LMFDB - Embedded newform 49.26.a.f.1.15

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			1.15
Root			$-5183.35$ 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)

$f(q)$	$=$	$q+10620.7 q^{2} +462798. q^{3} +7.92447e7 q^{4} -7.26756e8 q^{5} +4.91524e9 q^{6} +4.85262e11 q^{8} -6.33106e11 q^{9} +O(q^{10})$	\(q+10620.7 q^{2} +462798. q^{3} +7.92447e7 q^{4} -7.26756e8 q^{5} +4.91524e9 q^{6} +4.85262e11 q^{8} -6.33106e11 q^{9} -7.71865e12 q^{10} +1.89031e13 q^{11} +3.66743e13 q^{12} -1.00107e14 q^{13} -3.36342e14 q^{15} +2.49481e15 q^{16} -4.82905e14 q^{17} -6.72403e15 q^{18} +3.41110e15 q^{19} -5.75915e16 q^{20} +2.00764e17 q^{22} -8.11604e16 q^{23} +2.24578e17 q^{24} +2.30151e17 q^{25} -1.06320e18 q^{26} -6.85124e17 q^{27} +1.97993e17 q^{29} -3.57218e18 q^{30} -6.33560e18 q^{31} +1.02139e19 q^{32} +8.74831e18 q^{33} -5.12879e18 q^{34} -5.01703e19 q^{36} -4.34996e19 q^{37} +3.62282e19 q^{38} -4.63293e19 q^{39} -3.52667e20 q^{40} +3.51736e19 q^{41} +1.02055e20 q^{43} +1.49797e21 q^{44} +4.60114e20 q^{45} -8.61979e20 q^{46} +6.22189e20 q^{47} +1.15459e21 q^{48} +2.44437e21 q^{50} -2.23488e20 q^{51} -7.93293e21 q^{52} -2.75183e20 q^{53} -7.27649e21 q^{54} -1.37379e22 q^{55} +1.57865e21 q^{57} +2.10282e21 q^{58} -1.45313e22 q^{59} -2.66533e22 q^{60} -2.06025e22 q^{61} -6.72885e22 q^{62} +2.47667e22 q^{64} +7.27532e22 q^{65} +9.29131e22 q^{66} -3.80679e21 q^{67} -3.82677e22 q^{68} -3.75609e22 q^{69} -1.80688e23 q^{71} -3.07222e23 q^{72} +4.22315e22 q^{73} -4.61996e23 q^{74} +1.06514e23 q^{75} +2.70311e23 q^{76} -4.92049e23 q^{78} -2.63932e23 q^{79} -1.81312e24 q^{80} +2.19349e23 q^{81} +3.73568e23 q^{82} +5.25223e23 q^{83} +3.50954e23 q^{85} +1.08390e24 q^{86} +9.16308e22 q^{87} +9.17294e24 q^{88} -2.06756e24 q^{89} +4.88673e24 q^{90} -6.43153e24 q^{92} -2.93211e24 q^{93} +6.60808e24 q^{94} -2.47903e24 q^{95} +4.72697e24 q^{96} +6.63668e24 q^{97} -1.19677e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10620.7	1.83349	0.916744	−	0.399476i	$-0.130808\pi$
$2$	10620.7	1.83349	0.916744	+	0.399476i	$0.130808\pi$
$3$	462798.	0.502778	0.251389	−	0.967886i	$-0.419113\pi$
$3$	462798.	0.502778	0.251389	+	0.967886i	$0.419113\pi$
$4$	7.92447e7	2.36167
$5$	−7.26756e8	−1.33126	−0.665631	−	0.746281i	$-0.731838\pi$
$5$	−7.26756e8	−1.33126	−0.665631	+	0.746281i	$0.731838\pi$
$6$	4.91524e9	0.921837
$7$	0	0
$7$	0	0
$8$	4.85262e11	2.49661
$9$	−6.33106e11	−0.747214
$10$	−7.71865e12	−2.44085
$11$	1.89031e13	1.81603	0.908017	−	0.418933i	$-0.137596\pi$
$11$	1.89031e13	1.81603	0.908017	+	0.418933i	$0.137596\pi$
$12$	3.66743e13	1.18740
$13$	−1.00107e14	−1.19171	−0.595857	−	0.803091i	$-0.703187\pi$
$13$	−1.00107e14	−1.19171	−0.595857	+	0.803091i	$0.703187\pi$
$14$	0	0
$15$	−3.36342e14	−0.669329
$16$	2.49481e15	2.21583
$17$	−4.82905e14	−0.201025	−0.100513	−	0.994936i	$-0.532048\pi$
$17$	−4.82905e14	−0.201025	−0.100513	+	0.994936i	$0.532048\pi$
$18$	−6.72403e15	−1.37001
$19$	3.41110e15	0.353569	0.176784	−	0.984250i	$-0.443430\pi$
$19$	3.41110e15	0.353569	0.176784	+	0.984250i	$0.443430\pi$
$20$	−5.75915e16	−3.14401
$21$	0	0
$22$	2.00764e17	3.32967
$23$	−8.11604e16	−0.772229	−0.386114	−	0.922451i	$-0.626183\pi$
$23$	−8.11604e16	−0.772229	−0.386114	+	0.922451i	$0.626183\pi$
$24$	2.24578e17	1.25524
$25$	2.30151e17	0.772259
$26$	−1.06320e18	−2.18499
$27$	−6.85124e17	−0.878461
$28$	0	0
$29$	1.97993e17	0.103914	0.0519571	−	0.998649i	$-0.483454\pi$
$29$	1.97993e17	0.103914	0.0519571	+	0.998649i	$0.483454\pi$
$30$	−3.57218e18	−1.22721
$31$	−6.33560e18	−1.44466	−0.722332	−	0.691546i	$-0.756930\pi$
$31$	−6.33560e18	−1.44466	−0.722332	+	0.691546i	$0.756930\pi$
$32$	1.02139e19	1.56609
$33$	8.74831e18	0.913062
$34$	−5.12879e18	−0.368577
$35$	0	0
$36$	−5.01703e19	−1.76468
$37$	−4.34996e19	−1.08634	−0.543168	−	0.839624i	$-0.682775\pi$
$37$	−4.34996e19	−1.08634	−0.543168	+	0.839624i	$0.682775\pi$
$38$	3.62282e19	0.648264
$39$	−4.63293e19	−0.599167
$40$	−3.52667e20	−3.32365
$41$	3.51736e19	0.243455	0.121727	−	0.992564i	$-0.461157\pi$
$41$	3.51736e19	0.243455	0.121727	+	0.992564i	$0.461157\pi$
$42$	0	0
$43$	1.02055e20	0.389475	0.194738	−	0.980855i	$-0.437614\pi$
$43$	1.02055e20	0.389475	0.194738	+	0.980855i	$0.437614\pi$
$44$	1.49797e21	4.28888
$45$	4.60114e20	0.994738
$46$	−8.61979e20	−1.41587
$47$	6.22189e20	0.781086	0.390543	−	0.920585i	$-0.372287\pi$
$47$	6.22189e20	0.781086	0.390543	+	0.920585i	$0.372287\pi$
$48$	1.15459e21	1.11407
$49$	0	0
$50$	2.44437e21	1.41593
$51$	−2.23488e20	−0.101071
$52$	−7.93293e21	−2.81444
$53$	−2.75183e20	−0.0769436	−0.0384718	−	0.999260i	$-0.512249\pi$
$53$	−2.75183e20	−0.0769436	−0.0384718	+	0.999260i	$0.512249\pi$
$54$	−7.27649e21	−1.61065
$55$	−1.37379e22	−2.41762
$56$	0	0
$57$	1.57865e21	0.177767
$58$	2.10282e21	0.190525
$59$	−1.45313e22	−1.06329	−0.531647	−	0.846966i	$-0.678427\pi$
$59$	−1.45313e22	−1.06329	−0.531647	+	0.846966i	$0.678427\pi$
$60$	−2.66533e22	−1.58074
$61$	−2.06025e22	−0.993797	−0.496899	−	0.867809i	$-0.665528\pi$
$61$	−2.06025e22	−0.993797	−0.496899	+	0.867809i	$0.665528\pi$
$62$	−6.72885e22	−2.64877
$63$	0	0
$64$	2.47667e22	0.655570
$65$	7.27532e22	1.58648
$66$	9.29131e22	1.67409
$67$	−3.80679e21	−0.0568360	−0.0284180	−	0.999596i	$-0.509047\pi$
$67$	−3.80679e21	−0.0568360	−0.0284180	+	0.999596i	$0.509047\pi$
$68$	−3.82677e22	−0.474756
$69$	−3.75609e22	−0.388260
$70$	0	0
$71$	−1.80688e23	−1.30677	−0.653386	−	0.757025i	$-0.726652\pi$
$71$	−1.80688e23	−1.30677	−0.653386	+	0.757025i	$0.726652\pi$
$72$	−3.07222e23	−1.86551
$73$	4.22315e22	0.215825	0.107912	−	0.994160i	$-0.465583\pi$
$73$	4.22315e22	0.215825	0.107912	+	0.994160i	$0.465583\pi$
$74$	−4.61996e23	−1.99178
$75$	1.06514e23	0.388275
$76$	2.70311e23	0.835014
$77$	0	0
$78$	−4.92049e23	−1.09856
$79$	−2.63932e23	−0.502519	−0.251260	−	0.967920i	$-0.580845\pi$
$79$	−2.63932e23	−0.502519	−0.251260	+	0.967920i	$0.580845\pi$
$80$	−1.81312e24	−2.94986
$81$	2.19349e23	0.305544
$82$	3.73568e23	0.446371
$83$	5.25223e23	0.539346	0.269673	−	0.962952i	$-0.413084\pi$
$83$	5.25223e23	0.539346	0.269673	+	0.962952i	$0.413084\pi$
$84$	0	0
$85$	3.50954e23	0.267617
$86$	1.08390e24	0.714098
$87$	9.16308e22	0.0522457
$88$	9.17294e24	4.53393
$89$	−2.06756e24	−0.887327	−0.443663	−	0.896194i	$-0.646321\pi$
$89$	−2.06756e24	−0.887327	−0.443663	+	0.896194i	$0.646321\pi$
$90$	4.88673e24	1.82384
$91$	0	0
$92$	−6.43153e24	−1.82375
$93$	−2.93211e24	−0.726345
$94$	6.60808e24	1.43211
$95$	−2.47903e24	−0.470693
$96$	4.72697e24	0.787395
$97$	6.63668e24	0.971190	0.485595	−	0.874184i	$-0.338603\pi$
$97$	6.63668e24	0.971190	0.485595	+	0.874184i	$0.338603\pi$
$98$	0	0
$99$	−1.19677e25	−1.35697
$100$	1.82383e25	1.82383
$101$	−2.10560e25	−1.85934	−0.929668	−	0.368399i	$-0.879906\pi$
$101$	−2.10560e25	−1.85934	−0.929668	+	0.368399i	$0.879906\pi$
$102$	−2.37359e24	−0.185312
$103$	−2.33231e25	−1.61184	−0.805918	−	0.592027i	$-0.798328\pi$
$103$	−2.33231e25	−1.61184	−0.805918	+	0.592027i	$0.798328\pi$
$104$	−4.85780e25	−2.97525
$105$	0	0
$106$	−2.92263e24	−0.141075
$107$	−1.31949e25	−0.566381	−0.283191	−	0.959064i	$-0.591393\pi$
$107$	−1.31949e25	−0.566381	−0.283191	+	0.959064i	$0.591393\pi$
$108$	−5.42924e25	−2.07464
$109$	−2.76423e25	−0.941333	−0.470667	−	0.882311i	$-0.655987\pi$
$109$	−2.76423e25	−0.941333	−0.470667	+	0.882311i	$0.655987\pi$
$110$	−1.45906e26	−4.43267
$111$	−2.01316e25	−0.546185
$112$	0	0
$113$	2.44510e25	0.530660	0.265330	−	0.964158i	$-0.414519\pi$
$113$	2.44510e25	0.530660	0.265330	+	0.964158i	$0.414519\pi$
$114$	1.67663e25	0.325933
$115$	5.89838e25	1.02804
$116$	1.56899e25	0.245411
$117$	6.33783e25	0.890465
$118$	−1.54332e26	−1.94954
$119$	0	0
$120$	−1.63214e26	−1.67106
$121$	2.48979e26	2.29798
$122$	−2.18813e26	−1.82211
$123$	1.62783e25	0.122404
$124$	−5.02063e26	−3.41183
$125$	4.93264e25	0.303183
$126$	0	0
$127$	−3.51334e26	−1.77082	−0.885408	−	0.464815i	$-0.846121\pi$
$127$	−3.51334e26	−1.77082	−0.885408	+	0.464815i	$0.846121\pi$
$128$	−7.96814e25	−0.364110
$129$	4.72310e25	0.195820
$130$	7.72690e26	2.90880
$131$	2.65513e26	0.908226	0.454113	−	0.890944i	$-0.349956\pi$
$131$	2.65513e26	0.908226	0.454113	+	0.890944i	$0.349956\pi$
$132$	6.93257e26	2.15635
$133$	0	0
$134$	−4.04307e25	−0.104208
$135$	4.97918e26	1.16946
$136$	−2.34335e26	−0.501882
$137$	8.45387e26	1.65215	0.826073	−	0.563563i	$-0.190570\pi$
$137$	8.45387e26	1.65215	0.826073	+	0.563563i	$0.190570\pi$
$138$	−3.98923e26	−0.711869
$139$	−2.58974e26	−0.422251	−0.211126	−	0.977459i	$-0.567713\pi$
$139$	−2.58974e26	−0.422251	−0.211126	+	0.977459i	$0.567713\pi$
$140$	0	0
$141$	2.87948e26	0.392713
$142$	−1.91903e27	−2.39595
$143$	−1.89233e27	−2.16419
$144$	−1.57948e27	−1.65570
$145$	−1.43893e26	−0.138337
$146$	4.48528e26	0.395712
$147$	0	0
$148$	−3.44711e27	−2.56557
$149$	1.30264e27	0.891246	0.445623	−	0.895221i	$-0.352982\pi$
$149$	1.30264e27	0.891246	0.445623	+	0.895221i	$0.352982\pi$
$150$	1.13125e27	0.711897
$151$	−1.61225e26	−0.0933727	−0.0466864	−	0.998910i	$-0.514866\pi$
$151$	−1.61225e26	−0.0933727	−0.0466864	+	0.998910i	$0.514866\pi$
$152$	1.65527e27	0.882724
$153$	3.05730e26	0.150209
$154$	0	0
$155$	4.60444e27	1.92323
$156$	−3.67135e27	−1.41504
$157$	3.14816e27	1.12024	0.560120	−	0.828411i	$-0.310755\pi$
$157$	3.14816e27	1.12024	0.560120	+	0.828411i	$0.310755\pi$
$158$	−2.80314e27	−0.921363
$159$	−1.27354e26	−0.0386856
$160$	−7.42300e27	−2.08487
$161$	0	0
$162$	2.32964e27	0.560211
$163$	1.70639e27	0.379957	0.189978	−	0.981788i	$-0.439158\pi$
$163$	1.70639e27	0.379957	0.189978	+	0.981788i	$0.439158\pi$
$164$	2.78732e27	0.574961
$165$	−6.35789e27	−1.21552
$166$	5.57823e27	0.988884
$167$	−2.82156e27	−0.464017	−0.232009	−	0.972714i	$-0.574530\pi$
$167$	−2.82156e27	−0.464017	−0.232009	+	0.972714i	$0.574530\pi$
$168$	0	0
$169$	2.96497e27	0.420180
$170$	3.72738e27	0.490673
$171$	−2.15959e27	−0.264192
$172$	8.08734e27	0.919814
$173$	−6.04509e27	−0.639480	−0.319740	−	0.947505i	$-0.603595\pi$
$173$	−6.04509e27	−0.639480	−0.319740	+	0.947505i	$0.603595\pi$
$174$	9.73183e26	0.0957919
$175$	0	0
$176$	4.71595e28	4.02403
$177$	−6.72505e27	−0.534601
$178$	−2.19589e28	−1.62690
$179$	4.32380e27	0.298678	0.149339	−	0.988786i	$-0.452285\pi$
$179$	4.32380e27	0.298678	0.149339	+	0.988786i	$0.452285\pi$
$180$	3.64616e28	2.34925
$181$	4.82985e27	0.290370	0.145185	−	0.989405i	$-0.453622\pi$
$181$	4.82985e27	0.290370	0.145185	+	0.989405i	$0.453622\pi$
$182$	0	0
$183$	−9.53482e27	−0.499659
$184$	−3.93840e28	−1.92796
$185$	3.16136e28	1.44620
$186$	−3.11410e28	−1.33174
$187$	−9.12840e27	−0.365068
$188$	4.93052e28	1.84467
$189$	0	0
$190$	−2.63291e28	−0.863009
$191$	3.94729e28	1.21166	0.605832	−	0.795593i	$-0.292840\pi$
$191$	3.94729e28	1.21166	0.605832	+	0.795593i	$0.292840\pi$
$192$	1.14620e28	0.329606
$193$	1.82860e28	0.492779	0.246390	−	0.969171i	$-0.420756\pi$
$193$	1.82860e28	0.492779	0.246390	+	0.969171i	$0.420756\pi$
$194$	7.04861e28	1.78066
$195$	3.36701e28	0.797648
$196$	0	0
$197$	7.98007e27	0.166410	0.0832049	−	0.996532i	$-0.473484\pi$
$197$	7.98007e27	0.166410	0.0832049	+	0.996532i	$0.473484\pi$
$198$	−1.27105e29	−2.48798
$199$	8.13626e28	1.49541	0.747707	−	0.664029i	$-0.231155\pi$
$199$	8.13626e28	1.49541	0.747707	+	0.664029i	$0.231155\pi$
$200$	1.11684e29	1.92803
$201$	−1.76178e27	−0.0285759
$202$	−2.23629e29	−3.40907
$203$	0	0
$204$	−1.77102e28	−0.238697
$205$	−2.55626e28	−0.324102
$206$	−2.47707e29	−2.95528
$207$	5.13831e28	0.577021
$208$	−2.49747e29	−2.64064
$209$	6.44802e28	0.642093
$210$	0	0
$211$	1.91959e29	1.69698	0.848491	−	0.529210i	$-0.177512\pi$
$211$	1.91959e29	1.69698	0.848491	+	0.529210i	$0.177512\pi$
$212$	−2.18068e28	−0.181716
$213$	−8.36221e28	−0.657016
$214$	−1.40139e29	−1.03845
$215$	−7.41693e28	−0.518494
$216$	−3.32465e29	−2.19318
$217$	0	0
$218$	−2.93581e29	−1.72592
$219$	1.95447e28	0.108512
$220$	−1.08866e30	−5.70963
$221$	4.83421e28	0.239564
$222$	−2.13811e29	−1.00142
$223$	−3.51435e29	−1.55609	−0.778045	−	0.628209i	$-0.783788\pi$
$223$	−3.51435e29	−1.55609	−0.778045	+	0.628209i	$0.783788\pi$
$224$	0	0
$225$	−1.45710e29	−0.577043
$226$	2.59687e29	0.972958
$227$	1.63889e29	0.581067	0.290533	−	0.956865i	$-0.406167\pi$
$227$	1.63889e29	0.581067	0.290533	+	0.956865i	$0.406167\pi$
$228$	1.25100e29	0.419827
$229$	−2.51510e29	−0.799119	−0.399559	−	0.916707i	$-0.630837\pi$
$229$	−2.51510e29	−0.799119	−0.399559	+	0.916707i	$0.630837\pi$
$230$	6.26449e29	1.88490
$231$	0	0
$232$	9.60784e28	0.259433
$233$	6.08703e26	0.00155760	0.000778801	−	1.00000i	$-0.499752\pi$
$233$	6.08703e26	0.00155760	0.000778801		1.00000i	$0.499752\pi$
$234$	6.73121e29	1.63266
$235$	−4.52180e29	−1.03983
$236$	−1.15153e30	−2.51115
$237$	−1.22147e29	−0.252656
$238$	0	0
$239$	4.63291e28	0.0862741	0.0431371	−	0.999069i	$-0.486265\pi$
$239$	4.63291e28	0.0862741	0.0431371	+	0.999069i	$0.486265\pi$
$240$	−8.39107e29	−1.48312
$241$	−3.42417e29	−0.574569	−0.287284	−	0.957845i	$-0.592752\pi$
$241$	−3.42417e29	−0.574569	−0.287284	+	0.957845i	$0.592752\pi$
$242$	2.64433e30	4.21332
$243$	6.82013e29	1.03208
$244$	−1.63264e30	−2.34703
$245$	0	0
$246$	1.72887e29	0.224426
$247$	−3.41474e29	−0.421353
$248$	−3.07443e30	−3.60677
$249$	2.43072e29	0.271171
$250$	5.23880e29	0.555881
$251$	2.89774e29	0.292509	0.146254	−	0.989247i	$-0.453278\pi$
$251$	2.89774e29	0.292509	0.146254	+	0.989247i	$0.453278\pi$
$252$	0	0
$253$	−1.53418e30	−1.40239
$254$	−3.73141e30	−3.24677
$255$	1.62421e29	0.134552
$256$	−1.67731e30	−1.32316
$257$	1.36085e30	1.02246	0.511230	−	0.859444i	$-0.329190\pi$
$257$	1.36085e30	1.02246	0.511230	+	0.859444i	$0.329190\pi$
$258$	5.01626e29	0.359033
$259$	0	0
$260$	5.76531e30	3.74676
$261$	−1.25351e29	−0.0776462
$262$	2.81993e30	1.66522
$263$	−1.69869e30	−0.956464	−0.478232	−	0.878234i	$-0.658722\pi$
$263$	−1.69869e30	−0.956464	−0.478232	+	0.878234i	$0.658722\pi$
$264$	4.24522e30	2.27956
$265$	1.99991e29	0.102432
$266$	0	0
$267$	−9.56865e29	−0.446128
$268$	−3.01668e29	−0.134228
$269$	3.61152e29	0.153386	0.0766932	−	0.997055i	$-0.475564\pi$
$269$	3.61152e29	0.153386	0.0766932	+	0.997055i	$0.475564\pi$
$270$	5.28824e30	2.14419
$271$	−2.36332e30	−0.914968	−0.457484	−	0.889218i	$-0.651249\pi$
$271$	−2.36332e30	−0.914968	−0.457484	+	0.889218i	$0.651249\pi$
$272$	−1.20476e30	−0.445438
$273$	0	0
$274$	8.97860e30	3.02919
$275$	4.35057e30	1.40245
$276$	−2.97650e30	−0.916943
$277$	−4.03886e30	−1.18922	−0.594609	−	0.804015i	$-0.702693\pi$
$277$	−4.03886e30	−1.18922	−0.594609	+	0.804015i	$0.702693\pi$
$278$	−2.75048e30	−0.774192
$279$	4.01111e30	1.07947
$280$	0	0
$281$	−3.53953e30	−0.871197	−0.435599	−	0.900141i	$-0.643463\pi$
$281$	−3.53953e30	−0.871197	−0.435599	+	0.900141i	$0.643463\pi$
$282$	3.05821e30	0.720034
$283$	2.70985e30	0.610400	0.305200	−	0.952288i	$-0.401277\pi$
$283$	2.70985e30	0.610400	0.305200	+	0.952288i	$0.401277\pi$
$284$	−1.43186e31	−3.08617
$285$	−1.14729e30	−0.236654
$286$	−2.00978e31	−3.96802
$287$	0	0
$288$	−6.46648e30	−1.17020
$289$	−5.53743e30	−0.959589
$290$	−1.52824e30	−0.253639
$291$	3.07144e30	0.488293
$292$	3.34662e30	0.509708
$293$	9.51374e30	1.38837	0.694186	−	0.719796i	$-0.255764\pi$
$293$	9.51374e30	1.38837	0.694186	+	0.719796i	$0.255764\pi$
$294$	0	0
$295$	1.05607e31	1.41552
$296$	−2.11087e31	−2.71216
$297$	−1.29510e31	−1.59531
$298$	1.38350e31	1.63409
$299$	8.12471e30	0.920275
$300$	8.44063e30	0.916979
$301$	0	0
$302$	−1.71232e30	−0.171198
$303$	−9.74466e30	−0.934833
$304$	8.51002e30	0.783449
$305$	1.49730e31	1.32300
$306$	3.24707e30	0.275406
$307$	−7.32766e30	−0.596672	−0.298336	−	0.954461i	$-0.596432\pi$
$307$	−7.32766e30	−0.596672	−0.298336	+	0.954461i	$0.596432\pi$
$308$	0	0
$309$	−1.07939e31	−0.810396
$310$	4.89023e31	3.52621
$311$	1.87140e31	1.29617	0.648085	−	0.761568i	$-0.275570\pi$
$311$	1.87140e31	1.29617	0.648085	+	0.761568i	$0.275570\pi$
$312$	−2.24818e31	−1.49589
$313$	1.51596e30	0.0969134	0.0484567	−	0.998825i	$-0.484570\pi$
$313$	1.51596e30	0.0969134	0.0484567	+	0.998825i	$0.484570\pi$
$314$	3.34356e31	2.05395
$315$	0	0
$316$	−2.09152e31	−1.18679
$317$	1.36142e30	0.0742593	0.0371296	−	0.999310i	$-0.488179\pi$
$317$	1.36142e30	0.0742593	0.0371296	+	0.999310i	$0.488179\pi$
$318$	−1.35259e30	−0.0709295
$319$	3.74268e30	0.188712
$320$	−1.79994e31	−0.872735
$321$	−6.10658e30	−0.284764
$322$	0	0
$323$	−1.64724e30	−0.0710762
$324$	1.73823e31	0.721595
$325$	−2.30397e31	−0.920312
$326$	1.81231e31	0.696646
$327$	−1.27928e31	−0.473282
$328$	1.70684e31	0.607813
$329$	0	0
$330$	−6.75252e31	−2.22865
$331$	−1.41516e31	−0.449735	−0.224867	−	0.974389i	$-0.572195\pi$
$331$	−1.41516e31	−0.449735	−0.224867	+	0.974389i	$0.572195\pi$
$332$	4.16211e31	1.27376
$333$	2.75399e31	0.811726
$334$	−2.99670e31	−0.850770
$335$	2.76661e30	0.0756637
$336$	0	0
$337$	−3.73362e31	−0.947886	−0.473943	−	0.880556i	$-0.657170\pi$
$337$	−3.73362e31	−0.947886	−0.473943	+	0.880556i	$0.657170\pi$
$338$	3.14900e31	0.770395
$339$	1.13159e31	0.266804
$340$	2.78113e31	0.632025
$341$	−1.19762e32	−2.62356
$342$	−2.29363e31	−0.484392
$343$	0	0
$344$	4.95235e31	0.972369
$345$	2.72976e31	0.516875
$346$	−6.42031e31	−1.17248
$347$	−7.99786e31	−1.40882	−0.704410	−	0.709793i	$-0.748788\pi$
$347$	−7.99786e31	−1.40882	−0.704410	+	0.709793i	$0.748788\pi$
$348$	7.26125e30	0.123387
$349$	1.46039e31	0.239415	0.119707	−	0.992809i	$-0.461804\pi$
$349$	1.46039e31	0.239415	0.119707	+	0.992809i	$0.461804\pi$
$350$	0	0
$351$	6.85856e31	1.04687
$352$	1.93074e32	2.84407
$353$	2.15628e31	0.306564	0.153282	−	0.988182i	$-0.451016\pi$
$353$	2.15628e31	0.306564	0.153282	+	0.988182i	$0.451016\pi$
$354$	−7.14246e31	−0.980183
$355$	1.31316e32	1.73966
$356$	−1.63843e32	−2.09558
$357$	0	0
$358$	4.59218e31	0.547622
$359$	7.18637e31	0.827616	0.413808	−	0.910364i	$-0.364198\pi$
$359$	7.18637e31	0.827616	0.413808	+	0.910364i	$0.364198\pi$
$360$	2.23276e32	2.48348
$361$	−8.14409e31	−0.874989
$362$	5.12964e31	0.532389
$363$	1.15227e32	1.15537
$364$	0	0
$365$	−3.06920e31	−0.287319
$366$	−1.01266e32	−0.916119
$367$	1.80268e32	1.57613	0.788066	−	0.615591i	$-0.211083\pi$
$367$	1.80268e32	1.57613	0.788066	+	0.615591i	$0.211083\pi$
$368$	−2.02479e32	−1.71113
$369$	−2.22686e31	−0.181913
$370$	3.35759e32	2.65158
$371$	0	0
$372$	−2.32354e32	−1.71539
$373$	−2.30911e32	−1.64848	−0.824242	−	0.566238i	$-0.808398\pi$
$373$	−2.30911e32	−1.64848	−0.824242	+	0.566238i	$0.808398\pi$
$374$	−9.69499e31	−0.669348
$375$	2.28282e31	0.152433
$376$	3.01925e32	1.95007
$377$	−1.98204e31	−0.123836
$378$	0	0
$379$	2.72543e31	0.159384	0.0796920	−	0.996820i	$-0.474606\pi$
$379$	2.72543e31	0.159384	0.0796920	+	0.996820i	$0.474606\pi$
$380$	−1.96450e32	−1.11162
$381$	−1.62597e32	−0.890327
$382$	4.19230e32	2.22157
$383$	3.51608e32	1.80332	0.901662	−	0.432441i	$-0.142348\pi$
$383$	3.51608e32	1.80332	0.901662	+	0.432441i	$0.142348\pi$
$384$	−3.68764e31	−0.183066
$385$	0	0
$386$	1.94210e32	0.903505
$387$	−6.46119e31	−0.291022
$388$	5.25921e32	2.29363
$389$	3.20353e32	1.35288	0.676440	−	0.736498i	$-0.263522\pi$
$389$	3.20353e32	1.35288	0.676440	+	0.736498i	$0.263522\pi$
$390$	3.57600e32	1.46248
$391$	3.91928e31	0.155237
$392$	0	0
$393$	1.22879e32	0.456636
$394$	8.47538e31	0.305110
$395$	1.91814e32	0.668985
$396$	−9.48373e32	−3.20471
$397$	1.16866e32	0.382654	0.191327	−	0.981526i	$-0.438721\pi$
$397$	1.16866e32	0.382654	0.191327	+	0.981526i	$0.438721\pi$
$398$	8.64127e32	2.74182
$399$	0	0
$400$	5.74183e32	1.71120
$401$	3.51301e32	1.01479	0.507393	−	0.861715i	$-0.330609\pi$
$401$	3.51301e32	1.01479	0.507393	+	0.861715i	$0.330609\pi$
$402$	−1.87113e31	−0.0523936
$403$	6.34237e32	1.72163
$404$	−1.66857e33	−4.39115
$405$	−1.59413e32	−0.406759
$406$	0	0
$407$	−8.22277e32	−1.97282
$408$	−1.08450e32	−0.252335
$409$	−1.79509e32	−0.405085	−0.202542	−	0.979273i	$-0.564920\pi$
$409$	−1.79509e32	−0.405085	−0.202542	+	0.979273i	$0.564920\pi$
$410$	−2.71493e32	−0.594237
$411$	3.91244e32	0.830663
$412$	−1.84823e33	−3.80663
$413$	0	0
$414$	5.45724e32	1.05796
$415$	−3.81709e32	−0.718011
$416$	−1.02248e33	−1.86633
$417$	−1.19853e32	−0.212298
$418$	6.84824e32	1.17727
$419$	7.83929e32	1.30798	0.653991	−	0.756503i	$-0.273094\pi$
$419$	7.83929e32	1.30798	0.653991	+	0.756503i	$0.273094\pi$
$420$	0	0
$421$	5.64321e32	0.887156	0.443578	−	0.896236i	$-0.353709\pi$
$421$	5.64321e32	0.887156	0.443578	+	0.896236i	$0.353709\pi$
$422$	2.03873e33	3.11139
$423$	−3.93912e32	−0.583639
$424$	−1.33536e32	−0.192099
$425$	−1.11141e32	−0.155244
$426$	−8.88124e32	−1.20463
$427$	0	0
$428$	−1.04563e33	−1.33761
$429$	−8.75766e32	−1.08811
$430$	−7.87729e32	−0.950652
$431$	1.72017e32	0.201653	0.100827	−	0.994904i	$-0.467851\pi$
$431$	1.72017e32	0.201653	0.100827	+	0.994904i	$0.467851\pi$
$432$	−1.70925e33	−1.94652
$433$	1.53446e33	1.69769	0.848844	−	0.528643i	$-0.177299\pi$
$433$	1.53446e33	1.69769	0.848844	+	0.528643i	$0.177299\pi$
$434$	0	0
$435$	−6.65932e31	−0.0695528
$436$	−2.19051e33	−2.22312
$437$	−2.76846e32	−0.273036
$438$	2.07578e32	0.198955
$439$	−9.33238e32	−0.869332	−0.434666	−	0.900592i	$-0.643134\pi$
$439$	−9.33238e32	−0.869332	−0.434666	+	0.900592i	$0.643134\pi$
$440$	−6.66649e33	−6.03586
$441$	0	0
$442$	5.13427e32	0.439238
$443$	1.24372e32	0.103437	0.0517185	−	0.998662i	$-0.483530\pi$
$443$	1.24372e32	0.103437	0.0517185	+	0.998662i	$0.483530\pi$
$444$	−1.59532e33	−1.28991
$445$	1.50261e33	1.18126
$446$	−3.73249e33	−2.85307
$447$	6.02862e32	0.448099
$448$	0	0
$449$	−7.18416e32	−0.505006	−0.252503	−	0.967596i	$-0.581254\pi$
$449$	−7.18416e32	−0.505006	−0.252503	+	0.967596i	$0.581254\pi$
$450$	−1.54754e33	−1.05800
$451$	6.64889e32	0.442122
$452$	1.93761e33	1.25325
$453$	−7.46146e31	−0.0469457
$454$	1.74061e33	1.06538
$455$	0	0
$456$	7.66058e32	0.443814
$457$	−8.61958e32	−0.485885	−0.242943	−	0.970041i	$-0.578113\pi$
$457$	−8.61958e32	−0.485885	−0.242943	+	0.970041i	$0.578113\pi$
$458$	−2.67121e33	−1.46517
$459$	3.30850e32	0.176593
$460$	4.67415e33	2.42789
$461$	3.61625e33	1.82809	0.914043	−	0.405618i	$-0.132944\pi$
$461$	3.61625e33	1.82809	0.914043	+	0.405618i	$0.132944\pi$
$462$	0	0
$463$	−3.51337e33	−1.68252	−0.841262	−	0.540627i	$-0.818187\pi$
$463$	−3.51337e33	−1.68252	−0.841262	+	0.540627i	$0.818187\pi$
$464$	4.93954e32	0.230256
$465$	2.13093e33	0.966956
$466$	6.46485e30	0.00285584
$467$	2.86487e33	1.23209	0.616047	−	0.787710i	$-0.288733\pi$
$467$	2.86487e33	1.23209	0.616047	+	0.787710i	$0.288733\pi$
$468$	5.02239e33	2.10299
$469$	0	0
$470$	−4.80246e33	−1.90652
$471$	1.45696e33	0.563232
$472$	−7.05147e33	−2.65463
$473$	1.92916e33	0.707300
$474$	−1.29729e33	−0.463241
$475$	7.85068e32	0.273047
$476$	0	0
$477$	1.74220e32	0.0574934
$478$	4.92048e32	0.158182
$479$	−2.71322e32	−0.0849749	−0.0424875	−	0.999097i	$-0.513528\pi$
$479$	−2.71322e32	−0.0849749	−0.0424875	+	0.999097i	$0.513528\pi$
$480$	−3.43535e33	−1.04823
$481$	4.35461e33	1.29460
$482$	−3.63670e33	−1.05346
$483$	0	0
$484$	1.97303e34	5.42708
$485$	−4.82325e33	−1.29291
$486$	7.24345e33	1.89231
$487$	3.30062e33	0.840395	0.420197	−	0.907433i	$-0.361961\pi$
$487$	3.30062e33	0.840395	0.420197	+	0.907433i	$0.361961\pi$
$488$	−9.99762e33	−2.48113
$489$	7.89717e32	0.191034
$490$	0	0
$491$	−3.51808e33	−0.808698	−0.404349	−	0.914605i	$-0.632502\pi$
$491$	−3.51808e33	−0.808698	−0.404349	+	0.914605i	$0.632502\pi$
$492$	1.28997e33	0.289078
$493$	−9.56118e31	−0.0208894
$494$	−3.62669e33	−0.772544
$495$	8.69757e33	1.80648
$496$	−1.58061e34	−3.20113
$497$	0	0
$498$	2.58160e33	0.497189
$499$	2.95877e33	0.555718	0.277859	−	0.960622i	$-0.410375\pi$
$499$	2.95877e33	0.555718	0.277859	+	0.960622i	$0.410375\pi$
$500$	3.90885e33	0.716019
$501$	−1.30582e33	−0.233298
$502$	3.07760e33	0.536311
$503$	−9.10543e33	−1.54775	−0.773874	−	0.633339i	$-0.781684\pi$
$503$	−9.10543e33	−1.54775	−0.773874	+	0.633339i	$0.781684\pi$
$504$	0	0
$505$	1.53025e34	2.47526
$506$	−1.62941e34	−2.57127
$507$	1.37218e33	0.211257
$508$	−2.78413e34	−4.18209
$509$	3.59253e33	0.526536	0.263268	−	0.964723i	$-0.415200\pi$
$509$	3.59253e33	0.526536	0.263268	+	0.964723i	$0.415200\pi$
$510$	1.72502e33	0.246699
$511$	0	0
$512$	−1.51405e34	−2.06189
$513$	−2.33702e33	−0.310596
$514$	1.44532e34	1.87467
$515$	1.69502e34	2.14578
$516$	3.74281e33	0.462462
$517$	1.17613e34	1.41848
$518$	0	0
$519$	−2.79766e33	−0.321516
$520$	3.53044e34	3.96083
$521$	−8.62735e33	−0.944944	−0.472472	−	0.881346i	$-0.656638\pi$
$521$	−8.62735e33	−0.944944	−0.472472	+	0.881346i	$0.656638\pi$
$522$	−1.33131e33	−0.142363
$523$	−8.22313e33	−0.858551	−0.429275	−	0.903174i	$-0.641231\pi$
$523$	−8.22313e33	−0.858551	−0.429275	+	0.903174i	$0.641231\pi$
$524$	2.10405e34	2.14493
$525$	0	0
$526$	−1.80413e34	−1.75366
$527$	3.05950e33	0.290414
$528$	2.18254e34	2.02319
$529$	−4.45876e33	−0.403663
$530$	2.12404e33	0.187808
$531$	9.19984e33	0.794509
$532$	0	0
$533$	−3.52112e33	−0.290128
$534$	−1.01626e34	−0.817970
$535$	9.58948e33	0.754002
$536$	−1.84729e33	−0.141898
$537$	2.00105e33	0.150169
$538$	3.83569e33	0.281232
$539$	0	0
$540$	3.94574e34	2.76189
$541$	−2.51571e34	−1.72066	−0.860331	−	0.509736i	$-0.829743\pi$
$541$	−2.51571e34	−1.72066	−0.860331	+	0.509736i	$0.829743\pi$
$542$	−2.51001e34	−1.67758
$543$	2.23525e33	0.145992
$544$	−4.93234e33	−0.314823
$545$	2.00892e34	1.25316
$546$	0	0
$547$	−1.01748e34	−0.606298	−0.303149	−	0.952943i	$-0.598038\pi$
$547$	−1.01748e34	−0.606298	−0.303149	+	0.952943i	$0.598038\pi$
$548$	6.69924e34	3.90183
$549$	1.30436e34	0.742580
$550$	4.62060e34	2.57137
$551$	6.75373e32	0.0367408
$552$	−1.82269e34	−0.969334
$553$	0	0
$554$	−4.28955e34	−2.18042
$555$	1.46307e34	0.727116
$556$	−2.05223e34	−0.997220
$557$	−3.30597e32	−0.0157076	−0.00785378	−	0.999969i	$-0.502500\pi$
$557$	−3.30597e32	−0.0157076	−0.00785378	+	0.999969i	$0.502500\pi$
$558$	4.26008e34	1.97920
$559$	−1.02164e34	−0.464143
$560$	0	0
$561$	−4.22461e33	−0.183548
$562$	−3.75922e34	−1.59733
$563$	−9.83609e33	−0.408759	−0.204380	−	0.978892i	$-0.565518\pi$
$563$	−9.83609e33	−0.408759	−0.204380	+	0.978892i	$0.565518\pi$
$564$	2.28183e34	0.927460
$565$	−1.77699e34	−0.706448
$566$	2.87805e34	1.11916
$567$	0	0
$568$	−8.76810e34	−3.26250
$569$	2.48072e33	0.0902973	0.0451487	−	0.998980i	$-0.485624\pi$
$569$	2.48072e33	0.0902973	0.0451487	+	0.998980i	$0.485624\pi$
$570$	−1.21850e34	−0.433902
$571$	1.20298e34	0.419091	0.209546	−	0.977799i	$-0.432802\pi$
$571$	1.20298e34	0.419091	0.209546	+	0.977799i	$0.432802\pi$
$572$	−1.49957e35	−5.11112
$573$	1.82680e34	0.609198
$574$	0	0
$575$	−1.86792e34	−0.596361
$576$	−1.56800e34	−0.489851
$577$	4.27600e34	1.30720	0.653598	−	0.756842i	$-0.273259\pi$
$577$	4.27600e34	1.30720	0.653598	+	0.756842i	$0.273259\pi$
$578$	−5.88113e34	−1.75939
$579$	8.46273e33	0.247759
$580$	−1.14027e34	−0.326707
$581$	0	0
$582$	3.26209e34	0.895278
$583$	−5.20180e33	−0.139732
$584$	2.04933e34	0.538831
$585$	−4.60605e34	−1.18544
$586$	1.01042e35	2.54556
$587$	−4.35684e34	−1.07447	−0.537237	−	0.843431i	$-0.680532\pi$
$587$	−4.35684e34	−1.07447	−0.537237	+	0.843431i	$0.680532\pi$
$588$	0	0
$589$	−2.16113e34	−0.510788
$590$	1.12162e35	2.59534
$591$	3.69316e33	0.0836671
$592$	−1.08523e35	−2.40714
$593$	−7.25231e34	−1.57504	−0.787522	−	0.616287i	$-0.788636\pi$
$593$	−7.25231e34	−1.57504	−0.787522	+	0.616287i	$0.788636\pi$
$594$	−1.37548e35	−2.92499
$595$	0	0
$596$	1.03228e35	2.10483
$597$	3.76545e34	0.751861
$598$	8.62900e34	1.68731
$599$	6.74316e34	1.29130	0.645652	−	0.763632i	$-0.276586\pi$
$599$	6.74316e34	1.29130	0.645652	+	0.763632i	$0.276586\pi$
$600$	5.16870e34	0.969372
$601$	4.74903e34	0.872316	0.436158	−	0.899870i	$-0.356339\pi$
$601$	4.74903e34	0.872316	0.436158	+	0.899870i	$0.356339\pi$
$602$	0	0
$603$	2.41010e33	0.0424687
$604$	−1.27762e34	−0.220516
$605$	−1.80947e35	−3.05921
$606$	−1.03495e35	−1.71400
$607$	6.13342e33	0.0995047	0.0497524	−	0.998762i	$-0.484157\pi$
$607$	6.13342e33	0.0995047	0.0497524	+	0.998762i	$0.484157\pi$
$608$	3.48405e34	0.553720
$609$	0	0
$610$	1.59024e35	2.42571
$611$	−6.22854e34	−0.930831
$612$	2.42275e34	0.354745
$613$	9.67039e32	0.0138736	0.00693678	−	0.999976i	$-0.497792\pi$
$613$	9.67039e32	0.0138736	0.00693678	+	0.999976i	$0.497792\pi$
$614$	−7.78248e34	−1.09399
$615$	−1.18303e34	−0.162951
$616$	0	0
$617$	−1.38070e34	−0.182615	−0.0913073	−	0.995823i	$-0.529105\pi$
$617$	−1.38070e34	−0.182615	−0.0913073	+	0.995823i	$0.529105\pi$
$618$	−1.14639e35	−1.48585
$619$	−1.49788e34	−0.190259	−0.0951293	−	0.995465i	$-0.530326\pi$
$619$	−1.49788e34	−0.190259	−0.0951293	+	0.995465i	$0.530326\pi$
$620$	3.64877e35	4.54204
$621$	5.56049e34	0.678373
$622$	1.98756e35	2.37651
$623$	0	0
$624$	−1.15583e35	−1.32765
$625$	−1.04439e35	−1.17587
$626$	1.61006e34	0.177689
$627$	2.98413e34	0.322830
$628$	2.49475e35	2.64564
$629$	2.10062e34	0.218381
$630$	0	0
$631$	1.55673e35	1.55541	0.777706	−	0.628628i	$-0.216383\pi$
$631$	1.55673e35	1.55541	0.777706	+	0.628628i	$0.216383\pi$
$632$	−1.28076e35	−1.25460
$633$	8.88382e34	0.853205
$634$	1.44592e34	0.136153
$635$	2.55334e35	2.35742
$636$	−1.00921e34	−0.0913627
$637$	0	0
$638$	3.97498e34	0.346000
$639$	1.14395e35	0.976439
$640$	5.79089e34	0.484726
$641$	−1.54010e35	−1.26422	−0.632111	−	0.774878i	$-0.717811\pi$
$641$	−1.54010e35	−1.26422	−0.632111	+	0.774878i	$0.717811\pi$
$642$	−6.48561e34	−0.522111
$643$	−2.66772e34	−0.210622	−0.105311	−	0.994439i	$-0.533584\pi$
$643$	−2.66772e34	−0.210622	−0.105311	+	0.994439i	$0.533584\pi$
$644$	0	0
$645$	−3.43254e34	−0.260687
$646$	−1.74948e34	−0.130317
$647$	−1.35893e34	−0.0992874	−0.0496437	−	0.998767i	$-0.515809\pi$
$647$	−1.35893e34	−0.0992874	−0.0496437	+	0.998767i	$0.515809\pi$
$648$	1.06442e35	0.762825
$649$	−2.74686e35	−1.93098
$650$	−2.44698e35	−1.68738
$651$	0	0
$652$	1.35223e35	0.897335
$653$	2.42684e35	1.57989	0.789943	−	0.613180i	$-0.210110\pi$
$653$	2.42684e35	1.57989	0.789943	+	0.613180i	$0.210110\pi$
$654$	−1.35869e35	−0.867756
$655$	−1.92963e35	−1.20909
$656$	8.77513e34	0.539455
$657$	−2.67370e34	−0.161267
$658$	0	0
$659$	−1.83966e35	−1.06824	−0.534120	−	0.845409i	$-0.679357\pi$
$659$	−1.83966e35	−1.06824	−0.534120	+	0.845409i	$0.679357\pi$
$660$	−5.03829e35	−2.87067
$661$	2.05901e35	1.15117	0.575587	−	0.817740i	$-0.304774\pi$
$661$	2.05901e35	1.15117	0.575587	+	0.817740i	$0.304774\pi$
$662$	−1.50300e35	−0.824583
$663$	2.23726e34	0.120448
$664$	2.54871e35	1.34654
$665$	0	0
$666$	2.92493e35	1.48829
$667$	−1.60692e34	−0.0802455
$668$	−2.23594e35	−1.09586
$669$	−1.62644e35	−0.782367
$670$	2.93833e34	0.138728
$671$	−3.89451e35	−1.80477
$672$	0	0
$673$	−1.60111e35	−0.714878	−0.357439	−	0.933936i	$-0.616350\pi$
$673$	−1.60111e35	−0.714878	−0.357439	+	0.933936i	$0.616350\pi$
$674$	−3.96536e35	−1.73794
$675$	−1.57682e35	−0.678399
$676$	2.34958e35	0.992330
$677$	−4.10165e35	−1.70059	−0.850296	−	0.526305i	$-0.823577\pi$
$677$	−4.10165e35	−1.70059	−0.850296	+	0.526305i	$0.823577\pi$
$678$	1.20183e35	0.489182
$679$	0	0
$680$	1.70305e35	0.668137
$681$	7.58475e34	0.292148
$682$	−1.27196e36	−4.81026
$683$	−1.27532e35	−0.473545	−0.236772	−	0.971565i	$-0.576090\pi$
$683$	−1.27532e35	−0.473545	−0.236772	+	0.971565i	$0.576090\pi$
$684$	−1.71136e35	−0.623935
$685$	−6.14390e35	−2.19944
$686$	0	0
$687$	−1.16398e35	−0.401779
$688$	2.54608e35	0.863012
$689$	2.75477e34	0.0916947
$690$	2.89919e35	0.947684
$691$	−4.44974e35	−1.42843	−0.714215	−	0.699926i	$-0.753216\pi$
$691$	−4.44974e35	−1.42843	−0.714215	+	0.699926i	$0.753216\pi$
$692$	−4.79041e35	−1.51024
$693$	0	0
$694$	−8.49428e35	−2.58305
$695$	1.88211e35	0.562127
$696$	4.44649e34	0.130437
$697$	−1.69855e34	−0.0489406
$698$	1.55103e35	0.438964
$699$	2.81707e32	0.000783128 0
$700$	0	0
$701$	1.56793e35	0.420584	0.210292	−	0.977639i	$-0.432559\pi$
$701$	1.56793e35	0.420584	0.210292	+	0.977639i	$0.432559\pi$
$702$	7.28427e35	1.91943
$703$	−1.48381e35	−0.384094
$704$	4.68167e35	1.19054
$705$	−2.09268e35	−0.522804
$706$	2.29012e35	0.562081
$707$	0	0
$708$	−5.32924e35	−1.26255
$709$	1.18860e35	0.276667	0.138333	−	0.990386i	$-0.455825\pi$
$709$	1.18860e35	0.276667	0.138333	+	0.990386i	$0.455825\pi$
$710$	1.39467e36	3.18964
$711$	1.67097e35	0.375490
$712$	−1.00331e36	−2.21531
$713$	5.14200e35	1.11561
$714$	0	0
$715$	1.37526e36	2.88111
$716$	3.42638e35	0.705380
$717$	2.14411e34	0.0433767
$718$	7.63242e35	1.51742
$719$	3.53737e35	0.691145	0.345572	−	0.938392i	$-0.387685\pi$
$719$	3.53737e35	0.691145	0.345572	+	0.938392i	$0.387685\pi$
$720$	1.14790e36	2.20417
$721$	0	0
$722$	−8.64959e35	−1.60428
$723$	−1.58470e35	−0.288880
$724$	3.82740e35	0.685759
$725$	4.55683e34	0.0802487
$726$	1.22379e36	2.11836
$727$	−5.31713e35	−0.904685	−0.452342	−	0.891844i	$-0.649411\pi$
$727$	−5.31713e35	−0.904685	−0.452342	+	0.891844i	$0.649411\pi$
$728$	0	0
$729$	1.29782e35	0.213364
$730$	−3.25970e35	−0.526796
$731$	−4.92830e34	−0.0782943
$732$	−7.55584e35	−1.18003
$733$	−1.06594e36	−1.63656	−0.818280	−	0.574819i	$-0.805072\pi$
$733$	−1.06594e36	−1.63656	−0.818280	+	0.574819i	$0.805072\pi$
$734$	1.91457e36	2.88982
$735$	0	0
$736$	−8.28963e35	−1.20938
$737$	−7.19600e34	−0.103216
$738$	−2.36508e35	−0.333535
$739$	7.47492e35	1.03646	0.518228	−	0.855242i	$-0.326592\pi$
$739$	7.47492e35	1.03646	0.518228	+	0.855242i	$0.326592\pi$
$740$	2.50521e36	3.41545
$741$	−1.58034e35	−0.211847
$742$	0	0
$743$	−1.00025e35	−0.129643	−0.0648215	−	0.997897i	$-0.520648\pi$
$743$	−1.00025e35	−0.129643	−0.0648215	+	0.997897i	$0.520648\pi$
$744$	−1.42284e36	−1.81340
$745$	−9.46705e35	−1.18648
$746$	−2.45244e36	−3.02247
$747$	−3.32522e35	−0.403007
$748$	−7.23377e35	−0.862173
$749$	0	0
$750$	2.42451e35	0.279485
$751$	7.80838e35	0.885241	0.442621	−	0.896709i	$-0.354049\pi$
$751$	7.80838e35	0.885241	0.442621	+	0.896709i	$0.354049\pi$
$752$	1.55224e36	1.73076
$753$	1.34107e35	0.147067
$754$	−2.10507e35	−0.227051
$755$	1.17171e35	0.124304
$756$	0	0
$757$	−1.18318e36	−1.21438	−0.607188	−	0.794558i	$-0.707703\pi$
$757$	−1.18318e36	−1.21438	−0.607188	+	0.794558i	$0.707703\pi$
$758$	2.89459e35	0.292228
$759$	−7.10016e35	−0.705093
$760$	−1.20298e36	−1.17514
$761$	1.90333e36	1.82897	0.914486	−	0.404618i	$-0.132596\pi$
$761$	1.90333e36	1.82897	0.914486	+	0.404618i	$0.132596\pi$
$762$	−1.72689e36	−1.63240
$763$	0	0
$764$	3.12802e36	2.86156
$765$	−2.22191e35	−0.199967
$766$	3.73432e36	3.30637
$767$	1.45468e36	1.26714
$768$	−7.76254e35	−0.665256
$769$	−1.73117e36	−1.45969	−0.729844	−	0.683614i	$-0.760407\pi$
$769$	−1.73117e36	−1.45969	−0.729844	+	0.683614i	$0.760407\pi$
$770$	0	0
$771$	6.29799e35	0.514070
$772$	1.44907e36	1.16378
$773$	7.14423e35	0.564562	0.282281	−	0.959332i	$-0.408909\pi$
$773$	7.14423e35	0.564562	0.282281	+	0.959332i	$0.408909\pi$
$774$	−6.86223e35	−0.533584
$775$	−1.45815e36	−1.11566
$776$	3.22053e36	2.42469
$777$	0	0
$778$	3.40237e36	2.48049
$779$	1.19980e35	0.0860780
$780$	2.66817e36	1.88379
$781$	−3.41556e36	−2.37314
$782$	4.16254e35	0.284626
$783$	−1.35650e35	−0.0912845
$784$	0	0
$785$	−2.28795e36	−1.49133
$786$	1.30506e36	0.837236
$787$	−1.20748e36	−0.762423	−0.381211	−	0.924488i	$-0.624493\pi$
$787$	−1.20748e36	−0.762423	−0.381211	+	0.924488i	$0.624493\pi$
$788$	6.32378e35	0.393006
$789$	−7.86153e35	−0.480889
$790$	2.03720e36	1.22658
$791$	0	0
$792$	−5.80745e36	−3.38782
$793$	2.06245e36	1.18432
$794$	1.24119e36	0.701591
$795$	9.25554e34	0.0515006
$796$	6.44755e36	3.53168
$797$	1.13770e34	0.00613476	0.00306738	−	0.999995i	$-0.499024\pi$
$797$	1.13770e34	0.00613476	0.00306738	+	0.999995i	$0.499024\pi$
$798$	0	0
$799$	−3.00458e35	−0.157018
$800$	2.35074e36	1.20943
$801$	1.30899e36	0.663023
$802$	3.73106e36	1.86060
$803$	7.98306e35	0.391945
$804$	−1.39611e35	−0.0674870
$805$	0	0
$806$	6.73604e36	3.15658
$807$	1.67141e35	0.0771193
$808$	−1.02177e37	−4.64204
$809$	−1.92235e36	−0.859955	−0.429978	−	0.902840i	$-0.641479\pi$
$809$	−1.92235e36	−0.859955	−0.429978	+	0.902840i	$0.641479\pi$
$810$	−1.69308e36	−0.745787
$811$	9.14531e35	0.396678	0.198339	−	0.980134i	$-0.436445\pi$
$811$	9.14531e35	0.396678	0.198339	+	0.980134i	$0.436445\pi$
$812$	0	0
$813$	−1.09374e36	−0.460026
$814$	−8.73315e36	−3.61714
$815$	−1.24013e36	−0.505822
$816$	−5.57559e35	−0.223956
$817$	3.48120e35	0.137706
$818$	−1.90651e36	−0.742718
$819$	0	0
$820$	−2.02570e36	−0.765424
$821$	−5.27921e36	−1.96462	−0.982312	−	0.187251i	$-0.940042\pi$
$821$	−5.27921e36	−1.96462	−0.982312	+	0.187251i	$0.940042\pi$
$822$	4.15528e36	1.52301
$823$	5.08465e35	0.183554	0.0917768	−	0.995780i	$-0.470745\pi$
$823$	5.08465e35	0.183554	0.0917768	+	0.995780i	$0.470745\pi$
$824$	−1.13178e37	−4.02413
$825$	2.01344e36	0.705120
$826$	0	0
$827$	−2.13937e36	−0.726888	−0.363444	−	0.931616i	$-0.618399\pi$
$827$	−2.13937e36	−0.726888	−0.363444	+	0.931616i	$0.618399\pi$
$828$	4.07184e36	1.36273
$829$	−1.68108e36	−0.554188	−0.277094	−	0.960843i	$-0.589371\pi$
$829$	−1.68108e36	−0.554188	−0.277094	+	0.960843i	$0.589371\pi$
$830$	−4.05401e36	−1.31646
$831$	−1.86918e36	−0.597912
$832$	−2.47932e36	−0.781251
$833$	0	0
$834$	−1.27292e36	−0.389247
$835$	2.05059e36	0.617729
$836$	5.10971e36	1.51641
$837$	4.34068e36	1.26908
$838$	8.32587e36	2.39817
$839$	6.06533e36	1.72119	0.860597	−	0.509287i	$-0.170091\pi$
$839$	6.06533e36	1.72119	0.860597	+	0.509287i	$0.170091\pi$
$840$	0	0
$841$	−3.59116e36	−0.989202
$842$	5.99348e36	1.62659
$843$	−1.63809e36	−0.438019
$844$	1.52117e37	4.00772
$845$	−2.15481e36	−0.559370
$846$	−4.18362e36	−1.07009
$847$	0	0
$848$	−6.86528e35	−0.170494
$849$	1.25411e36	0.306896
$850$	−1.18040e36	−0.284637
$851$	3.53045e36	0.838900
$852$	−6.62660e36	−1.55166
$853$	−2.28852e36	−0.528071	−0.264035	−	0.964513i	$-0.585054\pi$
$853$	−2.28852e36	−0.528071	−0.264035	+	0.964513i	$0.585054\pi$
$854$	0	0
$855$	1.56949e36	0.351708
$856$	−6.40298e36	−1.41404
$857$	−1.91105e36	−0.415921	−0.207961	−	0.978137i	$-0.566683\pi$
$857$	−1.91105e36	−0.415921	−0.207961	+	0.978137i	$0.566683\pi$
$858$	−9.30124e36	−1.99503
$859$	−1.73980e36	−0.367777	−0.183889	−	0.982947i	$-0.558869\pi$
$859$	−1.73980e36	−0.367777	−0.183889	+	0.982947i	$0.558869\pi$
$860$	−5.87752e36	−1.22451
$861$	0	0
$862$	1.82694e36	0.369729
$863$	−4.58076e36	−0.913697	−0.456849	−	0.889544i	$-0.651022\pi$
$863$	−4.58076e36	−0.913697	−0.456849	+	0.889544i	$0.651022\pi$
$864$	−6.99778e36	−1.37575
$865$	4.39331e36	0.851315
$866$	1.62971e37	3.11269
$867$	−2.56271e36	−0.482460
$868$	0	0
$869$	−4.98912e36	−0.912592
$870$	−7.07266e35	−0.127524
$871$	3.81086e35	0.0677323
$872$	−1.34138e37	−2.35015
$873$	−4.20172e36	−0.725687
$874$	−2.94029e36	−0.500608
$875$	0	0
$876$	1.54881e36	0.256270
$877$	1.88890e35	0.0308116	0.0154058	−	0.999881i	$-0.495096\pi$
$877$	1.88890e35	0.0308116	0.0154058	+	0.999881i	$0.495096\pi$
$878$	−9.91163e36	−1.59391
$879$	4.40294e36	0.698043
$880$	−3.42735e37	−5.35704
$881$	−2.30697e36	−0.355502	−0.177751	−	0.984075i	$-0.556882\pi$
$881$	−2.30697e36	−0.355502	−0.177751	+	0.984075i	$0.556882\pi$
$882$	0	0
$883$	3.61124e36	0.540938	0.270469	−	0.962729i	$-0.412821\pi$
$883$	3.61124e36	0.540938	0.270469	+	0.962729i	$0.412821\pi$
$884$	3.83085e36	0.565773
$885$	4.88747e36	0.711694
$886$	1.32092e36	0.189650
$887$	3.14826e36	0.445683	0.222841	−	0.974855i	$-0.428467\pi$
$887$	3.14826e36	0.445683	0.222841	+	0.974855i	$0.428467\pi$
$888$	−9.76908e36	−1.36361
$889$	0	0
$890$	1.59588e37	2.16583
$891$	4.14638e36	0.554878
$892$	−2.78494e37	−3.67498
$893$	2.12235e36	0.276168
$894$	6.40281e36	0.821583
$895$	−3.14235e36	−0.397619
$896$	0	0
$897$	3.76010e36	0.462694
$898$	−7.63007e36	−0.925922
$899$	−1.25440e36	−0.150121
$900$	−1.15468e37	−1.36279
$901$	1.32887e35	0.0154676
$902$	7.06158e36	0.810626
$903$	0	0
$904$	1.18651e37	1.32485
$905$	−3.51012e36	−0.386558
$906$	−7.92458e35	−0.0860744
$907$	7.97194e36	0.854029	0.427015	−	0.904245i	$-0.359565\pi$
$907$	7.97194e36	0.854029	0.427015	+	0.904245i	$0.359565\pi$
$908$	1.29873e37	1.37229
$909$	1.33307e37	1.38932
$910$	0	0
$911$	−1.37224e37	−1.39140	−0.695698	−	0.718334i	$-0.744905\pi$
$911$	−1.37224e37	−1.39140	−0.695698	+	0.718334i	$0.744905\pi$
$912$	3.93842e36	0.393901
$913$	9.92833e36	0.979471
$914$	−9.15459e36	−0.890865
$915$	6.92949e36	0.665177
$916$	−1.99308e37	−1.88726
$917$	0	0
$918$	3.51386e36	0.323780
$919$	3.49900e36	0.318054	0.159027	−	0.987274i	$-0.449164\pi$
$919$	3.49900e36	0.318054	0.159027	+	0.987274i	$0.449164\pi$
$920$	2.86226e37	2.56662
$921$	−3.39123e36	−0.299993
$922$	3.84070e37	3.35177
$923$	1.80881e37	1.55730
$924$	0	0
$925$	−1.00115e37	−0.838933
$926$	−3.73144e37	−3.08489
$927$	1.47660e37	1.20439
$928$	2.02228e36	0.162739
$929$	−1.76139e37	−1.39849	−0.699246	−	0.714881i	$-0.746481\pi$
$929$	−1.76139e37	−1.39849	−0.699246	+	0.714881i	$0.746481\pi$
$930$	2.26319e37	1.77290
$931$	0	0
$932$	4.82365e34	0.00367855
$933$	8.66081e36	0.651686
$934$	3.04269e37	2.25903
$935$	6.63412e36	0.486002
$936$	3.07550e37	2.22315
$937$	2.25701e37	1.60986	0.804930	−	0.593370i	$-0.202203\pi$
$937$	2.25701e37	1.60986	0.804930	+	0.593370i	$0.202203\pi$
$938$	0	0
$939$	7.01584e35	0.0487259
$940$	−3.58328e37	−2.45574
$941$	−1.70977e37	−1.15629	−0.578147	−	0.815932i	$-0.696224\pi$
$941$	−1.70977e37	−1.15629	−0.578147	+	0.815932i	$0.696224\pi$
$942$	1.54740e37	1.03268
$943$	−2.85470e36	−0.188003
$944$	−3.62527e37	−2.35608
$945$	0	0
$946$	2.04890e37	1.29683
$947$	−6.18008e36	−0.386029	−0.193014	−	0.981196i	$-0.561826\pi$
$947$	−6.18008e36	−0.386029	−0.193014	+	0.981196i	$0.561826\pi$
$948$	−9.67951e36	−0.596690
$949$	−4.22766e36	−0.257201
$950$	8.33796e36	0.500628
$951$	6.30062e35	0.0373359
$952$	0	0
$953$	−2.46578e37	−1.42329	−0.711645	−	0.702539i	$-0.752050\pi$
$953$	−2.46578e37	−1.42329	−0.711645	+	0.702539i	$0.752050\pi$
$954$	1.85034e36	0.105413
$955$	−2.86872e37	−1.61304
$956$	3.67134e36	0.203751
$957$	1.73210e36	0.0948800
$958$	−2.88163e36	−0.155800
$959$	0	0
$960$	−8.33008e36	−0.438792
$961$	2.09071e37	1.08705
$962$	4.62490e37	2.37363
$963$	8.35378e36	0.423208
$964$	−2.71347e37	−1.35694
$965$	−1.32895e37	−0.656019
$966$	0	0
$967$	2.15136e37	1.03486	0.517432	−	0.855725i	$-0.326888\pi$
$967$	2.15136e37	1.03486	0.517432	+	0.855725i	$0.326888\pi$
$968$	1.20820e38	5.73717
$969$	−7.62338e35	−0.0357355
$970$	−5.12262e37	−2.37053
$971$	−2.14025e37	−0.977739	−0.488870	−	0.872357i	$-0.662591\pi$
$971$	−2.14025e37	−0.977739	−0.488870	+	0.872357i	$0.662591\pi$
$972$	5.40459e37	2.43744
$973$	0	0
$974$	3.50549e37	1.54085
$975$	−1.06627e37	−0.462712
$976$	−5.13993e37	−2.20209
$977$	2.72258e37	1.15159	0.575797	−	0.817593i	$-0.304692\pi$
$977$	2.72258e37	1.15159	0.575797	+	0.817593i	$0.304692\pi$
$978$	8.38734e36	0.350258
$979$	−3.90833e37	−1.61142
$980$	0	0
$981$	1.75005e37	0.703378
$982$	−3.73644e37	−1.48274
$983$	−1.97711e37	−0.774663	−0.387331	−	0.921941i	$-0.626603\pi$
$983$	−1.97711e37	−0.774663	−0.387331	+	0.921941i	$0.626603\pi$
$984$	7.89923e36	0.305595
$985$	−5.79956e36	−0.221535
$986$	−1.01546e36	−0.0383004
$987$	0	0
$988$	−2.70600e37	−0.995098
$989$	−8.28285e36	−0.300764
$990$	9.23742e37	3.31216
$991$	−3.22566e37	−1.14208	−0.571041	−	0.820921i	$-0.693460\pi$
$991$	−3.22566e37	−1.14208	−0.571041	+	0.820921i	$0.693460\pi$
$992$	−6.47111e37	−2.26247
$993$	−6.54935e36	−0.226117
$994$	0	0
$995$	−5.91308e37	−1.99079
$996$	1.92622e37	0.640418
$997$	−4.05678e37	−1.33196	−0.665981	−	0.745969i	$-0.731987\pi$
$997$	−4.05678e37	−1.33196	−0.665981	+	0.745969i	$0.731987\pi$
$998$	3.14242e37	1.01890
$999$	2.98027e37	0.954303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.f.1.15		16
7.2	even	3		7.26.c.a.4.2	yes	32
7.4	even	3		7.26.c.a.2.2	✓	32
7.6	odd	2		49.26.a.g.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.c.a.2.2	✓	32	7.4	even	3
7.26.c.a.4.2	yes	32	7.2	even	3
49.26.a.f.1.15		16	1.1	even	1	trivial
49.26.a.g.1.15		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)

\(f(q)\)	\(=\)	\(q+10620.7 q^{2} +462798. q^{3} +7.92447e7 q^{4} -7.26756e8 q^{5} +4.91524e9 q^{6} +4.85262e11 q^{8} -6.33106e11 q^{9} +O(q^{10})\)	\(q+10620.7 q^{2} +462798. q^{3} +7.92447e7 q^{4} -7.26756e8 q^{5} +4.91524e9 q^{6} +4.85262e11 q^{8} -6.33106e11 q^{9} -7.71865e12 q^{10} +1.89031e13 q^{11} +3.66743e13 q^{12} -1.00107e14 q^{13} -3.36342e14 q^{15} +2.49481e15 q^{16} -4.82905e14 q^{17} -6.72403e15 q^{18} +3.41110e15 q^{19} -5.75915e16 q^{20} +2.00764e17 q^{22} -8.11604e16 q^{23} +2.24578e17 q^{24} +2.30151e17 q^{25} -1.06320e18 q^{26} -6.85124e17 q^{27} +1.97993e17 q^{29} -3.57218e18 q^{30} -6.33560e18 q^{31} +1.02139e19 q^{32} +8.74831e18 q^{33} -5.12879e18 q^{34} -5.01703e19 q^{36} -4.34996e19 q^{37} +3.62282e19 q^{38} -4.63293e19 q^{39} -3.52667e20 q^{40} +3.51736e19 q^{41} +1.02055e20 q^{43} +1.49797e21 q^{44} +4.60114e20 q^{45} -8.61979e20 q^{46} +6.22189e20 q^{47} +1.15459e21 q^{48} +2.44437e21 q^{50} -2.23488e20 q^{51} -7.93293e21 q^{52} -2.75183e20 q^{53} -7.27649e21 q^{54} -1.37379e22 q^{55} +1.57865e21 q^{57} +2.10282e21 q^{58} -1.45313e22 q^{59} -2.66533e22 q^{60} -2.06025e22 q^{61} -6.72885e22 q^{62} +2.47667e22 q^{64} +7.27532e22 q^{65} +9.29131e22 q^{66} -3.80679e21 q^{67} -3.82677e22 q^{68} -3.75609e22 q^{69} -1.80688e23 q^{71} -3.07222e23 q^{72} +4.22315e22 q^{73} -4.61996e23 q^{74} +1.06514e23 q^{75} +2.70311e23 q^{76} -4.92049e23 q^{78} -2.63932e23 q^{79} -1.81312e24 q^{80} +2.19349e23 q^{81} +3.73568e23 q^{82} +5.25223e23 q^{83} +3.50954e23 q^{85} +1.08390e24 q^{86} +9.16308e22 q^{87} +9.17294e24 q^{88} -2.06756e24 q^{89} +4.88673e24 q^{90} -6.43153e24 q^{92} -2.93211e24 q^{93} +6.60808e24 q^{94} -2.47903e24 q^{95} +4.72697e24 q^{96} +6.63668e24 q^{97} -1.19677e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9}+O(q^{10}) \) 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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