LMFDB - Embedded newform 36.5.f.a.7.9

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			7.9
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85603 + 3.54333i) q^{2} +(6.53699 - 6.18609i) q^{3} +(-9.11034 - 13.1530i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(9.78653 + 34.6442i) q^{6} +(-51.8739 - 29.9494i) q^{7} +(63.5145 - 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +O(q^{10})$	\(q+(-1.85603 + 3.54333i) q^{2} +(6.53699 - 6.18609i) q^{3} +(-9.11034 - 13.1530i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(9.78653 + 34.6442i) 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} +(-140.920 - 29.6237i) q^{12} +(-85.8824 - 148.753i) q^{13} +(202.400 - 128.219i) q^{14} +(-256.785 - 76.4524i) q^{15} +(-90.0035 + 239.657i) q^{16} -99.0725 q^{17} +(278.287 + 165.929i) q^{18} +169.267i q^{19} +(-203.494 + 430.653i) q^{20} +(-524.369 + 125.118i) q^{21} +(-761.929 + 482.678i) q^{22} +(310.777 - 179.427i) q^{23} +(366.518 - 444.343i) 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} +(747.496 - 767.976i) q^{30} +(671.898 - 387.920i) q^{31} +(-682.133 - 763.721i) q^{32} +(1973.97 - 471.003i) q^{33} +(183.881 - 351.046i) q^{34} +1783.15i q^{35} +(-1104.45 + 678.094i) q^{36} +609.762 q^{37} +(-599.768 - 314.164i) q^{38} +(-1481.61 - 441.118i) q^{39} +(-1148.25 - 1520.35i) q^{40} +(206.545 + 357.747i) q^{41} +(529.909 - 2090.23i) 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} +(894.187 + 2123.40i) q^{48} +(593.432 + 1027.85i) q^{49} +(-559.161 - 882.661i) q^{50} +(-647.636 + 612.872i) q^{51} +(-1174.13 + 2484.80i) q^{52} +2034.30 q^{53} +(2845.61 - 636.835i) q^{54} -6712.63i q^{55} +(-3530.40 - 1494.05i) q^{56} +(1047.10 + 1106.50i) q^{57} +(38.6008 + 60.9330i) q^{58} +(-2250.48 + 1299.32i) q^{59} +(1333.82 + 4074.01i) 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} +(-1994.83 + 7868.63i) q^{66} +(5191.93 - 2997.56i) q^{67} +(902.584 + 1303.10i) q^{68} +(921.593 - 3095.41i) q^{69} +(-6318.29 - 3309.57i) q^{70} +1239.44i q^{71} +(-352.826 - 5171.98i) q^{72} -5060.60 q^{73} +(-1131.73 + 2160.59i) q^{74} +(545.636 + 2286.76i) q^{75} +(2226.37 - 1542.08i) q^{76} +(-6753.22 - 11696.9i) q^{77} +(4312.93 - 4431.11i) 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} +(6422.85 + 5757.16i) q^{84} +(1474.66 + 2554.19i) q^{85} +(-1035.91 + 656.246i) q^{86} +(-37.6671 - 157.863i) q^{87} +(13290.1 + 5624.30i) q^{88} +9436.67 q^{89} +(135.598 - 9644.33i) q^{90} +10288.5i q^{91} +(-5191.29 - 2453.01i) q^{92} +(1992.48 - 6692.25i) q^{93} +(-8859.31 + 5612.33i) q^{94} +(4363.88 - 2519.49i) q^{95} +(-9183.55 - 772.696i) 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 $

$2$	−1.85603	+	3.54333i	−0.464006	+	0.885832i
$2$	−1.85603	+	3.54333i	−0.464006	+	0.885832i
$3$	6.53699	−	6.18609i	0.726332	−	0.687344i
$3$	6.53699	−	6.18609i	0.726332	−	0.687344i
$4$	−9.11034	−	13.1530i	−0.569396	−	0.822063i
$5$	−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	$-0.369668\pi$
$6$	9.78653	+	34.6442i	0.271848	+	0.962340i
$7$	−51.8739	−	29.9494i	−1.05865	−	0.611212i	−0.133592	−	0.991036i	$-0.542651\pi$
$7$	−51.8739	−	29.9494i	−1.05865	−	0.611212i	−0.925059	+	0.379824i	$0.875984\pi$
$8$	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	$0.0483998\pi$
$11$	195.278	+	112.744i	1.61387	+	0.931767i	0.625406	+	0.780300i	$0.284934\pi$
$12$	−140.920	−	29.6237i	−0.978611	−	0.205720i
$13$	−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	$-0.336348\pi$
$14$	202.400	−	128.219i	1.03265	−	0.654180i
$15$	−256.785	−	76.4524i	−1.14127	−	0.339788i
$16$	−90.0035	+	239.657i	−0.351576	+	0.936159i
$17$	−99.0725			−0.342812			−0.171406	−	0.985201i	$-0.554831\pi$
$17$	−99.0725			−0.342812			−0.171406	+	0.985201i	$0.554831\pi$
$18$	278.287	+	165.929i	0.858911	+	0.512126i
$19$			169.267i			0.468884i	0.972130	+	0.234442i	$0.0753262\pi$
$19$			169.267i			0.468884i	−0.972130	+	0.234442i	$0.924674\pi$
$20$	−203.494	+	430.653i	−0.508735	+	1.07663i
$21$	−524.369	+	125.118i	−1.18904	+	0.283714i
$22$	−761.929	+	482.678i	−1.57423	+	0.997270i
$23$	310.777	−	179.427i	0.587480	−	0.339182i	−0.176620	−	0.984279i	$-0.556516\pi$
$23$	310.777	−	179.427i	0.587480	−	0.339182i	0.764101	+	0.645097i	$0.223183\pi$
$24$	366.518	−	444.343i	0.636315	−	0.771429i
$25$	−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	$0.163254\pi$
$30$	747.496	−	767.976i	0.830551	−	0.853307i
$31$	671.898	−	387.920i	0.699165	−	0.403663i	−0.107871	−	0.994165i	$-0.534403\pi$
$31$	671.898	−	387.920i	0.699165	−	0.403663i	0.807036	+	0.590502i	$0.201070\pi$
$32$	−682.133	−	763.721i	−0.666146	−	0.745821i
$33$	1973.97	−	471.003i	1.81265	−	0.432510i
$34$	183.881	−	351.046i	0.159067	−	0.303673i
$35$			1783.15i			1.45563i
$36$	−1104.45	+	678.094i	−0.852197	+	0.523221i
$37$	609.762			0.445407			0.222703	−	0.974886i	$-0.428512\pi$
$37$	609.762			0.445407			0.222703	+	0.974886i	$0.428512\pi$
$38$	−599.768	−	314.164i	−0.415352	−	0.217565i
$39$	−1481.61	−	441.118i	−0.974103	−	0.290019i
$40$	−1148.25	−	1520.35i	−0.717659	−	0.950218i
$41$	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	$0.794123\pi$
$42$	529.909	−	2090.23i	0.300402	−	1.18494i
$43$	265.498	+	153.286i	0.143590	+	0.0829019i	0.570074	−	0.821593i	$-0.306915\pi$
$43$	265.498	+	153.286i	0.143590	+	0.0829019i	−0.426484	+	0.904495i	$0.640248\pi$
$44$	−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	0.916377	−	0.400317i	$-0.131100\pi$
$47$	2270.59	+	1310.93i	1.02788	+	0.593447i	0.111504	+	0.993764i	$0.464433\pi$
$48$	894.187	+	2123.40i	0.388102	+	0.921616i
$49$	593.432	+	1027.85i	0.247160	+	0.428094i
$50$	−559.161	−	882.661i	−0.223665	−	0.353064i
$51$	−647.636	+	612.872i	−0.248995	+	0.235629i
$52$	−1174.13	+	2484.80i	−0.434219	+	0.918935i
$53$	2034.30			0.724209			0.362104	−	0.932138i	$-0.382058\pi$
$53$	2034.30			0.724209			0.362104	+	0.932138i	$0.382058\pi$
$54$	2845.61	−	636.835i	0.975861	−	0.218393i
$55$		−	6712.63i		−	2.21905i
$56$	−3530.40	−	1494.05i	−1.12577	−	0.476418i
$57$	1047.10	+	1106.50i	0.322284	+	0.340565i
$58$	38.6008	+	60.9330i	0.0114747	+	0.0181133i
$59$	−2250.48	+	1299.32i	−0.646505	+	0.373260i	−0.787116	−	0.616805i	$-0.788427\pi$
$59$	−2250.48	+	1299.32i	−0.646505	+	0.373260i	0.140611	+	0.990065i	$0.455093\pi$
$60$	1333.82	+	4074.01i	0.370506	+	1.13167i
$61$	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
$66$	−1994.83	+	7868.63i	−0.457950	+	1.80639i
$67$	5191.93	−	2997.56i	1.15659	−	0.667758i	0.206106	−	0.978530i	$-0.433921\pi$
$67$	5191.93	−	2997.56i	1.15659	−	0.667758i	0.950485	+	0.310772i	$0.100588\pi$
$68$	902.584	+	1303.10i	0.195196	+	0.281813i
$69$	921.593	−	3095.41i	0.193571	−	0.650160i
$70$	−6318.29	−	3309.57i	−1.28945	−	0.675423i
$71$			1239.44i			0.245872i	0.992415	+	0.122936i	$0.0392310\pi$
$71$			1239.44i			0.245872i	−0.992415	+	0.122936i	$0.960769\pi$
$72$	−352.826	−	5171.98i	−0.0680606	−	0.997681i
$73$	−5060.60			−0.949633			−0.474817	−	0.880085i	$-0.657486\pi$
$73$	−5060.60			−0.949633			−0.474817	+	0.880085i	$0.657486\pi$
$74$	−1131.73	+	2160.59i	−0.206672	+	0.394555i
$75$	545.636	+	2286.76i	0.0970019	+	0.406535i
$76$	2226.37	−	1542.08i	0.385452	−	0.266980i
$77$	−6753.22	−	11696.9i	−1.13901	−	1.97283i
$78$	4312.93	−	4431.11i	0.708898	−	0.728321i
$79$	1635.99	+	944.538i	0.262135	+	0.151344i	0.625308	−	0.780378i	$-0.284973\pi$
$79$	1635.99	+	944.538i	0.262135	+	0.151344i	−0.363173	+	0.931722i	$0.618307\pi$
$80$	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	0.0129681	−	0.999916i	$-0.495872\pi$
$83$	−5831.54	−	3366.84i	−0.846500	−	0.488727i	−0.859469	+	0.511189i	$0.829205\pi$
$84$	6422.85	+	5757.16i	0.910268	+	0.815925i
$85$	1474.66	+	2554.19i	0.204106	+	0.353522i
$86$	−1035.91	+	656.246i	−0.140064	+	0.0887298i
$87$	−37.6671	−	157.863i	−0.00497649	−	0.0208565i
$88$	13290.1	+	5624.30i	1.71618	+	0.726279i
$89$	9436.67			1.19135			0.595674	−	0.803226i	$-0.296885\pi$
$89$	9436.67			1.19135			0.595674	+	0.803226i	$0.296885\pi$
$90$	135.598	−	9644.33i	0.0167405	−	1.19066i
$91$			10288.5i			1.24242i
$92$	−5191.29	−	2453.01i	−0.613338	−	0.289817i
$93$	1992.48	−	6692.25i	0.230371	−	0.773760i
$94$	−8859.31	+	5612.33i	−1.00264	+	0.635166i
$95$	4363.88	−	2519.49i	0.483533	−	0.279168i
$96$	−9183.55	−	772.696i	−0.996479	−	0.0838429i
$97$	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	$0.269243\pi$
$102$	−969.576	−	3432.29i	−0.0931927	−	0.329901i
$103$	−13991.6	+	8078.04i	−1.31884	+	0.761432i	−0.983542	−	0.180680i	$-0.942170\pi$
$103$	−13991.6	+	8078.04i	−1.31884	+	0.761432i	−0.335298	+	0.942112i	$0.608837\pi$
$104$	−6625.25	−	8772.18i	−0.612541	−	0.811037i
$105$	11030.7	+	11656.4i	1.00052	+	1.05727i
$106$	−3775.72	+	7208.20i	−0.336037	+	0.641527i
$107$		−	3065.27i		−	0.267732i	−0.990999	−	0.133866i	$-0.957261\pi$
$107$		−	3065.27i		−	0.267732i	0.990999	−	0.133866i	$-0.0427392\pi$
$108$	−3025.01	+	11264.9i	−0.259346	+	0.965785i
$109$	−17728.8			−1.49220			−0.746098	−	0.665836i	$-0.768075\pi$
$109$	−17728.8			−1.49220			−0.746098	+	0.665836i	$0.768075\pi$
$110$	23785.1	+	12458.8i	1.96571	+	1.02965i
$111$	3986.01	−	3772.04i	0.323513	−	0.306147i
$112$	11846.4	−	9736.37i	0.944388	−	0.776178i
$113$	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	$0.636675\pi$
$114$	−5864.13	+	1656.54i	−0.451225	+	0.127465i
$115$	−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
$120$	−16911.1	−	2835.30i	−1.17438	−	0.196896i
$121$	18101.8	+	31353.3i	1.23638	+	2.14147i
$122$	3034.00	+	4789.31i	0.203843	+	0.321776i
$123$	3563.24	+	1060.88i	0.235524	+	0.0701223i
$124$	−11223.5	−	5303.40i	−0.729939	−	0.344914i
$125$	−10829.6			−0.693094
$126$	−9466.36	−	16941.9i	−0.596269	−	1.06714i
$127$			18478.7i			1.14568i	0.819667	+	0.572841i	$0.194159\pi$
$127$			18478.7i			1.14568i	−0.819667	+	0.572841i	$0.805841\pi$
$128$	−3830.77	+	15929.9i	−0.233812	+	0.972282i
$129$	2683.80	−	640.372i	0.161276	−	0.0384816i
$130$	−10945.6	−	17278.1i	−0.647669	−	1.02237i
$131$	7205.95	−	4160.35i	0.419902	−	0.242431i	−0.275133	−	0.961406i	$-0.588722\pi$
$131$	7205.95	−	4160.35i	0.419902	−	0.242431i	0.695036	+	0.718975i	$0.255389\pi$
$132$	−24178.7	−	21672.7i	−1.38767	−	1.24384i
$133$	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	$-0.0264938\pi$
$138$	9257.55	+	9010.67i	0.486114	+	0.473150i
$139$	−15783.6	+	9112.67i	−0.816915	+	0.471646i	−0.849351	−	0.527828i	$-0.823007\pi$
$139$	−15783.6	+	9112.67i	−0.816915	+	0.471646i	0.0324367	+	0.999474i	$0.489673\pi$
$140$	23453.8	−	16245.1i	1.19662	−	0.828832i
$141$	22952.3	−	5476.57i	1.15449	−	0.275468i
$142$	−4391.75	−	2300.44i	−0.217802	−	0.114086i
$143$		−	38730.8i		−	1.89402i
$144$	18980.9	+	8349.15i	0.915358	+	0.402640i
$145$	−536.823			−0.0255326
$146$	9392.60	−	17931.3i	0.440636	−	0.841215i
$147$	10237.7	+	3048.05i	0.473769	+	0.141055i
$148$	−5555.13	−	8020.20i	−0.253613	−	0.366152i
$149$	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	$0.714150\pi$
$150$	−9115.46	−	2310.92i	−0.405131	−	0.102708i
$151$	21240.4	+	12263.2i	0.931557	+	0.537835i	0.887304	−	0.461186i	$-0.152576\pi$
$151$	21240.4	+	12263.2i	0.931557	+	0.537835i	0.0442533	+	0.999020i	$0.485909\pi$
$152$	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
$156$	7695.94	+	23506.4i	0.316237	+	0.965910i
$157$	−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	$-0.464166\pi$
$158$	−6383.24	+	4043.75i	−0.255698	+	0.161983i
$159$	13298.2	−	12584.4i	0.526016	−	0.497780i
$160$	−9536.19	+	28953.9i	−0.372507	+	1.13101i
$161$	−21494.9			−0.829248
$162$	14662.2	−	21766.2i	0.558688	−	0.829378i
$163$		−	25324.6i		−	0.953162i	−0.879130	−	0.476581i	$-0.841876\pi$
$163$		−	25324.6i		−	0.953162i	0.879130	−	0.476581i	$-0.158124\pi$
$164$	2823.75	−	5975.89i	0.104988	−	0.222185i
$165$	−41525.0	−	43880.4i	−1.52525	−	1.61177i
$166$	22753.3	−	14414.1i	0.825712	−	0.523084i
$167$	−24109.7	+	13919.8i	−0.864490	+	0.499113i	−0.865513	−	0.500886i	$-0.833008\pi$
$167$	−24109.7	+	13919.8i	−0.864490	+	0.499113i	0.00102363	+	0.999999i	$0.499674\pi$
$168$	−32320.5	+	12072.8i	−1.14514	+	0.427750i
$169$	−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	$0.0465560\pi$
$174$	629.270	+	159.531i	0.0207845	+	0.00526921i
$175$	13550.4	−	7823.30i	0.442461	−	0.255455i
$176$	−44595.5	+	36652.4i	−1.43968	+	1.18325i
$177$	−6673.69	+	22415.3i	−0.213020	+	0.715482i
$178$	−17514.7	+	33437.2i	−0.552794	+	1.05533i
$179$			52513.4i			1.63895i	0.573118	+	0.819473i	$0.305734\pi$
$179$			52513.4i			1.63895i	−0.573118	+	0.819473i	$0.694266\pi$
$180$	33921.4	+	18380.6i	1.04696	+	0.567302i
$181$	−7223.25			−0.220483			−0.110242	−	0.993905i	$-0.535162\pi$
$181$	−7223.25			−0.220483			−0.110242	+	0.993905i	$0.535162\pi$
$182$	−36455.5	−	19095.7i	−1.10058	−	0.576492i
$183$	−2960.61	−	12407.9i	−0.0884056	−	0.370508i
$184$	18327.0	−	13841.6i	0.541322	−	0.408837i
$185$	−9076.12	−	15720.3i	−0.265190	−	0.459322i
$186$	20014.8	+	19481.0i	0.578528	+	0.563100i
$187$	−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	0.369100	−	0.929390i	$-0.379666\pi$
$191$	−9164.94	−	5291.38i	−0.251225	−	0.145045i	−0.620325	+	0.784345i	$0.712999\pi$
$192$	19782.8	−	31106.2i	0.536643	−	0.843809i
$193$	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	$0.657524\pi$
$194$	31243.8	+	49319.7i	0.830157	+	1.31044i
$195$	10680.8	+	44763.4i	0.280890	+	1.17721i
$196$	8113.02	−	17169.5i	0.211189	−	0.446937i
$197$	−10820.0			−0.278802			−0.139401	−	0.990236i	$-0.544518\pi$
$197$	−10820.0			−0.278802			−0.139401	+	0.990236i	$0.544518\pi$
$198$	35635.9	+	63777.4i	0.908986	+	1.62681i
$199$			807.389i			0.0203881i	0.999948	+	0.0101940i	$0.00324492\pi$
$199$			807.389i			0.0203881i	−0.999948	+	0.0101940i	$0.996755\pi$
$200$	−6515.50	+	15396.0i	−0.162888	+	0.384900i
$201$	15396.4	−	51712.8i	0.381090	−	1.27999i
$202$	−13831.3	−	21833.3i	−0.338970	−	0.535078i
$203$	−935.426	+	540.068i	−0.0226996	+	0.0131056i
$204$	13961.3	+	2934.90i	0.335479	+	0.0705233i
$205$	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
$210$	−61775.9	+	17450.9i	−1.40081	+	0.395711i
$211$	52683.9	−	30417.0i	1.18335	−	0.683207i	0.226562	−	0.973997i	$-0.427251\pi$
$211$	52683.9	−	30417.0i	1.18335	−	0.683207i	0.956787	+	0.290790i	$0.0939181\pi$
$212$	−18533.2	−	26757.2i	−0.412361	−	0.595345i
$213$	7667.31	+	8102.22i	0.168999	+	0.178585i
$214$	10861.2	+	5689.21i	0.237166	+	0.124229i
$215$		−	9126.44i		−	0.197435i
$216$	−34300.8	−	31626.6i	−0.735185	−	0.677867i
$217$	−46471.9			−0.986895
$218$	32905.1	−	62818.9i	0.692389	−	1.32184i
$219$	−33081.1	+	31305.3i	−0.689749	+	0.652724i
$220$	−88291.3	+	61154.3i	−1.82420	+	1.26352i
$221$	8508.59	+	14737.3i	0.174210	+	0.301741i
$222$	5967.45	+	21124.7i	0.121083	+	0.428633i
$223$	9292.11	+	5364.80i	0.186855	+	0.107881i	0.590509	−	0.807031i	$-0.298927\pi$
$223$	9292.11	+	5364.80i	0.186855	+	0.107881i	−0.403654	+	0.914912i	$0.632260\pi$
$224$	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	0.975511	−	0.219951i	$-0.0705898\pi$
$227$	65585.2	+	37865.7i	1.27278	+	0.734842i	0.297272	+	0.954793i	$0.403923\pi$
$228$	5014.32	−	23853.1i	0.0964589	−	0.458855i
$229$	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	$0.663413\pi$
$230$	36097.8	−	22867.8i	0.682378	−	0.432283i
$231$	−116504.	−	34686.6i	−2.18332	−	0.650036i
$232$	449.787	−	1062.84i	0.00835662	−	0.0197465i
$233$	56485.5			1.04046			0.520230	−	0.854026i	$-0.325846\pi$
$233$	56485.5			1.04046			0.520230	+	0.854026i	$0.325846\pi$
$234$	782.381	−	55646.3i	0.0142885	−	1.01626i
$235$		−	78050.9i		−	1.41333i
$236$	37592.6	+	17763.4i	0.674961	+	0.318935i
$237$	16537.4	−	3945.94i	0.294423	−	0.0702511i
$238$	−20052.3	+	12703.0i	−0.354005	+	0.224260i
$239$	41561.8	−	23995.7i	0.727610	−	0.420086i	−0.0899375	−	0.995947i	$-0.528667\pi$
$239$	41561.8	−	23995.7i	0.727610	−	0.420086i	0.817547	+	0.575862i	$0.195333\pi$
$240$	41433.9	−	54659.3i	0.719339	−	0.948947i
$241$	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
$246$	−10372.5	+	10656.7i	−0.171401	+	0.176097i
$247$	25178.9	−	14537.1i	0.412708	−	0.238277i
$248$	39622.8	−	29925.4i	0.644232	−	0.486561i
$249$	−58948.3	+	14065.4i	−0.950764	+	0.226858i
$250$	20100.0	−	38372.8i	0.321600	−	0.613965i
$251$			65230.8i			1.03539i	0.855564	+	0.517696i	$0.173210\pi$
$251$			65230.8i			1.03539i	−0.855564	+	0.517696i	$0.826790\pi$
$252$	77600.5	−	2097.83i	1.22198	−	0.0330346i
$253$	80917.3			1.26415
$254$	−65476.1	−	34296.9i	−1.01488	−	0.531604i
$255$	25440.4	+	7574.33i	0.391240	+	0.116483i
$256$	−49334.7	−	43139.9i	−0.752788	−	0.658263i
$257$	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	$0.726990\pi$
$258$	−2712.15	+	10698.1i	−0.0407451	+	0.160719i
$259$	−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	0.925929	−	0.377698i	$-0.123284\pi$
$263$	73443.4	+	42402.6i	1.06180	+	0.613029i	0.135868	+	0.990727i	$0.456618\pi$
$264$	121670.	−	45447.8i	1.74572	−	0.652087i
$265$	−30280.0	−	52446.5i	−0.431185	−	0.746835i
$266$	21703.3	+	34259.6i	0.306734	+	0.484193i
$267$	61687.4	−	58376.2i	0.865315	−	0.818866i
$268$	−86727.3	−	40980.8i	−1.20750	−	0.570572i
$269$	−66685.5			−0.921567			−0.460784	−	0.887513i	$-0.652432\pi$
$269$	−66685.5			−0.921567			−0.460784	+	0.887513i	$0.652432\pi$
$270$	−58774.3	−	63883.7i	−0.806232	−	0.876320i
$271$			122426.i			1.66700i	0.552516	+	0.833502i	$0.313668\pi$
$271$			122426.i			1.66700i	−0.552516	+	0.833502i	$0.686332\pi$
$272$	8916.88	−	23743.4i	0.120524	−	0.320926i
$273$	63645.7	+	67255.9i	0.853972	+	0.902412i
$274$	45823.2	+	72333.9i	0.610357	+	0.963475i
$275$	−51010.0	+	29450.6i	−0.674512	+	0.389430i
$276$	−49110.0	+	16078.5i	−0.644691	+	0.211070i
$277$	−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	$0.194929\pi$
$282$	−23194.8	+	91492.3i	−0.291671	+	1.15050i
$283$	−99634.2	+	57523.8i	−1.24404	+	0.718249i	−0.969915	−	0.243444i	$-0.921723\pi$
$283$	−99634.2	+	57523.8i	−1.24404	+	0.718249i	−0.274129	+	0.961693i	$0.588389\pi$
$284$	16302.4	−	11291.7i	0.202123	−	0.139999i
$285$	12940.9	−	43465.3i	0.159321	−	0.535122i
$286$	137236.	+	71885.5i	1.67778	+	0.878838i
$287$		−	24743.6i		−	0.300400i
$288$	−64812.8	+	51759.2i	−0.781404	+	0.624026i
$289$	−73705.6			−0.882480
$290$	996.357	−	1902.14i	0.0118473	−	0.0226176i
$291$	−30488.0	−	127775.i	−0.360034	−	1.50890i
$292$	46103.7	+	66562.1i	0.540717	+	0.780659i
$293$	−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	$0.886450\pi$
$294$	−29801.6	+	30618.1i	−0.344782	+	0.354229i
$295$	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
$300$	25106.9	−	28009.9i	0.278965	−	0.311221i
$301$	−9181.62	−	15903.0i	−0.101341	−	0.175528i
$302$	−82875.2	+	52501.0i	−0.908679	+	0.575644i
$303$	13496.7	+	56564.9i	0.147009	+	0.616115i
$304$	−40566.0	−	15234.6i	−0.438950	−	0.164848i
$305$	−42194.0			−0.453577
$306$	−27570.6	−	16439.0i	−0.294444	−	0.175563i
$307$		−	115338.i		−	1.22376i	−0.790952	−	0.611879i	$-0.790414\pi$
$307$		−	115338.i		−	1.22376i	0.790952	−	0.611879i	$-0.209586\pi$
$308$	−92325.6	+	195388.i	−0.973242	+	2.05966i
$309$	−41491.3	+	139359.i	−0.434550	+	1.45955i
$310$	78043.1	−	49439.9i	0.812103	−	0.514463i
$311$	85566.6	−	49401.9i	0.884674	−	0.510767i	0.0124776	−	0.999922i	$-0.496028\pi$
$311$	85566.6	−	49401.9i	0.884674	−	0.510767i	0.872197	+	0.489155i	$0.162695\pi$
$312$	−97574.7	−	16359.2i	−1.00237	−	0.168056i
$313$	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	$0.163318\pi$
$318$	19908.8	+	70476.9i	0.196875	+	0.696935i
$319$	3521.39	−	2033.08i	0.0346045	−	0.0199789i
$320$	−84893.7	−	87529.0i	−0.829040	−	0.854775i
$321$	−18962.0	−	20037.6i	−0.184024	−	0.194463i
$322$	39895.2	−	76163.6i	0.384777	−	0.734575i
$323$		−	16769.7i		−	0.160739i
$324$	49911.3	+	92351.6i	0.475455	+	0.879740i
$325$	44868.0			0.424785
$326$	89733.2	+	47003.1i	0.844342	+	0.442273i
$327$	−115893.	+	109672.i	−1.08383	+	1.02565i
$328$	15933.6	+	21096.9i	0.148104	+	0.196097i
$329$	−78522.8	−	136006.i	−0.725444	−	1.25651i
$330$	232554.	−	65693.4i	2.13548	−	0.603245i
$331$	12334.0	+	7121.02i	0.112576	+	0.0649960i	0.555231	−	0.831696i	$-0.312630\pi$
$331$	12334.0	+	7121.02i	0.112576	+	0.0649960i	−0.442655	+	0.896692i	$0.645963\pi$
$332$	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
$336$	17209.7	−	136930.i	0.152439	−	1.21288i
$337$	−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	$0.941077\pi$
$338$	−2016.79	−	3183.59i	−0.0176534	−	0.0278666i
$339$	127603.	+	37991.0i	1.11035	+	0.330584i
$340$	20160.7	−	42665.9i	0.174400	−	0.369082i
$341$	174942.			1.50448
$342$	−28086.2	+	47104.8i	−0.240127	+	0.402729i
$343$			72725.3i			0.618155i
$344$	18069.1	+	7646.75i	0.152693	+	0.0646190i
$345$	−93520.6	+	22314.6i	−0.785722	+	0.187478i
$346$	47209.9	+	74522.9i	0.394349	+	0.622498i
$347$	−128553.	+	74220.2i	−1.06764	+	0.616401i	−0.927535	−	0.373736i	$-0.878077\pi$
$347$	−128553.	+	74220.2i	−1.06764	+	0.616401i	−0.140103	+	0.990137i	$0.544743\pi$
$348$	−1733.21	+	1933.62i	−0.0143118	+	0.0159666i
$349$	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	$0.191437\pi$
$354$	−67038.3	−	65250.5i	−0.534954	−	0.520688i
$355$	31954.1	−	18448.7i	0.253554	−	0.146389i
$356$	−85971.3	−	124121.i	−0.678349	−	0.979364i
$357$	51950.5	−	12395.7i	0.407618	−	0.0972603i
$358$	−186072.	−	97466.3i	−1.45183	−	0.760481i
$359$		−	139927.i		−	1.08571i	−0.839827	−	0.542854i	$-0.817344\pi$
$359$		−	139927.i		−	1.08571i	0.839827	−	0.542854i	$-0.182656\pi$
$360$	−128087.	+	86079.6i	−0.988329	+	0.664194i
$361$	101670.			0.780148
$362$	13406.5	−	25594.4i	0.102306	−	0.195311i
$363$	312286.	+	92976.5i	2.36995	+	0.705603i
$364$	135325.	−	93731.7i	1.02135	−	0.707431i
$365$	75325.5	+	130468.i	0.565400	+	0.979302i
$366$	49460.4	+	12539.0i	0.369229	+	0.0936056i
$367$	−79304.5	−	45786.5i	−0.588797	−	0.339942i	0.175825	−	0.984421i	$-0.443741\pi$
$367$	−79304.5	−	45786.5i	−0.588797	−	0.339942i	−0.764622	+	0.644479i	$0.777074\pi$
$368$	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
$372$	−106175.	+	34761.6i	−0.767252	+	0.251197i
$373$	−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	$0.932845\pi$
$374$	75486.3	−	47820.2i	0.539666	−	0.341875i
$375$	−70792.9	+	66992.9i	−0.503416	+	0.476394i
$376$	154530.	+	65396.4i	1.09304	+	0.462571i
$377$	−3097.38			−0.0217928
$378$	−166686.	−	52189.2i	−1.16658	−	0.365256i
$379$			39838.1i			0.277345i	0.990338	+	0.138672i	$0.0442835\pi$
$379$			39838.1i			0.277345i	−0.990338	+	0.138672i	$0.955716\pi$
$380$	−72895.3	−	34444.8i	−0.504815	−	0.238537i
$381$	114311.	+	120795.i	0.787477	+	0.832146i
$382$	35759.4	−	22653.4i	0.245055	−	0.155241i
$383$	147816.	−	85341.8i	1.00769	−	0.581787i	0.0971722	−	0.995268i	$-0.469020\pi$
$383$	147816.	−	85341.8i	1.00769	−	0.581787i	0.910513	+	0.413480i	$0.135687\pi$
$384$	73501.9	+	127831.i	0.498467	+	0.866909i
$385$	−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	$0.913956\pi$
$390$	−178435.	−	45236.3i	−1.17314	−	0.297412i
$391$	−30789.5	+	17776.3i	−0.201395	+	0.116275i
$392$	45779.3	+	60614.2i	0.297918	+	0.394459i
$393$	21368.9	−	71772.9i	0.138355	−	0.464703i
$394$	20082.3	−	38338.9i	0.129366	−	0.246972i
$395$		−	56236.6i		−	0.360434i
$396$	−292125.	+	7897.23i	−1.86285	+	0.0503598i
$397$	292553.			1.85620			0.928098	−	0.372336i	$-0.121443\pi$
$397$	292553.			1.85620			0.928098	+	0.372336i	$0.121443\pi$
$398$	−2860.84	−	1498.53i	−0.0180604	−	0.00946021i
$399$	−21178.3	−	88758.3i	−0.133029	−	0.557524i
$400$	−42460.1	−	51661.9i	−0.265376	−	0.322887i
$401$	−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	$-0.385790\pi$
$402$	154659.	+	150535.i	0.957027	+	0.931505i
$403$	−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
$408$	−36311.8	+	44022.2i	−0.218136	+	0.264455i
$409$	−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	$0.866435\pi$
$410$	26323.9	+	41553.5i	0.156597	+	0.247195i
$411$	−44714.7	−	187400.i	−0.264708	−	1.10939i
$412$	233718.	+	110438.i	1.37689	+	0.650613i
$413$	155655.			0.912564
$414$	116257.	+	1634.57i	0.678297	+	0.00953678i
$415$			200458.i			1.16393i
$416$	−55022.3	+	167059.i	−0.317945	+	0.965349i
$417$	−46805.5	+	157208.i	−0.269169	+	0.904073i
$418$	−81701.5	−	128969.i	−0.467603	−	0.738132i
$419$	−277682.	+	160320.i	−1.58169	+	0.913187i	−0.587073	+	0.809534i	$0.699720\pi$
$419$	−277682.	+	160320.i	−1.58169	+	0.913187i	−0.994614	+	0.103653i	$0.966947\pi$
$420$	52823.6	−	251282.i	0.299453	−	1.42450i
$421$	−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
$426$	−42939.5	+	12129.8i	−0.236613	+	0.0668399i
$427$	−73524.1	+	42449.2i	−0.403250	+	0.232816i
$428$	−40317.5	+	27925.6i	−0.220093	+	0.152446i
$429$	−239593.	−	253183.i	−1.30184	−	1.37569i
$430$	32338.0	+	16938.9i	0.174894	+	0.0916112i
$431$		−	31343.0i		−	0.168728i	−0.996435	−	0.0843638i	$-0.973114\pi$
$431$		−	31343.0i		−	0.168728i	0.996435	−	0.0843638i	$-0.0268858\pi$
$432$	175726.	−	62839.1i	0.941607	−	0.336715i
$433$	101022.			0.538815			0.269407	−	0.963026i	$-0.413172\pi$
$433$	101022.			0.538815			0.269407	+	0.963026i	$0.413172\pi$
$434$	86253.1	−	164665.i	0.457926	−	0.874223i
$435$	−3509.21	+	3320.84i	−0.0185451	+	0.0175497i
$436$	161515.	+	233187.i	0.849651	+	1.22668i
$437$	30371.1	+	52604.3i	0.159037	+	0.275460i
$438$	−49525.7	−	175321.i	−0.258156	−	0.913870i
$439$	157593.	+	90986.2i	0.817724	+	0.472113i	0.849631	−	0.527378i	$-0.176825\pi$
$439$	157593.	+	90986.2i	0.817724	+	0.472113i	−0.0319068	+	0.999491i	$0.510158\pi$
$440$	−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	0.579806	−	0.814755i	$-0.303128\pi$
$443$	32206.4	+	18594.4i	0.164110	+	0.0947490i	−0.415696	+	0.909504i	$0.636462\pi$
$444$	−85927.6	−	18063.4i	−0.435880	−	0.0916292i
$445$	−140462.	−	243287.i	−0.709315	−	1.22857i
$446$	−36255.7	+	22967.8i	−0.182266	+	0.115465i
$447$	140078.	+	41705.3i	0.701061	+	0.208726i
$448$	−235987.	−	67114.3i	−1.17580	−	0.334395i
$449$	−20385.0			−0.101115			−0.0505577	−	0.998721i	$-0.516100\pi$
$449$	−20385.0			−0.101115			−0.0505577	+	0.998721i	$0.516100\pi$
$450$	−73883.2	+	41282.6i	−0.364855	+	0.203865i
$451$			93146.9i			0.457947i
$452$	101121.	−	214002.i	0.494953	−	1.04747i
$453$	214710.	−	51231.1i	1.04630	−	0.249653i
$454$	−255898.	+	162110.i	−1.24153	+	0.786501i
$455$	265249.	−	153141.i	1.28124	−	0.739724i
$456$	75212.6	+	62039.3i	0.361710	+	0.298358i
$457$	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	$0.0433344\pi$
$462$	339140.	−	348432.i	1.58890	−	1.63243i
$463$	−85869.5	+	49576.8i	−0.400569	+	0.231268i	−0.686729	−	0.726913i	$-0.740954\pi$
$463$	−85869.5	+	49576.8i	−0.400569	+	0.231268i	0.286161	+	0.958182i	$0.407621\pi$
$464$	2931.16	+	3566.39i	0.0136146	+	0.0165651i
$465$	−202191.	+	48244.0i	−0.935095	+	0.223120i
$466$	−104839.	+	200147.i	−0.482780	+	0.921673i
$467$			278790.i			1.27833i	0.769068	+	0.639167i	$0.220721\pi$
$467$			278790.i			1.27833i	−0.769068	+	0.639167i	$0.779279\pi$
$468$	195721.	+	106053.i	0.893605	+	0.484208i
$469$	−359101.			−1.63257
$470$	276560.	+	144865.i	1.25197	+	0.655792i
$471$	−342048.	−	101838.i	−1.54186	−	0.459057i
$472$	−132714.	+	100234.i	−0.595709	+	0.449913i
$473$	34564.0	+	59866.6i	0.154490	+	0.267585i
$474$	−16712.2	+	65921.3i	−0.0743833	+	0.293406i
$475$	−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	0.438407	−	0.898776i	$-0.355543\pi$
$479$	−27705.5	−	15995.8i	−0.120752	−	0.0697163i	−0.559160	+	0.829060i	$0.688876\pi$
$480$	116773.	+	248263.i	0.506829	+	1.07753i
$481$	−52367.8	−	90703.7i	−0.226347	−	0.392044i
$482$	137320.	+	216765.i	0.591070	+	0.933029i
$483$	−140512.	+	132970.i	−0.602310	+	0.569979i
$484$	247477.	−	523733.i	1.05644	−	2.23573i
$485$	−434509.			−1.84721
$486$	−38801.1	−	232987.i	−0.164275	−	0.986415i
$487$		−	346823.i		−	1.46235i	−0.682192	−	0.731173i	$-0.738973\pi$
$487$		−	346823.i		−	1.46235i	0.682192	−	0.731173i	$-0.261027\pi$
$488$	35353.1	−	83538.5i	0.148452	−	0.350790i
$489$	−156660.	−	165546.i	−0.655150	−	0.692313i
$490$	75632.1	+	119389.i	0.315003	+	0.497246i
$491$	207830.	−	119991.i	0.862076	−	0.497720i	−0.00263098	−	0.999997i	$-0.500837\pi$
$491$	207830.	−	119991.i	0.862076	−	0.497720i	0.864707	+	0.502277i	$0.167504\pi$
$492$	−18508.6	−	56532.4i	−0.0764614	−	0.233543i
$493$	−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
$498$	59571.1	−	234979.i	0.240202	−	0.947481i
$499$	295354.	−	170523.i	1.18616	−	0.684828i	0.228726	−	0.973491i	$-0.426544\pi$
$499$	295354.	−	170523.i	1.18616	−	0.684828i	0.957431	+	0.288663i	$0.0932107\pi$
$500$	98661.2	+	142442.i	0.394645	+	0.569767i
$501$	−71496.2	+	240139.i	−0.284844	+	0.956724i
$502$	−231134.	−	121070.i	−0.917184	−	0.480429i
$503$		−	3886.22i		−	0.0153600i	−0.999971	−	0.00768001i	$-0.997555\pi$
$503$		−	3886.22i		−	0.0153600i	0.999971	−	0.00768001i	$-0.00244465\pi$
$504$	−136595.	+	278857.i	−0.537742	+	1.09779i
$505$	192353.			0.754250
$506$	−150185.	+	286716.i	−0.586576	+	1.11983i
$507$	1968.01	+	8247.92i	0.00765616	+	0.0320870i
$508$	243051.	−	168347.i	0.941823	−	0.652347i
$509$	−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	$0.957705\pi$
$510$	−74056.3	+	76085.4i	−0.284722	+	0.292524i
$511$	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
$516$	−32873.1	−	29466.0i	−0.123464	−	0.110668i
$517$	295597.	+	511990.i	1.10591	+	1.91549i
$518$	123416.	−	78183.2i	0.459950	−	0.291376i
$519$	−46068.0	−	193071.i	−0.171027	−	0.716774i
$520$	−127541.	+	301377.i	−0.471676	+	1.11456i
$521$	229165.			0.844255			0.422127	−	0.906536i	$-0.361283\pi$
$521$	229165.			0.844255			0.422127	+	0.906536i	$0.361283\pi$
$522$	5100.41	−	2849.88i	0.0187182	−	0.0104589i
$523$		−	346673.i		−	1.26741i	−0.773575	−	0.633705i	$-0.781533\pi$
$523$		−	346673.i		−	1.26741i	0.773575	−	0.633705i	$-0.218467\pi$
$524$	−120370.	−	56877.7i	−0.438384	−	0.207147i
$525$	40182.9	−	134965.i	0.145788	−	0.489667i
$526$	−286559.	+	181534.i	−1.03572	+	0.656124i
$527$	−66566.6	+	38432.2i	−0.239682	+	0.138380i
$528$	−64785.6	+	515468.i	−0.232387	+	1.84899i
$529$	−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
$534$	92352.3	+	326926.i	0.323866	+	1.14648i
$535$	−79025.8	+	45625.6i	−0.276097	+	0.159405i
$536$	306176.	−	231242.i	1.06572	−	0.804890i
$537$	324853.	+	343280.i	1.12652	+	1.19042i
$538$	123770.	−	236289.i	0.427613	−	0.816353i
$539$			267623.i			0.921184i
$540$	335448.	−	89686.9i	1.15037	−	0.307568i
$541$	−287354.			−0.981799			−0.490900	−	0.871216i	$-0.663332\pi$
$541$	−287354.			−0.981799			−0.490900	+	0.871216i	$0.663332\pi$
$542$	−433797.	−	227227.i	−1.47669	−	0.773501i
$543$	−47218.3	+	44683.7i	−0.160144	+	0.151548i
$544$	67580.7	+	75663.8i	0.228362	+	0.255676i
$545$	263888.	+	457067.i	0.888436	+	1.53882i
$546$	−356438.	+	100689.i	−1.19563	+	0.337750i
$547$	−486589.	−	280932.i	−1.62625	−	0.938917i	−0.985198	−	0.171421i	$-0.945164\pi$
$547$	−486589.	−	280932.i	−1.62625	−	0.938917i	−0.641054	−	0.767496i	$-0.721502\pi$
$548$	−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
$552$	34178.0	−	203855.i	0.112168	−	0.669026i
$553$	−56576.7	−	97993.6i	−0.185006	−	0.320441i
$554$	−294230.	−	464455.i	−0.958666	−	1.51330i
$555$	−156578.	−	46617.7i	−0.508328	−	0.151344i
$556$	263653.	+	124583.i	0.852871	+	0.403002i
$557$	−393303.			−1.26770			−0.633850	−	0.773456i	$-0.718526\pi$
$557$	−393303.			−1.26770			−0.633850	+	0.773456i	$0.718526\pi$
$558$	251348.	+	3533.92i	0.807247	+	0.0113498i
$559$		−	52658.1i		−	0.168516i
$560$	−427344.	−	160490.i	−1.36270	−	0.511766i
$561$	−195567.	+	46663.4i	−0.621397	+	0.148269i
$562$	−29975.3	−	47317.3i	−0.0949054	−	0.149812i
$563$	−481867.	+	278206.i	−1.52023	+	0.877707i	−0.520518	+	0.853851i	$0.674261\pi$
$563$	−481867.	+	278206.i	−1.52023	+	0.877707i	−0.999715	+	0.0238561i	$0.992406\pi$
$564$	−281137.	−	251999.i	−0.883811	−	0.792210i
$565$	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	$0.257388\pi$
$570$	129993.	+	126526.i	0.400102	+	0.389432i
$571$	190279.	−	109858.i	0.583604	−	0.336944i	−0.178960	−	0.983856i	$-0.557273\pi$
$571$	190279.	−	109858.i	0.583604	−	0.336944i	0.762565	+	0.646912i	$0.223940\pi$
$572$	−509427.	+	352851.i	−1.55701	+	1.07845i
$573$	−92644.1	+	22105.5i	−0.282168	+	0.0673272i
$574$	87674.8	+	45924.8i	0.266104	+	0.139387i
$575$			93739.0i			0.283521i
$576$	−63105.6	−	325719.i	−0.190206	−	0.981744i
$577$	9527.81			0.0286181			0.0143091	−	0.999898i	$-0.495445\pi$
$577$	9527.81			0.0286181			0.0143091	+	0.999898i	$0.495445\pi$
$578$	136800.	−	261163.i	0.409477	−	0.781729i
$579$	337153.	+	100380.i	1.00570	+	0.299427i
$580$	4890.64	+	7060.84i	0.0145382	+	0.0209894i
$581$	201670.	+	349302.i	0.597432	+	1.03478i
$582$	509337.	+	129125.i	1.50369	+	0.381211i
$583$	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	0.512929	−	0.858431i	$-0.328560\pi$
$587$	8948.63	+	5166.49i	0.0259705	+	0.0149941i	−0.486959	+	0.873425i	$0.661894\pi$
$588$	−53177.5	−	162425.i	−0.153806	−	0.469784i
$589$	65662.1	+	113730.i	0.189271	+	0.327827i
$590$	−261401.	+	165596.i	−0.750937	+	0.475715i
$591$	−70730.4	+	66933.7i	−0.202503	+	0.191633i
$592$	−54880.7	+	146134.i	−0.156594	+	0.416972i
$593$	143639.			0.408473			0.204236	−	0.978922i	$-0.434529\pi$
$593$	143639.			0.408473			0.204236	+	0.978922i	$0.434529\pi$
$594$	627484.	+	196465.i	1.77840	+	0.556817i
$595$		−	176661.i		−	0.499008i
$596$	111007.	−	234924.i	0.312507	−	0.661356i
$597$	4994.58	+	5277.89i	0.0140136	+	0.0148085i
$598$	208279.	−	131943.i	0.582428	−	0.368965i
$599$	−305650.	+	176467.i	−0.851865	+	0.491824i	−0.861280	−	0.508131i	$-0.830336\pi$
$599$	−305650.	+	176467.i	−0.851865	+	0.491824i	0.00941494	+	0.999956i	$0.497003\pi$
$600$	52649.3	+	140949.i	0.146248	+	0.391525i
$601$	−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
$606$	−225478.	−	57162.5i	−0.613987	−	0.155656i
$607$	424309.	−	244975.i	1.15161	−	0.664881i	0.202330	−	0.979317i	$-0.435149\pi$
$607$	424309.	−	244975.i	1.15161	−	0.664881i	0.949279	+	0.314436i	$0.101815\pi$
$608$	129273.	−	115463.i	0.349703	−	0.312345i
$609$	−2773.96	+	9317.05i	−0.00747937	+	0.0251214i
$610$	78313.2	−	149507.i	0.210463	−	0.401793i
$611$		−	450342.i		−	1.20631i
$612$	109420.	−	67180.5i	0.292143	−	0.179366i
$613$	284390.			0.756821			0.378410	−	0.925638i	$-0.376471\pi$
$613$	284390.			0.756821			0.378410	+	0.925638i	$0.376471\pi$
$614$	408680.	+	214070.i	1.08404	+	0.567831i
$615$	−25687.2	−	107655.i	−0.0679151	−	0.284632i
$616$	−520965.	−	689785.i	−1.37293	−	1.81783i
$617$	−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	$0.916414\pi$
$618$	−416786.	−	405671.i	−1.09128	−	1.06218i
$619$	−58731.2	−	33908.5i	−0.153281	−	0.0884967i	0.421398	−	0.906876i	$-0.361540\pi$
$619$	−58731.2	−	33908.5i	−0.153281	−	0.0884967i	−0.574679	+	0.818379i	$0.694873\pi$
$620$	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
$624$	239067.	−	315376.i	0.613975	−	0.809952i
$625$	242826.	+	420586.i	0.621634	+	1.07670i
$626$	158687.	+	250495.i	0.404942	+	0.639219i
$627$	79725.2	+	334129.i	0.202797	+	0.849921i
$628$	−271062.	+	573647.i	−0.687306	+	1.45454i
$629$	−60410.6			−0.152691
$630$	−295876.	+	496228.i	−0.745467	+	1.25026i
$631$			716972.i			1.80071i	0.435158	+	0.900354i	$0.356692\pi$
$631$			716972.i			1.80071i	−0.435158	+	0.900354i	$0.643308\pi$
$632$	111341.	+	47118.9i	0.278754	+	0.117967i
$633$	156231.	−	524743.i	0.389907	−	1.30960i
$634$	4526.49	+	7145.27i	0.0112612	+	0.0177762i
$635$	476401.	−	275050.i	1.18148	−	0.682125i
$636$	−286674.	−	60263.6i	−0.708718	−	0.148984i
$637$	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	$0.880697\pi$
$642$	106194.	−	29998.3i	0.257650	−	0.0727825i
$643$	1326.59	−	765.910i	0.00320861	−	0.00185249i	−0.498395	−	0.866950i	$-0.666077\pi$
$643$	1326.59	−	765.910i	0.00320861	−	0.00185249i	0.501603	+	0.865098i	$0.332744\pi$
$644$	195826.	+	282723.i	0.472171	+	0.681695i
$645$	−56457.0	−	59659.4i	−0.135706	−	0.143403i
$646$	59420.6	+	31125.0i	0.142387	+	0.0745838i
$647$		−	106720.i		−	0.254938i	−0.991843	−	0.127469i	$-0.959315\pi$
$647$		−	106720.i		−	0.254938i	0.991843	−	0.127469i	$-0.0406854\pi$
$648$	−419869.	+	5445.23i	−0.999916	+	0.0129678i
$649$	−585960.			−1.39116
$650$	−83276.1	+	158982.i	−0.197103	+	0.376288i
$651$	−303786.	+	287480.i	−0.716814	+	0.678336i
$652$	−333094.	+	230715.i	−0.783560	+	0.542727i
$653$	−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	$0.920126\pi$
$654$	−173503.	−	614201.i	−0.405651	−	1.43600i
$655$	−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	0.0576633	−	0.998336i	$-0.481635\pi$
$659$	−337909.	−	195092.i	−0.778089	−	0.449230i	−0.835753	+	0.549106i	$0.814968\pi$
$660$	−198853.	+	945944.i	−0.456504	+	2.17159i
$661$	−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	$-0.337541\pi$
$662$	−48124.3	+	30486.5i	−0.109812	+	0.0695651i
$663$	146787.	+	43702.7i	0.333934	+	0.0994217i
$664$	−396879.	−	167957.i	−0.900166	−	0.380945i
$665$	−301829.			−0.682523
$666$	169689.	+	101177.i	0.382564	+	0.228104i
$667$		−	6471.12i		−	0.0145455i
$668$	402735.	+	190302.i	0.902540	+	0.426472i
$669$	93929.6	−	22412.2i	0.209870	−	0.0500763i
$670$	603060.	−	382036.i	1.34342	−	0.851048i
$671$	276780.	−	159799.i	0.614737	−	0.354919i
$672$	453244.	+	315124.i	1.00368	+	0.697820i
$673$	−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	$0.968976\pi$
$678$	−371448.	+	381626.i	−0.808051	+	0.830191i
$679$	−757142.	+	437136.i	−1.64224	+	0.948150i
$680$	113760.	+	150625.i	0.246022	+	0.325746i
$681$	662971.	−	158189.i	1.42955	−	0.341100i
$682$	−324698.	+	619878.i	−0.698089	+	1.33272i
$683$			175866.i			0.376999i	0.982073	+	0.188500i	$0.0603624\pi$
$683$			175866.i			0.376999i	−0.982073	+	0.188500i	$0.939638\pi$
$684$	−114779.	−	186946.i	−0.245330	−	0.399581i
$685$	−637265.			−1.35812
$686$	−257689.	−	134980.i	−0.547581	−	0.286828i
$687$	460330.	+	137054.i	0.975339	+	0.290387i
$688$	−60631.7	+	49832.2i	−0.128092	+	0.105277i
$689$	−174711.	−	302608.i	−0.368028	−	0.637444i
$690$	94508.7	−	372791.i	0.198506	−	0.783009i
$691$	203114.	+	117268.i	0.425386	+	0.245597i	0.697379	−	0.716702i	$-0.254349\pi$
$691$	203114.	+	117268.i	0.425386	+	0.245597i	−0.271993	+	0.962299i	$0.587683\pi$
$692$	−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
$696$	−3634.56	−	9730.18i	−0.00750296	−	0.0200864i
$697$	−20463.0	−	35442.9i	−0.0421214	−	0.0729565i
$698$	49942.0	+	78835.6i	0.102507	+	0.161812i
$699$	369245.	−	349425.i	0.755720	−	0.715154i
$700$	−226348.	−	106955.i	−0.461935	−	0.218276i
$701$	192485.			0.391707			0.195853	−	0.980633i	$-0.437252\pi$
$701$	192485.			0.391707			0.195853	+	0.980633i	$0.437252\pi$
$702$	−339119.	−	368599.i	−0.688141	−	0.747963i
$703$			103213.i			0.208844i
$704$	888369.	+	252650.i	1.79245	+	0.509770i
$705$	−482830.	−	510218.i	−0.971441	−	1.02654i
$706$	−41472.9	−	65466.7i	−0.0832060	−	0.131344i
$707$	335179.	−	193516.i	0.670561	−	0.387148i
$708$	355629.	−	116432.i	0.709464	−	0.232277i
$709$	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
$714$	−52499.4	+	207085.i	−0.102981	+	0.406211i
$715$	−998522.	+	576497.i	−1.95320	+	1.12768i
$716$	690710.	−	478415.i	1.34732	−	0.933209i
$717$	123249.	−	413965.i	0.239743	−	0.805240i
$718$	495808.	+	259708.i	0.961755	+	0.503776i
$719$		−	37302.4i		−	0.0721571i	−0.999349	−	0.0360786i	$-0.988513\pi$
$719$		−	37302.4i		−	0.0721571i	0.999349	−	0.0360786i	$-0.0114867\pi$
$720$	−67274.7	−	613622.i	−0.129774	−	1.18368i
$721$	967729.			1.86159
$722$	−188702.	+	360249.i	−0.361994	+	0.691080i
$723$	−133998.	−	561586.i	−0.256343	−	1.07433i
$724$	65806.3	+	95007.6i	0.125542	+	0.181251i
$725$	2355.23	+	4079.37i	0.00448081	+	0.00776099i
$726$	−909057.	+	933964.i	−1.72472	+	1.77197i
$727$	−647844.	−	374033.i	−1.22575	−	0.707686i	−0.259611	−	0.965713i	$-0.583594\pi$
$727$	−647844.	−	374033.i	−1.22575	−	0.707686i	−0.966138	+	0.258027i	$0.916928\pi$
$728$	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
$732$	−136230.	+	151982.i	−0.254243	+	0.283641i
$733$	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	$0.754501\pi$
$734$	309428.	−	196021.i	0.574337	−	0.363840i
$735$	−73802.7	−	309307.i	−0.136615	−	0.572552i
$736$	−349024.	−	114954.i	−0.644317	−	0.212211i
$737$	1.35183e6			2.48878
$738$	−1881.61	+	133828.i	−0.00345475	+	0.245717i
$739$			288908.i			0.529018i	0.964383	+	0.264509i	$0.0852099\pi$
$739$			288908.i			0.529018i	−0.964383	+	0.264509i	$0.914790\pi$
$740$	−124083.	+	262596.i	−0.226594	+	0.479539i
$741$	74666.8	−	250788.i	0.135985	−	0.456741i
$742$	411742.	−	260837.i	0.747855	−	0.473763i
$743$	−271416.	+	156702.i	−0.491651	+	0.283855i	−0.725259	−	0.688476i	$-0.758280\pi$
$743$	−271416.	+	156702.i	−0.491651	+	0.283855i	0.233608	+	0.972331i	$0.424947\pi$
$744$	73892.6	−	440733.i	0.133492	−	0.796213i
$745$	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
$750$	−105984.	−	375183.i	−0.188416	−	0.666992i
$751$	204539.	−	118091.i	0.362658	−	0.209381i	−0.307588	−	0.951520i	$-0.599522\pi$
$751$	204539.	−	118091.i	0.362658	−	0.209381i	0.670246	+	0.742139i	$0.266189\pi$
$752$	−518533.	+	426174.i	−0.916940	+	0.753618i
$753$	403524.	+	426413.i	0.711671	+	0.752039i
$754$	5748.83	−	10975.0i	0.0101120	−	0.0193047i
$755$		−	730134.i		−	1.28088i
$756$	494296.	−	493757.i	0.864856	−	0.863913i
$757$	−1.00219e6			−1.74888			−0.874438	−	0.485137i	$-0.838770\pi$
$757$	−1.00219e6			−1.74888			−0.874438	+	0.485137i	$0.838770\pi$
$758$	−141159.	−	73940.5i	−0.245681	−	0.128690i
$759$	528955.	−	500562.i	0.918196	−	0.868909i
$760$	257345.	−	194361.i	0.445542	−	0.336498i
$761$	−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	$-0.455608\pi$
$762$	−640181.	+	180842.i	−1.10254	+	0.311451i
$763$	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
$768$	−589368.	+	23184.0i	−0.999227	+	0.0393067i
$769$	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	$0.776883\pi$
$770$	−860689.	−	1.35863e6i	−1.45166	−	2.29151i
$771$	373634.	+	111242.i	0.628547	+	0.187137i
$772$	267183.	−	565437.i	0.448305	−	0.948744i
$773$	−661279.			−1.10669			−0.553345	−	0.832952i	$-0.686649\pi$
$773$	−661279.			−1.10669			−0.553345	+	0.832952i	$0.686649\pi$
$774$	48450.3	+	86711.2i	0.0808750	+	0.144742i
$775$			202663.i			0.337420i
$776$	364061.	−	860269.i	0.604576	−	1.42860i
$777$	−319740.	+	76292.0i	−0.529608	+	0.126368i
$778$	−461973.	−	729245.i	−0.763234	−	1.20480i
$779$	−60554.8	+	34961.3i	−0.0997869	+	0.0576120i
$780$	491468.	−	548295.i	0.807804	−	0.901208i
$781$	−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
$786$	214654.	+	208929.i	0.347451	+	0.338185i
$787$	−33656.2	+	19431.4i	−0.0543395	+	0.0313729i	−0.526924	−	0.849913i	$-0.676655\pi$
$787$	−33656.2	+	19431.4i	−0.0543395	+	0.0313729i	0.472584	+	0.881286i	$0.343321\pi$
$788$	98574.1	+	142316.i	0.158749	+	0.229193i
$789$	742405.	−	177143.i	1.19258	−	0.284557i
$790$	199265.	+	104377.i	0.319283	+	0.167243i
$791$		−	886090.i		−	1.41620i
$792$	514209.	−	1.04975e6i	0.819766	−	1.67354i
$793$	−243453.			−0.387141
$794$	−542986.	+	1.03661e6i	−0.861287	+	1.64428i
$795$	−522379.	−	155527.i	−0.826516	−	0.246078i
$796$	10619.6	−	7355.58i	0.0167603	−	0.0116089i
$797$	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	$0.664523\pi$
$798$	353807.	+	89696.1i	0.555598	+	0.140853i
$799$	−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
$804$	−820446.	+	268612.i	−1.26922	+	0.415541i
$805$	319946.	+	554163.i	0.493725	+	0.855156i
$806$	450297.	−	285261.i	0.693152	−	0.439109i
$807$	−435923.	+	412523.i	−0.669364	+	0.633433i
$808$	−161166.	+	380833.i	−0.246860	+	0.583326i
$809$	737297.			1.12654			0.563269	−	0.826274i	$-0.309544\pi$
$809$	737297.			1.12654			0.563269	+	0.826274i	$0.309544\pi$
$810$	−779398.	−	54023.7i	−1.18793	−	0.0823407i
$811$			823394.i			1.25189i	0.779867	+	0.625945i	$0.215286\pi$
$811$			823394.i			1.25189i	−0.779867	+	0.625945i	$0.784714\pi$
$812$	15625.6	+	7383.47i	0.0236987	+	0.0111982i
$813$	757341.	+	800301.i	1.14580	+	1.21080i
$814$	−464595.	+	294319.i	−0.701174	+	0.444190i
$815$	−652894.	+	376949.i	−0.982941	+	0.567501i
$816$	−88589.4	−	210371.i	−0.133046	−	0.315941i
$817$	−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	$0.0250308\pi$
$822$	747010.	+	189379.i	1.10556	+	0.280278i
$823$	400074.	−	230983.i	0.590664	−	0.341020i	−0.174696	−	0.984622i	$-0.555894\pi$
$823$	400074.	−	230983.i	0.590664	−	0.341020i	0.765360	+	0.643602i	$0.222561\pi$
$824$	−825104.	+	623166.i	−1.21522	+	0.917802i
$825$	−151267.	+	508071.i	−0.222248	+	0.746477i
$826$	−288900.	+	551537.i	−0.423435	+	0.808378i
$827$			1.11437e6i			1.62936i	0.579912	+	0.814679i	$0.303087\pi$
$827$			1.11437e6i			1.62936i	−0.579912	+	0.814679i	$0.696913\pi$
$828$	−221568.	+	408904.i	−0.323182	+	0.596432i
$829$	915553.			1.33222			0.666108	−	0.745856i	$-0.267959\pi$
$829$	915553.			1.33222			0.666108	+	0.745856i	$0.267959\pi$
$830$	−710287.	−	372055.i	−1.03105	−	0.540071i
$831$	287113.	+	1.20329e6i	0.415767	+	1.74248i
$832$	−489823.	−	505029.i	−0.707608	−	0.729574i
$833$	−58792.8	−	101832.i	−0.0847294	−	0.146756i
$834$	−470168.	−	457630.i	−0.675960	−	0.657934i
$835$	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	0.110101	−	0.993920i	$-0.464882\pi$
$839$	−489653.	−	282701.i	−0.695608	−	0.401610i	−0.805710	+	0.592311i	$0.798216\pi$
$840$	792331.	+	653556.i	1.12292	+	0.926242i
$841$	353478.	+	612242.i	0.499770	+	0.865627i
$842$	−290632.	−	458776.i	−0.409939	−	0.647107i
$843$	29250.2	+	122588.i	0.0411599	+	0.172501i
$844$	−880044.	−	415842.i	−1.23543	−	0.583772i
$845$	28047.6			0.0392810
$846$	414355.	+	741569.i	0.578938	+	1.03612i
$847$		−	2.16856e6i		−	3.02276i
$848$	−183094.	+	487534.i	−0.254615	+	0.677975i
$849$	−295460.	+	992379.i	−0.409905	+	1.37677i
$850$	55397.5	+	87447.5i	0.0766748	+	0.121035i
$851$	189500.	−	109408.i	0.261668	−	0.151074i
$852$	36716.9	−	174662.i	0.0505809	−	0.240613i
$853$	−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	$0.0551090\pi$
$858$	1.34180e6	−	379041.i	1.82269	−	0.514886i
$859$	662245.	−	382348.i	0.897496	−	0.518170i	0.0211092	−	0.999777i	$-0.493280\pi$
$859$	662245.	−	382348.i	0.897496	−	0.518170i	0.876387	+	0.481608i	$0.159947\pi$
$860$	−120040.	+	83144.9i	−0.162304	+	0.112419i
$861$	−153066.	−	161749.i	−0.206478	−	0.218190i
$862$	111059.	+	58173.5i	0.149464	+	0.0782907i
$863$			1.21817e6i			1.63564i	0.575477	+	0.817818i	$0.304817\pi$
$863$			1.21817e6i			1.63564i	−0.575477	+	0.817818i	$0.695183\pi$
$864$	−103493.	+	739287.i	−0.138638	+	0.990343i
$865$	−656551.			−0.877477
$866$	−187499.	+	357953.i	−0.250013	+	0.477299i
$867$	−481813.	+	455950.i	−0.640974	+	0.606567i
$868$	423375.	+	611246.i	0.561934	+	0.811290i
$869$	212982.	+	368895.i	0.282035	+	0.488498i
$870$	−5253.63	−	18597.8i	−0.00694099	−	0.0245710i
$871$	−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
$876$	713139.	+	149914.i	0.929321	+	0.195359i
$877$	−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	$0.928030\pi$
$878$	−614890.	+	389530.i	−0.797642	+	0.505303i
$879$	−245996.	−	73240.1i	−0.318383	−	0.0947918i
$880$	1.60873e6	+	604161.i	2.07739	+	0.780166i
$881$	−1.04312e6			−1.34395			−0.671974	−	0.740575i	$-0.734553\pi$
$881$	−1.04312e6			−1.34395			−0.671974	+	0.740575i	$0.734553\pi$
$882$	−5406.11	+	384506.i	−0.00694941	+	0.494272i
$883$		−	303710.i		−	0.389527i	−0.980850	−	0.194763i	$-0.937606\pi$
$883$		−	303710.i		−	0.389527i	0.980850	−	0.194763i	$-0.0623939\pi$
$884$	116324.	−	246175.i	0.148855	−	0.315021i
$885$	677227.	−	161591.i	0.864664	−	0.206314i
$886$	−125662.	+	79606.3i	−0.160080	+	0.101410i
$887$	587624.	−	339265.i	0.746882	−	0.431213i	−0.0776839	−	0.996978i	$-0.524752\pi$
$887$	587624.	−	339265.i	0.746882	−	0.431213i	0.824566	+	0.565765i	$0.191419\pi$
$888$	223488.	−	270943.i	0.283419	−	0.343600i
$889$	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
$894$	−407764.	+	418937.i	−0.510193	+	0.524172i
$895$	1.35385e6	−	781647.i	1.69015	−	0.975808i
$896$	675807.	−	711615.i	0.841795	−	0.886398i
$897$	−539599.	+	128752.i	−0.670636	+	0.160018i
$898$	37835.0	−	72230.6i	0.0469182	−	0.0895712i
$899$		−	13990.5i		−	0.0173107i
$900$	−9148.59	−	338414.i	−0.0112946	−	0.417795i
$901$	−201543.			−0.248267
$902$	−330050.	−	172883.i	−0.405664	−	0.212490i
$903$	−158398.	−	47159.6i	−0.194256	−	0.0578355i
$904$	570594.	+	755497.i	0.698217	+	0.924477i
$905$	107516.	+	186223.i	0.131273	+	0.227372i
$906$	−216978.	+	855873.i	−0.264338	+	1.04268i
$907$	−1.02766e6	−	593322.i	−1.24921	−	0.721233i	−0.278260	−	0.960506i	$-0.589758\pi$
$907$	−1.02766e6	−	593322.i	−1.24921	−	0.721233i	−0.970952	+	0.239273i	$0.923091\pi$
$908$	−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	0.879982	−	0.475007i	$-0.157554\pi$
$911$	754071.	+	435363.i	0.908606	+	0.524584i	0.0286234	+	0.999590i	$0.490888\pi$
$912$	−359422.	+	151356.i	−0.432131	+	0.181975i
$913$	−759181.	−	1.31494e6i	−0.910760	−	1.57748i
$914$	598635.	+	944971.i	0.716588	+	1.13117i
$915$	−275822.	+	261016.i	−0.329448	+	0.311764i
$916$	364797.	−	772016.i	0.434770	−	0.920101i
$917$	−498400.			−0.592706
$918$	−281922.	+	63092.9i	−0.334536	+	0.0748678i
$919$			60879.9i			0.0720847i	0.999350	+	0.0360423i	$0.0114751\pi$
$919$			60879.9i			0.0720847i	−0.999350	+	0.0360423i	$0.988525\pi$
$920$	−629643.	−	266462.i	−0.743907	−	0.314818i
$921$	−713491.	−	753963.i	−0.841142	−	0.888854i
$922$	343773.	+	542662.i	0.404399	+	0.638362i
$923$	184370.	−	106446.i	0.216415	−	0.124947i
$924$	605157.	+	1.84838e6i	0.708800	+	2.16495i
$925$	−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	$-0.0168246\pi$
$930$	204327.	−	805970.i	0.236244	−	0.931865i
$931$	−173982.	+	100448.i	−0.200726	+	0.115889i
$932$	−514602.	−	742955.i	−0.592434	−	0.855324i
$933$	253743.	−	852263.i	0.291495	−	0.979062i
$934$	−987846.	−	517442.i	−1.13239	−	0.593155i
$935$			665037.i			0.760717i
$936$	−739044.	+	496666.i	−0.843566	+	0.566908i
$937$	−634530.			−0.722725			−0.361362	−	0.932425i	$-0.617688\pi$
$937$	−634530.			−0.722725			−0.361362	+	0.932425i	$0.617688\pi$
$938$	666501.	−	1.27241e6i	0.757521	−	1.44618i
$939$	−154849.	−	648971.i	−0.175621	−	0.736028i
$940$	−1.02660e6	+	711070.i	−1.16184	+	0.804742i
$941$	−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	$0.845576\pi$
$942$	995695.	−	1.02298e6i	1.12208	−	1.15283i
$943$	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	0.734654	−	0.678442i	$-0.237344\pi$
$947$	461349.	+	266360.i	0.514434	+	0.297009i	−0.220220	+	0.975450i	$0.570678\pi$
$948$	−202563.	−	181568.i	−0.225394	−	0.202033i
$949$	434616.	+	752777.i	0.482585	+	0.835861i
$950$	149405.	−	94647.6i	0.165546	−	0.104873i
$951$	−4417.00	−	18511.7i	−0.00488390	−	0.0204684i
$952$	349766.	+	148019.i	0.385925	+	0.163321i
$953$	72542.5			0.0798742			0.0399371	−	0.999202i	$-0.487284\pi$
$953$	72542.5			0.0798742			0.0399371	+	0.999202i	$0.487284\pi$
$954$	566120.	+	337549.i	0.622030	+	0.370886i
$955$			315042.i			0.345432i
$956$	−694258.	−	328054.i	−0.759635	−	0.358946i
$957$	10442.5	−	35073.8i	0.0114020	−	0.0382965i
$958$	108100.	−	68481.1i	0.117787	−	0.0746173i
$959$	−1.11045e6	+	641118.i	−1.20743	+	0.697109i
$960$	−1.09641e6	−	47015.9i	−1.18968	−	0.0510155i
$961$	−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
$966$	−210361.	−	744676.i	−0.225430	−	0.798019i
$967$	−705768.	+	407475.i	−0.754760	+	0.435761i	−0.827411	−	0.561596i	$-0.810187\pi$
$967$	−705768.	+	407475.i	−0.754760	+	0.435761i	0.0726511	+	0.997357i	$0.476854\pi$
$968$	1.39643e6	+	1.84895e6i	1.49029	+	1.97322i
$969$	−103739.	−	109623.i	−0.110483	−	0.116750i
$970$	806460.	−	1.53961e6i	0.857115	−	1.63631i
$971$		−	939538.i		−	0.996496i	−0.867034	−	0.498248i	$-0.833977\pi$
$971$		−	939538.i		−	0.996496i	0.867034	−	0.498248i	$-0.166023\pi$
$972$	897566.	+	294945.i	0.950022	+	0.312183i
$973$	1.09168e6			1.15310
$974$	1.22891e6	+	643713.i	1.29539	+	0.678538i
$975$	293301.	−	277557.i	0.308535	−	0.291974i
$976$	230388.	+	280317.i	0.241858	+	0.294273i
$977$	−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	$-0.532169\pi$
$978$	877351.	−	247840.i	0.917266	−	0.259115i
$979$	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	0.940089	−	0.340929i	$-0.110741\pi$
$983$	1.07730e6	+	621978.i	1.11488	+	0.643677i	0.174792	+	0.984605i	$0.444075\pi$
$984$	234665.	+	39343.6i	0.242358	+	0.0406335i
$985$	161053.	+	278952.i	0.165995	+	0.287513i
$986$	−3824.28	−	6036.79i	−0.00393365	−	0.00620944i
$987$	−1.35465e6	−	403317.i	−1.39057	−	0.414012i
$988$	−420595.	−	198741.i	−0.430873	−	0.203598i
$989$	110014.			0.112475
$990$	1.11382e6	−	1.86804e6i	1.13643	−	1.90597i
$991$		−	766088.i		−	0.780066i	−0.920801	−	0.390033i	$-0.872464\pi$
$991$		−	766088.i		−	0.780066i	0.920801	−	0.390033i	$-0.127536\pi$
$992$	−754587.	−	248529.i	−0.766807	−	0.252554i
$993$	124678.	−	29749.1i	0.126442	−	0.0301700i
$994$	158920.	+	250863.i	0.160845	+	0.253900i
$995$	20815.3	−	12017.7i	0.0210251	−	0.0121388i
$996$	722042.	+	647207.i	0.727853	+	0.652416i
$997$	−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.7.9	yes	44
3.2	odd	2		108.5.f.a.19.14		44
4.3	odd	2	inner	36.5.f.a.7.8	✓	44
9.2	odd	6		324.5.d.e.163.2		22
9.4	even	3	inner	36.5.f.a.31.8	yes	44
9.5	odd	6		108.5.f.a.91.15		44
9.7	even	3		324.5.d.f.163.21		22
12.11	even	2		108.5.f.a.19.15		44
36.7	odd	6		324.5.d.f.163.22		22
36.11	even	6		324.5.d.e.163.1		22
36.23	even	6		108.5.f.a.91.14		44
36.31	odd	6	inner	36.5.f.a.31.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.8	✓	44	4.3	odd	2	inner
36.5.f.a.7.9	yes	44	1.1	even	1	trivial
36.5.f.a.31.8	yes	44	9.4	even	3	inner
36.5.f.a.31.9	yes	44	36.31	odd	6	inner
108.5.f.a.19.14		44	3.2	odd	2
108.5.f.a.19.15		44	12.11	even	2
108.5.f.a.91.14		44	36.23	even	6
108.5.f.a.91.15		44	9.5	odd	6
324.5.d.e.163.1		22	36.11	even	6
324.5.d.e.163.2		22	9.2	odd	6
324.5.d.f.163.21		22	9.7	even	3
324.5.d.f.163.22		22	36.7	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85603 + 3.54333i) q^{2} +(6.53699 - 6.18609i) q^{3} +(-9.11034 - 13.1530i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(9.78653 + 34.6442i) q^{6} +(-51.8739 - 29.9494i) q^{7} +(63.5145 - 7.86857i) q^{8} +(4.46449 - 80.8769i) q^{9} +O(q^{10})\)	\(q+(-1.85603 + 3.54333i) q^{2} +(6.53699 - 6.18609i) q^{3} +(-9.11034 - 13.1530i) q^{4} +(-14.8847 - 25.7811i) q^{5} +(9.78653 + 34.6442i) 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} +(-140.920 - 29.6237i) q^{12} +(-85.8824 - 148.753i) q^{13} +(202.400 - 128.219i) q^{14} +(-256.785 - 76.4524i) q^{15} +(-90.0035 + 239.657i) q^{16} -99.0725 q^{17} +(278.287 + 165.929i) q^{18} +169.267i q^{19} +(-203.494 + 430.653i) q^{20} +(-524.369 + 125.118i) q^{21} +(-761.929 + 482.678i) q^{22} +(310.777 - 179.427i) q^{23} +(366.518 - 444.343i) 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} +(747.496 - 767.976i) q^{30} +(671.898 - 387.920i) q^{31} +(-682.133 - 763.721i) q^{32} +(1973.97 - 471.003i) q^{33} +(183.881 - 351.046i) q^{34} +1783.15i q^{35} +(-1104.45 + 678.094i) q^{36} +609.762 q^{37} +(-599.768 - 314.164i) q^{38} +(-1481.61 - 441.118i) q^{39} +(-1148.25 - 1520.35i) q^{40} +(206.545 + 357.747i) q^{41} +(529.909 - 2090.23i) 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} +(894.187 + 2123.40i) q^{48} +(593.432 + 1027.85i) q^{49} +(-559.161 - 882.661i) q^{50} +(-647.636 + 612.872i) q^{51} +(-1174.13 + 2484.80i) q^{52} +2034.30 q^{53} +(2845.61 - 636.835i) q^{54} -6712.63i q^{55} +(-3530.40 - 1494.05i) q^{56} +(1047.10 + 1106.50i) q^{57} +(38.6008 + 60.9330i) q^{58} +(-2250.48 + 1299.32i) q^{59} +(1333.82 + 4074.01i) 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} +(-1994.83 + 7868.63i) q^{66} +(5191.93 - 2997.56i) q^{67} +(902.584 + 1303.10i) q^{68} +(921.593 - 3095.41i) q^{69} +(-6318.29 - 3309.57i) q^{70} +1239.44i q^{71} +(-352.826 - 5171.98i) q^{72} -5060.60 q^{73} +(-1131.73 + 2160.59i) q^{74} +(545.636 + 2286.76i) q^{75} +(2226.37 - 1542.08i) q^{76} +(-6753.22 - 11696.9i) q^{77} +(4312.93 - 4431.11i) 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} +(6422.85 + 5757.16i) q^{84} +(1474.66 + 2554.19i) q^{85} +(-1035.91 + 656.246i) q^{86} +(-37.6671 - 157.863i) q^{87} +(13290.1 + 5624.30i) q^{88} +9436.67 q^{89} +(135.598 - 9644.33i) q^{90} +10288.5i q^{91} +(-5191.29 - 2453.01i) q^{92} +(1992.48 - 6692.25i) q^{93} +(-8859.31 + 5612.33i) q^{94} +(4363.88 - 2519.49i) q^{95} +(-9183.55 - 772.696i) 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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