LMFDB - Embedded newform 950.2.bb.e.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.8
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.e.507.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 + 0.996195i) q^{2} +(0.202610 - 0.434499i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.450504 + 0.163970i) q^{6} +(-3.80940 - 1.02072i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.78062 + 2.12207i) q^{9} +O(q^{10})$	\(q+(0.0871557 + 0.996195i) q^{2} +(0.202610 - 0.434499i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.450504 + 0.163970i) q^{6} +(-3.80940 - 1.02072i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.78062 + 2.12207i) q^{9} +(1.98177 - 3.43252i) q^{11} +(-0.124082 + 0.463081i) q^{12} +(-1.51854 + 0.708105i) q^{13} +(0.684830 - 3.88386i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.76720 - 0.417076i) q^{17} +(-1.95880 + 1.95880i) q^{18} +(0.416317 + 4.33897i) q^{19} +(-1.21533 + 1.44837i) q^{21} +(3.59218 + 1.67506i) q^{22} +(3.68259 - 5.25928i) q^{23} +(-0.472133 - 0.0832498i) q^{24} +(-0.837759 - 1.45104i) q^{26} +(2.67205 - 0.715973i) q^{27} +(3.92877 + 0.343723i) q^{28} +(8.12456 - 6.81732i) q^{29} +(1.06152 - 0.612871i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-1.08990 - 1.55654i) q^{33} +(0.830978 + 4.71271i) q^{34} +(-2.12207 - 1.78062i) q^{36} +(2.79796 + 2.79796i) q^{37} +(-4.28618 + 0.792899i) q^{38} +0.803271i q^{39} +(0.178777 + 0.491185i) q^{41} +(-1.54878 - 1.08447i) q^{42} +(-0.194948 + 0.136504i) q^{43} +(-1.35561 + 3.72451i) q^{44} +(5.56022 + 3.21020i) q^{46} +(-0.0122621 + 0.140157i) q^{47} +(0.0417839 - 0.477592i) q^{48} +(7.40745 + 4.27669i) q^{49} +(0.784664 - 2.15585i) q^{51} +(1.37250 - 0.961038i) q^{52} +(11.1543 + 7.81035i) q^{53} +(0.946133 + 2.59948i) q^{54} +3.94378i q^{56} +(1.96963 + 0.698230i) q^{57} +(7.49948 + 7.49948i) q^{58} +(-6.90856 - 5.79697i) q^{59} +(-2.34513 - 13.2999i) q^{61} +(0.703057 + 1.00407i) q^{62} +(-4.61706 - 9.90132i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(1.45563 - 1.22141i) q^{66} +(-5.34318 - 0.467468i) q^{67} +(-4.62235 + 1.23856i) q^{68} +(-1.53902 - 2.66566i) q^{69} +(-4.12724 - 0.727743i) q^{71} +(1.58890 - 2.26918i) q^{72} +(2.15579 + 1.00526i) q^{73} +(-2.54346 + 3.03117i) q^{74} +(-1.16345 - 4.20076i) q^{76} +(-11.0530 + 11.0530i) q^{77} +(-0.800214 + 0.0700097i) q^{78} +(8.91892 - 3.24622i) q^{79} +(-1.21281 + 6.87816i) q^{81} +(-0.473734 + 0.220906i) q^{82} +(2.36349 - 8.82067i) q^{83} +(0.945356 - 1.63740i) q^{84} +(-0.152975 - 0.182309i) q^{86} +(-1.31600 - 4.91137i) q^{87} +(-3.82848 - 1.02584i) q^{88} +(4.74683 + 1.72770i) q^{89} +(6.50748 - 1.14745i) q^{91} +(-2.71337 + 5.81885i) q^{92} +(-0.0512163 - 0.585405i) q^{93} -0.140692 q^{94} +0.479416 q^{96} +(0.278881 + 3.18763i) q^{97} +(-3.61482 + 7.75200i) q^{98} +(10.8128 - 1.90659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$2$	0.0871557	+	0.996195i	0.0616284	+	0.704416i
$3$	0.202610	−	0.434499i	0.116977	−	0.250858i	−0.839098	−	0.543980i	$-0.816917\pi$
$3$	0.202610	−	0.434499i	0.116977	−	0.250858i	0.956075	+	0.293122i	$0.0946944\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	0.450504	+	0.163970i	0.183917	+	0.0669405i
$7$	−3.80940	−	1.02072i	−1.43982	−	0.385798i	−0.547347	−	0.836906i	$-0.684362\pi$
$7$	−3.80940	−	1.02072i	−1.43982	−	0.385798i	−0.892469	+	0.451108i	$0.851029\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	1.78062	+	2.12207i	0.593542	+	0.707355i
$10$		0			0
$11$	1.98177	−	3.43252i	0.597526	−	1.03494i	−0.395659	−	0.918397i	$-0.629484\pi$
$11$	1.98177	−	3.43252i	0.597526	−	1.03494i	0.993185	−	0.116548i	$-0.0371827\pi$
$12$	−0.124082	+	0.463081i	−0.0358194	+	0.133680i
$13$	−1.51854	+	0.708105i	−0.421166	+	0.196393i	−0.621635	−	0.783307i	$-0.713531\pi$
$13$	−1.51854	+	0.708105i	−0.421166	+	0.196393i	0.200469	+	0.979700i	$0.435753\pi$
$14$	0.684830	−	3.88386i	0.183028	−	1.03801i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	4.76720	−	0.417076i	1.15622	−	0.101156i	0.507129	−	0.861870i	$-0.330707\pi$
$17$	4.76720	−	0.417076i	1.15622	−	0.101156i	0.649087	+	0.760714i	$0.275151\pi$
$18$	−1.95880	+	1.95880i	−0.461693	+	0.461693i
$19$	0.416317	+	4.33897i	0.0955097	+	0.995429i
$19$	0.416317	+	4.33897i	0.0955097	+	0.995429i
$20$		0			0
$21$	−1.21533	+	1.44837i	−0.265206	+	0.316060i
$22$	3.59218	+	1.67506i	0.765856	+	0.357125i
$23$	3.68259	−	5.25928i	0.767872	−	1.09664i	−0.224634	−	0.974443i	$-0.572119\pi$
$23$	3.68259	−	5.25928i	0.767872	−	1.09664i	0.992506	−	0.122192i	$-0.0389924\pi$
$24$	−0.472133	−	0.0832498i	−0.0963737	−	0.0169933i
$25$		0			0
$26$	−0.837759	−	1.45104i	−0.164298	−	0.284573i
$27$	2.67205	−	0.715973i	0.514236	−	0.137789i
$28$	3.92877	+	0.343723i	0.742468	+	0.0649575i
$29$	8.12456	−	6.81732i	1.50869	−	1.26594i	0.642444	−	0.766333i	$-0.277921\pi$
$29$	8.12456	−	6.81732i	1.50869	−	1.26594i	0.866250	−	0.499612i	$-0.166524\pi$
$30$		0			0
$31$	1.06152	−	0.612871i	0.190655	−	0.110075i	−0.401634	−	0.915800i	$-0.631558\pi$
$31$	1.06152	−	0.612871i	0.190655	−	0.110075i	0.592289	+	0.805725i	$0.298224\pi$
$32$	0.422618	+	0.906308i	0.0747091	+	0.160214i
$33$	−1.08990	−	1.55654i	−0.189727	−	0.270959i
$34$	0.830978	+	4.71271i	0.142512	+	0.808223i
$35$		0			0
$36$	−2.12207	−	1.78062i	−0.353678	−	0.296771i
$37$	2.79796	+	2.79796i	0.459982	+	0.459982i	0.898649	−	0.438667i	$-0.144549\pi$
$37$	2.79796	+	2.79796i	0.459982	+	0.459982i	−0.438667	+	0.898649i	$0.644549\pi$
$38$	−4.28618	+	0.792899i	−0.695310	+	0.128625i
$39$			0.803271i			0.128626i
$40$		0			0
$41$	0.178777	+	0.491185i	0.0279202	+	0.0767101i	0.952870	−	0.303380i	$-0.0981152\pi$
$41$	0.178777	+	0.491185i	0.0279202	+	0.0767101i	−0.924949	+	0.380090i	$0.875893\pi$
$42$	−1.54878	−	1.08447i	−0.238982	−	0.167337i
$43$	−0.194948	+	0.136504i	−0.0297293	+	0.0208167i	−0.588347	−	0.808609i	$-0.700221\pi$
$43$	−0.194948	+	0.136504i	−0.0297293	+	0.0208167i	0.558617	+	0.829426i	$0.311332\pi$
$44$	−1.35561	+	3.72451i	−0.204366	+	0.561490i
$45$		0			0
$46$	5.56022	+	3.21020i	0.819810	+	0.473318i
$47$	−0.0122621	+	0.140157i	−0.00178861	+	0.0204439i	−0.997037	−	0.0769292i	$-0.975488\pi$
$47$	−0.0122621	+	0.140157i	−0.00178861	+	0.0204439i	0.995248	+	0.0973731i	$0.0310440\pi$
$48$	0.0417839	−	0.477592i	0.00603098	−	0.0689345i
$49$	7.40745	+	4.27669i	1.05821	+	0.610956i
$50$		0			0
$51$	0.784664	−	2.15585i	0.109875	−	0.301879i
$52$	1.37250	−	0.961038i	0.190332	−	0.133272i
$53$	11.1543	+	7.81035i	1.53217	+	1.07283i	0.969176	+	0.246370i	$0.0792378\pi$
$53$	11.1543	+	7.81035i	1.53217	+	1.07283i	0.562990	+	0.826464i	$0.309651\pi$
$54$	0.946133	+	2.59948i	0.128752	+	0.353744i
$55$		0			0
$56$			3.94378i			0.527009i
$57$	1.96963	+	0.698230i	0.260884	+	0.0924829i
$58$	7.49948	+	7.49948i	0.984730	+	0.984730i
$59$	−6.90856	−	5.79697i	−0.899417	−	0.754701i	0.0706591	−	0.997501i	$-0.477490\pi$
$59$	−6.90856	−	5.79697i	−0.899417	−	0.754701i	−0.970076	+	0.242800i	$0.921934\pi$
$60$		0			0
$61$	−2.34513	−	13.2999i	−0.300263	−	1.70287i	−0.645006	−	0.764178i	$-0.723145\pi$
$61$	−2.34513	−	13.2999i	−0.300263	−	1.70287i	0.344743	−	0.938697i	$-0.387966\pi$
$62$	0.703057	+	1.00407i	0.0892883	+	0.127517i
$63$	−4.61706	−	9.90132i	−0.581695	−	1.24745i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	1.45563	−	1.22141i	0.179175	−	0.150346i
$67$	−5.34318	−	0.467468i	−0.652774	−	0.0571103i	−0.244042	−	0.969765i	$-0.578473\pi$
$67$	−5.34318	−	0.467468i	−0.652774	−	0.0571103i	−0.408732	+	0.912654i	$0.634029\pi$
$68$	−4.62235	+	1.23856i	−0.560543	+	0.150197i
$69$	−1.53902	−	2.66566i	−0.185276	−	0.320908i
$70$		0			0
$71$	−4.12724	−	0.727743i	−0.489813	−	0.0863672i	−0.0767135	−	0.997053i	$-0.524443\pi$
$71$	−4.12724	−	0.727743i	−0.489813	−	0.0863672i	−0.413099	+	0.910686i	$0.635554\pi$
$72$	1.58890	−	2.26918i	0.187253	−	0.267426i
$73$	2.15579	+	1.00526i	0.252316	+	0.117657i	0.544662	−	0.838656i	$-0.316658\pi$
$73$	2.15579	+	1.00526i	0.252316	+	0.117657i	−0.292346	+	0.956313i	$0.594436\pi$
$74$	−2.54346	+	3.03117i	−0.295671	+	0.352367i
$75$		0			0
$76$	−1.16345	−	4.20076i	−0.133457	−	0.481860i
$77$	−11.0530	+	11.0530i	−1.25961	+	1.25961i
$78$	−0.800214	+	0.0700097i	−0.0906064	+	0.00792703i
$79$	8.91892	−	3.24622i	1.00346	−	0.365228i	0.212540	−	0.977152i	$-0.431826\pi$
$79$	8.91892	−	3.24622i	1.00346	−	0.365228i	0.790917	+	0.611924i	$0.209604\pi$
$80$		0			0
$81$	−1.21281	+	6.87816i	−0.134756	+	0.764240i
$82$	−0.473734	+	0.220906i	−0.0523152	+	0.0243950i
$83$	2.36349	−	8.82067i	0.259427	−	0.968195i	−0.706147	−	0.708065i	$-0.749568\pi$
$83$	2.36349	−	8.82067i	0.259427	−	0.968195i	0.965574	−	0.260129i	$-0.0837652\pi$
$84$	0.945356	−	1.63740i	0.103147	−	0.178655i
$85$		0			0
$86$	−0.152975	−	0.182309i	−0.0164958	−	0.0196589i
$87$	−1.31600	−	4.91137i	−0.141090	−	0.526554i
$88$	−3.82848	−	1.02584i	−0.408118	−	0.109355i
$89$	4.74683	+	1.72770i	0.503163	+	0.183136i	0.581116	−	0.813821i	$-0.302616\pi$
$89$	4.74683	+	1.72770i	0.503163	+	0.183136i	−0.0779532	+	0.996957i	$0.524838\pi$
$90$		0			0
$91$	6.50748	−	1.14745i	0.682170	−	0.120285i
$92$	−2.71337	+	5.81885i	−0.282889	+	0.606657i
$93$	−0.0512163	−	0.585405i	−0.00531088	−	0.0607036i
$94$	−0.140692			−0.0145113
$95$		0			0
$96$	0.479416			0.0489302
$97$	0.278881	+	3.18763i	0.0283161	+	0.323654i	0.997121	+	0.0758291i	$0.0241604\pi$
$97$	0.278881	+	3.18763i	0.0283161	+	0.323654i	−0.968805	+	0.247825i	$0.920284\pi$
$98$	−3.61482	+	7.75200i	−0.365152	+	0.783070i
$99$	10.8128	−	1.90659i	1.08673	−	0.191620i
$100$		0			0
$101$	−2.81842	−	1.02582i	−0.280443	−	0.102073i	0.197969	−	0.980208i	$-0.436565\pi$
$101$	−2.81842	−	1.02582i	−0.280443	−	0.102073i	−0.478412	+	0.878135i	$0.658788\pi$
$102$	2.21603	+	0.593784i	0.219420	+	0.0587934i
$103$	−0.350069	−	1.30647i	−0.0344933	−	0.128731i	0.946532	−	0.322609i	$-0.104560\pi$
$103$	−0.350069	−	1.30647i	−0.0344933	−	0.128731i	−0.981026	+	0.193878i	$0.937893\pi$
$104$	1.07700	+	1.28352i	0.105609	+	0.125860i
$105$		0			0
$106$	−6.80846	+	11.7926i	−0.661296	+	1.14540i
$107$	−4.68550	+	17.4865i	−0.452964	+	1.69048i	0.241042	+	0.970515i	$0.422511\pi$
$107$	−4.68550	+	17.4865i	−0.452964	+	1.69048i	−0.694006	+	0.719970i	$0.744156\pi$
$108$	−2.50713	+	1.16909i	−0.241248	+	0.112496i
$109$	−1.52919	+	8.67247i	−0.146470	+	0.830672i	0.819705	+	0.572786i	$0.194137\pi$
$109$	−1.52919	+	8.67247i	−0.146470	+	0.830672i	−0.966175	+	0.257887i	$0.916974\pi$
$110$		0			0
$111$	1.78261	−	0.648816i	0.169198	−	0.0615829i
$112$	−3.92877	+	0.343723i	−0.371234	+	0.0324788i
$113$	−3.41915	+	3.41915i	−0.321646	+	0.321646i	−0.849398	−	0.527752i	$-0.823035\pi$
$113$	−3.41915	+	3.41915i	−0.321646	+	0.321646i	0.527752	+	0.849398i	$0.323035\pi$
$114$	−0.523909	+	2.02299i	−0.0490686	+	0.189470i
$115$		0			0
$116$	−6.81732	+	8.12456i	−0.632972	+	0.754347i
$117$	−4.20659	−	1.96156i	−0.388899	−	0.181347i
$118$	5.17279	−	7.38751i	0.476194	−	0.680075i
$119$	−18.5859	−	3.27719i	−1.70377	−	0.300420i
$120$		0			0
$121$	−2.35481	−	4.07865i	−0.214074	−	0.370787i
$122$	13.0449	−	3.49536i	1.18103	−	0.316455i
$123$	0.249641	+	0.0218408i	0.0225094	+	0.00196931i
$124$	−0.938973	+	0.787892i	−0.0843222	+	0.0707548i
$125$		0			0
$126$	9.46124	−	5.46245i	0.842874	−	0.486634i
$127$	−4.95246	−	10.6206i	−0.439460	−	0.942424i	−0.993909	−	0.110206i	$-0.964849\pi$
$127$	−4.95246	−	10.6206i	−0.439460	−	0.942424i	0.554449	−	0.832218i	$-0.312929\pi$
$128$	−0.573576	−	0.819152i	−0.0506975	−	0.0724035i
$129$	0.0198124	+	0.112362i	0.00174439	+	0.00989290i
$130$		0			0
$131$	11.7431	+	9.85366i	1.02600	+	0.860918i	0.990370	−	0.138447i	$-0.0442109\pi$
$131$	11.7431	+	9.85366i	1.02600	+	0.860918i	0.0356327	+	0.999365i	$0.488655\pi$
$132$	1.34363	+	1.34363i	0.116948	+	0.116948i
$133$	2.84298	−	16.9538i	0.246518	−	1.47008i
$134$		−	5.36359i		−	0.463344i
$135$		0			0
$136$	−1.63671	−	4.49682i	−0.140347	−	0.385599i
$137$	−3.86135	−	2.70375i	−0.329897	−	0.230997i	0.396879	−	0.917871i	$-0.370093\pi$
$137$	−3.86135	−	2.70375i	−0.329897	−	0.230997i	−0.726776	+	0.686874i	$0.758982\pi$
$138$	2.52138	−	1.76549i	0.214634	−	0.150289i
$139$	−5.99212	+	16.4632i	−0.508245	+	1.39639i	0.374801	+	0.927105i	$0.377711\pi$
$139$	−5.99212	+	16.4632i	−0.508245	+	1.39639i	−0.883046	+	0.469286i	$0.844511\pi$
$140$		0			0
$141$	0.0584134	+	0.0337250i	0.00491930	+	0.00284016i
$142$	0.365261	−	4.17496i	0.0306521	−	0.350355i
$143$	−0.578799	+	6.61571i	−0.0484016	+	0.553233i
$144$	2.39903	+	1.38508i	0.199919	+	0.115423i
$145$		0			0
$146$	−0.813545	+	2.23520i	−0.0673295	+	0.184986i
$147$	3.35904	−	2.35203i	0.277049	−	0.193992i
$148$	−3.24132	−	2.26959i	−0.266434	−	0.186559i
$149$	−5.22965	−	14.3684i	−0.428430	−	1.17710i	−0.946765	−	0.321924i	$-0.895670\pi$
$149$	−5.22965	−	14.3684i	−0.428430	−	1.17710i	0.518336	−	0.855177i	$-0.326552\pi$
$150$		0			0
$151$		−	5.60463i		−	0.456098i	−0.973650	−	0.228049i	$-0.926765\pi$
$151$		−	5.60463i		−	0.456098i	0.973650	−	0.228049i	$-0.0732347\pi$
$152$	4.08337	−	1.52514i	0.331205	−	0.123705i
$153$	9.37366	+	9.37366i	0.757816	+	0.757816i
$154$	−11.9743	−	10.0476i	−0.964915	−	0.809660i
$155$		0			0
$156$	−0.139487	−	0.791067i	−0.0111679	−	0.0633361i
$157$	1.03737	+	1.48152i	0.0827911	+	0.118238i	0.858411	−	0.512962i	$-0.171452\pi$
$157$	1.03737	+	1.48152i	0.0827911	+	0.118238i	−0.775620	+	0.631200i	$0.782563\pi$
$158$	4.01120	+	8.60205i	0.319114	+	0.684343i
$159$	5.65357	−	3.26409i	0.448357	−	0.258859i
$160$		0			0
$161$	−19.3967	+	16.2758i	−1.52867	+	1.28271i
$162$	−6.95769	−	0.608719i	−0.546648	−	0.0478255i
$163$	2.73822	−	0.733705i	0.214474	−	0.0574682i	−0.149982	−	0.988689i	$-0.547922\pi$
$163$	2.73822	−	0.733705i	0.214474	−	0.0574682i	0.364456	+	0.931221i	$0.381255\pi$
$164$	−0.261354	−	0.452678i	−0.0204083	−	0.0353482i
$165$		0			0
$166$	8.99310	+	1.58573i	0.698000	+	0.123076i
$167$	11.9111	−	17.0109i	0.921711	−	1.31634i	−0.0268156	−	0.999640i	$-0.508537\pi$
$167$	11.9111	−	17.0109i	0.921711	−	1.31634i	0.948526	−	0.316699i	$-0.102574\pi$
$168$	1.71357	+	0.799049i	0.132205	+	0.0616480i
$169$	−6.55170	+	7.80801i	−0.503977	+	0.600616i
$170$		0			0
$171$	−8.46628	+	8.60953i	−0.647433	+	0.658387i
$172$	0.168283	−	0.168283i	0.0128314	−	0.0128314i
$173$	−5.44530	+	0.476402i	−0.413999	+	0.0362202i	−0.292253	−	0.956341i	$-0.594405\pi$
$173$	−5.44530	+	0.476402i	−0.413999	+	0.0362202i	−0.121746	+	0.992561i	$0.538849\pi$
$174$	4.77798	−	1.73904i	0.362218	−	0.131837i
$175$		0			0
$176$	0.688261	−	3.90332i	0.0518796	−	0.294224i
$177$	−3.91852	+	1.82724i	−0.294534	+	0.137343i
$178$	−1.30742	+	4.87935i	−0.0979950	+	0.365722i
$179$	0.495718	−	0.858609i	0.0370517	−	0.0641754i	−0.846905	−	0.531744i	$-0.821537\pi$
$179$	0.495718	−	0.858609i	0.0370517	−	0.0641754i	0.883957	+	0.467569i	$0.154870\pi$
$180$		0			0
$181$	−9.75951	−	11.6309i	−0.725419	−	0.864520i	0.269727	−	0.962937i	$-0.413067\pi$
$181$	−9.75951	−	11.6309i	−0.725419	−	0.864520i	−0.995145	+	0.0984165i	$0.968622\pi$
$182$	1.71024	+	6.38271i	0.126772	+	0.473118i
$183$	−6.25393	−	1.67573i	−0.462304	−	0.123874i
$184$	−6.03320	−	2.19590i	−0.444773	−	0.161884i
$185$		0			0
$186$	0.578713	−	0.102043i	0.0424333	−	0.00748214i
$187$	8.01587	−	17.1901i	0.586178	−	1.25706i
$188$	−0.0122621	−	0.140157i	−0.000894306	−	0.0102220i
$189$	−10.9097			−0.793565
$190$		0			0
$191$	−1.14767			−0.0830427			−0.0415213	−	0.999138i	$-0.513220\pi$
$191$	−1.14767			−0.0830427			−0.0415213	+	0.999138i	$0.513220\pi$
$192$	0.0417839	+	0.477592i	0.00301549	+	0.0344672i
$193$	−3.47773	+	7.45802i	−0.250333	+	0.536840i	−0.990813	−	0.135238i	$-0.956820\pi$
$193$	−3.47773	+	7.45802i	−0.250333	+	0.536840i	0.740481	+	0.672078i	$0.234598\pi$
$194$	−3.15119	+	0.555640i	−0.226242	+	0.0398926i
$195$		0			0
$196$	−8.03755	−	2.92543i	−0.574111	−	0.208959i
$197$	0.786915	+	0.210853i	0.0560653	+	0.0150227i	0.286743	−	0.958008i	$-0.407428\pi$
$197$	0.786915	+	0.210853i	0.0560653	+	0.0150227i	−0.230677	+	0.973030i	$0.574094\pi$
$198$	2.84174	+	10.6055i	0.201954	+	0.753701i
$199$	−8.05244	−	9.59653i	−0.570823	−	0.680280i	0.400977	−	0.916088i	$-0.368671\pi$
$199$	−8.05244	−	9.59653i	−0.570823	−	0.680280i	−0.971800	+	0.235808i	$0.924226\pi$
$200$		0			0
$201$	−1.28570	+	2.22689i	−0.0906861	+	0.157073i
$202$	0.776275	−	2.89710i	0.0546185	−	0.203839i
$203$	−37.9083	+	17.6769i	−2.66064	+	1.24068i
$204$	−0.398385	+	2.25935i	−0.0278925	+	0.158186i
$205$		0			0
$206$	1.27099	−	0.462603i	0.0885542	−	0.0322311i
$207$	17.7178	−	1.55011i	1.23147	−	0.107740i
$208$	−1.18477	+	1.18477i	−0.0821490	+	0.0821490i
$209$	15.7187	+	7.16982i	1.08728	+	0.495947i
$210$		0			0
$211$	3.92657	−	4.67951i	0.270317	−	0.322151i	−0.613760	−	0.789493i	$-0.710344\pi$
$211$	3.92657	−	4.67951i	0.270317	−	0.322151i	0.884077	+	0.467342i	$0.154788\pi$
$212$	−12.3411	−	5.75476i	−0.847592	−	0.395239i
$213$	−1.15242	+	1.64583i	−0.0789627	+	0.112770i
$214$	−17.8283	−	3.14362i	−1.21872	−	0.214893i
$215$		0			0
$216$	−1.38315	−	2.39569i	−0.0941117	−	0.163006i
$217$	−4.66934	+	1.25115i	−0.316975	+	0.0849333i
$218$	−8.77275	−	0.767516i	−0.594165	−	0.0519827i
$219$	0.873568	−	0.733011i	0.0590303	−	0.0495323i
$220$		0			0
$221$	−6.94383	+	4.00902i	−0.467093	+	0.269676i
$222$	0.801711	+	1.71927i	0.0538073	+	0.115390i
$223$	5.79740	+	8.27954i	0.388222	+	0.554439i	0.964929	−	0.262513i	$-0.0845511\pi$
$223$	5.79740	+	8.27954i	0.388222	+	0.554439i	−0.576706	+	0.816952i	$0.695662\pi$
$224$	−0.684830	−	3.88386i	−0.0457571	−	0.259502i
$225$		0			0
$226$	−3.70414	−	3.10814i	−0.246395	−	0.206750i
$227$	−15.8283	−	15.8283i	−1.05056	−	1.05056i	−0.998652	−	0.0519070i	$-0.983470\pi$
$227$	−15.8283	−	15.8283i	−1.05056	−	1.05056i	−0.0519070	−	0.998652i	$-0.516530\pi$
$228$	−2.06095	−	0.345600i	−0.136490	−	0.0228879i
$229$		−	14.0379i		−	0.927647i	−0.885928	−	0.463824i	$-0.846477\pi$
$229$		−	14.0379i		−	0.927647i	0.885928	−	0.463824i	$-0.153523\pi$
$230$		0			0
$231$	2.56307	+	7.04197i	0.168637	+	0.463327i
$232$	−8.68782	−	6.08327i	−0.570383	−	0.399386i
$233$	15.9469	−	11.1661i	1.04471	−	0.731516i	0.0805301	−	0.996752i	$-0.474339\pi$
$233$	15.9469	−	11.1661i	1.04471	−	0.731516i	0.964184	+	0.265236i	$0.0854498\pi$
$234$	1.58747	−	4.36154i	0.103776	−	0.285123i
$235$		0			0
$236$	7.81023	+	4.50924i	0.508403	+	0.293527i
$237$	0.396584	−	4.53298i	0.0257609	−	0.294448i
$238$	1.64486	−	18.8008i	0.106620	−	1.21867i
$239$	3.66297	+	2.11482i	0.236938	+	0.136796i	0.613769	−	0.789486i	$-0.289653\pi$
$239$	3.66297	+	2.11482i	0.236938	+	0.136796i	−0.376831	+	0.926282i	$0.622986\pi$
$240$		0			0
$241$	−3.83164	+	10.5274i	−0.246818	+	0.678126i	0.752981	+	0.658043i	$0.228615\pi$
$241$	−3.83164	+	10.5274i	−0.246818	+	0.678126i	−0.999798	+	0.0200835i	$0.993607\pi$
$242$	3.85790	−	2.70133i	0.247995	−	0.173648i
$243$	9.54091	+	6.68062i	0.612050	+	0.428562i
$244$	4.61900	+	12.6906i	0.295701	+	0.812432i
$245$		0			0
$246$			0.250595i			0.0159773i
$247$	−3.70464	−	6.29409i	−0.235721	−	0.400483i
$248$	−0.866730	−	0.866730i	−0.0550374	−	0.0550374i
$249$	−3.35370	−	2.81409i	−0.212532	−	0.178336i
$250$		0			0
$251$	1.72204	+	9.76617i	0.108694	+	0.616435i	0.989680	+	0.143293i	$0.0457692\pi$
$251$	1.72204	+	9.76617i	0.108694	+	0.616435i	−0.880986	+	0.473142i	$0.843120\pi$
$252$	6.26626	+	8.94915i	0.394737	+	0.563744i
$253$	−10.7546	−	23.0632i	−0.676134	−	1.44997i
$254$	10.1485	−	5.85926i	0.636775	−	0.367642i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−5.34746	−	0.467842i	−0.333565	−	0.0291832i	−0.0808571	−	0.996726i	$-0.525766\pi$
$257$	−5.34746	−	0.467842i	−0.333565	−	0.0291832i	−0.252708	+	0.967543i	$0.581321\pi$
$258$	−0.110207	+	0.0295300i	−0.00686122	+	0.00183846i
$259$	−7.80260	−	13.5145i	−0.484830	−	0.839750i
$260$		0			0
$261$	28.9336	+	5.10177i	1.79094	+	0.315792i
$262$	−8.79268	+	12.5573i	−0.543214	+	0.775790i
$263$	0.171100	+	0.0797854i	0.0105505	+	0.00491978i	0.427886	−	0.903833i	$-0.359258\pi$
$263$	0.171100	+	0.0797854i	0.0105505	+	0.00491978i	−0.417336	+	0.908752i	$0.637036\pi$
$264$	−1.22141	+	1.45563i	−0.0751729	+	0.0895876i
$265$		0			0
$266$	17.1371	+	1.35454i	1.05074	+	0.0830521i
$267$	1.71244	−	1.71244i	0.104800	−	0.104800i
$268$	5.34318	−	0.467468i	0.326387	−	0.0285552i
$269$	−22.6034	+	8.22695i	−1.37815	+	0.501606i	−0.921617	−	0.388100i	$-0.873132\pi$
$269$	−22.6034	+	8.22695i	−1.37815	+	0.501606i	−0.456534	+	0.889706i	$0.650909\pi$
$270$		0			0
$271$	3.08051	−	17.4704i	0.187127	−	1.06125i	−0.736064	−	0.676912i	$-0.763318\pi$
$271$	3.08051	−	17.4704i	0.187127	−	1.06125i	0.923191	−	0.384340i	$-0.125571\pi$
$272$	4.33706	−	2.02240i	0.262973	−	0.122626i
$273$	0.819919	−	3.05998i	0.0496237	−	0.185198i
$274$	2.35692	−	4.08230i	0.142387	−	0.246621i
$275$		0			0
$276$	1.97853	+	2.35792i	0.119093	+	0.141930i
$277$	3.18656	+	11.8924i	0.191462	+	0.714546i	0.993154	+	0.116809i	$0.0372665\pi$
$277$	3.18656	+	11.8924i	0.191462	+	0.714546i	−0.801692	+	0.597737i	$0.796067\pi$
$278$	−16.9228	−	4.53445i	−1.01496	−	0.271958i
$279$	3.19073	+	1.16133i	0.191024	+	0.0695270i
$280$		0			0
$281$	17.1607	−	3.02589i	1.02372	−	0.180509i	0.363510	−	0.931590i	$-0.381578\pi$
$281$	17.1607	−	3.02589i	1.02372	−	0.180509i	0.660210	+	0.751081i	$0.270467\pi$
$282$	−0.0285056	+	0.0611305i	−0.00169748	+	0.00364027i
$283$	−0.779840	−	8.91361i	−0.0463567	−	0.529859i	−0.983499	−	0.180912i	$-0.942095\pi$
$283$	−0.779840	−	8.91361i	−0.0463567	−	0.529859i	0.937143	−	0.348947i	$-0.113461\pi$
$284$	4.19091			0.248684
$285$		0			0
$286$	−6.64098			−0.392689
$287$	−0.179667	−	2.05360i	−0.0106054	−	0.121220i
$288$	−1.17072	+	2.51062i	−0.0689853	+	0.147940i
$289$	5.81054	−	1.02456i	0.341797	−	0.0602679i
$290$		0			0
$291$	1.44152	+	0.524672i	0.0845036	+	0.0307568i
$292$	−2.29760	−	0.615639i	−0.134457	−	0.0360276i
$293$	−3.62042	−	13.5116i	−0.211507	−	0.789355i	−0.987367	−	0.158450i	$-0.949350\pi$
$293$	−3.62042	−	13.5116i	−0.211507	−	0.789355i	0.775860	−	0.630905i	$-0.217316\pi$
$294$	2.63584	+	3.14127i	0.153725	+	0.183202i
$295$		0			0
$296$	1.97846	−	3.42679i	0.114996	−	0.199178i
$297$	2.83779	−	10.5908i	0.164665	−	0.614539i
$298$	13.8579	−	6.46204i	0.802766	−	0.374336i
$299$	−1.86802	+	10.5941i	−0.108030	+	0.612670i
$300$		0			0
$301$	0.881968	−	0.321010i	0.0508358	−	0.0185027i
$302$	5.58330	−	0.488475i	0.321283	−	0.0281086i
$303$	−1.01676	+	1.01676i	−0.0584112	+	0.0584112i
$304$	1.87523	+	3.93491i	0.107552	+	0.225683i
$305$		0			0
$306$	−8.52102	+	10.1550i	−0.487115	+	0.580520i
$307$	7.75210	+	3.61487i	0.442436	+	0.206311i	0.631053	−	0.775739i	$-0.282623\pi$
$307$	7.75210	+	3.61487i	0.442436	+	0.206311i	−0.188617	+	0.982051i	$0.560401\pi$
$308$	8.96575	−	12.8044i	0.510871	−	0.729599i
$309$	−0.638589	−	0.112600i	−0.0363280	−	0.00640561i
$310$		0			0
$311$	7.42425	+	12.8592i	0.420991	+	0.729177i	0.996037	−	0.0889440i	$-0.0283492\pi$
$311$	7.42425	+	12.8592i	0.420991	+	0.729177i	−0.575046	+	0.818121i	$0.695016\pi$
$312$	0.775900	−	0.207902i	0.0439267	−	0.0117701i
$313$	−9.45424	−	0.827139i	−0.534385	−	0.0467527i	−0.183230	−	0.983070i	$-0.558655\pi$
$313$	−9.45424	−	0.827139i	−0.534385	−	0.0467527i	−0.351155	+	0.936317i	$0.614211\pi$
$314$	−1.38547	+	1.16254i	−0.0781864	+	0.0656062i
$315$		0			0
$316$	−8.21972	+	4.74566i	−0.462395	+	0.266964i
$317$	7.44818	+	15.9727i	0.418332	+	0.897115i	0.996687	+	0.0813302i	$0.0259168\pi$
$317$	7.44818	+	15.9727i	0.418332	+	0.897115i	−0.578356	+	0.815785i	$0.696305\pi$
$318$	3.74441	+	5.34757i	0.209976	+	0.299877i
$319$	−7.29960	−	41.3981i	−0.408699	−	2.31785i
$320$		0			0
$321$	6.64854	+	5.57878i	0.371085	+	0.311377i
$322$	−17.9044	−	17.9044i	−0.997771	−	0.997771i
$323$	3.79435	+	20.5111i	0.211123	+	1.14127i
$324$		−	6.98427i		−	0.388015i
$325$		0			0
$326$	0.969564	+	2.66386i	0.0536992	+	0.147537i
$327$	3.45835	+	2.42156i	0.191247	+	0.133913i
$328$	0.428177	−	0.299813i	0.0236421	−	0.0165544i
$329$	0.189772	−	0.521396i	0.0104625	−	0.0287455i
$330$		0			0
$331$	0.953780	+	0.550665i	0.0524245	+	0.0302673i	0.525983	−	0.850495i	$-0.323697\pi$
$331$	0.953780	+	0.550665i	0.0524245	+	0.0302673i	−0.473559	+	0.880762i	$0.657031\pi$
$332$	−0.795892	+	9.09708i	−0.0436802	+	0.499267i
$333$	−0.955339	+	10.9196i	−0.0523523	+	0.598389i
$334$	17.9842	+	10.3832i	0.984054	+	0.568144i
$335$		0			0
$336$	−0.646661	+	1.77669i	−0.0352783	+	0.0969263i
$337$	9.70586	−	6.79611i	0.528712	−	0.370208i	−0.278531	−	0.960427i	$-0.589848\pi$
$337$	9.70586	−	6.79611i	0.528712	−	0.370208i	0.807243	+	0.590219i	$0.200959\pi$
$338$	−8.34932	−	5.84626i	−0.454143	−	0.317994i
$339$	0.792862	+	2.17837i	0.0430623	+	0.118313i
$340$		0			0
$341$		−	4.85827i		−	0.263090i
$342$	−9.31466	−	7.68369i	−0.503679	−	0.415487i
$343$	−4.33188	−	4.33188i	−0.233900	−	0.233900i
$344$	0.182309	+	0.152975i	0.00982945	+	0.00824789i
$345$		0			0
$346$	−0.949178	−	5.38306i	−0.0510282	−	0.289395i
$347$	3.94520	+	5.63432i	0.211789	+	0.302466i	0.910965	−	0.412483i	$-0.135338\pi$
$347$	3.94520	+	5.63432i	0.211789	+	0.302466i	−0.699176	+	0.714950i	$0.746450\pi$
$348$	2.14886	+	4.60823i	0.115191	+	0.247027i
$349$	−10.6745	+	6.16294i	−0.571394	+	0.329894i	−0.757706	−	0.652596i	$-0.773680\pi$
$349$	−10.6745	+	6.16294i	−0.571394	+	0.329894i	0.186312	+	0.982491i	$0.440346\pi$
$350$		0			0
$351$	−3.55062	+	2.97932i	−0.189518	+	0.159024i
$352$	3.94845	+	0.345445i	0.210453	+	0.0184123i
$353$	−11.2391	+	3.01151i	−0.598198	+	0.160287i	−0.545197	−	0.838308i	$-0.683545\pi$
$353$	−11.2391	+	3.01151i	−0.598198	+	0.160287i	−0.0530009	+	0.998594i	$0.516879\pi$
$354$	−2.16180	−	3.74435i	−0.114899	−	0.199010i
$355$		0			0
$356$	−4.97473	−	0.877179i	−0.263660	−	0.0464904i
$357$	−5.18963	+	7.41155i	−0.274664	+	0.392261i
$358$	0.898546	+	0.418999i	0.0474896	+	0.0221448i
$359$	1.81183	−	2.15926i	0.0956250	−	0.113961i	−0.716110	−	0.697988i	$-0.754079\pi$
$359$	1.81183	−	2.15926i	0.0956250	−	0.113961i	0.811735	+	0.584026i	$0.198523\pi$
$360$		0			0
$361$	−18.6534	+	3.61278i	−0.981756	+	0.190146i
$362$	10.7361	−	10.7361i	0.564276	−	0.564276i
$363$	−2.24928	+	0.196786i	−0.118057	+	0.0103286i
$364$	−6.20937	+	2.26003i	−0.325459	+	0.118458i
$365$		0			0
$366$	1.12429	−	6.37618i	0.0587677	−	0.333288i
$367$	−13.2065	+	6.15827i	−0.689372	+	0.321459i	−0.735547	−	0.677474i	$-0.763075\pi$
$367$	−13.2065	+	6.15827i	−0.689372	+	0.321459i	0.0461749	+	0.998933i	$0.485297\pi$
$368$	1.66172	−	6.20162i	0.0866231	−	0.323282i
$369$	−0.723992	+	1.25399i	−0.0376895	+	0.0652802i
$370$		0			0
$371$	−34.5191	−	41.1382i	−1.79214	−	2.13579i
$372$	0.152093	+	0.567617i	0.00788563	+	0.0294296i
$373$	22.2226	+	5.95452i	1.15064	+	0.308313i	0.783222	−	0.621742i	$-0.213575\pi$
$373$	22.2226	+	5.95452i	1.15064	+	0.308313i	0.367419	+	0.930055i	$0.380241\pi$
$374$	17.8233	+	6.48715i	0.921621	+	0.335443i
$375$		0			0
$376$	0.138554	−	0.0244309i	0.00714540	−	0.00125993i
$377$	−7.51006	+	16.1054i	−0.386788	+	0.829469i
$378$	−0.950844	−	10.8682i	−0.0489061	−	0.559000i
$379$	7.16506			0.368044			0.184022	−	0.982922i	$-0.441088\pi$
$379$	7.16506			0.368044			0.184022	+	0.982922i	$0.441088\pi$
$380$		0			0
$381$	−5.61805			−0.287821
$382$	−0.100026	−	1.14331i	−0.00511779	−	0.0584966i
$383$	−12.3266	+	26.4346i	−0.629862	+	1.35074i	0.289442	+	0.957196i	$0.406530\pi$
$383$	−12.3266	+	26.4346i	−0.629862	+	1.35074i	−0.919304	+	0.393548i	$0.871248\pi$
$384$	−0.472133	+	0.0832498i	−0.0240934	+	0.00424832i
$385$		0			0
$386$	−7.73274	−	2.81449i	−0.393586	−	0.143254i
$387$	−0.636800	−	0.170630i	−0.0323704	−	0.00867361i
$388$	−0.828170	−	3.09077i	−0.0420440	−	0.156910i
$389$	13.4228	+	15.9966i	0.680562	+	0.811062i	0.990180	−	0.139799i	$-0.0446457\pi$
$389$	13.4228	+	15.9966i	0.680562	+	0.811062i	−0.309618	+	0.950861i	$0.600201\pi$
$390$		0			0
$391$	15.3621	−	26.6080i	0.776896	−	1.34562i
$392$	2.21378	−	8.26193i	0.111813	−	0.417291i
$393$	6.66068	−	3.10593i	0.335987	−	0.156673i
$394$	−0.141467	+	0.802297i	−0.00712699	+	0.0404191i
$395$		0			0
$396$	−10.3175	+	3.75526i	−0.518473	+	0.188709i
$397$	−28.6522	+	2.50675i	−1.43801	+	0.125810i	−0.779332	−	0.626611i	$-0.784441\pi$
$397$	−28.6522	+	2.50675i	−1.43801	+	0.125810i	−0.658682	+	0.752421i	$0.728886\pi$
$398$	8.85819	−	8.85819i	0.444021	−	0.444021i
$399$	−6.79039	−	4.67028i	−0.339945	−	0.233807i
$400$		0			0
$401$	3.79236	−	4.51956i	0.189382	−	0.225696i	−0.662996	−	0.748623i	$-0.730715\pi$
$401$	3.79236	−	4.51956i	0.189382	−	0.225696i	0.852378	+	0.522927i	$0.175160\pi$
$402$	−2.33048	−	1.08672i	−0.116234	−	0.0542006i
$403$	−1.17798	+	1.68234i	−0.0586796	+	0.0838031i
$404$	2.95373	+	0.520823i	0.146954	+	0.0259119i
$405$		0			0
$406$	−20.9136	−	36.2234i	−1.03792	−	1.79774i
$407$	15.1490	−	4.05916i	0.750907	−	0.201205i
$408$	−2.28548	−	0.199953i	−0.113148	−	0.00989916i
$409$	−27.7673	+	23.2995i	−1.37301	+	1.15209i	−0.401285	+	0.915953i	$0.631436\pi$
$409$	−27.7673	+	23.2995i	−1.37301	+	1.15209i	−0.971720	+	0.236135i	$0.924119\pi$
$410$		0			0
$411$	−1.95712	+	1.12995i	−0.0965378	+	0.0557361i
$412$	0.571617	+	1.22584i	0.0281616	+	0.0603926i
$413$	20.4003	+	29.1347i	1.00383	+	1.43362i
$414$	3.08842	+	17.5153i	0.151788	+	0.860831i
$415$		0			0
$416$	−1.28352	−	1.07700i	−0.0629298	−	0.0528044i
$417$	5.93918	+	5.93918i	0.290843	+	0.290843i
$418$	−5.77256	+	16.2837i	−0.282345	+	0.796464i
$419$			31.6552i			1.54646i	0.634127	+	0.773229i	$0.281359\pi$
$419$			31.6552i			1.54646i	−0.634127	+	0.773229i	$0.718641\pi$
$420$		0			0
$421$	8.16158	+	22.4238i	0.397771	+	1.09287i	0.963367	+	0.268185i	$0.0864238\pi$
$421$	8.16158	+	22.4238i	0.397771	+	1.09287i	−0.565596	+	0.824682i	$0.691354\pi$
$422$	5.00393	+	3.50379i	0.243587	+	0.170562i
$423$	−0.319256	+	0.223545i	−0.0155227	+	0.0108691i
$424$	4.65726	−	12.7957i	0.226177	−	0.621415i
$425$		0			0
$426$	−1.74001	−	1.00459i	−0.0843037	−	0.0486728i
$427$	−4.64199	+	53.0582i	−0.224642	+	2.56767i
$428$	1.57781	−	18.0345i	0.0762664	−	0.871729i
$429$	2.75725	+	1.59190i	0.133121	+	0.0768575i
$430$		0			0
$431$	−6.37147	+	17.5055i	−0.306903	+	0.843209i	0.686353	+	0.727268i	$0.259210\pi$
$431$	−6.37147	+	17.5055i	−0.306903	+	0.843209i	−0.993256	+	0.115941i	$0.963012\pi$
$432$	2.26603	−	1.58669i	0.109024	−	0.0763396i
$433$	24.3541	+	17.0529i	1.17038	+	0.819511i	0.986552	−	0.163447i	$-0.0522612\pi$
$433$	24.3541	+	17.0529i	1.17038	+	0.819511i	0.183831	+	0.982958i	$0.441150\pi$
$434$	−1.65334	−	4.54252i	−0.0793630	−	0.218048i
$435$		0			0
$436$		−	8.80626i		−	0.421743i
$437$	24.3530	+	13.7891i	1.16496	+	0.659623i
$438$	0.806358	+	0.806358i	0.0385293	+	0.0385293i
$439$	24.1927	+	20.3001i	1.15465	+	0.968869i	0.999818	−	0.0190712i	$-0.00607093\pi$
$439$	24.1927	+	20.3001i	1.15465	+	0.968869i	0.154835	+	0.987940i	$0.450515\pi$
$440$		0			0
$441$	4.11446	+	23.3343i	0.195927	+	1.11116i
$442$	−4.59896	−	6.56800i	−0.218750	−	0.312408i
$443$	−4.44520	−	9.53277i	−0.211198	−	0.452915i	0.771961	−	0.635670i	$-0.219276\pi$
$443$	−4.44520	−	9.53277i	−0.211198	−	0.452915i	−0.983158	+	0.182755i	$0.941498\pi$
$444$	−1.64286	+	0.948505i	−0.0779666	+	0.0450141i
$445$		0			0
$446$	−7.74276	+	6.49695i	−0.366630	+	0.307639i
$447$	−7.30261	−	0.638896i	−0.345402	−	0.0302187i
$448$	3.80940	−	1.02072i	0.179977	−	0.0482247i
$449$	9.82833	+	17.0232i	0.463827	+	0.803373i	0.999148	−	0.0412764i	$-0.0131424\pi$
$449$	9.82833	+	17.0232i	0.463827	+	0.803373i	−0.535320	+	0.844649i	$0.679809\pi$
$450$		0			0
$451$	2.04030	+	0.359759i	0.0960738	+	0.0169404i
$452$	2.77347	−	3.96093i	0.130453	−	0.186307i
$453$	−2.43520	−	1.13555i	−0.114416	−	0.0533530i
$454$	14.3885	−	17.1476i	0.675286	−	0.804775i
$455$		0			0
$456$	0.164661	−	2.08323i	0.00771098	−	0.0975562i
$457$	24.6388	−	24.6388i	1.15256	−	1.15256i	0.166518	−	0.986038i	$-0.446748\pi$
$457$	24.6388	−	24.6388i	1.15256	−	1.15256i	0.986038	−	0.166518i	$-0.0532524\pi$
$458$	13.9844	−	1.22348i	0.653450	−	0.0571694i
$459$	12.4396	−	4.52764i	0.580630	−	0.211332i
$460$		0			0
$461$	2.17182	−	12.3170i	0.101152	−	0.573659i	−0.891536	−	0.452949i	$-0.850372\pi$
$461$	2.17182	−	12.3170i	0.101152	−	0.573659i	0.992688	−	0.120710i	$-0.0385170\pi$
$462$	−6.79178	+	3.16706i	−0.315982	+	0.147345i
$463$	0.230544	−	0.860402i	0.0107143	−	0.0399862i	−0.960362	−	0.278757i	$-0.910078\pi$
$463$	0.230544	−	0.860402i	0.0107143	−	0.0399862i	0.971076	+	0.238770i	$0.0767444\pi$
$464$	5.30293	−	9.18495i	0.246182	−	0.426401i
$465$		0			0
$466$	12.5135	+	14.9130i	0.579676	+	0.690831i
$467$	−5.49520	−	20.5084i	−0.254287	−	0.949013i	−0.968486	−	0.249070i	$-0.919875\pi$
$467$	−5.49520	−	20.5084i	−0.254287	−	0.949013i	0.714198	−	0.699944i	$-0.246792\pi$
$468$	4.48330	+	1.20130i	0.207241	+	0.0555300i
$469$	19.8772	+	7.23469i	0.917842	+	0.334067i
$470$		0			0
$471$	0.853899	−	0.150565i	0.0393456	−	0.00693769i
$472$	−3.81137	+	8.17352i	−0.175433	+	0.376217i
$473$	0.0822116	+	0.939683i	0.00378010	+	0.0432067i
$474$	4.55029			0.209002
$475$		0			0
$476$	18.8726			0.865024
$477$	3.28761	+	37.5775i	0.150529	+	1.72056i
$478$	−1.78752	+	3.83335i	−0.0817593	+	0.175333i
$479$	−10.0951	+	1.78004i	−0.461257	+	0.0813320i	−0.399448	−	0.916756i	$-0.630798\pi$
$479$	−10.0951	+	1.78004i	−0.461257	+	0.0813320i	−0.0618091	+	0.998088i	$0.519687\pi$
$480$		0			0
$481$	−6.23005	−	2.26755i	−0.284066	−	0.103392i
$482$	−10.8212	−	2.89954i	−0.492894	−	0.132071i
$483$	3.14183	+	11.7255i	0.142958	+	0.533528i
$484$	3.02729	+	3.60778i	0.137604	+	0.163990i
$485$		0			0
$486$	−5.82365	+	10.0869i	−0.264166	+	0.457549i
$487$	0.885650	−	3.30529i	0.0401326	−	0.149777i	−0.942952	−	0.332929i	$-0.891963\pi$
$487$	0.885650	−	3.30529i	0.0401326	−	0.149777i	0.983085	+	0.183151i	$0.0586299\pi$
$488$	−12.2397	+	5.70748i	−0.554067	+	0.258365i
$489$	0.235998	−	1.33841i	0.0106722	−	0.0605250i
$490$		0			0
$491$	17.8702	−	6.50422i	0.806471	−	0.293531i	0.0943054	−	0.995543i	$-0.469937\pi$
$491$	17.8702	−	6.50422i	0.806471	−	0.293531i	0.712165	+	0.702012i	$0.247715\pi$
$492$	−0.249641	+	0.0218408i	−0.0112547	+	0.000984657i
$493$	35.8881	−	35.8881i	1.61632	−	1.61632i
$494$	5.94726	−	4.23911i	0.267580	−	0.190726i
$495$		0			0
$496$	0.787892	−	0.938973i	0.0353774	−	0.0421611i
$497$	14.9795	+	6.98503i	0.671920	+	0.313322i
$498$	2.51109	−	3.58621i	0.112525	−	0.160702i
$499$	−18.7181	−	3.30050i	−0.837936	−	0.147751i	−0.261818	−	0.965117i	$-0.584322\pi$
$499$	−18.7181	−	3.30050i	−0.837936	−	0.147751i	−0.576118	+	0.817367i	$0.695433\pi$
$500$		0			0
$501$	−4.97788	−	8.62194i	−0.222395	−	0.385200i
$502$	−9.57892	+	2.56666i	−0.427528	+	0.114556i
$503$	−20.2133	−	1.76843i	−0.901265	−	0.0788505i	−0.372904	−	0.927870i	$-0.621638\pi$
$503$	−20.2133	−	1.76843i	−0.901265	−	0.0788505i	−0.528361	+	0.849020i	$0.677193\pi$
$504$	−8.36896	+	7.02239i	−0.372783	+	0.312802i
$505$		0			0
$506$	22.0381	−	12.7237i	0.979715	−	0.565639i
$507$	2.06513	+	4.42869i	0.0917157	+	0.196685i
$508$	6.72146	+	9.59924i	0.298217	+	0.425898i
$509$	0.555773	+	3.15194i	0.0246342	+	0.139707i	0.994644	−	0.103357i	$-0.0329584\pi$
$509$	0.555773	+	3.15194i	0.0246342	+	0.139707i	−0.970010	+	0.243064i	$0.921847\pi$
$510$		0			0
$511$	−7.18615	−	6.02990i	−0.317897	−	0.266747i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.21901	+	11.2959i	0.186274	+	0.498725i
$514$		−	5.36789i		−	0.236767i
$515$		0			0
$516$	−0.0390228	−	0.107214i	−0.00171788	−	0.00471985i
$517$	0.456790	+	0.319848i	0.0200896	+	0.0140669i
$518$	12.7830	−	8.95077i	0.561654	−	0.393274i
$519$	−0.896277	+	2.46250i	−0.0393422	+	0.108092i
$520$		0			0
$521$	11.9748	+	6.91365i	0.524625	+	0.302892i	0.738825	−	0.673898i	$-0.235381\pi$
$521$	11.9748	+	6.91365i	0.524625	+	0.302892i	−0.214200	+	0.976790i	$0.568714\pi$
$522$	−2.56063	+	29.2681i	−0.112076	+	1.28103i
$523$	1.87487	−	21.4299i	0.0819825	−	0.937064i	−0.838146	−	0.545447i	$-0.816360\pi$
$523$	1.87487	−	21.4299i	0.0819825	−	0.937064i	0.920128	−	0.391618i	$-0.128084\pi$
$524$	−13.2758	−	7.66479i	−0.579956	−	0.334838i
$525$		0			0
$526$	−0.0645694	+	0.177403i	−0.00281536	+	0.00773514i
$527$	4.80488	−	3.36442i	0.209304	−	0.146556i
$528$	−1.55654	−	1.08990i	−0.0677397	−	0.0474319i
$529$	−6.23210	−	17.1225i	−0.270961	−	0.744459i
$530$		0			0
$531$		−	24.9826i		−	1.08415i
$532$	0.144210	+	17.1899i	0.00625231	+	0.745278i
$533$	−0.619289	−	0.619289i	−0.0268244	−	0.0268244i
$534$	1.85517	+	1.55668i	0.0802812	+	0.0673639i
$535$		0			0
$536$	0.931378	+	5.28211i	0.0402294	+	0.228152i
$537$	−0.272627	−	0.389352i	−0.0117647	−	0.0168018i
$538$	−10.1657	−	21.8003i	−0.438273	−	0.939879i
$539$	29.3597	−	16.9508i	1.26461	−	0.730124i
$540$		0			0
$541$	−13.9852	+	11.7350i	−0.601271	+	0.504526i	−0.891854	−	0.452323i	$-0.850595\pi$
$541$	−13.9852	+	11.7350i	−0.601271	+	0.504526i	0.290583	+	0.956850i	$0.406151\pi$
$542$	17.6724	+	1.54614i	0.759096	+	0.0664123i
$543$	−7.03100	+	1.88395i	−0.301729	+	0.0808481i
$544$	2.39271	+	4.14429i	0.102586	+	0.177685i
$545$		0			0
$546$	3.11979	+	0.550104i	0.133515	+	0.0235423i
$547$	18.1445	−	25.9130i	0.775801	−	1.10796i	−0.215520	−	0.976499i	$-0.569145\pi$
$547$	18.1445	−	25.9130i	0.775801	−	1.10796i	0.991322	−	0.131459i	$-0.0419663\pi$
$548$	4.27219	+	1.99215i	0.182499	+	0.0851006i
$549$	24.0474	−	28.6586i	1.02632	−	1.22312i
$550$		0			0
$551$	32.9625	+	32.4141i	1.40425	+	1.38089i
$552$	−2.17650	+	2.17650i	−0.0926381	+	0.0926381i
$553$	−37.2892	+	3.26238i	−1.58570	+	0.138731i
$554$	−11.5694	+	4.21093i	−0.491538	+	0.178905i
$555$		0			0
$556$	3.04228	−	17.2536i	0.129021	−	0.731716i
$557$	−33.0238	+	15.3993i	−1.39926	+	0.652488i	−0.968279	−	0.249871i	$-0.919612\pi$
$557$	−33.0238	+	15.3993i	−1.39926	+	0.652488i	−0.430985	+	0.902359i	$0.641834\pi$
$558$	−0.878820	+	3.27980i	−0.0372034	+	0.138845i
$559$	0.199376	−	0.345330i	0.00843272	−	0.0146059i
$560$		0			0
$561$	−5.84498	−	6.96577i	−0.246775	−	0.294095i
$562$	4.51003	+	16.8317i	0.190244	+	0.710000i
$563$	11.3749	+	3.04788i	0.479393	+	0.128453i	0.490420	−	0.871486i	$-0.336843\pi$
$563$	11.3749	+	3.04788i	0.479393	+	0.128453i	−0.0110270	+	0.999939i	$0.503510\pi$
$564$	−0.0633823	−	0.0230693i	−0.00266887	−	0.000971391i
$565$		0			0
$566$	8.81173	−	1.55375i	0.370384	−	0.0653088i
$567$	11.6408	−	24.9637i	0.488866	−	1.04838i
$568$	0.365261	+	4.17496i	0.0153260	+	0.175177i
$569$	43.6972			1.83188			0.915941	−	0.401314i	$-0.131446\pi$
$569$	43.6972			1.83188			0.915941	+	0.401314i	$0.131446\pi$
$570$		0			0
$571$	20.2863			0.848953			0.424477	−	0.905439i	$-0.360458\pi$
$571$	20.2863			0.848953			0.424477	+	0.905439i	$0.360458\pi$
$572$	−0.578799	−	6.61571i	−0.0242008	−	0.276617i
$573$	−0.232530	+	0.498662i	−0.00971408	+	0.0208319i
$574$	2.03012	−	0.357966i	0.0847358	−	0.0149412i
$575$		0			0
$576$	−2.60310	−	0.947451i	−0.108462	−	0.0394771i
$577$	5.16771	+	1.38468i	0.215134	+	0.0576451i	0.364776	−	0.931095i	$-0.381145\pi$
$577$	5.16771	+	1.38468i	0.215134	+	0.0576451i	−0.149642	+	0.988740i	$0.547812\pi$
$578$	1.52708	+	5.69913i	0.0635181	+	0.237053i
$579$	2.53588	+	3.02214i	0.105387	+	0.125596i
$580$		0			0
$581$	−18.0070	+	31.1890i	−0.747055	+	1.29394i
$582$	−0.397038	+	1.48177i	−0.0164578	+	0.0614212i
$583$	48.9145	−	22.8092i	2.02583	−	0.944661i
$584$	0.413048	−	2.34251i	0.0170920	−	0.0969338i
$585$		0			0
$586$	13.1446	−	4.78425i	0.542999	−	0.197636i
$587$	−12.5936	+	1.10180i	−0.519795	+	0.0454762i	−0.344035	−	0.938957i	$-0.611794\pi$
$587$	−12.5936	+	1.10180i	−0.519795	+	0.0454762i	−0.175760	+	0.984433i	$0.556238\pi$
$588$	−2.89958	+	2.89958i	−0.119577	+	0.119577i
$589$	3.10116	+	4.35077i	0.127781	+	0.179270i
$590$		0			0
$591$	0.251052	−	0.299192i	0.0103269	−	0.0123071i
$592$	3.58618	+	1.67226i	0.147391	+	0.0687297i
$593$	−22.0064	+	31.4283i	−0.903693	+	1.29061i	0.0527263	+	0.998609i	$0.483209\pi$
$593$	−22.0064	+	31.4283i	−0.903693	+	1.29061i	−0.956419	+	0.291998i	$0.905680\pi$
$594$	10.7978	+	1.90394i	0.443039	+	0.0781197i
$595$		0			0
$596$	7.64524	+	13.2419i	0.313161	+	0.542411i
$597$	−5.80119	+	1.55442i	−0.237427	+	0.0636183i
$598$	−10.7165	−	0.937577i	−0.438232	−	0.0383404i
$599$	−17.1632	+	14.4016i	−0.701269	+	0.588435i	−0.922134	−	0.386870i	$-0.873556\pi$
$599$	−17.1632	+	14.4016i	−0.701269	+	0.588435i	0.220865	+	0.975304i	$0.429112\pi$
$600$		0			0
$601$	12.3801	−	7.14764i	0.504994	−	0.291558i	−0.225780	−	0.974178i	$-0.572493\pi$
$601$	12.3801	−	7.14764i	0.504994	−	0.291558i	0.730773	+	0.682620i	$0.239160\pi$
$602$	0.396657	+	0.850634i	0.0161665	+	0.0346692i
$603$	−8.52221	−	12.1710i	−0.347051	−	0.495640i
$604$	0.973233	+	5.51948i	0.0396003	+	0.224584i
$605$		0			0
$606$	−1.10150	−	0.924272i	−0.0447456	−	0.0375460i
$607$	28.6839	+	28.6839i	1.16424	+	1.16424i	0.983537	+	0.180707i	$0.0578385\pi$
$607$	28.6839	+	28.6839i	1.16424	+	1.16424i	0.180707	+	0.983537i	$0.442161\pi$
$608$	−3.75650	+	2.21104i	−0.152346	+	0.0896695i
$609$			20.0526i			0.812574i
$610$		0			0
$611$	−0.0806251	−	0.221516i	−0.00326174	−	0.00896156i
$612$	−10.8590	−	7.60354i	−0.438948	−	0.307355i
$613$	−30.0472	+	21.0393i	−1.21359	+	0.849768i	−0.992107	−	0.125395i	$-0.959980\pi$
$613$	−30.0472	+	21.0393i	−1.21359	+	0.849768i	−0.221488	+	0.975163i	$0.571091\pi$
$614$	−2.92547	+	8.03766i	−0.118062	+	0.324374i
$615$		0			0
$616$	13.5371	+	7.81565i	0.545426	+	0.314902i
$617$	2.76270	−	31.5779i	0.111222	−	1.27128i	−0.711440	−	0.702747i	$-0.751957\pi$
$617$	2.76270	−	31.5779i	0.111222	−	1.27128i	0.822663	−	0.568530i	$-0.192488\pi$
$618$	0.0565153	−	0.645973i	0.00227338	−	0.0259848i
$619$	−2.45898	−	1.41969i	−0.0988346	−	0.0570622i	0.449768	−	0.893145i	$-0.351507\pi$
$619$	−2.45898	−	1.41969i	−0.0988346	−	0.0570622i	−0.548603	+	0.836083i	$0.684840\pi$
$620$		0			0
$621$	6.07455	−	16.6897i	0.243763	−	0.669734i
$622$	−12.1632	+	8.51675i	−0.487699	+	0.341490i
$623$	−16.3190	−	11.4267i	−0.653809	−	0.457802i
$624$	0.274735	+	0.754828i	0.0109982	+	0.0302173i
$625$		0			0
$626$		−	9.49036i		−	0.379311i
$627$	6.30004	−	5.37706i	0.251599	−	0.214739i
$628$	−1.27887	−	1.27887i	−0.0510326	−	0.0510326i
$629$	14.5054	+	12.1715i	0.578369	+	0.485309i
$630$		0			0
$631$	−7.67304	−	43.5160i	−0.305459	−	1.73234i	−0.621337	−	0.783543i	$-0.713410\pi$
$631$	−7.67304	−	43.5160i	−0.305459	−	1.73234i	0.315878	−	0.948800i	$-0.397701\pi$
$632$	−5.44400	−	7.77483i	−0.216550	−	0.309266i
$633$	−1.23768	−	2.65421i	−0.0491933	−	0.105495i
$634$	−15.2627	+	8.81195i	−0.606161	+	0.349967i
$635$		0			0
$636$	−5.00087	+	4.19623i	−0.198298	+	0.166391i
$637$	−14.2768	−	1.24906i	−0.565668	−	0.0494895i
$638$	40.6044	−	10.8799i	1.60754	−	0.430740i
$639$	−5.80474	−	10.0541i	−0.229632	−	0.397734i
$640$		0			0
$641$	7.66169	+	1.35096i	0.302618	+	0.0533598i	0.322896	−	0.946435i	$-0.395344\pi$
$641$	7.66169	+	1.35096i	0.302618	+	0.0533598i	−0.0202772	+	0.999794i	$0.506455\pi$
$642$	−4.97810	+	7.10946i	−0.196470	+	0.280588i
$643$	−3.56957	−	1.66452i	−0.140770	−	0.0656422i	0.350957	−	0.936392i	$-0.385856\pi$
$643$	−3.56957	−	1.66452i	−0.140770	−	0.0656422i	−0.491727	+	0.870749i	$0.663634\pi$
$644$	16.2758	−	19.3967i	0.641355	−	0.764337i
$645$		0			0
$646$	−20.1024	+	5.56757i	−0.790917	+	0.219053i
$647$	−33.5534	+	33.5534i	−1.31912	+	1.31912i	−0.404645	+	0.914474i	$0.632605\pi$
$647$	−33.5534	+	33.5534i	−1.31912	+	1.31912i	−0.914474	+	0.404645i	$0.867395\pi$
$648$	6.95769	−	0.608719i	0.273324	−	0.0239127i
$649$	−33.5894	+	12.2255i	−1.31850	+	0.479894i
$650$		0			0
$651$	−0.402434	+	2.28232i	−0.0157726	+	0.0894510i
$652$	−2.56922	+	1.19805i	−0.100618	+	0.0469191i
$653$	8.77240	−	32.7390i	0.343291	−	1.28118i	−0.551306	−	0.834303i	$-0.685870\pi$
$653$	8.77240	−	32.7390i	0.343291	−	1.28118i	0.894597	−	0.446875i	$-0.147463\pi$
$654$	−2.11093	+	3.65624i	−0.0825440	+	0.142970i
$655$		0			0
$656$	0.335990	+	0.400417i	0.0131182	+	0.0156337i
$657$	1.70542	+	6.36471i	0.0665347	+	0.248311i
$658$	0.535951	+	0.143608i	0.0208936	+	0.00559841i
$659$	−40.8074	−	14.8527i	−1.58963	−	0.578579i	−0.612362	−	0.790577i	$-0.709781\pi$
$659$	−40.8074	−	14.8527i	−1.58963	−	0.578579i	−0.977270	+	0.211999i	$0.932003\pi$
$660$		0			0
$661$	−6.30664	+	1.11203i	−0.245300	+	0.0432530i	−0.294946	−	0.955514i	$-0.595302\pi$
$661$	−6.30664	+	1.11203i	−0.245300	+	0.0432530i	0.0496463	+	0.998767i	$0.484191\pi$
$662$	−0.465442	+	0.998144i	−0.0180899	+	0.0387940i
$663$	0.335025	+	3.82936i	0.0130113	+	0.148720i
$664$	−9.13183			−0.354384
$665$		0			0
$666$	−10.9613			−0.424741
$667$	−5.93477	−	67.8347i	−0.229795	−	2.62657i
$668$	−8.77627	+	18.8208i	−0.339564	+	0.728197i
$669$	4.77206	−	0.841443i	0.184499	−	0.0325321i
$670$		0			0
$671$	−50.2996	−	18.3076i	−1.94180	−	0.706756i
$672$	−1.82629	−	0.489352i	−0.0704506	−	0.0188772i
$673$	10.1071	+	37.7202i	0.389600	+	1.45401i	0.830787	+	0.556591i	$0.187891\pi$
$673$	10.1071	+	37.7202i	0.389600	+	1.45401i	−0.441187	+	0.897415i	$0.645442\pi$
$674$	7.61617	+	9.07660i	0.293364	+	0.349618i
$675$		0			0
$676$	5.09632	−	8.82708i	0.196012	−	0.339503i
$677$	−2.91465	+	10.8776i	−0.112019	+	0.418061i	−0.999047	−	0.0436556i	$-0.986100\pi$
$677$	−2.91465	+	10.8776i	−0.112019	+	0.418061i	0.887028	+	0.461716i	$0.152766\pi$
$678$	−2.10098	+	0.979702i	−0.0806876	+	0.0376252i
$679$	2.19132	−	12.4276i	0.0840952	−	0.476927i
$680$		0			0
$681$	−10.0843	+	3.67040i	−0.386432	+	0.140650i
$682$	4.83979	−	0.423426i	0.185325	−	0.0162138i
$683$	27.6455	−	27.6455i	1.05782	−	1.05782i	0.0596018	−	0.998222i	$-0.481017\pi$
$683$	27.6455	−	27.6455i	1.05782	−	1.05782i	0.998222	−	0.0596018i	$-0.0189831\pi$
$684$	6.84263	−	9.94889i	0.261634	−	0.380405i
$685$		0			0
$686$	3.93785	−	4.69294i	0.150348	−	0.179177i
$687$	−6.09943	−	2.84421i	−0.232708	−	0.108513i
$688$	−0.136504	+	0.194948i	−0.00520417	+	0.00743232i
$689$	−22.4688	−	3.96185i	−0.855993	−	0.150935i
$690$		0			0
$691$	8.59049	+	14.8792i	0.326798	+	0.566030i	0.981875	−	0.189532i	$-0.0606971\pi$
$691$	8.59049	+	14.8792i	0.326798	+	0.566030i	−0.655077	+	0.755562i	$0.727364\pi$
$692$	5.27985	−	1.41473i	0.200710	−	0.0537800i
$693$	−43.1365	−	3.77395i	−1.63862	−	0.143361i
$694$	−5.26904	+	4.42125i	−0.200010	+	0.167828i
$695$		0			0
$696$	−4.40341	+	2.54231i	−0.166911	+	0.0963661i
$697$	1.05713	+	2.26701i	0.0400415	+	0.0858692i
$698$	−7.06983	−	10.0968i	−0.267597	−	0.382168i
$699$	−1.62067	−	9.19126i	−0.0612993	−	0.347645i
$700$		0			0
$701$	−20.7726	−	17.4302i	−0.784568	−	0.658331i	0.159826	−	0.987145i	$-0.448907\pi$
$701$	−20.7726	−	17.4302i	−0.784568	−	0.658331i	−0.944395	+	0.328814i	$0.893351\pi$
$702$	−3.27744	−	3.27744i	−0.123699	−	0.123699i
$703$	−10.9754	+	13.3051i	−0.413947	+	0.501812i
$704$			3.96354i			0.149381i
$705$		0			0
$706$	−3.97961	−	10.9339i	−0.149775	−	0.411502i
$707$	9.68939	+	6.78458i	0.364407	+	0.255161i
$708$	3.54169	−	2.47992i	0.133105	−	0.0932011i
$709$	−7.35112	+	20.1970i	−0.276077	+	0.758515i	0.721721	+	0.692184i	$0.243351\pi$
$709$	−7.35112	+	20.1970i	−0.276077	+	0.758515i	−0.997798	+	0.0663308i	$0.978871\pi$
$710$		0			0
$711$	22.7699	+	13.1462i	0.853940	+	0.493022i
$712$	0.440265	−	5.03225i	0.0164996	−	0.188591i
$713$	0.685893	−	7.83980i	0.0256869	−	0.293603i
$714$	−7.83566	−	4.52392i	−0.293242	−	0.169303i
$715$		0			0
$716$	−0.339091	+	0.931645i	−0.0126724	+	0.0348172i
$717$	1.66104	−	1.16307i	0.0620327	−	0.0434358i
$718$	2.30896	+	1.61675i	0.0861694	+	0.0603365i
$719$	16.1748	+	44.4400i	0.603220	+	1.65733i	0.744705	+	0.667393i	$0.232590\pi$
$719$	16.1748	+	44.4400i	0.603220	+	1.65733i	−0.141485	+	0.989940i	$0.545188\pi$
$720$		0			0
$721$			5.33420i			0.198656i
$722$	−5.22478	−	18.2675i	−0.194446	−	0.679846i
$723$	3.79779	+	3.79779i	0.141241	+	0.141241i
$724$	11.6309	+	9.75951i	0.432260	+	0.362709i
$725$		0			0
$726$	−0.392075	−	2.22357i	−0.0145513	−	0.0825244i
$727$	−17.9595	−	25.6488i	−0.666079	−	0.951260i	−0.999963	−	0.00864549i	$-0.997248\pi$
$727$	−17.9595	−	25.6488i	−0.666079	−	0.951260i	0.333883	−	0.942614i	$-0.391641\pi$
$728$	−2.79261	−	5.98877i	−0.103501	−	0.221958i
$729$	−13.3099	+	7.68445i	−0.492957	+	0.284609i
$730$		0			0
$731$	−0.872424	+	0.732051i	−0.0322678	+	0.0270759i
$732$	6.44990	+	0.564293i	0.238395	+	0.0208569i
$733$	−7.77769	+	2.08403i	−0.287276	+	0.0769753i	−0.399579	−	0.916699i	$-0.630844\pi$
$733$	−7.77769	+	2.08403i	−0.287276	+	0.0769753i	0.112304	+	0.993674i	$0.464177\pi$
$734$	−7.28586	−	12.6195i	−0.268926	−	0.465793i
$735$		0			0
$736$	6.32285	+	1.11489i	0.233063	+	0.0410954i
$737$	−12.1935	+	17.4142i	−0.449155	+	0.641460i
$738$	−1.31232	−	0.611944i	−0.0483071	−	0.0225260i
$739$	15.9026	−	18.9519i	0.584986	−	0.697159i	−0.389648	−	0.920964i	$-0.627403\pi$
$739$	15.9026	−	18.9519i	0.584986	−	0.697159i	0.974634	+	0.223805i	$0.0718479\pi$
$740$		0			0
$741$	−3.48537	+	0.334415i	−0.128038	+	0.0122851i
$742$	37.9731	−	37.9731i	1.39404	−	1.39404i
$743$	−32.3885	+	2.83363i	−1.18822	+	0.103956i	−0.664070	−	0.747671i	$-0.731172\pi$
$743$	−32.3885	+	2.83363i	−1.18822	+	0.103956i	−0.524149	+	0.851626i	$0.675617\pi$
$744$	−0.552202	+	0.200985i	−0.0202447	+	0.00736847i
$745$		0			0
$746$	−3.99504	+	22.6570i	−0.146269	+	0.829531i
$747$	22.9265	−	10.6908i	0.838838	−	0.391157i
$748$	−4.90906	+	18.3209i	−0.179493	+	0.669877i
$749$	35.6978	−	61.8304i	1.30437	−	2.25924i
$750$		0			0
$751$	9.17626	+	10.9358i	0.334846	+	0.399054i	0.907026	−	0.421074i	$-0.138347\pi$
$751$	9.17626	+	10.9358i	0.334846	+	0.399054i	−0.572180	+	0.820128i	$0.693902\pi$
$752$	0.0364137	+	0.135898i	0.00132787	+	0.00495569i
$753$	4.59229	+	1.23050i	0.167352	+	0.0448419i
$754$	−16.6986	−	6.07781i	−0.608129	−	0.221341i
$755$		0			0
$756$	10.7440	−	1.89445i	0.390754	−	0.0689005i
$757$	13.5657	−	29.0917i	0.493052	−	1.05735i	−0.489609	−	0.871942i	$-0.662860\pi$
$757$	13.5657	−	29.0917i	0.493052	−	1.05735i	0.982661	−	0.185412i	$-0.0593619\pi$
$758$	0.624476	+	7.13779i	0.0226820	+	0.259256i
$759$	−12.1999			−0.442829
$760$		0			0
$761$	−24.3195			−0.881583			−0.440791	−	0.897610i	$-0.645302\pi$
$761$	−24.3195			−0.881583			−0.440791	+	0.897610i	$0.645302\pi$
$762$	−0.489645	−	5.59667i	−0.0177380	−	0.202746i
$763$	14.6775	−	31.4760i	0.531361	−	1.13951i
$764$	1.13024	−	0.199291i	0.0408905	−	0.00721010i
$765$		0			0
$766$	−27.4083	−	9.97581i	−0.990303	−	0.360441i
$767$	14.5957	+	3.91092i	0.527022	+	0.141215i
$768$	−0.124082	−	0.463081i	−0.00447743	−	0.0167100i
$769$	−4.80085	−	5.72143i	−0.173123	−	0.206320i	0.672505	−	0.740092i	$-0.265218\pi$
$769$	−4.80085	−	5.72143i	−0.173123	−	0.206320i	−0.845628	+	0.533773i	$0.820774\pi$
$770$		0			0
$771$	−1.28673	+	2.22868i	−0.0463403	+	0.0802638i
$772$	2.12983	−	7.94862i	0.0766541	−	0.286077i
$773$	18.7537	−	8.74499i	0.674523	−	0.314535i	−0.0550050	−	0.998486i	$-0.517517\pi$
$773$	18.7537	−	8.74499i	0.674523	−	0.314535i	0.729528	+	0.683951i	$0.239740\pi$
$774$	0.114480	−	0.649248i	0.00411490	−	0.0233367i
$775$		0			0
$776$	3.00683	−	1.09440i	0.107939	−	0.0392866i
$777$	−7.45292	+	0.652046i	−0.267372	+	0.0233920i
$778$	−14.7659	+	14.7659i	−0.529383	+	0.529383i
$779$	−2.05681	+	0.980195i	−0.0736928	+	0.0351191i
$780$		0			0
$781$	−10.6772	+	12.7246i	−0.382061	+	0.455323i
$782$	27.8456	+	12.9846i	0.995757	+	0.464329i
$783$	16.8282	−	24.0332i	0.601391	−	0.858876i
$784$	8.42344	+	1.48528i	0.300837	+	0.0530457i
$785$		0			0
$786$	3.67462	+	6.36464i	0.131070	+	0.227019i
$787$	14.3373	−	3.84167i	0.511070	−	0.136941i	0.00593723	−	0.999982i	$-0.498110\pi$
$787$	14.3373	−	3.84167i	0.511070	−	0.136941i	0.505133	+	0.863042i	$0.331443\pi$
$788$	−0.811574	−	0.0710035i	−0.0289111	−	0.00252940i
$789$	0.0693333	−	0.0581775i	0.00246833	−	0.00207118i
$790$		0			0
$791$	16.5149	−	9.53488i	0.587202	−	0.339021i
$792$	−4.64019	−	9.95093i	−0.164882	−	0.353591i
$793$	12.9789	+	18.5357i	0.460893	+	0.658223i
$794$	−4.99441	−	28.3247i	−0.177245	−	1.00521i
$795$		0			0
$796$	9.59653	+	8.05244i	0.340140	+	0.285411i
$797$	−7.78312	−	7.78312i	−0.275692	−	0.275692i	0.555694	−	0.831387i	$-0.312452\pi$
$797$	−7.78312	−	7.78312i	−0.275692	−	0.275692i	−0.831387	+	0.555694i	$0.812452\pi$
$798$	4.06069	−	7.17160i	0.143747	−	0.253872i
$799$			0.673269i			0.0238185i
$800$		0			0
$801$	4.78602	+	13.1495i	0.169106	+	0.464614i
$802$	4.83289	+	3.38403i	0.170655	+	0.119494i
$803$	7.72285	−	5.40760i	0.272533	−	0.190830i
$804$	0.879469	−	2.41632i	0.0310165	−	0.0852171i
$805$		0			0
$806$	−1.77860	−	1.02688i	−0.0626486	−	0.0361702i
$807$	−1.00507	+	11.4880i	−0.0353801	+	0.404397i
$808$	−0.261406	+	2.98788i	−0.00919623	+	0.105113i
$809$	−32.3031	−	18.6502i	−1.13572	−	0.655706i	−0.190350	−	0.981716i	$-0.560962\pi$
$809$	−32.3031	−	18.6502i	−1.13572	−	0.655706i	−0.945366	+	0.326010i	$0.894296\pi$
$810$		0			0
$811$	−10.0655	+	27.6547i	−0.353447	+	0.971086i	0.627808	+	0.778368i	$0.283952\pi$
$811$	−10.0655	+	27.6547i	−0.353447	+	0.971086i	−0.981254	+	0.192718i	$0.938270\pi$
$812$	34.2628	−	23.9911i	1.20239	−	0.841922i
$813$	−6.96673	−	4.87816i	−0.244334	−	0.171085i
$814$	5.36403	+	14.7376i	0.188009	+	0.516551i
$815$		0			0
$816$		−	2.29421i		−	0.0803132i
$817$	−0.673448	−	0.789045i	−0.0235610	−	0.0276052i
$818$	−25.6310	−	25.6310i	−0.896166	−	0.896166i
$819$	14.0223	+	11.7661i	0.489980	+	0.411142i
$820$		0			0
$821$	−2.73280	−	15.4985i	−0.0953754	−	0.540901i	−0.994632	−	0.103479i	$-0.967003\pi$
$821$	−2.73280	−	15.4985i	−0.0953754	−	0.540901i	0.899256	−	0.437422i	$-0.144108\pi$
$822$	−1.29622	−	1.85119i	−0.0452109	−	0.0645678i
$823$	−2.13952	−	4.58822i	−0.0745790	−	0.159935i	0.865483	−	0.500938i	$-0.167011\pi$
$823$	−2.13952	−	4.58822i	−0.0745790	−	0.159935i	−0.940062	+	0.341002i	$0.889234\pi$
$824$	−1.17135	+	0.676281i	−0.0408060	+	0.0235594i
$825$		0			0
$826$	−27.2458	+	22.8619i	−0.948003	+	0.795469i
$827$	−26.4080	−	2.31040i	−0.918296	−	0.0803405i	−0.381801	−	0.924244i	$-0.624696\pi$
$827$	−26.4080	−	2.31040i	−0.918296	−	0.0803405i	−0.536494	+	0.843904i	$0.680252\pi$
$828$	−17.1795	+	4.60323i	−0.597028	+	0.159973i
$829$	−19.4289	−	33.6518i	−0.674792	−	1.16877i	−0.976530	−	0.215384i	$-0.930900\pi$
$829$	−19.4289	−	33.6518i	−0.674792	−	1.16877i	0.301737	−	0.953391i	$-0.402433\pi$
$830$		0			0
$831$	5.81287	+	1.02497i	0.201646	+	0.0355557i
$832$	0.961038	−	1.37250i	0.0333180	−	0.0475830i
$833$	37.0965	+	17.2984i	1.28532	+	0.599354i
$834$	−5.39895	+	6.43422i	−0.186950	+	0.222799i
$835$		0			0
$836$	−16.7249	−	4.33138i	−0.578443	−	0.149804i
$837$	2.39764	−	2.39764i	0.0828747	−	0.0828747i
$838$	−31.5347	+	2.75893i	−1.08935	+	0.0953057i
$839$	12.3410	−	4.49176i	0.426059	−	0.155073i	−0.120086	−	0.992764i	$-0.538317\pi$
$839$	12.3410	−	4.49176i	0.426059	−	0.155073i	0.546145	+	0.837691i	$0.316095\pi$
$840$		0			0
$841$	14.4969	−	82.2160i	0.499893	−	2.83504i
$842$	−21.6271	+	10.0849i	−0.745319	+	0.347548i
$843$	2.16218	−	8.06937i	0.0744695	−	0.277924i
$844$	−3.05433	+	5.29026i	−0.105134	+	0.182098i
$845$		0			0
$846$	−0.250519	−	0.298557i	−0.00861304	−	0.0102646i
$847$	4.80723	+	17.9408i	0.165178	+	0.616454i
$848$	13.1529	+	3.52432i	0.451674	+	0.121026i
$849$	−4.03096	−	1.46715i	−0.138342	−	0.0503524i
$850$		0			0
$851$	25.0190	−	4.41152i	0.857640	−	0.151225i
$852$	0.849120	−	1.82094i	0.0290904	−	0.0623845i
$853$	0.609875	+	6.97090i	0.0208817	+	0.238679i	0.999462	+	0.0328115i	$0.0104461\pi$
$853$	0.609875	+	6.97090i	0.0208817	+	0.238679i	−0.978580	+	0.205868i	$0.933998\pi$
$854$	−53.2609			−1.82255
$855$		0			0
$856$	18.1034			0.618760
$857$	1.56786	+	17.9208i	0.0535572	+	0.612162i	0.974786	+	0.223141i	$0.0716310\pi$
$857$	1.56786	+	17.9208i	0.0535572	+	0.612162i	−0.921229	+	0.389021i	$0.872813\pi$
$858$	−1.34553	+	2.88550i	−0.0459356	+	0.0985092i
$859$	−12.9961	+	2.29156i	−0.443421	+	0.0781871i	−0.390901	−	0.920433i	$-0.627836\pi$
$859$	−12.9961	+	2.29156i	−0.443421	+	0.0781871i	−0.0525201	+	0.998620i	$0.516725\pi$
$860$		0			0
$861$	−0.928688	−	0.338015i	−0.0316496	−	0.0115195i
$862$	−17.9942	−	4.82152i	−0.612884	−	0.164222i
$863$	9.97309	+	37.2201i	0.339488	+	1.26699i	0.898921	+	0.438110i	$0.144352\pi$
$863$	9.97309	+	37.2201i	0.339488	+	1.26699i	−0.559433	+	0.828875i	$0.688981\pi$
$864$	1.77815	+	2.11912i	0.0604939	+	0.0720938i
$865$		0			0
$866$	−14.8654	+	25.7477i	−0.505148	+	0.874942i
$867$	0.732106	−	2.73226i	0.0248636	−	0.0927923i
$868$	4.38114	−	2.04296i	0.148706	−	0.0693426i
$869$	6.53250	−	37.0477i	0.221600	−	1.25676i
$870$		0			0
$871$	8.44483	−	3.07367i	0.286142	−	0.104147i
$872$	8.77275	−	0.767516i	0.297083	−	0.0259914i
$873$	−6.26777	+	6.26777i	−0.212132	+	0.212132i
$874$	−11.6141	+	25.4621i	−0.392854	+	0.861269i
$875$		0			0
$876$	−0.733011	+	0.873568i	−0.0247661	+	0.0295151i
$877$	36.6890	+	17.1084i	1.23890	+	0.577709i	0.927945	−	0.372716i	$-0.121574\pi$
$877$	36.6890	+	17.1084i	1.23890	+	0.577709i	0.310955	+	0.950425i	$0.399351\pi$
$878$	−18.1143	+	25.8699i	−0.611327	+	0.873066i
$879$	−6.60430	−	1.16452i	−0.222757	−	0.0392781i
$880$		0			0
$881$	9.76683	+	16.9166i	0.329053	+	0.569936i	0.982324	−	0.187188i	$-0.0599372\pi$
$881$	9.76683	+	16.9166i	0.329053	+	0.569936i	−0.653271	+	0.757124i	$0.726604\pi$
$882$	−22.8869	+	6.13252i	−0.770641	+	0.206493i
$883$	−28.9626	−	2.53390i	−0.974668	−	0.0852724i	−0.411319	−	0.911491i	$-0.634932\pi$
$883$	−28.9626	−	2.53390i	−0.974668	−	0.0852724i	−0.563349	+	0.826219i	$0.690487\pi$
$884$	6.14218	−	5.15390i	0.206584	−	0.173344i
$885$		0			0
$886$	9.10907	−	5.25912i	0.306025	−	0.176684i
$887$	−3.50708	−	7.52096i	−0.117756	−	0.252529i	0.838591	−	0.544761i	$-0.183380\pi$
$887$	−3.50708	−	7.52096i	−0.117756	−	0.252529i	−0.956347	+	0.292232i	$0.905602\pi$
$888$	−1.08808	−	1.55394i	−0.0365136	−	0.0521468i
$889$	8.02519	+	45.5131i	0.269156	+	1.52646i
$890$		0			0
$891$	21.2059	+	17.7939i	0.710426	+	0.596118i
$892$	−7.14705	−	7.14705i	−0.239301	−	0.239301i
$893$	−0.613240	+	0.00514461i	−0.0205213	+	0.000172158i
$894$		−	7.33051i		−	0.245169i
$895$		0			0
$896$	1.34885	+	3.70594i	0.0450620	+	0.123807i
$897$	4.22462	+	2.95811i	0.141056	+	0.0987685i
$898$	−16.1018	+	11.2746i	−0.537324	+	0.376238i
$899$	4.44628	−	12.2161i	0.148292	−	0.407428i
$900$		0			0
$901$	56.4325	+	32.5813i	1.88004	+	1.08544i
$902$	−0.180567	+	2.06389i	−0.00601222	+	0.0687199i
$903$	0.0392171	−	0.448254i	0.00130506	−	0.0149169i
$904$	4.18758	+	2.41770i	0.139277	+	0.0804116i
$905$		0			0
$906$	0.918991	−	2.52491i	0.0305314	−	0.0838844i
$907$	−28.6255	+	20.0438i	−0.950494	+	0.665543i	−0.942423	−	0.334425i	$-0.891458\pi$
$907$	−28.6255	+	20.0438i	−0.950494	+	0.665543i	−0.00807113	+	0.999967i	$0.502569\pi$
$908$	18.3363	+	12.8392i	0.608513	+	0.426085i
$909$	−2.84169	−	7.80747i	−0.0942528	−	0.258957i
$910$		0			0
$911$			38.3017i			1.26899i	0.772926	+	0.634497i	$0.218793\pi$
$911$			38.3017i			1.26899i	−0.772926	+	0.634497i	$0.781207\pi$
$912$	2.08965	−	0.0175306i	0.0691954	−	0.000580496i
$913$	−25.5933	−	25.5933i	−0.847014	−	0.847014i
$914$	26.6925	+	22.3977i	0.882910	+	0.740849i
$915$		0			0
$916$	2.43765	+	13.8246i	0.0805421	+	0.456777i
$917$	−34.6764	−	49.5230i	−1.14512	−	1.63539i
$918$	5.59459	+	11.9976i	0.184649	+	0.395981i
$919$	−46.8387	+	27.0424i	−1.54507	+	0.892045i	−0.546560	+	0.837420i	$0.684063\pi$
$919$	−46.8387	+	27.0424i	−1.54507	+	0.892045i	−0.998507	+	0.0546250i	$0.982604\pi$
$920$		0			0
$921$	3.14131	−	2.63587i	0.103510	−	0.0868549i
$922$	12.4594	+	1.09006i	0.410328	+	0.0358991i
$923$	6.78267	−	1.81741i	0.223254	−	0.0598208i
$924$	−3.74695	−	6.48991i	−0.123266	−	0.213502i
$925$		0			0
$926$	0.877221	+	0.154678i	0.0288273	+	0.00508302i
$927$	2.14908	−	3.06921i	0.0705851	−	0.100806i
$928$	9.61218	+	4.48223i	0.315535	+	0.147136i
$929$	13.3972	−	15.9662i	0.439548	−	0.523833i	−0.500104	−	0.865965i	$-0.666705\pi$
$929$	13.3972	−	15.9662i	0.439548	−	0.523833i	0.939652	+	0.342133i	$0.111149\pi$
$930$		0			0
$931$	−15.4726	+	33.9212i	−0.507094	+	1.11172i
$932$	−13.7656	+	13.7656i	−0.450908	+	0.450908i
$933$	7.09152	−	0.620428i	0.232166	−	0.0203119i
$934$	19.9514	−	7.26171i	0.652829	−	0.237610i
$935$		0			0
$936$	−0.805980	+	4.57094i	−0.0263443	+	0.149406i
$937$	−21.5664	+	10.0566i	−0.704543	+	0.328534i	−0.741659	−	0.670777i	$-0.765961\pi$
$937$	−21.5664	+	10.0566i	−0.704543	+	0.328534i	0.0371158	+	0.999311i	$0.488183\pi$
$938$	−5.47475	+	20.4321i	−0.178757	+	0.667130i
$939$	−2.27492	+	3.94027i	−0.0742391	+	0.128586i
$940$		0			0
$941$	−38.9456	−	46.4136i	−1.26959	−	1.51304i	−0.755221	−	0.655471i	$-0.772470\pi$
$941$	−38.9456	−	46.4136i	−1.26959	−	1.51304i	−0.514370	−	0.857568i	$-0.671974\pi$
$942$	0.224415	+	0.837527i	0.00731182	+	0.0272881i
$943$	3.24164	+	0.868594i	0.105562	+	0.0282853i
$944$	−8.47460	−	3.08450i	−0.275825	−	0.100392i
$945$		0			0
$946$	−0.928942	+	0.163798i	−0.0302025	+	0.00532552i
$947$	−0.763983	+	1.63837i	−0.0248261	+	0.0532398i	−0.918330	−	0.395816i	$-0.870462\pi$
$947$	−0.763983	+	1.63837i	−0.0248261	+	0.0532398i	0.893504	+	0.449056i	$0.148240\pi$
$948$	0.396584	+	4.53298i	0.0128805	+	0.147224i
$949$	−3.98547			−0.129374
$950$		0			0
$951$	8.44918			0.273984
$952$	1.64486	+	18.8008i	0.0533101	+	0.609337i
$953$	5.11590	−	10.9711i	0.165720	−	0.355388i	−0.805857	−	0.592110i	$-0.798295\pi$
$953$	5.11590	−	10.9711i	0.165720	−	0.355388i	0.971578	+	0.236722i	$0.0760729\pi$
$954$	−37.1480	+	6.55019i	−1.20271	+	0.212070i
$955$		0			0
$956$	−3.97456	−	1.44662i	−0.128546	−	0.0467871i
$957$	−19.4664	−	5.21601i	−0.629259	−	0.168610i
$958$	−2.65311	−	9.90154i	−0.0857181	−	0.319904i
$959$	11.9496	+	14.2410i	0.385874	+	0.459866i
$960$		0			0
$961$	−14.7488	+	25.5456i	−0.475767	+	0.824053i
$962$	1.71594	−	6.40398i	0.0553241	−	0.206472i
$963$	−45.4506	+	21.1940i	−1.46463	+	0.682966i
$964$	1.94538	−	11.0328i	0.0626563	−	0.355342i
$965$		0			0
$966$	−11.4070	+	4.15182i	−0.367015	+	0.133583i
$967$	−36.0478	+	3.15378i	−1.15922	+	0.101419i	−0.650495	−	0.759511i	$-0.725438\pi$
$967$	−36.0478	+	3.15378i	−1.15922	+	0.101419i	−0.508725	+	0.860929i	$0.669883\pi$
$968$	−3.33021	+	3.33021i	−0.107037	+	0.107037i
$969$	9.68083	+	2.50712i	0.310993	+	0.0805403i
$970$		0			0
$971$	−28.7356	+	34.2457i	−0.922168	+	1.09900i	0.0726529	+	0.997357i	$0.476853\pi$
$971$	−28.7356	+	34.2457i	−0.922168	+	1.09900i	−0.994821	+	0.101640i	$0.967591\pi$
$972$	−10.5560	−	4.92236i	−0.338585	−	0.157885i
$973$	39.6308	−	56.5986i	1.27050	−	1.81447i
$974$	3.36990	+	0.594205i	0.107979	+	0.0190395i
$975$		0			0
$976$	−6.75252	−	11.6957i	−0.216143	−	0.374371i
$977$	10.4561	−	2.80171i	0.334521	−	0.0896346i	−0.0876488	−	0.996151i	$-0.527935\pi$
$977$	10.4561	−	2.80171i	0.334521	−	0.0896346i	0.422170	+	0.906517i	$0.361269\pi$
$978$	1.35389	+	0.118450i	0.0432925	+	0.00378760i
$979$	15.3375	−	12.8697i	0.490189	−	0.411317i
$980$		0			0
$981$	−21.1265	+	12.1974i	−0.674516	+	0.389432i
$982$	8.03696	+	17.2353i	0.256470	+	0.550001i
$983$	4.84263	+	6.91599i	0.154456	+	0.220586i	0.888921	−	0.458061i	$-0.151456\pi$
$983$	4.84263	+	6.91599i	0.154456	+	0.220586i	−0.734465	+	0.678646i	$0.762567\pi$
$984$	−0.0435153	−	0.246788i	−0.00138722	−	0.00786730i
$985$		0			0
$986$	38.8794	+	32.6237i	1.23817	+	1.03895i
$987$	−0.188096	−	0.188096i	−0.00598716	−	0.00598716i
$988$	4.74131	+	5.55516i	0.150841	+	0.176733i
$989$			1.52797i			0.0485867i
$990$		0			0
$991$	11.0139	+	30.2605i	0.349869	+	0.961258i	0.982411	+	0.186732i	$0.0597895\pi$
$991$	11.0139	+	30.2605i	0.349869	+	0.961258i	−0.632542	+	0.774526i	$0.717988\pi$
$992$	1.00407	+	0.703057i	0.0318792	+	0.0223221i
$993$	0.432509	−	0.302846i	0.0137253	−	0.00961053i
$994$	−5.65291	+	15.5312i	−0.179299	+	0.492621i
$995$		0			0
$996$	3.79142	+	2.18898i	0.120136	+	0.0693603i
$997$	4.18037	−	47.7818i	0.132394	−	1.51327i	−0.581808	−	0.813326i	$-0.697654\pi$
$997$	4.18037	−	47.7818i	0.132394	−	1.51327i	0.714202	−	0.699940i	$-0.246790\pi$
$998$	1.65655	−	18.9345i	0.0524373	−	0.599361i
$999$	9.47956	+	5.47303i	0.299920	+	0.173159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.193.8		120
5.2	odd	4	inner	950.2.bb.e.307.3		120
5.3	odd	4		190.2.r.a.117.8	yes	120
5.4	even	2		190.2.r.a.3.3	✓	120
19.13	odd	18	inner	950.2.bb.e.393.3		120
95.13	even	36		190.2.r.a.127.3	yes	120
95.32	even	36	inner	950.2.bb.e.507.8		120
95.89	odd	18		190.2.r.a.13.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.3.3	✓	120	5.4	even	2
190.2.r.a.13.8	yes	120	95.89	odd	18
190.2.r.a.117.8	yes	120	5.3	odd	4
190.2.r.a.127.3	yes	120	95.13	even	36
950.2.bb.e.193.8		120	1.1	even	1	trivial
950.2.bb.e.307.3		120	5.2	odd	4	inner
950.2.bb.e.393.3		120	19.13	odd	18	inner
950.2.bb.e.507.8		120	95.32	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.202610 - 0.434499i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.450504 + 0.163970i) q^{6} +(-3.80940 - 1.02072i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.78062 + 2.12207i) q^{9} +O(q^{10})\)	\(q+(0.0871557 + 0.996195i) q^{2} +(0.202610 - 0.434499i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(0.450504 + 0.163970i) q^{6} +(-3.80940 - 1.02072i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(1.78062 + 2.12207i) q^{9} +(1.98177 - 3.43252i) q^{11} +(-0.124082 + 0.463081i) q^{12} +(-1.51854 + 0.708105i) q^{13} +(0.684830 - 3.88386i) q^{14} +(0.939693 - 0.342020i) q^{16} +(4.76720 - 0.417076i) q^{17} +(-1.95880 + 1.95880i) q^{18} +(0.416317 + 4.33897i) q^{19} +(-1.21533 + 1.44837i) q^{21} +(3.59218 + 1.67506i) q^{22} +(3.68259 - 5.25928i) q^{23} +(-0.472133 - 0.0832498i) q^{24} +(-0.837759 - 1.45104i) q^{26} +(2.67205 - 0.715973i) q^{27} +(3.92877 + 0.343723i) q^{28} +(8.12456 - 6.81732i) q^{29} +(1.06152 - 0.612871i) q^{31} +(0.422618 + 0.906308i) q^{32} +(-1.08990 - 1.55654i) q^{33} +(0.830978 + 4.71271i) q^{34} +(-2.12207 - 1.78062i) q^{36} +(2.79796 + 2.79796i) q^{37} +(-4.28618 + 0.792899i) q^{38} +0.803271i q^{39} +(0.178777 + 0.491185i) q^{41} +(-1.54878 - 1.08447i) q^{42} +(-0.194948 + 0.136504i) q^{43} +(-1.35561 + 3.72451i) q^{44} +(5.56022 + 3.21020i) q^{46} +(-0.0122621 + 0.140157i) q^{47} +(0.0417839 - 0.477592i) q^{48} +(7.40745 + 4.27669i) q^{49} +(0.784664 - 2.15585i) q^{51} +(1.37250 - 0.961038i) q^{52} +(11.1543 + 7.81035i) q^{53} +(0.946133 + 2.59948i) q^{54} +3.94378i q^{56} +(1.96963 + 0.698230i) q^{57} +(7.49948 + 7.49948i) q^{58} +(-6.90856 - 5.79697i) q^{59} +(-2.34513 - 13.2999i) q^{61} +(0.703057 + 1.00407i) q^{62} +(-4.61706 - 9.90132i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(1.45563 - 1.22141i) q^{66} +(-5.34318 - 0.467468i) q^{67} +(-4.62235 + 1.23856i) q^{68} +(-1.53902 - 2.66566i) q^{69} +(-4.12724 - 0.727743i) q^{71} +(1.58890 - 2.26918i) q^{72} +(2.15579 + 1.00526i) q^{73} +(-2.54346 + 3.03117i) q^{74} +(-1.16345 - 4.20076i) q^{76} +(-11.0530 + 11.0530i) q^{77} +(-0.800214 + 0.0700097i) q^{78} +(8.91892 - 3.24622i) q^{79} +(-1.21281 + 6.87816i) q^{81} +(-0.473734 + 0.220906i) q^{82} +(2.36349 - 8.82067i) q^{83} +(0.945356 - 1.63740i) q^{84} +(-0.152975 - 0.182309i) q^{86} +(-1.31600 - 4.91137i) q^{87} +(-3.82848 - 1.02584i) q^{88} +(4.74683 + 1.72770i) q^{89} +(6.50748 - 1.14745i) q^{91} +(-2.71337 + 5.81885i) q^{92} +(-0.0512163 - 0.585405i) q^{93} -0.140692 q^{94} +0.479416 q^{96} +(0.278881 + 3.18763i) q^{97} +(-3.61482 + 7.75200i) q^{98} +(10.8128 - 1.90659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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