LMFDB - Embedded newform 10.28.a.a.1.2

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			1.2
Root			$-4421.25$ 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)

$f(q)$	$=$	\(q-8192.00 q^{2} +186813. q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} -1.53037e9 q^{6} +1.52169e11 q^{7} -5.49756e11 q^{8} -7.59070e12 q^{9} -1.00000e13 q^{10} +5.20477e13 q^{11} +1.25368e13 q^{12} -9.66570e14 q^{13} -1.24656e15 q^{14} +2.28043e14 q^{15} +4.50360e15 q^{16} -8.84096e15 q^{17} +6.21830e16 q^{18} -4.96067e16 q^{19} +8.19200e16 q^{20} +2.84270e16 q^{21} -4.26375e17 q^{22} +2.39358e18 q^{23} -1.02701e17 q^{24} +1.49012e18 q^{25} +7.91814e18 q^{26} -2.84260e18 q^{27} +1.02119e19 q^{28} +5.37225e18 q^{29} -1.86813e18 q^{30} +1.60230e20 q^{31} -3.68935e19 q^{32} +9.72319e18 q^{33} +7.24251e19 q^{34} +1.85753e20 q^{35} -5.09403e20 q^{36} -2.24843e21 q^{37} +4.06378e20 q^{38} -1.80568e20 q^{39} -6.71089e20 q^{40} -4.36695e21 q^{41} -2.32874e20 q^{42} -5.19463e21 q^{43} +3.49286e21 q^{44} -9.26599e21 q^{45} -1.96082e22 q^{46} +1.42831e21 q^{47} +8.41330e20 q^{48} -4.25571e22 q^{49} -1.22070e22 q^{50} -1.65160e21 q^{51} -6.48654e22 q^{52} -2.24935e23 q^{53} +2.32866e22 q^{54} +6.35348e22 q^{55} -8.36555e22 q^{56} -9.26717e21 q^{57} -4.40094e22 q^{58} -1.17699e24 q^{59} +1.53037e22 q^{60} -2.05590e24 q^{61} -1.31261e24 q^{62} -1.15507e24 q^{63} +3.02231e23 q^{64} -1.17989e24 q^{65} -7.96523e22 q^{66} +3.81110e24 q^{67} -5.93307e23 q^{68} +4.47151e23 q^{69} -1.52169e24 q^{70} -3.12654e24 q^{71} +4.17303e24 q^{72} +1.49753e25 q^{73} +1.84191e25 q^{74} +2.78373e23 q^{75} -3.32905e24 q^{76} +7.92003e24 q^{77} +1.47921e24 q^{78} +1.41656e25 q^{79} +5.49756e24 q^{80} +5.73526e25 q^{81} +3.57740e25 q^{82} -7.95957e24 q^{83} +1.90771e24 q^{84} -1.07922e25 q^{85} +4.25544e25 q^{86} +1.00360e24 q^{87} -2.86135e25 q^{88} -1.05141e26 q^{89} +7.59070e25 q^{90} -1.47081e26 q^{91} +1.60630e26 q^{92} +2.99330e25 q^{93} -1.17007e25 q^{94} -6.05551e25 q^{95} -6.89218e24 q^{96} -2.67236e26 q^{97} +3.48628e26 q^{98} -3.95079e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	186813.	0.0676503	0.0338252	−	0.999428i	$-0.489231\pi$
$3$	186813.	0.0676503	0.0338252	+	0.999428i	$0.489231\pi$
$4$	6.71089e7	0.500000
$5$	1.22070e9	0.447214
$5$	1.22070e9	0.447214
$6$	−1.53037e9	−0.0478360
$7$	1.52169e11	0.593610	0.296805	−	0.954938i	$-0.404079\pi$
$7$	1.52169e11	0.593610	0.296805	+	0.954938i	$0.404079\pi$
$8$	−5.49756e11	−0.353553
$9$	−7.59070e12	−0.995423
$10$	−1.00000e13	−0.316228
$11$	5.20477e13	0.454570	0.227285	−	0.973828i	$-0.427015\pi$
$11$	5.20477e13	0.454570	0.227285	+	0.973828i	$0.427015\pi$
$12$	1.25368e13	0.0338252
$13$	−9.66570e14	−0.885111	−0.442556	−	0.896741i	$-0.645928\pi$
$13$	−9.66570e14	−0.885111	−0.442556	+	0.896741i	$0.645928\pi$
$14$	−1.24656e15	−0.419746
$15$	2.28043e14	0.0302541
$16$	4.50360e15	0.250000
$17$	−8.84096e15	−0.216491	−0.108245	−	0.994124i	$-0.534523\pi$
$17$	−8.84096e15	−0.216491	−0.108245	+	0.994124i	$0.534523\pi$
$18$	6.21830e16	0.703871
$19$	−4.96067e16	−0.270624	−0.135312	−	0.990803i	$-0.543204\pi$
$19$	−4.96067e16	−0.270624	−0.135312	+	0.990803i	$0.543204\pi$
$20$	8.19200e16	0.223607
$21$	2.84270e16	0.0401579
$22$	−4.26375e17	−0.321429
$23$	2.39358e18	0.990197	0.495098	−	0.868837i	$-0.335132\pi$
$23$	2.39358e18	0.990197	0.495098	+	0.868837i	$0.335132\pi$
$24$	−1.02701e17	−0.0239180
$25$	1.49012e18	0.200000
$26$	7.91814e18	0.625868
$27$	−2.84260e18	−0.134991
$28$	1.02119e19	0.296805
$29$	5.37225e18	0.0972261	0.0486131	−	0.998818i	$-0.484520\pi$
$29$	5.37225e18	0.0972261	0.0486131	+	0.998818i	$0.484520\pi$
$30$	−1.86813e18	−0.0213929
$31$	1.60230e20	1.17859	0.589293	−	0.807919i	$-0.299406\pi$
$31$	1.60230e20	1.17859	0.589293	+	0.807919i	$0.299406\pi$
$32$	−3.68935e19	−0.176777
$33$	9.72319e18	0.0307518
$34$	7.24251e19	0.153082
$35$	1.85753e20	0.265470
$36$	−5.09403e20	−0.497712
$37$	−2.24843e21	−1.51759	−0.758797	−	0.651327i	$-0.774213\pi$
$37$	−2.24843e21	−1.51759	−0.758797	+	0.651327i	$0.774213\pi$
$38$	4.06378e20	0.191360
$39$	−1.80568e20	−0.0598781
$40$	−6.71089e20	−0.158114
$41$	−4.36695e21	−0.737218	−0.368609	−	0.929585i	$-0.620166\pi$
$41$	−4.36695e21	−0.737218	−0.368609	+	0.929585i	$0.620166\pi$
$42$	−2.32874e20	−0.0283959
$43$	−5.19463e21	−0.461031	−0.230516	−	0.973069i	$-0.574041\pi$
$43$	−5.19463e21	−0.461031	−0.230516	+	0.973069i	$0.574041\pi$
$44$	3.49286e21	0.227285
$45$	−9.26599e21	−0.445167
$46$	−1.96082e22	−0.700175
$47$	1.42831e21	0.0381507	0.0190753	−	0.999818i	$-0.493928\pi$
$47$	1.42831e21	0.0381507	0.0190753	+	0.999818i	$0.493928\pi$
$48$	8.41330e20	0.0169126
$49$	−4.25571e22	−0.647627
$50$	−1.22070e22	−0.141421
$51$	−1.65160e21	−0.0146457
$52$	−6.48654e22	−0.442556
$53$	−2.24935e23	−1.18668	−0.593338	−	0.804953i	$-0.702190\pi$
$53$	−2.24935e23	−1.18668	−0.593338	+	0.804953i	$0.702190\pi$
$54$	2.32866e22	0.0954531
$55$	6.35348e22	0.203290
$56$	−8.36555e22	−0.209873
$57$	−9.26717e21	−0.0183078
$58$	−4.40094e22	−0.0687493
$59$	−1.17699e24	−1.45972	−0.729859	−	0.683598i	$-0.760414\pi$
$59$	−1.17699e24	−1.45972	−0.729859	+	0.683598i	$0.760414\pi$
$60$	1.53037e22	0.0151271
$61$	−2.05590e24	−1.62574	−0.812868	−	0.582448i	$-0.802095\pi$
$61$	−2.05590e24	−1.62574	−0.812868	+	0.582448i	$0.802095\pi$
$62$	−1.31261e24	−0.833386
$63$	−1.15507e24	−0.590893
$64$	3.02231e23	0.125000
$65$	−1.17989e24	−0.395834
$66$	−7.96523e22	−0.0217448
$67$	3.81110e24	0.849260	0.424630	−	0.905367i	$-0.360404\pi$
$67$	3.81110e24	0.849260	0.424630	+	0.905367i	$0.360404\pi$
$68$	−5.93307e23	−0.108245
$69$	4.47151e23	0.0669871
$70$	−1.52169e24	−0.187716
$71$	−3.12654e24	−0.318476	−0.159238	−	0.987240i	$-0.550904\pi$
$71$	−3.12654e24	−0.318476	−0.159238	+	0.987240i	$0.550904\pi$
$72$	4.17303e24	0.351935
$73$	1.49753e25	1.04838	0.524189	−	0.851602i	$-0.324369\pi$
$73$	1.49753e25	1.04838	0.524189	+	0.851602i	$0.324369\pi$
$74$	1.84191e25	1.07310
$75$	2.78373e23	0.0135301
$76$	−3.32905e24	−0.135312
$77$	7.92003e24	0.269837
$78$	1.47921e24	0.0423402
$79$	1.41656e25	0.341404	0.170702	−	0.985323i	$-0.445397\pi$
$79$	1.41656e25	0.341404	0.170702	+	0.985323i	$0.445397\pi$
$80$	5.49756e24	0.111803
$81$	5.73526e25	0.986291
$82$	3.57740e25	0.521292
$83$	−7.95957e24	−0.0984771	−0.0492385	−	0.998787i	$-0.515679\pi$
$83$	−7.95957e24	−0.0984771	−0.0492385	+	0.998787i	$0.515679\pi$
$84$	1.90771e24	0.0200790
$85$	−1.07922e25	−0.0968175
$86$	4.25544e25	0.325998
$87$	1.00360e24	0.00657738
$88$	−2.86135e25	−0.160715
$89$	−1.05141e26	−0.506998	−0.253499	−	0.967336i	$-0.581581\pi$
$89$	−1.05141e26	−0.506998	−0.253499	+	0.967336i	$0.581581\pi$
$90$	7.59070e25	0.314781
$91$	−1.47081e26	−0.525411
$92$	1.60630e26	0.495098
$93$	2.99330e25	0.0797317
$94$	−1.17007e25	−0.0269766
$95$	−6.05551e25	−0.121027
$96$	−6.89218e24	−0.0119590
$97$	−2.67236e26	−0.403159	−0.201580	−	0.979472i	$-0.564608\pi$
$97$	−2.67236e26	−0.403159	−0.201580	+	0.979472i	$0.564608\pi$
$98$	3.48628e26	0.457942
$99$	−3.95079e26	−0.452489
$100$	1.00000e26	0.100000
$101$	−4.51294e26	−0.394567	−0.197283	−	0.980346i	$-0.563212\pi$
$101$	−4.51294e26	−0.394567	−0.197283	+	0.980346i	$0.563212\pi$
$102$	1.35299e25	0.0103560
$103$	−2.25718e27	−1.51448	−0.757240	−	0.653137i	$-0.773453\pi$
$103$	−2.25718e27	−1.51448	−0.757240	+	0.653137i	$0.773453\pi$
$104$	5.31377e26	0.312934
$105$	3.47010e25	0.0179592
$106$	1.84267e27	0.839107
$107$	−2.71910e27	−1.09080	−0.545399	−	0.838177i	$-0.683622\pi$
$107$	−2.71910e27	−1.09080	−0.545399	+	0.838177i	$0.683622\pi$
$108$	−1.90764e26	−0.0674955
$109$	−4.53116e27	−1.41564	−0.707818	−	0.706395i	$-0.750320\pi$
$109$	−4.53116e27	−1.41564	−0.707818	+	0.706395i	$0.750320\pi$
$110$	−5.20477e26	−0.143748
$111$	−4.20035e26	−0.102666
$112$	6.85306e26	0.148403
$113$	−2.52001e27	−0.483998	−0.241999	−	0.970276i	$-0.577803\pi$
$113$	−2.52001e27	−0.483998	−0.241999	+	0.970276i	$0.577803\pi$
$114$	7.59167e25	0.0129456
$115$	2.92185e27	0.442829
$116$	3.60525e26	0.0486131
$117$	7.33694e27	0.881061
$118$	9.64187e27	1.03218
$119$	−1.34532e27	−0.128511
$120$	−1.25368e26	−0.0106965
$121$	−1.04010e28	−0.793366
$122$	1.68420e28	1.14957
$123$	−8.15802e26	−0.0498730
$124$	1.07529e28	0.589293
$125$	1.81899e27	0.0894427
$126$	9.46229e27	0.417825
$127$	4.15616e28	1.64946	0.824730	−	0.565526i	$-0.191327\pi$
$127$	4.15616e28	1.64946	0.824730	+	0.565526i	$0.191327\pi$
$128$	−2.47588e27	−0.0883883
$129$	−9.70423e26	−0.0311889
$130$	9.66570e27	0.279897
$131$	−5.42612e27	−0.141686	−0.0708430	−	0.997487i	$-0.522569\pi$
$131$	−5.42612e27	−0.141686	−0.0708430	+	0.997487i	$0.522569\pi$
$132$	6.52512e26	0.0153759
$133$	−7.54858e27	−0.160645
$134$	−3.12205e28	−0.600517
$135$	−3.46997e27	−0.0603698
$136$	4.86037e27	0.0765410
$137$	−2.10760e28	−0.300650	−0.150325	−	0.988637i	$-0.548032\pi$
$137$	−2.10760e28	−0.300650	−0.150325	+	0.988637i	$0.548032\pi$
$138$	−3.66306e27	−0.0473671
$139$	−7.38363e28	−0.866104	−0.433052	−	0.901369i	$-0.642563\pi$
$139$	−7.38363e28	−0.866104	−0.433052	+	0.901369i	$0.642563\pi$
$140$	1.24656e28	0.132735
$141$	2.66827e26	0.00258091
$142$	2.56126e28	0.225196
$143$	−5.03078e28	−0.402345
$144$	−3.41855e28	−0.248856
$145$	6.55792e27	0.0434808
$146$	−1.22678e29	−0.741315
$147$	−7.95022e27	−0.0438122
$148$	−1.50889e29	−0.758797
$149$	−1.91029e29	−0.877170	−0.438585	−	0.898690i	$-0.644520\pi$
$149$	−1.91029e29	−0.877170	−0.438585	+	0.898690i	$0.644520\pi$
$150$	−2.28043e27	−0.00956720
$151$	−8.87996e27	−0.0340583	−0.0170291	−	0.999855i	$-0.505421\pi$
$151$	−8.87996e27	−0.0340583	−0.0170291	+	0.999855i	$0.505421\pi$
$152$	2.72716e28	0.0956802
$153$	6.71091e28	0.215500
$154$	−6.48809e28	−0.190804
$155$	1.95593e29	0.527080
$156$	−1.21177e28	−0.0299390
$157$	6.26636e29	1.42027	0.710133	−	0.704067i	$-0.248635\pi$
$157$	6.26636e29	1.42027	0.710133	+	0.704067i	$0.248635\pi$
$158$	−1.16044e29	−0.241409
$159$	−4.20207e28	−0.0802790
$160$	−4.50360e28	−0.0790569
$161$	3.64227e29	0.587791
$162$	−4.69832e29	−0.697413
$163$	7.21779e28	0.0985988	0.0492994	−	0.998784i	$-0.484301\pi$
$163$	7.21779e28	0.0985988	0.0492994	+	0.998784i	$0.484301\pi$
$164$	−2.93061e29	−0.368609
$165$	1.18691e28	0.0137526
$166$	6.52048e28	0.0696338
$167$	6.72685e29	0.662429	0.331214	−	0.943556i	$-0.392542\pi$
$167$	6.72685e29	0.662429	0.331214	+	0.943556i	$0.392542\pi$
$168$	−1.56279e28	−0.0141980
$169$	−2.58277e29	−0.216578
$170$	8.84096e28	0.0684603
$171$	3.76550e29	0.269386
$172$	−3.48605e29	−0.230516
$173$	8.69859e29	0.531896	0.265948	−	0.963987i	$-0.414315\pi$
$173$	8.69859e29	0.531896	0.265948	+	0.963987i	$0.414315\pi$
$174$	−8.22153e27	−0.00465091
$175$	2.26749e29	0.118722
$176$	2.34402e29	0.113642
$177$	−2.19876e29	−0.0987504
$178$	8.61314e29	0.358502
$179$	3.70782e30	1.43088	0.715439	−	0.698675i	$-0.246227\pi$
$179$	3.70782e30	1.43088	0.715439	+	0.698675i	$0.246227\pi$
$180$	−6.21830e29	−0.222583
$181$	1.58156e30	0.525321	0.262661	−	0.964888i	$-0.415400\pi$
$181$	1.58156e30	0.525321	0.262661	+	0.964888i	$0.415400\pi$
$182$	1.20489e30	0.371522
$183$	−3.84069e29	−0.109982
$184$	−1.31588e30	−0.350087
$185$	−2.74466e30	−0.678689
$186$	−2.45212e29	−0.0563788
$187$	−4.60152e29	−0.0984101
$188$	9.58525e28	0.0190753
$189$	−4.32554e29	−0.0801320
$190$	4.96067e29	0.0855789
$191$	−8.65494e30	−1.39096	−0.695478	−	0.718547i	$-0.744807\pi$
$191$	−8.65494e30	−1.39096	−0.695478	+	0.718547i	$0.744807\pi$
$192$	5.64607e28	0.00845629
$193$	2.56974e30	0.358811	0.179405	−	0.983775i	$-0.442583\pi$
$193$	2.56974e30	0.358811	0.179405	+	0.983775i	$0.442583\pi$
$194$	2.18920e30	0.285077
$195$	−2.20419e29	−0.0267783
$196$	−2.85596e30	−0.323814
$197$	−1.43330e31	−1.51720	−0.758598	−	0.651559i	$-0.774115\pi$
$197$	−1.43330e31	−1.51720	−0.758598	+	0.651559i	$0.774115\pi$
$198$	3.23648e30	0.319958
$199$	−1.47927e31	−1.36626	−0.683128	−	0.730299i	$-0.739381\pi$
$199$	−1.47927e31	−1.36626	−0.683128	+	0.730299i	$0.739381\pi$
$200$	−8.19200e29	−0.0707107
$201$	7.11963e29	0.0574527
$202$	3.69700e30	0.279001
$203$	8.17487e29	0.0577144
$204$	−1.10837e29	−0.00732283
$205$	−5.33074e30	−0.329694
$206$	1.84908e31	1.07090
$207$	−1.81689e31	−0.985665
$208$	−4.35304e30	−0.221278
$209$	−2.58192e30	−0.123018
$210$	−2.84270e29	−0.0126990
$211$	2.00442e31	0.839800	0.419900	−	0.907570i	$-0.362065\pi$
$211$	2.00442e31	0.839800	0.419900	+	0.907570i	$0.362065\pi$
$212$	−1.50951e31	−0.593338
$213$	−5.84078e29	−0.0215450
$214$	2.22749e31	0.771310
$215$	−6.34110e30	−0.206179
$216$	1.56274e30	0.0477265
$217$	2.43820e31	0.699621
$218$	3.71192e31	1.00101
$219$	2.79758e30	0.0709231
$220$	4.26375e30	0.101645
$221$	8.54540e30	0.191618
$222$	3.44093e30	0.0725956
$223$	9.30611e31	1.84779	0.923894	−	0.382647i	$-0.124988\pi$
$223$	9.30611e31	1.84779	0.923894	+	0.382647i	$0.124988\pi$
$224$	−5.61403e30	−0.104936
$225$	−1.13110e31	−0.199085
$226$	2.06439e31	0.342238
$227$	2.62678e31	0.410274	0.205137	−	0.978733i	$-0.434236\pi$
$227$	2.62678e31	0.410274	0.205137	+	0.978733i	$0.434236\pi$
$228$	−6.21909e29	−0.00915391
$229$	−1.81385e31	−0.251665	−0.125832	−	0.992052i	$-0.540160\pi$
$229$	−1.81385e31	−0.251665	−0.125832	+	0.992052i	$0.540160\pi$
$230$	−2.39358e31	−0.313128
$231$	1.47956e30	0.0182546
$232$	−2.95342e30	−0.0343746
$233$	−1.08135e31	−0.118757	−0.0593786	−	0.998236i	$-0.518912\pi$
$233$	−1.08135e31	−0.118757	−0.0593786	+	0.998236i	$0.518912\pi$
$234$	−6.01042e31	−0.623004
$235$	1.74355e30	0.0170615
$236$	−7.89862e31	−0.729859
$237$	2.64631e30	0.0230961
$238$	1.10208e31	0.0908710
$239$	−2.49336e32	−1.94273	−0.971367	−	0.237586i	$-0.923644\pi$
$239$	−2.49336e32	−1.94273	−0.971367	+	0.237586i	$0.923644\pi$
$240$	1.02701e30	0.00756354
$241$	1.52145e32	1.05932	0.529662	−	0.848209i	$-0.322319\pi$
$241$	1.52145e32	1.05932	0.529662	+	0.848209i	$0.322319\pi$
$242$	8.52052e31	0.560995
$243$	3.23907e31	0.201714
$244$	−1.37969e32	−0.812868
$245$	−5.19496e31	−0.289628
$246$	6.68305e30	0.0352655
$247$	4.79483e31	0.239533
$248$	−8.80874e31	−0.416693
$249$	−1.48695e30	−0.00666201
$250$	−1.49012e31	−0.0632456
$251$	−1.40439e32	−0.564799	−0.282400	−	0.959297i	$-0.591130\pi$
$251$	−1.40439e32	−0.564799	−0.282400	+	0.959297i	$0.591130\pi$
$252$	−7.75151e31	−0.295447
$253$	1.24580e32	0.450114
$254$	−3.40473e32	−1.16634
$255$	−2.01612e30	−0.00654974
$256$	2.02824e31	0.0625000
$257$	4.52958e32	1.32422	0.662111	−	0.749406i	$-0.269661\pi$
$257$	4.52958e32	1.32422	0.662111	+	0.749406i	$0.269661\pi$
$258$	7.94971e30	0.0220539
$259$	−3.42140e32	−0.900859
$260$	−7.91814e31	−0.197917
$261$	−4.07791e31	−0.0967812
$262$	4.44508e31	0.100187
$263$	7.58089e32	1.62300	0.811499	−	0.584354i	$-0.198652\pi$
$263$	7.58089e32	1.62300	0.811499	+	0.584354i	$0.198652\pi$
$264$	−5.34538e30	−0.0108724
$265$	−2.74579e32	−0.530698
$266$	6.18380e31	0.113593
$267$	−1.96417e31	−0.0342986
$268$	2.55759e32	0.424630
$269$	−1.08950e33	−1.72016	−0.860082	−	0.510156i	$-0.829588\pi$
$269$	−1.08950e33	−1.72016	−0.860082	+	0.510156i	$0.829588\pi$
$270$	2.84260e31	0.0426879
$271$	9.86275e32	1.40900	0.704502	−	0.709702i	$-0.251170\pi$
$271$	9.86275e32	1.40900	0.704502	+	0.709702i	$0.251170\pi$
$272$	−3.98161e31	−0.0541226
$273$	−2.74767e31	−0.0355442
$274$	1.72655e32	0.212592
$275$	7.75572e31	0.0909140
$276$	3.00078e31	0.0334936
$277$	5.21841e32	0.554704	0.277352	−	0.960768i	$-0.410543\pi$
$277$	5.21841e32	0.554704	0.277352	+	0.960768i	$0.410543\pi$
$278$	6.04867e32	0.612428
$279$	−1.21626e33	−1.17319
$280$	−1.02119e32	−0.0938580
$281$	1.10443e33	0.967396	0.483698	−	0.875235i	$-0.339293\pi$
$281$	1.10443e33	0.967396	0.483698	+	0.875235i	$0.339293\pi$
$282$	−2.18585e30	−0.00182498
$283$	1.51510e33	1.20594	0.602968	−	0.797765i	$-0.293985\pi$
$283$	1.51510e33	1.20594	0.602968	+	0.797765i	$0.293985\pi$
$284$	−2.09819e32	−0.159238
$285$	−1.13125e31	−0.00818751
$286$	4.12121e32	0.284501
$287$	−6.64512e32	−0.437620
$288$	2.80047e32	0.175968
$289$	−1.58955e33	−0.953132
$290$	−5.37225e31	−0.0307456
$291$	−4.99231e31	−0.0272739
$292$	1.00498e33	0.524189
$293$	1.40575e33	0.700156	0.350078	−	0.936721i	$-0.386155\pi$
$293$	1.40575e33	0.700156	0.350078	+	0.936721i	$0.386155\pi$
$294$	6.51282e31	0.0309799
$295$	−1.43675e33	−0.652806
$296$	1.23609e33	0.536550
$297$	−1.47951e32	−0.0613628
$298$	1.56491e33	0.620253
$299$	−2.31356e33	−0.876434
$300$	1.86813e31	0.00676503
$301$	−7.90459e32	−0.273673
$302$	7.27447e31	0.0240828
$303$	−8.43075e31	−0.0266926
$304$	−2.23409e32	−0.0676561
$305$	−2.50965e33	−0.727051
$306$	−5.49757e32	−0.152381
$307$	−4.49630e33	−1.19258	−0.596290	−	0.802769i	$-0.703359\pi$
$307$	−4.49630e33	−1.19258	−0.596290	+	0.802769i	$0.703359\pi$
$308$	5.31504e32	0.134919
$309$	−4.21670e32	−0.102455
$310$	−1.60230e33	−0.372702
$311$	−2.75632e33	−0.613853	−0.306927	−	0.951733i	$-0.599301\pi$
$311$	−2.75632e33	−0.613853	−0.306927	+	0.951733i	$0.599301\pi$
$312$	9.92681e31	0.0211701
$313$	3.75694e33	0.767335	0.383668	−	0.923471i	$-0.374661\pi$
$313$	3.75694e33	0.767335	0.383668	+	0.923471i	$0.374661\pi$
$314$	−5.13340e33	−1.00428
$315$	−1.40999e33	−0.264256
$316$	9.50635e32	0.170702
$317$	−1.58056e33	−0.271964	−0.135982	−	0.990711i	$-0.543419\pi$
$317$	−1.58056e33	−0.271964	−0.135982	+	0.990711i	$0.543419\pi$
$318$	3.44234e32	0.0567658
$319$	2.79613e32	0.0441961
$320$	3.68935e32	0.0559017
$321$	−5.07963e32	−0.0737928
$322$	−2.98375e33	−0.415631
$323$	4.38571e32	0.0585876
$324$	3.84887e33	0.493146
$325$	−1.44030e33	−0.177022
$326$	−5.91281e32	−0.0697199
$327$	−8.46479e32	−0.0957682
$328$	2.40075e33	0.260646
$329$	2.17344e32	0.0226466
$330$	−9.72319e31	−0.00972457
$331$	1.82677e34	1.75390	0.876952	−	0.480578i	$-0.159573\pi$
$331$	1.82677e34	1.75390	0.876952	+	0.480578i	$0.159573\pi$
$332$	−5.34158e32	−0.0492385
$333$	1.70671e34	1.51065
$334$	−5.51063e33	−0.468408
$335$	4.65222e33	0.379801
$336$	1.28024e32	0.0100395
$337$	1.86275e34	1.40330	0.701650	−	0.712521i	$-0.252447\pi$
$337$	1.86275e34	1.40330	0.701650	+	0.712521i	$0.252447\pi$
$338$	2.11580e33	0.153144
$339$	−4.70771e32	−0.0327426
$340$	−7.24251e32	−0.0484088
$341$	8.33961e33	0.535750
$342$	−3.08469e33	−0.190485
$343$	−1.64752e34	−0.978048
$344$	2.85578e33	0.162999
$345$	5.45838e32	0.0299576
$346$	−7.12589e33	−0.376107
$347$	9.97856e33	0.506547	0.253274	−	0.967395i	$-0.418493\pi$
$347$	9.97856e33	0.506547	0.253274	+	0.967395i	$0.418493\pi$
$348$	6.73508e31	0.00328869
$349$	−1.32833e33	−0.0623969	−0.0311984	−	0.999513i	$-0.509932\pi$
$349$	−1.32833e33	−0.0623969	−0.0311984	+	0.999513i	$0.509932\pi$
$350$	−1.85753e33	−0.0839491
$351$	2.74757e33	0.119482
$352$	−1.92022e33	−0.0803573
$353$	5.06941e32	0.0204173	0.0102087	−	0.999948i	$-0.496750\pi$
$353$	5.06941e32	0.0204173	0.0102087	+	0.999948i	$0.496750\pi$
$354$	1.80122e33	0.0698271
$355$	−3.81658e33	−0.142427
$356$	−7.05588e33	−0.253499
$357$	−2.51322e32	−0.00869381
$358$	−3.03745e34	−1.01178
$359$	−1.29578e34	−0.415677	−0.207839	−	0.978163i	$-0.566643\pi$
$359$	−1.29578e34	−0.415677	−0.207839	+	0.978163i	$0.566643\pi$
$360$	5.09403e33	0.157390
$361$	−3.11398e34	−0.926762
$362$	−1.29561e34	−0.371458
$363$	−1.94305e33	−0.0536715
$364$	−9.87047e33	−0.262705
$365$	1.82804e34	0.468849
$366$	3.14630e33	0.0777687
$367$	−2.12850e34	−0.507087	−0.253543	−	0.967324i	$-0.581596\pi$
$367$	−2.12850e34	−0.507087	−0.253543	+	0.967324i	$0.581596\pi$
$368$	1.07797e34	0.247549
$369$	3.31482e34	0.733844
$370$	2.24843e34	0.479905
$371$	−3.42280e34	−0.704423
$372$	2.00877e33	0.0398659
$373$	−4.23988e34	−0.811492	−0.405746	−	0.913986i	$-0.632988\pi$
$373$	−4.23988e34	−0.811492	−0.405746	+	0.913986i	$0.632988\pi$
$374$	3.76956e33	0.0695864
$375$	3.39811e32	0.00605083
$376$	−7.85224e32	−0.0134883
$377$	−5.19265e33	−0.0860559
$378$	3.54348e33	0.0566619
$379$	−2.53814e34	−0.391639	−0.195820	−	0.980640i	$-0.562737\pi$
$379$	−2.53814e34	−0.391639	−0.195820	+	0.980640i	$0.562737\pi$
$380$	−4.06378e33	−0.0605134
$381$	7.76424e33	0.111587
$382$	7.09012e34	0.983555
$383$	−1.37667e35	−1.84351	−0.921755	−	0.387772i	$-0.873245\pi$
$383$	−1.37667e35	−1.84351	−0.921755	+	0.387772i	$0.873245\pi$
$384$	−4.62526e32	−0.00597950
$385$	9.66800e33	0.120675
$386$	−2.10513e34	−0.253717
$387$	3.94308e34	0.458921
$388$	−1.79339e34	−0.201580
$389$	1.31877e35	1.43169	0.715844	−	0.698260i	$-0.246042\pi$
$389$	1.31877e35	1.43169	0.715844	+	0.698260i	$0.246042\pi$
$390$	1.80568e33	0.0189351
$391$	−2.11615e34	−0.214368
$392$	2.33960e34	0.228971
$393$	−1.01367e33	−0.00958510
$394$	1.17416e35	1.07282
$395$	1.72920e34	0.152680
$396$	−2.65133e34	−0.226245
$397$	6.51145e34	0.537039	0.268520	−	0.963274i	$-0.413466\pi$
$397$	6.51145e34	0.537039	0.268520	+	0.963274i	$0.413466\pi$
$398$	1.21182e35	0.966089
$399$	−1.41017e33	−0.0108677
$400$	6.71089e33	0.0500000
$401$	−9.62542e34	−0.693379	−0.346690	−	0.937980i	$-0.612694\pi$
$401$	−9.62542e34	−0.693379	−0.346690	+	0.937980i	$0.612694\pi$
$402$	−5.83240e33	−0.0406252
$403$	−1.54874e35	−1.04318
$404$	−3.02858e34	−0.197283
$405$	7.00105e34	0.441083
$406$	−6.69685e33	−0.0408102
$407$	−1.17026e35	−0.689852
$408$	9.07979e32	0.00517802
$409$	3.10105e35	1.71098	0.855489	−	0.517821i	$-0.173257\pi$
$409$	3.10105e35	1.71098	0.855489	+	0.517821i	$0.173257\pi$
$410$	4.36695e34	0.233129
$411$	−3.93728e33	−0.0203391
$412$	−1.51477e35	−0.757240
$413$	−1.79100e35	−0.866503
$414$	1.48840e35	0.696970
$415$	−9.71627e33	−0.0440403
$416$	3.56601e34	0.156467
$417$	−1.37936e34	−0.0585922
$418$	2.11511e34	0.0869866
$419$	2.11087e35	0.840568	0.420284	−	0.907393i	$-0.361931\pi$
$419$	2.11087e35	0.840568	0.420284	+	0.907393i	$0.361931\pi$
$420$	2.32874e33	0.00897958
$421$	4.74937e35	1.77349	0.886743	−	0.462263i	$-0.152962\pi$
$421$	4.74937e35	1.77349	0.886743	+	0.462263i	$0.152962\pi$
$422$	−1.64202e35	−0.593828
$423$	−1.08419e34	−0.0379761
$424$	1.23659e35	0.419553
$425$	−1.31741e34	−0.0432981
$426$	4.78477e33	0.0152346
$427$	−3.12844e35	−0.965054
$428$	−1.82476e35	−0.545399
$429$	−9.39814e33	−0.0272188
$430$	5.19463e34	0.145791
$431$	−4.97520e35	−1.35322	−0.676608	−	0.736343i	$-0.736551\pi$
$431$	−4.97520e35	−1.35322	−0.676608	+	0.736343i	$0.736551\pi$
$432$	−1.28019e34	−0.0337478
$433$	1.48404e35	0.379191	0.189595	−	0.981862i	$-0.439282\pi$
$433$	1.48404e35	0.379191	0.189595	+	0.981862i	$0.439282\pi$
$434$	−1.99737e35	−0.494706
$435$	1.22510e33	0.00294149
$436$	−3.04081e35	−0.707818
$437$	−1.18737e35	−0.267971
$438$	−2.29178e34	−0.0501502
$439$	3.88897e35	0.825209	0.412604	−	0.910910i	$-0.364619\pi$
$439$	3.88897e35	0.825209	0.412604	+	0.910910i	$0.364619\pi$
$440$	−3.49286e34	−0.0718738
$441$	3.23038e35	0.644663
$442$	−7.00039e34	−0.135495
$443$	−7.59267e35	−1.42542	−0.712712	−	0.701457i	$-0.752533\pi$
$443$	−7.59267e35	−1.42542	−0.712712	+	0.701457i	$0.752533\pi$
$444$	−2.81881e34	−0.0513329
$445$	−1.28346e35	−0.226736
$446$	−7.62356e35	−1.30658
$447$	−3.56866e34	−0.0593408
$448$	4.59901e34	0.0742013
$449$	4.69834e33	0.00735562	0.00367781	−	0.999993i	$-0.498829\pi$
$449$	4.69834e33	0.00735562	0.00367781	+	0.999993i	$0.498829\pi$
$450$	9.26599e34	0.140774
$451$	−2.27290e35	−0.335117
$452$	−1.69115e35	−0.241999
$453$	−1.65889e33	−0.00230405
$454$	−2.15186e35	−0.290108
$455$	−1.79543e35	−0.234971
$456$	5.09468e33	0.00647279
$457$	1.07406e36	1.32483	0.662414	−	0.749138i	$-0.269532\pi$
$457$	1.07406e36	1.32483	0.662414	+	0.749138i	$0.269532\pi$
$458$	1.48591e35	0.177954
$459$	2.51313e34	0.0292243
$460$	1.96082e35	0.221415
$461$	9.20062e35	1.00892	0.504458	−	0.863436i	$-0.331692\pi$
$461$	9.20062e35	1.00892	0.504458	+	0.863436i	$0.331692\pi$
$462$	−1.21206e34	−0.0129079
$463$	5.38671e35	0.557161	0.278580	−	0.960413i	$-0.410136\pi$
$463$	5.38671e35	0.557161	0.278580	+	0.960413i	$0.410136\pi$
$464$	2.41944e34	0.0243065
$465$	3.65394e34	0.0356571
$466$	8.85839e34	0.0839740
$467$	−4.52515e35	−0.416731	−0.208365	−	0.978051i	$-0.566814\pi$
$467$	−4.52515e35	−0.416731	−0.208365	+	0.978051i	$0.566814\pi$
$468$	4.92374e35	0.440530
$469$	5.79929e35	0.504129
$470$	−1.42831e34	−0.0120643
$471$	1.17064e35	0.0960815
$472$	6.47055e35	0.516088
$473$	−2.70369e35	−0.209571
$474$	−2.16786e34	−0.0163314
$475$	−7.39198e34	−0.0541249
$476$	−9.02826e34	−0.0642555
$477$	1.70741e36	1.18125
$478$	2.04256e36	1.37372
$479$	−2.10559e36	−1.37672	−0.688359	−	0.725370i	$-0.741669\pi$
$479$	−2.10559e36	−1.37672	−0.688359	+	0.725370i	$0.741669\pi$
$480$	−8.41330e33	−0.00534823
$481$	2.17326e36	1.34324
$482$	−1.24638e36	−0.749055
$483$	6.80423e34	0.0397642
$484$	−6.98001e35	−0.396683
$485$	−3.26216e35	−0.180298
$486$	−2.65345e35	−0.142633
$487$	1.39900e36	0.731437	0.365718	−	0.930726i	$-0.380823\pi$
$487$	1.39900e36	0.731437	0.365718	+	0.930726i	$0.380823\pi$
$488$	1.13025e36	0.574785
$489$	1.34838e34	0.00667024
$490$	4.25571e35	0.204798
$491$	−1.78697e36	−0.836597	−0.418298	−	0.908310i	$-0.637373\pi$
$491$	−1.78697e36	−0.836597	−0.418298	+	0.908310i	$0.637373\pi$
$492$	−5.47475e34	−0.0249365
$493$	−4.74958e34	−0.0210485
$494$	−3.92793e35	−0.169375
$495$	−4.82274e35	−0.202359
$496$	7.21612e35	0.294647
$497$	−4.75761e35	−0.189050
$498$	1.21811e34	0.00471075
$499$	−5.03865e36	−1.89652	−0.948259	−	0.317499i	$-0.897157\pi$
$499$	−5.03865e36	−1.89652	−0.948259	+	0.317499i	$0.897157\pi$
$500$	1.22070e35	0.0447214
$501$	1.25666e35	0.0448135
$502$	1.15048e36	0.399373
$503$	−5.02862e36	−1.69934	−0.849671	−	0.527313i	$-0.823199\pi$
$503$	−5.02862e36	−1.69934	−0.849671	+	0.527313i	$0.823199\pi$
$504$	6.35004e35	0.208912
$505$	−5.50896e35	−0.176456
$506$	−1.02056e36	−0.318278
$507$	−4.82494e34	−0.0146516
$508$	2.78915e36	0.824730
$509$	−5.99564e36	−1.72642	−0.863209	−	0.504847i	$-0.831549\pi$
$509$	−5.99564e36	−1.72642	−0.863209	+	0.504847i	$0.831549\pi$
$510$	1.65160e34	0.00463136
$511$	2.27877e36	0.622327
$512$	−1.66153e35	−0.0441942
$513$	1.41012e35	0.0365319
$514$	−3.71063e36	−0.936366
$515$	−2.75535e36	−0.677296
$516$	−6.51240e34	−0.0155944
$517$	7.43405e34	0.0173422
$518$	2.80281e36	0.637004
$519$	1.62501e35	0.0359829
$520$	6.48654e35	0.139948
$521$	5.03095e36	1.05765	0.528824	−	0.848732i	$-0.322633\pi$
$521$	5.03095e36	1.05765	0.528824	+	0.848732i	$0.322633\pi$
$522$	3.34062e35	0.0684346
$523$	3.80823e36	0.760239	0.380119	−	0.924937i	$-0.375883\pi$
$523$	3.80823e36	0.760239	0.380119	+	0.924937i	$0.375883\pi$
$524$	−3.64141e35	−0.0708430
$525$	4.23596e34	0.00803158
$526$	−6.21027e36	−1.14763
$527$	−1.41659e36	−0.255153
$528$	4.37893e34	0.00768795
$529$	−1.14003e35	−0.0195103
$530$	2.24935e36	0.375260
$531$	8.93414e36	1.45304
$532$	−5.06577e35	−0.0803227
$533$	4.22096e36	0.652520
$534$	1.60904e35	0.0242528
$535$	−3.31921e36	−0.487820
$536$	−2.09517e36	−0.300259
$537$	6.92669e35	0.0967994
$538$	8.92515e36	1.21634
$539$	−2.21500e36	−0.294392
$540$	−2.32866e35	−0.0301849
$541$	8.39039e35	0.106076	0.0530382	−	0.998592i	$-0.483109\pi$
$541$	8.39039e35	0.106076	0.0530382	+	0.998592i	$0.483109\pi$
$542$	−8.07956e36	−0.996317
$543$	2.95456e35	0.0355381
$544$	3.26174e35	0.0382705
$545$	−5.53120e36	−0.633092
$546$	2.25089e35	0.0251336
$547$	5.66797e36	0.617445	0.308722	−	0.951152i	$-0.400099\pi$
$547$	5.66797e36	0.617445	0.308722	+	0.951152i	$0.400099\pi$
$548$	−1.41439e36	−0.150325
$549$	1.56058e37	1.61830
$550$	−6.35348e35	−0.0642859
$551$	−2.66500e35	−0.0263118
$552$	−2.45824e35	−0.0236835
$553$	2.15555e36	0.202661
$554$	−4.27492e36	−0.392235
$555$	−5.12738e35	−0.0459135
$556$	−4.95507e36	−0.433052
$557$	9.07435e36	0.774053	0.387026	−	0.922069i	$-0.373502\pi$
$557$	9.07435e36	0.774053	0.387026	+	0.922069i	$0.373502\pi$
$558$	9.96359e36	0.829572
$559$	5.02097e36	0.408064
$560$	8.36555e35	0.0663676
$561$	−8.59623e34	−0.00665747
$562$	−9.04752e36	−0.684052
$563$	−1.68489e37	−1.24368	−0.621840	−	0.783145i	$-0.713614\pi$
$563$	−1.68489e37	−1.24368	−0.621840	+	0.783145i	$0.713614\pi$
$564$	1.79065e34	0.00129045
$565$	−3.07619e36	−0.216451
$566$	−1.24117e37	−0.852726
$567$	8.72726e36	0.585472
$568$	1.71883e36	0.112598
$569$	−3.14141e36	−0.200960	−0.100480	−	0.994939i	$-0.532038\pi$
$569$	−3.14141e36	−0.200960	−0.100480	+	0.994939i	$0.532038\pi$
$570$	9.26717e34	0.00578944
$571$	2.78070e37	1.69655	0.848274	−	0.529557i	$-0.177642\pi$
$571$	2.78070e37	1.69655	0.848274	+	0.529557i	$0.177642\pi$
$572$	−3.37610e36	−0.201172
$573$	−1.61685e36	−0.0940986
$574$	5.44368e36	0.309444
$575$	3.56671e36	0.198039
$576$	−2.29415e36	−0.124428
$577$	−1.74113e37	−0.922482	−0.461241	−	0.887275i	$-0.652596\pi$
$577$	−1.74113e37	−0.922482	−0.461241	+	0.887275i	$0.652596\pi$
$578$	1.30216e37	0.673966
$579$	4.80060e35	0.0242737
$580$	4.40094e35	0.0217404
$581$	−1.21120e36	−0.0584570
$582$	4.08970e35	0.0192855
$583$	−1.17073e37	−0.539427
$584$	−8.23277e36	−0.370657
$585$	8.95622e36	0.394022
$586$	−1.15159e37	−0.495085
$587$	−2.14558e37	−0.901426	−0.450713	−	0.892669i	$-0.648830\pi$
$587$	−2.14558e37	−0.901426	−0.450713	+	0.892669i	$0.648830\pi$
$588$	−5.33530e35	−0.0219061
$589$	−7.94849e36	−0.318954
$590$	1.17699e37	0.461603
$591$	−2.67758e36	−0.102639
$592$	−1.01260e37	−0.379398
$593$	−4.77291e37	−1.74801	−0.874007	−	0.485913i	$-0.838487\pi$
$593$	−4.77291e37	−1.74801	−0.874007	+	0.485913i	$0.838487\pi$
$594$	1.21201e36	0.0433901
$595$	−1.64223e36	−0.0574719
$596$	−1.28197e37	−0.438585
$597$	−2.76347e36	−0.0924276
$598$	1.89527e37	0.619733
$599$	3.32612e37	1.06335	0.531674	−	0.846949i	$-0.321563\pi$
$599$	3.32612e37	1.06335	0.531674	+	0.846949i	$0.321563\pi$
$600$	−1.53037e35	−0.00478360
$601$	−1.18443e37	−0.361996	−0.180998	−	0.983483i	$-0.557933\pi$
$601$	−1.18443e37	−0.361996	−0.180998	+	0.983483i	$0.557933\pi$
$602$	6.47544e36	0.193516
$603$	−2.89289e37	−0.845373
$604$	−5.95924e35	−0.0170291
$605$	−1.26966e37	−0.354804
$606$	6.90647e35	0.0188745
$607$	1.62584e37	0.434540	0.217270	−	0.976112i	$-0.430285\pi$
$607$	1.62584e37	0.434540	0.217270	+	0.976112i	$0.430285\pi$
$608$	1.83016e36	0.0478401
$609$	1.52717e35	0.00390440
$610$	2.05590e37	0.514103
$611$	−1.38056e36	−0.0337676
$612$	4.50361e36	0.107750
$613$	−6.57104e37	−1.53786	−0.768932	−	0.639331i	$-0.779212\pi$
$613$	−6.57104e37	−1.53786	−0.768932	+	0.639331i	$0.779212\pi$
$614$	3.68337e37	0.843281
$615$	−9.95852e35	−0.0223039
$616$	−4.35408e36	−0.0954019
$617$	4.95910e37	1.06305	0.531524	−	0.847043i	$-0.321619\pi$
$617$	4.95910e37	1.06305	0.531524	+	0.847043i	$0.321619\pi$
$618$	3.45432e36	0.0724466
$619$	4.50080e37	0.923561	0.461781	−	0.886994i	$-0.347211\pi$
$619$	4.50080e37	0.923561	0.461781	+	0.886994i	$0.347211\pi$
$620$	1.31261e37	0.263540
$621$	−6.80398e36	−0.133668
$622$	2.25798e37	0.434060
$623$	−1.59991e37	−0.300959
$624$	−8.13204e35	−0.0149695
$625$	2.22045e36	0.0400000
$626$	−3.07768e37	−0.542588
$627$	−4.82335e35	−0.00832218
$628$	4.20528e37	0.710133
$629$	1.98783e37	0.328545
$630$	1.15507e37	0.186857
$631$	3.74258e37	0.592617	0.296309	−	0.955092i	$-0.404244\pi$
$631$	3.74258e37	0.592617	0.296309	+	0.955092i	$0.404244\pi$
$632$	−7.78760e36	−0.120704
$633$	3.74452e36	0.0568127
$634$	1.29480e37	0.192308
$635$	5.07344e37	0.737661
$636$	−2.81996e36	−0.0401395
$637$	4.11344e37	0.573222
$638$	−2.29059e36	−0.0312513
$639$	2.37326e37	0.317018
$640$	−3.02231e36	−0.0395285
$641$	−1.44495e37	−0.185042	−0.0925211	−	0.995711i	$-0.529493\pi$
$641$	−1.44495e37	−0.185042	−0.0925211	+	0.995711i	$0.529493\pi$
$642$	4.16123e36	0.0521794
$643$	−2.85263e37	−0.350265	−0.175133	−	0.984545i	$-0.556035\pi$
$643$	−2.85263e37	−0.350265	−0.175133	+	0.984545i	$0.556035\pi$
$644$	2.44429e37	0.293895
$645$	−1.18460e36	−0.0139481
$646$	−3.59277e36	−0.0414277
$647$	1.04680e38	1.18210	0.591050	−	0.806635i	$-0.298713\pi$
$647$	1.04680e38	1.18210	0.591050	+	0.806635i	$0.298713\pi$
$648$	−3.15299e37	−0.348707
$649$	−6.12594e37	−0.663544
$650$	1.17989e37	0.125174
$651$	4.55487e36	0.0473296
$652$	4.84378e36	0.0492994
$653$	−1.52185e38	−1.51720	−0.758600	−	0.651556i	$-0.774116\pi$
$653$	−1.52185e38	−1.51720	−0.758600	+	0.651556i	$0.774116\pi$
$654$	6.93435e36	0.0677183
$655$	−6.62368e36	−0.0633639
$656$	−1.96670e37	−0.184304
$657$	−1.13673e38	−1.04358
$658$	−1.78048e36	−0.0160136
$659$	1.20125e38	1.05847	0.529237	−	0.848474i	$-0.322478\pi$
$659$	1.20125e38	1.05847	0.529237	+	0.848474i	$0.322478\pi$
$660$	7.96523e35	0.00687631
$661$	1.16495e36	0.00985346	0.00492673	−	0.999988i	$-0.498432\pi$
$661$	1.16495e36	0.00985346	0.00492673	+	0.999988i	$0.498432\pi$
$662$	−1.49649e38	−1.24020
$663$	1.59639e36	0.0129630
$664$	4.37582e36	0.0348169
$665$	−9.21458e36	−0.0718428
$666$	−1.39814e38	−1.06819
$667$	1.28589e37	0.0962730
$668$	4.51431e37	0.331214
$669$	1.73850e37	0.125004
$670$	−3.81110e37	−0.268560
$671$	−1.07005e38	−0.739011
$672$	−1.04877e36	−0.00709898
$673$	−7.30965e37	−0.484946	−0.242473	−	0.970158i	$-0.577959\pi$
$673$	−7.30965e37	−0.484946	−0.242473	+	0.970158i	$0.577959\pi$
$674$	−1.52596e38	−0.992283
$675$	−4.23580e36	−0.0269982
$676$	−1.73326e37	−0.108289
$677$	−1.69952e38	−1.04083	−0.520415	−	0.853913i	$-0.674223\pi$
$677$	−1.69952e38	−1.04083	−0.520415	+	0.853913i	$0.674223\pi$
$678$	3.85655e36	0.0231525
$679$	−4.06649e37	−0.239319
$680$	5.93307e36	0.0342302
$681$	4.90716e36	0.0277552
$682$	−6.83181e37	−0.378832
$683$	3.18220e38	1.73001	0.865004	−	0.501765i	$-0.167316\pi$
$683$	3.18220e38	1.73001	0.865004	+	0.501765i	$0.167316\pi$
$684$	2.52698e37	0.134693
$685$	−2.57276e37	−0.134455
$686$	1.34965e38	0.691584
$687$	−3.38850e36	−0.0170252
$688$	−2.33945e37	−0.115258
$689$	2.17415e38	1.05034
$690$	−4.47151e36	−0.0211832
$691$	2.86475e38	1.33086	0.665432	−	0.746459i	$-0.268248\pi$
$691$	2.86475e38	1.33086	0.665432	+	0.746459i	$0.268248\pi$
$692$	5.83753e37	0.265948
$693$	−6.01185e37	−0.268602
$694$	−8.17443e37	−0.358183
$695$	−9.01322e37	−0.387334
$696$	−5.51738e35	−0.00232545
$697$	3.86080e37	0.159601
$698$	1.08817e37	0.0441213
$699$	−2.02009e36	−0.00803396
$700$	1.52169e37	0.0593610
$701$	3.03977e38	1.16318	0.581590	−	0.813482i	$-0.302431\pi$
$701$	3.03977e38	1.16318	0.581590	+	0.813482i	$0.302431\pi$
$702$	−2.25081e37	−0.0844866
$703$	1.11537e38	0.410698
$704$	1.57305e37	0.0568212
$705$	3.25717e35	0.00115422
$706$	−4.15286e36	−0.0144372
$707$	−6.86727e37	−0.234219
$708$	−1.47556e37	−0.0493752
$709$	−2.29087e38	−0.752103	−0.376051	−	0.926599i	$-0.622718\pi$
$709$	−2.29087e38	−0.752103	−0.376051	+	0.926599i	$0.622718\pi$
$710$	3.12654e37	0.100711
$711$	−1.07527e38	−0.339841
$712$	5.78018e37	0.179251
$713$	3.83523e38	1.16703
$714$	2.05883e36	0.00614745
$715$	−6.14108e37	−0.179934
$716$	2.48828e38	0.715439
$717$	−4.65792e37	−0.131427
$718$	1.06150e38	0.293928
$719$	−8.47935e37	−0.230421	−0.115211	−	0.993341i	$-0.536754\pi$
$719$	−8.47935e37	−0.230421	−0.115211	+	0.993341i	$0.536754\pi$
$720$	−4.17303e37	−0.111292
$721$	−3.43472e38	−0.899010
$722$	2.55097e38	0.655320
$723$	2.84227e37	0.0716636
$724$	1.06137e38	0.262661
$725$	8.00527e36	0.0194452
$726$	1.59174e37	0.0379515
$727$	6.68474e37	0.156448	0.0782240	−	0.996936i	$-0.475075\pi$
$727$	6.68474e37	0.156448	0.0782240	+	0.996936i	$0.475075\pi$
$728$	8.08589e37	0.185761
$729$	−4.31297e38	−0.972645
$730$	−1.49753e38	−0.331526
$731$	4.59255e37	0.0998089
$732$	−2.57745e37	−0.0549908
$733$	6.44770e38	1.35052	0.675260	−	0.737580i	$-0.264031\pi$
$733$	6.44770e38	1.35052	0.675260	+	0.737580i	$0.264031\pi$
$734$	1.74367e38	0.358564
$735$	−9.70485e36	−0.0195934
$736$	−8.83074e37	−0.175044
$737$	1.98359e38	0.386048
$738$	−2.71550e38	−0.518906
$739$	−9.08269e38	−1.70418	−0.852088	−	0.523398i	$-0.824664\pi$
$739$	−9.08269e38	−1.70418	−0.852088	+	0.523398i	$0.824664\pi$
$740$	−1.84191e38	−0.339344
$741$	8.95737e36	0.0162045
$742$	2.80396e38	0.498102
$743$	2.09598e38	0.365627	0.182813	−	0.983148i	$-0.441480\pi$
$743$	2.09598e38	0.365627	0.182813	+	0.983148i	$0.441480\pi$
$744$	−1.64559e37	−0.0281894
$745$	−2.33189e38	−0.392282
$746$	3.47331e38	0.573812
$747$	6.04187e37	0.0980264
$748$	−3.08803e37	−0.0492050
$749$	−4.13761e38	−0.647509
$750$	−2.78373e36	−0.00427858
$751$	−5.96152e38	−0.899949	−0.449975	−	0.893041i	$-0.648567\pi$
$751$	−5.96152e38	−0.899949	−0.449975	+	0.893041i	$0.648567\pi$
$752$	6.43255e36	0.00953767
$753$	−2.62359e37	−0.0382088
$754$	4.25382e37	0.0608507
$755$	−1.08398e37	−0.0152313
$756$	−2.90282e37	−0.0400660
$757$	−7.52761e38	−1.02062	−0.510309	−	0.859991i	$-0.670469\pi$
$757$	−7.52761e38	−1.02062	−0.510309	+	0.859991i	$0.670469\pi$
$758$	2.07924e38	0.276931
$759$	2.32732e37	0.0304503
$760$	3.32905e37	0.0427895
$761$	−4.68849e37	−0.0592025	−0.0296013	−	0.999562i	$-0.509424\pi$
$761$	−4.68849e37	−0.0592025	−0.0296013	+	0.999562i	$0.509424\pi$
$762$	−6.36047e37	−0.0789036
$763$	−6.89500e38	−0.840336
$764$	−5.80823e38	−0.695478
$765$	8.19202e37	0.0963744
$766$	1.12777e39	1.30356
$767$	1.13764e39	1.29201
$768$	3.78902e36	0.00422814
$769$	−1.28141e39	−1.40502	−0.702510	−	0.711674i	$-0.747937\pi$
$769$	−1.28141e39	−1.40502	−0.702510	+	0.711674i	$0.747937\pi$
$770$	−7.92003e37	−0.0853300
$771$	8.46184e37	0.0895840
$772$	1.72452e38	0.179405
$773$	1.05565e39	1.07918	0.539591	−	0.841927i	$-0.318579\pi$
$773$	1.05565e39	1.07918	0.539591	+	0.841927i	$0.318579\pi$
$774$	−3.23017e38	−0.324506
$775$	2.38761e38	0.235717
$776$	1.46915e38	0.142538
$777$	−6.39161e37	−0.0609434
$778$	−1.08033e39	−1.01236
$779$	2.16630e38	0.199509
$780$	−1.47921e37	−0.0133891
$781$	−1.62729e38	−0.144769
$782$	1.73355e38	0.151581
$783$	−1.52711e37	−0.0131247
$784$	−1.91660e38	−0.161907
$785$	7.64936e38	0.635162
$786$	8.30398e36	0.00677769
$787$	−2.14383e39	−1.72001	−0.860006	−	0.510283i	$-0.829540\pi$
$787$	−2.14383e39	−1.72001	−0.860006	+	0.510283i	$0.829540\pi$
$788$	−9.61868e38	−0.758598
$789$	1.41621e38	0.109796
$790$	−1.41656e38	−0.107961
$791$	−3.83466e38	−0.287306
$792$	2.17197e38	0.159979
$793$	1.98717e39	1.43896
$794$	−5.33418e38	−0.379744
$795$	−5.12948e37	−0.0359019
$796$	−9.92724e38	−0.683128
$797$	2.60844e39	1.76479	0.882395	−	0.470510i	$-0.155930\pi$
$797$	2.60844e39	1.76479	0.882395	+	0.470510i	$0.155930\pi$
$798$	1.15521e37	0.00768463
$799$	−1.26277e37	−0.00825927
$800$	−5.49756e37	−0.0353553
$801$	7.98092e38	0.504678
$802$	7.88514e38	0.490293
$803$	7.79432e38	0.476561
$804$	4.77790e37	0.0287263
$805$	4.44613e38	0.262868
$806$	1.26872e39	0.737639
$807$	−2.03532e38	−0.116370
$808$	2.48101e38	0.139500
$809$	3.01667e39	1.66810	0.834051	−	0.551688i	$-0.186016\pi$
$809$	3.01667e39	1.66810	0.834051	+	0.551688i	$0.186016\pi$
$810$	−5.73526e38	−0.311893
$811$	−6.69658e38	−0.358155	−0.179078	−	0.983835i	$-0.557311\pi$
$811$	−6.69658e38	−0.358155	−0.179078	+	0.983835i	$0.557311\pi$
$812$	5.48606e37	0.0288572
$813$	1.84249e38	0.0953196
$814$	9.58673e38	0.487799
$815$	8.81078e37	0.0440947
$816$	−7.43817e36	−0.00366141
$817$	2.57688e38	0.124766
$818$	−2.54038e39	−1.20984
$819$	1.11645e39	0.523006
$820$	−3.57740e38	−0.164847
$821$	−1.05326e39	−0.477422	−0.238711	−	0.971091i	$-0.576725\pi$
$821$	−1.05326e39	−0.477422	−0.238711	+	0.971091i	$0.576725\pi$
$822$	3.22542e37	0.0143819
$823$	2.68231e38	0.117655	0.0588276	−	0.998268i	$-0.481264\pi$
$823$	2.68231e38	0.117655	0.0588276	+	0.998268i	$0.481264\pi$
$824$	1.24090e39	0.535449
$825$	1.44887e37	0.00615036
$826$	1.46719e39	0.612710
$827$	−2.78651e39	−1.14482	−0.572409	−	0.819968i	$-0.693991\pi$
$827$	−2.78651e39	−1.14482	−0.572409	+	0.819968i	$0.693991\pi$
$828$	−1.21930e39	−0.492833
$829$	3.50578e39	1.39412	0.697058	−	0.717015i	$-0.254492\pi$
$829$	3.50578e39	1.39412	0.697058	+	0.717015i	$0.254492\pi$
$830$	7.95957e37	0.0311412
$831$	9.74867e37	0.0375259
$832$	−2.92128e38	−0.110639
$833$	3.76246e38	0.140205
$834$	1.12997e38	0.0414310
$835$	8.21148e38	0.296247
$836$	−1.73270e38	−0.0615088
$837$	−4.55470e38	−0.159099
$838$	−1.72923e39	−0.594371
$839$	−3.34496e39	−1.13137	−0.565685	−	0.824621i	$-0.691388\pi$
$839$	−3.34496e39	−1.13137	−0.565685	+	0.824621i	$0.691388\pi$
$840$	−1.90771e37	−0.00634952
$841$	−3.02427e39	−0.990547
$842$	−3.89068e39	−1.25404
$843$	2.06322e38	0.0654446
$844$	1.34514e39	0.419900
$845$	−3.15279e38	−0.0968566
$846$	8.88168e37	0.0268532
$847$	−1.58271e39	−0.470950
$848$	−1.01302e39	−0.296669
$849$	2.83040e38	0.0815820
$850$	1.07922e38	0.0306164
$851$	−5.38178e39	−1.50272
$852$	−3.91968e37	−0.0107725
$853$	−5.83249e39	−1.57776	−0.788882	−	0.614545i	$-0.789340\pi$
$853$	−5.83249e39	−1.57776	−0.788882	+	0.614545i	$0.789340\pi$
$854$	2.56282e39	0.682396
$855$	4.59655e38	0.120473
$856$	1.49484e39	0.385655
$857$	−3.39841e39	−0.863048	−0.431524	−	0.902102i	$-0.642024\pi$
$857$	−3.39841e39	−0.863048	−0.431524	+	0.902102i	$0.642024\pi$
$858$	7.69895e37	0.0192466
$859$	4.28955e39	1.05561	0.527805	−	0.849365i	$-0.323015\pi$
$859$	4.28955e39	1.05561	0.527805	+	0.849365i	$0.323015\pi$
$860$	−4.25544e38	−0.103090
$861$	−1.24139e38	−0.0296051
$862$	4.07568e39	0.956869
$863$	−1.58857e39	−0.367165	−0.183583	−	0.983004i	$-0.558770\pi$
$863$	−1.58857e39	−0.367165	−0.183583	+	0.983004i	$0.558770\pi$
$864$	1.04873e38	0.0238633
$865$	1.06184e39	0.237871
$866$	−1.21572e39	−0.268128
$867$	−2.96948e38	−0.0644797
$868$	1.63625e39	0.349810
$869$	7.37286e38	0.155192
$870$	−1.00360e37	−0.00207995
$871$	−3.68369e39	−0.751689
$872$	2.49103e39	0.500503
$873$	2.02851e39	0.401314
$874$	9.72697e38	0.189484
$875$	2.76793e38	0.0530941
$876$	1.87743e38	0.0354615
$877$	2.78657e39	0.518293	0.259147	−	0.965838i	$-0.416559\pi$
$877$	2.78657e39	0.518293	0.259147	+	0.965838i	$0.416559\pi$
$878$	−3.18585e39	−0.583511
$879$	2.62612e38	0.0473657
$880$	2.86135e38	0.0508224
$881$	1.86266e39	0.325806	0.162903	−	0.986642i	$-0.447914\pi$
$881$	1.86266e39	0.325806	0.162903	+	0.986642i	$0.447914\pi$
$882$	−2.64633e39	−0.455846
$883$	−1.12897e39	−0.191520	−0.0957601	−	0.995404i	$-0.530528\pi$
$883$	−1.12897e39	−0.191520	−0.0957601	+	0.995404i	$0.530528\pi$
$884$	5.73472e38	0.0958091
$885$	−2.68403e38	−0.0441625
$886$	6.21991e39	1.00793
$887$	−3.48784e39	−0.556656	−0.278328	−	0.960486i	$-0.589780\pi$
$887$	−3.48784e39	−0.556656	−0.278328	+	0.960486i	$0.589780\pi$
$888$	2.30917e38	0.0362978
$889$	6.32437e39	0.979136
$890$	1.05141e39	0.160327
$891$	2.98507e39	0.448338
$892$	6.24522e39	0.923894
$893$	−7.08540e37	−0.0103245
$894$	2.92345e38	0.0419603
$895$	4.52615e39	0.639908
$896$	−3.76751e38	−0.0524682
$897$	−4.32202e38	−0.0592911
$898$	−3.84888e37	−0.00520121
$899$	8.60796e38	0.114589
$900$	−7.59070e38	−0.0995423
$901$	1.98864e39	0.256904
$902$	1.86196e39	0.236963
$903$	−1.47668e38	−0.0185140
$904$	1.38539e39	0.171119
$905$	1.93062e39	0.234931
$906$	1.35896e37	0.00162921
$907$	−3.51472e39	−0.415138	−0.207569	−	0.978220i	$-0.566555\pi$
$907$	−3.51472e39	−0.415138	−0.207569	+	0.978220i	$0.566555\pi$
$908$	1.76280e39	0.205137
$909$	3.42563e39	0.392761
$910$	1.47081e39	0.166150
$911$	9.61927e38	0.107064	0.0535321	−	0.998566i	$-0.482952\pi$
$911$	9.61927e38	0.107064	0.0535321	+	0.998566i	$0.482952\pi$
$912$	−4.17356e37	−0.00457696
$913$	−4.14277e38	−0.0447647
$914$	−8.79869e39	−0.936795
$915$	−4.68835e38	−0.0491853
$916$	−1.21725e39	−0.125832
$917$	−8.25684e38	−0.0841062
$918$	−2.05876e38	−0.0206647
$919$	−4.28853e39	−0.424179	−0.212089	−	0.977250i	$-0.568027\pi$
$919$	−4.28853e39	−0.424179	−0.212089	+	0.977250i	$0.568027\pi$
$920$	−1.60630e39	−0.156564
$921$	−8.39967e38	−0.0806784
$922$	−7.53715e39	−0.713411
$923$	3.02202e39	0.281886
$924$	9.92918e37	0.00912729
$925$	−3.35042e39	−0.303519
$926$	−4.41279e39	−0.393972
$927$	1.71336e40	1.50755
$928$	−1.98201e38	−0.0171873
$929$	−2.10447e40	−1.79858	−0.899290	−	0.437353i	$-0.855916\pi$
$929$	−2.10447e40	−1.79858	−0.899290	+	0.437353i	$0.855916\pi$
$930$	−2.99330e38	−0.0252134
$931$	2.11112e39	0.175264
$932$	−7.25679e38	−0.0593786
$933$	−5.14916e38	−0.0415274
$934$	3.70700e39	0.294673
$935$	−5.61709e38	−0.0440103
$936$	−4.03352e39	−0.311502
$937$	1.07956e40	0.821795	0.410897	−	0.911682i	$-0.365215\pi$
$937$	1.07956e40	0.821795	0.410897	+	0.911682i	$0.365215\pi$
$938$	−4.75078e39	−0.356473
$939$	7.01844e38	0.0519105
$940$	1.17007e38	0.00853076
$941$	−6.73545e39	−0.484069	−0.242034	−	0.970268i	$-0.577815\pi$
$941$	−6.73545e39	−0.484069	−0.242034	+	0.970268i	$0.577815\pi$
$942$	−9.58985e38	−0.0679399
$943$	−1.04526e40	−0.729991
$944$	−5.30067e39	−0.364930
$945$	−5.28020e38	−0.0358361
$946$	2.21486e39	0.148189
$947$	1.10409e40	0.728249	0.364124	−	0.931350i	$-0.381368\pi$
$947$	1.10409e40	0.728249	0.364124	+	0.931350i	$0.381368\pi$
$948$	1.77591e38	0.0115480
$949$	−1.44747e40	−0.927930
$950$	6.05551e38	0.0382721
$951$	−2.95270e38	−0.0183985
$952$	7.39595e38	0.0454355
$953$	1.05932e40	0.641612	0.320806	−	0.947145i	$-0.396046\pi$
$953$	1.05932e40	0.641612	0.320806	+	0.947145i	$0.396046\pi$
$954$	−1.39871e40	−0.835267
$955$	−1.05651e40	−0.622055
$956$	−1.67326e40	−0.971367
$957$	5.22354e37	0.00298988
$958$	1.72490e40	0.973487
$959$	−3.20711e39	−0.178469
$960$	6.89218e37	0.00378177
$961$	7.19098e39	0.389065
$962$	−1.78034e40	−0.949814
$963$	2.06399e40	1.08581
$964$	1.02103e40	0.529662
$965$	3.13689e39	0.160465
$966$	−5.57402e38	−0.0281176
$967$	9.48098e39	0.471624	0.235812	−	0.971799i	$-0.424225\pi$
$967$	9.48098e39	0.471624	0.235812	+	0.971799i	$0.424225\pi$
$968$	5.71803e39	0.280497
$969$	8.19307e37	0.00396347
$970$	2.67236e39	0.127490
$971$	1.33762e40	0.629324	0.314662	−	0.949204i	$-0.398109\pi$
$971$	1.33762e40	0.629324	0.314662	+	0.949204i	$0.398109\pi$
$972$	2.17370e39	0.100857
$973$	−1.12356e40	−0.514128
$974$	−1.14606e40	−0.517204
$975$	−2.69067e38	−0.0119756
$976$	−9.25897e39	−0.406434
$977$	−2.56073e40	−1.10863	−0.554317	−	0.832306i	$-0.687020\pi$
$977$	−2.56073e40	−1.10863	−0.554317	+	0.832306i	$0.687020\pi$
$978$	−1.10459e38	−0.00471657
$979$	−5.47234e39	−0.230466
$980$	−3.48628e39	−0.144814
$981$	3.43947e40	1.40916
$982$	1.46388e40	0.591563
$983$	1.03636e39	0.0413085	0.0206543	−	0.999787i	$-0.493425\pi$
$983$	1.03636e39	0.0413085	0.0206543	+	0.999787i	$0.493425\pi$
$984$	4.48492e38	0.0176328
$985$	−1.74963e40	−0.678511
$986$	3.89086e38	0.0148836
$987$	4.06027e37	0.00153205
$988$	3.21776e39	0.119766
$989$	−1.24337e40	−0.456511
$990$	3.95079e39	0.143090
$991$	4.36938e40	1.56108	0.780541	−	0.625104i	$-0.214944\pi$
$991$	4.36938e40	1.56108	0.780541	+	0.625104i	$0.214944\pi$
$992$	−5.91145e39	−0.208347
$993$	3.41264e39	0.118652
$994$	3.89743e39	0.133679
$995$	−1.80575e40	−0.611008
$996$	−9.97875e37	−0.00333100
$997$	−3.43978e40	−1.13278	−0.566391	−	0.824137i	$-0.691661\pi$
$997$	−3.43978e40	−1.13278	−0.566391	+	0.824137i	$0.691661\pi$
$998$	4.12766e40	1.34104
$999$	6.39138e39	0.204862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.a.a.1.2	✓	2
5.2	odd	4		50.28.b.e.49.1		4
5.3	odd	4		50.28.b.e.49.4		4
5.4	even	2		50.28.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.a.1.2	✓	2	1.1	even	1	trivial
50.28.a.e.1.1		2	5.4	even	2
50.28.b.e.49.1		4	5.2	odd	4
50.28.b.e.49.4		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)

\(f(q)\)	\(=\)	\(q-8192.00 q^{2} +186813. q^{3} +6.71089e7 q^{4} +1.22070e9 q^{5} -1.53037e9 q^{6} +1.52169e11 q^{7} -5.49756e11 q^{8} -7.59070e12 q^{9} -1.00000e13 q^{10} +5.20477e13 q^{11} +1.25368e13 q^{12} -9.66570e14 q^{13} -1.24656e15 q^{14} +2.28043e14 q^{15} +4.50360e15 q^{16} -8.84096e15 q^{17} +6.21830e16 q^{18} -4.96067e16 q^{19} +8.19200e16 q^{20} +2.84270e16 q^{21} -4.26375e17 q^{22} +2.39358e18 q^{23} -1.02701e17 q^{24} +1.49012e18 q^{25} +7.91814e18 q^{26} -2.84260e18 q^{27} +1.02119e19 q^{28} +5.37225e18 q^{29} -1.86813e18 q^{30} +1.60230e20 q^{31} -3.68935e19 q^{32} +9.72319e18 q^{33} +7.24251e19 q^{34} +1.85753e20 q^{35} -5.09403e20 q^{36} -2.24843e21 q^{37} +4.06378e20 q^{38} -1.80568e20 q^{39} -6.71089e20 q^{40} -4.36695e21 q^{41} -2.32874e20 q^{42} -5.19463e21 q^{43} +3.49286e21 q^{44} -9.26599e21 q^{45} -1.96082e22 q^{46} +1.42831e21 q^{47} +8.41330e20 q^{48} -4.25571e22 q^{49} -1.22070e22 q^{50} -1.65160e21 q^{51} -6.48654e22 q^{52} -2.24935e23 q^{53} +2.32866e22 q^{54} +6.35348e22 q^{55} -8.36555e22 q^{56} -9.26717e21 q^{57} -4.40094e22 q^{58} -1.17699e24 q^{59} +1.53037e22 q^{60} -2.05590e24 q^{61} -1.31261e24 q^{62} -1.15507e24 q^{63} +3.02231e23 q^{64} -1.17989e24 q^{65} -7.96523e22 q^{66} +3.81110e24 q^{67} -5.93307e23 q^{68} +4.47151e23 q^{69} -1.52169e24 q^{70} -3.12654e24 q^{71} +4.17303e24 q^{72} +1.49753e25 q^{73} +1.84191e25 q^{74} +2.78373e23 q^{75} -3.32905e24 q^{76} +7.92003e24 q^{77} +1.47921e24 q^{78} +1.41656e25 q^{79} +5.49756e24 q^{80} +5.73526e25 q^{81} +3.57740e25 q^{82} -7.95957e24 q^{83} +1.90771e24 q^{84} -1.07922e25 q^{85} +4.25544e25 q^{86} +1.00360e24 q^{87} -2.86135e25 q^{88} -1.05141e26 q^{89} +7.59070e25 q^{90} -1.47081e26 q^{91} +1.60630e26 q^{92} +2.99330e25 q^{93} -1.17007e25 q^{94} -6.05551e25 q^{95} -6.89218e24 q^{96} -2.67236e26 q^{97} +3.48628e26 q^{98} -3.95079e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16384 q^{2} - 3340644 q^{3} + 134217728 q^{4} + 2441406250 q^{5} + 27366555648 q^{6} - 58706842292 q^{7} - 1099511627776 q^{8} - 2773343978406 q^{9} - 20000000000000 q^{10} - 148584207397296 q^{11}+ \cdots - 13\!\cdots\!12 q^{99}+O(q^{100}) \) 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

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Database

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