LMFDB - Embedded newform 91.8.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$23.0670$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.0670 q^{2} +71.8770 q^{3} +358.952 q^{4} +25.2300 q^{5} -1586.11 q^{6} +343.000 q^{7} -5096.40 q^{8} +2979.31 q^{9} +O(q^{10})$	\(q-22.0670 q^{2} +71.8770 q^{3} +358.952 q^{4} +25.2300 q^{5} -1586.11 q^{6} +343.000 q^{7} -5096.40 q^{8} +2979.31 q^{9} -556.750 q^{10} +6388.89 q^{11} +25800.4 q^{12} +2197.00 q^{13} -7568.97 q^{14} +1813.46 q^{15} +66516.5 q^{16} +16301.8 q^{17} -65744.4 q^{18} -28421.4 q^{19} +9056.35 q^{20} +24653.8 q^{21} -140983. q^{22} +59328.3 q^{23} -366315. q^{24} -77488.4 q^{25} -48481.2 q^{26} +56948.9 q^{27} +123120. q^{28} +253469. q^{29} -40017.5 q^{30} -195459. q^{31} -815477. q^{32} +459214. q^{33} -359732. q^{34} +8653.89 q^{35} +1.06943e6 q^{36} -189972. q^{37} +627174. q^{38} +157914. q^{39} -128582. q^{40} +172477. q^{41} -544036. q^{42} +101417. q^{43} +2.29330e6 q^{44} +75168.0 q^{45} -1.30920e6 q^{46} +286502. q^{47} +4.78101e6 q^{48} +117649. q^{49} +1.70994e6 q^{50} +1.17173e6 q^{51} +788617. q^{52} -1.57920e6 q^{53} -1.25669e6 q^{54} +161192. q^{55} -1.74807e6 q^{56} -2.04284e6 q^{57} -5.59329e6 q^{58} -56542.0 q^{59} +650943. q^{60} +2.02716e6 q^{61} +4.31318e6 q^{62} +1.02190e6 q^{63} +9.48102e6 q^{64} +55430.3 q^{65} -1.01335e7 q^{66} +1.14804e6 q^{67} +5.85156e6 q^{68} +4.26434e6 q^{69} -190965. q^{70} -1.98144e6 q^{71} -1.51838e7 q^{72} +5.52055e6 q^{73} +4.19212e6 q^{74} -5.56964e6 q^{75} -1.02019e7 q^{76} +2.19139e6 q^{77} -3.48468e6 q^{78} +1.22195e6 q^{79} +1.67821e6 q^{80} -2.42243e6 q^{81} -3.80605e6 q^{82} -667689. q^{83} +8.84953e6 q^{84} +411295. q^{85} -2.23796e6 q^{86} +1.82186e7 q^{87} -3.25604e7 q^{88} +1.22955e7 q^{89} -1.65873e6 q^{90} +753571. q^{91} +2.12960e7 q^{92} -1.40490e7 q^{93} -6.32223e6 q^{94} -717071. q^{95} -5.86141e7 q^{96} -8.75039e6 q^{97} -2.59616e6 q^{98} +1.90345e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	−22.0670	−1.95046	−0.975232	−	0.221185i	$-0.929008\pi$
$2$	−22.0670	−1.95046	−0.975232	+	0.221185i	$0.929008\pi$
$3$	71.8770	1.53697	0.768486	−	0.639867i	$-0.221011\pi$
$3$	71.8770	1.53697	0.768486	+	0.639867i	$0.221011\pi$
$4$	358.952	2.80431
$5$	25.2300	0.0902656	0.0451328	−	0.998981i	$-0.485629\pi$
$5$	25.2300	0.0902656	0.0451328	+	0.998981i	$0.485629\pi$
$6$	−1586.11	−2.99781
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−5096.40	−3.51924
$9$	2979.31	1.36228
$10$	−556.750	−0.176060
$11$	6388.89	1.44727	0.723637	−	0.690180i	$-0.242469\pi$
$11$	6388.89	1.44727	0.723637	+	0.690180i	$0.242469\pi$
$12$	25800.4	4.31014
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−7568.97	−0.737206
$15$	1813.46	0.138736
$16$	66516.5	4.05984
$17$	16301.8	0.804757	0.402379	−	0.915473i	$-0.368184\pi$
$17$	16301.8	0.804757	0.402379	+	0.915473i	$0.368184\pi$
$18$	−65744.4	−2.65708
$19$	−28421.4	−0.950621	−0.475310	−	0.879818i	$-0.657664\pi$
$19$	−28421.4	−0.950621	−0.475310	+	0.879818i	$0.657664\pi$
$20$	9056.35	0.253133
$21$	24653.8	0.580921
$22$	−140983.	−2.82286
$23$	59328.3	1.01675	0.508375	−	0.861136i	$-0.330246\pi$
$23$	59328.3	1.01675	0.508375	+	0.861136i	$0.330246\pi$
$24$	−366315.	−5.40897
$25$	−77488.4	−0.991852
$26$	−48481.2	−0.540961
$27$	56948.9	0.556817
$28$	123120.	1.05993
$29$	253469.	1.92988	0.964942	−	0.262463i	$-0.0845348\pi$
$29$	253469.	1.92988	0.964942	+	0.262463i	$0.0845348\pi$
$30$	−40017.5	−0.270599
$31$	−195459.	−1.17839	−0.589195	−	0.807991i	$-0.700555\pi$
$31$	−195459.	−1.17839	−0.589195	+	0.807991i	$0.700555\pi$
$32$	−815477.	−4.39934
$33$	459214.	2.22442
$34$	−359732.	−1.56965
$35$	8653.89	0.0341172
$36$	1.06943e6	3.82026
$37$	−189972.	−0.616573	−0.308286	−	0.951294i	$-0.599756\pi$
$37$	−189972.	−0.616573	−0.308286	+	0.951294i	$0.599756\pi$
$38$	627174.	1.85415
$39$	157914.	0.426279
$40$	−128582.	−0.317666
$41$	172477.	0.390830	0.195415	−	0.980721i	$-0.437395\pi$
$41$	172477.	0.390830	0.195415	+	0.980721i	$0.437395\pi$
$42$	−544036.	−1.13306
$43$	101417.	0.194523	0.0972614	−	0.995259i	$-0.468992\pi$
$43$	101417.	0.194523	0.0972614	+	0.995259i	$0.468992\pi$
$44$	2.29330e6	4.05861
$45$	75168.0	0.122967
$46$	−1.30920e6	−1.98313
$47$	286502.	0.402517	0.201259	−	0.979538i	$-0.435497\pi$
$47$	286502.	0.402517	0.201259	+	0.979538i	$0.435497\pi$
$48$	4.78101e6	6.23986
$49$	117649.	0.142857
$50$	1.70994e6	1.93457
$51$	1.17173e6	1.23689
$52$	788617.	0.777776
$53$	−1.57920e6	−1.45704	−0.728519	−	0.685026i	$-0.759791\pi$
$53$	−1.57920e6	−1.45704	−0.728519	+	0.685026i	$0.759791\pi$
$54$	−1.25669e6	−1.08605
$55$	161192.	0.130639
$56$	−1.74807e6	−1.33015
$57$	−2.04284e6	−1.46108
$58$	−5.59329e6	−3.76417
$59$	−56542.0	−0.0358417	−0.0179209	−	0.999839i	$-0.505705\pi$
$59$	−56542.0	−0.0358417	−0.0179209	+	0.999839i	$0.505705\pi$
$60$	650943.	0.389058
$61$	2.02716e6	1.14350	0.571748	−	0.820429i	$-0.306266\pi$
$61$	2.02716e6	1.14350	0.571748	+	0.820429i	$0.306266\pi$
$62$	4.31318e6	2.29841
$63$	1.02190e6	0.514894
$64$	9.48102e6	4.52090
$65$	55430.3	0.0250352
$66$	−1.01335e7	−4.33865
$67$	1.14804e6	0.466333	0.233167	−	0.972437i	$-0.425091\pi$
$67$	1.14804e6	0.466333	0.233167	+	0.972437i	$0.425091\pi$
$68$	5.85156e6	2.25679
$69$	4.26434e6	1.56272
$70$	−190965.	−0.0665443
$71$	−1.98144e6	−0.657018	−0.328509	−	0.944501i	$-0.606546\pi$
$71$	−1.98144e6	−0.657018	−0.328509	+	0.944501i	$0.606546\pi$
$72$	−1.51838e7	−4.79420
$73$	5.52055e6	1.66093	0.830467	−	0.557067i	$-0.188073\pi$
$73$	5.52055e6	1.66093	0.830467	+	0.557067i	$0.188073\pi$
$74$	4.19212e6	1.20260
$75$	−5.56964e6	−1.52445
$76$	−1.02019e7	−2.66583
$77$	2.19139e6	0.547018
$78$	−3.48468e6	−0.831442
$79$	1.22195e6	0.278843	0.139421	−	0.990233i	$-0.455476\pi$
$79$	1.22195e6	0.278843	0.139421	+	0.990233i	$0.455476\pi$
$80$	1.67821e6	0.366464
$81$	−2.42243e6	−0.506470
$82$	−3.80605e6	−0.762301
$83$	−667689.	−0.128174	−0.0640872	−	0.997944i	$-0.520414\pi$
$83$	−667689.	−0.128174	−0.0640872	+	0.997944i	$0.520414\pi$
$84$	8.84953e6	1.62908
$85$	411295.	0.0726419
$86$	−2.23796e6	−0.379410
$87$	1.82186e7	2.96618
$88$	−3.25604e7	−5.09331
$89$	1.22955e7	1.84876	0.924379	−	0.381475i	$-0.124584\pi$
$89$	1.22955e7	1.84876	0.924379	+	0.381475i	$0.124584\pi$
$90$	−1.65873e6	−0.239843
$91$	753571.	0.104828
$92$	2.12960e7	2.85128
$93$	−1.40490e7	−1.81115
$94$	−6.32223e6	−0.785096
$95$	−717071.	−0.0858083
$96$	−5.86141e7	−6.76165
$97$	−8.75039e6	−0.973478	−0.486739	−	0.873547i	$-0.661814\pi$
$97$	−8.75039e6	−0.973478	−0.486739	+	0.873547i	$0.661814\pi$
$98$	−2.59616e6	−0.278638
$99$	1.90345e7	1.97160
$100$	−2.78146e7	−2.78146
$101$	1.19449e7	1.15360	0.576801	−	0.816885i	$-0.304301\pi$
$101$	1.19449e7	1.15360	0.576801	+	0.816885i	$0.304301\pi$
$102$	−2.58565e7	−2.41251
$103$	1.48187e6	0.133622	0.0668112	−	0.997766i	$-0.478717\pi$
$103$	1.48187e6	0.133622	0.0668112	+	0.997766i	$0.478717\pi$
$104$	−1.11968e7	−0.976062
$105$	622016.	0.0524371
$106$	3.48481e7	2.84190
$107$	1.11066e7	0.876470	0.438235	−	0.898860i	$-0.355604\pi$
$107$	1.11066e7	0.876470	0.438235	+	0.898860i	$0.355604\pi$
$108$	2.04419e7	1.56149
$109$	1.40285e7	1.03758	0.518788	−	0.854903i	$-0.326383\pi$
$109$	1.40285e7	1.03758	0.518788	+	0.854903i	$0.326383\pi$
$110$	−3.55701e6	−0.254807
$111$	−1.36547e7	−0.947655
$112$	2.28151e7	1.53448
$113$	−9.36313e6	−0.610445	−0.305223	−	0.952281i	$-0.598731\pi$
$113$	−9.36313e6	−0.610445	−0.305223	+	0.952281i	$0.598731\pi$
$114$	4.50794e7	2.84978
$115$	1.49685e6	0.0917775
$116$	9.09830e7	5.41199
$117$	6.54554e6	0.377829
$118$	1.24771e6	0.0699080
$119$	5.59152e6	0.304170
$120$	−9.24211e6	−0.488244
$121$	2.13307e7	1.09460
$122$	−4.47334e7	−2.23035
$123$	1.23972e7	0.600695
$124$	−7.01602e7	−3.30457
$125$	−3.92613e6	−0.179796
$126$	−2.25503e7	−1.00428
$127$	3.15536e7	1.36690	0.683449	−	0.729998i	$-0.260479\pi$
$127$	3.15536e7	1.36690	0.683449	+	0.729998i	$0.260479\pi$
$128$	−1.04836e8	−4.41852
$129$	7.28955e6	0.298976
$130$	−1.22318e6	−0.0488302
$131$	3.23349e6	0.125667	0.0628337	−	0.998024i	$-0.479986\pi$
$131$	3.23349e6	0.125667	0.0628337	+	0.998024i	$0.479986\pi$
$132$	1.64836e8	6.23796
$133$	−9.74853e6	−0.359301
$134$	−2.53338e7	−0.909566
$135$	1.43682e6	0.0502614
$136$	−8.30807e7	−2.83213
$137$	−2.89986e7	−0.963509	−0.481754	−	0.876306i	$-0.660000\pi$
$137$	−2.89986e7	−0.963509	−0.481754	+	0.876306i	$0.660000\pi$
$138$	−9.41011e7	−3.04802
$139$	−1.93224e7	−0.610252	−0.305126	−	0.952312i	$-0.598699\pi$
$139$	−1.93224e7	−0.610252	−0.305126	+	0.952312i	$0.598699\pi$
$140$	3.10633e6	0.0956751
$141$	2.05929e7	0.618658
$142$	4.37245e7	1.28149
$143$	1.40364e7	0.401402
$144$	1.98173e8	5.53065
$145$	6.39501e6	0.174202
$146$	−1.21822e8	−3.23959
$147$	8.45626e6	0.219567
$148$	−6.81909e7	−1.72906
$149$	−2.17927e7	−0.539709	−0.269855	−	0.962901i	$-0.586976\pi$
$149$	−2.17927e7	−0.539709	−0.269855	+	0.962901i	$0.586976\pi$
$150$	1.22905e8	2.97338
$151$	−6.83968e7	−1.61665	−0.808326	−	0.588735i	$-0.799626\pi$
$151$	−6.83968e7	−1.61665	−0.808326	+	0.588735i	$0.799626\pi$
$152$	1.44847e8	3.34546
$153$	4.85682e7	1.09631
$154$	−4.83573e7	−1.06694
$155$	−4.93142e6	−0.106368
$156$	5.66834e7	1.19542
$157$	−9.59814e7	−1.97942	−0.989711	−	0.143083i	$-0.954299\pi$
$157$	−9.59814e7	−1.97942	−0.989711	+	0.143083i	$0.954299\pi$
$158$	−2.69648e7	−0.543873
$159$	−1.13508e8	−2.23943
$160$	−2.05745e7	−0.397108
$161$	2.03496e7	0.384295
$162$	5.34558e7	0.987852
$163$	8.19880e7	1.48284	0.741419	−	0.671042i	$-0.234153\pi$
$163$	8.19880e7	1.48284	0.741419	+	0.671042i	$0.234153\pi$
$164$	6.19110e7	1.09601
$165$	1.15860e7	0.200789
$166$	1.47339e7	0.249999
$167$	−2.82547e7	−0.469444	−0.234722	−	0.972063i	$-0.575418\pi$
$167$	−2.82547e7	−0.469444	−0.234722	+	0.972063i	$0.575418\pi$
$168$	−1.25646e8	−2.04440
$169$	4.82681e6	0.0769231
$170$	−9.07603e6	−0.141685
$171$	−8.46760e7	−1.29501
$172$	3.64037e7	0.545502
$173$	−1.02636e7	−0.150708	−0.0753541	−	0.997157i	$-0.524009\pi$
$173$	−1.02636e7	−0.150708	−0.0753541	+	0.997157i	$0.524009\pi$
$174$	−4.02029e8	−5.78542
$175$	−2.65785e7	−0.374885
$176$	4.24966e8	5.87571
$177$	−4.06407e6	−0.0550877
$178$	−2.71324e8	−3.60594
$179$	−1.02053e8	−1.32997	−0.664983	−	0.746859i	$-0.731561\pi$
$179$	−1.02053e8	−1.32997	−0.664983	+	0.746859i	$0.731561\pi$
$180$	2.69817e7	0.344838
$181$	−8.46935e7	−1.06163	−0.530817	−	0.847486i	$-0.678115\pi$
$181$	−8.46935e7	−1.06163	−0.530817	+	0.847486i	$0.678115\pi$
$182$	−1.66290e7	−0.204464
$183$	1.45707e8	1.75752
$184$	−3.02361e8	−3.57819
$185$	−4.79300e6	−0.0556553
$186$	3.10019e8	3.53259
$187$	1.04151e8	1.16470
$188$	1.02840e8	1.12878
$189$	1.95335e7	0.210457
$190$	1.58236e7	0.167366
$191$	9.02099e7	0.936780	0.468390	−	0.883522i	$-0.344834\pi$
$191$	9.02099e7	0.936780	0.468390	+	0.883522i	$0.344834\pi$
$192$	6.81468e8	6.94850
$193$	−6.42881e7	−0.643695	−0.321848	−	0.946792i	$-0.604304\pi$
$193$	−6.42881e7	−0.643695	−0.321848	+	0.946792i	$0.604304\pi$
$194$	1.93095e8	1.89873
$195$	3.98417e6	0.0384783
$196$	4.22303e7	0.400616
$197$	1.59236e7	0.148391	0.0741957	−	0.997244i	$-0.476361\pi$
$197$	1.59236e7	0.148391	0.0741957	+	0.997244i	$0.476361\pi$
$198$	−4.20034e8	−3.84553
$199$	2.11150e8	1.89935	0.949675	−	0.313238i	$-0.101414\pi$
$199$	2.11150e8	1.89935	0.949675	+	0.313238i	$0.101414\pi$
$200$	3.94912e8	3.49057
$201$	8.25179e7	0.716741
$202$	−2.63587e8	−2.25006
$203$	8.69397e7	0.729428
$204$	4.20593e8	3.46862
$205$	4.35160e6	0.0352785
$206$	−3.27003e7	−0.260626
$207$	1.76757e8	1.38510
$208$	1.46137e8	1.12600
$209$	−1.81581e8	−1.37581
$210$	−1.37260e7	−0.102277
$211$	−7.09909e7	−0.520252	−0.260126	−	0.965575i	$-0.583764\pi$
$211$	−7.09909e7	−0.520252	−0.260126	+	0.965575i	$0.583764\pi$
$212$	−5.66855e8	−4.08598
$213$	−1.42420e8	−1.00982
$214$	−2.45089e8	−1.70952
$215$	2.55875e6	0.0175587
$216$	−2.90235e8	−1.95957
$217$	−6.70423e7	−0.445390
$218$	−3.09568e8	−2.02375
$219$	3.96801e8	2.55281
$220$	5.78600e7	0.366352
$221$	3.58151e7	0.223199
$222$	3.01317e8	1.84837
$223$	1.13112e7	0.0683034	0.0341517	−	0.999417i	$-0.489127\pi$
$223$	1.13112e7	0.0683034	0.0341517	+	0.999417i	$0.489127\pi$
$224$	−2.79709e8	−1.66279
$225$	−2.30862e8	−1.35118
$226$	2.06616e8	1.19065
$227$	1.80865e8	1.02627	0.513137	−	0.858307i	$-0.328483\pi$
$227$	1.80865e8	1.02627	0.513137	+	0.858307i	$0.328483\pi$
$228$	−7.33282e8	−4.09731
$229$	2.20362e8	1.21258	0.606292	−	0.795242i	$-0.292656\pi$
$229$	2.20362e8	1.21258	0.606292	+	0.795242i	$0.292656\pi$
$230$	−3.30310e7	−0.179009
$231$	1.57511e8	0.840752
$232$	−1.29178e9	−6.79173
$233$	−2.89647e8	−1.50011	−0.750056	−	0.661374i	$-0.769974\pi$
$233$	−2.89647e8	−1.50011	−0.750056	+	0.661374i	$0.769974\pi$
$234$	−1.44440e8	−0.736942
$235$	7.22843e6	0.0363335
$236$	−2.02958e7	−0.100511
$237$	8.78303e7	0.428573
$238$	−1.23388e8	−0.593272
$239$	6.03205e7	0.285807	0.142903	−	0.989737i	$-0.454356\pi$
$239$	6.03205e7	0.285807	0.142903	+	0.989737i	$0.454356\pi$
$240$	1.20625e8	0.563245
$241$	−6.83456e7	−0.314522	−0.157261	−	0.987557i	$-0.550266\pi$
$241$	−6.83456e7	−0.314522	−0.157261	+	0.987557i	$0.550266\pi$
$242$	−4.70705e8	−2.13499
$243$	−2.98665e8	−1.33525
$244$	7.27654e8	3.20672
$245$	2.96828e6	0.0128951
$246$	−2.73568e8	−1.17163
$247$	−6.24417e7	−0.263655
$248$	9.96137e8	4.14704
$249$	−4.79915e7	−0.197000
$250$	8.66377e7	0.350685
$251$	1.07867e8	0.430557	0.215278	−	0.976553i	$-0.430934\pi$
$251$	1.07867e8	0.430557	0.215278	+	0.976553i	$0.430934\pi$
$252$	3.66814e8	1.44392
$253$	3.79042e8	1.47152
$254$	−6.96293e8	−2.66609
$255$	2.95627e7	0.111648
$256$	1.09985e9	4.09726
$257$	−4.62146e7	−0.169830	−0.0849148	−	0.996388i	$-0.527062\pi$
$257$	−4.62146e7	−0.169830	−0.0849148	+	0.996388i	$0.527062\pi$
$258$	−1.60858e8	−0.583142
$259$	−6.51605e7	−0.233043
$260$	1.98968e7	0.0702063
$261$	7.55162e8	2.62905
$262$	−7.13534e7	−0.245110
$263$	−1.01762e8	−0.344936	−0.172468	−	0.985015i	$-0.555174\pi$
$263$	−1.01762e8	−0.344936	−0.172468	+	0.985015i	$0.555174\pi$
$264$	−2.34034e9	−7.82827
$265$	−3.98431e7	−0.131520
$266$	2.15121e8	0.700803
$267$	8.83762e8	2.84149
$268$	4.12092e8	1.30774
$269$	−3.25193e8	−1.01861	−0.509305	−	0.860586i	$-0.670098\pi$
$269$	−3.25193e8	−1.01861	−0.509305	+	0.860586i	$0.670098\pi$
$270$	−3.17063e7	−0.0980330
$271$	−4.68308e8	−1.42935	−0.714675	−	0.699457i	$-0.753425\pi$
$271$	−4.68308e8	−1.42935	−0.714675	+	0.699457i	$0.753425\pi$
$272$	1.08434e9	3.26719
$273$	5.41645e7	0.161118
$274$	6.39913e8	1.87929
$275$	−4.95065e8	−1.43548
$276$	1.53069e9	4.38234
$277$	−1.84128e8	−0.520525	−0.260263	−	0.965538i	$-0.583809\pi$
$277$	−1.84128e8	−0.520525	−0.260263	+	0.965538i	$0.583809\pi$
$278$	4.26387e8	1.19027
$279$	−5.82332e8	−1.60530
$280$	−4.41037e7	−0.120067
$281$	−3.69283e8	−0.992858	−0.496429	−	0.868077i	$-0.665356\pi$
$281$	−3.69283e8	−0.992858	−0.496429	+	0.868077i	$0.665356\pi$
$282$	−4.54423e8	−1.20667
$283$	−5.57136e8	−1.46120	−0.730599	−	0.682807i	$-0.760759\pi$
$283$	−5.57136e8	−1.46120	−0.730599	+	0.682807i	$0.760759\pi$
$284$	−7.11242e8	−1.84248
$285$	−5.15409e7	−0.131885
$286$	−3.09741e8	−0.782920
$287$	5.91597e7	0.147720
$288$	−2.42956e9	−5.99313
$289$	−1.44589e8	−0.352366
$290$	−1.41119e8	−0.339775
$291$	−6.28952e8	−1.49621
$292$	1.98161e9	4.65778
$293$	5.49246e7	0.127565	0.0637823	−	0.997964i	$-0.479684\pi$
$293$	5.49246e7	0.127565	0.0637823	+	0.997964i	$0.479684\pi$
$294$	−1.86604e8	−0.428258
$295$	−1.42655e6	−0.00323527
$296$	9.68176e8	2.16987
$297$	3.63840e8	0.805866
$298$	4.80900e8	1.05268
$299$	1.30344e8	0.281996
$300$	−1.99923e9	−4.27503
$301$	3.47860e7	0.0735227
$302$	1.50931e9	3.15322
$303$	8.58561e8	1.77305
$304$	−1.89049e9	−3.85937
$305$	5.11453e7	0.103218
$306$	−1.07175e9	−2.13831
$307$	−9.84052e8	−1.94104	−0.970519	−	0.241026i	$-0.922516\pi$
$307$	−9.84052e8	−1.94104	−0.970519	+	0.241026i	$0.922516\pi$
$308$	7.86603e8	1.53401
$309$	1.06512e8	0.205374
$310$	1.08822e8	0.207467
$311$	7.13134e8	1.34434	0.672171	−	0.740395i	$-0.265362\pi$
$311$	7.13134e8	1.34434	0.672171	+	0.740395i	$0.265362\pi$
$312$	−8.04793e8	−1.50018
$313$	−7.89171e8	−1.45467	−0.727337	−	0.686280i	$-0.759242\pi$
$313$	−7.89171e8	−1.45467	−0.727337	+	0.686280i	$0.759242\pi$
$314$	2.11802e9	3.86079
$315$	2.57826e7	0.0464772
$316$	4.38622e8	0.781961
$317$	8.75475e8	1.54361	0.771803	−	0.635862i	$-0.219355\pi$
$317$	8.75475e8	1.54361	0.771803	+	0.635862i	$0.219355\pi$
$318$	2.50478e9	4.36792
$319$	1.61938e9	2.79307
$320$	2.39206e8	0.408082
$321$	7.98308e8	1.34711
$322$	−4.49054e8	−0.749554
$323$	−4.63320e8	−0.765019
$324$	−8.69536e8	−1.42030
$325$	−1.70242e8	−0.275090
$326$	−1.80923e9	−2.89222
$327$	1.00833e9	1.59473
$328$	−8.79014e8	−1.37543
$329$	9.82701e7	0.152137
$330$	−2.55668e8	−0.391631
$331$	5.87519e8	0.890480	0.445240	−	0.895411i	$-0.353118\pi$
$331$	5.87519e8	0.890480	0.445240	+	0.895411i	$0.353118\pi$
$332$	−2.39668e8	−0.359441
$333$	−5.65987e8	−0.839946
$334$	6.23497e8	0.915633
$335$	2.89651e7	0.0420938
$336$	1.63989e9	2.35845
$337$	−9.06553e8	−1.29029	−0.645147	−	0.764059i	$-0.723204\pi$
$337$	−9.06553e8	−1.29029	−0.645147	+	0.764059i	$0.723204\pi$
$338$	−1.06513e8	−0.150036
$339$	−6.72994e8	−0.938237
$340$	1.47635e8	0.203710
$341$	−1.24876e9	−1.70545
$342$	1.86854e9	2.52588
$343$	4.03536e7	0.0539949
$344$	−5.16861e8	−0.684573
$345$	1.07589e8	0.141059
$346$	2.26486e8	0.293951
$347$	−3.44710e7	−0.0442895	−0.0221447	−	0.999755i	$-0.507049\pi$
$347$	−3.44710e7	−0.0442895	−0.0221447	+	0.999755i	$0.507049\pi$
$348$	6.53959e9	8.31808
$349$	3.85687e7	0.0485676	0.0242838	−	0.999705i	$-0.492269\pi$
$349$	3.85687e7	0.0485676	0.0242838	+	0.999705i	$0.492269\pi$
$350$	5.86508e8	0.731199
$351$	1.25117e8	0.154433
$352$	−5.21000e9	−6.36705
$353$	−3.71741e8	−0.449810	−0.224905	−	0.974381i	$-0.572207\pi$
$353$	−3.71741e8	−0.449810	−0.224905	+	0.974381i	$0.572207\pi$
$354$	8.96818e7	0.107447
$355$	−4.99918e7	−0.0593061
$356$	4.41348e9	5.18449
$357$	4.01902e8	0.467500
$358$	2.25200e9	2.59405
$359$	−7.87106e8	−0.897848	−0.448924	−	0.893570i	$-0.648193\pi$
$359$	−7.87106e8	−0.897848	−0.448924	+	0.893570i	$0.648193\pi$
$360$	−3.83086e8	−0.432751
$361$	−8.60982e7	−0.0963205
$362$	1.86893e9	2.07068
$363$	1.53319e9	1.68238
$364$	2.70496e8	0.293972
$365$	1.39284e8	0.149925
$366$	−3.21530e9	−3.42798
$367$	−1.14315e7	−0.0120717	−0.00603587	−	0.999982i	$-0.501921\pi$
$367$	−1.14315e7	−0.0120717	−0.00603587	+	0.999982i	$0.501921\pi$
$368$	3.94631e9	4.12785
$369$	5.13863e8	0.532421
$370$	1.05767e8	0.108554
$371$	−5.41665e8	−0.550708
$372$	−5.04291e9	−5.07903
$373$	−1.02553e9	−1.02321	−0.511606	−	0.859220i	$-0.670949\pi$
$373$	−1.02553e9	−1.02321	−0.511606	+	0.859220i	$0.670949\pi$
$374$	−2.29829e9	−2.27171
$375$	−2.82198e8	−0.276341
$376$	−1.46013e9	−1.41656
$377$	5.56871e8	0.535254
$378$	−4.31045e8	−0.410489
$379$	−2.62836e7	−0.0247997	−0.0123999	−	0.999923i	$-0.503947\pi$
$379$	−2.62836e7	−0.0247997	−0.0123999	+	0.999923i	$0.503947\pi$
$380$	−2.57394e8	−0.240633
$381$	2.26798e9	2.10088
$382$	−1.99066e9	−1.82716
$383$	−1.44602e9	−1.31516	−0.657580	−	0.753385i	$-0.728420\pi$
$383$	−1.44602e9	−1.31516	−0.657580	+	0.753385i	$0.728420\pi$
$384$	−7.53533e9	−6.79114
$385$	5.52887e7	0.0493769
$386$	1.41864e9	1.25550
$387$	3.02152e8	0.264995
$388$	−3.14097e9	−2.72993
$389$	−6.96329e8	−0.599778	−0.299889	−	0.953974i	$-0.596950\pi$
$389$	−6.96329e8	−0.599778	−0.299889	+	0.953974i	$0.596950\pi$
$390$	−8.79185e7	−0.0750506
$391$	9.67159e8	0.818237
$392$	−5.99587e8	−0.502749
$393$	2.32414e8	0.193147
$394$	−3.51385e8	−0.289432
$395$	3.08298e7	0.0251699
$396$	6.83246e9	5.52896
$397$	1.08062e9	0.866771	0.433385	−	0.901209i	$-0.357319\pi$
$397$	1.08062e9	0.866771	0.433385	+	0.901209i	$0.357319\pi$
$398$	−4.65944e9	−3.70461
$399$	−7.00695e8	−0.552235
$400$	−5.15426e9	−4.02676
$401$	1.82256e9	1.41148	0.705742	−	0.708469i	$-0.250614\pi$
$401$	1.82256e9	1.41148	0.705742	+	0.708469i	$0.250614\pi$
$402$	−1.82092e9	−1.39798
$403$	−4.29423e8	−0.326827
$404$	4.28763e9	3.23506
$405$	−6.11179e7	−0.0457168
$406$	−1.91850e9	−1.42272
$407$	−1.21371e9	−0.892350
$408$	−5.97159e9	−4.35291
$409$	−4.85159e8	−0.350633	−0.175316	−	0.984512i	$-0.556095\pi$
$409$	−4.85159e8	−0.350633	−0.175316	+	0.984512i	$0.556095\pi$
$410$	−9.60267e7	−0.0688095
$411$	−2.08434e9	−1.48089
$412$	5.31919e8	0.374718
$413$	−1.93939e7	−0.0135469
$414$	−3.90050e9	−2.70159
$415$	−1.68458e7	−0.0115697
$416$	−1.79160e9	−1.22016
$417$	−1.38884e9	−0.937940
$418$	4.00694e9	2.68347
$419$	−1.05110e9	−0.698061	−0.349031	−	0.937111i	$-0.613489\pi$
$419$	−1.05110e9	−0.698061	−0.349031	+	0.937111i	$0.613489\pi$
$420$	2.23274e8	0.147050
$421$	−5.63072e8	−0.367770	−0.183885	−	0.982948i	$-0.558867\pi$
$421$	−5.63072e8	−0.367770	−0.183885	+	0.982948i	$0.558867\pi$
$422$	1.56655e9	1.01473
$423$	8.53577e8	0.548342
$424$	8.04823e9	5.12767
$425$	−1.26320e9	−0.798200
$426$	3.14279e9	1.96961
$427$	6.95317e8	0.432201
$428$	3.98672e9	2.45789
$429$	1.00889e9	0.616943
$430$	−5.64638e7	−0.0342476
$431$	1.59152e9	0.957507	0.478754	−	0.877949i	$-0.341089\pi$
$431$	1.59152e9	0.957507	0.478754	+	0.877949i	$0.341089\pi$
$432$	3.78804e9	2.26059
$433$	−3.02490e8	−0.179062	−0.0895310	−	0.995984i	$-0.528537\pi$
$433$	−3.02490e8	−0.179062	−0.0895310	+	0.995984i	$0.528537\pi$
$434$	1.47942e9	0.868716
$435$	4.59655e8	0.267744
$436$	5.03557e9	2.90968
$437$	−1.68619e9	−0.966544
$438$	−8.75620e9	−4.97916
$439$	1.49951e9	0.845909	0.422955	−	0.906151i	$-0.360993\pi$
$439$	1.49951e9	0.845909	0.422955	+	0.906151i	$0.360993\pi$
$440$	−8.21498e8	−0.459750
$441$	3.50513e8	0.194612
$442$	−7.90331e8	−0.435343
$443$	−2.94983e9	−1.61207	−0.806034	−	0.591869i	$-0.798390\pi$
$443$	−2.94983e9	−1.61207	−0.806034	+	0.591869i	$0.798390\pi$
$444$	−4.90136e9	−2.65752
$445$	3.10215e8	0.166879
$446$	−2.49604e8	−0.133223
$447$	−1.56640e9	−0.829518
$448$	3.25199e9	1.70874
$449$	−8.56831e8	−0.446717	−0.223359	−	0.974736i	$-0.571702\pi$
$449$	−8.56831e8	−0.446717	−0.223359	+	0.974736i	$0.571702\pi$
$450$	5.09443e9	2.63543
$451$	1.10194e9	0.565639
$452$	−3.36091e9	−1.71188
$453$	−4.91616e9	−2.48475
$454$	−3.99113e9	−2.00171
$455$	1.90126e7	0.00946240
$456$	1.04112e10	5.14188
$457$	1.91847e9	0.940262	0.470131	−	0.882597i	$-0.344207\pi$
$457$	1.91847e9	0.940262	0.470131	+	0.882597i	$0.344207\pi$
$458$	−4.86272e9	−2.36510
$459$	9.28371e8	0.448102
$460$	5.37297e8	0.257373
$461$	2.49708e9	1.18708	0.593538	−	0.804806i	$-0.297730\pi$
$461$	2.49708e9	1.18708	0.593538	+	0.804806i	$0.297730\pi$
$462$	−3.47578e9	−1.63986
$463$	−2.06821e9	−0.968412	−0.484206	−	0.874954i	$-0.660892\pi$
$463$	−2.06821e9	−0.968412	−0.484206	+	0.874954i	$0.660892\pi$
$464$	1.68598e10	7.83502
$465$	−3.54456e8	−0.163485
$466$	6.39164e9	2.92591
$467$	−2.87955e9	−1.30832	−0.654162	−	0.756354i	$-0.726979\pi$
$467$	−2.87955e9	−1.30832	−0.654162	+	0.756354i	$0.726979\pi$
$468$	2.34953e9	1.05955
$469$	3.93779e8	0.176257
$470$	−1.59510e8	−0.0708671
$471$	−6.89886e9	−3.04231
$472$	2.88161e8	0.126136
$473$	6.47941e8	0.281528
$474$	−1.93815e9	−0.835917
$475$	2.20233e9	0.942875
$476$	2.00709e9	0.852986
$477$	−4.70492e9	−1.98490
$478$	−1.33109e9	−0.557456
$479$	2.20214e9	0.915525	0.457762	−	0.889075i	$-0.348651\pi$
$479$	2.20214e9	0.915525	0.457762	+	0.889075i	$0.348651\pi$
$480$	−1.47883e9	−0.610344
$481$	−4.17369e8	−0.171007
$482$	1.50818e9	0.613463
$483$	1.46267e9	0.590651
$484$	7.65670e9	3.06961
$485$	−2.20772e8	−0.0878716
$486$	6.59062e9	2.60435
$487$	−1.45148e9	−0.569454	−0.284727	−	0.958609i	$-0.591903\pi$
$487$	−1.45148e9	−0.569454	−0.284727	+	0.958609i	$0.591903\pi$
$488$	−1.03312e10	−4.02424
$489$	5.89306e9	2.27908
$490$	−6.55010e7	−0.0251514
$491$	−6.71827e8	−0.256137	−0.128068	−	0.991765i	$-0.540878\pi$
$491$	−6.71827e8	−0.256137	−0.128068	+	0.991765i	$0.540878\pi$
$492$	4.44998e9	1.68454
$493$	4.13200e9	1.55309
$494$	1.37790e9	0.514249
$495$	4.80240e8	0.177967
$496$	−1.30012e10	−4.78408
$497$	−6.79635e8	−0.248330
$498$	1.05903e9	0.384242
$499$	1.16539e9	0.419873	0.209936	−	0.977715i	$-0.432674\pi$
$499$	1.16539e9	0.419873	0.209936	+	0.977715i	$0.432674\pi$
$500$	−1.40929e9	−0.504203
$501$	−2.03087e9	−0.721522
$502$	−2.38030e9	−0.839786
$503$	−1.27677e9	−0.447326	−0.223663	−	0.974667i	$-0.571802\pi$
$503$	−1.27677e9	−0.447326	−0.223663	+	0.974667i	$0.571802\pi$
$504$	−5.20803e9	−1.81204
$505$	3.01369e8	0.104131
$506$	−8.36431e9	−2.87014
$507$	3.46937e8	0.118229
$508$	1.13262e10	3.83321
$509$	4.74622e9	1.59527	0.797637	−	0.603138i	$-0.206083\pi$
$509$	4.74622e9	1.59527	0.797637	+	0.603138i	$0.206083\pi$
$510$	−6.52359e8	−0.217766
$511$	1.89355e9	0.627774
$512$	−1.08513e10	−3.57305
$513$	−1.61856e9	−0.529321
$514$	1.01982e9	0.331246
$515$	3.73875e7	0.0120615
$516$	2.61659e9	0.838421
$517$	1.83043e9	0.582553
$518$	1.43790e9	0.454541
$519$	−7.37715e8	−0.231634
$520$	−2.82495e8	−0.0881048
$521$	2.32160e9	0.719208	0.359604	−	0.933105i	$-0.382912\pi$
$521$	2.32160e9	0.719208	0.359604	+	0.933105i	$0.382912\pi$
$522$	−1.66641e10	−5.12786
$523$	−4.67046e9	−1.42759	−0.713795	−	0.700355i	$-0.753025\pi$
$523$	−4.67046e9	−1.42759	−0.713795	+	0.700355i	$0.753025\pi$
$524$	1.16067e9	0.352410
$525$	−1.91039e9	−0.576187
$526$	2.24557e9	0.672786
$527$	−3.18633e9	−0.948318
$528$	3.05453e10	9.03079
$529$	1.15018e8	0.0337808
$530$	8.79218e8	0.256526
$531$	−1.68456e8	−0.0488265
$532$	−3.49925e9	−1.00759
$533$	3.78933e8	0.108397
$534$	−1.95020e10	−5.54222
$535$	2.80219e8	0.0791151
$536$	−5.85089e9	−1.64114
$537$	−7.33527e9	−2.04412
$538$	7.17602e9	1.98676
$539$	7.51646e8	0.206754
$540$	5.15749e8	0.140948
$541$	1.18560e9	0.321919	0.160960	−	0.986961i	$-0.448541\pi$
$541$	1.18560e9	0.321919	0.160960	+	0.986961i	$0.448541\pi$
$542$	1.03341e10	2.78790
$543$	−6.08752e9	−1.63170
$544$	−1.32938e10	−3.54040
$545$	3.53940e8	0.0936574
$546$	−1.19525e9	−0.314256
$547$	7.17640e8	0.187478	0.0937392	−	0.995597i	$-0.470118\pi$
$547$	7.17640e8	0.187478	0.0937392	+	0.995597i	$0.470118\pi$
$548$	−1.04091e10	−2.70198
$549$	6.03955e9	1.55776
$550$	1.09246e10	2.79986
$551$	−7.20392e9	−1.83459
$552$	−2.17328e10	−5.49957
$553$	4.19129e8	0.105393
$554$	4.06316e9	1.01527
$555$	−3.44507e8	−0.0855406
$556$	−6.93581e9	−1.71134
$557$	6.16454e8	0.151150	0.0755749	−	0.997140i	$-0.475921\pi$
$557$	6.16454e8	0.151150	0.0755749	+	0.997140i	$0.475921\pi$
$558$	1.28503e10	3.13108
$559$	2.22813e8	0.0539509
$560$	5.75626e8	0.138510
$561$	7.48603e9	1.79012
$562$	8.14896e9	1.93653
$563$	−3.01375e8	−0.0711751	−0.0355875	−	0.999367i	$-0.511330\pi$
$563$	−3.01375e8	−0.0711751	−0.0355875	+	0.999367i	$0.511330\pi$
$564$	7.39185e9	1.73491
$565$	−2.36232e8	−0.0551022
$566$	1.22943e10	2.85001
$567$	−8.30894e8	−0.191428
$568$	1.00982e10	2.31221
$569$	−2.65389e9	−0.603936	−0.301968	−	0.953318i	$-0.597644\pi$
$569$	−2.65389e9	−0.603936	−0.301968	+	0.953318i	$0.597644\pi$
$570$	1.13735e9	0.257237
$571$	−8.38050e8	−0.188384	−0.0941919	−	0.995554i	$-0.530027\pi$
$571$	−8.38050e8	−0.188384	−0.0941919	+	0.995554i	$0.530027\pi$
$572$	5.03838e9	1.12565
$573$	6.48402e9	1.43980
$574$	−1.30548e9	−0.288123
$575$	−4.59726e9	−1.00847
$576$	2.82469e10	6.15874
$577$	−5.15958e9	−1.11815	−0.559074	−	0.829118i	$-0.688843\pi$
$577$	−5.15958e9	−1.11815	−0.559074	+	0.829118i	$0.688843\pi$
$578$	3.19065e9	0.687277
$579$	−4.62084e9	−0.989341
$580$	2.29550e9	0.488517
$581$	−2.29017e8	−0.0484454
$582$	1.38791e10	2.91830
$583$	−1.00893e10	−2.10873
$584$	−2.81350e10	−5.84523
$585$	1.65144e8	0.0341049
$586$	−1.21202e9	−0.248810
$587$	−5.34421e9	−1.09056	−0.545281	−	0.838253i	$-0.683577\pi$
$587$	−5.34421e9	−1.09056	−0.545281	+	0.838253i	$0.683577\pi$
$588$	3.03539e9	0.615735
$589$	5.55520e9	1.12020
$590$	3.14797e7	0.00631029
$591$	1.14454e9	0.228073
$592$	−1.26363e10	−2.50319
$593$	3.10578e9	0.611617	0.305808	−	0.952093i	$-0.401073\pi$
$593$	3.10578e9	0.611617	0.305808	+	0.952093i	$0.401073\pi$
$594$	−8.02885e9	−1.57181
$595$	1.41074e8	0.0274560
$596$	−7.82254e9	−1.51351
$597$	1.51768e10	2.91925
$598$	−2.87630e9	−0.550023
$599$	3.10216e9	0.589754	0.294877	−	0.955535i	$-0.404721\pi$
$599$	3.10216e9	0.589754	0.294877	+	0.955535i	$0.404721\pi$
$600$	2.83851e10	5.36490
$601$	6.33449e9	1.19029	0.595143	−	0.803620i	$-0.297095\pi$
$601$	6.33449e9	1.19029	0.595143	+	0.803620i	$0.297095\pi$
$602$	−7.67622e8	−0.143403
$603$	3.42038e9	0.635277
$604$	−2.45512e10	−4.53359
$605$	5.38174e8	0.0988050
$606$	−1.89459e10	−3.45828
$607$	−4.10229e9	−0.744501	−0.372251	−	0.928132i	$-0.621414\pi$
$607$	−4.10229e9	−0.744501	−0.372251	+	0.928132i	$0.621414\pi$
$608$	2.31770e10	4.18210
$609$	6.24897e9	1.12111
$610$	−1.12862e9	−0.201324
$611$	6.29444e8	0.111638
$612$	1.74336e10	3.07438
$613$	−3.75315e9	−0.658089	−0.329044	−	0.944314i	$-0.606727\pi$
$613$	−3.75315e9	−0.658089	−0.329044	+	0.944314i	$0.606727\pi$
$614$	2.17151e10	3.78592
$615$	3.12780e8	0.0542221
$616$	−1.11682e10	−1.92509
$617$	−1.90251e9	−0.326084	−0.163042	−	0.986619i	$-0.552131\pi$
$617$	−1.90251e9	−0.326084	−0.163042	+	0.986619i	$0.552131\pi$
$618$	−2.35040e9	−0.400574
$619$	4.03564e9	0.683905	0.341952	−	0.939717i	$-0.388912\pi$
$619$	4.03564e9	0.683905	0.341952	+	0.939717i	$0.388912\pi$
$620$	−1.77014e9	−0.298289
$621$	3.37868e9	0.566143
$622$	−1.57367e10	−2.62209
$623$	4.21735e9	0.698765
$624$	1.05039e10	1.73063
$625$	5.95473e9	0.975623
$626$	1.74146e10	2.83729
$627$	−1.30515e10	−2.11458
$628$	−3.44527e10	−5.55091
$629$	−3.09690e9	−0.496192
$630$	−5.68944e8	−0.0906521
$631$	7.23652e9	1.14664	0.573320	−	0.819332i	$-0.305655\pi$
$631$	7.23652e9	1.14664	0.573320	+	0.819332i	$0.305655\pi$
$632$	−6.22756e9	−0.981314
$633$	−5.10262e9	−0.799613
$634$	−1.93191e10	−3.01075
$635$	7.96098e8	0.123384
$636$	−4.07439e10	−6.28004
$637$	2.58475e8	0.0396214
$638$	−3.57349e10	−5.44779
$639$	−5.90333e9	−0.895044
$640$	−2.64502e9	−0.398840
$641$	1.86767e9	0.280089	0.140045	−	0.990145i	$-0.455275\pi$
$641$	1.86767e9	0.280089	0.140045	+	0.990145i	$0.455275\pi$
$642$	−1.76162e10	−2.62749
$643$	7.14319e9	1.05963	0.529814	−	0.848114i	$-0.322262\pi$
$643$	7.14319e9	1.05963	0.529814	+	0.848114i	$0.322262\pi$
$644$	7.30452e9	1.07768
$645$	1.83915e8	0.0269872
$646$	1.02241e10	1.49214
$647$	8.01022e9	1.16273	0.581366	−	0.813642i	$-0.302519\pi$
$647$	8.01022e9	1.16273	0.581366	+	0.813642i	$0.302519\pi$
$648$	1.23457e10	1.78239
$649$	−3.61240e8	−0.0518728
$650$	3.75673e9	0.536554
$651$	−4.81881e9	−0.684551
$652$	2.94297e10	4.15834
$653$	6.59916e8	0.0927454	0.0463727	−	0.998924i	$-0.485234\pi$
$653$	6.59916e8	0.0927454	0.0463727	+	0.998924i	$0.485234\pi$
$654$	−2.22508e10	−3.11045
$655$	8.15810e7	0.0113434
$656$	1.14726e10	1.58671
$657$	1.64474e10	2.26266
$658$	−2.16852e9	−0.296738
$659$	−1.28065e10	−1.74313	−0.871566	−	0.490277i	$-0.836895\pi$
$659$	−1.28065e10	−1.74313	−0.871566	+	0.490277i	$0.836895\pi$
$660$	4.15881e9	0.563073
$661$	−8.44083e8	−0.113679	−0.0568395	−	0.998383i	$-0.518102\pi$
$661$	−8.44083e8	−0.113679	−0.0568395	+	0.998383i	$0.518102\pi$
$662$	−1.29648e10	−1.73685
$663$	2.57428e9	0.343051
$664$	3.40282e9	0.451076
$665$	−2.45955e8	−0.0324325
$666$	1.24896e10	1.63828
$667$	1.50379e10	1.96221
$668$	−1.01421e10	−1.31647
$669$	8.13017e8	0.104980
$670$	−6.39173e8	−0.0821025
$671$	1.29513e10	1.65495
$672$	−2.01046e10	−2.55566
$673$	1.13326e10	1.43310	0.716550	−	0.697536i	$-0.245720\pi$
$673$	1.13326e10	1.43310	0.716550	+	0.697536i	$0.245720\pi$
$674$	2.00049e10	2.51667
$675$	−4.41288e9	−0.552280
$676$	1.73259e9	0.215716
$677$	1.27822e10	1.58323	0.791617	−	0.611018i	$-0.209240\pi$
$677$	1.27822e10	1.58323	0.791617	+	0.611018i	$0.209240\pi$
$678$	1.48510e10	1.83000
$679$	−3.00138e9	−0.367940
$680$	−2.09612e9	−0.255644
$681$	1.30000e10	1.57735
$682$	2.75565e10	3.32643
$683$	−2.50864e9	−0.301277	−0.150639	−	0.988589i	$-0.548133\pi$
$683$	−2.50864e9	−0.301277	−0.150639	+	0.988589i	$0.548133\pi$
$684$	−3.03946e10	−3.63162
$685$	−7.31636e8	−0.0869717
$686$	−8.90482e8	−0.105315
$687$	1.58389e10	1.86371
$688$	6.74589e9	0.789732
$689$	−3.46950e9	−0.404110
$690$	−2.37417e9	−0.275131
$691$	9.42715e9	1.08694	0.543472	−	0.839427i	$-0.317109\pi$
$691$	9.42715e9	1.08694	0.543472	+	0.839427i	$0.317109\pi$
$692$	−3.68412e9	−0.422632
$693$	6.52883e9	0.745193
$694$	7.60670e8	0.0863850
$695$	−4.87504e8	−0.0550847
$696$	−9.28492e10	−10.4387
$697$	2.81169e9	0.314524
$698$	−8.51095e8	−0.0947293
$699$	−2.08190e10	−2.30563
$700$	−9.54041e9	−1.05129
$701$	6.90377e9	0.756961	0.378480	−	0.925609i	$-0.376447\pi$
$701$	6.90377e9	0.756961	0.378480	+	0.925609i	$0.376447\pi$
$702$	−2.76095e9	−0.301216
$703$	5.39927e9	0.586127
$704$	6.05732e10	6.54299
$705$	5.19559e8	0.0558435
$706$	8.20321e9	0.877338
$707$	4.09709e9	0.436021
$708$	−1.45880e9	−0.154483
$709$	−4.74904e7	−0.00500431	−0.00250216	−	0.999997i	$-0.500796\pi$
$709$	−4.74904e7	−0.00500431	−0.00250216	+	0.999997i	$0.500796\pi$
$710$	1.10317e9	0.115674
$711$	3.64057e9	0.379862
$712$	−6.26627e10	−6.50622
$713$	−1.15962e10	−1.19813
$714$	−8.86877e9	−0.911842
$715$	3.54138e8	0.0362328
$716$	−3.66321e10	−3.72964
$717$	4.33566e9	0.439277
$718$	1.73691e10	1.75122
$719$	−9.56571e8	−0.0959768	−0.0479884	−	0.998848i	$-0.515281\pi$
$719$	−9.56571e8	−0.0959768	−0.0479884	+	0.998848i	$0.515281\pi$
$720$	4.99991e9	0.499227
$721$	5.08281e8	0.0505045
$722$	1.89993e9	0.187870
$723$	−4.91248e9	−0.483411
$724$	−3.04009e10	−2.97715
$725$	−1.96409e10	−1.91416
$726$	−3.38329e10	−3.28141
$727$	1.36680e10	1.31927	0.659636	−	0.751586i	$-0.270711\pi$
$727$	1.36680e10	1.31927	0.659636	+	0.751586i	$0.270711\pi$
$728$	−3.84050e9	−0.368917
$729$	−1.61693e10	−1.54577
$730$	−3.07357e9	−0.292424
$731$	1.65328e9	0.156544
$732$	5.23016e10	4.92863
$733$	1.15175e9	0.108017	0.0540087	−	0.998540i	$-0.482800\pi$
$733$	1.15175e9	0.108017	0.0540087	+	0.998540i	$0.482800\pi$
$734$	2.52258e8	0.0235455
$735$	2.13351e8	0.0198194
$736$	−4.83809e10	−4.47302
$737$	7.33472e9	0.674912
$738$	−1.13394e10	−1.03847
$739$	−9.36066e9	−0.853200	−0.426600	−	0.904440i	$-0.640289\pi$
$739$	−9.36066e9	−0.853200	−0.426600	+	0.904440i	$0.640289\pi$
$740$	−1.72046e9	−0.156075
$741$	−4.48813e9	−0.405230
$742$	1.19529e10	1.07414
$743$	−1.15076e10	−1.02926	−0.514628	−	0.857413i	$-0.672070\pi$
$743$	−1.15076e10	−1.02926	−0.514628	+	0.857413i	$0.672070\pi$
$744$	7.15994e10	6.37388
$745$	−5.49831e8	−0.0487172
$746$	2.26303e10	1.99574
$747$	−1.98925e9	−0.174610
$748$	3.73850e10	3.26619
$749$	3.80956e9	0.331274
$750$	6.22727e9	0.538993
$751$	−9.03982e9	−0.778789	−0.389395	−	0.921071i	$-0.627316\pi$
$751$	−9.03982e9	−0.778789	−0.389395	+	0.921071i	$0.627316\pi$
$752$	1.90571e10	1.63416
$753$	7.75316e9	0.661754
$754$	−1.22885e10	−1.04399
$755$	−1.72565e9	−0.145928
$756$	7.01157e9	0.590186
$757$	−5.89264e9	−0.493713	−0.246856	−	0.969052i	$-0.579398\pi$
$757$	−5.89264e9	−0.493713	−0.246856	+	0.969052i	$0.579398\pi$
$758$	5.79999e8	0.0483710
$759$	2.72444e10	2.26168
$760$	3.65448e9	0.301980
$761$	1.68791e10	1.38836	0.694182	−	0.719800i	$-0.255766\pi$
$761$	1.68791e10	1.38836	0.694182	+	0.719800i	$0.255766\pi$
$762$	−5.00475e10	−4.09770
$763$	4.81179e9	0.392167
$764$	3.23810e10	2.62702
$765$	1.22537e9	0.0989587
$766$	3.19093e10	2.56517
$767$	−1.24223e8	−0.00994071
$768$	7.90540e10	6.29738
$769$	−1.64383e10	−1.30351	−0.651756	−	0.758429i	$-0.725967\pi$
$769$	−1.64383e10	−1.30351	−0.651756	+	0.758429i	$0.725967\pi$
$770$	−1.22006e9	−0.0963079
$771$	−3.32177e9	−0.261023
$772$	−2.30763e10	−1.80512
$773$	−2.25705e10	−1.75757	−0.878786	−	0.477216i	$-0.841646\pi$
$773$	−2.25705e10	−1.75757	−0.878786	+	0.477216i	$0.841646\pi$
$774$	−6.66759e9	−0.516863
$775$	1.51458e10	1.16879
$776$	4.45955e10	3.42590
$777$	−4.68355e9	−0.358180
$778$	1.53659e10	1.16985
$779$	−4.90204e9	−0.371531
$780$	1.43012e9	0.107905
$781$	−1.26592e10	−0.950886
$782$	−2.13423e10	−1.59594
$783$	1.44348e10	1.07459
$784$	7.82559e9	0.579977
$785$	−2.42161e9	−0.178674
$786$	−5.12867e9	−0.376727
$787$	−9.22252e9	−0.674432	−0.337216	−	0.941427i	$-0.609485\pi$
$787$	−9.22252e9	−0.674432	−0.337216	+	0.941427i	$0.609485\pi$
$788$	5.71579e9	0.416136
$789$	−7.31432e9	−0.530157
$790$	−6.80321e8	−0.0490930
$791$	−3.21156e9	−0.230727
$792$	−9.70074e10	−6.93852
$793$	4.45368e9	0.317149
$794$	−2.38459e10	−1.69061
$795$	−2.86381e9	−0.202143
$796$	7.57926e10	5.32636
$797$	−9.19072e9	−0.643051	−0.321525	−	0.946901i	$-0.604196\pi$
$797$	−9.19072e9	−0.643051	−0.321525	+	0.946901i	$0.604196\pi$
$798$	1.54622e10	1.07711
$799$	4.67050e9	0.323929
$800$	6.31901e10	4.36349
$801$	3.66320e10	2.51853
$802$	−4.02184e10	−2.75305
$803$	3.52702e10	2.40383
$804$	2.96199e10	2.00996
$805$	5.13420e8	0.0346886
$806$	9.47607e9	0.637464
$807$	−2.33739e10	−1.56557
$808$	−6.08758e10	−4.05980
$809$	8.42433e9	0.559391	0.279696	−	0.960089i	$-0.409766\pi$
$809$	8.42433e9	0.559391	0.279696	+	0.960089i	$0.409766\pi$
$810$	1.34869e9	0.0891690
$811$	−2.76136e10	−1.81781	−0.908907	−	0.416999i	$-0.863082\pi$
$811$	−2.76136e10	−1.81781	−0.908907	+	0.416999i	$0.863082\pi$
$812$	3.12072e10	2.04554
$813$	−3.36606e10	−2.19687
$814$	2.67830e10	1.74050
$815$	2.06856e9	0.133849
$816$	7.79391e10	5.02157
$817$	−2.88241e9	−0.184917
$818$	1.07060e10	0.683896
$819$	2.24512e9	0.142806
$820$	1.56201e9	0.0989319
$821$	−1.00509e10	−0.633874	−0.316937	−	0.948447i	$-0.602654\pi$
$821$	−1.00509e10	−0.633874	−0.316937	+	0.948447i	$0.602654\pi$
$822$	4.59950e10	2.88841
$823$	−2.52454e10	−1.57864	−0.789321	−	0.613981i	$-0.789567\pi$
$823$	−2.52454e10	−1.57864	−0.789321	+	0.613981i	$0.789567\pi$
$824$	−7.55220e9	−0.470249
$825$	−3.55838e10	−2.20630
$826$	4.27965e8	0.0264227
$827$	1.30752e10	0.803857	0.401928	−	0.915671i	$-0.368340\pi$
$827$	1.30752e10	0.803857	0.401928	+	0.915671i	$0.368340\pi$
$828$	6.34473e10	3.88425
$829$	−1.50968e10	−0.920331	−0.460166	−	0.887833i	$-0.652210\pi$
$829$	−1.50968e10	−0.920331	−0.460166	+	0.887833i	$0.652210\pi$
$830$	3.71736e8	0.0225663
$831$	−1.32346e10	−0.800032
$832$	2.08298e10	1.25387
$833$	1.91789e9	0.114965
$834$	3.06474e10	1.82942
$835$	−7.12867e8	−0.0423746
$836$	−6.51788e10	−3.85819
$837$	−1.11312e10	−0.656147
$838$	2.31945e10	1.36154
$839$	−1.50199e9	−0.0878014	−0.0439007	−	0.999036i	$-0.513979\pi$
$839$	−1.50199e9	−0.0878014	−0.0439007	+	0.999036i	$0.513979\pi$
$840$	−3.17004e9	−0.184539
$841$	4.69965e10	2.72445
$842$	1.24253e10	0.717322
$843$	−2.65430e10	−1.52600
$844$	−2.54823e10	−1.45895
$845$	1.21780e8	0.00694350
$846$	−1.88359e10	−1.06952
$847$	7.31644e9	0.413721
$848$	−1.05043e11	−5.91534
$849$	−4.00453e10	−2.24582
$850$	2.78751e10	1.55686
$851$	−1.12707e10	−0.626901
$852$	−5.11220e10	−2.83184
$853$	−3.44502e9	−0.190051	−0.0950254	−	0.995475i	$-0.530293\pi$
$853$	−3.44502e9	−0.190051	−0.0950254	+	0.995475i	$0.530293\pi$
$854$	−1.53436e10	−0.842992
$855$	−2.13638e9	−0.116895
$856$	−5.66036e10	−3.08451
$857$	3.24249e10	1.75973	0.879864	−	0.475225i	$-0.157633\pi$
$857$	3.24249e10	1.75973	0.879864	+	0.475225i	$0.157633\pi$
$858$	−2.22632e10	−1.20333
$859$	−1.67291e10	−0.900526	−0.450263	−	0.892896i	$-0.648670\pi$
$859$	−1.67291e10	−0.900526	−0.450263	+	0.892896i	$0.648670\pi$
$860$	9.18466e8	0.0492401
$861$	4.25222e9	0.227041
$862$	−3.51201e10	−1.86758
$863$	−4.52178e9	−0.239481	−0.119741	−	0.992805i	$-0.538206\pi$
$863$	−4.52178e9	−0.239481	−0.119741	+	0.992805i	$0.538206\pi$
$864$	−4.64405e10	−2.44962
$865$	−2.58950e8	−0.0136038
$866$	6.67504e9	0.349254
$867$	−1.03927e10	−0.541576
$868$	−2.40650e10	−1.24901
$869$	7.80691e9	0.403562
$870$	−1.01432e10	−0.522224
$871$	2.52225e9	0.129338
$872$	−7.14952e10	−3.65148
$873$	−2.60701e10	−1.32615
$874$	3.72091e10	1.88521
$875$	−1.34666e9	−0.0679564
$876$	1.42432e11	7.15887
$877$	−1.50435e10	−0.753096	−0.376548	−	0.926397i	$-0.622889\pi$
$877$	−1.50435e10	−0.753096	−0.376548	+	0.926397i	$0.622889\pi$
$878$	−3.30897e10	−1.64992
$879$	3.94782e9	0.196063
$880$	1.07219e10	0.530374
$881$	1.52599e10	0.751860	0.375930	−	0.926648i	$-0.377323\pi$
$881$	1.52599e10	0.751860	0.375930	+	0.926648i	$0.377323\pi$
$882$	−7.73476e9	−0.379583
$883$	−8.87361e9	−0.433748	−0.216874	−	0.976200i	$-0.569586\pi$
$883$	−8.87361e9	−0.433748	−0.216874	+	0.976200i	$0.569586\pi$
$884$	1.28559e10	0.625920
$885$	−1.02536e8	−0.00497252
$886$	6.50938e10	3.14428
$887$	8.28980e9	0.398851	0.199426	−	0.979913i	$-0.436092\pi$
$887$	8.28980e9	0.398851	0.199426	+	0.979913i	$0.436092\pi$
$888$	6.95896e10	3.33503
$889$	1.08229e10	0.516639
$890$	−6.84550e9	−0.325492
$891$	−1.54767e10	−0.733002
$892$	4.06018e9	0.191544
$893$	−8.14277e9	−0.382641
$894$	3.45657e10	1.61794
$895$	−2.57480e9	−0.120050
$896$	−3.59589e10	−1.67004
$897$	9.36876e9	0.433419
$898$	1.89077e10	0.871306
$899$	−4.95427e10	−2.27416
$900$	−8.28683e10	−3.78913
$901$	−2.57438e10	−1.17256
$902$	−2.43164e10	−1.10326
$903$	2.50031e9	0.113002
$904$	4.77183e10	2.14830
$905$	−2.13682e9	−0.0958290
$906$	1.08485e11	4.84641
$907$	−1.95582e10	−0.870367	−0.435183	−	0.900342i	$-0.643316\pi$
$907$	−1.95582e10	−0.870367	−0.435183	+	0.900342i	$0.643316\pi$
$908$	6.49216e10	2.87799
$909$	3.55874e10	1.57153
$910$	−4.19550e8	−0.0184561
$911$	−3.73133e9	−0.163512	−0.0817559	−	0.996652i	$-0.526053\pi$
$911$	−3.73133e9	−0.163512	−0.0817559	+	0.996652i	$0.526053\pi$
$912$	−1.35883e11	−5.93174
$913$	−4.26579e9	−0.185503
$914$	−4.23349e10	−1.83395
$915$	3.67618e9	0.158644
$916$	7.90992e10	3.40046
$917$	1.10909e9	0.0474978
$918$	−2.04863e10	−0.874007
$919$	3.04633e10	1.29471	0.647356	−	0.762188i	$-0.275875\pi$
$919$	3.04633e10	1.29471	0.647356	+	0.762188i	$0.275875\pi$
$920$	−7.62856e9	−0.322987
$921$	−7.07308e10	−2.98332
$922$	−5.51030e10	−2.31535
$923$	−4.35323e9	−0.182224
$924$	5.65387e10	2.35773
$925$	1.47207e10	0.611549
$926$	4.56391e10	1.88885
$927$	4.41494e9	0.182031
$928$	−2.06698e11	−8.49021
$929$	−7.47892e9	−0.306044	−0.153022	−	0.988223i	$-0.548901\pi$
$929$	−7.47892e9	−0.306044	−0.153022	+	0.988223i	$0.548901\pi$
$930$	7.82177e9	0.318871
$931$	−3.34374e9	−0.135803
$932$	−1.03969e11	−4.20678
$933$	5.12580e10	2.06622
$934$	6.35430e10	2.55184
$935$	2.62772e9	0.105133
$936$	−3.33587e10	−1.32967
$937$	3.09080e10	1.22739	0.613695	−	0.789543i	$-0.289682\pi$
$937$	3.09080e10	1.22739	0.613695	+	0.789543i	$0.289682\pi$
$938$	−8.68951e9	−0.343784
$939$	−5.67233e10	−2.23579
$940$	2.59466e9	0.101890
$941$	−3.07895e10	−1.20459	−0.602295	−	0.798273i	$-0.705747\pi$
$941$	−3.07895e10	−1.20459	−0.602295	+	0.798273i	$0.705747\pi$
$942$	1.52237e11	5.93392
$943$	1.02328e10	0.397377
$944$	−3.76097e9	−0.145512
$945$	4.92829e8	0.0189970
$946$	−1.42981e10	−0.549110
$947$	4.75590e8	0.0181973	0.00909866	−	0.999959i	$-0.497104\pi$
$947$	4.75590e8	0.0181973	0.00909866	+	0.999959i	$0.497104\pi$
$948$	3.15268e10	1.20185
$949$	1.21287e10	0.460660
$950$	−4.85987e10	−1.83904
$951$	6.29265e10	2.37248
$952$	−2.84967e10	−1.07045
$953$	−1.12108e10	−0.419578	−0.209789	−	0.977747i	$-0.567278\pi$
$953$	−1.12108e10	−0.419578	−0.209789	+	0.977747i	$0.567278\pi$
$954$	1.03823e11	3.87147
$955$	2.27600e9	0.0845590
$956$	2.16521e10	0.801490
$957$	1.16396e11	4.29287
$958$	−4.85945e10	−1.78570
$959$	−9.94654e9	−0.364172
$960$	1.71934e10	0.627210
$961$	1.06915e10	0.388604
$962$	9.21008e9	0.333542
$963$	3.30899e10	1.19400
$964$	−2.45327e10	−0.882016
$965$	−1.62199e9	−0.0581035
$966$	−3.22767e10	−1.15204
$967$	−1.12392e10	−0.399706	−0.199853	−	0.979826i	$-0.564047\pi$
$967$	−1.12392e10	−0.399706	−0.199853	+	0.979826i	$0.564047\pi$
$968$	−1.08710e11	−3.85217
$969$	−3.33021e10	−1.17581
$970$	4.87178e9	0.171390
$971$	−4.85274e10	−1.70106	−0.850530	−	0.525926i	$-0.823719\pi$
$971$	−4.85274e10	−1.70106	−0.850530	+	0.525926i	$0.823719\pi$
$972$	−1.07206e11	−3.74445
$973$	−6.62758e9	−0.230654
$974$	3.20297e10	1.11070
$975$	−1.22365e10	−0.422806
$976$	1.34840e11	4.64241
$977$	−1.81742e10	−0.623484	−0.311742	−	0.950167i	$-0.600912\pi$
$977$	−1.81742e10	−0.623484	−0.311742	+	0.950167i	$0.600912\pi$
$978$	−1.30042e11	−4.44527
$979$	7.85544e10	2.67566
$980$	1.06547e9	0.0361618
$981$	4.17954e10	1.41347
$982$	1.48252e10	0.499586
$983$	2.48096e10	0.833073	0.416537	−	0.909119i	$-0.363244\pi$
$983$	2.48096e10	0.833073	0.416537	+	0.909119i	$0.363244\pi$
$984$	−6.31809e10	−2.11399
$985$	4.01752e8	0.0133946
$986$	−9.11808e10	−3.02924
$987$	7.06336e9	0.233831
$988$	−2.24136e10	−0.739369
$989$	6.01689e9	0.197781
$990$	−1.05974e10	−0.347119
$991$	−1.21078e10	−0.395192	−0.197596	−	0.980283i	$-0.563313\pi$
$991$	−1.21078e10	−0.395192	−0.197596	+	0.980283i	$0.563313\pi$
$992$	1.59392e11	5.18413
$993$	4.22292e10	1.36864
$994$	1.49975e10	0.484358
$995$	5.32731e9	0.171446
$996$	−1.72266e10	−0.552450
$997$	3.23614e10	1.03417	0.517087	−	0.855933i	$-0.327016\pi$
$997$	3.23614e10	1.03417	0.517087	+	0.855933i	$0.327016\pi$
$998$	−2.57165e10	−0.818947
$999$	−1.08187e10	−0.343318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.1	✓	12	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-22.0670 q^{2} +71.8770 q^{3} +358.952 q^{4} +25.2300 q^{5} -1586.11 q^{6} +343.000 q^{7} -5096.40 q^{8} +2979.31 q^{9} +O(q^{10})\)	\(q-22.0670 q^{2} +71.8770 q^{3} +358.952 q^{4} +25.2300 q^{5} -1586.11 q^{6} +343.000 q^{7} -5096.40 q^{8} +2979.31 q^{9} -556.750 q^{10} +6388.89 q^{11} +25800.4 q^{12} +2197.00 q^{13} -7568.97 q^{14} +1813.46 q^{15} +66516.5 q^{16} +16301.8 q^{17} -65744.4 q^{18} -28421.4 q^{19} +9056.35 q^{20} +24653.8 q^{21} -140983. q^{22} +59328.3 q^{23} -366315. q^{24} -77488.4 q^{25} -48481.2 q^{26} +56948.9 q^{27} +123120. q^{28} +253469. q^{29} -40017.5 q^{30} -195459. q^{31} -815477. q^{32} +459214. q^{33} -359732. q^{34} +8653.89 q^{35} +1.06943e6 q^{36} -189972. q^{37} +627174. q^{38} +157914. q^{39} -128582. q^{40} +172477. q^{41} -544036. q^{42} +101417. q^{43} +2.29330e6 q^{44} +75168.0 q^{45} -1.30920e6 q^{46} +286502. q^{47} +4.78101e6 q^{48} +117649. q^{49} +1.70994e6 q^{50} +1.17173e6 q^{51} +788617. q^{52} -1.57920e6 q^{53} -1.25669e6 q^{54} +161192. q^{55} -1.74807e6 q^{56} -2.04284e6 q^{57} -5.59329e6 q^{58} -56542.0 q^{59} +650943. q^{60} +2.02716e6 q^{61} +4.31318e6 q^{62} +1.02190e6 q^{63} +9.48102e6 q^{64} +55430.3 q^{65} -1.01335e7 q^{66} +1.14804e6 q^{67} +5.85156e6 q^{68} +4.26434e6 q^{69} -190965. q^{70} -1.98144e6 q^{71} -1.51838e7 q^{72} +5.52055e6 q^{73} +4.19212e6 q^{74} -5.56964e6 q^{75} -1.02019e7 q^{76} +2.19139e6 q^{77} -3.48468e6 q^{78} +1.22195e6 q^{79} +1.67821e6 q^{80} -2.42243e6 q^{81} -3.80605e6 q^{82} -667689. q^{83} +8.84953e6 q^{84} +411295. q^{85} -2.23796e6 q^{86} +1.82186e7 q^{87} -3.25604e7 q^{88} +1.22955e7 q^{89} -1.65873e6 q^{90} +753571. q^{91} +2.12960e7 q^{92} -1.40490e7 q^{93} -6.32223e6 q^{94} -717071. q^{95} -5.86141e7 q^{96} -8.75039e6 q^{97} -2.59616e6 q^{98} +1.90345e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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