LMFDB - Embedded newform 725.2.bh.a.4.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(4,725)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([7, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("725.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$725 = 5^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	725.bh (of order $70$ , degree $24$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$1728$
Relative dimension:	$72$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			4.20
Character	$\chi$	$=$	725.4
Dual form			725.2.bh.a.544.20

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30926 - 0.782244i) q^{2} +(2.06659 + 0.375031i) q^{3} +(0.154508 + 0.287124i) q^{4} +(-0.872774 - 2.05870i) q^{5} +(-2.41233 - 2.10759i) q^{6} +(1.84445 + 3.83004i) q^{7} +(-0.114540 + 2.55043i) q^{8} +(1.32145 + 0.495948i) q^{9} +(-0.467725 + 3.37809i) q^{10} +(1.69076 + 4.50501i) q^{11} +(0.211624 + 0.651313i) q^{12} +(-1.45362 - 0.959529i) q^{13} +(0.581169 - 6.45732i) q^{14} +(-1.03159 - 4.58182i) q^{15} +(2.50427 - 3.79380i) q^{16} +(-4.84238 + 3.51820i) q^{17} +(-1.34216 - 1.68302i) q^{18} +(1.34131 + 7.39121i) q^{19} +(0.456252 - 0.568680i) q^{20} +(2.37534 + 8.60686i) q^{21} +(1.31038 - 7.22080i) q^{22} +(-0.304087 + 3.37868i) q^{23} +(-1.19320 + 5.22774i) q^{24} +(-3.47653 + 3.59357i) q^{25} +(1.15258 + 2.39336i) q^{26} +(-2.86422 - 1.71129i) q^{27} +(-0.814714 + 1.12136i) q^{28} +(-4.97509 - 2.06119i) q^{29} +(-2.23349 + 6.80573i) q^{30} +(9.00003 - 3.84680i) q^{31} +(-1.64606 + 0.792699i) q^{32} +(1.80459 + 9.94411i) q^{33} +(9.09200 - 0.818295i) q^{34} +(6.27514 - 7.13994i) q^{35} +(0.0617757 + 0.456047i) q^{36} +(-0.167334 - 0.0628015i) q^{37} +(4.02562 - 10.7262i) q^{38} +(-2.64419 - 2.52811i) q^{39} +(5.35055 - 1.99015i) q^{40} +(1.61054 - 0.523297i) q^{41} +(3.62273 - 13.1267i) q^{42} +(-1.13959 - 4.99286i) q^{43} +(-1.03226 + 1.18152i) q^{44} +(-0.132316 - 3.15332i) q^{45} +(3.04108 - 4.18568i) q^{46} +(0.120973 + 2.69368i) q^{47} +(6.59809 - 6.90106i) q^{48} +(-6.90280 + 8.65584i) q^{49} +(7.36271 - 1.98541i) q^{50} +(-11.3267 + 5.45463i) q^{51} +(0.0509071 - 0.565624i) q^{52} +(1.35778 + 1.55411i) q^{53} +(2.41135 + 4.48103i) q^{54} +(7.79884 - 7.41263i) q^{55} +(-9.97952 + 4.26545i) q^{56} +15.7777i q^{57} +(4.90131 + 6.59036i) q^{58} +(-1.57784 - 4.85610i) q^{59} +(1.15616 - 1.00412i) q^{60} +(11.7716 - 1.59457i) q^{61} +(-14.7925 - 2.00378i) q^{62} +(0.537846 + 5.97596i) q^{63} +(-6.27981 - 0.565193i) q^{64} +(-0.706701 + 3.83003i) q^{65} +(5.41605 - 14.4310i) q^{66} +(-2.64653 - 0.118856i) q^{67} +(-1.75834 - 0.846773i) q^{68} +(-1.89553 + 6.86831i) q^{69} +(-13.8009 + 4.43932i) q^{70} +(-0.575620 - 12.8172i) q^{71} +(-1.41624 + 3.31346i) q^{72} +(13.7745 + 1.23973i) q^{73} +(0.169957 + 0.213119i) q^{74} +(-8.53227 + 6.12263i) q^{75} +(-1.91495 + 1.52712i) q^{76} +(-14.1359 + 14.7850i) q^{77} +(1.48433 + 5.37834i) q^{78} +(0.822741 + 2.98114i) q^{79} +(-9.99598 - 1.84441i) q^{80} +(-8.46615 - 7.39665i) q^{81} +(-2.51796 - 0.574708i) q^{82} +(1.49245 + 8.22406i) q^{83} +(-2.10422 + 2.01184i) q^{84} +(11.4692 + 6.89844i) q^{85} +(-2.41362 + 7.42836i) q^{86} +(-9.50847 - 6.12545i) q^{87} +(-11.6834 + 3.79616i) q^{88} +(3.88112 - 6.49591i) q^{89} +(-2.29343 + 4.23201i) q^{90} +(0.993897 - 7.33724i) q^{91} +(-1.01708 + 0.434722i) q^{92} +(20.0420 - 4.57447i) q^{93} +(1.94873 - 3.62134i) q^{94} +(14.0457 - 9.21222i) q^{95} +(-3.69901 + 1.02086i) q^{96} +(1.83594 + 3.41175i) q^{97} +(15.8085 - 5.93303i) q^{98} +6.79167i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1728 q - 35 q^{2} - 35 q^{3} + 53 q^{4} - 16 q^{5} - 19 q^{6} - 35 q^{8} + 49 q^{9} - 28 q^{10} - 21 q^{11} - 25 q^{13} - 21 q^{14} - 42 q^{15} + 37 q^{16} - 21 q^{19} + 54 q^{20} - 21 q^{21} - 25 q^{22}+ \cdots - 315 q^{98}+O(q^{100})$ 1728 * q - 35 * q^2 - 35 * q^3 + 53 * q^4 - 16 * q^5 - 19 * q^6 - 35 * q^8 + 49 * q^9 - 28 * q^10 - 21 * q^11 - 25 * q^13 - 21 * q^14 - 42 * q^15 + 37 * q^16 - 21 * q^19 + 54 * q^20 - 21 * q^21 - 25 * q^22 - 45 * q^23 - 68 * q^24 + 4 * q^25 - 14 * q^26 - 140 * q^27 - 40 * q^28 - 4 * q^29 - 154 * q^30 - 21 * q^31 - 5 * q^33 + 104 * q^34 - 50 * q^35 + 59 * q^36 - 35 * q^37 - 200 * q^38 - 21 * q^39 - 91 * q^40 - 65 * q^42 - 21 * q^44 - 114 * q^45 - 35 * q^47 - 35 * q^48 + 144 * q^49 + 196 * q^50 - 54 * q^51 + 180 * q^52 - 155 * q^53 - 25 * q^54 - 84 * q^55 - 49 * q^56 + 365 * q^58 - 204 * q^59 - 259 * q^60 - 105 * q^61 - 25 * q^62 - 95 * q^63 + 73 * q^64 - 22 * q^65 - 21 * q^66 + 15 * q^67 - 21 * q^69 + 58 * q^71 - 35 * q^72 - 35 * q^73 - 128 * q^74 - 168 * q^76 - 35 * q^77 + 165 * q^78 - 21 * q^79 - 377 * q^80 - 67 * q^81 - 25 * q^83 + 42 * q^84 + 77 * q^85 - 324 * q^86 + 285 * q^87 + 120 * q^88 - 21 * q^89 + 21 * q^90 + 37 * q^91 - 165 * q^92 - 77 * q^94 + 84 * q^95 + 313 * q^96 - 35 * q^97 - 315 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$ .

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{10}\right)$

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

)

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

$2$	−1.30926	−	0.782244i	−0.925784	−	0.553130i	−0.0309457	−	0.999521i	$-0.509852\pi$
$2$	−1.30926	−	0.782244i	−0.925784	−	0.553130i	−0.894838	+	0.446391i	$0.852709\pi$
$3$	2.06659	+	0.375031i	1.19315	+	0.216524i	0.738566	−	0.674181i	$-0.235503\pi$
$3$	2.06659	+	0.375031i	1.19315	+	0.216524i	0.454581	+	0.890705i	$0.349789\pi$
$4$	0.154508	+	0.287124i	0.0772539	+	0.143562i
$5$	−0.872774	−	2.05870i	−0.390316	−	0.920681i
$5$	−0.872774	−	2.05870i	−0.390316	−	0.920681i
$6$	−2.41233	−	2.10759i	−0.984830	−	0.860420i
$7$	1.84445	+	3.83004i	0.697137	+	1.44762i	0.885079	+	0.465440i	$0.154104\pi$
$7$	1.84445	+	3.83004i	0.697137	+	1.44762i	−0.187942	+	0.982180i	$0.560182\pi$
$8$	−0.114540	+	2.55043i	−0.0404960	+	0.901713i
$9$	1.32145	+	0.495948i	0.440483	+	0.165316i
$10$	−0.467725	+	3.37809i	−0.147908	+	1.06825i
$11$	1.69076	+	4.50501i	0.509783	+	1.35831i	0.899316	+	0.437300i	$0.144065\pi$
$11$	1.69076	+	4.50501i	0.509783	+	1.35831i	−0.389533	+	0.921013i	$0.627363\pi$
$12$	0.211624	+	0.651313i	0.0610907	+	0.188018i
$13$	−1.45362	−	0.959529i	−0.403163	−	0.266125i	0.333004	−	0.942925i	$-0.391938\pi$
$13$	−1.45362	−	0.959529i	−0.403163	−	0.266125i	−0.736167	+	0.676800i	$0.763366\pi$
$14$	0.581169	−	6.45732i	0.155324	−	1.72579i
$15$	−1.03159	−	4.58182i	−0.266355	−	1.18302i
$16$	2.50427	−	3.79380i	0.626067	−	0.948451i
$17$	−4.84238	+	3.51820i	−1.17445	+	0.853288i	−0.991535	−	0.129841i	$-0.958553\pi$
$17$	−4.84238	+	3.51820i	−1.17445	+	0.853288i	−0.182915	+	0.983129i	$0.558553\pi$
$18$	−1.34216	−	1.68302i	−0.316351	−	0.396691i
$19$	1.34131	+	7.39121i	0.307717	+	1.69566i	0.653159	+	0.757221i	$0.273443\pi$
$19$	1.34131	+	7.39121i	0.307717	+	1.69566i	−0.345442	+	0.938440i	$0.612271\pi$
$20$	0.456252	−	0.568680i	0.102021	−	0.127161i
$21$	2.37534	+	8.60686i	0.518342	+	1.87817i
$22$	1.31038	−	7.22080i	0.279374	−	1.53948i
$23$	−0.304087	+	3.37868i	−0.0634064	+	0.704503i	0.899900	+	0.436097i	$0.143640\pi$
$23$	−0.304087	+	3.37868i	−0.0634064	+	0.704503i	−0.963306	+	0.268406i	$0.913503\pi$
$24$	−1.19320	+	5.22774i	−0.243561	+	1.06711i
$25$	−3.47653	+	3.59357i	−0.695306	+	0.718714i
$26$	1.15258	+	2.39336i	0.226039	+	0.469376i
$27$	−2.86422	−	1.71129i	−0.551219	−	0.329338i
$28$	−0.814714	+	1.12136i	−0.153966	+	0.211917i
$29$	−4.97509	−	2.06119i	−0.923851	−	0.382753i
$29$	−4.97509	−	2.06119i	−0.923851	−	0.382753i
$30$	−2.23349	+	6.80573i	−0.407777	+	1.24255i
$31$	9.00003	−	3.84680i	1.61645	−	0.690905i	0.620793	−	0.783975i	$-0.286811\pi$
$31$	9.00003	−	3.84680i	1.61645	−	0.690905i	0.995660	+	0.0930699i	$0.0296680\pi$
$32$	−1.64606	+	0.792699i	−0.290984	+	0.140131i
$33$	1.80459	+	9.94411i	0.314139	+	1.73105i
$34$	9.09200	−	0.818295i	1.55927	−	0.140336i
$35$	6.27514	−	7.13994i	1.06069	−	1.20687i
$36$	0.0617757	+	0.456047i	0.0102960	+	0.0760078i
$37$	−0.167334	−	0.0628015i	−0.0275095	−	0.0103245i	0.337582	−	0.941296i	$-0.390391\pi$
$37$	−0.167334	−	0.0628015i	−0.0275095	−	0.0103245i	−0.365092	+	0.930972i	$0.618962\pi$
$38$	4.02562	−	10.7262i	0.653041	−	1.74002i
$39$	−2.64419	−	2.52811i	−0.423410	−	0.404821i
$40$	5.35055	−	1.99015i	0.845996	−	0.314670i
$41$	1.61054	−	0.523297i	0.251525	−	0.0817253i	−0.180541	−	0.983567i	$-0.557785\pi$
$41$	1.61054	−	0.523297i	0.251525	−	0.0817253i	0.432066	+	0.901842i	$0.357785\pi$
$42$	3.62273	−	13.1267i	0.559000	−	2.02549i
$43$	−1.13959	−	4.99286i	−0.173785	−	0.761403i	−0.984417	−	0.175848i	$-0.943733\pi$
$43$	−1.13959	−	4.99286i	−0.173785	−	0.761403i	0.810632	−	0.585556i	$-0.199124\pi$
$44$	−1.03226	+	1.18152i	−0.155619	+	0.178120i
$45$	−0.132316	−	3.15332i	−0.0197245	−	0.470070i
$46$	3.04108	−	4.18568i	0.448382	−	0.617145i
$47$	0.120973	+	2.69368i	0.0176458	+	0.392913i	0.988308	+	0.152468i	$0.0487221\pi$
$47$	0.120973	+	2.69368i	0.0176458	+	0.392913i	−0.970663	+	0.240445i	$0.922706\pi$
$48$	6.59809	−	6.90106i	0.952353	−	0.996083i
$49$	−6.90280	+	8.65584i	−0.986114	+	1.23655i
$50$	7.36271	−	1.98541i	1.04125	−	0.280779i
$51$	−11.3267	+	5.45463i	−1.58605	+	0.763801i
$52$	0.0509071	−	0.565624i	0.00705955	−	0.0784380i
$53$	1.35778	+	1.55411i	0.186506	+	0.213473i	0.838722	−	0.544560i	$-0.183303\pi$
$53$	1.35778	+	1.55411i	0.186506	+	0.213473i	−0.652216	+	0.758033i	$0.726161\pi$
$54$	2.41135	+	4.48103i	0.328143	+	0.609791i
$55$	7.79884	−	7.41263i	1.05160	−	0.999519i
$56$	−9.97952	+	4.26545i	−1.33357	+	0.569995i
$57$			15.7777i			2.08980i
$58$	4.90131	+	6.59036i	0.643574	+	0.865356i
$59$	−1.57784	−	4.85610i	−0.205417	−	0.632210i	−0.999696	−	0.0246562i	$-0.992151\pi$
$59$	−1.57784	−	4.85610i	−0.205417	−	0.632210i	0.794279	−	0.607554i	$-0.207849\pi$
$60$	1.15616	−	1.00412i	0.149260	−	0.129631i
$61$	11.7716	−	1.59457i	1.50720	−	0.204164i	0.666434	−	0.745564i	$-0.267820\pi$
$61$	11.7716	−	1.59457i	1.50720	−	0.204164i	0.840765	+	0.541400i	$0.182105\pi$
$62$	−14.7925	−	2.00378i	−1.87865	−	0.254480i
$63$	0.537846	+	5.97596i	0.0677622	+	0.752900i
$64$	−6.27981	−	0.565193i	−0.784976	−	0.0706491i
$65$	−0.706701	+	3.83003i	−0.0876555	+	0.475057i
$66$	5.41605	−	14.4310i	0.666670	−	1.77633i
$67$	−2.64653	−	0.118856i	−0.323325	−	0.0145205i	−0.117389	−	0.993086i	$-0.537452\pi$
$67$	−2.64653	−	0.118856i	−0.323325	−	0.0145205i	−0.205936	+	0.978565i	$0.566024\pi$
$68$	−1.75834	−	0.846773i	−0.213230	−	0.102686i
$69$	−1.89553	+	6.86831i	−0.228195	+	0.826847i
$70$	−13.8009	+	4.43932i	−1.64953	+	0.530601i
$71$	−0.575620	−	12.8172i	−0.0683136	−	1.52112i	−0.681873	−	0.731471i	$-0.738834\pi$
$71$	−0.575620	−	12.8172i	−0.0683136	−	1.52112i	0.613559	−	0.789649i	$-0.289737\pi$
$72$	−1.41624	+	3.31346i	−0.166905	+	0.390495i
$73$	13.7745	+	1.23973i	1.61218	+	0.145099i	0.858739	−	0.512413i	$-0.171248\pi$
$73$	13.7745	+	1.23973i	1.61218	+	0.145099i	0.753444	+	0.657512i	$0.228391\pi$
$74$	0.169957	+	0.213119i	0.0197571	+	0.0247746i
$75$	−8.53227	+	6.12263i	−0.985222	+	0.706981i
$76$	−1.91495	+	1.52712i	−0.219660	+	0.175173i
$77$	−14.1359	+	14.7850i	−1.61093	+	1.68490i
$78$	1.48433	+	5.37834i	0.168067	+	0.608978i
$79$	0.822741	+	2.98114i	0.0925656	+	0.335404i	0.995546	−	0.0942780i	$-0.0300542\pi$
$79$	0.822741	+	2.98114i	0.0925656	+	0.335404i	−0.902980	+	0.429682i	$0.858626\pi$
$80$	−9.99598	−	1.84441i	−1.11758	−	0.206212i
$81$	−8.46615	−	7.39665i	−0.940683	−	0.821850i
$82$	−2.51796	−	0.574708i	−0.278062	−	0.0634658i
$83$	1.49245	+	8.22406i	0.163817	+	0.902708i	0.956207	+	0.292692i	$0.0945511\pi$
$83$	1.49245	+	8.22406i	0.163817	+	0.902708i	−0.792389	+	0.610016i	$0.791163\pi$
$84$	−2.10422	+	2.01184i	−0.229590	+	0.219510i
$85$	11.4692	+	6.89844i	1.24401	+	0.748241i
$86$	−2.41362	+	7.42836i	−0.260267	+	0.801021i
$87$	−9.50847	−	6.12545i	−1.01941	−	0.656717i
$88$	−11.6834	+	3.79616i	−1.24545	+	0.404672i
$89$	3.88112	−	6.49591i	0.411398	−	0.688565i	−0.580688	−	0.814126i	$-0.697216\pi$
$89$	3.88112	−	6.49591i	0.411398	−	0.688565i	0.992086	+	0.125562i	$0.0400734\pi$
$90$	−2.29343	+	4.23201i	−0.241749	+	0.446093i
$91$	0.993897	−	7.33724i	0.104189	−	0.769152i
$92$	−1.01708	+	0.434722i	−0.106038	+	0.0453229i
$93$	20.0420	−	4.57447i	2.07826	−	0.474350i
$94$	1.94873	−	3.62134i	0.200996	−	0.373513i
$95$	14.0457	−	9.21222i	1.44106	−	0.945153i
$96$	−3.69901	+	1.02086i	−0.377529	+	0.104191i
$97$	1.83594	+	3.41175i	0.186412	+	0.346411i	0.956599	−	0.291406i	$-0.0941231\pi$
$97$	1.83594	+	3.41175i	0.186412	+	0.346411i	−0.770188	+	0.637817i	$0.779837\pi$
$98$	15.8085	−	5.93303i	1.59690	−	0.599327i
$99$			6.79167i			0.682588i
$100$	−1.56895	−	0.442960i	−0.156895	−	0.0442960i
$101$	−4.09944	+	0.935670i	−0.407909	+	0.0931027i	−0.421552	−	0.906804i	$-0.638514\pi$
$101$	−4.09944	+	0.935670i	−0.407909	+	0.0931027i	0.0136425	+	0.999907i	$0.495657\pi$
$102$	19.0963	+	1.71870i	1.89082	+	0.170177i
$103$	11.7963	−	0.529774i	1.16233	−	0.0522002i	0.544672	−	0.838649i	$-0.316654\pi$
$103$	11.7963	−	0.529774i	1.16233	−	0.0522002i	0.617655	+	0.786449i	$0.288083\pi$
$104$	2.61371	−	3.59746i	0.256295	−	0.352760i
$105$	15.6458	−	12.4020i	1.52688	−	1.21031i
$106$	−0.561993	−	3.09684i	−0.0545856	−	0.300791i
$107$	2.44375	+	1.94882i	0.236246	+	0.188400i	0.734456	−	0.678657i	$-0.237438\pi$
$107$	2.44375	+	1.94882i	0.236246	+	0.188400i	−0.498210	+	0.867057i	$0.666009\pi$
$108$	0.0488079	−	1.08679i	0.00469654	−	0.104577i
$109$	−2.14677	−	2.24535i	−0.205624	−	0.215065i	0.611939	−	0.790905i	$-0.290390\pi$
$109$	−2.14677	−	2.24535i	−0.205624	−	0.215065i	−0.817563	+	0.575839i	$0.804675\pi$
$110$	−16.0092	+	3.60444i	−1.52641	+	0.343670i
$111$	−0.322258	−	0.192540i	−0.0305874	−	0.0182751i
$112$	19.1494	+	2.59397i	1.80945	+	0.245107i
$113$	3.17457	+	3.32034i	0.298638	+	0.312351i	0.855040	−	0.518563i	$-0.173533\pi$
$113$	3.17457	+	3.32034i	0.298638	+	0.312351i	−0.556402	+	0.830914i	$0.687818\pi$
$114$	12.3420	−	20.6570i	1.15593	−	1.93470i
$115$	7.22110	−	2.32280i	0.673371	−	0.216602i
$116$	−0.176874	−	1.74693i	−0.0164223	−	0.162199i
$117$	−1.44501	−	1.98889i	−0.133591	−	0.183873i
$118$	−1.73285	+	7.59213i	−0.159522	+	0.698912i
$119$	−22.4064	−	12.0574i	−2.05399	−	1.10530i
$120$	11.8038	−	2.10620i	1.07753	−	0.192268i
$121$	−9.15268	+	7.99646i	−0.832062	+	0.726951i
$122$	−16.6594	−	7.12056i	−1.50827	−	0.644665i
$123$	3.52459	−	0.477438i	0.317801	−	0.0430491i
$124$	2.49508	+	1.98976i	0.224065	+	0.178686i
$125$	10.4323	+	4.02078i	0.933095	+	0.359629i
$126$	3.97048	−	8.24478i	0.353718	−	0.734503i
$127$	3.13841	−	1.17787i	0.278489	−	0.104519i	−0.208222	−	0.978081i	$-0.566768\pi$
$127$	3.13841	−	1.17787i	0.278489	−	0.104519i	0.486711	+	0.873563i	$0.338196\pi$
$128$	10.7359	+	7.80007i	0.948926	+	0.689435i
$129$	−0.482584	−	10.7456i	−0.0424892	−	0.946095i
$130$	3.92127	−	4.46168i	0.343918	−	0.391315i
$131$	2.69564	−	3.08541i	0.235519	−	0.269573i	−0.623151	−	0.782101i	$-0.714148\pi$
$131$	2.69564	−	3.08541i	0.235519	−	0.269573i	0.858671	+	0.512528i	$0.171291\pi$
$132$	−2.57637	+	2.05458i	−0.224244	+	0.178828i
$133$	−25.8347	+	18.7700i	−2.24015	+	1.62757i
$134$	3.37201	+	2.22584i	0.291297	+	0.192283i
$135$	−1.02323	+	7.39015i	−0.0880653	+	0.636043i
$136$	−8.41827	−	12.7531i	−0.721861	−	1.09357i
$137$	−14.7693	−	5.54301i	−1.26183	−	0.473571i	−0.371304	−	0.928512i	$-0.621089\pi$
$137$	−14.7693	−	5.54301i	−1.26183	−	0.473571i	−0.890522	+	0.454940i	$0.849661\pi$
$138$	7.85443	−	7.50960i	0.668613	−	0.639260i
$139$	−2.63390	−	0.237055i	−0.223404	−	0.0201068i	−0.0226284	−	0.999744i	$-0.507203\pi$
$139$	−2.63390	−	0.237055i	−0.223404	−	0.0201068i	−0.200776	+	0.979637i	$0.564346\pi$
$140$	3.01960	+	0.698563i	0.255203	+	0.0590394i
$141$	−0.760211	+	5.61210i	−0.0640213	+	0.472624i
$142$	−9.27253	+	17.2312i	−0.778133	+	1.44601i
$143$	1.86496	−	8.17092i	0.155956	−	0.683287i
$144$	5.19079	−	3.77133i	0.432566	−	0.314277i
$145$	0.0987483	+	12.0412i	0.00820060	+	0.999966i
$146$	−17.0646	−	12.3981i	−1.41227	−	1.02608i
$147$	−17.5115	+	15.2993i	−1.44432	+	1.26187i
$148$	−0.00782261	−	0.0577488i	−0.000643015	−	0.00474692i
$149$	0.348212	+	0.167690i	0.0285267	+	0.0137377i	0.448093	−	0.893987i	$-0.352103\pi$
$149$	0.348212	+	0.167690i	0.0285267	+	0.0137377i	−0.419566	+	0.907725i	$0.637818\pi$
$150$	15.9603	−	1.34177i	1.30315	−	0.109555i
$151$	2.78222	+	12.1897i	0.226413	+	0.991982i	0.952538	+	0.304419i	$0.0984624\pi$
$151$	2.78222	+	12.1897i	0.226413	+	0.991982i	−0.726125	+	0.687563i	$0.758680\pi$
$152$	−19.0044	+	2.57432i	−1.54146	+	0.208805i
$153$	−8.14380	+	2.24755i	−0.658387	+	0.181703i
$154$	30.0729	−	8.29959i	2.42334	−	0.668800i
$155$	−15.7744	−	15.1710i	−1.26703	−	1.21857i
$156$	0.317331	−	1.14982i	0.0254068	−	0.0920595i
$157$	−2.11729			−0.168979			−0.0844893	−	0.996424i	$-0.526926\pi$
$157$	−2.11729			−0.168979			−0.0844893	+	0.996424i	$0.526926\pi$
$158$	1.25480	−	4.54665i	0.0998263	−	0.361712i
$159$	2.22314	+	3.72091i	0.176307	+	0.295087i
$160$	3.06857	+	2.69690i	0.242592	+	0.213208i
$161$	−13.5014	+	5.06714i	−1.06406	+	0.399347i
$162$	5.29837	+	16.3067i	0.416279	+	1.28118i
$163$	−5.31101	+	8.04583i	−0.415990	+	0.630198i	−0.980798	−	0.195024i	$-0.937522\pi$
$163$	−5.31101	+	8.04583i	−0.415990	+	0.630198i	0.564808	+	0.825222i	$0.308950\pi$
$164$	0.399092	+	0.381571i	0.0311639	+	0.0297957i
$165$	18.8970	−	12.3941i	1.47113	−	0.964878i
$166$	4.47923	−	11.9349i	0.347655	−	0.926324i
$167$	4.48921	+	2.41575i	0.347386	+	0.186936i	0.638252	−	0.769827i	$-0.279658\pi$
$167$	4.48921	+	2.41575i	0.347386	+	0.186936i	−0.290866	+	0.956764i	$0.593943\pi$
$168$	−22.2233	+	5.07232i	−1.71456	+	0.391338i
$169$	−3.91700	−	9.16427i	−0.301308	−	0.704944i
$170$	−9.61989	−	18.0036i	−0.737812	−	1.38081i
$171$	−1.89319	+	10.4323i	−0.144776	+	0.797780i
$172$	1.25749	−	1.09864i	0.0958828	−	0.0837703i
$173$	−10.1083	−	3.28439i	−0.768520	−	0.249707i	−0.101589	−	0.994826i	$-0.532393\pi$
$173$	−10.1083	−	3.28439i	−0.768520	−	0.249707i	−0.666931	+	0.745119i	$0.732393\pi$
$174$	7.65742	+	15.4577i	0.580507	+	1.17185i
$175$	−20.1758	−	6.68710i	−1.52515	−	0.505497i
$176$	21.3252	+	4.86735i	1.60745	+	0.366890i
$177$	−1.43957	−	10.6273i	−0.108204	−	0.798798i
$178$	−10.1628	+	5.46882i	−0.761731	+	0.409905i
$179$	16.6601	−	14.5555i	1.24524	−	1.08793i	0.252502	−	0.967596i	$-0.418746\pi$
$179$	16.6601	−	14.5555i	1.24524	−	1.08793i	0.992734	−	0.120334i	$-0.0383964\pi$
$180$	0.884950	−	0.525204i	0.0659602	−	0.0391464i
$181$	−3.27605	+	6.08792i	−0.243507	+	0.452512i	−0.972786	−	0.231704i	$-0.925570\pi$
$181$	−3.27605	+	6.08792i	−0.243507	+	0.452512i	0.729279	+	0.684216i	$0.239855\pi$
$182$	−7.04078	+	8.82886i	−0.521897	+	0.654439i
$183$	24.9251	+	1.11939i	1.84252	+	0.0827475i
$184$	−8.58225	−	1.16255i	−0.632692	−	0.0857040i
$185$	0.0167550	+	0.399303i	0.00123185	+	0.0293573i
$186$	−29.8185	−	9.68862i	−2.18640	−	0.710404i
$187$	−24.0368	−	15.8666i	−1.75775	−	1.16028i
$188$	−0.754727	+	0.450929i	−0.0550442	+	0.0328873i
$189$	1.27141	−	14.1265i	0.0924811	−	1.02755i
$190$	−25.5956	+	1.07401i	−1.85690	+	0.0779167i
$191$	4.37368	−	1.42110i	0.316469	−	0.102827i	−0.146476	−	0.989214i	$-0.546793\pi$
$191$	4.37368	−	1.42110i	0.316469	−	0.102827i	0.462944	+	0.886387i	$0.346793\pi$
$192$	−12.7658	−	3.52315i	−0.921294	−	0.254261i
$193$	−5.19770	−	2.50308i	−0.374138	−	0.180176i	0.237359	−	0.971422i	$-0.423718\pi$
$193$	−5.19770	−	2.50308i	−0.374138	−	0.180176i	−0.611497	+	0.791246i	$0.709433\pi$
$194$	0.265105	−	5.90302i	0.0190334	−	0.423812i
$195$	−2.89684	+	7.65008i	−0.207447	+	0.547834i
$196$	−3.55183	−	0.644562i	−0.253702	−	0.0460402i
$197$	18.7875	+	8.03015i	1.33855	+	0.572125i	0.938789	−	0.344493i	$-0.111949\pi$
$197$	18.7875	+	8.03015i	1.33855	+	0.572125i	0.399764	+	0.916618i	$0.369092\pi$
$198$	5.31274	−	8.89203i	0.377560	−	0.631929i
$199$	3.44970	+	1.66129i	0.244543	+	0.117766i	0.552141	−	0.833751i	$-0.313811\pi$
$199$	3.44970	+	1.66129i	0.244543	+	0.117766i	−0.307598	+	0.951516i	$0.599525\pi$
$200$	−8.76694	−	9.27826i	−0.619917	−	0.656072i
$201$	−5.42472	−	1.23816i	−0.382630	−	0.0873328i
$202$	6.09914	+	1.98173i	0.429134	+	0.139434i
$203$	−1.28187	−	22.8566i	−0.0899694	−	1.60422i
$204$	−3.31621	−	2.40937i	−0.232181	−	0.168690i
$205$	−2.48295	−	2.85891i	−0.173417	−	0.199675i
$206$	−15.8588	−	8.53400i	−1.10494	−	0.594592i
$207$	−2.07748	+	4.31394i	−0.144395	+	0.299839i
$208$	−7.28052	+	3.11185i	−0.504814	+	0.215768i
$209$	−31.0297	+	18.5394i	−2.14637	+	1.28240i
$210$	−30.1858	+	3.99849i	−2.08302	+	0.275922i
$211$	10.0527	−	6.63572i	0.692055	−	0.456822i	−0.155287	−	0.987869i	$-0.549630\pi$
$211$	10.0527	−	6.63572i	0.692055	−	0.456822i	0.847342	+	0.531048i	$0.178202\pi$
$212$	−0.236433	+	0.629972i	−0.0162383	+	0.0432667i
$213$	3.61727	−	26.7038i	0.247851	−	1.82971i
$214$	−1.67504	−	4.46312i	−0.114503	−	0.305092i
$215$	−9.28421	+	6.70371i	−0.633178	+	0.457189i
$216$	4.69259	−	7.10898i	0.319291	−	0.483705i
$217$	31.3335	+	27.3753i	2.12706	+	1.85835i
$218$	1.05426	+	4.61903i	0.0714038	+	0.312840i
$219$	28.0013	+	7.72788i	1.89215	+	0.522202i
$220$	3.33332	+	1.09392i	0.224733	+	0.0737522i
$221$	10.4148	−	0.467730i	0.700576	−	0.0314629i
$222$	0.271305	+	0.504169i	0.0182088	+	0.0338376i
$223$	−14.3882	+	9.49759i	−0.963507	+	0.636005i	−0.931600	−	0.363485i	$-0.881587\pi$
$223$	−14.3882	+	9.49759i	−0.963507	+	0.636005i	−0.0319072	+	0.999491i	$0.510158\pi$
$224$	−6.07214	−	4.84237i	−0.405712	−	0.323545i
$225$	−6.37628	+	3.02454i	−0.425085	+	0.201636i
$226$	−1.55901	−	6.83046i	−0.103704	−	0.454355i
$227$	3.51803	−	5.88820i	0.233500	−	0.390813i	−0.719163	−	0.694841i	$-0.755475\pi$
$227$	3.51803	−	5.88820i	0.233500	−	0.390813i	0.952663	+	0.304028i	$0.0983317\pi$
$228$	−4.53014	+	2.43777i	−0.300016	+	0.161445i
$229$	1.00009	−	5.51096i	0.0660879	−	0.364174i	−0.933890	−	0.357560i	$-0.883609\pi$
$229$	1.00009	−	5.51096i	0.0660879	−	0.364174i	0.999978	−	0.00661440i	$-0.00210544\pi$
$230$	−11.2713	−	2.60752i	−0.743205	−	0.171935i
$231$	−34.7579	+	25.2531i	−2.28690	+	1.66153i
$232$	5.82676	−	12.4525i	0.382546	−	0.817548i
$233$	−10.4536	−	14.3882i	−0.684839	−	0.942599i	0.315141	−	0.949045i	$-0.397948\pi$
$233$	−10.4536	−	14.3882i	−0.684839	−	0.942599i	−0.999979	+	0.00644562i	$0.997948\pi$
$234$	0.336095	+	3.73432i	0.0219712	+	0.244120i
$235$	5.43991	−	2.60002i	0.354860	−	0.169607i
$236$	1.15051	−	1.20334i	0.0748919	−	0.0783308i
$237$	0.582252	+	6.46934i	0.0378213	+	0.420229i
$238$	19.9039	+	33.3135i	1.29018	+	2.15939i
$239$	3.32682	+	24.5596i	0.215194	+	1.58863i	0.700089	+	0.714055i	$0.253144\pi$
$239$	3.32682	+	24.5596i	0.215194	+	1.58863i	−0.484895	+	0.874572i	$0.661142\pi$
$240$	−19.9659	−	7.56045i	−1.28879	−	0.488025i
$241$	−28.7170	−	10.7777i	−1.84983	−	0.694252i	−0.979392	−	0.201969i	$-0.935266\pi$
$241$	−28.7170	−	10.7777i	−1.84983	−	0.694252i	−0.870435	−	0.492283i	$-0.836163\pi$
$242$	18.2384	−	3.30978i	1.17241	−	0.212761i
$243$	−8.48127	−	10.6352i	−0.544074	−	0.682247i
$244$	2.27664	+	3.13353i	0.145747	+	0.200604i
$245$	23.8444	+	6.65624i	1.52336	+	0.425251i
$246$	−4.98806	−	2.13200i	−0.318027	−	0.135931i
$247$	5.14232	−	12.0311i	0.327198	−	0.765518i
$248$	8.78012	+	23.3945i	0.557538	+	1.48556i
$249$			17.5555i			1.11253i
$250$	−10.5133	−	13.4248i	−0.664923	−	0.849062i
$251$	−9.80873	+	20.3680i	−0.619121	+	1.28562i	0.321740	+	0.946828i	$0.395732\pi$
$251$	−9.80873	+	20.3680i	−0.619121	+	1.28562i	−0.940862	+	0.338791i	$0.889982\pi$
$252$	−1.63274	+	1.07776i	−0.102853	+	0.0678925i
$253$	−15.7351	+	4.34262i	−0.989259	+	0.273018i
$254$	−5.03036	−	0.912876i	−0.315633	−	0.0572789i
$255$	21.1151	+	18.5576i	1.32228	+	1.16212i
$256$	−2.99826	−	7.01477i	−0.187391	−	0.438423i
$257$	11.4059	−	23.6847i	0.711483	−	1.47741i	−0.160069	−	0.987106i	$-0.551172\pi$
$257$	11.4059	−	23.6847i	0.711483	−	1.47741i	0.871552	−	0.490304i	$-0.163114\pi$
$258$	−7.77383	+	14.4462i	−0.483978	+	0.899381i
$259$	−0.0681070	−	0.756730i	−0.00423196	−	0.0470209i
$260$	−1.20888	+	0.388860i	−0.0749718	+	0.0241160i
$261$	−5.55208	−	5.19114i	−0.343665	−	0.321323i
$262$	−5.94283	+	1.93094i	−0.367149	+	0.119294i
$263$	−8.51501	+	0.766364i	−0.525058	+	0.0472561i	−0.348998	−	0.937123i	$-0.613478\pi$
$263$	−8.51501	+	0.766364i	−0.525058	+	0.0472561i	−0.176060	+	0.984379i	$0.556335\pi$
$264$	−25.5685	+	3.46348i	−1.57363	+	0.213163i
$265$	2.01441	−	4.15165i	0.123744	−	0.255034i
$266$	48.5069	−	4.36570i	2.97415	−	0.267678i
$267$	10.4569	−	11.9688i	0.639950	−	0.732481i
$268$	−0.374783	−	0.778245i	−0.0228935	−	0.0475389i
$269$	−15.4334	−	0.693113i	−0.940988	−	0.0422598i	−0.430917	−	0.902392i	$-0.641810\pi$
$269$	−15.4334	−	0.693113i	−0.940988	−	0.0422598i	−0.510072	+	0.860132i	$0.670381\pi$
$270$	7.12056	−	8.87518i	0.433344	−	0.540126i
$271$	12.1126	−	6.51805i	0.735786	−	0.395943i	−0.0626404	−	0.998036i	$-0.519952\pi$
$271$	12.1126	−	6.51805i	0.735786	−	0.395943i	0.798426	+	0.602093i	$0.205666\pi$
$272$	1.22072	+	27.1815i	0.0740173	+	1.64812i
$273$	4.80567	−	14.7903i	0.290853	−	0.895152i
$274$	15.0008	+	18.8104i	0.906231	+	1.13638i
$275$	−22.0670	−	9.58595i	−1.33069	−	0.578055i
$276$	−2.26493	+	0.516955i	−0.136333	+	0.0311170i
$277$	0.0812616	+	0.216521i	0.00488254	+	0.0130095i	0.938654	−	0.344862i	$-0.112074\pi$
$277$	0.0812616	+	0.216521i	0.00488254	+	0.0130095i	−0.933771	+	0.357871i	$0.883503\pi$
$278$	3.26301	+	2.37072i	0.195702	+	0.142186i
$279$	13.8009	−	0.619798i	0.826237	−	0.0371063i
$280$	17.4912	+	16.8221i	1.04530	+	1.00531i
$281$	1.17623	−	26.1908i	0.0701680	−	1.56241i	−0.587575	−	0.809170i	$-0.699917\pi$
$281$	1.17623	−	26.1908i	0.0701680	−	1.56241i	0.657743	−	0.753242i	$-0.271511\pi$
$282$	5.38534	−	6.75301i	0.320693	−	0.402136i
$283$	18.1053	+	9.74288i	1.07625	+	0.579154i	0.913220	−	0.407467i	$-0.133588\pi$
$283$	18.1053	+	9.74288i	1.07625	+	0.579154i	0.163029	+	0.986621i	$0.447874\pi$
$284$	3.59118	−	2.14563i	0.213097	−	0.127320i
$285$	32.4815	−	13.7703i	1.92404	−	0.815684i
$286$	−8.83336	+	9.23898i	−0.522328	+	0.546312i
$287$	4.97482	+	5.20325i	0.293654	+	0.307138i
$288$	−2.56832	+	0.231153i	−0.151340	+	0.0136208i
$289$	5.81767	−	17.9049i	0.342216	−	1.05323i
$290$	9.28986	−	15.8422i	0.545519	−	0.930288i
$291$	2.51463	+	7.73924i	0.147410	+	0.453682i
$292$	1.77231	+	4.14653i	0.103717	+	0.242657i
$293$	−21.6835	+	10.4422i	−1.26676	+	0.610040i	−0.941955	−	0.335740i	$-0.891014\pi$
$293$	−21.6835	+	10.4422i	−1.26676	+	0.610040i	−0.324807	+	0.945780i	$0.605299\pi$
$294$	34.8948	−	6.33247i	2.03511	−	0.369317i
$295$	−8.62017	+	7.48659i	−0.501886	+	0.435886i
$296$	0.179337	−	0.419580i	0.0104238	−	0.0243876i
$297$	2.86668	−	15.7967i	0.166342	−	0.916618i
$298$	−0.324724	−	0.491936i	−0.0188108	−	0.0284971i
$299$	3.68397	−	4.61955i	0.213049	−	0.267155i
$300$	−3.07625	−	1.50382i	−0.177608	−	0.0868232i
$301$	17.0209	−	13.5737i	0.981071	−	0.782378i
$302$	5.89267	−	18.1358i	0.339085	−	1.04360i
$303$	−8.82277	+	0.396231i	−0.506855	+	0.0227629i
$304$	31.3998	+	13.4209i	1.80090	+	0.769742i
$305$	−13.5567	−	22.8426i	−0.776255	−	1.30796i
$306$	12.4204	+	3.42783i	0.710030	+	0.195956i
$307$	−9.89132			−0.564528			−0.282264	−	0.959337i	$-0.591085\pi$
$307$	−9.89132			−0.564528			−0.282264	+	0.959337i	$0.591085\pi$
$308$	−6.42921	−	1.77435i	−0.366338	−	0.101103i
$309$	24.5769	+	3.32917i	1.39813	+	0.189390i
$310$	8.78530	+	32.2022i	0.498971	+	1.82896i
$311$	20.0897	−	13.2611i	1.13918	−	0.751967i	0.166944	−	0.985966i	$-0.446610\pi$
$311$	20.0897	−	13.2611i	1.13918	−	0.751967i	0.972237	+	0.234000i	$0.0751814\pi$
$312$	6.75063	−	6.45426i	0.382179	−	0.365401i
$313$	9.54581	+	15.9770i	0.539561	+	0.903074i	0.999883	+	0.0153211i	$0.00487706\pi$
$313$	9.54581	+	15.9770i	0.539561	+	0.903074i	−0.460321	+	0.887752i	$0.652266\pi$
$314$	2.77208	+	1.65624i	0.156438	+	0.0934671i
$315$	11.8333	−	6.32293i	0.666732	−	0.356256i
$316$	−0.728835	+	0.696837i	−0.0410001	+	0.0392002i
$317$	2.05513	+	4.80823i	0.115428	+	0.270057i	0.967274	−	0.253736i	$-0.0816594\pi$
$317$	2.05513	+	4.80823i	0.115428	+	0.270057i	−0.851846	+	0.523793i	$0.824517\pi$
$318$		−	6.61066i		−	0.370708i
$319$	0.874005	−	25.8978i	0.0489349	−	1.45000i
$320$	4.31729	+	13.4216i	0.241344	+	0.750288i
$321$	4.31936	+	4.94390i	0.241083	+	0.275942i
$322$	21.6405	+	3.92717i	1.20598	+	0.218852i
$323$	−32.4989	−	31.0721i	−1.80829	−	1.72890i
$324$	0.815667	−	3.57367i	0.0453148	−	0.198537i
$325$	8.50170	−	1.88787i	0.471589	−	0.104720i
$326$	13.2473	−	6.37955i	0.733698	−	0.353330i
$327$	−3.59443	−	5.44532i	−0.198772	−	0.301127i
$328$	1.15016	+	4.16752i	0.0635070	+	0.230113i
$329$	−10.0938	+	5.43169i	−0.556488	+	0.299459i
$330$	−34.4362	+	1.44497i	−1.89565	+	0.0795428i
$331$	13.5496	+	18.6494i	0.744752	+	1.02506i	0.998331	+	0.0577483i	$0.0183921\pi$
$331$	13.5496	+	18.6494i	0.744752	+	1.02506i	−0.253579	+	0.967315i	$0.581608\pi$
$332$	−2.13073	+	1.69920i	−0.116939	+	0.0932556i
$333$	−0.189977	−	0.165978i	−0.0104107	−	0.00909553i
$334$	−3.98782	−	6.67449i	−0.218204	−	0.365212i
$335$	2.06513	+	5.55215i	0.112830	+	0.303347i
$336$	38.6012	+	12.5423i	2.10587	+	0.684239i
$337$	9.13722	−	13.8423i	0.497736	−	0.754038i	−0.495692	−	0.868499i	$-0.665085\pi$
$337$	9.13722	−	13.8423i	0.497736	−	0.754038i	0.993428	+	0.114460i	$0.0365139\pi$
$338$	−2.04034	+	15.0624i	−0.110980	+	0.819288i
$339$	5.31530	+	8.05234i	0.288688	+	0.437343i
$340$	−0.208620	+	4.35895i	−0.0113140	+	0.236397i
$341$	32.5467	+	34.0412i	1.76250	+	1.84344i
$342$	10.6393	−	12.1776i	0.575307	−	0.658492i
$343$	−16.8730	−	3.85115i	−0.911056	−	0.207943i
$344$	12.8645	−	2.33455i	0.693605	−	0.125871i
$345$	15.7942	−	2.09214i	0.850330	−	0.112637i
$346$	10.6652	+	12.2073i	0.573363	+	0.656266i
$347$	−10.8155	+	14.8862i	−0.580604	+	0.799133i	−0.993761	−	0.111527i	$-0.964426\pi$
$347$	−10.8155	+	14.8862i	−0.580604	+	0.799133i	0.413157	+	0.910660i	$0.364426\pi$
$348$	0.289629	−	3.67653i	0.0155257	−	0.197083i
$349$	−9.57535			−0.512557			−0.256278	−	0.966603i	$-0.582496\pi$
$349$	−9.57535			−0.512557			−0.256278	+	0.966603i	$0.582496\pi$
$350$	21.1844	+	24.5375i	1.13235	+	1.31159i
$351$	2.52146	+	5.23587i	0.134586	+	0.279470i
$352$	−6.35421	−	6.07524i	−0.338680	−	0.323812i
$353$	22.8266	+	26.1272i	1.21494	+	1.39061i	0.896724	+	0.442590i	$0.145940\pi$
$353$	22.8266	+	26.1272i	1.21494	+	1.39061i	0.318214	+	0.948019i	$0.396917\pi$
$354$	−6.42839	+	15.0400i	−0.341665	+	0.799365i
$355$	−25.8844	+	12.3715i	−1.37380	+	0.656613i
$356$	2.46479	+	0.110694i	0.130634	+	0.00586677i
$357$	−41.7829	−	33.3208i	−2.21139	−	1.76352i
$358$	−33.1983	+	6.02461i	−1.75459	+	0.318410i
$359$	17.3626	+	11.4610i	0.916365	+	0.604887i	0.918634	−	0.395110i	$-0.129294\pi$
$359$	17.3626	+	11.4610i	0.916365	+	0.604887i	−0.00226851	+	0.999997i	$0.500722\pi$
$360$	8.05748	+	0.0237196i	0.424667	+	0.00125013i
$361$	−35.0425	+	13.1517i	−1.84434	+	0.692193i
$362$	9.05143	−	5.40798i	0.475732	−	0.284237i
$363$	−21.9138	+	13.0929i	−1.15017	+	0.687198i
$364$	2.26026	−	0.848290i	0.118470	−	0.0444625i
$365$	−9.46980	−	29.4396i	−0.495672	−	1.54094i
$366$	−31.7577	−	20.9631i	−1.66000	−	1.09576i
$367$	28.0429	−	5.08903i	1.46383	−	0.265645i	0.612579	−	0.790410i	$-0.290132\pi$
$367$	28.0429	−	5.08903i	1.46383	−	0.265645i	0.851248	+	0.524764i	$0.175847\pi$
$368$	12.0565	+	9.61476i	0.628490	+	0.501204i
$369$	2.38778	+	0.107235i	0.124303	+	0.00558244i
$370$	0.290415	−	0.535896i	0.0150980	−	0.0278599i
$371$	−3.44793	+	8.06683i	−0.179008	+	0.418809i
$372$	4.41009	+	5.04775i	0.228653	+	0.261714i
$373$	2.92712	+	2.79862i	0.151561	+	0.144907i	0.763034	−	0.646358i	$-0.223709\pi$
$373$	2.92712	+	2.79862i	0.151561	+	0.144907i	−0.611474	+	0.791265i	$0.709423\pi$
$374$	19.0588	+	39.5760i	0.985508	+	2.04643i
$375$	20.0514	+	12.2218i	1.03545	+	0.631128i
$376$	−6.88390			−0.355010
$377$	5.25414	+	7.76993i	0.270602	+	0.400172i
$378$	−12.7149	+	17.5006i	−0.653986	+	0.900134i
$379$	5.66816	+	6.48773i	0.291154	+	0.333252i	0.879983	−	0.475005i	$-0.157554\pi$
$379$	5.66816	+	6.48773i	0.291154	+	0.333252i	−0.588829	+	0.808257i	$0.700411\pi$
$380$	4.81521	+	2.60948i	0.247015	+	0.133864i
$381$	6.92755	−	1.25716i	0.354909	−	0.0644065i
$382$	−6.83791	−	1.56071i	−0.349858	−	0.0798528i
$383$	3.63435	−	4.15984i	0.185706	−	0.212558i	−0.652681	−	0.757633i	$-0.726356\pi$
$383$	3.63435	−	4.15984i	0.185706	−	0.212558i	0.838388	+	0.545075i	$0.183499\pi$
$384$	19.2614	+	20.1459i	0.982930	+	1.02806i
$385$	42.7753	+	16.1976i	2.18003	+	0.825509i
$386$	4.84710	+	7.34304i	0.246711	+	0.373751i
$387$	0.970291	−	7.16298i	0.0493227	−	0.364115i
$388$	−0.695928	+	1.05429i	−0.0353304	+	0.0535232i
$389$	20.3052	+	6.59755i	1.02951	+	0.334509i	0.774597	−	0.632455i	$-0.217952\pi$
$389$	20.3052	+	6.59755i	1.02951	+	0.334509i	0.254915	+	0.966963i	$0.417952\pi$
$390$	9.77694	−	7.74987i	0.495075	−	0.392430i
$391$	−10.4143	−	17.4307i	−0.526676	−	0.881508i
$392$	−21.2855	−	18.5965i	−1.07508	−	0.939267i
$393$	6.72791	−	5.36533i	0.339378	−	0.270645i
$394$	−18.3161	−	25.2099i	−0.922751	−	1.27006i
$395$	5.41921	−	4.29564i	0.272670	−	0.216137i
$396$	−1.95005	+	1.04937i	−0.0979936	+	0.0527326i
$397$	3.49270	+	12.6555i	0.175293	+	0.635161i	0.997793	+	0.0663961i	$0.0211501\pi$
$397$	3.49270	+	12.6555i	0.175293	+	0.635161i	−0.822500	+	0.568765i	$0.807421\pi$
$398$	−3.21701	−	4.87356i	−0.161254	−	0.244289i
$399$	−60.4291	+	29.1011i	−3.02524	+	1.45688i
$400$	4.92713	+	22.1885i	0.246356	+	1.10943i
$401$	1.74998	−	7.66718i	0.0873900	−	0.382881i	−0.912252	−	0.409629i	$-0.865658\pi$
$401$	1.74998	−	7.66718i	0.0873900	−	0.382881i	0.999642	+	0.0267483i	$0.00851527\pi$
$402$	6.13380	+	5.86451i	0.305926	+	0.292495i
$403$	−16.7738	−	3.04399i	−0.835560	−	0.151632i
$404$	−0.902048	−	1.03248i	−0.0448786	−	0.0513677i
$405$	−7.83849	+	23.8849i	−0.389498	+	1.18685i
$406$	−16.2011	+	30.9278i	−0.804048	+	1.53492i
$407$		−	0.860023i		−	0.0426298i
$408$	−12.6143	−	29.5126i	−0.624501	−	1.46109i
$409$	19.4197	−	18.5671i	0.960241	−	0.918084i	−0.0364526	−	0.999335i	$-0.511606\pi$
$409$	19.4197	−	18.5671i	0.960241	−	0.918084i	0.996694	+	0.0812509i	$0.0258915\pi$
$410$	1.01446	+	5.68532i	0.0501004	+	0.280778i
$411$	−28.4433	−	16.9941i	−1.40300	−	0.838256i
$412$	1.97474	+	3.30515i	0.0972883	+	0.162833i
$413$	15.6888	−	15.0000i	0.771996	−	0.738104i
$414$	6.09451	−	4.02295i	0.299529	−	0.197717i
$415$	15.6283	−	10.2503i	0.767165	−	0.503165i
$416$	3.15336	+	0.427152i	0.154606	+	0.0209429i
$417$	−5.35429	−	1.47769i	−0.262201	−	0.0723628i
$418$	55.1281			2.69640
$419$	6.00881	+	1.65833i	0.293550	+	0.0810145i	0.409710	−	0.912216i	$-0.365630\pi$
$419$	6.00881	+	1.65833i	0.293550	+	0.0810145i	−0.116160	+	0.993230i	$0.537059\pi$
$420$	5.97831	+	2.57609i	0.291711	+	0.125700i
$421$	−30.4117	−	12.9986i	−1.48218	−	0.633513i	−0.508421	−	0.861109i	$-0.669771\pi$
$421$	−30.4117	−	12.9986i	−1.48218	−	0.633513i	−0.973756	+	0.227596i	$0.926913\pi$
$422$	−18.3523	+	0.824202i	−0.893375	+	0.0401215i
$423$	−1.17606	+	3.61955i	−0.0571822	+	0.175989i
$424$	−4.11916	+	3.28492i	−0.200044	+	0.159530i
$425$	4.19181	−	29.6325i	0.203333	−	1.43739i
$426$	−25.6248	+	32.1325i	−1.24152	+	1.55682i
$427$	27.8194	+	42.1446i	1.34628	+	2.03952i
$428$	−0.181975	+	1.00277i	−0.00879610	+	0.0484705i
$429$	6.91846	−	16.1865i	0.334026	−	0.781494i
$430$	17.3993	−	1.51435i	0.839071	−	0.0730283i
$431$	29.2422	−	5.30667i	1.40855	−	0.255613i	0.579581	−	0.814915i	$-0.303216\pi$
$431$	29.2422	−	5.30667i	1.40855	−	0.255613i	0.828964	+	0.559301i	$0.188931\pi$
$432$	−13.6651	+	6.58075i	−0.657461	+	0.316616i
$433$	3.54834	+	8.30176i	0.170523	+	0.398957i	0.982891	−	0.184187i	$-0.0589651\pi$
$433$	3.54834	+	8.30176i	0.170523	+	0.398957i	−0.812369	+	0.583144i	$0.801822\pi$
$434$	−19.6094	−	60.3517i	−0.941283	−	2.89697i
$435$	−4.31175	+	24.9213i	−0.206733	+	1.19488i
$436$	0.312999	−	0.963313i	0.0149899	−	0.0461343i
$437$	−25.3804	+	2.28428i	−1.21411	+	0.109272i
$438$	−30.6158	−	32.0216i	−1.46288	−	1.53005i
$439$	−5.69306	+	5.95447i	−0.271715	+	0.284192i	−0.844547	−	0.535481i	$-0.820130\pi$
$439$	−5.69306	+	5.95447i	−0.271715	+	0.284192i	0.572832	+	0.819673i	$0.305845\pi$
$440$	18.0121	+	20.7394i	0.858694	+	0.988714i
$441$	−13.4145	+	8.01481i	−0.638787	+	0.381658i
$442$	−14.0015	−	7.53454i	−0.665985	−	0.358382i
$443$	3.99855	−	5.01403i	0.189977	−	0.238224i	−0.677716	−	0.735323i	$-0.737030\pi$
$443$	3.99855	−	5.01403i	0.189977	−	0.238224i	0.867693	+	0.497100i	$0.165602\pi$
$444$	0.00549146	−	0.122277i	0.000260613	−	0.00580301i
$445$	−16.7605	−	2.32063i	−0.794524	−	0.110008i
$446$	26.2673	−	1.17967i	1.24379	−	0.0558588i
$447$	0.656723	+	0.477137i	0.0310619	+	0.0225678i
$448$	−9.41808	−	25.0944i	−0.444963	−	1.18560i
$449$	−7.33523	+	1.67422i	−0.346171	+	0.0790113i	−0.392072	−	0.919935i	$-0.628241\pi$
$449$	−7.33523	+	1.67422i	−0.346171	+	0.0790113i	0.0459005	+	0.998946i	$0.485384\pi$
$450$	10.7141	+	1.02791i	0.505068	+	0.0484563i
$451$	5.08050	+	6.37075i	0.239231	+	0.299987i
$452$	−0.462852	+	1.42451i	−0.0217707	+	0.0670034i
$453$	1.17819	+	26.2345i	0.0553564	+	1.23260i
$454$	−9.21201	+	4.95719i	−0.432341	+	0.232653i
$455$	−15.9727	+	4.35762i	−0.748810	+	0.204288i
$456$	−40.2398	−	1.80717i	−1.88440	−	0.0846286i
$457$	16.6867	+	34.6503i	0.780572	+	1.62087i	0.783906	+	0.620879i	$0.213224\pi$
$457$	16.6867	+	34.6503i	0.780572	+	1.62087i	−0.00333454	+	0.999994i	$0.501061\pi$
$458$	−5.62029	+	6.43293i	−0.262619	+	0.300591i
$459$	19.8903	−	1.79016i	0.928399	−	0.0835574i
$460$	1.78265	+	1.71446i	0.0831163	+	0.0799370i
$461$	−15.9027	+	2.15417i	−0.740664	+	0.100330i	−0.494839	−	0.868985i	$-0.664773\pi$
$461$	−15.9027	+	2.15417i	−0.740664	+	0.100330i	−0.245825	+	0.969314i	$0.579059\pi$
$462$	65.2610	−	5.87360i	3.03622	−	0.273265i
$463$	33.1602	−	10.7744i	1.54108	−	0.500729i	0.589409	−	0.807834i	$-0.299361\pi$
$463$	33.1602	−	10.7744i	1.54108	−	0.500729i	0.951675	+	0.307106i	$0.0993605\pi$
$464$	−20.2787	+	13.7127i	−0.941415	+	0.636598i
$465$	−26.9097	−	37.2682i	−1.24791	−	1.72827i
$466$	2.43140	+	27.0150i	0.112632	+	1.25145i
$467$	−7.05539	+	13.1111i	−0.326484	+	0.606710i	−0.989937	−	0.141509i	$-0.954805\pi$
$467$	−7.05539	+	13.1111i	−0.326484	+	0.606710i	0.663453	+	0.748218i	$0.269090\pi$
$468$	0.347791	−	0.722196i	0.0160767	−	0.0333835i
$469$	−4.42617	−	10.3555i	−0.204381	−	0.478174i
$470$	−9.15608	−	0.851241i	−0.422338	−	0.0392648i
$471$	−4.37558	−	0.794051i	−0.201616	−	0.0365880i
$472$	12.5659	−	3.46796i	0.578391	−	0.159626i
$473$	20.5661	−	13.5756i	0.945631	−	0.624205i
$474$	4.29829	−	8.92549i	0.197427	−	0.409961i
$475$	−31.2239	−	20.8757i	−1.43265	−	0.957843i
$476$		−	8.29636i		−	0.380263i
$477$	1.02348	+	2.72706i	0.0468620	+	0.124863i
$478$	14.8559	−	34.7572i	0.679494	−	1.58976i
$479$	14.9541	+	6.39170i	0.683271	+	0.292044i	0.706528	−	0.707685i	$-0.250261\pi$
$479$	14.9541	+	6.39170i	0.683271	+	0.292044i	−0.0232566	+	0.999730i	$0.507403\pi$
$480$	5.33006	+	6.72420i	0.243283	+	0.306916i
$481$	0.182981	+	0.251851i	0.00834320	+	0.0114834i
$482$	29.1672	+	36.5745i	1.32853	+	1.66592i
$483$	−29.8021	+	5.40829i	−1.35604	+	0.246086i
$484$	−3.71013	−	1.39244i	−0.168642	−	0.0632925i
$485$	5.42143	−	6.75736i	0.246175	−	0.306836i
$486$	2.78485	+	20.5586i	0.126323	+	0.932557i
$487$	−5.88474	−	9.84939i	−0.266663	−	0.446318i	0.695604	−	0.718425i	$-0.255137\pi$
$487$	−5.88474	−	9.84939i	−0.266663	−	0.446318i	−0.962267	+	0.272107i	$0.912280\pi$
$488$	2.71853	+	30.2053i	0.123062	+	1.36733i
$489$	−13.9931	+	14.6357i	−0.632791	+	0.661847i
$490$	−26.0116	−	27.3668i	−1.17508	−	1.23631i
$491$	2.91256	+	32.3612i	0.131442	+	1.46044i	0.743027	+	0.669261i	$0.233389\pi$
$491$	2.91256	+	32.3612i	0.131442	+	1.46044i	−0.611585	+	0.791179i	$0.709468\pi$
$492$	0.681660	+	0.938224i	0.0307316	+	0.0422984i
$493$	31.3429	−	7.52227i	1.41162	−	0.338786i
$494$	−16.1438	+	11.7292i	−0.726346	+	0.527721i
$495$	13.9820	−	5.92759i	0.628446	−	0.266426i
$496$	7.94449	−	43.7777i	0.356718	−	1.96568i
$497$	48.0286	−	25.8453i	2.15438	−	1.15932i
$498$	13.7327	−	22.9846i	0.615376	−	1.02997i
$499$	−6.46168	−	28.3105i	−0.289265	−	1.26735i	−0.885537	−	0.464569i	$-0.846209\pi$
$499$	−6.46168	−	28.3105i	−0.289265	−	1.26735i	0.596272	−	0.802782i	$-0.296648\pi$
$500$	0.457415	+	3.61661i	0.0204562	+	0.161740i
$501$	8.37139	+	6.67596i	0.374006	+	0.298260i
$502$	28.7749	−	18.9941i	1.28429	−	0.847750i
$503$	−0.568938	−	1.05726i	−0.0253677	−	0.0471411i	0.867596	−	0.497269i	$-0.165664\pi$
$503$	−0.568938	−	1.05726i	−0.0253677	−	0.0471411i	−0.892964	+	0.450128i	$0.851378\pi$
$504$	−15.3029	+	0.687252i	−0.681644	+	0.0306127i
$505$	5.50415	+	7.62291i	0.244932	+	0.339215i
$506$	23.9983	+	6.62311i	1.06685	+	0.294433i
$507$	−4.65795	−	20.4078i	−0.206867	−	0.906343i
$508$	0.823102	+	0.719122i	0.0365192	+	0.0319059i
$509$	−1.97612	+	2.99369i	−0.0875900	+	0.132693i	−0.875727	−	0.482807i	$-0.839617\pi$
$509$	−1.97612	+	2.99369i	−0.0875900	+	0.132693i	0.788137	+	0.615500i	$0.211046\pi$
$510$	−13.1285	−	40.8138i	−0.581340	−	1.80726i
$511$	20.6582	+	55.0436i	0.913865	+	2.43498i
$512$	2.00085	−	14.7709i	0.0884258	−	0.652786i
$513$	8.80672	−	23.4654i	0.388826	−	1.03602i
$514$	−33.4605	+	22.0871i	−1.47588	+	0.974219i
$515$	−11.3862	−	23.8228i	−0.501735	−	1.04976i
$516$	3.01075	−	1.79884i	0.132541	−	0.0791894i
$517$	−11.9305	+	5.09935i	−0.524704	+	0.224269i
$518$	−0.502778	+	1.04403i	−0.0220908	+	0.0458720i
$519$	−19.6580	−	10.5784i	−0.862890	−	0.464341i
$520$	−9.68729	−	2.24108i	−0.424816	−	0.0982780i
$521$	−25.0878	−	18.2274i	−1.09912	−	0.798556i	−0.118203	−	0.992989i	$-0.537713\pi$
$521$	−25.0878	−	18.2274i	−1.09912	−	0.798556i	−0.980916	+	0.194433i	$0.937713\pi$
$522$	3.20836	+	11.1396i	0.140426	+	0.487567i
$523$	3.65587	+	1.18786i	0.159860	+	0.0519417i	0.387854	−	0.921721i	$-0.373217\pi$
$523$	3.65587	+	1.18786i	0.159860	+	0.0519417i	−0.227994	+	0.973663i	$0.573217\pi$
$524$	1.30239	+	0.297262i	0.0568952	+	0.0129860i
$525$	−39.1873	−	21.3861i	−1.71027	−	0.933364i
$526$	11.7478	+	5.65744i	0.512229	+	0.246676i
$527$	−30.0478	+	50.2915i	−1.30890	+	2.19073i
$528$	42.2452	+	18.0564i	1.83848	+	0.785806i
$529$	11.3074	+	2.05199i	0.491625	+	0.0892168i
$530$	−5.88498	+	3.85982i	−0.255627	+	0.167660i
$531$	0.323335	−	7.19961i	0.0140315	−	0.312436i
$532$	−9.38097	−	4.51764i	−0.406717	−	0.195864i
$533$	−2.84324	−	0.784685i	−0.123154	−	0.0339885i
$534$	−23.0533	+	7.49046i	−0.997612	+	0.324144i
$535$	1.87921	−	6.73184i	0.0812455	−	0.291043i
$536$	0.606266	−	6.73617i	0.0261867	−	0.290958i
$537$	39.8884	−	23.8322i	1.72131	−	1.02844i
$538$	19.6640	+	12.9801i	0.847776	+	0.559612i
$539$	−50.6656	−	16.4623i	−2.18232	−	0.709080i
$540$	−2.27998	+	0.848043i	−0.0981148	+	0.0364940i
$541$	−2.38840	−	0.323531i	−0.102685	−	0.0139097i	0.0827103	−	0.996574i	$-0.473642\pi$
$541$	−2.38840	−	0.323531i	−0.102685	−	0.0139097i	−0.185396	+	0.982664i	$0.559357\pi$
$542$	−20.9571	−	0.941186i	−0.900186	−	0.0404274i
$543$	−9.05342	+	11.3526i	−0.388519	+	0.487188i
$544$	5.18196	−	9.62970i	0.222175	−	0.412870i
$545$	−2.74886	+	6.37925i	−0.117748	+	0.273257i
$546$	−17.8615	+	15.6051i	−0.764402	+	0.667838i
$547$	−25.2239	+	13.5735i	−1.07850	+	0.580363i	−0.913876	−	0.405994i	$-0.866925\pi$
$547$	−25.2239	+	13.5735i	−1.07850	+	0.580363i	−0.164620	+	0.986357i	$0.552640\pi$
$548$	−0.690442	−	5.09705i	−0.0294942	−	0.217735i
$549$	16.3464	+	3.73096i	0.697647	+	0.159233i
$550$	21.3929	+	29.8123i	0.912194	+	1.27120i
$551$	8.56156	−	39.5366i	0.364735	−	1.68432i
$552$	−17.3000	−	5.62112i	−0.736338	−	0.239251i
$553$	−9.90037	+	8.64969i	−0.421007	+	0.367822i
$554$	0.0629798	−	0.347048i	0.00267576	−	0.0147446i
$555$	−0.115125	+	0.831479i	−0.00488679	+	0.0352943i
$556$	−0.338894	−	0.792881i	−0.0143723	−	0.0336257i
$557$	−22.7017	+	5.18151i	−0.961900	+	0.219547i	−0.674510	−	0.738266i	$-0.735645\pi$
$557$	−22.7017	+	5.18151i	−0.961900	+	0.219547i	−0.287391	+	0.957813i	$0.592788\pi$
$558$	−18.5537	−	9.98418i	−0.785441	−	0.422664i
$559$	−3.13426	+	8.35120i	−0.132565	+	0.353218i
$560$	−11.3729	−	41.6870i	−0.480593	−	1.76160i
$561$	−43.7238	−	41.8043i	−1.84602	−	1.76498i
$562$	−22.0276	+	33.3703i	−0.929177	+	1.40764i
$563$	−5.40807	−	16.6443i	−0.227923	−	0.701474i	−0.997982	−	0.0635016i	$-0.979773\pi$
$563$	−5.40807	−	16.6443i	−0.227923	−	0.701474i	0.770059	−	0.637973i	$-0.220227\pi$
$564$	−1.72883	+	0.648839i	−0.0727967	+	0.0273211i
$565$	4.06491	−	9.43340i	0.171012	−	0.396866i
$566$	−16.0832	−	26.9187i	−0.676026	−	1.13148i
$567$	12.7141	−	46.0685i	0.533942	−	1.93469i
$568$	32.7553			1.37438
$569$	7.11351	−	25.7752i	0.298214	−	1.08055i	−0.649220	−	0.760601i	$-0.724904\pi$
$569$	7.11351	−	25.7752i	0.298214	−	1.08055i	0.947434	−	0.319953i	$-0.103667\pi$
$570$	−53.2984	−	7.37960i	−2.23242	−	0.309097i
$571$	15.9152	−	4.39231i	0.666029	−	0.183812i	0.0833572	−	0.996520i	$-0.473436\pi$
$571$	15.9152	−	4.39231i	0.666029	−	0.183812i	0.582672	+	0.812707i	$0.302007\pi$
$572$	2.63422	−	0.726997i	0.110142	−	0.0303973i
$573$	9.57157	−	1.29656i	0.399858	−	0.0541645i
$574$	−2.44310	−	10.7039i	−0.101973	−	0.446773i
$575$	−11.0843	−	12.8388i	−0.462249	−	0.535416i
$576$	−8.01813	−	3.86133i	−0.334089	−	0.160889i
$577$	3.04530	+	22.4813i	0.126778	+	0.935909i	0.936887	+	0.349631i	$0.113693\pi$
$577$	3.04530	+	22.4813i	0.126778	+	0.935909i	−0.810110	+	0.586278i	$0.800593\pi$
$578$	−21.6228	+	18.8913i	−0.899392	+	0.785775i
$579$	−9.80279	−	7.12214i	−0.407390	−	0.295986i
$580$	−3.44205	+	1.88881i	−0.142923	+	0.0784286i
$581$	−28.7457	+	20.8850i	−1.19257	+	0.866456i
$582$	2.76168	−	12.0997i	0.114475	−	0.501549i
$583$	−4.70558	+	8.74444i	−0.194885	+	0.362158i
$584$	−4.73957	+	34.9889i	−0.196125	+	1.44785i
$585$	−2.83337	+	4.71070i	−0.117145	+	0.194764i
$586$	36.5576	+	3.29024i	1.51018	+	0.135919i
$587$	9.14257	−	8.74120i	0.377354	−	0.360788i	−0.478425	−	0.878128i	$-0.658792\pi$
$587$	9.14257	−	8.74120i	0.377354	−	0.360788i	0.855780	+	0.517341i	$0.173078\pi$
$588$	−7.09845	−	2.66409i	−0.292735	−	0.109865i
$589$	40.5043	+	61.3614i	1.66895	+	2.52835i
$590$	17.1423	−	3.05878i	0.705739	−	0.125928i
$591$	35.8145	+	23.6409i	1.47321	+	0.972458i
$592$	−0.657305	+	0.477560i	−0.0270151	+	0.0196276i
$593$	−29.2629	+	23.3364i	−1.20168	+	0.958311i	−0.999777	−	0.0210942i	$-0.993285\pi$
$593$	−29.2629	+	23.3364i	−1.20168	+	0.958311i	−0.201906	+	0.979405i	$0.564714\pi$
$594$	−16.1101	+	18.4395i	−0.661006	+	0.756582i
$595$	−5.26689	+	56.6515i	−0.215922	+	2.32248i
$596$	0.00565370	+	0.125889i	0.000231584	+	0.00515663i
$597$	6.50609	+	4.72695i	0.266277	+	0.193461i
$598$	−8.43687	+	3.16641i	−0.345009	+	0.129484i
$599$	−4.18257	+	8.68520i	−0.170895	+	0.354868i	−0.968772	−	0.247953i	$-0.920242\pi$
$599$	−4.18257	+	8.68520i	−0.170895	+	0.354868i	0.797877	+	0.602820i	$0.205956\pi$
$600$	−14.6381	−	22.4622i	−0.597596	−	0.917017i
$601$	−31.2066	−	24.8864i	−1.27294	−	1.01514i	−0.998567	−	0.0535163i	$-0.982957\pi$
$601$	−31.2066	−	24.8864i	−1.27294	−	1.01514i	−0.274377	−	0.961622i	$-0.588471\pi$
$602$	−32.9027	+	4.45698i	−1.34102	+	0.181653i
$603$	−3.43830	−	1.46960i	−0.140019	−	0.0598468i
$604$	−3.07007	+	2.68224i	−0.124919	+	0.109139i
$605$	24.4506	+	11.8636i	0.994057	+	0.482323i
$606$	11.8612	+	6.38279i	0.481829	+	0.259283i
$607$	3.81009	−	16.6931i	0.154647	−	0.677553i	−0.836851	−	0.547431i	$-0.815606\pi$
$607$	3.81009	−	16.6931i	0.154647	−	0.677553i	0.991498	−	0.130122i	$-0.0415369\pi$
$608$	−8.06688	−	11.1031i	−0.327155	−	0.450290i
$609$	5.92283	−	47.7159i	0.240005	−	1.93355i
$610$	−0.119257	+	40.5114i	−0.00482859	+	1.64026i
$611$	2.40881	−	4.03167i	0.0974501	−	0.163104i
$612$	−1.90360	−	1.99101i	−0.0769486	−	0.0804820i
$613$	20.6507	+	2.79733i	0.834075	+	0.112983i	0.538805	−	0.842431i	$-0.318876\pi$
$613$	20.6507	+	2.79733i	0.834075	+	0.112983i	0.295270	+	0.955414i	$0.404590\pi$
$614$	12.9503	+	7.73743i	0.522630	+	0.312257i
$615$	−4.05907	−	6.83939i	−0.163678	−	0.275791i
$616$	−36.0889	−	37.7460i	−1.45406	−	1.52083i
$617$	0.0953591	−	2.12333i	0.00383901	−	0.0854822i	−0.996159	−	0.0875649i	$-0.972091\pi$
$617$	0.0953591	−	2.12333i	0.00383901	−	0.0854822i	0.999998	+	0.00208263i	$0.000662921\pi$
$618$	−29.5732	−	23.5839i	−1.18961	−	0.948682i
$619$	0.466353	+	2.56982i	0.0187443	+	0.103290i	0.991945	−	0.126666i	$-0.0404276\pi$
$619$	0.466353	+	2.56982i	0.0187443	+	0.103290i	−0.973201	+	0.229956i	$0.926142\pi$
$620$	1.91869	−	6.87324i	0.0770563	−	0.276036i
$621$	6.65287	−	9.15689i	0.266970	−	0.367453i
$622$	−36.6759	+	1.64712i	−1.47057	+	0.0660434i
$623$	32.0381	+	2.88348i	1.28358	+	0.115524i
$624$	−16.2129	+	3.70049i	−0.649036	+	0.148138i
$625$	−0.827467	−	24.9863i	−0.0330987	−	0.999452i
$626$		−	28.3851i		−	1.13450i
$627$	−71.0785	+	26.6762i	−2.83860	+	1.06535i
$628$	−0.327139	−	0.607925i	−0.0130542	−	0.0242589i
$629$	1.03124	−	0.284605i	0.0411183	−	0.0113479i
$630$	−20.4389	−	0.978209i	−0.814305	−	0.0389728i
$631$	5.26726	−	9.78820i	0.209686	−	0.389662i	−0.753929	−	0.656956i	$-0.771844\pi$
$631$	5.26726	−	9.78820i	0.209686	−	0.389662i	0.963615	+	0.267294i	$0.0861294\pi$
$632$	−7.69742	+	1.75688i	−0.306187	+	0.0698851i
$633$	23.2634	−	9.94325i	0.924637	−	0.395209i
$634$	1.07051	−	7.90281i	0.0425153	−	0.313861i
$635$	−5.16400	−	5.43305i	−0.204927	−	0.215604i
$636$	−0.724869	+	1.21323i	−0.0287429	+	0.0481075i
$637$	18.3396	−	5.95889i	0.726641	−	0.236100i
$638$	−21.4027	+	33.2232i	−0.847341	+	1.31532i
$639$	5.59600	−	17.2227i	0.221374	−	0.681320i
$640$	6.68805	−	28.9097i	0.264368	−	1.14276i
$641$	14.8057	−	14.1557i	0.584789	−	0.559116i	−0.339598	−	0.940571i	$-0.610291\pi$
$641$	14.8057	−	14.1557i	0.584789	−	0.559116i	0.924387	+	0.381455i	$0.124577\pi$
$642$	−1.78781	−	9.85163i	−0.0705591	−	0.388813i
$643$	−24.4247	−	5.57478i	−0.963217	−	0.219848i	−0.288134	−	0.957590i	$-0.593035\pi$
$643$	−24.4247	−	5.57478i	−0.963217	−	0.219848i	−0.675083	+	0.737742i	$0.735892\pi$
$644$	−3.54096	−	3.09364i	−0.139533	−	0.121907i
$645$	−21.7008	+	10.3720i	−0.854467	+	0.408395i
$646$	18.2434	+	66.1034i	0.717776	+	2.60080i
$647$	−5.26407	−	19.0739i	−0.206952	−	0.749874i	−0.991534	−	0.129849i	$-0.958551\pi$
$647$	−5.26407	−	19.0739i	−0.206952	−	0.749874i	0.784582	−	0.620025i	$-0.212878\pi$
$648$	19.8344	−	20.7451i	0.779167	−	0.814945i
$649$	19.2090	−	15.3187i	0.754020	−	0.601311i
$650$	−12.6077	−	4.17870i	−0.494513	−	0.163902i
$651$	54.4870	+	68.3245i	2.13551	+	2.67785i
$652$	−3.13074	−	0.281772i	−0.122609	−	0.0110350i
$653$	−9.99347	+	23.3809i	−0.391075	+	0.914965i	0.602110	+	0.798413i	$0.294327\pi$
$653$	−9.99347	+	23.3809i	−0.391075	+	0.914965i	−0.993185	+	0.116552i	$0.962816\pi$
$654$	0.446453	+	9.94104i	0.0174577	+	0.388725i
$655$	−8.70463	−	2.85666i	−0.340118	−	0.111619i
$656$	2.04794	−	7.42056i	0.0799588	−	0.289724i
$657$	17.5875	+	8.46967i	0.686152	+	0.330433i
$658$	17.4642	+	0.784320i	0.680827	+	0.0305760i
$659$	−2.81990	+	7.51361i	−0.109848	+	0.292689i	−0.979650	−	0.200711i	$-0.935675\pi$
$659$	−2.81990	+	7.51361i	−0.109848	+	0.292689i	0.869803	+	0.493400i	$0.164246\pi$
$660$	6.47836	+	3.51079i	0.252170	+	0.136657i
$661$	14.9355	+	1.34422i	0.580925	+	0.0522842i	0.376205	−	0.926536i	$-0.377229\pi$
$661$	14.9355	+	1.34422i	0.580925	+	0.0522842i	0.204720	+	0.978821i	$0.434372\pi$
$662$	−3.15149	−	35.0159i	−0.122486	−	1.36093i
$663$	21.6986	+	2.93927i	0.842703	+	0.114152i
$664$	−21.1458	+	2.86440i	−0.820617	+	0.111160i
$665$	61.1897	+	36.8040i	2.37284	+	1.42720i
$666$	0.118893	+	0.365916i	0.00460702	+	0.0141789i
$667$	8.47695	−	16.1824i	0.328229	−	0.626587i
$668$			1.66221i			0.0643129i
$669$	−33.2965	+	14.2316i	−1.28732	+	0.550226i
$670$	1.63935	−	8.88462i	0.0633337	−	0.343243i
$671$	27.0865	+	50.3352i	1.04566	+	1.94317i
$672$	−10.7326	−	12.2845i	−0.414019	−	0.473883i
$673$	2.34913	−	26.1010i	0.0905525	−	1.00612i	−0.814314	−	0.580425i	$-0.802887\pi$
$673$	2.34913	−	26.1010i	0.0905525	−	1.00612i	0.904866	−	0.425696i	$-0.139971\pi$
$674$	−22.7910	+	10.9756i	−0.877877	+	0.422763i
$675$	16.1072	−	4.34341i	0.619966	−	0.167178i
$676$	2.02607	−	2.54061i	0.0779259	−	0.0977160i
$677$	17.9649	−	18.7898i	0.690448	−	0.722152i	−0.280920	−	0.959731i	$-0.590640\pi$
$677$	17.9649	−	18.7898i	0.690448	−	0.722152i	0.971368	+	0.237579i	$0.0763540\pi$
$678$	−0.660198	−	14.7004i	−0.0253547	−	0.564567i
$679$	−9.68086	+	13.3246i	−0.371517	+	0.511350i
$680$	−18.9077	+	28.4613i	−0.725077	+	1.09144i
$681$	9.47859	−	10.8491i	0.363221	−	0.415739i
$682$	−15.9835	−	70.0281i	−0.612039	−	2.68152i
$683$	0.691514	−	2.50565i	0.0264601	−	0.0958759i	−0.949540	−	0.313646i	$-0.898450\pi$
$683$	0.691514	−	2.50565i	0.0264601	−	0.0958759i	0.976000	+	0.217770i	$0.0698782\pi$
$684$	−3.28788	+	1.06830i	−0.125715	+	0.0408473i
$685$	1.47884	+	35.2434i	0.0565035	+	1.34658i
$686$	19.0785	+	18.2409i	0.728421	+	0.696442i
$687$	4.13356	−	11.0138i	0.157705	−	0.420204i
$688$	−21.7957	−	8.18008i	−0.830955	−	0.311863i
$689$	−0.482494	−	3.56191i	−0.0183816	−	0.135698i
$690$	−22.3152	−	9.61576i	−0.849525	−	0.366066i
$691$	−49.1159	+	4.42051i	−1.86846	+	0.168164i	−0.965300	−	0.261144i	$-0.915900\pi$
$691$	−49.1159	+	4.42051i	−1.86846	+	0.168164i	−0.903158	+	0.429308i	$0.858758\pi$
$692$	−0.618787	−	3.40980i	−0.0235227	−	0.129621i
$693$	−26.0124	+	12.5269i	−0.988129	+	0.475858i
$694$	25.8048	−	11.0295i	0.979538	−	0.418675i
$695$	1.81077	+	5.62931i	0.0686865	+	0.213532i
$696$	16.7116	−	23.5491i	0.633453	−	0.892625i
$697$	−5.95780	+	8.20021i	−0.225668	+	0.310605i
$698$	12.5366	+	7.49026i	0.474517	+	0.283510i
$699$	−16.2073	−	33.6549i	−0.613018	−	1.27294i
$700$	−1.19730	−	6.82616i	−0.0452535	−	0.258005i
$701$	−10.7775	+	47.2191i	−0.407059	+	1.78344i	0.190575	+	0.981673i	$0.438965\pi$
$701$	−10.7775	+	47.2191i	−0.407059	+	1.78344i	−0.597634	+	0.801769i	$0.703892\pi$
$702$	0.794489	−	8.82749i	0.0299860	−	0.333172i
$703$	0.239733	−	1.32104i	0.00904169	−	0.0498238i
$704$	−8.07144	−	29.2462i	−0.304204	−	1.10226i
$705$	12.2172	−	3.33305i	0.460125	−	0.125530i
$706$	−9.44806	−	52.0631i	−0.355583	−	1.95942i
$707$	−11.1449	−	13.9752i	−0.419146	−	0.525593i
$708$	2.82893	−	2.05534i	0.106318	−	0.0772443i
$709$	13.0586	−	19.7830i	0.490427	−	0.742965i	−0.502124	−	0.864796i	$-0.667448\pi$
$709$	13.0586	−	19.7830i	0.490427	−	0.742965i	0.992551	+	0.121831i	$0.0388765\pi$
$710$	43.5669	+	4.05041i	1.63504	+	0.152009i
$711$	−0.391278	+	4.34745i	−0.0146741	+	0.163042i
$712$	16.1228	+	10.6426i	0.604228	+	0.398847i
$713$	10.2603	+	31.5779i	0.384251	+	1.18260i
$714$	28.6396	+	76.3099i	1.07181	+	2.85583i
$715$	−18.4492	+	3.29197i	−0.689961	+	0.123113i
$716$	6.75335	+	2.53457i	0.252385	+	0.0947215i
$717$	−2.33543	+	52.0023i	−0.0872181	+	1.94206i
$718$	−13.7669	−	28.5872i	−0.513775	−	1.06686i
$719$	12.3764	+	10.8129i	0.461562	+	0.403255i	0.857064	−	0.515211i	$-0.172286\pi$
$719$	12.3764	+	10.8129i	0.461562	+	0.403255i	−0.395501	+	0.918465i	$0.629429\pi$
$720$	−12.2944	−	7.39478i	−0.458187	−	0.275587i
$721$	23.7868	+	44.2033i	0.885868	+	1.64622i
$722$	56.1674	+	10.1929i	2.09033	+	0.379339i
$723$	−55.3044	−	33.0429i	−2.05679	−	1.22888i
$724$	−2.25416			−0.0837752
$725$	24.7031	−	10.7125i	0.917449	−	0.397853i
$726$	38.9326			1.44492
$727$	−34.4600	−	20.5889i	−1.27805	−	0.763600i	−0.296543	−	0.955019i	$-0.595834\pi$
$727$	−34.4600	−	20.5889i	−1.27805	−	0.763600i	−0.981508	+	0.191419i	$0.938691\pi$
$728$	18.5993	+	3.37527i	0.689336	+	0.125096i
$729$	2.44312	+	4.54008i	0.0904859	+	0.168151i
$730$	−10.6306	+	45.9517i	−0.393456	+	1.70075i
$731$	23.0842	+	20.1680i	0.853798	+	0.745941i
$732$	3.52972	+	7.32954i	0.130462	+	0.270908i
$733$	1.50774	−	33.5724i	0.0556896	−	1.24003i	−0.755463	−	0.655191i	$-0.772588\pi$
$733$	1.50774	−	33.5724i	0.0556896	−	1.24003i	0.811153	−	0.584834i	$-0.198840\pi$
$734$	−40.6962	−	15.2735i	−1.50212	−	0.563756i
$735$	46.7803	+	22.6981i	1.72552	+	0.837232i
$736$	−2.17773	−	5.80255i	−0.0802723	−	0.213885i
$737$	−3.93919	−	12.1236i	−0.145102	−	0.446578i
$738$	−3.04233	−	2.00822i	−0.111990	−	0.0739237i
$739$	3.09742	−	34.4152i	0.113941	−	1.26598i	−0.711981	−	0.702198i	$-0.752202\pi$
$739$	3.09742	−	34.4152i	0.113941	−	1.26598i	0.825922	−	0.563785i	$-0.190655\pi$
$740$	−0.112060	+	0.0665061i	−0.00411942	+	0.00244481i
$741$	15.1391	−	22.9348i	0.556149	−	0.842530i
$742$	10.8245	−	7.86442i	0.397378	−	0.288712i
$743$	−32.0941	−	40.2447i	−1.17742	−	1.47644i	−0.846186	−	0.532888i	$-0.821107\pi$
$743$	−32.0941	−	40.2447i	−1.17742	−	1.47644i	−0.331233	−	0.943549i	$-0.607465\pi$
$744$	9.37124	+	51.6398i	0.343566	+	1.89321i
$745$	0.0413139	−	0.863222i	0.00151363	−	0.0316260i
$746$	−1.64315	−	5.95383i	−0.0601601	−	0.217985i
$747$	−2.10651	+	11.6078i	−0.0770733	+	0.424709i
$748$	0.841789	−	9.35305i	0.0307789	−	0.341981i
$749$	−2.95670	+	12.9542i	−0.108036	+	0.473335i
$750$	−16.6921	−	31.6865i	−0.609508	−	1.15703i
$751$	−4.84085	−	10.0521i	−0.176645	−	0.366807i	0.793782	−	0.608203i	$-0.208109\pi$
$751$	−4.84085	−	10.0521i	−0.176645	−	0.366807i	−0.970427	+	0.241395i	$0.922395\pi$
$752$	10.5222	+	6.28674i	0.383706	+	0.229254i
$753$	−27.9093	+	38.4138i	−1.01707	+	1.39988i
$754$	−0.801026	−	14.2828i	−0.0291716	−	0.520150i
$755$	22.6667	−	16.3666i	0.824926	−	0.595642i
$756$	4.25248	−	1.81760i	0.154661	−	0.0661054i
$757$	36.5449	−	17.5991i	1.32825	−	0.639650i	0.370921	−	0.928664i	$-0.379042\pi$
$757$	36.5449	−	17.5991i	1.32825	−	0.639650i	0.957325	+	0.289015i	$0.0933277\pi$
$758$	−2.34608	−	12.9280i	−0.0852135	−	0.469565i
$759$	−34.1467	+	3.07326i	−1.23945	+	0.111552i
$760$	21.8863	+	36.8777i	0.793900	+	1.33769i
$761$	3.63254	+	26.8165i	0.131679	+	0.972096i	0.929401	+	0.369071i	$0.120324\pi$
$761$	3.63254	+	26.8165i	0.131679	+	0.972096i	−0.797722	+	0.603025i	$0.793962\pi$
$762$	−10.0533	−	3.77308i	−0.364194	−	0.136684i
$763$	4.64016	−	12.3637i	0.167985	−	0.447595i
$764$	1.08380	+	1.03622i	0.0392105	+	0.0374890i
$765$	11.7347	+	14.8041i	0.424270	+	0.535243i
$766$	−8.01230	+	2.60335i	−0.289496	+	0.0940630i
$767$	−2.36598	+	8.57292i	−0.0854304	+	0.309550i
$768$	−3.56542	−	15.6211i	−0.128656	−	0.563678i
$769$	17.3924	−	19.9073i	0.627188	−	0.717874i	−0.348434	−	0.937333i	$-0.613286\pi$
$769$	17.3924	−	19.9073i	0.627188	−	0.717874i	0.975622	+	0.219459i	$0.0704293\pi$
$770$	−43.3333	−	54.6676i	−1.56162	−	1.97008i
$771$	32.4539	−	44.6690i	1.16880	−	1.60871i
$772$	−0.0843917	−	1.87913i	−0.00303732	−	0.0676313i
$773$	26.8996	−	28.1348i	0.967511	−	1.01194i	−0.0324112	−	0.999475i	$-0.510319\pi$
$773$	26.8996	−	28.1348i	0.967511	−	1.01194i	0.999922	−	0.0124627i	$-0.00396711\pi$
$774$	−6.87355	+	8.61916i	−0.247065	+	0.309809i
$775$	−17.4651	+	45.7157i	−0.627366	+	1.64216i
$776$	−8.91173	+	4.29166i	−0.319913	+	0.154062i
$777$	0.143048	−	1.58939i	0.00513182	−	0.0570192i
$778$	−21.4238	−	24.5215i	−0.768079	−	0.879137i
$779$	6.02803	+	11.2020i	0.215977	+	0.401352i
$780$	−2.64410	+	0.350245i	−0.0946741	+	0.0125408i
$781$	56.7683	−	24.2639i	2.03133	−	0.868232i
$782$			30.9678i			1.10741i
$783$	10.7224	+	14.4175i	0.383189	+	0.515240i
$784$	15.5521	+	47.8644i	0.555431	+	1.70944i
$785$	1.84792	+	4.35888i	0.0659551	+	0.155575i
$786$	−13.0056	+	1.76172i	−0.463893	+	0.0628386i
$787$	−27.8662	−	3.77473i	−0.993323	−	0.134555i	−0.380505	−	0.924779i	$-0.624250\pi$
$787$	−27.8662	−	3.77473i	−0.993323	−	0.134555i	−0.612818	+	0.790224i	$0.709964\pi$
$788$	0.597165	+	6.63505i	0.0212731	+	0.236364i
$789$	−17.8845	−	1.60963i	−0.636703	−	0.0573043i
$790$	−10.4554	+	1.38495i	−0.371985	+	0.0492741i
$791$	−6.86170	+	18.2829i	−0.243974	+	0.650066i
$792$	−17.3217	−	0.777918i	−0.615499	−	0.0276421i
$793$	−18.6415	−	8.97728i	−0.661980	−	0.318793i
$794$	5.32685	−	19.3014i	0.189043	−	0.684982i
$795$	5.71996	−	7.82431i	0.202866	−	0.277500i
$796$	0.0560106	+	1.24717i	0.00198524	+	0.0442049i
$797$	13.6476	−	31.9301i	0.483423	−	1.13102i	−0.483359	−	0.875422i	$-0.660584\pi$
$797$	13.6476	−	31.9301i	0.483423	−	1.13102i	0.966782	−	0.255602i	$-0.0822736\pi$
$798$	101.881	+	9.16948i	3.60656	+	0.324596i
$799$	−10.0627	−	12.6182i	−0.355992	−	0.446400i
$800$	2.87395	−	8.67106i	0.101609	−	0.306568i
$801$	8.35033	−	6.65917i	0.295045	−	0.235290i
$802$	−8.28878	+	8.66939i	−0.292687	+	0.306127i
$803$	17.7044	+	64.1504i	0.624774	+	2.26382i
$804$	−0.482657	−	1.74887i	−0.0170220	−	0.0616779i
$805$	22.2154	+	23.3728i	0.782989	+	0.823784i
$806$	19.5800	+	17.1065i	0.689676	+	0.602552i
$807$	−31.6345	−	7.22037i	−1.11359	−	0.254169i
$808$	−1.91681	−	10.5625i	−0.0674332	−	0.371588i
$809$	29.6637	−	28.3614i	1.04292	−	0.997132i	0.0429206	−	0.999078i	$-0.486334\pi$
$809$	29.6637	−	28.3614i	1.04292	−	0.997132i	0.999998	+	0.00194610i	$0.000619464\pi$
$810$	28.9464	−	25.1398i	1.01707	−	0.883324i
$811$	12.0013	−	36.9361i	0.421422	−	1.29700i	−0.484958	−	0.874538i	$-0.661165\pi$
$811$	12.0013	−	36.9361i	0.421422	−	1.29700i	0.906379	−	0.422465i	$-0.138835\pi$
$812$	6.36460	−	3.89957i	0.223354	−	0.136848i
$813$	27.4762	−	8.92755i	0.963632	−	0.313103i
$814$	−0.672748	+	1.12599i	−0.0235798	+	0.0394659i
$815$	21.1993	+	3.91160i	0.742579	+	0.137017i
$816$	−7.67119	+	56.6310i	−0.268545	+	1.98248i
$817$	35.3747	−	15.1199i	1.23760	−	0.528978i
$818$	−39.9493	+	9.11817i	−1.39680	+	0.318809i
$819$	4.95227	−	9.20287i	0.173046	−	0.321574i
$820$	0.437225	−	1.15464i	0.0152686	−	0.0403217i
$821$	−1.62750	+	0.449163i	−0.0568003	+	0.0156759i	−0.294322	−	0.955706i	$-0.595094\pi$
$821$	−1.62750	+	0.449163i	−0.0568003	+	0.0156759i	0.237521	+	0.971382i	$0.423665\pi$
$822$	23.9460	+	44.4992i	0.835214	+	1.55209i
$823$	−10.3903	+	3.89953i	−0.362182	+	0.135929i	−0.525830	−	0.850590i	$-0.676245\pi$
$823$	−10.3903	+	3.89953i	−0.362182	+	0.135929i	0.163648	+	0.986519i	$0.447674\pi$
$824$			30.1464i			1.05020i
$825$	−42.0085	−	28.0861i	−1.46255	−	0.977832i
$826$	−32.2744	+	7.36641i	−1.12297	+	0.256310i
$827$	27.5331	+	2.47803i	0.957420	+	0.0861694i	0.557316	−	0.830300i	$-0.311831\pi$
$827$	27.5331	+	2.47803i	0.957420	+	0.0861694i	0.400104	+	0.916470i	$0.368974\pi$
$828$	−1.55962	+	0.0700426i	−0.0542006	+	0.00243415i
$829$	−1.77854	+	2.44796i	−0.0617714	+	0.0850210i	−0.838785	−	0.544463i	$-0.816734\pi$
$829$	−1.77854	+	2.44796i	−0.0617714	+	0.0850210i	0.777014	+	0.629484i	$0.216734\pi$
$830$	−28.4797	+	1.19503i	−0.988544	+	0.0414800i
$831$	0.0867326	+	0.477936i	0.00300872	+	0.0165794i
$832$	8.58616	+	6.84723i	0.297671	+	0.237385i
$833$	2.97306	−	66.2003i	0.103010	−	2.29370i
$834$	5.85422	+	6.12303i	0.202715	+	0.212023i
$835$	1.05524	−	11.3504i	0.0365182	−	0.392796i
$836$	−10.1174	−	6.04488i	−0.349918	−	0.209066i
$837$	−32.3610	−	4.38360i	−1.11856	−	0.151519i
$838$	−6.56985	−	6.87153i	−0.226952	−	0.237373i
$839$	2.87969	−	4.81979i	0.0994180	−	0.166398i	−0.804699	−	0.593684i	$-0.797673\pi$
$839$	2.87969	−	4.81979i	0.0994180	−	0.166398i	0.904117	+	0.427286i	$0.140530\pi$
$840$	29.8383	+	41.3242i	1.02952	+	1.42582i
$841$	20.5030	+	20.5092i	0.707000	+	0.707214i
$842$	29.6486	+	40.8079i	1.02176	+	1.40633i
$843$	12.2531	−	53.6846i	0.422021	−	1.84899i
$844$	3.45849	+	1.86109i	0.119046	+	0.0640614i
$845$	−15.4479	+	16.0623i	−0.531423	+	0.552559i
$846$	4.37114	−	3.81895i	0.150283	−	0.131298i
$847$	−47.5084	−	20.3061i	−1.63241	−	0.697725i
$848$	9.29622	−	1.25926i	0.319233	−	0.0432431i
$849$	33.7624	+	26.9246i	1.15872	+	0.924050i
$850$	−28.6680	+	35.5176i	−0.983305	+	1.21824i
$851$	0.263070	−	0.546270i	0.00901792	−	0.0187259i
$852$	8.22617	−	3.08733i	0.281824	−	0.105770i
$853$	−38.5556	−	28.0123i	−1.32012	−	0.959122i	−0.999931	−	0.0117682i	$-0.996254\pi$
$853$	−38.5556	−	28.0123i	−1.32012	−	0.959122i	−0.320188	−	0.947354i	$-0.603746\pi$
$854$	−3.45537	−	76.9397i	−0.118240	−	2.63282i
$855$	23.1294	−	5.20755i	0.791009	−	0.178094i
$856$	−5.25025	+	6.00939i	−0.179450	+	0.205397i
$857$	−12.4572	+	9.93427i	−0.425529	+	0.339348i	−0.812723	−	0.582650i	$-0.802016\pi$
$857$	−12.4572	+	9.93427i	−0.425529	+	0.339348i	0.387194	+	0.921998i	$0.373444\pi$
$858$	−21.7199	+	15.7804i	−0.741504	+	0.538734i
$859$	−46.6829	−	30.8151i	−1.59280	−	1.05140i	−0.961106	−	0.276181i	$-0.910931\pi$
$859$	−46.6829	−	30.8151i	−1.59280	−	1.05140i	−0.631695	−	0.775217i	$-0.717640\pi$
$860$	−3.35928	−	1.62994i	−0.114550	−	0.0555806i
$861$	8.32954	+	12.6187i	0.283870	+	0.430045i
$862$	−42.4366	−	15.9267i	−1.44540	−	0.542466i
$863$	−13.9711	+	13.3578i	−0.475583	+	0.454704i	−0.890385	−	0.455207i	$-0.849565\pi$
$863$	−13.9711	+	13.3578i	−0.475583	+	0.454704i	0.414802	+	0.909912i	$0.363851\pi$
$864$	6.07120	+	0.546418i	0.206547	+	0.0185895i
$865$	2.06068	+	23.6765i	0.0700653	+	0.805027i
$866$	1.84831	−	13.6448i	0.0628083	−	0.463669i
$867$	18.7377	−	34.8204i	0.636364	−	1.18256i
$868$	−3.01881	+	13.2263i	−0.102465	+	0.448929i
$869$	−12.0390	+	8.74684i	−0.408395	+	0.296716i
$870$	25.1397	−	29.2555i	0.852315	−	0.991853i
$871$	3.73301	+	2.71219i	0.126488	+	0.0918991i
$872$	5.97249	−	5.21801i	0.202254	−	0.176704i
$873$	0.734052	+	5.41899i	0.0248439	+	0.183405i
$874$	35.0163	+	16.8630i	1.18444	+	0.570398i
$875$	3.84216	+	47.3724i	0.129889	+	1.60148i
$876$	2.10757	+	9.23386i	0.0712081	+	0.311983i
$877$	−36.9683	+	5.00769i	−1.24833	+	0.169098i	−0.728425	−	0.685126i	$-0.759747\pi$
$877$	−36.9683	+	5.00769i	−1.24833	+	0.169098i	−0.519905	+	0.854224i	$0.674033\pi$
$878$	12.1115	−	3.34257i	0.408744	−	0.112806i
$879$	−48.7270	+	13.4478i	−1.64352	+	0.453583i
$880$	−8.59169	−	48.1505i	−0.289626	−	1.62315i
$881$	−10.1692	+	36.8473i	−0.342609	+	1.24142i	0.566222	+	0.824253i	$0.308404\pi$
$881$	−10.1692	+	36.8473i	−0.342609	+	1.24142i	−0.908831	+	0.417164i	$0.863024\pi$
$882$	23.8326			0.802485
$883$	−6.21655	+	22.5252i	−0.209204	+	0.758032i	0.781723	+	0.623626i	$0.214341\pi$
$883$	−6.21655	+	22.5252i	−0.209204	+	0.758032i	−0.990926	+	0.134406i	$0.957087\pi$
$884$	1.74347	+	2.91807i	0.0586391	+	0.0981453i
$885$	−20.6221	+	12.2389i	−0.693204	+	0.411406i
$886$	−9.15732	+	3.43680i	−0.307646	+	0.115462i
$887$	10.2121	+	31.4295i	0.342888	+	1.05530i	0.962705	+	0.270554i	$0.0872068\pi$
$887$	10.2121	+	31.4295i	0.342888	+	1.05530i	−0.619817	+	0.784746i	$0.712793\pi$
$888$	0.527972	−	0.799844i	0.0177176	−	0.0268410i
$889$	10.2999	+	9.84773i	0.345448	+	0.330282i
$890$	20.1285	+	16.1491i	0.674708	+	0.541319i
$891$	19.0078	−	50.6461i	0.636785	−	1.69671i
$892$	−4.95008	−	2.66375i	−0.165741	−	0.0891889i
$893$	−19.7473	+	4.50719i	−0.660818	+	0.150827i
$894$	−0.486581	−	1.13841i	−0.0162737	−	0.0380742i
$895$	−44.5060	−	21.5946i	−1.48767	−	0.721828i
$896$	−10.0728	+	55.5057i	−0.336509	+	1.85432i
$897$	9.34573	−	8.16512i	0.312045	−	0.272625i
$898$	10.9133	+	3.54596i	0.364183	+	0.118330i
$899$	−52.7049	+	0.587393i	−1.75781	+	0.0195907i
$900$	−1.85360	−	1.36347i	−0.0617867	−	0.0454489i
$901$	−12.0425	−	2.74863i	−0.401195	−	0.0915702i
$902$	−1.66820	−	12.3151i	−0.0555449	−	0.410049i
$903$	40.2659	−	21.6680i	1.33997	−	0.721066i
$904$	−8.83190	+	7.71620i	−0.293745	+	0.256637i
$905$	15.3925	+	1.43104i	0.511663	+	0.0475694i
$906$	18.9792	−	35.2693i	0.630543	−	1.17174i
$907$	−18.3821	+	23.0504i	−0.610366	+	0.765375i	−0.986953	−	0.161006i	$-0.948526\pi$
$907$	−18.3821	+	23.0504i	−0.610366	+	0.765375i	0.376587	+	0.926381i	$0.377098\pi$
$908$	2.23420	+	0.100338i	0.0741446	+	0.00332984i
$909$	−5.88124	−	0.796668i	−0.195068	−	0.0264238i
$910$	24.3210	+	6.78929i	0.806234	+	0.225063i
$911$	10.8729	+	3.53280i	0.360234	+	0.117047i	0.483541	−	0.875321i	$-0.339350\pi$
$911$	10.8729	+	3.53280i	0.360234	+	0.117047i	−0.123308	+	0.992368i	$0.539350\pi$
$912$	59.8573	+	39.5115i	1.98207	+	1.30836i
$913$	−34.5261	+	20.6284i	−1.14265	+	0.682700i
$914$	5.25782	−	58.4192i	0.173913	−	1.93234i
$915$	−19.4495	−	52.2904i	−0.642981	−	1.72867i
$916$	1.73685	−	0.564336i	0.0573870	−	0.0186462i
$917$	16.7892	+	4.63353i	0.554429	+	0.153013i
$918$	−27.4418	−	13.2153i	−0.905715	−	0.436169i
$919$	−2.29971	+	51.2069i	−0.0758603	+	1.68916i	0.495616	+	0.868542i	$0.334942\pi$
$919$	−2.29971	+	51.2069i	−0.0758603	+	1.68916i	−0.571476	+	0.820619i	$0.693629\pi$
$920$	5.09703	+	18.6830i	0.168044	+	0.615959i
$921$	−20.4413	−	3.70955i	−0.673565	−	0.122234i
$922$	22.5058	+	9.61945i	0.741190	+	0.316800i
$923$	−11.4617	+	19.1837i	−0.377267	+	0.631438i
$924$	−12.6211	−	6.07801i	−0.415204	−	0.199952i
$925$	0.807423	−	0.382995i	0.0265479	−	0.0125928i
$926$	−51.8434	−	11.8329i	−1.70368	−	0.388854i
$927$	15.8510	+	5.15030i	0.520615	+	0.169158i
$928$	9.82318	−	0.550914i	0.322462	−	0.0180846i
$929$	−18.8324	−	13.6825i	−0.617870	−	0.448909i	0.234307	−	0.972163i	$-0.424718\pi$
$929$	−18.8324	−	13.6825i	−0.617870	−	0.448909i	−0.852177	+	0.523254i	$0.824718\pi$
$930$	6.07881	+	69.8435i	0.199332	+	2.29026i
$931$	−73.2359	−	39.4099i	−2.40021	−	1.29161i
$932$	2.51602	−	5.22456i	0.0824148	−	0.171136i
$933$	46.4905	−	19.8710i	1.52203	−	0.650547i
$934$	19.4934	−	11.6468i	0.637843	−	0.381094i
$935$	−11.6859	+	63.3326i	−0.382169	+	2.07120i
$936$	5.23803	−	3.45760i	0.171211	−	0.113015i
$937$	0.139338	−	0.371264i	0.00455196	−	0.0121287i	−0.933939	−	0.357432i	$-0.883652\pi$
$937$	0.139338	−	0.371264i	0.00455196	−	0.0121287i	0.938491	+	0.345303i	$0.112224\pi$
$938$	−2.30557	+	17.0204i	−0.0752795	+	0.555735i
$939$	13.7354	+	36.5979i	0.448239	+	1.19433i
$940$	1.58704	+	1.16020i	0.0517634	+	0.0378416i
$941$	−5.86888	+	8.89097i	−0.191320	+	0.289837i	−0.917555	−	0.397609i	$-0.869840\pi$
$941$	−5.86888	+	8.89097i	−0.191320	+	0.289837i	0.726235	+	0.687447i	$0.241268\pi$
$942$	5.10762	+	4.46239i	0.166415	+	0.145393i
$943$	1.27831	+	5.60063i	0.0416274	+	0.182382i
$944$	−22.3744	−	6.17495i	−0.728225	−	0.200977i
$945$	−30.1919	+	9.71177i	−0.982142	+	0.315924i
$946$	−37.5457	+	1.68618i	−1.22072	+	0.0548224i
$947$	4.56562	+	8.48434i	0.148363	+	0.275704i	0.943920	−	0.330174i	$-0.107108\pi$
$947$	4.56562	+	8.48434i	0.148363	+	0.275704i	−0.795557	+	0.605878i	$0.792822\pi$
$948$	−1.76754	+	1.16674i	−0.0574070	+	0.0378940i
$949$	−18.8334	−	15.0191i	−0.611358	−	0.487541i
$950$	24.5502	+	51.7564i	0.796514	+	1.67920i
$951$	2.44389	+	10.7074i	0.0792485	+	0.347211i
$952$	33.3180	−	55.7649i	1.07984	−	1.80735i
$953$	12.6763	−	6.82141i	0.410626	−	0.220967i	−0.255496	−	0.966810i	$-0.582239\pi$
$953$	12.6763	−	6.82141i	0.410626	−	0.220967i	0.666122	+	0.745843i	$0.267953\pi$
$954$	0.793225	−	4.37103i	0.0256816	−	0.141517i
$955$	−6.74286	−	7.76383i	−0.218194	−	0.251232i
$956$	−6.53762	+	4.74986i	−0.211442	+	0.153621i
$957$	11.5187	−	53.1924i	0.372346	−	1.71947i
$958$	−14.5789	−	20.0661i	−0.471023	−	0.648307i
$959$	−6.01128	−	66.7908i	−0.194114	−	2.15679i
$960$	3.88857	+	29.3560i	0.125503	+	0.947460i
$961$	44.7797	−	46.8359i	1.44451	−	1.51083i
$962$	−0.0425594	−	0.472873i	−0.00137217	−	0.0152460i
$963$	2.26277	+	3.78724i	0.0729168	+	0.122042i
$964$	−1.34248	−	9.91058i	−0.0432383	−	0.319198i
$965$	−0.616685	+	12.8851i	−0.0198518	+	0.414788i
$966$	43.2492	+	16.2317i	1.39152	+	0.522246i
$967$	−4.77853	+	0.867175i	−0.153667	+	0.0278865i	−0.254845	−	0.966982i	$-0.582025\pi$
$967$	−4.77853	+	0.867175i	−0.153667	+	0.0278865i	0.101178	+	0.994868i	$0.467739\pi$
$968$	−19.3461	−	24.2592i	−0.621806	−	0.779720i
$969$	−55.5089	−	76.4014i	−1.78320	−	2.45437i
$970$	−12.3839	+	4.60623i	−0.397624	+	0.147897i
$971$	−17.9129	−	7.65635i	−0.574853	−	0.245704i	0.0859047	−	0.996303i	$-0.472622\pi$
$971$	−17.9129	−	7.65635i	−0.574853	−	0.245704i	−0.660757	+	0.750599i	$0.729765\pi$
$972$	1.74319	−	4.07839i	0.0559128	−	0.130814i
$973$	−3.95017	−	10.5252i	−0.126637	−	0.337422i
$974$			17.4987i			0.560694i
$975$	18.2775	−	0.713045i	0.585350	−	0.0228357i
$976$	23.4297	−	48.6524i	0.749968	−	1.55732i
$977$	33.9647	−	22.4199i	1.08663	−	0.717275i	0.125142	−	0.992139i	$-0.460061\pi$
$977$	33.9647	−	22.4199i	1.08663	−	0.717275i	0.961483	+	0.274863i	$0.0886327\pi$
$978$	29.7692	−	8.21578i	0.951915	−	0.262712i
$979$	35.8262	+	6.50149i	1.14501	+	0.207789i
$980$	1.77298	+	7.87473i	0.0566359	+	0.251549i
$981$	−1.72327	−	4.03180i	−0.0550199	−	0.128725i
$982$	21.5011	−	44.6474i	0.686126	−	1.42476i
$983$	27.8802	−	51.8101i	0.889240	−	1.65249i	0.140036	−	0.990146i	$-0.455278\pi$
$983$	27.8802	−	51.8101i	0.889240	−	1.65249i	0.749204	−	0.662339i	$-0.230436\pi$
$984$	0.813966	+	9.04390i	0.0259483	+	0.288309i
$985$	0.134492	−	45.6864i	0.00428526	−	1.45569i
$986$	−46.9202	−	14.6692i	−1.49424	−	0.467164i
$987$	−22.8968	+	7.43961i	−0.728812	+	0.236805i
$988$	4.24893	−	0.382411i	0.135177	−	0.0121661i
$989$	17.2158	−	2.33204i	0.547430	−	0.0741544i
$990$	−22.9429	−	3.17663i	−0.729173	−	0.100960i
$991$	−29.0585	+	2.61532i	−0.923075	+	0.0830783i	−0.540971	−	0.841041i	$-0.681943\pi$
$991$	−29.0585	+	2.61532i	−0.923075	+	0.0830783i	−0.382104	+	0.924119i	$0.624800\pi$
$992$	−11.7652	+	13.4664i	−0.373546	+	0.427557i
$993$	21.0073	+	43.6222i	0.666648	+	1.38431i
$994$	−83.0991	−	3.73199i	−2.63574	−	0.118371i
$995$	0.409293	−	8.55185i	0.0129755	−	0.271112i
$996$	−5.04059	+	2.71246i	−0.159717	+	0.0859476i
$997$	−2.03746	−	45.3676i	−0.0645271	−	1.43681i	−0.726442	−	0.687228i	$-0.758827\pi$
$997$	−2.03746	−	45.3676i	−0.0645271	−	1.43681i	0.661915	−	0.749579i	$-0.269744\pi$
$998$	−13.6857	+	42.1203i	−0.433214	+	1.33329i
$999$	0.371809	+	0.466234i	0.0117635	+	0.0147510i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.bh.a.4.20	✓	1728
25.19	even	10	inner	725.2.bh.a.294.20	yes	1728
29.22	even	14	inner	725.2.bh.a.254.20	yes	1728
725.544	even	70	inner	725.2.bh.a.544.20	yes	1728

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.bh.a.4.20	✓	1728	1.1	even	1	trivial
725.2.bh.a.254.20	yes	1728	29.22	even	14	inner
725.2.bh.a.294.20	yes	1728	25.19	even	10	inner
725.2.bh.a.544.20	yes	1728	725.544	even	70	inner

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Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	725.2.bh.a.4.20

Level	$725$
Weight	$2$
Character	725.4
Analytic conductor	$5.789$
Analytic rank	$0$
Dimension	$1728$
Inner twists	$4$