LMFDB - Embedded newform 72.3.j.a.29.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, 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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.20
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86434 + 0.724045i) q^{2} +(-2.13383 + 2.10874i) q^{3} +(2.95152 + 2.69973i) q^{4} +(0.693019 + 1.20034i) q^{5} +(-5.50500 + 2.38642i) q^{6} +(-0.562989 + 0.975125i) q^{7} +(3.54790 + 7.17024i) q^{8} +(0.106423 - 8.99937i) q^{9} +O(q^{10})$	\(q+(1.86434 + 0.724045i) q^{2} +(-2.13383 + 2.10874i) q^{3} +(2.95152 + 2.69973i) q^{4} +(0.693019 + 1.20034i) q^{5} +(-5.50500 + 2.38642i) q^{6} +(-0.562989 + 0.975125i) q^{7} +(3.54790 + 7.17024i) q^{8} +(0.106423 - 8.99937i) q^{9} +(0.422919 + 2.73963i) q^{10} +(-1.11157 + 1.92529i) q^{11} +(-11.9911 + 0.463232i) q^{12} +(14.4573 - 8.34694i) q^{13} +(-1.75564 + 1.41033i) q^{14} +(-4.01000 - 1.09993i) q^{15} +(1.42291 + 15.9366i) q^{16} -20.2816i q^{17} +(6.71436 - 16.7008i) q^{18} -21.0174i q^{19} +(-1.19515 + 5.41380i) q^{20} +(-0.854966 - 3.26794i) q^{21} +(-3.46633 + 2.78457i) q^{22} +(-18.0360 + 10.4131i) q^{23} +(-22.6908 - 7.81844i) q^{24} +(11.5394 - 19.9869i) q^{25} +(32.9969 - 5.09377i) q^{26} +(18.7503 + 19.4275i) q^{27} +(-4.29425 + 1.35818i) q^{28} +(-26.9695 + 46.7126i) q^{29} +(-6.67960 - 4.95406i) q^{30} +(9.19365 + 15.9239i) q^{31} +(-8.88603 + 30.7415i) q^{32} +(-1.68805 - 6.45224i) q^{33} +(14.6848 - 37.8118i) q^{34} -1.56065 q^{35} +(24.6100 - 26.2745i) q^{36} -34.8194i q^{37} +(15.2175 - 39.1835i) q^{38} +(-13.2479 + 48.2977i) q^{39} +(-6.14800 + 9.22782i) q^{40} +(-15.1169 + 8.72774i) q^{41} +(0.772192 - 6.71159i) q^{42} +(-44.2282 - 25.5352i) q^{43} +(-8.47857 + 2.68160i) q^{44} +(10.8761 - 6.10899i) q^{45} +(-41.1649 + 6.35467i) q^{46} +(32.4750 + 18.7494i) q^{47} +(-36.6424 - 31.0054i) q^{48} +(23.8661 + 41.3373i) q^{49} +(35.9849 - 28.9073i) q^{50} +(42.7687 + 43.2774i) q^{51} +(65.2055 + 14.3947i) q^{52} -52.6541 q^{53} +(20.8904 + 49.7955i) q^{54} -3.08135 q^{55} +(-8.98931 - 0.577118i) q^{56} +(44.3202 + 44.8474i) q^{57} +(-84.1024 + 67.5609i) q^{58} +(-27.1346 - 46.9986i) q^{59} +(-8.86607 - 14.0724i) q^{60} +(76.5667 + 44.2058i) q^{61} +(5.61048 + 36.3441i) q^{62} +(8.71560 + 5.17032i) q^{63} +(-38.8248 + 50.8786i) q^{64} +(20.0384 + 11.5692i) q^{65} +(1.52462 - 13.2514i) q^{66} +(-66.0909 + 38.1576i) q^{67} +(54.7549 - 59.8615i) q^{68} +(16.5272 - 60.2531i) q^{69} +(-2.90958 - 1.12998i) q^{70} -69.4903i q^{71} +(64.9053 - 31.1658i) q^{72} -82.6983 q^{73} +(25.2108 - 64.9151i) q^{74} +(17.5240 + 66.9823i) q^{75} +(56.7412 - 62.0331i) q^{76} +(-1.25160 - 2.16783i) q^{77} +(-59.6682 + 80.4511i) q^{78} +(19.8580 - 34.3950i) q^{79} +(-18.1433 + 12.7524i) q^{80} +(-80.9773 - 1.91549i) q^{81} +(-34.5023 + 5.32616i) q^{82} +(56.9488 - 98.6383i) q^{83} +(6.29912 - 11.9536i) q^{84} +(24.3449 - 14.0555i) q^{85} +(-63.9677 - 79.6294i) q^{86} +(-40.9565 - 156.548i) q^{87} +(-17.7485 - 1.13946i) q^{88} -25.3593i q^{89} +(24.6999 - 3.51444i) q^{90} +18.7969i q^{91} +(-81.3463 - 17.9580i) q^{92} +(-53.1969 - 14.5917i) q^{93} +(46.9689 + 58.4686i) q^{94} +(25.2281 - 14.5654i) q^{95} +(-45.8646 - 84.3353i) q^{96} +(10.4267 - 18.0596i) q^{97} +(14.5644 + 94.3468i) q^{98} +(17.2081 + 10.2083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.86434	+	0.724045i	0.932169	+	0.362023i
$2$	1.86434	+	0.724045i	0.932169	+	0.362023i
$3$	−2.13383	+	2.10874i	−0.711275	+	0.702914i
$3$	−2.13383	+	2.10874i	−0.711275	+	0.702914i
$4$	2.95152	+	2.69973i	0.737879	+	0.674933i
$5$	0.693019	+	1.20034i	0.138604	+	0.240069i	0.926968	−	0.375139i	$-0.122405\pi$
$5$	0.693019	+	1.20034i	0.138604	+	0.240069i	−0.788365	+	0.615208i	$0.789072\pi$
$6$	−5.50500	+	2.38642i	−0.917500	+	0.397737i
$7$	−0.562989	+	0.975125i	−0.0804270	+	0.139304i	−0.903433	−	0.428728i	$-0.858962\pi$
$7$	−0.562989	+	0.975125i	−0.0804270	+	0.139304i	0.823006	+	0.568032i	$0.192295\pi$
$8$	3.54790	+	7.17024i	0.443488	+	0.896280i
$9$	0.106423	−	8.99937i	0.0118248	−	0.999930i
$10$	0.422919	+	2.73963i	0.0422919	+	0.273963i
$11$	−1.11157	+	1.92529i	−0.101052	+	0.175026i	−0.912118	−	0.409927i	$-0.865554\pi$
$11$	−1.11157	+	1.92529i	−0.101052	+	0.175026i	0.811067	+	0.584954i	$0.198887\pi$
$12$	−11.9911	+	0.463232i	−0.999255	+	0.0386026i
$13$	14.4573	−	8.34694i	1.11210	−	0.642072i	0.172729	−	0.984969i	$-0.444742\pi$
$13$	14.4573	−	8.34694i	1.11210	−	0.642072i	0.939373	+	0.342897i	$0.111408\pi$
$14$	−1.75564	+	1.41033i	−0.125403	+	0.100738i
$15$	−4.01000	−	1.09993i	−0.267333	−	0.0733285i
$16$	1.42291	+	15.9366i	0.0889319	+	0.996038i
$17$		−	20.2816i		−	1.19304i	−0.802600	−	0.596518i	$-0.796550\pi$
$17$		−	20.2816i		−	1.19304i	0.802600	−	0.596518i	$-0.203450\pi$
$18$	6.71436	−	16.7008i	0.373020	−	0.927823i
$19$		−	21.0174i		−	1.10618i	−0.833122	−	0.553089i	$-0.813449\pi$
$19$		−	21.0174i		−	1.10618i	0.833122	−	0.553089i	$-0.186551\pi$
$20$	−1.19515	+	5.41380i	−0.0597574	+	0.270690i
$21$	−0.854966	−	3.26794i	−0.0407127	−	0.155616i
$22$	−3.46633	+	2.78457i	−0.157561	+	0.126571i
$23$	−18.0360	+	10.4131i	−0.784176	+	0.452744i	−0.837908	−	0.545811i	$-0.816222\pi$
$23$	−18.0360	+	10.4131i	−0.784176	+	0.452744i	0.0537322	+	0.998555i	$0.482888\pi$
$24$	−22.6908	−	7.81844i	−0.945450	−	0.325769i
$25$	11.5394	−	19.9869i	0.461578	−	0.799476i
$26$	32.9969	−	5.09377i	1.26911	−	0.195914i
$27$	18.7503	+	19.4275i	0.694454	+	0.719537i
$28$	−4.29425	+	1.35818i	−0.153366	+	0.0485065i
$29$	−26.9695	+	46.7126i	−0.929984	+	1.61078i	−0.146640	+	0.989190i	$0.546846\pi$
$29$	−26.9695	+	46.7126i	−0.929984	+	1.61078i	−0.783343	+	0.621589i	$0.786487\pi$
$30$	−6.67960	−	4.95406i	−0.222653	−	0.165135i
$31$	9.19365	+	15.9239i	0.296569	+	0.513673i	0.975349	−	0.220669i	$-0.0708241\pi$
$31$	9.19365	+	15.9239i	0.296569	+	0.513673i	−0.678779	+	0.734342i	$0.737491\pi$
$32$	−8.88603	+	30.7415i	−0.277688	+	0.960671i
$33$	−1.68805	−	6.45224i	−0.0511530	−	0.195522i
$34$	14.6848	−	37.8118i	0.431906	−	1.11211i
$35$	−1.56065			−0.0445899
$36$	24.6100	−	26.2745i	0.683611	−	0.729847i
$37$		−	34.8194i		−	0.941065i	−0.882383	−	0.470532i	$-0.844062\pi$
$37$		−	34.8194i		−	0.941065i	0.882383	−	0.470532i	$-0.155938\pi$
$38$	15.2175	−	39.1835i	0.400461	−	1.03114i
$39$	−13.2479	+	48.2977i	−0.339689	+	1.23840i
$40$	−6.14800	+	9.22782i	−0.153700	+	0.230696i
$41$	−15.1169	+	8.72774i	−0.368705	+	0.212872i	−0.672892	−	0.739740i	$-0.734948\pi$
$41$	−15.1169	+	8.72774i	−0.368705	+	0.212872i	0.304188	+	0.952612i	$0.401615\pi$
$42$	0.772192	−	6.71159i	0.0183855	−	0.159800i
$43$	−44.2282	−	25.5352i	−1.02856	−	0.593841i	−0.111990	−	0.993709i	$-0.535722\pi$
$43$	−44.2282	−	25.5352i	−1.02856	−	0.593841i	−0.916573	+	0.399868i	$0.869056\pi$
$44$	−8.47857	+	2.68160i	−0.192695	+	0.0609454i
$45$	10.8761	−	6.10899i	0.241691	−	0.135755i
$46$	−41.1649	+	6.35467i	−0.894888	+	0.138145i
$47$	32.4750	+	18.7494i	0.690957	+	0.398924i	0.803970	−	0.594669i	$-0.202717\pi$
$47$	32.4750	+	18.7494i	0.690957	+	0.398924i	−0.113014	+	0.993593i	$0.536050\pi$
$48$	−36.6424	−	31.0054i	−0.763384	−	0.645945i
$49$	23.8661	+	41.3373i	0.487063	+	0.843618i
$50$	35.9849	−	28.9073i	0.719697	−	0.578146i
$51$	42.7687	+	43.2774i	0.838601	+	0.848577i
$52$	65.2055	+	14.3947i	1.25395	+	0.276822i
$53$	−52.6541			−0.993473			−0.496736	−	0.867901i	$-0.665468\pi$
$53$	−52.6541			−0.993473			−0.496736	+	0.867901i	$0.665468\pi$
$54$	20.8904	+	49.7955i	0.386860	+	0.922139i
$55$	−3.08135			−0.0560245
$56$	−8.98931	−	0.577118i	−0.160523	−	0.0103057i
$57$	44.3202	+	44.8474i	0.777547	+	0.786797i
$58$	−84.1024	+	67.5609i	−1.45004	+	1.16484i
$59$	−27.1346	−	46.9986i	−0.459909	−	0.796586i	0.539047	−	0.842276i	$-0.318785\pi$
$59$	−27.1346	−	46.9986i	−0.459909	−	0.796586i	−0.998956	+	0.0456902i	$0.985451\pi$
$60$	−8.86607	−	14.0724i	−0.147768	−	0.234539i
$61$	76.5667	+	44.2058i	1.25519	+	0.724686i	0.972136	−	0.234418i	$-0.0753184\pi$
$61$	76.5667	+	44.2058i	1.25519	+	0.724686i	0.283056	+	0.959103i	$0.408652\pi$
$62$	5.61048	+	36.3441i	0.0904915	+	0.586195i
$63$	8.71560	+	5.17032i	0.138343	+	0.0820686i
$64$	−38.8248	+	50.8786i	−0.606637	+	0.794979i
$65$	20.0384	+	11.5692i	0.308283	+	0.177987i
$66$	1.52462	−	13.2514i	0.0231003	−	0.200779i
$67$	−66.0909	+	38.1576i	−0.986432	+	0.569517i	−0.904206	−	0.427097i	$-0.859536\pi$
$67$	−66.0909	+	38.1576i	−0.986432	+	0.569517i	−0.0822260	+	0.996614i	$0.526203\pi$
$68$	54.7549	−	59.8615i	0.805219	−	0.880317i
$69$	16.5272	−	60.2531i	0.239525	−	0.873234i
$70$	−2.90958	−	1.12998i	−0.0415654	−	0.0161426i
$71$		−	69.4903i		−	0.978736i	−0.872077	−	0.489368i	$-0.837227\pi$
$71$		−	69.4903i		−	0.978736i	0.872077	−	0.489368i	$-0.162773\pi$
$72$	64.9053	−	31.1658i	0.901462	−	0.432858i
$73$	−82.6983			−1.13285			−0.566427	−	0.824112i	$-0.691675\pi$
$73$	−82.6983			−1.13285			−0.566427	+	0.824112i	$0.691675\pi$
$74$	25.2108	−	64.9151i	0.340687	−	0.877232i
$75$	17.5240	+	66.9823i	0.233654	+	0.893097i
$76$	56.7412	−	62.0331i	0.746595	−	0.816225i
$77$	−1.25160	−	2.16783i	−0.0162545	−	0.0281537i
$78$	−59.6682	+	80.4511i	−0.764977	+	1.03142i
$79$	19.8580	−	34.3950i	0.251366	−	0.435380i	−0.712536	−	0.701636i	$-0.752453\pi$
$79$	19.8580	−	34.3950i	0.251366	−	0.435380i	0.963902	+	0.266256i	$0.0857867\pi$
$80$	−18.1433	+	12.7524i	−0.226791	+	0.159404i
$81$	−80.9773	−	1.91549i	−0.999720	−	0.0236480i
$82$	−34.5023	+	5.32616i	−0.420760	+	0.0649531i
$83$	56.9488	−	98.6383i	0.686131	−	1.18841i	−0.286949	−	0.957946i	$-0.592641\pi$
$83$	56.9488	−	98.6383i	0.686131	−	1.18841i	0.973080	−	0.230467i	$-0.0740255\pi$
$84$	6.29912	−	11.9536i	0.0749895	−	0.142304i
$85$	24.3449	−	14.0555i	0.286411	−	0.165359i
$86$	−63.9677	−	79.6294i	−0.743811	−	0.925923i
$87$	−40.9565	−	156.548i	−0.470764	−	1.79941i
$88$	−17.7485	−	1.13946i	−0.201688	−	0.0129485i
$89$		−	25.3593i		−	0.284936i	−0.989799	−	0.142468i	$-0.954496\pi$
$89$		−	25.3593i		−	0.284936i	0.989799	−	0.142468i	$-0.0455038\pi$
$90$	24.6999	−	3.51444i	0.274444	−	0.0390494i
$91$			18.7969i			0.206560i
$92$	−81.3463	−	17.9580i	−0.884199	−	0.195195i
$93$	−53.1969	−	14.5917i	−0.572010	−	0.156900i
$94$	46.9689	+	58.4686i	0.499669	+	0.622007i
$95$	25.2281	−	14.5654i	0.265559	−	0.153320i
$96$	−45.8646	−	84.3353i	−0.477756	−	0.878493i
$97$	10.4267	−	18.0596i	0.107492	−	0.186182i	−0.807262	−	0.590194i	$-0.799051\pi$
$97$	10.4267	−	18.0596i	0.107492	−	0.186182i	0.914754	+	0.404012i	$0.132385\pi$
$98$	14.5644	+	94.3468i	0.148617	+	0.962723i
$99$	17.2081	+	10.2083i	0.173819	+	0.103114i
$100$	88.0182	−	27.8383i	0.880182	−	0.278383i
$101$	−37.6168	+	65.1543i	−0.372444	+	0.645092i	−0.989941	−	0.141481i	$-0.954813\pi$
$101$	−37.6168	+	65.1543i	−0.372444	+	0.645092i	0.617497	+	0.786573i	$0.288147\pi$
$102$	48.4005	+	111.650i	0.474514	+	1.09461i
$103$	−82.1673	−	142.318i	−0.797741	−	1.38173i	−0.921084	−	0.389364i	$-0.872695\pi$
$103$	−82.1673	−	142.318i	−0.797741	−	1.38173i	0.123343	−	0.992364i	$-0.460638\pi$
$104$	111.143	+	74.0484i	1.06868	+	0.712004i
$105$	3.33015	−	3.29100i	0.0317157	−	0.0313429i
$106$	−98.1650	−	38.1239i	−0.926085	−	0.359660i
$107$	136.212			1.27301			0.636504	−	0.771273i	$-0.280380\pi$
$107$	136.212			1.27301			0.636504	+	0.771273i	$0.280380\pi$
$108$	2.89266	+	107.961i	0.0267839	+	0.999641i
$109$			75.3671i			0.691441i	0.938337	+	0.345721i	$0.112366\pi$
$109$			75.3671i			0.691441i	−0.938337	+	0.345721i	$0.887634\pi$
$110$	−5.74468	−	2.23104i	−0.0522243	−	0.0202821i
$111$	73.4251	+	74.2985i	0.661487	+	0.669356i
$112$	−16.3413	−	7.58461i	−0.145904	−	0.0677197i
$113$	−95.2511	+	54.9933i	−0.842930	+	0.486666i	−0.858259	−	0.513217i	$-0.828454\pi$
$113$	−95.2511	+	54.9933i	−0.842930	+	0.486666i	0.0153290	+	0.999883i	$0.495120\pi$
$114$	50.1563	+	115.701i	0.439968	+	1.01492i
$115$	−24.9987	−	14.4330i	−0.217380	−	0.125504i
$116$	−205.712	+	65.0626i	−1.77338	+	0.560884i
$117$	−73.5786	−	130.995i	−0.628877	−	1.11962i
$118$	−16.5591	−	107.268i	−0.140331	−	0.909050i
$119$	19.7771	+	11.4183i	0.166194	+	0.0959523i
$120$	−6.34033	−	32.6551i	−0.0528361	−	0.272126i
$121$	58.0288	+	100.509i	0.479577	+	0.830652i
$122$	110.739	+	137.852i	0.907699	+	1.12994i
$123$	13.8523	−	50.5011i	0.112620	−	0.410578i
$124$	−15.8549	+	71.8199i	−0.127862	+	0.579193i
$125$	66.6392			0.533114
$126$	12.5053	+	15.9497i	0.0992482	+	0.126585i
$127$	139.760			1.10048			0.550238	−	0.835008i	$-0.314537\pi$
$127$	139.760			1.10048			0.550238	+	0.835008i	$0.314537\pi$
$128$	−109.221	+	66.7441i	−0.853289	+	0.521438i
$129$	148.222	−	38.7782i	1.14901	−	0.300606i
$130$	28.9818	+	36.0776i	0.222937	+	0.277520i
$131$	15.9691	+	27.6593i	0.121902	+	0.211140i	0.920518	−	0.390701i	$-0.127767\pi$
$131$	15.9691	+	27.6593i	0.121902	+	0.211140i	−0.798616	+	0.601841i	$0.794434\pi$
$132$	12.4370	−	23.6012i	0.0942197	−	0.178797i
$133$	20.4946	+	11.8325i	0.154094	+	0.0889665i
$134$	−150.844	+	23.2859i	−1.12570	+	0.173775i
$135$	−10.3254	+	35.9704i	−0.0764846	+	0.266447i
$136$	145.424	−	71.9572i	1.06929	−	0.529097i
$137$	67.6082	+	39.0336i	0.493491	+	0.284917i	0.726021	−	0.687672i	$-0.241367\pi$
$137$	67.6082	+	39.0336i	0.493491	+	0.284917i	−0.232531	+	0.972589i	$0.574701\pi$
$138$	74.4383	−	100.366i	0.539408	−	0.727288i
$139$	−22.9132	+	13.2289i	−0.164843	+	0.0951723i	−0.580152	−	0.814508i	$-0.697007\pi$
$139$	−22.9132	+	13.2289i	−0.164843	+	0.0951723i	0.415309	+	0.909680i	$0.363674\pi$
$140$	−4.60628	−	4.21333i	−0.0329020	−	0.0300952i
$141$	−108.834	+	28.4733i	−0.771870	+	0.201938i
$142$	50.3141	−	129.553i	0.354325	−	0.912348i
$143$			37.1127i			0.259529i
$144$	143.571	−	11.1093i	0.997020	−	0.0771477i
$145$	−74.7616			−0.515597
$146$	−154.178	−	59.8773i	−1.05601	−	0.410119i
$147$	−138.096	−	37.8791i	−0.939426	−	0.257681i
$148$	94.0030	−	102.770i	0.635155	−	0.694392i
$149$	60.9394	+	105.550i	0.408989	+	0.708390i	0.994777	−	0.102075i	$-0.0325481\pi$
$149$	60.9394	+	105.550i	0.408989	+	0.708390i	−0.585788	+	0.810465i	$0.699215\pi$
$150$	−15.8274	+	137.566i	−0.105516	+	0.917106i
$151$	−123.778	+	214.390i	−0.819724	+	1.41980i	0.0861624	+	0.996281i	$0.472540\pi$
$151$	−123.778	+	214.390i	−0.819724	+	1.41980i	−0.905886	+	0.423522i	$0.860794\pi$
$152$	150.700	−	74.5676i	0.991445	−	0.490576i
$153$	−182.522	−	2.15844i	−1.19295	−	0.0141074i
$154$	−0.763796	−	4.94779i	−0.00495971	−	0.0321285i
$155$	−12.7427	+	22.0711i	−0.0822113	+	0.142394i
$156$	−169.492	+	106.786i	−1.08649	+	0.684524i
$157$	25.8090	−	14.9009i	0.164389	−	0.0949099i	−0.415549	−	0.909571i	$-0.636410\pi$
$157$	25.8090	−	14.9009i	0.164389	−	0.0949099i	0.579937	+	0.814661i	$0.303077\pi$
$158$	61.9255	−	49.7458i	0.391933	−	0.314847i
$159$	112.355	−	111.034i	0.706633	−	0.698326i
$160$	−43.0586	+	10.6381i	−0.269116	+	0.0664883i
$161$		−	23.4499i		−	0.145651i
$162$	−149.582	−	62.2024i	−0.923348	−	0.383965i
$163$			107.162i			0.657434i	0.944428	+	0.328717i	$0.106616\pi$
$163$			107.162i			0.657434i	−0.944428	+	0.328717i	$0.893384\pi$
$164$	−68.1803	−	15.0515i	−0.415734	−	0.0917772i
$165$	6.57506	−	6.49777i	0.0398489	−	0.0393804i
$166$	177.590	−	142.662i	1.06982	−	0.859407i
$167$	−213.521	+	123.276i	−1.27857	+	0.738182i	−0.976585	−	0.215131i	$-0.930982\pi$
$167$	−213.521	+	123.276i	−1.27857	+	0.738182i	−0.301984	+	0.953313i	$0.597649\pi$
$168$	20.3986	−	17.7247i	0.121420	−	0.105504i
$169$	54.8427	−	94.9904i	0.324513	−	0.562074i
$170$	55.5640	−	8.57748i	0.326847	−	0.0504558i
$171$	−189.143	−	2.23674i	−1.10610	−	0.0130804i
$172$	−61.6022	−	194.772i	−0.358153	−	1.13239i
$173$	92.5883	−	160.368i	0.535192	−	0.926981i	−0.463962	−	0.885855i	$-0.653572\pi$
$173$	92.5883	−	160.368i	0.535192	−	0.926981i	0.999154	−	0.0411252i	$-0.0130942\pi$
$174$	36.9912	−	321.513i	0.212593	−	1.84778i
$175$	12.9932	+	22.5048i	0.0742466	+	0.128599i
$176$	−32.2642	−	14.9751i	−0.183320	−	0.0850857i
$177$	157.008	+	43.0668i	0.887053	+	0.243315i
$178$	18.3613	−	47.2783i	0.103153	−	0.265609i
$179$	15.9626			0.0891768			0.0445884	−	0.999005i	$-0.485802\pi$
$179$	15.9626			0.0891768			0.0445884	+	0.999005i	$0.485802\pi$
$180$	48.5936	+	11.3317i	0.269965	+	0.0629541i
$181$			6.32493i			0.0349443i	0.999847	+	0.0174722i	$0.00556185\pi$
$181$			6.32493i			0.0349443i	−0.999847	+	0.0174722i	$0.994438\pi$
$182$	−13.6098	+	35.0438i	−0.0747792	+	0.192549i
$183$	−256.599	+	67.1319i	−1.40218	+	0.366841i
$184$	−138.655	−	92.3781i	−0.753558	−	0.502055i
$185$	41.7953	−	24.1305i	0.225920	−	0.130435i
$186$	−88.6120	−	65.7209i	−0.476409	−	0.353338i
$187$	39.0480	+	22.5444i	0.208813	+	0.120558i
$188$	45.2320	+	143.013i	0.240596	+	0.760707i
$189$	−29.5004	+	7.34637i	−0.156087	+	0.0388697i
$190$	57.5797	−	8.88865i	0.303051	−	0.0467823i
$191$	196.282	+	113.324i	1.02766	+	0.593317i	0.916312	−	0.400465i	$-0.131151\pi$
$191$	196.282	+	113.324i	1.02766	+	0.593317i	0.111343	+	0.993782i	$0.464485\pi$
$192$	−24.4445	−	190.438i	−0.127315	−	0.991862i
$193$	−15.0900	−	26.1366i	−0.0781865	−	0.135423i	0.824281	−	0.566181i	$-0.191580\pi$
$193$	−15.0900	−	26.1366i	−0.0781865	−	0.135423i	−0.902468	+	0.430758i	$0.858246\pi$
$194$	32.5150	−	26.1199i	0.167603	−	0.134638i
$195$	−67.1549	+	17.5692i	−0.344384	+	0.0900984i
$196$	−41.1583	+	186.440i	−0.209991	+	0.951223i
$197$	133.378			0.677046			0.338523	−	0.940958i	$-0.390073\pi$
$197$	133.378			0.677046			0.338523	+	0.940958i	$0.390073\pi$
$198$	24.6905	+	31.4912i	0.124699	+	0.159046i
$199$	57.6075			0.289485			0.144743	−	0.989469i	$-0.453765\pi$
$199$	57.6075			0.289485			0.144743	+	0.989469i	$0.453765\pi$
$200$	184.252	+	11.8291i	0.921259	+	0.0591453i
$201$	60.5620	−	220.790i	0.301303	−	1.09846i
$202$	−117.305	+	94.2334i	−0.580719	+	0.466502i
$203$	−30.3671	−	52.5973i	−0.149592	−	0.259100i
$204$	9.39508	+	243.198i	0.0460543	+	1.19215i
$205$	−20.9526	−	12.0970i	−0.102208	−	0.0590097i
$206$	−50.1431	−	324.822i	−0.243413	−	1.57680i
$207$	91.7920	+	163.421i	0.443440	+	0.789475i
$208$	153.593	+	218.524i	0.738429	+	1.05059i
$209$	40.4645	+	23.3622i	0.193610	+	0.111781i
$210$	8.59136	−	3.72436i	0.0409112	−	0.0177351i
$211$	193.714	−	111.841i	0.918077	−	0.530052i	0.0350558	−	0.999385i	$-0.488839\pi$
$211$	193.714	−	111.841i	0.918077	−	0.530052i	0.883021	+	0.469333i	$0.155506\pi$
$212$	−155.409	−	142.152i	−0.733063	−	0.670527i
$213$	146.537	+	148.280i	0.687967	+	0.696151i
$214$	253.945	+	98.6236i	1.18666	+	0.460858i
$215$		−	70.7854i		−	0.329235i
$216$	−72.7759	+	203.371i	−0.336926	+	0.941531i
$217$	−20.7037			−0.0954086
$218$	−54.5692	+	140.510i	−0.250317	+	0.644540i
$219$	176.464	−	174.389i	0.805771	−	0.796298i
$220$	−9.09465	−	8.31881i	−0.0413393	−	0.0378128i
$221$	−169.289	−	293.218i	−0.766015	−	1.32678i
$222$	83.0937	+	191.681i	0.374296	+	0.863426i
$223$	−143.560	+	248.653i	−0.643766	+	1.11503i	0.340819	+	0.940129i	$0.389296\pi$
$223$	−143.560	+	248.653i	−0.643766	+	1.11503i	−0.984585	+	0.174906i	$0.944038\pi$
$224$	−24.9740	−	25.9721i	−0.111491	−	0.115947i
$225$	−178.642	−	105.975i	−0.793962	−	0.470999i
$226$	−217.398	+	33.5600i	−0.961938	+	0.148495i
$227$	−124.089	+	214.928i	−0.546647	+	0.946820i	0.451854	+	0.892092i	$0.350763\pi$
$227$	−124.089	+	214.928i	−0.546647	+	0.946820i	−0.998501	+	0.0547284i	$0.982571\pi$
$228$	9.73591	+	252.020i	0.0427014	+	1.10535i
$229$	−263.023	+	151.856i	−1.14857	+	0.663128i	−0.948539	−	0.316661i	$-0.897438\pi$
$229$	−263.023	+	151.856i	−1.14857	+	0.663128i	−0.200033	+	0.979789i	$0.564105\pi$
$230$	−36.1558	−	45.0081i	−0.157199	−	0.195687i
$231$	7.24209	+	1.98648i	0.0313510	+	0.00859948i
$232$	−430.626	−	27.6464i	−1.85615	−	0.119166i
$233$		−	191.277i		−	0.820933i	−0.911876	−	0.410466i	$-0.865366\pi$
$233$		−	191.277i		−	0.820933i	0.911876	−	0.410466i	$-0.134634\pi$
$234$	−42.3291	−	297.493i	−0.180893	−	1.27134i
$235$			51.9749i			0.221170i
$236$	46.7951	−	211.973i	0.198284	−	0.898192i
$237$	30.1567	+	115.268i	0.127243	+	0.486364i
$238$	28.6038	+	35.6071i	0.120184	+	0.149610i
$239$	114.707	−	66.2261i	0.479946	−	0.277097i	−0.240448	−	0.970662i	$-0.577294\pi$
$239$	114.707	−	66.2261i	0.479946	−	0.277097i	0.720394	+	0.693565i	$0.243961\pi$
$240$	11.8232	−	65.4708i	0.0492635	−	0.272795i
$241$	124.111	−	214.967i	0.514983	−	0.891978i	−0.484865	−	0.874589i	$-0.661131\pi$
$241$	124.111	−	214.967i	0.514983	−	0.891978i	0.999849	−	0.0173887i	$-0.00553528\pi$
$242$	35.4124	+	229.398i	0.146332	+	0.947926i
$243$	176.831	−	166.673i	0.727699	−	0.685897i
$244$	106.644	+	337.184i	0.437066	+	1.38190i
$245$	−33.0793	+	57.2951i	−0.135018	+	0.233857i
$246$	62.3904	−	84.1215i	0.253620	−	0.341957i
$247$	−175.431	−	303.855i	−0.710246	−	1.23018i
$248$	−81.5598	+	122.417i	−0.328870	+	0.493617i
$249$	86.4837	+	330.567i	0.347324	+	1.32758i
$250$	124.238	+	48.2498i	0.496952	+	0.192999i
$251$	−238.739			−0.951150			−0.475575	−	0.879675i	$-0.657760\pi$
$251$	−238.739			−0.951150			−0.475575	+	0.879675i	$0.657760\pi$
$252$	11.7658	+	38.7901i	0.0466895	+	0.153929i
$253$		−	46.2995i		−	0.183002i
$254$	260.561	+	101.193i	1.02583	+	0.398397i
$255$	−22.3083	+	81.3292i	−0.0874836	+	0.318938i
$256$	−251.951	+	45.3527i	−0.984182	+	0.177159i
$257$	41.8437	−	24.1585i	0.162816	−	0.0940018i	−0.416378	−	0.909192i	$-0.636701\pi$
$257$	41.8437	−	24.1585i	0.162816	−	0.0940018i	0.579194	+	0.815190i	$0.303367\pi$
$258$	304.414	+	35.0239i	1.17990	+	0.135751i
$259$	33.9533	+	19.6029i	0.131094	+	0.0756870i
$260$	27.9100	+	88.2449i	0.107346	+	0.339404i
$261$	417.514	+	247.680i	1.59967	+	0.948966i
$262$	9.74524	+	63.1287i	0.0371956	+	0.240949i
$263$	−332.934	−	192.220i	−1.26591	−	0.730873i	−0.291698	−	0.956510i	$-0.594220\pi$
$263$	−332.934	−	192.220i	−1.26591	−	0.730873i	−0.974211	+	0.225637i	$0.927554\pi$
$264$	40.2751	−	34.9956i	0.152557	−	0.132559i
$265$	−36.4903	−	63.2030i	−0.137699	−	0.238502i
$266$	29.6415	+	36.8989i	0.111434	+	0.138717i
$267$	53.4762	+	54.1123i	0.200285	+	0.202668i
$268$	−298.084	−	65.8048i	−1.11225	−	0.245540i
$269$	−113.224			−0.420909			−0.210454	−	0.977604i	$-0.567494\pi$
$269$	−113.224			−0.420909			−0.210454	+	0.977604i	$0.567494\pi$
$270$	−45.2943	+	59.5849i	−0.167757	+	0.220685i
$271$	399.534			1.47429			0.737147	−	0.675732i	$-0.236172\pi$
$271$	399.534			1.47429			0.737147	+	0.675732i	$0.236172\pi$
$272$	323.220	−	28.8589i	1.18831	−	0.106099i
$273$	−39.6378	−	40.1094i	−0.145194	−	0.146921i
$274$	97.7825	+	121.723i	0.356871	+	0.444246i
$275$	25.6537	+	44.4336i	0.0932863	+	0.161577i
$276$	211.448	−	133.219i	0.766114	−	0.482678i
$277$	−464.208	−	268.010i	−1.67584	−	0.967546i	−0.964267	−	0.264934i	$-0.914650\pi$
$277$	−464.208	−	268.010i	−1.67584	−	0.967546i	−0.711573	−	0.702612i	$-0.752017\pi$
$278$	−52.2963	+	8.07304i	−0.188116	+	0.0290397i
$279$	144.283	−	81.0424i	0.517144	−	0.290474i
$280$	−5.53703	−	11.1902i	−0.0197751	−	0.0399651i
$281$	−41.0005	−	23.6717i	−0.145909	−	0.0842407i	0.425268	−	0.905067i	$-0.360180\pi$
$281$	−41.0005	−	23.6717i	−0.145909	−	0.0842407i	−0.571177	+	0.820827i	$0.693513\pi$
$282$	−223.519	−	25.7166i	−0.792619	−	0.0911937i
$283$	247.514	−	142.902i	0.874608	−	0.504955i	0.00573140	−	0.999984i	$-0.498176\pi$
$283$	247.514	−	142.902i	0.874608	−	0.504955i	0.868877	+	0.495028i	$0.164842\pi$
$284$	187.605	−	205.102i	0.660581	−	0.722189i
$285$	−23.1176	+	84.2796i	−0.0811144	+	0.295718i
$286$	−26.8713	+	69.1907i	−0.0939555	+	0.241925i
$287$		−	19.6545i		−	0.0684825i
$288$	275.708	+	83.2403i	0.957320	+	0.289029i
$289$	−122.344			−0.423335
$290$	−139.381	−	54.1308i	−0.480624	−	0.186658i
$291$	15.8343	+	60.5234i	0.0544133	+	0.207984i
$292$	−244.086	−	223.263i	−0.835909	−	0.764600i
$293$	57.0269	+	98.7736i	0.194631	+	0.337111i	0.946780	−	0.321883i	$-0.104316\pi$
$293$	57.0269	+	98.7736i	0.194631	+	0.337111i	−0.752148	+	0.658994i	$0.770982\pi$
$294$	−230.031	−	170.607i	−0.782418	−	0.580296i
$295$	37.6096	−	65.1418i	0.127490	−	0.220820i
$296$	249.664	−	123.536i	0.843458	−	0.417351i
$297$	−58.2457	+	14.5047i	−0.196114	+	0.0488374i
$298$	37.1886	+	240.904i	0.124794	+	0.808402i
$299$	−173.835	+	301.092i	−0.581389	+	1.00700i
$300$	−129.112	+	245.010i	−0.430372	+	0.816699i
$301$	49.7999	−	28.7520i	0.165448	−	0.0955216i
$302$	−385.993	+	310.075i	−1.27812	+	1.02674i
$303$	−57.1257	−	218.352i	−0.188534	−	0.720634i
$304$	334.946	−	29.9058i	1.10179	−	0.0983745i
$305$			122.542i			0.401777i
$306$	−338.720	−	136.178i	−1.10693	−	0.445026i
$307$		−	178.258i		−	0.580644i	−0.956929	−	0.290322i	$-0.906238\pi$
$307$		−	178.258i		−	0.580644i	0.956929	−	0.290322i	$-0.0937624\pi$
$308$	2.15845	−	9.77738i	0.00700795	−	0.0317447i
$309$	475.443	+	130.412i	1.53865	+	0.422046i
$310$	−39.7373	+	31.9217i	−0.128185	+	0.102973i
$311$	148.082	−	85.4953i	0.476148	−	0.274904i	−0.242662	−	0.970111i	$-0.578020\pi$
$311$	148.082	−	85.4953i	0.476148	−	0.274904i	0.718810	+	0.695207i	$0.244687\pi$
$312$	−393.308	+	76.3649i	−1.26060	+	0.244759i
$313$	−51.7235	+	89.5878i	−0.165251	+	0.286223i	−0.936744	−	0.350014i	$-0.886177\pi$
$313$	−51.7235	+	89.5878i	−0.165251	+	0.286223i	0.771493	+	0.636237i	$0.219510\pi$
$314$	58.9057	−	9.09333i	0.187598	−	0.0289597i
$315$	−0.166089	+	14.0448i	−0.000527268	+	0.0445868i
$316$	151.468	−	47.9063i	0.479330	−	0.151602i
$317$	238.433	−	412.979i	0.752156	−	1.30277i	−0.194620	−	0.980879i	$-0.562347\pi$
$317$	238.433	−	412.979i	0.752156	−	1.30277i	0.946776	−	0.321893i	$-0.104319\pi$
$318$	289.860	−	125.655i	0.911511	−	0.395141i
$319$	−59.9569	−	103.848i	−0.187953	−	0.325543i
$320$	−87.9782	−	11.3432i	−0.274932	−	0.0354476i
$321$	−290.653	+	287.236i	−0.905460	+	0.894815i
$322$	16.9788	−	43.7185i	0.0527291	−	0.135772i
$323$	−426.266			−1.31971
$324$	−233.835	−	224.271i	−0.721712	−	0.692193i
$325$		−	385.276i		−	1.18547i
$326$	−77.5899	+	199.786i	−0.238006	+	0.612840i
$327$	−158.930	−	160.820i	−0.486024	−	0.491805i
$328$	−116.213	−	77.4267i	−0.354309	−	0.236057i
$329$	−36.5661	+	21.1114i	−0.111143	+	0.0641685i
$330$	16.9628	−	7.35340i	0.0514025	−	0.0222830i
$331$	146.687	+	84.6897i	0.443163	+	0.255860i	0.704938	−	0.709269i	$-0.250975\pi$
$331$	146.687	+	84.6897i	0.443163	+	0.255860i	−0.261775	+	0.965129i	$0.584308\pi$
$332$	434.382	−	137.386i	1.30838	−	0.413814i
$333$	−313.353	−	3.70560i	−0.940999	−	0.0111279i
$334$	−487.333	+	75.2302i	−1.45908	+	0.225240i
$335$	−91.6046	−	52.8879i	−0.273446	−	0.157874i
$336$	50.8634	−	18.2753i	0.151379	−	0.0543906i
$337$	296.462	+	513.487i	0.879709	+	1.52370i	0.851660	+	0.524094i	$0.175596\pi$
$337$	296.462	+	513.487i	0.879709	+	1.52370i	0.0280486	+	0.999607i	$0.491071\pi$
$338$	171.023	−	137.386i	0.505985	−	0.406467i
$339$	87.2827	−	318.206i	0.257471	−	0.938661i
$340$	109.801	+	24.2395i	0.322943	+	0.0712927i
$341$	−40.8774			−0.119875
$342$	−351.007	−	141.118i	−1.02634	−	0.412626i
$343$	−108.918			−0.317546
$344$	26.1760	−	407.723i	0.0760931	−	1.18524i
$345$	83.7782	−	21.9182i	0.242835	−	0.0635311i
$346$	288.729	−	231.941i	0.834478	−	0.670351i
$347$	173.414	+	300.362i	0.499752	+	0.865595i	1.00000		0.000286796i	$-9.12899e-5\pi$
$347$	173.414	+	300.362i	0.499752	+	0.865595i	−0.500248	+	0.865882i	$0.666758\pi$
$348$	301.754	−	572.626i	0.867110	−	1.64548i
$349$	197.166	+	113.834i	0.564945	+	0.326171i	0.755128	−	0.655578i	$-0.227575\pi$
$349$	197.166	+	113.834i	0.564945	+	0.326171i	−0.190183	+	0.981749i	$0.560908\pi$
$350$	7.92915	+	51.3642i	0.0226547	+	0.146755i
$351$	433.239	+	124.363i	1.23430	+	0.354309i
$352$	−49.3088	−	51.2794i	−0.140082	−	0.145680i
$353$	−133.728	−	77.2082i	−0.378834	−	0.218720i	0.298477	−	0.954417i	$-0.403521\pi$
$353$	−133.728	−	77.2082i	−0.378834	−	0.218720i	−0.677311	+	0.735697i	$0.736855\pi$
$354$	261.534	+	193.972i	0.738798	+	0.547944i
$355$	83.4123	−	48.1581i	0.234964	−	0.135657i
$356$	68.4633	−	74.8484i	0.192313	−	0.210248i
$357$	−66.2792	+	17.3401i	−0.185656	+	0.0485717i
$358$	29.7598	+	11.5577i	0.0831279	+	0.0322840i
$359$			10.6646i			0.0297064i	0.999890	+	0.0148532i	$0.00472809\pi$
$359$			10.6646i			0.0297064i	−0.999890	+	0.0148532i	$0.995272\pi$
$360$	82.3903	+	56.3102i	0.228862	+	0.156417i
$361$	−80.7299			−0.223628
$362$	−4.57953	+	11.7918i	−0.0126506	+	0.0325740i
$363$	−335.771	−	92.1007i	−0.924988	−	0.253721i
$364$	−50.7466	+	55.4795i	−0.139414	+	0.152416i
$365$	−57.3115	−	99.2665i	−0.157018	−	0.271963i
$366$	−526.993	−	60.6324i	−1.43987	−	0.165662i
$367$	9.10814	−	15.7758i	0.0248178	−	0.0429857i	−0.853350	−	0.521339i	$-0.825433\pi$
$367$	9.10814	−	15.7758i	0.0248178	−	0.0429857i	0.878168	+	0.478353i	$0.158766\pi$
$368$	−191.613	−	272.616i	−0.520689	−	0.740805i
$369$	76.9354	+	136.971i	0.208497	+	0.371196i
$370$	95.3921	−	14.7258i	0.257816	−	0.0397994i
$371$	29.6436	−	51.3443i	0.0799020	−	0.138394i
$372$	−117.618	−	186.685i	−0.316177	−	0.501842i
$373$	−88.6255	+	51.1680i	−0.237602	+	0.137180i	−0.614074	−	0.789248i	$-0.710470\pi$
$373$	−88.6255	+	51.1680i	−0.237602	+	0.137180i	0.376472	+	0.926428i	$0.377137\pi$
$374$	56.4755	+	70.3028i	0.151004	+	0.187975i
$375$	−142.196	+	140.525i	−0.379190	+	0.374733i
$376$	−19.2200	+	299.375i	−0.0511170	+	0.796209i
$377$			900.452i			2.38847i
$378$	−60.3179	−	7.66351i	−0.159571	−	0.0202738i
$379$		−	161.449i		−	0.425986i	−0.977054	−	0.212993i	$-0.931679\pi$
$379$		−	161.449i		−	0.425986i	0.977054	−	0.212993i	$-0.0683211\pi$
$380$	113.784	+	25.1189i	0.299431	+	0.0661023i
$381$	−298.224	+	294.718i	−0.782741	+	0.773539i
$382$	283.885	+	353.391i	0.743155	+	0.925106i
$383$	184.025	−	106.247i	0.480483	−	0.277407i	−0.240135	−	0.970740i	$-0.577192\pi$
$383$	184.025	−	106.247i	0.480483	−	0.277407i	0.720618	+	0.693333i	$0.243858\pi$
$384$	92.3125	−	372.739i	0.240397	−	0.970675i
$385$	1.73476	−	3.00470i	0.00450588	−	0.00780442i
$386$	−9.20876	−	59.6534i	−0.0238569	−	0.154543i
$387$	−234.507	+	395.308i	−0.605962	+	1.02147i
$388$	79.5309	−	25.1540i	0.204976	−	0.0648298i
$389$	−255.814	+	443.083i	−0.657620	+	1.13903i	0.323611	+	0.946190i	$0.395103\pi$
$389$	−255.814	+	443.083i	−0.657620	+	1.13903i	−0.981230	+	0.192840i	$0.938230\pi$
$390$	−137.920	−	15.8682i	−0.353642	−	0.0406877i
$391$	211.195	+	365.800i	0.540140	+	0.935550i
$392$	−211.724	+	317.786i	−0.540112	+	0.810679i
$393$	−92.4016	−	25.3454i	−0.235119	−	0.0644922i
$394$	248.662	+	96.5717i	0.631121	+	0.245106i
$395$	55.0478			0.139361
$396$	23.2304	+	76.5872i	0.0586625	+	0.193402i
$397$			198.582i			0.500206i	0.968219	+	0.250103i	$0.0804644\pi$
$397$			198.582i			0.500206i	−0.968219	+	0.250103i	$0.919536\pi$
$398$	107.400	+	41.7105i	0.269849	+	0.104800i
$399$	−68.6836	+	17.9691i	−0.172139	+	0.0450354i
$400$	334.943	+	155.460i	0.837358	+	0.388650i
$401$	357.504	−	206.405i	0.891532	−	0.514726i	0.0170888	−	0.999854i	$-0.494560\pi$
$401$	357.504	−	206.405i	0.891532	−	0.514726i	0.874443	+	0.485128i	$0.161227\pi$
$402$	272.770	−	367.778i	0.678533	−	0.914872i
$403$	265.831	+	153.478i	0.659630	+	0.380838i
$404$	−286.926	+	90.7487i	−0.710212	+	0.224625i
$405$	−53.8196	−	98.5282i	−0.132888	−	0.243279i
$406$	−18.5317	−	120.046i	−0.0456445	−	0.295681i
$407$	67.0374	+	38.7041i	0.164711	+	0.0950960i
$408$	−158.571	+	460.206i	−0.388654	+	1.12796i
$409$	104.695	+	181.337i	0.255978	+	0.443368i	0.965161	−	0.261657i	$-0.0842691\pi$
$409$	104.695	+	181.337i	0.255978	+	0.443368i	−0.709182	+	0.705025i	$0.750936\pi$
$410$	−30.3040	−	37.7235i	−0.0739121	−	0.0920086i
$411$	−226.576	+	59.2773i	−0.551280	+	0.144227i
$412$	141.702	−	641.884i	0.343937	−	1.55797i
$413$	61.1060			0.147956
$414$	52.8071	+	371.134i	0.127553	+	0.896459i
$415$	157.867			0.380401
$416$	128.129	+	518.611i	0.308002	+	1.24666i
$417$	20.9964	−	76.5463i	0.0503510	−	0.183564i
$418$	58.5243	+	72.8532i	0.140010	+	0.174290i
$419$	79.4861	+	137.674i	0.189704	+	0.328577i	0.945152	−	0.326632i	$-0.105914\pi$
$419$	79.4861	+	137.674i	0.189704	+	0.328577i	−0.755447	+	0.655209i	$0.772580\pi$
$420$	18.7138	−	0.722941i	0.0445567	−	0.00172129i
$421$	−186.964	−	107.944i	−0.444095	−	0.256399i	0.261238	−	0.965274i	$-0.415869\pi$
$421$	−186.964	−	107.944i	−0.444095	−	0.256399i	−0.705333	+	0.708876i	$0.749203\pi$
$422$	442.127	−	68.2516i	1.04769	−	0.161734i
$423$	172.189	−	290.259i	0.407067	−	0.686191i
$424$	−186.811	−	377.542i	−0.440593	−	0.890430i
$425$	−405.367	−	234.039i	−0.953804	−	0.550679i
$426$	165.833	+	382.544i	0.389280	+	0.897990i
$427$	−86.2124	+	49.7747i	−0.201903	+	0.116568i
$428$	402.032	+	367.736i	0.939327	+	0.859195i
$429$	−78.2611	−	79.1921i	−0.182427	−	0.184597i
$430$	51.2518	−	131.968i	0.119190	−	0.306902i
$431$			529.918i			1.22951i	0.788719	+	0.614754i	$0.210745\pi$
$431$			529.918i			1.22951i	−0.788719	+	0.614754i	$0.789255\pi$
$432$	−282.929	+	326.459i	−0.654927	+	0.755692i
$433$	−359.670			−0.830646			−0.415323	−	0.909674i	$-0.636332\pi$
$433$	−359.670			−0.830646			−0.415323	+	0.909674i	$0.636332\pi$
$434$	−38.5987	−	14.9904i	−0.0889370	−	0.0345401i
$435$	159.528	−	157.653i	0.366732	−	0.362420i
$436$	−203.471	+	222.447i	−0.466676	+	0.510200i
$437$	218.856	+	379.070i	0.500815	+	0.867438i
$438$	455.254	−	197.353i	1.03939	−	0.450578i
$439$	9.93781	−	17.2128i	0.0226374	−	0.0392091i	−0.854485	−	0.519476i	$-0.826127\pi$
$439$	9.93781	−	17.2128i	0.0226374	−	0.0392091i	0.877122	+	0.480267i	$0.159460\pi$
$440$	−10.9323	−	22.0940i	−0.0248462	−	0.0502137i
$441$	374.549	−	210.381i	0.849318	−	0.477053i
$442$	−103.310	−	669.230i	−0.233733	−	1.51410i
$443$	278.188	−	481.835i	0.627963	−	1.08766i	−0.359997	−	0.932954i	$-0.617222\pi$
$443$	278.188	−	481.835i	0.627963	−	1.08766i	0.987960	−	0.154710i	$-0.0494444\pi$
$444$	16.1294	+	417.521i	0.0363276	+	0.940363i
$445$	30.4399	−	17.5745i	0.0684043	−	0.0394932i
$446$	−447.680	+	359.629i	−1.00377	+	0.806344i
$447$	−352.612	−	96.7201i	−0.788841	−	0.216376i
$448$	−27.7551	−	66.5031i	−0.0619534	−	0.148444i
$449$		−	277.873i		−	0.618870i	−0.950921	−	0.309435i	$-0.899860\pi$
$449$		−	277.873i		−	0.618870i	0.950921	−	0.309435i	$-0.100140\pi$
$450$	−256.318	−	326.918i	−0.569595	−	0.726483i
$451$		−	38.8059i		−	0.0860441i
$452$	−429.602	−	94.8388i	−0.950447	−	0.209820i
$453$	−187.972	−	718.488i	−0.414950	−	1.58607i
$454$	−386.961	+	310.853i	−0.852338	+	0.684698i
$455$	−22.5628	+	13.0266i	−0.0495885	+	0.0286300i
$456$	−164.323	+	476.901i	−0.360358	+	1.04583i
$457$	354.954	−	614.799i	0.776705	−	1.34529i	−0.157125	−	0.987579i	$-0.550223\pi$
$457$	354.954	−	614.799i	0.776705	−	1.34529i	0.933831	−	0.357715i	$-0.116444\pi$
$458$	−600.315	+	92.6712i	−1.31073	+	0.202339i
$459$	394.021	−	380.285i	0.858434	−	0.828508i
$460$	−34.8188	−	110.089i	−0.0756931	−	0.239324i
$461$	266.139	−	460.966i	0.577308	−	0.999927i	−0.418479	−	0.908227i	$-0.637437\pi$
$461$	266.139	−	460.966i	0.577308	−	0.999927i	0.995787	−	0.0917001i	$-0.0292301\pi$
$462$	12.0634	+	8.94707i	0.0261113	+	0.0193660i
$463$	−116.898	−	202.473i	−0.252479	−	0.437306i	0.711729	−	0.702454i	$-0.247912\pi$
$463$	−116.898	−	202.473i	−0.252479	−	0.437306i	−0.964208	+	0.265148i	$0.914579\pi$
$464$	−782.815	−	363.335i	−1.68710	−	0.783049i
$465$	−19.3514	−	73.9670i	−0.0416159	−	0.159069i
$466$	138.493	−	356.606i	0.297196	−	0.765249i
$467$	602.162			1.28943			0.644713	−	0.764425i	$-0.276977\pi$
$467$	602.162			1.28943			0.644713	+	0.764425i	$0.276977\pi$
$468$	136.483	−	585.277i	0.291630	−	1.25059i
$469$		−	85.9292i		−	0.183218i
$470$	−37.6322	+	96.8988i	−0.0800684	+	0.206168i
$471$	−23.6499	+	86.2204i	−0.0502122	+	0.183058i
$472$	240.720	−	361.308i	0.510000	−	0.765483i
$473$	98.3252	−	56.7681i	0.207876	−	0.120017i
$474$	−27.2370	+	236.734i	−0.0574621	+	0.499438i
$475$	−420.072	−	242.529i	−0.884363	−	0.510587i
$476$	27.5461	+	87.0942i	0.0578699	+	0.182971i
$477$	−5.60363	+	473.853i	−0.0117476	+	0.993404i
$478$	261.803	−	40.4149i	0.547706	−	0.0845500i
$479$	−728.715	−	420.724i	−1.52133	−	0.878337i	−0.999683	−	0.0251729i	$-0.991986\pi$
$479$	−728.715	−	420.724i	−1.52133	−	0.878337i	−0.521642	−	0.853165i	$-0.674680\pi$
$480$	69.4464	−	113.499i	0.144680	−	0.236457i
$481$	−290.635	−	503.395i	−0.604231	−	1.04656i
$482$	387.030	−	310.909i	0.802968	−	0.645038i
$483$	49.4497	+	50.0379i	0.102380	+	0.103598i
$484$	−100.074	+	453.316i	−0.206764	+	0.936603i
$485$	28.9037			0.0595953
$486$	450.351	−	182.701i	0.926649	−	0.375929i
$487$	−475.714			−0.976826			−0.488413	−	0.872613i	$-0.662424\pi$
$487$	−475.714			−0.976826			−0.488413	+	0.872613i	$0.662424\pi$
$488$	−45.3153	+	705.840i	−0.0928592	+	1.44639i
$489$	−225.976	−	228.664i	−0.462119	−	0.467616i
$490$	−103.155	+	82.8665i	−0.210521	+	0.169115i
$491$	−110.548	−	191.474i	−0.225148	−	0.389968i	0.731216	−	0.682146i	$-0.238953\pi$
$491$	−110.548	−	191.474i	−0.225148	−	0.389968i	−0.956364	+	0.292178i	$0.905620\pi$
$492$	177.225	−	111.657i	0.360213	−	0.226946i
$493$	947.407	+	546.985i	1.92172	+	1.10950i
$494$	−107.058	−	693.508i	−0.216716	−	1.40386i
$495$	−0.327928	+	27.7302i	−0.000662480	+	0.0560206i
$496$	−240.691	+	169.174i	−0.485263	+	0.341076i
$497$	67.7617	+	39.1222i	0.136341	+	0.0787168i
$498$	−78.1107	+	678.907i	−0.156849	+	1.36327i
$499$	−687.365	+	396.850i	−1.37748	+	0.795291i	−0.991856	−	0.127363i	$-0.959349\pi$
$499$	−687.365	+	396.850i	−1.37748	+	0.795291i	−0.385628	+	0.922654i	$0.626015\pi$
$500$	196.687	+	179.908i	0.393374	+	0.359816i
$501$	195.659	−	713.311i	0.390536	−	1.42377i
$502$	−445.090	−	172.858i	−0.886633	−	0.344338i
$503$			60.2823i			0.119845i	0.998203	+	0.0599227i	$0.0190854\pi$
$503$			60.2823i			0.119845i	−0.998203	+	0.0599227i	$0.980915\pi$
$504$	−6.15038	+	80.8367i	−0.0122031	+	0.160390i
$505$	−104.277			−0.206489
$506$	33.5229	−	86.3179i	0.0662508	−	0.170589i
$507$	83.2853	+	318.342i	0.164271	+	0.627894i
$508$	412.505	+	377.315i	0.812018	+	0.742747i
$509$	−43.3811	−	75.1383i	−0.0852282	−	0.147619i	0.820260	−	0.571990i	$-0.193829\pi$
$509$	−43.3811	−	75.1383i	−0.0852282	−	0.147619i	−0.905488	+	0.424371i	$0.860495\pi$
$510$	−100.476	+	135.473i	−0.197012	+	0.265633i
$511$	46.5582	−	80.6412i	0.0911120	−	0.157811i
$512$	−502.559	−	97.8708i	−0.981560	−	0.191154i
$513$	408.315	−	394.081i	0.795936	−	0.768189i
$514$	95.5026	−	14.7428i	0.185803	−	0.0286826i
$515$	113.887	−	197.258i	0.221140	−	0.383026i
$516$	542.171	+	285.706i	1.05072	+	0.553693i
$517$	−72.1962	+	41.6825i	−0.139644	+	0.0806238i
$518$	49.1070	+	61.1302i	0.0948011	+	0.118012i
$519$	140.607	+	537.441i	0.270918	+	1.03553i
$520$	−11.8595	+	184.727i	−0.0228068	+	0.355243i
$521$		−	762.810i		−	1.46413i	−0.681237	−	0.732063i	$-0.738558\pi$
$521$		−	762.810i		−	1.46413i	0.681237	−	0.732063i	$-0.261442\pi$
$522$	599.055	+	764.058i	1.14762	+	1.46371i
$523$			921.604i			1.76215i	0.472978	+	0.881074i	$0.343179\pi$
$523$			921.604i			1.76215i	−0.472978	+	0.881074i	$0.656821\pi$
$524$	−27.5396	+	124.749i	−0.0525564	+	0.238071i
$525$	−75.1819	−	20.6221i	−0.143204	−	0.0392803i
$526$	−481.526	−	599.422i	−0.915450	−	1.13959i
$527$	322.962	−	186.462i	0.612830	−	0.353818i
$528$	100.425	−	36.0827i	0.190199	−	0.0683385i
$529$	−47.6340	+	82.5045i	−0.0900454	+	0.155963i
$530$	−22.2684	−	144.252i	−0.0420159	−	0.272174i
$531$	−425.845	+	239.193i	−0.801968	+	0.450457i
$532$	28.5454	+	90.2538i	0.0536567	+	0.169650i
$533$	−145.700	+	252.360i	−0.273358	+	0.473470i
$534$	60.5180	+	139.603i	0.113330	+	0.261429i
$535$	94.3975	+	163.501i	0.176444	+	0.305610i
$536$	−508.083	−	338.509i	−0.947917	−	0.631546i
$537$	−34.0615	+	33.6611i	−0.0634293	+	0.0626836i
$538$	−211.089	−	81.9796i	−0.392358	−	0.152378i
$539$	−106.115			−0.196874
$540$	−127.586	+	78.2914i	−0.236270	+	0.144984i
$541$			841.319i			1.55512i	0.628810	+	0.777559i	$0.283542\pi$
$541$			841.319i			1.55512i	−0.628810	+	0.777559i	$0.716458\pi$
$542$	744.866	+	289.280i	1.37429	+	0.533728i
$543$	−13.3376	−	13.4963i	−0.0245629	−	0.0248550i
$544$	623.487	+	180.223i	1.14612	+	0.331292i
$545$	−90.4665	+	52.2309i	−0.165994	+	0.0958364i
$546$	−44.8574	−	103.477i	−0.0821564	−	0.189518i
$547$	−282.340	−	163.009i	−0.516161	−	0.298006i	0.219201	−	0.975680i	$-0.429655\pi$
$547$	−282.340	−	163.009i	−0.516161	−	0.298006i	−0.735363	+	0.677674i	$0.762988\pi$
$548$	94.1666	+	297.732i	0.171837	+	0.543307i
$549$	405.973	−	684.348i	0.739477	−	1.24654i
$550$	15.6553	+	101.414i	0.0284643	+	0.184389i
$551$	981.776	+	566.829i	1.78181	+	1.02873i
$552$	490.667	−	95.2680i	0.888889	−	0.172587i
$553$	22.3596	+	38.7280i	0.0404333	+	0.0700325i
$554$	−671.388	−	835.769i	−1.21189	−	1.50861i
$555$	−38.2988	+	139.626i	−0.0690069	+	0.251578i
$556$	−103.343	−	22.8140i	−0.185869	−	0.0410324i
$557$	108.173			0.194206			0.0971029	−	0.995274i	$-0.469042\pi$
$557$	108.173			0.194206			0.0971029	+	0.995274i	$0.469042\pi$
$558$	327.671	−	46.6229i	0.587224	−	0.0835536i
$559$	−852.562			−1.52515
$560$	−2.22066	−	24.8714i	−0.00396547	−	0.0444133i
$561$	−130.862	+	34.2363i	−0.233265	+	0.0610273i
$562$	−59.2995	−	73.8182i	−0.105515	−	0.131349i
$563$	−408.191	−	707.008i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$563$	−408.191	−	707.008i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$564$	−398.095	−	209.782i	−0.705841	−	0.371954i
$565$	−132.022	−	76.2228i	−0.233667	−	0.134908i
$566$	564.918	−	87.2070i	0.998088	−	0.154076i
$567$	47.4572	−	77.8846i	0.0836987	−	0.137363i
$568$	498.262	−	246.545i	0.877222	−	0.434058i
$569$	339.011	+	195.728i	0.595801	+	0.343986i	0.767388	−	0.641183i	$-0.221556\pi$
$569$	339.011	+	195.728i	0.595801	+	0.343986i	−0.171587	+	0.985169i	$0.554889\pi$
$570$	−104.121	+	140.388i	−0.182669	+	0.246294i
$571$	−207.111	+	119.576i	−0.362717	+	0.209415i	−0.670272	−	0.742116i	$-0.733823\pi$
$571$	−207.111	+	119.576i	−0.362717	+	0.209415i	0.307555	+	0.951530i	$0.400489\pi$
$572$	−100.194	+	109.539i	−0.175165	+	0.191501i
$573$	−657.802	+	172.096i	−1.14800	+	0.300341i
$574$	14.2307	−	36.6426i	0.0247922	−	0.0638373i
$575$			480.647i			0.835907i
$576$	453.744	+	354.813i	0.787750	+	0.615995i
$577$	684.269			1.18591			0.592954	−	0.805236i	$-0.297961\pi$
$577$	684.269			1.18591			0.592954	+	0.805236i	$0.297961\pi$
$578$	−228.090	−	88.5824i	−0.394620	−	0.153257i
$579$	87.3149	+	23.9501i	0.150803	+	0.0413647i
$580$	−220.660	−	201.836i	−0.380449	−	0.347993i
$581$	64.1231	+	111.064i	0.110367	+	0.191161i
$582$	−14.3013	+	124.301i	−0.0245726	+	0.213575i
$583$	58.5285	−	101.374i	0.100392	−	0.173884i
$584$	−293.406	−	592.967i	−0.502407	−	1.01535i
$585$	106.248	−	179.102i	0.181620	−	0.306157i
$586$	34.8010	+	225.437i	0.0593874	+	0.384706i
$587$	483.688	−	837.773i	0.824001	−	1.42721i	−0.0786797	−	0.996900i	$-0.525070\pi$
$587$	483.688	−	837.773i	0.824001	−	1.42721i	0.902681	−	0.430311i	$-0.141596\pi$
$588$	−305.328	−	484.622i	−0.519266	−	0.824187i
$589$	334.678	−	193.226i	0.568213	−	0.328058i
$590$	117.283	−	94.2153i	0.198784	−	0.159687i
$591$	−284.605	+	281.260i	−0.481566	+	0.475905i
$592$	554.903	−	49.5449i	0.937336	−	0.0836907i
$593$			600.206i			1.01215i	0.862489	+	0.506076i	$0.168905\pi$
$593$			600.206i			1.01215i	−0.862489	+	0.506076i	$0.831095\pi$
$594$	−119.092	−	15.1309i	−0.200491	−	0.0254728i
$595$			31.6525i			0.0531974i
$596$	−105.093	+	476.053i	−0.176331	+	0.798746i
$597$	−122.924	+	121.479i	−0.205904	+	0.203483i
$598$	−542.092	+	435.472i	−0.906508	+	0.728214i
$599$	−509.888	+	294.384i	−0.851231	+	0.491459i	−0.861066	−	0.508493i	$-0.830203\pi$
$599$	−509.888	+	294.384i	−0.851231	+	0.491459i	0.00983473	+	0.999952i	$0.496869\pi$
$600$	−418.106	+	363.298i	−0.696843	+	0.605497i
$601$	−542.913	+	940.353i	−0.903349	+	1.56465i	−0.0802311	+	0.996776i	$0.525566\pi$
$601$	−542.913	+	940.353i	−0.903349	+	1.56465i	−0.823118	+	0.567870i	$0.807768\pi$
$602$	113.662	−	17.5461i	0.188807	−	0.0291463i
$603$	336.361	+	598.838i	0.557812	+	0.993097i
$604$	−944.129	+	298.609i	−1.56313	+	0.494385i
$605$	−80.4302	+	139.309i	−0.132942	+	0.230263i
$606$	51.5950	−	448.444i	0.0851403	−	0.740006i
$607$	150.149	+	260.065i	0.247362	+	0.428444i	0.962793	−	0.270240i	$-0.0871029\pi$
$607$	150.149	+	260.065i	0.247362	+	0.428444i	−0.715431	+	0.698684i	$0.753770\pi$
$608$	646.105	+	186.761i	1.06267	+	0.307173i
$609$	175.712	+	48.1972i	0.288526	+	0.0791416i
$610$	−88.7259	+	228.460i	−0.145452	+	0.374524i
$611$	626.001			1.02455
$612$	−532.889	−	499.130i	−0.870734	−	0.815572i
$613$		−	310.763i		−	0.506955i	−0.967341	−	0.253477i	$-0.918426\pi$
$613$		−	310.763i		−	0.506955i	0.967341	−	0.253477i	$-0.0815743\pi$
$614$	129.067	−	332.333i	0.210206	−	0.541258i
$615$	70.2186	−	18.3707i	0.114177	−	0.0298711i
$616$	11.1033	−	16.6655i	0.0180249	−	0.0270544i
$617$	378.986	−	218.808i	0.614240	−	0.354631i	−0.160383	−	0.987055i	$-0.551273\pi$
$617$	378.986	−	218.808i	0.614240	−	0.354631i	0.774623	+	0.632423i	$0.217940\pi$
$618$	791.962	+	587.374i	1.28149	+	0.950444i
$619$	−149.702	−	86.4306i	−0.241845	−	0.139629i	0.374179	−	0.927356i	$-0.377924\pi$
$619$	−149.702	−	86.4306i	−0.241845	−	0.139629i	−0.616025	+	0.787727i	$0.711258\pi$
$620$	−97.1964	+	30.7412i	−0.156768	+	0.0495826i
$621$	−540.481	−	155.147i	−0.870340	−	0.249834i
$622$	337.978	−	52.1740i	0.543373	−	0.0838810i
$623$	24.7285	+	14.2770i	0.0396926	+	0.0229165i
$624$	−788.551	−	142.403i	−1.26370	−	0.228210i
$625$	−242.304	−	419.683i	−0.387686	−	0.671492i
$626$	−161.296	+	129.572i	−0.257661	+	0.206984i
$627$	−135.609	+	35.4783i	−0.216282	+	0.0565843i
$628$	116.404	+	25.6973i	0.185357	+	0.0409193i
$629$	−706.193			−1.12272
$630$	−10.4788	+	26.0641i	−0.0166329	+	0.0413716i
$631$	1044.76			1.65572			0.827858	−	0.560937i	$-0.189559\pi$
$631$	1044.76			1.65572			0.827858	+	0.560937i	$0.189559\pi$
$632$	317.074	+	20.3563i	0.501700	+	0.0322094i
$633$	−177.509	+	647.142i	−0.280425	+	1.02234i
$634$	743.536	−	597.296i	1.17277	−	0.942107i
$635$	96.8566	+	167.761i	0.152530	+	0.264190i
$636$	631.378	−	24.3910i	0.992732	−	0.0383507i
$637$	690.079	+	398.418i	1.08333	+	0.625459i
$638$	−36.5890	−	237.020i	−0.0573496	−	0.371505i
$639$	−625.369	−	7.39539i	−0.978668	−	0.0115734i
$640$	−155.808	−	84.8479i	−0.243450	−	0.132575i
$641$	−66.0620	−	38.1409i	−0.103061	−	0.0595022i	0.447584	−	0.894242i	$-0.352285\pi$
$641$	−66.0620	−	38.1409i	−0.103061	−	0.0595022i	−0.550644	+	0.834740i	$0.685618\pi$
$642$	−749.846	+	325.059i	−1.16799	+	0.506323i
$643$	−195.821	+	113.057i	−0.304543	+	0.175828i	−0.644482	−	0.764620i	$-0.722927\pi$
$643$	−195.821	+	113.057i	−0.304543	+	0.175828i	0.339939	+	0.940447i	$0.389594\pi$
$644$	63.3083	−	69.2127i	0.0983048	−	0.107473i
$645$	149.268	+	151.044i	0.231423	+	0.234176i
$646$	−794.704	−	308.636i	−1.23019	−	0.477765i
$647$		−	619.832i		−	0.958010i	−0.877812	−	0.479005i	$-0.840998\pi$
$647$		−	619.832i		−	0.958010i	0.877812	−	0.479005i	$-0.159002\pi$
$648$	−273.565	−	587.423i	−0.422168	−	0.906517i
$649$	120.648			0.185898
$650$	278.957	−	718.285i	0.429165	−	1.10505i
$651$	44.1780	−	43.6587i	0.0678618	−	0.0670640i
$652$	−289.308	+	316.290i	−0.443724	+	0.485107i
$653$	−135.140	−	234.070i	−0.206953	−	0.358453i	0.743800	−	0.668402i	$-0.233021\pi$
$653$	−135.140	−	234.070i	−0.206953	−	0.358453i	−0.950753	+	0.309949i	$0.899688\pi$
$654$	−179.858	−	414.896i	−0.275012	−	0.634397i
$655$	−22.1338	+	38.3369i	−0.0337921	+	0.0585296i
$656$	−160.601	−	228.493i	−0.244818	−	0.348313i
$657$	−8.80104	+	744.233i	−0.0133958	+	1.13277i
$658$	−83.4572	+	12.8834i	−0.126835	+	0.0195796i
$659$	−171.355	+	296.796i	−0.260023	+	0.450373i	−0.966248	−	0.257615i	$-0.917064\pi$
$659$	−171.355	+	296.796i	−0.260023	+	0.450373i	0.706225	+	0.707988i	$0.250397\pi$
$660$	36.9486	−	1.42738i	0.0559828	−	0.00216269i
$661$	165.843	−	95.7496i	0.250897	−	0.144856i	−0.369278	−	0.929319i	$-0.620395\pi$
$661$	165.843	−	95.7496i	0.250897	−	0.144856i	0.620175	+	0.784463i	$0.287062\pi$
$662$	212.155	+	264.098i	0.320476	+	0.398940i
$663$	979.554	+	268.688i	1.47746	+	0.405261i
$664$	909.309	+	58.3781i	1.36944	+	0.0879189i
$665$			32.8007i			0.0493244i
$666$	−581.512	−	233.790i	−0.873142	−	0.351036i
$667$		−	1123.35i		−	1.68418i
$668$	−963.024	−	212.597i	−1.44165	−	0.318259i
$669$	−218.013	−	833.312i	−0.325879	−	1.24561i
$670$	−132.489	−	164.927i	−0.197744	−	0.246159i
$671$	−170.218	+	98.2754i	−0.253678	+	0.146461i
$672$	108.059	+	2.75613i	0.160802	+	0.00410138i
$673$	−163.581	+	283.331i	−0.243063	+	0.420997i	−0.961585	−	0.274507i	$-0.911485\pi$
$673$	−163.581	+	283.331i	−0.243063	+	0.420997i	0.718522	+	0.695504i	$0.244819\pi$
$674$	180.918	+	1171.97i	0.268424	+	1.73882i
$675$	604.663	−	150.577i	0.895798	−	0.223077i
$676$	418.318	−	132.305i	0.618813	−	0.195718i
$677$	−554.307	+	960.088i	−0.818770	+	1.41815i	0.0878198	+	0.996136i	$0.472010\pi$
$677$	−554.307	+	960.088i	−0.818770	+	1.41815i	−0.906589	+	0.422014i	$0.861323\pi$
$678$	393.120	−	530.047i	0.579823	−	0.781780i
$679$	11.7403	+	20.3347i	0.0172905	+	0.0299481i
$680$	187.155	+	124.691i	0.275228	+	0.183370i
$681$	−188.444	−	720.290i	−0.276716	−	1.05770i
$682$	−76.2093	−	29.5971i	−0.111744	−	0.0433975i
$683$	168.798			0.247142			0.123571	−	0.992336i	$-0.460565\pi$
$683$	168.798			0.247142			0.123571	+	0.992336i	$0.460565\pi$
$684$	−552.221	−	517.237i	−0.807340	−	0.756195i
$685$			108.204i			0.157962i
$686$	−203.060	−	78.8617i	−0.296007	−	0.114959i
$687$	241.019	−	878.682i	0.350829	−	1.27901i
$688$	344.011	−	741.181i	0.500016	−	1.07730i
$689$	−761.237	+	439.500i	−1.10484	+	0.637881i
$690$	172.061	+	19.7962i	0.249363	+	0.0286901i
$691$	−11.1188	−	6.41947i	−0.0160910	−	0.00929012i	0.491933	−	0.870633i	$-0.336291\pi$
$691$	−11.1188	−	6.41947i	−0.0160910	−	0.00929012i	−0.508024	+	0.861343i	$0.669624\pi$
$692$	706.225	−	223.364i	1.02056	−	0.322781i
$693$	−19.6423	+	11.0329i	−0.0283439	+	0.0159205i
$694$	105.827	+	685.535i	0.152488	+	0.987803i
$695$	−31.7586	−	18.3358i	−0.0456958	−	0.0263825i
$696$	977.180	−	849.086i	1.40399	−	1.21995i
$697$	177.013	+	306.595i	0.253964	+	0.439878i
$698$	285.163	+	354.982i	0.408543	+	0.508570i
$699$	403.354	+	408.153i	0.577045	+	0.583909i
$700$	−22.4074	+	101.501i	−0.0320106	+	0.145002i
$701$	−275.178			−0.392551			−0.196275	−	0.980549i	$-0.562885\pi$
$701$	−275.178			−0.392551			−0.196275	+	0.980549i	$0.562885\pi$
$702$	717.659	+	545.538i	1.02231	+	0.777120i
$703$	−731.812			−1.04098
$704$	−54.7998	−	131.304i	−0.0778406	−	0.186511i
$705$	−109.602	−	110.905i	−0.155463	−	0.157313i
$706$	−193.413	−	240.768i	−0.273956	−	0.341031i
$707$	−42.3557	−	73.3623i	−0.0599091	−	0.103766i
$708$	347.144	+	550.993i	0.490316	+	0.778238i
$709$	−1131.99	−	653.558i	−1.59661	−	0.921802i	−0.992134	−	0.125176i	$-0.960050\pi$
$709$	−1131.99	−	653.558i	−1.59661	−	0.921802i	−0.604473	−	0.796625i	$-0.706616\pi$
$710$	190.377	−	29.3888i	0.268137	−	0.0413926i
$711$	−307.420	−	182.370i	−0.432377	−	0.256497i
$712$	181.832	−	89.9723i	0.255383	−	0.126366i
$713$	−331.634	−	191.469i	−0.465125	−	0.268540i
$714$	−136.122	−	15.6613i	−0.190647	−	0.0219346i
$715$	−44.5480	+	25.7198i	−0.0623050	+	0.0359718i
$716$	47.1140	+	43.0949i	0.0658017	+	0.0601883i
$717$	−105.111	+	383.202i	−0.146598	+	0.534452i
$718$	−7.72164	+	19.8824i	−0.0107544	+	0.0276914i
$719$		−	697.960i		−	0.970737i	−0.874310	−	0.485368i	$-0.838686\pi$
$719$		−	697.960i		−	0.970737i	0.874310	−	0.485368i	$-0.161314\pi$
$720$	112.832	+	164.636i	0.156712	+	0.228660i
$721$	185.037			0.256640
$722$	−150.508	−	58.4521i	−0.208460	−	0.0809586i
$723$	188.478	+	720.419i	0.260688	+	0.996430i
$724$	−17.0756	+	18.6681i	−0.0235851	+	0.0257847i
$725$	622.427	+	1078.08i	0.858520	+	1.48700i
$726$	−559.305	−	414.820i	−0.770393	−	0.571377i
$727$	557.371	−	965.394i	0.766672	−	1.32791i	−0.172686	−	0.984977i	$-0.555245\pi$
$727$	557.371	−	965.394i	0.766672	−	1.32791i	0.939358	−	0.342938i	$-0.111422\pi$
$728$	−134.779	+	66.6896i	−0.185135	+	0.0916067i
$729$	−25.8561	+	728.541i	−0.0354679	+	0.999371i
$730$	−34.9747	−	226.562i	−0.0479105	−	0.310360i
$731$	−517.894	+	897.019i	−0.708474	+	1.22711i
$732$	−938.593	−	494.606i	−1.28223	−	0.675692i
$733$	1144.81	−	660.955i	1.56181	−	0.901712i	0.564736	−	0.825271i	$-0.308978\pi$
$733$	1144.81	−	660.955i	1.56181	−	0.901712i	0.997074	−	0.0764405i	$-0.0243555\pi$
$734$	28.4030	−	22.8166i	0.0386962	−	0.0310854i
$735$	−50.2349	−	192.013i	−0.0683469	−	0.261243i
$736$	−159.846	−	646.986i	−0.217182	−	0.879057i
$737$		−	169.659i		−	0.230202i
$738$	44.2602	+	311.066i	0.0599732	+	0.421498i
$739$		−	514.111i		−	0.695685i	−0.937553	−	0.347842i	$-0.886914\pi$
$739$		−	514.111i		−	0.695685i	0.937553	−	0.347842i	$-0.113086\pi$
$740$	188.505	+	41.6143i	0.254737	+	0.0562356i
$741$	1015.09	+	278.435i	1.36989	+	0.375756i
$742$	92.4414	−	74.2598i	0.124584	−	0.100081i
$743$	622.933	−	359.650i	0.838402	−	0.484052i	−0.0183187	−	0.999832i	$-0.505831\pi$
$743$	622.933	−	359.650i	0.838402	−	0.484052i	0.856721	+	0.515781i	$0.172498\pi$
$744$	−84.1113	−	433.205i	−0.113053	−	0.582265i
$745$	−84.4643	+	146.296i	−0.113375	+	0.196371i
$746$	−202.276	+	31.2255i	−0.271147	+	0.0418573i
$747$	−881.622	−	523.001i	−1.18022	−	0.700135i
$748$	54.3871	+	171.959i	0.0727100	+	0.229892i
$749$	−76.6858	+	132.824i	−0.102384	+	0.177335i
$750$	−366.849	+	159.029i	−0.489131	+	0.212039i
$751$	−125.288	−	217.005i	−0.166828	−	0.288955i	0.770475	−	0.637470i	$-0.220019\pi$
$751$	−125.288	−	217.005i	−0.166828	−	0.288955i	−0.937303	+	0.348516i	$0.886686\pi$
$752$	−252.593	+	544.220i	−0.335895	+	0.723696i
$753$	509.427	−	503.438i	0.676530	−	0.668576i
$754$	−651.968	+	1678.75i	−0.864679	+	2.22646i
$755$	−343.123			−0.454467
$756$	−106.904	−	57.9603i	−0.141408	−	0.0766670i
$757$		−	792.168i		−	1.04646i	−0.852192	−	0.523229i	$-0.824727\pi$
$757$		−	792.168i		−	1.04646i	0.852192	−	0.523229i	$-0.175273\pi$
$758$	116.896	−	300.995i	0.154216	−	0.397091i
$759$	97.6336	+	98.7951i	0.128635	+	0.130165i
$760$	193.945	+	129.215i	0.255190	+	0.170019i
$761$	−896.813	+	517.775i	−1.17847	+	0.680388i	−0.955659	−	0.294474i	$-0.904855\pi$
$761$	−896.813	+	517.775i	−1.17847	+	0.680388i	−0.222807	+	0.974863i	$0.571522\pi$
$762$	−769.380	+	333.527i	−1.00969	+	0.437700i
$763$	−73.4923	−	42.4308i	−0.0963202	−	0.0556105i
$764$	273.387	+	864.385i	0.357837	+	1.13139i
$765$	−123.900	−	220.585i	−0.161961	−	0.288346i
$766$	420.012	−	64.8378i	0.548319	−	0.0846446i
$767$	−784.588	−	452.982i	−1.02293	−	0.590589i
$768$	441.982	−	628.073i	0.575497	−	0.817804i
$769$	−75.7290	−	131.167i	−0.0984773	−	0.170568i	0.812577	−	0.582853i	$-0.198064\pi$
$769$	−75.7290	−	131.167i	−0.0984773	−	0.170568i	−0.911055	+	0.412286i	$0.864731\pi$
$770$	5.40973	−	4.34573i	0.00702562	−	0.00564381i
$771$	−38.3432	+	139.787i	−0.0497318	+	0.181307i
$772$	26.0235	−	117.882i	0.0337092	−	0.152697i
$773$	135.306			0.175040			0.0875199	−	0.996163i	$-0.472106\pi$
$773$	135.306			0.175040			0.0875199	+	0.996163i	$0.472106\pi$
$774$	−723.422	+	567.195i	−0.934654	+	0.732810i
$775$	424.358			0.547559
$776$	166.485	+	10.6884i	0.214543	+	0.0137737i
$777$	−113.788	+	29.7694i	−0.146445	+	0.0383133i
$778$	−797.736	+	640.836i	−1.02537	+	0.823696i
$779$	183.434	+	317.717i	0.235474	+	0.407853i
$780$	−245.641	−	129.444i	−0.314924	−	0.165954i
$781$	133.789	+	77.2431i	0.171305	+	0.0989028i
$782$	128.883	+	834.890i	0.164812	+	1.06763i
$783$	−1413.19	+	351.922i	−1.80485	+	0.449454i
$784$	−624.816	+	439.164i	−0.796960	+	0.560158i
$785$	35.7723	+	20.6532i	0.0455698	+	0.0263098i
$786$	−153.917	−	114.155i	−0.195823	−	0.145236i
$787$	682.754	−	394.188i	0.867541	−	0.500875i	0.00101045	−	0.999999i	$-0.499678\pi$
$787$	682.754	−	394.188i	0.867541	−	0.500875i	0.866530	+	0.499125i	$0.166345\pi$
$788$	393.667	+	360.085i	0.499578	+	0.456960i
$789$	1115.77	−	291.909i	1.41415	−	0.369973i
$790$	102.628	+	39.8571i	0.129908	+	0.0504520i
$791$		−	123.842i		−	0.156564i
$792$	−12.1433	+	159.604i	−0.0153325	+	0.201521i
$793$	1475.93			1.86120
$794$	−143.782	+	370.223i	−0.181086	+	0.466276i
$795$	211.143	+	57.9157i	0.265588	+	0.0728499i
$796$	170.030	+	155.525i	0.213605	+	0.195383i
$797$	−539.944	−	935.210i	−0.677470	−	1.17341i	−0.975740	−	0.218931i	$-0.929743\pi$
$797$	−539.944	−	935.210i	−0.677470	−	1.17341i	0.298270	−	0.954482i	$-0.403590\pi$
$798$	−141.060	−	16.2294i	−0.176767	−	0.0203376i
$799$	380.269	−	658.645i	0.475931	−	0.824336i
$800$	511.887	+	532.344i	0.639859	+	0.665430i
$801$	−228.218	−	2.69882i	−0.284916	−	0.00336932i
$802$	815.956	−	125.960i	1.01740	−	0.157057i
$803$	91.9247	−	159.218i	0.114477	−	0.198279i
$804$	774.824	−	488.165i	0.963712	−	0.607171i
$805$	28.1479	−	16.2512i	0.0349664	−	0.0201878i
$806$	384.474	+	478.608i	0.477015	+	0.593806i
$807$	241.601	−	238.761i	0.299382	−	0.295863i
$808$	−600.633	−	38.5609i	−0.743358	−	0.0477239i
$809$		−	81.1370i		−	0.100293i	−0.998742	−	0.0501465i	$-0.984031\pi$
$809$		−	81.1370i		−	0.100293i	0.998742	−	0.0501465i	$-0.0159688\pi$
$810$	−28.9991	−	222.658i	−0.0358014	−	0.274886i
$811$		−	129.860i		−	0.160124i	−0.996790	−	0.0800618i	$-0.974488\pi$
$811$		−	129.860i		−	0.160124i	0.996790	−	0.0800618i	$-0.0255118\pi$
$812$	52.3696	−	237.225i	0.0644946	−	0.292149i
$813$	−852.535	+	842.513i	−1.04863	+	1.03630i
$814$	96.9570	+	120.696i	0.119112	+	0.148275i
$815$	−128.631	+	74.2651i	−0.157829	+	0.0911229i
$816$	−628.839	+	743.167i	−0.770636	+	0.910744i
$817$	−536.682	+	929.560i	−0.656893	+	1.13777i
$818$	63.8908	+	413.878i	0.0781062	+	0.505964i
$819$	169.161	+	2.00043i	0.206545	+	0.00244253i
$820$	−29.1834	−	92.2709i	−0.0355895	−	0.112525i
$821$	98.1901	−	170.070i	0.119598	−	0.207150i	−0.800010	−	0.599986i	$-0.795173\pi$
$821$	98.1901	−	170.070i	0.119598	−	0.207150i	0.919608	+	0.392836i	$0.128506\pi$
$822$	−465.334	−	53.5383i	−0.566100	−	0.0651317i
$823$	404.339	+	700.336i	0.491299	+	0.850955i	0.999950	−	0.0100182i	$-0.00318895\pi$
$823$	404.339	+	700.336i	0.491299	+	0.850955i	−0.508651	+	0.860973i	$0.669856\pi$
$824$	728.933	−	1094.09i	0.884627	−	1.32778i
$825$	−148.439	−	40.7164i	−0.179927	−	0.0493532i
$826$	113.922	+	44.2435i	0.137920	+	0.0535635i
$827$	−832.552			−1.00671			−0.503357	−	0.864079i	$-0.667902\pi$
$827$	−832.552			−1.00671			−0.503357	+	0.864079i	$0.667902\pi$
$828$	−170.268	+	730.155i	−0.205637	+	0.881829i
$829$		−	316.550i		−	0.381845i	−0.981605	−	0.190923i	$-0.938852\pi$
$829$		−	316.550i		−	0.381845i	0.981605	−	0.190923i	$-0.0611479\pi$
$830$	294.317	+	114.303i	0.354598	+	0.137714i
$831$	1555.70	−	407.006i	1.87208	−	0.489779i
$832$	−136.622	+	1059.64i	−0.164209	+	1.27360i
$833$	838.387	−	484.043i	1.00647	−	0.581084i
$834$	94.5673	−	127.506i	0.113390	−	0.152885i
$835$	−295.948	−	170.866i	−0.354429	−	0.204630i
$836$	56.3601	+	178.197i	0.0674164	+	0.213155i
$837$	−136.978	+	477.186i	−0.163653	+	0.570115i
$838$	48.5068	+	314.222i	0.0578840	+	0.374967i
$839$	1011.15	+	583.790i	1.20519	+	0.695816i	0.961704	−	0.274089i	$-0.0883762\pi$
$839$	1011.15	+	583.790i	1.20519	+	0.695816i	0.243484	+	0.969905i	$0.421710\pi$
$840$	35.4123	+	12.2018i	0.0421575	+	0.0145260i
$841$	−1034.21	−	1791.31i	−1.22974	−	2.12997i
$842$	−270.408	−	336.614i	−0.321150	−	0.399780i
$843$	137.405	−	35.9483i	0.162996	−	0.0426433i
$844$	873.691	+	192.876i	1.03518	+	0.228526i
$845$	152.028			0.179915
$846$	531.180	−	416.468i	0.627872	−	0.492279i
$847$	−130.678			−0.154284
$848$	−74.9220	−	839.127i	−0.0883515	−	0.989537i
$849$	−226.808	+	826.872i	−0.267147	+	0.973936i
$850$	−586.286	−	729.831i	−0.689749	−	0.858625i
$851$	362.578	+	628.004i	0.426062	+	0.737960i
$852$	32.1901	+	833.262i	0.0377818	+	0.978007i
$853$	−152.565	−	88.0833i	−0.178857	−	0.103263i	0.407899	−	0.913027i	$-0.366262\pi$
$853$	−152.565	−	88.0833i	−0.178857	−	0.103263i	−0.586755	+	0.809764i	$0.699595\pi$
$854$	−196.768	+	30.3753i	−0.230408	+	0.0355683i
$855$	−128.395	−	228.587i	−0.150170	−	0.267353i
$856$	483.267	+	976.673i	0.564564	+	1.14097i
$857$	1034.77	+	597.426i	1.20744	+	0.697114i	0.962198	−	0.272349i	$-0.0878006\pi$
$857$	1034.77	+	597.426i	1.20744	+	0.697114i	0.245238	+	0.969463i	$0.421134\pi$
$858$	−88.5666	−	204.305i	−0.103224	−	0.238118i
$859$	438.348	−	253.080i	0.510300	−	0.294622i	−0.222657	−	0.974897i	$-0.571473\pi$
$859$	438.348	−	253.080i	0.510300	−	0.294622i	0.732957	+	0.680275i	$0.238140\pi$
$860$	191.102	−	208.924i	0.222211	−	0.242935i
$861$	41.4462	+	41.9392i	0.0481373	+	0.0487099i
$862$	−383.685	+	987.947i	−0.445110	+	1.14611i
$863$		−	214.021i		−	0.247997i	−0.992282	−	0.123998i	$-0.960428\pi$
$863$		−	214.021i		−	0.247997i	0.992282	−	0.123998i	$-0.0395718\pi$
$864$	−763.846	+	403.777i	−0.884081	+	0.467335i
$865$	256.662			0.296719
$866$	−670.547	−	260.417i	−0.774303	−	0.300713i
$867$	261.060	−	257.991i	0.301108	−	0.297568i
$868$	−61.1073	−	55.8943i	−0.0704001	−	0.0643944i
$869$	44.1469	+	76.4646i	0.0508019	+	0.0879915i
$870$	411.562	−	178.413i	0.473060	−	0.205072i
$871$	−636.998	+	1103.31i	−0.731342	+	1.26672i
$872$	−540.401	+	267.395i	−0.619725	+	0.306646i
$873$	−161.416	−	95.7561i	−0.184898	−	0.109686i
$874$	133.558	+	865.177i	0.152813	+	0.989905i
$875$	−37.5171	+	64.9816i	−0.0428767	+	0.0742646i
$876$	991.640	−	38.3085i	1.13201	−	0.0437311i
$877$	−720.576	+	416.025i	−0.821638	+	0.474373i	−0.850981	−	0.525197i	$-0.823992\pi$
$877$	−720.576	+	416.025i	−0.821638	+	0.474373i	0.0293431	+	0.999569i	$0.490658\pi$
$878$	30.9903	−	24.8950i	0.0352964	−	0.0283543i
$879$	−329.973	−	90.5105i	−0.375396	−	0.102970i
$880$	−4.38448	−	49.1062i	−0.00498237	−	0.0558025i
$881$		−	902.400i		−	1.02429i	−0.858899	−	0.512145i	$-0.828851\pi$
$881$		−	902.400i		−	1.02429i	0.858899	−	0.512145i	$-0.171149\pi$
$882$	850.612	−	121.030i	0.964413	−	0.137222i
$883$			1309.72i			1.48326i	0.670810	+	0.741630i	$0.265947\pi$
$883$			1309.72i			1.48326i	−0.670810	+	0.741630i	$0.734053\pi$
$884$	291.948	−	1322.47i	0.330258	−	1.49601i
$885$	57.1148	+	218.310i	0.0645365	+	0.246678i
$886$	867.506	−	696.883i	0.979127	−	0.786550i
$887$	−731.925	+	422.577i	−0.825169	+	0.476412i	−0.852196	−	0.523223i	$-0.824729\pi$
$887$	−731.925	+	422.577i	−0.825169	+	0.476412i	0.0270266	+	0.999635i	$0.491396\pi$
$888$	−272.233	+	790.079i	−0.306569	+	0.889729i
$889$	−78.6835	+	136.284i	−0.0885079	+	0.153300i
$890$	69.4750	−	10.7249i	0.0780618	−	0.0120505i
$891$	93.6996	−	153.776i	0.105162	−	0.172588i
$892$	−1095.01	+	346.330i	−1.22759	+	0.388263i
$893$	394.064	−	682.539i	0.441281	−	0.764321i
$894$	−587.358	−	435.626i	−0.657000	−	0.487277i
$895$	11.0624	+	19.1607i	0.0123602	+	0.0214086i
$896$	−3.59368	−	144.080i	−0.00401080	−	0.160804i
$897$	−263.990	−	1009.05i	−0.294303	−	1.12492i
$898$	201.192	−	518.049i	0.224045	−	0.576892i
$899$	−991.793			−1.10322
$900$	−241.160	−	795.071i	−0.267956	−	0.883412i
$901$			1067.91i			1.18525i
$902$	28.0972	−	72.3473i	0.0311499	−	0.0802077i
$903$	−45.6339	+	166.367i	−0.0505358	+	0.184238i
$904$	−732.257	−	487.863i	−0.810018	−	0.539671i
$905$	−7.59209	+	4.38330i	−0.00838905	+	0.00484342i
$906$	169.774	−	1475.60i	0.187388	−	1.62870i
$907$	757.357	+	437.260i	0.835013	+	0.482095i	0.855566	−	0.517694i	$-0.173209\pi$
$907$	757.357	+	437.260i	0.835013	+	0.482095i	−0.0205528	+	0.999789i	$0.506543\pi$
$908$	−946.499	+	299.358i	−1.04240	+	0.329689i
$909$	582.344	+	345.462i	0.640643	+	0.380046i
$910$	−51.4965	+	7.94958i	−0.0565896	+	0.00873580i
$911$	−669.345	−	386.447i	−0.734737	−	0.424201i	0.0854156	−	0.996345i	$-0.472778\pi$
$911$	−669.345	−	386.447i	−0.734737	−	0.424201i	−0.820153	+	0.572145i	$0.806112\pi$
$912$	−651.652	+	770.127i	−0.714530	+	0.844438i
$913$	126.605	+	219.286i	0.138669	+	0.240182i
$914$	1106.90	−	889.191i	1.21105	−	0.972856i
$915$	−258.409	−	261.483i	−0.282414	−	0.285774i
$916$	−1186.29	−	261.884i	−1.29507	−	0.285900i
$917$	−35.9617			−0.0392167
$918$	1009.93	−	423.692i	1.10014	−	0.461538i
$919$	−827.783			−0.900743			−0.450371	−	0.892841i	$-0.648708\pi$
$919$	−827.783			−0.900743			−0.450371	+	0.892841i	$0.648708\pi$
$920$	14.7952	−	230.453i	0.0160818	−	0.250493i
$921$	375.899	+	380.371i	0.408142	+	0.412998i
$922$	829.933	−	666.701i	0.900145	−	0.723103i
$923$	−580.031	−	1004.64i	−0.628419	−	1.08845i
$924$	16.0122	+	25.4148i	0.0173292	+	0.0275052i
$925$	−695.932	−	401.797i	−0.752359	−	0.434375i
$926$	−71.3375	−	462.117i	−0.0770383	−	0.499046i
$927$	−1289.52	+	724.308i	−1.39106	+	0.781347i
$928$	−1196.36	−	1244.17i	−1.28918	−	1.34070i
$929$	−318.846	−	184.086i	−0.343214	−	0.198155i	0.318478	−	0.947930i	$-0.396828\pi$
$929$	−318.846	−	184.086i	−0.343214	−	0.198155i	−0.661692	+	0.749775i	$0.730162\pi$
$930$	17.4779	−	151.911i	0.0187934	−	0.163345i
$931$	868.801	−	501.602i	0.933191	−	0.538778i
$932$	516.397	−	564.559i	0.554074	−	0.605749i
$933$	−135.694	+	494.699i	−0.145438	+	0.530224i
$934$	1122.63	+	435.992i	1.20196	+	0.466801i
$935$			62.4947i			0.0668393i
$936$	678.217	−	992.334i	0.724591	−	1.06019i
$937$	−733.051			−0.782339			−0.391169	−	0.920319i	$-0.627929\pi$
$937$	−733.051			−0.782339			−0.391169	+	0.920319i	$0.627929\pi$
$938$	62.2166	−	160.201i	0.0663290	−	0.170790i
$939$	−78.5485	−	300.236i	−0.0836512	−	0.319741i
$940$	−140.318	+	153.405i	−0.149275	+	0.163197i
$941$	−751.175	−	1301.07i	−0.798273	−	1.38265i	−0.920740	−	0.390177i	$-0.872414\pi$
$941$	−751.175	−	1301.07i	−0.798273	−	1.38265i	0.122467	−	0.992473i	$-0.460920\pi$
$942$	−106.519	+	143.620i	−0.113077	+	0.152463i
$943$	181.766	−	314.828i	0.192753	−	0.333858i
$944$	710.387	−	499.309i	0.752529	−	0.528929i
$945$	−29.2625	−	30.3195i	−0.0309657	−	0.0320841i
$946$	224.414	−	34.6430i	0.237224	−	0.0366206i
$947$	15.4857	−	26.8220i	0.0163524	−	0.0283232i	−0.857733	−	0.514095i	$-0.828128\pi$
$947$	15.4857	−	26.8220i	0.0163524	−	0.0283232i	0.874086	+	0.485772i	$0.161461\pi$
$948$	−222.185	+	421.631i	−0.234372	+	0.444758i
$949$	−1195.60	+	690.278i	−1.25985	+	0.727374i
$950$	−607.555	−	756.307i	−0.639532	−	0.796113i
$951$	362.090	+	1384.02i	0.380747	+	1.45533i
$952$	−11.7049	+	182.318i	−0.0122951	+	0.191510i
$953$		−	273.313i		−	0.286792i	−0.989665	−	0.143396i	$-0.954198\pi$
$953$		−	273.313i		−	0.286792i	0.989665	−	0.143396i	$-0.0458022\pi$
$954$	−353.538	+	879.366i	−0.370585	+	0.921767i
$955$			314.142i			0.328944i
$956$	517.352	+	114.210i	0.541164	+	0.119467i
$957$	346.927	+	95.1607i	0.362515	+	0.0994365i
$958$	−1053.95	−	1311.99i	−1.10015	−	1.36951i
$959$	−76.1253	+	43.9510i	−0.0793799	+	0.0458300i
$960$	211.650	−	161.319i	0.220469	−	0.168040i
$961$	311.454	−	539.454i	0.324093	−	0.561346i
$962$	−177.362	−	1148.93i	−0.184368	−	1.19432i
$963$	14.4961	−	1225.82i	0.0150531	−	1.27292i
$964$	946.668	−	299.411i	0.982020	−	0.310593i
$965$	20.9153	−	36.2264i	0.0216739	−	0.0375403i
$966$	55.9613	+	129.091i	0.0579309	+	0.133635i
$967$	276.224	+	478.433i	0.285650	+	0.494760i	0.972767	−	0.231787i	$-0.0744572\pi$
$967$	276.224	+	478.433i	0.285650	+	0.494760i	−0.687117	+	0.726547i	$0.741124\pi$
$968$	−514.793	+	772.677i	−0.531811	+	0.798220i
$969$	909.578	−	898.885i	0.938677	−	0.927642i
$970$	53.8863	+	20.9276i	0.0555529	+	0.0215748i
$971$	1433.59			1.47641			0.738203	−	0.674579i	$-0.235675\pi$
$971$	1433.59			1.47641			0.738203	+	0.674579i	$0.235675\pi$
$972$	971.891	−	14.5426i	0.999888	−	0.0149615i
$973$		−	29.7910i		−	0.0306177i
$974$	−886.893	−	344.439i	−0.910568	−	0.353633i
$975$	812.448	+	822.112i	0.833280	+	0.843192i
$976$	−595.543	+	1283.11i	−0.610187	+	1.31467i
$977$	−125.056	+	72.2010i	−0.128000	+	0.0739007i	−0.562633	−	0.826707i	$-0.690211\pi$
$977$	−125.056	+	72.2010i	−0.128000	+	0.0739007i	0.434633	+	0.900608i	$0.356878\pi$
$978$	−255.733	−	589.925i	−0.261486	−	0.603195i
$979$	48.8240	+	28.1886i	0.0498713	+	0.0287932i
$980$	−252.315	+	79.8021i	−0.257465	+	0.0814307i
$981$	678.257	+	8.02083i	0.691393	+	0.00817617i
$982$	−67.4623	−	437.014i	−0.0686989	−	0.445024i
$983$	1567.87	+	905.210i	1.59498	+	0.920865i	0.992433	+	0.122785i	$0.0391824\pi$
$983$	1567.87	+	905.210i	1.59498	+	0.920865i	0.602551	+	0.798080i	$0.294151\pi$
$984$	411.252	−	79.8488i	0.417939	−	0.0811472i
$985$	92.4335	+	160.100i	0.0938411	+	0.162538i
$986$	1370.24	+	1705.73i	1.38970	+	1.72995i
$987$	33.5071	−	122.157i	0.0339484	−	0.123765i
$988$	302.540	−	1370.45i	0.306214	−	1.38709i
$989$	1063.60			1.07543
$990$	−20.6893	+	51.4610i	−0.0208983	+	0.0519809i
$991$	−1230.50			−1.24167			−0.620836	−	0.783940i	$-0.713207\pi$
$991$	−1230.50			−1.24167			−0.620836	+	0.783940i	$0.713207\pi$
$992$	−571.218	+	141.126i	−0.575825	+	0.142264i
$993$	−491.593	+	128.612i	−0.495058	+	0.129518i
$994$	98.0045	+	122.000i	0.0985961	+	0.122736i
$995$	39.9231	+	69.1489i	0.0401238	+	0.0694964i
$996$	−637.184	+	1209.16i	−0.639743	+	1.21401i
$997$	−171.763	−	99.1676i	−0.172280	−	0.0994660i	0.411380	−	0.911464i	$-0.365047\pi$
$997$	−171.763	−	99.1676i	−0.172280	−	0.0994660i	−0.583661	+	0.811998i	$0.698380\pi$
$998$	−1568.82	+	242.180i	−1.57196	+	0.242666i
$999$	676.454	−	652.872i	0.677131	−	0.653526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.20	yes	44
3.2	odd	2		216.3.j.a.197.3		44
4.3	odd	2		288.3.n.a.209.17		44
8.3	odd	2		288.3.n.a.209.6		44
8.5	even	2	inner	72.3.j.a.29.19	yes	44
9.2	odd	6		648.3.h.a.485.24		44
9.4	even	3		216.3.j.a.125.4		44
9.5	odd	6	inner	72.3.j.a.5.19	✓	44
9.7	even	3		648.3.h.a.485.21		44
12.11	even	2		864.3.n.a.305.9		44
24.5	odd	2		216.3.j.a.197.4		44
24.11	even	2		864.3.n.a.305.14		44
36.7	odd	6		2592.3.h.a.1457.18		44
36.11	even	6		2592.3.h.a.1457.27		44
36.23	even	6		288.3.n.a.113.6		44
36.31	odd	6		864.3.n.a.17.14		44
72.5	odd	6	inner	72.3.j.a.5.20	yes	44
72.11	even	6		2592.3.h.a.1457.17		44
72.13	even	6		216.3.j.a.125.3		44
72.29	odd	6		648.3.h.a.485.22		44
72.43	odd	6		2592.3.h.a.1457.28		44
72.59	even	6		288.3.n.a.113.17		44
72.61	even	6		648.3.h.a.485.23		44
72.67	odd	6		864.3.n.a.17.9		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.19	✓	44	9.5	odd	6	inner
72.3.j.a.5.20	yes	44	72.5	odd	6	inner
72.3.j.a.29.19	yes	44	8.5	even	2	inner
72.3.j.a.29.20	yes	44	1.1	even	1	trivial
216.3.j.a.125.3		44	72.13	even	6
216.3.j.a.125.4		44	9.4	even	3
216.3.j.a.197.3		44	3.2	odd	2
216.3.j.a.197.4		44	24.5	odd	2
288.3.n.a.113.6		44	36.23	even	6
288.3.n.a.113.17		44	72.59	even	6
288.3.n.a.209.6		44	8.3	odd	2
288.3.n.a.209.17		44	4.3	odd	2
648.3.h.a.485.21		44	9.7	even	3
648.3.h.a.485.22		44	72.29	odd	6
648.3.h.a.485.23		44	72.61	even	6
648.3.h.a.485.24		44	9.2	odd	6
864.3.n.a.17.9		44	72.67	odd	6
864.3.n.a.17.14		44	36.31	odd	6
864.3.n.a.305.9		44	12.11	even	2
864.3.n.a.305.14		44	24.11	even	2
2592.3.h.a.1457.17		44	72.11	even	6
2592.3.h.a.1457.18		44	36.7	odd	6
2592.3.h.a.1457.27		44	36.11	even	6
2592.3.h.a.1457.28		44	72.43	odd	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86434 + 0.724045i) q^{2} +(-2.13383 + 2.10874i) q^{3} +(2.95152 + 2.69973i) q^{4} +(0.693019 + 1.20034i) q^{5} +(-5.50500 + 2.38642i) q^{6} +(-0.562989 + 0.975125i) q^{7} +(3.54790 + 7.17024i) q^{8} +(0.106423 - 8.99937i) q^{9} +O(q^{10})\)	\(q+(1.86434 + 0.724045i) q^{2} +(-2.13383 + 2.10874i) q^{3} +(2.95152 + 2.69973i) q^{4} +(0.693019 + 1.20034i) q^{5} +(-5.50500 + 2.38642i) q^{6} +(-0.562989 + 0.975125i) q^{7} +(3.54790 + 7.17024i) q^{8} +(0.106423 - 8.99937i) q^{9} +(0.422919 + 2.73963i) q^{10} +(-1.11157 + 1.92529i) q^{11} +(-11.9911 + 0.463232i) q^{12} +(14.4573 - 8.34694i) q^{13} +(-1.75564 + 1.41033i) q^{14} +(-4.01000 - 1.09993i) q^{15} +(1.42291 + 15.9366i) q^{16} -20.2816i q^{17} +(6.71436 - 16.7008i) q^{18} -21.0174i q^{19} +(-1.19515 + 5.41380i) q^{20} +(-0.854966 - 3.26794i) q^{21} +(-3.46633 + 2.78457i) q^{22} +(-18.0360 + 10.4131i) q^{23} +(-22.6908 - 7.81844i) q^{24} +(11.5394 - 19.9869i) q^{25} +(32.9969 - 5.09377i) q^{26} +(18.7503 + 19.4275i) q^{27} +(-4.29425 + 1.35818i) q^{28} +(-26.9695 + 46.7126i) q^{29} +(-6.67960 - 4.95406i) q^{30} +(9.19365 + 15.9239i) q^{31} +(-8.88603 + 30.7415i) q^{32} +(-1.68805 - 6.45224i) q^{33} +(14.6848 - 37.8118i) q^{34} -1.56065 q^{35} +(24.6100 - 26.2745i) q^{36} -34.8194i q^{37} +(15.2175 - 39.1835i) q^{38} +(-13.2479 + 48.2977i) q^{39} +(-6.14800 + 9.22782i) q^{40} +(-15.1169 + 8.72774i) q^{41} +(0.772192 - 6.71159i) q^{42} +(-44.2282 - 25.5352i) q^{43} +(-8.47857 + 2.68160i) q^{44} +(10.8761 - 6.10899i) q^{45} +(-41.1649 + 6.35467i) q^{46} +(32.4750 + 18.7494i) q^{47} +(-36.6424 - 31.0054i) q^{48} +(23.8661 + 41.3373i) q^{49} +(35.9849 - 28.9073i) q^{50} +(42.7687 + 43.2774i) q^{51} +(65.2055 + 14.3947i) q^{52} -52.6541 q^{53} +(20.8904 + 49.7955i) q^{54} -3.08135 q^{55} +(-8.98931 - 0.577118i) q^{56} +(44.3202 + 44.8474i) q^{57} +(-84.1024 + 67.5609i) q^{58} +(-27.1346 - 46.9986i) q^{59} +(-8.86607 - 14.0724i) q^{60} +(76.5667 + 44.2058i) q^{61} +(5.61048 + 36.3441i) q^{62} +(8.71560 + 5.17032i) q^{63} +(-38.8248 + 50.8786i) q^{64} +(20.0384 + 11.5692i) q^{65} +(1.52462 - 13.2514i) q^{66} +(-66.0909 + 38.1576i) q^{67} +(54.7549 - 59.8615i) q^{68} +(16.5272 - 60.2531i) q^{69} +(-2.90958 - 1.12998i) q^{70} -69.4903i q^{71} +(64.9053 - 31.1658i) q^{72} -82.6983 q^{73} +(25.2108 - 64.9151i) q^{74} +(17.5240 + 66.9823i) q^{75} +(56.7412 - 62.0331i) q^{76} +(-1.25160 - 2.16783i) q^{77} +(-59.6682 + 80.4511i) q^{78} +(19.8580 - 34.3950i) q^{79} +(-18.1433 + 12.7524i) q^{80} +(-80.9773 - 1.91549i) q^{81} +(-34.5023 + 5.32616i) q^{82} +(56.9488 - 98.6383i) q^{83} +(6.29912 - 11.9536i) q^{84} +(24.3449 - 14.0555i) q^{85} +(-63.9677 - 79.6294i) q^{86} +(-40.9565 - 156.548i) q^{87} +(-17.7485 - 1.13946i) q^{88} -25.3593i q^{89} +(24.6999 - 3.51444i) q^{90} +18.7969i q^{91} +(-81.3463 - 17.9580i) q^{92} +(-53.1969 - 14.5917i) q^{93} +(46.9689 + 58.4686i) q^{94} +(25.2281 - 14.5654i) q^{95} +(-45.8646 - 84.3353i) q^{96} +(10.4267 - 18.0596i) q^{97} +(14.5644 + 94.3468i) q^{98} +(17.2081 + 10.2083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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