	−	704.390i	0.489976	−	1.44342i
$489$	129.967	−	17.1105i	0.265781	−	0.0349908i
$490$	217.428	+	349.653i	0.443731	+	0.713578i
$491$	−93.5565	+	349.158i	−0.190543	+	0.711116i	0.802833	+	0.596204i	$0.203325\pi$
$491$	−93.5565	+	349.158i	−0.190543	+	0.711116i	−0.993376	+	0.114911i	$0.963342\pi$
$492$	70.4125	+	2.30507i	0.143115	+	0.00468510i
$493$	802.078	−	159.543i	1.62693	−	0.323617i
$494$	−425.981	−	326.867i	−0.862310	−	0.661674i
$495$	237.638	+	331.624i	0.480077	+	0.669947i
$496$	242.716	−	212.856i	0.489347	−	0.429145i
$497$	4.40152	−	22.1280i	0.00885619	−	0.0445230i
$498$	359.721	+	83.8752i	0.722332	+	0.168424i
$499$	−137.067	+	4.48711i	−0.274683	+	0.00899220i	−0.169750	−	0.985487i	$-0.554296\pi$
$499$	−137.067	+	4.48711i	−0.274683	+	0.00899220i	−0.104933	+	0.994479i	$0.533463\pi$
$500$	−8.80783	+	2.05370i	−0.0176157	+	0.00410739i
$501$	320.740	−	85.9420i	0.640199	−	0.171541i
$502$	377.352	−	402.894i	0.751697	−	0.802578i
$503$	209.187	+	139.774i	0.415879	+	0.277882i	0.745856	−	0.666108i	$-0.232041\pi$
$503$	209.187	+	139.774i	0.415879	+	0.277882i	−0.329977	+	0.943989i	$0.607041\pi$
$504$	−120.712	−	64.5221i	−0.239509	−	0.128020i
$505$	375.981	+	458.134i	0.744517	+	0.907197i
$506$	−85.0351	+	225.933i	−0.168054	+	0.446508i
$507$	134.827	−	134.827i	0.265931	−	0.265931i
$508$	−8.82199	+	3.99719i	−0.0173661	+	0.00786849i
$509$	−94.6978	+	719.301i	−0.186047	+	1.41317i	0.602465	+	0.798146i	$0.294185\pi$
$509$	−94.6978	+	719.301i	−0.186047	+	1.41317i	−0.788511	+	0.615020i	$0.789148\pi$
$510$	263.679	−	534.688i	0.517018	−	1.04841i
$511$	134.877	+	22.2683i	0.263948	+	0.0435779i
$512$	469.231	−	313.530i	0.916467	−	0.612364i
$513$	551.607	−	54.3285i	1.07526	−	0.105904i
$514$	−452.725	−	324.418i	−0.880789	−	0.631164i
$515$	−1179.67	+	357.848i	−2.29061	+	0.694850i
$516$	−31.6834	+	15.6245i	−0.0614019	+	0.0302800i
$517$	−1037.80	+	352.287i	−2.00736	+	0.681405i
$518$	99.6139	+	240.489i	0.192305	+	0.464265i
$519$	−386.820	+	471.342i	−0.745318	+	0.908173i
$520$	479.288	+	830.151i	0.921708	+	1.59645i
$521$	−788.123	−	455.023i	−1.51271	−	0.873365i	−0.999889	−	0.0148707i	$-0.995266\pi$
$521$	−788.123	−	455.023i	−1.51271	−	0.873365i	−0.512823	−	0.858494i	$-0.671400\pi$
$522$	94.1121	+	250.050i	0.180291	+	0.479023i
$523$	−636.423	−	288.359i	−1.21687	−	0.551356i	−0.301305	−	0.953528i	$-0.597422\pi$
$523$	−636.423	−	288.359i	−1.21687	−	0.551356i	−0.915564	+	0.402171i	$0.868256\pi$
$524$	−15.4644	+	24.8687i	−0.0295122	+	0.0474594i
$525$	−141.158	−	150.713i	−0.268873	−	0.287072i
$526$	91.0330	+	551.379i	0.173067	+	1.04825i
$527$	175.123	−	577.302i	0.332301	−	1.09545i
$528$	229.504	+	299.095i	0.434666	+	0.566468i
$529$	−290.199	+	330.909i	−0.548581	+	0.625537i
$530$	107.089	−	1087.30i	0.202055	−	2.05150i
$531$	144.029	−	76.9849i	0.271240	−	0.144981i
$532$	61.7330	+	25.5707i	0.116040	+	0.0480651i
$533$	37.0746	−	565.648i	0.0695583	−	1.06125i
$534$	509.031	+	33.3637i	0.953242	+	0.0624788i
$535$	402.209	−	971.018i	0.751793	−	1.81499i
$536$	−119.979	−	224.464i	−0.223841	−	0.418776i
$537$	235.920	+	23.2360i	0.439329	+	0.0432701i
$538$	605.542	+	531.046i	1.12554	+	0.987074i
$539$	−386.021	+	296.204i	−0.716180	+	0.549544i
$540$	−172.295	−	52.2650i	−0.319064	−	0.0967871i
$541$	643.925	−	106.312i	1.19025	−	0.196511i	0.465198	−	0.885207i	$-0.345983\pi$
$541$	643.925	−	106.312i	1.19025	−	0.196511i	0.725050	+	0.688696i	$0.241816\pi$
$542$	−186.840	+	174.995i	−0.344724	+	0.322869i
$543$	84.6745	+	52.6540i	0.155938	+	0.0969687i
$544$	125.322	−	276.593i	0.230372	−	0.508442i
$545$	198.415	−	74.6781i	0.364064	−	0.137024i
$546$	123.409	−	213.750i	0.226023	−	0.391484i
$547$	−695.242	+	401.398i	−1.27101	+	0.733818i	−0.975178	−	0.221422i	$-0.928930\pi$
$547$	−695.242	+	401.398i	−1.27101	+	0.733818i	−0.295832	+	0.955240i	$0.595597\pi$
$548$	76.1701	+	62.5112i	0.138997	+	0.114072i
$549$	321.393	−	133.125i	0.585415	−	0.242487i
$550$	−193.775	−	570.844i	−0.352319	−	1.03790i
$551$	−317.046	−	642.905i	−0.575401	−	1.16680i
$552$	−52.5938	−	173.378i	−0.0952786	−	0.314091i
$553$	23.7521	−	33.1460i	0.0429514	−	0.0599386i
$554$	−24.6067	−	249.836i	−0.0444164	−	0.450967i
$555$	323.517	+	484.177i	0.582913	+	0.872391i
$556$	−1.20663	+	7.30846i	−0.00217020	+	0.0131447i
$557$	113.359	+	55.9024i	0.203517	+	0.100363i	0.541191	−	0.840900i	$-0.317974\pi$
$557$	113.359	+	55.9024i	0.203517	+	0.100363i	−0.337674	+	0.941263i	$0.609640\pi$
$558$	195.406	+	25.7257i	0.350190	+	0.0461034i
$559$	117.311	+	258.910i	0.209858	+	0.463166i
$560$	225.883	+	225.883i	0.403362	+	0.403362i
$561$	659.356	+	248.164i	1.17532	+	0.442360i
$562$	−696.284	+	571.426i	−1.23894	+	1.01677i
$563$	458.213	−	857.257i	0.813878	−	1.52266i	−0.0382158	−	0.999270i	$-0.512167\pi$
$563$	458.213	−	857.257i	0.813878	−	1.52266i	0.852094	−	0.523389i	$-0.175333\pi$
$564$	83.1489	−	124.441i	0.147427	−	0.220640i
$565$	−702.750	−	658.197i	−1.24380	−	1.16495i
$566$	68.1687	+	254.409i	0.120439	+	0.449486i
$567$	25.4183	+	109.013i	0.0448294	+	0.192263i
$568$	1.61742	+	49.4070i	0.00284756	+	0.0869841i
$569$	149.932	−	643.021i	0.263500	−	1.13009i	−0.661446	−	0.749993i	$-0.730057\pi$
$569$	149.932	−	643.021i	0.263500	−	1.13009i	0.924946	−	0.380098i	$-0.124110\pi$
$570$	−512.528	−	101.948i	−0.899171	−	0.178856i
$571$	−349.910	−	398.996i	−0.612802	−	0.698767i	0.359327	−	0.933212i	$-0.383006\pi$
$571$	−349.910	−	398.996i	−0.612802	−	0.698767i	−0.972129	+	0.234445i	$0.924673\pi$
$572$	−167.537	+	120.055i	−0.292897	+	0.209887i
$573$	166.665	−	217.202i	0.290864	−	0.379061i
$574$	−48.1122	−	241.876i	−0.0838192	−	0.421388i
$575$	−7.26101	+	221.801i	−0.0126278	+	0.385741i
$576$	277.347	+	74.3149i	0.481505	+	0.129019i
$577$	135.711	−	84.3907i	0.235202	−	0.146258i	−0.405379	−	0.914149i	$-0.632860\pi$
$577$	135.711	−	84.3907i	0.235202	−	0.146258i	0.640581	+	0.767891i	$0.278694\pi$
$578$	42.5713	+	323.361i	0.0736528	+	0.559448i
$579$	178.608	+	60.6293i	0.308477	+	0.104714i
$580$	15.2292	+	232.352i	0.0262572	+	0.400607i
$581$			369.858i			0.636589i
$582$	−161.939	−	345.166i	−0.278246	−	0.593069i
$583$	1291.11			2.21459
$584$	−298.883	+	19.5898i	−0.511786	+	0.0335442i
$585$	−144.096	+	424.493i	−0.246318	+	0.725629i
$586$	−212.574	+	27.9859i	−0.362755	+	0.0477576i
$587$	244.578	+	393.313i	0.416657	+	0.670040i	0.988653	−	0.150217i	$-0.0479972\pi$
$587$	244.578	+	393.313i	0.416657	+	0.670040i	−0.571996	+	0.820257i	$0.693831\pi$
$588$	17.1973	−	64.1814i	0.0292472	−	0.109152i
$589$	−528.517	−	17.3019i	−0.897312	−	0.0293750i
$590$	−488.022	+	97.0737i	−0.827157	+	0.164532i
$591$	606.114	+	465.087i	1.02557	+	0.786950i
$592$	−254.473	−	355.117i	−0.429853	−	0.599860i
$593$	107.576	−	94.3413i	0.181409	−	0.159092i	−0.563825	−	0.825894i	$-0.690671\pi$
$593$	107.576	−	94.3413i	0.181409	−	0.159092i	0.745235	+	0.666802i	$0.232338\pi$
$594$	−145.112	+	729.529i	−0.244297	+	1.22816i
$595$	581.363	+	135.555i	0.977080	+	0.227823i
$596$	−28.3341	+	0.927564i	−0.0475405	+	0.00155632i
$597$	−774.961	+	180.696i	−1.29809	+	0.302673i
$598$	−256.216	+	68.6530i	−0.428456	+	0.114804i
$599$	−378.713	+	404.348i	−0.632242	+	0.675038i	−0.963255	−	0.268588i	$-0.913443\pi$
$599$	−378.713	+	404.348i	−0.632242	+	0.675038i	0.331013	+	0.943626i	$0.392610\pi$
$600$	376.191	+	251.363i	0.626985	+	0.418938i
$601$	−167.743	−	89.6604i	−0.279106	−	0.149185i	0.325905	−	0.945403i	$-0.394331\pi$
$601$	−167.743	−	89.6604i	−0.279106	−	0.149185i	−0.605011	+	0.796217i	$0.706831\pi$
$602$	78.4506	+	95.5923i	0.130317	+	0.158791i
$603$	41.9270	−	111.397i	0.0695307	−	0.184739i
$604$	93.1664	−	93.1664i	0.154249	−	0.154249i
$605$	570.116	−	258.316i	0.942341	−	0.426969i
$606$	−43.6423	+	331.496i	−0.0720170	+	0.547023i
$607$	−366.830	+	743.858i	−0.604333	+	1.22547i	0.352768	+	0.935711i	$0.385241\pi$
$607$	−366.830	+	743.858i	−0.604333	+	1.22547i	−0.957101	+	0.289755i	$0.906426\pi$
$608$	−262.616	−	43.3580i	−0.431934	−	0.0713126i
$609$	273.977	−	183.066i	0.449881	−	0.300601i
$610$	−1054.80	+	103.889i	−1.72919	+	0.170310i
$611$	−978.862	−	701.442i	−1.60206	−	1.14802i
$612$	74.7468	−	22.6742i	0.122135	−	0.0370493i
$613$	615.395	−	303.479i	1.00391	−	0.495072i	0.135422	−	0.990788i	$-0.456761\pi$
$613$	615.395	−	303.479i	1.00391	−	0.495072i	0.868485	+	0.495716i	$0.165094\pi$
$614$	314.915	−	106.899i	0.512892	−	0.174103i
$615$	−211.124	−	509.697i	−0.343290	−	0.828776i
$616$	−312.640	+	380.954i	−0.507533	+	0.618431i
$617$	435.940	+	755.070i	0.706547	+	1.22378i	0.966130	+	0.258055i	$0.0830816\pi$
$617$	435.940	+	755.070i	0.706547	+	1.22378i	−0.259583	+	0.965721i	$0.583585\pi$
$618$	−602.292	−	347.734i	−0.974583	−	0.562676i
$619$	202.707	+	538.579i	0.327475	+	0.870079i	0.992387	+	0.123158i	$0.0393022\pi$
$619$	202.707	+	538.579i	0.327475	+	0.870079i	−0.664912	+	0.746921i	$0.731531\pi$
$620$	156.461	+	70.8916i	0.252356	+	0.114341i
$621$	144.596	−	232.529i	0.232843	−	0.374442i
$622$	339.829	+	362.832i	0.546349	+	0.583331i
$623$	83.2066	+	503.975i	0.133558	+	0.808948i
$624$	−120.249	+	396.409i	−0.192707	+	0.635270i
$625$	401.385	+	523.096i	0.642216	+	0.836953i
$626$	−294.111	+	335.369i	−0.469826	+	0.535734i
$627$	60.5289	−	614.561i	0.0965374	−	0.980160i
$628$	−28.3512	+	15.1540i	−0.0451452	+	0.0241306i
$629$	−754.264	−	312.426i	−1.19915	−	0.496703i
$630$	−12.7554	+	194.609i	−0.0202466	+	0.308904i
$631$	552.342	+	36.2024i	0.875344	+	0.0573730i	0.496448	−	0.868066i	$-0.334637\pi$
$631$	552.342	+	36.2024i	0.875344	+	0.0573730i	0.378895	+	0.925439i	$0.376304\pi$
$632$	−34.1913	+	82.5452i	−0.0541002	+	0.130609i
$633$	−232.374	−	434.741i	−0.367099	−	0.686795i
$634$	−654.529	−	64.4655i	−1.03238	−	0.101681i
$635$	57.0234	+	50.0082i	0.0898006	+	0.0787530i
$636$	−139.878	+	107.332i	−0.219934	+	0.168761i
$637$	−511.617	−	155.197i	−0.803166	−	0.243638i
$638$	949.115	−	156.700i	1.48764	−	0.245611i
$639$	−16.8729	+	15.8032i	−0.0264051	+	0.0247311i
$640$	−412.806	−	256.699i	−0.645009	−	0.401093i
$641$	−171.679	+	378.905i	−0.267831	+	0.591115i	−0.995495	−	0.0948190i	$-0.969773\pi$
$641$	−171.679	+	378.905i	−0.267831	+	0.591115i	0.727664	+	0.685934i	$0.240606\pi$
$642$	554.941	−	208.865i	0.864394	−	0.325335i
$643$	459.708	−	796.237i	0.714942	−	1.23832i	−0.248040	−	0.968750i	$-0.579786\pi$
$643$	459.708	−	796.237i	0.714942	−	1.23832i	0.962982	−	0.269566i	$-0.0868804\pi$
$644$	28.5872	−	16.5049i	0.0443901	−	0.0256287i
$645$	213.846	+	175.499i	0.331543	+	0.272091i
$646$	676.875	−	280.371i	1.04779	−	0.434011i
$647$	−31.4042	−	92.5138i	−0.0485382	−	0.142989i	0.919958	−	0.392016i	$-0.128222\pi$
$647$	−31.4042	−	92.5138i	−0.0485382	−	0.142989i	−0.968496	+	0.249028i	$0.919889\pi$
$648$	−108.476	−	219.967i	−0.167401	−	0.339456i
$649$	−170.690	−	562.689i	−0.263004	−	0.867009i
$650$	385.829	−	538.423i	0.593582	−	0.828343i
$651$	−23.8257	−	241.906i	−0.0365986	−	0.371592i
$652$	−29.0729	−	43.5107i	−0.0445903	−	0.0667342i
$653$	38.5282	−	233.362i	0.0590018	−	0.357369i	−0.940827	−	0.338886i	$-0.889950\pi$
$653$	38.5282	−	233.362i	0.0590018	−	0.357369i	0.999829	−	0.0184825i	$-0.00588350\pi$
$654$	107.269	+	52.8994i	0.164020	+	0.0808859i
$655$	227.366	+	29.9333i	0.347124	+	0.0456997i
$656$	170.822	+	377.012i	0.260399	+	0.574714i
$657$	−99.0473	−	99.0473i	−0.150757	−	0.150757i
$658$	−490.328	−	184.547i	−0.745180	−	0.280466i
$659$	−62.7284	+	51.4799i	−0.0951873	+	0.0781182i	−0.680783	−	0.732485i	$-0.738360\pi$
$659$	−62.7284	+	51.4799i	−0.0951873	+	0.0781182i	0.585596	+	0.810603i	$0.300860\pi$
$660$	−94.5603	+	176.910i	−0.143273	+	0.268045i
$661$	−286.534	+	428.828i	−0.433486	+	0.648757i	−0.982328	−	0.187169i	$-0.940069\pi$
$661$	−286.534	+	428.828i	−0.433486	+	0.648757i	0.548842	+	0.835926i	$0.315069\pi$
$662$	−347.917	−	325.860i	−0.525554	−	0.492235i
$663$	200.355	+	747.734i	0.302194	+	1.12780i
$664$	−184.018	−	789.210i	−0.277136	−	1.18857i
$665$	−17.1206	−	522.979i	−0.0257452	−	0.786434i
$666$	60.5663	−	259.755i	0.0909404	−	0.390022i
$667$	−347.320	−	69.0862i	−0.520719	−	0.103578i
$668$	−87.3991	−	99.6596i	−0.130837	−	0.149191i
$669$	442.552	−	317.128i	0.661512	−	0.474033i
$670$	−220.768	+	287.711i	−0.329505	+	0.429419i
$671$	−244.355	−	1228.46i	−0.364165	−	1.83078i
$672$	4.00326	−	122.287i	0.00595723	−	0.181975i
$673$	468.528	+	125.542i	0.696178	+	0.186540i	0.589518	−	0.807755i	$-0.299318\pi$
$673$	468.528	+	125.542i	0.696178	+	0.186540i	0.106660	+	0.994296i	$0.465984\pi$
$674$	−586.349	+	364.615i	−0.869954	+	0.540972i
$675$	89.2514	+	677.932i	0.132224	+	1.00434i
$676$	−72.0766	−	24.4667i	−0.106622	−	0.0361934i
$677$	66.5939	+	1016.03i	0.0983662	+	1.50078i	0.706936	+	0.707278i	$0.250077\pi$
$677$	66.5939	+	1016.03i	0.0983662	+	1.50078i	−0.608570	+	0.793500i	$0.708256\pi$
$678$		−	543.202i		−	0.801182i
$679$	299.772	−	236.399i	0.441491	−	0.348158i
$680$	−1307.97			−1.92348
$681$	−818.518	+	53.6485i	−1.20194	+	0.0787790i
$682$	228.104	−	671.973i	0.334464	−	0.985298i
$683$	485.137	−	63.8695i	0.710303	−	0.0935131i	0.233287	−	0.972408i	$-0.425052\pi$
$683$	485.137	−	63.8695i	0.710303	−	0.0935131i	0.477016	+	0.878895i	$0.341718\pi$
$684$	−36.1552	−	58.1423i	−0.0528585	−	0.0850034i
$685$	199.715	−	745.345i	0.291554	−	1.08810i
$686$	−572.406	−	18.7386i	−0.834411	−	0.0273158i
$687$	275.793	−	54.8586i	0.401445	−	0.0798524i
$688$	−164.659	−	126.348i	−0.239331	−	0.183645i
$689$	826.337	+	1153.15i	1.19933	+	1.67366i
$690$	−194.092	+	170.214i	−0.281293	+	0.246687i
$691$	−206.023	+	1035.75i	−0.298152	+	1.49891i	0.483583	+	0.875298i	$0.339335\pi$
$691$	−206.023	+	1035.75i	−0.298152	+	1.49891i	−0.781735	+	0.623611i	$0.785665\pi$
$692$	237.050	+	55.2722i	0.342557	+	0.0798732i
$693$	−230.346	+	7.54073i	−0.332389	+	0.0108813i
$694$	−561.690	+	130.968i	−0.809352	+	0.188714i
$695$	56.0304	−	15.0133i	0.0806193	−	0.0216019i
$696$	−493.536	+	526.943i	−0.709103	+	0.757102i
$697$	643.122	+	429.720i	0.922700	+	0.616529i
$698$	−836.550	−	447.145i	−1.19849	−	0.640609i
$699$	73.2494	+	89.2547i	0.104792	+	0.127689i
$700$	−29.0365	+	77.1482i	−0.0414807	+	0.110212i
$701$	948.036	−	948.036i	1.35241	−	1.35241i	0.469442	−	0.882963i	$-0.344455\pi$
$701$	948.036	−	948.036i	1.35241	−	1.35241i	0.882963	−	0.469442i	$-0.155545\pi$
$702$	−744.454	+	337.308i	−1.06048	+	0.480495i
$703$	−93.4069	+	709.496i	−0.132869	+	1.00924i
$704$	457.246	−	927.203i	0.649497	−	1.31705i
$705$	−1156.36	−	190.916i	−1.64022	−	0.270802i
$706$	701.788	−	468.920i	0.994034	−	0.664192i
$707$	−333.186	+	32.8160i	−0.471268	+	0.0464158i
$708$	65.2699	+	46.7718i	0.0921892	+	0.0660618i
$709$	−1013.54	+	307.455i	−1.42954	+	0.433646i	−0.907780	−	0.419447i	$-0.862224\pi$
$709$	−1013.54	+	307.455i	−1.42954	+	0.433646i	−0.521759	+	0.853093i	$0.674724\pi$
$710$	63.1719	−	31.1529i	0.0889745	−	0.0438774i
$711$	−39.5658	+	13.4308i	−0.0556481	+	0.0188900i
$712$	−428.294	−	1033.99i	−0.601536	−	1.45224i
$713$	−165.726	+	201.937i	−0.232434	+	0.283222i
$714$	168.390	+	291.660i	0.235840	+	0.408487i
$715$	1397.81	+	807.025i	1.95498	+	1.12871i
$716$	−33.3347	−	88.5681i	−0.0465568	−	0.123698i
$717$	−295.829	−	134.038i	−0.412592	−	0.186943i
$718$	−417.524	+	671.434i	−0.581510	+	0.935145i
$719$	−182.624	−	194.985i	−0.253997	−	0.271189i	0.590160	−	0.807287i	$-0.299065\pi$
$719$	−182.624	−	194.985i	−0.253997	−	0.271189i	−0.844156	+	0.536097i	$0.819898\pi$
$720$	−53.3195	−	322.952i	−0.0740549	−	0.448544i
$721$	202.150	−	666.400i	0.280375	−	0.924272i
$722$	−3.36831	−	4.38966i	−0.00466524	−	0.00607986i
$723$	−233.774	+	266.568i	−0.323339	+	0.368698i
$724$	3.90147	−	39.6123i	0.00538877	−	0.0547131i
$725$	779.897	−	416.864i	1.07572	−	0.574984i
$726$	326.233	+	135.130i	0.449357	+	0.186130i
$727$	−33.6400	+	513.248i	−0.0462724	+	0.705980i	0.910202	+	0.414164i	$0.135926\pi$
$727$	−33.6400	+	513.248i	−0.0462724	+	0.705980i	−0.956475	+	0.291816i	$0.905741\pi$
$728$	−540.346	−	35.4161i	−0.742233	−	0.0486485i
$729$	266.854	−	644.244i	0.366056	−	0.883736i
$730$	201.183	+	376.387i	0.275593	+	0.515598i
$731$	−385.983	−	38.0160i	−0.528021	−	0.0520055i
$732$	128.597	+	112.777i	0.175679	+	0.154067i
$733$	327.766	−	251.504i	0.447157	−	0.343115i	−0.360509	−	0.932756i	$-0.617397\pi$
$733$	327.766	−	251.504i	0.447157	−	0.343115i	0.807666	+	0.589640i	$0.200730\pi$
$734$	−486.916	−	147.704i	−0.663373	−	0.201232i
$735$	−513.381	+	84.7595i	−0.698477	+	0.115319i
$736$	−95.9715	+	89.8871i	−0.130396	+	0.122129i
$737$	−363.930	−	226.307i	−0.493800	−	0.307064i
$738$	−104.290	+	230.172i	−0.141314	+	0.311886i
$739$	−182.229	+	68.5861i	−0.246589	+	0.0928094i	−0.472474	−	0.881344i	$-0.656639\pi$
$739$	−182.229	+	68.5861i	−0.246589	+	0.0928094i	0.225886	+	0.974154i	$0.427472\pi$
$740$	116.228	−	201.314i	0.157066	−	0.272045i
$741$	587.635	−	339.271i	0.793029	−	0.457856i
$742$	477.095	+	391.542i	0.642986	+	0.527685i
$743$	−1254.23	+	519.520i	−1.68807	+	0.699220i	−0.999659	−	0.0261046i	$-0.991690\pi$
$743$	−1254.23	+	519.520i	−1.68807	+	0.699220i	−0.688407	+	0.725325i	$0.741690\pi$
$744$	171.197	+	504.330i	0.230103	+	0.677863i
$745$	98.1890	+	199.108i	0.131797	+	0.267259i
$746$	−201.509	−	664.286i	−0.270119	−	0.890463i
$747$	220.746	−	308.051i	0.295511	−	0.412385i
$748$	−27.5660	−	279.883i	−0.0368530	−	0.374175i
$749$	329.858	+	493.667i	0.440398	+	0.659102i
$750$	−6.50864	+	39.4223i	−0.00867819	+	0.0525630i
$751$	1164.77	+	574.400i	1.55096	+	0.764846i	0.997675	−	0.0681490i	$-0.0217093\pi$
$751$	1164.77	+	574.400i	1.55096	+	0.764846i	0.553280	+	0.832995i	$0.313376\pi$
$752$	871.778	+	114.772i	1.15928	+	0.152622i
$753$	287.902	+	635.413i	0.382340	+	0.843842i
$754$	747.411	+	747.411i	0.991262	+	0.991262i
$755$	−965.652	−	363.446i	−1.27901	−	0.481385i
$756$	78.6228	−	64.5240i	0.103998	−	0.0853492i
$757$	−287.573	+	538.011i	−0.379885	+	0.710715i	−0.997102	−	0.0760782i	$-0.975760\pi$
$757$	−287.573	+	538.011i	−0.379885	+	0.710715i	0.617217	+	0.786793i	$0.288260\pi$
$758$	689.940	−	1032.57i	0.910211	−	1.36223i
$759$	−222.660	−	208.544i	−0.293360	−	0.274762i
$760$	296.733	+	1107.42i	0.390438	+	1.45714i
$761$	78.9451	+	338.577i	0.103739	+	0.444911i	0.999999	+	0.00138259i	$0.000440093\pi$
$761$	78.9451	+	338.577i	0.103739	+	0.444911i	−0.896260	+	0.443528i	$0.853727\pi$
$762$	1.40001	+	42.7659i	0.00183728	+	0.0561232i
$763$	−27.1951	+	116.633i	−0.0356423	+	0.152861i
$764$	−107.190	−	21.3215i	−0.140301	−	0.0279077i
$765$	−403.307	−	459.883i	−0.527198	−	0.601155i
$766$	736.110	−	527.489i	0.960979	−	0.688628i
$767$	393.320	−	512.585i	0.512804	−	0.668299i
$768$	70.3262	+	353.554i	0.0915706	+	0.460357i
$769$	−46.1999	+	1411.26i	−0.0600779	+	1.83519i	0.366129	+	0.930564i	$0.380683\pi$
$769$	−46.1999	+	1411.26i	−0.0600779	+	1.83519i	−0.426207	+	0.904625i	$0.640151\pi$
$770$	678.271	+	181.742i	0.880871	+	0.236029i
$771$	597.710	−	371.680i	0.775240	−	0.482075i
$772$	−9.82802	−	74.6512i	−0.0127306	−	0.0966985i
$773$	947.667	+	321.690i	1.22596	+	0.416157i	0.857983	−	0.513677i	$-0.171717\pi$
$773$	947.667	+	321.690i	1.22596	+	0.416157i	0.367977	+	0.929835i	$0.380051\pi$
$774$	−8.28734	−	126.440i	−0.0107072	−	0.163360i
$775$		−	652.353i		−	0.841746i
$776$	−522.042	+	653.581i	−0.672735	+	0.842244i
$777$	−328.953			−0.423363
$778$	47.3488	−	3.10340i	0.0608596	−	0.00398895i
$779$	217.931	−	642.005i	0.279758	−	0.824140i
$780$	−218.528	+	28.7697i	−0.280164	+	0.0368843i
$781$	43.9542	+	70.6842i	0.0562794	+	0.0905047i
$782$	93.6762	−	349.604i	0.119790	−	0.447064i
$783$	−1090.55	−	35.7008i	−1.39278	−	0.0455949i
$784$	382.876	−	76.1588i	0.488363	−	0.0971414i
$785$	199.720	+	153.251i	0.254421	+	0.195224i
$786$	75.3597	+	105.164i	0.0958774	+	0.133797i
$787$	−605.783	+	531.257i	−0.769737	+	0.675041i	−0.951275	−	0.308343i	$-0.900226\pi$
$787$	−605.783	+	531.257i	−0.769737	+	0.675041i	0.181539	+	0.983384i	$0.441892\pi$
$788$	59.4988	−	299.121i	0.0755061	−	0.379595i
$789$	−687.776	−	160.367i	−0.871706	−	0.203253i
$790$	127.238	−	4.16534i	0.161061	−	0.00527258i
$791$	529.710	−	123.511i	0.669672	−	0.156146i
$792$	487.764	−	130.696i	0.615863	−	0.165020i
$793$	940.803	−	1004.48i	1.18638	−	1.26669i
$794$	430.839	+	287.878i	0.542619	+	0.362566i
$795$	1217.66	+	650.854i	1.53165	+	0.818685i
$796$	201.521	+	245.553i	0.253166	+	0.308484i
$797$	−11.7283	+	31.1613i	−0.0147155	+	0.0390982i	−0.943060	−	0.332624i	$-0.892066\pi$
$797$	−11.7283	+	31.1613i	−0.0147155	+	0.0390982i	0.928344	+	0.371722i	$0.121233\pi$
$798$	208.739	−	208.739i	0.261578	−	0.261578i
$799$	1496.70	−	678.148i	1.87322	−	0.848745i
$800$	42.8598	−	325.552i	0.0535747	−	0.406940i
$801$	231.491	−	469.417i	0.289002	−	0.586039i
$802$	−196.312	−	32.4112i	−0.244778	−	0.0404130i
$803$	−419.342	+	280.196i	−0.522220	+	0.348936i
$804$	58.2414	−	5.73628i	0.0724396	−	0.00713468i
$805$	−210.119	−	150.569i	−0.261017	−	0.187042i
$806$	746.165	−	226.347i	0.925763	−	0.280827i
$807$	−912.857	+	450.171i	−1.13117	+	0.557833i
$808$	694.632	−	235.796i	0.859693	−	0.291826i
$809$	326.629	+	788.552i	0.403744	+	0.974724i	0.986749	+	0.162256i	$0.0518769\pi$
$809$	326.629	+	788.552i	0.403744	+	0.974724i	−0.583005	+	0.812469i	$0.698123\pi$
$810$	−221.696	+	270.138i	−0.273699	+	0.333503i
$811$	−379.018	−	656.479i	−0.467347	−	0.809468i	0.531957	−	0.846771i	$-0.321457\pi$
$811$	−379.018	−	656.479i	−0.467347	−	0.809468i	−0.999304	+	0.0373030i	$0.988123\pi$
$812$	−113.916	−	65.7693i	−0.140290	−	0.0809967i
$813$	−113.955	−	302.771i	−0.140166	−	0.372412i
$814$	−874.737	−	396.338i	−1.07462	−	0.486902i
$815$	−216.398	+	347.997i	−0.265519	+	0.426990i
$816$	−386.389	−	412.544i	−0.473516	−	0.505568i
$817$	55.3793	+	335.427i	0.0677837	+	0.410560i
$818$	−91.9496	+	303.117i	−0.112408	+	0.370559i
$819$	−154.161	−	200.907i	−0.188231	−	0.245308i
$820$	−145.210	+	165.580i	−0.177085	+	0.201926i
$821$	5.10107	−	51.7920i	0.00621324	−	0.0630841i	−0.991578	−	0.129510i	$-0.958660\pi$
$821$	5.10107	−	51.7920i	0.00621324	−	0.0630841i	0.997791	+	0.0664259i	$0.0211596\pi$
$822$	383.925	−	205.212i	0.467061	−	0.249650i
$823$	1265.06	+	524.005i	1.53713	+	0.636701i	0.980933	−	0.194347i	$-0.0622587\pi$
$823$	1265.06	+	524.005i	1.53713	+	0.636701i	0.556200	+	0.831048i	$0.312259\pi$
$824$	−99.7934	+	1522.55i	−0.121109	+	1.84776i
$825$	760.189	+	49.8254i	0.921441	+	0.0603944i
$826$	107.568	−	259.691i	0.130227	−	0.314396i
$827$	−239.995	−	448.999i	−0.290199	−	0.542925i	0.694003	−	0.719972i	$-0.255845\pi$
$827$	−239.995	−	448.999i	−0.290199	−	0.542925i	−0.984202	+	0.177047i	$0.943345\pi$
$828$	−33.6608	−	3.31530i	−0.0406532	−	0.00400399i
$829$	−223.449	−	195.959i	−0.269540	−	0.236380i	0.513896	−	0.857852i	$-0.328202\pi$
$829$	−223.449	−	195.959i	−0.269540	−	0.236380i	−0.783436	+	0.621472i	$0.786535\pi$
$830$	−916.068	+	702.924i	−1.10370	+	0.846896i
$831$	303.591	+	92.0934i	0.365332	+	0.110822i
$832$	1120.78	−	185.041i	1.34709	−	0.222405i
$833$	532.441	−	498.686i	0.639185	−	0.598662i
$834$	27.7903	+	17.2811i	0.0333217	+	0.0207208i
$835$	−428.401	+	945.501i	−0.513055	+	1.13234i
$836$	−230.716	+	86.8354i	−0.275976	+	0.103870i
$837$	−402.460	+	697.080i	−0.480836	+	0.832832i
$838$	526.518	−	303.985i	0.628303	−	0.362751i
$839$	−592.469	−	486.226i	−0.706160	−	0.579531i	0.211270	−	0.977428i	$-0.432240\pi$
$839$	−592.469	−	486.226i	−0.706160	−	0.579531i	−0.917430	+	0.397897i	$0.869740\pi$
$840$	−486.897	+	201.679i	−0.579640	+	0.240095i
$841$	183.262	+	539.873i	0.217910	+	0.641942i
$842$	118.287	+	239.863i	0.140484	+	0.284873i
$843$	−330.429	−	1089.28i	−0.391968	−	1.29215i
$844$	−114.621	+	159.954i	−0.135807	+	0.189519i
$845$	58.4242	+	593.191i	0.0691411	+	0.702001i
$846$	298.245	+	446.355i	0.352535	+	0.527606i
$847$	−57.5963	+	348.856i	−0.0680004	+	0.411872i
$848$	−929.037	−	458.151i	−1.09556	−	0.540272i
$849$	−329.997	−	43.4450i	−0.388690	−	0.0511719i
$850$	373.015	+	823.262i	0.438841	+	0.968544i
$851$	249.980	+	249.980i	0.293749	+	0.293749i
$852$	−10.6381	−	4.00390i	−0.0124860	−	0.00469941i
$853$	218.648	−	179.440i	0.256329	−	0.210363i	−0.497449	−	0.867493i	$-0.665730\pi$
$853$	218.648	−	179.440i	0.256329	−	0.210363i	0.753777	+	0.657130i	$0.228230\pi$
$854$	282.248	−	528.048i	0.330501	−	0.618323i
$855$	−297.875	+	445.802i	−0.348392	+	0.521406i
$856$	−949.474	−	889.280i	−1.10920	−	1.03888i
$857$	−189.260	−	706.327i	−0.220840	−	0.824185i	−0.984029	−	0.178010i	$-0.943034\pi$
$857$	−189.260	−	706.327i	−0.220840	−	0.824185i	0.763189	−	0.646175i	$-0.223633\pi$
$858$	206.772	+	886.796i	0.240993	+	1.03356i
$859$	−37.2039	−	1136.46i	−0.0433107	−	1.32300i	−0.770885	−	0.636975i	$-0.780185\pi$
$859$	−37.2039	−	1136.46i	−0.0433107	−	1.32300i	0.727574	−	0.686029i	$-0.240648\pi$
$860$	25.0768	−	107.548i	0.0291590	−	0.125056i
$861$	305.666	+	60.8007i	0.355012	+	0.0706164i
$862$	−34.0024	−	38.7723i	−0.0394459	−	0.0449795i
$863$	−733.968	+	525.954i	−0.850485	+	0.609449i	−0.921653	−	0.388016i	$-0.873161\pi$
$863$	−733.968	+	525.954i	−0.850485	+	0.609449i	0.0711682	+	0.997464i	$0.477327\pi$
$864$	−246.643	+	321.431i	−0.285466	+	0.372027i
$865$	−371.865	−	1869.49i	−0.429902	−	2.16126i
$866$	10.0554	−	307.161i	0.0116113	−	0.354690i
$867$	−398.122	−	106.676i	−0.459195	−	0.123041i
$868$	−82.4023	+	51.2411i	−0.0949336	+	0.0590335i
$869$	19.6365	+	149.154i	0.0225967	+	0.171639i
$870$	974.119	+	330.669i	1.11968	+	0.380079i
$871$	−30.7979	−	469.886i	−0.0353593	−	0.539479i
$872$		−	262.405i		−	0.300923i
$873$	−390.770	+	17.9784i	−0.447618	+	0.0205939i
$874$	−317.254			−0.362990
$875$	−39.9231	+	2.61670i	−0.0456264	+	0.00299051i
$876$	22.1382	−	65.2171i	0.0252719	−	0.0744487i
$877$	−441.261	+	58.0931i	−0.503148	+	0.0662407i	−0.377828	−	0.925876i	$-0.623329\pi$
$877$	−441.261	+	58.0931i	−0.503148	+	0.0662407i	−0.125320	+	0.992116i	$0.539996\pi$
$878$	313.344	+	503.898i	0.356883	+	0.573915i
$879$	70.1280	−	261.721i	0.0797816	−	0.297749i
$880$	−1177.90	−	38.5605i	−1.33852	−	0.0438188i
$881$	744.943	−	148.178i	0.845565	−	0.168193i	0.246749	−	0.969080i	$-0.420638\pi$
$881$	744.943	−	148.178i	0.845565	−	0.168193i	0.598817	+	0.800886i	$0.295638\pi$
$882$	189.081	+	145.087i	0.214378	+	0.164498i
$883$	154.025	+	214.941i	0.174433	+	0.243421i	0.890900	−	0.454200i	$-0.150075\pi$
$883$	154.025	+	214.941i	0.174433	+	0.243421i	−0.716466	+	0.697622i	$0.754242\pi$
$884$	232.334	−	203.752i	0.262822	−	0.230488i
$885$	122.675	−	616.727i	0.138615	−	0.696867i
$886$	298.295	+	69.5527i	0.336676	+	0.0785019i
$887$	−561.534	+	18.3827i	−0.633071	+	0.0207246i	−0.347570	−	0.937654i	$-0.612993\pi$
$887$	−561.534	+	18.3827i	−0.633071	+	0.0207246i	−0.285501	+	0.958379i	$0.592160\pi$
$888$	701.925	−	163.666i	0.790456	−	0.184309i
$889$	−41.3854	+	11.0892i	−0.0465528	+	0.0124738i
$890$	−1090.11	+	1163.90i	−1.22485	+	1.30776i
$891$	−343.371	−	229.433i	−0.385377	−	0.257501i
$892$	−191.677	−	102.453i	−0.214884	−	0.114858i
$893$	−913.723	−	1113.37i	−1.02321	−	1.24678i
$894$	−44.1175	+	117.217i	−0.0493484	+	0.131116i
$895$	−524.016	+	524.016i	−0.585493	+	0.585493i
$896$	250.129	−	113.332i	0.279162	−	0.126487i
$897$	43.7536	−	332.342i	0.0487777	−	0.370504i
$898$	444.531	−	901.419i	0.495023	−	1.00381i
$899$	1027.08	+	169.571i	1.14246	+	0.188622i
$900$	70.2294	−	46.9258i	0.0780327	−	0.0521398i
$901$	−1926.42	+	189.736i	−2.13809	+	0.210584i
$902$	739.557	+	529.959i	0.819908	+	0.587538i
$903$	−149.546	+	45.3644i	−0.165610	+	0.0502374i
$904$	−1068.85	+	527.101i	−1.18236	+	0.583076i
$905$	−295.161	+	100.194i	−0.326145	+	0.110711i
$906$	−222.757	−	537.782i	−0.245868	−	0.593578i
$907$	1045.59	−	1274.05i	1.15280	−	1.40469i	0.253513	−	0.967332i	$-0.418414\pi$
$907$	1045.59	−	1274.05i	1.15280	−	1.40469i	0.899287	−	0.437359i	$-0.144086\pi$
$908$	163.725	+	283.579i	0.180313	+	0.312312i
$909$	297.094	+	171.527i	0.326836	+	0.188699i
$910$	271.785	+	722.117i	0.298665	+	0.793535i
$911$	1492.26	+	676.134i	1.63804	+	0.742188i	0.999622	−	0.0274974i	$-0.00875379\pi$
$911$	1492.26	+	676.134i	1.63804	+	0.742188i	0.638423	+	0.769686i	$0.279587\pi$
$912$	−261.632	+	420.739i	−0.286877	+	0.461336i
$913$	−932.773	−	995.912i	−1.02166	−	1.09081i
$914$	−113.883	−	689.781i	−0.124599	−	0.754684i
$915$	388.817	−	1281.76i	0.424936	−	1.40083i
$916$	−68.3346	−	89.0554i	−0.0746011	−	0.0972221i
$917$	−85.4174	+	97.3999i	−0.0931487	+	0.106216i
$918$	109.309	−	1109.83i	0.119073	−	1.20897i
$919$	39.6215	−	21.1781i	0.0431137	−	0.0230447i	−0.449699	−	0.893180i	$-0.648469\pi$
$919$	39.6215	−	21.1781i	0.0431137	−	0.0230447i	0.492813	+	0.870135i	$0.335969\pi$
$920$	523.269	+	216.745i	0.568770	+	0.235592i
$921$	−27.4870	+	419.371i	−0.0298448	+	0.455343i
$922$	−854.049	−	55.9773i	−0.926301	−	0.0607129i
$923$	−34.9999	+	84.4972i	−0.0379197	+	0.0915462i
$924$	−53.4176	−	99.9373i	−0.0578113	−	0.108157i
$925$	−878.570	−	86.5316i	−0.949806	−	0.0935477i
$926$	834.112	+	731.496i	0.900768	+	0.789953i
$927$	−566.104	+	434.387i	−0.610684	+	0.468594i
$928$	501.414	+	152.102i	0.540317	+	0.163903i
$929$	−398.629	+	65.8139i	−0.429094	+	0.0708438i	−0.373545	−	0.927612i	$-0.621858\pi$
$929$	−398.629	+	65.8139i	−0.429094	+	0.0708438i	−0.0555496	+	0.998456i	$0.517691\pi$
$930$	553.875	−	518.760i	0.595564	−	0.557807i
$931$	−543.018	−	337.670i	−0.583263	−	0.362696i
$932$	19.0227	−	41.9840i	0.0204106	−	0.0450472i
$933$	−587.961	+	221.293i	−0.630183	+	0.237184i
$934$	−769.248	+	1332.38i	−0.823606	+	1.42653i
$935$	−1907.29	+	1101.18i	−2.03989	+	1.17773i
$936$	428.911	+	351.998i	0.458238	+	0.376066i
$937$	−951.350	+	394.062i	−1.01531	+	0.420557i	−0.827391	−	0.561627i	$-0.810176\pi$
$937$	−951.350	+	394.062i	−1.01531	+	0.420557i	−0.187924	+	0.982184i	$0.560176\pi$
$938$	−65.8513	−	193.992i	−0.0702040	−	0.206814i
$939$	−249.320	−	505.571i	−0.265517	−	0.538414i
$940$	135.813	+	447.715i	0.144482	+	0.476293i
$941$	−558.967	+	780.037i	−0.594014	+	0.828945i	−0.996244	−	0.0865937i	$-0.972402\pi$
$941$	−558.967	+	780.037i	−0.594014	+	0.828945i	0.402230	+	0.915539i	$0.368235\pi$
$942$	13.9207	+	141.339i	0.0147778	+	0.150041i
$943$	−186.080	−	278.488i	−0.197327	−	0.295321i
$944$	−76.8481	+	465.462i	−0.0814069	+	0.493074i
$945$	−714.345	−	352.276i	−0.755921	−	0.372779i
$946$	−452.324	−	59.5496i	−0.478144	−	0.0629488i
$947$	257.202	+	567.656i	0.271596	+	0.599426i	0.995941	−	0.0900125i	$-0.0286907\pi$
$947$	257.202	+	567.656i	0.271596	+	0.599426i	−0.724344	+	0.689438i	$0.757857\pi$
$948$	−14.5269	−	14.5269i	−0.0153237	−	0.0153237i
$949$	−518.645	−	195.204i	−0.546518	−	0.205695i
$950$	612.412	−	502.593i	0.644644	−	0.529046i
$951$	391.801	−	733.007i	0.411988	−	0.770775i
$952$	410.498	−	614.354i	0.431195	−	0.645330i
$953$	731.309	+	684.945i	0.767375	+	0.718725i	0.965200	−	0.261512i	$-0.0842211\pi$
$953$	731.309	+	684.945i	0.767375	+	0.718725i	−0.197825	+	0.980237i	$0.563388\pi$
$954$	−163.680	−	610.862i	−0.171572	−	0.640316i
$955$	194.342	+	833.490i	0.203500	+	0.872764i
$956$	4.24202	+	129.580i	0.00443726	+	0.135544i
$957$	−276.047	+	1183.90i	−0.288451	+	1.23710i
$958$	−405.956	−	80.7496i	−0.423753	−	0.0842898i
$959$	287.411	+	327.729i	0.299698	+	0.341740i
$960$	898.645	−	643.960i	0.936088	−	0.670791i
$961$	−117.538	+	153.178i	−0.122308	+	0.159395i
$962$	−205.862	−	1034.94i	−0.213993	−	1.07582i
$963$	19.9053	−	608.043i	0.0206701	−	0.631405i
$964$	136.714	+	36.6323i	0.141819	+	0.0380003i
$965$	−500.719	+	311.367i	−0.518880	+	0.322660i
$966$	−19.0351	−	144.586i	−0.0197051	−	0.149675i
$967$	329.608	+	111.887i	0.340857	+	0.115705i	0.486619	−	0.873614i	$-0.338230\pi$
$967$	329.608	+	111.887i	0.340857	+	0.115705i	−0.145762	+	0.989320i	$0.546563\pi$
$968$	−50.6684	−	773.051i	−0.0523434	−	0.798607i
$969$			925.863i			0.955483i
$970$	1155.24	+	293.197i	1.19097	+	0.302264i
$971$	1061.13			1.09282			0.546412	−	0.837517i	$-0.315993\pi$
$971$	1061.13			1.09282			0.546412	+	0.837517i	$0.315993\pi$
$972$	−175.810	+	11.5232i	−0.180874	+	0.0118551i
$973$	−10.5331	+	31.0294i	−0.0108254	+	0.0318905i
$974$	135.871	−	17.8878i	0.139498	−	0.0183653i
$975$	442.036	+	710.852i	0.453371	+	0.729079i
$976$	−260.089	+	970.666i	−0.266485	+	0.994535i
$977$	846.889	+	27.7243i	0.866826	+	0.0283770i	0.462896	−	0.886413i	$-0.346810\pi$
$977$	846.889	+	27.7243i	0.866826	+	0.0283770i	0.403931	+	0.914790i	$0.367644\pi$
$978$	−226.746	+	45.1026i	−0.231847	+	0.0461172i
$979$	−1495.06	−	1147.20i	−1.52713	−	1.17181i
$980$	120.988	+	168.839i	0.123458	+	0.172285i
$981$	92.2620	−	80.9116i	0.0940489	−	0.0824787i
$982$	124.370	−	625.250i	0.126650	−	0.636711i
$983$	−788.328	−	183.812i	−0.801961	−	0.186991i	−0.194045	−	0.980993i	$-0.562161\pi$
$983$	−788.328	−	183.812i	−0.801961	−	0.186991i	−0.607916	+	0.794001i	$0.707994\pi$
$984$	−682.486	+	22.3423i	−0.693583	+	0.0227056i
$985$	−2325.90	+	542.324i	−2.36132	+	0.550582i
$986$	−1393.12	+	373.285i	−1.41290	+	0.378585i
$987$	452.590	−	483.226i	0.458551	−	0.489590i
$988$	−225.221	−	150.488i	−0.227956	−	0.152315i
$989$	148.118	+	79.1707i	0.149765	+	0.0800513i
$990$	−456.454	−	556.191i	−0.461065	−	0.561809i
$991$	525.800	−	1397.02i	0.530575	−	1.40970i	−0.350427	−	0.936590i	$-0.613963\pi$
$991$	525.800	−	1397.02i	0.530575	−	1.40970i	0.881002	−	0.473113i	$-0.156870\pi$
$992$	273.320	−	273.320i	0.275525	−	0.275525i
$993$	548.706	−	248.616i	0.552575	−	0.250368i
$994$	−5.19358	+	39.4491i	−0.00522493	+	0.0396873i
$995$	1100.22	−	2231.03i	1.10575	−	2.24224i
$996$	183.848	+	30.3535i	0.184587	+	0.0304754i
$997$	672.865	−	449.594i	0.674889	−	0.450947i	−0.170315	−	0.985390i	$-0.554479\pi$
$997$	672.865	−	449.594i	0.674889	−	0.450947i	0.845205	+	0.534443i	$0.179479\pi$
$998$	240.697	−	23.7066i	0.241179	−	0.0237541i
$999$	885.423	+	634.485i	0.886309	+	0.635120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.7.5	✓	480
97.14	odd	96	inner	97.3.l.a.14.5	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.7.5	✓	480	1.1	even	1	trivial
97.3.l.a.14.5	yes	480	97.14	odd	96	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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	97.l (of order \(96\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75983 + 0.115345i) q^{2} +(0.716397 - 2.11044i) q^{3} +(-0.882081 + 0.116128i) q^{4} +(3.67912 + 5.91650i) q^{5} +(-1.01731 + 3.79665i) q^{6} +(-3.93366 - 0.128775i) q^{7} +(8.45779 - 1.68236i) q^{8} +(3.19945 + 2.45503i) q^{9} +(-7.15707 - 9.98768i) q^{10} +(10.9169 - 9.57385i) q^{11} +(-0.386839 + 1.94477i) q^{12} +(15.5379 + 3.62294i) q^{13} +(6.93744 - 0.227108i) q^{14} +(15.1221 - 3.52599i) q^{15} +(-11.2527 + 3.01516i) q^{16} +(-14.8818 + 15.8892i) q^{17} +(-5.91367 - 3.95139i) q^{18} +(16.8292 + 8.99537i) q^{19} +(-3.93235 - 4.79158i) q^{20} +(-3.08984 + 8.20950i) q^{21} +(-18.1076 + 18.1076i) q^{22} +(8.58669 - 3.89058i) q^{23} +(2.50862 - 19.0549i) q^{24} +(-10.4119 + 21.1132i) q^{25} +(-27.7620 - 4.58353i) q^{26} +(24.1513 - 16.1374i) q^{27} +(3.48476 - 0.343219i) q^{28} +(-30.5346 - 21.8808i) q^{29} +(-26.2057 + 7.94941i) q^{30} +(-24.8536 + 12.2564i) q^{31} +(-13.2083 + 4.48360i) q^{32} +(-12.3842 - 29.8981i) q^{33} +(24.3568 - 29.6788i) q^{34} +(-13.7105 - 23.7473i) q^{35} +(-3.10727 - 1.79398i) q^{36} +(13.2099 + 35.0979i) q^{37} +(-30.6540 - 13.8892i) q^{38} +(18.7773 - 30.1964i) q^{39} +(41.0709 + 43.8510i) q^{40} +(-5.78758 - 35.0549i) q^{41} +(4.49066 - 14.8037i) q^{42} +(10.8456 + 14.1342i) q^{43} +(-8.51778 + 9.71267i) q^{44} +(-2.75401 + 27.9619i) q^{45} +(-14.6624 + 7.83719i) q^{46} +(-69.7330 - 28.8844i) q^{47} +(-1.69812 + 25.9082i) q^{48} +(-33.4380 - 2.19164i) q^{49} +(15.8879 - 38.3567i) q^{50} +(22.8718 + 42.7901i) q^{51} +(-14.1264 - 1.39133i) q^{52} +(66.8519 + 58.6275i) q^{53} +(-40.6407 + 31.1847i) q^{54} +(96.8083 + 29.3665i) q^{55} +(-33.4868 + 5.52869i) q^{56} +(31.0406 - 29.0727i) q^{57} +(56.2596 + 34.9844i) q^{58} +(16.7129 - 36.8862i) q^{59} +(-12.9295 + 4.86631i) q^{60} +(43.1302 - 74.7038i) q^{61} +(42.3244 - 24.4360i) q^{62} +(-12.2694 - 10.0693i) q^{63} +(65.7788 - 27.2465i) q^{64} +(35.7308 + 105.260i) q^{65} +(25.2427 + 51.1871i) q^{66} +(-8.56757 - 28.2435i) q^{67} +(11.2818 - 15.7437i) q^{68} +(-2.05934 - 20.9089i) q^{69} +(26.8673 + 40.2098i) q^{70} +(-0.933784 + 5.65585i) q^{71} +(31.1906 + 15.3815i) q^{72} +(-34.4364 - 4.53363i) q^{73} +(-27.2956 - 60.2426i) q^{74} +(37.0991 + 37.0991i) q^{75} +(-15.8893 - 5.98031i) q^{76} +(-44.1762 + 36.2545i) q^{77} +(-29.5619 + 55.3064i) q^{78} +(-5.75615 + 8.61469i) q^{79} +(-59.2393 - 55.4837i) q^{80} +(-7.36106 - 27.4718i) q^{81} +(14.2286 + 61.0230i) q^{82} +(-3.07473 - 93.9232i) q^{83} +(1.77213 - 7.60026i) q^{84} +(-148.760 - 29.5903i) q^{85} +(-20.7167 - 23.6229i) q^{86} +(-68.0530 + 48.7661i) q^{87} +(76.2261 - 99.3398i) q^{88} +(-25.3195 - 127.290i) q^{89} +(1.62131 - 49.5259i) q^{90} +(-60.6545 - 16.2523i) q^{91} +(-7.12234 + 4.42896i) q^{92} +(8.06142 + 61.2325i) q^{93} +(126.050 + 42.7882i) q^{94} +(8.69531 + 132.665i) q^{95} +31.0873i q^{96} +(-74.1601 + 62.5243i) q^{97} +59.0979 q^{98} +(58.4321 - 3.82984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) \) 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Introduction

L-functions

Modular forms

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