LMFDB - Embedded newform 150.3.i.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(29,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("150.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.i (of order $10$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	150.29
Dual form			150.3.i.a.119.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.437016 + 1.34500i) q^{2} +(-2.70555 - 1.29615i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.68239 - 4.21957i) q^{5} +(2.92568 - 3.07252i) q^{6} +8.88015i q^{7} +(2.28825 - 1.66251i) q^{8} +(5.64000 + 7.01359i) q^{9} +O(q^{10})$	\(q+(-0.437016 + 1.34500i) q^{2} +(-2.70555 - 1.29615i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.68239 - 4.21957i) q^{5} +(2.92568 - 3.07252i) q^{6} +8.88015i q^{7} +(2.28825 - 1.66251i) q^{8} +(5.64000 + 7.01359i) q^{9} +(6.84756 - 1.76378i) q^{10} +(16.5303 + 5.37102i) q^{11} +(2.85396 + 5.27778i) q^{12} +(14.5516 - 4.72811i) q^{13} +(-11.9438 - 3.88077i) q^{14} +(1.78814 + 14.8930i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-8.28643 + 6.02044i) q^{17} +(-11.8980 + 4.52073i) q^{18} +(14.2114 - 10.3252i) q^{19} +(-0.620212 + 9.98075i) q^{20} +(11.5100 - 24.0257i) q^{21} +(-14.4480 + 19.8860i) q^{22} +(-8.91122 + 27.4259i) q^{23} +(-8.34582 + 1.53209i) q^{24} +(-10.6096 + 22.6371i) q^{25} +21.6381i q^{26} +(-6.16864 - 26.2859i) q^{27} +(10.4392 - 14.3684i) q^{28} +(-6.68922 + 9.20692i) q^{29} +(-20.8125 - 4.10345i) q^{30} +(33.0715 - 24.0278i) q^{31} -5.65685 q^{32} +(-37.7619 - 35.9573i) q^{33} +(-4.47618 - 13.7763i) q^{34} +(37.4705 - 23.8200i) q^{35} +(-0.880740 - 17.9784i) q^{36} +(1.47164 - 0.478166i) q^{37} +(7.67675 + 23.6266i) q^{38} +(-45.4985 - 6.06893i) q^{39} +(-13.1530 - 5.19593i) q^{40} +(5.18186 - 1.68369i) q^{41} +(27.2844 + 25.9805i) q^{42} +27.1575i q^{43} +(-20.4326 - 28.1230i) q^{44} +(14.4657 - 42.6115i) q^{45} +(-32.9934 - 23.9711i) q^{46} +(73.3819 + 53.3151i) q^{47} +(1.58660 - 11.8947i) q^{48} -29.8571 q^{49} +(-25.8102 - 24.1626i) q^{50} +(30.2227 - 5.54816i) q^{51} +(-29.1032 - 9.45621i) q^{52} +(-15.4590 - 11.2316i) q^{53} +(38.0502 + 3.19055i) q^{54} +(-21.6772 - 84.1579i) q^{55} +(14.7633 + 20.3200i) q^{56} +(-51.8327 + 9.51523i) q^{57} +(-9.45998 - 13.0205i) q^{58} +(36.4710 - 11.8502i) q^{59} +(14.6145 - 26.1995i) q^{60} +(-23.6592 + 72.8155i) q^{61} +(17.8646 + 54.9816i) q^{62} +(-62.2817 + 50.0840i) q^{63} +(2.47214 - 7.60845i) q^{64} +(-58.9837 - 48.7190i) q^{65} +(64.8650 - 35.0757i) q^{66} +(-29.7411 - 40.9351i) q^{67} +20.4852 q^{68} +(59.6578 - 62.6519i) q^{69} +(15.6627 + 60.8074i) q^{70} +(47.1092 - 64.8403i) q^{71} +(24.5658 + 6.67227i) q^{72} +(-20.6289 - 6.70273i) q^{73} +2.18832i q^{74} +(58.0458 - 47.4941i) q^{75} -35.1326 q^{76} +(-47.6955 + 146.792i) q^{77} +(28.0462 - 58.5431i) q^{78} +(56.9806 + 41.3989i) q^{79} +(12.7366 - 15.4201i) q^{80} +(-17.3809 + 79.1132i) q^{81} +7.70539i q^{82} +(-94.9893 + 69.0138i) q^{83} +(-46.8675 + 25.3436i) q^{84} +(47.6311 + 18.8160i) q^{85} +(-36.5267 - 11.8682i) q^{86} +(30.0315 - 16.2396i) q^{87} +(46.7547 - 15.1915i) q^{88} +(-135.505 - 44.0283i) q^{89} +(50.9907 + 38.0782i) q^{90} +(41.9863 + 129.221i) q^{91} +(46.6598 - 33.9003i) q^{92} +(-120.620 + 22.1430i) q^{93} +(-103.778 + 75.3989i) q^{94} +(-81.6885 - 32.2699i) q^{95} +(15.3049 + 7.33212i) q^{96} +(102.989 - 141.752i) q^{97} +(13.0480 - 40.1577i) q^{98} +(55.5607 + 146.229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 40 q^{4} + 20 q^{9}+O(q^{10}) $ 80 * q - 40 * q^4 + 20 * q^9	$ 80 q - 40 q^{4} + 20 q^{9} + 16 q^{10} + 20 q^{12} + 32 q^{15} - 80 q^{16} + 60 q^{19} - 60 q^{21} + 40 q^{22} + 116 q^{25} - 210 q^{27} - 40 q^{28} - 68 q^{30} + 180 q^{31} - 50 q^{33} - 120 q^{34} + 40 q^{36} - 40 q^{37} + 220 q^{39} + 32 q^{40} + 468 q^{45} + 120 q^{46} - 40 q^{48} - 680 q^{49} + 20 q^{51} - 120 q^{54} - 272 q^{55} - 156 q^{60} - 200 q^{61} - 830 q^{63} - 160 q^{64} + 160 q^{66} + 500 q^{67} - 280 q^{69} - 584 q^{70} + 120 q^{73} - 138 q^{75} - 80 q^{76} + 620 q^{78} + 400 q^{79} - 420 q^{81} + 180 q^{84} + 1632 q^{85} + 750 q^{87} + 160 q^{88} + 472 q^{90} - 340 q^{91} + 160 q^{94} + 20 q^{97} - 260 q^{99}+O(q^{100}) $ 80 * q - 40 * q^4 + 20 * q^9 + 16 * q^10 + 20 * q^12 + 32 * q^15 - 80 * q^16 + 60 * q^19 - 60 * q^21 + 40 * q^22 + 116 * q^25 - 210 * q^27 - 40 * q^28 - 68 * q^30 + 180 * q^31 - 50 * q^33 - 120 * q^34 + 40 * q^36 - 40 * q^37 + 220 * q^39 + 32 * q^40 + 468 * q^45 + 120 * q^46 - 40 * q^48 - 680 * q^49 + 20 * q^51 - 120 * q^54 - 272 * q^55 - 156 * q^60 - 200 * q^61 - 830 * q^63 - 160 * q^64 + 160 * q^66 + 500 * q^67 - 280 * q^69 - 584 * q^70 + 120 * q^73 - 138 * q^75 - 80 * q^76 + 620 * q^78 + 400 * q^79 - 420 * q^81 + 180 * q^84 + 1632 * q^85 + 750 * q^87 + 160 * q^88 + 472 * q^90 - 340 * q^91 + 160 * q^94 + 20 * q^97 - 260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.437016	+	1.34500i	−0.218508	+	0.672499i
$2$	−0.437016	+	1.34500i	−0.218508	+	0.672499i
$3$	−2.70555	−	1.29615i	−0.901850	−	0.432050i
$3$	−2.70555	−	1.29615i	−0.901850	−	0.432050i
$4$	−1.61803	−	1.17557i	−0.404508	−	0.293893i
$5$	−2.68239	−	4.21957i	−0.536477	−	0.843915i
$5$	−2.68239	−	4.21957i	−0.536477	−	0.843915i
$6$	2.92568	−	3.07252i	0.487614	−	0.512086i
$7$			8.88015i			1.26859i	0.773090	+	0.634297i	$0.218710\pi$
$7$			8.88015i			1.26859i	−0.773090	+	0.634297i	$0.781290\pi$
$8$	2.28825	−	1.66251i	0.286031	−	0.207813i
$9$	5.64000	+	7.01359i	0.626666	+	0.779288i
$10$	6.84756	−	1.76378i	0.684756	−	0.176378i
$11$	16.5303	+	5.37102i	1.50275	+	0.488274i	0.940820	−	0.338908i	$-0.110057\pi$
$11$	16.5303	+	5.37102i	1.50275	+	0.488274i	0.561934	+	0.827182i	$0.310057\pi$
$12$	2.85396	+	5.27778i	0.237830	+	0.439815i
$13$	14.5516	−	4.72811i	1.11936	−	0.363701i	0.309834	−	0.950791i	$-0.399727\pi$
$13$	14.5516	−	4.72811i	1.11936	−	0.363701i	0.809522	+	0.587090i	$0.199727\pi$
$14$	−11.9438	−	3.88077i	−0.853127	−	0.277198i
$15$	1.78814	+	14.8930i	0.119209	+	0.992869i
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	−8.28643	+	6.02044i	−0.487437	+	0.354144i	−0.804198	−	0.594362i	$-0.797405\pi$
$17$	−8.28643	+	6.02044i	−0.487437	+	0.354144i	0.316761	+	0.948505i	$0.397405\pi$
$18$	−11.8980	+	4.52073i	−0.661001	+	0.251152i
$19$	14.2114	−	10.3252i	0.747970	−	0.543432i	−0.147227	−	0.989103i	$-0.547035\pi$
$19$	14.2114	−	10.3252i	0.747970	−	0.543432i	0.895197	+	0.445671i	$0.147035\pi$
$20$	−0.620212	+	9.98075i	−0.0310106	+	0.499037i
$21$	11.5100	−	24.0257i	0.548095	−	1.14408i
$22$	−14.4480	+	19.8860i	−0.656728	+	0.903908i
$23$	−8.91122	+	27.4259i	−0.387444	+	1.19243i	0.547247	+	0.836971i	$0.315676\pi$
$23$	−8.91122	+	27.4259i	−0.387444	+	1.19243i	−0.934691	+	0.355460i	$0.884324\pi$
$24$	−8.34582	+	1.53209i	−0.347742	+	0.0638371i
$25$	−10.6096	+	22.6371i	−0.424384	+	0.905482i
$26$			21.6381i			0.832236i
$27$	−6.16864	−	26.2859i	−0.228468	−	0.973551i
$28$	10.4392	−	14.3684i	0.372830	−	0.513157i
$29$	−6.68922	+	9.20692i	−0.230663	+	0.317480i	−0.908622	−	0.417619i	$-0.862865\pi$
$29$	−6.68922	+	9.20692i	−0.230663	+	0.317480i	0.677959	+	0.735099i	$0.262865\pi$
$30$	−20.8125	−	4.10345i	−0.693751	−	0.136782i
$31$	33.0715	−	24.0278i	1.06682	−	0.775092i	0.0914841	−	0.995807i	$-0.470839\pi$
$31$	33.0715	−	24.0278i	1.06682	−	0.775092i	0.975338	+	0.220715i	$0.0708389\pi$
$32$	−5.65685			−0.176777
$33$	−37.7619	−	35.9573i	−1.14430	−	1.08961i
$34$	−4.47618	−	13.7763i	−0.131652	−	0.405184i
$35$	37.4705	−	23.8200i	1.07058	−	0.680572i
$36$	−0.880740	−	17.9784i	−0.0244650	−	0.499401i
$37$	1.47164	−	0.478166i	0.0397741	−	0.0129234i	−0.289062	−	0.957310i	$-0.593343\pi$
$37$	1.47164	−	0.478166i	0.0397741	−	0.0129234i	0.328836	+	0.944387i	$0.393343\pi$
$38$	7.67675	+	23.6266i	0.202020	+	0.621753i
$39$	−45.4985	−	6.06893i	−1.16663	−	0.155614i
$40$	−13.1530	−	5.19593i	−0.328826	−	0.129898i
$41$	5.18186	−	1.68369i	0.126387	−	0.0410656i	−0.245141	−	0.969488i	$-0.578834\pi$
$41$	5.18186	−	1.68369i	0.126387	−	0.0410656i	0.371528	+	0.928422i	$0.378834\pi$
$42$	27.2844	+	25.9805i	0.649629	+	0.618584i
$43$			27.1575i			0.631569i	0.948831	+	0.315784i	$0.102268\pi$
$43$			27.1575i			0.631569i	−0.948831	+	0.315784i	$0.897732\pi$
$44$	−20.4326	−	28.1230i	−0.464376	−	0.639159i
$45$	14.4657	−	42.6115i	0.321460	−	0.946923i
$46$	−32.9934	−	23.9711i	−0.717249	−	0.521112i
$47$	73.3819	+	53.3151i	1.56132	+	1.13436i	0.934920	+	0.354859i	$0.115471\pi$
$47$	73.3819	+	53.3151i	1.56132	+	1.13436i	0.626397	+	0.779504i	$0.284529\pi$
$48$	1.58660	−	11.8947i	0.0330541	−	0.247805i
$49$	−29.8571			−0.609329
$50$	−25.8102	−	24.1626i	−0.516204	−	0.483253i
$51$	30.2227	−	5.54816i	0.592603	−	0.108788i
$52$	−29.1032	−	9.45621i	−0.559678	−	0.181850i
$53$	−15.4590	−	11.2316i	−0.291680	−	0.211918i	0.432316	−	0.901722i	$-0.357697\pi$
$53$	−15.4590	−	11.2316i	−0.291680	−	0.211918i	−0.723996	+	0.689804i	$0.757697\pi$
$54$	38.0502	+	3.19055i	0.704634	+	0.0590843i
$55$	−21.6772	−	84.1579i	−0.394132	−	1.53014i
$56$	14.7633	+	20.3200i	0.263631	+	0.362857i
$57$	−51.8327	+	9.51523i	−0.909346	+	0.166934i
$58$	−9.45998	−	13.0205i	−0.163103	−	0.224492i
$59$	36.4710	−	11.8502i	0.618153	−	0.200850i	0.0168331	−	0.999858i	$-0.494642\pi$
$59$	36.4710	−	11.8502i	0.618153	−	0.200850i	0.601320	+	0.799008i	$0.294642\pi$
$60$	14.6145	−	26.1995i	0.243576	−	0.436659i
$61$	−23.6592	+	72.8155i	−0.387856	+	1.19370i	0.546532	+	0.837438i	$0.315948\pi$
$61$	−23.6592	+	72.8155i	−0.387856	+	1.19370i	−0.934387	+	0.356258i	$0.884052\pi$
$62$	17.8646	+	54.9816i	0.288139	+	0.886800i
$63$	−62.2817	+	50.0840i	−0.988599	+	0.794985i
$64$	2.47214	−	7.60845i	0.0386271	−	0.118882i
$65$	−58.9837	−	48.7190i	−0.907441	−	0.749523i
$66$	64.8650	−	35.0757i	0.982803	−	0.531450i
$67$	−29.7411	−	40.9351i	−0.443897	−	0.610972i	0.527175	−	0.849756i	$-0.323251\pi$
$67$	−29.7411	−	40.9351i	−0.443897	−	0.610972i	−0.971073	+	0.238784i	$0.923251\pi$
$68$	20.4852			0.301253
$69$	59.6578	−	62.6519i	0.864606	−	0.907999i
$70$	15.6627	+	60.8074i	0.223752	+	0.868677i
$71$	47.1092	−	64.8403i	0.663510	−	0.913244i	−0.336081	−	0.941833i	$-0.609102\pi$
$71$	47.1092	−	64.8403i	0.663510	−	0.913244i	0.999591	+	0.0285896i	$0.00910158\pi$
$72$	24.5658	+	6.67227i	0.341192	+	0.0926705i
$73$	−20.6289	−	6.70273i	−0.282587	−	0.0918182i	0.164294	−	0.986411i	$-0.447465\pi$
$73$	−20.6289	−	6.70273i	−0.282587	−	0.0918182i	−0.446881	+	0.894593i	$0.647465\pi$
$74$			2.18832i			0.0295719i
$75$	58.0458	−	47.4941i	0.773944	−	0.633254i
$76$	−35.1326			−0.462271
$77$	−47.6955	+	146.792i	−0.619422	+	1.90638i
$78$	28.0462	−	58.5431i	0.359567	−	0.750552i
$79$	56.9806	+	41.3989i	0.721274	+	0.524036i	0.886791	−	0.462171i	$-0.152929\pi$
$79$	56.9806	+	41.3989i	0.721274	+	0.524036i	−0.165517	+	0.986207i	$0.552929\pi$
$80$	12.7366	−	15.4201i	0.159207	−	0.192751i
$81$	−17.3809	+	79.1132i	−0.214578	+	0.976707i
$82$			7.70539i			0.0939682i
$83$	−94.9893	+	69.0138i	−1.14445	+	0.831491i	−0.987733	−	0.156152i	$-0.950091\pi$
$83$	−94.9893	+	69.0138i	−1.14445	+	0.831491i	−0.156717	+	0.987644i	$0.550091\pi$
$84$	−46.8675	+	25.3436i	−0.557946	+	0.301709i
$85$	47.6311	+	18.8160i	0.560366	+	0.221365i
$86$	−36.5267	−	11.8682i	−0.424729	−	0.138003i
$87$	30.0315	−	16.2396i	0.345190	−	0.186662i
$88$	46.7547	−	15.1915i	0.531304	−	0.172631i
$89$	−135.505	−	44.0283i	−1.52253	−	0.494701i	−0.576038	−	0.817423i	$-0.695402\pi$
$89$	−135.505	−	44.0283i	−1.52253	−	0.494701i	−0.946494	+	0.322722i	$0.895402\pi$
$90$	50.9907	+	38.0782i	0.566563	+	0.423092i
$91$	41.9863	+	129.221i	0.461388	+	1.42001i
$92$	46.6598	−	33.9003i	0.507171	−	0.368482i
$93$	−120.620	+	22.1430i	−1.29699	+	0.238096i
$94$	−103.778	+	75.3989i	−1.10402	+	0.802116i
$95$	−81.6885	−	32.2699i	−0.859879	−	0.339684i
$96$	15.3049	+	7.33212i	0.159426	+	0.0763763i
$97$	102.989	−	141.752i	1.06174	−	1.46136i	0.183580	−	0.983005i	$-0.441231\pi$
$97$	102.989	−	141.752i	1.06174	−	1.46136i	0.878164	−	0.478360i	$-0.158769\pi$
$98$	13.0480	−	40.1577i	0.133143	−	0.409773i
$99$	55.5607	+	146.229i	0.561219	+	1.47706i
$100$	43.7781	−	24.1552i	0.437781	−	0.241552i
$101$			67.3023i			0.666359i	0.942863	+	0.333180i	$0.108122\pi$
$101$			67.3023i			0.666359i	−0.942863	+	0.333180i	$0.891878\pi$
$102$	−5.74555	+	43.0741i	−0.0563290	+	0.422295i
$103$	−50.7074	+	69.7927i	−0.492305	+	0.677599i	−0.980811	−	0.194961i	$-0.937542\pi$
$103$	−50.7074	+	69.7927i	−0.492305	+	0.677599i	0.488506	+	0.872560i	$0.337542\pi$
$104$	25.4372	−	35.0112i	0.244588	−	0.336647i
$105$	−132.252	+	15.8789i	−1.25955	+	0.151228i
$106$	21.8624	−	15.8839i	0.206249	−	0.149849i
$107$	116.245			1.08640			0.543201	−	0.839603i	$-0.317212\pi$
$107$	116.245			1.08640			0.543201	+	0.839603i	$0.317212\pi$
$108$	−20.9198	+	49.7831i	−0.193702	+	0.460955i
$109$	−17.6420	−	54.2965i	−0.161853	−	0.498133i	0.836937	−	0.547299i	$-0.184344\pi$
$109$	−17.6420	−	54.2965i	−0.161853	−	0.498133i	−0.998791	+	0.0491655i	$0.984344\pi$
$110$	122.665	+	7.62253i	1.11514	+	0.0692957i
$111$	−4.60138	−	0.613767i	−0.0414538	−	0.00552943i
$112$	−33.7821	+	10.9765i	−0.301626	+	0.0980042i
$113$	−2.96339	−	9.12036i	−0.0262247	−	0.0807112i	0.937088	−	0.349094i	$-0.113511\pi$
$113$	−2.96339	−	9.12036i	−0.0262247	−	0.0807112i	−0.963312	+	0.268383i	$0.913511\pi$
$114$	9.85376	−	73.8731i	0.0864365	−	0.648010i
$115$	139.629	−	35.9654i	1.21417	−	0.312743i
$116$	21.6468	−	7.03346i	0.186610	−	0.0606333i
$117$	115.232	+	75.3925i	0.984890	+	0.644381i
$118$			54.2322i			0.459595i
$119$	−53.4625	−	73.5848i	−0.449264	−	0.618359i
$120$	28.8515	+	31.1061i	0.240429	+	0.259218i
$121$	146.512	+	106.447i	1.21084	+	0.879727i
$122$	−87.5972	−	63.6431i	−0.718010	−	0.521665i
$123$	−16.2021	−	2.16116i	−0.131724	−	0.0175704i
$124$	−81.7572			−0.659333
$125$	123.978	−	15.9534i	0.991822	−	0.127627i
$126$	−40.1448	−	105.656i	−0.318609	−	0.838542i
$127$	−130.689	−	42.4634i	−1.02905	−	0.334357i	−0.254633	−	0.967038i	$-0.581955\pi$
$127$	−130.689	−	42.4634i	−1.02905	−	0.334357i	−0.774413	+	0.632681i	$0.781955\pi$
$128$	9.15298	+	6.65003i	0.0715077	+	0.0519534i
$129$	35.2001	−	73.4759i	0.272869	−	0.569580i
$130$	91.3037	−	58.0419i	0.702336	−	0.446476i
$131$	33.6017	+	46.2488i	0.256502	+	0.353044i	0.917775	−	0.397101i	$-0.129984\pi$
$131$	33.6017	+	46.2488i	0.256502	+	0.353044i	−0.661273	+	0.750145i	$0.729984\pi$
$132$	18.8297	+	102.572i	0.142649	+	0.777059i
$133$	91.6894	+	126.200i	0.689394	+	0.948869i
$134$	68.0550	−	22.1124i	0.507873	−	0.165018i
$135$	−94.3685	+	96.5380i	−0.699026	+	0.715096i
$136$	−8.95235	+	27.5525i	−0.0658261	+	0.202592i
$137$	−51.2370	−	157.691i	−0.373992	−	1.15103i	−0.944156	−	0.329499i	$-0.893120\pi$
$137$	−51.2370	−	157.691i	−0.373992	−	1.15103i	0.570164	−	0.821531i	$-0.306880\pi$
$138$	58.1952	+	107.620i	0.421705	+	0.779851i
$139$	−1.12127	+	3.45092i	−0.00806671	+	0.0248268i	−0.955009	−	0.296577i	$-0.904155\pi$
$139$	−1.12127	+	3.45092i	−0.00806671	+	0.0248268i	0.946942	+	0.321404i	$0.104155\pi$
$140$	−88.6306	−	5.50757i	−0.633076	−	0.0393398i
$141$	−129.434	−	239.360i	−0.917972	−	1.69759i
$142$	66.6225	+	91.6980i	0.469173	+	0.645761i
$143$	265.937			1.85970
$144$	−19.7099	+	30.1251i	−0.136874	+	0.209202i
$145$	56.7923	+	3.52912i	0.391671	+	0.0243388i
$146$	18.0303	−	24.8166i	0.123495	−	0.169977i
$147$	80.7799	+	38.6993i	0.549523	+	0.263260i
$148$	−2.94329	−	0.956332i	−0.0198871	−	0.00646170i
$149$		−	30.0596i		−	0.201742i	−0.994900	−	0.100871i	$-0.967837\pi$
$149$		−	30.0596i		−	0.201742i	0.994900	−	0.100871i	$-0.0321630\pi$
$150$	38.5125	+	98.8271i	0.256750	+	0.658847i
$151$	−239.756			−1.58779			−0.793893	−	0.608058i	$-0.791949\pi$
$151$	−239.756			−1.58779			−0.793893	+	0.608058i	$0.791949\pi$
$152$	15.3535	−	47.2532i	0.101010	−	0.310876i
$153$	−88.9603	−	24.1623i	−0.581440	−	0.157924i
$154$	−176.591	−	128.301i	−1.14669	−	0.833120i
$155$	−190.098	−	75.0956i	−1.22644	−	0.484488i
$156$	66.4836	+	63.3064i	0.426177	+	0.405810i
$157$		−	285.668i		−	1.81954i	−0.415108	−	0.909772i	$-0.636256\pi$
$157$		−	285.668i		−	1.81954i	0.415108	−	0.909772i	$-0.363744\pi$
$158$	−80.5828	+	58.5468i	−0.510018	+	0.370550i
$159$	27.2673	+	50.4250i	0.171492	+	0.317138i
$160$	15.1739	+	23.8695i	0.0948367	+	0.149184i
$161$	−243.546	−	79.1330i	−1.51271	−	0.491510i
$162$	−98.8114	−	57.9510i	−0.609947	−	0.357722i
$163$	111.924	−	36.3663i	0.686650	−	0.223106i	0.0551454	−	0.998478i	$-0.482438\pi$
$163$	111.924	−	36.3663i	0.686650	−	0.223106i	0.631504	+	0.775372i	$0.282438\pi$
$164$	−10.3637	−	3.36738i	−0.0631935	−	0.0205328i
$165$	−50.4323	+	255.790i	−0.305650	+	1.55024i
$166$	−51.3115	−	157.920i	−0.309105	−	0.951328i
$167$	−16.3909	+	11.9087i	−0.0981492	+	0.0713096i	−0.635777	−	0.771872i	$-0.719320\pi$
$167$	−16.3909	+	11.9087i	−0.0981492	+	0.0713096i	0.537628	+	0.843182i	$0.319320\pi$
$168$	−13.6052	−	74.1122i	−0.0809833	−	0.441144i
$169$	52.6707	−	38.2675i	0.311661	−	0.226435i
$170$	−46.1231	+	55.8408i	−0.271312	+	0.328475i
$171$	152.569	+	41.4390i	0.892217	+	0.242333i
$172$	31.9255	−	43.9417i	0.185613	−	0.255475i
$173$	38.6233	−	118.870i	0.223256	−	0.687111i	−0.775208	−	0.631706i	$-0.782355\pi$
$173$	38.6233	−	118.870i	0.223256	−	0.687111i	0.998464	−	0.0554049i	$-0.0176450\pi$
$174$	8.71789	+	47.4893i	0.0501028	+	0.272927i
$175$	−201.021	−	94.2148i	−1.14869	−	0.538370i
$176$			69.5239i			0.395022i
$177$	−114.034	−	15.2107i	−0.644259	−	0.0859361i
$178$	118.436	−	163.013i	0.665371	−	0.915804i
$179$	−56.5615	+	77.8503i	−0.315986	+	0.434918i	−0.937236	−	0.348695i	$-0.886625\pi$
$179$	−56.5615	+	77.8503i	−0.315986	+	0.434918i	0.621250	+	0.783612i	$0.286625\pi$
$180$	−73.4989	+	51.9415i	−0.408327	+	0.288564i
$181$	−68.8447	+	50.0186i	−0.380357	+	0.276346i	−0.761493	−	0.648173i	$-0.775533\pi$
$181$	−68.8447	+	50.0186i	−0.380357	+	0.276346i	0.381135	+	0.924519i	$0.375533\pi$
$182$	−192.150			−1.05577
$183$	158.391	−	166.340i	0.865524	−	0.908962i
$184$	25.2047	+	77.5722i	0.136982	+	0.421588i
$185$	−5.96517	−	4.92708i	−0.0322442	−	0.0266329i
$186$	22.9308	−	171.911i	0.123284	−	0.924251i
$187$	−169.313	+	55.0131i	−0.905417	+	0.294188i
$188$	−56.0588	−	172.531i	−0.298185	−	0.917719i
$189$	233.423	−	54.7785i	1.23504	−	0.289833i
$190$	79.1022	−	95.7683i	0.416327	−	0.504044i
$191$	115.633	−	37.5714i	0.605407	−	0.196709i	0.00975672	−	0.999952i	$-0.496894\pi$
$191$	115.633	−	37.5714i	0.605407	−	0.196709i	0.595651	+	0.803244i	$0.296894\pi$
$192$	−16.5502	+	17.3808i	−0.0861988	+	0.0905249i
$193$		−	67.7539i		−	0.351056i	−0.984474	−	0.175528i	$-0.943837\pi$
$193$		−	67.7539i		−	0.351056i	0.984474	−	0.175528i	$-0.0561633\pi$
$194$	145.649	+	200.468i	0.750766	+	1.03334i
$195$	96.4362	+	208.263i	0.494545	+	1.06802i
$196$	48.3098	+	35.0992i	0.246479	+	0.179077i
$197$	133.793	+	97.2065i	0.679154	+	0.493434i	0.873077	−	0.487583i	$-0.162121\pi$
$197$	133.793	+	97.2065i	0.679154	+	0.493434i	−0.193923	+	0.981017i	$0.562121\pi$
$198$	−220.959	+	10.8245i	−1.11595	+	0.0546691i
$199$	−299.615			−1.50561			−0.752803	−	0.658246i	$-0.771298\pi$
$199$	−299.615			−1.50561			−0.752803	+	0.658246i	$0.771298\pi$
$200$	13.3569	+	69.4377i	0.0667846	+	0.347188i
$201$	27.4080	+	149.301i	0.136358	+	0.742791i
$202$	−90.5214	−	29.4122i	−0.448126	−	0.145605i
$203$	−81.7588	−	59.4013i	−0.402753	−	0.292617i
$204$	−55.4237	−	26.5518i	−0.271685	−	0.130156i
$205$	−21.0042	−	17.3489i	−0.102460	−	0.0846290i
$206$	−71.7111	−	98.7018i	−0.348112	−	0.479135i
$207$	−242.613	+	92.1825i	−1.17205	+	0.445326i
$208$	35.9736	+	49.5134i	0.172950	+	0.238045i
$209$	290.376	−	94.3488i	1.38936	−	0.451430i
$210$	36.4393	−	184.819i	0.173521	−	0.880088i
$211$	−45.0795	+	138.740i	−0.213647	+	0.657538i	0.785600	+	0.618735i	$0.212354\pi$
$211$	−45.0795	+	138.740i	−0.213647	+	0.657538i	−0.999247	+	0.0388029i	$0.987646\pi$
$212$	11.8097	+	36.3464i	0.0557059	+	0.171445i
$213$	−211.499	+	114.368i	−0.992953	+	0.536939i
$214$	−50.8009	+	156.349i	−0.237387	+	0.730603i
$215$	114.593	−	72.8468i	0.532990	−	0.338823i
$216$	−57.8159	−	49.8932i	−0.267666	−	0.230987i
$217$	213.371	+	293.680i	0.983276	+	1.35336i
$218$	80.7385			0.370360
$219$	47.1247	+	44.8727i	0.215181	+	0.204898i
$220$	−63.8591	+	161.654i	−0.290268	+	0.734789i
$221$	−92.1156	+	126.786i	−0.416813	+	0.573694i
$222$	2.83639	−	5.92061i	0.0127765	−	0.0266694i
$223$	338.042	+	109.836i	1.51588	+	0.492540i	0.944603	−	0.328216i	$-0.106447\pi$
$223$	338.042	+	109.836i	1.51588	+	0.492540i	0.571279	+	0.820756i	$0.306447\pi$
$224$		−	50.2337i		−	0.224258i
$225$	−218.605	+	53.2616i	−0.971578	+	0.236718i
$226$	13.5619			0.0600085
$227$	115.661	−	355.968i	0.509519	−	1.56814i	−0.283518	−	0.958967i	$-0.591502\pi$
$227$	115.661	−	355.968i	0.509519	−	1.56814i	0.793038	−	0.609173i	$-0.208498\pi$
$228$	95.0529	+	45.5370i	0.416899	+	0.199724i
$229$	145.582	+	105.771i	0.635729	+	0.461884i	0.858380	−	0.513014i	$-0.171471\pi$
$229$	145.582	+	105.771i	0.635729	+	0.461884i	−0.222651	+	0.974898i	$0.571471\pi$
$230$	−12.6468	+	203.518i	−0.0549860	+	0.884861i
$231$	319.306	−	335.331i	1.38228	−	1.45165i
$232$			32.1886i			0.138744i
$233$	20.8576	−	15.1539i	0.0895177	−	0.0650384i	−0.542126	−	0.840297i	$-0.682381\pi$
$233$	20.8576	−	15.1539i	0.0895177	−	0.0650384i	0.631644	+	0.775259i	$0.282381\pi$
$234$	−151.761	+	122.039i	−0.648551	+	0.521534i
$235$	28.1282	−	452.652i	0.119694	−	1.92618i
$236$	−72.9421	−	23.7003i	−0.309077	−	0.100425i
$237$	−100.505	−	185.862i	−0.424071	−	0.784228i
$238$	122.335	−	39.7491i	0.514014	−	0.167013i
$239$	56.1423	+	18.2417i	0.234905	+	0.0763253i	0.424104	−	0.905613i	$-0.360589\pi$
$239$	56.1423	+	18.2417i	0.234905	+	0.0763253i	−0.189199	+	0.981939i	$0.560589\pi$
$240$	−54.4462	+	25.2113i	−0.226859	+	0.105047i
$241$	−45.3121	−	139.456i	−0.188017	−	0.578657i	0.811970	−	0.583699i	$-0.198395\pi$
$241$	−45.3121	−	139.456i	−0.188017	−	0.578657i	−0.999987	+	0.00504186i	$0.998395\pi$
$242$	−207.199	+	150.539i	−0.856193	+	0.622061i
$243$	149.567	−	191.517i	0.615503	−	0.788134i
$244$	123.881	−	90.0049i	0.507710	−	0.368873i
$245$	80.0884	+	125.984i	0.326891	+	0.514222i
$246$	9.98733	−	20.8473i	0.0405989	−	0.0847452i
$247$	157.981	−	217.442i	0.639597	−	0.880330i
$248$	35.7292	−	109.963i	0.144069	−	0.443400i
$249$	346.450	−	63.5999i	1.39137	−	0.255421i
$250$	−32.7230	+	173.722i	−0.130892	+	0.694887i
$251$			101.467i			0.404252i	0.979359	+	0.202126i	$0.0647851\pi$
$251$			101.467i			0.404252i	−0.979359	+	0.202126i	$0.935215\pi$
$252$	159.651	−	7.82110i	0.633537	−	0.0310361i
$253$	−294.610	+	405.496i	−1.16447	+	1.60275i
$254$	114.226	−	157.219i	0.449709	−	0.618972i
$255$	−104.480	−	112.645i	−0.409725	−	0.441744i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−125.099			−0.486765			−0.243383	−	0.969930i	$-0.578257\pi$
$257$	−125.099			−0.486765			−0.243383	+	0.969930i	$0.578257\pi$
$258$	83.4418	+	79.4542i	0.323418	+	0.307962i
$259$	4.24619	+	13.0684i	0.0163945	+	0.0504572i
$260$	38.1650	+	148.168i	0.146788	+	0.569879i
$261$	−102.301	+	5.01158i	−0.391957	+	0.0192014i
$262$	−76.8890	+	24.9827i	−0.293469	+	0.0953540i
$263$	66.7110	+	205.315i	0.253654	+	0.780667i	0.994092	+	0.108542i	$0.0346182\pi$
$263$	66.7110	+	205.315i	0.253654	+	0.780667i	−0.740438	+	0.672125i	$0.765382\pi$
$264$	−146.188	−	19.4996i	−0.553741	−	0.0738622i
$265$	−5.92563	+	95.3582i	−0.0223609	+	0.359842i
$266$	−209.808	+	68.1707i	−0.788751	+	0.256281i
$267$	309.549	+	294.756i	1.15936	+	1.10395i
$268$			101.197i			0.377601i
$269$	14.5225	+	19.9886i	0.0539871	+	0.0743069i	0.835157	−	0.550012i	$-0.185377\pi$
$269$	14.5225	+	19.9886i	0.0539871	+	0.0743069i	−0.781170	+	0.624319i	$0.785377\pi$
$270$	−88.6027	−	169.114i	−0.328158	−	0.626348i
$271$	375.863	+	273.080i	1.38695	+	1.00768i	0.996192	+	0.0871815i	$0.0277860\pi$
$271$	375.863	+	273.080i	1.38695	+	1.00768i	0.390755	+	0.920495i	$0.372214\pi$
$272$	−33.1457	−	24.0818i	−0.121859	−	0.0885359i
$273$	53.8930	−	404.033i	0.197410	−	1.47998i
$274$	234.485			0.855786
$275$	−296.964	+	317.213i	−1.07987	+	1.15350i
$276$	−170.180	+	31.2410i	−0.616595	+	0.113192i
$277$	−225.091	−	73.1364i	−0.812601	−	0.264030i	−0.126902	−	0.991915i	$-0.540503\pi$
$277$	−225.091	−	73.1364i	−0.812601	−	0.264030i	−0.685699	+	0.727885i	$0.740503\pi$
$278$	−4.15147	−	3.01622i	−0.0149333	−	0.0108497i
$279$	355.045	+	96.4329i	1.27256	+	0.345638i
$280$	46.1407	−	116.801i	0.164788	−	0.417146i
$281$	−52.7516	−	72.6064i	−0.187728	−	0.258386i	0.704771	−	0.709435i	$-0.251050\pi$
$281$	−52.7516	−	72.6064i	−0.187728	−	0.258386i	−0.892499	+	0.451049i	$0.851050\pi$
$282$	378.504	−	69.4842i	1.34221	−	0.246398i
$283$	−296.551	−	408.168i	−1.04789	−	1.44229i	−0.890628	−	0.454732i	$-0.849735\pi$
$283$	−296.551	−	408.168i	−1.04789	−	1.44229i	−0.157257	−	0.987558i	$-0.550265\pi$
$284$	−152.449	+	49.5336i	−0.536791	+	0.174414i
$285$	179.186	+	193.188i	0.628721	+	0.677854i
$286$	−116.219	+	357.685i	−0.406360	+	1.25065i
$287$	14.9514	+	46.0157i	0.0520955	+	0.160334i
$288$	−31.9046	−	39.6748i	−0.110780	−	0.137760i
$289$	−56.8867	+	175.079i	−0.196840	+	0.605811i
$290$	−29.5658	+	74.8432i	−0.101951	+	0.258080i
$291$	−462.374	+	250.029i	−1.58892	+	0.859206i
$292$	25.4987	+	35.0959i	0.0873243	+	0.120192i
$293$	45.9329			0.156768			0.0783838	−	0.996923i	$-0.475024\pi$
$293$	45.9329			0.156768			0.0783838	+	0.996923i	$0.475024\pi$
$294$	−87.3525	+	91.7366i	−0.297117	+	0.312029i
$295$	−147.832	−	122.106i	−0.501126	−	0.413917i
$296$	2.57253	−	3.54078i	0.00869097	−	0.0119621i
$297$	39.2125	−	467.645i	0.132029	−	1.57456i
$298$	40.4300	+	13.1365i	0.135671	+	0.0440823i
$299$			441.225i			1.47567i
$300$	−149.753	+	8.61013i	−0.499176	+	0.0287004i
$301$	−241.162			−0.801204
$302$	104.777	−	322.471i	0.346944	−	1.06778i
$303$	87.2338	−	182.090i	0.287900	−	0.600956i
$304$	56.8457	+	41.3008i	0.186992	+	0.135858i
$305$	370.713	−	95.4877i	1.21545	−	0.313074i
$306$	71.3753	−	109.092i	0.233253	−	0.356510i
$307$			110.694i			0.360567i	0.983615	+	0.180284i	$0.0577015\pi$
$307$			110.694i			0.360567i	−0.983615	+	0.180284i	$0.942298\pi$
$308$	249.737	−	181.444i	0.810833	−	0.589105i
$309$	227.653	−	123.103i	0.736741	−	0.398393i
$310$	184.079	−	222.863i	0.593804	−	0.718913i
$311$	−320.823	−	104.242i	−1.03159	−	0.335182i	−0.256169	−	0.966632i	$-0.582460\pi$
$311$	−320.823	−	104.242i	−1.03159	−	0.335182i	−0.775417	+	0.631450i	$0.782460\pi$
$312$	−114.201	+	61.7543i	−0.366030	+	0.197931i
$313$	27.0113	−	8.77650i	0.0862981	−	0.0280399i	−0.265550	−	0.964097i	$-0.585553\pi$
$313$	27.0113	−	8.77650i	0.0862981	−	0.0280399i	0.351848	+	0.936057i	$0.385553\pi$
$314$	384.223	+	124.842i	1.22364	+	0.397585i
$315$	378.397	+	128.458i	1.20126	+	0.407802i
$316$	−43.5293	−	133.970i	−0.137751	−	0.423954i
$317$	−19.4846	+	14.1564i	−0.0614655	+	0.0446573i	−0.618094	−	0.786104i	$-0.712095\pi$
$317$	−19.4846	+	14.1564i	−0.0614655	+	0.0446573i	0.556628	+	0.830762i	$0.312095\pi$
$318$	−79.7377	+	14.6379i	−0.250747	+	0.0460312i
$319$	−160.025	+	116.265i	−0.501647	+	0.364468i
$320$	−38.7356	+	9.97746i	−0.121049	+	0.0311796i
$321$	−314.507	−	150.671i	−0.979771	−	0.469379i
$322$	212.867	−	292.987i	0.661079	−	0.909897i
$323$	−55.5996	+	171.118i	−0.172135	+	0.529777i
$324$	121.126	−	107.576i	0.373846	−	0.332023i
$325$	−47.3563	+	379.569i	−0.145712	+	1.16791i
$326$			166.430i			0.510521i
$327$	−22.6450	+	169.769i	−0.0692508	+	0.519170i
$328$	9.05823	−	12.4676i	0.0276166	−	0.0380109i
$329$	−473.446	+	651.643i	−1.43905	+	1.98068i
$330$	−321.998	−	179.616i	−0.975750	−	0.544290i
$331$	201.740	−	146.572i	0.609486	−	0.442817i	−0.239748	−	0.970835i	$-0.577065\pi$
$331$	201.740	−	146.572i	0.609486	−	0.442817i	0.849233	+	0.528018i	$0.177065\pi$
$332$	234.826			0.707309
$333$	11.6537	+	7.62464i	0.0349962	+	0.0228968i
$334$	−8.85407	−	27.2500i	−0.0265092	−	0.0815869i
$335$	−92.9516	+	235.299i	−0.277467	+	0.702384i
$336$	105.626	+	14.0892i	0.314364	+	0.0419323i
$337$	−108.391	+	35.2183i	−0.321634	+	0.104505i	−0.465384	−	0.885109i	$-0.654084\pi$
$337$	−108.391	+	35.2183i	−0.321634	+	0.104505i	0.143750	+	0.989614i	$0.454084\pi$
$338$	28.4517	+	87.5655i	0.0841768	+	0.259069i
$339$	−3.80376	+	28.5166i	−0.0112205	+	0.0841197i
$340$	−54.9492	−	86.4387i	−0.161615	−	0.254231i
$341$	675.736	−	219.560i	1.98163	−	0.643870i
$342$	−122.410	+	187.096i	−0.357925	+	0.547063i
$343$			169.992i			0.495602i
$344$	45.1495	+	62.1430i	0.131249	+	0.180648i
$345$	−424.390	−	83.6738i	−1.23012	−	0.242533i
$346$	143.001	+	103.896i	0.413298	+	0.300278i
$347$	−293.966	−	213.579i	−0.847166	−	0.615502i	0.0771974	−	0.997016i	$-0.475403\pi$
$347$	−293.966	−	213.579i	−0.847166	−	0.615502i	−0.924363	+	0.381514i	$0.875403\pi$
$348$	−67.6828	−	9.02805i	−0.194491	−	0.0259427i
$349$	−188.390			−0.539799			−0.269899	−	0.962889i	$-0.586990\pi$
$349$	−188.390			−0.539799			−0.269899	+	0.962889i	$0.586990\pi$
$350$	214.568	−	229.199i	0.613051	−	0.654853i
$351$	−214.046	−	353.336i	−0.609818	−	1.00666i
$352$	−93.5095	−	30.3831i	−0.265652	−	0.0863155i
$353$	−146.982	−	106.789i	−0.416380	−	0.302518i	0.359799	−	0.933030i	$-0.382845\pi$
$353$	−146.982	−	106.789i	−0.416380	−	0.302518i	−0.776180	+	0.630512i	$0.782845\pi$
$354$	70.2929	−	146.728i	0.198568	−	0.414485i
$355$	−399.964	−	24.8541i	−1.12666	−	0.0700114i
$356$	167.494	+	230.535i	0.470488	+	0.647571i
$357$	49.2685	+	268.382i	0.138007	+	0.751772i
$358$	−79.9901	−	110.097i	−0.223436	−	0.307533i
$359$	−274.660	+	89.2425i	−0.765070	+	0.248586i	−0.665453	−	0.746439i	$-0.731762\pi$
$359$	−274.660	+	89.2425i	−0.765070	+	0.248586i	−0.0996170	+	0.995026i	$0.531762\pi$
$360$	−37.7410	−	121.555i	−0.104836	−	0.337653i
$361$	−16.2004	+	49.8598i	−0.0448765	+	0.138116i
$362$	−37.1886	−	114.455i	−0.102731	−	0.316174i
$363$	−258.424	−	477.898i	−0.711911	−	1.31652i
$364$	83.9726	−	258.441i	0.230694	−	0.710003i
$365$	27.0520	+	105.024i	0.0741151	+	0.287738i
$366$	154.508	+	285.728i	0.422152	+	0.780679i
$367$	−104.081	−	143.255i	−0.283598	−	0.390340i	0.643323	−	0.765595i	$-0.277555\pi$
$367$	−104.081	−	143.255i	−0.283598	−	0.390340i	−0.926922	+	0.375255i	$0.877555\pi$
$368$	−115.349			−0.313449
$369$	41.0344	+	26.8475i	0.111204	+	0.0727573i
$370$	9.23378	−	5.86993i	0.0249562	−	0.0158647i
$371$	99.7387	−	137.279i	0.268838	−	0.370023i
$372$	221.198	+	105.970i	0.594619	+	0.284864i
$373$	278.407	+	90.4598i	0.746399	+	0.242520i	0.657431	−	0.753515i	$-0.271643\pi$
$373$	278.407	+	90.4598i	0.746399	+	0.242520i	0.0889679	+	0.996034i	$0.471643\pi$
$374$		−	251.767i		−	0.673174i
$375$	−356.106	−	117.531i	−0.949616	−	0.313416i
$376$	256.553			0.682321
$377$	−53.8076	+	165.603i	−0.142726	+	0.439265i
$378$	−28.3326	+	337.892i	−0.0749539	+	0.893894i
$379$	−456.223	−	331.465i	−1.20375	−	0.874579i	−0.209106	−	0.977893i	$-0.567055\pi$
$379$	−456.223	−	331.465i	−1.20375	−	0.874579i	−0.994649	+	0.103314i	$0.967055\pi$
$380$	94.2392	+	148.244i	0.247998	+	0.390117i
$381$	298.546	+	284.279i	0.783586	+	0.746139i
$382$			171.945i			0.450118i
$383$	−363.176	+	263.863i	−0.948241	+	0.688937i	−0.950390	−	0.311060i	$-0.899316\pi$
$383$	−363.176	+	263.863i	−0.948241	+	0.688937i	0.00214932	+	0.999998i	$0.499316\pi$
$384$	−16.1444	−	29.8556i	−0.0420428	−	0.0777490i
$385$	747.335	−	192.497i	1.94113	−	0.499993i
$386$	91.1288	+	29.6095i	0.236085	+	0.0767086i
$387$	−190.471	+	153.168i	−0.492174	+	0.395783i
$388$	−333.280	+	108.289i	−0.858969	+	0.279096i
$389$	512.841	+	166.632i	1.31836	+	0.428360i	0.881931	−	0.471379i	$-0.156244\pi$
$389$	512.841	+	166.632i	1.31836	+	0.428360i	0.436427	+	0.899740i	$0.356244\pi$
$390$	−322.258	+	38.6920i	−0.826302	+	0.0992102i
$391$	−91.2740	−	280.912i	−0.233437	−	0.718446i
$392$	−68.3204	+	49.6377i	−0.174287	+	0.126627i
$393$	−30.9658	−	168.681i	−0.0787934	−	0.429214i
$394$	−189.212	+	137.471i	−0.480234	+	0.348911i
$395$	21.8414	−	351.482i	0.0552946	−	0.889827i
$396$	82.0036	−	301.919i	0.207080	−	0.762423i
$397$	311.278	−	428.438i	0.784076	−	1.07919i	−0.210744	−	0.977541i	$-0.567589\pi$
$397$	311.278	−	428.438i	0.784076	−	1.07919i	0.994821	−	0.101647i	$-0.0324112\pi$
$398$	130.937	−	402.982i	0.328987	−	1.01252i
$399$	−84.4967	−	460.282i	−0.211771	−	1.15359i
$400$	−99.2307	−	12.3804i	−0.248077	−	0.0309509i
$401$		−	362.105i		−	0.903006i	−0.892270	−	0.451503i	$-0.850888\pi$
$401$		−	362.105i		−	0.903006i	0.892270	−	0.451503i	$-0.149112\pi$
$402$	−212.787	−	28.3832i	−0.529321	−	0.0706049i
$403$	367.638	−	506.010i	0.912252	−	1.25561i
$404$	79.1186	−	108.897i	0.195838	−	0.269548i
$405$	380.446	−	138.873i	0.939374	−	0.342895i
$406$	115.624	−	84.0061i	0.284789	−	0.206912i
$407$	26.8949			0.0660809
$408$	59.9332	−	62.9411i	0.146895	−	0.154267i
$409$	−118.845	−	365.769i	−0.290576	−	0.894300i	−0.984672	−	0.174418i	$-0.944196\pi$
$409$	−118.845	−	365.769i	−0.290576	−	0.894300i	0.694096	−	0.719882i	$-0.255804\pi$
$410$	32.5135	−	20.6688i	0.0793011	−	0.0504118i
$411$	−65.7670	+	493.052i	−0.160017	+	1.19964i
$412$	164.093	−	53.3169i	0.398283	−	0.129410i
$413$	105.231	+	323.868i	0.254797	+	0.784185i
$414$	−17.9592	−	366.600i	−0.0433798	−	0.885506i
$415$	546.007	+	215.693i	1.31568	+	0.519741i
$416$	−82.3164	+	26.7462i	−0.197876	+	0.0642938i
$417$	7.50657	−	7.88331i	0.0180014	−	0.0189048i
$418$			431.787i			1.03298i
$419$	−476.023	−	655.189i	−1.13609	−	1.56370i	−0.775943	−	0.630804i	$-0.782725\pi$
$419$	−476.023	−	655.189i	−1.13609	−	1.56370i	−0.360150	−	0.932894i	$-0.617275\pi$
$420$	232.656	+	129.779i	0.553942	+	0.308999i
$421$	−501.538	−	364.388i	−1.19130	−	0.865531i	−0.197899	−	0.980222i	$-0.563412\pi$
$421$	−501.538	−	364.388i	−1.19130	−	0.865531i	−0.993401	+	0.114692i	$0.963412\pi$
$422$	−166.905	−	121.264i	−0.395510	−	0.287355i
$423$	39.9438	+	815.367i	0.0944297	+	1.92758i
$424$	−54.0468			−0.127469
$425$	−48.3695	−	251.455i	−0.113811	−	0.591658i
$426$	−61.3962	−	334.446i	−0.144123	−	0.785085i
$427$	−646.613	−	210.097i	−1.51432	−	0.492031i
$428$	−188.088	−	136.654i	−0.439459	−	0.319285i
$429$	−719.506	−	344.694i	−1.67717	−	0.803483i
$430$	47.8999	+	185.962i	0.111395	+	0.432471i
$431$	57.0800	+	78.5638i	0.132436	+	0.182283i	0.870085	−	0.492902i	$-0.164064\pi$
$431$	57.0800	+	78.5638i	0.132436	+	0.182283i	−0.737649	+	0.675185i	$0.764064\pi$
$432$	92.3726	−	55.9580i	0.213825	−	0.129533i
$433$	47.8218	+	65.8210i	0.110443	+	0.152012i	0.860660	−	0.509180i	$-0.170051\pi$
$433$	47.8218	+	65.8210i	0.110443	+	0.152012i	−0.750217	+	0.661191i	$0.770051\pi$
$434$	−488.245	+	158.640i	−1.12499	+	0.365531i
$435$	−149.080	−	83.1595i	−0.342713	−	0.191171i
$436$	−35.2840	+	108.593i	−0.0809266	+	0.249067i
$437$	156.537	+	481.772i	0.358208	+	1.10245i
$438$	−80.9479	+	43.7725i	−0.184812	+	0.0999373i
$439$	−176.553	+	543.374i	−0.402171	+	1.23775i	0.521064	+	0.853518i	$0.325535\pi$
$439$	−176.553	+	543.374i	−0.402171	+	1.23775i	−0.923235	+	0.384236i	$0.874465\pi$
$440$	−189.516	−	156.535i	−0.430718	−	0.355762i
$441$	−168.394	−	209.406i	−0.381846	−	0.474843i
$442$	−130.271	−	179.303i	−0.294731	−	0.405663i
$443$	−307.905			−0.695044			−0.347522	−	0.937672i	$-0.612977\pi$
$443$	−307.905			−0.695044			−0.347522	+	0.937672i	$0.612977\pi$
$444$	6.72366	+	6.40234i	0.0151434	+	0.0144197i
$445$	177.697	+	689.876i	0.399319	+	1.55028i
$446$	−295.459	+	406.665i	−0.662465	+	0.911805i
$447$	−38.9617	+	81.3277i	−0.0871626	+	0.181941i
$448$	67.5642	+	21.9529i	0.150813	+	0.0490021i
$449$		−	730.520i		−	1.62699i	−0.581570	−	0.813497i	$-0.697561\pi$
$449$		−	730.520i		−	1.62699i	0.581570	−	0.813497i	$-0.302439\pi$
$450$	23.8972	−	317.299i	0.0531049	−	0.705110i
$451$	94.7008			0.209980
$452$	−5.92677	+	18.2407i	−0.0131123	+	0.0403556i
$453$	648.671	+	310.759i	1.43194	+	0.686002i
$454$	428.230	+	311.127i	0.943237	+	0.685302i
$455$	432.632	−	523.784i	0.950840	−	1.15117i
$456$	−102.787	+	107.945i	−0.225410	+	0.236723i
$457$			334.758i			0.732513i	0.930514	+	0.366256i	$0.119361\pi$
$457$			334.758i			0.732513i	−0.930514	+	0.366256i	$0.880639\pi$
$458$	−205.884	+	149.583i	−0.449528	+	0.326601i
$459$	209.369	+	180.678i	0.456141	+	0.393634i
$460$	−268.204	−	105.951i	−0.583053	−	0.230327i
$461$	385.182	+	125.153i	0.835536	+	0.271482i	0.695375	−	0.718647i	$-0.255238\pi$
$461$	385.182	+	125.153i	0.835536	+	0.271482i	0.140160	+	0.990129i	$0.455238\pi$
$462$	311.478	+	576.011i	0.674194	+	1.24678i
$463$	403.917	−	131.241i	0.872392	−	0.283457i	0.161597	−	0.986857i	$-0.448336\pi$
$463$	403.917	−	131.241i	0.872392	−	0.283457i	0.710795	+	0.703400i	$0.248336\pi$
$464$	−43.2935	−	14.0669i	−0.0933050	−	0.0303166i
$465$	416.984	+	449.570i	0.896740	+	0.966817i
$466$	11.2669	+	34.6759i	0.0241779	+	0.0744119i
$467$	251.589	−	182.790i	0.538734	−	0.391413i	−0.284881	−	0.958563i	$-0.591954\pi$
$467$	251.589	−	182.790i	0.538734	−	0.391413i	0.823615	+	0.567150i	$0.191954\pi$
$468$	−97.8202	−	257.451i	−0.209017	−	0.550109i
$469$	363.510	−	264.106i	0.775075	−	0.563125i
$470$	596.523	+	235.648i	1.26920	+	0.501380i
$471$	−370.269	+	772.890i	−0.786133	+	1.64096i
$472$	63.7537	−	87.7495i	0.135071	−	0.185910i
$473$	−145.863	+	448.921i	−0.308379	+	0.949093i
$474$	293.906	−	53.9541i	0.620055	−	0.113827i
$475$	82.9548	+	431.251i	0.174642	+	0.907897i
$476$			181.912i			0.382167i
$477$	−8.41477	−	171.770i	−0.0176410	−	0.360104i
$478$	−49.0702	+	67.5393i	−0.102657	+	0.141296i
$479$	113.399	−	156.080i	0.236741	−	0.325846i	−0.674071	−	0.738666i	$-0.735456\pi$
$479$	113.399	−	156.080i	0.236741	−	0.325846i	0.910813	+	0.412820i	$0.135456\pi$
$480$	−10.1152	−	84.2477i	−0.0210734	−	0.175516i
$481$	19.1540	−	13.9162i	0.0398211	−	0.0289317i
$482$	207.370			0.430229
$483$	556.359	+	529.771i	1.15188	+	1.09683i
$484$	−111.925	−	344.470i	−0.231250	−	0.711714i
$485$	−874.391	−	54.3354i	−1.80287	−	0.112032i
$486$	192.226	+	284.863i	0.395527	+	0.586139i
$487$	−485.583	+	157.776i	−0.997091	+	0.323974i	−0.761702	−	0.647927i	$-0.775636\pi$
$487$	−485.583	+	157.776i	−0.997091	+	0.323974i	−0.235388	+	0.971901i	$0.575636\pi$
$488$	66.9183	+	205.953i	0.137128	+	0.422036i
$489$	−349.952	−	46.6792i	−0.715648	−	0.0954586i
$490$	−204.448	+	52.6615i	−0.417242	+	0.107472i
$491$	553.144	−	179.727i	1.12657	−	0.366043i	0.314296	−	0.949325i	$-0.398232\pi$
$491$	553.144	−	179.727i	1.12657	−	0.366043i	0.812270	+	0.583282i	$0.198232\pi$
$492$	23.6750	+	22.5435i	0.0481198	+	0.0458202i
$493$		−	116.565i		−	0.236439i
$494$	223.418	+	307.509i	0.452264	+	0.622487i
$495$	467.989	−	626.686i	0.945433	−	1.26603i
$496$	132.286	+	96.1114i	0.266706	+	0.193773i
$497$	575.792	+	418.337i	1.15853	+	0.841725i
$498$	−65.8627	+	493.769i	−0.132254	+	0.991504i
$499$	281.894			0.564918			0.282459	−	0.959279i	$-0.408850\pi$
$499$	281.894			0.564918			0.282459	+	0.959279i	$0.408850\pi$
$500$	−219.355	−	119.931i	−0.438709	−	0.239863i
$501$	59.7819	−	10.9745i	0.119325	−	0.0219052i
$502$	−136.473	−	44.3429i	−0.271859	−	0.0883324i
$503$	−78.1333	−	56.7672i	−0.155335	−	0.112857i	0.507403	−	0.861709i	$-0.330606\pi$
$503$	−78.1333	−	56.7672i	−0.155335	−	0.112857i	−0.662738	+	0.748852i	$0.730606\pi$
$504$	−59.2508	+	218.148i	−0.117561	+	0.432834i
$505$	283.987	−	180.531i	0.562350	−	0.357487i
$506$	−416.642	−	573.458i	−0.823403	−	1.13332i
$507$	−192.104	+	35.2656i	−0.378903	+	0.0695574i
$508$	161.540	+	222.341i	0.317993	+	0.437679i
$509$	−42.5947	+	13.8399i	−0.0836832	+	0.0271903i	−0.350559	−	0.936541i	$-0.614009\pi$
$509$	−42.5947	+	13.8399i	−0.0836832	+	0.0271903i	0.266876	+	0.963731i	$0.414009\pi$
$510$	197.166	−	91.2977i	0.386600	−	0.179015i
$511$	59.5213	−	183.188i	0.116480	−	0.358489i
$512$	−6.99226	−	21.5200i	−0.0136568	−	0.0420312i
$513$	−359.072	−	309.867i	−0.699946	−	0.604030i
$514$	54.6701	−	168.257i	0.106362	−	0.327349i
$515$	430.512	+	26.7524i	0.835946	+	0.0519464i
$516$	−143.331	+	77.5062i	−0.277773	+	0.150206i
$517$	926.668	+	1275.45i	1.79239	+	2.46702i
$518$	−19.4326			−0.0375147
$519$	−258.571	+	271.548i	−0.498209	+	0.523213i
$520$	−215.965	−	13.4202i	−0.415317	−	0.0258081i
$521$	437.726	−	602.478i	0.840164	−	1.15639i	−0.145781	−	0.989317i	$-0.546569\pi$
$521$	437.726	−	602.478i	0.840164	−	1.15639i	0.985945	−	0.167070i	$-0.0534306\pi$
$522$	37.9665	−	139.784i	0.0727327	−	0.267786i
$523$	−427.802	−	139.001i	−0.817977	−	0.265777i	−0.130005	−	0.991513i	$-0.541499\pi$
$523$	−427.802	−	139.001i	−0.817977	−	0.265777i	−0.687973	+	0.725736i	$0.741499\pi$
$524$		−	114.333i		−	0.218193i
$525$	421.755	+	515.455i	0.803342	+	0.981820i
$526$	−305.302			−0.580423
$527$	−129.386	+	398.210i	−0.245515	+	0.755617i
$528$	90.1133	−	188.100i	0.170669	−	0.356251i
$529$	−244.801	−	177.859i	−0.462763	−	0.336217i
$530$	−125.667	−	49.6430i	−0.237107	−	0.0936660i
$531$	288.809	+	188.958i	0.543896	+	0.355853i
$532$		−	311.983i		−	0.586433i
$533$	67.4438	−	49.0008i	0.126536	−	0.0919340i
$534$	−531.724	+	287.530i	−0.995737	+	0.538445i
$535$	−311.814	−	490.504i	−0.582830	−	0.916830i
$536$	−136.110	−	44.2248i	−0.253936	−	0.0825089i
$537$	253.936	−	137.316i	0.472878	−	0.255709i
$538$	−33.2311	+	10.7975i	−0.0617679	+	0.0200696i
$539$	−493.547	−	160.363i	−0.915672	−	0.297520i
$540$	266.179	−	45.2648i	0.492923	−	0.0838238i
$541$	52.9898	+	163.086i	0.0979480	+	0.301453i	0.988011	−	0.154385i	$-0.0493397\pi$
$541$	52.9898	+	163.086i	0.0979480	+	0.301453i	−0.890063	+	0.455838i	$0.849340\pi$
$542$	−531.550	+	386.194i	−0.980720	+	0.712535i
$543$	251.094	−	46.0949i	0.462420	−	0.0848892i
$544$	46.8751	−	34.0568i	0.0861675	−	0.0626043i
$545$	−181.785	+	220.086i	−0.333551	+	0.403828i
$546$	519.871	+	249.055i	0.952145	+	0.456145i
$547$	−223.225	+	307.243i	−0.408090	+	0.561687i	−0.962751	−	0.270389i	$-0.912848\pi$
$547$	−223.225	+	307.243i	−0.408090	+	0.561687i	0.554661	+	0.832076i	$0.312848\pi$
$548$	−102.474	+	315.382i	−0.186996	+	0.575515i
$549$	−644.136	+	244.743i	−1.17329	+	0.445799i
$550$	−296.872	−	538.042i	−0.539768	−	0.978259i
$551$			199.911i			0.362815i
$552$	32.3524	−	242.545i	0.0586095	−	0.439392i
$553$	−367.628	+	505.997i	−0.664789	+	0.915003i
$554$	196.736	−	270.784i	0.355120	−	0.488780i
$555$	9.75284	+	21.0622i	0.0175727	+	0.0379499i
$556$	5.87106	−	4.26558i	0.0105595	−	0.00767190i
$557$	162.914			0.292485			0.146243	−	0.989249i	$-0.453282\pi$
$557$	162.914			0.292485			0.146243	+	0.989249i	$0.453282\pi$
$558$	−284.862	+	435.391i	−0.510506	+	0.780271i
$559$	128.403	+	395.185i	0.229702	+	0.706950i
$560$	136.933	+	113.103i	0.244523	+	0.201970i
$561$	529.390	+	70.6141i	0.943654	+	0.125872i
$562$	120.709	−	39.2206i	0.214784	−	0.0697876i
$563$	−18.6650	−	57.4448i	−0.0331527	−	0.102033i	0.933111	−	0.359589i	$-0.117083\pi$
$563$	−18.6650	−	57.4448i	−0.0331527	−	0.102033i	−0.966264	+	0.257555i	$0.917083\pi$
$564$	−71.9562	+	539.452i	−0.127582	+	0.956476i
$565$	−30.5351	+	36.9686i	−0.0540444	+	0.0654311i
$566$	678.583	−	220.485i	1.19891	−	0.389549i
$567$	−702.538	−	154.345i	−1.23904	−	0.272213i
$568$		−	226.690i		−	0.399102i
$569$	−306.353	−	421.658i	−0.538405	−	0.741051i	0.449977	−	0.893040i	$-0.351432\pi$
$569$	−306.353	−	421.658i	−0.538405	−	0.741051i	−0.988382	+	0.151989i	$0.951432\pi$
$570$	−338.145	+	156.578i	−0.593236	+	0.274698i
$571$	438.487	+	318.579i	0.767928	+	0.557932i	0.901332	−	0.433129i	$-0.142591\pi$
$571$	438.487	+	318.579i	0.767928	+	0.557932i	−0.133404	+	0.991062i	$0.542591\pi$
$572$	−430.296	−	312.628i	−0.752265	−	0.546552i
$573$	−361.548	−	48.2261i	−0.630974	−	0.0841642i
$574$	−68.4251			−0.119207
$575$	−526.298	−	492.702i	−0.915301	−	0.856873i
$576$	67.3054	−	25.5731i	0.116850	−	0.0443978i
$577$	789.861	+	256.641i	1.36891	+	0.444786i	0.899008	−	0.437933i	$-0.144289\pi$
$577$	789.861	+	256.641i	1.36891	+	0.444786i	0.469902	+	0.882719i	$0.344289\pi$
$578$	−210.621	−	153.025i	−0.364396	−	0.264749i
$579$	−87.8191	+	183.311i	−0.151674	+	0.316600i
$580$	−87.7432	−	72.4736i	−0.151281	−	0.124955i
$581$	−612.853	−	843.520i	−1.05482	−	1.45184i
$582$	−134.223	−	731.159i	−0.230624	−	1.25629i
$583$	−195.217	−	268.693i	−0.334849	−	0.460880i
$584$	−58.3473	+	18.9582i	−0.0999097	+	0.0324626i
$585$	9.02726	−	688.462i	0.0154312	−	1.17686i
$586$	−20.0734	+	61.7796i	−0.0342550	+	0.105426i
$587$	−87.1657	−	268.268i	−0.148494	−	0.457016i	0.848950	−	0.528473i	$-0.177235\pi$
$587$	−87.1657	−	268.268i	−0.148494	−	0.457016i	−0.997444	+	0.0714568i	$0.977235\pi$
$588$	−85.2110	−	157.579i	−0.144917	−	0.267992i
$589$	221.901	−	682.940i	0.376741	−	1.15949i
$590$	228.837	−	145.472i	0.387859	−	0.246562i
$591$	−235.990	−	436.413i	−0.399307	−	0.738432i
$592$	3.63810	+	5.00742i	0.00614544	+	0.00845847i
$593$	−737.541			−1.24374			−0.621872	−	0.783119i	$-0.713628\pi$
$593$	−737.541			−1.24374			−0.621872	+	0.783119i	$0.713628\pi$
$594$	611.845	+	257.109i	1.03004	+	0.432844i
$595$	−167.089	+	422.972i	−0.280822	+	0.710877i
$596$	−35.3372	+	48.6374i	−0.0592905	+	0.0816064i
$597$	810.624	+	388.346i	1.35783	+	0.650496i
$598$	−593.446	−	192.822i	−0.992385	−	0.322445i
$599$			494.412i			0.825396i	0.910868	+	0.412698i	$0.135414\pi$
$599$			494.412i			0.825396i	−0.910868	+	0.412698i	$0.864586\pi$
$600$	53.8637	−	205.180i	0.0897729	−	0.341966i
$601$	−547.684			−0.911288			−0.455644	−	0.890162i	$-0.650591\pi$
$601$	−547.684			−0.911288			−0.455644	+	0.890162i	$0.650591\pi$
$602$	105.392	−	324.363i	0.175070	−	0.538809i
$603$	119.362	−	439.466i	0.197947	−	0.728799i
$604$	387.933	+	281.850i	0.642273	+	0.466639i
$605$	56.1597	−	903.749i	0.0928259	−	1.49380i
$606$	206.788	+	196.905i	0.341234	+	0.324926i
$607$			414.860i			0.683459i	0.939798	+	0.341729i	$0.111013\pi$
$607$			414.860i			0.683459i	−0.939798	+	0.341729i	$0.888987\pi$
$608$	−80.3919	+	58.4082i	−0.132224	+	0.0960661i
$609$	144.210	+	266.685i	0.236798	+	0.437906i
$610$	−33.5770	+	540.338i	−0.0550443	+	0.885800i
$611$	1319.90	+	428.863i	2.16024	+	0.701903i
$612$	115.536	+	143.675i	0.188785	+	0.234762i
$613$	569.176	−	184.937i	0.928509	−	0.301691i	0.194556	−	0.980891i	$-0.437673\pi$
$613$	569.176	−	184.937i	0.928509	−	0.301691i	0.733953	+	0.679200i	$0.237673\pi$
$614$	−148.883	−	48.3751i	−0.242481	−	0.0787868i
$615$	34.3411	+	74.1630i	0.0558393	+	0.120590i
$616$	134.903	+	415.189i	0.218999	+	0.674008i
$617$	95.2613	−	69.2114i	0.154394	−	0.112174i	−0.507906	−	0.861412i	$-0.669580\pi$
$617$	95.2613	−	69.2114i	0.154394	−	0.112174i	0.662300	+	0.749238i	$0.269580\pi$
$618$	66.0856	+	359.991i	0.106935	+	0.582509i
$619$	279.977	−	203.415i	0.452305	−	0.328619i	−0.338200	−	0.941074i	$-0.609818\pi$
$619$	279.977	−	203.415i	0.452305	−	0.328619i	0.790505	+	0.612455i	$0.209818\pi$
$620$	219.305	+	344.981i	0.353717	+	0.556420i
$621$	775.885	+	65.0587i	1.24941	+	0.104764i
$622$	280.410	−	385.951i	0.450819	−	0.620500i
$623$	390.979	−	1203.31i	0.627574	−	1.93147i
$624$	−33.1516	−	180.588i	−0.0531276	−	0.289404i
$625$	−399.873	−	480.340i	−0.639797	−	0.768544i
$626$			40.1656i			0.0641623i
$627$	−907.916	−	121.105i	−1.44803	−	0.193150i
$628$	−335.823	+	462.221i	−0.534751	+	0.736021i
$629$	−9.31589	+	12.8222i	−0.0148106	+	0.0203851i
$630$	−338.141	+	452.805i	−0.536731	+	0.718738i
$631$	−70.4052	+	51.1524i	−0.111577	+	0.0810656i	−0.642175	−	0.766558i	$-0.721968\pi$
$631$	−70.4052	+	51.1524i	−0.111577	+	0.0810656i	0.530597	+	0.847624i	$0.321968\pi$
$632$	199.212			0.315208
$633$	301.793	−	316.939i	0.476766	−	0.500694i
$634$	−10.5252	−	32.3932i	−0.0166013	−	0.0510934i
$635$	171.381	+	665.354i	0.269891	+	1.04780i
$636$	15.1587	−	113.644i	0.0238344	−	0.178686i
$637$	−434.470	+	141.168i	−0.682056	+	0.221613i
$638$	−86.4427	−	266.043i	−0.135490	−	0.416996i
$639$	720.459	−	35.2943i	1.12748	−	0.0552337i
$640$	3.50845	−	56.4596i	0.00548195	−	0.0882182i
$641$	−564.370	+	183.375i	−0.880452	+	0.286076i	−0.714145	−	0.699998i	$-0.753184\pi$
$641$	−564.370	+	183.375i	−0.880452	+	0.286076i	−0.166307	+	0.986074i	$0.553184\pi$
$642$	340.096	−	357.165i	0.529745	−	0.556332i
$643$		−	555.696i		−	0.864224i	−0.901820	−	0.432112i	$-0.857768\pi$
$643$		−	555.696i		−	0.864224i	0.901820	−	0.432112i	$-0.142232\pi$
$644$	301.040	+	414.346i	0.467453	+	0.643394i
$645$	−404.457	+	48.5613i	−0.627065	+	0.0752889i
$646$	−205.855	−	149.563i	−0.318662	−	0.231521i
$647$	862.659	+	626.758i	1.33332	+	0.968715i	0.999661	+	0.0260212i	$0.00828373\pi$
$647$	862.659	+	626.758i	1.33332	+	0.968715i	0.333660	+	0.942693i	$0.391716\pi$
$648$	91.7547	+	209.926i	0.141597	+	0.323960i
$649$	666.524			1.02700
$650$	−489.824	−	229.572i	−0.753575	−	0.353188i
$651$	−196.633	−	1071.13i	−0.302048	−	1.64536i
$652$	−223.848	−	72.7326i	−0.343325	−	0.111553i
$653$	636.997	+	462.806i	0.975494	+	0.708738i	0.956697	−	0.291086i	$-0.0940165\pi$
$653$	636.997	+	462.806i	0.975494	+	0.708738i	0.0187968	+	0.999823i	$0.494016\pi$
$654$	−218.442	−	104.649i	−0.334009	−	0.160014i
$655$	105.017	−	265.842i	0.160332	−	0.405866i
$656$	12.8103	+	17.6318i	0.0195279	+	0.0268778i
$657$	−69.3367	−	182.486i	−0.105535	−	0.277756i
$658$	−669.554	−	921.562i	−1.01756	−	1.40055i
$659$	−233.655	+	75.9192i	−0.354560	+	0.115204i	−0.480881	−	0.876786i	$-0.659683\pi$
$659$	−233.655	+	75.9192i	−0.354560	+	0.115204i	0.126321	+	0.991989i	$0.459683\pi$
$660$	382.301	−	354.591i	0.579244	−	0.537259i
$661$	177.145	−	545.195i	0.267995	−	0.824804i	−0.722993	−	0.690855i	$-0.757234\pi$
$661$	177.145	−	545.195i	0.267995	−	0.824804i	0.990988	−	0.133949i	$-0.0427657\pi$
$662$	108.976	+	335.394i	0.164616	+	0.506637i
$663$	413.557	−	223.631i	0.623767	−	0.337302i
$664$	−102.623	+	315.841i	−0.154553	+	0.475664i
$665$	286.562	−	725.406i	0.430920	−	1.09084i
$666$	−15.3480	+	12.3421i	−0.0230450	+	0.0185317i
$667$	−192.899	−	265.503i	−0.289204	−	0.398055i
$668$	40.5206			0.0606595
$669$	−772.224	−	735.320i	−1.15430	−	1.09913i
$670$	−275.855	−	227.849i	−0.411723	−	0.340073i
$671$	−782.187	+	1076.59i	−1.16570	+	1.60445i
$672$	−65.1104	+	135.910i	−0.0968905	+	0.202247i
$673$	−1217.43	−	395.567i	−1.80896	−	0.587767i	−0.808961	−	0.587862i	$-0.799970\pi$
$673$	−1217.43	−	395.567i	−1.80896	−	0.587767i	−1.00000		9.49759e-5i	$0.999970\pi$
$674$		−	161.176i		−	0.239134i
$675$	660.482	+	139.243i	0.978492	+	0.206286i
$676$	−130.209			−0.192617
$677$	−21.7680	+	66.9952i	−0.0321537	+	0.0989589i	−0.965845	−	0.259119i	$-0.916568\pi$
$677$	−21.7680	+	66.9952i	−0.0321537	+	0.0989589i	0.933692	+	0.358078i	$0.116568\pi$
$678$	−36.6924	−	17.5783i	−0.0541186	−	0.0259266i
$679$	1258.78	+	914.559i	1.85388	+	1.34692i
$680$	140.273	−	36.1314i	0.206285	−	0.0531344i
$681$	−774.313	+	813.174i	−1.13702	+	1.19409i
$682$			1004.81i			1.47333i
$683$	50.6807	−	36.8217i	0.0742031	−	0.0539117i	−0.550065	−	0.835122i	$-0.685397\pi$
$683$	50.6807	−	36.8217i	0.0742031	−	0.0539117i	0.624268	+	0.781210i	$0.285397\pi$
$684$	−198.148	−	246.405i	−0.289689	−	0.360242i
$685$	−527.952	+	639.187i	−0.770733	+	0.933119i
$686$	−228.638	−	74.2891i	−0.333292	−	0.108293i
$687$	−256.784	−	474.866i	−0.373775	−	0.691217i
$688$	−103.313	+	33.5685i	−0.150164	+	0.0487914i
$689$	−278.058	−	90.3467i	−0.403568	−	0.131127i
$690$	298.006	−	534.236i	0.431893	−	0.774255i
$691$	−293.365	−	902.886i	−0.424552	−	1.30664i	−0.903423	−	0.428751i	$-0.858954\pi$
$691$	−293.365	−	902.886i	−0.424552	−	1.30664i	0.478871	−	0.877885i	$-0.341046\pi$
$692$	−202.234	+	146.932i	−0.292246	+	0.212329i
$693$	−1298.54	+	493.388i	−1.87379	+	0.711959i
$694$	415.731	−	302.047i	0.599037	−	0.435226i
$695$	17.5691	−	4.52542i	0.0252793	−	0.00651140i
$696$	41.7212	−	87.0878i	0.0599442	−	0.125126i
$697$	−32.8026	+	45.1489i	−0.0470625	+	0.0647760i
$698$	82.3293	−	253.384i	0.117950	−	0.363014i
$699$	−76.0731	+	13.9652i	−0.108831	+	0.0199788i
$700$	214.502	+	388.757i	0.306431	+	0.555367i
$701$			1169.75i			1.66868i	0.551247	+	0.834342i	$0.314152\pi$
$701$			1169.75i			1.66868i	−0.551247	+	0.834342i	$0.685848\pi$
$702$	568.778	−	133.478i	0.810225	−	0.190139i
$703$	15.9770	−	21.9904i	0.0227269	−	0.0312808i
$704$	81.7303	−	112.492i	0.116094	−	0.159790i
$705$	−662.806	+	1188.21i	−0.940151	+	1.68541i
$706$	207.864	−	151.022i	0.294425	−	0.213913i
$707$	−597.655			−0.845339
$708$	166.629	+	158.666i	0.235352	+	0.224105i
$709$	−153.546	−	472.565i	−0.216566	−	0.666523i	−0.999039	−	0.0438374i	$-0.986042\pi$
$709$	−153.546	−	472.565i	−0.216566	−	0.666523i	0.782472	−	0.622685i	$-0.213958\pi$
$710$	208.219	−	527.088i	0.293266	−	0.742378i
$711$	31.0161	+	633.128i	0.0436232	+	0.890476i
$712$	−383.267	+	124.531i	−0.538296	+	0.174903i
$713$	364.279	+	1121.13i	0.510910	+	1.57242i
$714$	−382.505	−	51.0214i	−0.535721	−	0.0714585i
$715$	−713.347	−	1122.14i	−0.997688	−	1.56943i
$716$	183.037	−	59.4723i	0.255638	−	0.0830619i
$717$	−128.252	−	122.123i	−0.178873	−	0.170325i
$718$		−	408.418i		−	0.568827i
$719$	−404.305	−	556.477i	−0.562315	−	0.773960i	0.429303	−	0.903160i	$-0.358759\pi$
$719$	−404.305	−	556.477i	−0.562315	−	0.773960i	−0.991619	+	0.129200i	$0.958759\pi$
$720$	179.985	+	2.35999i	0.249979	+	0.00327777i
$721$	−619.770	−	450.289i	−0.859598	−	0.624534i
$722$	−59.9814	−	43.5790i	−0.0830767	−	0.0603588i
$723$	−58.1620	+	436.037i	−0.0804453	+	0.603094i
$724$	170.193			0.235074
$725$	−137.448	−	249.106i	−0.189583	−	0.343594i
$726$	755.707	−	138.730i	1.04092	−	0.191088i
$727$	883.026	+	286.913i	1.21462	+	0.394653i	0.845119	−	0.534579i	$-0.179530\pi$
$727$	883.026	+	286.913i	1.21462	+	0.394653i	0.369498	+	0.929232i	$0.379530\pi$
$728$	310.905	+	225.886i	0.427068	+	0.310283i
$729$	−652.896	+	324.296i	−0.895605	+	0.444851i
$730$	−153.080	−	9.51249i	−0.209698	−	0.0130308i
$731$	−163.500	−	225.038i	−0.223666	−	0.307850i
$732$	−451.826	+	82.9444i	−0.617249	+	0.113312i
$733$	−143.420	−	197.401i	−0.195662	−	0.269306i	0.699902	−	0.714239i	$-0.253227\pi$
$733$	−143.420	−	197.401i	−0.195662	−	0.269306i	−0.895563	+	0.444934i	$0.853227\pi$
$734$	238.162	−	77.3835i	0.324471	−	0.105427i
$735$	−53.3887	−	444.663i	−0.0726377	−	0.604984i
$736$	50.4095	−	155.144i	0.0684912	−	0.210794i
$737$	−271.766	−	836.410i	−0.368746	−	1.13488i
$738$	−54.0424	+	43.4584i	−0.0732282	+	0.0588867i
$739$	−349.812	+	1076.61i	−0.473359	+	1.45685i	0.374800	+	0.927106i	$0.377711\pi$
$739$	−349.812	+	1076.61i	−0.473359	+	1.45685i	−0.848159	+	0.529742i	$0.822289\pi$
$740$	3.85972	+	14.9847i	0.00521584	+	0.0202495i
$741$	−709.261	+	383.533i	−0.957167	+	0.517588i
$742$	141.052	+	194.141i	0.190097	+	0.261646i
$743$	711.688			0.957857			0.478929	−	0.877854i	$-0.341025\pi$
$743$	711.688			0.957857			0.478929	+	0.877854i	$0.341025\pi$
$744$	−239.196	+	251.201i	−0.321500	+	0.337635i
$745$	−126.839	+	80.6314i	−0.170253	+	0.108230i
$746$	−243.336	+	334.924i	−0.326188	+	0.448960i
$747$	−1019.77	−	276.978i	−1.36516	−	0.370788i
$748$	338.626	+	110.026i	0.452709	+	0.147094i
$749$			1032.27i			1.37820i
$750$	313.703	−	427.599i	0.418270	−	0.570132i
$751$	1293.60			1.72251			0.861254	−	0.508175i	$-0.169680\pi$
$751$	1293.60			1.72251			0.861254	+	0.508175i	$0.169680\pi$
$752$	−112.118	+	345.062i	−0.149092	+	0.458860i
$753$	131.517	−	274.525i	0.174657	−	0.364575i
$754$	−199.221	−	144.742i	−0.264218	−	0.191966i
$755$	643.118	+	1011.67i	0.851811	+	1.33996i
$756$	−442.082	−	185.771i	−0.584764	−	0.245729i
$757$		−	1171.95i		−	1.54815i	−0.633092	−	0.774076i	$-0.718215\pi$
$757$		−	1171.95i		−	1.54815i	0.633092	−	0.774076i	$-0.281785\pi$
$758$	645.197	−	468.763i	0.851183	−	0.618421i
$759$	1322.67	−	715.232i	1.74264	−	0.942334i
$760$	−240.572	+	61.9662i	−0.316543	+	0.0815345i
$761$	−929.297	−	301.947i	−1.22115	−	0.396776i	−0.373651	−	0.927569i	$-0.621894\pi$
$761$	−929.297	−	301.947i	−1.22115	−	0.396776i	−0.847502	+	0.530793i	$0.821894\pi$
$762$	−512.824	+	277.309i	−0.672997	+	0.363923i
$763$	482.161	−	156.664i	0.631928	−	0.205326i
$764$	−231.266	−	75.1428i	−0.302704	−	0.0983544i
$765$	136.671	+	440.187i	0.178655	+	0.575408i
$766$	−196.181	−	603.783i	−0.256111	−	0.788229i
$767$	474.684	−	344.878i	0.618884	−	0.449645i
$768$	47.2111	−	8.66681i	0.0614728	−	0.0112849i
$769$	−6.70121	+	4.86871i	−0.00871418	+	0.00633122i	−0.592134	−	0.805840i	$-0.701714\pi$
$769$	−6.70121	+	4.86871i	−0.00871418	+	0.00633122i	0.583420	+	0.812171i	$0.301714\pi$
$770$	−67.6892	+	1089.29i	−0.0879081	+	1.41466i
$771$	338.461	+	162.147i	0.438989	+	0.210307i
$772$	−79.6494	+	109.628i	−0.103173	+	0.142005i
$773$	−182.178	+	560.686i	−0.235676	+	0.725337i	0.761355	+	0.648336i	$0.224535\pi$
$773$	−182.178	+	560.686i	−0.235676	+	0.725337i	−0.997031	+	0.0770017i	$0.975465\pi$
$774$	−122.772	−	323.120i	−0.158620	−	0.417468i
$775$	193.045	+	1003.57i	0.249090	+	1.29493i
$776$		−	495.585i		−	0.638640i
$777$	5.45034	−	40.8609i	0.00701460	−	0.0525881i
$778$	−448.240	+	616.949i	−0.576143	+	0.792993i
$779$	56.2572	−	77.4314i	0.0722172	−	0.0993985i
$780$	88.7911	−	450.345i	0.113835	−	0.577365i
$781$	1126.99	−	818.804i	1.44301	−	1.04841i
$782$	417.715			0.534162
$783$	283.275	+	119.038i	0.361782	+	0.152028i
$784$	−36.9054	−	113.583i	−0.0470733	−	0.144877i
$785$	−1205.40	+	766.273i	−1.53554	+	0.976145i
$786$	240.408	+	32.0675i	0.305863	+	0.0407983i
$787$	1289.88	−	419.107i	1.63898	−	0.532538i	0.662672	−	0.748909i	$-0.269422\pi$
$787$	1289.88	−	419.107i	1.63898	−	0.532538i	0.976311	+	0.216371i	$0.0694222\pi$
$788$	−102.209	−	314.567i	−0.129707	−	0.399197i
$789$	85.6293	−	641.958i	0.108529	−	0.813636i
$790$	463.197	+	182.980i	0.586325	+	0.231620i
$791$	80.9902	−	26.3153i	0.102390	−	0.0332684i
$792$	370.244	+	242.238i	0.467479	+	0.305856i
$793$			1171.45i			1.47723i
$794$	440.214	+	605.902i	0.554426	+	0.763101i
$795$	139.630	−	250.316i	0.175636	−	0.314863i
$796$	484.788	+	352.219i	0.609030	+	0.442486i
$797$	−273.643	−	198.813i	−0.343342	−	0.249452i	0.402729	−	0.915319i	$-0.368062\pi$
$797$	−273.643	−	198.813i	−0.343342	−	0.249452i	−0.746070	+	0.665867i	$0.768062\pi$
$798$	656.005	+	87.5029i	0.822061	+	0.109653i
$799$	−929.054			−1.16277
$800$	60.0169	−	128.055i	0.0750212	−	0.160068i
$801$	−455.453	−	1198.70i	−0.568605	−	1.49650i
$802$	487.031	+	158.246i	0.607270	+	0.197314i
$803$	−305.001	−	221.596i	−0.379827	−	0.275960i
$804$	131.167	−	273.794i	0.163143	−	0.340540i
$805$	319.378	+	1239.93i	0.396743	+	1.54028i
$806$	519.918	+	715.606i	0.645060	+	0.887848i
$807$	−13.3833	−	72.9034i	−0.0165840	−	0.0903388i
$808$	111.891	+	154.004i	0.138478	+	0.190599i
$809$	1309.19	−	425.381i	1.61828	−	0.525811i	0.646745	−	0.762706i	$-0.276130\pi$
$809$	1309.19	−	425.381i	1.61828	−	0.525811i	0.971535	+	0.236895i	$0.0761299\pi$
$810$	20.5221	+	572.389i	0.0253359	+	0.706653i
$811$	−90.6930	+	279.124i	−0.111829	+	0.344173i	−0.991272	−	0.131830i	$-0.957915\pi$
$811$	−90.6930	+	279.124i	−0.111829	+	0.344173i	0.879444	+	0.476003i	$0.157915\pi$
$812$	62.4582	+	192.227i	0.0769190	+	0.236732i
$813$	−662.963	−	1226.01i	−0.815452	−	1.50800i
$814$	−11.7535	+	36.1736i	−0.0144392	+	0.0444393i
$815$	−453.673	−	374.723i	−0.556655	−	0.459782i
$816$	58.4638	+	108.116i	0.0716468	+	0.132495i
$817$	280.406	+	385.946i	0.343215	+	0.472394i
$818$	543.895			0.664909
$819$	−669.497	+	1023.28i	−0.817457	+	1.24942i
$820$	13.5906	+	52.7631i	0.0165739	+	0.0643453i
$821$	−212.728	+	292.795i	−0.259108	+	0.356632i	−0.918675	−	0.395014i	$-0.870740\pi$
$821$	−212.728	+	292.795i	−0.259108	+	0.356632i	0.659567	+	0.751646i	$0.270740\pi$
$822$	−634.412	−	303.928i	−0.771791	−	0.369742i
$823$	−255.585	−	83.0445i	−0.310553	−	0.100905i	0.149594	−	0.988747i	$-0.452203\pi$
$823$	−255.585	−	83.0445i	−0.310553	−	0.100905i	−0.460147	+	0.887843i	$0.652203\pi$
$824$			244.004i			0.296122i
$825$	1214.61	−	473.326i	1.47225	−	0.573729i
$826$	−481.590			−0.583039
$827$	−268.822	+	827.349i	−0.325057	+	1.00042i	0.646358	+	0.763034i	$0.276291\pi$
$827$	−268.822	+	827.349i	−0.325057	+	1.00042i	−0.971415	+	0.237388i	$0.923709\pi$
$828$	500.924	+	136.055i	0.604980	+	0.164317i
$829$	498.059	+	361.861i	0.600795	+	0.436503i	0.846161	−	0.532927i	$-0.178908\pi$
$829$	498.059	+	361.861i	0.600795	+	0.436503i	−0.245366	+	0.969431i	$0.578908\pi$
$830$	−528.720	+	640.116i	−0.637012	+	0.771225i
$831$	514.198	+	489.625i	0.618770	+	0.589200i
$832$		−	122.404i		−	0.147120i
$833$	247.409	−	179.753i	0.297010	−	0.215790i
$834$	7.32253	+	13.5414i	0.00878002	+	0.0162367i
$835$	94.2164	+	37.2189i	0.112834	+	0.0445736i
$836$	−580.752	−	188.698i	−0.694679	−	0.225715i
$837$	−835.600	−	721.095i	−0.998327	−	0.861523i
$838$	1089.26	−	353.921i	1.29983	−	0.422340i
$839$	383.519	+	124.613i	0.457115	+	0.148526i	0.528518	−	0.848922i	$-0.322748\pi$
$839$	383.519	+	124.613i	0.457115	+	0.148526i	−0.0714035	+	0.997448i	$0.522748\pi$
$840$	−276.227	+	256.206i	−0.328842	+	0.305007i
$841$	219.862	+	676.664i	0.261429	+	0.804595i
$842$	709.281	−	515.323i	0.842377	−	0.612023i
$843$	48.6135	+	264.814i	0.0576672	+	0.314133i
$844$	236.039	−	171.493i	0.279667	−	0.203190i
$845$	−302.756	−	119.600i	−0.358291	−	0.141538i
$846$	−1114.12	−	302.604i	−1.31693	−	0.357688i
$847$	−945.265	+	1301.05i	−1.11602	+	1.53606i
$848$	23.6193	−	72.6927i	0.0278530	−	0.0857226i
$849$	273.288	+	1488.69i	0.321894	+	1.75347i
$850$	359.344	+	44.8330i	0.422758	+	0.0527447i
$851$			44.6222i			0.0524350i
$852$	476.660	+	63.5806i	0.559460	+	0.0746251i
$853$	384.635	−	529.404i	0.450920	−	0.620638i	−0.521675	−	0.853144i	$-0.674693\pi$
$853$	384.635	−	529.404i	0.450920	−	0.620638i	0.972595	+	0.232506i	$0.0746927\pi$
$854$	565.160	−	777.876i	0.661780	−	0.910862i
$855$	−234.395	−	754.932i	−0.274146	−	0.882961i
$856$	265.997	−	193.258i	0.310744	−	0.225769i
$857$	−668.295			−0.779808			−0.389904	−	0.920856i	$-0.627492\pi$
$857$	−668.295			−0.779808			−0.389904	+	0.920856i	$0.627492\pi$
$858$	778.049	−	817.097i	0.906816	−	0.952328i
$859$	161.884	+	498.228i	0.188456	+	0.580009i	0.999991	−	0.00429551i	$-0.00136731\pi$
$859$	161.884	+	498.228i	0.188456	+	0.580009i	−0.811534	+	0.584305i	$0.801367\pi$
$860$	−271.052	−	16.8434i	−0.315177	−	0.0195853i
$861$	19.1914	−	143.877i	0.0222897	−	0.167105i
$862$	−130.613	+	42.4387i	−0.151523	+	0.0492329i
$863$	74.8592	+	230.393i	0.0867430	+	0.266967i	0.985014	−	0.172474i	$-0.0551762\pi$
$863$	74.8592	+	230.393i	0.0867430	+	0.266967i	−0.898271	+	0.439442i	$0.855176\pi$
$864$	34.8951	+	148.695i	0.0403878	+	0.172101i
$865$	−605.184	+	155.882i	−0.699635	+	0.180211i
$866$	−109.428	+	35.5553i	−0.126360	+	0.0410569i
$867$	380.839	−	399.952i	0.439260	−	0.461306i
$868$		−	726.017i		−	0.836425i
$869$	719.553	+	990.379i	0.828024	+	1.13968i
$870$	177.000	−	164.170i	0.203448	−	0.188702i
$871$	−626.327	−	455.053i	−0.719089	−	0.522449i
$872$	−130.638	−	94.9138i	−0.149814	−	0.108846i
$873$	1575.05	−	77.1597i	1.80418	−	0.0883845i
$874$	−716.391			−0.819669
$875$	141.669	+	1100.94i	0.161907	+	1.25822i
$876$	−23.4984	−	128.004i	−0.0268247	−	0.146123i
$877$	−521.873	−	169.567i	−0.595066	−	0.193349i	−0.00402732	−	0.999992i	$-0.501282\pi$
$877$	−521.873	−	169.567i	−0.595066	−	0.193349i	−0.591039	+	0.806643i	$0.701282\pi$
$878$	−653.680	−	474.926i	−0.744510	−	0.540918i
$879$	−124.274	−	59.5359i	−0.141381	−	0.0677314i
$880$	293.361	−	186.490i	0.333365	−	0.211921i
$881$	−659.986	−	908.393i	−0.749133	−	1.03109i	−0.998041	−	0.0625660i	$-0.980072\pi$
$881$	−659.986	−	908.393i	−0.749133	−	1.03109i	0.248908	−	0.968527i	$-0.419928\pi$
$882$	355.241	−	134.976i	0.402767	−	0.153034i
$883$	252.897	+	348.083i	0.286407	+	0.394205i	0.927843	−	0.372972i	$-0.121661\pi$
$883$	252.897	+	348.083i	0.286407	+	0.394205i	−0.641436	+	0.767176i	$0.721661\pi$
$884$	298.092	−	96.8561i	0.337209	−	0.109566i
$885$	241.700	+	521.975i	0.273108	+	0.589802i
$886$	134.559	−	414.131i	0.151873	−	0.467416i
$887$	−98.4617	−	303.034i	−0.111005	−	0.341639i	0.880088	−	0.474811i	$-0.157484\pi$
$887$	−98.4617	−	303.034i	−0.111005	−	0.341639i	−0.991093	+	0.133172i	$0.957484\pi$
$888$	−11.5495	+	6.24538i	−0.0130062	+	0.00703308i
$889$	377.081	−	1160.54i	0.424163	−	1.30544i
$890$	−1005.54	−	62.4849i	−1.12982	−	0.0702077i
$891$	−712.229	+	1214.41i	−0.799359	+	1.36298i
$892$	−417.843	−	575.111i	−0.468433	−	0.644743i
$893$	1593.35			1.78427
$894$	−92.3586	−	87.9448i	−0.103309	−	0.0983723i
$895$	480.215	+	29.8409i	0.536553	+	0.0333418i
$896$	−59.0533	+	81.2799i	−0.0659077	+	0.0907142i
$897$	571.893	−	1193.76i	0.637562	−	1.33083i
$898$	982.547	+	319.249i	1.09415	+	0.355511i
$899$			465.214i			0.517480i
$900$	416.323	+	170.807i	0.462581	+	0.189785i
$901$	195.720			0.217225
$902$	−41.3858	+	127.372i	−0.0458822	+	0.141211i
$903$	652.477	+	312.582i	0.722566	+	0.346160i
$904$	−21.9436	−	15.9430i	−0.0242739	−	0.0176360i
$905$	395.725	+	156.326i	0.437266	+	0.172736i
$906$	−701.449	+	736.654i	−0.774227	+	0.813084i
$907$		−	87.2255i		−	0.0961692i	−0.998843	−	0.0480846i	$-0.984688\pi$
$907$		−	87.2255i		−	0.0961692i	0.998843	−	0.0480846i	$-0.0153117\pi$
$908$	−605.608	+	440.000i	−0.666970	+	0.484582i
$909$	−472.031	+	379.585i	−0.519286	+	0.417585i
$910$	515.421	+	810.791i	0.566396	+	0.890979i
$911$	−1467.29	−	476.753i	−1.61064	−	0.523329i	−0.640934	−	0.767596i	$-0.721453\pi$
$911$	−1467.29	−	476.753i	−1.61064	−	0.523329i	−0.969708	+	0.244267i	$0.921453\pi$
$912$	−100.267	−	185.422i	−0.109942	−	0.203313i
$913$	−1940.88	+	630.629i	−2.12582	+	0.690721i
$914$	−450.249	−	146.295i	−0.492614	−	0.160060i
$915$	−1126.75	−	222.153i	−1.23142	−	0.242790i
$916$	−111.215	−	342.284i	−0.121413	−	0.373672i
$917$	−410.696	+	298.388i	−0.447870	+	0.325396i
$918$	−334.509	+	202.641i	−0.364389	+	0.220742i
$919$	851.640	−	618.753i	0.926703	−	0.673289i	−0.0184806	−	0.999829i	$-0.505883\pi$
$919$	851.640	−	618.753i	0.926703	−	0.673289i	0.945183	+	0.326540i	$0.105883\pi$
$920$	259.713	−	314.432i	0.282297	−	0.341774i
$921$	143.476	−	299.488i	0.155783	−	0.325177i
$922$	−336.661	+	463.375i	−0.365142	+	0.502575i
$923$	378.944	−	1166.27i	0.410556	−	1.26356i
$924$	−910.854	+	167.211i	−0.985773	+	0.180964i
$925$	−4.78927	+	38.3868i	−0.00517759	+	0.0414993i
$926$			600.622i			0.648620i
$927$	−775.487	+	37.9901i	−0.836555	+	0.0409817i
$928$	37.8399	−	52.0822i	0.0407758	−	0.0561231i
$929$	495.358	−	681.801i	0.533216	−	0.733909i	−0.454400	−	0.890798i	$-0.650146\pi$
$929$	495.358	−	681.801i	0.533216	−	0.733909i	0.987616	+	0.156889i	$0.0501464\pi$
$930$	−786.899	+	364.373i	−0.846128	+	0.391799i
$931$	−424.312	+	308.281i	−0.455760	+	0.331129i
$932$	−51.5629			−0.0553250
$933$	732.890	+	697.865i	0.785520	+	0.747980i
$934$	135.904	+	418.268i	0.145507	+	0.447825i
$935$	686.295	+	566.862i	0.734005	+	0.606270i
$936$	389.020	−	19.0576i	0.415620	−	0.0203607i
$937$	869.531	−	282.528i	0.927995	−	0.301524i	0.194252	−	0.980952i	$-0.437772\pi$
$937$	869.531	−	282.528i	0.927995	−	0.301524i	0.733742	+	0.679428i	$0.237772\pi$
$938$	196.361	+	604.338i	0.209341	+	0.644284i
$939$	−84.4561	−	11.2654i	−0.0899426	−	0.0119972i
$940$	−577.637	+	699.340i	−0.614507	+	0.743978i
$941$	1446.35	−	469.947i	1.53703	−	0.499412i	0.586477	−	0.809966i	$-0.300514\pi$
$941$	1446.35	−	469.947i	1.53703	−	0.499412i	0.950556	+	0.310553i	$0.100514\pi$
$942$	−877.722	−	835.776i	−0.931764	−	0.887235i
$943$			157.121i			0.166618i
$944$	90.1614	+	124.096i	0.0955099	+	0.131458i
$945$	−857.272	−	838.007i	−0.907166	−	0.886780i
$946$	−540.053	−	392.371i	−0.570880	−	0.414769i
$947$	−418.835	−	304.301i	−0.442276	−	0.321332i	0.344263	−	0.938873i	$-0.388129\pi$
$947$	−418.835	−	304.301i	−0.442276	−	0.321332i	−0.786539	+	0.617541i	$0.788129\pi$
$948$	−55.8736	+	418.882i	−0.0589384	+	0.441858i
$949$	−331.875			−0.349710
$950$	−616.284	−	76.8897i	−0.648720	−	0.0809365i
$951$	71.0652	−	13.0459i	0.0747268	−	0.0137180i
$952$	−244.670	−	79.4982i	−0.257007	−	0.0835066i
$953$	−801.548	−	582.359i	−0.841079	−	0.611080i	0.0815929	−	0.996666i	$-0.473999\pi$
$953$	−801.548	−	582.359i	−0.841079	−	0.611080i	−0.922672	+	0.385586i	$0.873999\pi$
$954$	234.707	+	63.7483i	0.246024	+	0.0668221i
$955$	−468.707	−	387.140i	−0.490793	−	0.405382i
$956$	−69.3957	−	95.5150i	−0.0725897	−	0.0999111i
$957$	583.653	−	107.145i	0.609878	−	0.111959i
$958$	160.371	+	220.731i	0.167401	+	0.230408i
$959$	1400.32	−	454.992i	1.46019	−	0.474444i
$960$	117.733	+	23.2126i	0.122639	+	0.0241798i
$961$	219.421	−	675.309i	0.228326	−	0.702715i
$962$	10.3466	+	31.8436i	0.0107553	+	0.0331015i
$963$	655.621	+	815.294i	0.680811	+	0.846619i
$964$	−90.6242	+	278.913i	−0.0940085	+	0.289328i
$965$	−285.892	+	181.742i	−0.296262	+	0.188334i
$966$	−955.678	+	516.783i	−0.989314	+	0.534972i
$967$	−933.969	−	1285.50i	−0.965842	−	1.32937i	−0.944119	−	0.329603i	$-0.893085\pi$
$967$	−933.969	−	1285.50i	−0.965842	−	1.32937i	−0.0217225	−	0.999764i	$-0.506915\pi$
$968$	512.224			0.529157
$969$	372.222	−	390.903i	0.384130	−	0.403409i
$970$	455.204	−	1152.31i	0.469282	−	1.18795i
$971$	53.6223	−	73.8048i	0.0552238	−	0.0760091i	−0.780512	−	0.625141i	$-0.785042\pi$
$971$	53.6223	−	73.8048i	0.0552238	−	0.0760091i	0.835736	+	0.549132i	$0.185042\pi$
$972$	−467.146	+	134.054i	−0.480603	+	0.137915i
$973$	−30.6447	−	9.95708i	−0.0314951	−	0.0102334i
$974$		−	722.058i		−	0.741333i
$975$	620.103	−	965.562i	0.636003	−	0.990320i
$976$	−306.251			−0.313782
$977$	29.4896	−	90.7596i	0.0301838	−	0.0928962i	−0.934830	−	0.355096i	$-0.884448\pi$
$977$	29.4896	−	90.7596i	0.0301838	−	0.0928962i	0.965014	+	0.262200i	$0.0844481\pi$
$978$	215.718	−	450.285i	0.220571	−	0.460414i
$979$	−2003.47	−	1455.60i	−2.04644	−	1.48683i
$980$	18.5177	−	297.996i	0.0188957	−	0.304078i
$981$	281.313	−	429.966i	0.286761	−	0.438294i
$982$			822.520i			0.837597i
$983$	−566.239	+	411.397i	−0.576031	+	0.418511i	−0.837291	−	0.546757i	$-0.815862\pi$
$983$	−566.239	+	411.397i	−0.576031	+	0.418511i	0.261260	+	0.965269i	$0.415862\pi$
$984$	−40.6673	+	21.9909i	−0.0413286	+	0.0223484i
$985$	51.2846	−	825.296i	0.0520656	−	0.837864i
$986$	156.779	+	50.9406i	0.159005	+	0.0516639i
$987$	2125.56	−	1149.39i	2.15355	−	1.16453i
$988$	−511.236	+	166.111i	−0.517445	+	0.168128i
$989$	−744.819	−	242.006i	−0.753103	−	0.244698i
$990$	638.372	+	903.316i	0.644820	+	0.912441i
$991$	410.128	+	1262.24i	0.413852	+	1.27371i	0.913273	+	0.407347i	$0.133546\pi$
$991$	410.128	+	1262.24i	0.413852	+	1.27371i	−0.499421	+	0.866359i	$0.666454\pi$
$992$	−187.081	+	135.922i	−0.188589	+	0.137018i
$993$	−735.796	+	135.074i	−0.740983	+	0.136027i
$994$	−814.292	+	591.618i	−0.819208	+	0.595189i
$995$	803.685	+	1264.25i	0.807723	+	1.27060i
$996$	−635.335	−	304.370i	−0.637886	−	0.305592i
$997$	−873.173	+	1201.82i	−0.875800	+	1.20544i	0.101766	+	0.994808i	$0.467551\pi$
$997$	−873.173	+	1201.82i	−0.875800	+	1.20544i	−0.977566	+	0.210628i	$0.932449\pi$
$998$	−123.192	+	379.146i	−0.123439	+	0.379906i
$999$	−21.6470	−	35.7338i	−0.0216687	−	0.0357696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.i.a.29.3	✓	80
3.2	odd	2	inner	150.3.i.a.29.19	yes	80
25.19	even	10	inner	150.3.i.a.119.19	yes	80
75.44	odd	10	inner	150.3.i.a.119.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.i.a.29.3	✓	80	1.1	even	1	trivial
150.3.i.a.29.19	yes	80	3.2	odd	2	inner
150.3.i.a.119.3	yes	80	75.44	odd	10	inner
150.3.i.a.119.19	yes	80	25.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.437016 + 1.34500i) q^{2} +(-2.70555 - 1.29615i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.68239 - 4.21957i) q^{5} +(2.92568 - 3.07252i) q^{6} +8.88015i q^{7} +(2.28825 - 1.66251i) q^{8} +(5.64000 + 7.01359i) q^{9} +O(q^{10})\)	\(q+(-0.437016 + 1.34500i) q^{2} +(-2.70555 - 1.29615i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.68239 - 4.21957i) q^{5} +(2.92568 - 3.07252i) q^{6} +8.88015i q^{7} +(2.28825 - 1.66251i) q^{8} +(5.64000 + 7.01359i) q^{9} +(6.84756 - 1.76378i) q^{10} +(16.5303 + 5.37102i) q^{11} +(2.85396 + 5.27778i) q^{12} +(14.5516 - 4.72811i) q^{13} +(-11.9438 - 3.88077i) q^{14} +(1.78814 + 14.8930i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-8.28643 + 6.02044i) q^{17} +(-11.8980 + 4.52073i) q^{18} +(14.2114 - 10.3252i) q^{19} +(-0.620212 + 9.98075i) q^{20} +(11.5100 - 24.0257i) q^{21} +(-14.4480 + 19.8860i) q^{22} +(-8.91122 + 27.4259i) q^{23} +(-8.34582 + 1.53209i) q^{24} +(-10.6096 + 22.6371i) q^{25} +21.6381i q^{26} +(-6.16864 - 26.2859i) q^{27} +(10.4392 - 14.3684i) q^{28} +(-6.68922 + 9.20692i) q^{29} +(-20.8125 - 4.10345i) q^{30} +(33.0715 - 24.0278i) q^{31} -5.65685 q^{32} +(-37.7619 - 35.9573i) q^{33} +(-4.47618 - 13.7763i) q^{34} +(37.4705 - 23.8200i) q^{35} +(-0.880740 - 17.9784i) q^{36} +(1.47164 - 0.478166i) q^{37} +(7.67675 + 23.6266i) q^{38} +(-45.4985 - 6.06893i) q^{39} +(-13.1530 - 5.19593i) q^{40} +(5.18186 - 1.68369i) q^{41} +(27.2844 + 25.9805i) q^{42} +27.1575i q^{43} +(-20.4326 - 28.1230i) q^{44} +(14.4657 - 42.6115i) q^{45} +(-32.9934 - 23.9711i) q^{46} +(73.3819 + 53.3151i) q^{47} +(1.58660 - 11.8947i) q^{48} -29.8571 q^{49} +(-25.8102 - 24.1626i) q^{50} +(30.2227 - 5.54816i) q^{51} +(-29.1032 - 9.45621i) q^{52} +(-15.4590 - 11.2316i) q^{53} +(38.0502 + 3.19055i) q^{54} +(-21.6772 - 84.1579i) q^{55} +(14.7633 + 20.3200i) q^{56} +(-51.8327 + 9.51523i) q^{57} +(-9.45998 - 13.0205i) q^{58} +(36.4710 - 11.8502i) q^{59} +(14.6145 - 26.1995i) q^{60} +(-23.6592 + 72.8155i) q^{61} +(17.8646 + 54.9816i) q^{62} +(-62.2817 + 50.0840i) q^{63} +(2.47214 - 7.60845i) q^{64} +(-58.9837 - 48.7190i) q^{65} +(64.8650 - 35.0757i) q^{66} +(-29.7411 - 40.9351i) q^{67} +20.4852 q^{68} +(59.6578 - 62.6519i) q^{69} +(15.6627 + 60.8074i) q^{70} +(47.1092 - 64.8403i) q^{71} +(24.5658 + 6.67227i) q^{72} +(-20.6289 - 6.70273i) q^{73} +2.18832i q^{74} +(58.0458 - 47.4941i) q^{75} -35.1326 q^{76} +(-47.6955 + 146.792i) q^{77} +(28.0462 - 58.5431i) q^{78} +(56.9806 + 41.3989i) q^{79} +(12.7366 - 15.4201i) q^{80} +(-17.3809 + 79.1132i) q^{81} +7.70539i q^{82} +(-94.9893 + 69.0138i) q^{83} +(-46.8675 + 25.3436i) q^{84} +(47.6311 + 18.8160i) q^{85} +(-36.5267 - 11.8682i) q^{86} +(30.0315 - 16.2396i) q^{87} +(46.7547 - 15.1915i) q^{88} +(-135.505 - 44.0283i) q^{89} +(50.9907 + 38.0782i) q^{90} +(41.9863 + 129.221i) q^{91} +(46.6598 - 33.9003i) q^{92} +(-120.620 + 22.1430i) q^{93} +(-103.778 + 75.3989i) q^{94} +(-81.6885 - 32.2699i) q^{95} +(15.3049 + 7.33212i) q^{96} +(102.989 - 141.752i) q^{97} +(13.0480 - 40.1577i) q^{98} +(55.5607 + 146.229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 20 q^{9}+O(q^{10}) \) 80 * q - 40 * q^4 + 20 * q^9	\( 80 q - 40 q^{4} + 20 q^{9} + 16 q^{10} + 20 q^{12} + 32 q^{15} - 80 q^{16} + 60 q^{19} - 60 q^{21} + 40 q^{22} + 116 q^{25} - 210 q^{27} - 40 q^{28} - 68 q^{30} + 180 q^{31} - 50 q^{33} - 120 q^{34} + 40 q^{36} - 40 q^{37} + 220 q^{39} + 32 q^{40} + 468 q^{45} + 120 q^{46} - 40 q^{48} - 680 q^{49} + 20 q^{51} - 120 q^{54} - 272 q^{55} - 156 q^{60} - 200 q^{61} - 830 q^{63} - 160 q^{64} + 160 q^{66} + 500 q^{67} - 280 q^{69} - 584 q^{70} + 120 q^{73} - 138 q^{75} - 80 q^{76} + 620 q^{78} + 400 q^{79} - 420 q^{81} + 180 q^{84} + 1632 q^{85} + 750 q^{87} + 160 q^{88} + 472 q^{90} - 340 q^{91} + 160 q^{94} + 20 q^{97} - 260 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 20 * q^9 + 16 * q^10 + 20 * q^12 + 32 * q^15 - 80 * q^16 + 60 * q^19 - 60 * q^21 + 40 * q^22 + 116 * q^25 - 210 * q^27 - 40 * q^28 - 68 * q^30 + 180 * q^31 - 50 * q^33 - 120 * q^34 + 40 * q^36 - 40 * q^37 + 220 * q^39 + 32 * q^40 + 468 * q^45 + 120 * q^46 - 40 * q^48 - 680 * q^49 + 20 * q^51 - 120 * q^54 - 272 * q^55 - 156 * q^60 - 200 * q^61 - 830 * q^63 - 160 * q^64 + 160 * q^66 + 500 * q^67 - 280 * q^69 - 584 * q^70 + 120 * q^73 - 138 * q^75 - 80 * q^76 + 620 * q^78 + 400 * q^79 - 420 * q^81 + 180 * q^84 + 1632 * q^85 + 750 * q^87 + 160 * q^88 + 472 * q^90 - 340 * q^91 + 160 * q^94 + 20 * q^97 - 260 * q^99

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