LMFDB - Embedded newform 270.3.q.b.103.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(7,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([32, 9]))

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

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

chi := DirichletCharacter("270.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	270.q (of order $36$ , degree $12$ , 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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			103.14
Character	$\chi$	$=$	270.103
Dual form			270.3.q.b.97.14

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123257 + 1.40883i) q^{2} +(2.33981 - 1.87758i) q^{3} +(-1.96962 - 0.347296i) q^{4} +(4.99461 + 0.232069i) q^{5} +(2.35680 + 3.52782i) q^{6} +(-10.5915 - 7.41628i) q^{7} +(0.732051 - 2.73205i) q^{8} +(1.94940 - 8.78634i) q^{9} +(-0.942566 + 7.00796i) q^{10} +(18.1011 + 6.58827i) q^{11} +(-5.26060 + 2.88550i) q^{12} +(-0.453792 - 5.18687i) q^{13} +(11.7538 - 14.0076i) q^{14} +(12.1222 - 8.83478i) q^{15} +(3.75877 + 1.36808i) q^{16} +(-5.66531 - 21.1432i) q^{17} +(12.1382 + 3.82935i) q^{18} +(8.60490 - 4.96804i) q^{19} +(-9.75687 - 2.19170i) q^{20} +(-38.7068 + 2.53378i) q^{21} +(-11.5129 + 24.6894i) q^{22} +(-12.2632 + 8.58680i) q^{23} +(-3.41678 - 7.76696i) q^{24} +(24.8923 + 2.31819i) q^{25} +7.36336 q^{26} +(-11.9358 - 24.2185i) q^{27} +(18.2856 + 18.2856i) q^{28} +(11.3766 + 13.5581i) q^{29} +(10.9526 + 18.1670i) q^{30} +(3.94528 - 22.3748i) q^{31} +(-2.39069 + 5.12685i) q^{32} +(54.7231 - 18.5710i) q^{33} +(30.4856 - 5.37543i) q^{34} +(-51.1795 - 39.4994i) q^{35} +(-6.89103 + 16.6287i) q^{36} +(12.3371 + 46.0426i) q^{37} +(5.93852 + 12.7352i) q^{38} +(-10.8005 - 11.2842i) q^{39} +(4.29033 - 13.4756i) q^{40} +(-14.2759 - 11.9789i) q^{41} +(1.20120 - 54.8437i) q^{42} +(-9.53985 - 20.4583i) q^{43} +(-33.3642 - 19.2628i) q^{44} +(11.7755 - 43.4320i) q^{45} +(-10.5858 - 18.3352i) q^{46} +(40.1970 + 28.1462i) q^{47} +(11.3635 - 3.85634i) q^{48} +(40.4206 + 111.055i) q^{49} +(-6.33408 + 34.7833i) q^{50} +(-52.9538 - 38.8340i) q^{51} +(-0.907585 + 10.3737i) q^{52} +(46.1290 + 46.1290i) q^{53} +(35.5910 - 13.8305i) q^{54} +(88.8792 + 37.1066i) q^{55} +(-28.0152 + 23.5075i) q^{56} +(10.8059 - 27.7806i) q^{57} +(-20.5034 + 14.3566i) q^{58} +(-25.7670 - 70.7942i) q^{59} +(-26.9443 + 13.1911i) q^{60} +(15.7907 + 89.5537i) q^{61} +(31.0361 + 8.31609i) q^{62} +(-85.8091 + 78.6036i) q^{63} +(-6.92820 - 4.00000i) q^{64} +(-1.06280 - 26.0117i) q^{65} +(19.4184 + 79.3847i) q^{66} +(-72.2944 + 6.32494i) q^{67} +(3.81552 + 43.6116i) q^{68} +(-12.5712 + 43.1166i) q^{69} +(61.9562 - 67.2348i) q^{70} +(-54.4225 + 94.2626i) q^{71} +(-22.5777 - 11.7579i) q^{72} +(0.988798 - 3.69024i) q^{73} +(-66.3870 + 11.7058i) q^{74} +(62.5957 - 41.3131i) q^{75} +(-18.6737 + 6.79668i) q^{76} +(-142.858 - 204.023i) q^{77} +(17.2288 - 13.8253i) q^{78} +(12.7894 + 15.2418i) q^{79} +(18.4561 + 7.70532i) q^{80} +(-73.3997 - 34.2562i) q^{81} +(18.6359 - 18.6359i) q^{82} +(-106.494 - 9.31701i) q^{83} +(77.1175 + 8.45215i) q^{84} +(-23.3893 - 106.917i) q^{85} +(29.9981 - 10.9184i) q^{86} +(52.0756 + 10.3629i) q^{87} +(31.2504 - 44.6302i) q^{88} +(46.0129 - 26.5656i) q^{89} +(59.7369 + 21.9430i) q^{90} +(-33.6609 + 58.3024i) q^{91} +(27.1360 - 12.6537i) q^{92} +(-32.7793 - 59.7604i) q^{93} +(-44.6079 + 53.1616i) q^{94} +(44.1311 - 22.8165i) q^{95} +(4.03231 + 16.4846i) q^{96} +(-61.6919 + 28.7674i) q^{97} +(-161.439 + 43.2576i) q^{98} +(93.1732 - 146.200i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q + 12 q^{6} - 18 q^{7} - 216 q^{8} + 36 q^{11} + 18 q^{15} + 72 q^{20} - 288 q^{21} - 36 q^{22} + 36 q^{23} - 90 q^{25} + 66 q^{27} - 168 q^{30} + 432 q^{31} + 18 q^{33} - 162 q^{35} + 48 q^{36} + 108 q^{38}+ \cdots - 756 q^{98}+O(q^{100})$ 216 * q + 12 * q^6 - 18 * q^7 - 216 * q^8 + 36 * q^11 + 18 * q^15 + 72 * q^20 - 288 * q^21 - 36 * q^22 + 36 * q^23 - 90 * q^25 + 66 * q^27 - 168 * q^30 + 432 * q^31 + 18 * q^33 - 162 * q^35 + 48 * q^36 + 108 * q^38 + 36 * q^40 + 216 * q^41 + 144 * q^42 + 216 * q^43 - 78 * q^45 - 108 * q^46 + 108 * q^47 + 24 * q^48 - 126 * q^50 - 108 * q^51 - 540 * q^53 - 324 * q^55 - 72 * q^56 - 234 * q^57 - 72 * q^58 + 96 * q^60 - 216 * q^61 + 108 * q^63 - 144 * q^65 + 144 * q^66 + 864 * q^67 + 108 * q^68 - 72 * q^70 + 144 * q^72 + 216 * q^73 + 588 * q^75 - 216 * q^76 + 576 * q^77 + 216 * q^78 + 1044 * q^81 - 216 * q^83 - 576 * q^85 - 432 * q^86 - 900 * q^87 + 72 * q^88 + 606 * q^90 - 756 * q^91 - 252 * q^92 - 120 * q^93 + 108 * q^95 + 108 * q^97 - 756 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−0.123257	+	1.40883i	−0.0616284	+	0.704416i
$2$	−0.123257	+	1.40883i	−0.0616284	+	0.704416i
$3$	2.33981	−	1.87758i	0.779936	−	0.625859i
$3$	2.33981	−	1.87758i	0.779936	−	0.625859i
$4$	−1.96962	−	0.347296i	−0.492404	−	0.0868241i
$5$	4.99461	+	0.232069i	0.998922	+	0.0464138i
$5$	4.99461	+	0.232069i	0.998922	+	0.0464138i
$6$	2.35680	+	3.52782i	0.392799	+	0.587970i
$7$	−10.5915	−	7.41628i	−1.51308	−	1.05947i	−0.976475	−	0.215633i	$-0.930819\pi$
$7$	−10.5915	−	7.41628i	−1.51308	−	1.05947i	−0.536602	−	0.843835i	$-0.680293\pi$
$8$	0.732051	−	2.73205i	0.0915064	−	0.341506i
$9$	1.94940	−	8.78634i	0.216600	−	0.976260i
$10$	−0.942566	+	7.00796i	−0.0942566	+	0.700796i
$11$	18.1011	+	6.58827i	1.64556	+	0.598934i	0.987998	−	0.154469i	$-0.0493667\pi$
$11$	18.1011	+	6.58827i	1.64556	+	0.598934i	0.657559	+	0.753403i	$0.271589\pi$
$12$	−5.26060	+	2.88550i	−0.438383	+	0.240458i
$13$	−0.453792	−	5.18687i	−0.0349071	−	0.398990i	−0.993469	−	0.114105i	$-0.963600\pi$
$13$	−0.453792	−	5.18687i	−0.0349071	−	0.398990i	0.958562	−	0.284885i	$-0.0919555\pi$
$14$	11.7538	−	14.0076i	0.839555	−	1.00054i
$15$	12.1222	−	8.83478i	0.808144	−	0.588985i
$16$	3.75877	+	1.36808i	0.234923	+	0.0855050i
$17$	−5.66531	−	21.1432i	−0.333254	−	1.24372i	−0.905750	−	0.423812i	$-0.860692\pi$
$17$	−5.66531	−	21.1432i	−0.333254	−	1.24372i	0.572496	−	0.819907i	$-0.305975\pi$
$18$	12.1382	+	3.82935i	0.674345	+	0.212742i
$19$	8.60490	−	4.96804i	0.452889	−	0.261476i	−0.256160	−	0.966634i	$-0.582457\pi$
$19$	8.60490	−	4.96804i	0.452889	−	0.261476i	0.709050	+	0.705158i	$0.249124\pi$
$20$	−9.75687	−	2.19170i	−0.487843	−	0.109585i
$21$	−38.7068	+	2.53378i	−1.84318	+	0.120656i
$22$	−11.5129	+	24.6894i	−0.523312	+	1.12225i
$23$	−12.2632	+	8.58680i	−0.533184	+	0.373339i	−0.808943	−	0.587888i	$-0.799960\pi$
$23$	−12.2632	+	8.58680i	−0.533184	+	0.373339i	0.275759	+	0.961227i	$0.411071\pi$
$24$	−3.41678	−	7.76696i	−0.142366	−	0.323623i
$25$	24.8923	+	2.31819i	0.995692	+	0.0927275i
$26$	7.36336			0.283206
$27$	−11.9358	−	24.2185i	−0.442068	−	0.896982i
$28$	18.2856	+	18.2856i	0.653058	+	0.653058i
$29$	11.3766	+	13.5581i	0.392298	+	0.467522i	0.925655	−	0.378367i	$-0.123514\pi$
$29$	11.3766	+	13.5581i	0.392298	+	0.467522i	−0.533358	+	0.845890i	$0.679070\pi$
$30$	10.9526	+	18.1670i	0.365086	+	0.605568i
$31$	3.94528	−	22.3748i	0.127267	−	0.721768i	−0.852668	−	0.522453i	$-0.825017\pi$
$31$	3.94528	−	22.3748i	0.127267	−	0.721768i	0.979935	−	0.199315i	$-0.0638718\pi$
$32$	−2.39069	+	5.12685i	−0.0747091	+	0.160214i
$33$	54.7231	−	18.5710i	1.65828	−	0.562757i
$34$	30.4856	−	5.37543i	0.896634	−	0.158101i
$35$	−51.1795	−	39.4994i	−1.46227	−	1.12855i
$36$	−6.89103	+	16.6287i	−0.191418	+	0.461908i
$37$	12.3371	+	46.0426i	0.333435	+	1.24440i	0.905556	+	0.424226i	$0.139454\pi$
$37$	12.3371	+	46.0426i	0.333435	+	1.24440i	−0.572121	+	0.820169i	$0.693879\pi$
$38$	5.93852	+	12.7352i	0.156277	+	0.335137i
$39$	−10.8005	−	11.2842i	−0.276937	−	0.289340i
$40$	4.29033	−	13.4756i	0.107258	−	0.336891i
$41$	−14.2759	−	11.9789i	−0.348193	−	0.292169i	0.451871	−	0.892083i	$-0.350757\pi$
$41$	−14.2759	−	11.9789i	−0.348193	−	0.292169i	−0.800064	+	0.599915i	$0.795201\pi$
$42$	1.20120	−	54.8437i	0.0286000	−	1.30580i
$43$	−9.53985	−	20.4583i	−0.221857	−	0.475774i	0.763602	−	0.645687i	$-0.223429\pi$
$43$	−9.53985	−	20.4583i	−0.221857	−	0.475774i	−0.985459	+	0.169913i	$0.945651\pi$
$44$	−33.3642	−	19.2628i	−0.758277	−	0.437791i
$45$	11.7755	−	43.4320i	0.261679	−	0.965155i
$46$	−10.5858	−	18.3352i	−0.230127	−	0.398591i
$47$	40.1970	+	28.1462i	0.855255	+	0.598856i	0.916844	−	0.399246i	$-0.130728\pi$
$47$	40.1970	+	28.1462i	0.855255	+	0.598856i	−0.0615890	+	0.998102i	$0.519617\pi$
$48$	11.3635	−	3.85634i	0.236739	−	0.0803404i
$49$	40.4206	+	111.055i	0.824910	+	2.26642i
$50$	−6.33408	+	34.7833i	−0.126682	+	0.695666i
$51$	−52.9538	−	38.8340i	−1.03831	−	0.761452i
$52$	−0.907585	+	10.3737i	−0.0174535	+	0.199495i
$53$	46.1290	+	46.1290i	0.870359	+	0.870359i	0.992511	−	0.122153i	$-0.0389797\pi$
$53$	46.1290	+	46.1290i	0.870359	+	0.870359i	−0.122153	+	0.992511i	$0.538980\pi$
$54$	35.5910	−	13.8305i	0.659092	−	0.256120i
$55$	88.8792	+	37.1066i	1.61598	+	0.674665i
$56$	−28.0152	+	23.5075i	−0.500271	+	0.419777i
$57$	10.8059	−	27.7806i	0.189578	−	0.487380i
$58$	−20.5034	+	14.3566i	−0.353507	+	0.247528i
$59$	−25.7670	−	70.7942i	−0.436729	−	1.19990i	−0.941608	−	0.336712i	$-0.890685\pi$
$59$	−25.7670	−	70.7942i	−0.436729	−	1.19990i	0.504879	−	0.863190i	$-0.331537\pi$
$60$	−26.9443	+	13.1911i	−0.449071	+	0.219852i
$61$	15.7907	+	89.5537i	0.258864	+	1.46809i	0.785955	+	0.618284i	$0.212172\pi$
$61$	15.7907	+	89.5537i	0.258864	+	1.46809i	−0.527091	+	0.849809i	$0.676717\pi$
$62$	31.0361	+	8.31609i	0.500582	+	0.134131i
$63$	−85.8091	+	78.6036i	−1.36205	+	1.24768i
$64$	−6.92820	−	4.00000i	−0.108253	−	0.0625000i
$65$	−1.06280	−	26.0117i	−0.0163508	−	0.400180i
$66$	19.4184	+	79.3847i	0.294218	+	1.20280i
$67$	−72.2944	+	6.32494i	−1.07902	+	0.0944021i	−0.612779	−	0.790255i	$-0.709948\pi$
$67$	−72.2944	+	6.32494i	−1.07902	+	0.0944021i	−0.466243	+	0.884657i	$0.654393\pi$
$68$	3.81552	+	43.6116i	0.0561106	+	0.641347i
$69$	−12.5712	+	43.1166i	−0.182191	+	0.624879i
$70$	61.9562	−	67.2348i	0.885089	−	0.960497i
$71$	−54.4225	+	94.2626i	−0.766515	+	1.32764i	0.172927	+	0.984935i	$0.444677\pi$
$71$	−54.4225	+	94.2626i	−0.766515	+	1.32764i	−0.939442	+	0.342708i	$0.888656\pi$
$72$	−22.5777	−	11.7579i	−0.313579	−	0.163304i
$73$	0.988798	−	3.69024i	0.0135452	−	0.0505513i	−0.958822	−	0.284006i	$-0.908336\pi$
$73$	0.988798	−	3.69024i	0.0135452	−	0.0505513i	0.972368	+	0.233455i	$0.0750031\pi$
$74$	−66.3870	+	11.7058i	−0.897121	+	0.158187i
$75$	62.5957	−	41.3131i	0.834610	−	0.550841i
$76$	−18.6737	+	6.79668i	−0.245707	+	0.0894300i
$77$	−142.858	−	204.023i	−1.85530	−	2.64965i
$78$	17.2288	−	13.8253i	0.220883	−	0.177247i
$79$	12.7894	+	15.2418i	0.161891	+	0.192934i	0.840892	−	0.541203i	$-0.182031\pi$
$79$	12.7894	+	15.2418i	0.161891	+	0.192934i	−0.679001	+	0.734138i	$0.737587\pi$
$80$	18.4561	+	7.70532i	0.230701	+	0.0963166i
$81$	−73.3997	−	34.2562i	−0.906169	−	0.422916i
$82$	18.6359	−	18.6359i	0.227267	−	0.227267i
$83$	−106.494	−	9.31701i	−1.28306	−	0.112253i	−0.574851	−	0.818258i	$-0.694940\pi$
$83$	−106.494	−	9.31701i	−1.28306	−	0.112253i	−0.708207	+	0.706005i	$0.750496\pi$
$84$	77.1175	+	8.45215i	0.918065	+	0.100621i
$85$	−23.3893	−	106.917i	−0.275169	−	1.25785i
$86$	29.9981	−	10.9184i	0.348815	−	0.126958i
$87$	52.0756	+	10.3629i	0.598570	+	0.119114i
$88$	31.2504	−	44.6302i	0.355119	−	0.507162i
$89$	46.0129	−	26.5656i	0.516999	−	0.298490i	−0.218707	−	0.975791i	$-0.570184\pi$
$89$	46.0129	−	26.5656i	0.516999	−	0.298490i	0.735706	+	0.677301i	$0.236851\pi$
$90$	59.7369	+	21.9430i	0.663744	+	0.243812i
$91$	−33.6609	+	58.3024i	−0.369900	+	0.640685i
$92$	27.1360	−	12.6537i	0.294957	−	0.137541i
$93$	−32.7793	−	59.7604i	−0.352465	−	0.642584i
$94$	−44.6079	+	53.1616i	−0.474552	+	0.565549i
$95$	44.1311	−	22.8165i	0.464537	−	0.240174i
$96$	4.03231	+	16.4846i	0.0420032	+	0.171714i
$97$	−61.6919	+	28.7674i	−0.635999	+	0.296571i	−0.713749	−	0.700402i	$-0.753004\pi$
$97$	−61.6919	+	28.7674i	−0.635999	+	0.296571i	0.0777501	+	0.996973i	$0.475226\pi$
$98$	−161.439	+	43.2576i	−1.64734	+	0.441404i
$99$	93.1732	−	146.200i	0.941143	−	1.47676i
$100$	−48.2231	−	13.2109i	−0.482231	−	0.132109i
$101$	6.28254	+	35.6300i	0.0622034	+	0.352773i	0.999985	+	0.00554616i	$0.00176541\pi$
$101$	6.28254	+	35.6300i	0.0622034	+	0.352773i	−0.937781	+	0.347227i	$0.887123\pi$
$102$	61.2376	−	69.8165i	0.600368	−	0.684475i
$103$	−79.8649	−	37.2416i	−0.775387	−	0.361569i	−0.00569470	−	0.999984i	$-0.501813\pi$
$103$	−79.8649	−	37.2416i	−0.775387	−	0.361569i	−0.769693	+	0.638415i	$0.779590\pi$
$104$	−14.5030	−	2.55727i	−0.139452	−	0.0245891i
$105$	−193.913	+	3.67262i	−1.84679	+	0.0349773i
$106$	−70.6737	+	59.3023i	−0.666733	+	0.559456i
$107$	10.4357	−	10.4357i	0.0975302	−	0.0975302i	−0.656658	−	0.754188i	$-0.728031\pi$
$107$	10.4357	−	10.4357i	0.0975302	−	0.0975302i	0.754188	+	0.656658i	$0.228031\pi$
$108$	15.0980	+	51.8464i	0.139796	+	0.480059i
$109$		−	22.1508i		−	0.203218i	−0.994824	−	0.101609i	$-0.967601\pi$
$109$		−	22.1508i		−	0.203218i	0.994824	−	0.101609i	$-0.0323991\pi$
$110$	−63.2319	+	120.642i	−0.574835	+	1.09675i
$111$	115.315	+	84.5671i	1.03887	+	0.761865i
$112$	−29.6651	−	42.3662i	−0.264867	−	0.378269i
$113$	98.5787	+	45.9680i	0.872378	+	0.406796i	0.806642	−	0.591041i	$-0.201283\pi$
$113$	98.5787	+	45.9680i	0.872378	+	0.406796i	0.0657360	+	0.997837i	$0.479060\pi$
$114$	37.8063	+	18.6479i	0.331635	+	0.163578i
$115$	−63.2428	+	40.0418i	−0.549937	+	0.348190i
$116$	−17.6989	−	30.6554i	−0.152577	−	0.264271i
$117$	−46.4582	−	6.12411i	−0.397079	−	0.0523428i
$118$	102.913	−	27.5755i	0.872145	−	0.233691i
$119$	−96.7997	+	265.955i	−0.813443	+	2.23492i
$120$	−15.2630	−	39.5859i	−0.127192	−	0.329882i
$121$	191.554	+	160.733i	1.58309	+	1.32837i
$122$	−128.112	+	11.2084i	−1.05010	+	0.0918720i
$123$	−55.8942	−	1.22421i	−0.454425	−	0.00995294i
$124$	−15.5414	+	42.6996i	−0.125334	+	0.344352i
$125$	123.789	+	17.3552i	0.990315	+	0.138841i
$126$	−100.163	−	130.579i	−0.794942	−	1.03634i
$127$	0.707568	+	0.189592i	0.00557140	+	0.00149285i	0.261604	−	0.965175i	$-0.415749\pi$
$127$	0.707568	+	0.189592i	0.00557140	+	0.00149285i	−0.256032	+	0.966668i	$0.582415\pi$
$128$	6.48928	−	9.26765i	0.0506975	−	0.0724035i
$129$	−60.7334	−	29.9566i	−0.470802	−	0.232222i
$130$	36.7771	+	1.70881i	0.282901	+	0.0131447i
$131$	18.5559	−	105.236i	0.141648	−	0.803325i	−0.828350	−	0.560211i	$-0.810720\pi$
$131$	18.5559	−	105.236i	0.141648	−	0.803325i	0.969998	−	0.243114i	$-0.0781690\pi$
$132$	−114.233	+	17.5726i	−0.865403	+	0.133125i
$133$	−127.983	−	11.1971i	−0.962282	−	0.0841888i
$134$		−	102.630i		−	0.765898i
$135$	−53.9944	−	123.732i	−0.399959	−	0.916533i
$136$	−61.9117			−0.455233
$137$	−14.7502	+	168.595i	−0.107665	+	1.23062i	0.729619	+	0.683854i	$0.239697\pi$
$137$	−14.7502	+	168.595i	−0.107665	+	1.23062i	−0.837284	+	0.546768i	$0.815858\pi$
$138$	−59.1946	−	23.0251i	−0.428946	−	0.166849i
$139$	−54.8753	−	9.67599i	−0.394786	−	0.0696114i	−0.0272688	−	0.999628i	$-0.508681\pi$
$139$	−54.8753	−	9.67599i	−0.394786	−	0.0696114i	−0.367517	+	0.930017i	$0.619792\pi$
$140$	87.0860	+	95.5731i	0.622043	+	0.682665i
$141$	146.900	−	9.61621i	1.04184	−	0.0682001i
$142$	−126.092	−	88.2907i	−0.887973	−	0.621766i
$143$	25.9584	−	96.8779i	0.181527	−	0.677468i
$144$	19.3478	−	30.3589i	0.134360	−	0.210826i
$145$	53.6755	+	70.3579i	0.370176	+	0.485227i
$146$	5.07706	+	1.84790i	0.0347744	+	0.0126568i
$147$	303.090	+	183.954i	2.06184	+	1.25139i
$148$	−8.30888	−	94.9709i	−0.0561411	−	0.641695i
$149$	−111.724	+	133.147i	−0.749824	+	0.893605i	−0.997159	−	0.0753250i	$-0.976001\pi$
$149$	−111.724	+	133.147i	−0.749824	+	0.893605i	0.247336	+	0.968930i	$0.420445\pi$
$150$	50.4879	+	93.2790i	0.336586	+	0.621860i
$151$	185.341	+	67.4586i	1.22742	+	0.446745i	0.872714	−	0.488231i	$-0.162358\pi$
$151$	185.341	+	67.4586i	1.22742	+	0.446745i	0.354709	+	0.934977i	$0.384580\pi$
$152$	−7.27372	−	27.1459i	−0.0478534	−	0.178591i
$153$	−196.816	+	8.56076i	−1.28638	+	0.0559527i
$154$	305.042	−	176.116i	1.98079	−	1.14361i
$155$	24.8977	−	110.838i	0.160630	−	0.715084i
$156$	17.3539	+	25.9766i	0.111243	+	0.166517i
$157$	35.6396	−	76.4293i	0.227004	−	0.486811i	−0.759509	−	0.650497i	$-0.774561\pi$
$157$	35.6396	−	76.4293i	0.227004	−	0.486811i	0.986512	+	0.163686i	$0.0523384\pi$
$158$	−23.0495	+	16.1395i	−0.145883	+	0.102148i
$159$	194.544	+	21.3222i	1.22355	+	0.134102i
$160$	−13.1304	+	25.0518i	−0.0820647	+	0.156574i
$161$	193.569			1.20229
$162$	57.3082	−	99.1855i	0.353755	−	0.612256i
$163$	124.630	+	124.630i	0.764604	+	0.764604i	0.977151	−	0.212547i	$-0.0681759\pi$
$163$	124.630	+	124.630i	0.764604	+	0.764604i	−0.212547	+	0.977151i	$0.568176\pi$
$164$	23.9578	+	28.5518i	0.146084	+	0.174097i
$165$	277.631	−	80.0553i	1.68261	−	0.485184i
$166$	26.2522	−	148.884i	0.158146	−	0.896889i
$167$	15.9031	−	34.1044i	0.0952283	−	0.204218i	−0.852923	−	0.522036i	$-0.825173\pi$
$167$	15.9031	−	34.1044i	0.0952283	−	0.204218i	0.948152	+	0.317819i	$0.102950\pi$
$168$	−21.4129	+	107.604i	−0.127458	+	0.640499i
$169$	139.735	−	24.6390i	0.826833	−	0.145793i
$170$	153.511	−	19.7734i	0.903006	−	0.116314i
$171$	−26.8765	−	85.2903i	−0.157173	−	0.498774i
$172$	11.6848	+	43.6081i	0.0679346	+	0.253535i
$173$	−55.8513	−	119.773i	−0.322840	−	0.692332i	0.676174	−	0.736742i	$-0.263637\pi$
$173$	−55.8513	−	119.773i	−0.322840	−	0.692332i	−0.999013	+	0.0444101i	$0.985859\pi$
$174$	−21.0183	+	72.0885i	−0.120795	+	0.414302i
$175$	−246.455	−	209.161i	−1.40832	−	1.19521i
$176$	59.0247	+	49.5276i	0.335368	+	0.281407i
$177$	−193.211	−	117.265i	−1.09159	−	0.662516i
$178$	31.7550	+	68.0989i	0.178399	+	0.382578i
$179$	−77.3567	−	44.6619i	−0.432160	−	0.249508i	0.268106	−	0.963389i	$-0.413602\pi$
$179$	−77.3567	−	44.6619i	−0.432160	−	0.249508i	−0.700267	+	0.713882i	$0.746935\pi$
$180$	−38.2770	+	81.4547i	−0.212650	+	0.452526i
$181$	90.6246	+	156.966i	0.500688	+	0.867218i	1.00000		0.000794941i	$0.000253038\pi$
$181$	90.6246	+	156.966i	0.500688	+	0.867218i	−0.499311	+	0.866423i	$0.666414\pi$
$182$	−77.9893	−	54.6087i	−0.428513	−	0.300048i
$183$	205.091	+	179.890i	1.12072	+	0.983005i
$184$	14.4823	+	39.7897i	0.0787080	+	0.216249i
$185$	50.9339	+	232.828i	0.275318	+	1.25853i
$186$	88.2326	−	38.8146i	0.474369	−	0.208681i
$187$	36.7488	−	420.041i	0.196518	−	2.24621i
$188$	−69.3975	−	69.3975i	−0.369136	−	0.369136i
$189$	−53.1924	+	345.031i	−0.281441	+	1.82556i
$190$	26.7052	+	64.9855i	0.140554	+	0.342029i
$191$	120.592	−	101.189i	0.631371	−	0.529783i	−0.269984	−	0.962865i	$-0.587018\pi$
$191$	120.592	−	101.189i	0.631371	−	0.529783i	0.901355	+	0.433082i	$0.142574\pi$
$192$	−23.7210	+	3.64901i	−0.123547	+	0.0190053i
$193$	174.889	−	122.458i	0.906159	−	0.634499i	−0.0247726	−	0.999693i	$-0.507886\pi$
$193$	174.889	−	122.458i	0.906159	−	0.634499i	0.930932	+	0.365194i	$0.118997\pi$
$194$	−32.9245	−	90.4593i	−0.169714	−	0.466285i
$195$	−51.3258	−	58.8669i	−0.263209	−	0.301882i
$196$	−41.0441	−	232.773i	−0.209409	−	1.18762i
$197$	129.330	+	34.6539i	0.656499	+	0.175908i	0.571665	−	0.820487i	$-0.306298\pi$
$197$	129.330	+	34.6539i	0.656499	+	0.175908i	0.0848334	+	0.996395i	$0.472964\pi$
$198$	194.486	+	149.285i	0.982254	+	0.753967i
$199$	−50.0887	−	28.9187i	−0.251702	−	0.145320i	0.368841	−	0.929492i	$-0.379755\pi$
$199$	−50.0887	−	28.9187i	−0.251702	−	0.145320i	−0.620543	+	0.784172i	$0.713088\pi$
$200$	24.5558	−	66.3100i	0.122779	−	0.331550i
$201$	−157.280	+	150.538i	−0.782485	+	0.748943i
$202$	−50.9711	+	4.45939i	−0.252332	+	0.0220762i
$203$	−19.9451	−	227.974i	−0.0982519	−	1.12302i
$204$	90.8117	+	94.8788i	0.445156	+	0.465092i
$205$	−68.5227	−	63.1430i	−0.334257	−	0.308015i
$206$	62.3111	−	107.926i	0.302481	−	0.523912i
$207$	51.5407	+	124.488i	0.248989	+	0.601391i
$208$	5.39035	−	20.1171i	0.0259152	−	0.0967167i
$209$	188.489	−	33.2357i	0.901862	−	0.159023i
$210$	18.7271	−	273.644i	0.0891764	−	1.30307i
$211$	−243.436	+	88.6034i	−1.15372	+	0.419921i	−0.846851	−	0.531829i	$-0.821505\pi$
$211$	−243.436	+	88.6034i	−1.15372	+	0.419921i	−0.306873	+	0.951751i	$0.599283\pi$
$212$	−74.8360	−	106.877i	−0.353000	−	0.504136i
$213$	49.6471	+	322.739i	0.233085	+	1.51521i
$214$	13.4159	+	15.9885i	0.0626912	+	0.0747124i
$215$	−42.9001	−	104.395i	−0.199535	−	0.485558i
$216$	−74.9038	+	14.8801i	−0.346777	+	0.0688894i
$217$	−207.724	+	207.724i	−0.957256	+	0.957256i
$218$	31.2068	+	2.73024i	0.143150	+	0.0125240i
$219$	−4.61512	−	10.4910i	−0.0210736	−	0.0479041i
$220$	−162.171	−	103.953i	−0.737140	−	0.472514i
$221$	−107.096	+	38.9799i	−0.484599	+	0.176380i
$222$	−133.354	+	152.036i	−0.600694	+	0.684847i
$223$	−139.170	+	198.755i	−0.624080	+	0.891279i	−0.999365	−	0.0356309i	$-0.988656\pi$
$223$	−139.170	+	198.755i	−0.624080	+	0.891279i	0.375285	+	0.926909i	$0.377545\pi$
$224$	63.3432	−	36.5712i	0.282782	−	0.163264i
$225$	68.8934	−	214.193i	0.306193	−	0.951969i
$226$	−76.9117	+	133.215i	−0.340317	+	0.589447i
$227$	345.131	−	160.937i	1.52040	−	0.708975i	0.530103	−	0.847933i	$-0.322153\pi$
$227$	345.131	−	160.937i	1.52040	−	0.708975i	0.990298	+	0.138959i	$0.0443756\pi$
$228$	−30.9316	+	50.9643i	−0.135665	+	0.223528i
$229$	−163.771	+	195.174i	−0.715156	+	0.852289i	−0.994151	−	0.108003i	$-0.965554\pi$
$229$	−163.771	+	195.174i	−0.715156	+	0.852289i	0.278995	+	0.960293i	$0.409999\pi$
$230$	−48.6171	−	94.0339i	−0.211379	−	0.408843i
$231$	−717.330	−	209.147i	−3.10532	−	0.905396i
$232$	45.3698	−	21.1563i	0.195560	−	0.0911909i
$233$	270.893	−	72.5854i	1.16263	−	0.311525i	0.374614	−	0.927181i	$-0.377775\pi$
$233$	270.893	−	72.5854i	1.16263	−	0.311525i	0.788015	+	0.615656i	$0.211109\pi$
$234$	14.3541	−	64.6970i	0.0613425	−	0.276483i
$235$	194.236	+	149.908i	0.826538	+	0.637906i
$236$	26.1645	+	148.386i	0.110866	+	0.628755i
$237$	58.5424	+	11.6498i	0.247014	+	0.0491553i
$238$	−362.755	−	169.155i	−1.52418	−	0.710736i
$239$	−264.392	−	46.6195i	−1.10624	−	0.195061i	−0.409450	−	0.912333i	$-0.634279\pi$
$239$	−264.392	−	46.6195i	−1.10624	−	0.195061i	−0.696793	+	0.717272i	$0.745391\pi$
$240$	57.6511	−	16.6238i	0.240213	−	0.0692659i
$241$	178.530	−	149.804i	0.740787	−	0.621594i	−0.192262	−	0.981344i	$-0.561582\pi$
$241$	178.530	−	149.804i	0.740787	−	0.621594i	0.933049	+	0.359749i	$0.117138\pi$
$242$	−250.056	+	250.056i	−1.03329	+	1.03329i
$243$	−236.060	+	57.6607i	−0.971440	+	0.237287i
$244$		−	181.870i		−	0.745370i
$245$	176.113	+	564.055i	0.718827	+	2.30227i
$246$	8.61406	−	78.5947i	0.0350165	−	0.319491i
$247$	−29.6734	−	42.3780i	−0.120135	−	0.171571i
$248$	−58.2410	−	27.1582i	−0.234843	−	0.109509i
$249$	−266.669	+	178.151i	−1.07096	+	0.715464i
$250$	−39.7084	+	172.259i	−0.158834	+	0.689037i
$251$	−11.5975	−	20.0874i	−0.0462050	−	0.0800294i	0.841998	−	0.539481i	$-0.181379\pi$
$251$	−11.5975	−	20.0874i	−0.0462050	−	0.0800294i	−0.888203	+	0.459451i	$0.848046\pi$
$252$	196.310	−	125.018i	0.779007	−	0.496102i
$253$	−278.550	+	74.6374i	−1.10099	+	0.295009i
$254$	−0.354316	+	0.973476i	−0.00139495	+	0.00383258i
$255$	−255.472	−	206.250i	−1.00185	−	0.808823i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−106.914	+	9.35380i	−0.416009	+	0.0363961i	−0.293239	−	0.956039i	$-0.594733\pi$
$257$	−106.914	+	9.35380i	−0.416009	+	0.0363961i	−0.122770	+	0.992435i	$0.539178\pi$
$258$	49.6897	−	81.8708i	0.192596	−	0.317329i
$259$	210.796	−	579.158i	0.813885	−	2.23613i
$260$	−6.94045	+	51.6022i	−0.0266941	+	0.198470i
$261$	141.304	−	73.5288i	0.541395	−	0.281720i
$262$	145.972	+	39.1131i	0.557146	+	0.149287i
$263$	167.883	−	239.761i	0.638337	−	0.911640i	−0.361448	−	0.932392i	$-0.617717\pi$
$263$	167.883	−	239.761i	0.638337	−	0.911640i	0.999785	+	0.0207526i	$0.00660624\pi$
$264$	−10.6768	−	163.101i	−0.0404423	−	0.617808i
$265$	219.691	+	241.102i	0.829024	+	0.909817i
$266$	31.5497	−	178.927i	0.118608	−	0.672658i
$267$	57.7825	−	148.551i	0.216414	−	0.556372i
$268$	144.589	+	12.6499i	0.539511	+	0.0472011i
$269$		−	391.404i		−	1.45503i	−0.686090	−	0.727516i	$-0.740674\pi$
$269$		−	391.404i		−	1.45503i	0.686090	−	0.727516i	$-0.259326\pi$
$270$	180.973	−	60.8183i	0.670269	−	0.225253i
$271$	55.1204			0.203396			0.101698	−	0.994815i	$-0.467572\pi$
$271$	55.1204			0.203396			0.101698	+	0.994815i	$0.467572\pi$
$272$	7.63104	−	87.2232i	0.0280553	−	0.320673i
$273$	30.7073	+	199.617i	0.112481	+	0.731199i
$274$	−235.704	−	41.5610i	−0.860234	−	0.151683i
$275$	435.306	+	205.959i	1.58293	+	0.748942i
$276$	39.7347	−	80.5573i	0.143966	−	0.291874i
$277$	290.799	+	203.620i	1.04982	+	0.735089i	0.965250	−	0.261329i	$-0.0841608\pi$
$277$	290.799	+	203.620i	1.04982	+	0.735089i	0.0845657	+	0.996418i	$0.473050\pi$
$278$	20.3956	−	76.1174i	0.0733655	−	0.273804i
$279$	−188.902	−	78.2821i	−0.677068	−	0.280581i
$280$	−145.380	+	110.910i	−0.519215	+	0.396105i
$281$	59.4211	+	21.6275i	0.211463	+	0.0769663i	0.445580	−	0.895242i	$-0.352998\pi$
$281$	59.4211	+	21.6275i	0.211463	+	0.0769663i	−0.234117	+	0.972209i	$0.575220\pi$
$282$	−4.55880	+	208.143i	−0.0161659	+	0.738094i
$283$	−11.6588	−	133.261i	−0.0411973	−	0.470887i	−0.988571	−	0.150757i	$-0.951829\pi$
$283$	−11.6588	−	133.261i	−0.0411973	−	0.470887i	0.947374	−	0.320130i	$-0.103727\pi$
$284$	139.929	−	166.760i	0.492706	−	0.587184i
$285$	60.4184	−	136.246i	0.211994	−	0.478055i
$286$	133.285	+	48.5118i	0.466032	+	0.169622i
$287$	62.3650	+	232.749i	0.217300	+	0.810973i
$288$	40.3859	+	30.9997i	0.140229	+	0.107638i
$289$	−164.659	+	95.0661i	−0.569755	+	0.328948i
$290$	−105.738	+	66.9476i	−0.364615	+	0.230854i
$291$	−90.3341	+	183.141i	−0.310426	+	0.629352i
$292$	−3.22916	+	6.92496i	−0.0110588	+	0.0237156i
$293$	−127.494	+	89.2721i	−0.435132	+	0.304683i	−0.770542	−	0.637390i	$-0.780014\pi$
$293$	−127.494	+	89.2721i	−0.435132	+	0.304683i	0.335410	+	0.942072i	$0.391125\pi$
$294$	−296.518	+	404.329i	−1.00856	+	1.37527i
$295$	−112.267	−	359.569i	−0.380566	−	1.21888i
$296$	134.822			0.455480
$297$	−56.4938	−	517.019i	−0.190215	−	1.74080i
$298$	−173.811	−	173.811i	−0.583259	−	0.583259i
$299$	50.1036	+	59.7111i	0.167571	+	0.199703i
$300$	−137.637	+	59.6317i	−0.458791	+	0.198772i
$301$	−50.6825	+	287.435i	−0.168380	+	0.954933i
$302$	−117.882	+	252.799i	−0.390339	+	0.837084i
$303$	81.5981	+	71.5715i	0.269301	+	0.236210i
$304$	39.1405	−	6.90153i	0.128752	−	0.0227024i
$305$	58.0859	+	450.950i	0.190446	+	1.47853i
$306$	12.1982	−	278.335i	0.0398634	−	0.909593i
$307$	9.01338	+	33.6384i	0.0293595	+	0.109571i	0.979051	−	0.203617i	$-0.0652697\pi$
$307$	9.01338	+	33.6384i	0.0293595	+	0.109571i	−0.949691	+	0.313188i	$0.898603\pi$
$308$	210.520	+	451.461i	0.683505	+	1.46578i
$309$	−256.792	+	62.8144i	−0.831044	+	0.203283i
$310$	153.083	+	48.7382i	0.493817	+	0.157220i
$311$	50.4772	+	42.3554i	0.162306	+	0.136191i	0.720323	−	0.693638i	$-0.243993\pi$
$311$	50.4772	+	42.3554i	0.162306	+	0.136191i	−0.558018	+	0.829829i	$0.688438\pi$
$312$	−38.7357	+	21.2470i	−0.124153	+	0.0680993i
$313$	−71.2999	−	152.903i	−0.227795	−	0.488508i	0.758876	−	0.651235i	$-0.225749\pi$
$313$	−71.2999	−	152.903i	−0.227795	−	0.488508i	−0.986671	+	0.162727i	$0.947971\pi$
$314$	103.283	+	59.6306i	0.328927	+	0.189906i
$315$	−446.825	+	372.681i	−1.41849	+	1.18311i
$316$	−19.8968	−	34.4622i	−0.0629645	−	0.109058i
$317$	148.403	+	103.913i	0.468149	+	0.327802i	0.783735	−	0.621095i	$-0.213312\pi$
$317$	148.403	+	103.913i	0.468149	+	0.327802i	−0.315586	+	0.948897i	$0.602201\pi$
$318$	−54.0182	+	271.451i	−0.169869	+	0.853621i
$319$	116.605	+	320.370i	0.365534	+	1.00430i
$320$	−33.6754	−	21.5863i	−0.105236	−	0.0674571i
$321$	4.82370	−	44.0115i	0.0150271	−	0.137107i
$322$	−23.8586	+	272.706i	−0.0740952	+	0.846912i
$323$	−153.790	−	153.790i	−0.476130	−	0.476130i
$324$	132.672	+	92.9630i	0.409482	+	0.286923i
$325$	0.728211	−	130.165i	0.00224065	−	0.400508i
$326$	−190.945	+	160.222i	−0.585720	+	0.491478i
$327$	−41.5899	−	51.8286i	−0.127186	−	0.158497i
$328$	−43.1777	+	30.2334i	−0.131639	+	0.0921749i
$329$	−217.008	−	596.224i	−0.659598	−	1.81223i
$330$	78.5647	+	401.002i	0.238075	+	1.21516i
$331$	58.5161	+	331.861i	0.176786	+	1.00260i	0.936063	+	0.351834i	$0.114442\pi$
$331$	58.5161	+	331.861i	0.176786	+	1.00260i	−0.759277	+	0.650768i	$0.774447\pi$
$332$	206.516	+	55.3359i	0.622037	+	0.166674i
$333$	428.596	−	18.6424i	1.28708	−	0.0559831i
$334$	46.0872	+	26.6084i	0.137986	+	0.0796660i
$335$	−362.550	+	14.8133i	−1.08224	+	0.0442189i
$336$	−148.956	−	43.4301i	−0.443323	−	0.129256i
$337$	−504.960	+	44.1783i	−1.49840	+	0.131093i	−0.806643	−	0.591039i	$-0.798718\pi$
$337$	−504.960	+	44.1783i	−1.49840	+	0.131093i	−0.691756	+	0.722132i	$0.743162\pi$
$338$	17.4890	+	199.900i	0.0517425	+	0.591420i
$339$	316.964	−	77.5329i	0.934996	−	0.228711i
$340$	8.93614	+	218.708i	0.0262828	+	0.643260i
$341$	218.825	−	379.017i	0.641717	−	1.11149i
$342$	123.472	−	27.3519i	0.361031	−	0.0799763i
$343$	231.517	−	864.033i	0.674977	−	2.51905i
$344$	−62.8767	+	11.0869i	−0.182781	+	0.0322292i
$345$	−72.7943	+	212.433i	−0.210998	+	0.615749i
$346$	175.625	−	63.9222i	0.507586	−	0.184746i
$347$	21.0035	+	29.9961i	0.0605288	+	0.0864441i	0.848275	−	0.529555i	$-0.177641\pi$
$347$	21.0035	+	29.9961i	0.0605288	+	0.0864441i	−0.787747	+	0.615999i	$0.788752\pi$
$348$	−98.9700	−	38.4967i	−0.284396	−	0.110623i
$349$	−259.269	−	308.985i	−0.742891	−	0.885343i	0.253747	−	0.967271i	$-0.418337\pi$
$349$	−259.269	−	308.985i	−0.742891	−	0.885343i	−0.996638	+	0.0819276i	$0.973892\pi$
$350$	325.050	−	321.434i	0.928715	−	0.918382i
$351$	−120.202	+	72.8997i	−0.342455	+	0.207692i
$352$	−77.0513	+	77.0513i	−0.218896	+	0.218896i
$353$	−290.243	−	25.3930i	−0.822219	−	0.0719348i	−0.331721	−	0.943377i	$-0.607629\pi$
$353$	−290.243	−	25.3930i	−0.822219	−	0.0719348i	−0.490498	+	0.871443i	$0.663185\pi$
$354$	189.022	−	257.749i	0.533960	−	0.728104i
$355$	−293.695	+	458.175i	−0.827309	+	1.29063i
$356$	−99.8539	+	36.3438i	−0.280488	+	0.102089i
$357$	272.859	+	804.032i	0.764310	+	2.25219i
$358$	72.4559	−	103.478i	0.202391	−	0.289044i
$359$	−139.525	+	80.5547i	−0.388649	+	0.224386i	−0.681574	−	0.731749i	$-0.738704\pi$
$359$	−139.525	+	80.5547i	−0.388649	+	0.224386i	0.292926	+	0.956135i	$0.405371\pi$
$360$	−110.038	−	63.9658i	−0.305661	−	0.177683i
$361$	−131.137	+	227.136i	−0.363261	+	0.629186i
$362$	−232.309	+	108.328i	−0.641739	+	0.299248i
$363$	749.988	+	16.4265i	2.06608	+	0.0452519i
$364$	86.5472	−	103.143i	0.237767	−	0.283360i
$365$	5.79505	−	18.2019i	0.0158769	−	0.0498681i
$366$	−278.714	+	266.766i	−0.761513	+	0.728870i
$367$	98.0573	−	45.7249i	0.267186	−	0.124591i	−0.284409	−	0.958703i	$-0.591797\pi$
$367$	98.0573	−	45.7249i	0.267186	−	0.124591i	0.551595	+	0.834112i	$0.314019\pi$
$368$	−57.8421	+	15.4987i	−0.157180	+	0.0421161i
$369$	−133.080	+	102.081i	−0.360651	+	0.276643i
$370$	−334.294	+	43.0596i	−0.903496	+	0.116377i
$371$	−146.472	−	830.683i	−0.394803	−	2.23904i
$372$	43.8080	+	129.089i	0.117763	+	0.347014i
$373$	−135.761	−	63.3062i	−0.363969	−	0.169722i	0.232026	−	0.972710i	$-0.425465\pi$
$373$	−135.761	−	63.3062i	−0.363969	−	0.169722i	−0.595995	+	0.802988i	$0.703242\pi$
$374$	587.238	+	103.546i	1.57015	+	0.276861i
$375$	322.229	−	191.816i	0.859277	−	0.511510i
$376$	106.323	−	89.2157i	0.282774	−	0.237276i
$377$	65.1617	−	65.1617i	0.172843	−	0.172843i
$378$	−479.534	−	117.466i	−1.26861	−	0.310758i
$379$			457.821i			1.20797i	0.796995	+	0.603985i	$0.206421\pi$
$379$			457.821i			1.20797i	−0.796995	+	0.603985i	$0.793579\pi$
$380$	−94.8453	+	29.6132i	−0.249593	+	0.0779294i
$381$	2.01155	−	0.884904i	0.00527965	−	0.00232258i
$382$	127.694	+	182.366i	0.334277	+	0.477397i
$383$	−314.860	−	146.821i	−0.822088	−	0.383346i	−0.0343904	−	0.999408i	$-0.510949\pi$
$383$	−314.860	−	146.821i	−0.822088	−	0.383346i	−0.787697	+	0.616063i	$0.788727\pi$
$384$	−2.21707	−	33.8686i	−0.00577363	−	0.0881996i
$385$	−666.175	−	1052.17i	−1.73032	−	2.73290i
$386$	150.967	+	261.483i	0.391106	+	0.677416i
$387$	−198.350	+	43.9390i	−0.512533	+	0.113538i
$388$	131.500	−	35.2353i	0.338918	−	0.0908127i
$389$	174.865	−	480.438i	0.449524	−	1.23506i	−0.483532	−	0.875327i	$-0.660646\pi$
$389$	174.865	−	480.438i	0.449524	−	1.23506i	0.933056	−	0.359731i	$-0.117132\pi$
$390$	89.2598	−	65.0537i	0.228871	−	0.166804i
$391$	251.028	+	210.637i	0.642015	+	0.538714i
$392$	332.997	−	29.1334i	0.849481	−	0.0743200i
$393$	−154.171	−	281.071i	−0.392292	−	0.715194i
$394$	−64.7624	+	177.933i	−0.164372	+	0.451607i
$395$	60.3409	+	79.0949i	0.152762	+	0.200240i
$396$	−234.290	+	255.598i	−0.591641	+	0.645450i
$397$	−612.731	−	164.181i	−1.54340	−	0.413553i	−0.616039	−	0.787716i	$-0.711264\pi$
$397$	−612.731	−	164.181i	−1.54340	−	0.413553i	−0.927363	+	0.374163i	$0.877930\pi$
$398$	46.9154	−	67.0021i	0.117878	−	0.168347i
$399$	−320.480	+	214.100i	−0.803209	+	0.536591i
$400$	90.3929	+	42.7682i	0.225982	+	0.106920i
$401$	99.4497	−	564.007i	0.248004	−	1.40650i	−0.565406	−	0.824812i	$-0.691281\pi$
$401$	99.4497	−	564.007i	0.248004	−	1.40650i	0.813411	−	0.581690i	$-0.197608\pi$
$402$	−192.696	−	240.135i	−0.479344	−	0.597351i
$403$	−117.846	−	10.3102i	−0.292421	−	0.0255835i
$404$		−	72.3594i		−	0.179107i
$405$	−358.653	−	188.130i	−0.885563	−	0.464519i
$406$	323.635			0.797131
$407$	−80.0262	+	914.704i	−0.196625	+	2.24743i
$408$	−144.861	+	116.244i	−0.355053	+	0.284912i
$409$	258.532	+	45.5861i	0.632106	+	0.111457i	0.480516	−	0.876986i	$-0.340449\pi$
$409$	258.532	+	45.5861i	0.632106	+	0.111457i	0.151590	+	0.988443i	$0.451561\pi$
$410$	97.4038	−	88.7542i	0.237570	−	0.216474i
$411$	282.038	+	422.175i	0.686224	+	1.02719i
$412$	144.369	+	101.088i	0.350411	+	0.245360i
$413$	−252.117	+	940.915i	−0.610454	+	2.27824i
$414$	−181.735	+	57.2681i	−0.438975	+	0.138329i
$415$	−529.733	−	71.2487i	−1.27647	−	0.171684i
$416$	27.6772	+	10.0737i	0.0665317	+	0.0242156i
$417$	−146.565	+	80.3927i	−0.351475	+	0.192788i
$418$	23.5910	+	269.646i	0.0564377	+	0.645086i
$419$	−291.561	+	347.469i	−0.695850	+	0.829282i	−0.992050	−	0.125844i	$-0.959836\pi$
$419$	−291.561	+	347.469i	−0.695850	+	0.829282i	0.296200	+	0.955126i	$0.404281\pi$
$420$	383.210	+	60.1118i	0.912406	+	0.143123i
$421$	−555.988	−	202.363i	−1.32064	−	0.480673i	−0.416975	−	0.908918i	$-0.636910\pi$
$421$	−555.988	−	202.363i	−1.32064	−	0.480673i	−0.903663	+	0.428245i	$0.859132\pi$
$422$	−94.8221	−	353.881i	−0.224697	−	0.838581i
$423$	325.662	−	298.316i	0.769888	−	0.705239i
$424$	159.796	−	92.2580i	0.376876	−	0.217590i
$425$	−92.0086	−	539.437i	−0.216491	−	1.26926i
$426$	−460.804	+	30.1647i	−1.08170	+	0.0708091i
$427$	496.906	−	1065.62i	1.16372	−	2.49560i
$428$	−24.1787	+	16.9301i	−0.0564922	+	0.0395563i
$429$	−121.158	−	275.414i	−0.282420	−	0.641992i
$430$	152.363	−	47.5717i	0.354332	−	0.110632i
$431$	394.051			0.914273			0.457136	−	0.889397i	$-0.348875\pi$
$431$	394.051			0.914273			0.457136	+	0.889397i	$0.348875\pi$
$432$	−11.7312	−	107.361i	−0.0271555	−	0.248521i
$433$	403.434	+	403.434i	0.931719	+	0.931719i	0.997813	−	0.0660942i	$-0.0210538\pi$
$433$	403.434	+	403.434i	0.931719	+	0.931719i	−0.0660942	+	0.997813i	$0.521054\pi$
$434$	−267.045	−	318.252i	−0.615312	−	0.733300i
$435$	257.693	+	63.8440i	0.592397	+	0.146768i
$436$	−7.69289	+	43.6286i	−0.0176443	+	0.100066i
$437$	−62.8642	+	134.813i	−0.143854	+	0.308496i
$438$	15.3489	−	5.20885i	0.0350432	−	0.0118923i
$439$	343.289	−	60.5311i	0.781979	−	0.137884i	0.231613	−	0.972808i	$-0.425600\pi$
$439$	343.289	−	60.5311i	0.781979	−	0.137884i	0.550365	+	0.834924i	$0.314488\pi$
$440$	166.441	−	215.658i	0.378275	−	0.490133i
$441$	1054.56	−	138.659i	2.39129	−	0.314420i
$442$	−41.7157	−	155.685i	−0.0943795	−	0.352229i
$443$	261.271	+	560.297i	0.589776	+	1.26478i	0.944101	+	0.329656i	$0.106933\pi$
$443$	261.271	+	560.297i	0.589776	+	1.26478i	−0.354325	+	0.935122i	$0.615289\pi$
$444$	−197.756	−	206.613i	−0.445397	−	0.465345i
$445$	235.982	−	122.007i	0.530296	−	0.274172i
$446$	−262.859	−	220.565i	−0.589370	−	0.494540i
$447$	−11.4178	+	521.309i	−0.0255433	+	1.16624i
$448$	43.7152	+	93.7476i	0.0975786	+	0.209258i
$449$	442.558	+	255.511i	0.985654	+	0.569067i	0.903972	−	0.427591i	$-0.140638\pi$
$449$	442.558	+	255.511i	0.985654	+	0.569067i	0.0816813	+	0.996658i	$0.473971\pi$
$450$	293.271	+	123.460i	0.651712	+	0.274356i
$451$	−179.490	−	310.885i	−0.397982	−	0.689325i
$452$	−178.198	−	124.775i	−0.394242	−	0.276052i
$453$	560.321	−	190.152i	1.23691	−	0.419761i
$454$	184.194	+	506.068i	0.405713	+	1.11469i
$455$	−181.653	+	283.386i	−0.399238	+	0.622827i
$456$	−67.9876	−	49.8592i	−0.149096	−	0.109340i
$457$	−67.2631	+	768.821i	−0.147184	+	1.68232i	0.460124	+	0.887855i	$0.347805\pi$
$457$	−67.2631	+	768.821i	−0.147184	+	1.68232i	−0.607308	+	0.794467i	$0.707751\pi$
$458$	−254.782	−	254.782i	−0.556292	−	0.556292i
$459$	−444.437	+	389.567i	−0.968273	+	0.848731i
$460$	138.470	−	56.9030i	0.301022	−	0.123702i
$461$	−311.089	+	261.035i	−0.674813	+	0.566235i	−0.914486	−	0.404618i	$-0.867404\pi$
$461$	−311.089	+	261.035i	−0.674813	+	0.566235i	0.239673	+	0.970854i	$0.422960\pi$
$462$	383.068	−	984.819i	0.829152	−	2.13164i
$463$	587.606	−	411.446i	1.26913	−	0.888652i	0.271846	−	0.962341i	$-0.412366\pi$
$463$	587.606	−	411.446i	1.26913	−	0.888652i	0.997281	+	0.0736883i	$0.0234770\pi$
$464$	24.2135	+	66.5261i	0.0521843	+	0.143375i
$465$	−149.851	−	306.087i	−0.322261	−	0.658251i
$466$	68.8713	+	390.589i	0.147793	+	0.838173i
$467$	−45.7429	−	12.2568i	−0.0979505	−	0.0262458i	0.209511	−	0.977806i	$-0.432813\pi$
$467$	−45.7429	−	12.2568i	−0.0979505	−	0.0262458i	−0.307461	+	0.951561i	$0.599479\pi$
$468$	89.3780	+	28.1969i	0.190979	+	0.0602498i
$469$	812.617	+	469.165i	1.73266	+	1.00035i
$470$	−235.136	+	255.169i	−0.500290	+	0.542914i
$471$	−60.1123	−	245.746i	−0.127627	−	0.521754i
$472$	−212.276	+	18.5718i	−0.449738	+	0.0393469i
$473$	−37.8974	−	433.169i	−0.0801213	−	0.915791i
$474$	−23.6284	+	81.0405i	−0.0498489	+	0.170972i
$475$	225.712	−	103.718i	0.475184	−	0.218354i
$476$	283.023	−	490.211i	0.594587	−	1.02985i
$477$	495.229	−	315.381i	1.03822	−	0.661177i
$478$	98.2672	−	366.738i	0.205580	−	0.767234i
$479$	−647.354	+	114.146i	−1.35147	+	0.238301i	−0.802055	−	0.597250i	$-0.796260\pi$
$479$	−647.354	+	114.146i	−1.35147	+	0.238301i	−0.549414	+	0.835550i	$0.685149\pi$
$480$	16.3143	+	83.2697i	0.0339881	+	0.173479i
$481$	233.219	−	84.8846i	0.484862	−	0.176475i
$482$	189.044	+	269.983i	0.392207	+	0.560130i
$483$	452.913	−	363.440i	0.937708	−	0.752464i
$484$	−321.466	−	383.108i	−0.664186	−	0.791546i
$485$	−314.803	+	129.365i	−0.649078	+	0.266732i
$486$	−52.1383	−	339.676i	−0.107280	−	0.698921i
$487$	424.062	−	424.062i	0.870764	−	0.870764i	−0.121792	−	0.992556i	$-0.538864\pi$
$487$	424.062	−	424.062i	0.870764	−	0.870764i	0.992556	+	0.121792i	$0.0388641\pi$
$488$	256.225	+	22.4168i	0.525051	+	0.0459360i
$489$	525.614	+	57.6078i	1.07488	+	0.117807i
$490$	−816.366	+	178.590i	−1.66605	+	0.364469i
$491$	−598.206	+	217.729i	−1.21834	+	0.443441i	−0.869590	−	0.493774i	$-0.835617\pi$
$491$	−598.206	+	217.729i	−1.21834	+	0.443441i	−0.348753	+	0.937215i	$0.613395\pi$
$492$	109.665	+	21.8231i	0.222896	+	0.0443559i
$493$	222.211	−	317.350i	0.450732	−	0.643712i
$494$	63.3610	−	36.5815i	0.128261	−	0.0740516i
$495$	499.292	−	708.587i	1.00867	−	1.43149i
$496$	45.4400	−	78.7043i	0.0916129	−	0.158678i
$497$	1275.50	−	594.773i	2.56639	−	1.19673i
$498$	−218.115	−	397.650i	−0.437983	−	0.798493i
$499$	121.915	−	145.292i	0.244318	−	0.291167i	−0.629924	−	0.776656i	$-0.716914\pi$
$499$	121.915	−	145.292i	0.244318	−	0.291167i	0.874242	+	0.485490i	$0.161359\pi$
$500$	−237.790	−	77.1746i	−0.475580	−	0.154349i
$501$	−26.8234	−	109.657i	−0.0535397	−	0.218876i
$502$	29.7292	−	13.8630i	0.0592216	−	0.0276155i
$503$	−707.527	+	189.581i	−1.40661	+	0.376901i	−0.880716	−	0.473646i	$-0.842938\pi$
$503$	−707.527	+	189.581i	−1.40661	+	0.376901i	−0.525899	+	0.850547i	$0.676271\pi$
$504$	151.932	+	291.977i	0.301453	+	0.579319i
$505$	23.1102	+	179.416i	0.0457628	+	0.355280i
$506$	−70.8183	−	401.630i	−0.139957	−	0.793736i
$507$	280.691	−	320.014i	0.553631	−	0.631191i
$508$	−1.32779	−	0.619159i	−0.00261376	−	0.00121882i
$509$	−858.188	−	151.322i	−1.68603	−	0.297292i	−0.753248	−	0.657737i	$-0.771514\pi$
$509$	−858.188	−	151.322i	−1.68603	−	0.297292i	−0.932781	+	0.360445i	$0.882625\pi$
$510$	322.060	−	334.495i	0.631490	−	0.655872i
$511$	−37.8408	+	31.7522i	−0.0740524	+	0.0621373i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−223.025	−	149.100i	−0.434747	−	0.290644i
$514$		−	151.777i		−	0.295287i
$515$	−390.251	−	204.542i	−0.757770	−	0.397168i
$516$	109.218	+	80.0955i	0.211662	+	0.155224i
$517$	542.176	+	774.307i	1.04870	+	1.49769i
$518$	789.954	+	368.361i	1.52501	+	0.711122i
$519$	−355.565	−	175.382i	−0.685097	−	0.337922i
$520$	−71.8433	−	16.1383i	−0.138160	−	0.0310351i
$521$	−303.315	−	525.356i	−0.582178	−	1.00836i	−0.995221	−	0.0976498i	$-0.968867\pi$
$521$	−303.315	−	525.356i	−0.582178	−	1.00836i	0.413043	−	0.910711i	$-0.364466\pi$
$522$	86.1730	+	208.137i	0.165082	+	0.398729i
$523$	−5.99657	+	1.60678i	−0.0114657	+	0.00307223i	−0.264547	−	0.964373i	$-0.585223\pi$
$523$	−5.99657	+	1.60678i	−0.0114657	+	0.00307223i	0.253082	+	0.967445i	$0.418556\pi$
$524$	−73.0959	+	200.829i	−0.139496	+	0.383262i
$525$	−969.375	−	26.6580i	−1.84643	−	0.0507771i
$526$	317.091	+	266.071i	0.602834	+	0.505838i
$527$	−495.427	+	43.3443i	−0.940090	+	0.0822472i
$528$	231.098	+	5.06158i	0.437686	+	0.00958633i
$529$	−104.275	+	286.494i	−0.197117	+	0.541576i
$530$	−366.750	+	279.791i	−0.691981	+	0.527907i
$531$	−672.253	+	88.3914i	−1.26601	+	0.166462i
$532$	248.190	+	66.5022i	0.466522	+	0.125004i
$533$	−55.6548	+	79.4833i	−0.104418	+	0.149124i
$534$	202.162	+	99.7157i	0.378580	+	0.186734i
$535$	54.5442	−	49.7006i	0.101952	−	0.0928983i
$536$	−35.6431	+	202.142i	−0.0664984	+	0.377131i
$537$	−264.856	+	40.7430i	−0.493214	+	0.0758714i
$538$	551.422	+	48.2432i	1.02495	+	0.0896714i
$539$			2276.51i			4.22359i
$540$	63.3766	+	262.456i	0.117364	+	0.486031i
$541$	−118.379			−0.218815			−0.109408	−	0.993997i	$-0.534895\pi$
$541$	−118.379			−0.218815			−0.109408	+	0.993997i	$0.534895\pi$
$542$	−6.79397	+	77.6554i	−0.0125350	+	0.143276i
$543$	506.761	+	197.116i	0.933261	+	0.363014i
$544$	121.942	+	21.5017i	0.224158	+	0.0395252i
$545$	5.14051	−	110.635i	0.00943214	−	0.202999i
$546$	−285.012	+	18.6572i	−0.522000	+	0.0341706i
$547$	−384.610	−	269.307i	−0.703126	−	0.492334i	0.166503	−	0.986041i	$-0.446753\pi$
$547$	−384.610	−	269.307i	−0.703126	−	0.492334i	−0.869628	+	0.493707i	$0.835641\pi$
$548$	87.6046	−	326.945i	0.159862	−	0.596615i
$549$	817.632	+	35.8332i	1.48931	+	0.0652699i
$550$	−343.816	+	587.887i	−0.625120	+	1.06888i
$551$	165.252	+	60.1469i	0.299913	+	0.109160i
$552$	108.594	+	65.9087i	0.196728	+	0.119400i
$553$	−22.4219	−	256.284i	−0.0405460	−	0.463443i
$554$	−322.709	+	384.589i	−0.582507	+	0.694204i
$555$	556.328	+	449.141i	1.00239	+	0.809262i
$556$	104.723	+	38.1160i	0.188350	+	0.0685539i
$557$	60.2002	+	224.670i	0.108079	+	0.403358i	0.998676	−	0.0514357i	$-0.0163797\pi$
$557$	60.2002	+	224.670i	0.108079	+	0.403358i	−0.890597	+	0.454794i	$0.849713\pi$
$558$	133.570	−	256.482i	0.239372	−	0.459646i
$559$	−101.785	+	58.7658i	−0.182085	+	0.105127i
$560$	−138.334	−	218.487i	−0.247025	−	0.390155i
$561$	−702.675	−	1051.81i	−1.25254	−	1.87489i
$562$	−37.7936	+	81.0487i	−0.0672484	+	0.144215i
$563$	309.685	−	216.844i	0.550062	−	0.385158i	−0.265249	−	0.964180i	$-0.585454\pi$
$563$	309.685	−	216.844i	0.550062	−	0.385158i	0.815312	+	0.579022i	$0.196565\pi$
$564$	−292.676	−	32.0776i	−0.518929	−	0.0568751i
$565$	481.695	+	252.469i	0.852557	+	0.446848i
$566$	189.180			0.334239
$567$	523.362	+	907.178i	0.923037	+	1.59996i
$568$	217.690	+	217.690i	0.383257	+	0.383257i
$569$	−430.226	−	512.723i	−0.756109	−	0.901096i	0.241486	−	0.970404i	$-0.422365\pi$
$569$	−430.226	−	512.723i	−0.756109	−	0.901096i	−0.997595	+	0.0693087i	$0.977921\pi$
$570$	184.500	+	101.913i	0.323685	+	0.178794i
$571$	71.2732	−	404.211i	0.124822	−	0.707899i	−0.856592	−	0.515995i	$-0.827422\pi$
$571$	71.2732	−	404.211i	0.124822	−	0.707899i	0.981414	−	0.191905i	$-0.0614665\pi$
$572$	−84.7733	+	181.797i	−0.148205	+	0.317827i
$573$	92.1722	−	463.182i	0.160859	−	0.808346i
$574$	−335.592	+	59.1738i	−0.584654	+	0.103090i
$575$	−325.166	+	185.317i	−0.565505	+	0.322290i
$576$	−48.6512	+	53.0760i	−0.0844639	+	0.0921458i
$577$	−142.356	−	531.278i	−0.246717	−	0.920760i	−0.972513	−	0.232850i	$-0.925195\pi$
$577$	−142.356	−	531.278i	−0.246717	−	0.920760i	0.725796	−	0.687910i	$-0.241472\pi$
$578$	−113.637	−	243.695i	−0.196603	−	0.421617i
$579$	179.281	−	614.896i	0.309639	−	1.06200i
$580$	−81.2850	−	157.219i	−0.140147	−	0.271068i
$581$	1058.84	+	888.469i	1.82244	+	1.52921i
$582$	−246.881	−	149.839i	−0.424195	−	0.257455i
$583$	531.077	+	1138.90i	0.910938	+	1.95351i
$584$	−9.35808	−	5.40289i	−0.0160241	−	0.00925153i
$585$	−230.620	−	41.3691i	−0.394222	−	0.0707163i
$586$	−110.055	−	190.621i	−0.187807	−	0.325291i
$587$	−124.087	−	86.8864i	−0.211391	−	0.148018i	0.463086	−	0.886313i	$-0.346742\pi$
$587$	−124.087	−	86.8864i	−0.211391	−	0.148018i	−0.674477	+	0.738296i	$0.735631\pi$
$588$	−533.084	−	467.580i	−0.906606	−	0.795204i
$589$	−77.2102	−	212.133i	−0.131087	−	0.360159i
$590$	520.410	−	113.846i	0.882052	−	0.192959i
$591$	367.673	−	161.744i	0.622121	−	0.273679i
$592$	−16.6178	+	189.942i	−0.0280705	+	0.320848i
$593$	−627.362	−	627.362i	−1.05795	−	1.05795i	−0.998214	−	0.0597316i	$-0.980976\pi$
$593$	−627.362	−	627.362i	−1.05795	−	1.05795i	−0.0597316	−	0.998214i	$-0.519024\pi$
$594$	735.356	−	15.8642i	1.23797	−	0.0267074i
$595$	−545.197	+	1305.88i	−0.916297	+	2.19475i
$596$	266.294	−	223.447i	0.446802	−	0.374912i
$597$	−171.495	+	26.3812i	−0.287261	+	0.0441896i
$598$	−90.2986	+	63.2277i	−0.151001	+	0.105732i
$599$	−92.7352	−	254.788i	−0.154817	−	0.425355i	0.837901	−	0.545823i	$-0.183783\pi$
$599$	−92.7352	−	254.788i	−0.154817	−	0.425355i	−0.992717	+	0.120468i	$0.961561\pi$
$600$	−67.0462	−	201.258i	−0.111744	−	0.335430i
$601$	90.0728	+	510.828i	0.149872	+	0.849964i	0.963326	+	0.268335i	$0.0864733\pi$
$601$	90.0728	+	510.828i	0.149872	+	0.849964i	−0.813454	+	0.581629i	$0.802416\pi$
$602$	−398.700	−	106.831i	−0.662293	−	0.177461i
$603$	−85.3577	+	647.534i	−0.141555	+	1.07385i
$604$	−341.622	−	197.236i	−0.565600	−	0.326549i
$605$	919.437	+	847.252i	1.51973	+	1.40042i
$606$	−110.890	+	106.136i	−0.182986	+	0.175143i
$607$	−1183.24	+	103.520i	−1.94932	+	0.170543i	−0.992684	−	0.120740i	$-0.961473\pi$
$607$	−1183.24	+	103.520i	−1.94932	+	0.170543i	−0.956637	+	0.291284i	$0.905918\pi$
$608$	4.89876	+	55.9931i	0.00805717	+	0.0920939i
$609$	−474.707	−	495.967i	−0.779486	−	0.814395i
$610$	−642.473	+	26.2506i	−1.05323	+	0.0430338i
$611$	127.750	−	221.269i	0.209083	−	0.362142i
$612$	390.624	+	51.4920i	0.638275	+	0.0841372i
$613$	−82.2602	+	306.999i	−0.134193	+	0.500814i	0.865807	+	0.500378i	$0.166806\pi$
$613$	−82.2602	+	306.999i	−0.134193	+	0.500814i	−1.00000		0.000436377i	$0.999861\pi$
$614$	−48.5018	+	8.55218i	−0.0789932	+	0.0139286i
$615$	−278.886	−	19.0858i	−0.453473	−	0.0310338i
$616$	−661.980	+	240.941i	−1.07464	+	0.391138i
$617$	254.625	+	363.642i	0.412682	+	0.589371i	0.970651	−	0.240491i	$-0.0773083\pi$
$617$	254.625	+	363.642i	0.412682	+	0.589371i	−0.557970	+	0.829861i	$0.688419\pi$
$618$	−56.8435	−	369.520i	−0.0919797	−	0.597928i
$619$	130.811	+	155.895i	0.211327	+	0.251850i	0.861287	−	0.508119i	$-0.169659\pi$
$619$	130.811	+	155.895i	0.211327	+	0.251850i	−0.649960	+	0.759968i	$0.725214\pi$
$620$	−87.5324	+	209.661i	−0.141181	+	0.338163i
$621$	354.331	+	194.506i	0.570582	+	0.313215i
$622$	−65.8933	+	65.8933i	−0.105938	+	0.105938i
$623$	−684.365	−	59.8742i	−1.09850	−	0.0961063i
$624$	−25.1590	−	57.1909i	−0.0403189	−	0.0916521i
$625$	614.252	+	115.410i	0.982803	+	0.184656i
$626$	224.203	−	81.6032i	0.358152	−	0.130357i
$627$	378.626	−	431.668i	0.603869	−	0.688466i
$628$	−96.7399	+	138.159i	−0.154044	+	0.219998i
$629$	903.597	−	521.692i	1.43656	−	0.829399i
$630$	−469.971	−	675.436i	−0.745985	−	1.07212i
$631$	−14.4867	+	25.0917i	−0.0229583	+	0.0397649i	−0.877276	−	0.479986i	$-0.840642\pi$
$631$	−14.4867	+	25.0917i	−0.0229583	+	0.0397649i	0.854318	+	0.519751i	$0.173975\pi$
$632$	51.0039	−	23.7835i	0.0807023	−	0.0376321i
$633$	−403.233	+	664.385i	−0.637019	+	1.04958i
$634$	−164.688	+	196.267i	−0.259760	+	0.309570i
$635$	3.49003	+	1.11114i	0.00549611	+	0.00174983i
$636$	−375.771	−	109.561i	−0.590836	−	0.172266i
$637$	557.683	−	260.052i	0.875484	−	0.408245i
$638$	−465.720	+	124.789i	−0.729969	+	0.195595i
$639$	722.132	+	661.931i	1.13010	+	1.03589i
$640$	34.5621	−	44.7823i	0.0540034	−	0.0699724i
$641$	−90.4345	−	512.880i	−0.141084	−	0.800124i	−0.970429	−	0.241388i	$-0.922397\pi$
$641$	−90.4345	−	512.880i	−0.141084	−	0.800124i	0.829345	−	0.558737i	$-0.188714\pi$
$642$	61.4102	+	12.2205i	0.0956546	+	0.0190351i
$643$	−559.019	−	260.675i	−0.869392	−	0.405404i	−0.0638618	−	0.997959i	$-0.520342\pi$
$643$	−559.019	−	260.675i	−0.869392	−	0.405404i	−0.805530	+	0.592555i	$0.798119\pi$
$644$	−381.256	−	67.2256i	−0.592012	−	0.104388i
$645$	−296.388	−	163.716i	−0.459516	−	0.253823i
$646$	235.620	−	197.708i	0.364737	−	0.306050i
$647$	473.992	−	473.992i	0.732599	−	0.732599i	−0.238535	−	0.971134i	$-0.576667\pi$
$647$	473.992	−	473.992i	0.732599	−	0.732599i	0.971134	+	0.238535i	$0.0766671\pi$
$648$	−147.322	+	175.454i	−0.227349	+	0.270763i
$649$		−	1451.22i		−	2.23608i
$650$	183.291	+	17.0697i	0.281986	+	0.0262610i
$651$	−96.0164	+	876.054i	−0.147491	+	1.34571i
$652$	−202.190	−	288.758i	−0.310108	−	0.442880i
$653$	−722.570	−	336.940i	−1.10654	−	0.515988i	−0.218538	−	0.975829i	$-0.570129\pi$
$653$	−722.570	−	336.940i	−1.10654	−	0.515988i	−0.888001	+	0.459841i	$0.847906\pi$
$654$	78.1441	−	52.2049i	0.119486	−	0.0798240i
$655$	117.101	−	521.305i	0.178781	−	0.795885i
$656$	−37.2718	−	64.5566i	−0.0568167	−	0.0984094i
$657$	−30.4962	−	15.8817i	−0.0464173	−	0.0241730i
$658$	866.727	−	232.239i	1.31721	−	0.352946i
$659$	317.682	−	872.824i	0.482067	−	1.32447i	−0.425652	−	0.904887i	$-0.639955\pi$
$659$	317.682	−	872.824i	0.482067	−	1.32447i	0.907718	−	0.419580i	$-0.137823\pi$
$660$	−574.629	+	61.2582i	−0.870649	+	0.0928154i
$661$	98.2689	+	82.4574i	0.148667	+	0.124746i	0.714088	−	0.700056i	$-0.246842\pi$
$661$	98.2689	+	82.4574i	0.148667	+	0.124746i	−0.565421	+	0.824803i	$0.691286\pi$
$662$	−474.749	+	41.5352i	−0.717144	+	0.0627419i
$663$	−177.397	+	292.287i	−0.267567	+	0.440855i
$664$	−103.413	+	284.126i	−0.155743	+	0.427901i
$665$	−636.629	−	85.6262i	−0.957337	−	0.128761i
$666$	−26.5635	+	606.118i	−0.0398851	+	0.910087i
$667$	−255.935	−	68.5777i	−0.383711	−	0.102815i
$668$	−43.1674	+	61.6494i	−0.0646218	+	0.0922895i
$669$	47.5476	+	726.351i	0.0710727	+	1.08573i
$670$	23.8173	−	512.599i	0.0355482	−	0.765072i
$671$	−304.174	+	1725.06i	−0.453314	+	2.57087i
$672$	79.5456	−	204.501i	0.118371	−	0.304318i
$673$	−224.083	−	19.6047i	−0.332962	−	0.0291304i	−0.0805507	−	0.996751i	$-0.525668\pi$
$673$	−224.083	−	19.6047i	−0.332962	−	0.0291304i	−0.252411	+	0.967620i	$0.581223\pi$
$674$		−	716.850i		−	1.06358i
$675$	−240.967	−	630.524i	−0.356988	−	0.934109i
$676$	−283.781			−0.419794
$677$	15.7326	−	179.824i	0.0232387	−	0.265619i	−0.975683	−	0.219187i	$-0.929659\pi$
$677$	15.7326	−	179.824i	0.0232387	−	0.265619i	0.998921	−	0.0464319i	$-0.0147851\pi$
$678$	70.1629	+	456.105i	0.103485	+	0.672721i
$679$	866.759	+	152.833i	1.27652	+	0.225085i
$680$	−309.225	−	14.3678i	−0.454742	−	0.0211291i
$681$	505.368	−	1024.57i	0.742097	−	1.50451i
$682$	506.999	+	355.005i	0.743401	+	0.520535i
$683$	10.0260	−	37.4174i	0.0146793	−	0.0547838i	−0.958198	−	0.286107i	$-0.907639\pi$
$683$	10.0260	−	37.4174i	0.0146793	−	0.0547838i	0.972877	+	0.231323i	$0.0743054\pi$
$684$	23.3154	+	177.323i	0.0340868	+	0.259244i
$685$	−112.797	+	838.644i	−0.164667	+	1.22430i
$686$	1188.74	+	432.667i	1.73286	+	0.630709i
$687$	−16.7369	+	764.162i	−0.0243623	+	1.11232i
$688$	−7.86954	−	89.9492i	−0.0114383	−	0.130740i
$689$	218.332	−	260.198i	0.316883	−	0.377646i
$690$	−290.311	−	128.739i	−0.420740	−	0.186578i
$691$	−379.199	−	138.017i	−0.548768	−	0.199735i	0.0527310	−	0.998609i	$-0.483207\pi$
$691$	−379.199	−	138.017i	−0.548768	−	0.199735i	−0.601499	+	0.798874i	$0.705430\pi$
$692$	68.4087	+	255.305i	0.0988565	+	0.368937i
$693$	−2071.10	+	857.480i	−2.98860	+	1.23735i
$694$	−44.8483	+	25.8932i	−0.0646229	+	0.0373100i
$695$	−271.835	−	61.0627i	−0.391130	−	0.0878599i
$696$	66.4341	−	134.687i	0.0954513	−	0.193516i
$697$	−172.395	+	369.703i	−0.247339	+	0.530421i
$698$	467.264	−	327.182i	0.669433	−	0.468742i
$699$	497.552	−	678.458i	0.711805	−	0.970612i
$700$	412.781	+	497.560i	0.589688	+	0.710800i
$701$	−239.262			−0.341315			−0.170658	−	0.985330i	$-0.554589\pi$
$701$	−239.262			−0.341315			−0.170658	+	0.985330i	$0.554589\pi$
$702$	−87.8878	−	178.330i	−0.125196	−	0.254031i
$703$	334.901	+	334.901i	0.476388	+	0.476388i
$704$	−99.0552	−	118.049i	−0.140703	−	0.167684i
$705$	735.940	−	13.9383i	1.04389	−	0.0197707i
$706$	71.5489	−	405.774i	0.101344	−	0.574751i
$707$	197.700	−	423.970i	0.279633	−	0.599675i
$708$	339.827	+	298.069i	0.479981	+	0.421002i
$709$	−219.685	+	38.7364i	−0.309852	+	0.0546353i	−0.326412	−	0.945228i	$-0.605840\pi$
$709$	−219.685	+	38.7364i	−0.309852	+	0.0546353i	0.0165599	+	0.999863i	$0.494729\pi$
$710$	−609.292	−	470.240i	−0.858158	−	0.662310i
$711$	158.851	−	82.6596i	0.223420	−	0.116258i
$712$	−38.8947	−	145.157i	−0.0546274	−	0.203872i
$713$	143.746	+	308.265i	0.201608	+	0.432349i
$714$	−1166.38	+	285.309i	−1.63358	+	0.399593i
$715$	152.134	−	477.843i	0.212775	−	0.668312i
$716$	136.852	+	114.832i	0.191134	+	0.160381i
$717$	−706.159	+	387.336i	−0.984879	+	0.540218i
$718$	−96.2907	−	206.496i	−0.134110	−	0.287599i
$719$	−155.221	−	89.6167i	−0.215884	−	0.124641i	0.388159	−	0.921592i	$-0.373111\pi$
$719$	−155.221	−	89.6167i	−0.215884	−	0.124641i	−0.604043	+	0.796952i	$0.706444\pi$
$720$	103.680	−	147.141i	0.144000	−	0.204362i
$721$	569.698	+	986.746i	0.790150	+	1.36858i
$722$	−303.833	−	212.746i	−0.420822	−	0.294662i
$723$	136.456	−	685.717i	0.188736	−	0.948432i
$724$	−123.982	−	340.637i	−0.171245	−	0.470493i
$725$	251.760	+	363.867i	0.347255	+	0.501885i
$726$	−115.583	+	1054.58i	−0.159206	+	1.45259i
$727$	−45.3076	+	517.868i	−0.0623213	+	0.712335i	0.899188	+	0.437563i	$0.144158\pi$
$727$	−45.3076	+	517.868i	−0.0623213	+	0.712335i	−0.961509	+	0.274773i	$0.911397\pi$
$728$	134.644	+	134.644i	0.184950	+	0.184950i
$729$	−444.072	+	578.136i	−0.609152	+	0.793053i
$730$	24.9291	+	10.4078i	0.0341494	+	0.0142572i
$731$	−378.508	+	317.606i	−0.517795	+	0.434481i
$732$	−341.476	−	425.542i	−0.466497	−	0.581341i
$733$	−181.808	+	127.304i	−0.248033	+	0.173675i	−0.690981	−	0.722872i	$-0.742821\pi$
$733$	−181.808	+	127.304i	−0.248033	+	0.173675i	0.442948	+	0.896547i	$0.353933\pi$
$734$	52.3324	+	143.782i	0.0712976	+	0.195889i
$735$	1471.13	+	989.115i	2.00153	+	1.34573i
$736$	−14.7057	−	83.4001i	−0.0199806	−	0.113315i
$737$	−1350.28	−	361.807i	−1.83213	−	0.490918i
$738$	−127.412	−	200.070i	−0.172646	−	0.271098i
$739$	−1064.95	−	614.850i	−1.44107	−	0.832003i	−0.443150	−	0.896448i	$-0.646139\pi$
$739$	−1064.95	−	614.850i	−1.44107	−	0.832003i	−0.997921	+	0.0644448i	$0.979472\pi$
$740$	−19.4598	−	476.271i	−0.0262971	−	0.643609i
$741$	−148.998	−	43.4423i	−0.201077	−	0.0586266i
$742$	1188.35	−	103.967i	1.60154	−	0.140117i
$743$	21.6174	+	247.088i	0.0290948	+	0.332555i	0.996767	+	0.0803444i	$0.0256020\pi$
$743$	21.6174	+	247.088i	0.0290948	+	0.332555i	−0.967672	+	0.252211i	$0.918842\pi$
$744$	−187.264	+	45.8070i	−0.251699	+	0.0615686i
$745$	−588.916	+	639.091i	−0.790491	+	0.857840i
$746$	105.921	−	183.461i	0.141985	−	0.245926i
$747$	−289.462	+	917.529i	−0.387499	+	1.22829i
$748$	−218.260	+	814.556i	−0.291791	+	1.08898i
$749$	−187.925	+	33.1362i	−0.250901	+	0.0442406i
$750$	230.520	+	477.609i	0.307360	+	0.636812i
$751$	754.339	−	274.557i	1.00445	−	0.365588i	0.213149	−	0.977020i	$-0.431628\pi$
$751$	754.339	−	274.557i	1.00445	−	0.365588i	0.791297	+	0.611431i	$0.209406\pi$
$752$	112.585	+	160.788i	0.149714	+	0.213814i
$753$	−64.8515	−	25.2255i	−0.0861241	−	0.0335000i
$754$	83.7703	+	99.8336i	0.111101	+	0.132405i
$755$	910.051	+	379.941i	1.20536	+	0.503233i
$756$	224.596	−	661.104i	0.297085	−	0.874476i
$757$	200.685	−	200.685i	0.265106	−	0.265106i	−0.562019	−	0.827124i	$-0.689975\pi$
$757$	200.685	−	200.685i	0.265106	−	0.265106i	0.827124	+	0.562019i	$0.189975\pi$
$758$	−644.993	−	56.4296i	−0.850914	−	0.0744453i
$759$	−511.617	+	697.637i	−0.674067	+	0.919153i
$760$	−30.0297	−	137.271i	−0.0395127	−	0.180620i
$761$	435.835	−	158.631i	0.572713	−	0.208451i	−0.0393962	−	0.999224i	$-0.512543\pi$
$761$	435.835	−	158.631i	0.572713	−	0.208451i	0.612109	+	0.790773i	$0.290321\pi$
$762$	0.998745	+	2.94300i	0.00131069	+	0.00386221i
$763$	−164.276	+	234.611i	−0.215303	+	0.307485i
$764$	−272.662	+	157.421i	−0.356887	+	0.206049i
$765$	−985.005	−	2.91715i	−1.28759	−	0.00381327i
$766$	245.655	−	425.487i	0.320699	−	0.555467i
$767$	−355.508	+	165.776i	−0.463504	+	0.216135i
$768$	47.9885	+	1.05106i	0.0624850	+	0.00136856i
$769$	590.191	−	703.362i	0.767478	−	0.914645i	−0.230818	−	0.972997i	$-0.574140\pi$
$769$	590.191	−	703.362i	0.767478	−	0.914645i	0.998296	+	0.0583523i	$0.0185847\pi$
$770$	1564.44	−	808.841i	2.03174	−	1.05044i
$771$	−232.597	+	222.626i	−0.301682	+	0.288750i
$772$	−386.993	+	180.458i	−0.501286	+	0.233754i
$773$	−1224.43	+	328.086i	−1.58400	+	0.424432i	−0.940162	−	0.340727i	$-0.889327\pi$
$773$	−1224.43	+	328.086i	−1.58400	+	0.424432i	−0.643841	+	0.765160i	$0.722660\pi$
$774$	−37.4547	−	284.858i	−0.0483911	−	0.368034i
$775$	150.076	−	547.815i	0.193647	−	0.706857i
$776$	33.4324	+	189.605i	0.0430830	+	0.244336i
$777$	−594.191	−	1750.90i	−0.764725	−	2.25342i
$778$	655.303	+	305.573i	0.842291	+	0.392767i
$779$	−182.355	−	32.1540i	−0.234088	−	0.0412760i
$780$	80.6478	+	133.770i	0.103395	+	0.171501i
$781$	−1606.14	+	1347.71i	−2.05651	+	1.72562i
$782$	−327.694	+	327.694i	−0.419045	+	0.419045i
$783$	192.569	−	437.353i	0.245937	−	0.558561i
$784$			472.727i			0.602969i
$785$	195.743	−	373.464i	0.249354	−	0.475750i
$786$	414.985	−	182.557i	0.527971	−	0.232261i
$787$	873.208	+	1247.07i	1.10954	+	1.58459i	0.762810	+	0.646622i	$0.223819\pi$
$787$	873.208	+	1247.07i	1.10954	+	1.58459i	0.346730	+	0.937965i	$0.387292\pi$
$788$	−242.696	−	113.171i	−0.307989	−	0.143618i
$789$	−57.3574	−	876.208i	−0.0726963	−	1.11053i
$790$	−118.869	+	75.2612i	−0.150467	+	0.0952674i
$791$	−703.189	−	1217.96i	−0.888987	−	1.53977i
$792$	−331.217	−	361.579i	−0.418203	−	0.456540i
$793$	457.337	−	122.543i	0.576718	−	0.154531i
$794$	306.826	−	842.998i	0.386431	−	1.06171i
$795$	966.723	+	151.644i	1.21600	+	0.190747i
$796$	88.6121	+	74.3544i	0.111322	+	0.0934100i
$797$	450.571	−	39.4198i	0.565333	−	0.0494603i	0.199093	−	0.979981i	$-0.436200\pi$
$797$	450.571	−	39.4198i	0.565333	−	0.0494603i	0.366240	+	0.930520i	$0.380645\pi$
$798$	−262.129	−	477.892i	−0.328483	−	0.598862i
$799$	367.374	−	1009.35i	0.459792	−	1.26327i
$800$	−71.3947	+	122.077i	−0.0892434	+	0.152596i
$801$	−143.717	−	456.072i	−0.179422	−	0.569379i
$802$	782.334	+	209.626i	0.975479	+	0.261379i
$803$	42.2107	−	60.2831i	0.0525662	−	0.0750724i
$804$	362.061	−	241.879i	0.450325	−	0.300844i
$805$	966.800	+	44.9212i	1.20099	+	0.0558028i
$806$	29.0506	−	164.754i	0.0360429	−	0.204409i
$807$	−734.891	−	915.810i	−0.910646	−	1.13483i
$808$	101.942	+	8.91879i	0.126166	+	0.0110381i
$809$			934.323i			1.15491i	0.816422	+	0.577456i	$0.195954\pi$
$809$			934.323i			1.15491i	−0.816422	+	0.577456i	$0.804046\pi$
$810$	309.250	−	482.094i	0.381791	−	0.595177i
$811$	−984.919			−1.21445			−0.607225	−	0.794530i	$-0.707717\pi$
$811$	−984.919			−1.21445			−0.607225	+	0.794530i	$0.707717\pi$
$812$	−39.8903	+	455.948i	−0.0491260	+	0.561512i
$813$	128.971	−	103.493i	0.158636	−	0.127298i
$814$	−1278.80	−	225.487i	−1.57101	−	0.277011i
$815$	593.557	+	651.403i	0.728291	+	0.799268i
$816$	−145.913	−	218.413i	−0.178815	−	0.267663i
$817$	−183.727	−	128.647i	−0.224880	−	0.157463i
$818$	−96.0889	+	358.609i	−0.117468	+	0.438397i
$819$	446.646	+	409.411i	0.545356	+	0.499891i
$820$	113.034	+	148.165i	0.137846	+	0.180689i
$821$	492.715	+	179.334i	0.600140	+	0.218433i	0.624184	−	0.781278i	$-0.285432\pi$
$821$	492.715	+	179.334i	0.600140	+	0.218433i	−0.0240433	+	0.999711i	$0.507654\pi$
$822$	−629.537	+	345.308i	−0.765860	+	0.420083i
$823$	24.5376	+	280.466i	0.0298148	+	0.340785i	0.996422	+	0.0845213i	$0.0269361\pi$
$823$	24.5376	+	280.466i	0.0298148	+	0.340785i	−0.966607	+	0.256264i	$0.917508\pi$
$824$	−160.211	+	190.932i	−0.194431	+	0.231714i
$825$	1405.24	−	335.416i	1.70332	−	0.406565i
$826$	−1294.52	−	471.165i	−1.56721	−	0.570418i
$827$	85.9339	+	320.710i	0.103910	+	0.387799i	0.998219	−	0.0596513i	$-0.0189989\pi$
$827$	85.9339	+	320.710i	0.103910	+	0.387799i	−0.894309	+	0.447450i	$0.852332\pi$
$828$	−58.2811	−	263.093i	−0.0703878	−	0.317746i
$829$	−438.697	+	253.282i	−0.529189	+	0.305527i	−0.740686	−	0.671851i	$-0.765499\pi$
$829$	−438.697	+	253.282i	−0.529189	+	0.305527i	0.211497	+	0.977379i	$0.432166\pi$
$830$	165.671	−	737.523i	0.199603	−	0.888582i
$831$	1062.73	−	69.5670i	1.27885	−	0.0837148i
$832$	−17.6035	+	37.7509i	−0.0211581	+	0.0453736i
$833$	2119.06	−	1483.78i	2.54389	−	1.78125i
$834$	−95.1946	−	216.394i	−0.114142	−	0.259466i
$835$	87.3445	−	166.648i	0.104604	−	0.199578i
$836$	−382.794			−0.457887
$837$	−588.975	+	171.513i	−0.703674	+	0.204914i
$838$	−453.589	−	453.589i	−0.541275	−	0.541275i
$839$	948.982	+	1130.95i	1.13109	+	1.34798i	0.929636	+	0.368479i	$0.120121\pi$
$839$	948.982	+	1130.95i	1.13109	+	1.34798i	0.201451	+	0.979499i	$0.435434\pi$
$840$	−131.921	+	532.470i	−0.157048	+	0.633893i
$841$	91.6426	−	519.731i	0.108969	−	0.617992i
$842$	353.625	−	758.352i	0.419982	−	0.900655i
$843$	179.641	−	60.9636i	0.213098	−	0.0723174i
$844$	510.246	−	89.9702i	0.604557	−	0.106600i
$845$	703.639	−	90.6342i	0.832709	−	0.107259i
$846$	380.137	+	495.573i	0.449335	+	0.585784i
$847$	−836.813	−	3123.03i	−0.987972	−	3.68716i
$848$	110.280	+	236.497i	0.130047	+	0.278887i
$849$	−277.488	−	289.915i	−0.326840	−	0.341478i
$850$	771.316	−	63.1354i	0.907431	−	0.0742769i
$851$	−546.651	−	458.695i	−0.642364	−	0.539007i
$852$	14.3003	−	652.914i	0.0167844	−	0.766331i
$853$	−169.956	−	364.473i	−0.199245	−	0.427283i	0.781145	−	0.624350i	$-0.214636\pi$
$853$	−169.956	−	364.473i	−0.199245	−	0.427283i	−0.980390	+	0.197067i	$0.936858\pi$
$854$	1440.03	+	831.403i	1.68622	+	0.973539i
$855$	−114.445	−	432.229i	−0.133853	−	0.505531i
$856$	−20.8715	−	36.1504i	−0.0243825	−	0.0422318i
$857$	633.564	+	443.626i	0.739282	+	0.517650i	0.881500	−	0.472185i	$-0.156535\pi$
$857$	633.564	+	443.626i	0.739282	+	0.517650i	−0.142218	+	0.989835i	$0.545423\pi$
$858$	402.946	−	136.745i	0.469634	−	0.159376i
$859$	263.478	+	723.899i	0.306726	+	0.842723i	0.993290	+	0.115653i	$0.0368961\pi$
$859$	263.478	+	723.899i	0.306726	+	0.842723i	−0.686564	+	0.727070i	$0.740882\pi$
$860$	48.2407	+	220.517i	0.0560939	+	0.256415i
$861$	582.927	+	427.493i	0.677035	+	0.496508i
$862$	−48.5695	+	555.152i	−0.0563452	+	0.644028i
$863$	285.428	+	285.428i	0.330739	+	0.330739i	0.852867	−	0.522128i	$-0.174862\pi$
$863$	285.428	+	285.428i	0.330739	+	0.330739i	−0.522128	+	0.852867i	$0.674862\pi$
$864$	152.700	−	3.29426i	0.176736	−	0.00381280i
$865$	−251.160	−	611.183i	−0.290358	−	0.706570i
$866$	−618.097	+	518.645i	−0.713738	+	0.598898i
$867$	−206.777	+	531.597i	−0.238497	+	0.613145i
$868$	481.279	−	336.995i	0.554469	−	0.388244i
$869$	131.085	+	360.154i	0.150846	+	0.414446i
$870$	−121.708	+	355.176i	−0.139894	+	0.408249i
$871$	65.6133	+	372.112i	0.0753310	+	0.427223i
$872$	−60.5171	−	16.2155i	−0.0694004	−	0.0185958i
$873$	132.498	+	598.125i	0.151773	+	0.685138i
$874$	−182.180	−	105.182i	−0.208444	−	0.120345i
$875$	−1182.41	−	1101.87i	−1.35132	−	1.25928i
$876$	5.44653	+	22.2661i	0.00621750	+	0.0254179i
$877$	−520.997	+	45.5813i	−0.594067	+	0.0519741i	−0.380225	−	0.924894i	$-0.624153\pi$
$877$	−520.997	+	45.5813i	−0.594067	+	0.0519741i	−0.213842	+	0.976868i	$0.568598\pi$
$878$	42.9654	+	491.097i	0.0489356	+	0.559336i
$879$	−130.696	+	448.259i	−0.148687	+	0.509965i
$880$	283.312	+	261.069i	0.321945	+	0.296669i
$881$	−315.673	+	546.762i	−0.358312	+	0.620615i	−0.987679	−	0.156493i	$-0.949981\pi$
$881$	−315.673	+	546.762i	−0.358312	+	0.620615i	0.629367	+	0.777109i	$0.283314\pi$
$882$	65.3658	+	1502.79i	0.0741108	+	1.70384i
$883$	−333.416	+	1244.33i	−0.377595	+	1.40920i	0.471921	+	0.881641i	$0.343561\pi$
$883$	−333.416	+	1244.33i	−0.377595	+	1.40920i	−0.849516	+	0.527563i	$0.823106\pi$
$884$	224.476	−	39.5812i	0.253932	−	0.0447751i
$885$	−937.803	−	630.533i	−1.05966	−	0.712467i
$886$	−821.567	+	299.026i	−0.927277	+	0.337501i
$887$	515.424	+	736.102i	0.581087	+	0.829878i	0.996826	−	0.0796055i	$-0.0253661\pi$
$887$	515.424	+	736.102i	0.581087	+	0.829878i	−0.415739	+	0.909484i	$0.636477\pi$
$888$	315.458	−	253.139i	0.355245	−	0.285067i
$889$	−6.08816	−	7.25559i	−0.00684833	−	0.00816152i
$890$	142.800	+	347.497i	0.160450	+	0.390446i
$891$	−1102.93	−	1103.65i	−1.23785	−	1.23867i
$892$	343.138	−	343.138i	0.384684	−	0.384684i
$893$	485.723	+	42.4952i	0.543922	+	0.0475870i
$894$	−733.029	−	80.3407i	−0.819943	−	0.0898665i
$895$	−376.002	−	241.021i	−0.420114	−	0.269297i
$896$	−137.463	+	50.0324i	−0.153418	+	0.0558397i
$897$	229.345	+	45.6392i	0.255680	+	0.0508798i
$898$	−414.521	+	591.997i	−0.461604	+	0.659239i
$899$	348.245	−	201.059i	0.387370	−	0.223648i
$900$	−210.082	+	397.952i	−0.233425	+	0.442169i
$901$	713.981	−	1236.65i	0.792432	−	1.37253i
$902$	460.109	−	214.552i	0.510098	−	0.237863i
$903$	421.094	+	767.702i	0.466328	+	0.850169i
$904$	197.752	−	235.671i	0.218752	−	0.260698i
$905$	416.208	+	805.017i	0.459898	+	0.889522i
$906$	198.829	+	812.835i	0.219458	+	0.897169i
$907$	−453.408	+	211.428i	−0.499898	+	0.233106i	−0.656178	−	0.754607i	$-0.727828\pi$
$907$	−453.408	+	211.428i	−0.499898	+	0.233106i	0.156279	+	0.987713i	$0.450050\pi$
$908$	−735.668	+	197.122i	−0.810207	+	0.217094i
$909$	325.305	+	14.2567i	0.357871	+	0.0156839i
$910$	−376.853	−	290.848i	−0.414125	−	0.319613i
$911$	−220.309	−	1249.43i	−0.241832	−	1.37150i	−0.827737	−	0.561117i	$-0.810372\pi$
$911$	−220.309	−	1249.43i	−0.241832	−	1.37150i	0.585905	−	0.810380i	$-0.300739\pi$
$912$	78.6231	−	89.6376i	0.0862096	−	0.0982869i
$913$	−1866.28	−	870.259i	−2.04411	−	0.953186i
$914$	−1074.85	−	189.525i	−1.17598	−	0.207358i
$915$	982.604	+	946.076i	1.07388	+	1.03396i
$916$	390.348	−	327.541i	0.426145	−	0.357578i
$917$	−976.992	+	976.992i	−1.06542	+	1.06542i
$918$	−494.055	−	674.154i	−0.538186	−	0.734373i
$919$		−	1312.32i		−	1.42799i	−0.700150	−	0.713996i	$-0.746884\pi$
$919$		−	1312.32i		−	1.42799i	0.700150	−	0.713996i	$-0.253116\pi$
$920$	63.0994	+	202.095i	0.0685863	+	0.219669i
$921$	84.2483	+	61.7840i	0.0914748	+	0.0670836i
$922$	−329.410	−	470.446i	−0.357278	−	0.510245i
$923$	513.624	+	239.507i	0.556473	+	0.259487i
$924$	1340.23	+	661.064i	1.45046	+	0.715438i
$925$	200.363	+	1174.71i	0.216608	+	1.26995i
$926$	507.232	+	878.552i	0.547767	+	0.948760i
$927$	−482.906	+	629.122i	−0.520934	+	0.678664i
$928$	−96.7086	+	25.9130i	−0.104212	+	0.0279235i
$929$	−146.997	+	403.872i	−0.158232	+	0.434739i	−0.993322	−	0.115375i	$-0.963193\pi$
$929$	−146.997	+	403.872i	−0.158232	+	0.434739i	0.835090	+	0.550113i	$0.185415\pi$
$930$	449.695	−	173.388i	0.483543	−	0.186439i
$931$	899.539	+	754.803i	0.966207	+	0.810744i
$932$	−558.763	+	48.8854i	−0.599531	+	0.0524522i
$933$	197.632	+	4.32860i	0.211825	+	0.00463944i
$934$	22.9059	−	62.9333i	0.0245245	−	0.0673804i
$935$	281.025	−	2089.41i	0.300561	−	2.23467i
$936$	−50.7412	+	122.443i	−0.0542107	+	0.130815i
$937$	−1565.72	−	419.533i	−1.67099	−	0.447740i	−0.705612	−	0.708598i	$-0.749328\pi$
$937$	−1565.72	−	419.533i	−1.67099	−	0.447740i	−0.965377	+	0.260858i	$0.915994\pi$
$938$	−761.135	+	1087.01i	−0.811444	+	1.15886i
$939$	−453.915	−	223.893i	−0.483403	−	0.238437i
$940$	−330.509	−	362.719i	−0.351605	−	0.385871i
$941$	235.728	−	1336.88i	0.250508	−	1.42070i	−0.556836	−	0.830623i	$-0.687985\pi$
$941$	235.728	−	1336.88i	0.250508	−	1.42070i	0.807344	−	0.590081i	$-0.200904\pi$
$942$	353.624	−	54.3982i	0.375397	−	0.0577476i
$943$	277.929	+	24.3157i	0.294729	+	0.0257854i
$944$		−	301.351i		−	0.319227i
$945$	−345.746	+	1710.95i	−0.365869	+	1.81053i
$946$	614.933			0.650035
$947$	142.325	−	1626.78i	0.150290	−	1.71783i	−0.429506	−	0.903064i	$-0.641312\pi$
$947$	142.325	−	1626.78i	0.150290	−	1.71783i	0.579796	−	0.814762i	$-0.303132\pi$
$948$	−111.260	−	43.2772i	−0.117363	−	0.0456511i
$949$	−19.5895	−	3.45416i	−0.0206423	−	0.00363979i
$950$	118.301	+	330.775i	0.124527	+	0.348184i
$951$	542.340	−	35.5021i	0.570284	−	0.0373314i
$952$	655.740	+	459.154i	0.688803	+	0.482305i
$953$	58.0143	−	216.512i	0.0608754	−	0.227190i	−0.928785	−	0.370618i	$-0.879146\pi$
$953$	58.0143	−	216.512i	0.0608754	−	0.227190i	0.989661	+	0.143428i	$0.0458125\pi$
$954$	383.279	+	736.568i	0.401760	+	0.772084i
$955$	625.792	−	477.412i	0.655279	−	0.499908i
$956$	504.560	+	183.645i	0.527783	+	0.192097i
$957$	874.354	+	530.669i	0.913640	+	0.554513i
$958$	−81.0217	−	926.082i	−0.0845738	−	0.966683i
$959$	1406.57	−	1676.29i	1.46671	−	1.74796i
$960$	−119.324	+	12.7205i	−0.124296	+	0.0132505i
$961$	417.977	+	152.131i	0.434940	+	0.158305i
$962$	90.8424	+	339.029i	0.0944308	+	0.352420i
$963$	−71.3485	−	112.035i	−0.0740898	−	0.116340i
$964$	−403.661	+	233.054i	−0.418736	+	0.241757i
$965$	901.920	−	571.046i	0.934632	−	0.591757i
$966$	456.201	+	682.875i	0.472258	+	0.706910i
$967$	−234.447	+	502.774i	−0.242448	+	0.519932i	−0.989447	−	0.144893i	$-0.953716\pi$
$967$	−234.447	+	502.774i	−0.242448	+	0.519932i	0.746999	+	0.664825i	$0.231494\pi$
$968$	579.358	−	405.671i	0.598510	−	0.419081i
$969$	−648.591	−	71.0862i	−0.669341	−	0.0733604i
$970$	−143.452	−	459.450i	−0.147889	−	0.473659i
$971$	−956.983			−0.985565			−0.492782	−	0.870153i	$-0.664020\pi$
$971$	−956.983			−0.985565			−0.492782	+	0.870153i	$0.664020\pi$
$972$	484.972	−	31.5867i	0.498943	−	0.0324966i
$973$	509.454	+	509.454i	0.523591	+	0.523591i
$974$	545.163	+	649.701i	0.559716	+	0.667044i
$975$	−242.691	−	305.928i	−0.248914	−	0.313773i
$976$	−63.1629	+	358.215i	−0.0647161	+	0.367023i
$977$	441.881	−	947.618i	0.452284	−	0.969926i	−0.539498	−	0.841987i	$-0.681386\pi$
$977$	441.881	−	947.618i	0.452284	−	0.969926i	0.991782	−	0.127939i	$-0.0408363\pi$
$978$	−145.945	+	733.402i	−0.149228	+	0.749900i
$979$	1007.91	−	177.721i	1.02953	−	0.181533i
$980$	−150.980	−	1172.13i	−0.154061	−	1.19606i
$981$	−194.625	−	43.1808i	−0.198394	−	0.0440171i
$982$	−233.011	−	869.609i	−0.237282	−	0.885549i
$983$	463.280	+	993.506i	0.471292	+	1.01069i	0.987990	+	0.154520i	$0.0493832\pi$
$983$	463.280	+	993.506i	0.471292	+	1.01069i	−0.516698	+	0.856168i	$0.672839\pi$
$984$	−44.2620	+	151.810i	−0.0449817	+	0.154278i
$985$	637.912	+	203.097i	0.647627	+	0.206189i
$986$	419.704	+	352.173i	0.425663	+	0.357174i
$987$	−1627.21	−	987.600i	−1.64865	−	1.00061i
$988$	43.7275	+	93.7739i	0.0442586	+	0.0949129i
$989$	292.661	+	168.968i	0.295916	+	0.170847i
$990$	936.739	+	790.757i	0.946201	+	0.798744i
$991$	−174.588	−	302.395i	−0.176173	−	0.305141i	0.764393	−	0.644750i	$-0.223039\pi$
$991$	−174.588	−	302.395i	−0.176173	−	0.305141i	−0.940567	+	0.339609i	$0.889705\pi$
$992$	105.280	+	73.7181i	0.106129	+	0.0743126i
$993$	760.011	+	666.623i	0.765369	+	0.671322i
$994$	680.722	+	1870.27i	0.684831	+	1.88156i
$995$	−243.462	−	156.062i	−0.244686	−	0.156846i
$996$	587.106	−	258.275i	0.589463	−	0.259312i
$997$	23.0960	−	263.988i	0.0231655	−	0.264783i	−0.975776	−	0.218774i	$-0.929794\pi$
$997$	23.0960	−	263.988i	0.0231655	−	0.264783i	0.998941	−	0.0460087i	$-0.0146502\pi$
$998$	189.666	+	189.666i	0.190046	+	0.190046i
$999$	967.830	−	848.343i	0.968799	−	0.849192i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.q.b.103.14	yes	216
5.2	odd	4	inner	270.3.q.b.157.5	yes	216
27.16	even	9	inner	270.3.q.b.43.5	✓	216
135.97	odd	36	inner	270.3.q.b.97.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.q.b.43.5	✓	216	27.16	even	9	inner
270.3.q.b.97.14	yes	216	135.97	odd	36	inner
270.3.q.b.103.14	yes	216	1.1	even	1	trivial
270.3.q.b.157.5	yes	216	5.2	odd	4	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.3.q.b.103.14

Level	$270$
Weight	$3$
Character	270.103
Analytic conductor	$7.357$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$