LMFDB - Embedded newform 197.10.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,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, 10, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
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:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-28.5607 q^{2} -17.8798 q^{3} +303.711 q^{4} -2276.73 q^{5} +510.659 q^{6} +4449.75 q^{7} +5948.86 q^{8} -19363.3 q^{9} +O(q^{10})$	\(q-28.5607 q^{2} -17.8798 q^{3} +303.711 q^{4} -2276.73 q^{5} +510.659 q^{6} +4449.75 q^{7} +5948.86 q^{8} -19363.3 q^{9} +65025.0 q^{10} +83081.5 q^{11} -5430.29 q^{12} +187916. q^{13} -127088. q^{14} +40707.5 q^{15} -325404. q^{16} +667853. q^{17} +553029. q^{18} +411794. q^{19} -691470. q^{20} -79560.6 q^{21} -2.37286e6 q^{22} -775674. q^{23} -106364. q^{24} +3.23040e6 q^{25} -5.36702e6 q^{26} +698140. q^{27} +1.35144e6 q^{28} -3.43186e6 q^{29} -1.16263e6 q^{30} +8.79207e6 q^{31} +6.24792e6 q^{32} -1.48548e6 q^{33} -1.90743e7 q^{34} -1.01309e7 q^{35} -5.88086e6 q^{36} -814093. q^{37} -1.17611e7 q^{38} -3.35991e6 q^{39} -1.35440e7 q^{40} +4.73614e6 q^{41} +2.27230e6 q^{42} +3.02898e7 q^{43} +2.52328e7 q^{44} +4.40851e7 q^{45} +2.21538e7 q^{46} +2.02845e7 q^{47} +5.81815e6 q^{48} -2.05533e7 q^{49} -9.22622e7 q^{50} -1.19411e7 q^{51} +5.70723e7 q^{52} -3.68644e7 q^{53} -1.99393e7 q^{54} -1.89155e8 q^{55} +2.64710e7 q^{56} -7.36279e6 q^{57} +9.80162e7 q^{58} +1.23982e8 q^{59} +1.23633e7 q^{60} +9.31762e7 q^{61} -2.51107e8 q^{62} -8.61619e7 q^{63} -1.18382e7 q^{64} -4.27836e8 q^{65} +4.24263e7 q^{66} +3.56808e7 q^{67} +2.02834e8 q^{68} +1.38689e7 q^{69} +2.89345e8 q^{70} +4.86785e7 q^{71} -1.15190e8 q^{72} -1.24674e8 q^{73} +2.32510e7 q^{74} -5.77588e7 q^{75} +1.25066e8 q^{76} +3.69692e8 q^{77} +9.59611e7 q^{78} -1.55200e8 q^{79} +7.40858e8 q^{80} +3.68645e8 q^{81} -1.35267e8 q^{82} -6.28307e8 q^{83} -2.41634e7 q^{84} -1.52052e9 q^{85} -8.65097e8 q^{86} +6.13609e7 q^{87} +4.94241e8 q^{88} -1.00624e8 q^{89} -1.25910e9 q^{90} +8.36181e8 q^{91} -2.35581e8 q^{92} -1.57200e8 q^{93} -5.79339e8 q^{94} -9.37546e8 q^{95} -1.11712e8 q^{96} -1.05417e9 q^{97} +5.87017e8 q^{98} -1.60873e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) $ 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * 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 $

$2$	−28.5607	−1.26221	−0.631107	−	0.775695i	$-0.717399\pi$
$2$	−28.5607	−1.26221	−0.631107	+	0.775695i	$0.717399\pi$
$3$	−17.8798	−0.127443	−0.0637216	−	0.997968i	$-0.520297\pi$
$3$	−17.8798	−0.127443	−0.0637216	+	0.997968i	$0.520297\pi$
$4$	303.711	0.593186
$5$	−2276.73	−1.62910	−0.814549	−	0.580094i	$-0.803016\pi$
$5$	−2276.73	−1.62910	−0.814549	+	0.580094i	$0.803016\pi$
$6$	510.659	0.160861
$7$	4449.75	0.700478	0.350239	−	0.936660i	$-0.386100\pi$
$7$	4449.75	0.700478	0.350239	+	0.936660i	$0.386100\pi$
$8$	5948.86	0.513487
$9$	−19363.3	−0.983758
$10$	65025.0	2.05627
$11$	83081.5	1.71095	0.855475	−	0.517845i	$-0.173265\pi$
$11$	83081.5	1.71095	0.855475	+	0.517845i	$0.173265\pi$
$12$	−5430.29	−0.0755975
$13$	187916.	1.82482	0.912409	−	0.409280i	$-0.134220\pi$
$13$	187916.	1.82482	0.912409	+	0.409280i	$0.134220\pi$
$14$	−127088.	−0.884153
$15$	40707.5	0.207618
$16$	−325404.	−1.24132
$17$	667853.	1.93937	0.969685	−	0.244358i	$-0.0785773\pi$
$17$	667853.	1.93937	0.969685	+	0.244358i	$0.0785773\pi$
$18$	553029.	1.24171
$19$	411794.	0.724918	0.362459	−	0.932000i	$-0.381937\pi$
$19$	411794.	0.724918	0.362459	+	0.932000i	$0.381937\pi$
$20$	−691470.	−0.966359
$21$	−79560.6	−0.0892712
$22$	−2.37286e6	−2.15959
$23$	−775674.	−0.577968	−0.288984	−	0.957334i	$-0.593317\pi$
$23$	−775674.	−0.577968	−0.288984	+	0.957334i	$0.593317\pi$
$24$	−106364.	−0.0654404
$25$	3.23040e6	1.65396
$26$	−5.36702e6	−2.30331
$27$	698140.	0.252817
$28$	1.35144e6	0.415514
$29$	−3.43186e6	−0.901029	−0.450514	−	0.892769i	$-0.648759\pi$
$29$	−3.43186e6	−0.901029	−0.450514	+	0.892769i	$0.648759\pi$
$30$	−1.16263e6	−0.262058
$31$	8.79207e6	1.70987	0.854935	−	0.518734i	$-0.173597\pi$
$31$	8.79207e6	1.70987	0.854935	+	0.518734i	$0.173597\pi$
$32$	6.24792e6	1.05332
$33$	−1.48548e6	−0.218049
$34$	−1.90743e7	−2.44790
$35$	−1.01309e7	−1.14115
$36$	−5.88086e6	−0.583552
$37$	−814093.	−0.0714112	−0.0357056	−	0.999362i	$-0.511368\pi$
$37$	−814093.	−0.0714112	−0.0357056	+	0.999362i	$0.511368\pi$
$38$	−1.17611e7	−0.915002
$39$	−3.35991e6	−0.232561
$40$	−1.35440e7	−0.836520
$41$	4.73614e6	0.261756	0.130878	−	0.991398i	$-0.458220\pi$
$41$	4.73614e6	0.261756	0.130878	+	0.991398i	$0.458220\pi$
$42$	2.27230e6	0.112679
$43$	3.02898e7	1.35110	0.675552	−	0.737313i	$-0.263906\pi$
$43$	3.02898e7	1.35110	0.675552	+	0.737313i	$0.263906\pi$
$44$	2.52328e7	1.01491
$45$	4.40851e7	1.60264
$46$	2.21538e7	0.729520
$47$	2.02845e7	0.606351	0.303176	−	0.952935i	$-0.401953\pi$
$47$	2.02845e7	0.606351	0.303176	+	0.952935i	$0.401953\pi$
$48$	5.81815e6	0.158197
$49$	−2.05533e7	−0.509331
$50$	−9.22622e7	−2.08766
$51$	−1.19411e7	−0.247160
$52$	5.70723e7	1.08246
$53$	−3.68644e7	−0.641750	−0.320875	−	0.947122i	$-0.603977\pi$
$53$	−3.68644e7	−0.641750	−0.320875	+	0.947122i	$0.603977\pi$
$54$	−1.99393e7	−0.319109
$55$	−1.89155e8	−2.78731
$56$	2.64710e7	0.359686
$57$	−7.36279e6	−0.0923859
$58$	9.80162e7	1.13729
$59$	1.23982e8	1.33206	0.666031	−	0.745924i	$-0.267992\pi$
$59$	1.23982e8	1.33206	0.666031	+	0.745924i	$0.267992\pi$
$60$	1.23633e7	0.123156
$61$	9.31762e7	0.861630	0.430815	−	0.902440i	$-0.358226\pi$
$61$	9.31762e7	0.861630	0.430815	+	0.902440i	$0.358226\pi$
$62$	−2.51107e8	−2.15822
$63$	−8.61619e7	−0.689101
$64$	−1.18382e7	−0.0882011
$65$	−4.27836e8	−2.97281
$66$	4.24263e7	0.275225
$67$	3.56808e7	0.216321	0.108160	−	0.994133i	$-0.465504\pi$
$67$	3.56808e7	0.216321	0.108160	+	0.994133i	$0.465504\pi$
$68$	2.02834e8	1.15041
$69$	1.38689e7	0.0736581
$70$	2.89345e8	1.44037
$71$	4.86785e7	0.227339	0.113670	−	0.993519i	$-0.463739\pi$
$71$	4.86785e7	0.227339	0.113670	+	0.993519i	$0.463739\pi$
$72$	−1.15190e8	−0.505147
$73$	−1.24674e8	−0.513833	−0.256917	−	0.966434i	$-0.582707\pi$
$73$	−1.24674e8	−0.513833	−0.256917	+	0.966434i	$0.582707\pi$
$74$	2.32510e7	0.0901363
$75$	−5.77588e7	−0.210786
$76$	1.25066e8	0.430011
$77$	3.69692e8	1.19848
$78$	9.59611e7	0.293542
$79$	−1.55200e8	−0.448302	−0.224151	−	0.974554i	$-0.571961\pi$
$79$	−1.55200e8	−0.448302	−0.224151	+	0.974554i	$0.571961\pi$
$80$	7.40858e8	2.02223
$81$	3.68645e8	0.951538
$82$	−1.35267e8	−0.330393
$83$	−6.28307e8	−1.45318	−0.726592	−	0.687069i	$-0.758897\pi$
$83$	−6.28307e8	−1.45318	−0.726592	+	0.687069i	$0.758897\pi$
$84$	−2.41634e7	−0.0529544
$85$	−1.52052e9	−3.15943
$86$	−8.65097e8	−1.70538
$87$	6.13609e7	0.114830
$88$	4.94241e8	0.878550
$89$	−1.00624e8	−0.169998	−0.0849992	−	0.996381i	$-0.527089\pi$
$89$	−1.00624e8	−0.169998	−0.0849992	+	0.996381i	$0.527089\pi$
$90$	−1.25910e9	−2.02287
$91$	8.36181e8	1.27824
$92$	−2.35581e8	−0.342843
$93$	−1.57200e8	−0.217911
$94$	−5.79339e8	−0.765345
$95$	−9.37546e8	−1.18096
$96$	−1.11712e8	−0.134239
$97$	−1.05417e9	−1.20903	−0.604515	−	0.796594i	$-0.706633\pi$
$97$	−1.05417e9	−1.20903	−0.604515	+	0.796594i	$0.706633\pi$
$98$	5.87017e8	0.642885
$99$	−1.60873e9	−1.68316
$100$	9.81107e8	0.981107
$101$	−8.92308e8	−0.853235	−0.426617	−	0.904432i	$-0.640295\pi$
$101$	−8.92308e8	−0.853235	−0.426617	+	0.904432i	$0.640295\pi$
$102$	3.41045e8	0.311968
$103$	−1.65210e9	−1.44633	−0.723167	−	0.690673i	$-0.757314\pi$
$103$	−1.65210e9	−1.44633	−0.723167	+	0.690673i	$0.757314\pi$
$104$	1.11789e9	0.937020
$105$	1.81138e8	0.145432
$106$	1.05287e9	0.810026
$107$	1.26800e9	0.935172	0.467586	−	0.883948i	$-0.345124\pi$
$107$	1.26800e9	0.935172	0.467586	+	0.883948i	$0.345124\pi$
$108$	2.12033e8	0.149967
$109$	1.86438e9	1.26507	0.632535	−	0.774532i	$-0.282015\pi$
$109$	1.86438e9	1.26507	0.632535	+	0.774532i	$0.282015\pi$
$110$	5.40238e9	3.51818
$111$	1.45558e7	0.00910087
$112$	−1.44796e9	−0.869514
$113$	2.92077e9	1.68517	0.842586	−	0.538562i	$-0.181032\pi$
$113$	2.92077e9	1.68517	0.842586	+	0.538562i	$0.181032\pi$
$114$	2.10286e8	0.116611
$115$	1.76600e9	0.941567
$116$	−1.04229e9	−0.534478
$117$	−3.63868e9	−1.79518
$118$	−3.54101e9	−1.68135
$119$	2.97178e9	1.35849
$120$	2.42164e8	0.106609
$121$	4.54459e9	1.92735
$122$	−2.66117e9	−1.08756
$123$	−8.46812e7	−0.0333591
$124$	2.67025e9	1.01427
$125$	−2.90801e9	−1.06537
$126$	2.46084e9	0.869793
$127$	3.37479e9	1.15114	0.575572	−	0.817751i	$-0.304779\pi$
$127$	3.37479e9	1.15114	0.575572	+	0.817751i	$0.304779\pi$
$128$	−2.86083e9	−0.941992
$129$	−5.41575e8	−0.172189
$130$	1.22193e10	3.75232
$131$	1.95325e9	0.579478	0.289739	−	0.957106i	$-0.406431\pi$
$131$	1.95325e9	0.579478	0.289739	+	0.957106i	$0.406431\pi$
$132$	−4.51157e8	−0.129344
$133$	1.83238e9	0.507789
$134$	−1.01907e9	−0.273043
$135$	−1.58948e9	−0.411863
$136$	3.97297e9	0.995841
$137$	1.92199e9	0.466131	0.233066	−	0.972461i	$-0.425124\pi$
$137$	1.92199e9	0.466131	0.233066	+	0.972461i	$0.425124\pi$
$138$	−3.96104e8	−0.0929724
$139$	4.63980e9	1.05422	0.527112	−	0.849796i	$-0.323275\pi$
$139$	4.63980e9	1.05422	0.527112	+	0.849796i	$0.323275\pi$
$140$	−3.07687e9	−0.676913
$141$	−3.62683e8	−0.0772753
$142$	−1.39029e9	−0.286951
$143$	1.56124e10	3.12217
$144$	6.30089e9	1.22116
$145$	7.81344e9	1.46786
$146$	3.56076e9	0.648568
$147$	3.67489e8	0.0649108
$148$	−2.47249e8	−0.0423601
$149$	−4.27800e9	−0.711054	−0.355527	−	0.934666i	$-0.615699\pi$
$149$	−4.27800e9	−0.711054	−0.355527	+	0.934666i	$0.615699\pi$
$150$	1.64963e9	0.266058
$151$	8.83292e9	1.38264	0.691318	−	0.722550i	$-0.257030\pi$
$151$	8.83292e9	1.38264	0.691318	+	0.722550i	$0.257030\pi$
$152$	2.44971e9	0.372236
$153$	−1.29318e10	−1.90787
$154$	−1.05586e10	−1.51274
$155$	−2.00172e10	−2.78555
$156$	−1.02044e9	−0.137952
$157$	6.34702e9	0.833722	0.416861	−	0.908970i	$-0.363130\pi$
$157$	6.34702e9	0.833722	0.416861	+	0.908970i	$0.363130\pi$
$158$	4.43262e9	0.565853
$159$	6.59128e8	0.0817867
$160$	−1.42249e10	−1.71596
$161$	−3.45155e9	−0.404854
$162$	−1.05288e10	−1.20105
$163$	−8.68239e9	−0.963374	−0.481687	−	0.876343i	$-0.659976\pi$
$163$	−8.68239e9	−0.963374	−0.481687	+	0.876343i	$0.659976\pi$
$164$	1.43842e9	0.155270
$165$	3.38204e9	0.355223
$166$	1.79449e10	1.83423
$167$	2.39365e9	0.238142	0.119071	−	0.992886i	$-0.462008\pi$
$167$	2.39365e9	0.238142	0.119071	+	0.992886i	$0.462008\pi$
$168$	−4.73295e8	−0.0458395
$169$	2.47081e10	2.32996
$170$	4.34272e10	3.98787
$171$	−7.97370e9	−0.713144
$172$	9.19935e9	0.801455
$173$	−2.31540e10	−1.96525	−0.982627	−	0.185592i	$-0.940580\pi$
$173$	−2.31540e10	−1.96525	−0.982627	+	0.185592i	$0.940580\pi$
$174$	−1.75251e9	−0.144940
$175$	1.43744e10	1.15856
$176$	−2.70350e10	−2.12383
$177$	−2.21677e9	−0.169762
$178$	2.87388e9	0.214575
$179$	−1.77579e10	−1.29286	−0.646431	−	0.762973i	$-0.723739\pi$
$179$	−1.77579e10	−1.29286	−0.646431	+	0.762973i	$0.723739\pi$
$180$	1.33891e10	0.950663
$181$	1.60839e9	0.111388	0.0556941	−	0.998448i	$-0.482263\pi$
$181$	1.60839e9	0.111388	0.0556941	+	0.998448i	$0.482263\pi$
$182$	−2.38819e10	−1.61342
$183$	−1.66597e9	−0.109809
$184$	−4.61438e9	−0.296779
$185$	1.85347e9	0.116336
$186$	4.48974e9	0.275051
$187$	5.54862e10	3.31816
$188$	6.16063e9	0.359679
$189$	3.10655e9	0.177092
$190$	2.67769e10	1.49063
$191$	−1.53967e10	−0.837100	−0.418550	−	0.908194i	$-0.637462\pi$
$191$	−1.53967e10	−0.837100	−0.418550	+	0.908194i	$0.637462\pi$
$192$	2.11664e8	0.0112406
$193$	−2.25922e10	−1.17206	−0.586032	−	0.810288i	$-0.699311\pi$
$193$	−2.25922e10	−1.17206	−0.586032	+	0.810288i	$0.699311\pi$
$194$	3.01077e10	1.52606
$195$	7.64961e9	0.378864
$196$	−6.24228e9	−0.302128
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	4.59465e10	2.12451
$199$	−1.33320e10	−0.602636	−0.301318	−	0.953524i	$-0.597427\pi$
$199$	−1.33320e10	−0.602636	−0.301318	+	0.953524i	$0.597427\pi$
$200$	1.92172e10	0.849288
$201$	−6.37966e8	−0.0275686
$202$	2.54849e10	1.07697
$203$	−1.52709e10	−0.631151
$204$	−3.62664e9	−0.146612
$205$	−1.07829e10	−0.426427
$206$	4.71850e10	1.82558
$207$	1.50196e10	0.568581
$208$	−6.11487e10	−2.26518
$209$	3.42125e10	1.24030
$210$	−5.17343e9	−0.183566
$211$	−3.47005e10	−1.20522	−0.602609	−	0.798037i	$-0.705872\pi$
$211$	−3.47005e10	−1.20522	−0.602609	+	0.798037i	$0.705872\pi$
$212$	−1.11961e10	−0.380677
$213$	−8.70362e8	−0.0289729
$214$	−3.62149e10	−1.18039
$215$	−6.89619e10	−2.20108
$216$	4.15314e9	0.129818
$217$	3.91225e10	1.19773
$218$	−5.32478e10	−1.59679
$219$	2.22914e9	0.0654846
$220$	−5.74483e10	−1.65339
$221$	1.25500e11	3.53900
$222$	−4.15724e8	−0.0114873
$223$	5.02537e10	1.36081	0.680403	−	0.732838i	$-0.261805\pi$
$223$	5.02537e10	1.36081	0.680403	+	0.732838i	$0.261805\pi$
$224$	2.78017e10	0.737828
$225$	−6.25512e10	−1.62710
$226$	−8.34191e10	−2.12705
$227$	−1.30521e10	−0.326260	−0.163130	−	0.986605i	$-0.552159\pi$
$227$	−1.30521e10	−0.326260	−0.163130	+	0.986605i	$0.552159\pi$
$228$	−2.23616e9	−0.0548020
$229$	1.58312e10	0.380412	0.190206	−	0.981744i	$-0.439084\pi$
$229$	1.58312e10	0.380412	0.190206	+	0.981744i	$0.439084\pi$
$230$	−5.04382e10	−1.18846
$231$	−6.61001e9	−0.152738
$232$	−2.04157e10	−0.462666
$233$	3.20284e10	0.711924	0.355962	−	0.934500i	$-0.384153\pi$
$233$	3.20284e10	0.711924	0.355962	+	0.934500i	$0.384153\pi$
$234$	1.03923e11	2.26590
$235$	−4.61824e10	−0.987806
$236$	3.76547e10	0.790161
$237$	2.77495e9	0.0571330
$238$	−8.48759e10	−1.71470
$239$	−1.53258e10	−0.303832	−0.151916	−	0.988393i	$-0.548544\pi$
$239$	−1.53258e10	−0.303832	−0.151916	+	0.988393i	$0.548544\pi$
$240$	−1.32464e10	−0.257719
$241$	4.42326e10	0.844628	0.422314	−	0.906450i	$-0.361218\pi$
$241$	4.42326e10	0.844628	0.422314	+	0.906450i	$0.361218\pi$
$242$	−1.29796e11	−2.43273
$243$	−2.03328e10	−0.374084
$244$	2.82987e10	0.511107
$245$	4.67945e10	0.829750
$246$	2.41855e9	0.0421063
$247$	7.73828e10	1.32284
$248$	5.23028e10	0.877996
$249$	1.12340e10	0.185199
$250$	8.30546e10	1.34473
$251$	−4.58474e10	−0.729094	−0.364547	−	0.931185i	$-0.618776\pi$
$251$	−4.58474e10	−0.729094	−0.364547	+	0.931185i	$0.618776\pi$
$252$	−2.61683e10	−0.408765
$253$	−6.44441e10	−0.988874
$254$	−9.63862e10	−1.45299
$255$	2.71867e10	0.402647
$256$	8.77684e10	1.27720
$257$	−8.03885e9	−0.114946	−0.0574732	−	0.998347i	$-0.518304\pi$
$257$	−8.03885e9	−0.114946	−0.0574732	+	0.998347i	$0.518304\pi$
$258$	1.54678e10	0.217339
$259$	−3.62251e9	−0.0500220
$260$	−1.29939e11	−1.76343
$261$	6.64522e10	0.886394
$262$	−5.57861e10	−0.731426
$263$	−1.17791e11	−1.51813	−0.759066	−	0.651014i	$-0.774344\pi$
$263$	−1.17791e11	−1.51813	−0.759066	+	0.651014i	$0.774344\pi$
$264$	−8.83692e9	−0.111965
$265$	8.39305e10	1.04547
$266$	−5.23340e10	−0.640939
$267$	1.79913e9	0.0216651
$268$	1.08367e10	0.128318
$269$	−8.42977e10	−0.981591	−0.490796	−	0.871275i	$-0.663294\pi$
$269$	−8.42977e10	−0.981591	−0.490796	+	0.871275i	$0.663294\pi$
$270$	4.53966e10	0.519860
$271$	−8.41800e10	−0.948084	−0.474042	−	0.880502i	$-0.657206\pi$
$271$	−8.41800e10	−0.948084	−0.474042	+	0.880502i	$0.657206\pi$
$272$	−2.17322e11	−2.40737
$273$	−1.49507e10	−0.162904
$274$	−5.48933e10	−0.588358
$275$	2.68386e11	2.82985
$276$	4.21214e9	0.0436930
$277$	7.75886e10	0.791843	0.395921	−	0.918284i	$-0.370425\pi$
$277$	7.75886e10	0.791843	0.395921	+	0.918284i	$0.370425\pi$
$278$	−1.32516e11	−1.33066
$279$	−1.70244e11	−1.68210
$280$	−6.02673e10	−0.585964
$281$	1.00820e11	0.964647	0.482324	−	0.875993i	$-0.339793\pi$
$281$	1.00820e11	0.964647	0.482324	+	0.875993i	$0.339793\pi$
$282$	1.03585e10	0.0975381
$283$	9.78661e10	0.906971	0.453485	−	0.891264i	$-0.350180\pi$
$283$	9.78661e10	0.906971	0.453485	+	0.891264i	$0.350180\pi$
$284$	1.47842e10	0.134855
$285$	1.67631e10	0.150506
$286$	−4.45900e11	−3.94085
$287$	2.10746e10	0.183354
$288$	−1.20981e11	−1.03621
$289$	3.27440e11	2.76116
$290$	−2.23157e11	−1.85276
$291$	1.88483e10	0.154083
$292$	−3.78648e10	−0.304799
$293$	−1.72306e11	−1.36582	−0.682912	−	0.730500i	$-0.739287\pi$
$293$	−1.72306e11	−1.36582	−0.682912	+	0.730500i	$0.739287\pi$
$294$	−1.04957e10	−0.0819313
$295$	−2.82274e11	−2.17006
$296$	−4.84293e9	−0.0366687
$297$	5.80025e10	0.432556
$298$	1.22182e11	0.897502
$299$	−1.45762e11	−1.05469
$300$	−1.75420e10	−0.125036
$301$	1.34782e11	0.946418
$302$	−2.52274e11	−1.74518
$303$	1.59543e10	0.108739
$304$	−1.33999e11	−0.899853
$305$	−2.12137e11	−1.40368
$306$	3.69342e11	2.40814
$307$	−1.14465e10	−0.0735442	−0.0367721	−	0.999324i	$-0.511708\pi$
$307$	−1.14465e10	−0.0735442	−0.0367721	+	0.999324i	$0.511708\pi$
$308$	1.12280e11	0.710923
$309$	2.95392e10	0.184325
$310$	5.71704e11	3.51596
$311$	1.67055e11	1.01260	0.506299	−	0.862358i	$-0.331013\pi$
$311$	1.67055e11	1.01260	0.506299	+	0.862358i	$0.331013\pi$
$312$	−1.99876e10	−0.119417
$313$	1.96521e11	1.15734	0.578668	−	0.815563i	$-0.303573\pi$
$313$	1.96521e11	1.15734	0.578668	+	0.815563i	$0.303573\pi$
$314$	−1.81275e11	−1.05234
$315$	1.96168e11	1.12261
$316$	−4.71360e10	−0.265926
$317$	2.50443e10	0.139297	0.0696486	−	0.997572i	$-0.477812\pi$
$317$	2.50443e10	0.139297	0.0696486	+	0.997572i	$0.477812\pi$
$318$	−1.88251e10	−0.103232
$319$	−2.85124e11	−1.54161
$320$	2.69523e10	0.143688
$321$	−2.26715e10	−0.119181
$322$	9.85786e10	0.511012
$323$	2.75018e11	1.40588
$324$	1.11962e11	0.564439
$325$	6.07044e11	3.01818
$326$	2.47975e11	1.21598
$327$	−3.33347e10	−0.161225
$328$	2.81747e10	0.134408
$329$	9.02610e10	0.424735
$330$	−9.65934e10	−0.448368
$331$	1.35131e11	0.618772	0.309386	−	0.950937i	$-0.399877\pi$
$331$	1.35131e11	0.618772	0.309386	+	0.950937i	$0.399877\pi$
$332$	−1.90824e11	−0.862008
$333$	1.57635e10	0.0702513
$334$	−6.83642e10	−0.300586
$335$	−8.12358e10	−0.352408
$336$	2.58893e10	0.110814
$337$	−3.48004e11	−1.46977	−0.734885	−	0.678191i	$-0.762764\pi$
$337$	−3.48004e11	−1.46977	−0.734885	+	0.678191i	$0.762764\pi$
$338$	−7.05679e11	−2.94091
$339$	−5.22227e10	−0.214764
$340$	−4.61800e11	−1.87413
$341$	7.30458e11	2.92550
$342$	2.27734e11	0.900141
$343$	−2.71021e11	−1.05725
$344$	1.80190e11	0.693773
$345$	−3.15758e10	−0.119996
$346$	6.61294e11	2.48057
$347$	−2.52200e11	−0.933820	−0.466910	−	0.884305i	$-0.654633\pi$
$347$	−2.52200e11	−0.933820	−0.466910	+	0.884305i	$0.654633\pi$
$348$	1.86360e10	0.0681156
$349$	2.30487e10	0.0831633	0.0415816	−	0.999135i	$-0.486760\pi$
$349$	2.30487e10	0.0831633	0.0415816	+	0.999135i	$0.486760\pi$
$350$	−4.10544e11	−1.46236
$351$	1.31192e11	0.461344
$352$	5.19087e11	1.80218
$353$	1.13444e11	0.388863	0.194431	−	0.980916i	$-0.437714\pi$
$353$	1.13444e11	0.388863	0.194431	+	0.980916i	$0.437714\pi$
$354$	6.33125e10	0.214277
$355$	−1.10828e11	−0.370358
$356$	−3.05605e10	−0.100841
$357$	−5.31348e10	−0.173130
$358$	5.07176e11	1.63187
$359$	−9.87214e10	−0.313679	−0.156840	−	0.987624i	$-0.550131\pi$
$359$	−9.87214e10	−0.313679	−0.156840	+	0.987624i	$0.550131\pi$
$360$	2.62256e11	0.822934
$361$	−1.53113e11	−0.474494
$362$	−4.59368e10	−0.140596
$363$	−8.12563e10	−0.245627
$364$	2.53957e11	0.758237
$365$	2.83849e11	0.837085
$366$	4.75812e10	0.138602
$367$	−2.68609e11	−0.772899	−0.386449	−	0.922311i	$-0.626299\pi$
$367$	−2.68609e11	−0.772899	−0.386449	+	0.922311i	$0.626299\pi$
$368$	2.52407e11	0.717441
$369$	−9.17073e10	−0.257505
$370$	−5.29364e10	−0.146841
$371$	−1.64037e11	−0.449532
$372$	−4.77435e10	−0.129262
$373$	1.42556e11	0.381326	0.190663	−	0.981656i	$-0.438936\pi$
$373$	1.42556e11	0.381326	0.190663	+	0.981656i	$0.438936\pi$
$374$	−1.58472e12	−4.18824
$375$	5.19945e10	0.135774
$376$	1.20670e11	0.311353
$377$	−6.44903e11	−1.64421
$378$	−8.87250e10	−0.223529
$379$	−1.99498e11	−0.496664	−0.248332	−	0.968675i	$-0.579882\pi$
$379$	−1.99498e11	−0.496664	−0.248332	+	0.968675i	$0.579882\pi$
$380$	−2.84743e11	−0.700531
$381$	−6.03405e10	−0.146706
$382$	4.39740e11	1.05660
$383$	−3.17762e11	−0.754585	−0.377292	−	0.926094i	$-0.623145\pi$
$383$	−3.17762e11	−0.754585	−0.377292	+	0.926094i	$0.623145\pi$
$384$	5.11511e10	0.120051
$385$	−8.41690e11	−1.95245
$386$	6.45249e11	1.47940
$387$	−5.86511e11	−1.32916
$388$	−3.20163e11	−0.717180
$389$	6.17930e11	1.36825	0.684126	−	0.729364i	$-0.260184\pi$
$389$	6.17930e11	1.36825	0.684126	+	0.729364i	$0.260184\pi$
$390$	−2.18478e11	−0.478208
$391$	−5.18036e11	−1.12089
$392$	−1.22269e11	−0.261535
$393$	−3.49237e10	−0.0738506
$394$	−4.30163e10	−0.0899291
$395$	3.53350e11	0.730327
$396$	−4.88590e11	−0.998427
$397$	−3.96920e11	−0.801947	−0.400973	−	0.916090i	$-0.631328\pi$
$397$	−3.96920e11	−0.801947	−0.400973	+	0.916090i	$0.631328\pi$
$398$	3.80769e11	0.760656
$399$	−3.27626e10	−0.0647143
$400$	−1.05118e12	−2.05309
$401$	−1.57677e11	−0.304521	−0.152261	−	0.988340i	$-0.548655\pi$
$401$	−1.57677e11	−0.304521	−0.152261	+	0.988340i	$0.548655\pi$
$402$	1.82207e10	0.0347975
$403$	1.65217e12	3.12020
$404$	−2.71004e11	−0.506127
$405$	−8.39308e11	−1.55015
$406$	4.36147e11	0.796647
$407$	−6.76361e10	−0.122181
$408$	−7.10358e10	−0.126913
$409$	−3.65264e10	−0.0645435	−0.0322717	−	0.999479i	$-0.510274\pi$
$409$	−3.65264e10	−0.0645435	−0.0322717	+	0.999479i	$0.510274\pi$
$410$	3.07968e11	0.538242
$411$	−3.43648e10	−0.0594053
$412$	−5.01761e11	−0.857945
$413$	5.51689e11	0.933080
$414$	−4.28970e11	−0.717671
$415$	1.43049e12	2.36738
$416$	1.17409e12	1.92212
$417$	−8.29587e10	−0.134354
$418$	−9.77130e11	−1.56552
$419$	−5.44859e10	−0.0863617	−0.0431809	−	0.999067i	$-0.513749\pi$
$419$	−5.44859e10	−0.0863617	−0.0431809	+	0.999067i	$0.513749\pi$
$420$	5.50137e10	0.0862679
$421$	3.44841e11	0.534994	0.267497	−	0.963559i	$-0.413803\pi$
$421$	3.44841e11	0.534994	0.267497	+	0.963559i	$0.413803\pi$
$422$	9.91070e11	1.52124
$423$	−3.92775e11	−0.596503
$424$	−2.19301e11	−0.329530
$425$	2.15743e12	3.20765
$426$	2.48581e10	0.0365700
$427$	4.14611e11	0.603552
$428$	3.85105e11	0.554731
$429$	−2.79146e11	−0.397900
$430$	1.96960e12	2.77824
$431$	−7.66363e11	−1.06976	−0.534881	−	0.844928i	$-0.679643\pi$
$431$	−7.66363e11	−1.06976	−0.534881	+	0.844928i	$0.679643\pi$
$432$	−2.27177e11	−0.313825
$433$	6.30791e11	0.862362	0.431181	−	0.902265i	$-0.358097\pi$
$433$	6.30791e11	0.862362	0.431181	+	0.902265i	$0.358097\pi$
$434$	−1.11736e12	−1.51179
$435$	−1.39703e11	−0.187069
$436$	5.66232e11	0.750421
$437$	−3.19418e11	−0.418979
$438$	−6.36657e10	−0.0826556
$439$	3.44206e11	0.442312	0.221156	−	0.975238i	$-0.429017\pi$
$439$	3.44206e11	0.442312	0.221156	+	0.975238i	$0.429017\pi$
$440$	−1.12525e12	−1.43124
$441$	3.97981e11	0.501058
$442$	−3.58438e12	−4.46697
$443$	−1.46880e12	−1.81195	−0.905974	−	0.423333i	$-0.860860\pi$
$443$	−1.46880e12	−1.81195	−0.905974	+	0.423333i	$0.860860\pi$
$444$	4.42076e9	0.00539851
$445$	2.29093e11	0.276944
$446$	−1.43528e12	−1.71763
$447$	7.64897e10	0.0906190
$448$	−5.26768e10	−0.0617829
$449$	4.12349e11	0.478803	0.239401	−	0.970921i	$-0.423049\pi$
$449$	4.12349e11	0.478803	0.239401	+	0.970921i	$0.423049\pi$
$450$	1.78650e12	2.05375
$451$	3.93485e11	0.447852
$452$	8.87070e11	0.999620
$453$	−1.57931e11	−0.176208
$454$	3.72777e11	0.411811
$455$	−1.90376e12	−2.08239
$456$	−4.38003e10	−0.0474389
$457$	1.75908e12	1.88653	0.943263	−	0.332047i	$-0.107739\pi$
$457$	1.75908e12	1.88653	0.943263	+	0.332047i	$0.107739\pi$
$458$	−4.52150e11	−0.480162
$459$	4.66255e11	0.490305
$460$	5.36355e11	0.558524
$461$	−8.04922e11	−0.830041	−0.415020	−	0.909812i	$-0.636226\pi$
$461$	−8.04922e11	−0.830041	−0.415020	+	0.909812i	$0.636226\pi$
$462$	1.88786e11	0.192789
$463$	−1.37799e12	−1.39358	−0.696790	−	0.717276i	$-0.745389\pi$
$463$	−1.37799e12	−1.39358	−0.696790	+	0.717276i	$0.745389\pi$
$464$	1.11674e12	1.11846
$465$	3.57903e11	0.354999
$466$	−9.14752e11	−0.898601
$467$	−4.47324e10	−0.0435207	−0.0217604	−	0.999763i	$-0.506927\pi$
$467$	−4.47324e10	−0.0435207	−0.0217604	+	0.999763i	$0.506927\pi$
$468$	−1.10511e12	−1.06488
$469$	1.58771e11	0.151528
$470$	1.31900e12	1.24682
$471$	−1.13483e11	−0.106252
$472$	7.37552e11	0.683996
$473$	2.51652e12	2.31167
$474$	−7.92543e10	−0.0721141
$475$	1.33026e12	1.19899
$476$	9.02562e11	0.805835
$477$	7.13817e11	0.631327
$478$	4.37716e11	0.383501
$479$	−1.87671e12	−1.62887	−0.814435	−	0.580255i	$-0.802953\pi$
$479$	−1.87671e12	−1.62887	−0.814435	+	0.580255i	$0.802953\pi$
$480$	2.54338e11	0.218688
$481$	−1.52981e11	−0.130312
$482$	−1.26331e12	−1.06610
$483$	6.17131e10	0.0515959
$484$	1.38024e12	1.14328
$485$	2.40006e12	1.96963
$486$	5.80718e11	0.472174
$487$	1.18440e12	0.954157	0.477078	−	0.878861i	$-0.341696\pi$
$487$	1.18440e12	0.954157	0.477078	+	0.878861i	$0.341696\pi$
$488$	5.54293e11	0.442435
$489$	1.55239e11	0.122776
$490$	−1.33648e12	−1.04732
$491$	4.78870e11	0.371836	0.185918	−	0.982565i	$-0.440474\pi$
$491$	4.78870e11	0.371836	0.185918	+	0.982565i	$0.440474\pi$
$492$	−2.57186e10	−0.0197881
$493$	−2.29198e12	−1.74743
$494$	−2.21010e12	−1.66971
$495$	3.66266e12	2.74203
$496$	−2.86097e12	−2.12249
$497$	2.16607e11	0.159246
$498$	−3.20851e11	−0.233760
$499$	6.36936e10	0.0459879	0.0229939	−	0.999736i	$-0.492680\pi$
$499$	6.36936e10	0.0459879	0.0229939	+	0.999736i	$0.492680\pi$
$500$	−8.83194e11	−0.631962
$501$	−4.27979e10	−0.0303496
$502$	1.30943e12	0.920273
$503$	1.38419e12	0.964137	0.482069	−	0.876134i	$-0.339886\pi$
$503$	1.38419e12	0.964137	0.482069	+	0.876134i	$0.339886\pi$
$504$	−5.12565e11	−0.353844
$505$	2.03155e12	1.39000
$506$	1.84057e12	1.24817
$507$	−4.41775e11	−0.296938
$508$	1.02496e12	0.682843
$509$	−2.23851e12	−1.47819	−0.739093	−	0.673604i	$-0.764746\pi$
$509$	−2.23851e12	−1.47819	−0.739093	+	0.673604i	$0.764746\pi$
$510$	−7.76469e11	−0.508227
$511$	−5.54767e11	−0.359929
$512$	−1.04198e12	−0.670105
$513$	2.87490e11	0.183271
$514$	2.29595e11	0.145087
$515$	3.76139e12	2.35622
$516$	−1.64483e11	−0.102140
$517$	1.68527e12	1.03744
$518$	1.03461e11	0.0631384
$519$	4.13989e11	0.250458
$520$	−2.54514e12	−1.52650
$521$	2.37741e11	0.141363	0.0706813	−	0.997499i	$-0.477483\pi$
$521$	2.37741e11	0.141363	0.0706813	+	0.997499i	$0.477483\pi$
$522$	−1.89792e12	−1.11882
$523$	−1.10457e12	−0.645556	−0.322778	−	0.946475i	$-0.604617\pi$
$523$	−1.10457e12	−0.645556	−0.322778	+	0.946475i	$0.604617\pi$
$524$	5.93224e11	0.343738
$525$	−2.57012e11	−0.147651
$526$	3.36417e12	1.91621
$527$	5.87181e12	3.31607
$528$	4.83381e11	0.270668
$529$	−1.19948e12	−0.665953
$530$	−2.39711e12	−1.31961
$531$	−2.40070e12	−1.31043
$532$	5.56514e11	0.301213
$533$	8.89998e11	0.477658
$534$	−5.13843e10	−0.0273461
$535$	−2.88690e12	−1.52349
$536$	2.12260e11	0.111078
$537$	3.17507e11	0.164766
$538$	2.40760e12	1.23898
$539$	−1.70760e12	−0.871439
$540$	−4.82743e11	−0.244311
$541$	−3.75693e12	−1.88558	−0.942791	−	0.333383i	$-0.891810\pi$
$541$	−3.75693e12	−1.88558	−0.942791	+	0.333383i	$0.891810\pi$
$542$	2.40424e12	1.19669
$543$	−2.87578e10	−0.0141957
$544$	4.17269e12	2.04278
$545$	−4.24469e12	−2.06092
$546$	4.27003e11	0.205619
$547$	3.73656e12	1.78455	0.892276	−	0.451491i	$-0.149108\pi$
$547$	3.73656e12	1.78455	0.892276	+	0.451491i	$0.149108\pi$
$548$	5.83729e11	0.276503
$549$	−1.80420e12	−0.847635
$550$	−7.66528e12	−3.57187
$551$	−1.41322e12	−0.653172
$552$	8.25041e10	0.0378225
$553$	−6.90602e11	−0.314025
$554$	−2.21598e12	−0.999476
$555$	−3.31397e10	−0.0148262
$556$	1.40916e12	0.625351
$557$	2.84548e12	1.25258	0.626292	−	0.779589i	$-0.284572\pi$
$557$	2.84548e12	1.25258	0.626292	+	0.779589i	$0.284572\pi$
$558$	4.86227e12	2.12317
$559$	5.69195e12	2.46552
$560$	3.29663e12	1.41652
$561$	−9.92082e11	−0.422878
$562$	−2.87949e12	−1.21759
$563$	2.40414e12	1.00849	0.504246	−	0.863560i	$-0.331771\pi$
$563$	2.40414e12	1.00849	0.504246	+	0.863560i	$0.331771\pi$
$564$	−1.10151e11	−0.0458386
$565$	−6.64982e12	−2.74531
$566$	−2.79512e12	−1.14479
$567$	1.64038e12	0.666532
$568$	2.89582e11	0.116736
$569$	9.72582e11	0.388975	0.194487	−	0.980905i	$-0.437696\pi$
$569$	9.72582e11	0.388975	0.194487	+	0.980905i	$0.437696\pi$
$570$	−4.78766e11	−0.189971
$571$	1.03847e11	0.0408818	0.0204409	−	0.999791i	$-0.493493\pi$
$571$	1.03847e11	0.0408818	0.0204409	+	0.999791i	$0.493493\pi$
$572$	4.74165e12	1.85203
$573$	2.75290e11	0.106683
$574$	−6.01905e11	−0.231433
$575$	−2.50573e12	−0.955937
$576$	2.29226e11	0.0867686
$577$	−1.12680e12	−0.423210	−0.211605	−	0.977355i	$-0.567869\pi$
$577$	−1.12680e12	−0.423210	−0.211605	+	0.977355i	$0.567869\pi$
$578$	−9.35189e12	−3.48517
$579$	4.03945e11	0.149372
$580$	2.37303e12	0.870717
$581$	−2.79581e12	−1.01792
$582$	−5.38320e11	−0.194485
$583$	−3.06275e12	−1.09800
$584$	−7.41667e11	−0.263846
$585$	8.28432e12	2.92452
$586$	4.92116e12	1.72396
$587$	−6.60896e11	−0.229753	−0.114877	−	0.993380i	$-0.536647\pi$
$587$	−6.60896e11	−0.229753	−0.114877	+	0.993380i	$0.536647\pi$
$588$	1.11611e11	0.0385042
$589$	3.62052e12	1.23952
$590$	8.06194e12	2.73908
$591$	−2.69294e10	−0.00907996
$592$	2.64909e11	0.0886439
$593$	2.00492e12	0.665810	0.332905	−	0.942960i	$-0.391971\pi$
$593$	2.00492e12	0.665810	0.332905	+	0.942960i	$0.391971\pi$
$594$	−1.65659e12	−0.545979
$595$	−6.76595e12	−2.21311
$596$	−1.29928e12	−0.421787
$597$	2.38373e11	0.0768019
$598$	4.16305e12	1.33124
$599$	−9.03302e11	−0.286690	−0.143345	−	0.989673i	$-0.545786\pi$
$599$	−9.03302e11	−0.286690	−0.143345	+	0.989673i	$0.545786\pi$
$600$	−3.43599e11	−0.108236
$601$	4.35038e12	1.36017	0.680083	−	0.733135i	$-0.261944\pi$
$601$	4.35038e12	1.36017	0.680083	+	0.733135i	$0.261944\pi$
$602$	−3.84946e12	−1.19458
$603$	−6.90899e11	−0.212807
$604$	2.68266e12	0.820161
$605$	−1.03468e13	−3.13984
$606$	−4.55665e11	−0.137252
$607$	2.40048e12	0.717709	0.358854	−	0.933394i	$-0.383168\pi$
$607$	2.40048e12	0.717709	0.358854	+	0.933394i	$0.383168\pi$
$608$	2.57286e12	0.763571
$609$	2.73041e11	0.0804359
$610$	6.05879e12	1.77175
$611$	3.81179e12	1.10648
$612$	−3.92755e12	−1.13172
$613$	1.09621e12	0.313561	0.156780	−	0.987633i	$-0.449889\pi$
$613$	1.09621e12	0.313561	0.156780	+	0.987633i	$0.449889\pi$
$614$	3.26919e11	0.0928286
$615$	1.92797e11	0.0543452
$616$	2.19925e12	0.615404
$617$	−4.24776e12	−1.17999	−0.589993	−	0.807408i	$-0.700870\pi$
$617$	−4.24776e12	−1.17999	−0.589993	+	0.807408i	$0.700870\pi$
$618$	−8.43658e11	−0.232658
$619$	2.82470e12	0.773330	0.386665	−	0.922220i	$-0.373627\pi$
$619$	2.82470e12	0.773330	0.386665	+	0.922220i	$0.373627\pi$
$620$	−6.07945e12	−1.65235
$621$	−5.41529e11	−0.146120
$622$	−4.77119e12	−1.27812
$623$	−4.47750e11	−0.119080
$624$	1.09333e12	0.288681
$625$	3.11392e11	0.0816295
$626$	−5.61277e12	−1.46081
$627$	−6.11712e11	−0.158068
$628$	1.92766e12	0.494552
$629$	−5.43694e11	−0.138493
$630$	−5.60268e12	−1.41698
$631$	−2.97237e12	−0.746398	−0.373199	−	0.927751i	$-0.621739\pi$
$631$	−2.97237e12	−0.746398	−0.373199	+	0.927751i	$0.621739\pi$
$632$	−9.23265e11	−0.230197
$633$	6.20439e11	0.153597
$634$	−7.15282e11	−0.175823
$635$	−7.68350e12	−1.87533
$636$	2.00185e11	0.0485147
$637$	−3.86231e12	−0.929436
$638$	8.14333e12	1.94585
$639$	−9.42577e11	−0.223647
$640$	6.51335e12	1.53460
$641$	−2.12053e12	−0.496116	−0.248058	−	0.968745i	$-0.579792\pi$
$641$	−2.12053e12	−0.496116	−0.248058	+	0.968745i	$0.579792\pi$
$642$	6.47514e11	0.150432
$643$	−2.47068e12	−0.569990	−0.284995	−	0.958529i	$-0.591992\pi$
$643$	−2.47068e12	−0.569990	−0.284995	+	0.958529i	$0.591992\pi$
$644$	−1.04828e12	−0.240154
$645$	1.23302e12	0.280513
$646$	−7.85469e12	−1.77453
$647$	−4.76581e12	−1.06922	−0.534611	−	0.845099i	$-0.679542\pi$
$647$	−4.76581e12	−1.06922	−0.534611	+	0.845099i	$0.679542\pi$
$648$	2.19302e12	0.488602
$649$	1.03006e13	2.27909
$650$	−1.73376e13	−3.80959
$651$	−6.99502e11	−0.152642
$652$	−2.63694e12	−0.571460
$653$	7.64082e12	1.64449	0.822244	−	0.569136i	$-0.192722\pi$
$653$	7.64082e12	1.64449	0.822244	+	0.569136i	$0.192722\pi$
$654$	9.52060e11	0.203500
$655$	−4.44703e12	−0.944027
$656$	−1.54116e12	−0.324922
$657$	2.41410e12	0.505488
$658$	−2.57791e12	−0.536107
$659$	6.24994e12	1.29090	0.645448	−	0.763804i	$-0.276671\pi$
$659$	6.24994e12	1.29090	0.645448	+	0.763804i	$0.276671\pi$
$660$	1.02716e12	0.210713
$661$	−9.63418e11	−0.196294	−0.0981472	−	0.995172i	$-0.531292\pi$
$661$	−9.63418e11	−0.196294	−0.0981472	+	0.995172i	$0.531292\pi$
$662$	−3.85944e12	−0.781023
$663$	−2.24392e12	−0.451021
$664$	−3.73771e12	−0.746191
$665$	−4.17184e12	−0.827238
$666$	−4.50217e11	−0.0886723
$667$	2.66200e12	0.520766
$668$	7.26978e11	0.141263
$669$	−8.98526e11	−0.173426
$670$	2.32015e12	0.444814
$671$	7.74122e12	1.47420
$672$	−4.97088e11	−0.0940312
$673$	7.42899e12	1.39592	0.697962	−	0.716134i	$-0.254090\pi$
$673$	7.42899e12	1.39592	0.697962	+	0.716134i	$0.254090\pi$
$674$	9.93922e12	1.85517
$675$	2.25527e12	0.418149
$676$	7.50412e12	1.38210
$677$	3.66005e12	0.669634	0.334817	−	0.942283i	$-0.391325\pi$
$677$	3.66005e12	0.669634	0.334817	+	0.942283i	$0.391325\pi$
$678$	1.49152e12	0.271078
$679$	−4.69078e12	−0.846899
$680$	−9.04539e12	−1.62232
$681$	2.33369e11	0.0415797
$682$	−2.08624e13	−3.69261
$683$	−1.92837e12	−0.339076	−0.169538	−	0.985524i	$-0.554228\pi$
$683$	−1.92837e12	−0.339076	−0.169538	+	0.985524i	$0.554228\pi$
$684$	−2.42170e12	−0.423027
$685$	−4.37586e12	−0.759374
$686$	7.74053e12	1.33448
$687$	−2.83059e11	−0.0484810
$688$	−9.85641e12	−1.67715
$689$	−6.92743e12	−1.17108
$690$	9.01825e11	0.151461
$691$	−3.99370e12	−0.666384	−0.333192	−	0.942859i	$-0.608126\pi$
$691$	−3.99370e12	−0.666384	−0.333192	+	0.942859i	$0.608126\pi$
$692$	−7.03213e12	−1.16576
$693$	−7.15846e12	−1.17902
$694$	7.20301e12	1.17868
$695$	−1.05636e13	−1.71744
$696$	3.65028e11	0.0589637
$697$	3.16304e12	0.507642
$698$	−6.58285e11	−0.104970
$699$	−5.72661e11	−0.0907299
$700$	4.36568e12	0.687244
$701$	1.25989e13	1.97061	0.985307	−	0.170790i	$-0.0546319\pi$
$701$	1.25989e13	1.97061	0.985307	+	0.170790i	$0.0546319\pi$
$702$	−3.74693e12	−0.582315
$703$	−3.35239e11	−0.0517673
$704$	−9.83531e11	−0.150908
$705$	8.25732e11	0.125889
$706$	−3.24004e12	−0.490828
$707$	−3.97055e12	−0.597672
$708$	−6.73259e11	−0.100701
$709$	7.73619e12	1.14979	0.574896	−	0.818227i	$-0.305043\pi$
$709$	7.73619e12	1.14979	0.574896	+	0.818227i	$0.305043\pi$
$710$	3.16532e12	0.467472
$711$	3.00519e12	0.441020
$712$	−5.98596e11	−0.0872919
$713$	−6.81977e12	−0.988251
$714$	1.51756e12	0.218527
$715$	−3.55452e13	−5.08633
$716$	−5.39326e12	−0.766907
$717$	2.74023e11	0.0387213
$718$	2.81955e12	0.395931
$719$	1.27018e12	0.177250	0.0886251	−	0.996065i	$-0.471753\pi$
$719$	1.27018e12	0.177250	0.0886251	+	0.996065i	$0.471753\pi$
$720$	−1.43455e13	−1.98938
$721$	−7.35142e12	−1.01312
$722$	4.37302e12	0.598913
$723$	−7.90869e11	−0.107642
$724$	4.88488e11	0.0660739
$725$	−1.10863e13	−1.49027
$726$	2.32073e12	0.310035
$727$	4.61300e12	0.612462	0.306231	−	0.951957i	$-0.400932\pi$
$727$	4.61300e12	0.612462	0.306231	+	0.951957i	$0.400932\pi$
$728$	4.97433e12	0.656361
$729$	−6.89250e12	−0.903864
$730$	−8.10692e12	−1.05658
$731$	2.02291e13	2.62029
$732$	−5.05974e11	−0.0651371
$733$	−5.26445e12	−0.673573	−0.336787	−	0.941581i	$-0.609340\pi$
$733$	−5.26445e12	−0.673573	−0.336787	+	0.941581i	$0.609340\pi$
$734$	7.67164e12	0.975564
$735$	−8.36676e11	−0.105746
$736$	−4.84635e12	−0.608786
$737$	2.96442e12	0.370114
$738$	2.61922e12	0.325026
$739$	−4.10837e11	−0.0506721	−0.0253361	−	0.999679i	$-0.508066\pi$
$739$	−4.10837e11	−0.0506721	−0.0253361	+	0.999679i	$0.508066\pi$
$740$	5.62921e11	0.0690088
$741$	−1.38359e12	−0.168587
$742$	4.68502e12	0.567405
$743$	−1.50103e13	−1.80693	−0.903464	−	0.428663i	$-0.858985\pi$
$743$	−1.50103e13	−1.80693	−0.903464	+	0.428663i	$0.858985\pi$
$744$	−9.35163e11	−0.111895
$745$	9.73987e12	1.15838
$746$	−4.07150e12	−0.481315
$747$	1.21661e13	1.42958
$748$	1.68518e13	1.96829
$749$	5.64227e12	0.655067
$750$	−1.48500e12	−0.171376
$751$	−1.03516e13	−1.18749	−0.593744	−	0.804654i	$-0.702351\pi$
$751$	−1.03516e13	−1.18749	−0.593744	+	0.804654i	$0.702351\pi$
$752$	−6.60065e12	−0.752673
$753$	8.19742e11	0.0929180
$754$	1.84188e13	2.07535
$755$	−2.01102e13	−2.25245
$756$	9.43493e11	0.105049
$757$	1.33933e13	1.48237	0.741184	−	0.671302i	$-0.234265\pi$
$757$	1.33933e13	1.48237	0.741184	+	0.671302i	$0.234265\pi$
$758$	5.69780e12	0.626896
$759$	1.15225e12	0.126025
$760$	−5.57733e12	−0.606409
$761$	−9.94683e12	−1.07511	−0.537556	−	0.843228i	$-0.680652\pi$
$761$	−9.94683e12	−1.07511	−0.537556	+	0.843228i	$0.680652\pi$
$762$	1.72337e12	0.185174
$763$	8.29601e12	0.886153
$764$	−4.67615e12	−0.496556
$765$	2.94424e13	3.10811
$766$	9.07550e12	0.952448
$767$	2.32983e13	2.43077
$768$	−1.56928e12	−0.162770
$769$	1.31073e13	1.35159	0.675796	−	0.737089i	$-0.263800\pi$
$769$	1.31073e13	1.35159	0.675796	+	0.737089i	$0.263800\pi$
$770$	2.40392e13	2.46441
$771$	1.43733e11	0.0146491
$772$	−6.86152e12	−0.695252
$773$	−1.59306e13	−1.60481	−0.802405	−	0.596779i	$-0.796447\pi$
$773$	−1.59306e13	−1.60481	−0.802405	+	0.596779i	$0.796447\pi$
$774$	1.67511e13	1.67768
$775$	2.84018e13	2.82806
$776$	−6.27110e12	−0.620821
$777$	6.47697e10	0.00637496
$778$	−1.76485e13	−1.72703
$779$	1.95031e12	0.189752
$780$	2.32327e12	0.224737
$781$	4.04428e12	0.388966
$782$	1.47954e13	1.41481
$783$	−2.39592e12	−0.227795
$784$	6.68813e12	0.632241
$785$	−1.44505e13	−1.35822
$786$	9.97444e11	0.0932153
$787$	−8.47507e12	−0.787512	−0.393756	−	0.919215i	$-0.628824\pi$
$787$	−8.47507e12	−0.787512	−0.393756	+	0.919215i	$0.628824\pi$
$788$	4.57431e11	0.0422628
$789$	2.10607e12	0.193476
$790$	−1.00919e13	−0.921830
$791$	1.29967e13	1.18043
$792$	−9.57013e12	−0.864280
$793$	1.75093e13	1.57232
$794$	1.13363e13	1.01223
$795$	−1.50066e12	−0.133239
$796$	−4.04906e12	−0.357475
$797$	1.05177e13	0.923332	0.461666	−	0.887054i	$-0.347252\pi$
$797$	1.05177e13	0.923332	0.461666	+	0.887054i	$0.347252\pi$
$798$	9.35721e11	0.0816833
$799$	1.35471e13	1.17594
$800$	2.01833e13	1.74215
$801$	1.94841e12	0.167237
$802$	4.50334e12	0.384371
$803$	−1.03581e13	−0.879143
$804$	−1.93757e11	−0.0163533
$805$	7.85827e12	0.659547
$806$	−4.71872e13	−3.93837
$807$	1.50723e12	0.125097
$808$	−5.30822e12	−0.438125
$809$	9.42432e12	0.773538	0.386769	−	0.922177i	$-0.373591\pi$
$809$	9.42432e12	0.773538	0.386769	+	0.922177i	$0.373591\pi$
$810$	2.39712e13	1.95662
$811$	1.01147e13	0.821030	0.410515	−	0.911854i	$-0.365349\pi$
$811$	1.01147e13	0.821030	0.410515	+	0.911854i	$0.365349\pi$
$812$	−4.63795e12	−0.374390
$813$	1.50512e12	0.120827
$814$	1.93173e12	0.154219
$815$	1.97675e13	1.56943
$816$	3.88567e12	0.306803
$817$	1.24732e13	0.979439
$818$	1.04322e12	0.0814677
$819$	−1.61912e13	−1.25748
$820$	−3.27490e12	−0.252950
$821$	4.73633e12	0.363830	0.181915	−	0.983314i	$-0.441771\pi$
$821$	4.73633e12	0.363830	0.181915	+	0.983314i	$0.441771\pi$
$822$	9.81480e11	0.0749822
$823$	−1.13214e13	−0.860206	−0.430103	−	0.902780i	$-0.641523\pi$
$823$	−1.13214e13	−0.860206	−0.430103	+	0.902780i	$0.641523\pi$
$824$	−9.82811e12	−0.742673
$825$	−4.79869e12	−0.360645
$826$	−1.57566e13	−1.17775
$827$	−5.36374e11	−0.0398743	−0.0199372	−	0.999801i	$-0.506347\pi$
$827$	−5.36374e11	−0.0398743	−0.0199372	+	0.999801i	$0.506347\pi$
$828$	4.56162e12	0.337274
$829$	1.35509e12	0.0996491	0.0498245	−	0.998758i	$-0.484134\pi$
$829$	1.35509e12	0.0996491	0.0498245	+	0.998758i	$0.484134\pi$
$830$	−4.08557e13	−2.98814
$831$	−1.38727e12	−0.100915
$832$	−2.22458e12	−0.160951
$833$	−1.37266e13	−0.987781
$834$	2.36936e12	0.169583
$835$	−5.44970e12	−0.387957
$836$	1.03907e13	0.735727
$837$	6.13809e12	0.432284
$838$	1.55615e12	0.109007
$839$	1.93794e13	1.35024	0.675121	−	0.737707i	$-0.264092\pi$
$839$	1.93794e13	1.35024	0.675121	+	0.737707i	$0.264092\pi$
$840$	1.07757e12	0.0746771
$841$	−2.72948e12	−0.188147
$842$	−9.84888e12	−0.675277
$843$	−1.80264e12	−0.122938
$844$	−1.05389e13	−0.714918
$845$	−5.62537e13	−3.79574
$846$	1.12179e13	0.752915
$847$	2.02223e13	1.35006
$848$	1.19958e13	0.796615
$849$	−1.74983e12	−0.115587
$850$	−6.16176e13	−4.04874
$851$	6.31471e11	0.0412734
$852$	−2.64339e11	−0.0171863
$853$	1.56451e12	0.101183	0.0505917	−	0.998719i	$-0.483889\pi$
$853$	1.56451e12	0.101183	0.0505917	+	0.998719i	$0.483889\pi$
$854$	−1.18416e13	−0.761813
$855$	1.81540e13	1.16178
$856$	7.54315e12	0.480198
$857$	−1.98742e13	−1.25857	−0.629283	−	0.777176i	$-0.716651\pi$
$857$	−1.98742e13	−1.25857	−0.629283	+	0.777176i	$0.716651\pi$
$858$	7.97259e12	0.502235
$859$	−9.12312e12	−0.571708	−0.285854	−	0.958273i	$-0.592277\pi$
$859$	−9.12312e12	−0.571708	−0.285854	+	0.958273i	$0.592277\pi$
$860$	−2.09445e13	−1.30565
$861$	−3.76810e11	−0.0233673
$862$	2.18878e13	1.35027
$863$	3.18098e13	1.95215	0.976073	−	0.217441i	$-0.0697710\pi$
$863$	3.18098e13	1.95215	0.976073	+	0.217441i	$0.0697710\pi$
$864$	4.36193e12	0.266297
$865$	5.27155e13	3.20159
$866$	−1.80158e13	−1.08849
$867$	−5.85455e12	−0.351891
$868$	1.18819e13	0.710475
$869$	−1.28943e13	−0.767021
$870$	3.99000e12	0.236122
$871$	6.70501e12	0.394746
$872$	1.10909e13	0.649596
$873$	2.04122e13	1.18939
$874$	9.12278e12	0.528842
$875$	−1.29399e13	−0.746268
$876$	6.77015e11	0.0388445
$877$	−1.91391e13	−1.09251	−0.546253	−	0.837621i	$-0.683946\pi$
$877$	−1.91391e13	−1.09251	−0.546253	+	0.837621i	$0.683946\pi$
$878$	−9.83076e12	−0.558292
$879$	3.08079e12	0.174065
$880$	6.15516e13	3.45993
$881$	−3.44275e13	−1.92537	−0.962684	−	0.270627i	$-0.912769\pi$
$881$	−3.44275e13	−1.92537	−0.962684	+	0.270627i	$0.912769\pi$
$882$	−1.13666e13	−0.632443
$883$	1.54533e13	0.855455	0.427728	−	0.903908i	$-0.359314\pi$
$883$	1.54533e13	0.855455	0.427728	+	0.903908i	$0.359314\pi$
$884$	3.81159e13	2.09928
$885$	5.04700e12	0.276560
$886$	4.19499e13	2.28707
$887$	3.32028e13	1.80102	0.900511	−	0.434833i	$-0.143193\pi$
$887$	3.32028e13	1.80102	0.900511	+	0.434833i	$0.143193\pi$
$888$	8.65906e10	0.00467318
$889$	1.50170e13	0.806351
$890$	−6.54305e12	−0.349563
$891$	3.06276e13	1.62803
$892$	1.52626e13	0.807211
$893$	8.35304e12	0.439555
$894$	−2.18460e12	−0.114381
$895$	4.04299e13	2.10620
$896$	−1.27300e13	−0.659845
$897$	2.60619e12	0.134413
$898$	−1.17770e13	−0.604352
$899$	−3.01731e13	−1.54064
$900$	−1.89975e13	−0.965172
$901$	−2.46200e13	−1.24459
$902$	−1.12382e13	−0.565285
$903$	−2.40987e12	−0.120615
$904$	1.73753e13	0.865313
$905$	−3.66189e12	−0.181462
$906$	4.51061e12	0.222412
$907$	2.57281e13	1.26234	0.631168	−	0.775646i	$-0.282576\pi$
$907$	2.57281e13	1.26234	0.631168	+	0.775646i	$0.282576\pi$
$908$	−3.96407e12	−0.193533
$909$	1.72780e13	0.839377
$910$	5.43727e13	2.62842
$911$	2.90637e12	0.139803	0.0699017	−	0.997554i	$-0.477731\pi$
$911$	2.90637e12	0.139803	0.0699017	+	0.997554i	$0.477731\pi$
$912$	2.39588e12	0.114680
$913$	−5.22007e13	−2.48632
$914$	−5.02405e13	−2.38120
$915$	3.79297e12	0.178890
$916$	4.80812e12	0.225655
$917$	8.69148e12	0.405912
$918$	−1.33165e13	−0.618870
$919$	3.34790e13	1.54829	0.774146	−	0.633007i	$-0.218180\pi$
$919$	3.34790e13	1.54829	0.774146	+	0.633007i	$0.218180\pi$
$920$	1.05057e13	0.483482
$921$	2.04660e11	0.00937272
$922$	2.29891e13	1.04769
$923$	9.14749e12	0.414853
$924$	−2.00753e12	−0.0906023
$925$	−2.62984e12	−0.118111
$926$	3.93563e13	1.75900
$927$	3.19901e13	1.42284
$928$	−2.14420e13	−0.949073
$929$	−2.44771e13	−1.07817	−0.539087	−	0.842250i	$-0.681230\pi$
$929$	−2.44771e13	−1.07817	−0.539087	+	0.842250i	$0.681230\pi$
$930$	−1.02220e13	−0.448085
$931$	−8.46374e12	−0.369223
$932$	9.72739e12	0.422303
$933$	−2.98690e12	−0.129049
$934$	1.27759e12	0.0549325
$935$	−1.26327e14	−5.40562
$936$	−2.16460e13	−0.921801
$937$	2.38779e12	0.101197	0.0505985	−	0.998719i	$-0.483887\pi$
$937$	2.38779e12	0.101197	0.0505985	+	0.998719i	$0.483887\pi$
$938$	−4.53460e12	−0.191261
$939$	−3.51375e12	−0.147495
$940$	−1.40261e13	−0.585952
$941$	−8.72198e12	−0.362628	−0.181314	−	0.983425i	$-0.558035\pi$
$941$	−8.72198e12	−0.362628	−0.181314	+	0.983425i	$0.558035\pi$
$942$	3.24116e12	0.134113
$943$	−3.67370e12	−0.151287
$944$	−4.03442e13	−1.65351
$945$	−7.07278e12	−0.288501
$946$	−7.18735e13	−2.91782
$947$	9.75084e12	0.393973	0.196987	−	0.980406i	$-0.436884\pi$
$947$	9.75084e12	0.393973	0.196987	+	0.980406i	$0.436884\pi$
$948$	8.42782e11	0.0338905
$949$	−2.34282e13	−0.937652
$950$	−3.79930e13	−1.51338
$951$	−4.47787e11	−0.0177525
$952$	1.76787e13	0.697564
$953$	−3.04098e13	−1.19425	−0.597126	−	0.802148i	$-0.703691\pi$
$953$	−3.04098e13	−1.19425	−0.597126	+	0.802148i	$0.703691\pi$
$954$	−2.03871e13	−0.796870
$955$	3.50542e13	1.36372
$956$	−4.65462e12	−0.180229
$957$	5.09796e12	0.196468
$958$	5.35999e13	2.05598
$959$	8.55237e12	0.326515
$960$	−4.81902e11	−0.0183121
$961$	5.08608e13	1.92366
$962$	4.36925e12	0.164482
$963$	−2.45526e13	−0.919983
$964$	1.34339e13	0.501021
$965$	5.14365e13	1.90941
$966$	−1.76257e12	−0.0651251
$967$	−9.57947e10	−0.00352308	−0.00176154	−	0.999998i	$-0.500561\pi$
$967$	−9.57947e10	−0.00352308	−0.00176154	+	0.999998i	$0.500561\pi$
$968$	2.70351e13	0.989667
$969$	−4.91726e12	−0.179170
$970$	−6.85473e13	−2.48609
$971$	9.18567e12	0.331608	0.165804	−	0.986159i	$-0.446978\pi$
$971$	9.18567e12	0.331608	0.165804	+	0.986159i	$0.446978\pi$
$972$	−6.17530e12	−0.221901
$973$	2.06460e13	0.738461
$974$	−3.38274e13	−1.20435
$975$	−1.08538e13	−0.384647
$976$	−3.03199e13	−1.06956
$977$	1.86895e13	0.656253	0.328126	−	0.944634i	$-0.393583\pi$
$977$	1.86895e13	0.656253	0.328126	+	0.944634i	$0.393583\pi$
$978$	−4.43374e12	−0.154969
$979$	−8.35996e12	−0.290859
$980$	1.42120e13	0.492196
$981$	−3.61005e13	−1.24452
$982$	−1.36768e13	−0.469337
$983$	1.32422e13	0.452344	0.226172	−	0.974087i	$-0.427379\pi$
$983$	1.32422e13	0.452344	0.226172	+	0.974087i	$0.427379\pi$
$984$	−5.03757e11	−0.0171294
$985$	−3.42908e12	−0.116068
$986$	6.54604e13	2.20563
$987$	−1.61385e12	−0.0541297
$988$	2.35020e13	0.784692
$989$	−2.34950e13	−0.780894
$990$	−1.04608e14	−3.46104
$991$	−1.92235e13	−0.633143	−0.316571	−	0.948569i	$-0.602532\pi$
$991$	−1.92235e13	−0.633143	−0.316571	+	0.948569i	$0.602532\pi$
$992$	5.49322e13	1.80104
$993$	−2.41612e12	−0.0788583
$994$	−6.18644e12	−0.201003
$995$	3.03533e13	0.981753
$996$	3.41189e12	0.109857
$997$	−3.05605e12	−0.0979564	−0.0489782	−	0.998800i	$-0.515596\pi$
$997$	−3.05605e12	−0.0979564	−0.0489782	+	0.998800i	$0.515596\pi$
$998$	−1.81913e12	−0.0580466
$999$	−5.68351e11	−0.0180539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.17	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.17	✓	76	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-28.5607 q^{2} -17.8798 q^{3} +303.711 q^{4} -2276.73 q^{5} +510.659 q^{6} +4449.75 q^{7} +5948.86 q^{8} -19363.3 q^{9} +O(q^{10})\)	\(q-28.5607 q^{2} -17.8798 q^{3} +303.711 q^{4} -2276.73 q^{5} +510.659 q^{6} +4449.75 q^{7} +5948.86 q^{8} -19363.3 q^{9} +65025.0 q^{10} +83081.5 q^{11} -5430.29 q^{12} +187916. q^{13} -127088. q^{14} +40707.5 q^{15} -325404. q^{16} +667853. q^{17} +553029. q^{18} +411794. q^{19} -691470. q^{20} -79560.6 q^{21} -2.37286e6 q^{22} -775674. q^{23} -106364. q^{24} +3.23040e6 q^{25} -5.36702e6 q^{26} +698140. q^{27} +1.35144e6 q^{28} -3.43186e6 q^{29} -1.16263e6 q^{30} +8.79207e6 q^{31} +6.24792e6 q^{32} -1.48548e6 q^{33} -1.90743e7 q^{34} -1.01309e7 q^{35} -5.88086e6 q^{36} -814093. q^{37} -1.17611e7 q^{38} -3.35991e6 q^{39} -1.35440e7 q^{40} +4.73614e6 q^{41} +2.27230e6 q^{42} +3.02898e7 q^{43} +2.52328e7 q^{44} +4.40851e7 q^{45} +2.21538e7 q^{46} +2.02845e7 q^{47} +5.81815e6 q^{48} -2.05533e7 q^{49} -9.22622e7 q^{50} -1.19411e7 q^{51} +5.70723e7 q^{52} -3.68644e7 q^{53} -1.99393e7 q^{54} -1.89155e8 q^{55} +2.64710e7 q^{56} -7.36279e6 q^{57} +9.80162e7 q^{58} +1.23982e8 q^{59} +1.23633e7 q^{60} +9.31762e7 q^{61} -2.51107e8 q^{62} -8.61619e7 q^{63} -1.18382e7 q^{64} -4.27836e8 q^{65} +4.24263e7 q^{66} +3.56808e7 q^{67} +2.02834e8 q^{68} +1.38689e7 q^{69} +2.89345e8 q^{70} +4.86785e7 q^{71} -1.15190e8 q^{72} -1.24674e8 q^{73} +2.32510e7 q^{74} -5.77588e7 q^{75} +1.25066e8 q^{76} +3.69692e8 q^{77} +9.59611e7 q^{78} -1.55200e8 q^{79} +7.40858e8 q^{80} +3.68645e8 q^{81} -1.35267e8 q^{82} -6.28307e8 q^{83} -2.41634e7 q^{84} -1.52052e9 q^{85} -8.65097e8 q^{86} +6.13609e7 q^{87} +4.94241e8 q^{88} -1.00624e8 q^{89} -1.25910e9 q^{90} +8.36181e8 q^{91} -2.35581e8 q^{92} -1.57200e8 q^{93} -5.79339e8 q^{94} -9.37546e8 q^{95} -1.11712e8 q^{96} -1.05417e9 q^{97} +5.87017e8 q^{98} -1.60873e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

Introduction

L-functions

Modular forms

Varieties

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