LMFDB - Embedded newform 169.3.f.g.150.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(19,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("169.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.f (of order $12$, degree $4$, not 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:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			150.4
Character	$\chi$	$=$	169.150
Dual form			169.3.f.g.80.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92320 + 0.515320i) q^{2} +(0.299764 - 0.519206i) q^{3} +(-0.0309536 + 0.0178711i) q^{4} +(-5.65111 - 5.65111i) q^{5} +(-0.308949 + 1.15301i) q^{6} +(-1.96518 - 0.526568i) q^{7} +(5.68184 - 5.68184i) q^{8} +(4.32028 + 7.48295i) q^{9} +(13.7804 + 7.95610i) q^{10} +(3.76327 + 14.0447i) q^{11} +0.0214284i q^{12} +4.05079 q^{14} +(-4.62809 + 1.24009i) q^{15} +(-7.92788 + 13.7315i) q^{16} +(10.2245 - 5.90312i) q^{17} +(-12.1649 - 12.1649i) q^{18} +(-6.28035 + 23.4386i) q^{19} +(0.275914 + 0.0739308i) q^{20} +(-0.862488 + 0.862488i) q^{21} +(-14.4751 - 25.0716i) q^{22} +(-0.229705 - 0.132620i) q^{23} +(-1.24684 - 4.65326i) q^{24} +38.8702i q^{25} +10.5760 q^{27} +(0.0702397 - 0.0188207i) q^{28} +(-3.60897 + 6.25092i) q^{29} +(8.26171 - 4.76990i) q^{30} +(30.2298 + 30.2298i) q^{31} +(-0.148007 + 0.552371i) q^{32} +(8.42021 + 2.25619i) q^{33} +(-16.6218 + 16.6218i) q^{34} +(8.12976 + 14.0812i) q^{35} +(-0.267457 - 0.154416i) q^{36} +(3.53340 + 13.1868i) q^{37} -48.3135i q^{38} -64.2175 q^{40} +(33.6035 - 9.00403i) q^{41} +(1.21428 - 2.10319i) q^{42} +(-35.0467 + 20.2342i) q^{43} +(-0.367481 - 0.367481i) q^{44} +(17.8726 - 66.7014i) q^{45} +(0.510111 + 0.136684i) q^{46} +(9.87555 - 9.87555i) q^{47} +(4.75298 + 8.23241i) q^{48} +(-38.8506 - 22.4304i) q^{49} +(-20.0306 - 74.7552i) q^{50} -7.07817i q^{51} +77.1259 q^{53} +(-20.3398 + 5.45003i) q^{54} +(58.1017 - 100.635i) q^{55} +(-14.1577 + 8.17397i) q^{56} +(10.2868 + 10.2868i) q^{57} +(3.71955 - 13.8815i) q^{58} +(-34.8006 - 9.32480i) q^{59} +(0.121094 - 0.121094i) q^{60} +(15.4657 + 26.7873i) q^{61} +(-73.7160 - 42.5599i) q^{62} +(-4.54985 - 16.9803i) q^{63} -64.5616i q^{64} -17.3564 q^{66} +(-60.4589 + 16.1999i) q^{67} +(-0.210990 + 0.365445i) q^{68} +(-0.137715 + 0.0795095i) q^{69} +(-22.8915 - 22.8915i) q^{70} +(2.23685 - 8.34804i) q^{71} +(67.0641 + 17.9698i) q^{72} +(-23.3661 + 23.3661i) q^{73} +(-13.5909 - 23.5401i) q^{74} +(20.1816 + 11.6519i) q^{75} +(-0.224473 - 0.837745i) q^{76} -29.5820i q^{77} -49.8004 q^{79} +(122.400 - 32.7969i) q^{80} +(-35.7122 + 61.8554i) q^{81} +(-59.9863 + 34.6331i) q^{82} +(60.8000 + 60.8000i) q^{83} +(0.0112835 - 0.0421107i) q^{84} +(-91.1390 - 24.4206i) q^{85} +(56.9747 - 56.9747i) q^{86} +(2.16368 + 3.74760i) q^{87} +(101.182 + 58.4176i) q^{88} +(22.9556 + 85.6713i) q^{89} +137.490i q^{90} +0.00948026 q^{92} +(24.7573 - 6.63370i) q^{93} +(-13.9036 + 24.0818i) q^{94} +(167.945 - 96.9632i) q^{95} +(0.242427 + 0.242427i) q^{96} +(-8.75298 + 32.6665i) q^{97} +(86.2763 + 23.1177i) q^{98} +(-88.8376 + 88.8376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) $ 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.92320	+	0.515320i	−0.961601	+	0.257660i	−0.705278	−	0.708931i	$-0.749178\pi$
$2$	−1.92320	+	0.515320i	−0.961601	+	0.257660i	−0.256323	+	0.966591i	$0.582511\pi$
$3$	0.299764	−	0.519206i	0.0999213	−	0.173069i	−0.811731	−	0.584032i	$-0.801474\pi$
$3$	0.299764	−	0.519206i	0.0999213	−	0.173069i	0.911652	+	0.410963i	$0.134808\pi$
$4$	−0.0309536	+	0.0178711i	−0.00773840	+	0.00446777i
$5$	−5.65111	−	5.65111i	−1.13022	−	1.13022i	−0.990140	−	0.140083i	$-0.955263\pi$
$5$	−5.65111	−	5.65111i	−1.13022	−	1.13022i	−0.140083	−	0.990140i	$-0.544737\pi$
$6$	−0.308949	+	1.15301i	−0.0514915	+	0.192169i
$7$	−1.96518	−	0.526568i	−0.280740	−	0.0752241i	0.115702	−	0.993284i	$-0.463088\pi$
$7$	−1.96518	−	0.526568i	−0.280740	−	0.0752241i	−0.396442	+	0.918060i	$0.629755\pi$
$8$	5.68184	−	5.68184i	0.710231	−	0.710231i
$9$	4.32028	+	7.48295i	0.480031	+	0.831439i
$10$	13.7804	+	7.95610i	1.37804	+	0.795610i
$11$	3.76327	+	14.0447i	0.342116	+	1.27679i	0.895946	+	0.444164i	$0.146499\pi$
$11$	3.76327	+	14.0447i	0.342116	+	1.27679i	−0.553830	+	0.832630i	$0.686834\pi$
$12$			0.0214284i			0.00178570i
$13$		0			0
$13$		0			0
$14$	4.05079			0.289342
$15$	−4.62809	+	1.24009i	−0.308540	+	0.0826729i
$16$	−7.92788	+	13.7315i	−0.495492	+	0.858218i
$17$	10.2245	−	5.90312i	0.601441	−	0.347242i	−0.168167	−	0.985759i	$-0.553785\pi$
$17$	10.2245	−	5.90312i	0.601441	−	0.347242i	0.769608	+	0.638516i	$0.220451\pi$
$18$	−12.1649	−	12.1649i	−0.675827	−	0.675827i
$19$	−6.28035	+	23.4386i	−0.330545	+	1.23361i	0.578074	+	0.815984i	$0.303804\pi$
$19$	−6.28035	+	23.4386i	−0.330545	+	1.23361i	−0.908619	+	0.417626i	$0.862862\pi$
$20$	0.275914	+	0.0739308i	0.0137957	+	0.00369654i
$21$	−0.862488	+	0.862488i	−0.0410708	+	0.0410708i
$22$	−14.4751	−	25.0716i	−0.657958	−	1.13962i
$23$	−0.229705	−	0.132620i	−0.00998717	−	0.00576610i	0.494998	−	0.868894i	$-0.335169\pi$
$23$	−0.229705	−	0.132620i	−0.00998717	−	0.00576610i	−0.504985	+	0.863128i	$0.668502\pi$
$24$	−1.24684	−	4.65326i	−0.0519516	−	0.193886i
$25$			38.8702i			1.55481i
$26$		0			0
$27$	10.5760			0.391704
$28$	0.0702397	−	0.0188207i	0.00250856	−	0.000672167i
$29$	−3.60897	+	6.25092i	−0.124447	+	0.215549i	−0.921517	−	0.388339i	$-0.873049\pi$
$29$	−3.60897	+	6.25092i	−0.124447	+	0.215549i	0.797070	+	0.603888i	$0.206382\pi$
$30$	8.26171	−	4.76990i	0.275390	−	0.158997i
$31$	30.2298	+	30.2298i	0.975154	+	0.975154i	0.999699	−	0.0245446i	$-0.00781356\pi$
$31$	30.2298	+	30.2298i	0.975154	+	0.975154i	−0.0245446	+	0.999699i	$0.507814\pi$
$32$	−0.148007	+	0.552371i	−0.00462523	+	0.0172616i
$33$	8.42021	+	2.25619i	0.255158	+	0.0683693i
$34$	−16.6218	+	16.6218i	−0.488876	+	0.488876i
$35$	8.12976	+	14.0812i	0.232279	+	0.402319i
$36$	−0.267457	−	0.154416i	−0.00742935	−	0.00428934i
$37$	3.53340	+	13.1868i	0.0954973	+	0.356401i	0.997094	−	0.0761760i	$-0.0242711\pi$
$37$	3.53340	+	13.1868i	0.0954973	+	0.356401i	−0.901597	+	0.432577i	$0.857604\pi$
$38$		−	48.3135i		−	1.27141i
$39$		0			0
$40$	−64.2175			−1.60544
$41$	33.6035	−	9.00403i	0.819597	−	0.219610i	0.175427	−	0.984492i	$-0.443869\pi$
$41$	33.6035	−	9.00403i	0.819597	−	0.219610i	0.644170	+	0.764882i	$0.277203\pi$
$42$	1.21428	−	2.10319i	0.0289114	−	0.0500761i
$43$	−35.0467	+	20.2342i	−0.815039	+	0.470563i	−0.848703	−	0.528870i	$-0.822616\pi$
$43$	−35.0467	+	20.2342i	−0.815039	+	0.470563i	0.0336635	+	0.999433i	$0.489283\pi$
$44$	−0.367481	−	0.367481i	−0.00835184	−	0.00835184i
$45$	17.8726	−	66.7014i	0.397169	−	1.48225i
$46$	0.510111	+	0.136684i	0.0110894	+	0.00297139i
$47$	9.87555	−	9.87555i	0.210118	−	0.210118i	−0.594200	−	0.804318i	$-0.702531\pi$
$47$	9.87555	−	9.87555i	0.210118	−	0.210118i	0.804318	+	0.594200i	$0.202531\pi$
$48$	4.75298	+	8.23241i	0.0990205	+	0.171508i
$49$	−38.8506	−	22.4304i	−0.792869	−	0.457763i
$50$	−20.0306	−	74.7552i	−0.400612	−	1.49510i
$51$		−	7.07817i		−	0.138788i
$52$		0			0
$53$	77.1259			1.45521			0.727603	−	0.685999i	$-0.240635\pi$
$53$	77.1259			1.45521			0.727603	+	0.685999i	$0.240635\pi$
$54$	−20.3398	+	5.45003i	−0.376663	+	0.100927i
$55$	58.1017	−	100.635i	1.05639	−	1.82973i
$56$	−14.1577	+	8.17397i	−0.252817	+	0.145964i
$57$	10.2868	+	10.2868i	0.180471	+	0.180471i
$58$	3.71955	−	13.8815i	0.0641302	−	0.239337i
$59$	−34.8006	−	9.32480i	−0.589841	−	0.158048i	−0.0484607	−	0.998825i	$-0.515432\pi$
$59$	−34.8006	−	9.32480i	−0.589841	−	0.158048i	−0.541381	+	0.840778i	$0.682098\pi$
$60$	0.121094	−	0.121094i	0.00201824	−	0.00201824i
$61$	15.4657	+	26.7873i	0.253536	+	0.439137i	0.964497	−	0.264095i	$-0.0850732\pi$
$61$	15.4657	+	26.7873i	0.253536	+	0.439137i	−0.710961	+	0.703231i	$0.751740\pi$
$62$	−73.7160	−	42.5599i	−1.18897	−	0.686451i
$63$	−4.54985	−	16.9803i	−0.0722198	−	0.269528i
$64$		−	64.5616i		−	1.00878i
$65$		0			0
$66$	−17.3564			−0.262976
$67$	−60.4589	+	16.1999i	−0.902372	+	0.241790i	−0.680034	−	0.733180i	$-0.738035\pi$
$67$	−60.4589	+	16.1999i	−0.902372	+	0.241790i	−0.222337	+	0.974970i	$0.571369\pi$
$68$	−0.210990	+	0.365445i	−0.00310279	+	0.00537420i
$69$	−0.137715	+	0.0795095i	−0.00199586	+	0.00115231i
$70$	−22.8915	−	22.8915i	−0.327021	−	0.327021i
$71$	2.23685	−	8.34804i	0.0315049	−	0.117578i	−0.948383	−	0.317128i	$-0.897281\pi$
$71$	2.23685	−	8.34804i	0.0315049	−	0.117578i	0.979888	+	0.199550i	$0.0639481\pi$
$72$	67.0641	+	17.9698i	0.931446	+	0.249580i
$73$	−23.3661	+	23.3661i	−0.320084	+	0.320084i	−0.848799	−	0.528715i	$-0.822674\pi$
$73$	−23.3661	+	23.3661i	−0.320084	+	0.320084i	0.528715	+	0.848799i	$0.322674\pi$
$74$	−13.5909	−	23.5401i	−0.183661	−	0.318109i
$75$	20.1816	+	11.6519i	0.269089	+	0.155358i
$76$	−0.224473	−	0.837745i	−0.00295359	−	0.0110230i
$77$		−	29.5820i		−	0.384182i
$78$		0			0
$79$	−49.8004			−0.630385			−0.315193	−	0.949028i	$-0.602069\pi$
$79$	−49.8004			−0.630385			−0.315193	+	0.949028i	$0.602069\pi$
$80$	122.400	−	32.7969i	1.52999	−	0.409961i
$81$	−35.7122	+	61.8554i	−0.440892	+	0.763647i
$82$	−59.9863	+	34.6331i	−0.731541	+	0.422355i
$83$	60.8000	+	60.8000i	0.732530	+	0.732530i	0.971120	−	0.238590i	$-0.0766853\pi$
$83$	60.8000	+	60.8000i	0.732530	+	0.732530i	−0.238590	+	0.971120i	$0.576685\pi$
$84$	0.0112835	−	0.0421107i	0.000134328	−	0.000501317i
$85$	−91.1390	−	24.4206i	−1.07222	−	0.287302i
$86$	56.9747	−	56.9747i	0.662497	−	0.662497i
$87$	2.16368	+	3.74760i	0.0248699	+	0.0430758i
$88$	101.182	+	58.4176i	1.14980	+	0.663837i
$89$	22.9556	+	85.6713i	0.257928	+	0.962599i	0.966438	+	0.256899i	$0.0827007\pi$
$89$	22.9556	+	85.6713i	0.257928	+	0.962599i	−0.708511	+	0.705700i	$0.750633\pi$
$90$			137.490i			1.52767i
$91$		0			0
$92$	0.00948026			0.000103046
$93$	24.7573	−	6.63370i	0.266207	−	0.0713301i
$94$	−13.9036	+	24.0818i	−0.147911	+	0.256189i
$95$	167.945	−	96.9632i	1.76784	−	1.02066i
$96$	0.242427	+	0.242427i	0.00252528	+	0.00252528i
$97$	−8.75298	+	32.6665i	−0.0902369	+	0.336769i	−0.996254	−	0.0864718i	$-0.972441\pi$
$97$	−8.75298	+	32.6665i	−0.0902369	+	0.336769i	0.906017	+	0.423240i	$0.139107\pi$
$98$	86.2763	+	23.1177i	0.880371	+	0.235895i
$99$	−88.8376	+	88.8376i	−0.897350	+	0.897350i
$100$	−0.694651	−	1.20317i	−0.00694651	−	0.0120317i
$101$	14.4870	+	8.36406i	0.143435	+	0.0828125i	0.570000	−	0.821644i	$-0.306943\pi$
$101$	14.4870	+	8.36406i	0.143435	+	0.0828125i	−0.426565	+	0.904457i	$0.640276\pi$
$102$	3.64752	+	13.6127i	0.0357600	+	0.133458i
$103$			87.2313i			0.846906i	0.905918	+	0.423453i	$0.139182\pi$
$103$			87.2313i			0.846906i	−0.905918	+	0.423453i	$0.860818\pi$
$104$		0			0
$105$	9.74803			0.0928384
$106$	−148.329	+	39.7445i	−1.39933	+	0.374948i
$107$	−59.9117	+	103.770i	−0.559923	+	0.969815i	0.437579	+	0.899180i	$0.355836\pi$
$107$	−59.9117	+	103.770i	−0.559923	+	0.969815i	−0.997502	+	0.0706350i	$0.977497\pi$
$108$	−0.327365	+	0.189005i	−0.00303116	+	0.00175004i
$109$	−87.8195	−	87.8195i	−0.805684	−	0.805684i	0.178293	−	0.983977i	$-0.442942\pi$
$109$	−87.8195	−	87.8195i	−0.805684	−	0.805684i	−0.983977	+	0.178293i	$0.942942\pi$
$110$	−59.8820	+	223.482i	−0.544381	+	2.03166i
$111$	7.90587	+	2.11837i	0.0712241	+	0.0190844i
$112$	22.8103	−	22.8103i	0.203663	−	0.203663i
$113$	−84.8574	−	146.977i	−0.750950	−	1.30068i	−0.947363	−	0.320163i	$-0.896262\pi$
$113$	−84.8574	−	146.977i	−0.750950	−	1.30068i	0.196412	−	0.980521i	$-0.437071\pi$
$114$	−25.0847	−	14.4826i	−0.220041	−	0.127041i
$115$	0.548637	+	2.04754i	0.00477076	+	0.0178047i
$116$		−	0.257984i		−	0.00222400i
$117$		0			0
$118$	71.7339			0.607914
$119$	−23.2014	+	6.21679i	−0.194970	+	0.0522420i
$120$	−19.2501	+	33.3421i	−0.160417	+	0.277851i
$121$	−78.3032	+	45.2084i	−0.647134	+	0.373623i
$122$	−43.5477	−	43.5477i	−0.356948	−	0.356948i
$123$	5.39817	−	20.1462i	0.0438875	−	0.163790i
$124$	−1.47596	−	0.395482i	−0.0119029	−	0.00318937i
$125$	78.3820	−	78.3820i	0.627056	−	0.627056i
$126$	17.5006	+	30.3118i	0.138893	+	0.240570i
$127$	148.054	+	85.4792i	1.16578	+	0.673065i	0.952683	−	0.303966i	$-0.0983109\pi$
$127$	148.054	+	85.4792i	1.16578	+	0.673065i	0.213099	+	0.977031i	$0.431644\pi$
$128$	32.6779	+	121.955i	0.255296	+	0.952777i
$129$			24.2619i			0.188077i
$130$		0			0
$131$	109.132			0.833072			0.416536	−	0.909119i	$-0.363244\pi$
$131$	109.132			0.833072			0.416536	+	0.909119i	$0.363244\pi$
$132$	−0.300956	+	0.0806409i	−0.00227997	+	0.000610916i
$133$	24.6840	−	42.7540i	0.185594	−	0.321459i
$134$	107.926	−	62.3114i	0.805421	−	0.465010i
$135$	−59.7662	−	59.7662i	−0.442713	−	0.442713i
$136$	24.5534	−	91.6347i	0.180540	−	0.673784i
$137$	−138.193	−	37.0288i	−1.00871	−	0.270283i	−0.283620	−	0.958937i	$-0.591535\pi$
$137$	−138.193	−	37.0288i	−1.00871	−	0.270283i	−0.725090	+	0.688654i	$0.758202\pi$
$138$	0.223880	−	0.223880i	0.00162232	−	0.00162232i
$139$	83.8403	+	145.216i	0.603168	+	1.04472i	0.992338	+	0.123551i	$0.0394283\pi$
$139$	83.8403	+	145.216i	0.603168	+	1.04472i	−0.389171	+	0.921166i	$0.627238\pi$
$140$	−0.503290	−	0.290575i	−0.00359493	−	0.00207553i
$141$	−2.16712	−	8.08778i	−0.0153696	−	0.0573602i
$142$			17.2077i			0.121181i
$143$		0			0
$144$	−137.003			−0.951408
$145$	55.7193	−	14.9300i	0.384271	−	0.102965i
$146$	32.8967	−	56.9788i	0.225320	−	0.390266i
$147$	−23.2920	+	13.4476i	−0.158449	+	0.0914806i
$148$	−0.345034	−	0.345034i	−0.00233131	−	0.00233131i
$149$	−11.2189	+	41.8695i	−0.0752947	+	0.281004i	−0.993300	−	0.115565i	$-0.963132\pi$
$149$	−11.2189	+	41.8695i	−0.0752947	+	0.281004i	0.918005	+	0.396568i	$0.129799\pi$
$150$	−44.8178	−	12.0089i	−0.298785	−	0.0800593i
$151$	81.8840	−	81.8840i	0.542278	−	0.542278i	−0.381918	−	0.924196i	$-0.624736\pi$
$151$	81.8840	−	81.8840i	0.542278	−	0.542278i	0.924196	+	0.381918i	$0.124736\pi$
$152$	97.4904	+	168.858i	0.641384	+	1.11091i
$153$	88.3455	+	51.0063i	0.577422	+	0.333375i
$154$	15.2442	+	56.8922i	0.0989885	+	0.369430i
$155$		−	341.664i		−	2.20428i
$156$		0			0
$157$	−104.868			−0.667951			−0.333976	−	0.942582i	$-0.608390\pi$
$157$	−104.868			−0.667951			−0.333976	+	0.942582i	$0.608390\pi$
$158$	95.7763	−	25.6632i	0.606179	−	0.162425i
$159$	23.1196	−	40.0442i	0.145406	−	0.251851i
$160$	3.95792	−	2.28511i	0.0247370	−	0.0142819i
$161$	0.381578	+	0.381578i	0.00237005	+	0.00237005i
$162$	36.8065	−	137.364i	0.227200	−	0.847924i
$163$	309.120	+	82.8284i	1.89644	+	0.508149i	0.997549	+	0.0699767i	$0.0222925\pi$
$163$	309.120	+	82.8284i	1.89644	+	0.508149i	0.898891	+	0.438173i	$0.144374\pi$
$164$	−0.879237	+	0.879237i	−0.00536120	+	0.00536120i
$165$	−34.8336	−	60.3335i	−0.211113	−	0.365658i
$166$	−148.262	−	85.5991i	−0.893145	−	0.515657i
$167$	−51.1962	−	191.067i	−0.306564	−	1.14411i	−0.931590	−	0.363510i	$-0.881578\pi$
$167$	−51.1962	−	191.067i	−0.306564	−	1.14411i	0.625026	−	0.780604i	$-0.285088\pi$
$168$			9.80104i			0.0583395i
$169$		0			0
$170$	187.863			1.10508
$171$	−202.523	+	54.2658i	−1.18434	+	0.317344i
$172$	0.723214	−	1.25264i	0.00420473	−	0.00728281i
$173$	−241.095	+	139.196i	−1.39361	+	0.804604i	−0.993713	−	0.111955i	$-0.964289\pi$
$173$	−241.095	+	139.196i	−1.39361	+	0.804604i	−0.399901	+	0.916558i	$0.630956\pi$
$174$	−6.09240	−	6.09240i	−0.0350138	−	0.0350138i
$175$	20.4678	−	76.3869i	0.116959	−	0.436497i
$176$	−222.690	−	59.6696i	−1.26528	−	0.339032i
$177$	−15.2735	+	15.2735i	−0.0862908	+	0.0862908i
$178$	−88.2963	−	152.934i	−0.496047	−	0.859178i
$179$	−214.248	−	123.696i	−1.19692	−	0.691039i	−0.237049	−	0.971498i	$-0.576180\pi$
$179$	−214.248	−	123.696i	−1.19692	−	0.691039i	−0.959866	+	0.280458i	$0.909514\pi$
$180$	0.638804	+	2.38405i	0.00354891	+	0.0132447i
$181$			211.414i			1.16803i	0.811741	+	0.584017i	$0.198520\pi$
$181$			211.414i			1.16803i	−0.811741	+	0.584017i	$0.801480\pi$
$182$		0			0
$183$	18.5442			0.101334
$184$	−2.05868	+	0.551621i	−0.0111885	+	0.00299794i
$185$	54.5526	−	94.4879i	0.294879	−	0.510746i
$186$	−44.1948	+	25.5159i	−0.237606	+	0.137182i
$187$	121.385	+	121.385i	0.649120	+	0.649120i
$188$	−0.129197	+	0.482170i	−0.000687219	+	0.00256474i
$189$	−20.7838	−	5.56899i	−0.109967	−	0.0294656i
$190$	−273.025	+	273.025i	−1.43697	+	1.43697i
$191$	−26.6707	−	46.1950i	−0.139637	−	0.241859i	0.787722	−	0.616031i	$-0.211260\pi$
$191$	−26.6707	−	46.1950i	−0.139637	−	0.241859i	−0.927359	+	0.374172i	$0.877927\pi$
$192$	−33.5208	−	19.3532i	−0.174587	−	0.100798i
$193$	−49.1845	−	183.559i	−0.254842	−	0.951084i	−0.968178	−	0.250262i	$-0.919483\pi$
$193$	−49.1845	−	183.559i	−0.254842	−	0.951084i	0.713336	−	0.700822i	$-0.247183\pi$
$194$		−	67.3349i		−	0.347087i
$195$		0			0
$196$	1.60342			0.00818071
$197$	156.072	−	41.8194i	0.792244	−	0.212281i	0.160068	−	0.987106i	$-0.448829\pi$
$197$	156.072	−	41.8194i	0.792244	−	0.212281i	0.632176	+	0.774825i	$0.282162\pi$
$198$	125.073	−	216.632i	0.631681	−	1.09410i
$199$	269.633	−	155.673i	1.35494	−	0.782275i	0.366003	−	0.930613i	$-0.380726\pi$
$199$	269.633	−	155.673i	1.35494	−	0.782275i	0.988937	+	0.148338i	$0.0473925\pi$
$200$	220.854	+	220.854i	1.10427	+	1.10427i
$201$	−9.71230	+	36.2468i	−0.0483199	+	0.180332i
$202$	−32.1715	−	8.62034i	−0.159265	−	0.0426749i
$203$	10.3838	−	10.3838i	0.0511518	−	0.0511518i
$204$	0.126494	+	0.219095i	0.000620071	+	0.00107399i
$205$	−240.780	−	139.014i	−1.17454	−	0.678119i
$206$	−44.9521	−	167.763i	−0.218214	−	0.814385i
$207$		−	2.29183i		−	0.0110716i
$208$		0			0
$209$	−352.823			−1.68815
$210$	−18.7474	+	5.02336i	−0.0892735	+	0.0239208i
$211$	−160.126	+	277.347i	−0.758892	+	1.31444i	0.184524	+	0.982828i	$0.440926\pi$
$211$	−160.126	+	277.347i	−0.758892	+	1.31444i	−0.943416	+	0.331611i	$0.892408\pi$
$212$	−2.38732	+	1.37832i	−0.0112610	+	0.00650152i
$213$	−3.66383	−	3.66383i	−0.0172011	−	0.0172011i
$214$	61.7475	−	230.445i	0.288540	−	1.07684i
$215$	312.399	+	83.7070i	1.45302	+	0.389335i
$216$	60.0912	−	60.0912i	0.278200	−	0.278200i
$217$	−43.4889	−	75.3250i	−0.200410	−	0.347120i
$218$	214.150	+	123.639i	0.982339	+	0.567154i
$219$	5.12752	+	19.1362i	0.0234133	+	0.0873797i
$220$			4.15336i			0.0188789i
$221$		0			0
$222$	−16.2962			−0.0734064
$223$	319.945	−	85.7290i	1.43473	−	0.384435i	0.544046	−	0.839055i	$-0.316892\pi$
$223$	319.945	−	85.7290i	1.43473	−	0.384435i	0.890685	+	0.454620i	$0.150225\pi$
$224$	0.581722	−	1.00757i	0.00259698	−	0.00449809i
$225$	−290.864	+	167.930i	−1.29273	+	0.746356i
$226$	238.938	+	238.938i	1.05725	+	1.05725i
$227$	−41.8212	+	156.079i	−0.184234	+	0.687572i	0.810559	+	0.585657i	$0.199164\pi$
$227$	−41.8212	+	156.079i	−0.184234	+	0.687572i	−0.994793	+	0.101915i	$0.967503\pi$
$228$	−0.502251	−	0.134578i	−0.00220286	−	0.000590254i
$229$	−124.472	+	124.472i	−0.543547	+	0.543547i	−0.924567	−	0.381020i	$-0.875573\pi$
$229$	−124.472	+	124.472i	−0.543547	+	0.543547i	0.381020	+	0.924567i	$0.375573\pi$
$230$	−2.11028	−	3.65511i	−0.00917513	−	0.0158918i
$231$	−15.3592	−	8.86763i	−0.0664900	−	0.0383880i
$232$	15.0111	+	56.0223i	0.0647032	+	0.241476i
$233$		−	92.7546i		−	0.398088i	−0.979991	−	0.199044i	$-0.936216\pi$
$233$		−	92.7546i		−	0.398088i	0.979991	−	0.199044i	$-0.0637837\pi$
$234$		0			0
$235$	−111.616			−0.474961
$236$	1.24385	−	0.333288i	0.00527055	−	0.00141224i
$237$	−14.9284	+	25.8567i	−0.0629889	+	0.109100i
$238$	41.4173	−	23.9123i	0.174022	−	0.100472i
$239$	−26.1035	−	26.1035i	−0.109220	−	0.109220i	0.650385	−	0.759605i	$-0.274608\pi$
$239$	−26.1035	−	26.1035i	−0.109220	−	0.109220i	−0.759605	+	0.650385i	$0.774608\pi$
$240$	19.6626	−	73.3819i	0.0819276	−	0.305758i
$241$	−45.3667	−	12.1560i	−0.188244	−	0.0504397i	0.163466	−	0.986549i	$-0.447733\pi$
$241$	−45.3667	−	12.1560i	−0.188244	−	0.0504397i	−0.351709	+	0.936109i	$0.614399\pi$
$242$	127.296	−	127.296i	0.526017	−	0.526017i
$243$	69.0025	+	119.516i	0.283961	+	0.491835i
$244$	−0.957436	−	0.552776i	−0.00392392	−	0.00226548i
$245$	92.7924	+	346.306i	0.378744	+	1.41349i
$246$			41.5270i			0.168809i
$247$		0			0
$248$	343.522			1.38517
$249$	49.7934	−	13.3421i	0.199973	−	0.0535827i
$250$	−110.353	+	191.136i	−0.441410	+	0.764545i
$251$	156.585	−	90.4045i	0.623845	−	0.360177i	−0.154519	−	0.987990i	$-0.549383\pi$
$251$	156.585	−	90.4045i	0.623845	−	0.360177i	0.778365	+	0.627813i	$0.216050\pi$
$252$	0.444290	+	0.444290i	0.00176305	+	0.00176305i
$253$	0.998173	−	3.72523i	0.00394535	−	0.0147242i
$254$	−328.787	−	88.0983i	−1.29444	−	0.346844i
$255$	−39.9995	+	39.9995i	−0.156861	+	0.156861i
$256$	3.43097	+	5.94261i	0.0134022	+	0.0232133i
$257$	−153.535	−	88.6435i	−0.597413	−	0.344916i	0.170610	−	0.985339i	$-0.445426\pi$
$257$	−153.535	−	88.6435i	−0.597413	−	0.344916i	−0.768023	+	0.640422i	$0.778759\pi$
$258$	−12.5027	−	46.6606i	−0.0484600	−	0.180855i
$259$		−	27.7751i		−	0.107240i
$260$		0			0
$261$	−62.3671			−0.238954
$262$	−209.884	+	56.2381i	−0.801083	+	0.214649i
$263$	240.275	−	416.169i	0.913595	−	1.58239i	0.104649	−	0.994509i	$-0.466628\pi$
$263$	240.275	−	416.169i	0.913595	−	1.58239i	0.808946	−	0.587883i	$-0.200038\pi$
$264$	60.6616	−	35.0230i	0.229779	−	0.132663i
$265$	−435.847	−	435.847i	−1.64471	−	1.64471i
$266$	−25.4404	+	94.9447i	−0.0956405	+	0.356935i
$267$	51.3623	+	13.7625i	0.192368	+	0.0515449i
$268$	1.58191	−	1.58191i	0.00590265	−	0.00590265i
$269$	−53.3932	−	92.4798i	−0.198488	−	0.343791i	0.749550	−	0.661947i	$-0.230270\pi$
$269$	−53.3932	−	92.4798i	−0.198488	−	0.343791i	−0.948038	+	0.318156i	$0.896936\pi$
$270$	145.741	+	84.1438i	0.539782	+	0.311644i
$271$	−78.9475	−	294.636i	−0.291319	−	1.08722i	−0.944097	−	0.329669i	$-0.893063\pi$
$271$	−78.9475	−	294.636i	−0.291319	−	1.08722i	0.652777	−	0.757550i	$-0.273604\pi$
$272$			187.197i			0.688224i
$273$		0			0
$274$	284.855			1.03962
$275$	−545.921	+	146.279i	−1.98517	+	0.531924i
$276$	0.00284184	−	0.00492221i	1.02965e−5	−	1.78341e-5i
$277$	51.6492	−	29.8197i	0.186459	−	0.107652i	−0.403865	−	0.914819i	$-0.632333\pi$
$277$	51.6492	−	29.8197i	0.186459	−	0.107652i	0.590324	+	0.807166i	$0.299000\pi$
$278$	−236.074	−	236.074i	−0.849188	−	0.849188i
$279$	−95.6067	+	356.809i	−0.342676	+	1.27889i
$280$	126.199	+	33.8149i	0.450711	+	0.120768i
$281$	266.125	−	266.125i	0.947063	−	0.947063i	−0.0516049	−	0.998668i	$-0.516434\pi$
$281$	266.125	−	266.125i	0.947063	−	0.947063i	0.998668	+	0.0516049i	$0.0164337\pi$
$282$	8.33560	+	14.4377i	0.0295589	+	0.0511974i
$283$	372.572	+	215.104i	1.31651	+	0.760087i	0.983165	−	0.182719i	$-0.0584899\pi$
$283$	372.572	+	215.104i	1.31651	+	0.760087i	0.333343	+	0.942806i	$0.391823\pi$
$284$	0.0799498	+	0.298377i	0.000281513	+	0.00105062i
$285$		−	116.264i		−	0.407945i
$286$		0			0
$287$	−70.7781			−0.246614
$288$	−4.77280	+	1.27887i	−0.0165722	+	0.00444051i
$289$	−74.8063	+	129.568i	−0.258845	+	0.448333i
$290$	−99.4658	+	57.4266i	−0.342985	+	0.198023i
$291$	14.3369	+	14.3369i	0.0492675	+	0.0492675i
$292$	0.305688	−	1.14084i	0.00104688	−	0.00390699i
$293$	103.475	+	27.7261i	0.353158	+	0.0946284i	0.431037	−	0.902334i	$-0.358148\pi$
$293$	103.475	+	27.7261i	0.353158	+	0.0946284i	−0.0778785	+	0.996963i	$0.524815\pi$
$294$	37.8654	−	37.8654i	0.128794	−	0.128794i
$295$	143.967	+	249.358i	0.488023	+	0.845281i
$296$	95.0018	+	54.8493i	0.320952	+	0.185302i
$297$	39.8004	+	148.537i	0.134008	+	0.500125i
$298$		−	86.3049i		−	0.289614i
$299$		0			0
$300$	−0.832926			−0.00277642
$301$	79.5277	−	21.3094i	0.264212	−	0.0707953i
$302$	−115.283	+	199.676i	−0.381732	+	0.661178i
$303$	8.68535	−	5.01449i	0.0286645	−	0.0165495i
$304$	−272.057	−	272.057i	−0.894924	−	0.894924i
$305$	63.9800	−	238.777i	0.209770	−	0.782874i
$306$	−196.191	−	52.5692i	−0.641146	−	0.171795i
$307$	279.598	−	279.598i	0.910742	−	0.910742i	−0.0855884	−	0.996331i	$-0.527277\pi$
$307$	279.598	−	279.598i	0.910742	−	0.910742i	0.996331	+	0.0855884i	$0.0272770\pi$
$308$	0.528663	+	0.915670i	0.00171644	+	0.00297296i
$309$	45.2910	+	26.1488i	0.146573	+	0.0846239i
$310$	176.066	+	657.088i	0.567956	+	2.11964i
$311$			191.357i			0.615295i	0.951500	+	0.307648i	$0.0995418\pi$
$311$			191.357i			0.615295i	−0.951500	+	0.307648i	$0.900458\pi$
$312$		0			0
$313$	467.361			1.49317			0.746583	−	0.665292i	$-0.231693\pi$
$313$	467.361			1.49317			0.746583	+	0.665292i	$0.231693\pi$
$314$	201.683	−	54.0408i	0.642302	−	0.172104i
$315$	−70.2457	+	121.669i	−0.223002	+	0.386251i
$316$	1.54150	−	0.889987i	0.00487817	−	0.00281641i
$317$	−4.81422	−	4.81422i	−0.0151868	−	0.0151868i	0.699473	−	0.714659i	$-0.253418\pi$
$317$	−4.81422	−	4.81422i	−0.0151868	−	0.0151868i	−0.714659	+	0.699473i	$0.753418\pi$
$318$	−23.8279	+	88.9271i	−0.0749306	+	0.279645i
$319$	−101.374	−	27.1631i	−0.317787	−	0.0851507i
$320$	−364.845	+	364.845i	−1.14014	+	1.14014i
$321$	35.9188	+	62.2131i	0.111896	+	0.193810i
$322$	−0.930486	−	0.537216i	−0.00288971	−	0.00166837i
$323$	74.1473	+	276.722i	0.229558	+	0.856723i
$324$		−	2.55286i		−	0.00787921i
$325$		0			0
$326$	−637.182			−1.95455
$327$	−71.9216	+	19.2713i	−0.219944	+	0.0589337i
$328$	139.770	−	242.089i	0.426129	−	0.738077i
$329$	−24.6074	+	14.2071i	−0.0747945	+	0.0431826i
$330$	98.0831	+	98.0831i	0.297221	+	0.297221i
$331$	10.2911	−	38.4071i	0.0310911	−	0.116034i	−0.948636	−	0.316369i	$-0.897536\pi$
$331$	10.2911	−	38.4071i	0.0310911	−	0.116034i	0.979727	+	0.200335i	$0.0642031\pi$
$332$	−2.96854	−	0.795417i	−0.00894138	−	0.00239584i
$333$	−83.4111	+	83.4111i	−0.250484	+	0.250484i
$334$	196.921	+	341.078i	0.589585	+	1.02119i
$335$	433.208	+	250.113i	1.29316	+	0.746605i
$336$	−5.00554	−	18.6809i	−0.0148974	−	0.0555980i
$337$			84.6771i			0.251267i	0.992077	+	0.125634i	$0.0400964\pi$
$337$			84.6771i			0.251267i	−0.992077	+	0.125634i	$0.959904\pi$
$338$		0			0
$339$	−101.749			−0.300144
$340$	3.25750	−	0.872845i	0.00958089	−	0.00256719i
$341$	−310.806	+	538.332i	−0.911455	+	1.57869i
$342$	361.528	−	208.728i	1.05710	−	0.610316i
$343$	135.029	+	135.029i	0.393671	+	0.393671i
$344$	−84.1622	+	314.098i	−0.244657	+	0.913074i
$345$	1.22756	+	0.328923i	0.00355814	+	0.000953401i
$346$	391.944	−	391.944i	1.13279	−	1.13279i
$347$	−169.897	−	294.270i	−0.489616	−	0.848040i	0.510312	−	0.859989i	$-0.329530\pi$
$347$	−169.897	−	294.270i	−0.489616	−	0.848040i	−0.999929	+	0.0119488i	$0.996196\pi$
$348$	−0.133947	−	0.0773344i	−0.000384906	−	0.000222225i
$349$	−106.758	−	398.426i	−0.305897	−	1.14162i	−0.932171	−	0.362019i	$-0.882088\pi$
$349$	−106.758	−	398.426i	−0.305897	−	1.14162i	0.626274	−	0.779603i	$-0.284579\pi$
$350$			157.455i			0.449871i
$351$		0			0
$352$	−8.31490			−0.0236219
$353$	288.452	−	77.2905i	0.817145	−	0.218953i	0.174047	−	0.984737i	$-0.444316\pi$
$353$	288.452	−	77.2905i	0.817145	−	0.218953i	0.643098	+	0.765784i	$0.277649\pi$
$354$	21.5032	−	37.2447i	0.0607436	−	0.105211i
$355$	−59.8164	+	34.5350i	−0.168497	+	0.0972818i
$356$	−2.24159	−	2.24159i	−0.00629661	−	0.00629661i
$357$	−3.72714	+	13.9099i	−0.0104402	+	0.0389632i
$358$	475.785	+	127.486i	1.32901	+	0.356107i
$359$	−274.613	+	274.613i	−0.764940	+	0.764940i	−0.977211	−	0.212271i	$-0.931914\pi$
$359$	−274.613	+	274.613i	−0.764940	+	0.764940i	0.212271	+	0.977211i	$0.431914\pi$
$360$	−277.438	−	480.536i	−0.770661	−	1.33482i
$361$	−197.289	−	113.905i	−0.546508	−	0.315527i
$362$	−108.946	−	406.592i	−0.300956	−	1.12318i
$363$			54.2074i			0.149332i
$364$		0			0
$365$	264.089			0.723532
$366$	−35.6642	+	9.55620i	−0.0974433	+	0.0261098i
$367$	138.968	−	240.700i	0.378661	−	0.655860i	−0.612207	−	0.790698i	$-0.709718\pi$
$367$	138.968	−	240.700i	0.378661	−	0.655860i	0.990868	+	0.134838i	$0.0430514\pi$
$368$	3.64215	−	2.10279i	0.00989714	−	0.00571411i
$369$	212.553	+	212.553i	0.576025	+	0.576025i
$370$	−56.2241	+	209.831i	−0.151957	+	0.567112i
$371$	−151.566	−	40.6120i	−0.408534	−	0.109466i
$372$	−0.647776	+	0.647776i	−0.00174133	+	0.00174133i
$373$	−285.496	−	494.493i	−0.765404	−	1.32572i	−0.940033	−	0.341084i	$-0.889206\pi$
$373$	−285.496	−	494.493i	−0.765404	−	1.32572i	0.174629	−	0.984634i	$-0.444127\pi$
$374$	−296.001	−	170.896i	−0.791446	−	0.456942i
$375$	−17.2003	−	64.1925i	−0.0458676	−	0.171180i
$376$		−	112.223i		−	0.298465i
$377$		0			0
$378$	42.8412			0.113336
$379$	−246.885	+	66.1526i	−0.651411	+	0.174545i	−0.569367	−	0.822084i	$-0.692812\pi$
$379$	−246.885	+	66.1526i	−0.651411	+	0.174545i	−0.0820441	+	0.996629i	$0.526145\pi$
$380$	−3.46567	+	6.00272i	−0.00912018	+	0.0157966i
$381$	88.7627	−	51.2472i	0.232973	−	0.134507i
$382$	75.0983	+	75.0983i	0.196592	+	0.196592i
$383$	31.4773	−	117.475i	0.0821861	−	0.306723i	−0.912580	−	0.408897i	$-0.865913\pi$
$383$	31.4773	−	117.475i	0.0821861	−	0.306723i	0.994766	+	0.102175i	$0.0325800\pi$
$384$	73.1157	+	19.5913i	0.190405	+	0.0510190i
$385$	−167.172	+	167.172i	−0.434212	+	0.434212i
$386$	189.184	+	327.676i	0.490113	+	0.848900i
$387$	−302.823	−	174.835i	−0.782489	−	0.451770i
$388$	−0.312850	−	1.16757i	−0.000806314	−	0.00300921i
$389$			382.647i			0.983668i	0.870689	+	0.491834i	$0.163673\pi$
$389$			382.647i			0.983668i	−0.870689	+	0.491834i	$0.836327\pi$
$390$		0			0
$391$	−3.13149			−0.00800893
$392$	−348.189	+	93.2970i	−0.888237	+	0.238002i
$393$	32.7140	−	56.6622i	0.0832416	−	0.144179i
$394$	−278.608	+	160.854i	−0.707126	+	0.408259i
$395$	281.428	+	281.428i	0.712476	+	0.712476i
$396$	1.16222	−	4.33747i	0.00293490	−	0.0109532i
$397$	−670.261	−	179.596i	−1.68831	−	0.452382i	−0.718360	−	0.695671i	$-0.755107\pi$
$397$	−670.261	−	179.596i	−1.68831	−	0.452382i	−0.969954	+	0.243289i	$0.921774\pi$
$398$	−438.337	+	438.337i	−1.10135	+	1.10135i
$399$	−14.7988	−	25.6322i	−0.0370896	−	0.0642411i
$400$	−533.745	−	308.158i	−1.33436	−	0.770395i
$401$	39.0164	+	145.611i	0.0972977	+	0.363120i	0.997358	−	0.0726459i	$-0.0231443\pi$
$401$	39.0164	+	145.611i	0.0972977	+	0.363120i	−0.900060	+	0.435766i	$0.856478\pi$
$402$		−	74.7148i		−	0.185858i
$403$		0			0
$404$	−0.597899			−0.00147995
$405$	551.366	−	147.738i	1.36140	−	0.364785i
$406$	−14.6192	+	25.3211i	−0.0360078	+	0.0623673i
$407$	−171.908	+	99.2513i	−0.422379	+	0.243861i
$408$	−40.2171	−	40.2171i	−0.0985712	−	0.0985712i
$409$	80.8194	−	301.622i	0.197602	−	0.737462i	−0.793975	−	0.607950i	$-0.791992\pi$
$409$	80.8194	−	301.622i	0.197602	−	0.737462i	0.991578	−	0.129512i	$-0.0413412\pi$
$410$	534.705	+	143.274i	1.30416	+	0.349448i
$411$	−60.6510	+	60.6510i	−0.147569	+	0.147569i
$412$	−1.55892	−	2.70012i	−0.00378378	−	0.00655369i
$413$	63.4794	+	36.6498i	0.153703	+	0.0887405i
$414$	1.18103	+	4.40765i	0.00285272	+	0.0106465i
$415$		−	687.175i		−	1.65584i
$416$		0			0
$417$	100.529			0.241077
$418$	678.550	−	181.817i	1.62333	−	0.434969i
$419$	138.039	−	239.091i	0.329450	−	0.570624i	−0.652953	−	0.757398i	$-0.726470\pi$
$419$	138.039	−	239.091i	0.329450	−	0.570624i	0.982403	+	0.186775i	$0.0598034\pi$
$420$	−0.301737	+	0.174208i	−0.000718420	+	0.000414780i
$421$	188.700	+	188.700i	0.448218	+	0.448218i	0.894762	−	0.446544i	$-0.147345\pi$
$421$	188.700	+	188.700i	0.448218	+	0.448218i	−0.446544	+	0.894762i	$0.647345\pi$
$422$	165.033	−	615.910i	0.391072	−	1.45950i
$423$	116.563	+	31.2331i	0.275564	+	0.0738371i
$424$	438.217	−	438.217i	1.03353	−	1.03353i
$425$	229.455	+	397.428i	0.539895	+	0.935126i
$426$	8.93432	+	5.15823i	0.0209726	+	0.0121085i
$427$	−16.2875	−	60.7857i	−0.0381440	−	0.142355i
$428$		−	4.28275i		−	0.0100064i
$429$		0			0
$430$	−643.941			−1.49754
$431$	−332.145	+	88.9981i	−0.770639	+	0.206492i	−0.622654	−	0.782497i	$-0.713945\pi$
$431$	−332.145	+	88.9981i	−0.770639	+	0.206492i	−0.147985	+	0.988990i	$0.547279\pi$
$432$	−83.8453	+	145.224i	−0.194086	+	0.336167i
$433$	167.611	−	96.7701i	0.387092	−	0.223488i	−0.293807	−	0.955865i	$-0.594922\pi$
$433$	167.611	−	96.7701i	0.387092	−	0.223488i	0.680899	+	0.732377i	$0.261589\pi$
$434$	122.454	+	122.454i	0.282153	+	0.282153i
$435$	8.95092	−	33.4053i	0.0205768	−	0.0767938i
$436$	4.28776	+	1.14890i	0.00983431	+	0.00263509i
$437$	4.55106	−	4.55106i	0.0104143	−	0.0104143i
$438$	−19.7225	−	34.1604i	−0.0450285	−	0.0779917i
$439$	304.574	+	175.846i	0.693790	+	0.400560i	0.805030	−	0.593234i	$-0.202149\pi$
$439$	304.574	+	175.846i	0.693790	+	0.400560i	−0.111240	+	0.993794i	$0.535482\pi$
$440$	−241.668	−	901.918i	−0.549246	−	2.04981i
$441$		−	387.623i		−	0.878963i
$442$		0			0
$443$	−336.467			−0.759520			−0.379760	−	0.925085i	$-0.623993\pi$
$443$	−336.467			−0.759520			−0.379760	+	0.925085i	$0.623993\pi$
$444$	−0.282573	+	0.0757151i	−0.000636425	+	0.000170530i
$445$	354.414	−	613.863i	0.796435	−	1.37947i
$446$	−571.141	+	329.748i	−1.28058	+	0.739346i
$447$	18.3759	+	18.3759i	0.0411094	+	0.0411094i
$448$	−33.9961	+	126.875i	−0.0758842	+	0.283204i
$449$	132.735	+	35.5663i	0.295624	+	0.0792122i	0.403583	−	0.914943i	$-0.367765\pi$
$449$	132.735	+	35.5663i	0.295624	+	0.0792122i	−0.107959	+	0.994155i	$0.534431\pi$
$450$	472.851	−	472.851i	1.05078	−	1.05078i
$451$	252.918	+	438.067i	0.560795	+	0.971325i
$452$	5.25328	+	3.03298i	0.0116223	+	0.00671014i
$453$	−17.9688	−	67.0606i	−0.0396663	−	0.148037i
$454$		−	321.722i		−	0.708639i
$455$		0			0
$456$	116.896			0.256352
$457$	−191.805	+	51.3939i	−0.419704	+	0.112459i	−0.462489	−	0.886625i	$-0.653044\pi$
$457$	−191.805	+	51.3939i	−0.419704	+	0.112459i	0.0427852	+	0.999084i	$0.486377\pi$
$458$	175.242	−	303.529i	0.382625	−	0.662726i
$459$	108.134	−	62.4315i	0.235587	−	0.136016i
$460$	−0.0535740	−	0.0535740i	−0.000116465	−	0.000116465i
$461$	234.825	−	876.380i	0.509382	−	1.90104i	0.0828682	−	0.996561i	$-0.473592\pi$
$461$	234.825	−	876.380i	0.509382	−	1.90104i	0.426514	−	0.904481i	$-0.359741\pi$
$462$	34.1085	+	9.13934i	0.0738279	+	0.0197821i
$463$	−592.689	+	592.689i	−1.28011	+	1.28011i	−0.339498	+	0.940607i	$0.610257\pi$
$463$	−592.689	+	592.689i	−1.28011	+	1.28011i	−0.940607	+	0.339498i	$0.889743\pi$
$464$	−57.2229	−	99.1130i	−0.123325	−	0.213606i
$465$	−177.394	−	102.418i	−0.381493	−	0.220255i
$466$	47.7983	+	178.386i	0.102572	+	0.382802i
$467$			151.923i			0.325318i	0.986682	+	0.162659i	$0.0520070\pi$
$467$			151.923i			0.325318i	−0.986682	+	0.162659i	$0.947993\pi$
$468$		0			0
$469$	127.343			0.271520
$470$	214.660	−	57.5179i	0.456723	−	0.122378i
$471$	−31.4358	+	54.4483i	−0.0667426	+	0.115602i
$472$	−250.714	+	144.750i	−0.531174	+	0.306673i
$473$	−416.074	−	416.074i	−0.879650	−	0.879650i
$474$	15.3858	−	57.4205i	0.0324595	−	0.121140i
$475$	−911.062	−	244.118i	−1.91803	−	0.513933i
$476$	0.607065	−	0.607065i	0.00127535	−	0.00127535i
$477$	333.206	+	577.129i	0.698544	+	1.20991i
$478$	63.6539	+	36.7506i	0.133167	+	0.0768841i
$479$	130.457	+	486.873i	0.272353	+	1.01644i	0.957594	+	0.288120i	$0.0930301\pi$
$479$	130.457	+	486.873i	0.272353	+	1.01644i	−0.685241	+	0.728316i	$0.740303\pi$
$480$		−	2.73997i		−	0.00570827i
$481$		0			0
$482$	93.5136			0.194012
$483$	0.312501	−	0.0837344i	0.000647000	−	0.000173363i
$484$	1.61584	−	2.79872i	0.00333852	−	0.00578248i
$485$	234.066	−	135.138i	0.482611	−	0.278636i
$486$	−194.295	−	194.295i	−0.399783	−	0.399783i
$487$	−142.989	+	533.641i	−0.293611	+	1.09577i	0.648703	+	0.761042i	$0.275312\pi$
$487$	−142.989	+	533.641i	−0.293611	+	1.09577i	−0.942314	+	0.334730i	$0.891355\pi$
$488$	240.075	+	64.3279i	0.491957	+	0.131819i
$489$	135.668	−	135.668i	0.277439	−	0.277439i
$490$	−356.917	−	618.198i	−0.728402	−	1.26163i
$491$	−714.499	−	412.516i	−1.45519	−	0.840155i	−0.456422	−	0.889764i	$-0.650869\pi$
$491$	−714.499	−	412.516i	−1.45519	−	0.840155i	−0.998769	+	0.0496089i	$0.984203\pi$
$492$	0.192942	+	0.720069i	0.000392158	+	0.00146355i
$493$			85.2167i			0.172853i
$494$		0			0
$495$	1004.06			2.02841
$496$	−654.758	+	175.442i	−1.32008	+	0.353713i
$497$	−8.79163	+	15.2275i	−0.0176894	+	0.0306389i
$498$	−88.8872	+	51.3191i	−0.178488	+	0.103050i
$499$	225.404	+	225.404i	0.451711	+	0.451711i	0.895922	−	0.444211i	$-0.146516\pi$
$499$	225.404	+	225.404i	0.451711	+	0.451711i	−0.444211	+	0.895922i	$0.646516\pi$
$500$	−1.02543	+	3.82697i	−0.00205087	+	0.00765395i
$501$	−114.550	−	30.6936i	−0.228643	−	0.0612646i
$502$	−254.557	+	254.557i	−0.507087	+	0.507087i
$503$	−117.302	−	203.173i	−0.233205	−	0.403923i	0.725545	−	0.688175i	$-0.241588\pi$
$503$	−117.302	−	203.173i	−0.233205	−	0.403923i	−0.958749	+	0.284252i	$0.908255\pi$
$504$	−122.331	−	70.6277i	−0.242720	−	0.140134i
$505$	−34.6013	−	129.134i	−0.0685174	−	0.255711i
$506$			7.67875i			0.0151754i
$507$		0			0
$508$	−6.11042			−0.0120284
$509$	−668.249	+	179.057i	−1.31287	+	0.351782i	−0.846301	−	0.532705i	$-0.821176\pi$
$509$	−668.249	+	179.057i	−1.31287	+	0.351782i	−0.466566	+	0.884486i	$0.654509\pi$
$510$	56.3146	−	97.5398i	0.110421	−	0.191254i
$511$	58.2225	−	33.6148i	0.113938	−	0.0657823i
$512$	−366.771	−	366.771i	−0.716350	−	0.716350i
$513$	−66.4211	+	247.887i	−0.129476	+	0.483210i
$514$	340.959	+	91.3596i	0.663344	+	0.177742i
$515$	492.954	−	492.954i	0.957192	−	0.957192i
$516$	−0.433587	−	0.750994i	−0.000840284	−	0.00145542i
$517$	175.864	+	101.535i	0.340162	+	0.196393i
$518$	14.3131	+	53.4171i	0.0276314	+	0.103122i
$519$			166.904i			0.321588i
$520$		0			0
$521$	−297.695			−0.571391			−0.285695	−	0.958320i	$-0.592225\pi$
$521$	−297.695			−0.571391			−0.285695	+	0.958320i	$0.592225\pi$
$522$	119.944	−	32.1390i	0.229779	−	0.0615690i
$523$	−169.819	+	294.135i	−0.324701	+	0.562399i	−0.981452	−	0.191709i	$-0.938597\pi$
$523$	−169.819	+	294.135i	−0.324701	+	0.562399i	0.656751	+	0.754108i	$0.271930\pi$
$524$	−3.37804	+	1.95031i	−0.00644664	+	0.00372197i
$525$	−33.5251	−	33.5251i	−0.0638572	−	0.0638572i
$526$	−247.638	+	924.196i	−0.470794	+	1.75703i
$527$	487.535	+	130.634i	0.925113	+	0.247883i
$528$	−97.7352	+	97.7352i	−0.185105	+	0.185105i
$529$	−264.465	−	458.067i	−0.499934	−	0.865910i
$530$	1062.82	+	613.621i	2.00533	+	1.15778i
$531$	−80.5716	−	300.697i	−0.151736	−	0.566285i
$532$			1.76452i			0.00331677i
$533$		0			0
$534$	−105.872			−0.198262
$535$	924.985	−	247.849i	1.72894	−	0.463269i
$536$	−251.473	+	435.563i	−0.469165	+	0.812618i
$537$	−128.448	+	74.1592i	−0.239195	+	0.138099i
$538$	150.343	+	150.343i	0.279447	+	0.279447i
$539$	168.823	−	630.058i	0.313216	−	1.16894i
$540$	2.91807	+	0.781893i	0.00540383	+	0.00144795i
$541$	123.367	−	123.367i	0.228036	−	0.228036i	−0.583836	−	0.811872i	$-0.698449\pi$
$541$	123.367	−	123.367i	0.228036	−	0.228036i	0.811872	+	0.583836i	$0.198449\pi$
$542$	303.664	+	525.961i	0.560266	+	0.970408i
$543$	109.768	+	63.3744i	0.202150	+	0.116712i
$544$	1.74741	+	6.52143i	0.00321215	+	0.0119879i
$545$			992.557i			1.82120i
$546$		0			0
$547$	−193.679			−0.354074			−0.177037	−	0.984204i	$-0.556651\pi$
$547$	−193.679			−0.354074			−0.177037	+	0.984204i	$0.556651\pi$
$548$	4.93932	−	1.32349i	0.00901336	−	0.00241512i
$549$	−133.632	+	231.458i	−0.243410	+	0.421599i
$550$	974.536	−	562.649i	1.77188	−	1.02300i
$551$	−123.847	−	123.847i	−0.224768	−	0.224768i
$552$	−0.330712	+	1.23423i	−0.000599116	+	0.00223593i
$553$	97.8668	+	26.2233i	0.176974	+	0.0474201i
$554$	−83.9652	+	83.9652i	−0.151562	+	0.151562i
$555$	−32.7058	−	56.6481i	−0.0589294	−	0.102069i
$556$	−5.19032	−	2.99663i	−0.00933510	−	0.00538962i
$557$	233.565	+	871.675i	0.419326	+	1.56495i	0.776010	+	0.630721i	$0.217241\pi$
$557$	233.565	+	871.675i	0.419326	+	1.56495i	−0.356684	+	0.934225i	$0.616093\pi$
$558$		−	735.484i		−	1.31807i
$559$		0			0
$560$	−257.807			−0.460369
$561$	99.4110	−	26.6371i	0.177203	−	0.0474815i
$562$	−374.672	+	648.951i	−0.666676	+	1.15472i
$563$	412.904	−	238.390i	0.733399	−	0.423428i	−0.0862652	−	0.996272i	$-0.527493\pi$
$563$	412.904	−	238.390i	0.733399	−	0.423428i	0.819664	+	0.572844i	$0.194160\pi$
$564$	0.211617	+	0.211617i	0.000375208	+	0.000375208i
$565$	−351.047	+	1310.12i	−0.621322	+	2.31880i
$566$	−827.378	−	221.695i	−1.46180	−	0.391688i
$567$	102.752	−	102.752i	0.181221	−	0.181221i
$568$	−34.7228	−	60.1417i	−0.0611317	−	0.105883i
$569$	737.875	+	426.012i	1.29679	+	0.748704i	0.979849	−	0.199741i	$-0.0640100\pi$
$569$	737.875	+	426.012i	1.29679	+	0.748704i	0.316944	+	0.948444i	$0.397343\pi$
$570$	59.9133	+	223.600i	0.105111	+	0.392280i
$571$			839.202i			1.46971i	0.678227	+	0.734853i	$0.262749\pi$
$571$			839.202i			1.46971i	−0.678227	+	0.734853i	$0.737251\pi$
$572$		0			0
$573$	−31.9796			−0.0558109
$574$	136.121	−	36.4734i	0.237144	−	0.0635425i
$575$	5.15497	−	8.92868i	0.00896517	−	0.0155281i
$576$	483.111	−	278.924i	0.838735	−	0.484244i
$577$	699.005	+	699.005i	1.21145	+	1.21145i	0.970551	+	0.240897i	$0.0774417\pi$
$577$	699.005	+	699.005i	1.21145	+	1.21145i	0.240897	+	0.970551i	$0.422558\pi$
$578$	77.0984	−	287.735i	0.133388	−	0.497812i
$579$	−110.049	−	29.4875i	−0.190067	−	0.0509283i
$580$	−1.45790	+	1.45790i	−0.00251362	+	0.00251362i
$581$	−87.4676	−	151.498i	−0.150547	−	0.260754i
$582$	−34.9607	−	20.1846i	−0.0600700	−	0.0346814i
$583$	290.246	+	1083.21i	0.497849	+	1.85800i
$584$			265.525i			0.454667i
$585$		0			0
$586$	−213.292			−0.363979
$587$	224.194	−	60.0726i	0.381932	−	0.102338i	−0.0627446	−	0.998030i	$-0.519985\pi$
$587$	224.194	−	60.0726i	0.381932	−	0.102338i	0.444676	+	0.895691i	$0.353319\pi$
$588$	0.480647	−	0.832506i	0.000817428	−	0.00141583i
$589$	−898.397	+	518.690i	−1.52529	+	0.880628i
$590$	−405.376	−	405.376i	−0.687079	−	0.687079i
$591$	25.0719	−	93.5695i	0.0424228	−	0.158324i
$592$	−209.087	−	56.0247i	−0.353188	−	0.0946364i
$593$	−500.788	+	500.788i	−0.844499	+	0.844499i	−0.989440	−	0.144941i	$-0.953701\pi$
$593$	−500.788	+	500.788i	−0.844499	+	0.844499i	0.144941	+	0.989440i	$0.453701\pi$
$594$	−153.088	−	265.157i	−0.257725	−	0.446392i
$595$	166.245	+	95.9819i	0.279404	+	0.161314i
$596$	−0.400988	−	1.49651i	−0.000672798	−	0.00251092i
$597$		−	186.660i		−	0.312664i
$598$		0			0
$599$	563.203			0.940239			0.470119	−	0.882603i	$-0.344211\pi$
$599$	563.203			0.940239			0.470119	+	0.882603i	$0.344211\pi$
$600$	180.873	−	48.4648i	0.301455	−	0.0807747i
$601$	−67.6406	+	117.157i	−0.112547	+	0.194937i	−0.916796	−	0.399355i	$-0.869234\pi$
$601$	−67.6406	+	117.157i	−0.112547	+	0.194937i	0.804250	+	0.594292i	$0.202567\pi$
$602$	−141.967	+	81.9645i	−0.235825	+	0.136154i
$603$	−382.423	−	382.423i	−0.634200	−	0.634200i
$604$	−1.07125	+	3.99796i	−0.00177359	+	0.00661913i
$605$	697.978	+	187.023i	1.15368	+	0.309128i
$606$	−14.1196	+	14.1196i	−0.0232997	+	0.0232997i
$607$	−20.0524	−	34.7318i	−0.0330352	−	0.0572187i	0.849035	−	0.528336i	$-0.177184\pi$
$607$	−20.0524	−	34.7318i	−0.0330352	−	0.0572187i	−0.882070	+	0.471118i	$0.843851\pi$
$608$	−12.0173	−	6.93817i	−0.0197652	−	0.0114115i
$609$	−2.27865	−	8.50403i	−0.00374162	−	0.0139639i
$610$			492.185i			0.806861i
$611$		0			0
$612$	−3.64615			−0.00595776
$613$	−714.402	+	191.423i	−1.16542	+	0.312273i	−0.789128	−	0.614228i	$-0.789467\pi$
$613$	−714.402	+	191.423i	−1.16542	+	0.312273i	−0.376291	+	0.926501i	$0.622801\pi$
$614$	−393.640	+	681.805i	−0.641108	+	1.11043i
$615$	−144.354	+	83.3430i	−0.234722	+	0.135517i
$616$	−168.081	−	168.081i	−0.272858	−	0.272858i
$617$	−169.497	+	632.571i	−0.274712	+	1.02524i	0.681323	+	0.731983i	$0.261405\pi$
$617$	−169.497	+	632.571i	−0.274712	+	1.02524i	−0.956034	+	0.293254i	$0.905262\pi$
$618$	−100.579	−	26.9500i	−0.162749	−	0.0436084i
$619$	739.075	−	739.075i	1.19398	−	1.19398i	0.218042	−	0.975939i	$-0.430033\pi$
$619$	739.075	−	739.075i	1.19398	−	1.19398i	0.975939	−	0.218042i	$-0.0699671\pi$
$620$	6.10590	+	10.5757i	0.00984822	+	0.0170576i
$621$	−2.42936	−	1.40259i	−0.00391202	−	0.00225860i
$622$	−98.6100	−	368.018i	−0.158537	−	0.591668i
$623$		−	180.447i		−	0.289642i
$624$		0			0
$625$	85.8635			0.137382
$626$	−898.829	+	240.841i	−1.43583	+	0.384729i
$627$	−105.764	+	183.188i	−0.168682	+	0.292166i
$628$	3.24605	−	1.87411i	0.00516887	−	0.00298425i
$629$	113.971	+	113.971i	0.181194	+	0.181194i
$630$	72.3981	−	270.193i	0.114918	−	0.428878i
$631$	822.253	+	220.322i	1.30309	+	0.349163i	0.842620	−	0.538509i	$-0.181012\pi$
$631$	822.253	+	220.322i	1.30309	+	0.349163i	0.460475	+	0.887673i	$0.347679\pi$
$632$	−282.958	+	282.958i	−0.447719	+	0.447719i
$633$	96.0001	+	166.277i	0.151659	+	0.262681i
$634$	11.7396	+	6.77785i	0.0185167	+	0.0106906i
$635$	−353.619	−	1319.72i	−0.556881	−	2.07831i
$636$			1.65268i			0.00259856i
$637$		0			0
$638$	208.960			0.327524
$639$	72.1318	−	19.3277i	0.112882	−	0.0302467i
$640$	504.518	−	873.851i	0.788309	−	1.36539i
$641$	537.784	−	310.490i	0.838976	−	0.484383i	−0.0179397	−	0.999839i	$-0.505711\pi$
$641$	537.784	−	310.490i	0.838976	−	0.484383i	0.856916	+	0.515456i	$0.172377\pi$
$642$	−101.139	−	101.139i	−0.157537	−	0.157537i
$643$	33.3464	−	124.450i	0.0518607	−	0.193547i	−0.935136	−	0.354290i	$-0.884723\pi$
$643$	33.3464	−	124.450i	0.0518607	−	0.193547i	0.986996	+	0.160744i	$0.0513892\pi$
$644$	−0.0186304	−	0.00499200i	−2.89292e−5	−	7.75156e-6i
$645$	137.107	−	137.107i	0.212569	−	0.212569i
$646$	−285.200	−	493.982i	−0.441487	−	0.764678i
$647$	−492.538	−	284.367i	−0.761264	−	0.439516i	0.0684852	−	0.997652i	$-0.478183\pi$
$647$	−492.538	−	284.367i	−0.761264	−	0.439516i	−0.829750	+	0.558136i	$0.811517\pi$
$648$	148.541	+	554.364i	0.229231	+	0.855500i
$649$		−	523.857i		−	0.807176i
$650$		0			0
$651$	−52.1456			−0.0801008
$652$	−11.0486	+	2.96046i	−0.0169457	+	0.00454058i
$653$	498.955	−	864.215i	0.764096	−	1.32345i	−0.176627	−	0.984278i	$-0.556519\pi$
$653$	498.955	−	864.215i	0.764096	−	1.32345i	0.940723	−	0.339175i	$-0.110148\pi$
$654$	128.389	−	74.1253i	0.196313	−	0.113341i
$655$	−616.720	−	616.720i	−0.941557	−	0.941557i
$656$	−142.766	+	532.809i	−0.217631	+	0.812208i
$657$	−275.796	−	73.8992i	−0.419780	−	0.112480i
$658$	40.0038	−	40.0038i	0.0607960	−	0.0607960i
$659$	218.812	+	378.994i	0.332037	+	0.575105i	0.982911	−	0.184081i	$-0.0589308\pi$
$659$	218.812	+	378.994i	0.332037	+	0.575105i	−0.650874	+	0.759186i	$0.725598\pi$
$660$	2.15645	+	1.24503i	0.00326735	+	0.00188640i
$661$	−24.5675	−	91.6872i	−0.0371672	−	0.138710i	0.944849	−	0.327506i	$-0.106208\pi$
$661$	−24.5675	−	91.6872i	−0.0371672	−	0.138710i	−0.982016	+	0.188796i	$0.939541\pi$
$662$			79.1678i			0.119589i
$663$		0			0
$664$	690.912			1.04053
$665$	−381.100	+	102.115i	−0.573083	+	0.153557i
$666$	117.433	−	203.400i	0.176326	−	0.305405i
$667$	1.65800	−	0.957245i	0.00248575	−	0.00143515i
$668$	4.99928	+	4.99928i	0.00748395	+	0.00748395i
$669$	51.3969	−	191.816i	0.0768265	−	0.286720i
$670$	−962.034	−	257.776i	−1.43587	−	0.384740i
$671$	−318.019	+	318.019i	−0.473948	+	0.473948i
$672$	−0.348759	−	0.604068i	−0.000518986	−	0.000898911i
$673$	−263.517	−	152.141i	−0.391555	−	0.226064i	0.291279	−	0.956638i	$-0.405919\pi$
$673$	−263.517	−	152.141i	−0.391555	−	0.226064i	−0.682834	+	0.730574i	$0.739253\pi$
$674$	−43.6358	−	162.851i	−0.0647416	−	0.241619i
$675$			411.091i			0.609024i
$676$		0			0
$677$	−535.082			−0.790372			−0.395186	−	0.918601i	$-0.629320\pi$
$677$	−535.082			−0.790372			−0.395186	+	0.918601i	$0.629320\pi$
$678$	195.683	−	52.4332i	0.288618	−	0.0773351i
$679$	34.4023	−	59.5866i	0.0506662	−	0.0877564i
$680$	−656.592	+	379.084i	−0.965577	+	0.557476i
$681$	68.5006	+	68.5006i	0.100588	+	0.100588i
$682$	320.329	−	1195.49i	0.469691	−	1.75291i
$683$	−488.481	−	130.888i	−0.715199	−	0.191637i	−0.117171	−	0.993112i	$-0.537382\pi$
$683$	−488.481	−	130.888i	−0.715199	−	0.191637i	−0.598029	+	0.801475i	$0.704049\pi$
$684$	5.29902	−	5.29902i	0.00774710	−	0.00774710i
$685$	571.692	+	990.200i	0.834587	+	1.44555i
$686$	−329.272	−	190.105i	−0.479988	−	0.277121i
$687$	27.3145	+	101.939i	0.0397591	+	0.148383i
$688$		−	641.657i		−	0.932642i
$689$		0			0
$690$	−2.53034			−0.00366716
$691$	574.894	−	154.042i	0.831974	−	0.222927i	0.182399	−	0.983225i	$-0.441614\pi$
$691$	574.894	−	154.042i	0.831974	−	0.222927i	0.649575	+	0.760298i	$0.274947\pi$
$692$	4.97518	−	8.61726i	0.00718956	−	0.0124527i
$693$	221.361	−	127.803i	0.319424	−	0.184420i
$694$	478.389	+	478.389i	0.689322	+	0.689322i
$695$	346.839	−	1294.42i	0.499049	−	1.86248i
$696$	33.5869	+	8.99960i	0.0482571	+	0.0129305i
$697$	290.427	−	290.427i	0.416682	−	0.416682i
$698$	410.634	+	711.239i	0.588301	+	1.01897i
$699$	−48.1588	−	27.8045i	−0.0688967	−	0.0397775i
$700$	0.731563	+	2.73023i	0.00104509	+	0.00390033i
$701$		−	1080.69i		−	1.54164i	−0.637052	−	0.770821i	$-0.719846\pi$
$701$		−	1080.69i		−	1.54164i	0.637052	−	0.770821i	$-0.280154\pi$
$702$		0			0
$703$	−331.272			−0.471226
$704$	906.751	−	242.963i	1.28800	−	0.345118i
$705$	−33.4584	+	57.9516i	−0.0474587	+	0.0822009i
$706$	−514.922	+	297.290i	−0.729351	+	0.421091i
$707$	−24.0653	−	24.0653i	−0.0340386	−	0.0340386i
$708$	0.199816	−	0.745722i	0.000282225	−	0.00105328i
$709$	527.703	+	141.398i	0.744292	+	0.199432i	0.610985	−	0.791642i	$-0.290774\pi$
$709$	527.703	+	141.398i	0.744292	+	0.199432i	0.133307	+	0.991075i	$0.457440\pi$
$710$	97.2424	−	97.2424i	0.136961	−	0.136961i
$711$	−215.152	−	372.654i	−0.302605	−	0.524127i
$712$	617.201	+	356.341i	0.866855	+	0.500479i
$713$	−2.93485	−	10.9530i	−0.00411620	−	0.0153619i
$714$		−	28.6722i		−	0.0401571i
$715$		0			0
$716$	8.84232			0.0123496
$717$	−21.3780	+	5.72821i	−0.0298159	+	0.00798914i
$718$	386.623	−	669.651i	0.538472	−	0.932661i
$719$	−1155.86	+	667.337i	−1.60760	+	0.928146i	−0.617689	+	0.786422i	$0.711931\pi$
$719$	−1155.86	+	667.337i	−1.60760	+	0.928146i	−0.989906	+	0.141723i	$0.954736\pi$
$720$	774.218	+	774.218i	1.07530	+	1.07530i
$721$	45.9332	−	171.425i	0.0637077	−	0.237760i
$722$	438.125	+	117.395i	0.606821	+	0.162597i
$723$	−19.9108	+	19.9108i	−0.0275391	+	0.0275391i
$724$	−3.77820	−	6.54403i	−0.00521851	−	0.00903872i
$725$	−242.974	−	140.281i	−0.335137	−	0.193491i
$726$	−27.9341	−	104.252i	−0.0384768	−	0.143597i
$727$		−	1107.01i		−	1.52271i	−0.648335	−	0.761356i	$-0.724534\pi$
$727$		−	1107.01i		−	1.52271i	0.648335	−	0.761356i	$-0.275466\pi$
$728$		0			0
$729$	−560.082			−0.768289
$730$	−507.897	+	136.090i	−0.695749	+	0.186425i
$731$	−238.890	+	413.770i	−0.326799	+	0.566032i
$732$	−0.574010	+	0.331405i	−0.000784166	+	0.000452738i
$733$	−402.981	−	402.981i	−0.549769	−	0.549769i	0.376605	−	0.926374i	$-0.377091\pi$
$733$	−402.981	−	402.981i	−0.549769	−	0.549769i	−0.926374	+	0.376605i	$0.877091\pi$
$734$	−143.227	+	534.529i	−0.195132	+	0.728241i
$735$	207.620	+	55.6316i	0.282476	+	0.0756893i
$736$	0.107254	−	0.107254i	0.000145725	−	0.000145725i
$737$	−455.047	−	788.164i	−0.617431	−	1.06942i
$738$	−518.316	−	299.250i	−0.702325	−	0.405487i
$739$	−152.340	−	568.542i	−0.206144	−	0.769340i	−0.989098	−	0.147260i	$-0.952955\pi$
$739$	−152.340	−	568.542i	−0.206144	−	0.769340i	0.782954	−	0.622080i	$-0.213712\pi$
$740$			3.89965i			0.00526980i
$741$		0			0
$742$	312.421			0.421052
$743$	596.069	−	159.716i	0.802246	−	0.214961i	0.165676	−	0.986180i	$-0.447019\pi$
$743$	596.069	−	159.716i	0.802246	−	0.214961i	0.636570	+	0.771219i	$0.280353\pi$
$744$	102.975	−	178.359i	0.138408	−	0.239729i
$745$	300.009	−	173.210i	0.402697	−	0.232497i
$746$	803.888	+	803.888i	1.07760	+	1.07760i
$747$	−192.290	+	717.636i	−0.257416	+	0.960691i
$748$	−5.92660	−	1.58803i	−0.00792326	−	0.00212303i
$749$	172.379	−	172.379i	0.230146	−	0.230146i
$750$	66.1594	+	114.591i	0.0882125	+	0.152789i
$751$	−863.544	−	498.567i	−1.14986	−	0.663871i	−0.201006	−	0.979590i	$-0.564421\pi$
$751$	−863.544	−	498.567i	−1.14986	−	0.663871i	−0.948853	+	0.315719i	$0.897754\pi$
$752$	57.3139	+	213.898i	0.0762152	+	0.284439i
$753$		−	108.400i		−	0.143957i
$754$		0			0
$755$	−925.472			−1.22579
$756$	0.742856	−	0.199048i	0.000982614	−	0.000263290i
$757$	48.7879	−	84.5031i	0.0644490	−	0.111629i	−0.832000	−	0.554775i	$-0.812804\pi$
$757$	48.7879	−	84.5031i	0.0644490	−	0.111629i	0.896449	+	0.443146i	$0.146138\pi$
$758$	440.719	−	254.449i	0.581424	−	0.335685i
$759$	−1.63495	−	1.63495i	−0.00215408	−	0.00215408i
$760$	403.308	−	1505.17i	0.530669	−	1.98048i
$761$	−286.709	−	76.8236i	−0.376754	−	0.100951i	0.0654727	−	0.997854i	$-0.479144\pi$
$761$	−286.709	−	76.8236i	−0.376754	−	0.100951i	−0.442226	+	0.896904i	$0.645811\pi$
$762$	−144.300	+	144.300i	−0.189370	+	0.189370i
$763$	126.338	+	218.824i	0.165581	+	0.286795i
$764$	1.65111	+	0.953267i	0.00216113	+	0.00124773i
$765$	−211.008	−	787.493i	−0.275828	−	1.02940i
$766$			242.149i			0.316121i
$767$		0			0
$768$	4.11392			0.00535667
$769$	−137.314	+	36.7932i	−0.178562	+	0.0478455i	−0.346992	−	0.937868i	$-0.612797\pi$
$769$	−137.314	+	36.7932i	−0.178562	+	0.0478455i	0.168430	+	0.985714i	$0.446130\pi$
$770$	235.358	−	407.651i	0.305659	−	0.529417i
$771$	−92.0486	+	53.1443i	−0.119389	+	0.0689290i
$772$	4.80284	+	4.80284i	0.00622129	+	0.00622129i
$773$	−174.835	+	652.494i	−0.226178	+	0.844107i	0.755752	+	0.654858i	$0.227272\pi$
$773$	−174.835	+	652.494i	−0.226178	+	0.844107i	−0.981929	+	0.189248i	$0.939395\pi$
$774$	672.486	+	180.192i	0.868845	+	0.232806i
$775$	−1175.04	+	1175.04i	−1.51618	+	1.51618i
$776$	135.873	+	235.339i	0.175094	+	0.303272i
$777$	−14.4210	−	8.32596i	−0.0185598	−	0.0107155i
$778$	−197.186	−	735.907i	−0.253452	−	0.945895i
$779$			844.167i			1.08365i
$780$		0			0
$781$	125.664			0.160901
$782$	6.02249	−	1.61372i	0.00770140	−	0.00206358i
$783$	−38.1685	+	66.1098i	−0.0487465	+	0.0844314i
$784$	616.005	−	355.651i	0.785721	−	0.453636i
$785$	592.623	+	592.623i	0.754934	+	0.754934i
$786$	−33.7163	+	125.831i	−0.0428961	+	0.160090i
$787$	−653.790	−	175.182i	−0.830737	−	0.222595i	−0.181702	−	0.983354i	$-0.558161\pi$
$787$	−653.790	−	175.182i	−0.830737	−	0.222595i	−0.649035	+	0.760758i	$0.724827\pi$
$788$	−4.08363	+	4.08363i	−0.00518227	+	0.00518227i
$789$	−144.052	−	249.505i	−0.182575	−	0.316229i
$790$	−686.268	−	396.217i	−0.868694	−	0.501541i
$791$	89.3664	+	333.520i	0.112979	+	0.421644i
$792$			1009.52i			1.27465i
$793$		0			0
$794$	1381.60			1.74004
$795$	−356.946	+	95.6433i	−0.448988	+	0.120306i
$796$	−5.56407	+	9.63726i	−0.00699004	+	0.0121071i
$797$	827.418	−	477.710i	1.03817	−	0.599385i	0.118852	−	0.992912i	$-0.462078\pi$
$797$	827.418	−	477.710i	1.03817	−	0.599385i	0.919313	+	0.393527i	$0.128745\pi$
$798$	41.6698	+	41.6698i	0.0522178	+	0.0522178i
$799$	42.6761	−	159.269i	0.0534118	−	0.199336i
$800$	−21.4708	−	5.75308i	−0.0268385	−	0.00719134i
$801$	−541.899	+	541.899i	−0.676529	+	0.676529i
$802$	−150.073	−	259.933i	−0.187123	−	0.324107i
$803$	−416.104	−	240.238i	−0.518187	−	0.299175i
$804$	−0.347138	−	1.29554i	−0.000431764	−	0.00161136i
$805$		−	4.31268i		−	0.00535737i
$806$		0			0
$807$	−64.0215			−0.0793327
$808$	129.836	−	34.7895i	0.160688	−	0.0430563i
$809$	120.894	−	209.395i	0.149436	−	0.258831i	−0.781583	−	0.623801i	$-0.785587\pi$
$809$	120.894	−	209.395i	0.149436	−	0.258831i	0.931019	+	0.364970i	$0.118921\pi$
$810$	−984.255	+	568.260i	−1.21513	+	0.701556i
$811$	−444.795	−	444.795i	−0.548452	−	0.548452i	0.377541	−	0.925993i	$-0.376770\pi$
$811$	−444.795	−	444.795i	−0.548452	−	0.548452i	−0.925993	+	0.377541i	$0.876770\pi$
$812$	−0.135846	+	0.506986i	−0.000167299	+	0.000624367i
$813$	−176.643	−	47.3312i	−0.217273	−	0.0582180i
$814$	279.468	−	279.468i	0.343327	−	0.343327i
$815$	−1278.80	−	2214.94i	−1.56908	−	2.71772i
$816$	97.1938	+	56.1149i	0.119110	+	0.0687682i
$817$	−254.156	−	948.523i	−0.311084	−	1.16098i
$818$			621.728i			0.760059i
$819$		0			0
$820$	9.93734			0.0121187
$821$	352.928	−	94.5667i	0.429876	−	0.115185i	−0.0373921	−	0.999301i	$-0.511905\pi$
$821$	352.928	−	94.5667i	0.429876	−	0.115185i	0.467268	+	0.884116i	$0.345238\pi$
$822$	85.3893	−	147.899i	0.103880	−	0.179925i
$823$	−595.727	+	343.943i	−0.723848	+	0.417914i	−0.816167	−	0.577815i	$-0.803905\pi$
$823$	−595.727	+	343.943i	−0.723848	+	0.417914i	0.0923192	+	0.995729i	$0.470572\pi$
$824$	495.635	+	495.635i	0.601498	+	0.601498i
$825$	−87.6984	+	327.295i	−0.106301	+	0.396721i
$826$	−140.970	−	37.7728i	−0.170666	−	0.0457298i
$827$	486.409	−	486.409i	0.588161	−	0.588161i	−0.348972	−	0.937133i	$-0.613469\pi$
$827$	486.409	−	486.409i	0.588161	−	0.588161i	0.937133	+	0.348972i	$0.113469\pi$
$828$	0.0409574	+	0.0709403i	4.94655e−5	+	8.56767e-5i
$829$	617.844	+	356.712i	0.745288	+	0.430292i	0.823989	−	0.566606i	$-0.191744\pi$
$829$	617.844	+	356.712i	0.745288	+	0.430292i	−0.0787009	+	0.996898i	$0.525077\pi$
$830$	354.115	+	1321.58i	0.426645	+	1.59226i
$831$		−	35.7555i		−	0.0430270i
$832$		0			0
$833$	−529.637			−0.635819
$834$	−193.338	+	51.8047i	−0.231820	+	0.0621160i
$835$	−790.425	+	1369.06i	−0.946617	+	1.63959i
$836$	10.9211	−	6.30533i	0.0130636	−	0.00754226i
$837$	319.710	+	319.710i	0.381972	+	0.381972i
$838$	−142.269	+	530.955i	−0.169772	+	0.633598i
$839$	397.410	+	106.486i	0.473671	+	0.126920i	0.487754	−	0.872981i	$-0.337816\pi$
$839$	397.410	+	106.486i	0.473671	+	0.126920i	−0.0140828	+	0.999901i	$0.504483\pi$
$840$	55.3868	−	55.3868i	0.0659367	−	0.0659367i
$841$	394.451	+	683.209i	0.469026	+	0.812377i
$842$	−460.149	−	265.667i	−0.546495	−	0.315519i
$843$	−58.3990	−	217.948i	−0.0692752	−	0.258539i
$844$		−	11.4465i		−	0.0135622i
$845$		0			0
$846$	−240.270			−0.284007
$847$	177.685	−	47.6106i	0.209782	−	0.0562109i
$848$	−611.444	+	1059.05i	−0.721043	+	1.24888i
$849$	223.367	−	128.961i	0.263094	−	0.151898i
$850$	−646.092	−	646.092i	−0.760108	−	0.760108i
$851$	0.937201	−	3.49768i	0.00110129	−	0.00411008i
$852$	0.178885	+	0.0479321i	0.000209959	+	5.62584e-5i
$853$	−100.188	+	100.188i	−0.117454	+	0.117454i	−0.763391	−	0.645937i	$-0.776467\pi$
$853$	−100.188	+	100.188i	−0.117454	+	0.117454i	0.645937	+	0.763391i	$0.276467\pi$
$854$	62.6482	+	108.510i	0.0733585	+	0.127061i
$855$	1451.14	+	837.817i	1.69724	+	0.979902i
$856$	249.197	+	930.015i	0.291118	+	1.08647i
$857$		−	1105.86i		−	1.29039i	−0.764019	−	0.645194i	$-0.776776\pi$
$857$		−	1105.86i		−	1.29039i	0.764019	−	0.645194i	$-0.223224\pi$
$858$		0			0
$859$	−98.7915			−0.115008			−0.0575038	−	0.998345i	$-0.518314\pi$
$859$	−98.7915			−0.115008			−0.0575038	+	0.998345i	$0.518314\pi$
$860$	−11.1658	+	2.99187i	−0.0129835	+	0.00347891i
$861$	−21.2167	+	36.7485i	−0.0246420	+	0.0426811i
$862$	592.920	−	342.322i	0.687842	−	0.397126i
$863$	−14.6470	−	14.6470i	−0.0169722	−	0.0169722i	0.698570	−	0.715542i	$-0.253820\pi$
$863$	−14.6470	−	14.6470i	−0.0169722	−	0.0169722i	−0.715542	+	0.698570i	$0.753820\pi$
$864$	−1.56533	+	5.84188i	−0.00181172	+	0.00676144i
$865$	2149.07	+	575.842i	2.48448	+	0.665713i
$866$	−272.482	+	272.482i	−0.314644	+	0.314644i
$867$	44.8485	+	77.6799i	0.0517284	+	0.0895961i
$868$	2.69228	+	1.55439i	0.00310170	+	0.00179077i
$869$	−187.413	−	699.434i	−0.215665	−	0.804872i
$870$			68.8577i			0.0791468i
$871$		0			0
$872$	−997.954			−1.14444
$873$	−282.257	+	75.6307i	−0.323319	+	0.0866331i
$874$	−6.40735	+	11.0979i	−0.00733106	+	0.0126978i
$875$	−195.308	+	112.761i	−0.223209	+	0.128870i
$876$	−0.500698	−	0.500698i	−0.000571573	−	0.000571573i
$877$	196.106	−	731.877i	0.223610	−	0.834524i	−0.759347	−	0.650686i	$-0.774481\pi$
$877$	196.106	−	731.877i	0.223610	−	0.834524i	0.982957	−	0.183837i	$-0.0588520\pi$
$878$	−676.373	−	181.234i	−0.770357	−	0.206417i
$879$	45.4138	−	45.4138i	0.0516652	−	0.0516652i
$880$	921.246	+	1595.65i	1.04687	+	1.81323i
$881$	1427.91	+	824.403i	1.62078	+	0.935758i	0.986712	+	0.162481i	$0.0519498\pi$
$881$	1427.91	+	824.403i	1.62078	+	0.935758i	0.634069	+	0.773277i	$0.281384\pi$
$882$	199.750	+	745.476i	0.226474	+	0.845211i
$883$			360.322i			0.408065i	0.978964	+	0.204033i	$0.0654049\pi$
$883$			360.322i			0.408065i	−0.978964	+	0.204033i	$0.934595\pi$
$884$		0			0
$885$	172.624			0.195056
$886$	647.095	−	173.388i	0.730355	−	0.195698i
$887$	524.092	−	907.755i	0.590860	−	1.02340i	−0.403257	−	0.915087i	$-0.632122\pi$
$887$	524.092	−	907.755i	0.590860	−	1.02340i	0.994117	−	0.108312i	$-0.0345446\pi$
$888$	56.9562	−	32.8837i	0.0641399	−	0.0370312i
$889$	−245.943	−	245.943i	−0.276651	−	0.276651i
$890$	−365.273	+	1363.22i	−0.410419	+	1.53171i
$891$	−1003.14	−	268.790i	−1.12586	−	0.301672i
$892$	−8.37138	+	8.37138i	−0.00938495	+	0.00938495i
$893$	169.447	+	293.491i	0.189750	+	0.328657i
$894$	−44.8100	−	25.8711i	−0.0501231	−	0.0289386i
$895$	511.719	+	1909.76i	0.571753	+	2.13381i
$896$		−	256.872i		−	0.286687i
$897$		0			0
$898$	−273.604			−0.304682
$899$	−298.062	+	79.8655i	−0.331549	+	0.0888382i
$900$	6.00218	−	10.3961i	0.00666909	−	0.0115512i
$901$	788.574	−	455.283i	0.875221	−	0.505309i
$902$	−712.158	−	712.158i	−0.789532	−	0.789532i
$903$	12.7756	−	47.6791i	0.0141479	−	0.0528008i
$904$	−1317.25	−	352.956i	−1.45713	−	0.390438i
$905$	1194.73	−	1194.73i	1.32014	−	1.32014i
$906$	69.1153	+	119.711i	0.0762862	+	0.132132i
$907$	−141.664	−	81.7900i	−0.156190	−	0.0901764i	0.419868	−	0.907585i	$-0.362076\pi$
$907$	−141.664	−	81.7900i	−0.156190	−	0.0901764i	−0.576058	+	0.817409i	$0.695410\pi$
$908$	−1.49478	−	5.57859i	−0.00164623	−	0.00614382i
$909$			144.540i			0.159010i
$910$		0			0
$911$	826.177			0.906890			0.453445	−	0.891284i	$-0.350195\pi$
$911$	826.177			0.906890			0.453445	+	0.891284i	$0.350195\pi$
$912$	−222.806	+	59.7008i	−0.244305	+	0.0654614i
$913$	−625.112	+	1082.73i	−0.684680	+	1.18590i
$914$	342.395	−	197.682i	0.374611	−	0.216282i
$915$	−104.795	−	104.795i	−0.114530	−	0.114530i
$916$	1.62841	−	6.07732i	0.00177774	−	0.00663463i
$917$	−214.465	−	57.4657i	−0.233877	−	0.0626670i
$918$	−175.792	+	175.792i	−0.191495	+	0.191495i
$919$	−178.535	−	309.231i	−0.194271	−	0.336487i	0.752391	−	0.658717i	$-0.228901\pi$
$919$	−178.535	−	309.231i	−0.194271	−	0.336487i	−0.946661	+	0.322231i	$0.895567\pi$
$920$	14.7511	+	8.51654i	0.0160338	+	0.00925711i
$921$	−61.3556	−	228.982i	−0.0666185	−	0.248624i
$922$			1806.47i			1.95929i
$923$		0			0
$924$	0.633896			0.000686034
$925$	−512.574	+	137.344i	−0.554135	+	0.148480i
$926$	834.435	−	1445.28i	0.901118	−	1.56078i
$927$	−652.748	+	376.864i	−0.704150	+	0.406541i
$928$	−2.91867	−	2.91867i	−0.00314512	−	0.00314512i
$929$	−61.3191	+	228.846i	−0.0660055	+	0.246336i	−0.991044	−	0.133538i	$-0.957366\pi$
$929$	−61.3191	+	228.846i	−0.0660055	+	0.246336i	0.925038	+	0.379874i	$0.124033\pi$
$930$	393.943	+	105.557i	0.423594	+	0.113502i
$931$	769.732	−	769.732i	0.826780	−	0.826780i
$932$	1.65762	+	2.87109i	0.00177857	+	0.00308057i
$933$	99.3537	+	57.3619i	0.106488	+	0.0614811i
$934$	−78.2892	−	292.179i	−0.0838215	−	0.312826i
$935$		−	1371.93i		−	1.46730i
$936$		0			0
$937$	1610.13			1.71838			0.859192	−	0.511654i	$-0.170967\pi$
$937$	1610.13			1.71838			0.859192	+	0.511654i	$0.170967\pi$
$938$	−244.906	+	65.6224i	−0.261094	+	0.0699599i
$939$	140.098	−	242.657i	0.149199	−	0.258420i
$940$	3.45491	−	1.99469i	0.00367543	−	0.00212201i
$941$	−930.926	−	930.926i	−0.989295	−	0.989295i	0.0106488	−	0.999943i	$-0.496610\pi$
$941$	−930.926	−	930.926i	−0.989295	−	0.989295i	−0.999943	+	0.0106488i	$0.996610\pi$
$942$	32.3990	−	120.915i	0.0343938	−	0.128359i
$943$	−8.91301	−	2.38823i	−0.00945176	−	0.00253259i
$944$	403.939	−	403.939i	0.427901	−	0.427901i
$945$	85.9804	+	148.922i	0.0909846	+	0.157590i
$946$	1014.61	+	585.783i	1.07252	+	0.619221i
$947$	−51.1956	−	191.065i	−0.0540608	−	0.201758i	0.933613	−	0.358283i	$-0.116638\pi$
$947$	−51.1956	−	191.065i	−0.0540608	−	0.201758i	−0.987674	+	0.156525i	$0.949971\pi$
$948$		−	1.06714i		−	0.00112568i
$949$		0			0
$950$	1877.96			1.97679
$951$	−3.94270	+	1.05644i	−0.00414585	+	0.00111088i
$952$	−96.5038	+	167.150i	−0.101370	+	0.175577i
$953$	363.857	−	210.073i	0.381802	−	0.220433i	−0.296800	−	0.954940i	$-0.595920\pi$
$953$	363.857	−	210.073i	0.381802	−	0.220433i	0.678602	+	0.734506i	$0.262586\pi$
$954$	−938.228	−	938.228i	−0.983467	−	0.983467i
$955$	−110.334	+	411.772i	−0.115533	+	0.431175i
$956$	1.27449	+	0.341499i	0.00133315	+	0.000357217i
$957$	−44.4915	+	44.4915i	−0.0464906	+	0.0464906i
$958$	−501.791	−	869.127i	−0.523790	−	0.907231i
$959$	252.077	+	145.536i	0.262854	+	0.151759i
$960$	80.0625	+	298.797i	0.0833984	+	0.311247i
$961$			866.679i			0.901851i
$962$		0			0
$963$	−1035.34			−1.07512
$964$	1.62150	−	0.434480i	0.00168206	−	0.000450706i
$965$	−759.367	+	1315.26i	−0.786908	+	1.36297i
$966$	−0.557852	+	0.322076i	−0.000577487	+	0.000333412i
$967$	−957.774	−	957.774i	−0.990459	−	0.990459i	0.00949545	−	0.999955i	$-0.496977\pi$
$967$	−957.774	−	957.774i	−0.990459	−	0.990459i	−0.999955	+	0.00949545i	$0.996977\pi$
$968$	−188.040	+	701.774i	−0.194256	+	0.724973i
$969$	165.902	+	44.4534i	0.171210	+	0.0458755i
$970$	−380.517	+	380.517i	−0.392286	+	0.392286i
$971$	351.176	+	608.255i	0.361664	+	0.626421i	0.988235	−	0.152944i	$-0.0488753\pi$
$971$	351.176	+	608.255i	0.361664	+	0.626421i	−0.626571	+	0.779365i	$0.715542\pi$
$972$	−4.27175	−	2.46630i	−0.00439481	−	0.00253734i
$973$	−88.2953	−	329.523i	−0.0907454	−	0.338667i
$974$		−	1099.98i		−	1.12935i
$975$		0			0
$976$	−490.440			−0.502500
$977$	−645.113	+	172.858i	−0.660300	+	0.176927i	−0.573381	−	0.819289i	$-0.694369\pi$
$977$	−645.113	+	172.858i	−0.660300	+	0.176927i	−0.0869186	+	0.996215i	$0.527702\pi$
$978$	−191.004	+	330.829i	−0.195301	+	0.338271i
$979$	−1116.84	+	644.809i	−1.14080	+	0.658641i
$980$	−9.06111	−	9.06111i	−0.00924603	−	0.00924603i
$981$	277.744	−	1036.55i	0.283123	−	1.05663i
$982$	1586.70	+	425.156i	1.61579	+	0.432949i
$983$	507.852	−	507.852i	0.516635	−	0.516635i	−0.399916	−	0.916552i	$-0.630961\pi$
$983$	507.852	−	507.852i	0.516635	−	0.516635i	0.916552	+	0.399916i	$0.130961\pi$
$984$	−83.7962	−	145.139i	−0.0851587	−	0.147499i
$985$	−1118.31	−	645.655i	−1.13534	−	0.655487i
$986$	−43.9139	−	163.889i	−0.0445374	−	0.166216i
$987$			17.0351i			0.0172595i
$988$		0			0
$989$	10.7339			0.0108533
$990$	−1931.02	+	517.414i	−1.95052	+	0.522640i
$991$	418.667	−	725.153i	0.422469	−	0.731738i	−0.573711	−	0.819058i	$-0.694497\pi$
$991$	418.667	−	725.153i	0.422469	−	0.731738i	0.996180	+	0.0873195i	$0.0278301\pi$
$992$	−21.1723	+	12.2238i	−0.0213430	+	0.0123224i
$993$	−16.8563	−	16.8563i	−0.0169751	−	0.0169751i
$994$	9.06101	−	33.8161i	0.00911570	−	0.0340203i
$995$	−2403.45	−	644.003i	−2.41553	−	0.647239i
$996$	−1.30285	+	1.30285i	−0.00130808	+	0.00130808i
$997$	−305.867	−	529.777i	−0.306787	−	0.531371i	0.670870	−	0.741575i	$-0.265921\pi$
$997$	−305.867	−	529.777i	−0.306787	−	0.531371i	−0.977658	+	0.210204i	$0.932587\pi$
$998$	−549.651	−	317.341i	−0.550753	−	0.317977i
$999$	37.3693	+	139.464i	0.0374067	+	0.139604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.g.150.4		48
13.2	odd	12	inner	169.3.f.g.80.4		48
13.3	even	3	inner	169.3.f.g.89.9		48
13.4	even	6		169.3.d.e.99.4	yes	24
13.5	odd	4	inner	169.3.f.g.19.9		48
13.6	odd	12		169.3.d.e.70.9	yes	24
13.7	odd	12		169.3.d.e.70.4	✓	24
13.8	odd	4	inner	169.3.f.g.19.4		48
13.9	even	3		169.3.d.e.99.9	yes	24
13.10	even	6	inner	169.3.f.g.89.4		48
13.11	odd	12	inner	169.3.f.g.80.9		48
13.12	even	2	inner	169.3.f.g.150.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.4	✓	24	13.7	odd	12
169.3.d.e.70.9	yes	24	13.6	odd	12
169.3.d.e.99.4	yes	24	13.4	even	6
169.3.d.e.99.9	yes	24	13.9	even	3
169.3.f.g.19.4		48	13.8	odd	4	inner
169.3.f.g.19.9		48	13.5	odd	4	inner
169.3.f.g.80.4		48	13.2	odd	12	inner
169.3.f.g.80.9		48	13.11	odd	12	inner
169.3.f.g.89.4		48	13.10	even	6	inner
169.3.f.g.89.9		48	13.3	even	3	inner
169.3.f.g.150.4		48	1.1	even	1	trivial
169.3.f.g.150.9		48	13.12	even	2	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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.92320 + 0.515320i) q^{2} +(0.299764 - 0.519206i) q^{3} +(-0.0309536 + 0.0178711i) q^{4} +(-5.65111 - 5.65111i) q^{5} +(-0.308949 + 1.15301i) q^{6} +(-1.96518 - 0.526568i) q^{7} +(5.68184 - 5.68184i) q^{8} +(4.32028 + 7.48295i) q^{9} +(13.7804 + 7.95610i) q^{10} +(3.76327 + 14.0447i) q^{11} +0.0214284i q^{12} +4.05079 q^{14} +(-4.62809 + 1.24009i) q^{15} +(-7.92788 + 13.7315i) q^{16} +(10.2245 - 5.90312i) q^{17} +(-12.1649 - 12.1649i) q^{18} +(-6.28035 + 23.4386i) q^{19} +(0.275914 + 0.0739308i) q^{20} +(-0.862488 + 0.862488i) q^{21} +(-14.4751 - 25.0716i) q^{22} +(-0.229705 - 0.132620i) q^{23} +(-1.24684 - 4.65326i) q^{24} +38.8702i q^{25} +10.5760 q^{27} +(0.0702397 - 0.0188207i) q^{28} +(-3.60897 + 6.25092i) q^{29} +(8.26171 - 4.76990i) q^{30} +(30.2298 + 30.2298i) q^{31} +(-0.148007 + 0.552371i) q^{32} +(8.42021 + 2.25619i) q^{33} +(-16.6218 + 16.6218i) q^{34} +(8.12976 + 14.0812i) q^{35} +(-0.267457 - 0.154416i) q^{36} +(3.53340 + 13.1868i) q^{37} -48.3135i q^{38} -64.2175 q^{40} +(33.6035 - 9.00403i) q^{41} +(1.21428 - 2.10319i) q^{42} +(-35.0467 + 20.2342i) q^{43} +(-0.367481 - 0.367481i) q^{44} +(17.8726 - 66.7014i) q^{45} +(0.510111 + 0.136684i) q^{46} +(9.87555 - 9.87555i) q^{47} +(4.75298 + 8.23241i) q^{48} +(-38.8506 - 22.4304i) q^{49} +(-20.0306 - 74.7552i) q^{50} -7.07817i q^{51} +77.1259 q^{53} +(-20.3398 + 5.45003i) q^{54} +(58.1017 - 100.635i) q^{55} +(-14.1577 + 8.17397i) q^{56} +(10.2868 + 10.2868i) q^{57} +(3.71955 - 13.8815i) q^{58} +(-34.8006 - 9.32480i) q^{59} +(0.121094 - 0.121094i) q^{60} +(15.4657 + 26.7873i) q^{61} +(-73.7160 - 42.5599i) q^{62} +(-4.54985 - 16.9803i) q^{63} -64.5616i q^{64} -17.3564 q^{66} +(-60.4589 + 16.1999i) q^{67} +(-0.210990 + 0.365445i) q^{68} +(-0.137715 + 0.0795095i) q^{69} +(-22.8915 - 22.8915i) q^{70} +(2.23685 - 8.34804i) q^{71} +(67.0641 + 17.9698i) q^{72} +(-23.3661 + 23.3661i) q^{73} +(-13.5909 - 23.5401i) q^{74} +(20.1816 + 11.6519i) q^{75} +(-0.224473 - 0.837745i) q^{76} -29.5820i q^{77} -49.8004 q^{79} +(122.400 - 32.7969i) q^{80} +(-35.7122 + 61.8554i) q^{81} +(-59.9863 + 34.6331i) q^{82} +(60.8000 + 60.8000i) q^{83} +(0.0112835 - 0.0421107i) q^{84} +(-91.1390 - 24.4206i) q^{85} +(56.9747 - 56.9747i) q^{86} +(2.16368 + 3.74760i) q^{87} +(101.182 + 58.4176i) q^{88} +(22.9556 + 85.6713i) q^{89} +137.490i q^{90} +0.00948026 q^{92} +(24.7573 - 6.63370i) q^{93} +(-13.9036 + 24.0818i) q^{94} +(167.945 - 96.9632i) q^{95} +(0.242427 + 0.242427i) q^{96} +(-8.75298 + 32.6665i) q^{97} +(86.2763 + 23.1177i) q^{98} +(-88.8376 + 88.8376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) \) 48 * q - 12 * q^3 - 84 * q^9 + 376 * q^14 - 188 * q^16 + 136 * q^22 + 120 * q^27 - 84 * q^29 - 176 * q^35 - 1048 * q^40 + 368 * q^42 + 368 * q^48 - 88 * q^53 + 704 * q^55 + 8 * q^61 - 1480 * q^66 + 168 * q^68 - 744 * q^74 - 600 * q^79 - 240 * q^81 + 952 * q^87 + 3472 * q^92 - 1132 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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