LMFDB - Embedded newform 36.4.h.b.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, degree $2$, 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:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	36.23
Dual form			36.4.h.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52436 - 1.27578i) q^{2} +(5.18398 - 0.355390i) q^{3} +(4.74478 + 6.44105i) q^{4} +(-1.23846 - 0.715028i) q^{5} +(-13.5396 - 5.71649i) q^{6} +(23.8818 - 13.7882i) q^{7} +(-3.76017 - 22.3128i) q^{8} +(26.7474 - 3.68468i) q^{9} +O(q^{10})$	\(q+(-2.52436 - 1.27578i) q^{2} +(5.18398 - 0.355390i) q^{3} +(4.74478 + 6.44105i) q^{4} +(-1.23846 - 0.715028i) q^{5} +(-13.5396 - 5.71649i) q^{6} +(23.8818 - 13.7882i) q^{7} +(-3.76017 - 22.3128i) q^{8} +(26.7474 - 3.68468i) q^{9} +(2.21411 + 3.38499i) q^{10} +(-11.1087 - 19.2409i) q^{11} +(26.8859 + 31.7040i) q^{12} +(-34.5965 + 59.9229i) q^{13} +(-77.8769 + 4.33838i) q^{14} +(-6.67430 - 3.26656i) q^{15} +(-18.9742 + 61.1227i) q^{16} +31.4507i q^{17} +(-72.2209 - 24.8223i) q^{18} -11.4986i q^{19} +(-1.27071 - 11.3697i) q^{20} +(118.903 - 79.9650i) q^{21} +(3.49531 + 62.7433i) q^{22} +(-72.6810 + 125.887i) q^{23} +(-27.4224 - 114.333i) q^{24} +(-61.4775 - 106.482i) q^{25} +(163.782 - 107.129i) q^{26} +(137.349 - 28.6071i) q^{27} +(202.124 + 88.4021i) q^{28} +(-93.6986 + 54.0969i) q^{29} +(12.6809 + 16.7609i) q^{30} +(-102.800 - 59.3514i) q^{31} +(125.877 - 130.089i) q^{32} +(-64.4256 - 95.7966i) q^{33} +(40.1242 - 79.3929i) q^{34} -39.4357 q^{35} +(150.644 + 154.798i) q^{36} -300.439 q^{37} +(-14.6696 + 29.0265i) q^{38} +(-158.052 + 322.935i) q^{39} +(-11.2974 + 30.3222i) q^{40} +(344.853 + 199.101i) q^{41} +(-402.171 + 50.1668i) q^{42} +(173.261 - 100.032i) q^{43} +(71.2231 - 162.846i) q^{44} +(-35.7603 - 14.5618i) q^{45} +(344.077 - 225.060i) q^{46} +(-151.770 - 262.873i) q^{47} +(-76.6395 + 323.602i) q^{48} +(208.727 - 361.526i) q^{49} +(19.3436 + 347.231i) q^{50} +(11.1773 + 163.040i) q^{51} +(-550.119 + 61.4831i) q^{52} +243.342i q^{53} +(-383.213 - 103.012i) q^{54} +31.7722i q^{55} +(-397.452 - 481.024i) q^{56} +(-4.08648 - 59.6085i) q^{57} +(305.545 - 17.0213i) q^{58} +(-41.9197 + 72.6070i) q^{59} +(-10.6280 - 58.4885i) q^{60} +(199.218 + 345.055i) q^{61} +(183.784 + 280.974i) q^{62} +(587.971 - 456.794i) q^{63} +(-483.722 + 167.800i) q^{64} +(85.6931 - 49.4749i) q^{65} +(40.4180 + 324.018i) q^{66} +(-307.763 - 177.687i) q^{67} +(-202.576 + 149.227i) q^{68} +(-332.038 + 678.427i) q^{69} +(99.5499 + 50.3112i) q^{70} +866.235 q^{71} +(-182.790 - 582.954i) q^{72} +64.6645 q^{73} +(758.415 + 383.293i) q^{74} +(-356.541 - 530.153i) q^{75} +(74.0629 - 54.5582i) q^{76} +(-530.594 - 306.338i) q^{77} +(810.973 - 613.564i) q^{78} +(354.896 - 204.899i) q^{79} +(67.2033 - 62.1312i) q^{80} +(701.846 - 197.111i) q^{81} +(-616.524 - 942.559i) q^{82} +(79.8990 + 138.389i) q^{83} +(1079.23 + 386.442i) q^{84} +(22.4881 - 38.9506i) q^{85} +(-564.993 + 31.4747i) q^{86} +(-466.507 + 313.737i) q^{87} +(-387.548 + 320.216i) q^{88} -1493.47i q^{89} +(71.6943 + 82.3815i) q^{90} +1908.09i q^{91} +(-1155.70 + 129.165i) q^{92} +(-554.005 - 271.143i) q^{93} +(47.7536 + 857.209i) q^{94} +(-8.22181 + 14.2406i) q^{95} +(606.310 - 719.113i) q^{96} +(700.115 + 1212.63i) q^{97} +(-988.129 + 646.332i) q^{98} +(-368.026 - 473.712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.52436	−	1.27578i	−0.892496	−	0.451056i
$2$	−2.52436	−	1.27578i	−0.892496	−	0.451056i
$3$	5.18398	−	0.355390i	0.997658	−	0.0683949i
$3$	5.18398	−	0.355390i	0.997658	−	0.0683949i
$4$	4.74478	+	6.44105i	0.593097	+	0.805131i
$5$	−1.23846	−	0.715028i	−0.110772	−	0.0639540i	0.443591	−	0.896230i	$-0.353704\pi$
$5$	−1.23846	−	0.715028i	−0.110772	−	0.0639540i	−0.554362	+	0.832275i	$0.687038\pi$
$6$	−13.5396	−	5.71649i	−0.921256	−	0.388958i
$7$	23.8818	−	13.7882i	1.28950	−	0.744491i	0.310932	−	0.950432i	$-0.399359\pi$
$7$	23.8818	−	13.7882i	1.28950	−	0.744491i	0.978564	+	0.205941i	$0.0660255\pi$
$8$	−3.76017	−	22.3128i	−0.166177	−	0.986096i
$9$	26.7474	−	3.68468i	0.990644	−	0.136469i
$10$	2.21411	+	3.38499i	0.0700164	+	0.107043i
$11$	−11.1087	−	19.2409i	−0.304492	−	0.527396i	0.672656	−	0.739955i	$-0.265153\pi$
$11$	−11.1087	−	19.2409i	−0.304492	−	0.527396i	−0.977148	+	0.212560i	$0.931820\pi$
$12$	26.8859	+	31.7040i	0.646775	+	0.762681i
$13$	−34.5965	+	59.9229i	−0.738103	+	1.27843i	0.215245	+	0.976560i	$0.430945\pi$
$13$	−34.5965	+	59.9229i	−0.738103	+	1.27843i	−0.953348	+	0.301872i	$0.902388\pi$
$14$	−77.8769	+	4.33838i	−1.48668	+	0.0828201i
$15$	−6.67430	−	3.26656i	−0.114886	−	0.0562281i
$16$	−18.9742	+	61.1227i	−0.296472	+	0.955042i
$17$			31.4507i			0.448701i	0.974509	+	0.224351i	$0.0720261\pi$
$17$			31.4507i			0.448701i	−0.974509	+	0.224351i	$0.927974\pi$
$18$	−72.2209	−	24.8223i	−0.945701	−	0.325038i
$19$		−	11.4986i		−	0.138840i	−0.997588	−	0.0694199i	$-0.977885\pi$
$19$		−	11.4986i		−	0.138840i	0.997588	−	0.0694199i	$-0.0221148\pi$
$20$	−1.27071	−	11.3697i	−0.0142070	−	0.127117i
$21$	118.903	−	79.9650i	1.23556	−	0.830943i
$22$	3.49531	+	62.7433i	0.0338729	+	0.608041i
$23$	−72.6810	+	125.887i	−0.658914	+	1.14127i	0.321983	+	0.946746i	$0.395651\pi$
$23$	−72.6810	+	125.887i	−0.658914	+	1.14127i	−0.980897	+	0.194528i	$0.937683\pi$
$24$	−27.4224	−	114.333i	−0.233232	−	0.972421i
$25$	−61.4775	−	106.482i	−0.491820	−	0.851857i
$26$	163.782	−	107.129i	1.23540	−	0.808070i
$27$	137.349	−	28.6071i	0.978991	−	0.203905i
$28$	202.124	+	88.4021i	1.36421	+	0.596658i
$29$	−93.6986	+	54.0969i	−0.599979	+	0.346398i	−0.769033	−	0.639209i	$-0.779262\pi$
$29$	−93.6986	+	54.0969i	−0.599979	+	0.346398i	0.169054	+	0.985607i	$0.445929\pi$
$30$	12.6809	+	16.7609i	0.0771736	+	0.102003i
$31$	−102.800	−	59.3514i	−0.595592	−	0.343865i	0.171713	−	0.985147i	$-0.445070\pi$
$31$	−102.800	−	59.3514i	−0.595592	−	0.343865i	−0.767306	+	0.641282i	$0.778403\pi$
$32$	125.877	−	130.089i	0.695377	−	0.718645i
$33$	−64.4256	−	95.7966i	−0.339850	−	0.505335i
$34$	40.1242	−	79.3929i	0.202389	−	0.400464i
$35$	−39.4357			−0.190453
$36$	150.644	+	154.798i	0.697424	+	0.716659i
$37$	−300.439			−1.33491			−0.667457	−	0.744649i	$-0.732617\pi$
$37$	−300.439			−1.33491			−0.667457	+	0.744649i	$0.732617\pi$
$38$	−14.6696	+	29.0265i	−0.0626245	+	0.123914i
$39$	−158.052	+	322.935i	−0.648937	+	1.32592i
$40$	−11.2974	+	30.3222i	−0.0446571	+	0.119859i
$41$	344.853	+	199.101i	1.31359	+	0.758399i	0.982688	−	0.185268i	$-0.0593153\pi$
$41$	344.853	+	199.101i	1.31359	+	0.758399i	0.330897	+	0.943667i	$0.392649\pi$
$42$	−402.171	+	50.1668i	−1.47753	+	0.184307i
$43$	173.261	−	100.032i	0.614467	−	0.354763i	−0.160245	−	0.987077i	$-0.551228\pi$
$43$	173.261	−	100.032i	0.614467	−	0.354763i	0.774712	+	0.632315i	$0.217895\pi$
$44$	71.2231	−	162.846i	0.244029	−	0.557953i
$45$	−35.7603	−	14.5618i	−0.118463	−	0.0482388i
$46$	344.077	−	225.060i	1.10286	−	0.721374i
$47$	−151.770	−	262.873i	−0.471018	−	0.815828i	0.528432	−	0.848976i	$-0.322780\pi$
$47$	−151.770	−	262.873i	−0.471018	−	0.815828i	−0.999450	+	0.0331478i	$0.989447\pi$
$48$	−76.6395	+	323.602i	−0.230457	+	0.973082i
$49$	208.727	−	361.526i	0.608534	−	1.05401i
$50$	19.3436	+	347.231i	0.0547119	+	0.982117i
$51$	11.1773	+	163.040i	0.0306889	+	0.447650i
$52$	−550.119	+	61.4831i	−1.46707	+	0.163965i
$53$			243.342i			0.630673i	0.948980	+	0.315336i	$0.102117\pi$
$53$			243.342i			0.630673i	−0.948980	+	0.315336i	$0.897883\pi$
$54$	−383.213	−	103.012i	−0.965717	−	0.259595i
$55$			31.7722i			0.0778940i
$56$	−397.452	−	481.024i	−0.948425	−	1.14785i
$57$	−4.08648	−	59.6085i	−0.00949593	−	0.138515i
$58$	305.545	−	17.0213i	0.691724	−	0.0385347i
$59$	−41.9197	+	72.6070i	−0.0924996	+	0.160214i	−0.908562	−	0.417749i	$-0.862819\pi$
$59$	−41.9197	+	72.6070i	−0.0924996	+	0.160214i	0.816063	+	0.577963i	$0.196152\pi$
$60$	−10.6280	−	58.4885i	−0.0228678	−	0.125847i
$61$	199.218	+	345.055i	0.418151	+	0.724259i	0.995754	−	0.0920592i	$-0.0293449\pi$
$61$	199.218	+	345.055i	0.418151	+	0.724259i	−0.577602	+	0.816318i	$0.696012\pi$
$62$	183.784	+	280.974i	0.376461	+	0.575544i
$63$	587.971	−	456.794i	1.17583	−	0.913503i
$64$	−483.722	+	167.800i	−0.944770	+	0.327734i
$65$	85.6931	−	49.4749i	0.163522	−	0.0944094i
$66$	40.4180	+	324.018i	0.0753805	+	0.604301i
$67$	−307.763	−	177.687i	−0.561183	−	0.323999i	0.192437	−	0.981309i	$-0.438361\pi$
$67$	−307.763	−	177.687i	−0.561183	−	0.323999i	−0.753620	+	0.657310i	$0.771694\pi$
$68$	−202.576	+	149.227i	−0.361263	+	0.266123i
$69$	−332.038	+	678.427i	−0.579314	+	1.18367i
$70$	99.5499	+	50.3112i	0.169978	+	0.0859049i
$71$	866.235			1.44793			0.723966	−	0.689836i	$-0.242317\pi$
$71$	866.235			1.44793			0.723966	+	0.689836i	$0.242317\pi$
$72$	−182.790	−	582.954i	−0.299195	−	0.954192i
$73$	64.6645			0.103677			0.0518384	−	0.998655i	$-0.483492\pi$
$73$	64.6645			0.103677			0.0518384	+	0.998655i	$0.483492\pi$
$74$	758.415	+	383.293i	1.19140	+	0.602121i
$75$	−356.541	−	530.153i	−0.548931	−	0.816224i
$76$	74.0629	−	54.5582i	0.111784	−	0.0823455i
$77$	−530.594	−	306.338i	−0.785283	−	0.453383i
$78$	810.973	−	613.564i	1.17724	−	0.890672i
$79$	354.896	−	204.899i	0.505429	−	0.291809i	−0.225524	−	0.974238i	$-0.572409\pi$
$79$	354.896	−	204.899i	0.505429	−	0.291809i	0.730953	+	0.682428i	$0.239076\pi$
$80$	67.2033	−	62.1312i	0.0939194	−	0.0868310i
$81$	701.846	−	197.111i	0.962752	−	0.270385i
$82$	−616.524	−	942.559i	−0.830289	−	1.26937i
$83$	79.8990	+	138.389i	0.105663	+	0.183014i	0.914009	−	0.405694i	$-0.132970\pi$
$83$	79.8990	+	138.389i	0.105663	+	0.183014i	−0.808346	+	0.588708i	$0.799637\pi$
$84$	1079.23	+	386.442i	1.40182	+	0.501956i
$85$	22.4881	−	38.9506i	0.0286962	−	0.0497034i
$86$	−564.993	+	31.4747i	−0.708427	+	0.0394652i
$87$	−466.507	+	313.737i	−0.574882	+	0.386623i
$88$	−387.548	+	320.216i	−0.469463	+	0.387900i
$89$		−	1493.47i		−	1.77873i	−0.457195	−	0.889366i	$-0.651146\pi$
$89$		−	1493.47i		−	1.77873i	0.457195	−	0.889366i	$-0.348854\pi$
$90$	71.6943	+	82.3815i	0.0839694	+	0.0964863i
$91$			1908.09i			2.19805i
$92$	−1155.70	+	129.165i	−1.30967	+	0.146373i
$93$	−554.005	−	271.143i	−0.617716	−	0.302325i
$94$	47.7536	+	857.209i	0.0523979	+	0.940578i
$95$	−8.22181	+	14.2406i	−0.00887936	+	0.0153795i
$96$	606.310	−	719.113i	0.644597	−	0.764523i
$97$	700.115	+	1212.63i	0.732844	+	1.26932i	0.955663	+	0.294463i	$0.0951408\pi$
$97$	700.115	+	1212.63i	0.732844	+	1.26932i	−0.222819	+	0.974860i	$0.571526\pi$
$98$	−988.129	+	646.332i	−1.01853	+	0.666218i
$99$	−368.026	−	473.712i	−0.373617	−	0.480908i
$100$	394.159	−	901.213i	0.394159	−	0.901213i
$101$	−207.342	+	119.709i	−0.204270	+	0.117936i	−0.598646	−	0.801014i	$-0.704294\pi$
$101$	−207.342	+	119.709i	−0.204270	+	0.117936i	0.394375	+	0.918949i	$0.370961\pi$
$102$	179.788	−	425.831i	0.174526	−	0.413368i
$103$	−504.070	−	291.025i	−0.482208	−	0.278403i	0.239128	−	0.970988i	$-0.423138\pi$
$103$	−504.070	−	291.025i	−0.482208	−	0.278403i	−0.721336	+	0.692585i	$0.756472\pi$
$104$	1467.14	+	546.625i	1.38331	+	0.515394i
$105$	−204.434	+	14.0151i	−0.190007	+	0.0130260i
$106$	310.451	−	614.284i	0.284469	−	0.562873i
$107$	−1470.35			−1.32845			−0.664224	−	0.747533i	$-0.731238\pi$
$107$	−1470.35			−1.32845			−0.664224	+	0.747533i	$0.731238\pi$
$108$	835.948	+	748.935i	0.744807	+	0.667280i
$109$	−1.40399			−0.00123374			−0.000616870	−	1.00000i	$-0.500196\pi$
$109$	−1.40399			−0.00123374			−0.000616870		1.00000i	$0.500196\pi$
$110$	40.5344	−	80.2045i	0.0351345	−	0.0695200i
$111$	−1557.47	+	106.773i	−1.33179	+	0.0913013i
$112$	389.632	+	1721.34i	0.328721	+	1.45224i
$113$	−1174.77	−	678.256i	−0.977996	−	0.564646i	−0.0763312	−	0.997083i	$-0.524321\pi$
$113$	−1174.77	−	678.256i	−0.977996	−	0.564646i	−0.901664	+	0.432436i	$0.857654\pi$
$114$	−65.7315	+	155.687i	−0.0540028	+	0.127907i
$115$	180.026	−	103.938i	0.145978	−	0.0842805i
$116$	−793.020	−	346.840i	−0.634742	−	0.277614i
$117$	−704.570	+	1730.26i	−0.556731	+	1.36720i
$118$	198.451	−	129.806i	0.154821	−	0.101268i
$119$	433.648	+	751.100i	0.334054	+	0.578598i
$120$	−47.7895	+	161.205i	−0.0363547	+	0.122633i
$121$	418.692	−	725.195i	0.314569	−	0.544850i
$122$	−62.6829	−	1125.20i	−0.0465168	−	0.835008i
$123$	1858.47	+	909.579i	1.36238	+	0.666780i
$124$	−105.476	−	943.747i	−0.0763874	−	0.683475i
$125$			354.589i			0.253724i
$126$	−2067.02	+	402.992i	−1.46147	+	0.284931i
$127$		−	547.847i		−	0.382784i	−0.981514	−	0.191392i	$-0.938700\pi$
$127$		−	547.847i		−	0.382784i	0.981514	−	0.191392i	$-0.0613002\pi$
$128$	1435.16	+	193.536i	0.991030	+	0.133643i
$129$	862.633	−	580.142i	0.588764	−	0.395958i
$130$	−279.439	+	15.5670i	−0.188526	+	0.0105025i
$131$	931.609	−	1613.59i	0.621336	−	1.07619i	−0.367901	−	0.929865i	$-0.619923\pi$
$131$	931.609	−	1613.59i	0.621336	−	1.07619i	0.989237	−	0.146321i	$-0.0467433\pi$
$132$	311.346	−	869.502i	0.205297	−	0.573337i
$133$	−158.544	−	274.607i	−0.103365	−	0.179033i
$134$	550.216	+	841.185i	0.354712	+	0.542293i
$135$	−190.556	−	62.7792i	−0.121485	−	0.0400235i
$136$	701.754	−	118.260i	0.442462	−	0.0745640i
$137$	1253.96	−	723.973i	0.781992	−	0.451483i	−0.0551439	−	0.998478i	$-0.517562\pi$
$137$	1253.96	−	723.973i	0.781992	−	0.451483i	0.837136	+	0.546995i	$0.184228\pi$
$138$	1703.71	−	1288.99i	1.05094	−	0.795115i
$139$	324.131	+	187.137i	0.197787	+	0.114193i	0.595623	−	0.803264i	$-0.296905\pi$
$139$	324.131	+	187.137i	0.197787	+	0.114193i	−0.397836	+	0.917457i	$0.630239\pi$
$140$	−187.114	−	254.007i	−0.112957	−	0.153339i
$141$	−880.193	−	1308.79i	−0.525714	−	0.781702i
$142$	−2186.69	−	1105.12i	−1.29227	−	0.653098i
$143$	1537.29			0.898986
$144$	−282.293	+	1704.79i	−0.163364	+	0.986566i
$145$	154.723			0.0886143
$146$	−163.236	−	82.4976i	−0.0925311	−	0.0467640i
$147$	953.555	−	1948.32i	0.535020	−	1.09316i
$148$	−1425.51	−	1935.14i	−0.791733	−	1.07478i
$149$	2138.30	+	1234.55i	1.17568	+	0.678779i	0.955011	−	0.296570i	$-0.0958427\pi$
$149$	2138.30	+	1234.55i	1.17568	+	0.678779i	0.220669	+	0.975349i	$0.429176\pi$
$150$	223.679	+	1793.16i	0.121756	+	0.976075i
$151$	525.453	−	303.370i	0.283184	−	0.163496i	−0.351680	−	0.936120i	$-0.614390\pi$
$151$	525.453	−	303.370i	0.283184	−	0.163496i	0.634864	+	0.772624i	$0.281056\pi$
$152$	−256.566	+	43.2366i	−0.136909	+	0.0230720i
$153$	115.886	+	841.225i	0.0612340	+	0.444503i
$154$	948.589	+	1450.23i	0.496360	+	0.758849i
$155$	84.8758	+	147.009i	0.0439832	+	0.0761811i
$156$	−2829.96	+	514.234i	−1.45242	+	0.263921i
$157$	37.1699	−	64.3801i	0.0188948	−	0.0327267i	−0.856423	−	0.516274i	$-0.827319\pi$
$157$	37.1699	−	64.3801i	0.0188948	−	0.0327267i	0.875318	+	0.483547i	$0.160652\pi$
$158$	−1157.29	+	64.4705i	−0.582715	+	0.0324620i
$159$	86.4815	+	1261.48i	0.0431348	+	0.629196i
$160$	−248.911	+	71.1049i	−0.122988	+	0.0351333i
$161$			4008.55i			1.96222i
$162$	−2023.18	−	397.822i	−0.981211	−	0.192937i
$163$		−	40.4850i		−	0.0194542i	−0.999953	−	0.00972709i	$-0.996904\pi$
$163$		−	40.4850i		−	0.0194542i	0.999953	−	0.00972709i	$-0.00309628\pi$
$164$	353.832	+	3165.90i	0.168473	+	1.50741i
$165$	11.2915	+	164.707i	0.00532755	+	0.0777116i
$166$	−25.1398	−	451.277i	−0.0117544	−	0.211000i
$167$	−20.5614	+	35.6135i	−0.00952750	+	0.0165021i	−0.870750	−	0.491726i	$-0.836366\pi$
$167$	−20.5614	+	35.6135i	−0.00952750	+	0.0165021i	0.861222	+	0.508228i	$0.169699\pi$
$168$	−2231.34	−	2352.37i	−1.02471	−	1.08029i
$169$	−1295.34	−	2243.59i	−0.589593	−	1.02121i
$170$	−106.460	+	69.6354i	−0.0480303	+	0.0314164i
$171$	−42.3685	−	307.557i	−0.0189474	−	0.137541i
$172$	1466.40	+	641.352i	0.650069	+	0.284318i
$173$	−952.460	+	549.903i	−0.418579	+	0.241667i	−0.694469	−	0.719522i	$-0.744361\pi$
$173$	−952.460	+	549.903i	−0.418579	+	0.241667i	0.275890	+	0.961189i	$0.411027\pi$
$174$	1577.89	−	196.826i	0.687469	−	0.0857548i
$175$	−2936.39	−	1695.32i	−1.26840	−	0.732311i
$176$	1386.83	−	313.915i	0.593958	−	0.134445i
$177$	−191.507	+	391.291i	−0.0813252	+	0.166165i
$178$	−1905.33	+	3770.05i	−0.802308	+	1.58751i
$179$	−3849.91			−1.60757			−0.803787	−	0.594917i	$-0.797185\pi$
$179$	−3849.91			−1.60757			−0.803787	+	0.594917i	$0.797185\pi$
$180$	−75.8817	−	299.427i	−0.0314216	−	0.123989i
$181$	−1091.65			−0.448296			−0.224148	−	0.974555i	$-0.571960\pi$
$181$	−1091.65			−0.448296			−0.224148	+	0.974555i	$0.571960\pi$
$182$	2434.30	−	4816.70i	0.991441	−	1.96175i
$183$	1155.37	+	1717.96i	0.466708	+	0.693964i
$184$	3082.19	+	1148.36i	1.23490	+	0.460099i
$185$	372.083	+	214.822i	0.147871	+	0.0853731i
$186$	1052.59	+	1391.25i	0.414944	+	0.548448i
$187$	605.140	−	349.378i	0.236643	−	0.136626i
$188$	973.062	−	2224.83i	0.377489	−	0.863097i
$189$	2885.69	−	2576.97i	1.11060	−	0.991785i
$190$	38.9226	−	25.4591i	0.0148618	−	0.00972105i
$191$	319.673	+	553.690i	0.121103	+	0.209757i	0.920203	−	0.391441i	$-0.128023\pi$
$191$	319.673	+	553.690i	0.121103	+	0.209757i	−0.799100	+	0.601199i	$0.794690\pi$
$192$	−2447.97	+	1041.78i	−0.920142	+	0.391584i
$193$	−874.103	+	1513.99i	−0.326007	+	0.564660i	−0.981716	−	0.190353i	$-0.939037\pi$
$193$	−874.103	+	1513.99i	−0.326007	+	0.564660i	0.655709	+	0.755014i	$0.272370\pi$
$194$	−220.288	−	3954.31i	−0.0815244	−	1.46342i
$195$	426.649	−	286.932i	0.156682	−	0.105372i
$196$	3318.97	−	370.939i	1.20954	−	0.135182i
$197$		−	2079.55i		−	0.752089i	−0.926602	−	0.376044i	$-0.877284\pi$
$197$		−	2079.55i		−	0.752089i	0.926602	−	0.376044i	$-0.122716\pi$
$198$	324.679	+	1665.34i	0.116535	+	0.597730i
$199$		−	1834.81i		−	0.653598i	−0.945094	−	0.326799i	$-0.894030\pi$
$199$		−	1834.81i		−	0.653598i	0.945094	−	0.326799i	$-0.105970\pi$
$200$	−2144.75	+	1772.13i	−0.758283	+	0.626541i
$201$	−1658.59	−	811.752i	−0.582029	−	0.284859i
$202$	676.128	−	37.6659i	0.235506	−	0.0131196i
$203$	−1491.80	+	2583.86i	−0.515781	+	0.893358i
$204$	−997.115	+	845.582i	−0.342216	+	0.290209i
$205$	−284.726	−	493.159i	−0.0970053	−	0.168018i
$206$	901.169	+	1377.73i	0.304793	+	0.465976i
$207$	−1480.17	+	3634.96i	−0.497001	+	1.22052i
$208$	−3006.21	−	3251.62i	−1.00213	−	1.08394i
$209$	−221.243	+	127.735i	−0.0732235	+	0.0422756i
$210$	533.945	+	225.434i	0.175456	+	0.0740781i
$211$	4307.35	+	2486.85i	1.40536	+	0.811383i	0.994936	−	0.100513i	$-0.0320483\pi$
$211$	4307.35	+	2486.85i	1.40536	+	0.811383i	0.410421	+	0.911896i	$0.365382\pi$
$212$	−1567.38	+	1154.61i	−0.507774	+	0.374050i
$213$	4490.55	−	307.851i	1.44454	−	0.0990311i
$214$	3711.69	+	1875.84i	1.18563	+	0.599205i
$215$	−286.104			−0.0907540
$216$	−1154.76	−	2957.06i	−0.363756	−	0.931494i
$217$	−3273.39			−1.02402
$218$	3.54417	+	1.79118i	0.00110111	+	0.000556486i
$219$	335.220	−	22.9811i	0.103434	−	0.00709096i
$220$	−204.647	+	150.752i	−0.0627148	+	0.0461987i
$221$	−1884.62	−	1088.08i	−0.573634	−	0.331188i
$222$	4067.83	+	1717.45i	1.22980	+	0.519225i
$223$	611.995	−	353.335i	0.183777	−	0.106103i	−0.405289	−	0.914189i	$-0.632829\pi$
$223$	611.995	−	353.335i	0.183777	−	0.106103i	0.589066	+	0.808085i	$0.299496\pi$
$224$	1212.48	−	4842.36i	0.361661	−	1.44439i
$225$	−2036.71	−	2621.59i	−0.603471	−	0.776769i
$226$	2100.25	+	3210.92i	0.618170	+	0.945075i
$227$	−1604.80	−	2779.60i	−0.469227	−	0.812725i	0.530154	−	0.847901i	$-0.322134\pi$
$227$	−1604.80	−	2779.60i	−0.469227	−	0.812725i	−0.999381	+	0.0351765i	$0.988801\pi$
$228$	364.552	−	309.150i	0.105890	−	0.0897981i
$229$	−731.826	+	1267.56i	−0.211181	+	0.365776i	−0.952084	−	0.305836i	$-0.901064\pi$
$229$	−731.826	+	1267.56i	−0.211181	+	0.365776i	0.740904	+	0.671611i	$0.234398\pi$
$230$	−587.051	+	32.7035i	−0.168300	+	0.00937569i
$231$	−2859.46	−	1399.49i	−0.814453	−	0.398612i
$232$	1559.38	+	1887.27i	0.441285	+	0.534074i
$233$			1324.13i			0.372303i	0.982521	+	0.186152i	$0.0596015\pi$
$233$			1324.13i			0.372303i	−0.982521	+	0.186152i	$0.940398\pi$
$234$	3986.01	−	3468.92i	1.11356	−	0.969104i
$235$			434.078i			0.120494i
$236$	−666.564	+	74.4974i	−0.183854	+	0.0205482i
$237$	1766.95	−	1188.32i	0.484287	−	0.325695i
$238$	−136.445	−	2449.28i	−0.0371615	−	0.667074i
$239$	394.528	−	683.342i	0.106778	−	0.184944i	−0.807685	−	0.589614i	$-0.799280\pi$
$239$	394.528	−	683.342i	0.106778	−	0.184944i	0.914463	+	0.404669i	$0.132613\pi$
$240$	326.300	−	345.970i	0.0877607	−	0.0930512i
$241$	1170.39	+	2027.17i	0.312827	+	0.541832i	0.978973	−	0.203989i	$-0.0653907\pi$
$241$	1170.39	+	2027.17i	0.312827	+	0.541832i	−0.666146	+	0.745821i	$0.732057\pi$
$242$	−1982.12	+	1296.50i	−0.526509	+	0.344388i
$243$	3568.31	−	1271.25i	0.942005	−	0.335600i
$244$	−1277.27	+	2920.38i	−0.335119	+	0.766222i
$245$	−517.002	+	298.491i	−0.134817	+	0.0778364i
$246$	−3531.03	−	4667.10i	−0.915163	−	1.20961i
$247$	689.028	+	397.811i	0.177497	+	0.102478i
$248$	−937.752	+	2516.92i	−0.240110	+	0.644454i
$249$	463.377	+	689.012i	0.117933	+	0.175359i
$250$	452.378	−	895.111i	0.114443	−	0.226447i
$251$	938.044			0.235892			0.117946	−	0.993020i	$-0.462369\pi$
$251$	938.044			0.235892			0.117946	+	0.993020i	$0.462369\pi$
$252$	5732.03	+	1619.76i	1.43287	+	0.404903i
$253$	3229.58			0.802537
$254$	−698.932	+	1382.96i	−0.172657	+	0.341633i
$255$	102.735	−	209.911i	0.0252296	−	0.0515496i
$256$	−3375.96	−	2319.51i	−0.824209	−	0.566286i
$257$	143.756	+	82.9975i	0.0348920	+	0.0201449i	0.517345	−	0.855777i	$-0.326921\pi$
$257$	143.756	+	82.9975i	0.0348920	+	0.0201449i	−0.482453	+	0.875922i	$0.660254\pi$
$258$	−2917.73	+	363.957i	−0.704069	+	0.0878256i
$259$	−7175.02	+	4142.50i	−1.72137	+	0.993831i
$260$	725.265	+	317.206i	0.172996	+	0.0756626i
$261$	−2306.86	+	1792.20i	−0.547093	+	0.425036i
$262$	−4410.31	+	2884.76i	−1.03996	+	0.680234i
$263$	2415.87	+	4184.41i	0.566422	+	0.981072i	0.996916	+	0.0784782i	$0.0250061\pi$
$263$	2415.87	+	4184.41i	0.566422	+	0.981072i	−0.430494	+	0.902594i	$0.641661\pi$
$264$	−1895.24	+	1797.73i	−0.441833	+	0.419100i
$265$	173.997	−	301.371i	0.0403341	−	0.0698606i
$266$	49.8852	+	895.474i	0.0114987	+	0.206410i
$267$	−530.764	−	7742.11i	−0.121656	−	1.77457i
$268$	−315.776	−	2825.41i	−0.0719743	−	0.643989i
$269$		−	5581.42i		−	1.26508i	−0.774529	−	0.632538i	$-0.782013\pi$
$269$		−	5581.42i		−	1.26508i	0.774529	−	0.632538i	$-0.217987\pi$
$270$	400.940	+	401.585i	0.0903719	+	0.0905173i
$271$		−	8094.32i		−	1.81437i	−0.420729	−	0.907186i	$-0.638226\pi$
$271$		−	8094.32i		−	1.81437i	0.420729	−	0.907186i	$-0.361774\pi$
$272$	−1922.35	−	596.752i	−0.428528	−	0.133027i
$273$	678.117	+	9891.51i	0.150335	+	2.19290i
$274$	−4089.07	+	227.795i	−0.901568	+	0.0502247i
$275$	−1365.87	+	2365.76i	−0.299510	+	0.518767i
$276$	−5945.23	+	1080.31i	−1.29660	+	0.235606i
$277$	922.842	+	1598.41i	0.200174	+	0.346712i	0.948584	−	0.316524i	$-0.102516\pi$
$277$	922.842	+	1598.41i	0.200174	+	0.346712i	−0.748410	+	0.663236i	$0.769183\pi$
$278$	−579.477	−	885.921i	−0.125017	−	0.191130i
$279$	−2968.31	−	1208.71i	−0.636947	−	0.259368i
$280$	148.285	+	879.921i	0.0316490	+	0.187805i
$281$	−2195.00	+	1267.28i	−0.465987	+	0.269038i	−0.714558	−	0.699576i	$-0.753372\pi$
$281$	−2195.00	+	1267.28i	−0.465987	+	0.269038i	0.248571	+	0.968614i	$0.420039\pi$
$282$	552.198	+	4426.79i	0.116606	+	0.934792i
$283$	2691.52	+	1553.95i	0.565351	+	0.326405i	0.755290	−	0.655390i	$-0.227496\pi$
$283$	2691.52	+	1553.95i	0.565351	+	0.326405i	−0.189940	+	0.981796i	$0.560829\pi$
$284$	4110.09	+	5579.46i	0.858764	+	1.16577i
$285$	−37.5607	+	76.7449i	−0.00780669	+	0.0159508i
$286$	−3880.68	−	1961.25i	−0.802341	−	0.405493i
$287$	10981.0			2.25848
$288$	2887.54	−	3943.35i	0.590798	−	0.806819i
$289$	3923.85			0.798667
$290$	−390.577	−	197.393i	−0.0790878	−	0.0399700i
$291$	4060.34	+	6037.46i	0.817943	+	1.21623i
$292$	306.819	+	416.507i	0.0614904	+	0.0834734i
$293$	4824.35	+	2785.34i	0.961916	+	0.555363i	0.896762	−	0.442513i	$-0.145913\pi$
$293$	4824.35	+	2785.34i	0.961916	+	0.555363i	0.0651539	+	0.997875i	$0.479246\pi$
$294$	−4892.75	+	3701.75i	−0.970581	+	0.734320i
$295$	103.832	−	59.9475i	0.0204927	−	0.0118314i
$296$	1129.70	+	6703.63i	0.221833	+	1.31635i
$297$	−2076.20	−	2324.92i	−0.405633	−	0.454228i
$298$	−3822.83	−	5844.44i	−0.743122	−	1.13610i
$299$	−5029.02	−	8710.51i	−0.972694	−	1.68476i
$300$	1723.03	−	4811.96i	0.331598	−	0.926061i
$301$	2758.53	−	4777.91i	0.528235	−	0.914930i
$302$	−1713.47	+	95.4540i	−0.326486	+	0.0181880i
$303$	−1032.31	+	694.257i	−0.195726	+	0.131630i
$304$	702.824	+	218.176i	0.132598	+	0.0411621i
$305$		−	569.785i		−	0.106970i
$306$	780.680	−	2271.40i	0.145845	−	0.424337i
$307$			7746.70i			1.44016i	0.693893	+	0.720078i	$0.255894\pi$
$307$			7746.70i			1.44016i	−0.693893	+	0.720078i	$0.744106\pi$
$308$	−544.408	−	4871.09i	−0.100716	−	0.901156i
$309$	−2716.52	−	1329.53i	−0.500120	−	0.244771i
$310$	−26.7058	−	479.387i	−0.00489286	−	0.0878301i
$311$	2906.54	−	5034.28i	0.529951	−	0.917902i	−0.469438	−	0.882965i	$-0.655544\pi$
$311$	2906.54	−	5034.28i	0.529951	−	0.917902i	0.999390	−	0.0349372i	$-0.0111231\pi$
$312$	7799.88	+	2312.29i	1.41532	+	0.419576i
$313$	−1367.73	−	2368.98i	−0.246993	−	0.427805i	0.715697	−	0.698411i	$-0.246109\pi$
$313$	−1367.73	−	2368.98i	−0.246993	−	0.427805i	−0.962690	+	0.270606i	$0.912776\pi$
$314$	−175.965	+	115.098i	−0.0316251	+	0.0206858i
$315$	−1054.80	+	145.308i	−0.188671	+	0.0259910i
$316$	3003.67	+	1313.70i	0.534713	+	0.233865i
$317$	5434.46	−	3137.59i	0.962869	−	0.555913i	0.0658143	−	0.997832i	$-0.479035\pi$
$317$	5434.46	−	3137.59i	0.962869	−	0.555913i	0.897055	+	0.441919i	$0.145702\pi$
$318$	1391.06	−	3294.77i	0.245305	−	0.581011i
$319$	2081.75	+	1201.90i	0.365378	+	0.210951i
$320$	719.054	+	138.061i	0.125614	+	0.0241182i
$321$	−7622.27	+	522.548i	−1.32534	+	0.0908591i
$322$	5114.02	−	10119.0i	0.885073	−	1.75128i
$323$	361.639			0.0622976
$324$	4599.71	+	3585.38i	0.788701	+	0.614777i
$325$	8507.62			1.45206
$326$	−51.6499	+	102.199i	−0.00877492	+	0.0173628i
$327$	−7.27825	+	0.498964i	−0.00123085	+	8.43815e-5i
$328$	3145.80	−	8443.29i	0.529566	−	1.42135i
$329$	−7249.06	−	4185.25i	−1.21475	−	0.701338i
$330$	181.626	−	430.185i	0.0302974	−	0.0717603i
$331$	302.371	−	174.574i	0.0502110	−	0.0289893i	−0.474684	−	0.880156i	$-0.657438\pi$
$331$	302.371	−	174.574i	0.0502110	−	0.0289893i	0.524895	+	0.851167i	$0.324104\pi$
$332$	−512.268	+	1171.26i	−0.0846818	+	0.193618i
$333$	−8035.95	+	1107.02i	−1.32242	+	0.182175i
$334$	97.3394	−	63.6693i	0.0159466	−	0.0104306i
$335$	254.103	+	440.119i	0.0414421	+	0.0717799i
$336$	2631.59	+	8784.92i	0.427277	+	1.42636i
$337$	−4663.04	+	8076.62i	−0.753744	+	1.30552i	0.192252	+	0.981346i	$0.438421\pi$
$337$	−4663.04	+	8076.62i	−0.753744	+	1.30552i	−0.945996	+	0.324178i	$0.894912\pi$
$338$	407.571	+	7316.18i	0.0655886	+	1.17736i
$339$	−6331.06	−	3098.57i	−1.01432	−	0.496434i
$340$	357.584	−	39.9647i	0.0570374	−	0.00637468i
$341$			2637.28i			0.418817i
$342$	−285.421	+	830.437i	−0.0451281	+	0.131301i
$343$		−	2053.18i		−	0.323210i
$344$	−2883.49	−	3489.80i	−0.451941	−	0.546970i
$345$	896.312	−	602.792i	0.139872	−	0.0940673i
$346$	3105.91	−	173.024i	0.482586	−	0.0268840i
$347$	−2780.66	+	4816.24i	−0.430183	+	0.745098i	−0.996889	−	0.0788217i	$-0.974884\pi$
$347$	−2780.66	+	4816.24i	−0.430183	+	0.745098i	0.566706	+	0.823920i	$0.308218\pi$
$348$	−4234.27	−	1516.18i	−0.652243	−	0.233551i
$349$	−5336.11	−	9242.41i	−0.818439	−	1.41758i	−0.906832	−	0.421492i	$-0.861506\pi$
$349$	−5336.11	−	9242.41i	−0.818439	−	1.41758i	0.0883931	−	0.996086i	$-0.471827\pi$
$350$	5249.64	+	8025.78i	0.801728	+	1.22570i
$351$	−3037.56	+	9220.03i	−0.461918	+	1.40208i
$352$	−3901.36	−	976.860i	−0.590747	−	0.147917i
$353$	349.651	−	201.871i	0.0527196	−	0.0304377i	−0.473409	−	0.880843i	$-0.656977\pi$
$353$	349.651	−	201.871i	0.0527196	−	0.0304377i	0.526128	+	0.850405i	$0.323643\pi$
$354$	982.634	−	743.439i	0.147532	−	0.111620i
$355$	−1072.80	−	619.382i	−0.160390	−	0.0926011i
$356$	9619.50	−	7086.17i	1.43211	−	1.05496i
$357$	2514.96	+	3739.58i	0.372845	+	0.554396i
$358$	9718.55	+	4911.63i	1.43475	+	0.725106i
$359$	−6398.10			−0.940609			−0.470305	−	0.882504i	$-0.655856\pi$
$359$	−6398.10			−0.940609			−0.470305	+	0.882504i	$0.655856\pi$
$360$	−190.449	+	852.668i	−0.0278821	+	0.124832i
$361$	6726.78			0.980724
$362$	2755.71	+	1392.70i	0.400102	+	0.202207i
$363$	1912.76	−	3908.20i	0.276568	−	0.565089i
$364$	−12290.1	+	9053.46i	−1.76971	+	1.30365i
$365$	−80.0847	−	46.2369i	−0.0114844	−	0.00663055i
$366$	−724.833	−	5810.75i	−0.103518	−	0.829871i
$367$	−9573.58	+	5527.31i	−1.36168	+	0.786166i	−0.989848	−	0.142133i	$-0.954604\pi$
$367$	−9573.58	+	5527.31i	−1.36168	+	0.786166i	−0.371833	+	0.928300i	$0.621270\pi$
$368$	−6315.50	−	6831.06i	−0.894614	−	0.967646i
$369$	9957.54	+	4054.76i	1.40479	+	0.572039i
$370$	−665.205	−	1016.98i	−0.0934658	−	0.142893i
$371$	3355.25	+	5811.46i	0.469530	+	0.813250i
$372$	−882.185	−	4854.88i	−0.122955	−	0.676650i
$373$	−1756.18	+	3041.80i	−0.243785	+	0.422248i	−0.961789	−	0.273791i	$-0.911722\pi$
$373$	−1756.18	+	3041.80i	−0.243785	+	0.422248i	0.718004	+	0.696039i	$0.245056\pi$
$374$	−1973.32	+	109.930i	−0.272829	+	0.0151988i
$375$	126.018	+	1838.19i	0.0173534	+	0.253129i
$376$	−5294.74	+	4374.85i	−0.726212	+	0.600041i
$377$		−	7486.26i		−	1.02271i
$378$	−10572.2	+	2823.70i	−1.43856	+	0.384221i
$379$		−	1238.70i		−	0.167883i	−0.996471	−	0.0839413i	$-0.973249\pi$
$379$		−	1238.70i		−	0.167883i	0.996471	−	0.0839413i	$-0.0267508\pi$
$380$	−130.735	+	14.6114i	−0.0176488	+	0.00197249i
$381$	−194.700	−	2840.03i	−0.0261805	−	0.381888i
$382$	−100.584	−	1805.55i	−0.0134720	−	0.241832i
$383$	−853.999	+	1479.17i	−0.113936	+	0.197342i	−0.917354	−	0.398073i	$-0.869679\pi$
$383$	−853.999	+	1479.17i	−0.113936	+	0.197342i	0.803418	+	0.595415i	$0.203012\pi$
$384$	7508.65	+	493.244i	0.997849	+	0.0655488i
$385$	438.081	+	758.779i	0.0579914	+	0.100444i
$386$	4138.07	−	2706.69i	0.545653	−	0.356910i
$387$	4265.70	−	3314.02i	0.560304	−	0.435300i
$388$	−4488.75	+	10263.1i	−0.587324	+	1.34287i
$389$	−7751.80	+	4475.50i	−1.01036	+	0.583334i	−0.911298	−	0.411746i	$-0.864919\pi$
$389$	−7751.80	+	4475.50i	−1.01036	+	0.583334i	−0.0990663	+	0.995081i	$0.531586\pi$
$390$	−1443.08	+	180.009i	−0.187367	+	0.0233721i
$391$	−3959.24	−	2285.87i	−0.512091	−	0.295656i
$392$	−8851.51	−	3297.89i	−1.14048	−	0.424920i
$393$	4255.99	−	8695.93i	0.546276	−	1.11616i
$394$	−2653.04	+	5249.52i	−0.339234	+	0.671236i
$395$	−586.034			−0.0746496
$396$	1305.00	−	4618.13i	0.165603	−	0.586035i
$397$	−9391.26			−1.18724			−0.593619	−	0.804746i	$-0.702302\pi$
$397$	−9391.26			−1.18724			−0.593619	+	0.804746i	$0.702302\pi$
$398$	−2340.81	+	4631.71i	−0.294809	+	0.583334i
$399$	−919.484	−	1367.21i	−0.115368	−	0.171544i
$400$	7674.95	−	1737.26i	0.959369	−	0.217157i
$401$	3528.74	+	2037.32i	0.439444	+	0.253713i	0.703362	−	0.710832i	$-0.251681\pi$
$401$	3528.74	+	2037.32i	0.439444	+	0.253713i	−0.263918	+	0.964545i	$0.585015\pi$
$402$	3151.26	+	4165.15i	0.390971	+	0.516763i
$403$	7113.02	−	4106.70i	0.879217	−	0.507616i
$404$	−1754.84	−	767.508i	−0.216106	−	0.0945172i
$405$	−1010.15	−	257.725i	−0.123938	−	0.0316208i
$406$	7062.27	−	4619.40i	0.863287	−	0.564673i
$407$	3337.50	+	5780.71i	0.406471	+	0.704028i
$408$	3595.85	−	862.454i	0.436326	−	0.104652i
$409$	335.715	−	581.476i	0.0405869	−	0.0702986i	−0.845018	−	0.534737i	$-0.820411\pi$
$409$	335.715	−	581.476i	0.0405869	−	0.0702986i	0.885605	+	0.464439i	$0.153744\pi$
$410$	89.5875	+	1608.16i	0.0107913	+	0.193710i
$411$	6243.21	−	4198.71i	0.749281	−	0.503910i
$412$	−517.194	−	4627.58i	−0.0618454	−	0.553361i
$413$			2311.98i			0.275460i
$414$	8373.89	−	7287.57i	0.994093	−	0.865131i
$415$		−	228.520i		−	0.0270304i
$416$	3440.40	+	12043.5i	0.405479	+	1.41943i
$417$	1746.80	+	854.923i	0.205134	+	0.100398i
$418$	721.458	−	40.1911i	0.0844203	−	0.00470290i
$419$	4703.57	−	8146.83i	0.548412	−	0.949877i	−0.449972	−	0.893043i	$-0.648566\pi$
$419$	4703.57	−	8146.83i	0.548412	−	0.949877i	0.998384	−	0.0568346i	$-0.0181008\pi$
$420$	−1060.27	−	1250.27i	−0.123180	−	0.145255i
$421$	6156.19	+	10662.8i	0.712671	+	1.23438i	0.963851	+	0.266441i	$0.0858479\pi$
$421$	6156.19	+	10662.8i	0.712671	+	1.23438i	−0.251181	+	0.967940i	$0.580819\pi$
$422$	−7700.63	−	11772.9i	−0.888296	−	1.35805i
$423$	−5028.04	−	6471.93i	−0.577947	−	0.743915i
$424$	5429.65	−	915.008i	0.621904	−	0.104804i
$425$	3348.94	−	1933.51i	0.382229	−	0.220680i
$426$	−11728.5	−	4951.82i	−1.33392	−	0.563184i
$427$	9515.36	+	5493.70i	1.07841	+	0.622620i
$428$	−6976.48	−	9470.59i	−0.787899	−	1.06958i
$429$	7969.31	−	546.340i	0.896881	−	0.0614861i
$430$	722.229	+	365.005i	0.0809976	+	0.0409351i
$431$	−7647.49			−0.854679			−0.427340	−	0.904091i	$-0.640549\pi$
$431$	−7647.49			−0.854679			−0.427340	+	0.904091i	$0.640549\pi$
$432$	−857.538	+	8937.91i	−0.0955053	+	0.995429i
$433$	−13985.2			−1.55216			−0.776082	−	0.630632i	$-0.782796\pi$
$433$	−13985.2			−1.55216			−0.776082	+	0.630632i	$0.782796\pi$
$434$	8263.21	+	4176.12i	0.913932	+	0.461890i
$435$	802.083	−	54.9871i	0.0884067	−	0.00606076i
$436$	−6.66161	−	9.04315i	−0.000731727	−	0.000993322i
$437$	1447.52	+	835.728i	0.158454	+	0.0914835i
$438$	−875.534	−	369.654i	−0.0955128	−	0.0403259i
$439$	11706.7	−	6758.84i	1.27273	−	0.734811i	0.297228	−	0.954806i	$-0.403938\pi$
$439$	11706.7	−	6758.84i	1.27273	−	0.734811i	0.975501	+	0.219996i	$0.0706044\pi$
$440$	708.928	−	119.469i	0.0768109	−	0.0129442i
$441$	4250.80	−	10439.0i	0.459000	−	1.12720i
$442$	3369.30	+	5151.07i	0.362582	+	0.554325i
$443$	−3270.50	−	5664.67i	−0.350759	−	0.607532i	0.635624	−	0.771999i	$-0.280743\pi$
$443$	−3270.50	−	5664.67i	−0.350759	−	0.607532i	−0.986383	+	0.164467i	$0.947410\pi$
$444$	−8077.57	−	9525.12i	−0.863389	−	1.01811i
$445$	−1067.87	+	1849.61i	−0.113757	+	0.197033i
$446$	−1995.67	+	111.175i	−0.211878	+	0.0118034i
$447$	11523.7	+	5639.95i	1.21935	+	0.596779i
$448$	−9238.51	+	10677.0i	−0.974283	+	1.12598i
$449$			17599.7i			1.84984i	0.380158	+	0.924921i	$0.375870\pi$
$449$			17599.7i			1.84984i	−0.380158	+	0.924921i	$0.624130\pi$
$450$	1796.82	+	9216.24i	0.188229	+	0.965462i
$451$		−	8847.05i		−	0.923706i
$452$	−1205.36	−	10785.0i	−0.125432	−	1.12230i
$453$	2616.12	−	1759.41i	0.271338	−	0.182482i
$454$	504.943	+	9064.08i	0.0521986	+	0.937001i
$455$	1364.34	−	2363.10i	0.140574	−	0.243481i
$456$	−1314.67	+	315.319i	−0.135011	+	0.0323819i
$457$	1199.50	+	2077.59i	0.122779	+	0.212660i	0.920863	−	0.389887i	$-0.127486\pi$
$457$	1199.50	+	2077.59i	0.122779	+	0.212660i	−0.798083	+	0.602547i	$0.794153\pi$
$458$	3464.52	−	2266.13i	0.353463	−	0.231199i
$459$	899.713	+	4319.71i	0.0914924	+	0.439274i
$460$	1523.65	+	666.392i	0.154436	+	0.0675450i
$461$	−3237.72	+	1869.30i	−0.327106	+	0.188855i	−0.654555	−	0.756014i	$-0.727144\pi$
$461$	−3237.72	+	1869.30i	−0.327106	+	0.188855i	0.327450	+	0.944869i	$0.393811\pi$
$462$	5432.87	+	7180.84i	0.547099	+	0.723123i
$463$	−2167.70	−	1251.52i	−0.217585	−	0.125623i	0.387247	−	0.921976i	$-0.373426\pi$
$463$	−2167.70	−	1251.52i	−0.217585	−	0.125623i	−0.604831	+	0.796354i	$0.706760\pi$
$464$	−1528.69	−	6753.56i	−0.152948	−	0.675702i
$465$	492.241	+	731.929i	0.0490906	+	0.0729944i
$466$	1689.30	−	3342.58i	0.167930	−	0.332279i
$467$	−5361.30			−0.531245			−0.265622	−	0.964077i	$-0.585577\pi$
$467$	−5361.30			−0.531245			−0.265622	+	0.964077i	$0.585577\pi$
$468$	−14487.7	+	3671.52i	−1.43097	+	0.362641i
$469$	−9799.93			−0.964859
$470$	553.787	−	1095.77i	0.0543496	−	0.107540i
$471$	169.808	−	346.955i	0.0166122	−	0.0339424i
$472$	1777.69	+	662.331i	0.173358	+	0.0645895i
$473$	−3849.43	−	2222.47i	−0.374201	−	0.216045i
$474$	−5976.46	+	745.504i	−0.579131	+	0.0722408i
$475$	−1224.39	+	706.904i	−0.118272	+	0.0682841i
$476$	−2780.31	+	6356.95i	−0.267721	+	0.612122i
$477$	896.638	+	6508.77i	0.0860676	+	0.624772i
$478$	−1867.72	+	1221.67i	−0.178719	+	0.116899i
$479$	609.925	+	1056.42i	0.0581799	+	0.100771i	0.893648	−	0.448768i	$-0.148137\pi$
$479$	609.925	+	1056.42i	0.0581799	+	0.100771i	−0.835468	+	0.549538i	$0.814804\pi$
$480$	−1265.08	+	457.067i	−0.120297	+	0.0434628i
$481$	10394.1	−	18003.2i	0.985304	−	1.70660i
$482$	−368.257	−	6610.46i	−0.0348001	−	0.624685i
$483$	1424.60	+	20780.3i	0.134206	+	1.95763i
$484$	6657.62	−	744.076i	0.625246	−	0.0698795i
$485$		−	2002.41i		−	0.187473i
$486$	−10629.5	−	1343.28i	−0.992109	−	0.125376i
$487$		−	1483.03i		−	0.137993i	−0.997617	−	0.0689964i	$-0.978020\pi$
$487$		−	1483.03i		−	0.137993i	0.997617	−	0.0689964i	$-0.0219797\pi$
$488$	6950.06	−	5742.57i	0.644702	−	0.532693i
$489$	−14.3880	−	209.874i	−0.00133057	−	0.0194086i
$490$	1685.91	−	93.9189i	0.155432	−	0.00865882i
$491$	−6942.36	+	12024.5i	−0.638094	+	1.10521i	0.347756	+	0.937585i	$0.386944\pi$
$491$	−6942.36	+	12024.5i	−0.638094	+	1.10521i	−0.985851	+	0.167627i	$0.946390\pi$
$492$	2959.39	+	16286.3i	0.271178	+	1.49236i
$493$	−1701.39	−	2946.89i	−0.155429	−	0.269211i
$494$	−1231.84	−	1883.26i	−0.112192	−	0.171522i
$495$	117.070	+	849.825i	0.0106301	+	0.0771652i
$496$	5578.26	−	5157.24i	0.504982	−	0.466869i
$497$	20687.2	−	11943.8i	1.86710	−	1.07797i
$498$	−290.704	−	2330.48i	−0.0261582	−	0.209701i
$499$	−17493.2	−	10099.7i	−1.56935	−	0.906063i	−0.996245	−	0.0865784i	$-0.972407\pi$
$499$	−17493.2	−	10099.7i	−1.56935	−	0.906063i	−0.573102	−	0.819484i	$-0.694260\pi$
$500$	−2283.93	+	1682.45i	−0.204281	+	0.150483i
$501$	−93.9335	+	191.927i	−0.00837653	+	0.0171151i
$502$	−2367.96	−	1196.74i	−0.210532	−	0.106400i
$503$	−388.562			−0.0344436			−0.0172218	−	0.999852i	$-0.505482\pi$
$503$	−388.562			−0.0344436			−0.0172218	+	0.999852i	$0.505482\pi$
$504$	−12403.2	−	11401.7i	−1.09620	−	1.00768i
$505$	342.381			0.0301698
$506$	−8152.61	−	4120.23i	−0.716261	−	0.361989i
$507$	−7512.35	−	11170.4i	−0.658058	−	0.978489i
$508$	3528.71	−	2599.41i	0.308191	−	0.227028i
$509$	5854.78	+	3380.26i	0.509840	+	0.294356i	0.732768	−	0.680479i	$-0.238228\pi$
$509$	5854.78	+	3380.26i	0.509840	+	0.294356i	−0.222928	+	0.974835i	$0.571561\pi$
$510$	−527.142	+	398.824i	−0.0457691	+	0.0346279i
$511$	1544.30	−	891.605i	0.133691	−	0.0771864i
$512$	5562.96	+	10162.2i	0.480177	+	0.877172i
$513$	−328.941	−	1579.31i	−0.0283101	−	0.135923i
$514$	−257.005	−	392.916i	−0.0220545	−	0.0337175i
$515$	416.182	+	720.848i	0.0356100	+	0.0616783i
$516$	7829.72	+	2803.62i	0.667993	+	0.239191i
$517$	−3371.94	+	5840.37i	−0.286843	+	0.496826i
$518$	23397.2	−	1303.42i	1.98459	−	0.110558i
$519$	−4742.11	+	3189.19i	−0.401070	+	0.269730i
$520$	−1426.14	−	1726.02i	−0.120270	−	0.145559i
$521$			17324.6i			1.45683i	0.685139	+	0.728413i	$0.259742\pi$
$521$			17324.6i			1.45683i	−0.685139	+	0.728413i	$0.740258\pi$
$522$	8109.81	−	1581.11i	0.679994	−	0.132573i
$523$			16119.4i			1.34771i	0.738864	+	0.673855i	$0.235363\pi$
$523$			16119.4i			1.34771i	−0.738864	+	0.673855i	$0.764637\pi$
$524$	14813.5	−	1655.61i	1.23498	−	0.138026i
$525$	−15824.7	−	7744.97i	−1.31552	−	0.643844i
$526$	−760.142	−	13645.1i	−0.0630110	−	1.13109i
$527$	1866.64	−	3233.12i	0.154293	−	0.267243i
$528$	7077.77	−	2120.20i	0.583372	−	0.174754i
$529$	−4481.55	−	7762.27i	−0.368337	−	0.637978i
$530$	−823.712	+	538.787i	−0.0675090	+	0.0441574i
$531$	−853.709	+	2096.51i	−0.0697699	+	0.171338i
$532$	1016.50	−	2324.14i	0.0828398	−	0.189406i
$533$	−23861.4	+	13776.4i	−1.93912	+	1.11955i
$534$	−8537.38	+	20221.0i	−0.691852	+	1.63867i
$535$	1820.98	+	1051.34i	0.147154	+	0.0849597i
$536$	−2807.46	+	7535.20i	−0.226238	+	0.607222i
$537$	−19957.9	+	1368.22i	−1.60381	+	0.109950i
$538$	−7120.66	+	14089.5i	−0.570620	+	1.12907i
$539$	−9274.78			−0.741175
$540$	−499.783	−	1525.26i	−0.0398282	−	0.121549i
$541$	−4412.42			−0.350655			−0.175328	−	0.984510i	$-0.556099\pi$
$541$	−4412.42			−0.350655			−0.175328	+	0.984510i	$0.556099\pi$
$542$	−10326.6	+	20433.0i	−0.818384	+	1.61932i
$543$	−5659.09	+	387.961i	−0.447246	+	0.0306612i
$544$	4091.38	+	3958.91i	0.322457	+	0.312016i
$545$	1.73879	+	1.00389i	0.000136663	+	7.89026e-5i
$546$	10907.6	−	25834.8i	0.854946	−	2.02496i
$547$	−5985.94	+	3455.99i	−0.467898	+	0.270141i	−0.715360	−	0.698757i	$-0.753737\pi$
$547$	−5985.94	+	3455.99i	−0.467898	+	0.270141i	0.247461	+	0.968898i	$0.420404\pi$
$548$	10612.9	+	4641.71i	0.827300	+	0.361832i
$549$	6599.97	+	8495.28i	0.513078	+	0.660418i
$550$	6466.15	−	4229.49i	0.501305	−	0.327902i
$551$	622.038	+	1077.40i	0.0480938	+	0.0833010i
$552$	16386.1	+	4857.70i	1.26348	+	0.374561i
$553$	5650.37	−	9786.72i	0.434499	−	0.752574i
$554$	−290.368	−	5212.30i	−0.0222681	−	0.399728i
$555$	2005.22	+	981.399i	0.153363	+	0.0750596i
$556$	332.570	+	2975.67i	0.0253671	+	0.226972i
$557$		−	17257.6i		−	1.31280i	−0.754415	−	0.656398i	$-0.772079\pi$
$557$		−	17257.6i		−	1.31280i	0.754415	−	0.656398i	$-0.227921\pi$
$558$	5951.04	+	6838.13i	0.451483	+	0.518784i
$559$			13843.1i			1.04741i
$560$	748.260	−	2410.41i	0.0564639	−	0.181890i
$561$	3012.87	−	2026.23i	0.226744	−	0.152491i
$562$	7157.73	−	398.744i	0.537243	−	0.0299288i
$563$	12554.5	−	21745.1i	0.939805	−	1.62779i	0.173972	−	0.984751i	$-0.444340\pi$
$563$	12554.5	−	21745.1i	0.939805	−	1.62779i	0.765833	−	0.643039i	$-0.222327\pi$
$564$	4253.66	−	11879.3i	0.317573	−	0.886894i
$565$	969.945	+	1679.99i	0.0722228	+	0.125094i
$566$	−4811.86	−	7356.51i	−0.357346	−	0.546320i
$567$	14043.6	−	14384.5i	1.04017	−	1.06542i
$568$	−3257.19	−	19328.1i	−0.240614	−	1.42780i
$569$	14813.5	−	8552.60i	1.09142	−	0.630129i	0.157463	−	0.987525i	$-0.449669\pi$
$569$	14813.5	−	8552.60i	1.09142	−	0.630129i	0.933953	+	0.357396i	$0.116335\pi$
$570$	192.726	−	145.813i	0.0141621	−	0.0107148i
$571$	−4814.10	−	2779.42i	−0.352827	−	0.203705i	0.313103	−	0.949719i	$-0.398632\pi$
$571$	−4814.10	−	2779.42i	−0.352827	−	0.203705i	−0.665929	+	0.746015i	$0.731965\pi$
$572$	7294.12	+	9901.79i	0.533186	+	0.723802i
$573$	1853.96	+	2756.71i	0.135166	+	0.200983i
$574$	−27719.9	−	14009.3i	−2.01569	−	1.01870i
$575$	17873.0			1.29627
$576$	−12320.0	+	6270.57i	−0.891205	+	0.453600i
$577$	19014.3			1.37188			0.685939	−	0.727659i	$-0.259392\pi$
$577$	19014.3			1.37188			0.685939	+	0.727659i	$0.259392\pi$
$578$	−9905.21	−	5005.97i	−0.712807	−	0.360244i
$579$	−3993.28	+	8159.15i	−0.286624	+	0.585635i
$580$	734.127	+	996.580i	0.0525569	+	0.0713461i
$581$	3816.27	+	2203.32i	0.272505	+	0.157331i
$582$	−2547.29	−	20420.8i	−0.181424	−	1.45442i
$583$	4682.13	−	2703.23i	0.332614	−	0.192035i
$584$	−243.149	−	1442.85i	−0.0172287	−	0.102235i
$585$	2109.77	−	1639.08i	0.149108	−	0.115842i
$586$	−8624.91	−	13186.0i	−0.608006	−	0.929537i
$587$	12597.2	+	21818.9i	0.885759	+	1.53418i	0.844842	+	0.535017i	$0.179695\pi$
$587$	12597.2	+	21818.9i	0.885759	+	1.53418i	0.0409172	+	0.999163i	$0.486972\pi$
$588$	17073.7	−	3102.47i	1.19746	−	0.217591i
$589$	−682.457	+	1182.05i	−0.0477422	+	0.0826919i
$590$	−338.589	+	18.8622i	−0.0236263	+	0.00131618i
$591$	−739.050	−	10780.3i	−0.0514390	−	0.750327i
$592$	5700.58	−	18363.6i	0.395764	−	1.27490i
$593$		−	17307.5i		−	1.19854i	−0.800548	−	0.599269i	$-0.795458\pi$
$593$		−	17307.5i		−	1.19854i	0.800548	−	0.599269i	$-0.204542\pi$
$594$	2274.98	+	8517.71i	0.157144	+	0.588360i
$595$		−	1240.28i		−	0.0854564i
$596$	2193.97	+	19630.5i	0.150786	+	1.34916i
$597$	−652.073	−	9511.61i	−0.0447028	−	0.652068i
$598$	1582.36	+	28404.4i	0.108206	+	1.94238i
$599$	−10740.8	+	18603.5i	−0.732647	+	1.26898i	0.223101	+	0.974795i	$0.428382\pi$
$599$	−10740.8	+	18603.5i	−0.732647	+	1.26898i	−0.955748	+	0.294186i	$0.904951\pi$
$600$	−10488.5	+	9948.89i	−0.713655	+	0.676936i
$601$	2716.74	+	4705.53i	0.184390	+	0.319372i	0.943371	−	0.331741i	$-0.107636\pi$
$601$	2716.74	+	4705.53i	0.184390	+	0.319372i	−0.758981	+	0.651113i	$0.774303\pi$
$602$	−13059.1	+	8541.89i	−0.884133	+	0.578308i
$603$	−8886.59	−	3618.66i	−0.600149	−	0.244384i
$604$	4447.18	+	1945.04i	0.299591	+	0.131031i
$605$	−1037.07	+	598.752i	−0.0696907	+	0.0402359i
$606$	3491.65	−	435.549i	0.234057	−	0.0291963i
$607$	−11684.8	−	6746.19i	−0.781333	−	0.451103i	0.0555692	−	0.998455i	$-0.482303\pi$
$607$	−11684.8	−	6746.19i	−0.781333	−	0.451103i	−0.836903	+	0.547352i	$0.815636\pi$
$608$	−1495.84	−	1447.40i	−0.0997765	−	0.0965460i
$609$	−6815.16	+	13924.9i	−0.453472	+	0.926543i
$610$	−726.920	+	1438.34i	−0.0482494	+	0.0954701i
$611$	21002.8			1.39064
$612$	−4868.52	+	4737.85i	−0.321566	+	0.312935i
$613$	8330.79			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$613$	8330.79			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$614$	9883.08	−	19555.5i	0.649591	−	1.28533i
$615$	−1651.28	−	2455.34i	−0.108270	−	0.160990i
$616$	−4840.15	+	12990.9i	−0.316583	+	0.849706i
$617$	−17147.1	−	9899.88i	−1.11883	−	0.645955i	−0.177726	−	0.984080i	$-0.556874\pi$
$617$	−17147.1	−	9899.88i	−1.11883	−	0.645955i	−0.941101	+	0.338125i	$0.890207\pi$
$618$	5161.28	+	6821.88i	0.335950	+	0.444039i
$619$	22673.3	−	13090.4i	1.47224	−	0.849997i	0.472725	−	0.881210i	$-0.343270\pi$
$619$	22673.3	−	13090.4i	1.47224	−	0.849997i	0.999513	+	0.0312129i	$0.00993698\pi$
$620$	−544.177	+	1244.22i	−0.0352494	+	0.0805950i
$621$	−6381.37	+	19369.6i	−0.412360	+	1.25165i
$622$	−13759.8	+	9000.22i	−0.887005	+	0.580186i
$623$	−20592.2	−	35666.7i	−1.32425	−	2.29367i
$624$	−16739.7	−	15788.0i	−1.07392	−	1.01286i
$625$	−7431.14	+	12871.1i	−0.475593	+	0.823751i
$626$	430.351	+	7725.09i	0.0274765	+	0.493221i
$627$	−1101.53	+	740.803i	−0.0701606	+	0.0471847i
$628$	591.038	−	66.0563i	0.0375557	−	0.00419735i
$629$		−	9449.01i		−	0.598977i
$630$	2848.08	+	978.885i	0.180111	+	0.0619043i
$631$			24489.4i			1.54502i	0.635004	+	0.772509i	$0.280999\pi$
$631$			24489.4i			1.54502i	−0.635004	+	0.772509i	$0.719001\pi$
$632$	−5906.34	−	7148.26i	−0.371743	−	0.449909i
$633$	23213.1	+	11361.0i	1.45756	+	0.713364i
$634$	−17721.4	+	987.226i	−1.11010	+	0.0618419i
$635$	−391.726	+	678.489i	−0.0244806	+	0.0424016i
$636$	−7714.94	+	6542.49i	−0.481002	+	0.407903i
$637$	14442.5	+	25015.1i	0.898322	+	1.55594i
$638$	−3721.72	−	5689.87i	−0.230947	−	0.353079i
$639$	23169.5	−	3191.79i	1.43438	−	0.197598i
$640$	−1639.02	−	1265.87i	−0.101231	−	0.0781842i
$641$	−20279.7	+	11708.5i	−1.24961	+	0.721463i	−0.971032	−	0.238951i	$-0.923196\pi$
$641$	−20279.7	+	11708.5i	−1.24961	+	0.721463i	−0.278578	+	0.960414i	$0.589863\pi$
$642$	19908.0	+	8405.23i	1.22384	+	0.516710i
$643$	−1385.76	−	800.068i	−0.0849907	−	0.0490694i	0.456902	−	0.889517i	$-0.348959\pi$
$643$	−1385.76	−	800.068i	−0.0849907	−	0.0490694i	−0.541893	+	0.840447i	$0.682292\pi$
$644$	−25819.3	+	19019.7i	−1.57985	+	1.16379i
$645$	−1483.16	+	101.679i	−0.0905415	+	0.00620711i
$646$	−912.906	−	461.371i	−0.0556003	−	0.0280997i
$647$	−19887.1			−1.20841			−0.604206	−	0.796828i	$-0.706509\pi$
$647$	−19887.1			−1.20841			−0.604206	+	0.796828i	$0.706509\pi$
$648$	−7037.16	−	14919.0i	−0.426614	−	0.904434i
$649$	1862.70			0.112662
$650$	−21476.3	−	10853.8i	−1.29595	−	0.654958i
$651$	−16969.2	+	1163.33i	−1.02162	+	0.0700377i
$652$	260.766	−	192.092i	0.0156632	−	0.0115382i
$653$	3929.91	+	2268.93i	0.235512	+	0.135973i	0.613112	−	0.789996i	$-0.289917\pi$
$653$	3929.91	+	2268.93i	0.235512	+	0.135973i	−0.377600	+	0.925969i	$0.623251\pi$
$654$	19.0095	+	8.02587i	0.00113659	+	0.000479872i
$655$	−2307.53	+	1332.25i	−0.137653	+	0.0794739i
$656$	−18712.9	+	17300.6i	−1.11374	+	1.02968i
$657$	1729.61	−	238.268i	0.102707	−	0.0141487i
$658$	12959.8	+	19813.3i	0.767819	+	1.17386i
$659$	880.483	+	1525.04i	0.0520467	+	0.0901475i	0.890875	−	0.454249i	$-0.150092\pi$
$659$	880.483	+	1525.04i	0.0520467	+	0.0901475i	−0.838828	+	0.544396i	$0.816759\pi$
$660$	−1007.31	+	854.226i	−0.0594082	+	0.0503799i
$661$	3948.96	−	6839.80i	0.232370	−	0.402477i	−0.726135	−	0.687552i	$-0.758685\pi$
$661$	3948.96	−	6839.80i	0.232370	−	0.402477i	0.958505	+	0.285075i	$0.0920185\pi$
$662$	−986.012	+	54.9290i	−0.0578889	+	0.00322489i
$663$	−10156.5	−	4970.84i	−0.594942	−	0.291179i
$664$	2787.42	−	2303.14i	0.162911	−	0.134607i
$665$			453.455i			0.0264424i
$666$	21697.9	+	7457.58i	1.26243	+	0.433897i
$667$		−	15727.3i		−	0.912987i
$668$	−326.948	+	36.5407i	−0.0189371	+	0.00211647i
$669$	3047.00	−	2049.18i	0.176089	−	0.118424i
$670$	−79.9522	−	1435.20i	−0.00461018	−	0.0827560i
$671$	4426.12	−	7666.26i	0.254647	−	0.441062i
$672$	4564.54	−	25533.6i	0.262025	−	1.46575i
$673$	8028.88	+	13906.4i	0.459867	+	0.796513i	0.998953	−	0.0457375i	$-0.0145638\pi$
$673$	8028.88	+	13906.4i	0.459867	+	0.796513i	−0.539087	+	0.842250i	$0.681230\pi$
$674$	22075.2	−	14439.3i	1.26158	−	0.825193i
$675$	−11490.0	−	12866.5i	−0.655185	−	0.733675i
$676$	8304.98	−	18988.6i	0.472518	−	1.08037i
$677$	16512.7	−	9533.61i	0.937422	−	0.541221i	0.0482708	−	0.998834i	$-0.484629\pi$
$677$	16512.7	−	9533.61i	0.937422	−	0.541221i	0.889151	+	0.457613i	$0.151296\pi$
$678$	12028.8	+	15898.9i	0.681361	+	0.900582i
$679$	33440.0	+	19306.6i	1.89000	+	1.09119i
$680$	−953.656	−	355.313i	−0.0537809	−	0.0200377i
$681$	−9307.11	−	13839.1i	−0.523714	−	0.778729i
$682$	3364.58	−	6657.44i	0.188910	−	0.373792i
$683$	15166.6			0.849682			0.424841	−	0.905268i	$-0.360330\pi$
$683$	15166.6			0.849682			0.424841	+	0.905268i	$0.360330\pi$
$684$	1779.96	−	1732.19i	0.0995007	−	0.0968302i
$685$	−2070.64			−0.115497
$686$	−2619.40	+	5182.95i	−0.145786	+	0.288464i
$687$	−3343.29	+	6831.09i	−0.185669	+	0.379363i
$688$	2826.76	+	12488.2i	0.156641	+	0.692019i
$689$	−14581.8	−	8418.80i	−0.806272	−	0.465502i
$690$	−3031.64	+	378.167i	−0.167265	+	0.0208646i
$691$	−8692.79	+	5018.79i	−0.478567	+	0.276301i	−0.719819	−	0.694162i	$-0.755775\pi$
$691$	−8692.79	+	5018.79i	−0.478567	+	0.276301i	0.241252	+	0.970462i	$0.422442\pi$
$692$	−8061.16	−	3525.67i	−0.442832	−	0.193679i
$693$	−15320.8	−	6238.69i	−0.839809	−	0.341974i
$694$	13163.8	−	8610.41i	0.720017	−	0.470961i
$695$	−267.617	−	463.525i	−0.0146061	−	0.0252986i
$696$	8754.50	+	9229.37i	0.476779	+	0.502641i
$697$	−6261.87	+	10845.9i	−0.340294	+	0.589407i
$698$	1678.98	+	30138.8i	0.0910463	+	1.63434i
$699$	470.583	+	6864.27i	0.0254636	+	0.371431i
$700$	−3012.84	−	26957.3i	−0.162678	−	1.45556i
$701$		−	13222.0i		−	0.712394i	−0.934411	−	0.356197i	$-0.884073\pi$
$701$		−	13222.0i		−	0.712394i	0.934411	−	0.356197i	$-0.115927\pi$
$702$	19430.6	−	19399.4i	1.04467	−	1.04300i
$703$			3454.62i			0.185339i
$704$	8602.17	+	7443.21i	0.460520	+	0.398475i
$705$	154.267	+	2250.25i	0.00824118	+	0.120212i
$706$	−1140.19	+	63.5177i	−0.0607812	+	0.00338601i
$707$	−3301.14	+	5717.74i	−0.175604	+	0.304155i
$708$	−3428.98	+	623.084i	−0.182019	+	0.0330748i
$709$	−11792.3	−	20424.8i	−0.624636	−	1.08190i	−0.988611	−	0.150493i	$-0.951914\pi$
$709$	−11792.3	−	20424.8i	−0.624636	−	1.08190i	0.363975	−	0.931409i	$-0.381419\pi$
$710$	1917.94	+	2932.20i	0.101379	+	0.154991i
$711$	8737.55	−	6788.19i	0.460877	−	0.358055i
$712$	−33323.4	+	5615.69i	−1.75400	+	0.295585i
$713$	14943.2	−	8627.44i	0.784889	−	0.453156i
$714$	−1577.78	−	12648.6i	−0.0826989	−	0.662970i
$715$	−1903.89	−	1099.21i	−0.0995822	−	0.0574938i
$716$	−18267.0	−	24797.4i	−0.953447	−	1.29431i
$717$	1802.37	−	3682.65i	0.0938784	−	0.191814i
$718$	16151.1	+	8162.56i	0.839490	+	0.424267i
$719$	19376.4			1.00503			0.502517	−	0.864567i	$-0.332407\pi$
$719$	19376.4			1.00503			0.502517	+	0.864567i	$0.332407\pi$
$720$	1568.58	−	1909.47i	0.0811910	−	0.0988357i
$721$	−16050.8			−0.829074
$722$	−16980.8	−	8581.89i	−0.875292	−	0.442361i
$723$	6787.71	+	10092.9i	0.349153	+	0.519168i
$724$	−5179.63	−	7031.36i	−0.265883	−	0.360937i
$725$	11520.7	+	6651.48i	0.590163	+	0.340731i
$726$	−9814.50	+	7425.44i	−0.501722	+	0.379592i
$727$	−19193.8	+	11081.5i	−0.979172	+	0.565325i	−0.902020	−	0.431694i	$-0.857916\pi$
$727$	−19193.8	+	11081.5i	−0.979172	+	0.565325i	−0.0771518	+	0.997019i	$0.524583\pi$
$728$	42574.8	−	7174.74i	2.16748	−	0.365266i
$729$	18046.3	−	7858.28i	0.916846	−	0.399242i
$730$	143.174	+	218.889i	0.00725907	+	0.0110979i
$731$	3146.09	+	5449.19i	0.159182	+	0.275712i
$732$	−5583.49	+	15593.1i	−0.281929	+	0.787349i
$733$	14834.2	−	25693.7i	0.747497	−	1.29470i	−0.201522	−	0.979484i	$-0.564589\pi$
$733$	14834.2	−	25693.7i	0.747497	−	1.29470i	0.949019	−	0.315219i	$-0.102078\pi$
$734$	31218.8	−	1739.14i	1.56990	−	0.0874562i
$735$	−2574.05	+	1731.11i	−0.129177	+	0.0868749i
$736$	7227.65	+	25301.2i	0.361977	+	1.26714i
$737$			7895.53i			0.394621i
$738$	−19963.4	−	22939.3i	−0.995751	−	1.14418i
$739$		−	14616.0i		−	0.727549i	−0.931487	−	0.363774i	$-0.881488\pi$
$739$		−	14616.0i		−	0.727549i	0.931487	−	0.363774i	$-0.118512\pi$
$740$	381.770	+	3415.88i	0.0189651	+	0.169690i
$741$	3713.29	+	1817.37i	0.184091	+	0.0900982i
$742$	−1055.71	−	18950.8i	−0.0522323	−	0.937606i
$743$	−17948.9	+	31088.4i	−0.886246	+	1.53502i	−0.0419682	+	0.999119i	$0.513363\pi$
$743$	−17948.9	+	31088.4i	−0.886246	+	1.53502i	−0.844278	+	0.535905i	$0.819971\pi$
$744$	−3966.80	+	13380.9i	−0.195471	+	0.659367i
$745$	−1765.47	−	3057.89i	−0.0868213	−	0.150379i
$746$	8313.90	−	5438.09i	0.408034	−	0.266894i
$747$	2647.01	+	3407.15i	0.129651	+	0.166882i
$748$	5121.62	+	2240.02i	0.250354	+	0.109496i
$749$	−35114.6	+	20273.4i	−1.71303	+	0.989018i
$750$	2027.00	−	4801.01i	0.0986877	−	0.233744i
$751$	−23192.8	−	13390.4i	−1.12692	−	0.650627i	−0.183761	−	0.982971i	$-0.558827\pi$
$751$	−23192.8	−	13390.4i	−1.12692	−	0.650627i	−0.943158	+	0.332344i	$0.892161\pi$
$752$	18947.2	−	4288.77i	0.918793	−	0.207972i
$753$	4862.80	−	333.372i	0.235339	−	0.0161338i
$754$	−9550.81	+	18898.0i	−0.461300	+	0.912765i
$755$	−867.673			−0.0418250
$756$	30290.4	+	6359.72i	1.45721	+	0.305954i
$757$	1805.80			0.0867016			0.0433508	−	0.999060i	$-0.486197\pi$
$757$	1805.80			0.0867016			0.0433508	+	0.999060i	$0.486197\pi$
$758$	−1580.30	+	3126.91i	−0.0757244	+	0.149834i
$759$	16742.1	−	1147.76i	0.800657	−	0.0548894i
$760$	348.663	+	129.905i	0.0166412	+	0.00620017i
$761$	−3770.72	−	2177.03i	−0.179617	−	0.103702i	0.407496	−	0.913207i	$-0.366402\pi$
$761$	−3770.72	−	2177.03i	−0.179617	−	0.103702i	−0.587113	+	0.809505i	$0.699735\pi$
$762$	−3131.76	+	7417.65i	−0.148887	+	0.352642i
$763$	−33.5298	+	19.3584i	−0.00159090	+	0.000918508i
$764$	−2049.57	+	4686.17i	−0.0970560	+	0.221910i
$765$	457.979	−	1124.69i	0.0216448	−	0.0531545i
$766$	4042.89	−	2644.44i	0.190699	−	0.124736i
$767$	−2900.55	−	5023.90i	−0.136549	−	0.236509i
$768$	−18325.3	−	10824.5i	−0.861010	−	0.508588i
$769$	−1390.69	+	2408.74i	−0.0652138	+	0.112954i	−0.896789	−	0.442459i	$-0.854106\pi$
$769$	−1390.69	+	2408.74i	−0.0652138	+	0.112954i	0.831575	+	0.555412i	$0.187440\pi$
$770$	−137.840	−	2474.32i	−0.00645118	−	0.115803i
$771$	774.724	+	379.168i	0.0361881	+	0.0177113i
$772$	−13899.1	+	1553.41i	−0.647979	+	0.0724203i
$773$			7776.95i			0.361860i	0.983496	+	0.180930i	$0.0579107\pi$
$773$			7776.95i			0.361860i	−0.983496	+	0.180930i	$0.942089\pi$
$774$	−14996.1	+	2923.68i	−0.696413	+	0.135775i
$775$			14595.1i			0.676479i
$776$	24424.7	−	20181.2i	1.12989	−	0.933587i
$777$	−35723.0	+	24024.6i	−1.64936	+	1.10924i
$778$	25278.1	−	1408.20i	1.16486	−	0.0648924i
$779$	2289.38	−	3965.32i	0.105296	−	0.182378i
$780$	3872.49	+	1386.64i	0.177766	+	0.0636533i
$781$	−9622.78	−	16667.1i	−0.440884	−	0.763633i
$782$	7078.28	+	10821.5i	0.323681	+	0.494853i
$783$	−11321.8	+	10110.6i	−0.516742	+	0.461459i
$784$	18137.0	+	19617.6i	0.826212	+	0.893660i
$785$	−92.0672	+	53.1550i	−0.00418601	+	0.00241679i
$786$	−21837.7	+	16522.0i	−0.991000	+	0.749769i
$787$	−29197.6	−	16857.3i	−1.32247	−	0.763527i	−0.338347	−	0.941022i	$-0.609868\pi$
$787$	−29197.6	−	16857.3i	−1.32247	−	0.763527i	−0.984122	+	0.177494i	$0.943201\pi$
$788$	13394.4	−	9866.98i	0.605530	−	0.446062i
$789$	14010.9	+	20833.3i	0.632196	+	0.940034i
$790$	1479.36	+	747.650i	0.0666244	+	0.0336711i
$791$	−37407.7			−1.68150
$792$	−9186.00	+	9992.94i	−0.412134	+	0.448338i
$793$	−27569.0			−1.23456
$794$	23706.9	+	11981.2i	1.05961	+	0.535511i
$795$	794.891	−	1624.14i	0.0354615	−	0.0724557i
$796$	11818.1	−	8705.75i	0.526232	−	0.387647i
$797$	38099.8	+	21996.9i	1.69331	+	0.977631i	0.951817	+	0.306665i	$0.0992132\pi$
$797$	38099.8	+	21996.9i	1.69331	+	0.977631i	0.741489	+	0.670965i	$0.234120\pi$
$798$	576.847	+	4624.39i	0.0255892	+	0.205140i
$799$	8267.53	−	4773.26i	0.366063	−	0.211346i
$800$	−21590.7	−	5406.09i	−0.954183	−	0.238918i
$801$	−5502.94	−	39946.4i	−0.242743	−	1.76209i
$802$	−6308.65	−	9644.83i	−0.277763	−	0.424652i
$803$	−718.341	−	1244.20i	−0.0315688	−	0.0546787i
$804$	−2641.10	−	14534.6i	−0.115851	−	0.637558i
$805$	2866.23	−	4964.45i	0.125492	−	0.217359i
$806$	−23195.1	+	1292.15i	−1.01366	+	0.0564692i
$807$	−1983.58	−	28934.0i	−0.0865247	−	1.26211i
$808$	3450.68	+	4176.26i	0.150241	+	0.181832i
$809$			43059.9i			1.87133i	0.352893	+	0.935664i	$0.385198\pi$
$809$			43059.9i			1.87133i	−0.352893	+	0.935664i	$0.614802\pi$
$810$	2221.19	+	1939.32i	0.0963512	+	0.0841244i
$811$		−	17269.7i		−	0.747743i	−0.927480	−	0.373872i	$-0.878030\pi$
$811$		−	17269.7i		−	0.747743i	0.927480	−	0.373872i	$-0.121970\pi$
$812$	−23721.0	+	2651.14i	−1.02518	+	0.114577i
$813$	−2876.64	−	41960.8i	−0.124094	−	1.81012i
$814$	−1050.13	−	18850.5i	−0.0452174	−	0.811682i
$815$	−28.9479	+	50.1392i	−0.00124417	+	0.00215497i
$816$	−10177.5	−	2410.37i	−0.436623	−	0.103407i
$817$	−1150.23	−	1992.26i	−0.0492552	−	0.0853124i
$818$	−1589.30	+	1039.56i	−0.0679323	+	0.0444342i
$819$	7030.69	+	51036.4i	0.299966	+	2.17748i
$820$	1825.50	−	4173.86i	0.0777430	−	0.177753i
$821$	25271.0	−	14590.2i	1.07426	−	0.620222i	0.144915	−	0.989444i	$-0.453709\pi$
$821$	25271.0	−	14590.2i	1.07426	−	0.620222i	0.929341	+	0.369222i	$0.120376\pi$
$822$	−21116.7	+	2634.10i	−0.896022	+	0.111770i
$823$	32508.9	+	18769.0i	1.37690	+	0.794954i	0.991785	−	0.127914i	$-0.0408283\pi$
$823$	32508.9	+	18769.0i	1.37690	+	0.794954i	0.385115	+	0.922868i	$0.374162\pi$
$824$	−4598.19	+	12341.5i	−0.194400	+	0.521768i
$825$	−6239.90	+	12749.5i	−0.263328	+	0.538037i
$826$	2949.58	−	5836.27i	0.124248	−	0.245847i
$827$	14426.3			0.606594			0.303297	−	0.952896i	$-0.401913\pi$
$827$	14426.3			0.606594			0.303297	+	0.952896i	$0.401913\pi$
$828$	−30436.0	+	7713.20i	−1.27745	+	0.323735i
$829$	22149.2			0.927956			0.463978	−	0.885847i	$-0.346422\pi$
$829$	22149.2			0.927956			0.463978	+	0.885847i	$0.346422\pi$
$830$	−291.541	+	576.867i	−0.0121922	+	0.0241245i
$831$	5352.06	+	7958.16i	0.223419	+	0.332209i
$832$	6680.05	−	34791.3i	0.278352	−	1.44973i
$833$	11370.3	+	6564.62i	0.472936	+	0.273050i
$834$	−3318.85	−	4386.66i	−0.137797	−	0.182131i
$835$	50.9292	−	29.4040i	0.00211075	−	0.00121864i
$836$	−1872.49	−	818.965i	−0.0774660	−	0.0338810i
$837$	−15817.3	−	5211.03i	−0.653195	−	0.215197i
$838$	−22267.1	+	14564.8i	−0.917903	+	0.600397i
$839$	−8024.51	−	13898.9i	−0.330199	−	0.571921i	0.652352	−	0.757916i	$-0.273783\pi$
$839$	−8024.51	−	13898.9i	−0.330199	−	0.571921i	−0.982551	+	0.185995i	$0.940449\pi$
$840$	1081.42	+	4508.80i	0.0444197	+	0.185200i
$841$	−6341.54	+	10983.9i	−0.260017	+	0.450362i
$842$	−1937.02	−	34770.8i	−0.0792802	−	1.42313i
$843$	−10928.4	+	7349.65i	−0.446495	+	0.300279i
$844$	4419.50	+	39543.4i	0.180243	+	1.61273i
$845$			3704.81i			0.150827i
$846$	4435.82	+	22752.2i	0.180268	+	0.924628i
$847$		−	23092.0i		−	0.936776i
$848$	−14873.7	−	4617.22i	−0.602319	−	0.186977i
$849$	14505.1	+	7099.11i	0.586351	+	0.286974i
$850$	−10920.7	+	608.370i	−0.440677	+	0.0245493i
$851$	21836.2	−	37821.4i	0.879594	−	1.52350i
$852$	23289.5	+	27463.1i	0.936486	+	1.10431i
$853$	−12146.8	−	21038.9i	−0.487571	−	0.844498i	0.512327	−	0.858791i	$-0.328784\pi$
$853$	−12146.8	−	21038.9i	−0.487571	−	0.844498i	−0.999898	+	0.0142928i	$0.995450\pi$
$854$	−17011.4	−	26007.6i	−0.681639	−	1.04211i
$855$	−167.440	+	411.193i	−0.00669746	+	0.0164474i
$856$	5528.76	+	32807.6i	0.220758	+	1.30998i
$857$	−5106.52	+	2948.25i	−0.203542	+	0.117515i	−0.598306	−	0.801267i	$-0.704159\pi$
$857$	−5106.52	+	2948.25i	−0.203542	+	0.117515i	0.394765	+	0.918782i	$0.370826\pi$
$858$	−20814.4	−	8787.92i	−0.828196	−	0.349668i
$859$	31999.8	+	18475.1i	1.27103	+	0.733831i	0.975182	−	0.221403i	$-0.0710636\pi$
$859$	31999.8	+	18475.1i	1.27103	+	0.733831i	0.295851	+	0.955234i	$0.404397\pi$
$860$	−1357.50	−	1842.81i	−0.0538259	−	0.0730689i
$861$	56925.1	−	3902.52i	2.25320	−	0.154469i
$862$	19305.0	+	9756.51i	0.762797	+	0.385508i
$863$	−33898.3			−1.33709			−0.668546	−	0.743671i	$-0.733083\pi$
$863$	−33898.3			−1.33709			−0.668546	+	0.743671i	$0.733083\pi$
$864$	13567.5	−	21468.5i	0.534232	−	0.845338i
$865$	1572.78			0.0618223
$866$	35303.7	+	17842.1i	1.38530	+	0.700113i
$867$	20341.2	−	1394.50i	0.796797	−	0.0546248i
$868$	−15531.5	−	21084.1i	−0.607343	−	0.824469i
$869$	−7884.89	−	4552.34i	−0.307798	−	0.177707i
$870$	−2094.90	−	884.473i	−0.0816364	−	0.0344672i
$871$	21295.1	−	12294.7i	0.828423	−	0.478290i
$872$	5.27923	+	31.3269i	0.000205020	+	0.00121659i
$873$	23194.4	+	29855.1i	0.899211	+	1.15744i
$874$	−2587.86	−	3956.40i	−0.100155	−	0.153120i
$875$	4889.14	+	8468.23i	0.188895	+	0.327176i
$876$	1738.57	+	2050.13i	0.0670556	+	0.0790723i
$877$	−20850.0	+	36113.3i	−0.802800	+	1.39049i	0.114967	+	0.993369i	$0.463324\pi$
$877$	−20850.0	+	36113.3i	−0.802800	+	1.39049i	−0.917767	+	0.397120i	$0.870010\pi$
$878$	−38174.6	+	2126.64i	−1.46735	+	0.0817432i
$879$	25999.2	+	12724.6i	0.997648	+	0.488272i
$880$	−1942.00	−	602.853i	−0.0743920	−	0.0230934i
$881$			15865.5i			0.606723i	0.952876	+	0.303361i	$0.0981090\pi$
$881$			15865.5i			0.606723i	−0.952876	+	0.303361i	$0.901891\pi$
$882$	−24048.4	+	20928.6i	−0.918085	+	0.798984i
$883$		−	41172.6i		−	1.56916i	−0.620027	−	0.784581i	$-0.712878\pi$
$883$		−	41172.6i		−	1.56916i	0.620027	−	0.784581i	$-0.287122\pi$
$884$	−1933.69	−	17301.6i	−0.0735712	−	0.658277i
$885$	516.959	−	347.668i	0.0196355	−	0.0132053i
$886$	1029.05	+	18472.1i	0.0390198	+	0.700432i
$887$	9217.94	−	15965.9i	0.348938	−	0.604378i	−0.637123	−	0.770762i	$-0.719876\pi$
$887$	9217.94	−	15965.9i	0.348938	−	0.604378i	0.986061	+	0.166384i	$0.0532090\pi$
$888$	8238.75	+	34350.0i	0.311345	+	1.29810i
$889$	−7553.81	−	13083.6i	−0.284979	−	0.493599i
$890$	5055.38	−	3306.70i	0.190401	−	0.124540i
$891$	−11589.2	−	11314.5i	−0.435750	−	0.425421i
$892$	5179.63	+	2265.39i	0.194425	+	0.0850346i
$893$	−3022.66	+	1745.13i	−0.113269	+	0.0653961i
$894$	−21894.5	−	28938.9i	−0.819086	−	1.08262i
$895$	4767.98	+	2752.79i	0.178074	+	0.102811i
$896$	36942.8	−	15166.3i	1.37743	−	0.565480i
$897$	−29166.0	−	43367.9i	−1.08564	−	1.61428i
$898$	22453.3	−	44427.9i	0.834383	−	1.65098i
$899$	12842.9			0.476457
$900$	7222.06	−	25557.5i	0.267484	−	0.946572i
$901$	−7653.29			−0.282983
$902$	−11286.9	+	22333.1i	−0.416643	+	0.824403i
$903$	12602.1	−	25749.0i	0.464422	−	0.948917i
$904$	−10716.5	+	28762.9i	−0.394274	+	1.05823i
$905$	1351.97	+	780.559i	0.0496585	+	0.0286703i
$906$	−8848.65	+	1103.78i	−0.324478	+	0.0404754i
$907$	−7342.47	+	4239.18i	−0.268801	+	0.155192i	−0.628343	−	0.777937i	$-0.716266\pi$
$907$	−7342.47	+	4239.18i	−0.268801	+	0.155192i	0.359542	+	0.933129i	$0.382933\pi$
$908$	10289.1	−	23525.2i	0.376053	−	0.859814i
$909$	−5104.77	+	3965.89i	−0.186265	+	0.144709i
$910$	−6458.87	+	4224.72i	−0.235285	+	0.153899i
$911$	16805.6	+	29108.1i	0.611190	+	1.05861i	0.991040	+	0.133564i	$0.0426421\pi$
$911$	16805.6	+	29108.1i	0.611190	+	1.05861i	−0.379850	+	0.925048i	$0.624025\pi$
$912$	3720.97	+	881.245i	0.135103	+	0.0319967i
$913$	1775.16	−	3074.66i	0.0643473	−	0.111453i
$914$	−377.416	−	6774.87i	−0.0136584	−	0.245178i
$915$	−202.496	−	2953.76i	−0.00731619	−	0.106719i
$916$	−11636.8	+	1300.56i	−0.419748	+	0.0469124i
$917$		−	51380.7i		−	1.85032i
$918$	3239.80	−	12052.3i	0.116481	−	0.433319i
$919$		−	4323.08i		−	0.155174i	−0.996986	−	0.0775871i	$-0.975278\pi$
$919$		−	4323.08i		−	0.155174i	0.996986	−	0.0775871i	$-0.0247216\pi$
$920$	−2996.07	−	3626.05i	−0.107367	−	0.129943i
$921$	2753.10	+	40158.8i	0.0984993	+	1.43678i
$922$	10558.0	−	588.166i	0.377125	−	0.0210089i
$923$	−29968.7	+	51907.3i	−1.06872	+	1.85108i
$924$	−4553.34	−	25058.2i	−0.162115	−	0.892157i
$925$	18470.2	+	31991.3i	0.656537	+	1.13716i
$926$	3875.39	+	5924.81i	0.137531	+	0.210261i
$927$	−14554.9	−	5926.82i	−0.515690	−	0.209992i
$928$	−4757.07	+	18998.7i	−0.168274	+	0.672050i
$929$	−13142.9	+	7588.08i	−0.464161	+	0.267984i	−0.713792	−	0.700357i	$-0.753024\pi$
$929$	−13142.9	+	7588.08i	−0.464161	+	0.267984i	0.249631	+	0.968341i	$0.419691\pi$
$930$	−308.812	−	2475.64i	−0.0108885	−	0.0872898i
$931$	−4157.04	−	2400.07i	−0.146339	−	0.0844887i
$932$	−8528.78	+	6282.70i	−0.299753	+	0.220812i
$933$	13278.3	−	27130.6i	0.465930	−	0.951999i
$934$	13533.8	+	6839.83i	0.474134	+	0.239621i
$935$	−999.260			−0.0349511
$936$	41256.2	+	9214.87i	1.44071	+	0.321792i
$937$	13144.0			0.458266			0.229133	−	0.973395i	$-0.426411\pi$
$937$	13144.0			0.458266			0.229133	+	0.973395i	$0.426411\pi$
$938$	24738.5	+	12502.5i	0.861132	+	0.435205i
$939$	−7932.22	−	11794.7i	−0.275674	−	0.409910i
$940$	−2795.92	+	2059.60i	−0.0970135	+	0.0714647i
$941$	−29616.7	−	17099.2i	−1.02601	−	0.592368i	−0.110172	−	0.993913i	$-0.535140\pi$
$941$	−29616.7	−	17099.2i	−1.02601	−	0.592368i	−0.915839	+	0.401545i	$0.868473\pi$
$942$	−871.295	+	659.202i	−0.0301362	+	0.0228004i
$943$	−50128.5	+	28941.7i	−1.73108	+	0.999440i
$944$	−3642.54	−	3939.90i	−0.125588	−	0.135840i
$945$	−5416.44	+	1128.14i	−0.186452	+	0.0388343i
$946$	6881.96	+	10521.3i	0.236524	+	0.361604i
$947$	9574.22	+	16583.0i	0.328532	+	0.569035i	0.982221	−	0.187729i	$-0.0601126\pi$
$947$	9574.22	+	16583.0i	0.328532	+	0.569035i	−0.653688	+	0.756764i	$0.726779\pi$
$948$	16037.8	+	5742.72i	0.549456	+	0.196746i
$949$	−2237.17	+	3874.88i	−0.0765242	+	0.132544i
$950$	3992.66	−	222.424i	0.136357	−	0.00759619i
$951$	27057.1	−	18196.5i	0.922593	−	0.620466i
$952$	15128.6	−	12500.2i	0.515041	−	0.425559i
$953$			12906.3i			0.438696i	0.975647	+	0.219348i	$0.0703930\pi$
$953$			12906.3i			0.438696i	−0.975647	+	0.219348i	$0.929607\pi$
$954$	6040.32	−	17574.4i	0.204992	−	0.596428i
$955$		−	914.301i		−	0.0309802i
$956$	6273.38	−	701.133i	0.212234	−	0.0237200i
$957$	11218.9	+	5490.79i	0.378950	+	0.185467i
$958$	−191.910	−	3444.92i	−0.00647216	−	0.116180i
$959$	19964.5	−	34579.6i	0.672250	−	1.16437i
$960$	3776.63	+	460.160i	0.126969	+	0.0154704i
$961$	−7850.32	−	13597.2i	−0.263513	−	0.456418i
$962$	−49206.5	+	32185.8i	−1.64915	+	1.07870i
$963$	−39328.0	+	5417.76i	−1.31602	+	0.181293i
$964$	−7503.88	+	17157.0i	−0.250709	+	0.573226i
$965$	2165.09	−	1250.02i	0.0722246	−	0.0416989i
$966$	22914.8	−	54274.3i	0.763222	−	1.80771i
$967$	12026.9	+	6943.73i	0.399957	+	0.230916i	0.686466	−	0.727162i	$-0.259161\pi$
$967$	12026.9	+	6943.73i	0.399957	+	0.230916i	−0.286508	+	0.958078i	$0.592495\pi$
$968$	−17755.5	−	6615.33i	−0.589549	−	0.219654i
$969$	1874.73	−	128.523i	0.0621517	−	0.00426083i
$970$	−2554.63	+	5054.79i	−0.0845609	+	0.167319i
$971$	−42722.6			−1.41198			−0.705990	−	0.708222i	$-0.749498\pi$
$971$	−42722.6			−1.41198			−0.705990	+	0.708222i	$0.749498\pi$
$972$	25119.0	+	16951.9i	0.828902	+	0.559394i
$973$	10321.1			0.340061
$974$	−1892.02	+	3743.70i	−0.0622425	+	0.123158i
$975$	44103.4	−	3023.53i	1.44866	−	0.0993132i
$976$	−24870.7	+	5629.58i	−0.815668	+	0.184629i
$977$	−42433.4	−	24498.9i	−1.38952	−	0.802242i	−0.396262	−	0.918138i	$-0.629693\pi$
$977$	−42433.4	−	24498.9i	−1.38952	−	0.802242i	−0.993261	+	0.115896i	$0.963026\pi$
$978$	−231.432	+	548.152i	−0.00756685	+	0.0179223i
$979$	−28735.7	+	16590.5i	−0.938096	+	0.541610i
$980$	−4375.66	−	1913.76i	−0.142628	−	0.0623805i
$981$	−37.5530	+	5.17324i	−0.00122220	+	0.000168368i
$982$	32865.6	−	21497.3i	1.06801	−	0.698580i
$983$	−5783.64	−	10017.6i	−0.187660	−	0.325036i	0.756810	−	0.653635i	$-0.226757\pi$
$983$	−5783.64	−	10017.6i	−0.187660	−	0.325036i	−0.944469	+	0.328599i	$0.893424\pi$
$984$	13307.1	−	44887.9i	0.431113	−	1.45424i
$985$	−1486.93	+	2575.44i	−0.0480991	+	0.0833101i
$986$	535.333	+	9609.60i	0.0172906	+	0.310377i
$987$	−39066.4	−	19120.0i	−1.25988	−	0.616613i
$988$	706.968	+	6325.59i	0.0227648	+	0.203688i
$989$			29081.8i			0.935033i
$990$	788.661	−	2294.62i	0.0253185	−	0.0736644i
$991$			47618.2i			1.52638i	0.646174	+	0.763190i	$0.276368\pi$
$991$			47618.2i			1.52638i	−0.646174	+	0.763190i	$0.723632\pi$
$992$	−20661.0	+	5902.11i	−0.661278	+	0.188904i
$993$	1505.45	−	1012.45i	0.0481107	−	0.0323556i
$994$	−67459.7	+	3758.06i	−2.15261	+	0.119918i
$995$	−1311.94	+	2272.34i	−0.0418002	+	0.0724002i
$996$	−2239.34	+	6253.84i	−0.0712410	+	0.198956i
$997$	3447.14	+	5970.61i	0.109500	+	0.189660i	0.915568	−	0.402163i	$-0.131742\pi$
$997$	3447.14	+	5970.61i	0.109500	+	0.189660i	−0.806068	+	0.591823i	$0.798408\pi$
$998$	31274.2	+	47812.8i	0.991950	+	1.51652i
$999$	−41264.8	+	8594.67i	−1.30687	+	0.272195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.23.2	yes	24
3.2	odd	2		108.4.h.b.71.11		24
4.3	odd	2	inner	36.4.h.b.23.6	yes	24
9.2	odd	6	inner	36.4.h.b.11.6	yes	24
9.4	even	3		324.4.b.c.323.19		24
9.5	odd	6		324.4.b.c.323.6		24
9.7	even	3		108.4.h.b.35.7		24
12.11	even	2		108.4.h.b.71.7		24
36.7	odd	6		108.4.h.b.35.11		24
36.11	even	6	inner	36.4.h.b.11.2	✓	24
36.23	even	6		324.4.b.c.323.20		24
36.31	odd	6		324.4.b.c.323.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.2	✓	24	36.11	even	6	inner
36.4.h.b.11.6	yes	24	9.2	odd	6	inner
36.4.h.b.23.2	yes	24	1.1	even	1	trivial
36.4.h.b.23.6	yes	24	4.3	odd	2	inner
108.4.h.b.35.7		24	9.7	even	3
108.4.h.b.35.11		24	36.7	odd	6
108.4.h.b.71.7		24	12.11	even	2
108.4.h.b.71.11		24	3.2	odd	2
324.4.b.c.323.5		24	36.31	odd	6
324.4.b.c.323.6		24	9.5	odd	6
324.4.b.c.323.19		24	9.4	even	3
324.4.b.c.323.20		24	36.23	even	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52436 - 1.27578i) q^{2} +(5.18398 - 0.355390i) q^{3} +(4.74478 + 6.44105i) q^{4} +(-1.23846 - 0.715028i) q^{5} +(-13.5396 - 5.71649i) q^{6} +(23.8818 - 13.7882i) q^{7} +(-3.76017 - 22.3128i) q^{8} +(26.7474 - 3.68468i) q^{9} +O(q^{10})\)	\(q+(-2.52436 - 1.27578i) q^{2} +(5.18398 - 0.355390i) q^{3} +(4.74478 + 6.44105i) q^{4} +(-1.23846 - 0.715028i) q^{5} +(-13.5396 - 5.71649i) q^{6} +(23.8818 - 13.7882i) q^{7} +(-3.76017 - 22.3128i) q^{8} +(26.7474 - 3.68468i) q^{9} +(2.21411 + 3.38499i) q^{10} +(-11.1087 - 19.2409i) q^{11} +(26.8859 + 31.7040i) q^{12} +(-34.5965 + 59.9229i) q^{13} +(-77.8769 + 4.33838i) q^{14} +(-6.67430 - 3.26656i) q^{15} +(-18.9742 + 61.1227i) q^{16} +31.4507i q^{17} +(-72.2209 - 24.8223i) q^{18} -11.4986i q^{19} +(-1.27071 - 11.3697i) q^{20} +(118.903 - 79.9650i) q^{21} +(3.49531 + 62.7433i) q^{22} +(-72.6810 + 125.887i) q^{23} +(-27.4224 - 114.333i) q^{24} +(-61.4775 - 106.482i) q^{25} +(163.782 - 107.129i) q^{26} +(137.349 - 28.6071i) q^{27} +(202.124 + 88.4021i) q^{28} +(-93.6986 + 54.0969i) q^{29} +(12.6809 + 16.7609i) q^{30} +(-102.800 - 59.3514i) q^{31} +(125.877 - 130.089i) q^{32} +(-64.4256 - 95.7966i) q^{33} +(40.1242 - 79.3929i) q^{34} -39.4357 q^{35} +(150.644 + 154.798i) q^{36} -300.439 q^{37} +(-14.6696 + 29.0265i) q^{38} +(-158.052 + 322.935i) q^{39} +(-11.2974 + 30.3222i) q^{40} +(344.853 + 199.101i) q^{41} +(-402.171 + 50.1668i) q^{42} +(173.261 - 100.032i) q^{43} +(71.2231 - 162.846i) q^{44} +(-35.7603 - 14.5618i) q^{45} +(344.077 - 225.060i) q^{46} +(-151.770 - 262.873i) q^{47} +(-76.6395 + 323.602i) q^{48} +(208.727 - 361.526i) q^{49} +(19.3436 + 347.231i) q^{50} +(11.1773 + 163.040i) q^{51} +(-550.119 + 61.4831i) q^{52} +243.342i q^{53} +(-383.213 - 103.012i) q^{54} +31.7722i q^{55} +(-397.452 - 481.024i) q^{56} +(-4.08648 - 59.6085i) q^{57} +(305.545 - 17.0213i) q^{58} +(-41.9197 + 72.6070i) q^{59} +(-10.6280 - 58.4885i) q^{60} +(199.218 + 345.055i) q^{61} +(183.784 + 280.974i) q^{62} +(587.971 - 456.794i) q^{63} +(-483.722 + 167.800i) q^{64} +(85.6931 - 49.4749i) q^{65} +(40.4180 + 324.018i) q^{66} +(-307.763 - 177.687i) q^{67} +(-202.576 + 149.227i) q^{68} +(-332.038 + 678.427i) q^{69} +(99.5499 + 50.3112i) q^{70} +866.235 q^{71} +(-182.790 - 582.954i) q^{72} +64.6645 q^{73} +(758.415 + 383.293i) q^{74} +(-356.541 - 530.153i) q^{75} +(74.0629 - 54.5582i) q^{76} +(-530.594 - 306.338i) q^{77} +(810.973 - 613.564i) q^{78} +(354.896 - 204.899i) q^{79} +(67.2033 - 62.1312i) q^{80} +(701.846 - 197.111i) q^{81} +(-616.524 - 942.559i) q^{82} +(79.8990 + 138.389i) q^{83} +(1079.23 + 386.442i) q^{84} +(22.4881 - 38.9506i) q^{85} +(-564.993 + 31.4747i) q^{86} +(-466.507 + 313.737i) q^{87} +(-387.548 + 320.216i) q^{88} -1493.47i q^{89} +(71.6943 + 82.3815i) q^{90} +1908.09i q^{91} +(-1155.70 + 129.165i) q^{92} +(-554.005 - 271.143i) q^{93} +(47.7536 + 857.209i) q^{94} +(-8.22181 + 14.2406i) q^{95} +(606.310 - 719.113i) q^{96} +(700.115 + 1212.63i) q^{97} +(-988.129 + 646.332i) q^{98} +(-368.026 - 473.712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more