LMFDB - Embedded newform 10.28.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,28,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	10.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:	$46.1855574838$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 19551870 $ x^2 - x - 19551870
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4422.25$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8192.00 q^{2} -3.52746e6 q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} +2.88969e10 q^{6} -2.10875e11 q^{7} -5.49756e11 q^{8} +4.81735e12 q^{9} -1.00000e13 q^{10} -2.00632e14 q^{11} -2.36724e14 q^{12} +1.66667e15 q^{13} +1.72749e15 q^{14} -4.30598e15 q^{15} +4.50360e15 q^{16} +4.72049e16 q^{17} -3.94638e16 q^{18} +2.80684e17 q^{19} +8.19200e16 q^{20} +7.43854e17 q^{21} +1.64358e18 q^{22} -3.44510e18 q^{23} +1.93924e18 q^{24} +1.49012e18 q^{25} -1.36534e19 q^{26} +9.90596e18 q^{27} -1.41516e19 q^{28} +5.38410e19 q^{29} +3.52746e19 q^{30} -6.02019e19 q^{31} -3.68935e19 q^{32} +7.07721e20 q^{33} -3.86703e20 q^{34} -2.57416e20 q^{35} +3.23287e20 q^{36} +2.15489e21 q^{37} -2.29937e21 q^{38} -5.87910e21 q^{39} -6.71089e20 q^{40} -5.73864e21 q^{41} -6.09365e21 q^{42} +4.73192e20 q^{43} -1.34642e22 q^{44} +5.88056e21 q^{45} +2.82223e22 q^{46} -1.36579e22 q^{47} -1.58863e22 q^{48} -2.12439e22 q^{49} -1.22070e22 q^{50} -1.66513e23 q^{51} +1.11848e23 q^{52} +1.17314e23 q^{53} -8.11496e22 q^{54} -2.44912e23 q^{55} +1.15930e23 q^{56} -9.90101e23 q^{57} -4.41066e23 q^{58} -6.96143e23 q^{59} -2.88969e23 q^{60} -1.66138e24 q^{61} +4.93174e23 q^{62} -1.01586e24 q^{63} +3.02231e23 q^{64} +2.03451e24 q^{65} -5.79765e24 q^{66} -6.87655e22 q^{67} +3.16787e24 q^{68} +1.21524e25 q^{69} +2.10875e24 q^{70} -1.69024e24 q^{71} -2.64837e24 q^{72} -5.53884e24 q^{73} -1.76529e25 q^{74} -5.25632e24 q^{75} +1.88364e25 q^{76} +4.23083e25 q^{77} +4.81616e25 q^{78} -5.02072e24 q^{79} +5.49756e24 q^{80} -7.16780e25 q^{81} +4.70109e25 q^{82} +1.56395e26 q^{83} +4.99192e25 q^{84} +5.76232e25 q^{85} -3.87639e24 q^{86} -1.89922e26 q^{87} +1.10299e26 q^{88} -6.32996e25 q^{89} -4.81735e25 q^{90} -3.51459e26 q^{91} -2.31197e26 q^{92} +2.12360e26 q^{93} +1.11886e26 q^{94} +3.42632e26 q^{95} +1.30140e26 q^{96} -5.95949e26 q^{97} +1.74030e26 q^{98} -9.66515e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16384 q^{2} - 3340644 q^{3} + 134217728 q^{4} + 2441406250 q^{5} + 27366555648 q^{6} - 58706842292 q^{7} - 1099511627776 q^{8} - 2773343978406 q^{9} - 20000000000000 q^{10} - 148584207397296 q^{11}+ \cdots - 13\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 16384 * q^2 - 3340644 * q^3 + 134217728 * q^4 + 2441406250 * q^5 + 27366555648 * q^6 - 58706842292 * q^7 - 1099511627776 * q^8 - 2773343978406 * q^9 - 20000000000000 * q^10 - 148584207397296 * q^11 - 224186823868416 * q^12 + 700099119029596 * q^13 + 480926452056064 * q^14 - 4077934570312500 * q^15 + 9007199254740992 * q^16 + 38363966708465748 * q^17 + 22719233871101952 * q^18 + 231077489147345800 * q^19 + 163840000000000000 * q^20 + 772280752747638624 * q^21 + 1217201826998648832 * q^22 - 1051524217202377644 * q^23 + 1836538461130063872 * q^24 + 2980232238769531250 * q^25 - 5735211983090450432 * q^26 + 7063356285021193560 * q^27 - 3939749495243276288 * q^28 + 59213295656400885420 * q^29 + 33406440000000000000 * q^30 + 100028171637661559944 * q^31 - 73786976294838206464 * q^32 + 717443691297291752112 * q^33 - 314277615275751407616 * q^34 - 71663625844726562500 * q^35 - 186115963872067190784 * q^36 - 93534665260879182692 * q^37 - 1892986791095056793600 * q^38 - 6059669650423221487512 * q^39 - 1342177280000000000000 * q^40 - 10105587280937387464956 * q^41 - 6326523926508655607808 * q^42 - 4721434400282665756964 * q^43 - 9971317366772931231744 * q^44 - 3385429661140136718750 * q^45 + 8614086387321877659648 * q^46 - 12229615564061849682372 * q^47 - 15044923073577483239424 * q^48 - 63801053560061994186654 * q^49 - 24414062500000000000000 * q^50 - 168164944839408859896456 * q^51 + 46982856565476969938944 * q^52 - 107620760072906302379604 * q^53 - 57863014686893617643520 * q^54 - 181377206295527343750000 * q^55 + 32274427865032919351296 * q^56 - 999368617055941453508400 * q^57 - 485075318017236053360640 * q^58 - 1873128711713027366910360 * q^59 - 273665556480000000000000 * q^60 - 3717289232167725644025716 * q^61 - 819430782055723499061248 * q^62 - 2170926616021273562933124 * q^63 + 604462909807314587353088 * q^64 + 854613182409174804687500 * q^65 - 5877298719107414033301504 * q^66 + 3742334935347789083235028 * q^67 + 2574562224338955531190272 * q^68 + 12599594916132118555745568 * q^69 + 587068422920000000000000 * q^70 - 4816780974130885431148776 * q^71 + 1524661976039974426902528 * q^72 + 9436477395201058880013796 * q^73 + 766235977817122264612864 * q^74 - 4977947473526000976562500 * q^75 + 15507347792650705253171200 * q^76 + 50228356579868877749801616 * q^77 + 49640813776267030425698304 * q^78 + 9144841742084043183428080 * q^79 + 10995116277760000000000000 * q^80 - 14325462375198451093027998 * q^81 + 82784971005439078112919552 * q^82 + 148434950342238869610178716 * q^83 + 51826884005958906739163136 * q^84 + 46831014048420102539062500 * q^85 + 38677990607115597881049088 * q^86 - 188918373571694763982458840 * q^87 + 81685031868603852650446848 * q^88 - 168440373041146148645755980 * q^89 + 27733439784060000000000000 * q^90 - 498540814254851281271173816 * q^91 - 70566595684940821787836416 * q^92 + 242292812947742217165349632 * q^93 + 100185010700794672597991424 * q^94 + 282077013119318603515625000 * q^95 + 123248009818746742697361408 * q^96 - 863184664945605533733445292 * q^97 + 522658230764027856377069568 * q^98 - 1361593782715399520132408112 * 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 $

$2$	−8192.00	−0.707107
$2$	−8192.00	−0.707107
$3$	−3.52746e6	−1.27739	−0.638697	−	0.769458i	$-0.720526\pi$
$3$	−3.52746e6	−1.27739	−0.638697	+	0.769458i	$0.720526\pi$
$4$	6.71089e7	0.500000
$5$	1.22070e9	0.447214
$5$	1.22070e9	0.447214
$6$	2.88969e10	0.903254
$7$	−2.10875e11	−0.822626	−0.411313	−	0.911494i	$-0.634930\pi$
$7$	−2.10875e11	−0.822626	−0.411313	+	0.911494i	$0.634930\pi$
$8$	−5.49756e11	−0.353553
$9$	4.81735e12	0.631735
$10$	−1.00000e13	−0.316228
$11$	−2.00632e14	−1.75226	−0.876131	−	0.482074i	$-0.839884\pi$
$11$	−2.00632e14	−1.75226	−0.876131	+	0.482074i	$0.839884\pi$
$12$	−2.36724e14	−0.638697
$13$	1.66667e15	1.52621	0.763105	−	0.646275i	$-0.223674\pi$
$13$	1.66667e15	1.52621	0.763105	+	0.646275i	$0.223674\pi$
$14$	1.72749e15	0.581684
$15$	−4.30598e15	−0.571268
$16$	4.50360e15	0.250000
$17$	4.72049e16	1.15592	0.577959	−	0.816066i	$-0.303849\pi$
$17$	4.72049e16	1.15592	0.577959	+	0.816066i	$0.303849\pi$
$18$	−3.94638e16	−0.446704
$19$	2.80684e17	1.53124	0.765622	−	0.643291i	$-0.222431\pi$
$19$	2.80684e17	1.53124	0.765622	+	0.643291i	$0.222431\pi$
$20$	8.19200e16	0.223607
$21$	7.43854e17	1.05082
$22$	1.64358e18	1.23904
$23$	−3.44510e18	−1.42520	−0.712601	−	0.701570i	$-0.752483\pi$
$23$	−3.44510e18	−1.42520	−0.712601	+	0.701570i	$0.752483\pi$
$24$	1.93924e18	0.451627
$25$	1.49012e18	0.200000
$26$	−1.36534e19	−1.07919
$27$	9.90596e18	0.470420
$28$	−1.41516e19	−0.411313
$29$	5.38410e19	0.974407	0.487204	−	0.873288i	$-0.338017\pi$
$29$	5.38410e19	0.974407	0.487204	+	0.873288i	$0.338017\pi$
$30$	3.52746e19	0.403947
$31$	−6.02019e19	−0.442820	−0.221410	−	0.975181i	$-0.571066\pi$
$31$	−6.02019e19	−0.442820	−0.221410	+	0.975181i	$0.571066\pi$
$32$	−3.68935e19	−0.176777
$33$	7.07721e20	2.23833
$34$	−3.86703e20	−0.817357
$35$	−2.57416e20	−0.367889
$36$	3.23287e20	0.315867
$37$	2.15489e21	1.45446	0.727231	−	0.686393i	$-0.240807\pi$
$37$	2.15489e21	1.45446	0.727231	+	0.686393i	$0.240807\pi$
$38$	−2.29937e21	−1.08275
$39$	−5.87910e21	−1.94957
$40$	−6.71089e20	−0.158114
$41$	−5.73864e21	−0.968784	−0.484392	−	0.874851i	$-0.660959\pi$
$41$	−5.73864e21	−0.968784	−0.484392	+	0.874851i	$0.660959\pi$
$42$	−6.09365e21	−0.743040
$43$	4.73192e20	0.0419965	0.0209983	−	0.999780i	$-0.493316\pi$
$43$	4.73192e20	0.0419965	0.0209983	+	0.999780i	$0.493316\pi$
$44$	−1.34642e22	−0.876131
$45$	5.88056e21	0.282520
$46$	2.82223e22	1.00777
$47$	−1.36579e22	−0.364808	−0.182404	−	0.983224i	$-0.558388\pi$
$47$	−1.36579e22	−0.364808	−0.182404	+	0.983224i	$0.558388\pi$
$48$	−1.58863e22	−0.319348
$49$	−2.12439e22	−0.323287
$50$	−1.22070e22	−0.141421
$51$	−1.66513e23	−1.47656
$52$	1.11848e23	0.763105
$53$	1.17314e23	0.618907	0.309454	−	0.950915i	$-0.399854\pi$
$53$	1.17314e23	0.618907	0.309454	+	0.950915i	$0.399854\pi$
$54$	−8.11496e22	−0.332637
$55$	−2.44912e23	−0.783635
$56$	1.15930e23	0.290842
$57$	−9.90101e23	−1.95600
$58$	−4.41066e23	−0.689010
$59$	−6.96143e23	−0.863369	−0.431684	−	0.902025i	$-0.642081\pi$
$59$	−6.96143e23	−0.863369	−0.431684	+	0.902025i	$0.642081\pi$
$60$	−2.88969e23	−0.285634
$61$	−1.66138e24	−1.31376	−0.656882	−	0.753993i	$-0.728125\pi$
$61$	−1.66138e24	−1.31376	−0.656882	+	0.753993i	$0.728125\pi$
$62$	4.93174e23	0.313121
$63$	−1.01586e24	−0.519681
$64$	3.02231e23	0.125000
$65$	2.03451e24	0.682541
$66$	−5.79765e24	−1.58274
$67$	−6.87655e22	−0.0153236	−0.00766180	−	0.999971i	$-0.502439\pi$
$67$	−6.87655e22	−0.0153236	−0.00766180	+	0.999971i	$0.502439\pi$
$68$	3.16787e24	0.577959
$69$	1.21524e25	1.82054
$70$	2.10875e24	0.260137
$71$	−1.69024e24	−0.172171	−0.0860856	−	0.996288i	$-0.527436\pi$
$71$	−1.69024e24	−0.172171	−0.0860856	+	0.996288i	$0.527436\pi$
$72$	−2.64837e24	−0.223352
$73$	−5.53884e24	−0.387758	−0.193879	−	0.981025i	$-0.562107\pi$
$73$	−5.53884e24	−0.387758	−0.193879	+	0.981025i	$0.562107\pi$
$74$	−1.76529e25	−1.02846
$75$	−5.25632e24	−0.255479
$76$	1.88364e25	0.765622
$77$	4.23083e25	1.44146
$78$	4.81616e25	1.37855
$79$	−5.02072e24	−0.121004	−0.0605021	−	0.998168i	$-0.519270\pi$
$79$	−5.02072e24	−0.121004	−0.0605021	+	0.998168i	$0.519270\pi$
$80$	5.49756e24	0.111803
$81$	−7.16780e25	−1.23265
$82$	4.70109e25	0.685034
$83$	1.56395e26	1.93494	0.967470	−	0.252988i	$-0.0814132\pi$
$83$	1.56395e26	1.93494	0.967470	+	0.252988i	$0.0814132\pi$
$84$	4.99192e25	0.525408
$85$	5.76232e25	0.516942
$86$	−3.87639e24	−0.0296960
$87$	−1.89922e26	−1.24470
$88$	1.10299e26	0.619518
$89$	−6.32996e25	−0.305236	−0.152618	−	0.988285i	$-0.548770\pi$
$89$	−6.32996e25	−0.305236	−0.152618	+	0.988285i	$0.548770\pi$
$90$	−4.81735e25	−0.199772
$91$	−3.51459e26	−1.25550
$92$	−2.31197e26	−0.712601
$93$	2.12360e26	0.565656
$94$	1.11886e26	0.257958
$95$	3.42632e26	0.684793
$96$	1.30140e26	0.225813
$97$	−5.95949e26	−0.899063	−0.449532	−	0.893264i	$-0.648409\pi$
$97$	−5.95949e26	−0.899063	−0.449532	+	0.893264i	$0.648409\pi$
$98$	1.74030e26	0.228598
$99$	−9.66515e26	−1.10696
$100$	1.00000e26	0.100000
$101$	−6.01756e26	−0.526117	−0.263058	−	0.964780i	$-0.584731\pi$
$101$	−6.01756e26	−0.526117	−0.263058	+	0.964780i	$0.584731\pi$
$102$	1.36408e27	1.04409
$103$	5.34812e26	0.358838	0.179419	−	0.983773i	$-0.442578\pi$
$103$	5.34812e26	0.358838	0.179419	+	0.983773i	$0.442578\pi$
$104$	−9.16261e26	−0.539596
$105$	9.08025e26	0.469940
$106$	−9.61036e26	−0.437633
$107$	−2.27447e27	−0.912429	−0.456214	−	0.889870i	$-0.650795\pi$
$107$	−2.27447e27	−0.912429	−0.456214	+	0.889870i	$0.650795\pi$
$108$	6.64777e26	0.235210
$109$	−2.61656e27	−0.817472	−0.408736	−	0.912653i	$-0.634030\pi$
$109$	−2.61656e27	−0.817472	−0.408736	+	0.912653i	$0.634030\pi$
$110$	2.00632e27	0.554114
$111$	−7.60129e27	−1.85792
$112$	−9.49698e26	−0.205656
$113$	−9.28514e27	−1.78332	−0.891660	−	0.452705i	$-0.850459\pi$
$113$	−9.28514e27	−1.78332	−0.891660	+	0.452705i	$0.850459\pi$
$114$	8.11091e27	1.38310
$115$	−4.20545e27	−0.637369
$116$	3.61321e27	0.487204
$117$	8.02893e27	0.964159
$118$	5.70280e27	0.610494
$119$	−9.95436e27	−0.950888
$120$	2.36724e27	0.201974
$121$	2.71432e28	2.07042
$122$	1.36101e28	0.928972
$123$	2.02428e28	1.23752
$124$	−4.04008e27	−0.221410
$125$	1.81899e27	0.0894427
$126$	8.32194e27	0.367470
$127$	1.34819e28	0.535058	0.267529	−	0.963550i	$-0.413793\pi$
$127$	1.34819e28	0.535058	0.267529	+	0.963550i	$0.413793\pi$
$128$	−2.47588e27	−0.0883883
$129$	−1.66916e27	−0.0536461
$130$	−1.66667e28	−0.482630
$131$	−1.22819e28	−0.320703	−0.160351	−	0.987060i	$-0.551263\pi$
$131$	−1.22819e28	−0.320703	−0.160351	+	0.987060i	$0.551263\pi$
$132$	4.74943e28	1.11916
$133$	−5.91894e28	−1.25964
$134$	5.63327e26	0.0108354
$135$	1.20922e28	0.210378
$136$	−2.59512e28	−0.408679
$137$	7.77523e28	1.10914	0.554569	−	0.832138i	$-0.312883\pi$
$137$	7.77523e28	1.10914	0.554569	+	0.832138i	$0.312883\pi$
$138$	−9.95528e28	−1.28732
$139$	−6.09274e28	−0.714682	−0.357341	−	0.933974i	$-0.616317\pi$
$139$	−6.09274e28	−0.714682	−0.357341	+	0.933974i	$0.616317\pi$
$140$	−1.72749e28	−0.183945
$141$	4.81778e28	0.466003
$142$	1.38464e28	0.121743
$143$	−3.34387e29	−2.67432
$144$	2.16954e28	0.157934
$145$	6.57239e28	0.435768
$146$	4.53742e28	0.274186
$147$	7.49371e28	0.412965
$148$	1.44612e29	0.727231
$149$	−1.05900e29	−0.486276	−0.243138	−	0.969992i	$-0.578177\pi$
$149$	−1.05900e29	−0.486276	−0.243138	+	0.969992i	$0.578177\pi$
$150$	4.30598e28	0.180651
$151$	3.29076e28	0.126214	0.0631070	−	0.998007i	$-0.479899\pi$
$151$	3.29076e28	0.126214	0.0631070	+	0.998007i	$0.479899\pi$
$152$	−1.54308e29	−0.541376
$153$	2.27403e29	0.730233
$154$	−3.46590e29	−1.01926
$155$	−7.34887e28	−0.198035
$156$	−3.94540e29	−0.974785
$157$	−1.11931e29	−0.253692	−0.126846	−	0.991922i	$-0.540485\pi$
$157$	−1.11931e29	−0.253692	−0.126846	+	0.991922i	$0.540485\pi$
$158$	4.11298e28	0.0855629
$159$	−4.13820e29	−0.790588
$160$	−4.50360e28	−0.0790569
$161$	7.26487e29	1.17241
$162$	5.87186e29	0.871612
$163$	1.01040e30	1.38026	0.690128	−	0.723687i	$-0.257554\pi$
$163$	1.01040e30	1.38026	0.690128	+	0.723687i	$0.257554\pi$
$164$	−3.85114e29	−0.484392
$165$	8.63917e29	1.00101
$166$	−1.28118e30	−1.36821
$167$	−8.58149e29	−0.845065	−0.422533	−	0.906348i	$-0.638859\pi$
$167$	−8.58149e29	−0.845065	−0.422533	+	0.906348i	$0.638859\pi$
$168$	−4.08938e29	−0.371520
$169$	1.58525e30	1.32931
$170$	−4.72049e29	−0.365533
$171$	1.35216e30	0.967340
$172$	3.17554e28	0.0209983
$173$	1.28043e30	0.782949	0.391474	−	0.920189i	$-0.371965\pi$
$173$	1.28043e30	0.782949	0.391474	+	0.920189i	$0.371965\pi$
$174$	1.55584e30	0.880137
$175$	−3.14229e29	−0.164525
$176$	−9.03566e29	−0.438065
$177$	2.45561e30	1.10286
$178$	5.18550e29	0.215834
$179$	−4.74098e30	−1.82958	−0.914791	−	0.403928i	$-0.867645\pi$
$179$	−4.74098e30	−1.82958	−0.914791	+	0.403928i	$0.867645\pi$
$180$	3.94638e29	0.141260
$181$	−3.96469e30	−1.31689	−0.658443	−	0.752631i	$-0.728785\pi$
$181$	−3.96469e30	−1.31689	−0.658443	+	0.752631i	$0.728785\pi$
$182$	2.87916e30	0.887772
$183$	5.86046e30	1.67819
$184$	1.89396e30	0.503885
$185$	2.63048e30	0.650455
$186$	−1.73965e30	−0.399979
$187$	−9.47082e30	−2.02547
$188$	−9.16568e29	−0.182404
$189$	−2.08892e30	−0.386979
$190$	−2.80684e30	−0.484222
$191$	8.53219e30	1.37123	0.685615	−	0.727964i	$-0.259533\pi$
$191$	8.53219e30	1.37123	0.685615	+	0.727964i	$0.259533\pi$
$192$	−1.06611e30	−0.159674
$193$	−1.32910e31	−1.85582	−0.927908	−	0.372808i	$-0.878395\pi$
$193$	−1.32910e31	−1.85582	−0.927908	+	0.372808i	$0.878395\pi$
$194$	4.88201e30	0.635734
$195$	−7.17664e30	−0.871874
$196$	−1.42566e30	−0.161643
$197$	−8.40332e30	−0.889522	−0.444761	−	0.895649i	$-0.646711\pi$
$197$	−8.40332e30	−0.889522	−0.444761	+	0.895649i	$0.646711\pi$
$198$	7.91769e30	0.782742
$199$	1.87522e31	1.73195	0.865975	−	0.500088i	$-0.166699\pi$
$199$	1.87522e31	1.73195	0.865975	+	0.500088i	$0.166699\pi$
$200$	−8.19200e29	−0.0707107
$201$	2.42567e29	0.0195743
$202$	4.92959e30	0.372021
$203$	−1.13538e31	−0.801573
$204$	−1.11745e31	−0.738281
$205$	−7.00518e30	−0.433253
$206$	−4.38118e30	−0.253737
$207$	−1.65963e31	−0.900349
$208$	7.50601e30	0.381552
$209$	−5.63142e31	−2.68314
$210$	−7.43854e30	−0.332297
$211$	4.59140e31	1.92367	0.961837	−	0.273623i	$-0.0882219\pi$
$211$	4.59140e31	1.92367	0.961837	+	0.273623i	$0.0882219\pi$
$212$	7.87281e30	0.309454
$213$	5.96225e30	0.219931
$214$	1.86324e31	0.645185
$215$	5.77627e29	0.0187814
$216$	−5.44586e30	−0.166319
$217$	1.26951e31	0.364275
$218$	2.14348e31	0.578040
$219$	1.95380e31	0.495319
$220$	−1.64358e31	−0.391817
$221$	7.86750e31	1.76417
$222$	6.22698e31	1.31375
$223$	5.48895e31	1.08987	0.544933	−	0.838479i	$-0.316555\pi$
$223$	5.48895e31	1.08987	0.544933	+	0.838479i	$0.316555\pi$
$224$	7.77993e30	0.145421
$225$	7.17842e30	0.126347
$226$	7.60639e31	1.26100
$227$	−4.53524e31	−0.708355	−0.354178	−	0.935178i	$-0.615239\pi$
$227$	−4.53524e31	−0.708355	−0.354178	+	0.935178i	$0.615239\pi$
$228$	−6.64446e31	−0.978001
$229$	3.94248e30	0.0547004	0.0273502	−	0.999626i	$-0.491293\pi$
$229$	3.94248e30	0.0547004	0.0273502	+	0.999626i	$0.491293\pi$
$230$	3.44510e31	0.450688
$231$	−1.49241e32	−1.84131
$232$	−2.95994e31	−0.344505
$233$	4.71165e31	0.517449	0.258725	−	0.965951i	$-0.416698\pi$
$233$	4.71165e31	0.517449	0.258725	+	0.965951i	$0.416698\pi$
$234$	−6.57730e31	−0.681764
$235$	−1.66723e31	−0.163147
$236$	−4.67174e31	−0.431684
$237$	1.77104e31	0.154570
$238$	8.15461e31	0.672379
$239$	−5.90002e31	−0.459708	−0.229854	−	0.973225i	$-0.573825\pi$
$239$	−5.90002e31	−0.459708	−0.229854	+	0.973225i	$0.573825\pi$
$240$	−1.93924e31	−0.142817
$241$	−1.62357e32	−1.13042	−0.565212	−	0.824946i	$-0.691205\pi$
$241$	−1.62357e32	−1.13042	−0.565212	+	0.824946i	$0.691205\pi$
$242$	−2.22357e32	−1.46401
$243$	1.77302e32	1.10415
$244$	−1.11494e32	−0.656882
$245$	−2.59326e31	−0.144578
$246$	−1.65829e32	−0.875058
$247$	4.67808e32	2.33700
$248$	3.30964e31	0.156561
$249$	−5.51675e32	−2.47168
$250$	−1.49012e31	−0.0632456
$251$	2.64625e32	1.06423	0.532115	−	0.846672i	$-0.321397\pi$
$251$	2.64625e32	1.06423	0.532115	+	0.846672i	$0.321397\pi$
$252$	−6.81733e31	−0.259841
$253$	6.91197e32	2.49732
$254$	−1.10444e32	−0.378343
$255$	−2.03263e32	−0.660339
$256$	2.02824e31	0.0625000
$257$	2.74808e31	0.0803402	0.0401701	−	0.999193i	$-0.487210\pi$
$257$	2.74808e31	0.0803402	0.0401701	+	0.999193i	$0.487210\pi$
$258$	1.36738e31	0.0379335
$259$	−4.54414e32	−1.19648
$260$	1.36534e32	0.341271
$261$	2.59371e32	0.615567
$262$	1.00613e32	0.226771
$263$	−6.36864e32	−1.36346	−0.681732	−	0.731602i	$-0.738773\pi$
$263$	−6.36864e32	−1.36346	−0.681732	+	0.731602i	$0.738773\pi$
$264$	−3.89073e32	−0.791368
$265$	1.43206e32	0.276784
$266$	4.84879e32	0.890700
$267$	2.23286e32	0.389906
$268$	−4.61478e30	−0.00766180
$269$	−2.64799e32	−0.418080	−0.209040	−	0.977907i	$-0.567034\pi$
$269$	−2.64799e32	−0.418080	−0.209040	+	0.977907i	$0.567034\pi$
$270$	−9.90596e31	−0.148760
$271$	−9.06365e32	−1.29485	−0.647423	−	0.762131i	$-0.724153\pi$
$271$	−9.06365e32	−1.29485	−0.647423	+	0.762131i	$0.724153\pi$
$272$	2.12592e32	0.288979
$273$	1.23976e33	1.60377
$274$	−6.36947e32	−0.784279
$275$	−2.98965e32	−0.350452
$276$	8.15537e32	0.910271
$277$	6.76213e32	0.718798	0.359399	−	0.933184i	$-0.382982\pi$
$277$	6.76213e32	0.718798	0.359399	+	0.933184i	$0.382982\pi$
$278$	4.99117e32	0.505356
$279$	−2.90014e32	−0.279745
$280$	1.41516e32	0.130069
$281$	9.77731e32	0.856415	0.428207	−	0.903680i	$-0.359145\pi$
$281$	9.77731e32	0.856415	0.428207	+	0.903680i	$0.359145\pi$
$282$	−3.94672e32	−0.329514
$283$	1.47138e32	0.117113	0.0585567	−	0.998284i	$-0.481350\pi$
$283$	1.47138e32	0.117113	0.0585567	+	0.998284i	$0.481350\pi$
$284$	−1.13430e32	−0.0860856
$285$	−1.20862e33	−0.874750
$286$	2.73930e33	1.89103
$287$	1.21014e33	0.796947
$288$	−1.77729e32	−0.111676
$289$	5.60594e32	0.336146
$290$	−5.38410e32	−0.308135
$291$	2.10218e33	1.14846
$292$	−3.71706e32	−0.193879
$293$	−4.76752e32	−0.237454	−0.118727	−	0.992927i	$-0.537881\pi$
$293$	−4.76752e32	−0.237454	−0.118727	+	0.992927i	$0.537881\pi$
$294$	−6.13885e32	−0.292010
$295$	−8.49784e32	−0.386110
$296$	−1.18466e33	−0.514230
$297$	−1.98745e33	−0.824298
$298$	8.67536e32	0.343849
$299$	−5.74184e33	−2.17515
$300$	−3.52746e32	−0.127739
$301$	−9.97845e31	−0.0345474
$302$	−2.69579e32	−0.0892468
$303$	2.12267e33	0.672058
$304$	1.26409e33	0.382811
$305$	−2.02806e33	−0.587533
$306$	−1.86288e33	−0.516353
$307$	−1.97700e33	−0.524370	−0.262185	−	0.965018i	$-0.584443\pi$
$307$	−1.97700e33	−0.524370	−0.262185	+	0.965018i	$0.584443\pi$
$308$	2.83926e33	0.720728
$309$	−1.88653e33	−0.458377
$310$	6.02019e32	0.140032
$311$	−4.03023e33	−0.897562	−0.448781	−	0.893642i	$-0.648142\pi$
$311$	−4.03023e33	−0.897562	−0.448781	+	0.893642i	$0.648142\pi$
$312$	3.23207e33	0.689277
$313$	1.11971e33	0.228696	0.114348	−	0.993441i	$-0.463522\pi$
$313$	1.11971e33	0.228696	0.114348	+	0.993441i	$0.463522\pi$
$314$	9.16941e32	0.179387
$315$	−1.24007e33	−0.232409
$316$	−3.36935e32	−0.0605021
$317$	−6.02275e33	−1.03632	−0.518161	−	0.855283i	$-0.673383\pi$
$317$	−6.02275e33	−1.03632	−0.518161	+	0.855283i	$0.673383\pi$
$318$	3.39001e33	0.559030
$319$	−1.08022e34	−1.70742
$320$	3.68935e32	0.0559017
$321$	8.02309e33	1.16553
$322$	−5.95138e33	−0.829017
$323$	1.32497e34	1.76999
$324$	−4.81023e33	−0.616323
$325$	2.48353e33	0.305242
$326$	−8.27718e33	−0.975989
$327$	9.22980e33	1.04423
$328$	3.15485e33	0.342517
$329$	2.88012e33	0.300100
$330$	−7.07721e33	−0.707821
$331$	−3.93423e33	−0.377730	−0.188865	−	0.982003i	$-0.560481\pi$
$331$	−3.93423e33	−0.377730	−0.188865	+	0.982003i	$0.560481\pi$
$332$	1.04955e34	0.967470
$333$	1.03809e34	0.918834
$334$	7.02996e33	0.597551
$335$	−8.39423e31	−0.00685292
$336$	3.35002e33	0.262704
$337$	−1.77892e34	−1.34015	−0.670074	−	0.742294i	$-0.733738\pi$
$337$	−1.77892e34	−1.34015	−0.670074	+	0.742294i	$0.733738\pi$
$338$	−1.29864e34	−0.939967
$339$	3.27529e34	2.27800
$340$	3.86703e33	0.258471
$341$	1.20784e34	0.775937
$342$	−1.10769e34	−0.684013
$343$	1.83369e34	1.08857
$344$	−2.60140e32	−0.0148480
$345$	1.48345e34	0.814172
$346$	−1.04893e34	−0.553628
$347$	−6.67131e32	−0.0338660	−0.0169330	−	0.999857i	$-0.505390\pi$
$347$	−6.67131e32	−0.0338660	−0.0169330	+	0.999857i	$0.505390\pi$
$348$	−1.27454e34	−0.622351
$349$	−9.29683e33	−0.436708	−0.218354	−	0.975870i	$-0.570069\pi$
$349$	−9.29683e33	−0.436708	−0.218354	+	0.975870i	$0.570069\pi$
$350$	2.57416e33	0.116337
$351$	1.65099e34	0.717959
$352$	7.40201e33	0.309759
$353$	−2.79504e34	−1.12572	−0.562859	−	0.826553i	$-0.690299\pi$
$353$	−2.79504e34	−1.12572	−0.562859	+	0.826553i	$0.690299\pi$
$354$	−2.01164e34	−0.779841
$355$	−2.06328e33	−0.0769973
$356$	−4.24796e33	−0.152618
$357$	3.51136e34	1.21466
$358$	3.88381e34	1.29371
$359$	−4.42700e34	−1.42015	−0.710075	−	0.704126i	$-0.751339\pi$
$359$	−4.42700e34	−1.42015	−0.710075	+	0.704126i	$0.751339\pi$
$360$	−3.23287e33	−0.0998860
$361$	4.51830e34	1.34471
$362$	3.24787e34	0.931179
$363$	−9.57464e34	−2.64474
$364$	−2.35860e34	−0.627749
$365$	−6.76129e33	−0.173411
$366$	−4.80089e34	−1.18666
$367$	−4.21004e34	−1.00298	−0.501492	−	0.865162i	$-0.667215\pi$
$367$	−4.21004e34	−1.00298	−0.501492	+	0.865162i	$0.667215\pi$
$368$	−1.55154e34	−0.356300
$369$	−2.76451e34	−0.612015
$370$	−2.15489e34	−0.459941
$371$	−2.47386e34	−0.509129
$372$	1.42512e34	0.282828
$373$	−5.44723e34	−1.04257	−0.521287	−	0.853382i	$-0.674548\pi$
$373$	−5.44723e34	−1.04257	−0.521287	+	0.853382i	$0.674548\pi$
$374$	7.75849e34	1.43222
$375$	−6.41641e33	−0.114254
$376$	7.50853e33	0.128979
$377$	8.97352e34	1.48715
$378$	1.71124e34	0.273636
$379$	8.74120e34	1.34878	0.674391	−	0.738374i	$-0.264406\pi$
$379$	8.74120e34	1.34878	0.674391	+	0.738374i	$0.264406\pi$
$380$	2.29937e34	0.342397
$381$	−4.75568e34	−0.683480
$382$	−6.98957e34	−0.969606
$383$	−7.39769e34	−0.990632	−0.495316	−	0.868713i	$-0.664948\pi$
$383$	−7.39769e34	−0.990632	−0.495316	+	0.868713i	$0.664948\pi$
$384$	8.73356e33	0.112907
$385$	5.16459e34	0.644638
$386$	1.08880e35	1.31226
$387$	2.27953e33	0.0265307
$388$	−3.99934e34	−0.449532
$389$	6.86864e34	0.745677	0.372839	−	0.927896i	$-0.378385\pi$
$389$	6.86864e34	0.745677	0.372839	+	0.927896i	$0.378385\pi$
$390$	5.87910e34	0.616508
$391$	−1.62626e35	−1.64741
$392$	1.16790e34	0.114299
$393$	4.33238e34	0.409664
$394$	6.88400e34	0.628987
$395$	−6.12881e33	−0.0541147
$396$	−6.48617e34	−0.553482
$397$	1.09834e35	0.905868	0.452934	−	0.891544i	$-0.350377\pi$
$397$	1.09834e35	0.905868	0.452934	+	0.891544i	$0.350377\pi$
$398$	−1.53618e35	−1.22467
$399$	2.08788e35	1.60906
$400$	6.71089e33	0.0500000
$401$	1.31925e35	0.950336	0.475168	−	0.879895i	$-0.342387\pi$
$401$	1.31925e35	0.950336	0.475168	+	0.879895i	$0.342387\pi$
$402$	−1.98711e33	−0.0138411
$403$	−1.00337e35	−0.675837
$404$	−4.03832e34	−0.263058
$405$	−8.74976e34	−0.551256
$406$	9.30099e34	0.566797
$407$	−4.32340e35	−2.54860
$408$	9.15417e34	0.522043
$409$	1.07033e35	0.590544	0.295272	−	0.955413i	$-0.404590\pi$
$409$	1.07033e35	0.590544	0.295272	+	0.955413i	$0.404590\pi$
$410$	5.73864e34	0.306356
$411$	−2.74268e35	−1.41681
$412$	3.58906e34	0.179419
$413$	1.46799e35	0.710229
$414$	1.35957e35	0.636643
$415$	1.90911e35	0.865331
$416$	−6.14892e34	−0.269798
$417$	2.14919e35	0.912930
$418$	4.61326e35	1.89727
$419$	−2.62715e35	−1.04615	−0.523076	−	0.852286i	$-0.675216\pi$
$419$	−2.62715e35	−1.04615	−0.523076	+	0.852286i	$0.675216\pi$
$420$	6.09365e34	0.234970
$421$	−1.82406e35	−0.681131	−0.340566	−	0.940221i	$-0.610619\pi$
$421$	−1.82406e35	−0.681131	−0.340566	+	0.940221i	$0.610619\pi$
$422$	−3.76127e35	−1.36024
$423$	−6.57951e34	−0.230462
$424$	−6.44940e34	−0.218817
$425$	7.03408e34	0.231184
$426$	−4.88427e34	−0.155514
$427$	3.50345e35	1.08074
$428$	−1.52637e35	−0.456214
$429$	1.17954e36	3.41616
$430$	−4.73192e33	−0.0132805
$431$	1.35228e35	0.367810	0.183905	−	0.982944i	$-0.441126\pi$
$431$	1.35228e35	0.367810	0.183905	+	0.982944i	$0.441126\pi$
$432$	4.46125e34	0.117605
$433$	−3.26767e35	−0.834934	−0.417467	−	0.908692i	$-0.637082\pi$
$433$	−3.26767e35	−0.834934	−0.417467	+	0.908692i	$0.637082\pi$
$434$	−1.03998e35	−0.257582
$435$	−2.31838e35	−0.556648
$436$	−1.75594e35	−0.408736
$437$	−9.66985e35	−2.18233
$438$	−1.60056e35	−0.350244
$439$	−5.20602e35	−1.10468	−0.552338	−	0.833620i	$-0.686264\pi$
$439$	−5.20602e35	−1.10468	−0.552338	+	0.833620i	$0.686264\pi$
$440$	1.34642e35	0.277057
$441$	−1.02340e35	−0.204232
$442$	−6.44505e35	−1.24746
$443$	−7.68224e35	−1.44224	−0.721120	−	0.692810i	$-0.756372\pi$
$443$	−7.68224e35	−1.44224	−0.721120	+	0.692810i	$0.756372\pi$
$444$	−5.10114e35	−0.928960
$445$	−7.72700e34	−0.136506
$446$	−4.49655e35	−0.770652
$447$	3.73559e35	0.621166
$448$	−6.37332e34	−0.102828
$449$	5.97023e35	0.934686	0.467343	−	0.884076i	$-0.345211\pi$
$449$	5.97023e35	0.934686	0.467343	+	0.884076i	$0.345211\pi$
$450$	−5.88056e34	−0.0893408
$451$	1.15135e36	1.69756
$452$	−6.23115e35	−0.891660
$453$	−1.16080e35	−0.161225
$454$	3.71527e35	0.500883
$455$	−4.29028e35	−0.561476
$456$	5.44314e35	0.691551
$457$	1.24389e36	1.53431	0.767154	−	0.641463i	$-0.221672\pi$
$457$	1.24389e36	1.53431	0.767154	+	0.641463i	$0.221672\pi$
$458$	−3.22968e34	−0.0386790
$459$	4.67610e35	0.543767
$460$	−2.82223e35	−0.318685
$461$	−4.50718e35	−0.494245	−0.247122	−	0.968984i	$-0.579485\pi$
$461$	−4.50718e35	−0.494245	−0.247122	+	0.968984i	$0.579485\pi$
$462$	1.22258e36	1.30200
$463$	3.06062e35	0.316568	0.158284	−	0.987394i	$-0.449404\pi$
$463$	3.06062e35	0.316568	0.158284	+	0.987394i	$0.449404\pi$
$464$	2.42479e35	0.243602
$465$	2.59228e35	0.252969
$466$	−3.85978e35	−0.365892
$467$	2.48619e35	0.228958	0.114479	−	0.993426i	$-0.463480\pi$
$467$	2.48619e35	0.228958	0.114479	+	0.993426i	$0.463480\pi$
$468$	5.38813e35	0.482080
$469$	1.45010e34	0.0126056
$470$	1.36579e35	0.115362
$471$	3.94833e35	0.324064
$472$	3.82709e35	0.305247
$473$	−9.49374e34	−0.0735888
$474$	−1.45083e35	−0.109298
$475$	4.18252e35	0.306249
$476$	−6.68025e35	−0.475444
$477$	5.65143e35	0.390985
$478$	4.83330e35	0.325063
$479$	−2.43474e36	−1.59193	−0.795964	−	0.605344i	$-0.793036\pi$
$479$	−2.43474e36	−1.59193	−0.795964	+	0.605344i	$0.793036\pi$
$480$	1.58863e35	0.100987
$481$	3.59149e36	2.21981
$482$	1.33003e36	0.799330
$483$	−2.56265e36	−1.49763
$484$	1.82155e36	1.03521
$485$	−7.27476e35	−0.402073
$486$	−1.45246e36	−0.780755
$487$	−1.21293e35	−0.0634154	−0.0317077	−	0.999497i	$-0.510095\pi$
$487$	−1.21293e35	−0.0634154	−0.0317077	+	0.999497i	$0.510095\pi$
$488$	9.13356e35	0.464486
$489$	−3.56414e36	−1.76313
$490$	2.12439e35	0.102232
$491$	6.41302e35	0.300236	0.150118	−	0.988668i	$-0.452035\pi$
$491$	6.41302e35	0.300236	0.150118	+	0.988668i	$0.452035\pi$
$492$	1.35847e36	0.618759
$493$	2.54156e36	1.12633
$494$	−3.83228e36	−1.65251
$495$	−1.17983e36	−0.495049
$496$	−2.71125e35	−0.110705
$497$	3.56430e35	0.141633
$498$	4.51932e36	1.74774
$499$	−4.09067e36	−1.53970	−0.769851	−	0.638223i	$-0.779670\pi$
$499$	−4.09067e36	−1.53970	−0.769851	+	0.638223i	$0.779670\pi$
$500$	1.22070e35	0.0447214
$501$	3.02708e36	1.07948
$502$	−2.16781e36	−0.752524
$503$	−5.43130e35	−0.183542	−0.0917710	−	0.995780i	$-0.529253\pi$
$503$	−5.43130e35	−0.183542	−0.0917710	+	0.995780i	$0.529253\pi$
$504$	5.58476e35	0.183735
$505$	−7.34566e35	−0.235287
$506$	−5.66229e36	−1.76587
$507$	−5.59191e36	−1.69806
$508$	9.04756e35	0.267529
$509$	−1.01633e36	−0.292646	−0.146323	−	0.989237i	$-0.546744\pi$
$509$	−1.01633e36	−0.292646	−0.146323	+	0.989237i	$0.546744\pi$
$510$	1.66513e36	0.466930
$511$	1.16801e36	0.318980
$512$	−1.66153e35	−0.0441942
$513$	2.78045e36	0.720327
$514$	−2.25123e35	−0.0568091
$515$	6.52846e35	0.160477
$516$	−1.12016e35	−0.0268230
$517$	2.74022e36	0.639238
$518$	3.72256e36	0.846038
$519$	−4.51666e36	−1.00013
$520$	−1.11848e36	−0.241315
$521$	−5.75177e36	−1.20918	−0.604592	−	0.796536i	$-0.706664\pi$
$521$	−5.75177e36	−1.20918	−0.604592	+	0.796536i	$0.706664\pi$
$522$	−2.12477e36	−0.435272
$523$	−7.30952e35	−0.145920	−0.0729602	−	0.997335i	$-0.523245\pi$
$523$	−7.30952e35	−0.145920	−0.0729602	+	0.997335i	$0.523245\pi$
$524$	−8.24224e35	−0.160351
$525$	1.10843e36	0.210163
$526$	5.21719e36	0.964115
$527$	−2.84183e36	−0.511864
$528$	3.18729e36	0.559582
$529$	6.02551e36	1.03120
$530$	−1.17314e36	−0.195716
$531$	−3.35357e36	−0.545420
$532$	−3.97213e36	−0.629820
$533$	−9.56441e36	−1.47857
$534$	−1.82916e36	−0.275705
$535$	−2.77645e36	−0.408051
$536$	3.78042e34	0.00541771
$537$	1.67236e37	2.33710
$538$	2.16923e36	0.295628
$539$	4.26221e36	0.566483
$540$	8.11496e35	0.105189
$541$	1.06277e37	1.34362	0.671812	−	0.740721i	$-0.265516\pi$
$541$	1.06277e37	1.34362	0.671812	+	0.740721i	$0.265516\pi$
$542$	7.42494e36	0.915594
$543$	1.39853e37	1.68218
$544$	−1.74155e36	−0.204339
$545$	−3.19404e36	−0.365584
$546$	−1.01561e37	−1.13403
$547$	3.13391e36	0.341396	0.170698	−	0.985323i	$-0.445398\pi$
$547$	3.13391e36	0.341396	0.170698	+	0.985323i	$0.445398\pi$
$548$	5.21787e36	0.554569
$549$	−8.00348e36	−0.829950
$550$	2.44912e36	0.247807
$551$	1.51123e37	1.49206
$552$	−6.68088e36	−0.643659
$553$	1.05875e36	0.0995412
$554$	−5.53954e36	−0.508267
$555$	−9.27892e36	−0.830887
$556$	−4.08877e36	−0.357341
$557$	−1.82733e37	−1.55874	−0.779368	−	0.626566i	$-0.784460\pi$
$557$	−1.82733e37	−1.55874	−0.779368	+	0.626566i	$0.784460\pi$
$558$	2.37580e36	0.197810
$559$	7.88654e35	0.0640954
$560$	−1.15930e36	−0.0919724
$561$	3.34079e37	2.58732
$562$	−8.00958e36	−0.605577
$563$	−6.65901e36	−0.491526	−0.245763	−	0.969330i	$-0.579038\pi$
$563$	−6.65901e36	−0.491526	−0.245763	+	0.969330i	$0.579038\pi$
$564$	3.23315e36	0.233001
$565$	−1.13344e37	−0.797525
$566$	−1.20535e36	−0.0828117
$567$	1.51151e37	1.01401
$568$	9.29219e35	0.0608717
$569$	1.71644e37	1.09802	0.549012	−	0.835814i	$-0.315004\pi$
$569$	1.71644e37	1.09802	0.549012	+	0.835814i	$0.315004\pi$
$570$	9.90101e36	0.618542
$571$	−1.61696e37	−0.986535	−0.493267	−	0.869878i	$-0.664198\pi$
$571$	−1.61696e37	−0.986535	−0.493267	+	0.869878i	$0.664198\pi$
$572$	−2.24403e37	−1.33716
$573$	−3.00969e37	−1.75160
$574$	−9.91345e36	−0.563526
$575$	−5.13360e36	−0.285040
$576$	1.45596e36	0.0789668
$577$	2.68745e37	1.42386	0.711929	−	0.702251i	$-0.247822\pi$
$577$	2.68745e37	1.42386	0.711929	+	0.702251i	$0.247822\pi$
$578$	−4.59238e36	−0.237691
$579$	4.68835e37	2.37061
$580$	4.41066e36	0.217884
$581$	−3.29797e37	−1.59173
$582$	−1.72211e37	−0.812082
$583$	−2.35369e37	−1.08449
$584$	3.04501e36	0.137093
$585$	9.80094e36	0.431185
$586$	3.90555e36	0.167905
$587$	2.21802e37	0.931860	0.465930	−	0.884822i	$-0.345720\pi$
$587$	2.21802e37	0.931860	0.465930	+	0.884822i	$0.345720\pi$
$588$	5.02894e36	0.206482
$589$	−1.68977e37	−0.678066
$590$	6.96143e36	0.273021
$591$	2.96424e37	1.13627
$592$	9.70477e36	0.363615
$593$	−3.27250e37	−1.19851	−0.599255	−	0.800558i	$-0.704536\pi$
$593$	−3.27250e37	−1.19851	−0.599255	+	0.800558i	$0.704536\pi$
$594$	1.62812e37	0.582867
$595$	−1.21513e37	−0.425250
$596$	−7.10686e36	−0.243138
$597$	−6.61475e37	−2.21238
$598$	4.70372e37	1.53807
$599$	−5.26063e37	−1.68180	−0.840902	−	0.541187i	$-0.817975\pi$
$599$	−5.26063e37	−1.68180	−0.840902	+	0.541187i	$0.817975\pi$
$600$	2.88969e36	0.0903254
$601$	−3.25919e37	−0.996102	−0.498051	−	0.867148i	$-0.665951\pi$
$601$	−3.25919e37	−0.996102	−0.498051	+	0.867148i	$0.665951\pi$
$602$	8.17435e35	0.0244287
$603$	−3.31268e35	−0.00968045
$604$	2.20839e36	0.0631070
$605$	3.31338e37	0.925919
$606$	−1.73889e37	−0.475217
$607$	−1.02382e37	−0.273637	−0.136818	−	0.990596i	$-0.543688\pi$
$607$	−1.02382e37	−0.273637	−0.136818	+	0.990596i	$0.543688\pi$
$608$	−1.03554e37	−0.270688
$609$	4.00499e37	1.02392
$610$	1.66138e37	0.415449
$611$	−2.27632e37	−0.556773
$612$	1.52607e37	0.365117
$613$	−2.22273e37	−0.520201	−0.260100	−	0.965582i	$-0.583756\pi$
$613$	−2.22273e37	−0.520201	−0.260100	+	0.965582i	$0.583756\pi$
$614$	1.61956e37	0.370786
$615$	2.47105e37	0.553435
$616$	−2.32593e37	−0.509631
$617$	−3.05546e37	−0.654978	−0.327489	−	0.944855i	$-0.606202\pi$
$617$	−3.05546e37	−0.654978	−0.327489	+	0.944855i	$0.606202\pi$
$618$	1.54544e37	0.324122
$619$	−1.32801e37	−0.272507	−0.136254	−	0.990674i	$-0.543506\pi$
$619$	−1.32801e37	−0.272507	−0.136254	+	0.990674i	$0.543506\pi$
$620$	−4.93174e36	−0.0990177
$621$	−3.41270e37	−0.670443
$622$	3.30156e37	0.634672
$623$	1.33483e37	0.251095
$624$	−2.64771e37	−0.487392
$625$	2.22045e36	0.0400000
$626$	−9.17269e36	−0.161712
$627$	1.98646e38	3.42742
$628$	−7.51158e36	−0.126846
$629$	1.01722e38	1.68124
$630$	1.01586e37	0.164338
$631$	8.40893e37	1.33151	0.665755	−	0.746171i	$-0.268110\pi$
$631$	8.40893e37	1.33151	0.665755	+	0.746171i	$0.268110\pi$
$632$	2.76017e36	0.0427815
$633$	−1.61959e38	−2.45729
$634$	4.93384e37	0.732790
$635$	1.64574e37	0.239285
$636$	−2.77710e37	−0.395294
$637$	−3.54066e37	−0.493403
$638$	8.84919e37	1.20733
$639$	−8.14249e36	−0.108767
$640$	−3.02231e36	−0.0395285
$641$	7.86398e37	1.00707	0.503534	−	0.863975i	$-0.332033\pi$
$641$	7.86398e37	1.00707	0.503534	+	0.863975i	$0.332033\pi$
$642$	−6.57252e37	−0.824155
$643$	1.16284e38	1.42781	0.713904	−	0.700243i	$-0.246925\pi$
$643$	1.16284e38	1.42781	0.713904	+	0.700243i	$0.246925\pi$
$644$	4.87537e37	0.586204
$645$	−2.03755e36	−0.0239913
$646$	−1.08541e38	−1.25157
$647$	−7.65469e37	−0.864410	−0.432205	−	0.901775i	$-0.642264\pi$
$647$	−7.65469e37	−0.864410	−0.432205	+	0.901775i	$0.642264\pi$
$648$	3.94054e37	0.435806
$649$	1.39669e38	1.51285
$650$	−2.03451e37	−0.215839
$651$	−4.47814e37	−0.465323
$652$	6.78067e37	0.690128
$653$	−1.03403e38	−1.03087	−0.515436	−	0.856928i	$-0.672370\pi$
$653$	−1.03403e38	−1.03087	−0.515436	+	0.856928i	$0.672370\pi$
$654$	−7.56105e37	−0.738384
$655$	−1.49925e37	−0.143423
$656$	−2.58445e37	−0.242196
$657$	−2.66826e37	−0.244960
$658$	−2.35939e37	−0.212203
$659$	−5.24833e37	−0.462453	−0.231227	−	0.972900i	$-0.574274\pi$
$659$	−5.24833e37	−0.462453	−0.231227	+	0.972900i	$0.574274\pi$
$660$	5.79765e37	0.500505
$661$	−1.14190e38	−0.965846	−0.482923	−	0.875663i	$-0.660425\pi$
$661$	−1.14190e38	−0.965846	−0.482923	+	0.875663i	$0.660425\pi$
$662$	3.22292e37	0.267096
$663$	−2.77523e38	−2.25354
$664$	−8.59788e37	−0.684104
$665$	−7.22527e37	−0.563328
$666$	−8.50402e37	−0.649714
$667$	−1.85488e38	−1.38873
$668$	−5.75894e37	−0.422533
$669$	−1.93620e38	−1.39219
$670$	6.87655e35	0.00484575
$671$	3.33327e38	2.30206
$672$	−2.74434e37	−0.185760
$673$	3.00048e36	0.0199061	0.00995307	−	0.999950i	$-0.496832\pi$
$673$	3.00048e36	0.0199061	0.00995307	+	0.999950i	$0.496832\pi$
$674$	1.45729e38	0.947628
$675$	1.47610e37	0.0940840
$676$	1.06384e38	0.664657
$677$	2.27686e38	1.39441	0.697204	−	0.716873i	$-0.254427\pi$
$677$	2.27686e38	1.39441	0.697204	+	0.716873i	$0.254427\pi$
$678$	−2.68312e38	−1.61079
$679$	1.25671e38	0.739593
$680$	−3.16787e37	−0.182767
$681$	1.59979e38	0.904848
$682$	−9.89465e37	−0.548670
$683$	−1.59944e37	−0.0869538	−0.0434769	−	0.999054i	$-0.513843\pi$
$683$	−1.59944e37	−0.0869538	−0.0434769	+	0.999054i	$0.513843\pi$
$684$	9.07416e37	0.483670
$685$	9.49125e37	0.496022
$686$	−1.50216e38	−0.769735
$687$	−1.39069e37	−0.0698739
$688$	2.13107e36	0.0104991
$689$	1.95524e38	0.944582
$690$	−1.21524e38	−0.575706
$691$	1.56832e38	0.728586	0.364293	−	0.931284i	$-0.381311\pi$
$691$	1.56832e38	0.728586	0.364293	+	0.931284i	$0.381311\pi$
$692$	8.59282e37	0.391474
$693$	2.03814e38	0.910617
$694$	5.46514e36	0.0239469
$695$	−7.43743e37	−0.319616
$696$	1.04411e38	0.440069
$697$	−2.70892e38	−1.11983
$698$	7.61596e37	0.308799
$699$	−1.66201e38	−0.660987
$700$	−2.10875e37	−0.0822626
$701$	−2.65673e38	−1.01661	−0.508304	−	0.861178i	$-0.669727\pi$
$701$	−2.65673e38	−1.01661	−0.508304	+	0.861178i	$0.669727\pi$
$702$	−1.35249e38	−0.507674
$703$	6.04844e38	2.22714
$704$	−6.06373e37	−0.219033
$705$	5.88107e37	0.208403
$706$	2.28970e38	0.796004
$707$	1.26896e38	0.432797
$708$	1.64793e38	0.551431
$709$	−3.14013e38	−1.03092	−0.515458	−	0.856915i	$-0.672378\pi$
$709$	−3.14013e38	−1.03092	−0.515458	+	0.856915i	$0.672378\pi$
$710$	1.69024e37	0.0544453
$711$	−2.41866e37	−0.0764426
$712$	3.47993e37	0.107917
$713$	2.07402e38	0.631108
$714$	−2.87650e38	−0.858893
$715$	−4.08187e38	−1.19599
$716$	−3.18162e38	−0.914791
$717$	2.08121e38	0.587228
$718$	3.62660e38	1.00420
$719$	1.32586e38	0.360295	0.180147	−	0.983640i	$-0.442343\pi$
$719$	1.32586e38	0.360295	0.180147	+	0.983640i	$0.442343\pi$
$720$	2.64837e37	0.0706301
$721$	−1.12779e38	−0.295189
$722$	−3.70139e38	−0.950852
$723$	5.72708e38	1.44400
$724$	−2.66066e38	−0.658443
$725$	8.02294e37	0.194881
$726$	7.84354e38	1.87011
$727$	−3.02965e38	−0.709051	−0.354525	−	0.935046i	$-0.615358\pi$
$727$	−3.02965e38	−0.709051	−0.354525	+	0.935046i	$0.615358\pi$
$728$	1.93217e38	0.443886
$729$	−7.88385e37	−0.177794
$730$	5.53884e37	0.122620
$731$	2.23370e37	0.0485445
$732$	3.93289e38	0.839097
$733$	−6.47887e38	−1.35705	−0.678525	−	0.734578i	$-0.737380\pi$
$733$	−6.47887e38	−1.35705	−0.678525	+	0.734578i	$0.737380\pi$
$734$	3.44886e38	0.709217
$735$	9.14760e37	0.184683
$736$	1.27102e38	0.251942
$737$	1.37966e37	0.0268510
$738$	2.26468e38	0.432760
$739$	−5.25007e38	−0.985065	−0.492533	−	0.870294i	$-0.663929\pi$
$739$	−5.25007e38	−0.985065	−0.492533	+	0.870294i	$0.663929\pi$
$740$	1.76529e38	0.325228
$741$	−1.65017e39	−2.98527
$742$	2.02659e38	0.360009
$743$	1.07441e39	1.87423	0.937113	−	0.349027i	$-0.113488\pi$
$743$	1.07441e39	1.87423	0.937113	+	0.349027i	$0.113488\pi$
$744$	−1.16746e38	−0.199990
$745$	−1.29273e38	−0.217469
$746$	4.46237e38	0.737211
$747$	7.53408e38	1.22237
$748$	−6.35576e38	−1.01273
$749$	4.79629e38	0.750587
$750$	5.25632e37	0.0807895
$751$	−6.49718e38	−0.980812	−0.490406	−	0.871494i	$-0.663152\pi$
$751$	−6.49718e38	−0.980812	−0.490406	+	0.871494i	$0.663152\pi$
$752$	−6.15098e37	−0.0912019
$753$	−9.33453e38	−1.35944
$754$	−7.35111e38	−1.05157
$755$	4.01704e37	0.0564446
$756$	−1.40185e38	−0.193490
$757$	−1.41452e38	−0.191785	−0.0958926	−	0.995392i	$-0.530571\pi$
$757$	−1.41452e38	−0.191785	−0.0958926	+	0.995392i	$0.530571\pi$
$758$	−7.16079e38	−0.953733
$759$	−2.43817e39	−3.19007
$760$	−1.88364e38	−0.242111
$761$	1.02263e39	1.29130	0.645650	−	0.763634i	$-0.276587\pi$
$761$	1.02263e39	1.29130	0.645650	+	0.763634i	$0.276587\pi$
$762$	3.89586e38	0.483293
$763$	5.51768e38	0.672473
$764$	5.72586e38	0.685615
$765$	2.77591e38	0.326570
$766$	6.06019e38	0.700483
$767$	−1.16024e39	−1.31768
$768$	−7.15453e37	−0.0798371
$769$	2.43418e38	0.266899	0.133449	−	0.991056i	$-0.457395\pi$
$769$	2.43418e38	0.266899	0.133449	+	0.991056i	$0.457395\pi$
$770$	−4.23083e38	−0.455828
$771$	−9.69375e37	−0.102626
$772$	−8.91946e38	−0.927908
$773$	1.87371e39	1.91548	0.957741	−	0.287632i	$-0.0928679\pi$
$773$	1.87371e39	1.91548	0.957741	+	0.287632i	$0.0928679\pi$
$774$	−1.86739e37	−0.0187600
$775$	−8.97079e37	−0.0885641
$776$	3.27626e38	0.317867
$777$	1.60292e39	1.52837
$778$	−5.62679e38	−0.527273
$779$	−1.61075e39	−1.48344
$780$	−4.81616e38	−0.435937
$781$	3.39116e38	0.301689
$782$	1.33223e39	1.16490
$783$	5.33347e38	0.458380
$784$	−9.56742e37	−0.0808217
$785$	−1.36635e38	−0.113454
$786$	−3.54909e38	−0.289676
$787$	1.05821e39	0.849007	0.424503	−	0.905426i	$-0.360449\pi$
$787$	1.05821e39	0.849007	0.424503	+	0.905426i	$0.360449\pi$
$788$	−5.63937e38	−0.444761
$789$	2.24651e39	1.74168
$790$	5.02072e37	0.0382649
$791$	1.95801e39	1.46701
$792$	5.31347e38	0.391371
$793$	−2.76898e39	−2.00508
$794$	−8.99760e38	−0.640546
$795$	−5.05151e38	−0.353562
$796$	1.25844e39	0.865975
$797$	−1.98365e39	−1.34208	−0.671041	−	0.741421i	$-0.734152\pi$
$797$	−1.98365e39	−1.34208	−0.671041	+	0.741421i	$0.734152\pi$
$798$	−1.71039e39	−1.13778
$799$	−6.44722e38	−0.421687
$800$	−5.49756e37	−0.0353553
$801$	−3.04936e38	−0.192828
$802$	−1.08073e39	−0.671989
$803$	1.11127e39	0.679453
$804$	1.62784e37	0.00978714
$805$	8.86825e38	0.524316
$806$	8.21958e38	0.477889
$807$	9.34066e38	0.534053
$808$	3.30819e38	0.186010
$809$	2.34082e39	1.29438	0.647192	−	0.762327i	$-0.275943\pi$
$809$	2.34082e39	1.29438	0.647192	+	0.762327i	$0.275943\pi$
$810$	7.16780e38	0.389797
$811$	−1.86049e39	−0.995051	−0.497525	−	0.867449i	$-0.665758\pi$
$811$	−1.86049e39	−0.995051	−0.497525	+	0.867449i	$0.665758\pi$
$812$	−7.61937e38	−0.400786
$813$	3.19716e39	1.65403
$814$	3.54173e39	1.80213
$815$	1.23340e39	0.617270
$816$	−7.49909e38	−0.369140
$817$	1.32818e38	0.0643069
$818$	−8.76812e38	−0.417577
$819$	−1.69310e39	−0.793142
$820$	−4.70109e38	−0.216627
$821$	2.17461e39	0.985710	0.492855	−	0.870112i	$-0.335953\pi$
$821$	2.17461e39	0.985710	0.492855	+	0.870112i	$0.335953\pi$
$822$	2.24680e39	1.00183
$823$	−1.47840e39	−0.648477	−0.324239	−	0.945975i	$-0.605108\pi$
$823$	−1.47840e39	−0.648477	−0.324239	+	0.945975i	$0.605108\pi$
$824$	−2.94016e38	−0.126868
$825$	1.05459e39	0.447665
$826$	−1.20258e39	−0.502208
$827$	−1.81409e39	−0.745307	−0.372654	−	0.927971i	$-0.621552\pi$
$827$	−1.81409e39	−0.745307	−0.372654	+	0.927971i	$0.621552\pi$
$828$	−1.11376e39	−0.450174
$829$	3.68398e39	1.46498	0.732489	−	0.680779i	$-0.238359\pi$
$829$	3.68398e39	1.46498	0.732489	+	0.680779i	$0.238359\pi$
$830$	−1.56395e39	−0.611881
$831$	−2.38531e39	−0.918188
$832$	5.03720e38	0.190776
$833$	−1.00282e39	−0.373693
$834$	−1.76061e39	−0.645539
$835$	−1.04754e39	−0.377925
$836$	−3.77918e39	−1.34157
$837$	−5.96358e38	−0.208311
$838$	2.15216e39	0.739742
$839$	3.62449e39	1.22591	0.612957	−	0.790116i	$-0.289980\pi$
$839$	3.62449e39	1.22591	0.612957	+	0.790116i	$0.289980\pi$
$840$	−4.99192e38	−0.166149
$841$	−1.54276e38	−0.0505304
$842$	1.49427e39	0.481632
$843$	−3.44891e39	−1.09398
$844$	3.08123e39	0.961837
$845$	1.93512e39	0.594487
$846$	5.38993e38	0.162961
$847$	−5.72383e39	−1.70318
$848$	5.28335e38	0.154727
$849$	−5.19021e38	−0.149600
$850$	−5.76232e38	−0.163471
$851$	−7.42382e39	−2.07290
$852$	4.00120e38	0.109965
$853$	7.16984e39	1.93953	0.969767	−	0.244031i	$-0.0784699\pi$
$853$	7.16984e39	1.93953	0.969767	+	0.244031i	$0.0784699\pi$
$854$	−2.87003e39	−0.764196
$855$	1.65058e39	0.432608
$856$	1.25040e39	0.322592
$857$	−5.79545e39	−1.47179	−0.735896	−	0.677095i	$-0.763239\pi$
$857$	−5.79545e39	−1.47179	−0.735896	+	0.677095i	$0.763239\pi$
$858$	−9.66276e39	−2.41559
$859$	1.97147e39	0.485156	0.242578	−	0.970132i	$-0.422007\pi$
$859$	1.97147e39	0.485156	0.242578	+	0.970132i	$0.422007\pi$
$860$	3.87639e37	0.00939070
$861$	−4.26871e39	−1.01801
$862$	−1.10779e39	−0.260081
$863$	−1.32958e39	−0.307305	−0.153652	−	0.988125i	$-0.549104\pi$
$863$	−1.32958e39	−0.307305	−0.153652	+	0.988125i	$0.549104\pi$
$864$	−3.65465e38	−0.0831593
$865$	1.56302e39	0.350145
$866$	2.67688e39	0.590387
$867$	−1.97747e39	−0.429390
$868$	8.51954e38	0.182138
$869$	1.00732e39	0.212031
$870$	1.89922e39	0.393609
$871$	−1.14609e38	−0.0233870
$872$	1.43847e39	0.289020
$873$	−2.87090e39	−0.567970
$874$	7.92154e39	1.54314
$875$	−3.83580e38	−0.0735779
$876$	1.31118e39	0.247660
$877$	−7.27571e39	−1.35326	−0.676629	−	0.736324i	$-0.736560\pi$
$877$	−7.27571e39	−1.35326	−0.676629	+	0.736324i	$0.736560\pi$
$878$	4.26477e39	0.781124
$879$	1.68172e39	0.303322
$880$	−1.10299e39	−0.195909
$881$	−6.56252e39	−1.14788	−0.573939	−	0.818898i	$-0.694585\pi$
$881$	−6.56252e39	−1.14788	−0.573939	+	0.818898i	$0.694585\pi$
$882$	8.38366e38	0.144414
$883$	6.35223e39	1.07760	0.538799	−	0.842434i	$-0.318878\pi$
$883$	6.35223e39	1.07760	0.538799	+	0.842434i	$0.318878\pi$
$884$	5.27979e39	0.882086
$885$	2.99758e39	0.493215
$886$	6.29329e39	1.01982
$887$	4.10862e39	0.655732	0.327866	−	0.944724i	$-0.393670\pi$
$887$	4.10862e39	0.655732	0.327866	+	0.944724i	$0.393670\pi$
$888$	4.17885e39	0.656874
$889$	−2.84300e39	−0.440153
$890$	6.32996e38	0.0965241
$891$	1.43809e40	2.15992
$892$	3.68357e39	0.544933
$893$	−3.83357e39	−0.558609
$894$	−3.06020e39	−0.439231
$895$	−5.78732e39	−0.818214
$896$	5.22102e38	0.0727105
$897$	2.02541e40	2.77853
$898$	−4.89082e39	−0.660923
$899$	−3.24134e39	−0.431487
$900$	4.81735e38	0.0631735
$901$	5.53780e39	0.715406
$902$	−9.43190e39	−1.20036
$903$	3.51986e38	0.0441306
$904$	5.10456e39	0.630499
$905$	−4.83971e39	−0.588929
$906$	9.50929e38	0.114003
$907$	1.26175e40	1.49030	0.745152	−	0.666895i	$-0.232377\pi$
$907$	1.26175e40	1.49030	0.745152	+	0.666895i	$0.232377\pi$
$908$	−3.04355e39	−0.354178
$909$	−2.89887e39	−0.332366
$910$	3.51459e39	0.397024
$911$	−8.55940e39	−0.952676	−0.476338	−	0.879262i	$-0.658036\pi$
$911$	−8.55940e39	−0.952676	−0.476338	+	0.879262i	$0.658036\pi$
$912$	−4.45902e39	−0.489000
$913$	−3.13777e40	−3.39052
$914$	−1.01899e40	−1.08492
$915$	7.15389e39	0.750511
$916$	2.64575e38	0.0273502
$917$	2.58995e39	0.263818
$918$	−3.83066e39	−0.384501
$919$	4.48874e39	0.443982	0.221991	−	0.975049i	$-0.428744\pi$
$919$	4.48874e39	0.443982	0.221991	+	0.975049i	$0.428744\pi$
$920$	2.31197e39	0.225344
$921$	6.97378e39	0.669828
$922$	3.69228e39	0.349484
$923$	−2.81707e39	−0.262769
$924$	−1.00154e40	−0.920653
$925$	3.21104e39	0.290892
$926$	−2.50726e39	−0.223847
$927$	2.57638e39	0.226690
$928$	−1.98638e39	−0.172253
$929$	1.47342e40	1.25926	0.629631	−	0.776895i	$-0.283206\pi$
$929$	1.47342e40	1.25926	0.629631	+	0.776895i	$0.283206\pi$
$930$	−2.12360e39	−0.178876
$931$	−5.96284e39	−0.495031
$932$	3.16193e39	0.258725
$933$	1.42165e40	1.14654
$934$	−2.03669e39	−0.161898
$935$	−1.15611e40	−0.905817
$936$	−4.41395e39	−0.340882
$937$	−1.33104e40	−1.01323	−0.506614	−	0.862173i	$-0.669103\pi$
$937$	−1.33104e40	−1.01323	−0.506614	+	0.862173i	$0.669103\pi$
$938$	−1.18792e38	−0.00891350
$939$	−3.94974e39	−0.292135
$940$	−1.11886e39	−0.0815734
$941$	−1.28931e40	−0.926612	−0.463306	−	0.886198i	$-0.653337\pi$
$941$	−1.28931e40	−0.926612	−0.463306	+	0.886198i	$0.653337\pi$
$942$	−3.23447e39	−0.229148
$943$	1.97702e40	1.38071
$944$	−3.13515e39	−0.215842
$945$	−2.54995e39	−0.173062
$946$	7.77727e38	0.0520352
$947$	−1.41966e40	−0.936396	−0.468198	−	0.883624i	$-0.655097\pi$
$947$	−1.41966e40	−0.936396	−0.468198	+	0.883624i	$0.655097\pi$
$948$	1.18852e39	0.0772850
$949$	−9.23142e39	−0.591800
$950$	−3.42632e39	−0.216551
$951$	2.12450e40	1.32379
$952$	5.47246e39	0.336190
$953$	1.53298e40	0.928501	0.464251	−	0.885704i	$-0.346324\pi$
$953$	1.53298e40	0.928501	0.464251	+	0.885704i	$0.346324\pi$
$954$	−4.62965e39	−0.276468
$955$	1.04153e40	0.613233
$956$	−3.95944e39	−0.229854
$957$	3.81044e40	2.18104
$958$	1.99454e40	1.12566
$959$	−1.63961e40	−0.912406
$960$	−1.30140e39	−0.0714085
$961$	−1.48584e40	−0.803910
$962$	−2.94215e40	−1.56964
$963$	−1.09569e40	−0.576413
$964$	−1.08956e40	−0.565212
$965$	−1.62244e40	−0.829946
$966$	2.09932e40	1.05898
$967$	−6.60284e38	−0.0328453	−0.0164226	−	0.999865i	$-0.505228\pi$
$967$	−6.60284e38	−0.0328453	−0.0164226	+	0.999865i	$0.505228\pi$
$968$	−1.49221e40	−0.732004
$969$	−4.67377e40	−2.26098
$970$	5.95949e39	0.284309
$971$	1.76228e40	0.829117	0.414558	−	0.910023i	$-0.363936\pi$
$971$	1.76228e40	0.829117	0.414558	+	0.910023i	$0.363936\pi$
$972$	1.18986e40	0.552077
$973$	1.28481e40	0.587916
$974$	9.93633e38	0.0448415
$975$	−8.76054e39	−0.389914
$976$	−7.48221e39	−0.328441
$977$	2.50038e39	0.108250	0.0541251	−	0.998534i	$-0.482763\pi$
$977$	2.50038e39	0.108250	0.0541251	+	0.998534i	$0.482763\pi$
$978$	2.91974e40	1.24672
$979$	1.26999e40	0.534853
$980$	−1.74030e39	−0.0722892
$981$	−1.26049e40	−0.516425
$982$	−5.25355e39	−0.212299
$983$	2.38859e40	0.952069	0.476034	−	0.879427i	$-0.342074\pi$
$983$	2.38859e40	0.952069	0.476034	+	0.879427i	$0.342074\pi$
$984$	−1.11286e40	−0.437529
$985$	−1.02580e40	−0.397807
$986$	−2.08205e40	−0.796439
$987$	−1.01595e40	−0.383346
$988$	3.13940e40	1.16850
$989$	−1.63019e39	−0.0598535
$990$	9.66515e39	0.350053
$991$	−1.88335e40	−0.672879	−0.336440	−	0.941705i	$-0.609223\pi$
$991$	−1.88335e40	−0.672879	−0.336440	+	0.941705i	$0.609223\pi$
$992$	2.22106e39	0.0782803
$993$	1.38778e40	0.482510
$994$	−2.91987e39	−0.100149
$995$	2.28908e40	0.774551
$996$	−3.70223e40	−1.23584
$997$	−3.07289e40	−1.01196	−0.505979	−	0.862546i	$-0.668869\pi$
$997$	−3.07289e40	−1.01196	−0.505979	+	0.862546i	$0.668869\pi$
$998$	3.35107e40	1.08873
$999$	2.13463e40	0.684208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.a.1.1	✓	2
5.2	odd	4		50.28.b.e.49.2		4
5.3	odd	4		50.28.b.e.49.3		4
5.4	even	2		50.28.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.a.1.1	✓	2	1.1	even	1	trivial
50.28.a.e.1.2		2	5.4	even	2
50.28.b.e.49.2		4	5.2	odd	4
50.28.b.e.49.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} -3.52746e6 q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} +2.88969e10 q^{6} -2.10875e11 q^{7} -5.49756e11 q^{8} +4.81735e12 q^{9} -1.00000e13 q^{10} -2.00632e14 q^{11} -2.36724e14 q^{12} +1.66667e15 q^{13} +1.72749e15 q^{14} -4.30598e15 q^{15} +4.50360e15 q^{16} +4.72049e16 q^{17} -3.94638e16 q^{18} +2.80684e17 q^{19} +8.19200e16 q^{20} +7.43854e17 q^{21} +1.64358e18 q^{22} -3.44510e18 q^{23} +1.93924e18 q^{24} +1.49012e18 q^{25} -1.36534e19 q^{26} +9.90596e18 q^{27} -1.41516e19 q^{28} +5.38410e19 q^{29} +3.52746e19 q^{30} -6.02019e19 q^{31} -3.68935e19 q^{32} +7.07721e20 q^{33} -3.86703e20 q^{34} -2.57416e20 q^{35} +3.23287e20 q^{36} +2.15489e21 q^{37} -2.29937e21 q^{38} -5.87910e21 q^{39} -6.71089e20 q^{40} -5.73864e21 q^{41} -6.09365e21 q^{42} +4.73192e20 q^{43} -1.34642e22 q^{44} +5.88056e21 q^{45} +2.82223e22 q^{46} -1.36579e22 q^{47} -1.58863e22 q^{48} -2.12439e22 q^{49} -1.22070e22 q^{50} -1.66513e23 q^{51} +1.11848e23 q^{52} +1.17314e23 q^{53} -8.11496e22 q^{54} -2.44912e23 q^{55} +1.15930e23 q^{56} -9.90101e23 q^{57} -4.41066e23 q^{58} -6.96143e23 q^{59} -2.88969e23 q^{60} -1.66138e24 q^{61} +4.93174e23 q^{62} -1.01586e24 q^{63} +3.02231e23 q^{64} +2.03451e24 q^{65} -5.79765e24 q^{66} -6.87655e22 q^{67} +3.16787e24 q^{68} +1.21524e25 q^{69} +2.10875e24 q^{70} -1.69024e24 q^{71} -2.64837e24 q^{72} -5.53884e24 q^{73} -1.76529e25 q^{74} -5.25632e24 q^{75} +1.88364e25 q^{76} +4.23083e25 q^{77} +4.81616e25 q^{78} -5.02072e24 q^{79} +5.49756e24 q^{80} -7.16780e25 q^{81} +4.70109e25 q^{82} +1.56395e26 q^{83} +4.99192e25 q^{84} +5.76232e25 q^{85} -3.87639e24 q^{86} -1.89922e26 q^{87} +1.10299e26 q^{88} -6.32996e25 q^{89} -4.81735e25 q^{90} -3.51459e26 q^{91} -2.31197e26 q^{92} +2.12360e26 q^{93} +1.11886e26 q^{94} +3.42632e26 q^{95} +1.30140e26 q^{96} -5.95949e26 q^{97} +1.74030e26 q^{98} -9.66515e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 3340644 q^{3} + 134217728 q^{4} + 2441406250 q^{5} + 27366555648 q^{6} - 58706842292 q^{7} - 1099511627776 q^{8} - 2773343978406 q^{9} - 20000000000000 q^{10} - 148584207397296 q^{11}+ \cdots - 13\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 16384 * q^2 - 3340644 * q^3 + 134217728 * q^4 + 2441406250 * q^5 + 27366555648 * q^6 - 58706842292 * q^7 - 1099511627776 * q^8 - 2773343978406 * q^9 - 20000000000000 * q^10 - 148584207397296 * q^11 - 224186823868416 * q^12 + 700099119029596 * q^13 + 480926452056064 * q^14 - 4077934570312500 * q^15 + 9007199254740992 * q^16 + 38363966708465748 * q^17 + 22719233871101952 * q^18 + 231077489147345800 * q^19 + 163840000000000000 * q^20 + 772280752747638624 * q^21 + 1217201826998648832 * q^22 - 1051524217202377644 * q^23 + 1836538461130063872 * q^24 + 2980232238769531250 * q^25 - 5735211983090450432 * q^26 + 7063356285021193560 * q^27 - 3939749495243276288 * q^28 + 59213295656400885420 * q^29 + 33406440000000000000 * q^30 + 100028171637661559944 * q^31 - 73786976294838206464 * q^32 + 717443691297291752112 * q^33 - 314277615275751407616 * q^34 - 71663625844726562500 * q^35 - 186115963872067190784 * q^36 - 93534665260879182692 * q^37 - 1892986791095056793600 * q^38 - 6059669650423221487512 * q^39 - 1342177280000000000000 * q^40 - 10105587280937387464956 * q^41 - 6326523926508655607808 * q^42 - 4721434400282665756964 * q^43 - 9971317366772931231744 * q^44 - 3385429661140136718750 * q^45 + 8614086387321877659648 * q^46 - 12229615564061849682372 * q^47 - 15044923073577483239424 * q^48 - 63801053560061994186654 * q^49 - 24414062500000000000000 * q^50 - 168164944839408859896456 * q^51 + 46982856565476969938944 * q^52 - 107620760072906302379604 * q^53 - 57863014686893617643520 * q^54 - 181377206295527343750000 * q^55 + 32274427865032919351296 * q^56 - 999368617055941453508400 * q^57 - 485075318017236053360640 * q^58 - 1873128711713027366910360 * q^59 - 273665556480000000000000 * q^60 - 3717289232167725644025716 * q^61 - 819430782055723499061248 * q^62 - 2170926616021273562933124 * q^63 + 604462909807314587353088 * q^64 + 854613182409174804687500 * q^65 - 5877298719107414033301504 * q^66 + 3742334935347789083235028 * q^67 + 2574562224338955531190272 * q^68 + 12599594916132118555745568 * q^69 + 587068422920000000000000 * q^70 - 4816780974130885431148776 * q^71 + 1524661976039974426902528 * q^72 + 9436477395201058880013796 * q^73 + 766235977817122264612864 * q^74 - 4977947473526000976562500 * q^75 + 15507347792650705253171200 * q^76 + 50228356579868877749801616 * q^77 + 49640813776267030425698304 * q^78 + 9144841742084043183428080 * q^79 + 10995116277760000000000000 * q^80 - 14325462375198451093027998 * q^81 + 82784971005439078112919552 * q^82 + 148434950342238869610178716 * q^83 + 51826884005958906739163136 * q^84 + 46831014048420102539062500 * q^85 + 38677990607115597881049088 * q^86 - 188918373571694763982458840 * q^87 + 81685031868603852650446848 * q^88 - 168440373041146148645755980 * q^89 + 27733439784060000000000000 * q^90 - 498540814254851281271173816 * q^91 - 70566595684940821787836416 * q^92 + 242292812947742217165349632 * q^93 + 100185010700794672597991424 * q^94 + 282077013119318603515625000 * q^95 + 123248009818746742697361408 * q^96 - 863184664945605533733445292 * q^97 + 522658230764027856377069568 * q^98 - 1361593782715399520132408112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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