LMFDB - Embedded newform 197.14.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +O(q^{10})$	\(q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +6.59387e6 q^{10} +1.01012e7 q^{11} +2.35555e6 q^{12} +2.70916e7 q^{13} -2.19779e7 q^{14} -6.13857e6 q^{15} +6.26381e7 q^{16} -7.94734e7 q^{17} +2.45702e8 q^{18} -3.02415e8 q^{19} -6.83982e8 q^{20} +2.04604e7 q^{21} -1.57763e9 q^{22} +1.22651e9 q^{23} -1.81865e8 q^{24} +5.61759e8 q^{25} -4.23121e9 q^{26} -4.60548e8 q^{27} +2.27977e9 q^{28} -2.20816e9 q^{29} +9.58733e8 q^{30} -6.83081e8 q^{31} +4.63754e8 q^{32} +1.46869e9 q^{33} +1.24123e10 q^{34} -5.94110e9 q^{35} -2.54867e10 q^{36} +2.15026e10 q^{37} +4.72317e10 q^{38} +3.93906e9 q^{39} +5.28084e10 q^{40} -2.01349e10 q^{41} -3.19554e9 q^{42} -7.18113e10 q^{43} +1.63647e11 q^{44} +6.64185e10 q^{45} -1.91558e11 q^{46} +1.65782e10 q^{47} +9.10743e9 q^{48} -7.70868e10 q^{49} -8.77365e10 q^{50} -1.15552e10 q^{51} +4.38904e11 q^{52} +2.28728e11 q^{53} +7.19291e10 q^{54} -4.26466e11 q^{55} -1.76015e11 q^{56} -4.39705e10 q^{57} +3.44874e11 q^{58} -5.15415e11 q^{59} -9.94493e10 q^{60} +1.40601e11 q^{61} +1.06685e11 q^{62} -2.21379e11 q^{63} -5.85561e11 q^{64} -1.14379e12 q^{65} -2.29383e11 q^{66} +2.53048e11 q^{67} -1.28753e12 q^{68} +1.78331e11 q^{69} +9.27892e11 q^{70} -1.59034e12 q^{71} +1.96776e12 q^{72} +1.28348e12 q^{73} -3.35832e12 q^{74} +8.16784e10 q^{75} -4.89934e12 q^{76} +1.42145e12 q^{77} -6.15208e11 q^{78} -2.01437e12 q^{79} -2.64453e12 q^{80} +2.44120e12 q^{81} +3.14469e12 q^{82} +1.86340e12 q^{83} +3.31473e11 q^{84} +3.35530e12 q^{85} +1.12156e13 q^{86} -3.21061e11 q^{87} -1.26348e13 q^{88} +4.05006e12 q^{89} -1.03734e13 q^{90} +3.81234e12 q^{91} +1.98703e13 q^{92} -9.93184e10 q^{93} -2.58921e12 q^{94} +1.27677e13 q^{95} +6.74287e10 q^{96} +4.35140e12 q^{97} +1.20395e13 q^{98} -1.58911e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+O(q^{10}) $ 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	\( 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}+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

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 $

$2$	−156.182	−1.72558	−0.862790	−	0.505562i	$-0.831285\pi$
$2$	−156.182	−1.72558	−0.862790	+	0.505562i	$0.831285\pi$
$3$	145.398	0.115151	0.0575757	−	0.998341i	$-0.481663\pi$
$3$	145.398	0.115151	0.0575757	+	0.998341i	$0.481663\pi$
$4$	16200.7	1.97763
$5$	−42219.2	−1.20838	−0.604192	−	0.796839i	$-0.706504\pi$
$5$	−42219.2	−1.20838	−0.604192	+	0.796839i	$0.706504\pi$
$6$	−22708.4	−0.198703
$7$	140720.	0.452085	0.226042	−	0.974117i	$-0.427421\pi$
$7$	140720.	0.452085	0.226042	+	0.974117i	$0.427421\pi$
$8$	−1.25081e6	−1.68697
$9$	−1.57318e6	−0.986740
$10$	6.59387e6	2.08516
$11$	1.01012e7	1.71918	0.859590	−	0.510984i	$-0.170719\pi$
$11$	1.01012e7	1.71918	0.859590	+	0.510984i	$0.170719\pi$
$12$	2.35555e6	0.227726
$13$	2.70916e7	1.55669	0.778347	−	0.627835i	$-0.216059\pi$
$13$	2.70916e7	1.55669	0.778347	+	0.627835i	$0.216059\pi$
$14$	−2.19779e7	−0.780108
$15$	−6.13857e6	−0.139147
$16$	6.26381e7	0.933380
$17$	−7.94734e7	−0.798553	−0.399276	−	0.916831i	$-0.630739\pi$
$17$	−7.94734e7	−0.798553	−0.399276	+	0.916831i	$0.630739\pi$
$18$	2.45702e8	1.70270
$19$	−3.02415e8	−1.47471	−0.737353	−	0.675508i	$-0.763924\pi$
$19$	−3.02415e8	−1.47471	−0.737353	+	0.675508i	$0.763924\pi$
$20$	−6.83982e8	−2.38973
$21$	2.04604e7	0.0520582
$22$	−1.57763e9	−2.96658
$23$	1.22651e9	1.72758	0.863791	−	0.503850i	$-0.168084\pi$
$23$	1.22651e9	1.72758	0.863791	+	0.503850i	$0.168084\pi$
$24$	−1.81865e8	−0.194257
$25$	5.61759e8	0.460193
$26$	−4.23121e9	−2.68620
$27$	−4.60548e8	−0.228776
$28$	2.27977e9	0.894055
$29$	−2.20816e9	−0.689357	−0.344678	−	0.938721i	$-0.612012\pi$
$29$	−2.20816e9	−0.689357	−0.344678	+	0.938721i	$0.612012\pi$
$30$	9.58733e8	0.240110
$31$	−6.83081e8	−0.138236	−0.0691181	−	0.997608i	$-0.522019\pi$
$31$	−6.83081e8	−0.138236	−0.0691181	+	0.997608i	$0.522019\pi$
$32$	4.63754e8	0.0763507
$33$	1.46869e9	0.197966
$34$	1.24123e10	1.37797
$35$	−5.94110e9	−0.546292
$36$	−2.54867e10	−1.95140
$37$	2.15026e10	1.37778	0.688890	−	0.724865i	$-0.258098\pi$
$37$	2.15026e10	1.37778	0.688890	+	0.724865i	$0.258098\pi$
$38$	4.72317e10	2.54472
$39$	3.93906e9	0.179255
$40$	5.28084e10	2.03851
$41$	−2.01349e10	−0.661993	−0.330996	−	0.943632i	$-0.607385\pi$
$41$	−2.01349e10	−0.661993	−0.330996	+	0.943632i	$0.607385\pi$
$42$	−3.19554e9	−0.0898305
$43$	−7.18113e10	−1.73240	−0.866199	−	0.499700i	$-0.833444\pi$
$43$	−7.18113e10	−1.73240	−0.866199	+	0.499700i	$0.833444\pi$
$44$	1.63647e11	3.39990
$45$	6.64185e10	1.19236
$46$	−1.91558e11	−2.98108
$47$	1.65782e10	0.224337	0.112168	−	0.993689i	$-0.464220\pi$
$47$	1.65782e10	0.224337	0.112168	+	0.993689i	$0.464220\pi$
$48$	9.10743e9	0.107480
$49$	−7.70868e10	−0.795619
$50$	−8.77365e10	−0.794100
$51$	−1.15552e10	−0.0919545
$52$	4.38904e11	3.07856
$53$	2.28728e11	1.41751	0.708754	−	0.705455i	$-0.249257\pi$
$53$	2.28728e11	1.41751	0.708754	+	0.705455i	$0.249257\pi$
$54$	7.19291e10	0.394771
$55$	−4.26466e11	−2.07743
$56$	−1.76015e11	−0.762655
$57$	−4.39705e10	−0.169814
$58$	3.44874e11	1.18954
$59$	−5.15415e11	−1.59081	−0.795407	−	0.606076i	$-0.792743\pi$
$59$	−5.15415e11	−1.59081	−0.795407	+	0.606076i	$0.792743\pi$
$60$	−9.94493e10	−0.275181
$61$	1.40601e11	0.349418	0.174709	−	0.984620i	$-0.444102\pi$
$61$	1.40601e11	0.349418	0.174709	+	0.984620i	$0.444102\pi$
$62$	1.06685e11	0.238537
$63$	−2.21379e11	−0.446090
$64$	−5.85561e11	−1.06513
$65$	−1.14379e12	−1.88108
$66$	−2.29383e11	−0.341606
$67$	2.53048e11	0.341757	0.170878	−	0.985292i	$-0.445339\pi$
$67$	2.53048e11	0.341757	0.170878	+	0.985292i	$0.445339\pi$
$68$	−1.28753e12	−1.57924
$69$	1.78331e11	0.198933
$70$	9.27892e11	0.942671
$71$	−1.59034e12	−1.47337	−0.736685	−	0.676236i	$-0.763610\pi$
$71$	−1.59034e12	−1.47337	−0.736685	+	0.676236i	$0.763610\pi$
$72$	1.96776e12	1.66460
$73$	1.28348e12	0.992634	0.496317	−	0.868141i	$-0.334685\pi$
$73$	1.28348e12	0.992634	0.496317	+	0.868141i	$0.334685\pi$
$74$	−3.35832e12	−2.37747
$75$	8.16784e10	0.0529919
$76$	−4.89934e12	−2.91642
$77$	1.42145e12	0.777215
$78$	−6.15208e11	−0.309320
$79$	−2.01437e12	−0.932315	−0.466157	−	0.884702i	$-0.654362\pi$
$79$	−2.01437e12	−0.932315	−0.466157	+	0.884702i	$0.654362\pi$
$80$	−2.64453e12	−1.12788
$81$	2.44120e12	0.960396
$82$	3.14469e12	1.14232
$83$	1.86340e12	0.625602	0.312801	−	0.949819i	$-0.398733\pi$
$83$	1.86340e12	0.625602	0.312801	+	0.949819i	$0.398733\pi$
$84$	3.31473e11	0.102952
$85$	3.35530e12	0.964959
$86$	1.12156e13	2.98939
$87$	−3.21061e11	−0.0793804
$88$	−1.26348e13	−2.90021
$89$	4.05006e12	0.863826	0.431913	−	0.901915i	$-0.357839\pi$
$89$	4.05006e12	0.863826	0.431913	+	0.901915i	$0.357839\pi$
$90$	−1.03734e13	−2.05752
$91$	3.81234e12	0.703757
$92$	1.98703e13	3.41651
$93$	−9.93184e10	−0.0159181
$94$	−2.58921e12	−0.387111
$95$	1.27677e13	1.78201
$96$	6.74287e10	0.00879188
$97$	4.35140e12	0.530411	0.265206	−	0.964192i	$-0.414560\pi$
$97$	4.35140e12	0.530411	0.265206	+	0.964192i	$0.414560\pi$
$98$	1.20395e13	1.37291
$99$	−1.58911e13	−1.69638
$100$	9.10090e12	0.910090
$101$	−1.38940e13	−1.30238	−0.651192	−	0.758913i	$-0.725731\pi$
$101$	−1.38940e13	−1.30238	−0.651192	+	0.758913i	$0.725731\pi$
$102$	1.80472e12	0.158675
$103$	−2.39762e13	−1.97851	−0.989255	−	0.146203i	$-0.953295\pi$
$103$	−2.39762e13	−1.97851	−0.989255	+	0.146203i	$0.953295\pi$
$104$	−3.38866e13	−2.62610
$105$	−8.63822e11	−0.0629063
$106$	−3.57231e13	−2.44602
$107$	3.47469e12	0.223832	0.111916	−	0.993718i	$-0.464301\pi$
$107$	3.47469e12	0.223832	0.111916	+	0.993718i	$0.464301\pi$
$108$	−7.46120e12	−0.452433
$109$	1.17165e12	0.0669154	0.0334577	−	0.999440i	$-0.489348\pi$
$109$	1.17165e12	0.0669154	0.0334577	+	0.999440i	$0.489348\pi$
$110$	6.66061e13	3.58477
$111$	3.12643e12	0.158653
$112$	8.81446e12	0.421967
$113$	2.58831e13	1.16952	0.584758	−	0.811208i	$-0.301190\pi$
$113$	2.58831e13	1.16952	0.584758	+	0.811208i	$0.301190\pi$
$114$	6.86738e12	0.293028
$115$	−5.17821e13	−2.08758
$116$	−3.57738e13	−1.36329
$117$	−4.26201e13	−1.53605
$118$	8.04984e13	2.74508
$119$	−1.11835e13	−0.361014
$120$	7.67822e12	0.234737
$121$	6.75120e13	1.95558
$122$	−2.19593e13	−0.602949
$123$	−2.92756e12	−0.0762294
$124$	−1.10664e13	−0.273379
$125$	2.78201e13	0.652294
$126$	3.45753e13	0.769764
$127$	8.07463e13	1.70765	0.853825	−	0.520561i	$-0.174277\pi$
$127$	8.07463e13	1.70765	0.853825	+	0.520561i	$0.174277\pi$
$128$	8.76548e13	1.76162
$129$	−1.04412e13	−0.199488
$130$	1.78639e14	3.24596
$131$	8.22895e13	1.42259	0.711297	−	0.702892i	$-0.248108\pi$
$131$	8.22895e13	1.42259	0.711297	+	0.702892i	$0.248108\pi$
$132$	2.37939e13	0.391503
$133$	−4.25560e13	−0.666692
$134$	−3.95215e13	−0.589728
$135$	1.94440e13	0.276449
$136$	9.94065e13	1.34714
$137$	−4.05438e13	−0.523890	−0.261945	−	0.965083i	$-0.584364\pi$
$137$	−4.05438e13	−0.523890	−0.261945	+	0.965083i	$0.584364\pi$
$138$	−2.78520e13	−0.343276
$139$	−1.58298e14	−1.86157	−0.930783	−	0.365572i	$-0.880873\pi$
$139$	−1.58298e14	−1.86157	−0.930783	+	0.365572i	$0.880873\pi$
$140$	−9.62501e13	−1.08036
$141$	2.41043e12	0.0258327
$142$	2.48383e14	2.54242
$143$	2.73658e14	2.67624
$144$	−9.85411e13	−0.921004
$145$	9.32269e13	0.833008
$146$	−2.00455e14	−1.71287
$147$	−1.12082e13	−0.0916167
$148$	3.48358e14	2.72474
$149$	1.91701e14	1.43520	0.717602	−	0.696454i	$-0.245240\pi$
$149$	1.91701e14	1.43520	0.717602	+	0.696454i	$0.245240\pi$
$150$	−1.27567e13	−0.0914417
$151$	1.41076e14	0.968511	0.484255	−	0.874927i	$-0.339091\pi$
$151$	1.41076e14	0.968511	0.484255	+	0.874927i	$0.339091\pi$
$152$	3.78265e14	2.48779
$153$	1.25026e14	0.787964
$154$	−2.22004e14	−1.34115
$155$	2.88392e13	0.167042
$156$	6.38155e13	0.354500
$157$	4.64114e13	0.247330	0.123665	−	0.992324i	$-0.460535\pi$
$157$	4.64114e13	0.247330	0.123665	+	0.992324i	$0.460535\pi$
$158$	3.14607e14	1.60878
$159$	3.32565e13	0.163228
$160$	−1.95793e13	−0.0922610
$161$	1.72594e14	0.781013
$162$	−3.81270e14	−1.65724
$163$	2.55936e14	1.06884	0.534418	−	0.845220i	$-0.320531\pi$
$163$	2.55936e14	1.06884	0.534418	+	0.845220i	$0.320531\pi$
$164$	−3.26199e14	−1.30917
$165$	−6.20071e13	−0.239219
$166$	−2.91028e14	−1.07953
$167$	−9.12125e13	−0.325385	−0.162692	−	0.986677i	$-0.552018\pi$
$167$	−9.12125e13	−0.325385	−0.162692	+	0.986677i	$0.552018\pi$
$168$	−2.55922e13	−0.0878207
$169$	4.31081e14	1.42330
$170$	−5.24037e14	−1.66511
$171$	4.75754e14	1.45515
$172$	−1.16339e15	−3.42604
$173$	2.19464e13	0.0622392	0.0311196	−	0.999516i	$-0.490093\pi$
$173$	2.19464e13	0.0622392	0.0311196	+	0.999516i	$0.490093\pi$
$174$	5.01439e13	0.136977
$175$	7.90510e13	0.208046
$176$	6.32721e14	1.60465
$177$	−7.49402e13	−0.183184
$178$	−6.32545e14	−1.49060
$179$	−1.18994e14	−0.270384	−0.135192	−	0.990819i	$-0.543165\pi$
$179$	−1.18994e14	−0.270384	−0.135192	+	0.990819i	$0.543165\pi$
$180$	1.07603e15	2.35805
$181$	−2.24422e14	−0.474412	−0.237206	−	0.971459i	$-0.576232\pi$
$181$	−2.24422e14	−0.474412	−0.237206	+	0.971459i	$0.576232\pi$
$182$	−5.95418e14	−1.21439
$183$	2.04431e13	0.0402360
$184$	−1.53413e15	−2.91438
$185$	−9.07824e14	−1.66489
$186$	1.55117e13	0.0274679
$187$	−8.02778e14	−1.37286
$188$	2.68578e14	0.443655
$189$	−6.48085e13	−0.103426
$190$	−1.99409e15	−3.07500
$191$	1.02189e15	1.52295	0.761474	−	0.648195i	$-0.224476\pi$
$191$	1.02189e15	1.52295	0.761474	+	0.648195i	$0.224476\pi$
$192$	−8.51392e13	−0.122651
$193$	−1.32634e14	−0.184728	−0.0923640	−	0.995725i	$-0.529442\pi$
$193$	−1.32634e14	−0.184728	−0.0923640	+	0.995725i	$0.529442\pi$
$194$	−6.79609e14	−0.915267
$195$	−1.66304e14	−0.216609
$196$	−1.24886e15	−1.57344
$197$	−5.84517e13	−0.0712470
$197$	−5.84517e13	−0.0712470
$198$	2.48189e15	2.92725
$199$	−1.18083e15	−1.34785	−0.673925	−	0.738800i	$-0.735393\pi$
$199$	−1.18083e15	−1.34785	−0.673925	+	0.738800i	$0.735393\pi$
$200$	−7.02657e14	−0.776333
$201$	3.67926e13	0.0393537
$202$	2.16999e15	2.24737
$203$	−3.10733e14	−0.311648
$204$	−1.87203e14	−0.181852
$205$	8.50078e14	0.799942
$206$	3.74464e15	3.41408
$207$	−1.92952e15	−1.70467
$208$	1.69697e15	1.45299
$209$	−3.05476e15	−2.53529
$210$	1.34913e14	0.108550
$211$	−2.59301e14	−0.202287	−0.101143	−	0.994872i	$-0.532250\pi$
$211$	−2.59301e14	−0.202287	−0.101143	+	0.994872i	$0.532250\pi$
$212$	3.70555e15	2.80330
$213$	−2.31232e14	−0.169661
$214$	−5.42683e14	−0.386240
$215$	3.03181e15	2.09340
$216$	5.76060e14	0.385939
$217$	−9.61235e13	−0.0624944
$218$	−1.82990e14	−0.115468
$219$	1.86614e14	0.114303
$220$	−6.90905e15	−4.10838
$221$	−2.15306e15	−1.24310
$222$	−4.88291e14	−0.273769
$223$	−2.70804e15	−1.47460	−0.737299	−	0.675567i	$-0.763899\pi$
$223$	−2.70804e15	−1.47460	−0.737299	+	0.675567i	$0.763899\pi$
$224$	6.52596e13	0.0345170
$225$	−8.83750e14	−0.454091
$226$	−4.04246e15	−2.01809
$227$	6.30594e14	0.305902	0.152951	−	0.988234i	$-0.451122\pi$
$227$	6.30594e14	0.305902	0.152951	+	0.988234i	$0.451122\pi$
$228$	−7.12353e14	−0.335829
$229$	−1.68684e15	−0.772937	−0.386468	−	0.922303i	$-0.626305\pi$
$229$	−1.68684e15	−0.772937	−0.386468	+	0.922303i	$0.626305\pi$
$230$	8.08742e15	3.60229
$231$	2.06675e14	0.0894974
$232$	2.76200e15	1.16293
$233$	1.12024e15	0.458667	0.229334	−	0.973348i	$-0.426345\pi$
$233$	1.12024e15	0.458667	0.229334	+	0.973348i	$0.426345\pi$
$234$	6.65647e15	2.65058
$235$	−6.99918e14	−0.271085
$236$	−8.35010e15	−3.14603
$237$	−2.92884e14	−0.107357
$238$	1.74666e15	0.622958
$239$	5.25075e15	1.82236	0.911181	−	0.412006i	$-0.135172\pi$
$239$	5.25075e15	1.82236	0.911181	+	0.412006i	$0.135172\pi$
$240$	−3.84508e14	−0.129877
$241$	2.28199e15	0.750246	0.375123	−	0.926975i	$-0.377600\pi$
$241$	2.28199e15	0.750246	0.375123	+	0.926975i	$0.377600\pi$
$242$	−1.05441e16	−3.37451
$243$	1.08921e15	0.339367
$244$	2.27784e15	0.691018
$245$	3.25454e15	0.961414
$246$	4.57231e14	0.131540
$247$	−8.19292e15	−2.29566
$248$	8.54408e14	0.233201
$249$	2.70934e14	0.0720389
$250$	−4.34499e15	−1.12559
$251$	2.18163e15	0.550683	0.275342	−	0.961346i	$-0.411209\pi$
$251$	2.18163e15	0.550683	0.275342	+	0.961346i	$0.411209\pi$
$252$	−3.58650e15	−0.882200
$253$	1.23892e16	2.97003
$254$	−1.26111e16	−2.94669
$255$	4.87853e14	0.111116
$256$	−8.89316e15	−1.97468
$257$	−5.82816e14	−0.126173	−0.0630864	−	0.998008i	$-0.520094\pi$
$257$	−5.82816e14	−0.126173	−0.0630864	+	0.998008i	$0.520094\pi$
$258$	1.63072e15	0.344232
$259$	3.02586e15	0.622874
$260$	−1.85302e16	−3.72008
$261$	3.47384e15	0.680216
$262$	−1.28521e16	−2.45480
$263$	−8.54114e15	−1.59149	−0.795744	−	0.605633i	$-0.792920\pi$
$263$	−8.54114e15	−1.59149	−0.795744	+	0.605633i	$0.792920\pi$
$264$	−1.83706e15	−0.333963
$265$	−9.65671e15	−1.71290
$266$	6.64647e15	1.15043
$267$	5.88869e14	0.0994707
$268$	4.09956e15	0.675867
$269$	−2.03560e15	−0.327569	−0.163784	−	0.986496i	$-0.552370\pi$
$269$	−2.03560e15	−0.327569	−0.163784	+	0.986496i	$0.552370\pi$
$270$	−3.03679e15	−0.477035
$271$	−9.13857e15	−1.40145	−0.700726	−	0.713431i	$-0.747140\pi$
$271$	−9.13857e15	−1.40145	−0.700726	+	0.713431i	$0.747140\pi$
$272$	−4.97806e15	−0.745353
$273$	5.54306e14	0.0810386
$274$	6.33219e15	0.904015
$275$	5.67445e15	0.791155
$276$	2.88909e15	0.393416
$277$	−1.68445e15	−0.224048	−0.112024	−	0.993706i	$-0.535733\pi$
$277$	−1.68445e15	−0.224048	−0.112024	+	0.993706i	$0.535733\pi$
$278$	2.47232e16	3.21228
$279$	1.07461e15	0.136403
$280$	7.43122e15	0.921580
$281$	4.98535e15	0.604094	0.302047	−	0.953293i	$-0.402330\pi$
$281$	4.98535e15	0.604094	0.302047	+	0.953293i	$0.402330\pi$
$282$	−3.76465e14	−0.0445764
$283$	4.42735e15	0.512309	0.256154	−	0.966636i	$-0.417544\pi$
$283$	4.42735e15	0.512309	0.256154	+	0.966636i	$0.417544\pi$
$284$	−2.57647e16	−2.91378
$285$	1.85640e15	0.205201
$286$	−4.27404e16	−4.61806
$287$	−2.83338e15	−0.299277
$288$	−7.29570e14	−0.0753383
$289$	−3.58856e15	−0.362313
$290$	−1.45603e16	−1.43742
$291$	6.32683e14	0.0610776
$292$	2.07932e16	1.96306
$293$	1.20468e16	1.11233	0.556165	−	0.831072i	$-0.312272\pi$
$293$	1.20468e16	1.11233	0.556165	+	0.831072i	$0.312272\pi$
$294$	1.75052e15	0.158092
$295$	2.17604e16	1.92231
$296$	−2.68958e16	−2.32428
$297$	−4.65210e15	−0.393307
$298$	−2.99402e16	−2.47656
$299$	3.32280e16	2.68932
$300$	1.32325e15	0.104798
$301$	−1.01053e16	−0.783190
$302$	−2.20336e16	−1.67124
$303$	−2.02016e15	−0.149971
$304$	−1.89427e16	−1.37646
$305$	−5.93608e15	−0.422231
$306$	−1.95268e16	−1.35970
$307$	−9.26126e14	−0.0631351	−0.0315675	−	0.999502i	$-0.510050\pi$
$307$	−9.26126e14	−0.0631351	−0.0315675	+	0.999502i	$0.510050\pi$
$308$	2.30285e16	1.53704
$309$	−3.48608e15	−0.227828
$310$	−4.50415e15	−0.288245
$311$	−2.90105e16	−1.81808	−0.909038	−	0.416712i	$-0.863182\pi$
$311$	−2.90105e16	−1.81808	−0.909038	+	0.416712i	$0.863182\pi$
$312$	−4.92703e15	−0.302399
$313$	−5.07394e15	−0.305005	−0.152503	−	0.988303i	$-0.548733\pi$
$313$	−5.07394e15	−0.305005	−0.152503	+	0.988303i	$0.548733\pi$
$314$	−7.24860e15	−0.426788
$315$	9.34644e15	0.539048
$316$	−3.26342e16	−1.84377
$317$	9.04960e15	0.500892	0.250446	−	0.968131i	$-0.419423\pi$
$317$	9.04960e15	0.500892	0.250446	+	0.968131i	$0.419423\pi$
$318$	−5.19405e15	−0.281663
$319$	−2.23051e16	−1.18513
$320$	2.47219e16	1.28709
$321$	5.05212e14	0.0257745
$322$	−2.69561e16	−1.34770
$323$	2.40340e16	1.17763
$324$	3.95492e16	1.89931
$325$	1.52190e16	0.716380
$326$	−3.99724e16	−1.84436
$327$	1.70355e14	0.00770540
$328$	2.51850e16	1.11676
$329$	2.33289e15	0.101419
$330$	9.68437e15	0.412792
$331$	−3.09772e16	−1.29467	−0.647337	−	0.762204i	$-0.724117\pi$
$331$	−3.09772e16	−1.29467	−0.647337	+	0.762204i	$0.724117\pi$
$332$	3.01884e16	1.23721
$333$	−3.38275e16	−1.35951
$334$	1.42457e16	0.561478
$335$	−1.06835e16	−0.412973
$336$	1.28160e15	0.0485901
$337$	2.94553e16	1.09539	0.547696	−	0.836678i	$-0.315505\pi$
$337$	2.94553e16	1.09539	0.547696	+	0.836678i	$0.315505\pi$
$338$	−6.73269e16	−2.45601
$339$	3.76334e15	0.134671
$340$	5.43583e16	1.90833
$341$	−6.89996e15	−0.237653
$342$	−7.43041e16	−2.51098
$343$	−2.44819e16	−0.811772
$344$	8.98226e16	2.92251
$345$	−7.52900e15	−0.240388
$346$	−3.42763e15	−0.107399
$347$	−5.52018e16	−1.69751	−0.848753	−	0.528790i	$-0.822646\pi$
$347$	−5.52018e16	−1.69751	−0.848753	+	0.528790i	$0.822646\pi$
$348$	−5.20143e15	−0.156985
$349$	1.30873e16	0.387689	0.193845	−	0.981032i	$-0.437904\pi$
$349$	1.30873e16	0.387689	0.193845	+	0.981032i	$0.437904\pi$
$350$	−1.23463e16	−0.359000
$351$	−1.24770e16	−0.356134
$352$	4.68448e15	0.131261
$353$	6.32311e16	1.73938	0.869692	−	0.493595i	$-0.164318\pi$
$353$	6.32311e16	1.73938	0.869692	+	0.493595i	$0.164318\pi$
$354$	1.17043e16	0.316099
$355$	6.71431e16	1.78040
$356$	6.56138e16	1.70832
$357$	−1.62606e15	−0.0415712
$358$	1.85847e16	0.466569
$359$	−3.74200e14	−0.00922550	−0.00461275	−	0.999989i	$-0.501468\pi$
$359$	−3.74200e14	−0.00922550	−0.00461275	+	0.999989i	$0.501468\pi$
$360$	−8.30773e16	−2.01148
$361$	4.94020e16	1.17476
$362$	3.50507e16	0.818635
$363$	9.81608e15	0.225188
$364$	6.17627e16	1.39177
$365$	−5.41873e16	−1.19948
$366$	−3.19284e15	−0.0694304
$367$	−3.98708e16	−0.851775	−0.425888	−	0.904776i	$-0.640038\pi$
$367$	−3.98708e16	−0.851775	−0.425888	+	0.904776i	$0.640038\pi$
$368$	7.68260e16	1.61249
$369$	3.16758e16	0.653215
$370$	1.41785e17	2.87290
$371$	3.21867e16	0.640834
$372$	−1.60903e15	−0.0314800
$373$	−5.55924e16	−1.06883	−0.534414	−	0.845223i	$-0.679468\pi$
$373$	−5.55924e16	−1.06883	−0.534414	+	0.845223i	$0.679468\pi$
$374$	1.25379e17	2.36897
$375$	4.04498e15	0.0751126
$376$	−2.07362e16	−0.378450
$377$	−5.98227e16	−1.07312
$378$	1.01219e16	0.178470
$379$	−4.87769e16	−0.845394	−0.422697	−	0.906271i	$-0.638917\pi$
$379$	−4.87769e16	−0.845394	−0.422697	+	0.906271i	$0.638917\pi$
$380$	2.06846e17	3.52415
$381$	1.17403e16	0.196638
$382$	−1.59600e17	−2.62797
$383$	−3.53081e16	−0.571587	−0.285793	−	0.958291i	$-0.592257\pi$
$383$	−3.53081e16	−0.571587	−0.285793	+	0.958291i	$0.592257\pi$
$384$	1.27448e16	0.202852
$385$	−6.00124e16	−0.939175
$386$	2.07150e16	0.318763
$387$	1.12972e17	1.70943
$388$	7.04958e16	1.04896
$389$	4.31504e16	0.631411	0.315706	−	0.948857i	$-0.397759\pi$
$389$	4.31504e16	0.631411	0.315706	+	0.948857i	$0.397759\pi$
$390$	2.59736e16	0.373777
$391$	−9.74746e16	−1.37957
$392$	9.64213e16	1.34219
$393$	1.19647e16	0.163814
$394$	9.12909e15	0.122942
$395$	8.50450e16	1.12659
$396$	−2.57447e17	−3.35481
$397$	8.33842e15	0.106892	0.0534460	−	0.998571i	$-0.482979\pi$
$397$	8.33842e15	0.106892	0.0534460	+	0.998571i	$0.482979\pi$
$398$	1.84424e17	2.32582
$399$	−6.18754e15	−0.0767705
$400$	3.51875e16	0.429535
$401$	6.03120e16	0.724378	0.362189	−	0.932105i	$-0.382030\pi$
$401$	6.03120e16	0.724378	0.362189	+	0.932105i	$0.382030\pi$
$402$	−5.74633e15	−0.0679080
$403$	−1.85058e16	−0.215191
$404$	−2.25093e17	−2.57563
$405$	−1.03065e17	−1.16053
$406$	4.85309e16	0.537773
$407$	2.17203e17	2.36865
$408$	1.44535e16	0.155125
$409$	−4.61200e16	−0.487178	−0.243589	−	0.969879i	$-0.578325\pi$
$409$	−4.61200e16	−0.487178	−0.243589	+	0.969879i	$0.578325\pi$
$410$	−1.32767e17	−1.38036
$411$	−5.89497e15	−0.0603267
$412$	−3.88431e17	−3.91275
$413$	−7.25294e16	−0.719182
$414$	3.01355e17	2.94155
$415$	−7.86712e16	−0.755967
$416$	1.25638e16	0.118855
$417$	−2.30161e16	−0.214362
$418$	4.77098e17	4.37484
$419$	−1.76604e16	−0.159445	−0.0797223	−	0.996817i	$-0.525403\pi$
$419$	−1.76604e16	−0.159445	−0.0797223	+	0.996817i	$0.525403\pi$
$420$	−1.39945e16	−0.124405
$421$	−1.78240e17	−1.56016	−0.780082	−	0.625677i	$-0.784823\pi$
$421$	−1.78240e17	−1.56016	−0.780082	+	0.625677i	$0.784823\pi$
$422$	4.04980e16	0.349062
$423$	−2.60805e16	−0.221362
$424$	−2.86096e17	−2.39130
$425$	−4.46449e16	−0.367489
$426$	3.61142e16	0.292763
$427$	1.97855e16	0.157967
$428$	5.62925e16	0.442656
$429$	3.97893e16	0.308172
$430$	−4.73514e17	−3.61233
$431$	−1.68744e17	−1.26802	−0.634010	−	0.773325i	$-0.718592\pi$
$431$	−1.68744e17	−1.26802	−0.634010	+	0.773325i	$0.718592\pi$
$432$	−2.88478e16	−0.213535
$433$	−1.12283e17	−0.818737	−0.409368	−	0.912369i	$-0.634251\pi$
$433$	−1.12283e17	−0.818737	−0.409368	+	0.912369i	$0.634251\pi$
$434$	1.50127e16	0.107839
$435$	1.35550e16	0.0959220
$436$	1.89816e16	0.132334
$437$	−3.70914e17	−2.54767
$438$	−2.91457e16	−0.197239
$439$	1.39313e17	0.928907	0.464453	−	0.885598i	$-0.346251\pi$
$439$	1.39313e17	0.928907	0.464453	+	0.885598i	$0.346251\pi$
$440$	5.33430e17	3.50457
$441$	1.21272e17	0.785070
$442$	3.36269e17	2.14507
$443$	2.87843e17	1.80939	0.904694	−	0.426061i	$-0.140099\pi$
$443$	2.87843e17	1.80939	0.904694	+	0.426061i	$0.140099\pi$
$444$	5.06504e16	0.313757
$445$	−1.70990e17	−1.04383
$446$	4.22946e17	2.54454
$447$	2.78728e16	0.165266
$448$	−8.24004e16	−0.481529
$449$	−1.92688e17	−1.10982	−0.554911	−	0.831910i	$-0.687248\pi$
$449$	−1.92688e17	−1.10982	−0.554911	+	0.831910i	$0.687248\pi$
$450$	1.38025e17	0.783570
$451$	−2.03387e17	−1.13809
$452$	4.19324e17	2.31286
$453$	2.05122e16	0.111525
$454$	−9.84873e16	−0.527858
$455$	−1.60954e17	−0.850409
$456$	5.49989e16	0.286472
$457$	−1.94202e17	−0.997237	−0.498618	−	0.866822i	$-0.666159\pi$
$457$	−1.94202e17	−0.997237	−0.498618	+	0.866822i	$0.666159\pi$
$458$	2.63454e17	1.33376
$459$	3.66013e16	0.182690
$460$	−8.38907e17	−4.12846
$461$	−1.54263e17	−0.748524	−0.374262	−	0.927323i	$-0.622104\pi$
$461$	−1.54263e17	−0.748524	−0.374262	+	0.927323i	$0.622104\pi$
$462$	−3.22789e16	−0.154435
$463$	−5.96965e16	−0.281626	−0.140813	−	0.990036i	$-0.544972\pi$
$463$	−5.96965e16	−0.281626	−0.140813	+	0.990036i	$0.544972\pi$
$464$	−1.38315e17	−0.643432
$465$	4.19315e15	0.0192352
$466$	−1.74961e17	−0.791467
$467$	−2.22537e16	−0.0992754	−0.0496377	−	0.998767i	$-0.515807\pi$
$467$	−2.22537e16	−0.0992754	−0.0496377	+	0.998767i	$0.515807\pi$
$468$	−6.90476e17	−3.03774
$469$	3.56090e16	0.154503
$470$	1.09314e17	0.467779
$471$	6.74810e15	0.0284804
$472$	6.44689e17	2.68366
$473$	−7.25381e17	−2.97830
$474$	4.57431e16	0.185254
$475$	−1.69885e17	−0.678649
$476$	−1.81181e17	−0.713950
$477$	−3.59831e17	−1.39871
$478$	−8.20071e17	−3.14463
$479$	−7.45601e16	−0.282050	−0.141025	−	0.990006i	$-0.545040\pi$
$479$	−7.45601e16	−0.282050	−0.141025	+	0.990006i	$0.545040\pi$
$480$	−2.84679e15	−0.0106240
$481$	5.82541e17	2.14478
$482$	−3.56406e17	−1.29461
$483$	2.50948e16	0.0899348
$484$	1.09374e18	3.86741
$485$	−1.83713e17	−0.640941
$486$	−1.70114e17	−0.585605
$487$	4.65421e16	0.158091	0.0790456	−	0.996871i	$-0.474813\pi$
$487$	4.65421e16	0.158091	0.0790456	+	0.996871i	$0.474813\pi$
$488$	−1.75866e17	−0.589459
$489$	3.72124e16	0.123078
$490$	−5.08300e17	−1.65900
$491$	−5.75242e17	−1.85277	−0.926383	−	0.376583i	$-0.877099\pi$
$491$	−5.75242e17	−1.85277	−0.926383	+	0.376583i	$0.877099\pi$
$492$	−4.74286e16	−0.150753
$493$	1.75490e17	0.550488
$494$	1.27958e18	3.96135
$495$	6.70908e17	2.04988
$496$	−4.27869e16	−0.129027
$497$	−2.23794e17	−0.666088
$498$	−4.23148e16	−0.124309
$499$	−2.60876e16	−0.0756450	−0.0378225	−	0.999284i	$-0.512042\pi$
$499$	−2.60876e16	−0.0756450	−0.0378225	+	0.999284i	$0.512042\pi$
$500$	4.50706e17	1.28999
$501$	−1.32621e16	−0.0374685
$502$	−3.40731e17	−0.950248
$503$	−2.00565e17	−0.552159	−0.276080	−	0.961135i	$-0.589035\pi$
$503$	−2.00565e17	−0.552159	−0.276080	+	0.961135i	$0.589035\pi$
$504$	2.76904e17	0.752542
$505$	5.86594e17	1.57378
$506$	−1.93497e18	−5.12502
$507$	6.26781e16	0.163894
$508$	1.30815e18	3.37709
$509$	−2.45371e17	−0.625399	−0.312700	−	0.949852i	$-0.601233\pi$
$509$	−2.45371e17	−0.625399	−0.312700	+	0.949852i	$0.601233\pi$
$510$	−7.61937e16	−0.191740
$511$	1.80611e17	0.448755
$512$	6.70881e17	1.64585
$513$	1.39277e17	0.337377
$514$	9.10251e16	0.217721
$515$	1.01226e18	2.39080
$516$	−1.69155e17	−0.394513
$517$	1.67460e17	0.385676
$518$	−4.72583e17	−1.07482
$519$	3.19096e15	0.00716693
$520$	1.43067e18	3.17334
$521$	−1.71991e17	−0.376755	−0.188378	−	0.982097i	$-0.560323\pi$
$521$	−1.71991e17	−0.376755	−0.188378	+	0.982097i	$0.560323\pi$
$522$	−5.42550e17	−1.17377
$523$	−1.09598e17	−0.234176	−0.117088	−	0.993122i	$-0.537356\pi$
$523$	−1.09598e17	−0.234176	−0.117088	+	0.993122i	$0.537356\pi$
$524$	1.33315e18	2.81336
$525$	1.14938e16	0.0239568
$526$	1.33397e18	2.74624
$527$	5.42868e16	0.110389
$528$	9.19962e16	0.184778
$529$	1.00028e18	1.98454
$530$	1.50820e18	2.95574
$531$	8.10842e17	1.56972
$532$	−6.89438e17	−1.31847
$533$	−5.45486e17	−1.03052
$534$	−9.19705e16	−0.171645
$535$	−1.46699e17	−0.270475
$536$	−3.16516e17	−0.576534
$537$	−1.73014e16	−0.0311351
$538$	3.17923e17	0.565246
$539$	−7.78671e17	−1.36781
$540$	3.15006e17	0.546713
$541$	−1.00640e18	−1.72579	−0.862896	−	0.505381i	$-0.831352\pi$
$541$	−1.00640e18	−1.72579	−0.862896	+	0.505381i	$0.831352\pi$
$542$	1.42728e18	2.41832
$543$	−3.26305e16	−0.0546292
$544$	−3.68561e16	−0.0609701
$545$	−4.94662e16	−0.0808595
$546$	−8.65724e16	−0.139839
$547$	1.56743e17	0.250190	0.125095	−	0.992145i	$-0.460076\pi$
$547$	1.56743e17	0.250190	0.125095	+	0.992145i	$0.460076\pi$
$548$	−6.56838e17	−1.03606
$549$	−2.21191e17	−0.344785
$550$	−8.86246e17	−1.36520
$551$	6.67782e17	1.01660
$552$	−2.23059e17	−0.335595
$553$	−2.83463e17	−0.421485
$554$	2.63081e17	0.386612
$555$	−1.31995e17	−0.191714
$556$	−2.56454e18	−3.68148
$557$	7.98265e17	1.13263	0.566316	−	0.824188i	$-0.308368\pi$
$557$	7.98265e17	1.13263	0.566316	+	0.824188i	$0.308368\pi$
$558$	−1.67835e17	−0.235375
$559$	−1.94548e18	−2.69681
$560$	−3.72139e17	−0.509898
$561$	−1.16722e17	−0.158086
$562$	−7.78621e17	−1.04241
$563$	6.49635e17	0.859735	0.429867	−	0.902892i	$-0.358560\pi$
$563$	6.49635e17	0.859735	0.429867	+	0.902892i	$0.358560\pi$
$564$	3.90507e16	0.0510874
$565$	−1.09276e18	−1.41322
$566$	−6.91470e17	−0.884029
$567$	3.43526e17	0.434180
$568$	1.98923e18	2.48554
$569$	5.45655e17	0.674045	0.337022	−	0.941497i	$-0.390580\pi$
$569$	5.45655e17	0.674045	0.337022	+	0.941497i	$0.390580\pi$
$570$	−2.89935e17	−0.354091
$571$	5.26721e17	0.635983	0.317992	−	0.948094i	$-0.396992\pi$
$571$	5.26721e17	0.635983	0.317992	+	0.948094i	$0.396992\pi$
$572$	4.43346e18	5.29260
$573$	1.48580e17	0.175370
$574$	4.42523e17	0.516426
$575$	6.89001e17	0.795021
$576$	9.21194e17	1.05101
$577$	−1.14653e18	−1.29343	−0.646717	−	0.762730i	$-0.723858\pi$
$577$	−1.14653e18	−1.29343	−0.646717	+	0.762730i	$0.723858\pi$
$578$	5.60467e17	0.625200
$579$	−1.92847e16	−0.0212717
$580$	1.51034e18	1.64738
$581$	2.62218e17	0.282825
$582$	−9.88135e16	−0.105394
$583$	2.31043e18	2.43695
$584$	−1.60539e18	−1.67455
$585$	1.79939e18	1.85614
$586$	−1.88150e18	−1.91942
$587$	−2.89181e17	−0.291758	−0.145879	−	0.989302i	$-0.546601\pi$
$587$	−2.89181e17	−0.291758	−0.145879	+	0.989302i	$0.546601\pi$
$588$	−1.81581e17	−0.181184
$589$	2.06574e17	0.203858
$590$	−3.39858e18	−3.31711
$591$	−8.49874e15	−0.00820420
$592$	1.34688e18	1.28599
$593$	−7.69437e17	−0.726637	−0.363319	−	0.931665i	$-0.618356\pi$
$593$	−7.69437e17	−0.726637	−0.363319	+	0.931665i	$0.618356\pi$
$594$	7.26572e17	0.678683
$595$	4.72160e17	0.436243
$596$	3.10569e18	2.83830
$597$	−1.71689e17	−0.155207
$598$	−5.18961e18	−4.64063
$599$	−1.27078e18	−1.12407	−0.562037	−	0.827112i	$-0.689982\pi$
$599$	−1.27078e18	−1.12407	−0.562037	+	0.827112i	$0.689982\pi$
$600$	−1.02165e17	−0.0893958
$601$	−1.71100e18	−1.48104	−0.740519	−	0.672035i	$-0.765420\pi$
$601$	−1.71100e18	−1.48104	−0.740519	+	0.672035i	$0.765420\pi$
$602$	1.57826e18	1.35146
$603$	−3.98091e17	−0.337225
$604$	2.28554e18	1.91535
$605$	−2.85030e18	−2.36309
$606$	3.15511e17	0.258787
$607$	−1.97449e18	−1.60225	−0.801123	−	0.598500i	$-0.795764\pi$
$607$	−1.97449e18	−1.60225	−0.801123	+	0.598500i	$0.795764\pi$
$608$	−1.40246e17	−0.112595
$609$	−4.51799e16	−0.0358866
$610$	9.27106e17	0.728594
$611$	4.49130e17	0.349224
$612$	2.02551e18	1.55830
$613$	−1.66843e18	−1.27003	−0.635016	−	0.772499i	$-0.719007\pi$
$613$	−1.66843e18	−1.27003	−0.635016	+	0.772499i	$0.719007\pi$
$614$	1.44644e17	0.108945
$615$	1.23599e17	0.0921144
$616$	−1.77797e18	−1.31114
$617$	7.95080e17	0.580173	0.290086	−	0.957000i	$-0.406316\pi$
$617$	7.95080e17	0.580173	0.290086	+	0.957000i	$0.406316\pi$
$618$	5.44462e17	0.393136
$619$	1.95212e18	1.39482	0.697409	−	0.716673i	$-0.254336\pi$
$619$	1.95212e18	1.39482	0.697409	+	0.716673i	$0.254336\pi$
$620$	4.67215e17	0.330347
$621$	−5.64864e17	−0.395229
$622$	4.53090e18	3.13724
$623$	5.69926e17	0.390522
$624$	2.46735e17	0.167313
$625$	−1.86028e18	−1.24842
$626$	7.92457e17	0.526311
$627$	−4.44155e17	−0.291942
$628$	7.51897e17	0.489126
$629$	−1.70889e18	−1.10023
$630$	−1.45974e18	−0.930171
$631$	2.25291e18	1.42087	0.710434	−	0.703764i	$-0.248499\pi$
$631$	2.25291e18	1.42087	0.710434	+	0.703764i	$0.248499\pi$
$632$	2.51960e18	1.57279
$633$	−3.77017e16	−0.0232936
$634$	−1.41338e18	−0.864330
$635$	−3.40905e18	−2.06350
$636$	5.38779e17	0.322804
$637$	−2.08841e18	−1.23854
$638$	3.48365e18	2.04503
$639$	2.50190e18	1.45383
$640$	−3.70072e18	−2.12871
$641$	7.02648e17	0.400093	0.200046	−	0.979786i	$-0.435891\pi$
$641$	7.02648e17	0.400093	0.200046	+	0.979786i	$0.435891\pi$
$642$	−7.89049e16	−0.0444760
$643$	3.25156e17	0.181435	0.0907174	−	0.995877i	$-0.471084\pi$
$643$	3.25156e17	0.181435	0.0907174	+	0.995877i	$0.471084\pi$
$644$	2.79615e18	1.54455
$645$	4.40819e17	0.241058
$646$	−3.75367e18	−2.03210
$647$	7.77446e16	0.0416670	0.0208335	−	0.999783i	$-0.493368\pi$
$647$	7.77446e16	0.0416670	0.0208335	+	0.999783i	$0.493368\pi$
$648$	−3.05349e18	−1.62016
$649$	−5.20632e18	−2.73490
$650$	−2.37692e18	−1.23617
$651$	−1.39761e16	−0.00719632
$652$	4.14634e18	2.11376
$653$	3.53906e18	1.78629	0.893145	−	0.449769i	$-0.148494\pi$
$653$	3.53906e18	1.78629	0.893145	+	0.449769i	$0.148494\pi$
$654$	−2.66064e16	−0.0132963
$655$	−3.47420e18	−1.71904
$656$	−1.26121e18	−0.617891
$657$	−2.01914e18	−0.979472
$658$	−3.64354e17	−0.175007
$659$	−2.41172e18	−1.14702	−0.573512	−	0.819197i	$-0.694419\pi$
$659$	−2.41172e18	−1.14702	−0.573512	+	0.819197i	$0.694419\pi$
$660$	−1.00456e18	−0.473086
$661$	3.41467e18	1.59235	0.796175	−	0.605066i	$-0.206853\pi$
$661$	3.41467e18	1.59235	0.796175	+	0.605066i	$0.206853\pi$
$662$	4.83807e18	2.23406
$663$	−3.13050e17	−0.143145
$664$	−2.33076e18	−1.05537
$665$	1.79668e18	0.805620
$666$	5.28324e18	2.34595
$667$	−2.70832e18	−1.19092
$668$	−1.47771e18	−0.643490
$669$	−3.93743e17	−0.169802
$670$	1.66857e18	0.712619
$671$	1.42024e18	0.600713
$672$	9.48860e15	0.00397468
$673$	5.31727e17	0.220592	0.110296	−	0.993899i	$-0.464820\pi$
$673$	5.31727e17	0.220592	0.110296	+	0.993899i	$0.464820\pi$
$674$	−4.60038e18	−1.89018
$675$	−2.58717e17	−0.105281
$676$	6.98382e18	2.81475
$677$	−3.10744e18	−1.24044	−0.620221	−	0.784427i	$-0.712957\pi$
$677$	−3.10744e18	−1.24044	−0.620221	+	0.784427i	$0.712957\pi$
$678$	−5.87764e17	−0.232386
$679$	6.12331e17	0.239791
$680$	−4.19686e18	−1.62786
$681$	9.16869e16	0.0352250
$682$	1.07765e18	0.410089
$683$	2.49420e18	0.940151	0.470075	−	0.882626i	$-0.344227\pi$
$683$	2.49420e18	0.940151	0.470075	+	0.882626i	$0.344227\pi$
$684$	7.70756e18	2.87775
$685$	1.71173e18	0.633061
$686$	3.82363e18	1.40078
$687$	−2.45263e17	−0.0890047
$688$	−4.49812e18	−1.61699
$689$	6.19661e18	2.20663
$690$	1.17589e18	0.414809
$691$	6.96468e17	0.243385	0.121693	−	0.992568i	$-0.461168\pi$
$691$	6.96468e17	0.243385	0.121693	+	0.992568i	$0.461168\pi$
$692$	3.55548e17	0.123086
$693$	−2.23620e18	−0.766909
$694$	8.62150e18	2.92918
$695$	6.68321e18	2.24949
$696$	4.01588e17	0.133913
$697$	1.60018e18	0.528636
$698$	−2.04399e18	−0.668989
$699$	1.62880e17	0.0528162
$700$	1.28068e18	0.411438
$701$	1.48603e18	0.473000	0.236500	−	0.971632i	$-0.424000\pi$
$701$	1.48603e18	0.473000	0.236500	+	0.971632i	$0.424000\pi$
$702$	1.94868e18	0.614538
$703$	−6.50272e18	−2.03182
$704$	−5.91488e18	−1.83115
$705$	−1.01766e17	−0.0312158
$706$	−9.87554e18	−3.00145
$707$	−1.95517e18	−0.588787
$708$	−1.21408e18	−0.362270
$709$	−1.31649e18	−0.389240	−0.194620	−	0.980879i	$-0.562347\pi$
$709$	−1.31649e18	−0.389240	−0.194620	+	0.980879i	$0.562347\pi$
$710$	−1.04865e19	−3.07222
$711$	3.16897e18	0.919952
$712$	−5.06587e18	−1.45725
$713$	−8.37803e17	−0.238814
$714$	2.53960e17	0.0717344
$715$	−1.15536e19	−3.23392
$716$	−1.92779e18	−0.534718
$717$	7.63446e17	0.209848
$718$	5.84432e16	0.0159193
$719$	−4.49679e18	−1.21385	−0.606925	−	0.794759i	$-0.707597\pi$
$719$	−4.49679e18	−1.21385	−0.606925	+	0.794759i	$0.707597\pi$
$720$	4.16033e18	1.11293
$721$	−3.37394e18	−0.894454
$722$	−7.71569e18	−2.02714
$723$	3.31796e17	0.0863919
$724$	−3.63580e18	−0.938209
$725$	−1.24046e18	−0.317237
$726$	−1.53309e18	−0.388580
$727$	1.98219e18	0.497934	0.248967	−	0.968512i	$-0.419909\pi$
$727$	1.98219e18	0.497934	0.248967	+	0.968512i	$0.419909\pi$
$728$	−4.76854e18	−1.18722
$729$	−3.73369e18	−0.921318
$730$	8.46307e18	2.06980
$731$	5.70708e18	1.38341
$732$	3.31193e17	0.0795717
$733$	4.46397e18	1.06303	0.531515	−	0.847049i	$-0.321623\pi$
$733$	4.46397e18	1.06303	0.531515	+	0.847049i	$0.321623\pi$
$734$	6.22708e18	1.46981
$735$	4.73203e17	0.110708
$736$	5.68797e17	0.131902
$737$	2.55610e18	0.587541
$738$	−4.94718e18	−1.12717
$739$	7.78019e17	0.175712	0.0878560	−	0.996133i	$-0.471998\pi$
$739$	7.78019e17	0.175712	0.0878560	+	0.996133i	$0.471998\pi$
$740$	−1.47074e19	−3.29253
$741$	−1.19123e18	−0.264349
$742$	−5.02697e18	−1.10581
$743$	4.44055e18	0.968299	0.484150	−	0.874985i	$-0.339129\pi$
$743$	4.44055e18	0.968299	0.484150	+	0.874985i	$0.339129\pi$
$744$	1.24229e17	0.0268534
$745$	−8.09346e18	−1.73428
$746$	8.68251e18	1.84435
$747$	−2.93146e18	−0.617306
$748$	−1.30056e19	−2.71500
$749$	4.88960e17	0.101191
$750$	−6.31751e17	−0.129613
$751$	6.91924e18	1.40734	0.703670	−	0.710527i	$-0.251543\pi$
$751$	6.91924e18	1.40734	0.703670	+	0.710527i	$0.251543\pi$
$752$	1.03843e18	0.209392
$753$	3.17204e17	0.0634120
$754$	9.34321e18	1.85175
$755$	−5.95614e18	−1.17033
$756$	−1.04994e18	−0.204538
$757$	7.26685e17	0.140353	0.0701767	−	0.997535i	$-0.477644\pi$
$757$	7.26685e17	0.140353	0.0701767	+	0.997535i	$0.477644\pi$
$758$	7.61806e18	1.45880
$759$	1.80136e18	0.342002
$760$	−1.59701e19	−3.00620
$761$	3.74540e17	0.0699033	0.0349517	−	0.999389i	$-0.488872\pi$
$761$	3.74540e17	0.0699033	0.0349517	+	0.999389i	$0.488872\pi$
$762$	−1.83362e18	−0.339315
$763$	1.64875e17	0.0302514
$764$	1.65553e19	3.01182
$765$	−5.27851e18	−0.952164
$766$	5.51448e18	0.986319
$767$	−1.39634e19	−2.47641
$768$	−1.29304e18	−0.227387
$769$	6.50731e18	1.13470	0.567349	−	0.823478i	$-0.307969\pi$
$769$	6.50731e18	1.13470	0.567349	+	0.823478i	$0.307969\pi$
$770$	9.37284e18	1.62062
$771$	−8.47400e16	−0.0145290
$772$	−2.14877e18	−0.365323
$773$	−3.07419e18	−0.518279	−0.259140	−	0.965840i	$-0.583439\pi$
$773$	−3.07419e18	−0.518279	−0.259140	+	0.965840i	$0.583439\pi$
$774$	−1.76442e19	−2.94975
$775$	−3.83727e17	−0.0636153
$776$	−5.44280e18	−0.894789
$777$	4.39952e17	0.0717248
$778$	−6.73930e18	−1.08955
$779$	6.08909e18	0.976245
$780$	−2.69424e18	−0.428373
$781$	−1.60644e19	−2.53299
$782$	1.52237e19	2.38055
$783$	1.01696e18	0.157708
$784$	−4.82857e18	−0.742615
$785$	−1.95945e18	−0.298870
$786$	−1.86867e18	−0.282674
$787$	−6.74413e18	−1.01179	−0.505895	−	0.862595i	$-0.668838\pi$
$787$	−6.74413e18	−1.01179	−0.505895	+	0.862595i	$0.668838\pi$
$788$	−9.46960e17	−0.140900
$789$	−1.24186e18	−0.183262
$790$	−1.32825e19	−1.94403
$791$	3.64228e18	0.528720
$792$	1.98768e19	2.86175
$793$	3.80912e18	0.543937
$794$	−1.30231e18	−0.184451
$795$	−1.40406e18	−0.197242
$796$	−1.91302e19	−2.66554
$797$	−9.65539e18	−1.33442	−0.667208	−	0.744872i	$-0.732511\pi$
$797$	−9.65539e18	−1.33442	−0.667208	+	0.744872i	$0.732511\pi$
$798$	9.66380e17	0.132474
$799$	−1.31752e18	−0.179145
$800$	2.60518e17	0.0351360
$801$	−6.37148e18	−0.852372
$802$	−9.41962e18	−1.24997
$803$	1.29647e19	1.70652
$804$	5.96066e17	0.0778270
$805$	−7.28680e18	−0.943764
$806$	2.89026e18	0.371330
$807$	−2.95971e17	−0.0377200
$808$	1.73788e19	2.19709
$809$	−6.40206e18	−0.802886	−0.401443	−	0.915884i	$-0.631491\pi$
$809$	−6.40206e18	−0.802886	−0.401443	+	0.915884i	$0.631491\pi$
$810$	1.60969e19	2.00258
$811$	4.02888e18	0.497220	0.248610	−	0.968604i	$-0.420026\pi$
$811$	4.02888e18	0.497220	0.248610	+	0.968604i	$0.420026\pi$
$812$	−5.03410e18	−0.616322
$813$	−1.32873e18	−0.161379
$814$	−3.39231e19	−4.08730
$815$	−1.08054e19	−1.29156
$816$	−7.23798e17	−0.0858285
$817$	2.17168e19	2.55478
$818$	7.20310e18	0.840665
$819$	−5.99751e18	−0.694426
$820$	1.37719e19	1.58199
$821$	3.37777e18	0.384946	0.192473	−	0.981302i	$-0.438349\pi$
$821$	3.37777e18	0.384946	0.192473	+	0.981302i	$0.438349\pi$
$822$	9.20686e17	0.104099
$823$	−8.89092e17	−0.0997351	−0.0498675	−	0.998756i	$-0.515880\pi$
$823$	−8.89092e17	−0.0997351	−0.0498675	+	0.998756i	$0.515880\pi$
$824$	2.99898e19	3.33769
$825$	8.25052e17	0.0911026
$826$	1.13278e19	1.24101
$827$	4.34146e18	0.471900	0.235950	−	0.971765i	$-0.424180\pi$
$827$	4.34146e18	0.471900	0.235950	+	0.971765i	$0.424180\pi$
$828$	−3.12596e19	−3.37121
$829$	1.34365e19	1.43774	0.718870	−	0.695144i	$-0.244659\pi$
$829$	1.34365e19	1.43774	0.718870	+	0.695144i	$0.244659\pi$
$830$	1.22870e19	1.30448
$831$	−2.44916e17	−0.0257994
$832$	−1.58638e19	−1.65808
$833$	6.12635e18	0.635344
$834$	3.59470e18	0.369899
$835$	3.85092e18	0.393190
$836$	−4.94894e19	−5.01385
$837$	3.14592e17	0.0316251
$838$	2.75823e18	0.275135
$839$	−1.72037e19	−1.70282	−0.851412	−	0.524497i	$-0.824253\pi$
$839$	−1.72037e19	−1.70282	−0.851412	+	0.524497i	$0.824253\pi$
$840$	1.08048e18	0.106121
$841$	−5.38465e18	−0.524788
$842$	2.78377e19	2.69219
$843$	7.24858e17	0.0695623
$844$	−4.20086e18	−0.400048
$845$	−1.81999e19	−1.71989
$846$	4.07330e18	0.381978
$847$	9.50031e18	0.884088
$848$	1.43271e19	1.32307
$849$	6.43726e17	0.0589930
$850$	6.97271e18	0.634131
$851$	2.63731e19	2.38023
$852$	−3.74613e18	−0.335525
$853$	8.79218e18	0.781498	0.390749	−	0.920497i	$-0.372216\pi$
$853$	8.79218e18	0.781498	0.390749	+	0.920497i	$0.372216\pi$
$854$	−3.09013e18	−0.272584
$855$	−2.00860e19	−1.75838
$856$	−4.34620e18	−0.377598
$857$	7.90188e18	0.681326	0.340663	−	0.940185i	$-0.389348\pi$
$857$	7.90188e18	0.681326	0.340663	+	0.940185i	$0.389348\pi$
$858$	−6.21436e18	−0.531776
$859$	−1.16614e19	−0.990368	−0.495184	−	0.868788i	$-0.664899\pi$
$859$	−1.16614e19	−0.990368	−0.495184	+	0.868788i	$0.664899\pi$
$860$	4.91176e19	4.13997
$861$	−4.11967e17	−0.0344621
$862$	2.63547e19	2.18807
$863$	3.51764e18	0.289855	0.144928	−	0.989442i	$-0.453705\pi$
$863$	3.51764e18	0.289855	0.144928	+	0.989442i	$0.453705\pi$
$864$	−2.13581e17	−0.0174672
$865$	−9.26561e17	−0.0752089
$866$	1.75366e19	1.41280
$867$	−5.21768e17	−0.0417209
$868$	−1.55727e18	−0.123591
$869$	−2.03476e19	−1.60282
$870$	−2.11704e18	−0.165521
$871$	6.85548e18	0.532010
$872$	−1.46552e18	−0.112884
$873$	−6.84555e18	−0.523378
$874$	5.79300e19	4.39622
$875$	3.91486e18	0.294892
$876$	3.02329e18	0.226049
$877$	−3.25045e18	−0.241238	−0.120619	−	0.992699i	$-0.538488\pi$
$877$	−3.25045e18	−0.241238	−0.120619	+	0.992699i	$0.538488\pi$
$878$	−2.17581e19	−1.60290
$879$	1.75158e18	0.128086
$880$	−2.67130e19	−1.93903
$881$	−1.04161e19	−0.750522	−0.375261	−	0.926919i	$-0.622447\pi$
$881$	−1.04161e19	−0.750522	−0.375261	+	0.926919i	$0.622447\pi$
$882$	−1.89404e19	−1.35470
$883$	−5.27239e18	−0.374337	−0.187169	−	0.982328i	$-0.559931\pi$
$883$	−5.27239e18	−0.374337	−0.187169	+	0.982328i	$0.559931\pi$
$884$	−3.48812e19	−2.45839
$885$	3.16391e18	0.221357
$886$	−4.49558e19	−3.12225
$887$	−1.33763e19	−0.922214	−0.461107	−	0.887344i	$-0.652548\pi$
$887$	−1.33763e19	−0.922214	−0.461107	+	0.887344i	$0.652548\pi$
$888$	−3.91058e18	−0.267644
$889$	1.13627e19	0.772002
$890$	2.67055e19	1.80122
$891$	2.46591e19	1.65109
$892$	−4.38722e19	−2.91620
$893$	−5.01349e18	−0.330831
$894$	−4.35323e18	−0.285179
$895$	5.02383e18	0.326727
$896$	1.23348e19	0.796399
$897$	4.83128e18	0.309678
$898$	3.00943e19	1.91509
$899$	1.50835e18	0.0952940
$900$	−1.43174e19	−0.898022
$901$	−1.81778e19	−1.13196
$902$	3.17653e19	1.96386
$903$	−1.46929e18	−0.0901854
$904$	−3.23749e19	−1.97294
$905$	9.47494e18	0.573272
$906$	−3.20363e18	−0.192446
$907$	−1.98060e19	−1.18127	−0.590634	−	0.806939i	$-0.701122\pi$
$907$	−1.98060e19	−1.18127	−0.590634	+	0.806939i	$0.701122\pi$
$908$	1.02161e19	0.604959
$909$	2.18578e19	1.28511
$910$	2.51381e19	1.46745
$911$	9.01891e18	0.522739	0.261369	−	0.965239i	$-0.415826\pi$
$911$	9.01891e18	0.522739	0.261369	+	0.965239i	$0.415826\pi$
$912$	−2.75423e18	−0.158501
$913$	1.88226e19	1.07552
$914$	3.03308e19	1.72081
$915$	−8.63091e17	−0.0486205
$916$	−2.73281e19	−1.52858
$917$	1.15798e19	0.643133
$918$	−5.71645e18	−0.315246
$919$	3.82062e18	0.209210	0.104605	−	0.994514i	$-0.466642\pi$
$919$	3.82062e18	0.209210	0.104605	+	0.994514i	$0.466642\pi$
$920$	6.47698e19	3.52170
$921$	−1.34657e17	−0.00727009
$922$	2.40931e19	1.29164
$923$	−4.30850e19	−2.29359
$924$	3.34829e18	0.176992
$925$	1.20793e19	0.634045
$926$	9.32350e18	0.485968
$927$	3.77189e19	1.95227
$928$	−1.02404e18	−0.0526328
$929$	1.13165e19	0.577578	0.288789	−	0.957393i	$-0.406747\pi$
$929$	1.13165e19	0.577578	0.288789	+	0.957393i	$0.406747\pi$
$930$	−6.54893e17	−0.0331918
$931$	2.33122e19	1.17330
$932$	1.81487e19	0.907073
$933$	−4.21805e18	−0.209354
$934$	3.47561e18	0.171308
$935$	3.38927e19	1.65894
$936$	5.33098e19	2.59128
$937$	2.91885e19	1.40898	0.704489	−	0.709714i	$-0.251176\pi$
$937$	2.91885e19	1.40898	0.704489	+	0.709714i	$0.251176\pi$
$938$	−5.56148e18	−0.266607
$939$	−7.37739e17	−0.0351218
$940$	−1.13392e19	−0.536105
$941$	2.04885e19	0.962005	0.481003	−	0.876719i	$-0.340273\pi$
$941$	2.04885e19	0.962005	0.481003	+	0.876719i	$0.340273\pi$
$942$	−1.05393e18	−0.0491452
$943$	−2.46955e19	−1.14365
$944$	−3.22846e19	−1.48483
$945$	2.73616e18	0.124978
$946$	1.13291e20	5.13930
$947$	−3.42151e19	−1.54150	−0.770749	−	0.637139i	$-0.780118\pi$
$947$	−3.42151e19	−1.54150	−0.770749	+	0.637139i	$0.780118\pi$
$948$	−4.74493e18	−0.212313
$949$	3.47714e19	1.54523
$950$	2.65329e19	1.17106
$951$	1.31579e18	0.0576784
$952$	1.39885e19	0.609020
$953$	−2.46294e19	−1.06500	−0.532500	−	0.846430i	$-0.678747\pi$
$953$	−2.46294e19	−1.06500	−0.532500	+	0.846430i	$0.678747\pi$
$954$	5.61989e19	2.41359
$955$	−4.31432e19	−1.84031
$956$	8.50659e19	3.60395
$957$	−3.24311e18	−0.136469
$958$	1.16449e19	0.486699
$959$	−5.70533e18	−0.236843
$960$	3.59451e18	0.148210
$961$	−2.39509e19	−0.980891
$962$	−9.09822e19	−3.70099
$963$	−5.46633e18	−0.220864
$964$	3.69699e19	1.48371
$965$	5.59971e18	0.223222
$966$	−3.91935e18	−0.155190
$967$	2.16923e19	0.853166	0.426583	−	0.904449i	$-0.359717\pi$
$967$	2.16923e19	0.853166	0.426583	+	0.904449i	$0.359717\pi$
$968$	−8.44450e19	−3.29901
$969$	3.49448e18	0.135606
$970$	2.86926e19	1.10599
$971$	2.58227e19	0.988729	0.494365	−	0.869255i	$-0.335401\pi$
$971$	2.58227e19	0.988729	0.494365	+	0.869255i	$0.335401\pi$
$972$	1.76459e19	0.671141
$973$	−2.22757e19	−0.841585
$974$	−7.26903e18	−0.272799
$975$	2.21280e18	0.0824921
$976$	8.80699e18	0.326140
$977$	−4.80925e18	−0.176914	−0.0884571	−	0.996080i	$-0.528194\pi$
$977$	−4.80925e18	−0.176914	−0.0884571	+	0.996080i	$0.528194\pi$
$978$	−5.81190e18	−0.212381
$979$	4.09105e19	1.48507
$980$	5.27259e19	1.90132
$981$	−1.84322e18	−0.0660281
$982$	8.98422e19	3.19710
$983$	2.45382e18	0.0867451	0.0433725	−	0.999059i	$-0.486190\pi$
$983$	2.45382e18	0.0867451	0.0433725	+	0.999059i	$0.486190\pi$
$984$	3.66183e18	0.128597
$985$	2.46779e18	0.0860938
$986$	−2.74083e19	−0.949911
$987$	3.39196e17	0.0116786
$988$	−1.32731e20	−4.53997
$989$	−8.80769e19	−2.99286
$990$	−1.04784e20	−3.53724
$991$	−5.42214e19	−1.81841	−0.909205	−	0.416348i	$-0.863310\pi$
$991$	−5.42214e19	−1.81841	−0.909205	+	0.416348i	$0.863310\pi$
$992$	−3.16782e17	−0.0105544
$993$	−4.50401e18	−0.149083
$994$	3.49525e19	1.14939
$995$	4.98536e19	1.62872
$996$	4.38932e18	0.142466
$997$	−5.05255e18	−0.162927	−0.0814633	−	0.996676i	$-0.525959\pi$
$997$	−5.05255e18	−0.162927	−0.0814633	+	0.996676i	$0.525959\pi$
$998$	4.07440e18	0.130532
$999$	−9.90298e18	−0.315203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.a.1.10	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +O(q^{10})\)	\(q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +6.59387e6 q^{10} +1.01012e7 q^{11} +2.35555e6 q^{12} +2.70916e7 q^{13} -2.19779e7 q^{14} -6.13857e6 q^{15} +6.26381e7 q^{16} -7.94734e7 q^{17} +2.45702e8 q^{18} -3.02415e8 q^{19} -6.83982e8 q^{20} +2.04604e7 q^{21} -1.57763e9 q^{22} +1.22651e9 q^{23} -1.81865e8 q^{24} +5.61759e8 q^{25} -4.23121e9 q^{26} -4.60548e8 q^{27} +2.27977e9 q^{28} -2.20816e9 q^{29} +9.58733e8 q^{30} -6.83081e8 q^{31} +4.63754e8 q^{32} +1.46869e9 q^{33} +1.24123e10 q^{34} -5.94110e9 q^{35} -2.54867e10 q^{36} +2.15026e10 q^{37} +4.72317e10 q^{38} +3.93906e9 q^{39} +5.28084e10 q^{40} -2.01349e10 q^{41} -3.19554e9 q^{42} -7.18113e10 q^{43} +1.63647e11 q^{44} +6.64185e10 q^{45} -1.91558e11 q^{46} +1.65782e10 q^{47} +9.10743e9 q^{48} -7.70868e10 q^{49} -8.77365e10 q^{50} -1.15552e10 q^{51} +4.38904e11 q^{52} +2.28728e11 q^{53} +7.19291e10 q^{54} -4.26466e11 q^{55} -1.76015e11 q^{56} -4.39705e10 q^{57} +3.44874e11 q^{58} -5.15415e11 q^{59} -9.94493e10 q^{60} +1.40601e11 q^{61} +1.06685e11 q^{62} -2.21379e11 q^{63} -5.85561e11 q^{64} -1.14379e12 q^{65} -2.29383e11 q^{66} +2.53048e11 q^{67} -1.28753e12 q^{68} +1.78331e11 q^{69} +9.27892e11 q^{70} -1.59034e12 q^{71} +1.96776e12 q^{72} +1.28348e12 q^{73} -3.35832e12 q^{74} +8.16784e10 q^{75} -4.89934e12 q^{76} +1.42145e12 q^{77} -6.15208e11 q^{78} -2.01437e12 q^{79} -2.64453e12 q^{80} +2.44120e12 q^{81} +3.14469e12 q^{82} +1.86340e12 q^{83} +3.31473e11 q^{84} +3.35530e12 q^{85} +1.12156e13 q^{86} -3.21061e11 q^{87} -1.26348e13 q^{88} +4.05006e12 q^{89} -1.03734e13 q^{90} +3.81234e12 q^{91} +1.98703e13 q^{92} -9.93184e10 q^{93} -2.58921e12 q^{94} +1.27677e13 q^{95} +6.74287e10 q^{96} +4.35140e12 q^{97} +1.20395e13 q^{98} -1.58911e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) 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	\( 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}+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

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