LMFDB - Embedded newform 144.3.w.a.5.10

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			5.10
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59704 - 1.20393i) q^{2} +(-1.75135 - 2.43573i) q^{3} +(1.10109 + 3.84547i) q^{4} +(-2.49590 - 9.31484i) q^{5} +(-0.135487 + 5.99847i) q^{6} +(7.55275 - 4.36058i) q^{7} +(2.87120 - 7.46701i) q^{8} +(-2.86558 + 8.53161i) q^{9} +O(q^{10})$	\(q+(-1.59704 - 1.20393i) q^{2} +(-1.75135 - 2.43573i) q^{3} +(1.10109 + 3.84547i) q^{4} +(-2.49590 - 9.31484i) q^{5} +(-0.135487 + 5.99847i) q^{6} +(7.55275 - 4.36058i) q^{7} +(2.87120 - 7.46701i) q^{8} +(-2.86558 + 8.53161i) q^{9} +(-7.22838 + 17.8811i) q^{10} +(-8.59716 - 2.30360i) q^{11} +(7.43814 - 9.41669i) q^{12} +(-1.01775 - 3.79829i) q^{13} +(-17.3119 - 2.12897i) q^{14} +(-18.3173 + 22.3928i) q^{15} +(-13.5752 + 8.46840i) q^{16} +20.4214i q^{17} +(14.8480 - 10.1754i) q^{18} +(1.44592 - 1.44592i) q^{19} +(33.0717 - 19.8544i) q^{20} +(-23.8487 - 10.7596i) q^{21} +(10.9566 + 14.0294i) q^{22} +(6.97317 - 12.0779i) q^{23} +(-23.2161 + 6.08384i) q^{24} +(-58.8860 + 33.9979i) q^{25} +(-2.94750 + 7.29133i) q^{26} +(25.7993 - 7.96201i) q^{27} +(25.0847 + 24.2425i) q^{28} +(-8.45427 + 31.5518i) q^{29} +(56.2129 - 13.7096i) q^{30} +(12.0086 - 20.7996i) q^{31} +(31.8756 + 2.81926i) q^{32} +(9.44564 + 24.9748i) q^{33} +(24.5860 - 32.6139i) q^{34} +(-59.4691 - 59.4691i) q^{35} +(-35.9633 - 1.62543i) q^{36} +(-14.6915 - 14.6915i) q^{37} +(-4.04998 + 0.568403i) q^{38} +(-7.46919 + 9.13108i) q^{39} +(-76.7202 - 8.10783i) q^{40} +(29.9984 - 51.9587i) q^{41} +(25.1335 + 45.8958i) q^{42} +(9.90936 - 36.9823i) q^{43} +(-0.607813 - 35.5966i) q^{44} +(86.6228 + 5.39834i) q^{45} +(-25.6774 + 10.8937i) q^{46} +(31.8352 - 18.3801i) q^{47} +(44.4016 + 18.2345i) q^{48} +(13.5294 - 23.4336i) q^{49} +(134.975 + 16.5988i) q^{50} +(49.7411 - 35.7649i) q^{51} +(13.4856 - 8.09597i) q^{52} +(-41.8929 + 41.8929i) q^{53} +(-50.7884 - 18.3450i) q^{54} +85.8307i q^{55} +(-10.8751 - 68.9166i) q^{56} +(-6.05417 - 0.989567i) q^{57} +(51.4881 - 40.2111i) q^{58} +(-15.7167 - 58.6557i) q^{59} +(-106.280 - 45.7819i) q^{60} +(18.9131 + 5.06774i) q^{61} +(-44.2196 + 18.7602i) q^{62} +(15.5598 + 76.9328i) q^{63} +(-47.5124 - 42.8785i) q^{64} +(-32.8403 + 18.9603i) q^{65} +(14.9829 - 51.2577i) q^{66} +(9.28744 + 34.6612i) q^{67} +(-78.5298 + 22.4858i) q^{68} +(-41.6309 + 4.16777i) q^{69} +(23.3778 + 166.571i) q^{70} -22.7508 q^{71} +(55.4780 + 45.8933i) q^{72} -78.0968i q^{73} +(5.77535 + 41.1504i) q^{74} +(185.939 + 83.8886i) q^{75} +(7.15231 + 3.96814i) q^{76} +(-74.9773 + 20.0901i) q^{77} +(22.9218 - 5.59032i) q^{78} +(-9.92252 - 17.1863i) q^{79} +(112.764 + 105.315i) q^{80} +(-64.5769 - 48.8961i) q^{81} +(-110.463 + 46.8642i) q^{82} +(-20.4326 + 76.2556i) q^{83} +(15.1161 - 103.557i) q^{84} +(190.222 - 50.9699i) q^{85} +(-60.3498 + 47.1320i) q^{86} +(91.6580 - 34.6657i) q^{87} +(-41.8852 + 57.5810i) q^{88} -108.510 q^{89} +(-131.841 - 112.909i) q^{90} +(-24.2496 - 24.2496i) q^{91} +(54.1232 + 13.5163i) q^{92} +(-71.6934 + 7.17740i) q^{93} +(-72.9705 - 8.97372i) q^{94} +(-17.0773 - 9.85961i) q^{95} +(-48.9582 - 82.5778i) q^{96} +(5.21912 + 9.03978i) q^{97} +(-49.8195 + 21.1359i) q^{98} +(44.2893 - 66.7465i) 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.59704	−	1.20393i	−0.798521	−	0.601967i
$2$	−1.59704	−	1.20393i	−0.798521	−	0.601967i
$3$	−1.75135	−	2.43573i	−0.583782	−	0.811911i
$3$	−1.75135	−	2.43573i	−0.583782	−	0.811911i
$4$	1.10109	+	3.84547i	0.275272	+	0.961366i
$5$	−2.49590	−	9.31484i	−0.499181	−	1.86297i	−0.505228	−	0.862986i	$-0.668592\pi$
$5$	−2.49590	−	9.31484i	−0.499181	−	1.86297i	0.00604760	−	0.999982i	$-0.498075\pi$
$6$	−0.135487	+	5.99847i	−0.0225812	+	0.999745i
$7$	7.55275	−	4.36058i	1.07896	−	0.622941i	0.148348	−	0.988935i	$-0.452605\pi$
$7$	7.55275	−	4.36058i	1.07896	−	0.622941i	0.930617	+	0.365995i	$0.119271\pi$
$8$	2.87120	−	7.46701i	0.358900	−	0.933376i
$9$	−2.86558	+	8.53161i	−0.318398	+	0.947957i
$10$	−7.22838	+	17.8811i	−0.722838	+	1.78811i
$11$	−8.59716	−	2.30360i	−0.781560	−	0.209418i	−0.154088	−	0.988057i	$-0.549244\pi$
$11$	−8.59716	−	2.30360i	−0.781560	−	0.209418i	−0.627473	+	0.778639i	$0.715911\pi$
$12$	7.43814	−	9.41669i	0.619845	−	0.784724i
$13$	−1.01775	−	3.79829i	−0.0782884	−	0.292176i	0.915670	−	0.401930i	$-0.131660\pi$
$13$	−1.01775	−	3.79829i	−0.0782884	−	0.292176i	−0.993959	+	0.109754i	$0.964994\pi$
$14$	−17.3119	−	2.12897i	−1.23657	−	0.152070i
$15$	−18.3173	+	22.3928i	−1.22115	+	1.49286i
$16$	−13.5752	+	8.46840i	−0.848451	+	0.529275i
$17$			20.4214i			1.20126i	0.799527	+	0.600630i	$0.205083\pi$
$17$			20.4214i			1.20126i	−0.799527	+	0.600630i	$0.794917\pi$
$18$	14.8480	−	10.1754i	0.824886	−	0.565299i
$19$	1.44592	−	1.44592i	0.0761009	−	0.0761009i	−0.668032	−	0.744133i	$-0.732863\pi$
$19$	1.44592	−	1.44592i	0.0761009	−	0.0761009i	0.744133	+	0.668032i	$0.232863\pi$
$20$	33.0717	−	19.8544i	1.65358	−	0.992718i
$21$	−23.8487	−	10.7596i	−1.13565	−	0.512362i
$22$	10.9566	+	14.0294i	0.498030	+	0.637698i
$23$	6.97317	−	12.0779i	0.303181	−	0.525125i	−0.673673	−	0.739029i	$-0.735285\pi$
$23$	6.97317	−	12.0779i	0.303181	−	0.525125i	0.976855	+	0.213904i	$0.0686179\pi$
$24$	−23.2161	+	6.08384i	−0.967337	+	0.253493i
$25$	−58.8860	+	33.9979i	−2.35544	+	1.35991i
$26$	−2.94750	+	7.29133i	−0.113365	+	0.280436i
$27$	25.7993	−	7.96201i	0.955531	−	0.294889i
$28$	25.0847	+	24.2425i	0.895883	+	0.865802i
$29$	−8.45427	+	31.5518i	−0.291527	+	1.08799i	0.652410	+	0.757866i	$0.273758\pi$
$29$	−8.45427	+	31.5518i	−0.291527	+	1.08799i	−0.943937	+	0.330126i	$0.892909\pi$
$30$	56.2129	−	13.7096i	1.87376	−	0.456985i
$31$	12.0086	−	20.7996i	0.387375	−	0.670954i	−0.604720	−	0.796438i	$-0.706715\pi$
$31$	12.0086	−	20.7996i	0.387375	−	0.670954i	0.992096	+	0.125484i	$0.0400484\pi$
$32$	31.8756	+	2.81926i	0.996111	+	0.0881019i
$33$	9.44564	+	24.9748i	0.286232	+	0.756812i
$34$	24.5860	−	32.6139i	0.723118	−	0.959231i
$35$	−59.4691	−	59.4691i	−1.69912	−	1.69912i
$36$	−35.9633	−	1.62543i	−0.998980	−	0.0451508i
$37$	−14.6915	−	14.6915i	−0.397067	−	0.397067i	0.480130	−	0.877197i	$-0.340589\pi$
$37$	−14.6915	−	14.6915i	−0.397067	−	0.397067i	−0.877197	+	0.480130i	$0.840589\pi$
$38$	−4.04998	+	0.568403i	−0.106578	+	0.0149580i
$39$	−7.46919	+	9.13108i	−0.191518	+	0.234130i
$40$	−76.7202	−	8.10783i	−1.91801	−	0.202696i
$41$	29.9984	−	51.9587i	0.731667	−	1.26729i	−0.224503	−	0.974473i	$-0.572076\pi$
$41$	29.9984	−	51.9587i	0.731667	−	1.26729i	0.956170	−	0.292812i	$-0.0945909\pi$
$42$	25.1335	+	45.8958i	0.598417	+	1.09276i
$43$	9.90936	−	36.9823i	0.230450	−	0.860052i	−0.749697	−	0.661781i	$-0.769801\pi$
$43$	9.90936	−	36.9823i	0.230450	−	0.860052i	0.980147	−	0.198271i	$-0.0635326\pi$
$44$	−0.607813	−	35.5966i	−0.0138139	−	0.809013i
$45$	86.6228	+	5.39834i	1.92495	+	0.119963i
$46$	−25.6774	+	10.8937i	−0.558205	+	0.236819i
$47$	31.8352	−	18.3801i	0.677344	−	0.391065i	−0.121509	−	0.992590i	$-0.538773\pi$
$47$	31.8352	−	18.3801i	0.677344	−	0.391065i	0.798854	+	0.601525i	$0.205440\pi$
$48$	44.4016	+	18.2345i	0.925034	+	0.379885i
$49$	13.5294	−	23.4336i	0.276110	−	0.478236i
$50$	134.975	+	16.5988i	2.69949	+	0.331977i
$51$	49.7411	−	35.7649i	0.975316	−	0.701273i
$52$	13.4856	−	8.09597i	0.259338	−	0.155692i
$53$	−41.8929	+	41.8929i	−0.790433	+	0.790433i	−0.981564	−	0.191132i	$-0.938784\pi$
$53$	−41.8929	+	41.8929i	−0.790433	+	0.790433i	0.191132	+	0.981564i	$0.438784\pi$
$54$	−50.7884	−	18.3450i	−0.940526	−	0.339723i
$55$			85.8307i			1.56056i
$56$	−10.8751	−	68.9166i	−0.194197	−	1.23065i
$57$	−6.05417	−	0.989567i	−0.106213	−	0.0173608i
$58$	51.4881	−	40.2111i	0.887725	−	0.693295i
$59$	−15.7167	−	58.6557i	−0.266385	−	0.994164i	−0.961397	−	0.275165i	$-0.911267\pi$
$59$	−15.7167	−	58.6557i	−0.266385	−	0.994164i	0.695011	−	0.718999i	$-0.255399\pi$
$60$	−106.280	−	45.7819i	−1.77133	−	0.763031i
$61$	18.9131	+	5.06774i	0.310050	+	0.0830777i	0.410489	−	0.911866i	$-0.365358\pi$
$61$	18.9131	+	5.06774i	0.310050	+	0.0830777i	−0.100439	+	0.994943i	$0.532025\pi$
$62$	−44.2196	+	18.7602i	−0.713219	+	0.302584i
$63$	15.5598	+	76.9328i	0.246981	+	1.22116i
$64$	−47.5124	−	42.8785i	−0.742382	−	0.669977i
$65$	−32.8403	+	18.9603i	−0.505235	+	0.291697i
$66$	14.9829	−	51.2577i	0.227014	−	0.776632i
$67$	9.28744	+	34.6612i	0.138618	+	0.517331i	0.999957	+	0.00929939i	$0.00296013\pi$
$67$	9.28744	+	34.6612i	0.138618	+	0.517331i	−0.861338	+	0.508032i	$0.830373\pi$
$68$	−78.5298	+	22.4858i	−1.15485	+	0.330673i
$69$	−41.6309	+	4.16777i	−0.603347	+	0.0604025i
$70$	23.3778	+	166.571i	0.333969	+	2.37959i
$71$	−22.7508			−0.320434			−0.160217	−	0.987082i	$-0.551219\pi$
$71$	−22.7508			−0.320434			−0.160217	+	0.987082i	$0.551219\pi$
$72$	55.4780	+	45.8933i	0.770528	+	0.637407i
$73$		−	78.0968i		−	1.06982i	−0.844909	−	0.534910i	$-0.820346\pi$
$73$		−	78.0968i		−	1.06982i	0.844909	−	0.534910i	$-0.179654\pi$
$74$	5.77535	+	41.1504i	0.0780452	+	0.556087i
$75$	185.939	+	83.8886i	2.47919	+	1.11851i
$76$	7.15231	+	3.96814i	0.0941093	+	0.0522124i
$77$	−74.9773	+	20.0901i	−0.973731	+	0.260910i
$78$	22.9218	−	5.59032i	0.293870	−	0.0716707i
$79$	−9.92252	−	17.1863i	−0.125602	−	0.217548i	0.796366	−	0.604814i	$-0.206753\pi$
$79$	−9.92252	−	17.1863i	−0.125602	−	0.217548i	−0.921968	+	0.387266i	$0.873419\pi$
$80$	112.764	+	105.315i	1.40955	+	1.31643i
$81$	−64.5769	−	48.8961i	−0.797246	−	0.603655i
$82$	−110.463	+	46.8642i	−1.34712	+	0.571515i
$83$	−20.4326	+	76.2556i	−0.246176	+	0.918742i	0.726612	+	0.687048i	$0.241094\pi$
$83$	−20.4326	+	76.2556i	−0.246176	+	0.918742i	−0.972789	+	0.231694i	$0.925573\pi$
$84$	15.1161	−	103.557i	0.179954	−	1.23282i
$85$	190.222	−	50.9699i	2.23791	−	0.599646i
$86$	−60.3498	+	47.1320i	−0.701742	+	0.548047i
$87$	91.6580	−	34.6657i	1.05354	−	0.398456i
$88$	−41.8852	+	57.5810i	−0.475968	+	0.654329i
$89$	−108.510			−1.21922			−0.609608	−	0.792703i	$-0.708673\pi$
$89$	−108.510			−1.21922			−0.609608	+	0.792703i	$0.708673\pi$
$90$	−131.841	−	112.909i	−1.46490	−	1.25455i
$91$	−24.2496	−	24.2496i	−0.266479	−	0.266479i
$92$	54.1232	+	13.5163i	0.588295	+	0.146916i
$93$	−71.6934	+	7.17740i	−0.770897	+	0.0771764i
$94$	−72.9705	−	8.97372i	−0.776282	−	0.0954651i
$95$	−17.0773	−	9.85961i	−0.179762	−	0.103785i
$96$	−48.9582	−	82.5778i	−0.509981	−	0.860186i
$97$	5.21912	+	9.03978i	0.0538054	+	0.0931936i	0.891674	−	0.452679i	$-0.149532\pi$
$97$	5.21912	+	9.03978i	0.0538054	+	0.0931936i	−0.837868	+	0.545873i	$0.816198\pi$
$98$	−49.8195	+	21.1359i	−0.508362	+	0.215673i
$99$	44.2893	−	66.7465i	0.447367	−	0.674207i
$100$	−195.576	−	189.010i	−1.95576	−	1.89010i
$101$	58.5198	+	15.6803i	0.579404	+	0.155251i	0.536606	−	0.843833i	$-0.319706\pi$
$101$	58.5198	+	15.6803i	0.579404	+	0.155251i	0.0427979	+	0.999084i	$0.486373\pi$
$102$	−122.497	−	2.76684i	−1.20095	−	0.0271259i
$103$	−91.1270	−	52.6122i	−0.884728	−	0.510798i	−0.0125138	−	0.999922i	$-0.503983\pi$
$103$	−91.1270	−	52.6122i	−0.884728	−	0.510798i	−0.872215	+	0.489124i	$0.837317\pi$
$104$	−31.2840	−	3.30611i	−0.300808	−	0.0317895i
$105$	−40.6999	+	249.002i	−0.387618	+	2.37144i
$106$	117.341	−	16.4685i	1.10699	−	0.155363i
$107$	91.3826	−	91.3826i	0.854043	−	0.854043i	−0.136585	−	0.990628i	$-0.543613\pi$
$107$	91.3826	−	91.3826i	0.854043	−	0.854043i	0.990628	+	0.136585i	$0.0436127\pi$
$108$	59.0250	+	90.4436i	0.546528	+	0.837441i
$109$	88.9598	−	88.9598i	0.816145	−	0.816145i	−0.169402	−	0.985547i	$-0.554184\pi$
$109$	88.9598	−	88.9598i	0.816145	−	0.816145i	0.985547	+	0.169402i	$0.0541837\pi$
$110$	103.335	−	137.075i	0.939405	−	1.24614i
$111$	−10.0546	+	61.5143i	−0.0905824	+	0.554183i
$112$	−65.6030	+	123.156i	−0.585741	+	1.09960i
$113$	14.0397	+	8.10580i	0.124245	+	0.0717328i	0.560834	−	0.827928i	$-0.310480\pi$
$113$	14.0397	+	8.10580i	0.124245	+	0.0717328i	−0.436590	+	0.899661i	$0.643814\pi$
$114$	8.47739	+	8.86919i	0.0743630	+	0.0777999i
$115$	−129.908	−	34.8087i	−1.12963	−	0.302684i
$116$	−130.640	+	2.23068i	−1.12621	+	0.0192300i
$117$	35.3220	+	2.20127i	0.301897	+	0.0188143i
$118$	−45.5172	+	112.598i	−0.385739	+	0.954216i
$119$	89.0493	+	154.238i	0.748313	+	1.29612i
$120$	114.615	+	201.069i	0.955125	+	1.67558i
$121$	−36.1844	−	20.8911i	−0.299045	−	0.172654i
$122$	−24.1037	−	30.8635i	−0.197572	−	0.252979i
$123$	−179.095	+	17.9296i	−1.45606	+	0.145769i
$124$	93.2066	+	23.2766i	0.751666	+	0.187715i
$125$	293.185	+	293.185i	2.34548	+	2.34548i
$126$	67.7723	−	141.598i	0.537875	−	1.12379i
$127$	74.7359			0.588472			0.294236	−	0.955733i	$-0.404935\pi$
$127$	74.7359			0.588472			0.294236	+	0.955733i	$0.404935\pi$
$128$	24.2565	+	125.681i	0.189504	+	0.981880i
$129$	−107.434	+	40.6321i	−0.832818	+	0.314978i
$130$	75.2743	+	9.25703i	0.579033	+	0.0712079i
$131$	−109.153	+	29.2475i	−0.833229	+	0.223263i	−0.650122	−	0.759830i	$-0.725282\pi$
$131$	−109.153	+	29.2475i	−0.833229	+	0.223263i	−0.183107	+	0.983093i	$0.558616\pi$
$132$	−85.6392	+	63.8223i	−0.648782	+	0.483503i
$133$	4.61561	−	17.2257i	0.0347038	−	0.129516i
$134$	26.8973	−	66.5369i	0.200726	−	0.496544i
$135$	−138.558	−	220.444i	−1.02635	−	1.63292i
$136$	152.487	+	58.6339i	1.12123	+	0.431132i
$137$	−28.6355	−	49.5981i	−0.209018	−	0.362030i	0.742388	−	0.669971i	$-0.233693\pi$
$137$	−28.6355	−	49.5981i	−0.209018	−	0.362030i	−0.951405	+	0.307941i	$0.900360\pi$
$138$	71.5041	+	43.4647i	0.518145	+	0.314962i
$139$	113.758	−	30.4812i	0.818400	−	0.219290i	0.174753	−	0.984612i	$-0.444087\pi$
$139$	113.758	−	30.4812i	0.818400	−	0.219290i	0.643647	+	0.765323i	$0.277421\pi$
$140$	163.206	−	294.167i	1.16575	−	2.10119i
$141$	−100.523	−	45.3522i	−0.712931	−	0.321647i
$142$	36.3340	+	27.3905i	0.255873	+	0.192891i
$143$			34.9990i			0.244748i
$144$	−33.3482	−	140.085i	−0.231585	−	0.972815i
$145$	315.001			2.17242
$146$	−94.0234	+	124.724i	−0.643996	+	0.854274i
$147$	−80.7725	+	8.08633i	−0.549473	+	0.0550090i
$148$	40.3189	−	72.6721i	0.272425	−	0.491028i
$149$	−23.9955	−	89.5524i	−0.161044	−	0.601023i	−0.998512	−	0.0545367i	$-0.982632\pi$
$149$	−23.9955	−	89.5524i	−0.161044	−	0.601023i	0.837468	−	0.546486i	$-0.184035\pi$
$150$	−195.957	−	357.832i	−1.30638	−	2.38555i
$151$	44.1519	−	25.4911i	0.292397	−	0.168815i	−0.346626	−	0.938004i	$-0.612673\pi$
$151$	44.1519	−	25.4911i	0.292397	−	0.168815i	0.639022	+	0.769188i	$0.279339\pi$
$152$	−6.64516	−	14.9482i	−0.0437181	−	0.0983433i
$153$	−174.228	−	58.5192i	−1.13874	−	0.382479i
$154$	143.929	+	58.1829i	0.934604	+	0.377811i
$155$	−223.717	−	59.9448i	−1.44334	−	0.386741i
$156$	−43.3375	−	18.6684i	−0.277804	−	0.119669i
$157$	−10.8142	−	40.3590i	−0.0688800	−	0.257064i	0.922896	−	0.385049i	$-0.125816\pi$
$157$	−10.8142	−	40.3590i	−0.0688800	−	0.257064i	−0.991776	+	0.127986i	$0.959149\pi$
$158$	−4.84449	+	39.3933i	−0.0306613	+	0.249325i
$159$	175.409	+	28.6710i	1.10320	+	0.180321i
$160$	−53.2974	−	303.952i	−0.333109	−	1.89970i
$161$		−	121.628i		−	0.755456i
$162$	44.2644	+	155.835i	0.273237	+	0.961947i
$163$	−5.70764	+	5.70764i	−0.0350162	+	0.0350162i	−0.724398	−	0.689382i	$-0.757882\pi$
$163$	−5.70764	+	5.70764i	−0.0350162	+	0.0350162i	0.689382	+	0.724398i	$0.257882\pi$
$164$	232.836	+	58.1466i	1.41973	+	0.354552i
$165$	209.061	−	150.319i	1.26703	−	0.911026i
$166$	124.438	−	97.1839i	0.749629	−	0.585445i
$167$	76.5669	−	132.618i	0.458485	−	0.794118i	−0.540397	−	0.841410i	$-0.681726\pi$
$167$	76.5669	−	132.618i	0.458485	−	0.794118i	0.998881	+	0.0472920i	$0.0150591\pi$
$168$	−148.816	+	147.185i	−0.885811	+	0.876104i
$169$	132.967	−	76.7686i	0.786788	−	0.454252i
$170$	−365.157	−	147.614i	−2.14798	−	0.868316i
$171$	8.19261	+	16.4794i	0.0479100	+	0.0963707i
$172$	153.125	−	2.61462i	0.890262	−	0.0152013i
$173$	7.17021	−	26.7596i	0.0414463	−	0.154680i	−0.942101	−	0.335328i	$-0.891153\pi$
$173$	7.17021	−	26.7596i	0.0414463	−	0.154680i	0.983548	+	0.180648i	$0.0578196\pi$
$174$	−188.117	−	54.9875i	−1.08113	−	0.316020i
$175$	−296.501	+	513.555i	−1.69429	+	2.93460i
$176$	136.216	−	41.5323i	0.773955	−	0.235979i
$177$	−115.344	+	141.008i	−0.651662	+	0.796656i
$178$	173.295	+	130.639i	0.973570	+	0.733928i
$179$	−91.2881	−	91.2881i	−0.509989	−	0.509989i	0.404534	−	0.914523i	$-0.367434\pi$
$179$	−91.2881	−	91.2881i	−0.509989	−	0.509989i	−0.914523	+	0.404534i	$0.867434\pi$
$180$	74.6203	+	339.049i	0.414557	+	1.88361i
$181$	21.8441	+	21.8441i	0.120686	+	0.120686i	0.764870	−	0.644184i	$-0.222803\pi$
$181$	21.8441	+	21.8441i	0.120686	+	0.120686i	−0.644184	+	0.764870i	$0.722803\pi$
$182$	9.53272	+	67.9225i	0.0523776	+	0.373200i
$183$	−20.7796	−	54.9425i	−0.113550	−	0.300232i
$184$	−70.1643	−	86.7467i	−0.381328	−	0.471450i
$185$	−100.180	+	173.517i	−0.541514	+	0.937930i
$186$	123.139	+	74.8515i	0.662035	+	0.402428i
$187$	47.0428	−	175.566i	0.251566	−	0.938857i
$188$	105.733	+	102.183i	0.562411	+	0.543527i
$189$	160.137	−	172.635i	0.847286	−	0.913414i
$190$	15.4029	+	36.3062i	0.0810681	+	0.191085i
$191$	190.893	−	110.212i	0.999439	−	0.577026i	0.0913567	−	0.995818i	$-0.470880\pi$
$191$	190.893	−	110.212i	0.999439	−	0.577026i	0.908082	+	0.418792i	$0.137546\pi$
$192$	−21.2300	+	190.823i	−0.110573	+	0.993868i
$193$	−25.2352	+	43.7086i	−0.130752	+	0.226469i	−0.923967	−	0.382473i	$-0.875073\pi$
$193$	−25.2352	+	43.7086i	−0.130752	+	0.226469i	0.793215	+	0.608942i	$0.208406\pi$
$194$	2.54814	−	20.7204i	0.0131347	−	0.106806i
$195$	103.697	+	46.7840i	0.531779	+	0.239918i
$196$	105.010	+	26.2243i	0.535766	+	0.133798i
$197$	145.170	−	145.170i	0.736902	−	0.736902i	−0.235075	−	0.971977i	$-0.575534\pi$
$197$	145.170	−	145.170i	0.736902	−	0.736902i	0.971977	+	0.235075i	$0.0755337\pi$
$198$	−151.090	+	53.2756i	−0.763082	+	0.269069i
$199$			43.3365i			0.217771i	0.994054	+	0.108886i	$0.0347282\pi$
$199$			43.3365i			0.217771i	−0.994054	+	0.108886i	$0.965272\pi$
$200$	84.7888	+	537.317i	0.423944	+	2.68659i
$201$	68.1599	−	83.3254i	0.339104	−	0.414554i
$202$	−74.5805	−	95.4961i	−0.369210	−	0.472753i
$203$	73.7311	+	275.168i	0.363207	+	1.35551i
$204$	192.302	+	151.897i	0.942658	+	0.744595i
$205$	−558.860	−	149.746i	−2.72615	−	0.730468i
$206$	82.1921	+	193.735i	0.398991	+	0.940460i
$207$	83.0617	+	94.1026i	0.401264	+	0.454602i
$208$	45.9816	+	42.9439i	0.221065	+	0.206461i
$209$	−15.7616	+	9.09996i	−0.0754144	+	0.0435405i
$210$	364.781	−	348.666i	1.73705	−	1.66031i
$211$	83.9145	+	313.173i	0.397699	+	1.48423i	0.817134	+	0.576448i	$0.195562\pi$
$211$	83.9145	+	313.173i	0.397699	+	1.48423i	−0.419435	+	0.907785i	$0.637772\pi$
$212$	−207.226	−	114.970i	−0.977480	−	0.542311i
$213$	39.8445	+	55.4149i	0.187064	+	0.260164i
$214$	−255.961	+	35.9233i	−1.19608	+	0.167866i
$215$	−369.216			−1.71729
$216$	14.6227	−	215.504i	0.0676975	−	0.997706i
$217$		−	209.459i		−	0.965247i
$218$	−249.174	+	34.9709i	−1.14300	+	0.160417i
$219$	−190.223	+	136.775i	−0.868598	+	0.624541i
$220$	−330.059	+	94.5073i	−1.50027	+	0.429578i
$221$	77.5665	−	20.7839i	0.350980	−	0.0940447i
$222$	90.1168	−	86.1358i	0.405932	−	0.387999i
$223$	182.085	+	315.380i	0.816523	+	1.41426i	0.908229	+	0.418474i	$0.137435\pi$
$223$	182.085	+	315.380i	0.816523	+	1.41426i	−0.0917056	+	0.995786i	$0.529232\pi$
$224$	253.042	−	117.703i	1.12965	−	0.525459i
$225$	−121.314	−	599.817i	−0.539173	−	2.66585i
$226$	−12.6631	−	29.8481i	−0.0560314	−	0.132071i
$227$	83.0798	−	310.058i	0.365990	−	1.36589i	−0.500083	−	0.865978i	$-0.666697\pi$
$227$	83.0798	−	310.058i	0.365990	−	1.36589i	0.866073	−	0.499917i	$-0.166636\pi$
$228$	−2.86083	−	24.3707i	−0.0125475	−	0.106889i
$229$	−376.879	+	100.984i	−1.64576	+	0.440980i	−0.958421	−	0.285357i	$-0.907888\pi$
$229$	−376.879	+	100.984i	−1.64576	+	0.440980i	−0.687339	+	0.726337i	$0.741221\pi$
$230$	165.561	+	211.991i	0.719831	+	0.921702i
$231$	180.245	+	147.440i	0.780282	+	0.638268i
$232$	211.323	+	153.720i	0.910877	+	0.662584i
$233$	−88.1182			−0.378190			−0.189095	−	0.981959i	$-0.560555\pi$
$233$	−88.1182			−0.378190			−0.189095	+	0.981959i	$0.560555\pi$
$234$	−53.7605	−	46.0409i	−0.229746	−	0.196756i
$235$	−250.665	−	250.665i	−1.06666	−	1.06666i
$236$	208.253	−	125.023i	0.882427	−	0.529760i
$237$	−24.4835	+	54.2677i	−0.103306	+	0.228978i
$238$	43.4767	−	353.534i	0.182675	−	1.48544i
$239$	−361.872	−	208.927i	−1.51411	−	0.874171i	−0.999863	−	0.0165275i	$-0.994739\pi$
$239$	−361.872	−	208.927i	−1.51411	−	0.874171i	−0.514245	−	0.857643i	$-0.671928\pi$
$240$	59.0291	−	459.105i	0.245955	−	1.91294i
$241$	20.3206	+	35.1963i	0.0843179	+	0.146043i	0.905100	−	0.425198i	$-0.139796\pi$
$241$	20.3206	+	35.1963i	0.0843179	+	0.146043i	−0.820782	+	0.571241i	$0.806462\pi$
$242$	32.6366	+	76.9276i	0.134862	+	0.317883i
$243$	−6.00131	+	242.926i	−0.0246967	+	0.999695i
$244$	1.33714	+	78.3096i	0.00548008	+	0.320941i
$245$	−252.048	−	67.5360i	−1.02877	−	0.275657i
$246$	307.608	+	186.984i	1.25044	+	0.760098i
$247$	−6.96359	−	4.02043i	−0.0281927	−	0.0162771i
$248$	−120.831	−	149.388i	−0.487223	−	0.602372i
$249$	221.523	−	83.7815i	0.889650	−	0.336472i
$250$	−115.254	−	821.204i	−0.461015	−	3.28482i
$251$	−309.467	+	309.467i	−1.23294	+	1.23294i	−0.270106	+	0.962831i	$0.587059\pi$
$251$	−309.467	+	309.467i	−1.23294	+	1.23294i	−0.962831	+	0.270106i	$0.912941\pi$
$252$	−278.710	+	144.544i	−1.10599	+	0.573589i
$253$	−87.7721	+	87.7721i	−0.346925	+	0.346925i
$254$	−119.356	−	89.9771i	−0.469907	−	0.354240i
$255$	−457.294	−	374.064i	−1.79331	−	1.46692i
$256$	112.573	−	229.920i	0.439737	−	0.898127i
$257$	352.709	+	203.637i	1.37241	+	0.792361i	0.991231	−	0.132140i	$-0.0421849\pi$
$257$	352.709	+	203.637i	1.37241	+	0.792361i	0.381179	+	0.924501i	$0.375518\pi$
$258$	220.494	+	64.4516i	0.854629	+	0.249813i
$259$	−175.024	−	46.8976i	−0.675770	−	0.181072i
$260$	−109.071	−	105.409i	−0.419505	−	0.405420i
$261$	−244.961	−	162.543i	−0.938548	−	0.622769i
$262$	209.534	+	84.7035i	0.799748	+	0.323296i
$263$	193.599	+	335.324i	0.736119	+	1.27500i	0.954231	+	0.299072i	$0.0966769\pi$
$263$	193.599	+	335.324i	0.736119	+	1.27500i	−0.218112	+	0.975924i	$0.569990\pi$
$264$	213.607	+	1.17693i	0.809118	+	0.00445807i
$265$	494.787	+	285.665i	1.86712	+	1.07798i
$266$	−28.1099	+	21.9533i	−0.105676	+	0.0825311i
$267$	190.039	+	264.302i	0.711756	+	0.989895i
$268$	−123.062	+	73.8796i	−0.459187	+	0.275670i
$269$	361.010	+	361.010i	1.34204	+	1.34204i	0.894023	+	0.448022i	$0.147871\pi$
$269$	361.010	+	361.010i	1.34204	+	1.34204i	0.448022	+	0.894023i	$0.352129\pi$
$270$	−44.1181	+	518.873i	−0.163400	+	1.92175i
$271$	−226.147			−0.834489			−0.417244	−	0.908794i	$-0.637004\pi$
$271$	−226.147			−0.834489			−0.417244	+	0.908794i	$0.637004\pi$
$272$	−172.937	−	277.225i	−0.635796	−	1.01921i
$273$	−16.5961	+	101.535i	−0.0607916	+	0.371922i
$274$	−13.9807	+	113.685i	−0.0510246	+	0.414910i
$275$	584.570	−	156.635i	2.12571	−	0.569582i
$276$	−61.8663	−	155.501i	−0.224153	−	0.563410i
$277$	−30.8872	+	115.273i	−0.111506	+	0.416147i	−0.999002	−	0.0446692i	$-0.985777\pi$
$277$	−30.8872	+	115.273i	−0.111506	+	0.416147i	0.887496	+	0.460816i	$0.152443\pi$
$278$	−218.373	−	88.2767i	−0.785514	−	0.317542i
$279$	143.042	+	162.056i	0.512696	+	0.580846i
$280$	−614.804	+	273.308i	−2.19573	+	0.976102i
$281$	96.3536	+	166.889i	0.342895	+	0.593912i	0.984969	−	0.172731i	$-0.0552590\pi$
$281$	96.3536	+	166.889i	0.342895	+	0.593912i	−0.642074	+	0.766643i	$0.721926\pi$
$282$	105.939	+	193.453i	0.375670	+	0.686002i
$283$	130.006	−	34.8350i	0.459384	−	0.123092i	−0.0217027	−	0.999764i	$-0.506909\pi$
$283$	130.006	−	34.8350i	0.459384	−	0.123092i	0.481087	+	0.876673i	$0.340242\pi$
$284$	−25.0507	−	87.4875i	−0.0882066	−	0.308054i
$285$	5.89296	+	58.8634i	0.0206770	+	0.206538i
$286$	42.1365	−	55.8949i	0.147330	−	0.195437i
$287$		−	523.242i		−	1.82314i
$288$	−115.395	+	263.871i	−0.400677	+	0.916220i
$289$	−128.034			−0.443025
$290$	−503.069	−	379.240i	−1.73472	−	1.30772i
$291$	12.8780	−	28.5441i	0.0442543	−	0.0980899i
$292$	300.319	−	85.9915i	1.02849	−	0.294492i
$293$	109.866	+	410.025i	0.374969	+	1.39940i	0.853390	+	0.521273i	$0.174543\pi$
$293$	109.866	+	410.025i	0.374969	+	1.39940i	−0.478421	+	0.878130i	$0.658791\pi$
$294$	138.733	+	84.3305i	0.471879	+	0.286839i
$295$	−507.141	+	292.798i	−1.71912	+	0.992535i
$296$	−151.883	+	67.5192i	−0.513120	+	0.228105i
$297$	−240.143	+	9.01927i	−0.808561	+	0.0303679i
$298$	−69.4933	+	171.908i	−0.233199	+	0.576872i
$299$	−52.9723	−	14.1939i	−0.177165	−	0.0474712i
$300$	−117.855	+	807.392i	−0.392850	+	2.69131i
$301$	−86.4212	−	322.528i	−0.287114	−	1.07152i
$302$	−101.202	−	12.4456i	−0.335106	−	0.0412105i
$303$	−64.2953	−	170.000i	−0.212196	−	0.561057i
$304$	−7.38403	+	31.8732i	−0.0242896	+	0.104846i
$305$		−	188.821i		−	0.619084i
$306$	207.796	+	303.216i	0.679071	+	0.990902i
$307$	320.318	−	320.318i	1.04338	−	1.04338i	0.0443664	−	0.999015i	$-0.485873\pi$
$307$	320.318	−	320.318i	1.04338	−	1.04338i	0.999015	−	0.0443664i	$-0.0141269\pi$
$308$	−159.812	−	266.202i	−0.518872	−	0.864291i
$309$	31.4456	+	314.103i	0.101766	+	1.01651i
$310$	285.116	+	365.075i	0.919729	+	1.17766i
$311$	174.040	−	301.447i	0.559615	−	0.969281i	−0.437914	−	0.899017i	$-0.644282\pi$
$311$	174.040	−	301.447i	0.559615	−	0.969281i	0.997528	−	0.0702643i	$-0.0223843\pi$
$312$	46.7363	+	81.9897i	0.149796	+	0.262787i
$313$	193.014	−	111.437i	0.616657	−	0.356027i	−0.158909	−	0.987293i	$-0.550798\pi$
$313$	193.014	−	111.437i	0.616657	−	0.356027i	0.775566	+	0.631266i	$0.217464\pi$
$314$	−31.3189	+	77.4745i	−0.0997416	+	0.246734i
$315$	677.781	−	336.954i	2.15168	−	1.06969i
$316$	55.1638	−	57.0803i	0.174569	−	0.180634i
$317$	66.4963	−	248.167i	0.209767	−	0.782863i	−0.778176	−	0.628046i	$-0.783855\pi$
$317$	66.4963	−	248.167i	0.209767	−	0.782863i	0.987943	−	0.154816i	$-0.0494785\pi$
$318$	−245.618	−	256.970i	−0.772382	−	0.808080i
$319$	145.365	−	251.780i	0.455691	−	0.789280i
$320$	−280.820	+	549.591i	−0.877563	+	1.71747i
$321$	−382.626	−	62.5411i	−1.19198	−	0.194832i
$322$	−146.432	+	194.246i	−0.454759	+	0.603247i
$323$	29.5277	+	29.5277i	0.0914169	+	0.0914169i
$324$	116.923	−	302.167i	0.360874	−	0.932614i
$325$	189.065	+	189.065i	0.581738	+	0.581738i
$326$	15.9870	−	2.24372i	0.0490398	−	0.00688259i
$327$	−372.482	−	60.8829i	−1.13909	−	0.186186i
$328$	−301.845	−	373.182i	−0.920258	−	1.13775i
$329$	160.296	−	277.640i	0.487220	−	0.843891i
$330$	−514.853	−	11.6290i	−1.56016	−	0.0352393i
$331$	−11.8727	+	44.3094i	−0.0358691	+	0.133865i	−0.981539	−	0.191264i	$-0.938741\pi$
$331$	−11.8727	+	44.3094i	−0.0358691	+	0.133865i	0.945669	+	0.325130i	$0.105408\pi$
$332$	−315.736	+	5.39121i	−0.951013	+	0.0162386i
$333$	167.441	−	83.2423i	0.502827	−	0.249977i
$334$	−281.944	+	119.615i	−0.844142	+	0.358128i
$335$	299.683	−	173.022i	0.894576	−	0.516484i
$336$	414.867	−	55.8964i	1.23472	−	0.166358i
$337$	−121.097	+	209.747i	−0.359339	+	0.622394i	−0.987851	−	0.155407i	$-0.950331\pi$
$337$	−121.097	+	209.747i	−0.359339	+	0.622394i	0.628511	+	0.777800i	$0.283665\pi$
$338$	−304.778	−	37.4808i	−0.901711	−	0.110890i
$339$	−4.84473	−	48.3929i	−0.0142912	−	0.142752i
$340$	405.454	+	675.370i	1.19251	+	1.98638i
$341$	−151.154	+	151.154i	−0.443267	+	0.443267i
$342$	6.75615	−	36.1817i	0.0197548	−	0.105794i
$343$			191.353i			0.557881i
$344$	−247.695	−	180.177i	−0.720044	−	0.523770i
$345$	142.729	+	377.383i	0.413707	+	1.09386i
$346$	−43.6679	+	34.1037i	−0.126208	+	0.0985657i
$347$	−5.72586	−	21.3692i	−0.0165010	−	0.0615828i	0.957184	−	0.289479i	$-0.0934820\pi$
$347$	−5.72586	−	21.3692i	−0.0165010	−	0.0615828i	−0.973685	+	0.227896i	$0.926815\pi$
$348$	234.229	+	314.298i	0.673073	+	0.903154i
$349$	−49.8135	−	13.3475i	−0.142732	−	0.0382450i	0.186746	−	0.982408i	$-0.440206\pi$
$349$	−49.8135	−	13.3475i	−0.142732	−	0.0382450i	−0.329478	+	0.944163i	$0.606873\pi$
$350$	1091.81	−	463.201i	3.11946	−	1.32343i
$351$	−56.4993	−	89.8901i	−0.160967	−	0.256097i
$352$	−267.545	−	97.6663i	−0.760071	−	0.277461i
$353$	543.350	−	313.703i	1.53924	−	0.888678i	0.540351	−	0.841439i	$-0.318291\pi$
$353$	543.350	−	313.703i	1.53924	−	0.888678i	0.998884	−	0.0472383i	$-0.0150420\pi$
$354$	353.974	−	86.3293i	0.999926	−	0.243868i
$355$	56.7838	+	211.920i	0.159954	+	0.596958i
$356$	−119.479	−	417.272i	−0.335616	−	1.17211i
$357$	219.726	−	487.024i	0.615479	−	1.36421i
$358$	35.8862	+	255.696i	0.100241	+	0.714234i
$359$	619.161			1.72468			0.862341	−	0.506328i	$-0.168998\pi$
$359$	619.161			1.72468			0.862341	+	0.506328i	$0.168998\pi$
$360$	289.021	−	631.314i	0.802836	−	1.75365i
$361$			356.819i			0.988417i
$362$	−8.58711	−	61.1848i	−0.0237213	−	0.169019i
$363$	12.4863	+	124.723i	0.0343976	+	0.343590i
$364$	66.5500	−	119.952i	0.182830	−	0.329538i
$365$	−727.459	+	194.922i	−1.99304	+	0.534033i
$366$	−32.9612	+	112.763i	−0.0900578	+	0.308095i
$367$	−83.2812	−	144.247i	−0.226924	−	0.393044i	0.729971	−	0.683478i	$-0.239534\pi$
$367$	−83.2812	−	144.247i	−0.226924	−	0.393044i	−0.956895	+	0.290434i	$0.906200\pi$
$368$	7.61807	+	223.011i	0.0207013	+	0.606009i
$369$	357.329	+	404.826i	0.968371	+	1.09709i
$370$	368.895	−	156.504i	0.997013	−	0.422984i
$371$	−133.729	+	499.085i	−0.360456	+	1.34524i
$372$	−106.541	−	267.792i	−0.286401	−	0.719870i
$373$	−284.269	+	76.1698i	−0.762117	+	0.204209i	−0.618886	−	0.785481i	$-0.712416\pi$
$373$	−284.269	+	76.1698i	−0.762117	+	0.204209i	−0.143231	+	0.989689i	$0.545749\pi$
$374$	−286.499	+	223.750i	−0.766041	+	0.598263i
$375$	200.652	−	1227.59i	0.535072	−	3.27357i
$376$	−45.8388	−	290.486i	−0.121912	−	0.772570i
$377$	128.447			0.340709
$378$	−463.587	+	82.9116i	−1.22642	+	0.219343i
$379$	−126.432	−	126.432i	−0.333593	−	0.333593i	0.520356	−	0.853949i	$-0.325799\pi$
$379$	−126.432	−	126.432i	−0.333593	−	0.333593i	−0.853949	+	0.520356i	$0.825799\pi$
$380$	19.1111	−	76.5267i	0.0502924	−	0.201386i
$381$	−130.888	−	182.037i	−0.343539	−	0.477787i
$382$	−437.552	−	53.8090i	−1.14542	−	0.140861i
$383$	630.939	+	364.273i	1.64736	+	0.951103i	0.978116	+	0.208060i	$0.0667149\pi$
$383$	630.939	+	364.273i	1.64736	+	0.951103i	0.669243	+	0.743043i	$0.266618\pi$
$384$	263.643	−	279.192i	0.686570	−	0.727064i
$385$	374.272	+	648.258i	0.972136	+	1.68379i
$386$	92.9238	−	39.4230i	0.240735	−	0.102132i
$387$	287.122	+	190.519i	0.741918	+	0.492296i
$388$	−29.0154	+	30.0235i	−0.0747821	+	0.0773803i
$389$	30.6634	+	8.21624i	0.0788262	+	0.0211214i	0.298017	−	0.954561i	$-0.403675\pi$
$389$	30.6634	+	8.21624i	0.0788262	+	0.0211214i	−0.219190	+	0.975682i	$0.570342\pi$
$390$	−109.284	−	199.560i	−0.280214	−	0.511693i
$391$	246.647	+	142.402i	0.630812	+	0.364199i
$392$	−136.133	−	168.306i	−0.347278	−	0.429353i
$393$	262.404	+	214.645i	0.667694	+	0.546171i
$394$	−406.617	+	57.0675i	−1.03202	+	0.144841i
$395$	−135.322	+	135.322i	−0.342587	+	0.342587i
$396$	305.438	+	96.8192i	0.771308	+	0.244493i
$397$	113.569	−	113.569i	0.286068	−	0.286068i	−0.549455	−	0.835523i	$-0.685165\pi$
$397$	113.569	−	113.569i	0.286068	−	0.286068i	0.835523	+	0.549455i	$0.185165\pi$
$398$	52.1742	−	69.2102i	0.131091	−	0.173895i
$399$	−50.0407	+	18.9257i	−0.125415	+	0.0474329i
$400$	511.483	−	960.198i	1.27871	−	2.40050i
$401$	−343.971	−	198.592i	−0.857783	−	0.495242i	0.00548594	−	0.999985i	$-0.498254\pi$
$401$	−343.971	−	198.592i	−0.857783	−	0.495242i	−0.863269	+	0.504743i	$0.831587\pi$
$402$	−209.172	+	51.0143i	−0.520330	+	0.126901i
$403$	−91.2246	−	24.4436i	−0.226364	−	0.0606540i
$404$	4.13730	+	242.301i	0.0102408	+	0.599756i
$405$	−294.281	+	723.563i	−0.726620	+	1.78658i
$406$	213.533	−	528.223i	0.525942	−	1.30104i
$407$	92.4616	+	160.148i	0.227178	+	0.393485i
$408$	−124.241	−	474.105i	−0.304511	−	1.16202i
$409$	−448.224	−	258.782i	−1.09590	−	0.632720i	−0.160761	−	0.986993i	$-0.551395\pi$
$409$	−448.224	−	258.782i	−1.09590	−	0.632720i	−0.935142	+	0.354274i	$0.884728\pi$
$410$	712.239	+	911.981i	1.73717	+	2.22434i
$411$	−70.6570	+	156.612i	−0.171915	+	0.381050i
$412$	101.980	−	408.356i	0.247523	−	0.991157i
$413$	−374.478	−	374.478i	−0.906726	−	0.906726i
$414$	−19.3598	−	250.286i	−0.0467628	−	0.604557i
$415$	761.306			1.83447
$416$	−21.7330	−	123.942i	−0.0522427	−	0.297937i
$417$	−273.473	−	223.700i	−0.655810	−	0.536450i
$418$	36.1277	+	4.44289i	0.0864299	+	0.0106289i
$419$	−419.976	+	112.532i	−1.00233	+	0.268573i	−0.722421	−	0.691453i	$-0.756971\pi$
$419$	−419.976	+	112.532i	−1.00233	+	0.268573i	−0.279909	+	0.960027i	$0.590304\pi$
$420$	−1002.34	+	117.663i	−2.38653	+	0.280150i
$421$	159.837	−	596.521i	0.379661	−	1.41692i	−0.466752	−	0.884388i	$-0.654576\pi$
$421$	159.837	−	596.521i	0.379661	−	1.41692i	0.846413	−	0.532527i	$-0.178758\pi$
$422$	243.025	−	601.178i	0.575888	−	1.42459i
$423$	65.5852	+	324.275i	0.155048	+	0.766608i
$424$	192.532	+	433.098i	0.454085	+	1.02146i
$425$	−694.284	−	1202.54i	−1.63361	−	2.82950i
$426$	3.08244	−	136.470i	0.00723578	−	0.320352i
$427$	164.944	−	44.1966i	0.386286	−	0.103505i
$428$	452.029	+	250.788i	1.05614	+	0.585954i
$429$	85.2482	−	61.2954i	0.198714	−	0.142880i
$430$	589.654	+	444.512i	1.37129	+	1.03375i
$431$		−	427.020i		−	0.990765i	−0.868675	−	0.495382i	$-0.835028\pi$
$431$		−	427.020i		−	0.990765i	0.868675	−	0.495382i	$-0.164972\pi$
$432$	−282.806	+	326.565i	−0.654644	+	0.755938i
$433$	−598.712			−1.38271			−0.691353	−	0.722517i	$-0.742985\pi$
$433$	−598.712			−1.38271			−0.691353	+	0.722517i	$0.742985\pi$
$434$	−252.174	+	334.514i	−0.581047	+	0.770770i
$435$	−551.675	−	767.257i	−1.26822	−	1.76381i
$436$	440.044	+	244.139i	1.00928	+	0.559952i
$437$	−7.38099	−	27.5462i	−0.0168901	−	0.0630349i
$438$	468.462	+	10.5811i	1.06955	+	0.0241578i
$439$	109.152	−	63.0187i	0.248637	−	0.143551i	−0.370503	−	0.928831i	$-0.620815\pi$
$439$	109.152	−	63.0187i	0.248637	−	0.143551i	0.619140	+	0.785281i	$0.287481\pi$
$440$	640.899	+	246.437i	1.45659	+	0.560085i
$441$	161.157	+	182.578i	0.365435	+	0.414010i
$442$	−148.899	−	60.1921i	−0.336876	−	0.136181i
$443$	−172.539	−	46.2316i	−0.389478	−	0.104360i	0.0587654	−	0.998272i	$-0.481284\pi$
$443$	−172.539	−	46.2316i	−0.389478	−	0.104360i	−0.448244	+	0.893911i	$0.647950\pi$
$444$	−247.622	+	29.0679i	−0.557708	+	0.0654682i
$445$	270.831	+	1010.76i	0.608609	+	2.27136i
$446$	88.8995	−	722.893i	0.199326	−	1.62084i
$447$	−176.101	+	215.284i	−0.393962	+	0.481619i
$448$	−545.825	−	116.669i	−1.21836	−	0.260422i
$449$			219.897i			0.489748i	0.969555	+	0.244874i	$0.0787466\pi$
$449$			219.897i			0.489748i	−0.969555	+	0.244874i	$0.921253\pi$
$450$	−528.396	+	1103.99i	−1.17421	+	2.45330i
$451$	−377.593	+	377.593i	−0.837235	+	0.837235i
$452$	−15.7117	+	62.9142i	−0.0347603	+	0.139191i
$453$	−139.415	−	62.8984i	−0.307759	−	0.138849i
$454$	−505.971	+	395.153i	−1.11447	+	0.870382i
$455$	−165.356	+	286.405i	−0.363420	+	0.629462i
$456$	−24.7718	+	42.3653i	−0.0543242	+	0.0929063i
$457$	465.977	−	269.032i	1.01964	−	0.588692i	0.105643	−	0.994404i	$-0.466310\pi$
$457$	465.977	−	269.032i	1.01964	−	0.588692i	0.914001	+	0.405712i	$0.132977\pi$
$458$	723.471	+	292.461i	1.57963	+	0.638561i
$459$	162.596	+	526.859i	0.354239	+	1.14784i
$460$	−9.18438	−	537.884i	−0.0199660	−	1.16931i
$461$	−104.571	+	390.266i	−0.226836	+	0.846564i	0.754824	+	0.655927i	$0.227722\pi$
$461$	−104.571	+	390.266i	−0.226836	+	0.846564i	−0.981661	+	0.190637i	$0.938945\pi$
$462$	−110.351	−	452.471i	−0.238856	−	0.979375i
$463$	410.209	−	710.503i	0.885980	−	1.53456i	0.0413942	−	0.999143i	$-0.486820\pi$
$463$	410.209	−	710.503i	0.885980	−	1.53456i	0.844586	−	0.535420i	$-0.179847\pi$
$464$	−152.424	−	499.916i	−0.328501	−	1.07741i
$465$	245.796	+	649.899i	0.528594	+	1.39763i
$466$	140.729	+	106.088i	0.301993	+	0.227658i
$467$	66.4642	+	66.4642i	0.142322	+	0.142322i	0.774678	−	0.632356i	$-0.217912\pi$
$467$	66.4642	+	66.4642i	0.142322	+	0.142322i	−0.632356	+	0.774678i	$0.717912\pi$
$468$	30.4277	+	138.253i	0.0650165	+	0.295413i
$469$	221.289	+	221.289i	0.471831	+	0.471831i
$470$	98.5385	+	702.106i	0.209656	+	1.49384i
$471$	−79.3644	+	97.0229i	−0.168502	+	0.205993i
$472$	−483.108	−	51.0551i	−1.02353	−	0.108168i
$473$	−170.385	+	295.115i	−0.360222	+	0.623922i
$474$	104.436	−	57.1914i	0.220329	−	0.120657i
$475$	−35.9862	+	134.302i	−0.0757605	+	0.282742i
$476$	−495.065	+	512.266i	−1.04005	+	1.07619i
$477$	−237.367	−	477.462i	−0.497624	−	1.00097i
$478$	326.391	+	769.335i	0.682826	+	1.60949i
$479$	−402.738	+	232.521i	−0.840788	+	0.485429i	−0.857532	−	0.514430i	$-0.828003\pi$
$479$	−402.738	+	232.521i	−0.840788	+	0.485429i	0.0167438	+	0.999860i	$0.494670\pi$
$480$	−647.004	+	662.144i	−1.34793	+	1.37947i
$481$	−40.8502	+	70.7547i	−0.0849277	+	0.147099i
$482$	9.92116	−	80.6747i	0.0205833	−	0.167375i
$483$	−296.254	+	213.013i	−0.613363	+	0.441021i
$484$	40.4937	−	162.149i	0.0836647	−	0.335019i
$485$	71.1777	−	71.1777i	0.146758	−	0.146758i
$486$	302.051	−	380.738i	0.621504	−	0.783411i
$487$		−	262.515i		−	0.539045i	−0.962994	−	0.269522i	$-0.913134\pi$
$487$		−	262.515i		−	0.539045i	0.962994	−	0.269522i	$-0.0868658\pi$
$488$	92.1440	−	126.674i	0.188820	−	0.259577i
$489$	23.8983	+	3.90624i	0.0488719	+	0.00798821i
$490$	321.222	+	411.307i	0.655556	+	0.839402i
$491$	−77.3859	−	288.808i	−0.157609	−	0.588204i	−0.998868	−	0.0475716i	$-0.984852\pi$
$491$	−77.3859	−	288.808i	−0.157609	−	0.588204i	0.841259	−	0.540632i	$-0.181815\pi$
$492$	−266.147	−	668.961i	−0.540949	−	1.35968i
$493$	−644.332	−	172.648i	−1.30696	−	0.350199i
$494$	6.28082	+	14.8045i	0.0127142	+	0.0299686i
$495$	−732.275	−	245.955i	−1.47934	−	0.496879i
$496$	13.1192	+	384.052i	0.0264501	+	0.774299i
$497$	−171.831	+	99.2068i	−0.345737	+	0.199611i
$498$	−454.649	−	132.896i	−0.912949	−	0.266860i
$499$	−81.8323	−	305.402i	−0.163993	−	0.612029i	−0.998167	−	0.0605272i	$-0.980722\pi$
$499$	−81.8323	−	305.402i	−0.163993	−	0.612029i	0.834174	−	0.551501i	$-0.185945\pi$
$500$	−804.610	+	1450.26i	−1.60922	+	2.90051i
$501$	−457.116	+	45.7630i	−0.912408	+	0.0913433i
$502$	866.810	−	121.654i	1.72671	−	0.242339i
$503$	−67.4820			−0.134159			−0.0670795	−	0.997748i	$-0.521368\pi$
$503$	−67.4820			−0.134159			−0.0670795	+	0.997748i	$0.521368\pi$
$504$	619.133	+	104.704i	1.22844	+	0.207747i
$505$		−	584.239i		−	1.15691i
$506$	245.848	−	34.5040i	0.485865	−	0.0681897i
$507$	−419.859	−	189.424i	−0.828124	−	0.373617i
$508$	82.2909	+	287.394i	0.161990	+	0.565737i
$509$	186.107	−	49.8672i	0.365633	−	0.0979710i	−0.0713249	−	0.997453i	$-0.522723\pi$
$509$	186.107	−	49.8672i	0.365633	−	0.0979710i	0.436957	+	0.899482i	$0.356056\pi$
$510$	279.969	+	1147.95i	0.548958	+	2.25088i
$511$	−340.548	−	589.846i	−0.666434	−	1.15430i
$512$	−456.592	+	231.663i	−0.891781	+	0.452467i
$513$	25.7913	−	48.8161i	0.0502754	−	0.0951581i
$514$	−318.127	−	749.855i	−0.618923	−	1.45886i
$515$	−262.630	+	980.148i	−0.509961	+	1.90320i
$516$	−274.543	−	368.393i	−0.532061	−	0.713939i
$517$	−316.033	+	84.6807i	−0.611282	+	0.163792i
$518$	223.060	+	285.615i	0.430617	+	0.551381i
$519$	−77.7367	+	29.4006i	−0.149782	+	0.0566485i
$520$	47.2860	+	299.657i	0.0909347	+	0.576264i
$521$	861.429			1.65341			0.826707	−	0.562632i	$-0.190211\pi$
$521$	861.429			1.65341			0.826707	+	0.562632i	$0.190211\pi$
$522$	195.523	+	554.505i	0.374564	+	1.06227i
$523$	−9.70560	−	9.70560i	−0.0185576	−	0.0185576i	0.697767	−	0.716325i	$-0.254177\pi$
$523$	−9.70560	−	9.70560i	−0.0185576	−	0.0185576i	−0.716325	+	0.697767i	$0.754177\pi$
$524$	−232.657	−	387.540i	−0.444002	−	0.739580i
$525$	1770.16	−	177.215i	3.37173	−	0.337552i
$526$	94.5213	−	768.607i	0.179698	−	1.46123i
$527$	424.757	+	245.233i	0.805990	+	0.465338i
$528$	−339.723	−	259.049i	−0.643415	−	0.490622i
$529$	167.250	+	289.685i	0.316162	+	0.547609i
$530$	−446.273	−	1051.91i	−0.842025	−	1.98474i
$531$	545.465	+	33.9934i	1.02724	+	0.0640178i
$532$	71.3230	−	1.21784i	0.134066	−	0.00228918i
$533$	−227.885	−	61.0616i	−0.427552	−	0.114562i
$534$	14.7017	−	650.895i	0.0275313	−	1.21891i
$535$	−1079.30	−	623.132i	−2.01738	−	1.16473i
$536$	285.482	+	30.1698i	0.532615	+	0.0562870i
$537$	−62.4764	+	382.230i	−0.116343	+	0.711788i
$538$	−141.916	−	1011.18i	−0.263785	−	1.87952i
$539$	−170.296	+	170.296i	−0.315948	+	0.315948i
$540$	695.147	−	775.547i	1.28731	−	1.43620i
$541$	−29.9877	+	29.9877i	−0.0554301	+	0.0554301i	−0.734278	−	0.678848i	$-0.762479\pi$
$541$	−29.9877	+	29.9877i	−0.0554301	+	0.0554301i	0.678848	+	0.734278i	$0.262479\pi$
$542$	361.166	+	272.265i	0.666357	+	0.502335i
$543$	14.9498	−	91.4629i	0.0275319	−	0.168440i
$544$	−57.5733	+	650.944i	−0.105833	+	1.19659i
$545$	−1050.68	−	606.611i	−1.92786	−	1.11305i
$546$	148.746	−	142.175i	0.272428	−	0.260393i
$547$	1019.12	+	273.072i	1.86310	+	0.499217i	0.999983	−	0.00577947i	$-0.00183967\pi$
$547$	1019.12	+	273.072i	1.86310	+	0.499217i	0.863121	+	0.504997i	$0.168506\pi$
$548$	159.197	−	164.729i	0.290506	−	0.300599i
$549$	−97.4329	+	146.837i	−0.177473	+	0.267463i
$550$	−1122.16	−	453.631i	−2.04029	−	0.824783i
$551$	33.3971	+	57.8454i	0.0606117	+	0.104983i
$552$	−88.4099	+	322.825i	−0.160163	+	0.584828i
$553$	−149.885	−	86.5359i	−0.271039	−	0.156485i
$554$	188.109	−	146.909i	0.339547	−	0.265179i
$555$	598.091	−	59.8763i	1.07764	−	0.107885i
$556$	242.472	+	403.888i	0.436100	+	0.726418i
$557$	78.8086	+	78.8086i	0.141488	+	0.141488i	0.774303	−	0.632815i	$-0.218101\pi$
$557$	78.8086	+	78.8086i	0.141488	+	0.141488i	−0.632815	+	0.774303i	$0.718101\pi$
$558$	−33.3399	−	431.023i	−0.0597489	−	0.772443i
$559$	−150.555			−0.269328
$560$	1310.91	+	303.697i	2.34092	+	0.542317i
$561$	−510.021	+	192.893i	−0.909127	+	0.343838i
$562$	47.0429	−	382.533i	0.0837062	−	0.680663i
$563$	446.283	−	119.581i	0.792688	−	0.212400i	0.160317	−	0.987066i	$-0.448748\pi$
$563$	446.283	−	119.581i	0.792688	−	0.212400i	0.632371	+	0.774666i	$0.282082\pi$
$564$	63.7152	−	436.496i	0.112970	−	0.773928i
$565$	40.4626	−	151.008i	0.0716152	−	0.267272i
$566$	−249.564	−	100.885i	−0.440925	−	0.178243i
$567$	−700.949	−	87.7070i	−1.23624	−	0.154686i
$568$	−65.3221	+	169.881i	−0.115004	+	0.299085i
$569$	101.327	+	175.503i	0.178079	+	0.308441i	0.941222	−	0.337788i	$-0.109679\pi$
$569$	101.327	+	175.503i	0.178079	+	0.308441i	−0.763144	+	0.646229i	$0.776345\pi$
$570$	61.4563	−	101.102i	0.107818	−	0.177372i
$571$	372.354	−	99.7721i	0.652109	−	0.174732i	0.0824269	−	0.996597i	$-0.473733\pi$
$571$	372.354	−	99.7721i	0.652109	−	0.174732i	0.569682	+	0.821865i	$0.307066\pi$
$572$	−134.588	+	38.5370i	−0.235293	+	0.0673724i
$573$	−602.766	−	271.945i	−1.05195	−	0.474598i
$574$	−629.948	+	835.639i	−1.09747	+	1.45582i
$575$			948.292i			1.64920i
$576$	501.974	−	282.486i	0.871482	−	0.490427i
$577$	−297.597			−0.515765			−0.257883	−	0.966176i	$-0.583025\pi$
$577$	−297.597			−0.515765			−0.257883	+	0.966176i	$0.583025\pi$
$578$	204.476	+	154.145i	0.353765	+	0.266686i
$579$	150.658	−	15.0827i	0.260204	−	0.0260496i
$580$	346.844	+	1211.32i	0.598006	+	2.08849i
$581$	178.196	+	665.038i	0.306706	+	1.14464i
$582$	−54.9320	+	30.0820i	−0.0943848	+	0.0516872i
$583$	456.665	−	263.656i	0.783302	−	0.452240i
$584$	−583.150	−	224.232i	−0.998544	−	0.383958i
$585$	−67.6558	−	334.513i	−0.115651	−	0.571817i
$586$	318.182	−	787.099i	0.542973	−	1.34317i
$587$	−516.751	−	138.463i	−0.880325	−	0.235882i	−0.209778	−	0.977749i	$-0.567274\pi$
$587$	−516.751	−	138.463i	−0.880325	−	0.235882i	−0.670547	+	0.741867i	$0.733941\pi$
$588$	−120.033	−	301.704i	−0.204138	−	0.513102i
$589$	−12.7110	−	47.4379i	−0.0215806	−	0.0805398i
$590$	1162.43	+	142.953i	1.97023	+	0.242293i
$591$	−607.836	−	99.3522i	−1.02849	−	0.168109i
$592$	323.853	+	75.0265i	0.547049	+	0.126734i
$593$		−	181.495i		−	0.306063i	−0.988221	−	0.153031i	$-0.951096\pi$
$593$		−	181.495i		−	0.306063i	0.988221	−	0.153031i	$-0.0489035\pi$
$594$	394.376	+	274.711i	0.663933	+	0.462477i
$595$	1214.44	−	1214.44i	2.04108	−	2.04108i
$596$	317.949	−	190.879i	0.533472	−	0.320267i
$597$	105.556	−	75.8971i	0.176811	−	0.127131i
$598$	67.5105	+	86.4433i	0.112894	+	0.144554i
$599$	18.6182	−	32.2477i	0.0310821	−	0.0538358i	−0.850066	−	0.526676i	$-0.823438\pi$
$599$	18.6182	−	32.2477i	0.0310821	−	0.0538358i	0.881148	+	0.472841i	$0.156771\pi$
$600$	1160.27	−	1147.55i	1.93378	−	1.91258i
$601$	−583.511	+	336.890i	−0.970901	+	0.560550i	−0.899511	−	0.436899i	$-0.856077\pi$
$601$	−583.511	+	336.890i	−0.970901	+	0.560550i	−0.0713901	+	0.997448i	$0.522744\pi$
$602$	−250.284	+	619.137i	−0.415755	+	1.02847i
$603$	−322.330	−	20.0876i	−0.534544	−	0.0333128i
$604$	146.640	+	141.717i	0.242782	+	0.234630i
$605$	−104.284	+	389.194i	−0.172371	+	0.643296i
$606$	−101.987	+	348.905i	−0.168295	+	0.575750i
$607$	−85.4343	+	147.977i	−0.140748	+	0.243783i	−0.927779	−	0.373131i	$-0.878284\pi$
$607$	−85.4343	+	147.977i	−0.140748	+	0.243783i	0.787030	+	0.616914i	$0.211618\pi$
$608$	50.1658	−	42.0130i	0.0825096	−	0.0691003i
$609$	541.108	−	661.504i	0.888518	−	1.08621i
$610$	−227.328	+	301.555i	−0.372668	+	0.494352i
$611$	−102.213	−	102.213i	−0.167288	−	0.167288i
$612$	33.1936	−	734.421i	0.0542379	−	1.20003i
$613$	−357.490	−	357.490i	−0.583181	−	0.583181i	0.352595	−	0.935776i	$-0.385299\pi$
$613$	−357.490	−	357.490i	−0.583181	−	0.583181i	−0.935776	+	0.352595i	$0.885299\pi$
$614$	−897.203	+	125.920i	−1.46124	+	0.205081i
$615$	614.015	+	1623.49i	0.998399	+	2.63982i
$616$	−65.2618	+	617.539i	−0.105944	+	1.00250i
$617$	−425.433	+	736.871i	−0.689518	+	1.19428i	0.282476	+	0.959274i	$0.408844\pi$
$617$	−425.433	+	736.871i	−0.689518	+	1.19428i	−0.971994	+	0.235006i	$0.924489\pi$
$618$	327.939	−	539.494i	0.530646	−	0.872968i
$619$	−74.1354	+	276.677i	−0.119766	+	0.446974i	−0.999599	−	0.0283089i	$-0.990988\pi$
$619$	−74.1354	+	276.677i	−0.119766	+	0.446974i	0.879833	+	0.475283i	$0.157654\pi$
$620$	−15.8166	−	926.301i	−0.0255107	−	1.49403i
$621$	83.7390	−	367.122i	0.134845	−	0.591179i
$622$	−640.871	+	271.890i	−1.03034	+	0.437122i
$623$	−819.551	+	473.168i	−1.31549	+	0.759499i
$624$	24.0702	−	187.208i	0.0385740	−	0.300013i
$625$	1149.26	−	1990.58i	1.83882	−	3.18493i
$626$	−442.413	−	54.4068i	−0.706731	−	0.0869119i
$627$	49.7691	+	22.4539i	0.0793765	+	0.0358116i
$628$	143.292	−	86.0243i	0.228172	−	0.136981i
$629$	300.020	−	300.020i	0.476980	−	0.476980i
$630$	−1488.11	−	277.873i	−2.36209	−	0.441069i
$631$			193.264i			0.306282i	0.988204	+	0.153141i	$0.0489389\pi$
$631$			193.264i			0.306282i	−0.988204	+	0.153141i	$0.951061\pi$
$632$	−156.820	+	24.7462i	−0.248133	+	0.0391554i
$633$	615.843	−	752.868i	0.972895	−	1.18936i
$634$	−404.974	+	316.277i	−0.638761	+	0.498859i
$635$	−186.534	−	696.153i	−0.293754	−	1.09630i
$636$	82.8875	+	706.098i	0.130326	+	1.11022i
$637$	−102.777	−	27.5390i	−0.161345	−	0.0432324i
$638$	−535.282	+	227.094i	−0.839000	+	0.355946i
$639$	65.1943	−	194.101i	0.102026	−	0.303758i
$640$	1110.15	−	539.632i	1.73461	−	0.843174i
$641$	844.914	−	487.811i	1.31812	−	0.761016i	0.334693	−	0.942327i	$-0.391367\pi$
$641$	844.914	−	487.811i	1.31812	−	0.761016i	0.983426	+	0.181311i	$0.0580341\pi$
$642$	535.775	+	560.537i	0.834540	+	0.873111i
$643$	−87.1467	−	325.236i	−0.135531	−	0.505810i	−0.999995	−	0.00311486i	$-0.999009\pi$
$643$	−87.1467	−	325.236i	−0.135531	−	0.505810i	0.864464	−	0.502695i	$-0.167658\pi$
$644$	467.718	−	133.924i	0.726270	−	0.207956i
$645$	646.625	+	899.312i	1.00252	+	1.39428i
$646$	−11.6076	−	82.7063i	−0.0179684	−	0.128028i
$647$	136.600			0.211129			0.105564	−	0.994412i	$-0.466335\pi$
$647$	136.600			0.211129			0.105564	+	0.994412i	$0.466335\pi$
$648$	−550.520	+	341.806i	−0.849569	+	0.527478i
$649$			540.478i			0.832785i
$650$	−74.3231	−	529.566i	−0.114343	−	0.814718i
$651$	−510.185	+	366.834i	−0.783695	+	0.563494i
$652$	−28.2332	−	15.6639i	−0.0433024	−	0.0240244i
$653$	−614.540	+	164.666i	−0.941103	+	0.252168i	−0.696583	−	0.717476i	$-0.745297\pi$
$653$	−614.540	+	164.666i	−0.941103	+	0.252168i	−0.244520	+	0.969644i	$0.578630\pi$
$654$	521.570	+	545.676i	0.797507	+	0.834366i
$655$	544.871	+	943.744i	0.831864	+	1.44083i
$656$	32.7727	+	959.388i	0.0499584	+	1.46248i
$657$	666.292	+	223.793i	1.01414	+	0.340628i
$658$	−590.259	+	250.418i	−0.897050	+	0.380574i
$659$	233.363	−	870.921i	0.354116	−	1.32158i	−0.527477	−	0.849569i	$-0.676862\pi$
$659$	233.363	−	870.921i	0.354116	−	1.32158i	0.881593	−	0.472010i	$-0.156471\pi$
$660$	808.242	+	638.421i	1.22461	+	0.967304i
$661$	931.114	−	249.491i	1.40864	−	0.377445i	0.527204	−	0.849739i	$-0.323240\pi$
$661$	931.114	−	249.491i	1.40864	−	0.377445i	0.881441	+	0.472294i	$0.156574\pi$
$662$	72.3067	−	56.4701i	0.109225	−	0.0853022i
$663$	−186.470	−	152.531i	−0.281251	−	0.230062i
$664$	510.735	+	371.516i	0.769179	+	0.559511i
$665$	−171.975			−0.258608
$666$	−367.629	−	68.6469i	−0.551996	−	0.103073i
$667$	322.126	+	322.126i	0.482947	+	0.482947i
$668$	594.284	+	148.411i	0.889647	+	0.222173i
$669$	449.288	−	995.849i	0.671581	−	1.48856i
$670$	−686.913	−	84.4748i	−1.02524	−	0.126082i
$671$	−150.925	−	87.1364i	−0.224925	−	0.129860i
$672$	−729.856	−	410.204i	−1.08610	−	0.610422i
$673$	141.447	+	244.994i	0.210174	+	0.364033i	0.951769	−	0.306816i	$-0.0992635\pi$
$673$	141.447	+	244.994i	0.210174	+	0.364033i	−0.741595	+	0.670848i	$0.765930\pi$
$674$	445.919	−	189.181i	0.661600	−	0.280684i
$675$	−1248.53	+	1345.97i	−1.84967	+	1.99404i
$676$	441.619	+	426.791i	0.653283	+	0.631348i
$677$	630.350	+	168.902i	0.931094	+	0.249486i	0.692321	−	0.721590i	$-0.256588\pi$
$677$	630.350	+	168.902i	0.931094	+	0.249486i	0.238773	+	0.971076i	$0.423255\pi$
$678$	−50.5246	+	83.1183i	−0.0745201	+	0.122593i
$679$	78.8374	+	45.5168i	0.116108	+	0.0670351i
$680$	165.573	−	1566.74i	0.243490	−	2.30402i
$681$	−900.720	+	340.659i	−1.32264	+	0.500233i
$682$	423.379	−	59.4201i	0.620791	−	0.0871262i
$683$	−111.182	+	111.182i	−0.162785	+	0.162785i	−0.783799	−	0.621014i	$-0.786721\pi$
$683$	−111.182	+	111.182i	−0.162785	+	0.162785i	0.621014	+	0.783799i	$0.286721\pi$
$684$	−54.3502	+	49.6497i	−0.0794593	+	0.0725873i
$685$	−390.527	+	390.527i	−0.570112	+	0.570112i
$686$	230.377	−	305.599i	0.335826	−	0.445480i
$687$	906.016	+	741.118i	1.31880	+	1.07877i
$688$	178.659	+	585.958i	0.259678	+	0.851683i
$689$	201.758	+	116.485i	0.292827	+	0.169064i
$690$	226.400	−	774.532i	0.328116	−	1.12251i
$691$	−1237.17	−	331.499i	−1.79041	−	0.479739i	−0.797993	−	0.602667i	$-0.794105\pi$
$691$	−1237.17	−	331.499i	−1.79041	−	0.479739i	−0.992416	+	0.122928i	$0.960772\pi$
$692$	110.798	−	1.89188i	0.160113	−	0.00273393i
$693$	43.4525	−	697.247i	0.0627020	−	1.00613i
$694$	−16.5827	+	41.0211i	−0.0238943	+	0.0591082i
$695$	−567.856	−	983.555i	−0.817059	−	1.41519i
$696$	4.31936	−	783.943i	0.00620597	−	1.12636i
$697$	1061.07	+	612.609i	1.52234	+	0.878923i
$698$	63.4848	+	81.2887i	0.0909525	+	0.116459i
$699$	154.325	+	214.632i	0.220780	+	0.307056i
$700$	−2301.33	−	574.715i	−3.28762	−	0.821022i
$701$	184.271	+	184.271i	0.262869	+	0.262869i	0.826219	−	0.563350i	$-0.190488\pi$
$701$	184.271	+	184.271i	0.262869	+	0.262869i	−0.563350	+	0.826219i	$0.690488\pi$
$702$	−17.9899	+	211.580i	−0.0256267	+	0.301396i
$703$	−42.4853			−0.0604342
$704$	309.697	+	478.084i	0.439910	+	0.679096i
$705$	−171.552	+	1049.55i	−0.243336	+	1.48873i
$706$	−1245.43	−	153.160i	−1.76407	−	0.216940i
$707$	510.361	−	136.751i	0.721868	−	0.193424i
$708$	−669.246	−	288.289i	−0.945263	−	0.407188i
$709$	19.8003	−	73.8959i	0.0279271	−	0.104226i	−0.950555	−	0.310555i	$-0.899485\pi$
$709$	19.8003	−	73.8959i	0.0279271	−	0.104226i	0.978483	+	0.206329i	$0.0661518\pi$
$710$	164.452	−	406.809i	0.231622	−	0.572971i
$711$	175.061	−	35.4063i	0.246218	−	0.0497980i
$712$	−311.555	+	810.247i	−0.437577	+	1.13799i
$713$	−167.477	−	290.078i	−0.234890	−	0.406841i
$714$	−937.256	+	513.262i	−1.31268	+	0.718855i
$715$	326.010	−	87.3542i	0.455958	−	0.122174i
$716$	250.529	−	451.562i	0.349901	−	0.630673i
$717$	124.873	+	1247.33i	0.174160	+	1.73965i
$718$	−988.826	−	745.428i	−1.37719	−	1.03820i
$719$		−	357.779i		−	0.497606i	−0.968554	−	0.248803i	$-0.919963\pi$
$719$		−	357.779i		−	0.497606i	0.968554	−	0.248803i	$-0.0800372\pi$
$720$	−1221.64	+	660.273i	−1.69672	+	0.917045i
$721$	−917.680			−1.27279
$722$	429.586	−	569.854i	0.594994	−	0.789272i
$723$	50.1404	−	111.136i	0.0693505	−	0.153716i
$724$	−59.9484	+	108.053i	−0.0828017	+	0.149245i
$725$	−574.854	−	2145.39i	−0.792902	−	2.95915i
$726$	130.217	−	214.221i	0.179362	−	0.295070i
$727$	973.372	−	561.977i	1.33889	−	0.773008i	0.352246	−	0.935907i	$-0.385418\pi$
$727$	973.372	−	561.977i	1.33889	−	0.773008i	0.986643	+	0.162899i	$0.0520846\pi$
$728$	−250.697	+	111.446i	−0.344364	+	0.153086i
$729$	602.213	−	410.829i	0.826081	−	0.563552i
$730$	1396.46	+	564.514i	1.91295	+	0.773307i
$731$	755.230	+	202.363i	1.03315	+	0.276831i
$732$	188.399	−	140.404i	0.257376	−	0.191809i
$733$	−15.6674	−	58.4715i	−0.0213743	−	0.0797702i	0.954415	−	0.298483i	$-0.0964807\pi$
$733$	−15.6674	−	58.4715i	−0.0213743	−	0.0797702i	−0.975789	+	0.218713i	$0.929814\pi$
$734$	−40.6605	+	330.634i	−0.0553958	+	0.450455i
$735$	276.923	+	732.200i	0.376766	+	0.996191i
$736$	256.324	−	365.330i	0.348267	−	0.496373i
$737$		−	319.383i		−	0.433355i
$738$	−83.2852	−	1076.72i	−0.112853	−	1.45898i
$739$	−983.126	+	983.126i	−1.33035	+	1.33035i	−0.425288	+	0.905058i	$0.639827\pi$
$739$	−983.126	+	983.126i	−1.33035	+	1.33035i	−0.905058	+	0.425288i	$0.860173\pi$
$740$	−777.561	−	194.182i	−1.05076	−	0.262407i
$741$	2.40296	+	24.0026i	0.00324286	+	0.0323922i
$742$	814.436	−	636.058i	1.09762	−	0.857221i
$743$	−304.062	+	526.651i	−0.409236	+	0.708817i	−0.994804	−	0.101806i	$-0.967538\pi$
$743$	−304.062	+	526.651i	−0.409236	+	0.708817i	0.585569	+	0.810623i	$0.300871\pi$
$744$	−152.252	+	555.943i	−0.204640	+	0.747236i
$745$	−774.275	+	447.028i	−1.03930	+	0.600038i
$746$	545.694	+	220.595i	0.731493	+	0.295704i
$747$	−592.032	−	392.840i	−0.792546	−	0.525890i
$748$	726.932	−	12.4124i	0.971834	−	0.0165941i
$749$	291.709	−	1088.67i	0.389464	−	1.45350i
$750$	−1798.38	+	1718.94i	−2.39785	+	2.29192i
$751$	−36.5757	+	63.3510i	−0.0487027	+	0.0843555i	−0.889349	−	0.457229i	$-0.848842\pi$
$751$	−36.5757	+	63.3510i	−0.0487027	+	0.0843555i	0.840646	+	0.541584i	$0.182175\pi$
$752$	−276.520	+	519.106i	−0.367712	+	0.690301i
$753$	1295.76	+	211.795i	1.72080	+	0.281269i
$754$	−205.136	−	154.642i	−0.272063	−	0.205095i
$755$	−347.644	−	347.644i	−0.460456	−	0.460456i
$756$	840.188	+	425.715i	1.11136	+	0.563115i
$757$	863.777	+	863.777i	1.14105	+	1.14105i	0.988258	+	0.152794i	$0.0488272\pi$
$757$	863.777	+	863.777i	1.14105	+	1.14105i	0.152794	+	0.988258i	$0.451173\pi$
$758$	49.7015	+	354.133i	0.0655693	+	0.467193i
$759$	367.509	+	60.0701i	0.484201	+	0.0791438i
$760$	−122.654	+	99.2078i	−0.161387	+	0.130537i
$761$	−544.208	+	942.596i	−0.715122	+	1.23863i	0.247790	+	0.968814i	$0.420296\pi$
$761$	−544.208	+	942.596i	−0.715122	+	1.23863i	−0.962912	+	0.269815i	$0.913038\pi$
$762$	−10.1258	+	448.301i	−0.0132884	+	0.588322i
$763$	283.975	−	1059.81i	0.372182	−	1.38900i
$764$	634.007	+	612.719i	0.829851	+	0.801988i
$765$	−110.242	+	1768.96i	−0.144107	+	2.31237i
$766$	−569.076	−	1341.37i	−0.742919	−	1.75113i
$767$	−206.796	+	119.394i	−0.269616	+	0.155663i
$768$	−757.178	+	128.474i	−0.985909	+	0.167283i
$769$	−618.315	+	1070.95i	−0.804050	+	1.39266i	0.112880	+	0.993609i	$0.463993\pi$
$769$	−618.315	+	1070.95i	−0.804050	+	1.39266i	−0.916930	+	0.399048i	$0.869341\pi$
$770$	182.731	−	1485.89i	0.237314	−	1.92973i
$771$	−121.711	−	1215.74i	−0.157861	−	1.57684i
$772$	−195.866	−	48.9139i	−0.253712	−	0.0633600i
$773$	507.475	−	507.475i	0.656501	−	0.656501i	−0.298049	−	0.954550i	$-0.596336\pi$
$773$	507.475	−	507.475i	0.656501	−	0.656501i	0.954550	+	0.298049i	$0.0963360\pi$
$774$	−229.175	−	649.942i	−0.296091	−	0.839719i
$775$			1633.07i			2.10719i
$776$	82.4852	−	13.0162i	0.106295	−	0.0167735i
$777$	192.298	+	508.446i	0.247488	+	0.654371i
$778$	−39.0790	−	50.0384i	−0.0502300	−	0.0643167i
$779$	−31.7528	−	118.503i	−0.0407610	−	0.152122i
$780$	−65.7267	+	450.276i	−0.0842650	+	0.577277i
$781$	195.592	+	52.4088i	0.250439	+	0.0671048i
$782$	−222.464	−	524.369i	−0.284481	−	0.670549i
$783$	33.1009	+	881.328i	0.0422745	+	1.12558i
$784$	14.7806	+	432.688i	0.0188528	+	0.551898i
$785$	−348.946	+	201.464i	−0.444518	+	0.256642i
$786$	−160.651	−	658.714i	−0.204391	−	0.838058i
$787$	−118.586	−	442.568i	−0.150681	−	0.562348i	−0.999437	−	0.0335632i	$-0.989314\pi$
$787$	−118.586	−	442.568i	−0.150681	−	0.562348i	0.848756	−	0.528785i	$-0.177352\pi$
$788$	718.089	+	398.400i	0.911281	+	0.505584i
$789$	477.700	−	1058.82i	0.605450	−	1.34198i
$790$	379.034	−	53.1963i	0.479789	−	0.0673371i
$791$	141.384			0.178741
$792$	−371.233	−	522.351i	−0.468729	−	0.659534i
$793$		−	76.9950i		−	0.0970933i
$794$	−318.104	+	44.6450i	−0.400635	+	0.0562279i
$795$	−170.738	−	1705.47i	−0.214765	−	2.14524i
$796$	−166.649	+	47.7173i	−0.209358	+	0.0599463i
$797$	1432.08	−	383.725i	1.79684	−	0.481461i	0.803361	−	0.595492i	$-0.203043\pi$
$797$	1432.08	−	383.725i	1.79684	−	0.481461i	0.993477	+	0.114031i	$0.0363763\pi$
$798$	102.702	+	30.0205i	0.128700	+	0.0376196i
$799$	375.347	+	650.120i	0.469771	+	0.813666i
$800$	−1972.87	+	917.686i	−2.46609	+	1.14711i
$801$	310.945	−	925.768i	0.388196	−	1.15576i
$802$	310.245	+	731.278i	0.386839	+	0.911818i
$803$	−179.904	+	671.411i	−0.224040	+	0.836129i
$804$	395.475	+	170.358i	0.491884	+	0.211888i
$805$	−1132.95	+	303.573i	−1.40739	+	0.377109i
$806$	116.261	+	148.866i	0.144245	+	0.184697i
$807$	247.071	−	1511.58i	0.306159	−	1.87308i
$808$	285.107	−	391.946i	0.352855	−	0.485082i
$809$	−459.616			−0.568129			−0.284065	−	0.958805i	$-0.591683\pi$
$809$	−459.616			−0.568129			−0.284065	+	0.958805i	$0.591683\pi$
$810$	1341.10	−	801.266i	1.65568	−	0.989217i
$811$	394.415	+	394.415i	0.486332	+	0.486332i	0.907147	−	0.420815i	$-0.138256\pi$
$811$	394.415	+	394.415i	0.486332	+	0.486332i	−0.420815	+	0.907147i	$0.638256\pi$
$812$	−976.966	+	586.515i	−1.20316	+	0.722309i
$813$	396.061	+	550.832i	0.487159	+	0.677531i
$814$	45.1427	−	367.081i	0.0554578	−	0.450960i
$815$	67.4115	+	38.9200i	0.0827135	+	0.0477546i
$816$	−372.374	+	906.744i	−0.456341	+	1.11121i
$817$	−39.1451	−	67.8014i	−0.0479133	−	0.0829882i
$818$	404.276	+	952.919i	0.494225	+	1.16494i
$819$	276.377	−	137.399i	0.337457	−	0.167764i
$820$	−39.5109	−	2313.96i	−0.0481841	−	2.82190i
$821$	−656.567	−	175.926i	−0.799716	−	0.214283i	−0.164257	−	0.986418i	$-0.552522\pi$
$821$	−656.567	−	175.926i	−0.799716	−	0.214283i	−0.635459	+	0.772134i	$0.719189\pi$
$822$	301.392	−	165.049i	0.366657	−	0.200790i
$823$	−771.538	−	445.447i	−0.937470	−	0.541248i	−0.0483035	−	0.998833i	$-0.515381\pi$
$823$	−771.538	−	445.447i	−0.937470	−	0.541248i	−0.889166	+	0.457584i	$0.848715\pi$
$824$	−654.500	+	529.386i	−0.794296	+	0.642459i
$825$	−1405.31	−	1149.53i	−1.70340	−	1.39338i
$826$	147.211	+	1048.90i	0.178221	+	1.26986i
$827$	−564.117	+	564.117i	−0.682125	+	0.682125i	−0.960479	−	0.278354i	$-0.910211\pi$
$827$	−564.117	+	564.117i	−0.682125	+	0.682125i	0.278354	+	0.960479i	$0.410211\pi$
$828$	−270.410	+	423.026i	−0.326582	+	0.510901i
$829$	846.986	−	846.986i	1.02170	−	1.02170i	0.0219367	−	0.999759i	$-0.493017\pi$
$829$	846.986	−	846.986i	1.02170	−	1.02170i	0.999759	−	0.0219367i	$-0.00698324\pi$
$830$	−1215.84	−	916.562i	−1.46487	−	1.10429i
$831$	334.868	−	126.649i	0.402970	−	0.152406i
$832$	−114.509	+	224.106i	−0.137632	+	0.269358i
$833$	478.547	+	276.289i	0.574486	+	0.331680i
$834$	167.428	+	686.501i	0.200753	+	0.823143i
$835$	−1426.42	−	382.207i	−1.70828	−	0.457733i
$836$	−52.3485	−	50.5908i	−0.0626178	−	0.0605153i
$837$	144.209	−	632.228i	0.172292	−	0.755350i
$838$	806.201	+	325.905i	0.962054	+	0.388908i
$839$	548.425	+	949.899i	0.653665	+	1.13218i	0.982227	+	0.187698i	$0.0601026\pi$
$839$	548.425	+	949.899i	0.653665	+	1.13218i	−0.328562	+	0.944482i	$0.606564\pi$
$840$	1742.44	+	1018.84i	2.07433	+	1.21290i
$841$	−195.712	−	112.994i	−0.232713	−	0.134357i
$842$	−973.439	+	760.236i	−1.15610	+	0.902893i
$843$	237.749	−	526.972i	0.282028	−	0.625116i
$844$	−1111.90	+	667.522i	−1.31742	+	0.790903i
$845$	−1046.96	−	1046.96i	−1.23901	−	1.23901i
$846$	285.663	−	596.841i	0.337663	−	0.705486i
$847$	−364.390			−0.430212
$848$	213.939	−	923.471i	0.252287	−	1.08900i
$849$	−312.534	−	255.651i	−0.368120	−	0.301120i
$850$	−338.972	+	2756.37i	−0.398790	+	3.24279i
$851$	−279.888	+	74.9957i	−0.328893	+	0.0881266i
$852$	−169.224	+	214.237i	−0.198619	+	0.251452i
$853$	169.181	−	631.393i	0.198337	−	0.740202i	−0.793041	−	0.609168i	$-0.791504\pi$
$853$	169.181	−	631.393i	0.198337	−	0.740202i	0.991378	−	0.131034i	$-0.0418298\pi$
$854$	−316.632	−	127.998i	−0.370764	−	0.149880i
$855$	133.055	−	117.444i	0.155620	−	0.137361i
$856$	−419.977	−	944.733i	−0.490628	−	1.10366i
$857$	26.5621	+	46.0069i	0.0309943	+	0.0536837i	0.881106	−	0.472918i	$-0.156799\pi$
$857$	26.5621	+	46.0069i	0.0309943	+	0.0536837i	−0.850112	+	0.526602i	$0.823466\pi$
$858$	−209.941	−	4.74192i	−0.244686	−	0.00552671i
$859$	−826.689	+	221.511i	−0.962385	+	0.257870i	−0.705610	−	0.708601i	$-0.749327\pi$
$859$	−826.689	+	221.511i	−0.962385	+	0.257870i	−0.256775	+	0.966471i	$0.582660\pi$
$860$	−406.540	−	1419.81i	−0.472721	−	1.65094i
$861$	−1274.48	+	916.377i	−1.48023	+	1.06432i
$862$	−514.103	+	681.969i	−0.596408	+	0.791147i
$863$			509.555i			0.590447i	0.955428	+	0.295223i	$0.0953940\pi$
$863$			509.555i			0.590447i	−0.955428	+	0.295223i	$0.904606\pi$
$864$	844.816	−	181.059i	0.977796	−	0.209559i
$865$	−267.157			−0.308852
$866$	956.168	+	720.809i	1.10412	+	0.832343i
$867$	224.232	+	311.857i	0.258630	+	0.359696i
$868$	805.466	−	230.633i	0.927956	−	0.265706i
$869$	45.7151	+	170.611i	0.0526065	+	0.196330i
$870$	−42.6785	+	1889.52i	−0.0490558	+	2.17186i
$871$	122.201	−	70.5528i	0.140300	−	0.0810021i
$872$	−408.842	−	919.685i	−0.468856	−	1.05468i
$873$	−92.0797	+	18.6233i	−0.105475	+	0.0213325i
$874$	−21.3761	+	52.8787i	−0.0244578	+	0.0605020i
$875$	3492.81	+	935.896i	3.99179	+	1.06960i
$876$	−735.414	−	580.895i	−0.839514	−	0.663122i
$877$	133.688	+	498.931i	0.152438	+	0.568907i	0.999311	+	0.0371115i	$0.0118157\pi$
$877$	133.688	+	498.931i	0.152438	+	0.568907i	−0.846873	+	0.531795i	$0.821518\pi$
$878$	−250.190	−	30.7677i	−0.284955	−	0.0350430i
$879$	806.298	−	985.699i	0.917290	−	1.12139i
$880$	−726.849	−	1165.17i	−0.825964	−	1.32406i
$881$			57.0033i			0.0647030i	0.999477	+	0.0323515i	$0.0102996\pi$
$881$			57.0033i			0.0647030i	−0.999477	+	0.0323515i	$0.989700\pi$
$882$	−37.5620	−	485.607i	−0.0425873	−	0.550575i
$883$	478.007	−	478.007i	0.541344	−	0.541344i	−0.382579	−	0.923923i	$-0.624964\pi$
$883$	478.007	−	478.007i	0.541344	−	0.541344i	0.923923	+	0.382579i	$0.124964\pi$
$884$	165.331	+	275.394i	0.187026	+	0.311532i
$885$	1601.36	+	722.469i	1.80944	+	0.816349i
$886$	219.892	+	281.559i	0.248185	+	0.317787i
$887$	671.080	−	1162.35i	0.756573	−	1.31042i	−0.188015	−	0.982166i	$-0.560206\pi$
$887$	671.080	−	1162.35i	0.756573	−	1.31042i	0.944588	−	0.328257i	$-0.106461\pi$
$888$	430.459	+	251.698i	0.484751	+	0.283444i
$889$	564.462	−	325.892i	0.634940	−	0.366583i
$890$	784.353	−	1940.28i	0.881296	−	2.18009i
$891$	442.541	+	569.127i	0.496679	+	0.638751i
$892$	−1012.29	+	1047.46i	−1.13486	+	1.17428i
$893$	19.4550	−	72.6071i	0.0217861	−	0.0813069i
$894$	540.428	−	131.803i	0.604506	−	0.147431i
$895$	−622.488	+	1078.18i	−0.695517	+	1.20467i
$896$	731.244	+	843.463i	0.816120	+	0.941364i
$897$	58.2002	+	153.885i	0.0648832	+	0.171555i
$898$	264.741	−	351.184i	0.294812	−	0.391074i
$899$	554.739	+	554.739i	0.617062	+	0.617062i
$900$	2173.00	−	1126.96i	2.41444	−	1.25218i
$901$	−855.513	−	855.513i	−0.949515	−	0.949515i
$902$	1057.63	−	148.435i	1.17254	−	0.164562i
$903$	−634.239	+	775.358i	−0.702369	+	0.858646i
$904$	100.837	−	81.5609i	0.111545	−	0.0902222i
$905$	148.953	−	257.995i	0.164589	−	0.285077i
$906$	146.926	+	268.297i	0.162170	+	0.296134i
$907$	−235.273	+	878.052i	−0.259397	+	0.968083i	0.706194	+	0.708018i	$0.250411\pi$
$907$	−235.273	+	878.052i	−0.259397	+	0.968083i	−0.965591	+	0.260065i	$0.916256\pi$
$908$	1283.80	−	21.9209i	1.41387	−	0.0241419i
$909$	−301.472	+	454.335i	−0.331652	+	0.499818i
$910$	608.894	−	258.324i	0.669114	−	0.283872i
$911$	−1020.95	+	589.446i	−1.12069	+	0.647031i	−0.941577	−	0.336797i	$-0.890656\pi$
$911$	−1020.95	+	589.446i	−1.12069	+	0.647031i	−0.179114	+	0.983828i	$0.557323\pi$
$912$	90.5666	−	37.8355i	0.0993055	−	0.0414863i
$913$	351.325	−	608.513i	0.384803	−	0.666498i
$914$	−1068.08	−	131.350i	−1.16858	−	0.143709i
$915$	−459.917	+	330.690i	−0.502641	+	0.361410i
$916$	−803.310	−	1338.08i	−0.876975	−	1.46079i
$917$	−696.870	+	696.870i	−0.759945	+	0.759945i
$918$	374.631	−	1037.17i	0.408095	−	1.12982i
$919$			1362.05i			1.48210i	0.671450	+	0.741050i	$0.265672\pi$
$919$			1362.05i			1.48210i	−0.671450	+	0.741050i	$0.734328\pi$
$920$	−632.908	+	870.081i	−0.687944	+	0.945740i
$921$	−1341.20	−	219.222i	−1.45624	−	0.238026i
$922$	636.860	−	497.374i	0.690737	−	0.539452i
$923$	23.1546	+	86.4142i	0.0250863	+	0.0936232i
$924$	−368.509	+	855.471i	−0.398819	+	0.925835i
$925$	1364.60	+	365.644i	1.47524	+	0.395290i
$926$	−1510.52	+	640.839i	−1.63123	+	0.692050i
$927$	709.999	−	626.696i	0.765910	−	0.676047i
$928$	−358.437	+	981.896i	−0.386247	+	1.05808i
$929$	−887.320	+	512.294i	−0.955135	+	0.551447i	−0.894672	−	0.446723i	$-0.852591\pi$
$929$	−887.320	+	512.294i	−0.955135	+	0.551447i	−0.0604624	+	0.998170i	$0.519258\pi$
$930$	389.888	−	1333.84i	0.419234	−	1.43423i
$931$	−14.3206	−	53.4454i	−0.0153820	−	0.0574064i
$932$	−97.0259	−	338.856i	−0.104105	−	0.363579i
$933$	−1039.05	+	104.021i	−1.11366	+	0.111491i
$934$	−26.1277	−	186.165i	−0.0279740	−	0.199320i
$935$	−1752.79			−1.87464
$936$	117.853	−	257.429i	0.125912	−	0.275031i
$937$			776.183i			0.828370i	0.910193	+	0.414185i	$0.135933\pi$
$937$			776.183i			0.828370i	−0.910193	+	0.414185i	$0.864067\pi$
$938$	−86.9906	−	619.825i	−0.0927405	−	0.660794i
$939$	−609.463	−	274.966i	−0.649056	−	0.292829i
$940$	687.919	−	1239.93i	0.731828	−	1.31907i
$941$	1601.73	−	429.182i	1.70216	−	0.456092i	0.728676	−	0.684859i	$-0.240136\pi$
$941$	1601.73	−	429.182i	1.70216	−	0.456092i	0.973481	+	0.228767i	$0.0734694\pi$
$942$	243.557	−	59.4003i	0.258553	−	0.0630576i
$943$	−418.367	−	724.634i	−0.443656	−	0.768434i
$944$	710.078	+	663.168i	0.752201	+	0.702508i
$945$	−2007.76	−	1060.77i	−2.12461	−	1.12251i
$946$	627.411	−	266.179i	0.663225	−	0.281374i
$947$	190.158	−	709.679i	0.200800	−	0.749397i	−0.789888	−	0.613251i	$-0.789862\pi$
$947$	190.158	−	709.679i	0.200800	−	0.749397i	0.990689	−	0.136147i	$-0.0434718\pi$
$948$	−235.643	−	34.3968i	−0.248569	−	0.0362835i
$949$	−296.635	+	79.4830i	−0.312576	+	0.0837545i
$950$	219.163	−	171.162i	0.230698	−	0.180170i
$951$	−720.927	+	272.660i	−0.758073	+	0.286708i
$952$	1407.37	−	222.084i	1.47833	−	0.233282i
$953$	273.150			0.286621			0.143310	−	0.989678i	$-0.454225\pi$
$953$	273.150			0.286621			0.143310	+	0.989678i	$0.454225\pi$
$954$	−195.748	+	1048.30i	−0.205186	+	1.09885i
$955$	−1503.06	−	1503.06i	−1.57388	−	1.57388i
$956$	404.968	−	1621.61i	0.423607	−	1.69625i
$957$	−867.855	+	86.8830i	−0.906849	+	0.0907868i
$958$	923.128	+	113.524i	0.963600	+	0.118501i
$959$	−432.553	−	249.735i	−0.451046	−	0.260411i
$960$	1830.47	−	278.521i	1.90674	−	0.290126i
$961$	192.085	+	332.701i	0.199881	+	0.346203i
$962$	150.423	−	63.8173i	0.156365	−	0.0663381i
$963$	517.777	+	1041.51i	0.537671	+	1.08152i
$964$	−112.971	+	116.896i	−0.117190	+	0.121262i
$965$	470.123	+	125.969i	0.487174	+	0.130538i
$966$	729.584	+	16.4791i	0.755263	+	0.0170591i
$967$	−836.174	−	482.765i	−0.864709	−	0.499240i	0.000877061	−	1.00000i	$-0.499721\pi$
$967$	−836.174	−	482.765i	−0.864709	−	0.499240i	−0.865587	+	0.500759i	$0.833054\pi$
$968$	−259.887	+	210.207i	−0.268478	+	0.217156i
$969$	20.2084	−	123.635i	0.0208549	−	0.127590i
$970$	−199.367	+	27.9806i	−0.205533	+	0.0288460i
$971$	−21.8191	+	21.8191i	−0.0224708	+	0.0224708i	−0.718253	−	0.695782i	$-0.755058\pi$
$971$	−21.8191	+	21.8191i	−0.0224708	+	0.0224708i	0.695782	+	0.718253i	$0.255058\pi$
$972$	−940.771	+	244.405i	−0.967871	+	0.251446i
$973$	726.267	−	726.267i	0.746420	−	0.746420i
$974$	−316.050	+	419.247i	−0.324487	+	0.430439i
$975$	129.394	−	791.630i	0.132711	−	0.811928i
$976$	−299.664	+	91.3677i	−0.307033	+	0.0936144i
$977$	41.6980	+	24.0744i	0.0426796	+	0.0246411i	0.521188	−	0.853442i	$-0.325489\pi$
$977$	41.6980	+	24.0744i	0.0426796	+	0.0246411i	−0.478508	+	0.878083i	$0.658822\pi$
$978$	−33.4638	−	35.0104i	−0.0342166	−	0.0357980i
$979$	932.880	+	249.965i	0.952891	+	0.255326i
$980$	−17.8196	−	1043.60i	−0.0181833	−	1.06490i
$981$	504.049	+	1013.89i	0.513812	+	1.03353i
$982$	−224.117	+	554.406i	−0.228225	+	0.564568i
$983$	−182.725	−	316.488i	−0.185885	−	0.321962i	0.757990	−	0.652267i	$-0.226182\pi$
$983$	−182.725	−	316.488i	−0.185885	−	0.321962i	−0.943874	+	0.330305i	$0.892848\pi$
$984$	−380.337	+	1388.78i	−0.386521	+	1.41136i
$985$	−1714.56	−	989.902i	−1.74067	−	1.00498i
$986$	821.168	+	1051.46i	0.832828	+	1.06639i
$987$	−956.989	+	95.8065i	−0.969594	+	0.0970684i
$988$	7.79290	−	31.2051i	0.00788755	−	0.0315841i
$989$	−377.568	−	377.568i	−0.381767	−	0.381767i
$990$	873.361	+	1274.41i	0.882182	+	1.28728i
$991$	663.813			0.669842			0.334921	−	0.942246i	$-0.391290\pi$
$991$	663.813			0.669842			0.334921	+	0.942246i	$0.391290\pi$
$992$	441.422	−	629.143i	0.444981	−	0.634216i
$993$	128.719	−	48.6824i	0.129626	−	0.0490256i
$994$	393.860	+	48.4359i	0.396238	+	0.0487283i
$995$	403.672	−	108.164i	0.405701	−	0.108707i
$996$	566.095	+	759.607i	0.568368	+	0.762658i
$997$	−370.922	+	1384.30i	−0.372038	+	1.38847i	0.485586	+	0.874189i	$0.338606\pi$
$997$	−370.922	+	1384.30i	−0.372038	+	1.38847i	−0.857624	+	0.514277i	$0.828060\pi$
$998$	−236.994	+	586.261i	−0.237469	+	0.587436i
$999$	−496.004	−	262.057i	−0.496500	−	0.262319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.10	✓	184
3.2	odd	2		432.3.x.a.341.37		184
9.2	odd	6	inner	144.3.w.a.101.26	yes	184
9.7	even	3		432.3.x.a.197.21		184
16.13	even	4	inner	144.3.w.a.77.26	yes	184
48.29	odd	4		432.3.x.a.125.21		184
144.29	odd	12	inner	144.3.w.a.29.10	yes	184
144.61	even	12		432.3.x.a.413.37		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.10	✓	184	1.1	even	1	trivial
144.3.w.a.29.10	yes	184	144.29	odd	12	inner
144.3.w.a.77.26	yes	184	16.13	even	4	inner
144.3.w.a.101.26	yes	184	9.2	odd	6	inner
432.3.x.a.125.21		184	48.29	odd	4
432.3.x.a.197.21		184	9.7	even	3
432.3.x.a.341.37		184	3.2	odd	2
432.3.x.a.413.37		184	144.61	even	12

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)

\(f(q)\)	\(=\)	\(q+(-1.59704 - 1.20393i) q^{2} +(-1.75135 - 2.43573i) q^{3} +(1.10109 + 3.84547i) q^{4} +(-2.49590 - 9.31484i) q^{5} +(-0.135487 + 5.99847i) q^{6} +(7.55275 - 4.36058i) q^{7} +(2.87120 - 7.46701i) q^{8} +(-2.86558 + 8.53161i) q^{9} +O(q^{10})\)	\(q+(-1.59704 - 1.20393i) q^{2} +(-1.75135 - 2.43573i) q^{3} +(1.10109 + 3.84547i) q^{4} +(-2.49590 - 9.31484i) q^{5} +(-0.135487 + 5.99847i) q^{6} +(7.55275 - 4.36058i) q^{7} +(2.87120 - 7.46701i) q^{8} +(-2.86558 + 8.53161i) q^{9} +(-7.22838 + 17.8811i) q^{10} +(-8.59716 - 2.30360i) q^{11} +(7.43814 - 9.41669i) q^{12} +(-1.01775 - 3.79829i) q^{13} +(-17.3119 - 2.12897i) q^{14} +(-18.3173 + 22.3928i) q^{15} +(-13.5752 + 8.46840i) q^{16} +20.4214i q^{17} +(14.8480 - 10.1754i) q^{18} +(1.44592 - 1.44592i) q^{19} +(33.0717 - 19.8544i) q^{20} +(-23.8487 - 10.7596i) q^{21} +(10.9566 + 14.0294i) q^{22} +(6.97317 - 12.0779i) q^{23} +(-23.2161 + 6.08384i) q^{24} +(-58.8860 + 33.9979i) q^{25} +(-2.94750 + 7.29133i) q^{26} +(25.7993 - 7.96201i) q^{27} +(25.0847 + 24.2425i) q^{28} +(-8.45427 + 31.5518i) q^{29} +(56.2129 - 13.7096i) q^{30} +(12.0086 - 20.7996i) q^{31} +(31.8756 + 2.81926i) q^{32} +(9.44564 + 24.9748i) q^{33} +(24.5860 - 32.6139i) q^{34} +(-59.4691 - 59.4691i) q^{35} +(-35.9633 - 1.62543i) q^{36} +(-14.6915 - 14.6915i) q^{37} +(-4.04998 + 0.568403i) q^{38} +(-7.46919 + 9.13108i) q^{39} +(-76.7202 - 8.10783i) q^{40} +(29.9984 - 51.9587i) q^{41} +(25.1335 + 45.8958i) q^{42} +(9.90936 - 36.9823i) q^{43} +(-0.607813 - 35.5966i) q^{44} +(86.6228 + 5.39834i) q^{45} +(-25.6774 + 10.8937i) q^{46} +(31.8352 - 18.3801i) q^{47} +(44.4016 + 18.2345i) q^{48} +(13.5294 - 23.4336i) q^{49} +(134.975 + 16.5988i) q^{50} +(49.7411 - 35.7649i) q^{51} +(13.4856 - 8.09597i) q^{52} +(-41.8929 + 41.8929i) q^{53} +(-50.7884 - 18.3450i) q^{54} +85.8307i q^{55} +(-10.8751 - 68.9166i) q^{56} +(-6.05417 - 0.989567i) q^{57} +(51.4881 - 40.2111i) q^{58} +(-15.7167 - 58.6557i) q^{59} +(-106.280 - 45.7819i) q^{60} +(18.9131 + 5.06774i) q^{61} +(-44.2196 + 18.7602i) q^{62} +(15.5598 + 76.9328i) q^{63} +(-47.5124 - 42.8785i) q^{64} +(-32.8403 + 18.9603i) q^{65} +(14.9829 - 51.2577i) q^{66} +(9.28744 + 34.6612i) q^{67} +(-78.5298 + 22.4858i) q^{68} +(-41.6309 + 4.16777i) q^{69} +(23.3778 + 166.571i) q^{70} -22.7508 q^{71} +(55.4780 + 45.8933i) q^{72} -78.0968i q^{73} +(5.77535 + 41.1504i) q^{74} +(185.939 + 83.8886i) q^{75} +(7.15231 + 3.96814i) q^{76} +(-74.9773 + 20.0901i) q^{77} +(22.9218 - 5.59032i) q^{78} +(-9.92252 - 17.1863i) q^{79} +(112.764 + 105.315i) q^{80} +(-64.5769 - 48.8961i) q^{81} +(-110.463 + 46.8642i) q^{82} +(-20.4326 + 76.2556i) q^{83} +(15.1161 - 103.557i) q^{84} +(190.222 - 50.9699i) q^{85} +(-60.3498 + 47.1320i) q^{86} +(91.6580 - 34.6657i) q^{87} +(-41.8852 + 57.5810i) q^{88} -108.510 q^{89} +(-131.841 - 112.909i) q^{90} +(-24.2496 - 24.2496i) q^{91} +(54.1232 + 13.5163i) q^{92} +(-71.6934 + 7.17740i) q^{93} +(-72.9705 - 8.97372i) q^{94} +(-17.0773 - 9.85961i) q^{95} +(-48.9582 - 82.5778i) q^{96} +(5.21912 + 9.03978i) q^{97} +(-49.8195 + 21.1359i) q^{98} +(44.2893 - 66.7465i) 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

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