LMFDB - Embedded newform 91.10.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,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, 10, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 $ x^14 - x^13 - 4752x^12 + 9346x^11 + 8576824x^10 - 26923636x^9 - 7450416552x^8 + 31594524240x^7 + 3232668379296x^6 - 15784728192704x^5 - 654706244016512x^4 + 3031992312058112x^3 + 50459693673905664x^2 - 177878730644221952x - 247584423217725440
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$15.6702$ 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)

$f(q)$	$=$	$q-13.6702 q^{2} -25.3649 q^{3} -325.126 q^{4} +344.296 q^{5} +346.743 q^{6} +2401.00 q^{7} +11443.7 q^{8} -19039.6 q^{9} +O(q^{10})$	\(q-13.6702 q^{2} -25.3649 q^{3} -325.126 q^{4} +344.296 q^{5} +346.743 q^{6} +2401.00 q^{7} +11443.7 q^{8} -19039.6 q^{9} -4706.60 q^{10} +35993.7 q^{11} +8246.77 q^{12} -28561.0 q^{13} -32822.2 q^{14} -8733.03 q^{15} +10026.8 q^{16} -263368. q^{17} +260276. q^{18} -504621. q^{19} -111939. q^{20} -60901.1 q^{21} -492041. q^{22} -79329.8 q^{23} -290267. q^{24} -1.83459e6 q^{25} +390435. q^{26} +982195. q^{27} -780626. q^{28} -1.67250e6 q^{29} +119382. q^{30} +9.10824e6 q^{31} -5.99623e6 q^{32} -912974. q^{33} +3.60030e6 q^{34} +826655. q^{35} +6.19027e6 q^{36} -1.04185e7 q^{37} +6.89827e6 q^{38} +724446. q^{39} +3.94001e6 q^{40} -1.68104e7 q^{41} +832530. q^{42} +1.46059e7 q^{43} -1.17025e7 q^{44} -6.55527e6 q^{45} +1.08446e6 q^{46} -2.57006e6 q^{47} -254330. q^{48} +5.76480e6 q^{49} +2.50792e7 q^{50} +6.68031e6 q^{51} +9.28591e6 q^{52} +6.66482e7 q^{53} -1.34268e7 q^{54} +1.23925e7 q^{55} +2.74763e7 q^{56} +1.27996e7 q^{57} +2.28634e7 q^{58} +8.44876e7 q^{59} +2.83933e6 q^{60} +7.82544e7 q^{61} -1.24511e8 q^{62} -4.57141e7 q^{63} +7.68360e7 q^{64} -9.83344e6 q^{65} +1.24805e7 q^{66} +6.79359e7 q^{67} +8.56278e7 q^{68} +2.01219e6 q^{69} -1.13005e7 q^{70} +1.35632e8 q^{71} -2.17883e8 q^{72} +3.56746e8 q^{73} +1.42423e8 q^{74} +4.65340e7 q^{75} +1.64065e8 q^{76} +8.64208e7 q^{77} -9.90333e6 q^{78} +5.48862e8 q^{79} +3.45220e6 q^{80} +3.49844e8 q^{81} +2.29802e8 q^{82} +1.87931e8 q^{83} +1.98005e7 q^{84} -9.06767e7 q^{85} -1.99665e8 q^{86} +4.24227e7 q^{87} +4.11900e8 q^{88} -2.44441e8 q^{89} +8.96118e7 q^{90} -6.85750e7 q^{91} +2.57922e7 q^{92} -2.31029e8 q^{93} +3.51333e7 q^{94} -1.73739e8 q^{95} +1.52094e8 q^{96} -1.07571e9 q^{97} -7.88060e7 q^{98} -6.85306e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) $ 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * 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 $

$2$	−13.6702	−0.604143	−0.302072	−	0.953285i	$-0.597678\pi$
$2$	−13.6702	−0.604143	−0.302072	+	0.953285i	$0.597678\pi$
$3$	−25.3649	−0.180795	−0.0903976	−	0.995906i	$-0.528814\pi$
$3$	−25.3649	−0.180795	−0.0903976	+	0.995906i	$0.528814\pi$
$4$	−325.126	−0.635011
$5$	344.296	0.246358	0.123179	−	0.992384i	$-0.460691\pi$
$5$	344.296	0.246358	0.123179	+	0.992384i	$0.460691\pi$
$6$	346.743	0.109226
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	11443.7	0.987781
$9$	−19039.6	−0.967313
$10$	−4706.60	−0.148836
$11$	35993.7	0.741240	0.370620	−	0.928785i	$-0.379145\pi$
$11$	35993.7	0.741240	0.370620	+	0.928785i	$0.379145\pi$
$12$	8246.77	0.114807
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−32822.2	−0.228345
$15$	−8733.03	−0.0445404
$16$	10026.8	0.0382494
$17$	−263368.	−0.764792	−0.382396	−	0.923998i	$-0.624901\pi$
$17$	−263368.	−0.764792	−0.382396	+	0.923998i	$0.624901\pi$
$18$	260276.	0.584396
$19$	−504621.	−0.888330	−0.444165	−	0.895945i	$-0.646500\pi$
$19$	−504621.	−0.888330	−0.444165	+	0.895945i	$0.646500\pi$
$20$	−111939.	−0.156440
$21$	−60901.1	−0.0683342
$22$	−492041.	−0.447815
$23$	−79329.8	−0.0591100	−0.0295550	−	0.999563i	$-0.509409\pi$
$23$	−79329.8	−0.0591100	−0.0295550	+	0.999563i	$0.509409\pi$
$24$	−290267.	−0.178586
$25$	−1.83459e6	−0.939308
$26$	390435.	0.167559
$27$	982195.	0.355681
$28$	−780626.	−0.240012
$29$	−1.67250e6	−0.439111	−0.219556	−	0.975600i	$-0.570461\pi$
$29$	−1.67250e6	−0.439111	−0.219556	+	0.975600i	$0.570461\pi$
$30$	119382.	0.0269088
$31$	9.10824e6	1.77136	0.885680	−	0.464296i	$-0.153693\pi$
$31$	9.10824e6	1.77136	0.885680	+	0.464296i	$0.153693\pi$
$32$	−5.99623e6	−1.01089
$33$	−912974.	−0.134013
$34$	3.60030e6	0.462044
$35$	826655.	0.0931146
$36$	6.19027e6	0.614254
$37$	−1.04185e7	−0.913895	−0.456948	−	0.889494i	$-0.651057\pi$
$37$	−1.04185e7	−0.913895	−0.456948	+	0.889494i	$0.651057\pi$
$38$	6.89827e6	0.536678
$39$	724446.	0.0501436
$40$	3.94001e6	0.243348
$41$	−1.68104e7	−0.929077	−0.464539	−	0.885553i	$-0.653780\pi$
$41$	−1.68104e7	−0.929077	−0.464539	+	0.885553i	$0.653780\pi$
$42$	832530.	0.0412837
$43$	1.46059e7	0.651507	0.325754	−	0.945455i	$-0.394382\pi$
$43$	1.46059e7	0.651507	0.325754	+	0.945455i	$0.394382\pi$
$44$	−1.17025e7	−0.470695
$45$	−6.55527e6	−0.238305
$46$	1.08446e6	0.0357109
$47$	−2.57006e6	−0.0768252	−0.0384126	−	0.999262i	$-0.512230\pi$
$47$	−2.57006e6	−0.0768252	−0.0384126	+	0.999262i	$0.512230\pi$
$48$	−254330.	−0.00691531
$49$	5.76480e6	0.142857
$50$	2.50792e7	0.567477
$51$	6.68031e6	0.138271
$52$	9.28591e6	0.176120
$53$	6.66482e7	1.16024	0.580119	−	0.814532i	$-0.303006\pi$
$53$	6.66482e7	1.16024	0.580119	+	0.814532i	$0.303006\pi$
$54$	−1.34268e7	−0.214882
$55$	1.23925e7	0.182611
$56$	2.74763e7	0.373346
$57$	1.27996e7	0.160606
$58$	2.28634e7	0.265286
$59$	8.44876e7	0.907734	0.453867	−	0.891069i	$-0.350044\pi$
$59$	8.44876e7	0.907734	0.453867	+	0.891069i	$0.350044\pi$
$60$	2.83933e6	0.0282836
$61$	7.82544e7	0.723643	0.361822	−	0.932247i	$-0.382155\pi$
$61$	7.82544e7	0.723643	0.361822	+	0.932247i	$0.382155\pi$
$62$	−1.24511e8	−1.07016
$63$	−4.57141e7	−0.365610
$64$	7.68360e7	0.572473
$65$	−9.83344e6	−0.0683275
$66$	1.24805e7	0.0809629
$67$	6.79359e7	0.411872	0.205936	−	0.978565i	$-0.433976\pi$
$67$	6.79359e7	0.411872	0.205936	+	0.978565i	$0.433976\pi$
$68$	8.56278e7	0.485651
$69$	2.01219e6	0.0106868
$70$	−1.13005e7	−0.0562546
$71$	1.35632e8	0.633431	0.316716	−	0.948521i	$-0.397420\pi$
$71$	1.35632e8	0.633431	0.316716	+	0.948521i	$0.397420\pi$
$72$	−2.17883e8	−0.955493
$73$	3.56746e8	1.47030	0.735150	−	0.677904i	$-0.237112\pi$
$73$	3.56746e8	1.47030	0.735150	+	0.677904i	$0.237112\pi$
$74$	1.42423e8	0.552124
$75$	4.65340e7	0.169822
$76$	1.64065e8	0.564099
$77$	8.64208e7	0.280162
$78$	−9.90333e6	−0.0302939
$79$	5.48862e8	1.58541	0.792705	−	0.609606i	$-0.208672\pi$
$79$	5.48862e8	1.58541	0.792705	+	0.609606i	$0.208672\pi$
$80$	3.45220e6	0.00942305
$81$	3.49844e8	0.903008
$82$	2.29802e8	0.561296
$83$	1.87931e8	0.434658	0.217329	−	0.976098i	$-0.430266\pi$
$83$	1.87931e8	0.434658	0.217329	+	0.976098i	$0.430266\pi$
$84$	1.98005e7	0.0433929
$85$	−9.06767e7	−0.188413
$86$	−1.99665e8	−0.393604
$87$	4.24227e7	0.0793892
$88$	4.11900e8	0.732183
$89$	−2.44441e8	−0.412970	−0.206485	−	0.978450i	$-0.566203\pi$
$89$	−2.44441e8	−0.412970	−0.206485	+	0.978450i	$0.566203\pi$
$90$	8.96118e7	0.143971
$91$	−6.85750e7	−0.104828
$92$	2.57922e7	0.0375355
$93$	−2.31029e8	−0.320253
$94$	3.51333e7	0.0464134
$95$	−1.73739e8	−0.218847
$96$	1.52094e8	0.182764
$97$	−1.07571e9	−1.23373	−0.616867	−	0.787067i	$-0.711599\pi$
$97$	−1.07571e9	−1.23373	−0.616867	+	0.787067i	$0.711599\pi$
$98$	−7.88060e7	−0.0863062
$99$	−6.85306e8	−0.717011
$100$	5.96470e8	0.596470
$101$	−1.46814e9	−1.40385	−0.701926	−	0.712249i	$-0.747676\pi$
$101$	−1.46814e9	−1.40385	−0.701926	+	0.712249i	$0.747676\pi$
$102$	−9.13212e7	−0.0835354
$103$	1.14933e9	1.00619	0.503093	−	0.864232i	$-0.332195\pi$
$103$	1.14933e9	1.00619	0.503093	+	0.864232i	$0.332195\pi$
$104$	−3.26843e8	−0.273961
$105$	−2.09680e7	−0.0168347
$106$	−9.11095e8	−0.700951
$107$	1.71135e9	1.26215	0.631077	−	0.775720i	$-0.282613\pi$
$107$	1.71135e9	1.26215	0.631077	+	0.775720i	$0.282613\pi$
$108$	−3.19336e8	−0.225861
$109$	−5.85367e8	−0.397200	−0.198600	−	0.980081i	$-0.563639\pi$
$109$	−5.85367e8	−0.397200	−0.198600	+	0.980081i	$0.563639\pi$
$110$	−1.69408e8	−0.110323
$111$	2.64263e8	0.165228
$112$	2.40745e7	0.0144569
$113$	1.24200e9	0.716585	0.358292	−	0.933609i	$-0.383359\pi$
$113$	1.24200e9	0.716585	0.358292	+	0.933609i	$0.383359\pi$
$114$	−1.74974e8	−0.0970289
$115$	−2.73129e7	−0.0145622
$116$	5.43771e8	0.278840
$117$	5.43791e8	0.268284
$118$	−1.15496e9	−0.548402
$119$	−6.32348e8	−0.289064
$120$	−9.99379e7	−0.0439962
$121$	−1.06240e9	−0.450563
$122$	−1.06975e9	−0.437184
$123$	4.26395e8	0.167973
$124$	−2.96132e9	−1.12483
$125$	−1.30409e9	−0.477764
$126$	6.24922e8	0.220881
$127$	−1.33386e9	−0.454982	−0.227491	−	0.973780i	$-0.573052\pi$
$127$	−1.33386e9	−0.454982	−0.227491	+	0.973780i	$0.573052\pi$
$128$	2.01971e9	0.665034
$129$	−3.70476e8	−0.117789
$130$	1.34425e8	0.0412796
$131$	1.10115e9	0.326682	0.163341	−	0.986570i	$-0.447773\pi$
$131$	1.10115e9	0.326682	0.163341	+	0.986570i	$0.447773\pi$
$132$	2.96831e8	0.0850995
$133$	−1.21160e9	−0.335757
$134$	−9.28697e8	−0.248830
$135$	3.38166e8	0.0876249
$136$	−3.01390e9	−0.755447
$137$	−3.33341e9	−0.808438	−0.404219	−	0.914662i	$-0.632457\pi$
$137$	−3.33341e9	−0.808438	−0.404219	+	0.914662i	$0.632457\pi$
$138$	−2.75071e7	−0.00645637
$139$	2.93752e9	0.667444	0.333722	−	0.942672i	$-0.391695\pi$
$139$	2.93752e9	0.667444	0.333722	+	0.942672i	$0.391695\pi$
$140$	−2.68767e8	−0.0591288
$141$	6.51894e7	0.0138896
$142$	−1.85412e9	−0.382683
$143$	−1.02801e9	−0.205583
$144$	−1.90907e8	−0.0369991
$145$	−5.75834e8	−0.108179
$146$	−4.87679e9	−0.888272
$147$	−1.46223e8	−0.0258279
$148$	3.38731e9	0.580333
$149$	−3.64309e9	−0.605524	−0.302762	−	0.953066i	$-0.597909\pi$
$149$	−3.64309e9	−0.605524	−0.302762	+	0.953066i	$0.597909\pi$
$150$	−6.36130e8	−0.102597
$151$	6.28216e9	0.983361	0.491680	−	0.870776i	$-0.336383\pi$
$151$	6.28216e9	0.983361	0.491680	+	0.870776i	$0.336383\pi$
$152$	−5.77472e9	−0.877475
$153$	5.01444e9	0.739794
$154$	−1.18139e9	−0.169258
$155$	3.13593e9	0.436389
$156$	−2.35536e8	−0.0318417
$157$	9.01545e9	1.18424	0.592119	−	0.805851i	$-0.298292\pi$
$157$	9.01545e9	1.18424	0.592119	+	0.805851i	$0.298292\pi$
$158$	−7.50306e9	−0.957815
$159$	−1.69052e9	−0.209766
$160$	−2.06448e9	−0.249041
$161$	−1.90471e8	−0.0223415
$162$	−4.78243e9	−0.545546
$163$	−3.67475e9	−0.407741	−0.203870	−	0.978998i	$-0.565352\pi$
$163$	−3.67475e9	−0.407741	−0.203870	+	0.978998i	$0.565352\pi$
$164$	5.46550e9	0.589974
$165$	−3.14333e8	−0.0330151
$166$	−2.56906e9	−0.262596
$167$	−1.53442e10	−1.52659	−0.763293	−	0.646053i	$-0.776419\pi$
$167$	−1.53442e10	−1.52659	−0.763293	+	0.646053i	$0.776419\pi$
$168$	−6.96932e8	−0.0674992
$169$	8.15731e8	0.0769231
$170$	1.23957e9	0.113828
$171$	9.60779e9	0.859293
$172$	−4.74874e9	−0.413714
$173$	1.04174e10	0.884202	0.442101	−	0.896965i	$-0.354233\pi$
$173$	1.04174e10	0.884202	0.442101	+	0.896965i	$0.354233\pi$
$174$	−5.79927e8	−0.0479625
$175$	−4.40484e9	−0.355025
$176$	3.60903e8	0.0283520
$177$	−2.14302e9	−0.164114
$178$	3.34156e9	0.249493
$179$	2.23321e10	1.62589	0.812946	−	0.582340i	$-0.197863\pi$
$179$	2.23321e10	1.62589	0.812946	+	0.582340i	$0.197863\pi$
$180$	2.13128e9	0.151327
$181$	−1.71968e10	−1.19095	−0.595476	−	0.803373i	$-0.703037\pi$
$181$	−1.71968e10	−1.19095	−0.595476	+	0.803373i	$0.703037\pi$
$182$	9.37434e8	0.0633314
$183$	−1.98491e9	−0.130831
$184$	−9.07825e8	−0.0583878
$185$	−3.58704e9	−0.225146
$186$	3.15822e9	0.193479
$187$	−9.47959e9	−0.566895
$188$	8.35593e8	0.0487848
$189$	2.35825e9	0.134435
$190$	2.37505e9	0.132215
$191$	−1.51642e10	−0.824458	−0.412229	−	0.911080i	$-0.635250\pi$
$191$	−1.51642e10	−0.824458	−0.412229	+	0.911080i	$0.635250\pi$
$192$	−1.94893e9	−0.103500
$193$	3.49040e10	1.81079	0.905394	−	0.424572i	$-0.139575\pi$
$193$	3.49040e10	1.81079	0.905394	+	0.424572i	$0.139575\pi$
$194$	1.47052e10	0.745353
$195$	2.49424e8	0.0123533
$196$	−1.87428e9	−0.0907158
$197$	3.06985e10	1.45218	0.726088	−	0.687601i	$-0.241336\pi$
$197$	3.06985e10	1.45218	0.726088	+	0.687601i	$0.241336\pi$
$198$	9.36827e9	0.433178
$199$	1.51809e10	0.686215	0.343107	−	0.939296i	$-0.388521\pi$
$199$	1.51809e10	0.686215	0.343107	+	0.939296i	$0.388521\pi$
$200$	−2.09944e10	−0.927830
$201$	−1.72319e9	−0.0744646
$202$	2.00698e10	0.848128
$203$	−4.01567e9	−0.165968
$204$	−2.17194e9	−0.0878035
$205$	−5.78777e9	−0.228886
$206$	−1.57116e10	−0.607881
$207$	1.51041e9	0.0571779
$208$	−2.86377e8	−0.0106085
$209$	−1.81632e10	−0.658465
$210$	2.86637e8	0.0101706
$211$	−1.23472e10	−0.428842	−0.214421	−	0.976741i	$-0.568786\pi$
$211$	−1.23472e10	−0.428842	−0.214421	+	0.976741i	$0.568786\pi$
$212$	−2.16690e10	−0.736764
$213$	−3.44029e9	−0.114521
$214$	−2.33945e10	−0.762522
$215$	5.02874e9	0.160504
$216$	1.12399e10	0.351335
$217$	2.18689e10	0.669511
$218$	8.00209e9	0.239966
$219$	−9.04881e9	−0.265823
$220$	−4.02911e9	−0.115960
$221$	7.52207e9	0.212115
$222$	−3.61253e9	−0.0998214
$223$	4.73954e10	1.28341	0.641703	−	0.766953i	$-0.278228\pi$
$223$	4.73954e10	1.28341	0.641703	+	0.766953i	$0.278228\pi$
$224$	−1.43970e10	−0.382080
$225$	3.49298e10	0.908605
$226$	−1.69784e10	−0.432920
$227$	5.52538e10	1.38116	0.690582	−	0.723254i	$-0.257354\pi$
$227$	5.52538e10	1.38116	0.690582	+	0.723254i	$0.257354\pi$
$228$	−4.16149e9	−0.101986
$229$	1.69073e9	0.0406270	0.0203135	−	0.999794i	$-0.493534\pi$
$229$	1.69073e9	0.0406270	0.0203135	+	0.999794i	$0.493534\pi$
$230$	3.73374e8	0.00879768
$231$	−2.19205e9	−0.0506520
$232$	−1.91395e10	−0.433746
$233$	2.27459e10	0.505593	0.252797	−	0.967519i	$-0.418650\pi$
$233$	2.27459e10	0.505593	0.252797	+	0.967519i	$0.418650\pi$
$234$	−7.43373e9	−0.162082
$235$	−8.84863e8	−0.0189265
$236$	−2.74691e10	−0.576421
$237$	−1.39218e10	−0.286635
$238$	8.64432e9	0.174636
$239$	3.10640e10	0.615838	0.307919	−	0.951413i	$-0.400367\pi$
$239$	3.10640e10	0.615838	0.307919	+	0.951413i	$0.400367\pi$
$240$	−8.75647e7	−0.00170364
$241$	4.64625e10	0.887209	0.443605	−	0.896223i	$-0.353699\pi$
$241$	4.64625e10	0.887209	0.443605	+	0.896223i	$0.353699\pi$
$242$	1.45233e10	0.272205
$243$	−2.82063e10	−0.518940
$244$	−2.54425e10	−0.459521
$245$	1.98480e9	0.0351940
$246$	−5.82890e9	−0.101480
$247$	1.44125e10	0.246378
$248$	1.04232e11	1.74972
$249$	−4.76685e9	−0.0785840
$250$	1.78272e10	0.288638
$251$	4.74304e10	0.754267	0.377133	−	0.926159i	$-0.376910\pi$
$251$	4.74304e10	0.754267	0.377133	+	0.926159i	$0.376910\pi$
$252$	1.48628e10	0.232166
$253$	−2.85537e9	−0.0438147
$254$	1.82342e10	0.274874
$255$	2.30000e9	0.0340642
$256$	−6.69498e10	−0.974248
$257$	5.51800e10	0.789011	0.394505	−	0.918894i	$-0.370916\pi$
$257$	5.51800e10	0.789011	0.394505	+	0.918894i	$0.370916\pi$
$258$	5.06448e9	0.0711617
$259$	−2.50148e10	−0.345420
$260$	3.19710e9	0.0433887
$261$	3.18437e10	0.424758
$262$	−1.50529e10	−0.197363
$263$	4.26854e10	0.550146	0.275073	−	0.961423i	$-0.411298\pi$
$263$	4.26854e10	0.550146	0.275073	+	0.961423i	$0.411298\pi$
$264$	−1.04478e10	−0.132375
$265$	2.29467e10	0.285834
$266$	1.65628e10	0.202845
$267$	6.20021e9	0.0746631
$268$	−2.20877e10	−0.261543
$269$	−4.62546e10	−0.538604	−0.269302	−	0.963056i	$-0.586793\pi$
$269$	−4.62546e10	−0.538604	−0.269302	+	0.963056i	$0.586793\pi$
$270$	−4.62279e9	−0.0529380
$271$	−7.82930e10	−0.881782	−0.440891	−	0.897561i	$-0.645337\pi$
$271$	−7.82930e10	−0.881782	−0.440891	+	0.897561i	$0.645337\pi$
$272$	−2.64076e9	−0.0292529
$273$	1.73940e9	0.0189525
$274$	4.55684e10	0.488412
$275$	−6.60334e10	−0.696252
$276$	−6.54215e8	−0.00678624
$277$	−6.60686e10	−0.674274	−0.337137	−	0.941456i	$-0.609459\pi$
$277$	−6.60686e10	−0.674274	−0.337137	+	0.941456i	$0.609459\pi$
$278$	−4.01565e10	−0.403232
$279$	−1.73417e11	−1.71346
$280$	9.45997e9	0.0919769
$281$	7.05105e10	0.674645	0.337323	−	0.941389i	$-0.390479\pi$
$281$	7.05105e10	0.674645	0.337323	+	0.941389i	$0.390479\pi$
$282$	−8.91152e8	−0.00839133
$283$	−1.14764e11	−1.06357	−0.531786	−	0.846879i	$-0.678479\pi$
$283$	−1.14764e11	−1.06357	−0.531786	+	0.846879i	$0.678479\pi$
$284$	−4.40974e10	−0.402236
$285$	4.40687e9	0.0395665
$286$	1.40532e10	0.124202
$287$	−4.03619e10	−0.351158
$288$	1.14166e11	0.977846
$289$	−4.92249e10	−0.415092
$290$	7.87177e9	0.0653554
$291$	2.72852e10	0.223053
$292$	−1.15987e11	−0.933656
$293$	−4.35560e10	−0.345258	−0.172629	−	0.984987i	$-0.555226\pi$
$293$	−4.35560e10	−0.345258	−0.172629	+	0.984987i	$0.555226\pi$
$294$	1.99890e9	0.0156038
$295$	2.90887e10	0.223628
$296$	−1.19226e11	−0.902728
$297$	3.53528e10	0.263645
$298$	4.98018e10	0.365823
$299$	2.26574e9	0.0163942
$300$	−1.51294e10	−0.107839
$301$	3.50687e10	0.246247
$302$	−8.58784e10	−0.594091
$303$	3.72392e10	0.253810
$304$	−5.05976e9	−0.0339781
$305$	2.69427e10	0.178275
$306$	−6.85484e10	−0.446942
$307$	−1.14810e11	−0.737661	−0.368831	−	0.929497i	$-0.620242\pi$
$307$	−1.14810e11	−0.737661	−0.368831	+	0.929497i	$0.620242\pi$
$308$	−2.80976e10	−0.177906
$309$	−2.91527e10	−0.181914
$310$	−4.28688e10	−0.263642
$311$	1.68439e11	1.02099	0.510495	−	0.859881i	$-0.329462\pi$
$311$	1.68439e11	1.02099	0.510495	+	0.859881i	$0.329462\pi$
$312$	8.29033e9	0.0495309
$313$	−7.50797e10	−0.442153	−0.221077	−	0.975256i	$-0.570957\pi$
$313$	−7.50797e10	−0.442153	−0.221077	+	0.975256i	$0.570957\pi$
$314$	−1.23243e11	−0.715449
$315$	−1.57392e10	−0.0900710
$316$	−1.78449e11	−1.00675
$317$	−2.15188e11	−1.19688	−0.598442	−	0.801166i	$-0.704213\pi$
$317$	−2.15188e11	−1.19688	−0.598442	+	0.801166i	$0.704213\pi$
$318$	2.31098e10	0.126729
$319$	−6.01993e10	−0.325487
$320$	2.64543e10	0.141033
$321$	−4.34082e10	−0.228191
$322$	2.60378e9	0.0134975
$323$	1.32901e11	0.679388
$324$	−1.13743e11	−0.573420
$325$	5.23976e10	0.260517
$326$	5.02346e10	0.246334
$327$	1.48478e10	0.0718119
$328$	−1.92373e11	−0.917725
$329$	−6.17072e9	−0.0290372
$330$	4.29700e9	0.0199459
$331$	−3.75390e11	−1.71893	−0.859463	−	0.511198i	$-0.829202\pi$
$331$	−3.75390e11	−1.71893	−0.859463	+	0.511198i	$0.829202\pi$
$332$	−6.11012e10	−0.276012
$333$	1.98364e11	0.884023
$334$	2.09759e11	0.922277
$335$	2.33901e10	0.101468
$336$	−6.10646e8	−0.00261374
$337$	−3.79886e10	−0.160442	−0.0802212	−	0.996777i	$-0.525563\pi$
$337$	−3.79886e10	−0.160442	−0.0802212	+	0.996777i	$0.525563\pi$
$338$	−1.11512e10	−0.0464726
$339$	−3.15031e10	−0.129555
$340$	2.94813e10	0.119644
$341$	3.27839e11	1.31300
$342$	−1.31341e11	−0.519136
$343$	1.38413e10	0.0539949
$344$	1.67145e11	0.643546
$345$	6.92789e8	0.00263278
$346$	−1.42408e11	−0.534185
$347$	5.05460e11	1.87156	0.935781	−	0.352582i	$-0.114696\pi$
$347$	5.05460e11	1.87156	0.935781	+	0.352582i	$0.114696\pi$
$348$	−1.37927e10	−0.0504130
$349$	−2.27386e10	−0.0820445	−0.0410223	−	0.999158i	$-0.513061\pi$
$349$	−2.27386e10	−0.0820445	−0.0410223	+	0.999158i	$0.513061\pi$
$350$	6.02151e10	0.214486
$351$	−2.80525e10	−0.0986481
$352$	−2.15826e11	−0.749311
$353$	4.90907e10	0.168272	0.0841362	−	0.996454i	$-0.473187\pi$
$353$	4.90907e10	0.168272	0.0841362	+	0.996454i	$0.473187\pi$
$354$	2.92955e10	0.0991484
$355$	4.66976e10	0.156051
$356$	7.94740e10	0.262241
$357$	1.60394e10	0.0522615
$358$	−3.05285e11	−0.982271
$359$	1.77485e11	0.563945	0.281972	−	0.959423i	$-0.409011\pi$
$359$	1.77485e11	0.563945	0.281972	+	0.959423i	$0.409011\pi$
$360$	−7.50163e10	−0.235394
$361$	−6.80453e10	−0.210871
$362$	2.35084e11	0.719506
$363$	2.69478e10	0.0814597
$364$	2.22955e10	0.0665672
$365$	1.22826e11	0.362220
$366$	2.71342e10	0.0790409
$367$	5.44483e11	1.56671	0.783353	−	0.621577i	$-0.213508\pi$
$367$	5.44483e11	1.56671	0.783353	+	0.621577i	$0.213508\pi$
$368$	−7.95428e8	−0.00226092
$369$	3.20065e11	0.898709
$370$	4.90356e10	0.136020
$371$	1.60022e11	0.438529
$372$	7.51135e10	0.203364
$373$	−3.30520e10	−0.0884113	−0.0442057	−	0.999022i	$-0.514076\pi$
$373$	−3.30520e10	−0.0884113	−0.0442057	+	0.999022i	$0.514076\pi$
$374$	1.29588e11	0.342486
$375$	3.30782e10	0.0863775
$376$	−2.94110e10	−0.0758864
$377$	4.77682e10	0.121787
$378$	−3.22377e10	−0.0812179
$379$	2.97310e11	0.740174	0.370087	−	0.928997i	$-0.379328\pi$
$379$	2.97310e11	0.740174	0.370087	+	0.928997i	$0.379328\pi$
$380$	5.64870e10	0.138970
$381$	3.38332e10	0.0822586
$382$	2.07297e11	0.498091
$383$	−2.85231e11	−0.677334	−0.338667	−	0.940906i	$-0.609976\pi$
$383$	−2.85231e11	−0.677334	−0.338667	+	0.940906i	$0.609976\pi$
$384$	−5.12296e10	−0.120235
$385$	2.97543e10	0.0690203
$386$	−4.77145e11	−1.09398
$387$	−2.78090e11	−0.630211
$388$	3.49740e11	0.783435
$389$	−3.03770e11	−0.672622	−0.336311	−	0.941751i	$-0.609179\pi$
$389$	−3.03770e11	−0.672622	−0.336311	+	0.941751i	$0.609179\pi$
$390$	−3.40968e9	−0.00746315
$391$	2.08930e10	0.0452069
$392$	6.59705e10	0.141112
$393$	−2.79305e10	−0.0590626
$394$	−4.19655e11	−0.877323
$395$	1.88971e11	0.390579
$396$	2.22810e11	0.455310
$397$	4.67060e11	0.943660	0.471830	−	0.881690i	$-0.343594\pi$
$397$	4.67060e11	0.943660	0.471830	+	0.881690i	$0.343594\pi$
$398$	−2.07527e11	−0.414572
$399$	3.07320e10	0.0607033
$400$	−1.83951e10	−0.0359280
$401$	2.66725e11	0.515126	0.257563	−	0.966261i	$-0.417080\pi$
$401$	2.66725e11	0.515126	0.257563	+	0.966261i	$0.417080\pi$
$402$	2.35563e10	0.0449873
$403$	−2.60140e11	−0.491287
$404$	4.77330e11	0.891462
$405$	1.20450e11	0.222463
$406$	5.48950e10	0.100269
$407$	−3.74999e11	−0.677416
$408$	7.64473e10	0.136581
$409$	−3.58608e11	−0.633673	−0.316837	−	0.948480i	$-0.602621\pi$
$409$	−3.58608e11	−0.633673	−0.316837	+	0.948480i	$0.602621\pi$
$410$	7.91200e10	0.138280
$411$	8.45516e10	0.146162
$412$	−3.73677e11	−0.638939
$413$	2.02855e11	0.343091
$414$	−2.06476e10	−0.0345437
$415$	6.47039e10	0.107081
$416$	1.71258e11	0.280370
$417$	−7.45099e10	−0.120671
$418$	2.48294e11	0.397808
$419$	5.22372e11	0.827974	0.413987	−	0.910283i	$-0.364136\pi$
$419$	5.22372e11	0.827974	0.413987	+	0.910283i	$0.364136\pi$
$420$	6.81723e9	0.0106902
$421$	−5.33247e11	−0.827292	−0.413646	−	0.910438i	$-0.635745\pi$
$421$	−5.33247e11	−0.827292	−0.413646	+	0.910438i	$0.635745\pi$
$422$	1.68789e11	0.259082
$423$	4.89330e10	0.0743140
$424$	7.62701e11	1.14606
$425$	4.83172e11	0.718375
$426$	4.70294e10	0.0691874
$427$	1.87889e11	0.273511
$428$	−5.56404e11	−0.801481
$429$	2.60755e10	0.0371684
$430$	−6.87439e10	−0.0969675
$431$	1.19385e12	1.66648	0.833242	−	0.552909i	$-0.186482\pi$
$431$	1.19385e12	1.66648	0.833242	+	0.552909i	$0.186482\pi$
$432$	9.84832e9	0.0136046
$433$	4.83294e11	0.660717	0.330359	−	0.943855i	$-0.392830\pi$
$433$	4.83294e11	0.660717	0.330359	+	0.943855i	$0.392830\pi$
$434$	−2.98952e11	−0.404481
$435$	1.46060e10	0.0195582
$436$	1.90318e11	0.252226
$437$	4.00315e10	0.0525092
$438$	1.23699e11	0.160595
$439$	2.29672e11	0.295133	0.147567	−	0.989052i	$-0.452856\pi$
$439$	2.29672e11	0.295133	0.147567	+	0.989052i	$0.452856\pi$
$440$	1.41815e11	0.180379
$441$	−1.09760e11	−0.138188
$442$	−1.02828e11	−0.128148
$443$	−1.19208e12	−1.47058	−0.735289	−	0.677753i	$-0.762954\pi$
$443$	−1.19208e12	−1.47058	−0.735289	+	0.677753i	$0.762954\pi$
$444$	−8.59187e10	−0.104922
$445$	−8.41600e10	−0.101739
$446$	−6.47905e11	−0.775362
$447$	9.24065e10	0.109476
$448$	1.84483e11	0.216374
$449$	8.92348e11	1.03616	0.518079	−	0.855333i	$-0.326648\pi$
$449$	8.92348e11	1.03616	0.518079	+	0.855333i	$0.326648\pi$
$450$	−4.77498e11	−0.548927
$451$	−6.05069e11	−0.688669
$452$	−4.03805e11	−0.455039
$453$	−1.59346e11	−0.177787
$454$	−7.55330e11	−0.834422
$455$	−2.36101e10	−0.0258254
$456$	1.46475e11	0.158643
$457$	−1.16145e12	−1.24560	−0.622800	−	0.782381i	$-0.714005\pi$
$457$	−1.16145e12	−1.24560	−0.622800	+	0.782381i	$0.714005\pi$
$458$	−2.31126e10	−0.0245445
$459$	−2.58679e11	−0.272022
$460$	8.88013e9	0.00924718
$461$	−9.51529e11	−0.981223	−0.490612	−	0.871378i	$-0.663227\pi$
$461$	−9.51529e11	−0.981223	−0.490612	+	0.871378i	$0.663227\pi$
$462$	2.99658e10	0.0306011
$463$	−7.31799e11	−0.740078	−0.370039	−	0.929016i	$-0.620656\pi$
$463$	−7.31799e11	−0.740078	−0.370039	+	0.929016i	$0.620656\pi$
$464$	−1.67699e10	−0.0167957
$465$	−7.95425e10	−0.0788971
$466$	−3.10941e11	−0.305451
$467$	2.57187e10	0.0250221	0.0125111	−	0.999922i	$-0.496018\pi$
$467$	2.57187e10	0.0250221	0.0125111	+	0.999922i	$0.496018\pi$
$468$	−1.76800e11	−0.170363
$469$	1.63114e11	0.155673
$470$	1.20963e10	0.0114343
$471$	−2.28676e11	−0.214105
$472$	9.66848e11	0.896643
$473$	5.25718e11	0.482923
$474$	1.90314e11	0.173168
$475$	9.25770e11	0.834415
$476$	2.05592e11	0.183559
$477$	−1.26896e12	−1.12231
$478$	−4.24651e11	−0.372055
$479$	1.51678e12	1.31647	0.658237	−	0.752811i	$-0.271302\pi$
$479$	1.51678e12	1.31647	0.658237	+	0.752811i	$0.271302\pi$
$480$	5.23652e10	0.0450254
$481$	2.97562e11	0.253469
$482$	−6.35152e11	−0.536002
$483$	4.83127e9	0.00403924
$484$	3.45415e11	0.286113
$485$	−3.70362e11	−0.303941
$486$	3.85586e11	0.313514
$487$	−2.24128e12	−1.80558	−0.902788	−	0.430085i	$-0.858484\pi$
$487$	−2.24128e12	−1.80558	−0.902788	+	0.430085i	$0.858484\pi$
$488$	8.95518e11	0.714801
$489$	9.32097e10	0.0737176
$490$	−2.71326e10	−0.0212622
$491$	−1.10031e12	−0.854375	−0.427187	−	0.904163i	$-0.640496\pi$
$491$	−1.10031e12	−0.854375	−0.427187	+	0.904163i	$0.640496\pi$
$492$	−1.38632e11	−0.106665
$493$	4.40483e11	0.335829
$494$	−1.97022e11	−0.148848
$495$	−2.35948e11	−0.176642
$496$	9.13269e10	0.0677534
$497$	3.25652e11	0.239415
$498$	6.51638e10	0.0474760
$499$	−1.82750e11	−0.131948	−0.0659742	−	0.997821i	$-0.521016\pi$
$499$	−1.82750e11	−0.131948	−0.0659742	+	0.997821i	$0.521016\pi$
$500$	4.23994e11	0.303385
$501$	3.89205e11	0.275999
$502$	−6.48383e11	−0.455685
$503$	−2.30735e12	−1.60715	−0.803577	−	0.595201i	$-0.797072\pi$
$503$	−2.30735e12	−1.60715	−0.803577	+	0.595201i	$0.797072\pi$
$504$	−5.23138e11	−0.361143
$505$	−5.05475e11	−0.345851
$506$	3.90335e10	0.0264704
$507$	−2.06909e10	−0.0139073
$508$	4.33672e11	0.288918
$509$	1.53929e12	1.01646	0.508229	−	0.861222i	$-0.330300\pi$
$509$	1.53929e12	1.01646	0.508229	+	0.861222i	$0.330300\pi$
$510$	−3.14415e10	−0.0205796
$511$	8.56547e11	0.555721
$512$	−1.18872e11	−0.0764479
$513$	−4.95636e11	−0.315962
$514$	−7.54322e11	−0.476676
$515$	3.95711e11	0.247882
$516$	1.20451e11	0.0747975
$517$	−9.25060e10	−0.0569459
$518$	3.41957e11	0.208683
$519$	−2.64236e11	−0.159860
$520$	−1.12531e11	−0.0674926
$521$	1.17958e12	0.701387	0.350694	−	0.936490i	$-0.385946\pi$
$521$	1.17958e12	0.701387	0.350694	+	0.936490i	$0.385946\pi$
$522$	−4.35310e11	−0.256615
$523$	8.13940e11	0.475702	0.237851	−	0.971302i	$-0.423557\pi$
$523$	8.13940e11	0.475702	0.237851	+	0.971302i	$0.423557\pi$
$524$	−3.58012e11	−0.207447
$525$	1.11728e11	0.0641868
$526$	−5.83518e11	−0.332367
$527$	−2.39882e12	−1.35472
$528$	−9.15426e9	−0.00512590
$529$	−1.79486e12	−0.996506
$530$	−3.13686e11	−0.172685
$531$	−1.60861e12	−0.878063
$532$	3.93920e11	0.213209
$533$	4.80123e11	0.257680
$534$	−8.47582e10	−0.0451072
$535$	5.89212e11	0.310942
$536$	7.77436e11	0.406840
$537$	−5.66452e11	−0.293953
$538$	6.32309e11	0.325394
$539$	2.07496e11	0.105891
$540$	−1.09946e11	−0.0556428
$541$	−3.34130e12	−1.67698	−0.838490	−	0.544917i	$-0.816561\pi$
$541$	−3.34130e12	−1.67698	−0.838490	+	0.544917i	$0.816561\pi$
$542$	1.07028e12	0.532722
$543$	4.36195e11	0.215319
$544$	1.57922e12	0.773120
$545$	−2.01540e11	−0.0978535
$546$	−2.37779e10	−0.0114500
$547$	−2.94428e12	−1.40616	−0.703082	−	0.711109i	$-0.748193\pi$
$547$	−2.94428e12	−1.40616	−0.703082	+	0.711109i	$0.748193\pi$
$548$	1.08378e12	0.513367
$549$	−1.48993e12	−0.699990
$550$	9.02690e11	0.420636
$551$	8.43977e11	0.390075
$552$	2.30269e10	0.0105562
$553$	1.31782e12	0.599228
$554$	9.03171e11	0.407358
$555$	9.09848e10	0.0407053
$556$	−9.55064e11	−0.423834
$557$	2.56260e12	1.12806	0.564029	−	0.825755i	$-0.309251\pi$
$557$	2.56260e12	1.12806	0.564029	+	0.825755i	$0.309251\pi$
$558$	2.37065e12	1.03518
$559$	−4.17158e11	−0.180696
$560$	8.28874e9	0.00356158
$561$	2.40449e11	0.102492
$562$	−9.63893e11	−0.407582
$563$	−1.62703e10	−0.00682507	−0.00341253	−	0.999994i	$-0.501086\pi$
$563$	−1.62703e10	−0.00682507	−0.00341253	+	0.999994i	$0.501086\pi$
$564$	−2.11947e10	−0.00882006
$565$	4.27615e11	0.176537
$566$	1.56885e12	0.642550
$567$	8.39975e11	0.341305
$568$	1.55213e12	0.625691
$569$	−4.46269e12	−1.78481	−0.892404	−	0.451237i	$-0.850983\pi$
$569$	−4.46269e12	−1.78481	−0.892404	+	0.451237i	$0.850983\pi$
$570$	−6.02428e10	−0.0239039
$571$	−9.67227e11	−0.380773	−0.190386	−	0.981709i	$-0.560974\pi$
$571$	−9.67227e11	−0.380773	−0.190386	+	0.981709i	$0.560974\pi$
$572$	3.34234e11	0.130547
$573$	3.84637e11	0.149058
$574$	5.51755e11	0.212150
$575$	1.45537e11	0.0555225
$576$	−1.46293e12	−0.553760
$577$	4.50725e12	1.69286	0.846429	−	0.532502i	$-0.178748\pi$
$577$	4.50725e12	1.69286	0.846429	+	0.532502i	$0.178748\pi$
$578$	6.72915e11	0.250775
$579$	−8.85336e11	−0.327382
$580$	1.87218e11	0.0686946
$581$	4.51223e11	0.164285
$582$	−3.72994e11	−0.134756
$583$	2.39891e12	0.860015
$584$	4.08248e12	1.45233
$585$	1.87225e11	0.0660940
$586$	5.95420e11	0.208585
$587$	7.66315e11	0.266401	0.133201	−	0.991089i	$-0.457475\pi$
$587$	7.66315e11	0.266401	0.133201	+	0.991089i	$0.457475\pi$
$588$	4.75410e10	0.0164010
$589$	−4.59621e12	−1.57355
$590$	−3.97649e11	−0.135103
$591$	−7.78664e11	−0.262547
$592$	−1.04464e11	−0.0349559
$593$	2.26630e12	0.752613	0.376307	−	0.926495i	$-0.377194\pi$
$593$	2.26630e12	0.752613	0.376307	+	0.926495i	$0.377194\pi$
$594$	−4.83280e11	−0.159279
$595$	−2.17715e11	−0.0712134
$596$	1.18446e12	0.384514
$597$	−3.85063e11	−0.124064
$598$	−3.09731e10	−0.00990443
$599$	−1.58944e12	−0.504456	−0.252228	−	0.967668i	$-0.581163\pi$
$599$	−1.58944e12	−0.504456	−0.252228	+	0.967668i	$0.581163\pi$
$600$	5.32520e11	0.167747
$601$	−1.98361e11	−0.0620186	−0.0310093	−	0.999519i	$-0.509872\pi$
$601$	−1.98361e11	−0.0620186	−0.0310093	+	0.999519i	$0.509872\pi$
$602$	−4.79396e11	−0.148768
$603$	−1.29347e12	−0.398410
$604$	−2.04249e12	−0.624445
$605$	−3.65782e11	−0.111000
$606$	−5.09068e11	−0.153338
$607$	−2.18380e11	−0.0652927	−0.0326463	−	0.999467i	$-0.510393\pi$
$607$	−2.18380e11	−0.0652927	−0.0326463	+	0.999467i	$0.510393\pi$
$608$	3.02582e12	0.898003
$609$	1.01857e11	0.0300063
$610$	−3.68312e11	−0.107704
$611$	7.34036e10	0.0213075
$612$	−1.63032e12	−0.469777
$613$	−5.97188e12	−1.70820	−0.854100	−	0.520108i	$-0.825892\pi$
$613$	−5.97188e12	−1.70820	−0.854100	+	0.520108i	$0.825892\pi$
$614$	1.56948e12	0.445653
$615$	1.46806e11	0.0413815
$616$	9.88971e11	0.276739
$617$	−3.68385e12	−1.02334	−0.511668	−	0.859183i	$-0.670972\pi$
$617$	−3.68385e12	−1.02334	−0.511668	+	0.859183i	$0.670972\pi$
$618$	3.98523e11	0.109902
$619$	1.97374e12	0.540358	0.270179	−	0.962810i	$-0.412917\pi$
$619$	1.97374e12	0.540358	0.270179	+	0.962810i	$0.412917\pi$
$620$	−1.01957e12	−0.277112
$621$	−7.79173e10	−0.0210243
$622$	−2.30260e12	−0.616824
$623$	−5.86903e11	−0.156088
$624$	7.26391e9	0.00191796
$625$	3.13418e12	0.821607
$626$	1.02635e12	0.267124
$627$	4.60706e11	0.119047
$628$	−2.93115e12	−0.752003
$629$	2.74390e12	0.698940
$630$	2.15158e11	0.0544158
$631$	6.42247e12	1.61276	0.806381	−	0.591397i	$-0.201423\pi$
$631$	6.42247e12	1.61276	0.806381	+	0.591397i	$0.201423\pi$
$632$	6.28100e12	1.56604
$633$	3.13185e11	0.0775326
$634$	2.94167e12	0.723089
$635$	−4.59243e11	−0.112088
$636$	5.49633e11	0.133203
$637$	−1.64648e11	−0.0396214
$638$	8.22936e11	0.196641
$639$	−2.58238e12	−0.612726
$640$	6.95377e11	0.163836
$641$	7.58350e12	1.77422	0.887112	−	0.461555i	$-0.152708\pi$
$641$	7.58350e12	1.77422	0.887112	+	0.461555i	$0.152708\pi$
$642$	5.93399e11	0.137860
$643$	−6.67455e12	−1.53983	−0.769915	−	0.638147i	$-0.779701\pi$
$643$	−6.67455e12	−1.53983	−0.769915	+	0.638147i	$0.779701\pi$
$644$	6.19270e10	0.0141871
$645$	−1.27553e11	−0.0290184
$646$	−1.81679e12	−0.410448
$647$	−4.16412e12	−0.934229	−0.467115	−	0.884197i	$-0.654706\pi$
$647$	−4.16412e12	−0.934229	−0.467115	+	0.884197i	$0.654706\pi$
$648$	4.00350e12	0.891974
$649$	3.04102e12	0.672849
$650$	−7.16286e11	−0.157390
$651$	−5.54701e11	−0.121044
$652$	1.19476e12	0.258920
$653$	−4.52867e12	−0.974679	−0.487339	−	0.873213i	$-0.662033\pi$
$653$	−4.52867e12	−0.974679	−0.487339	+	0.873213i	$0.662033\pi$
$654$	−2.02972e11	−0.0433847
$655$	3.79121e11	0.0804808
$656$	−1.68556e11	−0.0355366
$657$	−6.79231e12	−1.42224
$658$	8.43551e10	0.0175426
$659$	3.08046e12	0.636254	0.318127	−	0.948048i	$-0.396946\pi$
$659$	3.08046e12	0.636254	0.318127	+	0.948048i	$0.396946\pi$
$660$	1.02198e11	0.0209650
$661$	1.11184e12	0.226535	0.113268	−	0.993565i	$-0.463868\pi$
$661$	1.11184e12	0.226535	0.113268	+	0.993565i	$0.463868\pi$
$662$	5.13166e12	1.03848
$663$	−1.90796e11	−0.0383494
$664$	2.15062e12	0.429346
$665$	−4.17147e11	−0.0827165
$666$	−2.71167e12	−0.534077
$667$	1.32679e11	0.0259559
$668$	4.98880e12	0.969398
$669$	−1.20218e12	−0.232034
$670$	−3.19747e11	−0.0613013
$671$	2.81666e12	0.536393
$672$	3.65177e11	0.0690783
$673$	6.85143e12	1.28740	0.643700	−	0.765278i	$-0.277399\pi$
$673$	6.85143e12	1.28740	0.643700	+	0.765278i	$0.277399\pi$
$674$	5.19312e11	0.0969302
$675$	−1.80192e12	−0.334094
$676$	−2.65215e11	−0.0488470
$677$	6.81551e12	1.24695	0.623475	−	0.781843i	$-0.285720\pi$
$677$	6.81551e12	1.24695	0.623475	+	0.781843i	$0.285720\pi$
$678$	4.30654e11	0.0782699
$679$	−2.58278e12	−0.466308
$680$	−1.03767e12	−0.186111
$681$	−1.40150e12	−0.249708
$682$	−4.48162e12	−0.793242
$683$	5.56934e12	0.979288	0.489644	−	0.871922i	$-0.337127\pi$
$683$	5.56934e12	0.979288	0.489644	+	0.871922i	$0.337127\pi$
$684$	−3.12374e12	−0.545660
$685$	−1.14768e12	−0.199165
$686$	−1.89213e11	−0.0326207
$687$	−4.28852e10	−0.00734517
$688$	1.46451e11	0.0249198
$689$	−1.90354e12	−0.321792
$690$	−9.47057e9	−0.00159058
$691$	6.68382e12	1.11525	0.557627	−	0.830092i	$-0.311712\pi$
$691$	6.68382e12	1.11525	0.557627	+	0.830092i	$0.311712\pi$
$692$	−3.38696e12	−0.561478
$693$	−1.64542e12	−0.271005
$694$	−6.90974e12	−1.13069
$695$	1.01138e12	0.164430
$696$	4.85471e11	0.0784191
$697$	4.42734e12	0.710551
$698$	3.10842e11	0.0495667
$699$	−5.76947e11	−0.0914089
$700$	1.43213e12	0.225445
$701$	1.03731e13	1.62247	0.811237	−	0.584718i	$-0.198795\pi$
$701$	1.03731e13	1.62247	0.811237	+	0.584718i	$0.198795\pi$
$702$	3.83483e11	0.0595976
$703$	5.25738e12	0.811840
$704$	2.76561e12	0.424340
$705$	2.24444e10	0.00342182
$706$	−6.71080e11	−0.101661
$707$	−3.52501e12	−0.530606
$708$	6.96749e11	0.104214
$709$	4.79725e12	0.712992	0.356496	−	0.934297i	$-0.383971\pi$
$709$	4.79725e12	0.712992	0.356496	+	0.934297i	$0.383971\pi$
$710$	−6.38365e11	−0.0942772
$711$	−1.04501e13	−1.53359
$712$	−2.79730e12	−0.407924
$713$	−7.22555e11	−0.104705
$714$	−2.19262e11	−0.0315734
$715$	−3.53941e11	−0.0506470
$716$	−7.26074e12	−1.03246
$717$	−7.87934e11	−0.111341
$718$	−2.42626e12	−0.340704
$719$	−1.36082e13	−1.89898	−0.949491	−	0.313793i	$-0.898400\pi$
$719$	−1.36082e13	−1.89898	−0.949491	+	0.313793i	$0.898400\pi$
$720$	−6.57287e10	−0.00911504
$721$	2.75955e12	0.380303
$722$	9.30194e11	0.127396
$723$	−1.17852e12	−0.160403
$724$	5.59112e12	0.756268
$725$	3.06834e12	0.412460
$726$	−3.68381e11	−0.0492134
$727$	3.58960e12	0.476586	0.238293	−	0.971193i	$-0.423412\pi$
$727$	3.58960e12	0.476586	0.238293	+	0.971193i	$0.423412\pi$
$728$	−7.84750e11	−0.103548
$729$	−6.17052e12	−0.809186
$730$	−1.67906e12	−0.218833
$731$	−3.84672e12	−0.498268
$732$	6.45346e11	0.0830793
$733$	−1.46498e13	−1.87441	−0.937203	−	0.348785i	$-0.886594\pi$
$733$	−1.46498e13	−1.87441	−0.937203	+	0.348785i	$0.886594\pi$
$734$	−7.44320e12	−0.946515
$735$	−5.03442e10	−0.00636291
$736$	4.75680e11	0.0597537
$737$	2.44526e12	0.305296
$738$	−4.37535e12	−0.542949
$739$	5.84726e12	0.721194	0.360597	−	0.932722i	$-0.382573\pi$
$739$	5.84726e12	0.721194	0.360597	+	0.932722i	$0.382573\pi$
$740$	1.16624e12	0.142970
$741$	−3.65571e11	−0.0445440
$742$	−2.18754e12	−0.264934
$743$	−1.00357e12	−0.120808	−0.0604041	−	0.998174i	$-0.519239\pi$
$743$	−1.00357e12	−0.120808	−0.0604041	+	0.998174i	$0.519239\pi$
$744$	−2.64383e12	−0.316340
$745$	−1.25430e12	−0.149176
$746$	4.51827e11	0.0534131
$747$	−3.57814e12	−0.420450
$748$	3.08206e12	0.359984
$749$	4.10896e12	0.477049
$750$	−4.52185e11	−0.0521844
$751$	−1.54982e13	−1.77787	−0.888937	−	0.458029i	$-0.848556\pi$
$751$	−1.54982e13	−1.77787	−0.888937	+	0.458029i	$0.848556\pi$
$752$	−2.57696e10	−0.00293852
$753$	−1.20307e12	−0.136368
$754$	−6.53001e11	−0.0735771
$755$	2.16292e12	0.242259
$756$	−7.66727e11	−0.0853675
$757$	8.62996e11	0.0955163	0.0477581	−	0.998859i	$-0.484792\pi$
$757$	8.62996e11	0.0955163	0.0477581	+	0.998859i	$0.484792\pi$
$758$	−4.06430e12	−0.447171
$759$	7.24261e10	0.00792150
$760$	−1.98821e12	−0.216173
$761$	1.39902e13	1.51214	0.756070	−	0.654491i	$-0.227117\pi$
$761$	1.39902e13	1.51214	0.756070	+	0.654491i	$0.227117\pi$
$762$	−4.62507e11	−0.0496960
$763$	−1.40547e12	−0.150127
$764$	4.93026e12	0.523540
$765$	1.72645e12	0.182254
$766$	3.89917e12	0.409207
$767$	−2.41305e12	−0.251760
$768$	1.69817e12	0.176139
$769$	−2.49263e10	−0.00257033	−0.00128517	−	0.999999i	$-0.500409\pi$
$769$	−2.49263e10	−0.00257033	−0.00128517	+	0.999999i	$0.500409\pi$
$770$	−4.06748e11	−0.0416981
$771$	−1.39963e12	−0.142649
$772$	−1.13482e13	−1.14987
$773$	−1.97915e12	−0.199375	−0.0996874	−	0.995019i	$-0.531784\pi$
$773$	−1.97915e12	−0.199375	−0.0996874	+	0.995019i	$0.531784\pi$
$774$	3.80155e12	0.380738
$775$	−1.67098e13	−1.66385
$776$	−1.23101e13	−1.21866
$777$	6.34496e11	0.0624503
$778$	4.15260e12	0.406360
$779$	8.48290e12	0.825327
$780$	−8.10941e10	−0.00784447
$781$	4.88189e12	0.469525
$782$	−2.85611e11	−0.0273115
$783$	−1.64272e12	−0.156183
$784$	5.78028e10	0.00546420
$785$	3.10398e12	0.291747
$786$	3.81816e11	0.0356823
$787$	7.78419e12	0.723315	0.361657	−	0.932311i	$-0.382211\pi$
$787$	7.78419e12	0.723315	0.361657	+	0.932311i	$0.382211\pi$
$788$	−9.98087e12	−0.922148
$789$	−1.08271e12	−0.0994639
$790$	−2.58327e12	−0.235965
$791$	2.98203e12	0.270844
$792$	−7.84242e12	−0.708250
$793$	−2.23502e12	−0.200703
$794$	−6.38481e12	−0.570106
$795$	−5.82041e11	−0.0516775
$796$	−4.93571e12	−0.435754
$797$	−2.48855e12	−0.218466	−0.109233	−	0.994016i	$-0.534839\pi$
$797$	−2.48855e12	−0.218466	−0.109233	+	0.994016i	$0.534839\pi$
$798$	−4.20112e11	−0.0366735
$799$	6.76874e11	0.0587553
$800$	1.10006e13	0.949536
$801$	4.65406e12	0.399472
$802$	−3.64618e12	−0.311210
$803$	1.28406e13	1.08985
$804$	5.60252e11	0.0472858
$805$	−6.55784e10	−0.00550401
$806$	3.55617e12	0.296808
$807$	1.17324e12	0.0973770
$808$	−1.68009e13	−1.38670
$809$	−2.01587e13	−1.65461	−0.827303	−	0.561756i	$-0.810126\pi$
$809$	−2.01587e13	−1.65461	−0.827303	+	0.561756i	$0.810126\pi$
$810$	−1.64657e12	−0.134400
$811$	1.64515e13	1.33540	0.667701	−	0.744429i	$-0.267278\pi$
$811$	1.64515e13	1.33540	0.667701	+	0.744429i	$0.267278\pi$
$812$	1.30560e12	0.105392
$813$	1.98589e12	0.159422
$814$	5.12631e12	0.409256
$815$	−1.26520e12	−0.100450
$816$	6.69824e10	0.00528878
$817$	−7.37043e12	−0.578753
$818$	4.90225e12	0.382830
$819$	1.30564e12	0.101402
$820$	1.88175e12	0.145345
$821$	9.70619e11	0.0745598	0.0372799	−	0.999305i	$-0.488131\pi$
$821$	9.70619e11	0.0745598	0.0372799	+	0.999305i	$0.488131\pi$
$822$	−1.15584e12	−0.0883026
$823$	−9.19346e12	−0.698521	−0.349261	−	0.937026i	$-0.613567\pi$
$823$	−9.19346e12	−0.698521	−0.349261	+	0.937026i	$0.613567\pi$
$824$	1.31526e13	0.993891
$825$	1.67493e12	0.125879
$826$	−2.77306e12	−0.207276
$827$	−2.59018e12	−0.192555	−0.0962777	−	0.995355i	$-0.530694\pi$
$827$	−2.59018e12	−0.192555	−0.0962777	+	0.995355i	$0.530694\pi$
$828$	−4.91073e11	−0.0363086
$829$	4.87377e12	0.358401	0.179201	−	0.983813i	$-0.442649\pi$
$829$	4.87377e12	0.358401	0.179201	+	0.983813i	$0.442649\pi$
$830$	−8.84516e11	−0.0646925
$831$	1.67582e12	0.121906
$832$	−2.19451e12	−0.158775
$833$	−1.51827e12	−0.109256
$834$	1.01857e12	0.0729024
$835$	−5.28296e12	−0.376087
$836$	5.90530e12	0.418133
$837$	8.94606e12	0.630039
$838$	−7.14093e12	−0.500215
$839$	−8.17102e11	−0.0569308	−0.0284654	−	0.999595i	$-0.509062\pi$
$839$	−8.17102e11	−0.0569308	−0.0284654	+	0.999595i	$0.509062\pi$
$840$	−2.39951e11	−0.0166290
$841$	−1.17099e13	−0.807182
$842$	7.28959e12	0.499803
$843$	−1.78849e12	−0.121973
$844$	4.01439e12	0.272319
$845$	2.80853e11	0.0189506
$846$	−6.68925e11	−0.0448963
$847$	−2.55083e12	−0.170297
$848$	6.68272e11	0.0443784
$849$	2.91098e12	0.192289
$850$	−6.60506e12	−0.434002
$851$	8.26496e11	0.0540204
$852$	1.11853e12	0.0727223
$853$	−1.31617e13	−0.851220	−0.425610	−	0.904907i	$-0.639941\pi$
$853$	−1.31617e13	−0.851220	−0.425610	+	0.904907i	$0.639941\pi$
$854$	−2.56848e12	−0.165240
$855$	3.30792e12	0.211694
$856$	1.95842e13	1.24673
$857$	3.09182e13	1.95795	0.978974	−	0.203986i	$-0.0653897\pi$
$857$	3.09182e13	1.95795	0.978974	+	0.203986i	$0.0653897\pi$
$858$	−3.56457e11	−0.0224551
$859$	5.44277e12	0.341075	0.170538	−	0.985351i	$-0.445450\pi$
$859$	5.44277e12	0.341075	0.170538	+	0.985351i	$0.445450\pi$
$860$	−1.63497e12	−0.101922
$861$	1.02377e12	0.0634877
$862$	−1.63201e13	−1.00680
$863$	1.82308e13	1.11881	0.559405	−	0.828895i	$-0.311030\pi$
$863$	1.82308e13	1.11881	0.559405	+	0.828895i	$0.311030\pi$
$864$	−5.88947e12	−0.359554
$865$	3.58667e12	0.217830
$866$	−6.60672e12	−0.399168
$867$	1.24858e12	0.0750468
$868$	−7.11013e12	−0.425147
$869$	1.97556e13	1.17517
$870$	−1.99666e11	−0.0118159
$871$	−1.94032e12	−0.114233
$872$	−6.69876e12	−0.392347
$873$	2.04811e13	1.19341
$874$	−5.47239e11	−0.0317231
$875$	−3.13113e12	−0.180578
$876$	2.94200e12	0.168801
$877$	1.71409e13	0.978441	0.489220	−	0.872160i	$-0.337281\pi$
$877$	1.71409e13	0.978441	0.489220	+	0.872160i	$0.337281\pi$
$878$	−3.13967e12	−0.178303
$879$	1.10479e12	0.0624211
$880$	1.24257e11	0.00698474
$881$	3.21025e13	1.79534	0.897670	−	0.440668i	$-0.145258\pi$
$881$	3.21025e13	1.79534	0.897670	+	0.440668i	$0.145258\pi$
$882$	1.50044e12	0.0834851
$883$	2.16643e13	1.19928	0.599641	−	0.800269i	$-0.295310\pi$
$883$	2.16643e13	1.19928	0.599641	+	0.800269i	$0.295310\pi$
$884$	−2.44562e12	−0.134695
$885$	−7.37832e11	−0.0404308
$886$	1.62960e13	0.888441
$887$	−1.98878e13	−1.07877	−0.539386	−	0.842059i	$-0.681344\pi$
$887$	−1.98878e13	−1.07877	−0.539386	+	0.842059i	$0.681344\pi$
$888$	3.02414e12	0.163209
$889$	−3.20260e12	−0.171967
$890$	1.15048e12	0.0614647
$891$	1.25922e13	0.669345
$892$	−1.54095e13	−0.814977
$893$	1.29691e12	0.0682461
$894$	−1.26322e12	−0.0661391
$895$	7.68886e12	0.400552
$896$	4.84932e12	0.251359
$897$	−5.74702e10	−0.00296399
$898$	−1.21986e13	−0.625987
$899$	−1.52335e13	−0.777824
$900$	−1.13566e13	−0.576974
$901$	−1.75530e13	−0.887342
$902$	8.27142e12	0.416055
$903$	−8.89513e11	−0.0445202
$904$	1.42130e13	0.707829
$905$	−5.92079e12	−0.293401
$906$	2.17830e12	0.107409
$907$	−3.25195e13	−1.59555	−0.797775	−	0.602955i	$-0.793990\pi$
$907$	−3.25195e13	−1.59555	−0.797775	+	0.602955i	$0.793990\pi$
$908$	−1.79644e13	−0.877054
$909$	2.79529e13	1.35797
$910$	3.22755e11	0.0156022
$911$	2.83544e13	1.36392	0.681959	−	0.731390i	$-0.261128\pi$
$911$	2.83544e13	1.36392	0.681959	+	0.731390i	$0.261128\pi$
$912$	1.28340e11	0.00614307
$913$	6.76433e12	0.322186
$914$	1.58773e13	0.752521
$915$	−6.83398e11	−0.0322314
$916$	−5.49700e11	−0.0257986
$917$	2.64386e12	0.123474
$918$	3.53620e12	0.164340
$919$	3.32705e13	1.53865	0.769324	−	0.638859i	$-0.220593\pi$
$919$	3.32705e13	1.53865	0.769324	+	0.638859i	$0.220593\pi$
$920$	−3.12561e11	−0.0143843
$921$	2.91214e12	0.133366
$922$	1.30076e13	0.592800
$923$	−3.87379e12	−0.175682
$924$	7.12692e11	0.0321646
$925$	1.91136e13	0.858429
$926$	1.00038e13	0.447113
$927$	−2.18829e13	−0.973297
$928$	1.00287e13	0.443893
$929$	−1.19302e13	−0.525505	−0.262753	−	0.964863i	$-0.584630\pi$
$929$	−1.19302e13	−0.525505	−0.262753	+	0.964863i	$0.584630\pi$
$930$	1.08736e12	0.0476651
$931$	−2.90904e12	−0.126904
$932$	−7.39527e12	−0.321057
$933$	−4.27244e12	−0.184590
$934$	−3.51581e11	−0.0151169
$935$	−3.26379e12	−0.139659
$936$	6.22296e12	0.265006
$937$	1.60828e13	0.681606	0.340803	−	0.940135i	$-0.389301\pi$
$937$	1.60828e13	0.681606	0.340803	+	0.940135i	$0.389301\pi$
$938$	−2.22980e12	−0.0940489
$939$	1.90439e12	0.0799393
$940$	2.87691e11	0.0120185
$941$	6.13920e11	0.0255246	0.0127623	−	0.999919i	$-0.495938\pi$
$941$	6.13920e11	0.0255246	0.0127623	+	0.999919i	$0.495938\pi$
$942$	3.12604e12	0.129350
$943$	1.33357e12	0.0549178
$944$	8.47144e11	0.0347203
$945$	8.11936e11	0.0331191
$946$	−7.18668e12	−0.291755
$947$	2.19411e13	0.886511	0.443256	−	0.896395i	$-0.353823\pi$
$947$	2.19411e13	0.886511	0.443256	+	0.896395i	$0.353823\pi$
$948$	4.52634e12	0.182016
$949$	−1.01890e13	−0.407788
$950$	−1.26555e13	−0.504106
$951$	5.45822e12	0.216391
$952$	−7.23638e12	−0.285532
$953$	−2.82211e13	−1.10830	−0.554148	−	0.832418i	$-0.686956\pi$
$953$	−2.82211e13	−1.10830	−0.554148	+	0.832418i	$0.686956\pi$
$954$	1.73469e13	0.678039
$955$	−5.22096e12	−0.203112
$956$	−1.00997e13	−0.391064
$957$	1.52695e12	0.0588464
$958$	−2.07347e13	−0.795339
$959$	−8.00352e12	−0.305561
$960$	−6.71010e11	−0.0254982
$961$	5.65204e13	2.13772
$962$	−4.06773e12	−0.153132
$963$	−3.25835e13	−1.22090
$964$	−1.51062e13	−0.563388
$965$	1.20173e13	0.446102
$966$	−6.60445e10	−0.00244028
$967$	−1.06711e13	−0.392456	−0.196228	−	0.980558i	$-0.562869\pi$
$967$	−1.06711e13	−0.392456	−0.196228	+	0.980558i	$0.562869\pi$
$968$	−1.21578e13	−0.445058
$969$	−3.37102e12	−0.122830
$970$	5.06293e12	0.183624
$971$	−1.12577e13	−0.406409	−0.203204	−	0.979136i	$-0.565136\pi$
$971$	−1.12577e13	−0.406409	−0.203204	+	0.979136i	$0.565136\pi$
$972$	9.17058e12	0.329533
$973$	7.05299e12	0.252270
$974$	3.06388e13	1.09083
$975$	−1.32906e12	−0.0471003
$976$	7.84645e11	0.0276789
$977$	−2.70189e13	−0.948730	−0.474365	−	0.880328i	$-0.657322\pi$
$977$	−2.70189e13	−0.948730	−0.474365	+	0.880328i	$0.657322\pi$
$978$	−1.27420e12	−0.0445360
$979$	−8.79832e12	−0.306110
$980$	−6.45308e11	−0.0223486
$981$	1.11452e13	0.384217
$982$	1.50415e13	0.516165
$983$	3.03511e13	1.03677	0.518386	−	0.855147i	$-0.326533\pi$
$983$	3.03511e13	1.03677	0.518386	+	0.855147i	$0.326533\pi$
$984$	4.87952e12	0.165920
$985$	1.05694e13	0.357756
$986$	−6.02149e12	−0.202889
$987$	1.56520e11	0.00524979
$988$	−4.68587e12	−0.156453
$989$	−1.15868e12	−0.0385106
$990$	3.22546e12	0.106717
$991$	−2.38842e13	−0.786647	−0.393324	−	0.919400i	$-0.628675\pi$
$991$	−2.38842e13	−0.786647	−0.393324	+	0.919400i	$0.628675\pi$
$992$	−5.46151e13	−1.79065
$993$	9.52173e12	0.310774
$994$	−4.45174e12	−0.144641
$995$	5.22674e12	0.169055
$996$	1.54982e12	0.0499017
$997$	−5.34756e13	−1.71407	−0.857033	−	0.515262i	$-0.827695\pi$
$997$	−5.34756e13	−1.71407	−0.857033	+	0.515262i	$0.827695\pi$
$998$	2.49823e12	0.0797158
$999$	−1.02330e13	−0.325055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.c.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.c.1.6	✓	14	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-13.6702 q^{2} -25.3649 q^{3} -325.126 q^{4} +344.296 q^{5} +346.743 q^{6} +2401.00 q^{7} +11443.7 q^{8} -19039.6 q^{9} +O(q^{10})\)	\(q-13.6702 q^{2} -25.3649 q^{3} -325.126 q^{4} +344.296 q^{5} +346.743 q^{6} +2401.00 q^{7} +11443.7 q^{8} -19039.6 q^{9} -4706.60 q^{10} +35993.7 q^{11} +8246.77 q^{12} -28561.0 q^{13} -32822.2 q^{14} -8733.03 q^{15} +10026.8 q^{16} -263368. q^{17} +260276. q^{18} -504621. q^{19} -111939. q^{20} -60901.1 q^{21} -492041. q^{22} -79329.8 q^{23} -290267. q^{24} -1.83459e6 q^{25} +390435. q^{26} +982195. q^{27} -780626. q^{28} -1.67250e6 q^{29} +119382. q^{30} +9.10824e6 q^{31} -5.99623e6 q^{32} -912974. q^{33} +3.60030e6 q^{34} +826655. q^{35} +6.19027e6 q^{36} -1.04185e7 q^{37} +6.89827e6 q^{38} +724446. q^{39} +3.94001e6 q^{40} -1.68104e7 q^{41} +832530. q^{42} +1.46059e7 q^{43} -1.17025e7 q^{44} -6.55527e6 q^{45} +1.08446e6 q^{46} -2.57006e6 q^{47} -254330. q^{48} +5.76480e6 q^{49} +2.50792e7 q^{50} +6.68031e6 q^{51} +9.28591e6 q^{52} +6.66482e7 q^{53} -1.34268e7 q^{54} +1.23925e7 q^{55} +2.74763e7 q^{56} +1.27996e7 q^{57} +2.28634e7 q^{58} +8.44876e7 q^{59} +2.83933e6 q^{60} +7.82544e7 q^{61} -1.24511e8 q^{62} -4.57141e7 q^{63} +7.68360e7 q^{64} -9.83344e6 q^{65} +1.24805e7 q^{66} +6.79359e7 q^{67} +8.56278e7 q^{68} +2.01219e6 q^{69} -1.13005e7 q^{70} +1.35632e8 q^{71} -2.17883e8 q^{72} +3.56746e8 q^{73} +1.42423e8 q^{74} +4.65340e7 q^{75} +1.64065e8 q^{76} +8.64208e7 q^{77} -9.90333e6 q^{78} +5.48862e8 q^{79} +3.45220e6 q^{80} +3.49844e8 q^{81} +2.29802e8 q^{82} +1.87931e8 q^{83} +1.98005e7 q^{84} -9.06767e7 q^{85} -1.99665e8 q^{86} +4.24227e7 q^{87} +4.11900e8 q^{88} -2.44441e8 q^{89} +8.96118e7 q^{90} -6.85750e7 q^{91} +2.57922e7 q^{92} -2.31029e8 q^{93} +3.51333e7 q^{94} -1.73739e8 q^{95} +1.52094e8 q^{96} -1.07571e9 q^{97} -7.88060e7 q^{98} -6.85306e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9}+O(q^{10}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9	\( 14 q + 27 q^{2} + 163 q^{3} + 2389 q^{4} + 2964 q^{5} + 471 q^{6} + 33614 q^{7} + 43263 q^{8} + 144129 q^{9} + 126524 q^{10} + 81825 q^{11} + 157399 q^{12} - 399854 q^{13} + 64827 q^{14} + 163856 q^{15} + 166361 q^{16} - 44922 q^{17} - 826396 q^{18} + 171756 q^{19} + 3899724 q^{20} + 391363 q^{21} + 917579 q^{22} + 1930479 q^{23} + 2992373 q^{24} + 8222344 q^{25} - 771147 q^{26} + 4139125 q^{27} + 5735989 q^{28} - 3799608 q^{29} - 5918004 q^{30} - 4392203 q^{31} + 3135663 q^{32} + 17499977 q^{33} - 20071132 q^{34} + 7116564 q^{35} + 2121398 q^{36} + 29198909 q^{37} - 44208366 q^{38} - 4655443 q^{39} + 134932928 q^{40} + 48410973 q^{41} + 1130871 q^{42} + 52650242 q^{43} - 14827353 q^{44} + 99215088 q^{45} - 34410455 q^{46} + 160580841 q^{47} + 227620515 q^{48} + 80707214 q^{49} + 149462949 q^{50} + 57114360 q^{51} - 68232229 q^{52} + 80753796 q^{53} + 301368833 q^{54} + 328919412 q^{55} + 103874463 q^{56} + 151101102 q^{57} + 335044204 q^{58} + 442445502 q^{59} + 561078360 q^{60} + 270199089 q^{61} + 543824517 q^{62} + 346053729 q^{63} + 223643137 q^{64} - 84654804 q^{65} + 317483345 q^{66} + 92500909 q^{67} + 255771204 q^{68} + 292017029 q^{69} + 303784124 q^{70} + 84383796 q^{71} + 1456696818 q^{72} + 367274315 q^{73} + 1091659407 q^{74} + 1154152501 q^{75} + 674789222 q^{76} + 196461825 q^{77} - 13452231 q^{78} + 434861545 q^{79} + 2644363752 q^{80} + 644207518 q^{81} + 634104331 q^{82} + 1013603934 q^{83} + 377914999 q^{84} + 1103701048 q^{85} + 2514069096 q^{86} + 1039292304 q^{87} + 1071310221 q^{88} + 1069739706 q^{89} - 1271572324 q^{90} - 960049454 q^{91} + 2301673917 q^{92} - 933838861 q^{93} + 2025486277 q^{94} + 2504029998 q^{95} - 116199027 q^{96} + 2839636281 q^{97} + 155649627 q^{98} + 5063037274 q^{99}+O(q^{100}) \) 14 * q + 27 * q^2 + 163 * q^3 + 2389 * q^4 + 2964 * q^5 + 471 * q^6 + 33614 * q^7 + 43263 * q^8 + 144129 * q^9 + 126524 * q^10 + 81825 * q^11 + 157399 * q^12 - 399854 * q^13 + 64827 * q^14 + 163856 * q^15 + 166361 * q^16 - 44922 * q^17 - 826396 * q^18 + 171756 * q^19 + 3899724 * q^20 + 391363 * q^21 + 917579 * q^22 + 1930479 * q^23 + 2992373 * q^24 + 8222344 * q^25 - 771147 * q^26 + 4139125 * q^27 + 5735989 * q^28 - 3799608 * q^29 - 5918004 * q^30 - 4392203 * q^31 + 3135663 * q^32 + 17499977 * q^33 - 20071132 * q^34 + 7116564 * q^35 + 2121398 * q^36 + 29198909 * q^37 - 44208366 * q^38 - 4655443 * q^39 + 134932928 * q^40 + 48410973 * q^41 + 1130871 * q^42 + 52650242 * q^43 - 14827353 * q^44 + 99215088 * q^45 - 34410455 * q^46 + 160580841 * q^47 + 227620515 * q^48 + 80707214 * q^49 + 149462949 * q^50 + 57114360 * q^51 - 68232229 * q^52 + 80753796 * q^53 + 301368833 * q^54 + 328919412 * q^55 + 103874463 * q^56 + 151101102 * q^57 + 335044204 * q^58 + 442445502 * q^59 + 561078360 * q^60 + 270199089 * q^61 + 543824517 * q^62 + 346053729 * q^63 + 223643137 * q^64 - 84654804 * q^65 + 317483345 * q^66 + 92500909 * q^67 + 255771204 * q^68 + 292017029 * q^69 + 303784124 * q^70 + 84383796 * q^71 + 1456696818 * q^72 + 367274315 * q^73 + 1091659407 * q^74 + 1154152501 * q^75 + 674789222 * q^76 + 196461825 * q^77 - 13452231 * q^78 + 434861545 * q^79 + 2644363752 * q^80 + 644207518 * q^81 + 634104331 * q^82 + 1013603934 * q^83 + 377914999 * q^84 + 1103701048 * q^85 + 2514069096 * q^86 + 1039292304 * q^87 + 1071310221 * q^88 + 1069739706 * q^89 - 1271572324 * q^90 - 960049454 * q^91 + 2301673917 * q^92 - 933838861 * q^93 + 2025486277 * q^94 + 2504029998 * q^95 - 116199027 * q^96 + 2839636281 * q^97 + 155649627 * q^98 + 5063037274 * q^99

Introduction

L-functions

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