LMFDB - Embedded newform 76.7.b.a.39.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.13
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.59318 - 5.71982i) q^{2} -42.2777i q^{3} +(-1.43269 + 63.9840i) q^{4} -135.842 q^{5} +(-241.821 + 236.467i) q^{6} -128.069i q^{7} +(373.990 - 349.679i) q^{8} -1058.40 q^{9} +O(q^{10})$	\(q+(-5.59318 - 5.71982i) q^{2} -42.2777i q^{3} +(-1.43269 + 63.9840i) q^{4} -135.842 q^{5} +(-241.821 + 236.467i) q^{6} -128.069i q^{7} +(373.990 - 349.679i) q^{8} -1058.40 q^{9} +(759.791 + 776.994i) q^{10} +2133.91i q^{11} +(2705.09 + 60.5706i) q^{12} -506.011 q^{13} +(-732.529 + 716.311i) q^{14} +5743.10i q^{15} +(-4091.89 - 183.338i) q^{16} +506.329 q^{17} +(5919.84 + 6053.87i) q^{18} +1573.56i q^{19} +(194.619 - 8691.73i) q^{20} -5414.44 q^{21} +(12205.6 - 11935.3i) q^{22} -10226.2i q^{23} +(-14783.6 - 15811.4i) q^{24} +2828.15 q^{25} +(2830.21 + 2894.29i) q^{26} +13926.4i q^{27} +(8194.34 + 183.482i) q^{28} +11663.3 q^{29} +(32849.5 - 32122.2i) q^{30} +16424.9i q^{31} +(21838.0 + 24430.3i) q^{32} +90216.8 q^{33} +(-2831.99 - 2896.11i) q^{34} +17397.1i q^{35} +(1516.36 - 67720.8i) q^{36} +61358.1 q^{37} +(9000.49 - 8801.22i) q^{38} +21393.0i q^{39} +(-50803.7 + 47501.2i) q^{40} -56680.7 q^{41} +(30284.0 + 30969.6i) q^{42} -118420. i q^{43} +(-136536. - 3057.22i) q^{44} +143776. q^{45} +(-58492.3 + 57197.2i) q^{46} +172279. i q^{47} +(-7751.10 + 172996. i) q^{48} +101247. q^{49} +(-15818.4 - 16176.5i) q^{50} -21406.4i q^{51} +(724.954 - 32376.6i) q^{52} -114873. q^{53} +(79656.4 - 77892.8i) q^{54} -289875. i q^{55} +(-44782.9 - 47896.4i) q^{56} +66526.6 q^{57} +(-65235.2 - 66712.2i) q^{58} +107818. i q^{59} +(-367466. - 8228.06i) q^{60} -89812.3 q^{61} +(93947.4 - 91867.4i) q^{62} +135548. i q^{63} +(17593.1 - 261553. i) q^{64} +68737.7 q^{65} +(-504599. - 516024. i) q^{66} +487498. i q^{67} +(-725.411 + 32397.0i) q^{68} -432342. q^{69} +(99508.5 - 97305.4i) q^{70} +605920. i q^{71} +(-395832. + 370101. i) q^{72} +411272. q^{73} +(-343187. - 350957. i) q^{74} -119568. i q^{75} +(-100683. - 2254.42i) q^{76} +273287. q^{77} +(122364. - 119655. i) q^{78} +351255. i q^{79} +(555853. + 24905.0i) q^{80} -182800. q^{81} +(317025. + 324203. i) q^{82} +954987. i q^{83} +(7757.19 - 346438. i) q^{84} -68781.0 q^{85} +(-677342. + 662345. i) q^{86} -493099. i q^{87} +(746184. + 798061. i) q^{88} -1.24076e6 q^{89} +(-804165. - 822373. i) q^{90} +64804.1i q^{91} +(654316. + 14651.0i) q^{92} +694406. q^{93} +(985405. - 963588. i) q^{94} -213756. i q^{95} +(1.03286e6 - 923262. i) q^{96} -786271. q^{97} +(-566295. - 579117. i) q^{98} -2.25854e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−5.59318	−	5.71982i	−0.699147	−	0.714978i
$2$	−5.59318	−	5.71982i	−0.699147	−	0.714978i
$3$		−	42.2777i		−	1.56584i	−0.622122	−	0.782920i	$-0.713729\pi$
$3$		−	42.2777i		−	1.56584i	0.622122	−	0.782920i	$-0.286271\pi$
$4$	−1.43269	+	63.9840i	−0.0223857	+	0.999749i
$5$	−135.842			−1.08674			−0.543370	−	0.839494i	$-0.682852\pi$
$5$	−135.842			−1.08674			−0.543370	+	0.839494i	$0.682852\pi$
$6$	−241.821	+	236.467i	−1.11954	+	1.09475i
$7$		−	128.069i		−	0.373378i	−0.982419	−	0.186689i	$-0.940224\pi$
$7$		−	128.069i		−	0.373378i	0.982419	−	0.186689i	$-0.0597756\pi$
$8$	373.990	−	349.679i	0.730449	−	0.682967i
$9$	−1058.40			−1.45186
$10$	759.791	+	776.994i	0.759791	+	0.776994i
$11$			2133.91i			1.60324i	0.597835	+	0.801619i	$0.296028\pi$
$11$			2133.91i			1.60324i	−0.597835	+	0.801619i	$0.703972\pi$
$12$	2705.09	+	60.5706i	1.56545	+	0.0350524i
$13$	−506.011			−0.230319			−0.115159	−	0.993347i	$-0.536738\pi$
$13$	−506.011			−0.230319			−0.115159	+	0.993347i	$0.536738\pi$
$14$	−732.529	+	716.311i	−0.266957	+	0.261046i
$15$			5743.10i			1.70166i
$16$	−4091.89	−	183.338i	−0.998998	−	0.0447602i
$17$	506.329			0.103059			0.0515296	−	0.998671i	$-0.483590\pi$
$17$	506.329			0.103059			0.0515296	+	0.998671i	$0.483590\pi$
$18$	5919.84	+	6053.87i	1.01506	+	1.03804i
$19$			1573.56i			0.229416i
$19$			1573.56i			0.229416i
$20$	194.619	−	8691.73i	0.0243274	−	1.08647i
$21$	−5414.44			−0.584650
$22$	12205.6	−	11935.3i	1.14628	−	1.12090i
$23$		−	10226.2i		−	0.840490i	−0.907411	−	0.420245i	$-0.861944\pi$
$23$		−	10226.2i		−	0.840490i	0.907411	−	0.420245i	$-0.138056\pi$
$24$	−14783.6	−	15811.4i	−1.06942	−	1.14377i
$25$	2828.15			0.181002
$26$	2830.21	+	2894.29i	0.161027	+	0.164673i
$27$			13926.4i			0.707534i
$28$	8194.34	+	183.482i	0.373284	+	0.00835833i
$29$	11663.3			0.478222			0.239111	−	0.970992i	$-0.423144\pi$
$29$	11663.3			0.478222			0.239111	+	0.970992i	$0.423144\pi$
$30$	32849.5	−	32122.2i	1.21665	−	1.18971i
$31$			16424.9i			0.551337i	0.961253	+	0.275669i	$0.0888992\pi$
$31$			16424.9i			0.551337i	−0.961253	+	0.275669i	$0.911101\pi$
$32$	21838.0	+	24430.3i	0.666444	+	0.745555i
$33$	90216.8			2.51042
$34$	−2831.99	−	2896.11i	−0.0720535	−	0.0736849i
$35$			17397.1i			0.405764i
$36$	1516.36	−	67720.8i	0.0325008	−	1.45149i
$37$	61358.1			1.21134			0.605671	−	0.795715i	$-0.292905\pi$
$37$	61358.1			1.21134			0.605671	+	0.795715i	$0.292905\pi$
$38$	9000.49	−	8801.22i	0.164027	−	0.160395i
$39$			21393.0i			0.360643i
$40$	−50803.7	+	47501.2i	−0.793808	+	0.742207i
$41$	−56680.7			−0.822401			−0.411200	−	0.911545i	$-0.634890\pi$
$41$	−56680.7			−0.822401			−0.411200	+	0.911545i	$0.634890\pi$
$42$	30284.0	+	30969.6i	0.408757	+	0.418012i
$43$		−	118420.i		−	1.48943i	−0.667383	−	0.744715i	$-0.732585\pi$
$43$		−	118420.i		−	1.48943i	0.667383	−	0.744715i	$-0.267415\pi$
$44$	−136536.	−	3057.22i	−1.60284	−	0.0358896i
$45$	143776.			1.57779
$46$	−58492.3	+	57197.2i	−0.600932	+	0.587627i
$47$			172279.i			1.65935i	0.558244	+	0.829677i	$0.311475\pi$
$47$			172279.i			1.65935i	−0.558244	+	0.829677i	$0.688525\pi$
$48$	−7751.10	+	172996.i	−0.0700873	+	1.56427i
$49$	101247.			0.860589
$50$	−15818.4	−	16176.5i	−0.126547	−	0.129412i
$51$		−	21406.4i		−	0.161374i
$52$	724.954	−	32376.6i	0.00515585	−	0.230261i
$53$	−114873.			−0.771599			−0.385799	−	0.922583i	$-0.626074\pi$
$53$	−114873.			−0.771599			−0.385799	+	0.922583i	$0.626074\pi$
$54$	79656.4	−	77892.8i	0.505871	−	0.494670i
$55$		−	289875.i		−	1.74230i
$56$	−44782.9	−	47896.4i	−0.255005	−	0.272734i
$57$	66526.6			0.359228
$58$	−65235.2	−	66712.2i	−0.334347	−	0.341918i
$59$			107818.i			0.524972i	0.964936	+	0.262486i	$0.0845423\pi$
$59$			107818.i			0.524972i	−0.964936	+	0.262486i	$0.915458\pi$
$60$	−367466.	−	8228.06i	−1.70123	−	0.0380929i
$61$	−89812.3			−0.395682			−0.197841	−	0.980234i	$-0.563393\pi$
$61$	−89812.3			−0.395682			−0.197841	+	0.980234i	$0.563393\pi$
$62$	93947.4	−	91867.4i	0.394194	−	0.385466i
$63$			135548.i			0.542091i
$64$	17593.1	−	261553.i	0.0671123	−	0.997745i
$65$	68737.7			0.250297
$66$	−504599.	−	516024.i	−1.75515	−	1.79489i
$67$			487498.i			1.62087i	0.585827	+	0.810436i	$0.300770\pi$
$67$			487498.i			1.62087i	−0.585827	+	0.810436i	$0.699230\pi$
$68$	−725.411	+	32397.0i	−0.00230705	+	0.103033i
$69$	−432342.			−1.31607
$70$	99508.5	−	97305.4i	0.290112	−	0.283689i
$71$			605920.i			1.69294i	0.532440	+	0.846468i	$0.321275\pi$
$71$			605920.i			1.69294i	−0.532440	+	0.846468i	$0.678725\pi$
$72$	−395832.	+	370101.i	−1.06051	+	0.991569i
$73$	411272.			1.05721			0.528605	−	0.848868i	$-0.322715\pi$
$73$	411272.			1.05721			0.528605	+	0.848868i	$0.322715\pi$
$74$	−343187.	−	350957.i	−0.846906	−	0.866082i
$75$		−	119568.i		−	0.283420i
$76$	−100683.	−	2254.42i	−0.229358	−	0.00513563i
$77$	273287.			0.598614
$78$	122364.	−	119655.i	0.257851	−	0.252142i
$79$			351255.i			0.712428i	0.934404	+	0.356214i	$0.115933\pi$
$79$			351255.i			0.712428i	−0.934404	+	0.356214i	$0.884067\pi$
$80$	555853.	+	24905.0i	1.08565	+	0.0486427i
$81$	−182800.			−0.343971
$82$	317025.	+	324203.i	0.574980	+	0.587998i
$83$			954987.i			1.67018i	0.550114	+	0.835090i	$0.314584\pi$
$83$			954987.i			1.67018i	−0.550114	+	0.835090i	$0.685416\pi$
$84$	7757.19	−	346438.i	0.0130878	−	0.584504i
$85$	−68781.0			−0.111998
$86$	−677342.	+	662345.i	−1.06491	+	1.04133i
$87$		−	493099.i		−	0.748819i
$88$	746184.	+	798061.i	1.09496	+	1.17108i
$89$	−1.24076e6			−1.76002			−0.880009	−	0.474957i	$-0.842464\pi$
$89$	−1.24076e6			−1.76002			−0.880009	+	0.474957i	$0.842464\pi$
$90$	−804165.	−	822373.i	−1.10311	−	1.12808i
$91$			64804.1i			0.0859960i
$92$	654316.	+	14651.0i	0.840280	+	0.0188150i
$93$	694406.			0.863306
$94$	985405.	−	963588.i	1.18640	−	1.16013i
$95$		−	213756.i		−	0.249315i
$96$	1.03286e6	−	923262.i	1.16742	−	1.04355i
$97$	−786271.			−0.861504			−0.430752	−	0.902470i	$-0.641752\pi$
$97$	−786271.			−0.861504			−0.430752	+	0.902470i	$0.641752\pi$
$98$	−566295.	−	579117.i	−0.601679	−	0.615302i
$99$		−	2.25854e6i		−	2.32767i
$100$	−4051.86	+	180957.i	−0.00405186	+	0.180957i
$101$	683726.			0.663618			0.331809	−	0.943347i	$-0.392341\pi$
$101$	683726.			0.663618			0.331809	+	0.943347i	$0.392341\pi$
$102$	−122441.	+	119730.i	−0.115379	+	0.112824i
$103$		−	1.39493e6i		−	1.27656i	−0.769805	−	0.638279i	$-0.779647\pi$
$103$		−	1.39493e6i		−	1.27656i	0.769805	−	0.638279i	$-0.220353\pi$
$104$	−189243.	+	176941.i	−0.168236	+	0.157300i
$105$	735511.			0.635362
$106$	642507.	+	657055.i	0.539461	+	0.551676i
$107$			1.39953e6i			1.14243i	0.820800	+	0.571216i	$0.193528\pi$
$107$			1.39953e6i			1.14243i	−0.820800	+	0.571216i	$0.806472\pi$
$108$	−891065.	−	19952.1i	−0.707356	−	0.0158386i
$109$	1.94508e6			1.50196			0.750980	−	0.660325i	$-0.229581\pi$
$109$	1.94508e6			1.50196			0.750980	+	0.660325i	$0.229581\pi$
$110$	−1.65804e6	+	1.62133e6i	−1.24571	+	1.21813i
$111$		−	2.59408e6i		−	1.89677i
$112$	−23479.8	+	524043.i	−0.0167125	+	0.373004i
$113$	1.77736e6			1.23180			0.615900	−	0.787824i	$-0.288793\pi$
$113$	1.77736e6			1.23180			0.615900	+	0.787824i	$0.288793\pi$
$114$	−372095.	−	380520.i	−0.251154	−	0.256840i
$115$			1.38916e6i			0.913394i
$116$	−16709.9	+	746267.i	−0.0107053	+	0.478102i
$117$	535563.			0.334390
$118$	616701.	−	603046.i	0.375343	−	0.367033i
$119$		−	64844.9i		−	0.0384800i
$120$	2.00824e6	+	2.14786e6i	1.16218	+	1.24298i
$121$	−2.78201e6			−1.57037
$122$	502336.	+	513710.i	0.276640	+	0.282904i
$123$			2.39633e6i			1.28775i
$124$	−1.05093e6	−	23531.7i	−0.551199	−	0.0123421i
$125$	1.73835e6			0.890037
$126$	775311.	−	758145.i	0.387583	−	0.379001i
$127$		−	321283.i		−	0.156847i	−0.996920	−	0.0784235i	$-0.975011\pi$
$127$		−	321283.i		−	0.156847i	0.996920	−	0.0784235i	$-0.0249886\pi$
$128$	−1.59444e6	+	1.36228e6i	−0.760287	+	0.649587i
$129$	−5.00653e6			−2.33221
$130$	−384462.	−	393167.i	−0.174994	−	0.178956i
$131$			2.33586e6i			1.03904i	0.854458	+	0.519520i	$0.173889\pi$
$131$			2.33586e6i			1.03904i	−0.854458	+	0.519520i	$0.826111\pi$
$132$	−129252.	+	5.77243e6i	−0.0561974	+	2.50979i
$133$	201524.			0.0856588
$134$	2.78840e6	−	2.72667e6i	1.15889	−	1.13323i
$135$		−	1.89179e6i		−	0.768904i
$136$	189362.	−	177053.i	0.0752795	−	0.0703860i
$137$	−1.47868e6			−0.575059			−0.287530	−	0.957772i	$-0.592834\pi$
$137$	−1.47868e6			−0.575059			−0.287530	+	0.957772i	$0.592834\pi$
$138$	2.41817e6	+	2.47292e6i	0.920129	+	0.940963i
$139$		−	2.28582e6i		−	0.851134i	−0.904927	−	0.425567i	$-0.860075\pi$
$139$		−	2.28582e6i		−	0.851134i	0.904927	−	0.425567i	$-0.139925\pi$
$140$	−1.11314e6	−	24924.6i	−0.405663	−	0.00908332i
$141$	7.28356e6			2.59828
$142$	3.46575e6	−	3.38902e6i	1.21041	−	1.18361i
$143$		−	1.07978e6i		−	0.369256i
$144$	4.33087e6	+	194045.i	1.45040	+	0.0649853i
$145$	−1.58438e6			−0.519702
$146$	−2.30032e6	−	2.35240e6i	−0.739145	−	0.755881i
$147$		−	4.28051e6i		−	1.34754i
$148$	−87906.8	+	3.92593e6i	−0.0271167	+	1.21104i
$149$	−4.57881e6			−1.38418			−0.692092	−	0.721809i	$-0.743311\pi$
$149$	−4.57881e6			−1.38418			−0.692092	+	0.721809i	$0.743311\pi$
$150$	−683906.	+	668764.i	−0.202639	+	0.198152i
$151$		−	1.06339e6i		−	0.308861i	−0.988004	−	0.154430i	$-0.950646\pi$
$151$		−	1.06339e6i		−	0.308861i	0.988004	−	0.154430i	$-0.0493542\pi$
$152$	550242.	+	588497.i	0.156683	+	0.167577i
$153$	−535900.			−0.149627
$154$	−1.52854e6	−	1.56315e6i	−0.418519	−	0.427995i
$155$		−	2.23120e6i		−	0.599160i
$156$	−1.36881e6	−	30649.4i	−0.360552	−	0.00807324i
$157$	−254950.			−0.0658803			−0.0329402	−	0.999457i	$-0.510487\pi$
$157$	−254950.			−0.0658803			−0.0329402	+	0.999457i	$0.510487\pi$
$158$	2.00911e6	−	1.96463e6i	0.509370	−	0.498092i
$159$			4.85658e6i			1.20820i
$160$	−2.96653e6	−	3.31868e6i	−0.724251	−	0.810224i
$161$	−1.30966e6			−0.313820
$162$	1.02243e6	+	1.04558e6i	0.240486	+	0.245932i
$163$			1.22136e6i			0.282019i	0.990008	+	0.141010i	$0.0450349\pi$
$163$			1.22136e6i			0.282019i	−0.990008	+	0.141010i	$0.954965\pi$
$164$	81205.6	−	3.62666e6i	0.0184100	−	0.822195i
$165$	−1.22553e7			−2.72817
$166$	5.46235e6	−	5.34141e6i	1.19414	−	1.16770i
$167$		−	4.85716e6i		−	1.04288i	−0.853289	−	0.521439i	$-0.825395\pi$
$167$		−	4.85716e6i		−	1.04288i	0.853289	−	0.521439i	$-0.174605\pi$
$168$	−2.02495e6	+	1.89332e6i	−0.427057	+	0.399297i
$169$	−4.57076e6			−0.946953
$170$	384704.	+	393415.i	0.0783034	+	0.0800763i
$171$		−	1.66546e6i		−	0.333079i
$172$	7.57699e6	+	169659.i	1.48906	+	0.0333419i
$173$	−5.91797e6			−1.14297			−0.571484	−	0.820613i	$-0.693632\pi$
$173$	−5.91797e6			−1.14297			−0.571484	+	0.820613i	$0.693632\pi$
$174$	−2.82044e6	+	2.75799e6i	−0.535388	+	0.523535i
$175$		−	362198.i		−	0.0675821i
$176$	391226.	−	8.73174e6i	0.0717613	−	1.60163i
$177$	4.55830e6			0.822022
$178$	6.93978e6	+	7.09691e6i	1.23051	+	1.25837i
$179$			6.77457e6i			1.18120i	0.806965	+	0.590599i	$0.201109\pi$
$179$			6.77457e6i			1.18120i	−0.806965	+	0.590599i	$0.798891\pi$
$180$	−205986.	+	9.19936e6i	−0.0353199	+	1.57739i
$181$	1.01498e7			1.71168			0.855838	−	0.517245i	$-0.173042\pi$
$181$	1.01498e7			1.71168			0.855838	+	0.517245i	$0.173042\pi$
$182$	370668.	−	362461.i	0.0614852	−	0.0601239i
$183$			3.79706e6i			0.619575i
$184$	−3.57590e6	−	3.82451e6i	−0.574027	−	0.613936i
$185$	−8.33503e6			−1.31641
$186$	−3.88394e6	−	3.97188e6i	−0.603578	−	0.617244i
$187$			1.08046e6i			0.165228i
$188$	−1.10231e7	−	246822.i	−1.65894	−	0.0371458i
$189$	1.78353e6			0.264177
$190$	−1.22265e6	+	1.19558e6i	−0.178255	+	0.174308i
$191$			1.35214e6i			0.194053i	0.995282	+	0.0970267i	$0.0309332\pi$
$191$			1.35214e6i			0.194053i	−0.995282	+	0.0970267i	$0.969067\pi$
$192$	−1.10579e7	−	743794.i	−1.56231	−	0.105087i
$193$	−6.10922e6			−0.849794			−0.424897	−	0.905242i	$-0.639690\pi$
$193$	−6.10922e6			−0.849794			−0.424897	+	0.905242i	$0.639690\pi$
$194$	4.39776e6	+	4.49733e6i	0.602318	+	0.615956i
$195$		−	2.90607e6i		−	0.391924i
$196$	−145056.	+	6.47821e6i	−0.0192649	+	0.860373i
$197$	−4.05456e6			−0.530329			−0.265164	−	0.964203i	$-0.585426\pi$
$197$	−4.05456e6			−0.530329			−0.265164	+	0.964203i	$0.585426\pi$
$198$	−1.29184e7	+	1.26324e7i	−1.66423	+	1.62739i
$199$		−	9.59076e6i		−	1.21701i	−0.793550	−	0.608505i	$-0.791770\pi$
$199$		−	9.59076e6i		−	1.21701i	0.793550	−	0.608505i	$-0.208230\pi$
$200$	1.05770e6	−	988946.i	0.132213	−	0.123618i
$201$	2.06103e7			2.53803
$202$	−3.82420e6	−	3.91079e6i	−0.463967	−	0.474472i
$203$		−	1.49371e6i		−	0.178557i
$204$	1.36967e6	+	30668.7i	0.161334	+	0.00361247i
$205$	7.69964e6			0.893735
$206$	−7.97874e6	+	7.80209e6i	−0.912710	+	0.892502i
$207$			1.08235e7i			1.22027i
$208$	2.07054e6	+	92770.9i	0.230088	+	0.0103091i
$209$	−3.35784e6			−0.367808
$210$	−4.11385e6	−	4.20699e6i	−0.444212	−	0.454270i
$211$			1.50061e7i			1.59743i	0.601709	+	0.798715i	$0.294487\pi$
$211$			1.50061e7i			1.59743i	−0.601709	+	0.798715i	$0.705513\pi$
$212$	164577.	−	7.35005e6i	0.0172728	−	0.771405i
$213$	2.56169e7			2.65087
$214$	8.00506e6	−	7.82782e6i	0.816814	−	0.798729i
$215$			1.60865e7i			1.61862i
$216$	4.86977e6	+	5.20833e6i	0.483222	+	0.516817i
$217$	2.10351e6			0.205857
$218$	−1.08792e7	−	1.11255e7i	−1.05009	−	1.07387i
$219$		−	1.73876e7i		−	1.65542i
$220$	1.85474e7	+	415300.i	1.74187	+	0.0390027i
$221$	−256208.			−0.0237365
$222$	−1.48377e7	+	1.45091e7i	−1.35615	+	1.32612i
$223$			1.25571e7i			1.13233i	0.824292	+	0.566165i	$0.191574\pi$
$223$			1.25571e7i			1.13233i	−0.824292	+	0.566165i	$0.808426\pi$
$224$	3.12876e6	−	2.79677e6i	0.278374	−	0.248835i
$225$	−2.99333e6			−0.262789
$226$	−9.94109e6	−	1.01662e7i	−0.861210	−	0.880709i
$227$		−	1.52227e7i		−	1.30141i	−0.759332	−	0.650703i	$-0.774474\pi$
$227$		−	1.52227e7i		−	1.30141i	0.759332	−	0.650703i	$-0.225526\pi$
$228$	−95311.7	+	4.25663e6i	−0.00804158	+	0.359138i
$229$	1.08681e7			0.904999			0.452499	−	0.891765i	$-0.350532\pi$
$229$	1.08681e7			0.904999			0.452499	+	0.891765i	$0.350532\pi$
$230$	7.94573e6	−	7.76981e6i	0.653056	−	0.638597i
$231$		−	1.15539e7i		−	0.937333i
$232$	4.36198e6	−	4.07843e6i	0.349317	−	0.326610i
$233$	−1.51934e7			−1.20112			−0.600561	−	0.799579i	$-0.705056\pi$
$233$	−1.51934e7			−1.20112			−0.600561	+	0.799579i	$0.705056\pi$
$234$	−2.99550e6	−	3.06332e6i	−0.233788	−	0.239081i
$235$		−	2.34028e7i		−	1.80328i
$236$	−6.89863e6	−	154470.i	−0.524840	−	0.0117519i
$237$	1.48502e7			1.11555
$238$	−370901.	+	362689.i	−0.0275123	+	0.0269032i
$239$			3.15586e6i			0.231166i	0.993298	+	0.115583i	$0.0368736\pi$
$239$			3.15586e6i			0.231166i	−0.993298	+	0.115583i	$0.963126\pi$
$240$	1.05293e6	−	2.35002e7i	0.0761666	−	1.69995i
$241$	−1.79761e7			−1.28424			−0.642118	−	0.766606i	$-0.721944\pi$
$241$	−1.79761e7			−1.28424			−0.642118	+	0.766606i	$0.721944\pi$
$242$	1.55603e7	+	1.59126e7i	1.09792	+	1.12278i
$243$			1.78807e7i			1.24614i
$244$	128673.	−	5.74655e6i	0.00885762	−	0.395583i
$245$	−1.37537e7			−0.935236
$246$	1.37066e7	−	1.34031e7i	0.920711	−	0.900326i
$247$		−	796239.i		−	0.0528388i
$248$	5.74344e6	+	6.14274e6i	0.376545	+	0.402724i
$249$	4.03746e7			2.61523
$250$	−9.72293e6	−	9.94307e6i	−0.622267	−	0.636357i
$251$			4.62501e6i			0.292477i	0.989249	+	0.146238i	$0.0467167\pi$
$251$			4.62501e6i			0.292477i	−0.989249	+	0.146238i	$0.953283\pi$
$252$	−8.67291e6	−	194198.i	−0.541955	−	0.0121351i
$253$	2.18219e7			1.34751
$254$	−1.83768e6	+	1.79699e6i	−0.112142	+	0.109659i
$255$			2.90790e6i			0.175372i
$256$	1.67100e7	+	1.50040e6i	0.995993	+	0.0894307i
$257$	−7.08799e6			−0.417564			−0.208782	−	0.977962i	$-0.566950\pi$
$257$	−7.08799e6			−0.417564			−0.208782	+	0.977962i	$0.566950\pi$
$258$	2.80024e7	+	2.86364e7i	1.63056	+	1.66748i
$259$		−	7.85804e6i		−	0.452288i
$260$	−98479.5	+	4.39811e6i	−0.00560307	+	0.250234i
$261$	−1.23445e7			−0.694309
$262$	1.33607e7	−	1.30649e7i	0.742890	−	0.726442i
$263$			3.36544e6i			0.185001i	0.995713	+	0.0925005i	$0.0294860\pi$
$263$			3.36544e6i			0.185001i	−0.995713	+	0.0925005i	$0.970514\pi$
$264$	3.37402e7	−	3.15469e7i	1.83373	−	1.71453i
$265$	1.56047e7			0.838527
$266$	−1.12716e6	−	1.15268e6i	−0.0598881	−	0.0612441i
$267$			5.24564e7i			2.75591i
$268$	−3.11921e7	−	698432.i	−1.62047	−	0.0362844i
$269$	3.09506e7			1.59005			0.795027	−	0.606573i	$-0.207456\pi$
$269$	3.09506e7			1.59005			0.795027	+	0.606573i	$0.207456\pi$
$270$	−1.08207e7	+	1.05811e7i	−0.549749	+	0.537578i
$271$			1.00907e7i			0.507006i	0.967335	+	0.253503i	$0.0815828\pi$
$271$			1.00907e7i			0.507006i	−0.967335	+	0.253503i	$0.918417\pi$
$272$	−2.07185e6	−	92829.3i	−0.102956	−	0.00461295i
$273$	2.73977e6			0.134656
$274$	8.27052e6	+	8.45778e6i	0.402051	+	0.411154i
$275$			6.03503e6i			0.290189i
$276$	619410.	−	2.76630e7i	0.0294612	−	1.31574i
$277$	−3.75660e7			−1.76748			−0.883742	−	0.467975i	$-0.844984\pi$
$277$	−3.75660e7			−1.76748			−0.883742	+	0.467975i	$0.844984\pi$
$278$	−1.30745e7	+	1.27850e7i	−0.608542	+	0.595068i
$279$		−	1.73841e7i		−	0.800462i
$280$	6.08342e6	+	6.50636e6i	0.277124	+	0.296390i
$281$	−2.51670e7			−1.13426			−0.567129	−	0.823629i	$-0.691946\pi$
$281$	−2.51670e7			−1.13426			−0.567129	+	0.823629i	$0.691946\pi$
$282$	−4.07383e7	−	4.16607e7i	−1.81658	−	1.85771i
$283$			1.92125e7i			0.847668i	0.905740	+	0.423834i	$0.139316\pi$
$283$			1.92125e7i			0.847668i	−0.905740	+	0.423834i	$0.860684\pi$
$284$	−3.87692e7	−	868093.i	−1.69251	−	0.0378976i
$285$	−9.03713e6			−0.390388
$286$	−6.17615e6	+	6.03941e6i	−0.264010	+	0.258164i
$287$			7.25902e6i			0.307066i
$288$	−2.31134e7	−	2.58571e7i	−0.967581	−	1.08244i
$289$	−2.38812e7			−0.989379
$290$	8.86170e6	+	9.06235e6i	0.363348	+	0.371575i
$291$			3.32417e7i			1.34898i
$292$	−589224.	+	2.63148e7i	−0.0236664	+	1.05694i
$293$	3.32410e7			1.32151			0.660756	−	0.750601i	$-0.270236\pi$
$293$	3.32410e7			1.32151			0.660756	+	0.750601i	$0.270236\pi$
$294$	−2.44837e7	+	2.39416e7i	−0.963464	+	0.942133i
$295$		−	1.46463e7i		−	0.570507i
$296$	2.29473e7	−	2.14556e7i	0.884824	−	0.827306i
$297$	−2.97177e7			−1.13435
$298$	2.56101e7	+	2.61900e7i	0.967749	+	0.989661i
$299$			5.17459e6i			0.193581i
$300$	7.65042e6	+	171303.i	0.283349	+	0.00634456i
$301$	−1.51659e7			−0.556120
$302$	−6.08241e6	+	5.94775e6i	−0.220829	+	0.215939i
$303$		−	2.89064e7i		−	1.03912i
$304$	288493.	−	6.43885e6i	0.0102687	−	0.229186i
$305$	1.22003e7			0.430003
$306$	2.99739e6	+	3.06525e6i	0.104611	+	0.106980i
$307$		−	4.96436e6i		−	0.171573i	−0.996314	−	0.0857863i	$-0.972660\pi$
$307$		−	4.96436e6i		−	0.171573i	0.996314	−	0.0857863i	$-0.0273402\pi$
$308$	−391534.	+	1.74860e7i	−0.0134004	+	0.598464i
$309$	−5.89744e7			−1.99888
$310$	−1.27620e7	+	1.24795e7i	−0.428386	+	0.418901i
$311$		−	4.34971e7i		−	1.44603i	−0.690830	−	0.723017i	$-0.742755\pi$
$311$		−	4.34971e7i		−	1.44603i	0.690830	−	0.723017i	$-0.257245\pi$
$312$	7.48067e6	+	8.00075e6i	0.246307	+	0.263431i
$313$	1.59172e7			0.519079			0.259539	−	0.965733i	$-0.416429\pi$
$313$	1.59172e7			0.519079			0.259539	+	0.965733i	$0.416429\pi$
$314$	1.42598e6	+	1.45827e6i	0.0460601	+	0.0471029i
$315$		−	1.84132e7i		−	0.589111i
$316$	−2.24747e7	−	503238.i	−0.712249	−	0.0159482i
$317$	−2.86581e7			−0.899642			−0.449821	−	0.893119i	$-0.648512\pi$
$317$	−2.86581e7			−0.899642			−0.449821	+	0.893119i	$0.648512\pi$
$318$	2.77788e7	−	2.71637e7i	0.863836	−	0.844710i
$319$			2.48885e7i			0.766703i
$320$	−2.38989e6	+	3.55300e7i	−0.0729335	+	1.08429i
$321$	5.91689e7			1.78887
$322$	7.32517e6	+	7.49103e6i	0.219407	+	0.224375i
$323$			796741.i			0.0236434i
$324$	261895.	−	1.16963e7i	0.00770003	−	0.343885i
$325$	−1.43108e6			−0.0416882
$326$	6.98593e6	−	6.83126e6i	0.201638	−	0.197173i
$327$		−	8.22335e7i		−	2.35183i
$328$	−2.11980e7	+	1.98201e7i	−0.600722	+	0.561673i
$329$	2.20635e7			0.619566
$330$	6.85459e7	+	7.00979e7i	1.90739	+	1.95058i
$331$			3.91798e7i			1.08039i	0.841541	+	0.540193i	$0.181649\pi$
$331$			3.91798e7i			1.08039i	−0.841541	+	0.540193i	$0.818351\pi$
$332$	−6.11038e7	−	1.36820e6i	−1.66976	−	0.0373882i
$333$	−6.49416e7			−1.75869
$334$	−2.77821e7	+	2.71670e7i	−0.745634	+	0.729125i
$335$		−	6.62229e7i		−	1.76147i
$336$	2.21553e7	+	992672.i	0.584064	+	0.0261691i
$337$	−1.28414e7			−0.335524			−0.167762	−	0.985828i	$-0.553654\pi$
$337$	−1.28414e7			−0.335524			−0.167762	+	0.985828i	$0.553654\pi$
$338$	2.55651e7	+	2.61439e7i	0.662060	+	0.677050i
$339$		−	7.51427e7i		−	1.92880i
$340$	98541.5	−	4.40088e6i	0.00250716	−	0.111970i
$341$	−3.50492e7			−0.883925
$342$	−9.52615e6	+	9.31523e6i	−0.238144	+	0.232871i
$343$		−	2.80338e7i		−	0.694703i
$344$	−4.14090e7	−	4.42879e7i	−1.01723	−	1.08795i
$345$	5.87304e7			1.43023
$346$	3.31003e7	+	3.38497e7i	0.799104	+	0.817197i
$347$			1.91750e7i			0.458931i	0.973317	+	0.229466i	$0.0736979\pi$
$347$			1.91750e7i			0.458931i	−0.973317	+	0.229466i	$0.926302\pi$
$348$	3.15504e7	+	706456.i	0.748631	+	0.0167628i
$349$	−1.22976e7			−0.289297			−0.144649	−	0.989483i	$-0.546205\pi$
$349$	−1.22976e7			−0.289297			−0.144649	+	0.989483i	$0.546205\pi$
$350$	−2.07171e6	+	2.02584e6i	−0.0483197	+	0.0472498i
$351$		−	7.04690e6i		−	0.162958i
$352$	−5.21322e7	+	4.66004e7i	−1.19530	+	1.06847i
$353$	−1.19218e7			−0.271030			−0.135515	−	0.990775i	$-0.543269\pi$
$353$	−1.19218e7			−0.271030			−0.135515	+	0.990775i	$0.543269\pi$
$354$	−2.54954e7	−	2.60727e7i	−0.574715	−	0.587727i
$355$		−	8.23096e7i		−	1.83978i
$356$	1.77762e6	−	7.93886e7i	0.0393992	−	1.75958i
$357$	−2.74149e6			−0.0602535
$358$	3.87493e7	−	3.78914e7i	0.844530	−	0.825832i
$359$			4.71015e7i			1.01801i	0.860764	+	0.509004i	$0.169986\pi$
$359$			4.71015e7i			1.01801i	−0.860764	+	0.509004i	$0.830014\pi$
$360$	5.37708e7	−	5.02754e7i	1.15249	−	1.07758i
$361$	−2.47610e6			−0.0526316
$362$	−5.67696e7	−	5.80550e7i	−1.19671	−	1.22381i
$363$			1.17617e8i			2.45895i
$364$	−4.14642e6	−	92843.8i	−0.0859744	−	0.00192508i
$365$	−5.58682e7			−1.14891
$366$	2.17185e7	−	2.12376e7i	0.442982	−	0.433174i
$367$			1.10353e7i			0.223248i	0.993751	+	0.111624i	$0.0356052\pi$
$367$			1.10353e7i			0.223248i	−0.993751	+	0.111624i	$0.964395\pi$
$368$	−1.87486e6	+	4.18447e7i	−0.0376205	+	0.839648i
$369$	5.99910e7			1.19401
$370$	4.66193e7	+	4.76749e7i	0.920366	+	0.941205i
$371$			1.47117e7i			0.288098i
$372$	−994866.	+	4.44309e7i	−0.0193257	+	0.863090i
$373$	2.77202e7			0.534159			0.267079	−	0.963675i	$-0.413941\pi$
$373$	2.77202e7			0.534159			0.267079	+	0.963675i	$0.413941\pi$
$374$	6.18005e6	−	6.04322e6i	0.118135	−	0.115519i
$375$		−	7.34936e7i		−	1.39366i
$376$	6.02424e7	+	6.44307e7i	1.13328	+	1.21207i
$377$	−5.90178e6			−0.110143
$378$	−9.97562e6	−	1.02015e7i	−0.184699	−	0.188881i
$379$			1.49573e7i			0.274749i	0.990519	+	0.137374i	$0.0438663\pi$
$379$			1.49573e7i			0.274749i	−0.990519	+	0.137374i	$0.956134\pi$
$380$	1.36770e7	+	306246.i	0.249253	+	0.00558109i
$381$	−1.35831e7			−0.245597
$382$	7.73399e6	−	7.56276e6i	0.138744	−	0.135672i
$383$			1.09639e7i			0.195150i	0.995228	+	0.0975750i	$0.0311086\pi$
$383$			1.09639e7i			0.195150i	−0.995228	+	0.0975750i	$0.968891\pi$
$384$	5.75942e7	+	6.74091e7i	1.01715	+	1.19049i
$385$	−3.71239e7			−0.650537
$386$	3.41699e7	+	3.49436e7i	0.594131	+	0.607584i
$387$			1.25336e8i			2.16244i
$388$	1.12648e6	−	5.03088e7i	0.0192854	−	0.861288i
$389$	263243.			0.00447206			0.00223603	−	0.999998i	$-0.499288\pi$
$389$	263243.			0.00447206			0.00223603	+	0.999998i	$0.499288\pi$
$390$	−1.66222e7	+	1.62542e7i	−0.280217	+	0.274013i
$391$		−	5.17785e6i		−	0.0866202i
$392$	3.78655e7	−	3.54041e7i	0.628617	−	0.587754i
$393$	9.87546e7			1.62697
$394$	2.26779e7	+	2.31914e7i	0.370778	+	0.379173i
$395$		−	4.77153e7i		−	0.774223i
$396$	1.44510e8	+	3.23577e6i	2.32709	+	0.0521066i
$397$	−6.51444e6			−0.104113			−0.0520566	−	0.998644i	$-0.516578\pi$
$397$	−6.51444e6			−0.104113			−0.0520566	+	0.998644i	$0.516578\pi$
$398$	−5.48574e7	+	5.36428e7i	−0.870134	+	0.850869i
$399$		−	8.51997e6i		−	0.134128i
$400$	−1.15725e7	−	518507.i	−0.180820	−	0.00810168i
$401$	5.00404e7			0.776047			0.388024	−	0.921649i	$-0.373158\pi$
$401$	5.00404e7			0.776047			0.388024	+	0.921649i	$0.373158\pi$
$402$	−1.15277e8	−	1.17887e8i	−1.77445	−	1.81463i
$403$		−	8.31117e6i		−	0.126983i
$404$	−979565.	+	4.37475e7i	−0.0148556	+	0.663452i
$405$	2.48320e7			0.373807
$406$	−8.54374e6	+	8.35458e6i	−0.127664	+	0.124838i
$407$			1.30933e8i			1.94207i
$408$	−7.48538e6	−	8.00579e6i	−0.110213	−	0.117876i
$409$	−8.81335e7			−1.28816			−0.644082	−	0.764957i	$-0.722760\pi$
$409$	−8.81335e7			−1.28816			−0.644082	+	0.764957i	$0.722760\pi$
$410$	−4.30655e7	−	4.40406e7i	−0.624853	−	0.639001i
$411$			6.25152e7i			0.900451i
$412$	8.92531e7	+	1.99849e6i	1.27624	+	0.0285766i
$413$	1.38081e7			0.196013
$414$	6.19084e7	−	6.05377e7i	0.872466	−	0.853149i
$415$		−	1.29728e8i		−	1.81505i
$416$	−1.10503e7	−	1.23620e7i	−0.153495	−	0.171715i
$417$	−9.66393e7			−1.33274
$418$	1.87810e7	+	1.92062e7i	0.257152	+	0.262975i
$419$			8.33112e7i			1.13256i	0.824213	+	0.566280i	$0.191618\pi$
$419$			8.33112e7i			1.13256i	−0.824213	+	0.566280i	$0.808382\pi$
$420$	−1.05376e6	+	4.70609e7i	−0.0142230	+	0.635203i
$421$	−4.06740e7			−0.545093			−0.272546	−	0.962143i	$-0.587866\pi$
$421$	−4.06740e7			−0.545093			−0.272546	+	0.962143i	$0.587866\pi$
$422$	8.58325e7	−	8.39321e7i	1.14213	−	1.11684i
$423$		−	1.82341e8i		−	2.40914i
$424$	−4.29615e7	+	4.01688e7i	−0.563614	+	0.526976i
$425$	1.43198e6			0.0186539
$426$	−1.43280e8	−	1.46524e8i	−1.85335	−	1.89531i
$427$			1.15021e7i			0.147739i
$428$	−8.95474e7	−	2.00508e6i	−1.14215	−	0.0255742i
$429$	−4.56507e7			−0.578196
$430$	9.20117e7	−	8.99745e7i	1.15728	−	1.13166i
$431$			9.01015e6i			0.112538i	0.998416	+	0.0562692i	$0.0179205\pi$
$431$			9.01015e6i			0.112538i	−0.998416	+	0.0562692i	$0.982080\pi$
$432$	2.55323e6	−	5.69853e7i	0.0316693	−	0.706825i
$433$	8.87569e7			1.09330			0.546649	−	0.837362i	$-0.315903\pi$
$433$	8.87569e7			1.09330			0.546649	+	0.837362i	$0.315903\pi$
$434$	−1.17653e7	−	1.20317e7i	−0.143924	−	0.147183i
$435$			6.69838e7i			0.813770i
$436$	−2.78669e6	+	1.24454e8i	−0.0336224	+	1.50158i
$437$	1.60916e7			0.192822
$438$	−9.94542e7	+	9.72522e7i	−1.18359	+	1.15738i
$439$			3.17656e7i			0.375460i	0.982221	+	0.187730i	$0.0601130\pi$
$439$			3.17656e7i			0.375460i	−0.982221	+	0.187730i	$0.939887\pi$
$440$	−1.01363e8	−	1.08411e8i	−1.18993	−	1.27266i
$441$	−1.07161e8			−1.24945
$442$	1.43302e6	+	1.46546e6i	0.0165953	+	0.0169710i
$443$		−	3.24377e7i		−	0.373112i	−0.982444	−	0.186556i	$-0.940267\pi$
$443$		−	3.24377e7i		−	0.373112i	0.982444	−	0.186556i	$-0.0597326\pi$
$444$	1.65979e8	+	3.71650e6i	1.89629	+	0.0424605i
$445$	1.68548e8			1.91268
$446$	7.18241e7	−	7.02339e7i	0.809591	−	0.791666i
$447$			1.93582e8i			2.16741i
$448$	−3.34967e7	−	2.25312e6i	−0.372536	−	0.0250582i
$449$	8.18077e7			0.903765			0.451882	−	0.892078i	$-0.350753\pi$
$449$	8.18077e7			0.903765			0.451882	+	0.892078i	$0.350753\pi$
$450$	1.67422e7	+	1.71213e7i	0.183728	+	0.187888i
$451$		−	1.20952e8i		−	1.31850i
$452$	−2.54640e6	+	1.13723e8i	−0.0275747	+	1.23149i
$453$	−4.49578e7			−0.483627
$454$	−8.70708e7	+	8.51430e7i	−0.930476	+	0.909875i
$455$		−	8.80314e6i		−	0.0934552i
$456$	2.48803e7	−	2.32630e7i	0.262398	−	0.245341i
$457$	−6.54954e7			−0.686218			−0.343109	−	0.939296i	$-0.611480\pi$
$457$	−6.54954e7			−0.686218			−0.343109	+	0.939296i	$0.611480\pi$
$458$	−6.07873e7	−	6.21637e7i	−0.632728	−	0.647054i
$459$			7.05134e6i			0.0729178i
$460$	−8.88838e7	−	1.99023e6i	−0.913165	−	0.0204470i
$461$	8.74406e7			0.892505			0.446252	−	0.894907i	$-0.352758\pi$
$461$	8.74406e7			0.892505			0.446252	+	0.894907i	$0.352758\pi$
$462$	−6.60865e7	+	6.46233e7i	−0.670172	+	0.655334i
$463$		−	9.21088e7i		−	0.928022i	−0.885829	−	0.464011i	$-0.846410\pi$
$463$		−	9.21088e7i		−	0.928022i	0.885829	−	0.464011i	$-0.153590\pi$
$464$	−4.77252e7	−	2.13833e6i	−0.477742	−	0.0214053i
$465$	−9.43298e7			−0.938188
$466$	8.49794e7	+	8.69035e7i	0.839761	+	0.858775i
$467$		−	1.67302e7i		−	0.164267i	−0.996621	−	0.0821337i	$-0.973827\pi$
$467$		−	1.67302e7i		−	0.164267i	0.996621	−	0.0821337i	$-0.0261734\pi$
$468$	−767293.	+	3.42674e7i	−0.00748555	+	0.334306i
$469$	6.24332e7			0.605198
$470$	−1.33860e8	+	1.30896e8i	−1.28931	+	1.26076i
$471$			1.07787e7i			0.103158i
$472$	3.77018e7	+	4.03229e7i	0.358538	+	0.383465i
$473$	2.52698e8			2.38791
$474$	−8.30601e7	−	8.49407e7i	−0.779933	−	0.797592i
$475$			4.45028e6i			0.0415247i
$476$	4.14903e6	+	92902.3i	0.0384703	+	0.000861402i
$477$	1.21582e8			1.12025
$478$	1.80509e7	−	1.76513e7i	0.165278	−	0.161619i
$479$		−	1.87423e8i		−	1.70536i	−0.522434	−	0.852680i	$-0.674976\pi$
$479$		−	1.87423e8i		−	1.70536i	0.522434	−	0.852680i	$-0.325024\pi$
$480$	−1.40306e8	+	1.25418e8i	−1.26868	+	1.13406i
$481$	−3.10478e7			−0.278995
$482$	1.00544e8	+	1.02820e8i	0.897870	+	0.918200i
$483$			5.53694e7i			0.491393i
$484$	3.98575e6	−	1.78004e8i	0.0351539	−	1.56998i
$485$	1.06809e8			0.936230
$486$	1.02274e8	−	1.00010e8i	0.890960	−	0.871234i
$487$		−	5.54808e6i		−	0.0480348i	−0.999712	−	0.0240174i	$-0.992354\pi$
$487$		−	5.54808e6i		−	0.0480348i	0.999712	−	0.0240174i	$-0.00764571\pi$
$488$	−3.35889e7	+	3.14055e7i	−0.289026	+	0.270238i
$489$	5.16361e7			0.441597
$490$	7.69269e7	+	7.86687e7i	0.653868	+	0.668673i
$491$			8.66911e7i			0.732369i	0.930542	+	0.366184i	$0.119336\pi$
$491$			8.66911e7i			0.732369i	−0.930542	+	0.366184i	$0.880664\pi$
$492$	−1.53327e8	−	3.43319e6i	−1.28743	−	0.0288272i
$493$	5.90550e6			0.0492851
$494$	−4.55435e6	+	4.45351e6i	−0.0377785	+	0.0369421i
$495$			3.06805e8i			2.52957i
$496$	3.01130e6	−	6.72089e7i	0.0246780	−	0.550785i
$497$	7.75993e7			0.632104
$498$	−2.25823e8	−	2.30936e8i	−1.82843	−	1.86983i
$499$		−	2.25615e7i		−	0.181580i	−0.995870	−	0.0907898i	$-0.971061\pi$
$499$		−	2.25615e7i		−	0.181580i	0.995870	−	0.0907898i	$-0.0289391\pi$
$500$	−2.49051e6	+	1.11227e8i	−0.0199241	+	0.889814i
$501$	−2.05350e8			−1.63298
$502$	2.64542e7	−	2.58685e7i	0.209114	−	0.204484i
$503$		−	2.11929e8i		−	1.66527i	−0.553820	−	0.832637i	$-0.686830\pi$
$503$		−	2.11929e8i		−	1.66527i	0.553820	−	0.832637i	$-0.313170\pi$
$504$	4.73984e7	+	5.06937e7i	0.370230	+	0.395970i
$505$	−9.28790e7			−0.721180
$506$	−1.22054e8	−	1.24817e8i	−0.942106	−	0.963437i
$507$			1.93241e8i			1.48278i
$508$	2.05569e7	+	460297.i	0.156808	+	0.00351113i
$509$	−1.91979e7			−0.145580			−0.0727899	−	0.997347i	$-0.523190\pi$
$509$	−1.91979e7			−0.145580			−0.0727899	+	0.997347i	$0.523190\pi$
$510$	1.66327e7	−	1.62644e7i	0.125387	−	0.122611i
$511$		−	5.26711e7i		−	0.394738i
$512$	−8.48800e7	−	1.03970e8i	−0.632405	−	0.774638i
$513$	−2.19140e7			−0.162319
$514$	3.96444e7	+	4.05420e7i	0.291939	+	0.298549i
$515$			1.89490e8i			1.38728i
$516$	7.17278e6	−	3.20337e8i	0.0522082	−	2.33162i
$517$	−3.67628e8			−2.66034
$518$	−4.49466e7	+	4.39515e7i	−0.323376	+	0.316216i
$519$			2.50198e8i			1.78971i
$520$	2.57072e7	−	2.40361e7i	0.182829	−	0.170944i
$521$	−2.13789e7			−0.151172			−0.0755860	−	0.997139i	$-0.524083\pi$
$521$	−2.13789e7			−0.151172			−0.0755860	+	0.997139i	$0.524083\pi$
$522$	6.90451e7	+	7.06084e7i	0.485424	+	0.496415i
$523$		−	4.99582e7i		−	0.349222i	−0.984638	−	0.174611i	$-0.944133\pi$
$523$		−	4.99582e7i		−	0.349222i	0.984638	−	0.174611i	$-0.0558668\pi$
$524$	−1.49457e8	−	3.34655e6i	−1.03878	−	0.0232596i
$525$	−1.53129e7			−0.105823
$526$	1.92497e7	−	1.88235e7i	0.132272	−	0.129343i
$527$			8.31640e6i			0.0568203i
$528$	−3.69158e8	−	1.65401e7i	−2.50790	−	0.112367i
$529$	4.34598e7			0.293576
$530$	−8.72797e7	−	8.92559e7i	−0.586254	−	0.599528i
$531$		−	1.14115e8i		−	0.762183i
$532$	−288720.	+	1.28943e7i	−0.00191753	+	0.0856373i
$533$	2.86810e7			0.189414
$534$	3.00041e8	−	2.93398e8i	1.97041	−	1.92678i
$535$		−	1.90115e8i		−	1.24153i
$536$	1.70468e8	+	1.82320e8i	1.10700	+	1.18396i
$537$	2.86413e8			1.84957
$538$	−1.73112e8	−	1.77032e8i	−1.11168	−	1.13685i
$539$			2.16053e8i			1.37973i
$540$	1.21044e8	+	2.71034e6i	0.768712	+	0.0172125i
$541$	2.12244e8			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$541$	2.12244e8			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$542$	5.77170e7	−	5.64391e7i	0.362498	−	0.354472i
$543$		−	4.29110e8i		−	2.68021i
$544$	1.10572e7	+	1.23698e7i	0.0686831	+	0.0768362i
$545$	−2.64225e8			−1.63224
$546$	−1.53240e7	−	1.56710e7i	−0.0941444	−	0.0962760i
$547$		−	2.77586e8i		−	1.69604i	−0.529965	−	0.848020i	$-0.677795\pi$
$547$		−	2.77586e8i		−	1.69604i	0.529965	−	0.848020i	$-0.322205\pi$
$548$	2.11848e6	−	9.46118e7i	0.0128731	−	0.574915i
$549$	9.50576e7			0.574473
$550$	3.45193e7	−	3.37550e7i	0.207479	−	0.202885i
$551$			1.83530e7i			0.109712i
$552$	−1.61692e8	+	1.51181e8i	−0.961325	+	0.898835i
$553$	4.49847e7			0.266005
$554$	2.10113e8	+	2.14871e8i	1.23573	+	1.26371i
$555$			3.52386e8i			2.06129i
$556$	1.46256e8	+	3.27486e6i	0.850921	+	0.0190532i
$557$	−4.69393e7			−0.271626			−0.135813	−	0.990735i	$-0.543365\pi$
$557$	−4.69393e7			−0.271626			−0.135813	+	0.990735i	$0.543365\pi$
$558$	−9.94342e7	+	9.72327e7i	−0.572312	+	0.559641i
$559$			5.99218e7i			0.343044i
$560$	3.18955e6	−	7.11873e7i	0.0181621	−	0.405358i
$561$	4.56794e7			0.258721
$562$	1.40763e8	+	1.43951e8i	0.793014	+	0.810969i
$563$		−	4.15903e7i		−	0.233059i	−0.993187	−	0.116530i	$-0.962823\pi$
$563$		−	4.15903e7i		−	0.233059i	0.993187	−	0.116530i	$-0.0371770\pi$
$564$	−1.04351e7	+	4.66031e8i	−0.0581644	+	2.59763i
$565$	−2.41441e8			−1.33864
$566$	1.09892e8	−	1.07459e8i	0.606063	−	0.592645i
$567$			2.34110e7i			0.128431i
$568$	2.11878e8	+	2.26608e8i	1.15622	+	1.23660i
$569$	−2.21825e8			−1.20413			−0.602065	−	0.798447i	$-0.705655\pi$
$569$	−2.21825e8			−1.20413			−0.602065	+	0.798447i	$0.705655\pi$
$570$	5.05463e7	+	5.16908e7i	0.272938	+	0.279118i
$571$			2.33659e8i			1.25509i	0.778580	+	0.627545i	$0.215940\pi$
$571$			2.33659e8i			1.25509i	−0.778580	+	0.627545i	$0.784060\pi$
$572$	6.90887e7	+	1.54699e6i	0.369164	+	0.00826606i
$573$	5.71653e7			0.303857
$574$	4.15203e7	−	4.06010e7i	0.219546	−	0.214685i
$575$		−	2.89214e7i		−	0.152130i
$576$	−1.86206e7	+	2.76828e8i	−0.0974373	+	1.44858i
$577$	−3.57501e8			−1.86101			−0.930507	−	0.366275i	$-0.880633\pi$
$577$	−3.57501e8			−1.86101			−0.930507	+	0.366275i	$0.880633\pi$
$578$	1.33572e8	+	1.36596e8i	0.691722	+	0.707384i
$579$			2.58284e8i			1.33064i
$580$	2.26991e6	−	1.01375e8i	0.0116339	−	0.519572i
$581$	1.22304e8			0.623608
$582$	1.90137e8	−	1.85927e8i	0.964489	−	0.943134i
$583$		−	2.45129e8i		−	1.23706i
$584$	1.53812e8	−	1.43813e8i	0.772238	−	0.722039i
$585$	−7.27522e7			−0.363394
$586$	−1.85923e8	−	1.90133e8i	−0.923932	−	0.944852i
$587$			3.60885e7i			0.178425i	0.996013	+	0.0892123i	$0.0284350\pi$
$587$			3.60885e7i			0.178425i	−0.996013	+	0.0892123i	$0.971565\pi$
$588$	2.73884e8	+	6.13262e6i	1.34721	+	0.0301657i
$589$	−2.58456e7			−0.126485
$590$	−8.37741e7	+	8.19193e7i	−0.407900	+	0.398869i
$591$			1.71417e8i			0.830410i
$592$	−2.51071e8	−	1.12493e7i	−1.21013	−	0.0542199i
$593$	8.06897e7			0.386949			0.193475	−	0.981105i	$-0.438024\pi$
$593$	8.06897e7			0.386949			0.193475	+	0.981105i	$0.438024\pi$
$594$	1.66216e8	+	1.69980e8i	0.793075	+	0.811031i
$595$			8.80869e6i			0.0418177i
$596$	6.55999e6	−	2.92970e8i	0.0309859	−	1.38384i
$597$	−4.05475e8			−1.90564
$598$	2.95977e7	−	2.89424e7i	0.138406	−	0.135342i
$599$			2.50847e8i			1.16716i	0.812057	+	0.583578i	$0.198348\pi$
$599$			2.50847e8i			1.16716i	−0.812057	+	0.583578i	$0.801652\pi$
$600$	−4.18104e7	−	4.47172e7i	−0.193567	−	0.207024i
$601$	9.73770e7			0.448573			0.224286	−	0.974523i	$-0.427995\pi$
$601$	9.73770e7			0.448573			0.224286	+	0.974523i	$0.427995\pi$
$602$	8.48256e7	+	8.67462e7i	0.388810	+	0.397613i
$603$		−	5.15970e8i		−	2.35327i
$604$	6.80401e7	+	1.52351e6i	0.308783	+	0.00691407i
$605$	3.77915e8			1.70659
$606$	−1.65339e8	+	1.61679e8i	−0.742947	+	0.726498i
$607$			7.72034e7i			0.345200i	0.984992	+	0.172600i	$0.0552167\pi$
$607$			7.72034e7i			0.345200i	−0.984992	+	0.172600i	$0.944783\pi$
$608$	−3.84427e7	+	3.43635e7i	−0.171042	+	0.152893i
$609$	−6.31505e7			−0.279592
$610$	−6.82385e7	−	6.97836e7i	−0.300636	−	0.307442i
$611$		−	8.71750e7i		−	0.382180i
$612$	767777.	−	3.42890e7i	0.00334951	−	0.149589i
$613$	2.48876e8			1.08044			0.540222	−	0.841523i	$-0.318340\pi$
$613$	2.48876e8			1.08044			0.540222	+	0.841523i	$0.318340\pi$
$614$	−2.83952e7	+	2.77666e7i	−0.122671	+	0.119955i
$615$		−	3.25523e8i		−	1.39945i
$616$	1.02207e8	−	9.55627e7i	0.437257	−	0.408833i
$617$	2.15582e8			0.917821			0.458910	−	0.888483i	$-0.348240\pi$
$617$	2.15582e8			0.917821			0.458910	+	0.888483i	$0.348240\pi$
$618$	3.29854e8	+	3.37323e8i	1.39752	+	1.42916i
$619$		−	3.44973e8i		−	1.45450i	−0.686374	−	0.727248i	$-0.740799\pi$
$619$		−	3.44973e8i		−	1.45450i	0.686374	−	0.727248i	$-0.259201\pi$
$620$	1.42761e8	+	3.19660e6i	0.599010	+	0.0134126i
$621$	1.42415e8			0.594675
$622$	−2.48795e8	+	2.43287e8i	−1.03388	+	1.01099i
$623$			1.58902e8i			0.657152i
$624$	3.92214e6	−	8.75377e7i	0.0161424	−	0.360281i
$625$	−2.80332e8			−1.14824
$626$	−8.90277e7	−	9.10434e7i	−0.362913	−	0.371130i
$627$			1.41962e8i			0.575929i
$628$	365263.	−	1.63127e7i	0.00147478	−	0.0658638i
$629$	3.10674e7			0.124840
$630$	−1.05320e8	+	1.02988e8i	−0.421201	+	0.411876i
$631$			2.53122e8i			1.00749i	0.863852	+	0.503746i	$0.168045\pi$
$631$			2.53122e8i			1.00749i	−0.863852	+	0.503746i	$0.831955\pi$
$632$	1.22826e8	+	1.31366e8i	0.486565	+	0.520392i
$633$	6.34425e8			2.50132
$634$	1.60290e8	+	1.63919e8i	0.628982	+	0.643224i
$635$			4.36438e7i			0.170452i
$636$	−3.10743e8	−	6.95795e6i	−1.20790	−	0.0270464i
$637$	−5.12323e7			−0.198210
$638$	1.42358e8	−	1.39206e8i	0.548176	−	0.536039i
$639$		−	6.41307e8i		−	2.45790i
$640$	2.16592e8	−	1.85056e8i	0.826234	−	0.705932i
$641$	−5.68594e7			−0.215888			−0.107944	−	0.994157i	$-0.534427\pi$
$641$	−5.68594e7			−0.215888			−0.107944	+	0.994157i	$0.534427\pi$
$642$	−3.30942e8	−	3.38435e8i	−1.25068	−	1.27900i
$643$		−	1.90203e8i		−	0.715457i	−0.933826	−	0.357729i	$-0.883551\pi$
$643$		−	1.90203e8i		−	0.715457i	0.933826	−	0.357729i	$-0.116449\pi$
$644$	1.87633e6	−	8.37973e7i	0.00702509	−	0.313742i
$645$	6.80099e8			2.53450
$646$	4.55722e6	−	4.45632e6i	0.0169045	−	0.0165302i
$647$		−	2.82051e8i		−	1.04139i	−0.853742	−	0.520696i	$-0.825673\pi$
$647$		−	2.82051e8i		−	1.04139i	0.853742	−	0.520696i	$-0.174327\pi$
$648$	−6.83655e7	+	6.39214e7i	−0.251253	+	0.234921i
$649$	−2.30074e8			−0.841655
$650$	8.00427e6	+	8.18550e6i	0.0291462	+	0.0298061i
$651$		−	8.89316e7i		−	0.322339i
$652$	−7.81471e7	−	1.74982e6i	−0.281949	−	0.00631321i
$653$	4.11184e7			0.147671			0.0738357	−	0.997270i	$-0.476476\pi$
$653$	4.11184e7			0.147671			0.0738357	+	0.997270i	$0.476476\pi$
$654$	−4.70361e8	+	4.59947e8i	−1.68150	+	1.64428i
$655$		−	3.17308e8i		−	1.12916i
$656$	2.31931e8	+	1.03917e7i	0.821577	+	0.0368108i
$657$	−4.35292e8			−1.53491
$658$	−1.23405e8	−	1.26199e8i	−0.433168	−	0.442976i
$659$		−	2.03687e8i		−	0.711717i	−0.934540	−	0.355858i	$-0.884189\pi$
$659$		−	2.03687e8i		−	0.711717i	0.934540	−	0.355858i	$-0.115811\pi$
$660$	1.75579e7	−	7.84140e8i	0.0610719	−	2.72748i
$661$	−1.05851e8			−0.366513			−0.183257	−	0.983065i	$-0.558664\pi$
$661$	−1.05851e8			−0.366513			−0.183257	+	0.983065i	$0.558664\pi$
$662$	2.24102e8	−	2.19140e8i	0.772451	−	0.755349i
$663$			1.08319e7i			0.0371675i
$664$	3.33939e8	+	3.57156e8i	1.14068	+	1.21998i
$665$	−2.73755e7			−0.0930887
$666$	3.63230e8	+	3.71454e8i	1.22959	+	1.25743i
$667$		−	1.19272e8i		−	0.401941i
$668$	3.10781e8	+	6.95879e6i	1.04262	+	0.0233456i
$669$	5.30883e8			1.77305
$670$	−3.78783e8	+	3.70397e8i	−1.25941	+	1.23152i
$671$		−	1.91651e8i		−	0.634372i
$672$	−1.18241e8	−	1.32277e8i	−0.389637	−	0.435889i
$673$	−3.40279e8			−1.11632			−0.558161	−	0.829733i	$-0.688493\pi$
$673$	−3.40279e8			−1.11632			−0.558161	+	0.829733i	$0.688493\pi$
$674$	7.18243e7	+	7.34506e7i	0.234580	+	0.239892i
$675$			3.93860e7i			0.128065i
$676$	6.54846e6	−	2.92455e8i	0.0211982	−	0.946716i
$677$	−4.85228e8			−1.56380			−0.781898	−	0.623407i	$-0.785748\pi$
$677$	−4.85228e8			−1.56380			−0.781898	+	0.623407i	$0.785748\pi$
$678$	−4.29803e8	+	4.20286e8i	−1.37905	+	1.34852i
$679$			1.00697e8i			0.321666i
$680$	−2.57234e7	+	2.40513e7i	−0.0818091	+	0.0764912i
$681$	−6.43579e8			−2.03779
$682$	1.96037e8	+	2.00475e8i	0.617994	+	0.631987i
$683$			1.82779e8i			0.573671i	0.957980	+	0.286836i	$0.0926034\pi$
$683$			1.82779e8i			0.573671i	−0.957980	+	0.286836i	$0.907397\pi$
$684$	1.06563e8	+	2.38608e6i	0.332995	+	0.00745620i
$685$	2.00867e8			0.624939
$686$	−1.60348e8	+	1.56798e8i	−0.496697	+	0.485700i
$687$		−	4.59479e8i		−	1.41708i
$688$	−2.17109e7	+	4.84563e8i	−0.0666672	+	1.48794i
$689$	5.81271e7			0.177714
$690$	−3.28489e8	−	3.35927e8i	−0.999941	−	1.02258i
$691$			3.49632e8i			1.05969i	0.848096	+	0.529843i	$0.177749\pi$
$691$			3.49632e8i			1.05969i	−0.848096	+	0.529843i	$0.822251\pi$
$692$	8.47859e6	−	3.78655e8i	0.0255862	−	1.14268i
$693$	−2.89248e8			−0.869101
$694$	1.09678e8	−	1.07249e8i	0.328126	−	0.320861i
$695$			3.10511e8i			0.924961i
$696$	−1.72427e8	−	1.84414e8i	−0.511418	−	0.546974i
$697$	−2.86991e7			−0.0847559
$698$	6.87828e7	+	7.03401e7i	0.202262	+	0.206841i
$699$			6.42342e8i			1.88076i
$700$	2.31748e7	+	518915.i	0.0675652	+	0.00151287i
$701$	2.11545e7			0.0614113			0.0307057	−	0.999528i	$-0.490225\pi$
$701$	2.11545e7			0.0614113			0.0307057	+	0.999528i	$0.490225\pi$
$702$	−4.03070e7	+	3.94146e7i	−0.116512	+	0.113932i
$703$			9.65508e7i			0.277901i
$704$	5.58131e8	+	3.75420e7i	1.59962	+	0.107597i
$705$	−9.89416e8			−2.82366
$706$	6.66808e7	+	6.81905e7i	0.189490	+	0.193780i
$707$		−	8.75639e7i		−	0.247780i
$708$	−6.53061e6	+	2.91658e8i	−0.0184015	+	0.821816i
$709$	−6.02503e8			−1.69052			−0.845261	−	0.534354i	$-0.820555\pi$
$709$	−6.02503e8			−1.69052			−0.845261	+	0.534354i	$0.820555\pi$
$710$	−4.70796e8	+	4.60373e8i	−1.31540	+	1.28628i
$711$		−	3.71769e8i		−	1.03434i
$712$	−4.64031e8	+	4.33867e8i	−1.28560	+	1.20203i
$713$	1.67965e8			0.463394
$714$	1.53337e7	+	1.56808e7i	0.0421261	+	0.0430799i
$715$			1.46680e8i			0.401285i
$716$	−4.33464e8	−	9.70583e6i	−1.18090	−	0.0264420i
$717$	1.33422e8			0.361969
$718$	2.69412e8	−	2.63447e8i	0.727854	−	0.711738i
$719$			1.96584e8i			0.528886i	0.964401	+	0.264443i	$0.0851881\pi$
$719$			1.96584e8i			0.528886i	−0.964401	+	0.264443i	$0.914812\pi$
$720$	−5.88316e8	−	2.63596e7i	−1.57621	−	0.0706221i
$721$	−1.78647e8			−0.476638
$722$	1.38493e7	+	1.41628e7i	0.0367972	+	0.0376304i
$723$			7.59988e8i			2.01091i
$724$	−1.45415e7	+	6.49424e8i	−0.0383171	+	1.71125i
$725$	3.29857e7			0.0865590
$726$	6.72748e8	−	6.57853e8i	1.75810	−	1.71917i
$727$			3.68545e8i			0.959150i	0.877501	+	0.479575i	$0.159209\pi$
$727$			3.68545e8i			0.959150i	−0.877501	+	0.479575i	$0.840791\pi$
$728$	2.26606e7	+	2.42361e7i	0.0587324	+	0.0628157i
$729$	6.22694e8			1.60728
$730$	3.12481e8	+	3.19556e8i	0.803258	+	0.821445i
$731$		−	5.99596e7i		−	0.153499i
$732$	−2.42951e8	−	5.43999e6i	−0.619419	−	0.0138696i
$733$	1.90708e8			0.484236			0.242118	−	0.970247i	$-0.422158\pi$
$733$	1.90708e8			0.484236			0.242118	+	0.970247i	$0.422158\pi$
$734$	6.31200e7	−	6.17225e7i	0.159617	−	0.156083i
$735$			5.81474e8i			1.46443i
$736$	2.49831e8	−	2.23321e8i	0.626632	−	0.560140i
$737$	−1.04028e9			−2.59864
$738$	−3.35540e8	−	3.43138e8i	−0.834787	−	0.853689i
$739$			2.33066e8i			0.577491i	0.957406	+	0.288745i	$0.0932381\pi$
$739$			2.33066e8i			0.577491i	−0.957406	+	0.288745i	$0.906762\pi$
$740$	1.19415e7	−	5.33308e8i	0.0294688	−	1.31608i
$741$	−3.36632e7			−0.0827371
$742$	8.41481e7	−	8.22850e7i	0.205984	−	0.201423i
$743$			6.00511e8i			1.46405i	0.681280	+	0.732023i	$0.261423\pi$
$743$			6.00511e8i			1.46405i	−0.681280	+	0.732023i	$0.738577\pi$
$744$	2.59701e8	−	2.42819e8i	0.630601	−	0.589610i
$745$	6.21997e8			1.50425
$746$	−1.55044e8	−	1.58555e8i	−0.373456	−	0.381911i
$747$		−	1.01076e9i		−	2.42486i
$748$	−6.91322e7	−	1.54796e6i	−0.165187	−	0.00369875i
$749$	1.79236e8			0.426559
$750$	−4.20370e8	+	4.11063e8i	−0.996433	+	0.974371i
$751$			7.18571e8i			1.69648i	0.529609	+	0.848242i	$0.322339\pi$
$751$			7.18571e8i			1.69648i	−0.529609	+	0.848242i	$0.677661\pi$
$752$	3.15853e7	−	7.04948e8i	0.0742730	−	1.65769i
$753$	1.95535e8			0.457972
$754$	3.30097e7	+	3.37571e7i	0.0770065	+	0.0787501i
$755$			1.44454e8i			0.335651i
$756$	−2.55524e6	+	1.14117e8i	−0.00591380	+	0.264111i
$757$	−4.86002e7			−0.112034			−0.0560171	−	0.998430i	$-0.517840\pi$
$757$	−4.86002e7			−0.112034			−0.0560171	+	0.998430i	$0.517840\pi$
$758$	8.55531e7	−	8.36589e7i	0.196439	−	0.192090i
$759$		−	9.22579e8i		−	2.10998i
$760$	−7.47462e7	−	7.99428e7i	−0.170274	−	0.182112i
$761$	5.98328e8			1.35764			0.678821	−	0.734303i	$-0.262491\pi$
$761$	5.98328e8			1.35764			0.678821	+	0.734303i	$0.262491\pi$
$762$	7.59726e7	+	7.76928e7i	0.171709	+	0.175597i
$763$		−	2.49104e8i		−	0.560799i
$764$	−8.65152e7	−	1.93719e6i	−0.194005	−	0.00434402i
$765$	7.27980e7			0.162605
$766$	6.27115e7	−	6.13230e7i	0.139528	−	0.136439i
$767$		−	5.45571e7i		−	0.120911i
$768$	6.34333e7	−	7.06460e8i	0.140034	−	1.55957i
$769$	3.01756e6			0.00663554			0.00331777	−	0.999994i	$-0.498944\pi$
$769$	3.01756e6			0.00663554			0.00331777	+	0.999994i	$0.498944\pi$
$770$	2.07641e8	+	2.12342e8i	0.454821	+	0.465119i
$771$			2.99664e8i			0.653839i
$772$	8.75259e6	−	3.90892e8i	0.0190232	−	0.849581i
$773$	7.62345e8			1.65049			0.825245	−	0.564775i	$-0.191037\pi$
$773$	7.62345e8			1.65049			0.825245	+	0.564775i	$0.191037\pi$
$774$	7.16900e8	−	7.01028e8i	1.54609	−	1.51186i
$775$			4.64521e7i			0.0997931i
$776$	−2.94058e8	+	2.74943e8i	−0.629285	+	0.588379i
$777$	−3.32220e8			−0.708211
$778$	−1.47237e6	−	1.50570e6i	−0.00312663	−	0.00319743i
$779$		−	8.91906e7i		−	0.188672i
$780$	1.85942e8	+	4.16348e6i	0.391826	+	0.00877351i
$781$	−1.29298e9			−2.71418
$782$	−2.96164e7	+	2.89606e7i	−0.0619315	+	0.0605603i
$783$			1.62428e8i			0.338358i
$784$	−4.14294e8	−	1.85625e7i	−0.859726	−	0.0385201i
$785$	3.46330e7			0.0715947
$786$	−5.52352e8	−	5.64858e8i	−1.13749	−	1.16325i
$787$		−	1.28417e8i		−	0.263450i	−0.991286	−	0.131725i	$-0.957948\pi$
$787$		−	1.28417e8i		−	0.263450i	0.991286	−	0.131725i	$-0.0420515\pi$
$788$	5.80891e6	−	2.59427e8i	0.0118718	−	0.530196i
$789$	1.42283e8			0.289682
$790$	−2.72923e8	+	2.66880e8i	−0.553552	+	0.541296i
$791$		−	2.27624e8i		−	0.459927i
$792$	−7.89763e8	−	8.44670e8i	−1.58972	−	1.70025i
$793$	4.54460e7			0.0911330
$794$	3.64365e7	+	3.72614e7i	0.0727905	+	0.0744386i
$795$		−	6.59729e8i		−	1.31300i
$796$	6.13655e8	+	1.37405e7i	1.21670	+	0.0272436i
$797$	4.26277e8			0.842010			0.421005	−	0.907058i	$-0.361677\pi$
$797$	4.26277e8			0.842010			0.421005	+	0.907058i	$0.361677\pi$
$798$	−4.87327e7	+	4.76537e7i	−0.0958984	+	0.0937752i
$799$			8.72300e7i			0.171012i
$800$	6.17614e7	+	6.90928e7i	0.120628	+	0.134947i
$801$	1.31322e9			2.55529
$802$	−2.79885e8	−	2.86222e8i	−0.542571	−	0.554856i
$803$			8.77618e8i			1.69496i
$804$	−2.95281e7	+	1.31873e9i	−0.0568155	+	2.53739i
$805$	1.77907e8			0.341041
$806$	−4.75384e7	+	4.64859e7i	−0.0907903	+	0.0887801i
$807$		−	1.30852e9i		−	2.48977i
$808$	2.55707e8	−	2.39085e8i	0.484739	−	0.453229i
$809$	9.49579e8			1.79344			0.896718	−	0.442603i	$-0.145945\pi$
$809$	9.49579e8			1.79344			0.896718	+	0.442603i	$0.145945\pi$
$810$	−1.38890e8	−	1.42035e8i	−0.261346	−	0.267263i
$811$		−	2.68143e8i		−	0.502694i	−0.967897	−	0.251347i	$-0.919127\pi$
$811$		−	2.68143e8i		−	0.502694i	0.967897	−	0.251347i	$-0.0808735\pi$
$812$	9.55734e7	+	2.14001e6i	0.178513	+	0.00399713i
$813$	4.26611e8			0.793891
$814$	7.48911e8	−	7.32330e8i	1.38854	−	1.35779i
$815$		−	1.65912e8i		−	0.306482i
$816$	−3.92461e6	+	8.75929e7i	−0.00722314	+	0.161212i
$817$	1.86341e8			0.341699
$818$	4.92946e8	+	5.04108e8i	0.900616	+	0.921008i
$819$		−	6.85888e7i		−	0.124854i
$820$	−1.10312e7	+	4.92654e8i	−0.0200069	+	0.893511i
$821$	1.54998e8			0.280089			0.140045	−	0.990145i	$-0.455275\pi$
$821$	1.54998e8			0.280089			0.140045	+	0.990145i	$0.455275\pi$
$822$	3.57575e8	−	3.49659e8i	0.643802	−	0.629548i
$823$		−	7.64754e7i		−	0.137190i	−0.997645	−	0.0685950i	$-0.978148\pi$
$823$		−	7.64754e7i		−	0.137190i	0.997645	−	0.0685950i	$-0.0218516\pi$
$824$	−4.87777e8	−	5.21689e8i	−0.871847	−	0.932460i
$825$	2.55147e8			0.454390
$826$	−7.72313e7	−	7.89800e7i	−0.137042	−	0.140145i
$827$			6.84111e8i			1.20951i	0.796411	+	0.604756i	$0.206729\pi$
$827$			6.84111e8i			1.20951i	−0.796411	+	0.604756i	$0.793271\pi$
$828$	−6.92530e8	−	1.55066e7i	−1.21996	−	0.0273166i
$829$	−1.44498e8			−0.253629			−0.126814	−	0.991926i	$-0.540475\pi$
$829$	−1.44498e8			−0.253629			−0.126814	+	0.991926i	$0.540475\pi$
$830$	−7.42019e8	+	7.25590e8i	−1.29772	+	1.26899i
$831$			1.58820e9i			2.76760i
$832$	−8.90228e6	+	1.32349e8i	−0.0154572	+	0.229800i
$833$	5.12646e7			0.0886915
$834$	5.40521e8	+	5.52759e8i	0.931782	+	0.952879i
$835$			6.59809e8i			1.13334i
$836$	4.81073e6	−	2.14848e8i	0.00823365	−	0.367716i
$837$	−2.28739e8			−0.390090
$838$	4.76525e8	−	4.65974e8i	0.809755	−	0.791826i
$839$		−	1.01838e9i		−	1.72434i	−0.506618	−	0.862171i	$-0.669104\pi$
$839$		−	1.01838e9i		−	1.72434i	0.506618	−	0.862171i	$-0.330896\pi$
$840$	2.75074e8	−	2.57193e8i	0.464100	−	0.433931i
$841$	−4.58790e8			−0.771304
$842$	2.27497e8	+	2.32648e8i	0.381100	+	0.389729i
$843$			1.06400e9i			1.77607i
$844$	−9.60153e8	−	2.14991e7i	−1.59703	−	0.0357596i
$845$	6.20903e8			1.02909
$846$	−1.04296e9	+	1.01986e9i	−1.72248	+	1.68435i
$847$			3.56289e8i			0.586343i
$848$	4.70050e8	+	2.10606e7i	0.770825	+	0.0345369i
$849$	8.12262e8			1.32731
$850$	−8.00931e6	−	8.19065e6i	−0.0130418	−	0.0133371i
$851$		−	6.27463e8i		−	1.01812i
$852$	−3.67010e7	+	1.63907e9i	−0.0593415	+	2.65020i
$853$	−2.87246e8			−0.462815			−0.231407	−	0.972857i	$-0.574333\pi$
$853$	−2.87246e8			−0.462815			−0.231407	+	0.972857i	$0.574333\pi$
$854$	6.57901e7	−	6.43335e7i	0.105630	−	0.103291i
$855$			2.26240e8i			0.361969i
$856$	4.89386e8	+	5.23410e8i	0.780244	+	0.834489i
$857$	4.89934e8			0.778386			0.389193	−	0.921156i	$-0.372754\pi$
$857$	4.89934e8			0.778386			0.389193	+	0.921156i	$0.372754\pi$
$858$	2.55332e8	+	2.61114e8i	0.404244	+	0.413397i
$859$		−	3.97304e8i		−	0.626821i	−0.949618	−	0.313411i	$-0.898528\pi$
$859$		−	3.97304e8i		−	0.626821i	0.949618	−	0.313411i	$-0.101472\pi$
$860$	−1.02928e9	−	2.30468e7i	−1.61822	−	0.0362340i
$861$	3.06894e8			0.480817
$862$	5.15365e7	−	5.03954e7i	0.0804624	−	0.0786809i
$863$		−	8.53576e8i		−	1.32804i	−0.747716	−	0.664018i	$-0.768850\pi$
$863$		−	8.53576e8i		−	1.32804i	0.747716	−	0.664018i	$-0.231150\pi$
$864$	−3.40226e8	+	3.04125e8i	−0.527505	+	0.471532i
$865$	8.03911e8			1.24211
$866$	−4.96433e8	−	5.07673e8i	−0.764376	−	0.781683i
$867$			1.00964e9i			1.54921i
$868$	−3.01367e6	+	1.34591e8i	−0.00460826	+	0.205806i
$869$	−7.49546e8			−1.14219
$870$	3.83135e8	−	3.74652e8i	0.581828	−	0.568946i
$871$		−	2.46679e8i		−	0.373317i
$872$	7.27441e8	−	6.80154e8i	1.09711	−	1.02579i
$873$	8.32192e8			1.25078
$874$	−9.00034e7	−	9.20413e7i	−0.134811	−	0.137863i
$875$		−	2.22629e8i		−	0.332320i
$876$	1.11253e9	+	2.49110e7i	1.65501	+	0.0370578i
$877$	−3.34379e8			−0.495724			−0.247862	−	0.968795i	$-0.579728\pi$
$877$	−3.34379e8			−0.495724			−0.247862	+	0.968795i	$0.579728\pi$
$878$	1.81694e8	−	1.77671e8i	0.268445	−	0.262502i
$879$		−	1.40535e9i		−	2.06928i
$880$	−5.31451e7	+	1.18614e9i	−0.0779858	+	1.74056i
$881$	−6.63559e8			−0.970402			−0.485201	−	0.874403i	$-0.661254\pi$
$881$	−6.63559e8			−0.970402			−0.485201	+	0.874403i	$0.661254\pi$
$882$	5.99368e8	+	6.12939e8i	0.873550	+	0.893329i
$883$		−	5.06966e7i		−	0.0736371i	−0.999322	−	0.0368186i	$-0.988278\pi$
$883$		−	5.06966e7i		−	0.0736371i	0.999322	−	0.0368186i	$-0.0117224\pi$
$884$	367066.	−	1.63932e7i	0.000531357	−	0.0237305i
$885$	−6.19211e8			−0.893323
$886$	−1.85538e8	+	1.81430e8i	−0.266767	+	0.260860i
$887$			1.32162e9i			1.89380i	0.321522	+	0.946902i	$0.395806\pi$
$887$			1.32162e9i			1.89380i	−0.321522	+	0.946902i	$0.604194\pi$
$888$	−9.07095e8	−	9.70159e8i	−1.29543	−	1.38549i
$889$	−4.11462e7			−0.0585632
$890$	−9.42717e8	−	9.64061e8i	−1.33725	−	1.36752i
$891$		−	3.90079e8i		−	0.551467i
$892$	−8.03450e8	−	1.79903e7i	−1.13205	−	0.0253480i
$893$	−2.71092e8			−0.380682
$894$	1.10725e9	−	1.08274e9i	1.54965	−	1.51534i
$895$		−	9.20274e8i		−	1.28365i
$896$	1.74466e8	+	2.04197e8i	0.242542	+	0.283874i
$897$	2.18770e8			0.303117
$898$	−4.57565e8	−	4.67926e8i	−0.631865	−	0.646171i
$899$			1.91569e8i			0.263661i
$900$	4.28849e6	−	1.91525e8i	0.00588271	−	0.262723i
$901$	−5.81637e7			−0.0795203
$902$	−6.91821e8	+	6.76504e8i	−0.942701	+	0.921829i
$903$			6.41179e8i			0.870795i
$904$	6.64715e8	−	6.21506e8i	0.899767	−	0.841279i
$905$	−1.37877e9			−1.86014
$906$	2.51457e8	+	2.57150e8i	0.338126	+	0.345782i
$907$		−	8.07780e8i		−	1.08261i	−0.840827	−	0.541304i	$-0.817931\pi$
$907$		−	8.07780e8i		−	1.08261i	0.840827	−	0.541304i	$-0.182069\pi$
$908$	9.74006e8	+	2.18093e7i	1.30108	+	0.0291329i
$909$	−7.23658e8			−0.963478
$910$	−5.03524e7	+	4.92375e7i	−0.0668184	+	0.0653390i
$911$		−	1.65125e6i		−	0.00218403i	−0.999999	−	0.00109201i	$-0.999652\pi$
$911$		−	1.65125e6i		−	0.00218403i	0.999999	−	0.00109201i	$-0.000347599\pi$
$912$	−2.72220e8	−	1.21968e7i	−0.358868	−	0.0160791i
$913$	−2.03786e9			−2.67770
$914$	3.66327e8	+	3.74622e8i	0.479767	+	0.490630i
$915$		−	5.15801e8i		−	0.673316i
$916$	−1.55706e7	+	6.95385e8i	−0.0202590	+	0.904772i
$917$	2.99150e8			0.387954
$918$	4.03324e7	−	3.94394e7i	0.0521346	−	0.0509803i
$919$			9.07976e8i			1.16984i	0.811090	+	0.584922i	$0.198875\pi$
$919$			9.07976e8i			1.16984i	−0.811090	+	0.584922i	$0.801125\pi$
$920$	4.85759e8	+	5.19531e8i	0.623818	+	0.667188i
$921$	−2.09882e8			−0.268655
$922$	−4.89071e8	−	5.00145e8i	−0.623992	−	0.638121i
$923$		−	3.06602e8i		−	0.389915i
$924$	7.39267e8	+	1.65532e7i	0.937099	+	0.0209829i
$925$	1.73530e8			0.219255
$926$	−5.26846e8	+	5.15181e8i	−0.663515	+	0.648824i
$927$			1.47640e9i			1.85338i
$928$	2.54705e8	+	2.84940e8i	0.318708	+	0.356540i
$929$	7.16460e8			0.893603			0.446802	−	0.894633i	$-0.352563\pi$
$929$	7.16460e8			0.893603			0.446802	+	0.894633i	$0.352563\pi$
$930$	5.27604e8	+	5.39550e8i	0.655932	+	0.670784i
$931$			1.59319e8i			0.197433i
$932$	2.17674e7	−	9.72134e8i	0.0268880	−	1.20082i
$933$	−1.83896e9			−2.26426
$934$	−9.56939e7	+	9.35752e7i	−0.117447	+	0.114847i
$935$		−	1.46772e8i		−	0.179560i
$936$	2.00295e8	−	1.87275e8i	0.244255	−	0.228377i
$937$	1.22416e9			1.48806			0.744031	−	0.668145i	$-0.232911\pi$
$937$	1.22416e9			1.48806			0.744031	+	0.668145i	$0.232911\pi$
$938$	−3.49200e8	−	3.57107e8i	−0.423122	−	0.432703i
$939$		−	6.72942e8i		−	0.812794i
$940$	1.49740e9	+	3.35288e7i	1.80283	+	0.0403678i
$941$	−6.48273e8			−0.778016			−0.389008	−	0.921234i	$-0.627182\pi$
$941$	−6.48273e8			−0.778016			−0.389008	+	0.921234i	$0.627182\pi$
$942$	6.16522e7	−	6.02871e7i	0.0737557	−	0.0721227i
$943$			5.79631e8i			0.691220i
$944$	1.97671e7	−	4.41181e8i	0.0234978	−	0.524446i
$945$	−2.42279e8			−0.287092
$946$	−1.41338e9	−	1.44539e9i	−1.66950	−	1.70730i
$947$			7.86022e8i			0.925518i	0.886484	+	0.462759i	$0.153141\pi$
$947$			7.86022e8i			0.925518i	−0.886484	+	0.462759i	$0.846859\pi$
$948$	−2.12757e7	+	9.50177e8i	−0.0249723	+	1.11527i
$949$	−2.08108e8			−0.243495
$950$	2.54548e7	−	2.48912e7i	0.0296892	−	0.0290319i
$951$			1.21160e9i			1.40870i
$952$	−2.26749e7	−	2.42513e7i	−0.0262806	−	0.0281077i
$953$	−2.08176e8			−0.240521			−0.120260	−	0.992742i	$-0.538373\pi$
$953$	−2.08176e8			−0.240521			−0.120260	+	0.992742i	$0.538373\pi$
$954$	−6.80031e8	−	6.95428e8i	−0.783220	−	0.800954i
$955$		−	1.83678e8i		−	0.210885i
$956$	−2.01924e8	−	4.52135e6i	−0.231108	−	0.00517481i
$957$	1.05223e9			1.20053
$958$	−1.07202e9	+	1.04829e9i	−1.21929	+	1.19230i
$959$			1.89372e8i			0.214714i
$960$	1.50213e9	+	1.01039e8i	1.69782	+	0.114202i
$961$	6.17727e8			0.696027
$962$	1.73656e8	+	1.77588e8i	0.195059	+	0.199475i
$963$		−	1.48127e9i		−	1.65865i
$964$	2.57541e7	−	1.15018e9i	0.0287485	−	1.28391i
$965$	8.29891e8			0.923504
$966$	3.16703e8	−	3.09691e8i	0.351335	−	0.343556i
$967$		−	1.32763e9i		−	1.46824i	−0.679020	−	0.734119i	$-0.737595\pi$
$967$		−	1.32763e9i		−	1.46824i	0.679020	−	0.734119i	$-0.262405\pi$
$968$	−1.04045e9	+	9.72812e8i	−1.14708	+	1.07251i
$969$	3.36844e7			0.0370218
$970$	−5.97402e8	−	6.10928e8i	−0.654563	−	0.669383i
$971$		−	5.15383e8i		−	0.562953i	−0.959568	−	0.281477i	$-0.909176\pi$
$971$		−	5.15383e8i		−	0.562953i	0.959568	−	0.281477i	$-0.0908242\pi$
$972$	−1.14408e9	−	2.56174e7i	−1.24582	−	0.0278957i
$973$	−2.92742e8			−0.317795
$974$	−3.17340e7	+	3.10314e7i	−0.0343438	+	0.0335834i
$975$			6.05026e7i			0.0652770i
$976$	3.67502e8	+	1.64660e7i	0.395285	+	0.0177108i
$977$	−1.20775e9			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$977$	−1.20775e9			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$978$	−2.88810e8	−	2.95349e8i	−0.308742	−	0.315732i
$979$		−	2.64767e9i		−	2.82173i
$980$	1.97047e7	−	8.80016e8i	0.0209359	−	0.935001i
$981$	−2.05868e9			−2.18063
$982$	4.95857e8	−	4.84879e8i	0.523627	−	0.512034i
$983$			4.78603e8i			0.503865i	0.967745	+	0.251933i	$0.0810662\pi$
$983$			4.78603e8i			0.503865i	−0.967745	+	0.251933i	$0.918934\pi$
$984$	8.37946e8	+	8.96203e8i	0.879490	+	0.940635i
$985$	5.50781e8			0.576329
$986$	−3.30305e7	−	3.37784e7i	−0.0344575	−	0.0352377i
$987$		−	9.32795e8i		−	0.970141i
$988$	5.09465e7	+	1.14076e6i	0.0528255	+	0.00118283i
$989$	−1.21099e9			−1.25185
$990$	1.75487e9	−	1.71602e9i	1.80859	−	1.76854i
$991$			1.73239e8i			0.178002i	0.996032	+	0.0890011i	$0.0283675\pi$
$991$			1.73239e8i			0.178002i	−0.996032	+	0.0890011i	$0.971633\pi$
$992$	−4.01266e8	+	3.58687e8i	−0.411052	+	0.367436i
$993$	1.65643e9			1.69171
$994$	−4.34027e8	−	4.43854e8i	−0.441934	−	0.451940i
$995$			1.30283e9i			1.32257i
$996$	−5.78442e7	+	2.58333e9i	−0.0585439	+	2.61458i
$997$	1.27881e9			1.29039			0.645195	−	0.764018i	$-0.276776\pi$
$997$	1.27881e9			1.29039			0.645195	+	0.764018i	$0.276776\pi$
$998$	−1.29048e8	+	1.26191e8i	−0.129825	+	0.126951i
$999$			8.54496e8i			0.857065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.13	✓	54
4.3	odd	2	inner	76.7.b.a.39.14	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.13	✓	54	1.1	even	1	trivial
76.7.b.a.39.14	yes	54	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.59318 - 5.71982i) q^{2} -42.2777i q^{3} +(-1.43269 + 63.9840i) q^{4} -135.842 q^{5} +(-241.821 + 236.467i) q^{6} -128.069i q^{7} +(373.990 - 349.679i) q^{8} -1058.40 q^{9} +O(q^{10})\)	\(q+(-5.59318 - 5.71982i) q^{2} -42.2777i q^{3} +(-1.43269 + 63.9840i) q^{4} -135.842 q^{5} +(-241.821 + 236.467i) q^{6} -128.069i q^{7} +(373.990 - 349.679i) q^{8} -1058.40 q^{9} +(759.791 + 776.994i) q^{10} +2133.91i q^{11} +(2705.09 + 60.5706i) q^{12} -506.011 q^{13} +(-732.529 + 716.311i) q^{14} +5743.10i q^{15} +(-4091.89 - 183.338i) q^{16} +506.329 q^{17} +(5919.84 + 6053.87i) q^{18} +1573.56i q^{19} +(194.619 - 8691.73i) q^{20} -5414.44 q^{21} +(12205.6 - 11935.3i) q^{22} -10226.2i q^{23} +(-14783.6 - 15811.4i) q^{24} +2828.15 q^{25} +(2830.21 + 2894.29i) q^{26} +13926.4i q^{27} +(8194.34 + 183.482i) q^{28} +11663.3 q^{29} +(32849.5 - 32122.2i) q^{30} +16424.9i q^{31} +(21838.0 + 24430.3i) q^{32} +90216.8 q^{33} +(-2831.99 - 2896.11i) q^{34} +17397.1i q^{35} +(1516.36 - 67720.8i) q^{36} +61358.1 q^{37} +(9000.49 - 8801.22i) q^{38} +21393.0i q^{39} +(-50803.7 + 47501.2i) q^{40} -56680.7 q^{41} +(30284.0 + 30969.6i) q^{42} -118420. i q^{43} +(-136536. - 3057.22i) q^{44} +143776. q^{45} +(-58492.3 + 57197.2i) q^{46} +172279. i q^{47} +(-7751.10 + 172996. i) q^{48} +101247. q^{49} +(-15818.4 - 16176.5i) q^{50} -21406.4i q^{51} +(724.954 - 32376.6i) q^{52} -114873. q^{53} +(79656.4 - 77892.8i) q^{54} -289875. i q^{55} +(-44782.9 - 47896.4i) q^{56} +66526.6 q^{57} +(-65235.2 - 66712.2i) q^{58} +107818. i q^{59} +(-367466. - 8228.06i) q^{60} -89812.3 q^{61} +(93947.4 - 91867.4i) q^{62} +135548. i q^{63} +(17593.1 - 261553. i) q^{64} +68737.7 q^{65} +(-504599. - 516024. i) q^{66} +487498. i q^{67} +(-725.411 + 32397.0i) q^{68} -432342. q^{69} +(99508.5 - 97305.4i) q^{70} +605920. i q^{71} +(-395832. + 370101. i) q^{72} +411272. q^{73} +(-343187. - 350957. i) q^{74} -119568. i q^{75} +(-100683. - 2254.42i) q^{76} +273287. q^{77} +(122364. - 119655. i) q^{78} +351255. i q^{79} +(555853. + 24905.0i) q^{80} -182800. q^{81} +(317025. + 324203. i) q^{82} +954987. i q^{83} +(7757.19 - 346438. i) q^{84} -68781.0 q^{85} +(-677342. + 662345. i) q^{86} -493099. i q^{87} +(746184. + 798061. i) q^{88} -1.24076e6 q^{89} +(-804165. - 822373. i) q^{90} +64804.1i q^{91} +(654316. + 14651.0i) q^{92} +694406. q^{93} +(985405. - 963588. i) q^{94} -213756. i q^{95} +(1.03286e6 - 923262. i) q^{96} -786271. q^{97} +(-566295. - 579117. i) q^{98} -2.25854e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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