LMFDB - Embedded newform 363.3.h.q.245.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-4,18,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.2
Character	$\chi$	$=$	363.245
Dual form			363.3.h.q.323.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69141 - 2.32802i) q^{2} +(2.68453 + 1.33914i) q^{3} +(-1.32276 + 4.07105i) q^{4} +(2.90829 - 4.00292i) q^{5} +(-1.42308 - 8.51468i) q^{6} +(-3.45484 + 10.6329i) q^{7} +(0.767802 - 0.249474i) q^{8} +(5.41340 + 7.18993i) q^{9} -14.2380 q^{10} +(-9.00271 + 9.15748i) q^{12} +(13.6720 - 9.93330i) q^{13} +(30.5972 - 9.94163i) q^{14} +(13.1679 - 6.85133i) q^{15} +(11.9727 + 8.69868i) q^{16} +(0.0367864 - 0.0506321i) q^{17} +(7.58207 - 24.7636i) q^{18} +(1.66282 + 5.11764i) q^{19} +(12.4491 + 17.1347i) q^{20} +(-23.5136 + 23.9178i) q^{21} +8.69537i q^{23} +(2.39527 + 0.358475i) q^{24} +(0.160235 + 0.493153i) q^{25} +(-46.2499 - 15.0275i) q^{26} +(4.90408 + 26.5509i) q^{27} +(-38.7171 - 28.1296i) q^{28} +(47.5106 + 15.4371i) q^{29} +(-38.2223 - 19.0667i) q^{30} +(19.8827 - 14.4457i) q^{31} -45.8150i q^{32} -0.180094 q^{34} +(32.5149 + 44.7530i) q^{35} +(-36.4312 + 12.5276i) q^{36} +(-12.1319 + 37.3382i) q^{37} +(9.10148 - 12.5271i) q^{38} +(50.0050 - 8.35747i) q^{39} +(1.23437 - 3.79899i) q^{40} +(41.7596 - 13.5685i) q^{41} +(95.4523 + 14.2854i) q^{42} +0.201842 q^{43} +(44.5244 - 0.758975i) q^{45} +(20.2430 - 14.7074i) q^{46} +(-14.1766 + 4.60627i) q^{47} +(20.4923 + 39.3850i) q^{48} +(-61.4808 - 44.6684i) q^{49} +(0.877048 - 1.20715i) q^{50} +(0.166558 - 0.0866612i) q^{51} +(22.3541 + 68.7988i) q^{52} +(-57.5690 - 79.2369i) q^{53} +(53.5163 - 56.3252i) q^{54} +9.02585i q^{56} +(-2.38935 + 15.9652i) q^{57} +(-44.4218 - 136.716i) q^{58} +(13.7827 + 4.47826i) q^{59} +(10.4741 + 62.6697i) q^{60} +(-23.7229 - 17.2357i) q^{61} +(-67.2596 - 21.8540i) q^{62} +(-95.1523 + 32.7201i) q^{63} +(-58.7676 + 42.6972i) q^{64} -83.6168i q^{65} +82.8515 q^{67} +(0.157466 + 0.216733i) q^{68} +(-11.6443 + 23.3430i) q^{69} +(49.1899 - 151.391i) q^{70} +(-15.6972 + 21.6053i) q^{71} +(5.95012 + 4.16994i) q^{72} +(4.31706 - 13.2865i) q^{73} +(107.444 - 34.9108i) q^{74} +(-0.230246 + 1.53846i) q^{75} -23.0337 q^{76} +(-104.035 - 102.277i) q^{78} +(-40.6025 + 29.4994i) q^{79} +(69.6402 - 22.6275i) q^{80} +(-22.3903 + 77.8439i) q^{81} +(-102.220 - 74.2674i) q^{82} +(35.4092 - 48.7366i) q^{83} +(-66.2676 - 127.362i) q^{84} +(-0.0956907 - 0.294506i) q^{85} +(-0.341398 - 0.469894i) q^{86} +(106.871 + 105.065i) q^{87} -40.3489i q^{89} +(-77.0758 - 102.370i) q^{90} +(58.3852 + 179.691i) q^{91} +(-35.3993 - 11.5019i) q^{92} +(72.7206 - 12.1540i) q^{93} +(34.7020 + 25.2125i) q^{94} +(25.3215 + 8.22744i) q^{95} +(61.3528 - 122.992i) q^{96} +(24.9281 - 18.1114i) q^{97} +218.681i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.69141	−	2.32802i	−0.845704	−	1.16401i	−0.984793	−	0.173732i	$-0.944417\pi$
$2$	−1.69141	−	2.32802i	−0.845704	−	1.16401i	0.139089	−	0.990280i	$-0.455583\pi$
$3$	2.68453	+	1.33914i	0.894843	+	0.446381i
$3$	2.68453	+	1.33914i	0.894843	+	0.446381i
$4$	−1.32276	+	4.07105i	−0.330691	+	1.01776i
$5$	2.90829	−	4.00292i	0.581658	−	0.800583i	−0.412218	−	0.911085i	$-0.635246\pi$
$5$	2.90829	−	4.00292i	0.581658	−	0.800583i	0.993876	+	0.110502i	$0.0352459\pi$
$6$	−1.42308	−	8.51468i	−0.237180	−	1.41911i
$7$	−3.45484	+	10.6329i	−0.493548	+	1.51899i	0.325658	+	0.945488i	$0.394414\pi$
$7$	−3.45484	+	10.6329i	−0.493548	+	1.51899i	−0.819207	+	0.573498i	$0.805586\pi$
$8$	0.767802	−	0.249474i	0.0959752	−	0.0311842i
$9$	5.41340	+	7.18993i	0.601489	+	0.798881i
$10$	−14.2380			−1.42380
$11$		0			0
$11$		0			0
$12$	−9.00271	+	9.15748i	−0.750226	+	0.763123i
$13$	13.6720	−	9.93330i	1.05169	−	0.764100i	0.0791598	−	0.996862i	$-0.474776\pi$
$13$	13.6720	−	9.93330i	1.05169	−	0.764100i	0.972534	+	0.232762i	$0.0747763\pi$
$14$	30.5972	−	9.94163i	2.18551	−	0.710116i
$15$	13.1679	−	6.85133i	0.877857	−	0.456756i
$16$	11.9727	+	8.69868i	0.748294	+	0.543668i
$17$	0.0367864	−	0.0506321i	0.00216391	−	0.00297836i	−0.807934	−	0.589273i	$-0.799414\pi$
$17$	0.0367864	−	0.0506321i	0.00216391	−	0.00297836i	0.810098	+	0.586295i	$0.199414\pi$
$18$	7.58207	−	24.7636i	0.421226	−	1.37576i
$19$	1.66282	+	5.11764i	0.0875170	+	0.269350i	0.985231	−	0.171228i	$-0.0547735\pi$
$19$	1.66282	+	5.11764i	0.0875170	+	0.269350i	−0.897714	+	0.440578i	$0.854774\pi$
$20$	12.4491	+	17.1347i	0.622454	+	0.856734i
$21$	−23.5136	+	23.9178i	−1.11969	+	1.13894i
$22$		0			0
$23$			8.69537i			0.378060i	0.981971	+	0.189030i	$0.0605343\pi$
$23$			8.69537i			0.378060i	−0.981971	+	0.189030i	$0.939466\pi$
$24$	2.39527	+	0.358475i	0.0998028	+	0.0149365i
$25$	0.160235	+	0.493153i	0.00640940	+	0.0197261i
$26$	−46.2499	−	15.0275i	−1.77884	−	0.577981i
$27$	4.90408	+	26.5509i	0.181633	+	0.983366i
$28$	−38.7171	−	28.1296i	−1.38275	−	1.00463i
$29$	47.5106	+	15.4371i	1.63830	+	0.532315i	0.976157	−	0.217066i	$-0.0696488\pi$
$29$	47.5106	+	15.4371i	1.63830	+	0.532315i	0.662139	+	0.749381i	$0.269649\pi$
$30$	−38.2223	−	19.0667i	−1.27408	−	0.635556i
$31$	19.8827	−	14.4457i	0.641379	−	0.465989i	−0.218945	−	0.975737i	$-0.570261\pi$
$31$	19.8827	−	14.4457i	0.641379	−	0.465989i	0.860324	+	0.509748i	$0.170261\pi$
$32$		−	45.8150i		−	1.43172i
$33$		0			0
$34$	−0.180094			−0.00529687
$35$	32.5149	+	44.7530i	0.928998	+	1.27866i
$36$	−36.4312	+	12.5276i	−1.01198	+	0.347989i
$37$	−12.1319	+	37.3382i	−0.327890	+	1.00914i	0.642229	+	0.766512i	$0.278010\pi$
$37$	−12.1319	+	37.3382i	−0.327890	+	1.00914i	−0.970119	+	0.242629i	$0.921990\pi$
$38$	9.10148	−	12.5271i	0.239513	−	0.329661i
$39$	50.0050	−	8.35747i	1.28218	−	0.214294i
$40$	1.23437	−	3.79899i	0.0308591	−	0.0949747i
$41$	41.7596	−	13.5685i	1.01853	−	0.330940i	0.248282	−	0.968688i	$-0.420134\pi$
$41$	41.7596	−	13.5685i	1.01853	−	0.330940i	0.770245	+	0.637748i	$0.220134\pi$
$42$	95.4523	+	14.2854i	2.27267	+	0.340128i
$43$	0.201842			0.00469401			0.00234701	−	0.999997i	$-0.499253\pi$
$43$	0.201842			0.00469401			0.00234701	+	0.999997i	$0.499253\pi$
$44$		0			0
$45$	44.5244	−	0.758975i	0.989431	−	0.0168661i
$46$	20.2430	−	14.7074i	0.440066	−	0.319726i
$47$	−14.1766	+	4.60627i	−0.301631	+	0.0980058i	−0.455922	−	0.890020i	$-0.650691\pi$
$47$	−14.1766	+	4.60627i	−0.301631	+	0.0980058i	0.154291	+	0.988025i	$0.450691\pi$
$48$	20.4923	+	39.3850i	0.426923	+	0.820521i
$49$	−61.4808	−	44.6684i	−1.25471	−	0.911601i
$50$	0.877048	−	1.20715i	0.0175410	−	0.0241431i
$51$	0.166558	−	0.0866612i	0.00326584	−	0.00169924i
$52$	22.3541	+	68.7988i	0.429886	+	1.32305i
$53$	−57.5690	−	79.2369i	−1.08621	−	1.49504i	−0.852499	−	0.522729i	$-0.824914\pi$
$53$	−57.5690	−	79.2369i	−1.08621	−	1.49504i	−0.233709	−	0.972307i	$-0.575086\pi$
$54$	53.5163	−	56.3252i	0.991042	−	1.04306i
$55$		0			0
$56$			9.02585i			0.161176i
$57$	−2.38935	+	15.9652i	−0.0419185	+	0.280092i
$58$	−44.4218	−	136.716i	−0.765893	−	2.35718i
$59$	13.7827	+	4.47826i	0.233605	+	0.0759028i	0.423480	−	0.905905i	$-0.360808\pi$
$59$	13.7827	+	4.47826i	0.233605	+	0.0759028i	−0.189875	+	0.981808i	$0.560808\pi$
$60$	10.4741	+	62.6697i	0.174569	+	1.04449i
$61$	−23.7229	−	17.2357i	−0.388900	−	0.282552i	0.376105	−	0.926577i	$-0.377263\pi$
$61$	−23.7229	−	17.2357i	−0.388900	−	0.282552i	−0.765005	+	0.644025i	$0.777263\pi$
$62$	−67.2596	−	21.8540i	−1.08483	−	0.352484i
$63$	−95.1523	+	32.7201i	−1.51035	+	0.519366i
$64$	−58.7676	+	42.6972i	−0.918244	+	0.667143i
$65$		−	83.6168i		−	1.28641i
$66$		0			0
$67$	82.8515			1.23659			0.618294	−	0.785947i	$-0.287824\pi$
$67$	82.8515			1.23659			0.618294	+	0.785947i	$0.287824\pi$
$68$	0.157466	+	0.216733i	0.00231568	+	0.00318726i
$69$	−11.6443	+	23.3430i	−0.168758	+	0.338304i
$70$	49.1899	−	151.391i	0.702713	−	2.16273i
$71$	−15.6972	+	21.6053i	−0.221087	+	0.304301i	−0.905125	−	0.425147i	$-0.860223\pi$
$71$	−15.6972	+	21.6053i	−0.221087	+	0.304301i	0.684037	+	0.729447i	$0.260223\pi$
$72$	5.95012	+	4.16994i	0.0826405	+	0.0579158i
$73$	4.31706	−	13.2865i	0.0591378	−	0.182007i	−0.917124	−	0.398603i	$-0.869495\pi$
$73$	4.31706	−	13.2865i	0.0591378	−	0.182007i	0.976261	+	0.216595i	$0.0694952\pi$
$74$	107.444	−	34.9108i	1.45195	−	0.471767i
$75$	−0.230246	+	1.53846i	−0.00306995	+	0.0205128i
$76$	−23.0337			−0.303075
$77$		0			0
$78$	−104.035	−	102.277i	−1.33379	−	1.31124i
$79$	−40.6025	+	29.4994i	−0.513956	+	0.373411i	−0.814322	−	0.580413i	$-0.802891\pi$
$79$	−40.6025	+	29.4994i	−0.513956	+	0.373411i	0.300366	+	0.953824i	$0.402891\pi$
$80$	69.6402	−	22.6275i	0.870502	−	0.282843i
$81$	−22.3903	+	77.8439i	−0.276423	+	0.961036i
$82$	−102.220	−	74.2674i	−1.24659	−	0.905700i
$83$	35.4092	−	48.7366i	0.426617	−	0.587188i	−0.540556	−	0.841308i	$-0.681786\pi$
$83$	35.4092	−	48.7366i	0.426617	−	0.587188i	0.967173	+	0.254120i	$0.0817860\pi$
$84$	−66.2676	−	127.362i	−0.788901	−	1.51622i
$85$	−0.0956907	−	0.294506i	−0.00112577	−	0.00346477i
$86$	−0.341398	−	0.469894i	−0.00396974	−	0.00546388i
$87$	106.871	+	105.065i	1.22840	+	1.20764i
$88$		0			0
$89$		−	40.3489i		−	0.453359i	−0.973969	−	0.226679i	$-0.927213\pi$
$89$		−	40.3489i		−	0.453359i	0.973969	−	0.226679i	$-0.0727869\pi$
$90$	−77.0758	−	102.370i	−0.856398	−	1.13745i
$91$	58.3852	+	179.691i	0.641596	+	1.97463i
$92$	−35.3993	−	11.5019i	−0.384774	−	0.125021i
$93$	72.7206	−	12.1540i	0.781942	−	0.130688i
$94$	34.7020	+	25.2125i	0.369170	+	0.268218i
$95$	25.3215	+	8.22744i	0.266542	+	0.0866047i
$96$	61.3528	−	122.992i	0.639092	−	1.28116i
$97$	24.9281	−	18.1114i	0.256991	−	0.186715i	−0.451828	−	0.892105i	$-0.649228\pi$
$97$	24.9281	−	18.1114i	0.256991	−	0.186715i	0.708820	+	0.705390i	$0.249228\pi$
$98$			218.681i			2.23144i
$99$		0			0
$100$	−2.21960			−0.0221960
$101$	−30.5189	−	42.0057i	−0.302167	−	0.415898i	0.630751	−	0.775985i	$-0.282747\pi$
$101$	−30.5189	−	42.0057i	−0.302167	−	0.415898i	−0.932919	+	0.360087i	$0.882747\pi$
$102$	−0.483466	−	0.241171i	−0.00473987	−	0.00236442i
$103$	−15.8074	+	48.6501i	−0.153470	+	0.472331i	−0.998003	−	0.0631724i	$-0.979878\pi$
$103$	−15.8074	+	48.6501i	−0.153470	+	0.472331i	0.844533	+	0.535504i	$0.179878\pi$
$104$	8.01930	−	11.0376i	0.0771086	−	0.106131i
$105$	27.3567	+	163.683i	0.260540	+	1.55888i
$106$	−87.0927	+	268.044i	−0.821630	+	2.52872i
$107$	−65.0929	+	21.1500i	−0.608345	+	0.197663i	−0.596959	−	0.802272i	$-0.703624\pi$
$107$	−65.0929	+	21.1500i	−0.608345	+	0.197663i	−0.0113861	+	0.999935i	$0.503624\pi$
$108$	−114.577	−	15.1558i	−1.06090	−	0.140331i
$109$	−125.737			−1.15355			−0.576773	−	0.816904i	$-0.695688\pi$
$109$	−125.737			−1.15355			−0.576773	+	0.816904i	$0.695688\pi$
$110$		0			0
$111$	−82.5697	+	83.9892i	−0.743871	+	0.756659i
$112$	−133.856	+	97.2521i	−1.19514	+	0.868322i
$113$	−93.8997	+	30.5099i	−0.830971	+	0.269999i	−0.693454	−	0.720501i	$-0.743912\pi$
$113$	−93.8997	+	30.5099i	−0.830971	+	0.269999i	−0.137516	+	0.990499i	$0.543912\pi$
$114$	41.2088	−	21.4412i	0.361481	−	0.188081i
$115$	34.8068	+	25.2886i	0.302668	+	0.219901i
$116$	−125.691	+	172.998i	−1.08354	+	1.49136i
$117$	145.432	+	44.5280i	1.24301	+	0.380581i
$118$	−12.8866	−	39.6610i	−0.109209	−	0.336110i
$119$	0.411275	+	0.566072i	0.00345609	+	0.00475691i
$120$	8.40107	−	8.54550i	0.0700089	−	0.0712125i
$121$		0			0
$122$			84.3801i			0.691640i
$123$	130.275	+	19.4970i	1.05915	+	0.158512i
$124$	32.5088	+	100.052i	0.262168	+	0.806869i
$125$	120.083	+	39.0173i	0.960662	+	0.312138i
$126$	237.114	+	166.174i	1.88186	+	1.31884i
$127$	16.8672	+	12.2547i	0.132813	+	0.0964940i	0.652208	−	0.758040i	$-0.273843\pi$
$127$	16.8672	+	12.2547i	0.132813	+	0.0964940i	−0.519395	+	0.854534i	$0.673843\pi$
$128$	24.5092	+	7.96353i	0.191478	+	0.0622151i
$129$	0.541852	+	0.270296i	0.00420040	+	0.00209532i
$130$	−194.662	+	141.430i	−1.49740	+	1.08792i
$131$			29.0290i			0.221595i	0.993843	+	0.110798i	$0.0353405\pi$
$131$			29.0290i			0.221595i	−0.993843	+	0.110798i	$0.964659\pi$
$132$		0			0
$133$	−60.1602			−0.452332
$134$	−140.136	−	192.880i	−1.04579	−	1.43940i
$135$	120.543	+	57.5870i	0.892915	+	0.426570i
$136$	0.0156133	−	0.0480527i	0.000114803	−	0.000353328i
$137$	89.1732	−	122.736i	0.650899	−	0.895886i	−0.348238	−	0.937406i	$-0.613220\pi$
$137$	89.1732	−	122.736i	0.650899	−	0.895886i	0.999138	+	0.0415199i	$0.0132200\pi$
$138$	74.0383	−	12.3742i	0.536509	−	0.0896682i
$139$	−5.94013	+	18.2818i	−0.0427348	+	0.131524i	−0.970148	−	0.242515i	$-0.922028\pi$
$139$	−5.94013	+	18.2818i	−0.0427348	+	0.131524i	0.927413	+	0.374039i	$0.122028\pi$
$140$	−225.201	+	73.1722i	−1.60858	+	0.522659i
$141$	−44.2261	−	6.61887i	−0.313660	−	0.0469424i
$142$	76.8481			0.541184
$143$		0			0
$144$	2.27009	+	133.172i	0.0157645	+	0.924808i
$145$	199.968	−	145.285i	1.37909	−	1.00197i
$146$	−38.2333	+	12.4227i	−0.261872	+	0.0850873i
$147$	−105.230	−	202.245i	−0.715848	−	1.37582i
$148$	−135.958	−	98.7793i	−0.918635	−	0.667427i
$149$	−106.781	+	146.971i	−0.716651	+	0.986385i	0.282978	+	0.959127i	$0.408678\pi$
$149$	−106.781	+	146.971i	−0.716651	+	0.986385i	−0.999628	+	0.0272587i	$0.991322\pi$
$150$	3.97101	−	2.06615i	0.0264734	−	0.0137743i
$151$	43.3216	+	133.330i	0.286898	+	0.882982i	0.985823	+	0.167787i	$0.0536621\pi$
$151$	43.3216	+	133.330i	0.286898	+	0.882982i	−0.698925	+	0.715195i	$0.746338\pi$
$152$	2.55344	+	3.51451i	0.0167989	+	0.0231217i
$153$	0.563181	−	0.00960013i	0.00368092	−	6.27460e-5i
$154$		0			0
$155$		−	121.601i		−	0.784523i
$156$	−32.1212	+	214.628i	−0.205905	+	1.37582i
$157$	−55.5031	−	170.821i	−0.353523	−	1.08803i	−0.956861	−	0.290547i	$-0.906163\pi$
$157$	−55.5031	−	170.821i	−0.353523	−	1.08803i	0.603338	−	0.797486i	$-0.293837\pi$
$158$	137.351	+	44.6280i	0.869309	+	0.282456i
$159$	−48.4362	−	289.807i	−0.304630	−	1.82268i
$160$	−183.394	−	133.243i	−1.14621	−	0.832771i
$161$	−92.4570	−	30.0411i	−0.574267	−	0.186591i
$162$	219.094	−	79.5408i	1.35243	−	0.490992i
$163$	−179.001	+	130.052i	−1.09816	+	0.797863i	−0.980759	−	0.195222i	$-0.937457\pi$
$163$	−179.001	+	130.052i	−1.09816	+	0.797863i	−0.117404	+	0.993084i	$0.537457\pi$
$164$			187.953i			1.14606i
$165$		0			0
$166$	−173.351			−1.04428
$167$	108.399	+	149.198i	0.649095	+	0.893402i	0.999059	−	0.0433607i	$-0.0138065\pi$
$167$	108.399	+	149.198i	0.649095	+	0.893402i	−0.349965	+	0.936763i	$0.613806\pi$
$168$	−12.0869	+	24.2302i	−0.0719458	+	0.144227i
$169$	36.0297	−	110.888i	0.213193	−	0.656142i
$170$	−0.523764	+	0.720899i	−0.00308096	+	0.00424058i
$171$	−27.7940	+	39.6594i	−0.162538	+	0.231927i
$172$	−0.266990	+	0.821710i	−0.00155227	+	0.00477739i
$173$	−231.626	+	75.2598i	−1.33888	+	0.435028i	−0.888937	−	0.458030i	$-0.848555\pi$
$173$	−231.626	+	75.2598i	−1.33888	+	0.435028i	−0.449941	+	0.893058i	$0.648555\pi$
$174$	63.8308	−	426.506i	0.366844	−	2.45118i
$175$	−5.79723			−0.0331270
$176$		0			0
$177$	31.0030	+	30.4790i	0.175158	+	0.172198i
$178$	−93.9332	+	68.2465i	−0.527715	+	0.383407i
$179$	−301.127	+	97.8421i	−1.68227	+	0.546604i	−0.985350	−	0.170542i	$-0.945448\pi$
$179$	−301.127	+	97.8421i	−1.68227	+	0.546604i	−0.696923	+	0.717146i	$0.745448\pi$
$180$	−55.8054	+	182.265i	−0.310030	+	1.01258i
$181$	24.9975	+	18.1618i	0.138108	+	0.100341i	0.654694	−	0.755894i	$-0.272797\pi$
$181$	24.9975	+	18.1618i	0.138108	+	0.100341i	−0.516586	+	0.856235i	$0.672797\pi$
$182$	319.572	−	439.853i	1.75589	−	2.41678i
$183$	−40.6038	−	78.0381i	−0.221879	−	0.426438i
$184$	2.16927	+	6.67632i	0.0117895	+	0.0362843i
$185$	114.179	+	157.153i	0.617182	+	0.849478i
$186$	−151.295	−	148.738i	−0.813413	−	0.799666i
$187$		0			0
$188$		−	63.8068i		−	0.339398i
$189$	−299.256	−	39.5844i	−1.58336	−	0.209441i
$190$	−23.6752	−	72.8649i	−0.124607	−	0.383500i
$191$	−281.437	−	91.4445i	−1.47349	−	0.478767i	−0.541332	−	0.840809i	$-0.682080\pi$
$191$	−281.437	−	91.4445i	−1.47349	−	0.478767i	−0.932162	+	0.362042i	$0.882080\pi$
$192$	−214.941	+	35.9236i	−1.11948	+	0.187102i
$193$	64.3229	+	46.7333i	0.333279	+	0.242142i	0.741821	−	0.670598i	$-0.233962\pi$
$193$	64.3229	+	46.7333i	0.333279	+	0.242142i	−0.408541	+	0.912740i	$0.633962\pi$
$194$	−84.3273	−	27.3996i	−0.434677	−	0.141235i
$195$	111.975	−	224.472i	0.574230	−	1.15114i
$196$	263.172	−	191.206i	1.34271	−	0.975539i
$197$		−	360.331i		−	1.82909i	−0.404485	−	0.914544i	$-0.632549\pi$
$197$		−	360.331i		−	1.82909i	0.404485	−	0.914544i	$-0.367451\pi$
$198$		0			0
$199$	369.874			1.85866			0.929332	−	0.369245i	$-0.120384\pi$
$199$	369.874			1.85866			0.929332	+	0.369245i	$0.120384\pi$
$200$	0.246058	+	0.338669i	0.00123029	+	0.00169335i
$201$	222.417	+	110.950i	1.10655	+	0.551989i
$202$	−46.1703	+	142.097i	−0.228566	+	0.703453i
$203$	−328.283	+	451.843i	−1.61716	+	2.22583i
$204$	0.132485	+	0.792697i	0.000649438	+	0.00388577i
$205$	67.1353	−	206.621i	0.327489	−	1.00791i
$206$	139.995	−	45.4872i	0.679589	−	0.220812i
$207$	−62.5191	+	47.0715i	−0.302025	+	0.227398i
$208$	250.098			1.20239
$209$		0			0
$210$	334.786	−	340.541i	1.59422	−	1.62163i
$211$	125.195	−	90.9598i	0.593343	−	0.431089i	−0.250167	−	0.968203i	$-0.580485\pi$
$211$	125.195	−	90.9598i	0.593343	−	0.431089i	0.843510	+	0.537114i	$0.180485\pi$
$212$	398.727	−	129.554i	1.88079	−	0.611105i
$213$	−71.0722	+	36.9794i	−0.333672	+	0.173612i
$214$	159.336	+	115.765i	0.744562	+	0.540956i
$215$	0.587016	−	0.807958i	0.00273031	−	0.00375795i
$216$	10.3891	+	19.1624i	0.0480978	+	0.0887147i
$217$	84.9076	+	261.319i	0.391279	+	1.20423i
$218$	212.672	+	292.718i	0.975559	+	1.34274i
$219$	29.3818	−	29.8870i	0.134164	−	0.136470i
$220$		0			0
$221$		−	1.05765i		−	0.00478576i
$222$	335.188	+	50.1642i	1.50985	+	0.225965i
$223$	−110.417	−	339.829i	−0.495145	−	1.52390i	−0.816731	−	0.577018i	$-0.804216\pi$
$223$	−110.417	−	339.829i	−0.495145	−	1.52390i	0.321587	−	0.946880i	$-0.395784\pi$
$224$	487.147	+	158.284i	2.17476	+	0.706623i
$225$	−2.67832	+	3.82171i	−0.0119036	+	0.0169854i
$226$	229.850	+	166.996i	1.01704	+	0.738920i
$227$	−97.5400	−	31.6927i	−0.429692	−	0.139615i	0.0861831	−	0.996279i	$-0.472533\pi$
$227$	−97.5400	−	31.6927i	−0.429692	−	0.139615i	−0.515875	+	0.856664i	$0.672533\pi$
$228$	−61.8346	−	30.8454i	−0.271205	−	0.135287i
$229$	298.821	−	217.106i	1.30490	−	0.948063i	0.304906	−	0.952382i	$-0.401375\pi$
$229$	298.821	−	217.106i	1.30490	−	0.948063i	0.999991	+	0.00431926i	$0.00137487\pi$
$230$		−	123.804i		−	0.538280i
$231$		0			0
$232$	40.3299			0.173836
$233$	−10.1837	−	14.0166i	−0.0437067	−	0.0601571i	0.786604	−	0.617457i	$-0.211837\pi$
$233$	−10.1837	−	14.0166i	−0.0437067	−	0.0601571i	−0.830311	+	0.557300i	$0.811837\pi$
$234$	−142.322	−	413.884i	−0.608215	−	1.76873i
$235$	−22.7913	+	70.1443i	−0.0969841	+	0.298486i
$236$	−36.4624	+	50.1862i	−0.154502	+	0.212654i
$237$	−148.503	+	24.8196i	−0.626593	+	0.104724i
$238$	0.622194	−	1.91492i	0.00261426	−	0.00804587i
$239$	208.117	−	67.6212i	0.870781	−	0.282934i	0.160657	−	0.987010i	$-0.448639\pi$
$239$	208.117	−	67.6212i	0.870781	−	0.282934i	0.710124	+	0.704077i	$0.248639\pi$
$240$	217.253	+	32.5140i	0.905219	+	0.135475i
$241$	118.033			0.489765			0.244883	−	0.969553i	$-0.421251\pi$
$241$	118.033			0.489765			0.244883	+	0.969553i	$0.421251\pi$
$242$		0			0
$243$	−164.351	+	178.991i	−0.676343	+	0.736587i
$244$	101.547	−	73.7783i	0.416177	−	0.302370i
$245$	−357.608	+	116.194i	−1.45962	+	0.474261i
$246$	−174.959	−	336.261i	−0.711215	−	1.36691i
$247$	73.5693	+	53.4512i	0.297851	+	0.216402i
$248$	11.6622	−	16.0516i	0.0470249	−	0.0647243i
$249$	160.322	−	83.4169i	0.643865	−	0.335007i
$250$	−112.276	−	345.550i	−0.449103	−	1.38220i
$251$	−94.3753	−	129.896i	−0.375997	−	0.517516i	0.578521	−	0.815667i	$-0.303630\pi$
$251$	−94.3753	−	129.896i	−0.375997	−	0.517516i	−0.954519	+	0.298151i	$0.903630\pi$
$252$	−7.34098	−	430.650i	−0.0291309	−	1.70893i
$253$		0			0
$254$		−	59.9950i		−	0.236201i
$255$	0.137500	−	0.918752i	0.000539217	−	0.00360295i
$256$	66.8731	+	205.814i	0.261223	+	0.803962i
$257$	24.9007	+	8.09071i	0.0968897	+	0.0314814i	0.357061	−	0.934081i	$-0.383779\pi$
$257$	24.9007	+	8.09071i	0.0968897	+	0.0314814i	−0.260171	+	0.965563i	$0.583779\pi$
$258$	−0.287238	−	1.71862i	−0.00111333	−	0.00666134i
$259$	−355.100	−	257.995i	−1.37104	−	0.996120i
$260$	340.408	+	110.605i	1.30926	+	0.425405i
$261$	146.202	+	425.165i	0.560160	+	1.62899i
$262$	67.5801	−	49.0998i	0.257939	−	0.187404i
$263$			221.020i			0.840378i	0.907437	+	0.420189i	$0.138036\pi$
$263$			221.020i			0.840378i	−0.907437	+	0.420189i	$0.861964\pi$
$264$		0			0
$265$	−484.606			−1.82870
$266$	101.755	+	140.054i	0.382539	+	0.526520i
$267$	54.0329	−	108.318i	0.202370	−	0.405685i
$268$	−109.593	+	337.292i	−0.408929	+	1.25855i
$269$	73.7314	−	101.483i	0.274094	−	0.377259i	−0.649672	−	0.760214i	$-0.725094\pi$
$269$	73.7314	−	101.483i	0.274094	−	0.377259i	0.923767	+	0.382956i	$0.125094\pi$
$270$	−69.8242	−	378.031i	−0.258608	−	1.40012i
$271$	123.585	−	380.355i	0.456032	−	1.40352i	−0.413887	−	0.910328i	$-0.635829\pi$
$271$	123.585	−	380.355i	0.456032	−	1.40352i	0.869919	−	0.493195i	$-0.164171\pi$
$272$	0.880865	−	0.286211i	0.00323848	−	0.00105224i
$273$	−83.8952	+	560.572i	−0.307308	+	2.05338i
$274$	−436.561			−1.59329
$275$		0			0
$276$	−79.6276	−	78.2819i	−0.288506	−	0.283630i
$277$	−59.5551	+	43.2693i	−0.215000	+	0.156207i	−0.690073	−	0.723740i	$-0.742422\pi$
$277$	−59.5551	+	43.2693i	−0.215000	+	0.156207i	0.475073	+	0.879946i	$0.342422\pi$
$278$	52.6077	−	17.0933i	0.189236	−	0.0614866i
$279$	211.496	+	64.7555i	0.758052	+	0.232098i
$280$	36.1297	+	26.2498i	0.129035	+	0.0937492i
$281$	246.506	−	339.286i	0.877244	−	1.20742i	−0.0999321	−	0.994994i	$-0.531863\pi$
$281$	246.506	−	339.286i	0.877244	−	1.20742i	0.977176	−	0.212429i	$-0.0681374\pi$
$282$	59.3955	+	114.155i	0.210622	+	0.404803i
$283$	−81.9963	−	252.359i	−0.289739	−	0.891726i	−0.984938	−	0.172909i	$-0.944683\pi$
$283$	−81.9963	−	252.359i	−0.289739	−	0.891726i	0.695198	−	0.718818i	$-0.255317\pi$
$284$	−67.1927	−	92.4828i	−0.236594	−	0.325644i
$285$	56.9585	+	55.9959i	0.199854	+	0.196477i
$286$		0			0
$287$			490.903i			1.71046i
$288$	329.407	−	248.015i	1.14377	−	0.861163i
$289$	89.3047	+	274.852i	0.309013	+	0.951044i
$290$	−676.455	−	219.793i	−2.33260	−	0.757908i
$291$	91.1740	−	15.2381i	0.313313	−	0.0523648i
$292$	48.3797	+	35.1499i	0.165684	+	0.120376i
$293$	−181.199	−	58.8752i	−0.618427	−	0.200939i	−0.0169852	−	0.999856i	$-0.505407\pi$
$293$	−181.199	−	58.8752i	−0.618427	−	0.200939i	−0.601442	+	0.798917i	$0.705407\pi$
$294$	−292.845	+	587.057i	−0.996073	+	1.99679i
$295$	58.0101	−	42.1468i	0.196644	−	0.142871i
$296$			31.6949i			0.107078i
$297$		0			0
$298$	522.763			1.75424
$299$	86.3737	+	118.883i	0.288875	+	0.397603i
$300$	−5.95859	−	2.97236i	−0.0198620	−	0.00990787i
$301$	−0.697333	+	2.14617i	−0.00231672	+	0.00713014i
$302$	237.121	−	326.370i	0.785170	−	1.08069i
$303$	−25.6774	−	153.635i	−0.0847437	−	0.507045i
$304$	−24.6083	+	75.7365i	−0.0809482	+	0.249133i
$305$	−137.986	+	44.8344i	−0.452413	+	0.146998i
$306$	−0.974918	−	1.29486i	−0.00318601	−	0.00423157i
$307$	−285.254			−0.929166			−0.464583	−	0.885530i	$-0.653796\pi$
$307$	−285.254			−0.929166			−0.464583	+	0.885530i	$0.653796\pi$
$308$		0			0
$309$	−107.585	+	109.434i	−0.348171	+	0.354156i
$310$	−283.090	+	205.677i	−0.913194	+	0.663474i
$311$	480.177	−	156.019i	1.54398	−	0.501669i	0.591507	−	0.806300i	$-0.298533\pi$
$311$	480.177	−	156.019i	1.54398	−	0.501669i	0.952470	+	0.304631i	$0.0985333\pi$
$312$	36.3090	−	18.8918i	0.116375	−	0.0605507i
$313$	−64.8592	−	47.1229i	−0.207218	−	0.150553i	0.479336	−	0.877631i	$-0.340877\pi$
$313$	−64.8592	−	47.1229i	−0.207218	−	0.150553i	−0.686554	+	0.727079i	$0.740877\pi$
$314$	−303.797	+	418.141i	−0.967507	+	1.33166i
$315$	−145.755	+	476.046i	−0.462713	+	1.51126i
$316$	−66.3861	−	204.315i	−0.210083	−	0.646568i
$317$	5.08824	+	7.00336i	0.0160512	+	0.0220926i	0.816967	−	0.576684i	$-0.195654\pi$
$317$	5.08824	+	7.00336i	0.0160512	+	0.0220926i	−0.800916	+	0.598777i	$0.795654\pi$
$318$	−592.752	+	602.942i	−1.86400	+	1.89604i
$319$		0			0
$320$			359.417i			1.12318i
$321$	−203.067	−	30.3909i	−0.632606	−	0.0946758i
$322$	86.4461	+	266.054i	0.268466	+	0.826254i
$323$	0.320286	+	0.104067i	0.000991599	+	0.000322190i
$324$	−287.289	−	194.121i	−0.886695	−	0.599138i
$325$	7.08937	+	5.15073i	0.0218135	+	0.0158484i
$326$	605.526	+	196.747i	1.85744	+	0.603520i
$327$	−337.544	−	168.379i	−1.03224	−	0.514921i
$328$	28.6781	−	20.8359i	0.0874333	−	0.0635240i
$329$		−	166.653i		−	0.506544i
$330$		0			0
$331$	28.2554			0.0853638			0.0426819	−	0.999089i	$-0.486410\pi$
$331$	28.2554			0.0853638			0.0426819	+	0.999089i	$0.486410\pi$
$332$	151.571	+	208.619i	0.456539	+	0.628372i
$333$	−334.134	+	114.899i	−1.00341	+	0.345042i
$334$	163.990	−	504.710i	0.490989	−	1.51111i
$335$	240.956	−	331.647i	0.719271	−	0.989992i
$336$	−489.575	+	81.8239i	−1.45707	+	0.243523i
$337$	−89.1584	+	274.401i	−0.264565	+	0.814247i	0.727228	+	0.686396i	$0.240808\pi$
$337$	−89.1584	+	274.401i	−0.264565	+	0.814247i	−0.991793	+	0.127851i	$0.959192\pi$
$338$	−319.091	+	103.679i	−0.944055	+	0.306742i
$339$	−292.933	−	43.8404i	−0.864111	−	0.129323i
$340$	1.32552			0.00389859
$341$		0			0
$342$	139.339	−	2.37521i	0.407424	−	0.00694506i
$343$	244.162	−	177.394i	0.711843	−	0.517184i
$344$	0.154975	−	0.0503544i	0.000450509	−	0.000146379i
$345$	59.5749	+	114.499i	0.172681	+	0.331882i
$346$	566.980	+	411.935i	1.63867	+	1.19056i
$347$	−154.947	+	213.267i	−0.446534	+	0.614602i	−0.971648	−	0.236430i	$-0.924023\pi$
$347$	−154.947	+	213.267i	−0.446534	+	0.614602i	0.525114	+	0.851032i	$0.324023\pi$
$348$	−569.089	+	296.101i	−1.63531	+	0.850865i
$349$	−150.777	−	464.043i	−0.432025	−	1.32964i	−0.896105	−	0.443842i	$-0.853615\pi$
$349$	−150.777	−	464.043i	−0.432025	−	1.32964i	0.464080	−	0.885793i	$-0.346385\pi$
$350$	9.80548	+	13.4961i	0.0280157	+	0.0385603i
$351$	330.787	+	314.291i	0.942412	+	0.895415i
$352$		0			0
$353$		−	437.345i		−	1.23894i	−0.785021	−	0.619469i	$-0.787348\pi$
$353$		−	437.345i		−	1.23894i	0.785021	−	0.619469i	$-0.212652\pi$
$354$	18.5171	−	123.728i	0.0523083	−	0.349514i
$355$	40.8324	+	125.669i	0.115021	+	0.353997i
$356$	164.262	+	53.3721i	0.461411	+	0.149922i
$357$	0.346030	+	2.07039i	0.000969272	+	0.00579942i
$358$	737.107	+	535.540i	2.05896	+	1.49592i
$359$	−233.007	−	75.7087i	−0.649046	−	0.210888i	−0.0340525	−	0.999420i	$-0.510841\pi$
$359$	−233.007	−	75.7087i	−0.649046	−	0.210888i	−0.614993	+	0.788532i	$0.710841\pi$
$360$	33.9966	−	11.6904i	0.0944349	−	0.0324734i
$361$	268.630	−	195.171i	0.744127	−	0.540640i
$362$		−	88.9137i		−	0.245618i
$363$		0			0
$364$	−808.761			−2.22187
$365$	−40.6296	−	55.9219i	−0.111314	−	0.153211i
$366$	−112.997	+	226.521i	−0.308735	+	0.618909i
$367$	69.5602	−	214.084i	0.189537	−	0.583336i	−0.810460	−	0.585795i	$-0.800783\pi$
$367$	69.5602	−	214.084i	0.189537	−	0.583336i	0.999997	+	0.00245833i	$0.000782511\pi$
$368$	−75.6383	+	104.107i	−0.205539	+	0.282900i
$369$	323.618	+	226.797i	0.877014	+	0.614626i
$370$	172.734	−	531.621i	0.466849	−	1.43681i
$371$	1041.41	−	338.375i	2.80703	−	0.912061i
$372$	−46.7127	+	312.126i	−0.125572	+	0.839048i
$373$	−283.156			−0.759131			−0.379566	−	0.925165i	$-0.623927\pi$
$373$	−283.156			−0.759131			−0.379566	+	0.925165i	$0.623927\pi$
$374$		0			0
$375$	270.116	+	265.551i	0.720310	+	0.708136i
$376$	−9.73571	+	7.07341i	−0.0258928	+	0.0188123i
$377$	802.907	−	260.880i	2.12973	−	0.691990i
$378$	414.010	+	763.628i	1.09527	+	2.02018i
$379$	369.384	+	268.373i	0.974627	+	0.708108i	0.956501	−	0.291727i	$-0.0942300\pi$
$379$	369.384	+	268.373i	0.974627	+	0.708108i	0.0181260	+	0.999836i	$0.494230\pi$
$380$	−66.9886	+	92.2019i	−0.176286	+	0.242637i
$381$	28.8697	+	55.4858i	0.0757734	+	0.145632i
$382$	263.140	+	809.863i	0.688849	+	2.12006i
$383$	−188.834	−	259.908i	−0.493040	−	0.678611i	0.487905	−	0.872897i	$-0.337761\pi$
$383$	−188.834	−	259.908i	−0.493040	−	0.678611i	−0.980945	+	0.194285i	$0.937761\pi$
$384$	55.1314	+	54.1997i	0.143571	+	0.141145i
$385$		0			0
$386$		−	228.790i		−	0.592721i
$387$	1.09265	+	1.45123i	0.00282339	+	0.00374996i
$388$	40.7581	+	125.441i	0.105047	+	0.323301i
$389$	−299.994	−	97.4741i	−0.771194	−	0.250576i	−0.103118	−	0.994669i	$-0.532882\pi$
$389$	−299.994	−	97.4741i	−0.771194	−	0.250576i	−0.668076	+	0.744093i	$0.732882\pi$
$390$	−711.971	+	118.993i	−1.82557	+	0.305111i
$391$	0.440265	+	0.319871i	0.00112600	+	0.000818085i
$392$	−58.3487	−	18.9586i	−0.148849	−	0.0483639i
$393$	−38.8739	+	77.9291i	−0.0989157	+	0.198293i
$394$	−838.858	+	609.466i	−2.12908	+	1.54687i
$395$			248.321i			0.628661i
$396$		0			0
$397$	−338.199			−0.851885			−0.425943	−	0.904750i	$-0.640057\pi$
$397$	−338.199			−0.851885			−0.425943	+	0.904750i	$0.640057\pi$
$398$	−625.608	−	861.076i	−1.57188	−	2.16351i
$399$	−161.502	−	80.5630i	−0.404766	−	0.201912i
$400$	−2.37133	+	7.29821i	−0.00592833	+	0.0182455i
$401$	−212.161	+	292.015i	−0.529080	+	0.728216i	−0.986990	−	0.160782i	$-0.948598\pi$
$401$	−212.161	+	292.015i	−0.529080	+	0.728216i	0.457910	+	0.888999i	$0.348598\pi$
$402$	−117.904	−	705.454i	−0.293294	−	1.75486i
$403$	128.344	−	395.002i	0.318472	−	0.980155i
$404$	211.376	−	68.6803i	0.523209	−	0.170001i
$405$	246.485	+	316.019i	0.608606	+	0.780293i
$406$	1607.16			3.95852
$407$		0			0
$408$	0.106264	−	0.108090i	0.000260450	−	0.000264928i
$409$	−356.891	+	259.297i	−0.872595	+	0.633978i	−0.931282	−	0.364299i	$-0.881309\pi$
$409$	−356.891	+	259.297i	−0.872595	+	0.633978i	0.0586868	+	0.998276i	$0.481309\pi$
$410$	−594.572	+	193.188i	−1.45018	+	0.471191i
$411$	403.750	−	210.074i	0.982359	−	0.511129i
$412$	−177.147	−	128.705i	−0.429970	−	0.312391i
$413$	−95.2338	+	131.078i	−0.230590	+	0.317380i
$414$	215.329	+	65.9289i	0.520118	+	0.159248i
$415$	−92.1083	−	283.480i	−0.221948	−	0.683085i
$416$	−455.094	−	626.384i	−1.09398	−	1.50573i
$417$	−40.4284	+	41.1235i	−0.0969507	+	0.0986174i
$418$		0			0
$419$		−	393.180i		−	0.938377i	−0.883098	−	0.469188i	$-0.844547\pi$
$419$		−	393.180i		−	0.938377i	0.883098	−	0.469188i	$-0.155453\pi$
$420$	−702.547	−	105.143i	−1.67273	−	0.250341i
$421$	−217.358	−	668.959i	−0.516289	−	1.58898i	−0.780924	−	0.624627i	$-0.785251\pi$
$421$	−217.358	−	668.959i	−0.516289	−	1.58898i	0.264634	−	0.964349i	$-0.414749\pi$
$422$	−423.513	−	137.608i	−1.00359	−	0.326085i
$423$	−109.863	−	76.9936i	−0.259722	−	0.182018i
$424$	−63.9691	−	46.4763i	−0.150871	−	0.109614i
$425$	0.0308638	+	0.0100283i	7.26208e−5	+	2.35959e-5i
$426$	206.301	+	102.911i	0.484275	+	0.241574i
$427$	265.224	−	192.697i	0.621134	−	0.451280i
$428$		−	292.973i		−	0.684515i
$429$		0			0
$430$	−2.87383			−0.00668332
$431$	−88.9050	−	122.367i	−0.206276	−	0.283915i	0.693327	−	0.720623i	$-0.256144\pi$
$431$	−88.9050	−	122.367i	−0.206276	−	0.283915i	−0.899603	+	0.436708i	$0.856144\pi$
$432$	−172.243	+	360.545i	−0.398710	+	0.834595i
$433$	−145.735	+	448.525i	−0.336569	+	1.03585i	0.629375	+	0.777102i	$0.283311\pi$
$433$	−145.735	+	448.525i	−0.336569	+	1.03585i	−0.965944	+	0.258752i	$0.916689\pi$
$434$	464.742	−	639.663i	1.07084	−	1.47388i
$435$	731.377	−	122.237i	1.68133	−	0.281005i
$436$	166.320	−	511.880i	0.381467	−	1.17404i
$437$	−44.4998	+	14.4589i	−0.101830	+	0.0330866i
$438$	−119.274	−	17.8506i	−0.272316	−	0.0407547i
$439$	506.417			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$439$	506.417			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$440$		0			0
$441$	−11.6571	−	683.851i	−0.0264334	−	1.55068i
$442$	−2.46224	+	1.78892i	−0.00557068	+	0.00404734i
$443$	−607.289	+	197.320i	−1.37086	+	0.445418i	−0.899652	−	0.436607i	$-0.856180\pi$
$443$	−607.289	+	197.320i	−1.37086	+	0.445418i	−0.471203	+	0.882025i	$0.656180\pi$
$444$	−232.704	−	447.243i	−0.524108	−	1.00730i
$445$	−161.513	−	117.346i	−0.362951	−	0.263699i
$446$	−604.370	+	831.844i	−1.35509	+	1.86512i
$447$	−483.472	+	251.554i	−1.08159	+	0.562761i
$448$	−250.962	−	772.382i	−0.560183	−	1.72407i
$449$	−194.835	−	268.168i	−0.433931	−	0.597255i	0.534919	−	0.844904i	$-0.320342\pi$
$449$	−194.835	−	268.168i	−0.433931	−	0.597255i	−0.968850	+	0.247648i	$0.920342\pi$
$450$	13.4272	−	0.228883i	0.0298381	−	0.000508629i
$451$		0			0
$452$		−	422.627i		−	0.935016i
$453$	−62.2500	+	415.943i	−0.137417	+	0.918196i
$454$	91.1986	+	280.681i	0.200878	+	0.618239i
$455$	889.089	+	288.883i	1.95404	+	0.634907i
$456$	2.14836	+	12.8542i	0.00471131	+	0.0281891i
$457$	69.5244	+	50.5125i	0.152132	+	0.110531i	0.661248	−	0.750168i	$-0.270027\pi$
$457$	69.5244	+	50.5125i	0.152132	+	0.110531i	−0.509115	+	0.860698i	$0.670027\pi$
$458$	−1010.86	−	328.448i	−2.20711	−	0.717134i
$459$	1.52473	+	0.728407i	0.00332186	+	0.00158694i
$460$	−148.992	+	108.249i	−0.323897	+	0.235325i
$461$		−	65.3245i		−	0.141702i	−0.997487	−	0.0708508i	$-0.977429\pi$
$461$		−	65.3245i		−	0.141702i	0.997487	−	0.0708508i	$-0.0225714\pi$
$462$		0			0
$463$	535.374			1.15632			0.578158	−	0.815925i	$-0.303772\pi$
$463$	535.374			1.15632			0.578158	+	0.815925i	$0.303772\pi$
$464$	434.548	+	598.104i	0.936525	+	1.28902i
$465$	162.841	−	326.442i	0.350196	−	0.702025i
$466$	−15.4063	+	47.4156i	−0.0330607	+	0.101750i
$467$	−292.723	+	402.899i	−0.626817	+	0.862739i	−0.997827	−	0.0658897i	$-0.979011\pi$
$467$	−292.723	+	402.899i	−0.626817	+	0.862739i	0.371010	+	0.928629i	$0.379011\pi$
$468$	−373.647	+	533.160i	−0.798392	+	1.13923i
$469$	−286.238	+	880.951i	−0.610317	+	1.87836i
$470$	201.847	−	65.5840i	0.429461	−	0.139540i
$471$	79.7539	−	532.901i	0.169329	−	1.13142i
$472$	11.6996			0.0247872
$473$		0			0
$474$	308.959	+	303.737i	0.651812	+	0.640796i
$475$	−2.25734	+	1.64005i	−0.00475229	+	0.00345274i
$476$	−2.84852	+	0.925542i	−0.00598430	+	0.00194442i
$477$	258.064	−	842.858i	0.541015	−	1.76700i
$478$	−509.434	−	370.125i	−1.06576	−	0.774321i
$479$	510.599	−	702.779i	1.06597	−	1.46718i	0.191875	−	0.981419i	$-0.438543\pi$
$479$	510.599	−	702.779i	1.06597	−	1.46718i	0.874093	−	0.485759i	$-0.161457\pi$
$480$	−313.894	−	603.286i	−0.653946	−	1.25685i
$481$	205.024	+	630.999i	0.426245	+	1.31185i
$482$	−199.643	−	274.784i	−0.414196	−	0.570092i
$483$	−207.974	−	204.459i	−0.430588	−	0.423311i
$484$		0			0
$485$		−	152.458i		−	0.314347i
$486$	694.679	+	79.8678i	1.42938	+	0.164337i
$487$	74.5091	+	229.315i	0.152996	+	0.470873i	0.997952	−	0.0639620i	$-0.0203736\pi$
$487$	74.5091	+	229.315i	0.152996	+	0.470873i	−0.844956	+	0.534835i	$0.820374\pi$
$488$	−22.5143	−	7.31535i	−0.0461359	−	0.0149905i
$489$	−654.690	+	109.420i	−1.33883	+	0.223763i
$490$	875.363	+	635.988i	1.78645	+	1.29794i
$491$	475.575	+	154.524i	0.968585	+	0.314712i	0.750245	−	0.661160i	$-0.229936\pi$
$491$	475.575	+	154.524i	0.968585	+	0.314712i	0.218340	+	0.975873i	$0.429936\pi$
$492$	−251.696	+	504.566i	−0.511577	+	1.02554i
$493$	2.52936	−	1.83769i	0.00513054	−	0.00372756i
$494$		−	261.679i		−	0.529714i
$495$		0			0
$496$	363.708			0.733283
$497$	−175.496	−	241.550i	−0.353111	−	0.486016i
$498$	−465.367	−	232.142i	−0.934471	−	0.466149i
$499$	−171.447	+	527.660i	−0.343582	+	1.05744i	0.618757	+	0.785582i	$0.287637\pi$
$499$	−171.447	+	527.660i	−0.343582	+	1.05744i	−0.962339	+	0.271853i	$0.912363\pi$
$500$	−317.682	+	437.252i	−0.635364	+	0.874504i
$501$	91.2023	+	545.688i	0.182040	+	1.08920i
$502$	−142.775	+	439.416i	−0.284412	+	0.875330i
$503$	−639.571	+	207.809i	−1.27151	+	0.413140i	−0.865583	−	0.500765i	$-0.833052\pi$
$503$	−639.571	+	207.809i	−1.27151	+	0.413140i	−0.405929	+	0.913904i	$0.633052\pi$
$504$	−64.8953	+	48.8605i	−0.128760	+	0.0969455i
$505$	−256.903			−0.508719
$506$		0			0
$507$	245.217	−	249.433i	0.483664	−	0.491979i
$508$	−72.2010	+	52.4571i	−0.142128	+	0.103262i
$509$	612.141	−	198.897i	1.20264	−	0.390760i	0.361906	−	0.932215i	$-0.382126\pi$
$509$	612.141	−	198.897i	1.20264	−	0.390760i	0.840730	+	0.541455i	$0.182126\pi$
$510$	−2.37145	+	1.23388i	−0.00464989	+	0.00241937i
$511$	126.360	+	91.8057i	0.247279	+	0.179659i
$512$	426.621	−	587.193i	0.833243	−	1.14686i
$513$	−127.723	+	69.2468i	−0.248974	+	0.134984i
$514$	−23.2818	−	71.6540i	−0.0452953	−	0.139405i
$515$	148.770	+	204.764i	0.288874	+	0.397600i
$516$	−1.81713	+	1.84837i	−0.00352157	+	0.00358211i
$517$		0			0
$518$			1263.06i			2.43833i
$519$	−722.590	−	108.143i	−1.39227	−	0.208368i
$520$	−20.8602	−	64.2011i	−0.0401158	−	0.123464i
$521$	−507.873	−	165.018i	−0.974803	−	0.316733i	−0.222050	−	0.975035i	$-0.571275\pi$
$521$	−507.873	−	165.018i	−0.974803	−	0.316733i	−0.752753	+	0.658303i	$0.771275\pi$
$522$	742.508	−	1059.49i	1.42243	−	2.02967i
$523$	−805.063	−	584.913i	−1.53932	−	1.11838i	−0.950761	−	0.309924i	$-0.899696\pi$
$523$	−805.063	−	584.913i	−1.53932	−	1.11838i	−0.588557	−	0.808456i	$-0.700304\pi$
$524$	−118.178	−	38.3984i	−0.225531	−	0.0732794i
$525$	−15.5628	−	7.76332i	−0.0296435	−	0.0147873i
$526$	514.539	−	373.834i	0.978210	−	0.710711i
$527$		−	1.53811i		−	0.00291861i
$528$		0			0
$529$	453.391			0.857071
$530$	819.666	+	1128.17i	1.54654	+	2.12863i
$531$	42.4127	+	123.339i	0.0798732	+	0.232277i
$532$	79.5777	−	244.915i	0.149582	−	0.460366i
$533$	436.158	−	600.320i	0.818307	−	1.12630i
$534$	−343.558	+	57.4198i	−0.643367	+	0.107528i
$535$	−104.647	+	322.071i	−0.195603	+	0.602003i
$536$	63.6135	−	20.6693i	0.118682	−	0.0385621i
$537$	−939.408	−	140.592i	−1.74936	−	0.261810i
$538$	−360.964			−0.670936
$539$		0			0
$540$	−393.890	+	414.564i	−0.729426	+	0.767711i
$541$	−558.792	+	405.986i	−1.03289	+	0.750436i	−0.968884	−	0.247513i	$-0.920387\pi$
$541$	−558.792	+	405.986i	−1.03289	+	0.750436i	−0.0640026	+	0.997950i	$0.520387\pi$
$542$	−1094.51	+	355.627i	−2.01939	+	0.656138i
$543$	42.7854	+	82.2310i	0.0787944	+	0.151438i
$544$	−2.31971	−	1.68537i	−0.00426418	−	0.00309811i
$545$	−365.678	+	503.313i	−0.670969	+	0.923510i
$546$	1446.93	−	752.846i	2.65005	−	1.37884i
$547$	26.8715	+	82.7020i	0.0491253	+	0.151192i	0.972610	−	0.232443i	$-0.0746720\pi$
$547$	26.8715	+	82.7020i	0.0491253	+	0.151192i	−0.923485	+	0.383635i	$0.874672\pi$
$548$	381.711	+	525.380i	0.696552	+	0.958722i
$549$	−4.49800	−	263.870i	−0.00819307	−	0.480637i
$550$		0			0
$551$			268.812i			0.487861i
$552$	−3.11708	+	20.8277i	−0.00564688	+	0.0377314i
$553$	−173.390	−	533.638i	−0.313544	−	0.964988i
$554$	201.464	+	65.4595i	0.363653	+	0.118158i
$555$	96.0652	+	574.784i	0.173090	+	1.03565i
$556$	−66.5688	−	48.3651i	−0.119728	−	0.0869876i
$557$	699.473	+	227.272i	1.25579	+	0.408029i	0.859991	−	0.510309i	$-0.170469\pi$
$557$	699.473	+	227.272i	1.25579	+	0.408029i	0.395795	+	0.918339i	$0.370469\pi$
$558$	−206.975	−	601.897i	−0.370922	−	1.07867i
$559$	2.75959	−	2.00496i	0.00493666	−	0.00358669i
$560$			818.651i			1.46188i
$561$		0			0
$562$	−1206.81			−2.14734
$563$	−335.019	−	461.115i	−0.595061	−	0.819031i	0.400184	−	0.916435i	$-0.368946\pi$
$563$	−335.019	−	461.115i	−0.595061	−	0.819031i	−0.995245	+	0.0974037i	$0.968946\pi$
$564$	85.4464	−	171.291i	0.151501	−	0.303708i
$565$	−150.959	+	464.604i	−0.267184	+	0.822308i
$566$	−448.807	+	617.730i	−0.792946	+	1.09140i
$567$	−750.352	−	507.012i	−1.32337	−	0.894200i
$568$	−6.66237	+	20.5047i	−0.0117295	+	0.0360997i
$569$	−540.055	+	175.474i	−0.949130	+	0.308391i	−0.742362	−	0.669999i	$-0.766294\pi$
$569$	−540.055	+	175.474i	−0.949130	+	0.308391i	−0.206768	+	0.978390i	$0.566294\pi$
$570$	34.0196	−	227.313i	0.0596835	−	0.398794i
$571$	229.442			0.401825			0.200912	−	0.979609i	$-0.435609\pi$
$571$	229.442			0.401825			0.200912	+	0.979609i	$0.435609\pi$
$572$		0			0
$573$	−633.070	−	622.370i	−1.10483	−	1.08616i
$574$	1142.83	−	830.317i	1.99100	−	1.44655i
$575$	−4.28815	+	1.39330i	−0.00745765	+	0.00242314i
$576$	−625.122	−	191.398i	−1.08528	−	0.332289i
$577$	581.714	+	422.640i	1.00817	+	0.732479i	0.963825	−	0.266538i	$-0.0858797\pi$
$577$	581.714	+	422.640i	1.00817	+	0.732479i	0.0443458	+	0.999016i	$0.485880\pi$
$578$	488.810	−	672.790i	0.845692	−	1.16400i
$579$	110.094	+	211.595i	0.190145	+	0.365448i
$580$	326.953	+	1006.26i	0.563712	+	1.73493i
$581$	395.878	+	544.880i	0.681374	+	0.937831i
$582$	−189.687	−	186.481i	−0.325923	−	0.320415i
$583$		0			0
$584$		−	11.2784i		−	0.0193124i
$585$	601.199	−	452.651i	1.02769	−	0.773763i
$586$	169.419	+	521.418i	0.289111	+	0.889791i
$587$	486.604	+	158.107i	0.828968	+	0.269348i	0.692611	−	0.721312i	$-0.256460\pi$
$587$	486.604	+	158.107i	0.828968	+	0.269348i	0.136358	+	0.990660i	$0.456460\pi$
$588$	962.544	−	160.872i	1.63698	−	0.273593i
$589$	106.989	+	77.7322i	0.181646	+	0.131973i
$590$	−196.237	−	63.7614i	−0.332606	−	0.108070i
$591$	482.534	−	967.318i	0.816470	−	1.63675i
$592$	−470.045	+	341.508i	−0.793996	+	0.576872i
$593$			241.775i			0.407715i	0.979001	+	0.203858i	$0.0653480\pi$
$593$			241.775i			0.407715i	−0.979001	+	0.203858i	$0.934652\pi$
$594$		0			0
$595$	3.46204			0.00581856
$596$	−457.081	−	629.119i	−0.766915	−	1.05557i
$597$	992.938	+	495.314i	1.66321	+	0.829672i
$598$	130.670	−	402.160i	0.218511	−	0.672508i
$599$	284.669	−	391.813i	0.475240	−	0.654112i	−0.502341	−	0.864669i	$-0.667528\pi$
$599$	284.669	−	391.813i	0.475240	−	0.654112i	0.977582	+	0.210557i	$0.0675279\pi$
$600$	0.207023	+	1.23867i	0.000345038	+	0.00206446i
$601$	149.380	−	459.745i	0.248553	−	0.764966i	−0.746479	−	0.665409i	$-0.768257\pi$
$601$	149.380	−	459.745i	0.248553	−	0.764966i	0.995032	−	0.0995576i	$-0.0317428\pi$
$602$	6.17581	−	2.00664i	0.0102588	−	0.00333329i
$603$	448.508	+	595.696i	0.743794	+	0.987888i
$604$	−600.098			−0.993540
$605$		0			0
$606$	−314.234	+	319.636i	−0.518538	+	0.527453i
$607$	402.569	−	292.483i	0.663211	−	0.481851i	−0.204535	−	0.978859i	$-0.565568\pi$
$607$	402.569	−	292.483i	0.663211	−	0.481851i	0.867746	+	0.497009i	$0.165568\pi$
$608$	234.465	−	76.1823i	0.385633	−	0.125300i
$609$	−1486.37	+	773.367i	−2.44067	+	1.26990i
$610$	337.766	+	245.402i	0.553715	+	0.402298i
$611$	−148.068	+	203.798i	−0.242337	+	0.333548i
$612$	−0.705872	+	2.30543i	−0.00115339	+	0.00376705i
$613$	−323.828	−	996.640i	−0.528267	−	1.62584i	−0.757763	−	0.652530i	$-0.773708\pi$
$613$	−323.828	−	996.640i	−0.528267	−	1.62584i	0.229496	−	0.973310i	$-0.426292\pi$
$614$	482.481	+	664.078i	0.785799	+	1.08156i
$615$	456.922	−	464.777i	0.742963	−	0.755735i
$616$		0			0
$617$		−	322.739i		−	0.523078i	−0.965193	−	0.261539i	$-0.915770\pi$
$617$		−	322.739i		−	0.523078i	0.965193	−	0.261539i	$-0.0842301\pi$
$618$	436.735	+	65.3618i	0.706692	+	0.105763i
$619$	166.334	+	511.925i	0.268715	+	0.827019i	0.990814	+	0.135230i	$0.0431773\pi$
$619$	166.334	+	511.925i	0.268715	+	0.827019i	−0.722099	+	0.691789i	$0.756823\pi$
$620$	495.044	+	160.849i	0.798457	+	0.259435i
$621$	−230.870	+	42.6428i	−0.371771	+	0.0686680i
$622$	−1175.39	−	853.971i	−1.88970	−	1.37294i
$623$	429.026	+	139.399i	0.688645	+	0.223754i
$624$	671.395	+	334.916i	1.07595	+	0.536725i
$625$	494.931	−	359.588i	0.791889	−	0.575341i
$626$			230.698i			0.368527i
$627$		0			0
$628$	768.838			1.22426
$629$	1.44422	+	1.98780i	0.00229606	+	0.00316026i
$630$	1354.78	−	465.868i	2.15044	−	0.739472i
$631$	272.965	−	840.101i	0.432591	−	1.33138i	−0.462943	−	0.886388i	$-0.653207\pi$
$631$	272.965	−	840.101i	0.432591	−	1.33138i	0.895535	−	0.444992i	$-0.146793\pi$
$632$	−23.8153	+	32.7790i	−0.0376825	+	0.0518655i
$633$	457.899	−	76.5298i	0.723379	−	0.120900i
$634$	7.69770	−	23.6911i	0.0121415	−	0.0373676i
$635$	98.1094	−	31.8777i	0.154503	−	0.0502011i
$636$	1243.89	+	186.160i	1.95580	+	0.292704i
$637$	−1284.27			−2.01613
$638$		0			0
$639$	−240.316	+	4.09649i	−0.376082	+	0.00641079i
$640$	103.157	−	74.9481i	0.161183	−	0.117106i
$641$	280.561	−	91.1597i	0.437692	−	0.142215i	−0.0818783	−	0.996642i	$-0.526092\pi$
$641$	280.561	−	91.1597i	0.437692	−	0.142215i	0.519571	+	0.854427i	$0.326092\pi$
$642$	272.718	+	524.147i	0.424794	+	0.816429i
$643$	−675.938	−	491.098i	−1.05123	−	0.763760i	−0.0787805	−	0.996892i	$-0.525103\pi$
$643$	−675.938	−	491.098i	−1.05123	−	0.763760i	−0.972445	+	0.233132i	$0.925103\pi$
$644$	244.597	−	336.659i	0.379810	−	0.522763i
$645$	2.65783	−	1.38289i	0.00412067	−	0.00214402i
$646$	−0.299464	−	0.921655i	−0.000463566	−	0.00142671i
$647$	480.606	+	661.498i	0.742823	+	1.02241i	0.998451	+	0.0556327i	$0.0177176\pi$
$647$	480.606	+	661.498i	0.742823	+	1.02241i	−0.255629	+	0.966775i	$0.582282\pi$
$648$	2.22875	+	65.3545i	0.00343943	+	0.100856i
$649$		0			0
$650$		−	25.2162i		−	0.0387942i
$651$	−122.006	+	815.221i	−0.187413	+	1.25226i
$652$	−292.671	−	900.748i	−0.448881	−	1.38151i
$653$	262.841	+	85.4023i	0.402514	+	0.130785i	0.503276	−	0.864126i	$-0.332128\pi$
$653$	262.841	+	85.4023i	0.402514	+	0.130785i	−0.100762	+	0.994911i	$0.532128\pi$
$654$	178.933	+	1070.61i	0.273598	+	1.63701i
$655$	116.200	+	84.4246i	0.177405	+	0.128892i
$656$	618.004	+	200.802i	0.942079	+	0.306100i
$657$	118.899	−	40.8860i	0.180973	−	0.0622313i
$658$	−387.972	+	281.878i	−0.589623	+	0.428386i
$659$			881.372i			1.33744i	0.743515	+	0.668719i	$0.233157\pi$
$659$			881.372i			1.33744i	−0.743515	+	0.668719i	$0.766843\pi$
$660$		0			0
$661$	−501.036			−0.757997			−0.378999	−	0.925397i	$-0.623731\pi$
$661$	−501.036			−0.757997			−0.378999	+	0.925397i	$0.623731\pi$
$662$	−47.7915	−	65.7793i	−0.0721925	−	0.0993645i
$663$	1.41635	−	2.83930i	0.00213627	−	0.00428251i
$664$	15.0287	−	46.2537i	0.0226336	−	0.0696592i
$665$	−174.963	+	240.816i	−0.263103	+	0.362130i
$666$	832.645	+	583.531i	1.25022	+	0.876173i
$667$	−134.231	+	413.122i	−0.201247	+	0.619373i
$668$	−750.779	+	243.943i	−1.12392	+	0.365184i
$669$	158.661	−	1060.15i	0.237162	−	1.58467i
$670$	−1179.64			−1.76065
$671$		0			0
$672$	1095.80	+	1077.28i	1.63065	+	1.60309i
$673$	3.60405	−	2.61850i	0.00535520	−	0.00389078i	−0.585104	−	0.810958i	$-0.698946\pi$
$673$	3.60405	−	2.61850i	0.00535520	−	0.00389078i	0.590460	+	0.807067i	$0.298946\pi$
$674$	789.616	−	256.562i	1.17154	−	0.380655i
$675$	−12.3078	+	6.67285i	−0.0182338	+	0.00988570i
$676$	403.771	+	293.357i	0.597295	+	0.433960i
$677$	−10.1571	+	13.9800i	−0.0150031	+	0.0206500i	−0.816453	−	0.577412i	$-0.804062\pi$
$677$	−10.1571	+	13.9800i	−0.0150031	+	0.0206500i	0.801450	+	0.598062i	$0.204062\pi$
$678$	393.409	+	756.108i	0.580249	+	1.11520i
$679$	106.454	+	327.630i	0.156780	+	0.482519i
$680$	−0.146943	−	0.202250i	−0.000216092	−	0.000297426i
$681$	−219.408	−	215.700i	−0.322185	−	0.316740i
$682$		0			0
$683$			1085.69i			1.58958i	0.606882	+	0.794792i	$0.292420\pi$
$683$			1085.69i			1.58958i	−0.606882	+	0.794792i	$0.707580\pi$
$684$	−124.691	−	165.611i	−0.182296	−	0.242121i
$685$	−231.962	−	713.906i	−0.338631	−	1.04220i
$686$	−825.955	−	268.369i	−1.20402	−	0.391209i
$687$	1092.93	−	182.664i	1.59088	−	0.265887i
$688$	2.41660	+	1.75576i	0.00351250	+	0.00255198i
$689$	−1574.17	−	511.478i	−2.28471	−	0.742349i
$690$	165.792	−	332.357i	0.240278	−	0.481677i
$691$	163.068	−	118.476i	0.235988	−	0.171456i	−0.463506	−	0.886094i	$-0.653409\pi$
$691$	163.068	−	118.476i	0.235988	−	0.171456i	0.699494	+	0.714638i	$0.253409\pi$
$692$		−	1042.51i		−	1.50652i
$693$		0			0
$694$	758.569			1.09304
$695$	55.9050	+	76.9467i	0.0804389	+	0.110715i
$696$	108.267	+	54.0074i	0.155556	+	0.0775969i
$697$	0.849182	−	2.61351i	0.00121834	−	0.00374966i
$698$	−825.278	+	1135.90i	−1.18235	+	1.62736i
$699$	−8.56812	−	51.2654i	−0.0122577	−	0.0733410i
$700$	7.66836	−	23.6008i	0.0109548	−	0.0337154i
$701$	−408.672	+	132.785i	−0.582984	+	0.189423i	−0.585637	−	0.810574i	$-0.699155\pi$
$701$	−408.672	+	132.785i	−0.582984	+	0.189423i	0.00265309	+	0.999996i	$0.499155\pi$
$702$	172.180	−	1301.67i	0.245271	−	1.85423i
$703$	−211.257			−0.300508
$704$		0			0
$705$	−155.117	+	157.784i	−0.220024	+	0.223807i
$706$	−1018.15	+	739.729i	−1.44214	+	1.04777i
$707$	552.080	−	179.382i	0.780877	−	0.253722i
$708$	−165.091	+	85.8980i	−0.233179	+	0.121325i
$709$	−606.394	−	440.571i	−0.855281	−	0.621398i	0.0713162	−	0.997454i	$-0.477280\pi$
$709$	−606.394	−	440.571i	−0.855281	−	0.621398i	−0.926597	+	0.376056i	$0.877280\pi$
$710$	223.496	−	307.616i	0.314784	−	0.433263i
$711$	−431.897	−	132.237i	−0.607449	−	0.185987i
$712$	−10.0660	−	30.9800i	−0.0141376	−	0.0435112i
$713$	125.610	+	172.888i	0.176172	+	0.242479i
$714$	4.23464	−	4.30744i	0.00593087	−	0.00603283i
$715$		0			0
$716$		−	1355.32i		−	1.89291i
$717$	649.250	+	97.1666i	0.905508	+	0.135518i
$718$	217.859	+	670.501i	0.303425	+	0.933845i
$719$	429.113	+	139.427i	0.596820	+	0.193919i	0.591822	−	0.806069i	$-0.298409\pi$
$719$	429.113	+	139.427i	0.596820	+	0.193919i	0.00499824	+	0.999988i	$0.498409\pi$
$720$	539.680	+	378.217i	0.749555	+	0.525301i
$721$	−462.680	−	336.157i	−0.641720	−	0.466237i
$722$	−908.725	−	295.263i	−1.25862	−	0.408951i
$723$	316.864	+	158.063i	0.438263	+	0.218622i
$724$	−107.003	+	77.7423i	−0.147794	+	0.107379i
$725$			25.9035i			0.0357290i
$726$		0			0
$727$	300.631			0.413523			0.206761	−	0.978391i	$-0.433708\pi$
$727$	300.631			0.413523			0.206761	+	0.978391i	$0.433708\pi$
$728$	89.6565	+	123.402i	0.123155	+	0.169508i
$729$	−680.900	+	260.416i	−0.934019	+	0.357223i
$730$	−61.4662	+	189.174i	−0.0842003	+	0.259142i
$731$	0.00742506	−	0.0102197i	1.01574e−5	−	1.39805e-5i
$732$	371.406	−	62.0740i	0.507385	−	0.0848006i
$733$	412.036	−	1268.12i	0.562122	−	1.73003i	−0.114228	−	0.993455i	$-0.536439\pi$
$733$	412.036	−	1268.12i	0.562122	−	1.73003i	0.676350	−	0.736580i	$-0.263561\pi$
$734$	−616.048	+	200.166i	−0.839303	+	0.272706i
$735$	−1115.61	−	166.962i	−1.51784	−	0.227159i
$736$	398.379			0.541275
$737$		0			0
$738$	−19.3815	−	1137.00i	−0.0262623	−	1.54065i
$739$	854.307	−	620.691i	1.15603	−	0.839906i	0.166760	−	0.985997i	$-0.446669\pi$
$739$	854.307	−	620.691i	1.15603	−	0.839906i	0.989271	+	0.146091i	$0.0466693\pi$
$740$	−790.810	+	256.950i	−1.06866	+	0.347229i
$741$	125.920	+	242.011i	0.169933	+	0.326601i
$742$	−2549.19	−	1852.10i	−3.43557	−	2.49609i
$743$	593.078	−	816.301i	0.798220	−	1.09866i	−0.194815	−	0.980840i	$-0.562411\pi$
$743$	593.078	−	816.301i	0.798220	−	1.09866i	0.993035	−	0.117816i	$-0.0375892\pi$
$744$	52.8029	−	27.4737i	0.0709716	−	0.0369271i
$745$	277.764	+	854.870i	0.372838	+	1.14748i
$746$	478.932	+	659.193i	0.642000	+	0.883637i
$747$	542.097	−	9.24073i	0.725699	−	0.0123705i
$748$		0			0
$749$		−	765.196i		−	1.02162i
$750$	161.332	−	1077.99i	0.215109	−	1.43732i
$751$	−15.5397	−	47.8263i	−0.0206920	−	0.0636836i	0.940177	−	0.340686i	$-0.110659\pi$
$751$	−15.5397	−	47.8263i	−0.0206920	−	0.0636836i	−0.960869	+	0.277002i	$0.910659\pi$
$752$	−209.801	−	68.1686i	−0.278991	−	0.0906497i
$753$	−79.4035	−	475.093i	−0.105450	−	0.630933i
$754$	−1965.38	−	1427.93i	−2.60660	−	1.89381i
$755$	659.702	+	214.350i	0.873777	+	0.283907i
$756$	556.995	−	1165.92i	0.736765	−	1.54223i
$757$	−256.265	+	186.187i	−0.338527	+	0.245954i	−0.744040	−	0.668135i	$-0.767093\pi$
$757$	−256.265	+	186.187i	−0.338527	+	0.245954i	0.405513	+	0.914089i	$0.367093\pi$
$758$		−	1313.86i		−	1.73333i
$759$		0			0
$760$	21.4944			0.0282821
$761$	41.9533	+	57.7438i	0.0551292	+	0.0758788i	0.835692	−	0.549199i	$-0.185067\pi$
$761$	41.9533	+	57.7438i	0.0551292	+	0.0758788i	−0.780562	+	0.625078i	$0.785067\pi$
$762$	80.3419	−	161.058i	0.105436	−	0.211363i
$763$	434.400	−	1336.94i	0.569331	−	1.75222i
$764$	744.550	−	1024.79i	0.974542	−	1.34134i
$765$	1.59946	−	2.28229i	0.00209080	−	0.00298338i
$766$	−285.676	+	879.221i	−0.372945	+	1.14781i
$767$	232.921	−	75.6806i	0.303678	−	0.0986709i
$768$	−96.0917	+	642.067i	−0.125119	+	0.836024i
$769$	634.282			0.824814			0.412407	−	0.911000i	$-0.364688\pi$
$769$	634.282			0.824814			0.412407	+	0.911000i	$0.364688\pi$
$770$		0			0
$771$	56.0119	+	55.0653i	0.0726484	+	0.0714206i
$772$	−275.338	+	200.045i	−0.356655	+	0.259125i
$773$	−821.374	+	266.881i	−1.06258	+	0.345253i	−0.787593	−	0.616195i	$-0.788673\pi$
$773$	−821.374	+	266.881i	−1.06258	+	0.345253i	−0.274986	+	0.961448i	$0.588673\pi$
$774$	1.53038	−	4.99835i	0.00197724	−	0.00645782i
$775$	10.3098	+	7.49053i	0.0133030	+	0.00966520i
$776$	14.6216	−	20.1248i	0.0188422	−	0.0259341i
$777$	−607.784	−	1168.12i	−0.782218	−	1.50338i
$778$	280.491	+	863.262i	0.360528	+	1.10959i
$779$	138.878	+	191.149i	0.178277	+	0.245377i
$780$	765.719	+	752.778i	0.981691	+	0.965100i
$781$		0			0
$782$		−	1.56598i		−	0.00200253i
$783$	−176.874	+	1337.15i	−0.225892	+	1.70773i
$784$	−347.536	−	1069.60i	−0.443285	−	1.36429i
$785$	−845.202	−	274.623i	−1.07669	−	0.349838i
$786$	247.172	−	41.3105i	0.314469	−	0.0525579i
$787$	973.760	+	707.478i	1.23731	+	0.898956i	0.997416	−	0.0718441i	$-0.0228884\pi$
$787$	973.760	+	707.478i	1.23731	+	0.898956i	0.239891	+	0.970800i	$0.422888\pi$
$788$	1466.92	+	476.632i	1.86158	+	0.604863i
$789$	−295.977	+	593.333i	−0.375129	+	0.752007i
$790$	578.098	−	420.013i	0.731769	−	0.531661i
$791$		−	1103.83i		−	1.39549i
$792$		0			0
$793$	−495.547			−0.624902
$794$	572.032	+	787.334i	0.720443	+	0.991604i
$795$	−1300.94	−	648.956i	−1.63640	−	0.816297i
$796$	−489.256	+	1505.77i	−0.614643	+	1.89168i
$797$	368.331	−	506.965i	0.462147	−	0.636091i	−0.512805	−	0.858505i	$-0.671394\pi$
$797$	368.331	−	506.965i	0.462147	−	0.636091i	0.974952	+	0.222414i	$0.0713936\pi$
$798$	85.6128	+	512.245i	0.107284	+	0.641911i
$799$	−0.288282	+	0.887242i	−0.000360804	+	0.00111044i
$800$	22.5938	−	7.34117i	0.0282423	−	0.00917647i
$801$	290.106	−	218.425i	0.362180	−	0.272690i
$802$	1038.67			1.29510
$803$		0			0
$804$	−745.887	+	758.710i	−0.927721	+	0.943670i
$805$	−389.144	+	282.729i	−0.483408	+	0.351217i
$806$	−1136.66	+	369.322i	−1.41024	+	0.458216i
$807$	333.834	−	173.696i	0.413672	−	0.215237i
$808$	−33.9118	−	24.6384i	−0.0419700	−	0.0304930i
$809$	−236.367	+	325.331i	−0.292171	+	0.402139i	−0.929718	−	0.368272i	$-0.879949\pi$
$809$	−236.367	+	325.331i	−0.292171	+	0.402139i	0.637547	+	0.770412i	$0.279949\pi$
$810$	318.792	−	1108.34i	0.393570	−	1.36832i
$811$	−171.141	−	526.717i	−0.211024	−	0.649466i	−0.999412	−	0.0342874i	$-0.989084\pi$
$811$	−171.141	−	526.717i	−0.211024	−	0.649466i	0.788388	−	0.615179i	$-0.210916\pi$
$812$	−1405.23	−	1934.14i	−1.73058	−	2.38194i
$813$	841.116	−	855.576i	1.03458	−	1.05237i
$814$		0			0
$815$			1094.75i			1.34325i
$816$	2.74799	+	0.411263i	0.00336763	+	0.000503999i
$817$	0.335628	+	1.03296i	0.000410806	+	0.00126433i
$818$	1207.30	+	392.275i	1.47591	+	0.479554i
$819$	−975.905	+	1392.53i	−1.19158	+	1.70027i
$820$	752.361	+	546.622i	0.917513	+	0.666612i
$821$	210.185	+	68.2932i	0.256011	+	0.0831829i	0.434211	−	0.900811i	$-0.357027\pi$
$821$	210.185	+	68.2932i	0.256011	+	0.0831829i	−0.178200	+	0.983994i	$0.557027\pi$
$822$	−1171.96	−	584.618i	−1.42574	−	0.711214i
$823$	−581.483	+	422.472i	−0.706541	+	0.513332i	−0.882056	−	0.471145i	$-0.843841\pi$
$823$	−581.483	+	422.472i	−0.706541	+	0.513332i	0.175515	+	0.984477i	$0.443841\pi$
$824$			41.2972i			0.0501179i
$825$		0			0
$826$	466.232			0.564446
$827$	−377.587	−	519.704i	−0.456574	−	0.628421i	0.517220	−	0.855853i	$-0.326967\pi$
$827$	−377.587	−	519.704i	−0.456574	−	0.628421i	−0.973794	+	0.227432i	$0.926967\pi$
$828$	−108.932	−	316.783i	−0.131561	−	0.382588i
$829$	253.712	−	780.846i	0.306046	−	0.941913i	−0.673239	−	0.739425i	$-0.735097\pi$
$829$	253.712	−	780.846i	0.306046	−	0.941913i	0.979285	−	0.202488i	$-0.0649027\pi$
$830$	−504.156	+	693.911i	−0.607416	+	0.836037i
$831$	−217.821	+	36.4050i	−0.262119	+	0.0438086i
$832$	−379.348	+	1167.51i	−0.455947	+	1.40326i
$833$	−4.52332	+	1.46971i	−0.00543015	+	0.00176436i
$834$	164.117	+	24.5618i	0.196783	+	0.0294506i
$835$	912.483			1.09279
$836$		0			0
$837$	481.052	+	457.062i	0.574733	+	0.546071i
$838$	−915.332	+	665.027i	−1.09228	+	0.793589i
$839$	−327.020	+	106.255i	−0.389774	+	0.126645i	−0.497346	−	0.867552i	$-0.665692\pi$
$839$	−327.020	+	106.255i	−0.389774	+	0.126645i	0.107573	+	0.994197i	$0.465692\pi$
$840$	61.8391	+	118.851i	0.0736180	+	0.141489i
$841$	1338.57	+	972.526i	1.59164	+	1.15639i
$842$	−1189.71	+	1637.50i	−1.41296	+	1.94477i
$843$	1116.10	−	580.717i	1.32397	−	0.688870i
$844$	204.698	+	629.995i	0.242533	+	0.746439i
$845$	−339.090	−	466.718i	−0.401290	−	0.552329i
$846$	6.57969	+	385.990i	0.00777741	+	0.456253i
$847$		0			0
$848$		−	1449.45i		−	1.70926i
$849$	117.823	−	787.269i	0.138778	−	0.927289i
$850$	−0.0288573	−	0.0888136i	−3.39498e−5	−	0.000104487i
$851$	−324.670	−	105.492i	−0.381515	−	0.123962i
$852$	−56.5331	−	338.253i	−0.0663534	−	0.397011i
$853$	276.697	+	201.032i	0.324381	+	0.235677i	0.738043	−	0.674754i	$-0.235750\pi$
$853$	276.697	+	201.032i	0.324381	+	0.235677i	−0.413661	+	0.910431i	$0.635750\pi$
$854$	−897.205	−	291.520i	−1.05059	−	0.341358i
$855$	77.9204	+	226.598i	0.0911350	+	0.265027i
$856$	−44.7021	+	32.4780i	−0.0522220	+	0.0379415i
$857$			1404.79i			1.63920i	0.572937	+	0.819600i	$0.305804\pi$
$857$			1404.79i			1.63920i	−0.572937	+	0.819600i	$0.694196\pi$
$858$		0			0
$859$	759.128			0.883735			0.441867	−	0.897080i	$-0.354316\pi$
$859$	759.128			0.883735			0.441867	+	0.897080i	$0.354316\pi$
$860$	2.51275	+	3.45851i	0.00292181	+	0.00402152i
$861$	−657.389	+	1317.84i	−0.763518	+	1.53060i
$862$	−134.499	+	413.946i	−0.156031	+	0.480215i
$863$	−232.529	+	320.049i	−0.269443	+	0.370856i	−0.922202	−	0.386710i	$-0.873612\pi$
$863$	−232.529	+	320.049i	−0.269443	+	0.370856i	0.652759	+	0.757566i	$0.273612\pi$
$864$	1216.43	−	224.681i	1.40790	−	0.260047i
$865$	−372.376	+	1146.06i	−0.430493	+	1.32492i
$866$	1290.67	−	419.365i	1.49038	−	0.484255i
$867$	−128.324	+	857.439i	−0.148009	+	0.988972i
$868$	−1176.15			−1.35501
$869$		0			0
$870$	−1521.63	−	1495.91i	−1.74900	−	1.71944i
$871$	1132.75	−	822.989i	1.30051	−	0.944878i
$872$	−96.5408	+	31.3680i	−0.110712	+	0.0359725i
$873$	265.165	+	81.1877i	0.303740	+	0.0929985i
$874$	108.928	+	79.1407i	0.124631	+	0.0905501i
$875$	−829.733	+	1142.03i	−0.948267	+	1.30518i
$876$	82.8060	+	159.148i	0.0945274	+	0.181676i
$877$	350.305	+	1078.13i	0.399436	+	1.22934i	0.925453	+	0.378863i	$0.123685\pi$
$877$	350.305	+	1078.13i	0.399436	+	1.22934i	−0.526017	+	0.850474i	$0.676315\pi$
$878$	−856.557	−	1178.95i	−0.975577	−	1.34277i
$879$	−407.592	−	400.703i	−0.463700	−	0.455863i
$880$		0			0
$881$			894.628i			1.01547i	0.861514	+	0.507735i	$0.169517\pi$
$881$			894.628i			1.01547i	−0.861514	+	0.507735i	$0.830483\pi$
$882$	−1572.30	+	1183.81i	−1.78266	+	1.34219i
$883$	9.80769	+	30.1850i	0.0111072	+	0.0341846i	0.956457	−	0.291875i	$-0.0942791\pi$
$883$	9.80769	+	30.1850i	0.0111072	+	0.0341846i	−0.945349	+	0.326059i	$0.894279\pi$
$884$	4.30576	+	1.39903i	0.00487077	+	0.00158261i
$885$	212.170	−	35.4606i	0.239741	−	0.0400684i
$886$	1486.54	+	1080.03i	1.67781	+	1.21900i
$887$	−1289.18	−	418.881i	−1.45342	−	0.472244i	−0.527366	−	0.849638i	$-0.676820\pi$
$887$	−1289.18	−	418.881i	−1.45342	−	0.472244i	−0.926053	+	0.377394i	$0.876820\pi$
$888$	−42.4440	+	85.0860i	−0.0477973	+	0.0958176i
$889$	−188.577	+	137.009i	−0.212123	+	0.154116i
$890$			574.487i			0.645491i
$891$		0			0
$892$	1529.52			1.71470
$893$	−47.1465	−	64.8916i	−0.0527957	−	0.0726670i
$894$	1403.37	+	700.054i	1.56977	+	0.783058i
$895$	−484.110	+	1489.94i	−0.540905	+	1.66474i
$896$	−169.351	+	233.091i	−0.189008	+	0.260147i
$897$	72.6713	+	434.812i	0.0810159	+	0.484740i
$898$	−294.755	+	907.162i	−0.328235	+	1.01020i
$899$	1167.64	−	379.389i	1.29882	−	0.422012i
$900$	−12.0156	−	15.9588i	−0.0133506	−	0.0177320i
$901$	−6.12969			−0.00680321
$902$		0			0
$903$	−4.74604	+	4.82763i	−0.00525586	+	0.00534621i
$904$	−64.4849	+	46.8510i	−0.0713329	+	0.0518264i
$905$	145.400	−	47.2433i	0.160663	−	0.0522025i
$906$	1073.61	−	558.610i	1.18501	−	0.616567i
$907$	−728.063	−	528.968i	−0.802715	−	0.583207i	0.108994	−	0.994042i	$-0.465237\pi$
$907$	−728.063	−	528.968i	−0.802715	−	0.583207i	−0.911709	+	0.410836i	$0.865237\pi$
$908$	258.045	−	355.168i	0.284190	−	0.391154i
$909$	136.807	−	446.822i	0.150503	−	0.491554i
$910$	−831.287	−	2558.44i	−0.913502	−	2.81147i
$911$	−188.025	−	258.794i	−0.206394	−	0.284077i	0.693254	−	0.720694i	$-0.256177\pi$
$911$	−188.025	−	258.794i	−0.206394	−	0.284077i	−0.899648	+	0.436617i	$0.856177\pi$
$912$	−167.483	+	170.363i	−0.183644	+	0.186801i
$913$		0			0
$914$		−	247.292i		−	0.270560i
$915$	−430.467	−	64.4237i	−0.470456	−	0.0704084i
$916$	488.581	+	1503.70i	0.533385	+	1.64159i
$917$	−308.662	−	100.290i	−0.336600	−	0.109368i
$918$	−0.883194	−	4.78164i	−0.000962085	−	0.00520876i
$919$	362.706	+	263.522i	0.394675	+	0.286748i	0.767369	−	0.641206i	$-0.221566\pi$
$919$	362.706	+	263.522i	0.394675	+	0.286748i	−0.372693	+	0.927955i	$0.621566\pi$
$920$	33.0336	+	10.7333i	0.0359061	+	0.0116666i
$921$	−765.773	−	381.996i	−0.831458	−	0.414762i
$922$	−152.077	+	110.490i	−0.164942	+	0.119838i
$923$			451.314i			0.488964i
$924$		0			0
$925$	−20.3574			−0.0220080
$926$	−905.536	−	1246.36i	−0.977901	−	1.34597i
$927$	−435.363	+	149.708i	−0.469647	+	0.161498i
$928$	707.252	−	2176.70i	0.762125	−	2.34558i
$929$	172.146	−	236.939i	0.185303	−	0.255047i	−0.706252	−	0.707961i	$-0.749615\pi$
$929$	172.146	−	236.939i	0.185303	−	0.255047i	0.891554	+	0.452914i	$0.149615\pi$
$930$	−1035.39	+	173.048i	−1.11333	+	0.186073i
$931$	126.365	−	388.913i	0.135731	−	0.417737i
$932$	70.5329	−	22.9175i	0.0756791	−	0.0245896i
$933$	1497.98	+	224.188i	1.60555	+	0.240287i
$934$	1433.07			1.53434
$935$		0			0
$936$	122.771	−	2.09279i	0.131166	−	0.00223589i
$937$	−119.433	+	86.7730i	−0.127463	+	0.0926073i	−0.649690	−	0.760199i	$-0.725101\pi$
$937$	−119.433	+	86.7730i	−0.127463	+	0.0926073i	0.522227	+	0.852806i	$0.325101\pi$
$938$	2535.02	−	823.678i	2.70258	−	0.878122i
$939$	−111.012	−	213.359i	−0.118224	−	0.227219i
$940$	−255.413	−	185.569i	−0.271716	−	0.197413i
$941$	−20.5137	+	28.2347i	−0.0217999	+	0.0300049i	−0.819778	−	0.572682i	$-0.805903\pi$
$941$	−20.5137	+	28.2347i	−0.0217999	+	0.0300049i	0.797978	+	0.602687i	$0.205903\pi$
$942$	−1375.50	+	715.684i	−1.46019	+	0.759749i
$943$	117.983	+	363.115i	0.125115	+	0.385064i
$944$	126.061	+	173.508i	0.133539	+	0.183801i
$945$	−1028.78	+	1082.77i	−1.08865	+	1.14579i
$946$		0			0
$947$			867.513i			0.916064i	0.888936	+	0.458032i	$0.151446\pi$
$947$			867.513i			0.916064i	−0.888936	+	0.458032i	$0.848554\pi$
$948$	95.3919	−	637.391i	0.100624	−	0.672354i
$949$	−72.9563	−	224.536i	−0.0768771	−	0.236603i
$950$	7.63616	+	2.48114i	0.00803806	+	0.00261172i
$951$	4.28103	+	25.6146i	0.00450161	+	0.0269344i
$952$	0.456998	+	0.332028i	0.000480040	+	0.000348769i
$953$	1236.76	+	401.847i	1.29775	+	0.421666i	0.874799	−	0.484485i	$-0.160993\pi$
$953$	1236.76	+	401.847i	1.29775	+	0.421666i	0.422954	+	0.906151i	$0.360993\pi$
$954$	−2398.68	+	824.837i	−2.51434	+	0.864609i
$955$	−1184.55	+	860.623i	−1.24036	+	0.901176i
$956$			936.699i			0.979811i
$957$		0			0
$958$	−2499.72			−2.60931
$959$	996.965	+	1372.20i	1.03959	+	1.43087i
$960$	−481.311	+	964.866i	−0.501365	+	1.00507i
$961$	−110.319	+	339.527i	−0.114796	+	0.353306i
$962$	1122.20	−	1544.58i	1.16653	−	1.60559i
$963$	−504.440	−	353.520i	−0.523822	−	0.367103i
$964$	−156.130	+	480.520i	−0.161961	+	0.498464i
$965$	374.139	−	121.565i	0.387709	−	0.125974i
$966$	−124.217	+	829.993i	−0.128589	+	0.859206i
$967$	−1422.62			−1.47117			−0.735585	−	0.677433i	$-0.763093\pi$
$967$	−1422.62			−1.47117			−0.735585	+	0.677433i	$0.763093\pi$
$968$		0			0
$969$	0.720457	+	0.708281i	0.000743506	+	0.000730940i
$970$	−354.926	+	257.869i	−0.365903	+	0.265844i
$971$	330.282	−	107.315i	0.340146	−	0.110520i	−0.133963	−	0.990986i	$-0.542770\pi$
$971$	330.282	−	107.315i	0.340146	−	0.110520i	0.474109	+	0.880466i	$0.342770\pi$
$972$	−511.281	−	905.844i	−0.526009	−	0.931939i
$973$	−173.867	−	126.322i	−0.178691	−	0.129827i
$974$	407.826	−	561.325i	0.418713	−	0.576309i
$975$	12.1341	+	23.3210i	0.0124452	+	0.0239189i
$976$	−134.100	−	412.716i	−0.137397	−	0.422865i
$977$	−274.257	−	377.482i	−0.280713	−	0.386369i	0.645257	−	0.763966i	$-0.276750\pi$
$977$	−274.257	−	377.482i	−0.280713	−	0.386369i	−0.925970	+	0.377597i	$0.876750\pi$
$978$	1362.08	+	1339.06i	1.39272	+	1.36918i
$979$		0			0
$980$		−	1609.54i		−	1.64238i
$981$	−680.662	−	904.038i	−0.693845	−	0.921547i
$982$	−444.657	−	1368.51i	−0.452807	−	1.39360i
$983$	−963.856	−	313.176i	−0.980525	−	0.318592i	−0.225467	−	0.974251i	$-0.572391\pi$
$983$	−963.856	−	313.176i	−0.980525	−	0.318592i	−0.755057	+	0.655659i	$0.772391\pi$
$984$	104.889	−	17.5304i	0.106595	−	0.0178155i
$985$	−1442.37	−	1047.94i	−1.46434	−	1.06390i
$986$	−8.55635	−	2.78013i	−0.00867784	−	0.00281960i
$987$	223.172	−	447.384i	0.226111	−	0.453277i
$988$	−314.917	+	228.801i	−0.318742	+	0.231580i
$989$			1.75510i			0.00177462i
$990$		0			0
$991$	−1208.63			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$991$	−1208.63			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$992$	−661.828	−	910.928i	−0.667165	−	0.918274i
$993$	75.8525	+	37.8380i	0.0763873	+	0.0381048i
$994$	−265.498	+	817.118i	−0.267100	+	0.822050i
$995$	1075.70	−	1480.57i	1.08111	−	1.48801i
$996$	127.526	+	763.020i	0.128038	+	0.766085i
$997$	44.6144	−	137.309i	0.0447486	−	0.137722i	−0.926186	−	0.377067i	$-0.876933\pi$
$997$	44.6144	−	137.309i	0.0447486	−	0.137722i	0.970935	+	0.239345i	$0.0769326\pi$
$998$	1518.39	−	493.356i	1.52144	−	0.494344i
$999$	−1050.86	−	139.004i	−1.05191	−	0.139143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.245.2		24
3.2	odd	2	inner	363.3.h.q.245.5		24
11.2	odd	10		363.3.b.k.122.2	yes	6
11.3	even	5	inner	363.3.h.q.269.2		24
11.4	even	5	inner	363.3.h.q.323.5		24
11.5	even	5	inner	363.3.h.q.251.5		24
11.6	odd	10		363.3.h.p.251.2		24
11.7	odd	10		363.3.h.p.323.2		24
11.8	odd	10		363.3.h.p.269.5		24
11.9	even	5		363.3.b.j.122.5	yes	6
11.10	odd	2		363.3.h.p.245.5		24
33.2	even	10		363.3.b.k.122.5	yes	6
33.5	odd	10	inner	363.3.h.q.251.2		24
33.8	even	10		363.3.h.p.269.2		24
33.14	odd	10	inner	363.3.h.q.269.5		24
33.17	even	10		363.3.h.p.251.5		24
33.20	odd	10		363.3.b.j.122.2	✓	6
33.26	odd	10	inner	363.3.h.q.323.2		24
33.29	even	10		363.3.h.p.323.5		24
33.32	even	2		363.3.h.p.245.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.2	✓	6	33.20	odd	10
363.3.b.j.122.5	yes	6	11.9	even	5
363.3.b.k.122.2	yes	6	11.2	odd	10
363.3.b.k.122.5	yes	6	33.2	even	10
363.3.h.p.245.2		24	33.32	even	2
363.3.h.p.245.5		24	11.10	odd	2
363.3.h.p.251.2		24	11.6	odd	10
363.3.h.p.251.5		24	33.17	even	10
363.3.h.p.269.2		24	33.8	even	10
363.3.h.p.269.5		24	11.8	odd	10
363.3.h.p.323.2		24	11.7	odd	10
363.3.h.p.323.5		24	33.29	even	10
363.3.h.q.245.2		24	1.1	even	1	trivial
363.3.h.q.245.5		24	3.2	odd	2	inner
363.3.h.q.251.2		24	33.5	odd	10	inner
363.3.h.q.251.5		24	11.5	even	5	inner
363.3.h.q.269.2		24	11.3	even	5	inner
363.3.h.q.269.5		24	33.14	odd	10	inner
363.3.h.q.323.2		24	33.26	odd	10	inner
363.3.h.q.323.5		24	11.4	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69141 - 2.32802i) q^{2} +(2.68453 + 1.33914i) q^{3} +(-1.32276 + 4.07105i) q^{4} +(2.90829 - 4.00292i) q^{5} +(-1.42308 - 8.51468i) q^{6} +(-3.45484 + 10.6329i) q^{7} +(0.767802 - 0.249474i) q^{8} +(5.41340 + 7.18993i) q^{9} -14.2380 q^{10} +(-9.00271 + 9.15748i) q^{12} +(13.6720 - 9.93330i) q^{13} +(30.5972 - 9.94163i) q^{14} +(13.1679 - 6.85133i) q^{15} +(11.9727 + 8.69868i) q^{16} +(0.0367864 - 0.0506321i) q^{17} +(7.58207 - 24.7636i) q^{18} +(1.66282 + 5.11764i) q^{19} +(12.4491 + 17.1347i) q^{20} +(-23.5136 + 23.9178i) q^{21} +8.69537i q^{23} +(2.39527 + 0.358475i) q^{24} +(0.160235 + 0.493153i) q^{25} +(-46.2499 - 15.0275i) q^{26} +(4.90408 + 26.5509i) q^{27} +(-38.7171 - 28.1296i) q^{28} +(47.5106 + 15.4371i) q^{29} +(-38.2223 - 19.0667i) q^{30} +(19.8827 - 14.4457i) q^{31} -45.8150i q^{32} -0.180094 q^{34} +(32.5149 + 44.7530i) q^{35} +(-36.4312 + 12.5276i) q^{36} +(-12.1319 + 37.3382i) q^{37} +(9.10148 - 12.5271i) q^{38} +(50.0050 - 8.35747i) q^{39} +(1.23437 - 3.79899i) q^{40} +(41.7596 - 13.5685i) q^{41} +(95.4523 + 14.2854i) q^{42} +0.201842 q^{43} +(44.5244 - 0.758975i) q^{45} +(20.2430 - 14.7074i) q^{46} +(-14.1766 + 4.60627i) q^{47} +(20.4923 + 39.3850i) q^{48} +(-61.4808 - 44.6684i) q^{49} +(0.877048 - 1.20715i) q^{50} +(0.166558 - 0.0866612i) q^{51} +(22.3541 + 68.7988i) q^{52} +(-57.5690 - 79.2369i) q^{53} +(53.5163 - 56.3252i) q^{54} +9.02585i q^{56} +(-2.38935 + 15.9652i) q^{57} +(-44.4218 - 136.716i) q^{58} +(13.7827 + 4.47826i) q^{59} +(10.4741 + 62.6697i) q^{60} +(-23.7229 - 17.2357i) q^{61} +(-67.2596 - 21.8540i) q^{62} +(-95.1523 + 32.7201i) q^{63} +(-58.7676 + 42.6972i) q^{64} -83.6168i q^{65} +82.8515 q^{67} +(0.157466 + 0.216733i) q^{68} +(-11.6443 + 23.3430i) q^{69} +(49.1899 - 151.391i) q^{70} +(-15.6972 + 21.6053i) q^{71} +(5.95012 + 4.16994i) q^{72} +(4.31706 - 13.2865i) q^{73} +(107.444 - 34.9108i) q^{74} +(-0.230246 + 1.53846i) q^{75} -23.0337 q^{76} +(-104.035 - 102.277i) q^{78} +(-40.6025 + 29.4994i) q^{79} +(69.6402 - 22.6275i) q^{80} +(-22.3903 + 77.8439i) q^{81} +(-102.220 - 74.2674i) q^{82} +(35.4092 - 48.7366i) q^{83} +(-66.2676 - 127.362i) q^{84} +(-0.0956907 - 0.294506i) q^{85} +(-0.341398 - 0.469894i) q^{86} +(106.871 + 105.065i) q^{87} -40.3489i q^{89} +(-77.0758 - 102.370i) q^{90} +(58.3852 + 179.691i) q^{91} +(-35.3993 - 11.5019i) q^{92} +(72.7206 - 12.1540i) q^{93} +(34.7020 + 25.2125i) q^{94} +(25.3215 + 8.22744i) q^{95} +(61.3528 - 122.992i) q^{96} +(24.9281 - 18.1114i) q^{97} +218.681i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

L-functions

Modular forms

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Database

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