LMFDB - Embedded newform 45.5.k.a.7.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, 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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.20
Character	$\chi$	$=$	45.7
Dual form			45.5.k.a.13.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.12130 - 1.64020i) q^{2} +(2.33917 - 8.69070i) q^{3} +(20.9237 - 12.0803i) q^{4} +(-20.7596 + 13.9297i) q^{5} +(0.0642868 - 57.0351i) q^{6} +(76.3600 - 20.4606i) q^{7} +(36.5683 - 36.5683i) q^{8} +(-70.0566 - 40.6580i) q^{9} +(-104.228 + 119.318i) q^{10} +(-59.3466 + 102.791i) q^{11} +(-56.0421 - 210.099i) q^{12} +(-23.9591 - 6.41983i) q^{13} +(433.863 - 250.491i) q^{14} +(72.4989 + 213.000i) q^{15} +(-29.4183 + 50.9540i) q^{16} +(192.494 + 192.494i) q^{17} +(-495.524 - 133.973i) q^{18} +129.326i q^{19} +(-266.092 + 542.243i) q^{20} +(0.801944 - 711.482i) q^{21} +(-194.680 + 726.556i) q^{22} +(527.562 + 141.360i) q^{23} +(-232.264 - 403.343i) q^{24} +(236.925 - 578.352i) q^{25} -157.191 q^{26} +(-517.221 + 513.735i) q^{27} +(1350.56 - 1350.56i) q^{28} +(-1250.58 - 722.025i) q^{29} +(793.149 + 1184.92i) q^{30} +(-90.3066 - 156.416i) q^{31} +(-310.662 + 1159.41i) q^{32} +(754.506 + 756.209i) q^{33} +(1494.04 + 862.585i) q^{34} +(-1300.19 + 1488.43i) q^{35} +(-1957.00 - 4.41165i) q^{36} +(-779.690 - 779.690i) q^{37} +(212.120 + 791.641i) q^{38} +(-111.837 + 193.205i) q^{39} +(-249.758 + 1268.53i) q^{40} +(-368.068 - 637.513i) q^{41} +(-1162.06 - 4356.51i) q^{42} +(-600.059 - 2239.45i) q^{43} +2867.69i q^{44} +(2020.70 - 131.824i) q^{45} +3461.22 q^{46} +(-2215.11 + 593.536i) q^{47} +(374.012 + 374.856i) q^{48} +(3332.88 - 1924.24i) q^{49} +(501.677 - 3928.87i) q^{50} +(2123.18 - 1222.63i) q^{51} +(-578.866 + 155.107i) q^{52} +(1921.37 - 1921.37i) q^{53} +(-2323.44 + 3993.07i) q^{54} +(-199.842 - 2960.59i) q^{55} +(2044.14 - 3540.56i) q^{56} +(1123.93 + 302.515i) q^{57} +(-8839.47 - 2368.53i) q^{58} +(1869.79 - 1079.52i) q^{59} +(4090.04 + 3580.93i) q^{60} +(-1816.59 + 3146.42i) q^{61} +(-809.346 - 809.346i) q^{62} +(-6181.41 - 1671.25i) q^{63} +6665.24i q^{64} +(586.810 - 200.471i) q^{65} +(5858.89 + 3391.44i) q^{66} +(1220.93 - 4556.55i) q^{67} +(6353.05 + 1702.30i) q^{68} +(2462.57 - 4254.22i) q^{69} +(-5517.56 + 11243.7i) q^{70} +2400.17 q^{71} +(-4048.64 + 1075.05i) q^{72} +(-2342.00 + 2342.00i) q^{73} +(-6051.56 - 3493.87i) q^{74} +(-4472.08 - 3411.91i) q^{75} +(1562.29 + 2705.96i) q^{76} +(-2428.53 + 9063.40i) q^{77} +(-367.696 + 1366.10i) q^{78} +(6340.19 + 3660.51i) q^{79} +(-99.0624 - 1467.58i) q^{80} +(3254.85 + 5696.73i) q^{81} +(-3298.70 - 3298.70i) q^{82} +(1184.41 + 4420.26i) q^{83} +(-8578.12 - 14896.5i) q^{84} +(-6677.49 - 1314.71i) q^{85} +(-7346.28 - 12724.1i) q^{86} +(-9200.24 + 9179.52i) q^{87} +(1588.70 + 5929.10i) q^{88} +11661.0i q^{89} +(12153.1 - 4121.29i) q^{90} -1960.87 q^{91} +(12746.2 - 3415.33i) q^{92} +(-1570.60 + 418.945i) q^{93} +(-12585.8 + 7266.42i) q^{94} +(-1801.47 - 2684.75i) q^{95} +(9349.37 + 5411.92i) q^{96} +(12098.3 - 3241.73i) q^{97} +(17245.4 - 17245.4i) q^{98} +(8336.91 - 4788.29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) $ 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	6.12130	−	1.64020i	1.53032	−	0.410049i	0.607200	−	0.794549i	$-0.292293\pi$
$2$	6.12130	−	1.64020i	1.53032	−	0.410049i	0.923125	+	0.384500i	$0.125626\pi$
$3$	2.33917	−	8.69070i	0.259908	−	0.965633i
$3$	2.33917	−	8.69070i	0.259908	−	0.965633i
$4$	20.9237	−	12.0803i	1.30773	−	0.755017i
$5$	−20.7596	+	13.9297i	−0.830385	+	0.557189i
$5$	−20.7596	+	13.9297i	−0.830385	+	0.557189i
$6$	0.0642868	−	57.0351i	0.00178574	−	1.58431i
$7$	76.3600	−	20.4606i	1.55837	−	0.417563i	0.626221	−	0.779646i	$-0.284601\pi$
$7$	76.3600	−	20.4606i	1.55837	−	0.417563i	0.932146	+	0.362083i	$0.117934\pi$
$8$	36.5683	−	36.5683i	0.571379	−	0.571379i
$9$	−70.0566	−	40.6580i	−0.864896	−	0.501951i
$10$	−104.228	+	119.318i	−1.04228	+	1.19318i
$11$	−59.3466	+	102.791i	−0.490467	+	0.849514i	−0.999940	−	0.0109726i	$-0.996507\pi$
$11$	−59.3466	+	102.791i	−0.490467	+	0.849514i	0.509472	+	0.860487i	$0.329841\pi$
$12$	−56.0421	−	210.099i	−0.389181	−	1.45902i
$13$	−23.9591	−	6.41983i	−0.141770	−	0.0379872i	0.187236	−	0.982315i	$-0.440047\pi$
$13$	−23.9591	−	6.41983i	−0.141770	−	0.0379872i	−0.329006	+	0.944328i	$0.606714\pi$
$14$	433.863	−	250.491i	2.21359	−	1.27801i
$15$	72.4989	+	213.000i	0.322217	+	0.946666i
$16$	−29.4183	+	50.9540i	−0.114915	+	0.199039i
$17$	192.494	+	192.494i	0.666069	+	0.666069i	0.956804	−	0.290735i	$-0.0938998\pi$
$17$	192.494	+	192.494i	0.666069	+	0.666069i	−0.290735	+	0.956804i	$0.593900\pi$
$18$	−495.524	−	133.973i	−1.52940	−	0.413498i
$19$			129.326i			0.358243i	0.983827	+	0.179121i	$0.0573255\pi$
$19$			129.326i			0.358243i	−0.983827	+	0.179121i	$0.942675\pi$
$20$	−266.092	+	542.243i	−0.665231	+	1.35561i
$21$	0.801944	−	711.482i	0.00181847	−	1.61334i
$22$	−194.680	+	726.556i	−0.402232	+	1.50115i
$23$	527.562	+	141.360i	0.997281	+	0.267221i	0.720306	−	0.693657i	$-0.244001\pi$
$23$	527.562	+	141.360i	0.997281	+	0.267221i	0.276975	+	0.960877i	$0.410668\pi$
$24$	−232.264	−	403.343i	−0.403237	−	0.700248i
$25$	236.925	−	578.352i	0.379080	−	0.925364i
$26$	−157.191			−0.232531
$27$	−517.221	+	513.735i	−0.709494	+	0.704712i
$28$	1350.56	−	1350.56i	1.72265	−	1.72265i
$29$	−1250.58	−	722.025i	−1.48702	−	0.858532i	−0.487131	−	0.873329i	$-0.661956\pi$
$29$	−1250.58	−	722.025i	−1.48702	−	0.858532i	−0.999891	+	0.0147970i	$0.995290\pi$
$30$	793.149	+	1184.92i	0.881277	+	1.31658i
$31$	−90.3066	−	156.416i	−0.0939715	−	0.162763i	0.815207	−	0.579169i	$-0.196623\pi$
$31$	−90.3066	−	156.416i	−0.0939715	−	0.162763i	−0.909179	+	0.416406i	$0.863290\pi$
$32$	−310.662	+	1159.41i	−0.303381	+	1.13223i
$33$	754.506	+	756.209i	0.692843	+	0.694407i
$34$	1494.04	+	862.585i	1.29242	+	0.746180i
$35$	−1300.19	+	1488.43i	−1.06138	+	1.21504i
$36$	−1957.00	−	4.41165i	−1.51003	−	0.00340405i
$37$	−779.690	−	779.690i	−0.569532	−	0.569532i	0.362465	−	0.931997i	$-0.381935\pi$
$37$	−779.690	−	779.690i	−0.569532	−	0.569532i	−0.931997	+	0.362465i	$0.881935\pi$
$38$	212.120	+	791.641i	0.146897	+	0.548228i
$39$	−111.837	+	193.205i	−0.0735288	+	0.127025i
$40$	−249.758	+	1268.53i	−0.156098	+	0.792831i
$41$	−368.068	−	637.513i	−0.218958	−	0.379246i	0.735532	−	0.677490i	$-0.236932\pi$
$41$	−368.068	−	637.513i	−0.218958	−	0.379246i	−0.954490	+	0.298244i	$0.903599\pi$
$42$	−1162.06	−	4356.51i	−0.658766	−	2.46968i
$43$	−600.059	−	2239.45i	−0.324532	−	1.21117i	−0.914782	−	0.403948i	$-0.867638\pi$
$43$	−600.059	−	2239.45i	−0.324532	−	1.21117i	0.590250	−	0.807220i	$-0.299029\pi$
$44$			2867.69i			1.48125i
$45$	2020.70	−	131.824i	0.997879	−	0.0650981i
$46$	3461.22			1.63574
$47$	−2215.11	+	593.536i	−1.00276	+	0.268690i	−0.722603	−	0.691263i	$-0.757055\pi$
$47$	−2215.11	+	593.536i	−1.00276	+	0.268690i	−0.280161	+	0.959953i	$0.590388\pi$
$48$	374.012	+	374.856i	0.162331	+	0.162698i
$49$	3332.88	−	1924.24i	1.38812	−	0.801433i
$50$	501.677	−	3928.87i	0.200671	−	1.57155i
$51$	2123.18	−	1222.63i	0.816294	−	0.470062i
$52$	−578.866	+	155.107i	−0.214078	+	0.0573619i
$53$	1921.37	−	1921.37i	0.684005	−	0.684005i	−0.276895	−	0.960900i	$-0.589305\pi$
$53$	1921.37	−	1921.37i	0.684005	−	0.684005i	0.960900	+	0.276895i	$0.0893054\pi$
$54$	−2323.44	+	3993.07i	−0.796789	+	1.36937i
$55$	−199.842	−	2960.59i	−0.0660634	−	0.978708i
$56$	2044.14	−	3540.56i	0.651831	−	1.12900i
$57$	1123.93	+	302.515i	0.345931	+	0.0931100i
$58$	−8839.47	−	2368.53i	−2.62767	−	0.704081i
$59$	1869.79	−	1079.52i	0.537141	−	0.310119i	−0.206778	−	0.978388i	$-0.566298\pi$
$59$	1869.79	−	1079.52i	0.537141	−	0.310119i	0.743920	+	0.668269i	$0.232965\pi$
$60$	4090.04	+	3580.93i	1.13612	+	0.994702i
$61$	−1816.59	+	3146.42i	−0.488198	+	0.845584i	−0.999908	−	0.0135745i	$-0.995679\pi$
$61$	−1816.59	+	3146.42i	−0.488198	+	0.845584i	0.511710	+	0.859158i	$0.329012\pi$
$62$	−809.346	−	809.346i	−0.210548	−	0.210548i
$63$	−6181.41	−	1671.25i	−1.55742	−	0.421075i
$64$			6665.24i			1.62726i
$65$	586.810	−	200.471i	0.138890	−	0.0474488i
$66$	5858.89	+	3391.44i	1.34502	+	0.778568i
$67$	1220.93	−	4556.55i	0.271982	−	1.01505i	−0.685856	−	0.727738i	$-0.740572\pi$
$67$	1220.93	−	4556.55i	0.271982	−	1.01505i	0.957837	−	0.287311i	$-0.0927614\pi$
$68$	6353.05	+	1702.30i	1.37393	+	0.368143i
$69$	2462.57	−	4254.22i	0.517238	−	0.893555i
$70$	−5517.56	+	11243.7i	−1.12603	+	2.29463i
$71$	2400.17			0.476129			0.238065	−	0.971249i	$-0.423487\pi$
$71$	2400.17			0.476129			0.238065	+	0.971249i	$0.423487\pi$
$72$	−4048.64	+	1075.05i	−0.780988	+	0.207379i
$73$	−2342.00	+	2342.00i	−0.439483	+	0.439483i	−0.891838	−	0.452355i	$-0.850584\pi$
$73$	−2342.00	+	2342.00i	−0.439483	+	0.439483i	0.452355	+	0.891838i	$0.350584\pi$
$74$	−6051.56	−	3493.87i	−1.10511	−	0.638033i
$75$	−4472.08	−	3411.91i	−0.795037	−	0.606561i
$76$	1562.29	+	2705.96i	0.270479	+	0.468484i
$77$	−2428.53	+	9063.40i	−0.409602	+	1.52866i
$78$	−367.696	+	1366.10i	−0.0604365	+	0.224540i
$79$	6340.19	+	3660.51i	1.01589	+	0.586526i	0.912912	−	0.408157i	$-0.133828\pi$
$79$	6340.19	+	3660.51i	1.01589	+	0.586526i	0.102982	+	0.994683i	$0.467162\pi$
$80$	−99.0624	−	1467.58i	−0.0154785	−	0.229309i
$81$	3254.85	+	5696.73i	0.496090	+	0.868271i
$82$	−3298.70	−	3298.70i	−0.490587	−	0.490587i
$83$	1184.41	+	4420.26i	0.171927	+	0.641641i	0.997055	+	0.0766942i	$0.0244365\pi$
$83$	1184.41	+	4420.26i	0.171927	+	0.641641i	−0.825128	+	0.564946i	$0.808897\pi$
$84$	−8578.12	−	14896.5i	−1.21572	−	2.11118i
$85$	−6677.49	−	1314.71i	−0.924220	−	0.181967i
$86$	−7346.28	−	12724.1i	−0.993277	−	1.72041i
$87$	−9200.24	+	9179.52i	−1.21552	+	1.21278i
$88$	1588.70	+	5929.10i	0.205152	+	0.765637i
$89$			11661.0i			1.47216i	0.676895	+	0.736079i	$0.263325\pi$
$89$			11661.0i			1.47216i	−0.676895	+	0.736079i	$0.736675\pi$
$90$	12153.1	−	4121.29i	1.50039	−	0.508801i
$91$	−1960.87			−0.236792
$92$	12746.2	−	3415.33i	1.50593	−	0.403512i
$93$	−1570.60	+	418.945i	−0.181594	+	0.0484386i
$94$	−12585.8	+	7266.42i	−1.42438	+	0.822366i
$95$	−1801.47	−	2684.75i	−0.199609	−	0.297480i
$96$	9349.37	+	5411.92i	1.01447	+	0.587231i
$97$	12098.3	−	3241.73i	1.28582	−	0.344535i	0.449749	−	0.893155i	$-0.351513\pi$
$97$	12098.3	−	3241.73i	1.28582	−	0.344535i	0.836072	+	0.548620i	$0.184847\pi$
$98$	17245.4	−	17245.4i	1.79565	−	1.79565i
$99$	8336.91	−	4788.29i	0.850618	−	0.488551i
$100$	−2029.32	−	14963.4i	−0.202932	−	1.49634i
$101$	−1738.66	+	3011.46i	−0.170441	+	0.295212i	−0.938574	−	0.345078i	$-0.887852\pi$
$101$	−1738.66	+	3011.46i	−0.170441	+	0.295212i	0.768133	+	0.640290i	$0.221186\pi$
$102$	10991.3	−	10966.5i	1.05645	−	1.05407i
$103$	3361.04	+	900.588i	0.316810	+	0.0848890i	0.413720	−	0.910404i	$-0.364229\pi$
$103$	3361.04	+	900.588i	0.316810	+	0.0848890i	−0.0969099	+	0.995293i	$0.530896\pi$
$104$	−1110.91	+	641.382i	−0.102710	+	0.0592994i
$105$	9894.11	+	14781.3i	0.897425	+	1.34071i
$106$	8609.86	−	14912.7i	0.766275	−	1.32723i
$107$	−5567.92	−	5567.92i	−0.486323	−	0.486323i	0.420821	−	0.907144i	$-0.361742\pi$
$107$	−5567.92	−	5567.92i	−0.486323	−	0.486323i	−0.907144	+	0.420821i	$0.861742\pi$
$108$	−4616.09	+	16997.4i	−0.395756	+	1.45725i
$109$		−	15519.4i		−	1.30624i	−0.757256	−	0.653119i	$-0.773460\pi$
$109$		−	15519.4i		−	1.30624i	0.757256	−	0.653119i	$-0.226540\pi$
$110$	−6079.24	−	17794.9i	−0.502417	−	1.47065i
$111$	−8599.88	+	4952.23i	−0.697985	+	0.401934i
$112$	−1203.83	+	4492.76i	−0.0959688	+	0.358160i
$113$	−11644.5	−	3120.14i	−0.911936	−	0.244353i	−0.227801	−	0.973708i	$-0.573154\pi$
$113$	−11644.5	−	3120.14i	−0.911936	−	0.244353i	−0.684135	+	0.729355i	$0.739820\pi$
$114$	7376.10	+	8.31393i	0.567567	+	0.000639730i
$115$	−12921.1	+	4414.22i	−0.977020	+	0.333778i
$116$	−34889.1			−2.59283
$117$	1417.48	+	1423.88i	0.103549	+	0.104017i
$118$	9674.91	−	9674.91i	0.694837	−	0.694837i
$119$	18637.4	+	10760.3i	1.31610	+	0.759854i
$120$	10440.2	+	5137.87i	0.725013	+	0.356797i
$121$	276.473	+	478.866i	0.0188835	+	0.0327072i
$122$	−5959.12	+	22239.7i	−0.400371	+	1.49420i
$123$	−6401.41	+	1707.52i	−0.423122	+	0.112864i
$124$	−3779.09	−	2181.86i	−0.245778	−	0.141900i
$125$	3137.82	+	15306.7i	0.200820	+	0.979628i
$126$	−40579.4	−	91.4778i	−2.55602	−	0.00576202i
$127$	3421.89	+	3421.89i	0.212158	+	0.212158i	0.805183	−	0.593026i	$-0.202067\pi$
$127$	3421.89	+	3421.89i	0.212158	+	0.212158i	−0.593026	+	0.805183i	$0.702067\pi$
$128$	5961.71	+	22249.4i	0.363874	+	1.35800i
$129$	−20866.0	−	23.5190i	−1.25389	−	0.00141332i
$130$	3263.22	−	2189.63i	0.193090	−	0.129564i
$131$	−6806.61	−	11789.4i	−0.396633	−	0.686988i	0.596675	−	0.802483i	$-0.296488\pi$
$131$	−6806.61	−	11789.4i	−0.396633	−	0.686988i	−0.993308	+	0.115495i	$0.963155\pi$
$132$	24922.2	+	6708.01i	1.43034	+	0.384987i
$133$	2646.08	+	9875.30i	0.149589	+	0.558274i
$134$		−	29894.6i		−	1.66488i
$135$	3581.13	−	17869.7i	0.196495	−	0.980505i
$136$	14078.3			0.761155
$137$	2159.53	−	578.645i	0.115058	−	0.0308298i	−0.200830	−	0.979626i	$-0.564364\pi$
$137$	2159.53	−	578.645i	0.115058	−	0.0308298i	0.315889	+	0.948796i	$0.397697\pi$
$138$	8096.38	−	30080.4i	0.425141	−	1.57952i
$139$	18980.7	−	10958.5i	0.982388	−	0.567182i	0.0793979	−	0.996843i	$-0.474700\pi$
$139$	18980.7	−	10958.5i	0.982388	−	0.567182i	0.902990	+	0.429661i	$0.141367\pi$
$140$	−9224.19	+	46850.1i	−0.470622	+	2.39031i
$141$	−23.2634	+	20639.2i	−0.00117013	+	1.03814i
$142$	14692.1	−	3936.75i	0.728632	−	0.195236i
$143$	2081.79	−	2081.79i	0.101804	−	0.101804i
$144$	4132.64	−	2373.57i	0.199298	−	0.114466i
$145$	36019.3	−	2431.33i	1.71317	−	0.115640i
$146$	−10494.8	+	18177.4i	−0.492342	+	0.852761i
$147$	−8926.83	−	33466.2i	−0.413107	−	1.54872i
$148$	−25732.8	−	6895.09i	−1.17480	−	0.314787i
$149$	5737.43	−	3312.51i	0.258431	−	0.149205i	−0.365187	−	0.930934i	$-0.618995\pi$
$149$	5737.43	−	3312.51i	0.258431	−	0.149205i	0.623619	+	0.781729i	$0.285662\pi$
$150$	−32971.1	−	13550.2i	−1.46538	−	0.602232i
$151$	−4922.16	+	8525.43i	−0.215875	+	0.373906i	−0.953543	−	0.301258i	$-0.902594\pi$
$151$	−4922.16	+	8525.43i	−0.215875	+	0.373906i	0.737668	+	0.675163i	$0.235927\pi$
$152$	4729.21	+	4729.21i	0.204692	+	0.204692i
$153$	−5659.04	−	21311.9i	−0.241746	−	0.910414i
$154$			59463.1i			2.50730i
$155$	4053.56	+	1989.18i	0.168723	+	0.0827965i
$156$	−6.07934	+	5393.57i	−0.000249808	+	0.221629i
$157$	−6069.32	+	22651.0i	−0.246230	+	0.918943i	0.726531	+	0.687133i	$0.241131\pi$
$157$	−6069.32	+	22651.0i	−0.246230	+	0.918943i	−0.972761	+	0.231809i	$0.925535\pi$
$158$	44814.2	+	12007.9i	1.79515	+	0.481009i
$159$	−12203.7	−	21192.5i	−0.482720	−	0.838277i
$160$	−9701.00	−	28396.3i	−0.378945	−	1.10923i
$161$	43176.9			1.66571
$162$	29267.7	+	29532.8i	1.11521	+	1.12531i
$163$	−20736.6	+	20736.6i	−0.780483	+	0.780483i	−0.979912	−	0.199430i	$-0.936091\pi$
$163$	−20736.6	+	20736.6i	−0.780483	+	0.780483i	0.199430	+	0.979912i	$0.436091\pi$
$164$	−15402.7	−	8892.74i	−0.572675	−	0.330634i
$165$	−26197.1	−	5188.55i	−0.962243	−	0.190580i
$166$	14500.2	+	25115.1i	0.526209	+	0.911420i
$167$	4853.83	−	18114.7i	0.174041	−	0.649529i	−0.822672	−	0.568516i	$-0.807518\pi$
$167$	4853.83	−	18114.7i	0.174041	−	0.649529i	0.996713	−	0.0810133i	$-0.0258156\pi$
$168$	−25988.3	−	26047.0i	−0.920789	−	0.922867i
$169$	−24201.7	−	13972.9i	−0.847370	−	0.489229i
$170$	−43031.3	+	2904.64i	−1.48897	+	0.100507i
$171$	5258.13	−	9060.11i	0.179820	−	0.309843i
$172$	−39608.6	−	39608.6i	−1.33885	−	1.33885i
$173$	7407.64	+	27645.7i	0.247507	+	0.923709i	0.972107	+	0.234539i	$0.0753581\pi$
$173$	7407.64	+	27645.7i	0.247507	+	0.923709i	−0.724600	+	0.689170i	$0.757975\pi$
$174$	−41261.2	+	71280.8i	−1.36283	+	2.35437i
$175$	6258.15	−	49010.6i	0.204348	−	1.60035i
$176$	−3491.75	−	6047.89i	−0.112724	−	0.195244i
$177$	−5008.06	−	18775.0i	−0.159854	−	0.599284i
$178$	19126.3	+	71380.3i	0.603658	+	2.25288i
$179$		−	45816.0i		−	1.42992i	−0.699167	−	0.714958i	$-0.746446\pi$
$179$		−	45816.0i		−	1.42992i	0.699167	−	0.714958i	$-0.253554\pi$
$180$	40688.1	−	27168.9i	1.25580	−	0.838546i
$181$	32346.3			0.987343			0.493671	−	0.869649i	$-0.335655\pi$
$181$	32346.3			0.987343			0.493671	+	0.869649i	$0.335655\pi$
$182$	−12003.1	+	3216.22i	−0.362368	+	0.0970963i
$183$	23095.3	+	23147.4i	0.689638	+	0.691194i
$184$	24461.3	−	14122.7i	0.722510	−	0.417141i
$185$	27047.0	+	5325.21i	0.790269	+	0.155594i
$186$	−8926.99	+	5140.59i	−0.258035	+	0.148589i
$187$	−31210.5	+	8362.84i	−0.892520	+	0.239150i
$188$	−39178.0	+	39178.0i	−1.10848	+	1.10848i
$189$	−28983.7	+	49811.4i	−0.811390	+	1.39446i
$190$	−15430.9	−	13479.4i	−0.427448	−	0.373391i
$191$	11348.8	−	19656.8i	0.311089	−	0.538822i	−0.667509	−	0.744601i	$-0.732640\pi$
$191$	11348.8	−	19656.8i	0.311089	−	0.538822i	0.978598	+	0.205779i	$0.0659729\pi$
$192$	57925.6	+	15591.1i	1.57133	+	0.422936i
$193$	−18890.7	−	5061.74i	−0.507146	−	0.135889i	−0.00383125	−	0.999993i	$-0.501220\pi$
$193$	−18890.7	−	5061.74i	−0.507146	−	0.135889i	−0.503314	+	0.864103i	$0.667886\pi$
$194$	68740.2	−	39687.1i	1.82645	−	1.05450i
$195$	−369.588	−	5568.72i	−0.00971960	−	0.146449i
$196$	46490.7	−	80524.3i	1.21019	−	2.09611i
$197$	34046.6	+	34046.6i	0.877285	+	0.877285i	0.993253	−	0.115968i	$-0.0369969\pi$
$197$	34046.6	+	34046.6i	0.877285	+	0.877285i	−0.115968	+	0.993253i	$0.536997\pi$
$198$	43179.0	−	42984.7i	1.10139	−	1.09644i
$199$			29758.3i			0.751454i	0.926730	+	0.375727i	$0.122607\pi$
$199$			29758.3i			0.751454i	−0.926730	+	0.375727i	$0.877393\pi$
$200$	−12485.4	−	29813.3i	−0.312135	−	0.745332i
$201$	−36743.7	−	21269.2i	−0.909475	−	0.526453i
$202$	−5703.51	+	21285.8i	−0.139778	+	0.521659i
$203$	−110268.	−	29546.1i	−2.67582	−	0.716983i
$204$	29655.0	−	51230.5i	0.712586	−	1.23103i
$205$	16521.4	+	8107.45i	0.393132	+	0.192920i
$206$	22051.1			0.519631
$207$	−31211.7	−	31352.8i	−0.728413	−	0.731704i
$208$	1031.95	−	1031.95i	0.0238525	−	0.0238525i
$209$	−13293.5	−	7675.03i	−0.304332	−	0.175706i
$210$	84809.1	+	74252.4i	1.92311	+	1.68373i
$211$	22206.3	+	38462.4i	0.498782	+	0.863916i	0.999999	−	0.00140548i	$-0.000447379\pi$
$211$	22206.3	+	38462.4i	0.498782	+	0.863916i	−0.501217	+	0.865322i	$0.667114\pi$
$212$	16991.4	−	63412.8i	0.378057	−	1.41093i
$213$	5614.39	−	20859.1i	0.123750	−	0.459766i
$214$	−43215.4	−	24950.4i	−0.943649	−	0.544816i
$215$	43651.9	+	38131.5i	0.944336	+	0.824911i
$216$	−127.481	+	37700.3i	−0.00273237	+	0.808047i
$217$	−10096.2	−	10096.2i	−0.214406	−	0.214406i
$218$	−25454.9	−	94998.9i	−0.535622	−	1.99897i
$219$	14875.3	+	25832.0i	0.310154	+	0.538604i
$220$	−39946.2	−	59532.2i	−0.825334	−	1.23000i
$221$	−3376.21	−	5847.76i	−0.0691265	−	0.119731i
$222$	−44519.8	+	44419.6i	−0.903332	+	0.901298i
$223$	−99.1807	−	370.148i	−0.00199442	−	0.00744329i	0.964921	−	0.262539i	$-0.0845598\pi$
$223$	−99.1807	−	370.148i	−0.00199442	−	0.00744329i	−0.966916	+	0.255095i	$0.917893\pi$
$224$			94888.6i			1.89112i
$225$	−40112.8	+	30884.5i	−0.792352	+	0.610064i
$226$	−76397.2			−1.49576
$227$	−49850.8	+	13357.5i	−0.967431	+	0.259222i	−0.707743	−	0.706470i	$-0.750286\pi$
$227$	−49850.8	+	13357.5i	−0.967431	+	0.259222i	−0.259688	+	0.965692i	$0.583620\pi$
$228$	27171.2	−	7247.68i	0.522684	−	0.139421i
$229$	16793.7	−	9695.84i	0.320240	−	0.184891i	−0.331260	−	0.943540i	$-0.607474\pi$
$229$	16793.7	−	9695.84i	0.320240	−	0.184891i	0.651499	+	0.758649i	$0.274140\pi$
$230$	−71853.7	+	48213.9i	−1.35829	+	0.911415i
$231$	73086.6	+	42306.5i	1.36966	+	0.792835i
$232$	−72134.9	+	19328.5i	−1.34020	+	0.359105i
$233$	19744.0	−	19744.0i	0.363683	−	0.363683i	−0.501484	−	0.865167i	$-0.667212\pi$
$233$	19744.0	−	19744.0i	0.363683	−	0.363683i	0.865167	+	0.501484i	$0.167212\pi$
$234$	11012.3	+	6391.07i	0.201115	+	0.116719i
$235$	37717.0	−	43177.4i	0.682970	−	0.781846i
$236$	26081.9	−	45175.1i	0.468290	−	0.811102i
$237$	46643.2	−	46538.2i	0.830408	−	0.828538i
$238$	131734.	+	35298.0i	2.32565	+	0.623155i
$239$	5365.08	−	3097.53i	0.0939248	−	0.0542275i	−0.452302	−	0.891865i	$-0.649397\pi$
$239$	5365.08	−	3097.53i	0.0939248	−	0.0542275i	0.546227	+	0.837637i	$0.316064\pi$
$240$	−12986.0	−	2571.99i	−0.225451	−	0.0446525i
$241$	27498.9	−	47629.4i	0.473457	−	0.820052i	−0.526081	−	0.850434i	$-0.676339\pi$
$241$	27498.9	−	47629.4i	0.473457	−	0.820052i	0.999538	+	0.0303824i	$0.00967250\pi$
$242$	2477.81	+	2477.81i	0.0423095	+	0.0423095i
$243$	57122.2	−	14961.3i	0.967369	−	0.253371i
$244$			87779.4i			1.47439i
$245$	−42385.3	+	86372.7i	−0.706127	+	1.43895i
$246$	−36384.3	+	20951.8i	−0.601234	+	0.346220i
$247$	830.249	−	3098.53i	0.0136086	−	0.0507881i
$248$	−9022.20	−	2417.49i	−0.146693	−	0.0393063i
$249$	41185.7	+	46.4222i	0.664275	+	0.000748734i
$250$	44313.5	+	88550.2i	0.709016	+	1.41680i
$251$	−104801.			−1.66348			−0.831738	−	0.555168i	$-0.812654\pi$
$251$	−104801.			−1.66348			−0.831738	+	0.555168i	$0.812654\pi$
$252$	−149527.	+	39704.5i	−2.35460	+	0.625228i
$253$	−45839.5	+	45839.5i	−0.716141	+	0.716141i
$254$	26559.0	+	15333.8i	0.411665	+	0.237675i
$255$	−27045.6	+	54956.7i	−0.415926	+	0.845163i
$256$	19664.9	+	34060.6i	0.300063	+	0.519724i
$257$	17482.3	−	65245.0i	0.264688	−	0.987827i	−0.697754	−	0.716338i	$-0.745817\pi$
$257$	17482.3	−	65245.0i	0.264688	−	0.987827i	0.962441	−	0.271490i	$-0.0875163\pi$
$258$	−127766.	+	34080.4i	−1.91944	+	0.511995i
$259$	−75490.0	−	43584.2i	−1.12536	−	0.649725i
$260$	9856.45	−	11283.4i	0.145806	−	0.166914i
$261$	58255.6	+	101429.i	0.855178	+	1.48895i
$262$	−61002.3	−	61002.3i	−0.888676	−	0.888676i
$263$	−7192.99	−	26844.6i	−0.103992	−	0.388102i	0.894237	−	0.447593i	$-0.147719\pi$
$263$	−7192.99	−	26844.6i	−0.103992	−	0.388102i	−0.998229	+	0.0594916i	$0.981052\pi$
$264$	55244.2	+	62.2682i	0.792646	+	0.000893426i
$265$	−13122.8	+	66651.2i	−0.186868	+	0.949109i
$266$	32394.9	+	56109.6i	0.457839	+	0.793001i
$267$	101342.	+	27277.0i	1.42157	+	0.382625i
$268$	−29498.2	−	110089.i	−0.410701	−	1.53276i
$269$		−	37997.6i		−	0.525112i	−0.964917	−	0.262556i	$-0.915435\pi$
$269$		−	37997.6i		−	0.525112i	0.964917	−	0.262556i	$-0.0845654\pi$
$270$	−7388.67	−	115260.i	−0.101353	−	1.58106i
$271$	−127096.			−1.73059			−0.865293	−	0.501267i	$-0.832867\pi$
$271$	−127096.			−1.73059			−0.865293	+	0.501267i	$0.832867\pi$
$272$	−15471.2	+	4145.49i	−0.209115	+	0.0560322i
$273$	−4586.81	+	17041.4i	−0.0615440	+	0.228654i
$274$	12270.1	−	7084.12i	0.163435	−	0.0943593i
$275$	45388.9	+	58677.0i	0.600184	+	0.775895i
$276$	133.862	−	118762.i	0.00175728	−	1.55905i
$277$	84525.9	−	22648.7i	1.10162	−	0.295177i	0.338194	−	0.941076i	$-0.390184\pi$
$277$	84525.9	−	22648.7i	1.10162	−	0.295177i	0.763423	+	0.645899i	$0.223517\pi$
$278$	98212.5	−	98212.5i	1.27080	−	1.27080i
$279$	−32.9795	+	14629.6i	−0.000423677	+	0.187943i
$280$	6883.39	+	101975.i	0.0877983	+	1.30070i
$281$	46420.3	−	80402.3i	0.587889	−	1.01825i	−0.406620	−	0.913597i	$-0.633293\pi$
$281$	46420.3	−	80402.3i	0.587889	−	1.01825i	0.994509	−	0.104656i	$-0.0333740\pi$
$282$	33710.0	+	126377.i	0.423897	+	1.58917i
$283$	−50067.3	−	13415.5i	−0.625146	−	0.167507i	−0.0676798	−	0.997707i	$-0.521560\pi$
$283$	−50067.3	−	13415.5i	−0.625146	−	0.167507i	−0.557466	+	0.830200i	$0.688226\pi$
$284$	50220.2	−	28994.7i	0.622647	−	0.359486i
$285$	−27546.3	+	9375.97i	−0.339136	+	0.115432i
$286$	9328.74	−	16157.8i	0.114049	−	0.197538i
$287$	−41149.6	−	41149.6i	−0.499576	−	0.499576i
$288$	68903.2	−	68593.2i	0.830719	−	0.826982i
$289$		−	9413.25i		−	0.112705i
$290$	216497.	−	73961.7i	2.57428	−	0.879449i
$291$	127.058	−	112726.i	0.00150043	−	1.33118i
$292$	−20711.2	+	77295.3i	−0.242907	+	0.906541i
$293$	144202.	+	38638.8i	1.67972	+	0.450079i	0.967704	−	0.252088i	$-0.0811172\pi$
$293$	144202.	+	38638.8i	1.67972	+	0.450079i	0.712013	+	0.702167i	$0.247784\pi$
$294$	−109535.	−	190215.i	−1.26724	−	2.20064i
$295$	−23778.7	+	48456.2i	−0.273239	+	0.556807i
$296$	−57023.8			−0.650838
$297$	−22112.2	−	83654.2i	−0.250679	−	0.948363i
$298$	29687.4	−	29687.4i	0.334302	−	0.334302i
$299$	−11732.4	−	6773.71i	−0.131234	−	0.0757678i
$300$	−134789.	−	17365.6i	−1.49766	−	0.192951i
$301$	−91640.9	−	158727.i	−1.01148	−	1.75193i
$302$	−16146.6	+	60260.0i	−0.177039	+	0.660717i
$303$	22104.6	+	22154.5i	0.240768	+	0.241311i
$304$	−6589.66	−	3804.54i	−0.0713043	−	0.0411676i
$305$	−6117.12	−	90623.0i	−0.0657578	−	0.974179i
$306$	−69596.4	−	121174.i	−0.743265	−	1.29410i
$307$	121429.	+	121429.i	1.28839	+	1.28839i	0.935765	+	0.352626i	$0.114711\pi$
$307$	121429.	+	121429.i	1.28839	+	1.28839i	0.352626	+	0.935765i	$0.385289\pi$
$308$	58674.7	+	218977.i	0.618513	+	2.30832i
$309$	15688.8	−	27103.2i	0.164313	−	0.283859i
$310$	28075.7	+	5527.76i	0.292151	+	0.0575209i
$311$	10591.5	+	18344.9i	0.109505	+	0.189669i	0.915570	−	0.402159i	$-0.131740\pi$
$311$	10591.5	+	18344.9i	0.109505	+	0.189669i	−0.806065	+	0.591827i	$0.798407\pi$
$312$	2975.46	+	11154.9i	0.0305665	+	0.114592i
$313$	26039.8	+	97181.9i	0.265797	+	0.991966i	0.961761	+	0.273890i	$0.0883104\pi$
$313$	26039.8	+	97181.9i	0.265797	+	0.991966i	−0.695965	+	0.718076i	$0.745023\pi$
$314$			148609.i			1.50725i
$315$	151604.	−	51410.9i	1.52788	−	0.518124i
$316$	176880.			1.77135
$317$	−189428.	+	50757.2i	−1.88507	+	0.505102i	−0.885917	+	0.463844i	$0.846470\pi$
$317$	−189428.	+	50757.2i	−1.88507	+	0.505102i	−0.999149	+	0.0412579i	$0.986863\pi$
$318$	−109462.	−	109709.i	−1.08245	−	1.08490i
$319$	148436.	−	85699.4i	1.45867	−	0.842164i
$320$	−92845.0	−	138368.i	−0.906690	−	1.35125i
$321$	−61413.4	+	35364.8i	−0.596009	+	0.343211i
$322$	264299.	−	70818.6i	2.54908	−	0.683023i
$323$	−24894.4	+	24894.4i	−0.238614	+	0.238614i
$324$	136921.	+	79876.8i	1.30431	+	0.760905i
$325$	−9389.44	+	12335.8i	−0.0888941	+	0.116789i
$326$	−92923.0	+	160947.i	−0.874356	+	1.51443i
$327$	−134875.	−	36302.5i	−1.26135	−	0.339501i
$328$	−36772.4	−	9853.13i	−0.341801	−	0.0915854i
$329$	−157001.	+	90644.8i	−1.45048	+	0.837435i
$330$	−168870.	+	11207.7i	−1.55069	+	0.102917i
$331$	−69173.2	+	119811.i	−0.631367	+	1.09356i	0.355906	+	0.934522i	$0.384172\pi$
$331$	−69173.2	+	119811.i	−0.631367	+	1.09356i	−0.987273	+	0.159038i	$0.949161\pi$
$332$	78180.1	+	78180.1i	0.709284	+	0.709284i
$333$	22921.8	+	86323.1i	0.206709	+	0.778464i
$334$		−	118847.i		−	1.06536i
$335$	38125.6	+	111600.i	0.339725	+	0.994427i
$336$	36229.3	+	20971.5i	0.320909	+	0.185759i
$337$	10095.9	−	37678.5i	0.0888967	−	0.331767i	−0.907127	−	0.420857i	$-0.861729\pi$
$337$	10095.9	−	37678.5i	0.0888967	−	0.331767i	0.996024	+	0.0890903i	$0.0283960\pi$
$338$	−171064.	−	45836.5i	−1.49736	−	0.401216i
$339$	−54354.7	+	93900.5i	−0.472974	+	0.817087i
$340$	−155600.	+	53157.3i	−1.34602	+	0.459838i
$341$	21437.5			0.184360
$342$	17326.2	−	64084.0i	0.148133	−	0.547895i
$343$	80913.3	−	80913.3i	0.687752	−	0.687752i
$344$	−103836.	−	59949.7i	−0.877467	−	0.506606i
$345$	8138.03	+	122619.i	0.0683725	+	1.03019i
$346$	90688.8	+	157078.i	0.757533	+	1.31208i
$347$	−13691.2	+	51096.1i	−0.113706	+	0.424355i	−0.999187	−	0.0403203i	$-0.987162\pi$
$347$	−13691.2	+	51096.1i	−0.113706	+	0.424355i	0.885481	+	0.464675i	$0.153829\pi$
$348$	−81611.4	+	303210.i	−0.673895	+	2.50372i
$349$	−90420.5	−	52204.3i	−0.742362	−	0.428603i	0.0805653	−	0.996749i	$-0.474327\pi$
$349$	−90420.5	−	52204.3i	−0.742362	−	0.428603i	−0.822928	+	0.568146i	$0.807661\pi$
$350$	−42079.0	−	310273.i	−0.343502	−	2.53284i
$351$	15690.3	−	8988.17i	0.127355	−	0.0729554i
$352$	−100740.	−	100740.i	−0.813050	−	0.813050i
$353$	14615.6	+	54546.2i	0.117292	+	0.437738i	0.999448	−	0.0332180i	$-0.0105756\pi$
$353$	14615.6	+	54546.2i	0.117292	+	0.437738i	−0.882156	+	0.470956i	$0.843909\pi$
$354$	−61450.5	−	106713.i	−0.490364	−	0.851551i
$355$	−49826.6	+	33433.7i	−0.395371	+	0.265294i
$356$	140868.	+	243990.i	1.11151	+	1.92518i
$357$	137110.	−	136802.i	1.07581	−	1.07338i
$358$	−75147.2	−	280453.i	−0.586336	−	2.18824i
$359$			6031.74i			0.0468008i	0.999726	+	0.0234004i	$0.00744926\pi$
$359$			6031.74i			0.0468008i	−0.999726	+	0.0234004i	$0.992551\pi$
$360$	69073.1	−	78714.2i	0.532971	−	0.607363i
$361$	113596.			0.871662
$362$	198002.	−	53054.4i	1.51095	−	0.404859i
$363$	4808.40	−	1282.60i	0.0364911	−	0.00973370i
$364$	−41028.6	+	23687.9i	−0.309659	+	0.178782i
$365$	15995.6	−	81242.6i	0.120065	−	0.609815i
$366$	179339.	+	103811.i	1.33879	+	0.774966i
$367$	−69478.5	+	18616.7i	−0.515844	+	0.138220i	−0.507343	−	0.861744i	$-0.669372\pi$
$367$	−69478.5	+	18616.7i	−0.515844	+	0.138220i	−0.00850033	+	0.999964i	$0.502706\pi$
$368$	−22722.8	+	22722.8i	−0.167790	+	0.167790i
$369$	−134.417	+	59626.9i	−0.000987188	+	0.437915i
$370$	174297.	−	11765.2i	1.27317	−	0.0859398i
$371$	107403.	−	186028.i	0.780316	−	1.35155i
$372$	−27801.8	+	27739.2i	−0.200903	+	0.200451i
$373$	−152773.	−	40935.4i	−1.09807	−	0.294226i	−0.336090	−	0.941830i	$-0.609105\pi$
$373$	−152773.	−	40935.4i	−1.09807	−	0.294226i	−0.761978	+	0.647603i	$0.775771\pi$
$374$	−177332.	+	102383.i	−1.26778	+	0.731954i
$375$	140366.	+	8535.07i	0.998156	+	0.0606938i
$376$	−59298.0	+	102707.i	−0.419435	+	0.726482i
$377$	25327.7	+	25327.7i	0.178202	+	0.178202i
$378$	−95717.1	+	352450.i	−0.669894	+	2.46668i
$379$			158266.i			1.10182i	0.834566	+	0.550908i	$0.185718\pi$
$379$			158266.i			1.10182i	−0.834566	+	0.550908i	$0.814282\pi$
$380$	−70125.9	−	34412.6i	−0.485637	−	0.238314i
$381$	37743.0	−	21734.2i	0.260008	−	0.149725i
$382$	37228.7	−	138939.i	0.255124	−	0.952135i
$383$	−85820.7	−	22995.6i	−0.585052	−	0.156764i	−0.0458612	−	0.998948i	$-0.514603\pi$
$383$	−85820.7	−	22995.6i	−0.585052	−	0.156764i	−0.539191	+	0.842184i	$0.681270\pi$
$384$	207308.	+	233.667i	1.40590	+	0.00158465i
$385$	−75835.4	−	221982.i	−0.511623	−	1.49760i
$386$	−123938.			−0.831819
$387$	−49013.6	+	181285.i	−0.327261	+	1.21043i
$388$	213979.	−	213979.i	1.42137	−	1.42137i
$389$	−75804.8	−	43765.9i	−0.500953	−	0.289226i	0.228154	−	0.973625i	$-0.426731\pi$
$389$	−75804.8	−	43765.9i	−0.500953	−	0.289226i	−0.729107	+	0.684399i	$0.760064\pi$
$390$	−11396.2	−	33481.6i	−0.0749254	−	0.220129i
$391$	74341.5	+	128763.i	0.486270	+	0.842245i
$392$	51511.6	−	192244.i	0.335222	−	1.25107i
$393$	−118380.	+	31576.8i	−0.766466	+	0.204448i
$394$	264252.	+	152566.i	1.70226	+	0.982801i
$395$	−182610.	+	12326.3i	−1.17039	+	0.0790021i
$396$	116595.	−	200901.i	0.743513	−	1.28112i
$397$	137399.	+	137399.i	0.871769	+	0.871769i	0.992665	−	0.120896i	$-0.0385769\pi$
$397$	137399.	+	137399.i	0.871769	+	0.871769i	−0.120896	+	0.992665i	$0.538577\pi$
$398$	48809.5	+	182160.i	0.308133	+	1.14997i
$399$	92012.9	+	103.712i	0.577967	+	0.000651452i
$400$	22499.4	+	29086.4i	0.140622	+	0.181790i
$401$	15915.4	+	27566.3i	0.0989757	+	0.171431i	0.911261	−	0.411829i	$-0.135110\pi$
$401$	15915.4	+	27566.3i	0.0989757	+	0.171431i	−0.812285	+	0.583260i	$0.801777\pi$
$402$	−259805.	−	69928.5i	−1.60766	−	0.432715i
$403$	1159.51	+	4327.34i	0.00713942	+	0.0266447i
$404$			84014.2i			0.514742i
$405$	−146923.	−	72922.8i	−0.895738	−	0.444583i
$406$	−723443.			−4.38887
$407$	126417.	−	33873.4i	0.763163	−	0.204489i
$408$	32931.6	−	122351.i	0.197830	−	0.734997i
$409$	60286.8	−	34806.6i	0.360393	−	0.208073i	−0.308860	−	0.951107i	$-0.599948\pi$
$409$	60286.8	−	34806.6i	0.360393	−	0.208073i	0.669253	+	0.743035i	$0.266614\pi$
$410$	114430.	+	22529.8i	0.680726	+	0.134026i
$411$	22.6797	−	20121.4i	0.000134262	−	0.119117i
$412$	81204.5	−	21758.7i	0.478394	−	0.128185i
$413$	120689.	−	120689.i	0.707569	−	0.707569i
$414$	−242481.	−	140726.i	−1.41474	−	0.821060i
$415$	−86160.9	−	75264.6i	−0.500281	−	0.437013i
$416$	14886.4	−	25784.0i	0.0860207	−	0.148992i
$417$	−50838.2	−	190590.i	−0.292360	−	1.09604i
$418$	−93962.3	−	25177.1i	−0.537776	−	0.144097i
$419$	197901.	−	114258.i	1.12725	−	0.650817i	0.184007	−	0.982925i	$-0.441093\pi$
$419$	197901.	−	114258.i	1.12725	−	0.650817i	0.943241	+	0.332108i	$0.107760\pi$
$420$	385583.	+	189755.i	2.18584	+	1.07571i
$421$	−148888.	+	257881.i	−0.840029	+	1.45497i	0.0498398	+	0.998757i	$0.484129\pi$
$421$	−148888.	+	257881.i	−0.840029	+	1.45497i	−0.889869	+	0.456216i	$0.849204\pi$
$422$	199017.	+	199017.i	1.11755	+	1.11755i
$423$	179315.	+	48480.8i	1.00216	+	0.270950i
$424$		−	140522.i		−	0.781653i
$425$	156936.	−	65722.7i	0.868849	−	0.363863i
$426$	154.299	−	136894.i	0.000850244	−	0.754335i
$427$	−74336.8	+	277429.i	−0.407707	+	1.52158i
$428$	−183763.	−	49239.2i	−1.00316	−	0.268796i
$429$	−13222.6	−	22961.9i	−0.0718459	−	0.124765i
$430$	329750.	+	161817.i	1.78340	+	0.875157i
$431$	78059.0			0.420212			0.210106	−	0.977679i	$-0.432619\pi$
$431$	78059.0			0.420212			0.210106	+	0.977679i	$0.432619\pi$
$432$	−10961.1	−	41467.7i	−0.0587335	−	0.222199i
$433$	−58064.1	+	58064.1i	−0.309693	+	0.309693i	−0.844791	−	0.535097i	$-0.820275\pi$
$433$	−58064.1	+	58064.1i	−0.309693	+	0.309693i	0.535097	+	0.844791i	$0.320275\pi$
$434$	−78361.4	−	45242.0i	−0.416028	−	0.240194i
$435$	63125.3	−	318720.i	0.333599	−	1.68435i
$436$	−187479.	−	324723.i	−0.986232	−	1.70820i
$437$	−18281.4	+	68227.2i	−0.0957299	+	0.357269i
$438$	133426.	+	133727.i	0.695491	+	0.697060i
$439$	131727.	+	76052.4i	0.683509	+	0.394624i	0.801176	−	0.598429i	$-0.204208\pi$
$439$	131727.	+	76052.4i	0.683509	+	0.394624i	−0.117667	+	0.993053i	$0.537541\pi$
$440$	−115572.	−	100956.i	−0.596960	−	0.521466i
$441$	−311726.	−	702.722i	−1.60286	−	0.00361332i
$442$	−30258.3	−	30258.3i	−0.154882	−	0.154882i
$443$	−82919.3	−	309459.i	−0.422521	−	1.57687i	−0.769277	−	0.638915i	$-0.779384\pi$
$443$	−82919.3	−	309459.i	−0.422521	−	1.57687i	0.346756	−	0.937955i	$-0.387283\pi$
$444$	−120117.	+	207508.i	−0.609308	+	1.05261i
$445$	−162434.	−	242077.i	−0.820271	−	1.22246i
$446$	−1214.23	−	2103.11i	−0.00610423	−	0.0105728i
$447$	−15367.2	−	57610.8i	−0.0769094	−	0.288330i
$448$	136375.	+	508958.i	0.679482	+	2.53586i
$449$		−	165.469i		−	0.000820773i	−1.00000		0.000410386i	$-0.999869\pi$
$449$		−	165.469i		−	0.000820773i	1.00000		0.000410386i	$-0.000130630\pi$
$450$	−194886.	+	254846.i	−0.962400	+	1.25850i
$451$	87374.4			0.429567
$452$	−281338.	+	75384.3i	−1.37706	+	0.368981i
$453$	62578.2	+	62719.4i	0.304949	+	0.305637i
$454$	−283243.	+	163530.i	−1.37419	+	0.793389i
$455$	40707.0	−	27314.4i	0.196628	−	0.131938i
$456$	52162.6	−	30037.8i	0.250859	−	0.144457i
$457$	22771.3	−	6101.56i	0.109032	−	0.0292152i	−0.203890	−	0.978994i	$-0.565359\pi$
$457$	22771.3	−	6101.56i	0.109032	−	0.0292152i	0.312923	+	0.949779i	$0.398692\pi$
$458$	86896.1	−	86896.1i	0.414257	−	0.414257i
$459$	−198453.	−	671.057i	−0.941958	−	0.00318518i
$460$	−217031.	+	248452.i	−1.02567	+	1.17416i
$461$	−18240.5	+	31593.4i	−0.0858291	+	0.148660i	−0.905744	−	0.423825i	$-0.860687\pi$
$461$	−18240.5	+	31593.4i	−0.0858291	+	0.148660i	0.819915	+	0.572485i	$0.194021\pi$
$462$	516776.	+	139094.i	2.42113	+	0.651666i
$463$	7242.12	+	1940.52i	0.0337834	+	0.00905225i	0.275671	−	0.961252i	$-0.411100\pi$
$463$	7242.12	+	1940.52i	0.0337834	+	0.00905225i	−0.241888	+	0.970304i	$0.577767\pi$
$464$	73580.2	−	42481.5i	0.341763	−	0.197317i
$465$	26769.4	−	30575.3i	0.123803	−	0.141405i
$466$	88474.8	−	153243.i	0.407425	−	0.705681i
$467$	−76390.2	−	76390.2i	−0.350271	−	0.350271i	0.509940	−	0.860210i	$-0.329668\pi$
$467$	−76390.2	−	76390.2i	−0.350271	−	0.350271i	−0.860210	+	0.509940i	$0.829668\pi$
$468$	46859.7	+	12669.3i	0.213948	+	0.0578444i
$469$		−	372919.i		−	1.69539i
$470$	160058.	−	326165.i	0.724570	−	1.47653i
$471$	182656.	+	105731.i	0.823365	+	0.476608i
$472$	28898.6	−	107851.i	0.129716	−	0.484107i
$473$	265807.	+	71222.8i	1.18808	+	0.318344i
$474$	209185.	−	361378.i	0.931052	−	1.60844i
$475$	74795.8	+	30640.5i	0.331505	+	0.135803i
$476$	519949.			2.29481
$477$	−212724.	+	56485.5i	−0.934931	+	0.248256i
$478$	27760.7	−	27760.7i	0.121500	−	0.121500i
$479$	−18040.6	−	10415.8i	−0.0786286	−	0.0453962i	0.460170	−	0.887831i	$-0.347788\pi$
$479$	−18040.6	−	10415.8i	−0.0786286	−	0.0453962i	−0.538799	+	0.842434i	$0.681122\pi$
$480$	−269476.	+	17884.7i	−1.16960	+	0.0776247i
$481$	13675.2	+	23686.2i	0.0591077	+	0.102378i
$482$	90207.1	−	336658.i	0.388282	−	1.44909i
$483$	100998.	−	375237.i	0.432931	−	1.60847i
$484$	11569.7	+	6679.75i	0.0493890	+	0.0285147i
$485$	−206000.	+	235823.i	−0.875756	+	1.00254i
$486$	325122.	−	185274.i	1.37649	−	0.784409i
$487$	149834.	+	149834.i	0.631759	+	0.631759i	0.948509	−	0.316750i	$-0.102592\pi$
$487$	149834.	+	149834.i	0.631759	+	0.631759i	−0.316750	+	0.948509i	$0.602592\pi$
$488$	48629.7	+	181488.i	0.204203	+	0.762095i
$489$	131709.	+	228722.i	0.550807	+	0.956513i
$490$	−117785.	+	598233.i	−0.490565	+	2.49160i
$491$	−76853.4	−	133114.i	−0.318787	−	0.552155i	0.661449	−	0.749991i	$-0.269942\pi$
$491$	−76853.4	−	133114.i	−0.318787	−	0.552155i	−0.980235	+	0.197836i	$0.936609\pi$
$492$	−113314.	+	113058.i	−0.468114	+	0.467060i
$493$	−101744.	−	379715.i	−0.418617	−	1.56230i
$494$		−	20328.8i		−	0.0833025i
$495$	−106372.	+	215534.i	−0.434125	+	0.879641i
$496$	10626.7			0.0431951
$497$	183277.	−	49108.8i	0.741984	−	0.198814i
$498$	252186.	−	67268.5i	1.01686	−	0.271240i
$499$	12447.8	−	7186.76i	0.0499911	−	0.0288624i	−0.474796	−	0.880096i	$-0.657478\pi$
$499$	12447.8	−	7186.76i	0.0499911	−	0.0288624i	0.524787	+	0.851233i	$0.324145\pi$
$500$	250564.	+	282366.i	1.00225	+	1.12946i
$501$	−146076.	−	84556.6i	−0.581973	−	0.336877i
$502$	−641516.	+	171894.i	−2.54566	+	0.682107i
$503$	−127228.	+	127228.i	−0.502859	+	0.502859i	−0.912325	−	0.409466i	$-0.865715\pi$
$503$	−127228.	+	127228.i	−0.502859	+	0.502859i	0.409466	+	0.912325i	$0.365715\pi$
$504$	−287158.	+	164929.i	−1.13047	+	0.649285i
$505$	−5854.73	−	86735.9i	−0.0229575	−	0.340107i
$506$	−205411.	+	355783.i	−0.802276	+	1.38958i
$507$	−178046.	+	177645.i	−0.692654	+	0.691094i
$508$	112936.	+	30261.0i	0.437627	+	0.117262i
$509$	−12915.1	+	7456.54i	−0.0498497	+	0.0287807i	−0.524718	−	0.851276i	$-0.675829\pi$
$509$	−12915.1	+	7456.54i	−0.0498497	+	0.0287807i	0.474868	+	0.880057i	$0.342496\pi$
$510$	−75414.1	+	380767.i	−0.289943	+	1.46392i
$511$	−130916.	+	226754.i	−0.501363	+	0.868387i
$512$	−84362.1	−	84362.1i	−0.321816	−	0.321816i
$513$	−66439.1	−	66889.9i	−0.252458	−	0.254171i
$514$		−	428059.i		−	1.62023i
$515$	−82318.9	+	28122.5i	−0.310374	+	0.106033i
$516$	−436878.	+	251575.i	−1.64082	+	0.944862i
$517$	70448.6	−	262918.i	0.263567	−	0.983647i
$518$	−533584.	−	142973.i	−1.98858	−	0.532838i
$519$	257588.	+	290.339i	0.956293	+	0.00107788i
$520$	14127.7	−	28789.5i	0.0522475	−	0.106470i
$521$	−106128.			−0.390980			−0.195490	−	0.980706i	$-0.562630\pi$
$521$	−106128.			−0.390980			−0.195490	+	0.980706i	$0.562630\pi$
$522$	522963.	+	525326.i	1.91924	+	1.92792i
$523$	−119078.	+	119078.i	−0.435339	+	0.435339i	−0.890440	−	0.455101i	$-0.849603\pi$
$523$	−119078.	+	119078.i	−0.435339	+	0.435339i	0.455101	+	0.890440i	$0.349603\pi$
$524$	−284838.	−	164452.i	−1.03738	−	0.598929i
$525$	−411298.	−	169032.i	−1.49224	−	0.613267i
$526$	−88060.9	−	152526.i	−0.318282	−	0.551280i
$527$	12725.6	−	47492.5i	0.0458201	−	0.171003i
$528$	−60728.2	+	16198.7i	−0.217832	+	0.0581049i
$529$	15989.2	+	9231.36i	0.0571367	+	0.0329879i
$530$	28992.6	+	429516.i	0.103213	+	1.52907i
$531$	−174882.	−	394.236i	−0.620236	−	0.00139819i
$532$	174662.	+	174662.i	0.617128	+	0.617128i
$533$	4725.87	+	17637.2i	0.0166352	+	0.0620834i
$534$	665084.	+	749.646i	2.33235	+	0.00262890i
$535$	193147.	+	38028.3i	0.674810	+	0.132862i
$536$	−121978.	−	211272.i	−0.424573	−	0.735382i
$537$	−398173.	−	107171.i	−1.38078	−	0.371646i
$538$	−62323.6	−	232595.i	−0.215322	−	0.803592i
$539$			456788.i			1.57231i
$540$	−140941.	−	417160.i	−0.483335	−	1.43059i
$541$	510441.			1.74402			0.872009	−	0.489490i	$-0.162817\pi$
$541$	510441.			1.74402			0.872009	+	0.489490i	$0.162817\pi$
$542$	−777992.	+	208462.i	−2.64836	+	0.709625i
$543$	75663.5	−	281112.i	0.256618	−	0.953411i
$544$	−282979.	+	163378.i	−0.956218	+	0.552073i
$545$	216181.	+	322177.i	0.727822	+	1.08468i
$546$	−126.058	+	111839.i	−0.000422849	+	0.375151i
$547$	−38316.7	+	10266.9i	−0.128060	+	0.0343136i	−0.322280	−	0.946644i	$-0.604449\pi$
$547$	−38316.7	+	10266.9i	−0.128060	+	0.0343136i	0.194220	+	0.980958i	$0.437783\pi$
$548$	38195.1	−	38195.1i	0.127188	−	0.127188i
$549$	255191.	−	146568.i	0.846682	−	0.486291i
$550$	374081.	+	284733.i	1.23663	+	0.941266i
$551$	93376.4	−	161733.i	0.307563	−	0.532715i
$552$	−65517.3	−	245621.i	−0.215020	−	0.806098i
$553$	559033.	+	149792.i	1.82805	+	0.489824i
$554$	480260.	−	277278.i	1.56479	−	0.903434i
$555$	109547.	−	222600.i	0.355644	−	0.722670i
$556$	264764.	−	458585.i	0.856464	−	1.48344i
$557$	219561.	+	219561.i	0.707693	+	0.707693i	0.966050	−	0.258357i	$-0.0831810\pi$
$557$	219561.	+	219561.i	0.707693	+	0.707693i	−0.258357	+	0.966050i	$0.583181\pi$
$558$	23793.6	+	89606.5i	0.0764173	+	0.287787i
$559$			57507.6i			0.184035i
$560$	−37591.9	−	110037.i	−0.119872	−	0.350884i
$561$	−327.778	+	290803.i	−0.00104149	+	0.924004i
$562$	152277.	−	568305.i	0.482127	−	1.79932i
$563$	−408199.	−	109377.i	−1.28782	−	0.345070i	−0.450988	−	0.892530i	$-0.648928\pi$
$563$	−408199.	−	109377.i	−1.28782	−	0.345070i	−0.836832	+	0.547460i	$0.815595\pi$
$564$	248841.	+	432129.i	0.782281	+	1.35849i
$565$	285199.	−	97432.1i	0.893409	−	0.305214i
$566$	−328481.			−1.02536
$567$	365099.	+	368406.i	1.13565	+	1.14594i
$568$	87769.9	−	87769.9i	0.272050	−	0.272050i
$569$	53184.4	+	30706.0i	0.164271	+	0.0948416i	0.579881	−	0.814701i	$-0.303099\pi$
$569$	53184.4	+	30706.0i	0.164271	+	0.0948416i	−0.415611	+	0.909543i	$0.636432\pi$
$570$	−153241.	+	102575.i	−0.471656	+	0.315711i
$571$	−219870.	−	380825.i	−0.674362	−	1.16803i	−0.976655	−	0.214814i	$-0.931085\pi$
$571$	−219870.	−	380825.i	−0.674362	−	1.16803i	0.302293	−	0.953215i	$-0.402248\pi$
$572$	18410.1	−	68707.4i	0.0562683	−	0.209996i
$573$	−144284.	−	144610.i	−0.439450	−	0.440442i
$574$	−319382.	−	184396.i	−0.969365	−	0.559663i
$575$	206748.	−	271625.i	0.625325	−	0.821550i
$576$	270996.	−	466944.i	0.816803	−	1.40741i
$577$	−262979.	−	262979.i	−0.789894	−	0.789894i	0.191582	−	0.981477i	$-0.438638\pi$
$577$	−262979.	−	262979.i	−0.789894	−	0.789894i	−0.981477	+	0.191582i	$0.938638\pi$
$578$	−15439.6	−	57621.3i	−0.0462147	−	0.172475i
$579$	−88178.5	+	152333.i	−0.263030	+	0.454398i
$580$	724284.	−	485995.i	2.15304	−	1.44470i
$581$	180882.	+	313298.i	0.535851	+	0.928121i
$582$	−184114.	−	690235.i	−0.543553	−	2.03775i
$583$	83473.4	+	311527.i	0.245590	+	0.916555i
$584$			171286.i			0.502222i
$585$	−49260.6	−	9814.20i	−0.143942	−	0.0286776i
$586$	946079.			2.75507
$587$	214167.	−	57385.9i	0.621550	−	0.166544i	0.0657179	−	0.997838i	$-0.479066\pi$
$587$	214167.	−	57385.9i	0.621550	−	0.166544i	0.555832	+	0.831294i	$0.312400\pi$
$588$	−591063.	−	592397.i	−1.70954	−	1.71340i
$589$	20228.6	−	11679.0i	0.0583088	−	0.0336646i
$590$	−66078.6	+	335616.i	−0.189827	+	0.964138i
$591$	375529.	−	216248.i	1.07515	−	0.619123i
$592$	62665.5	−	16791.2i	0.178807	−	0.0479113i
$593$	−51232.2	+	51232.2i	−0.145691	+	0.145691i	−0.776190	−	0.630499i	$-0.782850\pi$
$593$	−51232.2	+	51232.2i	−0.145691	+	0.145691i	0.630499	+	0.776190i	$0.282850\pi$
$594$	−272565.	−	475804.i	−0.772496	−	1.34851i
$595$	−536793.	+	36233.9i	−1.51626	+	0.102348i
$596$	80032.0	−	138620.i	0.225305	−	0.390240i
$597$	258621.	+	69609.8i	0.725629	+	0.195309i
$598$	−82927.8	−	22220.4i	−0.231899	−	0.0621370i
$599$	−350023.	+	202086.i	−0.975536	+	0.563226i	−0.900919	−	0.433986i	$-0.857107\pi$
$599$	−350023.	+	202086.i	−0.975536	+	0.563226i	−0.0746166	+	0.997212i	$0.523773\pi$
$600$	−288304.	+	38768.7i	−0.800844	+	0.107691i
$601$	17891.6	−	30989.1i	0.0495336	−	0.0857947i	−0.840196	−	0.542284i	$-0.817560\pi$
$601$	17891.6	−	30989.1i	0.0495336	−	0.0857947i	0.889729	+	0.456489i	$0.150893\pi$
$602$	−821305.	−	821305.i	−2.26627	−	2.26627i
$603$	−270794.	+	269576.i	−0.744741	+	0.741390i
$604$			237844.i			0.651956i
$605$	−12410.0	−	6089.88i	−0.0339047	−	0.0166379i
$606$	171647.	+	99358.5i	0.467402	+	0.270558i
$607$	−175576.	+	655259.i	−0.476527	+	1.77842i	0.138982	+	0.990295i	$0.455617\pi$
$607$	−175576.	+	655259.i	−0.476527	+	1.77842i	−0.615509	+	0.788130i	$0.711050\pi$
$608$	−149941.	−	40176.6i	−0.405615	−	0.108684i
$609$	−514711.	+	889190.i	−1.38781	+	2.39751i
$610$	−186084.	−	544697.i	−0.500092	−	1.46385i
$611$	56882.5			0.152369
$612$	−375861.	−	377560.i	−1.00352	−	1.00805i
$613$	−171923.	+	171923.i	−0.457522	+	0.457522i	−0.897841	−	0.440319i	$-0.854865\pi$
$613$	−171923.	+	171923.i	−0.457522	+	0.457522i	0.440319	+	0.897841i	$0.354865\pi$
$614$	942474.	+	544138.i	2.49996	+	1.44335i
$615$	109106.	−	124617.i	0.288468	−	0.329480i
$616$	242626.	+	420240.i	0.639404	+	1.10748i
$617$	22636.8	−	84481.6i	0.0594627	−	0.221918i	−0.929800	−	0.368065i	$-0.880021\pi$
$617$	22636.8	−	84481.6i	0.0594627	−	0.221918i	0.989263	+	0.146147i	$0.0466872\pi$
$618$	51581.2	−	191639.i	0.135056	−	0.501773i
$619$	−25542.0	−	14746.7i	−0.0666613	−	0.0384869i	0.466299	−	0.884627i	$-0.345587\pi$
$619$	−25542.0	−	14746.7i	−0.0666613	−	0.0384869i	−0.532960	+	0.846140i	$0.678920\pi$
$620$	108845.	−	7347.13i	0.283156	−	0.0191132i
$621$	−345487.	+	197913.i	−0.895878	+	0.513204i
$622$	94922.7	+	94922.7i	0.245352	+	0.245352i
$623$	238590.	+	890431.i	0.614719	+	2.29416i
$624$	−6554.49	−	11382.3i	−0.0168333	−	0.0292322i
$625$	−278358.	−	274052.i	−0.712597	−	0.701574i
$626$	318795.	+	552169.i	0.813510	+	1.40904i
$627$	−97797.3	+	97577.0i	−0.248766	+	0.248206i
$628$	146638.	+	547261.i	0.371816	+	1.38763i
$629$		−	300171.i		−	0.758695i
$630$	843688.	−	563361.i	2.12569	−	1.41940i
$631$	73195.8			0.183835			0.0919174	−	0.995767i	$-0.470700\pi$
$631$	73195.8			0.183835			0.0919174	+	0.995767i	$0.470700\pi$
$632$	365708.	−	97991.2i	0.915589	−	0.245331i
$633$	386210.	−	103018.i	0.963864	−	0.257102i
$634$	−1.07630e6	+	621400.i	−2.67765	+	1.54594i
$635$	−118703.	−	23371.2i	−0.294384	−	0.0579606i
$636$	−511356.	−	296000.i	−1.26418	−	0.731776i
$637$	−92206.3	+	24706.6i	−0.227238	+	0.0608883i
$638$	768056.	−	768056.i	1.88691	−	1.88691i
$639$	−168147.	−	97586.0i	−0.411802	−	0.238993i
$640$	−433691.	−	378845.i	−1.05882	−	0.924914i
$641$	−295383.	+	511618.i	−0.718902	+	1.24517i	0.242533	+	0.970143i	$0.422022\pi$
$641$	−295383.	+	511618.i	−0.718902	+	1.24517i	−0.961435	+	0.275031i	$0.911312\pi$
$642$	−317924.	+	317209.i	−0.771354	+	0.769617i
$643$	358081.	+	95947.5i	0.866083	+	0.232066i	0.664393	−	0.747383i	$-0.268690\pi$
$643$	358081.	+	95947.5i	0.866083	+	0.232066i	0.201690	+	0.979449i	$0.435357\pi$
$644$	903418.	−	521589.i	2.17830	−	1.25764i
$645$	433499.	−	290170.i	1.04200	−	0.697482i
$646$	−111554.	+	193218.i	−0.267314	+	0.463001i
$647$	−112032.	−	112032.i	−0.267629	−	0.267629i	0.560515	−	0.828144i	$-0.310603\pi$
$647$	−112032.	−	112032.i	−0.267629	−	0.267629i	−0.828144	+	0.560515i	$0.810603\pi$
$648$	327343.	+	89295.2i	0.779567	+	0.212656i
$649$			256264.i			0.608412i
$650$	−37242.4	+	90911.7i	−0.0881478	+	0.215176i
$651$	−111359.	+	64126.1i	−0.262763	+	0.151312i
$652$	−183382.	+	684391.i	−0.431381	+	1.60994i
$653$	227655.	+	61000.1i	0.533890	+	0.143055i	0.515684	−	0.856779i	$-0.327538\pi$
$653$	227655.	+	61000.1i	0.533890	+	0.143055i	0.0182058	+	0.999834i	$0.494205\pi$
$654$	−885151.	−	997.693i	−2.06948	−	0.00233261i
$655$	305526.	+	149929.i	0.712140	+	0.349465i
$656$	43311.8			0.100646
$657$	259294.	−	68851.5i	0.600705	−	0.159508i
$658$	−812377.	+	812377.i	−1.87632	+	1.87632i
$659$	−474328.	−	273853.i	−1.09221	−	0.630590i	−0.158049	−	0.987431i	$-0.550521\pi$
$659$	−474328.	−	273853.i	−1.09221	−	0.630590i	−0.934165	+	0.356841i	$0.883854\pi$
$660$	−610818.	+	207904.i	−1.40224	+	0.477283i
$661$	−262409.	−	454506.i	−0.600587	−	1.04025i	−0.992732	−	0.120344i	$-0.961600\pi$
$661$	−262409.	−	454506.i	−0.600587	−	1.04025i	0.392145	−	0.919903i	$-0.371733\pi$
$662$	−226915.	+	846859.i	−0.517783	+	1.93239i
$663$	−58718.7	+	15662.7i	−0.133582	+	0.0356320i
$664$	204953.	+	118330.i	0.464856	+	0.268384i
$665$	−192492.	−	168149.i	−0.435281	−	0.380233i
$666$	281898.	+	490813.i	0.635540	+	1.10654i
$667$	−557695.	−	557695.i	−1.25356	−	1.25356i
$668$	−117271.	−	437662.i	−0.262808	−	0.980812i
$669$	−3448.84	−	3.88734i	−0.00770586	−	8.68562e-6i
$670$	416424.	+	620601.i	0.927654	+	1.38249i
$671$	−215616.	−	373458.i	−0.478890	−	0.829463i
$672$	824649.	+	221961.i	1.82613	+	0.491515i
$673$	−166405.	−	621032.i	−0.367398	−	1.37115i	−0.864141	−	0.503250i	$-0.832138\pi$
$673$	−166405.	−	621032.i	−0.367398	−	1.37115i	0.496743	−	0.867898i	$-0.334529\pi$
$674$		−	247200.i		−	0.544163i
$675$	174577.	+	420853.i	0.383160	+	0.923682i
$676$	−675185.			−1.47751
$677$	550746.	−	147572.i	1.20164	−	0.321978i	0.398162	−	0.917315i	$-0.369648\pi$
$677$	550746.	−	147572.i	1.20164	−	0.321978i	0.803476	+	0.595337i	$0.202981\pi$
$678$	−178706.	+	663945.i	−0.388758	+	1.44435i
$679$	857497.	−	495076.i	1.85991	−	1.07382i
$680$	−292261.	+	196107.i	−0.632052	+	0.424108i
$681$	−523.540	+	464483.i	−0.00112890	+	1.00156i
$682$	131226.	−	35161.8i	0.282130	−	0.0755966i
$683$	−234909.	+	234909.i	−0.503569	+	0.503569i	−0.912545	−	0.408976i	$-0.865886\pi$
$683$	−234909.	+	234909.i	−0.503569	+	0.503569i	0.408976	+	0.912545i	$0.365886\pi$
$684$	570.539	−	253090.i	0.00121948	−	0.540958i
$685$	−36770.7	+	42094.2i	−0.0783648	+	0.0897100i
$686$	362581.	−	628008.i	0.770471	−	1.33450i
$687$	−44980.4	−	168629.i	−0.0953037	−	0.357289i
$688$	131762.	+	35305.4i	0.278363	+	0.0745873i
$689$	−58369.3	+	33699.5i	−0.122955	+	0.0709881i
$690$	250935.	+	737239.i	0.527063	+	1.54850i
$691$	139383.	−	241419.i	0.291914	−	0.505609i	−0.682348	−	0.731027i	$-0.739041\pi$
$691$	139383.	−	241419.i	0.291914	−	0.505609i	0.974262	+	0.225418i	$0.0723746\pi$
$692$	488962.	+	488962.i	1.02109	+	1.02109i
$693$	538635.	−	536212.i	1.12157	−	1.11653i
$694$			335231.i			0.696025i
$695$	−241384.	+	491891.i	−0.499733	+	1.01836i
$696$	−757.571	+	672116.i	−0.00156389	+	1.38748i
$697$	51866.5	−	193568.i	0.106763	−	0.398445i
$698$	−639116.	−	171251.i	−1.31180	−	0.351497i
$699$	−125405.	−	217773.i	−0.256660	−	0.445708i
$700$	−461118.	−	1.10108e6i	−0.941058	−	2.24710i
$701$	172371.			0.350775			0.175387	−	0.984500i	$-0.443882\pi$
$701$	172371.			0.350775			0.175387	+	0.984500i	$0.443882\pi$
$702$	81302.4	−	80754.4i	0.164979	−	0.163867i
$703$	100834.	−	100834.i	0.204031	−	0.204031i
$704$	−685128.	−	395559.i	−1.38238	−	0.798116i
$705$	−287016.	−	428787.i	−0.577468	−	0.862706i
$706$	178933.	+	309921.i	0.358989	+	0.621787i
$707$	−71148.2	+	265529.i	−0.142339	+	0.531218i
$708$	−331594.	−	332342.i	−0.661515	−	0.663008i
$709$	768996.	+	443980.i	1.52979	+	0.883224i	0.999370	+	0.0354886i	$0.0112987\pi$
$709$	768996.	+	443980.i	1.52979	+	0.883224i	0.530419	+	0.847736i	$0.322035\pi$
$710$	−250166.	+	286383.i	−0.496262	+	0.568107i
$711$	−295343.	−	514223.i	−0.584235	−	1.01721i
$712$	426421.	+	426421.i	0.841160	+	0.841160i
$713$	−25531.4	−	95284.6i	−0.0502222	−	0.187432i
$714$	614912.	−	1.06229e6i	1.20619	−	2.08376i
$715$	−14218.5	+	72216.2i	−0.0278125	+	0.141261i
$716$	−553469.	−	958637.i	−1.07961	−	1.86994i
$717$	−14369.9	−	53872.0i	−0.0279521	−	0.104791i
$718$	9893.24	+	36922.1i	0.0191907	+	0.0716205i
$719$		−	282634.i		−	0.546722i	−0.961912	−	0.273361i	$-0.911865\pi$
$719$		−	282634.i		−	0.546722i	0.961912	−	0.273361i	$-0.0881353\pi$
$720$	−52728.8	+	106841.i	−0.101714	+	0.206098i
$721$	275075.			0.529153
$722$	695354.	−	186320.i	1.33393	−	0.357424i
$723$	−349609.	−	350398.i	−0.668815	−	0.670324i
$724$	676803.	−	390753.i	1.29118	−	0.745461i
$725$	−713880.	+	552213.i	−1.35815	+	1.05058i
$726$	27329.9	−	15737.9i	0.0518520	−	0.0298589i
$727$	−542766.	+	145434.i	−1.02694	+	0.275167i	−0.732690	−	0.680563i	$-0.761735\pi$
$727$	−542766.	+	145434.i	−1.02694	+	0.275167i	−0.294246	+	0.955730i	$0.595069\pi$
$728$	−71705.7	+	71705.7i	−0.135298	+	0.135298i
$729$	3594.04	−	531429.i	0.00676281	−	0.999977i
$730$	−35339.7	−	523546.i	−0.0663159	−	0.982448i
$731$	315573.	−	546588.i	0.590561	−	1.02288i
$732$	762864.	+	205331.i	1.42372	+	0.383206i
$733$	−44673.4	−	11970.2i	−0.0831460	−	0.0222789i	0.217006	−	0.976170i	$-0.430371\pi$
$733$	−44673.4	−	11970.2i	−0.0831460	−	0.0222789i	−0.300152	+	0.953891i	$0.597037\pi$
$734$	−394764.	+	227917.i	−0.732732	+	0.423043i
$735$	651493.	+	570398.i	1.20597	+	1.05585i
$736$	−327787.	+	567744.i	−0.605112	+	1.04809i
$737$	395916.	+	395916.i	0.728901	+	0.728901i
$738$	96977.1	+	365215.i	0.178056	+	0.670557i
$739$		−	756555.i		−	1.38532i	−0.721262	−	0.692662i	$-0.756438\pi$
$739$		−	756555.i		−	1.38532i	0.721262	−	0.692662i	$-0.243562\pi$
$740$	630251.	−	215312.i	1.15093	−	0.393192i
$741$	−24986.3	−	14463.4i	−0.0455057	−	0.0263412i
$742$	352326.	−	1.31490e6i	0.639936	−	2.38827i
$743$	707138.	+	189477.i	1.28093	+	0.343225i	0.834210	−	0.551447i	$-0.185924\pi$
$743$	707138.	+	189477.i	1.28093	+	0.343225i	0.446724	+	0.894672i	$0.352591\pi$
$744$	−42114.2	+	72754.4i	−0.0760821	+	0.131436i
$745$	−72964.7	+	148687.i	−0.131462	+	0.267893i
$746$	−1.00231e6			−1.80105
$747$	96743.8	−	357824.i	0.173373	−	0.641251i
$748$	−552013.	+	552013.i	−0.986611	+	0.986611i
$749$	−539089.	−	311243.i	−0.960941	−	0.554799i
$750$	873220.	−	177982.i	1.55239	−	0.316412i
$751$	67617.3	+	117117.i	0.119889	+	0.207653i	0.919723	−	0.392567i	$-0.128413\pi$
$751$	67617.3	+	117117.i	0.119889	+	0.207653i	−0.799835	+	0.600220i	$0.795080\pi$
$752$	34921.7	−	130329.i	0.0617532	−	0.230466i
$753$	−245146.	+	910791.i	−0.432350	+	1.60631i
$754$	196580.	+	113496.i	0.345778	+	0.199635i
$755$	−16574.7	−	245549.i	−0.0290772	−	0.430769i
$756$	−4708.21	+	1.39237e6i	−0.00823783	+	2.43618i
$757$	525216.	+	525216.i	0.916528	+	0.916528i	0.996775	−	0.0802469i	$-0.0255709\pi$
$757$	525216.	+	525216.i	0.916528	+	0.916528i	−0.0802469	+	0.996775i	$0.525571\pi$
$758$	259587.	+	968793.i	0.451799	+	1.68614i
$759$	291151.	+	505604.i	0.505400	+	0.877661i
$760$	−164053.	−	32300.1i	−0.284026	−	0.0559212i
$761$	−70184.9	−	121564.i	−0.121192	−	0.209911i	0.799046	−	0.601270i	$-0.205338\pi$
$761$	−70184.9	−	121564.i	−0.121192	−	0.209911i	−0.920238	+	0.391359i	$0.872005\pi$
$762$	195388.	−	194948.i	0.336502	−	0.335744i
$763$	−317536.	−	1.18506e6i	−0.545437	−	2.03560i
$764$		−	548388.i		−	0.939510i
$765$	414348.	+	363598.i	0.708016	+	0.621296i
$766$	−563052.			−0.959601
$767$	−51728.9	+	13860.7i	−0.0879311	+	0.0235611i
$768$	342010.	−	91228.4i	0.579852	−	0.154671i
$769$	−598783.	+	345707.i	−1.01255	+	0.584596i	−0.911937	−	0.410330i	$-0.865414\pi$
$769$	−598783.	+	345707.i	−1.01255	+	0.584596i	−0.100613	+	0.994926i	$0.532080\pi$
$770$	−828305.	−	1.23443e6i	−1.39704	−	2.08202i
$771$	−526131.	−	304553.i	−0.885085	−	0.512335i
$772$	−456409.	+	122294.i	−0.765807	+	0.205197i
$773$	81071.7	−	81071.7i	0.135678	−	0.135678i	−0.636006	−	0.771684i	$-0.719415\pi$
$773$	81071.7	−	81071.7i	0.135678	−	0.135678i	0.771684	+	0.636006i	$0.219415\pi$
$774$	−2682.82	+	1.19009e6i	−0.00447826	+	1.98655i
$775$	−111859.	+	15170.3i	−0.186238	+	0.0252575i
$776$	323869.	−	560957.i	0.537831	−	0.931551i
$777$	−555361.	+	554110.i	−0.919885	+	0.917813i
$778$	−535808.	−	143569.i	−0.885218	−	0.237194i
$779$	82446.8	−	47600.7i	0.135862	−	0.0784401i
$780$	−75004.8	−	112053.i	−0.123282	−	0.184177i
$781$	−142442.	+	246716.i	−0.233526	+	0.404478i
$782$	666263.	+	666263.i	1.08951	+	1.08951i
$783$	1.01776e6	−	269022.i	1.66005	−	0.438798i
$784$			226432.i			0.368388i
$785$	−189526.	−	554771.i	−0.307559	−	0.900273i
$786$	−672847.	+	387458.i	−1.08911	+	0.627161i
$787$	261554.	−	976134.i	0.422291	−	1.57601i	−0.347476	−	0.937689i	$-0.612961\pi$
$787$	261554.	−	976134.i	0.422291	−	1.57601i	0.769768	−	0.638324i	$-0.220372\pi$
$788$	1.12367e6	+	301087.i	1.80962	+	0.484885i
$789$	−250124.	−	281.926i	−0.401792	−	0.000452878i
$790$	−1.09759e6	+	374969.i	−1.75868	+	0.600816i
$791$	−953015.			−1.52316
$792$	129767.	−	479966.i	0.206877	−	0.765173i
$793$	63723.3	−	63723.3i	0.101333	−	0.101333i
$794$	1.06642e6	+	615697.i	1.69156	+	0.976621i
$795$	548549.	+	269954.i	0.867923	+	0.427126i
$796$	359489.	+	622653.i	0.567361	+	0.982698i
$797$	247043.	−	921978.i	0.388916	−	1.45146i	−0.442984	−	0.896530i	$-0.646080\pi$
$797$	247043.	−	921978.i	0.388916	−	1.45146i	0.831900	−	0.554926i	$-0.187253\pi$
$798$	563409.	−	150285.i	0.884745	−	0.235998i
$799$	−540646.	−	312142.i	−0.846876	−	0.488944i
$800$	596942.	+	454365.i	0.932722	+	0.709945i
$801$	474112.	−	816928.i	0.738951	−	1.27326i
$802$	142637.	+	142637.i	0.221760	+	0.221760i
$803$	−101748.	−	379727.i	−0.157795	−	0.588899i
$804$	−1.02575e6	−	1156.17i	−1.58683	−	0.00178858i
$805$	−896336.	+	601443.i	−1.38318	+	0.928116i
$806$	14195.4	+	24587.1i	0.0218513	+	0.0378475i
$807$	−330226.	−	88882.8i	−0.507066	−	0.136481i
$808$	46543.7	+	173704.i	0.0712916	+	0.266064i
$809$		−	177471.i		−	0.271163i	−0.990766	−	0.135581i	$-0.956710\pi$
$809$		−	177471.i		−	0.271163i	0.990766	−	0.135581i	$-0.0432902\pi$
$810$	−1.01897e6	−	205399.i	−1.55307	−	0.313060i
$811$	487458.			0.741132			0.370566	−	0.928806i	$-0.379164\pi$
$811$	487458.			0.741132			0.370566	+	0.928806i	$0.379164\pi$
$812$	−2.66413e6	+	713851.i	−4.04057	+	1.08267i
$813$	−297299.	+	1.10455e6i	−0.449792	+	1.67111i
$814$	718279.	−	414698.i	1.08404	−	0.625869i
$815$	141629.	−	719341.i	0.213225	−	1.08298i
$816$	−162.481	+	144152.i	−0.000244018	+	0.216492i
$817$	289618.	−	77603.0i	0.433892	−	0.116261i
$818$	311944.	−	311944.i	0.466198	−	0.466198i
$819$	137372.	+	79725.2i	0.204800	+	0.118858i
$820$	443627.	−	29945.2i	0.659767	−	0.0445347i
$821$	−265363.	+	459622.i	−0.393689	+	0.681890i	−0.992933	−	0.118677i	$-0.962135\pi$
$821$	−265363.	+	459622.i	−0.393689	+	0.681890i	0.599244	+	0.800567i	$0.295468\pi$
$822$	−32864.2	−	123206.i	−0.0486385	−	0.182343i
$823$	−412650.	−	110569.i	−0.609231	−	0.163243i	−0.0590035	−	0.998258i	$-0.518792\pi$
$823$	−412650.	−	110569.i	−0.609231	−	0.163243i	−0.550227	+	0.835015i	$0.685459\pi$
$824$	155840.	−	89974.4i	0.229522	−	0.132515i
$825$	616117.	−	257206.i	0.905222	−	0.377896i
$826$	540821.	−	936730.i	0.792672	−	1.37295i
$827$	704209.	+	704209.i	1.02965	+	1.02965i	0.999547	+	0.0301049i	$0.00958415\pi$
$827$	704209.	+	704209.i	1.02965	+	1.02965i	0.0301049	+	0.999547i	$0.490416\pi$
$828$	−1.03181e6	−	278968.i	−1.50501	−	0.406906i
$829$			433124.i			0.630236i	0.949053	+	0.315118i	$0.102044\pi$
$829$			433124.i			0.630236i	−0.949053	+	0.315118i	$0.897956\pi$
$830$	−650866.	−	319396.i	−0.944790	−	0.463632i
$831$	887.704	−	787569.i	0.00128548	−	1.14048i
$832$	42789.7	−	159693.i	0.0618148	−	0.230696i
$833$	1.01196e6	+	271155.i	1.45839	+	0.390776i
$834$	−623800.	−	1.08327e6i	−0.896837	−	1.55742i
$835$	151570.	+	443668.i	0.217390	+	0.636334i
$836$	−370866.			−0.530645
$837$	127065.	+	34507.8i	0.181373	+	0.0492568i
$838$	1.02400e6	−	1.02400e6i	1.45819	−	1.45819i
$839$	−567106.	−	327419.i	−0.805639	−	0.465136i	0.0398002	−	0.999208i	$-0.487328\pi$
$839$	−567106.	−	327419.i	−0.805639	−	0.465136i	−0.845439	+	0.534072i	$0.820661\pi$
$840$	902336.	+	178715.i	1.27882	+	0.253282i
$841$	689001.	+	1.19338e6i	0.974155	+	1.68729i
$842$	−488410.	+	1.82277e6i	−0.688907	+	2.57104i
$843$	−590167.	−	591499.i	−0.830462	−	0.832337i
$844$	929273.	+	536516.i	1.30454	+	0.753178i
$845$	697057.	−	47051.9i	0.976237	−	0.0658967i
$846$	1.17716e6	+	2653.66i	1.64473	+	0.00370770i
$847$	30909.4	+	30909.4i	0.0430847	+	0.0430847i
$848$	41378.1	+	154425.i	0.0575412	+	0.214747i
$849$	−233706.	+	403739.i	−0.324231	+	0.560125i
$850$	852853.	−	659714.i	1.18042	−	0.913099i
$851$	−301118.	−	521551.i	−0.415793	−	0.720175i
$852$	−134510.	−	504273.i	−0.185301	−	0.694682i
$853$	294765.	+	1.10008e6i	0.405115	+	1.51191i	0.803844	+	0.594840i	$0.202785\pi$
$853$	294765.	+	1.10008e6i	0.405115	+	1.51191i	−0.398729	+	0.917069i	$0.630549\pi$
$854$			1.82015e6i			2.49570i
$855$	17048.2	+	261329.i	0.0233209	+	0.357483i
$856$	−407218.			−0.555750
$857$	390354.	−	104595.i	0.531492	−	0.142413i	0.0169148	−	0.999857i	$-0.494616\pi$
$857$	390354.	−	104595.i	0.531492	−	0.142413i	0.514577	+	0.857444i	$0.327949\pi$
$858$	−118602.	−	118869.i	−0.161107	−	0.161471i
$859$	−755361.	+	436108.i	−1.02369	+	0.591028i	−0.915171	−	0.403067i	$-0.867944\pi$
$859$	−755361.	+	436108.i	−1.02369	+	0.591028i	−0.108519	+	0.994094i	$0.534611\pi$
$860$	1.37400e6	+	270523.i	1.85776	+	0.365769i
$861$	−453875.	+	261363.i	−0.612251	+	0.352564i
$862$	477822.	−	128032.i	0.643060	−	0.172308i
$863$	264532.	−	264532.i	0.355187	−	0.355187i	−0.506848	−	0.862035i	$-0.669190\pi$
$863$	264532.	−	264532.i	0.355187	−	0.355187i	0.862035	+	0.506848i	$0.169190\pi$
$864$	−434947.	−	759268.i	−0.582651	−	1.01711i
$865$	−538877.	−	470728.i	−0.720207	−	0.629126i
$866$	−260191.	+	450664.i	−0.346942	+	0.600921i
$867$	−81807.7	−	22019.2i	−0.108832	−	0.0292929i
$868$	−333213.	−	89284.2i	−0.442265	−	0.118505i
$869$	−752537.	+	434477.i	−0.996525	+	0.575344i
$870$	−136355.	−	2.05452e6i	−0.180150	−	2.71439i
$871$	−58504.6	+	101333.i	−0.0771177	+	0.133572i
$872$	−567518.	−	567518.i	−0.746357	−	0.746357i
$873$	−979367.	−	264788.i	−1.28504	−	0.347432i
$874$			447625.i			0.585991i
$875$	552788.	+	1.10462e6i	0.722009	+	1.44276i
$876$	623303.	+	360802.i	0.812253	+	0.470176i
$877$	−311875.	+	1.16393e6i	−0.405492	+	1.51332i	0.397656	+	0.917535i	$0.369824\pi$
$877$	−311875.	+	1.16393e6i	−0.405492	+	1.51332i	−0.803147	+	0.595781i	$0.796843\pi$
$878$	931079.	+	249482.i	1.20781	+	0.323631i
$879$	673111.	−	1.16283e6i	0.871182	−	1.50501i
$880$	156733.	+	76912.8i	0.202393	+	0.0993193i
$881$	869341.			1.12005			0.560026	−	0.828475i	$-0.310791\pi$
$881$	869341.			1.12005			0.560026	+	0.828475i	$0.310791\pi$
$882$	−1.90932e6	+	506991.i	−2.45438	+	0.651723i
$883$	−907638.	+	907638.i	−1.16410	+	1.16410i	−0.180534	+	0.983569i	$0.557783\pi$
$883$	−907638.	+	907638.i	−1.16410	+	1.16410i	−0.983569	+	0.180534i	$0.942217\pi$
$884$	−141285.	−	81571.1i	−0.180797	−	0.104383i
$885$	365496.	+	320000.i	0.466655	+	0.408568i
$886$	−1.01515e6	−	1.75829e6i	−1.29319	−	2.23987i
$887$	350090.	−	1.30655e6i	0.444972	−	1.66066i	−0.271040	−	0.962568i	$-0.587368\pi$
$887$	350090.	−	1.30655e6i	0.444972	−	1.66066i	0.716012	−	0.698088i	$-0.245966\pi$
$888$	−133388.	+	495577.i	−0.169158	+	0.628471i
$889$	331309.	+	191281.i	0.419208	+	0.242030i
$890$	−1.39136e6	−	1.21540e6i	−1.75655	−	1.53441i
$891$	−778738.	−	3511.02i	−0.980925	−	0.00442260i
$892$	−6546.71	−	6546.71i	−0.00822798	−	0.00822798i
$893$	−76759.4	−	286470.i	−0.0962562	−	0.359233i
$894$	−188560.	−	327448.i	−0.235926	−	0.409701i
$895$	638204.	+	951122.i	0.796734	+	1.18738i
$896$	910472.	+	1.57698e6i	1.13410	+	1.96432i
$897$	−86312.4	+	86118.1i	−0.107272	+	0.107031i
$898$	−271.401	−	1012.88i	−0.000336557	−	0.00125605i
$899$			260815.i			0.322710i
$900$	−466214.	+	1.13079e6i	−0.575572	+	1.39604i
$901$	739704.			0.911189
$902$	534845.	−	143311.i	0.657377	−	0.176144i
$903$	−1.59381e6	+	425135.i	−1.95461	+	0.521377i
$904$	−539918.	+	311722.i	−0.660679	+	0.381443i
$905$	−671498.	+	450576.i	−0.819875	+	0.550137i
$906$	485932.	+	281284.i	0.591997	+	0.342680i
$907$	601812.	−	161255.i	0.731553	−	0.196019i	0.126232	−	0.992001i	$-0.459711\pi$
$907$	601812.	−	161255.i	0.731553	−	0.196019i	0.605321	+	0.795982i	$0.293045\pi$
$908$	−881698.	+	881698.i	−1.06942	+	1.06942i
$909$	244245.	−	140282.i	0.295595	−	0.169775i
$910$	204379.	−	233967.i	0.246804	−	0.282535i
$911$	−145988.	+	252859.i	−0.175906	+	0.304678i	−0.940475	−	0.339864i	$-0.889619\pi$
$911$	−145988.	+	252859.i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$912$	−48478.5	+	48369.3i	−0.0582853	+	0.0581541i
$913$	−524655.	−	140581.i	−0.629408	−	0.168649i
$914$	129382.	−	74698.9i	0.154875	−	0.0894174i
$915$	−801887.	−	158821.i	−0.957791	−	0.189699i
$916$	234257.	−	405745.i	0.279191	−	0.483573i
$917$	−760971.	−	760971.i	−0.904960	−	0.904960i
$918$	−1.21589e6	+	321394.i	−1.44281	+	0.381375i
$919$			1.10906e6i			1.31318i	0.754246	+	0.656592i	$0.228003\pi$
$919$			1.10906e6i			1.31318i	−0.754246	+	0.656592i	$0.771997\pi$
$920$	−311081.	+	633922.i	−0.367535	+	0.748962i
$921$	1.33935e6	−	771263.i	1.57897	−	0.909250i
$922$	−59836.0	+	223311.i	−0.0703883	+	0.262693i
$923$	−57505.9	−	15408.7i	−0.0675008	−	0.0180868i
$924$	2.04031e6	+	2299.73i	2.38975	+	0.00269359i
$925$	−635664.	+	266208.i	−0.742923	+	0.311126i
$926$	47514.0			0.0554115
$927$	−198847.	−	199745.i	−0.231398	−	0.232443i
$928$	1.22563e6	−	1.22563e6i	1.42319	−	1.42319i
$929$	1.30303e6	+	752306.i	1.50981	+	0.871692i	0.999934	+	0.0114458i	$0.00364340\pi$
$929$	1.30303e6	+	752306.i	1.50981	+	0.871692i	0.509880	+	0.860246i	$0.329690\pi$
$930$	113714.	−	231067.i	0.131476	−	0.267161i
$931$	248854.	+	431027.i	0.287108	+	0.497285i
$932$	174603.	−	651629.i	0.201011	−	0.750185i
$933$	184206.	−	49135.3i	0.211612	−	0.0564456i
$934$	−592902.	−	342312.i	−0.679656	−	0.392400i
$935$	531427.	−	608364.i	0.607884	−	0.695889i
$936$	103904.	+	234.229i	0.118598	+	0.000267355i
$937$	−1.06969e6	−	1.06969e6i	−1.21837	−	1.21837i	−0.968201	−	0.250172i	$-0.919513\pi$
$937$	−1.06969e6	−	1.06969e6i	−1.21837	−	1.21837i	−0.250172	−	0.968201i	$-0.580487\pi$
$938$	−611661.	−	2.28275e6i	−0.695193	−	2.59449i
$939$	905491.	+	1020.62i	1.02696	+	0.00115753i
$940$	267582.	−	1.35906e6i	0.302832	−	1.53810i
$941$	90685.3	+	157072.i	0.102414	+	0.177386i	0.912679	−	0.408678i	$-0.134010\pi$
$941$	90685.3	+	157072.i	0.102414	+	0.177386i	−0.810265	+	0.586064i	$0.800677\pi$
$942$	1.29151e6	+	347620.i	1.45545	+	0.391745i
$943$	−104060.	−	388357.i	−0.117020	−	0.436725i
$944$			127031.i			0.142549i
$945$	−92169.7	−	1.43780e6i	−0.103211	−	1.61004i
$946$	1.74391e6			1.94868
$947$	−1.55342e6	+	416239.i	−1.73217	+	0.464133i	−0.980681	−	0.195614i	$-0.937330\pi$
$947$	−1.55342e6	+	416239.i	−1.73217	+	0.464133i	−0.751488	+	0.659747i	$0.770663\pi$
$948$	413752.	−	1.53721e6i	0.460387	−	1.71047i
$949$	71147.6	−	41077.1i	0.0790002	−	0.0456108i
$950$	508104.	+	64879.7i	0.562996	+	0.0718888i
$951$	−1989.40	+	1.76499e6i	−0.00219969	+	1.95156i
$952$	1.07502e6	−	288051.i	1.18616	−	0.317830i
$953$	−837262.	+	837262.i	−0.921883	+	0.921883i	−0.997162	−	0.0752797i	$-0.976015\pi$
$953$	−837262.	+	837262.i	−0.921883	+	0.921883i	0.0752797	+	0.997162i	$0.476015\pi$
$954$	−1.20950e6	+	694674.i	−1.32895	+	0.763281i
$955$	38215.8	+	566154.i	0.0419021	+	0.620765i
$956$	74838.1	−	129623.i	0.0818854	−	0.141830i
$957$	−397572.	−	1.49048e6i	−0.434102	−	1.62743i
$958$	−127516.	−	34167.8i	−0.138942	−	0.0372294i
$959$	153062.	−	88370.6i	0.166430	−	0.0960883i
$960$	−1.41969e6	+	483222.i	−1.54047	+	0.524330i
$961$	445450.	−	771542.i	0.482339	−	0.835435i
$962$	122560.	+	122560.i	0.132434	+	0.132434i
$963$	163689.	+	616450.i	0.176509	+	0.664730i
$964$		−	1.32878e6i		−	1.42987i
$965$	462672.	−	158062.i	0.496842	−	0.169736i
$966$	2775.70	−	2.46260e6i	0.00297453	−	2.63900i
$967$	−197297.	+	736322.i	−0.210993	+	0.787435i	0.776546	+	0.630060i	$0.216970\pi$
$967$	−197297.	+	736322.i	−0.210993	+	0.787435i	−0.987539	+	0.157375i	$0.949697\pi$
$968$	27621.4	+	7401.14i	0.0294778	+	0.00789856i
$969$	158118.	+	274582.i	0.168396	+	0.292432i
$970$	−874189.	+	1.78142e6i	−0.929099	+	1.89332i
$971$	1.03063e6			1.09311			0.546557	−	0.837422i	$-0.315938\pi$
$971$	1.03063e6			1.09311			0.546557	+	0.837422i	$0.315938\pi$
$972$	1.01447e6	−	1.00310e6i	1.07376	−	1.06172i
$973$	1.22515e6	−	1.22515e6i	1.29409	−	1.29409i
$974$	1.16293e6	+	671420.i	1.22585	+	0.707744i
$975$	85243.3	+	110456.i	0.0896708	+	0.116193i
$976$	−106882.	−	185125.i	−0.112203	−	0.194341i
$977$	368390.	−	1.37485e6i	0.385939	−	1.44034i	−0.450742	−	0.892654i	$-0.648840\pi$
$977$	368390.	−	1.37485e6i	0.385939	−	1.44034i	0.836681	−	0.547690i	$-0.184493\pi$
$978$	1.18138e6	+	1.18405e6i	1.23513	+	1.23792i
$979$	−1.19865e6	−	692038.i	−1.25062	−	0.722046i
$980$	156552.	+	2.31926e6i	0.163007	+	2.41489i
$981$	−630989.	+	1.08724e6i	−0.655667	+	1.12976i
$982$	−688776.	−	688776.i	−0.714258	−	0.714258i
$983$	48915.0	+	182553.i	0.0506215	+	0.188922i	0.986607	−	0.163117i	$-0.0521549\pi$
$983$	48915.0	+	182553.i	0.0506215	+	0.188922i	−0.935985	+	0.352040i	$0.885488\pi$
$984$	−171647.	+	296530.i	−0.177275	+	0.306251i
$985$	−1.18105e6	−	232535.i	−1.21730	−	0.239671i
$986$	−1.24562e6	−	2.15747e6i	−1.28124	−	2.21917i
$987$	420514.	+	1.57649e6i	0.431664	+	1.61829i
$988$	−20059.3	−	74862.2i	−0.0205495	−	0.0766918i
$989$		−	1.26627e6i		−	1.29460i
$990$	−297614.	+	1.49382e6i	−0.303656	+	1.52415i
$991$	−338833.			−0.345016			−0.172508	−	0.985008i	$-0.555187\pi$
$991$	−338833.			−0.345016			−0.172508	+	0.985008i	$0.555187\pi$
$992$	209404.	−	56109.7i	0.212795	−	0.0570184i
$993$	879438.	+	881423.i	0.891881	+	0.893893i
$994$	1.04134e6	−	601220.i	1.05395	−	0.608500i
$995$	−414526.	−	617772.i	−0.418702	−	0.623997i
$996$	862316.	−	496563.i	0.869256	−	0.500560i
$997$	877346.	−	235084.i	0.882634	−	0.236501i	0.211091	−	0.977467i	$-0.432299\pi$
$997$	877346.	−	235084.i	0.882634	−	0.236501i	0.671543	+	0.740966i	$0.265632\pi$
$998$	64409.2	−	64409.2i	0.0646676	−	0.0646676i
$999$	803826.	+	2718.09i	0.805436	+	0.00272354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.k.a.7.20	✓	88
3.2	odd	2		135.5.l.a.127.3		88
5.3	odd	4	inner	45.5.k.a.43.3	yes	88
9.4	even	3	inner	45.5.k.a.22.3	yes	88
9.5	odd	6		135.5.l.a.37.20		88
15.8	even	4		135.5.l.a.73.20		88
45.13	odd	12	inner	45.5.k.a.13.20	yes	88
45.23	even	12		135.5.l.a.118.3		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.k.a.7.20	✓	88	1.1	even	1	trivial
45.5.k.a.13.20	yes	88	45.13	odd	12	inner
45.5.k.a.22.3	yes	88	9.4	even	3	inner
45.5.k.a.43.3	yes	88	5.3	odd	4	inner
135.5.l.a.37.20		88	9.5	odd	6
135.5.l.a.73.20		88	15.8	even	4
135.5.l.a.118.3		88	45.23	even	12
135.5.l.a.127.3		88	3.2	odd	2

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(6.12130 - 1.64020i) q^{2} +(2.33917 - 8.69070i) q^{3} +(20.9237 - 12.0803i) q^{4} +(-20.7596 + 13.9297i) q^{5} +(0.0642868 - 57.0351i) q^{6} +(76.3600 - 20.4606i) q^{7} +(36.5683 - 36.5683i) q^{8} +(-70.0566 - 40.6580i) q^{9} +(-104.228 + 119.318i) q^{10} +(-59.3466 + 102.791i) q^{11} +(-56.0421 - 210.099i) q^{12} +(-23.9591 - 6.41983i) q^{13} +(433.863 - 250.491i) q^{14} +(72.4989 + 213.000i) q^{15} +(-29.4183 + 50.9540i) q^{16} +(192.494 + 192.494i) q^{17} +(-495.524 - 133.973i) q^{18} +129.326i q^{19} +(-266.092 + 542.243i) q^{20} +(0.801944 - 711.482i) q^{21} +(-194.680 + 726.556i) q^{22} +(527.562 + 141.360i) q^{23} +(-232.264 - 403.343i) q^{24} +(236.925 - 578.352i) q^{25} -157.191 q^{26} +(-517.221 + 513.735i) q^{27} +(1350.56 - 1350.56i) q^{28} +(-1250.58 - 722.025i) q^{29} +(793.149 + 1184.92i) q^{30} +(-90.3066 - 156.416i) q^{31} +(-310.662 + 1159.41i) q^{32} +(754.506 + 756.209i) q^{33} +(1494.04 + 862.585i) q^{34} +(-1300.19 + 1488.43i) q^{35} +(-1957.00 - 4.41165i) q^{36} +(-779.690 - 779.690i) q^{37} +(212.120 + 791.641i) q^{38} +(-111.837 + 193.205i) q^{39} +(-249.758 + 1268.53i) q^{40} +(-368.068 - 637.513i) q^{41} +(-1162.06 - 4356.51i) q^{42} +(-600.059 - 2239.45i) q^{43} +2867.69i q^{44} +(2020.70 - 131.824i) q^{45} +3461.22 q^{46} +(-2215.11 + 593.536i) q^{47} +(374.012 + 374.856i) q^{48} +(3332.88 - 1924.24i) q^{49} +(501.677 - 3928.87i) q^{50} +(2123.18 - 1222.63i) q^{51} +(-578.866 + 155.107i) q^{52} +(1921.37 - 1921.37i) q^{53} +(-2323.44 + 3993.07i) q^{54} +(-199.842 - 2960.59i) q^{55} +(2044.14 - 3540.56i) q^{56} +(1123.93 + 302.515i) q^{57} +(-8839.47 - 2368.53i) q^{58} +(1869.79 - 1079.52i) q^{59} +(4090.04 + 3580.93i) q^{60} +(-1816.59 + 3146.42i) q^{61} +(-809.346 - 809.346i) q^{62} +(-6181.41 - 1671.25i) q^{63} +6665.24i q^{64} +(586.810 - 200.471i) q^{65} +(5858.89 + 3391.44i) q^{66} +(1220.93 - 4556.55i) q^{67} +(6353.05 + 1702.30i) q^{68} +(2462.57 - 4254.22i) q^{69} +(-5517.56 + 11243.7i) q^{70} +2400.17 q^{71} +(-4048.64 + 1075.05i) q^{72} +(-2342.00 + 2342.00i) q^{73} +(-6051.56 - 3493.87i) q^{74} +(-4472.08 - 3411.91i) q^{75} +(1562.29 + 2705.96i) q^{76} +(-2428.53 + 9063.40i) q^{77} +(-367.696 + 1366.10i) q^{78} +(6340.19 + 3660.51i) q^{79} +(-99.0624 - 1467.58i) q^{80} +(3254.85 + 5696.73i) q^{81} +(-3298.70 - 3298.70i) q^{82} +(1184.41 + 4420.26i) q^{83} +(-8578.12 - 14896.5i) q^{84} +(-6677.49 - 1314.71i) q^{85} +(-7346.28 - 12724.1i) q^{86} +(-9200.24 + 9179.52i) q^{87} +(1588.70 + 5929.10i) q^{88} +11661.0i q^{89} +(12153.1 - 4121.29i) q^{90} -1960.87 q^{91} +(12746.2 - 3415.33i) q^{92} +(-1570.60 + 418.945i) q^{93} +(-12585.8 + 7266.42i) q^{94} +(-1801.47 - 2684.75i) q^{95} +(9349.37 + 5411.92i) q^{96} +(12098.3 - 3241.73i) q^{97} +(17245.4 - 17245.4i) q^{98} +(8336.91 - 4788.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 120 q^{6} - 2 q^{7} - 72 q^{8} - 8 q^{10} - 160 q^{11} + 186 q^{12} - 2 q^{13} + 270 q^{15} + 2044 q^{16} - 908 q^{17} - 1656 q^{18} - 834 q^{20} - 1428 q^{21} + 62 q^{22}+ \cdots + 193724 q^{98}+O(q^{100}) \) 88 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 120 * q^6 - 2 * q^7 - 72 * q^8 - 8 * q^10 - 160 * q^11 + 186 * q^12 - 2 * q^13 + 270 * q^15 + 2044 * q^16 - 908 * q^17 - 1656 * q^18 - 834 * q^20 - 1428 * q^21 + 62 * q^22 + 778 * q^23 + 292 * q^25 + 4112 * q^26 + 126 * q^27 - 1096 * q^28 - 4158 * q^30 - 4 * q^31 + 3874 * q^32 + 828 * q^33 - 2528 * q^35 - 7320 * q^36 + 2092 * q^37 - 1590 * q^38 + 510 * q^40 - 4732 * q^41 - 14382 * q^42 - 2 * q^43 + 7308 * q^45 + 2984 * q^46 + 7348 * q^47 + 5850 * q^48 + 12982 * q^50 + 16716 * q^51 - 1058 * q^52 + 25792 * q^53 + 3944 * q^55 - 15312 * q^56 - 4830 * q^57 - 4866 * q^58 - 8238 * q^60 - 5572 * q^61 - 26404 * q^62 - 10476 * q^63 + 22354 * q^65 + 13260 * q^66 - 2732 * q^67 - 39694 * q^68 - 2502 * q^70 + 16712 * q^71 + 80910 * q^72 - 8 * q^73 - 6570 * q^75 - 1632 * q^76 + 14642 * q^77 + 9222 * q^78 - 125516 * q^80 - 67764 * q^81 - 15304 * q^82 - 37022 * q^83 + 14782 * q^85 - 31432 * q^86 - 78786 * q^87 - 4986 * q^88 + 44502 * q^90 - 22360 * q^91 + 47692 * q^92 + 33378 * q^93 + 51120 * q^95 + 163716 * q^96 - 15272 * q^97 + 193724 * q^98

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