LMFDB - Embedded newform 49.26.a.f.1.16

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			1.16
Root			$-5263.74$ 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)

$f(q)$	$=$	$q+10781.5 q^{2} -1.64286e6 q^{3} +8.26859e7 q^{4} +5.33897e8 q^{5} -1.77124e10 q^{6} +5.29710e11 q^{8} +1.85169e12 q^{9} +O(q^{10})$	\(q+10781.5 q^{2} -1.64286e6 q^{3} +8.26859e7 q^{4} +5.33897e8 q^{5} -1.77124e10 q^{6} +5.29710e11 q^{8} +1.85169e12 q^{9} +5.75620e12 q^{10} -2.57148e12 q^{11} -1.35841e14 q^{12} -5.77974e13 q^{13} -8.77116e14 q^{15} +2.93658e15 q^{16} -1.56167e15 q^{17} +1.99639e16 q^{18} -6.12730e15 q^{19} +4.41457e16 q^{20} -2.77244e16 q^{22} -5.06226e16 q^{23} -8.70236e17 q^{24} -1.29772e16 q^{25} -6.23141e17 q^{26} -1.65008e18 q^{27} +5.40685e17 q^{29} -9.45661e18 q^{30} -5.98731e18 q^{31} +1.38865e19 q^{32} +4.22458e18 q^{33} -1.68371e19 q^{34} +1.53108e20 q^{36} +6.79054e19 q^{37} -6.60613e19 q^{38} +9.49527e19 q^{39} +2.82810e20 q^{40} +3.81906e19 q^{41} -2.63312e20 q^{43} -2.12625e20 q^{44} +9.88610e20 q^{45} -5.45786e20 q^{46} +5.17657e20 q^{47} -4.82437e21 q^{48} -1.39913e20 q^{50} +2.56559e21 q^{51} -4.77902e21 q^{52} -3.50250e21 q^{53} -1.77903e22 q^{54} -1.37291e21 q^{55} +1.00663e22 q^{57} +5.82938e21 q^{58} +1.82634e22 q^{59} -7.25251e22 q^{60} -2.40034e22 q^{61} -6.45520e22 q^{62} +5.11822e22 q^{64} -3.08578e22 q^{65} +4.55472e22 q^{66} -4.58271e21 q^{67} -1.29128e23 q^{68} +8.31656e22 q^{69} +1.62887e23 q^{71} +9.80856e23 q^{72} -1.99573e23 q^{73} +7.32120e23 q^{74} +2.13197e22 q^{75} -5.06641e23 q^{76} +1.02373e24 q^{78} -8.29880e23 q^{79} +1.56783e24 q^{80} +1.14193e24 q^{81} +4.11751e23 q^{82} -1.45624e24 q^{83} -8.33769e23 q^{85} -2.83889e24 q^{86} -8.88267e23 q^{87} -1.36214e24 q^{88} -5.46454e23 q^{89} +1.06587e25 q^{90} -4.18577e24 q^{92} +9.83628e24 q^{93} +5.58111e24 q^{94} -3.27135e24 q^{95} -2.28136e25 q^{96} -1.09756e24 q^{97} -4.76158e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10781.5	1.86124	0.930622	−	0.365981i	$-0.119267\pi$
$2$	10781.5	1.86124	0.930622	+	0.365981i	$0.119267\pi$
$3$	−1.64286e6	−1.78478	−0.892388	−	0.451269i	$-0.850972\pi$
$3$	−1.64286e6	−1.78478	−0.892388	+	0.451269i	$0.850972\pi$
$4$	8.26859e7	2.46423
$5$	5.33897e8	0.977986	0.488993	−	0.872288i	$-0.337364\pi$
$5$	5.33897e8	0.977986	0.488993	+	0.872288i	$0.337364\pi$
$6$	−1.77124e10	−3.32190
$7$	0	0
$7$	0	0
$8$	5.29710e11	2.72529
$9$	1.85169e12	2.18543
$10$	5.75620e12	1.82027
$11$	−2.57148e12	−0.247044	−0.123522	−	0.992342i	$-0.539419\pi$
$11$	−2.57148e12	−0.247044	−0.123522	+	0.992342i	$0.539419\pi$
$12$	−1.35841e14	−4.39810
$13$	−5.77974e13	−0.688044	−0.344022	−	0.938962i	$-0.611789\pi$
$13$	−5.77974e13	−0.688044	−0.344022	+	0.938962i	$0.611789\pi$
$14$	0	0
$15$	−8.77116e14	−1.74549
$16$	2.93658e15	2.60820
$17$	−1.56167e15	−0.650095	−0.325047	−	0.945698i	$-0.605380\pi$
$17$	−1.56167e15	−0.650095	−0.325047	+	0.945698i	$0.605380\pi$
$18$	1.99639e16	4.06761
$19$	−6.12730e15	−0.635110	−0.317555	−	0.948240i	$-0.602862\pi$
$19$	−6.12730e15	−0.635110	−0.317555	+	0.948240i	$0.602862\pi$
$20$	4.41457e16	2.40998
$21$	0	0
$22$	−2.77244e16	−0.459810
$23$	−5.06226e16	−0.481666	−0.240833	−	0.970567i	$-0.577421\pi$
$23$	−5.06226e16	−0.481666	−0.240833	+	0.970567i	$0.577421\pi$
$24$	−8.70236e17	−4.86404
$25$	−1.29772e16	−0.0435443
$26$	−6.23141e17	−1.28062
$27$	−1.65008e18	−2.11572
$28$	0	0
$29$	5.40685e17	0.283772	0.141886	−	0.989883i	$-0.454683\pi$
$29$	5.40685e17	0.283772	0.141886	+	0.989883i	$0.454683\pi$
$30$	−9.45661e18	−3.24877
$31$	−5.98731e18	−1.36524	−0.682622	−	0.730772i	$-0.739160\pi$
$31$	−5.98731e18	−1.36524	−0.682622	+	0.730772i	$0.739160\pi$
$32$	1.38865e19	2.12921
$33$	4.22458e18	0.440919
$34$	−1.68371e19	−1.20999
$35$	0	0
$36$	1.53108e20	5.38539
$37$	6.79054e19	1.69583	0.847916	−	0.530131i	$-0.177857\pi$
$37$	6.79054e19	1.69583	0.847916	+	0.530131i	$0.177857\pi$
$38$	−6.60613e19	−1.18209
$39$	9.49527e19	1.22800
$40$	2.82810e20	2.66530
$41$	3.81906e19	0.264337	0.132169	−	0.991227i	$-0.457806\pi$
$41$	3.81906e19	0.264337	0.132169	+	0.991227i	$0.457806\pi$
$42$	0	0
$43$	−2.63312e20	−1.00488	−0.502441	−	0.864612i	$-0.667564\pi$
$43$	−2.63312e20	−1.00488	−0.502441	+	0.864612i	$0.667564\pi$
$44$	−2.12625e20	−0.608774
$45$	9.88610e20	2.13732
$46$	−5.45786e20	−0.896499
$47$	5.17657e20	0.649859	0.324930	−	0.945738i	$-0.394659\pi$
$47$	5.17657e20	0.649859	0.324930	+	0.945738i	$0.394659\pi$
$48$	−4.82437e21	−4.65506
$49$	0	0
$50$	−1.39913e20	−0.0810465
$51$	2.56559e21	1.16027
$52$	−4.77902e21	−1.69550
$53$	−3.50250e21	−0.979331	−0.489666	−	0.871910i	$-0.662881\pi$
$53$	−3.50250e21	−0.979331	−0.489666	+	0.871910i	$0.662881\pi$
$54$	−1.77903e22	−3.93787
$55$	−1.37291e21	−0.241606
$56$	0	0
$57$	1.00663e22	1.13353
$58$	5.82938e21	0.528169
$59$	1.82634e22	1.33638	0.668192	−	0.743989i	$-0.267069\pi$
$59$	1.82634e22	1.33638	0.668192	+	0.743989i	$0.267069\pi$
$60$	−7.25251e22	−4.30128
$61$	−2.40034e22	−1.15784	−0.578922	−	0.815383i	$-0.696526\pi$
$61$	−2.40034e22	−1.15784	−0.578922	+	0.815383i	$0.696526\pi$
$62$	−6.45520e22	−2.54105
$63$	0	0
$64$	5.11822e22	1.35478
$65$	−3.08578e22	−0.672897
$66$	4.55472e22	0.820658
$67$	−4.58271e21	−0.0684207	−0.0342104	−	0.999415i	$-0.510892\pi$
$67$	−4.58271e21	−0.0684207	−0.0342104	+	0.999415i	$0.510892\pi$
$68$	−1.29128e23	−1.60198
$69$	8.31656e22	0.859666
$70$	0	0
$71$	1.62887e23	1.17803	0.589016	−	0.808121i	$-0.299515\pi$
$71$	1.62887e23	1.17803	0.589016	+	0.808121i	$0.299515\pi$
$72$	9.80856e23	5.95592
$73$	−1.99573e23	−1.01992	−0.509959	−	0.860199i	$-0.670340\pi$
$73$	−1.99573e23	−1.01992	−0.509959	+	0.860199i	$0.670340\pi$
$74$	7.32120e23	3.15636
$75$	2.13197e22	0.0777168
$76$	−5.06641e23	−1.56506
$77$	0	0
$78$	1.02373e24	2.28562
$79$	−8.29880e23	−1.58007	−0.790036	−	0.613061i	$-0.789938\pi$
$79$	−8.29880e23	−1.58007	−0.790036	+	0.613061i	$0.789938\pi$
$80$	1.56783e24	2.55079
$81$	1.14193e24	1.59066
$82$	4.11751e23	0.491996
$83$	−1.45624e24	−1.49540	−0.747698	−	0.664038i	$-0.768841\pi$
$83$	−1.45624e24	−1.49540	−0.747698	+	0.664038i	$0.768841\pi$
$84$	0	0
$85$	−8.33769e23	−0.635783
$86$	−2.83889e24	−1.87033
$87$	−8.88267e23	−0.506469
$88$	−1.36214e24	−0.673268
$89$	−5.46454e23	−0.234519	−0.117260	−	0.993101i	$-0.537411\pi$
$89$	−5.46454e23	−0.234519	−0.117260	+	0.993101i	$0.537411\pi$
$90$	1.06587e25	3.97807
$91$	0	0
$92$	−4.18577e24	−1.18694
$93$	9.83628e24	2.43666
$94$	5.58111e24	1.20955
$95$	−3.27135e24	−0.621128
$96$	−2.28136e25	−3.80017
$97$	−1.09756e24	−0.160614	−0.0803068	−	0.996770i	$-0.525590\pi$
$97$	−1.09756e24	−0.160614	−0.0803068	+	0.996770i	$0.525590\pi$
$98$	0	0
$99$	−4.76158e24	−0.539897
$100$	−1.07303e24	−0.107303
$101$	2.61297e24	0.230737	0.115369	−	0.993323i	$-0.463195\pi$
$101$	2.61297e24	0.230737	0.115369	+	0.993323i	$0.463195\pi$
$102$	2.76609e25	2.15955
$103$	9.00503e24	0.622329	0.311165	−	0.950356i	$-0.399281\pi$
$103$	9.00503e24	0.622329	0.311165	+	0.950356i	$0.399281\pi$
$104$	−3.06158e25	−1.87512
$105$	0	0
$106$	−3.77621e25	−1.82277
$107$	−7.06838e24	−0.303405	−0.151702	−	0.988426i	$-0.548476\pi$
$107$	−7.06838e24	−0.303405	−0.151702	+	0.988426i	$0.548476\pi$
$108$	−1.36438e26	−5.21362
$109$	−4.85024e24	−0.165170	−0.0825852	−	0.996584i	$-0.526318\pi$
$109$	−4.85024e24	−0.165170	−0.0825852	+	0.996584i	$0.526318\pi$
$110$	−1.48020e25	−0.449688
$111$	−1.11559e26	−3.02668
$112$	0	0
$113$	5.65679e25	1.22769	0.613846	−	0.789426i	$-0.289621\pi$
$113$	5.65679e25	1.22769	0.613846	+	0.789426i	$0.289621\pi$
$114$	1.08529e26	2.10977
$115$	−2.70272e25	−0.471063
$116$	4.47070e25	0.699279
$117$	−1.07023e26	−1.50367
$118$	1.96906e26	2.48734
$119$	0	0
$120$	−4.64617e26	−4.75696
$121$	−1.01735e26	−0.938969
$122$	−2.58792e26	−2.15503
$123$	−6.27417e25	−0.471783
$124$	−4.95066e26	−3.36428
$125$	−1.66042e26	−1.02057
$126$	0	0
$127$	−2.84321e26	−1.43305	−0.716527	−	0.697560i	$-0.754269\pi$
$127$	−2.84321e26	−1.43305	−0.716527	+	0.697560i	$0.754269\pi$
$128$	8.58651e25	0.392367
$129$	4.32583e26	1.79349
$130$	−3.32693e26	−1.25243
$131$	−1.78887e26	−0.611908	−0.305954	−	0.952046i	$-0.598975\pi$
$131$	−1.78887e26	−0.611908	−0.305954	+	0.952046i	$0.598975\pi$
$132$	3.49313e26	1.08653
$133$	0	0
$134$	−4.94084e25	−0.127348
$135$	−8.80973e26	−2.06914
$136$	−8.27230e26	−1.77170
$137$	4.98659e26	0.974533	0.487266	−	0.873253i	$-0.337994\pi$
$137$	4.98659e26	0.974533	0.487266	+	0.873253i	$0.337994\pi$
$138$	8.96648e26	1.60005
$139$	6.22773e26	1.01542	0.507709	−	0.861529i	$-0.330493\pi$
$139$	6.22773e26	1.01542	0.507709	+	0.861529i	$0.330493\pi$
$140$	0	0
$141$	−8.50436e26	−1.15985
$142$	1.75616e27	2.19261
$143$	1.48625e26	0.169977
$144$	5.43762e27	5.70004
$145$	2.88670e26	0.277525
$146$	−2.15169e27	−1.89832
$147$	0	0
$148$	5.61482e27	4.17892
$149$	−1.26987e27	−0.868823	−0.434411	−	0.900715i	$-0.643044\pi$
$149$	−1.26987e27	−0.868823	−0.434411	+	0.900715i	$0.643044\pi$
$150$	2.29858e26	0.144650
$151$	−3.03779e27	−1.75932	−0.879662	−	0.475600i	$-0.842231\pi$
$151$	−3.03779e27	−1.75932	−0.879662	+	0.475600i	$0.842231\pi$
$152$	−3.24569e27	−1.73086
$153$	−2.89172e27	−1.42073
$154$	0	0
$155$	−3.19660e27	−1.33519
$156$	7.85125e27	3.02609
$157$	4.66710e27	1.66074	0.830369	−	0.557214i	$-0.188130\pi$
$157$	4.66710e27	1.66074	0.830369	+	0.557214i	$0.188130\pi$
$158$	−8.94733e27	−2.94090
$159$	5.75410e27	1.74789
$160$	7.41398e27	2.08234
$161$	0	0
$162$	1.23117e28	2.96061
$163$	−6.06308e27	−1.35004	−0.675022	−	0.737797i	$-0.735866\pi$
$163$	−6.06308e27	−1.35004	−0.675022	+	0.737797i	$0.735866\pi$
$164$	3.15782e27	0.651388
$165$	2.25549e27	0.431212
$166$	−1.57004e28	−2.78330
$167$	−5.86300e27	−0.964193	−0.482097	−	0.876118i	$-0.660125\pi$
$167$	−5.86300e27	−0.964193	−0.482097	+	0.876118i	$0.660125\pi$
$168$	0	0
$169$	−3.71588e27	−0.526596
$170$	−8.98926e27	−1.18335
$171$	−1.13458e28	−1.38799
$172$	−2.17722e28	−2.47626
$173$	1.07564e28	1.13787	0.568935	−	0.822383i	$-0.307356\pi$
$173$	1.07564e28	1.13787	0.568935	+	0.822383i	$0.307356\pi$
$174$	−9.57683e27	−0.942663
$175$	0	0
$176$	−7.55135e27	−0.644342
$177$	−3.00041e28	−2.38515
$178$	−5.89159e27	−0.436498
$179$	−1.93159e28	−1.33430	−0.667149	−	0.744924i	$-0.732486\pi$
$179$	−1.93159e28	−1.33430	−0.667149	+	0.744924i	$0.732486\pi$
$180$	8.17441e28	5.26684
$181$	−1.20639e28	−0.725279	−0.362640	−	0.931929i	$-0.618124\pi$
$181$	−1.20639e28	−0.725279	−0.362640	+	0.931929i	$0.618124\pi$
$182$	0	0
$183$	3.94341e28	2.06649
$184$	−2.68153e28	−1.31268
$185$	3.62545e28	1.65850
$186$	1.06050e29	4.53521
$187$	4.01580e27	0.160602
$188$	4.28029e28	1.60140
$189$	0	0
$190$	−3.52699e28	−1.15607
$191$	3.47936e28	1.06803	0.534013	−	0.845476i	$-0.320683\pi$
$191$	3.47936e28	1.06803	0.534013	+	0.845476i	$0.320683\pi$
$192$	−8.40849e28	−2.41798
$193$	1.13307e28	0.305346	0.152673	−	0.988277i	$-0.451212\pi$
$193$	1.13307e28	0.305346	0.152673	+	0.988277i	$0.451212\pi$
$194$	−1.18333e28	−0.298941
$195$	5.06950e28	1.20097
$196$	0	0
$197$	−6.44599e28	−1.34419	−0.672097	−	0.740463i	$-0.734606\pi$
$197$	−6.44599e28	−1.34419	−0.672097	+	0.740463i	$0.734606\pi$
$198$	−5.13369e28	−1.00488
$199$	−5.31432e28	−0.976752	−0.488376	−	0.872633i	$-0.662410\pi$
$199$	−5.31432e28	−0.976752	−0.488376	+	0.872633i	$0.662410\pi$
$200$	−6.87415e27	−0.118671
$201$	7.52874e27	0.122116
$202$	2.81717e28	0.429458
$203$	0	0
$204$	2.12138e29	2.85918
$205$	2.03899e28	0.258518
$206$	9.70876e28	1.15831
$207$	−9.37371e28	−1.05265
$208$	−1.69726e29	−1.79456
$209$	1.57562e28	0.156900
$210$	0	0
$211$	−5.10346e28	−0.451163	−0.225582	−	0.974224i	$-0.572428\pi$
$211$	−5.10346e28	−0.451163	−0.225582	+	0.974224i	$0.572428\pi$
$212$	−2.89607e29	−2.41330
$213$	−2.67600e29	−2.10252
$214$	−7.62075e28	−0.564710
$215$	−1.40581e29	−0.982759
$216$	−8.74064e29	−5.76596
$217$	0	0
$218$	−5.22928e28	−0.307422
$219$	3.27869e29	1.82033
$220$	−1.13520e29	−0.595373
$221$	9.02602e28	0.447294
$222$	−1.20277e30	−5.63339
$223$	−2.08285e29	−0.922246	−0.461123	−	0.887336i	$-0.652553\pi$
$223$	−2.08285e29	−0.922246	−0.461123	+	0.887336i	$0.652553\pi$
$224$	0	0
$225$	−2.40297e28	−0.0951628
$226$	6.09886e29	2.28504
$227$	−4.11168e28	−0.145780	−0.0728898	−	0.997340i	$-0.523222\pi$
$227$	−4.11168e28	−0.145780	−0.0728898	+	0.997340i	$0.523222\pi$
$228$	8.32338e29	2.79328
$229$	3.11794e29	0.990658	0.495329	−	0.868705i	$-0.335047\pi$
$229$	3.11794e29	0.990658	0.495329	+	0.868705i	$0.335047\pi$
$230$	−2.91394e29	−0.876763
$231$	0	0
$232$	2.86406e29	0.773361
$233$	1.38688e28	0.0354888	0.0177444	−	0.999843i	$-0.494351\pi$
$233$	1.38688e28	0.0354888	0.0177444	+	0.999843i	$0.494351\pi$
$234$	−1.15386e30	−2.79870
$235$	2.76376e29	0.635553
$236$	1.51012e30	3.29316
$237$	1.36337e30	2.82007
$238$	0	0
$239$	2.65772e29	0.494920	0.247460	−	0.968898i	$-0.420404\pi$
$239$	2.65772e29	0.494920	0.247460	+	0.968898i	$0.420404\pi$
$240$	−2.57572e30	−4.55258
$241$	4.83254e29	0.810890	0.405445	−	0.914119i	$-0.367117\pi$
$241$	4.83254e29	0.810890	0.405445	+	0.914119i	$0.367117\pi$
$242$	−1.09685e30	−1.74765
$243$	−4.77935e29	−0.723254
$244$	−1.98474e30	−2.85319
$245$	0	0
$246$	−6.76448e29	−0.878103
$247$	3.54142e29	0.436983
$248$	−3.17153e30	−3.72069
$249$	2.39239e30	2.66895
$250$	−1.79018e30	−1.89953
$251$	8.39992e29	0.847917	0.423959	−	0.905682i	$-0.360640\pi$
$251$	8.39992e29	0.847917	0.423959	+	0.905682i	$0.360640\pi$
$252$	0	0
$253$	1.30175e29	0.118993
$254$	−3.06540e30	−2.66726
$255$	1.36976e30	1.13473
$256$	−7.91636e29	−0.624491
$257$	1.26054e30	0.947090	0.473545	−	0.880770i	$-0.342974\pi$
$257$	1.26054e30	0.947090	0.473545	+	0.880770i	$0.342974\pi$
$258$	4.66389e30	3.33812
$259$	0	0
$260$	−2.55151e30	−1.65817
$261$	1.00118e30	0.620162
$262$	−1.92866e30	−1.13891
$263$	2.81072e30	1.58260	0.791301	−	0.611427i	$-0.209404\pi$
$263$	2.81072e30	1.58260	0.791301	+	0.611427i	$0.209404\pi$
$264$	2.23780e30	1.20163
$265$	−1.86997e30	−0.957772
$266$	0	0
$267$	8.97746e29	0.418565
$268$	−3.78926e29	−0.168604
$269$	−6.27718e29	−0.266601	−0.133300	−	0.991076i	$-0.542557\pi$
$269$	−6.27718e29	−0.266601	−0.133300	+	0.991076i	$0.542557\pi$
$270$	−9.49820e30	−3.85118
$271$	5.30988e29	0.205574	0.102787	−	0.994703i	$-0.467224\pi$
$271$	5.30988e29	0.205574	0.102787	+	0.994703i	$0.467224\pi$
$272$	−4.58595e30	−1.69558
$273$	0	0
$274$	5.37628e30	1.81384
$275$	3.33706e28	0.0107574
$276$	6.87662e30	2.11842
$277$	−4.21390e30	−1.24076	−0.620379	−	0.784302i	$-0.713021\pi$
$277$	−4.21390e30	−1.24076	−0.620379	+	0.784302i	$0.713021\pi$
$278$	6.71441e30	1.88994
$279$	−1.10866e31	−2.98364
$280$	0	0
$281$	4.06909e30	1.00154	0.500770	−	0.865580i	$-0.333050\pi$
$281$	4.06909e30	1.00154	0.500770	+	0.865580i	$0.333050\pi$
$282$	−9.16896e30	−2.15877
$283$	−2.98435e30	−0.672231	−0.336116	−	0.941821i	$-0.609113\pi$
$283$	−2.98435e30	−0.672231	−0.336116	+	0.941821i	$0.609113\pi$
$284$	1.34685e31	2.90294
$285$	5.37435e30	1.10858
$286$	1.60240e30	0.316369
$287$	0	0
$288$	2.57135e31	4.65324
$289$	−3.33183e30	−0.577377
$290$	3.11229e30	0.516541
$291$	1.80314e30	0.286659
$292$	−1.65018e31	−2.51332
$293$	3.55815e30	0.519253	0.259627	−	0.965709i	$-0.416401\pi$
$293$	3.55815e30	0.519253	0.259627	+	0.965709i	$0.416401\pi$
$294$	0	0
$295$	9.75077e30	1.30696
$296$	3.59701e31	4.62163
$297$	4.24315e30	0.522677
$298$	−1.36911e31	−1.61709
$299$	2.92585e30	0.331407
$300$	1.76284e30	0.191512
$301$	0	0
$302$	−3.27519e31	−3.27453
$303$	−4.29273e30	−0.411814
$304$	−1.79933e31	−1.65650
$305$	−1.28153e31	−1.13235
$306$	−3.11770e31	−2.64433
$307$	−9.19775e30	−0.748949	−0.374474	−	0.927237i	$-0.622177\pi$
$307$	−9.19775e30	−0.748949	−0.374474	+	0.927237i	$0.622177\pi$
$308$	0	0
$309$	−1.47940e31	−1.11072
$310$	−3.44641e31	−2.48511
$311$	7.76536e30	0.537844	0.268922	−	0.963162i	$-0.413333\pi$
$311$	7.76536e30	0.537844	0.268922	+	0.963162i	$0.413333\pi$
$312$	5.02974e31	3.34667
$313$	1.72138e31	1.10046	0.550228	−	0.835015i	$-0.314541\pi$
$313$	1.72138e31	1.10046	0.550228	+	0.835015i	$0.314541\pi$
$314$	5.03182e31	3.09104
$315$	0	0
$316$	−6.86193e31	−3.89366
$317$	−5.60573e30	−0.305768	−0.152884	−	0.988244i	$-0.548856\pi$
$317$	−5.60573e30	−0.305768	−0.152884	+	0.988244i	$0.548856\pi$
$318$	6.20377e31	3.25324
$319$	−1.39036e30	−0.0701042
$320$	2.73260e31	1.32496
$321$	1.16123e31	0.541510
$322$	0	0
$323$	9.56879e30	0.412882
$324$	9.44217e31	3.91976
$325$	7.50048e29	0.0299604
$326$	−6.53690e31	−2.51276
$327$	7.96825e30	0.294792
$328$	2.02299e31	0.720396
$329$	0	0
$330$	2.43175e31	0.802592
$331$	−2.24176e31	−0.712424	−0.356212	−	0.934405i	$-0.615932\pi$
$331$	−2.24176e31	−0.712424	−0.356212	+	0.934405i	$0.615932\pi$
$332$	−1.20410e32	−3.68500
$333$	1.25739e32	3.70611
$334$	−6.32118e31	−1.79460
$335$	−2.44670e30	−0.0669145
$336$	0	0
$337$	1.01894e31	0.258687	0.129343	−	0.991600i	$-0.458713\pi$
$337$	1.01894e31	0.258687	0.129343	+	0.991600i	$0.458713\pi$
$338$	−4.00626e31	−0.980123
$339$	−9.29329e31	−2.19116
$340$	−6.89409e31	−1.56672
$341$	1.53963e31	0.337276
$342$	−1.22325e32	−2.58338
$343$	0	0
$344$	−1.39479e32	−2.73859
$345$	4.44019e31	0.840741
$346$	1.15970e32	2.11785
$347$	8.98333e31	1.58241	0.791204	−	0.611552i	$-0.209454\pi$
$347$	8.98333e31	1.58241	0.791204	+	0.611552i	$0.209454\pi$
$348$	−7.34471e31	−1.24806
$349$	−2.35931e30	−0.0386783	−0.0193391	−	0.999813i	$-0.506156\pi$
$349$	−2.35931e30	−0.0386783	−0.0193391	+	0.999813i	$0.506156\pi$
$350$	0	0
$351$	9.53703e31	1.45571
$352$	−3.57090e31	−0.526010
$353$	−6.66779e31	−0.947978	−0.473989	−	0.880531i	$-0.657186\pi$
$353$	−6.66779e31	−0.947978	−0.473989	+	0.880531i	$0.657186\pi$
$354$	−3.23489e32	−4.43934
$355$	8.69649e31	1.15210
$356$	−4.51841e31	−0.577910
$357$	0	0
$358$	−2.08254e32	−2.48345
$359$	2.62511e31	0.302320	0.151160	−	0.988509i	$-0.451699\pi$
$359$	2.62511e31	0.302320	0.151160	+	0.988509i	$0.451699\pi$
$360$	5.23676e32	5.82481
$361$	−5.55327e31	−0.596635
$362$	−1.30067e32	−1.34992
$363$	1.67135e32	1.67585
$364$	0	0
$365$	−1.06551e32	−0.997466
$366$	4.25158e32	3.84625
$367$	−4.46907e31	−0.390744	−0.195372	−	0.980729i	$-0.562591\pi$
$367$	−4.46907e31	−0.390744	−0.195372	+	0.980729i	$0.562591\pi$
$368$	−1.48657e32	−1.25628
$369$	7.07171e31	0.577690
$370$	3.90877e32	3.08687
$371$	0	0
$372$	8.13321e32	6.00448
$373$	1.93050e32	1.37819	0.689096	−	0.724670i	$-0.258008\pi$
$373$	1.93050e32	1.37819	0.689096	+	0.724670i	$0.258008\pi$
$374$	4.32962e31	0.298920
$375$	2.72783e32	1.82149
$376$	2.74208e32	1.77106
$377$	−3.12501e31	−0.195247
$378$	0	0
$379$	−1.74269e32	−1.01913	−0.509566	−	0.860431i	$-0.670194\pi$
$379$	−1.74269e32	−1.01913	−0.509566	+	0.860431i	$0.670194\pi$
$380$	−2.70494e32	−1.53060
$381$	4.67098e32	2.55768
$382$	3.75126e32	1.98786
$383$	3.55708e31	0.182435	0.0912176	−	0.995831i	$-0.470924\pi$
$383$	3.55708e31	0.182435	0.0912176	+	0.995831i	$0.470924\pi$
$384$	−1.41064e32	−0.700286
$385$	0	0
$386$	1.22162e32	0.568323
$387$	−4.87571e32	−2.19609
$388$	−9.07529e31	−0.395789
$389$	3.50480e31	0.148011	0.0740054	−	0.997258i	$-0.476422\pi$
$389$	3.50480e31	0.148011	0.0740054	+	0.997258i	$0.476422\pi$
$390$	5.46567e32	2.23530
$391$	7.90556e31	0.313129
$392$	0	0
$393$	2.93885e32	1.09212
$394$	−6.94973e32	−2.50187
$395$	−4.43070e32	−1.54529
$396$	−3.93715e32	−1.33043
$397$	1.65589e32	0.542187	0.271094	−	0.962553i	$-0.412615\pi$
$397$	1.65589e32	0.542187	0.271094	+	0.962553i	$0.412615\pi$
$398$	−5.72962e32	−1.81797
$399$	0	0
$400$	−3.81085e31	−0.113572
$401$	3.14036e32	0.907141	0.453570	−	0.891220i	$-0.350150\pi$
$401$	3.14036e32	0.907141	0.453570	+	0.891220i	$0.350150\pi$
$402$	8.11709e31	0.227287
$403$	3.46050e32	0.939348
$404$	2.16056e32	0.568589
$405$	6.09674e32	1.55564
$406$	0	0
$407$	−1.74617e32	−0.418946
$408$	1.35902e33	3.16209
$409$	−2.66869e31	−0.0602223	−0.0301112	−	0.999547i	$-0.509586\pi$
$409$	−2.66869e31	−0.0602223	−0.0301112	+	0.999547i	$0.509586\pi$
$410$	2.19833e32	0.481165
$411$	−8.19225e32	−1.73932
$412$	7.44589e32	1.53356
$413$	0	0
$414$	−1.01062e33	−1.95923
$415$	−7.77482e32	−1.46248
$416$	−8.02605e32	−1.46499
$417$	−1.02313e33	−1.81229
$418$	1.69876e32	0.292030
$419$	−6.60692e32	−1.10236	−0.551180	−	0.834386i	$-0.685822\pi$
$419$	−6.60692e32	−1.10236	−0.551180	+	0.834386i	$0.685822\pi$
$420$	0	0
$421$	−1.58685e32	−0.249464	−0.124732	−	0.992190i	$-0.539807\pi$
$421$	−1.58685e32	−0.249464	−0.124732	+	0.992190i	$0.539807\pi$
$422$	−5.50228e32	−0.839725
$423$	9.58539e32	1.42022
$424$	−1.85531e33	−2.66896
$425$	2.02661e31	0.0283079
$426$	−2.88512e33	−3.91331
$427$	0	0
$428$	−5.84455e32	−0.747659
$429$	−2.44169e32	−0.303372
$430$	−1.51568e33	−1.82916
$431$	−6.76895e31	−0.0793515	−0.0396758	−	0.999213i	$-0.512633\pi$
$431$	−6.76895e31	−0.0793515	−0.0396758	+	0.999213i	$0.512633\pi$
$432$	−4.84559e33	−5.51823
$433$	6.14348e32	0.679697	0.339849	−	0.940480i	$-0.389624\pi$
$433$	6.14348e32	0.679697	0.339849	+	0.940480i	$0.389624\pi$
$434$	0	0
$435$	−4.74243e32	−0.495319
$436$	−4.01046e32	−0.407018
$437$	3.10179e32	0.305911
$438$	3.53492e33	3.38807
$439$	1.56594e33	1.45871	0.729356	−	0.684134i	$-0.239820\pi$
$439$	1.56594e33	1.45871	0.729356	+	0.684134i	$0.239820\pi$
$440$	−7.27242e32	−0.658446
$441$	0	0
$442$	9.73138e32	0.832523
$443$	−4.23752e32	−0.352424	−0.176212	−	0.984352i	$-0.556384\pi$
$443$	−4.23752e32	−0.352424	−0.176212	+	0.984352i	$0.556384\pi$
$444$	−9.22433e33	−7.45844
$445$	−2.91750e32	−0.229357
$446$	−2.24562e33	−1.71652
$447$	2.08621e33	1.55065
$448$	0	0
$449$	−2.77398e33	−1.94995	−0.974976	−	0.222311i	$-0.928640\pi$
$449$	−2.77398e33	−1.94995	−0.974976	+	0.222311i	$0.928640\pi$
$450$	−2.59076e32	−0.177121
$451$	−9.82065e31	−0.0653031
$452$	4.67737e33	3.02532
$453$	4.99065e33	3.14000
$454$	−4.43300e32	−0.271331
$455$	0	0
$456$	5.33220e33	3.08920
$457$	1.99795e33	1.12624	0.563121	−	0.826375i	$-0.309601\pi$
$457$	1.99795e33	1.12624	0.563121	+	0.826375i	$0.309601\pi$
$458$	3.36160e33	1.84386
$459$	2.57688e33	1.37542
$460$	−2.23477e33	−1.16081
$461$	2.44261e33	1.23479	0.617395	−	0.786653i	$-0.288188\pi$
$461$	2.44261e33	1.23479	0.617395	+	0.786653i	$0.288188\pi$
$462$	0	0
$463$	3.01274e33	1.44278	0.721388	−	0.692531i	$-0.243504\pi$
$463$	3.01274e33	1.44278	0.721388	+	0.692531i	$0.243504\pi$
$464$	1.58776e33	0.740134
$465$	5.25156e33	2.38301
$466$	1.49527e32	0.0660533
$467$	−4.08771e33	−1.75800	−0.878999	−	0.476823i	$-0.841788\pi$
$467$	−4.08771e33	−1.75800	−0.878999	+	0.476823i	$0.841788\pi$
$468$	−8.84926e33	−3.70539
$469$	0	0
$470$	2.97974e33	1.18292
$471$	−7.66737e33	−2.96405
$472$	9.67429e33	3.64203
$473$	6.77102e32	0.248250
$474$	1.46992e34	5.24885
$475$	7.95152e31	0.0276554
$476$	0	0
$477$	−6.48553e33	−2.14026
$478$	2.86541e33	0.921167
$479$	−4.93079e33	−1.54427	−0.772134	−	0.635460i	$-0.780811\pi$
$479$	−4.93079e33	−1.54427	−0.772134	+	0.635460i	$0.780811\pi$
$480$	−1.21801e34	−3.71651
$481$	−3.92475e33	−1.16681
$482$	5.21019e33	1.50927
$483$	0	0
$484$	−8.41201e33	−2.31384
$485$	−5.85985e32	−0.157078
$486$	−5.15285e33	−1.34615
$487$	−4.81451e33	−1.22586	−0.612929	−	0.790138i	$-0.710009\pi$
$487$	−4.81451e33	−1.22586	−0.612929	+	0.790138i	$0.710009\pi$
$488$	−1.27148e34	−3.15546
$489$	9.96077e33	2.40953
$490$	0	0
$491$	2.25523e33	0.518409	0.259204	−	0.965822i	$-0.416540\pi$
$491$	2.25523e33	0.518409	0.259204	+	0.965822i	$0.416540\pi$
$492$	−5.18785e33	−1.16258
$493$	−8.44369e32	−0.184479
$494$	3.81817e33	0.813333
$495$	−2.54219e33	−0.528012
$496$	−1.75822e34	−3.56083
$497$	0	0
$498$	2.57935e34	4.96757
$499$	1.46100e33	0.274406	0.137203	−	0.990543i	$-0.456189\pi$
$499$	1.46100e33	0.274406	0.137203	+	0.990543i	$0.456189\pi$
$500$	−1.37293e34	−2.51492
$501$	9.63206e33	1.72087
$502$	9.05635e33	1.57818
$503$	−1.51539e33	−0.257587	−0.128793	−	0.991671i	$-0.541110\pi$
$503$	−1.51539e33	−0.257587	−0.128793	+	0.991671i	$0.541110\pi$
$504$	0	0
$505$	1.39506e33	0.225658
$506$	1.40348e33	0.221475
$507$	6.10465e33	0.939856
$508$	−2.35093e34	−3.53137
$509$	−2.44504e32	−0.0358355	−0.0179177	−	0.999839i	$-0.505704\pi$
$509$	−2.44504e32	−0.0358355	−0.0179177	+	0.999839i	$0.505704\pi$
$510$	1.47681e34	2.11201
$511$	0	0
$512$	−1.14162e34	−1.55470
$513$	1.01105e34	1.34371
$514$	1.35904e34	1.76277
$515$	4.80776e33	0.608629
$516$	3.57685e34	4.41957
$517$	−1.33115e33	−0.160544
$518$	0	0
$519$	−1.76713e34	−2.03084
$520$	−1.63457e34	−1.83384
$521$	6.09190e33	0.667239	0.333619	−	0.942708i	$-0.391730\pi$
$521$	6.09190e33	0.667239	0.333619	+	0.942708i	$0.391730\pi$
$522$	1.07942e34	1.15427
$523$	1.87427e33	0.195686	0.0978432	−	0.995202i	$-0.468806\pi$
$523$	1.87427e33	0.195686	0.0978432	+	0.995202i	$0.468806\pi$
$524$	−1.47914e34	−1.50788
$525$	0	0
$526$	3.03038e34	2.94561
$527$	9.35018e33	0.887538
$528$	1.24058e34	1.15001
$529$	−8.48312e33	−0.767998
$530$	−2.01611e34	−1.78265
$531$	3.38181e34	2.92057
$532$	0	0
$533$	−2.20732e33	−0.181876
$534$	9.67903e33	0.779051
$535$	−3.77378e33	−0.296725
$536$	−2.42751e33	−0.186466
$537$	3.17333e34	2.38142
$538$	−6.76773e33	−0.496209
$539$	0	0
$540$	−7.28441e34	−5.09885
$541$	−4.07532e33	−0.278738	−0.139369	−	0.990241i	$-0.544507\pi$
$541$	−4.07532e33	−0.278738	−0.139369	+	0.990241i	$0.544507\pi$
$542$	5.72484e33	0.382624
$543$	1.98192e34	1.29446
$544$	−2.16861e34	−1.38419
$545$	−2.58953e33	−0.161534
$546$	0	0
$547$	1.84107e34	1.09706	0.548529	−	0.836131i	$-0.315188\pi$
$547$	1.84107e34	1.09706	0.548529	+	0.836131i	$0.315188\pi$
$548$	4.12320e34	2.40147
$549$	−4.44468e34	−2.53038
$550$	3.59785e32	0.0200221
$551$	−3.31294e33	−0.180226
$552$	4.40536e34	2.34284
$553$	0	0
$554$	−4.54321e34	−2.30935
$555$	−5.95609e34	−2.96005
$556$	5.14945e34	2.50222
$557$	4.11261e34	1.95401	0.977007	−	0.213206i	$-0.0683906\pi$
$557$	4.11261e34	1.95401	0.977007	+	0.213206i	$0.0683906\pi$
$558$	−1.19530e35	−5.55328
$559$	1.52187e34	0.691402
$560$	0	0
$561$	−6.59738e33	−0.286639
$562$	4.38708e34	1.86411
$563$	2.85205e34	1.18523	0.592614	−	0.805487i	$-0.298096\pi$
$563$	2.85205e34	1.18523	0.592614	+	0.805487i	$0.298096\pi$
$564$	−7.03191e34	−2.85815
$565$	3.02014e34	1.20067
$566$	−3.21757e34	−1.25119
$567$	0	0
$568$	8.62828e34	3.21048
$569$	−1.96964e34	−0.716942	−0.358471	−	0.933541i	$-0.616702\pi$
$569$	−1.96964e34	−0.716942	−0.358471	+	0.933541i	$0.616702\pi$
$570$	5.79434e34	2.06333
$571$	1.92430e34	0.670380	0.335190	−	0.942151i	$-0.391200\pi$
$571$	1.92430e34	0.670380	0.335190	+	0.942151i	$0.391200\pi$
$572$	1.22892e34	0.418863
$573$	−5.71608e34	−1.90619
$574$	0	0
$575$	6.56939e32	0.0209738
$576$	9.47734e34	2.96077
$577$	−5.68085e34	−1.73666	−0.868331	−	0.495985i	$-0.834807\pi$
$577$	−5.68085e34	−1.73666	−0.868331	+	0.495985i	$0.834807\pi$
$578$	−3.59220e34	−1.07464
$579$	−1.86148e34	−0.544973
$580$	2.38689e34	0.683885
$581$	0	0
$582$	1.94405e34	0.533543
$583$	9.00661e33	0.241938
$584$	−1.05716e35	−2.77958
$585$	−5.71390e34	−1.47057
$586$	3.83621e34	0.966457
$587$	−3.27785e34	−0.808376	−0.404188	−	0.914676i	$-0.632446\pi$
$587$	−3.27785e34	−0.808376	−0.404188	+	0.914676i	$0.632446\pi$
$588$	0	0
$589$	3.66860e34	0.867080
$590$	1.05128e35	2.43258
$591$	1.05898e35	2.39909
$592$	1.99409e35	4.42307
$593$	−1.15377e34	−0.250573	−0.125287	−	0.992121i	$-0.539985\pi$
$593$	−1.15377e34	−0.250573	−0.125287	+	0.992121i	$0.539985\pi$
$594$	4.57475e34	0.972829
$595$	0	0
$596$	−1.05000e35	−2.14098
$597$	8.73066e34	1.74328
$598$	3.15450e34	0.616830
$599$	2.23010e34	0.427059	0.213530	−	0.976937i	$-0.431504\pi$
$599$	2.23010e34	0.427059	0.213530	+	0.976937i	$0.431504\pi$
$600$	1.12932e34	0.211801
$601$	−1.14471e34	−0.210263	−0.105132	−	0.994458i	$-0.533526\pi$
$601$	−1.14471e34	−0.210263	−0.105132	+	0.994458i	$0.533526\pi$
$602$	0	0
$603$	−8.48575e33	−0.149528
$604$	−2.51182e35	−4.33538
$605$	−5.43158e34	−0.918298
$606$	−4.62820e34	−0.766487
$607$	3.74162e34	0.607017	0.303509	−	0.952829i	$-0.401842\pi$
$607$	3.74162e34	0.607017	0.303509	+	0.952829i	$0.401842\pi$
$608$	−8.50869e34	−1.35228
$609$	0	0
$610$	−1.38168e35	−2.10759
$611$	−2.99192e34	−0.447131
$612$	−2.39104e35	−3.50102
$613$	−7.15551e34	−1.02656	−0.513280	−	0.858221i	$-0.671570\pi$
$613$	−7.15551e34	−1.02656	−0.513280	+	0.858221i	$0.671570\pi$
$614$	−9.91654e34	−1.39398
$615$	−3.34976e34	−0.461397
$616$	0	0
$617$	5.87751e33	0.0777372	0.0388686	−	0.999244i	$-0.487625\pi$
$617$	5.87751e33	0.0777372	0.0388686	+	0.999244i	$0.487625\pi$
$618$	−1.59501e35	−2.06732
$619$	4.26019e34	0.541123	0.270562	−	0.962703i	$-0.412791\pi$
$619$	4.26019e34	0.541123	0.270562	+	0.962703i	$0.412791\pi$
$620$	−2.64314e35	−3.29021
$621$	8.35313e34	1.01907
$622$	8.37220e34	1.00106
$623$	0	0
$624$	2.78836e35	3.20288
$625$	−8.47819e34	−0.954560
$626$	1.85590e35	2.04822
$627$	−2.58852e34	−0.280032
$628$	3.85903e35	4.09244
$629$	−1.06046e35	−1.10245
$630$	0	0
$631$	1.32275e34	0.132163	0.0660815	−	0.997814i	$-0.478950\pi$
$631$	1.32275e34	0.132163	0.0660815	+	0.997814i	$0.478950\pi$
$632$	−4.39595e35	−4.30615
$633$	8.38425e34	0.805226
$634$	−6.04381e34	−0.569108
$635$	−1.51798e35	−1.40151
$636$	4.75783e35	4.30720
$637$	0	0
$638$	−1.49902e34	−0.130481
$639$	3.01616e35	2.57450
$640$	4.58431e34	0.383729
$641$	1.84013e35	1.51051	0.755253	−	0.655433i	$-0.227514\pi$
$641$	1.84013e35	1.51051	0.755253	+	0.655433i	$0.227514\pi$
$642$	1.25198e35	1.00788
$643$	1.95791e35	1.54581	0.772903	−	0.634524i	$-0.218804\pi$
$643$	1.95791e35	1.54581	0.772903	+	0.634524i	$0.218804\pi$
$644$	0	0
$645$	2.30955e35	1.75401
$646$	1.03166e35	0.768474
$647$	−1.26386e35	−0.923411	−0.461705	−	0.887033i	$-0.652762\pi$
$647$	−1.26386e35	−0.923411	−0.461705	+	0.887033i	$0.652762\pi$
$648$	6.04893e35	4.33502
$649$	−4.69640e34	−0.330146
$650$	8.08663e33	0.0557636
$651$	0	0
$652$	−5.01331e35	−3.32682
$653$	2.07143e34	0.134851	0.0674257	−	0.997724i	$-0.478521\pi$
$653$	2.07143e34	0.134851	0.0674257	+	0.997724i	$0.478521\pi$
$654$	8.59095e34	0.548680
$655$	−9.55070e34	−0.598438
$656$	1.12150e35	0.689445
$657$	−3.69546e35	−2.22896
$658$	0	0
$659$	−2.47161e34	−0.143520	−0.0717598	−	0.997422i	$-0.522862\pi$
$659$	−2.47161e34	−0.143520	−0.0717598	+	0.997422i	$0.522862\pi$
$660$	1.86497e35	1.06261
$661$	−2.17055e35	−1.21354	−0.606768	−	0.794879i	$-0.707534\pi$
$661$	−2.17055e35	−1.21354	−0.606768	+	0.794879i	$0.707534\pi$
$662$	−2.41695e35	−1.32600
$663$	−1.48284e35	−0.798319
$664$	−7.71384e35	−4.07539
$665$	0	0
$666$	1.35566e36	6.89798
$667$	−2.73708e34	−0.136683
$668$	−4.84787e35	−2.37599
$669$	3.42182e35	1.64600
$670$	−2.63790e34	−0.124544
$671$	6.17243e34	0.286039
$672$	0	0
$673$	−1.44204e35	−0.643856	−0.321928	−	0.946764i	$-0.604331\pi$
$673$	−1.44204e35	−0.643856	−0.321928	+	0.946764i	$0.604331\pi$
$674$	1.09857e35	0.481479
$675$	2.14134e34	0.0921275
$676$	−3.07250e35	−1.29765
$677$	−1.82203e35	−0.755434	−0.377717	−	0.925921i	$-0.623291\pi$
$677$	−1.82203e35	−0.755434	−0.377717	+	0.925921i	$0.623291\pi$
$678$	−1.00195e36	−4.07828
$679$	0	0
$680$	−4.41655e35	−1.73270
$681$	6.75490e34	0.260184
$682$	1.65994e35	0.627753
$683$	−1.65440e35	−0.614300	−0.307150	−	0.951661i	$-0.599375\pi$
$683$	−1.65440e35	−0.614300	−0.307150	+	0.951661i	$0.599375\pi$
$684$	−9.38140e35	−3.42032
$685$	2.66233e35	0.953079
$686$	0	0
$687$	−5.12232e35	−1.76810
$688$	−7.73235e35	−2.62093
$689$	2.02435e35	0.673823
$690$	4.78718e35	1.56483
$691$	−1.75082e35	−0.562037	−0.281019	−	0.959702i	$-0.590672\pi$
$691$	−1.75082e35	−0.562037	−0.281019	+	0.959702i	$0.590672\pi$
$692$	8.89406e35	2.80397
$693$	0	0
$694$	9.68535e35	2.94525
$695$	3.32496e35	0.993063
$696$	−4.70524e35	−1.38028
$697$	−5.96410e34	−0.171844
$698$	−2.54368e34	−0.0719897
$699$	−2.27845e34	−0.0633395
$700$	0	0
$701$	1.28650e35	0.345091	0.172545	−	0.985002i	$-0.444801\pi$
$701$	1.28650e35	0.345091	0.172545	+	0.985002i	$0.444801\pi$
$702$	1.02823e36	2.70943
$703$	−4.16076e35	−1.07704
$704$	−1.31614e35	−0.334691
$705$	−4.54045e35	−1.13432
$706$	−7.18887e35	−1.76442
$707$	0	0
$708$	−2.48092e36	−5.87755
$709$	4.83883e35	1.12632	0.563160	−	0.826348i	$-0.309585\pi$
$709$	4.83883e35	1.12632	0.563160	+	0.826348i	$0.309585\pi$
$710$	9.37610e35	2.14434
$711$	−1.53668e36	−3.45313
$712$	−2.89462e35	−0.639134
$713$	3.03093e35	0.657592
$714$	0	0
$715$	7.93504e34	0.166235
$716$	−1.59715e36	−3.28802
$717$	−4.36625e35	−0.883322
$718$	2.83026e35	0.562691
$719$	2.47823e35	0.484206	0.242103	−	0.970251i	$-0.422163\pi$
$719$	2.47823e35	0.484206	0.242103	+	0.970251i	$0.422163\pi$
$720$	2.90313e36	5.57455
$721$	0	0
$722$	−5.98725e35	−1.11048
$723$	−7.93916e35	−1.44726
$724$	−9.97514e35	−1.78726
$725$	−7.01657e33	−0.0123566
$726$	1.80196e36	3.11917
$727$	−1.07202e36	−1.82399	−0.911995	−	0.410201i	$-0.865459\pi$
$727$	−1.07202e36	−1.82399	−0.911995	+	0.410201i	$0.865459\pi$
$728$	0	0
$729$	−1.82367e35	−0.299815
$730$	−1.14878e36	−1.85653
$731$	4.11205e35	0.653268
$732$	3.26064e36	5.09231
$733$	5.51981e34	0.0847471	0.0423735	−	0.999102i	$-0.486508\pi$
$733$	5.51981e34	0.0847471	0.0423735	+	0.999102i	$0.486508\pi$
$734$	−4.81832e35	−0.727269
$735$	0	0
$736$	−7.02972e35	−1.02557
$737$	1.17844e34	0.0169030
$738$	7.62434e35	1.07522
$739$	−4.81720e35	−0.667942	−0.333971	−	0.942583i	$-0.608389\pi$
$739$	−4.81720e35	−0.667942	−0.333971	+	0.942583i	$0.608389\pi$
$740$	2.99773e36	4.08692
$741$	−5.81804e35	−0.779918
$742$	0	0
$743$	3.06034e35	0.396652	0.198326	−	0.980136i	$-0.436449\pi$
$743$	3.06034e35	0.396652	0.198326	+	0.980136i	$0.436449\pi$
$744$	5.21037e36	6.64060
$745$	−6.77980e35	−0.849696
$746$	2.08137e36	2.56515
$747$	−2.69650e36	−3.26808
$748$	3.32050e35	0.395761
$749$	0	0
$750$	2.94101e36	3.39024
$751$	−3.57907e34	−0.0405762	−0.0202881	−	0.999794i	$-0.506458\pi$
$751$	−3.57907e34	−0.0405762	−0.0202881	+	0.999794i	$0.506458\pi$
$752$	1.52014e36	1.69496
$753$	−1.37999e36	−1.51334
$754$	−3.36923e35	−0.363403
$755$	−1.62187e36	−1.72059
$756$	0	0
$757$	−7.29146e35	−0.748369	−0.374184	−	0.927354i	$-0.622077\pi$
$757$	−7.29146e35	−0.748369	−0.374184	+	0.927354i	$0.622077\pi$
$758$	−1.87888e36	−1.89685
$759$	−2.13859e35	−0.212376
$760$	−1.73286e36	−1.69276
$761$	1.33811e36	1.28583	0.642915	−	0.765938i	$-0.277725\pi$
$761$	1.33811e36	1.28583	0.642915	+	0.765938i	$0.277725\pi$
$762$	5.03601e36	4.76047
$763$	0	0
$764$	2.87694e36	2.63186
$765$	−1.54388e36	−1.38946
$766$	3.83505e35	0.339556
$767$	−1.05558e36	−0.919490
$768$	1.30054e36	1.11458
$769$	1.28652e35	0.108477	0.0542386	−	0.998528i	$-0.482727\pi$
$769$	1.28652e35	0.108477	0.0542386	+	0.998528i	$0.482727\pi$
$770$	0	0
$771$	−2.07088e36	−1.69034
$772$	9.36891e35	0.752442
$773$	2.48561e36	1.96422	0.982110	−	0.188309i	$-0.0603007\pi$
$773$	2.48561e36	1.96422	0.982110	+	0.188309i	$0.0603007\pi$
$774$	−5.25674e36	−4.08747
$775$	7.76985e34	0.0594485
$776$	−5.81389e35	−0.437719
$777$	0	0
$778$	3.77870e35	0.275484
$779$	−2.34005e35	−0.167883
$780$	4.19176e36	2.95947
$781$	−4.18861e35	−0.291026
$782$	8.52336e35	0.582809
$783$	−8.92174e35	−0.600382
$784$	0	0
$785$	2.49175e36	1.62418
$786$	3.16851e36	2.03270
$787$	7.13099e35	0.450262	0.225131	−	0.974328i	$-0.427719\pi$
$787$	7.13099e35	0.450262	0.225131	+	0.974328i	$0.427719\pi$
$788$	−5.32993e36	−3.31240
$789$	−4.61762e36	−2.82459
$790$	−4.77695e36	−2.87616
$791$	0	0
$792$	−2.52225e36	−1.47138
$793$	1.38733e36	0.796647
$794$	1.78529e36	1.00914
$795$	3.07210e36	1.70941
$796$	−4.39419e36	−2.40694
$797$	7.07210e35	0.381346	0.190673	−	0.981654i	$-0.438933\pi$
$797$	7.07210e35	0.381346	0.190673	+	0.981654i	$0.438933\pi$
$798$	0	0
$799$	−8.08408e35	−0.422470
$800$	−1.80208e35	−0.0927150
$801$	−1.01186e36	−0.512525
$802$	3.38577e36	1.68841
$803$	5.13198e35	0.251965
$804$	6.22520e35	0.300921
$805$	0	0
$806$	3.73094e36	1.74836
$807$	1.03125e36	0.475823
$808$	1.38412e36	0.628826
$809$	3.05232e36	1.36544	0.682721	−	0.730679i	$-0.260796\pi$
$809$	3.05232e36	1.36544	0.682721	+	0.730679i	$0.260796\pi$
$810$	6.57319e36	2.89543
$811$	3.08503e36	1.33813	0.669065	−	0.743204i	$-0.266695\pi$
$811$	3.08503e36	1.33813	0.669065	+	0.743204i	$0.266695\pi$
$812$	0	0
$813$	−8.72337e35	−0.366904
$814$	−1.88264e36	−0.779760
$815$	−3.23706e36	−1.32032
$816$	7.53406e36	3.02623
$817$	1.61339e36	0.638210
$818$	−2.87725e35	−0.112088
$819$	0	0
$820$	1.68595e36	0.637048
$821$	2.69666e36	1.00355	0.501773	−	0.864999i	$-0.332681\pi$
$821$	2.69666e36	1.00355	0.501773	+	0.864999i	$0.332681\pi$
$822$	−8.83245e36	−3.23731
$823$	3.56657e36	1.28752	0.643759	−	0.765229i	$-0.277374\pi$
$823$	3.56657e36	1.28752	0.643759	+	0.765229i	$0.277374\pi$
$824$	4.77005e36	1.69603
$825$	−5.48232e34	−0.0191995
$826$	0	0
$827$	3.35602e36	1.14027	0.570133	−	0.821552i	$-0.306892\pi$
$827$	3.35602e36	1.14027	0.570133	+	0.821552i	$0.306892\pi$
$828$	−7.75074e36	−2.59396
$829$	−8.99807e35	−0.296632	−0.148316	−	0.988940i	$-0.547385\pi$
$829$	−8.99807e35	−0.296632	−0.148316	+	0.988940i	$0.547385\pi$
$830$	−8.38240e36	−2.72203
$831$	6.92283e36	2.21448
$832$	−2.95819e36	−0.932149
$833$	0	0
$834$	−1.10308e37	−3.37312
$835$	−3.13024e36	−0.942967
$836$	1.30282e36	0.386639
$837$	9.87954e36	2.88847
$838$	−7.12324e36	−2.05176
$839$	1.93037e36	0.547794	0.273897	−	0.961759i	$-0.411687\pi$
$839$	1.93037e36	0.547794	0.273897	+	0.961759i	$0.411687\pi$
$840$	0	0
$841$	−3.33802e36	−0.919474
$842$	−1.71085e36	−0.464314
$843$	−6.68493e36	−1.78753
$844$	−4.21984e36	−1.11177
$845$	−1.98389e36	−0.515003
$846$	1.03345e37	2.64337
$847$	0	0
$848$	−1.02854e37	−2.55429
$849$	4.90285e36	1.19978
$850$	2.18498e35	0.0526879
$851$	−3.43754e36	−0.816825
$852$	−2.21267e37	−5.18110
$853$	2.43710e35	0.0562355	0.0281178	−	0.999605i	$-0.491049\pi$
$853$	2.43710e35	0.0562355	0.0281178	+	0.999605i	$0.491049\pi$
$854$	0	0
$855$	−6.05751e36	−1.35743
$856$	−3.74419e36	−0.826867
$857$	8.66652e36	1.88619	0.943093	−	0.332530i	$-0.107902\pi$
$857$	8.66652e36	1.88619	0.943093	+	0.332530i	$0.107902\pi$
$858$	−2.63251e36	−0.564649
$859$	−3.87843e36	−0.819862	−0.409931	−	0.912116i	$-0.634447\pi$
$859$	−3.87843e36	−0.819862	−0.409931	+	0.912116i	$0.634447\pi$
$860$	−1.16241e37	−2.42175
$861$	0	0
$862$	−7.29793e35	−0.147693
$863$	8.92425e36	1.78007	0.890034	−	0.455894i	$-0.150680\pi$
$863$	8.92425e36	1.78007	0.890034	+	0.455894i	$0.150680\pi$
$864$	−2.29139e37	−4.50482
$865$	5.74284e36	1.11282
$866$	6.62358e36	1.26508
$867$	5.47371e36	1.03049
$868$	0	0
$869$	2.13402e36	0.390348
$870$	−5.11304e36	−0.921910
$871$	2.64869e35	0.0470765
$872$	−2.56922e36	−0.450137
$873$	−2.03234e36	−0.351009
$874$	3.34419e36	0.569375
$875$	0	0
$876$	2.71102e37	4.48571
$877$	−2.23456e36	−0.364500	−0.182250	−	0.983252i	$-0.558338\pi$
$877$	−2.23456e36	−0.364500	−0.182250	+	0.983252i	$0.558338\pi$
$878$	1.68832e37	2.71502
$879$	−5.84553e36	−0.926751
$880$	−4.03165e36	−0.630157
$881$	9.64654e36	1.48653	0.743264	−	0.668999i	$-0.233277\pi$
$881$	9.64654e36	1.48653	0.743264	+	0.668999i	$0.233277\pi$
$882$	0	0
$883$	−2.16701e36	−0.324603	−0.162301	−	0.986741i	$-0.551892\pi$
$883$	−2.16701e36	−0.324603	−0.162301	+	0.986741i	$0.551892\pi$
$884$	7.46324e36	1.10224
$885$	−1.60191e37	−2.33264
$886$	−4.56867e36	−0.655946
$887$	−1.16431e37	−1.64825	−0.824126	−	0.566406i	$-0.808333\pi$
$887$	−1.16431e37	−1.64825	−0.824126	+	0.566406i	$0.808333\pi$
$888$	−5.90937e37	−8.24858
$889$	0	0
$890$	−3.14550e36	−0.426889
$891$	−2.93646e36	−0.392964
$892$	−1.72222e37	−2.27263
$893$	−3.17184e36	−0.412732
$894$	2.24925e37	2.88615
$895$	−1.03127e37	−1.30492
$896$	0	0
$897$	−4.80675e36	−0.591488
$898$	−2.99076e37	−3.62934
$899$	−3.23724e36	−0.387418
$900$	−1.98692e36	−0.234503
$901$	5.46973e36	0.636658
$902$	−1.05881e36	−0.121545
$903$	0	0
$904$	2.99646e37	3.34582
$905$	−6.44088e36	−0.709313
$906$	5.38066e37	5.84431
$907$	9.35920e36	1.00265	0.501323	−	0.865260i	$-0.332847\pi$
$907$	9.35920e36	1.00265	0.501323	+	0.865260i	$0.332847\pi$
$908$	−3.39978e36	−0.359234
$909$	4.83840e36	0.504259
$910$	0	0
$911$	5.42856e35	0.0550433	0.0275217	−	0.999621i	$-0.491238\pi$
$911$	5.42856e35	0.0550433	0.0275217	+	0.999621i	$0.491238\pi$
$912$	2.95604e37	2.95647
$913$	3.74469e36	0.369429
$914$	2.15408e37	2.09621
$915$	2.10538e37	2.02100
$916$	2.57809e37	2.44121
$917$	0	0
$918$	2.77825e37	2.55999
$919$	−1.74669e37	−1.58772	−0.793858	−	0.608103i	$-0.791931\pi$
$919$	−1.74669e37	−1.58772	−0.793858	+	0.608103i	$0.791931\pi$
$920$	−1.43166e37	−1.28378
$921$	1.51106e37	1.33671
$922$	2.63350e37	2.29825
$923$	−9.41444e36	−0.810538
$924$	0	0
$925$	−8.81222e35	−0.0738437
$926$	3.24818e37	2.68536
$927$	1.66745e37	1.36005
$928$	7.50823e36	0.604210
$929$	1.32802e37	1.05441	0.527204	−	0.849739i	$-0.323240\pi$
$929$	1.32802e37	1.05441	0.527204	+	0.849739i	$0.323240\pi$
$930$	5.66196e37	4.43537
$931$	0	0
$932$	1.14676e36	0.0874525
$933$	−1.27574e37	−0.959932
$934$	−4.40715e37	−3.27207
$935$	2.14402e36	0.157067
$936$	−5.66909e37	−4.09794
$937$	−1.24053e37	−0.884834	−0.442417	−	0.896809i	$-0.645879\pi$
$937$	−1.24053e37	−0.884834	−0.442417	+	0.896809i	$0.645879\pi$
$938$	0	0
$939$	−2.82798e37	−1.96407
$940$	2.28524e37	1.56615
$941$	−2.66478e37	−1.80215	−0.901075	−	0.433663i	$-0.857221\pi$
$941$	−2.66478e37	−1.80215	−0.901075	+	0.433663i	$0.857221\pi$
$942$	−8.26656e37	−5.51681
$943$	−1.93331e36	−0.127322
$944$	5.36318e37	3.48556
$945$	0	0
$946$	7.30016e36	0.462054
$947$	2.39011e36	0.149294	0.0746471	−	0.997210i	$-0.476217\pi$
$947$	2.39011e36	0.149294	0.0746471	+	0.997210i	$0.476217\pi$
$948$	1.12732e38	6.94931
$949$	1.15348e37	0.701749
$950$	8.57291e35	0.0514735
$951$	9.20941e36	0.545727
$952$	0	0
$953$	5.16541e36	0.298156	0.149078	−	0.988825i	$-0.452369\pi$
$953$	5.16541e36	0.298156	0.149078	+	0.988825i	$0.452369\pi$
$954$	−6.99236e37	−3.98354
$955$	1.85762e37	1.04451
$956$	2.19756e37	1.21960
$957$	2.28416e36	0.125120
$958$	−5.31612e37	−2.87426
$959$	0	0
$960$	−4.48927e37	−2.36475
$961$	1.66150e37	0.863891
$962$	−4.23146e37	−2.17171
$963$	−1.30884e37	−0.663069
$964$	3.99583e37	1.99822
$965$	6.04944e36	0.298624
$966$	0	0
$967$	−5.51627e36	−0.265347	−0.132674	−	0.991160i	$-0.542356\pi$
$967$	−5.51627e36	−0.265347	−0.132674	+	0.991160i	$0.542356\pi$
$968$	−5.38898e37	−2.55896
$969$	−1.57201e37	−0.736902
$970$	−6.31779e36	−0.292360
$971$	−1.58448e37	−0.723845	−0.361922	−	0.932208i	$-0.617879\pi$
$971$	−1.58448e37	−0.723845	−0.361922	+	0.932208i	$0.617879\pi$
$972$	−3.95185e37	−1.78226
$973$	0	0
$974$	−5.19076e37	−2.28162
$975$	−1.23222e36	−0.0534725
$976$	−7.04878e37	−3.01989
$977$	1.49299e37	0.631501	0.315750	−	0.948842i	$-0.397744\pi$
$977$	1.49299e37	0.631501	0.315750	+	0.948842i	$0.397744\pi$
$978$	1.07392e38	4.48472
$979$	1.40520e36	0.0579367
$980$	0	0
$981$	−8.98113e36	−0.360968
$982$	2.43147e37	0.964886
$983$	3.78511e37	1.48306	0.741531	−	0.670919i	$-0.234100\pi$
$983$	3.78511e37	1.48306	0.741531	+	0.670919i	$0.234100\pi$
$984$	−3.32349e37	−1.28575
$985$	−3.44150e37	−1.31460
$986$	−9.10355e36	−0.343360
$987$	0	0
$988$	2.92825e37	1.07683
$989$	1.33295e37	0.484017
$990$	−2.74086e37	−0.982759
$991$	1.83850e37	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$991$	1.83850e37	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$992$	−8.31429e37	−2.90689
$993$	3.68289e37	1.27152
$994$	0	0
$995$	−2.83730e37	−0.955249
$996$	1.97817e38	6.57691
$997$	−1.81883e37	−0.597176	−0.298588	−	0.954382i	$-0.596516\pi$
$997$	−1.81883e37	−0.597176	−0.298588	+	0.954382i	$0.596516\pi$
$998$	1.57517e37	0.510736
$999$	−1.12049e38	−3.58790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.f.1.16		16
7.2	even	3		7.26.c.a.4.1	yes	32
7.4	even	3		7.26.c.a.2.1	✓	32
7.6	odd	2		49.26.a.g.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.c.a.2.1	✓	32	7.4	even	3
7.26.c.a.4.1	yes	32	7.2	even	3
49.26.a.f.1.16		16	1.1	even	1	trivial
49.26.a.g.1.16		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)

\(f(q)\)	\(=\)	\(q+10781.5 q^{2} -1.64286e6 q^{3} +8.26859e7 q^{4} +5.33897e8 q^{5} -1.77124e10 q^{6} +5.29710e11 q^{8} +1.85169e12 q^{9} +O(q^{10})\)	\(q+10781.5 q^{2} -1.64286e6 q^{3} +8.26859e7 q^{4} +5.33897e8 q^{5} -1.77124e10 q^{6} +5.29710e11 q^{8} +1.85169e12 q^{9} +5.75620e12 q^{10} -2.57148e12 q^{11} -1.35841e14 q^{12} -5.77974e13 q^{13} -8.77116e14 q^{15} +2.93658e15 q^{16} -1.56167e15 q^{17} +1.99639e16 q^{18} -6.12730e15 q^{19} +4.41457e16 q^{20} -2.77244e16 q^{22} -5.06226e16 q^{23} -8.70236e17 q^{24} -1.29772e16 q^{25} -6.23141e17 q^{26} -1.65008e18 q^{27} +5.40685e17 q^{29} -9.45661e18 q^{30} -5.98731e18 q^{31} +1.38865e19 q^{32} +4.22458e18 q^{33} -1.68371e19 q^{34} +1.53108e20 q^{36} +6.79054e19 q^{37} -6.60613e19 q^{38} +9.49527e19 q^{39} +2.82810e20 q^{40} +3.81906e19 q^{41} -2.63312e20 q^{43} -2.12625e20 q^{44} +9.88610e20 q^{45} -5.45786e20 q^{46} +5.17657e20 q^{47} -4.82437e21 q^{48} -1.39913e20 q^{50} +2.56559e21 q^{51} -4.77902e21 q^{52} -3.50250e21 q^{53} -1.77903e22 q^{54} -1.37291e21 q^{55} +1.00663e22 q^{57} +5.82938e21 q^{58} +1.82634e22 q^{59} -7.25251e22 q^{60} -2.40034e22 q^{61} -6.45520e22 q^{62} +5.11822e22 q^{64} -3.08578e22 q^{65} +4.55472e22 q^{66} -4.58271e21 q^{67} -1.29128e23 q^{68} +8.31656e22 q^{69} +1.62887e23 q^{71} +9.80856e23 q^{72} -1.99573e23 q^{73} +7.32120e23 q^{74} +2.13197e22 q^{75} -5.06641e23 q^{76} +1.02373e24 q^{78} -8.29880e23 q^{79} +1.56783e24 q^{80} +1.14193e24 q^{81} +4.11751e23 q^{82} -1.45624e24 q^{83} -8.33769e23 q^{85} -2.83889e24 q^{86} -8.88267e23 q^{87} -1.36214e24 q^{88} -5.46454e23 q^{89} +1.06587e25 q^{90} -4.18577e24 q^{92} +9.83628e24 q^{93} +5.58111e24 q^{94} -3.27135e24 q^{95} -2.28136e25 q^{96} -1.09756e24 q^{97} -4.76158e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4050 q^{2} - 531440 q^{3} + 286295596 q^{4} - 288173088 q^{5} - 6531645442 q^{6} + 137183373360 q^{8} + 5146896583216 q^{9}+O(q^{10}) \) 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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