LMFDB - Embedded newform 144.3.w.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	144.29
Dual form			144.3.w.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99458 - 0.147176i) q^{2} +(-2.86084 - 0.903108i) q^{3} +(3.95668 + 0.587107i) q^{4} +(-0.0992523 + 0.370415i) q^{5} +(5.57325 + 2.22237i) q^{6} +(3.11010 + 1.79562i) q^{7} +(-7.80549 - 1.75336i) q^{8} +(7.36879 + 5.16729i) q^{9} +O(q^{10})$	\(q+(-1.99458 - 0.147176i) q^{2} +(-2.86084 - 0.903108i) q^{3} +(3.95668 + 0.587107i) q^{4} +(-0.0992523 + 0.370415i) q^{5} +(5.57325 + 2.22237i) q^{6} +(3.11010 + 1.79562i) q^{7} +(-7.80549 - 1.75336i) q^{8} +(7.36879 + 5.16729i) q^{9} +(0.252482 - 0.724213i) q^{10} +(-6.39886 + 1.71457i) q^{11} +(-10.7892 - 5.25293i) q^{12} +(4.35132 - 16.2393i) q^{13} +(-5.93907 - 4.03923i) q^{14} +(0.618469 - 0.970060i) q^{15} +(15.3106 + 4.64599i) q^{16} -24.3572i q^{17} +(-13.9371 - 11.3911i) q^{18} +(-16.6582 - 16.6582i) q^{19} +(-0.610182 + 1.40734i) q^{20} +(-7.27586 - 7.94573i) q^{21} +(13.0154 - 2.47808i) q^{22} +(-12.0564 - 20.8824i) q^{23} +(20.7468 + 12.0653i) q^{24} +(21.5233 + 12.4265i) q^{25} +(-11.0691 + 31.7502i) q^{26} +(-16.4143 - 21.4376i) q^{27} +(11.2515 + 8.93065i) q^{28} +(-3.62146 - 13.5155i) q^{29} +(-1.37635 + 1.84384i) q^{30} +(-4.04605 - 7.00797i) q^{31} +(-29.8544 - 11.5201i) q^{32} +(19.8545 + 0.873759i) q^{33} +(-3.58480 + 48.5824i) q^{34} +(-0.973808 + 0.973808i) q^{35} +(26.1222 + 24.7716i) q^{36} +(23.2472 - 23.2472i) q^{37} +(30.7744 + 35.6778i) q^{38} +(-27.1143 + 42.5284i) q^{39} +(1.42418 - 2.71724i) q^{40} +(25.7565 + 44.6115i) q^{41} +(13.3428 + 16.9192i) q^{42} +(2.25526 + 8.41674i) q^{43} +(-26.3249 + 3.02718i) q^{44} +(-2.64541 + 2.21664i) q^{45} +(20.9741 + 43.4259i) q^{46} +(6.02413 + 3.47803i) q^{47} +(-39.6053 - 27.1186i) q^{48} +(-18.0515 - 31.2661i) q^{49} +(-41.1010 - 27.9533i) q^{50} +(-21.9972 + 69.6821i) q^{51} +(26.7510 - 61.6992i) q^{52} +(12.8444 + 12.8444i) q^{53} +(29.5845 + 45.1748i) q^{54} -2.54041i q^{55} +(-21.1275 - 19.4688i) q^{56} +(32.6123 + 62.7006i) q^{57} +(5.23413 + 27.4906i) q^{58} +(20.9700 - 78.2612i) q^{59} +(3.01661 - 3.47511i) q^{60} +(-71.0232 + 19.0306i) q^{61} +(7.03876 + 14.5734i) q^{62} +(13.6392 + 29.3023i) q^{63} +(57.8515 + 27.3717i) q^{64} +(5.58341 + 3.22358i) q^{65} +(-39.4728 - 4.66489i) q^{66} +(3.25953 - 12.1647i) q^{67} +(14.3003 - 96.3738i) q^{68} +(15.6325 + 70.6293i) q^{69} +(2.08566 - 1.79901i) q^{70} +79.2346 q^{71} +(-48.4569 - 53.2534i) q^{72} -88.5296i q^{73} +(-49.7897 + 42.9469i) q^{74} +(-50.3522 - 54.9880i) q^{75} +(-56.1310 - 75.6913i) q^{76} +(-22.9798 - 6.15742i) q^{77} +(60.3408 - 80.8357i) q^{78} +(-57.3999 + 99.4195i) q^{79} +(-3.24056 + 5.21015i) q^{80} +(27.5981 + 76.1534i) q^{81} +(-44.8076 - 92.7719i) q^{82} +(-4.32178 - 16.1291i) q^{83} +(-24.1232 - 35.7104i) q^{84} +(9.02227 + 2.41751i) q^{85} +(-3.25955 - 17.1198i) q^{86} +(-1.84553 + 41.9361i) q^{87} +(52.9525 - 2.16356i) q^{88} +95.2289 q^{89} +(5.60271 - 4.03192i) q^{90} +(42.6927 - 42.6927i) q^{91} +(-35.4433 - 89.7032i) q^{92} +(5.24615 + 23.7027i) q^{93} +(-11.5037 - 7.82381i) q^{94} +(7.82380 - 4.51708i) q^{95} +(75.0047 + 59.9190i) q^{96} +(32.5843 - 56.4377i) q^{97} +(31.4035 + 65.0195i) q^{98} +(-56.0115 - 20.4305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.99458	−	0.147176i	−0.997289	−	0.0735880i
$2$	−1.99458	−	0.147176i	−0.997289	−	0.0735880i
$3$	−2.86084	−	0.903108i	−0.953613	−	0.301036i
$3$	−2.86084	−	0.903108i	−0.953613	−	0.301036i
$4$	3.95668	+	0.587107i	0.989170	+	0.146777i
$5$	−0.0992523	+	0.370415i	−0.0198505	+	0.0740829i	−0.975141	−	0.221587i	$-0.928876\pi$
$5$	−0.0992523	+	0.370415i	−0.0198505	+	0.0740829i	0.955290	+	0.295670i	$0.0955429\pi$
$6$	5.57325	+	2.22237i	0.928875	+	0.370394i
$7$	3.11010	+	1.79562i	0.444300	+	0.256517i	0.705420	−	0.708790i	$-0.250758\pi$
$7$	3.11010	+	1.79562i	0.444300	+	0.256517i	−0.261120	+	0.965306i	$0.584092\pi$
$8$	−7.80549	−	1.75336i	−0.975687	−	0.219170i
$9$	7.36879	+	5.16729i	0.818754	+	0.574144i
$10$	0.252482	−	0.724213i	0.0252482	−	0.0724213i
$11$	−6.39886	+	1.71457i	−0.581715	+	0.155870i	−0.537664	−	0.843159i	$-0.680693\pi$
$11$	−6.39886	+	1.71457i	−0.581715	+	0.155870i	−0.0440508	+	0.999029i	$0.514026\pi$
$12$	−10.7892	−	5.25293i	−0.899100	−	0.437744i
$13$	4.35132	−	16.2393i	0.334717	−	1.24918i	−0.569459	−	0.822020i	$-0.692847\pi$
$13$	4.35132	−	16.2393i	0.334717	−	1.24918i	0.904176	−	0.427161i	$-0.140486\pi$
$14$	−5.93907	−	4.03923i	−0.424219	−	0.288517i
$15$	0.618469	−	0.970060i	0.0412313	−	0.0646707i
$16$	15.3106	+	4.64599i	0.956913	+	0.290374i
$17$		−	24.3572i		−	1.43278i	−0.697701	−	0.716389i	$-0.745793\pi$
$17$		−	24.3572i		−	1.43278i	0.697701	−	0.716389i	$-0.254207\pi$
$18$	−13.9371	−	11.3911i	−0.774285	−	0.632838i
$19$	−16.6582	−	16.6582i	−0.876747	−	0.876747i	0.116449	−	0.993197i	$-0.462849\pi$
$19$	−16.6582	−	16.6582i	−0.876747	−	0.876747i	−0.993197	+	0.116449i	$0.962849\pi$
$20$	−0.610182	+	1.40734i	−0.0305091	+	0.0703670i
$21$	−7.27586	−	7.94573i	−0.346470	−	0.378368i
$22$	13.0154	−	2.47808i	0.591607	−	0.112640i
$23$	−12.0564	−	20.8824i	−0.524193	−	0.907929i	−0.999603	−	0.0281647i	$-0.991034\pi$
$23$	−12.0564	−	20.8824i	−0.524193	−	0.907929i	0.475410	−	0.879764i	$-0.342300\pi$
$24$	20.7468	+	12.0653i	0.864449	+	0.502720i
$25$	21.5233	+	12.4265i	0.860931	+	0.497059i
$26$	−11.0691	+	31.7502i	−0.425734	+	1.22116i
$27$	−16.4143	−	21.4376i	−0.607937	−	0.793986i
$28$	11.2515	+	8.93065i	0.401838	+	0.318952i
$29$	−3.62146	−	13.5155i	−0.124878	−	0.466050i	0.874957	−	0.484200i	$-0.160889\pi$
$29$	−3.62146	−	13.5155i	−0.124878	−	0.466050i	−0.999835	+	0.0181494i	$0.994223\pi$
$30$	−1.37635	+	1.84384i	−0.0458785	+	0.0614612i
$31$	−4.04605	−	7.00797i	−0.130518	−	0.226063i	0.793358	−	0.608755i	$-0.208331\pi$
$31$	−4.04605	−	7.00797i	−0.130518	−	0.226063i	−0.923876	+	0.382691i	$0.874997\pi$
$32$	−29.8544	−	11.5201i	−0.932951	−	0.360004i
$33$	19.8545	+	0.873759i	0.601653	+	0.0264776i
$34$	−3.58480	+	48.5824i	−0.105435	+	1.42889i
$35$	−0.973808	+	0.973808i	−0.0278231	+	0.0278231i
$36$	26.1222	+	24.7716i	0.725616	+	0.688100i
$37$	23.2472	−	23.2472i	0.628302	−	0.628302i	−0.319338	−	0.947641i	$-0.603461\pi$
$37$	23.2472	−	23.2472i	0.628302	−	0.628302i	0.947641	+	0.319338i	$0.103461\pi$
$38$	30.7744	+	35.6778i	0.809852	+	0.938888i
$39$	−27.1143	+	42.5284i	−0.695239	+	1.09047i
$40$	1.42418	−	2.71724i	0.0356046	−	0.0679311i
$41$	25.7565	+	44.6115i	0.628207	+	1.08809i	0.987911	+	0.155020i	$0.0495442\pi$
$41$	25.7565	+	44.6115i	0.628207	+	1.08809i	−0.359704	+	0.933066i	$0.617122\pi$
$42$	13.3428	+	16.9192i	0.317687	+	0.402838i
$43$	2.25526	+	8.41674i	0.0524479	+	0.195738i	0.987179	−	0.159618i	$-0.0510263\pi$
$43$	2.25526	+	8.41674i	0.0524479	+	0.195738i	−0.934731	+	0.355356i	$0.884360\pi$
$44$	−26.3249	+	3.02718i	−0.598292	+	0.0687996i
$45$	−2.64541	+	2.21664i	−0.0587869	+	0.0492587i
$46$	20.9741	+	43.4259i	0.455959	+	0.944042i
$47$	6.02413	+	3.47803i	0.128173	+	0.0740006i	0.562716	−	0.826651i	$-0.309757\pi$
$47$	6.02413	+	3.47803i	0.128173	+	0.0740006i	−0.434543	+	0.900651i	$0.643090\pi$
$48$	−39.6053	−	27.1186i	−0.825111	−	0.564970i
$49$	−18.0515	−	31.2661i	−0.368398	−	0.638084i
$50$	−41.1010	−	27.9533i	−0.822019	−	0.559065i
$51$	−21.9972	+	69.6821i	−0.431318	+	1.36632i
$52$	26.7510	−	61.6992i	0.514443	−	1.18652i
$53$	12.8444	+	12.8444i	0.242346	+	0.242346i	0.817820	−	0.575474i	$-0.195182\pi$
$53$	12.8444	+	12.8444i	0.242346	+	0.242346i	−0.575474	+	0.817820i	$0.695182\pi$
$54$	29.5845	+	45.1748i	0.547861	+	0.836570i
$55$		−	2.54041i		−	0.0461892i
$56$	−21.1275	−	19.4688i	−0.377277	−	0.347657i
$57$	32.6123	+	62.7006i	0.572145	+	1.10001i
$58$	5.23413	+	27.4906i	0.0902436	+	0.473976i
$59$	20.9700	−	78.2612i	0.355424	−	1.32646i	−0.524526	−	0.851395i	$-0.675757\pi$
$59$	20.9700	−	78.2612i	0.355424	−	1.32646i	0.879950	−	0.475067i	$-0.157576\pi$
$60$	3.01661	−	3.47511i	0.0502769	−	0.0579185i
$61$	−71.0232	+	19.0306i	−1.16431	+	0.311977i	−0.788688	−	0.614794i	$-0.789239\pi$
$61$	−71.0232	+	19.0306i	−1.16431	+	0.311977i	−0.375627	+	0.926771i	$0.622573\pi$
$62$	7.03876	+	14.5734i	0.113528	+	0.235055i
$63$	13.6392	+	29.3023i	0.216495	+	0.465117i
$64$	57.8515	+	27.3717i	0.903929	+	0.427682i
$65$	5.58341	+	3.22358i	0.0858986	+	0.0495936i
$66$	−39.4728	−	4.66489i	−0.598073	−	0.0706802i
$67$	3.25953	−	12.1647i	0.0486498	−	0.181563i	−0.937325	−	0.348455i	$-0.886706\pi$
$67$	3.25953	−	12.1647i	0.0486498	−	0.181563i	0.985975	+	0.166892i	$0.0533730\pi$
$68$	14.3003	−	96.3738i	0.210299	−	1.41726i
$69$	15.6325	+	70.6293i	0.226558	+	1.02361i
$70$	2.08566	−	1.79901i	0.0297951	−	0.0257002i
$71$	79.2346			1.11598			0.557990	−	0.829847i	$-0.311573\pi$
$71$	79.2346			1.11598			0.557990	+	0.829847i	$0.311573\pi$
$72$	−48.4569	−	53.2534i	−0.673013	−	0.739631i
$73$		−	88.5296i		−	1.21273i	−0.795185	−	0.606367i	$-0.792626\pi$
$73$		−	88.5296i		−	1.21273i	0.795185	−	0.606367i	$-0.207374\pi$
$74$	−49.7897	+	42.9469i	−0.672834	+	0.580363i
$75$	−50.3522	−	54.9880i	−0.671362	−	0.733173i
$76$	−56.1310	−	75.6913i	−0.738566	−	0.995938i
$77$	−22.9798	−	6.15742i	−0.298439	−	0.0799665i
$78$	60.3408	−	80.8357i	0.773599	−	1.03635i
$79$	−57.3999	+	99.4195i	−0.726581	+	1.25848i	0.231739	+	0.972778i	$0.425558\pi$
$79$	−57.3999	+	99.4195i	−0.726581	+	1.25848i	−0.958320	+	0.285697i	$0.907775\pi$
$80$	−3.24056	+	5.21015i	−0.0405069	+	0.0651268i
$81$	27.5981	+	76.1534i	0.340718	+	0.940166i
$82$	−44.8076	−	92.7719i	−0.546434	−	1.13136i
$83$	−4.32178	−	16.1291i	−0.0520697	−	0.194327i	0.934992	−	0.354670i	$-0.115407\pi$
$83$	−4.32178	−	16.1291i	−0.0520697	−	0.194327i	−0.987061	+	0.160343i	$0.948740\pi$
$84$	−24.1232	−	35.7104i	−0.287181	−	0.425124i
$85$	9.02227	+	2.41751i	0.106144	+	0.0284413i
$86$	−3.25955	−	17.1198i	−0.0379017	−	0.199067i
$87$	−1.84553	+	41.9361i	−0.0212129	+	0.482024i
$88$	52.9525	−	2.16356i	0.601733	−	0.0245859i
$89$	95.2289			1.06999			0.534994	−	0.844856i	$-0.320314\pi$
$89$	95.2289			1.06999			0.534994	+	0.844856i	$0.320314\pi$
$90$	5.60271	−	4.03192i	0.0622523	−	0.0447991i
$91$	42.6927	−	42.6927i	0.469151	−	0.469151i
$92$	−35.4433	−	89.7032i	−0.385253	−	0.975035i
$93$	5.24615	+	23.7027i	0.0564102	+	0.254868i
$94$	−11.5037	−	7.82381i	−0.122380	−	0.0832320i
$95$	7.82380	−	4.51708i	0.0823558	−	0.0475482i
$96$	75.0047	+	59.9190i	0.781299	+	0.624157i
$97$	32.5843	−	56.4377i	0.335921	−	0.581832i	−0.647741	−	0.761861i	$-0.724286\pi$
$97$	32.5843	−	56.4377i	0.335921	−	0.581832i	0.983661	+	0.180029i	$0.0576193\pi$
$98$	31.4035	+	65.0195i	0.320444	+	0.663464i
$99$	−56.0115	−	20.4305i	−0.565773	−	0.206369i
$100$	77.8650	+	61.8040i	0.778650	+	0.618040i
$101$	−127.848	+	34.2567i	−1.26582	+	0.339176i	−0.828428	−	0.560095i	$-0.810764\pi$
$101$	−127.848	+	34.2567i	−1.26582	+	0.339176i	−0.437392	+	0.899271i	$0.644098\pi$
$102$	54.1307	−	135.749i	0.530693	−	1.33087i
$103$	−96.1033	+	55.4853i	−0.933042	+	0.538692i	−0.887772	−	0.460283i	$-0.847748\pi$
$103$	−96.1033	+	55.4853i	−0.933042	+	0.538692i	−0.0452697	+	0.998975i	$0.514415\pi$
$104$	−62.4376	+	119.127i	−0.600362	+	1.14545i
$105$	3.66536	−	1.90645i	0.0349082	−	0.0181567i
$106$	−23.7287	−	27.5095i	−0.223856	−	0.259523i
$107$	53.3528	+	53.3528i	0.498625	+	0.498625i	0.911010	−	0.412385i	$-0.135304\pi$
$107$	53.3528	+	53.3528i	0.498625	+	0.498625i	−0.412385	+	0.911010i	$0.635304\pi$
$108$	−52.3599	−	94.4587i	−0.484814	−	0.874617i
$109$	−64.1974	−	64.1974i	−0.588967	−	0.588967i	0.348385	−	0.937352i	$-0.386730\pi$
$109$	−64.1974	−	64.1974i	−0.588967	−	0.588967i	−0.937352	+	0.348385i	$0.886730\pi$
$110$	−0.373886	+	5.06704i	−0.00339897	+	0.0460640i
$111$	−87.5012	+	45.5117i	−0.788299	+	0.410015i
$112$	39.2751	+	41.9415i	0.350671	+	0.374478i
$113$	124.049	−	71.6198i	1.09778	−	0.633804i	0.162143	−	0.986767i	$-0.448159\pi$
$113$	124.049	−	71.6198i	1.09778	−	0.633804i	0.935637	+	0.352964i	$0.114826\pi$
$114$	−55.8197	−	129.861i	−0.489646	−	1.13913i
$115$	8.93176	−	2.39326i	0.0776675	−	0.0208109i
$116$	−6.39391	−	55.6025i	−0.0551199	−	0.479332i
$117$	115.977	−	97.1798i	0.991260	−	0.830596i
$118$	−53.3445	+	153.012i	−0.452072	+	1.29671i
$119$	43.7363	−	75.7535i	0.367532	−	0.636584i
$120$	−6.52832	+	6.48740i	−0.0544027	+	0.0540617i
$121$	−66.7834	+	38.5574i	−0.551929	+	0.318656i
$122$	144.462	−	27.5051i	1.18412	−	0.225452i
$123$	−33.3961	−	150.887i	−0.271513	−	1.22673i
$124$	−11.8945	−	30.1037i	−0.0959234	−	0.242772i
$125$	−13.5182	+	13.5182i	−0.108146	+	0.108146i
$126$	−22.8918	−	60.4532i	−0.181681	−	0.479787i
$127$	−145.624			−1.14664			−0.573322	−	0.819330i	$-0.694346\pi$
$127$	−145.624			−1.14664			−0.573322	+	0.819330i	$0.694346\pi$
$128$	−111.361	−	63.1092i	−0.870006	−	0.493041i
$129$	1.14930	−	26.1157i	0.00890929	−	0.202447i
$130$	−10.6621	−	7.25143i	−0.0820162	−	0.0557802i
$131$	156.168	+	41.8452i	1.19212	+	0.319429i	0.799725	−	0.600366i	$-0.204979\pi$
$131$	156.168	+	41.8452i	1.19212	+	0.319429i	0.392399	+	0.919795i	$0.371645\pi$
$132$	78.0451	+	15.1139i	0.591250	+	0.114500i
$133$	−21.8969	−	81.7205i	−0.164639	−	0.614440i
$134$	−8.29175	+	23.7838i	−0.0618787	+	0.177491i
$135$	9.56996	−	3.95236i	0.0708886	−	0.0292767i
$136$	−42.7070	+	190.120i	−0.314022	+	1.39794i
$137$	−101.494	+	175.792i	−0.740830	+	1.28316i	0.211287	+	0.977424i	$0.432234\pi$
$137$	−101.494	+	175.792i	−0.740830	+	1.28316i	−0.952118	+	0.305732i	$0.901099\pi$
$138$	−20.7853	−	143.176i	−0.150618	−	1.03751i
$139$	41.3576	+	11.0817i	0.297536	+	0.0797247i	0.404499	−	0.914538i	$-0.367446\pi$
$139$	41.3576	+	11.0817i	0.297536	+	0.0797247i	−0.106963	+	0.994263i	$0.534113\pi$
$140$	−4.42477	+	3.28131i	−0.0316055	+	0.0234380i
$141$	−14.0930	−	15.3905i	−0.0999504	−	0.109153i
$142$	−158.040	−	11.6614i	−1.11296	−	0.0821227i
$143$			111.374i			0.778839i
$144$	88.8135	+	113.350i	0.616760	+	0.787151i
$145$	5.36576			0.0370052
$146$	−13.0294	+	176.579i	−0.0892427	+	1.20945i
$147$	23.4057	+	105.750i	0.159223	+	0.719387i
$148$	105.630	−	78.3330i	0.713718	−	0.529277i
$149$	−67.0629	+	250.282i	−0.450087	+	1.67975i	0.252058	+	0.967712i	$0.418893\pi$
$149$	−67.0629	+	250.282i	−0.450087	+	1.67975i	−0.702145	+	0.712034i	$0.747774\pi$
$150$	92.3384	+	117.088i	0.615589	+	0.780589i
$151$	248.718	+	143.597i	1.64714	+	0.950975i	0.978202	+	0.207655i	$0.0665831\pi$
$151$	248.718	+	143.597i	1.64714	+	0.950975i	0.668936	+	0.743320i	$0.266750\pi$
$152$	100.818	+	159.233i	0.663274	+	1.04759i
$153$	125.861	−	179.483i	0.822621	−	1.17309i
$154$	44.9288	+	15.6635i	0.291745	+	0.101711i
$155$	2.99743	−	0.803160i	0.0193383	−	0.00518168i
$156$	−132.251	+	152.352i	−0.847765	+	0.976617i
$157$	−80.1572	+	299.151i	−0.510555	+	1.90542i	−0.0960379	+	0.995378i	$0.530617\pi$
$157$	−80.1572	+	299.151i	−0.510555	+	1.90542i	−0.414518	+	0.910041i	$0.636050\pi$
$158$	129.121	−	189.852i	0.817220	−	1.20160i
$159$	−25.1458	−	48.3455i	−0.158150	−	0.304060i
$160$	7.23035	−	9.91511i	0.0451897	−	0.0619694i
$161$		−	86.5950i		−	0.537857i
$162$	−43.8387	−	155.956i	−0.270609	−	0.962689i
$163$	4.21083	+	4.21083i	0.0258333	+	0.0258333i	0.719905	−	0.694072i	$-0.244185\pi$
$163$	4.21083	+	4.21083i	0.0258333	+	0.0258333i	−0.694072	+	0.719905i	$0.744185\pi$
$164$	75.7184	+	191.635i	0.461697	+	1.16851i
$165$	−2.29426	+	7.26769i	−0.0139046	+	0.0440466i
$166$	6.24632	+	32.8068i	0.0376284	+	0.197632i
$167$	−76.5369	−	132.566i	−0.458305	−	0.793807i	0.540567	−	0.841301i	$-0.318210\pi$
$167$	−76.5369	−	132.566i	−0.458305	−	0.793807i	−0.998872	+	0.0474942i	$0.984876\pi$
$168$	42.8600	+	74.7776i	0.255119	+	0.445105i
$169$	−98.4241	−	56.8252i	−0.582391	−	0.336244i
$170$	−17.6398	−	6.14977i	−0.103764	−	0.0361751i
$171$	−36.6730	−	208.829i	−0.214462	−	1.22122i
$172$	3.98180	+	34.6264i	0.0231500	+	0.201316i
$173$	−5.37712	−	20.0677i	−0.0310816	−	0.115998i	0.948642	−	0.316351i	$-0.102458\pi$
$173$	−5.37712	−	20.0677i	−0.0310816	−	0.115998i	−0.979724	+	0.200353i	$0.935791\pi$
$174$	9.85303	−	83.3732i	0.0566266	−	0.479156i
$175$	44.6264	+	77.2952i	0.255008	+	0.441687i
$176$	−105.936	−	3.47794i	−0.601911	−	0.0197610i
$177$	−130.670	+	204.954i	−0.738250	+	1.15793i
$178$	−189.941	−	14.0154i	−1.06709	−	0.0787382i
$179$	104.907	−	104.907i	0.586071	−	0.586071i	−0.350494	−	0.936565i	$-0.613986\pi$
$179$	104.907	−	104.907i	0.586071	−	0.586071i	0.936565	+	0.350494i	$0.113986\pi$
$180$	−11.7684	+	7.21740i	−0.0653802	+	0.0400966i
$181$	178.510	−	178.510i	0.986241	−	0.986241i	−0.0136654	−	0.999907i	$-0.504350\pi$
$181$	178.510	−	178.510i	0.986241	−	0.986241i	0.999907	+	0.0136654i	$0.00434995\pi$
$182$	−91.4373	+	78.8706i	−0.502403	+	0.433355i
$183$	220.373	+	9.69816i	1.20422	+	0.0529954i
$184$	57.4922	+	184.136i	0.312457	+	1.00074i
$185$	6.30376	+	10.9184i	0.0340744	+	0.0590185i
$186$	−6.97538	−	48.0490i	−0.0375020	−	0.258328i
$187$	41.7622	+	155.859i	0.223327	+	0.833468i
$188$	21.7936	+	17.2983i	0.115923	+	0.0920120i
$189$	−12.5563	−	96.1469i	−0.0664357	−	0.508714i
$190$	−16.2700	+	7.85818i	−0.0856315	+	0.0413588i
$191$	−78.4442	−	45.2898i	−0.410703	−	0.237119i	0.280389	−	0.959887i	$-0.409537\pi$
$191$	−78.4442	−	45.2898i	−0.410703	−	0.237119i	−0.691092	+	0.722767i	$0.742870\pi$
$192$	−140.784	−	130.552i	−0.733250	−	0.679959i
$193$	−141.170	−	244.514i	−0.731451	−	1.26691i	−0.956263	−	0.292508i	$-0.905510\pi$
$193$	−141.170	−	244.514i	−0.731451	−	1.26691i	0.224812	−	0.974402i	$-0.427823\pi$
$194$	−73.2982	+	107.774i	−0.377826	+	0.555534i
$195$	−13.0620	−	14.2646i	−0.0669846	−	0.0731517i
$196$	−53.0674	−	134.308i	−0.270752	−	0.685246i
$197$	−137.726	−	137.726i	−0.699116	−	0.699116i	0.265104	−	0.964220i	$-0.414594\pi$
$197$	−137.726	−	137.726i	−0.699116	−	0.699116i	−0.964220	+	0.265104i	$0.914594\pi$
$198$	108.712	+	48.9937i	0.549053	+	0.247443i
$199$			206.381i			1.03709i	0.855050	+	0.518545i	$0.173526\pi$
$199$			206.381i			1.03709i	−0.855050	+	0.518545i	$0.826474\pi$
$200$	−146.212	−	134.733i	−0.731059	−	0.673664i
$201$	−20.3111	+	31.8577i	−0.101050	+	0.158496i
$202$	260.044	−	49.5116i	1.28735	−	0.245107i
$203$	13.0055	−	48.5372i	0.0640665	−	0.239100i
$204$	−127.947	+	262.795i	−0.627190	+	1.28821i
$205$	−19.0812	+	5.11278i	−0.0930788	+	0.0249404i
$206$	199.852	−	96.5256i	0.970154	−	0.468571i
$207$	19.0640	−	216.177i	0.0920964	−	1.04433i
$208$	142.069	−	228.418i	0.683025	−	1.09816i
$209$	135.155	+	78.0319i	0.646675	+	0.373358i
$210$	−7.59143	+	3.26311i	−0.0361497	+	0.0155386i
$211$	81.2026	−	303.052i	0.384847	−	1.43627i	−0.453562	−	0.891225i	$-0.649847\pi$
$211$	81.2026	−	303.052i	0.384847	−	1.43627i	0.838409	−	0.545042i	$-0.183486\pi$
$212$	43.2800	+	58.3620i	0.204151	+	0.275293i
$213$	−226.677	−	71.5575i	−1.06421	−	0.335951i
$214$	−98.5641	−	114.269i	−0.460580	−	0.533966i
$215$	−3.34152			−0.0155420
$216$	90.5338	+	196.111i	0.419138	+	0.907923i
$217$		−	29.0607i		−	0.133920i
$218$	118.598	+	137.495i	0.544029	+	0.630711i
$219$	−79.9519	+	253.269i	−0.365077	+	1.15648i
$220$	1.49149	−	10.0516i	0.00677950	−	0.0456889i
$221$	−395.546	−	105.986i	−1.78980	−	0.479575i
$222$	181.226	−	77.8986i	0.816334	−	0.350894i
$223$	138.941	−	240.652i	0.623052	−	1.07916i	−0.365862	−	0.930669i	$-0.619226\pi$
$223$	138.941	−	240.652i	0.623052	−	1.07916i	0.988914	−	0.148488i	$-0.0474407\pi$
$224$	−72.1645	−	89.4359i	−0.322163	−	0.399268i
$225$	94.3893	+	202.785i	0.419508	+	0.901267i
$226$	−257.966	+	124.594i	−1.14144	+	0.551302i
$227$	26.2636	+	98.0172i	0.115699	+	0.431794i	0.999338	−	0.0363741i	$-0.0115808\pi$
$227$	26.2636	+	98.0172i	0.115699	+	0.431794i	−0.883639	+	0.468168i	$0.844914\pi$
$228$	92.2242	+	267.233i	0.404492	+	1.17207i
$229$	−27.1599	−	7.27747i	−0.118602	−	0.0317794i	0.199030	−	0.979993i	$-0.436221\pi$
$229$	−27.1599	−	7.27747i	−0.118602	−	0.0317794i	−0.317632	+	0.948214i	$0.602888\pi$
$230$	−18.1673	+	3.45900i	−0.0789883	+	0.0150391i
$231$	60.1807	+	38.3687i	0.260523	+	0.166098i
$232$	4.56980	+	111.845i	0.0196974	+	0.482089i
$233$	−276.964			−1.18869			−0.594343	−	0.804212i	$-0.702588\pi$
$233$	−276.964			−1.18869			−0.594343	+	0.804212i	$0.702588\pi$
$234$	−245.629	+	176.764i	−1.04969	+	0.755400i
$235$	−1.88622	+	1.88622i	−0.00802647	+	0.00802647i
$236$	128.919	−	297.343i	0.546269	−	1.25993i
$237$	253.998	−	232.585i	1.07172	−	0.981371i
$238$	−98.3845	+	144.659i	−0.413380	+	0.607812i
$239$	254.577	−	146.980i	1.06518	−	0.614979i	0.138316	−	0.990388i	$-0.455831\pi$
$239$	254.577	−	146.980i	1.06518	−	0.614979i	0.926859	+	0.375409i	$0.122498\pi$
$240$	13.9760	−	11.9788i	0.0582335	−	0.0499117i
$241$	99.8099	−	172.876i	0.414149	−	0.717327i	−0.581190	−	0.813768i	$-0.697413\pi$
$241$	99.8099	−	172.876i	0.414149	−	0.717327i	0.995339	+	0.0964412i	$0.0307460\pi$
$242$	138.879	−	67.0769i	0.573882	−	0.277177i
$243$	−10.1790	−	242.787i	−0.0418889	−	0.999122i
$244$	−292.189	+	33.5998i	−1.19750	+	0.137704i
$245$	13.3731	−	3.58331i	0.0545840	−	0.0146257i
$246$	44.4041	+	305.872i	0.180504	+	1.24338i
$247$	−343.003	+	198.033i	−1.38868	+	0.801754i
$248$	19.2940	+	61.7948i	0.0777982	+	0.249173i
$249$	−2.20242	+	50.0458i	−0.00884505	+	0.200987i
$250$	28.9527	−	24.9736i	0.115811	−	0.0998944i
$251$	154.182	+	154.182i	0.614271	+	0.614271i	0.944056	−	0.329785i	$-0.106976\pi$
$251$	154.182	+	154.182i	0.614271	+	0.614271i	−0.329785	+	0.944056i	$0.606976\pi$
$252$	36.7623	+	123.948i	0.145882	+	0.491856i
$253$	112.952	+	112.952i	0.446449	+	0.446449i
$254$	290.458	+	21.4323i	1.14354	+	0.0843792i
$255$	−23.6280	−	15.0642i	−0.0926588	−	0.0590753i
$256$	212.830	+	142.266i	0.831365	+	0.555726i
$257$	−127.793	+	73.7813i	−0.497249	+	0.287087i	−0.727577	−	0.686026i	$-0.759353\pi$
$257$	−127.793	+	73.7813i	−0.497249	+	0.287087i	0.230328	+	0.973113i	$0.426020\pi$
$258$	−6.13596	+	51.9206i	−0.0237828	+	0.201243i
$259$	114.044	−	30.5580i	0.440325	−	0.117985i
$260$	20.1992	+	16.0327i	0.0776891	+	0.0616644i
$261$	43.1526	−	118.306i	0.165336	−	0.453279i
$262$	−305.331	−	106.448i	−1.16539	−	0.406289i
$263$	200.555	−	347.372i	0.762567	−	1.32080i	−0.178957	−	0.983857i	$-0.557272\pi$
$263$	200.555	−	347.372i	0.762567	−	1.32080i	0.941524	−	0.336947i	$-0.109394\pi$
$264$	−153.443	−	41.6323i	−0.581222	−	0.157698i
$265$	−6.03257	+	3.48291i	−0.0227644	+	0.0131430i
$266$	31.6478	+	166.221i	0.118977	+	0.624889i
$267$	−272.435	−	86.0021i	−1.02035	−	0.322105i
$268$	20.0389	−	46.2183i	0.0747722	−	0.172456i
$269$	−38.4599	+	38.4599i	−0.142974	+	0.142974i	−0.774971	−	0.631997i	$-0.782235\pi$
$269$	−38.4599	+	38.4599i	−0.142974	+	0.142974i	0.631997	+	0.774971i	$0.282235\pi$
$270$	−19.6697	+	6.47482i	−0.0728508	+	0.0239808i
$271$	78.7332			0.290528			0.145264	−	0.989393i	$-0.453597\pi$
$271$	78.7332			0.290528			0.145264	+	0.989393i	$0.453597\pi$
$272$	113.164	−	372.924i	0.416042	−	1.37104i
$273$	−160.693	+	83.5808i	−0.588619	+	0.306157i
$274$	228.310	−	335.694i	0.833247	−	1.22516i
$275$	−159.030	−	42.6121i	−0.578293	−	0.154953i
$276$	20.3857	+	288.636i	0.0738612	+	1.04578i
$277$	82.6913	+	308.608i	0.298524	+	1.11411i	0.938378	+	0.345611i	$0.112328\pi$
$277$	82.6913	+	308.608i	0.298524	+	1.11411i	−0.639853	+	0.768497i	$0.721005\pi$
$278$	−80.8599	−	28.1902i	−0.290863	−	0.101404i
$279$	6.39773	−	72.5474i	0.0229309	−	0.260026i
$280$	9.30848	−	5.89361i	0.0332446	−	0.0210486i
$281$	65.8614	−	114.075i	0.234382	−	0.405962i	−0.724711	−	0.689053i	$-0.758027\pi$
$281$	65.8614	−	114.075i	0.234382	−	0.405962i	0.959093	+	0.283091i	$0.0913600\pi$
$282$	25.8445	+	32.7717i	0.0916471	+	0.116212i
$283$	258.450	+	69.2515i	0.913251	+	0.244705i	0.684698	−	0.728827i	$-0.259934\pi$
$283$	258.450	+	69.2515i	0.913251	+	0.244705i	0.228553	+	0.973532i	$0.426601\pi$
$284$	313.506	+	46.5192i	1.10389	+	0.163800i
$285$	−26.4620	+	5.85688i	−0.0928493	+	0.0205504i
$286$	16.3916	−	222.144i	0.0573131	−	0.776727i
$287$			184.995i			0.644583i
$288$	−160.463	−	239.156i	−0.557163	−	0.830403i
$289$	−304.275			−1.05286
$290$	−10.7024	−	0.789711i	−0.0369049	−	0.00272314i
$291$	−144.188	+	132.032i	−0.495490	+	0.453718i
$292$	51.9764	−	350.283i	0.178001	−	1.19960i
$293$	−24.7756	+	92.4639i	−0.0845585	+	0.315576i	−0.995230	−	0.0975542i	$-0.968898\pi$
$293$	−24.7756	+	92.4639i	−0.0845585	+	0.315576i	0.910672	+	0.413131i	$0.135565\pi$
$294$	−31.1207	−	214.371i	−0.105853	−	0.729153i
$295$	26.9078	+	15.5352i	0.0912128	+	0.0526617i
$296$	−222.216	+	140.695i	−0.750731	+	0.475321i
$297$	141.789	+	109.033i	0.477404	+	0.367114i
$298$	170.598	−	489.337i	0.572476	−	1.64207i
$299$	−391.577	+	104.923i	−1.30962	+	0.350913i
$300$	−166.943	−	247.132i	−0.556478	−	0.823773i
$301$	−8.09916	+	30.2265i	−0.0269075	+	0.100420i
$302$	−474.953	−	323.021i	−1.57269	−	1.06961i
$303$	396.690	+	17.4575i	1.30921	+	0.0576156i
$304$	−177.653	−	332.441i	−0.584386	−	1.09356i
$305$		−	28.1969i		−	0.0924487i
$306$	−277.455	+	339.470i	−0.906716	+	1.10938i
$307$	102.660	+	102.660i	0.334399	+	0.334399i	0.854254	−	0.519855i	$-0.174014\pi$
$307$	102.660	+	102.660i	0.334399	+	0.334399i	−0.519855	+	0.854254i	$0.674014\pi$
$308$	−87.3087	−	37.8546i	−0.283470	−	0.122904i
$309$	325.045	−	71.9427i	1.05193	−	0.232824i
$310$	−6.09682	+	1.16081i	−0.0196672	+	0.00374456i
$311$	−299.135	−	518.117i	−0.961849	−	1.66597i	−0.717852	−	0.696195i	$-0.754875\pi$
$311$	−299.135	−	518.117i	−0.961849	−	1.66597i	−0.243997	−	0.969776i	$-0.578459\pi$
$312$	286.208	−	284.414i	0.917334	−	0.911584i
$313$	95.0121	+	54.8552i	0.303553	+	0.175256i	0.644038	−	0.764994i	$-0.277258\pi$
$313$	95.0121	+	54.8552i	0.303553	+	0.175256i	−0.340485	+	0.940250i	$0.610591\pi$
$314$	203.908	−	584.882i	0.649387	−	1.86268i
$315$	−12.2077	+	2.14383i	−0.0387547	+	0.00680582i
$316$	−285.483	+	359.671i	−0.903427	+	1.13820i
$317$	24.7168	+	92.2444i	0.0779710	+	0.290992i	0.993891	−	0.110370i	$-0.0352036\pi$
$317$	24.7168	+	92.2444i	0.0779710	+	0.290992i	−0.915920	+	0.401362i	$0.868537\pi$
$318$	43.0399	+	100.130i	0.135346	+	0.314873i
$319$	46.3464	+	80.2743i	0.145286	+	0.251644i
$320$	−15.8808	+	18.7123i	−0.0496273	+	0.0584760i
$321$	−104.450	−	200.817i	−0.325391	−	0.625599i
$322$	−12.7447	+	172.721i	−0.0395798	+	0.536399i
$323$	−405.748	+	405.748i	−1.25619	+	1.25619i
$324$	64.4867	+	317.518i	0.199033	+	0.979993i
$325$	295.452	−	295.452i	0.909084	−	0.909084i
$326$	−7.77909	−	9.01855i	−0.0238622	−	0.0276643i
$327$	125.681	+	241.635i	0.384346	+	0.738946i
$328$	−122.822	−	393.376i	−0.374457	−	1.19932i
$329$	12.4904	+	21.6341i	0.0379648	+	0.0657570i
$330$	5.64571	−	14.1583i	0.0171082	−	0.0429040i
$331$	139.717	+	521.431i	0.422106	+	1.57532i	0.770163	+	0.637848i	$0.220175\pi$
$331$	139.717	+	521.431i	0.422106	+	1.57532i	−0.348057	+	0.937474i	$0.613158\pi$
$332$	−7.63038	−	66.3551i	−0.0229831	−	0.199865i
$333$	291.429	−	51.1786i	0.875161	−	0.153689i
$334$	133.148	+	275.677i	0.398647	+	0.825380i
$335$	4.18248	+	2.41476i	0.0124850	+	0.00720823i
$336$	−74.4821	−	155.458i	−0.221673	−	0.462671i
$337$	151.381	+	262.200i	0.449202	+	0.778041i	0.998334	−	0.0576947i	$-0.0183750\pi$
$337$	151.381	+	262.200i	0.449202	+	0.778041i	−0.549132	+	0.835736i	$0.685042\pi$
$338$	187.951	+	127.828i	0.556069	+	0.378189i
$339$	−419.565	+	92.8629i	−1.23766	+	0.273932i
$340$	34.2789	+	14.8624i	0.100820	+	0.0437128i
$341$	37.9058	+	37.9058i	0.111161	+	0.111161i
$342$	42.4125	+	421.922i	0.124013	+	1.23369i
$343$		−	305.625i		−	0.891035i
$344$	−2.84584	−	69.6511i	−0.00827279	−	0.202474i
$345$	−27.7137	−	1.21962i	−0.0803295	−	0.00353514i
$346$	7.77160	+	40.8179i	0.0224613	+	0.117971i
$347$	−126.962	+	473.828i	−0.365885	+	1.36550i	0.500333	+	0.865833i	$0.333211\pi$
$347$	−126.962	+	473.828i	−0.365885	+	1.36550i	−0.866218	+	0.499667i	$0.833456\pi$
$348$	−31.9232	+	164.844i	−0.0917332	+	0.473690i
$349$	507.053	−	135.864i	1.45287	−	0.389296i	0.555851	−	0.831282i	$-0.312392\pi$
$349$	507.053	−	135.864i	1.45287	−	0.389296i	0.897022	+	0.441985i	$0.145726\pi$
$350$	−77.6348	−	160.739i	−0.221814	−	0.459255i
$351$	−419.557	+	173.275i	−1.19532	+	0.493662i
$352$	210.786	+	22.5283i	0.598825	+	0.0640009i
$353$	505.800	+	292.024i	1.43286	+	0.827262i	0.997338	−	0.0729160i	$-0.0232305\pi$
$353$	505.800	+	292.024i	1.43286	+	0.827262i	0.435522	+	0.900178i	$0.356564\pi$
$354$	290.796	−	389.566i	0.821458	−	1.10047i
$355$	−7.86422	+	29.3497i	−0.0221527	+	0.0826751i
$356$	376.790	+	55.9096i	1.05840	+	0.157049i
$357$	−193.536	+	177.220i	−0.542118	+	0.496414i
$358$	−224.684	+	193.805i	−0.627609	+	0.541354i
$359$	−654.682			−1.82363			−0.911813	−	0.410605i	$-0.865318\pi$
$359$	−654.682			−1.82363			−0.911813	+	0.410605i	$0.865318\pi$
$360$	24.5353	−	12.6636i	0.0681536	−	0.0351767i
$361$			193.991i			0.537372i
$362$	−382.324	+	329.779i	−1.05614	+	0.910992i
$363$	225.878	−	49.9939i	0.622254	−	0.137724i
$364$	193.987	−	143.856i	0.532930	−	0.395209i
$365$	32.7927	+	8.78677i	0.0898429	+	0.0240733i
$366$	−438.123	−	51.7773i	−1.19706	−	0.141468i
$367$	6.22505	−	10.7821i	0.0169620	−	0.0293790i	−0.857420	−	0.514618i	$-0.827934\pi$
$367$	6.22505	−	10.7821i	0.0169620	−	0.0293790i	0.874382	+	0.485239i	$0.161267\pi$
$368$	−87.5722	−	375.736i	−0.237968	−	1.02102i
$369$	−40.7268	+	461.824i	−0.110371	+	1.25156i
$370$	−10.9664	−	22.7054i	−0.0296389	−	0.0613660i
$371$	16.8837	+	63.0108i	0.0455086	+	0.169841i
$372$	6.84129	+	96.8640i	0.0183906	+	0.260387i
$373$	−137.239	−	36.7732i	−0.367934	−	0.0985876i	0.0701145	−	0.997539i	$-0.477664\pi$
$373$	−137.239	−	36.7732i	−0.367934	−	0.0985876i	−0.438049	+	0.898951i	$0.644330\pi$
$374$	−60.3593	−	317.018i	−0.161388	−	0.847643i
$375$	50.8819	−	26.4651i	0.135685	−	0.0705735i
$376$	−40.9230	−	37.7102i	−0.108838	−	0.100293i
$377$	−235.240			−0.623980
$378$	10.8941	+	193.621i	0.0288204	+	0.512224i
$379$	248.467	−	248.467i	0.655587	−	0.655587i	−0.298746	−	0.954333i	$-0.596568\pi$
$379$	248.467	−	248.467i	0.655587	−	0.655587i	0.954333	+	0.298746i	$0.0965683\pi$
$380$	33.6083	−	13.2792i	0.0884429	−	0.0349453i
$381$	416.606	+	131.514i	1.09345	+	0.345181i
$382$	149.798	+	101.879i	0.392140	+	0.266699i
$383$	97.1783	−	56.1059i	0.253729	−	0.146491i	−0.367741	−	0.929928i	$-0.619869\pi$
$383$	97.1783	−	56.1059i	0.253729	−	0.146491i	0.621471	+	0.783437i	$0.286536\pi$
$384$	261.591	+	281.116i	0.681226	+	0.732073i
$385$	4.56160	−	7.90092i	0.0118483	−	0.0205219i
$386$	245.588	+	508.478i	0.636238	+	1.31730i
$387$	−26.8732	+	73.6748i	−0.0694399	+	0.190374i
$388$	162.061	−	204.175i	0.417682	−	0.526225i
$389$	6.90940	−	1.85137i	0.0177620	−	0.00475930i	−0.249927	−	0.968265i	$-0.580407\pi$
$389$	6.90940	−	1.85137i	0.0177620	−	0.00475930i	0.267689	+	0.963505i	$0.413740\pi$
$390$	23.9537	+	30.3742i	0.0614199	+	0.0778826i
$391$	−508.637	+	293.662i	−1.30086	+	0.751053i
$392$	86.0802	+	275.698i	0.219592	+	0.703312i
$393$	−408.981	−	260.749i	−1.04067	−	0.663484i
$394$	254.435	+	294.975i	0.645774	+	0.748667i
$395$	−31.1294	−	31.1294i	−0.0788085	−	0.0788085i
$396$	−209.625	−	113.722i	−0.529355	−	0.287176i
$397$	466.538	+	466.538i	1.17516	+	1.17516i	0.980963	+	0.194197i	$0.0622100\pi$
$397$	466.538	+	466.538i	1.17516	+	1.17516i	0.194197	+	0.980963i	$0.437790\pi$
$398$	30.3743	−	411.643i	0.0763174	−	1.03428i
$399$	−11.1589	+	253.564i	−0.0279671	+	0.635500i
$400$	271.801	+	290.254i	0.679503	+	0.725635i
$401$	3.66564	−	2.11636i	0.00914124	−	0.00527770i	−0.495422	−	0.868652i	$-0.664987\pi$
$401$	3.66564	−	2.11636i	0.00914124	−	0.00527770i	0.504564	+	0.863374i	$0.331653\pi$
$402$	45.2007	−	60.5533i	0.112440	−	0.150630i
$403$	−131.410	+	35.2113i	−0.326081	+	0.0873730i
$404$	−525.965	+	60.4824i	−1.30189	+	0.149709i
$405$	−30.9475	+	2.66435i	−0.0764136	+	0.00657864i
$406$	−33.0840	+	94.8971i	−0.0814877	+	0.233737i
$407$	−108.897	+	188.614i	−0.267559	+	0.463426i
$408$	293.877	−	505.334i	0.720287	−	1.23856i
$409$	337.198	−	194.681i	0.824445	−	0.475994i	−0.0275017	−	0.999622i	$-0.508755\pi$
$409$	337.198	−	194.681i	0.824445	−	0.475994i	0.851947	+	0.523628i	$0.175422\pi$
$410$	38.8113	−	7.38955i	0.0946617	−	0.0180233i
$411$	449.117	−	411.254i	1.09274	−	1.00062i
$412$	−412.826	+	163.114i	−1.00200	+	0.395909i
$413$	205.746	−	205.746i	0.498175	−	0.498175i
$414$	−69.8406	+	428.376i	−0.168697	+	1.03472i
$415$	6.40341			0.0154299
$416$	−316.986	+	434.688i	−0.761985	+	1.04492i
$417$	−108.309	−	69.0534i	−0.259735	−	0.165596i
$418$	−258.093	−	175.532i	−0.617447	−	0.419933i
$419$	634.715	+	170.071i	1.51483	+	0.405898i	0.918037	−	0.396495i	$-0.129774\pi$
$419$	634.715	+	170.071i	1.51483	+	0.405898i	0.596795	+	0.802393i	$0.296440\pi$
$420$	15.6219	−	5.39126i	0.0371951	−	0.0128363i
$421$	189.826	+	708.442i	0.450894	+	1.68276i	0.699886	+	0.714254i	$0.253234\pi$
$421$	189.826	+	708.442i	0.450894	+	1.68276i	−0.248992	+	0.968506i	$0.580099\pi$
$422$	−206.567	+	592.510i	−0.489495	+	1.40405i
$423$	26.4185	+	56.7573i	0.0624551	+	0.134178i
$424$	−77.7358	−	122.777i	−0.183339	−	0.289569i
$425$	302.675	−	524.248i	0.712175	−	1.23352i
$426$	441.594	+	176.088i	1.03661	+	0.413353i
$427$	−255.061	−	68.3434i	−0.597333	−	0.160055i
$428$	179.776	+	242.424i	0.420038	+	0.566411i
$429$	100.583	−	318.623i	0.234459	−	0.742711i
$430$	6.66492	+	0.491791i	0.0154998	+	0.00114370i
$431$			31.2114i			0.0724162i	0.999344	+	0.0362081i	$0.0115279\pi$
$431$			31.2114i			0.0724162i	−0.999344	+	0.0362081i	$0.988472\pi$
$432$	−151.714	−	404.484i	−0.351189	−	0.936304i
$433$	−649.978			−1.50110			−0.750552	−	0.660812i	$-0.770212\pi$
$433$	−649.978			−1.50110			−0.750552	+	0.660812i	$0.770212\pi$
$434$	−4.27703	+	57.9637i	−0.00985490	+	0.133557i
$435$	−15.3506	−	4.84586i	−0.0352887	−	0.0111399i
$436$	−216.318	−	291.699i	−0.496141	−	0.669035i
$437$	−147.024	+	548.701i	−0.336439	+	1.25561i
$438$	196.745	−	493.398i	0.449190	−	1.12648i
$439$	−554.380	−	320.072i	−1.26283	−	0.729093i	−0.289205	−	0.957267i	$-0.593391\pi$
$439$	−554.380	−	320.072i	−1.26283	−	0.729093i	−0.973620	+	0.228175i	$0.926724\pi$
$440$	−4.45424	+	19.8291i	−0.0101233	+	0.0450662i
$441$	28.5435	−	323.671i	0.0647246	−	0.733948i
$442$	773.348	+	269.612i	1.74966	+	0.609983i
$443$	−149.735	+	40.1214i	−0.338003	+	0.0905675i	−0.423828	−	0.905743i	$-0.639314\pi$
$443$	−149.735	+	40.1214i	−0.338003	+	0.0905675i	0.0858255	+	0.996310i	$0.472647\pi$
$444$	−372.934	+	128.703i	−0.839942	+	0.289871i
$445$	−9.45169	+	35.2742i	−0.0212397	+	0.0792678i
$446$	−312.546	+	459.550i	−0.700775	+	1.03038i
$447$	417.888	−	655.452i	0.934873	−	1.46634i
$448$	130.775	+	189.008i	0.291908	+	0.421892i
$449$		−	638.864i		−	1.42286i	−0.702757	−	0.711430i	$-0.748048\pi$
$449$		−	638.864i		−	1.42286i	0.702757	−	0.711430i	$-0.251952\pi$
$450$	−158.422	−	418.363i	−0.352048	−	0.929695i
$451$	−241.302	−	241.302i	−0.535037	−	0.535037i
$452$	532.871	−	210.546i	1.17892	−	0.465811i
$453$	−581.857	−	635.428i	−1.28445	−	1.40271i
$454$	−37.9591	−	199.368i	−0.0836103	−	0.439137i
$455$	11.5767	+	20.0513i	0.0254432	+	0.0440689i
$456$	−144.618	−	546.590i	−0.317145	−	1.19866i
$457$	−131.301	−	75.8068i	−0.287311	−	0.165879i	0.349417	−	0.936967i	$-0.386380\pi$
$457$	−131.301	−	75.8068i	−0.287311	−	0.165879i	−0.636729	+	0.771088i	$0.719713\pi$
$458$	53.1015	+	18.5128i	0.115942	+	0.0404209i
$459$	−522.161	+	399.807i	−1.13761	+	0.871039i
$460$	36.7452	−	4.22545i	0.0798809	−	0.00918576i
$461$	−78.9392	−	294.605i	−0.171235	−	0.639056i	−0.997162	−	0.0752804i	$-0.976015\pi$
$461$	−78.9392	−	294.605i	−0.171235	−	0.639056i	0.825928	−	0.563776i	$-0.190652\pi$
$462$	−114.388	−	85.3864i	−0.247593	−	0.184819i
$463$	−79.3585	−	137.453i	−0.171401	−	0.296875i	0.767509	−	0.641038i	$-0.221496\pi$
$463$	−79.3585	−	137.453i	−0.171401	−	0.296875i	−0.938910	+	0.344163i	$0.888163\pi$
$464$	7.34600	−	223.755i	0.0158319	−	0.482231i
$465$	−9.30051	−	0.409297i	−0.0200011	−	0.000880209i
$466$	552.426	+	40.7624i	1.18546	+	0.0874729i
$467$	246.433	−	246.433i	0.527693	−	0.527693i	−0.392191	−	0.919884i	$-0.628283\pi$
$467$	246.433	−	246.433i	0.527693	−	0.527693i	0.919884	+	0.392191i	$0.128283\pi$
$468$	515.940	−	316.418i	1.10244	−	0.676107i
$469$	31.9807	−	31.9807i	0.0681892	−	0.0681892i
$470$	4.03982	−	3.48461i	0.00859536	−	0.00741406i
$471$	499.482	−	783.431i	1.06047	−	1.66334i
$472$	−300.901	+	574.099i	−0.637503	+	1.21631i
$473$	−28.8622	−	49.9907i	−0.0610194	−	0.105689i
$474$	−540.850	+	426.526i	−1.14103	+	0.899844i
$475$	−151.536	−	565.542i	−0.319024	−	1.19061i
$476$	217.526	−	274.054i	0.456987	−	0.575744i
$477$	28.2768	+	161.018i	0.0592805	+	0.337564i
$478$	−529.405	+	255.696i	−1.10754	+	0.534928i
$479$	−437.680	−	252.694i	−0.913736	−	0.527546i	−0.0321049	−	0.999485i	$-0.510221\pi$
$479$	−437.680	−	252.694i	−0.913736	−	0.527546i	−0.881631	+	0.471939i	$0.843554\pi$
$480$	−29.6393	+	21.8357i	−0.0617485	+	0.0454911i
$481$	−276.363	−	478.675i	−0.574560	−	0.995166i
$482$	−224.522	+	330.124i	−0.465813	+	0.684906i
$483$	−78.2047	+	247.734i	−0.161915	+	0.512908i
$484$	−286.878	+	113.350i	−0.592723	+	0.234195i
$485$	17.6713	+	17.6713i	0.0364356	+	0.0364356i
$486$	−15.4295	+	485.755i	−0.0317480	+	0.999496i
$487$			85.1544i			0.174855i	0.996171	+	0.0874275i	$0.0278646\pi$
$487$			85.1544i			0.174855i	−0.996171	+	0.0874275i	$0.972135\pi$
$488$	587.739	−	24.0141i	1.20438	−	0.0492093i
$489$	−8.24366	−	15.8493i	−0.0168582	−	0.0324117i
$490$	−27.2010	+	5.17899i	−0.0555123	+	0.0105694i
$491$	−40.6464	+	151.694i	−0.0827829	+	0.308950i	−0.994885	−	0.101013i	$-0.967792\pi$
$491$	−40.6464	+	151.694i	−0.0827829	+	0.308950i	0.912102	+	0.409963i	$0.134458\pi$
$492$	−43.5505	−	616.620i	−0.0885172	−	1.25329i
$493$	−329.199	+	88.2087i	−0.667747	+	0.178922i
$494$	713.293	−	344.511i	1.44391	−	0.697390i
$495$	13.1270	−	18.7197i	0.0265192	−	0.0378176i
$496$	−29.3886	−	126.094i	−0.0592511	−	0.254222i
$497$	246.428	+	142.275i	0.495831	+	0.286268i
$498$	11.7584	−	99.4961i	0.0236113	−	0.199791i
$499$	112.759	−	420.823i	0.225970	−	0.843332i	−0.756043	−	0.654521i	$-0.772870\pi$
$499$	112.759	−	420.823i	0.225970	−	0.843332i	0.982014	−	0.188810i	$-0.0604632\pi$
$500$	−61.4240	+	45.5507i	−0.122848	+	0.0911013i
$501$	99.2383	+	448.370i	0.198081	+	0.894951i
$502$	−284.836	−	330.220i	−0.567403	−	0.657809i
$503$	731.836			1.45494			0.727471	−	0.686138i	$-0.240695\pi$
$503$	731.836			1.45494			0.727471	+	0.686138i	$0.240695\pi$
$504$	−55.0832	−	252.634i	−0.109292	−	0.501257i
$505$		−	50.7568i		−	0.100508i
$506$	−208.667	−	241.915i	−0.412386	−	0.478092i
$507$	230.256	+	251.455i	0.454154	+	0.495967i
$508$	−576.187	−	85.4968i	−1.13423	−	0.168301i
$509$	288.023	+	77.1756i	0.565861	+	0.151622i	0.530398	−	0.847749i	$-0.322043\pi$
$509$	288.023	+	77.1756i	0.565861	+	0.151622i	0.0354635	+	0.999371i	$0.488709\pi$
$510$	44.9108	+	33.5242i	0.0880603	+	0.0657337i
$511$	158.965	−	275.336i	0.311087	−	0.538818i
$512$	−403.567	−	315.084i	−0.788217	−	0.615398i
$513$	−83.6795	+	630.545i	−0.163118	+	1.22913i
$514$	265.752	−	128.355i	0.517027	−	0.249717i
$515$	−11.0141	−	41.1051i	−0.0213866	−	0.0798158i
$516$	19.8801	−	102.657i	0.0385273	−	0.198947i
$517$	−44.5109	−	11.9266i	−0.0860945	−	0.0230690i
$518$	−231.967	+	44.1658i	−0.447813	+	0.0852622i
$519$	−2.74023	+	62.2665i	−0.00527982	+	0.119974i
$520$	−37.9292	−	34.9514i	−0.0729407	−	0.0672142i
$521$	421.221			0.808486			0.404243	−	0.914652i	$-0.367535\pi$
$521$	421.221			0.808486			0.404243	+	0.914652i	$0.367535\pi$
$522$	−103.483	+	229.619i	−0.198243	+	0.439883i
$523$	121.842	−	121.842i	0.232968	−	0.232968i	−0.580963	−	0.813930i	$-0.697324\pi$
$523$	121.842	−	121.842i	0.232968	−	0.232968i	0.813930	+	0.580963i	$0.197324\pi$
$524$	593.340	+	257.255i	1.13233	+	0.490946i
$525$	−57.8630	−	261.431i	−0.110215	−	0.497965i
$526$	−451.147	+	663.342i	−0.857694	+	1.26111i
$527$	−170.695	+	98.5507i	−0.323899	+	0.187003i
$528$	299.926	+	105.622i	0.568041	+	0.200041i
$529$	−26.2155	+	45.4065i	−0.0495566	+	0.0858346i
$530$	12.5450	−	6.05908i	0.0236699	−	0.0114322i
$531$	558.922	−	468.332i	1.05258	−	0.881981i
$532$	−38.6604	−	336.197i	−0.0726700	−	0.631950i
$533$	836.537	−	224.149i	1.56949	−	0.420543i
$534$	530.734	+	211.634i	0.993885	+	0.396318i
$535$	−25.0581	+	14.4673i	−0.0468375	+	0.0270416i
$536$	−46.7714	+	89.2367i	−0.0872602	+	0.166486i
$537$	−394.863	+	205.379i	−0.735313	+	0.382456i
$538$	82.3717	−	71.0509i	0.153107	−	0.132065i
$539$	169.117	+	169.117i	0.313761	+	0.313761i
$540$	40.1857	−	10.0196i	0.0744180	−	0.0185549i
$541$	−387.104	−	387.104i	−0.715534	−	0.715534i	0.252153	−	0.967687i	$-0.418861\pi$
$541$	−387.104	−	387.104i	−0.715534	−	0.715534i	−0.967687	+	0.252153i	$0.918861\pi$
$542$	−157.039	−	11.5876i	−0.289741	−	0.0213794i
$543$	−671.901	+	349.474i	−1.23739	+	0.643598i
$544$	−280.599	+	727.171i	−0.515807	+	1.33671i
$545$	30.1514	−	17.4079i	0.0553236	−	0.0319411i
$546$	332.816	−	143.058i	0.609553	−	0.262011i
$547$	−571.389	+	153.103i	−1.04459	+	0.279896i	−0.740013	−	0.672593i	$-0.765181\pi$
$547$	−571.389	+	153.103i	−1.04459	+	0.279896i	−0.304573	+	0.952489i	$0.598514\pi$
$548$	−504.787	+	635.966i	−0.921144	+	1.16052i
$549$	−621.692	−	226.765i	−1.13241	−	0.413051i
$550$	310.927	+	108.399i	0.565322	+	0.197088i
$551$	−164.816	+	285.470i	−0.299122	+	0.518095i
$552$	1.81937	−	578.706i	0.00329596	−	1.04838i
$553$	−357.039	+	206.137i	−0.645640	+	0.372761i
$554$	−119.514	−	627.713i	−0.215730	−	1.13306i
$555$	−8.17351	−	36.9288i	−0.0147270	−	0.0665385i
$556$	157.132	+	68.1282i	0.282612	+	0.122533i
$557$	406.323	−	406.323i	0.729484	−	0.729484i	−0.241033	−	0.970517i	$-0.577486\pi$
$557$	406.323	−	406.323i	0.729484	−	0.729484i	0.970517	+	0.241033i	$0.0774861\pi$
$558$	−23.4380	+	143.760i	−0.0420036	+	0.257634i
$559$	146.496			0.262067
$560$	−19.4339	+	10.3853i	−0.0347034	+	0.0185452i
$561$	21.2824	−	483.602i	0.0379365	−	0.862035i
$562$	−148.155	+	217.839i	−0.263621	+	0.387613i
$563$	532.100	+	142.576i	0.945116	+	0.253243i	0.698289	−	0.715816i	$-0.253945\pi$
$563$	532.100	+	142.576i	0.945116	+	0.253243i	0.246828	+	0.969059i	$0.420612\pi$
$564$	−46.7256	−	69.1695i	−0.0828468	−	0.122641i
$565$	14.2169	+	53.0580i	0.0251626	+	0.0939080i
$566$	−505.306	−	176.165i	−0.892767	−	0.311246i
$567$	−50.9094	+	286.401i	−0.0897874	+	0.505116i
$568$	−618.465	−	138.927i	−1.08885	−	0.244589i
$569$	29.5231	−	51.1356i	0.0518860	−	0.0898692i	−0.838916	−	0.544261i	$-0.816810\pi$
$569$	29.5231	−	51.1356i	0.0518860	−	0.0898692i	0.890802	+	0.454392i	$0.150143\pi$
$570$	53.6426	−	7.78742i	0.0941098	−	0.0136621i
$571$	460.662	+	123.434i	0.806764	+	0.216172i	0.638552	−	0.769579i	$-0.279534\pi$
$571$	460.662	+	123.434i	0.806764	+	0.216172i	0.168212	+	0.985751i	$0.446201\pi$
$572$	−65.3885	+	440.671i	−0.114316	+	0.770404i
$573$	183.515	+	200.410i	0.320270	+	0.349757i
$574$	27.2268	−	368.987i	0.0474335	−	0.642835i
$575$		−	599.276i		−	1.04222i
$576$	284.858	+	500.632i	0.494545	+	0.869152i
$577$	−27.7037			−0.0480133			−0.0240066	−	0.999712i	$-0.507642\pi$
$577$	−27.7037			−0.0480133			−0.0240066	+	0.999712i	$0.507642\pi$
$578$	606.900	+	44.7820i	1.05000	+	0.0774774i
$579$	183.042	+	827.006i	0.316135	+	1.42833i
$580$	21.2306	+	3.15028i	0.0366045	+	0.00543151i
$581$	15.5205	−	57.9235i	0.0267135	−	0.0996962i
$582$	307.026	−	242.127i	0.527535	−	0.416025i
$583$	−104.212	−	60.1667i	−0.178751	−	0.103202i
$584$	−155.224	+	691.018i	−0.265795	+	1.18325i
$585$	24.4858	+	52.6050i	0.0418560	+	0.0899232i
$586$	63.0254	−	180.780i	0.107552	−	0.308498i
$587$	−790.936	+	211.931i	−1.34742	+	0.361040i	−0.859182	−	0.511670i	$-0.829027\pi$
$587$	−790.936	+	211.931i	−1.34742	+	0.361040i	−0.488239	+	0.872710i	$0.662360\pi$
$588$	30.5225	+	432.160i	0.0519090	+	0.734966i
$589$	−49.3402	+	184.140i	−0.0837694	+	0.312632i
$590$	−51.3832	−	34.9463i	−0.0870902	−	0.0592311i
$591$	269.630	+	518.393i	0.456227	+	0.877146i
$592$	463.935	−	247.922i	0.783674	−	0.418788i
$593$			150.135i			0.253179i	0.991955	+	0.126589i	$0.0404030\pi$
$593$			150.135i			0.253179i	−0.991955	+	0.126589i	$0.959597\pi$
$594$	−266.762	−	238.342i	−0.449094	−	0.401250i
$595$	23.7193	+	23.7193i	0.0398643	+	0.0398643i
$596$	−412.289	+	950.913i	−0.691760	+	1.59549i
$597$	186.384	−	590.423i	0.312202	−	0.988983i
$598$	796.474	−	151.646i	1.33190	−	0.253589i
$599$	225.177	+	390.018i	0.375922	+	0.651116i	0.990465	−	0.137768i	$-0.0439928\pi$
$599$	225.177	+	390.018i	0.375922	+	0.651116i	−0.614543	+	0.788884i	$0.710659\pi$
$600$	296.610	+	517.494i	0.494350	+	0.862490i
$601$	−126.281	−	72.9085i	−0.210118	−	0.121312i	0.391248	−	0.920285i	$-0.372043\pi$
$601$	−126.281	−	72.9085i	−0.210118	−	0.121312i	−0.601366	+	0.798973i	$0.705377\pi$
$602$	20.6030	−	59.0971i	0.0342243	−	0.0981679i
$603$	86.8777	−	72.7965i	0.144076	−	0.120724i
$604$	899.789	+	714.192i	1.48972	+	1.18244i
$605$	−7.65382	−	28.5645i	−0.0126509	−	0.0472140i
$606$	−788.659	−	93.2035i	−1.30142	−	0.153801i
$607$	−59.7022	−	103.407i	−0.0983562	−	0.170358i	0.812648	−	0.582755i	$-0.198025\pi$
$607$	−59.7022	−	103.407i	−0.0983562	−	0.170358i	−0.911004	+	0.412397i	$0.864692\pi$
$608$	305.416	+	689.226i	0.502329	+	1.13360i
$609$	−81.0410	+	127.112i	−0.133072	+	0.208722i
$610$	−4.14990	+	56.2408i	−0.00680311	+	0.0921981i
$611$	82.6938	−	82.6938i	0.135342	−	0.135342i
$612$	603.368	−	636.264i	0.985895	−	1.03965i
$613$	−129.429	+	129.429i	−0.211140	+	0.211140i	−0.804752	−	0.593612i	$-0.797702\pi$
$613$	−129.429	+	129.429i	−0.211140	+	0.211140i	0.593612	+	0.804752i	$0.297702\pi$
$614$	−189.655	−	219.873i	−0.308885	−	0.358100i
$615$	59.2055	+	2.60552i	0.0962691	+	0.00423661i
$616$	168.573	+	88.3536i	0.273657	+	0.143431i
$617$	154.999	+	268.465i	0.251213	+	0.435114i	0.963860	−	0.266409i	$-0.0858371\pi$
$617$	154.999	+	268.465i	0.251213	+	0.435114i	−0.712647	+	0.701523i	$0.752504\pi$
$618$	−658.916	+	95.6564i	−1.06621	+	0.154784i
$619$	−192.204	−	717.315i	−0.310507	−	1.15883i	−0.928100	−	0.372331i	$-0.878559\pi$
$619$	−192.204	−	717.315i	−0.310507	−	1.15883i	0.617593	−	0.786498i	$-0.288108\pi$
$620$	12.3314	−	1.41803i	0.0198894	−	0.00228714i
$621$	−249.770	+	601.230i	−0.402206	+	0.968165i
$622$	520.394	+	1077.45i	0.836646	+	1.73223i
$623$	296.172	+	170.995i	0.475396	+	0.274470i
$624$	−612.723	+	525.163i	−0.981928	+	0.841608i
$625$	306.996	+	531.733i	0.491194	+	0.850773i
$626$	−181.436	−	123.397i	−0.289833	−	0.197119i
$627$	−316.186	−	345.296i	−0.504283	−	0.550712i
$628$	−492.790	+	1136.58i	−0.784697	+	1.80984i
$629$	−566.237	−	566.237i	−0.900218	−	0.900218i
$630$	24.6648	−	2.47936i	0.0391505	−	0.00393549i
$631$		−	804.718i		−	1.27531i	−0.770324	−	0.637653i	$-0.779906\pi$
$631$		−	804.718i		−	1.27531i	0.770324	−	0.637653i	$-0.220094\pi$
$632$	622.353	−	675.376i	0.984735	−	1.06863i
$633$	−505.997	+	793.649i	−0.799363	+	1.25379i
$634$	−35.7234	−	187.626i	−0.0563461	−	0.295940i
$635$	14.4535	−	53.9412i	0.0227614	−	0.0849467i
$636$	−71.1098	−	206.051i	−0.111808	−	0.323979i
$637$	−586.289	+	157.096i	−0.920392	+	0.246618i
$638$	−80.6270	−	166.934i	−0.126375	−	0.261653i
$639$	583.863	+	409.429i	0.913714	+	0.640733i
$640$	34.4294	−	34.9859i	0.0537959	−	0.0546655i
$641$	282.229	+	162.945i	0.440294	+	0.254204i	0.703722	−	0.710475i	$-0.251520\pi$
$641$	282.229	+	162.945i	0.440294	+	0.254204i	−0.263428	+	0.964679i	$0.584853\pi$
$642$	178.779	+	415.918i	0.278472	+	0.647848i
$643$	20.1141	−	75.0669i	0.0312817	−	0.116745i	−0.948520	−	0.316718i	$-0.897419\pi$
$643$	20.1141	−	75.0669i	0.0312817	−	0.116745i	0.979801	+	0.199974i	$0.0640856\pi$
$644$	50.8406	−	342.629i	0.0789450	−	0.532032i
$645$	9.55955	+	3.01776i	0.0148210	+	0.00467869i
$646$	869.012	−	749.579i	1.34522	−	1.16034i
$647$	−126.316			−0.195233			−0.0976165	−	0.995224i	$-0.531122\pi$
$647$	−126.316			−0.195233			−0.0976165	+	0.995224i	$0.531122\pi$
$648$	−81.8928	−	642.804i	−0.126378	−	0.991982i
$649$			536.737i			0.827022i
$650$	−632.786	+	545.819i	−0.973517	+	0.839722i
$651$	−26.2449	+	83.1378i	−0.0403148	+	0.127708i
$652$	14.1887	+	19.1331i	0.0217618	+	0.0293452i
$653$	−616.426	−	165.171i	−0.943991	−	0.252942i	−0.246180	−	0.969224i	$-0.579176\pi$
$653$	−616.426	−	165.171i	−0.943991	−	0.252942i	−0.697810	+	0.716282i	$0.745842\pi$
$654$	−215.118	−	500.458i	−0.328926	−	0.765226i
$655$	−31.0001	+	53.6938i	−0.0473284	+	0.0819752i
$656$	187.083	+	802.694i	0.285187	+	1.22362i
$657$	457.459	−	652.356i	0.696284	−	0.992932i
$658$	−21.7291	−	44.9891i	−0.0330230	−	0.0683725i
$659$	−113.770	−	424.595i	−0.172640	−	0.644302i	−0.996942	−	0.0781507i	$-0.975098\pi$
$659$	−113.770	−	424.595i	−0.172640	−	0.644302i	0.824301	−	0.566151i	$-0.191568\pi$
$660$	−13.3446	+	27.4089i	−0.0202190	+	0.0415287i
$661$	−125.488	−	33.6243i	−0.189845	−	0.0508688i	0.162644	−	0.986685i	$-0.447998\pi$
$661$	−125.488	−	33.6243i	−0.189845	−	0.0508688i	−0.352489	+	0.935816i	$0.614665\pi$
$662$	−201.934	−	1060.60i	−0.305037	−	1.60211i
$663$	1035.88	+	660.430i	1.56241	+	0.996123i
$664$	5.45352	+	133.473i	0.00821314	+	0.201014i
$665$	32.4438			0.0487876
$666$	−588.809	+	59.1884i	−0.884098	+	0.0888714i
$667$	−238.573	+	238.573i	−0.357681	+	0.357681i
$668$	−225.001	−	569.455i	−0.336829	−	0.852478i
$669$	−614.821	+	562.988i	−0.919015	+	0.841537i
$670$	−7.98689	−	5.43198i	−0.0119207	−	0.00810743i
$671$	421.838	−	243.548i	0.628671	−	0.362963i
$672$	125.681	+	321.034i	0.187025	+	0.477729i
$673$	217.925	−	377.457i	0.323812	−	0.560858i	−0.657460	−	0.753490i	$-0.728369\pi$
$673$	217.925	−	377.457i	0.323812	−	0.560858i	0.981271	+	0.192632i	$0.0617023\pi$
$674$	−263.352	−	545.257i	−0.390730	−	0.808987i
$675$	−86.8955	−	665.379i	−0.128734	−	0.985747i
$676$	−356.070	−	282.624i	−0.526731	−	0.418084i
$677$	431.171	−	115.532i	0.636885	−	0.170653i	0.0740929	−	0.997251i	$-0.476394\pi$
$677$	431.171	−	115.532i	0.636885	−	0.170653i	0.562792	+	0.826599i	$0.309727\pi$
$678$	850.522	−	123.472i	1.25446	−	0.182113i
$679$	202.681	−	117.018i	0.298499	−	0.172339i
$680$	−66.1845	−	34.6892i	−0.0973302	−	0.0510135i
$681$	13.3842	−	304.130i	0.0196537	−	0.446594i
$682$	−70.0272	−	81.1848i	−0.102679	−	0.119039i
$683$	300.065	+	300.065i	0.439334	+	0.439334i	0.891788	−	0.452454i	$-0.149451\pi$
$683$	300.065	+	300.065i	0.439334	+	0.439334i	−0.452454	+	0.891788i	$0.649451\pi$
$684$	−22.4983	−	847.799i	−0.0328922	−	1.23947i
$685$	−55.0426	−	55.0426i	−0.0803541	−	0.0803541i
$686$	−44.9806	+	609.593i	−0.0655695	+	0.888619i
$687$	71.1277	+	45.3480i	0.103534	+	0.0660088i
$688$	−4.57471	+	139.343i	−0.00664929	+	0.202534i
$689$	264.474	−	152.694i	0.383852	−	0.221617i
$690$	55.0976	+	6.51142i	0.0798516	+	0.00943685i
$691$	−616.504	+	165.192i	−0.892192	+	0.239062i	−0.675660	−	0.737214i	$-0.736141\pi$
$691$	−616.504	+	165.192i	−0.892192	+	0.239062i	−0.216532	+	0.976276i	$0.569475\pi$
$692$	−9.49364	−	82.5583i	−0.0137191	−	0.119304i
$693$	−137.516	−	164.116i	−0.198436	−	0.236820i
$694$	322.972	−	926.402i	0.465377	−	1.33487i
$695$	−8.20967	+	14.2196i	−0.0118125	+	0.0204598i
$696$	87.9343	−	324.096i	0.126342	−	0.465656i
$697$	1086.61	−	627.357i	1.55899	−	0.900082i
$698$	−1031.35	+	196.366i	−1.47758	+	0.281327i
$699$	792.348	+	250.128i	1.13355	+	0.357837i
$700$	131.192	+	332.033i	0.187417	+	0.474332i
$701$	−693.443	+	693.443i	−0.989219	+	0.989219i	−0.999943	−	0.0107235i	$-0.996587\pi$
$701$	−693.443	+	693.443i	−0.989219	+	0.989219i	0.0107235	+	0.999943i	$0.496587\pi$
$702$	862.340	−	283.863i	1.22840	−	0.404363i
$703$	−774.513			−1.10172
$704$	−417.114	−	75.9571i	−0.592491	−	0.107894i
$705$	7.09964	−	3.69271i	0.0100704	−	0.00523789i
$706$	−965.878	−	656.905i	−1.36810	−	0.930460i
$707$	−459.132	−	123.024i	−0.649409	−	0.174008i
$708$	−637.350	+	734.221i	−0.900212	+	1.03704i
$709$	113.078	+	422.013i	0.159489	+	0.595223i	0.998679	+	0.0513837i	$0.0163631\pi$
$709$	113.078	+	422.013i	0.159489	+	0.595223i	−0.839190	+	0.543839i	$0.816970\pi$
$710$	20.0054	−	57.3827i	0.0281766	−	0.0808208i
$711$	−936.698	+	436.000i	−1.31744	+	0.613220i
$712$	−743.309	−	166.971i	−1.04397	−	0.234509i
$713$	−97.5620	+	168.982i	−0.136833	+	0.237002i
$714$	412.105	−	324.995i	0.577178	−	0.455175i
$715$	−41.2545	−	11.0541i	−0.0576986	−	0.0154603i
$716$	476.673	−	353.490i	0.665745	−	0.493702i
$717$	−861.043	+	190.576i	−1.20090	+	0.265796i
$718$	1305.81	+	96.3534i	1.81868	+	0.134197i
$719$			814.721i			1.13313i	0.824017	+	0.566565i	$0.191728\pi$
$719$			814.721i			1.13313i	−0.824017	+	0.566565i	$0.808272\pi$
$720$	−50.8013	+	21.6476i	−0.0705574	+	0.0300661i
$721$	−398.522			−0.552734
$722$	28.5509	−	386.931i	0.0395441	−	0.535915i
$723$	−441.665	+	404.430i	−0.610879	+	0.559378i
$724$	811.110	−	601.501i	1.12032	−	0.830802i
$725$	90.0039	−	335.899i	0.124143	−	0.463309i
$726$	−457.889	+	66.4729i	−0.630701	+	0.0915604i
$727$	1132.29	+	653.729i	1.55749	+	0.899215i	0.997497	+	0.0707154i	$0.0225282\pi$
$727$	1132.29	+	653.729i	1.55749	+	0.899215i	0.559990	+	0.828500i	$0.310805\pi$
$728$	−408.093	+	258.382i	−0.560568	+	0.354920i
$729$	−190.142	+	703.766i	−0.260826	+	0.965386i
$730$	−64.1143	−	22.3522i	−0.0878278	−	0.0306194i
$731$	205.009	−	54.9319i	0.280449	−	0.0751462i
$732$	866.250	+	167.755i	1.18340	+	0.229173i
$733$	250.467	−	934.755i	0.341701	−	1.27525i	−0.554718	−	0.832039i	$-0.687174\pi$
$733$	250.467	−	934.755i	0.341701	−	1.27525i	0.896419	−	0.443208i	$-0.146160\pi$
$734$	−14.0032	+	20.5896i	−0.0190779	+	0.0280512i
$735$	−41.4943	−	1.82608i	−0.0564549	−	0.00248447i
$736$	119.370	+	762.323i	0.162188	+	1.03576i
$737$			83.4292i			0.113201i
$738$	149.202	−	915.151i	0.202171	−	1.24004i
$739$	821.104	+	821.104i	1.11110	+	1.11110i	0.993002	+	0.118100i	$0.0376805\pi$
$739$	821.104	+	821.104i	1.11110	+	1.11110i	0.118100	+	0.993002i	$0.462320\pi$
$740$	18.5317	+	46.9017i	0.0250428	+	0.0633807i
$741$	1160.12	−	256.771i	1.56562	−	0.346520i
$742$	−24.4022	−	128.165i	−0.0328870	−	0.172729i
$743$	510.682	+	884.527i	0.687324	+	1.19048i	0.972700	+	0.232065i	$0.0745483\pi$
$743$	510.682	+	884.527i	0.687324	+	1.19048i	−0.285376	+	0.958416i	$0.592118\pi$
$744$	0.610567	−	194.210i	0.000820654	−	0.261034i
$745$	−86.0520	−	49.6822i	−0.115506	−	0.0666875i
$746$	268.322	+	93.5453i	0.359682	+	0.125396i
$747$	51.4976	−	141.184i	0.0689392	−	0.189001i
$748$	73.7338	+	641.201i	0.0985746	+	0.857221i
$749$	70.1314	+	261.734i	0.0936334	+	0.349445i
$750$	−105.383	+	45.2980i	−0.140511	+	0.0603973i
$751$	542.086	+	938.921i	0.721819	+	1.25023i	0.960270	+	0.279073i	$0.0900270\pi$
$751$	542.086	+	938.921i	0.721819	+	1.25023i	−0.238451	+	0.971155i	$0.576640\pi$
$752$	76.0741	+	81.2388i	0.101162	+	0.108030i
$753$	−301.847	−	580.333i	−0.400859	−	0.770694i
$754$	469.205	+	34.6217i	0.622288	+	0.0459174i
$755$	−77.8763	+	77.8763i	−0.103147	+	0.103147i
$756$	6.76716	−	387.794i	0.00895127	−	0.512956i
$757$	−7.99210	+	7.99210i	−0.0105576	+	0.0105576i	−0.712366	−	0.701808i	$-0.752376\pi$
$757$	−7.99210	+	7.99210i	−0.0105576	+	0.0105576i	0.701808	+	0.712366i	$0.252376\pi$
$758$	−532.156	+	459.019i	−0.702053	+	0.605566i
$759$	−221.129	−	425.144i	−0.291342	−	0.560137i
$760$	−68.9887	+	21.5401i	−0.0907746	+	0.0283422i
$761$	−306.450	−	530.786i	−0.402693	−	0.697485i	0.591357	−	0.806410i	$-0.298593\pi$
$761$	−306.450	−	530.786i	−0.402693	−	0.697485i	−0.994050	+	0.108925i	$0.965259\pi$
$762$	−811.598	−	323.630i	−1.06509	−	0.424711i
$763$	−84.3864	−	314.934i	−0.110598	−	0.412758i
$764$	−283.789	−	225.252i	−0.371451	−	0.294833i
$765$	53.9913	+	64.4349i	0.0705768	+	0.0842286i
$766$	−202.087	+	97.6053i	−0.263821	+	0.127422i
$767$	−1179.66	−	681.079i	−1.53802	−	0.887978i
$768$	−480.389	−	599.208i	−0.625507	−	0.780219i
$769$	570.212	+	987.637i	0.741499	+	1.28431i	0.951813	+	0.306679i	$0.0992179\pi$
$769$	570.212	+	987.637i	0.741499	+	1.28431i	−0.210314	+	0.977634i	$0.567449\pi$
$770$	−10.2613	+	15.0876i	−0.0133263	+	0.0195943i
$771$	432.228	−	95.6655i	0.560606	−	0.124080i
$772$	−415.008	−	1050.34i	−0.537576	−	1.36055i
$773$	143.006	+	143.006i	0.185001	+	0.185001i	0.793531	−	0.608530i	$-0.208241\pi$
$773$	143.006	+	143.006i	0.185001	+	0.185001i	−0.608530	+	0.793531i	$0.708241\pi$
$774$	64.4439	−	142.995i	0.0832609	−	0.184748i
$775$		−	201.113i		−	0.259500i
$776$	−353.292	+	383.392i	−0.455273	+	0.494062i
$777$	−353.859	−	15.5726i	−0.455417	−	0.0200420i
$778$	−14.0538	+	2.67580i	−0.0180640	+	0.00343933i
$779$	314.091	−	1172.20i	0.403198	−	1.50476i
$780$	−43.3073	−	64.1091i	−0.0555221	−	0.0821912i
$781$	−507.011	+	135.853i	−0.649182	+	0.173948i
$782$	1057.74	−	510.872i	1.35260	−	0.653289i
$783$	−230.296	+	299.482i	−0.294119	+	0.382480i
$784$	−131.117	−	562.571i	−0.167242	−	0.717565i
$785$	−102.854	−	59.3828i	−0.131024	−	0.0756469i
$786$	777.369	+	580.277i	0.989019	+	0.738265i
$787$	372.792	−	1391.28i	0.473687	−	1.76782i	−0.152660	−	0.988279i	$-0.548784\pi$
$787$	372.792	−	1391.28i	0.473687	−	1.76782i	0.626347	−	0.779545i	$-0.284549\pi$
$788$	−464.077	−	625.797i	−0.588931	−	0.794159i
$789$	−887.470	+	812.651i	−1.12480	+	1.02998i
$790$	57.5084	+	66.6714i	0.0727955	+	0.0843942i
$791$	514.407			0.650325
$792$	401.376	+	257.678i	0.506788	+	0.325352i
$793$			1236.18i			1.55886i
$794$	−861.884	−	999.210i	−1.08550	−	1.25845i
$795$	20.4037	−	4.51597i	0.0256650	−	0.00568046i
$796$	−121.168	+	816.583i	−0.152221	+	1.02586i
$797$	−802.616	−	215.060i	−1.00705	−	0.269837i	−0.282652	−	0.959223i	$-0.591214\pi$
$797$	−802.616	−	215.060i	−1.00705	−	0.269837i	−0.724395	+	0.689385i	$0.757881\pi$
$798$	59.5758	−	504.111i	0.0746564	−	0.631719i
$799$	84.7152	−	146.731i	0.106027	−	0.183643i
$800$	−499.410	−	618.936i	−0.624263	−	0.773670i
$801$	701.722	+	492.076i	0.876058	+	0.614327i
$802$	−7.62287	+	3.68174i	−0.00950483	+	0.00459070i
$803$	151.790	+	566.489i	0.189029	+	0.705465i
$804$	−99.0683	+	114.126i	−0.123219	+	0.141947i
$805$	32.0761	+	8.59475i	0.0398460	+	0.0106767i
$806$	267.291	−	50.8913i	0.331626	−	0.0631405i
$807$	144.761	−	75.2941i	0.179382	−	0.0933013i
$808$	1057.98	−	43.2275i	1.30938	−	0.0534994i
$809$	452.170			0.558924			0.279462	−	0.960157i	$-0.409844\pi$
$809$	452.170			0.558924			0.279462	+	0.960157i	$0.409844\pi$
$810$	62.1193	−	0.759525i	0.0766905	−	0.000937686i
$811$	−158.561	+	158.561i	−0.195513	+	0.195513i	−0.798073	−	0.602561i	$-0.794147\pi$
$811$	−158.561	+	158.561i	−0.195513	+	0.195513i	0.602561	+	0.798073i	$0.294147\pi$
$812$	79.9552	−	184.411i	0.0984670	−	0.227107i
$813$	−225.243	−	71.1046i	−0.277051	−	0.0874595i
$814$	244.962	−	360.179i	0.300936	−	0.442480i
$815$	−1.97768	+	1.14182i	−0.00242661	+	0.00140100i
$816$	−660.534	+	964.677i	−0.809477	+	1.18220i
$817$	102.639	−	177.776i	0.125629	−	0.217596i
$818$	−701.220	+	338.680i	−0.857237	+	0.414034i
$819$	535.199	−	93.9878i	0.653479	−	0.114759i
$820$	−78.4997	+	9.02694i	−0.0957314	+	0.0110085i
$821$	−317.564	+	85.0910i	−0.386802	+	0.103643i	−0.446979	−	0.894545i	$-0.647500\pi$
$821$	−317.564	+	85.0910i	−0.386802	+	0.103643i	0.0601773	+	0.998188i	$0.480833\pi$
$822$	−956.325	+	754.178i	−1.16341	+	0.917491i
$823$	618.573	−	357.133i	0.751608	−	0.433941i	−0.0746668	−	0.997209i	$-0.523789\pi$
$823$	618.573	−	357.133i	0.751608	−	0.433941i	0.826274	+	0.563268i	$0.190456\pi$
$824$	847.420	−	264.586i	1.02842	−	0.321100i
$825$	416.477	+	265.528i	0.504821	+	0.321852i
$826$	−440.658	+	380.096i	−0.533484	+	0.460164i
$827$	−562.041	−	562.041i	−0.679614	−	0.679614i	0.280299	−	0.959913i	$-0.409566\pi$
$827$	−562.041	−	562.041i	−0.679614	−	0.679614i	−0.959913	+	0.280299i	$0.909566\pi$
$828$	202.349	−	844.150i	0.244383	−	1.01950i
$829$	−171.040	−	171.040i	−0.206321	−	0.206321i	0.596381	−	0.802702i	$-0.296605\pi$
$829$	−171.040	−	171.040i	−0.206321	−	0.206321i	−0.802702	+	0.596381i	$0.796605\pi$
$830$	−12.7721	−	0.942427i	−0.0153881	−	0.00113545i
$831$	42.1402	−	957.557i	0.0507102	−	1.15229i
$832$	696.228	−	820.367i	0.836813	−	0.986018i
$833$	−761.557	+	439.685i	−0.914234	+	0.527833i
$834$	205.868	+	153.673i	0.246845	+	0.184260i
$835$	56.7007	−	15.1929i	0.0679051	−	0.0181951i
$836$	488.952	+	388.098i	0.584871	+	0.464232i
$837$	−83.8210	+	201.769i	−0.100145	+	0.241062i
$838$	−1240.96	−	432.635i	−1.48086	−	0.516271i
$839$	−423.711	+	733.889i	−0.505019	+	0.874719i	0.494964	+	0.868914i	$0.335181\pi$
$839$	−423.711	+	733.889i	−0.505019	+	0.874719i	−0.999983	+	0.00580563i	$0.998152\pi$
$840$	−31.9526	+	8.45411i	−0.0380389	+	0.0100644i
$841$	558.775	−	322.609i	0.664417	−	0.383601i
$842$	−274.358	−	1440.98i	−0.325841	−	1.71138i
$843$	−291.441	+	266.871i	−0.345719	+	0.316573i
$844$	499.217	−	1151.41i	0.591489	−	1.36423i
$845$	30.8177	−	30.8177i	0.0364706	−	0.0364706i
$846$	−44.3405	−	117.095i	−0.0524119	−	0.138410i
$847$	−276.938			−0.326963
$848$	136.980	+	256.330i	0.161533	+	0.302276i
$849$	−676.842	−	431.526i	−0.797223	−	0.508275i
$850$	−680.864	+	1001.11i	−0.801017	+	1.17777i
$851$	−765.734	−	205.178i	−0.899805	−	0.241102i
$852$	−854.878	−	416.214i	−1.00338	−	0.488514i
$853$	−198.844	−	742.097i	−0.233112	−	0.869985i	−0.978991	−	0.203904i	$-0.934637\pi$
$853$	−198.844	−	742.097i	−0.233112	−	0.869985i	0.745879	−	0.666081i	$-0.232030\pi$
$854$	498.681	+	173.855i	0.583935	+	0.203577i
$855$	80.9930	+	7.14252i	0.0947287	+	0.00835382i
$856$	−322.899	−	509.992i	−0.377218	−	0.595785i
$857$	−126.433	+	218.988i	−0.147530	+	0.255529i	−0.930314	−	0.366764i	$-0.880465\pi$
$857$	−126.433	+	218.988i	−0.147530	+	0.255529i	0.782784	+	0.622293i	$0.213799\pi$
$858$	−247.514	+	620.715i	−0.288477	+	0.723443i
$859$	455.076	+	121.937i	0.529774	+	0.141953i	0.513784	−	0.857920i	$-0.328243\pi$
$859$	455.076	+	121.937i	0.529774	+	0.141953i	0.0159902	+	0.999872i	$0.494910\pi$
$860$	−13.2213	−	1.96183i	−0.0153736	−	0.00228120i
$861$	167.071	−	529.242i	0.194043	−	0.614682i
$862$	4.59356	−	62.2535i	0.00532896	−	0.0722199i
$863$			1193.75i			1.38326i	0.722252	+	0.691630i	$0.243107\pi$
$863$			1193.75i			1.38326i	−0.722252	+	0.691630i	$0.756893\pi$
$864$	243.075	+	829.102i	0.281336	+	0.959609i
$865$	7.96705			0.00921046
$866$	1296.43	+	95.6610i	1.49703	+	0.110463i
$867$	870.482	+	274.793i	1.00402	+	0.316947i
$868$	17.0617	−	114.984i	0.0196564	−	0.132470i
$869$	196.832	−	734.588i	0.226504	−	0.845325i
$870$	29.9047	+	11.9247i	0.0343732	+	0.0137065i
$871$	−183.364	−	105.865i	−0.210522	−	0.121545i
$872$	388.531	+	613.653i	0.445563	+	0.703731i
$873$	531.737	−	247.505i	0.609091	−	0.283510i
$874$	374.006	−	1072.79i	0.427925	−	1.22745i
$875$	−66.3167	+	17.7695i	−0.0757905	+	0.0203080i
$876$	−465.040	+	955.164i	−0.530868	+	1.09037i
$877$	−160.079	+	597.424i	−0.182530	+	0.681213i	0.812615	+	0.582800i	$0.198043\pi$
$877$	−160.079	+	597.424i	−0.182530	+	0.681213i	−0.995146	+	0.0984124i	$0.968624\pi$
$878$	1058.65	+	719.999i	1.20575	+	0.820045i
$879$	154.384	−	242.149i	0.175636	−	0.275483i
$880$	11.8027	−	38.8952i	0.0134122	−	0.0441990i
$881$		−	659.188i		−	0.748227i	−0.927383	−	0.374114i	$-0.877947\pi$
$881$		−	659.188i		−	0.748227i	0.927383	−	0.374114i	$-0.122053\pi$
$882$	−104.569	+	641.386i	−0.118559	+	0.727195i
$883$	348.148	+	348.148i	0.394279	+	0.394279i	0.876209	−	0.481931i	$-0.160064\pi$
$883$	348.148	+	348.148i	0.394279	+	0.394279i	−0.481931	+	0.876209i	$0.660064\pi$
$884$	−1502.82	−	651.581i	−1.70002	−	0.737082i
$885$	−62.9488	−	68.7443i	−0.0711286	−	0.0776772i
$886$	304.563	−	57.9879i	0.343751	−	0.0654490i
$887$	−346.677	−	600.462i	−0.390842	−	0.676959i	0.601719	−	0.798708i	$-0.294483\pi$
$887$	−346.677	−	600.462i	−0.390842	−	0.676959i	−0.992561	+	0.121750i	$0.961150\pi$
$888$	762.788	−	201.820i	0.858996	−	0.227275i
$889$	−452.905	−	261.485i	−0.509454	−	0.294134i
$890$	24.0436	−	68.9660i	0.0270153	−	0.0774899i
$891$	−307.167	−	439.976i	−0.344744	−	0.493800i
$892$	691.032	−	870.610i	0.774699	−	0.976020i
$893$	−42.4134	−	158.289i	−0.0474954	−	0.177255i
$894$	−929.977	+	1245.85i	−1.04024	+	1.39356i
$895$	28.4467	+	49.2712i	0.0317840	+	0.0550516i
$896$	−233.023	−	396.238i	−0.260071	−	0.442229i
$897$	1215.00	+	53.4696i	1.35451	+	0.0596093i
$898$	−94.0254	+	1274.26i	−0.104705	+	1.41900i
$899$	−80.0633	+	80.0633i	−0.0890582	+	0.0890582i
$900$	254.411	+	857.772i	0.282679	+	0.953080i
$901$	312.853	−	312.853i	0.347229	−	0.347229i
$902$	445.781	+	516.809i	0.494214	+	0.572959i
$903$	50.4682	−	79.1587i	0.0558895	−	0.0876619i
$904$	−1093.84	+	341.525i	−1.21000	+	0.377794i
$905$	48.4051	+	83.8401i	0.0534863	+	0.0926410i
$906$	1067.04	+	1353.05i	1.17775	+	1.49343i
$907$	−156.029	−	582.306i	−0.172027	−	0.642014i	−0.997039	−	0.0768983i	$-0.975498\pi$
$907$	−156.029	−	582.306i	−0.172027	−	0.642014i	0.825012	−	0.565115i	$-0.191168\pi$
$908$	46.3701	+	403.242i	0.0510684	+	0.444099i
$909$	−1119.10	−	408.197i	−1.23113	−	0.449061i
$910$	−20.1395	−	41.6978i	−0.0221313	−	0.0458217i
$911$	611.260	+	352.911i	0.670977	+	0.387389i	0.796447	−	0.604708i	$-0.206710\pi$
$911$	611.260	+	352.911i	0.670977	+	0.387389i	−0.125469	+	0.992097i	$0.540044\pi$
$912$	208.007	+	1111.50i	0.228078	+	1.21875i
$913$	55.3090	+	95.7980i	0.0605794	+	0.104927i
$914$	250.734	+	170.527i	0.274326	+	0.186572i
$915$	−25.4648	+	80.6666i	−0.0278304	+	0.0881603i
$916$	−103.190	−	44.7404i	−0.112653	−	0.0488432i
$917$	410.561	+	410.561i	0.447722	+	0.447722i
$918$	1100.33	−	720.596i	1.19862	−	0.784963i
$919$			523.158i			0.569269i	0.958636	+	0.284634i	$0.0918722\pi$
$919$			523.158i			0.569269i	−0.958636	+	0.284634i	$0.908128\pi$
$920$	−73.9130	+	3.01998i	−0.0803403	+	0.00328258i
$921$	−200.981	−	386.409i	−0.218221	−	0.419553i
$922$	114.092	+	599.230i	0.123744	+	0.649924i
$923$	344.775	−	1286.72i	0.373538	−	1.39406i
$924$	215.589	+	187.145i	0.233322	+	0.202538i
$925$	789.236	−	211.475i	0.853228	−	0.228622i
$926$	138.057	+	285.840i	0.149090	+	0.308683i
$927$	−994.874	−	87.7348i	−1.07322	−	0.0946438i
$928$	−47.5835	+	445.216i	−0.0512754	+	0.479759i
$929$	−1174.21	−	677.929i	−1.26395	−	0.729740i	−0.290112	−	0.956993i	$-0.593692\pi$
$929$	−1174.21	−	677.929i	−1.26395	−	0.729740i	−0.973836	+	0.227252i	$0.927026\pi$
$930$	18.4904	+	2.18519i	0.0198821	+	0.00234966i
$931$	−220.132	+	821.543i	−0.236447	+	0.882431i
$932$	−1095.86	−	162.607i	−1.17581	−	0.174472i
$933$	387.861	+	1752.40i	0.415714	+	1.87824i
$934$	−527.798	+	455.260i	−0.565094	+	0.487430i
$935$	−61.8773			−0.0661789
$936$	−1075.65	+	555.186i	−1.14920	+	0.593148i
$937$			640.967i			0.684062i	0.939689	+	0.342031i	$0.111115\pi$
$937$			640.967i			0.684062i	−0.939689	+	0.342031i	$0.888885\pi$
$938$	−68.4948	+	59.0812i	−0.0730222	+	0.0629864i
$939$	−222.274	−	242.738i	−0.236713	−	0.258507i
$940$	−8.57058	+	6.35576i	−0.00911764	+	0.00676144i
$941$	1703.77	+	456.525i	1.81060	+	0.485149i	0.995549	−	0.0942413i	$-0.0300425\pi$
$941$	1703.77	+	456.525i	1.81060	+	0.485149i	0.815050	+	0.579390i	$0.196709\pi$
$942$	−1111.56	+	1489.10i	−1.18000	+	1.58079i
$943$	621.063	−	1075.71i	0.658603	−	1.14073i
$944$	684.665	−	1100.80i	0.725280	−	1.16610i
$945$	36.8605	+	4.89175i	0.0390058	+	0.00517645i
$946$	50.2104	+	103.958i	0.0530765	+	0.109892i
$947$	−249.302	−	930.409i	−0.263255	−	0.982481i	−0.963310	−	0.268392i	$-0.913508\pi$
$947$	−249.302	−	930.409i	−0.263255	−	0.982481i	0.700055	−	0.714089i	$-0.253159\pi$
$948$	1141.54	−	771.139i	1.20416	−	0.813438i
$949$	−1437.66	−	385.221i	−1.51492	−	0.405923i
$950$	219.017	+	1150.32i	0.230544	+	1.21086i
$951$	12.5959	−	286.218i	0.0132449	−	0.300966i
$952$	−474.206	+	514.608i	−0.498116	+	0.540555i
$953$	−666.795			−0.699680			−0.349840	−	0.936809i	$-0.613764\pi$
$953$	−666.795			−0.699680			−0.349840	+	0.936809i	$0.613764\pi$
$954$	−32.7023	−	325.325i	−0.0342792	−	0.341011i
$955$	24.5618	−	24.5618i	0.0257191	−	0.0257191i
$956$	1093.57	−	432.089i	1.14390	−	0.451976i
$957$	−60.0931	−	271.508i	−0.0627932	−	0.283707i
$958$	835.795	+	568.435i	0.872438	+	0.593356i
$959$	−631.312	+	364.488i	−0.658302	+	0.380071i
$960$	62.3315	−	39.1909i	0.0649287	−	0.0408238i
$961$	447.759	−	775.541i	0.465930	−	0.807015i
$962$	480.778	+	995.428i	0.499770	+	1.03475i
$963$	117.456	+	668.836i	0.121969	+	0.694533i
$964$	496.412	−	625.415i	0.514950	−	0.648770i
$965$	104.583	−	28.0229i	0.108376	−	0.0290393i
$966$	192.446	−	482.616i	0.199219	−	0.499602i
$967$	−355.090	+	205.011i	−0.367208	+	0.212007i	−0.672238	−	0.740335i	$-0.734667\pi$
$967$	−355.090	+	205.011i	−0.367208	+	0.212007i	0.305030	+	0.952343i	$0.401333\pi$
$968$	588.883	−	183.864i	0.608350	−	0.189943i
$969$	1527.21	−	794.345i	1.57607	−	0.819757i
$970$	−32.6459	−	37.8475i	−0.0336556	−	0.0390180i
$971$	−64.7037	−	64.7037i	−0.0666361	−	0.0666361i	0.673003	−	0.739639i	$-0.265004\pi$
$971$	−64.7037	−	64.7037i	−0.0666361	−	0.0666361i	−0.739639	+	0.673003i	$0.765004\pi$
$972$	102.267	−	966.605i	0.105213	−	0.994450i
$973$	108.728	+	108.728i	0.111745	+	0.111745i
$974$	12.5327	−	169.847i	0.0128672	−	0.174381i
$975$	−1112.07	+	578.416i	−1.14058	+	0.593247i
$976$	−1175.82	−	38.6029i	−1.20474	−	0.0395522i
$977$	146.768	−	84.7367i	0.150223	−	0.0867315i	−0.423004	−	0.906128i	$-0.639024\pi$
$977$	146.768	−	84.7367i	0.150223	−	0.0867315i	0.573228	+	0.819396i	$0.305691\pi$
$978$	14.1100	+	32.8260i	0.0144274	+	0.0335644i
$979$	−609.357	+	163.277i	−0.622428	+	0.166779i
$980$	55.0168	−	6.32656i	0.0561396	−	0.00645567i
$981$	−141.330	−	804.783i	−0.144067	−	0.820371i
$982$	103.398	−	296.584i	0.105293	−	0.302021i
$983$	198.220	−	343.328i	0.201648	−	0.349265i	−0.747411	−	0.664362i	$-0.768703\pi$
$983$	198.220	−	343.328i	0.201648	−	0.349265i	0.949060	+	0.315096i	$0.102037\pi$
$984$	−3.88677	+	1236.31i	−0.00394997	+	1.25641i
$985$	64.6853	−	37.3461i	0.0656703	−	0.0379148i
$986$	669.596	−	127.489i	0.679103	−	0.129299i
$987$	−16.1952	−	73.1717i	−0.0164085	−	0.0741355i
$988$	−1473.42	+	582.174i	−1.49132	+	0.589245i
$989$	148.571	−	148.571i	0.150223	−	0.150223i
$990$	−28.9380	+	35.4059i	−0.0292303	+	0.0357636i
$991$	−1432.51			−1.44552			−0.722760	−	0.691099i	$-0.757127\pi$
$991$	−1432.51			−1.44552			−0.722760	+	0.691099i	$0.757127\pi$
$992$	40.0598	+	255.830i	0.0403828	+	0.257893i
$993$	71.2010	−	1617.91i	0.0717030	−	1.62932i
$994$	−470.580	−	320.047i	−0.473420	−	0.321979i
$995$	−76.4465	−	20.4838i	−0.0768307	−	0.0205867i
$996$	−38.0965	+	196.722i	−0.0382495	+	0.197512i
$997$	190.632	+	711.447i	0.191205	+	0.713587i	0.993217	+	0.116279i	$0.0370966\pi$
$997$	190.632	+	711.447i	0.191205	+	0.713587i	−0.802011	+	0.597309i	$0.796237\pi$
$998$	−286.842	+	822.768i	−0.287416	+	0.824417i
$999$	−879.950	−	116.778i	−0.880831	−	0.116895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.29.2	yes	184
3.2	odd	2		432.3.x.a.413.45		184
9.4	even	3		432.3.x.a.125.32		184
9.5	odd	6	inner	144.3.w.a.77.15	yes	184
16.5	even	4	inner	144.3.w.a.101.15	yes	184
48.5	odd	4		432.3.x.a.197.32		184
144.5	odd	12	inner	144.3.w.a.5.2	✓	184
144.85	even	12		432.3.x.a.341.45		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.2	✓	184	144.5	odd	12	inner
144.3.w.a.29.2	yes	184	1.1	even	1	trivial
144.3.w.a.77.15	yes	184	9.5	odd	6	inner
144.3.w.a.101.15	yes	184	16.5	even	4	inner
432.3.x.a.125.32		184	9.4	even	3
432.3.x.a.197.32		184	48.5	odd	4
432.3.x.a.341.45		184	144.85	even	12
432.3.x.a.413.45		184	3.2	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99458 - 0.147176i) q^{2} +(-2.86084 - 0.903108i) q^{3} +(3.95668 + 0.587107i) q^{4} +(-0.0992523 + 0.370415i) q^{5} +(5.57325 + 2.22237i) q^{6} +(3.11010 + 1.79562i) q^{7} +(-7.80549 - 1.75336i) q^{8} +(7.36879 + 5.16729i) q^{9} +O(q^{10})\)	\(q+(-1.99458 - 0.147176i) q^{2} +(-2.86084 - 0.903108i) q^{3} +(3.95668 + 0.587107i) q^{4} +(-0.0992523 + 0.370415i) q^{5} +(5.57325 + 2.22237i) q^{6} +(3.11010 + 1.79562i) q^{7} +(-7.80549 - 1.75336i) q^{8} +(7.36879 + 5.16729i) q^{9} +(0.252482 - 0.724213i) q^{10} +(-6.39886 + 1.71457i) q^{11} +(-10.7892 - 5.25293i) q^{12} +(4.35132 - 16.2393i) q^{13} +(-5.93907 - 4.03923i) q^{14} +(0.618469 - 0.970060i) q^{15} +(15.3106 + 4.64599i) q^{16} -24.3572i q^{17} +(-13.9371 - 11.3911i) q^{18} +(-16.6582 - 16.6582i) q^{19} +(-0.610182 + 1.40734i) q^{20} +(-7.27586 - 7.94573i) q^{21} +(13.0154 - 2.47808i) q^{22} +(-12.0564 - 20.8824i) q^{23} +(20.7468 + 12.0653i) q^{24} +(21.5233 + 12.4265i) q^{25} +(-11.0691 + 31.7502i) q^{26} +(-16.4143 - 21.4376i) q^{27} +(11.2515 + 8.93065i) q^{28} +(-3.62146 - 13.5155i) q^{29} +(-1.37635 + 1.84384i) q^{30} +(-4.04605 - 7.00797i) q^{31} +(-29.8544 - 11.5201i) q^{32} +(19.8545 + 0.873759i) q^{33} +(-3.58480 + 48.5824i) q^{34} +(-0.973808 + 0.973808i) q^{35} +(26.1222 + 24.7716i) q^{36} +(23.2472 - 23.2472i) q^{37} +(30.7744 + 35.6778i) q^{38} +(-27.1143 + 42.5284i) q^{39} +(1.42418 - 2.71724i) q^{40} +(25.7565 + 44.6115i) q^{41} +(13.3428 + 16.9192i) q^{42} +(2.25526 + 8.41674i) q^{43} +(-26.3249 + 3.02718i) q^{44} +(-2.64541 + 2.21664i) q^{45} +(20.9741 + 43.4259i) q^{46} +(6.02413 + 3.47803i) q^{47} +(-39.6053 - 27.1186i) q^{48} +(-18.0515 - 31.2661i) q^{49} +(-41.1010 - 27.9533i) q^{50} +(-21.9972 + 69.6821i) q^{51} +(26.7510 - 61.6992i) q^{52} +(12.8444 + 12.8444i) q^{53} +(29.5845 + 45.1748i) q^{54} -2.54041i q^{55} +(-21.1275 - 19.4688i) q^{56} +(32.6123 + 62.7006i) q^{57} +(5.23413 + 27.4906i) q^{58} +(20.9700 - 78.2612i) q^{59} +(3.01661 - 3.47511i) q^{60} +(-71.0232 + 19.0306i) q^{61} +(7.03876 + 14.5734i) q^{62} +(13.6392 + 29.3023i) q^{63} +(57.8515 + 27.3717i) q^{64} +(5.58341 + 3.22358i) q^{65} +(-39.4728 - 4.66489i) q^{66} +(3.25953 - 12.1647i) q^{67} +(14.3003 - 96.3738i) q^{68} +(15.6325 + 70.6293i) q^{69} +(2.08566 - 1.79901i) q^{70} +79.2346 q^{71} +(-48.4569 - 53.2534i) q^{72} -88.5296i q^{73} +(-49.7897 + 42.9469i) q^{74} +(-50.3522 - 54.9880i) q^{75} +(-56.1310 - 75.6913i) q^{76} +(-22.9798 - 6.15742i) q^{77} +(60.3408 - 80.8357i) q^{78} +(-57.3999 + 99.4195i) q^{79} +(-3.24056 + 5.21015i) q^{80} +(27.5981 + 76.1534i) q^{81} +(-44.8076 - 92.7719i) q^{82} +(-4.32178 - 16.1291i) q^{83} +(-24.1232 - 35.7104i) q^{84} +(9.02227 + 2.41751i) q^{85} +(-3.25955 - 17.1198i) q^{86} +(-1.84553 + 41.9361i) q^{87} +(52.9525 - 2.16356i) q^{88} +95.2289 q^{89} +(5.60271 - 4.03192i) q^{90} +(42.6927 - 42.6927i) q^{91} +(-35.4433 - 89.7032i) q^{92} +(5.24615 + 23.7027i) q^{93} +(-11.5037 - 7.82381i) q^{94} +(7.82380 - 4.51708i) q^{95} +(75.0047 + 59.9190i) q^{96} +(32.5843 - 56.4377i) q^{97} +(31.4035 + 65.0195i) q^{98} +(-56.0115 - 20.4305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Introduction

L-functions

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