LMFDB - Embedded newform 75.3.k.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.75152 - 0.594183i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-4.60913 - 1.93801i) q^{5} +(-2.03297 + 6.25683i) q^{6} +(-5.76987 + 5.76987i) q^{7} +(21.7507 - 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(3.75152 - 0.594183i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-4.60913 - 1.93801i) q^{5} +(-2.03297 + 6.25683i) q^{6} +(-5.76987 + 5.76987i) q^{7} +(21.7507 - 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-18.4428 - 4.53182i) q^{10} +(-8.57269 - 6.22843i) q^{11} +(-2.82521 + 17.8377i) q^{12} +(8.56755 + 1.35697i) q^{13} +(-18.2174 + 25.0741i) q^{14} +(6.61519 - 5.58921i) q^{15} +(41.2709 - 29.9851i) q^{16} +(9.18644 + 18.0294i) q^{17} +(-8.05738 - 8.05738i) q^{18} +(-9.04167 - 2.93782i) q^{19} +(-51.9516 - 4.36741i) q^{20} +(-4.36741 - 13.4415i) q^{21} +(-35.8615 - 18.2723i) q^{22} +(-4.80786 - 30.3556i) q^{23} +42.2818i q^{24} +(17.4882 + 17.8651i) q^{25} +32.9476 q^{26} +(5.13218 - 0.812857i) q^{27} +(-38.6265 + 75.8088i) q^{28} +(15.8984 - 5.16571i) q^{29} +(21.4960 - 24.8987i) q^{30} +(-8.39189 + 25.8276i) q^{31} +(67.9662 - 67.9662i) q^{32} +(16.3531 - 8.33234i) q^{33} +(45.1759 + 62.1792i) q^{34} +(37.7761 - 15.4120i) q^{35} +(-25.3068 - 18.3864i) q^{36} +(-0.661704 + 4.17784i) q^{37} +(-35.6656 - 5.64887i) q^{38} +(-8.83112 + 12.1550i) q^{39} +(-121.730 + 8.92781i) q^{40} +(8.18348 - 5.94565i) q^{41} +(-24.3711 - 47.8310i) q^{42} +(14.3428 + 14.3428i) q^{43} +(-105.081 - 34.1428i) q^{44} +(3.42389 + 14.6040i) q^{45} +(-36.0736 - 111.023i) q^{46} +(21.1998 + 10.8018i) q^{47} +(13.8223 + 87.2704i) q^{48} -17.5827i q^{49} +(76.2226 + 56.6301i) q^{50} -35.0478 q^{51} +(89.3335 - 14.1490i) q^{52} +(32.8517 - 64.4751i) q^{53} +(18.7705 - 6.09890i) q^{54} +(27.4419 + 45.3216i) q^{55} +(-61.5540 + 189.444i) q^{56} +(11.6436 - 11.6436i) q^{57} +(56.5739 - 28.8258i) q^{58} +(-59.3161 - 81.6416i) q^{59} +(47.5914 - 76.7410i) q^{60} +(-21.3169 - 15.4876i) q^{61} +(-16.1361 + 101.879i) q^{62} +(24.1781 + 3.82943i) q^{63} +(94.6519 - 130.277i) q^{64} +(-36.8592 - 22.8584i) q^{65} +(56.3982 - 40.9757i) q^{66} +(46.3389 + 90.9453i) q^{67} +(149.191 + 149.191i) q^{68} +(50.6275 + 16.4499i) q^{69} +(132.560 - 80.2644i) q^{70} +(-5.29227 - 16.2879i) q^{71} +(-65.2522 - 33.2477i) q^{72} +(-5.05041 - 31.8870i) q^{73} +16.0664i q^{74} +(-41.3222 + 12.9411i) q^{75} -99.1288 q^{76} +(85.4005 - 13.5261i) q^{77} +(-25.9079 + 50.8470i) q^{78} +(-114.576 + 37.2281i) q^{79} +(-248.335 + 58.2218i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(27.1677 - 27.1677i) q^{82} +(-107.103 + 54.5720i) q^{83} +(-86.6199 - 119.222i) q^{84} +(-7.40035 - 100.903i) q^{85} +(62.3293 + 45.2849i) q^{86} +(-4.52940 + 28.5975i) q^{87} +(-255.489 - 40.4655i) q^{88} +(-55.9848 + 77.0565i) q^{89} +(21.5222 + 52.7528i) q^{90} +(-57.2631 + 41.6041i) q^{91} +(-145.487 - 285.534i) q^{92} +(-33.2601 - 33.2601i) q^{93} +(85.9498 + 27.9268i) q^{94} +(35.9807 + 31.0636i) q^{95} +(51.4459 + 158.334i) q^{96} +(-52.6386 - 26.8207i) q^{97} +(-10.4473 - 65.9619i) q^{98} +31.7893i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	3.75152	−	0.594183i	1.87576	−	0.297091i	0.888830	−	0.458237i	$-0.151519\pi$
$2$	3.75152	−	0.594183i	1.87576	−	0.297091i	0.986931	+	0.161146i	$0.0515191\pi$
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$4$	9.91663	−	3.22211i	2.47916	−	0.805527i
$5$	−4.60913	−	1.93801i	−0.921827	−	0.387602i
$5$	−4.60913	−	1.93801i	−0.921827	−	0.387602i
$6$	−2.03297	+	6.25683i	−0.338828	+	1.04281i
$7$	−5.76987	+	5.76987i	−0.824267	+	0.824267i	−0.986717	−	0.162450i	$-0.948060\pi$
$7$	−5.76987	+	5.76987i	−0.824267	+	0.824267i	0.162450	+	0.986717i	$0.448060\pi$
$8$	21.7507	−	11.0826i	2.71884	−	1.38532i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	−18.4428	−	4.53182i	−1.84428	−	0.453182i
$11$	−8.57269	−	6.22843i	−0.779336	−	0.566220i	0.125444	−	0.992101i	$-0.459964\pi$
$11$	−8.57269	−	6.22843i	−0.779336	−	0.566220i	−0.904780	+	0.425880i	$0.859964\pi$
$12$	−2.82521	+	17.8377i	−0.235434	+	1.48647i
$13$	8.56755	+	1.35697i	0.659042	+	0.104382i	0.476993	−	0.878907i	$-0.341727\pi$
$13$	8.56755	+	1.35697i	0.659042	+	0.104382i	0.182050	+	0.983289i	$0.441727\pi$
$14$	−18.2174	+	25.0741i	−1.30124	+	1.79101i
$15$	6.61519	−	5.58921i	0.441013	−	0.372614i
$16$	41.2709	−	29.9851i	2.57943	−	1.87407i
$17$	9.18644	+	18.0294i	0.540379	+	1.06055i	0.986220	+	0.165441i	$0.0529046\pi$
$17$	9.18644	+	18.0294i	0.540379	+	1.06055i	−0.445841	+	0.895112i	$0.647095\pi$
$18$	−8.05738	−	8.05738i	−0.447632	−	0.447632i
$19$	−9.04167	−	2.93782i	−0.475877	−	0.154622i	0.0612512	−	0.998122i	$-0.480491\pi$
$19$	−9.04167	−	2.93782i	−0.475877	−	0.154622i	−0.537128	+	0.843501i	$0.680491\pi$
$20$	−51.9516	−	4.36741i	−2.59758	−	0.218370i
$21$	−4.36741	−	13.4415i	−0.207972	−	0.640071i
$22$	−35.8615	−	18.2723i	−1.63007	−	0.830560i
$23$	−4.80786	−	30.3556i	−0.209037	−	1.31981i	−0.839402	−	0.543511i	$-0.817095\pi$
$23$	−4.80786	−	30.3556i	−0.209037	−	1.31981i	0.630365	−	0.776299i	$-0.282905\pi$
$24$			42.2818i			1.76174i
$25$	17.4882	+	17.8651i	0.699529	+	0.714604i
$26$	32.9476			1.26722
$27$	5.13218	−	0.812857i	0.190081	−	0.0301058i
$28$	−38.6265	+	75.8088i	−1.37952	+	2.70746i
$29$	15.8984	−	5.16571i	0.548221	−	0.178128i	−0.0217932	−	0.999762i	$-0.506938\pi$
$29$	15.8984	−	5.16571i	0.548221	−	0.178128i	0.570015	+	0.821635i	$0.306938\pi$
$30$	21.4960	−	24.8987i	0.716534	−	0.829955i
$31$	−8.39189	+	25.8276i	−0.270706	+	0.833148i	0.719617	+	0.694371i	$0.244317\pi$
$31$	−8.39189	+	25.8276i	−0.270706	+	0.833148i	−0.990324	+	0.138777i	$0.955683\pi$
$32$	67.9662	−	67.9662i	2.12394	−	2.12394i
$33$	16.3531	−	8.33234i	0.495550	−	0.252495i
$34$	45.1759	+	62.1792i	1.32870	+	1.82880i
$35$	37.7761	−	15.4120i	1.07932	−	0.440343i
$36$	−25.3068	−	18.3864i	−0.702966	−	0.510734i
$37$	−0.661704	+	4.17784i	−0.0178839	+	0.112914i	−0.995015	−	0.0997215i	$-0.968205\pi$
$37$	−0.661704	+	4.17784i	−0.0178839	+	0.112914i	0.977131	+	0.212636i	$0.0682048\pi$
$38$	−35.6656	−	5.64887i	−0.938568	−	0.148655i
$39$	−8.83112	+	12.1550i	−0.226439	+	0.311667i
$40$	−121.730	+	8.92781i	−3.04325	+	0.223195i
$41$	8.18348	−	5.94565i	0.199597	−	0.145016i	−0.483497	−	0.875346i	$-0.660634\pi$
$41$	8.18348	−	5.94565i	0.199597	−	0.145016i	0.683094	+	0.730330i	$0.260634\pi$
$42$	−24.3711	−	47.8310i	−0.580265	−	1.13883i
$43$	14.3428	+	14.3428i	0.333552	+	0.333552i	0.853934	−	0.520382i	$-0.174210\pi$
$43$	14.3428	+	14.3428i	0.333552	+	0.333552i	−0.520382	+	0.853934i	$0.674210\pi$
$44$	−105.081	−	34.1428i	−2.38820	−	0.775974i
$45$	3.42389	+	14.6040i	0.0760865	+	0.324533i
$46$	−36.0736	−	111.023i	−0.784208	−	2.41354i
$47$	21.1998	+	10.8018i	0.451060	+	0.229826i	0.664736	−	0.747078i	$-0.268544\pi$
$47$	21.1998	+	10.8018i	0.451060	+	0.229826i	−0.213677	+	0.976904i	$0.568544\pi$
$48$	13.8223	+	87.2704i	0.287964	+	1.81813i
$49$		−	17.5827i		−	0.358831i
$50$	76.2226	+	56.6301i	1.52445	+	1.13260i
$51$	−35.0478			−0.687212
$52$	89.3335	−	14.1490i	1.71795	−	0.272097i
$53$	32.8517	−	64.4751i	0.619843	−	1.21651i	−0.341168	−	0.940002i	$-0.610823\pi$
$53$	32.8517	−	64.4751i	0.619843	−	1.21651i	0.961011	−	0.276509i	$-0.0891775\pi$
$54$	18.7705	−	6.09890i	0.347602	−	0.112943i
$55$	27.4419	+	45.3216i	0.498944	+	0.824029i
$56$	−61.5540	+	189.444i	−1.09918	+	3.38292i
$57$	11.6436	−	11.6436i	0.204274	−	0.204274i
$58$	56.5739	−	28.8258i	0.975412	−	0.496997i
$59$	−59.3161	−	81.6416i	−1.00536	−	1.38376i	−0.921980	−	0.387238i	$-0.873429\pi$
$59$	−59.3161	−	81.6416i	−1.00536	−	1.38376i	−0.0833777	−	0.996518i	$-0.526571\pi$
$60$	47.5914	−	76.7410i	0.793190	−	1.27902i
$61$	−21.3169	−	15.4876i	−0.349458	−	0.253896i	0.399184	−	0.916871i	$-0.369294\pi$
$61$	−21.3169	−	15.4876i	−0.349458	−	0.253896i	−0.748641	+	0.662975i	$0.769294\pi$
$62$	−16.1361	+	101.879i	−0.260259	+	1.64321i
$63$	24.1781	+	3.82943i	0.383779	+	0.0607846i
$64$	94.6519	−	130.277i	1.47894	−	2.03558i
$65$	−36.8592	−	22.8584i	−0.567064	−	0.351668i
$66$	56.3982	−	40.9757i	0.854518	−	0.620844i
$67$	46.3389	+	90.9453i	0.691626	+	1.35739i	0.923103	+	0.384552i	$0.125644\pi$
$67$	46.3389	+	90.9453i	0.691626	+	1.35739i	−0.231477	+	0.972840i	$0.574356\pi$
$68$	149.191	+	149.191i	2.19399	+	2.19399i
$69$	50.6275	+	16.4499i	0.733731	+	0.238404i
$70$	132.560	−	80.2644i	1.89372	−	1.14663i
$71$	−5.29227	−	16.2879i	−0.0745390	−	0.229408i	0.906845	−	0.421465i	$-0.138484\pi$
$71$	−5.29227	−	16.2879i	−0.0745390	−	0.229408i	−0.981384	+	0.192057i	$0.938484\pi$
$72$	−65.2522	−	33.2477i	−0.906281	−	0.461773i
$73$	−5.05041	−	31.8870i	−0.0691837	−	0.436809i	−0.997830	−	0.0658425i	$-0.979027\pi$
$73$	−5.05041	−	31.8870i	−0.0691837	−	0.436809i	0.928646	−	0.370966i	$-0.120973\pi$
$74$			16.0664i			0.217114i
$75$	−41.3222	+	12.9411i	−0.550963	+	0.172548i
$76$	−99.1288			−1.30433
$77$	85.4005	−	13.5261i	1.10910	−	0.175664i
$78$	−25.9079	+	50.8470i	−0.332152	+	0.651885i
$79$	−114.576	+	37.2281i	−1.45033	+	0.471241i	−0.925102	−	0.379719i	$-0.876021\pi$
$79$	−114.576	+	37.2281i	−1.45033	+	0.471241i	−0.525230	+	0.850960i	$0.676021\pi$
$80$	−248.335	+	58.2218i	−3.10418	+	0.727772i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	27.1677	−	27.1677i	0.331314	−	0.331314i
$83$	−107.103	+	54.5720i	−1.29040	+	0.657493i	−0.958304	−	0.285751i	$-0.907757\pi$
$83$	−107.103	+	54.5720i	−1.29040	+	0.657493i	−0.332100	+	0.943244i	$0.607757\pi$
$84$	−86.6199	−	119.222i	−1.03119	−	1.41931i
$85$	−7.40035	−	100.903i	−0.0870630	−	1.18710i
$86$	62.3293	+	45.2849i	0.724760	+	0.526569i
$87$	−4.52940	+	28.5975i	−0.0520621	+	0.328707i
$88$	−255.489	−	40.4655i	−2.90329	−	0.459835i
$89$	−55.9848	+	77.0565i	−0.629043	+	0.865803i	−0.997972	−	0.0636543i	$-0.979724\pi$
$89$	−55.9848	+	77.0565i	−0.629043	+	0.865803i	0.368929	+	0.929458i	$0.379724\pi$
$90$	21.5222	+	52.7528i	0.239136	+	0.586142i
$91$	−57.2631	+	41.6041i	−0.629265	+	0.457188i
$92$	−145.487	−	285.534i	−1.58138	−	3.10363i
$93$	−33.2601	−	33.2601i	−0.357635	−	0.357635i
$94$	85.9498	+	27.9268i	0.914359	+	0.297093i
$95$	35.9807	+	31.0636i	0.378744	+	0.326986i
$96$	51.4459	+	158.334i	0.535895	+	1.64932i
$97$	−52.6386	−	26.8207i	−0.542666	−	0.276502i	0.161095	−	0.986939i	$-0.448498\pi$
$97$	−52.6386	−	26.8207i	−0.542666	−	0.276502i	−0.703761	+	0.710437i	$0.748498\pi$
$98$	−10.4473	−	65.9619i	−0.106605	−	0.673081i
$99$			31.7893i			0.321104i
$100$	230.988	+	120.813i	2.30988	+	1.20813i
$101$	−18.0818			−0.179027			−0.0895136	−	0.995986i	$-0.528531\pi$
$101$	−18.0818			−0.179027			−0.0895136	+	0.995986i	$0.528531\pi$
$102$	−131.483	+	20.8248i	−1.28905	+	0.204165i
$103$	44.2825	−	86.9093i	0.429927	−	0.843779i	−0.569830	−	0.821762i	$-0.692991\pi$
$103$	44.2825	−	86.9093i	0.429927	−	0.843779i	0.999758	−	0.0220172i	$-0.00700886\pi$
$104$	201.389	−	65.4353i	1.93643	−	0.629186i
$105$	−5.91980	+	70.4177i	−0.0563791	+	0.670645i
$106$	84.9339	−	261.400i	0.801263	−	2.46603i
$107$	−37.6236	+	37.6236i	−0.351622	+	0.351622i	−0.860713	−	0.509091i	$-0.829982\pi$
$107$	−37.6236	+	37.6236i	−0.351622	+	0.351622i	0.509091	+	0.860713i	$0.329982\pi$
$108$	48.2748	−	24.5972i	0.446989	−	0.227752i
$109$	49.2625	+	67.8040i	0.451950	+	0.622055i	0.972815	−	0.231583i	$-0.0743906\pi$
$109$	49.2625	+	67.8040i	0.451950	+	0.622055i	−0.520865	+	0.853639i	$0.674391\pi$
$110$	129.878	+	153.719i	1.18071	+	1.39745i
$111$	−5.92720	−	4.30636i	−0.0533982	−	0.0387961i
$112$	−65.1178	+	411.138i	−0.581409	+	3.67087i
$113$	98.6277	+	15.6211i	0.872812	+	0.138240i	0.576742	−	0.816926i	$-0.304324\pi$
$113$	98.6277	+	15.6211i	0.872812	+	0.138240i	0.296070	+	0.955166i	$0.404324\pi$
$114$	36.7628	−	50.5997i	0.322481	−	0.443857i
$115$	−36.6695	+	149.231i	−0.318865	+	1.29766i
$116$	141.014	−	102.453i	1.21564	−	0.883214i
$117$	−11.8142	−	23.1867i	−0.100976	−	0.198177i
$118$	−271.036	−	271.036i	−2.29691	−	2.29691i
$119$	−157.032	−	51.0227i	−1.31959	−	0.428762i
$120$	81.9426	−	194.883i	0.682855	−	1.62402i
$121$	−2.69329	−	8.28909i	−0.0222586	−	0.0685049i
$122$	−89.1733	−	45.4361i	−0.730929	−	0.372427i
$123$	2.74078	+	17.3046i	0.0222827	+	0.140688i
$124$			283.162i			2.28357i
$125$	−45.9828	−	116.235i	−0.367863	−	0.929880i
$126$	92.9800			0.737936
$127$	−75.6911	+	11.9883i	−0.595993	+	0.0943960i	−0.447141	−	0.894463i	$-0.647558\pi$
$127$	−75.6911	+	11.9883i	−0.595993	+	0.0943960i	−0.148852	+	0.988859i	$0.547558\pi$
$128$	103.132	−	202.409i	0.805721	−	1.58132i
$129$	−33.4129	+	10.8565i	−0.259015	+	0.0841590i
$130$	−151.860	−	63.8529i	−1.16815	−	0.491176i
$131$	−14.5474	+	44.7722i	−0.111049	+	0.341772i	−0.991102	−	0.133102i	$-0.957506\pi$
$131$	−14.5474	+	44.7722i	−0.111049	+	0.341772i	0.880054	+	0.474874i	$0.157506\pi$
$132$	135.320	−	135.320i	1.02515	−	1.02515i
$133$	69.1200	−	35.2184i	0.519699	−	0.264800i
$134$	227.880	+	313.649i	1.70059	+	2.34067i
$135$	−25.2302	−	6.19965i	−0.186891	−	0.0459233i
$136$	399.624	+	290.343i	2.93841	+	2.13488i
$137$	−31.2075	+	197.036i	−0.227792	+	1.43822i	0.563163	+	0.826346i	$0.309584\pi$
$137$	−31.2075	+	197.036i	−0.227792	+	1.43822i	−0.790955	+	0.611875i	$0.790416\pi$
$138$	199.704	+	31.6300i	1.44713	+	0.229203i
$139$	96.9324	−	133.416i	0.697355	−	0.959827i	−0.302622	−	0.953111i	$-0.597862\pi$
$139$	96.9324	−	133.416i	0.697355	−	0.959827i	0.999977	−	0.00671658i	$-0.00213797\pi$
$140$	324.953	−	274.554i	2.32109	−	1.96110i
$141$	−33.3403	+	24.2231i	−0.236456	+	0.171795i
$142$	−29.5321	−	57.9600i	−0.207972	−	0.408169i
$143$	−64.9952	−	64.9952i	−0.454512	−	0.454512i
$144$	−145.551	−	47.2923i	−1.01077	−	0.328419i
$145$	−83.2891	−	7.00186i	−0.574408	−	0.0482887i
$146$	−37.8934	−	116.624i	−0.259544	−	0.798795i
$147$	27.1348	+	13.8259i	0.184591	+	0.0940537i
$148$	6.89956	+	43.5621i	0.0466187	+	0.294339i
$149$		−	212.069i		−	1.42328i	−0.702542	−	0.711642i	$-0.747952\pi$
$149$		−	212.069i		−	1.42328i	0.702542	−	0.711642i	$-0.252048\pi$
$150$	−147.332	+	73.1017i	−0.982213	+	0.487345i
$151$	−29.7291			−0.196882			−0.0984408	−	0.995143i	$-0.531385\pi$
$151$	−29.7291			−0.196882			−0.0984408	+	0.995143i	$0.531385\pi$
$152$	−229.221	+	36.3051i	−1.50804	+	0.238849i
$153$	27.5593	−	54.0882i	0.180126	−	0.353518i
$154$	312.345	−	101.487i	2.02821	−	0.659006i
$155$	88.7335	−	102.779i	0.572474	−	0.663092i
$156$	−48.4103	+	148.991i	−0.310322	+	0.955073i
$157$	126.157	−	126.157i	0.803546	−	0.803546i	−0.180102	−	0.983648i	$-0.557643\pi$
$157$	126.157	−	126.157i	0.803546	−	0.803546i	0.983648	+	0.180102i	$0.0576428\pi$
$158$	−407.715	+	207.741i	−2.58047	+	1.31482i
$159$	73.6700	+	101.398i	0.463333	+	0.637723i
$160$	−444.984	+	181.546i	−2.78115	+	1.13466i
$161$	202.889	+	147.407i	1.26018	+	0.915572i
$162$	−5.34764	+	33.7637i	−0.0330101	+	0.208418i
$163$	275.324	+	43.6071i	1.68911	+	0.267528i	0.925664	−	0.378347i	$-0.123507\pi$
$163$	275.324	+	43.6071i	1.68911	+	0.267528i	0.763443	+	0.645875i	$0.223507\pi$
$164$	61.9951	−	85.3289i	0.378019	−	0.520298i
$165$	−91.5220	+	6.71231i	−0.554679	+	0.0406807i
$166$	−369.375	+	268.367i	−2.22515	+	1.61667i
$167$	83.7861	+	164.439i	0.501713	+	0.984667i	0.993487	+	0.113944i	$0.0363486\pi$
$167$	83.7861	+	164.439i	0.501713	+	0.984667i	−0.491774	+	0.870723i	$0.663651\pi$
$168$	−243.960	−	243.960i	−1.45215	−	1.45215i
$169$	−89.1670	−	28.9721i	−0.527615	−	0.171433i
$170$	−87.7176	−	374.144i	−0.515986	−	2.20085i
$171$	8.81345	+	27.1250i	0.0515406	+	0.158626i
$172$	188.446	+	96.0179i	1.09561	+	0.558243i
$173$	−7.21329	−	45.5429i	−0.0416953	−	0.263254i	0.958031	−	0.286666i	$-0.0925470\pi$
$173$	−7.21329	−	45.5429i	−0.0416953	−	0.263254i	−0.999726	+	0.0234122i	$0.992547\pi$
$174$			109.975i			0.632043i
$175$	−203.984	−	2.17450i	−1.16562	−	0.0124257i
$176$	−540.563			−3.07138
$177$	172.637	−	27.3430i	0.975352	−	0.154481i
$178$	−164.243	+	322.344i	−0.922711	+	1.81092i
$179$	187.032	−	60.7705i	1.04487	−	0.339500i	0.264219	−	0.964463i	$-0.414886\pi$
$179$	187.032	−	60.7705i	1.04487	−	0.339500i	0.780655	+	0.624963i	$0.214886\pi$
$180$	81.0091	+	133.790i	0.450051	+	0.743280i
$181$	53.3319	−	164.139i	0.294652	−	0.906844i	−0.688687	−	0.725059i	$-0.741812\pi$
$181$	53.3319	−	164.139i	0.294652	−	0.906844i	0.983338	−	0.181785i	$-0.0581875\pi$
$182$	−190.103	+	190.103i	−1.04452	+	1.04452i
$183$	40.6638	−	20.7193i	0.222207	−	0.113220i
$184$	−440.992	−	606.974i	−2.39670	−	3.29877i
$185$	11.1466	−	17.9738i	0.0602517	−	0.0971558i
$186$	−144.538	−	105.013i	−0.777088	−	0.564588i
$187$	33.5423	−	211.778i	0.179370	−	1.13250i
$188$	245.035	+	38.8098i	1.30338	+	0.206435i
$189$	−24.9219	+	34.3021i	−0.131862	+	0.181492i
$190$	153.440	+	95.1567i	0.807578	+	0.500825i
$191$	45.7324	−	33.2265i	0.239437	−	0.173961i	−0.461596	−	0.887090i	$-0.652723\pi$
$191$	45.7324	−	33.2265i	0.239437	−	0.173961i	0.701032	+	0.713130i	$0.252723\pi$
$192$	126.625	+	248.515i	0.659503	+	1.29435i
$193$	172.829	+	172.829i	0.895487	+	0.895487i	0.995033	−	0.0995457i	$-0.0317390\pi$
$193$	172.829	+	172.829i	0.895487	+	0.895487i	−0.0995457	+	0.995033i	$0.531739\pi$
$194$	−213.411	−	69.3416i	−1.10006	−	0.357431i
$195$	64.2604	−	38.9092i	0.329540	−	0.199534i
$196$	−56.6534	−	174.361i	−0.289048	−	0.889598i
$197$	56.7764	+	28.9290i	0.288205	+	0.146848i	0.592116	−	0.805853i	$-0.298293\pi$
$197$	56.7764	+	28.9290i	0.288205	+	0.146848i	−0.303911	+	0.952700i	$0.598293\pi$
$198$	18.8886	+	119.258i	0.0953972	+	0.602314i
$199$		−	120.112i		−	0.603576i	−0.953375	−	0.301788i	$-0.902417\pi$
$199$		−	120.112i		−	0.603576i	0.953375	−	0.301788i	$-0.0975835\pi$
$200$	578.373	+	194.765i	2.89186	+	0.973824i
$201$	−176.791			−0.879557
$202$	−67.8341	+	10.7439i	−0.335812	+	0.0531874i
$203$	−61.9263	+	121.537i	−0.305056	+	0.598705i
$204$	−347.556	+	112.928i	−1.70371	+	0.553568i
$205$	−49.2415	+	11.5446i	−0.240202	+	0.0563152i
$206$	114.487	−	352.354i	0.555761	−	1.71046i
$207$	−65.1967	+	65.1967i	−0.314960	+	0.314960i
$208$	394.279	−	200.895i	1.89557	−	0.965843i
$209$	59.2134	+	81.5003i	0.283318	+	0.389954i
$210$	19.6327	+	267.691i	0.0934892	+	1.27472i
$211$	193.529	+	140.607i	0.917200	+	0.666385i	0.942825	−	0.333287i	$-0.108158\pi$
$211$	193.529	+	140.607i	0.917200	+	0.666385i	−0.0256257	+	0.999672i	$0.508158\pi$
$212$	118.032	−	745.227i	0.556757	−	3.51522i
$213$	29.2982	+	4.64037i	0.137550	+	0.0217858i
$214$	−118.790	+	163.501i	−0.555095	+	0.764023i
$215$	−38.3113	−	93.9041i	−0.178192	−	0.436763i
$216$	102.620	−	74.5579i	0.475093	−	0.345175i
$217$	−100.602	−	197.442i	−0.463602	−	0.909870i
$218$	225.097	+	225.097i	1.03256	+	1.03256i
$219$	53.1816	+	17.2797i	0.242838	+	0.0789029i
$220$	418.163	+	361.017i	1.90074	+	1.64099i
$221$	54.2400	+	166.933i	0.245430	+	0.755355i
$222$	−24.7948	−	12.6336i	−0.111688	−	0.0569080i
$223$	−31.2037	−	197.012i	−0.139927	−	0.883463i	−0.953367	−	0.301814i	$-0.902408\pi$
$223$	−31.2037	−	197.012i	−0.139927	−	0.883463i	0.813440	−	0.581649i	$-0.197592\pi$
$224$			784.312i			3.50139i
$225$	12.5215	−	73.9474i	0.0556513	−	0.328655i
$226$	379.286			1.67826
$227$	−223.393	+	35.3820i	−0.984110	+	0.155868i	−0.627694	−	0.778460i	$-0.716001\pi$
$227$	−223.393	+	35.3820i	−0.984110	+	0.155868i	−0.356415	+	0.934328i	$0.616001\pi$
$228$	77.9484	−	152.982i	0.341879	−	0.670975i
$229$	296.158	−	96.2275i	1.29327	−	0.420207i	0.420032	−	0.907509i	$-0.362019\pi$
$229$	296.158	−	96.2275i	1.29327	−	0.420207i	0.873234	+	0.487302i	$0.162019\pi$
$230$	−48.8959	+	581.631i	−0.212591	+	2.52883i
$231$	−46.2789	+	142.432i	−0.200342	+	0.616588i
$232$	288.553	−	288.553i	1.24376	−	1.24376i
$233$	−372.857	+	189.980i	−1.60024	+	0.815365i	−0.600366	+	0.799726i	$0.704978\pi$
$233$	−372.857	+	189.980i	−1.60024	+	0.815365i	−0.999878	+	0.0156392i	$0.995022\pi$
$234$	−58.0984	−	79.9656i	−0.248284	−	0.341733i
$235$	−76.7786	−	90.8726i	−0.326718	−	0.386692i
$236$	−851.274	−	618.487i	−3.60709	−	2.62071i
$237$	32.6423	−	206.096i	0.137731	−	0.869601i
$238$	−619.425	−	98.1072i	−2.60262	−	0.412215i
$239$	−36.4395	+	50.1547i	−0.152467	+	0.209852i	−0.878417	−	0.477895i	$-0.841400\pi$
$239$	−36.4395	+	50.1547i	−0.152467	+	0.209852i	0.725951	+	0.687747i	$0.241400\pi$
$240$	105.422	−	429.029i	0.439260	−	1.78762i
$241$	6.33519	−	4.60279i	0.0262871	−	0.0190987i	−0.574564	−	0.818460i	$-0.694828\pi$
$241$	6.33519	−	4.60279i	0.0262871	−	0.0190987i	0.600851	+	0.799361i	$0.294828\pi$
$242$	−15.0292	−	29.4964i	−0.0621040	−	0.121886i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	−261.295	−	84.8998i	−1.07088	−	0.347950i
$245$	−34.0755	+	81.0411i	−0.139084	+	0.330780i
$246$	20.5642	+	63.2900i	0.0835942	+	0.257276i
$247$	−73.4784	−	37.4391i	−0.297483	−	0.151575i
$248$	103.706	+	654.773i	0.418169	+	2.64021i
$249$		−	208.201i		−	0.836150i
$250$	−241.570	−	408.736i	−0.966281	−	1.63494i
$251$	231.377			0.921822			0.460911	−	0.887446i	$-0.347523\pi$
$251$	231.377			0.921822			0.460911	+	0.887446i	$0.347523\pi$
$252$	252.104	−	39.9293i	1.00041	−	0.158450i
$253$	−147.851	+	290.175i	−0.584393	+	1.14694i
$254$	−276.834	+	89.9487i	−1.08990	+	0.354129i
$255$	161.540	+	67.9230i	0.633490	+	0.266365i
$256$	67.5895	−	208.019i	0.264022	−	0.812575i
$257$	222.364	−	222.364i	0.865229	−	0.865229i	−0.126710	−	0.991940i	$-0.540442\pi$
$257$	222.364	−	222.364i	0.865229	−	0.865229i	0.991940	+	0.126710i	$0.0404419\pi$
$258$	−118.899	+	60.5818i	−0.460847	+	0.234813i
$259$	−20.2876	−	27.9235i	−0.0783305	−	0.107813i
$260$	−439.171	−	107.914i	−1.68912	−	0.415056i
$261$	−40.5720	−	29.4773i	−0.155448	−	0.112940i
$262$	−27.9719	+	176.608i	−0.106763	+	0.674075i
$263$	−129.506	−	20.5117i	−0.492418	−	0.0779914i	−0.0947130	−	0.995505i	$-0.530193\pi$
$263$	−129.506	−	20.5117i	−0.492418	−	0.0779914i	−0.397705	+	0.917513i	$0.630193\pi$
$264$	263.349	−	362.469i	0.997535	−	1.37299i
$265$	−276.371	+	233.507i	−1.04291	+	0.881160i
$266$	238.379	−	173.192i	0.896161	−	0.651099i
$267$	−74.8961	−	146.992i	−0.280510	−	0.550531i
$268$	752.562	+	752.562i	2.80807	+	2.80807i
$269$	172.494	+	56.0466i	0.641241	+	0.208352i	0.611548	−	0.791207i	$-0.290547\pi$
$269$	172.494	+	56.0466i	0.641241	+	0.208352i	0.0296926	+	0.999559i	$0.490547\pi$
$270$	−98.3354	−	8.26676i	−0.364205	−	0.0306176i
$271$	68.6682	+	211.339i	0.253388	+	0.779849i	0.994143	+	0.108073i	$0.0344681\pi$
$271$	68.6682	+	211.339i	0.253388	+	0.779849i	−0.740755	+	0.671776i	$0.765532\pi$
$272$	919.746	+	468.634i	3.38142	+	1.72292i
$273$	−19.1783	−	121.087i	−0.0702502	−	0.443543i
$274$			757.728i			2.76543i
$275$	−38.6498	−	262.076i	−0.140545	−	0.953004i
$276$	555.057			2.01108
$277$	−32.5716	+	5.15883i	−0.117587	+	0.0186239i	−0.214951	−	0.976625i	$-0.568959\pi$
$277$	−32.5716	+	5.15883i	−0.117587	+	0.0186239i	0.0973636	+	0.995249i	$0.468959\pi$
$278$	284.370	−	558.108i	1.02292	−	2.00758i
$279$	77.4828	−	25.1757i	0.277716	−	0.0902354i
$280$	650.854	−	753.879i	2.32448	−	2.69243i
$281$	−92.8454	+	285.749i	−0.330411	+	1.01690i	0.638528	+	0.769598i	$0.279544\pi$
$281$	−92.8454	+	285.749i	−0.330411	+	1.01690i	−0.968939	+	0.247301i	$0.920456\pi$
$282$	−110.684	+	110.684i	−0.392496	+	0.392496i
$283$	−320.713	+	163.411i	−1.13326	+	0.577425i	−0.916991	−	0.398908i	$-0.869389\pi$
$283$	−320.713	+	163.411i	−1.13326	+	0.577425i	−0.216270	+	0.976334i	$0.569389\pi$
$284$	−104.963	−	144.469i	−0.369588	−	0.508694i
$285$	−76.2324	+	31.1015i	−0.267482	+	0.109128i
$286$	−282.450	−	205.212i	−0.987587	−	0.717524i
$287$	−12.9120	+	81.5232i	−0.0449896	+	0.284053i
$288$	−284.806	−	45.1088i	−0.988910	−	0.156628i
$289$	−70.7986	+	97.4459i	−0.244978	+	0.337183i
$290$	−316.621	+	23.2213i	−1.09180	+	0.0800735i
$291$	82.7832	−	60.1455i	0.284478	−	0.206686i
$292$	−152.827	−	299.939i	−0.523379	−	1.02719i
$293$	−43.2558	−	43.2558i	−0.147631	−	0.147631i	0.629428	−	0.777059i	$-0.283289\pi$
$293$	−43.2558	−	43.2558i	−0.147631	−	0.147631i	−0.777059	+	0.629428i	$0.783289\pi$
$294$	110.012	+	35.7451i	0.374191	+	0.121582i
$295$	115.174	+	491.252i	0.390419	+	1.66526i
$296$	31.9085	+	98.2044i	0.107799	+	0.331772i
$297$	−49.0594	−	24.9970i	−0.165183	−	0.0841650i
$298$	−126.008	−	795.583i	−0.422845	−	2.66974i
$299$		−	266.597i		−	0.891630i
$300$	−368.080	+	261.477i	−1.22693	+	0.871589i
$301$	−165.512			−0.549872
$302$	−111.529	+	17.6645i	−0.369303	+	0.0584918i
$303$	14.2183	−	27.9050i	0.0469251	−	0.0920957i
$304$	−461.249	+	149.869i	−1.51726	+	0.492989i
$305$	68.2373	+	112.697i	0.223729	+	0.369498i
$306$	71.2511	−	219.288i	0.232847	−	0.716628i
$307$	−264.280	+	264.280i	−0.860845	+	0.860845i	−0.991436	−	0.130591i	$-0.958313\pi$
$307$	−264.280	+	264.280i	−0.860845	+	0.860845i	0.130591	+	0.991436i	$0.458313\pi$
$308$	803.302	−	409.303i	2.60812	−	1.32891i
$309$	99.3035	+	136.680i	0.321371	+	0.442329i
$310$	271.816	−	438.302i	0.876826	−	1.41388i
$311$	−99.7735	−	72.4897i	−0.320815	−	0.233086i	0.415708	−	0.909498i	$-0.363534\pi$
$311$	−99.7735	−	72.4897i	−0.320815	−	0.233086i	−0.736523	+	0.676412i	$0.763534\pi$
$312$	−57.3750	+	362.252i	−0.183894	+	1.16106i
$313$	524.250	+	83.0331i	1.67492	+	0.265281i	0.920395	−	0.390989i	$-0.127867\pi$
$313$	524.250	+	83.0331i	1.67492	+	0.265281i	0.754525	+	0.656271i	$0.227867\pi$
$314$	398.319	−	548.240i	1.26853	−	1.74599i
$315$	−104.019	−	64.5078i	−0.330218	−	0.204787i
$316$	−1016.26	+	738.354i	−3.21600	+	2.33656i
$317$	−10.6377	−	20.8776i	−0.0335573	−	0.0658600i	0.873619	−	0.486610i	$-0.161767\pi$
$317$	−10.6377	−	20.8776i	−0.0335573	−	0.0658600i	−0.907176	+	0.420750i	$0.861767\pi$
$318$	336.623	+	336.623i	1.05856	+	1.05856i
$319$	−168.466	−	54.7381i	−0.528108	−	0.171593i
$320$	−688.742	+	417.029i	−2.15232	+	1.30321i
$321$	−28.4785	−	87.6480i	−0.0887182	−	0.273047i
$322$	848.727	+	432.448i	2.63580	+	1.34301i
$323$	−30.0936	−	190.004i	−0.0931692	−	0.588247i
$324$			93.8426i			0.289638i
$325$	125.589	+	176.791i	0.386427	+	0.543973i
$326$	1058.80			3.24784
$327$	−143.377	+	22.7086i	−0.438461	+	0.0694454i
$328$	112.104	−	220.016i	0.341780	−	0.670781i
$329$	−184.645	+	59.9949i	−0.561232	+	0.182355i
$330$	−339.358	+	79.5621i	−1.02836	+	0.241097i
$331$	86.1347	−	265.095i	0.260226	−	0.800893i	−0.732529	−	0.680736i	$-0.761660\pi$
$331$	86.1347	−	265.095i	0.260226	−	0.800893i	0.992755	−	0.120157i	$-0.0383398\pi$
$332$	−886.269	+	886.269i	−2.66948	+	2.66948i
$333$	11.3066	−	5.76102i	0.0339539	−	0.0173004i
$334$	412.032	+	567.114i	1.23363	+	1.69795i
$335$	−37.3294	−	508.984i	−0.111431	−	1.51936i
$336$	−583.291	−	423.786i	−1.73599	−	1.26127i
$337$	41.2850	−	260.663i	0.122507	−	0.773481i	−0.847570	−	0.530684i	$-0.821935\pi$
$337$	41.2850	−	260.663i	0.122507	−	0.773481i	0.970077	−	0.242797i	$-0.0780649\pi$
$338$	−351.727	−	55.7080i	−1.04061	−	0.164817i
$339$	−101.662	+	139.926i	−0.299888	+	0.412760i
$340$	−398.508	−	976.776i	−1.17208	−	2.87287i
$341$	232.806	−	169.144i	0.682717	−	0.496023i
$342$	49.1810	+	96.5232i	0.143804	+	0.282232i
$343$	−181.274	−	181.274i	−0.528494	−	0.528494i
$344$	470.920	+	153.011i	1.36895	+	0.444800i
$345$	−201.469	−	173.936i	−0.583967	−	0.504163i
$346$	−54.1216	−	166.569i	−0.156421	−	0.481414i
$347$	129.934	+	66.2046i	0.374449	+	0.190791i	0.631079	−	0.775718i	$-0.282612\pi$
$347$	129.934	+	66.2046i	0.374449	+	0.190791i	−0.256630	+	0.966510i	$0.582612\pi$
$348$	47.2279	+	298.185i	0.135712	+	0.856854i
$349$			51.9592i			0.148880i	0.997225	+	0.0744401i	$0.0237170\pi$
$349$			51.9592i			0.148880i	−0.997225	+	0.0744401i	$0.976283\pi$
$350$	−766.542	+	113.046i	−2.19012	+	0.322989i
$351$	45.0732			0.128414
$352$	−1005.98	+	159.331i	−2.85789	+	0.452645i
$353$	−304.680	+	597.969i	−0.863117	+	1.69396i	−0.154945	+	0.987923i	$0.549520\pi$
$353$	−304.680	+	597.969i	−0.863117	+	1.69396i	−0.708172	+	0.706040i	$0.750480\pi$
$354$	631.405	−	205.156i	1.78363	−	0.579537i
$355$	−7.17341	+	85.3298i	−0.0202068	+	0.240366i
$356$	−306.896	+	944.530i	−0.862068	+	2.65317i
$357$	202.221	−	202.221i	0.566446	−	0.566446i
$358$	665.547	−	339.113i	1.85907	−	0.947243i
$359$	−194.075	−	267.121i	−0.540599	−	0.744071i	0.448100	−	0.893983i	$-0.352101\pi$
$359$	−194.075	−	267.121i	−0.540599	−	0.744071i	−0.988699	+	0.149913i	$0.952101\pi$
$360$	236.322	+	279.702i	0.656450	+	0.776951i
$361$	−218.934	−	159.065i	−0.606466	−	0.440623i
$362$	102.547	−	647.459i	0.283280	−	1.78856i
$363$	14.9101	+	2.36153i	0.0410747	+	0.00650560i
$364$	−433.804	+	597.080i	−1.19177	+	1.64033i
$365$	−38.5194	+	156.759i	−0.105533	+	0.429478i
$366$	140.240	−	101.890i	0.383170	−	0.278389i
$367$	240.780	+	472.558i	0.656077	+	1.28762i	0.943992	+	0.329967i	$0.107038\pi$
$367$	240.780	+	472.558i	0.656077	+	1.28762i	−0.287916	+	0.957656i	$0.592962\pi$
$368$	−1108.64	−	1108.64i	−3.01261	−	3.01261i
$369$	−28.8608	−	9.37744i	−0.0782135	−	0.0254131i
$370$	31.1369	−	74.0522i	0.0841537	−	0.200141i
$371$	182.463	+	561.563i	0.491813	+	1.51365i
$372$	−436.995	−	222.660i	−1.17472	−	0.598549i
$373$	−19.6626	−	124.145i	−0.0527148	−	0.332828i	−0.999925	−	0.0122162i	$-0.996111\pi$
$373$	−19.6626	−	124.145i	−0.0527148	−	0.332828i	0.947211	−	0.320612i	$-0.103889\pi$
$374$		−	814.418i		−	2.17759i
$375$	215.540	+	20.4358i	0.574773	+	0.0544954i
$376$	580.823			1.54474
$377$	143.220	−	22.6838i	0.379894	−	0.0601694i
$378$	−73.1134	+	143.493i	−0.193422	+	0.379611i
$379$	348.309	−	113.173i	0.919022	−	0.298608i	0.188956	−	0.981986i	$-0.439490\pi$
$379$	348.309	−	113.173i	0.919022	−	0.298608i	0.730065	+	0.683377i	$0.239490\pi$
$380$	456.898	+	192.113i	1.20236	+	0.505560i
$381$	41.0174	−	126.239i	0.107657	−	0.331335i
$382$	151.823	−	151.823i	0.397443	−	0.397443i
$383$	89.5224	−	45.6139i	0.233740	−	0.119096i	−0.333198	−	0.942857i	$-0.608128\pi$
$383$	89.5224	−	45.6139i	0.233740	−	0.119096i	0.566938	+	0.823760i	$0.308128\pi$
$384$	231.274	+	318.322i	0.602277	+	0.828963i
$385$	−419.836	−	103.163i	−1.09048	−	0.267957i
$386$	751.064	+	545.680i	1.94576	+	1.41368i
$387$	9.51922	−	60.1020i	0.0245975	−	0.155302i
$388$	−608.417	−	96.3638i	−1.56809	−	0.248360i
$389$	−379.989	+	523.009i	−0.976834	+	1.34450i	−0.0383170	+	0.999266i	$0.512200\pi$
$389$	−379.989	+	523.009i	−0.976834	+	1.34450i	−0.938517	+	0.345232i	$0.887800\pi$
$390$	217.955	−	184.151i	0.558859	−	0.472182i
$391$	503.126	−	365.543i	1.28677	−	0.934892i
$392$	−194.861	−	382.437i	−0.497095	−	0.975604i
$393$	−57.6564	−	57.6564i	−0.146708	−	0.146708i
$394$	230.187	+	74.7923i	0.584231	+	0.189828i
$395$	600.245	+	50.4608i	1.51961	+	0.127749i
$396$	102.429	+	315.243i	0.258658	+	0.796067i
$397$	−656.562	−	334.535i	−1.65381	−	0.842657i	−0.995989	−	0.0894813i	$-0.971479\pi$
$397$	−656.562	−	334.535i	−1.65381	−	0.842657i	−0.657819	−	0.753176i	$-0.728521\pi$
$398$	−71.3682	−	450.601i	−0.179317	−	1.13216i
$399$			134.364i			0.336752i
$400$	1257.44	+	212.923i	3.14360	+	0.532308i
$401$	−549.240			−1.36968			−0.684838	−	0.728696i	$-0.740127\pi$
$401$	−549.240			−1.36968			−0.684838	+	0.728696i	$0.740127\pi$
$402$	−663.235	+	105.046i	−1.64984	+	0.261309i
$403$	−106.945	+	209.892i	−0.265373	+	0.520823i
$404$	−179.310	+	58.2614i	−0.443837	+	0.144211i
$405$	29.4071	−	34.0620i	0.0726102	−	0.0841037i
$406$	−160.103	+	492.745i	−0.394341	+	1.21366i
$407$	31.6939	−	31.6939i	0.0778720	−	0.0778720i
$408$	−762.316	+	388.419i	−1.86842	+	0.952008i
$409$	312.156	+	429.646i	0.763219	+	1.05048i	0.996940	+	0.0781765i	$0.0249098\pi$
$409$	312.156	+	429.646i	0.763219	+	1.05048i	−0.233721	+	0.972304i	$0.575090\pi$
$410$	−177.871	+	72.5683i	−0.433832	+	0.176996i
$411$	−279.540	−	203.098i	−0.680147	−	0.494155i
$412$	159.102	−	1004.53i	0.386170	−	2.43818i
$413$	813.307	+	128.815i	1.96927	+	0.311901i
$414$	−205.848	+	283.325i	−0.497217	+	0.684361i
$415$	599.415	−	43.9617i	1.44437	−	0.105932i
$416$	674.532	−	490.076i	1.62147	−	1.17807i
$417$	129.675	+	254.502i	0.310972	+	0.610317i
$418$	270.567	+	270.567i	0.647288	+	0.647288i
$419$	−2.59910	−	0.844497i	−0.00620309	−	0.00201551i	0.305914	−	0.952059i	$-0.401038\pi$
$419$	−2.59910	−	0.844497i	−0.00620309	−	0.00201551i	−0.312117	+	0.950044i	$0.601038\pi$
$420$	168.189	+	717.381i	0.400450	+	1.70805i
$421$	−103.538	−	318.658i	−0.245934	−	0.756906i	−0.995481	−	0.0949560i	$-0.969729\pi$
$421$	−103.538	−	318.658i	−0.245934	−	0.756906i	0.749548	−	0.661950i	$-0.230271\pi$
$422$	809.575	+	412.499i	1.91842	+	0.977486i
$423$	−11.1662	−	70.5005i	−0.0263976	−	0.166668i
$424$		−	1766.46i		−	4.16618i
$425$	−161.443	+	479.419i	−0.379865	+	1.12804i
$426$	112.670			0.264483
$427$	212.357	−	33.6341i	0.497324	−	0.0787684i
$428$	−251.872	+	494.326i	−0.588485	+	1.15497i
$429$	151.413	−	49.1971i	0.352944	−	0.114678i
$430$	−199.522	−	329.519i	−0.464004	−	0.766324i
$431$	198.585	−	611.181i	0.460753	−	1.41805i	−0.403493	−	0.914983i	$-0.632204\pi$
$431$	198.585	−	611.181i	0.460753	−	1.41805i	0.864246	−	0.503069i	$-0.167796\pi$
$432$	187.436	−	187.436i	0.433880	−	0.433880i
$433$	−46.6581	+	23.7735i	−0.107755	+	0.0549041i	−0.507037	−	0.861924i	$-0.669259\pi$
$433$	−46.6581	+	23.7735i	−0.107755	+	0.0549041i	0.399282	+	0.916828i	$0.369259\pi$
$434$	−494.726	−	680.932i	−1.13992	−	1.56897i
$435$	76.2989	−	123.032i	0.175400	−	0.282832i
$436$	706.990	+	513.658i	1.62154	+	1.17812i
$437$	−45.7082	+	288.590i	−0.104595	+	0.660389i
$438$	209.779	+	33.2257i	0.478948	+	0.0758579i
$439$	166.038	−	228.532i	0.378219	−	0.520574i	−0.576893	−	0.816820i	$-0.695735\pi$
$439$	166.038	−	228.532i	0.378219	−	0.520574i	0.955112	+	0.296246i	$0.0957349\pi$
$440$	1099.16	+	681.652i	2.49809	+	1.54921i
$441$	−42.6741	+	31.0046i	−0.0967667	+	0.0703051i
$442$	302.671	+	594.026i	0.684777	+	1.34395i
$443$	−338.562	−	338.562i	−0.764248	−	0.764248i	0.212839	−	0.977087i	$-0.431729\pi$
$443$	−338.562	−	338.562i	−0.764248	−	0.764248i	−0.977087	+	0.212839i	$0.931729\pi$
$444$	−72.6534	−	23.6065i	−0.163634	−	0.0531679i
$445$	407.378	−	246.664i	0.915456	−	0.554302i
$446$	−234.122	−	720.555i	−0.524938	−	1.61559i
$447$	327.280	+	166.757i	0.732170	+	0.373059i
$448$	205.553	+	1297.81i	0.458824	+	2.89690i
$449$			511.774i			1.13981i	0.821711	+	0.569904i	$0.193020\pi$
$449$			511.774i			1.13981i	−0.821711	+	0.569904i	$0.806980\pi$
$450$	3.03660	−	284.855i	0.00674801	−	0.633011i
$451$	−107.187			−0.237664
$452$	1028.39	−	162.881i	2.27519	−	0.360355i
$453$	23.3770	−	45.8800i	0.0516049	−	0.101280i
$454$	−817.040	+	265.472i	−1.79965	+	0.584741i
$455$	344.563	−	80.7823i	0.757280	−	0.177544i
$456$	124.216	−	382.298i	0.272404	−	0.838373i
$457$	−545.786	+	545.786i	−1.19428	+	1.19428i	−0.218425	+	0.975854i	$0.570092\pi$
$457$	−545.786	+	545.786i	−1.19428	+	1.19428i	−0.975854	+	0.218425i	$0.929908\pi$
$458$	1053.87	−	536.971i	2.30102	−	1.17243i
$459$	61.8018	+	85.0628i	0.134644	+	0.185322i
$460$	117.200	+	1598.02i	0.254783	+	3.47395i
$461$	−732.858	−	532.452i	−1.58971	−	1.15499i	−0.904349	−	0.426795i	$-0.859643\pi$
$461$	−732.858	−	532.452i	−1.58971	−	1.15499i	−0.685365	−	0.728200i	$-0.740357\pi$
$462$	−88.9858	+	561.834i	−0.192610	+	1.21609i
$463$	−135.873	−	21.5202i	−0.293462	−	0.0464799i	0.00796733	−	0.999968i	$-0.497464\pi$
$463$	−135.873	−	21.5202i	−0.293462	−	0.0464799i	−0.301430	+	0.953488i	$0.597464\pi$
$464$	501.248	−	689.909i	1.08028	−	1.48687i
$465$	88.8418	+	217.759i	0.191058	+	0.468298i
$466$	−1285.90	+	934.259i	−2.75944	+	2.00485i
$467$	−247.420	−	485.589i	−0.529807	−	1.03981i	−0.988502	−	0.151211i	$-0.951683\pi$
$467$	−247.420	−	485.589i	−0.529807	−	1.03981i	0.458694	−	0.888594i	$-0.348317\pi$
$468$	−191.867	−	191.867i	−0.409973	−	0.409973i
$469$	−792.112	−	257.373i	−1.68894	−	0.548769i
$470$	−342.032	−	295.290i	−0.727727	−	0.628276i
$471$	95.4923	+	293.895i	0.202744	+	0.623981i
$472$	−2194.97	−	1118.39i	−4.65035	−	2.36947i
$473$	−33.6232	−	212.289i	−0.0710851	−	0.448813i
$474$		−	792.567i		−	1.67208i
$475$	−105.638	−	212.907i	−0.222397	−	0.448226i
$476$	−1721.63			−3.61686
$477$	−214.414	+	33.9598i	−0.449504	+	0.0711945i
$478$	−106.903	+	209.808i	−0.223646	+	0.438929i
$479$	243.720	−	79.1895i	0.508810	−	0.165323i	−0.0433508	−	0.999060i	$-0.513803\pi$
$479$	243.720	−	79.1895i	0.508810	−	0.165323i	0.552161	+	0.833737i	$0.313803\pi$
$480$	69.7324	−	829.487i	0.145276	−	1.72810i
$481$	−11.3384	+	34.8959i	−0.0235725	+	0.0725487i
$482$	21.0317	−	21.0317i	0.0436342	−	0.0436342i
$483$	−387.027	+	197.200i	−0.801298	+	0.408282i
$484$	−53.4167	−	73.5218i	−0.110365	−	0.151905i
$485$	190.640	+	225.635i	0.393072	+	0.465226i
$486$	−47.9014	−	34.8024i	−0.0985626	−	0.0716099i
$487$	−12.9195	+	81.5705i	−0.0265288	+	0.167496i	−0.997396	−	0.0721231i	$-0.977023\pi$
$487$	−12.9195	+	81.5705i	−0.0265288	+	0.167496i	0.970867	+	0.239619i	$0.0770226\pi$
$488$	−635.301	−	100.622i	−1.30185	−	0.206192i
$489$	−283.795	+	390.610i	−0.580357	+	0.798793i
$490$	−79.6817	+	324.274i	−0.162616	+	0.661784i
$491$	−348.669	+	253.323i	−0.710121	+	0.515933i	−0.883213	−	0.468973i	$-0.844624\pi$
$491$	−348.669	+	253.323i	−0.710121	+	0.515933i	0.173092	+	0.984906i	$0.444624\pi$
$492$	82.9365	+	162.772i	0.168570	+	0.330838i
$493$	239.184	+	239.184i	0.485161	+	0.485161i
$494$	−297.901	−	96.7940i	−0.603039	−	0.195939i
$495$	61.6080	−	146.521i	0.124461	−	0.296002i
$496$	428.101	+	1317.56i	0.863107	+	2.65637i
$497$	124.515	+	63.4435i	0.250533	+	0.127653i
$498$	−123.710	−	781.071i	−0.248413	−	1.56842i
$499$		−	651.682i		−	1.30598i	−0.757368	−	0.652988i	$-0.773515\pi$
$499$		−	651.682i		−	1.30598i	0.757368	−	0.652988i	$-0.226485\pi$
$500$	−830.516	−	1004.50i	−1.66103	−	2.00900i
$501$	−319.658			−0.638040
$502$	868.017	−	137.480i	1.72912	−	0.273865i
$503$	130.915	−	256.936i	0.260269	−	0.510807i	−0.723482	−	0.690343i	$-0.757460\pi$
$503$	130.915	−	256.936i	0.260269	−	0.510807i	0.983751	+	0.179536i	$0.0574596\pi$
$504$	568.331	−	184.662i	1.12764	−	0.366393i
$505$	83.3412	+	35.0426i	0.165032	+	0.0693913i
$506$	−382.251	+	1176.45i	−0.755437	+	2.32499i
$507$	114.827	−	114.827i	0.226483	−	0.226483i
$508$	−711.973	+	362.768i	−1.40152	+	0.714111i
$509$	302.452	+	416.290i	0.594208	+	0.817858i	0.995163	−	0.0982404i	$-0.0313214\pi$
$509$	302.452	+	416.290i	0.594208	+	0.817858i	−0.400954	+	0.916098i	$0.631321\pi$
$510$	646.380	+	158.830i	1.26741	+	0.311432i
$511$	213.124	+	154.844i	0.417073	+	0.303021i
$512$	−12.1857	+	76.9377i	−0.0238002	+	0.150269i
$513$	−48.7915	−	7.72781i	−0.0951101	−	0.0150640i
$514$	702.078	−	966.328i	1.36591	−	1.88001i
$515$	−372.535	+	314.757i	−0.723369	+	0.611178i
$516$	−296.363	+	215.320i	−0.574346	+	0.417287i
$517$	−114.461	−	224.642i	−0.221394	−	0.434511i
$518$	−92.7010	−	92.7010i	−0.178960	−	0.178960i
$519$	75.9570	+	24.6799i	0.146353	+	0.0475528i
$520$	−1055.04	−	88.6943i	−2.02893	−	0.170566i
$521$	−32.3038	−	99.4209i	−0.0620035	−	0.190827i	0.915257	−	0.402872i	$-0.131988\pi$
$521$	−32.3038	−	99.4209i	−0.0620035	−	0.190827i	−0.977260	+	0.212044i	$0.931988\pi$
$522$	−169.722	−	86.4775i	−0.325137	−	0.165666i
$523$	69.8213	+	440.834i	0.133501	+	0.842895i	0.960009	+	0.279969i	$0.0903243\pi$
$523$	69.8213	+	440.834i	0.133501	+	0.842895i	−0.826508	+	0.562926i	$0.809676\pi$
$524$			490.862i			0.936760i
$525$	163.756	−	313.092i	0.311915	−	0.596366i
$526$	−498.032			−0.946829
$527$	−542.748	+	85.9628i	−1.02988	+	0.163117i
$528$	425.063	−	834.234i	0.805044	−	1.57999i
$529$	−395.239	+	128.421i	−0.747144	+	0.242762i
$530$	−898.067	+	1040.22i	−1.69447	+	1.96268i
$531$	−93.5530	+	287.926i	−0.176183	+	0.542234i
$532$	571.960	−	571.960i	1.07511	−	1.07511i
$533$	78.1805	−	39.8349i	0.146680	−	0.0747372i
$534$	−368.314	−	506.941i	−0.689727	−	0.949327i
$535$	246.327	−	100.497i	0.460424	−	0.187845i
$536$	2015.81	+	1464.57i	3.76084	+	2.73241i
$537$	−53.2848	+	336.427i	−0.0992268	+	0.626494i
$538$	680.416	+	107.767i	1.26471	+	0.200311i
$539$	−109.513	+	150.731i	−0.203177	+	0.279650i
$540$	−270.175	+	19.8149i	−0.500324	+	0.0366942i
$541$	725.813	−	527.334i	1.34161	−	0.974740i	0.342231	−	0.939616i	$-0.388817\pi$
$541$	725.813	−	527.334i	1.34161	−	0.974740i	0.999383	−	0.0351241i	$-0.0111827\pi$
$542$	383.184	+	752.041i	0.706982	+	1.38753i
$543$	211.373	+	211.373i	0.389270	+	0.389270i
$544$	1849.76	+	601.022i	3.40029	+	1.10482i
$545$	−95.6526	−	407.989i	−0.175509	−	0.748604i
$546$	−143.896	−	442.865i	−0.263545	−	0.811109i
$547$	93.0075	+	47.3897i	0.170032	+	0.0866357i	0.536935	−	0.843623i	$-0.319582\pi$
$547$	93.0075	+	47.3897i	0.170032	+	0.0866357i	−0.366903	+	0.930259i	$0.619582\pi$
$548$	325.399	+	2054.49i	0.593794	+	3.74907i
$549$			79.0475i			0.143984i
$550$	−300.716	−	960.219i	−0.546757	−	1.74585i
$551$	−158.924			−0.288428
$552$	1283.49	−	203.285i	2.32516	−	0.368270i
$553$	446.288	−	875.890i	0.807031	−	1.58389i
$554$	−119.128	+	38.7069i	−0.215032	+	0.0698681i
$555$	18.9735	+	31.3356i	0.0341865	+	0.0564605i
$556$	531.362	−	1635.36i	0.955687	−	2.94130i
$557$	510.800	−	510.800i	0.917056	−	0.917056i	−0.0797580	−	0.996814i	$-0.525415\pi$
$557$	510.800	−	510.800i	0.917056	−	0.917056i	0.996814	+	0.0797580i	$0.0254148\pi$
$558$	275.719	−	140.486i	0.494121	−	0.251767i
$559$	103.420	+	142.345i	0.185008	+	0.254642i
$560$	1096.93	−	1768.79i	1.95880	−	3.15855i
$561$	300.454	+	218.293i	0.535569	+	0.389114i
$562$	−178.524	+	1127.16i	−0.317659	+	2.00562i
$563$	277.173	+	43.8999i	0.492314	+	0.0779749i	0.397655	−	0.917535i	$-0.369824\pi$
$563$	277.173	+	43.8999i	0.492314	+	0.0779749i	0.0946589	+	0.995510i	$0.469824\pi$
$564$	−252.574	+	347.638i	−0.447826	+	0.616379i
$565$	−424.315	−	263.141i	−0.750999	−	0.465737i
$566$	−1106.06	+	803.603i	−1.95418	+	1.41979i
$567$	−33.3403	−	65.4341i	−0.0588013	−	0.115404i
$568$	−295.623	−	295.623i	−0.520463	−	0.520463i
$569$	434.760	+	141.262i	0.764077	+	0.248264i	0.665027	−	0.746819i	$-0.268420\pi$
$569$	434.760	+	141.262i	0.764077	+	0.248264i	0.0990493	+	0.995083i	$0.468420\pi$
$570$	−267.507	+	161.974i	−0.469311	+	0.284165i
$571$	−17.3540	−	53.4102i	−0.0303924	−	0.0935380i	0.934710	−	0.355412i	$-0.115659\pi$
$571$	−17.3540	−	53.4102i	−0.0303924	−	0.0935380i	−0.965102	+	0.261874i	$0.915659\pi$
$572$	−853.955	−	435.112i	−1.49293	−	0.760685i
$573$	15.3165	+	96.7045i	0.0267303	+	0.168769i
$574$			313.508i			0.546181i
$575$	458.225	−	616.759i	0.796913	−	1.07262i
$576$	−483.094			−0.838706
$577$	450.487	−	71.3502i	0.780741	−	0.123657i	0.246673	−	0.969099i	$-0.420663\pi$
$577$	450.487	−	71.3502i	0.780741	−	0.123657i	0.534068	+	0.845442i	$0.320663\pi$
$578$	−207.702	+	407.638i	−0.359346	+	0.705256i
$579$	−402.623	+	130.820i	−0.695377	+	0.225942i
$580$	−848.508	+	198.932i	−1.46295	+	0.342986i
$581$	303.100	−	932.846i	0.521687	−	1.60559i
$582$	274.825	−	274.825i	0.472209	−	0.472209i
$583$	−683.206	+	348.111i	−1.17188	+	0.597102i
$584$	−463.240	−	637.595i	−0.793219	−	1.09177i
$585$	9.51722	+	129.767i	0.0162687	+	0.221823i
$586$	−187.977	−	136.573i	−0.320779	−	0.233060i
$587$	−26.2626	+	165.815i	−0.0447404	+	0.282480i	−0.999908	−	0.0135870i	$-0.995675\pi$
$587$	−26.2626	+	165.815i	−0.0447404	+	0.282480i	0.955167	+	0.296066i	$0.0956750\pi$
$588$	313.635	+	49.6749i	0.533392	+	0.0844810i
$589$	151.753	−	208.871i	0.257646	−	0.354619i
$590$	723.969	+	1774.51i	1.22707	+	3.00764i
$591$	−89.2905	+	64.8734i	−0.151084	+	0.109769i
$592$	97.9636	+	192.264i	0.165479	+	0.324771i
$593$	−365.800	−	365.800i	−0.616863	−	0.616863i	0.327862	−	0.944726i	$-0.393672\pi$
$593$	−365.800	−	365.800i	−0.616863	−	0.616863i	−0.944726	+	0.327862i	$0.893672\pi$
$594$	−198.900	−	64.6266i	−0.334849	−	0.108799i
$595$	624.898	+	539.500i	1.05025	+	0.906722i
$596$	−683.310	−	2103.01i	−1.14649	−	3.52855i
$597$	185.364	+	94.4479i	0.310493	+	0.158204i
$598$	−158.407	−	1000.15i	−0.264895	−	1.67248i
$599$			783.143i			1.30742i	0.756746	+	0.653709i	$0.226788\pi$
$599$			783.143i			1.30742i	−0.756746	+	0.653709i	$0.773212\pi$
$600$	−755.369	+	739.434i	−1.25895	+	1.23239i
$601$	−144.125			−0.239809			−0.119904	−	0.992785i	$-0.538259\pi$
$601$	−144.125			−0.239809			−0.119904	+	0.992785i	$0.538259\pi$
$602$	−620.920	+	98.3440i	−1.03143	+	0.163362i
$603$	139.017	−	272.836i	0.230542	−	0.452464i
$604$	−294.813	+	95.7904i	−0.488100	+	0.158593i
$605$	−3.65062	+	43.4252i	−0.00603408	+	0.0717771i
$606$	36.7596	−	113.134i	0.0606594	−	0.186691i
$607$	−200.753	+	200.753i	−0.330729	+	0.330729i	−0.852863	−	0.522134i	$-0.825136\pi$
$607$	−200.753	+	200.753i	−0.330729	+	0.330729i	0.522134	+	0.852863i	$0.325136\pi$
$608$	−814.200	+	414.855i	−1.33914	+	0.682328i
$609$	−138.870	−	191.138i	−0.228029	−	0.313855i
$610$	322.956	+	382.240i	0.529436	+	0.626623i
$611$	166.973	+	121.313i	0.273278	+	0.198548i
$612$	99.0175	−	625.172i	0.161793	−	1.02152i
$613$	−83.2322	−	13.1827i	−0.135778	−	0.0215052i	0.0881752	−	0.996105i	$-0.471896\pi$
$613$	−83.2322	−	13.1827i	−0.135778	−	0.0215052i	−0.223954	+	0.974600i	$0.571896\pi$
$614$	−834.420	+	1148.48i	−1.35899	+	1.87049i
$615$	20.9039	−	85.0708i	0.0339900	−	0.138327i
$616$	1707.62	−	1240.66i	2.77211	−	2.01406i
$617$	206.931	+	406.125i	0.335382	+	0.658225i	0.995687	−	0.0927727i	$-0.0295730\pi$
$617$	206.931	+	406.125i	0.335382	+	0.658225i	−0.660305	+	0.750998i	$0.729573\pi$
$618$	453.752	+	453.752i	0.734226	+	0.734226i
$619$	−828.947	−	269.341i	−1.33917	−	0.435123i	−0.450135	−	0.892960i	$-0.648624\pi$
$619$	−828.947	−	269.341i	−1.33917	−	0.435123i	−0.889036	+	0.457837i	$0.848624\pi$
$620$	548.772	−	1305.13i	0.885115	−	2.10505i
$621$	−49.3496	−	151.882i	−0.0794679	−	0.244577i
$622$	−417.375	−	212.663i	−0.671020	−	0.341902i
$623$	−121.581	−	767.630i	−0.195154	−	1.23215i
$624$			766.450i			1.22829i
$625$	−13.3237	+	624.858i	−0.0213179	+	0.999773i
$626$	2016.07			3.22056
$627$	−172.338	+	27.2957i	−0.274862	+	0.0435339i
$628$	844.559	−	1657.54i	1.34484	−	2.63940i
$629$	−81.4026	+	26.4493i	−0.129416	+	0.0420498i
$630$	−428.557	−	180.196i	−0.680249	−	0.286026i
$631$	30.0827	−	92.5850i	0.0476746	−	0.146727i	−0.924385	−	0.381460i	$-0.875421\pi$
$631$	30.0827	−	92.5850i	0.0476746	−	0.146727i	0.972060	+	0.234733i	$0.0754214\pi$
$632$	−2079.53	+	2079.53i	−3.29040	+	3.29040i
$633$	−369.173	+	188.103i	−0.583212	+	0.297161i
$634$	−52.3126	−	72.0021i	−0.0825119	−	0.113568i
$635$	372.104	+	91.4346i	0.585991	+	0.143991i
$636$	1057.27	+	768.154i	1.66238	+	1.20779i
$637$	23.8591	−	150.641i	0.0374555	−	0.236485i
$638$	−664.530	−	105.251i	−1.04158	−	0.164971i
$639$	−30.1995	+	41.5660i	−0.0472606	+	0.0650486i
$640$	−867.621	+	733.057i	−1.35566	+	1.14540i
$641$	449.534	−	326.605i	0.701301	−	0.509525i	−0.179055	−	0.983839i	$-0.557304\pi$
$641$	449.534	−	326.605i	0.701301	−	0.509525i	0.880356	+	0.474314i	$0.157304\pi$
$642$	−158.917	−	311.892i	−0.247534	−	0.485813i
$643$	8.96968	+	8.96968i	0.0139497	+	0.0139497i	0.714047	−	0.700098i	$-0.246860\pi$
$643$	8.96968	+	8.96968i	0.0139497	+	0.0139497i	−0.700098	+	0.714047i	$0.746860\pi$
$644$	2486.93	+	808.053i	3.86170	+	1.25474i
$645$	175.045	+	14.7155i	0.271387	+	0.0228147i
$646$	−225.794	−	694.922i	−0.349526	−	1.07573i
$647$	−368.471	−	187.745i	−0.569506	−	0.290178i	0.145429	−	0.989369i	$-0.453544\pi$
$647$	−368.471	−	187.745i	−0.569506	−	0.290178i	−0.714935	+	0.699191i	$0.753544\pi$
$648$	34.3691	+	216.998i	0.0530387	+	0.334873i
$649$			1069.33i			1.64766i
$650$	576.196	+	588.613i	0.886455	+	0.905558i
$651$	383.812			0.589574
$652$	2870.80	−	454.689i	4.40306	−	0.697377i
$653$	231.525	−	454.393i	0.354555	−	0.695854i	−0.642990	−	0.765874i	$-0.722306\pi$
$653$	231.525	−	454.393i	0.354555	−	0.695854i	0.997546	+	0.0700205i	$0.0223065\pi$
$654$	−524.387	+	170.384i	−0.801816	+	0.260526i
$655$	153.820	−	178.168i	0.234839	−	0.272012i
$656$	159.459	−	490.765i	0.243078	−	0.748117i
$657$	−68.4858	+	68.4858i	−0.104240	+	0.104240i
$658$	−657.052	+	334.785i	−0.998560	+	0.508792i
$659$	15.3369	+	21.1094i	0.0232730	+	0.0320325i	0.820495	−	0.571654i	$-0.193698\pi$
$659$	15.3369	+	21.1094i	0.0232730	+	0.0320325i	−0.797222	+	0.603686i	$0.793698\pi$
$660$	−885.962	+	361.457i	−1.34237	+	0.547662i
$661$	445.887	+	323.956i	0.674564	+	0.490099i	0.871550	−	0.490307i	$-0.163115\pi$
$661$	445.887	+	323.956i	0.674564	+	0.490099i	−0.196986	+	0.980406i	$0.563115\pi$
$662$	165.621	−	1045.69i	0.250183	−	1.57959i
$663$	−300.274	−	47.5587i	−0.452902	−	0.0717326i
$664$	−1724.78	+	2373.96i	−2.59756	+	3.57524i
$665$	−386.837	+	28.3710i	−0.581710	+	0.0426632i
$666$	38.9940	−	28.3308i	0.0585495	−	0.0425387i
$667$	−233.246	−	457.770i	−0.349694	−	0.686312i
$668$	1360.72	+	1360.72i	2.03700	+	2.03700i
$669$	328.579	+	106.762i	0.491150	+	0.159584i
$670$	−442.472	−	1887.29i	−0.660406	−	2.81684i
$671$	86.2797	+	265.542i	0.128584	+	0.395740i
$672$	−1210.40	−	616.731i	−1.80120	−	0.917755i
$673$	28.1223	+	177.557i	0.0417865	+	0.263829i	0.999733	−	0.0231183i	$-0.00735944\pi$
$673$	28.1223	+	177.557i	0.0417865	+	0.263829i	−0.957946	+	0.286948i	$0.907359\pi$
$674$		−	1002.41i		−	1.48726i
$675$	104.275	+	77.4715i	0.154481	+	0.114773i
$676$	−977.587			−1.44614
$677$	−171.834	+	27.2158i	−0.253817	+	0.0402006i	−0.282046	−	0.959401i	$-0.591013\pi$
$677$	−171.834	+	27.2158i	−0.253817	+	0.0402006i	0.0282294	+	0.999601i	$0.491013\pi$
$678$	−298.246	+	585.340i	−0.439890	+	0.863333i
$679$	458.470	−	148.966i	0.675213	−	0.219390i
$680$	−1279.23	−	2112.71i	−1.88122	−	3.10692i
$681$	121.058	−	372.577i	0.177765	−	0.547103i
$682$	772.876	−	772.876i	1.13325	−	1.13325i
$683$	−542.106	+	276.217i	−0.793713	+	0.404417i	−0.803328	−	0.595537i	$-0.796939\pi$
$683$	−542.106	+	276.217i	−0.793713	+	0.404417i	0.00961491	+	0.999954i	$0.496939\pi$
$684$	174.799	+	240.591i	0.255555	+	0.351741i
$685$	525.698	−	847.686i	0.767442	−	1.23750i
$686$	−787.761	−	572.342i	−1.14834	−	0.834318i
$687$	−84.3743	+	532.718i	−0.122816	+	0.775427i
$688$	1022.01	+	161.870i	1.48548	+	0.235276i
$689$	368.949	−	507.815i	0.535485	−	0.737032i
$690$	−859.164	−	532.816i	−1.24516	−	0.772197i
$691$	−33.4189	+	24.2803i	−0.0483631	+	0.0351379i	−0.611704	−	0.791087i	$-0.709516\pi$
$691$	−33.4189	+	24.2803i	−0.0483631	+	0.0351379i	0.563341	+	0.826224i	$0.309516\pi$
$692$	−218.276	−	428.390i	−0.315427	−	0.619061i
$693$	−183.420	−	183.420i	−0.264675	−	0.264675i
$694$	526.787	+	171.163i	0.759059	+	0.246633i
$695$	−705.336	+	427.076i	−1.01487	+	0.614498i
$696$	218.416	+	672.214i	0.313816	+	0.965825i
$697$	182.374	+	92.9240i	0.261655	+	0.133320i
$698$	30.8732	+	194.926i	0.0442310	+	0.279264i
$699$		−	724.806i		−	1.03692i
$700$	−2029.84	+	635.695i	−2.89977	+	0.908135i
$701$	−1169.75			−1.66869			−0.834344	−	0.551244i	$-0.814153\pi$
$701$	−1169.75			−1.66869			−0.834344	+	0.551244i	$0.814153\pi$
$702$	169.093	−	26.7817i	0.240873	−	0.0381506i
$703$	18.2566	−	35.8306i	0.0259696	−	0.0509682i
$704$	−1622.84	+	527.294i	−2.30518	+	0.748997i
$705$	200.614	−	47.0338i	0.284560	−	0.0667146i
$706$	−787.712	+	2424.33i	−1.11574	+	3.43389i
$707$	104.329	−	104.329i	0.147566	−	0.147566i
$708$	1623.88	−	827.407i	2.29361	−	1.16865i
$709$	426.559	+	587.108i	0.601635	+	0.828079i	0.995857	−	0.0909363i	$-0.0289860\pi$
$709$	426.559	+	587.108i	0.601635	+	0.828079i	−0.394222	+	0.919015i	$0.628986\pi$
$710$	23.7903	+	324.379i	0.0335074	+	0.456871i
$711$	292.393	+	212.436i	0.411242	+	0.298785i
$712$	−363.728	+	2296.49i	−0.510854	+	3.22541i
$713$	824.360	+	130.566i	1.15618	+	0.183122i
$714$	638.481	−	878.793i	0.894231	−	1.23080i
$715$	173.610	+	425.533i	0.242811	+	0.595151i
$716$	1658.92	−	1205.28i	2.31693	−	1.68335i
$717$	−48.7485	−	95.6743i	−0.0679895	−	0.133437i
$718$	−886.795	−	886.795i	−1.23509	−	1.23509i
$719$	455.491	+	147.998i	0.633506	+	0.205839i	0.608128	−	0.793839i	$-0.291921\pi$
$719$	455.491	+	147.998i	0.633506	+	0.205839i	0.0253785	+	0.999678i	$0.491921\pi$
$720$	579.209	+	500.055i	0.804458	+	0.694521i
$721$	245.951	+	756.959i	0.341125	+	1.04987i
$722$	−915.850	−	466.649i	−1.26849	−	0.646328i
$723$	2.12175	+	13.3962i	0.00293465	+	0.0185287i
$724$		−	1799.54i		−	2.48556i
$725$	370.321	+	193.688i	0.510788	+	0.267156i
$726$	57.3388			0.0789791
$727$	−455.141	+	72.0872i	−0.626053	+	0.0991571i	−0.461397	−	0.887194i	$-0.652652\pi$
$727$	−455.141	+	72.0872i	−0.626053	+	0.0991571i	−0.164656	+	0.986351i	$0.552652\pi$
$728$	−784.436	+	1539.54i	−1.07752	+	2.11475i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	−51.3627	+	610.974i	−0.0703598	+	0.836950i
$731$	−126.832	+	390.350i	−0.173505	+	0.533994i
$732$	336.488	−	336.488i	0.459684	−	0.459684i
$733$	1148.56	−	585.221i	1.56693	−	0.798391i	0.567248	−	0.823547i	$-0.308008\pi$
$733$	1148.56	−	585.221i	1.56693	−	0.798391i	0.999684	+	0.0251561i	$0.00800829\pi$
$734$	1184.08	+	1629.74i	1.61318	+	2.22036i
$735$	−98.2734	−	116.313i	−0.133705	−	0.158249i
$736$	−2389.93	−	1736.38i	−3.24718	−	2.35922i
$737$	169.197	−	1068.26i	0.229575	−	1.44948i
$738$	−113.844	−	18.0311i	−0.154260	−	0.0244324i
$739$	337.918	−	465.105i	0.457264	−	0.629370i	−0.516674	−	0.856182i	$-0.672830\pi$
$739$	337.918	−	465.105i	0.457264	−	0.629370i	0.973939	+	0.226812i	$0.0728302\pi$
$740$	52.6229	−	214.155i	0.0711120	−	0.289399i
$741$	115.557	−	83.9572i	0.155948	−	0.113303i
$742$	1018.18	+	1998.30i	1.37221	+	2.69312i
$743$	440.338	+	440.338i	0.592649	+	0.592649i	0.938346	−	0.345697i	$-0.112357\pi$
$743$	440.338	+	440.338i	0.592649	+	0.592649i	−0.345697	+	0.938346i	$0.612357\pi$
$744$	−1092.04	−	354.825i	−1.46779	−	0.476915i
$745$	−410.993	+	977.456i	−0.551668	+	1.31202i
$746$	−147.530	−	454.049i	−0.197761	−	0.608645i
$747$	321.310	+	163.716i	0.430134	+	0.219164i
$748$	−349.744	−	2208.20i	−0.467572	−	2.95213i
$749$		−	434.166i		−	0.579661i
$750$	820.744	−	51.4048i	1.09433	−	0.0685397i
$751$	−393.993			−0.524624			−0.262312	−	0.964983i	$-0.584485\pi$
$751$	−393.993			−0.524624			−0.262312	+	0.964983i	$0.584485\pi$
$752$	1198.83	−	189.876i	1.59419	−	0.252495i
$753$	−181.940	+	357.077i	−0.241620	+	0.474206i
$754$	523.815	−	170.198i	0.694715	−	0.225727i
$755$	137.025	+	57.6153i	0.181491	+	0.0763117i
$756$	−136.616	+	420.462i	−0.180709	+	0.556167i
$757$	−517.043	+	517.043i	−0.683016	+	0.683016i	−0.960679	−	0.277663i	$-0.910440\pi$
$757$	−517.043	+	517.043i	−0.683016	+	0.683016i	0.277663	+	0.960679i	$0.410440\pi$
$758$	1239.44	−	631.528i	1.63515	−	0.833151i
$759$	−331.557	−	456.349i	−0.436834	−	0.601250i
$760$	1126.87	+	276.898i	1.48273	+	0.364340i
$761$	−290.456	−	211.029i	−0.381677	−	0.277304i	0.380360	−	0.924839i	$-0.375800\pi$
$761$	−290.456	−	211.029i	−0.381677	−	0.277304i	−0.762036	+	0.647534i	$0.775800\pi$
$762$	78.8689	−	497.958i	0.103502	−	0.653489i
$763$	−675.458	−	106.982i	−0.885266	−	0.140212i
$764$	346.452	−	476.850i	0.453471	−	0.624149i
$765$	−231.848	+	195.889i	−0.303069	+	0.256065i
$766$	308.742	−	224.314i	0.403058	−	0.292838i
$767$	−397.409	−	779.958i	−0.518134	−	1.01689i
$768$	267.881	+	267.881i	0.348804	+	0.348804i
$769$	−1299.32	−	422.175i	−1.68962	−	0.548992i	−0.702885	−	0.711304i	$-0.748105\pi$
$769$	−1299.32	−	422.175i	−1.68962	−	0.548992i	−0.986740	+	0.162312i	$0.948105\pi$
$770$	−1636.32	−	137.560i	−2.12509	−	0.178650i
$771$	168.315	+	518.020i	0.218307	+	0.671880i
$772$	2270.76	+	1157.01i	2.94139	+	1.49871i
$773$	157.447	+	994.081i	0.203683	+	1.28600i	0.851559	+	0.524258i	$0.175657\pi$
$773$	157.447	+	994.081i	0.203683	+	1.28600i	−0.647876	+	0.761746i	$0.724343\pi$
$774$		−	231.130i		−	0.298617i
$775$	−608.172	+	301.757i	−0.784738	+	0.389364i
$776$	−1442.17			−1.85847
$777$	59.0463	−	9.35202i	0.0759927	−	0.0120361i
$778$	−1114.77	+	2187.86i	−1.43287	+	2.81216i
$779$	−91.4595	+	29.7170i	−0.117406	+	0.0381476i
$780$	511.876	−	592.902i	0.656252	−	0.760131i
$781$	−56.0792	+	172.594i	−0.0718043	+	0.220991i
$782$	1670.29	−	1670.29i	2.13592	−	2.13592i
$783$	77.3945	−	39.4345i	0.0988436	−	0.0503633i
$784$	−527.219	−	725.655i	−0.672473	−	0.925580i
$785$	−825.966	+	336.980i	−1.05219	+	0.429274i
$786$	−250.558	−	182.041i	−0.318776	−	0.231604i
$787$	−180.846	+	1141.82i	−0.229791	+	1.45085i	0.555395	+	0.831587i	$0.312567\pi$
$787$	−180.846	+	1141.82i	−0.229791	+	1.45085i	−0.785186	+	0.619259i	$0.787433\pi$
$788$	656.243	+	103.939i	0.832796	+	0.131902i
$789$	133.490	−	183.733i	0.169189	−	0.232869i
$790$	2281.82	−	167.351i	2.88837	−	0.211836i
$791$	−659.200	+	478.937i	−0.833376	+	0.605483i
$792$	352.307	+	691.440i	0.444831	+	0.873031i
$793$	−161.617	−	161.617i	−0.203805	−	0.203805i
$794$	−2661.88	−	864.897i	−3.35249	−	1.08929i
$795$	−143.044	−	610.130i	−0.179930	−	0.767459i
$796$	−387.013	−	1191.10i	−0.486197	−	1.49636i
$797$	−685.540	−	349.300i	−0.860150	−	0.438269i	−0.0324730	−	0.999473i	$-0.510338\pi$
$797$	−685.540	−	349.300i	−0.860150	−	0.438269i	−0.827677	+	0.561204i	$0.810338\pi$
$798$	79.8368	+	504.070i	0.100046	+	0.631667i
$799$			481.450i			0.602566i
$800$	2402.83	+	25.6146i	3.00354	+	0.0320182i
$801$	285.741			0.356731
$802$	−2060.48	+	326.349i	−2.56918	+	0.406918i
$803$	−155.310	+	304.814i	−0.193413	+	0.379594i
$804$	−1753.17	+	569.640i	−2.18056	+	0.708507i
$805$	−649.464	−	1072.62i	−0.806787	−	1.33245i
$806$	−276.493	+	850.958i	−0.343043	+	1.05578i
$807$	−222.133	+	222.133i	−0.275257	+	0.275257i
$808$	−393.291	+	200.392i	−0.486747	+	0.248010i
$809$	−190.387	−	262.045i	−0.235336	−	0.323912i	0.674972	−	0.737843i	$-0.264156\pi$
$809$	−190.387	−	262.045i	−0.235336	−	0.323912i	−0.910308	+	0.413931i	$0.864156\pi$
$810$	90.0824	−	145.258i	0.111213	−	0.179330i
$811$	−741.264	−	538.560i	−0.914012	−	0.664069i	0.0280143	−	0.999608i	$-0.491082\pi$
$811$	−741.264	−	538.560i	−0.914012	−	0.664069i	−0.942026	+	0.335539i	$0.891082\pi$
$812$	−222.494	+	1404.77i	−0.274008	+	1.73002i
$813$	−380.149	−	60.2097i	−0.467588	−	0.0740587i
$814$	100.068	−	137.732i	0.122934	−	0.169204i
$815$	−1184.50	−	734.573i	−1.45337	−	0.901316i
$816$	−1446.46	+	1050.91i	−1.77262	+	1.28788i
$817$	−87.5460	−	171.819i	−0.107155	−	0.210304i
$818$	1426.35	+	1426.35i	1.74370	+	1.74370i
$819$	201.951	+	65.6177i	0.246582	+	0.0801193i
$820$	−451.112	+	273.145i	−0.550136	+	0.333104i
$821$	−214.758	−	660.957i	−0.261581	−	0.805064i	−0.992461	−	0.122558i	$-0.960890\pi$
$821$	−214.758	−	660.957i	−0.261581	−	0.805064i	0.730880	−	0.682506i	$-0.239110\pi$
$822$	−1169.38	−	595.828i	−1.42260	−	0.724851i
$823$	208.667	+	1317.47i	0.253544	+	1.60081i	0.705457	+	0.708752i	$0.250742\pi$
$823$	208.667	+	1317.47i	0.253544	+	1.60081i	−0.451913	+	0.892062i	$0.649258\pi$
$824$		−	2381.10i		−	2.88969i
$825$	434.846	+	146.433i	0.527085	+	0.177494i
$826$	3127.68			3.78654
$827$	927.959	−	146.974i	1.12208	−	0.177720i	0.432293	−	0.901733i	$-0.357705\pi$
$827$	927.959	−	146.974i	1.12208	−	0.177720i	0.689786	+	0.724013i	$0.257705\pi$
$828$	−436.460	+	856.602i	−0.527126	+	1.03454i
$829$	−264.382	+	85.9029i	−0.318917	+	0.103622i	−0.464101	−	0.885782i	$-0.653622\pi$
$829$	−264.382	+	85.9029i	−0.318917	+	0.103622i	0.145184	+	0.989405i	$0.453622\pi$
$830$	2222.60	−	521.085i	2.67783	−	0.627814i
$831$	17.6507	−	54.3233i	0.0212403	−	0.0653710i
$832$	987.717	−	987.717i	1.18716	−	1.18716i
$833$	317.006	−	161.522i	0.380559	−	0.193904i
$834$	637.701	+	877.720i	0.764629	+	1.05242i
$835$	−67.4958	−	920.302i	−0.0808333	−	1.10216i
$836$	849.801	+	617.416i	1.01651	+	0.738536i
$837$	−22.0746	+	139.373i	−0.0263734	+	0.166515i
$838$	−10.2523	−	1.62381i	−0.0122343	−	0.00193772i
$839$	95.4951	−	131.438i	0.113820	−	0.156660i	−0.748306	−	0.663354i	$-0.769133\pi$
$839$	95.4951	−	131.438i	0.113820	−	0.156660i	0.862126	+	0.506694i	$0.169133\pi$
$840$	651.648	+	1597.24i	0.775772	+	1.90148i
$841$	−454.308	+	330.074i	−0.540200	+	0.392478i
$842$	−577.766	−	1133.93i	−0.686183	−	1.34671i
$843$	−367.979	−	367.979i	−0.436512	−	0.436512i
$844$	2372.21	+	770.777i	2.81067	+	0.913243i
$845$	354.834	+	306.343i	0.419922	+	0.362536i
$846$	−83.7803	−	257.849i	−0.0990311	−	0.304786i
$847$	63.3669	+	32.2870i	0.0748133	+	0.0381193i
$848$	−577.471	−	3646.01i	−0.680980	−	4.29954i
$849$		−	623.442i		−	0.734325i
$850$	−320.793	+	1894.48i	−0.377403	+	2.22880i
$851$	130.002			0.152764
$852$	305.491	−	48.3850i	0.358557	−	0.0567899i
$853$	−580.664	+	1139.62i	−0.680732	+	1.33601i	0.249262	+	0.968436i	$0.419812\pi$
$853$	−580.664	+	1139.62i	−0.680732	+	1.33601i	−0.929994	+	0.367575i	$0.880188\pi$
$854$	776.678	−	252.358i	0.909459	−	0.295501i
$855$	11.9462	−	142.103i	0.0139721	−	0.166203i
$856$	−401.375	+	1235.31i	−0.468896	+	1.44311i
$857$	215.985	−	215.985i	0.252025	−	0.252025i	−0.569776	−	0.821800i	$-0.692970\pi$
$857$	215.985	−	215.985i	0.252025	−	0.252025i	0.821800	+	0.569776i	$0.192970\pi$
$858$	538.797	−	274.531i	0.627969	−	0.319966i
$859$	−773.813	−	1065.06i	−0.900830	−	1.23989i	−0.970202	−	0.242296i	$-0.922100\pi$
$859$	−773.813	−	1065.06i	−0.900830	−	1.23989i	0.0693723	−	0.997591i	$-0.477900\pi$
$860$	−682.488	−	807.769i	−0.793590	−	0.939266i
$861$	−115.659	−	84.0312i	−0.134331	−	0.0975972i
$862$	381.841	−	2410.85i	0.442971	−	2.79681i
$863$	−736.931	−	116.718i	−0.853918	−	0.135247i	−0.285896	−	0.958261i	$-0.592291\pi$
$863$	−736.931	−	116.718i	−0.853918	−	0.135247i	−0.568022	+	0.823013i	$0.692291\pi$
$864$	293.568	−	404.061i	0.339778	−	0.467664i
$865$	−55.0156	+	223.893i	−0.0636019	+	0.258836i
$866$	−160.913	+	116.910i	−0.185812	+	0.135000i
$867$	−94.7138	−	185.886i	−0.109243	−	0.214402i
$868$	−1633.81	−	1633.81i	−1.88227	−	1.88227i
$869$	1214.10	+	394.485i	1.39712	+	0.453952i
$870$	213.134	−	506.891i	0.244981	−	0.582634i
$871$	273.601	+	842.059i	0.314123	+	0.966772i
$872$	1822.94	+	928.833i	2.09053	+	1.06518i
$873$	27.7254	+	175.051i	0.0317587	+	0.200517i
$874$			1109.81i			1.26981i
$875$	935.975	+	405.346i	1.06969	+	0.463252i
$876$	583.059			0.665593
$877$	1231.98	−	195.126i	1.40477	−	0.222493i	0.592401	−	0.805643i	$-0.298180\pi$
$877$	1231.98	−	195.126i	1.40477	−	0.222493i	0.812364	+	0.583150i	$0.198180\pi$
$878$	487.106	−	955.999i	0.554790	−	1.08884i
$879$	100.769	−	32.7418i	0.114640	−	0.0372489i
$880$	2491.53	+	1047.62i	2.83128	+	1.19047i
$881$	−263.341	+	810.479i	−0.298911	+	0.919954i	0.682968	+	0.730448i	$0.260689\pi$
$881$	−263.341	+	810.479i	−0.298911	+	0.919954i	−0.981880	+	0.189506i	$0.939311\pi$
$882$	−141.671	+	141.671i	−0.160624	+	0.160624i
$883$	−1428.74	+	727.978i	−1.61805	+	0.824437i	−0.618805	+	0.785545i	$0.712383\pi$
$883$	−1428.74	+	727.978i	−1.61805	+	0.824437i	−0.999243	+	0.0388919i	$0.987617\pi$
$884$	1075.76	+	1480.65i	1.21692	+	1.67494i
$885$	−848.699	−	208.545i	−0.958982	−	0.235644i
$886$	−1471.29	−	1068.95i	−1.66060	−	1.20649i
$887$	−19.8592	+	125.386i	−0.0223891	+	0.141359i	−0.996351	−	0.0853537i	$-0.972798\pi$
$887$	−19.8592	+	125.386i	−0.0223891	+	0.141359i	0.973962	+	0.226713i	$0.0727980\pi$
$888$	−176.647	−	27.9781i	−0.198926	−	0.0315068i
$889$	367.557	−	505.899i	0.413450	−	0.569065i
$890$	1381.72	−	1167.42i	1.55250	−	1.31171i
$891$	77.1542	−	56.0558i	0.0865928	−	0.0629134i
$892$	−944.230	−	1853.16i	−1.05855	−	2.07753i
$893$	−159.948	−	159.948i	−0.179113	−	0.179113i
$894$	1326.88	+	431.130i	1.48421	+	0.482248i
$895$	−979.831	−	82.3713i	−1.09478	−	0.0920350i
$896$	572.811	+	1762.93i	0.639298	+	1.96756i
$897$	411.431	+	209.635i	0.458675	+	0.233706i
$898$	304.087	+	1919.93i	0.338627	+	2.13801i
$899$			453.968i			0.504970i
$900$	−114.095	−	773.654i	−0.126772	−	0.859616i
$901$	1464.24			1.62512
$902$	−402.112	+	63.6884i	−0.445801	+	0.0706079i
$903$	130.147	−	255.429i	0.144128	−	0.282867i
$904$	2318.35	−	753.277i	2.56454	−	0.833271i
$905$	−563.917	+	653.180i	−0.623112	+	0.721746i
$906$	60.4383	−	186.010i	0.0667090	−	0.205309i
$907$	626.637	−	626.637i	0.690889	−	0.690889i	−0.271538	−	0.962428i	$-0.587532\pi$
$907$	626.637	−	626.637i	0.690889	−	0.690889i	0.962428	+	0.271538i	$0.0875323\pi$
$908$	−2101.30	+	1070.67i	−2.31421	+	1.17915i
$909$	31.8846	+	43.8853i	0.0350765	+	0.0482787i
$910$	1244.63	−	507.790i	1.36773	−	0.558010i
$911$	1053.95	+	765.743i	1.15692	+	0.840552i	0.989386	−	0.145314i	$-0.0464192\pi$
$911$	1053.95	+	765.743i	1.15692	+	0.840552i	0.167535	+	0.985866i	$0.446419\pi$
$912$	131.408	−	829.677i	0.144088	−	0.909734i
$913$	1258.06	+	199.258i	1.37794	+	0.218245i
$914$	−1723.23	+	2371.82i	−1.88537	+	2.59499i
$915$	−227.579	+	16.6909i	−0.248720	+	0.0182414i
$916$	2626.83	−	1908.51i	2.86772	−	2.08352i
$917$	−174.393	−	342.266i	−0.190178	−	0.373245i
$918$	282.393	+	282.393i	0.307618	+	0.307618i
$919$	1388.79	+	451.245i	1.51120	+	0.491017i	0.943260	−	0.332056i	$-0.107742\pi$
$919$	1388.79	+	451.245i	1.51120	+	0.491017i	0.567936	+	0.823073i	$0.307742\pi$
$920$	856.271	+	3652.27i	0.930729	+	3.96986i
$921$	−200.042	−	615.666i	−0.217201	−	0.668476i
$922$	−3065.71	−	1562.06i	−3.32506	−	1.69420i
$923$	−23.2396	−	146.729i	−0.0251783	−	0.158970i
$924$			1561.56i			1.69000i
$925$	−86.2095	+	61.2415i	−0.0931995	+	0.0662071i
$926$	−522.518			−0.564274
$927$	−289.019	+	45.7761i	−0.311779	+	0.0493809i
$928$	729.461	−	1431.65i	0.786058	−	1.54272i
$929$	−225.655	+	73.3196i	−0.242901	+	0.0789232i	−0.427937	−	0.903808i	$-0.640760\pi$
$929$	−225.655	+	73.3196i	−0.242901	+	0.0789232i	0.185037	+	0.982732i	$0.440760\pi$
$930$	462.680	+	764.137i	0.497505	+	0.821653i
$931$	−51.6547	+	158.977i	−0.0554831	+	0.170759i
$932$	−3085.35	+	3085.35i	−3.31046	+	3.31046i
$933$	190.326	−	96.9762i	0.203994	−	0.103940i
$934$	−1216.73	−	1674.68i	−1.30271	−	1.79302i
$935$	−565.028	+	911.106i	−0.604308	+	0.974445i
$936$	−513.936	−	373.396i	−0.549076	−	0.398927i
$937$	278.872	−	1760.73i	0.297622	−	1.87911i	−0.155759	−	0.987795i	$-0.549782\pi$
$937$	278.872	−	1760.73i	0.297622	−	1.87911i	0.453381	−	0.891317i	$-0.350218\pi$
$938$	−3124.55	−	494.880i	−3.33108	−	0.527591i
$939$	−540.378	+	743.767i	−0.575483	+	0.792084i
$940$	−1054.19	−	653.760i	−1.12148	−	0.695490i
$941$	−364.279	+	264.664i	−0.387119	+	0.281258i	−0.764274	−	0.644892i	$-0.776902\pi$
$941$	−364.279	+	264.664i	−0.387119	+	0.281258i	0.377155	+	0.926150i	$0.376902\pi$
$942$	532.869	+	1045.81i	0.565678	+	1.11021i
$943$	−219.829	−	219.829i	−0.233117	−	0.233117i
$944$	−4896.06	−	1590.83i	−5.18650	−	1.68520i
$945$	181.346	−	109.804i	0.191901	−	0.116195i
$946$	−252.277	−	776.427i	−0.266677	−	0.820748i
$947$	727.461	+	370.660i	0.768174	+	0.391404i	0.793731	−	0.608269i	$-0.208136\pi$
$947$	727.461	+	370.660i	0.768174	+	0.391404i	−0.0255566	+	0.999673i	$0.508136\pi$
$948$	−340.360	−	2148.95i	−0.359030	−	2.26683i
$949$		−	280.047i		−	0.295097i
$950$	−522.810	−	735.958i	−0.550327	−	0.774693i
$951$	40.5845			0.0426756
$952$	−3981.02	+	630.531i	−4.18174	+	0.662323i
$953$	539.470	−	1058.77i	0.566075	−	1.11099i	−0.413612	−	0.910453i	$-0.635733\pi$
$953$	539.470	−	1058.77i	0.566075	−	1.11099i	0.979687	−	0.200532i	$-0.0642671\pi$
$954$	−784.199	+	254.802i	−0.822011	+	0.267088i
$955$	−275.180	+	64.5156i	−0.288147	+	0.0675556i
$956$	−199.753	+	614.777i	−0.208947	+	0.643073i
$957$	216.947	−	216.947i	0.226694	−	0.226694i
$958$	867.268	−	441.895i	0.905290	−	0.461269i
$959$	−956.809	−	1316.94i	−0.997716	−	1.37324i
$960$	−102.005	−	1390.84i	−0.106256	−	1.44879i
$961$	180.825	+	131.377i	0.188163	+	0.136708i
$962$	−21.8016	+	137.650i	−0.0226628	+	0.143087i
$963$	157.658	+	24.9706i	0.163715	+	0.0259300i
$964$	47.9931	−	66.0568i	0.0497853	−	0.0685236i
$965$	−461.648	−	1131.54i	−0.478391	−	1.17258i
$966$	−1334.77	+	969.765i	−1.38175	+	1.00390i
$967$	714.594	+	1402.47i	0.738980	+	1.45033i	0.887205	+	0.461376i	$0.152644\pi$
$967$	714.594	+	1402.47i	0.738980	+	1.45033i	−0.148225	+	0.988954i	$0.547356\pi$
$968$	−150.445	−	150.445i	−0.155419	−	0.155419i
$969$	316.891	+	102.964i	0.327028	+	0.106258i
$970$	849.257	+	733.198i	0.875522	+	0.755874i
$971$	193.680	+	596.085i	0.199464	+	0.613887i	0.999895	+	0.0144629i	$0.00460386\pi$
$971$	193.680	+	596.085i	0.199464	+	0.613887i	−0.800431	+	0.599425i	$0.795396\pi$
$972$	−144.824	−	73.7917i	−0.148996	−	0.0759174i
$973$	210.505	+	1329.08i	0.216347	+	1.36596i
$974$			313.690i			0.322064i
$975$	−371.591	+	54.8005i	−0.381119	+	0.0562056i
$976$	−1344.17			−1.37722
$977$	522.903	−	82.8198i	0.535213	−	0.0847695i	0.117024	−	0.993129i	$-0.462665\pi$
$977$	522.903	−	82.8198i	0.535213	−	0.0847695i	0.418190	+	0.908360i	$0.362665\pi$
$978$	−832.568	+	1634.01i	−0.851296	+	1.67076i
$979$	959.881	−	311.884i	0.980471	−	0.318574i
$980$	−76.7908	+	913.449i	−0.0783580	+	0.932091i
$981$	77.6965	−	239.125i	0.0792013	−	0.243757i
$982$	−1157.52	+	1157.52i	−1.17874	+	1.17874i
$983$	745.712	−	379.959i	0.758608	−	0.386530i	−0.0314952	−	0.999504i	$-0.510027\pi$
$983$	745.712	−	379.959i	0.758608	−	0.386530i	0.790103	+	0.612974i	$0.210027\pi$
$984$	251.393	+	346.013i	0.255481	+	0.351639i
$985$	−205.625	−	243.371i	−0.208757	−	0.247077i
$986$	1039.42	+	755.186i	1.05418	+	0.765909i
$987$	52.6047	−	332.133i	0.0532976	−	0.336508i
$988$	−849.291	−	134.514i	−0.859606	−	0.136148i
$989$	366.425	−	504.341i	0.370501	−	0.509950i
$990$	144.063	−	586.283i	0.145519	−	0.592205i
$991$	533.102	−	387.322i	0.537944	−	0.390839i	−0.285377	−	0.958415i	$-0.592119\pi$
$991$	533.102	−	387.322i	0.537944	−	0.390839i	0.823321	+	0.567576i	$0.192119\pi$
$992$	1185.04	+	2325.77i	1.19459	+	2.34452i
$993$	341.383	+	341.383i	0.343789	+	0.343789i
$994$	504.817	+	164.025i	0.507865	+	0.165015i
$995$	−232.778	+	553.610i	−0.233947	+	0.556392i
$996$	−670.847	−	2064.65i	−0.673541	−	2.07295i
$997$	−310.548	−	158.232i	−0.311482	−	0.158708i	0.291260	−	0.956644i	$-0.405925\pi$
$997$	−310.548	−	158.232i	−0.311482	−	0.158708i	−0.602743	+	0.797936i	$0.705925\pi$
$998$	−387.218	−	2444.80i	−0.387994	−	2.44970i
$999$			21.9793i			0.0220013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.10	✓	80
3.2	odd	2		225.3.r.b.163.1		80
5.2	odd	4		375.3.k.c.82.10		80
5.3	odd	4		375.3.k.b.82.1		80
5.4	even	2		375.3.k.a.43.1		80
25.2	odd	20	inner	75.3.k.a.52.10	yes	80
25.11	even	5		375.3.k.c.343.10		80
25.14	even	10		375.3.k.b.343.1		80
25.23	odd	20		375.3.k.a.157.1		80
75.2	even	20		225.3.r.b.127.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.10	✓	80	1.1	even	1	trivial
75.3.k.a.52.10	yes	80	25.2	odd	20	inner
225.3.r.b.127.1		80	75.2	even	20
225.3.r.b.163.1		80	3.2	odd	2
375.3.k.a.43.1		80	5.4	even	2
375.3.k.a.157.1		80	25.23	odd	20
375.3.k.b.82.1		80	5.3	odd	4
375.3.k.b.343.1		80	25.14	even	10
375.3.k.c.82.10		80	5.2	odd	4
375.3.k.c.343.10		80	25.11	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(3.75152 - 0.594183i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-4.60913 - 1.93801i) q^{5} +(-2.03297 + 6.25683i) q^{6} +(-5.76987 + 5.76987i) q^{7} +(21.7507 - 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(3.75152 - 0.594183i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(9.91663 - 3.22211i) q^{4} +(-4.60913 - 1.93801i) q^{5} +(-2.03297 + 6.25683i) q^{6} +(-5.76987 + 5.76987i) q^{7} +(21.7507 - 11.0826i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-18.4428 - 4.53182i) q^{10} +(-8.57269 - 6.22843i) q^{11} +(-2.82521 + 17.8377i) q^{12} +(8.56755 + 1.35697i) q^{13} +(-18.2174 + 25.0741i) q^{14} +(6.61519 - 5.58921i) q^{15} +(41.2709 - 29.9851i) q^{16} +(9.18644 + 18.0294i) q^{17} +(-8.05738 - 8.05738i) q^{18} +(-9.04167 - 2.93782i) q^{19} +(-51.9516 - 4.36741i) q^{20} +(-4.36741 - 13.4415i) q^{21} +(-35.8615 - 18.2723i) q^{22} +(-4.80786 - 30.3556i) q^{23} +42.2818i q^{24} +(17.4882 + 17.8651i) q^{25} +32.9476 q^{26} +(5.13218 - 0.812857i) q^{27} +(-38.6265 + 75.8088i) q^{28} +(15.8984 - 5.16571i) q^{29} +(21.4960 - 24.8987i) q^{30} +(-8.39189 + 25.8276i) q^{31} +(67.9662 - 67.9662i) q^{32} +(16.3531 - 8.33234i) q^{33} +(45.1759 + 62.1792i) q^{34} +(37.7761 - 15.4120i) q^{35} +(-25.3068 - 18.3864i) q^{36} +(-0.661704 + 4.17784i) q^{37} +(-35.6656 - 5.64887i) q^{38} +(-8.83112 + 12.1550i) q^{39} +(-121.730 + 8.92781i) q^{40} +(8.18348 - 5.94565i) q^{41} +(-24.3711 - 47.8310i) q^{42} +(14.3428 + 14.3428i) q^{43} +(-105.081 - 34.1428i) q^{44} +(3.42389 + 14.6040i) q^{45} +(-36.0736 - 111.023i) q^{46} +(21.1998 + 10.8018i) q^{47} +(13.8223 + 87.2704i) q^{48} -17.5827i q^{49} +(76.2226 + 56.6301i) q^{50} -35.0478 q^{51} +(89.3335 - 14.1490i) q^{52} +(32.8517 - 64.4751i) q^{53} +(18.7705 - 6.09890i) q^{54} +(27.4419 + 45.3216i) q^{55} +(-61.5540 + 189.444i) q^{56} +(11.6436 - 11.6436i) q^{57} +(56.5739 - 28.8258i) q^{58} +(-59.3161 - 81.6416i) q^{59} +(47.5914 - 76.7410i) q^{60} +(-21.3169 - 15.4876i) q^{61} +(-16.1361 + 101.879i) q^{62} +(24.1781 + 3.82943i) q^{63} +(94.6519 - 130.277i) q^{64} +(-36.8592 - 22.8584i) q^{65} +(56.3982 - 40.9757i) q^{66} +(46.3389 + 90.9453i) q^{67} +(149.191 + 149.191i) q^{68} +(50.6275 + 16.4499i) q^{69} +(132.560 - 80.2644i) q^{70} +(-5.29227 - 16.2879i) q^{71} +(-65.2522 - 33.2477i) q^{72} +(-5.05041 - 31.8870i) q^{73} +16.0664i q^{74} +(-41.3222 + 12.9411i) q^{75} -99.1288 q^{76} +(85.4005 - 13.5261i) q^{77} +(-25.9079 + 50.8470i) q^{78} +(-114.576 + 37.2281i) q^{79} +(-248.335 + 58.2218i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(27.1677 - 27.1677i) q^{82} +(-107.103 + 54.5720i) q^{83} +(-86.6199 - 119.222i) q^{84} +(-7.40035 - 100.903i) q^{85} +(62.3293 + 45.2849i) q^{86} +(-4.52940 + 28.5975i) q^{87} +(-255.489 - 40.4655i) q^{88} +(-55.9848 + 77.0565i) q^{89} +(21.5222 + 52.7528i) q^{90} +(-57.2631 + 41.6041i) q^{91} +(-145.487 - 285.534i) q^{92} +(-33.2601 - 33.2601i) q^{93} +(85.9498 + 27.9268i) q^{94} +(35.9807 + 31.0636i) q^{95} +(51.4459 + 158.334i) q^{96} +(-52.6386 - 26.8207i) q^{97} +(-10.4473 - 65.9619i) q^{98} +31.7893i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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