LMFDB - Embedded newform 197.14.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,14,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	197.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:	$211.244930035$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-146.034 q^{2} -203.966 q^{3} +13133.8 q^{4} -50263.7 q^{5} +29785.9 q^{6} -418854. q^{7} -721672. q^{8} -1.55272e6 q^{9} +7.34019e6 q^{10} -3.57704e6 q^{11} -2.67886e6 q^{12} -3.21000e7 q^{13} +6.11668e7 q^{14} +1.02521e7 q^{15} -2.20388e6 q^{16} -7.27608e7 q^{17} +2.26749e8 q^{18} -7.39711e7 q^{19} -6.60155e8 q^{20} +8.54321e7 q^{21} +5.22368e8 q^{22} -6.55864e8 q^{23} +1.47197e8 q^{24} +1.30574e9 q^{25} +4.68767e9 q^{26} +6.41891e8 q^{27} -5.50116e9 q^{28} -3.76330e9 q^{29} -1.49715e9 q^{30} -3.37261e9 q^{31} +6.23378e9 q^{32} +7.29595e8 q^{33} +1.06255e10 q^{34} +2.10532e10 q^{35} -2.03932e10 q^{36} +2.33861e10 q^{37} +1.08023e10 q^{38} +6.54731e9 q^{39} +3.62739e10 q^{40} -1.28633e10 q^{41} -1.24760e10 q^{42} +1.05664e10 q^{43} -4.69802e10 q^{44} +7.80455e10 q^{45} +9.57782e10 q^{46} -2.28358e10 q^{47} +4.49518e8 q^{48} +7.85499e10 q^{49} -1.90682e11 q^{50} +1.48407e10 q^{51} -4.21595e11 q^{52} +1.04399e11 q^{53} -9.37376e10 q^{54} +1.79795e11 q^{55} +3.02275e11 q^{56} +1.50876e10 q^{57} +5.49568e11 q^{58} -1.62045e11 q^{59} +1.34649e11 q^{60} -4.12566e11 q^{61} +4.92514e11 q^{62} +6.50364e11 q^{63} -8.92287e11 q^{64} +1.61346e12 q^{65} -1.06545e11 q^{66} -7.46287e11 q^{67} -9.55627e11 q^{68} +1.33774e11 q^{69} -3.07447e12 q^{70} -1.39356e12 q^{71} +1.12056e12 q^{72} -1.34651e12 q^{73} -3.41516e12 q^{74} -2.66326e11 q^{75} -9.71524e11 q^{76} +1.49826e12 q^{77} -9.56127e11 q^{78} -1.02991e12 q^{79} +1.10775e11 q^{80} +2.34461e12 q^{81} +1.87847e12 q^{82} -1.85519e12 q^{83} +1.12205e12 q^{84} +3.65723e12 q^{85} -1.54305e12 q^{86} +7.67586e11 q^{87} +2.58145e12 q^{88} +7.32016e12 q^{89} -1.13973e13 q^{90} +1.34452e13 q^{91} -8.61400e12 q^{92} +6.87898e11 q^{93} +3.33480e12 q^{94} +3.71806e12 q^{95} -1.27148e12 q^{96} -9.99692e12 q^{97} -1.14709e13 q^{98} +5.55414e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14}+ \cdots - 8666459567773 q^{99}+O(q^{100}) $ 104 * q - 128 * q^2 - 8020 * q^3 + 409600 * q^4 - 99004 * q^5 - 83328 * q^6 - 2084037 * q^7 - 2111301 * q^8 + 51549776 * q^9 - 9626347 * q^10 - 10688800 * q^11 - 68157440 * q^12 - 94762650 * q^13 - 52465903 * q^14 - 186128761 * q^15 + 1543503872 * q^16 - 109572251 * q^17 - 449658263 * q^18 - 1495268031 * q^19 - 1194030741 * q^20 - 832275538 * q^21 - 2695120703 * q^22 - 2632554532 * q^23 - 190649667 * q^24 + 22696779124 * q^25 - 2460454754 * q^26 - 16267542277 * q^27 - 18137835250 * q^28 + 47556769 * q^29 - 9613748117 * q^30 - 24774628288 * q^31 - 29246249180 * q^32 - 42367036666 * q^33 - 39395206606 * q^34 - 26216433864 * q^35 + 190013501626 * q^36 - 82419664050 * q^37 - 34593622142 * q^38 - 39498281801 * q^39 - 150303128514 * q^40 - 25862853768 * q^41 - 138889965149 * q^42 - 258164897781 * q^43 - 197365738094 * q^44 - 240782892021 * q^45 - 218441397971 * q^46 - 208905762731 * q^47 - 664063830814 * q^48 + 1113758315863 * q^49 - 1516068087607 * q^50 - 1019253294393 * q^51 - 1162941441840 * q^52 + 161684855900 * q^53 + 1679137315823 * q^54 - 557952233701 * q^55 + 2842561845328 * q^56 + 801593765429 * q^57 - 7249760433 * q^58 - 775487110641 * q^59 - 57598844627 * q^60 - 36786715662 * q^61 + 681529132643 * q^62 - 4349115033663 * q^63 + 4600420238797 * q^64 - 2531819073161 * q^65 - 3958922748734 * q^66 - 7314072405766 * q^67 - 10297353950393 * q^68 - 2089200206275 * q^69 - 14268943913713 * q^70 - 6055724651085 * q^71 - 26860198563805 * q^72 - 7572811533391 * q^73 - 11175265675817 * q^74 - 24431657592434 * q^75 - 26425925198106 * q^76 - 9735327037686 * q^77 - 35310017230907 * q^78 - 8981210762721 * q^79 - 25913753436330 * q^80 + 15437375349812 * q^81 - 19721330628227 * q^82 - 22209909714532 * q^83 - 18837805278768 * q^84 - 5905005171430 * q^85 - 8913876797772 * q^86 - 7341562344401 * q^87 - 35154329886441 * q^88 - 4646484034146 * q^89 + 9564902968095 * q^90 - 22752431457047 * q^91 - 13601121953458 * q^92 - 9615114240293 * q^93 + 15352521272967 * q^94 + 5258551767043 * q^95 + 87277848810881 * q^96 - 42298840804040 * q^97 + 27000102375354 * q^98 - 8666459567773 * q^99

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 $

$2$	−146.034	−1.61346	−0.806729	−	0.590921i	$-0.798764\pi$
$2$	−146.034	−1.61346	−0.806729	+	0.590921i	$0.798764\pi$
$3$	−203.966	−0.161536	−0.0807682	−	0.996733i	$-0.525737\pi$
$3$	−203.966	−0.161536	−0.0807682	+	0.996733i	$0.525737\pi$
$4$	13133.8	1.60325
$5$	−50263.7	−1.43863	−0.719316	−	0.694683i	$-0.755545\pi$
$5$	−50263.7	−1.43863	−0.719316	+	0.694683i	$0.755545\pi$
$6$	29785.9	0.260632
$7$	−418854.	−1.34563	−0.672815	−	0.739811i	$-0.734915\pi$
$7$	−418854.	−1.34563	−0.672815	+	0.739811i	$0.734915\pi$
$8$	−721672.	−0.973318
$9$	−1.55272e6	−0.973906
$10$	7.34019e6	2.32117
$11$	−3.57704e6	−0.608795	−0.304397	−	0.952545i	$-0.598455\pi$
$11$	−3.57704e6	−0.608795	−0.304397	+	0.952545i	$0.598455\pi$
$12$	−2.67886e6	−0.258983
$13$	−3.21000e7	−1.84447	−0.922237	−	0.386624i	$-0.873641\pi$
$13$	−3.21000e7	−1.84447	−0.922237	+	0.386624i	$0.873641\pi$
$14$	6.11668e7	2.17112
$15$	1.02521e7	0.232391
$16$	−2.20388e6	−0.0328404
$17$	−7.27608e7	−0.731104	−0.365552	−	0.930791i	$-0.619120\pi$
$17$	−7.27608e7	−0.731104	−0.365552	+	0.930791i	$0.619120\pi$
$18$	2.26749e8	1.57136
$19$	−7.39711e7	−0.360715	−0.180357	−	0.983601i	$-0.557725\pi$
$19$	−7.39711e7	−0.360715	−0.180357	+	0.983601i	$0.557725\pi$
$20$	−6.60155e8	−2.30649
$21$	8.54321e7	0.217368
$22$	5.22368e8	0.982266
$23$	−6.55864e8	−0.923811	−0.461905	−	0.886929i	$-0.652834\pi$
$23$	−6.55864e8	−0.923811	−0.461905	+	0.886929i	$0.652834\pi$
$24$	1.47197e8	0.157226
$25$	1.30574e9	1.06966
$26$	4.68767e9	2.97598
$27$	6.41891e8	0.318857
$28$	−5.50116e9	−2.15738
$29$	−3.76330e9	−1.17485	−0.587424	−	0.809279i	$-0.699858\pi$
$29$	−3.76330e9	−1.17485	−0.587424	+	0.809279i	$0.699858\pi$
$30$	−1.49715e9	−0.374954
$31$	−3.37261e9	−0.682519	−0.341259	−	0.939969i	$-0.610853\pi$
$31$	−3.37261e9	−0.682519	−0.341259	+	0.939969i	$0.610853\pi$
$32$	6.23378e9	1.02631
$33$	7.29595e8	0.0983425
$34$	1.06255e10	1.17961
$35$	2.10532e10	1.93587
$36$	−2.03932e10	−1.56141
$37$	2.33861e10	1.49846	0.749232	−	0.662307i	$-0.230423\pi$
$37$	2.33861e10	1.49846	0.749232	+	0.662307i	$0.230423\pi$
$38$	1.08023e10	0.581998
$39$	6.54731e9	0.297950
$40$	3.62739e10	1.40025
$41$	−1.28633e10	−0.422918	−0.211459	−	0.977387i	$-0.567822\pi$
$41$	−1.28633e10	−0.422918	−0.211459	+	0.977387i	$0.567822\pi$
$42$	−1.24760e10	−0.350715
$43$	1.05664e10	0.254907	0.127454	−	0.991845i	$-0.459320\pi$
$43$	1.05664e10	0.254907	0.127454	+	0.991845i	$0.459320\pi$
$44$	−4.69802e10	−0.976050
$45$	7.80455e10	1.40109
$46$	9.57782e10	1.49053
$47$	−2.28358e10	−0.309016	−0.154508	−	0.987992i	$-0.549379\pi$
$47$	−2.28358e10	−0.309016	−0.154508	+	0.987992i	$0.549379\pi$
$48$	4.49518e8	0.00530492
$49$	7.85499e10	0.810721
$50$	−1.90682e11	−1.72585
$51$	1.48407e10	0.118100
$52$	−4.21595e11	−2.95715
$53$	1.04399e11	0.647000	0.323500	−	0.946228i	$-0.395140\pi$
$53$	1.04399e11	0.647000	0.323500	+	0.946228i	$0.395140\pi$
$54$	−9.37376e10	−0.514463
$55$	1.79795e11	0.875832
$56$	3.02275e11	1.30973
$57$	1.50876e10	0.0582685
$58$	5.49568e11	1.89557
$59$	−1.62045e11	−0.500146	−0.250073	−	0.968227i	$-0.580455\pi$
$59$	−1.62045e11	−0.500146	−0.250073	+	0.968227i	$0.580455\pi$
$60$	1.34649e11	0.372581
$61$	−4.12566e11	−1.02530	−0.512648	−	0.858599i	$-0.671335\pi$
$61$	−4.12566e11	−1.02530	−0.512648	+	0.858599i	$0.671335\pi$
$62$	4.92514e11	1.10122
$63$	6.50364e11	1.31052
$64$	−8.92287e11	−1.62306
$65$	1.61346e12	2.65352
$66$	−1.06545e11	−0.158672
$67$	−7.46287e11	−1.00791	−0.503953	−	0.863731i	$-0.668121\pi$
$67$	−7.46287e11	−1.00791	−0.503953	+	0.863731i	$0.668121\pi$
$68$	−9.55627e11	−1.17214
$69$	1.33774e11	0.149229
$70$	−3.07447e12	−3.12344
$71$	−1.39356e12	−1.29106	−0.645531	−	0.763734i	$-0.723364\pi$
$71$	−1.39356e12	−1.29106	−0.645531	+	0.763734i	$0.723364\pi$
$72$	1.12056e12	0.947921
$73$	−1.34651e12	−1.04139	−0.520693	−	0.853744i	$-0.674326\pi$
$73$	−1.34651e12	−1.04139	−0.520693	+	0.853744i	$0.674326\pi$
$74$	−3.41516e12	−2.41771
$75$	−2.66326e11	−0.172789
$76$	−9.71524e11	−0.578316
$77$	1.49826e12	0.819213
$78$	−9.56127e11	−0.480730
$79$	−1.02991e12	−0.476675	−0.238338	−	0.971182i	$-0.576602\pi$
$79$	−1.02991e12	−0.476675	−0.238338	+	0.971182i	$0.576602\pi$
$80$	1.10775e11	0.0472453
$81$	2.34461e12	0.922399
$82$	1.87847e12	0.682361
$83$	−1.85519e12	−0.622847	−0.311424	−	0.950271i	$-0.600806\pi$
$83$	−1.85519e12	−0.622847	−0.311424	+	0.950271i	$0.600806\pi$
$84$	1.12205e12	0.348495
$85$	3.65723e12	1.05179
$86$	−1.54305e12	−0.411282
$87$	7.67586e11	0.189781
$88$	2.58145e12	0.592551
$89$	7.32016e12	1.56130	0.780648	−	0.624971i	$-0.214889\pi$
$89$	7.32016e12	1.56130	0.780648	+	0.624971i	$0.214889\pi$
$90$	−1.13973e13	−2.26060
$91$	1.34452e13	2.48198
$92$	−8.61400e12	−1.48110
$93$	6.87898e11	0.110252
$94$	3.33480e12	0.498584
$95$	3.71806e12	0.518936
$96$	−1.27148e12	−0.165786
$97$	−9.99692e12	−1.21857	−0.609284	−	0.792952i	$-0.708543\pi$
$97$	−9.99692e12	−1.21857	−0.609284	+	0.792952i	$0.708543\pi$
$98$	−1.14709e13	−1.30806
$99$	5.55414e12	0.592909
$100$	1.71493e13	1.71493
$101$	7.93968e12	0.744242	0.372121	−	0.928184i	$-0.378631\pi$
$101$	7.93968e12	0.744242	0.372121	+	0.928184i	$0.378631\pi$
$102$	−2.16725e12	−0.190549
$103$	1.36027e13	1.12249	0.561244	−	0.827650i	$-0.310323\pi$
$103$	1.36027e13	1.12249	0.561244	+	0.827650i	$0.310323\pi$
$104$	2.31656e13	1.79526
$105$	−4.29414e12	−0.312713
$106$	−1.52458e13	−1.04391
$107$	−9.30370e11	−0.0599323	−0.0299662	−	0.999551i	$-0.509540\pi$
$107$	−9.30370e11	−0.0599323	−0.0299662	+	0.999551i	$0.509540\pi$
$108$	8.43048e12	0.511208
$109$	2.77639e13	1.58565	0.792825	−	0.609449i	$-0.208609\pi$
$109$	2.77639e13	1.58565	0.792825	+	0.609449i	$0.208609\pi$
$110$	−2.62561e13	−1.41312
$111$	−4.76997e12	−0.242056
$112$	9.23106e11	0.0441911
$113$	−3.76219e12	−0.169993	−0.0849965	−	0.996381i	$-0.527088\pi$
$113$	−3.76219e12	−0.169993	−0.0849965	+	0.996381i	$0.527088\pi$
$114$	−2.20330e12	−0.0940139
$115$	3.29662e13	1.32902
$116$	−4.94265e13	−1.88357
$117$	4.98423e13	1.79635
$118$	2.36640e13	0.806965
$119$	3.04762e13	0.983796
$120$	−7.39865e12	−0.226191
$121$	−2.17275e13	−0.629369
$122$	6.02484e13	1.65427
$123$	2.62367e12	0.0683167
$124$	−4.42952e13	−1.09425
$125$	−4.27416e12	−0.100216
$126$	−9.49750e13	−2.11447
$127$	6.61939e13	1.39989	0.699945	−	0.714197i	$-0.253208\pi$
$127$	6.61939e13	1.39989	0.699945	+	0.714197i	$0.253208\pi$
$128$	7.92368e13	1.59244
$129$	−2.15519e12	−0.0411768
$130$	−2.35620e14	−4.28134
$131$	−2.16973e13	−0.375096	−0.187548	−	0.982255i	$-0.560054\pi$
$131$	−2.16973e13	−0.375096	−0.187548	+	0.982255i	$0.560054\pi$
$132$	9.58237e12	0.157668
$133$	3.09831e13	0.485389
$134$	1.08983e14	1.62621
$135$	−3.22638e13	−0.458718
$136$	5.25094e13	0.711597
$137$	3.31332e13	0.428134	0.214067	−	0.976819i	$-0.431329\pi$
$137$	3.31332e13	0.428134	0.214067	+	0.976819i	$0.431329\pi$
$138$	−1.95355e13	−0.240775
$139$	−1.28112e13	−0.150658	−0.0753290	−	0.997159i	$-0.524001\pi$
$139$	−1.28112e13	−0.150658	−0.0753290	+	0.997159i	$0.524001\pi$
$140$	2.76509e14	3.10368
$141$	4.65774e12	0.0499173
$142$	2.03507e14	2.08307
$143$	1.14823e14	1.12291
$144$	3.42202e12	0.0319835
$145$	1.89157e14	1.69017
$146$	1.96636e14	1.68023
$147$	−1.60215e13	−0.130961
$148$	3.07149e14	2.40241
$149$	2.35853e13	0.176576	0.0882878	−	0.996095i	$-0.471860\pi$
$149$	2.35853e13	0.176576	0.0882878	+	0.996095i	$0.471860\pi$
$150$	3.88926e13	0.278788
$151$	−3.09147e13	−0.212234	−0.106117	−	0.994354i	$-0.533842\pi$
$151$	−3.09147e13	−0.212234	−0.106117	+	0.994354i	$0.533842\pi$
$152$	5.33829e13	0.351090
$153$	1.12977e14	0.712027
$154$	−2.18796e14	−1.32177
$155$	1.69520e14	0.981893
$156$	8.59912e13	0.477688
$157$	−2.65473e14	−1.41473	−0.707363	−	0.706851i	$-0.750115\pi$
$157$	−2.65473e14	−1.41473	−0.707363	+	0.706851i	$0.750115\pi$
$158$	1.50401e14	0.769096
$159$	−2.12939e13	−0.104514
$160$	−3.13333e14	−1.47647
$161$	2.74712e14	1.24311
$162$	−3.42393e14	−1.48825
$163$	1.66316e14	0.694566	0.347283	−	0.937760i	$-0.387104\pi$
$163$	1.66316e14	0.694566	0.347283	+	0.937760i	$0.387104\pi$
$164$	−1.68944e14	−0.678044
$165$	−3.66721e13	−0.141479
$166$	2.70921e14	1.00494
$167$	2.03524e14	0.726035	0.363018	−	0.931782i	$-0.381746\pi$
$167$	2.03524e14	0.726035	0.363018	+	0.931782i	$0.381746\pi$
$168$	−6.16540e13	−0.211568
$169$	7.27532e14	2.40209
$170$	−5.34078e14	−1.69702
$171$	1.14857e14	0.351302
$172$	1.38777e14	0.408680
$173$	−2.86935e13	−0.0813738	−0.0406869	−	0.999172i	$-0.512955\pi$
$173$	−2.86935e13	−0.0813738	−0.0406869	+	0.999172i	$0.512955\pi$
$174$	−1.12093e14	−0.306203
$175$	−5.46914e14	−1.43937
$176$	7.88337e12	0.0199931
$177$	3.30517e13	0.0807918
$178$	−1.06899e15	−2.51909
$179$	−9.20345e12	−0.0209125	−0.0104563	−	0.999945i	$-0.503328\pi$
$179$	−9.20345e12	−0.0209125	−0.0104563	+	0.999945i	$0.503328\pi$
$180$	1.02504e15	2.24630
$181$	−6.16406e13	−0.130304	−0.0651518	−	0.997875i	$-0.520753\pi$
$181$	−6.16406e13	−0.130304	−0.0651518	+	0.997875i	$0.520753\pi$
$182$	−1.96345e15	−4.00457
$183$	8.41495e13	0.165622
$184$	4.73319e14	0.899162
$185$	−1.17547e15	−2.15574
$186$	−1.00456e14	−0.177886
$187$	2.60268e14	0.445093
$188$	−2.99922e14	−0.495429
$189$	−2.68859e14	−0.429064
$190$	−5.42962e14	−0.837281
$191$	−7.53720e14	−1.12329	−0.561647	−	0.827377i	$-0.689832\pi$
$191$	−7.53720e14	−1.12329	−0.561647	+	0.827377i	$0.689832\pi$
$192$	1.81996e14	0.262183
$193$	−9.91457e14	−1.38087	−0.690433	−	0.723396i	$-0.742580\pi$
$193$	−9.91457e14	−1.38087	−0.690433	+	0.723396i	$0.742580\pi$
$194$	1.45989e15	1.96611
$195$	−3.29092e14	−0.428640
$196$	1.03166e15	1.29979
$197$	−5.84517e13	−0.0712470
$197$	−5.84517e13	−0.0712470
$198$	−8.11091e14	−0.956634
$199$	−9.04020e14	−1.03189	−0.515944	−	0.856622i	$-0.672559\pi$
$199$	−9.04020e14	−1.03189	−0.515944	+	0.856622i	$0.672559\pi$
$200$	−9.42314e14	−1.04112
$201$	1.52217e14	0.162813
$202$	−1.15946e15	−1.20080
$203$	1.57627e15	1.58091
$204$	1.94916e14	0.189344
$205$	6.46556e14	0.608424
$206$	−1.98645e15	−1.81109
$207$	1.01837e15	0.899705
$208$	7.07446e13	0.0605733
$209$	2.64598e14	0.219601
$210$	6.27088e14	0.504549
$211$	1.90858e15	1.48893	0.744466	−	0.667660i	$-0.232704\pi$
$211$	1.90858e15	1.48893	0.744466	+	0.667660i	$0.232704\pi$
$212$	1.37116e15	1.03730
$213$	2.84239e14	0.208553
$214$	1.35865e14	0.0966983
$215$	−5.31107e14	−0.366718
$216$	−4.63235e14	−0.310350
$217$	1.41263e15	0.918418
$218$	−4.05446e15	−2.55838
$219$	2.74643e14	0.168222
$220$	2.36140e15	1.40418
$221$	2.33562e15	1.34850
$222$	6.96577e14	0.390548
$223$	−2.49410e15	−1.35810	−0.679051	−	0.734091i	$-0.737608\pi$
$223$	−2.49410e15	−1.35810	−0.679051	+	0.734091i	$0.737608\pi$
$224$	−2.61104e15	−1.38103
$225$	−2.02745e15	−1.04175
$226$	5.49406e14	0.274277
$227$	3.25549e14	0.157924	0.0789620	−	0.996878i	$-0.474839\pi$
$227$	3.25549e14	0.157924	0.0789620	+	0.996878i	$0.474839\pi$
$228$	1.98158e14	0.0934190
$229$	1.09573e15	0.502081	0.251040	−	0.967977i	$-0.419227\pi$
$229$	1.09573e15	0.502081	0.251040	+	0.967977i	$0.419227\pi$
$230$	−4.81417e15	−2.14432
$231$	−3.05594e14	−0.132333
$232$	2.71587e15	1.14350
$233$	−2.46372e15	−1.00874	−0.504368	−	0.863489i	$-0.668275\pi$
$233$	−2.46372e15	−1.00874	−0.504368	+	0.863489i	$0.668275\pi$
$234$	−7.27865e15	−2.89833
$235$	1.14781e15	0.444560
$236$	−2.12827e15	−0.801859
$237$	2.10067e14	0.0770004
$238$	−4.45055e15	−1.58731
$239$	1.31872e15	0.457686	0.228843	−	0.973463i	$-0.426506\pi$
$239$	1.31872e15	0.457686	0.228843	+	0.973463i	$0.426506\pi$
$240$	−2.25944e13	−0.00763183
$241$	2.24478e15	0.738011	0.369006	−	0.929427i	$-0.379698\pi$
$241$	2.24478e15	0.738011	0.369006	+	0.929427i	$0.379698\pi$
$242$	3.17295e15	1.01546
$243$	−1.50160e15	−0.467858
$244$	−5.41856e15	−1.64380
$245$	−3.94821e15	−1.16633
$246$	−3.83145e14	−0.110226
$247$	2.37447e15	0.665329
$248$	2.43392e15	0.664308
$249$	3.78397e14	0.100612
$250$	6.24172e14	0.161694
$251$	−2.36311e15	−0.596491	−0.298246	−	0.954489i	$-0.596401\pi$
$251$	−2.36311e15	−0.596491	−0.298246	+	0.954489i	$0.596401\pi$
$252$	8.54176e15	2.10109
$253$	2.34605e15	0.562411
$254$	−9.66653e15	−2.25866
$255$	−7.45951e14	−0.169902
$256$	−4.26162e15	−0.946270
$257$	8.01003e15	1.73408	0.867040	−	0.498239i	$-0.166020\pi$
$257$	8.01003e15	1.73408	0.867040	+	0.498239i	$0.166020\pi$
$258$	3.14730e14	0.0664370
$259$	−9.79537e15	−2.01638
$260$	2.11909e16	4.25425
$261$	5.84335e15	1.14419
$262$	3.16853e15	0.605202
$263$	−3.03022e15	−0.564627	−0.282314	−	0.959322i	$-0.591102\pi$
$263$	−3.03022e15	−0.564627	−0.282314	+	0.959322i	$0.591102\pi$
$264$	−5.26528e14	−0.0957185
$265$	−5.24749e15	−0.930794
$266$	−4.52458e15	−0.783155
$267$	−1.49307e15	−0.252206
$268$	−9.80160e15	−1.61592
$269$	9.34088e15	1.50313	0.751567	−	0.659657i	$-0.229298\pi$
$269$	9.34088e15	1.50313	0.751567	+	0.659657i	$0.229298\pi$
$270$	4.71160e15	0.740123
$271$	1.00893e16	1.54725	0.773627	−	0.633641i	$-0.218440\pi$
$271$	1.00893e16	1.54725	0.773627	+	0.633641i	$0.218440\pi$
$272$	1.60356e14	0.0240098
$273$	−2.74237e15	−0.400930
$274$	−4.83856e15	−0.690776
$275$	−4.67067e15	−0.651204
$276$	1.75697e15	0.239251
$277$	−1.38991e16	−1.84870	−0.924351	−	0.381542i	$-0.875393\pi$
$277$	−1.38991e16	−1.84870	−0.924351	+	0.381542i	$0.875393\pi$
$278$	1.87086e15	0.243081
$279$	5.23672e15	0.664709
$280$	−1.51935e16	−1.88421
$281$	−5.72722e15	−0.693989	−0.346994	−	0.937867i	$-0.612798\pi$
$281$	−5.72722e15	−0.693989	−0.346994	+	0.937867i	$0.612798\pi$
$282$	−6.80186e14	−0.0805395
$283$	−1.05835e16	−1.22467	−0.612334	−	0.790599i	$-0.709769\pi$
$283$	−1.05835e16	−1.22467	−0.612334	+	0.790599i	$0.709769\pi$
$284$	−1.83028e16	−2.06989
$285$	−7.58360e14	−0.0838269
$286$	−1.67680e16	−1.81176
$287$	5.38784e15	0.569092
$288$	−9.67932e15	−0.999525
$289$	−4.61045e15	−0.465486
$290$	−2.76233e16	−2.72702
$291$	2.03903e15	0.196843
$292$	−1.76849e16	−1.66960
$293$	−2.10081e16	−1.93976	−0.969878	−	0.243591i	$-0.921675\pi$
$293$	−2.10081e16	−1.93976	−0.969878	+	0.243591i	$0.921675\pi$
$294$	2.33968e15	0.211300
$295$	8.14497e15	0.719526
$296$	−1.68771e16	−1.45848
$297$	−2.29607e15	−0.194119
$298$	−3.44425e15	−0.284897
$299$	2.10532e16	1.70395
$300$	−3.49788e15	−0.277024
$301$	−4.42578e15	−0.343011
$302$	4.51459e15	0.342431
$303$	−1.61943e15	−0.120222
$304$	1.63024e14	0.0118460
$305$	2.07371e16	1.47502
$306$	−1.64985e16	−1.14883
$307$	−1.52897e16	−1.04232	−0.521158	−	0.853460i	$-0.674500\pi$
$307$	−1.52897e16	−1.04232	−0.521158	+	0.853460i	$0.674500\pi$
$308$	1.96778e16	1.31340
$309$	−2.77448e15	−0.181323
$310$	−2.47556e16	−1.58424
$311$	1.80466e16	1.13098	0.565488	−	0.824757i	$-0.308688\pi$
$311$	1.80466e16	1.13098	0.565488	+	0.824757i	$0.308688\pi$
$312$	−4.72501e15	−0.290000
$313$	−2.53518e15	−0.152395	−0.0761975	−	0.997093i	$-0.524278\pi$
$313$	−2.53518e15	−0.152395	−0.0761975	+	0.997093i	$0.524278\pi$
$314$	3.87679e16	2.28260
$315$	−3.26897e16	−1.88535
$316$	−1.35266e16	−0.764229
$317$	−3.87801e15	−0.214646	−0.107323	−	0.994224i	$-0.534228\pi$
$317$	−3.87801e15	−0.214646	−0.107323	+	0.994224i	$0.534228\pi$
$318$	3.10963e15	0.168629
$319$	1.34615e16	0.715241
$320$	4.48497e16	2.33499
$321$	1.89764e14	0.00968125
$322$	−4.01171e16	−2.00570
$323$	5.38220e15	0.263720
$324$	3.07937e16	1.47884
$325$	−4.19141e16	−1.97296
$326$	−2.42877e16	−1.12065
$327$	−5.66289e15	−0.256140
$328$	9.28307e15	0.411634
$329$	9.56489e15	0.415821
$330$	5.35537e15	0.228270
$331$	2.14217e15	0.0895308	0.0447654	−	0.998998i	$-0.485746\pi$
$331$	2.14217e15	0.0895308	0.0447654	+	0.998998i	$0.485746\pi$
$332$	−2.43658e16	−0.998580
$333$	−3.63121e16	−1.45936
$334$	−2.97213e16	−1.17143
$335$	3.75112e16	1.45000
$336$	−1.88282e14	−0.00713846
$337$	−4.65719e16	−1.73193	−0.865963	−	0.500108i	$-0.833294\pi$
$337$	−4.65719e16	−1.73193	−0.865963	+	0.500108i	$0.833294\pi$
$338$	−1.06244e17	−3.87567
$339$	7.67360e14	0.0274600
$340$	4.80334e16	1.68628
$341$	1.20639e16	0.415514
$342$	−1.67729e16	−0.566812
$343$	7.68141e15	0.254700
$344$	−7.62548e15	−0.248106
$345$	−6.72399e15	−0.214686
$346$	4.19022e15	0.131293
$347$	5.68681e16	1.74875	0.874374	−	0.485252i	$-0.161272\pi$
$347$	5.68681e16	1.74875	0.874374	+	0.485252i	$0.161272\pi$
$348$	1.00813e16	0.304266
$349$	−1.79320e16	−0.531206	−0.265603	−	0.964083i	$-0.585571\pi$
$349$	−1.79320e16	−0.531206	−0.265603	+	0.964083i	$0.585571\pi$
$350$	7.98678e16	2.32236
$351$	−2.06047e16	−0.588125
$352$	−2.22985e16	−0.624809
$353$	−1.38653e16	−0.381411	−0.190705	−	0.981647i	$-0.561077\pi$
$353$	−1.38653e16	−0.381411	−0.190705	+	0.981647i	$0.561077\pi$
$354$	−4.82666e15	−0.130354
$355$	7.00456e16	1.85736
$356$	9.61416e16	2.50315
$357$	−6.21611e15	−0.158919
$358$	1.34401e15	0.0337415
$359$	7.30117e16	1.80002	0.900012	−	0.435864i	$-0.143557\pi$
$359$	7.30117e16	1.80002	0.900012	+	0.435864i	$0.143557\pi$
$360$	−5.63233e16	−1.36371
$361$	−3.65813e16	−0.869885
$362$	9.00161e15	0.210239
$363$	4.43168e15	0.101666
$364$	1.76587e17	3.97923
$365$	6.76807e16	1.49817
$366$	−1.22886e16	−0.267225
$367$	−7.32278e16	−1.56440	−0.782198	−	0.623030i	$-0.785901\pi$
$367$	−7.32278e16	−1.56440	−0.782198	+	0.623030i	$0.785901\pi$
$368$	1.44545e15	0.0303383
$369$	1.99731e16	0.411883
$370$	1.71658e17	3.47819
$371$	−4.37281e16	−0.870622
$372$	9.03473e15	0.176761
$373$	5.75065e16	1.10563	0.552814	−	0.833304i	$-0.313554\pi$
$373$	5.75065e16	1.10563	0.552814	+	0.833304i	$0.313554\pi$
$374$	−3.80079e16	−0.718139
$375$	8.71785e14	0.0161885
$376$	1.64800e16	0.300771
$377$	1.20802e17	2.16698
$378$	3.92624e16	0.692278
$379$	1.37477e16	0.238272	0.119136	−	0.992878i	$-0.461987\pi$
$379$	1.37477e16	0.238272	0.119136	+	0.992878i	$0.461987\pi$
$380$	4.88324e16	0.831983
$381$	−1.35013e16	−0.226133
$382$	1.10068e17	1.81239
$383$	−1.01565e17	−1.64420	−0.822098	−	0.569345i	$-0.807197\pi$
$383$	−1.01565e17	−1.64420	−0.822098	+	0.569345i	$0.807197\pi$
$384$	−1.61616e16	−0.257236
$385$	−7.53080e16	−1.17855
$386$	1.44786e17	2.22797
$387$	−1.64067e16	−0.248256
$388$	−1.31298e17	−1.95367
$389$	−3.11554e16	−0.455891	−0.227945	−	0.973674i	$-0.573201\pi$
$389$	−3.11554e16	−0.455891	−0.227945	+	0.973674i	$0.573201\pi$
$390$	4.80585e16	0.691593
$391$	4.77212e16	0.675402
$392$	−5.66873e16	−0.789089
$393$	4.42552e15	0.0605916
$394$	8.53592e15	0.114954
$395$	5.17670e16	0.685760
$396$	7.29471e16	0.950581
$397$	−1.26117e17	−1.61673	−0.808363	−	0.588684i	$-0.799646\pi$
$397$	−1.26117e17	−1.61673	−0.808363	+	0.588684i	$0.799646\pi$
$398$	1.32017e17	1.66491
$399$	−6.31951e15	−0.0784079
$400$	−2.87769e15	−0.0351281
$401$	−2.07320e16	−0.249002	−0.124501	−	0.992219i	$-0.539733\pi$
$401$	−2.07320e16	−0.249002	−0.124501	+	0.992219i	$0.539733\pi$
$402$	−2.22289e16	−0.262693
$403$	1.08261e17	1.25889
$404$	1.04278e17	1.19321
$405$	−1.17849e17	−1.32699
$406$	−2.30189e17	−2.55073
$407$	−8.36529e16	−0.912258
$408$	−1.07102e16	−0.114949
$409$	−6.61620e16	−0.698887	−0.349443	−	0.936957i	$-0.613629\pi$
$409$	−6.61620e16	−0.698887	−0.349443	+	0.936957i	$0.613629\pi$
$410$	−9.44189e16	−0.981667
$411$	−6.75805e15	−0.0691591
$412$	1.78655e17	1.79963
$413$	6.78732e16	0.673012
$414$	−1.48717e17	−1.45164
$415$	9.32489e16	0.896048
$416$	−2.00104e17	−1.89299
$417$	2.61305e15	0.0243367
$418$	−3.86401e16	−0.354318
$419$	9.29004e16	0.838739	0.419369	−	0.907816i	$-0.362251\pi$
$419$	9.29004e16	0.838739	0.419369	+	0.907816i	$0.362251\pi$
$420$	−5.63984e16	−0.501356
$421$	1.35585e17	1.18681	0.593403	−	0.804906i	$-0.297784\pi$
$421$	1.35585e17	1.18681	0.593403	+	0.804906i	$0.297784\pi$
$422$	−2.78717e17	−2.40233
$423$	3.54577e16	0.300952
$424$	−7.53420e16	−0.629737
$425$	−9.50065e16	−0.782034
$426$	−4.15085e16	−0.336492
$427$	1.72805e17	1.37967
$428$	−1.22193e16	−0.0960865
$429$	−2.34200e16	−0.181390
$430$	7.75594e16	0.591684
$431$	−2.01800e17	−1.51641	−0.758207	−	0.652014i	$-0.773924\pi$
$431$	−2.01800e17	−1.51641	−0.758207	+	0.652014i	$0.773924\pi$
$432$	−1.41465e15	−0.0104714
$433$	−9.34070e15	−0.0681095	−0.0340548	−	0.999420i	$-0.510842\pi$
$433$	−9.34070e15	−0.0681095	−0.0340548	+	0.999420i	$0.510842\pi$
$434$	−2.06292e17	−1.48183
$435$	−3.85817e16	−0.273024
$436$	3.64645e17	2.54219
$437$	4.85150e16	0.333232
$438$	−4.01071e16	−0.271419
$439$	−1.03148e17	−0.687766	−0.343883	−	0.939012i	$-0.611742\pi$
$439$	−1.03148e17	−0.687766	−0.343883	+	0.939012i	$0.611742\pi$
$440$	−1.29753e17	−0.852463
$441$	−1.21966e17	−0.789566
$442$	−3.41079e17	−2.17576
$443$	−1.49111e17	−0.937314	−0.468657	−	0.883380i	$-0.655262\pi$
$443$	−1.49111e17	−0.937314	−0.468657	+	0.883380i	$0.655262\pi$
$444$	−6.26480e16	−0.388077
$445$	−3.67938e17	−2.24613
$446$	3.64223e17	2.19124
$447$	−4.81061e15	−0.0285234
$448$	3.73738e17	2.18404
$449$	−1.40368e17	−0.808475	−0.404237	−	0.914654i	$-0.632463\pi$
$449$	−1.40368e17	−0.808475	−0.404237	+	0.914654i	$0.632463\pi$
$450$	2.96075e17	1.68082
$451$	4.60124e16	0.257471
$452$	−4.94119e16	−0.272541
$453$	6.30556e15	0.0342835
$454$	−4.75411e16	−0.254804
$455$	−6.75806e17	−3.57066
$456$	−1.08883e16	−0.0567138
$457$	8.31704e16	0.427084	0.213542	−	0.976934i	$-0.431500\pi$
$457$	8.31704e16	0.427084	0.213542	+	0.976934i	$0.431500\pi$
$458$	−1.60014e17	−0.810087
$459$	−4.67045e16	−0.233118
$460$	4.32972e17	2.13076
$461$	2.31638e17	1.12397	0.561983	−	0.827149i	$-0.310039\pi$
$461$	2.31638e17	1.12397	0.561983	+	0.827149i	$0.310039\pi$
$462$	4.46270e16	0.213513
$463$	−3.05029e17	−1.43901	−0.719507	−	0.694485i	$-0.755632\pi$
$463$	−3.05029e17	−1.43901	−0.719507	+	0.694485i	$0.755632\pi$
$464$	8.29387e15	0.0385825
$465$	−3.45763e16	−0.158611
$466$	3.59786e17	1.62755
$467$	−1.86370e17	−0.831410	−0.415705	−	0.909500i	$-0.636465\pi$
$467$	−1.86370e17	−0.831410	−0.415705	+	0.909500i	$0.636465\pi$
$468$	6.54620e17	2.87999
$469$	3.12585e17	1.35627
$470$	−1.67619e17	−0.717279
$471$	5.41475e16	0.228529
$472$	1.16943e17	0.486802
$473$	−3.77964e16	−0.155186
$474$	−3.06768e16	−0.124237
$475$	−9.65869e16	−0.385842
$476$	4.00269e17	1.57727
$477$	−1.62103e17	−0.630117
$478$	−1.92578e17	−0.738458
$479$	4.69474e17	1.77595	0.887975	−	0.459892i	$-0.152112\pi$
$479$	4.69474e17	1.77595	0.887975	+	0.459892i	$0.152112\pi$
$480$	6.39093e16	0.238504
$481$	−7.50693e17	−2.76388
$482$	−3.27813e17	−1.19075
$483$	−5.60319e16	−0.200807
$484$	−2.85365e17	−1.00904
$485$	5.02482e17	1.75307
$486$	2.19285e17	0.754870
$487$	−1.69302e17	−0.575075	−0.287538	−	0.957769i	$-0.592837\pi$
$487$	−1.69302e17	−0.575075	−0.287538	+	0.957769i	$0.592837\pi$
$488$	2.97737e17	0.997939
$489$	−3.39228e16	−0.112198
$490$	5.76572e17	1.88182
$491$	1.93030e17	0.621720	0.310860	−	0.950456i	$-0.399383\pi$
$491$	1.93030e17	0.621720	0.310860	+	0.950456i	$0.399383\pi$
$492$	3.44589e16	0.109529
$493$	2.73821e17	0.858936
$494$	−3.46753e17	−1.07348
$495$	−2.79172e17	−0.852978
$496$	7.43283e15	0.0224142
$497$	5.83699e17	1.73729
$498$	−5.52587e16	−0.162334
$499$	−2.97960e17	−0.863980	−0.431990	−	0.901878i	$-0.642188\pi$
$499$	−2.97960e17	−0.863980	−0.431990	+	0.901878i	$0.642188\pi$
$500$	−5.61361e16	−0.160671
$501$	−4.15120e16	−0.117281
$502$	3.45093e17	0.962414
$503$	4.06755e17	1.11980	0.559901	−	0.828560i	$-0.310839\pi$
$503$	4.06755e17	1.11980	0.559901	+	0.828560i	$0.310839\pi$
$504$	−4.69349e17	−1.27555
$505$	−3.99078e17	−1.07069
$506$	−3.42602e17	−0.907428
$507$	−1.48392e17	−0.388024
$508$	8.69379e17	2.24437
$509$	1.55951e17	0.397487	0.198744	−	0.980052i	$-0.436314\pi$
$509$	1.55951e17	0.397487	0.198744	+	0.980052i	$0.436314\pi$
$510$	1.08934e17	0.274130
$511$	5.63993e17	1.40132
$512$	−2.67677e16	−0.0656685
$513$	−4.74814e16	−0.115017
$514$	−1.16973e18	−2.79787
$515$	−6.83720e17	−1.61485
$516$	−2.83059e16	−0.0660167
$517$	8.16846e16	0.188127
$518$	1.43045e18	3.25334
$519$	5.85251e15	0.0131448
$520$	−1.16439e18	−2.58272
$521$	−3.63157e16	−0.0795516	−0.0397758	−	0.999209i	$-0.512664\pi$
$521$	−3.63157e16	−0.0795516	−0.0397758	+	0.999209i	$0.512664\pi$
$522$	−8.53326e17	−1.84611
$523$	2.88190e17	0.615769	0.307884	−	0.951424i	$-0.400379\pi$
$523$	2.88190e17	0.615769	0.307884	+	0.951424i	$0.400379\pi$
$524$	−2.84968e17	−0.601372
$525$	1.11552e17	0.232510
$526$	4.42514e17	0.911003
$527$	2.45394e17	0.498993
$528$	−1.60794e15	−0.00322961
$529$	−7.38784e16	−0.146574
$530$	7.66310e17	1.50180
$531$	2.51610e17	0.487095
$532$	4.06927e17	0.778199
$533$	4.12911e17	0.780062
$534$	2.18038e17	0.406924
$535$	4.67639e16	0.0862205
$536$	5.38574e17	0.981012
$537$	1.87719e15	0.00337813
$538$	−1.36408e18	−2.42525
$539$	−2.80976e17	−0.493563
$540$	−4.23747e17	−0.735440
$541$	−9.27419e17	−1.59035	−0.795177	−	0.606377i	$-0.792622\pi$
$541$	−9.27419e17	−1.59035	−0.795177	+	0.606377i	$0.792622\pi$
$542$	−1.47338e18	−2.49643
$543$	1.25726e16	0.0210488
$544$	−4.53575e17	−0.750336
$545$	−1.39551e18	−2.28117
$546$	4.00478e17	0.646884
$547$	6.03525e17	0.963335	0.481668	−	0.876354i	$-0.340031\pi$
$547$	6.03525e17	0.963335	0.481668	+	0.876354i	$0.340031\pi$
$548$	4.35165e17	0.686405
$549$	6.40599e17	0.998541
$550$	6.82075e17	1.05069
$551$	2.78375e17	0.423785
$552$	−9.65411e16	−0.145247
$553$	4.31382e17	0.641429
$554$	2.02973e18	2.98281
$555$	2.39757e17	0.348230
$556$	−1.68260e17	−0.241542
$557$	1.13063e18	1.60421	0.802106	−	0.597182i	$-0.203713\pi$
$557$	1.13063e18	1.60421	0.802106	+	0.597182i	$0.203713\pi$
$558$	−7.64737e17	−1.07248
$559$	−3.39181e17	−0.470170
$560$	−4.63987e16	−0.0635746
$561$	−5.30859e16	−0.0718986
$562$	8.36366e17	1.11972
$563$	−1.45239e17	−0.192212	−0.0961058	−	0.995371i	$-0.530639\pi$
$563$	−1.45239e17	−0.192212	−0.0961058	+	0.995371i	$0.530639\pi$
$564$	6.11739e16	0.0800299
$565$	1.89102e17	0.244557
$566$	1.54555e18	1.97595
$567$	−9.82052e17	−1.24121
$568$	1.00569e18	1.25661
$569$	7.14874e17	0.883080	0.441540	−	0.897242i	$-0.354432\pi$
$569$	7.14874e17	0.883080	0.441540	+	0.897242i	$0.354432\pi$
$570$	1.10746e17	0.135251
$571$	6.34516e17	0.766139	0.383070	−	0.923720i	$-0.374867\pi$
$571$	6.34516e17	0.766139	0.383070	+	0.923720i	$0.374867\pi$
$572$	1.50806e18	1.80030
$573$	1.53733e17	0.181453
$574$	−7.86806e17	−0.918206
$575$	−8.56387e17	−0.988164
$576$	1.38547e18	1.58071
$577$	−1.12169e17	−0.126540	−0.0632702	−	0.997996i	$-0.520153\pi$
$577$	−1.12169e17	−0.126540	−0.0632702	+	0.997996i	$0.520153\pi$
$578$	6.73280e17	0.751043
$579$	2.02224e17	0.223060
$580$	2.48436e18	2.70977
$581$	7.77056e17	0.838122
$582$	−2.97768e17	−0.317598
$583$	−3.73440e17	−0.393890
$584$	9.71740e17	1.01360
$585$	−2.50526e18	−2.58428
$586$	3.06789e18	3.12972
$587$	−8.35807e17	−0.843254	−0.421627	−	0.906769i	$-0.638541\pi$
$587$	−8.35807e17	−0.843254	−0.421627	+	0.906769i	$0.638541\pi$
$588$	−2.10424e17	−0.209963
$589$	2.49476e17	0.246195
$590$	−1.18944e18	−1.16093
$591$	1.19222e16	0.0115090
$592$	−5.15402e16	−0.0492102
$593$	3.24648e16	0.0306589	0.0153295	−	0.999882i	$-0.495120\pi$
$593$	3.24648e16	0.0306589	0.0153295	+	0.999882i	$0.495120\pi$
$594$	3.35303e17	0.313203
$595$	−1.53185e18	−1.41532
$596$	3.09765e17	0.283095
$597$	1.84389e17	0.166687
$598$	−3.07448e18	−2.74925
$599$	2.70986e17	0.239703	0.119851	−	0.992792i	$-0.461758\pi$
$599$	2.70986e17	0.239703	0.119851	+	0.992792i	$0.461758\pi$
$600$	1.92200e17	0.168179
$601$	1.06437e18	0.921320	0.460660	−	0.887577i	$-0.347613\pi$
$601$	1.06437e18	0.921320	0.460660	+	0.887577i	$0.347613\pi$
$602$	6.46313e17	0.553434
$603$	1.15878e18	0.981605
$604$	−4.06028e17	−0.340264
$605$	1.09211e18	0.905430
$606$	2.36491e17	0.193973
$607$	−1.95225e18	−1.58420	−0.792098	−	0.610394i	$-0.791011\pi$
$607$	−1.95225e18	−1.58420	−0.792098	+	0.610394i	$0.791011\pi$
$608$	−4.61120e17	−0.370203
$609$	−3.21507e17	−0.255374
$610$	−3.02831e18	−2.37989
$611$	7.33029e17	0.569972
$612$	1.48382e18	1.14156
$613$	9.41311e17	0.716540	0.358270	−	0.933618i	$-0.383367\pi$
$613$	9.41311e17	0.716540	0.358270	+	0.933618i	$0.383367\pi$
$614$	2.23281e18	1.68173
$615$	−1.31876e17	−0.0982825
$616$	−1.08125e18	−0.797355
$617$	6.07523e17	0.443312	0.221656	−	0.975125i	$-0.428854\pi$
$617$	6.07523e17	0.443312	0.221656	+	0.975125i	$0.428854\pi$
$618$	4.05168e17	0.292557
$619$	−2.65867e18	−1.89966	−0.949828	−	0.312774i	$-0.898742\pi$
$619$	−2.65867e18	−1.89966	−0.949828	+	0.312774i	$0.898742\pi$
$620$	2.22644e18	1.57422
$621$	−4.20993e17	−0.294564
$622$	−2.63541e18	−1.82478
$623$	−3.06608e18	−2.10093
$624$	−1.44295e16	−0.00978479
$625$	−1.37908e18	−0.925487
$626$	3.70221e17	0.245883
$627$	−5.39690e16	−0.0354736
$628$	−3.48667e18	−2.26816
$629$	−1.70159e18	−1.09553
$630$	4.77380e18	3.04194
$631$	−4.04336e17	−0.255006	−0.127503	−	0.991838i	$-0.540696\pi$
$631$	−4.04336e17	−0.255006	−0.127503	+	0.991838i	$0.540696\pi$
$632$	7.43256e17	0.463957
$633$	−3.89287e17	−0.240517
$634$	5.66319e17	0.346323
$635$	−3.32715e18	−2.01392
$636$	−2.79670e17	−0.167562
$637$	−2.52145e18	−1.49535
$638$	−1.96583e18	−1.15401
$639$	2.16381e18	1.25737
$640$	−3.98274e18	−2.29093
$641$	7.36613e17	0.419433	0.209716	−	0.977762i	$-0.432746\pi$
$641$	7.36613e17	0.419433	0.209716	+	0.977762i	$0.432746\pi$
$642$	−2.77119e16	−0.0156203
$643$	−3.64324e17	−0.203290	−0.101645	−	0.994821i	$-0.532411\pi$
$643$	−3.64324e17	−0.203290	−0.101645	+	0.994821i	$0.532411\pi$
$644$	3.60801e18	1.99301
$645$	1.08328e17	0.0592382
$646$	−7.85982e17	−0.425502
$647$	3.67191e17	0.196795	0.0983974	−	0.995147i	$-0.468628\pi$
$647$	3.67191e17	0.196795	0.0983974	+	0.995147i	$0.468628\pi$
$648$	−1.69204e18	−0.897788
$649$	5.79640e17	0.304487
$650$	6.12087e18	3.18329
$651$	−2.88129e17	−0.148358
$652$	2.18436e18	1.11356
$653$	1.48824e18	0.751168	0.375584	−	0.926788i	$-0.377442\pi$
$653$	1.48824e18	0.751168	0.375584	+	0.926788i	$0.377442\pi$
$654$	8.26972e17	0.413272
$655$	1.09059e18	0.539625
$656$	2.83492e16	0.0138888
$657$	2.09076e18	1.01421
$658$	−1.39679e18	−0.670910
$659$	1.65430e18	0.786792	0.393396	−	0.919369i	$-0.371300\pi$
$659$	1.65430e18	0.786792	0.393396	+	0.919369i	$0.371300\pi$
$660$	−4.81645e17	−0.226825
$661$	−3.63502e18	−1.69511	−0.847553	−	0.530710i	$-0.821925\pi$
$661$	−3.63502e18	−1.69511	−0.847553	+	0.530710i	$0.821925\pi$
$662$	−3.12829e17	−0.144454
$663$	−4.76387e17	−0.217832
$664$	1.33884e18	0.606229
$665$	−1.55733e18	−0.698295
$666$	5.30278e18	2.35462
$667$	2.46821e18	1.08534
$668$	2.67304e18	1.16402
$669$	5.08712e17	0.219383
$670$	−5.47789e18	−2.33952
$671$	1.47576e18	0.624195
$672$	5.32565e17	0.223086
$673$	−4.58195e18	−1.90087	−0.950435	−	0.310922i	$-0.899362\pi$
$673$	−4.58195e18	−1.90087	−0.950435	+	0.310922i	$0.899362\pi$
$674$	6.80106e18	2.79439
$675$	8.38141e17	0.341069
$676$	9.55528e18	3.85115
$677$	1.72187e17	0.0687345	0.0343672	−	0.999409i	$-0.489058\pi$
$677$	1.72187e17	0.0687345	0.0343672	+	0.999409i	$0.489058\pi$
$678$	−1.12060e17	−0.0443056
$679$	4.18725e18	1.63974
$680$	−2.63932e18	−1.02373
$681$	−6.64010e16	−0.0255105
$682$	−1.76174e18	−0.670415
$683$	4.78259e17	0.180272	0.0901361	−	0.995929i	$-0.471270\pi$
$683$	4.78259e17	0.180272	0.0901361	+	0.995929i	$0.471270\pi$
$684$	1.50850e18	0.563225
$685$	−1.66540e18	−0.615926
$686$	−1.12174e18	−0.410948
$687$	−2.23492e17	−0.0811043
$688$	−2.32871e16	−0.00837126
$689$	−3.35121e18	−1.19337
$690$	9.81928e17	0.346386
$691$	−4.75450e18	−1.66149	−0.830745	−	0.556654i	$-0.812085\pi$
$691$	−4.75450e18	−1.66149	−0.830745	+	0.556654i	$0.812085\pi$
$692$	−3.76856e17	−0.130462
$693$	−2.32638e18	−0.797836
$694$	−8.30466e18	−2.82153
$695$	6.43937e17	0.216741
$696$	−5.53945e17	−0.184717
$697$	9.35942e17	0.309198
$698$	2.61867e18	0.857079
$699$	5.02516e17	0.162948
$700$	−7.18307e18	−2.30767
$701$	3.59960e18	1.14574	0.572872	−	0.819645i	$-0.305829\pi$
$701$	3.59960e18	1.14574	0.572872	+	0.819645i	$0.305829\pi$
$702$	3.00897e18	0.948915
$703$	−1.72990e18	−0.540518
$704$	3.19174e18	0.988111
$705$	−2.34115e17	−0.0718126
$706$	2.02480e18	0.615390
$707$	−3.32557e18	−1.00147
$708$	4.34095e17	0.129529
$709$	2.92359e18	0.864401	0.432200	−	0.901778i	$-0.357737\pi$
$709$	2.92359e18	0.864401	0.432200	+	0.901778i	$0.357737\pi$
$710$	−1.02290e19	−2.99678
$711$	1.59916e18	0.464237
$712$	−5.28275e18	−1.51964
$713$	2.21197e18	0.630518
$714$	9.07761e17	0.256409
$715$	−5.77142e18	−1.61545
$716$	−1.20876e17	−0.0335280
$717$	−2.68975e17	−0.0739329
$718$	−1.06622e19	−2.90427
$719$	−1.30924e18	−0.353411	−0.176705	−	0.984264i	$-0.556544\pi$
$719$	−1.30924e18	−0.353411	−0.176705	+	0.984264i	$0.556544\pi$
$720$	−1.72003e17	−0.0460124
$721$	−5.69753e18	−1.51045
$722$	5.34209e18	1.40352
$723$	−4.57859e17	−0.119216
$724$	−8.09577e17	−0.208909
$725$	−4.91388e18	−1.25669
$726$	−6.47174e17	−0.164034
$727$	6.43459e18	1.61639	0.808197	−	0.588913i	$-0.200444\pi$
$727$	6.43459e18	1.61639	0.808197	+	0.588913i	$0.200444\pi$
$728$	−9.70303e18	−2.41576
$729$	−3.43180e18	−0.846823
$730$	−9.88366e18	−2.41724
$731$	−7.68820e17	−0.186364
$732$	1.10520e18	0.265534
$733$	3.52248e18	0.838827	0.419413	−	0.907795i	$-0.362236\pi$
$733$	3.52248e18	0.838827	0.419413	+	0.907795i	$0.362236\pi$
$734$	1.06937e19	2.52409
$735$	8.05302e17	0.188404
$736$	−4.08851e18	−0.948112
$737$	2.66950e18	0.613607
$738$	−2.91674e18	−0.664556
$739$	7.12146e18	1.60835	0.804175	−	0.594393i	$-0.202608\pi$
$739$	7.12146e18	1.60835	0.804175	+	0.594393i	$0.202608\pi$
$740$	−1.54384e19	−3.45619
$741$	−4.84312e17	−0.107475
$742$	6.38577e18	1.40471
$743$	3.83815e18	0.836940	0.418470	−	0.908231i	$-0.362567\pi$
$743$	3.83815e18	0.836940	0.418470	+	0.908231i	$0.362567\pi$
$744$	−4.96437e17	−0.107310
$745$	−1.18548e18	−0.254027
$746$	−8.39788e18	−1.78389
$747$	2.88060e18	0.606595
$748$	3.41831e18	0.713595
$749$	3.89689e17	0.0806467
$750$	−1.27310e17	−0.0261195
$751$	4.88087e18	0.992746	0.496373	−	0.868109i	$-0.334665\pi$
$751$	4.88087e18	0.992746	0.496373	+	0.868109i	$0.334665\pi$
$752$	5.03275e16	0.0101482
$753$	4.81994e17	0.0963550
$754$	−1.76411e19	−3.49633
$755$	1.55389e18	0.305326
$756$	−3.53114e18	−0.687897
$757$	5.87358e18	1.13444	0.567218	−	0.823568i	$-0.308020\pi$
$757$	5.87358e18	1.13444	0.567218	+	0.823568i	$0.308020\pi$
$758$	−2.00762e18	−0.384443
$759$	−4.78515e17	−0.0908499
$760$	−2.68322e18	−0.505090
$761$	−2.00830e18	−0.374825	−0.187413	−	0.982281i	$-0.560010\pi$
$761$	−2.00830e18	−0.374825	−0.187413	+	0.982281i	$0.560010\pi$
$762$	1.97165e18	0.364856
$763$	−1.16290e19	−2.13370
$764$	−9.89922e18	−1.80092
$765$	−5.67865e18	−1.02434
$766$	1.48320e19	2.65284
$767$	5.20163e18	0.922507
$768$	8.69227e17	0.152857
$769$	−6.28602e17	−0.109611	−0.0548056	−	0.998497i	$-0.517454\pi$
$769$	−6.28602e17	−0.109611	−0.0548056	+	0.998497i	$0.517454\pi$
$770$	1.09975e19	1.90153
$771$	−1.63378e18	−0.280117
$772$	−1.30216e19	−2.21387
$773$	−2.08070e18	−0.350786	−0.175393	−	0.984498i	$-0.556120\pi$
$773$	−2.08070e18	−0.350786	−0.175393	+	0.984498i	$0.556120\pi$
$774$	2.39593e18	0.400550
$775$	−4.40374e18	−0.730064
$776$	7.21450e18	1.18605
$777$	1.99792e18	0.325718
$778$	4.54974e18	0.735561
$779$	9.51511e17	0.152553
$780$	−4.32224e18	−0.687216
$781$	4.98482e18	0.785991
$782$	−6.96890e18	−1.08973
$783$	−2.41563e18	−0.374609
$784$	−1.73115e17	−0.0266244
$785$	1.33436e19	2.03527
$786$	−6.46274e17	−0.0977620
$787$	−1.31588e19	−1.97415	−0.987075	−	0.160257i	$-0.948768\pi$
$787$	−1.31588e19	−1.97415	−0.987075	+	0.160257i	$0.948768\pi$
$788$	−7.67694e17	−0.114227
$789$	6.18063e17	0.0912078
$790$	−7.55973e18	−1.10645
$791$	1.57581e18	0.228748
$792$	−4.00827e18	−0.577089
$793$	1.32433e19	1.89113
$794$	1.84174e19	2.60852
$795$	1.07031e18	0.150357
$796$	−1.18732e19	−1.65437
$797$	−5.33017e18	−0.736651	−0.368325	−	0.929697i	$-0.620069\pi$
$797$	−5.33017e18	−0.736651	−0.368325	+	0.929697i	$0.620069\pi$
$798$	9.22861e17	0.126508
$799$	1.66155e18	0.225923
$800$	8.13968e18	1.09780
$801$	−1.13662e19	−1.52056
$802$	3.02757e18	0.401754
$803$	4.81653e18	0.633991
$804$	1.99920e18	0.261030
$805$	−1.38080e19	−1.78837
$806$	−1.58097e19	−2.03117
$807$	−1.90522e18	−0.242811
$808$	−5.72985e18	−0.724384
$809$	−1.21598e19	−1.52496	−0.762482	−	0.647010i	$-0.776019\pi$
$809$	−1.21598e19	−1.52496	−0.762482	+	0.647010i	$0.776019\pi$
$810$	1.72099e19	2.14105
$811$	1.03518e18	0.127755	0.0638776	−	0.997958i	$-0.479653\pi$
$811$	1.03518e18	0.127755	0.0638776	+	0.997958i	$0.479653\pi$
$812$	2.07025e19	2.53459
$813$	−2.05788e18	−0.249938
$814$	1.22161e19	1.47189
$815$	−8.35964e18	−0.999224
$816$	−3.27073e16	−0.00387845
$817$	−7.81609e17	−0.0919488
$818$	9.66187e18	1.12763
$819$	−2.08767e19	−2.41722
$820$	8.49175e18	0.975455
$821$	5.96819e18	0.680162	0.340081	−	0.940396i	$-0.389546\pi$
$821$	5.96819e18	0.680162	0.340081	+	0.940396i	$0.389546\pi$
$822$	9.86902e17	0.111585
$823$	−5.87796e18	−0.659367	−0.329684	−	0.944091i	$-0.606942\pi$
$823$	−5.87796e18	−0.659367	−0.329684	+	0.944091i	$0.606942\pi$
$824$	−9.81666e18	−1.09254
$825$	9.52660e17	0.105193
$826$	−9.91176e18	−1.08588
$827$	−1.22284e19	−1.32918	−0.664592	−	0.747206i	$-0.731395\pi$
$827$	−1.22284e19	−1.32918	−0.664592	+	0.747206i	$0.731395\pi$
$828$	1.33751e19	1.44245
$829$	4.06181e18	0.434626	0.217313	−	0.976102i	$-0.430271\pi$
$829$	4.06181e18	0.434626	0.217313	+	0.976102i	$0.430271\pi$
$830$	−1.36175e19	−1.44574
$831$	2.83494e18	0.298633
$832$	2.86424e19	2.99369
$833$	−5.71535e18	−0.592721
$834$	−3.81592e17	−0.0392663
$835$	−1.02299e19	−1.04450
$836$	3.47518e18	0.352076
$837$	−2.16484e18	−0.217626
$838$	−1.35666e19	−1.35327
$839$	−5.90693e18	−0.584667	−0.292334	−	0.956316i	$-0.594432\pi$
$839$	−5.90693e18	−0.584667	−0.292334	+	0.956316i	$0.594432\pi$
$840$	3.09896e18	0.304369
$841$	3.90178e18	0.380267
$842$	−1.98000e19	−1.91486
$843$	1.16816e18	0.112104
$844$	2.50670e19	2.38713
$845$	−3.65685e19	−3.45572
$846$	−5.17801e18	−0.485574
$847$	9.10066e18	0.846898
$848$	−2.30084e17	−0.0212477
$849$	2.15868e18	0.197828
$850$	1.38741e19	1.26178
$851$	−1.53381e19	−1.38430
$852$	3.73315e18	0.334363
$853$	−1.16071e19	−1.03171	−0.515854	−	0.856677i	$-0.672525\pi$
$853$	−1.16071e19	−1.03171	−0.515854	+	0.856677i	$0.672525\pi$
$854$	−2.52353e19	−2.22604
$855$	−5.77312e18	−0.505394
$856$	6.71422e17	0.0583332
$857$	−1.09084e19	−0.940560	−0.470280	−	0.882517i	$-0.655847\pi$
$857$	−1.09084e19	−0.940560	−0.470280	+	0.882517i	$0.655847\pi$
$858$	3.42010e18	0.292666
$859$	1.05481e19	0.895814	0.447907	−	0.894080i	$-0.352170\pi$
$859$	1.05481e19	0.895814	0.447907	+	0.894080i	$0.352170\pi$
$860$	−6.97546e18	−0.587940
$861$	−1.09894e18	−0.0919290
$862$	2.94695e19	2.44667
$863$	−2.01877e18	−0.166348	−0.0831739	−	0.996535i	$-0.526506\pi$
$863$	−2.01877e18	−0.166348	−0.0831739	+	0.996535i	$0.526506\pi$
$864$	4.00140e18	0.327245
$865$	1.44224e18	0.117067
$866$	1.36406e18	0.109892
$867$	9.40375e17	0.0751929
$868$	1.85532e19	1.47245
$869$	3.68402e18	0.290197
$870$	5.63423e18	0.440513
$871$	2.39558e19	1.85906
$872$	−2.00364e19	−1.54334
$873$	1.55224e19	1.18677
$874$	−7.08483e18	−0.537656
$875$	1.79025e18	0.134853
$876$	3.60711e18	0.269701
$877$	1.67018e19	1.23956	0.619779	−	0.784776i	$-0.287222\pi$
$877$	1.67018e19	1.23956	0.619779	+	0.784776i	$0.287222\pi$
$878$	1.50631e19	1.10968
$879$	4.28494e18	0.313341
$880$	−3.96248e17	−0.0287627
$881$	2.08672e18	0.150356	0.0751781	−	0.997170i	$-0.476047\pi$
$881$	2.08672e18	0.150356	0.0751781	+	0.997170i	$0.476047\pi$
$882$	1.78112e19	1.27393
$883$	1.41111e19	1.00188	0.500941	−	0.865482i	$-0.332987\pi$
$883$	1.41111e19	1.00188	0.500941	+	0.865482i	$0.332987\pi$
$884$	3.06756e19	2.16199
$885$	−1.66130e18	−0.116230
$886$	2.17752e19	1.51232
$887$	2.77985e19	1.91654	0.958269	−	0.285868i	$-0.0922819\pi$
$887$	2.77985e19	1.91654	0.958269	+	0.285868i	$0.0922819\pi$
$888$	3.44236e18	0.235598
$889$	−2.77256e19	−1.88373
$890$	5.37314e19	3.62404
$891$	−8.38677e18	−0.561552
$892$	−3.27571e19	−2.17738
$893$	1.68919e18	0.111467
$894$	7.02510e17	0.0460213
$895$	4.62600e17	0.0300854
$896$	−3.31887e19	−2.14283
$897$	−4.29415e18	−0.275249
$898$	2.04984e19	1.30444
$899$	1.26921e19	0.801856
$900$	−2.66281e19	−1.67018
$901$	−7.59617e18	−0.473024
$902$	−6.71936e18	−0.415418
$903$	9.02711e17	0.0554087
$904$	2.71507e18	0.165457
$905$	3.09829e18	0.187459
$906$	−9.20823e17	−0.0553150
$907$	−5.92017e18	−0.353091	−0.176546	−	0.984292i	$-0.556492\pi$
$907$	−5.92017e18	−0.353091	−0.176546	+	0.984292i	$0.556492\pi$
$908$	4.27570e18	0.253192
$909$	−1.23281e19	−0.724822
$910$	9.86904e19	5.76111
$911$	2.45208e19	1.42124	0.710618	−	0.703578i	$-0.248416\pi$
$911$	2.45208e19	1.42124	0.710618	+	0.703578i	$0.248416\pi$
$912$	−3.32513e16	−0.00191356
$913$	6.63610e18	0.379186
$914$	−1.21457e19	−0.689083
$915$	−4.22966e18	−0.238270
$916$	1.43911e19	0.804961
$917$	9.08800e18	0.504740
$918$	6.82042e18	0.376127
$919$	−1.23801e19	−0.677915	−0.338957	−	0.940802i	$-0.610074\pi$
$919$	−1.23801e19	−0.677915	−0.338957	+	0.940802i	$0.610074\pi$
$920$	−2.37908e19	−1.29356
$921$	3.11858e18	0.168372
$922$	−3.38269e19	−1.81347
$923$	4.47333e19	2.38133
$924$	−4.01362e18	−0.212162
$925$	3.05361e19	1.60285
$926$	4.45445e19	2.32179
$927$	−2.11211e19	−1.09320
$928$	−2.34596e19	−1.20575
$929$	1.13560e19	0.579594	0.289797	−	0.957088i	$-0.406412\pi$
$929$	1.13560e19	0.579594	0.289797	+	0.957088i	$0.406412\pi$
$930$	5.04930e18	0.255913
$931$	−5.81043e18	−0.292439
$932$	−3.23580e19	−1.61726
$933$	−3.68090e18	−0.182694
$934$	2.72162e19	1.34145
$935$	−1.30820e19	−0.640324
$936$	−3.59698e19	−1.74842
$937$	1.75029e18	0.0844896	0.0422448	−	0.999107i	$-0.486549\pi$
$937$	1.75029e18	0.0844896	0.0422448	+	0.999107i	$0.486549\pi$
$938$	−4.56480e19	−2.18828
$939$	5.17091e17	0.0246173
$940$	1.50752e19	0.712740
$941$	−2.26832e19	−1.06505	−0.532527	−	0.846413i	$-0.678757\pi$
$941$	−2.26832e19	−1.06505	−0.532527	+	0.846413i	$0.678757\pi$
$942$	−7.90735e18	−0.368723
$943$	8.43656e18	0.390697
$944$	3.57128e17	0.0164250
$945$	1.35138e19	0.617265
$946$	5.51955e18	0.250387
$947$	1.76557e19	0.795443	0.397722	−	0.917506i	$-0.369801\pi$
$947$	1.76557e19	0.795443	0.397722	+	0.917506i	$0.369801\pi$
$948$	2.75898e18	0.123451
$949$	4.32230e19	1.92081
$950$	1.41049e19	0.622541
$951$	7.90983e17	0.0346732
$952$	−2.19938e19	−0.957547
$953$	4.39762e19	1.90158	0.950788	−	0.309842i	$-0.100276\pi$
$953$	4.39762e19	1.90158	0.950788	+	0.309842i	$0.100276\pi$
$954$	2.36725e19	1.01667
$955$	3.78848e19	1.61600
$956$	1.73199e19	0.733785
$957$	−2.74568e18	−0.115537
$958$	−6.85590e19	−2.86542
$959$	−1.38780e19	−0.576110
$960$	−9.14782e18	−0.377185
$961$	−1.30431e19	−0.534168
$962$	1.09626e20	4.45941
$963$	1.44460e18	0.0583685
$964$	2.94825e19	1.18322
$965$	4.98343e19	1.98656
$966$	8.18254e18	0.323994
$967$	2.96455e19	1.16597	0.582983	−	0.812484i	$-0.301885\pi$
$967$	2.96455e19	1.16597	0.582983	+	0.812484i	$0.301885\pi$
$968$	1.56801e19	0.612576
$969$	−1.09779e18	−0.0426004
$970$	−7.33793e19	−2.82851
$971$	2.48779e19	0.952553	0.476276	−	0.879296i	$-0.341986\pi$
$971$	2.48779e19	0.952553	0.476276	+	0.879296i	$0.341986\pi$
$972$	−1.97218e19	−0.750094
$973$	5.36601e18	0.202730
$974$	2.47238e19	0.927861
$975$	8.54907e18	0.318705
$976$	9.09246e17	0.0336711
$977$	−1.58078e19	−0.581510	−0.290755	−	0.956798i	$-0.593906\pi$
$977$	−1.58078e19	−0.581510	−0.290755	+	0.956798i	$0.593906\pi$
$978$	4.95386e18	0.181026
$979$	−2.61845e19	−0.950509
$980$	−5.18551e19	−1.86992
$981$	−4.31095e19	−1.54427
$982$	−2.81889e19	−1.00312
$983$	3.22371e19	1.13962	0.569808	−	0.821778i	$-0.307017\pi$
$983$	3.22371e19	1.13962	0.569808	+	0.821778i	$0.307017\pi$
$984$	−1.89343e18	−0.0664939
$985$	2.93800e18	0.102498
$986$	−3.99870e19	−1.38586
$987$	−1.95091e18	−0.0671702
$988$	3.11859e19	1.06669
$989$	−6.93013e18	−0.235486
$990$	4.07685e19	1.37624
$991$	5.60470e18	0.187963	0.0939817	−	0.995574i	$-0.470040\pi$
$991$	5.60470e18	0.187963	0.0939817	+	0.995574i	$0.470040\pi$
$992$	−2.10241e19	−0.700473
$993$	−4.36931e17	−0.0144625
$994$	−8.52397e19	−2.80305
$995$	4.54394e19	1.48451
$996$	4.96980e18	0.161307
$997$	−3.36491e19	−1.08506	−0.542531	−	0.840036i	$-0.682534\pi$
$997$	−3.36491e19	−1.08506	−0.542531	+	0.840036i	$0.682534\pi$
$998$	4.35121e19	1.39400
$999$	1.50113e19	0.477797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.a.1.13	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.a.1.13	✓	104	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-146.034 q^{2} -203.966 q^{3} +13133.8 q^{4} -50263.7 q^{5} +29785.9 q^{6} -418854. q^{7} -721672. q^{8} -1.55272e6 q^{9} +7.34019e6 q^{10} -3.57704e6 q^{11} -2.67886e6 q^{12} -3.21000e7 q^{13} +6.11668e7 q^{14} +1.02521e7 q^{15} -2.20388e6 q^{16} -7.27608e7 q^{17} +2.26749e8 q^{18} -7.39711e7 q^{19} -6.60155e8 q^{20} +8.54321e7 q^{21} +5.22368e8 q^{22} -6.55864e8 q^{23} +1.47197e8 q^{24} +1.30574e9 q^{25} +4.68767e9 q^{26} +6.41891e8 q^{27} -5.50116e9 q^{28} -3.76330e9 q^{29} -1.49715e9 q^{30} -3.37261e9 q^{31} +6.23378e9 q^{32} +7.29595e8 q^{33} +1.06255e10 q^{34} +2.10532e10 q^{35} -2.03932e10 q^{36} +2.33861e10 q^{37} +1.08023e10 q^{38} +6.54731e9 q^{39} +3.62739e10 q^{40} -1.28633e10 q^{41} -1.24760e10 q^{42} +1.05664e10 q^{43} -4.69802e10 q^{44} +7.80455e10 q^{45} +9.57782e10 q^{46} -2.28358e10 q^{47} +4.49518e8 q^{48} +7.85499e10 q^{49} -1.90682e11 q^{50} +1.48407e10 q^{51} -4.21595e11 q^{52} +1.04399e11 q^{53} -9.37376e10 q^{54} +1.79795e11 q^{55} +3.02275e11 q^{56} +1.50876e10 q^{57} +5.49568e11 q^{58} -1.62045e11 q^{59} +1.34649e11 q^{60} -4.12566e11 q^{61} +4.92514e11 q^{62} +6.50364e11 q^{63} -8.92287e11 q^{64} +1.61346e12 q^{65} -1.06545e11 q^{66} -7.46287e11 q^{67} -9.55627e11 q^{68} +1.33774e11 q^{69} -3.07447e12 q^{70} -1.39356e12 q^{71} +1.12056e12 q^{72} -1.34651e12 q^{73} -3.41516e12 q^{74} -2.66326e11 q^{75} -9.71524e11 q^{76} +1.49826e12 q^{77} -9.56127e11 q^{78} -1.02991e12 q^{79} +1.10775e11 q^{80} +2.34461e12 q^{81} +1.87847e12 q^{82} -1.85519e12 q^{83} +1.12205e12 q^{84} +3.65723e12 q^{85} -1.54305e12 q^{86} +7.67586e11 q^{87} +2.58145e12 q^{88} +7.32016e12 q^{89} -1.13973e13 q^{90} +1.34452e13 q^{91} -8.61400e12 q^{92} +6.87898e11 q^{93} +3.33480e12 q^{94} +3.71806e12 q^{95} -1.27148e12 q^{96} -9.99692e12 q^{97} -1.14709e13 q^{98} +5.55414e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14}+ \cdots - 8666459567773 q^{99}+O(q^{100}) \) 104 * q - 128 * q^2 - 8020 * q^3 + 409600 * q^4 - 99004 * q^5 - 83328 * q^6 - 2084037 * q^7 - 2111301 * q^8 + 51549776 * q^9 - 9626347 * q^10 - 10688800 * q^11 - 68157440 * q^12 - 94762650 * q^13 - 52465903 * q^14 - 186128761 * q^15 + 1543503872 * q^16 - 109572251 * q^17 - 449658263 * q^18 - 1495268031 * q^19 - 1194030741 * q^20 - 832275538 * q^21 - 2695120703 * q^22 - 2632554532 * q^23 - 190649667 * q^24 + 22696779124 * q^25 - 2460454754 * q^26 - 16267542277 * q^27 - 18137835250 * q^28 + 47556769 * q^29 - 9613748117 * q^30 - 24774628288 * q^31 - 29246249180 * q^32 - 42367036666 * q^33 - 39395206606 * q^34 - 26216433864 * q^35 + 190013501626 * q^36 - 82419664050 * q^37 - 34593622142 * q^38 - 39498281801 * q^39 - 150303128514 * q^40 - 25862853768 * q^41 - 138889965149 * q^42 - 258164897781 * q^43 - 197365738094 * q^44 - 240782892021 * q^45 - 218441397971 * q^46 - 208905762731 * q^47 - 664063830814 * q^48 + 1113758315863 * q^49 - 1516068087607 * q^50 - 1019253294393 * q^51 - 1162941441840 * q^52 + 161684855900 * q^53 + 1679137315823 * q^54 - 557952233701 * q^55 + 2842561845328 * q^56 + 801593765429 * q^57 - 7249760433 * q^58 - 775487110641 * q^59 - 57598844627 * q^60 - 36786715662 * q^61 + 681529132643 * q^62 - 4349115033663 * q^63 + 4600420238797 * q^64 - 2531819073161 * q^65 - 3958922748734 * q^66 - 7314072405766 * q^67 - 10297353950393 * q^68 - 2089200206275 * q^69 - 14268943913713 * q^70 - 6055724651085 * q^71 - 26860198563805 * q^72 - 7572811533391 * q^73 - 11175265675817 * q^74 - 24431657592434 * q^75 - 26425925198106 * q^76 - 9735327037686 * q^77 - 35310017230907 * q^78 - 8981210762721 * q^79 - 25913753436330 * q^80 + 15437375349812 * q^81 - 19721330628227 * q^82 - 22209909714532 * q^83 - 18837805278768 * q^84 - 5905005171430 * q^85 - 8913876797772 * q^86 - 7341562344401 * q^87 - 35154329886441 * q^88 - 4646484034146 * q^89 + 9564902968095 * q^90 - 22752431457047 * q^91 - 13601121953458 * q^92 - 9615114240293 * q^93 + 15352521272967 * q^94 + 5258551767043 * q^95 + 87277848810881 * q^96 - 42298840804040 * q^97 + 27000102375354 * q^98 - 8666459567773 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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