LMFDB - Embedded newform 98.10.c.g.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{106})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 106x^{2} + 11236 $ x^4 + 106*x^2 + 11236
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-5.14782 + 8.91628i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.10.c.g.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 - 13.8564i) q^{2} +(-61.7738 + 106.995i) q^{3} +(-128.000 + 221.703i) q^{4} +(638.329 + 1105.62i) q^{5} +1976.76 q^{6} +4096.00 q^{8} +(2209.50 + 3826.97i) q^{9} +(10213.3 - 17689.9i) q^{10} +(13822.0 - 23940.4i) q^{11} +(-15814.1 - 27390.8i) q^{12} +83312.2 q^{13} -157728. q^{15} +(-32768.0 - 56755.8i) q^{16} +(277117. - 479981. i) q^{17} +(35352.0 - 61231.5i) q^{18} +(-171752. - 297483. i) q^{19} -326824. q^{20} -442304. q^{22} +(267852. + 463933. i) q^{23} +(-253025. + 438253. i) q^{24} +(161634. - 279959. i) q^{25} +(-666498. - 1.15441e6i) q^{26} -2.97774e6 q^{27} -2.59101e6 q^{29} +(1.26182e6 + 2.18554e6i) q^{30} +(3.04862e6 - 5.28036e6i) q^{31} +(-524288. + 908093. i) q^{32} +(1.70767e6 + 2.95778e6i) q^{33} -8.86775e6 q^{34} -1.13126e6 q^{36} +(8.90396e6 + 1.54221e7i) q^{37} +(-2.74803e6 + 4.75972e6i) q^{38} +(-5.14651e6 + 8.91402e6i) q^{39} +(2.61460e6 + 4.52861e6i) q^{40} +3.05338e7 q^{41} -8.75976e6 q^{43} +(3.53843e6 + 6.12874e6i) q^{44} +(-2.82078e6 + 4.88573e6i) q^{45} +(4.28563e6 - 7.42293e6i) q^{46} +(-1.36365e7 - 2.36191e7i) q^{47} +8.09681e6 q^{48} -5.17230e6 q^{50} +(3.42372e7 + 5.93005e7i) q^{51} +(-1.06640e7 + 1.84705e7i) q^{52} +(4.17442e7 - 7.23032e7i) q^{53} +(2.38219e7 + 4.12608e7i) q^{54} +3.52919e7 q^{55} +4.24390e7 q^{57} +(2.07280e7 + 3.59020e7i) q^{58} +(-4.07738e7 + 7.06222e7i) q^{59} +(2.01892e7 - 3.49687e7i) q^{60} +(-2.49221e7 - 4.31664e7i) q^{61} -9.75558e7 q^{62} +1.67772e7 q^{64} +(5.31806e7 + 9.21115e7i) q^{65} +(2.73228e7 - 4.73245e7i) q^{66} +(9.27465e7 - 1.60642e8i) q^{67} +(7.09420e7 + 1.22875e8i) q^{68} -6.61849e7 q^{69} +3.70271e8 q^{71} +(9.05011e6 + 1.56753e7i) q^{72} +(1.23005e8 - 2.13051e8i) q^{73} +(1.42463e8 - 2.46754e8i) q^{74} +(1.99695e7 + 3.45883e7i) q^{75} +8.79369e7 q^{76} +1.64688e8 q^{78} +(2.59954e8 + 4.50253e8i) q^{79} +(4.18335e7 - 7.24578e7i) q^{80} +(1.40457e8 - 2.43278e8i) q^{81} +(-2.44270e8 - 4.23089e8i) q^{82} -2.98889e8 q^{83} +7.07568e8 q^{85} +(7.00780e7 + 1.21379e8i) q^{86} +(1.60056e8 - 2.77226e8i) q^{87} +(5.66149e7 - 9.80599e7i) q^{88} +(-1.48763e8 - 2.57666e8i) q^{89} +9.02648e7 q^{90} -1.37140e8 q^{92} +(3.76649e8 + 6.52376e8i) q^{93} +(-2.18184e8 + 3.77905e8i) q^{94} +(2.19268e8 - 3.79784e8i) q^{95} +(-6.47745e7 - 1.12193e8i) q^{96} +7.80734e8 q^{97} +1.22159e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} - 512 q^{4} + 16384 q^{8} + 8838 q^{9} + 55288 q^{11} - 630912 q^{15} - 131072 q^{16} + 141408 q^{18} - 1769216 q^{22} + 1071408 q^{23} + 646538 q^{25} - 10364024 q^{29} + 5047296 q^{30}+ \cdots + 488635344 q^{99}+O(q^{100}) $ 4 * q - 32 * q^2 - 512 * q^4 + 16384 * q^8 + 8838 * q^9 + 55288 * q^11 - 630912 * q^15 - 131072 * q^16 + 141408 * q^18 - 1769216 * q^22 + 1071408 * q^23 + 646538 * q^25 - 10364024 * q^29 + 5047296 * q^30 - 2097152 * q^32 - 4525056 * q^36 + 35615820 * q^37 - 20586048 * q^39 - 35039024 * q^43 + 14153728 * q^44 + 17142528 * q^46 - 20689216 * q^50 + 136948608 * q^51 + 166976980 * q^53 + 169756032 * q^57 + 82912192 * q^58 + 80756736 * q^60 + 67108864 * q^64 + 212722496 * q^65 + 370985848 * q^67 + 1481082688 * q^71 + 36200448 * q^72 + 569853120 * q^74 + 658753536 * q^78 + 1039814512 * q^79 + 561827502 * q^81 + 2830271232 * q^85 + 280312192 * q^86 + 226459648 * q^88 - 548560896 * q^92 + 1506597504 * q^93 + 877072832 * q^95 + 488635344 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$	−61.7738	+	106.995i	−0.440310	+	0.762639i	−0.997712	−	0.0676033i	$-0.978465\pi$
$3$	−61.7738	+	106.995i	−0.440310	+	0.762639i	0.557402	+	0.830243i	$0.311798\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	638.329	+	1105.62i	0.456751	+	0.791116i	0.998787	−	0.0492392i	$-0.0156797\pi$
$5$	638.329	+	1105.62i	0.456751	+	0.791116i	−0.542036	+	0.840355i	$0.682346\pi$
$6$	1976.76			0.622692
$7$		0			0
$7$		0			0
$8$	4096.00			0.353553
$9$	2209.50	+	3826.97i	0.112254	+	0.194430i
$10$	10213.3	−	17689.9i	0.322972	−	0.559404i
$11$	13822.0	−	23940.4i	0.284645	−	0.493020i	−0.687878	−	0.725826i	$-0.741458\pi$
$11$	13822.0	−	23940.4i	0.284645	−	0.493020i	0.972523	+	0.232807i	$0.0747909\pi$
$12$	−15814.1	−	27390.8i	−0.220155	−	0.381320i
$13$	83312.2			0.809028			0.404514	−	0.914532i	$-0.367441\pi$
$13$	83312.2			0.809028			0.404514	+	0.914532i	$0.367441\pi$
$14$		0			0
$15$	−157728.			−0.804448
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	277117.	−	479981.i	0.804717	−	1.39381i	−0.111765	−	0.993735i	$-0.535650\pi$
$17$	277117.	−	479981.i	0.804717	−	1.39381i	0.916482	−	0.400076i	$-0.131016\pi$
$18$	35352.0	−	61231.5i	0.0793757	−	0.137483i
$19$	−171752.	−	297483.i	−0.302350	−	0.523685i	0.674318	−	0.738441i	$-0.264438\pi$
$19$	−171752.	−	297483.i	−0.302350	−	0.523685i	−0.976668	+	0.214756i	$0.931104\pi$
$20$	−326824.			−0.456751
$21$		0			0
$22$	−442304.			−0.402549
$23$	267852.	+	463933.i	0.199581	+	0.345685i	0.948393	−	0.317098i	$-0.102709\pi$
$23$	267852.	+	463933.i	0.199581	+	0.345685i	−0.748811	+	0.662783i	$0.769375\pi$
$24$	−253025.	+	438253.i	−0.155673	+	0.269634i
$25$	161634.	−	279959.i	0.0827569	−	0.143339i
$26$	−666498.	−	1.15441e6i	−0.286035	−	0.495427i
$27$	−2.97774e6			−1.07833
$28$		0			0
$29$	−2.59101e6			−0.680264			−0.340132	−	0.940378i	$-0.610472\pi$
$29$	−2.59101e6			−0.680264			−0.340132	+	0.940378i	$0.610472\pi$
$30$	1.26182e6	+	2.18554e6i	0.284415	+	0.492622i
$31$	3.04862e6	−	5.28036e6i	0.592892	−	1.02692i	−0.400949	−	0.916100i	$-0.631320\pi$
$31$	3.04862e6	−	5.28036e6i	0.592892	−	1.02692i	0.993841	−	0.110818i	$-0.0353472\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	1.70767e6	+	2.95778e6i	0.250664	+	0.434163i
$34$	−8.86775e6			−1.13804
$35$		0			0
$36$	−1.13126e6			−0.112254
$37$	8.90396e6	+	1.54221e7i	0.781043	+	1.35281i	0.931334	+	0.364165i	$0.118646\pi$
$37$	8.90396e6	+	1.54221e7i	0.781043	+	1.35281i	−0.150291	+	0.988642i	$0.548021\pi$
$38$	−2.74803e6	+	4.75972e6i	−0.213794	+	0.370302i
$39$	−5.14651e6	+	8.91402e6i	−0.356223	+	0.616997i
$40$	2.61460e6	+	4.52861e6i	0.161486	+	0.279702i
$41$	3.05338e7			1.68754			0.843769	−	0.536707i	$-0.180332\pi$
$41$	3.05338e7			1.68754			0.843769	+	0.536707i	$0.180332\pi$
$42$		0			0
$43$	−8.75976e6			−0.390736			−0.195368	−	0.980730i	$-0.562590\pi$
$43$	−8.75976e6			−0.390736			−0.195368	+	0.980730i	$0.562590\pi$
$44$	3.53843e6	+	6.12874e6i	0.142323	+	0.246510i
$45$	−2.82078e6	+	4.88573e6i	−0.102544	+	0.177612i
$46$	4.28563e6	−	7.42293e6i	0.141125	−	0.244436i
$47$	−1.36365e7	−	2.36191e7i	−0.407626	−	0.706029i	0.586997	−	0.809589i	$-0.300310\pi$
$47$	−1.36365e7	−	2.36191e7i	−0.407626	−	0.706029i	−0.994623	+	0.103560i	$0.966977\pi$
$48$	8.09681e6			0.220155
$49$		0			0
$50$	−5.17230e6			−0.117036
$51$	3.42372e7	+	5.93005e7i	0.708650	+	1.22742i
$52$	−1.06640e7	+	1.84705e7i	−0.202257	+	0.350320i
$53$	4.17442e7	−	7.23032e7i	0.726700	−	1.25868i	−0.231570	−	0.972818i	$-0.574386\pi$
$53$	4.17442e7	−	7.23032e7i	0.726700	−	1.25868i	0.958270	−	0.285863i	$-0.0922803\pi$
$54$	2.38219e7	+	4.12608e7i	0.381246	+	0.660337i
$55$	3.52919e7			0.520048
$56$		0			0
$57$	4.24390e7			0.532511
$58$	2.07280e7	+	3.59020e7i	0.240510	+	0.416575i
$59$	−4.07738e7	+	7.06222e7i	−0.438073	+	0.758765i	−0.997541	−	0.0700871i	$-0.977672\pi$
$59$	−4.07738e7	+	7.06222e7i	−0.438073	+	0.758765i	0.559468	+	0.828852i	$0.311006\pi$
$60$	2.01892e7	−	3.49687e7i	0.201112	−	0.348336i
$61$	−2.49221e7	−	4.31664e7i	−0.230463	−	0.399173i	0.727482	−	0.686127i	$-0.240691\pi$
$61$	−2.49221e7	−	4.31664e7i	−0.230463	−	0.399173i	−0.957944	+	0.286954i	$0.907357\pi$
$62$	−9.75558e7			−0.838476
$63$		0			0
$64$	1.67772e7			0.125000
$65$	5.31806e7	+	9.21115e7i	0.369525	+	0.640035i
$66$	2.73228e7	−	4.73245e7i	0.177246	−	0.307000i
$67$	9.27465e7	−	1.60642e8i	0.562290	−	0.973916i	−0.435006	−	0.900428i	$-0.643254\pi$
$67$	9.27465e7	−	1.60642e8i	0.562290	−	0.973916i	0.997296	−	0.0734880i	$-0.0234130\pi$
$68$	7.09420e7	+	1.22875e8i	0.402359	+	0.696906i
$69$	−6.61849e7			−0.351510
$70$		0			0
$71$	3.70271e8			1.72925			0.864623	−	0.502421i	$-0.167557\pi$
$71$	3.70271e8			1.72925			0.864623	+	0.502421i	$0.167557\pi$
$72$	9.05011e6	+	1.56753e7i	0.0396879	+	0.0687414i
$73$	1.23005e8	−	2.13051e8i	0.506957	−	0.878075i	−0.493011	−	0.870023i	$-0.664104\pi$
$73$	1.23005e8	−	2.13051e8i	0.506957	−	0.878075i	0.999968	−	0.00805160i	$-0.00256293\pi$
$74$	1.42463e8	−	2.46754e8i	0.552281	−	0.956579i
$75$	1.99695e7	+	3.45883e7i	0.0728773	+	0.126227i
$76$	8.79369e7			0.302350
$77$		0			0
$78$	1.64688e8			0.503776
$79$	2.59954e8	+	4.50253e8i	0.750886	+	1.30057i	0.947394	+	0.320070i	$0.103707\pi$
$79$	2.59954e8	+	4.50253e8i	0.750886	+	1.30057i	−0.196508	+	0.980502i	$0.562960\pi$
$80$	4.18335e7	−	7.24578e7i	0.114188	−	0.197779i
$81$	1.40457e8	−	2.43278e8i	0.362544	−	0.627944i
$82$	−2.44270e8	−	4.23089e8i	−0.596635	−	1.03340i
$83$	−2.98889e8			−0.691287			−0.345643	−	0.938366i	$-0.612339\pi$
$83$	−2.98889e8			−0.691287			−0.345643	+	0.938366i	$0.612339\pi$
$84$		0			0
$85$	7.07568e8			1.47022
$86$	7.00780e7	+	1.21379e8i	0.138146	+	0.239276i
$87$	1.60056e8	−	2.77226e8i	0.299527	−	0.518796i
$88$	5.66149e7	−	9.80599e7i	0.100637	−	0.174309i
$89$	−1.48763e8	−	2.57666e8i	−0.251328	−	0.435313i	0.712564	−	0.701608i	$-0.247534\pi$
$89$	−1.48763e8	−	2.57666e8i	−0.251328	−	0.435313i	−0.963892	+	0.266294i	$0.914201\pi$
$90$	9.02648e7			0.145020
$91$		0			0
$92$	−1.37140e8			−0.199581
$93$	3.76649e8	+	6.52376e8i	0.522112	+	0.904325i
$94$	−2.18184e8	+	3.77905e8i	−0.288235	+	0.499238i
$95$	2.19268e8	−	3.79784e8i	0.276197	−	0.478388i
$96$	−6.47745e7	−	1.12193e8i	−0.0778365	−	0.134817i
$97$	7.80734e8			0.895427			0.447713	−	0.894177i	$-0.352238\pi$
$97$	7.80734e8			0.895427			0.447713	+	0.894177i	$0.352238\pi$
$98$		0			0
$99$	1.22159e8			0.127810
$100$	4.13784e7	+	7.16695e7i	0.0413784	+	0.0716695i
$101$	−6.51159e8	+	1.12784e9i	−0.622646	+	1.07845i	0.366346	+	0.930479i	$0.380609\pi$
$101$	−6.51159e8	+	1.12784e9i	−0.622646	+	1.07845i	−0.988991	+	0.147975i	$0.952725\pi$
$102$	5.47794e8	−	9.48808e8i	0.501091	−	0.867916i
$103$	1.07474e9	+	1.86151e9i	0.940887	+	1.62966i	0.763784	+	0.645472i	$0.223339\pi$
$103$	1.07474e9	+	1.86151e9i	0.940887	+	1.62966i	0.177104	+	0.984192i	$0.443327\pi$
$104$	3.41247e8			0.286035
$105$		0			0
$106$	−1.33582e9			−1.02771
$107$	4.17444e8	+	7.23034e8i	0.307873	+	0.533251i	0.977897	−	0.209088i	$-0.0670496\pi$
$107$	4.17444e8	+	7.23034e8i	0.307873	+	0.533251i	−0.670024	+	0.742339i	$0.733716\pi$
$108$	3.81151e8	−	6.60173e8i	0.269582	−	0.466929i
$109$	−5.12813e8	+	8.88219e8i	−0.347969	+	0.602699i	−0.985888	−	0.167403i	$-0.946462\pi$
$109$	−5.12813e8	+	8.88219e8i	−0.347969	+	0.602699i	0.637920	+	0.770103i	$0.279795\pi$
$110$	−2.82336e8	−	4.89019e8i	−0.183865	−	0.318463i
$111$	−2.20012e9			−1.37560
$112$		0			0
$113$	−4.65902e8			−0.268808			−0.134404	−	0.990927i	$-0.542912\pi$
$113$	−4.65902e8			−0.268808			−0.134404	+	0.990927i	$0.542912\pi$
$114$	−3.39512e8	−	5.88052e8i	−0.188271	−	0.326095i
$115$	−3.41955e8	+	5.92284e8i	−0.182318	+	0.315784i
$116$	3.31649e8	−	5.74433e8i	0.170066	−	0.294563i
$117$	1.84078e8	+	3.18833e8i	0.0908169	+	0.157299i
$118$	1.30476e9			0.619529
$119$		0			0
$120$	−6.46054e8			−0.284415
$121$	7.96878e8	+	1.38023e9i	0.337954	+	0.585354i
$122$	−3.98754e8	+	6.90662e8i	−0.162962	+	0.282258i
$123$	−1.88619e9	+	3.26697e9i	−0.743040	+	1.28698i
$124$	7.80446e8	+	1.35177e9i	0.296446	+	0.513459i
$125$	2.90618e9			1.06470
$126$		0			0
$127$	−7.84044e8			−0.267438			−0.133719	−	0.991019i	$-0.542692\pi$
$127$	−7.84044e8			−0.267438			−0.133719	+	0.991019i	$0.542692\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	5.41123e8	−	9.37253e8i	0.172045	−	0.297991i
$130$	8.50890e8	−	1.47378e9i	0.261293	−	0.452573i
$131$	−2.88682e9	−	5.00012e9i	−0.856444	−	1.48340i	−0.875299	−	0.483582i	$-0.839335\pi$
$131$	−2.88682e9	−	5.00012e9i	−0.856444	−	1.48340i	0.0188547	−	0.999822i	$-0.493998\pi$
$132$	−8.74329e8			−0.250664
$133$		0			0
$134$	−2.96789e9			−0.795199
$135$	−1.90078e9	−	3.29225e9i	−0.492527	−	0.853082i
$136$	1.13507e9	−	1.96600e9i	0.284511	−	0.492787i
$137$	−3.58836e9	+	6.21523e9i	−0.870269	+	1.50735i	−0.00855148	+	0.999963i	$0.502722\pi$
$137$	−3.58836e9	+	6.21523e9i	−0.870269	+	1.50735i	−0.861718	+	0.507388i	$0.830611\pi$
$138$	5.29479e8	+	9.17085e8i	0.124278	+	0.215255i
$139$	−3.11320e9			−0.707359			−0.353679	−	0.935367i	$-0.615070\pi$
$139$	−3.11320e9			−0.707359			−0.353679	+	0.935367i	$0.615070\pi$
$140$		0			0
$141$	3.36951e9			0.717927
$142$	−2.96217e9	−	5.13062e9i	−0.611381	−	1.05894i
$143$	1.15154e9	−	1.99453e9i	0.230286	−	0.398867i
$144$	1.44802e8	−	2.50804e8i	0.0280636	−	0.0486075i
$145$	−1.65391e9	−	2.86466e9i	−0.310711	−	0.538168i
$146$	−3.93617e9			−0.716945
$147$		0			0
$148$	−4.55882e9			−0.781043
$149$	−3.43535e9	−	5.95020e9i	−0.570996	−	0.988993i	−0.996464	−	0.0840202i	$-0.973224\pi$
$149$	−3.43535e9	−	5.95020e9i	−0.570996	−	0.988993i	0.425468	−	0.904973i	$-0.360109\pi$
$150$	3.19513e8	−	5.53412e8i	0.0515321	−	0.0892562i
$151$	−4.53378e9	+	7.85273e9i	−0.709682	+	1.22921i	0.255293	+	0.966864i	$0.417828\pi$
$151$	−4.53378e9	+	7.85273e9i	−0.709682	+	1.22921i	−0.964975	+	0.262342i	$0.915505\pi$
$152$	−7.03495e8	−	1.21849e9i	−0.106897	−	0.185151i
$153$	2.44916e9			0.361332
$154$		0			0
$155$	7.78409e9			1.08322
$156$	−1.31751e9	−	2.28199e9i	−0.178112	−	0.308498i
$157$	1.67744e9	−	2.90541e9i	0.220343	−	0.381645i	−0.734569	−	0.678534i	$-0.762616\pi$
$157$	1.67744e9	−	2.90541e9i	0.220343	−	0.381645i	0.954912	+	0.296889i	$0.0959491\pi$
$158$	4.15926e9	−	7.20405e9i	0.530957	−	0.919644i
$159$	5.15740e9	+	8.93288e9i	0.639947	+	1.10842i
$160$	−1.33867e9			−0.161486
$161$		0			0
$162$	−4.49462e9			−0.512714
$163$	−3.28981e9	−	5.69812e9i	−0.365028	−	0.632247i	0.623752	−	0.781622i	$-0.285607\pi$
$163$	−3.28981e9	−	5.69812e9i	−0.365028	−	0.632247i	−0.988781	+	0.149374i	$0.952274\pi$
$164$	−3.90833e9	+	6.76942e9i	−0.421884	+	0.730725i
$165$	−2.18012e9	+	3.77607e9i	−0.228982	+	0.396609i
$166$	2.39111e9	+	4.14153e9i	0.244407	+	0.423325i
$167$	3.22471e8			0.0320824			0.0160412	−	0.999871i	$-0.494894\pi$
$167$	3.22471e8			0.0320824			0.0160412	+	0.999871i	$0.494894\pi$
$168$		0			0
$169$	−3.66357e9			−0.345473
$170$	−5.66054e9	−	9.80435e9i	−0.519802	−	0.900323i
$171$	7.58971e8	−	1.31458e9i	0.0678801	−	0.117572i
$172$	1.12125e9	−	1.94206e9i	0.0976841	−	0.169194i
$173$	8.36145e8	+	1.44825e9i	0.0709699	+	0.122923i	0.899327	−	0.437277i	$-0.144057\pi$
$173$	8.36145e8	+	1.44825e9i	0.0709699	+	0.122923i	−0.828357	+	0.560201i	$0.810724\pi$
$174$	−5.12180e9			−0.423595
$175$		0			0
$176$	−1.81168e9			−0.142323
$177$	−5.03750e9	−	8.72520e9i	−0.385776	−	0.668184i
$178$	−2.38022e9	+	4.12265e9i	−0.177716	+	0.307813i
$179$	−4.21451e9	+	7.29975e9i	−0.306838	+	0.531458i	−0.977669	−	0.210152i	$-0.932604\pi$
$179$	−4.21451e9	+	7.29975e9i	−0.306838	+	0.531458i	0.670831	+	0.741610i	$0.265937\pi$
$180$	−7.22119e8	−	1.25075e9i	−0.0512722	−	0.0888061i
$181$	2.02316e10			1.40113			0.700563	−	0.713591i	$-0.252932\pi$
$181$	2.02316e10			1.40113			0.700563	+	0.713591i	$0.252932\pi$
$182$		0			0
$183$	6.15813e9			0.405900
$184$	1.09712e9	+	1.90027e9i	0.0705626	+	0.122218i
$185$	−1.13673e10	+	1.96888e10i	−0.713485	+	1.23579i
$186$	6.02639e9	−	1.04380e10i	0.369189	−	0.639454i
$187$	−7.66063e9	−	1.32686e10i	−0.458118	−	0.793483i
$188$	6.98188e9			0.407626
$189$		0			0
$190$	−7.01658e9			−0.390602
$191$	8.91139e9	+	1.54350e10i	0.484502	+	0.839182i	0.999841	−	0.0178042i	$-0.00566754\pi$
$191$	8.91139e9	+	1.54350e10i	0.484502	+	0.839182i	−0.515340	+	0.856986i	$0.672334\pi$
$192$	−1.03639e9	+	1.79508e9i	−0.0550387	+	0.0953299i
$193$	−7.72836e9	+	1.33859e10i	−0.400940	+	0.694449i	−0.993840	−	0.110828i	$-0.964650\pi$
$193$	−7.72836e9	+	1.33859e10i	−0.400940	+	0.694449i	0.592899	+	0.805277i	$0.297983\pi$
$194$	−6.24587e9	−	1.08182e10i	−0.316581	−	0.548335i
$195$	−1.31407e10			−0.650821
$196$		0			0
$197$	2.03655e10			0.963376			0.481688	−	0.876343i	$-0.340024\pi$
$197$	2.03655e10			0.963376			0.481688	+	0.876343i	$0.340024\pi$
$198$	−9.77271e8	−	1.69268e9i	−0.0451878	−	0.0782676i
$199$	1.38513e10	−	2.39911e10i	0.626109	−	1.08445i	−0.362216	−	0.932094i	$-0.617980\pi$
$199$	1.38513e10	−	2.39911e10i	0.626109	−	1.08445i	0.988325	−	0.152359i	$-0.0486870\pi$
$200$	6.62055e8	−	1.14671e9i	0.0292590	−	0.0506780i
$201$	1.14586e10	+	1.98469e10i	0.495164	+	0.857650i
$202$	2.08371e10			0.880554
$203$		0			0
$204$	−1.75294e10			−0.708650
$205$	1.94906e10	+	3.37587e10i	0.770785	+	1.33504i
$206$	1.71959e10	−	2.97842e10i	0.665308	−	1.15235i
$207$	−1.18364e9	+	2.05012e9i	−0.0448077	+	0.0776092i
$208$	−2.72998e9	−	4.72846e9i	−0.101129	−	0.175160i
$209$	−9.49581e9			−0.344250
$210$		0			0
$211$	−1.30691e10			−0.453914			−0.226957	−	0.973905i	$-0.572878\pi$
$211$	−1.30691e10			−0.453914			−0.226957	+	0.973905i	$0.572878\pi$
$212$	1.06865e10	+	1.85096e10i	0.363350	+	0.629341i
$213$	−2.28730e10	+	3.96172e10i	−0.761404	+	1.31879i
$214$	6.67910e9	−	1.15685e10i	0.217699	−	0.377065i
$215$	−5.59161e9	−	9.68495e9i	−0.178469	−	0.309118i
$216$	−1.21968e10			−0.381246
$217$		0			0
$218$	1.64100e10			0.492102
$219$	1.51970e10	+	2.63220e10i	0.446436	+	0.773250i
$220$	−4.51737e9	+	7.82431e9i	−0.130012	+	0.225187i
$221$	2.30873e10	−	3.99883e10i	0.651039	−	1.12763i
$222$	1.76010e10	+	3.04858e10i	0.486350	+	0.842383i
$223$	−4.18178e10			−1.13237			−0.566187	−	0.824277i	$-0.691582\pi$
$223$	−4.18178e10			−1.13237			−0.566187	+	0.824277i	$0.691582\pi$
$224$		0			0
$225$	1.42853e9			0.0371592
$226$	3.72722e9	+	6.45573e9i	0.0950379	+	0.164610i
$227$	2.80611e10	−	4.86033e10i	0.701438	−	1.21493i	−0.266524	−	0.963828i	$-0.585875\pi$
$227$	2.80611e10	−	4.86033e10i	0.701438	−	1.21493i	0.967962	−	0.251097i	$-0.0807914\pi$
$228$	−5.43219e9	+	9.40883e9i	−0.133128	+	0.230584i
$229$	2.24541e9	+	3.88917e9i	0.0539556	+	0.0934538i	0.891742	−	0.452545i	$-0.149484\pi$
$229$	2.24541e9	+	3.88917e9i	0.0539556	+	0.0934538i	−0.837786	+	0.545999i	$0.816150\pi$
$230$	1.09426e10			0.257836
$231$		0			0
$232$	−1.06128e10			−0.240510
$233$	3.22331e10	+	5.58294e10i	0.716475	+	1.24097i	0.962388	+	0.271679i	$0.0875788\pi$
$233$	3.22331e10	+	5.58294e10i	0.716475	+	1.24097i	−0.245913	+	0.969292i	$0.579088\pi$
$234$	2.94525e9	−	5.10133e9i	0.0642172	−	0.111227i
$235$	1.74091e10	−	3.01535e10i	0.372367	−	0.644959i
$236$	−1.04381e10	−	1.80793e10i	−0.219037	−	0.379383i
$237$	−6.42333e10			−1.32249
$238$		0			0
$239$	−1.23198e9			−0.0244238			−0.0122119	−	0.999925i	$-0.503887\pi$
$239$	−1.23198e9			−0.0244238			−0.0122119	+	0.999925i	$0.503887\pi$
$240$	5.16843e9	+	8.95199e9i	0.100556	+	0.174168i
$241$	4.44175e9	−	7.69334e9i	0.0848160	−	0.146906i	−0.820497	−	0.571651i	$-0.806303\pi$
$241$	4.44175e9	−	7.69334e9i	0.0848160	−	0.146906i	0.905313	+	0.424746i	$0.139636\pi$
$242$	1.27501e10	−	2.20837e10i	0.238970	−	0.413908i
$243$	−1.19524e10	−	2.07021e10i	−0.219900	−	0.380878i
$244$	1.27601e10			0.230463
$245$		0			0
$246$	6.03580e10			1.05082
$247$	−1.43090e10	−	2.47839e10i	−0.244610	−	0.423676i
$248$	1.24871e10	−	2.16284e10i	0.209619	−	0.363071i
$249$	1.84635e10	−	3.19797e10i	0.304381	−	0.527203i
$250$	−2.32494e10	−	4.02692e10i	−0.376428	−	0.651993i
$251$	9.92817e10			1.57884			0.789419	−	0.613855i	$-0.210382\pi$
$251$	9.92817e10			1.57884			0.789419	+	0.613855i	$0.210382\pi$
$252$		0			0
$253$	1.48090e10			0.227239
$254$	6.27235e9	+	1.08640e10i	0.0945538	+	0.163772i
$255$	−4.37091e10	+	7.57064e10i	−0.647353	+	1.12125i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	2.78328e10	+	4.82079e10i	0.397977	+	0.689317i	0.993476	−	0.114039i	$-0.0363789\pi$
$257$	2.78328e10	+	4.82079e10i	0.397977	+	0.689317i	−0.595499	+	0.803356i	$0.703046\pi$
$258$	−1.73159e10			−0.243309
$259$		0			0
$260$	−2.72285e10			−0.369525
$261$	−5.72483e9	−	9.91569e9i	−0.0763625	−	0.132264i
$262$	−4.61891e10	+	8.00019e10i	−0.605597	+	1.04893i
$263$	4.98863e10	−	8.64057e10i	0.642955	−	1.11363i	−0.341814	−	0.939768i	$-0.611041\pi$
$263$	4.98863e10	−	8.64057e10i	0.642955	−	1.11363i	0.984770	−	0.173864i	$-0.0556253\pi$
$264$	6.99463e9	+	1.21151e10i	0.0886232	+	0.153500i
$265$	1.06586e11			1.32768
$266$		0			0
$267$	3.67587e10			0.442649
$268$	2.37431e10	+	4.11242e10i	0.281145	+	0.486958i
$269$	9.86745e9	−	1.70909e10i	0.114900	−	0.199012i	−0.802840	−	0.596195i	$-0.796679\pi$
$269$	9.86745e9	−	1.70909e10i	0.114900	−	0.199012i	0.917740	+	0.397182i	$0.130012\pi$
$270$	−3.04125e10	+	5.26760e10i	−0.348269	+	0.603220i
$271$	−2.94220e10	−	5.09604e10i	−0.331368	−	0.573946i	0.651413	−	0.758724i	$-0.274177\pi$
$271$	−2.94220e10	−	5.09604e10i	−0.331368	−	0.573946i	−0.982780	+	0.184778i	$0.940843\pi$
$272$	−3.63223e10			−0.402359
$273$		0			0
$274$	1.14828e11			1.23075
$275$	−4.46822e9	−	7.73919e9i	−0.0471127	−	0.0816016i
$276$	8.47167e9	−	1.46734e10i	0.0878776	−	0.152208i
$277$	2.09747e10	−	3.63293e10i	0.214061	−	0.370764i	−0.738921	−	0.673792i	$-0.764664\pi$
$277$	2.09747e10	−	3.63293e10i	0.214061	−	0.370764i	0.952982	+	0.303028i	$0.0979976\pi$
$278$	2.49056e10	+	4.31377e10i	0.250089	+	0.433167i
$279$	2.69437e10			0.266218
$280$		0			0
$281$	2.62716e10			0.251367			0.125684	−	0.992070i	$-0.459888\pi$
$281$	2.62716e10			0.251367			0.125684	+	0.992070i	$0.459888\pi$
$282$	−2.69561e10	−	4.66893e10i	−0.253826	−	0.439639i
$283$	6.18584e10	−	1.07142e11i	0.573271	−	0.992935i	−0.422956	−	0.906150i	$-0.639008\pi$
$283$	6.18584e10	−	1.07142e11i	0.573271	−	0.992935i	0.996227	−	0.0867843i	$-0.0276591\pi$
$284$	−4.73946e10	+	8.20899e10i	−0.432311	+	0.748785i
$285$	2.70901e10	+	4.69213e10i	0.243225	+	0.421278i
$286$	−3.68493e10			−0.325674
$287$		0			0
$288$	−4.63366e9			−0.0396879
$289$	−9.42939e10	−	1.63322e11i	−0.795140	−	1.37722i
$290$	−2.64626e10	+	4.58346e10i	−0.219706	+	0.380542i
$291$	−4.82289e10	+	8.35349e10i	−0.394265	+	0.682888i
$292$	3.14893e10	+	5.45412e10i	0.253478	+	0.439037i
$293$	3.33848e10			0.264633			0.132316	−	0.991208i	$-0.457758\pi$
$293$	3.33848e10			0.264633			0.132316	+	0.991208i	$0.457758\pi$
$294$		0			0
$295$	−1.04108e11			−0.800362
$296$	3.64706e10	+	6.31689e10i	0.276141	+	0.478289i
$297$	−4.11584e10	+	7.12884e10i	−0.306940	+	0.531636i
$298$	−5.49656e10	+	9.52032e10i	−0.403755	+	0.699324i
$299$	2.23153e10	+	3.86513e10i	0.161467	+	0.279669i
$300$	−1.02244e10			−0.0728773
$301$		0			0
$302$	1.45081e11			1.00364
$303$	−8.04491e10	−	1.39342e11i	−0.548314	−	0.949708i
$304$	−1.12559e10	+	1.94958e10i	−0.0755875	+	0.130921i
$305$	3.18170e10	−	5.51087e10i	0.210528	−	0.364646i
$306$	−1.95933e10	−	3.39366e10i	−0.127750	−	0.221270i
$307$	−2.32773e11			−1.49558			−0.747791	−	0.663935i	$-0.768885\pi$
$307$	−2.32773e11			−1.49558			−0.747791	+	0.663935i	$0.768885\pi$
$308$		0			0
$309$	−2.65564e11			−1.65713
$310$	−6.22727e10	−	1.07859e11i	−0.382975	−	0.663332i
$311$	−3.81408e9	+	6.60617e9i	−0.0231189	+	0.0400431i	−0.877353	−	0.479845i	$-0.840693\pi$
$311$	−3.81408e9	+	6.60617e9i	−0.0231189	+	0.0400431i	0.854234	+	0.519888i	$0.174026\pi$
$312$	−2.10801e10	+	3.65118e10i	−0.125944	+	0.218141i
$313$	−8.48334e10	−	1.46936e11i	−0.499594	−	0.865322i	0.500406	−	0.865791i	$-0.333184\pi$
$313$	−8.48334e10	−	1.46936e11i	−0.499594	−	0.865322i	−1.00000		0.000468677i	$0.999851\pi$
$314$	−5.36781e10			−0.311612
$315$		0			0
$316$	−1.33096e11			−0.750886
$317$	4.30026e10	+	7.44826e10i	0.239182	+	0.414275i	0.960480	−	0.278350i	$-0.0897876\pi$
$317$	4.30026e10	+	7.44826e10i	0.239182	+	0.414275i	−0.721298	+	0.692625i	$0.756454\pi$
$318$	8.25184e10	−	1.42926e11i	0.452511	−	0.783771i
$319$	−3.58129e10	+	6.20297e10i	−0.193634	+	0.335384i
$320$	1.07094e10	+	1.85492e10i	0.0570939	+	0.0988895i
$321$	−1.03148e11			−0.542237
$322$		0			0
$323$	−1.90381e11			−0.973225
$324$	3.59570e10	+	6.22793e10i	0.181272	+	0.313972i
$325$	1.34661e10	−	2.33240e10i	0.0669526	−	0.115965i
$326$	−5.26369e10	+	9.11699e10i	−0.258114	+	0.447066i
$327$	−6.33569e10	−	1.09737e11i	−0.306428	−	0.530749i
$328$	1.25066e11			0.596635
$329$		0			0
$330$	6.97637e10			0.323830
$331$	−1.79638e11	−	3.11142e11i	−0.822568	−	1.42473i	−0.903764	−	0.428031i	$-0.859207\pi$
$331$	−1.79638e11	−	3.11142e11i	−0.822568	−	1.42473i	0.0811963	−	0.996698i	$-0.474126\pi$
$332$	3.82578e10	−	6.62644e10i	0.172822	−	0.299336i
$333$	−3.93466e10	+	6.81503e10i	−0.175351	+	0.303717i
$334$	−2.57977e9	−	4.46829e9i	−0.0113428	−	0.0196464i
$335$	2.36811e11			1.02731
$336$		0			0
$337$	−2.23831e11			−0.945335			−0.472668	−	0.881241i	$-0.656709\pi$
$337$	−2.23831e11			−0.945335			−0.472668	+	0.881241i	$0.656709\pi$
$338$	2.93086e10	+	5.07639e10i	0.122143	+	0.211558i
$339$	2.87805e10	−	4.98494e10i	0.118359	−	0.205003i
$340$	−9.05687e10	+	1.56870e11i	−0.367555	+	0.636625i
$341$	−8.42760e10	−	1.45970e11i	−0.337528	−	0.584615i
$342$	−2.42871e10			−0.0959970
$343$		0			0
$344$	−3.58800e10			−0.138146
$345$	−4.22478e10	−	7.31753e10i	−0.160553	−	0.278086i
$346$	1.33783e10	−	2.31719e10i	0.0501833	−	0.0869200i
$347$	−6.24477e10	+	1.08163e11i	−0.231224	+	0.400492i	−0.958169	−	0.286204i	$-0.907606\pi$
$347$	−6.24477e10	+	1.08163e11i	−0.231224	+	0.400492i	0.726944	+	0.686696i	$0.240940\pi$
$348$	4.09744e10	+	7.09697e10i	0.149763	+	0.259398i
$349$	−4.14076e9			−0.0149405			−0.00747025	−	0.999972i	$-0.502378\pi$
$349$	−4.14076e9			−0.0149405			−0.00747025	+	0.999972i	$0.502378\pi$
$350$		0			0
$351$	−2.48082e11			−0.872397
$352$	1.44934e10	+	2.51033e10i	0.0503186	+	0.0871544i
$353$	8.63964e10	−	1.49643e11i	0.296149	−	0.512944i	−0.679103	−	0.734043i	$-0.737631\pi$
$353$	8.63964e10	−	1.49643e11i	0.296149	−	0.512944i	0.975251	+	0.221099i	$0.0709643\pi$
$354$	−8.06000e10	+	1.39603e11i	−0.272785	+	0.472477i
$355$	2.36355e11	+	4.09378e11i	0.789835	+	1.36803i
$356$	7.61669e10			0.251328
$357$		0			0
$358$	1.34864e11			0.433934
$359$	1.07540e10	+	1.86264e10i	0.0341699	+	0.0591839i	0.882605	−	0.470116i	$-0.155788\pi$
$359$	1.07540e10	+	1.86264e10i	0.0341699	+	0.0591839i	−0.848435	+	0.529300i	$0.822455\pi$
$360$	−1.15539e10	+	2.00119e10i	−0.0362550	+	0.0627954i
$361$	1.02347e11	−	1.77269e11i	0.317169	−	0.549353i
$362$	−1.61853e11	−	2.80337e11i	−0.495373	−	0.858010i
$363$	−1.96905e11			−0.595219
$364$		0			0
$365$	3.14071e11			0.926212
$366$	−4.92651e10	−	8.53296e10i	−0.143507	−	0.248562i
$367$	−2.74298e11	+	4.75098e11i	−0.789270	+	1.36706i	0.137145	+	0.990551i	$0.456207\pi$
$367$	−2.74298e11	+	4.75098e11i	−0.789270	+	1.36706i	−0.926415	+	0.376504i	$0.877126\pi$
$368$	1.75539e10	−	3.04043e10i	0.0498953	−	0.0864212i
$369$	6.74644e10	+	1.16852e11i	0.189433	+	0.328108i
$370$	3.63754e11			1.00902
$371$		0			0
$372$	−1.92844e11			−0.522112
$373$	6.30120e10	+	1.09140e11i	0.168552	+	0.291941i	0.937911	−	0.346876i	$-0.112758\pi$
$373$	6.30120e10	+	1.09140e11i	0.168552	+	0.291941i	−0.769359	+	0.638817i	$0.779424\pi$
$374$	−1.22570e11	+	2.12298e11i	−0.323938	+	0.561077i
$375$	−1.79526e11	+	3.10947e11i	−0.468798	+	0.811982i
$376$	−5.58550e10	−	9.67437e10i	−0.144118	−	0.249619i
$377$	−2.15863e11			−0.550353
$378$		0			0
$379$	−5.31002e10			−0.132197			−0.0660983	−	0.997813i	$-0.521055\pi$
$379$	−5.31002e10			−0.132197			−0.0660983	+	0.997813i	$0.521055\pi$
$380$	5.61327e10	+	9.72246e10i	0.138099	+	0.239194i
$381$	4.84334e10	−	8.38891e10i	0.117756	−	0.203959i
$382$	1.42582e11	−	2.46960e11i	0.342595	−	0.593391i
$383$	3.11345e11	+	5.39266e11i	0.739346	+	1.28058i	0.952790	+	0.303630i	$0.0981985\pi$
$383$	3.11345e11	+	5.39266e11i	0.739346	+	1.28058i	−0.213444	+	0.976955i	$0.568468\pi$
$384$	3.31645e10			0.0778365
$385$		0			0
$386$	2.47308e11			0.567015
$387$	−1.93547e10	−	3.35233e10i	−0.0438618	−	0.0759709i
$388$	−9.99339e10	+	1.73091e11i	−0.223857	+	0.387731i
$389$	1.18940e11	−	2.06009e11i	0.263362	−	0.456157i	−0.703771	−	0.710427i	$-0.748502\pi$
$389$	1.18940e11	−	2.06009e11i	0.263362	−	0.456157i	0.967133	+	0.254270i	$0.0818353\pi$
$390$	1.05125e11	+	1.82083e11i	0.230100	+	0.398545i
$391$	2.96906e11			0.642426
$392$		0			0
$393$	7.13319e11			1.50840
$394$	−1.62924e11	−	2.82192e11i	−0.340605	−	0.589945i
$395$	−3.31872e11	+	5.74819e11i	−0.685936	+	1.18808i
$396$	−1.56363e10	+	2.70829e10i	−0.0319526	+	0.0553436i
$397$	−8.47727e10	−	1.46831e11i	−0.171277	−	0.296660i	0.767590	−	0.640942i	$-0.221456\pi$
$397$	−8.47727e10	−	1.46831e11i	−0.171277	−	0.296660i	−0.938867	+	0.344281i	$0.888123\pi$
$398$	−4.43240e11			−0.885453
$399$		0			0
$400$	−2.11858e10			−0.0413784
$401$	4.51773e11	+	7.82494e11i	0.872510	+	1.51123i	0.859392	+	0.511318i	$0.170842\pi$
$401$	4.51773e11	+	7.82494e11i	0.872510	+	1.51123i	0.0131183	+	0.999914i	$0.495824\pi$
$402$	1.83338e11	−	3.17550e11i	0.350134	−	0.606450i
$403$	2.53987e11	−	4.39919e11i	0.479666	−	0.830806i
$404$	−1.66697e11	−	2.88727e11i	−0.311323	−	0.539227i
$405$	3.58631e11			0.662369
$406$		0			0
$407$	4.92282e11			0.889281
$408$	1.40235e11	+	2.42895e11i	0.250546	+	0.433958i
$409$	5.22550e11	−	9.05082e11i	0.923363	−	1.59931i	0.129191	−	0.991620i	$-0.458762\pi$
$409$	5.22550e11	−	9.05082e11i	0.923363	−	1.59931i	0.794173	−	0.607692i	$-0.207905\pi$
$410$	3.11850e11	−	5.40140e11i	0.545027	−	0.944014i
$411$	−4.43333e11	−	7.67876e11i	−0.766377	−	1.32740i
$412$	−5.50269e11			−0.940887
$413$		0			0
$414$	3.78764e10			0.0633676
$415$	−1.90789e11	−	3.30457e11i	−0.315746	−	0.546888i
$416$	−4.36796e10	+	7.56553e10i	−0.0715087	+	0.123857i
$417$	1.92314e11	−	3.33097e11i	0.311457	−	0.539460i
$418$	7.59665e10	+	1.31578e11i	0.121711	+	0.210809i
$419$	−4.17508e11			−0.661761			−0.330881	−	0.943673i	$-0.607346\pi$
$419$	−4.17508e11			−0.661761			−0.330881	+	0.943673i	$0.607346\pi$
$420$		0			0
$421$	1.67897e11			0.260480			0.130240	−	0.991482i	$-0.458425\pi$
$421$	1.67897e11			0.260480			0.130240	+	0.991482i	$0.458425\pi$
$422$	1.04553e11	+	1.81090e11i	0.160483	+	0.277964i
$423$	6.02596e10	−	1.04373e11i	0.0915155	−	0.158509i
$424$	1.70984e11	−	2.96154e11i	0.256927	−	0.445011i
$425$	−8.95834e10	−	1.55163e11i	−0.133192	−	0.230695i
$426$	7.31937e11			1.07679
$427$		0			0
$428$	−2.13731e11			−0.307873
$429$	1.42270e11	+	2.46419e11i	0.202794	+	0.351250i
$430$	−8.94657e10	+	1.54959e11i	−0.126197	+	0.218579i
$431$	8.01996e10	−	1.38910e11i	0.111950	−	0.193903i	−0.804606	−	0.593809i	$-0.797624\pi$
$431$	8.01996e10	−	1.38910e11i	0.111950	−	0.193903i	0.916556	+	0.399905i	$0.130957\pi$
$432$	9.75747e10	+	1.69004e11i	0.134791	+	0.233465i
$433$	4.44852e10			0.0608163			0.0304081	−	0.999538i	$-0.490319\pi$
$433$	4.44852e10			0.0608163			0.0304081	+	0.999538i	$0.490319\pi$
$434$		0			0
$435$	4.08674e11			0.547237
$436$	−1.31280e11	−	2.27384e11i	−0.173984	−	0.301350i
$437$	9.20081e10	−	1.59363e11i	0.120687	−	0.209036i
$438$	2.43152e11	−	4.21152e11i	0.315678	−	0.546770i
$439$	2.87543e11	+	4.98038e11i	0.369498	+	0.639989i	0.989487	−	0.144621i	$-0.0461964\pi$
$439$	2.87543e11	+	4.98038e11i	0.369498	+	0.639989i	−0.619989	+	0.784610i	$0.712863\pi$
$440$	1.44556e11			0.183865
$441$		0			0
$442$	−7.38792e11			−0.920708
$443$	4.14919e11	+	7.18661e11i	0.511855	+	0.886559i	0.999906	+	0.0137433i	$0.00437476\pi$
$443$	4.14919e11	+	7.18661e11i	0.511855	+	0.886559i	−0.488051	+	0.872815i	$0.662292\pi$
$444$	2.81616e11	−	4.87773e11i	0.343901	−	0.595654i
$445$	1.89920e11	−	3.28951e11i	0.229589	−	0.397660i
$446$	3.34543e11	+	5.79445e11i	0.400355	+	0.693434i
$447$	8.48858e11			1.00566
$448$		0			0
$449$	8.23705e11			0.956452			0.478226	−	0.878237i	$-0.341280\pi$
$449$	8.23705e11			0.956452			0.478226	+	0.878237i	$0.341280\pi$
$450$	−1.14282e10	−	1.97942e10i	−0.0131378	−	0.0227553i
$451$	4.22038e11	−	7.30991e11i	0.480349	−	0.831989i
$452$	5.96355e10	−	1.03292e11i	0.0672019	−	0.116397i
$453$	−5.60137e11	−	9.70186e11i	−0.624960	−	1.08246i
$454$	−8.97957e11			−0.991983
$455$		0			0
$456$	1.73830e11			0.188271
$457$	7.99141e11	+	1.38415e12i	0.857039	+	1.48443i	0.874741	+	0.484591i	$0.161032\pi$
$457$	7.99141e11	+	1.38415e12i	0.857039	+	1.48443i	−0.0177019	+	0.999843i	$0.505635\pi$
$458$	3.59266e10	−	6.22267e10i	0.0381523	−	0.0660818i
$459$	−8.25184e11	+	1.42926e12i	−0.867748	+	1.50298i
$460$	−8.75406e10	−	1.51625e11i	−0.0911589	−	0.157892i
$461$	−1.27501e12			−1.31480			−0.657402	−	0.753540i	$-0.728345\pi$
$461$	−1.27501e12			−1.31480			−0.657402	+	0.753540i	$0.728345\pi$
$462$		0			0
$463$	−3.13766e11			−0.317316			−0.158658	−	0.987334i	$-0.550717\pi$
$463$	−3.13766e11			−0.317316			−0.158658	+	0.987334i	$0.550717\pi$
$464$	8.49021e10	+	1.47055e11i	0.0850330	+	0.147281i
$465$	−4.80852e11	+	8.32861e11i	−0.476951	+	0.826103i
$466$	5.15730e11	−	8.93271e11i	0.506624	−	0.877499i
$467$	−4.70743e11	−	8.15351e11i	−0.457992	−	0.793266i	0.540863	−	0.841111i	$-0.318098\pi$
$467$	−4.70743e11	−	8.15351e11i	−0.457992	−	0.793266i	−0.998855	+	0.0478453i	$0.984765\pi$
$468$	−9.42481e10			−0.0908169
$469$		0			0
$470$	−5.57092e11			−0.526607
$471$	2.07244e11	+	3.58957e11i	0.194038	+	0.336084i
$472$	−1.67009e11	+	2.89269e11i	−0.154882	+	0.268264i
$473$	−1.21077e11	+	2.09712e11i	−0.111221	+	0.192641i
$474$	5.13866e11	+	8.90042e11i	0.467571	+	0.809857i
$475$	−1.11044e11			−0.100086
$476$		0			0
$477$	3.68936e11			0.326301
$478$	9.85584e9	+	1.70708e10i	0.00863512	+	0.0149565i
$479$	−3.55020e11	+	6.14913e11i	−0.308137	+	0.533708i	−0.977955	−	0.208817i	$-0.933039\pi$
$479$	−3.55020e11	+	6.14913e11i	−0.308137	+	0.533708i	0.669818	+	0.742525i	$0.266372\pi$
$480$	8.26949e10	−	1.43232e11i	0.0711039	−	0.123155i
$481$	7.41808e11	+	1.28485e12i	0.631886	+	1.09446i
$482$	−1.42136e11			−0.119948
$483$		0			0
$484$	−4.08002e11			−0.337954
$485$	4.98365e11	+	8.63194e11i	0.408987	+	0.708387i
$486$	−1.91238e11	+	3.31233e11i	−0.155493	+	0.269321i
$487$	−6.09315e11	+	1.05536e12i	−0.490864	+	0.850202i	−0.999945	−	0.0105170i	$-0.996652\pi$
$487$	−6.09315e11	+	1.05536e12i	−0.490864	+	0.850202i	0.509080	+	0.860719i	$0.329986\pi$
$488$	−1.02081e11	−	1.76809e11i	−0.0814809	−	0.141129i
$489$	8.12896e11			0.642902
$490$		0			0
$491$	−5.76219e10			−0.0447426			−0.0223713	−	0.999750i	$-0.507122\pi$
$491$	−5.76219e10			−0.0447426			−0.0223713	+	0.999750i	$0.507122\pi$
$492$	−4.82864e11	−	8.36345e11i	−0.371520	−	0.643491i
$493$	−7.18012e11	+	1.24363e12i	−0.547420	+	0.948159i
$494$	−2.28944e11	+	3.96543e11i	−0.172965	+	0.299584i
$495$	7.79775e10	+	1.35061e11i	0.0583776	+	0.101113i
$496$	−3.99589e11			−0.296446
$497$		0			0
$498$	−5.90832e11			−0.430459
$499$	−1.19437e12	−	2.06871e12i	−0.862357	−	1.49365i	−0.869648	−	0.493673i	$-0.835654\pi$
$499$	−1.19437e12	−	2.06871e12i	−0.862357	−	1.49365i	0.00729029	−	0.999973i	$-0.497679\pi$
$500$	−3.71991e11	+	6.44307e11i	−0.266175	+	0.461028i
$501$	−1.99203e10	+	3.45029e10i	−0.0141262	+	0.0244673i
$502$	−7.94253e11	−	1.37569e12i	−0.558203	−	0.966836i
$503$	1.80042e12			1.25406			0.627030	−	0.778995i	$-0.284270\pi$
$503$	1.80042e12			1.25406			0.627030	+	0.778995i	$0.284270\pi$
$504$		0			0
$505$	−1.66261e12			−1.13758
$506$	−1.18472e11	−	2.05200e11i	−0.0803412	−	0.139155i
$507$	2.26313e11	−	3.91985e11i	0.152115	−	0.263471i
$508$	1.00358e11	−	1.73825e11i	0.0668596	−	0.115804i
$509$	6.64302e11	+	1.15061e12i	0.438668	+	0.759795i	0.997587	−	0.0694273i	$-0.0221172\pi$
$509$	6.64302e11	+	1.15061e12i	0.438668	+	0.759795i	−0.558919	+	0.829222i	$0.688784\pi$
$510$	1.39869e12			0.915496
$511$		0			0
$512$	6.87195e10			0.0441942
$513$	5.11432e11	+	8.85827e11i	0.326032	+	0.564704i
$514$	4.45325e11	−	7.71326e11i	0.281412	−	0.487421i
$515$	−1.37208e12	+	2.37651e12i	−0.859503	+	1.48870i
$516$	1.38528e11	+	2.39937e11i	0.0860226	+	0.148995i
$517$	−7.53934e11			−0.464115
$518$		0			0
$519$	−2.06607e11			−0.124995
$520$	2.17828e11	+	3.77289e11i	0.130647	+	0.226287i
$521$	1.09541e12	−	1.89731e12i	0.651341	−	1.12816i	−0.331457	−	0.943470i	$-0.607540\pi$
$521$	1.09541e12	−	1.89731e12i	0.651341	−	1.12816i	0.982798	−	0.184685i	$-0.0591265\pi$
$522$	−9.15972e10	+	1.58651e11i	−0.0539964	+	0.0935246i
$523$	2.54118e11	+	4.40145e11i	0.148518	+	0.257240i	0.930680	−	0.365835i	$-0.119216\pi$
$523$	2.54118e11	+	4.40145e11i	0.148518	+	0.257240i	−0.782162	+	0.623075i	$0.785883\pi$
$524$	1.47805e12			0.856444
$525$		0			0
$526$	−1.59636e12			−0.909276
$527$	−1.68965e12	−	2.92656e12i	−0.954221	−	1.65276i
$528$	1.11914e11	−	1.93841e11i	0.0626661	−	0.108541i
$529$	7.57087e11	−	1.31131e12i	0.420335	−	0.728041i
$530$	−8.52690e11	−	1.47690e12i	−0.469407	−	0.813037i
$531$	−3.60359e11			−0.196702
$532$		0			0
$533$	2.54384e12			1.36527
$534$	−2.94070e11	−	5.09344e11i	−0.156500	−	0.271066i
$535$	−5.32933e11	+	9.23067e11i	−0.281242	+	0.487126i
$536$	3.79890e11	−	6.57988e11i	0.198800	−	0.344331i
$537$	−5.20693e11	−	9.01866e11i	−0.270207	−	0.468013i
$538$	−3.15758e11			−0.162493
$539$		0			0
$540$	9.73199e11			0.492527
$541$	−5.00073e11	−	8.66152e11i	−0.250984	−	0.434717i	0.712813	−	0.701354i	$-0.247421\pi$
$541$	−5.00073e11	−	8.66152e11i	−0.250984	−	0.434717i	−0.963797	+	0.266637i	$0.914087\pi$
$542$	−4.70752e11	+	8.15366e11i	−0.234312	+	0.405841i
$543$	−1.24978e12	+	2.16469e12i	−0.616929	+	1.06855i
$544$	2.90578e11	+	5.03297e11i	0.142255	+	0.246393i
$545$	−1.30937e12			−0.635740
$546$		0			0
$547$	−3.35970e12			−1.60457			−0.802283	−	0.596944i	$-0.796381\pi$
$547$	−3.35970e12			−1.60457			−0.802283	+	0.596944i	$0.796381\pi$
$548$	−9.18621e11	−	1.59110e12i	−0.435135	−	0.753675i
$549$	1.10131e11	−	1.90752e11i	0.0517408	−	0.0896177i
$550$	−7.14916e10	+	1.23827e11i	−0.0333137	+	0.0577010i
$551$	4.45010e11	+	7.70779e11i	0.205678	+	0.356244i
$552$	−2.71093e11			−0.124278
$553$		0			0
$554$	−6.71191e11			−0.302728
$555$	−1.40440e12	−	2.43250e12i	−0.628309	−	1.08826i
$556$	3.98489e11	−	6.90203e11i	0.176840	−	0.306295i
$557$	−6.95038e10	+	1.20384e11i	−0.0305957	+	0.0529933i	−0.880918	−	0.473269i	$-0.843074\pi$
$557$	−6.95038e10	+	1.20384e11i	−0.0305957	+	0.0529933i	0.850322	+	0.526263i	$0.176407\pi$
$558$	−2.15550e11	−	3.73343e11i	−0.0941224	−	0.163025i
$559$	−7.29795e11			−0.316117
$560$		0			0
$561$	1.89290e12			0.806855
$562$	−2.10173e11	−	3.64030e11i	−0.0888717	−	0.153930i
$563$	1.94083e12	−	3.36162e12i	0.814143	−	1.41014i	−0.0957985	−	0.995401i	$-0.530540\pi$
$563$	1.94083e12	−	3.36162e12i	0.814143	−	1.41014i	0.909942	−	0.414736i	$-0.136126\pi$
$564$	−4.31297e11	+	7.47028e11i	−0.179482	+	0.310872i
$565$	−2.97399e11	−	5.15110e11i	−0.122778	−	0.212658i
$566$	−1.97947e12			−0.810728
$567$		0			0
$568$	1.51663e12			0.611381
$569$	−6.22799e11	−	1.07872e12i	−0.249082	−	0.431423i	0.714189	−	0.699953i	$-0.246796\pi$
$569$	−6.22799e11	−	1.07872e12i	−0.249082	−	0.431423i	−0.963271	+	0.268530i	$0.913462\pi$
$570$	4.33441e11	−	7.50742e11i	0.171986	−	0.297888i
$571$	1.28293e12	−	2.22211e12i	0.505059	−	0.874788i	−0.494924	−	0.868936i	$-0.664804\pi$
$571$	1.28293e12	−	2.22211e12i	0.505059	−	0.874788i	0.999983	−	0.00585145i	$-0.00186258\pi$
$572$	2.94795e11	+	5.10599e11i	0.115143	+	0.199434i
$573$	−2.20196e12			−0.853324
$574$		0			0
$575$	1.73176e11			0.0660669
$576$	3.70693e10	+	6.42058e10i	0.0140318	+	0.0243038i
$577$	−1.89405e12	+	3.28059e12i	−0.711378	+	1.23214i	0.252963	+	0.967476i	$0.418595\pi$
$577$	−1.89405e12	+	3.28059e12i	−0.711378	+	1.23214i	−0.964340	+	0.264666i	$0.914738\pi$
$578$	−1.50870e12	+	2.61315e12i	−0.562249	+	0.973843i
$579$	−9.54821e11	−	1.65380e12i	−0.353076	−	0.611546i
$580$	8.46804e11			0.310711
$581$		0			0
$582$	1.54332e12			0.557575
$583$	−1.15398e12	−	1.99875e12i	−0.413703	−	0.716555i
$584$	5.03830e11	−	8.72658e11i	0.179236	−	0.310446i
$585$	−2.35005e11	+	4.07041e11i	−0.0829614	+	0.143693i
$586$	−2.67078e11	−	4.62593e11i	−0.0935619	−	0.162054i
$587$	−2.25752e12			−0.784802			−0.392401	−	0.919794i	$-0.628355\pi$
$587$	−2.25752e12			−0.784802			−0.392401	+	0.919794i	$0.628355\pi$
$588$		0			0
$589$	−2.09442e12			−0.717043
$590$	8.32867e11	+	1.44257e12i	0.282971	+	0.490119i
$591$	−1.25805e12	+	2.17901e12i	−0.424184	+	0.734709i
$592$	5.83530e11	−	1.01070e12i	0.195261	−	0.338202i
$593$	2.26382e12	+	3.92106e12i	0.751790	+	1.30214i	0.946954	+	0.321368i	$0.104143\pi$
$593$	2.26382e12	+	3.92106e12i	0.751790	+	1.30214i	−0.195164	+	0.980771i	$0.562524\pi$
$594$	1.31707e12			0.434079
$595$		0			0
$596$	1.75890e12			0.570996
$597$	1.71129e12	+	2.96404e12i	0.551365	+	0.954991i
$598$	3.57046e11	−	6.18421e11i	0.114174	−	0.197756i
$599$	−1.94812e12	+	3.37424e12i	−0.618293	+	1.07092i	0.371504	+	0.928431i	$0.378842\pi$
$599$	−1.94812e12	+	3.37424e12i	−0.618293	+	1.07092i	−0.989797	+	0.142484i	$0.954491\pi$
$600$	8.17953e10	+	1.41674e11i	0.0257660	+	0.0446281i
$601$	4.27283e12			1.33592			0.667960	−	0.744197i	$-0.267168\pi$
$601$	4.27283e12			1.33592			0.667960	+	0.744197i	$0.267168\pi$
$602$		0			0
$603$	8.19693e11			0.252478
$604$	−1.16065e12	−	2.01030e12i	−0.354841	−	0.614603i
$605$	−1.01734e12	+	1.76209e12i	−0.308722	+	0.534722i
$606$	−1.28719e12	+	2.22947e12i	−0.387717	+	0.671545i
$607$	−2.42051e12	−	4.19245e12i	−0.723699	−	1.25348i	−0.959507	−	0.281683i	$-0.909107\pi$
$607$	−2.42051e12	−	4.19245e12i	−0.723699	−	1.25348i	0.235809	−	0.971799i	$-0.424226\pi$
$608$	3.60189e11			0.106897
$609$		0			0
$610$	−1.01814e12			−0.297732
$611$	−1.13609e12	−	1.96776e12i	−0.329781	−	0.571197i
$612$	−3.13493e11	+	5.42985e11i	−0.0903329	+	0.156461i
$613$	3.36194e12	−	5.82305e12i	0.961652	−	1.66563i	0.243298	−	0.969952i	$-0.421771\pi$
$613$	3.36194e12	−	5.82305e12i	0.961652	−	1.66563i	0.718354	−	0.695678i	$-0.244896\pi$
$614$	1.86218e12	+	3.22540e12i	0.528768	+	0.915853i
$615$	−4.81603e12			−1.35754
$616$		0			0
$617$	8.50617e11			0.236293			0.118146	−	0.992996i	$-0.462305\pi$
$617$	8.50617e11			0.236293			0.118146	+	0.992996i	$0.462305\pi$
$618$	2.12451e12	+	3.67976e12i	0.585883	+	1.01478i
$619$	2.98722e12	−	5.17402e12i	0.817823	−	1.41651i	−0.0894592	−	0.995990i	$-0.528514\pi$
$619$	2.98722e12	−	5.17402e12i	0.817823	−	1.41651i	0.907283	−	0.420521i	$-0.138153\pi$
$620$	−9.96363e11	+	1.72575e12i	−0.270804	+	0.469046i
$621$	−7.97595e11	−	1.38147e12i	−0.215214	−	0.372761i
$622$	1.22050e11			0.0326951
$623$		0			0
$624$	6.74564e11			0.178112
$625$	1.53940e12	+	2.66633e12i	0.403546	+	0.698962i
$626$	−1.35733e12	+	2.35097e12i	−0.353266	+	0.611875i
$627$	5.86592e11	−	1.01601e12i	0.151577	−	0.262538i
$628$	4.29425e11	+	7.43786e11i	0.110171	+	0.190822i
$629$	9.86976e12			2.51408
$630$		0			0
$631$	−5.96909e12			−1.49891			−0.749455	−	0.662055i	$-0.769685\pi$
$631$	−5.96909e12			−1.49891			−0.749455	+	0.662055i	$0.769685\pi$
$632$	1.06477e12	+	1.84424e12i	0.265478	+	0.459822i
$633$	8.07326e11	−	1.39833e12i	0.199863	−	0.346173i
$634$	6.88041e11	−	1.19172e12i	0.169127	−	0.292936i
$635$	−5.00478e11	−	8.66854e11i	−0.122153	−	0.211575i
$636$	−2.64059e12			−0.639947
$637$		0			0
$638$	1.14601e12			0.273840
$639$	8.18113e11	+	1.41701e12i	0.194115	+	0.336217i
$640$	1.71350e11	−	2.96787e11i	0.0403715	−	0.0699254i
$641$	2.10779e12	−	3.65080e12i	0.493136	−	0.854136i	−0.506833	−	0.862044i	$-0.669184\pi$
$641$	2.10779e12	−	3.65080e12i	0.493136	−	0.854136i	0.999969	+	0.00790799i	$0.00251722\pi$
$642$	8.25187e11	+	1.42927e12i	0.191710	+	0.332051i
$643$	5.53403e12			1.27671			0.638354	−	0.769743i	$-0.279615\pi$
$643$	5.53403e12			1.27671			0.638354	+	0.769743i	$0.279615\pi$
$644$		0			0
$645$	1.38166e12			0.314327
$646$	1.52305e12	+	2.63800e12i	0.344087	+	0.595976i
$647$	−1.25955e12	+	2.18160e12i	−0.282582	+	0.489447i	−0.972020	−	0.234898i	$-0.924524\pi$
$647$	−1.25955e12	+	2.18160e12i	−0.282582	+	0.489447i	0.689438	+	0.724345i	$0.257858\pi$
$648$	5.75311e11	−	9.96469e11i	0.128179	−	0.222012i
$649$	1.12715e12	+	1.95228e12i	0.249391	+	0.431958i
$650$	−4.30916e11			−0.0946853
$651$		0			0
$652$	1.68438e12			0.365028
$653$	3.80173e12	+	6.58478e12i	0.818223	+	1.41720i	0.906991	+	0.421151i	$0.138374\pi$
$653$	3.80173e12	+	6.58478e12i	0.818223	+	1.41720i	−0.0887679	+	0.996052i	$0.528293\pi$
$654$	−1.01371e12	+	1.75580e12i	−0.216677	+	0.375296i
$655$	3.68548e12	−	6.38344e12i	0.782364	−	1.35509i
$656$	−1.00053e12	−	1.73297e12i	−0.210942	−	0.365363i
$657$	1.08712e12			0.227632
$658$		0			0
$659$	−4.45281e12			−0.919708			−0.459854	−	0.887994i	$-0.652098\pi$
$659$	−4.45281e12			−0.919708			−0.459854	+	0.887994i	$0.652098\pi$
$660$	−5.58110e11	−	9.66675e11i	−0.114491	−	0.198304i
$661$	−2.65674e12	+	4.60161e12i	−0.541305	+	0.937569i	0.457524	+	0.889197i	$0.348736\pi$
$661$	−2.65674e12	+	4.60161e12i	−0.541305	+	0.937569i	−0.998829	+	0.0483713i	$0.984597\pi$
$662$	−2.87420e12	+	4.97827e12i	−0.581643	+	1.00744i
$663$	2.85237e12	+	4.94046e12i	0.573318	+	0.993016i
$664$	−1.22425e12			−0.244407
$665$		0			0
$666$	1.25909e12			0.247984
$667$	−6.94006e11	−	1.20205e12i	−0.135768	−	0.235157i
$668$	−4.12763e10	+	7.14927e10i	−0.00802060	+	0.0138921i
$669$	2.58325e12	−	4.47431e12i	0.498595	−	0.863593i
$670$	−1.89449e12	−	3.28135e12i	−0.363208	−	0.629095i
$671$	−1.37789e12			−0.262400
$672$		0			0
$673$	−2.03778e12			−0.382904			−0.191452	−	0.981502i	$-0.561320\pi$
$673$	−2.03778e12			−0.382904			−0.191452	+	0.981502i	$0.561320\pi$
$674$	1.79065e12	+	3.10150e12i	0.334227	+	0.578897i
$675$	−4.81306e11	+	8.33647e11i	−0.0892389	+	0.154566i
$676$	4.68937e11	−	8.12223e11i	0.0863683	−	0.149594i
$677$	−5.04490e12	−	8.73803e12i	−0.923004	−	1.59869i	−0.794740	−	0.606950i	$-0.792393\pi$
$677$	−5.04490e12	−	8.73803e12i	−0.923004	−	1.59869i	−0.128264	−	0.991740i	$-0.540941\pi$
$678$	−9.20977e11			−0.167385
$679$		0			0
$680$	2.89820e12			0.519802
$681$	3.46689e12	+	6.00482e12i	0.617700	+	1.06989i
$682$	−1.34842e12	+	2.33553e12i	−0.238668	+	0.413385i
$683$	−4.64538e12	+	8.04603e12i	−0.816823	+	1.41478i	0.0911884	+	0.995834i	$0.470933\pi$
$683$	−4.64538e12	+	8.04603e12i	−0.816823	+	1.41478i	−0.908011	+	0.418945i	$0.862400\pi$
$684$	1.94297e11	+	3.36531e11i	0.0339401	+	0.0587859i
$685$	−9.16222e12			−1.58999
$686$		0			0
$687$	−5.54830e11			−0.0950287
$688$	2.87040e11	+	4.97167e11i	0.0488421	+	0.0845969i
$689$	3.47781e12	−	6.02374e12i	0.587921	−	1.01831i
$690$	−6.75964e11	+	1.17080e12i	−0.113528	+	0.196636i
$691$	3.42773e12	+	5.93700e12i	0.571947	+	0.990641i	0.996366	+	0.0851749i	$0.0271449\pi$
$691$	3.42773e12	+	5.93700e12i	0.571947	+	0.990641i	−0.424419	+	0.905466i	$0.639522\pi$
$692$	−4.28106e11			−0.0709699
$693$		0			0
$694$	1.99833e12			0.327001
$695$	−1.98724e12	−	3.44201e12i	−0.323087	−	0.559603i
$696$	6.55590e11	−	1.13552e12i	0.105899	−	0.183422i
$697$	8.46144e12	−	1.46556e13i	1.35799	−	2.35211i
$698$	3.31260e10	+	5.73760e10i	0.00528226	+	0.00914915i
$699$	−7.96465e12			−1.26188
$700$		0			0
$701$	2.51709e12			0.393702			0.196851	−	0.980433i	$-0.436928\pi$
$701$	2.51709e12			0.393702			0.196851	+	0.980433i	$0.436928\pi$
$702$	1.98466e12	+	3.43753e12i	0.308439	+	0.534232i
$703$	3.05854e12	−	5.29754e12i	0.472297	−	0.818042i
$704$	2.31895e11	−	4.01653e11i	0.0355806	−	0.0616275i
$705$	2.15085e12	+	3.72539e12i	0.327914	+	0.567964i
$706$	−2.76469e12			−0.418817
$707$		0			0
$708$	2.57920e12			0.385776
$709$	3.29616e12	+	5.70912e12i	0.489892	+	0.848519i	0.999932	−	0.0116322i	$-0.00370273\pi$
$709$	3.29616e12	+	5.70912e12i	0.489892	+	0.848519i	−0.510040	+	0.860151i	$0.670369\pi$
$710$	3.78167e12	−	6.55005e12i	0.558498	−	0.967346i
$711$	−1.14874e12	+	1.98967e12i	−0.168580	+	0.291990i
$712$	−6.09335e11	−	1.05540e12i	−0.0888579	−	0.153906i
$713$	3.26631e12			0.473320
$714$		0			0
$715$	2.94025e12			0.420734
$716$	−1.07891e12	−	1.86874e12i	−0.153419	−	0.265729i
$717$	7.61041e10	−	1.31816e11i	0.0107540	−	0.0186265i
$718$	1.72063e11	−	2.98022e11i	0.0241617	−	0.0418494i
$719$	−3.94608e11	−	6.83480e11i	−0.0550662	−	0.0953775i	0.837178	−	0.546930i	$-0.184204\pi$
$719$	−3.94608e11	−	6.83480e11i	−0.0550662	−	0.0953775i	−0.892245	+	0.451553i	$0.850870\pi$
$720$	3.69725e11			0.0512722
$721$		0			0
$722$	−3.27509e12			−0.448545
$723$	5.48768e11	+	9.50493e11i	0.0746906	+	0.129368i
$724$	−2.58965e12	+	4.48540e12i	−0.350281	+	0.606705i
$725$	−4.18796e11	+	7.25376e11i	−0.0562965	+	0.0975084i
$726$	1.57524e12	+	2.72839e12i	0.210442	+	0.364495i
$727$	4.67869e12			0.621183			0.310592	−	0.950543i	$-0.399473\pi$
$727$	4.67869e12			0.621183			0.310592	+	0.950543i	$0.399473\pi$
$728$		0			0
$729$	8.48259e12			1.11238
$730$	−2.51257e12	−	4.35190e12i	−0.327465	−	0.567187i
$731$	−2.42748e12	+	4.20452e12i	−0.314432	+	0.544613i
$732$	−7.88241e11	+	1.36527e12i	−0.101475	+	0.175760i
$733$	−3.69124e12	−	6.39342e12i	−0.472285	−	0.818022i	0.527212	−	0.849734i	$-0.323238\pi$
$733$	−3.69124e12	−	6.39342e12i	−0.472285	−	0.818022i	−0.999497	+	0.0317116i	$0.989904\pi$
$734$	8.77754e12			1.11620
$735$		0			0
$736$	−5.61726e11			−0.0705626
$737$	−2.56388e12	−	4.44078e12i	−0.320107	−	0.554441i
$738$	1.07943e12	−	1.86963e12i	0.133949	−	0.232007i
$739$	1.86389e12	−	3.22835e12i	0.229890	−	0.398181i	−0.727885	−	0.685699i	$-0.759497\pi$
$739$	1.86389e12	−	3.22835e12i	0.229890	−	0.398181i	0.957775	+	0.287518i	$0.0928301\pi$
$740$	−2.91003e12	−	5.04032e12i	−0.356742	−	0.617896i
$741$	3.53569e12			0.430816
$742$		0			0
$743$	8.63062e12			1.03894			0.519472	−	0.854487i	$-0.326129\pi$
$743$	8.63062e12			1.03894			0.519472	+	0.854487i	$0.326129\pi$
$744$	1.54276e12	+	2.67213e12i	0.184595	+	0.319727i
$745$	4.38577e12	−	7.59637e12i	0.521606	−	0.903448i
$746$	1.00819e12	−	1.74624e12i	0.119184	−	0.206433i
$747$	−6.60395e11	−	1.14384e12i	−0.0775999	−	0.134407i
$748$	3.92224e12			0.458118
$749$		0			0
$750$	5.74482e12			0.662980
$751$	−8.57905e12	−	1.48594e13i	−0.984146	−	1.70459i	−0.645671	−	0.763616i	$-0.723422\pi$
$751$	−8.57905e12	−	1.48594e13i	−0.984146	−	1.70459i	−0.338475	−	0.940975i	$-0.609911\pi$
$752$	−8.93680e11	+	1.54790e12i	−0.101907	+	0.176507i
$753$	−6.13300e12	+	1.06227e13i	−0.695178	+	1.20408i
$754$	1.72690e12	+	2.99108e12i	0.194579	+	0.337021i
$755$	−1.15762e13			−1.29659
$756$		0			0
$757$	−6.69732e12			−0.741258			−0.370629	−	0.928781i	$-0.620858\pi$
$757$	−6.69732e12			−0.741258			−0.370629	+	0.928781i	$0.620858\pi$
$758$	4.24802e11	+	7.35778e11i	0.0467385	+	0.0809535i
$759$	−9.14808e11	+	1.58449e12i	−0.100056	+	0.173302i
$760$	8.98123e11	−	1.55559e12i	0.0976505	−	0.169136i
$761$	1.54048e12	+	2.66819e12i	0.166504	+	0.288393i	0.937188	−	0.348824i	$-0.113419\pi$
$761$	1.54048e12	+	2.66819e12i	0.166504	+	0.288393i	−0.770684	+	0.637217i	$0.780085\pi$
$762$	−1.54987e12			−0.166532
$763$		0			0
$764$	−4.56263e12			−0.484502
$765$	1.56337e12	+	2.70784e12i	0.165039	+	0.285855i
$766$	4.98152e12	−	8.62825e12i	0.522797	−	0.905510i
$767$	−3.39695e12	+	5.88370e12i	−0.354414	+	0.613862i
$768$	−2.65316e11	−	4.59541e11i	−0.0275194	−	0.0476650i
$769$	3.26639e11			0.0336821			0.0168410	−	0.999858i	$-0.494639\pi$
$769$	3.26639e11			0.0336821			0.0168410	+	0.999858i	$0.494639\pi$
$770$		0			0
$771$	−6.87736e12			−0.700934
$772$	−1.97846e12	−	3.42680e12i	−0.200470	−	0.347224i
$773$	−9.81182e12	+	1.69946e13i	−0.988421	+	1.71200i	−0.362803	+	0.931866i	$0.618180\pi$
$773$	−9.81182e12	+	1.69946e13i	−0.988421	+	1.71200i	−0.625618	+	0.780129i	$0.715153\pi$
$774$	−3.09675e11	+	5.36373e11i	−0.0310150	+	0.0537195i
$775$	−9.85524e11	−	1.70698e12i	−0.0981317	−	0.169969i
$776$	3.19789e12			0.316581
$777$		0			0
$778$	−3.80607e12			−0.372450
$779$	−5.24423e12	−	9.08327e12i	−0.510227	−	0.883739i
$780$	1.68201e12	−	2.91332e12i	0.162705	−	0.281814i
$781$	5.11788e12	−	8.86443e12i	0.492221	−	0.852553i
$782$	−2.37524e12	−	4.11404e12i	−0.227132	−	0.393404i
$783$	7.71535e12			0.733547
$784$		0			0
$785$	4.28304e12			0.402567
$786$	−5.70655e12	−	9.88404e12i	−0.533301	−	0.923705i
$787$	−7.33958e12	+	1.27125e13i	−0.682001	+	1.18126i	0.292368	+	0.956306i	$0.405557\pi$
$787$	−7.33958e12	+	1.27125e13i	−0.682001	+	1.18126i	−0.974369	+	0.224954i	$0.927777\pi$
$788$	−2.60678e12	+	4.51507e12i	−0.240844	+	0.417154i
$789$	6.16334e12	+	1.06752e13i	0.566199	+	0.980686i
$790$	1.06199e13			0.970060
$791$		0			0
$792$	5.00363e11			0.0451878
$793$	−2.07632e12	−	3.59629e12i	−0.186451	−	0.322942i
$794$	−1.35636e12	+	2.34929e12i	−0.121111	+	0.209770i
$795$	−6.58424e12	+	1.14042e13i	−0.584593	+	1.01254i
$796$	3.54592e12	+	6.14172e12i	0.313055	+	0.542227i
$797$	−9.49591e12			−0.833632			−0.416816	−	0.908991i	$-0.636854\pi$
$797$	−9.49591e12			−0.833632			−0.416816	+	0.908991i	$0.636854\pi$
$798$		0			0
$799$	−1.51156e13			−1.31209
$800$	1.69486e11	+	2.93558e11i	0.0146295	+	0.0253390i
$801$	6.57386e11	−	1.13863e12i	0.0564253	−	0.0977315i
$802$	7.22837e12	−	1.25199e13i	0.616958	−	1.06860i
$803$	−3.40036e12	−	5.88959e12i	−0.288606	−	0.499879i
$804$	−5.86680e12			−0.495164
$805$		0			0
$806$	−8.12759e12			−0.678351
$807$	1.21910e12	+	2.11154e12i	0.101183	+	0.175254i
$808$	−2.66715e12	+	4.61963e12i	−0.220138	+	0.381291i
$809$	−7.23685e12	+	1.25346e13i	−0.593993	+	1.02883i	0.399695	+	0.916648i	$0.369116\pi$
$809$	−7.23685e12	+	1.25346e13i	−0.593993	+	1.02883i	−0.993688	+	0.112178i	$0.964217\pi$
$810$	−2.86905e12	−	4.96933e12i	−0.234183	−	0.405617i
$811$	7.11471e12			0.577516			0.288758	−	0.957402i	$-0.406758\pi$
$811$	7.11471e12			0.577516			0.288758	+	0.957402i	$0.406758\pi$
$812$		0			0
$813$	7.27003e12			0.583618
$814$	−3.93825e12	−	6.82126e12i	−0.314408	−	0.544571i
$815$	4.19996e12	−	7.27455e12i	0.333454	−	0.577559i
$816$	2.24377e12	−	3.88632e12i	0.177163	−	0.306854i
$817$	1.50450e12	+	2.60588e12i	0.118139	+	0.204623i
$818$	−1.67216e13			−1.30583
$819$		0			0
$820$	−9.97919e12			−0.770785
$821$	−3.73509e12	−	6.46937e12i	−0.286918	−	0.496956i	0.686155	−	0.727456i	$-0.259297\pi$
$821$	−3.73509e12	−	6.46937e12i	−0.286918	−	0.496956i	−0.973072	+	0.230500i	$0.925964\pi$
$822$	−7.09333e12	+	1.22860e13i	−0.541910	+	0.938616i
$823$	−7.92422e12	+	1.37252e13i	−0.602085	+	1.04284i	0.390420	+	0.920637i	$0.372330\pi$
$823$	−7.92422e12	+	1.37252e13i	−0.602085	+	1.04284i	−0.992505	+	0.122204i	$0.961004\pi$
$824$	4.40215e12	+	7.62475e12i	0.332654	+	0.576173i
$825$	1.10408e12			0.0829767
$826$		0			0
$827$	2.27588e12			0.169190			0.0845948	−	0.996415i	$-0.473040\pi$
$827$	2.27588e12			0.169190			0.0845948	+	0.996415i	$0.473040\pi$
$828$	−3.03011e11	−	5.24831e11i	−0.0224038	−	0.0388046i
$829$	6.39444e12	−	1.10755e13i	0.470226	−	0.814456i	−0.529194	−	0.848501i	$-0.677506\pi$
$829$	6.39444e12	−	1.10755e13i	0.470226	−	0.814456i	0.999420	+	0.0340449i	$0.0108389\pi$
$830$	−3.05263e12	+	5.28731e12i	−0.223266	+	0.386708i
$831$	2.59138e12	+	4.48840e12i	0.188506	+	0.326503i
$832$	1.39775e12			0.101129
$833$		0			0
$834$	−6.15404e12			−0.440467
$835$	2.05843e11	+	3.56530e11i	0.0146537	+	0.0253809i
$836$	1.21546e12	−	2.10524e12i	0.0860624	−	0.149065i
$837$	−9.07800e12	+	1.57236e13i	−0.639331	+	1.10735i
$838$	3.34006e12	+	5.78515e12i	0.233968	+	0.405244i
$839$	1.07948e13			0.752119			0.376060	−	0.926595i	$-0.377279\pi$
$839$	1.07948e13			0.752119			0.376060	+	0.926595i	$0.377279\pi$
$840$		0			0
$841$	−7.79383e12			−0.537241
$842$	−1.34318e12	−	2.32646e12i	−0.0920936	−	0.159511i
$843$	−1.62290e12	+	2.81094e12i	−0.110679	+	0.191703i
$844$	1.67284e12	−	2.89745e12i	0.113479	−	0.196551i
$845$	−2.33856e12	−	4.05051e12i	−0.157795	−	0.273309i
$846$	−1.92831e12			−0.129422
$847$		0			0
$848$	−5.47150e12			−0.363350
$849$	7.64246e12	+	1.32371e13i	0.504834	+	0.874398i
$850$	−1.43333e12	+	2.48261e12i	−0.0941808	+	0.163126i
$851$	−4.76988e12	+	8.26168e12i	−0.311763	+	0.539990i
$852$	−5.85549e12	−	1.01420e13i	−0.380702	−	0.659395i
$853$	−1.76557e13			−1.14187			−0.570933	−	0.820997i	$-0.693418\pi$
$853$	−1.76557e13			−1.14187			−0.570933	+	0.820997i	$0.693418\pi$
$854$		0			0
$855$	1.93789e12			0.124017
$856$	1.70985e12	+	2.96155e12i	0.108849	+	0.188533i
$857$	8.21628e12	−	1.42310e13i	0.520309	−	0.901202i	−0.479412	−	0.877590i	$-0.659150\pi$
$857$	8.21628e12	−	1.42310e13i	0.520309	−	0.901202i	0.999721	−	0.0236121i	$-0.00751667\pi$
$858$	2.27632e12	−	3.94271e12i	0.143397	−	0.248371i
$859$	−4.22012e11	−	7.30946e11i	−0.0264457	−	0.0458053i	0.852500	−	0.522728i	$-0.175086\pi$
$859$	−4.22012e11	−	7.30946e11i	−0.0264457	−	0.0458053i	−0.878945	+	0.476922i	$0.841752\pi$
$860$	2.86290e12			0.178469
$861$		0			0
$862$	−2.56639e12			−0.158321
$863$	1.23131e12	+	2.13270e12i	0.0755649	+	0.130882i	0.901332	−	0.433129i	$-0.142591\pi$
$863$	1.23131e12	+	2.13270e12i	0.0755649	+	0.130882i	−0.825767	+	0.564012i	$0.809257\pi$
$864$	1.56120e12	−	2.70407e12i	0.0953115	−	0.165084i
$865$	−1.06747e12	+	1.84891e12i	−0.0648312	+	0.112291i
$866$	−3.55882e11	−	6.16405e11i	−0.0215018	−	0.0372422i
$867$	2.32996e13			1.40043
$868$		0			0
$869$	1.43723e13			0.854944
$870$	−3.26939e12	−	5.66276e12i	−0.193478	−	0.335113i
$871$	7.72692e12	−	1.33834e13i	0.454909	−	0.787925i
$872$	−2.10048e12	+	3.63814e12i	−0.123026	+	0.213086i
$873$	1.72503e12	+	2.98784e12i	0.100515	+	0.174098i
$874$	−2.94426e12			−0.170677
$875$		0			0
$876$	−7.78086e12			−0.446436
$877$	−1.50166e12	−	2.60096e12i	−0.0857184	−	0.148469i	0.819979	−	0.572394i	$-0.193985\pi$
$877$	−1.50166e12	−	2.60096e12i	−0.0857184	−	0.148469i	−0.905697	+	0.423925i	$0.860652\pi$
$878$	4.60068e12	−	7.96861e12i	0.261274	−	0.452540i
$879$	−2.06230e12	+	3.57201e12i	−0.116521	+	0.201819i
$880$	−1.15645e12	−	2.00302e12i	−0.0650060	−	0.112594i
$881$	−4.67820e11			−0.0261630			−0.0130815	−	0.999914i	$-0.504164\pi$
$881$	−4.67820e11			−0.0261630			−0.0130815	+	0.999914i	$0.504164\pi$
$882$		0			0
$883$	−9.28272e12			−0.513869			−0.256934	−	0.966429i	$-0.582712\pi$
$883$	−9.28272e12			−0.513869			−0.256934	+	0.966429i	$0.582712\pi$
$884$	5.91034e12	+	1.02370e13i	0.325520	+	0.563816i
$885$	6.43116e12	−	1.11391e13i	0.352407	−	0.610387i
$886$	6.63871e12	−	1.14986e13i	0.361936	−	0.626892i
$887$	−4.98915e12	−	8.64147e12i	−0.270627	−	0.468739i	0.698396	−	0.715712i	$-0.253898\pi$
$887$	−4.98915e12	−	8.64147e12i	−0.270627	−	0.468739i	−0.969022	+	0.246973i	$0.920564\pi$
$888$	−9.01171e12			−0.486350
$889$		0			0
$890$	−6.07744e12			−0.324688
$891$	−3.88279e12	−	6.72519e12i	−0.206393	−	0.357483i
$892$	5.35268e12	−	9.27112e12i	0.283093	−	0.490332i
$893$	−4.68418e12	+	8.11323e12i	−0.246491	+	0.426936i
$894$	−6.79087e12	−	1.17621e13i	−0.355555	−	0.615839i
$895$	−1.07610e13			−0.560594
$896$		0			0
$897$	−5.51401e12			−0.284382
$898$	−6.58964e12	−	1.14136e13i	−0.338157	−	0.585705i
$899$	−7.89899e12	+	1.36814e13i	−0.403323	+	0.698576i
$900$	−1.82851e11	+	3.16708e11i	−0.00928981	+	0.0160904i
$901$	−2.31361e13	−	4.00729e13i	−1.16958	−	2.02577i
$902$	−1.35052e13			−0.679317
$903$		0			0
$904$	−1.90834e12			−0.0950379
$905$	1.29144e13	+	2.23684e13i	0.639965	+	1.10845i
$906$	−8.96220e12	+	1.55230e13i	−0.441914	+	0.765417i
$907$	5.19978e11	−	9.00628e11i	0.0255124	−	0.0441888i	−0.852987	−	0.521932i	$-0.825212\pi$
$907$	5.19978e11	−	9.00628e11i	0.0255124	−	0.0441888i	0.878500	+	0.477743i	$0.158545\pi$
$908$	7.18365e12	+	1.24425e13i	0.350719	+	0.607463i
$909$	−5.75494e12			−0.279578
$910$		0			0
$911$	2.92798e13			1.40843			0.704215	−	0.709986i	$-0.251299\pi$
$911$	2.92798e13			1.40843			0.704215	+	0.709986i	$0.251299\pi$
$912$	−1.39064e12	−	2.40866e12i	−0.0665638	−	0.115292i
$913$	−4.13124e12	+	7.15552e12i	−0.196771	+	0.340818i
$914$	1.27863e13	−	2.21464e13i	0.606018	−	1.04965i
$915$	3.93092e12	+	6.80855e12i	0.185395	+	0.321114i
$916$	−1.14965e12			−0.0539556
$917$		0			0
$918$	2.64059e13			1.22718
$919$	6.57595e12	+	1.13899e13i	0.304115	+	0.526743i	0.977064	−	0.212946i	$-0.0683058\pi$
$919$	6.57595e12	+	1.13899e13i	0.304115	+	0.526743i	−0.672949	+	0.739689i	$0.734972\pi$
$920$	−1.40065e12	+	2.42600e12i	−0.0644591	+	0.111646i
$921$	1.43793e13	−	2.49056e13i	0.658519	−	1.14059i
$922$	1.02001e13	+	1.76671e13i	0.464853	+	0.805149i
$923$	3.08481e13			1.39901
$924$		0			0
$925$	5.75675e12			0.258547
$926$	2.51013e12	+	4.34767e12i	0.112188	+	0.194315i
$927$	−4.74929e12	+	8.22602e12i	−0.211237	+	0.365873i
$928$	1.35843e12	−	2.35288e12i	0.0601274	−	0.104144i
$929$	1.68476e13	+	2.91809e13i	0.742108	+	1.28537i	0.951534	+	0.307545i	$0.0995074\pi$
$929$	1.68476e13	+	2.91809e13i	0.742108	+	1.28537i	−0.209425	+	0.977825i	$0.567159\pi$
$930$	1.53873e13			0.674510
$931$		0			0
$932$	−1.65034e13			−0.716475
$933$	−4.71220e11	−	8.16176e11i	−0.0203590	−	0.0352628i
$934$	−7.53189e12	+	1.30456e13i	−0.323849	+	0.560924i
$935$	9.78000e12	−	1.69395e13i	0.418492	−	0.724849i
$936$	7.53985e11	+	1.30594e12i	0.0321086	+	0.0556137i
$937$	−1.90556e13			−0.807598			−0.403799	−	0.914848i	$-0.632311\pi$
$937$	−1.90556e13			−0.807598			−0.403799	+	0.914848i	$0.632311\pi$
$938$		0			0
$939$	2.09619e13			0.879905
$940$	4.45674e12	+	7.71929e12i	0.186184	+	0.322480i
$941$	−8.37175e12	+	1.45003e13i	−0.348067	+	0.602870i	−0.985906	−	0.167300i	$-0.946495\pi$
$941$	−8.37175e12	+	1.45003e13i	−0.348067	+	0.602870i	0.637839	+	0.770170i	$0.279829\pi$
$942$	3.31590e12	−	5.74331e12i	0.137206	−	0.237647i
$943$	8.17854e12	+	1.41656e13i	0.336801	+	0.583356i
$944$	5.34430e12			0.219037
$945$		0			0
$946$	3.87448e12			0.157291
$947$	1.17483e13	+	2.03486e13i	0.474677	+	0.822165i	0.999579	−	0.0289973i	$-0.00923141\pi$
$947$	1.17483e13	+	2.03486e13i	0.474677	+	0.822165i	−0.524902	+	0.851163i	$0.675898\pi$
$948$	8.22186e12	−	1.42407e13i	0.330623	−	0.572655i
$949$	1.02478e13	−	1.77498e13i	0.410142	−	0.710387i
$950$	8.88352e11	+	1.53867e12i	0.0353858	+	0.0612900i
$951$	−1.06257e13			−0.421256
$952$		0			0
$953$	2.77607e13			1.09022			0.545108	−	0.838366i	$-0.316489\pi$
$953$	2.77607e13			1.09022			0.545108	+	0.838366i	$0.316489\pi$
$954$	−2.95149e12	−	5.11212e12i	−0.115365	−	0.199818i
$955$	−1.13768e13	+	1.97052e13i	−0.442594	+	0.766594i
$956$	1.57693e11	−	2.73133e11i	0.00610595	−	0.0105758i
$957$	−4.42459e12	−	7.66362e12i	−0.170518	−	0.295346i
$958$	1.13606e13			0.435771
$959$		0			0
$960$	−2.64624e12			−0.100556
$961$	−5.36834e12	−	9.29823e12i	−0.203041	−	0.351678i
$962$	1.18689e13	−	2.05576e13i	0.446811	−	0.773899i
$963$	−1.84468e12	+	3.19509e12i	−0.0691200	+	0.119719i
$964$	1.13709e12	+	1.96949e12i	0.0424080	+	0.0734528i
$965$	−1.97330e13			−0.732520
$966$		0			0
$967$	−1.72985e13			−0.636193			−0.318097	−	0.948058i	$-0.603044\pi$
$967$	−1.72985e13			−0.636193			−0.318097	+	0.948058i	$0.603044\pi$
$968$	3.26401e12	+	5.65344e12i	0.119485	+	0.206954i
$969$	1.17606e13	−	2.03699e13i	0.428521	−	0.742219i
$970$	7.97384e12	−	1.38111e13i	0.289198	−	0.500905i
$971$	6.05022e12	+	1.04793e13i	0.218416	+	0.378308i	0.954324	−	0.298774i	$-0.0965777\pi$
$971$	6.05022e12	+	1.04793e13i	0.218416	+	0.378308i	−0.735908	+	0.677082i	$0.763244\pi$
$972$	6.11961e12			0.219900
$973$		0			0
$974$	1.94981e13			0.694187
$975$	1.66371e12	+	2.88163e12i	0.0589598	+	0.102121i
$976$	−1.63330e12	+	2.82895e12i	−0.0576157	+	0.0997933i
$977$	1.49843e13	−	2.59535e13i	0.526151	−	0.911320i	−0.473385	−	0.880856i	$-0.656968\pi$
$977$	1.49843e13	−	2.59535e13i	0.526151	−	0.911320i	0.999536	−	0.0304647i	$-0.00969871\pi$
$978$	−6.50317e12	−	1.12638e13i	−0.227300	−	0.393696i
$979$	−8.22483e12			−0.286157
$980$		0			0
$981$	−4.53225e12			−0.156244
$982$	4.60975e11	+	7.98432e11i	0.0158189	+	0.0273991i
$983$	−3.81824e11	+	6.61338e11i	−0.0130428	+	0.0225909i	−0.872473	−	0.488662i	$-0.837485\pi$
$983$	−3.81824e11	+	6.61338e11i	−0.0130428	+	0.0225909i	0.859430	+	0.511253i	$0.170818\pi$
$984$	−7.72582e12	+	1.33815e13i	−0.262704	+	0.455017i
$985$	1.29999e13	+	2.25164e13i	0.440023	+	0.762143i
$986$	2.29764e13			0.774169
$987$		0			0
$988$	7.32622e12			0.244610
$989$	−2.34632e12	−	4.06394e12i	−0.0779837	−	0.135072i
$990$	1.24764e12	−	2.16098e12i	0.0412792	−	0.0714976i
$991$	2.07406e13	−	3.59237e13i	0.683107	−	1.18318i	−0.290921	−	0.956747i	$-0.593962\pi$
$991$	2.07406e13	−	3.59237e13i	0.683107	−	1.18318i	0.974028	−	0.226429i	$-0.0727051\pi$
$992$	3.19671e12	+	5.53686e12i	0.104809	+	0.181535i
$993$	4.43876e13			1.44874
$994$		0			0
$995$	3.53666e13			1.14390
$996$	4.72665e12	+	8.18681e12i	0.152190	+	0.263601i
$997$	−2.54631e13	+	4.41033e13i	−0.816173	+	1.41365i	0.0923096	+	0.995730i	$0.470575\pi$
$997$	−2.54631e13	+	4.41033e13i	−0.816173	+	1.41365i	−0.908483	+	0.417923i	$0.862758\pi$
$998$	−1.91100e13	+	3.30994e13i	−0.609779	+	1.05617i
$999$	−2.65137e13	−	4.59231e13i	−0.842220	−	1.45877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.g.67.1		4
7.2	even	3	inner	98.10.c.g.79.1		4
7.3	odd	6		98.10.a.f.1.1	✓	2
7.4	even	3		98.10.a.f.1.2	yes	2
7.5	odd	6	inner	98.10.c.g.79.2		4
7.6	odd	2	inner	98.10.c.g.67.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.f.1.1	✓	2	7.3	odd	6
98.10.a.f.1.2	yes	2	7.4	even	3
98.10.c.g.67.1		4	1.1	even	1	trivial
98.10.c.g.67.2		4	7.6	odd	2	inner
98.10.c.g.79.1		4	7.2	even	3	inner
98.10.c.g.79.2		4	7.5	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-61.7738 + 106.995i) q^{3} +(-128.000 + 221.703i) q^{4} +(638.329 + 1105.62i) q^{5} +1976.76 q^{6} +4096.00 q^{8} +(2209.50 + 3826.97i) q^{9} +(10213.3 - 17689.9i) q^{10} +(13822.0 - 23940.4i) q^{11} +(-15814.1 - 27390.8i) q^{12} +83312.2 q^{13} -157728. q^{15} +(-32768.0 - 56755.8i) q^{16} +(277117. - 479981. i) q^{17} +(35352.0 - 61231.5i) q^{18} +(-171752. - 297483. i) q^{19} -326824. q^{20} -442304. q^{22} +(267852. + 463933. i) q^{23} +(-253025. + 438253. i) q^{24} +(161634. - 279959. i) q^{25} +(-666498. - 1.15441e6i) q^{26} -2.97774e6 q^{27} -2.59101e6 q^{29} +(1.26182e6 + 2.18554e6i) q^{30} +(3.04862e6 - 5.28036e6i) q^{31} +(-524288. + 908093. i) q^{32} +(1.70767e6 + 2.95778e6i) q^{33} -8.86775e6 q^{34} -1.13126e6 q^{36} +(8.90396e6 + 1.54221e7i) q^{37} +(-2.74803e6 + 4.75972e6i) q^{38} +(-5.14651e6 + 8.91402e6i) q^{39} +(2.61460e6 + 4.52861e6i) q^{40} +3.05338e7 q^{41} -8.75976e6 q^{43} +(3.53843e6 + 6.12874e6i) q^{44} +(-2.82078e6 + 4.88573e6i) q^{45} +(4.28563e6 - 7.42293e6i) q^{46} +(-1.36365e7 - 2.36191e7i) q^{47} +8.09681e6 q^{48} -5.17230e6 q^{50} +(3.42372e7 + 5.93005e7i) q^{51} +(-1.06640e7 + 1.84705e7i) q^{52} +(4.17442e7 - 7.23032e7i) q^{53} +(2.38219e7 + 4.12608e7i) q^{54} +3.52919e7 q^{55} +4.24390e7 q^{57} +(2.07280e7 + 3.59020e7i) q^{58} +(-4.07738e7 + 7.06222e7i) q^{59} +(2.01892e7 - 3.49687e7i) q^{60} +(-2.49221e7 - 4.31664e7i) q^{61} -9.75558e7 q^{62} +1.67772e7 q^{64} +(5.31806e7 + 9.21115e7i) q^{65} +(2.73228e7 - 4.73245e7i) q^{66} +(9.27465e7 - 1.60642e8i) q^{67} +(7.09420e7 + 1.22875e8i) q^{68} -6.61849e7 q^{69} +3.70271e8 q^{71} +(9.05011e6 + 1.56753e7i) q^{72} +(1.23005e8 - 2.13051e8i) q^{73} +(1.42463e8 - 2.46754e8i) q^{74} +(1.99695e7 + 3.45883e7i) q^{75} +8.79369e7 q^{76} +1.64688e8 q^{78} +(2.59954e8 + 4.50253e8i) q^{79} +(4.18335e7 - 7.24578e7i) q^{80} +(1.40457e8 - 2.43278e8i) q^{81} +(-2.44270e8 - 4.23089e8i) q^{82} -2.98889e8 q^{83} +7.07568e8 q^{85} +(7.00780e7 + 1.21379e8i) q^{86} +(1.60056e8 - 2.77226e8i) q^{87} +(5.66149e7 - 9.80599e7i) q^{88} +(-1.48763e8 - 2.57666e8i) q^{89} +9.02648e7 q^{90} -1.37140e8 q^{92} +(3.76649e8 + 6.52376e8i) q^{93} +(-2.18184e8 + 3.77905e8i) q^{94} +(2.19268e8 - 3.79784e8i) q^{95} +(-6.47745e7 - 1.12193e8i) q^{96} +7.80734e8 q^{97} +1.22159e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} - 512 q^{4} + 16384 q^{8} + 8838 q^{9} + 55288 q^{11} - 630912 q^{15} - 131072 q^{16} + 141408 q^{18} - 1769216 q^{22} + 1071408 q^{23} + 646538 q^{25} - 10364024 q^{29} + 5047296 q^{30}+ \cdots + 488635344 q^{99}+O(q^{100}) \) 4 * q - 32 * q^2 - 512 * q^4 + 16384 * q^8 + 8838 * q^9 + 55288 * q^11 - 630912 * q^15 - 131072 * q^16 + 141408 * q^18 - 1769216 * q^22 + 1071408 * q^23 + 646538 * q^25 - 10364024 * q^29 + 5047296 * q^30 - 2097152 * q^32 - 4525056 * q^36 + 35615820 * q^37 - 20586048 * q^39 - 35039024 * q^43 + 14153728 * q^44 + 17142528 * q^46 - 20689216 * q^50 + 136948608 * q^51 + 166976980 * q^53 + 169756032 * q^57 + 82912192 * q^58 + 80756736 * q^60 + 67108864 * q^64 + 212722496 * q^65 + 370985848 * q^67 + 1481082688 * q^71 + 36200448 * q^72 + 569853120 * q^74 + 658753536 * q^78 + 1039814512 * q^79 + 561827502 * q^81 + 2830271232 * q^85 + 280312192 * q^86 + 226459648 * q^88 - 548560896 * q^92 + 1506597504 * q^93 + 877072832 * q^95 + 488635344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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