LMFDB - Embedded newform 35.10.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("35.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3018x^{4} + 3368x^{3} + 2066979x^{2} - 6329061x - 14714266 $ x^6 - 3x^5 - 3018x^4 + 3368x^3 + 2066979x^2 - 6329061*x - 14714266
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-39.7818$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+42.7818 q^{2} -260.219 q^{3} +1318.28 q^{4} +625.000 q^{5} -11132.6 q^{6} -2401.00 q^{7} +34494.1 q^{8} +48030.7 q^{9} +26738.6 q^{10} +41568.7 q^{11} -343041. q^{12} +103859. q^{13} -102719. q^{14} -162637. q^{15} +800760. q^{16} +355256. q^{17} +2.05484e6 q^{18} -349126. q^{19} +823925. q^{20} +624785. q^{21} +1.77838e6 q^{22} +228204. q^{23} -8.97601e6 q^{24} +390625. q^{25} +4.44327e6 q^{26} -7.37660e6 q^{27} -3.16519e6 q^{28} +4.02216e6 q^{29} -6.95788e6 q^{30} -3.29476e6 q^{31} +1.65969e7 q^{32} -1.08169e7 q^{33} +1.51985e7 q^{34} -1.50062e6 q^{35} +6.33179e7 q^{36} -2.13083e7 q^{37} -1.49362e7 q^{38} -2.70260e7 q^{39} +2.15588e7 q^{40} +1.05289e7 q^{41} +2.67294e7 q^{42} +3.89712e6 q^{43} +5.47991e7 q^{44} +3.00192e7 q^{45} +9.76296e6 q^{46} -3.31846e7 q^{47} -2.08373e8 q^{48} +5.76480e6 q^{49} +1.67116e7 q^{50} -9.24443e7 q^{51} +1.36915e8 q^{52} -6.31880e7 q^{53} -3.15584e8 q^{54} +2.59804e7 q^{55} -8.28203e7 q^{56} +9.08490e7 q^{57} +1.72075e8 q^{58} +5.86733e7 q^{59} -2.14401e8 q^{60} +1.37845e8 q^{61} -1.40956e8 q^{62} -1.15322e8 q^{63} +3.00057e8 q^{64} +6.49118e7 q^{65} -4.62768e8 q^{66} +8.36796e7 q^{67} +4.68327e8 q^{68} -5.93829e7 q^{69} -6.41994e7 q^{70} +1.50169e8 q^{71} +1.65678e9 q^{72} -2.74817e8 q^{73} -9.11609e8 q^{74} -1.01648e8 q^{75} -4.60246e8 q^{76} -9.98063e7 q^{77} -1.15622e9 q^{78} -2.75964e8 q^{79} +5.00475e8 q^{80} +9.74140e8 q^{81} +4.50444e8 q^{82} +2.32312e8 q^{83} +8.23642e8 q^{84} +2.22035e8 q^{85} +1.66726e8 q^{86} -1.04664e9 q^{87} +1.43387e9 q^{88} +2.71482e8 q^{89} +1.28427e9 q^{90} -2.49365e8 q^{91} +3.00837e8 q^{92} +8.57358e8 q^{93} -1.41969e9 q^{94} -2.18204e8 q^{95} -4.31883e9 q^{96} -9.76607e8 q^{97} +2.46628e8 q^{98} +1.99657e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} - 124 q^{3} + 3009 q^{4} + 3750 q^{5} + 4888 q^{6} - 14406 q^{7} + 22041 q^{8} + 111090 q^{9} + 9375 q^{10} - 47796 q^{11} - 541656 q^{12} + 102168 q^{13} - 36015 q^{14} - 77500 q^{15} + 2371065 q^{16}+ \cdots + 3571968784 q^{99}+O(q^{100}) $ 6 * q + 15 * q^2 - 124 * q^3 + 3009 * q^4 + 3750 * q^5 + 4888 * q^6 - 14406 * q^7 + 22041 * q^8 + 111090 * q^9 + 9375 * q^10 - 47796 * q^11 - 541656 * q^12 + 102168 * q^13 - 36015 * q^14 - 77500 * q^15 + 2371065 * q^16 - 38472 * q^17 + 1837015 * q^18 + 361056 * q^19 + 1880625 * q^20 + 297724 * q^21 + 2068680 * q^22 + 697032 * q^23 + 4828076 * q^24 + 2343750 * q^25 + 10847622 * q^26 + 1653188 * q^27 - 7224609 * q^28 + 16028184 * q^29 + 3055000 * q^30 + 1362912 * q^31 - 1148823 * q^32 + 14059020 * q^33 - 9216294 * q^34 - 9003750 * q^35 + 92319641 * q^36 - 3912924 * q^37 + 39877140 * q^38 - 20341868 * q^39 + 13775625 * q^40 + 22452756 * q^41 - 11736088 * q^42 - 29998992 * q^43 - 94378728 * q^44 + 69431250 * q^45 + 49589520 * q^46 - 121271508 * q^47 - 327116052 * q^48 + 34588806 * q^49 + 5859375 * q^50 - 281338180 * q^51 - 44528550 * q^52 - 20308596 * q^53 - 290104308 * q^54 - 29872500 * q^55 - 52920441 * q^56 + 186940744 * q^57 + 256759494 * q^58 + 120280392 * q^59 - 338535000 * q^60 - 87693540 * q^61 - 344802528 * q^62 - 266727090 * q^63 + 640647105 * q^64 + 63855000 * q^65 - 1393970692 * q^66 + 495050664 * q^67 - 141443706 * q^68 + 1031633640 * q^69 - 22509375 * q^70 + 253762512 * q^71 + 856452205 * q^72 + 187195308 * q^73 - 418806054 * q^74 - 48437500 * q^75 - 584719476 * q^76 + 114758196 * q^77 - 1728062324 * q^78 + 831079500 * q^79 + 1481915625 * q^80 + 1869314710 * q^81 + 2286848814 * q^82 - 767650536 * q^83 + 1300516056 * q^84 - 24045000 * q^85 + 566199948 * q^86 + 1303216852 * q^87 + 2952495444 * q^88 + 582579684 * q^89 + 1148134375 * q^90 - 245305368 * q^91 - 4259382384 * q^92 + 15388800 * q^93 - 1115946660 * q^94 + 225660000 * q^95 + 989345252 * q^96 - 1184506872 * q^97 + 86472015 * q^98 + 3571968784 * q^99

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 $

$2$	42.7818	1.89071	0.945353	−	0.326050i	$-0.105718\pi$
$2$	42.7818	1.89071	0.945353	+	0.326050i	$0.105718\pi$
$3$	−260.219	−1.85478	−0.927391	−	0.374095i	$-0.877954\pi$
$3$	−260.219	−1.85478	−0.927391	+	0.374095i	$0.877954\pi$
$4$	1318.28	2.57477
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−11132.6	−3.50684
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	34494.1	2.97742
$9$	48030.7	2.44021
$10$	26738.6	0.845549
$11$	41568.7	0.856050	0.428025	−	0.903767i	$-0.359210\pi$
$11$	41568.7	0.856050	0.428025	+	0.903767i	$0.359210\pi$
$12$	−343041.	−4.77563
$13$	103859.	1.00855	0.504277	−	0.863542i	$-0.331759\pi$
$13$	103859.	1.00855	0.504277	+	0.863542i	$0.331759\pi$
$14$	−102719.	−0.714619
$15$	−162637.	−0.829483
$16$	800760.	3.05466
$17$	355256.	1.03162	0.515812	−	0.856702i	$-0.327490\pi$
$17$	355256.	1.03162	0.515812	+	0.856702i	$0.327490\pi$
$18$	2.05484e6	4.61372
$19$	−349126.	−0.614597	−0.307299	−	0.951613i	$-0.599425\pi$
$19$	−349126.	−0.614597	−0.307299	+	0.951613i	$0.599425\pi$
$20$	823925.	1.15147
$21$	624785.	0.701041
$22$	1.77838e6	1.61854
$23$	228204.	0.170039	0.0850193	−	0.996379i	$-0.472905\pi$
$23$	228204.	0.170039	0.0850193	+	0.996379i	$0.472905\pi$
$24$	−8.97601e6	−5.52246
$25$	390625.	0.200000
$26$	4.44327e6	1.90688
$27$	−7.37660e6	−2.67128
$28$	−3.16519e6	−0.973170
$29$	4.02216e6	1.05601	0.528005	−	0.849241i	$-0.322940\pi$
$29$	4.02216e6	1.05601	0.528005	+	0.849241i	$0.322940\pi$
$30$	−6.95788e6	−1.56831
$31$	−3.29476e6	−0.640761	−0.320381	−	0.947289i	$-0.603811\pi$
$31$	−3.29476e6	−0.640761	−0.320381	+	0.947289i	$0.603811\pi$
$32$	1.65969e7	2.79803
$33$	−1.08169e7	−1.58778
$34$	1.51985e7	1.95050
$35$	−1.50062e6	−0.169031
$36$	6.33179e7	6.28298
$37$	−2.13083e7	−1.86914	−0.934570	−	0.355778i	$-0.884216\pi$
$37$	−2.13083e7	−1.86914	−0.934570	+	0.355778i	$0.884216\pi$
$38$	−1.49362e7	−1.16202
$39$	−2.70260e7	−1.87065
$40$	2.15588e7	1.33154
$41$	1.05289e7	0.581909	0.290954	−	0.956737i	$-0.406027\pi$
$41$	1.05289e7	0.581909	0.290954	+	0.956737i	$0.406027\pi$
$42$	2.67294e7	1.32546
$43$	3.89712e6	0.173835	0.0869173	−	0.996216i	$-0.472298\pi$
$43$	3.89712e6	0.173835	0.0869173	+	0.996216i	$0.472298\pi$
$44$	5.47991e7	2.20413
$45$	3.00192e7	1.09130
$46$	9.76296e6	0.321493
$47$	−3.31846e7	−0.991964	−0.495982	−	0.868333i	$-0.665192\pi$
$47$	−3.31846e7	−0.991964	−0.495982	+	0.868333i	$0.665192\pi$
$48$	−2.08373e8	−5.66572
$49$	5.76480e6	0.142857
$50$	1.67116e7	0.378141
$51$	−9.24443e7	−1.91344
$52$	1.36915e8	2.59679
$53$	−6.31880e7	−1.10000	−0.550001	−	0.835164i	$-0.685373\pi$
$53$	−6.31880e7	−1.10000	−0.550001	+	0.835164i	$0.685373\pi$
$54$	−3.15584e8	−5.05060
$55$	2.59804e7	0.382837
$56$	−8.28203e7	−1.12536
$57$	9.08490e7	1.13994
$58$	1.72075e8	1.99660
$59$	5.86733e7	0.630386	0.315193	−	0.949028i	$-0.397931\pi$
$59$	5.86733e7	0.630386	0.315193	+	0.949028i	$0.397931\pi$
$60$	−2.14401e8	−2.13573
$61$	1.37845e8	1.27470	0.637348	−	0.770576i	$-0.280032\pi$
$61$	1.37845e8	1.27470	0.637348	+	0.770576i	$0.280032\pi$
$62$	−1.40956e8	−1.21149
$63$	−1.15322e8	−0.922314
$64$	3.00057e8	2.23560
$65$	6.49118e7	0.451039
$66$	−4.62768e8	−3.00203
$67$	8.36796e7	0.507321	0.253660	−	0.967293i	$-0.418365\pi$
$67$	8.36796e7	0.507321	0.253660	+	0.967293i	$0.418365\pi$
$68$	4.68327e8	2.65619
$69$	−5.93829e7	−0.315384
$70$	−6.41994e7	−0.319588
$71$	1.50169e8	0.701322	0.350661	−	0.936503i	$-0.385957\pi$
$71$	1.50169e8	0.701322	0.350661	+	0.936503i	$0.385957\pi$
$72$	1.65678e9	7.26554
$73$	−2.74817e8	−1.13264	−0.566318	−	0.824187i	$-0.691633\pi$
$73$	−2.74817e8	−1.13264	−0.566318	+	0.824187i	$0.691633\pi$
$74$	−9.11609e8	−3.53399
$75$	−1.01648e8	−0.370956
$76$	−4.60246e8	−1.58244
$77$	−9.98063e7	−0.323556
$78$	−1.15622e9	−3.53684
$79$	−2.75964e8	−0.797133	−0.398566	−	0.917139i	$-0.630492\pi$
$79$	−2.75964e8	−0.797133	−0.398566	+	0.917139i	$0.630492\pi$
$80$	5.00475e8	1.36608
$81$	9.74140e8	2.51443
$82$	4.50444e8	1.10022
$83$	2.32312e8	0.537304	0.268652	−	0.963237i	$-0.413422\pi$
$83$	2.32312e8	0.537304	0.268652	+	0.963237i	$0.413422\pi$
$84$	8.23642e8	1.80502
$85$	2.22035e8	0.461356
$86$	1.66726e8	0.328670
$87$	−1.04664e9	−1.95867
$88$	1.43387e9	2.54882
$89$	2.71482e8	0.458654	0.229327	−	0.973349i	$-0.426347\pi$
$89$	2.71482e8	0.458654	0.229327	+	0.973349i	$0.426347\pi$
$90$	1.28427e9	2.06332
$91$	−2.49365e8	−0.381197
$92$	3.00837e8	0.437810
$93$	8.57358e8	1.18847
$94$	−1.41969e9	−1.87551
$95$	−2.18204e8	−0.274856
$96$	−4.31883e9	−5.18974
$97$	−9.76607e8	−1.12007	−0.560037	−	0.828467i	$-0.689213\pi$
$97$	−9.76607e8	−1.12007	−0.560037	+	0.828467i	$0.689213\pi$
$98$	2.46628e8	0.270101
$99$	1.99657e9	2.08894
$100$	5.14953e8	0.514953
$101$	1.11904e9	1.07004	0.535019	−	0.844840i	$-0.320304\pi$
$101$	1.11904e9	1.07004	0.535019	+	0.844840i	$0.320304\pi$
$102$	−3.95493e9	−3.61775
$103$	1.01154e9	0.885559	0.442779	−	0.896631i	$-0.353993\pi$
$103$	1.01154e9	0.885559	0.442779	+	0.896631i	$0.353993\pi$
$104$	3.58252e9	3.00289
$105$	3.90490e8	0.313515
$106$	−2.70329e9	−2.07978
$107$	−1.47411e9	−1.08719	−0.543593	−	0.839349i	$-0.682936\pi$
$107$	−1.47411e9	−1.08719	−0.543593	+	0.839349i	$0.682936\pi$
$108$	−9.72443e9	−6.87792
$109$	−1.79852e9	−1.22038	−0.610190	−	0.792255i	$-0.708907\pi$
$109$	−1.79852e9	−1.22038	−0.610190	+	0.792255i	$0.708907\pi$
$110$	1.11149e9	0.723832
$111$	5.54483e9	3.46685
$112$	−1.92262e9	−1.15455
$113$	1.09680e9	0.632812	0.316406	−	0.948624i	$-0.397524\pi$
$113$	1.09680e9	0.632812	0.316406	+	0.948624i	$0.397524\pi$
$114$	3.88668e9	2.15530
$115$	1.42627e8	0.0760436
$116$	5.30233e9	2.71898
$117$	4.98842e9	2.46108
$118$	2.51015e9	1.19187
$119$	−8.52970e8	−0.389917
$120$	−5.61000e9	−2.46972
$121$	−6.29995e8	−0.267179
$122$	5.89725e9	2.41007
$123$	−2.73981e9	−1.07931
$124$	−4.34342e9	−1.64981
$125$	2.44141e8	0.0894427
$126$	−4.93367e9	−1.74382
$127$	−3.23678e8	−0.110407	−0.0552035	−	0.998475i	$-0.517581\pi$
$127$	−3.23678e8	−0.110407	−0.0552035	+	0.998475i	$0.517581\pi$
$128$	4.33936e9	1.42883
$129$	−1.01410e9	−0.322425
$130$	2.77704e9	0.852781
$131$	−4.60246e9	−1.36543	−0.682714	−	0.730686i	$-0.739200\pi$
$131$	−4.60246e9	−1.36543	−0.682714	+	0.730686i	$0.739200\pi$
$132$	−1.42598e10	−4.08817
$133$	8.38251e8	0.232296
$134$	3.57996e9	0.959194
$135$	−4.61037e9	−1.19463
$136$	1.22542e10	3.07158
$137$	−3.07931e9	−0.746812	−0.373406	−	0.927668i	$-0.621810\pi$
$137$	−3.07931e9	−0.746812	−0.373406	+	0.927668i	$0.621810\pi$
$138$	−2.54050e9	−0.596299
$139$	−6.80655e9	−1.54654	−0.773268	−	0.634079i	$-0.781379\pi$
$139$	−6.80655e9	−1.54654	−0.773268	+	0.634079i	$0.781379\pi$
$140$	−1.97824e9	−0.435215
$141$	8.63524e9	1.83988
$142$	6.42449e9	1.32599
$143$	4.31728e9	0.863371
$144$	3.84610e10	7.45401
$145$	2.51385e9	0.472262
$146$	−1.17572e10	−2.14148
$147$	−1.50011e9	−0.264969
$148$	−2.80904e10	−4.81260
$149$	1.11783e10	1.85796	0.928981	−	0.370127i	$-0.120686\pi$
$149$	1.11783e10	1.85796	0.928981	+	0.370127i	$0.120686\pi$
$150$	−4.34868e9	−0.701369
$151$	−4.87685e9	−0.763384	−0.381692	−	0.924290i	$-0.624658\pi$
$151$	−4.87685e9	−0.763384	−0.381692	+	0.924290i	$0.624658\pi$
$152$	−1.20428e10	−1.82991
$153$	1.70632e10	2.51738
$154$	−4.26989e9	−0.611750
$155$	−2.05923e9	−0.286557
$156$	−3.56279e10	−4.81647
$157$	−5.01169e9	−0.658318	−0.329159	−	0.944274i	$-0.606765\pi$
$157$	−5.01169e9	−0.658318	−0.329159	+	0.944274i	$0.606765\pi$
$158$	−1.18062e10	−1.50714
$159$	1.64427e10	2.04026
$160$	1.03731e10	1.25132
$161$	−5.47917e8	−0.0642686
$162$	4.16754e10	4.75404
$163$	−1.45416e10	−1.61349	−0.806746	−	0.590899i	$-0.798773\pi$
$163$	−1.45416e10	−1.61349	−0.806746	+	0.590899i	$0.798773\pi$
$164$	1.38800e10	1.49828
$165$	−6.76058e9	−0.710079
$166$	9.93872e9	1.01588
$167$	−4.62247e8	−0.0459886	−0.0229943	−	0.999736i	$-0.507320\pi$
$167$	−4.62247e8	−0.0459886	−0.0229943	+	0.999736i	$0.507320\pi$
$168$	2.15514e10	2.08729
$169$	1.82180e8	0.0171795
$170$	9.49906e9	0.872289
$171$	−1.67688e10	−1.49975
$172$	5.13750e9	0.447583
$173$	1.02318e9	0.0868449	0.0434224	−	0.999057i	$-0.486174\pi$
$173$	1.02318e9	0.0868449	0.0434224	+	0.999057i	$0.486174\pi$
$174$	−4.47771e10	−3.70326
$175$	−9.37891e8	−0.0755929
$176$	3.32865e10	2.61494
$177$	−1.52679e10	−1.16923
$178$	1.16145e10	0.867180
$179$	1.42460e10	1.03718	0.518590	−	0.855023i	$-0.326457\pi$
$179$	1.42460e10	1.03718	0.518590	+	0.855023i	$0.326457\pi$
$180$	3.95737e10	2.80983
$181$	1.83877e10	1.27343	0.636714	−	0.771100i	$-0.280293\pi$
$181$	1.83877e10	1.27343	0.636714	+	0.771100i	$0.280293\pi$
$182$	−1.06683e10	−0.720732
$183$	−3.58698e10	−2.36428
$184$	7.87168e9	0.506276
$185$	−1.33177e10	−0.835905
$186$	3.66793e10	2.24705
$187$	1.47675e10	0.883121
$188$	−4.37466e10	−2.55408
$189$	1.77112e10	1.00965
$190$	−9.33514e9	−0.519672
$191$	−2.65507e10	−1.44353	−0.721766	−	0.692137i	$-0.756669\pi$
$191$	−2.65507e10	−1.44353	−0.721766	+	0.692137i	$0.756669\pi$
$192$	−7.80805e10	−4.14655
$193$	5.84127e9	0.303040	0.151520	−	0.988454i	$-0.451583\pi$
$193$	5.84127e9	0.303040	0.151520	+	0.988454i	$0.451583\pi$
$194$	−4.17810e10	−2.11773
$195$	−1.68913e10	−0.836578
$196$	7.59962e9	0.367824
$197$	−2.06491e10	−0.976793	−0.488397	−	0.872622i	$-0.662418\pi$
$197$	−2.06491e10	−0.976793	−0.488397	+	0.872622i	$0.662418\pi$
$198$	8.54169e10	3.94958
$199$	−2.66301e10	−1.20374	−0.601871	−	0.798593i	$-0.705578\pi$
$199$	−2.66301e10	−1.20374	−0.601871	+	0.798593i	$0.705578\pi$
$200$	1.34743e10	0.595484
$201$	−2.17750e10	−0.940969
$202$	4.78745e10	2.02313
$203$	−9.65720e9	−0.399134
$204$	−1.21867e11	−4.92665
$205$	6.58055e9	0.260238
$206$	4.32756e10	1.67433
$207$	1.09608e10	0.414930
$208$	8.31660e10	3.08078
$209$	−1.45127e10	−0.526126
$210$	1.67059e10	0.592765
$211$	1.35165e10	0.469454	0.234727	−	0.972061i	$-0.424580\pi$
$211$	1.35165e10	0.469454	0.234727	+	0.972061i	$0.424580\pi$
$212$	−8.32995e10	−2.83225
$213$	−3.90767e10	−1.30080
$214$	−6.30652e10	−2.05555
$215$	2.43570e9	0.0777412
$216$	−2.54449e11	−7.95352
$217$	7.91072e9	0.242185
$218$	−7.69437e10	−2.30738
$219$	7.15125e10	2.10079
$220$	3.42495e10	0.985716
$221$	3.68965e10	1.04045
$222$	2.37218e11	6.55479
$223$	4.47296e10	1.21122	0.605610	−	0.795762i	$-0.292929\pi$
$223$	4.47296e10	1.21122	0.605610	+	0.795762i	$0.292929\pi$
$224$	−3.98492e10	−1.05756
$225$	1.87620e10	0.488043
$226$	4.69231e10	1.19646
$227$	2.46775e10	0.616858	0.308429	−	0.951247i	$-0.400197\pi$
$227$	2.46775e10	0.616858	0.308429	+	0.951247i	$0.400197\pi$
$228$	1.19764e11	2.93509
$229$	−5.44437e10	−1.30824	−0.654121	−	0.756390i	$-0.726961\pi$
$229$	−5.44437e10	−1.30824	−0.654121	+	0.756390i	$0.726961\pi$
$230$	6.10185e9	0.143776
$231$	2.59715e10	0.600126
$232$	1.38741e11	3.14418
$233$	−5.82731e10	−1.29529	−0.647644	−	0.761943i	$-0.724246\pi$
$233$	−5.82731e10	−1.29529	−0.647644	+	0.761943i	$0.724246\pi$
$234$	2.13413e11	4.65318
$235$	−2.07404e10	−0.443620
$236$	7.73478e10	1.62310
$237$	7.18110e10	1.47851
$238$	−3.64916e10	−0.737219
$239$	5.53754e10	1.09781	0.548904	−	0.835885i	$-0.315045\pi$
$239$	5.53754e10	1.09781	0.548904	+	0.835885i	$0.315045\pi$
$240$	−1.30233e11	−2.53379
$241$	6.01280e10	1.14815	0.574077	−	0.818802i	$-0.305361\pi$
$241$	6.01280e10	1.14815	0.574077	+	0.818802i	$0.305361\pi$
$242$	−2.69523e10	−0.505157
$243$	−1.08296e11	−1.99243
$244$	1.81718e11	3.28204
$245$	3.60300e9	0.0638877
$246$	−1.17214e11	−2.04066
$247$	−3.62598e10	−0.619854
$248$	−1.13650e11	−1.90781
$249$	−6.04519e10	−0.996582
$250$	1.04448e10	0.169110
$251$	1.01611e9	0.0161588	0.00807938	−	0.999967i	$-0.497428\pi$
$251$	1.01611e9	0.0161588	0.00807938	+	0.999967i	$0.497428\pi$
$252$	−1.52026e11	−2.37474
$253$	9.48612e9	0.145561
$254$	−1.38475e10	−0.208747
$255$	−5.77777e10	−0.855715
$256$	3.20161e10	0.465895
$257$	−1.10965e11	−1.58667	−0.793334	−	0.608787i	$-0.791657\pi$
$257$	−1.10965e11	−1.58667	−0.793334	+	0.608787i	$0.791657\pi$
$258$	−4.33852e10	−0.609611
$259$	5.11613e10	0.706469
$260$	8.55720e10	1.16132
$261$	1.93187e11	2.57689
$262$	−1.96901e11	−2.58162
$263$	1.21172e11	1.56171	0.780856	−	0.624711i	$-0.214783\pi$
$263$	1.21172e11	1.56171	0.780856	+	0.624711i	$0.214783\pi$
$264$	−3.73121e11	−4.72750
$265$	−3.94925e10	−0.491936
$266$	3.58619e10	0.439203
$267$	−7.06446e10	−0.850704
$268$	1.10313e11	1.30623
$269$	5.16654e10	0.601609	0.300805	−	0.953686i	$-0.402745\pi$
$269$	5.16654e10	0.601609	0.300805	+	0.953686i	$0.402745\pi$
$270$	−1.97240e11	−2.25870
$271$	−2.49166e10	−0.280626	−0.140313	−	0.990107i	$-0.544811\pi$
$271$	−2.49166e10	−0.280626	−0.140313	+	0.990107i	$0.544811\pi$
$272$	2.84475e11	3.15126
$273$	6.48895e10	0.707037
$274$	−1.31738e11	−1.41200
$275$	1.62378e10	0.171210
$276$	−7.82833e10	−0.812041
$277$	−2.22882e10	−0.227466	−0.113733	−	0.993511i	$-0.536281\pi$
$277$	−2.22882e10	−0.227466	−0.113733	+	0.993511i	$0.536281\pi$
$278$	−2.91196e11	−2.92404
$279$	−1.58250e11	−1.56359
$280$	−5.17627e10	−0.503276
$281$	9.03151e10	0.864135	0.432068	−	0.901841i	$-0.357784\pi$
$281$	9.03151e10	0.864135	0.432068	+	0.901841i	$0.357784\pi$
$282$	3.69431e11	3.47866
$283$	−9.63268e10	−0.892706	−0.446353	−	0.894857i	$-0.647277\pi$
$283$	−9.63268e10	−0.892706	−0.446353	+	0.894857i	$0.647277\pi$
$284$	1.97965e11	1.80574
$285$	5.67806e10	0.509798
$286$	1.84701e11	1.63238
$287$	−2.52798e10	−0.219941
$288$	7.97162e11	6.82780
$289$	7.61912e9	0.0642487
$290$	1.07547e11	0.892908
$291$	2.54131e11	2.07749
$292$	−3.62286e11	−2.91627
$293$	−4.21047e10	−0.333754	−0.166877	−	0.985978i	$-0.553368\pi$
$293$	−4.21047e10	−0.333754	−0.166877	+	0.985978i	$0.553368\pi$
$294$	−6.41773e10	−0.500978
$295$	3.66708e10	0.281917
$296$	−7.35012e11	−5.56521
$297$	−3.06635e11	−2.28675
$298$	4.78227e11	3.51286
$299$	2.37010e10	0.171493
$300$	−1.34000e11	−0.955126
$301$	−9.35700e9	−0.0657033
$302$	−2.08640e11	−1.44333
$303$	−2.91195e11	−1.98469
$304$	−2.79566e11	−1.87738
$305$	8.61531e10	0.570061
$306$	7.29994e11	4.75963
$307$	9.28980e10	0.596875	0.298438	−	0.954429i	$-0.403534\pi$
$307$	9.28980e10	0.596875	0.298438	+	0.954429i	$0.403534\pi$
$308$	−1.31573e11	−0.833082
$309$	−2.63223e11	−1.64252
$310$	−8.80973e10	−0.541795
$311$	−1.56495e11	−0.948588	−0.474294	−	0.880366i	$-0.657297\pi$
$311$	−1.56495e11	−0.948588	−0.474294	+	0.880366i	$0.657297\pi$
$312$	−9.32239e11	−5.56969
$313$	8.88488e10	0.523242	0.261621	−	0.965171i	$-0.415743\pi$
$313$	8.88488e10	0.523242	0.261621	+	0.965171i	$0.415743\pi$
$314$	−2.14409e11	−1.24469
$315$	−7.20761e10	−0.412471
$316$	−3.63798e11	−2.05243
$317$	6.19880e10	0.344779	0.172389	−	0.985029i	$-0.444851\pi$
$317$	6.19880e10	0.344779	0.172389	+	0.985029i	$0.444851\pi$
$318$	7.03448e11	3.85753
$319$	1.67196e11	0.903997
$320$	1.87536e11	0.999791
$321$	3.83591e11	2.01649
$322$	−2.34409e10	−0.121513
$323$	−1.24029e11	−0.634034
$324$	1.28419e12	6.47406
$325$	4.05699e10	0.201711
$326$	−6.22114e11	−3.05064
$327$	4.68007e11	2.26354
$328$	3.63184e11	1.73259
$329$	7.96762e10	0.374927
$330$	−2.89230e11	−1.34255
$331$	3.65322e11	1.67282	0.836410	−	0.548104i	$-0.184650\pi$
$331$	3.65322e11	1.67282	0.836410	+	0.548104i	$0.184650\pi$
$332$	3.06252e11	1.38343
$333$	−1.02345e12	−4.56110
$334$	−1.97757e10	−0.0869508
$335$	5.22997e10	0.226881
$336$	5.00302e11	2.14144
$337$	1.45738e11	0.615514	0.307757	−	0.951465i	$-0.400422\pi$
$337$	1.45738e11	0.615514	0.307757	+	0.951465i	$0.400422\pi$
$338$	7.79400e9	0.0324815
$339$	−2.85408e11	−1.17373
$340$	2.92705e11	1.18788
$341$	−1.36959e11	−0.548523
$342$	−7.17397e11	−2.83558
$343$	−1.38413e10	−0.0539949
$344$	1.34428e11	0.517578
$345$	−3.71143e10	−0.141044
$346$	4.37734e10	0.164198
$347$	2.96112e11	1.09641	0.548206	−	0.836343i	$-0.315311\pi$
$347$	2.96112e11	1.09641	0.548206	+	0.836343i	$0.315311\pi$
$348$	−1.37976e12	−5.04311
$349$	3.01854e11	1.08914	0.544569	−	0.838716i	$-0.316693\pi$
$349$	3.01854e11	1.08914	0.544569	+	0.838716i	$0.316693\pi$
$350$	−4.01246e10	−0.142924
$351$	−7.66126e11	−2.69413
$352$	6.89912e11	2.39526
$353$	−1.99229e11	−0.682916	−0.341458	−	0.939897i	$-0.610921\pi$
$353$	−1.99229e11	−0.682916	−0.341458	+	0.939897i	$0.610921\pi$
$354$	−6.53187e11	−2.21066
$355$	9.38555e10	0.313641
$356$	3.57889e11	1.18093
$357$	2.21959e11	0.723211
$358$	6.09469e11	1.96100
$359$	−6.48945e10	−0.206197	−0.103099	−	0.994671i	$-0.532876\pi$
$359$	−6.48945e10	−0.206197	−0.103099	+	0.994671i	$0.532876\pi$
$360$	1.03549e12	3.24925
$361$	−2.00799e11	−0.622270
$362$	7.86660e11	2.40768
$363$	1.63936e11	0.495559
$364$	−3.28733e11	−0.981494
$365$	−1.71761e11	−0.506530
$366$	−1.53457e12	−4.47016
$367$	−4.27450e10	−0.122995	−0.0614976	−	0.998107i	$-0.519588\pi$
$367$	−4.27450e10	−0.122995	−0.0614976	+	0.998107i	$0.519588\pi$
$368$	1.82736e11	0.519409
$369$	5.05710e11	1.41998
$370$	−5.69756e11	−1.58045
$371$	1.51714e11	0.415761
$372$	1.13024e12	3.06004
$373$	5.72742e11	1.53204	0.766018	−	0.642819i	$-0.222235\pi$
$373$	5.72742e11	1.53204	0.766018	+	0.642819i	$0.222235\pi$
$374$	6.31781e11	1.66972
$375$	−6.35299e10	−0.165897
$376$	−1.14467e12	−2.95349
$377$	4.17737e11	1.06504
$378$	7.57717e11	1.90895
$379$	−2.28088e11	−0.567840	−0.283920	−	0.958848i	$-0.591635\pi$
$379$	−2.28088e11	−0.567840	−0.283920	+	0.958848i	$0.591635\pi$
$380$	−2.87654e11	−0.707691
$381$	8.42271e10	0.204781
$382$	−1.13589e12	−2.72929
$383$	8.33542e11	1.97940	0.989699	−	0.143162i	$-0.0457271\pi$
$383$	8.33542e11	1.97940	0.989699	+	0.143162i	$0.0457271\pi$
$384$	−1.12918e12	−2.65017
$385$	−6.23790e10	−0.144699
$386$	2.49900e11	0.572959
$387$	1.87182e11	0.424193
$388$	−1.28744e12	−2.88393
$389$	−3.47070e11	−0.768501	−0.384251	−	0.923229i	$-0.625540\pi$
$389$	−3.47070e11	−0.768501	−0.384251	+	0.923229i	$0.625540\pi$
$390$	−7.22638e11	−1.58172
$391$	8.10708e10	0.175416
$392$	1.98852e11	0.425346
$393$	1.19764e12	2.53257
$394$	−8.83404e11	−1.84683
$395$	−1.72478e11	−0.356489
$396$	2.63204e12	5.37854
$397$	5.31999e11	1.07486	0.537432	−	0.843307i	$-0.319394\pi$
$397$	5.31999e11	1.07486	0.537432	+	0.843307i	$0.319394\pi$
$398$	−1.13928e12	−2.27592
$399$	−2.18129e11	−0.430858
$400$	3.12797e11	0.610931
$401$	−1.10007e11	−0.212456	−0.106228	−	0.994342i	$-0.533877\pi$
$401$	−1.10007e11	−0.212456	−0.106228	+	0.994342i	$0.533877\pi$
$402$	−9.31572e11	−1.77910
$403$	−3.42190e11	−0.646242
$404$	1.47521e12	2.75510
$405$	6.08837e11	1.12449
$406$	−4.13152e11	−0.754645
$407$	−8.85759e11	−1.60008
$408$	−3.18878e12	−5.69710
$409$	5.36319e11	0.947694	0.473847	−	0.880607i	$-0.342865\pi$
$409$	5.36319e11	0.947694	0.473847	+	0.880607i	$0.342865\pi$
$410$	2.81528e11	0.492032
$411$	8.01294e11	1.38517
$412$	1.33350e12	2.28011
$413$	−1.40875e11	−0.238263
$414$	4.68922e11	0.784511
$415$	1.45195e11	0.240290
$416$	1.72374e12	2.82197
$417$	1.77119e12	2.86849
$418$	−6.20879e11	−0.994749
$419$	2.77847e11	0.440395	0.220198	−	0.975455i	$-0.429330\pi$
$419$	2.77847e11	0.440395	0.220198	+	0.975455i	$0.429330\pi$
$420$	5.14776e11	0.807228
$421$	5.42301e11	0.841339	0.420670	−	0.907214i	$-0.361795\pi$
$421$	5.42301e11	0.841339	0.420670	+	0.907214i	$0.361795\pi$
$422$	5.78260e11	0.887599
$423$	−1.59388e12	−2.42060
$424$	−2.17961e12	−3.27516
$425$	1.38772e11	0.206325
$426$	−1.67177e12	−2.45943
$427$	−3.30966e11	−0.481790
$428$	−1.94329e12	−2.79925
$429$	−1.12344e12	−1.60137
$430$	1.04204e11	0.146986
$431$	−5.57666e11	−0.778442	−0.389221	−	0.921144i	$-0.627256\pi$
$431$	−5.57666e11	−0.778442	−0.389221	+	0.921144i	$0.627256\pi$
$432$	−5.90688e12	−8.15984
$433$	2.13337e11	0.291656	0.145828	−	0.989310i	$-0.453415\pi$
$433$	2.13337e11	0.291656	0.145828	+	0.989310i	$0.453415\pi$
$434$	3.38435e11	0.457900
$435$	−6.54150e11	−0.875942
$436$	−2.37095e12	−3.14219
$437$	−7.96718e10	−0.104505
$438$	3.05943e12	3.97198
$439$	−1.05316e12	−1.35334	−0.676668	−	0.736289i	$-0.736577\pi$
$439$	−1.05316e12	−1.35334	−0.676668	+	0.736289i	$0.736577\pi$
$440$	8.96171e11	1.13987
$441$	2.76887e11	0.348602
$442$	1.57850e12	1.96718
$443$	−7.98551e11	−0.985113	−0.492556	−	0.870281i	$-0.663937\pi$
$443$	−7.98551e11	−0.985113	−0.492556	+	0.870281i	$0.663937\pi$
$444$	7.30964e12	8.92632
$445$	1.69676e11	0.205117
$446$	1.91361e12	2.29006
$447$	−2.90880e12	−3.44611
$448$	−7.20438e11	−0.844978
$449$	−9.80369e11	−1.13836	−0.569182	−	0.822211i	$-0.692740\pi$
$449$	−9.80369e11	−1.13836	−0.569182	+	0.822211i	$0.692740\pi$
$450$	8.02671e11	0.922745
$451$	4.37671e11	0.498143
$452$	1.44589e12	1.62934
$453$	1.26905e12	1.41591
$454$	1.05575e12	1.16630
$455$	−1.55853e11	−0.170477
$456$	3.13376e12	3.39409
$457$	7.38737e11	0.792259	0.396130	−	0.918195i	$-0.370353\pi$
$457$	7.38737e11	0.792259	0.396130	+	0.918195i	$0.370353\pi$
$458$	−2.32920e12	−2.47350
$459$	−2.62058e12	−2.75576
$460$	1.88023e11	0.195794
$461$	−8.57026e11	−0.883771	−0.441885	−	0.897072i	$-0.645690\pi$
$461$	−8.57026e11	−0.883771	−0.441885	+	0.897072i	$0.645690\pi$
$462$	1.11111e12	1.13466
$463$	−8.66003e11	−0.875800	−0.437900	−	0.899024i	$-0.644278\pi$
$463$	−8.66003e11	−0.875800	−0.437900	+	0.899024i	$0.644278\pi$
$464$	3.22078e12	3.22575
$465$	5.35849e11	0.531501
$466$	−2.49303e12	−2.44901
$467$	−1.74446e12	−1.69721	−0.848606	−	0.529025i	$-0.822558\pi$
$467$	−1.74446e12	−1.69721	−0.848606	+	0.529025i	$0.822558\pi$
$468$	6.57613e12	6.33672
$469$	−2.00915e11	−0.191749
$470$	−8.87309e11	−0.838754
$471$	1.30414e12	1.22104
$472$	2.02388e12	1.87692
$473$	1.61998e11	0.148811
$474$	3.07220e12	2.79542
$475$	−1.36377e11	−0.122919
$476$	−1.12445e12	−1.00395
$477$	−3.03496e12	−2.68424
$478$	2.36906e12	2.07563
$479$	−6.51076e11	−0.565096	−0.282548	−	0.959253i	$-0.591180\pi$
$479$	−6.51076e11	−0.565096	−0.282548	+	0.959253i	$0.591180\pi$
$480$	−2.69927e12	−2.32092
$481$	−2.21306e12	−1.88513
$482$	2.57238e12	2.17082
$483$	1.42578e11	0.119204
$484$	−8.30510e11	−0.687924
$485$	−6.10379e11	−0.500913
$486$	−4.63308e12	−3.76710
$487$	9.91101e8	0.000798432 0	0.000399216	−	1.00000i	$-0.499873\pi$
$487$	9.91101e8	0.000798432 0	0.000399216		1.00000i	$0.499873\pi$
$488$	4.75484e12	3.79530
$489$	3.78398e12	2.99267
$490$	1.54143e11	0.120793
$491$	8.38408e11	0.651012	0.325506	−	0.945540i	$-0.394465\pi$
$491$	8.38408e11	0.651012	0.325506	+	0.945540i	$0.394465\pi$
$492$	−3.61184e12	−2.77898
$493$	1.42890e12	1.08941
$494$	−1.55126e12	−1.17196
$495$	1.24786e12	0.934204
$496$	−2.63831e12	−1.95730
$497$	−3.60555e11	−0.265075
$498$	−2.58624e12	−1.88424
$499$	2.48735e12	1.79591	0.897955	−	0.440088i	$-0.145053\pi$
$499$	2.48735e12	1.79591	0.897955	+	0.440088i	$0.145053\pi$
$500$	3.21846e11	0.230294
$501$	1.20285e11	0.0852987
$502$	4.34709e10	0.0305515
$503$	−1.40863e12	−0.981163	−0.490582	−	0.871395i	$-0.663216\pi$
$503$	−1.40863e12	−0.981163	−0.490582	+	0.871395i	$0.663216\pi$
$504$	−3.97792e12	−2.74611
$505$	6.99400e11	0.478536
$506$	4.05833e11	0.275214
$507$	−4.74067e10	−0.0318643
$508$	−4.26699e11	−0.284272
$509$	−8.28720e11	−0.547240	−0.273620	−	0.961838i	$-0.588221\pi$
$509$	−8.28720e11	−0.547240	−0.273620	+	0.961838i	$0.588221\pi$
$510$	−2.47183e12	−1.61791
$511$	6.59835e11	0.428096
$512$	−8.52047e11	−0.547960
$513$	2.57536e12	1.64176
$514$	−4.74727e12	−2.99992
$515$	6.32215e11	0.396034
$516$	−1.33687e12	−0.830169
$517$	−1.37944e12	−0.849170
$518$	2.18877e12	1.33572
$519$	−2.66250e11	−0.161078
$520$	2.23908e12	1.34293
$521$	−8.58369e11	−0.510393	−0.255196	−	0.966889i	$-0.582140\pi$
$521$	−8.58369e11	−0.510393	−0.255196	+	0.966889i	$0.582140\pi$
$522$	8.26488e12	4.87214
$523$	1.43567e12	0.839069	0.419534	−	0.907739i	$-0.362193\pi$
$523$	1.43567e12	0.839069	0.419534	+	0.907739i	$0.362193\pi$
$524$	−6.06733e12	−3.51566
$525$	2.44057e11	0.140208
$526$	5.18395e12	2.95274
$527$	−1.17048e12	−0.661025
$528$	−8.66176e12	−4.85013
$529$	−1.74908e12	−0.971087
$530$	−1.68956e12	−0.930105
$531$	2.81812e12	1.53827
$532$	1.10505e12	0.598108
$533$	1.09352e12	0.586886
$534$	−3.02230e12	−1.60843
$535$	−9.21320e11	−0.486204
$536$	2.88645e12	1.51051
$537$	−3.70707e12	−1.92374
$538$	2.21034e12	1.13747
$539$	2.39635e11	0.122293
$540$	−6.07777e12	−3.07590
$541$	3.25599e12	1.63416	0.817081	−	0.576523i	$-0.195591\pi$
$541$	3.25599e12	1.63416	0.817081	+	0.576523i	$0.195591\pi$
$542$	−1.06598e12	−0.530581
$543$	−4.78483e12	−2.36193
$544$	5.89616e12	2.88652
$545$	−1.12407e12	−0.545770
$546$	2.77609e12	1.33680
$547$	−1.31051e12	−0.625887	−0.312944	−	0.949772i	$-0.601315\pi$
$547$	−1.31051e12	−0.625887	−0.312944	+	0.949772i	$0.601315\pi$
$548$	−4.05940e12	−1.92287
$549$	6.62079e12	3.11053
$550$	6.94680e11	0.323707
$551$	−1.40424e12	−0.649021
$552$	−2.04836e12	−0.939031
$553$	6.62590e11	0.301288
$554$	−9.53528e11	−0.430070
$555$	3.46552e12	1.55042
$556$	−8.97294e12	−3.98197
$557$	6.12448e11	0.269600	0.134800	−	0.990873i	$-0.456961\pi$
$557$	6.12448e11	0.269600	0.134800	+	0.990873i	$0.456961\pi$
$558$	−6.77020e12	−2.95630
$559$	4.04751e11	0.175321
$560$	−1.20164e12	−0.516331
$561$	−3.84278e12	−1.63800
$562$	3.86384e12	1.63383
$563$	2.74733e12	1.15245	0.576227	−	0.817290i	$-0.304524\pi$
$563$	2.74733e12	1.15245	0.576227	+	0.817290i	$0.304524\pi$
$564$	1.13837e13	4.73725
$565$	6.85500e11	0.283002
$566$	−4.12103e12	−1.68784
$567$	−2.33891e12	−0.950363
$568$	5.17994e12	2.08813
$569$	−7.10003e11	−0.283958	−0.141979	−	0.989870i	$-0.545347\pi$
$569$	−7.10003e11	−0.283958	−0.141979	+	0.989870i	$0.545347\pi$
$570$	2.42918e12	0.963878
$571$	2.87190e12	1.13060	0.565298	−	0.824887i	$-0.308761\pi$
$571$	2.87190e12	1.13060	0.565298	+	0.824887i	$0.308761\pi$
$572$	5.69138e12	2.22298
$573$	6.90899e12	2.67744
$574$	−1.08152e12	−0.415843
$575$	8.91421e10	0.0340077
$576$	1.44120e13	5.45534
$577$	−5.13479e12	−1.92855	−0.964277	−	0.264897i	$-0.914662\pi$
$577$	−5.13479e12	−1.92855	−0.964277	+	0.264897i	$0.914662\pi$
$578$	3.25959e11	0.121475
$579$	−1.52001e12	−0.562072
$580$	3.31396e12	1.21596
$581$	−5.57781e11	−0.203082
$582$	1.08722e13	3.92793
$583$	−2.62664e12	−0.941656
$584$	−9.47956e12	−3.37233
$585$	3.11776e12	1.10063
$586$	−1.80131e12	−0.631030
$587$	2.46529e12	0.857031	0.428515	−	0.903535i	$-0.359037\pi$
$587$	2.46529e12	0.857031	0.428515	+	0.903535i	$0.359037\pi$
$588$	−1.97756e12	−0.682233
$589$	1.15029e12	0.393810
$590$	1.56884e12	0.533022
$591$	5.37327e12	1.81174
$592$	−1.70629e13	−5.70958
$593$	−1.51279e12	−0.502379	−0.251189	−	0.967938i	$-0.580822\pi$
$593$	−1.51279e12	−0.502379	−0.251189	+	0.967938i	$0.580822\pi$
$594$	−1.31184e13	−4.32356
$595$	−5.33106e11	−0.174376
$596$	1.47361e13	4.78382
$597$	6.92964e12	2.23268
$598$	1.01397e12	0.324243
$599$	−5.89069e12	−1.86959	−0.934794	−	0.355191i	$-0.884416\pi$
$599$	−5.89069e12	−1.86959	−0.934794	+	0.355191i	$0.884416\pi$
$600$	−3.50625e12	−1.10449
$601$	−3.78551e12	−1.18356	−0.591779	−	0.806101i	$-0.701574\pi$
$601$	−3.78551e12	−1.18356	−0.591779	+	0.806101i	$0.701574\pi$
$602$	−4.00309e11	−0.124226
$603$	4.01919e12	1.23797
$604$	−6.42905e12	−1.96553
$605$	−3.93747e11	−0.119486
$606$	−1.24578e13	−3.75246
$607$	4.65336e12	1.39129	0.695645	−	0.718386i	$-0.255119\pi$
$607$	4.65336e12	1.39129	0.695645	+	0.718386i	$0.255119\pi$
$608$	−5.79442e12	−1.71966
$609$	2.51298e12	0.740306
$610$	3.68578e12	1.07782
$611$	−3.44651e12	−1.00045
$612$	2.24941e13	6.48167
$613$	5.65330e12	1.61707	0.808537	−	0.588445i	$-0.200260\pi$
$613$	5.65330e12	1.61707	0.808537	+	0.588445i	$0.200260\pi$
$614$	3.97434e12	1.12852
$615$	−1.71238e12	−0.482684
$616$	−3.44273e12	−0.963363
$617$	−4.91335e12	−1.36488	−0.682441	−	0.730941i	$-0.739081\pi$
$617$	−4.91335e12	−1.36488	−0.682441	+	0.730941i	$0.739081\pi$
$618$	−1.12611e13	−3.10552
$619$	1.31898e12	0.361101	0.180551	−	0.983566i	$-0.442212\pi$
$619$	1.31898e12	0.361101	0.180551	+	0.983566i	$0.442212\pi$
$620$	−2.71464e12	−0.737818
$621$	−1.68337e12	−0.454221
$622$	−6.69512e12	−1.79350
$623$	−6.51828e11	−0.173355
$624$	−2.16413e13	−5.71418
$625$	1.52588e11	0.0400000
$626$	3.80111e12	0.989296
$627$	3.77647e12	0.975848
$628$	−6.60681e12	−1.69502
$629$	−7.56992e12	−1.92825
$630$	−3.08354e12	−0.779862
$631$	−1.26560e12	−0.317808	−0.158904	−	0.987294i	$-0.550796\pi$
$631$	−1.26560e12	−0.317808	−0.158904	+	0.987294i	$0.550796\pi$
$632$	−9.51913e12	−2.37340
$633$	−3.51724e12	−0.870735
$634$	2.65196e12	0.651875
$635$	−2.02299e11	−0.0493755
$636$	2.16761e13	5.25320
$637$	5.98726e11	0.144079
$638$	7.15293e12	1.70919
$639$	7.21271e12	1.71137
$640$	2.71210e12	0.638992
$641$	7.10592e12	1.66249	0.831246	−	0.555905i	$-0.187628\pi$
$641$	7.10592e12	1.66249	0.831246	+	0.555905i	$0.187628\pi$
$642$	1.64107e13	3.81259
$643$	4.17010e12	0.962049	0.481024	−	0.876707i	$-0.340265\pi$
$643$	4.17010e12	0.962049	0.481024	+	0.876707i	$0.340265\pi$
$644$	−7.22309e11	−0.165477
$645$	−6.33815e11	−0.144193
$646$	−5.30619e12	−1.19877
$647$	−5.36916e12	−1.20458	−0.602292	−	0.798276i	$-0.705746\pi$
$647$	−5.36916e12	−1.20458	−0.602292	+	0.798276i	$0.705746\pi$
$648$	3.36021e13	7.48650
$649$	2.43897e12	0.539641
$650$	1.73565e12	0.381375
$651$	−2.05852e12	−0.449200
$652$	−1.91699e13	−4.15436
$653$	2.71691e12	0.584744	0.292372	−	0.956305i	$-0.405555\pi$
$653$	2.71691e12	0.584744	0.292372	+	0.956305i	$0.405555\pi$
$654$	2.00222e13	4.27968
$655$	−2.87653e12	−0.610638
$656$	8.43110e12	1.77753
$657$	−1.31996e13	−2.76387
$658$	3.40869e12	0.708877
$659$	6.36955e12	1.31560	0.657801	−	0.753192i	$-0.271487\pi$
$659$	6.36955e12	1.31560	0.657801	+	0.753192i	$0.271487\pi$
$660$	−8.91235e12	−1.82829
$661$	−5.58167e12	−1.13725	−0.568627	−	0.822596i	$-0.692525\pi$
$661$	−5.58167e12	−1.13725	−0.568627	+	0.822596i	$0.692525\pi$
$662$	1.56291e13	3.16281
$663$	−9.60116e12	−1.92980
$664$	8.01340e12	1.59978
$665$	5.23907e11	0.103886
$666$	−4.37852e13	−8.62370
$667$	9.17871e11	0.179562
$668$	−6.09371e11	−0.118410
$669$	−1.16395e13	−2.24655
$670$	2.23748e12	0.428965
$671$	5.73003e12	1.09120
$672$	1.03695e13	1.96154
$673$	4.49826e12	0.845234	0.422617	−	0.906308i	$-0.361112\pi$
$673$	4.49826e12	0.845234	0.422617	+	0.906308i	$0.361112\pi$
$674$	6.23492e12	1.16376
$675$	−2.88148e12	−0.534256
$676$	2.40165e11	0.0442333
$677$	5.35625e12	0.979969	0.489984	−	0.871731i	$-0.337002\pi$
$677$	5.35625e12	0.979969	0.489984	+	0.871731i	$0.337002\pi$
$678$	−1.22103e13	−2.21917
$679$	2.34483e12	0.423349
$680$	7.65890e12	1.37365
$681$	−6.42155e12	−1.14414
$682$	−5.85934e12	−1.03710
$683$	−2.20240e12	−0.387261	−0.193630	−	0.981075i	$-0.562026\pi$
$683$	−2.20240e12	−0.387261	−0.193630	+	0.981075i	$0.562026\pi$
$684$	−2.21059e13	−3.86150
$685$	−1.92457e12	−0.333984
$686$	−5.92155e11	−0.102088
$687$	1.41673e13	2.42650
$688$	3.12066e12	0.531005
$689$	−6.56264e12	−1.10941
$690$	−1.58782e12	−0.266673
$691$	4.30201e12	0.717827	0.358913	−	0.933371i	$-0.383147\pi$
$691$	4.30201e12	0.717827	0.358913	+	0.933371i	$0.383147\pi$
$692$	1.34884e12	0.223605
$693$	−4.79377e12	−0.789546
$694$	1.26682e13	2.07299
$695$	−4.25409e12	−0.691632
$696$	−3.61029e13	−5.83177
$697$	3.74045e12	0.600311
$698$	1.29139e13	2.05924
$699$	1.51637e13	2.40248
$700$	−1.23640e12	−0.194634
$701$	9.24701e12	1.44634	0.723170	−	0.690670i	$-0.242684\pi$
$701$	9.24701e12	1.44634	0.723170	+	0.690670i	$0.242684\pi$
$702$	−3.27762e13	−5.09380
$703$	7.43929e12	1.14877
$704$	1.24730e13	1.91379
$705$	5.39703e12	0.822817
$706$	−8.52339e12	−1.29119
$707$	−2.68681e12	−0.404436
$708$	−2.01273e13	−3.01049
$709$	−1.08956e13	−1.61936	−0.809680	−	0.586872i	$-0.800359\pi$
$709$	−1.08956e13	−1.61936	−0.809680	+	0.586872i	$0.800359\pi$
$710$	4.01531e12	0.593002
$711$	−1.32548e13	−1.94517
$712$	9.36452e12	1.36561
$713$	−7.51877e11	−0.108954
$714$	9.49579e12	1.36738
$715$	2.69830e12	0.386111
$716$	1.87802e13	2.67050
$717$	−1.44097e13	−2.03619
$718$	−2.77630e12	−0.389858
$719$	−6.34998e12	−0.886120	−0.443060	−	0.896492i	$-0.646107\pi$
$719$	−6.34998e12	−0.886120	−0.443060	+	0.896492i	$0.646107\pi$
$720$	2.40382e13	3.33353
$721$	−2.42872e12	−0.334710
$722$	−8.59053e12	−1.17653
$723$	−1.56464e13	−2.12957
$724$	2.42402e13	3.27878
$725$	1.57115e12	0.211202
$726$	7.01349e12	0.936956
$727$	4.81017e12	0.638639	0.319319	−	0.947647i	$-0.396546\pi$
$727$	4.81017e12	0.638639	0.319319	+	0.947647i	$0.396546\pi$
$728$	−8.60163e12	−1.13498
$729$	9.00655e12	1.18109
$730$	−7.34822e12	−0.957700
$731$	1.38448e12	0.179332
$732$	−4.72865e13	−6.08747
$733$	−1.10839e13	−1.41816	−0.709082	−	0.705126i	$-0.750890\pi$
$733$	−1.10839e13	−1.41816	−0.709082	+	0.705126i	$0.750890\pi$
$734$	−1.82871e12	−0.232548
$735$	−9.37568e11	−0.118498
$736$	3.78748e12	0.475774
$737$	3.47845e12	0.434292
$738$	2.16352e13	2.68477
$739$	−1.33603e13	−1.64784	−0.823922	−	0.566704i	$-0.808218\pi$
$739$	−1.33603e13	−1.64784	−0.823922	+	0.566704i	$0.808218\pi$
$740$	−1.75565e13	−2.15226
$741$	9.43548e12	1.14969
$742$	6.49061e12	0.786082
$743$	2.12151e12	0.255384	0.127692	−	0.991814i	$-0.459243\pi$
$743$	2.12151e12	0.255384	0.127692	+	0.991814i	$0.459243\pi$
$744$	2.95738e13	3.53858
$745$	6.98643e12	0.830906
$746$	2.45029e13	2.89663
$747$	1.11581e13	1.31114
$748$	1.94677e13	2.27383
$749$	3.53934e12	0.410918
$750$	−2.71792e12	−0.313662
$751$	2.36099e12	0.270841	0.135420	−	0.990788i	$-0.456762\pi$
$751$	2.36099e12	0.270841	0.135420	+	0.990788i	$0.456762\pi$
$752$	−2.65729e13	−3.03011
$753$	−2.64410e11	−0.0299710
$754$	1.78715e13	2.01368
$755$	−3.04803e12	−0.341396
$756$	2.33483e13	2.59961
$757$	6.53431e12	0.723217	0.361608	−	0.932330i	$-0.382228\pi$
$757$	6.53431e12	0.723217	0.361608	+	0.932330i	$0.382228\pi$
$758$	−9.75801e12	−1.07362
$759$	−2.46847e12	−0.269985
$760$	−7.52674e12	−0.818363
$761$	−7.47260e12	−0.807682	−0.403841	−	0.914829i	$-0.632325\pi$
$761$	−7.47260e12	−0.807682	−0.403841	+	0.914829i	$0.632325\pi$
$762$	3.60339e12	0.387180
$763$	4.31824e12	0.461260
$764$	−3.50013e13	−3.71676
$765$	1.06645e13	1.12581
$766$	3.56604e13	3.74246
$767$	6.09374e12	0.635777
$768$	−8.33117e12	−0.864133
$769$	3.53111e12	0.364119	0.182059	−	0.983288i	$-0.441724\pi$
$769$	3.53111e12	0.364119	0.182059	+	0.983288i	$0.441724\pi$
$770$	−2.66868e12	−0.273583
$771$	2.88751e13	2.94292
$772$	7.70043e12	0.780256
$773$	4.38854e12	0.442092	0.221046	−	0.975263i	$-0.429053\pi$
$773$	4.38854e12	0.442092	0.221046	+	0.975263i	$0.429053\pi$
$774$	8.00796e12	0.802025
$775$	−1.28702e12	−0.128152
$776$	−3.36872e13	−3.33493
$777$	−1.33131e13	−1.31034
$778$	−1.48483e13	−1.45301
$779$	−3.67591e12	−0.357640
$780$	−2.22674e13	−2.15399
$781$	6.24232e12	0.600366
$782$	3.46835e12	0.331660
$783$	−2.96698e13	−2.82090
$784$	4.61622e12	0.436379
$785$	−3.13231e12	−0.294409
$786$	5.12374e13	4.78834
$787$	−8.78357e12	−0.816178	−0.408089	−	0.912942i	$-0.633805\pi$
$787$	−8.78357e12	−0.816178	−0.408089	+	0.912942i	$0.633805\pi$
$788$	−2.72213e13	−2.51501
$789$	−3.15312e13	−2.89663
$790$	−7.37890e12	−0.674015
$791$	−2.63342e12	−0.239180
$792$	6.88700e13	6.21966
$793$	1.43164e13	1.28560
$794$	2.27599e13	2.03225
$795$	1.02767e13	0.912433
$796$	−3.51059e13	−3.09935
$797$	−3.11376e12	−0.273352	−0.136676	−	0.990616i	$-0.543642\pi$
$797$	−3.11376e12	−0.273352	−0.136676	+	0.990616i	$0.543642\pi$
$798$	−9.33193e12	−0.814626
$799$	−1.17890e13	−1.02333
$800$	6.48318e12	0.559607
$801$	1.30395e13	1.11921
$802$	−4.70628e12	−0.401692
$803$	−1.14238e13	−0.969593
$804$	−2.87055e13	−2.42278
$805$	−3.42448e11	−0.0287418
$806$	−1.46395e13	−1.22185
$807$	−1.34443e13	−1.11585
$808$	3.86003e13	3.18595
$809$	2.27913e13	1.87068	0.935341	−	0.353747i	$-0.115093\pi$
$809$	2.27913e13	1.87068	0.935341	+	0.353747i	$0.115093\pi$
$810$	2.60471e13	2.12607
$811$	6.23133e12	0.505810	0.252905	−	0.967491i	$-0.418614\pi$
$811$	6.23133e12	0.505810	0.252905	+	0.967491i	$0.418614\pi$
$812$	−1.27309e13	−1.02768
$813$	6.48377e12	0.520499
$814$	−3.78944e13	−3.02527
$815$	−9.08847e12	−0.721575
$816$	−7.40256e13	−5.84489
$817$	−1.36059e12	−0.106838
$818$	2.29447e13	1.79181
$819$	−1.19772e13	−0.930202
$820$	8.67501e12	0.670051
$821$	−6.34294e12	−0.487244	−0.243622	−	0.969870i	$-0.578336\pi$
$821$	−6.34294e12	−0.487244	−0.243622	+	0.969870i	$0.578336\pi$
$822$	3.42808e13	2.61895
$823$	−1.01100e13	−0.768158	−0.384079	−	0.923300i	$-0.625481\pi$
$823$	−1.01100e13	−0.768158	−0.384079	+	0.923300i	$0.625481\pi$
$824$	3.48923e13	2.63668
$825$	−4.22537e12	−0.317557
$826$	−6.02686e12	−0.450486
$827$	−2.09841e11	−0.0155997	−0.00779984	−	0.999970i	$-0.502483\pi$
$827$	−2.09841e11	−0.0155997	−0.00779984	+	0.999970i	$0.502483\pi$
$828$	1.44494e13	1.06835
$829$	−1.42099e13	−1.04495	−0.522474	−	0.852655i	$-0.674991\pi$
$829$	−1.42099e13	−1.04495	−0.522474	+	0.852655i	$0.674991\pi$
$830$	6.21170e12	0.454317
$831$	5.79980e12	0.421899
$832$	3.11636e13	2.25472
$833$	2.04798e12	0.147375
$834$	7.57746e13	5.42346
$835$	−2.88904e11	−0.0205667
$836$	−1.91318e13	−1.35465
$837$	2.43041e13	1.71165
$838$	1.18868e13	0.832658
$839$	6.20295e12	0.432185	0.216092	−	0.976373i	$-0.430669\pi$
$839$	6.20295e12	0.432185	0.216092	+	0.976373i	$0.430669\pi$
$840$	1.34696e13	0.933466
$841$	1.67059e12	0.115157
$842$	2.32006e13	1.59072
$843$	−2.35017e13	−1.60278
$844$	1.78185e13	1.20873
$845$	1.13863e11	0.00768292
$846$	−6.81890e13	−4.57665
$847$	1.51262e12	0.100984
$848$	−5.05984e13	−3.36012
$849$	2.50660e13	1.65577
$850$	5.93691e12	0.390099
$851$	−4.86265e12	−0.317826
$852$	−5.15141e13	−3.34925
$853$	−3.60370e12	−0.233066	−0.116533	−	0.993187i	$-0.537178\pi$
$853$	−3.60370e12	−0.233066	−0.116533	+	0.993187i	$0.537178\pi$
$854$	−1.41593e13	−0.910922
$855$	−1.04805e13	−0.670708
$856$	−5.08482e13	−3.23701
$857$	−4.01270e12	−0.254110	−0.127055	−	0.991896i	$-0.540553\pi$
$857$	−4.01270e12	−0.254110	−0.127055	+	0.991896i	$0.540553\pi$
$858$	−4.80626e13	−3.02771
$859$	2.02534e13	1.26919	0.634597	−	0.772843i	$-0.281166\pi$
$859$	2.02534e13	1.26919	0.634597	+	0.772843i	$0.281166\pi$
$860$	3.21094e12	0.200165
$861$	6.57829e12	0.407942
$862$	−2.38579e13	−1.47180
$863$	1.57831e13	0.968598	0.484299	−	0.874903i	$-0.339075\pi$
$863$	1.57831e13	0.968598	0.484299	+	0.874903i	$0.339075\pi$
$864$	−1.22429e14	−7.47433
$865$	6.39487e11	0.0388382
$866$	9.12694e12	0.551435
$867$	−1.98264e12	−0.119167
$868$	1.04285e13	0.623570
$869$	−1.14715e13	−0.682385
$870$	−2.79857e13	−1.65615
$871$	8.69087e12	0.511660
$872$	−6.20382e13	−3.63358
$873$	−4.69071e13	−2.73322
$874$	−3.40850e12	−0.197589
$875$	−5.86182e11	−0.0338062
$876$	9.42735e13	5.40905
$877$	−8.86665e12	−0.506129	−0.253065	−	0.967449i	$-0.581439\pi$
$877$	−8.86665e12	−0.506129	−0.253065	+	0.967449i	$0.581439\pi$
$878$	−4.50562e13	−2.55876
$879$	1.09564e13	0.619040
$880$	2.08041e13	1.16943
$881$	−1.22614e13	−0.685720	−0.342860	−	0.939387i	$-0.611396\pi$
$881$	−1.22614e13	−0.685720	−0.342860	+	0.939387i	$0.611396\pi$
$882$	1.18457e13	0.659103
$883$	1.90484e13	1.05447	0.527236	−	0.849719i	$-0.323228\pi$
$883$	1.90484e13	1.05447	0.527236	+	0.849719i	$0.323228\pi$
$884$	4.86400e13	2.67891
$885$	−9.54242e12	−0.522894
$886$	−3.41634e13	−1.86256
$887$	2.67439e13	1.45067	0.725335	−	0.688396i	$-0.241685\pi$
$887$	2.67439e13	1.45067	0.725335	+	0.688396i	$0.241685\pi$
$888$	1.91264e14	10.3223
$889$	7.77152e11	0.0417300
$890$	7.25904e12	0.387815
$891$	4.04937e13	2.15247
$892$	5.89661e13	3.11861
$893$	1.15856e13	0.609659
$894$	−1.24443e14	−6.51558
$895$	8.90375e12	0.463841
$896$	−1.04188e13	−0.540047
$897$	−6.16744e12	−0.318082
$898$	−4.19419e13	−2.15231
$899$	−1.32520e13	−0.676650
$900$	2.47336e13	1.25660
$901$	−2.24479e13	−1.13479
$902$	1.87244e13	0.941841
$903$	2.43486e12	0.121865
$904$	3.78332e13	1.88415
$905$	1.14923e13	0.569495
$906$	5.42920e13	2.67707
$907$	3.03949e13	1.49131	0.745655	−	0.666332i	$-0.232137\pi$
$907$	3.03949e13	1.49131	0.745655	+	0.666332i	$0.232137\pi$
$908$	3.25319e13	1.58827
$909$	5.37483e13	2.61112
$910$	−6.66768e12	−0.322321
$911$	1.77272e13	0.852721	0.426361	−	0.904553i	$-0.359795\pi$
$911$	1.77272e13	0.852721	0.426361	+	0.904553i	$0.359795\pi$
$912$	7.27482e13	3.48214
$913$	9.65690e12	0.459959
$914$	3.16045e13	1.49793
$915$	−2.24186e13	−1.05734
$916$	−7.17721e13	−3.36842
$917$	1.10505e13	0.516083
$918$	−1.12113e14	−5.21032
$919$	−3.30500e13	−1.52845	−0.764226	−	0.644948i	$-0.776879\pi$
$919$	−3.30500e13	−1.52845	−0.764226	+	0.644948i	$0.776879\pi$
$920$	4.91980e12	0.226414
$921$	−2.41738e13	−1.10707
$922$	−3.66651e13	−1.67095
$923$	1.55964e13	0.707320
$924$	3.42377e13	1.54518
$925$	−8.32357e12	−0.373828
$926$	−3.70491e13	−1.65588
$927$	4.85852e13	2.16095
$928$	6.67555e13	2.95475
$929$	−3.62767e13	−1.59793	−0.798963	−	0.601380i	$-0.794618\pi$
$929$	−3.62767e13	−1.59793	−0.798963	+	0.601380i	$0.794618\pi$
$930$	2.29246e13	1.00491
$931$	−2.01264e12	−0.0877996
$932$	−7.68203e13	−3.33506
$933$	4.07228e13	1.75942
$934$	−7.46313e13	−3.20893
$935$	9.22970e12	0.394944
$936$	1.72071e14	7.32768
$937$	8.07643e11	0.0342288	0.0171144	−	0.999854i	$-0.494552\pi$
$937$	8.07643e11	0.0342288	0.0171144	+	0.999854i	$0.494552\pi$
$938$	−8.59548e12	−0.362541
$939$	−2.31201e13	−0.970499
$940$	−2.73416e13	−1.14222
$941$	−2.62828e13	−1.09274	−0.546371	−	0.837543i	$-0.683991\pi$
$941$	−2.62828e13	−1.09274	−0.546371	+	0.837543i	$0.683991\pi$
$942$	5.57932e13	2.30862
$943$	2.40273e12	0.0989470
$944$	4.69832e13	1.92561
$945$	1.10695e13	0.451529
$946$	6.93057e12	0.281358
$947$	1.64435e13	0.664384	0.332192	−	0.943212i	$-0.392212\pi$
$947$	1.64435e13	0.664384	0.332192	+	0.943212i	$0.392212\pi$
$948$	9.46670e13	3.80681
$949$	−2.85422e13	−1.14232
$950$	−5.83446e12	−0.232405
$951$	−1.61304e13	−0.639489
$952$	−2.94224e13	−1.16095
$953$	−1.18588e13	−0.465717	−0.232859	−	0.972511i	$-0.574808\pi$
$953$	−1.18588e13	−0.465717	−0.232859	+	0.972511i	$0.574808\pi$
$954$	−1.29841e14	−5.07510
$955$	−1.65942e13	−0.645567
$956$	7.30003e13	2.82660
$957$	−4.35074e13	−1.67672
$958$	−2.78542e13	−1.06843
$959$	7.39343e12	0.282268
$960$	−4.88003e13	−1.85439
$961$	−1.55842e13	−0.589425
$962$	−9.46787e13	−3.56422
$963$	−7.08027e13	−2.65296
$964$	7.92655e13	2.95623
$965$	3.65079e12	0.135523
$966$	6.09975e12	0.225380
$967$	1.14207e13	0.420023	0.210011	−	0.977699i	$-0.432650\pi$
$967$	1.14207e13	0.420023	0.210011	+	0.977699i	$0.432650\pi$
$968$	−2.17311e13	−0.795505
$969$	3.22747e13	1.17599
$970$	−2.61131e13	−0.947078
$971$	8.26707e12	0.298446	0.149223	−	0.988804i	$-0.452323\pi$
$971$	8.26707e12	0.298446	0.149223	+	0.988804i	$0.452323\pi$
$972$	−1.42764e14	−5.13004
$973$	1.63425e13	0.584536
$974$	4.24011e10	0.00150960
$975$	−1.05570e13	−0.374129
$976$	1.10381e14	3.89375
$977$	−5.06889e13	−1.77987	−0.889934	−	0.456090i	$-0.849250\pi$
$977$	−5.06889e13	−1.77987	−0.889934	+	0.456090i	$0.849250\pi$
$978$	1.61886e14	5.65826
$979$	1.12851e13	0.392631
$980$	4.74976e12	0.164496
$981$	−8.63840e13	−2.97799
$982$	3.58686e13	1.23087
$983$	1.12786e13	0.385268	0.192634	−	0.981271i	$-0.438297\pi$
$983$	1.12786e13	0.385268	0.192634	+	0.981271i	$0.438297\pi$
$984$	−9.45073e13	−3.21357
$985$	−1.29057e13	−0.436835
$986$	6.11307e13	2.05974
$987$	−2.07332e13	−0.695408
$988$	−4.78006e13	−1.59598
$989$	8.89338e11	0.0295586
$990$	5.33856e13	1.76630
$991$	5.17189e13	1.70340	0.851702	−	0.524027i	$-0.175571\pi$
$991$	5.17189e13	1.70340	0.851702	+	0.524027i	$0.175571\pi$
$992$	−5.46829e13	−1.79287
$993$	−9.50635e13	−3.10272
$994$	−1.54252e13	−0.501178
$995$	−1.66438e13	−0.538330
$996$	−7.96926e13	−2.56597
$997$	1.92951e13	0.618471	0.309235	−	0.950986i	$-0.399927\pi$
$997$	1.92951e13	0.618471	0.309235	+	0.950986i	$0.399927\pi$
$998$	1.06413e14	3.39554
$999$	1.57183e14	4.99300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.a.e.1.6	✓	6
3.2	odd	2		315.10.a.l.1.1		6
5.2	odd	4		175.10.b.g.99.11		12
5.3	odd	4		175.10.b.g.99.2		12
5.4	even	2		175.10.a.g.1.1		6
7.6	odd	2		245.10.a.g.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.6	✓	6	1.1	even	1	trivial
175.10.a.g.1.1		6	5.4	even	2
175.10.b.g.99.2		12	5.3	odd	4
175.10.b.g.99.11		12	5.2	odd	4
245.10.a.g.1.6		6	7.6	odd	2
315.10.a.l.1.1		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+42.7818 q^{2} -260.219 q^{3} +1318.28 q^{4} +625.000 q^{5} -11132.6 q^{6} -2401.00 q^{7} +34494.1 q^{8} +48030.7 q^{9} +26738.6 q^{10} +41568.7 q^{11} -343041. q^{12} +103859. q^{13} -102719. q^{14} -162637. q^{15} +800760. q^{16} +355256. q^{17} +2.05484e6 q^{18} -349126. q^{19} +823925. q^{20} +624785. q^{21} +1.77838e6 q^{22} +228204. q^{23} -8.97601e6 q^{24} +390625. q^{25} +4.44327e6 q^{26} -7.37660e6 q^{27} -3.16519e6 q^{28} +4.02216e6 q^{29} -6.95788e6 q^{30} -3.29476e6 q^{31} +1.65969e7 q^{32} -1.08169e7 q^{33} +1.51985e7 q^{34} -1.50062e6 q^{35} +6.33179e7 q^{36} -2.13083e7 q^{37} -1.49362e7 q^{38} -2.70260e7 q^{39} +2.15588e7 q^{40} +1.05289e7 q^{41} +2.67294e7 q^{42} +3.89712e6 q^{43} +5.47991e7 q^{44} +3.00192e7 q^{45} +9.76296e6 q^{46} -3.31846e7 q^{47} -2.08373e8 q^{48} +5.76480e6 q^{49} +1.67116e7 q^{50} -9.24443e7 q^{51} +1.36915e8 q^{52} -6.31880e7 q^{53} -3.15584e8 q^{54} +2.59804e7 q^{55} -8.28203e7 q^{56} +9.08490e7 q^{57} +1.72075e8 q^{58} +5.86733e7 q^{59} -2.14401e8 q^{60} +1.37845e8 q^{61} -1.40956e8 q^{62} -1.15322e8 q^{63} +3.00057e8 q^{64} +6.49118e7 q^{65} -4.62768e8 q^{66} +8.36796e7 q^{67} +4.68327e8 q^{68} -5.93829e7 q^{69} -6.41994e7 q^{70} +1.50169e8 q^{71} +1.65678e9 q^{72} -2.74817e8 q^{73} -9.11609e8 q^{74} -1.01648e8 q^{75} -4.60246e8 q^{76} -9.98063e7 q^{77} -1.15622e9 q^{78} -2.75964e8 q^{79} +5.00475e8 q^{80} +9.74140e8 q^{81} +4.50444e8 q^{82} +2.32312e8 q^{83} +8.23642e8 q^{84} +2.22035e8 q^{85} +1.66726e8 q^{86} -1.04664e9 q^{87} +1.43387e9 q^{88} +2.71482e8 q^{89} +1.28427e9 q^{90} -2.49365e8 q^{91} +3.00837e8 q^{92} +8.57358e8 q^{93} -1.41969e9 q^{94} -2.18204e8 q^{95} -4.31883e9 q^{96} -9.76607e8 q^{97} +2.46628e8 q^{98} +1.99657e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} - 124 q^{3} + 3009 q^{4} + 3750 q^{5} + 4888 q^{6} - 14406 q^{7} + 22041 q^{8} + 111090 q^{9} + 9375 q^{10} - 47796 q^{11} - 541656 q^{12} + 102168 q^{13} - 36015 q^{14} - 77500 q^{15} + 2371065 q^{16}+ \cdots + 3571968784 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 - 124 * q^3 + 3009 * q^4 + 3750 * q^5 + 4888 * q^6 - 14406 * q^7 + 22041 * q^8 + 111090 * q^9 + 9375 * q^10 - 47796 * q^11 - 541656 * q^12 + 102168 * q^13 - 36015 * q^14 - 77500 * q^15 + 2371065 * q^16 - 38472 * q^17 + 1837015 * q^18 + 361056 * q^19 + 1880625 * q^20 + 297724 * q^21 + 2068680 * q^22 + 697032 * q^23 + 4828076 * q^24 + 2343750 * q^25 + 10847622 * q^26 + 1653188 * q^27 - 7224609 * q^28 + 16028184 * q^29 + 3055000 * q^30 + 1362912 * q^31 - 1148823 * q^32 + 14059020 * q^33 - 9216294 * q^34 - 9003750 * q^35 + 92319641 * q^36 - 3912924 * q^37 + 39877140 * q^38 - 20341868 * q^39 + 13775625 * q^40 + 22452756 * q^41 - 11736088 * q^42 - 29998992 * q^43 - 94378728 * q^44 + 69431250 * q^45 + 49589520 * q^46 - 121271508 * q^47 - 327116052 * q^48 + 34588806 * q^49 + 5859375 * q^50 - 281338180 * q^51 - 44528550 * q^52 - 20308596 * q^53 - 290104308 * q^54 - 29872500 * q^55 - 52920441 * q^56 + 186940744 * q^57 + 256759494 * q^58 + 120280392 * q^59 - 338535000 * q^60 - 87693540 * q^61 - 344802528 * q^62 - 266727090 * q^63 + 640647105 * q^64 + 63855000 * q^65 - 1393970692 * q^66 + 495050664 * q^67 - 141443706 * q^68 + 1031633640 * q^69 - 22509375 * q^70 + 253762512 * q^71 + 856452205 * q^72 + 187195308 * q^73 - 418806054 * q^74 - 48437500 * q^75 - 584719476 * q^76 + 114758196 * q^77 - 1728062324 * q^78 + 831079500 * q^79 + 1481915625 * q^80 + 1869314710 * q^81 + 2286848814 * q^82 - 767650536 * q^83 + 1300516056 * q^84 - 24045000 * q^85 + 566199948 * q^86 + 1303216852 * q^87 + 2952495444 * q^88 + 582579684 * q^89 + 1148134375 * q^90 - 245305368 * q^91 - 4259382384 * q^92 + 15388800 * q^93 - 1115946660 * q^94 + 225660000 * q^95 + 989345252 * q^96 - 1184506872 * q^97 + 86472015 * q^98 + 3571968784 * q^99

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