LMFDB - Embedded newform 72.3.j.a.29.17

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			29.17
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45018 - 1.37730i) q^{2} +(1.79120 - 2.40657i) q^{3} +(0.206068 - 3.99469i) q^{4} +(1.89538 + 3.28290i) q^{5} +(-0.717012 - 5.95700i) q^{6} +(-5.70744 + 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(-2.58320 - 8.62132i) q^{9} +O(q^{10})$	\(q+(1.45018 - 1.37730i) q^{2} +(1.79120 - 2.40657i) q^{3} +(0.206068 - 3.99469i) q^{4} +(1.89538 + 3.28290i) q^{5} +(-0.717012 - 5.95700i) q^{6} +(-5.70744 + 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(-2.58320 - 8.62132i) q^{9} +(7.27021 + 2.15029i) q^{10} +(-3.47103 + 6.01200i) q^{11} +(-9.24440 - 7.65121i) q^{12} +(14.6939 - 8.48351i) q^{13} +(5.33861 + 22.1968i) q^{14} +(11.2956 + 1.31895i) q^{15} +(-15.9151 - 1.64636i) q^{16} +22.9919i q^{17} +(-15.6203 - 8.94465i) q^{18} -21.7334i q^{19} +(13.5047 - 6.89497i) q^{20} +(13.5672 + 31.4425i) q^{21} +(3.24672 + 13.4992i) q^{22} +(-13.7369 + 7.93101i) q^{23} +(-23.9441 + 1.63669i) q^{24} +(5.31504 - 9.20592i) q^{25} +(9.62445 - 32.5406i) q^{26} +(-25.3749 - 9.22586i) q^{27} +(38.3137 + 24.8366i) q^{28} +(-6.57213 + 11.3833i) q^{29} +(18.1972 - 13.6447i) q^{30} +(3.45597 + 5.98592i) q^{31} +(-25.3473 + 19.5324i) q^{32} +(8.25100 + 19.1220i) q^{33} +(31.6668 + 33.3424i) q^{34} -43.2712 q^{35} +(-34.9718 + 8.54249i) q^{36} -1.75177i q^{37} +(-29.9335 - 31.5174i) q^{38} +(5.90348 - 50.5576i) q^{39} +(10.0879 - 28.5991i) q^{40} +(33.1748 - 19.1535i) q^{41} +(62.9808 + 26.9112i) q^{42} +(-10.9120 - 6.30005i) q^{43} +(23.3008 + 15.1046i) q^{44} +(23.4068 - 24.8211i) q^{45} +(-8.99764 + 30.4213i) q^{46} +(-28.8738 - 16.6703i) q^{47} +(-32.4692 + 35.3518i) q^{48} +(-40.6498 - 70.4076i) q^{49} +(-4.97156 - 20.6707i) q^{50} +(55.3316 + 41.1830i) q^{51} +(-30.8610 - 60.4456i) q^{52} +1.96807 q^{53} +(-49.5050 + 21.5697i) q^{54} -26.3157 q^{55} +(89.7694 - 16.7520i) q^{56} +(-52.3030 - 38.9289i) q^{57} +(6.14741 + 25.5596i) q^{58} +(-10.5216 - 18.2239i) q^{59} +(7.59647 - 44.8504i) q^{60} +(-48.0654 - 27.7506i) q^{61} +(13.2562 + 3.92076i) q^{62} +(99.9702 + 23.6693i) q^{63} +(-9.85628 + 63.2365i) q^{64} +(55.7011 + 32.1590i) q^{65} +(38.3022 + 16.3663i) q^{66} +(75.4627 - 43.5684i) q^{67} +(91.8453 + 4.73789i) q^{68} +(-5.51901 + 47.2649i) q^{69} +(-62.7512 + 59.5976i) q^{70} -38.7491i q^{71} +(-38.9499 + 60.5550i) q^{72} +31.7926 q^{73} +(-2.41272 - 2.54039i) q^{74} +(-12.6344 - 29.2807i) q^{75} +(-86.8181 - 4.47856i) q^{76} +(-39.6214 - 68.6263i) q^{77} +(-61.0720 - 81.4487i) q^{78} +(-68.7491 + 119.077i) q^{79} +(-24.7603 - 55.3681i) q^{80} +(-67.6542 + 44.5411i) q^{81} +(21.7294 - 73.4679i) q^{82} +(-33.5423 + 58.0970i) q^{83} +(128.399 - 47.7175i) q^{84} +(-75.4800 + 43.5784i) q^{85} +(-24.5015 + 5.89291i) q^{86} +(15.6227 + 36.2060i) q^{87} +(54.5940 - 10.1879i) q^{88} +159.426i q^{89} +(-0.242031 - 68.2334i) q^{90} +193.677i q^{91} +(28.8512 + 56.5090i) q^{92} +(20.5959 + 2.40493i) q^{93} +(-64.8323 + 15.5930i) q^{94} +(71.3485 - 41.1931i) q^{95} +(1.60394 + 95.9866i) q^{96} +(42.5296 - 73.6635i) q^{97} +(-155.922 - 46.1168i) q^{98} +(60.7977 + 14.3947i) 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 $

$2$	1.45018	−	1.37730i	0.725092	−	0.688652i
$2$	1.45018	−	1.37730i	0.725092	−	0.688652i
$3$	1.79120	−	2.40657i	0.597067	−	0.802191i
$3$	1.79120	−	2.40657i	0.597067	−	0.802191i
$4$	0.206068	−	3.99469i	0.0515171	−	0.998672i
$5$	1.89538	+	3.28290i	0.379077	+	0.656580i	0.990928	−	0.134393i	$-0.0429083\pi$
$5$	1.89538	+	3.28290i	0.379077	+	0.656580i	−0.611851	+	0.790973i	$0.709575\pi$
$6$	−0.717012	−	5.95700i	−0.119502	−	0.992834i
$7$	−5.70744	+	9.88558i	−0.815349	+	1.41223i	0.0937277	+	0.995598i	$0.470122\pi$
$7$	−5.70744	+	9.88558i	−0.815349	+	1.41223i	−0.909077	+	0.416628i	$0.863212\pi$
$8$	−5.20306	−	6.07685i	−0.650383	−	0.759607i
$9$	−2.58320	−	8.62132i	−0.287022	−	0.957924i
$10$	7.27021	+	2.15029i	0.727021	+	0.215029i
$11$	−3.47103	+	6.01200i	−0.315548	+	0.546545i	−0.979554	−	0.201182i	$-0.935522\pi$
$11$	−3.47103	+	6.01200i	−0.315548	+	0.546545i	0.664006	+	0.747727i	$0.268855\pi$
$12$	−9.24440	−	7.65121i	−0.770367	−	0.637601i
$13$	14.6939	−	8.48351i	1.13030	−	0.652578i	0.186288	−	0.982495i	$-0.440354\pi$
$13$	14.6939	−	8.48351i	1.13030	−	0.652578i	0.944010	+	0.329917i	$0.107021\pi$
$14$	5.33861	+	22.1968i	0.381329	+	1.58549i
$15$	11.2956	+	1.31895i	0.753037	+	0.0879303i
$16$	−15.9151	−	1.64636i	−0.994692	−	0.102897i
$17$			22.9919i			1.35246i	0.736690	+	0.676231i	$0.236388\pi$
$17$			22.9919i			1.35246i	−0.736690	+	0.676231i	$0.763612\pi$
$18$	−15.6203	−	8.94465i	−0.867794	−	0.496925i
$19$		−	21.7334i		−	1.14386i	−0.820302	−	0.571931i	$-0.806194\pi$
$19$		−	21.7334i		−	1.14386i	0.820302	−	0.571931i	$-0.193806\pi$
$20$	13.5047	−	6.89497i	0.675237	−	0.344748i
$21$	13.5672	+	31.4425i	0.646057	+	1.49726i
$22$	3.24672	+	13.4992i	0.147578	+	0.613598i
$23$	−13.7369	+	7.93101i	−0.597257	+	0.344826i	−0.767962	−	0.640496i	$-0.778729\pi$
$23$	−13.7369	+	7.93101i	−0.597257	+	0.344826i	0.170705	+	0.985322i	$0.445396\pi$
$24$	−23.9441	+	1.63669i	−0.997672	+	0.0681954i
$25$	5.31504	−	9.20592i	0.212602	−	0.368237i
$26$	9.62445	−	32.5406i	0.370171	−	1.25156i
$27$	−25.3749	−	9.22586i	−0.939810	−	0.341698i
$28$	38.3137	+	24.8366i	1.36835	+	0.887020i
$29$	−6.57213	+	11.3833i	−0.226625	+	0.392526i	−0.956806	−	0.290728i	$-0.906103\pi$
$29$	−6.57213	+	11.3833i	−0.226625	+	0.392526i	0.730181	+	0.683254i	$0.239436\pi$
$30$	18.1972	−	13.6447i	0.606575	−	0.454823i
$31$	3.45597	+	5.98592i	0.111483	+	0.193094i	0.916368	−	0.400336i	$-0.131107\pi$
$31$	3.45597	+	5.98592i	0.111483	+	0.193094i	−0.804885	+	0.593430i	$0.797773\pi$
$32$	−25.3473	+	19.5324i	−0.792104	+	0.610386i
$33$	8.25100	+	19.1220i	0.250030	+	0.579454i
$34$	31.6668	+	33.3424i	0.931376	+	0.980660i
$35$	−43.2712			−1.23632
$36$	−34.9718	+	8.54249i	−0.971439	+	0.237291i
$37$		−	1.75177i		−	0.0473452i	−0.999720	−	0.0236726i	$-0.992464\pi$
$37$		−	1.75177i		−	0.0473452i	0.999720	−	0.0236726i	$-0.00753592\pi$
$38$	−29.9335	−	31.5174i	−0.787723	−	0.829405i
$39$	5.90348	−	50.5576i	0.151371	−	1.29635i
$40$	10.0879	−	28.5991i	0.252198	−	0.714978i
$41$	33.1748	−	19.1535i	0.809142	−	0.467159i	−0.0375156	−	0.999296i	$-0.511944\pi$
$41$	33.1748	−	19.1535i	0.809142	−	0.467159i	0.846658	+	0.532137i	$0.178611\pi$
$42$	62.9808	+	26.9112i	1.49954	+	0.640743i
$43$	−10.9120	−	6.30005i	−0.253768	−	0.146513i	0.367721	−	0.929936i	$-0.380138\pi$
$43$	−10.9120	−	6.30005i	−0.253768	−	0.146513i	−0.621488	+	0.783424i	$0.713472\pi$
$44$	23.3008	+	15.1046i	0.529563	+	0.343285i
$45$	23.4068	−	24.8211i	0.520151	−	0.551580i
$46$	−8.99764	+	30.4213i	−0.195601	+	0.661333i
$47$	−28.8738	−	16.6703i	−0.614335	−	0.354687i	0.160325	−	0.987064i	$-0.448746\pi$
$47$	−28.8738	−	16.6703i	−0.614335	−	0.354687i	−0.774660	+	0.632378i	$0.782079\pi$
$48$	−32.4692	+	35.3518i	−0.676441	+	0.736497i
$49$	−40.6498	−	70.4076i	−0.829589	−	1.43689i
$50$	−4.97156	−	20.6707i	−0.0994312	−	0.413414i
$51$	55.3316	+	41.1830i	1.08493	+	0.807511i
$52$	−30.8610	−	60.4456i	−0.593482	−	1.16242i
$53$	1.96807			0.0371334			0.0185667	−	0.999828i	$-0.494090\pi$
$53$	1.96807			0.0371334			0.0185667	+	0.999828i	$0.494090\pi$
$54$	−49.5050	+	21.5697i	−0.916760	+	0.399439i
$55$	−26.3157			−0.478468
$56$	89.7694	−	16.7520i	1.60303	−	0.299143i
$57$	−52.3030	−	38.9289i	−0.917596	−	0.682962i
$58$	6.14741	+	25.5596i	0.105990	+	0.440683i
$59$	−10.5216	−	18.2239i	−0.178332	−	0.308880i	0.762977	−	0.646425i	$-0.223737\pi$
$59$	−10.5216	−	18.2239i	−0.178332	−	0.308880i	−0.941309	+	0.337545i	$0.890404\pi$
$60$	7.59647	−	44.8504i	0.126608	−	0.747507i
$61$	−48.0654	−	27.7506i	−0.787958	−	0.454928i	0.0512853	−	0.998684i	$-0.483668\pi$
$61$	−48.0654	−	27.7506i	−0.787958	−	0.454928i	−0.839243	+	0.543756i	$0.817002\pi$
$62$	13.2562	+	3.92076i	0.213810	+	0.0632381i
$63$	99.9702	+	23.6693i	1.58683	+	0.375703i
$64$	−9.85628	+	63.2365i	−0.154004	+	0.988070i
$65$	55.7011	+	32.1590i	0.856939	+	0.494754i
$66$	38.3022	+	16.3663i	0.580337	+	0.247973i
$67$	75.4627	−	43.5684i	1.12631	−	0.650275i	0.183305	−	0.983056i	$-0.441320\pi$
$67$	75.4627	−	43.5684i	1.12631	−	0.650275i	0.943004	+	0.332781i	$0.107987\pi$
$68$	91.8453	+	4.73789i	1.35067	+	0.0696749i
$69$	−5.51901	+	47.2649i	−0.0799856	+	0.684999i
$70$	−62.7512	+	59.5976i	−0.896446	+	0.851394i
$71$		−	38.7491i		−	0.545762i	−0.962048	−	0.272881i	$-0.912023\pi$
$71$		−	38.7491i		−	0.545762i	0.962048	−	0.272881i	$-0.0879765\pi$
$72$	−38.9499	+	60.5550i	−0.540971	+	0.841041i
$73$	31.7926			0.435515			0.217758	−	0.976003i	$-0.430126\pi$
$73$	31.7926			0.435515			0.217758	+	0.976003i	$0.430126\pi$
$74$	−2.41272	−	2.54039i	−0.0326044	−	0.0343296i
$75$	−12.6344	−	29.2807i	−0.168459	−	0.390409i
$76$	−86.8181	−	4.47856i	−1.14234	−	0.0589284i
$77$	−39.6214	−	68.6263i	−0.514564	−	0.891250i
$78$	−61.0720	−	81.4487i	−0.782974	−	1.04421i
$79$	−68.7491	+	119.077i	−0.870241	+	1.50730i	−0.00849443	+	0.999964i	$0.502704\pi$
$79$	−68.7491	+	119.077i	−0.870241	+	1.50730i	−0.861747	+	0.507338i	$0.830629\pi$
$80$	−24.7603	−	55.3681i	−0.309504	−	0.692101i
$81$	−67.6542	+	44.5411i	−0.835237	+	0.549890i
$82$	21.7294	−	73.4679i	0.264993	−	0.895950i
$83$	−33.5423	+	58.0970i	−0.404124	+	0.699964i	−0.994219	−	0.107370i	$-0.965757\pi$
$83$	−33.5423	+	58.0970i	−0.404124	+	0.699964i	0.590095	+	0.807334i	$0.299090\pi$
$84$	128.399	−	47.7175i	1.52855	−	0.568065i
$85$	−75.4800	+	43.5784i	−0.888000	+	0.512687i
$86$	−24.5015	+	5.89291i	−0.284901	+	0.0685223i
$87$	15.6227	+	36.2060i	0.179571	+	0.416161i
$88$	54.5940	−	10.1879i	0.620386	−	0.115771i
$89$			159.426i			1.79130i	0.444762	+	0.895649i	$0.353288\pi$
$89$			159.426i			1.79130i	−0.444762	+	0.895649i	$0.646712\pi$
$90$	−0.242031	−	68.2334i	−0.00268924	−	0.758149i
$91$			193.677i			2.12832i
$92$	28.8512	+	56.5090i	0.313600	+	0.614228i
$93$	20.5959	+	2.40493i	0.221461	+	0.0258595i
$94$	−64.8323	+	15.5930i	−0.689705	+	0.165883i
$95$	71.3485	−	41.1931i	0.751037	−	0.433611i
$96$	1.60394	+	95.9866i	0.0167077	+	0.999860i
$97$	42.5296	−	73.6635i	0.438450	−	0.759418i	−0.559120	−	0.829087i	$-0.688861\pi$
$97$	42.5296	−	73.6635i	0.438450	−	0.759418i	0.997570	+	0.0696690i	$0.0221943\pi$
$98$	−155.922	−	46.1168i	−1.59104	−	0.470579i
$99$	60.7977	+	14.3947i	0.614118	+	0.145401i
$100$	−35.6795	−	23.1290i	−0.356795	−	0.231290i
$101$	14.8145	−	25.6594i	0.146678	−	0.254053i	−0.783320	−	0.621619i	$-0.786475\pi$
$101$	14.8145	−	25.6594i	0.146678	−	0.254053i	0.929998	+	0.367565i	$0.119809\pi$
$102$	136.963	−	16.4854i	1.34277	−	0.161622i
$103$	1.31615	+	2.27965i	0.0127782	+	0.0221325i	0.872344	−	0.488893i	$-0.162599\pi$
$103$	1.31615	+	2.27965i	0.0127782	+	0.0221325i	−0.859566	+	0.511025i	$0.829266\pi$
$104$	−128.006	−	45.1523i	−1.23083	−	0.434156i
$105$	−77.5074	+	104.135i	−0.738166	+	0.991765i
$106$	2.85406	−	2.71063i	0.0269251	−	0.0255720i
$107$	204.119			1.90766			0.953828	−	0.300352i	$-0.0971041\pi$
$107$	204.119			1.90766			0.953828	+	0.300352i	$0.0971041\pi$
$108$	−42.0834	+	99.4635i	−0.389661	+	0.920958i
$109$		−	106.708i		−	0.978974i	−0.872011	−	0.489487i	$-0.837184\pi$
$109$		−	106.708i		−	0.978974i	0.872011	−	0.489487i	$-0.162816\pi$
$110$	−38.1626	+	36.2447i	−0.346933	+	0.329498i
$111$	−4.21577	−	3.13778i	−0.0379799	−	0.0282683i
$112$	107.110	−	147.933i	0.956336	−	1.32083i
$113$	65.8775	−	38.0344i	0.582986	−	0.336587i	−0.179333	−	0.983788i	$-0.557394\pi$
$113$	65.8775	−	38.0344i	0.582986	−	0.336587i	0.762319	+	0.647201i	$0.224061\pi$
$114$	−129.466	+	15.5831i	−1.13567	+	0.136694i
$115$	−52.0734	−	30.0646i	−0.452812	−	0.261431i
$116$	44.1183	+	28.5993i	0.380330	+	0.246546i
$117$	−111.096	−	104.766i	−0.949540	−	0.895436i
$118$	−40.3582	−	11.9366i	−0.342018	−	0.101158i
$119$	−227.288	−	131.225i	−1.90998	−	1.10273i
$120$	−50.7564	−	75.5040i	−0.422970	−	0.629200i
$121$	36.4039	+	63.0535i	0.300859	+	0.521103i
$122$	−107.925	+	25.9572i	−0.884629	+	0.212764i
$123$	13.3285	−	114.145i	0.108362	−	0.928012i
$124$	24.6240	−	12.5720i	0.198581	−	0.101387i
$125$	135.065			1.08052
$126$	177.575	−	103.365i	1.40933	−	0.820353i
$127$	196.308			1.54573			0.772865	−	0.634570i	$-0.218823\pi$
$127$	196.308			1.54573			0.772865	+	0.634570i	$0.218823\pi$
$128$	72.8024	+	105.280i	0.568769	+	0.822497i
$129$	−34.7071	+	14.9759i	−0.269047	+	0.116092i
$130$	125.070	−	30.0808i	0.962073	−	0.231391i
$131$	8.60811	+	14.9097i	0.0657108	+	0.113814i	0.897009	−	0.442012i	$-0.145735\pi$
$131$	8.60811	+	14.9097i	0.0657108	+	0.113814i	−0.831298	+	0.555827i	$0.812402\pi$
$132$	78.0866	−	29.0198i	0.591565	−	0.219847i
$133$	214.847	+	124.042i	1.61539	+	0.932647i
$134$	49.4279	−	167.117i	0.368865	−	1.24714i
$135$	−17.8075	−	100.790i	−0.131908	−	0.746590i
$136$	139.718	−	119.628i	1.02734	−	0.879618i
$137$	−158.315	−	91.4032i	−1.15558	−	0.667176i	−0.205342	−	0.978690i	$-0.565831\pi$
$137$	−158.315	−	91.4032i	−1.15558	−	0.667176i	−0.950242	+	0.311514i	$0.899164\pi$
$138$	57.0946	+	76.1442i	0.413729	+	0.551769i
$139$	84.6463	−	48.8706i	0.608966	−	0.351587i	−0.163595	−	0.986528i	$-0.552309\pi$
$139$	84.6463	−	48.8706i	0.608966	−	0.351587i	0.772561	+	0.634941i	$0.218976\pi$
$140$	−8.91682	+	172.855i	−0.0636916	+	1.23468i
$141$	−91.8370	+	39.6270i	−0.651326	+	0.281043i
$142$	−53.3693	−	56.1933i	−0.375840	−	0.395728i
$143$			117.786i			0.823678i
$144$	26.9180	+	141.462i	0.186930	+	0.982373i
$145$	−49.8268			−0.343633
$146$	46.1051	−	43.7881i	0.315789	−	0.299918i
$147$	−242.253	−	28.2873i	−1.64798	−	0.192431i
$148$	−6.99778	−	0.360985i	−0.0472823	−	0.00243909i
$149$	−14.1349	−	24.4823i	−0.0948650	−	0.164311i	0.814687	−	0.579901i	$-0.196909\pi$
$149$	−14.1349	−	24.4823i	−0.0948650	−	0.164311i	−0.909552	+	0.415590i	$0.863575\pi$
$150$	−58.6507	−	25.0610i	−0.391004	−	0.167073i
$151$	22.1105	−	38.2965i	0.146427	−	0.253619i	−0.783477	−	0.621420i	$-0.786556\pi$
$151$	22.1105	−	38.2965i	0.146427	−	0.253619i	0.929904	+	0.367801i	$0.119889\pi$
$152$	−132.071	+	113.080i	−0.868885	+	0.743948i
$153$	198.220	−	59.3925i	1.29556	−	0.388186i
$154$	−151.978	−	44.9500i	−0.986867	−	0.291883i
$155$	−13.1008	+	22.6912i	−0.0845212	+	0.146395i
$156$	−200.745	−	34.0009i	−1.28683	−	0.217954i
$157$	−199.188	+	115.001i	−1.26871	+	0.732492i	−0.974744	−	0.223324i	$-0.928309\pi$
$157$	−199.188	+	115.001i	−1.26871	+	0.732492i	−0.293968	+	0.955815i	$0.594976\pi$
$158$	64.3062	+	267.372i	0.407001	+	1.69223i
$159$	3.52521	−	4.73630i	0.0221711	−	0.0297881i
$160$	−112.166	−	46.1914i	−0.701036	−	0.288696i
$161$		−	181.063i		−	1.12462i
$162$	−36.7644	+	157.773i	−0.226941	+	0.973909i
$163$			38.2483i			0.234652i	0.993093	+	0.117326i	$0.0374322\pi$
$163$			38.2483i			0.234652i	−0.993093	+	0.117326i	$0.962568\pi$
$164$	−69.6760	−	136.470i	−0.424854	−	0.832135i
$165$	−47.1367	+	63.3307i	−0.285677	+	0.383823i
$166$	31.3747	+	130.449i	0.189004	+	0.785839i
$167$	19.3179	−	11.1532i	0.115676	−	0.0667857i	−0.441046	−	0.897485i	$-0.645392\pi$
$167$	19.3179	−	11.1532i	0.115676	−	0.0667857i	0.556722	+	0.830699i	$0.312059\pi$
$168$	120.480	−	246.043i	0.717144	−	1.46454i
$169$	59.4400	−	102.953i	0.351716	−	0.609190i
$170$	−49.4392	+	167.156i	−0.290819	+	0.983268i
$171$	−187.370	+	56.1416i	−1.09573	+	0.328313i
$172$	−27.4153	+	42.2918i	−0.159392	+	0.245883i
$173$	−63.8618	+	110.612i	−0.369143	+	0.639375i	−0.989432	−	0.144999i	$-0.953682\pi$
$173$	−63.8618	+	110.612i	−0.369143	+	0.639375i	0.620289	+	0.784374i	$0.287015\pi$
$174$	72.5224	+	30.9883i	0.416795	+	0.178093i
$175$	60.6706	+	105.085i	0.346689	+	0.600483i
$176$	65.1395	−	89.9668i	0.370111	−	0.511175i
$177$	−62.7036	−	7.32174i	−0.354258	−	0.0413658i
$178$	219.577	+	231.196i	1.23358	+	1.29886i
$179$	−103.043			−0.575660			−0.287830	−	0.957682i	$-0.592934\pi$
$179$	−103.043			−0.575660			−0.287830	+	0.957682i	$0.592934\pi$
$180$	−94.3291	−	98.6176i	−0.524050	−	0.547876i
$181$		−	71.5305i		−	0.395196i	−0.980283	−	0.197598i	$-0.936686\pi$
$181$		−	71.5305i		−	0.395196i	0.980283	−	0.197598i	$-0.0633141\pi$
$182$	266.752	+	280.867i	1.46567	+	1.54322i
$183$	−152.879	+	65.9661i	−0.835403	+	0.360471i
$184$	119.670	+	42.2116i	0.650378	+	0.229411i
$185$	5.75089	−	3.32028i	0.0310859	−	0.0179475i
$186$	33.1802	−	24.8792i	0.178388	−	0.133759i
$187$	−138.227	−	79.8054i	−0.739182	−	0.426767i
$188$	−72.5425	+	111.906i	−0.385865	+	0.595247i
$189$	236.029	−	198.189i	1.24883	−	1.04862i
$190$	46.7331	−	158.006i	0.245964	−	0.831611i
$191$	150.886	+	87.1141i	0.789979	+	0.456095i	0.839955	−	0.542656i	$-0.182581\pi$
$191$	150.886	+	87.1141i	0.789979	+	0.456095i	−0.0499759	+	0.998750i	$0.515914\pi$
$192$	134.529	+	136.989i	0.700670	+	0.713485i
$193$	104.945	+	181.771i	0.543759	+	0.941818i	0.998684	+	0.0512883i	$0.0163327\pi$
$193$	104.945	+	181.771i	0.543759	+	0.941818i	−0.454925	+	0.890530i	$0.650334\pi$
$194$	−39.7812	−	165.402i	−0.205058	−	0.852587i
$195$	177.165	−	76.4454i	0.908538	−	0.392028i
$196$	−289.633	+	147.875i	−1.47772	+	0.754463i
$197$	75.9883			0.385727			0.192864	−	0.981226i	$-0.438223\pi$
$197$	75.9883			0.385727			0.192864	+	0.981226i	$0.438223\pi$
$198$	107.994	−	62.8620i	0.545422	−	0.317485i
$199$	−278.786			−1.40094			−0.700468	−	0.713684i	$-0.747025\pi$
$199$	−278.786			−1.40094			−0.700468	+	0.713684i	$0.747025\pi$
$200$	−83.5975	+	15.6003i	−0.417988	+	0.0780013i
$201$	30.3183	−	259.647i	0.150837	−	1.29177i
$202$	−13.8571	−	57.6149i	−0.0685994	−	0.285222i
$203$	−75.0201	−	129.939i	−0.369557	−	0.640092i
$204$	175.916	−	212.546i	0.862331	−	1.04189i
$205$	125.758	+	72.6065i	0.613454	+	0.354178i
$206$	5.04843	+	1.49316i	0.0245070	+	0.00724836i
$207$	103.861	+	97.9429i	0.501743	+	0.473154i
$208$	−247.821	+	110.824i	−1.19145	+	0.532809i
$209$	130.661	+	75.4371i	0.625172	+	0.360943i
$210$	31.0260	+	257.767i	0.147743	+	1.22746i
$211$	−132.352	+	76.4132i	−0.627259	+	0.362148i	−0.779690	−	0.626166i	$-0.784623\pi$
$211$	−132.352	+	76.4132i	−0.627259	+	0.362148i	0.152431	+	0.988314i	$0.451290\pi$
$212$	0.405557	−	7.86182i	0.00191300	−	0.0370840i
$213$	−93.2526	−	69.4075i	−0.437806	−	0.325857i
$214$	296.011	−	281.134i	1.38323	−	1.31371i
$215$		−	47.7640i		−	0.222158i
$216$	75.9628	+	202.202i	0.351680	+	0.936120i
$217$	−78.8990			−0.363590
$218$	−146.970	−	154.747i	−0.674173	−	0.709847i
$219$	56.9469	−	76.5112i	0.260032	−	0.349366i
$220$	−5.42284	+	105.123i	−0.0246493	+	0.477832i
$221$	195.052	+	337.839i	0.882587	+	1.52869i
$222$	−10.4353	+	1.25604i	−0.0470059	+	0.00565784i
$223$	119.959	−	207.776i	0.537934	−	0.931729i	−0.461081	−	0.887358i	$-0.652538\pi$
$223$	119.959	−	207.776i	0.537934	−	0.931729i	0.999015	−	0.0443711i	$-0.0141284\pi$
$224$	−48.4204	−	362.053i	−0.216163	−	1.61631i
$225$	−93.0970	−	22.0419i	−0.413764	−	0.0979642i
$226$	43.1496	−	145.890i	0.190927	−	0.645532i
$227$	134.662	−	233.242i	0.593227	−	1.02750i	−0.400568	−	0.916267i	$-0.631187\pi$
$227$	134.662	−	233.242i	0.593227	−	1.02750i	0.993795	−	0.111231i	$-0.0354795\pi$
$228$	−166.287	+	200.912i	−0.729327	+	0.881193i
$229$	3.17890	−	1.83534i	0.0138816	−	0.00801457i	−0.493043	−	0.870005i	$-0.664116\pi$
$229$	3.17890	−	1.83534i	0.0138816	−	0.00801457i	0.506925	+	0.861990i	$0.330782\pi$
$230$	−116.924	+	28.1217i	−0.508366	+	0.122268i
$231$	−236.124	−	27.5716i	−1.02218	−	0.119358i
$232$	103.370	−	19.2900i	0.445559	−	0.0831464i
$233$		−	22.7345i		−	0.0975731i	−0.998809	−	0.0487865i	$-0.984465\pi$
$233$		−	22.7345i		−	0.0975731i	0.998809	−	0.0487865i	$-0.0155354\pi$
$234$	−305.405	+	1.08330i	−1.30515	+	0.00462950i
$235$		−	126.386i		−	0.537814i
$236$	−74.9672	+	38.2751i	−0.317657	+	0.162183i
$237$	163.424	+	378.740i	0.689552	+	1.59806i
$238$	−510.346	+	122.744i	−2.14431	+	0.515733i
$239$	67.2142	−	38.8061i	0.281231	−	0.162369i	−0.352750	−	0.935718i	$-0.614753\pi$
$239$	67.2142	−	38.8061i	0.281231	−	0.162369i	0.633981	+	0.773349i	$0.281420\pi$
$240$	−177.598	−	39.5878i	−0.739992	−	0.164949i
$241$	−99.9215	+	173.069i	−0.414612	+	0.718129i	−0.995388	−	0.0959348i	$-0.969416\pi$
$241$	−99.9215	+	173.069i	−0.414612	+	0.718129i	0.580776	+	0.814064i	$0.302749\pi$
$242$	139.636	+	41.2999i	0.577009	+	0.170661i
$243$	−13.9908	+	242.597i	−0.0575752	+	0.998341i
$244$	−120.760	+	186.288i	−0.494917	+	0.763475i
$245$	154.094	−	266.899i	0.628955	−	1.08938i
$246$	−137.884	−	183.889i	−0.560505	−	0.747518i
$247$	−184.375	−	319.348i	−0.746459	−	1.29290i
$248$	18.3939	−	52.1465i	0.0741690	−	0.210268i
$249$	79.7337	+	184.785i	0.320216	+	0.742110i
$250$	195.870	−	186.026i	0.783479	−	0.744104i
$251$	−250.203			−0.996825			−0.498412	−	0.866940i	$-0.666083\pi$
$251$	−250.203			−0.996825			−0.498412	+	0.866940i	$0.666083\pi$
$252$	115.152	−	394.472i	0.456953	−	1.56537i
$253$		−	110.115i		−	0.435237i
$254$	284.682	−	270.375i	1.12080	−	1.06447i
$255$	−30.3252	+	259.706i	−0.118922	+	1.01845i
$256$	250.579	+	52.4038i	0.978824	+	0.204702i
$257$	−287.367	+	165.911i	−1.11816	+	0.645570i	−0.940930	−	0.338600i	$-0.890047\pi$
$257$	−287.367	+	165.911i	−1.11816	+	0.645570i	−0.177229	+	0.984170i	$0.556713\pi$
$258$	−29.7054	+	69.5201i	−0.115137	+	0.269458i
$259$	17.3173	+	9.99814i	0.0668621	+	0.0386029i
$260$	139.943	−	215.881i	0.538244	−	0.830313i
$261$	115.116	+	27.2552i	0.441057	+	0.104426i
$262$	33.0185	+	9.76580i	0.126025	+	0.0372741i
$263$	301.212	+	173.905i	1.14529	+	0.661235i	0.947736	−	0.319057i	$-0.103366\pi$
$263$	301.212	+	173.905i	1.14529	+	0.661235i	0.197557	+	0.980291i	$0.436699\pi$
$264$	73.2710	−	149.633i	0.277541	−	0.566792i
$265$	3.73024	+	6.46097i	0.0140764	+	0.0243810i
$266$	482.411	−	116.026i	1.81358	−	0.436188i
$267$	383.669	+	285.563i	1.43696	+	1.06953i
$268$	−158.492	−	310.428i	−0.591387	−	1.15831i
$269$	−507.709			−1.88740			−0.943698	−	0.330809i	$-0.892678\pi$
$269$	−507.709			−1.88740			−0.943698	+	0.330809i	$0.892678\pi$
$270$	−164.642	−	121.637i	−0.609786	−	0.450508i
$271$	85.0065			0.313677			0.156839	−	0.987624i	$-0.449870\pi$
$271$	85.0065			0.313677			0.156839	+	0.987624i	$0.449870\pi$
$272$	37.8528	−	365.917i	0.139165	−	1.34528i
$273$	466.097	+	346.914i	1.70732	+	1.27075i
$274$	−355.476	+	85.4963i	−1.29736	+	0.312030i
$275$	36.8973	+	63.9080i	0.134172	+	0.232393i
$276$	187.671	+	31.7865i	0.679968	+	0.115169i
$277$	159.497	+	92.0857i	0.575802	+	0.332439i	0.759463	−	0.650550i	$-0.225462\pi$
$277$	159.497	+	92.0857i	0.575802	+	0.332439i	−0.183661	+	0.982990i	$0.558795\pi$
$278$	55.4431	−	187.455i	0.199436	−	0.674299i
$279$	42.6790	−	45.2578i	0.152971	−	0.162214i
$280$	225.143	+	262.953i	0.804081	+	0.939117i
$281$	−244.767	−	141.316i	−0.871057	−	0.502905i	−0.00335771	−	0.999994i	$-0.501069\pi$
$281$	−244.767	−	141.316i	−0.871057	−	0.502905i	−0.867699	+	0.497089i	$0.834402\pi$
$282$	−78.6021	+	183.954i	−0.278731	+	0.652319i
$283$	210.985	−	121.812i	0.745529	−	0.430431i	−0.0785474	−	0.996910i	$-0.525028\pi$
$283$	210.985	−	121.812i	0.745529	−	0.430431i	0.824076	+	0.566479i	$0.191695\pi$
$284$	−154.791	−	7.98497i	−0.545037	−	0.0281161i
$285$	28.6653	−	245.491i	0.100580	−	0.861371i
$286$	162.227	+	170.811i	0.567228	+	0.597243i
$287$			437.270i			1.52359i
$288$	233.872	+	168.071i	0.812055	+	0.583581i
$289$	−239.626			−0.829154
$290$	−72.2581	+	68.6267i	−0.249166	+	0.236644i
$291$	−101.098	−	234.297i	−0.347414	−	0.805144i
$292$	6.55145	−	127.002i	0.0224365	−	0.434937i
$293$	−285.189	−	493.962i	−0.973342	−	1.68588i	−0.685303	−	0.728258i	$-0.740330\pi$
$293$	−285.189	−	493.962i	−0.973342	−	1.68588i	−0.288039	−	0.957619i	$-0.593003\pi$
$294$	−390.272	+	292.634i	−1.32746	+	0.995355i
$295$	39.8849	−	69.0827i	0.135203	−	0.234179i
$296$	−10.6453	+	9.11458i	−0.0359637	+	0.0307925i
$297$	143.543	−	120.530i	0.483309	−	0.405826i
$298$	−54.2178	−	16.0359i	−0.181939	−	0.0538116i
$299$	−134.566	+	233.074i	−0.450052	+	0.779513i
$300$	−119.571	+	44.4368i	−0.398569	+	0.148123i
$301$	124.559	−	71.9143i	0.413818	−	0.238918i
$302$	−20.6816	−	85.9899i	−0.0684822	−	0.284735i
$303$	−35.2156	−	81.6132i	−0.116223	−	0.269351i
$304$	−35.7809	+	345.888i	−0.117700	+	1.13779i
$305$		−	210.392i		−	0.689810i
$306$	205.654	−	359.139i	0.672072	−	1.17366i
$307$			147.169i			0.479377i	0.970850	+	0.239688i	$0.0770453\pi$
$307$			147.169i			0.479377i	−0.970850	+	0.239688i	$0.922955\pi$
$308$	−282.305	+	144.133i	−0.916575	+	0.467966i
$309$	7.84364	+	0.915882i	0.0253839	+	0.00296402i
$310$	12.2542	+	50.9502i	0.0395295	+	0.164355i
$311$	−140.255	+	80.9762i	−0.450981	+	0.260374i	−0.708244	−	0.705967i	$-0.750512\pi$
$311$	−140.255	+	80.9762i	−0.450981	+	0.260374i	0.257264	+	0.966341i	$0.417179\pi$
$312$	−337.947	+	227.180i	−1.08316	+	0.728140i
$313$	−217.298	+	376.370i	−0.694241	+	1.20246i	0.276195	+	0.961102i	$0.410927\pi$
$313$	−217.298	+	376.370i	−0.694241	+	1.20246i	−0.970436	+	0.241359i	$0.922407\pi$
$314$	−130.468	+	441.115i	−0.415502	+	1.40483i
$315$	111.778	+	373.055i	0.354851	+	1.18430i
$316$	461.508	+	299.169i	1.46047	+	0.946738i
$317$	−303.122	+	525.022i	−0.956219	+	1.65622i	−0.224667	+	0.974436i	$0.572129\pi$
$317$	−303.122	+	525.022i	−0.956219	+	1.65622i	−0.731553	+	0.681785i	$0.761204\pi$
$318$	−1.41113	−	11.7238i	−0.00443751	−	0.0368673i
$319$	−45.6241	−	79.0232i	−0.143022	−	0.247722i
$320$	−226.281	+	87.5002i	−0.707127	+	0.273438i
$321$	365.619	−	491.228i	1.13900	−	1.53031i
$322$	−249.379	−	262.575i	−0.774469	−	0.815450i
$323$	499.691			1.54703
$324$	163.986	+	279.436i	0.506131	+	0.862457i
$325$		−	180.361i		−	0.554957i
$326$	52.6795	+	55.4670i	0.161594	+	0.170144i
$327$	−256.801	−	191.136i	−0.785325	−	0.584513i
$328$	−289.004	−	101.942i	−0.881109	−	0.310798i
$329$	329.591	−	190.289i	1.00180	−	0.578387i
$330$	18.8687	+	156.763i	0.0571778	+	0.475039i
$331$	−339.693	−	196.122i	−1.02626	−	0.592514i	−0.110352	−	0.993893i	$-0.535198\pi$
$331$	−339.693	−	196.122i	−1.02626	−	0.592514i	−0.915912	+	0.401379i	$0.868531\pi$
$332$	225.167	+	145.963i	0.678215	+	0.439648i
$333$	−15.1026	+	4.52517i	−0.0453531	+	0.0135891i
$334$	12.6532	−	42.7808i	0.0378838	−	0.128086i
$335$	286.062	+	165.158i	0.853916	+	0.493008i
$336$	−164.158	−	522.745i	−0.488564	−	1.55579i
$337$	3.96893	+	6.87439i	0.0117772	+	0.0203988i	0.871854	−	0.489766i	$-0.162918\pi$
$337$	3.96893	+	6.87439i	0.0117772	+	0.0203988i	−0.860077	+	0.510165i	$0.829584\pi$
$338$	−55.5987	−	231.168i	−0.164493	−	0.683928i
$339$	26.4673	−	226.666i	0.0780745	−	0.668632i
$340$	158.528	+	310.499i	0.466259	+	0.913233i
$341$	−47.9831			−0.140713
$342$	−194.397	+	339.482i	−0.568414	+	0.992636i
$343$	368.697			1.07492
$344$	18.4914	+	99.0902i	0.0537540	+	0.288053i
$345$	−165.627	+	71.4668i	−0.480077	+	0.207150i
$346$	59.7348	+	248.365i	0.172644	+	0.717817i
$347$	108.377	+	187.715i	0.312326	+	0.540965i	0.978866	−	0.204505i	$-0.0655584\pi$
$347$	108.377	+	187.715i	0.312326	+	0.540965i	−0.666539	+	0.745470i	$0.732225\pi$
$348$	147.851	−	54.9467i	0.424859	−	0.157893i
$349$	−434.379	−	250.789i	−1.24464	−	0.718593i	−0.274605	−	0.961557i	$-0.588547\pi$
$349$	−434.379	−	250.789i	−1.24464	−	0.718593i	−0.970035	+	0.242964i	$0.921880\pi$
$350$	232.717	+	68.8301i	0.664906	+	0.196658i
$351$	−451.123	+	79.7044i	−1.28525	+	0.227078i
$352$	−29.4473	−	220.185i	−0.0836570	−	0.625527i
$353$	−140.586	−	81.1674i	−0.398261	−	0.229936i	0.287472	−	0.957789i	$-0.407185\pi$
$353$	−140.586	−	81.1674i	−0.398261	−	0.229936i	−0.685733	+	0.727853i	$0.740518\pi$
$354$	−101.016	+	75.7440i	−0.285356	+	0.213966i
$355$	127.209	−	73.4444i	0.358337	−	0.206886i
$356$	636.855	+	32.8526i	1.78892	+	0.0922825i
$357$	−722.920	+	311.935i	−2.02499	+	0.873768i
$358$	−149.431	+	141.922i	−0.417406	+	0.396429i
$359$		−	245.739i		−	0.684509i	−0.939607	−	0.342255i	$-0.888809\pi$
$359$		−	245.739i		−	0.684509i	0.939607	−	0.342255i	$-0.111191\pi$
$360$	−272.621	−	13.0939i	−0.757280	−	0.0363719i
$361$	−111.340			−0.308420
$362$	−98.5192	−	103.732i	−0.272153	−	0.286554i
$363$	216.950	+	25.3327i	0.597657	+	0.0697870i
$364$	773.678	+	39.9106i	2.12549	+	0.109645i
$365$	60.2592	+	104.372i	0.165094	+	0.285951i
$366$	−130.847	+	306.223i	−0.357505	+	0.836676i
$367$	13.1011	−	22.6918i	0.0356979	−	0.0618305i	−0.847624	−	0.530597i	$-0.821968\pi$
$367$	13.1011	−	22.6918i	0.0356979	−	0.0618305i	0.883322	+	0.468766i	$0.155301\pi$
$368$	231.681	−	103.607i	0.629568	−	0.281540i
$369$	−250.826	−	236.534i	−0.679744	−	0.641012i
$370$	3.76682	−	12.7357i	0.0101806	−	0.0344209i
$371$	−11.2326	+	19.4555i	−0.0302767	+	0.0524407i
$372$	13.8511	−	81.7786i	0.0372342	−	0.219835i
$373$	−19.4643	+	11.2377i	−0.0521831	+	0.0301279i	−0.525865	−	0.850568i	$-0.676258\pi$
$373$	−19.4643	+	11.2377i	−0.0521831	+	0.0301279i	0.473681	+	0.880696i	$0.342925\pi$
$374$	−310.371	+	74.6480i	−0.829868	+	0.199594i
$375$	241.929	−	325.045i	0.645145	−	0.866786i
$376$	48.9292	+	262.198i	0.130131	+	0.697335i
$377$			223.019i			0.591562i
$378$	69.3181	−	612.494i	0.183381	−	1.62035i
$379$			170.148i			0.448940i	0.974481	+	0.224470i	$0.0720650\pi$
$379$			170.148i			0.448940i	−0.974481	+	0.224470i	$0.927935\pi$
$380$	−149.851	−	293.504i	−0.394344	−	0.772378i
$381$	351.627	−	472.429i	0.922905	−	1.23997i
$382$	338.795	−	81.4844i	0.886898	−	0.213310i
$383$	83.5469	−	48.2358i	0.218138	−	0.125942i	−0.386950	−	0.922101i	$-0.626471\pi$
$383$	83.5469	−	48.2358i	0.218138	−	0.125942i	0.605088	+	0.796159i	$0.293138\pi$
$384$	383.767	+	13.3726i	0.999393	+	0.0348244i
$385$	150.195	−	260.146i	0.390118	−	0.675704i
$386$	402.544	+	119.059i	1.04286	+	0.308444i
$387$	−26.1269	+	110.350i	−0.0675113	+	0.285142i
$388$	−285.499	−	185.072i	−0.735822	−	0.476991i
$389$	55.8230	−	96.6882i	0.143504	−	0.248556i	−0.785310	−	0.619103i	$-0.787496\pi$
$389$	55.8230	−	96.6882i	0.143504	−	0.248556i	0.928814	+	0.370547i	$0.120830\pi$
$390$	151.633	−	354.870i	0.388803	−	0.909923i
$391$	−182.349	−	315.837i	−0.466365	−	0.807767i
$392$	−216.353	+	613.358i	−0.551921	+	1.56469i
$393$	51.3001	+	5.99019i	0.130535	+	0.0152422i
$394$	110.197	−	104.659i	0.279688	−	0.265632i
$395$	−521.223			−1.31955
$396$	70.0306	−	239.901i	0.176845	−	0.605812i
$397$		−	582.265i		−	1.46666i	−0.679871	−	0.733332i	$-0.737964\pi$
$397$		−	582.265i		−	1.46666i	0.679871	−	0.733332i	$-0.262036\pi$
$398$	−404.292	+	383.973i	−1.01581	+	0.964758i
$399$	683.351	−	294.861i	1.71266	−	0.739001i
$400$	−99.7455	+	137.762i	−0.249364	+	0.344406i
$401$	−530.337	+	306.190i	−1.32254	+	0.763567i	−0.984133	−	0.177434i	$-0.943220\pi$
$401$	−530.337	+	306.190i	−1.32254	+	0.763567i	−0.338404	+	0.941001i	$0.609887\pi$
$402$	−313.645	−	418.293i	−0.780211	−	1.04053i
$403$	101.563	+	58.6375i	0.252018	+	0.145503i
$404$	−99.4485	−	64.4667i	−0.246160	−	0.159571i
$405$	−274.455	−	137.679i	−0.677666	−	0.339949i
$406$	−287.758	−	85.1095i	−0.708763	−	0.209629i
$407$	10.5316	+	6.08045i	0.0258763	+	0.0149397i
$408$	−37.6305	−	550.520i	−0.0922317	−	1.34931i
$409$	169.968	+	294.393i	0.415569	+	0.719786i	0.995488	−	0.0948878i	$-0.0302492\pi$
$409$	169.968	+	294.393i	0.415569	+	0.719786i	−0.579919	+	0.814674i	$0.696916\pi$
$410$	282.374	−	67.9144i	0.688716	−	0.165645i
$411$	−503.542	+	217.275i	−1.22516	+	0.528650i
$412$	9.37770	−	4.78787i	0.0227614	−	0.0116210i
$413$	240.206			0.581612
$414$	285.514	−	1.01275i	0.689648	−	0.00244626i
$415$	−254.302			−0.612776
$416$	−206.747	+	502.040i	−0.496989	+	1.20683i
$417$	34.0079	−	291.245i	0.0815538	−	0.698428i
$418$	293.382	−	70.5621i	0.701872	−	0.168809i
$419$	38.4222	+	66.5492i	0.0916998	+	0.158829i	0.908226	−	0.418479i	$-0.137437\pi$
$419$	38.4222	+	66.5492i	0.0916998	+	0.158829i	−0.816527	+	0.577308i	$0.804103\pi$
$420$	400.016	+	331.077i	0.952420	+	0.788278i
$421$	697.260	+	402.563i	1.65620	+	0.956207i	0.974445	+	0.224627i	$0.0721162\pi$
$421$	697.260	+	402.563i	1.65620	+	0.956207i	0.681755	+	0.731581i	$0.261217\pi$
$422$	−86.6900	+	293.102i	−0.205426	+	0.694554i
$423$	−69.1331	+	291.992i	−0.163435	+	0.690290i
$424$	−10.2400	−	11.9597i	−0.0241509	−	0.0282067i
$425$	211.661	+	122.203i	0.498027	+	0.287536i
$426$	−230.829	+	27.7836i	−0.541851	+	0.0652197i
$427$	548.661	−	316.770i	1.28492	−	0.741850i
$428$	42.0625	−	815.393i	0.0982769	−	1.90512i
$429$	283.461	+	210.978i	0.660748	+	0.491791i
$430$	−65.7856	−	69.2666i	−0.152990	−	0.161085i
$431$		−	713.531i		−	1.65552i	−0.561080	−	0.827762i	$-0.689614\pi$
$431$		−	713.531i		−	1.65552i	0.561080	−	0.827762i	$-0.310386\pi$
$432$	388.654	+	188.606i	0.899661	+	0.436589i
$433$	488.389			1.12792			0.563960	−	0.825802i	$-0.309277\pi$
$433$	488.389			1.12792			0.563960	+	0.825802i	$0.309277\pi$
$434$	−114.418	+	108.668i	−0.263636	+	0.250387i
$435$	−89.2498	+	119.912i	−0.205172	+	0.275660i
$436$	−426.266	−	21.9892i	−0.977674	−	0.0504339i
$437$	172.368	+	298.549i	0.394434	+	0.683179i
$438$	−22.7957	−	189.389i	−0.0520449	−	0.432394i
$439$	−190.893	+	330.636i	−0.434836	+	0.753158i	−0.997282	−	0.0736756i	$-0.976527\pi$
$439$	−190.893	+	330.636i	−0.434836	+	0.753158i	0.562446	+	0.826834i	$0.309860\pi$
$440$	136.922	+	159.917i	0.311187	+	0.363447i
$441$	−502.000	+	532.332i	−1.13832	+	1.20710i
$442$	748.169	+	221.284i	1.69269	+	0.500643i
$443$	271.361	−	470.011i	0.612554	−	1.06097i	−0.378255	−	0.925702i	$-0.623476\pi$
$443$	271.361	−	470.011i	0.612554	−	1.06097i	0.990808	−	0.135272i	$-0.0431910\pi$
$444$	−13.4032	+	16.1941i	−0.0301873	+	0.0364732i
$445$	−523.378	+	302.173i	−1.17613	+	0.679039i
$446$	−112.207	−	466.533i	−0.251585	−	1.04604i
$447$	−84.2370	−	9.83615i	−0.188450	−	0.0220048i
$448$	−568.875	−	458.354i	−1.26981	−	1.02311i
$449$		−	131.985i		−	0.293953i	−0.989140	−	0.146976i	$-0.953046\pi$
$449$		−	131.985i		−	0.293953i	0.989140	−	0.146976i	$-0.0469542\pi$
$450$	−165.366	+	96.2579i	−0.367480	+	0.213906i
$451$			265.929i			0.589644i
$452$	−138.360	−	270.998i	−0.306107	−	0.599552i
$453$	−52.5590	−	121.807i	−0.116024	−	0.268890i
$454$	−125.960	−	523.715i	−0.277445	−	1.15356i
$455$	−635.821	+	367.092i	−1.39741	+	0.806795i
$456$	35.5708	+	520.387i	0.0780061	+	1.14120i
$457$	127.088	−	220.122i	0.278091	−	0.481668i	−0.692819	−	0.721111i	$-0.743632\pi$
$457$	127.088	−	220.122i	0.278091	−	0.481668i	0.970910	+	0.239443i	$0.0769649\pi$
$458$	2.08217	−	7.03988i	0.00454622	−	0.0153709i
$459$	212.120	−	583.415i	0.462134	−	1.27106i
$460$	−130.829	+	201.822i	−0.284412	+	0.438743i
$461$	247.923	−	429.415i	0.537794	−	0.931487i	−0.461228	−	0.887281i	$-0.652591\pi$
$461$	247.923	−	429.415i	0.537794	−	0.931487i	0.999022	−	0.0442051i	$-0.0140755\pi$
$462$	−380.398	+	285.231i	−0.823372	+	0.617382i
$463$	188.880	+	327.149i	0.407947	+	0.706586i	0.994660	−	0.103210i	$-0.0329113\pi$
$463$	188.880	+	327.149i	0.407947	+	0.706586i	−0.586712	+	0.809796i	$0.699578\pi$
$464$	123.337	−	170.345i	0.265812	−	0.367124i
$465$	31.1420	+	72.1725i	0.0669720	+	0.155210i
$466$	−31.3124	−	32.9693i	−0.0671939	−	0.0707495i
$467$	−134.451			−0.287904			−0.143952	−	0.989585i	$-0.545981\pi$
$467$	−134.451			−0.287904			−0.143952	+	0.989585i	$0.545981\pi$
$468$	−441.401	+	422.206i	−0.943164	+	0.902149i
$469$			994.658i			2.12081i
$470$	−174.072	−	183.283i	−0.370367	−	0.389965i
$471$	−80.0267	+	685.351i	−0.169908	+	1.45510i
$472$	−55.9997	+	158.759i	−0.118643	+	0.336353i
$473$	75.7517	−	43.7353i	0.160152	−	0.0924636i
$474$	758.635	+	324.159i	1.60050	+	0.683880i
$475$	−200.076	−	115.514i	−0.421212	−	0.243187i
$476$	−571.039	+	880.903i	−1.19966	+	1.85064i
$477$	−5.08391	−	16.9673i	−0.0106581	−	0.0355709i
$478$	44.0251	−	148.850i	0.0921028	−	0.311402i
$479$	−266.094	−	153.630i	−0.555521	−	0.320730i	0.195825	−	0.980639i	$-0.437262\pi$
$479$	−266.094	−	153.630i	−0.555521	−	0.320730i	−0.751346	+	0.659909i	$0.770595\pi$
$480$	−312.074	+	187.197i	−0.650155	+	0.389994i
$481$	−14.8612	−	25.7403i	−0.0308964	−	0.0535142i
$482$	93.4641	+	388.604i	0.193909	+	0.806233i
$483$	−435.742	−	324.320i	−0.902157	−	0.671471i
$484$	259.381	−	132.429i	0.535910	−	0.273614i
$485$	322.440			0.664825
$486$	313.840	+	371.080i	0.645762	+	0.763539i
$487$	489.926			1.00601			0.503005	−	0.864284i	$-0.332228\pi$
$487$	489.926			1.00601			0.503005	+	0.864284i	$0.332228\pi$
$488$	81.4512	+	436.475i	0.166908	+	0.894415i
$489$	92.0473	+	68.5103i	0.188236	+	0.140103i
$490$	−144.136	−	599.287i	−0.294155	−	1.22303i
$491$	45.0122	+	77.9634i	0.0916745	+	0.158785i	0.908216	−	0.418502i	$-0.137445\pi$
$491$	45.0122	+	77.9634i	0.0916745	+	0.158785i	−0.816541	+	0.577287i	$0.804111\pi$
$492$	−453.229	−	76.7649i	−0.921197	−	0.156026i
$493$	−261.722	−	151.105i	−0.530877	−	0.306502i
$494$	−707.217	−	209.172i	−1.43161	−	0.423425i
$495$	67.9787	+	226.876i	0.137331	+	0.458336i
$496$	−45.1471	−	100.956i	−0.0910223	−	0.203540i
$497$	383.058	+	221.158i	0.770740	+	0.444987i
$498$	370.134	+	158.155i	0.743242	+	0.317581i
$499$	−471.622	+	272.291i	−0.945134	+	0.545673i	−0.891566	−	0.452891i	$-0.850393\pi$
$499$	−471.622	+	272.291i	−0.945134	+	0.545673i	−0.0535679	+	0.998564i	$0.517059\pi$
$500$	27.8327	−	539.544i	0.0556654	−	1.07909i
$501$	7.76126	−	66.4676i	0.0154915	−	0.132670i
$502$	−362.840	+	344.605i	−0.722790	+	0.686465i
$503$		−	59.9114i		−	0.119108i	−0.998225	−	0.0595541i	$-0.981032\pi$
$503$		−	59.9114i		−	0.119108i	0.998225	−	0.0595541i	$-0.0189679\pi$
$504$	−376.316	−	730.657i	−0.746660	−	1.44972i
$505$	112.316			0.222409
$506$	−151.662	−	159.687i	−0.299727	−	0.315587i
$507$	−141.295	−	327.456i	−0.278689	−	0.645870i
$508$	40.4528	−	784.188i	0.0796315	−	1.54368i
$509$	328.303	+	568.638i	0.644996	+	1.11717i	0.984302	+	0.176490i	$0.0564744\pi$
$509$	328.303	+	568.638i	0.644996	+	1.11717i	−0.339306	+	0.940676i	$0.610192\pi$
$510$	313.717	+	418.388i	0.615131	+	0.820369i
$511$	−181.454	+	314.288i	−0.355097	+	0.615046i
$512$	435.562	−	269.128i	0.850706	−	0.525641i
$513$	−200.509	+	551.481i	−0.390856	+	1.07501i
$514$	−188.225	+	636.394i	−0.366196	+	1.23812i
$515$	−4.98924	+	8.64161i	−0.00968784	+	0.0167798i
$516$	52.6720	+	141.730i	0.102077	+	0.274671i
$517$	200.443	−	115.726i	0.387705	−	0.223841i
$518$	38.8837	−	9.35202i	0.0750651	−	0.0180541i
$519$	151.806	+	351.816i	0.292498	+	0.677873i
$520$	−94.3905	−	505.813i	−0.181520	−	0.972716i
$521$		−	657.693i		−	1.26237i	−0.775634	−	0.631184i	$-0.782569\pi$
$521$		−	657.693i		−	1.26237i	0.775634	−	0.631184i	$-0.217431\pi$
$522$	204.478	−	119.024i	0.391720	−	0.228016i
$523$			534.207i			1.02143i	0.859750	+	0.510714i	$0.170619\pi$
$523$			534.207i			1.02143i	−0.859750	+	0.510714i	$0.829381\pi$
$524$	61.3334	−	31.3143i	0.117048	−	0.0597601i
$525$	361.567	+	42.2193i	0.688699	+	0.0804177i
$526$	676.332	−	162.666i	1.28580	−	0.309252i
$527$	−137.627	+	79.4592i	−0.261152	+	0.150776i
$528$	−99.8337	−	317.912i	−0.189079	−	0.602106i
$529$	−138.698	+	240.232i	−0.262190	+	0.454126i
$530$	14.3083	+	4.23192i	0.0269967	+	0.00798475i
$531$	−129.935	+	137.786i	−0.244699	+	0.259484i
$532$	539.783	−	832.686i	1.01463	−	1.56520i
$533$	324.978	−	562.878i	0.609715	−	1.05606i
$534$	949.698	−	114.310i	1.77846	−	0.214064i
$535$	386.884	+	670.103i	0.723148	+	1.25253i
$536$	−657.396	−	231.887i	−1.22649	−	0.432624i
$537$	−184.571	+	247.981i	−0.343707	+	0.461789i
$538$	−736.272	+	699.270i	−1.36854	+	1.29976i
$539$	564.387			1.04710
$540$	−406.293	+	50.3659i	−0.752394	+	0.0932702i
$541$		−	41.7800i		−	0.0772273i	−0.999254	−	0.0386137i	$-0.987706\pi$
$541$		−	41.7800i		−	0.0772273i	0.999254	−	0.0386137i	$-0.0122942\pi$
$542$	123.275	−	117.080i	0.227445	−	0.216014i
$543$	−172.143	−	128.125i	−0.317023	−	0.235959i
$544$	−449.085	−	582.782i	−0.825525	−	1.07129i
$545$	350.312	−	202.253i	0.642775	−	0.371106i
$546$	1153.73	−	138.869i	2.11306	−	0.254338i
$547$	−72.1250	−	41.6414i	−0.131855	−	0.0761268i	0.432621	−	0.901576i	$-0.357589\pi$
$547$	−72.1250	−	41.6414i	−0.131855	−	0.0761268i	−0.564477	+	0.825449i	$0.690922\pi$
$548$	−397.751	+	613.584i	−0.725823	+	1.11968i
$549$	−115.084	+	486.072i	−0.209625	+	0.885378i
$550$	141.529	+	41.8596i	0.257325	+	0.0761083i
$551$	247.397	+	142.835i	0.448996	+	0.259228i
$552$	315.938	−	212.384i	0.572351	−	0.384754i
$553$	−784.763	−	1359.25i	−1.41910	−	2.45796i
$554$	358.130	−	86.1348i	0.646445	−	0.155478i
$555$	2.31051	−	19.7872i	0.00416308	−	0.0356527i
$556$	−177.780	−	348.206i	−0.319748	−	0.626270i
$557$	−233.457			−0.419133			−0.209566	−	0.977794i	$-0.567205\pi$
$557$	−233.457			−0.419133			−0.209566	+	0.977794i	$0.567205\pi$
$558$	−0.441311	−	124.414i	−0.000790880	−	0.222964i
$559$	−213.786			−0.382444
$560$	688.664	+	71.2399i	1.22976	+	0.127214i
$561$	−439.650	+	189.706i	−0.783690	+	0.338157i
$562$	−549.593	+	132.184i	−0.977923	+	0.235203i
$563$	−314.155	−	544.133i	−0.558002	−	0.966488i	−0.997663	−	0.0683244i	$-0.978235\pi$
$563$	−314.155	−	544.133i	−0.558002	−	0.966488i	0.439661	−	0.898164i	$-0.355099\pi$
$564$	139.373	+	375.026i	0.247115	+	0.664940i
$565$	249.726	+	144.179i	0.441993	+	0.255185i
$566$	138.194	−	467.240i	0.244160	−	0.825512i
$567$	−54.1824	−	923.017i	−0.0955598	−	1.62790i
$568$	−235.473	+	201.614i	−0.414565	+	0.354954i
$569$	584.843	+	337.660i	1.02784	+	0.593426i	0.916366	−	0.400341i	$-0.131108\pi$
$569$	584.843	+	337.660i	1.02784	+	0.593426i	0.111478	+	0.993767i	$0.464442\pi$
$570$	−296.545	−	395.487i	−0.520255	−	0.693838i
$571$	−637.313	+	367.953i	−1.11613	+	0.644400i	−0.940411	−	0.340039i	$-0.889560\pi$
$571$	−637.313	+	367.953i	−1.11613	+	0.644400i	−0.175723	+	0.984440i	$0.556226\pi$
$572$	470.518	+	24.2720i	0.822585	+	0.0424335i
$573$	479.914	−	207.080i	0.837546	−	0.361395i
$574$	602.254	+	634.122i	1.04922	+	1.10474i
$575$			168.615i			0.293243i
$576$	570.642	−	78.3782i	0.990699	−	0.136073i
$577$	180.595			0.312990			0.156495	−	0.987679i	$-0.449981\pi$
$577$	180.595			0.312990			0.156495	+	0.987679i	$0.449981\pi$
$578$	−347.501	+	330.037i	−0.601213	+	0.570999i
$579$	625.424	+	73.0292i	1.08018	+	0.126130i
$580$	−10.2677	+	199.043i	−0.0177030	+	0.343177i
$581$	−382.882	−	663.171i	−0.659005	−	1.14143i
$582$	−469.308	−	200.532i	−0.806371	−	0.344556i
$583$	−6.83122	+	11.8320i	−0.0117174	+	0.0202951i
$584$	−165.419	−	193.199i	−0.283251	−	0.330820i
$585$	133.366	−	563.290i	0.227977	−	0.962888i
$586$	−1093.91	−	323.544i	−1.86674	−	0.552123i
$587$	134.034	−	232.154i	0.228338	−	0.395493i	−0.728978	−	0.684537i	$-0.760004\pi$
$587$	134.034	−	232.154i	0.228338	−	0.395493i	0.957316	+	0.289045i	$0.0933376\pi$
$588$	−162.920	+	961.897i	−0.277074	+	1.63588i
$589$	130.094	−	75.1099i	0.220873	−	0.127521i
$590$	−37.3074	−	155.116i	−0.0632329	−	0.262909i
$591$	136.110	−	182.871i	0.230305	−	0.309427i
$592$	−2.88404	+	27.8796i	−0.00487170	+	0.0470939i
$593$			195.220i			0.329208i	0.986360	+	0.164604i	$0.0526345\pi$
$593$			195.220i			0.329208i	−0.986360	+	0.164604i	$0.947365\pi$
$594$	42.1564	−	372.493i	0.0709703	−	0.627093i
$595$		−	994.885i		−	1.67208i
$596$	−100.712	+	51.4194i	−0.168980	+	0.0862742i
$597$	−499.362	+	670.920i	−0.836453	+	1.12382i
$598$	125.869	+	523.339i	0.210484	+	0.875148i
$599$	733.133	−	423.274i	1.22393	−	0.706635i	0.258175	−	0.966098i	$-0.416879\pi$
$599$	733.133	−	423.274i	1.22393	−	0.706635i	0.965753	+	0.259463i	$0.0835456\pi$
$600$	−112.197	+	229.127i	−0.186995	+	0.381878i
$601$	400.778	−	694.167i	0.666851	−	1.15502i	−0.311928	−	0.950106i	$-0.600975\pi$
$601$	400.778	−	694.167i	0.666851	−	1.15502i	0.978780	−	0.204915i	$-0.0656918\pi$
$602$	81.5860	−	275.845i	0.135525	−	0.458214i
$603$	−570.552	−	538.042i	−0.946190	−	0.892276i
$604$	−148.426	−	96.2163i	−0.245739	−	0.159298i
$605$	−137.999	+	239.021i	−0.228097	+	0.395076i
$606$	−163.475	−	69.8517i	−0.269761	−	0.115267i
$607$	−269.066	−	466.036i	−0.443272	−	0.767770i	0.554658	−	0.832078i	$-0.312849\pi$
$607$	−269.066	−	466.036i	−0.443272	−	0.767770i	−0.997930	+	0.0643086i	$0.979516\pi$
$608$	424.504	+	550.883i	0.698198	+	0.906057i
$609$	−447.083	−	52.2048i	−0.734126	−	0.0857222i
$610$	−289.774	−	305.107i	−0.475039	−	0.500176i
$611$	−565.690			−0.925843
$612$	−196.408	−	804.066i	−0.320928	−	1.31383i
$613$			977.999i			1.59543i	0.603034	+	0.797715i	$0.293958\pi$
$613$			977.999i			1.59543i	−0.603034	+	0.797715i	$0.706042\pi$
$614$	202.696	+	213.422i	0.330124	+	0.347592i
$615$	399.991	−	172.593i	0.650392	−	0.280640i
$616$	−210.879	+	597.840i	−0.342336	+	0.970520i
$617$	−174.494	+	100.744i	−0.282810	+	0.163280i	−0.634695	−	0.772763i	$-0.718874\pi$
$617$	−174.494	+	100.744i	−0.282810	+	0.163280i	0.351885	+	0.936043i	$0.385541\pi$
$618$	12.6362	−	9.47487i	0.0204469	−	0.0153315i
$619$	646.869	+	373.470i	1.04502	+	0.603344i	0.921252	−	0.388967i	$-0.127168\pi$
$619$	646.869	+	373.470i	1.04502	+	0.603344i	0.123771	+	0.992311i	$0.460501\pi$
$620$	87.9447	+	57.0095i	0.141846	+	0.0919508i
$621$	421.742	−	74.5134i	0.679134	−	0.119989i
$622$	−91.8666	+	310.604i	−0.147696	+	0.499364i
$623$	−1576.01	−	909.912i	−2.52972	−	1.46053i
$624$	−177.190	+	794.908i	−0.283959	+	1.27389i
$625$	123.125	+	213.258i	0.196999	+	0.341213i
$626$	203.255	+	845.091i	0.324688	+	1.34999i
$627$	415.585	−	179.322i	0.662815	−	0.286000i
$628$	418.348	+	819.392i	0.666158	+	1.30476i
$629$	40.2765			0.0640326
$630$	675.908	+	387.046i	1.07287	+	0.614358i
$631$	−700.521			−1.11018			−0.555088	−	0.831792i	$-0.687315\pi$
$631$	−700.521			−1.11018			−0.555088	+	0.831792i	$0.687315\pi$
$632$	1081.32	−	201.786i	1.71095	−	0.319282i
$633$	−53.1742	+	455.385i	−0.0840035	+	0.719408i
$634$	283.533	+	1178.87i	0.447212	+	1.85941i
$635$	372.079	+	644.459i	0.585950	+	1.01490i
$636$	−18.1936	−	15.0581i	−0.0286063	−	0.0236763i
$637$	−1194.61	−	689.707i	−1.87536	−	1.08274i
$638$	−175.002	−	51.7600i	−0.274298	−	0.0811285i
$639$	−334.068	+	100.097i	−0.522799	+	0.156646i
$640$	−207.634	+	438.549i	−0.324428	+	0.685232i
$641$	271.932	+	157.000i	0.424231	+	0.244930i	0.696886	−	0.717182i	$-0.254568\pi$
$641$	271.932	+	157.000i	0.424231	+	0.244930i	−0.272655	+	0.962112i	$0.587902\pi$
$642$	−146.356	−	1215.94i	−0.227969	−	1.89399i
$643$	31.2886	−	18.0645i	0.0486603	−	0.0280940i	−0.475472	−	0.879731i	$-0.657723\pi$
$643$	31.2886	−	18.0645i	0.0486603	−	0.0280940i	0.524133	+	0.851637i	$0.324390\pi$
$644$	−723.291	−	37.3114i	−1.12312	−	0.0579369i
$645$	−114.948	−	85.5550i	−0.178213	−	0.132643i
$646$	724.644	−	688.226i	1.12174	−	1.06537i
$647$		−	750.073i		−	1.15931i	−0.814862	−	0.579655i	$-0.803187\pi$
$647$		−	750.073i		−	1.15931i	0.814862	−	0.579655i	$-0.196813\pi$
$648$	622.679	+	179.374i	0.960924	+	0.276812i
$649$	146.083			0.225089
$650$	−248.412	−	261.556i	−0.382172	−	0.402395i
$651$	−141.324	+	189.876i	−0.217088	+	0.291669i
$652$	152.790	+	7.88176i	0.234340	+	0.0120886i
$653$	10.5807	+	18.3264i	0.0162033	+	0.0280649i	0.874013	−	0.485902i	$-0.161509\pi$
$653$	10.5807	+	18.3264i	0.0162033	+	0.0280649i	−0.857810	+	0.513967i	$0.828175\pi$
$654$	−635.661	+	76.5111i	−0.971959	+	0.116989i
$655$	−32.6313	+	56.5191i	−0.0498188	+	0.0862888i
$656$	−559.513	+	250.212i	−0.852917	+	0.381420i
$657$	−82.1265	−	274.094i	−0.125002	−	0.417190i
$658$	215.881	−	729.901i	0.328087	−	1.10927i
$659$	−566.376	+	980.992i	−0.859448	+	1.48861i	0.0130092	+	0.999915i	$0.495859\pi$
$659$	−566.376	+	980.992i	−0.859448	+	1.48861i	−0.872457	+	0.488691i	$0.837474\pi$
$660$	243.273	+	201.347i	0.368596	+	0.305071i
$661$	478.603	−	276.322i	0.724060	−	0.418036i	−0.0921855	−	0.995742i	$-0.529385\pi$
$661$	478.603	−	276.322i	0.724060	−	0.418036i	0.816245	+	0.577706i	$0.196052\pi$
$662$	−762.737	+	183.448i	−1.15217	+	0.277111i
$663$	1162.41	+	135.732i	1.75326	+	0.204724i
$664$	527.570	−	98.4506i	0.794533	−	0.148269i
$665$			940.429i			1.41418i
$666$	−15.6690	+	27.3632i	−0.0235270	+	0.0410858i
$667$		−	208.494i		−	0.312585i
$668$	−40.5728	−	79.4674i	−0.0607377	−	0.118963i
$669$	−285.156	−	660.859i	−0.426242	−	0.987831i
$670$	642.315	−	154.485i	0.958679	−	0.230574i
$671$	333.673	−	192.646i	0.497277	−	0.287103i
$672$	−958.038	−	531.982i	−1.42565	−	0.791640i
$673$	82.2812	−	142.515i	0.122260	−	0.211761i	−0.798398	−	0.602130i	$-0.794319\pi$
$673$	82.2812	−	142.515i	0.122260	−	0.211761i	0.920659	+	0.390368i	$0.127652\pi$
$674$	15.2238	+	4.50271i	0.0225872	+	0.00668057i
$675$	−219.801	+	184.563i	−0.325631	+	0.273427i
$676$	−399.017	−	258.659i	−0.590261	−	0.382632i
$677$	303.242	−	525.230i	0.447920	−	0.775819i	−0.550331	−	0.834947i	$-0.685498\pi$
$677$	303.242	−	525.230i	0.447920	−	0.775819i	0.998250	+	0.0591273i	$0.0188318\pi$
$678$	−273.806	−	365.161i	−0.403843	−	0.538586i
$679$	485.471	+	840.861i	0.714980	+	1.23838i
$680$	657.547	+	231.940i	0.966980	+	0.341088i
$681$	−320.107	−	741.859i	−0.470054	−	1.08937i
$682$	−69.5843	+	66.0873i	−0.102030	+	0.0969021i
$683$	−117.424			−0.171924			−0.0859619	−	0.996298i	$-0.527396\pi$
$683$	−117.424			−0.171924			−0.0859619	+	0.996298i	$0.527396\pi$
$684$	185.657	+	760.055i	0.271428	+	1.11119i
$685$		−	692.976i		−	1.01164i
$686$	534.679	−	507.808i	0.779415	−	0.740245i
$687$	1.27717	−	10.9377i	0.00185905	−	0.0159210i
$688$	163.293	+	118.231i	0.237345	+	0.171847i
$689$	28.9185	−	16.6961i	0.0419718	−	0.0242324i
$690$	−141.758	+	331.758i	−0.205446	+	0.480809i
$691$	787.615	+	454.730i	1.13982	+	0.658075i	0.946386	−	0.323038i	$-0.104704\pi$
$691$	787.615	+	454.730i	1.13982	+	0.658075i	0.193434	+	0.981113i	$0.438038\pi$
$692$	428.700	+	277.901i	0.619508	+	0.401592i
$693$	−489.299	+	518.864i	−0.706059	+	0.748721i
$694$	415.708	+	122.953i	0.599002	+	0.177165i
$695$	320.874	+	185.257i	0.461690	+	0.266557i
$696$	138.733	−	283.319i	0.199329	−	0.407067i
$697$	440.375	+	762.751i	0.631814	+	1.09433i
$698$	−975.343	+	234.582i	−1.39734	+	0.336077i
$699$	−54.7123	−	40.7221i	−0.0782723	−	0.0582577i
$700$	432.282	−	220.706i	0.617546	−	0.315294i
$701$	−190.527			−0.271793			−0.135896	−	0.990723i	$-0.543391\pi$
$701$	−190.527			−0.271793			−0.135896	+	0.990723i	$0.543391\pi$
$702$	−544.434	+	736.919i	−0.775547	+	1.04974i
$703$	−38.0719			−0.0541564
$704$	−345.966	−	278.751i	−0.491429	−	0.395954i
$705$	−304.158	−	226.383i	−0.431430	−	0.321111i
$706$	−315.668	+	75.9220i	−0.447122	+	0.107538i
$707$	169.105	+	292.899i	0.239187	+	0.414284i
$708$	−42.1693	+	248.972i	−0.0595612	+	0.351656i
$709$	−890.120	−	513.911i	−1.25546	−	0.724839i	−0.283270	−	0.959040i	$-0.591419\pi$
$709$	−890.120	−	513.911i	−1.25546	−	0.724839i	−0.972188	+	0.234201i	$0.924753\pi$
$710$	83.3219	−	281.714i	0.117355	−	0.396780i
$711$	1204.19	+	285.108i	1.69366	+	0.400996i
$712$	968.805	−	829.501i	1.36068	−	1.16503i
$713$	−94.9487	−	54.8186i	−0.133168	−	0.0768845i
$714$	−618.738	+	1448.04i	−0.866580	+	2.02807i
$715$	−386.680	+	223.250i	−0.540811	+	0.312237i
$716$	−21.2339	+	411.625i	−0.0296563	+	0.574895i
$717$	27.0043	−	231.265i	0.0376629	−	0.322546i
$718$	−338.457	−	356.367i	−0.471389	−	0.496332i
$719$			548.905i			0.763428i	0.924281	+	0.381714i	$0.124666\pi$
$719$			548.905i			0.763428i	−0.924281	+	0.381714i	$0.875334\pi$
$720$	−413.385	+	356.493i	−0.574146	+	0.495130i
$721$	−30.0475			−0.0416748
$722$	−161.463	+	153.349i	−0.223633	+	0.212394i
$723$	237.524	+	550.470i	0.328526	+	0.761369i
$724$	−285.742	−	14.7402i	−0.394671	−	0.0203594i
$725$	69.8623	+	121.005i	0.0963617	+	0.166903i
$726$	349.508	−	262.068i	0.481416	−	0.360976i
$727$	−180.113	+	311.965i	−0.247749	+	0.429113i	−0.962901	−	0.269856i	$-0.913024\pi$
$727$	−180.113	+	311.965i	−0.247749	+	0.429113i	0.715152	+	0.698969i	$0.246357\pi$
$728$	1176.94	−	1007.71i	1.61668	−	1.38422i
$729$	558.767	+	468.210i	0.766484	+	0.642263i
$730$	231.139	+	68.3634i	0.316628	+	0.0936484i
$731$	144.850	−	250.887i	0.198153	−	0.343211i
$732$	232.011	+	624.296i	0.316954	+	0.852864i
$733$	557.115	−	321.651i	0.760048	−	0.438814i	−0.0692647	−	0.997598i	$-0.522065\pi$
$733$	557.115	−	321.651i	0.760048	−	0.438814i	0.829313	+	0.558784i	$0.188732\pi$
$734$	−12.2545	−	50.9515i	−0.0166955	−	0.0694163i
$735$	−366.298	−	848.908i	−0.498365	−	1.15498i
$736$	193.282	−	469.344i	0.262612	−	0.637696i
$737$			604.909i			0.820772i
$738$	−689.522	+	2.44581i	−0.934311	+	0.00331411i
$739$		−	948.427i		−	1.28339i	−0.766959	−	0.641696i	$-0.778231\pi$
$739$		−	948.427i		−	1.28339i	0.766959	−	0.641696i	$-0.221769\pi$
$740$	−12.0784	−	23.6572i	−0.0163222	−	0.0319692i
$741$	−1098.79	−	128.303i	−1.48284	−	0.173148i
$742$	10.5067	+	43.6848i	0.0141600	+	0.0588744i
$743$	−832.510	+	480.650i	−1.12047	+	0.646904i	−0.941521	−	0.336954i	$-0.890603\pi$
$743$	−832.510	+	480.650i	−1.12047	+	0.646904i	−0.178950	+	0.983858i	$0.557270\pi$
$744$	−92.5473	−	137.671i	−0.124392	−	0.185042i
$745$	53.5821	−	92.8068i	0.0719222	−	0.124573i
$746$	−12.7491	+	43.1050i	−0.0170899	+	0.0577815i
$747$	587.519	+	139.103i	0.786505	+	0.186215i
$748$	−347.282	+	535.728i	−0.464280	+	0.716214i
$749$	−1165.00	+	2017.84i	−1.55541	+	2.69404i
$750$	−96.8435	−	804.585i	−0.129125	−	1.07278i
$751$	−80.1757	−	138.868i	−0.106759	−	0.184911i	0.807697	−	0.589598i	$-0.200714\pi$
$751$	−80.1757	−	138.868i	−0.106759	−	0.184911i	−0.914455	+	0.404687i	$0.867381\pi$
$752$	432.083	+	312.845i	0.574578	+	0.416018i
$753$	−448.164	+	602.132i	−0.595171	+	0.799644i
$754$	307.165	+	323.418i	0.407380	+	0.428937i
$755$	167.632			0.222029
$756$	−743.066	−	983.701i	−0.982892	−	1.30119i
$757$		−	43.6832i		−	0.0577057i	−0.999584	−	0.0288529i	$-0.990815\pi$
$757$		−	43.6832i		−	0.0577057i	0.999584	−	0.0288529i	$-0.00918543\pi$
$758$	234.346	+	246.746i	0.309163	+	0.325523i
$759$	−265.000	−	197.238i	−0.349143	−	0.259866i
$760$	−621.555	−	219.244i	−0.817836	−	0.288479i
$761$	−787.821	+	454.849i	−1.03524	+	0.597699i	−0.918483	−	0.395461i	$-0.870585\pi$
$761$	−787.821	+	454.849i	−1.03524	+	0.597699i	−0.116762	+	0.993160i	$0.537251\pi$
$762$	−140.755	−	1169.41i	−0.184718	−	1.53465i
$763$	1054.87	+	609.031i	1.38253	+	0.798206i
$764$	379.087	−	584.791i	0.496187	−	0.765434i
$765$	570.683	+	538.165i	0.745991	+	0.703484i
$766$	54.7230	−	185.020i	0.0714400	−	0.241541i
$767$	−309.206	−	178.520i	−0.403137	−	0.232751i
$768$	574.951	−	509.171i	0.748634	−	0.662983i
$769$	−407.652	−	706.074i	−0.530106	−	0.918171i	−0.999383	−	0.0351200i	$-0.988819\pi$
$769$	−407.652	−	706.074i	−0.530106	−	0.918171i	0.469277	−	0.883051i	$-0.344515\pi$
$770$	−140.489	−	584.125i	−0.182454	−	0.758603i
$771$	−115.454	+	988.751i	−0.149746	+	1.28243i
$772$	747.744	−	381.767i	0.968580	−	0.494517i
$773$	−199.902			−0.258606			−0.129303	−	0.991605i	$-0.541274\pi$
$773$	−199.902			−0.258606			−0.129303	+	0.991605i	$0.541274\pi$
$774$	114.097	+	196.013i	0.147412	+	0.253246i
$775$	73.4745			0.0948058
$776$	−668.927	+	124.829i	−0.862019	+	0.160863i
$777$	55.0800	−	23.7667i	0.0708880	−	0.0305877i
$778$	−52.2155	−	217.101i	−0.0671150	−	0.279050i
$779$	−416.270	−	721.001i	−0.534365	−	0.925547i
$780$	−268.868	−	723.471i	−0.344702	−	0.927527i
$781$	232.959	+	134.499i	0.298284	+	0.172214i
$782$	−699.443	−	206.872i	−0.894428	−	0.264543i
$783$	271.787	−	228.215i	0.347110	−	0.291462i
$784$	531.029	+	1187.47i	0.677333	+	1.51462i
$785$	−755.075	−	435.943i	−0.961879	−	0.555341i
$786$	82.6449	−	61.9690i	0.105146	−	0.0788409i
$787$	950.172	−	548.582i	1.20733	−	0.697055i	0.245158	−	0.969483i	$-0.421160\pi$
$787$	950.172	−	548.582i	1.20733	−	0.697055i	0.962176	+	0.272428i	$0.0878267\pi$
$788$	15.6588	−	303.549i	0.0198715	−	0.385215i
$789$	958.046	−	413.390i	1.21425	−	0.523942i
$790$	−755.870	+	717.883i	−0.956797	+	0.908713i
$791$			868.316i			1.09774i
$792$	−228.860	−	444.355i	−0.288964	−	0.561054i
$793$	−941.690			−1.18750
$794$	−801.956	−	844.392i	−1.01002	−	1.06347i
$795$	22.2304	+	2.59579i	0.0279628	+	0.00326515i
$796$	−57.4490	+	1113.66i	−0.0721722	+	1.39908i
$797$	−297.651	−	515.547i	−0.373465	−	0.646860i	0.616631	−	0.787252i	$-0.288497\pi$
$797$	−297.651	−	515.547i	−0.373465	−	0.646860i	−0.990096	+	0.140392i	$0.955164\pi$
$798$	584.871	−	1368.78i	0.732921	−	1.71527i
$799$	383.281	−	663.862i	0.479700	−	0.830866i
$800$	45.0914	+	337.161i	0.0563642	+	0.421451i
$801$	1374.46	−	411.828i	1.71593	−	0.514142i
$802$	−347.370	+	1174.47i	−0.433129	+	1.46442i
$803$	−110.353	+	191.137i	−0.137426	+	0.238029i
$804$	−1030.96	−	174.617i	−1.28229	−	0.217185i
$805$	594.412	−	343.184i	0.738400	−	0.426316i
$806$	228.047	−	54.8481i	0.282937	−	0.0680498i
$807$	−909.410	+	1221.84i	−1.12690	+	1.51405i
$808$	−233.009	+	43.4821i	−0.288377	+	0.0538145i
$809$		−	578.133i		−	0.714627i	−0.933985	−	0.357313i	$-0.883693\pi$
$809$		−	578.133i		−	0.714627i	0.933985	−	0.357313i	$-0.116307\pi$
$810$	−587.636	+	178.347i	−0.725477	+	0.220181i
$811$		−	870.431i		−	1.07328i	−0.843811	−	0.536641i	$-0.819693\pi$
$811$		−	870.431i		−	1.07328i	0.843811	−	0.536641i	$-0.180307\pi$
$812$	−534.524	+	272.906i	−0.658280	+	0.336091i
$813$	152.264	−	204.574i	0.187286	−	0.251629i
$814$	23.6474	−	5.68751i	0.0290509	−	0.00698711i
$815$	−125.565	+	72.4951i	−0.154068	+	0.0889511i
$816$	−812.805	−	746.527i	−0.996084	−	0.914861i
$817$	−136.921	+	237.155i	−0.167590	+	0.290275i
$818$	651.952	+	192.826i	0.797008	+	0.235729i
$819$	1669.75	−	500.305i	2.03876	−	0.610873i
$820$	315.955	−	487.403i	0.385311	−	0.594393i
$821$	610.012	−	1056.57i	0.743011	−	1.28693i	−0.208108	−	0.978106i	$-0.566731\pi$
$821$	610.012	−	1056.57i	0.743011	−	1.28693i	0.951118	−	0.308826i	$-0.0999362\pi$
$822$	−430.975	+	1008.62i	−0.524301	+	1.22703i
$823$	184.322	+	319.255i	0.223964	+	0.387916i	0.956008	−	0.293341i	$-0.0947670\pi$
$823$	184.322	+	319.255i	0.223964	+	0.387916i	−0.732044	+	0.681257i	$0.761434\pi$
$824$	7.00504	−	19.8592i	0.00850127	−	0.0241010i
$825$	219.890	+	25.6760i	0.266533	+	0.0311224i
$826$	348.343	−	330.836i	0.421722	−	0.400528i
$827$	754.669			0.912538			0.456269	−	0.889842i	$-0.349185\pi$
$827$	754.669			0.912538			0.456269	+	0.889842i	$0.349185\pi$
$828$	412.654	−	394.709i	0.498374	−	0.476701i
$829$		−	257.000i		−	0.310012i	−0.987914	−	0.155006i	$-0.950460\pi$
$829$		−	257.000i		−	0.310012i	0.987914	−	0.155006i	$-0.0495397\pi$
$830$	−368.785	+	350.251i	−0.444319	+	0.421990i
$831$	507.303	−	218.898i	0.610472	−	0.263415i
$832$	391.641	+	1012.80i	0.470722	+	1.21731i
$833$	1618.80	−	934.615i	1.94334	−	1.12199i
$834$	−351.815	−	469.198i	−0.421840	−	0.562587i
$835$	73.2297	+	42.2792i	0.0877003	+	0.0506338i
$836$	328.273	−	506.405i	0.392671	−	0.605747i
$837$	−32.4696	−	183.776i	−0.0387928	−	0.219565i
$838$	147.378	+	43.5896i	0.175868	+	0.0520162i
$839$	1439.78	+	831.258i	1.71607	+	0.990773i	0.925801	+	0.378011i	$0.123392\pi$
$839$	1439.78	+	831.258i	1.71607	+	0.990773i	0.790268	+	0.612762i	$0.209941\pi$
$840$	1036.09	−	70.8215i	1.23344	−	0.0843113i
$841$	334.114	+	578.703i	0.397282	+	0.688113i
$842$	1565.61	−	376.548i	1.85939	−	0.447207i
$843$	−778.515	+	335.924i	−0.923506	+	0.398486i
$844$	277.974	+	544.450i	0.329353	+	0.645083i
$845$	450.646			0.533309
$846$	301.907	+	518.660i	0.356864	+	0.613073i
$847$	−831.094			−0.981221
$848$	−31.3219	−	3.24014i	−0.0369363	−	0.00382092i
$849$	84.7662	−	725.940i	0.0998424	−	0.855053i
$850$	475.258	−	114.305i	0.559127	−	0.134477i
$851$	13.8933	+	24.0639i	0.0163259	+	0.0282772i
$852$	−296.478	+	358.212i	−0.347978	+	0.420437i
$853$	435.489	+	251.429i	0.510538	+	0.294759i	0.733055	−	0.680170i	$-0.238094\pi$
$853$	435.489	+	251.429i	0.510538	+	0.294759i	−0.222517	+	0.974929i	$0.571427\pi$
$854$	359.372	−	1215.05i	0.420810	−	1.42277i
$855$	−539.446	−	508.708i	−0.630931	−	0.594981i
$856$	−1062.05	−	1240.40i	−1.24071	−	1.44907i
$857$	270.221	+	156.012i	0.315310	+	0.182045i	0.649300	−	0.760532i	$-0.275062\pi$
$857$	270.221	+	156.012i	0.315310	+	0.182045i	−0.333990	+	0.942577i	$0.608395\pi$
$858$	701.652	−	84.4540i	0.817776	−	0.0984312i
$859$	−890.067	+	513.880i	−1.03617	+	0.598231i	−0.918745	−	0.394852i	$-0.870796\pi$
$859$	−890.067	+	513.880i	−1.03617	+	0.598231i	−0.117421	+	0.993082i	$0.537463\pi$
$860$	−190.802	−	9.84266i	−0.221863	−	0.0114449i
$861$	1052.32	+	783.239i	1.22221	+	0.909685i
$862$	−982.748	−	1034.75i	−1.14008	−	1.20041i
$863$			749.389i			0.868354i	0.900828	+	0.434177i	$0.142961\pi$
$863$			749.389i			0.868354i	−0.900828	+	0.434177i	$0.857039\pi$
$864$	823.388	−	261.780i	0.952995	−	0.302986i
$865$	−484.170			−0.559734
$866$	708.255	−	672.661i	0.817846	−	0.776744i
$867$	−429.218	+	576.677i	−0.495061	+	0.665140i
$868$	−16.2586	+	315.177i	−0.0187311	+	0.363107i
$869$	−477.260	−	826.638i	−0.549206	−	0.951252i
$870$	35.7264	+	296.819i	0.0410649	+	0.341171i
$871$	739.227	−	1280.38i	0.848710	−	1.47001i
$872$	−648.450	+	555.209i	−0.743635	+	0.636708i
$873$	−744.939	−	176.374i	−0.853309	−	0.202032i
$874$	661.158	+	195.549i	0.756474	+	0.223740i
$875$	−770.878	+	1335.20i	−0.881003	+	1.52594i
$876$	−293.904	−	243.252i	−0.335506	−	0.277685i
$877$	−1288.44	+	743.881i	−1.46914	+	0.848211i	−0.999402	−	0.0345923i	$-0.988987\pi$
$877$	−1288.44	+	743.881i	−1.46914	+	0.848211i	−0.469743	+	0.882803i	$0.655653\pi$
$878$	178.557	+	742.402i	0.203368	+	0.845560i
$879$	−1699.59	−	198.457i	−1.93355	−	0.225775i
$880$	418.816	+	43.3251i	0.475928	+	0.0492330i
$881$			970.067i			1.10110i	0.834803	+	0.550549i	$0.185582\pi$
$881$			970.067i			1.10110i	−0.834803	+	0.550549i	$0.814418\pi$
$882$	5.19079	+	1463.38i	0.00588525	+	1.65917i
$883$		−	468.838i		−	0.530960i	−0.964116	−	0.265480i	$-0.914470\pi$
$883$		−	468.838i		−	0.530960i	0.964116	−	0.265480i	$-0.0855305\pi$
$884$	1389.76	−	709.553i	1.57212	−	0.802662i
$885$	−94.8108	−	219.727i	−0.107131	−	0.248279i
$886$	−253.825	−	1055.35i	−0.286484	−	1.19114i
$887$	358.011	−	206.698i	0.403620	−	0.233030i	−0.284425	−	0.958698i	$-0.591803\pi$
$887$	358.011	−	206.698i	0.403620	−	0.233030i	0.688045	+	0.725668i	$0.258469\pi$
$888$	2.86711	+	41.9446i	0.00322872	+	0.0472350i
$889$	−1120.42	+	1940.62i	−1.26031	+	2.18292i
$890$	−342.811	+	1159.06i	−0.385181	+	1.30231i
$891$	−32.9514	−	561.340i	−0.0369825	−	0.630011i
$892$	−805.279	−	522.016i	−0.902779	−	0.585220i
$893$	−362.301	+	627.524i	−0.405713	+	0.702715i
$894$	−135.707	+	101.756i	−0.151797	+	0.113821i
$895$	−195.306	−	338.280i	−0.218219	−	0.377967i
$896$	−1456.27	+	118.817i	−1.62530	+	0.132608i
$897$	319.877	+	741.325i	0.356607	+	0.826449i
$898$	−181.783	−	191.402i	−0.202431	−	0.213143i
$899$	−90.8523			−0.101059
$900$	−107.235	+	367.351i	−0.119150	+	0.408168i
$901$			45.2495i			0.0502215i
$902$	366.265	+	385.646i	0.406059	+	0.427546i
$903$	50.0436	−	428.574i	0.0554192	−	0.474612i
$904$	−573.894	−	202.432i	−0.634838	−	0.223930i
$905$	234.828	−	135.578i	0.259478	−	0.149810i
$906$	−243.986	−	104.253i	−0.269300	−	0.115070i
$907$	−1337.74	−	772.343i	−1.47490	−	0.851536i	−0.475304	−	0.879822i	$-0.657662\pi$
$907$	−1337.74	−	772.343i	−1.47490	−	0.851536i	−0.999600	+	0.0282854i	$0.990995\pi$
$908$	−903.980	−	585.998i	−0.995573	−	0.645373i
$909$	−259.486	−	61.4369i	−0.285464	−	0.0675873i
$910$	−416.461	+	1408.07i	−0.457650	+	1.54733i
$911$	73.7841	+	42.5993i	0.0809924	+	0.0467610i	0.539949	−	0.841698i	$-0.318443\pi$
$911$	73.7841	+	42.5993i	0.0809924	+	0.0467610i	−0.458957	+	0.888459i	$0.651777\pi$
$912$	768.315	+	705.665i	0.842451	+	0.773755i
$913$	−232.853	−	403.313i	−0.255041	−	0.441744i
$914$	−118.875	−	494.256i	−0.130060	−	0.540762i
$915$	−506.324	−	376.854i	−0.553360	−	0.411863i
$916$	−6.67653	−	13.0769i	−0.00728879	−	0.0142761i
$917$	−196.521			−0.214309
$918$	−495.928	−	1138.21i	−0.540226	−	1.23988i
$919$	−125.501			−0.136563			−0.0682815	−	0.997666i	$-0.521752\pi$
$919$	−125.501			−0.136563			−0.0682815	+	0.997666i	$0.521752\pi$
$920$	88.2431	+	472.870i	0.0959164	+	0.513990i
$921$	354.172	+	263.609i	0.384552	+	0.286220i
$922$	−231.901	−	964.197i	−0.251520	−	1.04577i
$923$	−328.729	−	569.375i	−0.356152	−	0.616874i
$924$	−158.798	+	937.560i	−0.171859	+	1.01468i
$925$	−16.1267	−	9.31074i	−0.0174342	−	0.0100657i
$926$	724.494	+	214.282i	0.782391	+	0.231406i
$927$	16.2537	−	17.2358i	0.0175336	−	0.0185931i
$928$	−55.7562	−	416.904i	−0.0600821	−	0.449250i
$929$	−1474.21	−	851.134i	−1.58688	−	0.916183i	−0.993818	−	0.111024i	$-0.964587\pi$
$929$	−1474.21	−	851.134i	−1.58688	−	0.916183i	−0.593059	−	0.805159i	$-0.702080\pi$
$930$	144.565	+	61.7715i	0.155446	+	0.0664210i
$931$	−1530.19	+	883.458i	−1.64360	+	0.948935i
$932$	−90.8174	−	4.68487i	−0.0974435	−	0.00502668i
$933$	−56.3495	+	482.579i	−0.0603961	+	0.517233i
$934$	−194.979	+	185.180i	−0.208757	+	0.198266i
$935$		−	605.047i		−	0.647109i
$936$	−58.6068	+	1220.22i	−0.0626140	+	1.30365i
$937$	1629.91			1.73950			0.869748	−	0.493496i	$-0.164281\pi$
$937$	1629.91			1.73950			0.869748	+	0.493496i	$0.164281\pi$
$938$	1369.95	+	1442.44i	1.46050	+	1.53778i
$939$	516.540	+	1197.10i	0.550095	+	1.27486i
$940$	−504.874	−	26.0442i	−0.537100	−	0.0277066i
$941$	847.730	+	1468.31i	0.900882	+	1.56037i	0.826352	+	0.563155i	$0.190412\pi$
$941$	847.730	+	1468.31i	0.900882	+	1.56037i	0.0745304	+	0.997219i	$0.476254\pi$
$942$	827.883	+	1104.11i	0.878856	+	1.17209i
$943$	−303.813	+	526.220i	−0.322177	+	0.558027i
$944$	137.449	+	307.358i	0.145603	+	0.325591i
$945$	1098.00	+	399.214i	1.16191	+	0.422448i
$946$	49.6172	−	167.757i	0.0524495	−	0.177333i
$947$	759.787	−	1315.99i	0.802310	−	1.38964i	−0.115783	−	0.993275i	$-0.536938\pi$
$947$	759.787	−	1315.99i	0.802310	−	1.38964i	0.918092	−	0.396367i	$-0.129729\pi$
$948$	1546.63	−	574.781i	1.63146	−	0.606309i
$949$	467.156	−	269.713i	0.492262	−	0.284207i
$950$	−449.244	+	108.049i	−0.472889	+	0.113736i
$951$	720.552	+	1669.90i	0.757679	+	1.75595i
$952$	385.160	+	2063.97i	0.404580	+	2.16803i
$953$		−	330.801i		−	0.347115i	−0.984824	−	0.173558i	$-0.944474\pi$
$953$		−	330.801i		−	0.347115i	0.984824	−	0.173558i	$-0.0555263\pi$
$954$	−30.7418	−	17.6037i	−0.0322241	−	0.0184525i
$955$			660.459i			0.691580i
$956$	−141.168	−	276.496i	−0.147665	−	0.289222i
$957$	−271.897	−	31.7488i	−0.284114	−	0.0331753i
$958$	−597.481	+	143.702i	−0.623675	+	0.150002i
$959$	1807.15	−	1043.36i	1.88441	−	1.08796i
$960$	−194.738	+	701.291i	−0.202852	+	0.730512i
$961$	456.613	−	790.876i	0.475143	−	0.822972i
$962$	−57.0037	−	16.8598i	−0.0592554	−	0.0175258i
$963$	−527.280	−	1759.78i	−0.547539	−	1.82739i
$964$	670.766	+	434.819i	0.695816	+	0.451057i
$965$	−397.824	+	689.051i	−0.412253	+	0.714043i
$966$	−1078.59	+	129.824i	−1.11656	+	0.134394i
$967$	−272.891	−	472.661i	−0.282204	−	0.488791i	0.689723	−	0.724073i	$-0.257732\pi$
$967$	−272.891	−	472.661i	−0.282204	−	0.488791i	−0.971927	+	0.235281i	$0.924399\pi$
$968$	193.755	−	549.293i	0.200160	−	0.567451i
$969$	895.047	−	1202.54i	0.923681	−	1.24101i
$970$	467.597	−	444.098i	0.482059	−	0.457833i
$971$	−661.647			−0.681408			−0.340704	−	0.940171i	$-0.610665\pi$
$971$	−661.647			−0.681408			−0.340704	+	0.940171i	$0.610665\pi$
$972$	966.216	+	105.880i	0.994049	+	0.108930i
$973$			1115.70i			1.14666i
$974$	710.484	−	674.778i	0.729449	−	0.692790i
$975$	−434.052	−	323.063i	−0.445181	−	0.331346i
$976$	719.277	+	520.785i	0.736964	+	0.533592i
$977$	137.933	−	79.6354i	0.141180	−	0.0815102i	−0.427746	−	0.903899i	$-0.640692\pi$
$977$	137.933	−	79.6354i	0.141180	−	0.0815102i	0.568926	+	0.822389i	$0.307359\pi$
$978$	227.845	−	27.4245i	0.232970	−	0.0280414i
$979$	−958.466	−	553.370i	−0.979025	−	0.565240i
$980$	−1034.42	−	670.557i	−1.05553	−	0.684242i
$981$	−919.965	+	275.648i	−0.937783	+	0.280987i
$982$	172.655	+	51.0658i	0.175820	+	0.0520019i
$983$	−488.957	−	282.299i	−0.497413	−	0.287181i	0.230232	−	0.973136i	$-0.426052\pi$
$983$	−488.957	−	282.299i	−0.497413	−	0.287181i	−0.727644	+	0.685955i	$0.759385\pi$
$984$	−762.994	+	512.911i	−0.775401	+	0.521251i
$985$	144.027	+	249.462i	0.146220	+	0.253261i
$986$	−587.664	+	141.340i	−0.596008	+	0.143347i
$987$	132.418	−	1134.03i	0.134162	−	1.14897i
$988$	−1313.69	+	670.715i	−1.32964	+	0.678861i
$989$	199.863			0.202086
$990$	411.059	+	235.385i	0.415211	+	0.237762i
$991$	259.373			0.261729			0.130864	−	0.991400i	$-0.458225\pi$
$991$	259.373			0.261729			0.130864	+	0.991400i	$0.458225\pi$
$992$	−204.519	−	84.2237i	−0.206168	−	0.0849029i
$993$	−1080.44	+	466.203i	−1.08806	+	0.469489i
$994$	860.106	−	206.866i	0.865298	−	0.208115i
$995$	−528.407	−	915.228i	−0.531062	−	0.919827i
$996$	754.591	−	280.433i	0.757622	−	0.281559i
$997$	1549.08	+	894.362i	1.55374	+	0.897053i	0.997832	+	0.0658097i	$0.0209630\pi$
$997$	1549.08	+	894.362i	1.55374	+	0.897053i	0.555909	+	0.831243i	$0.312370\pi$
$998$	−308.911	+	1044.44i	−0.309530	+	1.04653i
$999$	−16.1616	+	44.4510i	−0.0161778	+	0.0444955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.17	yes	44
3.2	odd	2		216.3.j.a.197.6		44
4.3	odd	2		288.3.n.a.209.7		44
8.3	odd	2		288.3.n.a.209.16		44
8.5	even	2	inner	72.3.j.a.29.10	yes	44
9.2	odd	6		648.3.h.a.485.42		44
9.4	even	3		216.3.j.a.125.13		44
9.5	odd	6	inner	72.3.j.a.5.10	✓	44
9.7	even	3		648.3.h.a.485.3		44
12.11	even	2		864.3.n.a.305.6		44
24.5	odd	2		216.3.j.a.197.13		44
24.11	even	2		864.3.n.a.305.17		44
36.7	odd	6		2592.3.h.a.1457.12		44
36.11	even	6		2592.3.h.a.1457.33		44
36.23	even	6		288.3.n.a.113.16		44
36.31	odd	6		864.3.n.a.17.17		44
72.5	odd	6	inner	72.3.j.a.5.17	yes	44
72.11	even	6		2592.3.h.a.1457.11		44
72.13	even	6		216.3.j.a.125.6		44
72.29	odd	6		648.3.h.a.485.4		44
72.43	odd	6		2592.3.h.a.1457.34		44
72.59	even	6		288.3.n.a.113.7		44
72.61	even	6		648.3.h.a.485.41		44
72.67	odd	6		864.3.n.a.17.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.10	✓	44	9.5	odd	6	inner
72.3.j.a.5.17	yes	44	72.5	odd	6	inner
72.3.j.a.29.10	yes	44	8.5	even	2	inner
72.3.j.a.29.17	yes	44	1.1	even	1	trivial
216.3.j.a.125.6		44	72.13	even	6
216.3.j.a.125.13		44	9.4	even	3
216.3.j.a.197.6		44	3.2	odd	2
216.3.j.a.197.13		44	24.5	odd	2
288.3.n.a.113.7		44	72.59	even	6
288.3.n.a.113.16		44	36.23	even	6
288.3.n.a.209.7		44	4.3	odd	2
288.3.n.a.209.16		44	8.3	odd	2
648.3.h.a.485.3		44	9.7	even	3
648.3.h.a.485.4		44	72.29	odd	6
648.3.h.a.485.41		44	72.61	even	6
648.3.h.a.485.42		44	9.2	odd	6
864.3.n.a.17.6		44	72.67	odd	6
864.3.n.a.17.17		44	36.31	odd	6
864.3.n.a.305.6		44	12.11	even	2
864.3.n.a.305.17		44	24.11	even	2
2592.3.h.a.1457.11		44	72.11	even	6
2592.3.h.a.1457.12		44	36.7	odd	6
2592.3.h.a.1457.33		44	36.11	even	6
2592.3.h.a.1457.34		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)

\(f(q)\)	\(=\)	\(q+(1.45018 - 1.37730i) q^{2} +(1.79120 - 2.40657i) q^{3} +(0.206068 - 3.99469i) q^{4} +(1.89538 + 3.28290i) q^{5} +(-0.717012 - 5.95700i) q^{6} +(-5.70744 + 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(-2.58320 - 8.62132i) q^{9} +O(q^{10})\)	\(q+(1.45018 - 1.37730i) q^{2} +(1.79120 - 2.40657i) q^{3} +(0.206068 - 3.99469i) q^{4} +(1.89538 + 3.28290i) q^{5} +(-0.717012 - 5.95700i) q^{6} +(-5.70744 + 9.88558i) q^{7} +(-5.20306 - 6.07685i) q^{8} +(-2.58320 - 8.62132i) q^{9} +(7.27021 + 2.15029i) q^{10} +(-3.47103 + 6.01200i) q^{11} +(-9.24440 - 7.65121i) q^{12} +(14.6939 - 8.48351i) q^{13} +(5.33861 + 22.1968i) q^{14} +(11.2956 + 1.31895i) q^{15} +(-15.9151 - 1.64636i) q^{16} +22.9919i q^{17} +(-15.6203 - 8.94465i) q^{18} -21.7334i q^{19} +(13.5047 - 6.89497i) q^{20} +(13.5672 + 31.4425i) q^{21} +(3.24672 + 13.4992i) q^{22} +(-13.7369 + 7.93101i) q^{23} +(-23.9441 + 1.63669i) q^{24} +(5.31504 - 9.20592i) q^{25} +(9.62445 - 32.5406i) q^{26} +(-25.3749 - 9.22586i) q^{27} +(38.3137 + 24.8366i) q^{28} +(-6.57213 + 11.3833i) q^{29} +(18.1972 - 13.6447i) q^{30} +(3.45597 + 5.98592i) q^{31} +(-25.3473 + 19.5324i) q^{32} +(8.25100 + 19.1220i) q^{33} +(31.6668 + 33.3424i) q^{34} -43.2712 q^{35} +(-34.9718 + 8.54249i) q^{36} -1.75177i q^{37} +(-29.9335 - 31.5174i) q^{38} +(5.90348 - 50.5576i) q^{39} +(10.0879 - 28.5991i) q^{40} +(33.1748 - 19.1535i) q^{41} +(62.9808 + 26.9112i) q^{42} +(-10.9120 - 6.30005i) q^{43} +(23.3008 + 15.1046i) q^{44} +(23.4068 - 24.8211i) q^{45} +(-8.99764 + 30.4213i) q^{46} +(-28.8738 - 16.6703i) q^{47} +(-32.4692 + 35.3518i) q^{48} +(-40.6498 - 70.4076i) q^{49} +(-4.97156 - 20.6707i) q^{50} +(55.3316 + 41.1830i) q^{51} +(-30.8610 - 60.4456i) q^{52} +1.96807 q^{53} +(-49.5050 + 21.5697i) q^{54} -26.3157 q^{55} +(89.7694 - 16.7520i) q^{56} +(-52.3030 - 38.9289i) q^{57} +(6.14741 + 25.5596i) q^{58} +(-10.5216 - 18.2239i) q^{59} +(7.59647 - 44.8504i) q^{60} +(-48.0654 - 27.7506i) q^{61} +(13.2562 + 3.92076i) q^{62} +(99.9702 + 23.6693i) q^{63} +(-9.85628 + 63.2365i) q^{64} +(55.7011 + 32.1590i) q^{65} +(38.3022 + 16.3663i) q^{66} +(75.4627 - 43.5684i) q^{67} +(91.8453 + 4.73789i) q^{68} +(-5.51901 + 47.2649i) q^{69} +(-62.7512 + 59.5976i) q^{70} -38.7491i q^{71} +(-38.9499 + 60.5550i) q^{72} +31.7926 q^{73} +(-2.41272 - 2.54039i) q^{74} +(-12.6344 - 29.2807i) q^{75} +(-86.8181 - 4.47856i) q^{76} +(-39.6214 - 68.6263i) q^{77} +(-61.0720 - 81.4487i) q^{78} +(-68.7491 + 119.077i) q^{79} +(-24.7603 - 55.3681i) q^{80} +(-67.6542 + 44.5411i) q^{81} +(21.7294 - 73.4679i) q^{82} +(-33.5423 + 58.0970i) q^{83} +(128.399 - 47.7175i) q^{84} +(-75.4800 + 43.5784i) q^{85} +(-24.5015 + 5.89291i) q^{86} +(15.6227 + 36.2060i) q^{87} +(54.5940 - 10.1879i) q^{88} +159.426i q^{89} +(-0.242031 - 68.2334i) q^{90} +193.677i q^{91} +(28.8512 + 56.5090i) q^{92} +(20.5959 + 2.40493i) q^{93} +(-64.8323 + 15.5930i) q^{94} +(71.3485 - 41.1931i) q^{95} +(1.60394 + 95.9866i) q^{96} +(42.5296 - 73.6635i) q^{97} +(-155.922 - 46.1168i) q^{98} +(60.7977 + 14.3947i) 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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