LMFDB - Embedded newform 49.26.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} - 102767646 x^{14} - 8353831787 x^{13} + \cdots - 19\!\cdots\!25 $ x^16 - 7x^15 - 102767646x^14 - 8353831787x^13 + 4185677643993650x^12 + 562220204331364005x^11 - 86550668488721547269166x^10 - 13503515603113660531891071x^9 + 965826847827056947570287718668x^8 + 141116151744976015884635882704475x^7 - 5675610476525345365812557283872525546x^6 - 593990079927536831972725284276336402609x^5 + 15609742817644324006868027509950928439202734x^4 + 683352175430176911712808313009743940208537543x^3 - 14770680754658171625578497787051039244458614700106x^2 - 1172311978858441138365483619399458802951554523682085*x - 19070924863597306950463678441239105954656943770460525
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{65}\cdot 3^{19}\cdot 5^{9}\cdot 7^{31} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-3416.50$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7087.00 q^{2} +1.56615e6 q^{3} +1.66712e7 q^{4} +7.06414e7 q^{5} +1.10993e10 q^{6} -1.19652e11 q^{8} +1.60553e12 q^{9} +O(q^{10})$	\(q+7087.00 q^{2} +1.56615e6 q^{3} +1.66712e7 q^{4} +7.06414e7 q^{5} +1.10993e10 q^{6} -1.19652e11 q^{8} +1.60553e12 q^{9} +5.00636e11 q^{10} -9.77647e12 q^{11} +2.61095e13 q^{12} -1.48152e14 q^{13} +1.10635e14 q^{15} -1.40736e15 q^{16} +1.69008e15 q^{17} +1.13784e16 q^{18} +4.74456e15 q^{19} +1.17768e15 q^{20} -6.92859e16 q^{22} +2.62589e16 q^{23} -1.87392e17 q^{24} -2.93033e17 q^{25} -1.04996e18 q^{26} +1.18751e18 q^{27} -1.29880e18 q^{29} +7.84069e17 q^{30} +8.61295e17 q^{31} -5.95915e18 q^{32} -1.53114e19 q^{33} +1.19776e19 q^{34} +2.67660e19 q^{36} -5.29791e19 q^{37} +3.36247e19 q^{38} -2.32028e20 q^{39} -8.45235e18 q^{40} +2.47110e20 q^{41} -3.01446e20 q^{43} -1.62985e20 q^{44} +1.13416e20 q^{45} +1.86097e20 q^{46} -1.34257e21 q^{47} -2.20414e21 q^{48} -2.07673e21 q^{50} +2.64691e21 q^{51} -2.46988e21 q^{52} +9.39086e20 q^{53} +8.41588e21 q^{54} -6.90623e20 q^{55} +7.43067e21 q^{57} -9.20462e21 q^{58} +1.96529e21 q^{59} +1.84441e21 q^{60} +1.38068e21 q^{61} +6.10400e21 q^{62} +4.99073e21 q^{64} -1.04657e22 q^{65} -1.08512e23 q^{66} -1.55703e22 q^{67} +2.81756e22 q^{68} +4.11252e22 q^{69} -2.34235e23 q^{71} -1.92104e23 q^{72} -1.63638e23 q^{73} -3.75463e23 q^{74} -4.58933e23 q^{75} +7.90975e22 q^{76} -1.64439e24 q^{78} +1.09298e21 q^{79} -9.94181e22 q^{80} +4.99470e23 q^{81} +1.75127e24 q^{82} +8.71053e23 q^{83} +1.19389e23 q^{85} -2.13635e24 q^{86} -2.03412e24 q^{87} +1.16977e24 q^{88} +1.89918e24 q^{89} +8.03783e23 q^{90} +4.37767e23 q^{92} +1.34891e24 q^{93} -9.51478e24 q^{94} +3.35162e23 q^{95} -9.33291e24 q^{96} -5.81746e24 q^{97} -1.56964e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9}+O(q^{10}) $ 16 * q + 4050 * q^2 - 531440 * q^3 + 286295596 * q^4 - 288173088 * q^5 - 6531645442 * q^6 + 137183373360 * q^8 + 5146896583216 * q^9	$ 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9} + 918803280822 q^{10} - 253661467680 q^{11} - 59498382182260 q^{12} + 68129645475920 q^{13} - 14\!\cdots\!08 q^{15}+ \cdots + 21\!\cdots\!28 q^{99}+O(q^{100}) $ 16 * q + 4050 * q^2 - 531440 * q^3 + 286295596 * q^4 - 288173088 * q^5 - 6531645442 * q^6 + 137183373360 * q^8 + 5146896583216 * q^9 + 918803280822 * q^10 - 253661467680 * q^11 - 59498382182260 * q^12 + 68129645475920 * q^13 - 1404332214639008 * q^15 + 5327562569765872 * q^16 - 5022112861130400 * q^17 - 1957025270033980 * q^18 - 10588631642557696 * q^19 + 12365603244583092 * q^20 - 94651471756449330 * q^22 - 20610047702550960 * q^23 - 573793671932159616 * q^24 + 958211520923613472 * q^25 - 2724774668939531124 * q^26 - 1103054793716345120 * q^27 - 4344632493050616336 * q^29 + 2619504629356224458 * q^30 - 10841379318391039264 * q^31 - 6763645131553838880 * q^32 + 11546953084647657040 * q^33 + 6541316394798823806 * q^34 + 141226019822573256728 * q^36 - 29321738000603330320 * q^37 + 70525127026788123690 * q^38 - 25840220465930531024 * q^39 + 85110519871079993136 * q^40 - 165270014614023120144 * q^41 + 215507582734291457600 * q^43 + 879888416642398340460 * q^44 - 485170985786336771600 * q^45 - 1667203425207259516686 * q^46 - 2014371898465936816800 * q^47 - 5831281959829213328560 * q^48 - 836396256472298102808 * q^50 + 7525441297042267778496 * q^51 - 6992249387859106251160 * q^52 - 8918984691607286334960 * q^53 - 34981309708344282421726 * q^54 - 32943212576578456921776 * q^55 + 28344067162748052349840 * q^57 + 26386021221286483940940 * q^58 + 10935316261765587024144 * q^59 - 139984946157807148568716 * q^60 + 17484129051186787701488 * q^61 - 131394252459900844408050 * q^62 + 165809551263124614802048 * q^64 + 60109967964600925224336 * q^65 - 61498292814044614748374 * q^66 - 218997561331718103994960 * q^67 - 482184105822238591781100 * q^68 - 407858979455444402603424 * q^69 - 278059426277993021419488 * q^71 + 332574755512105623952800 * q^72 - 181923789786333620742640 * q^73 + 788377165482644151934950 * q^74 + 66014699727433523602592 * q^75 + 631386434812602470719172 * q^76 + 155695476291097040159540 * q^78 - 438039985868556642949360 * q^79 + 1229118480867135510718416 * q^80 + 738103636463171961601504 * q^81 + 4913051673767471255932260 * q^82 + 2177700923800256297617440 * q^83 - 252838841319017848403856 * q^85 - 5848093469680723949747688 * q^86 + 2195492958449506107537040 * q^87 + 10064215655338142337197760 * q^88 - 449697822243925695740496 * q^89 + 20875370857270558016637452 * q^90 - 9256057866243149752728540 * q^92 + 2539354660954665131215920 * q^93 + 1689612490320614160295890 * q^94 + 2244103526711501036678160 * q^95 + 3851732620967552391601888 * q^96 - 8537037301155842764342960 * q^97 + 2136810407699986619975728 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	7087.00	1.22345	0.611727	−	0.791069i	$-0.290475\pi$
$2$	7087.00	1.22345	0.611727	+	0.791069i	$0.290475\pi$
$3$	1.56615e6	1.70144	0.850720	−	0.525619i	$-0.176166\pi$
$3$	1.56615e6	1.70144	0.850720	+	0.525619i	$0.176166\pi$
$4$	1.66712e7	0.496841
$5$	7.06414e7	0.129400	0.0647000	−	0.997905i	$-0.479391\pi$
$5$	7.06414e7	0.129400	0.0647000	+	0.997905i	$0.479391\pi$
$6$	1.10993e10	2.08163
$7$	0	0
$7$	0	0
$8$	−1.19652e11	−0.615593
$9$	1.60553e12	1.89490
$10$	5.00636e11	0.158315
$11$	−9.77647e12	−0.939233	−0.469617	−	0.882871i	$-0.655608\pi$
$11$	−9.77647e12	−0.939233	−0.469617	+	0.882871i	$0.655608\pi$
$12$	2.61095e13	0.845344
$13$	−1.48152e14	−1.76367	−0.881834	−	0.471559i	$-0.843691\pi$
$13$	−1.48152e14	−1.76367	−0.881834	+	0.471559i	$0.843691\pi$
$14$	0	0
$15$	1.10635e14	0.220166
$16$	−1.40736e15	−1.24999
$17$	1.69008e15	0.703550	0.351775	−	0.936085i	$-0.385578\pi$
$17$	1.69008e15	0.703550	0.351775	+	0.936085i	$0.385578\pi$
$18$	1.13784e16	2.31832
$19$	4.74456e15	0.491785	0.245893	−	0.969297i	$-0.420919\pi$
$19$	4.74456e15	0.491785	0.245893	+	0.969297i	$0.420919\pi$
$20$	1.17768e15	0.0642911
$21$	0	0
$22$	−6.92859e16	−1.14911
$23$	2.62589e16	0.249849	0.124925	−	0.992166i	$-0.460131\pi$
$23$	2.62589e16	0.249849	0.124925	+	0.992166i	$0.460131\pi$
$24$	−1.87392e17	−1.04739
$25$	−2.93033e17	−0.983256
$26$	−1.04996e18	−2.15777
$27$	1.18751e18	1.52261
$28$	0	0
$29$	−1.29880e18	−0.681661	−0.340830	−	0.940125i	$-0.610708\pi$
$29$	−1.29880e18	−0.681661	−0.340830	+	0.940125i	$0.610708\pi$
$30$	7.84069e17	0.269363
$31$	8.61295e17	0.196395	0.0981976	−	0.995167i	$-0.468692\pi$
$31$	8.61295e17	0.196395	0.0981976	+	0.995167i	$0.468692\pi$
$32$	−5.95915e18	−0.913713
$33$	−1.53114e19	−1.59805
$34$	1.19776e19	0.860761
$35$	0	0
$36$	2.67660e19	0.941462
$37$	−5.29791e19	−1.32307	−0.661535	−	0.749914i	$-0.730095\pi$
$37$	−5.29791e19	−1.32307	−0.661535	+	0.749914i	$0.730095\pi$
$38$	3.36247e19	0.601677
$39$	−2.32028e20	−3.00078
$40$	−8.45235e18	−0.0796576
$41$	2.47110e20	1.71038	0.855189	−	0.518316i	$-0.173441\pi$
$41$	2.47110e20	1.71038	0.855189	+	0.518316i	$0.173441\pi$
$42$	0	0
$43$	−3.01446e20	−1.15041	−0.575207	−	0.818008i	$-0.695079\pi$
$43$	−3.01446e20	−1.15041	−0.575207	+	0.818008i	$0.695079\pi$
$44$	−1.62985e20	−0.466649
$45$	1.13416e20	0.245200
$46$	1.86097e20	0.305679
$47$	−1.34257e21	−1.68544	−0.842719	−	0.538354i	$-0.819046\pi$
$47$	−1.34257e21	−1.68544	−0.842719	+	0.538354i	$0.819046\pi$
$48$	−2.20414e21	−2.12678
$49$	0	0
$50$	−2.07673e21	−1.20297
$51$	2.64691e21	1.19705
$52$	−2.46988e21	−0.876262
$53$	9.39086e20	0.262577	0.131289	−	0.991344i	$-0.458089\pi$
$53$	9.39086e20	0.262577	0.131289	+	0.991344i	$0.458089\pi$
$54$	8.41588e21	1.86285
$55$	−6.90623e20	−0.121537
$56$	0	0
$57$	7.43067e21	0.836743
$58$	−9.20462e21	−0.833981
$59$	1.96529e21	0.143806	0.0719029	−	0.997412i	$-0.477093\pi$
$59$	1.96529e21	0.143806	0.0719029	+	0.997412i	$0.477093\pi$
$60$	1.84441e21	0.109388
$61$	1.38068e21	0.0665993	0.0332996	−	0.999445i	$-0.489398\pi$
$61$	1.38068e21	0.0665993	0.0332996	+	0.999445i	$0.489398\pi$
$62$	6.10400e21	0.240281
$63$	0	0
$64$	4.99073e21	0.132104
$65$	−1.04657e22	−0.228219
$66$	−1.08512e23	−1.95514
$67$	−1.55703e22	−0.232467	−0.116234	−	0.993222i	$-0.537082\pi$
$67$	−1.55703e22	−0.232467	−0.116234	+	0.993222i	$0.537082\pi$
$68$	2.81756e22	0.349552
$69$	4.11252e22	0.425103
$70$	0	0
$71$	−2.34235e23	−1.69403	−0.847017	−	0.531565i	$-0.821604\pi$
$71$	−2.34235e23	−1.69403	−0.847017	+	0.531565i	$0.821604\pi$
$72$	−1.92104e23	−1.16648
$73$	−1.63638e23	−0.836275	−0.418138	−	0.908384i	$-0.637317\pi$
$73$	−1.63638e23	−0.836275	−0.418138	+	0.908384i	$0.637317\pi$
$74$	−3.75463e23	−1.61872
$75$	−4.58933e23	−1.67295
$76$	7.90975e22	0.244339
$77$	0	0
$78$	−1.64439e24	−3.67131
$79$	1.09298e21	0.00208100	0.00104050	−	0.999999i	$-0.499669\pi$
$79$	1.09298e21	0.00208100	0.00104050	+	0.999999i	$0.499669\pi$
$80$	−9.94181e22	−0.161749
$81$	4.99470e23	0.695739
$82$	1.75127e24	2.09257
$83$	8.71053e23	0.894475	0.447238	−	0.894415i	$-0.352408\pi$
$83$	8.71053e23	0.894475	0.447238	+	0.894415i	$0.352408\pi$
$84$	0	0
$85$	1.19389e23	0.0910393
$86$	−2.13635e24	−1.40748
$87$	−2.03412e24	−1.15980
$88$	1.16977e24	0.578185
$89$	1.89918e24	0.815061	0.407531	−	0.913192i	$-0.366390\pi$
$89$	1.89918e24	0.815061	0.407531	+	0.913192i	$0.366390\pi$
$90$	8.03783e23	0.299991
$91$	0	0
$92$	4.37767e23	0.124135
$93$	1.34891e24	0.334155
$94$	−9.51478e24	−2.06206
$95$	3.35162e23	0.0636370
$96$	−9.33291e24	−1.55463
$97$	−5.81746e24	−0.851308	−0.425654	−	0.904886i	$-0.639956\pi$
$97$	−5.81746e24	−0.851308	−0.425654	+	0.904886i	$0.639956\pi$
$98$	0	0
$99$	−1.56964e25	−1.77975
$100$	−4.88521e24	−0.488521
$101$	4.19327e24	0.370284	0.185142	−	0.982712i	$-0.440725\pi$
$101$	4.19327e24	0.370284	0.185142	+	0.982712i	$0.440725\pi$
$102$	1.87586e25	1.46453
$103$	−1.95543e25	−1.35138	−0.675690	−	0.737186i	$-0.736154\pi$
$103$	−1.95543e25	−1.35138	−0.675690	+	0.737186i	$0.736154\pi$
$104$	1.77267e25	1.08570
$105$	0	0
$106$	6.65531e24	0.321251
$107$	4.40077e25	1.88900	0.944499	−	0.328514i	$-0.106548\pi$
$107$	4.40077e25	1.88900	0.944499	+	0.328514i	$0.106548\pi$
$108$	1.97972e25	0.756497
$109$	−3.83580e25	−1.30624	−0.653122	−	0.757253i	$-0.726541\pi$
$109$	−3.83580e25	−1.30624	−0.653122	+	0.757253i	$0.726541\pi$
$110$	−4.89445e24	−0.148695
$111$	−8.29730e25	−2.25113
$112$	0	0
$113$	−7.29362e24	−0.158293	−0.0791467	−	0.996863i	$-0.525220\pi$
$113$	−7.29362e24	−0.158293	−0.0791467	+	0.996863i	$0.525220\pi$
$114$	5.26612e25	1.02372
$115$	1.85496e24	0.0323305
$116$	−2.16526e25	−0.338677
$117$	−2.37863e26	−3.34197
$118$	1.39280e25	0.175940
$119$	0	0
$120$	−1.32376e25	−0.135533
$121$	−1.27678e25	−0.117841
$122$	9.78487e24	0.0814812
$123$	3.87011e26	2.91011
$124$	1.43588e25	0.0975771
$125$	−4.17530e25	−0.256633
$126$	0	0
$127$	2.04035e26	1.02839	0.514196	−	0.857672i	$-0.328090\pi$
$127$	2.04035e26	1.02839	0.514196	+	0.857672i	$0.328090\pi$
$128$	2.35325e26	1.07534
$129$	−4.72109e26	−1.95736
$130$	−7.41704e25	−0.279215
$131$	−2.20402e26	−0.753919	−0.376959	−	0.926230i	$-0.623030\pi$
$131$	−2.20402e26	−0.753919	−0.376959	+	0.926230i	$0.623030\pi$
$132$	−2.55259e26	−0.793975
$133$	0	0
$134$	−1.10347e26	−0.284413
$135$	8.38873e25	0.197026
$136$	−2.02220e26	−0.433100
$137$	6.06697e26	1.18567	0.592837	−	0.805323i	$-0.298008\pi$
$137$	6.06697e26	1.18567	0.592837	+	0.805323i	$0.298008\pi$
$138$	2.91455e26	0.520095
$139$	8.57157e26	1.39758	0.698788	−	0.715329i	$-0.253723\pi$
$139$	8.57157e26	1.39758	0.698788	+	0.715329i	$0.253723\pi$
$140$	0	0
$141$	−2.10266e27	−2.86767
$142$	−1.66002e27	−2.07257
$143$	1.44841e27	1.65650
$144$	−2.25956e27	−2.36860
$145$	−9.17492e25	−0.0882069
$146$	−1.15971e27	−1.02314
$147$	0	0
$148$	−8.83226e26	−0.657355
$149$	1.72373e27	1.17934	0.589671	−	0.807644i	$-0.299257\pi$
$149$	1.72373e27	1.17934	0.589671	+	0.807644i	$0.299257\pi$
$150$	−3.25246e27	−2.04678
$151$	1.47861e27	0.856331	0.428165	−	0.903700i	$-0.359160\pi$
$151$	1.47861e27	0.856331	0.428165	+	0.903700i	$0.359160\pi$
$152$	−5.67693e26	−0.302739
$153$	2.71346e27	1.33316
$154$	0	0
$155$	6.08431e25	0.0254135
$156$	−3.86819e27	−1.49091
$157$	−4.45497e27	−1.58525	−0.792627	−	0.609707i	$-0.791287\pi$
$157$	−4.45497e27	−1.58525	−0.792627	+	0.609707i	$0.791287\pi$
$158$	7.74594e24	0.00254601
$159$	1.47075e27	0.446759
$160$	−4.20963e26	−0.118234
$161$	0	0
$162$	3.53975e27	0.851205
$163$	−2.66902e27	−0.594301	−0.297151	−	0.954831i	$-0.596036\pi$
$163$	−2.66902e27	−0.594301	−0.297151	+	0.954831i	$0.596036\pi$
$164$	4.11962e27	0.849786
$165$	−1.08162e27	−0.206787
$166$	6.17316e27	1.09435
$167$	−3.86218e27	−0.635151	−0.317576	−	0.948233i	$-0.602869\pi$
$167$	−3.86218e27	−0.635151	−0.317576	+	0.948233i	$0.602869\pi$
$168$	0	0
$169$	1.48928e28	2.11053
$170$	8.46113e26	0.111382
$171$	7.61750e27	0.931883
$172$	−5.02547e27	−0.571573
$173$	1.07350e28	1.13560	0.567799	−	0.823167i	$-0.307795\pi$
$173$	1.07350e28	1.13560	0.567799	+	0.823167i	$0.307795\pi$
$174$	−1.44158e28	−1.41897
$175$	0	0
$176$	1.37590e28	1.17403
$177$	3.07793e27	0.244677
$178$	1.34595e28	0.997190
$179$	9.07363e27	0.626784	0.313392	−	0.949624i	$-0.398535\pi$
$179$	9.07363e27	0.626784	0.313392	+	0.949624i	$0.398535\pi$
$180$	1.89079e27	0.121825
$181$	1.95774e28	1.17699	0.588496	−	0.808500i	$-0.299720\pi$
$181$	1.95774e28	1.17699	0.588496	+	0.808500i	$0.299720\pi$
$182$	0	0
$183$	2.16234e27	0.113315
$184$	−3.14191e27	−0.153805
$185$	−3.74252e27	−0.171205
$186$	9.55976e27	0.408823
$187$	−1.65230e28	−0.660797
$188$	−2.23822e28	−0.837394
$189$	0	0
$190$	2.37529e27	0.0778569
$191$	5.34224e27	0.163986	0.0819929	−	0.996633i	$-0.473872\pi$
$191$	5.34224e27	0.163986	0.0819929	+	0.996633i	$0.473872\pi$
$192$	7.81621e27	0.224766
$193$	−4.46018e28	−1.20195	−0.600974	−	0.799269i	$-0.705220\pi$
$193$	−4.46018e28	−1.20195	−0.600974	+	0.799269i	$0.705220\pi$
$194$	−4.12284e28	−1.04154
$195$	−1.63908e28	−0.388300
$196$	0	0
$197$	5.67147e28	1.18268	0.591341	−	0.806422i	$-0.298599\pi$
$197$	5.67147e28	1.18268	0.591341	+	0.806422i	$0.298599\pi$
$198$	−1.11240e29	−2.17744
$199$	−2.21806e28	−0.407671	−0.203835	−	0.979005i	$-0.565341\pi$
$199$	−2.21806e28	−0.407671	−0.203835	+	0.979005i	$0.565341\pi$
$200$	3.50618e28	0.605285
$201$	−2.43853e28	−0.395529
$202$	2.97177e28	0.453026
$203$	0	0
$204$	4.41271e28	0.594742
$205$	1.74562e28	0.221323
$206$	−1.38582e29	−1.65335
$207$	4.21593e28	0.473439
$208$	2.08504e29	2.20457
$209$	−4.63850e28	−0.461901
$210$	0	0
$211$	−4.57666e28	−0.404592	−0.202296	−	0.979324i	$-0.564840\pi$
$211$	−4.57666e28	−0.404592	−0.202296	+	0.979324i	$0.564840\pi$
$212$	1.56557e28	0.130459
$213$	−3.66846e29	−2.88230
$214$	3.11883e29	2.31110
$215$	−2.12946e28	−0.148864
$216$	−1.42087e29	−0.937310
$217$	0	0
$218$	−2.71843e29	−1.59813
$219$	−2.56281e29	−1.42287
$220$	−1.15135e28	−0.0603844
$221$	−2.50389e29	−1.24083
$222$	−5.88030e29	−2.75415
$223$	−3.56999e29	−1.58072	−0.790362	−	0.612640i	$-0.790108\pi$
$223$	−3.56999e29	−1.58072	−0.790362	+	0.612640i	$0.790108\pi$
$224$	0	0
$225$	−4.70472e29	−1.86317
$226$	−5.16899e28	−0.193665
$227$	−1.59840e29	−0.566711	−0.283355	−	0.959015i	$-0.591448\pi$
$227$	−1.59840e29	−0.566711	−0.283355	+	0.959015i	$0.591448\pi$
$228$	1.23878e29	0.415728
$229$	−2.57686e29	−0.818743	−0.409371	−	0.912368i	$-0.634252\pi$
$229$	−2.57686e29	−0.818743	−0.409371	+	0.912368i	$0.634252\pi$
$230$	1.31461e28	0.0395548
$231$	0	0
$232$	1.55404e29	0.419625
$233$	−4.42391e29	−1.13203	−0.566015	−	0.824395i	$-0.691515\pi$
$233$	−4.42391e29	−1.13203	−0.566015	+	0.824395i	$0.691515\pi$
$234$	−1.68573e30	−4.08875
$235$	−9.48408e28	−0.218096
$236$	3.27638e28	0.0714486
$237$	1.71176e27	0.00354070
$238$	0	0
$239$	7.09748e28	0.132169	0.0660846	−	0.997814i	$-0.478949\pi$
$239$	7.09748e28	0.132169	0.0660846	+	0.997814i	$0.478949\pi$
$240$	−1.55703e29	−0.275206
$241$	1.07042e30	1.79615	0.898074	−	0.439845i	$-0.144966\pi$
$241$	1.07042e30	1.79615	0.898074	+	0.439845i	$0.144966\pi$
$242$	−9.04852e28	−0.144174
$243$	−2.23920e29	−0.338856
$244$	2.30176e28	0.0330892
$245$	0	0
$246$	2.74275e30	3.56038
$247$	−7.02918e29	−0.867346
$248$	−1.03055e29	−0.120899
$249$	1.36420e30	1.52190
$250$	−2.95904e29	−0.313979
$251$	−4.99218e28	−0.0503929	−0.0251964	−	0.999683i	$-0.508021\pi$
$251$	−4.99218e28	−0.0503929	−0.0251964	+	0.999683i	$0.508021\pi$
$252$	0	0
$253$	−2.56719e29	−0.234667
$254$	1.44600e30	1.25819
$255$	1.86981e29	0.154898
$256$	1.50029e30	1.18352
$257$	7.11597e29	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$257$	7.11597e29	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$258$	−3.34584e30	−2.39474
$259$	0	0
$260$	−1.74476e29	−0.113388
$261$	−2.08526e30	−1.29168
$262$	−1.56199e30	−0.922385
$263$	−2.56524e29	−0.144438	−0.0722189	−	0.997389i	$-0.523008\pi$
$263$	−2.56524e29	−0.144438	−0.0722189	+	0.997389i	$0.523008\pi$
$264$	1.83203e30	0.983747
$265$	6.63383e28	0.0339775
$266$	0	0
$267$	2.97439e30	1.38678
$268$	−2.59575e29	−0.115499
$269$	−4.45536e29	−0.189226	−0.0946128	−	0.995514i	$-0.530161\pi$
$269$	−4.45536e29	−0.189226	−0.0946128	+	0.995514i	$0.530161\pi$
$270$	5.94510e29	0.241053
$271$	−3.02931e30	−1.17281	−0.586406	−	0.810017i	$-0.699458\pi$
$271$	−3.02931e30	−1.17281	−0.586406	+	0.810017i	$0.699458\pi$
$272$	−2.37855e30	−0.879431
$273$	0	0
$274$	4.29967e30	1.45062
$275$	2.86483e30	0.923506
$276$	6.85607e29	0.211209
$277$	−4.21800e30	−1.24196	−0.620982	−	0.783825i	$-0.713266\pi$
$277$	−4.21800e30	−1.24196	−0.620982	+	0.783825i	$0.713266\pi$
$278$	6.07467e30	1.70987
$279$	1.38283e30	0.372149
$280$	0	0
$281$	−9.66797e29	−0.237961	−0.118981	−	0.992897i	$-0.537963\pi$
$281$	−9.66797e29	−0.237961	−0.118981	+	0.992897i	$0.537963\pi$
$282$	−1.49015e31	−3.50846
$283$	1.01331e30	0.228250	0.114125	−	0.993466i	$-0.463594\pi$
$283$	1.01331e30	0.228250	0.114125	+	0.993466i	$0.463594\pi$
$284$	−3.90498e30	−0.841665
$285$	5.24913e29	0.108274
$286$	1.02649e31	2.02665
$287$	0	0
$288$	−9.56757e30	−1.73139
$289$	−2.91427e30	−0.505017
$290$	−6.50227e29	−0.107917
$291$	−9.11099e30	−1.44845
$292$	−2.72805e30	−0.415495
$293$	−1.66683e30	−0.243246	−0.121623	−	0.992576i	$-0.538810\pi$
$293$	−1.66683e30	−0.243246	−0.121623	+	0.992576i	$0.538810\pi$
$294$	0	0
$295$	1.38831e29	0.0186085
$296$	6.33903e30	0.814473
$297$	−1.16096e31	−1.43009
$298$	1.22160e31	1.44287
$299$	−3.89032e30	−0.440651
$300$	−7.65096e30	−0.831190
$301$	0	0
$302$	1.04789e31	1.04768
$303$	6.56727e30	0.630016
$304$	−6.67732e30	−0.614727
$305$	9.75330e28	0.00861794
$306$	1.92303e31	1.63105
$307$	5.00339e30	0.407413	0.203706	−	0.979032i	$-0.434701\pi$
$307$	5.00339e30	0.407413	0.203706	+	0.979032i	$0.434701\pi$
$308$	0	0
$309$	−3.06249e31	−2.29929
$310$	4.31195e29	0.0310923
$311$	4.17643e30	0.289268	0.144634	−	0.989485i	$-0.453800\pi$
$311$	4.17643e30	0.289268	0.144634	+	0.989485i	$0.453800\pi$
$312$	2.77626e31	1.84726
$313$	−1.88231e30	−0.120334	−0.0601669	−	0.998188i	$-0.519163\pi$
$313$	−1.88231e30	−0.120334	−0.0601669	+	0.998188i	$0.519163\pi$
$314$	−3.15724e31	−1.93949
$315$	0	0
$316$	1.82213e28	0.00103393
$317$	1.62969e31	0.888921	0.444460	−	0.895799i	$-0.353395\pi$
$317$	1.62969e31	0.888921	0.444460	+	0.895799i	$0.353395\pi$
$318$	1.04232e31	0.546590
$319$	1.26977e31	0.640238
$320$	3.52552e29	0.0170942
$321$	6.89225e31	3.21402
$322$	0	0
$323$	8.01866e30	0.345996
$324$	8.32676e30	0.345672
$325$	4.34136e31	1.73414
$326$	−1.89154e31	−0.727101
$327$	−6.00742e31	−2.22250
$328$	−2.95671e31	−1.05290
$329$	0	0
$330$	−7.66542e30	−0.252995
$331$	−2.71797e30	−0.0863764	−0.0431882	−	0.999067i	$-0.513752\pi$
$331$	−2.71797e30	−0.0863764	−0.0431882	+	0.999067i	$0.513752\pi$
$332$	1.45215e31	0.444412
$333$	−8.50593e31	−2.50708
$334$	−2.73713e31	−0.777079
$335$	−1.09991e30	−0.0300812
$336$	0	0
$337$	1.22398e31	0.310743	0.155372	−	0.987856i	$-0.450342\pi$
$337$	1.22398e31	0.310743	0.155372	+	0.987856i	$0.450342\pi$
$338$	1.05545e32	2.58213
$339$	−1.14229e31	−0.269327
$340$	1.99036e30	0.0452320
$341$	−8.42042e30	−0.184461
$342$	5.39853e31	1.14012
$343$	0	0
$344$	3.60685e31	0.708187
$345$	2.90514e30	0.0550083
$346$	7.60789e31	1.38935
$347$	7.57823e31	1.33490	0.667451	−	0.744654i	$-0.267385\pi$
$347$	7.57823e31	1.33490	0.667451	+	0.744654i	$0.267385\pi$
$348$	−3.39112e31	−0.576238
$349$	−2.92088e31	−0.478847	−0.239423	−	0.970915i	$-0.576958\pi$
$349$	−2.92088e31	−0.478847	−0.239423	+	0.970915i	$0.576958\pi$
$350$	0	0
$351$	−1.75932e32	−2.68539
$352$	5.82595e31	0.858190
$353$	3.98467e31	0.566511	0.283255	−	0.959044i	$-0.408586\pi$
$353$	3.98467e31	0.566511	0.283255	+	0.959044i	$0.408586\pi$
$354$	2.18133e31	0.299351
$355$	−1.65467e31	−0.219208
$356$	3.16616e31	0.404955
$357$	0	0
$358$	6.43049e31	0.766842
$359$	−3.34764e31	−0.385529	−0.192765	−	0.981245i	$-0.561745\pi$
$359$	−3.34764e31	−0.385529	−0.192765	+	0.981245i	$0.561745\pi$
$360$	−1.35705e31	−0.150943
$361$	−7.05657e31	−0.758147
$362$	1.38745e32	1.44000
$363$	−1.99962e31	−0.200500
$364$	0	0
$365$	−1.15596e31	−0.108214
$366$	1.53245e31	0.138635
$367$	6.50253e31	0.568534	0.284267	−	0.958745i	$-0.408250\pi$
$367$	6.50253e31	0.568534	0.284267	+	0.958745i	$0.408250\pi$
$368$	−3.69558e31	−0.312309
$369$	3.96742e32	3.24099
$370$	−2.65232e31	−0.209462
$371$	0	0
$372$	2.24880e31	0.166022
$373$	−3.43708e31	−0.245374	−0.122687	−	0.992445i	$-0.539151\pi$
$373$	−3.43708e31	−0.245374	−0.122687	+	0.992445i	$0.539151\pi$
$374$	−1.17098e32	−0.808456
$375$	−6.53913e31	−0.436646
$376$	1.60640e32	1.03754
$377$	1.92421e32	1.20222
$378$	0	0
$379$	1.36008e32	0.795378	0.397689	−	0.917520i	$-0.369812\pi$
$379$	1.36008e32	0.795378	0.397689	+	0.917520i	$0.369812\pi$
$380$	5.58755e30	0.0316174
$381$	3.19549e32	1.74975
$382$	3.78605e31	0.200629
$383$	−2.49543e32	−1.27986	−0.639928	−	0.768435i	$-0.721036\pi$
$383$	−2.49543e32	−1.27986	−0.639928	+	0.768435i	$0.721036\pi$
$384$	3.68554e32	1.82962
$385$	0	0
$386$	−3.16093e32	−1.47053
$387$	−4.83980e32	−2.17992
$388$	−9.69840e31	−0.422964
$389$	−1.97032e32	−0.832082	−0.416041	−	0.909346i	$-0.636583\pi$
$389$	−1.97032e32	−0.832082	−0.416041	+	0.909346i	$0.636583\pi$
$390$	−1.16162e32	−0.475068
$391$	4.43795e31	0.175781
$392$	0	0
$393$	−3.45182e32	−1.28275
$394$	4.01937e32	1.44696
$395$	7.72094e28	0.000269282 0
$396$	−2.61677e32	−0.884252
$397$	−2.71861e32	−0.890156	−0.445078	−	0.895492i	$-0.646824\pi$
$397$	−2.71861e32	−0.890156	−0.445078	+	0.895492i	$0.646824\pi$
$398$	−1.57194e32	−0.498767
$399$	0	0
$400$	4.12404e32	1.22906
$401$	1.01099e32	0.292040	0.146020	−	0.989282i	$-0.453354\pi$
$401$	1.01099e32	0.292040	0.146020	+	0.989282i	$0.453354\pi$
$402$	−1.72819e32	−0.483912
$403$	−1.27603e32	−0.346376
$404$	6.99068e31	0.183972
$405$	3.52832e31	0.0900286
$406$	0	0
$407$	5.17948e32	1.24267
$408$	−3.16707e32	−0.736894
$409$	4.49821e32	1.01508	0.507538	−	0.861630i	$-0.330556\pi$
$409$	4.49821e32	1.01508	0.507538	+	0.861630i	$0.330556\pi$
$410$	1.23712e32	0.270778
$411$	9.50177e32	2.01735
$412$	−3.25994e32	−0.671420
$413$	0	0
$414$	2.98783e32	0.579231
$415$	6.15324e31	0.115745
$416$	8.82864e32	1.61149
$417$	1.34243e33	2.37789
$418$	−3.28731e32	−0.565115
$419$	−5.88886e32	−0.982554	−0.491277	−	0.871004i	$-0.663470\pi$
$419$	−5.88886e32	−0.982554	−0.491277	+	0.871004i	$0.663470\pi$
$420$	0	0
$421$	3.45046e32	0.542439	0.271220	−	0.962517i	$-0.412573\pi$
$421$	3.45046e32	0.542439	0.271220	+	0.962517i	$0.412573\pi$
$422$	−3.24348e32	−0.495000
$423$	−2.15552e33	−3.19373
$424$	−1.12363e32	−0.161641
$425$	−4.95248e32	−0.691770
$426$	−2.59984e33	−3.52636
$427$	0	0
$428$	7.33662e32	0.938531
$429$	2.26842e33	2.81843
$430$	−1.50915e32	−0.182128
$431$	1.65146e33	1.93599	0.967994	−	0.250973i	$-0.0807505\pi$
$431$	1.65146e33	1.93599	0.967994	+	0.250973i	$0.0807505\pi$
$432$	−1.67126e33	−1.90325
$433$	1.17184e33	1.29649	0.648245	−	0.761432i	$-0.275503\pi$
$433$	1.17184e33	1.29649	0.648245	+	0.761432i	$0.275503\pi$
$434$	0	0
$435$	−1.43693e32	−0.150079
$436$	−6.39473e32	−0.648995
$437$	1.24587e32	0.122872
$438$	−1.81627e33	−1.74082
$439$	−5.58259e32	−0.520031	−0.260015	−	0.965604i	$-0.583728\pi$
$439$	−5.58259e32	−0.520031	−0.260015	+	0.965604i	$0.583728\pi$
$440$	8.26341e31	0.0748171
$441$	0	0
$442$	−1.77451e33	−1.51810
$443$	−1.63479e33	−1.35961	−0.679806	−	0.733392i	$-0.737936\pi$
$443$	−1.63479e33	−1.35961	−0.679806	+	0.733392i	$0.737936\pi$
$444$	−1.38326e33	−1.11845
$445$	1.34160e32	0.105469
$446$	−2.53005e33	−1.93394
$447$	2.69961e33	2.00658
$448$	0	0
$449$	−1.25741e32	−0.0883890	−0.0441945	−	0.999023i	$-0.514072\pi$
$449$	−1.25741e32	−0.0883890	−0.0441945	+	0.999023i	$0.514072\pi$
$450$	−3.33424e33	−2.27950
$451$	−2.41586e33	−1.60644
$452$	−1.21593e32	−0.0786465
$453$	2.31572e33	1.45700
$454$	−1.13279e33	−0.693345
$455$	0	0
$456$	−8.89091e32	−0.515093
$457$	7.20556e32	0.406177	0.203089	−	0.979160i	$-0.434902\pi$
$457$	7.20556e32	0.406177	0.203089	+	0.979160i	$0.434902\pi$
$458$	−1.82622e33	−1.00169
$459$	2.00698e33	1.07124
$460$	3.09244e31	0.0160631
$461$	−5.78511e32	−0.292449	−0.146224	−	0.989251i	$-0.546712\pi$
$461$	−5.78511e32	−0.292449	−0.146224	+	0.989251i	$0.546712\pi$
$462$	0	0
$463$	−1.12689e33	−0.539659	−0.269830	−	0.962908i	$-0.586967\pi$
$463$	−1.12689e33	−0.539659	−0.269830	+	0.962908i	$0.586967\pi$
$464$	1.82789e33	0.852069
$465$	9.52891e31	0.0432396
$466$	−3.13523e33	−1.38499
$467$	2.27324e32	0.0977651	0.0488825	−	0.998805i	$-0.484434\pi$
$467$	2.27324e32	0.0977651	0.0488825	+	0.998805i	$0.484434\pi$
$468$	−3.96546e33	−1.66043
$469$	0	0
$470$	−6.72137e32	−0.266830
$471$	−6.97713e33	−2.69721
$472$	−2.35150e32	−0.0885258
$473$	2.94708e33	1.08051
$474$	1.21313e31	0.00433189
$475$	−1.39031e33	−0.483551
$476$	0	0
$477$	1.50773e33	0.497557
$478$	5.02999e32	0.161703
$479$	−4.13052e31	−0.0129363	−0.00646817	−	0.999979i	$-0.502059\pi$
$479$	−4.13052e31	−0.0129363	−0.00646817	+	0.999979i	$0.502059\pi$
$480$	−6.59289e32	−0.201169
$481$	7.84899e33	2.33346
$482$	7.58609e33	2.19750
$483$	0	0
$484$	−2.12854e32	−0.0585484
$485$	−4.10953e32	−0.110159
$486$	−1.58692e33	−0.414575
$487$	6.09569e33	1.55207	0.776034	−	0.630691i	$-0.217229\pi$
$487$	6.09569e33	1.55207	0.776034	+	0.630691i	$0.217229\pi$
$488$	−1.65200e32	−0.0409980
$489$	−4.18007e33	−1.01117
$490$	0	0
$491$	2.24832e33	0.516821	0.258410	−	0.966035i	$-0.416801\pi$
$491$	2.24832e33	0.516821	0.258410	+	0.966035i	$0.416801\pi$
$492$	6.45193e33	1.44586
$493$	−2.19508e33	−0.479583
$494$	−4.98158e33	−1.06116
$495$	−1.10881e33	−0.230300
$496$	−1.21216e33	−0.245492
$497$	0	0
$498$	9.66806e33	1.86197
$499$	−1.92303e33	−0.361184	−0.180592	−	0.983558i	$-0.557801\pi$
$499$	−1.92303e33	−0.361184	−0.180592	+	0.983558i	$0.557801\pi$
$500$	−6.96073e32	−0.127506
$501$	−6.04875e33	−1.08067
$502$	−3.53796e32	−0.0616534
$503$	−2.11881e33	−0.360158	−0.180079	−	0.983652i	$-0.557635\pi$
$503$	−2.11881e33	−0.360158	−0.180079	+	0.983652i	$0.557635\pi$
$504$	0	0
$505$	2.96218e32	0.0479148
$506$	−1.81937e33	−0.287104
$507$	2.33242e34	3.59094
$508$	3.40152e33	0.510947
$509$	−5.48810e32	−0.0804359	−0.0402179	−	0.999191i	$-0.512805\pi$
$509$	−5.48810e32	−0.0804359	−0.0402179	+	0.999191i	$0.512805\pi$
$510$	1.32514e33	0.189511
$511$	0	0
$512$	2.73636e33	0.372648
$513$	5.63420e33	0.748799
$514$	5.04309e33	0.654120
$515$	−1.38134e33	−0.174868
$516$	−7.87063e33	−0.972497
$517$	1.31256e34	1.58302
$518$	0	0
$519$	1.68125e34	1.93215
$520$	1.25224e33	0.140490
$521$	−4.72187e33	−0.517181	−0.258591	−	0.965987i	$-0.583258\pi$
$521$	−4.72187e33	−0.517181	−0.258591	+	0.965987i	$0.583258\pi$
$522$	−1.47783e34	−1.58031
$523$	4.55154e33	0.475212	0.237606	−	0.971362i	$-0.423637\pi$
$523$	4.55154e33	0.475212	0.237606	+	0.971362i	$0.423637\pi$
$524$	−3.67437e33	−0.374577
$525$	0	0
$526$	−1.81799e33	−0.176713
$527$	1.45566e33	0.138174
$528$	2.15487e34	1.99754
$529$	−1.03562e34	−0.937575
$530$	4.70140e32	0.0415699
$531$	3.15532e33	0.272497
$532$	0	0
$533$	−3.66100e34	−3.01654
$534$	2.10795e34	1.69666
$535$	3.10876e33	0.244436
$536$	1.86301e33	0.143105
$537$	1.42106e34	1.06644
$538$	−3.15752e33	−0.231509
$539$	0	0
$540$	1.39850e33	0.0978906
$541$	−3.46675e33	−0.237114	−0.118557	−	0.992947i	$-0.537827\pi$
$541$	−3.46675e33	−0.237114	−0.118557	+	0.992947i	$0.537827\pi$
$542$	−2.14688e34	−1.43488
$543$	3.06611e34	2.00258
$544$	−1.00714e34	−0.642843
$545$	−2.70966e33	−0.169028
$546$	0	0
$547$	−5.02878e33	−0.299654	−0.149827	−	0.988712i	$-0.547872\pi$
$547$	−5.02878e33	−0.299654	−0.149827	+	0.988712i	$0.547872\pi$
$548$	1.01144e34	0.589091
$549$	2.21671e33	0.126199
$550$	2.03030e34	1.12987
$551$	−6.16224e33	−0.335231
$552$	−4.92069e33	−0.261690
$553$	0	0
$554$	−2.98930e34	−1.51949
$555$	−5.86133e33	−0.291295
$556$	1.42898e34	0.694372
$557$	2.28502e34	1.08568	0.542838	−	0.839838i	$-0.317350\pi$
$557$	2.28502e34	1.08568	0.542838	+	0.839838i	$0.317350\pi$
$558$	9.80013e33	0.455307
$559$	4.46600e34	2.02895
$560$	0	0
$561$	−2.58774e34	−1.12431
$562$	−6.85169e33	−0.291135
$563$	−2.84599e34	−1.18271	−0.591355	−	0.806412i	$-0.701407\pi$
$563$	−2.84599e34	−1.18271	−0.591355	+	0.806412i	$0.701407\pi$
$564$	−3.50538e34	−1.42478
$565$	−5.15231e32	−0.0204831
$566$	7.18132e33	0.279253
$567$	0	0
$568$	2.80266e34	1.04284
$569$	2.01138e34	0.732136	0.366068	−	0.930588i	$-0.380704\pi$
$569$	2.01138e34	0.732136	0.366068	+	0.930588i	$0.380704\pi$
$570$	3.72006e33	0.132469
$571$	−5.44944e34	−1.89845	−0.949227	−	0.314591i	$-0.898133\pi$
$571$	−5.44944e34	−1.89845	−0.949227	+	0.314591i	$0.898133\pi$
$572$	2.41467e34	0.823015
$573$	8.36672e33	0.279012
$574$	0	0
$575$	−7.69471e33	−0.245666
$576$	8.01274e33	0.250323
$577$	−4.43086e34	−1.35454	−0.677268	−	0.735736i	$-0.736836\pi$
$577$	−4.43086e34	−1.35454	−0.677268	+	0.735736i	$0.736836\pi$
$578$	−2.06534e34	−0.617866
$579$	−6.98529e34	−2.04504
$580$	−1.52957e33	−0.0438248
$581$	0	0
$582$	−6.45696e34	−1.77211
$583$	−9.18094e33	−0.246621
$584$	1.95796e34	0.514805
$585$	−1.68029e34	−0.432451
$586$	−1.18128e34	−0.297601
$587$	3.57998e34	0.882886	0.441443	−	0.897289i	$-0.354467\pi$
$587$	3.57998e34	0.882886	0.441443	+	0.897289i	$0.354467\pi$
$588$	0	0
$589$	4.08646e33	0.0965843
$590$	9.83895e32	0.0227666
$591$	8.88235e34	2.01226
$592$	7.45609e34	1.65383
$593$	−2.69114e34	−0.584458	−0.292229	−	0.956348i	$-0.594397\pi$
$593$	−2.69114e34	−0.584458	−0.292229	+	0.956348i	$0.594397\pi$
$594$	−8.22776e34	−1.74965
$595$	0	0
$596$	2.87366e34	0.585945
$597$	−3.47380e34	−0.693627
$598$	−2.75707e34	−0.539117
$599$	−1.19323e34	−0.228501	−0.114250	−	0.993452i	$-0.536447\pi$
$599$	−1.19323e34	−0.228501	−0.114250	+	0.993452i	$0.536447\pi$
$600$	5.49120e34	1.02986
$601$	−2.49574e34	−0.458425	−0.229213	−	0.973376i	$-0.573615\pi$
$601$	−2.49574e34	−0.458425	−0.229213	+	0.973376i	$0.573615\pi$
$602$	0	0
$603$	−2.49985e34	−0.440502
$604$	2.46502e34	0.425460
$605$	−9.01932e32	−0.0152487
$606$	4.65423e34	0.770796
$607$	−7.20312e33	−0.116859	−0.0584295	−	0.998292i	$-0.518609\pi$
$607$	−7.20312e33	−0.116859	−0.0584295	+	0.998292i	$0.518609\pi$
$608$	−2.82735e34	−0.449351
$609$	0	0
$610$	6.91217e32	0.0105437
$611$	1.98905e35	2.97255
$612$	4.52367e34	0.662366
$613$	−3.43976e34	−0.493482	−0.246741	−	0.969081i	$-0.579360\pi$
$613$	−3.43976e34	−0.493482	−0.246741	+	0.969081i	$0.579360\pi$
$614$	3.54590e34	0.498451
$615$	2.73390e34	0.376568
$616$	0	0
$617$	1.17716e35	1.55694	0.778470	−	0.627682i	$-0.215996\pi$
$617$	1.17716e35	1.55694	0.778470	+	0.627682i	$0.215996\pi$
$618$	−2.17039e35	−2.81308
$619$	2.79144e34	0.354565	0.177283	−	0.984160i	$-0.443269\pi$
$619$	2.79144e34	0.354565	0.177283	+	0.984160i	$0.443269\pi$
$620$	1.01433e33	0.0126265
$621$	3.11826e34	0.380424
$622$	2.95984e34	0.353906
$623$	0	0
$624$	3.26548e35	3.75094
$625$	8.43812e34	0.950047
$626$	−1.33400e34	−0.147223
$627$	−7.26457e34	−0.785897
$628$	−7.42696e34	−0.787618
$629$	−8.95388e34	−0.930847
$630$	0	0
$631$	7.93622e33	0.0792951	0.0396476	−	0.999214i	$-0.487376\pi$
$631$	7.93622e33	0.0792951	0.0396476	+	0.999214i	$0.487376\pi$
$632$	−1.30776e32	−0.00128105
$633$	−7.16771e34	−0.688389
$634$	1.15496e35	1.08755
$635$	1.44133e34	0.133074
$636$	2.45191e34	0.221968
$637$	0	0
$638$	8.99887e34	0.783302
$639$	−3.76070e35	−3.21002
$640$	1.66237e34	0.139148
$641$	1.30136e35	1.06825	0.534124	−	0.845406i	$-0.320642\pi$
$641$	1.30136e35	1.06825	0.534124	+	0.845406i	$0.320642\pi$
$642$	4.88454e35	3.93220
$643$	−9.50824e34	−0.750694	−0.375347	−	0.926884i	$-0.622476\pi$
$643$	−9.50824e34	−0.750694	−0.375347	+	0.926884i	$0.622476\pi$
$644$	0	0
$645$	−3.33504e34	−0.253282
$646$	5.68283e34	0.423310
$647$	1.47524e35	1.07785	0.538924	−	0.842354i	$-0.318831\pi$
$647$	1.47524e35	1.07785	0.538924	+	0.842354i	$0.318831\pi$
$648$	−5.97623e34	−0.428292
$649$	−1.92136e34	−0.135067
$650$	3.07672e35	2.12164
$651$	0	0
$652$	−4.44958e34	−0.295273
$653$	−1.44013e35	−0.937535	−0.468767	−	0.883322i	$-0.655302\pi$
$653$	−1.44013e35	−0.937535	−0.468767	+	0.883322i	$0.655302\pi$
$654$	−4.25746e35	−2.71912
$655$	−1.55695e34	−0.0975570
$656$	−3.47774e35	−2.13796
$657$	−2.62725e35	−1.58466
$658$	0	0
$659$	−1.60205e35	−0.930271	−0.465135	−	0.885240i	$-0.653994\pi$
$659$	−1.60205e35	−0.930271	−0.465135	+	0.885240i	$0.653994\pi$
$660$	−1.80319e34	−0.102740
$661$	−8.33273e34	−0.465875	−0.232937	−	0.972492i	$-0.574834\pi$
$661$	−8.33273e34	−0.465875	−0.232937	+	0.972492i	$0.574834\pi$
$662$	−1.92623e34	−0.105678
$663$	−3.92146e35	−2.11120
$664$	−1.04223e35	−0.550632
$665$	0	0
$666$	−6.02816e35	−3.06730
$667$	−3.41051e34	−0.170312
$668$	−6.43873e34	−0.315569
$669$	−5.59112e35	−2.68951
$670$	−7.79504e33	−0.0368030
$671$	−1.34982e34	−0.0625522
$672$	0	0
$673$	1.71504e35	0.765750	0.382875	−	0.923800i	$-0.374934\pi$
$673$	1.71504e35	0.765750	0.382875	+	0.923800i	$0.374934\pi$
$674$	8.67438e34	0.380180
$675$	−3.47979e35	−1.49712
$676$	2.48280e35	1.04860
$677$	1.20664e35	0.500286	0.250143	−	0.968209i	$-0.419522\pi$
$677$	1.20664e35	0.500286	0.250143	+	0.968209i	$0.419522\pi$
$678$	−8.09540e34	−0.329509
$679$	0	0
$680$	−1.42851e34	−0.0560431
$681$	−2.50332e35	−0.964224
$682$	−5.96756e34	−0.225679
$683$	4.16108e35	1.54507	0.772534	−	0.634973i	$-0.218989\pi$
$683$	4.16108e35	1.54507	0.772534	+	0.634973i	$0.218989\pi$
$684$	1.26993e35	0.462997
$685$	4.28579e34	0.153426
$686$	0	0
$687$	−4.03574e35	−1.39304
$688$	4.24245e35	1.43801
$689$	−1.39128e35	−0.463099
$690$	2.05887e34	0.0673002
$691$	2.36157e35	0.758097	0.379049	−	0.925377i	$-0.376251\pi$
$691$	2.36157e35	0.758097	0.379049	+	0.925377i	$0.376251\pi$
$692$	1.78965e35	0.564212
$693$	0	0
$694$	5.37070e35	1.63319
$695$	6.05507e34	0.180846
$696$	2.43385e35	0.713967
$697$	4.17635e35	1.20334
$698$	−2.07003e35	−0.585847
$699$	−6.92850e35	−1.92608
$700$	0	0
$701$	5.29957e35	1.42156	0.710780	−	0.703414i	$-0.248342\pi$
$701$	5.29957e35	1.42156	0.710780	+	0.703414i	$0.248342\pi$
$702$	−1.24683e36	−3.28545
$703$	−2.51362e35	−0.650667
$704$	−4.87917e34	−0.124076
$705$	−1.48534e35	−0.371076
$706$	2.82394e35	0.693100
$707$	0	0
$708$	5.13128e34	0.121566
$709$	7.05743e35	1.64274	0.821369	−	0.570397i	$-0.193211\pi$
$709$	7.05743e35	1.64274	0.821369	+	0.570397i	$0.193211\pi$
$710$	−1.17266e35	−0.268191
$711$	1.75480e33	0.00394329
$712$	−2.27239e35	−0.501745
$713$	2.26166e34	0.0490692
$714$	0	0
$715$	1.02318e35	0.214350
$716$	1.51268e35	0.311412
$717$	1.11157e35	0.224878
$718$	−2.37247e35	−0.471678
$719$	−3.68289e35	−0.719577	−0.359789	−	0.933034i	$-0.617151\pi$
$719$	−3.68289e35	−0.719577	−0.359789	+	0.933034i	$0.617151\pi$
$720$	−1.59618e35	−0.306497
$721$	0	0
$722$	−5.00099e35	−0.927559
$723$	1.67644e36	3.05604
$724$	3.26379e35	0.584778
$725$	3.80592e35	0.670247
$726$	−1.41713e35	−0.245303
$727$	8.39885e35	1.42902	0.714512	−	0.699623i	$-0.246649\pi$
$727$	8.39885e35	1.42902	0.714512	+	0.699623i	$0.246649\pi$
$728$	0	0
$729$	−7.73887e35	−1.27228
$730$	−8.19232e34	−0.132395
$731$	−5.09468e35	−0.809374
$732$	3.60489e34	0.0562993
$733$	−9.75132e35	−1.49714	−0.748572	−	0.663053i	$-0.769260\pi$
$733$	−9.75132e35	−1.49714	−0.748572	+	0.663053i	$0.769260\pi$
$734$	4.60835e35	0.695576
$735$	0	0
$736$	−1.56481e35	−0.228290
$737$	1.52222e35	0.218341
$738$	2.81171e36	3.96521
$739$	−8.42530e35	−1.16823	−0.584117	−	0.811670i	$-0.698559\pi$
$739$	−8.42530e35	−1.16823	−0.584117	+	0.811670i	$0.698559\pi$
$740$	−6.23923e34	−0.0850617
$741$	−1.10087e36	−1.47574
$742$	0	0
$743$	1.05572e36	1.36833	0.684164	−	0.729329i	$-0.260167\pi$
$743$	1.05572e36	1.36833	0.684164	+	0.729329i	$0.260167\pi$
$744$	−1.61400e35	−0.205703
$745$	1.21766e35	0.152607
$746$	−2.43586e35	−0.300204
$747$	1.39850e36	1.69494
$748$	−2.75458e35	−0.328311
$749$	0	0
$750$	−4.63429e35	−0.534216
$751$	−6.35711e35	−0.720710	−0.360355	−	0.932815i	$-0.617344\pi$
$751$	−6.35711e35	−0.720710	−0.360355	+	0.932815i	$0.617344\pi$
$752$	1.88948e36	2.10678
$753$	−7.81849e34	−0.0857404
$754$	1.36369e36	1.47087
$755$	1.04451e35	0.110809
$756$	0	0
$757$	2.79575e35	0.286946	0.143473	−	0.989654i	$-0.454173\pi$
$757$	2.79575e35	0.286946	0.143473	+	0.989654i	$0.454173\pi$
$758$	9.63887e35	0.973108
$759$	−4.02059e35	−0.399271
$760$	−4.01026e34	−0.0391745
$761$	−1.52024e35	−0.146084	−0.0730421	−	0.997329i	$-0.523271\pi$
$761$	−1.52024e35	−0.146084	−0.0730421	+	0.997329i	$0.523271\pi$
$762$	2.26465e36	2.14074
$763$	0	0
$764$	8.90615e34	0.0814748
$765$	1.91683e35	0.172510
$766$	−1.76851e36	−1.56585
$767$	−2.91163e35	−0.253626
$768$	2.34967e36	2.01369
$769$	1.38528e36	1.16804	0.584020	−	0.811739i	$-0.301479\pi$
$769$	1.38528e36	1.16804	0.584020	+	0.811739i	$0.301479\pi$
$770$	0	0
$771$	1.11446e36	0.909676
$772$	−7.43565e35	−0.597176
$773$	1.31899e36	1.04231	0.521156	−	0.853461i	$-0.325501\pi$
$773$	1.31899e36	1.04231	0.521156	+	0.853461i	$0.325501\pi$
$774$	−3.42997e36	−2.66703
$775$	−2.52388e35	−0.193107
$776$	6.96068e35	0.524059
$777$	0	0
$778$	−1.39636e36	−1.01801
$779$	1.17243e36	0.841139
$780$	−2.73255e35	−0.192923
$781$	2.28999e36	1.59109
$782$	3.14518e35	0.215061
$783$	−1.54234e36	−1.03791
$784$	0	0
$785$	−3.14705e35	−0.205132
$786$	−2.44631e36	−1.56938
$787$	−9.39629e35	−0.593297	−0.296648	−	0.954987i	$-0.595869\pi$
$787$	−9.39629e35	−0.593297	−0.296648	+	0.954987i	$0.595869\pi$
$788$	9.45502e35	0.587604
$789$	−4.01754e35	−0.245752
$790$	5.47184e32	0.000329454 0
$791$	0	0
$792$	1.87809e36	1.09560
$793$	−2.04551e35	−0.117459
$794$	−1.92668e36	−1.08906
$795$	1.03895e35	0.0578106
$796$	−3.69777e35	−0.202547
$797$	3.55270e34	0.0191571	0.00957853	−	0.999954i	$-0.496951\pi$
$797$	3.55270e34	0.0191571	0.00957853	+	0.999954i	$0.496951\pi$
$798$	0	0
$799$	−2.26904e36	−1.18579
$800$	1.74623e36	0.898414
$801$	3.04917e36	1.54446
$802$	7.16489e35	0.357297
$803$	1.59980e36	0.785457
$804$	−4.06533e35	−0.196515
$805$	0	0
$806$	−9.04323e35	−0.423775
$807$	−6.97775e35	−0.321956
$808$	−5.01731e35	−0.227944
$809$	−2.42442e36	−1.08455	−0.542276	−	0.840200i	$-0.682437\pi$
$809$	−2.42442e36	−1.08455	−0.542276	+	0.840200i	$0.682437\pi$
$810$	2.50052e35	0.110146
$811$	−2.97257e36	−1.28935	−0.644676	−	0.764456i	$-0.723008\pi$
$811$	−2.97257e36	−1.28935	−0.644676	+	0.764456i	$0.723008\pi$
$812$	0	0
$813$	−4.74435e36	−1.99547
$814$	3.67070e36	1.52035
$815$	−1.88543e35	−0.0769026
$816$	−3.72516e36	−1.49630
$817$	−1.43023e36	−0.565757
$818$	3.18788e36	1.24190
$819$	0	0
$820$	2.91016e35	0.109962
$821$	−3.48601e36	−1.29730	−0.648648	−	0.761089i	$-0.724665\pi$
$821$	−3.48601e36	−1.29730	−0.648648	+	0.761089i	$0.724665\pi$
$822$	6.73391e36	2.46814
$823$	4.20170e36	1.51680	0.758398	−	0.651792i	$-0.225983\pi$
$823$	4.20170e36	1.51680	0.758398	+	0.651792i	$0.225983\pi$
$824$	2.33970e36	0.831899
$825$	4.48674e36	1.57129
$826$	0	0
$827$	−8.95283e35	−0.304188	−0.152094	−	0.988366i	$-0.548602\pi$
$827$	−8.95283e35	−0.304188	−0.152094	+	0.988366i	$0.548602\pi$
$828$	7.02846e35	0.235224
$829$	−3.80704e36	−1.25503	−0.627517	−	0.778603i	$-0.715929\pi$
$829$	−3.80704e36	−1.25503	−0.627517	+	0.778603i	$0.715929\pi$
$830$	4.36080e35	0.141609
$831$	−6.60600e36	−2.11313
$832$	−7.39389e35	−0.232987
$833$	0	0
$834$	9.51383e36	2.90924
$835$	−2.72830e35	−0.0821885
$836$	−7.73294e35	−0.229491
$837$	1.02280e36	0.299034
$838$	−4.17344e36	−1.20211
$839$	2.65827e36	0.754354	0.377177	−	0.926141i	$-0.376895\pi$
$839$	2.65827e36	0.754354	0.377177	+	0.926141i	$0.376895\pi$
$840$	0	0
$841$	−1.94347e36	−0.535338
$842$	2.44534e36	0.663650
$843$	−1.51414e36	−0.404877
$844$	−7.62984e35	−0.201018
$845$	1.05204e36	0.273102
$846$	−1.52762e37	−3.90738
$847$	0	0
$848$	−1.32164e36	−0.328219
$849$	1.58699e36	0.388354
$850$	−3.50983e36	−0.846349
$851$	−1.39117e36	−0.330568
$852$	−6.11577e36	−1.43204
$853$	1.25520e36	0.289635	0.144818	−	0.989458i	$-0.453740\pi$
$853$	1.25520e36	0.289635	0.144818	+	0.989458i	$0.453740\pi$
$854$	0	0
$855$	5.38111e35	0.120586
$856$	−5.26559e36	−1.16285
$857$	−4.19375e36	−0.912729	−0.456364	−	0.889793i	$-0.650849\pi$
$857$	−4.19375e36	−0.912729	−0.456364	+	0.889793i	$0.650849\pi$
$858$	1.60763e37	3.44822
$859$	−1.71325e36	−0.362165	−0.181082	−	0.983468i	$-0.557960\pi$
$859$	−1.71325e36	−0.362165	−0.181082	+	0.983468i	$0.557960\pi$
$860$	−3.55006e35	−0.0739615
$861$	0	0
$862$	1.17039e37	2.36859
$863$	5.70992e36	1.13892	0.569462	−	0.822017i	$-0.307151\pi$
$863$	5.70992e36	1.13892	0.569462	+	0.822017i	$0.307151\pi$
$864$	−7.07655e36	−1.39123
$865$	7.58334e35	0.146946
$866$	8.30482e36	1.58620
$867$	−4.56417e36	−0.859257
$868$	0	0
$869$	−1.06855e34	−0.00195455
$870$	−1.01835e36	−0.183614
$871$	2.30678e36	0.409995
$872$	4.58959e36	0.804114
$873$	−9.34008e36	−1.61314
$874$	8.82946e35	0.150328
$875$	0	0
$876$	−4.27252e36	−0.706940
$877$	−6.49394e36	−1.05929	−0.529643	−	0.848221i	$-0.677674\pi$
$877$	−6.49394e36	−1.05929	−0.529643	+	0.848221i	$0.677674\pi$
$878$	−3.95638e36	−0.636234
$879$	−2.61050e36	−0.413869
$880$	9.71958e35	0.151920
$881$	−5.60014e36	−0.862979	−0.431490	−	0.902118i	$-0.642012\pi$
$881$	−5.60014e36	−0.862979	−0.431490	+	0.902118i	$0.642012\pi$
$882$	0	0
$883$	−4.46810e36	−0.669289	−0.334645	−	0.942344i	$-0.608616\pi$
$883$	−4.46810e36	−0.669289	−0.334645	+	0.942344i	$0.608616\pi$
$884$	−4.17429e36	−0.616494
$885$	2.17429e35	0.0316612
$886$	−1.15858e37	−1.66342
$887$	−9.27605e35	−0.131316	−0.0656580	−	0.997842i	$-0.520915\pi$
$887$	−9.27605e35	−0.131316	−0.0656580	+	0.997842i	$0.520915\pi$
$888$	9.92785e36	1.38578
$889$	0	0
$890$	9.50795e35	0.129036
$891$	−4.88305e36	−0.653461
$892$	−5.95160e36	−0.785368
$893$	−6.36988e36	−0.828873
$894$	1.91321e37	2.45496
$895$	6.40974e35	0.0811059
$896$	0	0
$897$	−6.09280e36	−0.749742
$898$	−8.91129e35	−0.108140
$899$	−1.11865e36	−0.133875
$900$	−7.84333e36	−0.925698
$901$	1.58713e36	0.184736
$902$	−1.71212e37	−1.96541
$903$	0	0
$904$	8.72693e35	0.0974442
$905$	1.38298e36	0.152303
$906$	1.64115e37	1.78257
$907$	1.97302e35	0.0211369	0.0105684	−	0.999944i	$-0.496636\pi$
$907$	1.97302e35	0.0211369	0.0105684	+	0.999944i	$0.496636\pi$
$908$	−2.66472e36	−0.281565
$909$	6.73239e36	0.701651
$910$	0	0
$911$	−1.68805e37	−1.71161	−0.855804	−	0.517299i	$-0.826937\pi$
$911$	−1.68805e37	−1.71161	−0.855804	+	0.517299i	$0.826937\pi$
$912$	−1.04577e37	−1.04592
$913$	−8.51582e36	−0.840121
$914$	5.10659e36	0.496939
$915$	1.52751e35	0.0146629
$916$	−4.29594e36	−0.406785
$917$	0	0
$918$	1.42235e37	1.31061
$919$	−1.45150e37	−1.31939	−0.659695	−	0.751534i	$-0.729314\pi$
$919$	−1.45150e37	−1.31939	−0.659695	+	0.751534i	$0.729314\pi$
$920$	−2.21949e35	−0.0199024
$921$	7.83604e36	0.693188
$922$	−4.09991e36	−0.357798
$923$	3.47025e37	2.98772
$924$	0	0
$925$	1.55246e37	1.30092
$926$	−7.98629e36	−0.660249
$927$	−3.13949e37	−2.56073
$928$	7.73977e36	0.622843
$929$	−9.68926e36	−0.769298	−0.384649	−	0.923063i	$-0.625677\pi$
$929$	−9.68926e36	−0.769298	−0.384649	+	0.923063i	$0.625677\pi$
$930$	6.75315e35	0.0529017
$931$	0	0
$932$	−7.37520e36	−0.562438
$933$	6.54090e36	0.492172
$934$	1.61104e36	0.119611
$935$	−1.16721e36	−0.0855071
$936$	2.84606e37	2.05729
$937$	−2.59067e37	−1.84785	−0.923926	−	0.382571i	$-0.875039\pi$
$937$	−2.59067e37	−1.84785	−0.923926	+	0.382571i	$0.875039\pi$
$938$	0	0
$939$	−2.94798e36	−0.204741
$940$	−1.58111e36	−0.108359
$941$	2.44770e37	1.65534	0.827670	−	0.561215i	$-0.189666\pi$
$941$	2.44770e37	1.65534	0.827670	+	0.561215i	$0.189666\pi$
$942$	−4.94469e37	−3.29992
$943$	6.48883e36	0.427337
$944$	−2.76588e36	−0.179756
$945$	0	0
$946$	2.08860e37	1.32195
$947$	2.45761e37	1.53511	0.767553	−	0.640986i	$-0.221474\pi$
$947$	2.45761e37	1.53511	0.767553	+	0.640986i	$0.221474\pi$
$948$	2.85371e34	0.00175916
$949$	2.42434e37	1.47491
$950$	−9.85314e36	−0.591602
$951$	2.55233e37	1.51245
$952$	0	0
$953$	1.86800e37	1.07824	0.539120	−	0.842229i	$-0.318757\pi$
$953$	1.86800e37	1.07824	0.539120	+	0.842229i	$0.318757\pi$
$954$	1.06853e37	0.608738
$955$	3.77383e35	0.0212197
$956$	1.18323e36	0.0656670
$957$	1.98865e37	1.08933
$958$	−2.92730e35	−0.0158270
$959$	0	0
$960$	5.52148e35	0.0290847
$961$	−1.84910e37	−0.961429
$962$	5.56258e37	2.85488
$963$	7.06555e37	3.57946
$964$	1.78452e37	0.892399
$965$	−3.15073e36	−0.155532
$966$	0	0
$967$	−1.21475e37	−0.584327	−0.292164	−	0.956368i	$-0.594375\pi$
$967$	−1.21475e37	−0.584327	−0.292164	+	0.956368i	$0.594375\pi$
$968$	1.52768e36	0.0725423
$969$	1.25584e37	0.588691
$970$	−2.91243e36	−0.134775
$971$	−2.38178e37	−1.08808	−0.544040	−	0.839059i	$-0.683106\pi$
$971$	−2.38178e37	−1.08808	−0.544040	+	0.839059i	$0.683106\pi$
$972$	−3.73302e36	−0.168357
$973$	0	0
$974$	4.32002e37	1.89888
$975$	6.79920e37	2.95053
$976$	−1.94312e36	−0.0832484
$977$	−2.27147e37	−0.960781	−0.480391	−	0.877055i	$-0.659505\pi$
$977$	−2.27147e37	−0.960781	−0.480391	+	0.877055i	$0.659505\pi$
$978$	−2.96242e37	−1.23712
$979$	−1.85672e37	−0.765532
$980$	0	0
$981$	−6.15847e37	−2.47520
$982$	1.59339e37	0.632307
$983$	2.90751e37	1.13921	0.569604	−	0.821920i	$-0.307097\pi$
$983$	2.90751e37	1.13921	0.569604	+	0.821920i	$0.307097\pi$
$984$	−4.63064e37	−1.79144
$985$	4.00640e36	0.153039
$986$	−1.55565e37	−0.586747
$987$	0	0
$988$	−1.17185e37	−0.430933
$989$	−7.91564e36	−0.287430
$990$	−7.85816e36	−0.281761
$991$	−2.66029e37	−0.941909	−0.470954	−	0.882158i	$-0.656090\pi$
$991$	−2.66029e37	−0.941909	−0.470954	+	0.882158i	$0.656090\pi$
$992$	−5.13259e36	−0.179449
$993$	−4.25674e36	−0.146964
$994$	0	0
$995$	−1.56687e36	−0.0527526
$996$	2.27428e37	0.756140
$997$	−2.67868e37	−0.879492	−0.439746	−	0.898122i	$-0.644932\pi$
$997$	−2.67868e37	−0.879492	−0.439746	+	0.898122i	$0.644932\pi$
$998$	−1.36285e37	−0.441892
$999$	−6.29132e37	−2.01453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.f.1.13		16
7.2	even	3		7.26.c.a.4.4	yes	32
7.4	even	3		7.26.c.a.2.4	✓	32
7.6	odd	2		49.26.a.g.1.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.c.a.2.4	✓	32	7.4	even	3
7.26.c.a.4.4	yes	32	7.2	even	3
49.26.a.f.1.13		16	1.1	even	1	trivial
49.26.a.g.1.13		16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+7087.00 q^{2} +1.56615e6 q^{3} +1.66712e7 q^{4} +7.06414e7 q^{5} +1.10993e10 q^{6} -1.19652e11 q^{8} +1.60553e12 q^{9} +O(q^{10})\)	\(q+7087.00 q^{2} +1.56615e6 q^{3} +1.66712e7 q^{4} +7.06414e7 q^{5} +1.10993e10 q^{6} -1.19652e11 q^{8} +1.60553e12 q^{9} +5.00636e11 q^{10} -9.77647e12 q^{11} +2.61095e13 q^{12} -1.48152e14 q^{13} +1.10635e14 q^{15} -1.40736e15 q^{16} +1.69008e15 q^{17} +1.13784e16 q^{18} +4.74456e15 q^{19} +1.17768e15 q^{20} -6.92859e16 q^{22} +2.62589e16 q^{23} -1.87392e17 q^{24} -2.93033e17 q^{25} -1.04996e18 q^{26} +1.18751e18 q^{27} -1.29880e18 q^{29} +7.84069e17 q^{30} +8.61295e17 q^{31} -5.95915e18 q^{32} -1.53114e19 q^{33} +1.19776e19 q^{34} +2.67660e19 q^{36} -5.29791e19 q^{37} +3.36247e19 q^{38} -2.32028e20 q^{39} -8.45235e18 q^{40} +2.47110e20 q^{41} -3.01446e20 q^{43} -1.62985e20 q^{44} +1.13416e20 q^{45} +1.86097e20 q^{46} -1.34257e21 q^{47} -2.20414e21 q^{48} -2.07673e21 q^{50} +2.64691e21 q^{51} -2.46988e21 q^{52} +9.39086e20 q^{53} +8.41588e21 q^{54} -6.90623e20 q^{55} +7.43067e21 q^{57} -9.20462e21 q^{58} +1.96529e21 q^{59} +1.84441e21 q^{60} +1.38068e21 q^{61} +6.10400e21 q^{62} +4.99073e21 q^{64} -1.04657e22 q^{65} -1.08512e23 q^{66} -1.55703e22 q^{67} +2.81756e22 q^{68} +4.11252e22 q^{69} -2.34235e23 q^{71} -1.92104e23 q^{72} -1.63638e23 q^{73} -3.75463e23 q^{74} -4.58933e23 q^{75} +7.90975e22 q^{76} -1.64439e24 q^{78} +1.09298e21 q^{79} -9.94181e22 q^{80} +4.99470e23 q^{81} +1.75127e24 q^{82} +8.71053e23 q^{83} +1.19389e23 q^{85} -2.13635e24 q^{86} -2.03412e24 q^{87} +1.16977e24 q^{88} +1.89918e24 q^{89} +8.03783e23 q^{90} +4.37767e23 q^{92} +1.34891e24 q^{93} -9.51478e24 q^{94} +3.35162e23 q^{95} -9.33291e24 q^{96} -5.81746e24 q^{97} -1.56964e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9}+O(q^{10}) \) 16 * q + 4050 * q^2 - 531440 * q^3 + 286295596 * q^4 - 288173088 * q^5 - 6531645442 * q^6 + 137183373360 * q^8 + 5146896583216 * q^9	\( 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9} + 918803280822 q^{10} - 253661467680 q^{11} - 59498382182260 q^{12} + 68129645475920 q^{13} - 14\!\cdots\!08 q^{15}+ \cdots + 21\!\cdots\!28 q^{99}+O(q^{100}) \) 16 * q + 4050 * q^2 - 531440 * q^3 + 286295596 * q^4 - 288173088 * q^5 - 6531645442 * q^6 + 137183373360 * q^8 + 5146896583216 * q^9 + 918803280822 * q^10 - 253661467680 * q^11 - 59498382182260 * q^12 + 68129645475920 * q^13 - 1404332214639008 * q^15 + 5327562569765872 * q^16 - 5022112861130400 * q^17 - 1957025270033980 * q^18 - 10588631642557696 * q^19 + 12365603244583092 * q^20 - 94651471756449330 * q^22 - 20610047702550960 * q^23 - 573793671932159616 * q^24 + 958211520923613472 * q^25 - 2724774668939531124 * q^26 - 1103054793716345120 * q^27 - 4344632493050616336 * q^29 + 2619504629356224458 * q^30 - 10841379318391039264 * q^31 - 6763645131553838880 * q^32 + 11546953084647657040 * q^33 + 6541316394798823806 * q^34 + 141226019822573256728 * q^36 - 29321738000603330320 * q^37 + 70525127026788123690 * q^38 - 25840220465930531024 * q^39 + 85110519871079993136 * q^40 - 165270014614023120144 * q^41 + 215507582734291457600 * q^43 + 879888416642398340460 * q^44 - 485170985786336771600 * q^45 - 1667203425207259516686 * q^46 - 2014371898465936816800 * q^47 - 5831281959829213328560 * q^48 - 836396256472298102808 * q^50 + 7525441297042267778496 * q^51 - 6992249387859106251160 * q^52 - 8918984691607286334960 * q^53 - 34981309708344282421726 * q^54 - 32943212576578456921776 * q^55 + 28344067162748052349840 * q^57 + 26386021221286483940940 * q^58 + 10935316261765587024144 * q^59 - 139984946157807148568716 * q^60 + 17484129051186787701488 * q^61 - 131394252459900844408050 * q^62 + 165809551263124614802048 * q^64 + 60109967964600925224336 * q^65 - 61498292814044614748374 * q^66 - 218997561331718103994960 * q^67 - 482184105822238591781100 * q^68 - 407858979455444402603424 * q^69 - 278059426277993021419488 * q^71 + 332574755512105623952800 * q^72 - 181923789786333620742640 * q^73 + 788377165482644151934950 * q^74 + 66014699727433523602592 * q^75 + 631386434812602470719172 * q^76 + 155695476291097040159540 * q^78 - 438039985868556642949360 * q^79 + 1229118480867135510718416 * q^80 + 738103636463171961601504 * q^81 + 4913051673767471255932260 * q^82 + 2177700923800256297617440 * q^83 - 252838841319017848403856 * q^85 - 5848093469680723949747688 * q^86 + 2195492958449506107537040 * q^87 + 10064215655338142337197760 * q^88 - 449697822243925695740496 * q^89 + 20875370857270558016637452 * q^90 - 9256057866243149752728540 * q^92 + 2539354660954665131215920 * q^93 + 1689612490320614160295890 * q^94 + 2244103526711501036678160 * q^95 + 3851732620967552391601888 * q^96 - 8537037301155842764342960 * q^97 + 2136810407699986619975728 * q^99

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