LMFDB - Embedded newform 197.14.a.b.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:	$0$
Dimension:	$109$
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)

$f(q)$	$=$	$q-145.155 q^{2} -2025.07 q^{3} +12878.0 q^{4} -10162.8 q^{5} +293949. q^{6} +345875. q^{7} -680200. q^{8} +2.50658e6 q^{9} +O(q^{10})$	\(q-145.155 q^{2} -2025.07 q^{3} +12878.0 q^{4} -10162.8 q^{5} +293949. q^{6} +345875. q^{7} -680200. q^{8} +2.50658e6 q^{9} +1.47518e6 q^{10} +1.29462e6 q^{11} -2.60789e7 q^{12} -2.93098e7 q^{13} -5.02055e7 q^{14} +2.05804e7 q^{15} -6.76221e6 q^{16} -7.66490e7 q^{17} -3.63843e8 q^{18} +1.13939e8 q^{19} -1.30877e8 q^{20} -7.00421e8 q^{21} -1.87921e8 q^{22} -9.76784e8 q^{23} +1.37745e9 q^{24} -1.11742e9 q^{25} +4.25447e9 q^{26} -1.84739e9 q^{27} +4.45418e9 q^{28} +4.14550e9 q^{29} -2.98735e9 q^{30} -5.83659e9 q^{31} +6.55377e9 q^{32} -2.62170e9 q^{33} +1.11260e10 q^{34} -3.51506e9 q^{35} +3.22798e10 q^{36} +3.87665e9 q^{37} -1.65388e10 q^{38} +5.93545e10 q^{39} +6.91274e9 q^{40} -3.31987e10 q^{41} +1.01670e11 q^{42} -4.34571e10 q^{43} +1.66722e10 q^{44} -2.54739e10 q^{45} +1.41785e11 q^{46} +1.16895e11 q^{47} +1.36939e10 q^{48} +2.27405e10 q^{49} +1.62199e11 q^{50} +1.55219e11 q^{51} -3.77453e11 q^{52} +3.23420e10 q^{53} +2.68158e11 q^{54} -1.31570e10 q^{55} -2.35264e11 q^{56} -2.30734e11 q^{57} -6.01741e11 q^{58} -4.58259e11 q^{59} +2.65034e11 q^{60} -7.04452e11 q^{61} +8.47211e11 q^{62} +8.66964e11 q^{63} -8.95917e11 q^{64} +2.97870e11 q^{65} +3.80553e11 q^{66} +7.66795e11 q^{67} -9.87087e11 q^{68} +1.97806e12 q^{69} +5.10229e11 q^{70} -1.10301e12 q^{71} -1.70498e12 q^{72} +2.36793e12 q^{73} -5.62715e11 q^{74} +2.26285e12 q^{75} +1.46731e12 q^{76} +4.47777e11 q^{77} -8.61560e12 q^{78} +7.79158e11 q^{79} +6.87229e10 q^{80} -2.55213e11 q^{81} +4.81896e12 q^{82} -6.47070e11 q^{83} -9.02003e12 q^{84} +7.78968e11 q^{85} +6.30802e12 q^{86} -8.39492e12 q^{87} -8.80601e11 q^{88} +1.00322e12 q^{89} +3.69767e12 q^{90} -1.01375e13 q^{91} -1.25790e13 q^{92} +1.18195e13 q^{93} -1.69679e13 q^{94} -1.15794e12 q^{95} -1.32718e13 q^{96} +1.52626e13 q^{97} -3.30090e12 q^{98} +3.24507e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) $ 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14} + 87246239 q^{15} + 2130706432 q^{16} + 228353715 q^{17} + 400647337 q^{18} + 1139301305 q^{19} + 1109969259 q^{20} + 539982398 q^{21} + 1613315649 q^{22} + 920306804 q^{23} + 5542439613 q^{24} + 31241700999 q^{25} + 1864366110 q^{26} + 17825460755 q^{27} + 20413389070 q^{28} + 7185436621 q^{29} + 2050251883 q^{30} + 28475592572 q^{31} + 8334714660 q^{32} + 19623425846 q^{33} + 37845014194 q^{34} + 25255003636 q^{35} + 287968706746 q^{36} + 71523920490 q^{37} + 67778214914 q^{38} + 44951568463 q^{39} + 169184871486 q^{40} + 69139231052 q^{41} + 58715177635 q^{42} + 247544146139 q^{43} + 63861560722 q^{44} + 257443045479 q^{45} + 160530477869 q^{46} + 308496573061 q^{47} + 412228130018 q^{48} + 1736616239908 q^{49} + 1680360028531 q^{50} + 756579032995 q^{51} + 928015404666 q^{52} + 342783723680 q^{53} - 597894730601 q^{54} + 59276330527 q^{55} - 3822929869144 q^{56} - 562905761941 q^{57} + 62740419347 q^{58} + 827401964151 q^{59} - 2247133283907 q^{60} + 988213134514 q^{61} + 1937380192071 q^{62} + 1788190111357 q^{63} + 11682175668457 q^{64} + 2494670804291 q^{65} + 11819807890512 q^{66} + 8038740399790 q^{67} + 10126245189885 q^{68} + 5225665164579 q^{69} + 11464042631319 q^{70} + 4867145119603 q^{71} + 18133468947055 q^{72} + 9684156738615 q^{73} + 16996786880941 q^{74} + 16718732018262 q^{75} + 21454522032798 q^{76} + 6593100920650 q^{77} + 33749579076633 q^{78} + 7591753073823 q^{79} + 24349241260570 q^{80} + 38778649605417 q^{81} + 25555033184251 q^{82} + 16945724819556 q^{83} + 21855489402730 q^{84} + 15544906794766 q^{85} + 18664144286914 q^{86} + 19049540636401 q^{87} + 17318749473003 q^{88} + 11289674998576 q^{89} + 20983303956671 q^{90} + 47242561944227 q^{91} - 25046698097386 q^{92} - 5411884145985 q^{93} + 18338784709341 q^{94} + 6784117894603 q^{95} - 36827486682955 q^{96} + 45969533477736 q^{97} - 42983409526150 q^{98} + 12084396239183 q^{99}+O(q^{100}) \) 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * 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 $

$2$	−145.155	−1.60375	−0.801877	−	0.597490i	$-0.796165\pi$
$2$	−145.155	−1.60375	−0.801877	+	0.597490i	$0.796165\pi$
$3$	−2025.07	−1.60381	−0.801903	−	0.597455i	$-0.796179\pi$
$3$	−2025.07	−1.60381	−0.801903	+	0.597455i	$0.796179\pi$
$4$	12878.0	1.57202
$5$	−10162.8	−0.290876	−0.145438	−	0.989367i	$-0.546459\pi$
$5$	−10162.8	−0.290876	−0.145438	+	0.989367i	$0.546459\pi$
$6$	293949.	2.57211
$7$	345875.	1.11117	0.555587	−	0.831459i	$-0.312494\pi$
$7$	345875.	1.11117	0.555587	+	0.831459i	$0.312494\pi$
$8$	−680200.	−0.917385
$9$	2.50658e6	1.57219
$10$	1.47518e6	0.466494
$11$	1.29462e6	0.220338	0.110169	−	0.993913i	$-0.464861\pi$
$11$	1.29462e6	0.220338	0.110169	+	0.993913i	$0.464861\pi$
$12$	−2.60789e7	−2.52122
$13$	−2.93098e7	−1.68415	−0.842077	−	0.539358i	$-0.818667\pi$
$13$	−2.93098e7	−1.68415	−0.842077	+	0.539358i	$0.818667\pi$
$14$	−5.02055e7	−1.78205
$15$	2.05804e7	0.466509
$16$	−6.76221e6	−0.100765
$17$	−7.66490e7	−0.770173	−0.385087	−	0.922880i	$-0.625828\pi$
$17$	−7.66490e7	−0.770173	−0.385087	+	0.922880i	$0.625828\pi$
$18$	−3.63843e8	−2.52141
$19$	1.13939e8	0.555614	0.277807	−	0.960637i	$-0.410392\pi$
$19$	1.13939e8	0.555614	0.277807	+	0.960637i	$0.410392\pi$
$20$	−1.30877e8	−0.457265
$21$	−7.00421e8	−1.78211
$22$	−1.87921e8	−0.353368
$23$	−9.76784e8	−1.37584	−0.687920	−	0.725787i	$-0.741476\pi$
$23$	−9.76784e8	−1.37584	−0.687920	+	0.725787i	$0.741476\pi$
$24$	1.37745e9	1.47131
$25$	−1.11742e9	−0.915391
$26$	4.25447e9	2.70097
$27$	−1.84739e9	−0.917685
$28$	4.45418e9	1.74679
$29$	4.14550e9	1.29417	0.647083	−	0.762420i	$-0.275989\pi$
$29$	4.14550e9	1.29417	0.647083	+	0.762420i	$0.275989\pi$
$30$	−2.98735e9	−0.748165
$31$	−5.83659e9	−1.18116	−0.590579	−	0.806980i	$-0.701101\pi$
$31$	−5.83659e9	−1.18116	−0.590579	+	0.806980i	$0.701101\pi$
$32$	6.55377e9	1.07899
$33$	−2.62170e9	−0.353380
$34$	1.11260e10	1.23517
$35$	−3.51506e9	−0.323214
$36$	3.22798e10	2.47152
$37$	3.87665e9	0.248396	0.124198	−	0.992257i	$-0.460364\pi$
$37$	3.87665e9	0.248396	0.124198	+	0.992257i	$0.460364\pi$
$38$	−1.65388e10	−0.891068
$39$	5.93545e10	2.70105
$40$	6.91274e9	0.266846
$41$	−3.31987e10	−1.09151	−0.545753	−	0.837946i	$-0.683756\pi$
$41$	−3.31987e10	−1.09151	−0.545753	+	0.837946i	$0.683756\pi$
$42$	1.01670e11	2.85806
$43$	−4.34571e10	−1.04837	−0.524186	−	0.851604i	$-0.675631\pi$
$43$	−4.34571e10	−1.04837	−0.524186	+	0.851604i	$0.675631\pi$
$44$	1.66722e10	0.346377
$45$	−2.54739e10	−0.457313
$46$	1.41785e11	2.20651
$47$	1.16895e11	1.58183	0.790916	−	0.611925i	$-0.209605\pi$
$47$	1.16895e11	1.58183	0.790916	+	0.611925i	$0.209605\pi$
$48$	1.36939e10	0.161607
$49$	2.27405e10	0.234707
$50$	1.62199e11	1.46806
$51$	1.55219e11	1.23521
$52$	−3.77453e11	−2.64753
$53$	3.23420e10	0.200435	0.100218	−	0.994966i	$-0.468046\pi$
$53$	3.23420e10	0.200435	0.100218	+	0.994966i	$0.468046\pi$
$54$	2.68158e11	1.47174
$55$	−1.31570e10	−0.0640912
$56$	−2.35264e11	−1.01937
$57$	−2.30734e11	−0.891098
$58$	−6.01741e11	−2.07552
$59$	−4.58259e11	−1.41440	−0.707202	−	0.707012i	$-0.750043\pi$
$59$	−4.58259e11	−1.41440	−0.707202	+	0.707012i	$0.750043\pi$
$60$	2.65034e11	0.733363
$61$	−7.04452e11	−1.75068	−0.875342	−	0.483505i	$-0.839364\pi$
$61$	−7.04452e11	−1.75068	−0.875342	+	0.483505i	$0.839364\pi$
$62$	8.47211e11	1.89429
$63$	8.66964e11	1.74698
$64$	−8.95917e11	−1.62966
$65$	2.97870e11	0.489880
$66$	3.80553e11	0.566734
$67$	7.66795e11	1.03560	0.517801	−	0.855501i	$-0.326751\pi$
$67$	7.66795e11	1.03560	0.517801	+	0.855501i	$0.326751\pi$
$68$	−9.87087e11	−1.21073
$69$	1.97806e12	2.20658
$70$	5.10229e11	0.518356
$71$	−1.10301e12	−1.02188	−0.510939	−	0.859617i	$-0.670702\pi$
$71$	−1.10301e12	−1.02188	−0.510939	+	0.859617i	$0.670702\pi$
$72$	−1.70498e12	−1.44231
$73$	2.36793e12	1.83135	0.915674	−	0.401921i	$-0.131657\pi$
$73$	2.36793e12	1.83135	0.915674	+	0.401921i	$0.131657\pi$
$74$	−5.62715e11	−0.398366
$75$	2.26285e12	1.46811
$76$	1.46731e12	0.873439
$77$	4.47777e11	0.244834
$78$	−8.61560e12	−4.33182
$79$	7.79158e11	0.360620	0.180310	−	0.983610i	$-0.442290\pi$
$79$	7.79158e11	0.360620	0.180310	+	0.983610i	$0.442290\pi$
$80$	6.87229e10	0.0293101
$81$	−2.55213e11	−0.100404
$82$	4.81896e12	1.75050
$83$	−6.47070e11	−0.217242	−0.108621	−	0.994083i	$-0.534643\pi$
$83$	−6.47070e11	−0.217242	−0.108621	+	0.994083i	$0.534643\pi$
$84$	−9.02003e12	−2.80151
$85$	7.78968e11	0.224025
$86$	6.30802e12	1.68133
$87$	−8.39492e12	−2.07559
$88$	−8.80601e11	−0.202135
$89$	1.00322e12	0.213974	0.106987	−	0.994260i	$-0.465880\pi$
$89$	1.00322e12	0.213974	0.106987	+	0.994260i	$0.465880\pi$
$90$	3.69767e12	0.733418
$91$	−1.01375e13	−1.87139
$92$	−1.25790e13	−2.16285
$93$	1.18195e13	1.89435
$94$	−1.69679e13	−2.53687
$95$	−1.15794e12	−0.161615
$96$	−1.32718e13	−1.73049
$97$	1.52626e13	1.86043	0.930213	−	0.367020i	$-0.119622\pi$
$97$	1.52626e13	1.86043	0.930213	+	0.367020i	$0.119622\pi$
$98$	−3.30090e12	−0.376411
$99$	3.24507e12	0.346414
$100$	−1.43902e13	−1.43902
$101$	−1.76318e13	−1.65275	−0.826374	−	0.563121i	$-0.809600\pi$
$101$	−1.76318e13	−1.65275	−0.826374	+	0.563121i	$0.809600\pi$
$102$	−2.25309e13	−1.98097
$103$	−4.93405e12	−0.407157	−0.203578	−	0.979059i	$-0.565257\pi$
$103$	−4.93405e12	−0.407157	−0.203578	+	0.979059i	$0.565257\pi$
$104$	1.99366e13	1.54502
$105$	7.11824e12	0.518372
$106$	−4.69461e12	−0.321448
$107$	−2.84116e13	−1.83021	−0.915105	−	0.403216i	$-0.867892\pi$
$107$	−2.84116e13	−1.83021	−0.915105	+	0.403216i	$0.867892\pi$
$108$	−2.37907e13	−1.44262
$109$	−1.38782e13	−0.792614	−0.396307	−	0.918118i	$-0.629708\pi$
$109$	−1.38782e13	−0.792614	−0.396307	+	0.918118i	$0.629708\pi$
$110$	1.90980e12	0.102787
$111$	−7.85048e12	−0.398379
$112$	−2.33888e12	−0.111967
$113$	1.35222e13	0.610993	0.305497	−	0.952193i	$-0.401178\pi$
$113$	1.35222e13	0.610993	0.305497	+	0.952193i	$0.401178\pi$
$114$	3.34922e13	1.42910
$115$	9.92686e12	0.400199
$116$	5.33858e13	2.03446
$117$	−7.34675e13	−2.64781
$118$	6.65187e13	2.26835
$119$	−2.65110e13	−0.855796
$120$	−1.39988e13	−0.427968
$121$	−3.28467e13	−0.951451
$122$	1.02255e14	2.80766
$123$	6.72296e13	1.75056
$124$	−7.51637e13	−1.85681
$125$	2.37619e13	0.557142
$126$	−1.25844e14	−2.80172
$127$	−5.73033e13	−1.21187	−0.605934	−	0.795515i	$-0.707201\pi$
$127$	−5.73033e13	−1.21187	−0.605934	+	0.795515i	$0.707201\pi$
$128$	7.63585e13	1.53459
$129$	8.80036e13	1.68139
$130$	−4.32374e13	−0.785647
$131$	−1.03566e13	−0.179041	−0.0895205	−	0.995985i	$-0.528533\pi$
$131$	−1.03566e13	−0.179041	−0.0895205	+	0.995985i	$0.528533\pi$
$132$	−3.37623e13	−0.555522
$133$	3.94086e13	0.617384
$134$	−1.11304e14	−1.66085
$135$	1.87746e13	0.266933
$136$	5.21366e13	0.706545
$137$	−5.90787e13	−0.763392	−0.381696	−	0.924288i	$-0.624660\pi$
$137$	−5.90787e13	−0.763392	−0.381696	+	0.924288i	$0.624660\pi$
$138$	−2.87125e14	−3.53881
$139$	8.92735e13	1.04985	0.524924	−	0.851149i	$-0.324094\pi$
$139$	8.92735e13	1.04985	0.524924	+	0.851149i	$0.324094\pi$
$140$	−4.52670e13	−0.508100
$141$	−2.36721e14	−2.53695
$142$	1.60107e14	1.63884
$143$	−3.79451e13	−0.371084
$144$	−1.69500e13	−0.158422
$145$	−4.21299e13	−0.376442
$146$	−3.43718e14	−2.93703
$147$	−4.60511e13	−0.376424
$148$	4.99235e13	0.390485
$149$	−3.00467e13	−0.224950	−0.112475	−	0.993655i	$-0.535878\pi$
$149$	−3.00467e13	−0.224950	−0.112475	+	0.993655i	$0.535878\pi$
$150$	−3.28465e14	−2.35448
$151$	−1.09032e14	−0.748521	−0.374260	−	0.927324i	$-0.622103\pi$
$151$	−1.09032e14	−0.748521	−0.374260	+	0.927324i	$0.622103\pi$
$152$	−7.75012e13	−0.509712
$153$	−1.92127e14	−1.21086
$154$	−6.49972e13	−0.392654
$155$	5.93161e13	0.343571
$156$	7.64368e14	4.24612
$157$	2.21346e14	1.17957	0.589784	−	0.807561i	$-0.299213\pi$
$157$	2.21346e14	1.17957	0.589784	+	0.807561i	$0.299213\pi$
$158$	−1.13099e14	−0.578345
$159$	−6.54948e13	−0.321459
$160$	−6.66046e13	−0.313852
$161$	−3.37845e14	−1.52880
$162$	3.70455e13	0.161023
$163$	2.75363e14	1.14997	0.574985	−	0.818164i	$-0.305008\pi$
$163$	2.75363e14	1.14997	0.574985	+	0.818164i	$0.305008\pi$
$164$	−4.27533e14	−1.71587
$165$	2.66438e13	0.102790
$166$	9.39255e13	0.348402
$167$	−4.51190e14	−1.60954	−0.804771	−	0.593586i	$-0.797712\pi$
$167$	−4.51190e14	−1.60954	−0.804771	+	0.593586i	$0.797712\pi$
$168$	4.76426e14	1.63488
$169$	5.56192e14	1.83637
$170$	−1.13071e14	−0.359281
$171$	2.85597e14	0.873533
$172$	−5.59641e14	−1.64807
$173$	−3.30467e14	−0.937193	−0.468596	−	0.883412i	$-0.655240\pi$
$173$	−3.30467e14	−0.937193	−0.468596	+	0.883412i	$0.655240\pi$
$174$	1.21857e15	3.32873
$175$	−3.86488e14	−1.01716
$176$	−8.75450e12	−0.0222023
$177$	9.28007e14	2.26843
$178$	−1.45622e14	−0.343161
$179$	−4.56742e13	−0.103783	−0.0518915	−	0.998653i	$-0.516525\pi$
$179$	−4.56742e13	−0.103783	−0.0518915	+	0.998653i	$0.516525\pi$
$180$	−3.28053e14	−0.718908
$181$	−6.46033e14	−1.36567	−0.682833	−	0.730575i	$-0.739252\pi$
$181$	−6.46033e14	−1.36567	−0.682833	+	0.730575i	$0.739252\pi$
$182$	1.47152e15	3.00124
$183$	1.42656e15	2.80776
$184$	6.64409e14	1.26217
$185$	−3.93976e13	−0.0722526
$186$	−1.71566e15	−3.03807
$187$	−9.92314e13	−0.169699
$188$	1.50538e15	2.48668
$189$	−6.38965e14	−1.01971
$190$	1.68081e14	0.259191
$191$	5.19900e14	0.774825	0.387412	−	0.921907i	$-0.373369\pi$
$191$	5.19900e14	0.774825	0.387412	+	0.921907i	$0.373369\pi$
$192$	1.81429e15	2.61366
$193$	5.43076e14	0.756376	0.378188	−	0.925729i	$-0.376547\pi$
$193$	5.43076e14	0.756376	0.378188	+	0.925729i	$0.376547\pi$
$194$	−2.21545e15	−2.98366
$195$	−6.03207e14	−0.785673
$196$	2.92852e14	0.368964
$197$	5.84517e13	0.0712470
$197$	5.84517e13	0.0712470
$198$	−4.71039e14	−0.555563
$199$	−5.89769e14	−0.673189	−0.336594	−	0.941650i	$-0.609275\pi$
$199$	−5.89769e14	−0.673189	−0.336594	+	0.941650i	$0.609275\pi$
$200$	7.60069e14	0.839766
$201$	−1.55281e15	−1.66091
$202$	2.55934e15	2.65060
$203$	1.43382e15	1.43804
$204$	1.99892e15	1.94178
$205$	3.37392e14	0.317493
$206$	7.16203e14	0.652979
$207$	−2.44839e15	−2.16308
$208$	1.98199e14	0.169703
$209$	1.47508e14	0.122423
$210$	−1.03325e15	−0.831341
$211$	7.79987e14	0.608487	0.304244	−	0.952594i	$-0.401596\pi$
$211$	7.79987e14	0.608487	0.304244	+	0.952594i	$0.401596\pi$
$212$	4.16501e14	0.315089
$213$	2.23367e15	1.63889
$214$	4.12409e15	2.93520
$215$	4.41646e14	0.304947
$216$	1.25659e15	0.841871
$217$	−2.01873e15	−1.31247
$218$	2.01450e15	1.27116
$219$	−4.79523e15	−2.93713
$220$	−1.69436e14	−0.100753
$221$	2.24657e15	1.29709
$222$	1.13954e15	0.638902
$223$	1.43792e15	0.782985	0.391493	−	0.920181i	$-0.371959\pi$
$223$	1.43792e15	0.782985	0.391493	+	0.920181i	$0.371959\pi$
$224$	2.26678e15	1.19894
$225$	−2.80091e15	−1.43917
$226$	−1.96281e15	−0.979882
$227$	−3.72324e15	−1.80615	−0.903073	−	0.429486i	$-0.858695\pi$
$227$	−3.72324e15	−1.80615	−0.903073	+	0.429486i	$0.858695\pi$
$228$	−2.97140e15	−1.40083
$229$	−2.18510e15	−1.00125	−0.500623	−	0.865666i	$-0.666896\pi$
$229$	−2.18510e15	−1.00125	−0.500623	+	0.865666i	$0.666896\pi$
$230$	−1.44094e15	−0.641821
$231$	−9.06780e14	−0.392667
$232$	−2.81977e15	−1.18725
$233$	−2.22110e15	−0.909401	−0.454700	−	0.890645i	$-0.650254\pi$
$233$	−2.22110e15	−0.909401	−0.454700	+	0.890645i	$0.650254\pi$
$234$	1.06642e16	4.24644
$235$	−1.18798e15	−0.460117
$236$	−5.90147e15	−2.22348
$237$	−1.57785e15	−0.578364
$238$	3.84820e15	1.37249
$239$	−4.73143e15	−1.64212	−0.821062	−	0.570838i	$-0.806618\pi$
$239$	−4.73143e15	−1.64212	−0.821062	+	0.570838i	$0.806618\pi$
$240$	−1.39169e14	−0.0470077
$241$	1.43724e15	0.472519	0.236259	−	0.971690i	$-0.424078\pi$
$241$	1.43724e15	0.472519	0.236259	+	0.971690i	$0.424078\pi$
$242$	4.76786e15	1.52589
$243$	3.46216e15	1.07871
$244$	−9.07195e15	−2.75212
$245$	−2.31107e14	−0.0682706
$246$	−9.75873e15	−2.80747
$247$	−3.33953e15	−0.935740
$248$	3.97005e15	1.08358
$249$	1.31036e15	0.348414
$250$	−3.44916e15	−0.893518
$251$	1.08501e15	0.273875	0.136938	−	0.990580i	$-0.456274\pi$
$251$	1.08501e15	0.273875	0.136938	+	0.990580i	$0.456274\pi$
$252$	1.11648e16	2.74629
$253$	−1.26457e15	−0.303150
$254$	8.31787e15	1.94354
$255$	−1.57746e15	−0.359293
$256$	−3.74448e15	−0.831442
$257$	4.84146e15	1.04812	0.524060	−	0.851682i	$-0.324417\pi$
$257$	4.84146e15	1.04812	0.524060	+	0.851682i	$0.324417\pi$
$258$	−1.27742e16	−2.69653
$259$	1.34083e15	0.276011
$260$	3.83598e15	0.770104
$261$	1.03910e16	2.03468
$262$	1.50331e15	0.287138
$263$	−4.14252e15	−0.771885	−0.385942	−	0.922523i	$-0.626124\pi$
$263$	−4.14252e15	−0.771885	−0.385942	+	0.922523i	$0.626124\pi$
$264$	1.78328e15	0.324186
$265$	−3.28685e14	−0.0583018
$266$	−5.72036e15	−0.990132
$267$	−2.03159e15	−0.343172
$268$	9.87480e15	1.62799
$269$	8.88717e15	1.43012	0.715062	−	0.699061i	$-0.246399\pi$
$269$	8.88717e15	1.43012	0.715062	+	0.699061i	$0.246399\pi$
$270$	−2.72524e15	−0.428094
$271$	5.37246e15	0.823896	0.411948	−	0.911207i	$-0.364848\pi$
$271$	5.37246e15	0.823896	0.411948	+	0.911207i	$0.364848\pi$
$272$	5.18316e14	0.0776063
$273$	2.05292e16	3.00134
$274$	8.57558e15	1.22429
$275$	−1.44664e15	−0.201696
$276$	2.54734e16	3.46879
$277$	9.67553e15	1.28693	0.643467	−	0.765474i	$-0.277495\pi$
$277$	9.67553e15	1.28693	0.643467	+	0.765474i	$0.277495\pi$
$278$	−1.29585e16	−1.68370
$279$	−1.46299e16	−1.85701
$280$	2.39094e15	0.296512
$281$	−9.60785e15	−1.16422	−0.582110	−	0.813110i	$-0.697773\pi$
$281$	−9.60785e15	−1.16422	−0.582110	+	0.813110i	$0.697773\pi$
$282$	3.43612e16	4.06864
$283$	−1.56977e16	−1.81645	−0.908225	−	0.418482i	$-0.862562\pi$
$283$	−1.56977e16	−1.81645	−0.908225	+	0.418482i	$0.862562\pi$
$284$	−1.42045e16	−1.60642
$285$	2.34490e15	0.259199
$286$	5.50793e15	0.595127
$287$	−1.14826e16	−1.21285
$288$	1.64276e16	1.69637
$289$	−4.02951e15	−0.406833
$290$	6.11537e15	0.603720
$291$	−3.09078e16	−2.98376
$292$	3.04943e16	2.87892
$293$	8.90199e14	0.0821954	0.0410977	−	0.999155i	$-0.486915\pi$
$293$	8.90199e14	0.0821954	0.0410977	+	0.999155i	$0.486915\pi$
$294$	6.68455e15	0.603691
$295$	4.65720e15	0.411417
$296$	−2.63689e15	−0.227875
$297$	−2.39167e15	−0.202201
$298$	4.36143e15	0.360764
$299$	2.86294e16	2.31712
$300$	2.91411e16	2.30790
$301$	−1.50307e16	−1.16492
$302$	1.58266e16	1.20044
$303$	3.57055e16	2.65069
$304$	−7.70478e14	−0.0559863
$305$	7.15921e15	0.509232
$306$	2.78882e16	1.94192
$307$	1.77890e16	1.21270	0.606348	−	0.795200i	$-0.292634\pi$
$307$	1.77890e16	1.21270	0.606348	+	0.795200i	$0.292634\pi$
$308$	5.76648e15	0.384885
$309$	9.99179e15	0.653000
$310$	−8.61004e15	−0.551003
$311$	−4.48278e15	−0.280934	−0.140467	−	0.990085i	$-0.544860\pi$
$311$	−4.48278e15	−0.280934	−0.140467	+	0.990085i	$0.544860\pi$
$312$	−4.03729e16	−2.47791
$313$	−1.49198e16	−0.896862	−0.448431	−	0.893817i	$-0.648017\pi$
$313$	−1.49198e16	−0.896862	−0.448431	+	0.893817i	$0.648017\pi$
$314$	−3.21294e16	−1.89174
$315$	−8.81078e15	−0.508155
$316$	1.00340e16	0.566903
$317$	−1.64023e16	−0.907859	−0.453930	−	0.891038i	$-0.649978\pi$
$317$	−1.64023e16	−0.907859	−0.453930	+	0.891038i	$0.649978\pi$
$318$	9.50691e15	0.515541
$319$	5.36685e15	0.285154
$320$	9.10503e15	0.474031
$321$	5.75354e16	2.93530
$322$	4.90400e16	2.45181
$323$	−8.73330e15	−0.427919
$324$	−3.28664e15	−0.157837
$325$	3.27514e16	1.54166
$326$	−3.99704e16	−1.84427
$327$	2.81044e16	1.27120
$328$	2.25817e16	1.00133
$329$	4.04311e16	1.75769
$330$	−3.86748e15	−0.164850
$331$	−4.04451e16	−1.69038	−0.845188	−	0.534469i	$-0.820512\pi$
$331$	−4.04451e16	−1.69038	−0.845188	+	0.534469i	$0.820512\pi$
$332$	−8.33298e15	−0.341509
$333$	9.71713e15	0.390527
$334$	6.54925e16	2.58131
$335$	−7.79279e15	−0.301232
$336$	4.73639e15	0.179573
$337$	−3.09233e16	−1.14998	−0.574991	−	0.818160i	$-0.694994\pi$
$337$	−3.09233e16	−1.14998	−0.574991	+	0.818160i	$0.694994\pi$
$338$	−8.07341e16	−2.94509
$339$	−2.73833e16	−0.979914
$340$	1.00316e16	0.352173
$341$	−7.55617e15	−0.260255
$342$	−4.14559e16	−1.40093
$343$	−2.56461e16	−0.850374
$344$	2.95595e16	0.961762
$345$	−2.01026e16	−0.641842
$346$	4.79690e16	1.50303
$347$	−4.75672e16	−1.46274	−0.731368	−	0.681983i	$-0.761118\pi$
$347$	−4.75672e16	−1.46274	−0.731368	+	0.681983i	$0.761118\pi$
$348$	−1.08110e17	−3.26288
$349$	1.75469e16	0.519797	0.259899	−	0.965636i	$-0.416311\pi$
$349$	1.75469e16	0.519797	0.259899	+	0.965636i	$0.416311\pi$
$350$	5.61007e16	1.63127
$351$	5.41466e16	1.54552
$352$	8.48465e15	0.237742
$353$	2.14820e16	0.590933	0.295467	−	0.955353i	$-0.404525\pi$
$353$	2.14820e16	0.590933	0.295467	+	0.955353i	$0.404525\pi$
$354$	−1.34705e17	−3.63800
$355$	1.12096e16	0.297240
$356$	1.29195e16	0.336372
$357$	5.36865e16	1.37253
$358$	6.62985e15	0.166442
$359$	9.72533e15	0.239768	0.119884	−	0.992788i	$-0.461748\pi$
$359$	9.72533e15	0.239768	0.119884	+	0.992788i	$0.461748\pi$
$360$	1.73273e16	0.419533
$361$	−2.90709e16	−0.691293
$362$	9.37751e16	2.19019
$363$	6.65168e16	1.52594
$364$	−1.30551e17	−2.94186
$365$	−2.40648e16	−0.532696
$366$	−2.07073e17	−4.50295
$367$	−2.51912e16	−0.538171	−0.269085	−	0.963116i	$-0.586721\pi$
$367$	−2.51912e16	−0.538171	−0.269085	+	0.963116i	$0.586721\pi$
$368$	6.60522e15	0.138636
$369$	−8.32152e16	−1.71606
$370$	5.71876e15	0.115875
$371$	1.11863e16	0.222718
$372$	1.52212e17	2.97796
$373$	5.80195e16	1.11549	0.557746	−	0.830011i	$-0.311666\pi$
$373$	5.80195e16	1.11549	0.557746	+	0.830011i	$0.311666\pi$
$374$	1.44040e16	0.272155
$375$	−4.81195e16	−0.893547
$376$	−7.95121e16	−1.45115
$377$	−1.21504e17	−2.17957
$378$	9.27491e16	1.63536
$379$	2.67049e16	0.462845	0.231423	−	0.972853i	$-0.425662\pi$
$379$	2.67049e16	0.462845	0.231423	+	0.972853i	$0.425662\pi$
$380$	−1.49119e16	−0.254063
$381$	1.16043e17	1.94360
$382$	−7.54662e16	−1.24263
$383$	−8.05130e16	−1.30339	−0.651695	−	0.758481i	$-0.725942\pi$
$383$	−8.05130e16	−1.30339	−0.651695	+	0.758481i	$0.725942\pi$
$384$	−1.54631e17	−2.46119
$385$	−4.55067e15	−0.0712165
$386$	−7.88302e16	−1.21304
$387$	−1.08929e17	−1.64824
$388$	1.96552e17	2.92463
$389$	−1.30815e17	−1.91419	−0.957094	−	0.289779i	$-0.906418\pi$
$389$	−1.30815e17	−1.91419	−0.957094	+	0.289779i	$0.906418\pi$
$390$	8.75587e16	1.26003
$391$	7.48695e16	1.05963
$392$	−1.54681e16	−0.215316
$393$	2.09728e16	0.287147
$394$	−8.48457e15	−0.114263
$395$	−7.91842e15	−0.104896
$396$	4.17901e16	0.544572
$397$	1.86167e16	0.238651	0.119326	−	0.992855i	$-0.461927\pi$
$397$	1.86167e16	0.238651	0.119326	+	0.992855i	$0.461927\pi$
$398$	8.56080e16	1.07963
$399$	−7.98052e16	−0.990164
$400$	7.55623e15	0.0922391
$401$	−1.20070e17	−1.44210	−0.721052	−	0.692881i	$-0.756341\pi$
$401$	−1.20070e17	−1.44210	−0.721052	+	0.692881i	$0.756341\pi$
$402$	2.25399e17	2.66368
$403$	1.71069e17	1.98925
$404$	−2.27062e17	−2.59816
$405$	2.59368e15	0.0292051
$406$	−2.08127e17	−2.30626
$407$	5.01879e15	0.0547312
$408$	−1.05580e17	−1.13316
$409$	−1.76100e17	−1.86020	−0.930098	−	0.367313i	$-0.880278\pi$
$409$	−1.76100e17	−1.86020	−0.930098	+	0.367313i	$0.880278\pi$
$410$	−4.89741e16	−0.509180
$411$	1.19638e17	1.22433
$412$	−6.35408e16	−0.640060
$413$	−1.58500e17	−1.57165
$414$	3.55396e17	3.46905
$415$	6.57604e15	0.0631905
$416$	−1.92090e17	−1.81718
$417$	−1.80785e17	−1.68375
$418$	−2.14115e16	−0.196337
$419$	9.38626e16	0.847426	0.423713	−	0.905797i	$-0.360727\pi$
$419$	9.38626e16	0.847426	0.423713	+	0.905797i	$0.360727\pi$
$420$	9.16688e16	0.814894
$421$	1.10977e17	0.971407	0.485703	−	0.874124i	$-0.338563\pi$
$421$	1.10977e17	0.971407	0.485703	+	0.874124i	$0.338563\pi$
$422$	−1.13219e17	−0.975863
$423$	2.93007e17	2.48694
$424$	−2.19990e16	−0.183876
$425$	8.56492e16	0.705010
$426$	−3.24228e17	−2.62838
$427$	−2.43652e17	−1.94531
$428$	−3.65885e17	−2.87713
$429$	7.68415e16	0.595146
$430$	−6.41072e16	−0.489059
$431$	−1.35233e17	−1.01620	−0.508102	−	0.861297i	$-0.669653\pi$
$431$	−1.35233e17	−1.01620	−0.508102	+	0.861297i	$0.669653\pi$
$432$	1.24924e16	0.0924703
$433$	9.96386e16	0.726534	0.363267	−	0.931685i	$-0.381661\pi$
$433$	9.96386e16	0.726534	0.363267	+	0.931685i	$0.381661\pi$
$434$	2.93029e17	2.10488
$435$	8.53159e16	0.603740
$436$	−1.78724e17	−1.24601
$437$	−1.11294e17	−0.764436
$438$	6.96052e17	4.71043
$439$	1.63741e17	1.09178	0.545892	−	0.837855i	$-0.316191\pi$
$439$	1.63741e17	1.09178	0.545892	+	0.837855i	$0.316191\pi$
$440$	8.94938e15	0.0587963
$441$	5.70009e16	0.369004
$442$	−3.26101e17	−2.08021
$443$	7.00534e16	0.440357	0.220178	−	0.975460i	$-0.429336\pi$
$443$	7.00534e16	0.440357	0.220178	+	0.975460i	$0.429336\pi$
$444$	−1.01099e17	−0.626262
$445$	−1.01955e16	−0.0622399
$446$	−2.08722e17	−1.25571
$447$	6.08465e16	0.360776
$448$	−3.09875e17	−1.81084
$449$	7.90873e16	0.455518	0.227759	−	0.973718i	$-0.426860\pi$
$449$	7.90873e16	0.455518	0.227759	+	0.973718i	$0.426860\pi$
$450$	4.06566e17	2.30807
$451$	−4.29797e16	−0.240501
$452$	1.74139e17	0.960496
$453$	2.20797e17	1.20048
$454$	5.40448e17	2.89661
$455$	1.03026e17	0.544342
$456$	1.56945e17	0.817480
$457$	6.98717e16	0.358795	0.179397	−	0.983777i	$-0.442585\pi$
$457$	6.98717e16	0.358795	0.179397	+	0.983777i	$0.442585\pi$
$458$	3.17179e17	1.60575
$459$	1.41600e17	0.706776
$460$	1.27838e17	0.629123
$461$	1.57968e17	0.766502	0.383251	−	0.923644i	$-0.374804\pi$
$461$	1.57968e17	0.766502	0.383251	+	0.923644i	$0.374804\pi$
$462$	1.31624e17	0.629740
$463$	−2.34071e17	−1.10426	−0.552131	−	0.833758i	$-0.686185\pi$
$463$	−2.34071e17	−1.10426	−0.552131	+	0.833758i	$0.686185\pi$
$464$	−2.80327e16	−0.130406
$465$	−1.20119e17	−0.551021
$466$	3.22405e17	1.45845
$467$	−5.92394e16	−0.264272	−0.132136	−	0.991232i	$-0.542184\pi$
$467$	−5.92394e16	−0.264272	−0.132136	+	0.991232i	$0.542184\pi$
$468$	−9.46116e17	−4.16243
$469$	2.65215e17	1.15073
$470$	1.72442e17	0.737915
$471$	−4.48240e17	−1.89180
$472$	3.11708e17	1.29755
$473$	−5.62605e16	−0.230997
$474$	2.29033e17	0.927553
$475$	−1.27318e17	−0.508604
$476$	−3.41409e17	−1.34533
$477$	8.10679e16	0.315123
$478$	6.86792e17	2.63356
$479$	−2.37177e17	−0.897205	−0.448603	−	0.893731i	$-0.648078\pi$
$479$	−2.37177e17	−0.897205	−0.448603	+	0.893731i	$0.648078\pi$
$480$	1.34879e17	0.503357
$481$	−1.13624e17	−0.418337
$482$	−2.08623e17	−0.757804
$483$	6.84160e17	2.45189
$484$	−4.23000e17	−1.49570
$485$	−1.55111e17	−0.541154
$486$	−5.02550e17	−1.72999
$487$	1.18832e17	0.403641	0.201821	−	0.979423i	$-0.435314\pi$
$487$	1.18832e17	0.403641	0.201821	+	0.979423i	$0.435314\pi$
$488$	4.79168e17	1.60605
$489$	−5.57630e17	−1.84433
$490$	3.35464e16	0.109489
$491$	−1.43052e17	−0.460750	−0.230375	−	0.973102i	$-0.573995\pi$
$491$	−1.43052e17	−0.460750	−0.230375	+	0.973102i	$0.573995\pi$
$492$	8.65784e17	2.75193
$493$	−3.17748e17	−0.996732
$494$	4.84750e17	1.50070
$495$	−3.29790e16	−0.100764
$496$	3.94682e16	0.119019
$497$	−3.81503e17	−1.13548
$498$	−1.90206e17	−0.558770
$499$	6.60855e15	0.0191625	0.00958126	−	0.999954i	$-0.496950\pi$
$499$	6.60855e15	0.0191625	0.00958126	+	0.999954i	$0.496950\pi$
$500$	3.06006e17	0.875840
$501$	9.13691e17	2.58139
$502$	−1.57494e17	−0.439228
$503$	−6.41119e17	−1.76501	−0.882504	−	0.470304i	$-0.844144\pi$
$503$	−6.41119e17	−1.76501	−0.882504	+	0.470304i	$0.844144\pi$
$504$	−5.89709e17	−1.60265
$505$	1.79188e17	0.480745
$506$	1.83558e17	0.486178
$507$	−1.12633e18	−2.94518
$508$	−7.37953e17	−1.90509
$509$	−5.47621e17	−1.39577	−0.697887	−	0.716208i	$-0.745876\pi$
$509$	−5.47621e17	−1.39577	−0.697887	+	0.716208i	$0.745876\pi$
$510$	2.28977e17	0.576217
$511$	8.19009e17	2.03495
$512$	−8.19983e16	−0.201164
$513$	−2.10489e17	−0.509879
$514$	−7.02762e17	−1.68092
$515$	5.01438e16	0.118432
$516$	1.13331e18	2.64318
$517$	1.51335e17	0.348538
$518$	−1.94629e17	−0.442654
$519$	6.69219e17	1.50308
$520$	−2.02611e17	−0.449409
$521$	−1.31923e15	−0.00288985	−0.00144492	−	0.999999i	$-0.500460\pi$
$521$	−1.31923e15	−0.00288985	−0.00144492	+	0.999999i	$0.500460\pi$
$522$	−1.50831e18	−3.26312
$523$	−5.26578e17	−1.12513	−0.562564	−	0.826754i	$-0.690185\pi$
$523$	−5.26578e17	−1.12513	−0.562564	+	0.826754i	$0.690185\pi$
$524$	−1.33372e17	−0.281457
$525$	7.82665e17	1.63132
$526$	6.01309e17	1.23791
$527$	4.47369e17	0.909696
$528$	1.77285e16	0.0356082
$529$	4.50071e17	0.892934
$530$	4.77104e16	0.0935017
$531$	−1.14867e18	−2.22371
$532$	5.07505e17	0.970543
$533$	9.73048e17	1.83826
$534$	2.94895e17	0.550364
$535$	2.88741e17	0.532365
$536$	−5.21574e17	−0.950046
$537$	9.24935e16	0.166448
$538$	−1.29002e18	−2.29356
$539$	2.94403e16	0.0517149
$540$	2.41780e17	0.419625
$541$	−7.09136e16	−0.121604	−0.0608020	−	0.998150i	$-0.519366\pi$
$541$	−7.09136e16	−0.121604	−0.0608020	+	0.998150i	$0.519366\pi$
$542$	−7.79840e17	−1.32133
$543$	1.30826e18	2.19026
$544$	−5.02340e17	−0.831007
$545$	1.41042e17	0.230553
$546$	−2.97992e18	−4.81341
$547$	−2.39261e17	−0.381903	−0.190952	−	0.981599i	$-0.561157\pi$
$547$	−2.39261e17	−0.381903	−0.190952	+	0.981599i	$0.561157\pi$
$548$	−7.60817e17	−1.20007
$549$	−1.76577e18	−2.75241
$550$	2.09987e17	0.323470
$551$	4.72333e17	0.719057
$552$	−1.34547e18	−2.02428
$553$	2.69491e17	0.400711
$554$	−1.40445e18	−2.06392
$555$	7.97828e16	0.115879
$556$	1.14967e18	1.65039
$557$	2.71586e17	0.385344	0.192672	−	0.981263i	$-0.438285\pi$
$557$	2.71586e17	0.385344	0.192672	+	0.981263i	$0.438285\pi$
$558$	2.12360e18	2.97818
$559$	1.27372e18	1.76562
$560$	2.37695e16	0.0325686
$561$	2.00950e17	0.272164
$562$	1.39463e18	1.86712
$563$	6.09127e17	0.806127	0.403064	−	0.915172i	$-0.367945\pi$
$563$	6.09127e17	0.806127	0.403064	+	0.915172i	$0.367945\pi$
$564$	−3.04849e18	−3.98815
$565$	−1.37423e17	−0.177723
$566$	2.27860e18	2.91314
$567$	−8.82719e16	−0.111566
$568$	7.50265e17	0.937456
$569$	5.16902e17	0.638525	0.319263	−	0.947666i	$-0.396565\pi$
$569$	5.16902e17	0.638525	0.319263	+	0.947666i	$0.396565\pi$
$570$	−3.40375e17	−0.415691
$571$	−1.84006e17	−0.222176	−0.111088	−	0.993811i	$-0.535434\pi$
$571$	−1.84006e17	−0.222176	−0.111088	+	0.993811i	$0.535434\pi$
$572$	−4.88658e17	−0.583353
$573$	−1.05283e18	−1.24267
$574$	1.66676e18	1.94511
$575$	1.09148e18	1.25943
$576$	−2.24569e18	−2.56214
$577$	5.01932e16	0.0566243	0.0283121	−	0.999599i	$-0.490987\pi$
$577$	5.01932e16	0.0566243	0.0283121	+	0.999599i	$0.490987\pi$
$578$	5.84904e17	0.652460
$579$	−1.09977e18	−1.21308
$580$	−5.42549e17	−0.591776
$581$	−2.23805e17	−0.241393
$582$	4.48643e18	4.78522
$583$	4.18706e16	0.0441636
$584$	−1.61067e18	−1.68005
$585$	7.46636e17	0.770186
$586$	−1.29217e17	−0.131821
$587$	1.04740e18	1.05674	0.528368	−	0.849016i	$-0.322804\pi$
$587$	1.04740e18	1.05674	0.528368	+	0.849016i	$0.322804\pi$
$588$	−5.93046e17	−0.591747
$589$	−6.65014e17	−0.656269
$590$	−6.76016e17	−0.659810
$591$	−1.18369e17	−0.114266
$592$	−2.62147e16	−0.0250296
$593$	1.41371e18	1.33507	0.667534	−	0.744579i	$-0.267350\pi$
$593$	1.41371e18	1.33507	0.667534	+	0.744579i	$0.267350\pi$
$594$	3.47163e17	0.324281
$595$	2.69426e17	0.248931
$596$	−3.86941e17	−0.353626
$597$	1.19432e18	1.07966
$598$	−4.15570e18	−3.71610
$599$	−2.05968e17	−0.182191	−0.0910954	−	0.995842i	$-0.529037\pi$
$599$	−2.05968e17	−0.182191	−0.0910954	+	0.995842i	$0.529037\pi$
$600$	−1.53919e18	−1.34682
$601$	−9.31064e17	−0.805927	−0.402963	−	0.915216i	$-0.632020\pi$
$601$	−9.31064e17	−0.805927	−0.402963	+	0.915216i	$0.632020\pi$
$602$	2.18179e18	1.86825
$603$	1.92204e18	1.62817
$604$	−1.40412e18	−1.17669
$605$	3.33814e17	0.276755
$606$	−5.18284e18	−4.25105
$607$	2.63045e17	0.213454	0.106727	−	0.994288i	$-0.465963\pi$
$607$	2.63045e17	0.213454	0.106727	+	0.994288i	$0.465963\pi$
$608$	7.46729e17	0.599501
$609$	−2.90359e18	−2.30634
$610$	−1.03920e18	−0.816683
$611$	−3.42618e18	−2.66405
$612$	−2.47422e18	−1.90350
$613$	−1.16532e18	−0.887060	−0.443530	−	0.896259i	$-0.646274\pi$
$613$	−1.16532e18	−0.887060	−0.443530	+	0.896259i	$0.646274\pi$
$614$	−2.58216e18	−1.94486
$615$	−6.83241e17	−0.509197
$616$	−3.04578e17	−0.224607
$617$	−4.22470e17	−0.308278	−0.154139	−	0.988049i	$-0.549260\pi$
$617$	−4.22470e17	−0.308278	−0.154139	+	0.988049i	$0.549260\pi$
$618$	−1.45036e18	−1.04725
$619$	2.34248e18	1.67373	0.836866	−	0.547407i	$-0.184385\pi$
$619$	2.34248e18	1.67373	0.836866	+	0.547407i	$0.184385\pi$
$620$	7.63874e17	0.540102
$621$	1.80450e18	1.26259
$622$	6.50698e17	0.450549
$623$	3.46988e17	0.237762
$624$	−4.01367e17	−0.272171
$625$	1.12255e18	0.753332
$626$	2.16569e18	1.43835
$627$	−2.98713e17	−0.196343
$628$	2.85049e18	1.85431
$629$	−2.97141e17	−0.191308
$630$	1.27893e18	0.814954
$631$	−1.03646e18	−0.653678	−0.326839	−	0.945080i	$-0.605983\pi$
$631$	−1.03646e18	−0.653678	−0.326839	+	0.945080i	$0.605983\pi$
$632$	−5.29983e17	−0.330827
$633$	−1.57953e18	−0.975895
$634$	2.38087e18	1.45598
$635$	5.82362e17	0.352504
$636$	−8.43443e17	−0.505341
$637$	−6.66520e17	−0.395282
$638$	−7.79026e17	−0.457317
$639$	−2.76478e18	−1.60659
$640$	−7.76016e17	−0.446376
$641$	2.48877e18	1.41712	0.708561	−	0.705650i	$-0.249345\pi$
$641$	2.48877e18	1.41712	0.708561	+	0.705650i	$0.249345\pi$
$642$	−8.35156e18	−4.70750
$643$	1.68962e18	0.942797	0.471399	−	0.881920i	$-0.343749\pi$
$643$	1.68962e18	0.942797	0.471399	+	0.881920i	$0.343749\pi$
$644$	−4.35078e18	−2.40330
$645$	−8.94363e17	−0.489075
$646$	1.26768e18	0.686277
$647$	3.24216e18	1.73763	0.868813	−	0.495141i	$-0.164884\pi$
$647$	3.24216e18	1.73763	0.868813	+	0.495141i	$0.164884\pi$
$648$	1.73596e17	0.0921090
$649$	−5.93272e17	−0.311647
$650$	−4.75404e18	−2.47244
$651$	4.08807e18	2.10495
$652$	3.54614e18	1.80778
$653$	−2.68182e18	−1.35361	−0.676806	−	0.736161i	$-0.736637\pi$
$653$	−2.68182e18	−1.35361	−0.676806	+	0.736161i	$0.736637\pi$
$654$	−4.07949e18	−2.03869
$655$	1.05252e17	0.0520788
$656$	2.24496e17	0.109985
$657$	5.93542e18	2.87923
$658$	−5.86878e18	−2.81890
$659$	6.03146e17	0.286858	0.143429	−	0.989661i	$-0.454187\pi$
$659$	6.03146e17	0.286858	0.143429	+	0.989661i	$0.454187\pi$
$660$	3.43119e17	0.161588
$661$	2.93438e18	1.36838	0.684190	−	0.729304i	$-0.260156\pi$
$661$	2.93438e18	1.36838	0.684190	+	0.729304i	$0.260156\pi$
$662$	5.87081e18	2.71095
$663$	−4.54946e18	−2.08028
$664$	4.40137e17	0.199295
$665$	−4.00502e17	−0.179582
$666$	−1.41049e18	−0.626308
$667$	−4.04926e18	−1.78056
$668$	−5.81043e18	−2.53024
$669$	−2.91189e18	−1.25576
$670$	1.13116e18	0.483102
$671$	−9.11999e17	−0.385743
$672$	−4.59039e18	−1.92287
$673$	3.11819e18	1.29361	0.646807	−	0.762654i	$-0.276104\pi$
$673$	3.11819e18	1.29361	0.646807	+	0.762654i	$0.276104\pi$
$674$	4.48867e18	1.84429
$675$	2.06431e18	0.840041
$676$	7.16265e18	2.88682
$677$	2.72429e18	1.08749	0.543747	−	0.839249i	$-0.317005\pi$
$677$	2.72429e18	1.08749	0.543747	+	0.839249i	$0.317005\pi$
$678$	3.97483e18	1.57154
$679$	5.27895e18	2.06726
$680$	−5.29854e17	−0.205517
$681$	7.53982e18	2.89671
$682$	1.09682e18	0.417384
$683$	3.95022e18	1.48897	0.744487	−	0.667637i	$-0.232694\pi$
$683$	3.95022e18	1.48897	0.744487	+	0.667637i	$0.232694\pi$
$684$	3.67793e18	1.37321
$685$	6.00405e17	0.222053
$686$	3.72267e18	1.36379
$687$	4.42498e18	1.60580
$688$	2.93866e17	0.105639
$689$	−9.47939e17	−0.337563
$690$	2.91799e18	1.02936
$691$	3.49814e18	1.22245	0.611223	−	0.791458i	$-0.290678\pi$
$691$	3.49814e18	1.22245	0.611223	+	0.791458i	$0.290678\pi$
$692$	−4.25577e18	−1.47329
$693$	1.12239e18	0.384926
$694$	6.90462e18	2.34587
$695$	−9.07269e17	−0.305376
$696$	5.71023e18	1.90412
$697$	2.54465e18	0.840648
$698$	−2.54702e18	−0.833626
$699$	4.49789e18	1.45850
$700$	−4.97720e18	−1.59900
$701$	−2.04271e18	−0.650190	−0.325095	−	0.945681i	$-0.605396\pi$
$701$	−2.04271e18	−0.650190	−0.325095	+	0.945681i	$0.605396\pi$
$702$	−7.85966e18	−2.47864
$703$	4.41701e17	0.138013
$704$	−1.15987e18	−0.359078
$705$	2.40575e18	0.737939
$706$	−3.11822e18	−0.947711
$707$	−6.09839e18	−1.83649
$708$	1.19509e19	3.56602
$709$	6.55708e17	0.193870	0.0969348	−	0.995291i	$-0.469096\pi$
$709$	6.55708e17	0.193870	0.0969348	+	0.995291i	$0.469096\pi$
$710$	−1.62714e18	−0.476700
$711$	1.95302e18	0.566963
$712$	−6.82389e17	−0.196296
$713$	5.70109e18	1.62508
$714$	−7.79288e18	−2.20120
$715$	3.85629e17	0.107939
$716$	−5.88194e17	−0.163149
$717$	9.58148e18	2.63365
$718$	−1.41168e18	−0.384528
$719$	3.13690e18	0.846765	0.423382	−	0.905951i	$-0.360843\pi$
$719$	3.13690e18	0.846765	0.423382	+	0.905951i	$0.360843\pi$
$720$	1.72260e17	0.0460811
$721$	−1.70656e18	−0.452422
$722$	4.21979e18	1.10866
$723$	−2.91052e18	−0.757829
$724$	−8.31963e18	−2.14686
$725$	−4.63227e18	−1.18467
$726$	−9.65525e18	−2.44723
$727$	−3.16136e18	−0.794146	−0.397073	−	0.917787i	$-0.629974\pi$
$727$	−3.16136e18	−0.794146	−0.397073	+	0.917787i	$0.629974\pi$
$728$	6.89555e18	1.71678
$729$	−6.60422e18	−1.62964
$730$	3.49314e18	0.854313
$731$	3.33094e18	0.807429
$732$	1.83713e19	4.41386
$733$	−3.49551e18	−0.832405	−0.416202	−	0.909272i	$-0.636639\pi$
$733$	−3.49551e18	−0.832405	−0.416202	+	0.909272i	$0.636639\pi$
$734$	3.65664e18	0.863093
$735$	4.68008e17	0.109493
$736$	−6.40162e18	−1.48451
$737$	9.92709e17	0.228183
$738$	1.20791e19	2.75213
$739$	6.65779e18	1.50363	0.751816	−	0.659374i	$-0.229178\pi$
$739$	6.65779e18	1.50363	0.751816	+	0.659374i	$0.229178\pi$
$740$	−5.07363e17	−0.113583
$741$	6.76278e18	1.50075
$742$	−1.62375e18	−0.357185
$743$	6.25592e18	1.36416	0.682078	−	0.731279i	$-0.261076\pi$
$743$	6.25592e18	1.36416	0.682078	+	0.731279i	$0.261076\pi$
$744$	−8.03962e18	−1.73785
$745$	3.05358e17	0.0654325
$746$	−8.42183e18	−1.78897
$747$	−1.62193e18	−0.341546
$748$	−1.27790e18	−0.266771
$749$	−9.82685e18	−2.03368
$750$	6.98479e18	1.43303
$751$	−2.91968e18	−0.593849	−0.296925	−	0.954901i	$-0.595961\pi$
$751$	−2.91968e18	−0.593849	−0.296925	+	0.954901i	$0.595961\pi$
$752$	−7.90469e17	−0.159393
$753$	−2.19721e18	−0.439242
$754$	1.76369e19	3.49550
$755$	1.10807e18	0.217727
$756$	−8.22861e18	−1.60300
$757$	−1.42277e17	−0.0274796	−0.0137398	−	0.999906i	$-0.504374\pi$
$757$	−1.42277e17	−0.0274796	−0.0137398	+	0.999906i	$0.504374\pi$
$758$	−3.87635e18	−0.742289
$759$	2.56083e18	0.486194
$760$	7.87629e17	0.148263
$761$	−1.21558e16	−0.00226874	−0.00113437	−	0.999999i	$-0.500361\pi$
$761$	−1.21558e16	−0.00226874	−0.00113437	+	0.999999i	$0.500361\pi$
$762$	−1.68443e19	−3.11706
$763$	−4.80013e18	−0.880732
$764$	6.69529e18	1.21804
$765$	1.95255e18	0.352211
$766$	1.16869e19	2.09031
$767$	1.34315e19	2.38207
$768$	7.58283e18	1.33347
$769$	−2.25480e18	−0.393175	−0.196588	−	0.980486i	$-0.562986\pi$
$769$	−2.25480e18	−0.393175	−0.196588	+	0.980486i	$0.562986\pi$
$770$	6.60553e17	0.114214
$771$	−9.80428e18	−1.68098
$772$	6.99374e18	1.18904
$773$	−1.60398e17	−0.0270415	−0.0135208	−	0.999909i	$-0.504304\pi$
$773$	−1.60398e17	−0.0270415	−0.0135208	+	0.999909i	$0.504304\pi$
$774$	1.58116e19	2.64338
$775$	6.52192e18	1.08122
$776$	−1.03816e19	−1.70673
$777$	−2.71528e18	−0.442668
$778$	1.89884e19	3.06988
$779$	−3.78262e18	−0.606456
$780$	−7.76812e18	−1.23510
$781$	−1.42798e18	−0.225159
$782$	−1.08677e19	−1.69939
$783$	−7.65834e18	−1.18764
$784$	−1.53776e17	−0.0236501
$785$	−2.24949e18	−0.343108
$786$	−3.04431e18	−0.460513
$787$	1.55309e17	0.0233002	0.0116501	−	0.999932i	$-0.496292\pi$
$787$	1.55309e17	0.0233002	0.0116501	+	0.999932i	$0.496292\pi$
$788$	7.52743e17	0.112002
$789$	8.38889e18	1.23795
$790$	1.14940e18	0.168227
$791$	4.67698e18	0.678919
$792$	−2.20730e18	−0.317795
$793$	2.06474e19	2.94842
$794$	−2.70231e18	−0.382738
$795$	6.65611e17	0.0935048
$796$	−7.59506e18	−1.05827
$797$	8.03018e18	1.10980	0.554902	−	0.831916i	$-0.312756\pi$
$797$	8.03018e18	1.10980	0.554902	+	0.831916i	$0.312756\pi$
$798$	1.15841e19	1.58798
$799$	−8.95989e18	−1.21828
$800$	−7.32331e18	−0.987695
$801$	2.51465e18	0.336408
$802$	1.74288e19	2.31278
$803$	3.06558e18	0.403516
$804$	−1.99972e19	−2.61098
$805$	3.43345e18	0.444691
$806$	−2.48316e19	−3.19027
$807$	−1.79971e19	−2.29364
$808$	1.19931e19	1.51621
$809$	−1.04069e19	−1.30513	−0.652567	−	0.757731i	$-0.726308\pi$
$809$	−1.04069e19	−1.30513	−0.652567	+	0.757731i	$0.726308\pi$
$810$	−3.76486e17	−0.0468378
$811$	4.35231e18	0.537136	0.268568	−	0.963261i	$-0.413450\pi$
$811$	4.35231e18	0.537136	0.268568	+	0.963261i	$0.413450\pi$
$812$	1.84648e19	2.26064
$813$	−1.08796e19	−1.32137
$814$	−7.28503e17	−0.0877754
$815$	−2.79846e18	−0.334499
$816$	−1.04963e18	−0.124465
$817$	−4.95145e18	−0.582491
$818$	2.55619e19	2.98329
$819$	−2.54106e19	−2.94218
$820$	4.34494e18	0.499107
$821$	−4.07100e18	−0.463949	−0.231975	−	0.972722i	$-0.574519\pi$
$821$	−4.07100e18	−0.463949	−0.231975	+	0.972722i	$0.574519\pi$
$822$	−1.73661e19	−1.96353
$823$	−1.12410e19	−1.26097	−0.630484	−	0.776202i	$-0.717144\pi$
$823$	−1.12410e19	−1.26097	−0.630484	+	0.776202i	$0.717144\pi$
$824$	3.35614e18	0.373519
$825$	2.92954e18	0.323481
$826$	2.30072e19	2.52054
$827$	−5.36960e18	−0.583655	−0.291828	−	0.956471i	$-0.594263\pi$
$827$	−5.36960e18	−0.583655	−0.291828	+	0.956471i	$0.594263\pi$
$828$	−3.15304e19	−3.40042
$829$	−1.15117e19	−1.23179	−0.615893	−	0.787830i	$-0.711205\pi$
$829$	−1.15117e19	−1.23179	−0.615893	+	0.787830i	$0.711205\pi$
$830$	−9.54546e17	−0.101342
$831$	−1.95936e19	−2.06399
$832$	2.62592e19	2.74460
$833$	−1.74303e18	−0.180765
$834$	2.62419e19	2.70032
$835$	4.58535e18	0.468178
$836$	1.89961e18	0.192452
$837$	1.07824e19	1.08393
$838$	−1.36246e19	−1.35906
$839$	−4.36647e18	−0.432193	−0.216097	−	0.976372i	$-0.569333\pi$
$839$	−4.36647e18	−0.432193	−0.216097	+	0.976372i	$0.569333\pi$
$840$	−4.84182e18	−0.475547
$841$	6.92453e18	0.674864
$842$	−1.61090e19	−1.55790
$843$	1.94566e19	1.86718
$844$	1.00447e19	0.956557
$845$	−5.65246e18	−0.534157
$846$	−4.25315e19	−3.98844
$847$	−1.13608e19	−1.05723
$848$	−2.18703e17	−0.0201968
$849$	3.17889e19	2.91323
$850$	−1.24324e19	−1.13066
$851$	−3.78665e18	−0.341753
$852$	2.87652e19	2.57638
$853$	−6.93088e17	−0.0616056	−0.0308028	−	0.999525i	$-0.509806\pi$
$853$	−6.93088e17	−0.0616056	−0.0308028	+	0.999525i	$0.509806\pi$
$854$	3.53674e19	3.11980
$855$	−2.90247e18	−0.254090
$856$	1.93256e19	1.67901
$857$	9.79130e18	0.844239	0.422119	−	0.906540i	$-0.361286\pi$
$857$	9.79130e18	0.844239	0.422119	+	0.906540i	$0.361286\pi$
$858$	−1.11539e19	−0.954467
$859$	8.47286e18	0.719572	0.359786	−	0.933035i	$-0.382850\pi$
$859$	8.47286e18	0.719572	0.359786	+	0.933035i	$0.382850\pi$
$860$	5.68752e18	0.479384
$861$	2.32530e19	1.94518
$862$	1.96298e19	1.62974
$863$	1.39686e18	0.115102	0.0575508	−	0.998343i	$-0.481671\pi$
$863$	1.39686e18	0.115102	0.0575508	+	0.998343i	$0.481671\pi$
$864$	−1.21074e19	−0.990170
$865$	3.35847e18	0.272607
$866$	−1.44631e19	−1.16518
$867$	8.16004e18	0.652481
$868$	−2.59972e19	−2.06324
$869$	1.00871e18	0.0794584
$870$	−1.23840e19	−0.968250
$871$	−2.24746e19	−1.74411
$872$	9.43997e18	0.727132
$873$	3.82570e19	2.92495
$874$	1.61549e19	1.22597
$875$	8.21864e18	0.619081
$876$	−6.17531e19	−4.61723
$877$	8.92989e18	0.662748	0.331374	−	0.943499i	$-0.392488\pi$
$877$	8.92989e18	0.662748	0.331374	+	0.943499i	$0.392488\pi$
$878$	−2.37678e19	−1.75095
$879$	−1.80271e18	−0.131825
$880$	8.89702e16	0.00645814
$881$	1.28545e19	0.926218	0.463109	−	0.886301i	$-0.346734\pi$
$881$	1.28545e19	0.926218	0.463109	+	0.886301i	$0.346734\pi$
$882$	−8.27397e18	−0.591791
$883$	−6.29105e18	−0.446661	−0.223331	−	0.974743i	$-0.571693\pi$
$883$	−6.29105e18	−0.446661	−0.223331	+	0.974743i	$0.571693\pi$
$884$	2.89314e19	2.03906
$885$	−9.43115e18	−0.659832
$886$	−1.01686e19	−0.706224
$887$	8.99934e18	0.620450	0.310225	−	0.950663i	$-0.399596\pi$
$887$	8.99934e18	0.620450	0.310225	+	0.950663i	$0.399596\pi$
$888$	5.33989e18	0.365467
$889$	−1.98198e19	−1.34660
$890$	1.47993e18	0.0998175
$891$	−3.30404e17	−0.0221228
$892$	1.85176e19	1.23087
$893$	1.33189e19	0.878889
$894$	−8.83219e18	−0.578595
$895$	4.64178e17	0.0301880
$896$	2.64105e19	1.70520
$897$	−5.79765e19	−3.71622
$898$	−1.14799e19	−0.730539
$899$	−2.41956e19	−1.52861
$900$	−3.60701e19	−2.26241
$901$	−2.47898e18	−0.154370
$902$	6.23873e18	0.385703
$903$	3.04383e19	1.86831
$904$	−9.19777e18	−0.560516
$905$	6.56551e18	0.397240
$906$	−3.20499e19	−1.92528
$907$	2.22298e19	1.32583	0.662915	−	0.748694i	$-0.269319\pi$
$907$	2.22298e19	1.32583	0.662915	+	0.748694i	$0.269319\pi$
$908$	−4.79480e19	−2.83931
$909$	−4.41955e19	−2.59844
$910$	−1.49547e19	−0.872990
$911$	2.10175e18	0.121818	0.0609091	−	0.998143i	$-0.480600\pi$
$911$	2.10175e18	0.121818	0.0609091	+	0.998143i	$0.480600\pi$
$912$	1.56027e18	0.0897912
$913$	−8.37711e17	−0.0478667
$914$	−1.01422e19	−0.575418
$915$	−1.44979e19	−0.816710
$916$	−2.81398e19	−1.57398
$917$	−3.58208e18	−0.198946
$918$	−2.05540e19	−1.13349
$919$	−2.10844e19	−1.15454	−0.577272	−	0.816552i	$-0.695883\pi$
$919$	−2.10844e19	−1.15454	−0.577272	+	0.816552i	$0.695883\pi$
$920$	−6.75225e18	−0.367137
$921$	−3.60239e19	−1.94493
$922$	−2.29299e19	−1.22928
$923$	3.23290e19	1.72100
$924$	−1.16775e19	−0.617281
$925$	−4.33184e18	−0.227380
$926$	3.39767e19	1.77096
$927$	−1.23676e19	−0.640129
$928$	2.71686e19	1.39639
$929$	−2.72627e18	−0.139145	−0.0695723	−	0.997577i	$-0.522163\pi$
$929$	−2.72627e18	−0.139145	−0.0695723	+	0.997577i	$0.522163\pi$
$930$	1.74359e19	0.883702
$931$	2.59103e18	0.130406
$932$	−2.86034e19	−1.42960
$933$	9.07793e18	0.450564
$934$	8.59890e18	0.423827
$935$	1.00847e18	0.0493614
$936$	4.99726e19	2.42906
$937$	−3.00915e19	−1.45257	−0.726285	−	0.687394i	$-0.758755\pi$
$937$	−3.00915e19	−1.45257	−0.726285	+	0.687394i	$0.758755\pi$
$938$	−3.84974e19	−1.84549
$939$	3.02137e19	1.43839
$940$	−1.52989e19	−0.723316
$941$	−1.54939e19	−0.727490	−0.363745	−	0.931499i	$-0.618502\pi$
$941$	−1.54939e19	−0.727490	−0.363745	+	0.931499i	$0.618502\pi$
$942$	6.50643e19	3.03398
$943$	3.24280e19	1.50174
$944$	3.09884e18	0.142522
$945$	6.49368e18	0.296609
$946$	8.16650e18	0.370462
$947$	−7.49897e18	−0.337852	−0.168926	−	0.985629i	$-0.554030\pi$
$947$	−7.49897e18	−0.337852	−0.168926	+	0.985629i	$0.554030\pi$
$948$	−2.03196e19	−0.909202
$949$	−6.94038e19	−3.08427
$950$	1.84808e19	0.815676
$951$	3.32157e19	1.45603
$952$	1.80328e19	0.785095
$953$	6.28397e18	0.271725	0.135863	−	0.990728i	$-0.456619\pi$
$953$	6.28397e18	0.271725	0.135863	+	0.990728i	$0.456619\pi$
$954$	−1.17674e19	−0.505379
$955$	−5.28364e18	−0.225378
$956$	−6.09315e19	−2.58146
$957$	−1.08682e19	−0.457332
$958$	3.44275e19	1.43890
$959$	−2.04338e19	−0.848261
$960$	−1.84383e19	−0.760253
$961$	9.64822e18	0.395135
$962$	1.64931e19	0.670910
$963$	−7.12160e19	−2.87744
$964$	1.85088e19	0.742811
$965$	−5.51917e18	−0.220012
$966$	−9.93094e19	−3.93223
$967$	−4.43950e19	−1.74607	−0.873035	−	0.487657i	$-0.837852\pi$
$967$	−4.43950e19	−1.74607	−0.873035	+	0.487657i	$0.837852\pi$
$968$	2.23423e19	0.872847
$969$	1.76855e19	0.686300
$970$	2.25151e19	0.867877
$971$	−2.37034e19	−0.907581	−0.453790	−	0.891108i	$-0.649929\pi$
$971$	−2.37034e19	−0.907581	−0.453790	+	0.891108i	$0.649929\pi$
$972$	4.45857e19	1.69576
$973$	3.08775e19	1.16656
$974$	−1.72491e19	−0.647341
$975$	−6.63239e19	−2.47252
$976$	4.76365e18	0.176407
$977$	−2.43638e19	−0.896254	−0.448127	−	0.893970i	$-0.647909\pi$
$977$	−2.43638e19	−0.896254	−0.448127	+	0.893970i	$0.647909\pi$
$978$	8.09429e19	2.95785
$979$	1.29879e18	0.0471467
$980$	−2.97620e18	−0.107323
$981$	−3.47869e19	−1.24614
$982$	2.07648e19	0.738930
$983$	−1.91129e19	−0.675662	−0.337831	−	0.941207i	$-0.609693\pi$
$983$	−1.91129e19	−0.675662	−0.337831	+	0.941207i	$0.609693\pi$
$984$	−4.57296e19	−1.60594
$985$	−5.94033e17	−0.0207241
$986$	4.61228e19	1.59851
$987$	−8.18758e19	−2.81899
$988$	−4.30065e19	−1.47101
$989$	4.24482e19	1.44239
$990$	4.78708e18	0.161600
$991$	2.98770e19	1.00198	0.500989	−	0.865453i	$-0.332970\pi$
$991$	2.98770e19	1.00198	0.500989	+	0.865453i	$0.332970\pi$
$992$	−3.82516e19	−1.27445
$993$	8.19040e19	2.71104
$994$	5.53771e19	1.82104
$995$	5.99370e18	0.195815
$996$	1.68749e19	0.547715
$997$	−2.20460e19	−0.710905	−0.355453	−	0.934694i	$-0.615673\pi$
$997$	−2.20460e19	−0.710905	−0.355453	+	0.934694i	$0.615673\pi$
$998$	−9.59265e17	−0.0307320
$999$	−7.16167e18	−0.227949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.14.a.b.1.13	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.14.a.b.1.13	✓	109	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)

\(f(q)\)	\(=\)	\(q-145.155 q^{2} -2025.07 q^{3} +12878.0 q^{4} -10162.8 q^{5} +293949. q^{6} +345875. q^{7} -680200. q^{8} +2.50658e6 q^{9} +O(q^{10})\)	\(q-145.155 q^{2} -2025.07 q^{3} +12878.0 q^{4} -10162.8 q^{5} +293949. q^{6} +345875. q^{7} -680200. q^{8} +2.50658e6 q^{9} +1.47518e6 q^{10} +1.29462e6 q^{11} -2.60789e7 q^{12} -2.93098e7 q^{13} -5.02055e7 q^{14} +2.05804e7 q^{15} -6.76221e6 q^{16} -7.66490e7 q^{17} -3.63843e8 q^{18} +1.13939e8 q^{19} -1.30877e8 q^{20} -7.00421e8 q^{21} -1.87921e8 q^{22} -9.76784e8 q^{23} +1.37745e9 q^{24} -1.11742e9 q^{25} +4.25447e9 q^{26} -1.84739e9 q^{27} +4.45418e9 q^{28} +4.14550e9 q^{29} -2.98735e9 q^{30} -5.83659e9 q^{31} +6.55377e9 q^{32} -2.62170e9 q^{33} +1.11260e10 q^{34} -3.51506e9 q^{35} +3.22798e10 q^{36} +3.87665e9 q^{37} -1.65388e10 q^{38} +5.93545e10 q^{39} +6.91274e9 q^{40} -3.31987e10 q^{41} +1.01670e11 q^{42} -4.34571e10 q^{43} +1.66722e10 q^{44} -2.54739e10 q^{45} +1.41785e11 q^{46} +1.16895e11 q^{47} +1.36939e10 q^{48} +2.27405e10 q^{49} +1.62199e11 q^{50} +1.55219e11 q^{51} -3.77453e11 q^{52} +3.23420e10 q^{53} +2.68158e11 q^{54} -1.31570e10 q^{55} -2.35264e11 q^{56} -2.30734e11 q^{57} -6.01741e11 q^{58} -4.58259e11 q^{59} +2.65034e11 q^{60} -7.04452e11 q^{61} +8.47211e11 q^{62} +8.66964e11 q^{63} -8.95917e11 q^{64} +2.97870e11 q^{65} +3.80553e11 q^{66} +7.66795e11 q^{67} -9.87087e11 q^{68} +1.97806e12 q^{69} +5.10229e11 q^{70} -1.10301e12 q^{71} -1.70498e12 q^{72} +2.36793e12 q^{73} -5.62715e11 q^{74} +2.26285e12 q^{75} +1.46731e12 q^{76} +4.47777e11 q^{77} -8.61560e12 q^{78} +7.79158e11 q^{79} +6.87229e10 q^{80} -2.55213e11 q^{81} +4.81896e12 q^{82} -6.47070e11 q^{83} -9.02003e12 q^{84} +7.78968e11 q^{85} +6.30802e12 q^{86} -8.39492e12 q^{87} -8.80601e11 q^{88} +1.00322e12 q^{89} +3.69767e12 q^{90} -1.01375e13 q^{91} -1.25790e13 q^{92} +1.18195e13 q^{93} -1.69679e13 q^{94} -1.15794e12 q^{95} -1.32718e13 q^{96} +1.52626e13 q^{97} -3.30090e12 q^{98} +3.24507e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) \) 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9	\( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14} + 87246239 q^{15} + 2130706432 q^{16} + 228353715 q^{17} + 400647337 q^{18} + 1139301305 q^{19} + 1109969259 q^{20} + 539982398 q^{21} + 1613315649 q^{22} + 920306804 q^{23} + 5542439613 q^{24} + 31241700999 q^{25} + 1864366110 q^{26} + 17825460755 q^{27} + 20413389070 q^{28} + 7185436621 q^{29} + 2050251883 q^{30} + 28475592572 q^{31} + 8334714660 q^{32} + 19623425846 q^{33} + 37845014194 q^{34} + 25255003636 q^{35} + 287968706746 q^{36} + 71523920490 q^{37} + 67778214914 q^{38} + 44951568463 q^{39} + 169184871486 q^{40} + 69139231052 q^{41} + 58715177635 q^{42} + 247544146139 q^{43} + 63861560722 q^{44} + 257443045479 q^{45} + 160530477869 q^{46} + 308496573061 q^{47} + 412228130018 q^{48} + 1736616239908 q^{49} + 1680360028531 q^{50} + 756579032995 q^{51} + 928015404666 q^{52} + 342783723680 q^{53} - 597894730601 q^{54} + 59276330527 q^{55} - 3822929869144 q^{56} - 562905761941 q^{57} + 62740419347 q^{58} + 827401964151 q^{59} - 2247133283907 q^{60} + 988213134514 q^{61} + 1937380192071 q^{62} + 1788190111357 q^{63} + 11682175668457 q^{64} + 2494670804291 q^{65} + 11819807890512 q^{66} + 8038740399790 q^{67} + 10126245189885 q^{68} + 5225665164579 q^{69} + 11464042631319 q^{70} + 4867145119603 q^{71} + 18133468947055 q^{72} + 9684156738615 q^{73} + 16996786880941 q^{74} + 16718732018262 q^{75} + 21454522032798 q^{76} + 6593100920650 q^{77} + 33749579076633 q^{78} + 7591753073823 q^{79} + 24349241260570 q^{80} + 38778649605417 q^{81} + 25555033184251 q^{82} + 16945724819556 q^{83} + 21855489402730 q^{84} + 15544906794766 q^{85} + 18664144286914 q^{86} + 19049540636401 q^{87} + 17318749473003 q^{88} + 11289674998576 q^{89} + 20983303956671 q^{90} + 47242561944227 q^{91} - 25046698097386 q^{92} - 5411884145985 q^{93} + 18338784709341 q^{94} + 6784117894603 q^{95} - 36827486682955 q^{96} + 45969533477736 q^{97} - 42983409526150 q^{98} + 12084396239183 q^{99}+O(q^{100}) \) 109 * q + 192 * q^2 + 8018 * q^3 + 471040 * q^4 + 88496 * q^5 + 383232 * q^6 + 1680731 * q^7 + 1820859 * q^8 + 59521391 * q^9 + 16373653 * q^10 + 21199298 * q^11 + 63225856 * q^12 + 59695238 * q^13 + 37888529 * q^14 + 87246239 * q^15 + 2130706432 * q^16 + 228353715 * q^17 + 400647337 * q^18 + 1139301305 * q^19 + 1109969259 * q^20 + 539982398 * q^21 + 1613315649 * q^22 + 920306804 * q^23 + 5542439613 * q^24 + 31241700999 * q^25 + 1864366110 * q^26 + 17825460755 * q^27 + 20413389070 * q^28 + 7185436621 * q^29 + 2050251883 * q^30 + 28475592572 * q^31 + 8334714660 * q^32 + 19623425846 * q^33 + 37845014194 * q^34 + 25255003636 * q^35 + 287968706746 * q^36 + 71523920490 * q^37 + 67778214914 * q^38 + 44951568463 * q^39 + 169184871486 * q^40 + 69139231052 * q^41 + 58715177635 * q^42 + 247544146139 * q^43 + 63861560722 * q^44 + 257443045479 * q^45 + 160530477869 * q^46 + 308496573061 * q^47 + 412228130018 * q^48 + 1736616239908 * q^49 + 1680360028531 * q^50 + 756579032995 * q^51 + 928015404666 * q^52 + 342783723680 * q^53 - 597894730601 * q^54 + 59276330527 * q^55 - 3822929869144 * q^56 - 562905761941 * q^57 + 62740419347 * q^58 + 827401964151 * q^59 - 2247133283907 * q^60 + 988213134514 * q^61 + 1937380192071 * q^62 + 1788190111357 * q^63 + 11682175668457 * q^64 + 2494670804291 * q^65 + 11819807890512 * q^66 + 8038740399790 * q^67 + 10126245189885 * q^68 + 5225665164579 * q^69 + 11464042631319 * q^70 + 4867145119603 * q^71 + 18133468947055 * q^72 + 9684156738615 * q^73 + 16996786880941 * q^74 + 16718732018262 * q^75 + 21454522032798 * q^76 + 6593100920650 * q^77 + 33749579076633 * q^78 + 7591753073823 * q^79 + 24349241260570 * q^80 + 38778649605417 * q^81 + 25555033184251 * q^82 + 16945724819556 * q^83 + 21855489402730 * q^84 + 15544906794766 * q^85 + 18664144286914 * q^86 + 19049540636401 * q^87 + 17318749473003 * q^88 + 11289674998576 * q^89 + 20983303956671 * q^90 + 47242561944227 * q^91 - 25046698097386 * q^92 - 5411884145985 * q^93 + 18338784709341 * q^94 + 6784117894603 * q^95 - 36827486682955 * q^96 + 45969533477736 * q^97 - 42983409526150 * q^98 + 12084396239183 * q^99

Introduction

L-functions

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