LMFDB - Embedded newform 98.13.b.c.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(97,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("98.97");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$89.5713940931$
Analytic rank:	$0$
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} + 6613776 x^{14} + 17532494948988 x^{12} + \cdots + 16\!\cdots\!41 $ x^16 + 6613776x^14 + 17532494948988x^12 + 23874431083308410544x^10 + 17814546644991454004799078x^8 + 7194684838492777650788022411888x^6 + 1439579890626389563511626657632573372x^4 + 111400901558110496276819595183126508110288*x^2 + 166146008225686888975158615912586831592255841
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{8}\cdot 7^{24} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.6
Root			$512.782i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.13.b.c.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548 q^{2} +512.782i q^{3} +2048.00 q^{4} -14650.7i q^{5} -23205.9i q^{6} -92681.9 q^{8} +268495. q^{9} +O(q^{10})$	\(q-45.2548 q^{2} +512.782i q^{3} +2048.00 q^{4} -14650.7i q^{5} -23205.9i q^{6} -92681.9 q^{8} +268495. q^{9} +663015. i q^{10} -2.68298e6 q^{11} +1.05018e6i q^{12} -1.34691e6i q^{13} +7.51261e6 q^{15} +4.19430e6 q^{16} -7.16465e6i q^{17} -1.21507e7 q^{18} +7.31436e7i q^{19} -3.00046e7i q^{20} +1.21418e8 q^{22} +2.28225e8 q^{23} -4.75256e7i q^{24} +2.94979e7 q^{25} +6.09543e7i q^{26} +4.10193e8i q^{27} -5.69081e8 q^{29} -3.39982e8 q^{30} -3.08915e8i q^{31} -1.89813e8 q^{32} -1.37578e9i q^{33} +3.24235e8i q^{34} +5.49879e8 q^{36} +1.70366e9 q^{37} -3.31010e9i q^{38} +6.90673e8 q^{39} +1.35785e9i q^{40} -5.37658e9i q^{41} -9.19904e9 q^{43} -5.49474e9 q^{44} -3.93364e9i q^{45} -1.03283e10 q^{46} +1.09163e10i q^{47} +2.15076e9i q^{48} -1.33492e9 q^{50} +3.67391e9 q^{51} -2.75848e9i q^{52} -1.58563e10 q^{53} -1.85632e10i q^{54} +3.93075e10i q^{55} -3.75067e10 q^{57} +2.57537e10 q^{58} -2.02600e10i q^{59} +1.53858e10 q^{60} +2.75345e10i q^{61} +1.39799e10i q^{62} +8.58993e9 q^{64} -1.97332e10 q^{65} +6.22608e10i q^{66} +6.70111e10 q^{67} -1.46732e10i q^{68} +1.17030e11i q^{69} +7.34393e10 q^{71} -2.48847e10 q^{72} -6.49049e10i q^{73} -7.70990e10 q^{74} +1.51260e10i q^{75} +1.49798e11i q^{76} -3.12563e10 q^{78} +6.32826e9 q^{79} -6.14495e10i q^{80} -6.76503e10 q^{81} +2.43316e11i q^{82} -5.07191e11i q^{83} -1.04967e11 q^{85} +4.16301e11 q^{86} -2.91815e11i q^{87} +2.48663e11 q^{88} -6.34733e11i q^{89} +1.78016e11i q^{90} +4.67404e11 q^{92} +1.58406e11 q^{93} -4.94016e11i q^{94} +1.07160e12 q^{95} -9.73325e10i q^{96} +3.89725e11i q^{97} -7.20367e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32768 q^{4} - 4724496 q^{9}+O(q^{10}) $ 16 * q + 32768 * q^4 - 4724496 * q^9	$ 16 q + 32768 q^{4} - 4724496 q^{9} - 4144176 q^{11} - 27163728 q^{15} + 67108864 q^{16} + 9185280 q^{18} + 62776320 q^{22} - 51261120 q^{23} - 1042411616 q^{25} + 532360944 q^{29} + 4303835136 q^{30} - 9675767808 q^{36} - 11529048080 q^{37} - 21052166544 q^{39} - 66929432000 q^{43} - 8487272448 q^{44} - 14406426624 q^{46} - 99248080896 q^{50} + 46598512752 q^{51} - 78268323600 q^{53} - 328243960080 q^{57} - 59274792960 q^{58} - 55631314944 q^{60} + 137438953472 q^{64} - 316645407792 q^{65} - 215534239840 q^{67} - 1150259029344 q^{71} + 18811453440 q^{72} - 9805556736 q^{74} - 786088888320 q^{78} - 455264129536 q^{79} + 783968356800 q^{81} + 710209696080 q^{85} + 76210384896 q^{86} + 128565903360 q^{88} - 104982773760 q^{92} + 917337537360 q^{93} + 373007725920 q^{95} + 3921180354576 q^{99}+O(q^{100}) $ 16 * q + 32768 * q^4 - 4724496 * q^9 - 4144176 * q^11 - 27163728 * q^15 + 67108864 * q^16 + 9185280 * q^18 + 62776320 * q^22 - 51261120 * q^23 - 1042411616 * q^25 + 532360944 * q^29 + 4303835136 * q^30 - 9675767808 * q^36 - 11529048080 * q^37 - 21052166544 * q^39 - 66929432000 * q^43 - 8487272448 * q^44 - 14406426624 * q^46 - 99248080896 * q^50 + 46598512752 * q^51 - 78268323600 * q^53 - 328243960080 * q^57 - 59274792960 * q^58 - 55631314944 * q^60 + 137438953472 * q^64 - 316645407792 * q^65 - 215534239840 * q^67 - 1150259029344 * q^71 + 18811453440 * q^72 - 9805556736 * q^74 - 786088888320 * q^78 - 455264129536 * q^79 + 783968356800 * q^81 + 710209696080 * q^85 + 76210384896 * q^86 + 128565903360 * q^88 - 104982773760 * q^92 + 917337537360 * q^93 + 373007725920 * q^95 + 3921180354576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−45.2548	−0.707107
$2$	−45.2548	−0.707107
$3$	512.782i	0.703405i	0.936112	+	0.351702i	$0.114397\pi$
$3$	512.782i	0.703405i	−0.936112	+	0.351702i	$0.885603\pi$
$4$	2048.00	0.500000
$5$	− 14650.7i	− 0.937644i	−0.883293	−	0.468822i	$-0.844679\pi$
$5$	− 14650.7i	− 0.937644i	0.883293	−	0.468822i	$-0.155321\pi$
$6$	− 23205.9i	− 0.497382i
$7$	0	0
$7$	0	0
$8$	−92681.9	−0.353553
$9$	268495.	0.505222
$10$	663015.i	0.663015i
$11$	−2.68298e6	−1.51447	−0.757235	−	0.653142i	$-0.773450\pi$
$11$	−2.68298e6	−1.51447	−0.757235	+	0.653142i	$0.773450\pi$
$12$	1.05018e6i	0.351702i
$13$	− 1.34691e6i	− 0.279048i	−0.990219	−	0.139524i	$-0.955443\pi$
$13$	− 1.34691e6i	− 0.279048i	0.990219	−	0.139524i	$-0.0445573\pi$
$14$	0	0
$15$	7.51261e6	0.659544
$16$	4.19430e6	0.250000
$17$	− 7.16465e6i	− 0.296826i	−0.988925	−	0.148413i	$-0.952584\pi$
$17$	− 7.16465e6i	− 0.296826i	0.988925	−	0.148413i	$-0.0474165\pi$
$18$	−1.21507e7	−0.357246
$19$	7.31436e7i	1.55473i	0.629050	+	0.777365i	$0.283444\pi$
$19$	7.31436e7i	1.55473i	−0.629050	+	0.777365i	$0.716556\pi$
$20$	− 3.00046e7i	− 0.468822i
$21$	0	0
$22$	1.21418e8	1.07089
$23$	2.28225e8	1.54169	0.770843	−	0.637025i	$-0.219835\pi$
$23$	2.28225e8	1.54169	0.770843	+	0.637025i	$0.219835\pi$
$24$	− 4.75256e7i	− 0.248691i
$25$	2.94979e7	0.120823
$26$	6.09543e7i	0.197317i
$27$	4.10193e8i	1.05878i
$28$	0	0
$29$	−5.69081e8	−0.956723	−0.478362	−	0.878163i	$-0.658769\pi$
$29$	−5.69081e8	−0.956723	−0.478362	+	0.878163i	$0.658769\pi$
$30$	−3.39982e8	−0.466368
$31$	− 3.08915e8i	− 0.348071i	−0.984739	−	0.174036i	$-0.944319\pi$
$31$	− 3.08915e8i	− 0.348071i	0.984739	−	0.174036i	$-0.0556808\pi$
$32$	−1.89813e8	−0.176777
$33$	− 1.37578e9i	− 1.06529i
$34$	3.24235e8i	0.209888i
$35$	0	0
$36$	5.49879e8	0.252611
$37$	1.70366e9	0.664008	0.332004	−	0.943278i	$-0.392275\pi$
$37$	1.70366e9	0.664008	0.332004	+	0.943278i	$0.392275\pi$
$38$	− 3.31010e9i	− 1.09936i
$39$	6.90673e8	0.196284
$40$	1.35785e9i	0.331507i
$41$	− 5.37658e9i	− 1.13189i	−0.824444	−	0.565944i	$-0.808512\pi$
$41$	− 5.37658e9i	− 1.13189i	0.824444	−	0.565944i	$-0.191488\pi$
$42$	0	0
$43$	−9.19904e9	−1.45523	−0.727615	−	0.685985i	$-0.759371\pi$
$43$	−9.19904e9	−1.45523	−0.727615	+	0.685985i	$0.759371\pi$
$44$	−5.49474e9	−0.757235
$45$	− 3.93364e9i	− 0.473718i
$46$	−1.03283e10	−1.09014
$47$	1.09163e10i	1.01272i	0.862322	+	0.506360i	$0.169009\pi$
$47$	1.09163e10i	1.01272i	−0.862322	+	0.506360i	$0.830991\pi$
$48$	2.15076e9i	0.175851i
$49$	0	0
$50$	−1.33492e9	−0.0854350
$51$	3.67391e9	0.208789
$52$	− 2.75848e9i	− 0.139524i
$53$	−1.58563e10	−0.715397	−0.357698	−	0.933837i	$-0.616438\pi$
$53$	−1.58563e10	−0.715397	−0.357698	+	0.933837i	$0.616438\pi$
$54$	− 1.85632e10i	− 0.748671i
$55$	3.93075e10i	1.42003i
$56$	0	0
$57$	−3.75067e10	−1.09360
$58$	2.57537e10	0.676506
$59$	− 2.02600e10i	− 0.480317i	−0.970734	−	0.240159i	$-0.922801\pi$
$59$	− 2.02600e10i	− 0.480317i	0.970734	−	0.240159i	$-0.0771995\pi$
$60$	1.53858e10	0.329772
$61$	2.75345e10i	0.534438i	0.963636	+	0.267219i	$0.0861047\pi$
$61$	2.75345e10i	0.534438i	−0.963636	+	0.267219i	$0.913895\pi$
$62$	1.39799e10i	0.246124i
$63$	0	0
$64$	8.58993e9	0.125000
$65$	−1.97332e10	−0.261648
$66$	6.22608e10i	0.753271i
$67$	6.70111e10	0.740795	0.370398	−	0.928873i	$-0.379221\pi$
$67$	6.70111e10	0.740795	0.370398	+	0.928873i	$0.379221\pi$
$68$	− 1.46732e10i	− 0.148413i
$69$	1.17030e11i	1.08443i
$70$	0	0
$71$	7.34393e10	0.573295	0.286648	−	0.958036i	$-0.407459\pi$
$71$	7.34393e10	0.573295	0.286648	+	0.958036i	$0.407459\pi$
$72$	−2.48847e10	−0.178623
$73$	− 6.49049e10i	− 0.428885i	−0.976737	−	0.214442i	$-0.931207\pi$
$73$	− 6.49049e10i	− 0.428885i	0.976737	−	0.214442i	$-0.0687934\pi$
$74$	−7.70990e10	−0.469525
$75$	1.51260e10i	0.0849877i
$76$	1.49798e11i	0.777365i
$77$	0	0
$78$	−3.12563e10	−0.138794
$79$	6.32826e9	0.0260328	0.0130164	−	0.999915i	$-0.495857\pi$
$79$	6.32826e9	0.0260328	0.0130164	+	0.999915i	$0.495857\pi$
$80$	− 6.14495e10i	− 0.234411i
$81$	−6.76503e10	−0.239530
$82$	2.43316e11i	0.800365i
$83$	− 5.07191e11i	− 1.55133i	−0.631147	−	0.775663i	$-0.717415\pi$
$83$	− 5.07191e11i	− 1.55133i	0.631147	−	0.775663i	$-0.282585\pi$
$84$	0	0
$85$	−1.04967e11	−0.278317
$86$	4.16301e11	1.02900
$87$	− 2.91815e11i	− 0.672964i
$88$	2.48663e11	0.535446
$89$	− 6.34733e11i	− 1.27718i	−0.769548	−	0.638589i	$-0.779518\pi$
$89$	− 6.34733e11i	− 1.27718i	0.769548	−	0.638589i	$-0.220482\pi$
$90$	1.78016e11i	0.334969i
$91$	0	0
$92$	4.67404e11	0.770843
$93$	1.58406e11	0.244835
$94$	− 4.94016e11i	− 0.716101i
$95$	1.07160e12	1.45778
$96$	− 9.73325e10i	− 0.124346i
$97$	3.89725e11i	0.467873i	0.972252	+	0.233937i	$0.0751609\pi$
$97$	3.89725e11i	0.467873i	−0.972252	+	0.233937i	$0.924839\pi$
$98$	0	0
$99$	−7.20367e11	−0.765143
$100$	6.04117e10	0.0604117
$101$	− 2.73813e9i	− 0.00257944i	−0.999999	−	0.00128972i	$-0.999589\pi$
$101$	− 2.73813e9i	− 0.00257944i	0.999999	−	0.00128972i	$-0.000410531\pi$
$102$	−1.66262e11	−0.147636
$103$	− 2.12461e12i	− 1.77933i	−0.456618	−	0.889663i	$-0.650939\pi$
$103$	− 2.12461e12i	− 1.77933i	0.456618	−	0.889663i	$-0.349061\pi$
$104$	1.24834e11i	0.0986585i
$105$	0	0
$106$	7.17575e11	0.505862
$107$	1.88366e12	1.25516	0.627582	−	0.778550i	$-0.284045\pi$
$107$	1.88366e12	1.25516	0.627582	+	0.778550i	$0.284045\pi$
$108$	8.40076e11i	0.529390i
$109$	−2.61810e12	−1.56109	−0.780544	−	0.625101i	$-0.785058\pi$
$109$	−2.61810e12	−1.56109	−0.780544	+	0.625101i	$0.785058\pi$
$110$	− 1.77885e12i	− 1.00412i
$111$	8.73608e11i	0.467067i
$112$	0	0
$113$	2.59357e12	1.24574	0.622869	−	0.782326i	$-0.285967\pi$
$113$	2.59357e12	1.24574	0.622869	+	0.782326i	$0.285967\pi$
$114$	1.69736e12	0.773295
$115$	− 3.34365e12i	− 1.44555i
$116$	−1.16548e12	−0.478362
$117$	− 3.61640e11i	− 0.140981i
$118$	9.16865e11i	0.339636i
$119$	0	0
$120$	−6.96283e11	−0.233184
$121$	4.05993e12	1.29362
$122$	− 1.24607e12i	− 0.377905i
$123$	2.75702e12	0.796175
$124$	− 6.32657e11i	− 0.174036i
$125$	− 4.00899e12i	− 1.05093i
$126$	0	0
$127$	6.80221e12	1.62117	0.810583	−	0.585623i	$-0.199150\pi$
$127$	6.80221e12	1.62117	0.810583	+	0.585623i	$0.199150\pi$
$128$	−3.88736e11	−0.0883883
$129$	− 4.71711e12i	− 1.02362i
$130$	8.93023e11	0.185013
$131$	− 8.15579e12i	− 1.61376i	−0.590718	−	0.806878i	$-0.701155\pi$
$131$	− 8.15579e12i	− 1.61376i	0.590718	−	0.806878i	$-0.298845\pi$
$132$	− 2.81760e12i	− 0.532643i
$133$	0	0
$134$	−3.03258e12	−0.523821
$135$	6.00961e12	0.992759
$136$	6.64034e11i	0.104944i
$137$	8.14193e12	1.23141	0.615707	−	0.787975i	$-0.288870\pi$
$137$	8.14193e12	1.23141	0.615707	+	0.787975i	$0.288870\pi$
$138$	− 5.29616e12i	− 0.766807i
$139$	1.24727e13i	1.72930i	0.502371	+	0.864652i	$0.332461\pi$
$139$	1.24727e13i	1.72930i	−0.502371	+	0.864652i	$0.667539\pi$
$140$	0	0
$141$	−5.59769e12	−0.712352
$142$	−3.32348e12	−0.405381
$143$	3.61374e12i	0.422610i
$144$	1.12615e12	0.126305
$145$	8.33744e12i	0.897066i
$146$	2.93726e12i	0.303267i
$147$	0	0
$148$	3.48910e12	0.332004
$149$	5.83715e12	0.533437	0.266719	−	0.963774i	$-0.414061\pi$
$149$	5.83715e12	0.533437	0.266719	+	0.963774i	$0.414061\pi$
$150$	− 6.84524e11i	− 0.0600954i
$151$	8.12255e12	0.685221	0.342610	−	0.939478i	$-0.388689\pi$
$151$	8.12255e12	0.685221	0.342610	+	0.939478i	$0.388689\pi$
$152$	− 6.77909e12i	− 0.549680i
$153$	− 1.92368e12i	− 0.149963i
$154$	0	0
$155$	−4.52581e12	−0.326367
$156$	1.41450e12	0.0981420
$157$	− 2.31549e13i	− 1.54613i	−0.634327	−	0.773065i	$-0.718723\pi$
$157$	− 2.31549e13i	− 1.54613i	0.634327	−	0.773065i	$-0.281277\pi$
$158$	−2.86384e11	−0.0184080
$159$	− 8.13084e12i	− 0.503214i
$160$	2.78088e12i	0.165754i
$161$	0	0
$162$	3.06150e12	0.169373
$163$	8.52361e12	0.454462	0.227231	−	0.973841i	$-0.427033\pi$
$163$	8.52361e12	0.454462	0.227231	+	0.973841i	$0.427033\pi$
$164$	− 1.10112e13i	− 0.565944i
$165$	−2.01562e13	−0.998859
$166$	2.29529e13i	1.09695i
$167$	2.04015e13i	0.940509i	0.882531	+	0.470255i	$0.155838\pi$
$167$	2.04015e13i	0.940509i	−0.882531	+	0.470255i	$0.844162\pi$
$168$	0	0
$169$	2.14839e13	0.922132
$170$	4.75027e12	0.196800
$171$	1.96387e13i	0.785483i
$172$	−1.88396e13	−0.727615
$173$	− 8.50196e12i	− 0.317134i	−0.987348	−	0.158567i	$-0.949313\pi$
$173$	− 8.50196e12i	− 0.317134i	0.987348	−	0.158567i	$-0.0506873\pi$
$174$	1.32060e13i	0.475857i
$175$	0	0
$176$	−1.12532e13	−0.378618
$177$	1.03890e13	0.337858
$178$	2.87248e13i	0.903101i
$179$	−1.97772e13	−0.601240	−0.300620	−	0.953744i	$-0.597194\pi$
$179$	−1.97772e13	−0.601240	−0.300620	+	0.953744i	$0.597194\pi$
$180$	− 8.05610e12i	− 0.236859i
$181$	− 2.46719e13i	− 0.701667i	−0.936438	−	0.350833i	$-0.885898\pi$
$181$	− 2.46719e13i	− 0.701667i	0.936438	−	0.350833i	$-0.114102\pi$
$182$	0	0
$183$	−1.41192e13	−0.375926
$184$	−2.11523e13	−0.545068
$185$	− 2.49598e13i	− 0.622603i
$186$	−7.16864e12	−0.173125
$187$	1.92226e13i	0.449534i
$188$	2.23566e13i	0.506360i
$189$	0	0
$190$	−4.84953e13	−1.03081
$191$	−4.15018e13	−0.854805	−0.427403	−	0.904061i	$-0.640571\pi$
$191$	−4.15018e13	−0.854805	−0.427403	+	0.904061i	$0.640571\pi$
$192$	4.40477e12i	0.0879256i
$193$	5.97986e13	1.15704	0.578519	−	0.815669i	$-0.303631\pi$
$193$	5.97986e13	1.15704	0.578519	+	0.815669i	$0.303631\pi$
$194$	− 1.76370e13i	− 0.330836i
$195$	− 1.01188e13i	− 0.184045i
$196$	0	0
$197$	−5.28263e13	−0.903760	−0.451880	−	0.892079i	$-0.649246\pi$
$197$	−5.28263e13	−0.903760	−0.451880	+	0.892079i	$0.649246\pi$
$198$	3.26001e13	0.541038
$199$	− 7.64701e13i	− 1.23133i	−0.788009	−	0.615663i	$-0.788888\pi$
$199$	− 7.64701e13i	− 1.23133i	0.788009	−	0.615663i	$-0.211112\pi$
$200$	−2.73392e12	−0.0427175
$201$	3.43621e13i	0.521079i
$202$	1.23913e11i	0.00182394i
$203$	0	0
$204$	7.52416e12	0.104394
$205$	−7.87706e13	−1.06131
$206$	9.61488e13i	1.25817i
$207$	6.12773e13	0.778893
$208$	− 5.64936e12i	− 0.0697621i
$209$	− 1.96243e14i	− 2.35459i
$210$	0	0
$211$	5.17345e13	0.586254	0.293127	−	0.956074i	$-0.405304\pi$
$211$	5.17345e13	0.586254	0.293127	+	0.956074i	$0.405304\pi$
$212$	−3.24737e13	−0.357698
$213$	3.76584e13i	0.403259i
$214$	−8.52449e13	−0.887535
$215$	1.34772e14i	1.36449i
$216$	− 3.80175e13i	− 0.374335i
$217$	0	0
$218$	1.18482e14	1.10386
$219$	3.32821e13	0.301680
$220$	8.05017e13i	0.710017i
$221$	−9.65017e12	−0.0828288
$222$	− 3.95350e13i	− 0.330266i
$223$	− 6.07846e13i	− 0.494270i	−0.968981	−	0.247135i	$-0.920511\pi$
$223$	− 6.07846e13i	− 0.494270i	0.968981	−	0.247135i	$-0.0794891\pi$
$224$	0	0
$225$	7.92005e12	0.0610425
$226$	−1.17371e14	−0.880870
$227$	1.61792e14i	1.18250i	0.806487	+	0.591251i	$0.201366\pi$
$227$	1.61792e14i	1.18250i	−0.806487	+	0.591251i	$0.798634\pi$
$228$	−7.68138e13	−0.546802
$229$	8.61634e13i	0.597462i	0.954337	+	0.298731i	$0.0965633\pi$
$229$	8.61634e13i	0.597462i	−0.954337	+	0.298731i	$0.903437\pi$
$230$	1.51316e14i	1.02216i
$231$	0	0
$232$	5.27435e13	0.338253
$233$	−1.55626e14	−0.972628	−0.486314	−	0.873784i	$-0.661659\pi$
$233$	−1.55626e14	−0.972628	−0.486314	+	0.873784i	$0.661659\pi$
$234$	1.63660e13i	0.0996888i
$235$	1.59932e14	0.949570
$236$	− 4.14926e13i	− 0.240159i
$237$	3.24502e12i	0.0183116i
$238$	0	0
$239$	2.13466e14	1.14536	0.572679	−	0.819780i	$-0.305904\pi$
$239$	2.13466e14	1.14536	0.572679	+	0.819780i	$0.305904\pi$
$240$	3.15102e13	0.164886
$241$	1.15381e14i	0.588885i	0.955669	+	0.294442i	$0.0951339\pi$
$241$	1.15381e14i	0.588885i	−0.955669	+	0.294442i	$0.904866\pi$
$242$	−1.83732e14	−0.914727
$243$	1.83304e14i	0.890294i
$244$	5.63906e13i	0.267219i
$245$	0	0
$246$	−1.24768e14	−0.562981
$247$	9.85181e13	0.433845
$248$	2.86308e13i	0.123062i
$249$	2.60079e14	1.09121
$250$	1.81426e14i	0.743122i
$251$	− 3.21279e14i	− 1.28481i	−0.766364	−	0.642406i	$-0.777936\pi$
$251$	− 3.21279e14i	− 1.28481i	0.766364	−	0.642406i	$-0.222064\pi$
$252$	0	0
$253$	−6.12322e14	−2.33484
$254$	−3.07833e14	−1.14634
$255$	− 5.38253e13i	− 0.195770i
$256$	1.75922e13	0.0625000
$257$	− 3.42124e14i	− 1.18737i	−0.804699	−	0.593683i	$-0.797673\pi$
$257$	− 3.42124e14i	− 1.18737i	0.804699	−	0.593683i	$-0.202327\pi$
$258$	2.13472e14i	0.723806i
$259$	0	0
$260$	−4.04136e13	−0.130824
$261$	−1.52796e14	−0.483357
$262$	3.69089e14i	1.14110i
$263$	−1.03152e14	−0.311705	−0.155853	−	0.987780i	$-0.549812\pi$
$263$	−1.03152e14	−0.311705	−0.155853	+	0.987780i	$0.549812\pi$
$264$	1.27510e14i	0.376635i
$265$	2.32306e14i	0.670788i
$266$	0	0
$267$	3.25480e14	0.898373
$268$	1.37239e14	0.370398
$269$	− 4.68801e14i	− 1.23730i	−0.785667	−	0.618650i	$-0.787680\pi$
$269$	− 4.68801e14i	− 1.23730i	0.785667	−	0.618650i	$-0.212320\pi$
$270$	−2.71964e14	−0.701987
$271$	4.36618e14i	1.10226i	0.834418	+	0.551132i	$0.185804\pi$
$271$	4.36618e14i	1.10226i	−0.834418	+	0.551132i	$0.814196\pi$
$272$	− 3.00507e13i	− 0.0742065i
$273$	0	0
$274$	−3.68462e14	−0.870741
$275$	−7.91421e13	−0.182983
$276$	2.39677e14i	0.542215i
$277$	−1.97438e14	−0.437071	−0.218536	−	0.975829i	$-0.570128\pi$
$277$	−1.97438e14	−0.437071	−0.218536	+	0.975829i	$0.570128\pi$
$278$	− 5.64450e14i	− 1.22280i
$279$	− 8.29422e13i	− 0.175853i
$280$	0	0
$281$	8.30058e13	0.168605	0.0843025	−	0.996440i	$-0.473134\pi$
$281$	8.30058e13	0.168605	0.0843025	+	0.996440i	$0.473134\pi$
$282$	2.53323e14	0.503709
$283$	− 7.09553e14i	− 1.38123i	−0.723223	−	0.690615i	$-0.757340\pi$
$283$	− 7.09553e14i	− 1.38123i	0.723223	−	0.690615i	$-0.242660\pi$
$284$	1.50404e14	0.286648
$285$	5.49500e14i	1.02541i
$286$	− 1.63539e14i	− 0.298831i
$287$	0	0
$288$	−5.09638e13	−0.0893114
$289$	5.31290e14	0.911894
$290$	− 3.77309e14i	− 0.634322i
$291$	−1.99844e14	−0.329104
$292$	− 1.32925e14i	− 0.214442i
$293$	− 1.90883e14i	− 0.301691i	−0.988557	−	0.150845i	$-0.951800\pi$
$293$	− 1.90883e14i	− 0.301691i	0.988557	−	0.150845i	$-0.0481996\pi$
$294$	0	0
$295$	−2.96824e14	−0.450367
$296$	−1.57899e14	−0.234762
$297$	− 1.10054e15i	− 1.60349i
$298$	−2.64159e14	−0.377197
$299$	− 3.07399e14i	− 0.430205i
$300$	3.09780e13i	0.0424939i
$301$	0	0
$302$	−3.67585e14	−0.484524
$303$	1.40406e12	0.00181439
$304$	3.06787e14i	0.388682i
$305$	4.03399e14	0.501113
$306$	8.70557e13i	0.106040i
$307$	6.74575e14i	0.805750i	0.915255	+	0.402875i	$0.131989\pi$
$307$	6.74575e14i	0.805750i	−0.915255	+	0.402875i	$0.868011\pi$
$308$	0	0
$309$	1.08946e15	1.25159
$310$	2.04815e14	0.230776
$311$	6.49614e14i	0.717949i	0.933347	+	0.358974i	$0.116873\pi$
$311$	6.49614e14i	0.717949i	−0.933347	+	0.358974i	$0.883127\pi$
$312$	−6.40129e13	−0.0693969
$313$	− 1.15629e15i	− 1.22971i	−0.788642	−	0.614853i	$-0.789215\pi$
$313$	− 1.15629e15i	− 1.22971i	0.788642	−	0.614853i	$-0.210785\pi$
$314$	1.04787e15i	1.09328i
$315$	0	0
$316$	1.29603e13	0.0130164
$317$	1.79232e15	1.76628	0.883140	−	0.469110i	$-0.155425\pi$
$317$	1.79232e15	1.76628	0.883140	+	0.469110i	$0.155425\pi$
$318$	3.67960e14i	0.355826i
$319$	1.52683e15	1.44893
$320$	− 1.25848e14i	− 0.117206i
$321$	9.65909e14i	0.882889i
$322$	0	0
$323$	5.24049e14	0.461484
$324$	−1.38548e14	−0.119765
$325$	− 3.97311e13i	− 0.0337155i
$326$	−3.85735e14	−0.321354
$327$	− 1.34252e15i	− 1.09808i
$328$	4.98312e14i	0.400183i
$329$	0	0
$330$	9.12164e14	0.706300
$331$	2.66229e14	0.202436	0.101218	−	0.994864i	$-0.467726\pi$
$331$	2.66229e14	0.202436	0.101218	+	0.994864i	$0.467726\pi$
$332$	− 1.03873e15i	− 0.775663i
$333$	4.57426e14	0.335471
$334$	− 9.23266e14i	− 0.665040i
$335$	− 9.81759e14i	− 0.694602i
$336$	0	0
$337$	−2.34808e14	−0.160300	−0.0801498	−	0.996783i	$-0.525540\pi$
$337$	−2.34808e14	−0.160300	−0.0801498	+	0.996783i	$0.525540\pi$
$338$	−9.72251e14	−0.652046
$339$	1.32994e15i	0.876258i
$340$	−2.14973e14	−0.139159
$341$	8.28811e14i	0.527144i
$342$	− 8.88747e14i	− 0.555420i
$343$	0	0
$344$	8.52585e14	0.514502
$345$	1.71456e15	1.01681
$346$	3.84755e14i	0.224247i
$347$	1.32679e15	0.760018	0.380009	−	0.924983i	$-0.375921\pi$
$347$	1.32679e15	0.760018	0.380009	+	0.924983i	$0.375921\pi$
$348$	− 5.97637e14i	− 0.336482i
$349$	− 2.62751e15i	− 1.45409i	−0.686590	−	0.727045i	$-0.740893\pi$
$349$	− 2.62751e15i	− 1.45409i	0.686590	−	0.727045i	$-0.259107\pi$
$350$	0	0
$351$	5.52494e14	0.295451
$352$	5.09262e14	0.267723
$353$	− 2.53804e15i	− 1.31175i	−0.754871	−	0.655873i	$-0.772301\pi$
$353$	− 2.53804e15i	− 1.31175i	0.754871	−	0.655873i	$-0.227699\pi$
$354$	−4.70152e14	−0.238901
$355$	− 1.07594e15i	− 0.537547i
$356$	− 1.29993e15i	− 0.638589i
$357$	0	0
$358$	8.95016e14	0.425141
$359$	1.16042e15	0.542060	0.271030	−	0.962571i	$-0.412636\pi$
$359$	1.16042e15	0.542060	0.271030	+	0.962571i	$0.412636\pi$
$360$	3.64578e14i	0.167485i
$361$	−3.13667e15	−1.41718
$362$	1.11652e15i	0.496153i
$363$	2.08186e15i	0.909938i
$364$	0	0
$365$	−9.50902e14	−0.402141
$366$	6.38961e14	0.265820
$367$	− 1.78981e15i	− 0.732504i	−0.930516	−	0.366252i	$-0.880641\pi$
$367$	− 1.78981e15i	− 0.732504i	0.930516	−	0.366252i	$-0.119359\pi$
$368$	9.57244e14	0.385421
$369$	− 1.44359e15i	− 0.571854i
$370$	1.12955e15i	0.440247i
$371$	0	0
$372$	3.24415e14	0.122418
$373$	−4.78396e15	−1.77637	−0.888187	−	0.459483i	$-0.848035\pi$
$373$	−4.78396e15	−1.77637	−0.888187	+	0.459483i	$0.848035\pi$
$374$	− 8.69915e14i	− 0.317868i
$375$	2.05574e15	0.739232
$376$	− 1.01175e15i	− 0.358050i
$377$	7.66503e14i	0.266972i
$378$	0	0
$379$	−1.31568e15	−0.443931	−0.221965	−	0.975055i	$-0.571247\pi$
$379$	−1.31568e15	−0.443931	−0.221965	+	0.975055i	$0.571247\pi$
$380$	2.19465e15	0.728891
$381$	3.48805e15i	1.14034i
$382$	1.87816e15	0.604439
$383$	− 1.51566e15i	− 0.480187i	−0.970750	−	0.240093i	$-0.922822\pi$
$383$	− 1.51566e15i	− 0.480187i	0.970750	−	0.240093i	$-0.0771780\pi$
$384$	− 1.99337e14i	− 0.0621728i
$385$	0	0
$386$	−2.70618e15	−0.818149
$387$	−2.46990e15	−0.735214
$388$	7.98158e14i	0.233937i
$389$	−2.77117e15	−0.799772	−0.399886	−	0.916565i	$-0.630950\pi$
$389$	−2.77117e15	−0.799772	−0.399886	+	0.916565i	$0.630950\pi$
$390$	4.57926e14i	0.130139i
$391$	− 1.63515e15i	− 0.457612i
$392$	0	0
$393$	4.18214e15	1.13512
$394$	2.39065e15	0.639055
$395$	− 9.27134e13i	− 0.0244095i
$396$	−1.47531e15	−0.382571
$397$	3.51793e15i	0.898555i	0.893392	+	0.449278i	$0.148319\pi$
$397$	3.51793e15i	0.898555i	−0.893392	+	0.449278i	$0.851681\pi$
$398$	3.46064e15i	0.870679i
$399$	0	0
$400$	1.23723e14	0.0302058
$401$	4.91780e15	1.18278	0.591391	−	0.806385i	$-0.298579\pi$
$401$	4.91780e15	1.18278	0.591391	+	0.806385i	$0.298579\pi$
$402$	− 1.55505e15i	− 0.368458i
$403$	−4.16081e14	−0.0971288
$404$	− 5.60768e12i	− 0.00128972i
$405$	9.91123e14i	0.224594i
$406$	0	0
$407$	−4.57089e15	−1.00562
$408$	−3.40505e14	−0.0738180
$409$	− 2.91085e15i	− 0.621843i	−0.950436	−	0.310921i	$-0.899362\pi$
$409$	− 2.91085e15i	− 0.621843i	0.950436	−	0.310921i	$-0.100638\pi$
$410$	3.56475e15	0.750458
$411$	4.17504e15i	0.866183i
$412$	− 4.35120e15i	− 0.889663i
$413$	0	0
$414$	−2.77310e15	−0.550760
$415$	−7.43070e15	−1.45459
$416$	2.55661e14i	0.0493292i
$417$	−6.39577e15	−1.21640
$418$	8.88092e15i	1.66495i
$419$	− 1.87176e14i	− 0.0345912i	−0.999850	−	0.0172956i	$-0.994494\pi$
$419$	− 1.87176e14i	− 0.0345912i	0.999850	−	0.0172956i	$-0.00550564\pi$
$420$	0	0
$421$	−2.95025e15	−0.529866	−0.264933	−	0.964267i	$-0.585350\pi$
$421$	−2.95025e15	−0.529866	−0.264933	+	0.964267i	$0.585350\pi$
$422$	−2.34124e15	−0.414544
$423$	2.93098e15i	0.511648i
$424$	1.46959e15	0.252931
$425$	− 2.11342e14i	− 0.0358635i
$426$	− 1.70422e15i	− 0.285147i
$427$	0	0
$428$	3.85774e15	0.627582
$429$	−1.85306e15	−0.297266
$430$	− 6.09910e15i	− 0.964839i
$431$	−1.86609e15	−0.291118	−0.145559	−	0.989350i	$-0.546498\pi$
$431$	−1.86609e15	−0.291118	−0.145559	+	0.989350i	$0.546498\pi$
$432$	1.72047e15i	0.264695i
$433$	6.43623e15i	0.976572i	0.872684	+	0.488286i	$0.162378\pi$
$433$	6.43623e15i	0.976572i	−0.872684	+	0.488286i	$0.837622\pi$
$434$	0	0
$435$	−4.27529e15	−0.631001
$436$	−5.36187e15	−0.780544
$437$	1.66932e16i	2.39690i
$438$	−1.50618e15	−0.213320
$439$	4.23331e15i	0.591416i	0.955278	+	0.295708i	$0.0955556\pi$
$439$	4.23331e15i	0.591416i	−0.955278	+	0.295708i	$0.904444\pi$
$440$	− 3.64309e15i	− 0.502058i
$441$	0	0
$442$	4.36717e14	0.0585688
$443$	−7.07275e15	−0.935764	−0.467882	−	0.883791i	$-0.654983\pi$
$443$	−7.07275e15	−0.935764	−0.467882	+	0.883791i	$0.654983\pi$
$444$	1.78915e15i	0.233533i
$445$	−9.29928e15	−1.19754
$446$	2.75080e15i	0.349502i
$447$	2.99319e15i	0.375223i
$448$	0	0
$449$	−7.31324e15	−0.892549	−0.446274	−	0.894896i	$-0.647249\pi$
$449$	−7.31324e15	−0.892549	−0.446274	+	0.894896i	$0.647249\pi$
$450$	−3.58420e14	−0.0431636
$451$	1.44252e16i	1.71421i
$452$	5.31163e15	0.622869
$453$	4.16510e15i	0.481988i
$454$	− 7.32188e15i	− 0.836156i
$455$	0	0
$456$	3.47620e15	0.386647
$457$	−1.30291e16	−1.43026	−0.715131	−	0.698990i	$-0.753633\pi$
$457$	−1.30291e16	−1.43026	−0.715131	+	0.698990i	$0.753633\pi$
$458$	− 3.89931e15i	− 0.422469i
$459$	2.93889e15	0.314273
$460$	− 6.84780e15i	− 0.722776i
$461$	− 2.39251e15i	− 0.249257i	−0.992203	−	0.124629i	$-0.960226\pi$
$461$	− 2.39251e15i	− 0.249257i	0.992203	−	0.124629i	$-0.0397739\pi$
$462$	0	0
$463$	7.43873e15	0.755115	0.377557	−	0.925986i	$-0.376764\pi$
$463$	7.43873e15	0.755115	0.377557	+	0.925986i	$0.376764\pi$
$464$	−2.38690e15	−0.239181
$465$	− 2.32076e15i	− 0.229568i
$466$	7.04283e15	0.687752
$467$	− 2.52191e15i	− 0.243125i	−0.992584	−	0.121562i	$-0.961210\pi$
$467$	− 2.52191e15i	− 0.243125i	0.992584	−	0.121562i	$-0.0387904\pi$
$468$	− 7.40639e14i	− 0.0704906i
$469$	0	0
$470$	−7.23768e15	−0.671448
$471$	1.18734e16	1.08755
$472$	1.87774e15i	0.169818i
$473$	2.46808e16	2.20390
$474$	− 1.46853e14i	− 0.0129483i
$475$	2.15758e15i	0.187848i
$476$	0	0
$477$	−4.25735e15	−0.361434
$478$	−9.66036e15	−0.809890
$479$	− 2.81554e15i	− 0.233103i	−0.993185	−	0.116552i	$-0.962816\pi$
$479$	− 2.81554e15i	− 0.233103i	0.993185	−	0.116552i	$-0.0371840\pi$
$480$	−1.42599e15	−0.116592
$481$	− 2.29469e15i	− 0.185290i
$482$	− 5.22153e15i	− 0.416404i
$483$	0	0
$484$	8.31474e15	0.646810
$485$	5.70975e15	0.438699
$486$	− 8.29537e15i	− 0.629533i
$487$	−2.22273e16	−1.66615	−0.833074	−	0.553161i	$-0.813421\pi$
$487$	−2.22273e16	−1.66615	−0.833074	+	0.553161i	$0.813421\pi$
$488$	− 2.55195e15i	− 0.188952i
$489$	4.37076e15i	0.319671i
$490$	0	0
$491$	2.73159e16	1.94952	0.974758	−	0.223265i	$-0.0716714\pi$
$491$	2.73159e16	1.94952	0.974758	+	0.223265i	$0.0716714\pi$
$492$	5.64637e15	0.398087
$493$	4.07727e15i	0.283980i
$494$	−4.45842e15	−0.306774
$495$	1.05539e16i	0.717432i
$496$	− 1.29568e15i	− 0.0870179i
$497$	0	0
$498$	−1.17698e16	−0.771603
$499$	1.99078e16	1.28950	0.644748	−	0.764395i	$-0.276962\pi$
$499$	1.99078e16	1.28950	0.644748	+	0.764395i	$0.276962\pi$
$500$	− 8.21042e15i	− 0.525467i
$501$	−1.04615e16	−0.661559
$502$	1.45394e16i	0.908500i
$503$	6.87587e15i	0.424541i	0.977211	+	0.212271i	$0.0680858\pi$
$503$	6.87587e15i	0.424541i	−0.977211	+	0.212271i	$0.931914\pi$
$504$	0	0
$505$	−4.01154e13	−0.00241860
$506$	2.77105e16	1.65098
$507$	1.10166e16i	0.648632i
$508$	1.39309e16	0.810583
$509$	− 7.74934e15i	− 0.445613i	−0.974863	−	0.222807i	$-0.928478\pi$
$509$	− 7.74934e15i	− 0.445613i	0.974863	−	0.222807i	$-0.0715218\pi$
$510$	2.43585e15i	0.138430i
$511$	0	0
$512$	−7.96131e14	−0.0441942
$513$	−3.00030e16	−1.64612
$514$	1.54828e16i	0.839594i
$515$	−3.11270e16	−1.66837
$516$	− 9.66063e15i	− 0.511808i
$517$	− 2.92882e16i	− 1.53373i
$518$	0	0
$519$	4.35965e15	0.223073
$520$	1.82891e15	0.0925066
$521$	− 2.38722e16i	− 1.19362i	−0.802382	−	0.596811i	$-0.796434\pi$
$521$	− 2.38722e16i	− 1.19362i	0.802382	−	0.596811i	$-0.203566\pi$
$522$	6.91475e15	0.341785
$523$	− 2.08819e16i	− 1.02037i	−0.860064	−	0.510187i	$-0.829576\pi$
$523$	− 2.08819e16i	− 1.02037i	0.860064	−	0.510187i	$-0.170424\pi$
$524$	− 1.67031e16i	− 0.806878i
$525$	0	0
$526$	4.66814e15	0.220409
$527$	−2.21327e15	−0.103317
$528$	− 5.77045e15i	− 0.266321i
$529$	3.01719e16	1.37680
$530$	− 1.05130e16i	− 0.474319i
$531$	− 5.43973e15i	− 0.242667i
$532$	0	0
$533$	−7.24179e15	−0.315851
$534$	−1.47295e16	−0.635246
$535$	− 2.75970e16i	− 1.17690i
$536$	−6.21072e15	−0.261911
$537$	− 1.01414e16i	− 0.422915i
$538$	2.12155e16i	0.874903i
$539$	0	0
$540$	1.23077e16	0.496380
$541$	3.20200e16	1.27714	0.638569	−	0.769564i	$-0.279526\pi$
$541$	3.20200e16	1.27714	0.638569	+	0.769564i	$0.279526\pi$
$542$	− 1.97591e16i	− 0.779419i
$543$	1.26513e16	0.493556
$544$	1.35994e15i	0.0524719i
$545$	3.83570e16i	1.46375i
$546$	0	0
$547$	−3.33242e16	−1.24404	−0.622022	−	0.783000i	$-0.713688\pi$
$547$	−3.33242e16	−1.24404	−0.622022	+	0.783000i	$0.713688\pi$
$548$	1.66747e16	0.615707
$549$	7.39288e15i	0.270010i
$550$	3.58156e15	0.129389
$551$	− 4.16247e16i	− 1.48745i
$552$	− 1.08465e16i	− 0.383404i
$553$	0	0
$554$	8.93503e15	0.309056
$555$	1.27990e16	0.437942
$556$	2.55441e16i	0.864652i
$557$	3.00335e15	0.100571	0.0502857	−	0.998735i	$-0.483987\pi$
$557$	3.00335e15	0.100571	0.0502857	+	0.998735i	$0.483987\pi$
$558$	3.75353e15i	0.124347i
$559$	1.23903e16i	0.406080i
$560$	0	0
$561$	−9.85701e15	−0.316204
$562$	−3.75641e15	−0.119222
$563$	− 2.99743e16i	− 0.941237i	−0.882337	−	0.470618i	$-0.844031\pi$
$563$	− 2.99743e16i	− 0.941237i	0.882337	−	0.470618i	$-0.155969\pi$
$564$	−1.14641e16	−0.356176
$565$	− 3.79975e16i	− 1.16806i
$566$	3.21107e16i	0.976677i
$567$	0	0
$568$	−6.80650e15	−0.202691
$569$	−2.71521e16	−0.800073	−0.400037	−	0.916499i	$-0.631003\pi$
$569$	−2.71521e16	−0.800073	−0.400037	+	0.916499i	$0.631003\pi$
$570$	− 2.48675e16i	− 0.725076i
$571$	7.01921e15	0.202522	0.101261	−	0.994860i	$-0.467712\pi$
$571$	7.01921e15	0.202522	0.101261	+	0.994860i	$0.467712\pi$
$572$	7.40093e15i	0.211305i
$573$	− 2.12814e16i	− 0.601274i
$574$	0	0
$575$	6.73215e15	0.186272
$576$	2.30636e15	0.0631527
$577$	5.11563e16i	1.38626i	0.720814	+	0.693129i	$0.243768\pi$
$577$	5.11563e16i	1.38626i	−0.720814	+	0.693129i	$0.756232\pi$
$578$	−2.40434e16	−0.644807
$579$	3.06637e16i	0.813866i
$580$	1.70751e16i	0.448533i
$581$	0	0
$582$	9.04392e15	0.232712
$583$	4.25421e16	1.08345
$584$	6.01551e15i	0.151634i
$585$	−5.29828e15	−0.132190
$586$	8.63839e15i	0.213328i
$587$	2.97094e16i	0.726216i	0.931747	+	0.363108i	$0.118284\pi$
$587$	2.97094e16i	0.726216i	−0.931747	+	0.363108i	$0.881716\pi$
$588$	0	0
$589$	2.25951e16	0.541157
$590$	1.34327e16	0.318457
$591$	− 2.70884e16i	− 0.635709i
$592$	7.14568e15	0.166002
$593$	4.63002e16i	1.06477i	0.846503	+	0.532384i	$0.178704\pi$
$593$	4.63002e16i	1.06477i	−0.846503	+	0.532384i	$0.821296\pi$
$594$	4.98047e16i	1.13384i
$595$	0	0
$596$	1.19545e16	0.266719
$597$	3.92125e16	0.866121
$598$	1.39113e16i	0.304201i
$599$	4.11717e16	0.891329	0.445664	−	0.895200i	$-0.352967\pi$
$599$	4.11717e16	0.891329	0.445664	+	0.895200i	$0.352967\pi$
$600$	− 1.40191e15i	− 0.0300477i
$601$	− 1.89158e15i	− 0.0401402i	−0.999799	−	0.0200701i	$-0.993611\pi$
$601$	− 1.89158e15i	− 0.0401402i	0.999799	−	0.0200701i	$-0.00638893\pi$
$602$	0	0
$603$	1.79922e16	0.374266
$604$	1.66350e16	0.342610
$605$	− 5.94808e16i	− 1.21296i
$606$	−6.35406e13	−0.00128297
$607$	8.60862e15i	0.172108i	0.996290	+	0.0860541i	$0.0274258\pi$
$607$	8.60862e15i	0.172108i	−0.996290	+	0.0860541i	$0.972574\pi$
$608$	− 1.38836e16i	− 0.274840i
$609$	0	0
$610$	−1.82557e16	−0.354340
$611$	1.47033e16	0.282598
$612$	− 3.93969e15i	− 0.0749814i
$613$	−1.55125e16	−0.292360	−0.146180	−	0.989258i	$-0.546698\pi$
$613$	−1.55125e16	−0.292360	−0.146180	+	0.989258i	$0.546698\pi$
$614$	− 3.05278e16i	− 0.569751i
$615$	− 4.03922e16i	− 0.746529i
$616$	0	0
$617$	6.49218e16	1.17674	0.588368	−	0.808593i	$-0.299770\pi$
$617$	6.49218e16	1.17674	0.588368	+	0.808593i	$0.299770\pi$
$618$	−4.93034e16	−0.885005
$619$	− 3.48235e16i	− 0.619055i	−0.950891	−	0.309527i	$-0.899829\pi$
$619$	− 3.48235e16i	− 0.619055i	0.950891	−	0.309527i	$-0.100171\pi$
$620$	−9.26887e15	−0.163184
$621$	9.36163e16i	1.63231i
$622$	− 2.93982e16i	− 0.507666i
$623$	0	0
$624$	2.89689e15	0.0490710
$625$	−5.15329e16	−0.864578
$626$	5.23277e16i	0.869533i
$627$	1.00630e17	1.65623
$628$	− 4.74213e16i	− 0.773065i
$629$	− 1.22062e16i	− 0.197095i
$630$	0	0
$631$	−6.99817e16	−1.10869	−0.554343	−	0.832289i	$-0.687030\pi$
$631$	−6.99817e16	−1.10869	−0.554343	+	0.832289i	$0.687030\pi$
$632$	−5.86515e14	−0.00920400
$633$	2.65285e16i	0.412374i
$634$	−8.11110e16	−1.24895
$635$	− 9.96571e16i	− 1.52008i
$636$	− 1.66520e16i	− 0.251607i
$637$	0	0
$638$	−6.90965e16	−1.02455
$639$	1.97181e16	0.289641
$640$	5.69525e15i	0.0828768i
$641$	1.65253e16	0.238233	0.119117	−	0.992880i	$-0.461994\pi$
$641$	1.65253e16	0.238233	0.119117	+	0.992880i	$0.461994\pi$
$642$	− 4.37120e16i	− 0.624297i
$643$	2.58392e16i	0.365605i	0.983150	+	0.182803i	$0.0585170\pi$
$643$	2.58392e16i	0.365605i	−0.983150	+	0.182803i	$0.941483\pi$
$644$	0	0
$645$	−6.91088e16	−0.959788
$646$	−2.37157e16	−0.326318
$647$	− 1.00097e17i	− 1.36457i	−0.731087	−	0.682284i	$-0.760987\pi$
$647$	− 1.00097e17i	− 1.36457i	0.731087	−	0.682284i	$-0.239013\pi$
$648$	6.26996e15	0.0846865
$649$	5.43572e16i	0.727426i
$650$	1.79802e15i	0.0238405i
$651$	0	0
$652$	1.74564e16	0.227231
$653$	3.07131e16	0.396136	0.198068	−	0.980188i	$-0.436533\pi$
$653$	3.07131e16	0.396136	0.198068	+	0.980188i	$0.436533\pi$
$654$	6.07553e16i	0.776458i
$655$	−1.19488e17	−1.51313
$656$	− 2.25510e16i	− 0.282972i
$657$	− 1.74267e16i	− 0.216682i
$658$	0	0
$659$	1.64417e16	0.200740	0.100370	−	0.994950i	$-0.467997\pi$
$659$	1.64417e16	0.200740	0.100370	+	0.994950i	$0.467997\pi$
$660$	−4.12798e16	−0.499430
$661$	7.43082e16i	0.890898i	0.895307	+	0.445449i	$0.146956\pi$
$661$	7.43082e16i	0.890898i	−0.895307	+	0.445449i	$0.853044\pi$
$662$	−1.20482e16	−0.143144
$663$	− 4.94843e15i	− 0.0582622i
$664$	4.70075e16i	0.548477i
$665$	0	0
$666$	−2.07007e16	−0.237214
$667$	−1.29878e17	−1.47497
$668$	4.17823e16i	0.470255i
$669$	3.11692e16	0.347672
$670$	4.44294e16i	0.491158i
$671$	− 7.38743e16i	− 0.809391i
$672$	0	0
$673$	1.00460e17	1.08119	0.540596	−	0.841283i	$-0.318199\pi$
$673$	1.00460e17	1.08119	0.540596	+	0.841283i	$0.318199\pi$
$674$	1.06262e16	0.113349
$675$	1.20998e16i	0.127925i
$676$	4.39990e16	0.461066
$677$	− 3.28661e16i	− 0.341363i	−0.985326	−	0.170681i	$-0.945403\pi$
$677$	− 3.28661e16i	− 0.341363i	0.985326	−	0.170681i	$-0.0545969\pi$
$678$	− 6.01860e16i	− 0.619608i
$679$	0	0
$680$	9.72855e15	0.0983999
$681$	−8.29641e16	−0.831778
$682$	− 3.75077e16i	− 0.372747i
$683$	4.01889e16	0.395897	0.197949	−	0.980212i	$-0.436572\pi$
$683$	4.01889e16	0.395897	0.197949	+	0.980212i	$0.436572\pi$
$684$	4.02201e16i	0.392741i
$685$	− 1.19285e17i	− 1.15463i
$686$	0	0
$687$	−4.41831e16	−0.420258
$688$	−3.85836e16	−0.363808
$689$	2.13571e16i	0.199630i
$690$	−7.75923e16	−0.718992
$691$	1.59780e17i	1.46776i	0.679281	+	0.733878i	$0.262292\pi$
$691$	1.59780e17i	1.46776i	−0.679281	+	0.733878i	$0.737708\pi$
$692$	− 1.74120e16i	− 0.158567i
$693$	0	0
$694$	−6.00435e16	−0.537414
$695$	1.82734e17	1.62147
$696$	2.70459e16i	0.237929i
$697$	−3.85213e16	−0.335973
$698$	1.18907e17i	1.02820i
$699$	− 7.98023e16i	− 0.684152i
$700$	0	0
$701$	1.35098e17	1.13852	0.569262	−	0.822156i	$-0.307229\pi$
$701$	1.35098e17	1.13852	0.569262	+	0.822156i	$0.307229\pi$
$702$	−2.50030e16	−0.208915
$703$	1.24612e17i	1.03235i
$704$	−2.30466e16	−0.189309
$705$	8.20101e16i	0.667933i
$706$	1.14858e17i	0.927544i
$707$	0	0
$708$	2.12766e16	0.168929
$709$	−7.02992e15	−0.0553443	−0.0276722	−	0.999617i	$-0.508809\pi$
$709$	−7.02992e15	−0.0553443	−0.0276722	+	0.999617i	$0.508809\pi$
$710$	4.86913e16i	0.380103i
$711$	1.69911e15	0.0131524
$712$	5.88283e16i	0.451550i
$713$	− 7.05020e16i	− 0.536617i
$714$	0	0
$715$	5.29437e16	0.396258
$716$	−4.05038e16	−0.300620
$717$	1.09461e17i	0.805650i
$718$	−5.25144e16	−0.383294
$719$	− 1.57564e17i	− 1.14047i	−0.821482	−	0.570234i	$-0.806852\pi$
$719$	− 1.57564e17i	− 1.14047i	0.821482	−	0.570234i	$-0.193148\pi$
$720$	− 1.64989e16i	− 0.118430i
$721$	0	0
$722$	1.41950e17	1.00210
$723$	−5.91651e16	−0.414224
$724$	− 5.05280e16i	− 0.350833i
$725$	−1.67867e16	−0.115595
$726$	− 9.42143e16i	− 0.643424i
$727$	1.73285e17i	1.17370i	0.809697	+	0.586848i	$0.199631\pi$
$727$	1.73285e17i	1.17370i	−0.809697	+	0.586848i	$0.800369\pi$
$728$	0	0
$729$	−1.29947e17	−0.865767
$730$	4.30329e16	0.284357
$731$	6.59080e16i	0.431950i
$732$	−2.89161e16	−0.187963
$733$	1.53480e17i	0.989529i	0.869027	+	0.494764i	$0.164746\pi$
$733$	1.53480e17i	0.989529i	−0.869027	+	0.494764i	$0.835254\pi$
$734$	8.09975e16i	0.517959i
$735$	0	0
$736$	−4.33199e16	−0.272534
$737$	−1.79789e17	−1.12191
$738$	6.53293e16i	0.404362i
$739$	1.55258e17	0.953204	0.476602	−	0.879119i	$-0.341868\pi$
$739$	1.55258e17	0.953204	0.476602	+	0.879119i	$0.341868\pi$
$740$	− 5.11177e16i	− 0.311302i
$741$	5.05183e16i	0.305168i
$742$	0	0
$743$	−1.55426e17	−0.923830	−0.461915	−	0.886924i	$-0.652838\pi$
$743$	−1.55426e17	−0.923830	−0.461915	+	0.886924i	$0.652838\pi$
$744$	−1.46814e16	−0.0865623
$745$	− 8.55183e16i	− 0.500175i
$746$	2.16497e17	1.25609
$747$	− 1.36179e17i	− 0.783764i
$748$	3.93679e16i	0.224767i
$749$	0	0
$750$	−9.30322e16	−0.522716
$751$	−2.96504e17	−1.65269	−0.826344	−	0.563166i	$-0.809583\pi$
$751$	−2.96504e17	−1.65269	−0.826344	+	0.563166i	$0.809583\pi$
$752$	4.57864e16i	0.253180i
$753$	1.64746e17	0.903744
$754$	− 3.46880e16i	− 0.188778i
$755$	− 1.19001e17i	− 0.642493i
$756$	0	0
$757$	−2.70923e16	−0.143970	−0.0719848	−	0.997406i	$-0.522933\pi$
$757$	−2.70923e16	−0.143970	−0.0719848	+	0.997406i	$0.522933\pi$
$758$	5.95409e16	0.313906
$759$	− 3.13988e17i	− 1.64234i
$760$	−9.93183e16	−0.515404
$761$	3.41053e17i	1.75596i	0.478698	+	0.877980i	$0.341109\pi$
$761$	3.41053e17i	1.75596i	−0.478698	+	0.877980i	$0.658891\pi$
$762$	− 1.57851e17i	− 0.806340i
$763$	0	0
$764$	−8.49958e16	−0.427403
$765$	−2.81832e16	−0.140612
$766$	6.85911e16i	0.339543i
$767$	−2.72885e16	−0.134032
$768$	9.02096e15i	0.0439628i
$769$	1.79123e17i	0.866153i	0.901357	+	0.433076i	$0.142572\pi$
$769$	1.79123e17i	0.866153i	−0.901357	+	0.433076i	$0.857428\pi$
$770$	0	0
$771$	1.75435e17	0.835199
$772$	1.22468e17	0.578519
$773$	6.02147e16i	0.282244i	0.989992	+	0.141122i	$0.0450710\pi$
$773$	6.02147e16i	0.282244i	−0.989992	+	0.141122i	$0.954929\pi$
$774$	1.11775e17	0.519875
$775$	− 9.11233e15i	− 0.0420552i
$776$	− 3.61205e16i	− 0.165418i
$777$	0	0
$778$	1.25409e17	0.565524
$779$	3.93263e17	1.75978
$780$	− 2.07234e16i	− 0.0920223i
$781$	−1.97036e17	−0.868239
$782$	7.39985e16i	0.323581i
$783$	− 2.33433e17i	− 1.01296i
$784$	0	0
$785$	−3.39236e17	−1.44972
$786$	−1.89262e17	−0.802654
$787$	− 1.73136e16i	− 0.0728685i	−0.999336	−	0.0364343i	$-0.988400\pi$
$787$	− 1.73136e16i	− 0.0728685i	0.999336	−	0.0364343i	$-0.0116000\pi$
$788$	−1.08188e17	−0.451880
$789$	− 5.28946e16i	− 0.219255i
$790$	4.19573e15i	0.0172602i
$791$	0	0
$792$	6.67650e16	0.270519
$793$	3.70865e16	0.149134
$794$	− 1.59204e17i	− 0.635374i
$795$	−1.19122e17	−0.471835
$796$	− 1.56611e17i	− 0.615663i
$797$	1.59583e17i	0.622640i	0.950305	+	0.311320i	$0.100771\pi$
$797$	1.59583e17i	0.622640i	−0.950305	+	0.311320i	$0.899229\pi$
$798$	0	0
$799$	7.82117e16	0.300601
$800$	−5.59907e15	−0.0213588
$801$	− 1.70423e17i	− 0.645258i
$802$	−2.22554e17	−0.836353
$803$	1.74138e17i	0.649533i
$804$	7.03736e16i	0.260539i
$805$	0	0
$806$	1.88297e16	0.0686804
$807$	2.40393e17	0.870322
$808$	2.53775e14i	0 0.000911970i
$809$	−1.92801e16	−0.0687729	−0.0343864	−	0.999409i	$-0.510948\pi$
$809$	−1.92801e16	−0.0687729	−0.0343864	+	0.999409i	$0.510948\pi$
$810$	− 4.48531e16i	− 0.158812i
$811$	3.01693e17i	1.06033i	0.847896	+	0.530163i	$0.177869\pi$
$811$	3.01693e17i	1.06033i	−0.847896	+	0.530163i	$0.822131\pi$
$812$	0	0
$813$	−2.23890e17	−0.775338
$814$	2.06855e17	0.711081
$815$	− 1.24877e17i	− 0.426124i
$816$	1.54095e16	0.0521972
$817$	− 6.72851e17i	− 2.26249i
$818$	1.31730e17i	0.439709i
$819$	0	0
$820$	−1.61322e17	−0.530654
$821$	−1.60131e17	−0.522897	−0.261448	−	0.965217i	$-0.584200\pi$
$821$	−1.60131e17	−0.522897	−0.261448	+	0.965217i	$0.584200\pi$
$822$	− 1.88941e17i	− 0.612484i
$823$	−4.22232e17	−1.35879	−0.679395	−	0.733773i	$-0.737757\pi$
$823$	−4.22232e17	−1.35879	−0.679395	+	0.733773i	$0.737757\pi$
$824$	1.96913e17i	0.629087i
$825$	− 4.05827e16i	− 0.128711i
$826$	0	0
$827$	2.73276e17	0.854218	0.427109	−	0.904200i	$-0.359532\pi$
$827$	2.73276e17	0.854218	0.427109	+	0.904200i	$0.359532\pi$
$828$	1.25496e17	0.389446
$829$	3.83464e17i	1.18140i	0.806891	+	0.590701i	$0.201149\pi$
$829$	3.83464e17i	1.18140i	−0.806891	+	0.590701i	$0.798851\pi$
$830$	3.36275e17	1.02855
$831$	− 1.01243e17i	− 0.307438i
$832$	− 1.15699e16i	− 0.0348810i
$833$	0	0
$834$	2.89440e17	0.860125
$835$	2.98896e17	0.881863
$836$	− 4.01905e17i	− 1.17730i
$837$	1.26715e17	0.368531
$838$	8.47062e15i	0.0244597i
$839$	3.51637e17i	1.00814i	0.863662	+	0.504072i	$0.168165\pi$
$839$	3.51637e17i	1.00814i	−0.863662	+	0.504072i	$0.831835\pi$
$840$	0	0
$841$	−2.99612e16	−0.0846804
$842$	1.33513e17	0.374672
$843$	4.25639e16i	0.118598i
$844$	1.05952e17	0.293127
$845$	− 3.14754e17i	− 0.864632i
$846$	− 1.32641e17i	− 0.361789i
$847$	0	0
$848$	−6.65062e16	−0.178849
$849$	3.63846e17	0.971564
$850$	9.56425e15i	0.0253593i
$851$	3.88818e17	1.02369
$852$	7.71243e16i	0.201629i
$853$	− 7.08810e13i	0 0.000184008i	−1.00000		9.20038e-5i	$-0.999971\pi$
$853$	− 7.08810e13i	0 0.000184008i	1.00000		9.20038e-5i	$-2.92857e-5\pi$
$854$	0	0
$855$	2.87721e17	0.736503
$856$	−1.74581e17	−0.443768
$857$	1.50325e14i	0 0.000379443i	1.00000		0.000189722i	$6.03903e-5\pi$
$857$	1.50325e14i	0 0.000379443i	−1.00000		0.000189722i	$0.999940\pi$
$858$	8.38599e16	0.210199
$859$	− 6.67721e17i	− 1.66202i	−0.556258	−	0.831009i	$-0.687763\pi$
$859$	− 6.67721e17i	− 1.66202i	0.556258	−	0.831009i	$-0.312237\pi$
$860$	2.76014e17i	0.682244i
$861$	0	0
$862$	8.44497e16	0.205852
$863$	4.09646e17	0.991617	0.495808	−	0.868432i	$-0.334872\pi$
$863$	4.09646e17	0.991617	0.495808	+	0.868432i	$0.334872\pi$
$864$	− 7.78598e16i	− 0.187168i
$865$	−1.24560e17	−0.297359
$866$	− 2.91270e17i	− 0.690540i
$867$	2.72436e17i	0.641431i
$868$	0	0
$869$	−1.69786e16	−0.0394260
$870$	1.93477e17	0.446185
$871$	− 9.02582e16i	− 0.206718i
$872$	2.42651e17	0.551928
$873$	1.04640e17i	0.236380i
$874$	− 7.55447e17i	− 1.69487i
$875$	0	0
$876$	6.81617e16	0.150840
$877$	−7.79893e17	−1.71410	−0.857052	−	0.515230i	$-0.827707\pi$
$877$	−7.79893e17	−1.71410	−0.857052	+	0.515230i	$0.827707\pi$
$878$	− 1.91578e17i	− 0.418194i
$879$	9.78815e16	0.212211
$880$	1.64867e17i	0.355009i
$881$	− 5.86771e17i	− 1.25491i	−0.778652	−	0.627456i	$-0.784096\pi$
$881$	− 5.86771e17i	− 1.25491i	0.778652	−	0.627456i	$-0.215904\pi$
$882$	0	0
$883$	1.02492e17	0.216235	0.108117	−	0.994138i	$-0.465518\pi$
$883$	1.02492e17	0.216235	0.108117	+	0.994138i	$0.465518\pi$
$884$	−1.97635e16	−0.0414144
$885$	− 1.52206e17i	− 0.316790i
$886$	3.20076e17	0.661685
$887$	− 3.55881e17i	− 0.730741i	−0.930862	−	0.365370i	$-0.880942\pi$
$887$	− 3.55881e17i	− 0.730741i	0.930862	−	0.365370i	$-0.119058\pi$
$888$	− 8.09676e16i	− 0.165133i
$889$	0	0
$890$	4.20837e17	0.846787
$891$	1.81504e17	0.362761
$892$	− 1.24487e17i	− 0.247135i
$893$	−7.98459e17	−1.57450
$894$	− 1.35456e17i	− 0.265322i
$895$	2.89750e17i	0.563749i
$896$	0	0
$897$	1.57629e17	0.302608
$898$	3.30960e17	0.631127
$899$	1.75798e17i	0.333008i
$900$	1.62203e16	0.0305213
$901$	1.13605e17i	0.212348i
$902$	− 6.52812e17i	− 1.21213i
$903$	0	0
$904$	−2.40377e17	−0.440435
$905$	−3.61460e17	−0.657914
$906$	− 1.88491e17i	− 0.340817i
$907$	2.34779e17	0.421711	0.210856	−	0.977517i	$-0.432375\pi$
$907$	2.34779e17	0.421711	0.210856	+	0.977517i	$0.432375\pi$
$908$	3.31350e17i	0.591251i
$909$	− 7.35175e14i	− 0.00130319i
$910$	0	0
$911$	2.85714e17	0.499829	0.249915	−	0.968268i	$-0.419597\pi$
$911$	2.85714e17	0.499829	0.249915	+	0.968268i	$0.419597\pi$
$912$	−1.57315e17	−0.273401
$913$	1.36078e18i	2.34944i
$914$	5.89628e17	1.01135
$915$	2.06856e17i	0.352485i
$916$	1.76463e17i	0.298731i
$917$	0	0
$918$	−1.32999e17	−0.222225
$919$	4.04408e17	0.671316	0.335658	−	0.941984i	$-0.391041\pi$
$919$	4.04408e17	0.671316	0.335658	+	0.941984i	$0.391041\pi$
$920$	3.09896e17i	0.511080i
$921$	−3.45910e17	−0.566768
$922$	1.08272e17i	0.176251i
$923$	− 9.89164e16i	− 0.159977i
$924$	0	0
$925$	5.02545e16	0.0802277
$926$	−3.36639e17	−0.533947
$927$	− 5.70447e17i	− 0.898954i
$928$	1.08019e17	0.169126
$929$	1.21219e18i	1.88571i	0.333200	+	0.942856i	$0.391872\pi$
$929$	1.21219e18i	1.88571i	−0.333200	+	0.942856i	$0.608128\pi$
$930$	1.05025e17i	0.162329i
$931$	0	0
$932$	−3.18722e17	−0.486314
$933$	−3.33111e17	−0.505009
$934$	1.14129e17i	0.171915i
$935$	2.81624e17	0.421503
$936$	3.35175e16i	0.0498444i
$937$	1.24564e17i	0.184058i	0.995756	+	0.0920292i	$0.0293353\pi$
$937$	1.24564e17i	0.184058i	−0.995756	+	0.0920292i	$0.970665\pi$
$938$	0	0
$939$	5.92925e17	0.864981
$940$	3.27540e17	0.474785
$941$	− 7.88539e17i	− 1.13576i	−0.823112	−	0.567878i	$-0.807764\pi$
$941$	− 7.88539e17i	− 1.13576i	0.823112	−	0.567878i	$-0.192236\pi$
$942$	−5.37331e17	−0.769017
$943$	− 1.22707e18i	− 1.74501i
$944$	− 8.49768e16i	− 0.120079i
$945$	0	0
$946$	−1.11693e18	−1.55840
$947$	−5.04323e17	−0.699213	−0.349606	−	0.936897i	$-0.613685\pi$
$947$	−5.04323e17	−0.699213	−0.349606	+	0.936897i	$0.613685\pi$
$948$	6.64580e15i	0.00915582i
$949$	−8.74213e16	−0.119680
$950$	− 9.76410e16i	− 0.132828i
$951$	9.19068e17i	1.24241i
$952$	0	0
$953$	−1.53450e17	−0.204837	−0.102419	−	0.994741i	$-0.532658\pi$
$953$	−1.53450e17	−0.204837	−0.102419	+	0.994741i	$0.532658\pi$
$954$	1.92666e17	0.255572
$955$	6.08031e17i	0.801503i
$956$	4.37178e17	0.572679
$957$	7.82932e17i	1.01918i
$958$	1.27417e17i	0.164829i
$959$	0	0
$960$	6.45329e16	0.0824429
$961$	6.92234e17	0.878846
$962$	1.03846e17i	0.131020i
$963$	5.05755e17	0.634136
$964$	2.36299e17i	0.294442i
$965$	− 8.76091e17i	− 1.08489i
$966$	0	0
$967$	−7.09549e17	−0.867807	−0.433904	−	0.900959i	$-0.642864\pi$
$967$	−7.09549e17	−0.867807	−0.433904	+	0.900959i	$0.642864\pi$
$968$	−3.76282e17	−0.457364
$969$	2.68723e17i	0.324610i
$970$	−2.58394e17	−0.310207
$971$	− 2.10255e17i	− 0.250860i	−0.992102	−	0.125430i	$-0.959969\pi$
$971$	− 2.10255e17i	− 0.250860i	0.992102	−	0.125430i	$-0.0400310\pi$
$972$	3.75406e17i	0.445147i
$973$	0	0
$974$	1.00589e18	1.17814
$975$	2.03734e16	0.0237157
$976$	1.15488e17i	0.133610i
$977$	−7.34560e17	−0.844618	−0.422309	−	0.906452i	$-0.638780\pi$
$977$	−7.34560e17	−0.844618	−0.422309	+	0.906452i	$0.638780\pi$
$978$	− 1.97798e17i	− 0.226042i
$979$	1.70297e18i	1.93425i
$980$	0	0
$981$	−7.02948e17	−0.788695
$982$	−1.23618e18	−1.37852
$983$	8.45345e17i	0.936942i	0.883479	+	0.468471i	$0.155195\pi$
$983$	8.45345e17i	0.936942i	−0.883479	+	0.468471i	$0.844805\pi$
$984$	−2.55525e17	−0.281490
$985$	7.73942e17i	0.847405i
$986$	− 1.84516e17i	− 0.200804i
$987$	0	0
$988$	2.01765e17	0.216922
$989$	−2.09945e18	−2.24351
$990$	− 4.77614e17i	− 0.507301i
$991$	−1.57176e18	−1.65937	−0.829685	−	0.558232i	$-0.811480\pi$
$991$	−1.57176e18	−1.65937	−0.829685	+	0.558232i	$0.811480\pi$
$992$	5.86359e16i	0.0615309i
$993$	1.36518e17i	0.142394i
$994$	0	0
$995$	−1.12034e18	−1.15455
$996$	5.32641e17	0.545605
$997$	5.11638e17i	0.520945i	0.965481	+	0.260473i	$0.0838783\pi$
$997$	5.11638e17i	0.520945i	−0.965481	+	0.260473i	$0.916122\pi$
$998$	−9.00924e17	−0.911811
$999$	6.98831e17i	0.703039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.b.c.97.6		16
7.2	even	3		14.13.d.a.3.6	✓	16
7.3	odd	6		14.13.d.a.5.6	yes	16
7.4	even	3		98.13.d.a.19.7		16
7.5	odd	6		98.13.d.a.31.7		16
7.6	odd	2	inner	98.13.b.c.97.3		16
21.2	odd	6		126.13.n.a.73.4		16
21.17	even	6		126.13.n.a.19.4		16
28.3	even	6		112.13.s.c.33.6		16
28.23	odd	6		112.13.s.c.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.6	✓	16	7.2	even	3
14.13.d.a.5.6	yes	16	7.3	odd	6
98.13.b.c.97.3		16	7.6	odd	2	inner
98.13.b.c.97.6		16	1.1	even	1	trivial
98.13.d.a.19.7		16	7.4	even	3
98.13.d.a.31.7		16	7.5	odd	6
112.13.s.c.17.6		16	28.23	odd	6
112.13.s.c.33.6		16	28.3	even	6
126.13.n.a.19.4		16	21.17	even	6
126.13.n.a.73.4		16	21.2	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548 q^{2} +512.782i q^{3} +2048.00 q^{4} -14650.7i q^{5} -23205.9i q^{6} -92681.9 q^{8} +268495. q^{9} +O(q^{10})\)	\(q-45.2548 q^{2} +512.782i q^{3} +2048.00 q^{4} -14650.7i q^{5} -23205.9i q^{6} -92681.9 q^{8} +268495. q^{9} +663015. i q^{10} -2.68298e6 q^{11} +1.05018e6i q^{12} -1.34691e6i q^{13} +7.51261e6 q^{15} +4.19430e6 q^{16} -7.16465e6i q^{17} -1.21507e7 q^{18} +7.31436e7i q^{19} -3.00046e7i q^{20} +1.21418e8 q^{22} +2.28225e8 q^{23} -4.75256e7i q^{24} +2.94979e7 q^{25} +6.09543e7i q^{26} +4.10193e8i q^{27} -5.69081e8 q^{29} -3.39982e8 q^{30} -3.08915e8i q^{31} -1.89813e8 q^{32} -1.37578e9i q^{33} +3.24235e8i q^{34} +5.49879e8 q^{36} +1.70366e9 q^{37} -3.31010e9i q^{38} +6.90673e8 q^{39} +1.35785e9i q^{40} -5.37658e9i q^{41} -9.19904e9 q^{43} -5.49474e9 q^{44} -3.93364e9i q^{45} -1.03283e10 q^{46} +1.09163e10i q^{47} +2.15076e9i q^{48} -1.33492e9 q^{50} +3.67391e9 q^{51} -2.75848e9i q^{52} -1.58563e10 q^{53} -1.85632e10i q^{54} +3.93075e10i q^{55} -3.75067e10 q^{57} +2.57537e10 q^{58} -2.02600e10i q^{59} +1.53858e10 q^{60} +2.75345e10i q^{61} +1.39799e10i q^{62} +8.58993e9 q^{64} -1.97332e10 q^{65} +6.22608e10i q^{66} +6.70111e10 q^{67} -1.46732e10i q^{68} +1.17030e11i q^{69} +7.34393e10 q^{71} -2.48847e10 q^{72} -6.49049e10i q^{73} -7.70990e10 q^{74} +1.51260e10i q^{75} +1.49798e11i q^{76} -3.12563e10 q^{78} +6.32826e9 q^{79} -6.14495e10i q^{80} -6.76503e10 q^{81} +2.43316e11i q^{82} -5.07191e11i q^{83} -1.04967e11 q^{85} +4.16301e11 q^{86} -2.91815e11i q^{87} +2.48663e11 q^{88} -6.34733e11i q^{89} +1.78016e11i q^{90} +4.67404e11 q^{92} +1.58406e11 q^{93} -4.94016e11i q^{94} +1.07160e12 q^{95} -9.73325e10i q^{96} +3.89725e11i q^{97} -7.20367e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32768 q^{4} - 4724496 q^{9}+O(q^{10}) \) 16 * q + 32768 * q^4 - 4724496 * q^9	\( 16 q + 32768 q^{4} - 4724496 q^{9} - 4144176 q^{11} - 27163728 q^{15} + 67108864 q^{16} + 9185280 q^{18} + 62776320 q^{22} - 51261120 q^{23} - 1042411616 q^{25} + 532360944 q^{29} + 4303835136 q^{30} - 9675767808 q^{36} - 11529048080 q^{37} - 21052166544 q^{39} - 66929432000 q^{43} - 8487272448 q^{44} - 14406426624 q^{46} - 99248080896 q^{50} + 46598512752 q^{51} - 78268323600 q^{53} - 328243960080 q^{57} - 59274792960 q^{58} - 55631314944 q^{60} + 137438953472 q^{64} - 316645407792 q^{65} - 215534239840 q^{67} - 1150259029344 q^{71} + 18811453440 q^{72} - 9805556736 q^{74} - 786088888320 q^{78} - 455264129536 q^{79} + 783968356800 q^{81} + 710209696080 q^{85} + 76210384896 q^{86} + 128565903360 q^{88} - 104982773760 q^{92} + 917337537360 q^{93} + 373007725920 q^{95} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q + 32768 * q^4 - 4724496 * q^9 - 4144176 * q^11 - 27163728 * q^15 + 67108864 * q^16 + 9185280 * q^18 + 62776320 * q^22 - 51261120 * q^23 - 1042411616 * q^25 + 532360944 * q^29 + 4303835136 * q^30 - 9675767808 * q^36 - 11529048080 * q^37 - 21052166544 * q^39 - 66929432000 * q^43 - 8487272448 * q^44 - 14406426624 * q^46 - 99248080896 * q^50 + 46598512752 * q^51 - 78268323600 * q^53 - 328243960080 * q^57 - 59274792960 * q^58 - 55631314944 * q^60 + 137438953472 * q^64 - 316645407792 * q^65 - 215534239840 * q^67 - 1150259029344 * q^71 + 18811453440 * q^72 - 9805556736 * q^74 - 786088888320 * q^78 - 455264129536 * q^79 + 783968356800 * q^81 + 710209696080 * q^85 + 76210384896 * q^86 + 128565903360 * q^88 - 104982773760 * q^92 + 917337537360 * q^93 + 373007725920 * q^95 + 3921180354576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more