LMFDB - Embedded newform 29.9.c.a.12.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.18
Character	$\chi$	$=$	29.12
Dual form			29.9.c.a.17.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.3086 + 19.3086i) q^{2} +(104.909 + 104.909i) q^{3} +489.642i q^{4} -703.899i q^{5} +4051.27i q^{6} +1720.21 q^{7} +(-4511.30 + 4511.30i) q^{8} +15450.6i q^{9} +O(q^{10})$	\(q+(19.3086 + 19.3086i) q^{2} +(104.909 + 104.909i) q^{3} +489.642i q^{4} -703.899i q^{5} +4051.27i q^{6} +1720.21 q^{7} +(-4511.30 + 4511.30i) q^{8} +15450.6i q^{9} +(13591.3 - 13591.3i) q^{10} +(-10409.2 - 10409.2i) q^{11} +(-51367.6 + 51367.6i) q^{12} -45920.6i q^{13} +(33214.8 + 33214.8i) q^{14} +(73845.0 - 73845.0i) q^{15} -48865.2 q^{16} +(21798.7 + 21798.7i) q^{17} +(-298329. + 298329. i) q^{18} +(-100538. - 100538. i) q^{19} +344659. q^{20} +(180465. + 180465. i) q^{21} -401975. i q^{22} -371944. q^{23} -946548. q^{24} -104849. q^{25} +(886661. - 886661. i) q^{26} +(-932594. + 932594. i) q^{27} +842288. i q^{28} +(352328. + 613279. i) q^{29} +2.85168e6 q^{30} +(742488. + 742488. i) q^{31} +(211376. + 211376. i) q^{32} -2.18403e6i q^{33} +841804. i q^{34} -1.21085e6i q^{35} -7.56526e6 q^{36} +(-1.38707e6 + 1.38707e6i) q^{37} -3.88249e6i q^{38} +(4.81746e6 - 4.81746e6i) q^{39} +(3.17550e6 + 3.17550e6i) q^{40} +(1.11426e6 - 1.11426e6i) q^{41} +6.96904e6i q^{42} +(-308251. - 308251. i) q^{43} +(5.09680e6 - 5.09680e6i) q^{44} +1.08757e7 q^{45} +(-7.18171e6 - 7.18171e6i) q^{46} +(-2.34971e6 + 2.34971e6i) q^{47} +(-5.12637e6 - 5.12637e6i) q^{48} -2.80568e6 q^{49} +(-2.02448e6 - 2.02448e6i) q^{50} +4.57374e6i q^{51} +2.24847e7 q^{52} -2.43738e6 q^{53} -3.60141e7 q^{54} +(-7.32704e6 + 7.32704e6i) q^{55} +(-7.76039e6 + 7.76039e6i) q^{56} -2.10946e7i q^{57} +(-5.03858e6 + 1.86445e7i) q^{58} +1.50512e7 q^{59} +(3.61576e7 + 3.61576e7i) q^{60} +(-5.29417e6 - 5.29417e6i) q^{61} +2.86728e7i q^{62} +2.65783e7i q^{63} +2.06722e7i q^{64} -3.23235e7 q^{65} +(4.21706e7 - 4.21706e7i) q^{66} -307461. i q^{67} +(-1.06736e7 + 1.06736e7i) q^{68} +(-3.90201e7 - 3.90201e7i) q^{69} +(2.33799e7 - 2.33799e7i) q^{70} +3.43659e7i q^{71} +(-6.97023e7 - 6.97023e7i) q^{72} +(2.97294e7 - 2.97294e7i) q^{73} -5.35648e7 q^{74} +(-1.09995e7 - 1.09995e7i) q^{75} +(4.92276e7 - 4.92276e7i) q^{76} +(-1.79061e7 - 1.79061e7i) q^{77} +1.86037e8 q^{78} +(-2.34290e7 - 2.34290e7i) q^{79} +3.43961e7i q^{80} -9.43027e7 q^{81} +4.30297e7 q^{82} +3.11154e7 q^{83} +(-8.83632e7 + 8.83632e7i) q^{84} +(1.53441e7 - 1.53441e7i) q^{85} -1.19038e7i q^{86} +(-2.73759e7 + 1.01300e8i) q^{87} +9.39183e7 q^{88} +(-7.74500e7 - 7.74500e7i) q^{89} +(2.09993e8 + 2.09993e8i) q^{90} -7.89931e7i q^{91} -1.82120e8i q^{92} +1.55787e8i q^{93} -9.07390e7 q^{94} +(-7.07685e7 + 7.07685e7i) q^{95} +4.43503e7i q^{96} +(1.09854e7 - 1.09854e7i) q^{97} +(-5.41736e7 - 5.41736e7i) q^{98} +(1.60829e8 - 1.60829e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) $ 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

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

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 $

$2$	19.3086	+	19.3086i	1.20679	+	1.20679i	0.972062	+	0.234724i	$0.0754186\pi$
$2$	19.3086	+	19.3086i	1.20679	+	1.20679i	0.234724	+	0.972062i	$0.424581\pi$
$3$	104.909	+	104.909i	1.29517	+	1.29517i	0.931548	+	0.363619i	$0.118459\pi$
$3$	104.909	+	104.909i	1.29517	+	1.29517i	0.363619	+	0.931548i	$0.381541\pi$
$4$			489.642i			1.91267i
$5$		−	703.899i		−	1.12624i	−0.826376	−	0.563119i	$-0.809601\pi$
$5$		−	703.899i		−	1.12624i	0.826376	−	0.563119i	$-0.190399\pi$
$6$			4051.27i			3.12598i
$7$	1720.21			0.716456			0.358228	−	0.933634i	$-0.383381\pi$
$7$	1720.21			0.716456			0.358228	+	0.933634i	$0.383381\pi$
$8$	−4511.30	+	4511.30i	−1.10139	+	1.10139i
$9$			15450.6i			2.35491i
$10$	13591.3	−	13591.3i	1.35913	−	1.35913i
$11$	−10409.2	−	10409.2i	−0.710964	−	0.710964i	0.255773	−	0.966737i	$-0.417670\pi$
$11$	−10409.2	−	10409.2i	−0.710964	−	0.710964i	−0.966737	+	0.255773i	$0.917670\pi$
$12$	−51367.6	+	51367.6i	−2.47722	+	2.47722i
$13$		−	45920.6i		−	1.60781i	−0.594759	−	0.803904i	$-0.702753\pi$
$13$		−	45920.6i		−	1.60781i	0.594759	−	0.803904i	$-0.297247\pi$
$14$	33214.8	+	33214.8i	0.864609	+	0.864609i
$15$	73845.0	−	73845.0i	1.45867	−	1.45867i
$16$	−48865.2			−0.745623
$17$	21798.7	+	21798.7i	0.260997	+	0.260997i	0.825459	−	0.564462i	$-0.190916\pi$
$17$	21798.7	+	21798.7i	0.260997	+	0.260997i	−0.564462	+	0.825459i	$0.690916\pi$
$18$	−298329.	+	298329.i	−2.84188	+	2.84188i
$19$	−100538.	−	100538.i	−0.771463	−	0.771463i	0.206899	−	0.978362i	$-0.433663\pi$
$19$	−100538.	−	100538.i	−0.771463	−	0.771463i	−0.978362	+	0.206899i	$0.933663\pi$
$20$	344659.			2.15412
$21$	180465.	+	180465.i	0.927930	+	0.927930i
$22$		−	401975.i		−	1.71596i
$23$	−371944.			−1.32913			−0.664563	−	0.747232i	$-0.731382\pi$
$23$	−371944.			−1.32913			−0.664563	+	0.747232i	$0.731382\pi$
$24$	−946548.			−2.85297
$25$	−104849.			−0.268412
$26$	886661.	−	886661.i	1.94028	−	1.94028i
$27$	−932594.	+	932594.i	−1.75484	+	1.75484i
$28$			842288.i			1.37034i
$29$	352328.	+	613279.i	0.498145	+	0.867094i
$29$	352328.	+	613279.i	0.498145	+	0.867094i
$30$	2.85168e6			3.52060
$31$	742488.	+	742488.i	0.803975	+	0.803975i	0.983714	−	0.179739i	$-0.0575255\pi$
$31$	742488.	+	742488.i	0.803975	+	0.803975i	−0.179739	+	0.983714i	$0.557525\pi$
$32$	211376.	+	211376.i	0.201584	+	0.201584i
$33$		−	2.18403e6i		−	1.84163i
$34$			841804.i			0.629935i
$35$		−	1.21085e6i		−	0.806900i
$36$	−7.56526e6			−4.50416
$37$	−1.38707e6	+	1.38707e6i	−0.740104	+	0.740104i	−0.972598	−	0.232494i	$-0.925311\pi$
$37$	−1.38707e6	+	1.38707e6i	−0.740104	+	0.740104i	0.232494	+	0.972598i	$0.425311\pi$
$38$		−	3.88249e6i		−	1.86198i
$39$	4.81746e6	−	4.81746e6i	2.08238	−	2.08238i
$40$	3.17550e6	+	3.17550e6i	1.24043	+	1.24043i
$41$	1.11426e6	−	1.11426e6i	0.394324	−	0.394324i	−0.481902	−	0.876225i	$-0.660054\pi$
$41$	1.11426e6	−	1.11426e6i	0.394324	−	0.394324i	0.876225	+	0.481902i	$0.160054\pi$
$42$			6.96904e6i			2.23963i
$43$	−308251.	−	308251.i	−0.0901636	−	0.0901636i	0.660586	−	0.750750i	$-0.270308\pi$
$43$	−308251.	−	308251.i	−0.0901636	−	0.0901636i	−0.750750	+	0.660586i	$0.770308\pi$
$44$	5.09680e6	−	5.09680e6i	1.35984	−	1.35984i
$45$	1.08757e7			2.65219
$46$	−7.18171e6	−	7.18171e6i	−1.60397	−	1.60397i
$47$	−2.34971e6	+	2.34971e6i	−0.481529	+	0.481529i	−0.905620	−	0.424091i	$-0.860594\pi$
$47$	−2.34971e6	+	2.34971e6i	−0.481529	+	0.481529i	0.424091	+	0.905620i	$0.360594\pi$
$48$	−5.12637e6	−	5.12637e6i	−0.965706	−	0.965706i
$49$	−2.80568e6			−0.486691
$50$	−2.02448e6	−	2.02448e6i	−0.323916	−	0.323916i
$51$			4.57374e6i			0.676069i
$52$	2.24847e7			3.07520
$53$	−2.43738e6			−0.308901			−0.154451	−	0.988001i	$-0.549361\pi$
$53$	−2.43738e6			−0.308901			−0.154451	+	0.988001i	$0.549361\pi$
$54$	−3.60141e7			−4.23543
$55$	−7.32704e6	+	7.32704e6i	−0.800715	+	0.800715i
$56$	−7.76039e6	+	7.76039e6i	−0.789099	+	0.789099i
$57$		−	2.10946e7i		−	1.99835i
$58$	−5.03858e6	+	1.86445e7i	−0.445242	+	1.64755i
$59$	1.50512e7			1.24212			0.621058	−	0.783765i	$-0.286703\pi$
$59$	1.50512e7			1.24212			0.621058	+	0.783765i	$0.286703\pi$
$60$	3.61576e7	+	3.61576e7i	2.78994	+	2.78994i
$61$	−5.29417e6	−	5.29417e6i	−0.382365	−	0.382365i	0.489588	−	0.871954i	$-0.337147\pi$
$61$	−5.29417e6	−	5.29417e6i	−0.382365	−	0.382365i	−0.871954	+	0.489588i	$0.837147\pi$
$62$			2.86728e7i			1.94045i
$63$			2.65783e7i			1.68719i
$64$			2.06722e7i			1.23216i
$65$	−3.23235e7			−1.81077
$66$	4.21706e7	−	4.21706e7i	2.22246	−	2.22246i
$67$		−	307461.i		−	0.0152578i	−0.999971	−	0.00762889i	$-0.997572\pi$
$67$		−	307461.i		−	0.0152578i	0.999971	−	0.00762889i	$-0.00242837\pi$
$68$	−1.06736e7	+	1.06736e7i	−0.499199	+	0.499199i
$69$	−3.90201e7	−	3.90201e7i	−1.72144	−	1.72144i
$70$	2.33799e7	−	2.33799e7i	0.973756	−	0.973756i
$71$			3.43659e7i			1.35237i	0.736733	+	0.676184i	$0.236368\pi$
$71$			3.43659e7i			1.35237i	−0.736733	+	0.676184i	$0.763632\pi$
$72$	−6.97023e7	−	6.97023e7i	−2.59368	−	2.59368i
$73$	2.97294e7	−	2.97294e7i	1.04688	−	1.04688i	0.0480292	−	0.998846i	$-0.484706\pi$
$73$	2.97294e7	−	2.97294e7i	1.04688	−	1.04688i	0.998846	−	0.0480292i	$-0.0152940\pi$
$74$	−5.35648e7			−1.78629
$75$	−1.09995e7	−	1.09995e7i	−0.347639	−	0.347639i
$76$	4.92276e7	−	4.92276e7i	1.47555	−	1.47555i
$77$	−1.79061e7	−	1.79061e7i	−0.509375	−	0.509375i
$78$	1.86037e8			5.02597
$79$	−2.34290e7	−	2.34290e7i	−0.601515	−	0.601515i	0.339200	−	0.940714i	$-0.389844\pi$
$79$	−2.34290e7	−	2.34290e7i	−0.601515	−	0.601515i	−0.940714	+	0.339200i	$0.889844\pi$
$80$			3.43961e7i			0.839749i
$81$	−9.43027e7			−2.19071
$82$	4.30297e7			0.951729
$83$	3.11154e7			0.655637			0.327819	−	0.944741i	$-0.393686\pi$
$83$	3.11154e7			0.655637			0.327819	+	0.944741i	$0.393686\pi$
$84$	−8.83632e7	+	8.83632e7i	−1.77482	+	1.77482i
$85$	1.53441e7	−	1.53441e7i	0.293945	−	0.293945i
$86$		−	1.19038e7i		−	0.217616i
$87$	−2.73759e7	+	1.01300e8i	−0.477850	+	1.76821i
$88$	9.39183e7			1.56610
$89$	−7.74500e7	−	7.74500e7i	−1.23442	−	1.23442i	−0.962250	−	0.272166i	$-0.912260\pi$
$89$	−7.74500e7	−	7.74500e7i	−1.23442	−	1.23442i	−0.272166	−	0.962250i	$-0.587740\pi$
$90$	2.09993e8	+	2.09993e8i	3.20063	+	3.20063i
$91$		−	7.89931e7i		−	1.15192i
$92$		−	1.82120e8i		−	2.54217i
$93$			1.55787e8i			2.08256i
$94$	−9.07390e7			−1.16220
$95$	−7.07685e7	+	7.07685e7i	−0.868851	+	0.868851i
$96$			4.43503e7i			0.522170i
$97$	1.09854e7	−	1.09854e7i	0.124088	−	0.124088i	−0.642335	−	0.766424i	$-0.722034\pi$
$97$	1.09854e7	−	1.09854e7i	0.124088	−	0.124088i	0.766424	+	0.642335i	$0.222034\pi$
$98$	−5.41736e7	−	5.41736e7i	−0.587332	−	0.587332i
$99$	1.60829e8	−	1.60829e8i	1.67426	−	1.67426i
$100$		−	5.13383e7i		−	0.513383i
$101$	5.11322e7	+	5.11322e7i	0.491370	+	0.491370i	0.908738	−	0.417368i	$-0.137047\pi$
$101$	5.11322e7	+	5.11322e7i	0.491370	+	0.491370i	−0.417368	+	0.908738i	$0.637047\pi$
$102$	−8.83124e7	+	8.83124e7i	−0.815870	+	0.815870i
$103$	−8.91246e7			−0.791860			−0.395930	−	0.918281i	$-0.629578\pi$
$103$	−8.91246e7			−0.791860			−0.395930	+	0.918281i	$0.629578\pi$
$104$	2.07162e8	+	2.07162e8i	1.77083	+	1.77083i
$105$	1.27029e8	−	1.27029e8i	1.04507	−	1.04507i
$106$	−4.70623e7	−	4.70623e7i	−0.372778	−	0.372778i
$107$	3.30736e7			0.252317			0.126158	−	0.992010i	$-0.459735\pi$
$107$	3.30736e7			0.252317			0.126158	+	0.992010i	$0.459735\pi$
$108$	−4.56637e8	−	4.56637e8i	−3.35642	−	3.35642i
$109$		−	7.36332e7i		−	0.521636i	−0.965388	−	0.260818i	$-0.916008\pi$
$109$		−	7.36332e7i		−	0.521636i	0.965388	−	0.260818i	$-0.0839923\pi$
$110$	−2.82950e8			−1.93258
$111$	−2.91032e8			−1.91712
$112$	−8.40584e7			−0.534206
$113$	−4.59421e7	+	4.59421e7i	−0.281772	+	0.281772i	−0.833815	−	0.552044i	$-0.813848\pi$
$113$	−4.59421e7	+	4.59421e7i	−0.281772	+	0.281772i	0.552044	+	0.833815i	$0.313848\pi$
$114$	4.07306e8	−	4.07306e8i	2.41158	−	2.41158i
$115$			2.61811e8i			1.49691i
$116$	−3.00287e8	+	1.72515e8i	−1.65846	+	0.952785i
$117$	7.09500e8			3.78625
$118$	2.90617e8	+	2.90617e8i	1.49897	+	1.49897i
$119$	3.74984e7	+	3.74984e7i	0.186993	+	0.186993i
$120$			6.66274e8i			3.21313i
$121$			2.34518e6i			0.0109405i
$122$		−	2.04446e8i		−	0.922866i
$123$	2.33792e8			1.02143
$124$	−3.63553e8	+	3.63553e8i	−1.53773	+	1.53773i
$125$		−	2.01158e8i		−	0.823942i
$126$	−5.13189e8	+	5.13189e8i	−2.03608	+	2.03608i
$127$	−1.01036e8	−	1.01036e8i	−0.388384	−	0.388384i	0.485727	−	0.874111i	$-0.338555\pi$
$127$	−1.01036e8	−	1.01036e8i	−0.388384	−	0.388384i	−0.874111	+	0.485727i	$0.838555\pi$
$128$	−3.45039e8	+	3.45039e8i	−1.28537	+	1.28537i
$129$		−	6.46764e7i		−	0.233554i
$130$	−6.24120e8	−	6.24120e8i	−2.18522	−	2.18522i
$131$	2.35431e8	−	2.35431e8i	0.799426	−	0.799426i	−0.183579	−	0.983005i	$-0.558768\pi$
$131$	2.35431e8	−	2.35431e8i	0.799426	−	0.799426i	0.983005	+	0.183579i	$0.0587684\pi$
$132$	1.06940e9			3.52243
$133$	−1.72946e8	−	1.72946e8i	−0.552719	−	0.552719i
$134$	5.93664e6	−	5.93664e6i	0.0184129	−	0.0184129i
$135$	6.56452e8	+	6.56452e8i	1.97637	+	1.97637i
$136$	−1.96681e8			−0.574919
$137$	4.84224e7	+	4.84224e7i	0.137456	+	0.137456i	0.772487	−	0.635031i	$-0.219013\pi$
$137$	4.84224e7	+	4.84224e7i	0.137456	+	0.137456i	−0.635031	+	0.772487i	$0.719013\pi$
$138$		−	1.50685e9i		−	4.15482i
$139$	−5.84969e7			−0.156702			−0.0783509	−	0.996926i	$-0.524965\pi$
$139$	−5.84969e7			−0.156702			−0.0783509	+	0.996926i	$0.524965\pi$
$140$	5.92886e8			1.54333
$141$	−4.93009e8			−1.24732
$142$	−6.63557e8	+	6.63557e8i	−1.63202	+	1.63202i
$143$	−4.77998e8	+	4.77998e8i	−1.14309	+	1.14309i
$144$		−	7.54996e8i		−	1.75588i
$145$	4.31686e8	−	2.48004e8i	0.976554	−	0.561030i
$146$	1.14807e9			2.52671
$147$	−2.94339e8	−	2.94339e8i	−0.630346	−	0.630346i
$148$	−6.79170e8	−	6.79170e8i	−1.41557	−	1.41557i
$149$			5.18371e8i			1.05171i	0.850575	+	0.525854i	$0.176254\pi$
$149$			5.18371e8i			1.05171i	−0.850575	+	0.525854i	$0.823746\pi$
$150$		−	4.24770e8i		−	0.839051i
$151$			5.66749e8i			1.09014i	0.838390	+	0.545071i	$0.183497\pi$
$151$			5.66749e8i			1.09014i	−0.838390	+	0.545071i	$0.816503\pi$
$152$	9.07113e8			1.69937
$153$	−3.36803e8	+	3.36803e8i	−0.614625	+	0.614625i
$154$		−	6.91481e8i		−	1.22941i
$155$	5.22636e8	−	5.22636e8i	0.905467	−	0.905467i
$156$	2.35883e9	+	2.35883e9i	3.98289	+	3.98289i
$157$	−9.14232e7	+	9.14232e7i	−0.150473	+	0.150473i	−0.778329	−	0.627856i	$-0.783932\pi$
$157$	−9.14232e7	+	9.14232e7i	−0.150473	+	0.150473i	0.627856	+	0.778329i	$0.283932\pi$
$158$		−	9.04763e8i		−	1.45180i
$159$	−2.55702e8	−	2.55702e8i	−0.400079	−	0.400079i
$160$	1.48787e8	−	1.48787e8i	0.227032	−	0.227032i
$161$	−6.39822e8			−0.952261
$162$	−1.82085e9	−	1.82085e9i	−2.64371	−	2.64371i
$163$	−1.49329e7	+	1.49329e7i	−0.0211540	+	0.0211540i	−0.717605	−	0.696451i	$-0.754762\pi$
$163$	−1.49329e7	+	1.49329e7i	−0.0211540	+	0.0211540i	0.696451	+	0.717605i	$0.254762\pi$
$164$	5.45591e8	+	5.45591e8i	0.754209	+	0.754209i
$165$	−1.53734e9			−2.07412
$166$	6.00795e8	+	6.00795e8i	0.791214	+	0.791214i
$167$			1.45226e8i			0.186715i	0.995633	+	0.0933573i	$0.0297599\pi$
$167$			1.45226e8i			0.186715i	−0.995633	+	0.0933573i	$0.970240\pi$
$168$	−1.62826e9			−2.04403
$169$	−1.29297e9			−1.58505
$170$	5.92545e8			0.709456
$171$	1.55337e9	−	1.55337e9i	1.81673	−	1.81673i
$172$	1.50933e8	−	1.50933e8i	0.172453	−	0.172453i
$173$		−	4.11645e8i		−	0.459556i	−0.973243	−	0.229778i	$-0.926200\pi$
$173$		−	4.11645e8i		−	0.459556i	0.973243	−	0.229778i	$-0.0738000\pi$
$174$	−2.48456e9	+	1.42738e9i	−2.71052	+	1.55719i
$175$	−1.80362e8			−0.192306
$176$	5.08649e8	+	5.08649e8i	0.530111	+	0.530111i
$177$	1.57900e9	+	1.57900e9i	1.60875	+	1.60875i
$178$		−	2.99090e9i		−	2.97935i
$179$			1.55746e9i			1.51706i	0.651637	+	0.758531i	$0.274083\pi$
$179$			1.55746e9i			1.51706i	−0.651637	+	0.758531i	$0.725917\pi$
$180$			5.32518e9i			5.07276i
$181$	2.08542e9			1.94303			0.971513	−	0.236985i	$-0.0761593\pi$
$181$	2.08542e9			1.94303			0.971513	+	0.236985i	$0.0761593\pi$
$182$	1.52524e9	−	1.52524e9i	1.39013	−	1.39013i
$183$		−	1.11081e9i		−	0.990454i
$184$	1.67795e9	−	1.67795e9i	1.46389	−	1.46389i
$185$	9.76359e8	+	9.76359e8i	0.833533	+	0.833533i
$186$	−3.00802e9	+	3.00802e9i	−2.51321	+	2.51321i
$187$		−	4.53816e8i		−	0.371119i
$188$	−1.15052e9	−	1.15052e9i	−0.921004	−	0.921004i
$189$	−1.60426e9	+	1.60426e9i	−1.25727	+	1.25727i
$190$	−2.73288e9			−2.09704
$191$	9.19955e8	+	9.19955e8i	0.691247	+	0.691247i	0.962506	−	0.271259i	$-0.0874401\pi$
$191$	9.19955e8	+	9.19955e8i	0.691247	+	0.691247i	−0.271259	+	0.962506i	$0.587440\pi$
$192$	−2.16869e9	+	2.16869e9i	−1.59585	+	1.59585i
$193$	−1.85847e8	−	1.85847e8i	−0.133945	−	0.133945i	0.636955	−	0.770901i	$-0.280194\pi$
$193$	−1.85847e8	−	1.85847e8i	−0.133945	−	0.133945i	−0.770901	+	0.636955i	$0.780194\pi$
$194$	4.24227e8			0.299496
$195$	−3.39101e9	−	3.39101e9i	−2.34525	−	2.34525i
$196$		−	1.37378e9i		−	0.930877i
$197$	2.03206e9			1.34919			0.674594	−	0.738189i	$-0.264319\pi$
$197$	2.03206e9			1.34919			0.674594	+	0.738189i	$0.264319\pi$
$198$	6.21075e9			4.04095
$199$	−5.73555e7			−0.0365732			−0.0182866	−	0.999833i	$-0.505821\pi$
$199$	−5.73555e7			−0.0365732			−0.0182866	+	0.999833i	$0.505821\pi$
$200$	4.73004e8	−	4.73004e8i	0.295627	−	0.295627i
$201$	3.22553e7	−	3.22553e7i	0.0197614	−	0.0197614i
$202$			1.97458e9i			1.18596i
$203$	6.06079e8	+	1.05497e9i	0.356899	+	0.621235i
$204$	−2.23950e9			−1.29309
$205$	−7.84330e8	−	7.84330e8i	−0.444103	−	0.444103i
$206$	−1.72087e9	−	1.72087e9i	−0.955606	−	0.955606i
$207$		−	5.74676e9i		−	3.12998i
$208$			2.24392e9i			1.19882i
$209$			2.09304e9i			1.09697i
$210$	4.90550e9			2.52235
$211$	−7.66465e8	+	7.66465e8i	−0.386690	+	0.386690i	−0.873505	−	0.486815i	$-0.838158\pi$
$211$	−7.66465e8	+	7.66465e8i	−0.386690	+	0.386690i	0.486815	+	0.873505i	$0.338158\pi$
$212$		−	1.19344e9i		−	0.590825i
$213$	−3.60528e9	+	3.60528e9i	−1.75154	+	1.75154i
$214$	6.38604e8	+	6.38604e8i	0.304493	+	0.304493i
$215$	−2.16978e8	+	2.16978e8i	−0.101546	+	0.101546i
$216$		−	8.41442e9i		−	3.86553i
$217$	1.27724e9	+	1.27724e9i	0.576013	+	0.576013i
$218$	1.42175e9	−	1.42175e9i	0.629504	−	0.629504i
$219$	6.23774e9			2.71176
$220$	−3.58763e9	−	3.58763e9i	−1.53150	−	1.53150i
$221$	1.00101e9	−	1.00101e9i	0.419633	−	0.419633i
$222$	−5.61941e9	−	5.61941e9i	−2.31355	−	2.31355i
$223$	6.65420e8			0.269077			0.134538	−	0.990908i	$-0.457045\pi$
$223$	6.65420e8			0.269077			0.134538	+	0.990908i	$0.457045\pi$
$224$	3.63612e8	+	3.63612e8i	0.144426	+	0.144426i
$225$		−	1.61997e9i		−	0.632088i
$226$	−1.77415e9			−0.680076
$227$	1.48619e9			0.559719			0.279859	−	0.960041i	$-0.409712\pi$
$227$	1.48619e9			0.559719			0.279859	+	0.960041i	$0.409712\pi$
$228$	1.03288e10			3.82217
$229$	−1.99672e9	+	1.99672e9i	−0.726065	+	0.726065i	−0.969833	−	0.243769i	$-0.921616\pi$
$229$	−1.99672e9	+	1.99672e9i	−0.726065	+	0.726065i	0.243769	+	0.969833i	$0.421616\pi$
$230$	−5.05520e9	+	5.05520e9i	−1.80645	+	1.80645i
$231$		−	3.75700e9i		−	1.31945i
$232$	−4.35615e9	−	1.17723e9i	−1.50366	−	0.406357i
$233$	−4.79139e9			−1.62569			−0.812844	−	0.582481i	$-0.802082\pi$
$233$	−4.79139e9			−1.62569			−0.812844	+	0.582481i	$0.802082\pi$
$234$	1.36994e10	+	1.36994e10i	4.56919	+	4.56919i
$235$	1.65396e9	+	1.65396e9i	0.542316	+	0.542316i
$236$			7.36969e9i			2.37575i
$237$		−	4.91581e9i		−	1.55812i
$238$			1.44808e9i			0.451320i
$239$	3.32623e9			1.01944			0.509718	−	0.860341i	$-0.329750\pi$
$239$	3.32623e9			1.01944			0.509718	+	0.860341i	$0.329750\pi$
$240$	−3.60845e9	+	3.60845e9i	−1.08762	+	1.08762i
$241$		−	5.41707e9i		−	1.60582i	−0.596102	−	0.802909i	$-0.703285\pi$
$241$		−	5.41707e9i		−	1.60582i	0.596102	−	0.802909i	$-0.296715\pi$
$242$	−4.52822e7	+	4.52822e7i	−0.0132028	+	0.0132028i
$243$	−3.77441e9	−	3.77441e9i	−1.08249	−	1.08249i
$244$	2.59225e9	−	2.59225e9i	0.731337	−	0.731337i
$245$			1.97491e9i			0.548130i
$246$	4.51419e9	+	4.51419e9i	1.23265	+	1.23265i
$247$	−4.61676e9	+	4.61676e9i	−1.24036	+	1.24036i
$248$	−6.69917e9			−1.77098
$249$	3.26428e9	+	3.26428e9i	0.849160	+	0.849160i
$250$	3.88407e9	−	3.88407e9i	0.994322	−	0.994322i
$251$	−1.43376e9	−	1.43376e9i	−0.361229	−	0.361229i	0.503036	−	0.864265i	$-0.332216\pi$
$251$	−1.43376e9	−	1.43376e9i	−0.361229	−	0.361229i	−0.864265	+	0.503036i	$0.832216\pi$
$252$	−1.30138e10			−3.22703
$253$	3.87165e9	+	3.87165e9i	0.944962	+	0.944962i
$254$		−	3.90173e9i		−	0.937394i
$255$	3.21945e9			0.761414
$256$	−8.03233e9			−1.87017
$257$	−3.30811e9			−0.758312			−0.379156	−	0.925333i	$-0.623786\pi$
$257$	−3.30811e9			−0.758312			−0.379156	+	0.925333i	$0.623786\pi$
$258$	1.24881e9	−	1.24881e9i	0.281849	−	0.281849i
$259$	−2.38606e9	+	2.38606e9i	−0.530252	+	0.530252i
$260$		−	1.58269e10i		−	3.46341i
$261$	−9.47552e9	+	5.44368e9i	−2.04193	+	1.17309i
$262$	9.09167e9			1.92947
$263$	−7.94098e8	−	7.94098e8i	−0.165978	−	0.165978i	0.619231	−	0.785209i	$-0.287445\pi$
$263$	−7.94098e8	−	7.94098e8i	−0.165978	−	0.165978i	−0.785209	+	0.619231i	$0.787445\pi$
$264$	9.85283e9	+	9.85283e9i	2.02836	+	2.02836i
$265$			1.71567e9i			0.347896i
$266$		−	6.67869e9i		−	1.33403i
$267$		−	1.62503e10i		−	3.19755i
$268$	1.50546e8			0.0291830
$269$	−6.56214e9	+	6.56214e9i	−1.25325	+	1.25325i	−0.298989	+	0.954257i	$0.596649\pi$
$269$	−6.56214e9	+	6.56214e9i	−1.25325	+	1.25325i	−0.954257	+	0.298989i	$0.903351\pi$
$270$			2.53503e10i			4.77011i
$271$	4.59769e9	−	4.59769e9i	0.852437	−	0.852437i	−0.137996	−	0.990433i	$-0.544066\pi$
$271$	4.59769e9	−	4.59769e9i	0.852437	−	0.852437i	0.990433	+	0.137996i	$0.0440661\pi$
$272$	−1.06520e9	−	1.06520e9i	−0.194605	−	0.194605i
$273$	8.28705e9	−	8.28705e9i	1.49193	−	1.49193i
$274$			1.86994e9i			0.331760i
$275$	1.09139e9	+	1.09139e9i	0.190832	+	0.190832i
$276$	1.91059e10	−	1.91059e10i	3.29254	−	3.29254i
$277$	3.73726e9			0.634796			0.317398	−	0.948292i	$-0.397191\pi$
$277$	3.73726e9			0.634796			0.317398	+	0.948292i	$0.397191\pi$
$278$	−1.12949e9	−	1.12949e9i	−0.189106	−	0.189106i
$279$	−1.14719e10	+	1.14719e10i	−1.89329	+	1.89329i
$280$	5.46253e9	+	5.46253e9i	0.888713	+	0.888713i
$281$	−2.40573e9			−0.385852			−0.192926	−	0.981213i	$-0.561798\pi$
$281$	−2.40573e9			−0.385852			−0.192926	+	0.981213i	$0.561798\pi$
$282$	−9.51930e9	−	9.51930e9i	−1.50525	−	1.50525i
$283$			5.25499e8i			0.0819269i	0.999161	+	0.0409634i	$0.0130427\pi$
$283$			5.25499e8i			0.0819269i	−0.999161	+	0.0409634i	$0.986957\pi$
$284$	−1.68270e10			−2.58663
$285$	−1.48484e10			−2.25061
$286$	−1.84589e10			−2.75894
$287$	1.91677e9	−	1.91677e9i	0.282516	−	0.282516i
$288$	−3.26589e9	+	3.26589e9i	−0.474713	+	0.474713i
$289$		−	6.02539e9i		−	0.863761i
$290$	1.31238e10	+	3.54665e9i	1.85553	+	0.501449i
$291$	2.30493e9			0.321430
$292$	1.45568e10	+	1.45568e10i	2.00232	+	2.00232i
$293$	5.07476e9	+	5.07476e9i	0.688565	+	0.688565i	0.961915	−	0.273350i	$-0.0881316\pi$
$293$	5.07476e9	+	5.07476e9i	0.688565	+	0.688565i	−0.273350	+	0.961915i	$0.588132\pi$
$294$		−	1.13665e10i		−	1.52139i
$295$		−	1.05945e10i		−	1.39892i
$296$		−	1.25150e10i		−	1.63029i
$297$	1.94152e10			2.49526
$298$	−1.00090e10	+	1.00090e10i	−1.26919	+	1.26919i
$299$			1.70799e10i			2.13698i
$300$	5.38583e9	−	5.38583e9i	0.664917	−	0.664917i
$301$	−5.30257e8	−	5.30257e8i	−0.0645982	−	0.0645982i
$302$	−1.09431e10	+	1.09431e10i	−1.31557	+	1.31557i
$303$			1.07284e10i			1.27281i
$304$	4.91280e9	+	4.91280e9i	0.575221	+	0.575221i
$305$	−3.72656e9	+	3.72656e9i	−0.430634	+	0.430634i
$306$	−1.30064e10			−1.48344
$307$	1.25835e9	+	1.25835e9i	0.141660	+	0.141660i	0.774380	−	0.632720i	$-0.218062\pi$
$307$	1.25835e9	+	1.25835e9i	0.141660	+	0.141660i	−0.632720	+	0.774380i	$0.718062\pi$
$308$	8.76757e9	−	8.76757e9i	0.974263	−	0.974263i
$309$	−9.34993e9	−	9.34993e9i	−1.02559	−	1.02559i
$310$	2.01827e10			2.18541
$311$	−3.16257e9	−	3.16257e9i	−0.338064	−	0.338064i	0.517575	−	0.855638i	$-0.326835\pi$
$311$	−3.16257e9	−	3.16257e9i	−0.338064	−	0.338064i	−0.855638	+	0.517575i	$0.826835\pi$
$312$			4.34660e10i			4.58703i
$313$	1.47896e10			1.54091			0.770456	−	0.637493i	$-0.220028\pi$
$313$	1.47896e10			1.54091			0.770456	+	0.637493i	$0.220028\pi$
$314$	−3.53050e9			−0.363177
$315$	1.87084e10			1.90018
$316$	1.14719e10	−	1.14719e10i	1.15050	−	1.15050i
$317$	−5.66224e9	+	5.66224e9i	−0.560727	+	0.560727i	−0.929514	−	0.368787i	$-0.879773\pi$
$317$	−5.66224e9	+	5.66224e9i	−0.560727	+	0.560727i	0.368787	+	0.929514i	$0.379773\pi$
$318$		−	9.87448e9i		−	0.965619i
$319$	2.71629e9	−	1.00512e10i	0.262309	−	0.970636i
$320$	1.45512e10			1.38771
$321$	3.46970e9	+	3.46970e9i	0.326793	+	0.326793i
$322$	−1.23541e10	−	1.23541e10i	−1.14917	−	1.14917i
$323$		−	4.38319e9i		−	0.402699i
$324$		−	4.61746e10i		−	4.19009i
$325$			4.81471e9i			0.431556i
$326$	−5.76665e8			−0.0510568
$327$	7.72475e9	−	7.72475e9i	0.675606	−	0.675606i
$328$			1.00536e10i			0.868610i
$329$	−4.04199e9	+	4.04199e9i	−0.344994	+	0.344994i
$330$	−2.96838e10	−	2.96838e10i	−2.50302	−	2.50302i
$331$	8.66884e8	−	8.66884e8i	0.0722186	−	0.0722186i	−0.670075	−	0.742293i	$-0.733738\pi$
$331$	8.66884e8	−	8.66884e8i	0.0722186	−	0.0722186i	0.742293	+	0.670075i	$0.233738\pi$
$332$			1.52354e10i			1.25401i
$333$	−2.14311e10	−	2.14311e10i	−1.74288	−	1.74288i
$334$	−2.80411e9	+	2.80411e9i	−0.225325	+	0.225325i
$335$	−2.16422e8			−0.0171839
$336$	−8.81844e9	−	8.81844e9i	−0.691886	−	0.691886i
$337$	2.47591e9	−	2.47591e9i	0.191962	−	0.191962i	−0.604581	−	0.796543i	$-0.706660\pi$
$337$	2.47591e9	−	2.47591e9i	0.191962	−	0.191962i	0.796543	+	0.604581i	$0.206660\pi$
$338$	−2.49654e10	−	2.49654e10i	−1.91281	−	1.91281i
$339$	−9.63944e9			−0.729882
$340$	7.51311e9	+	7.51311e9i	0.562217	+	0.562217i
$341$		−	1.54574e10i		−	1.14319i
$342$	5.99867e10			4.38481
$343$	−1.47430e10			−1.06515
$344$	2.78123e9			0.198611
$345$	−2.74662e10	+	2.74662e10i	−1.93875	+	1.93875i
$346$	7.94828e9	−	7.94828e9i	0.554586	−	0.554586i
$347$			4.15846e9i			0.286824i	0.989663	+	0.143412i	$0.0458073\pi$
$347$			4.15846e9i			0.286824i	−0.989663	+	0.143412i	$0.954193\pi$
$348$	−4.96010e10	−	1.34044e10i	−3.38200	−	0.913968i
$349$	1.22040e9			0.0822620			0.0411310	−	0.999154i	$-0.486904\pi$
$349$	1.22040e9			0.0822620			0.0411310	+	0.999154i	$0.486904\pi$
$350$	−3.48253e9	−	3.48253e9i	−0.232072	−	0.232072i
$351$	4.28253e10	+	4.28253e10i	2.82144	+	2.82144i
$352$		−	4.40053e9i		−	0.286638i
$353$			2.15653e10i			1.38886i	0.719563	+	0.694428i	$0.244342\pi$
$353$			2.15653e10i			1.38886i	−0.719563	+	0.694428i	$0.755658\pi$
$354$			6.09763e10i			3.88283i
$355$	2.41901e10			1.52309
$356$	3.79228e10	−	3.79228e10i	2.36103	−	2.36103i
$357$			7.86780e9i			0.484373i
$358$	−3.00722e10	+	3.00722e10i	−1.83077	+	1.83077i
$359$	3.97287e9	+	3.97287e9i	0.239181	+	0.239181i	0.816511	−	0.577330i	$-0.195905\pi$
$359$	3.97287e9	+	3.97287e9i	0.239181	+	0.239181i	−0.577330	+	0.816511i	$0.695905\pi$
$360$	−4.90633e10	+	4.90633e10i	−2.92110	+	2.92110i
$361$			3.23216e9i			0.190311i
$362$	4.02664e10	+	4.02664e10i	2.34482	+	2.34482i
$363$	−2.46030e8	+	2.46030e8i	−0.0141697	+	0.0141697i
$364$	3.86784e10			2.20324
$365$	−2.09265e10	−	2.09265e10i	−1.17903	−	1.17903i
$366$	2.14481e10	−	2.14481e10i	1.19527	−	1.19527i
$367$	−5.86602e9	−	5.86602e9i	−0.323355	−	0.323355i	0.526698	−	0.850053i	$-0.323430\pi$
$367$	−5.86602e9	−	5.86602e9i	−0.323355	−	0.323355i	−0.850053	+	0.526698i	$0.823430\pi$
$368$	1.81751e10			0.991028
$369$	1.72161e10	+	1.72161e10i	0.928599	+	0.928599i
$370$			3.77042e10i			2.01179i
$371$	−4.19281e9			−0.221314
$372$	−7.62797e10			−3.98325
$373$	−2.05713e9			−0.106274			−0.0531368	−	0.998587i	$-0.516922\pi$
$373$	−2.05713e9			−0.106274			−0.0531368	+	0.998587i	$0.516922\pi$
$374$	8.76253e9	−	8.76253e9i	0.447861	−	0.447861i
$375$	2.11032e10	−	2.11032e10i	1.06714	−	1.06714i
$376$		−	2.12005e10i		−	1.06070i
$377$	2.81621e10	−	1.61791e10i	1.39412	−	0.800921i
$378$	−6.19519e10			−3.03450
$379$	−2.16312e10	−	2.16312e10i	−1.04839	−	1.04839i	−0.998768	−	0.0496268i	$-0.984197\pi$
$379$	−2.16312e10	−	2.16312e10i	−1.04839	−	1.04839i	−0.0496268	−	0.998768i	$-0.515803\pi$
$380$	−3.46512e10	−	3.46512e10i	−1.66182	−	1.66182i
$381$		−	2.11991e10i		−	1.00604i
$382$			3.55260e10i			1.66837i
$383$			4.09090e10i			1.90118i	0.310446	+	0.950591i	$0.399522\pi$
$383$			4.09090e10i			1.90118i	−0.310446	+	0.950591i	$0.600478\pi$
$384$	−7.23951e10			−3.32954
$385$	−1.26041e10	+	1.26041e10i	−0.573677	+	0.573677i
$386$		−	7.17690e9i		−	0.323287i
$387$	4.76266e9	−	4.76266e9i	0.212327	−	0.212327i
$388$	5.37894e9	+	5.37894e9i	0.237339	+	0.237339i
$389$	2.17589e10	−	2.17589e10i	0.950251	−	0.950251i	−0.0485686	−	0.998820i	$-0.515466\pi$
$389$	2.17589e10	−	2.17589e10i	0.950251	−	0.950251i	0.998820	+	0.0485686i	$0.0154659\pi$
$390$		−	1.30951e11i		−	5.66044i
$391$	−8.10790e9	−	8.10790e9i	−0.346898	−	0.346898i
$392$	1.26572e10	−	1.26572e10i	0.536037	−	0.536037i
$393$	4.93974e10			2.07078
$394$	3.92363e10	+	3.92363e10i	1.62818	+	1.62818i
$395$	−1.64917e10	+	1.64917e10i	−0.677449	+	0.677449i
$396$	7.87486e10	+	7.87486e10i	3.20230	+	3.20230i
$397$	−2.31260e10			−0.930977			−0.465488	−	0.885054i	$-0.654121\pi$
$397$	−2.31260e10			−0.930977			−0.465488	+	0.885054i	$0.654121\pi$
$398$	−1.10745e9	−	1.10745e9i	−0.0441360	−	0.0441360i
$399$		−	3.62871e10i		−	1.43173i
$400$	5.12344e9			0.200135
$401$	2.54777e9			0.0985333			0.0492667	−	0.998786i	$-0.484312\pi$
$401$	2.54777e9			0.0985333			0.0492667	+	0.998786i	$0.484312\pi$
$402$	1.24561e9			0.0476955
$403$	3.40955e10	−	3.40955e10i	1.29264	−	1.29264i
$404$	−2.50365e10	+	2.50365e10i	−0.939826	+	0.939826i
$405$			6.63796e10i			2.46726i
$406$	−8.66742e9	+	3.20725e10i	−0.318996	+	1.18040i
$407$	2.88767e10			1.05237
$408$	−2.06335e10	−	2.06335e10i	−0.744616	−	0.744616i
$409$	−3.20843e10	−	3.20843e10i	−1.14657	−	1.14657i	−0.987223	−	0.159344i	$-0.949062\pi$
$409$	−3.20843e10	−	3.20843e10i	−1.14657	−	1.14657i	−0.159344	−	0.987223i	$-0.550938\pi$
$410$		−	3.02886e10i		−	1.07187i
$411$			1.01598e10i			0.356057i
$412$		−	4.36392e10i		−	1.51456i
$413$	2.58912e10			0.889921
$414$	1.10962e11	−	1.10962e11i	3.77721	−	3.77721i
$415$		−	2.19021e10i		−	0.738404i
$416$	9.70652e9	−	9.70652e9i	0.324108	−	0.324108i
$417$	−6.13683e9	−	6.13683e9i	−0.202955	−	0.202955i
$418$	−4.04137e10	+	4.04137e10i	−1.32380	+	1.32380i
$419$			4.54308e10i			1.47399i	0.675899	+	0.736994i	$0.263755\pi$
$419$			4.54308e10i			1.47399i	−0.675899	+	0.736994i	$0.736245\pi$
$420$	6.21987e10	+	6.21987e10i	1.99887	+	1.99887i
$421$	−1.05155e10	+	1.05155e10i	−0.334734	+	0.334734i	−0.854381	−	0.519647i	$-0.826064\pi$
$421$	−1.05155e10	+	1.05155e10i	−0.334734	+	0.334734i	0.519647	+	0.854381i	$0.326064\pi$
$422$	−2.95987e10			−0.933304
$423$	−3.63044e10	−	3.63044e10i	−1.13396	−	1.13396i
$424$	1.09958e10	−	1.09958e10i	0.340221	−	0.340221i
$425$	−2.28556e9	−	2.28556e9i	−0.0700548	−	0.0700548i
$426$	−1.39226e11			−4.22747
$427$	−9.10709e9	−	9.10709e9i	−0.273948	−	0.273948i
$428$			1.61942e10i			0.482598i
$429$	−1.00292e11			−2.96099
$430$	−8.37906e9			−0.245088
$431$	−2.23729e10			−0.648354			−0.324177	−	0.945996i	$-0.605087\pi$
$431$	−2.23729e10			−0.648354			−0.324177	+	0.945996i	$0.605087\pi$
$432$	4.55713e10	−	4.55713e10i	1.30845	−	1.30845i
$433$	2.88082e9	−	2.88082e9i	0.0819529	−	0.0819529i	−0.664942	−	0.746895i	$-0.731544\pi$
$433$	2.88082e9	−	2.88082e9i	0.0819529	−	0.0819529i	0.746895	+	0.664942i	$0.231544\pi$
$434$			4.93232e10i			1.39025i
$435$	7.13053e10	+	1.92699e10i	1.99143	+	0.538173i
$436$	3.60539e10			0.997716
$437$	3.73945e10	+	3.73945e10i	1.02537	+	1.02537i
$438$	1.20442e11	+	1.20442e11i	3.27251	+	3.27251i
$439$		−	1.58831e10i		−	0.427640i	−0.976873	−	0.213820i	$-0.931409\pi$
$439$		−	1.58831e10i		−	0.427640i	0.976873	−	0.213820i	$-0.0685906\pi$
$440$		−	6.61090e10i		−	1.76380i
$441$		−	4.33493e10i		−	1.14612i
$442$	3.86562e10			1.01281
$443$	4.65864e10	−	4.65864e10i	1.20961	−	1.20961i	0.238453	−	0.971154i	$-0.423360\pi$
$443$	4.65864e10	−	4.65864e10i	1.20961	−	1.20961i	0.971154	−	0.238453i	$-0.0766402\pi$
$444$		−	1.42501e11i		−	3.66680i
$445$	−5.45170e10	+	5.45170e10i	−1.39025	+	1.39025i
$446$	1.28483e10	+	1.28483e10i	0.324718	+	0.324718i
$447$	−5.43815e10	+	5.43815e10i	−1.36214	+	1.36214i
$448$			3.55606e10i			0.882789i
$449$	6.57060e9	+	6.57060e9i	0.161666	+	0.161666i	0.783305	−	0.621638i	$-0.213533\pi$
$449$	6.57060e9	+	6.57060e9i	0.161666	+	0.161666i	−0.621638	+	0.783305i	$0.713533\pi$
$450$	3.12794e10	−	3.12794e10i	0.762795	−	0.762795i
$451$	−2.31973e10			−0.560700
$452$	−2.24952e10	−	2.24952e10i	−0.538935	−	0.538935i
$453$	−5.94568e10	+	5.94568e10i	−1.41192	+	1.41192i
$454$	2.86961e10	+	2.86961e10i	0.675461	+	0.675461i
$455$	−5.56032e10			−1.29734
$456$	9.51639e10	+	9.51639e10i	2.20096	+	2.20096i
$457$		−	3.74567e10i		−	0.858746i	−0.903127	−	0.429373i	$-0.858735\pi$
$457$		−	3.74567e10i		−	0.858746i	0.903127	−	0.429373i	$-0.141265\pi$
$458$	−7.71077e10			−1.75241
$459$	−4.06587e10			−0.916015
$460$	−1.28194e11			−2.86309
$461$	−7.11547e9	+	7.11547e9i	−0.157543	+	0.157543i	−0.781477	−	0.623934i	$-0.785533\pi$
$461$	−7.11547e9	+	7.11547e9i	−0.157543	+	0.157543i	0.623934	+	0.781477i	$0.285533\pi$
$462$	7.25423e10	−	7.25423e10i	1.59229	−	1.59229i
$463$		−	5.51420e10i		−	1.19994i	−0.800024	−	0.599969i	$-0.795180\pi$
$463$		−	5.51420e10i		−	1.19994i	0.800024	−	0.599969i	$-0.204820\pi$
$464$	−1.72166e10	−	2.99680e10i	−0.371428	−	0.646525i
$465$	1.09658e11			2.34546
$466$	−9.25148e10	−	9.25148e10i	−1.96186	−	1.96186i
$467$	−5.57661e10	−	5.57661e10i	−1.17247	−	1.17247i	−0.981618	−	0.190855i	$-0.938874\pi$
$467$	−5.57661e10	−	5.57661e10i	−1.17247	−	1.17247i	−0.190855	−	0.981618i	$-0.561126\pi$
$468$			3.47401e11i			7.24183i
$469$		−	5.28898e8i		−	0.0109315i
$470$			6.38711e10i			1.30892i
$471$	−1.91821e10			−0.389774
$472$	−6.79003e10	+	6.79003e10i	−1.36806	+	1.36806i
$473$			6.41732e9i			0.128206i
$474$	9.49173e10	−	9.49173e10i	1.88032	−	1.88032i
$475$	1.05413e10	+	1.05413e10i	0.207070	+	0.207070i
$476$	−1.83608e10	+	1.83608e10i	−0.357654	+	0.357654i
$477$		−	3.76590e10i		−	0.727436i
$478$	6.42247e10	+	6.42247e10i	1.23024	+	1.23024i
$479$	−4.53189e10	+	4.53189e10i	−0.860869	+	0.860869i	−0.991439	−	0.130570i	$-0.958319\pi$
$479$	−4.53189e10	+	4.53189e10i	−0.860869	+	0.860869i	0.130570	+	0.991439i	$0.458319\pi$
$480$	3.12181e10			0.588088
$481$	6.36952e10	+	6.36952e10i	1.18994	+	1.18994i
$482$	1.04596e11	−	1.04596e11i	1.93788	−	1.93788i
$483$	−6.71228e10	−	6.71228e10i	−1.23334	−	1.23334i
$484$	−1.14830e9			−0.0209254
$485$	−7.73264e9	−	7.73264e9i	−0.139753	−	0.139753i
$486$		−	1.45757e11i		−	2.61267i
$487$	1.09086e11			1.93933			0.969667	−	0.244429i	$-0.0786006\pi$
$487$	1.09086e11			1.93933			0.969667	+	0.244429i	$0.0786006\pi$
$488$	4.77672e10			0.842268
$489$	−3.13317e9			−0.0547960
$490$	−3.81327e10	+	3.81327e10i	−0.661475	+	0.661475i
$491$	8.42240e9	−	8.42240e9i	0.144914	−	0.144914i	−0.630928	−	0.775842i	$-0.717326\pi$
$491$	8.42240e9	−	8.42240e9i	0.144914	−	0.144914i	0.775842	+	0.630928i	$0.217326\pi$
$492$			1.14474e11i			1.95365i
$493$	−5.68838e9	+	2.10490e10i	−0.0962944	+	0.356323i
$494$	−1.78286e11			−2.99371
$495$	−1.13207e11	−	1.13207e11i	−1.88562	−	1.88562i
$496$	−3.62818e10	−	3.62818e10i	−0.599462	−	0.599462i
$497$			5.91167e10i			0.968912i
$498$			1.26057e11i			2.04951i
$499$			1.93592e10i			0.312238i	0.987738	+	0.156119i	$0.0498983\pi$
$499$			1.93592e10i			0.312238i	−0.987738	+	0.156119i	$0.950102\pi$
$500$	9.84953e10			1.57592
$501$	−1.52354e10	+	1.52354e10i	−0.241827	+	0.241827i
$502$		−	5.53679e10i		−	0.871853i
$503$	1.49471e10	−	1.49471e10i	0.233500	−	0.233500i	−0.580652	−	0.814152i	$-0.697202\pi$
$503$	1.49471e10	−	1.49471e10i	0.233500	−	0.233500i	0.814152	+	0.580652i	$0.197202\pi$
$504$	−1.19903e11	−	1.19903e11i	−1.85826	−	1.85826i
$505$	3.59919e10	−	3.59919e10i	0.553400	−	0.553400i
$506$			1.49512e11i			2.28073i
$507$	−1.35644e11	−	1.35644e11i	−2.05290	−	2.05290i
$508$	4.94715e10	−	4.94715e10i	0.742849	−	0.742849i
$509$	−1.56855e10			−0.233684			−0.116842	−	0.993151i	$-0.537277\pi$
$509$	−1.56855e10			−0.233684			−0.116842	+	0.993151i	$0.537277\pi$
$510$	6.21630e10	+	6.21630e10i	0.918864	+	0.918864i
$511$	5.11409e10	−	5.11409e10i	0.750040	−	0.750040i
$512$	−6.67630e10	−	6.67630e10i	−0.971529	−	0.971529i
$513$	1.87522e11			2.70759
$514$	−6.38750e10	−	6.38750e10i	−0.915121	−	0.915121i
$515$			6.27347e10i			0.891823i
$516$	3.16683e10			0.446710
$517$	4.89173e10			0.684700
$518$	−9.21428e10			−1.27980
$519$	4.31851e10	−	4.31851e10i	0.595201	−	0.595201i
$520$	1.45821e11	−	1.45821e11i	1.99437	−	1.99437i
$521$		−	1.63296e10i		−	0.221628i	−0.993841	−	0.110814i	$-0.964654\pi$
$521$		−	1.63296e10i		−	0.221628i	0.993841	−	0.110814i	$-0.0353458\pi$
$522$	−2.88069e11	−	7.78491e10i	−3.87984	−	1.04851i
$523$	9.94172e10			1.32879			0.664393	−	0.747384i	$-0.268690\pi$
$523$	9.94172e10			1.32879			0.664393	+	0.747384i	$0.268690\pi$
$524$	1.15277e11	+	1.15277e11i	1.52903	+	1.52903i
$525$	−1.89215e10	−	1.89215e10i	−0.249068	−	0.249068i
$526$		−	3.06658e10i		−	0.400600i
$527$			3.23705e10i			0.419670i
$528$			1.06723e11i			1.37317i
$529$	6.00314e10			0.766578
$530$	−3.31271e10	+	3.31271e10i	−0.419836	+	0.419836i
$531$			2.32549e11i			2.92508i
$532$	8.46818e10	−	8.46818e10i	1.05717	−	1.05717i
$533$	−5.11677e10	−	5.11677e10i	−0.633997	−	0.633997i
$534$	3.13771e11	−	3.13771e11i	3.85876	−	3.85876i
$535$		−	2.32805e10i		−	0.284169i
$536$	1.38705e9	+	1.38705e9i	0.0168048	+	0.0168048i
$537$	−1.63390e11	+	1.63390e11i	−1.96485	+	1.96485i
$538$	−2.53411e11			−3.02480
$539$	2.92049e10	+	2.92049e10i	0.346020	+	0.346020i
$540$	−3.21427e11	+	3.21427e11i	−3.78013	+	3.78013i
$541$	−5.88937e10	−	5.88937e10i	−0.687511	−	0.687511i	0.274170	−	0.961681i	$-0.411597\pi$
$541$	−5.88937e10	−	5.88937e10i	−0.687511	−	0.687511i	−0.961681	+	0.274170i	$0.911597\pi$
$542$	1.77550e11			2.05742
$543$	2.18778e11	+	2.18778e11i	2.51654	+	2.51654i
$544$			9.21546e9i			0.105226i
$545$	−5.18304e10			−0.587487
$546$	3.20022e11			3.60089
$547$	5.09654e10			0.569281			0.284640	−	0.958634i	$-0.408126\pi$
$547$	5.09654e10			0.569281			0.284640	+	0.958634i	$0.408126\pi$
$548$	−2.37097e10	+	2.37097e10i	−0.262908	+	0.262908i
$549$	8.17981e10	−	8.17981e10i	0.900438	−	0.900438i
$550$			4.21465e10i			0.460586i
$551$	2.62354e10	−	9.70801e10i	0.284630	−	1.05323i
$552$	3.52063e11			3.79196
$553$	−4.03029e10	−	4.03029e10i	−0.430959	−	0.430959i
$554$	7.21611e10	+	7.21611e10i	0.766062	+	0.766062i
$555$			2.04857e11i			2.15913i
$556$		−	2.86426e10i		−	0.299718i
$557$		−	1.01258e11i		−	1.05198i	−0.850490	−	0.525991i	$-0.823694\pi$
$557$		−	1.01258e11i		−	1.05198i	0.850490	−	0.525991i	$-0.176306\pi$
$558$	−4.43011e11			−4.56960
$559$	−1.41551e10	+	1.41551e10i	−0.144966	+	0.144966i
$560$			5.91686e10i			0.601643i
$561$	4.76091e10	−	4.76091e10i	0.480661	−	0.480661i
$562$	−4.64512e10	−	4.64512e10i	−0.465641	−	0.465641i
$563$	−9.05581e10	+	9.05581e10i	−0.901351	+	0.901351i	−0.995553	−	0.0942022i	$-0.969970\pi$
$563$	−9.05581e10	+	9.05581e10i	−0.901351	+	0.901351i	0.0942022	+	0.995553i	$0.469970\pi$
$564$		−	2.41398e11i		−	2.38571i
$565$	3.23386e10	+	3.23386e10i	0.317342	+	0.317342i
$566$	−1.01466e10	+	1.01466e10i	−0.0988682	+	0.0988682i
$567$	−1.62221e11			−1.56954
$568$	−1.55035e11	−	1.55035e11i	−1.48949	−	1.48949i
$569$	5.36057e10	−	5.36057e10i	0.511401	−	0.511401i	−0.403555	−	0.914956i	$-0.632225\pi$
$569$	5.36057e10	−	5.36057e10i	0.511401	−	0.511401i	0.914956	+	0.403555i	$0.132225\pi$
$570$	−2.86702e11	−	2.86702e11i	−2.71601	−	2.71601i
$571$	1.22087e11			1.14848			0.574240	−	0.818687i	$-0.305298\pi$
$571$	1.22087e11			1.14848			0.574240	+	0.818687i	$0.305298\pi$
$572$	−2.34048e11	−	2.34048e11i	−2.18636	−	2.18636i
$573$			1.93022e11i			1.79056i
$574$	7.40202e10			0.681872
$575$	3.89978e10			0.356754
$576$	−3.19398e11			−2.90163
$577$	3.83445e10	−	3.83445e10i	0.345939	−	0.345939i	−0.512655	−	0.858594i	$-0.671338\pi$
$577$	3.83445e10	−	3.83445e10i	0.345939	−	0.345939i	0.858594	+	0.512655i	$0.171338\pi$
$578$	1.16342e11	−	1.16342e11i	1.04238	−	1.04238i
$579$		−	3.89940e10i		−	0.346963i
$580$	1.21433e11	+	2.11372e11i	1.07306	+	1.86782i
$581$	5.35251e10			0.469735
$582$	4.45050e10	+	4.45050e10i	0.387897	+	0.387897i
$583$	2.53712e10	+	2.53712e10i	0.219618	+	0.219618i
$584$			2.68237e11i			2.30604i
$585$		−	4.99416e11i		−	4.26422i
$586$			1.95973e11i			1.66190i
$587$	−4.78063e10			−0.402655			−0.201327	−	0.979524i	$-0.564525\pi$
$587$	−4.78063e10			−0.402655			−0.201327	+	0.979524i	$0.564525\pi$
$588$	1.44121e11	−	1.44121e11i	1.20564	−	1.20564i
$589$		−	1.49296e11i		−	1.24047i
$590$	2.04565e11	−	2.04565e11i	1.68819	−	1.68819i
$591$	2.13181e11	+	2.13181e11i	1.74742	+	1.74742i
$592$	6.77796e10	−	6.77796e10i	0.551838	−	0.551838i
$593$		−	1.35497e11i		−	1.09575i	−0.836560	−	0.547875i	$-0.815437\pi$
$593$		−	1.35497e11i		−	1.09575i	0.836560	−	0.547875i	$-0.184563\pi$
$594$	3.74879e11	+	3.74879e11i	3.01124	+	3.01124i
$595$	2.63951e10	−	2.63951e10i	0.210598	−	0.210598i
$596$	−2.53816e11			−2.01157
$597$	−6.01708e9	−	6.01708e9i	−0.0473684	−	0.0473684i
$598$	−3.29788e11	+	3.29788e11i	−2.57888	+	2.57888i
$599$	1.05733e11	+	1.05733e11i	0.821301	+	0.821301i	0.986295	−	0.164993i	$-0.0527603\pi$
$599$	1.05733e11	+	1.05733e11i	0.821301	+	0.821301i	−0.164993	+	0.986295i	$0.552760\pi$
$600$	9.92442e10			0.765773
$601$	−4.26099e10	−	4.26099e10i	−0.326597	−	0.326597i	0.524694	−	0.851291i	$-0.324180\pi$
$601$	−4.26099e10	−	4.26099e10i	−0.326597	−	0.326597i	−0.851291	+	0.524694i	$0.824180\pi$
$602$		−	2.04770e10i		−	0.155912i
$603$	4.75046e9			0.0359307
$604$	−2.77504e11			−2.08508
$605$	1.65077e9			0.0123216
$606$	−2.07150e11	+	2.07150e11i	−1.53601	+	1.53601i
$607$	−1.55757e11	+	1.55757e11i	−1.14734	+	1.14734i	−0.160266	+	0.987074i	$0.551235\pi$
$607$	−1.55757e11	+	1.55757e11i	−1.14734	+	1.14734i	−0.987074	+	0.160266i	$0.948765\pi$
$608$		−	4.25026e10i		−	0.311029i
$609$	−4.70924e10	+	1.74258e11i	−0.342359	+	1.26685i
$610$	−1.43909e11			−1.03937
$611$	1.07900e11	+	1.07900e11i	0.774206	+	0.774206i
$612$	−1.64913e11	−	1.64913e11i	−1.17557	−	1.17557i
$613$			8.48091e10i			0.600621i	0.953841	+	0.300311i	$0.0970903\pi$
$613$			8.48091e10i			0.600621i	−0.953841	+	0.300311i	$0.902910\pi$
$614$			4.85939e10i			0.341907i
$615$		−	1.64566e11i		−	1.15037i
$616$	1.61559e11			1.12204
$617$	5.29081e9	−	5.29081e9i	0.0365074	−	0.0365074i	−0.688617	−	0.725125i	$-0.741782\pi$
$617$	5.29081e9	−	5.29081e9i	0.0365074	−	0.0365074i	0.725125	+	0.688617i	$0.241782\pi$
$618$		−	3.61068e11i		−	2.47534i
$619$	−1.25958e11	+	1.25958e11i	−0.857955	+	0.857955i	−0.991097	−	0.133142i	$-0.957493\pi$
$619$	−1.25958e11	+	1.25958e11i	−0.857955	+	0.857955i	0.133142	+	0.991097i	$0.457493\pi$
$620$	2.55905e11	+	2.55905e11i	1.73186	+	1.73186i
$621$	3.46873e11	−	3.46873e11i	2.33240	−	2.33240i
$622$		−	1.22129e11i		−	0.815941i
$623$	−1.33230e11	−	1.33230e11i	−0.884405	−	0.884405i
$624$	−2.35406e11	+	2.35406e11i	−1.55267	+	1.55267i
$625$	−1.82551e11			−1.19637
$626$	2.85565e11	+	2.85565e11i	1.85955	+	1.85955i
$627$	−2.19578e11	+	2.19578e11i	−1.42075	+	1.42075i
$628$	−4.47647e10	−	4.47647e10i	−0.287804	−	0.287804i
$629$	−6.04728e10			−0.386329
$630$	3.61233e11	+	3.61233e11i	2.29311	+	2.29311i
$631$		−	1.30063e10i		−	0.0820421i	−0.999158	−	0.0410210i	$-0.986939\pi$
$631$		−	1.30063e10i		−	0.0820421i	0.999158	−	0.0410210i	$-0.0130611\pi$
$632$	2.11391e11			1.32501
$633$	−1.60817e11			−1.00166
$634$	−2.18660e11			−1.35335
$635$	−7.11192e10	+	7.11192e10i	−0.437413	+	0.437413i
$636$	1.25202e11	−	1.25202e11i	0.765217	−	0.765217i
$637$			1.28838e11i			0.782505i
$638$	2.46523e11	−	1.41627e11i	1.48790	−	0.854799i
$639$	−5.30974e11			−3.18471
$640$	2.42873e11	+	2.42873e11i	1.44763	+	1.44763i
$641$	−6.21710e10	−	6.21710e10i	−0.368261	−	0.368261i	0.498582	−	0.866843i	$-0.333854\pi$
$641$	−6.21710e10	−	6.21710e10i	−0.368261	−	0.368261i	−0.866843	+	0.498582i	$0.833854\pi$
$642$			1.33990e11i			0.788738i
$643$			2.86390e11i			1.67538i	0.546143	+	0.837692i	$0.316096\pi$
$643$			2.86390e11i			1.67538i	−0.546143	+	0.837692i	$0.683904\pi$
$644$		−	3.13284e11i		−	1.82136i
$645$	−4.55256e10			−0.263037
$646$	8.46332e10	−	8.46332e10i	0.485971	−	0.485971i
$647$		−	2.70519e10i		−	0.154376i	−0.997017	−	0.0771882i	$-0.975406\pi$
$647$		−	2.70519e10i		−	0.154376i	0.997017	−	0.0771882i	$-0.0245942\pi$
$648$	4.25428e11	−	4.25428e11i	2.41283	−	2.41283i
$649$	−1.56671e11	−	1.56671e11i	−0.883100	−	0.883100i
$650$	−9.29652e10	+	9.29652e10i	−0.520795	+	0.520795i
$651$			2.67986e11i			1.49206i
$652$	−7.31177e9	−	7.31177e9i	−0.0404606	−	0.0404606i
$653$	−6.34357e10	+	6.34357e10i	−0.348884	+	0.348884i	−0.859694	−	0.510810i	$-0.829346\pi$
$653$	−6.34357e10	+	6.34357e10i	−0.348884	+	0.348884i	0.510810	+	0.859694i	$0.329346\pi$
$654$	2.98308e11			1.63062
$655$	−1.65719e11	−	1.65719e11i	−0.900344	−	0.900344i
$656$	−5.44487e10	+	5.44487e10i	−0.294017	+	0.294017i
$657$	4.59337e11	+	4.59337e11i	2.46530	+	2.46530i
$658$	−1.56090e11			−0.832669
$659$	−1.94352e11	−	1.94352e11i	−1.03050	−	1.03050i	−0.999520	−	0.0309758i	$-0.990139\pi$
$659$	−1.94352e11	−	1.94352e11i	−1.03050	−	1.03050i	−0.0309758	−	0.999520i	$-0.509861\pi$
$660$		−	7.52746e11i		−	3.96710i
$661$	2.65475e11			1.39065			0.695324	−	0.718696i	$-0.255261\pi$
$661$	2.65475e11			1.39065			0.695324	+	0.718696i	$0.255261\pi$
$662$	3.34766e10			0.174305
$663$	2.10029e11			1.08699
$664$	−1.40371e11	+	1.40371e11i	−0.722114	+	0.722114i
$665$	−1.21737e11	+	1.21737e11i	−0.622494	+	0.622494i
$666$		−	8.27608e11i		−	4.20657i
$667$	−1.31047e11	−	2.28105e11i	−0.662098	−	1.15248i
$668$	−7.11087e10			−0.357122
$669$	6.98082e10	+	6.98082e10i	0.348499	+	0.348499i
$670$	−4.17879e9	−	4.17879e9i	−0.0207373	−	0.0207373i
$671$			1.10216e11i			0.543696i
$672$			7.62919e10i			0.374112i
$673$		−	1.24317e11i		−	0.605996i	−0.952991	−	0.302998i	$-0.902012\pi$
$673$		−	1.24317e11i		−	0.605996i	0.952991	−	0.302998i	$-0.0979876\pi$
$674$	9.56127e10			0.463315
$675$	9.77812e10	−	9.77812e10i	0.471021	−	0.471021i
$676$		−	6.33093e11i		−	3.03166i
$677$	1.51687e11	−	1.51687e11i	0.722094	−	0.722094i	−0.246937	−	0.969031i	$-0.579424\pi$
$677$	1.51687e11	−	1.51687e11i	0.722094	−	0.722094i	0.969031	+	0.246937i	$0.0794242\pi$
$678$	−1.86124e11	−	1.86124e11i	−0.880812	−	0.880812i
$679$	1.88973e10	−	1.88973e10i	0.0889038	−	0.0889038i
$680$			1.38444e11i			0.647496i
$681$	1.55914e11	+	1.55914e11i	0.724929	+	0.724929i
$682$	2.98461e11	−	2.98461e11i	1.37959	−	1.37959i
$683$	4.58526e10			0.210708			0.105354	−	0.994435i	$-0.466402\pi$
$683$	4.58526e10			0.210708			0.105354	+	0.994435i	$0.466402\pi$
$684$	7.60595e11	+	7.60595e11i	3.47480	+	3.47480i
$685$	3.40845e10	−	3.40845e10i	0.154808	−	0.154808i
$686$	−2.84667e11	−	2.84667e11i	−1.28541	−	1.28541i
$687$	−4.18946e11			−1.88075
$688$	1.50627e10	+	1.50627e10i	0.0672280	+	0.0672280i
$689$			1.11926e11i			0.496654i
$690$	−1.06067e12			−4.67932
$691$	2.94434e11			1.29145			0.645723	−	0.763571i	$-0.276556\pi$
$691$	2.94434e11			1.29145			0.645723	+	0.763571i	$0.276556\pi$
$692$	2.01559e11			0.878977
$693$	2.76659e11	−	2.76659e11i	1.19953	−	1.19953i
$694$	−8.02940e10	+	8.02940e10i	−0.346135	+	0.346135i
$695$			4.11759e10i			0.176484i
$696$	−3.33496e11	−	5.80498e11i	−1.42119	−	2.47379i
$697$	4.85791e10			0.205834
$698$	2.35641e10	+	2.35641e10i	0.0992726	+	0.0992726i
$699$	−5.02657e11	−	5.02657e11i	−2.10554	−	2.10554i
$700$		−	8.83127e10i		−	0.367816i
$701$		−	3.17317e11i		−	1.31408i	−0.753856	−	0.657040i	$-0.771808\pi$
$701$		−	3.17317e11i		−	1.31408i	0.753856	−	0.657040i	$-0.228192\pi$
$702$			1.65379e12i			6.80976i
$703$	2.78907e11			1.14193
$704$	2.15182e11	−	2.15182e11i	0.876022	−	0.876022i
$705$			3.47028e11i			1.40478i
$706$	−4.16396e11	+	4.16396e11i	−1.67605	+	1.67605i
$707$	8.79581e10	+	8.79581e10i	0.352045	+	0.352045i
$708$	−7.73143e11	+	7.73143e11i	−3.07699	+	3.07699i
$709$		−	4.31380e11i		−	1.70716i	−0.520961	−	0.853581i	$-0.674426\pi$
$709$		−	4.31380e11i		−	1.70716i	0.520961	−	0.853581i	$-0.325574\pi$
$710$	4.67077e11	+	4.67077e11i	1.83804	+	1.83804i
$711$	3.61993e11	−	3.61993e11i	1.41652	−	1.41652i
$712$	6.98801e11			2.71915
$713$	−2.76164e11	−	2.76164e11i	−1.06858	−	1.06858i
$714$	−1.51916e11	+	1.51916e11i	−0.584535	+	0.584535i
$715$	3.36462e11	+	3.36462e11i	1.28740	+	1.28740i
$716$	−7.62596e11			−2.90163
$717$	3.48949e11	+	3.48949e11i	1.32034	+	1.32034i
$718$			1.53421e11i			0.577281i
$719$	3.12468e11			1.16920			0.584602	−	0.811320i	$-0.301251\pi$
$719$	3.12468e11			1.16920			0.584602	+	0.811320i	$0.301251\pi$
$720$	−5.31441e11			−1.97754
$721$	−1.53313e11			−0.567333
$722$	−6.24084e10	+	6.24084e10i	−0.229665	+	0.229665i
$723$	5.68297e11	−	5.68297e11i	2.07980	−	2.07980i
$724$			1.02111e12i			3.71636i
$725$	−3.69411e10	−	6.43014e10i	−0.133708	−	0.232739i
$726$	−9.50097e9			−0.0341996
$727$	−3.07044e11	−	3.07044e11i	−1.09917	−	1.09917i	−0.994508	−	0.104657i	$-0.966625\pi$
$727$	−3.07044e11	−	3.07044e11i	−1.09917	−	1.09917i	−0.104657	−	0.994508i	$-0.533375\pi$
$728$	3.56362e11	+	3.56362e11i	1.26872	+	1.26872i
$729$		−	1.73215e11i		−	0.613304i
$730$		−	8.08122e11i		−	2.84568i
$731$		−	1.34390e10i		−	0.0470648i
$732$	5.43898e11			1.89441
$733$	−3.36144e11	+	3.36144e11i	−1.16442	+	1.16442i	−0.180924	+	0.983497i	$0.557909\pi$
$733$	−3.36144e11	+	3.36144e11i	−1.16442	+	1.16442i	−0.983497	+	0.180924i	$0.942091\pi$
$734$		−	2.26529e11i		−	0.780440i
$735$	−2.07185e11	+	2.07185e11i	−0.709919	+	0.709919i
$736$	−7.86201e10	−	7.86201e10i	−0.267931	−	0.267931i
$737$	−3.20043e9	+	3.20043e9i	−0.0108477	+	0.0108477i
$738$			6.64835e11i			2.24124i
$739$	3.63967e11	+	3.63967e11i	1.22035	+	1.22035i	0.967507	+	0.252844i	$0.0813659\pi$
$739$	3.63967e11	+	3.63967e11i	1.22035	+	1.22035i	0.252844	+	0.967507i	$0.418634\pi$
$740$	−4.78067e11	+	4.78067e11i	−1.59427	+	1.59427i
$741$	−9.68675e11			−3.21296
$742$	−8.09571e10	−	8.09571e10i	−0.267079	−	0.267079i
$743$	1.93810e10	−	1.93810e10i	0.0635949	−	0.0635949i	−0.674594	−	0.738189i	$-0.735681\pi$
$743$	1.93810e10	−	1.93810e10i	0.0635949	−	0.0635949i	0.738189	+	0.674594i	$0.235681\pi$
$744$	−7.02800e11	−	7.02800e11i	−2.29372	−	2.29372i
$745$	3.64881e11			1.18447
$746$	−3.97202e10	−	3.97202e10i	−0.128250	−	0.128250i
$747$			4.80752e11i			1.54397i
$748$	2.22207e11			0.709826
$749$	5.68936e10			0.180774
$750$	8.14944e11			2.57562
$751$	−5.15512e10	+	5.15512e10i	−0.162061	+	0.162061i	−0.783479	−	0.621418i	$-0.786557\pi$
$751$	−5.15512e10	+	5.15512e10i	−0.162061	+	0.162061i	0.621418	+	0.783479i	$0.286557\pi$
$752$	1.14819e11	−	1.14819e11i	0.359039	−	0.359039i
$753$		−	3.00828e11i		−	0.935705i
$754$	8.56167e11	+	2.31375e11i	2.64895	+	0.715864i
$755$	3.98934e11			1.22776
$756$	−7.85513e11	−	7.85513e11i	−2.40473	−	2.40473i
$757$	3.52050e11	+	3.52050e11i	1.07206	+	1.07206i	0.997193	+	0.0748694i	$0.0238540\pi$
$757$	3.52050e11	+	3.52050e11i	1.07206	+	1.07206i	0.0748694	+	0.997193i	$0.476146\pi$
$758$		−	8.35337e11i		−	2.53038i
$759$			8.12338e11i			2.44777i
$760$		−	6.38516e11i		−	1.91389i
$761$	−3.76190e11			−1.12168			−0.560839	−	0.827925i	$-0.689521\pi$
$761$	−3.76190e11			−1.12168			−0.560839	+	0.827925i	$0.689521\pi$
$762$	4.09324e11	−	4.09324e11i	1.21408	−	1.21408i
$763$		−	1.26665e11i		−	0.373730i
$764$	−4.50449e11	+	4.50449e11i	−1.32212	+	1.32212i
$765$	2.37075e11	+	2.37075e11i	0.692214	+	0.692214i
$766$	−7.89895e11	+	7.89895e11i	−2.29432	+	2.29432i
$767$		−	6.91158e11i		−	1.99708i
$768$	−8.42660e11	−	8.42660e11i	−2.42219	−	2.42219i
$769$	−3.96761e11	+	3.96761e11i	−1.13455	+	1.13455i	−0.145140	+	0.989411i	$0.546363\pi$
$769$	−3.96761e11	+	3.96761e11i	−1.13455	+	1.13455i	−0.989411	+	0.145140i	$0.953637\pi$
$770$	−4.86733e11			−1.38461
$771$	−3.47049e11	−	3.47049e11i	−0.982141	−	0.982141i
$772$	9.09988e10	−	9.09988e10i	0.256192	−	0.256192i
$773$	3.72854e11	+	3.72854e11i	1.04429	+	1.04429i	0.998973	+	0.0453166i	$0.0144297\pi$
$773$	3.72854e11	+	3.72854e11i	1.04429	+	1.04429i	0.0453166	+	0.998973i	$0.485570\pi$
$774$	1.83921e11			0.512468
$775$	−7.78488e10	−	7.78488e10i	−0.215797	−	0.215797i
$776$			9.91173e10i			0.273340i
$777$	−5.00636e11			−1.37353
$778$	8.40267e11			2.29350
$779$	−2.24052e11			−0.608413
$780$	1.66038e12	−	1.66038e12i	4.48569	−	4.48569i
$781$	3.57723e11	−	3.57723e11i	0.961485	−	0.961485i
$782$		−	3.13104e11i		−	0.837263i
$783$	−9.00519e11	−	2.43361e11i	−2.39578	−	0.647446i
$784$	1.37100e11			0.362888
$785$	6.43527e10	+	6.43527e10i	0.169468	+	0.169468i
$786$	9.53793e11	+	9.53793e11i	2.49899	+	2.49899i
$787$		−	5.03270e11i		−	1.31190i	−0.754803	−	0.655952i	$-0.772268\pi$
$787$		−	5.03270e11i		−	1.31190i	0.754803	−	0.655952i	$-0.227732\pi$
$788$			9.94985e11i			2.58055i
$789$		−	1.66615e11i		−	0.429939i
$790$	−6.36862e11			−1.63507
$791$	−7.90301e10	+	7.90301e10i	−0.201877	+	0.201877i
$792$			1.45109e12i			3.68803i
$793$	−2.43111e11	+	2.43111e11i	−0.614770	+	0.614770i
$794$	−4.46530e11	−	4.46530e11i	−1.12349	−	1.12349i
$795$	−1.79988e11	+	1.79988e11i	−0.450584	+	0.450584i
$796$		−	2.80837e10i		−	0.0699523i
$797$	−2.97788e11	−	2.97788e11i	−0.738030	−	0.738030i	0.234167	−	0.972197i	$-0.424764\pi$
$797$	−2.97788e11	−	2.97788e11i	−0.738030	−	0.738030i	−0.972197	+	0.234167i	$0.924764\pi$
$798$	7.00652e11	−	7.00652e11i	1.72779	−	1.72779i
$799$	−1.02441e11			−0.251355
$800$	−2.21625e10	−	2.21625e10i	−0.0541077	−	0.0541077i
$801$	1.19665e12	−	1.19665e12i	2.90694	−	2.90694i
$802$	4.91939e10	+	4.91939e10i	0.118909	+	0.118909i
$803$	−6.18920e11			−1.48858
$804$	1.57936e10	+	1.57936e10i	0.0377969	+	0.0377969i
$805$			4.50370e11i			1.07247i
$806$	1.31667e12			3.11987
$807$	−1.37685e12			−3.24632
$808$	−4.61345e11			−1.08238
$809$	−4.97072e11	+	4.97072e11i	−1.16045	+	1.16045i	−0.176068	+	0.984378i	$0.556338\pi$
$809$	−4.97072e11	+	4.97072e11i	−1.16045	+	1.16045i	−0.984378	+	0.176068i	$0.943662\pi$
$810$	−1.28170e12	+	1.28170e12i	−2.97745	+	2.97745i
$811$		−	5.20856e11i		−	1.20402i	−0.798488	−	0.602011i	$-0.794366\pi$
$811$		−	5.20856e11i		−	1.20402i	0.798488	−	0.602011i	$-0.205634\pi$
$812$	−5.16557e11	+	2.96762e11i	−1.18821	+	0.682628i
$813$	9.64673e11			2.20810
$814$	5.57568e11	+	5.57568e11i	1.26999	+	1.26999i
$815$	1.05112e10	+	1.05112e10i	0.0238245	+	0.0238245i
$816$		−	2.23497e11i		−	0.504092i
$817$			6.19818e10i			0.139116i
$818$		−	1.23900e12i		−	2.76732i
$819$	1.22049e12			2.71268
$820$	3.84041e11	−	3.84041e11i	0.849419	−	0.849419i
$821$			8.38056e11i			1.84459i	0.386483	+	0.922296i	$0.373690\pi$
$821$			8.38056e11i			1.84459i	−0.386483	+	0.922296i	$0.626310\pi$
$822$	−1.96172e11	+	1.96172e11i	−0.429685	+	0.429685i
$823$	5.90785e11	+	5.90785e11i	1.28775	+	1.28775i	0.936153	+	0.351592i	$0.114359\pi$
$823$	5.90785e11	+	5.90785e11i	1.28775	+	1.28775i	0.351592	+	0.936153i	$0.385641\pi$
$824$	4.02068e11	−	4.02068e11i	0.872148	−	0.872148i
$825$			2.28993e11i			0.494318i
$826$	4.99922e11	+	4.99922e11i	1.07394	+	1.07394i
$827$	−6.00262e10	+	6.00262e10i	−0.128327	+	0.128327i	−0.768353	−	0.640026i	$-0.778924\pi$
$827$	−6.00262e10	+	6.00262e10i	−0.128327	+	0.128327i	0.640026	+	0.768353i	$0.278924\pi$
$828$	2.81386e12			5.98660
$829$	−4.17735e11	−	4.17735e11i	−0.884469	−	0.884469i	0.109516	−	0.993985i	$-0.465070\pi$
$829$	−4.17735e11	−	4.17735e11i	−0.884469	−	0.884469i	−0.993985	+	0.109516i	$0.965070\pi$
$830$	4.22899e11	−	4.22899e11i	0.891095	−	0.891095i
$831$	3.92070e11	+	3.92070e11i	0.822166	+	0.822166i
$832$	9.49281e11			1.98108
$833$	−6.11601e10	−	6.11601e10i	−0.127025	−	0.127025i
$834$		−	2.36987e11i		−	0.489846i
$835$	1.02224e11			0.210285
$836$	−1.02484e12			−2.09813
$837$	−1.38488e12			−2.82169
$838$	−8.77204e11	+	8.77204e11i	−1.77879	+	1.77879i
$839$	2.36983e11	−	2.36983e11i	0.478266	−	0.478266i	−0.426311	−	0.904577i	$-0.640187\pi$
$839$	2.36983e11	−	2.36983e11i	0.478266	−	0.478266i	0.904577	+	0.426311i	$0.140187\pi$
$840$			1.14613e12i			2.30206i
$841$	−2.51976e11	+	4.32151e11i	−0.503703	+	0.863877i
$842$	−4.06077e11			−0.807905
$843$	−2.52381e11	−	2.52381e11i	−0.499743	−	0.499743i
$844$	−3.75294e11	−	3.75294e11i	−0.739608	−	0.739608i
$845$			9.10120e11i			1.78514i
$846$		−	1.40197e12i		−	2.73689i
$847$			4.03421e9i			0.00783836i
$848$	1.19103e11			0.230324
$849$	−5.51293e10	+	5.51293e10i	−0.106109	+	0.106109i
$850$		−	8.82620e10i		−	0.169082i
$851$	5.15914e11	−	5.15914e11i	0.983691	−	0.983691i
$852$	−1.76530e12	−	1.76530e12i	−3.35011	−	3.35011i
$853$	2.59292e11	−	2.59292e11i	0.489772	−	0.489772i	−0.418463	−	0.908234i	$-0.637431\pi$
$853$	2.59292e11	−	2.59292e11i	0.489772	−	0.489772i	0.908234	+	0.418463i	$0.137431\pi$
$854$		−	3.51690e11i		−	0.661193i
$855$	−1.09341e12	−	1.09341e12i	−2.04607	−	2.04607i
$856$	−1.49205e11	+	1.49205e11i	−0.277900	+	0.277900i
$857$	−3.44705e10			−0.0639035			−0.0319517	−	0.999489i	$-0.510172\pi$
$857$	−3.44705e10			−0.0639035			−0.0319517	+	0.999489i	$0.510172\pi$
$858$	−1.93650e12	−	1.93650e12i	−3.57329	−	3.57329i
$859$	1.17488e11	−	1.17488e11i	0.215785	−	0.215785i	−0.590934	−	0.806720i	$-0.701241\pi$
$859$	1.17488e11	−	1.17488e11i	0.215785	−	0.215785i	0.806720	+	0.590934i	$0.201241\pi$
$860$	−1.06241e11	−	1.06241e11i	−0.194223	−	0.194223i
$861$	4.02171e11			0.731810
$862$	−4.31988e11	−	4.31988e11i	−0.782425	−	0.782425i
$863$		−	1.03455e11i		−	0.186512i	−0.995642	−	0.0932562i	$-0.970272\pi$
$863$		−	1.03455e11i		−	0.186512i	0.995642	−	0.0932562i	$-0.0297276\pi$
$864$	−3.94256e11			−0.707496
$865$	−2.89756e11			−0.517569
$866$	1.11249e11			0.197799
$867$	6.32115e11	−	6.32115e11i	1.11872	−	1.11872i
$868$	−6.25388e11	+	6.25388e11i	−1.10172	+	1.10172i
$869$			4.87757e11i			0.855311i
$870$	1.00473e12	+	1.74888e12i	1.75377	+	3.05269i
$871$	−1.41188e10			−0.0245316
$872$	3.32182e11	+	3.32182e11i	0.574526	+	0.574526i
$873$	1.69732e11	+	1.69732e11i	0.292217	+	0.292217i
$874$			1.44407e12i			2.47481i
$875$		−	3.46034e11i		−	0.590318i
$876$			3.05426e12i			5.18668i
$877$	6.76530e11			1.14364			0.571819	−	0.820380i	$-0.306238\pi$
$877$	6.76530e11			1.14364			0.571819	+	0.820380i	$0.306238\pi$
$878$	3.06681e11	−	3.06681e11i	0.516070	−	0.516070i
$879$			1.06477e12i			1.78361i
$880$	3.58037e11	−	3.58037e11i	0.597032	−	0.597032i
$881$	−6.61015e10	−	6.61015e10i	−0.109726	−	0.109726i	0.650112	−	0.759838i	$-0.274722\pi$
$881$	−6.61015e10	−	6.61015e10i	−0.109726	−	0.109726i	−0.759838	+	0.650112i	$0.774722\pi$
$882$	8.37014e11	−	8.37014e11i	1.38312	−	1.38312i
$883$		−	8.40441e10i		−	0.138250i	−0.997608	−	0.0691249i	$-0.977979\pi$
$883$		−	8.40441e10i		−	0.138250i	0.997608	−	0.0691249i	$-0.0220207\pi$
$884$	4.90137e11	+	4.90137e11i	0.802617	+	0.802617i
$885$	1.11145e12	−	1.11145e12i	1.81183	−	1.81183i
$886$	1.79903e12			2.91947
$887$	6.45103e11	+	6.45103e11i	1.04216	+	1.04216i	0.999071	+	0.0430900i	$0.0137202\pi$
$887$	6.45103e11	+	6.45103e11i	1.04216	+	1.04216i	0.0430900	+	0.999071i	$0.486280\pi$
$888$	1.31293e12	−	1.31293e12i	2.11149	−	2.11149i
$889$	−1.73803e11	−	1.73803e11i	−0.278260	−	0.278260i
$890$	−2.10529e12			−3.35546
$891$	9.81618e11	+	9.81618e11i	1.55751	+	1.55751i
$892$			3.25818e11i			0.514654i
$893$	4.72469e11			0.742964
$894$	−2.10006e12			−3.28762
$895$	1.09629e12			1.70857
$896$	−5.93540e11	+	5.93540e11i	−0.920911	+	0.920911i
$897$	−1.79183e12	+	1.79183e12i	−2.76775	+	2.76775i
$898$			2.53738e11i			0.390193i
$899$	−1.93752e11	+	7.16952e11i	−0.296626	+	1.09762i
$900$	7.93207e11			1.20897
$901$	−5.31317e10	−	5.31317e10i	−0.0806222	−	0.0806222i
$902$	−4.47906e11	−	4.47906e11i	−0.676645	−	0.676645i
$903$		−	1.11257e11i		−	0.167331i
$904$		−	4.14517e11i		−	0.620682i
$905$		−	1.46792e12i		−	2.18831i
$906$	−2.29605e12			−3.40776
$907$	3.71208e11	−	3.71208e11i	0.548515	−	0.548515i	−0.377496	−	0.926011i	$-0.623215\pi$
$907$	3.71208e11	−	3.71208e11i	0.548515	−	0.548515i	0.926011	+	0.377496i	$0.123215\pi$
$908$			7.27700e11i			1.07055i
$909$	−7.90022e11	+	7.90022e11i	−1.15713	+	1.15713i
$910$	−1.07362e12	−	1.07362e12i	−1.56561	−	1.56561i
$911$	−4.23505e11	+	4.23505e11i	−0.614873	+	0.614873i	−0.944212	−	0.329339i	$-0.893174\pi$
$911$	−4.23505e11	+	4.23505e11i	−0.614873	+	0.614873i	0.329339	+	0.944212i	$0.393174\pi$
$912$			1.03079e12i			1.49001i
$913$	−3.23888e11	−	3.23888e11i	−0.466135	−	0.466135i
$914$	7.23235e11	−	7.23235e11i	1.03632	−	1.03632i
$915$	−7.81896e11			−1.11549
$916$	−9.77679e11	−	9.77679e11i	−1.38872	−	1.38872i
$917$	4.04991e11	−	4.04991e11i	0.572753	−	0.572753i
$918$	−7.85061e11	−	7.85061e11i	−1.10543	−	1.10543i
$919$	−5.38385e10			−0.0754799			−0.0377399	−	0.999288i	$-0.512016\pi$
$919$	−5.38385e10			−0.0754799			−0.0377399	+	0.999288i	$0.512016\pi$
$920$	−1.18111e12	−	1.18111e12i	−1.64869	−	1.64869i
$921$			2.64023e11i			0.366947i
$922$	−2.74779e11			−0.380242
$923$	1.57810e12			2.17435
$924$	1.83958e12			2.52367
$925$	1.45433e11	−	1.45433e11i	0.198653	−	0.198653i
$926$	1.06471e12	−	1.06471e12i	1.44807	−	1.44807i
$927$		−	1.37703e12i		−	1.86476i
$928$	−5.51587e10	+	2.04106e11i	−0.0743742	+	0.275210i
$929$	−6.28458e10			−0.0843750			−0.0421875	−	0.999110i	$-0.513433\pi$
$929$	−6.28458e10			−0.0843750			−0.0421875	+	0.999110i	$0.513433\pi$
$930$	2.11734e12	+	2.11734e12i	2.83047	+	2.83047i
$931$	2.82077e11	+	2.82077e11i	0.375464	+	0.375464i
$932$		−	2.34606e12i		−	3.10940i
$933$		−	6.63561e11i		−	0.875697i
$934$		−	2.15353e12i		−	2.82985i
$935$	−3.19440e11			−0.417968
$936$	−3.20077e12	+	3.20077e12i	−4.17014	+	4.17014i
$937$			1.94226e11i			0.251970i	0.992032	+	0.125985i	$0.0402091\pi$
$937$			1.94226e11i			0.251970i	−0.992032	+	0.125985i	$0.959791\pi$
$938$	1.02123e10	−	1.02123e10i	0.0131920	−	0.0131920i
$939$	1.55155e12	+	1.55155e12i	1.99574	+	1.99574i
$940$	−8.09847e11	+	8.09847e11i	−1.03727	+	1.03727i
$941$			9.43609e11i			1.20347i	0.798698	+	0.601733i	$0.205523\pi$
$941$			9.43609e11i			1.20347i	−0.798698	+	0.601733i	$0.794477\pi$
$942$	−3.70380e11	−	3.70380e11i	−0.470374	−	0.470374i
$943$	−4.14444e11	+	4.14444e11i	−0.524106	+	0.524106i
$944$	−7.35478e11			−0.926150
$945$	1.12924e12	+	1.12924e12i	1.41598	+	1.41598i
$946$	−1.23909e11	+	1.23909e11i	−0.154717	+	0.154717i
$947$	−2.84760e11	−	2.84760e11i	−0.354062	−	0.354062i	0.507557	−	0.861618i	$-0.330549\pi$
$947$	−2.84760e11	−	2.84760e11i	−0.354062	−	0.354062i	−0.861618	+	0.507557i	$0.830549\pi$
$948$	2.40699e12			2.98017
$949$	−1.36519e12	−	1.36519e12i	−1.68317	−	1.68317i
$950$			4.07073e11i			0.499779i
$951$	−1.18803e12			−1.45247
$952$	−3.38333e11			−0.411904
$953$	−1.38857e12			−1.68343			−0.841717	−	0.539919i	$-0.818455\pi$
$953$	−1.38857e12			−1.68343			−0.841717	+	0.539919i	$0.818455\pi$
$954$	7.27141e11	−	7.27141e11i	0.877859	−	0.877859i
$955$	6.47555e11	−	6.47555e11i	0.778509	−	0.778509i
$956$			1.62866e12i			1.94984i
$957$	1.33942e12	−	7.69497e11i	1.59687	−	0.917401i
$958$	−1.75009e12			−2.07777
$959$	8.32968e10	+	8.32968e10i	0.0984813	+	0.0984813i
$960$	1.52654e12	+	1.52654e12i	1.79731	+	1.79731i
$961$			2.49685e11i			0.292751i
$962$			2.45973e12i			2.87202i
$963$			5.11007e11i			0.594185i
$964$	2.65243e12			3.07139
$965$	−1.30818e11	+	1.30818e11i	−0.150854	+	0.150854i
$966$		−	2.59209e12i		−	2.97675i
$967$	5.11763e11	−	5.11763e11i	0.585279	−	0.585279i	−0.351070	−	0.936349i	$-0.614182\pi$
$967$	5.11763e11	−	5.11763e11i	0.585279	−	0.585279i	0.936349	+	0.351070i	$0.114182\pi$
$968$	−1.05798e10	−	1.05798e10i	−0.0120497	−	0.0120497i
$969$	4.59834e11	−	4.59834e11i	0.521562	−	0.521562i
$970$		−	2.98613e11i		−	0.337304i
$971$	6.89667e11	+	6.89667e11i	0.775823	+	0.775823i	0.979118	−	0.203295i	$-0.0651649\pi$
$971$	6.89667e11	+	6.89667e11i	0.775823	+	0.775823i	−0.203295	+	0.979118i	$0.565165\pi$
$972$	1.84811e12	−	1.84811e12i	2.07044	−	2.07044i
$973$	−1.00627e11			−0.112270
$974$	2.10629e12	+	2.10629e12i	2.34036	+	2.34036i
$975$	−5.05104e11	+	5.05104e11i	−0.558936	+	0.558936i
$976$	2.58700e11	+	2.58700e11i	0.285100	+	0.285100i
$977$	9.34051e11			1.02516			0.512581	−	0.858639i	$-0.328690\pi$
$977$	9.34051e11			1.02516			0.512581	+	0.858639i	$0.328690\pi$
$978$	−6.04971e10	−	6.04971e10i	−0.0661271	−	0.0661271i
$979$			1.61239e12i			1.75525i
$980$	−9.67000e11			−1.04839
$981$	1.13768e12			1.22841
$982$	3.25249e11			0.349760
$983$	−3.24743e11	+	3.24743e11i	−0.347797	+	0.347797i	−0.859289	−	0.511491i	$-0.829093\pi$
$983$	−3.24743e11	+	3.24743e11i	−0.347797	+	0.347797i	0.511491	+	0.859289i	$0.329093\pi$
$984$	−1.05470e12	+	1.05470e12i	−1.12499	+	1.12499i
$985$		−	1.43037e12i		−	1.51951i
$986$	−5.16261e11	+	2.96592e11i	−0.546212	+	0.313799i
$987$	−8.48079e11			−0.893650
$988$	−2.26056e12	−	2.26056e12i	−2.37240	−	2.37240i
$989$	1.14652e11	+	1.14652e11i	0.119839	+	0.119839i
$990$		−	4.37174e12i		−	4.55107i
$991$		−	1.54204e12i		−	1.59882i	−0.600785	−	0.799411i	$-0.705145\pi$
$991$		−	1.54204e12i		−	1.59882i	0.600785	−	0.799411i	$-0.294855\pi$
$992$			3.13888e11i			0.324137i
$993$	1.81887e11			0.187070
$994$	−1.14146e12	+	1.14146e12i	−1.16927	+	1.16927i
$995$			4.03725e10i			0.0411901i
$996$	−1.59833e12	+	1.59833e12i	−1.62416	+	1.62416i
$997$	−1.36280e12	−	1.36280e12i	−1.37928	−	1.37928i	−0.845842	−	0.533433i	$-0.820901\pi$
$997$	−1.36280e12	−	1.36280e12i	−1.37928	−	1.37928i	−0.533433	−	0.845842i	$-0.679099\pi$
$998$	−3.73799e11	+	3.73799e11i	−0.376804	+	0.376804i
$999$		−	2.58715e12i		−	2.59753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.c.a.12.18	✓	38
29.17	odd	4	inner	29.9.c.a.17.18	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.c.a.12.18	✓	38	1.1	even	1	trivial
29.9.c.a.17.18	yes	38	29.17	odd	4	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(19.3086 + 19.3086i) q^{2} +(104.909 + 104.909i) q^{3} +489.642i q^{4} -703.899i q^{5} +4051.27i q^{6} +1720.21 q^{7} +(-4511.30 + 4511.30i) q^{8} +15450.6i q^{9} +O(q^{10})\)	\(q+(19.3086 + 19.3086i) q^{2} +(104.909 + 104.909i) q^{3} +489.642i q^{4} -703.899i q^{5} +4051.27i q^{6} +1720.21 q^{7} +(-4511.30 + 4511.30i) q^{8} +15450.6i q^{9} +(13591.3 - 13591.3i) q^{10} +(-10409.2 - 10409.2i) q^{11} +(-51367.6 + 51367.6i) q^{12} -45920.6i q^{13} +(33214.8 + 33214.8i) q^{14} +(73845.0 - 73845.0i) q^{15} -48865.2 q^{16} +(21798.7 + 21798.7i) q^{17} +(-298329. + 298329. i) q^{18} +(-100538. - 100538. i) q^{19} +344659. q^{20} +(180465. + 180465. i) q^{21} -401975. i q^{22} -371944. q^{23} -946548. q^{24} -104849. q^{25} +(886661. - 886661. i) q^{26} +(-932594. + 932594. i) q^{27} +842288. i q^{28} +(352328. + 613279. i) q^{29} +2.85168e6 q^{30} +(742488. + 742488. i) q^{31} +(211376. + 211376. i) q^{32} -2.18403e6i q^{33} +841804. i q^{34} -1.21085e6i q^{35} -7.56526e6 q^{36} +(-1.38707e6 + 1.38707e6i) q^{37} -3.88249e6i q^{38} +(4.81746e6 - 4.81746e6i) q^{39} +(3.17550e6 + 3.17550e6i) q^{40} +(1.11426e6 - 1.11426e6i) q^{41} +6.96904e6i q^{42} +(-308251. - 308251. i) q^{43} +(5.09680e6 - 5.09680e6i) q^{44} +1.08757e7 q^{45} +(-7.18171e6 - 7.18171e6i) q^{46} +(-2.34971e6 + 2.34971e6i) q^{47} +(-5.12637e6 - 5.12637e6i) q^{48} -2.80568e6 q^{49} +(-2.02448e6 - 2.02448e6i) q^{50} +4.57374e6i q^{51} +2.24847e7 q^{52} -2.43738e6 q^{53} -3.60141e7 q^{54} +(-7.32704e6 + 7.32704e6i) q^{55} +(-7.76039e6 + 7.76039e6i) q^{56} -2.10946e7i q^{57} +(-5.03858e6 + 1.86445e7i) q^{58} +1.50512e7 q^{59} +(3.61576e7 + 3.61576e7i) q^{60} +(-5.29417e6 - 5.29417e6i) q^{61} +2.86728e7i q^{62} +2.65783e7i q^{63} +2.06722e7i q^{64} -3.23235e7 q^{65} +(4.21706e7 - 4.21706e7i) q^{66} -307461. i q^{67} +(-1.06736e7 + 1.06736e7i) q^{68} +(-3.90201e7 - 3.90201e7i) q^{69} +(2.33799e7 - 2.33799e7i) q^{70} +3.43659e7i q^{71} +(-6.97023e7 - 6.97023e7i) q^{72} +(2.97294e7 - 2.97294e7i) q^{73} -5.35648e7 q^{74} +(-1.09995e7 - 1.09995e7i) q^{75} +(4.92276e7 - 4.92276e7i) q^{76} +(-1.79061e7 - 1.79061e7i) q^{77} +1.86037e8 q^{78} +(-2.34290e7 - 2.34290e7i) q^{79} +3.43961e7i q^{80} -9.43027e7 q^{81} +4.30297e7 q^{82} +3.11154e7 q^{83} +(-8.83632e7 + 8.83632e7i) q^{84} +(1.53441e7 - 1.53441e7i) q^{85} -1.19038e7i q^{86} +(-2.73759e7 + 1.01300e8i) q^{87} +9.39183e7 q^{88} +(-7.74500e7 - 7.74500e7i) q^{89} +(2.09993e8 + 2.09993e8i) q^{90} -7.89931e7i q^{91} -1.82120e8i q^{92} +1.55787e8i q^{93} -9.07390e7 q^{94} +(-7.07685e7 + 7.07685e7i) q^{95} +4.43503e7i q^{96} +(1.09854e7 - 1.09854e7i) q^{97} +(-5.41736e7 - 5.41736e7i) q^{98} +(1.60829e8 - 1.60829e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8}+O(q^{10}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8	\( 38 q - 8 q^{2} - 2 q^{3} - 4 q^{7} - 3678 q^{8} + 15870 q^{10} - 8390 q^{11} + 5022 q^{12} + 12728 q^{14} - 35530 q^{15} - 245912 q^{16} + 76234 q^{17} - 465022 q^{18} - 164488 q^{19} + 4092 q^{20} - 514620 q^{21} + 733568 q^{23} - 482376 q^{24} - 1528354 q^{25} + 1405470 q^{26} - 1279754 q^{27} + 1420996 q^{29} + 3659852 q^{30} + 291062 q^{31} + 1592134 q^{32} - 10223688 q^{36} + 7994574 q^{37} - 309930 q^{39} + 9093994 q^{40} + 9561658 q^{41} - 5181022 q^{43} - 11400526 q^{44} + 9526060 q^{45} - 32561820 q^{46} + 5445034 q^{47} - 17683542 q^{48} + 45106458 q^{49} + 3122002 q^{50} + 56198616 q^{52} - 25331452 q^{53} - 42307016 q^{54} + 3037606 q^{55} - 25661184 q^{56} - 33846328 q^{58} + 27333008 q^{59} + 30592014 q^{60} - 49572406 q^{61} - 121974972 q^{65} + 133443354 q^{66} + 21192980 q^{68} - 28739184 q^{69} - 17976124 q^{70} - 186114192 q^{72} + 45787870 q^{73} + 91919252 q^{74} - 159074460 q^{75} + 243795016 q^{76} + 59851916 q^{77} + 163580208 q^{78} - 99827470 q^{79} - 75138586 q^{81} - 18178416 q^{82} - 177270160 q^{83} - 9436684 q^{84} + 156307616 q^{85} - 20584526 q^{87} + 563433236 q^{88} - 388451858 q^{89} + 306402752 q^{90} + 81569204 q^{94} - 44386260 q^{95} - 121157834 q^{97} - 129908712 q^{98} - 216447384 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 2 * q^3 - 4 * q^7 - 3678 * q^8 + 15870 * q^10 - 8390 * q^11 + 5022 * q^12 + 12728 * q^14 - 35530 * q^15 - 245912 * q^16 + 76234 * q^17 - 465022 * q^18 - 164488 * q^19 + 4092 * q^20 - 514620 * q^21 + 733568 * q^23 - 482376 * q^24 - 1528354 * q^25 + 1405470 * q^26 - 1279754 * q^27 + 1420996 * q^29 + 3659852 * q^30 + 291062 * q^31 + 1592134 * q^32 - 10223688 * q^36 + 7994574 * q^37 - 309930 * q^39 + 9093994 * q^40 + 9561658 * q^41 - 5181022 * q^43 - 11400526 * q^44 + 9526060 * q^45 - 32561820 * q^46 + 5445034 * q^47 - 17683542 * q^48 + 45106458 * q^49 + 3122002 * q^50 + 56198616 * q^52 - 25331452 * q^53 - 42307016 * q^54 + 3037606 * q^55 - 25661184 * q^56 - 33846328 * q^58 + 27333008 * q^59 + 30592014 * q^60 - 49572406 * q^61 - 121974972 * q^65 + 133443354 * q^66 + 21192980 * q^68 - 28739184 * q^69 - 17976124 * q^70 - 186114192 * q^72 + 45787870 * q^73 + 91919252 * q^74 - 159074460 * q^75 + 243795016 * q^76 + 59851916 * q^77 + 163580208 * q^78 - 99827470 * q^79 - 75138586 * q^81 - 18178416 * q^82 - 177270160 * q^83 - 9436684 * q^84 + 156307616 * q^85 - 20584526 * q^87 + 563433236 * q^88 - 388451858 * q^89 + 306402752 * q^90 + 81569204 * q^94 - 44386260 * q^95 - 121157834 * q^97 - 129908712 * q^98 - 216447384 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more