LMFDB - Embedded newform 103.16.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,16,Mod(1,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("103.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	103.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:	$146.974310253$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-182.639 q^{2} -3002.52 q^{3} +589.102 q^{4} +37324.2 q^{5} +548379. q^{6} +4.15954e6 q^{7} +5.87713e6 q^{8} -5.33376e6 q^{9} +O(q^{10})$	\(q-182.639 q^{2} -3002.52 q^{3} +589.102 q^{4} +37324.2 q^{5} +548379. q^{6} +4.15954e6 q^{7} +5.87713e6 q^{8} -5.33376e6 q^{9} -6.81686e6 q^{10} +2.55774e7 q^{11} -1.76879e6 q^{12} +3.68304e8 q^{13} -7.59695e8 q^{14} -1.12067e8 q^{15} -1.09270e9 q^{16} -8.33124e8 q^{17} +9.74155e8 q^{18} +6.37975e9 q^{19} +2.19878e7 q^{20} -1.24891e10 q^{21} -4.67143e9 q^{22} -2.63612e10 q^{23} -1.76462e10 q^{24} -2.91245e10 q^{25} -6.72668e10 q^{26} +5.90977e10 q^{27} +2.45039e9 q^{28} +1.70843e10 q^{29} +2.04678e10 q^{30} -2.38558e11 q^{31} +6.98784e9 q^{32} -7.67966e10 q^{33} +1.52161e11 q^{34} +1.55251e11 q^{35} -3.14213e9 q^{36} -3.20053e11 q^{37} -1.16519e12 q^{38} -1.10584e12 q^{39} +2.19359e11 q^{40} -1.37788e12 q^{41} +2.28100e12 q^{42} +1.78730e12 q^{43} +1.50677e10 q^{44} -1.99078e11 q^{45} +4.81459e12 q^{46} +1.06573e12 q^{47} +3.28085e12 q^{48} +1.25542e13 q^{49} +5.31927e12 q^{50} +2.50147e12 q^{51} +2.16969e11 q^{52} -1.22504e13 q^{53} -1.07936e13 q^{54} +9.54654e11 q^{55} +2.44461e13 q^{56} -1.91553e13 q^{57} -3.12027e12 q^{58} -4.26050e12 q^{59} -6.60187e10 q^{60} -3.24464e13 q^{61} +4.35701e13 q^{62} -2.21860e13 q^{63} +3.45293e13 q^{64} +1.37466e13 q^{65} +1.40261e13 q^{66} -3.59168e13 q^{67} -4.90795e11 q^{68} +7.91500e13 q^{69} -2.83550e13 q^{70} -9.91821e13 q^{71} -3.13472e13 q^{72} +1.67791e14 q^{73} +5.84542e13 q^{74} +8.74469e13 q^{75} +3.75832e12 q^{76} +1.06390e14 q^{77} +2.01970e14 q^{78} +4.17611e13 q^{79} -4.07841e13 q^{80} -1.00908e14 q^{81} +2.51655e14 q^{82} -1.73954e14 q^{83} -7.35736e12 q^{84} -3.10957e13 q^{85} -3.26431e14 q^{86} -5.12960e13 q^{87} +1.50321e14 q^{88} +9.08463e13 q^{89} +3.63595e13 q^{90} +1.53197e15 q^{91} -1.55294e13 q^{92} +7.16276e14 q^{93} -1.94644e14 q^{94} +2.38119e14 q^{95} -2.09812e13 q^{96} +3.05146e14 q^{97} -2.29289e15 q^{98} -1.36424e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 857 q^{2} - 3932 q^{3} + 952767 q^{4} - 439140 q^{5} + 743647 q^{6} - 3190353 q^{7} - 33093708 q^{8} + 233430375 q^{9}+O(q^{10}) $ 61 * q - 857 * q^2 - 3932 * q^3 + 952767 * q^4 - 439140 * q^5 + 743647 * q^6 - 3190353 * q^7 - 33093708 * q^8 + 233430375 * q^9	\( 61 q - 857 q^{2} - 3932 q^{3} + 952767 q^{4} - 439140 q^{5} + 743647 q^{6} - 3190353 q^{7} - 33093708 q^{8} + 233430375 q^{9} - 63234482 q^{10} - 103748368 q^{11} - 331520313 q^{12} - 313165161 q^{13} - 755555817 q^{14} - 674398526 q^{15} + 14512908187 q^{16} - 12083282787 q^{17} - 13168798944 q^{18} - 5361319119 q^{19} - 9305646747 q^{20} - 16461308876 q^{21} - 28941029471 q^{22} - 66168004047 q^{23} + 7802762994 q^{24} + 303234371695 q^{25} + 182749185334 q^{26} - 156925014338 q^{27} - 664627255237 q^{28} - 645743643657 q^{29} - 1069618618594 q^{30} - 122874478996 q^{31} - 269627394831 q^{32} + 46150978058 q^{33} + 969116824174 q^{34} - 478522677982 q^{35} + 4223214984684 q^{36} + 819999551780 q^{37} - 1018697698883 q^{38} - 991652931072 q^{39} - 6174778893965 q^{40} - 7325440107283 q^{41} - 9956139869801 q^{42} - 8612850695736 q^{43} - 13352142895690 q^{44} - 15559896379366 q^{45} - 32065613137770 q^{46} - 15984352430276 q^{47} - 41506324107117 q^{48} + 17231550044622 q^{49} - 33888000032918 q^{50} - 27907219770060 q^{51} - 57828879269473 q^{52} - 37355418884312 q^{53} - 49810074049935 q^{54} - 46090202313238 q^{55} - 31772217542854 q^{56} - 57782774436846 q^{57} - 36740035491030 q^{58} - 41266858463091 q^{59} + 44989673695855 q^{60} - 45509082837011 q^{61} + 9938607229349 q^{62} + 47160755658129 q^{63} + 422835893804094 q^{64} - 177125638146712 q^{65} + 310487514411959 q^{66} + 91080256620398 q^{67} - 256019865760105 q^{68} + 80891639918642 q^{69} + 384378270951236 q^{70} - 46207729769832 q^{71} - 56835727444502 q^{72} - 114864967341268 q^{73} + 673296051484809 q^{74} + 251412324545408 q^{75} - 92392796537324 q^{76} - 426424980478584 q^{77} + 860430952610076 q^{78} + 27257492827013 q^{79} + 12\!\cdots\!86 q^{80}+ \cdots - 24\!\cdots\!92 q^{99}+O(q^{100}) \) 61 * q - 857 * q^2 - 3932 * q^3 + 952767 * q^4 - 439140 * q^5 + 743647 * q^6 - 3190353 * q^7 - 33093708 * q^8 + 233430375 * q^9 - 63234482 * q^10 - 103748368 * q^11 - 331520313 * q^12 - 313165161 * q^13 - 755555817 * q^14 - 674398526 * q^15 + 14512908187 * q^16 - 12083282787 * q^17 - 13168798944 * q^18 - 5361319119 * q^19 - 9305646747 * q^20 - 16461308876 * q^21 - 28941029471 * q^22 - 66168004047 * q^23 + 7802762994 * q^24 + 303234371695 * q^25 + 182749185334 * q^26 - 156925014338 * q^27 - 664627255237 * q^28 - 645743643657 * q^29 - 1069618618594 * q^30 - 122874478996 * q^31 - 269627394831 * q^32 + 46150978058 * q^33 + 969116824174 * q^34 - 478522677982 * q^35 + 4223214984684 * q^36 + 819999551780 * q^37 - 1018697698883 * q^38 - 991652931072 * q^39 - 6174778893965 * q^40 - 7325440107283 * q^41 - 9956139869801 * q^42 - 8612850695736 * q^43 - 13352142895690 * q^44 - 15559896379366 * q^45 - 32065613137770 * q^46 - 15984352430276 * q^47 - 41506324107117 * q^48 + 17231550044622 * q^49 - 33888000032918 * q^50 - 27907219770060 * q^51 - 57828879269473 * q^52 - 37355418884312 * q^53 - 49810074049935 * q^54 - 46090202313238 * q^55 - 31772217542854 * q^56 - 57782774436846 * q^57 - 36740035491030 * q^58 - 41266858463091 * q^59 + 44989673695855 * q^60 - 45509082837011 * q^61 + 9938607229349 * q^62 + 47160755658129 * q^63 + 422835893804094 * q^64 - 177125638146712 * q^65 + 310487514411959 * q^66 + 91080256620398 * q^67 - 256019865760105 * q^68 + 80891639918642 * q^69 + 384378270951236 * q^70 - 46207729769832 * q^71 - 56835727444502 * q^72 - 114864967341268 * q^73 + 673296051484809 * q^74 + 251412324545408 * q^75 - 92392796537324 * q^76 - 426424980478584 * q^77 + 860430952610076 * q^78 + 27257492827013 * q^79 + 1261262804917286 * q^80 + 970042227882689 * q^81 + 1867558085467524 * q^82 - 67054622423409 * q^83 + 2889728360587655 * q^84 + 35781044772768 * q^85 + 935963078541511 * q^86 + 200876689178626 * q^87 + 748805894780353 * q^88 - 584912027466128 * q^89 + 1478961422736826 * q^90 + 1070772310581326 * q^91 - 630612477352560 * q^92 - 625157665750792 * q^93 + 1462001220045896 * q^94 - 1523943242724438 * q^95 + 1053537706701997 * q^96 - 786010536406413 * q^97 - 5974525724410954 * q^98 - 2483530260497592 * 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 $

$2$	−182.639	−1.00895	−0.504474	−	0.863427i	$-0.668314\pi$
$2$	−182.639	−1.00895	−0.504474	+	0.863427i	$0.668314\pi$
$3$	−3002.52	−0.792642	−0.396321	−	0.918112i	$-0.629713\pi$
$3$	−3002.52	−0.792642	−0.396321	+	0.918112i	$0.629713\pi$
$4$	589.102	0.0179780
$5$	37324.2	0.213656	0.106828	−	0.994278i	$-0.465931\pi$
$5$	37324.2	0.213656	0.106828	+	0.994278i	$0.465931\pi$
$6$	548379.	0.799735
$7$	4.15954e6	1.90902	0.954508	−	0.298184i	$-0.0963809\pi$
$7$	4.15954e6	1.90902	0.954508	+	0.298184i	$0.0963809\pi$
$8$	5.87713e6	0.990810
$9$	−5.33376e6	−0.371719
$10$	−6.81686e6	−0.215568
$11$	2.55774e7	0.395740	0.197870	−	0.980228i	$-0.436598\pi$
$11$	2.55774e7	0.395740	0.197870	+	0.980228i	$0.436598\pi$
$12$	−1.76879e6	−0.0142501
$13$	3.68304e8	1.62791	0.813957	−	0.580925i	$-0.197309\pi$
$13$	3.68304e8	1.62791	0.813957	+	0.580925i	$0.197309\pi$
$14$	−7.59695e8	−1.92610
$15$	−1.12067e8	−0.169353
$16$	−1.09270e9	−1.01765
$17$	−8.33124e8	−0.492428	−0.246214	−	0.969216i	$-0.579187\pi$
$17$	−8.33124e8	−0.492428	−0.246214	+	0.969216i	$0.579187\pi$
$18$	9.74155e8	0.375046
$19$	6.37975e9	1.63739	0.818694	−	0.574231i	$-0.194699\pi$
$19$	6.37975e9	1.63739	0.818694	+	0.574231i	$0.194699\pi$
$20$	2.19878e7	0.00384110
$21$	−1.24891e10	−1.51317
$22$	−4.67143e9	−0.399282
$23$	−2.63612e10	−1.61438	−0.807190	−	0.590291i	$-0.799013\pi$
$23$	−2.63612e10	−1.61438	−0.807190	+	0.590291i	$0.799013\pi$
$24$	−1.76462e10	−0.785357
$25$	−2.91245e10	−0.954351
$26$	−6.72668e10	−1.64248
$27$	5.90977e10	1.08728
$28$	2.45039e9	0.0343202
$29$	1.70843e10	0.183913	0.0919565	−	0.995763i	$-0.470688\pi$
$29$	1.70843e10	0.183913	0.0919565	+	0.995763i	$0.470688\pi$
$30$	2.04678e10	0.170868
$31$	−2.38558e11	−1.55733	−0.778666	−	0.627438i	$-0.784104\pi$
$31$	−2.38558e11	−1.55733	−0.778666	+	0.627438i	$0.784104\pi$
$32$	6.98784e9	0.0359516
$33$	−7.67966e10	−0.313680
$34$	1.52161e11	0.496835
$35$	1.55251e11	0.407873
$36$	−3.14213e9	−0.00668276
$37$	−3.20053e11	−0.554253	−0.277127	−	0.960833i	$-0.589382\pi$
$37$	−3.20053e11	−0.554253	−0.277127	+	0.960833i	$0.589382\pi$
$38$	−1.16519e12	−1.65204
$39$	−1.10584e12	−1.29035
$40$	2.19359e11	0.211693
$41$	−1.37788e12	−1.10492	−0.552462	−	0.833538i	$-0.686311\pi$
$41$	−1.37788e12	−1.10492	−0.552462	+	0.833538i	$0.686311\pi$
$42$	2.28100e12	1.52671
$43$	1.78730e12	1.00273	0.501365	−	0.865236i	$-0.332831\pi$
$43$	1.78730e12	1.00273	0.501365	+	0.865236i	$0.332831\pi$
$44$	1.50677e10	0.00711461
$45$	−1.99078e11	−0.0794201
$46$	4.81459e12	1.62883
$47$	1.06573e12	0.306841	0.153420	−	0.988161i	$-0.450971\pi$
$47$	1.06573e12	0.306841	0.153420	+	0.988161i	$0.450971\pi$
$48$	3.28085e12	0.806636
$49$	1.25542e13	2.64435
$50$	5.31927e12	0.962892
$51$	2.50147e12	0.390319
$52$	2.16969e11	0.0292666
$53$	−1.22504e13	−1.43245	−0.716225	−	0.697869i	$-0.754132\pi$
$53$	−1.22504e13	−1.43245	−0.716225	+	0.697869i	$0.754132\pi$
$54$	−1.07936e13	−1.09701
$55$	9.54654e11	0.0845523
$56$	2.44461e13	1.89147
$57$	−1.91553e13	−1.29786
$58$	−3.12027e12	−0.185559
$59$	−4.26050e12	−0.222880	−0.111440	−	0.993771i	$-0.535546\pi$
$59$	−4.26050e12	−0.222880	−0.111440	+	0.993771i	$0.535546\pi$
$60$	−6.60187e10	−0.00304462
$61$	−3.24464e13	−1.32188	−0.660942	−	0.750437i	$-0.729843\pi$
$61$	−3.24464e13	−1.32188	−0.660942	+	0.750437i	$0.729843\pi$
$62$	4.35701e13	1.57127
$63$	−2.21860e13	−0.709618
$64$	3.45293e13	0.981381
$65$	1.37466e13	0.347814
$66$	1.40261e13	0.316488
$67$	−3.59168e13	−0.723997	−0.361998	−	0.932179i	$-0.617905\pi$
$67$	−3.59168e13	−0.723997	−0.361998	+	0.932179i	$0.617905\pi$
$68$	−4.90795e11	−0.00885285
$69$	7.91500e13	1.27963
$70$	−2.83550e13	−0.411523
$71$	−9.91821e13	−1.29418	−0.647092	−	0.762412i	$-0.724015\pi$
$71$	−9.91821e13	−1.29418	−0.647092	+	0.762412i	$0.724015\pi$
$72$	−3.13472e13	−0.368303
$73$	1.67791e14	1.77765	0.888827	−	0.458242i	$-0.151521\pi$
$73$	1.67791e14	1.77765	0.888827	+	0.458242i	$0.151521\pi$
$74$	5.84542e13	0.559213
$75$	8.74469e13	0.756458
$76$	3.75832e12	0.0294369
$77$	1.06390e14	0.755475
$78$	2.01970e14	1.30190
$79$	4.17611e13	0.244663	0.122332	−	0.992489i	$-0.460963\pi$
$79$	4.17611e13	0.244663	0.122332	+	0.992489i	$0.460963\pi$
$80$	−4.07841e13	−0.217428
$81$	−1.00908e14	−0.490106
$82$	2.51655e14	1.11481
$83$	−1.73954e14	−0.703636	−0.351818	−	0.936068i	$-0.614436\pi$
$83$	−1.73954e14	−0.703636	−0.351818	+	0.936068i	$0.614436\pi$
$84$	−7.35736e12	−0.0272037
$85$	−3.10957e13	−0.105210
$86$	−3.26431e14	−1.01170
$87$	−5.12960e13	−0.145777
$88$	1.50321e14	0.392104
$89$	9.08463e13	0.217712	0.108856	−	0.994058i	$-0.465281\pi$
$89$	9.08463e13	0.217712	0.108856	+	0.994058i	$0.465281\pi$
$90$	3.63595e13	0.0801308
$91$	1.53197e15	3.10771
$92$	−1.55294e13	−0.0290233
$93$	7.16276e14	1.23441
$94$	−1.94644e14	−0.309587
$95$	2.38119e14	0.349838
$96$	−2.09812e13	−0.0284967
$97$	3.05146e14	0.383460	0.191730	−	0.981448i	$-0.438590\pi$
$97$	3.05146e14	0.383460	0.191730	+	0.981448i	$0.438590\pi$
$98$	−2.29289e15	−2.66801
$99$	−1.36424e14	−0.147104
$100$	−1.71573e13	−0.0171573
$101$	−1.53032e15	−1.42027	−0.710134	−	0.704066i	$-0.751366\pi$
$101$	−1.53032e15	−1.42027	−0.710134	+	0.704066i	$0.751366\pi$
$102$	−4.56867e14	−0.393812
$103$	1.22987e14	0.0985329
$103$	1.22987e14	0.0985329
$104$	2.16457e15	1.61295
$105$	−4.66146e14	−0.323297
$106$	2.23740e15	1.44527
$107$	−1.80751e15	−1.08819	−0.544093	−	0.839025i	$-0.683126\pi$
$107$	−1.80751e15	−1.08819	−0.544093	+	0.839025i	$0.683126\pi$
$108$	3.48146e13	0.0195471
$109$	7.52029e14	0.394036	0.197018	−	0.980400i	$-0.436874\pi$
$109$	7.52029e14	0.394036	0.197018	+	0.980400i	$0.436874\pi$
$110$	−1.74357e14	−0.0853090
$111$	9.60965e14	0.439324
$112$	−4.54512e15	−1.94272
$113$	2.94889e15	1.17915	0.589577	−	0.807712i	$-0.299295\pi$
$113$	2.94889e15	1.17915	0.589577	+	0.807712i	$0.299295\pi$
$114$	3.49852e15	1.30948
$115$	−9.83909e14	−0.344922
$116$	1.00644e13	0.00330638
$117$	−1.96445e15	−0.605127
$118$	7.78135e14	0.224874
$119$	−3.46541e15	−0.940053
$120$	−6.58631e14	−0.167796
$121$	−3.52305e15	−0.843389
$122$	5.92599e15	1.33371
$123$	4.13711e15	0.875808
$124$	−1.40535e14	−0.0279977
$125$	−2.22609e15	−0.417559
$126$	4.05203e15	0.715969
$127$	−2.11616e15	−0.352388	−0.176194	−	0.984355i	$-0.556379\pi$
$127$	−2.11616e15	−0.352388	−0.176194	+	0.984355i	$0.556379\pi$
$128$	−6.53538e15	−1.02612
$129$	−5.36641e15	−0.794806
$130$	−2.51068e15	−0.350926
$131$	−1.30266e16	−1.71908	−0.859540	−	0.511069i	$-0.829250\pi$
$131$	−1.30266e16	−1.71908	−0.859540	+	0.511069i	$0.829250\pi$
$132$	−4.52410e13	−0.00563934
$133$	2.65368e16	3.12580
$134$	6.55982e15	0.730476
$135$	2.20577e15	0.232304
$136$	−4.89638e15	−0.487902
$137$	1.07514e16	1.01406	0.507028	−	0.861930i	$-0.330744\pi$
$137$	1.07514e16	1.01406	0.507028	+	0.861930i	$0.330744\pi$
$138$	−1.44559e16	−1.29108
$139$	−9.15057e15	−0.774172	−0.387086	−	0.922044i	$-0.626518\pi$
$139$	−9.15057e15	−0.774172	−0.387086	+	0.922044i	$0.626518\pi$
$140$	9.14589e13	0.00733273
$141$	−3.19988e15	−0.243215
$142$	1.81146e16	1.30576
$143$	9.42024e15	0.644231
$144$	5.82820e15	0.378282
$145$	6.37658e14	0.0392941
$146$	−3.06452e16	−1.79356
$147$	−3.76942e16	−2.09602
$148$	−1.88544e14	−0.00996435
$149$	−1.60097e16	−0.804425	−0.402213	−	0.915546i	$-0.631759\pi$
$149$	−1.60097e16	−0.804425	−0.402213	+	0.915546i	$0.631759\pi$
$150$	−1.59712e16	−0.763228
$151$	−2.47484e16	−1.12518	−0.562588	−	0.826738i	$-0.690194\pi$
$151$	−2.47484e16	−1.12518	−0.562588	+	0.826738i	$0.690194\pi$
$152$	3.74946e16	1.62234
$153$	4.44369e15	0.183045
$154$	−1.94310e16	−0.762236
$155$	−8.90398e15	−0.332734
$156$	−6.51453e14	−0.0231979
$157$	−3.67263e14	−0.0124661	−0.00623303	−	0.999981i	$-0.501984\pi$
$157$	−3.67263e14	−0.0124661	−0.00623303	+	0.999981i	$0.501984\pi$
$158$	−7.62722e15	−0.246853
$159$	3.67820e16	1.13542
$160$	2.60815e14	0.00768128
$161$	−1.09650e17	−3.08188
$162$	1.84298e16	0.494492
$163$	−2.37947e16	−0.609639	−0.304819	−	0.952410i	$-0.598596\pi$
$163$	−2.37947e16	−0.609639	−0.304819	+	0.952410i	$0.598596\pi$
$164$	−8.11711e14	−0.0198643
$165$	−2.86637e15	−0.0670197
$166$	3.17708e16	0.709933
$167$	7.39985e16	1.58070	0.790350	−	0.612656i	$-0.209899\pi$
$167$	7.39985e16	1.58070	0.790350	+	0.612656i	$0.209899\pi$
$168$	−7.34001e16	−1.49926
$169$	8.44620e16	1.65010
$170$	5.67929e15	0.106152
$171$	−3.40281e16	−0.608648
$172$	1.05290e15	0.0180271
$173$	−1.68651e16	−0.276468	−0.138234	−	0.990400i	$-0.544143\pi$
$173$	−1.68651e16	−0.276468	−0.138234	+	0.990400i	$0.544143\pi$
$174$	9.36867e15	0.147082
$175$	−1.21144e17	−1.82187
$176$	−2.79483e16	−0.402727
$177$	1.27923e16	0.176664
$178$	−1.65921e16	−0.219660
$179$	3.62431e16	0.460073	0.230037	−	0.973182i	$-0.426115\pi$
$179$	3.62431e16	0.460073	0.230037	+	0.973182i	$0.426115\pi$
$180$	−1.17277e14	−0.00142781
$181$	−4.61834e16	−0.539382	−0.269691	−	0.962947i	$-0.586922\pi$
$181$	−4.61834e16	−0.539382	−0.269691	+	0.962947i	$0.586922\pi$
$182$	−2.79799e17	−3.13553
$183$	9.74211e16	1.04778
$184$	−1.54928e17	−1.59954
$185$	−1.19457e16	−0.118420
$186$	−1.30820e17	−1.24545
$187$	−2.13091e16	−0.194874
$188$	6.27824e14	0.00551638
$189$	2.45819e17	2.07564
$190$	−4.34898e16	−0.352968
$191$	−1.61917e17	−1.26340	−0.631701	−	0.775212i	$-0.717643\pi$
$191$	−1.61917e17	−1.26340	−0.631701	+	0.775212i	$0.717643\pi$
$192$	−1.03675e17	−0.777884
$193$	−8.41301e16	−0.607116	−0.303558	−	0.952813i	$-0.598175\pi$
$193$	−8.41301e16	−0.607116	−0.303558	+	0.952813i	$0.598175\pi$
$194$	−5.57316e16	−0.386891
$195$	−4.12746e16	−0.275692
$196$	7.39570e15	0.0475400
$197$	4.62983e16	0.286463	0.143231	−	0.989689i	$-0.454251\pi$
$197$	4.62983e16	0.286463	0.143231	+	0.989689i	$0.454251\pi$
$198$	2.49163e16	0.148421
$199$	−2.43706e17	−1.39787	−0.698936	−	0.715184i	$-0.746343\pi$
$199$	−2.43706e17	−1.39787	−0.698936	+	0.715184i	$0.746343\pi$
$200$	−1.71168e17	−0.945581
$201$	1.07841e17	0.573870
$202$	2.79496e17	1.43298
$203$	7.10629e16	0.351093
$204$	1.47362e15	0.00701714
$205$	−5.14282e16	−0.236074
$206$	−2.24623e16	−0.0994147
$207$	1.40604e17	0.600096
$208$	−4.02445e17	−1.65665
$209$	1.63177e17	0.647980
$210$	8.51365e16	0.326190
$211$	−1.79905e17	−0.665157	−0.332579	−	0.943076i	$-0.607919\pi$
$211$	−1.79905e17	−0.665157	−0.332579	+	0.943076i	$0.607919\pi$
$212$	−7.21671e15	−0.0257526
$213$	2.97797e17	1.02582
$214$	3.30123e17	1.09792
$215$	6.67095e16	0.214239
$216$	3.47325e17	1.07729
$217$	−9.92291e17	−2.97297
$218$	−1.37350e17	−0.397562
$219$	−5.03797e17	−1.40904
$220$	5.62389e14	0.00152008
$221$	−3.06843e17	−0.801630
$222$	−1.75510e17	−0.443256
$223$	3.74822e17	0.915247	0.457623	−	0.889146i	$-0.348701\pi$
$223$	3.74822e17	0.915247	0.457623	+	0.889146i	$0.348701\pi$
$224$	2.90662e16	0.0686322
$225$	1.55343e17	0.354751
$226$	−5.38583e17	−1.18971
$227$	7.23982e17	1.54715	0.773577	−	0.633702i	$-0.218465\pi$
$227$	7.23982e17	1.54715	0.773577	+	0.633702i	$0.218465\pi$
$228$	−1.12844e16	−0.0233329
$229$	−4.49356e17	−0.899133	−0.449567	−	0.893247i	$-0.648422\pi$
$229$	−4.49356e17	−0.899133	−0.449567	+	0.893247i	$0.648422\pi$
$230$	1.79700e17	0.348009
$231$	−3.19438e17	−0.598821
$232$	1.00407e17	0.182223
$233$	−5.25478e17	−0.923390	−0.461695	−	0.887039i	$-0.652759\pi$
$233$	−5.25478e17	−0.923390	−0.461695	+	0.887039i	$0.652759\pi$
$234$	3.58785e17	0.610542
$235$	3.97775e16	0.0655584
$236$	−2.50987e15	−0.00400693
$237$	−1.25389e17	−0.193930
$238$	6.32920e17	0.948465
$239$	2.22271e17	0.322774	0.161387	−	0.986891i	$-0.448403\pi$
$239$	2.22271e17	0.322774	0.161387	+	0.986891i	$0.448403\pi$
$240$	1.22455e17	0.172343
$241$	3.73706e17	0.509802	0.254901	−	0.966967i	$-0.417957\pi$
$241$	3.73706e17	0.509802	0.254901	+	0.966967i	$0.417957\pi$
$242$	6.43447e17	0.850937
$243$	−5.45007e17	−0.698804
$244$	−1.91143e16	−0.0237648
$245$	4.68575e17	0.564980
$246$	−7.55599e17	−0.883646
$247$	2.34969e18	2.66552
$248$	−1.40204e18	−1.54302
$249$	5.22300e17	0.557731
$250$	4.06572e17	0.421296
$251$	1.43991e18	1.44805	0.724025	−	0.689774i	$-0.242290\pi$
$251$	1.43991e18	1.44805	0.724025	+	0.689774i	$0.242290\pi$
$252$	−1.30698e16	−0.0127575
$253$	−6.74249e17	−0.638876
$254$	3.86495e17	0.355542
$255$	9.33654e16	0.0833940
$256$	6.21616e16	0.0539166
$257$	−9.26977e17	−0.780855	−0.390428	−	0.920634i	$-0.627673\pi$
$257$	−9.26977e17	−0.780855	−0.390428	+	0.920634i	$0.627673\pi$
$258$	9.80117e17	0.801918
$259$	−1.33127e18	−1.05808
$260$	8.09818e15	0.00625298
$261$	−9.11237e16	−0.0683640
$262$	2.37917e18	1.73446
$263$	−2.72439e16	−0.0193020	−0.00965098	−	0.999953i	$-0.503072\pi$
$263$	−2.72439e16	−0.0193020	−0.00965098	+	0.999953i	$0.503072\pi$
$264$	−4.51344e17	−0.310798
$265$	−4.57234e17	−0.306052
$266$	−4.84666e18	−3.15377
$267$	−2.72768e17	−0.172568
$268$	−2.11587e16	−0.0130160
$269$	2.03449e18	1.21707	0.608533	−	0.793529i	$-0.291758\pi$
$269$	2.03449e18	1.21707	0.608533	+	0.793529i	$0.291758\pi$
$270$	−4.02861e17	−0.234383
$271$	2.06113e18	1.16637	0.583184	−	0.812340i	$-0.301807\pi$
$271$	2.06113e18	1.16637	0.583184	+	0.812340i	$0.301807\pi$
$272$	9.10353e17	0.501122
$273$	−4.59979e18	−2.46330
$274$	−1.96363e18	−1.02313
$275$	−7.44927e17	−0.377675
$276$	4.66275e16	0.0230051
$277$	6.04945e16	0.0290481	0.0145240	−	0.999895i	$-0.495377\pi$
$277$	6.04945e16	0.0290481	0.0145240	+	0.999895i	$0.495377\pi$
$278$	1.67125e18	0.781100
$279$	1.27241e18	0.578890
$280$	9.12432e17	0.404125
$281$	8.60576e17	0.371101	0.185550	−	0.982635i	$-0.440593\pi$
$281$	8.60576e17	0.371101	0.185550	+	0.982635i	$0.440593\pi$
$282$	5.84424e17	0.245391
$283$	1.43294e18	0.585907	0.292953	−	0.956127i	$-0.405362\pi$
$283$	1.43294e18	0.585907	0.292953	+	0.956127i	$0.405362\pi$
$284$	−5.84284e16	−0.0232668
$285$	−7.14957e17	−0.277296
$286$	−1.72051e18	−0.649997
$287$	−5.73134e18	−2.10932
$288$	−3.72715e16	−0.0133639
$289$	−2.16833e18	−0.757515
$290$	−1.16461e17	−0.0396458
$291$	−9.16208e17	−0.303946
$292$	9.88461e16	0.0319586
$293$	3.30061e18	1.04013	0.520064	−	0.854127i	$-0.325908\pi$
$293$	3.30061e18	1.04013	0.520064	+	0.854127i	$0.325908\pi$
$294$	6.88445e18	2.11478
$295$	−1.59020e17	−0.0476196
$296$	−1.88099e18	−0.549160
$297$	1.51156e18	0.430281
$298$	2.92400e18	0.811624
$299$	−9.70893e18	−2.62807
$300$	5.15152e16	0.0135996
$301$	7.43434e18	1.91423
$302$	4.52003e18	1.13524
$303$	4.59481e18	1.12576
$304$	−6.97114e18	−1.66629
$305$	−1.21104e18	−0.282428
$306$	−8.11591e17	−0.184683
$307$	2.01059e18	0.446462	0.223231	−	0.974766i	$-0.428340\pi$
$307$	2.01059e18	0.446462	0.223231	+	0.974766i	$0.428340\pi$
$308$	6.26746e16	0.0135819
$309$	−3.69272e17	−0.0781013
$310$	1.62622e18	0.335711
$311$	−1.56066e18	−0.314488	−0.157244	−	0.987560i	$-0.550261\pi$
$311$	−1.56066e18	−0.314488	−0.157244	+	0.987560i	$0.550261\pi$
$312$	−6.49917e18	−1.27849
$313$	1.89021e18	0.363017	0.181509	−	0.983389i	$-0.441902\pi$
$313$	1.89021e18	0.363017	0.181509	+	0.983389i	$0.441902\pi$
$314$	6.70766e16	0.0125776
$315$	−8.28074e17	−0.151614
$316$	2.46016e16	0.00439855
$317$	−3.08095e18	−0.537948	−0.268974	−	0.963147i	$-0.586685\pi$
$317$	−3.08095e18	−0.537948	−0.268974	+	0.963147i	$0.586685\pi$
$318$	−6.71783e18	−1.14558
$319$	4.36972e17	0.0727818
$320$	1.28878e18	0.209678
$321$	5.42710e18	0.862542
$322$	2.00265e19	3.10946
$323$	−5.31512e18	−0.806295
$324$	−5.94454e16	−0.00881111
$325$	−1.07267e19	−1.55360
$326$	4.34584e18	0.615094
$327$	−2.25799e18	−0.312329
$328$	−8.09797e18	−1.09477
$329$	4.43295e18	0.585765
$330$	5.23512e17	0.0676195
$331$	1.61350e18	0.203732	0.101866	−	0.994798i	$-0.467519\pi$
$331$	1.61350e18	0.203732	0.101866	+	0.994798i	$0.467519\pi$
$332$	−1.02477e17	−0.0126499
$333$	1.70708e18	0.206027
$334$	−1.35150e19	−1.59485
$335$	−1.34056e18	−0.154686
$336$	1.36468e19	1.53988
$337$	1.04347e19	1.15147	0.575737	−	0.817635i	$-0.304715\pi$
$337$	1.04347e19	1.15147	0.575737	+	0.817635i	$0.304715\pi$
$338$	−1.54261e19	−1.66487
$339$	−8.85411e18	−0.934646
$340$	−1.83185e16	−0.00189147
$341$	−6.10168e18	−0.616300
$342$	6.21486e18	0.614095
$343$	3.24720e19	3.13908
$344$	1.05042e19	0.993515
$345$	2.95421e18	0.273400
$346$	3.08024e18	0.278942
$347$	4.28859e18	0.380053	0.190026	−	0.981779i	$-0.439143\pi$
$347$	4.28859e18	0.380053	0.190026	+	0.981779i	$0.439143\pi$
$348$	−3.02186e16	−0.00262078
$349$	6.87478e18	0.583536	0.291768	−	0.956489i	$-0.405756\pi$
$349$	6.87478e18	0.583536	0.291768	+	0.956489i	$0.405756\pi$
$350$	2.21257e19	1.83818
$351$	2.17659e19	1.77000
$352$	1.78731e17	0.0142275
$353$	−2.17136e18	−0.169208	−0.0846042	−	0.996415i	$-0.526963\pi$
$353$	−2.17136e18	−0.169208	−0.0846042	+	0.996415i	$0.526963\pi$
$354$	−2.33637e18	−0.178245
$355$	−3.70189e18	−0.276510
$356$	5.35178e16	0.00391402
$357$	1.04050e19	0.745125
$358$	−6.61941e18	−0.464191
$359$	−5.49966e18	−0.377683	−0.188842	−	0.982008i	$-0.560473\pi$
$359$	−5.49966e18	−0.377683	−0.188842	+	0.982008i	$0.560473\pi$
$360$	−1.17001e18	−0.0786902
$361$	2.55200e19	1.68104
$362$	8.43490e18	0.544209
$363$	1.05780e19	0.668506
$364$	9.02490e17	0.0558704
$365$	6.26266e18	0.379807
$366$	−1.77929e19	−1.05716
$367$	−1.58717e19	−0.923904	−0.461952	−	0.886905i	$-0.652851\pi$
$367$	−1.58717e19	−0.923904	−0.461952	+	0.886905i	$0.652851\pi$
$368$	2.88048e19	1.64288
$369$	7.34928e18	0.410721
$370$	2.18175e18	0.119479
$371$	−5.09558e19	−2.73457
$372$	4.21960e17	0.0221921
$373$	−1.13393e19	−0.584481	−0.292241	−	0.956345i	$-0.594401\pi$
$373$	−1.13393e19	−0.584481	−0.292241	+	0.956345i	$0.594401\pi$
$374$	3.89188e18	0.196618
$375$	6.68389e18	0.330975
$376$	6.26344e18	0.304021
$377$	6.29222e18	0.299395
$378$	−4.48962e19	−2.09421
$379$	−3.80637e19	−1.74067	−0.870335	−	0.492460i	$-0.836098\pi$
$379$	−3.80637e19	−1.74067	−0.870335	+	0.492460i	$0.836098\pi$
$380$	1.40276e17	0.00628937
$381$	6.35383e18	0.279318
$382$	2.95724e19	1.27471
$383$	2.79381e19	1.18088	0.590440	−	0.807082i	$-0.298954\pi$
$383$	2.79381e19	1.18088	0.590440	+	0.807082i	$0.298954\pi$
$384$	1.96226e19	0.813342
$385$	3.97092e18	0.161412
$386$	1.53655e19	0.612549
$387$	−9.53304e18	−0.372734
$388$	1.79762e17	0.00689383
$389$	−1.13708e19	−0.427728	−0.213864	−	0.976863i	$-0.568605\pi$
$389$	−1.13708e19	−0.427728	−0.213864	+	0.976863i	$0.568605\pi$
$390$	7.53837e18	0.278159
$391$	2.19621e19	0.794966
$392$	7.37826e19	2.62004
$393$	3.91126e19	1.36261
$394$	−8.45589e18	−0.289027
$395$	1.55870e18	0.0522738
$396$	−8.03674e16	−0.00264464
$397$	4.36971e19	1.41099	0.705495	−	0.708715i	$-0.250725\pi$
$397$	4.36971e19	1.41099	0.705495	+	0.708715i	$0.250725\pi$
$398$	4.45102e19	1.41038
$399$	−7.96773e19	−2.47764
$400$	3.18243e19	0.971200
$401$	2.89024e19	0.865666	0.432833	−	0.901474i	$-0.357514\pi$
$401$	2.89024e19	0.865666	0.432833	+	0.901474i	$0.357514\pi$
$402$	−1.96960e19	−0.579005
$403$	−8.78619e19	−2.53520
$404$	−9.01512e17	−0.0255336
$405$	−3.76632e18	−0.104714
$406$	−1.29789e19	−0.354235
$407$	−8.18610e18	−0.219340
$408$	1.47015e19	0.386732
$409$	−5.67302e19	−1.46518	−0.732588	−	0.680673i	$-0.761688\pi$
$409$	−5.67302e19	−1.46518	−0.732588	+	0.680673i	$0.761688\pi$
$410$	9.39281e18	0.238186
$411$	−3.22814e19	−0.803783
$412$	7.24521e16	0.00177142
$413$	−1.77217e19	−0.425481
$414$	−2.56799e19	−0.605467
$415$	−6.49268e18	−0.150336
$416$	2.57365e18	0.0585261
$417$	2.74748e19	0.613641
$418$	−2.98025e19	−0.653779
$419$	−6.59074e19	−1.42013	−0.710067	−	0.704134i	$-0.751335\pi$
$419$	−6.59074e19	−1.42013	−0.710067	+	0.704134i	$0.751335\pi$
$420$	−2.74607e17	−0.00581223
$421$	−1.22703e18	−0.0255117	−0.0127559	−	0.999919i	$-0.504060\pi$
$421$	−1.22703e18	−0.0255117	−0.0127559	+	0.999919i	$0.504060\pi$
$422$	3.28577e19	0.671109
$423$	−5.68435e18	−0.114059
$424$	−7.19969e19	−1.41929
$425$	2.42643e19	0.469949
$426$	−5.43893e19	−1.03500
$427$	−1.34962e20	−2.52350
$428$	−1.06481e18	−0.0195634
$429$	−2.82845e19	−0.510645
$430$	−1.21838e19	−0.216157
$431$	−5.68448e19	−0.991086	−0.495543	−	0.868583i	$-0.665031\pi$
$431$	−5.68448e19	−0.991086	−0.495543	+	0.868583i	$0.665031\pi$
$432$	−6.45759e19	−1.10648
$433$	−8.11057e18	−0.136582	−0.0682908	−	0.997665i	$-0.521755\pi$
$433$	−8.11057e18	−0.136582	−0.0682908	+	0.997665i	$0.521755\pi$
$434$	1.81231e20	2.99958
$435$	−1.91458e18	−0.0311462
$436$	4.43022e17	0.00708397
$437$	−1.68178e20	−2.64337
$438$	9.20130e19	1.42165
$439$	−1.27136e20	−1.93101	−0.965504	−	0.260387i	$-0.916150\pi$
$439$	−1.27136e20	−1.93101	−0.965504	+	0.260387i	$0.916150\pi$
$440$	5.61062e18	0.0837753
$441$	−6.69611e19	−0.982954
$442$	5.60415e19	0.808804
$443$	4.50608e19	0.639397	0.319698	−	0.947519i	$-0.396418\pi$
$443$	4.50608e19	0.639397	0.319698	+	0.947519i	$0.396418\pi$
$444$	5.66107e17	0.00789816
$445$	3.39076e18	0.0465155
$446$	−6.84572e19	−0.923437
$447$	4.80694e19	0.637621
$448$	1.43626e20	1.87347
$449$	−1.23573e20	−1.58517	−0.792585	−	0.609762i	$-0.791265\pi$
$449$	−1.23573e20	−1.58517	−0.792585	+	0.609762i	$0.791265\pi$
$450$	−2.83718e19	−0.357925
$451$	−3.52425e19	−0.437263
$452$	1.73720e18	0.0211988
$453$	7.43077e19	0.891861
$454$	−1.32227e20	−1.56100
$455$	5.71797e19	0.663982
$456$	−1.12578e20	−1.28593
$457$	1.59593e20	1.79326	0.896629	−	0.442783i	$-0.146009\pi$
$457$	1.59593e20	1.79326	0.896629	+	0.442783i	$0.146009\pi$
$458$	8.20700e19	0.907180
$459$	−4.92357e19	−0.535408
$460$	−5.79623e17	−0.00620100
$461$	1.35074e20	1.42172	0.710861	−	0.703332i	$-0.248305\pi$
$461$	1.35074e20	1.42172	0.710861	+	0.703332i	$0.248305\pi$
$462$	5.83420e19	0.604180
$463$	−3.12305e19	−0.318215	−0.159108	−	0.987261i	$-0.550862\pi$
$463$	−3.12305e19	−0.318215	−0.159108	+	0.987261i	$0.550862\pi$
$464$	−1.86680e19	−0.187160
$465$	2.67344e19	0.263738
$466$	9.59729e19	0.931653
$467$	−1.27500e20	−1.21797	−0.608983	−	0.793183i	$-0.708422\pi$
$467$	−1.27500e20	−1.21797	−0.608983	+	0.793183i	$0.708422\pi$
$468$	−1.15726e18	−0.0108790
$469$	−1.49397e20	−1.38212
$470$	−7.26493e18	−0.0661451
$471$	1.10271e18	0.00988112
$472$	−2.50395e19	−0.220832
$473$	4.57144e19	0.396821
$474$	2.29009e19	0.195666
$475$	−1.85807e20	−1.56264
$476$	−2.04148e18	−0.0169002
$477$	6.53405e19	0.532469
$478$	−4.05954e19	−0.325662
$479$	2.75649e19	0.217691	0.108845	−	0.994059i	$-0.465285\pi$
$479$	2.75649e19	0.217691	0.108845	+	0.994059i	$0.465285\pi$
$480$	−7.83104e17	−0.00608850
$481$	−1.17877e20	−0.902277
$482$	−6.82533e19	−0.514365
$483$	3.29228e20	2.44283
$484$	−2.07543e18	−0.0151624
$485$	1.13893e19	0.0819285
$486$	9.95397e19	0.705057
$487$	5.14686e19	0.358984	0.179492	−	0.983759i	$-0.442555\pi$
$487$	5.14686e19	0.358984	0.179492	+	0.983759i	$0.442555\pi$
$488$	−1.90692e20	−1.30974
$489$	7.14440e19	0.483225
$490$	−8.55802e19	−0.570036
$491$	−1.10111e20	−0.722301	−0.361151	−	0.932507i	$-0.617616\pi$
$491$	−1.10111e20	−0.722301	−0.361151	+	0.932507i	$0.617616\pi$
$492$	2.43718e18	0.0157453
$493$	−1.42333e19	−0.0905639
$494$	−4.29145e20	−2.68938
$495$	−5.09190e18	−0.0314297
$496$	2.60672e20	1.58483
$497$	−4.12552e20	−2.47062
$498$	−9.53925e19	−0.562722
$499$	2.94624e19	0.171204	0.0856020	−	0.996329i	$-0.472719\pi$
$499$	2.94624e19	0.171204	0.0856020	+	0.996329i	$0.472719\pi$
$500$	−1.31139e18	−0.00750686
$501$	−2.22182e20	−1.25293
$502$	−2.62985e20	−1.46101
$503$	−1.58394e20	−0.866917	−0.433459	−	0.901173i	$-0.642707\pi$
$503$	−1.58394e20	−0.866917	−0.433459	+	0.901173i	$0.642707\pi$
$504$	−1.30390e20	−0.703097
$505$	−5.71178e19	−0.303449
$506$	1.23144e20	0.644593
$507$	−2.53599e20	−1.30794
$508$	−1.24664e18	−0.00633522
$509$	7.03779e19	0.352414	0.176207	−	0.984353i	$-0.443617\pi$
$509$	7.03779e19	0.352414	0.176207	+	0.984353i	$0.443617\pi$
$510$	−1.70522e19	−0.0841403
$511$	6.97933e20	3.39357
$512$	2.02798e20	0.971716
$513$	3.77028e20	1.78030
$514$	1.69302e20	0.787843
$515$	4.59040e18	0.0210522
$516$	−3.16136e18	−0.0142890
$517$	2.72586e19	0.121429
$518$	2.43142e20	1.06755
$519$	5.06380e19	0.219140
$520$	8.07908e19	0.344617
$521$	−2.08453e20	−0.876444	−0.438222	−	0.898867i	$-0.644392\pi$
$521$	−2.08453e20	−0.876444	−0.438222	+	0.898867i	$0.644392\pi$
$522$	1.66428e19	0.0689758
$523$	−1.57349e20	−0.642837	−0.321419	−	0.946937i	$-0.604160\pi$
$523$	−1.57349e20	−0.642837	−0.321419	+	0.946937i	$0.604160\pi$
$524$	−7.67399e18	−0.0309056
$525$	3.63739e20	1.44409
$526$	4.97581e18	0.0194747
$527$	1.98748e20	0.766874
$528$	8.39155e19	0.319218
$529$	4.28276e20	1.60623
$530$	8.35090e19	0.308791
$531$	2.27245e19	0.0828487
$532$	1.56329e19	0.0561955
$533$	−5.07478e20	−1.79872
$534$	4.98182e19	0.174112
$535$	−6.74640e19	−0.232498
$536$	−2.11088e20	−0.717343
$537$	−1.08821e20	−0.364673
$538$	−3.71578e20	−1.22796
$539$	3.21103e20	1.04647
$540$	1.29942e18	0.00417636
$541$	−9.78179e19	−0.310055	−0.155028	−	0.987910i	$-0.549547\pi$
$541$	−9.78179e19	−0.310055	−0.155028	+	0.987910i	$0.549547\pi$
$542$	−3.76443e20	−1.17681
$543$	1.38667e20	0.427537
$544$	−5.82174e18	−0.0177036
$545$	2.80689e19	0.0841882
$546$	8.40102e20	2.48535
$547$	1.83263e20	0.534774	0.267387	−	0.963589i	$-0.413840\pi$
$547$	1.83263e20	0.534774	0.267387	+	0.963589i	$0.413840\pi$
$548$	6.33369e18	0.0182307
$549$	1.73062e20	0.491369
$550$	1.36053e20	0.381055
$551$	1.08994e20	0.301137
$552$	4.65175e20	1.26787
$553$	1.73707e20	0.467066
$554$	−1.10487e19	−0.0293080
$555$	3.58672e19	0.0938643
$556$	−5.39062e18	−0.0139180
$557$	5.04506e20	1.28515	0.642573	−	0.766224i	$-0.277867\pi$
$557$	5.04506e20	1.28515	0.642573	+	0.766224i	$0.277867\pi$
$558$	−2.32392e20	−0.584071
$559$	6.58270e20	1.63236
$560$	−1.69643e20	−0.415074
$561$	6.39811e19	0.154465
$562$	−1.57175e20	−0.374422
$563$	−8.18105e20	−1.92307	−0.961537	−	0.274675i	$-0.911430\pi$
$563$	−8.18105e20	−1.92307	−0.961537	+	0.274675i	$0.911430\pi$
$564$	−1.88506e18	−0.00437251
$565$	1.10065e20	0.251933
$566$	−2.61710e20	−0.591150
$567$	−4.19732e20	−0.935620
$568$	−5.82906e20	−1.28229
$569$	2.61938e20	0.568666	0.284333	−	0.958726i	$-0.408228\pi$
$569$	2.61938e20	0.568666	0.284333	+	0.958726i	$0.408228\pi$
$570$	1.30579e20	0.279777
$571$	−4.25835e19	−0.0900474	−0.0450237	−	0.998986i	$-0.514336\pi$
$571$	−4.25835e19	−0.0900474	−0.0450237	+	0.998986i	$0.514336\pi$
$572$	5.54949e18	0.0115820
$573$	4.86159e20	1.00143
$574$	1.04677e21	2.12819
$575$	7.67756e20	1.54069
$576$	−1.84171e20	−0.364798
$577$	−7.35877e20	−1.43875	−0.719377	−	0.694620i	$-0.755572\pi$
$577$	−7.35877e20	−1.43875	−0.719377	+	0.694620i	$0.755572\pi$
$578$	3.96022e20	0.764294
$579$	2.52602e20	0.481225
$580$	3.75646e17	0.000706429 0
$581$	−7.23567e20	−1.34325
$582$	1.67336e20	0.306666
$583$	−3.13332e20	−0.566879
$584$	9.86130e20	1.76132
$585$	−7.33214e19	−0.129289
$586$	−6.02821e20	−1.04944
$587$	2.47060e20	0.424636	0.212318	−	0.977201i	$-0.431899\pi$
$587$	2.47060e20	0.424636	0.212318	+	0.977201i	$0.431899\pi$
$588$	−2.22058e19	−0.0376822
$589$	−1.52194e21	−2.54996
$590$	2.90432e19	0.0480458
$591$	−1.39012e20	−0.227062
$592$	3.49721e20	0.564039
$593$	−6.88185e20	−1.09596	−0.547980	−	0.836491i	$-0.684603\pi$
$593$	−6.88185e20	−1.09596	−0.547980	+	0.836491i	$0.684603\pi$
$594$	−2.76071e20	−0.434132
$595$	−1.29344e20	−0.200848
$596$	−9.43134e18	−0.0144619
$597$	7.31732e20	1.10801
$598$	1.77323e21	2.65159
$599$	3.18221e20	0.469924	0.234962	−	0.972005i	$-0.424503\pi$
$599$	3.18221e20	0.469924	0.234962	+	0.972005i	$0.424503\pi$
$600$	5.13937e20	0.749507
$601$	−1.13299e21	−1.63180	−0.815899	−	0.578195i	$-0.803757\pi$
$601$	−1.13299e21	−1.63180	−0.815899	+	0.578195i	$0.803757\pi$
$602$	−1.35780e21	−1.93136
$603$	1.91572e20	0.269123
$604$	−1.45793e19	−0.0202284
$605$	−1.31495e20	−0.180195
$606$	−8.39192e20	−1.13584
$607$	−4.93271e20	−0.659433	−0.329716	−	0.944080i	$-0.606953\pi$
$607$	−4.93271e20	−0.659433	−0.329716	+	0.944080i	$0.606953\pi$
$608$	4.45807e19	0.0588667
$609$	−2.13368e20	−0.278291
$610$	2.21183e20	0.284956
$611$	3.92513e20	0.499511
$612$	2.61778e18	0.00329078
$613$	1.29975e21	1.61401	0.807004	−	0.590545i	$-0.201087\pi$
$613$	1.29975e21	1.61401	0.807004	+	0.590545i	$0.201087\pi$
$614$	−3.67212e20	−0.450458
$615$	1.54414e20	0.187122
$616$	6.25268e20	0.748533
$617$	−6.69656e19	−0.0791978	−0.0395989	−	0.999216i	$-0.512608\pi$
$617$	−6.69656e19	−0.0791978	−0.0395989	+	0.999216i	$0.512608\pi$
$618$	6.74436e19	0.0788002
$619$	−1.52441e21	−1.75964	−0.879819	−	0.475309i	$-0.842336\pi$
$619$	−1.52441e21	−1.75964	−0.879819	+	0.475309i	$0.842336\pi$
$620$	−5.24536e18	−0.00598187
$621$	−1.55788e21	−1.75529
$622$	2.85037e20	0.317303
$623$	3.77879e20	0.415616
$624$	1.20835e21	1.31313
$625$	8.05722e20	0.865137
$626$	−3.45226e20	−0.366266
$627$	−4.89943e20	−0.513616
$628$	−2.16355e17	−0.000224114 0
$629$	2.66643e20	0.272930
$630$	1.51239e20	0.152971
$631$	−1.11186e21	−1.11130	−0.555650	−	0.831416i	$-0.687531\pi$
$631$	−1.11186e21	−1.11130	−0.555650	+	0.831416i	$0.687531\pi$
$632$	2.45436e20	0.242415
$633$	5.40168e20	0.527231
$634$	5.62702e20	0.542762
$635$	−7.89841e19	−0.0752899
$636$	2.16683e19	0.0204125
$637$	4.62376e21	4.30477
$638$	−7.98082e19	−0.0734332
$639$	5.29014e20	0.481073
$640$	−2.43928e20	−0.219236
$641$	6.55583e20	0.582361	0.291181	−	0.956668i	$-0.405952\pi$
$641$	6.55583e20	0.582361	0.291181	+	0.956668i	$0.405952\pi$
$642$	−9.91202e20	−0.870261
$643$	−5.69690e20	−0.494374	−0.247187	−	0.968968i	$-0.579506\pi$
$643$	−5.69690e20	−0.494374	−0.247187	+	0.968968i	$0.579506\pi$
$644$	−6.45952e19	−0.0554060
$645$	−2.00297e20	−0.169815
$646$	9.70749e20	0.813510
$647$	1.10363e21	0.914197	0.457098	−	0.889416i	$-0.348889\pi$
$647$	1.10363e21	0.914197	0.457098	+	0.889416i	$0.348889\pi$
$648$	−5.93052e20	−0.485602
$649$	−1.08972e20	−0.0882025
$650$	1.95911e21	1.56750
$651$	2.97938e21	2.35650
$652$	−1.40175e19	−0.0109601
$653$	−7.48550e20	−0.578592	−0.289296	−	0.957240i	$-0.593421\pi$
$653$	−7.48550e20	−0.578592	−0.289296	+	0.957240i	$0.593421\pi$
$654$	4.12397e20	0.315125
$655$	−4.86207e20	−0.367292
$656$	1.50561e21	1.12443
$657$	−8.94958e20	−0.660788
$658$	−8.09630e20	−0.591007
$659$	−1.49585e21	−1.07956	−0.539779	−	0.841807i	$-0.681492\pi$
$659$	−1.49585e21	−1.07956	−0.539779	+	0.841807i	$0.681492\pi$
$660$	−1.68858e18	−0.00120488
$661$	−2.19783e20	−0.155054	−0.0775270	−	0.996990i	$-0.524702\pi$
$661$	−2.19783e20	−0.155054	−0.0775270	+	0.996990i	$0.524702\pi$
$662$	−2.94689e20	−0.205556
$663$	9.21303e20	0.635405
$664$	−1.02235e21	−0.697170
$665$	9.90464e20	0.667846
$666$	−3.11781e20	−0.207870
$667$	−4.50363e20	−0.296906
$668$	4.35927e19	0.0284178
$669$	−1.12541e21	−0.725463
$670$	2.44840e20	0.156071
$671$	−8.29894e20	−0.523123
$672$	−8.72719e19	−0.0544008
$673$	1.24909e21	0.769980	0.384990	−	0.922921i	$-0.374205\pi$
$673$	1.24909e21	0.769980	0.384990	+	0.922921i	$0.374205\pi$
$674$	−1.90578e21	−1.16178
$675$	−1.72119e21	−1.03765
$676$	4.97567e19	0.0296655
$677$	−1.72387e21	−1.01646	−0.508230	−	0.861221i	$-0.669700\pi$
$677$	−1.72387e21	−1.01646	−0.508230	+	0.861221i	$0.669700\pi$
$678$	1.61711e21	0.943010
$679$	1.26927e21	0.732031
$680$	−1.82753e20	−0.104243
$681$	−2.17377e21	−1.22634
$682$	1.11441e21	0.621815
$683$	9.49624e20	0.524078	0.262039	−	0.965057i	$-0.415605\pi$
$683$	9.49624e20	0.524078	0.262039	+	0.965057i	$0.415605\pi$
$684$	−2.00460e19	−0.0109423
$685$	4.01288e20	0.216659
$686$	−5.93066e21	−3.16717
$687$	1.34920e21	0.712691
$688$	−1.95298e21	−1.02043
$689$	−4.51186e21	−2.33191
$690$	−5.39555e20	−0.275846
$691$	1.50723e21	0.762246	0.381123	−	0.924524i	$-0.375537\pi$
$691$	1.50723e21	0.762246	0.381123	+	0.924524i	$0.375537\pi$
$692$	−9.93529e18	−0.00497032
$693$	−5.67459e20	−0.280825
$694$	−7.83266e20	−0.383454
$695$	−3.41538e20	−0.165406
$696$	−3.01474e20	−0.144437
$697$	1.14794e21	0.544095
$698$	−1.25560e21	−0.588758
$699$	1.57776e21	0.731917
$700$	−7.13664e19	−0.0327536
$701$	6.85021e20	0.311042	0.155521	−	0.987833i	$-0.450294\pi$
$701$	6.85021e20	0.311042	0.155521	+	0.987833i	$0.450294\pi$
$702$	−3.97531e21	−1.78584
$703$	−2.04185e21	−0.907527
$704$	8.83168e20	0.388372
$705$	−1.19433e20	−0.0519643
$706$	3.96576e20	0.170723
$707$	−6.36540e21	−2.71132
$708$	7.53594e18	0.00317606
$709$	1.69771e21	0.707973	0.353987	−	0.935251i	$-0.384826\pi$
$709$	1.69771e21	0.707973	0.353987	+	0.935251i	$0.384826\pi$
$710$	6.76111e20	0.278985
$711$	−2.22744e20	−0.0909461
$712$	5.33916e20	0.215711
$713$	6.28867e21	2.51413
$714$	−1.90036e21	−0.751793
$715$	3.51603e20	0.137644
$716$	2.13509e19	0.00827119
$717$	−6.67373e20	−0.255844
$718$	1.00445e21	0.381063
$719$	4.54618e20	0.170679	0.0853395	−	0.996352i	$-0.472803\pi$
$719$	4.54618e20	0.170679	0.0853395	+	0.996352i	$0.472803\pi$
$720$	2.17533e20	0.0808222
$721$	5.11571e20	0.188101
$722$	−4.66096e21	−1.69608
$723$	−1.12206e21	−0.404091
$724$	−2.72067e19	−0.00969700
$725$	−4.97572e20	−0.175518
$726$	−1.93196e21	−0.674488
$727$	−2.02009e21	−0.698010	−0.349005	−	0.937121i	$-0.613480\pi$
$727$	−2.02009e21	−0.698010	−0.349005	+	0.937121i	$0.613480\pi$
$728$	9.00361e21	3.07915
$729$	3.08432e21	1.04401
$730$	−1.14381e21	−0.383206
$731$	−1.48904e21	−0.493772
$732$	5.73910e19	0.0188370
$733$	9.17603e20	0.298109	0.149055	−	0.988829i	$-0.452377\pi$
$733$	9.17603e20	0.298109	0.149055	+	0.988829i	$0.452377\pi$
$734$	2.89879e21	0.932172
$735$	−1.40691e21	−0.447827
$736$	−1.84208e20	−0.0580396
$737$	−9.18656e20	−0.286515
$738$	−1.34227e21	−0.414397
$739$	3.88029e21	1.18585	0.592927	−	0.805256i	$-0.297972\pi$
$739$	3.88029e21	1.18585	0.592927	+	0.805256i	$0.297972\pi$
$740$	−7.03724e18	−0.00212894
$741$	−7.05499e21	−2.11281
$742$	9.30653e21	2.75904
$743$	6.33048e21	1.85789	0.928946	−	0.370216i	$-0.120716\pi$
$743$	6.33048e21	1.85789	0.928946	+	0.370216i	$0.120716\pi$
$744$	4.20965e21	1.22306
$745$	−5.97548e20	−0.171870
$746$	2.07100e21	0.589712
$747$	9.27828e20	0.261555
$748$	−1.25532e19	−0.00350343
$749$	−7.51842e21	−2.07737
$750$	−1.22074e21	−0.333936
$751$	5.18962e21	1.40552	0.702758	−	0.711429i	$-0.251952\pi$
$751$	5.18962e21	1.40552	0.702758	+	0.711429i	$0.251952\pi$
$752$	−1.16452e21	−0.312258
$753$	−4.32337e21	−1.14778
$754$	−1.14921e21	−0.302074
$755$	−9.23714e20	−0.240401
$756$	1.44812e20	0.0373158
$757$	−4.42113e21	−1.12801	−0.564007	−	0.825770i	$-0.690741\pi$
$757$	−4.42113e21	−1.12801	−0.564007	+	0.825770i	$0.690741\pi$
$758$	6.95192e21	1.75625
$759$	2.02445e21	0.506400
$760$	1.39945e21	0.346623
$761$	−2.58173e21	−0.633179	−0.316589	−	0.948563i	$-0.602538\pi$
$761$	−2.58173e21	−0.633179	−0.316589	+	0.948563i	$0.602538\pi$
$762$	−1.16046e21	−0.281817
$763$	3.12809e21	0.752222
$764$	−9.53856e19	−0.0227134
$765$	1.65857e20	0.0391086
$766$	−5.10259e21	−1.19145
$767$	−1.56916e21	−0.362829
$768$	−1.86642e20	−0.0427365
$769$	−5.29368e20	−0.120036	−0.0600178	−	0.998197i	$-0.519116\pi$
$769$	−5.29368e20	−0.120036	−0.0600178	+	0.998197i	$0.519116\pi$
$770$	−7.25246e20	−0.162856
$771$	2.78327e21	0.618938
$772$	−4.95612e19	−0.0109147
$773$	−7.43993e21	−1.62264	−0.811321	−	0.584601i	$-0.801251\pi$
$773$	−7.43993e21	−1.62264	−0.811321	+	0.584601i	$0.801251\pi$
$774$	1.74111e21	0.376070
$775$	6.94788e21	1.48624
$776$	1.79338e21	0.379936
$777$	3.99717e21	0.838678
$778$	2.07675e21	0.431556
$779$	−8.79052e21	−1.80919
$780$	−2.43150e19	−0.00495637
$781$	−2.53682e21	−0.512161
$782$	−4.01115e21	−0.802080
$783$	1.00964e21	0.199965
$784$	−1.37179e22	−2.69103
$785$	−1.37078e19	−0.00266345
$786$	−7.14350e21	−1.37481
$787$	6.59425e21	1.25706	0.628529	−	0.777787i	$-0.283658\pi$
$787$	6.59425e21	1.25706	0.628529	+	0.777787i	$0.283658\pi$
$788$	2.72744e19	0.00515002
$789$	8.18005e19	0.0152995
$790$	−2.84680e20	−0.0527416
$791$	1.22660e22	2.25102
$792$	−8.01779e20	−0.145752
$793$	−1.19501e22	−2.15191
$794$	−7.98081e21	−1.42362
$795$	1.37286e21	0.242589
$796$	−1.43568e20	−0.0251309
$797$	−1.00670e21	−0.174567	−0.0872836	−	0.996184i	$-0.527819\pi$
$797$	−1.00670e21	−0.174567	−0.0872836	+	0.996184i	$0.527819\pi$
$798$	1.45522e22	2.49981
$799$	−8.87885e20	−0.151097
$800$	−2.03517e20	−0.0343105
$801$	−4.84553e20	−0.0809277
$802$	−5.27871e21	−0.873413
$803$	4.29165e21	0.703490
$804$	6.35294e19	0.0103170
$805$	−4.09261e21	−0.658462
$806$	1.60470e22	2.55789
$807$	−6.10861e21	−0.964697
$808$	−8.99386e21	−1.40722
$809$	−7.07231e21	−1.09634	−0.548172	−	0.836365i	$-0.684676\pi$
$809$	−7.07231e21	−1.09634	−0.548172	+	0.836365i	$0.684676\pi$
$810$	6.87878e20	0.105651
$811$	−1.99393e21	−0.303427	−0.151713	−	0.988425i	$-0.548479\pi$
$811$	−1.99393e21	−0.303427	−0.151713	+	0.988425i	$0.548479\pi$
$812$	4.18633e19	0.00631194
$813$	−6.18858e21	−0.924511
$814$	1.49510e21	0.221303
$815$	−8.88116e20	−0.130253
$816$	−2.73336e21	−0.397210
$817$	1.14025e22	1.64186
$818$	1.03612e22	1.47829
$819$	−8.17119e21	−1.15520
$820$	−3.02965e19	−0.00424412
$821$	1.75488e21	0.243599	0.121799	−	0.992555i	$-0.461134\pi$
$821$	1.75488e21	0.243599	0.121799	+	0.992555i	$0.461134\pi$
$822$	5.89585e21	0.810976
$823$	−2.53418e21	−0.345413	−0.172707	−	0.984973i	$-0.555251\pi$
$823$	−2.53418e21	−0.345413	−0.172707	+	0.984973i	$0.555251\pi$
$824$	7.22813e20	0.0976274
$825$	2.23666e21	0.299361
$826$	3.23668e21	0.429289
$827$	−1.27678e22	−1.67813	−0.839066	−	0.544029i	$-0.816898\pi$
$827$	−1.27678e22	−1.67813	−0.839066	+	0.544029i	$0.816898\pi$
$828$	8.28303e19	0.0107885
$829$	−5.37743e21	−0.694090	−0.347045	−	0.937849i	$-0.612815\pi$
$829$	−5.37743e21	−0.694090	−0.347045	+	0.937849i	$0.612815\pi$
$830$	1.18582e21	0.151681
$831$	−1.81636e20	−0.0230247
$832$	1.27173e22	1.59760
$833$	−1.04592e22	−1.30215
$834$	−5.01798e21	−0.619132
$835$	2.76193e21	0.337726
$836$	9.61279e19	0.0116494
$837$	−1.40982e22	−1.69326
$838$	1.20373e22	1.43284
$839$	−5.66557e21	−0.668388	−0.334194	−	0.942504i	$-0.608464\pi$
$839$	−5.66557e21	−0.668388	−0.334194	+	0.942504i	$0.608464\pi$
$840$	−2.73960e21	−0.320326
$841$	−8.33731e21	−0.966176
$842$	2.24104e20	0.0257400
$843$	−2.58390e21	−0.294150
$844$	−1.05982e20	−0.0119582
$845$	3.15247e21	0.352554
$846$	1.03819e21	0.115079
$847$	−1.46542e22	−1.61004
$848$	1.33859e22	1.45774
$849$	−4.30242e21	−0.464414
$850$	−4.43161e21	−0.474155
$851$	8.43696e21	0.894776
$852$	1.75433e20	0.0184422
$853$	−4.84523e21	−0.504890	−0.252445	−	0.967611i	$-0.581235\pi$
$853$	−4.84523e21	−0.504890	−0.252445	+	0.967611i	$0.581235\pi$
$854$	2.46494e22	2.54608
$855$	−1.27007e21	−0.130041
$856$	−1.06230e22	−1.07819
$857$	1.05223e22	1.05866	0.529330	−	0.848416i	$-0.322443\pi$
$857$	1.05223e22	1.05866	0.529330	+	0.848416i	$0.322443\pi$
$858$	5.16586e21	0.515214
$859$	−9.07381e21	−0.897100	−0.448550	−	0.893758i	$-0.648059\pi$
$859$	−9.07381e21	−0.897100	−0.448550	+	0.893758i	$0.648059\pi$
$860$	3.92987e19	0.00385159
$861$	1.72085e22	1.67193
$862$	1.03821e22	0.999955
$863$	−7.11537e21	−0.679386	−0.339693	−	0.940536i	$-0.610323\pi$
$863$	−7.11537e21	−0.679386	−0.339693	+	0.940536i	$0.610323\pi$
$864$	4.12965e20	0.0390895
$865$	−6.29477e20	−0.0590690
$866$	1.48131e21	0.137804
$867$	6.51045e21	0.600438
$868$	−5.84561e20	−0.0534481
$869$	1.06814e21	0.0968232
$870$	3.49678e20	0.0314249
$871$	−1.32283e22	−1.17860
$872$	4.41977e21	0.390415
$873$	−1.62758e21	−0.142539
$874$	3.07158e22	2.66702
$875$	−9.25951e21	−0.797127
$876$	−2.96788e20	−0.0253317
$877$	−1.22185e22	−1.03400	−0.517000	−	0.855986i	$-0.672951\pi$
$877$	−1.22185e22	−1.03400	−0.517000	+	0.855986i	$0.672951\pi$
$878$	2.32200e22	1.94829
$879$	−9.91016e21	−0.824449
$880$	−1.04315e21	−0.0860451
$881$	4.45088e21	0.364021	0.182010	−	0.983297i	$-0.441740\pi$
$881$	4.45088e21	0.364021	0.182010	+	0.983297i	$0.441740\pi$
$882$	1.22297e22	0.991750
$883$	2.28202e22	1.83490	0.917452	−	0.397847i	$-0.130242\pi$
$883$	2.28202e22	1.83490	0.917452	+	0.397847i	$0.130242\pi$
$884$	−1.80762e20	−0.0144117
$885$	4.77460e20	0.0377453
$886$	−8.22986e21	−0.645119
$887$	−2.48008e22	−1.92769	−0.963847	−	0.266455i	$-0.914148\pi$
$887$	−2.48008e22	−1.92769	−0.963847	+	0.266455i	$0.914148\pi$
$888$	5.64772e21	0.435287
$889$	−8.80226e21	−0.672715
$890$	−6.19287e20	−0.0469318
$891$	−2.58097e21	−0.193955
$892$	2.20808e20	0.0164543
$893$	6.79909e21	0.502417
$894$	−8.77937e21	−0.643327
$895$	1.35274e21	0.0982975
$896$	−2.71842e22	−1.95887
$897$	2.91513e22	2.08312
$898$	2.25693e22	1.59936
$899$	−4.07560e21	−0.286414
$900$	9.15130e19	0.00637770
$901$	1.02061e22	0.705378
$902$	6.43666e21	0.441176
$903$	−2.23218e22	−1.51730
$904$	1.73310e22	1.16832
$905$	−1.72376e21	−0.115242
$906$	−1.35715e22	−0.899842
$907$	8.19687e20	0.0539006	0.0269503	−	0.999637i	$-0.491420\pi$
$907$	8.19687e20	0.0539006	0.0269503	+	0.999637i	$0.491420\pi$
$908$	4.26499e20	0.0278147
$909$	8.16234e21	0.527941
$910$	−1.04433e22	−0.669924
$911$	1.17749e22	0.749149	0.374575	−	0.927197i	$-0.377789\pi$
$911$	1.17749e22	0.749149	0.374575	+	0.927197i	$0.377789\pi$
$912$	2.09310e22	1.32077
$913$	−4.44928e21	−0.278457
$914$	−2.91480e22	−1.80931
$915$	3.63616e21	0.223864
$916$	−2.64716e20	−0.0161646
$917$	−5.41846e22	−3.28175
$918$	8.99237e21	0.540199
$919$	−8.16981e21	−0.486794	−0.243397	−	0.969927i	$-0.578262\pi$
$919$	−8.16981e21	−0.486794	−0.243397	+	0.969927i	$0.578262\pi$
$920$	−5.78256e21	−0.341752
$921$	−6.03683e21	−0.353885
$922$	−2.46698e22	−1.43444
$923$	−3.65292e22	−2.10682
$924$	−1.88182e20	−0.0107656
$925$	9.32136e21	0.528952
$926$	5.70391e21	0.321063
$927$	−6.55986e20	−0.0366266
$928$	1.19383e20	0.00661197
$929$	3.59969e21	0.197764	0.0988819	−	0.995099i	$-0.468473\pi$
$929$	3.59969e21	0.197764	0.0988819	+	0.995099i	$0.468473\pi$
$930$	−4.88275e21	−0.266099
$931$	8.00926e22	4.32982
$932$	−3.09560e20	−0.0166007
$933$	4.68591e21	0.249277
$934$	2.32866e22	1.22887
$935$	−7.95345e20	−0.0416359
$936$	−1.15453e22	−0.599566
$937$	1.30337e22	0.671459	0.335730	−	0.941958i	$-0.391017\pi$
$937$	1.30337e22	0.671459	0.335730	+	0.941958i	$0.391017\pi$
$938$	2.72858e22	1.39449
$939$	−5.67540e21	−0.287743
$940$	2.34330e19	0.00117861
$941$	−2.65951e22	−1.32703	−0.663514	−	0.748164i	$-0.730936\pi$
$941$	−2.65951e22	−1.32703	−0.663514	+	0.748164i	$0.730936\pi$
$942$	−2.01399e20	−0.00996954
$943$	3.63225e22	1.78377
$944$	4.65544e21	0.226815
$945$	9.17499e21	0.443473
$946$	−8.34925e21	−0.400372
$947$	1.47805e22	0.703175	0.351587	−	0.936155i	$-0.385642\pi$
$947$	1.47805e22	0.703175	0.351587	+	0.936155i	$0.385642\pi$
$948$	−7.38667e19	−0.00348647
$949$	6.17981e22	2.89387
$950$	3.39356e22	1.57663
$951$	9.25062e21	0.426400
$952$	−2.03667e22	−0.931414
$953$	−3.55337e22	−1.61229	−0.806147	−	0.591715i	$-0.798451\pi$
$953$	−3.55337e22	−1.61229	−0.806147	+	0.591715i	$0.798451\pi$
$954$	−1.19337e22	−0.537234
$955$	−6.04341e21	−0.269934
$956$	1.30940e20	0.00580281
$957$	−1.31202e21	−0.0576899
$958$	−5.03443e21	−0.219639
$959$	4.47210e22	1.93585
$960$	−3.86958e21	−0.166200
$961$	3.34447e22	1.42529
$962$	2.15289e22	0.910351
$963$	9.64086e21	0.404500
$964$	2.20151e20	0.00916521
$965$	−3.14009e21	−0.129714
$966$	−6.01299e22	−2.46469
$967$	4.28632e22	1.74335	0.871677	−	0.490080i	$-0.163033\pi$
$967$	4.28632e22	1.74335	0.871677	+	0.490080i	$0.163033\pi$
$968$	−2.07054e22	−0.835639
$969$	1.59588e22	0.639103
$970$	−2.08014e21	−0.0826616
$971$	1.70953e22	0.674111	0.337056	−	0.941485i	$-0.390569\pi$
$971$	1.70953e22	0.674111	0.337056	+	0.941485i	$0.390569\pi$
$972$	−3.21065e20	−0.0125631
$973$	−3.80622e22	−1.47791
$974$	−9.40019e21	−0.362197
$975$	3.22071e22	1.23145
$976$	3.54542e22	1.34522
$977$	−1.11034e22	−0.418068	−0.209034	−	0.977908i	$-0.567032\pi$
$977$	−1.11034e22	−0.418068	−0.209034	+	0.977908i	$0.567032\pi$
$978$	−1.30485e22	−0.487549
$979$	2.32361e21	0.0861575
$980$	2.76038e20	0.0101572
$981$	−4.01115e21	−0.146471
$982$	2.01105e22	0.728765
$983$	−1.16429e22	−0.418706	−0.209353	−	0.977840i	$-0.567136\pi$
$983$	−1.16429e22	−0.418706	−0.209353	+	0.977840i	$0.567136\pi$
$984$	2.43144e22	0.867760
$985$	1.72805e21	0.0612045
$986$	2.59957e21	0.0913744
$987$	−1.33100e22	−0.464301
$988$	1.38421e21	0.0479207
$989$	−4.71153e22	−1.61879
$990$	9.29980e20	0.0317110
$991$	5.08313e22	1.72020	0.860100	−	0.510125i	$-0.170401\pi$
$991$	5.08313e22	1.72020	0.860100	+	0.510125i	$0.170401\pi$
$992$	−1.66701e21	−0.0559886
$993$	−4.84458e21	−0.161487
$994$	7.53482e22	2.49273
$995$	−9.09612e21	−0.298664
$996$	3.07688e20	0.0100269
$997$	2.89386e22	0.935975	0.467987	−	0.883735i	$-0.344979\pi$
$997$	2.89386e22	0.935975	0.467987	+	0.883735i	$0.344979\pi$
$998$	−5.38099e21	−0.172736
$999$	−1.89144e22	−0.602630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.16.a.a.1.19	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.16.a.a.1.19	✓	61	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	103.a (trivial)

\(f(q)\)	\(=\)	\(q-182.639 q^{2} -3002.52 q^{3} +589.102 q^{4} +37324.2 q^{5} +548379. q^{6} +4.15954e6 q^{7} +5.87713e6 q^{8} -5.33376e6 q^{9} +O(q^{10})\)	\(q-182.639 q^{2} -3002.52 q^{3} +589.102 q^{4} +37324.2 q^{5} +548379. q^{6} +4.15954e6 q^{7} +5.87713e6 q^{8} -5.33376e6 q^{9} -6.81686e6 q^{10} +2.55774e7 q^{11} -1.76879e6 q^{12} +3.68304e8 q^{13} -7.59695e8 q^{14} -1.12067e8 q^{15} -1.09270e9 q^{16} -8.33124e8 q^{17} +9.74155e8 q^{18} +6.37975e9 q^{19} +2.19878e7 q^{20} -1.24891e10 q^{21} -4.67143e9 q^{22} -2.63612e10 q^{23} -1.76462e10 q^{24} -2.91245e10 q^{25} -6.72668e10 q^{26} +5.90977e10 q^{27} +2.45039e9 q^{28} +1.70843e10 q^{29} +2.04678e10 q^{30} -2.38558e11 q^{31} +6.98784e9 q^{32} -7.67966e10 q^{33} +1.52161e11 q^{34} +1.55251e11 q^{35} -3.14213e9 q^{36} -3.20053e11 q^{37} -1.16519e12 q^{38} -1.10584e12 q^{39} +2.19359e11 q^{40} -1.37788e12 q^{41} +2.28100e12 q^{42} +1.78730e12 q^{43} +1.50677e10 q^{44} -1.99078e11 q^{45} +4.81459e12 q^{46} +1.06573e12 q^{47} +3.28085e12 q^{48} +1.25542e13 q^{49} +5.31927e12 q^{50} +2.50147e12 q^{51} +2.16969e11 q^{52} -1.22504e13 q^{53} -1.07936e13 q^{54} +9.54654e11 q^{55} +2.44461e13 q^{56} -1.91553e13 q^{57} -3.12027e12 q^{58} -4.26050e12 q^{59} -6.60187e10 q^{60} -3.24464e13 q^{61} +4.35701e13 q^{62} -2.21860e13 q^{63} +3.45293e13 q^{64} +1.37466e13 q^{65} +1.40261e13 q^{66} -3.59168e13 q^{67} -4.90795e11 q^{68} +7.91500e13 q^{69} -2.83550e13 q^{70} -9.91821e13 q^{71} -3.13472e13 q^{72} +1.67791e14 q^{73} +5.84542e13 q^{74} +8.74469e13 q^{75} +3.75832e12 q^{76} +1.06390e14 q^{77} +2.01970e14 q^{78} +4.17611e13 q^{79} -4.07841e13 q^{80} -1.00908e14 q^{81} +2.51655e14 q^{82} -1.73954e14 q^{83} -7.35736e12 q^{84} -3.10957e13 q^{85} -3.26431e14 q^{86} -5.12960e13 q^{87} +1.50321e14 q^{88} +9.08463e13 q^{89} +3.63595e13 q^{90} +1.53197e15 q^{91} -1.55294e13 q^{92} +7.16276e14 q^{93} -1.94644e14 q^{94} +2.38119e14 q^{95} -2.09812e13 q^{96} +3.05146e14 q^{97} -2.29289e15 q^{98} -1.36424e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 857 q^{2} - 3932 q^{3} + 952767 q^{4} - 439140 q^{5} + 743647 q^{6} - 3190353 q^{7} - 33093708 q^{8} + 233430375 q^{9}+O(q^{10}) \) 61 * q - 857 * q^2 - 3932 * q^3 + 952767 * q^4 - 439140 * q^5 + 743647 * q^6 - 3190353 * q^7 - 33093708 * q^8 + 233430375 * q^9	\( 61 q - 857 q^{2} - 3932 q^{3} + 952767 q^{4} - 439140 q^{5} + 743647 q^{6} - 3190353 q^{7} - 33093708 q^{8} + 233430375 q^{9} - 63234482 q^{10} - 103748368 q^{11} - 331520313 q^{12} - 313165161 q^{13} - 755555817 q^{14} - 674398526 q^{15} + 14512908187 q^{16} - 12083282787 q^{17} - 13168798944 q^{18} - 5361319119 q^{19} - 9305646747 q^{20} - 16461308876 q^{21} - 28941029471 q^{22} - 66168004047 q^{23} + 7802762994 q^{24} + 303234371695 q^{25} + 182749185334 q^{26} - 156925014338 q^{27} - 664627255237 q^{28} - 645743643657 q^{29} - 1069618618594 q^{30} - 122874478996 q^{31} - 269627394831 q^{32} + 46150978058 q^{33} + 969116824174 q^{34} - 478522677982 q^{35} + 4223214984684 q^{36} + 819999551780 q^{37} - 1018697698883 q^{38} - 991652931072 q^{39} - 6174778893965 q^{40} - 7325440107283 q^{41} - 9956139869801 q^{42} - 8612850695736 q^{43} - 13352142895690 q^{44} - 15559896379366 q^{45} - 32065613137770 q^{46} - 15984352430276 q^{47} - 41506324107117 q^{48} + 17231550044622 q^{49} - 33888000032918 q^{50} - 27907219770060 q^{51} - 57828879269473 q^{52} - 37355418884312 q^{53} - 49810074049935 q^{54} - 46090202313238 q^{55} - 31772217542854 q^{56} - 57782774436846 q^{57} - 36740035491030 q^{58} - 41266858463091 q^{59} + 44989673695855 q^{60} - 45509082837011 q^{61} + 9938607229349 q^{62} + 47160755658129 q^{63} + 422835893804094 q^{64} - 177125638146712 q^{65} + 310487514411959 q^{66} + 91080256620398 q^{67} - 256019865760105 q^{68} + 80891639918642 q^{69} + 384378270951236 q^{70} - 46207729769832 q^{71} - 56835727444502 q^{72} - 114864967341268 q^{73} + 673296051484809 q^{74} + 251412324545408 q^{75} - 92392796537324 q^{76} - 426424980478584 q^{77} + 860430952610076 q^{78} + 27257492827013 q^{79} + 12\!\cdots\!86 q^{80}+ \cdots - 24\!\cdots\!92 q^{99}+O(q^{100}) \) 61 * q - 857 * q^2 - 3932 * q^3 + 952767 * q^4 - 439140 * q^5 + 743647 * q^6 - 3190353 * q^7 - 33093708 * q^8 + 233430375 * q^9 - 63234482 * q^10 - 103748368 * q^11 - 331520313 * q^12 - 313165161 * q^13 - 755555817 * q^14 - 674398526 * q^15 + 14512908187 * q^16 - 12083282787 * q^17 - 13168798944 * q^18 - 5361319119 * q^19 - 9305646747 * q^20 - 16461308876 * q^21 - 28941029471 * q^22 - 66168004047 * q^23 + 7802762994 * q^24 + 303234371695 * q^25 + 182749185334 * q^26 - 156925014338 * q^27 - 664627255237 * q^28 - 645743643657 * q^29 - 1069618618594 * q^30 - 122874478996 * q^31 - 269627394831 * q^32 + 46150978058 * q^33 + 969116824174 * q^34 - 478522677982 * q^35 + 4223214984684 * q^36 + 819999551780 * q^37 - 1018697698883 * q^38 - 991652931072 * q^39 - 6174778893965 * q^40 - 7325440107283 * q^41 - 9956139869801 * q^42 - 8612850695736 * q^43 - 13352142895690 * q^44 - 15559896379366 * q^45 - 32065613137770 * q^46 - 15984352430276 * q^47 - 41506324107117 * q^48 + 17231550044622 * q^49 - 33888000032918 * q^50 - 27907219770060 * q^51 - 57828879269473 * q^52 - 37355418884312 * q^53 - 49810074049935 * q^54 - 46090202313238 * q^55 - 31772217542854 * q^56 - 57782774436846 * q^57 - 36740035491030 * q^58 - 41266858463091 * q^59 + 44989673695855 * q^60 - 45509082837011 * q^61 + 9938607229349 * q^62 + 47160755658129 * q^63 + 422835893804094 * q^64 - 177125638146712 * q^65 + 310487514411959 * q^66 + 91080256620398 * q^67 - 256019865760105 * q^68 + 80891639918642 * q^69 + 384378270951236 * q^70 - 46207729769832 * q^71 - 56835727444502 * q^72 - 114864967341268 * q^73 + 673296051484809 * q^74 + 251412324545408 * q^75 - 92392796537324 * q^76 - 426424980478584 * q^77 + 860430952610076 * q^78 + 27257492827013 * q^79 + 1261262804917286 * q^80 + 970042227882689 * q^81 + 1867558085467524 * q^82 - 67054622423409 * q^83 + 2889728360587655 * q^84 + 35781044772768 * q^85 + 935963078541511 * q^86 + 200876689178626 * q^87 + 748805894780353 * q^88 - 584912027466128 * q^89 + 1478961422736826 * q^90 + 1070772310581326 * q^91 - 630612477352560 * q^92 - 625157665750792 * q^93 + 1462001220045896 * q^94 - 1523943242724438 * q^95 + 1053537706701997 * q^96 - 786010536406413 * q^97 - 5974525724410954 * q^98 - 2483530260497592 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more