LMFDB - Embedded newform 36.5.f.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (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:	$3.72131867102$
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			7.8
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14060 + 3.37903i) q^{2} +(-6.53699 + 6.18609i) q^{3} +(-6.83568 - 14.4663i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(-6.90992 - 35.3306i) q^{6} +(51.8739 + 29.9494i) q^{7} +(63.5145 + 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +O(q^{10})$	\(q+(-2.14060 + 3.37903i) q^{2} +(-6.53699 + 6.18609i) q^{3} +(-6.83568 - 14.4663i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(-6.90992 - 35.3306i) q^{6} +(51.8739 + 29.9494i) q^{7} +(63.5145 + 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +(118.977 + 4.89106i) q^{10} +(-195.278 - 112.744i) q^{11} +(134.175 + 52.2799i) q^{12} +(-85.8824 - 148.753i) q^{13} +(-212.241 + 111.174i) q^{14} +(256.785 + 76.4524i) q^{15} +(-162.547 + 197.774i) q^{16} -99.0725 q^{17} +(263.729 + 188.211i) q^{18} -169.267i q^{19} +(-271.209 + 391.557i) q^{20} +(-524.369 + 125.118i) q^{21} +(798.976 - 418.511i) q^{22} +(-310.777 + 179.427i) q^{23} +(-463.869 + 341.470i) q^{24} +(-130.609 + 226.221i) q^{25} +(686.480 + 28.2206i) q^{26} +(471.128 + 556.309i) q^{27} +(78.6636 - 955.147i) q^{28} +(9.01635 - 15.6168i) q^{29} +(-808.009 + 704.031i) q^{30} +(-671.898 + 387.920i) q^{31} +(-320.335 - 972.605i) q^{32} +(1973.97 - 471.003i) q^{33} +(212.075 - 334.769i) q^{34} -1783.15i q^{35} +(-1200.51 + 488.264i) q^{36} +609.762 q^{37} +(571.958 + 362.333i) q^{38} +(1481.61 + 441.118i) q^{39} +(-742.534 - 1754.59i) q^{40} +(206.545 + 357.747i) q^{41} +(699.686 - 2039.68i) q^{42} +(-265.498 - 153.286i) q^{43} +(-296.127 + 3595.63i) q^{44} +(-2151.54 + 1088.73i) q^{45} +(58.9591 - 1434.21i) q^{46} +(-2270.59 - 1310.93i) q^{47} +(-160.878 - 2298.38i) q^{48} +(593.432 + 1027.85i) q^{49} +(-484.826 - 925.578i) q^{50} +(647.636 - 612.872i) q^{51} +(-1564.84 + 2259.23i) q^{52} +2034.30 q^{53} +(-2888.28 + 401.120i) q^{54} +6712.63i q^{55} +(3059.08 + 2310.39i) q^{56} +(1047.10 + 1106.50i) q^{57} +(33.4692 + 63.8958i) q^{58} +(2250.48 - 1299.32i) q^{59} +(-649.318 - 4237.33i) q^{60} +(708.681 - 1227.47i) q^{61} +(127.469 - 3100.74i) q^{62} +(2653.80 - 4061.69i) q^{63} +(3972.17 + 999.536i) q^{64} +(-2556.67 + 4428.28i) q^{65} +(-2633.95 + 7678.34i) q^{66} +(-5191.93 + 2997.56i) q^{67} +(677.228 + 1433.21i) q^{68} +(921.593 - 3095.41i) q^{69} +(6025.32 + 3817.01i) q^{70} -1239.44i q^{71} +(919.945 - 5101.72i) q^{72} -5060.60 q^{73} +(-1305.25 + 2060.40i) q^{74} +(-545.636 - 2286.76i) q^{75} +(-2448.66 + 1157.05i) q^{76} +(-6753.22 - 11696.9i) q^{77} +(-4662.09 + 4062.15i) q^{78} +(-1635.99 - 944.538i) q^{79} +(7518.28 + 1246.83i) q^{80} +(-6521.14 - 722.147i) q^{81} +(-1650.97 - 67.8700i) q^{82} +(5831.54 + 3366.84i) q^{83} +(5394.40 + 6730.41i) q^{84} +(1474.66 + 2554.19i) q^{85} +(1086.28 - 569.004i) q^{86} +(37.6671 + 157.863i) q^{87} +(-11515.8 - 8697.42i) q^{88} +9436.67 q^{89} +(926.745 - 9600.66i) q^{90} -10288.5i q^{91} +(4720.02 + 3269.29i) q^{92} +(1992.48 - 6692.25i) q^{93} +(9290.07 - 4866.22i) q^{94} +(-4363.88 + 2519.49i) q^{95} +(8110.66 + 4376.29i) q^{96} +(7297.91 - 12640.4i) q^{97} +(-4743.45 - 195.000i) q^{98} +(-9990.18 + 15290.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.14060	+	3.37903i	−0.535150	+	0.844757i
$2$	−2.14060	+	3.37903i	−0.535150	+	0.844757i
$3$	−6.53699	+	6.18609i	−0.726332	+	0.687344i
$3$	−6.53699	+	6.18609i	−0.726332	+	0.687344i
$4$	−6.83568	−	14.4663i	−0.427230	−	0.904143i
$5$	−14.8847	−	25.7811i	−0.595388	−	1.03124i	−0.993492	−	0.113902i	$-0.963665\pi$
$5$	−14.8847	−	25.7811i	−0.595388	−	1.03124i	0.398104	−	0.917340i	$-0.369668\pi$
$6$	−6.90992	−	35.3306i	−0.191942	−	0.981406i
$7$	51.8739	+	29.9494i	1.05865	+	0.611212i	0.925059	−	0.379824i	$-0.124016\pi$
$7$	51.8739	+	29.9494i	1.05865	+	0.611212i	0.133592	+	0.991036i	$0.457349\pi$
$8$	63.5145	+	7.86857i	0.992413	+	0.122946i
$9$	4.46449	−	80.8769i	0.0551171	−	0.998480i
$10$	118.977	+	4.89106i	1.18977	+	0.0489106i
$11$	−195.278	−	112.744i	−1.61387	−	0.931767i	−0.988462	−	0.151467i	$-0.951600\pi$
$11$	−195.278	−	112.744i	−1.61387	−	0.931767i	−0.625406	−	0.780300i	$-0.715066\pi$
$12$	134.175	+	52.2799i	0.931768	+	0.363055i
$13$	−85.8824	−	148.753i	−0.508180	−	0.880194i	−0.999955	−	0.00947137i	$-0.996985\pi$
$13$	−85.8824	−	148.753i	−0.508180	−	0.880194i	0.491775	−	0.870722i	$-0.336348\pi$
$14$	−212.241	+	111.174i	−1.08286	+	0.567213i
$15$	256.785	+	76.4524i	1.14127	+	0.339788i
$16$	−162.547	+	197.774i	−0.634949	+	0.772554i
$17$	−99.0725			−0.342812			−0.171406	−	0.985201i	$-0.554831\pi$
$17$	−99.0725			−0.342812			−0.171406	+	0.985201i	$0.554831\pi$
$18$	263.729	+	188.211i	0.813977	+	0.580897i
$19$		−	169.267i		−	0.468884i	−0.972130	−	0.234442i	$-0.924674\pi$
$19$		−	169.267i		−	0.468884i	0.972130	−	0.234442i	$-0.0753262\pi$
$20$	−271.209	+	391.557i	−0.678023	+	0.978893i
$21$	−524.369	+	125.118i	−1.18904	+	0.283714i
$22$	798.976	−	418.511i	1.65078	−	0.864692i
$23$	−310.777	+	179.427i	−0.587480	+	0.339182i	−0.764101	−	0.645097i	$-0.776817\pi$
$23$	−310.777	+	179.427i	−0.587480	+	0.339182i	0.176620	+	0.984279i	$0.443484\pi$
$24$	−463.869	+	341.470i	−0.805328	+	0.592829i
$25$	−130.609	+	226.221i	−0.208974	+	0.361953i
$26$	686.480	+	28.2206i	1.01550	+	0.0417465i
$27$	471.128	+	556.309i	0.646266	+	0.763113i
$28$	78.6636	−	955.147i	0.100336	−	1.21830i
$29$	9.01635	−	15.6168i	0.0107210	−	0.0185693i	−0.860615	−	0.509256i	$-0.829921\pi$
$29$	9.01635	−	15.6168i	0.0107210	−	0.0185693i	0.871336	+	0.490687i	$0.163254\pi$
$30$	−808.009	+	704.031i	−0.897788	+	0.782256i
$31$	−671.898	+	387.920i	−0.699165	+	0.403663i	−0.807036	−	0.590502i	$-0.798930\pi$
$31$	−671.898	+	387.920i	−0.699165	+	0.403663i	0.107871	+	0.994165i	$0.465597\pi$
$32$	−320.335	−	972.605i	−0.312827	−	0.949810i
$33$	1973.97	−	471.003i	1.81265	−	0.432510i
$34$	212.075	−	334.769i	0.183455	−	0.289593i
$35$		−	1783.15i		−	1.45563i
$36$	−1200.51	+	488.264i	−0.926316	+	0.376747i
$37$	609.762			0.445407			0.222703	−	0.974886i	$-0.428512\pi$
$37$	609.762			0.445407			0.222703	+	0.974886i	$0.428512\pi$
$38$	571.958	+	362.333i	0.396093	+	0.250923i
$39$	1481.61	+	441.118i	0.974103	+	0.290019i
$40$	−742.534	−	1754.59i	−0.464083	−	1.09662i
$41$	206.545	+	357.747i	0.122871	+	0.212818i	0.920899	−	0.389802i	$-0.127457\pi$
$41$	206.545	+	357.747i	0.122871	+	0.212818i	−0.798028	+	0.602620i	$0.794123\pi$
$42$	699.686	−	2039.68i	0.396648	−	1.15628i
$43$	−265.498	−	153.286i	−0.143590	−	0.0829019i	0.426484	−	0.904495i	$-0.359752\pi$
$43$	−265.498	−	153.286i	−0.143590	−	0.0829019i	−0.570074	+	0.821593i	$0.693085\pi$
$44$	−296.127	+	3595.63i	−0.152958	+	1.85725i
$45$	−2151.54	+	1088.73i	−1.06249	+	0.537644i
$46$	58.9591	−	1434.21i	0.0278635	−	0.677791i
$47$	−2270.59	−	1310.93i	−1.02788	−	0.593447i	−0.111504	−	0.993764i	$-0.535567\pi$
$47$	−2270.59	−	1310.93i	−1.02788	−	0.593447i	−0.916377	+	0.400317i	$0.868900\pi$
$48$	−160.878	−	2298.38i	−0.0698256	−	0.997559i
$49$	593.432	+	1027.85i	0.247160	+	0.428094i
$50$	−484.826	−	925.578i	−0.193930	−	0.370231i
$51$	647.636	−	612.872i	0.248995	−	0.235629i
$52$	−1564.84	+	2259.23i	−0.578711	+	0.835512i
$53$	2034.30			0.724209			0.362104	−	0.932138i	$-0.382058\pi$
$53$	2034.30			0.724209			0.362104	+	0.932138i	$0.382058\pi$
$54$	−2888.28	+	401.120i	−0.990494	+	0.137558i
$55$			6712.63i			2.21905i
$56$	3059.08	+	2310.39i	0.975472	+	0.736732i
$57$	1047.10	+	1106.50i	0.322284	+	0.340565i
$58$	33.4692	+	63.8958i	0.00994922	+	0.0189940i
$59$	2250.48	−	1299.32i	0.646505	−	0.373260i	−0.140611	−	0.990065i	$-0.544907\pi$
$59$	2250.48	−	1299.32i	0.646505	−	0.373260i	0.787116	+	0.616805i	$0.211573\pi$
$60$	−649.318	−	4237.33i	−0.180366	−	1.17704i
$61$	708.681	−	1227.47i	0.190455	−	0.329877i	−0.754946	−	0.655786i	$-0.772337\pi$
$61$	708.681	−	1227.47i	0.190455	−	0.329877i	0.945401	+	0.325910i	$0.105670\pi$
$62$	127.469	−	3100.74i	0.0331606	−	0.806645i
$63$	2653.80	−	4061.69i	0.668633	−	1.02335i
$64$	3972.17	+	999.536i	0.969768	+	0.244027i
$65$	−2556.67	+	4428.28i	−0.605129	+	1.04811i
$66$	−2633.95	+	7678.34i	−0.604673	+	1.76271i
$67$	−5191.93	+	2997.56i	−1.15659	+	0.667758i	−0.950485	−	0.310772i	$-0.899412\pi$
$67$	−5191.93	+	2997.56i	−1.15659	+	0.667758i	−0.206106	+	0.978530i	$0.566079\pi$
$68$	677.228	+	1433.21i	0.146459	+	0.309951i
$69$	921.593	−	3095.41i	0.193571	−	0.650160i
$70$	6025.32	+	3817.01i	1.22966	+	0.778982i
$71$		−	1239.44i		−	0.245872i	−0.992415	−	0.122936i	$-0.960769\pi$
$71$		−	1239.44i		−	0.245872i	0.992415	−	0.122936i	$-0.0392310\pi$
$72$	919.945	−	5101.72i	0.177458	−	0.984128i
$73$	−5060.60			−0.949633			−0.474817	−	0.880085i	$-0.657486\pi$
$73$	−5060.60			−0.949633			−0.474817	+	0.880085i	$0.657486\pi$
$74$	−1305.25	+	2060.40i	−0.238359	+	0.376260i
$75$	−545.636	−	2286.76i	−0.0970019	−	0.406535i
$76$	−2448.66	+	1157.05i	−0.423938	+	0.200321i
$77$	−6753.22	−	11696.9i	−1.13901	−	1.97283i
$78$	−4662.09	+	4062.15i	−0.766286	+	0.667677i
$79$	−1635.99	−	944.538i	−0.262135	−	0.151344i	0.363173	−	0.931722i	$-0.381693\pi$
$79$	−1635.99	−	944.538i	−0.262135	−	0.151344i	−0.625308	+	0.780378i	$0.715027\pi$
$80$	7518.28	+	1246.83i	1.17473	+	0.194818i
$81$	−6521.14	−	722.147i	−0.993924	−	0.110067i
$82$	−1650.97	−	67.8700i	−0.245534	−	0.0100937i
$83$	5831.54	+	3366.84i	0.846500	+	0.488727i	0.859469	−	0.511189i	$-0.170795\pi$
$83$	5831.54	+	3366.84i	0.846500	+	0.488727i	−0.0129681	+	0.999916i	$0.504128\pi$
$84$	5394.40	+	6730.41i	0.764513	+	0.953856i
$85$	1474.66	+	2554.19i	0.204106	+	0.353522i
$86$	1086.28	−	569.004i	0.146874	−	0.0769340i
$87$	37.6671	+	157.863i	0.00497649	+	0.0208565i
$88$	−11515.8	−	8697.42i	−1.48707	−	1.12312i
$89$	9436.67			1.19135			0.595674	−	0.803226i	$-0.296885\pi$
$89$	9436.67			1.19135			0.595674	+	0.803226i	$0.296885\pi$
$90$	926.745	−	9600.66i	0.114413	−	1.18527i
$91$		−	10288.5i		−	1.24242i
$92$	4720.02	+	3269.29i	0.557658	+	0.386258i
$93$	1992.48	−	6692.25i	0.230371	−	0.773760i
$94$	9290.07	−	4866.22i	1.05139	−	0.550727i
$95$	−4363.88	+	2519.49i	−0.483533	+	0.279168i
$96$	8110.66	+	4376.29i	0.880063	+	0.474858i
$97$	7297.91	−	12640.4i	0.775631	−	1.34343i	−0.158808	−	0.987309i	$-0.550765\pi$
$97$	7297.91	−	12640.4i	0.775631	−	1.34343i	0.934439	−	0.356123i	$-0.115902\pi$
$98$	−4743.45	−	195.000i	−0.493904	−	0.0203040i
$99$	−9990.18	+	15290.1i	−1.01930	+	1.56006i
$100$	4165.37	+	343.050i	0.416537	+	0.0343050i
$101$	−3230.71	+	5595.76i	−0.316705	+	0.548550i	−0.979799	−	0.199987i	$-0.935910\pi$
$101$	−3230.71	+	5595.76i	−0.316705	+	0.548550i	0.663093	+	0.748537i	$0.269243\pi$
$102$	684.583	+	3500.29i	0.0658000	+	0.336437i
$103$	13991.6	−	8078.04i	1.31884	−	0.761432i	0.335298	−	0.942112i	$-0.391163\pi$
$103$	13991.6	−	8078.04i	1.31884	−	0.761432i	0.983542	+	0.180680i	$0.0578298\pi$
$104$	−4284.30	−	10123.7i	−0.396108	−	0.935995i
$105$	11030.7	+	11656.4i	1.00052	+	1.05727i
$106$	−4354.62	+	6873.97i	−0.387560	+	0.611780i
$107$			3065.27i			0.267732i	0.990999	+	0.133866i	$0.0427392\pi$
$107$			3065.27i			0.267732i	−0.990999	+	0.133866i	$0.957261\pi$
$108$	4827.25	−	10618.2i	0.413859	−	0.910341i
$109$	−17728.8			−1.49220			−0.746098	−	0.665836i	$-0.768075\pi$
$109$	−17728.8			−1.49220			−0.746098	+	0.665836i	$0.768075\pi$
$110$	−22682.2	−	14369.0i	−1.87456	−	1.18752i
$111$	−3986.01	+	3772.04i	−0.323513	+	0.306147i
$112$	−14355.1	+	5391.10i	−1.14438	+	0.429775i
$113$	7396.56	+	12811.2i	0.579259	+	1.00331i	0.995565	+	0.0940814i	$0.0299914\pi$
$113$	7396.56	+	12811.2i	0.579259	+	1.00331i	−0.416305	+	0.909225i	$0.636675\pi$
$114$	−5980.31	+	1169.62i	−0.460165	+	0.0899985i
$115$	9251.65	+	5341.44i	0.699558	+	0.403890i
$116$	−287.550	−	23.6819i	−0.0213696	−	0.00175995i
$117$	−12414.1	+	6281.80i	−0.906865	+	0.458894i
$118$	−426.951	+	10385.8i	−0.0306629	+	0.745890i
$119$	−5139.28	−	2967.16i	−0.362918	−	0.209531i
$120$	15708.0	+	6876.36i	1.09083	+	0.477525i
$121$	18101.8	+	31353.3i	1.23638	+	2.14147i
$122$	2630.66	+	5022.18i	0.176744	+	0.337421i
$123$	−3563.24	−	1060.88i	−0.235524	−	0.0701223i
$124$	10204.6	+	7068.17i	0.663673	+	0.459688i
$125$	−10829.6			−0.693094
$126$	8043.83	+	17661.7i	0.506666	+	1.11248i
$127$		−	18478.7i		−	1.14568i	−0.819667	−	0.572841i	$-0.805841\pi$
$127$		−	18478.7i		−	1.14568i	0.819667	−	0.572841i	$-0.194159\pi$
$128$	−11880.3	+	11282.5i	−0.725115	+	0.688628i
$129$	2683.80	−	640.372i	0.161276	−	0.0384816i
$130$	−9490.49	−	18118.2i	−0.561567	−	1.07208i
$131$	−7205.95	+	4160.35i	−0.419902	+	0.242431i	−0.695036	−	0.718975i	$-0.744611\pi$
$131$	−7205.95	+	4160.35i	−0.419902	+	0.242431i	0.275133	+	0.961406i	$0.411278\pi$
$132$	−20307.1	−	25336.5i	−1.16547	−	1.45411i
$133$	5069.44	−	8780.53i	0.286587	−	0.496384i
$134$	984.989	−	23960.3i	0.0548557	−	1.33439i
$135$	7329.64	−	20426.7i	0.402175	−	1.12080i
$136$	−6292.54	−	779.559i	−0.340211	−	0.0421474i
$137$	10703.4	−	18538.7i	0.570268	−	0.987732i	−0.426271	−	0.904596i	$-0.640173\pi$
$137$	10703.4	−	18538.7i	0.570268	−	0.987732i	0.996538	−	0.0831367i	$-0.0264938\pi$
$138$	8486.72	+	9740.12i	0.445638	+	0.511454i
$139$	15783.6	−	9112.67i	0.816915	−	0.471646i	−0.0324367	−	0.999474i	$-0.510327\pi$
$139$	15783.6	−	9112.67i	0.816915	−	0.471646i	0.849351	+	0.527828i	$0.176993\pi$
$140$	−25795.6	+	12189.0i	−1.31610	+	0.621890i
$141$	22952.3	−	5476.57i	1.15449	−	0.275468i
$142$	4188.11	+	2653.15i	0.207702	+	0.131578i
$143$			38730.8i			1.89402i
$144$	15269.6	+	14029.3i	0.736383	+	0.676565i
$145$	−536.823			−0.0255326
$146$	10832.7	−	17099.9i	0.508196	−	0.802210i
$147$	−10237.7	−	3048.05i	−0.473769	−	0.141055i
$148$	−4168.13	−	8820.99i	−0.190291	−	0.402711i
$149$	8119.72	+	14063.8i	0.365736	+	0.633474i	0.988894	−	0.148622i	$-0.0474838\pi$
$149$	8119.72	+	14063.8i	0.365736	+	0.633474i	−0.623158	+	0.782096i	$0.714150\pi$
$150$	8895.02	+	3051.32i	0.395334	+	0.135614i
$151$	−21240.4	−	12263.2i	−0.931557	−	0.537835i	−0.0442533	−	0.999020i	$-0.514091\pi$
$151$	−21240.4	−	12263.2i	−0.931557	−	0.537835i	−0.887304	+	0.461186i	$0.847424\pi$
$152$	1331.89	−	10750.9i	0.0576476	−	0.465326i
$153$	−442.308	+	8012.68i	−0.0188948	+	0.342290i
$154$	53980.1	+	2219.08i	2.27611	+	0.0935690i
$155$	20002.0	+	11548.2i	0.832549	+	0.480672i
$156$	−3746.47	−	24448.8i	−0.153947	−	1.00463i
$157$	−19827.0	−	34341.4i	−0.804375	−	1.39322i	−0.916712	−	0.399548i	$-0.869167\pi$
$157$	−19827.0	−	34341.4i	−0.804375	−	1.39322i	0.112337	−	0.993670i	$-0.464166\pi$
$158$	6693.61	−	3506.17i	0.268131	−	0.140449i
$159$	−13298.2	+	12584.4i	−0.526016	+	0.497780i
$160$	−20306.7	+	22735.5i	−0.793231	+	0.888106i
$161$	−21494.9			−0.829248
$162$	16399.3	−	20489.3i	0.624878	−	0.780723i
$163$			25324.6i			0.953162i	0.879130	+	0.476581i	$0.158124\pi$
$163$			25324.6i			0.953162i	−0.879130	+	0.476581i	$0.841876\pi$
$164$	3763.40	−	5433.39i	0.139924	−	0.202015i
$165$	−41525.0	−	43880.4i	−1.52525	−	1.61177i
$166$	−23859.6	+	12497.9i	−0.865860	+	0.453545i
$167$	24109.7	−	13919.8i	0.864490	−	0.499113i	−0.00102363	−	0.999999i	$-0.500326\pi$
$167$	24109.7	−	13919.8i	0.864490	−	0.499113i	0.865513	+	0.500886i	$0.166992\pi$
$168$	−34289.5	+	3820.75i	−1.21491	+	0.135372i
$169$	−471.081	+	815.937i	−0.0164939	+	0.0285682i
$170$	−11787.4	−	484.569i	−0.407867	−	0.0167671i
$171$	−13689.8	−	755.690i	−0.468171	−	0.0258435i
$172$	−402.612	+	4888.59i	−0.0136091	+	0.165244i
$173$	11027.3	−	19099.8i	0.368448	−	0.638170i	−0.620875	−	0.783909i	$-0.713223\pi$
$173$	11027.3	−	19099.8i	0.368448	−	0.638170i	0.989323	+	0.145739i	$0.0465560\pi$
$174$	−614.053	−	210.643i	−0.0202818	−	0.00695741i
$175$	−13550.4	+	7823.30i	−0.442461	+	0.255455i
$176$	54039.6	−	20294.7i	1.74456	−	0.655174i
$177$	−6673.69	+	22415.3i	−0.213020	+	0.715482i
$178$	−20200.1	+	31886.8i	−0.637550	+	1.00640i
$179$		−	52513.4i		−	1.63895i	−0.573118	−	0.819473i	$-0.694266\pi$
$179$		−	52513.4i		−	1.63895i	0.573118	−	0.819473i	$-0.305734\pi$
$180$	30457.1	+	23682.7i	0.940035	+	0.730946i
$181$	−7223.25			−0.220483			−0.110242	−	0.993905i	$-0.535162\pi$
$181$	−7223.25			−0.220483			−0.110242	+	0.993905i	$0.535162\pi$
$182$	34765.2	+	22023.6i	1.04955	+	0.664882i
$183$	2960.61	+	12407.9i	0.0884056	+	0.370508i
$184$	−21150.7	+	8950.85i	−0.624725	+	0.264380i
$185$	−9076.12	−	15720.3i	−0.265190	−	0.459322i
$186$	18348.2	+	21058.1i	0.530357	+	0.608685i
$187$	19346.7	+	11169.8i	0.553252	+	0.319420i
$188$	−3443.21	+	41808.1i	−0.0974200	+	1.18289i
$189$	7778.09	+	42967.9i	0.217746	+	1.20287i
$190$	827.894	−	20138.9i	0.0229334	−	0.557864i
$191$	9164.94	+	5291.38i	0.251225	+	0.145045i	0.620325	−	0.784345i	$-0.287001\pi$
$191$	9164.94	+	5291.38i	0.251225	+	0.145045i	−0.369100	+	0.929390i	$0.620334\pi$
$192$	−32149.3	+	18038.3i	−0.872105	+	0.489319i
$193$	19543.2	+	33849.9i	0.524665	+	0.908746i	0.999588	+	0.0287188i	$0.00914273\pi$
$193$	19543.2	+	33849.9i	0.524665	+	0.908746i	−0.474923	+	0.880028i	$0.657524\pi$
$194$	27090.2	+	51717.8i	0.719796	+	1.37416i
$195$	−10680.8	−	44763.4i	−0.280890	−	1.17721i
$196$	10812.7	−	15610.8i	0.281464	−	0.406363i
$197$	−10820.0			−0.278802			−0.139401	−	0.990236i	$-0.544518\pi$
$197$	−10820.0			−0.278802			−0.139401	+	0.990236i	$0.544518\pi$
$198$	−30280.8	−	66487.1i	−0.772391	−	1.69593i
$199$		−	807.389i		−	0.0203881i	−0.999948	−	0.0101940i	$-0.996755\pi$
$199$		−	807.389i		−	0.0203881i	0.999948	−	0.0101940i	$-0.00324492\pi$
$200$	−10075.6	+	13340.6i	−0.251889	+	0.333515i
$201$	15396.4	−	51712.8i	0.381090	−	1.27999i
$202$	−11992.6	−	22894.9i	−0.293907	−	0.561095i
$203$	935.426	−	540.068i	0.0226996	−	0.0131056i
$204$	−13293.0	−	5179.50i	−0.319421	−	0.124459i
$205$	6148.73	−	10649.9i	0.146311	−	0.253419i
$206$	−2654.41	+	64569.8i	−0.0625510	+	1.52158i
$207$	13124.1	+	25935.7i	0.306286	+	0.605282i
$208$	43379.3	+	7194.03i	1.00267	+	0.166282i
$209$	−19083.8	+	33054.1i	−0.436890	+	0.756716i
$210$	−62999.8	+	12321.4i	−1.42857	+	0.279397i
$211$	−52683.9	+	30417.0i	−1.18335	+	0.683207i	−0.956787	−	0.290790i	$-0.906082\pi$
$211$	−52683.9	+	30417.0i	−1.18335	+	0.683207i	−0.226562	+	0.973997i	$0.572749\pi$
$212$	−13905.8	−	29428.8i	−0.309403	−	0.654788i
$213$	7667.31	+	8102.22i	0.168999	+	0.178585i
$214$	−10357.6	−	6561.51i	−0.226169	−	0.143277i
$215$			9126.44i			0.197435i
$216$	25546.1	+	39040.8i	0.547541	+	0.836779i
$217$	−46471.9			−0.986895
$218$	37950.2	−	59906.1i	0.798549	−	1.26054i
$219$	33081.1	−	31305.3i	0.689749	−	0.652724i
$220$	97106.9	−	45885.4i	2.00634	−	0.948045i
$221$	8508.59	+	14737.3i	0.174210	+	0.301741i
$222$	−4213.40	−	21543.3i	−0.0854923	−	0.437125i
$223$	−9292.11	−	5364.80i	−0.186855	−	0.107881i	0.403654	−	0.914912i	$-0.367740\pi$
$223$	−9292.11	−	5364.80i	−0.186855	−	0.107881i	−0.590509	+	0.807031i	$0.701073\pi$
$224$	12511.9	−	60046.6i	0.249361	−	1.19672i
$225$	17712.9	+	11573.2i	0.349885	+	0.228606i
$226$	−59122.5	−	2430.48i	−1.15754	−	0.0475856i
$227$	−65585.2	−	37865.7i	−1.27278	−	0.734842i	−0.297272	−	0.954793i	$-0.596077\pi$
$227$	−65585.2	−	37865.7i	−1.27278	−	0.734842i	−0.975511	+	0.219951i	$0.929410\pi$
$228$	8849.25	−	22711.3i	0.170230	−	0.436891i
$229$	26683.3	+	46216.8i	0.508825	+	0.881311i	0.999948	+	0.0102204i	$0.00325330\pi$
$229$	26683.3	+	46216.8i	0.508825	+	0.881311i	−0.491123	+	0.871090i	$0.663413\pi$
$230$	−37853.0	+	19827.7i	−0.715557	+	0.374815i
$231$	116504.	+	34686.6i	2.18332	+	0.650036i
$232$	695.550	−	920.945i	0.0129227	−	0.0171103i
$233$	56485.5			1.04046			0.520230	−	0.854026i	$-0.325846\pi$
$233$	56485.5			1.04046			0.520230	+	0.854026i	$0.325846\pi$
$234$	5347.18	−	55394.3i	0.0976546	−	1.01166i
$235$			78050.9i			1.41333i
$236$	−34179.9	−	23674.4i	−0.613686	−	0.425065i
$237$	16537.4	−	3945.94i	0.294423	−	0.0702511i
$238$	21027.3	−	11014.3i	0.371218	−	0.194447i
$239$	−41561.8	+	23995.7i	−0.727610	+	0.420086i	−0.817547	−	0.575862i	$-0.804667\pi$
$239$	−41561.8	+	23995.7i	−0.727610	+	0.420086i	0.0899375	+	0.995947i	$0.471333\pi$
$240$	−56860.0	+	38358.3i	−0.987152	+	0.665942i
$241$	32075.1	−	55555.6i	0.552247	−	0.956520i	−0.445865	−	0.895100i	$-0.647104\pi$
$241$	32075.1	−	55555.6i	0.552247	−	0.956520i	0.998112	−	0.0614196i	$-0.0195628\pi$
$242$	−144692.	−	5948.19i	−2.47067	−	0.101567i
$243$	47095.9	−	35619.7i	0.797573	−	0.603223i
$244$	−22601.3	−	1861.39i	−0.379624	−	0.0312649i
$245$	17666.1	−	30598.6i	0.294313	−	0.509764i
$246$	11212.2	−	9769.38i	0.185277	−	0.161435i
$247$	−25178.9	+	14537.1i	−0.412708	+	0.238277i
$248$	−45727.6	+	19351.7i	−0.743490	+	0.314641i
$249$	−58948.3	+	14065.4i	−0.950764	+	0.226858i
$250$	23181.8	−	36593.5i	0.370909	−	0.585496i
$251$		−	65230.8i		−	1.03539i	−0.855564	−	0.517696i	$-0.826790\pi$
$251$		−	65230.8i		−	1.03539i	0.855564	−	0.517696i	$-0.173210\pi$
$252$	−76898.1	−	10626.3i	−1.21092	−	0.167333i
$253$	80917.3			1.26415
$254$	62440.1	+	39555.5i	0.967823	+	0.613111i
$255$	−25440.4	−	7574.33i	−0.391240	−	0.116483i
$256$	−12692.9	−	64295.1i	−0.193678	−	0.981065i
$257$	21657.9	+	37512.6i	0.327907	+	0.567951i	0.982096	−	0.188380i	$-0.0603235\pi$
$257$	21657.9	+	37512.6i	0.327907	+	0.567951i	−0.654190	+	0.756331i	$0.726990\pi$
$258$	−3581.10	+	10439.4i	−0.0537994	+	0.156833i
$259$	31630.7	+	18262.0i	0.471530	+	0.272238i
$260$	81537.3	+	6715.22i	1.20617	+	0.0993376i
$261$	−1222.78	−	798.935i	−0.0179502	−	0.0117282i
$262$	1367.08	−	33254.7i	0.0199155	−	0.484452i
$263$	−73443.4	−	42402.6i	−1.06180	−	0.613029i	−0.135868	−	0.990727i	$-0.543382\pi$
$263$	−73443.4	−	42402.6i	−1.06180	−	0.613029i	−0.925929	+	0.377698i	$0.876716\pi$
$264$	129082.	−	14383.1i	1.85207	−	0.206370i
$265$	−30280.0	−	52446.5i	−0.431185	−	0.746835i
$266$	18818.0	+	35925.4i	0.265957	+	0.507736i
$267$	−61687.4	+	58376.2i	−0.865315	+	0.818866i
$268$	78854.0	+	54617.6i	1.09788	+	0.760437i
$269$	−66685.5			−0.921567			−0.460784	−	0.887513i	$-0.652432\pi$
$269$	−66685.5			−0.921567			−0.460784	+	0.887513i	$0.652432\pi$
$270$	53332.5	+	68492.4i	0.731584	+	0.939539i
$271$		−	122426.i		−	1.66700i	−0.552516	−	0.833502i	$-0.686332\pi$
$271$		−	122426.i		−	1.66700i	0.552516	−	0.833502i	$-0.313668\pi$
$272$	16103.9	−	19593.9i	0.217668	−	0.264840i
$273$	63645.7	+	67255.9i	0.853972	+	0.902412i
$274$	39731.4	+	75851.0i	0.529216	+	1.01032i
$275$	51010.0	−	29450.6i	0.674512	−	0.389430i
$276$	−51078.8	+	7827.19i	−0.670537	+	0.102751i
$277$	−68726.1	+	119037.i	−0.895699	+	1.55140i	−0.0627613	+	0.998029i	$0.519991\pi$
$277$	−68726.1	+	119037.i	−0.895699	+	1.55140i	−0.832937	+	0.553367i	$0.813343\pi$
$278$	−2994.39	+	72839.8i	−0.0387453	+	0.942496i
$279$	28374.1	+	56072.9i	0.364514	+	0.720351i
$280$	14030.8	−	113256.i	0.178965	−	1.44459i
$281$	−7001.61	+	12127.2i	−0.0886718	+	0.153584i	−0.906950	−	0.421238i	$-0.861596\pi$
$281$	−7001.61	+	12127.2i	−0.0886718	+	0.153584i	0.818278	+	0.574822i	$0.194929\pi$
$282$	−30626.2	+	89279.7i	−0.385119	+	1.12268i
$283$	99634.2	−	57523.8i	1.24404	−	0.718249i	0.274129	−	0.961693i	$-0.411611\pi$
$283$	99634.2	−	57523.8i	1.24404	−	0.718249i	0.969915	+	0.243444i	$0.0782773\pi$
$284$	−17930.1	+	8472.43i	−0.222304	+	0.105044i
$285$	12940.9	−	43465.3i	0.159321	−	0.535122i
$286$	−130873.	−	82907.2i	−1.59999	−	1.01358i
$287$			24743.6i			0.300400i
$288$	−80091.4	+	21565.5i	−0.965608	+	0.260001i
$289$	−73705.6			−0.882480
$290$	1149.12	−	1813.94i	0.0136638	−	0.0215688i
$291$	30488.0	+	127775.i	0.360034	+	1.50890i
$292$	34592.6	+	73208.0i	0.405712	+	0.858604i
$293$	−14259.3	−	24697.8i	−0.166097	−	0.287689i	0.770947	−	0.636899i	$-0.219783\pi$
$293$	−14259.3	−	24697.8i	−0.166097	−	0.287689i	−0.937044	+	0.349210i	$0.886450\pi$
$294$	32214.2	−	28068.7i	0.372694	−	0.324734i
$295$	−66995.6	−	38679.9i	−0.769843	−	0.444469i
$296$	38728.7	+	4797.95i	0.442027	+	0.0547611i
$297$	−29280.5	−	161752.i	−0.331944	−	1.83373i
$298$	−64902.9	−	2668.11i	−0.730856	−	0.0300449i
$299$	53380.6	+	30819.3i	0.597092	+	0.344731i
$300$	−29351.2	+	23524.9i	−0.326124	+	0.261388i
$301$	−9181.62	−	15903.0i	−0.101341	−	0.175528i
$302$	86904.8	−	45521.5i	0.952862	−	0.499117i
$303$	−13496.7	−	56564.9i	−0.147009	−	0.616115i
$304$	33476.6	+	27513.8i	0.362238	+	0.297717i
$305$	−42194.0			−0.453577
$306$	−26128.3	−	18646.5i	−0.279041	−	0.199138i
$307$			115338.i			1.22376i	0.790952	+	0.611879i	$0.209586\pi$
$307$			115338.i			1.22376i	−0.790952	+	0.611879i	$0.790414\pi$
$308$	−123048.	+	177650.i	−1.29710	+	1.87268i
$309$	−41491.3	+	139359.i	−0.434550	+	1.45955i
$310$	−81837.8	+	42867.4i	−0.851590	+	0.446070i
$311$	−85566.6	+	49401.9i	−0.884674	+	0.510767i	−0.872197	−	0.489155i	$-0.837305\pi$
$311$	−85566.6	+	49401.9i	−0.884674	+	0.510767i	−0.0124776	+	0.999922i	$0.503972\pi$
$312$	90632.7	+	39675.6i	0.931056	+	0.407581i
$313$	37066.1	−	64200.3i	0.378345	−	0.655313i	−0.612477	−	0.790489i	$-0.709827\pi$
$313$	37066.1	−	64200.3i	0.378345	−	0.655313i	0.990822	+	0.135176i	$0.0431600\pi$
$314$	158482.	+	6515.09i	1.60739	+	0.0660786i
$315$	−144216.	−	7960.85i	−1.45342	−	0.0802303i
$316$	−2480.88	+	30123.2i	−0.0248445	+	0.301667i
$317$	1057.30	−	1831.29i	0.0105215	−	0.0182238i	−0.860717	−	0.509084i	$-0.829984\pi$
$317$	1057.30	−	1831.29i	0.0105215	−	0.0182238i	0.871238	+	0.490860i	$0.163318\pi$
$318$	−14056.9	−	71873.2i	−0.139006	−	0.710743i
$319$	−3521.39	+	2033.08i	−0.0346045	+	0.0199789i
$320$	−33355.5	−	117285.i	−0.325737	−	1.14536i
$321$	−18962.0	−	20037.6i	−0.184024	−	0.194463i
$322$	46012.1	−	72632.1i	0.443772	−	0.700514i
$323$			16769.7i			0.160739i
$324$	34129.6	+	99273.0i	0.325118	+	0.945673i
$325$	44868.0			0.424785
$326$	−85572.5	−	54209.7i	−0.805191	−	0.510084i
$327$	115893.	−	109672.i	1.08383	−	1.02565i
$328$	10303.7	+	24347.3i	0.0957731	+	0.226310i
$329$	−78522.8	−	136006.i	−0.725444	−	1.25651i
$330$	237161.	−	46383.7i	2.17779	−	0.425930i
$331$	−12334.0	−	7121.02i	−0.112576	−	0.0649960i	0.442655	−	0.896692i	$-0.354037\pi$
$331$	−12334.0	−	7121.02i	−0.112576	−	0.0649960i	−0.555231	+	0.831696i	$0.687370\pi$
$332$	8843.19	−	107375.i	0.0802292	−	0.974156i
$333$	2722.27	−	49315.6i	0.0245495	−	0.444730i
$334$	−4573.98	+	111264.i	−0.0410017	+	0.997384i
$335$	154561.	+	89235.7i	1.37724	+	0.795150i
$336$	60489.6	−	124044.i	0.535799	−	1.09874i
$337$	−37711.8	−	65318.7i	−0.332061	−	0.575146i	0.650855	−	0.759202i	$-0.274411\pi$
$337$	−37711.8	−	65318.7i	−0.332061	−	0.575146i	−0.982916	+	0.184056i	$0.941077\pi$
$338$	−1748.68	−	3338.39i	−0.0153065	−	0.0292216i
$339$	−127603.	−	37991.0i	−1.11035	−	0.330584i
$340$	26869.4	−	38792.6i	0.232434	−	0.335576i
$341$	174942.			1.50448
$342$	31857.8	−	44640.5i	0.272373	−	0.381661i
$343$		−	72725.3i		−	0.618155i
$344$	−15656.8	−	11824.9i	−0.132308	−	0.0999268i
$345$	−93520.6	+	22314.6i	−0.785722	+	0.187478i
$346$	40933.8	+	78146.5i	0.341924	+	0.652765i
$347$	128553.	−	74220.2i	1.06764	−	0.616401i	0.140103	−	0.990137i	$-0.455257\pi$
$347$	128553.	−	74220.2i	1.06764	−	0.616401i	0.927535	+	0.373736i	$0.121923\pi$
$348$	2026.21	−	1624.00i	0.0167311	−	0.0134100i
$349$	11665.4	−	20205.1i	0.0957745	−	0.165886i	−0.814157	−	0.580645i	$-0.802801\pi$
$349$	11665.4	−	20205.1i	0.0957745	−	0.165886i	0.909932	+	0.414758i	$0.136134\pi$
$350$	2570.71	−	62533.6i	0.0209854	−	0.510478i
$351$	42290.9	−	117859.i	0.343268	−	0.956637i
$352$	−47100.8	+	226044.i	−0.380140	+	1.82435i
$353$	−9687.21	+	16778.7i	−0.0777409	+	0.134651i	−0.902275	−	0.431161i	$-0.858104\pi$
$353$	−9687.21	+	16778.7i	−0.0777409	+	0.134651i	0.824534	+	0.565812i	$0.191437\pi$
$354$	−61456.4	−	70532.8i	−0.490411	−	0.562840i
$355$	−31954.1	+	18448.7i	−0.253554	+	0.146389i
$356$	−64506.0	−	136514.i	−0.508980	−	1.07715i
$357$	51950.5	−	12395.7i	0.407618	−	0.0972603i
$358$	177444.	+	112410.i	1.38451	+	0.877081i
$359$			139927.i			1.08571i	0.839827	+	0.542854i	$0.182656\pi$
$359$			139927.i			1.08571i	−0.839827	+	0.542854i	$0.817344\pi$
$360$	−145221.	+	52220.4i	−1.12053	+	0.402936i
$361$	101670.			0.780148
$362$	15462.1	−	24407.6i	0.117992	−	0.186255i
$363$	−312286.	−	92976.5i	−2.36995	−	0.705603i
$364$	−148836.	+	70328.9i	−1.12333	+	0.530800i
$365$	75325.5	+	130468.i	0.565400	+	0.979302i
$366$	−48264.3	−	16556.4i	−0.360300	−	0.123596i
$367$	79304.5	+	45786.5i	0.588797	+	0.339942i	0.764622	−	0.644479i	$-0.222926\pi$
$367$	79304.5	+	45786.5i	0.588797	+	0.339942i	−0.175825	+	0.984421i	$0.556259\pi$
$368$	15029.9	−	90628.9i	0.110984	−	0.669224i
$369$	29855.6	−	15107.6i	0.219267	−	0.110954i
$370$	72547.7	+	2982.38i	0.529932	+	0.0217851i
$371$	105527.	+	60926.1i	0.766684	+	0.442645i
$372$	−110432.	+	16922.3i	−0.798011	+	0.122285i
$373$	−42790.4	−	74115.1i	−0.307559	−	0.532708i	0.670269	−	0.742118i	$-0.266179\pi$
$373$	−42790.4	−	74115.1i	−0.307559	−	0.532708i	−0.977828	+	0.209411i	$0.932845\pi$
$374$	−79156.6	+	41462.9i	−0.565906	+	0.296426i
$375$	70792.9	−	66992.9i	0.503416	−	0.476394i
$376$	−133900.	−	101129.i	−0.947120	−	0.715319i
$377$	−3097.38			−0.0217928
$378$	−161840.	−	65694.6i	−1.13266	−	0.459776i
$379$		−	39838.1i		−	0.277345i	−0.990338	−	0.138672i	$-0.955716\pi$
$379$		−	39838.1i		−	0.277345i	0.990338	−	0.138672i	$-0.0442835\pi$
$380$	66277.7	+	45906.8i	0.458987	+	0.317914i
$381$	114311.	+	120795.i	0.787477	+	0.832146i
$382$	−37498.2	+	19641.9i	−0.256971	+	0.134603i
$383$	−147816.	+	85341.8i	−1.00769	+	0.581787i	−0.910513	−	0.413480i	$-0.864313\pi$
$383$	−147816.	+	85341.8i	−1.00769	+	0.581787i	−0.0971722	+	0.995268i	$0.530980\pi$
$384$	7866.84	−	147246.i	0.0533504	−	0.998576i
$385$	−201039.	+	348210.i	−1.35631	+	2.34920i
$386$	−156214.	−	6421.84i	−1.04844	−	0.0431007i
$387$	−13582.6	+	20788.3i	−0.0906901	+	0.138803i
$388$	−232745.	−	19168.3i	−1.54603	−	0.127327i
$389$	−107907.	+	186901.i	−0.713103	+	1.23513i	0.250583	+	0.968095i	$0.419378\pi$
$389$	−107907.	+	186901.i	−0.713103	+	1.23513i	−0.963687	+	0.267036i	$0.913956\pi$
$390$	174120.	+	59729.6i	1.14477	+	0.392700i
$391$	30789.5	−	17776.3i	0.201395	−	0.116275i
$392$	29603.8	+	69953.1i	0.192653	+	0.455234i
$393$	21368.9	−	71772.9i	0.138355	−	0.464703i
$394$	23161.3	−	36561.2i	0.149201	−	0.235520i
$395$			56236.6i			0.360434i
$396$	289481.	+	40002.5i	1.84599	+	0.255092i
$397$	292553.			1.85620			0.928098	−	0.372336i	$-0.121443\pi$
$397$	292553.			1.85620			0.928098	+	0.372336i	$0.121443\pi$
$398$	2728.19	+	1728.30i	0.0172230	+	0.0109107i
$399$	21178.3	+	88758.3i	0.133029	+	0.557524i
$400$	−23510.5	−	62602.5i	−0.146941	−	0.391266i
$401$	−102157.	−	176941.i	−0.635300	−	1.10037i	−0.986452	−	0.164053i	$-0.947543\pi$
$401$	−102157.	−	176941.i	−0.635300	−	1.10037i	0.351152	−	0.936318i	$-0.385790\pi$
$402$	141782.	+	162721.i	0.877340	+	1.00691i
$403$	115408.	+	66631.1i	0.710604	+	0.410267i
$404$	103034.	+	8485.63i	0.631274	+	0.0519902i
$405$	78447.5	+	178871.i	0.478265	+	1.09051i
$406$	−177.464	+	4316.90i	−0.00107661	+	0.0261891i
$407$	−119073.	−	68746.9i	−0.718827	−	0.415015i
$408$	45956.7	−	33830.3i	0.276076	−	0.203229i
$409$	−17364.4	−	30076.0i	−0.103804	−	0.179793i	0.809445	−	0.587196i	$-0.199768\pi$
$409$	−17364.4	−	30076.0i	−0.103804	−	0.179793i	−0.913249	+	0.407402i	$0.866435\pi$
$410$	22824.4	+	43573.9i	0.135779	+	0.259214i
$411$	44714.7	+	187400.i	0.264708	+	1.10939i
$412$	−212501.	−	147187.i	−1.25189	−	0.867113i
$413$	155655.			0.912564
$414$	−115731.	−	11171.4i	−0.675225	−	0.0651790i
$415$		−	200458.i		−	1.16393i
$416$	−117167.	+	131180.i	−0.677044	+	0.758023i
$417$	−46805.5	+	157208.i	−0.269169	+	0.904073i
$418$	−70840.1	−	135240.i	−0.405440	−	0.774023i
$419$	277682.	−	160320.i	1.58169	−	0.913187i	0.587073	−	0.809534i	$-0.300280\pi$
$419$	277682.	−	160320.i	1.58169	−	0.913187i	0.994614	−	0.103653i	$-0.0330530\pi$
$420$	93222.9	−	239254.i	0.528474	−	1.35631i
$421$	−67885.7	+	117582.i	−0.383014	+	0.663399i	−0.991491	−	0.130172i	$-0.958447\pi$
$421$	−67885.7	+	117582.i	−0.383014	+	0.663399i	0.608478	+	0.793571i	$0.291780\pi$
$422$	9994.93	−	243131.i	0.0561248	−	1.36526i
$423$	−116161.	+	177786.i	−0.649199	+	0.993609i
$424$	129208.	+	16007.0i	0.718714	+	0.0890388i
$425$	12939.7	−	22412.3i	0.0716386	−	0.124082i
$426$	−43790.3	+	8564.45i	−0.241301	+	0.0471933i
$427$	73524.1	−	42449.2i	0.403250	−	0.232816i
$428$	44343.0	−	20953.2i	0.242068	−	0.114383i
$429$	−239593.	−	253183.i	−1.30184	−	1.37569i
$430$	−30838.5	−	19536.0i	−0.166785	−	0.105657i
$431$			31343.0i			0.168728i	0.996435	+	0.0843638i	$0.0268858\pi$
$431$			31343.0i			0.168728i	−0.996435	+	0.0843638i	$0.973114\pi$
$432$	−186604.	+	2750.26i	−0.999891	+	0.0147369i
$433$	101022.			0.538815			0.269407	−	0.963026i	$-0.413172\pi$
$433$	101022.			0.538815			0.269407	+	0.963026i	$0.413172\pi$
$434$	99477.7	−	157030.i	0.528137	−	0.833687i
$435$	3509.21	−	3320.84i	0.0185451	−	0.0175497i
$436$	121188.	+	256470.i	0.637511	+	1.34916i
$437$	30371.1	+	52604.3i	0.159037	+	0.275460i
$438$	34968.3	+	178794.i	0.182275	+	0.931976i
$439$	−157593.	−	90986.2i	−0.817724	−	0.472113i	0.0319068	−	0.999491i	$-0.489842\pi$
$439$	−157593.	−	90986.2i	−0.817724	−	0.472113i	−0.849631	+	0.527378i	$0.823175\pi$
$440$	−52818.8	+	426349.i	−0.272824	+	2.20222i
$441$	85779.0	−	43406.1i	0.441066	−	0.223189i
$442$	−68011.3	−	2795.89i	−0.348126	−	0.0143112i
$443$	−32206.4	−	18594.4i	−0.164110	−	0.0947490i	0.415696	−	0.909504i	$-0.363538\pi$
$443$	−32206.4	−	18594.4i	−0.164110	−	0.0947490i	−0.579806	+	0.814755i	$0.696872\pi$
$444$	81814.5	+	31878.3i	0.415016	+	0.161707i
$445$	−140462.	−	243287.i	−0.709315	−	1.22857i
$446$	38018.5	−	19914.4i	0.191128	−	0.100115i
$447$	−140078.	−	41705.3i	−0.701061	−	0.208726i
$448$	176116.	+	170814.i	0.877493	+	0.851074i
$449$	−20385.0			−0.101115			−0.0505577	−	0.998721i	$-0.516100\pi$
$449$	−20385.0			−0.101115			−0.0505577	+	0.998721i	$0.516100\pi$
$450$	−77022.4	+	35079.0i	−0.380357	+	0.173230i
$451$		−	93146.9i		−	0.457947i
$452$	134770.	−	194574.i	0.659656	−	0.952375i
$453$	214710.	−	51231.1i	1.04630	−	0.249653i
$454$	268341.	−	140559.i	1.30189	−	0.681943i
$455$	−265249.	+	153141.i	−1.28124	+	0.739724i
$456$	57799.5	+	78517.7i	0.277968	+	0.377605i
$457$	139829.	−	242191.i	0.669521	−	1.15964i	−0.308517	−	0.951219i	$-0.599833\pi$
$457$	139829.	−	242191.i	0.669521	−	1.15964i	0.978038	−	0.208426i	$-0.0668340\pi$
$458$	−213286.	−	8768.03i	−1.01679	−	0.0417995i
$459$	−46675.8	−	55114.9i	−0.221547	−	0.261604i
$460$	14029.6	−	170349.i	0.0663023	−	0.805054i
$461$	80298.4	−	139081.i	0.377838	−	0.654434i	−0.612910	−	0.790153i	$-0.710001\pi$
$461$	80298.4	−	139081.i	0.377838	−	0.654434i	0.990747	+	0.135719i	$0.0433344\pi$
$462$	−366595.	+	319420.i	−1.71752	+	1.49651i
$463$	85869.5	−	49576.8i	0.400569	−	0.231268i	−0.286161	−	0.958182i	$-0.592379\pi$
$463$	85869.5	−	49576.8i	0.400569	−	0.231268i	0.686729	+	0.726913i	$0.259046\pi$
$464$	1623.01	+	4321.66i	0.00753849	+	0.0200731i
$465$	−202191.	+	48244.0i	−0.935095	+	0.223120i
$466$	−120913.	+	190866.i	−0.556802	+	0.878936i
$467$		−	278790.i		−	1.27833i	−0.769068	−	0.639167i	$-0.779279\pi$
$467$		−	278790.i		−	1.27833i	0.769068	−	0.639167i	$-0.220721\pi$
$468$	175733.	+	136645.i	0.802345	+	0.623883i
$469$	−359101.			−1.63257
$470$	−263736.	−	167076.i	−1.19392	−	0.756341i
$471$	342048.	+	101838.i	1.54186	+	0.459057i
$472$	153162.	−	64817.3i	0.687491	−	0.290943i
$473$	34564.0	+	59866.6i	0.154490	+	0.267585i
$474$	−22066.6	+	64327.1i	−0.0982150	+	0.286311i
$475$	38291.7	+	22107.7i	0.169714	+	0.0979844i
$476$	−7793.40	+	94628.8i	−0.0343964	+	0.417647i
$477$	9082.11	−	164528.i	0.0399163	−	0.723108i
$478$	7884.90	−	191804.i	0.0345096	−	0.839462i
$479$	27705.5	+	15995.8i	0.120752	+	0.0697163i	0.559160	−	0.829060i	$-0.311124\pi$
$479$	27705.5	+	15995.8i	0.120752	+	0.0697163i	−0.438407	+	0.898776i	$0.644457\pi$
$480$	−7899.34	−	274241.i	−0.0342853	−	1.19028i
$481$	−52367.8	−	90703.7i	−0.226347	−	0.392044i
$482$	119064.	+	227305.i	0.512492	+	0.978396i
$483$	140512.	−	132970.i	0.602310	−	0.569979i
$484$	329828.	−	476187.i	1.40798	−	2.03276i
$485$	−434509.			−1.84721
$486$	19546.6	+	235386.i	0.0827559	+	0.996570i
$487$			346823.i			1.46235i	0.682192	+	0.731173i	$0.261027\pi$
$487$			346823.i			1.46235i	−0.682192	+	0.731173i	$0.738973\pi$
$488$	54670.0	−	72385.9i	0.229567	−	0.303959i
$489$	−156660.	−	165546.i	−0.655150	−	0.692313i
$490$	65577.5	+	125194.i	0.273126	+	0.521423i
$491$	−207830.	+	119991.i	−0.862076	+	0.497720i	−0.864707	−	0.502277i	$-0.832496\pi$
$491$	−207830.	+	119991.i	−0.862076	+	0.497720i	0.00263098	+	0.999997i	$0.499163\pi$
$492$	9010.17	+	58798.7i	0.0372223	+	0.242906i
$493$	−893.273	+	1547.19i	−0.00367528	+	0.00636577i
$494$	4776.82	−	116198.i	0.0195743	−	0.476152i
$495$	542897.	+	29968.4i	2.21568	+	0.122308i
$496$	32494.6	−	195939.i	0.132083	−	0.796448i
$497$	37120.5	−	64294.7i	0.150280	−	0.260293i
$498$	78657.2	−	229297.i	0.317161	−	0.924568i
$499$	−295354.	+	170523.i	−1.18616	+	0.684828i	−0.957431	−	0.288663i	$-0.906789\pi$
$499$	−295354.	+	170523.i	−1.18616	+	0.684828i	−0.228726	+	0.973491i	$0.573456\pi$
$500$	74027.6	+	156664.i	0.296110	+	0.626656i
$501$	−71496.2	+	240139.i	−0.284844	+	0.956724i
$502$	220417.	+	139633.i	0.874655	+	0.554090i
$503$			3886.22i			0.0153600i	0.999971	+	0.00768001i	$0.00244465\pi$
$503$			3886.22i			0.0153600i	−0.999971	+	0.00768001i	$0.997555\pi$
$504$	200515.	−	237094.i	0.789378	−	0.933383i
$505$	192353.			0.754250
$506$	−173211.	+	273422.i	−0.676512	+	1.06790i
$507$	−1968.01	−	8247.92i	−0.00765616	−	0.0320870i
$508$	−267318.	+	126314.i	−1.03586	+	0.489469i
$509$	−98673.1	−	170907.i	−0.380858	−	0.659666i	0.610327	−	0.792150i	$-0.291038\pi$
$509$	−98673.1	−	170907.i	−0.380858	−	0.659666i	−0.991185	+	0.132484i	$0.957705\pi$
$510$	80051.5	−	69750.1i	0.307772	−	0.268167i
$511$	−262513.	−	151562.i	−1.00533	−	0.580427i
$512$	244425.	+	94740.3i	0.932409	+	0.361405i
$513$	94164.7	−	79746.3i	0.357811	−	0.303023i
$514$	−173117.	−	7116.71i	−0.655260	−	0.0269372i
$515$	−416521.	−	240478.i	−1.57044	−	0.906696i
$516$	−27609.4	−	34447.2i	−0.103695	−	0.129376i
$517$	295597.	+	511990.i	1.10591	+	1.91549i
$518$	−129416.	+	67789.5i	−0.482314	+	0.252640i
$519$	46068.0	+	193071.i	0.171027	+	0.716774i
$520$	−197230.	+	261142.i	−0.729399	+	0.965763i
$521$	229165.			0.844255			0.422127	−	0.906536i	$-0.361283\pi$
$521$	229165.			0.844255			0.422127	+	0.906536i	$0.361283\pi$
$522$	5317.11	−	2421.62i	0.0195135	−	0.00888720i
$523$			346673.i			1.26741i	0.773575	+	0.633705i	$0.218467\pi$
$523$			346673.i			1.26741i	−0.773575	+	0.633705i	$0.781533\pi$
$524$	109442.	+	75804.5i	0.398587	+	0.276078i
$525$	40182.9	−	134965.i	0.145788	−	0.489667i
$526$	300492.	−	157401.i	1.08608	−	0.568899i
$527$	66566.6	−	38432.2i	0.239682	−	0.138380i
$528$	−227712.	+	466960.i	−0.816803	+	1.67499i
$529$	−75532.2	+	130826.i	−0.269911	+	0.467500i
$530$	242035.	+	9949.89i	0.861642	+	0.0354215i
$531$	−95037.5	−	187813.i	−0.337059	−	0.666095i
$532$	−161675.	−	13315.2i	−0.571241	−	0.0470460i
$533$	35477.2	−	61448.4i	0.124881	−	0.216300i
$534$	−65206.7	−	333404.i	−0.228670	−	1.16920i
$535$	79025.8	−	45625.6i	0.276097	−	0.159405i
$536$	−353349.	+	149536.i	−1.22991	+	0.520493i
$537$	324853.	+	343280.i	1.12652	+	1.19042i
$538$	142747.	−	225332.i	0.493176	−	0.778500i
$539$		−	267623.i		−	0.921184i
$540$	−345601.	+	33597.3i	−1.18519	+	0.115217i
$541$	−287354.			−0.981799			−0.490900	−	0.871216i	$-0.663332\pi$
$541$	−287354.			−0.981799			−0.490900	+	0.871216i	$0.663332\pi$
$542$	413683.	+	262066.i	1.40821	+	0.892097i
$543$	47218.3	−	44683.7i	0.160144	−	0.151548i
$544$	31736.4	+	96358.5i	0.107241	+	0.325606i
$545$	263888.	+	457067.i	0.888436	+	1.53882i
$546$	−363499.	+	71092.7i	−1.21932	+	0.238473i
$547$	486589.	+	280932.i	1.62625	+	0.938917i	0.985198	+	0.171421i	$0.0548357\pi$
$547$	486589.	+	280932.i	1.62625	+	0.938917i	0.641054	+	0.767496i	$0.278498\pi$
$548$	−341352.	−	28112.9i	−1.13669	−	0.0936148i
$549$	−96110.2	−	62796.0i	−0.318878	−	0.208347i
$550$	−9677.37	+	235406.i	−0.0319913	+	0.778203i
$551$	−2643.40	−	1526.17i	−0.00870684	−	0.00502689i
$552$	82890.9	−	189352.i	0.272038	−	0.621428i
$553$	−56576.7	−	97993.6i	−0.185006	−	0.320441i
$554$	−255115.	−	487038.i	−0.831220	−	1.58688i
$555$	156578.	+	46617.7i	0.508328	+	0.151344i
$556$	−239718.	−	166039.i	−0.775446	−	0.537107i
$557$	−393303.			−1.26770			−0.633850	−	0.773456i	$-0.718526\pi$
$557$	−393303.			−1.26770			−0.633850	+	0.773456i	$0.718526\pi$
$558$	−250209.	−	24152.5i	−0.803591	−	0.0775701i
$559$			52658.1i			0.168516i
$560$	352660.	+	289846.i	1.12455	+	0.924254i
$561$	−195567.	+	46663.4i	−0.621397	+	0.148269i
$562$	−25990.4	−	49618.0i	−0.0822886	−	0.157097i
$563$	481867.	−	278206.i	1.52023	−	0.877707i	0.520518	−	0.853851i	$-0.325739\pi$
$563$	481867.	−	278206.i	1.52023	−	0.877707i	0.999715	−	0.0238561i	$-0.00759436\pi$
$564$	−236120.	−	294599.i	−0.742293	−	0.926132i
$565$	220191.	−	381382.i	0.689768	−	1.19471i
$566$	−18902.1	+	459802.i	−0.0590035	+	1.43529i
$567$	−316649.	−	232765.i	−0.984944	−	0.724021i
$568$	9752.64	−	78722.5i	0.0302291	−	0.244007i
$569$	−91030.8	+	157670.i	−0.281167	+	0.486995i	−0.971672	−	0.236332i	$-0.924055\pi$
$569$	−91030.8	+	157670.i	−0.281167	+	0.486995i	0.690506	+	0.723327i	$0.257388\pi$
$570$	119169.	+	136769.i	0.366787	+	0.420958i
$571$	−190279.	+	109858.i	−0.583604	+	0.336944i	−0.762565	−	0.646912i	$-0.776060\pi$
$571$	−190279.	+	109858.i	−0.583604	+	0.336944i	0.178960	+	0.983856i	$0.442727\pi$
$572$	560292.	−	264752.i	1.71247	−	0.809182i
$573$	−92644.1	+	22105.5i	−0.282168	+	0.0673272i
$574$	−83609.5	−	52966.2i	−0.253765	−	0.160759i
$575$		−	93739.0i		−	0.283521i
$576$	98573.0	−	316794.i	0.297107	−	0.954844i
$577$	9527.81			0.0286181			0.0143091	−	0.999898i	$-0.495445\pi$
$577$	9527.81			0.0286181			0.0143091	+	0.999898i	$0.495445\pi$
$578$	157774.	−	249053.i	0.472259	−	0.745482i
$579$	−337153.	−	100380.i	−1.00570	−	0.299427i
$580$	3669.55	+	7765.83i	0.0109083	+	0.0230851i
$581$	201670.	+	349302.i	0.597432	+	1.03478i
$582$	−497020.	−	170496.i	−1.46733	−	0.503348i
$583$	−397254.	−	229355.i	−1.16878	−	0.674794i
$584$	−321421.	−	39819.7i	−0.942429	−	0.116754i
$585$	346731.	+	226545.i	1.01317	+	0.661978i
$586$	113978.	+	4685.55i	0.331914	+	0.0136447i
$587$	−8948.63	−	5166.49i	−0.0259705	−	0.0149941i	0.486959	−	0.873425i	$-0.338106\pi$
$587$	−8948.63	−	5166.49i	−0.0259705	−	0.0149941i	−0.512929	+	0.858431i	$0.671440\pi$
$588$	25887.4	+	168936.i	0.0748745	+	0.488617i
$589$	65662.1	+	113730.i	0.189271	+	0.327827i
$590$	274111.	−	143582.i	0.787449	−	0.412473i
$591$	70730.4	−	66933.7i	0.202503	−	0.191633i
$592$	−99115.0	+	120595.i	−0.282811	+	0.344101i
$593$	143639.			0.408473			0.204236	−	0.978922i	$-0.434529\pi$
$593$	143639.			0.408473			0.204236	+	0.978922i	$0.434529\pi$
$594$	609241.	+	247306.i	1.72670	+	0.700909i
$595$			176661.i			0.499008i
$596$	147947.	−	213597.i	0.416498	−	0.601317i
$597$	4994.58	+	5277.89i	0.0140136	+	0.0148085i
$598$	−218406.	+	114403.i	−0.610747	+	0.319915i
$599$	305650.	−	176467.i	0.851865	−	0.491824i	−0.00941494	−	0.999956i	$-0.502997\pi$
$599$	305650.	−	176467.i	0.851865	−	0.491824i	0.861280	+	0.508131i	$0.169664\pi$
$600$	−16662.2	−	149536.i	−0.0462839	−	0.415377i
$601$	−17733.8	+	30715.9i	−0.0490969	+	0.0850382i	−0.889529	−	0.456878i	$-0.848968\pi$
$601$	−17733.8	+	30715.9i	−0.0490969	+	0.0850382i	0.840433	+	0.541916i	$0.182301\pi$
$602$	73390.9	+	3017.04i	0.202511	+	0.00832509i
$603$	219254.	+	433290.i	0.602995	+	1.19164i
$604$	−32209.8	+	391097.i	−0.0882907	+	1.07204i
$605$	538881.	−	933369.i	1.47225	−	2.55001i
$606$	220026.	+	75476.8i	0.599139	+	0.205527i
$607$	−424309.	+	244975.i	−1.15161	+	0.664881i	−0.949279	−	0.314436i	$-0.898185\pi$
$607$	−424309.	+	244975.i	−1.15161	+	0.664881i	−0.202330	+	0.979317i	$0.564851\pi$
$608$	−164630.	+	54222.2i	−0.445350	+	0.146680i
$609$	−2773.96	+	9317.05i	−0.00747937	+	0.0251214i
$610$	90320.5	−	142575.i	0.242732	−	0.383163i
$611$			450342.i			1.20631i
$612$	118937.	−	48373.5i	0.317552	−	0.129153i
$613$	284390.			0.756821			0.378410	−	0.925638i	$-0.376471\pi$
$613$	284390.			0.756821			0.378410	+	0.925638i	$0.376471\pi$
$614$	−389730.	−	246892.i	−1.03378	−	0.654893i
$615$	25687.2	+	107655.i	0.0679151	+	0.284632i
$616$	−336889.	−	796061.i	−0.887821	−	2.09790i
$617$	−98237.4	−	170152.i	−0.258052	−	0.446958i	0.707668	−	0.706545i	$-0.249747\pi$
$617$	−98237.4	−	170152.i	−0.258052	−	0.446958i	−0.965720	+	0.259586i	$0.916414\pi$
$618$	−382083.	−	438512.i	−1.00042	−	1.14817i
$619$	58731.2	+	33908.5i	0.153281	+	0.0884967i	0.574679	−	0.818379i	$-0.305127\pi$
$619$	58731.2	+	33908.5i	0.153281	+	0.0884967i	−0.421398	+	0.906876i	$0.638460\pi$
$620$	30331.8	−	368294.i	0.0789069	−	0.958101i
$621$	−246233.	−	88355.0i	−0.638502	−	0.229112i
$622$	16233.3	−	394882.i	0.0419590	−	1.02067i
$623$	489517.	+	282623.i	1.26122	+	0.728167i
$624$	−328073.	+	221321.i	−0.842561	+	0.568400i
$625$	242826.	+	420586.i	0.621634	+	1.07670i
$626$	137591.	+	262674.i	0.351109	+	0.670300i
$627$	−79725.2	−	334129.i	−0.202797	−	0.849921i
$628$	−361262.	+	521571.i	−0.916016	+	1.32249i
$629$	−60410.6			−0.152691
$630$	335608.	−	470268.i	0.845573	−	1.18485i
$631$		−	716972.i		−	1.80071i	−0.435158	−	0.900354i	$-0.643308\pi$
$631$		−	716972.i		−	1.80071i	0.435158	−	0.900354i	$-0.356692\pi$
$632$	−96476.7	−	72864.7i	−0.241539	−	0.182424i
$633$	156231.	−	524743.i	0.389907	−	1.30960i
$634$	3924.74	+	7492.69i	0.00976409	+	0.0186406i
$635$	−476401.	+	275050.i	−1.18148	+	0.682125i
$636$	272952.	+	106353.i	0.674794	+	0.262927i
$637$	101931.	−	176549.i	0.251204	−	0.435098i
$638$	668.061	−	16250.9i	0.00164125	−	0.0399241i
$639$	−100242.	−	5533.47i	−0.245499	−	0.0135518i
$640$	467709.	+	138350.i	1.14187	+	0.337769i
$641$	−321445.	+	556760.i	−0.782332	+	1.35504i	0.148248	+	0.988950i	$0.452637\pi$
$641$	−321445.	+	556760.i	−0.782332	+	1.35504i	−0.930580	+	0.366089i	$0.880697\pi$
$642$	108298.	−	21180.7i	0.262754	−	0.0513891i
$643$	−1326.59	+	765.910i	−0.00320861	+	0.00185249i	−0.501603	−	0.865098i	$-0.667256\pi$
$643$	−1326.59	+	765.910i	−0.00320861	+	0.00185249i	0.498395	+	0.866950i	$0.333923\pi$
$644$	146933.	+	310952.i	0.354280	+	0.749759i
$645$	−56457.0	−	59659.4i	−0.135706	−	0.143403i
$646$	−56665.3	−	35897.2i	−0.135785	−	0.0860192i
$647$			106720.i			0.254938i	0.991843	+	0.127469i	$0.0406854\pi$
$647$			106720.i			0.254938i	−0.991843	+	0.127469i	$0.959315\pi$
$648$	−408504.	−	97178.8i	−0.972851	−	0.231431i
$649$	−585960.			−1.39116
$650$	−96044.3	+	151610.i	−0.227324	+	0.358841i
$651$	303786.	−	287480.i	0.716814	−	0.678336i
$652$	366353.	−	173111.i	0.861795	−	0.407219i
$653$	−114833.	−	198896.i	−0.269301	−	0.466444i	0.699380	−	0.714750i	$-0.253459\pi$
$653$	−114833.	−	198896.i	−0.269301	−	0.466444i	−0.968682	+	0.248306i	$0.920126\pi$
$654$	122505.	+	626369.i	0.286416	+	1.46445i
$655$	214517.	+	123851.i	0.500010	+	0.288681i
$656$	−104326.	−	17301.5i	−0.242430	−	0.0402046i
$657$	−22593.0	+	409285.i	−0.0523410	+	0.948190i
$658$	627652.	+	25802.3i	1.44966	+	0.0595946i
$659$	337909.	+	195092.i	0.778089	+	0.449230i	0.835753	−	0.549106i	$-0.185032\pi$
$659$	337909.	+	195092.i	0.778089	+	0.449230i	−0.0576633	+	0.998336i	$0.518365\pi$
$660$	−350935.	+	900664.i	−0.805637	+	2.06764i
$661$	−223443.	−	387014.i	−0.511403	−	0.885776i	−0.999913	−	0.0132177i	$-0.995793\pi$
$661$	−223443.	−	387014.i	−0.511403	−	0.885776i	0.488509	−	0.872559i	$-0.337541\pi$
$662$	50464.2	−	26433.6i	0.115151	−	0.0603171i
$663$	−146787.	−	43702.7i	−0.333934	−	0.0994217i
$664$	343895.	+	259729.i	0.779991	+	0.589094i
$665$	−301829.			−0.682523
$666$	160812.	+	114764.i	0.362551	+	0.258735i
$667$			6471.12i			0.0145455i
$668$	−366174.	−	253628.i	−0.820605	−	0.568386i
$669$	93929.6	−	22412.2i	0.209870	−	0.0500763i
$670$	−632383.	+	331248.i	−1.40874	+	0.737909i
$671$	−276780.	+	159799.i	−0.614737	+	0.354919i
$672$	289664.	+	469924.i	0.641440	+	1.04061i
$673$	−169746.	+	294009.i	−0.374774	+	0.649128i	−0.990293	−	0.138994i	$-0.955613\pi$
$673$	−169746.	+	294009.i	−0.374774	+	0.649128i	0.615519	+	0.788122i	$0.288946\pi$
$674$	301440.	+	12392.0i	0.663561	+	0.0272785i
$675$	−187382.	+	33920.1i	−0.411264	+	0.0744474i
$676$	15023.7	+	1237.32i	0.0328764	+	0.00270762i
$677$	−266702.	+	461941.i	−0.581900	+	1.00788i	0.413354	+	0.910570i	$0.364357\pi$
$677$	−266702.	+	461941.i	−0.581900	+	1.00788i	−0.995254	+	0.0973098i	$0.968976\pi$
$678$	401519.	−	349850.i	0.873467	−	0.761065i
$679$	757142.	−	437136.i	1.64224	−	0.948150i
$680$	73564.7	+	173832.i	0.159093	+	0.375934i
$681$	662971.	−	158189.i	1.42955	−	0.341100i
$682$	−374482.	+	591136.i	−0.805122	+	1.27092i
$683$		−	175866.i		−	0.376999i	−0.982073	−	0.188500i	$-0.939638\pi$
$683$		−	175866.i		−	0.376999i	0.982073	−	0.188500i	$-0.0603624\pi$
$684$	82646.9	+	203206.i	0.176650	+	0.434335i
$685$	−637265.			−1.35812
$686$	245741.	+	155676.i	0.522191	+	0.330805i
$687$	−460330.	−	137054.i	−0.975339	−	0.290387i
$688$	73471.8	−	27592.5i	0.155219	−	0.0582927i
$689$	−174711.	−	302608.i	−0.368028	−	0.637444i
$690$	124788.	−	363776.i	0.262105	−	0.764074i
$691$	−203114.	−	117268.i	−0.425386	−	0.245597i	0.271993	−	0.962299i	$-0.412317\pi$
$691$	−203114.	−	117268.i	−0.425386	−	0.245597i	−0.697379	+	0.716702i	$0.745651\pi$
$692$	−351682.	−	28963.7i	−0.734409	−	0.0604842i
$693$	−976160.	+	493958.i	−2.03261	+	1.02855i
$694$	−24388.5	+	593261.i	−0.0506368	+	1.23176i
$695$	−469869.	−	271279.i	−0.972762	−	0.561625i
$696$	1150.25	+	10322.9i	0.00237451	+	0.0213101i
$697$	−20463.0	−	35442.9i	−0.0421214	−	0.0729565i
$698$	43302.7	+	82668.8i	0.0888799	+	0.169680i
$699$	−369245.	+	349425.i	−0.755720	+	0.715154i
$700$	205800.	+	142546.i	0.420000	+	0.290910i
$701$	192485.			0.391707			0.195853	−	0.980633i	$-0.437252\pi$
$701$	192485.			0.391707			0.195853	+	0.980633i	$0.437252\pi$
$702$	307720.	+	395190.i	0.624427	+	0.801922i
$703$		−	103213.i		−	0.208844i
$704$	−662986.	−	643025.i	−1.33770	−	1.29743i
$705$	−482830.	−	510218.i	−0.971441	−	1.02654i
$706$	−35959.4	−	68649.9i	−0.0721445	−	0.137731i
$707$	−335179.	+	193516.i	−0.670561	+	0.387148i
$708$	369886.	−	56680.4i	0.737906	−	0.113075i
$709$	300439.	−	520376.i	0.597674	−	1.03520i	−0.395489	−	0.918471i	$-0.629425\pi$
$709$	300439.	−	520376.i	0.597674	−	1.03520i	0.993164	−	0.116731i	$-0.0372417\pi$
$710$	6062.18	−	147465.i	0.0120258	−	0.292532i
$711$	−83695.1	+	128097.i	−0.165562	+	0.253395i
$712$	599365.	+	74253.1i	1.18231	+	0.146472i
$713$	139207.	−	241114.i	0.273831	−	0.474288i
$714$	−69319.7	+	202077.i	−0.135975	+	0.396387i
$715$	998522.	−	576497.i	1.95320	−	1.12768i
$716$	−759675.	+	358965.i	−1.48184	+	0.700206i
$717$	123249.	−	413965.i	0.239743	−	0.805240i
$718$	−472818.	−	299528.i	−0.917160	−	0.581016i
$719$			37302.4i			0.0721571i	0.999349	+	0.0360786i	$0.0114867\pi$
$719$			37302.4i			0.0721571i	−0.999349	+	0.0360786i	$0.988513\pi$
$720$	134405.	−	602489.i	0.259269	−	1.16221i
$721$	967729.			1.86159
$722$	−217634.	+	343545.i	−0.417496	+	0.659036i
$723$	133998.	+	561586.i	0.256343	+	1.07433i
$724$	49375.8	+	104494.i	0.0941970	+	0.199348i
$725$	2355.23	+	4079.37i	0.00448081	+	0.00776099i
$726$	982649.	−	856198.i	1.86434	−	1.62443i
$727$	647844.	+	374033.i	1.22575	+	0.707686i	0.966138	−	0.258027i	$-0.0830723\pi$
$727$	647844.	+	374033.i	1.22575	+	0.707686i	0.259611	+	0.965713i	$0.416406\pi$
$728$	80955.8	−	653469.i	0.152751	−	1.23300i
$729$	−87518.5	+	524185.i	−0.164682	+	0.986347i
$730$	−602095.	−	24751.7i	−1.12985	−	0.0464471i
$731$	26303.6	+	15186.4i	0.0492244	+	0.0284197i
$732$	159259.	−	127646.i	0.297223	−	0.238223i
$733$	131709.	+	228126.i	0.245136	+	0.424588i	0.962170	−	0.272450i	$-0.0878341\pi$
$733$	131709.	+	228126.i	0.245136	+	0.424588i	−0.717034	+	0.697038i	$0.754501\pi$
$734$	−324473.	+	169962.i	−0.602263	+	0.315471i
$735$	73802.7	+	309307.i	0.136615	+	0.572552i
$736$	274065.	+	244787.i	0.505938	+	0.451889i
$737$	1.35183e6			2.48878
$738$	−12859.8	+	133222.i	−0.0236115	+	0.244604i
$739$		−	288908.i		−	0.529018i	−0.964383	−	0.264509i	$-0.914790\pi$
$739$		−	288908.i		−	0.529018i	0.964383	−	0.264509i	$-0.0852099\pi$
$740$	−165373.	+	238757.i	−0.301996	+	0.436006i
$741$	74666.8	−	250788.i	0.135985	−	0.456741i
$742$	−431762.	+	226161.i	−0.784218	+	0.410780i
$743$	271416.	−	156702.i	0.491651	−	0.283855i	−0.233608	−	0.972331i	$-0.575053\pi$
$743$	271416.	−	156702.i	0.491651	−	0.283855i	0.725259	+	0.688476i	$0.241720\pi$
$744$	179210.	−	409377.i	0.323754	−	0.739567i
$745$	241719.	−	418670.i	0.435510	−	0.754326i
$746$	342034.	+	14060.8i	0.614599	+	0.0252657i
$747$	298334.	−	456606.i	0.534641	−	0.818276i
$748$	29338.1	−	356228.i	0.0524359	−	0.636685i
$749$	−91802.9	+	159007.i	−0.163641	+	0.283435i
$750$	74831.6	+	382616.i	0.133034	+	0.680207i
$751$	−204539.	+	118091.i	−0.362658	+	0.209381i	−0.670246	−	0.742139i	$-0.733811\pi$
$751$	−204539.	+	118091.i	−0.362658	+	0.209381i	0.307588	+	0.951520i	$0.400478\pi$
$752$	628344.	−	235976.i	1.11112	−	0.417284i
$753$	403524.	+	426413.i	0.711671	+	0.752039i
$754$	6630.26	−	10466.2i	0.0116624	−	0.0184096i
$755$			730134.i			1.28088i
$756$	568417.	−	406235.i	0.994543	−	0.710777i
$757$	−1.00219e6			−1.74888			−0.874438	−	0.485137i	$-0.838770\pi$
$757$	−1.00219e6			−1.74888			−0.874438	+	0.485137i	$0.838770\pi$
$758$	134614.	+	85277.4i	0.234289	+	0.148421i
$759$	−528955.	+	500562.i	−0.918196	+	0.868909i
$760$	−296994.	+	125686.i	−0.514187	+	0.217601i
$761$	−456412.	−	790529.i	−0.788112	−	1.36505i	−0.927122	−	0.374759i	$-0.877725\pi$
$761$	−456412.	−	790529.i	−0.788112	−	1.36505i	0.139010	−	0.990291i	$-0.455608\pi$
$762$	−652864.	+	127686.i	−1.12438	+	0.219905i
$763$	−919661.	−	530967.i	−1.57971	−	0.912049i
$764$	13898.1	−	168753.i	0.0238105	−	0.289111i
$765$	213159.	−	107863.i	0.364234	−	0.184311i
$766$	28043.0	−	682158.i	0.0477933	−	1.16259i
$767$	−386554.	−	223177.i	−0.657082	−	0.379366i
$768$	480709.	+	341777.i	0.815004	+	0.579456i
$769$	104325.	+	180697.i	0.176416	+	0.305561i	0.940650	−	0.339378i	$-0.110216\pi$
$769$	104325.	+	180697.i	0.176416	+	0.305561i	−0.764235	+	0.644938i	$0.776883\pi$
$770$	−746268.	−	1.42470e6i	−1.25867	−	2.40293i
$771$	−373634.	−	111242.i	−0.628547	−	0.187137i
$772$	356091.	−	514105.i	0.597484	−	0.862616i
$773$	−661279.			−1.10669			−0.553345	−	0.832952i	$-0.686649\pi$
$773$	−661279.			−1.10669			−0.553345	+	0.832952i	$0.686649\pi$
$774$	−41169.6	−	90395.4i	−0.0687218	−	0.150891i
$775$		−	202663.i		−	0.337420i
$776$	562984.	−	745421.i	0.934917	−	1.23788i
$777$	−319740.	+	76292.0i	−0.529608	+	0.126368i
$778$	−400558.	−	764703.i	−0.661769	−	1.26338i
$779$	60554.8	−	34961.3i	0.0997869	−	0.0576120i
$780$	−574550.	+	460500.i	−0.944362	+	0.756904i
$781$	−139739.	+	242036.i	−0.229096	+	0.396805i
$782$	−5841.23	+	142090.i	−0.00955192	+	0.232355i
$783$	12935.6	−	2341.62i	0.0210991	−	0.00381938i
$784$	−299743.	−	49709.5i	−0.487660	−	0.0808736i
$785$	−590239.	+	1.02232e6i	−0.957830	+	1.65901i
$786$	196780.	+	225843.i	0.318520	+	0.365562i
$787$	33656.2	−	19431.4i	0.0543395	−	0.0313729i	−0.472584	−	0.881286i	$-0.656679\pi$
$787$	33656.2	−	19431.4i	0.0543395	−	0.0313729i	0.526924	+	0.849913i	$0.323345\pi$
$788$	73962.2	+	156526.i	0.119113	+	0.252077i
$789$	742405.	−	177143.i	1.19258	−	0.284557i
$790$	−190025.	−	120380.i	−0.304479	−	0.192886i
$791$			886090.i			1.41620i
$792$	−754832.	+	892536.i	−1.20337	+	1.42290i
$793$	−243453.			−0.387141
$794$	−626239.	+	988546.i	−0.993343	+	1.56804i
$795$	522379.	+	155527.i	0.826516	+	0.246078i
$796$	−11679.9	+	5519.05i	−0.0184338	+	0.00871040i
$797$	321301.	+	556510.i	0.505820	+	0.876105i	0.999977	+	0.00673297i	$0.00214319\pi$
$797$	321301.	+	556510.i	0.505820	+	0.876105i	−0.494158	+	0.869372i	$0.664523\pi$
$798$	−345251.	−	118434.i	−0.542162	−	0.185982i
$799$	224953.	+	129877.i	0.352369	+	0.203441i
$800$	261862.	+	54564.2i	0.409160	+	0.0852566i
$801$	42129.9	−	763209.i	0.0656637	−	1.18954i
$802$	816565.	+	33568.3i	1.26953	+	0.0521893i
$803$	988223.	+	570551.i	1.53258	+	0.884837i
$804$	−853338.	+	130763.i	−1.32011	+	0.202290i
$805$	319946.	+	554163.i	0.493725	+	0.855156i
$806$	−472191.	+	247338.i	−0.726855	+	0.380733i
$807$	435923.	−	412523.i	0.669364	−	0.633433i
$808$	−249228.	+	329990.i	−0.381745	+	0.505450i
$809$	737297.			1.12654			0.563269	−	0.826274i	$-0.309544\pi$
$809$	737297.			1.12654			0.563269	+	0.826274i	$0.309544\pi$
$810$	−772334.	−	117814.i	−1.17716	−	0.179568i
$811$		−	823394.i		−	1.25189i	−0.779867	−	0.625945i	$-0.784714\pi$
$811$		−	823394.i		−	1.25189i	0.779867	−	0.625945i	$-0.215286\pi$
$812$	−14207.1	−	9840.41i	−0.0215473	−	0.0149245i
$813$	757341.	+	800301.i	1.14580	+	1.21080i
$814$	487185.	−	255192.i	0.735267	−	0.385139i
$815$	652894.	−	376949.i	0.982941	−	0.567501i
$816$	15938.6	+	227706.i	0.0239370	+	0.341975i
$817$	−25946.2	+	44940.1i	−0.0388713	+	0.0673271i
$818$	138798.	+	5705.87i	0.207432	+	0.00852738i
$819$	−832102.	−	45932.9i	−1.24053	−	0.0684788i
$820$	−196096.	−	16150.0i	−0.291635	−	0.0240184i
$821$	290123.	−	502508.i	0.430424	−	0.745516i	−0.566486	−	0.824071i	$-0.691697\pi$
$821$	290123.	−	502508.i	0.430424	−	0.745516i	0.996910	+	0.0785556i	$0.0250308\pi$
$822$	−728945.	−	250055.i	−1.07883	−	0.370077i
$823$	−400074.	+	230983.i	−0.590664	+	0.341020i	−0.765360	−	0.643602i	$-0.777439\pi$
$823$	−400074.	+	230983.i	−0.590664	+	0.341020i	0.174696	+	0.984622i	$0.444106\pi$
$824$	952230.	−	402978.i	1.40245	−	0.593509i
$825$	−151267.	+	508071.i	−0.222248	+	0.746477i
$826$	−333195.	+	525963.i	−0.488358	+	0.770895i
$827$		−	1.11437e6i		−	1.62936i	−0.579912	−	0.814679i	$-0.696913\pi$
$827$		−	1.11437e6i		−	1.62936i	0.579912	−	0.814679i	$-0.303087\pi$
$828$	285482.	−	367145.i	0.416407	−	0.535521i
$829$	915553.			1.33222			0.666108	−	0.745856i	$-0.267959\pi$
$829$	915553.			1.33222			0.666108	+	0.745856i	$0.267959\pi$
$830$	677353.	+	429100.i	0.983238	+	0.622876i
$831$	−287113.	−	1.20329e6i	−0.415767	−	1.74248i
$832$	−192456.	−	676714.i	−0.278026	−	0.977594i
$833$	−58792.8	−	101832.i	−0.0847294	−	0.146756i
$834$	−431020.	−	494677.i	−0.619677	−	0.711196i
$835$	−717733.	−	414383.i	−1.02941	−	0.594332i
$836$	608621.	+	50124.6i	0.870832	+	0.0717197i
$837$	−532353.	−	191023.i	−0.759887	−	0.272668i
$838$	−52680.6	+	1.28148e6i	−0.0750175	+	1.82483i
$839$	489653.	+	282701.i	0.695608	+	0.401610i	0.805710	−	0.592311i	$-0.201784\pi$
$839$	489653.	+	282701.i	0.695608	+	0.401610i	−0.110101	+	0.993920i	$0.535118\pi$
$840$	608892.	+	827149.i	0.862942	+	1.17226i
$841$	353478.	+	612242.i	0.499770	+	0.865627i
$842$	−251995.	−	481083.i	−0.355442	−	0.678572i
$843$	−29250.2	−	122588.i	−0.0411599	−	0.172501i
$844$	800152.	+	554219.i	1.12328	+	0.778030i
$845$	28047.6			0.0392810
$846$	−352089.	−	773077.i	−0.491940	−	1.08015i
$847$			2.16856e6i			3.02276i
$848$	−330670.	+	402331.i	−0.459836	+	0.559490i
$849$	−295460.	+	992379.i	−0.409905	+	1.37677i
$850$	48032.9	+	91699.4i	0.0664816	+	0.126920i
$851$	−189500.	+	109408.i	−0.261668	+	0.151074i
$852$	64797.9	−	166302.i	0.0892651	−	0.229096i
$853$	−100990.	+	174919.i	−0.138796	+	0.240402i	−0.927041	−	0.374959i	$-0.877657\pi$
$853$	−100990.	+	174919.i	−0.138796	+	0.240402i	0.788245	+	0.615362i	$0.210990\pi$
$854$	−13948.6	+	339307.i	−0.0191256	+	0.465240i
$855$	184286.	+	364185.i	0.252092	+	0.498184i
$856$	−24119.3	+	194689.i	−0.0329167	+	0.265701i
$857$	252164.	−	436762.i	0.343338	−	0.594679i	−0.641712	−	0.766946i	$-0.721776\pi$
$857$	252164.	−	436762.i	0.343338	−	0.594679i	0.985050	+	0.172266i	$0.0551090\pi$
$858$	1.36838e6	−	267627.i	1.85880	−	0.363543i
$859$	−662245.	+	382348.i	−0.897496	+	0.518170i	−0.876387	−	0.481608i	$-0.840053\pi$
$859$	−662245.	+	382348.i	−0.897496	+	0.518170i	−0.0211092	+	0.999777i	$0.506720\pi$
$860$	132026.	−	62385.4i	0.178510	−	0.0843501i
$861$	−153066.	−	161749.i	−0.206478	−	0.218190i
$862$	−105909.	−	67092.8i	−0.142534	−	0.0902946i
$863$		−	1.21817e6i		−	1.63564i	−0.575477	−	0.817818i	$-0.695183\pi$
$863$		−	1.21817e6i		−	1.63564i	0.575477	−	0.817818i	$-0.304817\pi$
$864$	390150.	−	636427.i	0.522642	−	0.852552i
$865$	−656551.			−0.877477
$866$	−216247.	+	341356.i	−0.288346	+	0.455168i
$867$	481813.	−	455950.i	0.640974	−	0.606567i
$868$	317667.	+	672276.i	0.421631	+	0.892295i
$869$	212982.	+	368895.i	0.282035	+	0.488498i
$870$	3709.40	+	18966.3i	0.00490078	+	0.0250578i
$871$	891792.	+	514876.i	1.17551	+	0.678682i
$872$	−1.12603e6	−	139500.i	−1.48088	−	0.183460i
$873$	−989731.	−	646665.i	−1.29864	−	0.848498i
$874$	−242764.	−	9979.83i	−0.317805	−	0.0130647i
$875$	−561773.	−	324340.i	−0.733744	−	0.423627i
$876$	−679003.	−	264567.i	−0.884838	−	0.344769i
$877$	−225455.	−	390499.i	−0.293130	−	0.507716i	0.681418	−	0.731894i	$-0.261364\pi$
$877$	−225455.	−	390499.i	−0.293130	−	0.507716i	−0.974548	+	0.224178i	$0.928030\pi$
$878$	644787.	−	337745.i	0.836426	−	0.438127i
$879$	245996.	+	73240.1i	0.318383	+	0.0947918i
$880$	−1.32758e6	−	1.09112e6i	−1.71434	−	1.40899i
$881$	−1.04312e6			−1.34395			−0.671974	−	0.740575i	$-0.734553\pi$
$881$	−1.04312e6			−1.34395			−0.671974	+	0.740575i	$0.734553\pi$
$882$	−36948.0	+	382765.i	−0.0474957	+	0.492034i
$883$			303710.i			0.389527i	0.980850	+	0.194763i	$0.0623939\pi$
$883$			303710.i			0.389527i	−0.980850	+	0.194763i	$0.937606\pi$
$884$	155032.	−	223827.i	0.198389	−	0.286423i
$885$	677227.	−	161591.i	0.864664	−	0.206314i
$886$	131772.	−	69023.4i	0.167863	−	0.0879283i
$887$	−587624.	+	339265.i	−0.746882	+	0.431213i	−0.824566	−	0.565765i	$-0.808581\pi$
$887$	−587624.	+	339265.i	−0.746882	+	0.431213i	0.0776839	+	0.996978i	$0.475248\pi$
$888$	−282850.	+	208215.i	−0.358699	+	0.264050i
$889$	553426.	−	958562.i	0.700255	−	1.21288i
$890$	1.12275e6	+	46155.3i	1.41743	+	0.0582696i
$891$	1.19202e6	+	876237.i	1.50151	+	1.10374i
$892$	−14090.9	+	171094.i	−0.0177097	+	0.215034i
$893$	−221896.	+	384336.i	−0.278258	+	0.481956i
$894$	440775.	−	384054.i	0.551495	−	0.480526i
$895$	−1.35385e6	+	781647.i	−1.69015	+	0.975808i
$896$	−954180.	+	229458.i	−1.18854	+	0.285817i
$897$	−539599.	+	128752.i	−0.670636	+	0.160018i
$898$	43636.0	−	68881.4i	0.0541119	−	0.0854179i
$899$			13990.5i			0.0173107i
$900$	46341.1	−	335351.i	0.0572112	−	0.414013i
$901$	−201543.			−0.248267
$902$	314746.	+	199390.i	0.386854	+	0.245070i
$903$	158398.	+	47159.6i	0.194256	+	0.0578355i
$904$	368983.	+	871898.i	0.451512	+	1.06691i
$905$	107516.	+	186223.i	0.131273	+	0.227372i
$906$	−286496.	+	835175.i	−0.349029	+	1.01747i
$907$	1.02766e6	+	593322.i	1.24921	+	0.721233i	0.970952	−	0.239273i	$-0.0769090\pi$
$907$	1.02766e6	+	593322.i	1.24921	+	0.721233i	0.278260	+	0.960506i	$0.410242\pi$
$908$	−99456.1	+	1.20761e6i	−0.120631	+	1.46472i
$909$	438144.	+	286272.i	0.530260	+	0.346458i
$910$	50321.7	−	1.22410e6i	0.0607676	−	1.47820i
$911$	−754071.	−	435363.i	−0.908606	−	0.524584i	−0.0286234	−	0.999590i	$-0.509112\pi$
$911$	−754071.	−	435363.i	−0.908606	−	0.524584i	−0.879982	+	0.475007i	$0.842446\pi$
$912$	−389039.	+	27231.4i	−0.467739	+	0.0327401i
$913$	−759181.	−	1.31494e6i	−0.910760	−	1.57748i
$914$	519052.	+	990919.i	0.621324	+	1.18617i
$915$	275822.	−	261016.i	0.329448	−	0.311764i
$916$	486188.	−	701931.i	0.579446	−	0.836573i
$917$	−498400.			−0.592706
$918$	286149.	−	39739.9i	0.339553	−	0.0471565i
$919$		−	60879.9i		−	0.0720847i	−0.999350	−	0.0360423i	$-0.988525\pi$
$919$		−	60879.9i		−	0.0720847i	0.999350	−	0.0360423i	$-0.0114751\pi$
$920$	545584.	+	412056.i	0.644594	+	0.486834i
$921$	−713491.	−	753963.i	−0.841142	−	0.888854i
$922$	298072.	+	569047.i	0.350638	+	0.669401i
$923$	−184370.	+	106446.i	−0.216415	+	0.124947i
$924$	−294597.	−	1.92249e6i	−0.345052	−	2.25174i
$925$	−79640.2	+	137941.i	−0.0930783	+	0.161216i
$926$	−16290.7	+	396280.i	−0.0189985	+	0.462147i
$927$	−590861.	−	1.16766e6i	−0.687584	−	1.35880i
$928$	−18077.2	−	3766.75i	−0.0209911	−	0.00437392i
$929$	470405.	−	814765.i	0.545055	−	0.944063i	−0.453548	−	0.891232i	$-0.649842\pi$
$929$	470405.	−	814765.i	0.545055	−	0.944063i	0.998603	−	0.0528314i	$-0.0168246\pi$
$930$	269791.	−	786480.i	0.311934	−	0.909330i
$931$	173982.	−	100448.i	0.200726	−	0.115889i
$932$	−386117.	−	817136.i	−0.444516	−	0.940725i
$933$	253743.	−	852263.i	0.291495	−	0.979062i
$934$	942041.	+	596778.i	1.07988	+	0.684100i
$935$		−	665037.i		−	0.760717i
$936$	−837902.	+	301304.i	−0.956404	+	0.343917i
$937$	−634530.			−0.722725			−0.361362	−	0.932425i	$-0.617688\pi$
$937$	−634530.			−0.722725			−0.361362	+	0.932425i	$0.617688\pi$
$938$	768691.	−	1.21341e6i	0.873667	−	1.37912i
$939$	154849.	+	648971.i	0.175621	+	0.736028i
$940$	1.12911e6	−	533531.i	1.27785	−	0.603815i
$941$	−34049.0	−	58974.5i	−0.0384525	−	0.0666017i	0.846159	−	0.532931i	$-0.178909\pi$
$941$	−34049.0	−	58974.5i	−0.0384525	−	0.0666017i	−0.884611	+	0.466329i	$0.845576\pi$
$942$	−1.07630e6	+	937798.i	−1.21292	+	1.05684i
$943$	−128379.	−	74119.7i	−0.144368	−	0.0833509i
$944$	−108839.	+	656287.i	−0.122135	+	0.736461i
$945$	991983.	−	840092.i	1.11081	−	0.940726i
$946$	−276279.	−	11357.6i	−0.308720	−	0.0126912i
$947$	−461349.	−	266360.i	−0.514434	−	0.297009i	0.220220	−	0.975450i	$-0.429322\pi$
$947$	−461349.	−	266360.i	−0.514434	−	0.297009i	−0.734654	+	0.678442i	$0.762656\pi$
$948$	−170128.	−	212262.i	−0.189303	−	0.236187i
$949$	434616.	+	752777.i	0.482585	+	0.835861i
$950$	−156670.	+	82065.0i	−0.173595	+	0.0909308i
$951$	4417.00	+	18511.7i	0.00488390	+	0.0204684i
$952$	−303071.	−	228896.i	−0.334403	−	0.252560i
$953$	72542.5			0.0798742			0.0399371	−	0.999202i	$-0.487284\pi$
$953$	72542.5			0.0798742			0.0399371	+	0.999202i	$0.487284\pi$
$954$	536504.	+	382877.i	0.589489	+	0.420690i
$955$		−	315042.i		−	0.345432i
$956$	631232.	+	437218.i	0.690674	+	0.478390i
$957$	10442.5	−	35073.8i	0.0114020	−	0.0382965i
$958$	−113357.	+	59377.1i	−0.123514	+	0.0646976i
$959$	1.11045e6	−	641118.i	1.20743	−	0.697109i
$960$	943578.	+	560348.i	1.02385	+	0.608016i
$961$	−160796.	+	278507.i	−0.174112	+	0.301571i
$962$	418589.	+	17207.9i	0.452311	+	0.0185942i
$963$	247909.	+	13684.8i	0.267325	+	0.0147566i
$964$	−1.02294e6	−	84246.8i	−1.10077	−	0.0906566i
$965$	581791.	−	1.00769e6i	0.624759	−	1.08211i
$966$	148528.	+	759430.i	0.159168	+	0.813830i
$967$	705768.	−	407475.i	0.754760	−	0.435761i	−0.0726511	−	0.997357i	$-0.523146\pi$
$967$	705768.	−	407475.i	0.754760	−	0.435761i	0.827411	+	0.561596i	$0.189813\pi$
$968$	903022.	+	2.13382e6i	0.963713	+	2.27723i
$969$	−103739.	−	109623.i	−0.110483	−	0.116750i
$970$	930109.	−	1.46822e6i	0.988532	−	1.56044i
$971$			939538.i			0.996496i	0.867034	+	0.498248i	$0.166023\pi$
$971$			939538.i			0.996496i	−0.867034	+	0.498248i	$0.833977\pi$
$972$	−837217.	−	437818.i	−0.886146	−	0.463405i
$973$	1.09168e6			1.15310
$974$	−1.17193e6	−	742409.i	−1.23533	−	0.782574i
$975$	−293301.	+	277557.i	−0.308535	+	0.291974i
$976$	127568.	+	339681.i	0.133919	+	0.356592i
$977$	−870579.	−	1.50789e6i	−0.912051	−	1.57972i	−0.811162	−	0.584821i	$-0.801165\pi$
$977$	−870579.	−	1.50789e6i	−0.912051	−	1.57972i	−0.100889	−	0.994898i	$-0.532169\pi$
$978$	894733.	−	174991.i	0.935440	−	0.182952i
$979$	−1.84277e6	−	1.06393e6i	−1.92268	−	1.11006i
$980$	−563408.	−	46401.0i	−0.586639	−	0.0483142i
$981$	−79149.9	+	1.43385e6i	−0.0822456	+	1.48993i
$982$	39428.5	−	959116.i	0.0408872	−	0.994599i
$983$	−1.07730e6	−	621978.i	−1.11488	−	0.643677i	−0.174792	−	0.984605i	$-0.555925\pi$
$983$	−1.07730e6	−	621978.i	−1.11488	−	0.643677i	−0.940089	+	0.340929i	$0.889259\pi$
$984$	−217970.	−	95418.8i	−0.225116	−	0.0985471i
$985$	161053.	+	278952.i	0.165995	+	0.287513i
$986$	−3315.87	−	6330.31i	−0.00341071	−	0.00651136i
$987$	1.35465e6	+	403317.i	1.39057	+	0.414012i
$988$	382412.	+	264875.i	0.391758	+	0.271348i
$989$	110014.			0.112475
$990$	−1.26339e6	+	1.77031e6i	−1.28904	+	1.80626i
$991$			766088.i			0.780066i	0.920801	+	0.390033i	$0.127536\pi$
$991$			766088.i			0.780066i	−0.920801	+	0.390033i	$0.872464\pi$
$992$	592526.	+	529227.i	0.602121	+	0.537797i
$993$	124678.	−	29749.1i	0.126442	−	0.0301700i
$994$	137793.	+	263060.i	0.139462	+	0.266246i
$995$	−20815.3	+	12017.7i	−0.0210251	+	0.0121388i
$996$	606427.	+	756617.i	0.611307	+	0.762706i
$997$	−192679.	+	333731.i	−0.193841	+	0.335742i	−0.946520	−	0.322645i	$-0.895428\pi$
$997$	−192679.	+	333731.i	−0.193841	+	0.335742i	0.752679	+	0.658388i	$0.228761\pi$
$998$	56033.2	−	1.36303e6i	0.0562580	−	1.36850i
$999$	287276.	+	339216.i	0.287851	+	0.339895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.7.8	✓	44
3.2	odd	2		108.5.f.a.19.15		44
4.3	odd	2	inner	36.5.f.a.7.9	yes	44
9.2	odd	6		324.5.d.e.163.1		22
9.4	even	3	inner	36.5.f.a.31.9	yes	44
9.5	odd	6		108.5.f.a.91.14		44
9.7	even	3		324.5.d.f.163.22		22
12.11	even	2		108.5.f.a.19.14		44
36.7	odd	6		324.5.d.f.163.21		22
36.11	even	6		324.5.d.e.163.2		22
36.23	even	6		108.5.f.a.91.15		44
36.31	odd	6	inner	36.5.f.a.31.8	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.8	✓	44	1.1	even	1	trivial
36.5.f.a.7.9	yes	44	4.3	odd	2	inner
36.5.f.a.31.8	yes	44	36.31	odd	6	inner
36.5.f.a.31.9	yes	44	9.4	even	3	inner
108.5.f.a.19.14		44	12.11	even	2
108.5.f.a.19.15		44	3.2	odd	2
108.5.f.a.91.14		44	9.5	odd	6
108.5.f.a.91.15		44	36.23	even	6
324.5.d.e.163.1		22	9.2	odd	6
324.5.d.e.163.2		22	36.11	even	6
324.5.d.f.163.21		22	36.7	odd	6
324.5.d.f.163.22		22	9.7	even	3

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14060 + 3.37903i) q^{2} +(-6.53699 + 6.18609i) q^{3} +(-6.83568 - 14.4663i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(-6.90992 - 35.3306i) q^{6} +(51.8739 + 29.9494i) q^{7} +(63.5145 + 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +O(q^{10})\)	\(q+(-2.14060 + 3.37903i) q^{2} +(-6.53699 + 6.18609i) q^{3} +(-6.83568 - 14.4663i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(-6.90992 - 35.3306i) q^{6} +(51.8739 + 29.9494i) q^{7} +(63.5145 + 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +(118.977 + 4.89106i) q^{10} +(-195.278 - 112.744i) q^{11} +(134.175 + 52.2799i) q^{12} +(-85.8824 - 148.753i) q^{13} +(-212.241 + 111.174i) q^{14} +(256.785 + 76.4524i) q^{15} +(-162.547 + 197.774i) q^{16} -99.0725 q^{17} +(263.729 + 188.211i) q^{18} -169.267i q^{19} +(-271.209 + 391.557i) q^{20} +(-524.369 + 125.118i) q^{21} +(798.976 - 418.511i) q^{22} +(-310.777 + 179.427i) q^{23} +(-463.869 + 341.470i) q^{24} +(-130.609 + 226.221i) q^{25} +(686.480 + 28.2206i) q^{26} +(471.128 + 556.309i) q^{27} +(78.6636 - 955.147i) q^{28} +(9.01635 - 15.6168i) q^{29} +(-808.009 + 704.031i) q^{30} +(-671.898 + 387.920i) q^{31} +(-320.335 - 972.605i) q^{32} +(1973.97 - 471.003i) q^{33} +(212.075 - 334.769i) q^{34} -1783.15i q^{35} +(-1200.51 + 488.264i) q^{36} +609.762 q^{37} +(571.958 + 362.333i) q^{38} +(1481.61 + 441.118i) q^{39} +(-742.534 - 1754.59i) q^{40} +(206.545 + 357.747i) q^{41} +(699.686 - 2039.68i) q^{42} +(-265.498 - 153.286i) q^{43} +(-296.127 + 3595.63i) q^{44} +(-2151.54 + 1088.73i) q^{45} +(58.9591 - 1434.21i) q^{46} +(-2270.59 - 1310.93i) q^{47} +(-160.878 - 2298.38i) q^{48} +(593.432 + 1027.85i) q^{49} +(-484.826 - 925.578i) q^{50} +(647.636 - 612.872i) q^{51} +(-1564.84 + 2259.23i) q^{52} +2034.30 q^{53} +(-2888.28 + 401.120i) q^{54} +6712.63i q^{55} +(3059.08 + 2310.39i) q^{56} +(1047.10 + 1106.50i) q^{57} +(33.4692 + 63.8958i) q^{58} +(2250.48 - 1299.32i) q^{59} +(-649.318 - 4237.33i) q^{60} +(708.681 - 1227.47i) q^{61} +(127.469 - 3100.74i) q^{62} +(2653.80 - 4061.69i) q^{63} +(3972.17 + 999.536i) q^{64} +(-2556.67 + 4428.28i) q^{65} +(-2633.95 + 7678.34i) q^{66} +(-5191.93 + 2997.56i) q^{67} +(677.228 + 1433.21i) q^{68} +(921.593 - 3095.41i) q^{69} +(6025.32 + 3817.01i) q^{70} -1239.44i q^{71} +(919.945 - 5101.72i) q^{72} -5060.60 q^{73} +(-1305.25 + 2060.40i) q^{74} +(-545.636 - 2286.76i) q^{75} +(-2448.66 + 1157.05i) q^{76} +(-6753.22 - 11696.9i) q^{77} +(-4662.09 + 4062.15i) q^{78} +(-1635.99 - 944.538i) q^{79} +(7518.28 + 1246.83i) q^{80} +(-6521.14 - 722.147i) q^{81} +(-1650.97 - 67.8700i) q^{82} +(5831.54 + 3366.84i) q^{83} +(5394.40 + 6730.41i) q^{84} +(1474.66 + 2554.19i) q^{85} +(1086.28 - 569.004i) q^{86} +(37.6671 + 157.863i) q^{87} +(-11515.8 - 8697.42i) q^{88} +9436.67 q^{89} +(926.745 - 9600.66i) q^{90} -10288.5i q^{91} +(4720.02 + 3269.29i) q^{92} +(1992.48 - 6692.25i) q^{93} +(9290.07 - 4866.22i) q^{94} +(-4363.88 + 2519.49i) q^{95} +(8110.66 + 4376.29i) q^{96} +(7297.91 - 12640.4i) q^{97} +(-4743.45 - 195.000i) q^{98} +(-9990.18 + 15290.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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