LMFDB - Embedded newform 169.3.f.g.89.9

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			89.9
Character	$\chi$	$=$	169.89
Dual form			169.3.f.g.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.515320 - 1.92320i) q^{2} +(0.299764 + 0.519206i) q^{3} +(0.0309536 + 0.0178711i) q^{4} +(-5.65111 - 5.65111i) q^{5} +(1.15301 - 0.308949i) q^{6} +(0.526568 + 1.96518i) q^{7} +(5.68184 - 5.68184i) q^{8} +(4.32028 - 7.48295i) q^{9} +(-13.7804 + 7.95610i) q^{10} +(-14.0447 - 3.76327i) q^{11} +0.0214284i q^{12} +4.05079 q^{14} +(1.24009 - 4.62809i) q^{15} +(-7.92788 - 13.7315i) q^{16} +(-10.2245 - 5.90312i) q^{17} +(-12.1649 - 12.1649i) q^{18} +(23.4386 - 6.28035i) q^{19} +(-0.0739308 - 0.275914i) q^{20} +(-0.862488 + 0.862488i) q^{21} +(-14.4751 + 25.0716i) q^{22} +(0.229705 - 0.132620i) q^{23} +(4.65326 + 1.24684i) q^{24} +38.8702i q^{25} +10.5760 q^{27} +(-0.0188207 + 0.0702397i) q^{28} +(-3.60897 - 6.25092i) q^{29} +(-8.26171 - 4.76990i) q^{30} +(30.2298 + 30.2298i) q^{31} +(0.552371 - 0.148007i) q^{32} +(-2.25619 - 8.42021i) q^{33} +(-16.6218 + 16.6218i) q^{34} +(8.12976 - 14.0812i) q^{35} +(0.267457 - 0.154416i) q^{36} +(-13.1868 - 3.53340i) q^{37} -48.3135i q^{38} -64.2175 q^{40} +(-9.00403 + 33.6035i) q^{41} +(1.21428 + 2.10319i) q^{42} +(35.0467 + 20.2342i) q^{43} +(-0.367481 - 0.367481i) q^{44} +(-66.7014 + 17.8726i) q^{45} +(-0.136684 - 0.510111i) q^{46} +(9.87555 - 9.87555i) q^{47} +(4.75298 - 8.23241i) q^{48} +(38.8506 - 22.4304i) q^{49} +(74.7552 + 20.0306i) q^{50} -7.07817i q^{51} +77.1259 q^{53} +(5.45003 - 20.3398i) q^{54} +(58.1017 + 100.635i) q^{55} +(14.1577 + 8.17397i) q^{56} +(10.2868 + 10.2868i) q^{57} +(-13.8815 + 3.71955i) q^{58} +(9.32480 + 34.8006i) q^{59} +(0.121094 - 0.121094i) q^{60} +(15.4657 - 26.7873i) q^{61} +(73.7160 - 42.5599i) q^{62} +(16.9803 + 4.54985i) q^{63} -64.5616i q^{64} -17.3564 q^{66} +(16.1999 - 60.4589i) q^{67} +(-0.210990 - 0.365445i) q^{68} +(0.137715 + 0.0795095i) q^{69} +(-22.8915 - 22.8915i) q^{70} +(-8.34804 + 2.23685i) q^{71} +(-17.9698 - 67.0641i) q^{72} +(-23.3661 + 23.3661i) q^{73} +(-13.5909 + 23.5401i) q^{74} +(-20.1816 + 11.6519i) q^{75} +(0.837745 + 0.224473i) q^{76} -29.5820i q^{77} -49.8004 q^{79} +(-32.7969 + 122.400i) q^{80} +(-35.7122 - 61.8554i) q^{81} +(59.9863 + 34.6331i) q^{82} +(60.8000 + 60.8000i) q^{83} +(-0.0421107 + 0.0112835i) q^{84} +(24.4206 + 91.1390i) q^{85} +(56.9747 - 56.9747i) q^{86} +(2.16368 - 3.74760i) q^{87} +(-101.182 + 58.4176i) q^{88} +(-85.6713 - 22.9556i) q^{89} +137.490i q^{90} +0.00948026 q^{92} +(-6.63370 + 24.7573i) q^{93} +(-13.9036 - 24.0818i) q^{94} +(-167.945 - 96.9632i) q^{95} +(0.242427 + 0.242427i) q^{96} +(32.6665 - 8.75298i) q^{97} +(-23.1177 - 86.2763i) 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.515320	−	1.92320i	0.257660	−	0.961601i	−0.708931	−	0.705278i	$-0.750822\pi$
$2$	0.515320	−	1.92320i	0.257660	−	0.961601i	0.966591	−	0.256323i	$-0.0825110\pi$
$3$	0.299764	+	0.519206i	0.0999213	+	0.173069i	0.911652	−	0.410963i	$-0.134808\pi$
$3$	0.299764	+	0.519206i	0.0999213	+	0.173069i	−0.811731	+	0.584032i	$0.801474\pi$
$4$	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	$-0.544737\pi$
$6$	1.15301	−	0.308949i	0.192169	−	0.0514915i
$7$	0.526568	+	1.96518i	0.0752241	+	0.280740i	0.993284	−	0.115702i	$-0.0369116\pi$
$7$	0.526568	+	1.96518i	0.0752241	+	0.280740i	−0.918060	+	0.396442i	$0.870245\pi$
$8$	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
$11$	−14.0447	−	3.76327i	−1.27679	−	0.342116i	−0.444164	−	0.895946i	$-0.646499\pi$
$11$	−14.0447	−	3.76327i	−1.27679	−	0.342116i	−0.832630	+	0.553830i	$0.813166\pi$
$12$			0.0214284i			0.00178570i
$13$		0			0
$13$		0			0
$14$	4.05079			0.289342
$15$	1.24009	−	4.62809i	0.0826729	−	0.308540i
$16$	−7.92788	−	13.7315i	−0.495492	−	0.858218i
$17$	−10.2245	−	5.90312i	−0.601441	−	0.347242i	0.168167	−	0.985759i	$-0.446215\pi$
$17$	−10.2245	−	5.90312i	−0.601441	−	0.347242i	−0.769608	+	0.638516i	$0.779549\pi$
$18$	−12.1649	−	12.1649i	−0.675827	−	0.675827i
$19$	23.4386	−	6.28035i	1.23361	−	0.330545i	0.417626	−	0.908619i	$-0.362862\pi$
$19$	23.4386	−	6.28035i	1.23361	−	0.330545i	0.815984	+	0.578074i	$0.196196\pi$
$20$	−0.0739308	−	0.275914i	−0.00369654	−	0.0137957i
$21$	−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	$-0.664831\pi$
$23$	0.229705	−	0.132620i	0.00998717	−	0.00576610i	0.504985	+	0.863128i	$0.331498\pi$
$24$	4.65326	+	1.24684i	0.193886	+	0.0519516i
$25$			38.8702i			1.55481i
$26$		0			0
$27$	10.5760			0.391704
$28$	−0.0188207	+	0.0702397i	−0.000672167	+	0.00250856i
$29$	−3.60897	−	6.25092i	−0.124447	−	0.215549i	0.797070	−	0.603888i	$-0.206382\pi$
$29$	−3.60897	−	6.25092i	−0.124447	−	0.215549i	−0.921517	+	0.388339i	$0.873049\pi$
$30$	−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	$0.507814\pi$
$32$	0.552371	−	0.148007i	0.0172616	−	0.00462523i
$33$	−2.25619	−	8.42021i	−0.0683693	−	0.255158i
$34$	−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
$37$	−13.1868	−	3.53340i	−0.356401	−	0.0954973i	0.0761760	−	0.997094i	$-0.475729\pi$
$37$	−13.1868	−	3.53340i	−0.356401	−	0.0954973i	−0.432577	+	0.901597i	$0.642396\pi$
$38$		−	48.3135i		−	1.27141i
$39$		0			0
$40$	−64.2175			−1.60544
$41$	−9.00403	+	33.6035i	−0.219610	+	0.819597i	0.764882	+	0.644170i	$0.222797\pi$
$41$	−9.00403	+	33.6035i	−0.219610	+	0.819597i	−0.984492	+	0.175427i	$0.943869\pi$
$42$	1.21428	+	2.10319i	0.0289114	+	0.0500761i
$43$	35.0467	+	20.2342i	0.815039	+	0.470563i	0.848703	−	0.528870i	$-0.177384\pi$
$43$	35.0467	+	20.2342i	0.815039	+	0.470563i	−0.0336635	+	0.999433i	$0.510717\pi$
$44$	−0.367481	−	0.367481i	−0.00835184	−	0.00835184i
$45$	−66.7014	+	17.8726i	−1.48225	+	0.397169i
$46$	−0.136684	−	0.510111i	−0.00297139	−	0.0110894i
$47$	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
$50$	74.7552	+	20.0306i	1.49510	+	0.400612i
$51$		−	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	$0.240635\pi$
$54$	5.45003	−	20.3398i	0.100927	−	0.376663i
$55$	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
$58$	−13.8815	+	3.71955i	−0.239337	+	0.0641302i
$59$	9.32480	+	34.8006i	0.158048	+	0.589841i	0.998825	+	0.0484607i	$0.0154315\pi$
$59$	9.32480	+	34.8006i	0.158048	+	0.589841i	−0.840778	+	0.541381i	$0.817902\pi$
$60$	0.121094	−	0.121094i	0.00201824	−	0.00201824i
$61$	15.4657	−	26.7873i	0.253536	−	0.439137i	−0.710961	−	0.703231i	$-0.751740\pi$
$61$	15.4657	−	26.7873i	0.253536	−	0.439137i	0.964497	+	0.264095i	$0.0850732\pi$
$62$	73.7160	−	42.5599i	1.18897	−	0.686451i
$63$	16.9803	+	4.54985i	0.269528	+	0.0722198i
$64$		−	64.5616i		−	1.00878i
$65$		0			0
$66$	−17.3564			−0.262976
$67$	16.1999	−	60.4589i	0.241790	−	0.902372i	−0.733180	−	0.680034i	$-0.761965\pi$
$67$	16.1999	−	60.4589i	0.241790	−	0.902372i	0.974970	−	0.222337i	$-0.0713685\pi$
$68$	−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
$71$	−8.34804	+	2.23685i	−0.117578	+	0.0315049i	−0.317128	−	0.948383i	$-0.602719\pi$
$71$	−8.34804	+	2.23685i	−0.117578	+	0.0315049i	0.199550	+	0.979888i	$0.436052\pi$
$72$	−17.9698	−	67.0641i	−0.249580	−	0.931446i
$73$	−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
$76$	0.837745	+	0.224473i	0.0110230	+	0.00295359i
$77$		−	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	$0.602069\pi$
$80$	−32.7969	+	122.400i	−0.409961	+	1.52999i
$81$	−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	$0.576685\pi$
$84$	−0.0421107	+	0.0112835i	−0.000501317	+	0.000134328i
$85$	24.4206	+	91.1390i	0.287302	+	1.07222i
$86$	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
$89$	−85.6713	−	22.9556i	−0.962599	−	0.257928i	−0.256899	−	0.966438i	$-0.582701\pi$
$89$	−85.6713	−	22.9556i	−0.962599	−	0.257928i	−0.705700	+	0.708511i	$0.749367\pi$
$90$			137.490i			1.52767i
$91$		0			0
$92$	0.00948026			0.000103046
$93$	−6.63370	+	24.7573i	−0.0713301	+	0.266207i
$94$	−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
$97$	32.6665	−	8.75298i	0.336769	−	0.0902369i	−0.0864718	−	0.996254i	$-0.527559\pi$
$97$	32.6665	−	8.75298i	0.336769	−	0.0902369i	0.423240	+	0.906017i	$0.360893\pi$
$98$	−23.1177	−	86.2763i	−0.235895	−	0.880371i
$99$	−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	$-0.693057\pi$
$101$	−14.4870	+	8.36406i	−0.143435	+	0.0828125i	0.426565	+	0.904457i	$0.359724\pi$
$102$	−13.6127	−	3.64752i	−0.133458	−	0.0357600i
$103$			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
$106$	39.7445	−	148.329i	0.374948	−	1.39933i
$107$	−59.9117	−	103.770i	−0.559923	−	0.969815i	−0.997502	−	0.0706350i	$-0.977497\pi$
$107$	−59.9117	−	103.770i	−0.559923	−	0.969815i	0.437579	−	0.899180i	$-0.355836\pi$
$108$	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	$0.942942\pi$
$110$	223.482	−	59.8820i	2.03166	−	0.544381i
$111$	−2.11837	−	7.90587i	−0.0190844	−	0.0712241i
$112$	22.8103	−	22.8103i	0.203663	−	0.203663i
$113$	−84.8574	+	146.977i	−0.750950	+	1.30068i	0.196412	+	0.980521i	$0.437071\pi$
$113$	−84.8574	+	146.977i	−0.750950	+	1.30068i	−0.947363	+	0.320163i	$0.896262\pi$
$114$	25.0847	−	14.4826i	0.220041	−	0.127041i
$115$	−2.04754	−	0.548637i	−0.0178047	−	0.00477076i
$116$		−	0.257984i		−	0.00222400i
$117$		0			0
$118$	71.7339			0.607914
$119$	6.21679	−	23.2014i	0.0522420	−	0.194970i
$120$	−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
$123$	−20.1462	+	5.39817i	−0.163790	+	0.0438875i
$124$	0.395482	+	1.47596i	0.00318937	+	0.0119029i
$125$	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	$-0.901689\pi$
$127$	−148.054	+	85.4792i	−1.16578	+	0.673065i	−0.213099	+	0.977031i	$0.568356\pi$
$128$	−121.955	−	32.6779i	−0.952777	−	0.255296i
$129$			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	$0.363244\pi$
$132$	0.0806409	−	0.300956i	0.000610916	−	0.00227997i
$133$	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
$136$	−91.6347	+	24.5534i	−0.673784	+	0.180540i
$137$	37.0288	+	138.193i	0.270283	+	1.00871i	0.958937	+	0.283620i	$0.0915354\pi$
$137$	37.0288	+	138.193i	0.270283	+	1.00871i	−0.688654	+	0.725090i	$0.741798\pi$
$138$	0.223880	−	0.223880i	0.00162232	−	0.00162232i
$139$	83.8403	−	145.216i	0.603168	−	1.04472i	−0.389171	−	0.921166i	$-0.627238\pi$
$139$	83.8403	−	145.216i	0.603168	−	1.04472i	0.992338	−	0.123551i	$-0.0394283\pi$
$140$	0.503290	−	0.290575i	0.00359493	−	0.00207553i
$141$	8.08778	+	2.16712i	0.0573602	+	0.0153696i
$142$			17.2077i			0.121181i
$143$		0			0
$144$	−137.003			−0.951408
$145$	−14.9300	+	55.7193i	−0.102965	+	0.384271i
$146$	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
$149$	41.8695	−	11.2189i	0.281004	−	0.0752947i	−0.115565	−	0.993300i	$-0.536868\pi$
$149$	41.8695	−	11.2189i	0.281004	−	0.0752947i	0.396568	+	0.918005i	$0.370201\pi$
$150$	12.0089	+	44.8178i	0.0800593	+	0.298785i
$151$	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
$154$	−56.8922	−	15.2442i	−0.369430	−	0.0989885i
$155$		−	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	$0.608390\pi$
$158$	−25.6632	+	95.7763i	−0.162425	+	0.606179i
$159$	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
$162$	−137.364	+	36.8065i	−0.847924	+	0.227200i
$163$	−82.8284	−	309.120i	−0.508149	−	1.89644i	−0.438173	−	0.898891i	$-0.644374\pi$
$163$	−82.8284	−	309.120i	−0.508149	−	1.89644i	−0.0699767	−	0.997549i	$-0.522292\pi$
$164$	−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
$167$	191.067	+	51.1962i	1.14411	+	0.306564i	0.780604	−	0.625026i	$-0.214912\pi$
$167$	191.067	+	51.1962i	1.14411	+	0.306564i	0.363510	+	0.931590i	$0.381578\pi$
$168$			9.80104i			0.0583395i
$169$		0			0
$170$	187.863			1.10508
$171$	54.2658	−	202.523i	0.317344	−	1.18434i
$172$	0.723214	+	1.25264i	0.00420473	+	0.00728281i
$173$	241.095	+	139.196i	1.39361	+	0.804604i	0.993713	−	0.111955i	$-0.0357111\pi$
$173$	241.095	+	139.196i	1.39361	+	0.804604i	0.399901	+	0.916558i	$0.369044\pi$
$174$	−6.09240	−	6.09240i	−0.0350138	−	0.0350138i
$175$	−76.3869	+	20.4678i	−0.436497	+	0.116959i
$176$	59.6696	+	222.690i	0.339032	+	1.26528i
$177$	−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	$-0.423820\pi$
$179$	214.248	−	123.696i	1.19692	−	0.691039i	0.959866	+	0.280458i	$0.0904864\pi$
$180$	−2.38405	−	0.638804i	−0.0132447	−	0.00354891i
$181$			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
$184$	0.551621	−	2.05868i	0.00299794	−	0.0111885i
$185$	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
$188$	0.482170	−	0.129197i	0.00256474	−	0.000687219i
$189$	5.56899	+	20.7838i	0.0294656	+	0.109967i
$190$	−273.025	+	273.025i	−1.43697	+	1.43697i
$191$	−26.6707	+	46.1950i	−0.139637	+	0.241859i	−0.927359	−	0.374172i	$-0.877927\pi$
$191$	−26.6707	+	46.1950i	−0.139637	+	0.241859i	0.787722	+	0.616031i	$0.211260\pi$
$192$	33.5208	−	19.3532i	0.174587	−	0.100798i
$193$	183.559	+	49.1845i	0.951084	+	0.254842i	0.700822	−	0.713336i	$-0.252817\pi$
$193$	183.559	+	49.1845i	0.951084	+	0.254842i	0.250262	+	0.968178i	$0.419483\pi$
$194$		−	67.3349i		−	0.347087i
$195$		0			0
$196$	1.60342			0.00818071
$197$	−41.8194	+	156.072i	−0.212281	+	0.792244i	0.774825	+	0.632176i	$0.217838\pi$
$197$	−41.8194	+	156.072i	−0.212281	+	0.792244i	−0.987106	+	0.160068i	$0.948829\pi$
$198$	125.073	+	216.632i	0.631681	+	1.09410i
$199$	−269.633	−	155.673i	−1.35494	−	0.782275i	−0.366003	−	0.930613i	$-0.619274\pi$
$199$	−269.633	−	155.673i	−1.35494	−	0.782275i	−0.988937	+	0.148338i	$0.952607\pi$
$200$	220.854	+	220.854i	1.10427	+	1.10427i
$201$	36.2468	−	9.71230i	0.180332	−	0.0483199i
$202$	8.62034	+	32.1715i	0.0426749	+	0.159265i
$203$	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
$206$	167.763	+	44.9521i	0.814385	+	0.218214i
$207$		−	2.29183i		−	0.0110716i
$208$		0			0
$209$	−352.823			−1.68815
$210$	5.02336	−	18.7474i	0.0239208	−	0.0892735i
$211$	−160.126	−	277.347i	−0.758892	−	1.31444i	−0.943416	−	0.331611i	$-0.892408\pi$
$211$	−160.126	−	277.347i	−0.758892	−	1.31444i	0.184524	−	0.982828i	$-0.440926\pi$
$212$	2.38732	+	1.37832i	0.0112610	+	0.00650152i
$213$	−3.66383	−	3.66383i	−0.0172011	−	0.0172011i
$214$	−230.445	+	61.7475i	−1.07684	+	0.288540i
$215$	−83.7070	−	312.399i	−0.389335	−	1.45302i
$216$	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
$219$	−19.1362	−	5.12752i	−0.0873797	−	0.0234133i
$220$			4.15336i			0.0188789i
$221$		0			0
$222$	−16.2962			−0.0734064
$223$	−85.7290	+	319.945i	−0.384435	+	1.43473i	0.454620	+	0.890685i	$0.349775\pi$
$223$	−85.7290	+	319.945i	−0.384435	+	1.43473i	−0.839055	+	0.544046i	$0.816892\pi$
$224$	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
$227$	156.079	−	41.8212i	0.687572	−	0.184234i	0.101915	−	0.994793i	$-0.467503\pi$
$227$	156.079	−	41.8212i	0.687572	−	0.184234i	0.585657	+	0.810559i	$0.300836\pi$
$228$	0.134578	+	0.502251i	0.000590254	+	0.00220286i
$229$	−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
$232$	−56.0223	−	15.0111i	−0.241476	−	0.0647032i
$233$		−	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
$236$	−0.333288	+	1.24385i	−0.00141224	+	0.00527055i
$237$	−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	$0.774608\pi$
$240$	−73.3819	+	19.6626i	−0.305758	+	0.0819276i
$241$	12.1560	+	45.3667i	0.0504397	+	0.188244i	0.986549	−	0.163466i	$-0.0522673\pi$
$241$	12.1560	+	45.3667i	0.0504397	+	0.188244i	−0.936109	+	0.351709i	$0.885601\pi$
$242$	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
$245$	−346.306	−	92.7924i	−1.41349	−	0.378744i
$246$			41.5270i			0.168809i
$247$		0			0
$248$	343.522			1.38517
$249$	−13.3421	+	49.7934i	−0.0535827	+	0.199973i
$250$	−110.353	−	191.136i	−0.441410	−	0.764545i
$251$	−156.585	−	90.4045i	−0.623845	−	0.360177i	0.154519	−	0.987990i	$-0.450617\pi$
$251$	−156.585	−	90.4045i	−0.623845	−	0.360177i	−0.778365	+	0.627813i	$0.783950\pi$
$252$	0.444290	+	0.444290i	0.00176305	+	0.00176305i
$253$	−3.72523	+	0.998173i	−0.0147242	+	0.00394535i
$254$	88.0983	+	328.787i	0.346844	+	1.29444i
$255$	−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	$-0.554574\pi$
$257$	153.535	−	88.6435i	0.597413	−	0.344916i	0.768023	+	0.640422i	$0.221241\pi$
$258$	46.6606	+	12.5027i	0.180855	+	0.0484600i
$259$		−	27.7751i		−	0.107240i
$260$		0			0
$261$	−62.3671			−0.238954
$262$	56.2381	−	209.884i	0.214649	−	0.801083i
$263$	240.275	+	416.169i	0.913595	+	1.58239i	0.808946	+	0.587883i	$0.200038\pi$
$263$	240.275	+	416.169i	0.913595	+	1.58239i	0.104649	+	0.994509i	$0.466628\pi$
$264$	−60.6616	−	35.0230i	−0.229779	−	0.132663i
$265$	−435.847	−	435.847i	−1.64471	−	1.64471i
$266$	94.9447	−	25.4404i	0.356935	−	0.0956405i
$267$	−13.7625	−	51.3623i	−0.0515449	−	0.192368i
$268$	1.58191	−	1.58191i	0.00590265	−	0.00590265i
$269$	−53.3932	+	92.4798i	−0.198488	+	0.343791i	−0.948038	−	0.318156i	$-0.896936\pi$
$269$	−53.3932	+	92.4798i	−0.198488	+	0.343791i	0.749550	+	0.661947i	$0.230270\pi$
$270$	−145.741	+	84.1438i	−0.539782	+	0.311644i
$271$	294.636	+	78.9475i	1.08722	+	0.291319i	0.757550	−	0.652777i	$-0.226396\pi$
$271$	294.636	+	78.9475i	1.08722	+	0.291319i	0.329669	+	0.944097i	$0.393063\pi$
$272$			187.197i			0.688224i
$273$		0			0
$274$	284.855			1.03962
$275$	146.279	−	545.921i	0.531924	−	1.98517i
$276$	0.00284184	+	0.00492221i	1.02965e−5	+	1.78341e-5i
$277$	−51.6492	−	29.8197i	−0.186459	−	0.107652i	0.403865	−	0.914819i	$-0.367667\pi$
$277$	−51.6492	−	29.8197i	−0.186459	−	0.107652i	−0.590324	+	0.807166i	$0.701000\pi$
$278$	−236.074	−	236.074i	−0.849188	−	0.849188i
$279$	356.809	−	95.6067i	1.27889	−	0.342676i
$280$	−33.8149	−	126.199i	−0.120768	−	0.450711i
$281$	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	$-0.941510\pi$
$283$	−372.572	+	215.104i	−1.31651	+	0.760087i	−0.333343	+	0.942806i	$0.608177\pi$
$284$	−0.298377	−	0.0799498i	−0.00105062	−	0.000281513i
$285$		−	116.264i		−	0.407945i
$286$		0			0
$287$	−70.7781			−0.246614
$288$	1.27887	−	4.77280i	0.00444051	−	0.0165722i
$289$	−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
$292$	−1.14084	+	0.305688i	−0.00390699	+	0.00104688i
$293$	−27.7261	−	103.475i	−0.0946284	−	0.353158i	0.902334	−	0.431037i	$-0.141852\pi$
$293$	−27.7261	−	103.475i	−0.0946284	−	0.353158i	−0.996963	+	0.0778785i	$0.975185\pi$
$294$	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
$297$	−148.537	−	39.8004i	−0.500125	−	0.134008i
$298$		−	86.3049i		−	0.289614i
$299$		0			0
$300$	−0.832926			−0.00277642
$301$	−21.3094	+	79.5277i	−0.0707953	+	0.264212i
$302$	−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
$305$	−238.777	+	63.9800i	−0.782874	+	0.209770i
$306$	52.5692	+	196.191i	0.171795	+	0.641146i
$307$	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
$310$	−657.088	−	176.066i	−2.11964	−	0.567956i
$311$			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	$0.231693\pi$
$314$	−54.0408	+	201.683i	−0.172104	+	0.642302i
$315$	−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	$0.753418\pi$
$318$	88.9271	−	23.8279i	0.279645	−	0.0749306i
$319$	27.1631	+	101.374i	0.0851507	+	0.317787i
$320$	−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
$323$	−276.722	−	74.1473i	−0.856723	−	0.229558i
$324$		−	2.55286i		−	0.00787921i
$325$		0			0
$326$	−637.182			−1.95455
$327$	19.2713	−	71.9216i	0.0589337	−	0.219944i
$328$	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
$331$	−38.4071	+	10.2911i	−0.116034	+	0.0310911i	−0.316369	−	0.948636i	$-0.602464\pi$
$331$	−38.4071	+	10.2911i	−0.116034	+	0.0310911i	0.200335	+	0.979727i	$0.435797\pi$
$332$	0.795417	+	2.96854i	0.00239584	+	0.00894138i
$333$	−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
$336$	18.6809	+	5.00554i	0.0555980	+	0.0148974i
$337$			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
$340$	−0.872845	+	3.25750i	−0.00256719	+	0.00958089i
$341$	−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
$344$	314.098	−	84.1622i	0.913074	−	0.244657i
$345$	−0.328923	−	1.22756i	−0.000953401	−	0.00355814i
$346$	391.944	−	391.944i	1.13279	−	1.13279i
$347$	−169.897	+	294.270i	−0.489616	+	0.848040i	−0.999929	−	0.0119488i	$-0.996196\pi$
$347$	−169.897	+	294.270i	−0.489616	+	0.848040i	0.510312	+	0.859989i	$0.329530\pi$
$348$	0.133947	−	0.0773344i	0.000384906	−	0.000222225i
$349$	398.426	+	106.758i	1.14162	+	0.305897i	0.779603	−	0.626274i	$-0.215421\pi$
$349$	398.426	+	106.758i	1.14162	+	0.305897i	0.362019	+	0.932171i	$0.382088\pi$
$350$			157.455i			0.449871i
$351$		0			0
$352$	−8.31490			−0.0236219
$353$	−77.2905	+	288.452i	−0.218953	+	0.817145i	0.765784	+	0.643098i	$0.222351\pi$
$353$	−77.2905	+	288.452i	−0.218953	+	0.817145i	−0.984737	+	0.174047i	$0.944316\pi$
$354$	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
$357$	13.9099	−	3.72714i	0.0389632	−	0.0104402i
$358$	−127.486	−	475.785i	−0.356107	−	1.32901i
$359$	−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
$362$	406.592	+	108.946i	1.12318	+	0.300956i
$363$			54.2074i			0.149332i
$364$		0			0
$365$	264.089			0.723532
$366$	9.55620	−	35.6642i	0.0261098	−	0.0974433i
$367$	138.968	+	240.700i	0.378661	+	0.655860i	0.990868	−	0.134838i	$-0.0430514\pi$
$367$	138.968	+	240.700i	0.378661	+	0.655860i	−0.612207	+	0.790698i	$0.709718\pi$
$368$	−3.64215	−	2.10279i	−0.00989714	−	0.00571411i
$369$	212.553	+	212.553i	0.576025	+	0.576025i
$370$	209.831	−	56.2241i	0.567112	−	0.151957i
$371$	40.6120	+	151.566i	0.109466	+	0.408534i
$372$	−0.647776	+	0.647776i	−0.00174133	+	0.00174133i
$373$	−285.496	+	494.493i	−0.765404	+	1.32572i	0.174629	+	0.984634i	$0.444127\pi$
$373$	−285.496	+	494.493i	−0.765404	+	1.32572i	−0.940033	+	0.341084i	$0.889206\pi$
$374$	296.001	−	170.896i	0.791446	−	0.456942i
$375$	64.1925	+	17.2003i	0.171180	+	0.0458676i
$376$		−	112.223i		−	0.298465i
$377$		0			0
$378$	42.8412			0.113336
$379$	66.1526	−	246.885i	0.174545	−	0.651411i	−0.822084	−	0.569367i	$-0.807188\pi$
$379$	66.1526	−	246.885i	0.174545	−	0.651411i	0.996629	−	0.0820441i	$-0.0261448\pi$
$380$	−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
$383$	−117.475	+	31.4773i	−0.306723	+	0.0821861i	−0.408897	−	0.912580i	$-0.634087\pi$
$383$	−117.475	+	31.4773i	−0.306723	+	0.0821861i	0.102175	+	0.994766i	$0.467420\pi$
$384$	−19.5913	−	73.1157i	−0.0510190	−	0.190405i
$385$	−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
$388$	1.16757	+	0.312850i	0.00300921	+	0.000806314i
$389$			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
$392$	93.2970	−	348.189i	0.238002	−	0.888237i
$393$	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
$396$	−4.33747	+	1.16222i	−0.0109532	+	0.00293490i
$397$	179.596	+	670.261i	0.452382	+	1.68831i	0.695671	+	0.718360i	$0.255107\pi$
$397$	179.596	+	670.261i	0.452382	+	1.68831i	−0.243289	+	0.969954i	$0.578226\pi$
$398$	−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
$401$	−145.611	−	39.0164i	−0.363120	−	0.0972977i	0.0726459	−	0.997358i	$-0.476856\pi$
$401$	−145.611	−	39.0164i	−0.363120	−	0.0972977i	−0.435766	+	0.900060i	$0.643522\pi$
$402$		−	74.7148i		−	0.185858i
$403$		0			0
$404$	−0.597899			−0.00147995
$405$	−147.738	+	551.366i	−0.364785	+	1.36140i
$406$	−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
$409$	−301.622	+	80.8194i	−0.737462	+	0.197602i	−0.607950	−	0.793975i	$-0.708008\pi$
$409$	−301.622	+	80.8194i	−0.737462	+	0.197602i	−0.129512	+	0.991578i	$0.541341\pi$
$410$	−143.274	−	534.705i	−0.349448	−	1.30416i
$411$	−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
$414$	−4.40765	−	1.18103i	−0.0106465	−	0.00285272i
$415$		−	687.175i		−	1.65584i
$416$		0			0
$417$	100.529			0.241077
$418$	−181.817	+	678.550i	−0.434969	+	1.62333i
$419$	138.039	+	239.091i	0.329450	+	0.570624i	0.982403	−	0.186775i	$-0.0598034\pi$
$419$	138.039	+	239.091i	0.329450	+	0.570624i	−0.652953	+	0.757398i	$0.726470\pi$
$420$	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	$0.647345\pi$
$422$	−615.910	+	165.033i	−1.45950	+	0.391072i
$423$	−31.2331	−	116.563i	−0.0738371	−	0.275564i
$424$	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
$427$	60.7857	+	16.2875i	0.142355	+	0.0381440i
$428$		−	4.28275i		−	0.0100064i
$429$		0			0
$430$	−643.941			−1.49754
$431$	88.9981	−	332.145i	0.206492	−	0.770639i	−0.782497	−	0.622654i	$-0.786055\pi$
$431$	88.9981	−	332.145i	0.206492	−	0.770639i	0.988990	−	0.147985i	$-0.0472788\pi$
$432$	−83.8453	−	145.224i	−0.194086	−	0.336167i
$433$	−167.611	−	96.7701i	−0.387092	−	0.223488i	0.293807	−	0.955865i	$-0.405078\pi$
$433$	−167.611	−	96.7701i	−0.387092	−	0.223488i	−0.680899	+	0.732377i	$0.738411\pi$
$434$	122.454	+	122.454i	0.282153	+	0.282153i
$435$	−33.4053	+	8.95092i	−0.0767938	+	0.0205768i
$436$	−1.14890	−	4.28776i	−0.00263509	−	0.00983431i
$437$	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	$-0.797851\pi$
$439$	−304.574	+	175.846i	−0.693790	+	0.400560i	0.111240	+	0.993794i	$0.464518\pi$
$440$	901.918	+	241.668i	2.04981	+	0.549246i
$441$		−	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	$0.623993\pi$
$444$	0.0757151	−	0.282573i	0.000170530	−	0.000636425i
$445$	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
$448$	126.875	−	33.9961i	0.283204	−	0.0758842i
$449$	−35.5663	−	132.735i	−0.0792122	−	0.295624i	0.914943	−	0.403583i	$-0.132235\pi$
$449$	−35.5663	−	132.735i	−0.0792122	−	0.295624i	−0.994155	+	0.107959i	$0.965569\pi$
$450$	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
$453$	67.0606	+	17.9688i	0.148037	+	0.0396663i
$454$		−	321.722i		−	0.708639i
$455$		0			0
$456$	116.896			0.256352
$457$	51.3939	−	191.805i	0.112459	−	0.419704i	−0.886625	−	0.462489i	$-0.846956\pi$
$457$	51.3939	−	191.805i	0.112459	−	0.419704i	0.999084	+	0.0427852i	$0.0136231\pi$
$458$	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
$461$	−876.380	+	234.825i	−1.90104	+	0.509382i	−0.904481	+	0.426514i	$0.859741\pi$
$461$	−876.380	+	234.825i	−1.90104	+	0.509382i	−0.996561	+	0.0828682i	$0.973592\pi$
$462$	−9.13934	−	34.1085i	−0.0197821	−	0.0738279i
$463$	−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
$466$	−178.386	−	47.7983i	−0.382802	−	0.102572i
$467$			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
$470$	−57.5179	+	214.660i	−0.122378	+	0.456723i
$471$	−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
$474$	−57.4205	+	15.3858i	−0.121140	+	0.0324595i
$475$	244.118	+	911.062i	0.513933	+	1.91803i
$476$	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
$479$	−486.873	−	130.457i	−1.01644	−	0.272353i	−0.288120	−	0.957594i	$-0.593030\pi$
$479$	−486.873	−	130.457i	−1.01644	−	0.272353i	−0.728316	+	0.685241i	$0.759697\pi$
$480$		−	2.73997i		−	0.00570827i
$481$		0			0
$482$	93.5136			0.194012
$483$	−0.0837344	+	0.312501i	−0.000173363	+	0.000647000i
$484$	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
$487$	533.641	−	142.989i	1.09577	−	0.293611i	0.334730	−	0.942314i	$-0.391355\pi$
$487$	533.641	−	142.989i	1.09577	−	0.293611i	0.761042	+	0.648703i	$0.224688\pi$
$488$	−64.3279	−	240.075i	−0.131819	−	0.491957i
$489$	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	$-0.349131\pi$
$491$	714.499	−	412.516i	1.45519	−	0.840155i	0.998769	+	0.0496089i	$0.0157975\pi$
$492$	−0.720069	−	0.192942i	−0.00146355	−	0.000392158i
$493$			85.2167i			0.172853i
$494$		0			0
$495$	1004.06			2.02841
$496$	175.442	−	654.758i	0.353713	−	1.32008i
$497$	−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	$0.646516\pi$
$500$	3.82697	−	1.02543i	0.00765395	−	0.00205087i
$501$	30.6936	+	114.550i	0.0612646	+	0.228643i
$502$	−254.557	+	254.557i	−0.507087	+	0.507087i
$503$	−117.302	+	203.173i	−0.233205	+	0.403923i	−0.958749	−	0.284252i	$-0.908255\pi$
$503$	−117.302	+	203.173i	−0.233205	+	0.403923i	0.725545	+	0.688175i	$0.241588\pi$
$504$	122.331	−	70.6277i	0.242720	−	0.140134i
$505$	129.134	+	34.6013i	0.255711	+	0.0685174i
$506$			7.67875i			0.0151754i
$507$		0			0
$508$	−6.11042			−0.0120284
$509$	179.057	−	668.249i	0.351782	−	1.31287i	−0.532705	−	0.846301i	$-0.678824\pi$
$509$	179.057	−	668.249i	0.351782	−	1.31287i	0.884486	−	0.466566i	$-0.154509\pi$
$510$	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
$513$	247.887	−	66.4211i	0.483210	−	0.129476i
$514$	−91.3596	−	340.959i	−0.177742	−	0.663344i
$515$	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
$518$	−53.4171	−	14.3131i	−0.103122	−	0.0276314i
$519$			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	$0.592225\pi$
$522$	−32.1390	+	119.944i	−0.0615690	+	0.229779i
$523$	−169.819	−	294.135i	−0.324701	−	0.562399i	0.656751	−	0.754108i	$-0.271930\pi$
$523$	−169.819	−	294.135i	−0.324701	−	0.562399i	−0.981452	+	0.191709i	$0.938597\pi$
$524$	3.37804	+	1.95031i	0.00644664	+	0.00372197i
$525$	−33.5251	−	33.5251i	−0.0638572	−	0.0638572i
$526$	924.196	−	247.638i	1.75703	−	0.470794i
$527$	−130.634	−	487.535i	−0.247883	−	0.925113i
$528$	−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
$531$	300.697	+	80.5716i	0.566285	+	0.151736i
$532$			1.76452i			0.00331677i
$533$		0			0
$534$	−105.872			−0.198262
$535$	−247.849	+	924.985i	−0.463269	+	1.72894i
$536$	−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
$539$	−630.058	+	168.823i	−1.16894	+	0.313216i
$540$	−0.781893	−	2.91807i	−0.00144795	−	0.00540383i
$541$	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
$544$	−6.52143	−	1.74741i	−0.0119879	−	0.00321215i
$545$			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	$0.556651\pi$
$548$	−1.32349	+	4.93932i	−0.00241512	+	0.00901336i
$549$	−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
$552$	1.23423	−	0.330712i	0.00223593	−	0.000599116i
$553$	−26.2233	−	97.8668i	−0.0474201	−	0.176974i
$554$	−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
$557$	−871.675	−	233.565i	−1.56495	−	0.419326i	−0.630721	−	0.776010i	$-0.717241\pi$
$557$	−871.675	−	233.565i	−1.56495	−	0.419326i	−0.934225	+	0.356684i	$0.883907\pi$
$558$		−	735.484i		−	1.31807i
$559$		0			0
$560$	−257.807			−0.460369
$561$	−26.6371	+	99.4110i	−0.0474815	+	0.177203i
$562$	−374.672	−	648.951i	−0.666676	−	1.15472i
$563$	−412.904	−	238.390i	−0.733399	−	0.423428i	0.0862652	−	0.996272i	$-0.472507\pi$
$563$	−412.904	−	238.390i	−0.733399	−	0.423428i	−0.819664	+	0.572844i	$0.805840\pi$
$564$	0.211617	+	0.211617i	0.000375208	+	0.000375208i
$565$	1310.12	−	351.047i	2.31880	−	0.621322i
$566$	221.695	+	827.378i	0.391688	+	1.46180i
$567$	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	$-0.935990\pi$
$569$	−737.875	+	426.012i	−1.29679	+	0.748704i	−0.316944	+	0.948444i	$0.602657\pi$
$570$	−223.600	−	59.9133i	−0.392280	−	0.105111i
$571$			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
$574$	−36.4734	+	136.121i	−0.0635425	+	0.237144i
$575$	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	$0.422558\pi$
$578$	−287.735	+	77.0984i	−0.497812	+	0.133388i
$579$	29.4875	+	110.049i	0.0509283	+	0.190067i
$580$	−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
$583$	−1083.21	−	290.246i	−1.85800	−	0.497849i
$584$			265.525i			0.454667i
$585$		0			0
$586$	−213.292			−0.363979
$587$	−60.0726	+	224.194i	−0.102338	+	0.381932i	−0.998030	−	0.0627446i	$-0.980015\pi$
$587$	−60.0726	+	224.194i	−0.102338	+	0.381932i	0.895691	+	0.444676i	$0.146681\pi$
$588$	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
$591$	−93.5695	+	25.0719i	−0.158324	+	0.0424228i
$592$	56.0247	+	209.087i	0.0946364	+	0.353188i
$593$	−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
$596$	1.49651	+	0.400988i	0.00251092	+	0.000672798i
$597$		−	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	$0.344211\pi$
$600$	−48.4648	+	180.873i	−0.0807747	+	0.301455i
$601$	−67.6406	−	117.157i	−0.112547	−	0.194937i	0.804250	−	0.594292i	$-0.202567\pi$
$601$	−67.6406	−	117.157i	−0.112547	−	0.194937i	−0.916796	+	0.399355i	$0.869234\pi$
$602$	141.967	+	81.9645i	0.235825	+	0.136154i
$603$	−382.423	−	382.423i	−0.634200	−	0.634200i
$604$	3.99796	−	1.07125i	0.00661913	−	0.00177359i
$605$	−187.023	−	697.978i	−0.309128	−	1.15368i
$606$	−14.1196	+	14.1196i	−0.0232997	+	0.0232997i
$607$	−20.0524	+	34.7318i	−0.0330352	+	0.0572187i	−0.882070	−	0.471118i	$-0.843851\pi$
$607$	−20.0524	+	34.7318i	−0.0330352	+	0.0572187i	0.849035	+	0.528336i	$0.177184\pi$
$608$	12.0173	−	6.93817i	0.0197652	−	0.0114115i
$609$	8.50403	+	2.27865i	0.0139639	+	0.00374162i
$610$			492.185i			0.806861i
$611$		0			0
$612$	−3.64615			−0.00595776
$613$	191.423	−	714.402i	0.312273	−	1.16542i	−0.614228	−	0.789128i	$-0.710533\pi$
$613$	191.423	−	714.402i	0.312273	−	1.16542i	0.926501	−	0.376291i	$-0.122801\pi$
$614$	−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
$617$	632.571	−	169.497i	1.02524	−	0.274712i	0.293254	−	0.956034i	$-0.405262\pi$
$617$	632.571	−	169.497i	1.02524	−	0.274712i	0.731983	+	0.681323i	$0.238595\pi$
$618$	26.9500	+	100.579i	0.0436084	+	0.162749i
$619$	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
$622$	368.018	+	98.6100i	0.591668	+	0.158537i
$623$		−	180.447i		−	0.289642i
$624$		0			0
$625$	85.8635			0.137382
$626$	240.841	−	898.829i	0.384729	−	1.43583i
$627$	−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
$630$	−270.193	+	72.3981i	−0.428878	+	0.114918i
$631$	−220.322	−	822.253i	−0.349163	−	1.30309i	−0.887673	−	0.460475i	$-0.847679\pi$
$631$	−220.322	−	822.253i	−0.349163	−	1.30309i	0.538509	−	0.842620i	$-0.318988\pi$
$632$	−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
$635$	1319.72	+	353.619i	2.07831	+	0.556881i
$636$			1.65268i			0.00259856i
$637$		0			0
$638$	208.960			0.327524
$639$	−19.3277	+	72.1318i	−0.0302467	+	0.112882i
$640$	504.518	+	873.851i	0.788309	+	1.36539i
$641$	−537.784	−	310.490i	−0.838976	−	0.484383i	0.0179397	−	0.999839i	$-0.494289\pi$
$641$	−537.784	−	310.490i	−0.838976	−	0.484383i	−0.856916	+	0.515456i	$0.827623\pi$
$642$	−101.139	−	101.139i	−0.157537	−	0.157537i
$643$	−124.450	+	33.3464i	−0.193547	+	0.0518607i	−0.354290	−	0.935136i	$-0.615277\pi$
$643$	−124.450	+	33.3464i	−0.193547	+	0.0518607i	0.160744	+	0.986996i	$0.448611\pi$
$644$	0.00499200	+	0.0186304i	7.75156e−6	+	2.89292e-5i
$645$	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	$-0.521817\pi$
$647$	492.538	−	284.367i	0.761264	−	0.439516i	0.829750	+	0.558136i	$0.188483\pi$
$648$	−554.364	−	148.541i	−0.855500	−	0.229231i
$649$		−	523.857i		−	0.807176i
$650$		0			0
$651$	−52.1456			−0.0801008
$652$	2.96046	−	11.0486i	0.00454058	−	0.0169457i
$653$	498.955	+	864.215i	0.764096	+	1.32345i	0.940723	+	0.339175i	$0.110148\pi$
$653$	498.955	+	864.215i	0.764096	+	1.32345i	−0.176627	+	0.984278i	$0.556519\pi$
$654$	−128.389	−	74.1253i	−0.196313	−	0.113341i
$655$	−616.720	−	616.720i	−0.941557	−	0.941557i
$656$	532.809	−	142.766i	0.812208	−	0.217631i
$657$	73.8992	+	275.796i	0.112480	+	0.419780i
$658$	40.0038	−	40.0038i	0.0607960	−	0.0607960i
$659$	218.812	−	378.994i	0.332037	−	0.575105i	−0.650874	−	0.759186i	$-0.725598\pi$
$659$	218.812	−	378.994i	0.332037	−	0.575105i	0.982911	+	0.184081i	$0.0589308\pi$
$660$	−2.15645	+	1.24503i	−0.00326735	+	0.00188640i
$661$	91.6872	+	24.5675i	0.138710	+	0.0371672i	0.327506	−	0.944849i	$-0.393792\pi$
$661$	91.6872	+	24.5675i	0.138710	+	0.0371672i	−0.188796	+	0.982016i	$0.560459\pi$
$662$			79.1678i			0.119589i
$663$		0			0
$664$	690.912			1.04053
$665$	102.115	−	381.100i	0.153557	−	0.573083i
$666$	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
$669$	−191.816	+	51.3969i	−0.286720	+	0.0768265i
$670$	257.776	+	962.034i	0.384740	+	1.43587i
$671$	−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	$-0.594081\pi$
$673$	263.517	−	152.141i	0.391555	−	0.226064i	0.682834	+	0.730574i	$0.260747\pi$
$674$	162.851	+	43.6358i	0.241619	+	0.0647416i
$675$			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	$0.629320\pi$
$678$	−52.4332	+	195.683i	−0.0773351	+	0.288618i
$679$	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
$682$	−1195.49	+	320.329i	−1.75291	+	0.469691i
$683$	130.888	+	488.481i	0.191637	+	0.715199i	0.993112	+	0.117171i	$0.0373824\pi$
$683$	130.888	+	488.481i	0.191637	+	0.715199i	−0.801475	+	0.598029i	$0.795951\pi$
$684$	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
$687$	−101.939	−	27.3145i	−0.148383	−	0.0397591i
$688$		−	641.657i		−	0.932642i
$689$		0			0
$690$	−2.53034			−0.00366716
$691$	−154.042	+	574.894i	−0.222927	+	0.831974i	0.760298	+	0.649575i	$0.225053\pi$
$691$	−154.042	+	574.894i	−0.222927	+	0.831974i	−0.983225	+	0.182399i	$0.941614\pi$
$692$	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
$695$	−1294.42	+	346.839i	−1.86248	+	0.499049i
$696$	−8.99960	−	33.5869i	−0.0129305	−	0.0482571i
$697$	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
$700$	−2.73023	−	0.731563i	−0.00390033	−	0.00104509i
$701$		−	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
$704$	−242.963	+	906.751i	−0.345118	+	1.28800i
$705$	−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
$708$	−0.745722	+	0.199816i	−0.00105328	+	0.000282225i
$709$	−141.398	−	527.703i	−0.199432	−	0.744292i	−0.991075	−	0.133307i	$-0.957440\pi$
$709$	−141.398	−	527.703i	−0.199432	−	0.744292i	0.791642	−	0.610985i	$-0.209226\pi$
$710$	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
$713$	10.9530	+	2.93485i	0.0153619	+	0.00411620i
$714$		−	28.6722i		−	0.0401571i
$715$		0			0
$716$	8.84232			0.0123496
$717$	5.72821	−	21.3780i	0.00798914	−	0.0298159i
$718$	386.623	+	669.651i	0.538472	+	0.932661i
$719$	1155.86	+	667.337i	1.60760	+	0.928146i	0.989906	+	0.141723i	$0.0452644\pi$
$719$	1155.86	+	667.337i	1.60760	+	0.928146i	0.617689	+	0.786422i	$0.288069\pi$
$720$	774.218	+	774.218i	1.07530	+	1.07530i
$721$	−171.425	+	45.9332i	−0.237760	+	0.0637077i
$722$	−117.395	−	438.125i	−0.162597	−	0.606821i
$723$	−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
$726$	104.252	+	27.9341i	0.143597	+	0.0384768i
$727$		−	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
$730$	136.090	−	507.897i	0.186425	−	0.695749i
$731$	−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	$0.877091\pi$
$734$	534.529	−	143.227i	0.728241	−	0.195132i
$735$	−55.6316	−	207.620i	−0.0756893	−	0.282476i
$736$	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
$739$	568.542	+	152.340i	0.769340	+	0.206144i	0.622080	−	0.782954i	$-0.286288\pi$
$739$	568.542	+	152.340i	0.769340	+	0.206144i	0.147260	+	0.989098i	$0.452955\pi$
$740$			3.89965i			0.00526980i
$741$		0			0
$742$	312.421			0.421052
$743$	−159.716	+	596.069i	−0.214961	+	0.802246i	0.771219	+	0.636570i	$0.219647\pi$
$743$	−159.716	+	596.069i	−0.214961	+	0.802246i	−0.986180	+	0.165676i	$0.947019\pi$
$744$	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
$747$	717.636	−	192.290i	0.960691	−	0.257416i
$748$	1.58803	+	5.92660i	0.00212303	+	0.00792326i
$749$	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	$-0.435579\pi$
$751$	863.544	−	498.567i	1.14986	−	0.663871i	0.948853	+	0.315719i	$0.102246\pi$
$752$	−213.898	−	57.3139i	−0.284439	−	0.0762152i
$753$		−	108.400i		−	0.143957i
$754$		0			0
$755$	−925.472			−1.22579
$756$	−0.199048	+	0.742856i	−0.000263290	+	0.000982614i
$757$	48.7879	+	84.5031i	0.0644490	+	0.111629i	0.896449	−	0.443146i	$-0.146138\pi$
$757$	48.7879	+	84.5031i	0.0644490	+	0.111629i	−0.832000	+	0.554775i	$0.812804\pi$
$758$	−440.719	−	254.449i	−0.581424	−	0.335685i
$759$	−1.63495	−	1.63495i	−0.00215408	−	0.00215408i
$760$	−1505.17	+	403.308i	−1.98048	+	0.530669i
$761$	76.8236	+	286.709i	0.100951	+	0.376754i	0.997854	−	0.0654727i	$-0.0208555\pi$
$761$	76.8236	+	286.709i	0.100951	+	0.376754i	−0.896904	+	0.442226i	$0.854189\pi$
$762$	−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
$765$	787.493	+	211.008i	1.02940	+	0.275828i
$766$			242.149i			0.316121i
$767$		0			0
$768$	4.11392			0.00535667
$769$	36.7932	−	137.314i	0.0478455	−	0.178562i	−0.937868	−	0.346992i	$-0.887203\pi$
$769$	36.7932	−	137.314i	0.0478455	−	0.178562i	0.985714	+	0.168430i	$0.0538698\pi$
$770$	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
$773$	652.494	−	174.835i	0.844107	−	0.226178i	0.189248	−	0.981929i	$-0.439395\pi$
$773$	652.494	−	174.835i	0.844107	−	0.226178i	0.654858	+	0.755752i	$0.272728\pi$
$774$	−180.192	−	672.486i	−0.232806	−	0.868845i
$775$	−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
$778$	735.907	+	197.186i	0.945895	+	0.253452i
$779$			844.167i			1.08365i
$780$		0			0
$781$	125.664			0.160901
$782$	−1.61372	+	6.02249i	−0.00206358	+	0.00770140i
$783$	−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
$786$	125.831	−	33.7163i	0.160090	−	0.0428961i
$787$	175.182	+	653.790i	0.222595	+	0.830737i	0.983354	+	0.181702i	$0.0581605\pi$
$787$	175.182	+	653.790i	0.222595	+	0.830737i	−0.760758	+	0.649035i	$0.775173\pi$
$788$	−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
$791$	−333.520	−	89.3664i	−0.421644	−	0.112979i
$792$			1009.52i			1.27465i
$793$		0			0
$794$	1381.60			1.74004
$795$	95.6433	−	356.946i	0.120306	−	0.448988i
$796$	−5.56407	−	9.63726i	−0.00699004	−	0.0121071i
$797$	−827.418	−	477.710i	−1.03817	−	0.599385i	−0.118852	−	0.992912i	$-0.537922\pi$
$797$	−827.418	−	477.710i	−1.03817	−	0.599385i	−0.919313	+	0.393527i	$0.871255\pi$
$798$	41.6698	+	41.6698i	0.0522178	+	0.0522178i
$799$	−159.269	+	42.6761i	−0.199336	+	0.0534118i
$800$	5.75308	+	21.4708i	0.00719134	+	0.0268385i
$801$	−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
$804$	1.29554	+	0.347138i	0.00161136	+	0.000431764i
$805$		−	4.31268i		−	0.00535737i
$806$		0			0
$807$	−64.0215			−0.0793327
$808$	−34.7895	+	129.836i	−0.0430563	+	0.160688i
$809$	120.894	+	209.395i	0.149436	+	0.258831i	0.931019	−	0.364970i	$-0.118921\pi$
$809$	120.894	+	209.395i	0.149436	+	0.258831i	−0.781583	+	0.623801i	$0.785587\pi$
$810$	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	$0.876770\pi$
$812$	0.506986	−	0.135846i	0.000624367	−	0.000167299i
$813$	47.3312	+	176.643i	0.0582180	+	0.217273i
$814$	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
$817$	948.523	+	254.156i	1.16098	+	0.311084i
$818$			621.728i			0.760059i
$819$		0			0
$820$	9.93734			0.0121187
$821$	−94.5667	+	352.928i	−0.115185	+	0.429876i	−0.999301	−	0.0373921i	$-0.988095\pi$
$821$	−94.5667	+	352.928i	−0.115185	+	0.429876i	0.884116	+	0.467268i	$0.154762\pi$
$822$	85.3893	+	147.899i	0.103880	+	0.179925i
$823$	595.727	+	343.943i	0.723848	+	0.417914i	0.816167	−	0.577815i	$-0.196095\pi$
$823$	595.727	+	343.943i	0.723848	+	0.417914i	−0.0923192	+	0.995729i	$0.529428\pi$
$824$	495.635	+	495.635i	0.601498	+	0.601498i
$825$	327.295	−	87.6984i	0.396721	−	0.106301i
$826$	37.7728	+	140.970i	0.0457298	+	0.170666i
$827$	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	$-0.808256\pi$
$829$	−617.844	+	356.712i	−0.745288	+	0.430292i	0.0787009	+	0.996898i	$0.474923\pi$
$830$	−1321.58	−	354.115i	−1.59226	−	0.426645i
$831$		−	35.7555i		−	0.0430270i
$832$		0			0
$833$	−529.637			−0.635819
$834$	51.8047	−	193.338i	0.0621160	−	0.231820i
$835$	−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
$838$	530.955	−	142.269i	0.633598	−	0.169772i
$839$	−106.486	−	397.410i	−0.126920	−	0.473671i	0.872981	−	0.487754i	$-0.162184\pi$
$839$	−106.486	−	397.410i	−0.126920	−	0.473671i	−0.999901	+	0.0140828i	$0.995517\pi$
$840$	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
$843$	217.948	+	58.3990i	0.258539	+	0.0692752i
$844$		−	11.4465i		−	0.0135622i
$845$		0			0
$846$	−240.270			−0.284007
$847$	−47.6106	+	177.685i	−0.0562109	+	0.209782i
$848$	−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
$851$	−3.49768	+	0.937201i	−0.00411008	+	0.00110129i
$852$	−0.0479321	−	0.178885i	−5.62584e−5	−	0.000209959i
$853$	−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
$856$	−930.015	−	249.197i	−1.08647	−	0.291118i
$857$		−	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	$0.518314\pi$
$860$	2.99187	−	11.1658i	0.00347891	−	0.0129835i
$861$	−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	$0.753820\pi$
$864$	5.84188	−	1.56533i	0.00676144	−	0.00181172i
$865$	−575.842	−	2149.07i	−0.665713	−	2.48448i
$866$	−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
$869$	699.434	+	187.413i	0.804872	+	0.215665i
$870$			68.8577i			0.0791468i
$871$		0			0
$872$	−997.954			−1.14444
$873$	75.6307	−	282.257i	0.0866331	−	0.323319i
$874$	−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
$877$	−731.877	+	196.106i	−0.834524	+	0.223610i	−0.650686	−	0.759347i	$-0.725519\pi$
$877$	−731.877	+	196.106i	−0.834524	+	0.223610i	−0.183837	+	0.982957i	$0.558852\pi$
$878$	181.234	+	676.373i	0.206417	+	0.770357i
$879$	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	−0.634069	+	0.773277i	$0.718616\pi$
$881$	−1427.91	+	824.403i	−1.62078	+	0.935758i	−0.986712	+	0.162481i	$0.948050\pi$
$882$	−745.476	−	199.750i	−0.845211	−	0.226474i
$883$			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
$886$	−173.388	+	647.095i	−0.195698	+	0.730355i
$887$	524.092	+	907.755i	0.590860	+	1.02340i	0.994117	+	0.108312i	$0.0345446\pi$
$887$	524.092	+	907.755i	0.590860	+	1.02340i	−0.403257	+	0.915087i	$0.632122\pi$
$888$	−56.9562	−	32.8837i	−0.0641399	−	0.0370312i
$889$	−245.943	−	245.943i	−0.276651	−	0.276651i
$890$	1363.22	−	365.273i	1.53171	−	0.410419i
$891$	268.790	+	1003.14i	0.301672	+	1.12586i
$892$	−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
$895$	−1909.76	−	511.719i	−2.13381	−	0.571753i
$896$		−	256.872i		−	0.286687i
$897$		0			0
$898$	−273.604			−0.304682
$899$	79.8655	−	298.062i	0.0888382	−	0.331549i
$900$	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
$903$	−47.6791	+	12.7756i	−0.0528008	+	0.0141479i
$904$	352.956	+	1317.25i	0.390438	+	1.45713i
$905$	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	$-0.637924\pi$
$907$	141.664	−	81.7900i	0.156190	−	0.0901764i	0.576058	+	0.817409i	$0.304590\pi$
$908$	5.57859	+	1.49478i	0.00614382	+	0.00164623i
$909$			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	$0.350195\pi$
$912$	59.7008	−	222.806i	0.0654614	−	0.244305i
$913$	−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
$916$	−6.07732	+	1.62841i	−0.00663463	+	0.00177774i
$917$	57.4657	+	214.465i	0.0626670	+	0.233877i
$918$	−175.792	+	175.792i	−0.191495	+	0.191495i
$919$	−178.535	+	309.231i	−0.194271	+	0.336487i	−0.946661	−	0.322231i	$-0.895567\pi$
$919$	−178.535	+	309.231i	−0.194271	+	0.336487i	0.752391	+	0.658717i	$0.228901\pi$
$920$	−14.7511	+	8.51654i	−0.0160338	+	0.00925711i
$921$	228.982	+	61.3556i	0.248624	+	0.0666185i
$922$			1806.47i			1.95929i
$923$		0			0
$924$	0.633896			0.000686034
$925$	137.344	−	512.574i	0.148480	−	0.554135i
$926$	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
$929$	228.846	−	61.3191i	0.246336	−	0.0660055i	−0.133538	−	0.991044i	$-0.542634\pi$
$929$	228.846	−	61.3191i	0.246336	−	0.0660055i	0.379874	+	0.925038i	$0.375967\pi$
$930$	−105.557	−	393.943i	−0.113502	−	0.423594i
$931$	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
$934$	292.179	+	78.2892i	0.312826	+	0.0838215i
$935$		−	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	$0.170967\pi$
$938$	65.6224	−	244.906i	0.0699599	−	0.261094i
$939$	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	$0.996610\pi$
$942$	−120.915	+	32.3990i	−0.128359	+	0.0343938i
$943$	2.38823	+	8.91301i	0.00253259	+	0.00945176i
$944$	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
$947$	191.065	+	51.1956i	0.201758	+	0.0540608i	0.358283	−	0.933613i	$-0.383362\pi$
$947$	191.065	+	51.1956i	0.201758	+	0.0540608i	−0.156525	+	0.987674i	$0.550029\pi$
$948$		−	1.06714i		−	0.00112568i
$949$		0			0
$950$	1877.96			1.97679
$951$	1.05644	−	3.94270i	0.00111088	−	0.00414585i
$952$	−96.5038	−	167.150i	−0.101370	−	0.175577i
$953$	−363.857	−	210.073i	−0.381802	−	0.220433i	0.296800	−	0.954940i	$-0.404080\pi$
$953$	−363.857	−	210.073i	−0.381802	−	0.220433i	−0.678602	+	0.734506i	$0.737414\pi$
$954$	−938.228	−	938.228i	−0.983467	−	0.983467i
$955$	411.772	−	110.334i	0.431175	−	0.115533i
$956$	−0.341499	−	1.27449i	−0.000357217	−	0.00133315i
$957$	−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
$960$	−298.797	−	80.0625i	−0.311247	−	0.0833984i
$961$			866.679i			0.901851i
$962$		0			0
$963$	−1035.34			−1.07512
$964$	−0.434480	+	1.62150i	−0.000450706	+	0.00168206i
$965$	−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	$0.996977\pi$
$968$	701.774	−	188.040i	0.724973	−	0.194256i
$969$	−44.4534	−	165.902i	−0.0458755	−	0.171210i
$970$	−380.517	+	380.517i	−0.392286	+	0.392286i
$971$	351.176	−	608.255i	0.361664	−	0.626421i	−0.626571	−	0.779365i	$-0.715542\pi$
$971$	351.176	−	608.255i	0.361664	−	0.626421i	0.988235	+	0.152944i	$0.0488753\pi$
$972$	4.27175	−	2.46630i	0.00439481	−	0.00253734i
$973$	329.523	+	88.2953i	0.338667	+	0.0907454i
$974$		−	1099.98i		−	1.12935i
$975$		0			0
$976$	−490.440			−0.502500
$977$	172.858	−	645.113i	0.176927	−	0.660300i	−0.819289	−	0.573381i	$-0.805631\pi$
$977$	172.858	−	645.113i	0.176927	−	0.660300i	0.996215	−	0.0869186i	$-0.0277020\pi$
$978$	−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
$981$	−1036.55	+	277.744i	−1.05663	+	0.283123i
$982$	−425.156	−	1586.70i	−0.432949	−	1.61579i
$983$	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
$986$	163.889	+	43.9139i	0.166216	+	0.0445374i
$987$			17.0351i			0.0172595i
$988$		0			0
$989$	10.7339			0.0108533
$990$	517.414	−	1931.02i	0.522640	−	1.95052i
$991$	418.667	+	725.153i	0.422469	+	0.731738i	0.996180	−	0.0873195i	$-0.0278301\pi$
$991$	418.667	+	725.153i	0.422469	+	0.731738i	−0.573711	+	0.819058i	$0.694497\pi$
$992$	21.1723	+	12.2238i	0.0213430	+	0.0123224i
$993$	−16.8563	−	16.8563i	−0.0169751	−	0.0169751i
$994$	−33.8161	+	9.06101i	−0.0340203	+	0.00911570i
$995$	644.003	+	2403.45i	0.647239	+	2.41553i
$996$	−1.30285	+	1.30285i	−0.00130808	+	0.00130808i
$997$	−305.867	+	529.777i	−0.306787	+	0.531371i	−0.977658	−	0.210204i	$-0.932587\pi$
$997$	−305.867	+	529.777i	−0.306787	+	0.531371i	0.670870	+	0.741575i	$0.265921\pi$
$998$	549.651	−	317.341i	0.550753	−	0.317977i
$999$	−139.464	−	37.3693i	−0.139604	−	0.0374067i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.e.70.4	✓	24	13.11	odd	12
169.3.d.e.70.9	yes	24	13.2	odd	12
169.3.d.e.99.4	yes	24	13.10	even	6
169.3.d.e.99.9	yes	24	13.3	even	3
169.3.f.g.19.4		48	13.7	odd	12	inner
169.3.f.g.19.9		48	13.6	odd	12	inner
169.3.f.g.80.4		48	13.5	odd	4	inner
169.3.f.g.80.9		48	13.8	odd	4	inner
169.3.f.g.89.4		48	13.12	even	2	inner
169.3.f.g.89.9		48	1.1	even	1	trivial
169.3.f.g.150.4		48	13.9	even	3	inner
169.3.f.g.150.9		48	13.4	even	6	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+(0.515320 - 1.92320i) q^{2} +(0.299764 + 0.519206i) q^{3} +(0.0309536 + 0.0178711i) q^{4} +(-5.65111 - 5.65111i) q^{5} +(1.15301 - 0.308949i) q^{6} +(0.526568 + 1.96518i) q^{7} +(5.68184 - 5.68184i) q^{8} +(4.32028 - 7.48295i) q^{9} +(-13.7804 + 7.95610i) q^{10} +(-14.0447 - 3.76327i) q^{11} +0.0214284i q^{12} +4.05079 q^{14} +(1.24009 - 4.62809i) q^{15} +(-7.92788 - 13.7315i) q^{16} +(-10.2245 - 5.90312i) q^{17} +(-12.1649 - 12.1649i) q^{18} +(23.4386 - 6.28035i) q^{19} +(-0.0739308 - 0.275914i) q^{20} +(-0.862488 + 0.862488i) q^{21} +(-14.4751 + 25.0716i) q^{22} +(0.229705 - 0.132620i) q^{23} +(4.65326 + 1.24684i) q^{24} +38.8702i q^{25} +10.5760 q^{27} +(-0.0188207 + 0.0702397i) q^{28} +(-3.60897 - 6.25092i) q^{29} +(-8.26171 - 4.76990i) q^{30} +(30.2298 + 30.2298i) q^{31} +(0.552371 - 0.148007i) q^{32} +(-2.25619 - 8.42021i) q^{33} +(-16.6218 + 16.6218i) q^{34} +(8.12976 - 14.0812i) q^{35} +(0.267457 - 0.154416i) q^{36} +(-13.1868 - 3.53340i) q^{37} -48.3135i q^{38} -64.2175 q^{40} +(-9.00403 + 33.6035i) q^{41} +(1.21428 + 2.10319i) q^{42} +(35.0467 + 20.2342i) q^{43} +(-0.367481 - 0.367481i) q^{44} +(-66.7014 + 17.8726i) q^{45} +(-0.136684 - 0.510111i) q^{46} +(9.87555 - 9.87555i) q^{47} +(4.75298 - 8.23241i) q^{48} +(38.8506 - 22.4304i) q^{49} +(74.7552 + 20.0306i) q^{50} -7.07817i q^{51} +77.1259 q^{53} +(5.45003 - 20.3398i) q^{54} +(58.1017 + 100.635i) q^{55} +(14.1577 + 8.17397i) q^{56} +(10.2868 + 10.2868i) q^{57} +(-13.8815 + 3.71955i) q^{58} +(9.32480 + 34.8006i) q^{59} +(0.121094 - 0.121094i) q^{60} +(15.4657 - 26.7873i) q^{61} +(73.7160 - 42.5599i) q^{62} +(16.9803 + 4.54985i) q^{63} -64.5616i q^{64} -17.3564 q^{66} +(16.1999 - 60.4589i) q^{67} +(-0.210990 - 0.365445i) q^{68} +(0.137715 + 0.0795095i) q^{69} +(-22.8915 - 22.8915i) q^{70} +(-8.34804 + 2.23685i) q^{71} +(-17.9698 - 67.0641i) q^{72} +(-23.3661 + 23.3661i) q^{73} +(-13.5909 + 23.5401i) q^{74} +(-20.1816 + 11.6519i) q^{75} +(0.837745 + 0.224473i) q^{76} -29.5820i q^{77} -49.8004 q^{79} +(-32.7969 + 122.400i) q^{80} +(-35.7122 - 61.8554i) q^{81} +(59.9863 + 34.6331i) q^{82} +(60.8000 + 60.8000i) q^{83} +(-0.0421107 + 0.0112835i) q^{84} +(24.4206 + 91.1390i) q^{85} +(56.9747 - 56.9747i) q^{86} +(2.16368 - 3.74760i) q^{87} +(-101.182 + 58.4176i) q^{88} +(-85.6713 - 22.9556i) q^{89} +137.490i q^{90} +0.00948026 q^{92} +(-6.63370 + 24.7573i) q^{93} +(-13.9036 - 24.0818i) q^{94} +(-167.945 - 96.9632i) q^{95} +(0.242427 + 0.242427i) q^{96} +(32.6665 - 8.75298i) q^{97} +(-23.1177 - 86.2763i) 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

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