LMFDB - Embedded newform 28.9.c.a.15.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,9,Mod(15,28)] 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("28.15"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	28.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.4066010817$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.17
Character	$\chi$	$=$	28.15
Dual form			28.9.c.a.15.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.1564 - 12.3632i) q^{2} +137.158i q^{3} +(-49.6953 - 251.130i) q^{4} -657.296 q^{5} +(1695.70 + 1393.03i) q^{6} -907.493i q^{7} +(-3609.49 - 1936.19i) q^{8} -12251.2 q^{9} +(-6675.76 + 8126.25i) q^{10} -26916.6i q^{11} +(34444.4 - 6816.09i) q^{12} -16111.5 q^{13} +(-11219.5 - 9216.85i) q^{14} -90153.2i q^{15} +(-60596.8 + 24960.0i) q^{16} -56012.3 q^{17} +(-124428. + 151464. i) q^{18} +238923. i q^{19} +(32664.5 + 165067. i) q^{20} +124470. q^{21} +(-332774. - 273376. i) q^{22} +127908. i q^{23} +(265563. - 495069. i) q^{24} +41412.9 q^{25} +(-163635. + 199189. i) q^{26} -780460. i q^{27} +(-227899. + 45098.1i) q^{28} +199470. q^{29} +(-1.11458e6 - 915631. i) q^{30} -947271. i q^{31} +(-306860. + 1.00267e6i) q^{32} +3.69182e6 q^{33} +(-568883. + 692489. i) q^{34} +596491. i q^{35} +(608829. + 3.07666e6i) q^{36} -1.15282e6 q^{37} +(2.95385e6 + 2.42660e6i) q^{38} -2.20982e6i q^{39} +(2.37250e6 + 1.27265e6i) q^{40} -2.28391e6 q^{41} +(1.26416e6 - 1.53884e6i) q^{42} -123118. i q^{43} +(-6.75957e6 + 1.33763e6i) q^{44} +8.05269e6 q^{45} +(1.58135e6 + 1.29908e6i) q^{46} -1.80641e6i q^{47} +(-3.42345e6 - 8.31131e6i) q^{48} -823543. q^{49} +(420606. - 511994. i) q^{50} -7.68253e6i q^{51} +(800667. + 4.04609e6i) q^{52} +9.83342e6 q^{53} +(-9.64895e6 - 7.92666e6i) q^{54} +1.76922e7i q^{55} +(-1.75708e6 + 3.27558e6i) q^{56} -3.27702e7 q^{57} +(2.02590e6 - 2.46608e6i) q^{58} -1.11306e6i q^{59} +(-2.26402e7 + 4.48019e6i) q^{60} +6.24258e6 q^{61} +(-1.17113e7 - 9.62086e6i) q^{62} +1.11179e7i q^{63} +(9.27958e6 + 1.39773e7i) q^{64} +1.05900e7 q^{65} +(3.74956e7 - 4.56425e7i) q^{66} -1.95228e7i q^{67} +(2.78355e6 + 1.40664e7i) q^{68} -1.75436e7 q^{69} +(7.37451e6 + 6.05820e6i) q^{70} +5.89294e6i q^{71} +(4.42207e7 + 2.37207e7i) q^{72} -4.26337e7 q^{73} +(-1.17085e7 + 1.42524e7i) q^{74} +5.68010e6i q^{75} +(6.00009e7 - 1.18734e7i) q^{76} -2.44266e7 q^{77} +(-2.73204e7 - 2.24438e7i) q^{78} +5.91774e7i q^{79} +(3.98300e7 - 1.64061e7i) q^{80} +2.66657e7 q^{81} +(-2.31963e7 + 2.82363e7i) q^{82} -4.35428e7i q^{83} +(-6.18556e6 - 3.12581e7i) q^{84} +3.68167e7 q^{85} +(-1.52213e6 - 1.25044e6i) q^{86} +2.73589e7i q^{87} +(-5.21156e7 + 9.71551e7i) q^{88} +4.27703e6 q^{89} +(8.17863e7 - 9.95566e7i) q^{90} +1.46211e7i q^{91} +(3.21215e7 - 6.35642e6i) q^{92} +1.29926e8 q^{93} +(-2.23330e7 - 1.83467e7i) q^{94} -1.57043e8i q^{95} +(-1.37524e8 - 4.20883e7i) q^{96} -7.85671e7 q^{97} +(-8.36423e6 + 1.01816e7i) q^{98} +3.29762e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) $ 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	10.1564	−	12.3632i	0.634775	−	0.772697i
$2$	10.1564	−	12.3632i	0.634775	−	0.772697i
$3$			137.158i			1.69331i	0.532146	+	0.846653i	$0.321386\pi$
$3$			137.158i			1.69331i	−0.532146	+	0.846653i	$0.678614\pi$
$4$	−49.6953	−	251.130i	−0.194122	−	0.980977i
$5$	−657.296			−1.05167			−0.525837	−	0.850586i	$-0.676248\pi$
$5$	−657.296			−1.05167			−0.525837	+	0.850586i	$0.676248\pi$
$6$	1695.70	+	1393.03i	1.30841	+	1.07487i
$7$		−	907.493i		−	0.377964i
$7$		−	907.493i		−	0.377964i
$8$	−3609.49	−	1936.19i	−0.881222	−	0.472702i
$9$	−12251.2			−1.86728
$10$	−6675.76	+	8126.25i	−0.667576	+	0.812625i
$11$		−	26916.6i		−	1.83844i	−0.393744	−	0.919220i	$-0.628820\pi$
$11$		−	26916.6i		−	1.83844i	0.393744	−	0.919220i	$-0.371180\pi$
$12$	34444.4	−	6816.09i	1.66109	−	0.328708i
$13$	−16111.5			−0.564110			−0.282055	−	0.959398i	$-0.591016\pi$
$13$	−16111.5			−0.564110			−0.282055	+	0.959398i	$0.591016\pi$
$14$	−11219.5	−	9216.85i	−0.292052	−	0.239922i
$15$		−	90153.2i		−	1.78080i
$16$	−60596.8	+	24960.0i	−0.924633	+	0.380859i
$17$	−56012.3			−0.670638			−0.335319	−	0.942105i	$-0.608844\pi$
$17$	−56012.3			−0.670638			−0.335319	+	0.942105i	$0.608844\pi$
$18$	−124428.	+	151464.i	−1.18530	+	1.44284i
$19$			238923.i			1.83334i	0.399640	+	0.916672i	$0.369135\pi$
$19$			238923.i			1.83334i	−0.399640	+	0.916672i	$0.630865\pi$
$20$	32664.5	+	165067.i	0.204153	+	1.03167i
$21$	124470.			0.640009
$22$	−332774.	−	273376.i	−1.42056	−	1.16700i
$23$			127908.i			0.457073i	0.973535	+	0.228537i	$0.0733941\pi$
$23$			127908.i			0.457073i	−0.973535	+	0.228537i	$0.926606\pi$
$24$	265563.	−	495069.i	0.800428	−	1.49218i
$25$	41412.9			0.106017
$26$	−163635.	+	199189.i	−0.358082	+	0.435886i
$27$		−	780460.i		−	1.46857i
$28$	−227899.	+	45098.1i	−0.370775	+	0.0733713i
$29$	199470.			0.282024			0.141012	−	0.990008i	$-0.454964\pi$
$29$	199470.			0.282024			0.141012	+	0.990008i	$0.454964\pi$
$30$	−1.11458e6	−	915631.i	−1.37602	−	1.13041i
$31$		−	947271.i		−	1.02572i	−0.858473	−	0.512858i	$-0.828587\pi$
$31$		−	947271.i		−	1.02572i	0.858473	−	0.512858i	$-0.171413\pi$
$32$	−306860.	+	1.00267e6i	−0.292645	+	0.956221i
$33$	3.69182e6			3.11304
$34$	−568883.	+	692489.i	−0.425704	+	0.518200i
$35$			596491.i			0.397495i
$36$	608829.	+	3.07666e6i	0.362481	+	1.83176i
$37$	−1.15282e6			−0.615110			−0.307555	−	0.951530i	$-0.599511\pi$
$37$	−1.15282e6			−0.615110			−0.307555	+	0.951530i	$0.599511\pi$
$38$	2.95385e6	+	2.42660e6i	1.41662	+	1.16376i
$39$		−	2.20982e6i		−	0.955210i
$40$	2.37250e6	+	1.27265e6i	0.926758	+	0.497128i
$41$	−2.28391e6			−0.808246			−0.404123	−	0.914705i	$-0.632423\pi$
$41$	−2.28391e6			−0.808246			−0.404123	+	0.914705i	$0.632423\pi$
$42$	1.26416e6	−	1.53884e6i	0.406262	−	0.494533i
$43$		−	123118.i		−	0.0360122i	−0.999838	−	0.0180061i	$-0.994268\pi$
$43$		−	123118.i		−	0.0360122i	0.999838	−	0.0180061i	$-0.00573182\pi$
$44$	−6.75957e6	+	1.33763e6i	−1.80347	+	0.356882i
$45$	8.05269e6			1.96377
$46$	1.58135e6	+	1.29908e6i	0.353179	+	0.290139i
$47$		−	1.80641e6i		−	0.370191i	−0.982721	−	0.185096i	$-0.940741\pi$
$47$		−	1.80641e6i		−	0.370191i	0.982721	−	0.185096i	$-0.0592595\pi$
$48$	−3.42345e6	−	8.31131e6i	−0.644911	−	1.56569i
$49$	−823543.			−0.142857
$50$	420606.	−	511994.i	0.0672969	−	0.0819190i
$51$		−	7.68253e6i		−	1.13559i
$52$	800667.	+	4.04609e6i	0.109506	+	0.553379i
$53$	9.83342e6			1.24624			0.623119	−	0.782127i	$-0.285865\pi$
$53$	9.83342e6			1.24624			0.623119	+	0.782127i	$0.285865\pi$
$54$	−9.64895e6	−	7.92666e6i	−1.13476	−	0.932213i
$55$			1.76922e7i			1.93344i
$56$	−1.75708e6	+	3.27558e6i	−0.178664	+	0.333071i
$57$	−3.27702e7			−3.10441
$58$	2.02590e6	−	2.46608e6i	0.179022	−	0.217919i
$59$		−	1.11306e6i		−	0.0918564i	−0.998945	−	0.0459282i	$-0.985375\pi$
$59$		−	1.11306e6i		−	0.0918564i	0.998945	−	0.0459282i	$-0.0146245\pi$
$60$	−2.26402e7	+	4.48019e6i	−1.74693	+	0.345694i
$61$	6.24258e6			0.450863			0.225432	−	0.974259i	$-0.427621\pi$
$61$	6.24258e6			0.450863			0.225432	+	0.974259i	$0.427621\pi$
$62$	−1.17113e7	−	9.62086e6i	−0.792569	−	0.651099i
$63$			1.11179e7i			0.705766i
$64$	9.27958e6	+	1.39773e7i	0.553106	+	0.833111i
$65$	1.05900e7			0.593259
$66$	3.74956e7	−	4.56425e7i	1.97608	−	2.40544i
$67$		−	1.95228e7i		−	0.968818i	−0.874842	−	0.484409i	$-0.839035\pi$
$67$		−	1.95228e7i		−	0.968818i	0.874842	−	0.484409i	$-0.160965\pi$
$68$	2.78355e6	+	1.40664e7i	0.130186	+	0.657881i
$69$	−1.75436e7			−0.773965
$70$	7.37451e6	+	6.05820e6i	0.307143	+	0.252320i
$71$			5.89294e6i			0.231899i	0.993255	+	0.115949i	$0.0369910\pi$
$71$			5.89294e6i			0.231899i	−0.993255	+	0.115949i	$0.963009\pi$
$72$	4.42207e7	+	2.37207e7i	1.64549	+	0.882668i
$73$	−4.26337e7			−1.50128			−0.750639	−	0.660712i	$-0.770254\pi$
$73$	−4.26337e7			−1.50128			−0.750639	+	0.660712i	$0.770254\pi$
$74$	−1.17085e7	+	1.42524e7i	−0.390456	+	0.475294i
$75$			5.68010e6i			0.179519i
$76$	6.00009e7	−	1.18734e7i	1.79847	−	0.355893i
$77$	−2.44266e7			−0.694865
$78$	−2.73204e7	−	2.24438e7i	−0.738088	−	0.606343i
$79$			5.91774e7i			1.51931i	0.650324	+	0.759657i	$0.274633\pi$
$79$			5.91774e7i			1.51931i	−0.650324	+	0.759657i	$0.725367\pi$
$80$	3.98300e7	−	1.64061e7i	0.972412	−	0.400539i
$81$	2.66657e7			0.619460
$82$	−2.31963e7	+	2.82363e7i	−0.513054	+	0.624529i
$83$		−	4.35428e7i		−	0.917497i	−0.888566	−	0.458748i	$-0.848298\pi$
$83$		−	4.35428e7i		−	0.917497i	0.888566	−	0.458748i	$-0.151702\pi$
$84$	−6.18556e6	−	3.12581e7i	−0.124240	−	0.627834i
$85$	3.68167e7			0.705292
$86$	−1.52213e6	−	1.25044e6i	−0.0278265	−	0.0228596i
$87$			2.73589e7i			0.477552i
$88$	−5.21156e7	+	9.71551e7i	−0.869034	+	1.62007i
$89$	4.27703e6			0.0681683			0.0340842	−	0.999419i	$-0.489149\pi$
$89$	4.27703e6			0.0681683			0.0340842	+	0.999419i	$0.489149\pi$
$90$	8.17863e7	−	9.95566e7i	1.24655	−	1.51740i
$91$			1.46211e7i			0.213213i
$92$	3.21215e7	−	6.35642e6i	0.448379	−	0.0887281i
$93$	1.29926e8			1.73685
$94$	−2.23330e7	−	1.83467e7i	−0.286046	−	0.234988i
$95$		−	1.57043e8i		−	1.92808i
$96$	−1.37524e8	−	4.20883e7i	−1.61917	−	0.495537i
$97$	−7.85671e7			−0.887470			−0.443735	−	0.896158i	$-0.646347\pi$
$97$	−7.85671e7			−0.887470			−0.443735	+	0.896158i	$0.646347\pi$
$98$	−8.36423e6	+	1.01816e7i	−0.0906821	+	0.110385i
$99$			3.29762e8i			3.43289i
$100$	−2.05803e6	−	1.04000e7i	−0.0205803	−	0.104000i
$101$	−4.90488e7			−0.471349			−0.235675	−	0.971832i	$-0.575730\pi$
$101$	−4.90488e7			−0.471349			−0.235675	+	0.971832i	$0.575730\pi$
$102$	−9.49803e7	−	7.80268e7i	−0.877471	−	0.720847i
$103$		−	4.96179e7i		−	0.440849i	−0.975404	−	0.220424i	$-0.929256\pi$
$103$		−	4.96179e7i		−	0.440849i	0.975404	−	0.220424i	$-0.0707442\pi$
$104$	5.81544e7	+	3.11949e7i	0.497106	+	0.266656i
$105$	−8.18134e7			−0.673081
$106$	9.98721e7	−	1.21572e8i	0.791081	−	0.962965i
$107$		−	1.52716e8i		−	1.16506i	−0.812809	−	0.582530i	$-0.802063\pi$
$107$		−	1.52716e8i		−	1.16506i	0.812809	−	0.582530i	$-0.197937\pi$
$108$	−1.95997e8	+	3.87852e7i	−1.44064	+	0.285083i
$109$	1.35471e8			0.959711			0.479855	−	0.877348i	$-0.340689\pi$
$109$	1.35471e8			0.959711			0.479855	+	0.877348i	$0.340689\pi$
$110$	2.18731e8	+	1.79689e8i	1.49396	+	1.22730i
$111$		−	1.58118e8i		−	1.04157i
$112$	2.26510e7	+	5.49911e7i	0.143951	+	0.349478i
$113$	4.55043e6			0.0279087			0.0139543	−	0.999903i	$-0.495558\pi$
$113$	4.55043e6			0.0279087			0.0139543	+	0.999903i	$0.495558\pi$
$114$	−3.32827e8	+	4.05143e8i	−1.97060	+	2.39877i
$115$		−	8.40733e7i		−	0.480692i
$116$	−9.91273e6	−	5.00930e7i	−0.0547471	−	0.276659i
$117$	1.97386e8			1.05335
$118$	−1.37609e7	−	1.13046e7i	−0.0709772	−	0.0583081i
$119$			5.08308e7i			0.253477i
$120$	−1.74553e8	+	3.25407e8i	−0.841789	+	1.56928i
$121$	−5.10144e8			−2.37986
$122$	6.34021e7	−	7.71780e7i	0.286197	−	0.348381i
$123$		−	3.13256e8i		−	1.36861i
$124$	−2.37888e8	+	4.70749e7i	−1.00620	+	0.199114i
$125$	2.29536e8			0.940178
$126$	1.37452e8	+	1.12918e8i	0.545344	+	0.448003i
$127$		−	4.34916e8i		−	1.67182i	−0.548864	−	0.835911i	$-0.684940\pi$
$127$		−	4.34916e8i		−	1.67182i	0.548864	−	0.835911i	$-0.315060\pi$
$128$	2.67050e8	+	2.72339e7i	0.994840	+	0.101454i
$129$	1.68866e7			0.0609796
$130$	1.07557e8	−	1.30926e8i	0.376586	−	0.458410i
$131$			3.31733e8i			1.12643i	0.826311	+	0.563215i	$0.190436\pi$
$131$			3.31733e8i			1.12643i	−0.826311	+	0.563215i	$0.809564\pi$
$132$	−1.83466e8	−	9.27127e8i	−0.604310	−	3.05382i
$133$	2.16821e8			0.692939
$134$	−2.41363e8	−	1.98281e8i	−0.748603	−	0.614981i
$135$			5.12993e8i			1.54446i
$136$	2.02176e8	+	1.08450e8i	0.590981	+	0.317012i
$137$	4.22491e8			1.19932			0.599660	−	0.800255i	$-0.295302\pi$
$137$	4.22491e8			1.19932			0.599660	+	0.800255i	$0.295302\pi$
$138$	−1.78179e8	+	2.16894e8i	−0.491293	+	0.598040i
$139$		−	3.11063e8i		−	0.833276i	−0.909072	−	0.416638i	$-0.863208\pi$
$139$		−	3.11063e8i		−	0.833276i	0.909072	−	0.416638i	$-0.136792\pi$
$140$	1.49797e8	−	2.96428e7i	0.389934	−	0.0771627i
$141$	2.47764e8			0.626846
$142$	7.28553e7	+	5.98510e7i	0.179187	+	0.147203i
$143$			4.33668e8i			1.03708i
$144$	7.42385e8	−	3.05791e8i	1.72655	−	0.711171i
$145$	−1.31111e8			−0.296597
$146$	−4.33004e8	+	5.27087e8i	−0.952973	+	1.16003i
$147$		−	1.12955e8i		−	0.241901i
$148$	5.72895e7	+	2.89507e8i	0.119407	+	0.603409i
$149$	−3.44721e8			−0.699395			−0.349698	−	0.936863i	$-0.613716\pi$
$149$	−3.44721e8			−0.699395			−0.349698	+	0.936863i	$0.613716\pi$
$150$	7.02239e7	+	5.76893e7i	0.138714	+	0.113954i
$151$			3.44226e8i			0.662119i	0.943610	+	0.331059i	$0.107406\pi$
$151$			3.44226e8i			0.662119i	−0.943610	+	0.331059i	$0.892594\pi$
$152$	4.62600e8	−	8.62391e8i	0.866625	−	1.61558i
$153$	6.86221e8			1.25227
$154$	−2.48086e8	+	3.01990e8i	−0.441083	+	0.536920i
$155$			6.22637e8i			1.07872i
$156$	−5.54953e8	+	1.09818e8i	−0.937039	+	0.185427i
$157$	−1.67311e8			−0.275375			−0.137688	−	0.990476i	$-0.543967\pi$
$157$	−1.67311e8			−0.275375			−0.137688	+	0.990476i	$0.543967\pi$
$158$	7.31620e8	+	6.01029e8i	1.17397	+	0.964422i
$159$			1.34873e9i			2.11026i
$160$	2.01698e8	−	6.59051e8i	0.307767	−	1.00563i
$161$	1.16075e8			0.172757
$162$	2.70828e8	−	3.29673e8i	0.393218	−	0.478655i
$163$			1.69789e7i			0.0240525i	0.999928	+	0.0120262i	$0.00382816\pi$
$163$			1.69789e7i			0.0240525i	−0.999928	+	0.0120262i	$0.996172\pi$
$164$	1.13500e8	+	5.73559e8i	0.156898	+	0.792871i
$165$	−2.42662e9			−3.27390
$166$	−5.38327e8	−	4.42238e8i	−0.708947	−	0.582404i
$167$		−	1.24502e9i		−	1.60070i	−0.599533	−	0.800350i	$-0.704647\pi$
$167$		−	1.24502e9i		−	1.60070i	0.599533	−	0.800350i	$-0.295353\pi$
$168$	−4.49271e8	−	2.40996e8i	−0.563990	−	0.302533i
$169$	−5.56149e8			−0.681780
$170$	3.73925e8	−	4.55170e8i	0.447702	−	0.544977i
$171$		−	2.92711e9i		−	3.42337i
$172$	−3.09187e7	+	6.11841e6i	−0.0353271	+	0.00699076i
$173$	−2.11604e8			−0.236233			−0.118116	−	0.993000i	$-0.537686\pi$
$173$	−2.11604e8			−0.236233			−0.118116	+	0.993000i	$0.537686\pi$
$174$	3.38242e8	+	2.77867e8i	0.369003	+	0.303138i
$175$		−	3.75819e7i		−	0.0400707i
$176$	6.71838e8	+	1.63106e9i	0.700187	+	1.69988i
$177$	1.52664e8			0.155541
$178$	4.34392e7	−	5.28776e7i	0.0432715	−	0.0526735i
$179$			1.94146e8i			0.189111i	0.995520	+	0.0945553i	$0.0301429\pi$
$179$			1.94146e8i			0.189111i	−0.995520	+	0.0945553i	$0.969857\pi$
$180$	−4.00181e8	−	2.02227e9i	−0.381212	−	1.92641i
$181$	−1.18768e9			−1.10659			−0.553293	−	0.832986i	$-0.686629\pi$
$181$	−1.18768e9			−1.10659			−0.553293	+	0.832986i	$0.686629\pi$
$182$	1.80763e8	+	1.48498e8i	0.164749	+	0.135342i
$183$			8.56218e8i			0.763449i
$184$	2.47654e8	−	4.61682e8i	0.216059	−	0.402783i
$185$	7.57741e8			0.646895
$186$	1.31957e9	−	1.60629e9i	1.10251	−	1.34206i
$187$			1.50766e9i			1.23293i
$188$	−4.53645e8	+	8.97703e7i	−0.363149	+	0.0718623i
$189$	−7.08262e8			−0.555068
$190$	−1.94155e9	−	1.59499e9i	−1.48982	−	1.22390i
$191$			4.94298e8i			0.371411i	0.982605	+	0.185706i	$0.0594571\pi$
$191$			4.94298e8i			0.371411i	−0.982605	+	0.185706i	$0.940543\pi$
$192$	−1.91709e9	+	1.27277e9i	−1.41071	+	0.936577i
$193$	−2.53453e9			−1.82670			−0.913352	−	0.407172i	$-0.866515\pi$
$193$	−2.53453e9			−1.82670			−0.913352	+	0.407172i	$0.866515\pi$
$194$	−7.97958e8	+	9.71337e8i	−0.563343	+	0.685746i
$195$			1.45251e9i			1.00457i
$196$	4.09262e7	+	2.06817e8i	0.0277318	+	0.140140i
$197$	2.42762e9			1.61182			0.805909	−	0.592040i	$-0.201677\pi$
$197$	2.42762e9			1.61182			0.805909	+	0.592040i	$0.201677\pi$
$198$	4.07690e9	+	3.34919e9i	2.65258	+	2.17911i
$199$			1.60689e9i			1.02465i	0.858792	+	0.512324i	$0.171215\pi$
$199$			1.60689e9i			1.02465i	−0.858792	+	0.512324i	$0.828785\pi$
$200$	−1.49479e8	−	8.01831e7i	−0.0934245	−	0.0501144i
$201$	2.67770e9			1.64051
$202$	−4.98159e8	+	6.06398e8i	−0.299200	+	0.364210i
$203$		−	1.81018e8i		−	0.106595i
$204$	−1.92931e9	+	3.81785e8i	−1.11399	+	0.220444i
$205$	1.50120e9			0.850010
$206$	−6.13434e8	−	5.03939e8i	−0.340643	−	0.279840i
$207$		−	1.56703e9i		−	0.853485i
$208$	9.76307e8	−	4.02144e8i	0.521594	−	0.214846i
$209$	6.43100e9			3.37049
$210$	−8.30929e8	+	1.01147e9i	−0.427255	+	0.520088i
$211$		−	1.85374e9i		−	0.935231i	−0.883932	−	0.467615i	$-0.845113\pi$
$211$		−	1.85374e9i		−	0.935231i	0.883932	−	0.467615i	$-0.154887\pi$
$212$	−4.88675e8	−	2.46947e9i	−0.241923	−	1.22253i
$213$	−8.08262e8			−0.392675
$214$	−1.88805e9	−	1.55104e9i	−0.900239	−	0.739551i
$215$			8.09252e7i			0.0378730i
$216$	−1.51112e9	+	2.81706e9i	−0.694197	+	1.29414i
$217$	−8.59641e8			−0.387684
$218$	1.37590e9	−	1.67485e9i	0.609200	−	0.741566i
$219$		−	5.84754e9i		−	2.54212i
$220$	4.44304e9	−	8.79218e8i	1.89666	−	0.375323i
$221$	9.02445e8			0.378313
$222$	−1.95483e9	−	1.60590e9i	−0.804818	−	0.661162i
$223$			4.02348e9i			1.62698i	0.581578	+	0.813491i	$0.302436\pi$
$223$			4.02348e9i			1.62698i	−0.581578	+	0.813491i	$0.697564\pi$
$224$	9.09916e8	+	2.78474e8i	0.361418	+	0.110609i
$225$	−5.07359e8			−0.197964
$226$	4.62160e7	−	5.62577e7i	0.0177157	−	0.0215649i
$227$		−	2.84223e9i		−	1.07043i	−0.844717	−	0.535213i	$-0.820231\pi$
$227$		−	2.84223e9i		−	1.07043i	0.844717	−	0.535213i	$-0.179769\pi$
$228$	1.62852e9	+	8.22958e9i	0.602635	+	3.04536i
$229$	1.06468e9			0.387148			0.193574	−	0.981086i	$-0.437992\pi$
$229$	1.06468e9			0.387148			0.193574	+	0.981086i	$0.437992\pi$
$230$	−1.03941e9	−	8.53882e8i	−0.371429	−	0.305131i
$231$		−	3.35030e9i		−	1.17662i
$232$	−7.19985e8	−	3.86211e8i	−0.248526	−	0.133313i
$233$	−4.20140e9			−1.42551			−0.712755	−	0.701413i	$-0.752553\pi$
$233$	−4.20140e9			−1.42551			−0.712755	+	0.701413i	$0.752553\pi$
$234$	2.00473e9	−	2.44032e9i	0.668641	−	0.813922i
$235$			1.18735e9i			0.389320i
$236$	−2.79522e8	+	5.53137e7i	−0.0901091	+	0.0178314i
$237$	−8.11664e9			−2.57266
$238$	6.28429e8	+	5.16258e8i	0.195861	+	0.160901i
$239$			4.83554e9i			1.48202i	0.671496	+	0.741008i	$0.265652\pi$
$239$			4.83554e9i			1.48202i	−0.671496	+	0.741008i	$0.734348\pi$
$240$	2.25022e9	+	5.46299e9i	0.678235	+	1.64659i
$241$	1.91794e9			0.568547			0.284274	−	0.958743i	$-0.408248\pi$
$241$	1.91794e9			0.568547			0.284274	+	0.958743i	$0.408248\pi$
$242$	−5.18123e9	+	6.30700e9i	−1.51068	+	1.83891i
$243$		−	1.46319e9i		−	0.419638i
$244$	−3.10227e8	−	1.56770e9i	−0.0875226	−	0.442287i
$245$	5.41311e8			0.150239
$246$	−3.87283e9	−	3.18155e9i	−1.05752	−	0.868757i
$247$		−	3.84942e9i		−	1.03421i
$248$	−1.83409e9	+	3.41916e9i	−0.484858	+	0.903885i
$249$	5.97224e9			1.55360
$250$	2.33126e9	−	2.83779e9i	0.596801	−	0.726473i
$251$		−	6.47351e8i		−	0.163097i	−0.996669	−	0.0815483i	$-0.974014\pi$
$251$		−	6.47351e8i		−	0.163097i	0.996669	−	0.0815483i	$-0.0259865\pi$
$252$	2.79204e9	−	5.52508e8i	0.692341	−	0.137005i
$253$	3.44284e9			0.840302
$254$	−5.37693e9	−	4.41718e9i	−1.29181	−	1.06123i
$255$			5.04969e9i			1.19427i
$256$	3.04897e9	−	3.02499e9i	0.709893	−	0.704310i
$257$	1.70764e9			0.391439			0.195720	−	0.980660i	$-0.437296\pi$
$257$	1.70764e9			0.391439			0.195720	+	0.980660i	$0.437296\pi$
$258$	1.71507e8	−	2.08772e8i	0.0387083	−	0.0471187i
$259$			1.04617e9i			0.232490i
$260$	−5.26275e8	−	2.65948e9i	−0.115165	−	0.581974i
$261$	−2.44376e9			−0.526618
$262$	4.10127e9	+	3.36922e9i	0.870389	+	0.715029i
$263$		−	5.47987e9i		−	1.14537i	−0.819774	−	0.572686i	$-0.805901\pi$
$263$		−	5.47987e9i		−	1.14537i	0.819774	−	0.572686i	$-0.194099\pi$
$264$	−1.33256e10	−	7.14805e9i	−2.74328	−	1.47154i
$265$	−6.46347e9			−1.31064
$266$	2.20212e9	−	2.68059e9i	0.439860	−	0.535432i
$267$			5.86628e8i			0.115430i
$268$	−4.90276e9	+	9.70190e8i	−0.950389	+	0.188069i
$269$	−4.59540e9			−0.877636			−0.438818	−	0.898576i	$-0.644603\pi$
$269$	−4.59540e9			−0.877636			−0.438818	+	0.898576i	$0.644603\pi$
$270$	6.34221e9	+	5.21016e9i	1.19340	+	0.980384i
$271$			9.79974e9i			1.81693i	0.417965	+	0.908463i	$0.362744\pi$
$271$			9.79974e9i			1.81693i	−0.417965	+	0.908463i	$0.637256\pi$
$272$	3.39417e9	−	1.39807e9i	0.620094	−	0.255419i
$273$	−2.00540e9			−0.361035
$274$	4.29099e9	−	5.22332e9i	0.761298	−	0.926712i
$275$		−	1.11469e9i		−	0.194906i
$276$	8.71832e8	+	4.40572e9i	0.150244	+	0.759242i
$277$	−3.80877e9			−0.646942			−0.323471	−	0.946238i	$-0.604850\pi$
$277$	−3.80877e9			−0.646942			−0.323471	+	0.946238i	$0.604850\pi$
$278$	−3.84572e9	−	3.15928e9i	−0.643870	−	0.528943i
$279$			1.16052e10i			1.91530i
$280$	1.15492e9	−	2.15303e9i	0.187897	−	0.350282i
$281$	−4.81849e9			−0.772833			−0.386416	−	0.922324i	$-0.626287\pi$
$281$	−4.81849e9			−0.772833			−0.386416	+	0.922324i	$0.626287\pi$
$282$	2.51639e9	−	3.06314e9i	0.397906	−	0.484363i
$283$			3.67318e9i			0.572659i	0.958131	+	0.286330i	$0.0924353\pi$
$283$			3.67318e9i			0.572659i	−0.958131	+	0.286330i	$0.907565\pi$
$284$	1.47989e9	−	2.92851e8i	0.227487	−	0.0450167i
$285$	2.15397e10			3.26483
$286$	5.36150e9	+	4.40450e9i	0.801350	+	0.658313i
$287$			2.07263e9i			0.305488i
$288$	3.75942e9	−	1.22840e10i	0.546450	−	1.78553i
$289$	−3.83837e9			−0.550245
$290$	−1.33161e9	+	1.62094e9i	−0.188272	+	0.229180i
$291$		−	1.07761e10i		−	1.50276i
$292$	2.11869e9	+	1.07066e10i	0.291432	+	1.47272i
$293$	1.25889e9			0.170812			0.0854059	−	0.996346i	$-0.472781\pi$
$293$	1.25889e9			0.170812			0.0854059	+	0.996346i	$0.472781\pi$
$294$	−1.39648e9	−	1.14722e9i	−0.186916	−	0.153552i
$295$			7.31608e8i			0.0966029i
$296$	4.16107e9	+	2.23207e9i	0.542049	+	0.290764i
$297$	−2.10073e10			−2.69988
$298$	−3.50112e9	+	4.26184e9i	−0.443958	+	0.540421i
$299$		−	2.06079e9i		−	0.257839i
$300$	1.42644e9	−	2.82274e8i	0.176104	−	0.0348487i
$301$	−1.11729e8			−0.0136113
$302$	4.25572e9	+	3.49609e9i	0.511617	+	0.420296i
$303$		−	6.72742e9i		−	0.798138i
$304$	−5.96352e9	−	1.44780e10i	−0.698246	−	1.69517i
$305$	−4.10322e9			−0.474161
$306$	6.96953e9	−	8.48385e9i	0.794909	−	0.967626i
$307$			1.03282e10i			1.16270i	0.813652	+	0.581352i	$0.197476\pi$
$307$			1.03282e10i			1.16270i	−0.813652	+	0.581352i	$0.802524\pi$
$308$	1.21389e9	+	6.13426e9i	0.134889	+	0.681647i
$309$	6.80548e9			0.746491
$310$	7.69776e9	+	6.32375e9i	0.833523	+	0.684743i
$311$		−	7.35432e9i		−	0.786142i	−0.919508	−	0.393071i	$-0.871413\pi$
$311$		−	7.35432e9i		−	0.786142i	0.919508	−	0.393071i	$-0.128587\pi$
$312$	−4.27863e9	+	7.97632e9i	−0.451529	+	0.841752i
$313$	−2.25389e9			−0.234831			−0.117415	−	0.993083i	$-0.537461\pi$
$313$	−2.25389e9			−0.234831			−0.117415	+	0.993083i	$0.537461\pi$
$314$	−1.69927e9	+	2.06849e9i	−0.174801	+	0.212782i
$315$		−	7.30776e9i		−	0.742236i
$316$	1.48612e10	−	2.94084e9i	1.49041	−	0.294933i
$317$	4.74392e9			0.469786			0.234893	−	0.972021i	$-0.424526\pi$
$317$	4.74392e9			0.469786			0.234893	+	0.972021i	$0.424526\pi$
$318$	1.66746e10	+	1.36982e10i	1.63059	+	1.33954i
$319$		−	5.36906e9i		−	0.518484i
$320$	−6.09943e9	−	9.18721e9i	−0.581687	−	0.876161i
$321$	2.09461e10			1.97280
$322$	1.17891e9	−	1.43506e9i	0.109662	−	0.133489i
$323$		−	1.33827e10i		−	1.22951i
$324$	−1.32516e9	−	6.69657e9i	−0.120251	−	0.607676i
$325$	−6.67225e8			−0.0598052
$326$	2.09913e8	+	1.72445e8i	0.0185853	+	0.0152679i
$327$			1.85809e10i			1.62508i
$328$	8.24374e9	+	4.42207e9i	0.712244	+	0.382059i
$329$	−1.63931e9			−0.139919
$330$	−2.46457e10	+	3.00007e10i	−2.07819	+	2.52973i
$331$			1.36551e9i			0.113758i	0.998381	+	0.0568791i	$0.0181149\pi$
$331$			1.36551e9i			0.113758i	−0.998381	+	0.0568791i	$0.981885\pi$
$332$	−1.09349e10	+	2.16388e9i	−0.900043	+	0.178107i
$333$	1.41234e10			1.14858
$334$	−1.53924e10	−	1.26449e10i	−1.23686	−	1.01608i
$335$			1.28322e10i			1.01888i
$336$	−7.54246e9	+	3.10676e9i	−0.591774	+	0.243753i
$337$	−1.36727e9			−0.106007			−0.0530034	−	0.998594i	$-0.516879\pi$
$337$	−1.36727e9			−0.106007			−0.0530034	+	0.998594i	$0.516879\pi$
$338$	−5.64847e9	+	6.87576e9i	−0.432777	+	0.526810i
$339$			6.24127e8i			0.0472579i
$340$	−1.82962e9	−	9.24578e9i	−0.136913	−	0.691875i
$341$	−2.54973e10			−1.88572
$342$	−3.61883e10	−	2.97288e10i	−2.64523	−	2.17307i
$343$			7.47359e8i			0.0539949i
$344$	−2.38380e8	+	4.44394e8i	−0.0170230	+	0.0317347i
$345$	1.15313e10			0.813958
$346$	−2.14913e9	+	2.61609e9i	−0.149954	+	0.182536i
$347$			3.33594e9i			0.230092i	0.993360	+	0.115046i	$0.0367015\pi$
$347$			3.33594e9i			0.230092i	−0.993360	+	0.115046i	$0.963299\pi$
$348$	6.87064e9	−	1.35961e9i	0.468468	−	0.0927035i
$349$	6.17677e9			0.416351			0.208176	−	0.978091i	$-0.433247\pi$
$349$	6.17677e9			0.416351			0.208176	+	0.978091i	$0.433247\pi$
$350$	−4.64631e8	−	3.81696e8i	−0.0309625	−	0.0254358i
$351$			1.25744e10i			0.828436i
$352$	2.69885e10	+	8.25964e9i	1.75796	+	0.538010i
$353$	5.75284e9			0.370496			0.185248	−	0.982692i	$-0.440691\pi$
$353$	5.75284e9			0.370496			0.185248	+	0.982692i	$0.440691\pi$
$354$	1.55052e9	−	1.88741e9i	0.0987334	−	0.120186i
$355$		−	3.87340e9i		−	0.243882i
$356$	−2.12548e8	−	1.07409e9i	−0.0132330	−	0.0668716i
$357$	−6.97184e9			−0.429214
$358$	2.40025e9	+	1.97182e9i	0.146125	+	0.120043i
$359$			4.65457e9i			0.280222i	0.990136	+	0.140111i	$0.0447459\pi$
$359$			4.65457e9i			0.280222i	−0.990136	+	0.140111i	$0.955254\pi$
$360$	−2.90661e10	−	1.55915e10i	−1.73052	−	0.928278i
$361$	−4.01008e10			−2.36115
$362$	−1.20626e10	+	1.46835e10i	−0.702433	+	0.855057i
$363$		−	6.99702e10i		−	4.02983i
$364$	3.67180e9	−	7.26600e8i	0.209157	−	0.0413895i
$365$	2.80229e10			1.57885
$366$	1.05856e10	+	8.69609e9i	0.589915	+	0.484618i
$367$		−	1.54218e10i		−	0.850099i	−0.905170	−	0.425049i	$-0.860257\pi$
$367$		−	1.54218e10i		−	0.850099i	0.905170	−	0.425049i	$-0.139743\pi$
$368$	−3.19258e9	−	7.75080e9i	−0.174081	−	0.422625i
$369$	2.79807e10			1.50922
$370$	7.69592e9	−	9.36807e9i	0.410633	−	0.499854i
$371$		−	8.92376e9i		−	0.471034i
$372$	−6.45669e9	−	3.26282e10i	−0.337162	−	1.70381i
$373$	−2.30539e10			−1.19099			−0.595495	−	0.803359i	$-0.703044\pi$
$373$	−2.30539e10			−1.19099			−0.595495	+	0.803359i	$0.703044\pi$
$374$	1.86395e10	+	1.53124e10i	0.952680	+	0.782631i
$375$			3.14826e10i			1.59201i
$376$	−3.49756e9	+	6.52023e9i	−0.174990	+	0.326221i
$377$	−3.21377e9			−0.159092
$378$	−7.19339e9	+	8.75635e9i	−0.352343	+	0.428900i
$379$			1.21581e10i			0.589264i	0.955611	+	0.294632i	$0.0951971\pi$
$379$			1.21581e10i			0.589264i	−0.955611	+	0.294632i	$0.904803\pi$
$380$	−3.94383e10	+	7.80431e9i	−1.89140	+	0.374283i
$381$	5.96520e10			2.83091
$382$	6.11108e9	+	5.02028e9i	0.286988	+	0.235762i
$383$		−	1.95573e10i		−	0.908893i	−0.890774	−	0.454446i	$-0.849837\pi$
$383$		−	1.95573e10i		−	0.908893i	0.890774	−	0.454446i	$-0.150163\pi$
$384$	−3.73534e9	+	3.66280e10i	−0.171793	+	1.68457i
$385$	1.60555e10			0.730771
$386$	−2.57417e10	+	3.13348e10i	−1.15954	+	1.41149i
$387$			1.50835e9i			0.0672449i
$388$	3.90441e9	+	1.97306e10i	0.172278	+	0.870588i
$389$	−2.79258e10			−1.21957			−0.609785	−	0.792566i	$-0.708744\pi$
$389$	−2.79258e10			−1.21957			−0.609785	+	0.792566i	$0.708744\pi$
$390$	1.79576e10	+	1.47522e10i	0.776227	+	0.637675i
$391$		−	7.16442e9i		−	0.306531i
$392$	2.97257e9	+	1.59453e9i	0.125889	+	0.0675288i
$393$	−4.54998e10			−1.90739
$394$	2.46559e10	−	3.00131e10i	1.02314	−	1.24545i
$395$		−	3.88971e10i		−	1.59782i
$396$	8.28131e10	−	1.63876e10i	3.36758	−	0.666400i
$397$	−2.77813e10			−1.11838			−0.559192	−	0.829038i	$-0.688889\pi$
$397$	−2.77813e10			−1.11838			−0.559192	+	0.829038i	$0.688889\pi$
$398$	1.98663e10	+	1.63203e10i	0.791743	+	0.650421i
$399$			2.97387e10i			1.17336i
$400$	−2.50949e9	+	1.03366e9i	−0.0980268	+	0.0403775i
$401$	2.15513e10			0.833482			0.416741	−	0.909025i	$-0.363172\pi$
$401$	2.15513e10			0.833482			0.416741	+	0.909025i	$0.363172\pi$
$402$	2.71958e10	−	3.31048e10i	1.04135	−	1.26761i
$403$			1.52620e10i			0.578617i
$404$	2.43749e9	+	1.23176e10i	0.0914994	+	0.462383i
$405$	−1.75273e10			−0.651470
$406$	−2.23795e9	−	1.83849e9i	−0.0823657	−	0.0676638i
$407$			3.10299e10i			1.13084i
$408$	−1.48748e10	+	2.77300e10i	−0.536798	+	1.00071i
$409$	3.19218e10			1.14076			0.570380	−	0.821381i	$-0.306796\pi$
$409$	3.19218e10			1.14076			0.570380	+	0.821381i	$0.306796\pi$
$410$	1.52468e10	−	1.85596e10i	0.539565	−	0.656801i
$411$			5.79479e10i			2.03082i
$412$	−1.24606e10	+	2.46578e9i	−0.432463	+	0.0855785i
$413$	−1.01009e9			−0.0347185
$414$	−1.93734e10	−	1.59154e10i	−0.659485	−	0.541771i
$415$			2.86205e10i			0.964907i
$416$	4.94399e9	−	1.61546e10i	0.165084	−	0.539414i
$417$	4.26647e10			1.41099
$418$	6.53158e10	−	7.95075e10i	2.13950	−	2.60437i
$419$		−	2.54225e9i		−	0.0824827i	−0.999149	−	0.0412413i	$-0.986869\pi$
$419$		−	2.54225e9i		−	0.0824827i	0.999149	−	0.0412413i	$-0.0131312\pi$
$420$	4.06574e9	+	2.05458e10i	0.130660	+	0.660277i
$421$	8.41539e9			0.267884			0.133942	−	0.990989i	$-0.457236\pi$
$421$	8.41539e9			0.267884			0.133942	+	0.990989i	$0.457236\pi$
$422$	−2.29181e10	−	1.88273e10i	−0.722650	−	0.593661i
$423$			2.21308e10i			0.691251i
$424$	−3.54936e10	−	1.90393e10i	−1.09821	−	0.589099i
$425$	−2.31963e9			−0.0710990
$426$	−8.20902e9	+	9.99266e9i	−0.249260	+	0.303419i
$427$		−	5.66510e9i		−	0.170410i
$428$	−3.83515e10	+	7.58925e9i	−1.14290	+	0.226164i
$429$	−5.94809e10			−1.75610
$430$	1.00049e9	+	8.21908e8i	0.0292644	+	0.0240408i
$431$		−	5.29025e10i		−	1.53309i	−0.642192	−	0.766544i	$-0.721975\pi$
$431$		−	5.29025e10i		−	1.53309i	0.642192	−	0.766544i	$-0.278025\pi$
$432$	1.94803e10	+	4.72933e10i	0.559319	+	1.35789i
$433$	−2.93322e10			−0.834437			−0.417219	−	0.908806i	$-0.636995\pi$
$433$	−2.93322e10			−0.834437			−0.417219	+	0.908806i	$0.636995\pi$
$434$	−8.73086e9	+	1.06279e10i	−0.246092	+	0.299563i
$435$		−	1.79829e10i		−	0.502229i
$436$	−6.73227e9	−	3.40209e10i	−0.186301	−	0.941455i
$437$	−3.05602e10			−0.837973
$438$	−7.22940e10	−	5.93899e10i	−1.96429	−	1.61367i
$439$		−	3.98026e10i		−	1.07165i	−0.844329	−	0.535826i	$-0.820000\pi$
$439$		−	3.98026e10i		−	1.07165i	0.844329	−	0.535826i	$-0.180000\pi$
$440$	3.42553e10	−	6.38597e10i	0.913940	−	1.70379i
$441$	1.00894e10			0.266755
$442$	9.16558e9	−	1.11571e10i	0.240144	−	0.292322i
$443$			4.91921e10i			1.27726i	0.769512	+	0.638632i	$0.220499\pi$
$443$			4.91921e10i			1.27726i	−0.769512	+	0.638632i	$0.779501\pi$
$444$	−3.97081e10	+	7.85770e9i	−1.02176	+	0.202192i
$445$	−2.81128e9			−0.0716908
$446$	4.97430e10	+	4.08641e10i	1.25716	+	1.03277i
$447$		−	4.72811e10i		−	1.18429i
$448$	1.26843e10	−	8.42115e9i	0.314886	−	0.209054i
$449$	4.51734e10			1.11147			0.555735	−	0.831360i	$-0.312437\pi$
$449$	4.51734e10			1.11147			0.555735	+	0.831360i	$0.312437\pi$
$450$	−5.15294e9	+	6.27256e9i	−0.125662	+	0.152966i
$451$			6.14751e10i			1.48591i
$452$	−2.26135e8	−	1.14275e9i	−0.00541769	−	0.0273778i
$453$	−4.72132e10			−1.12117
$454$	−3.51390e10	−	2.88668e10i	−0.827115	−	0.679479i
$455$		−	9.61039e9i		−	0.224231i
$456$	1.18284e11	+	6.34492e10i	2.73568	+	1.46746i
$457$	−5.68697e9			−0.130382			−0.0651908	−	0.997873i	$-0.520766\pi$
$457$	−5.68697e9			−0.130382			−0.0651908	+	0.997873i	$0.520766\pi$
$458$	1.08133e10	−	1.31628e10i	0.245752	−	0.299148i
$459$			4.37154e10i			0.984881i
$460$	−2.11133e10	+	4.17805e9i	−0.471548	+	0.0933130i
$461$	7.76005e10			1.71815			0.859075	−	0.511850i	$-0.171040\pi$
$461$	7.76005e10			1.71815			0.859075	+	0.511850i	$0.171040\pi$
$462$	−4.14203e10	−	3.40270e10i	−0.909170	−	0.746888i
$463$		−	9.21711e9i		−	0.200572i	−0.994959	−	0.100286i	$-0.968024\pi$
$463$		−	9.21711e9i		−	0.200572i	0.994959	−	0.100286i	$-0.0319758\pi$
$464$	−1.20872e10	+	4.97877e9i	−0.260769	+	0.107411i
$465$	−8.53995e10			−1.82660
$466$	−4.26711e10	+	5.19426e10i	−0.904878	+	1.10149i
$467$			1.01081e10i			0.212520i	0.994338	+	0.106260i	$0.0338876\pi$
$467$			1.01081e10i			0.212520i	−0.994338	+	0.106260i	$0.966112\pi$
$468$	−9.80917e9	−	4.95696e10i	−0.204479	−	1.03331i
$469$	−1.77168e10			−0.366179
$470$	1.46794e10	+	1.20592e10i	0.300827	+	0.247131i
$471$		−	2.29479e10i		−	0.466294i
$472$	−2.15509e9	+	4.01757e9i	−0.0434207	+	0.0809459i
$473$	−3.31393e9			−0.0662062
$474$	−8.24358e10	+	1.00347e11i	−1.63306	+	1.98789i
$475$			9.89450e9i			0.194366i
$476$	1.27651e10	−	2.52605e9i	0.248655	−	0.0492056i
$477$	−1.20472e11			−2.32708
$478$	5.97825e10	+	4.91116e10i	1.14515	+	0.940747i
$479$			2.74724e10i			0.521861i	0.965358	+	0.260930i	$0.0840293\pi$
$479$			2.74724e10i			0.521861i	−0.965358	+	0.260930i	$0.915971\pi$
$480$	9.03940e10	+	2.76644e10i	1.70284	+	0.521143i
$481$	1.85736e10			0.346990
$482$	1.94793e10	−	2.37118e10i	0.360899	−	0.439315i
$483$			1.59206e10i			0.292531i
$484$	2.53518e10	+	1.28113e11i	0.461984	+	2.33459i
$485$	5.16418e10			0.933328
$486$	−1.80896e10	−	1.48607e10i	−0.324253	−	0.266376i
$487$		−	7.18816e9i		−	0.127792i	−0.997957	−	0.0638958i	$-0.979647\pi$
$487$		−	7.18816e9i		−	0.127792i	0.997957	−	0.0638958i	$-0.0203525\pi$
$488$	−2.25325e10	−	1.20868e10i	−0.397311	−	0.213124i
$489$	−2.32879e9			−0.0407281
$490$	5.49777e9	−	6.69232e9i	0.0953679	−	0.116089i
$491$		−	7.61869e10i		−	1.31085i	−0.755259	−	0.655427i	$-0.772489\pi$
$491$		−	7.61869e10i		−	1.31085i	0.755259	−	0.655427i	$-0.227511\pi$
$492$	−7.86680e10	+	1.55673e10i	−1.34257	+	0.265677i
$493$	−1.11728e10			−0.189136
$494$	−4.75910e10	−	3.90962e10i	−0.799129	−	0.656489i
$495$		−	2.16751e11i		−	3.61027i
$496$	2.36439e10	+	5.74015e10i	0.390654	+	0.948412i
$497$	5.34780e9			0.0876495
$498$	6.06564e10	−	7.38357e10i	0.986187	−	1.20046i
$499$		−	1.21901e10i		−	0.196609i	−0.995156	−	0.0983047i	$-0.968658\pi$
$499$		−	1.21901e10i		−	0.196609i	0.995156	−	0.0983047i	$-0.0313420\pi$
$500$	−1.14068e10	−	5.76433e10i	−0.182510	−	0.922293i
$501$	1.70764e11			2.71047
$502$	−8.00330e9	−	6.57475e9i	−0.126024	−	0.103530i
$503$			1.06919e11i			1.67026i	0.550052	+	0.835130i	$0.314608\pi$
$503$			1.06919e11i			1.67026i	−0.550052	+	0.835130i	$0.685392\pi$
$504$	2.15263e10	−	4.01299e10i	0.333617	−	0.621937i
$505$	3.22396e10			0.495705
$506$	3.49669e10	−	4.25644e10i	0.533402	−	0.649299i
$507$		−	7.62802e10i		−	1.15446i
$508$	−1.09220e11	+	2.16133e10i	−1.64002	+	0.324538i
$509$	−4.83273e10			−0.719982			−0.359991	−	0.932956i	$-0.617220\pi$
$509$	−4.83273e10			−0.719982			−0.359991	+	0.932956i	$0.617220\pi$
$510$	6.24301e10	+	5.12867e10i	0.922813	+	0.758095i
$511$			3.86897e10i			0.567430i
$512$	−6.43190e9	−	6.84178e10i	−0.0935964	−	0.995610i
$513$	1.86470e11			2.69240
$514$	1.73435e10	−	2.11119e10i	0.248476	−	0.302464i
$515$			3.26136e10i			0.463629i
$516$	−8.39186e8	−	4.24074e9i	−0.0118375	−	0.0598196i
$517$	−4.86225e10			−0.680574
$518$	1.29340e10	+	1.06253e10i	0.179644	+	0.147579i
$519$		−	2.90231e10i		−	0.400014i
$520$	−3.82246e10	−	2.05043e10i	−0.522793	−	0.280435i
$521$	6.18916e10			0.840003			0.420002	−	0.907523i	$-0.362030\pi$
$521$	6.18916e10			0.840003			0.420002	+	0.907523i	$0.362030\pi$
$522$	−2.48197e10	+	3.02125e10i	−0.334284	+	0.406916i
$523$			4.49254e10i			0.600462i	0.953867	+	0.300231i	$0.0970638\pi$
$523$			4.49254e10i			0.600462i	−0.953867	+	0.300231i	$0.902936\pi$
$524$	8.33083e10	−	1.64856e10i	1.10500	−	0.218665i
$525$	5.15465e9			0.0678518
$526$	−6.77484e10	−	5.56557e10i	−0.885027	−	0.727054i
$527$			5.30589e10i			0.687884i
$528$	−2.23712e11	+	9.21477e10i	−2.87842	+	1.18563i
$529$	6.19506e10			0.791084
$530$	−6.56455e10	+	7.99089e10i	−0.831959	+	1.01272i
$531$			1.36363e10i			0.171522i
$532$	−1.07750e10	−	5.44503e10i	−0.134515	−	0.679758i
$533$	3.67973e10			0.455939
$534$	7.25257e9	+	5.95803e9i	0.0891923	+	0.0732719i
$535$			1.00379e11i			1.22526i
$536$	−3.77997e10	+	7.04672e10i	−0.457962	+	0.853744i
$537$	−2.66286e10			−0.320222
$538$	−4.66727e10	+	5.68137e10i	−0.557101	+	0.678147i
$539$			2.21670e10i			0.262634i
$540$	1.28828e11	−	2.54933e10i	1.51508	−	0.299814i
$541$	1.19284e11			1.39249			0.696247	−	0.717802i	$-0.254852\pi$
$541$	1.19284e11			1.39249			0.696247	+	0.717802i	$0.254852\pi$
$542$	1.21156e11	+	9.95300e10i	1.40393	+	1.15334i
$543$		−	1.62900e11i		−	1.87379i
$544$	1.71880e10	−	5.61619e10i	0.196259	−	0.641278i
$545$	−8.90445e10			−1.00930
$546$	−2.03676e10	+	2.47930e10i	−0.229176	+	0.278971i
$547$		−	7.40033e10i		−	0.826612i	−0.910592	−	0.413306i	$-0.864374\pi$
$547$		−	7.40033e10i		−	0.826612i	0.910592	−	0.413306i	$-0.135626\pi$
$548$	−2.09958e10	−	1.06100e11i	−0.232815	−	1.17651i
$549$	−7.64793e10			−0.841889
$550$	−1.37811e10	−	1.13213e10i	−0.150603	−	0.123721i
$551$			4.76581e10i			0.517047i
$552$	6.33232e10	+	3.39676e10i	0.682035	+	0.365854i
$553$	5.37031e10			0.574247
$554$	−3.86834e10	+	4.70884e10i	−0.410663	+	0.499891i
$555$			1.03930e11i			1.09539i
$556$	−7.81173e10	+	1.54584e10i	−0.817425	+	0.161757i
$557$	6.40251e10			0.665166			0.332583	−	0.943074i	$-0.392080\pi$
$557$	6.40251e10			0.665166			0.332583	+	0.943074i	$0.392080\pi$
$558$	1.43477e11	+	1.17867e11i	1.47995	+	1.21579i
$559$			1.98363e9i			0.0203148i
$560$	−1.48884e10	−	3.61454e10i	−0.151390	−	0.367537i
$561$	−2.06787e11			−2.08772
$562$	−4.89385e10	+	5.95717e10i	−0.490575	+	0.597166i
$563$			1.71348e10i			0.170547i	0.996358	+	0.0852737i	$0.0271765\pi$
$563$			1.71348e10i			0.170547i	−0.996358	+	0.0852737i	$0.972824\pi$
$564$	−1.23127e10	−	6.22209e10i	−0.121685	−	0.614922i
$565$	−2.99098e9			−0.0293508
$566$	4.54121e10	+	3.73063e10i	0.442492	+	0.363510i
$567$		−	2.41990e10i		−	0.234134i
$568$	1.14098e10	−	2.12705e10i	0.109619	−	0.204354i
$569$	−1.46030e11			−1.39313			−0.696567	−	0.717492i	$-0.745290\pi$
$569$	−1.46030e11			−1.39313			−0.696567	+	0.717492i	$0.745290\pi$
$570$	2.18766e11	−	2.66299e11i	2.07243	−	2.52272i
$571$			2.01677e11i			1.89719i	0.316487	+	0.948597i	$0.397497\pi$
$571$			2.01677e11i			1.89719i	−0.316487	+	0.948597i	$0.602503\pi$
$572$	1.08907e11	−	2.15512e10i	1.01735	−	0.201321i
$573$	−6.77967e10			−0.628912
$574$	2.56243e10	+	2.10505e10i	0.236050	+	0.193916i
$575$			5.29703e9i			0.0484575i
$576$	−1.13686e11	−	1.71239e11i	−1.03280	−	1.55565i
$577$	−1.01108e11			−0.912184			−0.456092	−	0.889933i	$-0.650751\pi$
$577$	−1.01108e11			−0.912184			−0.456092	+	0.889933i	$0.650751\pi$
$578$	−3.89840e10	+	4.74544e10i	−0.349281	+	0.425173i
$579$		−	3.47630e11i		−	3.09317i
$580$	6.51559e9	+	3.29259e10i	0.0575761	+	0.290955i
$581$	−3.95148e10			−0.346781
$582$	−1.33226e11	−	1.09446e11i	−1.16118	−	0.953912i
$583$		−	2.64682e11i		−	2.29113i
$584$	1.53886e11	+	8.25467e10i	1.32296	+	0.709657i
$585$	−1.29741e11			−1.10778
$586$	1.27858e10	−	1.55639e10i	0.108427	−	0.131986i
$587$		−	2.93518e10i		−	0.247219i	−0.992331	−	0.123609i	$-0.960553\pi$
$587$		−	2.93518e10i		−	0.247219i	0.992331	−	0.123609i	$-0.0394470\pi$
$588$	−2.83665e10	+	5.61335e9i	−0.237299	+	0.0469583i
$589$	2.26325e11			1.88049
$590$	9.04498e9	+	7.43050e9i	0.0746448	+	0.0613211i
$591$			3.32967e11i			2.72930i
$592$	6.98569e10	−	2.87743e10i	0.568751	−	0.234270i
$593$	−9.94526e10			−0.804261			−0.402131	−	0.915582i	$-0.631730\pi$
$593$	−9.94526e10			−0.804261			−0.402131	+	0.915582i	$0.631730\pi$
$594$	−2.13359e11	+	2.59717e11i	−1.71382	+	2.08619i
$595$		−	3.34109e10i		−	0.266575i
$596$	1.71310e10	+	8.65699e10i	0.135768	+	0.686091i
$597$	−2.20398e11			−1.73504
$598$	−2.54779e10	−	2.09302e10i	−0.199232	−	0.163670i
$599$		−	1.41709e11i		−	1.10075i	−0.834916	−	0.550377i	$-0.814484\pi$
$599$		−	1.41709e11i		−	1.10075i	0.834916	−	0.550377i	$-0.185516\pi$
$600$	1.09977e10	−	2.05022e10i	0.0848590	−	0.158196i
$601$	−1.56728e11			−1.20129			−0.600645	−	0.799516i	$-0.705090\pi$
$601$	−1.56728e11			−1.20129			−0.600645	+	0.799516i	$0.705090\pi$
$602$	−1.13476e9	+	1.38132e9i	−0.00864012	+	0.0105174i
$603$			2.39178e11i			1.80906i
$604$	8.64455e10	−	1.71064e10i	0.649523	−	0.128532i
$605$	3.35316e11			2.50284
$606$	−8.31721e10	−	6.83263e10i	−0.616719	−	0.506638i
$607$		−	9.53187e10i		−	0.702139i	−0.936349	−	0.351070i	$-0.885818\pi$
$607$		−	9.53187e10i		−	0.702139i	0.936349	−	0.351070i	$-0.114182\pi$
$608$	−2.39561e11	−	7.33161e10i	−1.75308	−	0.536519i
$609$	2.48280e10			0.180498
$610$	−4.16740e10	+	5.07288e10i	−0.300985	+	0.366383i
$611$			2.91041e10i			0.208828i
$612$	−3.41019e10	−	1.72331e11i	−0.243094	−	1.22845i
$613$	−2.79765e10			−0.198131			−0.0990655	−	0.995081i	$-0.531585\pi$
$613$	−2.79765e10			−0.198131			−0.0990655	+	0.995081i	$0.531585\pi$
$614$	1.27689e11	+	1.04897e11i	0.898418	+	0.738055i
$615$			2.05902e11i			1.43933i
$616$	8.81676e10	+	4.72945e10i	0.612331	+	0.328464i
$617$	−1.32782e11			−0.916216			−0.458108	−	0.888897i	$-0.651473\pi$
$617$	−1.32782e11			−0.916216			−0.458108	+	0.888897i	$0.651473\pi$
$618$	6.91191e10	−	8.41372e10i	0.473854	−	0.576812i
$619$		−	2.52840e11i		−	1.72220i	−0.508438	−	0.861098i	$-0.669777\pi$
$619$		−	2.52840e11i		−	1.72220i	0.508438	−	0.861098i	$-0.330223\pi$
$620$	1.56363e11	−	3.09421e10i	1.05820	−	0.209403i
$621$	9.98270e10			0.671246
$622$	−9.09226e10	−	7.46934e10i	−0.607450	−	0.499023i
$623$		−	3.88138e9i		−	0.0257652i
$624$	5.51571e10	+	1.33908e11i	0.363800	+	0.883218i
$625$	−1.67050e11			−1.09478
$626$	−2.28914e10	+	2.78652e10i	−0.149065	+	0.181453i
$627$			8.82062e11i			5.70727i
$628$	8.31455e9	+	4.20168e10i	0.0534565	+	0.270137i
$629$	6.45719e10			0.412516
$630$	−9.03469e10	−	7.42204e10i	−0.573523	−	0.471152i
$631$		−	2.94434e11i		−	1.85725i	−0.371022	−	0.928624i	$-0.620993\pi$
$631$		−	2.94434e11i		−	1.85725i	0.371022	−	0.928624i	$-0.379007\pi$
$632$	1.14579e11	−	2.13600e11i	0.718183	−	1.33885i
$633$	2.54255e11			1.58363
$634$	4.81811e10	−	5.86498e10i	0.298208	−	0.363003i
$635$			2.85868e11i			1.75821i
$636$	3.38707e11	−	6.70255e10i	2.07012	−	0.409649i
$637$	1.32685e10			0.0805871
$638$	−6.63785e10	−	5.45303e10i	−0.400631	−	0.329120i
$639$		−	7.21957e10i		−	0.433020i
$640$	−1.75531e11	−	1.79007e10i	−1.04625	−	0.106697i
$641$	−8.62098e9			−0.0510651			−0.0255326	−	0.999674i	$-0.508128\pi$
$641$	−8.62098e9			−0.0510651			−0.0255326	+	0.999674i	$0.508128\pi$
$642$	2.12737e11	−	2.58960e11i	1.25228	−	1.52438i
$643$			6.56298e10i			0.383934i	0.981401	+	0.191967i	$0.0614867\pi$
$643$			6.56298e10i			0.383934i	−0.981401	+	0.191967i	$0.938513\pi$
$644$	−5.76840e9	−	2.91501e10i	−0.0335361	−	0.169471i
$645$	−1.10995e10			−0.0641306
$646$	−1.65452e11	−	1.35920e11i	−0.950039	−	0.780462i
$647$		−	2.20959e11i		−	1.26094i	−0.776214	−	0.630469i	$-0.782862\pi$
$647$		−	2.20959e11i		−	1.26094i	0.776214	−	0.630469i	$-0.217138\pi$
$648$	−9.62496e10	−	5.16298e10i	−0.545882	−	0.292820i
$649$	−2.99597e10			−0.168872
$650$	−6.77660e9	+	8.24901e9i	−0.0379628	+	0.0462113i
$651$		−	1.17906e11i		−	0.656468i
$652$	4.26392e9	−	8.43772e8i	0.0235949	−	0.00466912i
$653$	2.14034e11			1.17714			0.588572	−	0.808445i	$-0.299690\pi$
$653$	2.14034e11			1.17714			0.588572	+	0.808445i	$0.299690\pi$
$654$	2.29719e11	+	1.88715e11i	1.25570	+	1.03156i
$655$		−	2.18047e11i		−	1.18464i
$656$	1.38397e11	−	5.70063e10i	0.747331	−	0.307828i
$657$	5.22315e11			2.80331
$658$	−1.66495e10	+	2.02670e10i	−0.0888171	+	0.108115i
$659$		−	1.08027e11i		−	0.572782i	−0.958113	−	0.286391i	$-0.907544\pi$
$659$		−	1.08027e11i		−	0.572782i	0.958113	−	0.286391i	$-0.0924556\pi$
$660$	1.20591e11	+	6.09397e11i	0.635537	+	3.21162i
$661$	7.81382e10			0.409315			0.204657	−	0.978834i	$-0.434392\pi$
$661$	7.81382e10			0.409315			0.204657	+	0.978834i	$0.434392\pi$
$662$	1.68820e10	+	1.38686e10i	0.0879006	+	0.0722108i
$663$			1.23777e11i			0.640600i
$664$	−8.43071e10	+	1.57167e11i	−0.433702	+	0.808519i
$665$	−1.42516e11			−0.728746
$666$	1.43443e11	−	1.74610e11i	0.729092	−	0.887508i
$667$			2.55138e10i			0.128906i
$668$	−3.12662e11	+	6.18715e10i	−1.57025	+	0.310731i
$669$	−5.51852e11			−2.75498
$670$	1.58647e11	+	1.30329e11i	0.787286	+	0.646760i
$671$		−	1.68029e11i		−	0.828885i
$672$	−3.81948e10	+	1.24802e11i	−0.187295	+	0.611990i
$673$	2.32190e11			1.13184			0.565918	−	0.824462i	$-0.308522\pi$
$673$	2.32190e11			1.13184			0.565918	+	0.824462i	$0.308522\pi$
$674$	−1.38865e10	+	1.69037e10i	−0.0672904	+	0.0819111i
$675$		−	3.23211e10i		−	0.155694i
$676$	2.76380e10	+	1.39666e11i	0.132349	+	0.668811i
$677$	−1.77300e11			−0.844022			−0.422011	−	0.906591i	$-0.638676\pi$
$677$	−1.77300e11			−0.844022			−0.422011	+	0.906591i	$0.638676\pi$
$678$	7.71618e9	+	6.33888e9i	0.0365160	+	0.0299981i
$679$			7.12990e10i			0.335432i
$680$	−1.32889e11	−	7.12840e10i	−0.621519	−	0.333393i
$681$	3.89834e11			1.81256
$682$	−2.58961e11	+	3.15227e11i	−1.19701	+	1.45709i
$683$		−	1.20209e11i		−	0.552399i	−0.961100	−	0.276199i	$-0.910925\pi$
$683$		−	1.20209e11i		−	0.552399i	0.961100	−	0.276199i	$-0.0890750\pi$
$684$	−7.35085e11	+	1.45463e11i	−3.35825	+	0.664553i
$685$	−2.77702e11			−1.26129
$686$	9.23972e9	+	7.59048e9i	0.0417217	+	0.0342746i
$687$			1.46029e11i			0.655560i
$688$	3.07303e9	+	7.46057e9i	0.0137156	+	0.0332980i
$689$	−1.58431e11			−0.703015
$690$	1.17116e11	−	1.42563e11i	0.516680	−	0.628943i
$691$			8.98059e10i			0.393906i	0.980413	+	0.196953i	$0.0631047\pi$
$691$			8.98059e10i			0.393906i	−0.980413	+	0.196953i	$0.936895\pi$
$692$	1.05157e10	+	5.31402e10i	0.0458580	+	0.231739i
$693$	2.99256e11			1.29751
$694$	4.12428e10	+	3.38811e10i	0.177791	+	0.146056i
$695$			2.04460e11i			0.876334i
$696$	5.29719e10	−	9.87515e10i	0.225740	−	0.420830i
$697$	1.27927e11			0.542040
$698$	6.27337e10	−	7.63644e10i	0.264289	−	0.321713i
$699$		−	5.76254e11i		−	2.41382i
$700$	−9.43795e9	+	1.86764e9i	−0.0393084	+	0.00777861i
$701$	−3.54522e11			−1.46815			−0.734077	−	0.679066i	$-0.762385\pi$
$701$	−3.54522e11			−1.46815			−0.734077	+	0.679066i	$0.762385\pi$
$702$	1.55459e11	+	1.27711e11i	0.640130	+	0.525870i
$703$		−	2.75435e11i		−	1.12771i
$704$	3.76221e11	−	2.49775e11i	1.53162	−	1.01685i
$705$	−1.62854e11			−0.659238
$706$	5.84281e10	−	7.11232e10i	0.235181	−	0.286281i
$707$			4.45114e10i			0.178153i
$708$	−7.58670e9	−	3.83386e10i	−0.0301940	−	0.152582i
$709$	2.53353e11			1.00263			0.501316	−	0.865264i	$-0.332850\pi$
$709$	2.53353e11			1.00263			0.501316	+	0.865264i	$0.332850\pi$
$710$	−4.78875e10	−	3.93398e10i	−0.188447	−	0.154810i
$711$		−	7.24997e11i		−	2.83699i
$712$	−1.54379e10	−	8.28113e9i	−0.0600714	−	0.0322233i
$713$	1.21163e11			0.468828
$714$	−7.08087e10	+	8.61939e10i	−0.272454	+	0.331653i
$715$		−	2.85048e11i		−	1.09067i
$716$	4.87559e10	−	9.64813e9i	0.185513	−	0.0367106i
$717$	−6.63231e11			−2.50951
$718$	5.75451e10	+	4.72736e10i	0.216526	+	0.177878i
$719$		−	1.05815e11i		−	0.395941i	−0.980208	−	0.197970i	$-0.936565\pi$
$719$		−	1.05815e11i		−	0.395941i	0.980208	−	0.197970i	$-0.0634350\pi$
$720$	−4.87967e11	+	2.00995e11i	−1.81577	+	0.747920i
$721$	−4.50279e10			−0.166625
$722$	−4.07279e11	+	4.95772e11i	−1.49880	+	1.82446i
$723$			2.63060e11i			0.962724i
$724$	5.90222e10	+	2.98263e11i	0.214813	+	1.08554i
$725$	8.26063e9			0.0298993
$726$	−8.65053e11	−	7.10645e11i	−3.11384	−	2.55803i
$727$			3.46349e11i			1.23987i	0.784653	+	0.619935i	$0.212841\pi$
$727$			3.46349e11i			1.23987i	−0.784653	+	0.619935i	$0.787159\pi$
$728$	2.83092e10	−	5.27747e10i	0.100786	−	0.187888i
$729$	3.75641e11			1.33004
$730$	2.84612e11	−	3.46452e11i	1.00222	−	1.21998i
$731$			6.89615e9i			0.0241511i
$732$	2.15022e11	−	4.25500e10i	0.748926	−	0.148202i
$733$	4.60065e11			1.59369			0.796844	−	0.604185i	$-0.206501\pi$
$733$	4.60065e11			1.59369			0.796844	+	0.604185i	$0.206501\pi$
$734$	−1.90662e11	−	1.56629e11i	−0.656869	−	0.539621i
$735$			7.42450e10i			0.254401i
$736$	−1.28249e11	−	3.92499e10i	−0.437063	−	0.133760i
$737$	−5.25487e11			−1.78111
$738$	2.84183e11	−	3.45930e11i	0.958016	−	1.16617i
$739$			1.47154e11i			0.493394i	0.969093	+	0.246697i	$0.0793453\pi$
$739$			1.47154e11i			0.493394i	−0.969093	+	0.246697i	$0.920655\pi$
$740$	−3.76562e10	−	1.90292e11i	−0.125577	−	0.634589i
$741$	5.27978e11			1.75123
$742$	−1.10326e11	−	9.06332e10i	−0.363967	−	0.299000i
$743$			5.11405e11i			1.67807i	0.544078	+	0.839035i	$0.316880\pi$
$743$			5.11405e11i			1.67807i	−0.544078	+	0.839035i	$0.683120\pi$
$744$	−4.68964e11	−	2.51560e11i	−1.53055	−	0.821013i
$745$	2.26584e11			0.735535
$746$	−2.34144e11	+	2.85018e11i	−0.756011	+	0.920275i
$747$			5.33454e11i			1.71322i
$748$	3.78619e11	−	7.49237e10i	1.20947	−	0.239339i
$749$	−1.38588e11			−0.440351
$750$	3.89224e11	+	3.19750e11i	1.23014	+	1.01057i
$751$			1.62445e11i			0.510678i	0.966852	+	0.255339i	$0.0821870\pi$
$751$			1.62445e11i			0.510678i	−0.966852	+	0.255339i	$0.917813\pi$
$752$	4.50881e10	+	1.09463e11i	0.140991	+	0.342291i
$753$	8.87892e10			0.276172
$754$	−3.26403e10	+	3.97323e10i	−0.100988	+	0.122930i
$755$		−	2.26258e11i		−	0.696333i
$756$	3.51973e10	+	1.77866e11i	0.107751	+	0.544510i
$757$	5.36933e11			1.63507			0.817535	−	0.575879i	$-0.195340\pi$
$757$	5.36933e11			1.63507			0.817535	+	0.575879i	$0.195340\pi$
$758$	1.50313e11	+	1.23483e11i	0.455323	+	0.374050i
$759$			4.72213e11i			1.42289i
$760$	−3.04065e11	+	5.66846e11i	−0.911407	+	1.69907i
$761$	−6.67048e10			−0.198893			−0.0994463	−	0.995043i	$-0.531707\pi$
$761$	−6.67048e10			−0.198893			−0.0994463	+	0.995043i	$0.531707\pi$
$762$	6.05850e11	−	7.37488e11i	1.79699	−	2.18743i
$763$		−	1.22939e11i		−	0.362737i
$764$	1.24133e11	−	2.45643e10i	0.364346	−	0.0720992i
$765$	−4.51050e11			−1.31698
$766$	−2.41789e11	−	1.98631e11i	−0.702299	−	0.576942i
$767$			1.79331e10i			0.0518171i
$768$	4.14900e11	+	4.18189e11i	1.19261	+	1.20206i
$769$	−7.77898e10			−0.222442			−0.111221	−	0.993796i	$-0.535476\pi$
$769$	−7.77898e10			−0.222442			−0.111221	+	0.993796i	$0.535476\pi$
$770$	1.63066e11	−	1.98497e11i	0.463875	−	0.564665i
$771$			2.34216e11i			0.662826i
$772$	1.25954e11	+	6.36497e11i	0.354604	+	1.79195i
$773$	−5.17211e11			−1.44860			−0.724302	−	0.689483i	$-0.757838\pi$
$773$	−5.17211e11			−1.44860			−0.724302	+	0.689483i	$0.757838\pi$
$774$	1.86480e10	+	1.53194e10i	0.0519599	+	0.0426853i
$775$		−	3.92292e10i		−	0.108743i
$776$	2.83587e11	+	1.52120e11i	0.782058	+	0.419509i
$777$	−1.43491e11			−0.393676
$778$	−2.83625e11	+	3.45251e11i	−0.774153	+	0.942359i
$779$		−	5.45679e11i		−	1.48179i
$780$	3.64768e11	−	7.21827e10i	0.985459	−	0.195009i
$781$	1.58618e11			0.426332
$782$	−8.85748e10	−	7.27647e10i	−0.236855	−	0.194578i
$783$		−	1.55678e11i		−	0.414173i
$784$	4.99040e10	−	2.05556e10i	0.132090	−	0.0544084i
$785$	1.09973e11			0.289605
$786$	−4.62114e11	+	5.62521e11i	−1.21076	+	1.47383i
$787$		−	4.36437e10i		−	0.113769i	−0.998381	−	0.0568843i	$-0.981883\pi$
$787$		−	4.36437e10i		−	0.113769i	0.998381	−	0.0568843i	$-0.0181166\pi$
$788$	−1.20641e11	−	6.09649e11i	−0.312890	−	1.58116i
$789$	7.51606e11			1.93947
$790$	−4.80891e11	−	3.95054e11i	−1.23463	−	1.01426i
$791$		−	4.12948e9i		−	0.0105485i
$792$	6.38480e11	−	1.19027e12i	1.62273	−	3.02514i
$793$	−1.00578e11			−0.254336
$794$	−2.82158e11	+	3.43465e11i	−0.709922	+	0.864172i
$795$		−	8.86514e11i		−	2.21931i
$796$	4.03540e11	−	7.98551e10i	1.00516	−	0.198907i
$797$	−7.00915e11			−1.73713			−0.868565	−	0.495576i	$-0.834957\pi$
$797$	−7.00915e11			−1.73713			−0.868565	+	0.495576i	$0.834957\pi$
$798$	3.67664e11	+	3.02038e11i	0.906650	+	0.744818i
$799$			1.01182e11i			0.248264i
$800$	−1.27080e10	+	4.15235e10i	−0.0310253	+	0.101376i
$801$	−5.23989e10			−0.127289
$802$	2.18884e11	−	2.66442e11i	0.529073	−	0.644029i
$803$			1.14755e12i			2.76001i
$804$	−1.33069e11	−	6.72451e11i	−0.318459	−	1.60930i
$805$	−7.62959e10			−0.181684
$806$	1.88686e11	+	1.55007e11i	0.447095	+	0.367291i
$807$		−	6.30295e11i		−	1.48611i
$808$	1.77041e11	+	9.49676e10i	0.415363	+	0.222808i
$809$	7.69699e11			1.79691			0.898457	−	0.439062i	$-0.144689\pi$
$809$	7.69699e11			1.79691			0.898457	+	0.439062i	$0.144689\pi$
$810$	−1.78014e11	+	2.16692e11i	−0.413537	+	0.503389i
$811$			1.74434e11i			0.403226i	0.979465	+	0.201613i	$0.0646184\pi$
$811$			1.74434e11i			0.403226i	−0.979465	+	0.201613i	$0.935382\pi$
$812$	−4.54590e10	+	8.99573e9i	−0.104567	+	0.0206925i
$813$	−1.34411e12			−3.07661
$814$	3.83627e11	+	3.15152e11i	0.873800	+	0.717831i
$815$		−	1.11602e10i		−	0.0252953i
$816$	1.91756e11	+	4.65536e11i	0.432502	+	1.05001i
$817$	2.94159e10			0.0660227
$818$	3.24211e11	−	3.94655e11i	0.724126	−	0.881463i
$819$		−	1.79127e11i		−	0.398129i
$820$	−7.46028e10	−	3.76998e11i	−0.165006	−	0.833841i
$821$	−4.95290e11			−1.09015			−0.545075	−	0.838387i	$-0.683499\pi$
$821$	−4.95290e11			−1.09015			−0.545075	+	0.838387i	$0.683499\pi$
$822$	7.16419e11	+	5.88542e11i	1.56921	+	1.28911i
$823$		−	1.70543e11i		−	0.371736i	−0.982575	−	0.185868i	$-0.940490\pi$
$823$		−	1.70543e11i		−	0.371736i	0.982575	−	0.185868i	$-0.0595097\pi$
$824$	−9.60695e10	+	1.79095e11i	−0.208390	+	0.388486i
$825$	1.52889e11			0.330035
$826$	−1.02589e10	+	1.24879e10i	−0.0220384	+	0.0268269i
$827$			1.94768e9i			0.00416386i	0.999998	+	0.00208193i	$0.000662699\pi$
$827$			1.94768e9i			0.00416386i	−0.999998	+	0.00208193i	$0.999337\pi$
$828$	−3.93528e11	+	7.78740e10i	−0.837249	+	0.165680i
$829$	3.99121e11			0.845057			0.422528	−	0.906350i	$-0.361143\pi$
$829$	3.99121e11			0.845057			0.422528	+	0.906350i	$0.361143\pi$
$830$	3.53840e11	+	2.90681e11i	0.745581	+	0.612498i
$831$		−	5.22402e11i		−	1.09547i
$832$	−1.49508e11	−	2.25195e11i	−0.312012	−	0.469966i
$833$	4.61286e10			0.0958054
$834$	4.33319e11	−	5.27470e11i	0.895661	−	1.09027i
$835$			8.18345e11i			1.68341i
$836$	−3.19591e11	−	1.61502e12i	−0.654288	−	3.30638i
$837$	−7.39307e11			−1.50634
$838$	−3.14303e10	−	2.58201e10i	−0.0637341	−	0.0523579i
$839$			8.25578e11i			1.66613i	0.553172	+	0.833067i	$0.313417\pi$
$839$			8.25578e11i			1.66613i	−0.553172	+	0.833067i	$0.686583\pi$
$840$	2.95304e11	+	1.58406e11i	0.593134	+	0.318166i
$841$	−4.60458e11			−0.920463
$842$	8.54701e10	−	1.04041e11i	0.170046	−	0.206993i
$843$		−	6.60893e11i		−	1.30864i
$844$	−4.65530e11	+	9.21221e10i	−0.917440	+	0.181549i
$845$	3.65555e11			0.717010
$846$	2.73607e11	+	2.24769e11i	0.534128	+	0.438789i
$847$			4.62952e11i			0.899503i
$848$	−5.95873e11	+	2.45442e11i	−1.15231	+	0.474641i
$849$	−5.03805e11			−0.969687
$850$	−2.35591e10	+	2.86780e10i	−0.0451318	+	0.0549380i
$851$		−	1.47454e11i		−	0.281151i
$852$	4.01668e10	+	2.02979e11i	0.0762270	+	0.385205i
$853$	−1.07813e11			−0.203646			−0.101823	−	0.994803i	$-0.532468\pi$
$853$	−1.07813e11			−0.203646			−0.101823	+	0.994803i	$0.532468\pi$
$854$	−7.00385e10	−	5.75370e10i	−0.131676	−	0.108172i
$855$			1.92397e12i			3.60027i
$856$	−2.95686e11	+	5.51225e11i	−0.550726	+	1.02668i
$857$	3.23082e11			0.598949			0.299475	−	0.954104i	$-0.403189\pi$
$857$	3.23082e11			0.598949			0.299475	+	0.954104i	$0.403189\pi$
$858$	−6.04111e11	+	7.35371e11i	−1.11472	+	1.35693i
$859$		−	1.29588e11i		−	0.238009i	−0.992894	−	0.119005i	$-0.962030\pi$
$859$		−	1.29588e11i		−	0.238009i	0.992894	−	0.119005i	$-0.0379703\pi$
$860$	2.03228e10	−	4.02160e9i	0.0371526	−	0.00735200i
$861$	−2.84277e11			−0.517285
$862$	−6.54042e11	−	5.37299e11i	−1.18461	−	0.973165i
$863$		−	5.55601e11i		−	1.00166i	−0.865546	−	0.500830i	$-0.833028\pi$
$863$		−	5.55601e11i		−	1.00166i	0.865546	−	0.500830i	$-0.166972\pi$
$864$	7.82544e11	+	2.39492e11i	1.40428	+	0.429770i
$865$	1.39087e11			0.248439
$866$	−2.97910e11	+	3.62639e11i	−0.529680	+	0.644767i
$867$		−	5.26463e11i		−	0.931732i
$868$	4.27201e10	+	2.15882e11i	0.0752582	+	0.380310i
$869$	1.59285e12			2.79317
$870$	−2.22325e11	−	1.82641e11i	−0.388071	−	0.318802i
$871$			3.14542e11i			0.546520i
$872$	−4.88981e11	−	2.62297e11i	−0.845719	−	0.453657i
$873$	9.62544e11			1.65716
$874$	−3.10381e11	+	3.77820e11i	−0.531924	+	0.647500i
$875$		−	2.08302e11i		−	0.355354i
$876$	−1.46849e12	+	2.90595e11i	−2.49376	+	0.493482i
$877$	5.99578e11			1.01356			0.506778	−	0.862077i	$-0.330836\pi$
$877$	5.99578e11			1.01356			0.506778	+	0.862077i	$0.330836\pi$
$878$	−4.92086e11	−	4.04251e11i	−0.828062	−	0.680257i
$879$			1.72667e11i			0.289236i
$880$	−4.41596e11	−	1.07209e12i	−0.736368	−	1.78772i
$881$	−9.53880e11			−1.58340			−0.791699	−	0.610911i	$-0.790803\pi$
$881$	−9.53880e11			−1.58340			−0.791699	+	0.610911i	$0.790803\pi$
$882$	1.02472e11	−	1.24737e11i	0.169329	−	0.206121i
$883$		−	6.75733e11i		−	1.11156i	−0.831330	−	0.555779i	$-0.812420\pi$
$883$		−	6.75733e11i		−	1.11156i	0.831330	−	0.555779i	$-0.187580\pi$
$884$	−4.48473e10	−	2.26631e11i	−0.0734390	−	0.371117i
$885$	−1.00346e11			−0.163578
$886$	6.08170e11	+	4.99615e11i	0.986938	+	0.810775i
$887$			3.84198e11i			0.620670i	0.950627	+	0.310335i	$0.100441\pi$
$887$			3.84198e11i			0.620670i	−0.950627	+	0.310335i	$0.899559\pi$
$888$	−3.06145e11	+	5.70723e11i	−0.492352	+	0.917854i
$889$	−3.94683e11			−0.631890
$890$	−2.85524e10	+	3.47562e10i	−0.0455075	+	0.0553953i
$891$		−	7.17751e11i		−	1.13884i
$892$	1.01042e12	−	1.99948e11i	1.59603	−	0.315833i
$893$	4.31595e11			0.678688
$894$	−5.84544e11	−	4.80206e11i	−0.915097	−	0.751757i
$895$		−	1.27611e11i		−	0.198883i
$896$	2.47146e10	−	2.42346e11i	0.0383461	−	0.376014i
$897$	2.82653e11			0.436601
$898$	4.58799e11	−	5.58486e11i	0.705533	−	0.858829i
$899$		−	1.88952e11i		−	0.289277i
$900$	2.52134e10	+	1.27413e11i	0.0384291	+	0.194198i
$901$	−5.50793e11			−0.835775
$902$	7.60026e11	+	6.24365e11i	1.14816	+	0.943219i
$903$		−	1.53245e10i		−	0.0230481i
$904$	−1.64247e10	−	8.81049e9i	−0.0245937	−	0.0131925i
$905$	7.80658e11			1.16377
$906$	−4.79516e11	+	5.83705e11i	−0.711690	+	0.866324i
$907$		−	5.25447e11i		−	0.776425i	−0.921570	−	0.388212i	$-0.873093\pi$
$907$		−	5.25447e11i		−	0.776425i	0.921570	−	0.388212i	$-0.126907\pi$
$908$	−7.13771e11	+	1.41246e11i	−1.05006	+	0.207793i
$909$	6.00908e11			0.880142
$910$	−1.18815e11	−	9.76069e10i	−0.173263	−	0.142336i
$911$		−	7.54377e11i		−	1.09525i	−0.836722	−	0.547627i	$-0.815531\pi$
$911$		−	7.54377e11i		−	1.09525i	0.836722	−	0.547627i	$-0.184469\pi$
$912$	1.98577e12	−	8.17943e11i	2.87044	−	1.18234i
$913$	−1.17203e12			−1.68676
$914$	−5.77591e10	+	7.03089e10i	−0.0827629	+	0.100745i
$915$		−	5.62789e11i		−	0.802899i
$916$	−5.29096e10	−	2.67373e11i	−0.0751541	−	0.379784i
$917$	3.01046e11			0.425750
$918$	5.40460e11	+	4.43991e11i	0.761015	+	0.625177i
$919$			4.15366e11i			0.582330i	0.956673	+	0.291165i	$0.0940429\pi$
$919$			4.15366e11i			0.582330i	−0.956673	+	0.291165i	$0.905957\pi$
$920$	−1.62782e11	+	3.03462e11i	−0.227224	+	0.423597i
$921$	−1.41659e12			−1.96881
$922$	7.88142e11	−	9.59388e11i	1.09064	−	1.32761i
$923$		−	9.49442e10i		−	0.130816i
$924$	−8.41361e11	+	1.66494e11i	−1.15424	+	0.228408i
$925$	−4.77414e10			−0.0652121
$926$	−1.13953e11	−	9.36126e10i	−0.154982	−	0.127318i
$927$			6.07881e11i			0.823189i
$928$	−6.12095e10	+	2.00003e11i	−0.0825328	+	0.269677i
$929$	−8.20816e11			−1.10200			−0.551002	−	0.834504i	$-0.685754\pi$
$929$	−8.20816e11			−1.10200			−0.551002	+	0.834504i	$0.685754\pi$
$930$	−8.67351e11	+	1.05581e12i	−1.15948	+	1.41141i
$931$		−	1.96764e11i		−	0.261906i
$932$	2.08790e11	+	1.05510e12i	0.276723	+	1.39839i
$933$	1.00870e12			1.33118
$934$	1.24968e11	+	1.02661e11i	0.164214	+	0.134902i
$935$		−	9.90980e11i		−	1.29664i
$936$	−7.12463e11	−	3.82177e11i	−0.928237	−	0.497921i
$937$	4.95698e10			0.0643070			0.0321535	−	0.999483i	$-0.489763\pi$
$937$	4.95698e10			0.0643070			0.0321535	+	0.999483i	$0.489763\pi$
$938$	−1.79939e11	+	2.19035e11i	−0.232441	+	0.282945i
$939$		−	3.09138e11i		−	0.397640i
$940$	2.98179e11	−	5.90057e10i	0.381914	−	0.0755757i
$941$	5.18442e11			0.661214			0.330607	−	0.943769i	$-0.392747\pi$
$941$	5.18442e11			0.661214			0.330607	+	0.943769i	$0.392747\pi$
$942$	−2.83709e11	−	2.33068e11i	−0.360304	−	0.295992i
$943$		−	2.92130e11i		−	0.369428i
$944$	2.77819e10	+	6.74477e10i	0.0349843	+	0.0849335i
$945$	4.65538e11			0.583751
$946$	−3.36576e10	+	4.09706e10i	−0.0420260	+	0.0511573i
$947$		−	3.10319e11i		−	0.385841i	−0.981214	−	0.192921i	$-0.938204\pi$
$947$		−	3.10319e11i		−	0.385841i	0.981214	−	0.192921i	$-0.0617960\pi$
$948$	4.03359e11	+	2.03833e12i	0.499411	+	2.52372i
$949$	6.86894e11			0.846885
$950$	1.22327e11	+	1.00492e11i	0.150186	+	0.123378i
$951$			6.50665e11i			0.795492i
$952$	9.84179e10	−	1.83473e11i	0.119819	−	0.223370i
$953$	2.93068e11			0.355302			0.177651	−	0.984094i	$-0.443150\pi$
$953$	2.93068e11			0.355302			0.177651	+	0.984094i	$0.443150\pi$
$954$	−1.22356e12	+	1.48941e12i	−1.47717	+	1.79813i
$955$		−	3.24900e11i		−	0.390603i
$956$	1.21435e12	−	2.40303e11i	1.45382	−	0.287692i
$957$	7.36407e11			0.877951
$958$	3.39646e11	+	2.79020e11i	0.403240	+	0.331264i
$959$		−	3.83407e11i		−	0.453300i
$960$	1.26010e12	−	8.36584e11i	1.48361	−	0.984973i
$961$	−4.44311e10			−0.0520947
$962$	1.88641e11	−	2.29629e11i	0.220260	−	0.268118i
$963$			1.87096e12i			2.17550i
$964$	−9.53125e10	−	4.81652e11i	−0.110368	−	0.557732i
$965$	1.66594e12			1.92110
$966$	1.96829e11	+	1.61696e11i	0.226038	+	0.185691i
$967$			5.11470e11i			0.584944i	0.956274	+	0.292472i	$0.0944779\pi$
$967$			5.11470e11i			0.584944i	−0.956274	+	0.292472i	$0.905522\pi$
$968$	1.84136e12	+	9.87735e11i	2.09719	+	1.12496i
$969$	1.83553e12			2.08194
$970$	5.24495e11	−	6.38456e11i	0.592453	−	0.721180i
$971$			9.37891e11i			1.05506i	0.849538	+	0.527528i	$0.176881\pi$
$971$			9.37891e11i			1.05506i	−0.849538	+	0.527528i	$0.823119\pi$
$972$	−3.67450e11	+	7.27135e10i	−0.411655	+	0.0814611i
$973$	−2.82287e11			−0.314949
$974$	−8.88684e10	−	7.30058e10i	−0.0987442	−	0.0811188i
$975$		−	9.15151e10i		−	0.101268i
$976$	−3.78280e11	+	1.55815e11i	−0.416883	+	0.171715i
$977$	−6.09361e11			−0.668800			−0.334400	−	0.942431i	$-0.608534\pi$
$977$	−6.09361e11			−0.668800			−0.334400	+	0.942431i	$0.608534\pi$
$978$	−2.36521e10	+	2.87912e10i	−0.0258532	+	0.0314705i
$979$		−	1.15123e11i		−	0.125323i
$980$	−2.69006e10	−	1.35940e11i	−0.0291647	−	0.147381i
$981$	−1.65969e12			−1.79205
$982$	−9.41910e11	−	7.73784e11i	−1.01289	−	0.832096i
$983$		−	1.43805e12i		−	1.54014i	−0.637958	−	0.770071i	$-0.720221\pi$
$983$		−	1.43805e12i		−	1.54014i	0.637958	−	0.770071i	$-0.279779\pi$
$984$	−6.06522e11	+	1.13069e12i	−0.646943	+	1.20605i
$985$	−1.59566e12			−1.69511
$986$	−1.13475e11	+	1.38131e11i	−0.120059	+	0.146145i
$987$		−	2.24844e11i		−	0.236926i
$988$	−9.66706e11	+	1.91298e11i	−1.01453	+	0.200763i
$989$	1.57478e10			0.0164602
$990$	−2.67973e12	−	2.20141e12i	−2.78965	−	2.29171i
$991$			1.83354e12i			1.90106i	0.310639	+	0.950528i	$0.399457\pi$
$991$			1.83354e12i			1.90106i	−0.310639	+	0.950528i	$0.600543\pi$
$992$	9.49801e11	+	2.90680e11i	0.980812	+	0.300171i
$993$	−1.87290e11			−0.192627
$994$	5.43143e10	−	6.61156e10i	0.0556377	−	0.0677265i
$995$		−	1.05620e12i		−	1.07760i
$996$	−2.96792e11	−	1.49981e12i	−0.301589	−	1.52405i
$997$	−1.14913e12			−1.16302			−0.581512	−	0.813538i	$-0.697539\pi$
$997$	−1.14913e12			−1.16302			−0.581512	+	0.813538i	$0.697539\pi$
$998$	−1.50708e11	−	1.23807e11i	−0.151919	−	0.124803i
$999$			8.99726e11i			0.903334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.9.c.a.15.17	✓	24
4.3	odd	2	inner	28.9.c.a.15.18	yes	24
8.3	odd	2		448.9.d.d.127.23		24
8.5	even	2		448.9.d.d.127.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.c.a.15.17	✓	24	1.1	even	1	trivial
28.9.c.a.15.18	yes	24	4.3	odd	2	inner
448.9.d.d.127.2		24	8.5	even	2
448.9.d.d.127.23		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(10.1564 - 12.3632i) q^{2} +137.158i q^{3} +(-49.6953 - 251.130i) q^{4} -657.296 q^{5} +(1695.70 + 1393.03i) q^{6} -907.493i q^{7} +(-3609.49 - 1936.19i) q^{8} -12251.2 q^{9} +(-6675.76 + 8126.25i) q^{10} -26916.6i q^{11} +(34444.4 - 6816.09i) q^{12} -16111.5 q^{13} +(-11219.5 - 9216.85i) q^{14} -90153.2i q^{15} +(-60596.8 + 24960.0i) q^{16} -56012.3 q^{17} +(-124428. + 151464. i) q^{18} +238923. i q^{19} +(32664.5 + 165067. i) q^{20} +124470. q^{21} +(-332774. - 273376. i) q^{22} +127908. i q^{23} +(265563. - 495069. i) q^{24} +41412.9 q^{25} +(-163635. + 199189. i) q^{26} -780460. i q^{27} +(-227899. + 45098.1i) q^{28} +199470. q^{29} +(-1.11458e6 - 915631. i) q^{30} -947271. i q^{31} +(-306860. + 1.00267e6i) q^{32} +3.69182e6 q^{33} +(-568883. + 692489. i) q^{34} +596491. i q^{35} +(608829. + 3.07666e6i) q^{36} -1.15282e6 q^{37} +(2.95385e6 + 2.42660e6i) q^{38} -2.20982e6i q^{39} +(2.37250e6 + 1.27265e6i) q^{40} -2.28391e6 q^{41} +(1.26416e6 - 1.53884e6i) q^{42} -123118. i q^{43} +(-6.75957e6 + 1.33763e6i) q^{44} +8.05269e6 q^{45} +(1.58135e6 + 1.29908e6i) q^{46} -1.80641e6i q^{47} +(-3.42345e6 - 8.31131e6i) q^{48} -823543. q^{49} +(420606. - 511994. i) q^{50} -7.68253e6i q^{51} +(800667. + 4.04609e6i) q^{52} +9.83342e6 q^{53} +(-9.64895e6 - 7.92666e6i) q^{54} +1.76922e7i q^{55} +(-1.75708e6 + 3.27558e6i) q^{56} -3.27702e7 q^{57} +(2.02590e6 - 2.46608e6i) q^{58} -1.11306e6i q^{59} +(-2.26402e7 + 4.48019e6i) q^{60} +6.24258e6 q^{61} +(-1.17113e7 - 9.62086e6i) q^{62} +1.11179e7i q^{63} +(9.27958e6 + 1.39773e7i) q^{64} +1.05900e7 q^{65} +(3.74956e7 - 4.56425e7i) q^{66} -1.95228e7i q^{67} +(2.78355e6 + 1.40664e7i) q^{68} -1.75436e7 q^{69} +(7.37451e6 + 6.05820e6i) q^{70} +5.89294e6i q^{71} +(4.42207e7 + 2.37207e7i) q^{72} -4.26337e7 q^{73} +(-1.17085e7 + 1.42524e7i) q^{74} +5.68010e6i q^{75} +(6.00009e7 - 1.18734e7i) q^{76} -2.44266e7 q^{77} +(-2.73204e7 - 2.24438e7i) q^{78} +5.91774e7i q^{79} +(3.98300e7 - 1.64061e7i) q^{80} +2.66657e7 q^{81} +(-2.31963e7 + 2.82363e7i) q^{82} -4.35428e7i q^{83} +(-6.18556e6 - 3.12581e7i) q^{84} +3.68167e7 q^{85} +(-1.52213e6 - 1.25044e6i) q^{86} +2.73589e7i q^{87} +(-5.21156e7 + 9.71551e7i) q^{88} +4.27703e6 q^{89} +(8.17863e7 - 9.95566e7i) q^{90} +1.46211e7i q^{91} +(3.21215e7 - 6.35642e6i) q^{92} +1.29926e8 q^{93} +(-2.23330e7 - 1.83467e7i) q^{94} -1.57043e8i q^{95} +(-1.37524e8 - 4.20883e7i) q^{96} -7.85671e7 q^{97} +(-8.36423e6 + 1.01816e7i) q^{98} +3.29762e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) \) 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more