LMFDB - Embedded newform 19.12.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,12,Mod(1,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("19.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	19.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:	$14.5985204306$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 10491x^{5} + 5390x^{4} + 33206195x^{3} + 155482410x^{2} - 32794886585x - 417193412918 $ x^7 - 2x^6 - 10491x^5 + 5390x^4 + 33206195x^3 + 155482410x^2 - 32794886585x - 417193412918
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-76.9480$ of defining polynomial
Character	$\chi$	$=$	19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+75.9480 q^{2} -578.534 q^{3} +3720.10 q^{4} -559.147 q^{5} -43938.5 q^{6} -42737.5 q^{7} +126992. q^{8} +157554. q^{9} +O(q^{10})$	\(q+75.9480 q^{2} -578.534 q^{3} +3720.10 q^{4} -559.147 q^{5} -43938.5 q^{6} -42737.5 q^{7} +126992. q^{8} +157554. q^{9} -42466.1 q^{10} -760245. q^{11} -2.15220e6 q^{12} -1.08264e6 q^{13} -3.24583e6 q^{14} +323485. q^{15} +2.02605e6 q^{16} -147825. q^{17} +1.19659e7 q^{18} +2.47610e6 q^{19} -2.08008e6 q^{20} +2.47251e7 q^{21} -5.77391e7 q^{22} +4.63915e7 q^{23} -7.34693e7 q^{24} -4.85155e7 q^{25} -8.22242e7 q^{26} +1.13352e7 q^{27} -1.58988e8 q^{28} -6.40882e7 q^{29} +2.45680e7 q^{30} +2.79716e8 q^{31} -1.06206e8 q^{32} +4.39827e8 q^{33} -1.12270e7 q^{34} +2.38966e7 q^{35} +5.86116e8 q^{36} -2.37124e8 q^{37} +1.88055e8 q^{38} +6.26342e8 q^{39} -7.10073e7 q^{40} -9.81332e8 q^{41} +1.87782e9 q^{42} +4.72722e7 q^{43} -2.82818e9 q^{44} -8.80959e7 q^{45} +3.52334e9 q^{46} +1.85661e9 q^{47} -1.17214e9 q^{48} -1.50830e8 q^{49} -3.68465e9 q^{50} +8.55218e7 q^{51} -4.02752e9 q^{52} -2.12327e9 q^{53} +8.60882e8 q^{54} +4.25088e8 q^{55} -5.42734e9 q^{56} -1.43251e9 q^{57} -4.86737e9 q^{58} -2.01394e9 q^{59} +1.20340e9 q^{60} +1.20487e10 q^{61} +2.12439e10 q^{62} -6.73347e9 q^{63} -1.22155e10 q^{64} +6.05353e8 q^{65} +3.34040e10 q^{66} -2.14288e10 q^{67} -5.49924e8 q^{68} -2.68390e10 q^{69} +1.81490e9 q^{70} +5.76489e9 q^{71} +2.00082e10 q^{72} -2.64202e10 q^{73} -1.80091e10 q^{74} +2.80678e10 q^{75} +9.21133e9 q^{76} +3.24910e10 q^{77} +4.75694e10 q^{78} -1.83608e10 q^{79} -1.13286e9 q^{80} -3.44680e10 q^{81} -7.45302e10 q^{82} -2.66752e10 q^{83} +9.19798e10 q^{84} +8.26560e7 q^{85} +3.59023e9 q^{86} +3.70772e10 q^{87} -9.65452e10 q^{88} +2.35606e10 q^{89} -6.69070e9 q^{90} +4.62693e10 q^{91} +1.72581e11 q^{92} -1.61825e11 q^{93} +1.41006e11 q^{94} -1.38450e9 q^{95} +6.14435e10 q^{96} -1.06270e10 q^{97} -1.14552e10 q^{98} -1.19780e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 9 q^{2} + 10 q^{3} + 6661 q^{4} - 14307 q^{5} - 66435 q^{6} - 2209 q^{7} - 72891 q^{8} + 346867 q^{9}+O(q^{10}) $ 7 * q - 9 * q^2 + 10 * q^3 + 6661 * q^4 - 14307 * q^5 - 66435 * q^6 - 2209 * q^7 - 72891 * q^8 + 346867 * q^9	\( 7 q - 9 q^{2} + 10 q^{3} + 6661 q^{4} - 14307 q^{5} - 66435 q^{6} - 2209 q^{7} - 72891 q^{8} + 346867 q^{9} + 610116 q^{10} - 1399461 q^{11} - 500945 q^{12} - 2639296 q^{13} - 6202863 q^{14} - 10553670 q^{15} - 11910239 q^{16} - 9760773 q^{17} - 27428622 q^{18} + 17332693 q^{19} - 60822132 q^{20} - 51652462 q^{21} - 96770562 q^{22} - 117151884 q^{23} - 129456201 q^{24} - 40644056 q^{25} - 140205807 q^{26} + 123768280 q^{27} - 95042353 q^{28} - 380102178 q^{29} + 336001500 q^{30} + 108083372 q^{31} + 639362133 q^{32} + 292307766 q^{33} + 632902677 q^{34} + 258176013 q^{35} + 1082564974 q^{36} + 470630222 q^{37} - 22284891 q^{38} + 1096564364 q^{39} + 1263596868 q^{40} - 572622810 q^{41} + 3526613691 q^{42} + 1170836039 q^{43} + 1857175194 q^{44} + 325468269 q^{45} + 6333771957 q^{46} - 3485769735 q^{47} - 3849252725 q^{48} + 2791682862 q^{49} - 6699338667 q^{50} - 3006308190 q^{51} - 4968372073 q^{52} - 9143305584 q^{53} - 8531659545 q^{54} - 18483973467 q^{55} - 11872570905 q^{56} + 24760990 q^{57} + 10101698853 q^{58} - 847227714 q^{59} - 6348541140 q^{60} - 8144938567 q^{61} + 21626318880 q^{62} - 43596471133 q^{63} - 14662293047 q^{64} - 9033654252 q^{65} + 45199579482 q^{66} - 5797397824 q^{67} - 6895758945 q^{68} - 54587710308 q^{69} + 63346638156 q^{70} - 4538589186 q^{71} + 85775462646 q^{72} - 1815379657 q^{73} + 52966894338 q^{74} + 24070734700 q^{75} + 16493295439 q^{76} + 77952325659 q^{77} + 110360547051 q^{78} - 54907201480 q^{79} + 77197994292 q^{80} + 33147767443 q^{81} + 66047089392 q^{82} - 68609936724 q^{83} + 117356373533 q^{84} + 50328221961 q^{85} + 11262589308 q^{86} - 128062398816 q^{87} - 118799781006 q^{88} - 105124973892 q^{89} + 10463980248 q^{90} - 53584340240 q^{91} + 22337690499 q^{92} - 294151780936 q^{93} + 203078543976 q^{94} - 35425548393 q^{95} + 219060245223 q^{96} - 386940894664 q^{97} - 357308952786 q^{98} - 392424818133 q^{99}+O(q^{100}) \) 7 * q - 9 * q^2 + 10 * q^3 + 6661 * q^4 - 14307 * q^5 - 66435 * q^6 - 2209 * q^7 - 72891 * q^8 + 346867 * q^9 + 610116 * q^10 - 1399461 * q^11 - 500945 * q^12 - 2639296 * q^13 - 6202863 * q^14 - 10553670 * q^15 - 11910239 * q^16 - 9760773 * q^17 - 27428622 * q^18 + 17332693 * q^19 - 60822132 * q^20 - 51652462 * q^21 - 96770562 * q^22 - 117151884 * q^23 - 129456201 * q^24 - 40644056 * q^25 - 140205807 * q^26 + 123768280 * q^27 - 95042353 * q^28 - 380102178 * q^29 + 336001500 * q^30 + 108083372 * q^31 + 639362133 * q^32 + 292307766 * q^33 + 632902677 * q^34 + 258176013 * q^35 + 1082564974 * q^36 + 470630222 * q^37 - 22284891 * q^38 + 1096564364 * q^39 + 1263596868 * q^40 - 572622810 * q^41 + 3526613691 * q^42 + 1170836039 * q^43 + 1857175194 * q^44 + 325468269 * q^45 + 6333771957 * q^46 - 3485769735 * q^47 - 3849252725 * q^48 + 2791682862 * q^49 - 6699338667 * q^50 - 3006308190 * q^51 - 4968372073 * q^52 - 9143305584 * q^53 - 8531659545 * q^54 - 18483973467 * q^55 - 11872570905 * q^56 + 24760990 * q^57 + 10101698853 * q^58 - 847227714 * q^59 - 6348541140 * q^60 - 8144938567 * q^61 + 21626318880 * q^62 - 43596471133 * q^63 - 14662293047 * q^64 - 9033654252 * q^65 + 45199579482 * q^66 - 5797397824 * q^67 - 6895758945 * q^68 - 54587710308 * q^69 + 63346638156 * q^70 - 4538589186 * q^71 + 85775462646 * q^72 - 1815379657 * q^73 + 52966894338 * q^74 + 24070734700 * q^75 + 16493295439 * q^76 + 77952325659 * q^77 + 110360547051 * q^78 - 54907201480 * q^79 + 77197994292 * q^80 + 33147767443 * q^81 + 66047089392 * q^82 - 68609936724 * q^83 + 117356373533 * q^84 + 50328221961 * q^85 + 11262589308 * q^86 - 128062398816 * q^87 - 118799781006 * q^88 - 105124973892 * q^89 + 10463980248 * q^90 - 53584340240 * q^91 + 22337690499 * q^92 - 294151780936 * q^93 + 203078543976 * q^94 - 35425548393 * q^95 + 219060245223 * q^96 - 386940894664 * q^97 - 357308952786 * q^98 - 392424818133 * 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 $

$2$	75.9480	1.67823	0.839115	−	0.543955i	$-0.183074\pi$
$2$	75.9480	1.67823	0.839115	+	0.543955i	$0.183074\pi$
$3$	−578.534	−1.37455	−0.687277	−	0.726396i	$-0.741194\pi$
$3$	−578.534	−1.37455	−0.687277	+	0.726396i	$0.741194\pi$
$4$	3720.10	1.81645
$5$	−559.147	−0.0800186	−0.0400093	−	0.999199i	$-0.512739\pi$
$5$	−559.147	−0.0800186	−0.0400093	+	0.999199i	$0.512739\pi$
$6$	−43938.5	−2.30682
$7$	−42737.5	−0.961104	−0.480552	−	0.876966i	$-0.659564\pi$
$7$	−42737.5	−0.961104	−0.480552	+	0.876966i	$0.659564\pi$
$8$	126992.	1.37020
$9$	157554.	0.889397
$10$	−42466.1	−0.134289
$11$	−760245.	−1.42329	−0.711645	−	0.702539i	$-0.752050\pi$
$11$	−760245.	−1.42329	−0.711645	+	0.702539i	$0.752050\pi$
$12$	−2.15220e6	−2.49681
$13$	−1.08264e6	−0.808714	−0.404357	−	0.914601i	$-0.632505\pi$
$13$	−1.08264e6	−0.808714	−0.404357	+	0.914601i	$0.632505\pi$
$14$	−3.24583e6	−1.61295
$15$	323485.	0.109990
$16$	2.02605e6	0.483049
$17$	−147825.	−0.0252510	−0.0126255	−	0.999920i	$-0.504019\pi$
$17$	−147825.	−0.0252510	−0.0126255	+	0.999920i	$0.504019\pi$
$18$	1.19659e7	1.49261
$19$	2.47610e6	0.229416
$19$	2.47610e6	0.229416
$20$	−2.08008e6	−0.145350
$21$	2.47251e7	1.32109
$22$	−5.77391e7	−2.38861
$23$	4.63915e7	1.50292	0.751459	−	0.659780i	$-0.229351\pi$
$23$	4.63915e7	1.50292	0.751459	+	0.659780i	$0.229351\pi$
$24$	−7.34693e7	−1.88341
$25$	−4.85155e7	−0.993597
$26$	−8.22242e7	−1.35721
$27$	1.13352e7	0.152029
$28$	−1.58988e8	−1.74580
$29$	−6.40882e7	−0.580215	−0.290108	−	0.956994i	$-0.593691\pi$
$29$	−6.40882e7	−0.580215	−0.290108	+	0.956994i	$0.593691\pi$
$30$	2.45680e7	0.184588
$31$	2.79716e8	1.75480	0.877402	−	0.479757i	$-0.159275\pi$
$31$	2.79716e8	1.75480	0.877402	+	0.479757i	$0.159275\pi$
$32$	−1.06206e8	−0.559529
$33$	4.39827e8	1.95639
$34$	−1.12270e7	−0.0423770
$35$	2.38966e7	0.0769061
$36$	5.86116e8	1.61555
$37$	−2.37124e8	−0.562167	−0.281084	−	0.959683i	$-0.590694\pi$
$37$	−2.37124e8	−0.562167	−0.281084	+	0.959683i	$0.590694\pi$
$38$	1.88055e8	0.385012
$39$	6.26342e8	1.11162
$40$	−7.10073e7	−0.109641
$41$	−9.81332e8	−1.32283	−0.661416	−	0.750019i	$-0.730044\pi$
$41$	−9.81332e8	−1.32283	−0.661416	+	0.750019i	$0.730044\pi$
$42$	1.87782e9	2.21709
$43$	4.72722e7	0.0490376	0.0245188	−	0.999699i	$-0.492195\pi$
$43$	4.72722e7	0.0490376	0.0245188	+	0.999699i	$0.492195\pi$
$44$	−2.82818e9	−2.58534
$45$	−8.80959e7	−0.0711683
$46$	3.52334e9	2.52224
$47$	1.85661e9	1.18082	0.590409	−	0.807104i	$-0.298966\pi$
$47$	1.85661e9	1.18082	0.590409	+	0.807104i	$0.298966\pi$
$48$	−1.17214e9	−0.663977
$49$	−1.50830e8	−0.0762796
$50$	−3.68465e9	−1.66748
$51$	8.55218e7	0.0347089
$52$	−4.02752e9	−1.46899
$53$	−2.12327e9	−0.697409	−0.348704	−	0.937233i	$-0.613378\pi$
$53$	−2.12327e9	−0.697409	−0.348704	+	0.937233i	$0.613378\pi$
$54$	8.60882e8	0.255140
$55$	4.25088e8	0.113890
$56$	−5.42734e9	−1.31690
$57$	−1.43251e9	−0.315344
$58$	−4.86737e9	−0.973734
$59$	−2.01394e9	−0.366743	−0.183371	−	0.983044i	$-0.558701\pi$
$59$	−2.01394e9	−0.366743	−0.183371	+	0.983044i	$0.558701\pi$
$60$	1.20340e9	0.199791
$61$	1.20487e10	1.82653	0.913263	−	0.407371i	$-0.133554\pi$
$61$	1.20487e10	1.82653	0.913263	+	0.407371i	$0.133554\pi$
$62$	2.12439e10	2.94496
$63$	−6.73347e9	−0.854803
$64$	−1.22155e10	−1.42207
$65$	6.05353e8	0.0647121
$66$	3.34040e10	3.28327
$67$	−2.14288e10	−1.93904	−0.969520	−	0.245012i	$-0.921208\pi$
$67$	−2.14288e10	−1.93904	−0.969520	+	0.245012i	$0.921208\pi$
$68$	−5.49924e8	−0.0458673
$69$	−2.68390e10	−2.06584
$70$	1.81490e9	0.129066
$71$	5.76489e9	0.379201	0.189601	−	0.981861i	$-0.439281\pi$
$71$	5.76489e9	0.379201	0.189601	+	0.981861i	$0.439281\pi$
$72$	2.00082e10	1.21865
$73$	−2.64202e10	−1.49163	−0.745814	−	0.666154i	$-0.767939\pi$
$73$	−2.64202e10	−1.49163	−0.745814	+	0.666154i	$0.767939\pi$
$74$	−1.80091e10	−0.943445
$75$	2.80678e10	1.36575
$76$	9.21133e9	0.416723
$77$	3.24910e10	1.36793
$78$	4.75694e10	1.86555
$79$	−1.83608e10	−0.671342	−0.335671	−	0.941979i	$-0.608963\pi$
$79$	−1.83608e10	−0.671342	−0.335671	+	0.941979i	$0.608963\pi$
$80$	−1.13286e9	−0.0386529
$81$	−3.44680e10	−1.09837
$82$	−7.45302e10	−2.22002
$83$	−2.66752e10	−0.743324	−0.371662	−	0.928368i	$-0.621212\pi$
$83$	−2.66752e10	−0.743324	−0.371662	+	0.928368i	$0.621212\pi$
$84$	9.19798e10	2.39970
$85$	8.26560e7	0.00202055
$86$	3.59023e9	0.0822964
$87$	3.70772e10	0.797537
$88$	−9.65452e10	−1.95019
$89$	2.35606e10	0.447241	0.223620	−	0.974676i	$-0.428212\pi$
$89$	2.35606e10	0.447241	0.223620	+	0.974676i	$0.428212\pi$
$90$	−6.69070e9	−0.119437
$91$	4.62693e10	0.777258
$92$	1.72581e11	2.72998
$93$	−1.61825e11	−2.41207
$94$	1.41006e11	1.98168
$95$	−1.38450e9	−0.0183575
$96$	6.14435e10	0.769102
$97$	−1.06270e10	−0.125651	−0.0628257	−	0.998025i	$-0.520011\pi$
$97$	−1.06270e10	−0.125651	−0.0628257	+	0.998025i	$0.520011\pi$
$98$	−1.14552e10	−0.128015
$99$	−1.19780e11	−1.26587
$100$	−1.80482e11	−1.80482
$101$	−6.85020e10	−0.648539	−0.324269	−	0.945965i	$-0.605118\pi$
$101$	−6.85020e10	−0.648539	−0.324269	+	0.945965i	$0.605118\pi$
$102$	6.49521e9	0.0582495
$103$	2.94639e9	0.0250430	0.0125215	−	0.999922i	$-0.496014\pi$
$103$	2.94639e9	0.0250430	0.0125215	+	0.999922i	$0.496014\pi$
$104$	−1.37487e11	−1.10810
$105$	−1.38250e10	−0.105712
$106$	−1.61258e11	−1.17041
$107$	7.18708e10	0.495384	0.247692	−	0.968839i	$-0.420328\pi$
$107$	7.18708e10	0.495384	0.247692	+	0.968839i	$0.420328\pi$
$108$	4.21679e10	0.276154
$109$	−2.37162e11	−1.47639	−0.738194	−	0.674589i	$-0.764321\pi$
$109$	−2.37162e11	−1.47639	−0.738194	+	0.674589i	$0.764321\pi$
$110$	3.22846e10	0.191133
$111$	1.37184e11	0.772729
$112$	−8.65886e10	−0.464260
$113$	2.89617e11	1.47874	0.739371	−	0.673298i	$-0.235123\pi$
$113$	2.89617e11	1.47874	0.739371	+	0.673298i	$0.235123\pi$
$114$	−1.08796e11	−0.529220
$115$	−2.59396e10	−0.120261
$116$	−2.38414e11	−1.05393
$117$	−1.70574e11	−0.719268
$118$	−1.52955e11	−0.615478
$119$	6.31768e9	0.0242689
$120$	4.10801e10	0.150708
$121$	2.92660e11	1.02576
$122$	9.15074e11	3.06533
$123$	5.67734e11	1.81830
$124$	1.04057e12	3.18752
$125$	5.44294e10	0.159525
$126$	−5.11394e11	−1.43456
$127$	6.97694e11	1.87389	0.936945	−	0.349476i	$-0.113640\pi$
$127$	6.97694e11	1.87389	0.936945	+	0.349476i	$0.113640\pi$
$128$	−7.10230e11	−1.82702
$129$	−2.73486e10	−0.0674049
$130$	4.59754e10	0.108602
$131$	−3.48233e8	−0.000788638 0	−0.000394319	−	1.00000i	$-0.500126\pi$
$131$	−3.48233e8	−0.000788638 0	−0.000394319		1.00000i	$0.500126\pi$
$132$	1.63620e12	3.55369
$133$	−1.05822e11	−0.220492
$134$	−1.62748e12	−3.25415
$135$	−6.33801e9	−0.0121651
$136$	−1.87727e10	−0.0345989
$137$	−3.68529e11	−0.652391	−0.326196	−	0.945302i	$-0.605767\pi$
$137$	−3.68529e11	−0.652391	−0.326196	+	0.945302i	$0.605767\pi$
$138$	−2.03837e12	−3.46695
$139$	−5.82223e11	−0.951718	−0.475859	−	0.879522i	$-0.657863\pi$
$139$	−5.82223e11	−0.951718	−0.475859	+	0.879522i	$0.657863\pi$
$140$	8.88975e10	0.139696
$141$	−1.07411e12	−1.62310
$142$	4.37831e11	0.636387
$143$	8.23070e11	1.15103
$144$	3.19213e11	0.429623
$145$	3.58347e10	0.0464280
$146$	−2.00656e12	−2.50329
$147$	8.72600e10	0.104850
$148$	−8.82123e11	−1.02115
$149$	8.65612e11	0.965603	0.482801	−	0.875730i	$-0.339619\pi$
$149$	8.65612e11	0.965603	0.482801	+	0.875730i	$0.339619\pi$
$150$	2.13170e12	2.29205
$151$	−1.29180e12	−1.33913	−0.669563	−	0.742755i	$-0.733519\pi$
$151$	−1.29180e12	−1.33913	−0.669563	+	0.742755i	$0.733519\pi$
$152$	3.14446e11	0.314344
$153$	−2.32905e10	−0.0224582
$154$	2.46762e12	2.29570
$155$	−1.56402e11	−0.140417
$156$	2.33005e12	2.01921
$157$	3.77137e11	0.315537	0.157769	−	0.987476i	$-0.449570\pi$
$157$	3.77137e11	0.315537	0.157769	+	0.987476i	$0.449570\pi$
$158$	−1.39447e12	−1.12667
$159$	1.22838e12	0.958626
$160$	5.93845e10	0.0447727
$161$	−1.98266e12	−1.44446
$162$	−2.61778e12	−1.84332
$163$	1.43201e12	0.974795	0.487397	−	0.873180i	$-0.337946\pi$
$163$	1.43201e12	0.974795	0.487397	+	0.873180i	$0.337946\pi$
$164$	−3.65065e12	−2.40286
$165$	−2.45928e11	−0.156547
$166$	−2.02593e12	−1.24747
$167$	−5.48607e11	−0.326829	−0.163415	−	0.986557i	$-0.552251\pi$
$167$	−5.48607e11	−0.326829	−0.163415	+	0.986557i	$0.552251\pi$
$168$	3.13990e12	1.81015
$169$	−6.20056e11	−0.345982
$170$	6.27755e9	0.00339095
$171$	3.90120e11	0.204042
$172$	1.75857e11	0.0890746
$173$	2.36053e12	1.15813	0.579064	−	0.815282i	$-0.303418\pi$
$173$	2.36053e12	1.15813	0.579064	+	0.815282i	$0.303418\pi$
$174$	2.81594e12	1.33845
$175$	2.07343e12	0.954950
$176$	−1.54030e12	−0.687519
$177$	1.16513e12	0.504107
$178$	1.78938e12	0.750572
$179$	−1.03168e12	−0.419615	−0.209808	−	0.977743i	$-0.567284\pi$
$179$	−1.03168e12	−0.419615	−0.209808	+	0.977743i	$0.567284\pi$
$180$	−3.27725e11	−0.129274
$181$	9.06364e11	0.346793	0.173397	−	0.984852i	$-0.444526\pi$
$181$	9.06364e11	0.346793	0.173397	+	0.984852i	$0.444526\pi$
$182$	3.51406e12	1.30442
$183$	−6.97057e12	−2.51066
$184$	5.89136e12	2.05929
$185$	1.32587e11	0.0449838
$186$	−1.22903e13	−4.04801
$187$	1.12383e11	0.0359396
$188$	6.90678e12	2.14490
$189$	−4.84437e11	−0.146116
$190$	−1.05150e11	−0.0308081
$191$	−5.75476e12	−1.63811	−0.819056	−	0.573713i	$-0.805502\pi$
$191$	−5.75476e12	−1.63811	−0.819056	+	0.573713i	$0.805502\pi$
$192$	7.06705e12	1.95471
$193$	6.35485e12	1.70821	0.854103	−	0.520104i	$-0.174107\pi$
$193$	6.35485e12	1.70821	0.854103	+	0.520104i	$0.174107\pi$
$194$	−8.07101e11	−0.210872
$195$	−3.50217e11	−0.0889503
$196$	−5.61101e11	−0.138558
$197$	−3.53349e12	−0.848476	−0.424238	−	0.905551i	$-0.639458\pi$
$197$	−3.53349e12	−0.848476	−0.424238	+	0.905551i	$0.639458\pi$
$198$	−9.09702e12	−2.12442
$199$	3.79492e12	0.862008	0.431004	−	0.902350i	$-0.358160\pi$
$199$	3.79492e12	0.862008	0.431004	+	0.902350i	$0.358160\pi$
$200$	−6.16109e12	−1.36142
$201$	1.23973e13	2.66531
$202$	−5.20259e12	−1.08840
$203$	2.73897e12	0.557647
$204$	3.18149e11	0.0630471
$205$	5.48709e11	0.105851
$206$	2.23773e11	0.0420278
$207$	7.30917e12	1.33669
$208$	−2.19348e12	−0.390648
$209$	−1.88244e12	−0.326525
$210$	−1.04998e12	−0.177408
$211$	1.53937e12	0.253390	0.126695	−	0.991942i	$-0.459563\pi$
$211$	1.53937e12	0.253390	0.126695	+	0.991942i	$0.459563\pi$
$212$	−7.89876e12	−1.26681
$213$	−3.33518e12	−0.521232
$214$	5.45844e12	0.831367
$215$	−2.64321e10	−0.00392392
$216$	1.43948e12	0.208310
$217$	−1.19544e13	−1.68655
$218$	−1.80120e13	−2.47772
$219$	1.52850e13	2.05032
$220$	1.58137e12	0.206875
$221$	1.60041e11	0.0204209
$222$	1.04189e13	1.29682
$223$	−5.61894e12	−0.682304	−0.341152	−	0.940008i	$-0.610817\pi$
$223$	−5.61894e12	−0.682304	−0.341152	+	0.940008i	$0.610817\pi$
$224$	4.53896e12	0.537765
$225$	−7.64381e12	−0.883703
$226$	2.19958e13	2.48167
$227$	−8.78670e12	−0.967573	−0.483786	−	0.875186i	$-0.660739\pi$
$227$	−8.78670e12	−0.967573	−0.483786	+	0.875186i	$0.660739\pi$
$228$	−5.32906e12	−0.572808
$229$	1.78937e12	0.187761	0.0938806	−	0.995583i	$-0.470073\pi$
$229$	1.78937e12	0.187761	0.0938806	+	0.995583i	$0.470073\pi$
$230$	−1.97006e12	−0.201826
$231$	−1.87971e13	−1.88029
$232$	−8.13871e12	−0.795008
$233$	−1.49446e13	−1.42570	−0.712850	−	0.701317i	$-0.752596\pi$
$233$	−1.49446e13	−1.42570	−0.712850	+	0.701317i	$0.752596\pi$
$234$	−1.29548e13	−1.20710
$235$	−1.03812e12	−0.0944874
$236$	−7.49206e12	−0.666171
$237$	1.06224e13	0.922795
$238$	4.79815e11	0.0407287
$239$	−7.59815e12	−0.630259	−0.315130	−	0.949049i	$-0.602048\pi$
$239$	−7.59815e12	−0.630259	−0.315130	+	0.949049i	$0.602048\pi$
$240$	6.55399e11	0.0531305
$241$	−1.75241e13	−1.38849	−0.694243	−	0.719741i	$-0.744261\pi$
$241$	−1.75241e13	−1.38849	−0.694243	+	0.719741i	$0.744261\pi$
$242$	2.22270e13	1.72145
$243$	1.79329e13	1.35774
$244$	4.48223e13	3.31780
$245$	8.43359e10	0.00610378
$246$	4.31182e13	3.05153
$247$	−2.68072e12	−0.185532
$248$	3.55218e13	2.40442
$249$	1.54325e13	1.02174
$250$	4.13380e12	0.267719
$251$	−2.73332e13	−1.73175	−0.865876	−	0.500259i	$-0.833238\pi$
$251$	−2.73332e13	−1.73175	−0.865876	+	0.500259i	$0.833238\pi$
$252$	−2.50492e13	−1.55271
$253$	−3.52689e13	−2.13909
$254$	5.29884e13	3.14482
$255$	−4.78193e10	−0.00277736
$256$	−2.89233e13	−1.64410
$257$	1.03532e13	0.576025	0.288013	−	0.957627i	$-0.407005\pi$
$257$	1.03532e13	0.576025	0.288013	+	0.957627i	$0.407005\pi$
$258$	−2.07707e12	−0.113121
$259$	1.01341e13	0.540301
$260$	2.25197e12	0.117547
$261$	−1.00974e13	−0.516042
$262$	−2.64476e10	−0.00132352
$263$	−1.68167e11	−0.00824109	−0.00412055	−	0.999992i	$-0.501312\pi$
$263$	−1.68167e11	−0.00824109	−0.00412055	+	0.999992i	$0.501312\pi$
$264$	5.58547e13	2.68064
$265$	1.18722e12	0.0558057
$266$	−8.03700e12	−0.370037
$267$	−1.36306e13	−0.614756
$268$	−7.97173e13	−3.52218
$269$	7.11871e12	0.308151	0.154075	−	0.988059i	$-0.450760\pi$
$269$	7.11871e12	0.308151	0.154075	+	0.988059i	$0.450760\pi$
$270$	−4.81359e11	−0.0204159
$271$	4.18480e13	1.73918	0.869588	−	0.493778i	$-0.164385\pi$
$271$	4.18480e13	1.73918	0.869588	+	0.493778i	$0.164385\pi$
$272$	−2.99502e11	−0.0121975
$273$	−2.67683e13	−1.06838
$274$	−2.79890e13	−1.09486
$275$	3.68836e13	1.41418
$276$	−9.98438e13	−3.75250
$277$	−4.34333e12	−0.160024	−0.0800118	−	0.996794i	$-0.525496\pi$
$277$	−4.34333e12	−0.160024	−0.0800118	+	0.996794i	$0.525496\pi$
$278$	−4.42187e13	−1.59720
$279$	4.40704e13	1.56072
$280$	3.03468e12	0.105376
$281$	2.12282e13	0.722816	0.361408	−	0.932408i	$-0.382296\pi$
$281$	2.12282e13	0.722816	0.361408	+	0.932408i	$0.382296\pi$
$282$	−8.15767e13	−2.72393
$283$	−1.29126e13	−0.422851	−0.211425	−	0.977394i	$-0.567811\pi$
$283$	−1.29126e13	−0.422851	−0.211425	+	0.977394i	$0.567811\pi$
$284$	2.14459e13	0.688801
$285$	8.00981e11	0.0252334
$286$	6.25105e13	1.93170
$287$	4.19397e13	1.27138
$288$	−1.67331e13	−0.497643
$289$	−3.42500e13	−0.999362
$290$	2.72157e12	0.0779168
$291$	6.14809e12	0.172714
$292$	−9.82857e13	−2.70947
$293$	1.15382e13	0.312153	0.156076	−	0.987745i	$-0.450115\pi$
$293$	1.15382e13	0.312153	0.156076	+	0.987745i	$0.450115\pi$
$294$	6.62722e12	0.175963
$295$	1.12609e12	0.0293462
$296$	−3.01129e13	−0.770279
$297$	−8.61749e12	−0.216382
$298$	6.57415e13	1.62050
$299$	−5.02252e13	−1.21543
$300$	1.04415e14	2.48083
$301$	−2.02030e12	−0.0471303
$302$	−9.81095e13	−2.24736
$303$	3.96307e13	0.891451
$304$	5.01671e12	0.110819
$305$	−6.73699e12	−0.146156
$306$	−1.76886e12	−0.0376900
$307$	8.77982e13	1.83749	0.918744	−	0.394854i	$-0.129205\pi$
$307$	8.77982e13	1.83749	0.918744	+	0.394854i	$0.129205\pi$
$308$	1.20870e14	2.48478
$309$	−1.70459e12	−0.0344229
$310$	−1.18785e13	−0.235652
$311$	5.44838e13	1.06190	0.530952	−	0.847402i	$-0.321835\pi$
$311$	5.44838e13	1.06190	0.530952	+	0.847402i	$0.321835\pi$
$312$	7.95407e13	1.52314
$313$	1.17147e13	0.220413	0.110206	−	0.993909i	$-0.464849\pi$
$313$	1.17147e13	0.220413	0.110206	+	0.993909i	$0.464849\pi$
$314$	2.86428e13	0.529544
$315$	3.76500e12	0.0684001
$316$	−6.83041e13	−1.21946
$317$	−4.61261e13	−0.809320	−0.404660	−	0.914467i	$-0.632610\pi$
$317$	−4.61261e13	−0.809320	−0.404660	+	0.914467i	$0.632610\pi$
$318$	9.32931e13	1.60879
$319$	4.87227e13	0.825815
$320$	6.83023e12	0.113792
$321$	−4.15797e13	−0.680931
$322$	−1.50579e14	−2.42413
$323$	−3.66030e11	−0.00579299
$324$	−1.28224e14	−1.99514
$325$	5.25247e13	0.803535
$326$	1.08758e14	1.63593
$327$	1.37206e14	2.02937
$328$	−1.24622e14	−1.81254
$329$	−7.93471e13	−1.13489
$330$	−1.86777e13	−0.262723
$331$	−2.72631e12	−0.0377157	−0.0188578	−	0.999822i	$-0.506003\pi$
$331$	−2.72631e12	−0.0377157	−0.0188578	+	0.999822i	$0.506003\pi$
$332$	−9.92343e13	−1.35021
$333$	−3.73598e13	−0.499990
$334$	−4.16656e13	−0.548494
$335$	1.19819e13	0.155159
$336$	5.00944e13	0.638151
$337$	6.31846e13	0.791857	0.395929	−	0.918281i	$-0.370423\pi$
$337$	6.31846e13	0.791857	0.395929	+	0.918281i	$0.370423\pi$
$338$	−4.70920e13	−0.580638
$339$	−1.67553e14	−2.03261
$340$	3.07488e11	0.00367024
$341$	−2.12653e14	−2.49760
$342$	2.96288e13	0.342429
$343$	9.09522e13	1.03442
$344$	6.00321e12	0.0671912
$345$	1.50070e13	0.165306
$346$	1.79278e14	1.94360
$347$	4.91646e13	0.524614	0.262307	−	0.964984i	$-0.415517\pi$
$347$	4.91646e13	0.524614	0.262307	+	0.964984i	$0.415517\pi$
$348$	1.37931e14	1.44869
$349$	6.23394e13	0.644500	0.322250	−	0.946655i	$-0.395561\pi$
$349$	6.23394e13	0.644500	0.322250	+	0.946655i	$0.395561\pi$
$350$	1.57473e14	1.60262
$351$	−1.22719e13	−0.122948
$352$	8.07422e13	0.796372
$353$	−1.18251e14	−1.14827	−0.574135	−	0.818761i	$-0.694662\pi$
$353$	−1.18251e14	−1.14827	−0.574135	+	0.818761i	$0.694662\pi$
$354$	8.84896e13	0.846007
$355$	−3.22342e12	−0.0303431
$356$	8.76477e13	0.812392
$357$	−3.65499e12	−0.0333589
$358$	−7.83536e13	−0.704211
$359$	−7.39160e13	−0.654213	−0.327106	−	0.944987i	$-0.606074\pi$
$359$	−7.39160e13	−0.654213	−0.327106	+	0.944987i	$0.606074\pi$
$360$	−1.11875e13	−0.0975145
$361$	6.13107e12	0.0526316
$362$	6.88365e13	0.581998
$363$	−1.69314e14	−1.40996
$364$	1.72126e14	1.41185
$365$	1.47728e13	0.119358
$366$	−5.29401e14	−4.21346
$367$	2.23518e14	1.75247	0.876233	−	0.481887i	$-0.160048\pi$
$367$	2.23518e14	1.75247	0.876233	+	0.481887i	$0.160048\pi$
$368$	9.39916e13	0.725983
$369$	−1.54613e14	−1.17652
$370$	1.00697e13	0.0754932
$371$	9.07432e13	0.670282
$372$	−6.02006e14	−4.38141
$373$	1.48916e14	1.06793	0.533966	−	0.845506i	$-0.320701\pi$
$373$	1.48916e14	1.06793	0.533966	+	0.845506i	$0.320701\pi$
$374$	8.53529e12	0.0603149
$375$	−3.14892e13	−0.219275
$376$	2.35776e14	1.61795
$377$	6.93843e13	0.469228
$378$	−3.67920e13	−0.245216
$379$	−3.63324e13	−0.238659	−0.119330	−	0.992855i	$-0.538075\pi$
$379$	−3.63324e13	−0.238659	−0.119330	+	0.992855i	$0.538075\pi$
$380$	−5.15048e12	−0.0333456
$381$	−4.03639e14	−2.57576
$382$	−4.37062e14	−2.74913
$383$	−5.78932e13	−0.358950	−0.179475	−	0.983763i	$-0.557440\pi$
$383$	−5.78932e13	−0.358950	−0.179475	+	0.983763i	$0.557440\pi$
$384$	4.10892e14	2.51134
$385$	−1.81672e13	−0.109460
$386$	4.82638e14	2.86676
$387$	7.44793e12	0.0436140
$388$	−3.95335e13	−0.228240
$389$	2.33229e13	0.132758	0.0663789	−	0.997794i	$-0.478855\pi$
$389$	2.33229e13	0.132758	0.0663789	+	0.997794i	$0.478855\pi$
$390$	−2.65983e13	−0.149279
$391$	−6.85783e12	−0.0379502
$392$	−1.91542e13	−0.104518
$393$	2.01464e11	0.00108403
$394$	−2.68361e14	−1.42394
$395$	1.02664e13	0.0537198
$396$	−4.45592e14	−2.29940
$397$	1.46796e14	0.747081	0.373540	−	0.927614i	$-0.378144\pi$
$397$	1.46796e14	0.747081	0.373540	+	0.927614i	$0.378144\pi$
$398$	2.88217e14	1.44665
$399$	6.12218e13	0.303079
$400$	−9.82950e13	−0.479956
$401$	2.02235e12	0.00974010	0.00487005	−	0.999988i	$-0.498450\pi$
$401$	2.02235e12	0.00974010	0.00487005	+	0.999988i	$0.498450\pi$
$402$	9.41549e14	4.47301
$403$	−3.02831e14	−1.41913
$404$	−2.54834e14	−1.17804
$405$	1.92727e13	0.0878900
$406$	2.08019e14	0.935859
$407$	1.80272e14	0.800127
$408$	1.08606e13	0.0475580
$409$	−4.39137e13	−0.189724	−0.0948619	−	0.995490i	$-0.530241\pi$
$409$	−4.39137e13	−0.189724	−0.0948619	+	0.995490i	$0.530241\pi$
$410$	4.16733e13	0.177643
$411$	2.13206e14	0.896747
$412$	1.09609e13	0.0454894
$413$	8.60710e13	0.352478
$414$	5.55116e14	2.24327
$415$	1.49154e13	0.0594797
$416$	1.14982e14	0.452498
$417$	3.36836e14	1.30819
$418$	−1.42968e14	−0.547984
$419$	−2.82908e14	−1.07021	−0.535104	−	0.844786i	$-0.679728\pi$
$419$	−2.82908e14	−1.07021	−0.535104	+	0.844786i	$0.679728\pi$
$420$	−5.14302e13	−0.192020
$421$	−2.07413e14	−0.764336	−0.382168	−	0.924093i	$-0.624822\pi$
$421$	−2.07413e14	−0.764336	−0.382168	+	0.924093i	$0.624822\pi$
$422$	1.16912e14	0.425246
$423$	2.92517e14	1.05022
$424$	−2.69639e14	−0.955587
$425$	7.17181e12	0.0250894
$426$	−2.53300e14	−0.874747
$427$	−5.14931e14	−1.75548
$428$	2.67366e14	0.899841
$429$	−4.76173e14	−1.58216
$430$	−2.00747e12	−0.00658524
$431$	4.80227e14	1.55533	0.777664	−	0.628680i	$-0.216405\pi$
$431$	4.80227e14	1.55533	0.777664	+	0.628680i	$0.216405\pi$
$432$	2.29656e13	0.0734375
$433$	1.91065e14	0.603250	0.301625	−	0.953427i	$-0.402471\pi$
$433$	1.91065e14	0.603250	0.301625	+	0.953427i	$0.402471\pi$
$434$	−9.07911e14	−2.83041
$435$	−2.07316e13	−0.0638177
$436$	−8.82267e14	−2.68179
$437$	1.14870e14	0.344793
$438$	1.16086e15	3.44091
$439$	2.19249e14	0.641774	0.320887	−	0.947118i	$-0.396019\pi$
$439$	2.19249e14	0.641774	0.320887	+	0.947118i	$0.396019\pi$
$440$	5.39830e13	0.156051
$441$	−2.37638e13	−0.0678428
$442$	1.21548e13	0.0342709
$443$	−5.02480e14	−1.39926	−0.699629	−	0.714506i	$-0.746652\pi$
$443$	−5.02480e14	−1.39926	−0.699629	+	0.714506i	$0.746652\pi$
$444$	5.10338e14	1.40363
$445$	−1.31738e13	−0.0357876
$446$	−4.26748e14	−1.14506
$447$	−5.00785e14	−1.32727
$448$	5.22059e14	1.36675
$449$	−5.06653e14	−1.31026	−0.655128	−	0.755518i	$-0.727385\pi$
$449$	−5.06653e14	−1.31026	−0.655128	+	0.755518i	$0.727385\pi$
$450$	−5.80532e14	−1.48306
$451$	7.46053e14	1.88278
$452$	1.07740e15	2.68607
$453$	7.47349e14	1.84070
$454$	−6.67332e14	−1.62381
$455$	−2.58713e13	−0.0621950
$456$	−1.81917e14	−0.432083
$457$	5.36557e14	1.25915	0.629574	−	0.776941i	$-0.283230\pi$
$457$	5.36557e14	1.25915	0.629574	+	0.776941i	$0.283230\pi$
$458$	1.35899e14	0.315106
$459$	−1.67562e12	−0.00383889
$460$	−9.64980e13	−0.218449
$461$	−4.03273e14	−0.902077	−0.451039	−	0.892504i	$-0.648946\pi$
$461$	−4.03273e14	−0.902077	−0.451039	+	0.892504i	$0.648946\pi$
$462$	−1.42760e15	−3.15556
$463$	−7.11827e14	−1.55482	−0.777408	−	0.628997i	$-0.783466\pi$
$463$	−7.11827e14	−1.55482	−0.777408	+	0.628997i	$0.783466\pi$
$464$	−1.29846e14	−0.280272
$465$	9.04841e13	0.193010
$466$	−1.13502e15	−2.39265
$467$	−8.38289e14	−1.74643	−0.873215	−	0.487336i	$-0.837969\pi$
$467$	−8.38289e14	−1.74643	−0.873215	+	0.487336i	$0.837969\pi$
$468$	−6.34552e14	−1.30652
$469$	9.15815e14	1.86362
$470$	−7.88431e13	−0.158572
$471$	−2.18186e14	−0.433723
$472$	−2.55755e14	−0.502509
$473$	−3.59385e13	−0.0697948
$474$	8.06747e14	1.54866
$475$	−1.20129e14	−0.227947
$476$	2.35024e13	0.0440833
$477$	−3.34530e14	−0.620274
$478$	−5.77064e14	−1.05772
$479$	5.73586e14	1.03933	0.519665	−	0.854370i	$-0.326057\pi$
$479$	5.73586e14	1.03933	0.519665	+	0.854370i	$0.326057\pi$
$480$	−3.43559e13	−0.0615424
$481$	2.56719e14	0.454632
$482$	−1.33092e15	−2.33020
$483$	1.14703e15	1.98549
$484$	1.08872e15	1.86324
$485$	5.94207e12	0.0100544
$486$	1.36197e15	2.27860
$487$	5.05893e14	0.836853	0.418427	−	0.908251i	$-0.362582\pi$
$487$	5.05893e14	0.836853	0.418427	+	0.908251i	$0.362582\pi$
$488$	1.53009e15	2.50270
$489$	−8.28464e14	−1.33991
$490$	6.40514e12	0.0102435
$491$	6.80267e14	1.07580	0.537899	−	0.843009i	$-0.319218\pi$
$491$	6.80267e14	1.07580	0.537899	+	0.843009i	$0.319218\pi$
$492$	2.11202e15	3.30286
$493$	9.47385e12	0.0146510
$494$	−2.03595e14	−0.311365
$495$	6.69744e13	0.101293
$496$	5.66720e14	0.847656
$497$	−2.46377e14	−0.364452
$498$	1.17207e15	1.71471
$499$	−3.65905e13	−0.0529439	−0.0264719	−	0.999650i	$-0.508427\pi$
$499$	−3.65905e13	−0.0529439	−0.0264719	+	0.999650i	$0.508427\pi$
$500$	2.02482e14	0.289769
$501$	3.17387e14	0.449244
$502$	−2.07590e15	−2.90628
$503$	7.50275e14	1.03895	0.519477	−	0.854484i	$-0.326127\pi$
$503$	7.50275e14	1.03895	0.519477	+	0.854484i	$0.326127\pi$
$504$	−8.55100e14	−1.17125
$505$	3.83027e13	0.0518951
$506$	−2.67860e15	−3.58988
$507$	3.58723e14	0.475571
$508$	2.59549e15	3.40384
$509$	−9.81460e14	−1.27328	−0.636641	−	0.771160i	$-0.719677\pi$
$509$	−9.81460e14	−1.27328	−0.636641	+	0.771160i	$0.719677\pi$
$510$	−3.63178e12	−0.00466104
$511$	1.12913e15	1.43361
$512$	−7.42115e14	−0.932151
$513$	2.80670e13	0.0348779
$514$	7.86303e14	0.966703
$515$	−1.64747e12	−0.00200390
$516$	−1.01739e14	−0.122438
$517$	−1.41148e15	−1.68065
$518$	7.69663e14	0.906749
$519$	−1.36565e15	−1.59191
$520$	7.68752e13	0.0886682
$521$	−1.10841e15	−1.26500	−0.632502	−	0.774558i	$-0.717972\pi$
$521$	−1.10841e15	−1.26500	−0.632502	+	0.774558i	$0.717972\pi$
$522$	−7.66874e14	−0.866036
$523$	−4.97440e14	−0.555881	−0.277940	−	0.960598i	$-0.589652\pi$
$523$	−4.97440e14	−0.555881	−0.277940	+	0.960598i	$0.589652\pi$
$524$	−1.29546e12	−0.00143252
$525$	−1.19955e15	−1.31263
$526$	−1.27720e13	−0.0138304
$527$	−4.13491e13	−0.0443106
$528$	8.91114e14	0.945032
$529$	1.19936e15	1.25876
$530$	9.01668e13	0.0936547
$531$	−3.17305e14	−0.326180
$532$	−3.93669e14	−0.400514
$533$	1.06243e15	1.06979
$534$	−1.03522e15	−1.03170
$535$	−4.01863e13	−0.0396399
$536$	−2.72130e15	−2.65686
$537$	5.96859e14	0.576784
$538$	5.40651e14	0.517148
$539$	1.14667e14	0.108568
$540$	−2.35780e13	−0.0220974
$541$	−5.29002e14	−0.490764	−0.245382	−	0.969426i	$-0.578913\pi$
$541$	−5.29002e14	−0.490764	−0.245382	+	0.969426i	$0.578913\pi$
$542$	3.17827e15	2.91874
$543$	−5.24362e14	−0.476686
$544$	1.56999e13	0.0141287
$545$	1.32609e14	0.118138
$546$	−2.03300e15	−1.79299
$547$	−2.95428e14	−0.257942	−0.128971	−	0.991648i	$-0.541167\pi$
$547$	−2.95428e14	−0.257942	−0.128971	+	0.991648i	$0.541167\pi$
$548$	−1.37096e15	−1.18504
$549$	1.89832e15	1.62451
$550$	2.80124e15	2.37331
$551$	−1.58689e14	−0.133110
$552$	−3.40835e15	−2.83061
$553$	7.84697e14	0.645229
$554$	−3.29867e14	−0.268556
$555$	−7.67060e13	−0.0618327
$556$	−2.16593e15	−1.72875
$557$	4.35634e14	0.344285	0.172142	−	0.985072i	$-0.444931\pi$
$557$	4.35634e14	0.344285	0.172142	+	0.985072i	$0.444931\pi$
$558$	3.34706e15	2.61924
$559$	−5.11787e13	−0.0396574
$560$	4.84157e13	0.0371494
$561$	−6.50175e13	−0.0494009
$562$	1.61224e15	1.21305
$563$	2.30001e15	1.71369	0.856847	−	0.515570i	$-0.172420\pi$
$563$	2.30001e15	1.71369	0.856847	+	0.515570i	$0.172420\pi$
$564$	−3.99580e15	−2.94828
$565$	−1.61938e14	−0.118327
$566$	−9.80683e14	−0.709640
$567$	1.47308e15	1.05565
$568$	7.32096e14	0.519580
$569$	−9.08105e14	−0.638291	−0.319145	−	0.947706i	$-0.603396\pi$
$569$	−9.08105e14	−0.638291	−0.319145	+	0.947706i	$0.603396\pi$
$570$	6.08329e13	0.0423474
$571$	−1.56459e15	−1.07870	−0.539351	−	0.842081i	$-0.681331\pi$
$571$	−1.56459e15	−1.07870	−0.539351	+	0.842081i	$0.681331\pi$
$572$	3.06190e15	2.09080
$573$	3.32932e15	2.25167
$574$	3.18524e15	2.13367
$575$	−2.25070e15	−1.49329
$576$	−1.92460e15	−1.26478
$577$	1.87429e14	0.122003	0.0610015	−	0.998138i	$-0.480571\pi$
$577$	1.87429e14	0.122003	0.0610015	+	0.998138i	$0.480571\pi$
$578$	−2.60122e15	−1.67716
$579$	−3.67650e15	−2.34802
$580$	1.33309e14	0.0843343
$581$	1.14003e15	0.714412
$582$	4.66935e14	0.289854
$583$	1.61420e15	0.992616
$584$	−3.35516e15	−2.04382
$585$	9.53759e13	0.0575548
$586$	8.76306e14	0.523864
$587$	−1.82614e15	−1.08149	−0.540746	−	0.841186i	$-0.681858\pi$
$587$	−1.82614e15	−1.08149	−0.540746	+	0.841186i	$0.681858\pi$
$588$	3.24616e14	0.190456
$589$	6.92605e14	0.402579
$590$	8.55243e13	0.0492497
$591$	2.04424e15	1.16628
$592$	−4.80426e14	−0.271554
$593$	−1.26725e15	−0.709678	−0.354839	−	0.934927i	$-0.615464\pi$
$593$	−1.26725e15	−0.709678	−0.354839	+	0.934927i	$0.615464\pi$
$594$	−6.54481e14	−0.363138
$595$	−3.53251e12	−0.00194196
$596$	3.22016e15	1.75397
$597$	−2.19549e15	−1.18488
$598$	−3.81450e15	−2.03977
$599$	2.10895e15	1.11742	0.558712	−	0.829361i	$-0.311296\pi$
$599$	2.10895e15	1.11742	0.558712	+	0.829361i	$0.311296\pi$
$600$	3.56440e15	1.87135
$601$	6.37611e14	0.331701	0.165850	−	0.986151i	$-0.446963\pi$
$601$	6.37611e14	0.331701	0.165850	+	0.986151i	$0.446963\pi$
$602$	−1.53438e14	−0.0790954
$603$	−3.37620e15	−1.72458
$604$	−4.80562e15	−2.43246
$605$	−1.63640e14	−0.0820796
$606$	3.00987e15	1.49606
$607$	9.44930e14	0.465438	0.232719	−	0.972544i	$-0.425238\pi$
$607$	9.44930e14	0.465438	0.232719	+	0.972544i	$0.425238\pi$
$608$	−2.62975e14	−0.128365
$609$	−1.58459e15	−0.766516
$610$	−5.11660e14	−0.245283
$611$	−2.01004e15	−0.954944
$612$	−8.66428e13	−0.0407943
$613$	1.58352e14	0.0738910	0.0369455	−	0.999317i	$-0.488237\pi$
$613$	1.58352e14	0.0738910	0.0369455	+	0.999317i	$0.488237\pi$
$614$	6.66809e15	3.08373
$615$	−3.17446e14	−0.145498
$616$	4.12611e15	1.87433
$617$	3.98602e15	1.79462	0.897308	−	0.441405i	$-0.145520\pi$
$617$	3.98602e15	1.79462	0.897308	+	0.441405i	$0.145520\pi$
$618$	−1.29460e14	−0.0577695
$619$	−3.48649e15	−1.54202	−0.771010	−	0.636823i	$-0.780248\pi$
$619$	−3.48649e15	−1.54202	−0.771010	+	0.636823i	$0.780248\pi$
$620$	−5.81832e14	−0.255061
$621$	5.25854e14	0.228487
$622$	4.13793e15	1.78212
$623$	−1.00692e15	−0.429845
$624$	1.26900e15	0.536967
$625$	2.33849e15	0.980832
$626$	8.89707e14	0.369903
$627$	1.08906e15	0.448827
$628$	1.40299e15	0.573159
$629$	3.50529e13	0.0141953
$630$	2.85944e14	0.114791
$631$	−2.15442e15	−0.857371	−0.428686	−	0.903454i	$-0.641023\pi$
$631$	−2.15442e15	−0.857371	−0.428686	+	0.903454i	$0.641023\pi$
$632$	−2.33169e15	−0.919870
$633$	−8.90576e14	−0.348298
$634$	−3.50318e15	−1.35823
$635$	−3.90113e14	−0.149946
$636$	4.56970e15	1.74130
$637$	1.63294e14	0.0616883
$638$	3.70039e15	1.38591
$639$	9.08281e14	0.337261
$640$	3.97123e14	0.146196
$641$	−2.90418e14	−0.106000	−0.0529998	−	0.998595i	$-0.516878\pi$
$641$	−2.90418e14	−0.106000	−0.0529998	+	0.998595i	$0.516878\pi$
$642$	−3.15789e15	−1.14276
$643$	−1.83731e15	−0.659206	−0.329603	−	0.944120i	$-0.606915\pi$
$643$	−1.83731e15	−0.659206	−0.329603	+	0.944120i	$0.606915\pi$
$644$	−7.37568e15	−2.62379
$645$	1.52919e13	0.00539364
$646$	−2.77992e13	−0.00972196
$647$	−4.64352e15	−1.61018	−0.805089	−	0.593154i	$-0.797882\pi$
$647$	−4.64352e15	−1.61018	−0.805089	+	0.593154i	$0.797882\pi$
$648$	−4.37717e15	−1.50498
$649$	1.53109e15	0.521981
$650$	3.98914e15	1.34852
$651$	6.91601e15	2.31825
$652$	5.32720e15	1.77067
$653$	−2.90253e15	−0.956652	−0.478326	−	0.878182i	$-0.658756\pi$
$653$	−2.90253e15	−0.956652	−0.478326	+	0.878182i	$0.658756\pi$
$654$	1.04206e16	3.40575
$655$	1.94713e11	6.31057e−5 0
$656$	−1.98823e15	−0.638993
$657$	−4.16261e15	−1.32665
$658$	−6.02625e15	−1.90460
$659$	3.52056e15	1.10342	0.551711	−	0.834036i	$-0.313975\pi$
$659$	3.52056e15	1.10342	0.551711	+	0.834036i	$0.313975\pi$
$660$	−9.14875e14	−0.284361
$661$	−1.40798e15	−0.433998	−0.216999	−	0.976172i	$-0.569627\pi$
$661$	−1.40798e15	−0.433998	−0.216999	+	0.976172i	$0.569627\pi$
$662$	−2.07058e14	−0.0632956
$663$	−9.25892e13	−0.0280696
$664$	−3.38755e15	−1.01850
$665$	5.91702e13	0.0176435
$666$	−2.83740e15	−0.839098
$667$	−2.97315e15	−0.872015
$668$	−2.04087e15	−0.593670
$669$	3.25075e15	0.937864
$670$	9.09998e14	0.260393
$671$	−9.15995e15	−2.59968
$672$	−2.62594e15	−0.739187
$673$	−2.28201e15	−0.637139	−0.318569	−	0.947900i	$-0.603202\pi$
$673$	−2.28201e15	−0.637139	−0.318569	+	0.947900i	$0.603202\pi$
$674$	4.79874e15	1.32892
$675$	−5.49930e14	−0.151056
$676$	−2.30667e15	−0.628461
$677$	−9.49590e14	−0.256625	−0.128312	−	0.991734i	$-0.540956\pi$
$677$	−9.49590e14	−0.256625	−0.128312	+	0.991734i	$0.540956\pi$
$678$	−1.27253e16	−3.41119
$679$	4.54173e14	0.120764
$680$	1.04967e13	0.00276855
$681$	5.08340e15	1.32998
$682$	−1.61506e16	−4.19154
$683$	−4.27936e15	−1.10170	−0.550852	−	0.834603i	$-0.685697\pi$
$683$	−4.27936e15	−1.10170	−0.550852	+	0.834603i	$0.685697\pi$
$684$	1.45128e15	0.370632
$685$	2.06062e14	0.0522034
$686$	6.90763e15	1.73599
$687$	−1.03521e15	−0.258088
$688$	9.57761e13	0.0236876
$689$	2.29873e15	0.564004
$690$	1.13975e15	0.277421
$691$	−3.20692e15	−0.774388	−0.387194	−	0.921998i	$-0.626556\pi$
$691$	−3.20692e15	−0.774388	−0.387194	+	0.921998i	$0.626556\pi$
$692$	8.78141e15	2.10369
$693$	5.11909e15	1.21663
$694$	3.73395e15	0.880423
$695$	3.25548e14	0.0761551
$696$	4.70852e15	1.09278
$697$	1.45066e14	0.0334029
$698$	4.73455e15	1.08162
$699$	8.64598e15	1.95970
$700$	7.71337e15	1.73462
$701$	−8.97609e14	−0.200280	−0.100140	−	0.994973i	$-0.531929\pi$
$701$	−8.97609e14	−0.200280	−0.100140	+	0.994973i	$0.531929\pi$
$702$	−9.32023e14	−0.206335
$703$	−5.87142e14	−0.128970
$704$	9.28674e15	2.02401
$705$	6.00587e14	0.129878
$706$	−8.98093e15	−1.92706
$707$	2.92761e15	0.623313
$708$	4.33441e15	0.915687
$709$	−2.08099e15	−0.436230	−0.218115	−	0.975923i	$-0.569991\pi$
$709$	−2.08099e15	−0.436230	−0.218115	+	0.975923i	$0.569991\pi$
$710$	−2.44812e14	−0.0509227
$711$	−2.89283e15	−0.597090
$712$	2.99202e15	0.612807
$713$	1.29765e16	2.63732
$714$	−2.77589e14	−0.0559838
$715$	−4.60217e14	−0.0921041
$716$	−3.83793e15	−0.762212
$717$	4.39578e15	0.866325
$718$	−5.61377e15	−1.09792
$719$	−8.09021e15	−1.57019	−0.785093	−	0.619378i	$-0.787385\pi$
$719$	−8.09021e15	−1.57019	−0.785093	+	0.619378i	$0.787385\pi$
$720$	−1.78487e14	−0.0343778
$721$	−1.25922e14	−0.0240689
$722$	4.65642e14	0.0883279
$723$	1.01383e16	1.90855
$724$	3.37176e15	0.629933
$725$	3.10927e15	0.576500
$726$	−1.28590e16	−2.36623
$727$	3.88682e15	0.709832	0.354916	−	0.934898i	$-0.384510\pi$
$727$	3.88682e15	0.709832	0.354916	+	0.934898i	$0.384510\pi$
$728$	5.87584e15	1.06499
$729$	−4.26889e15	−0.767915
$730$	1.12196e15	0.200310
$731$	−6.98803e12	−0.00123825
$732$	−2.59312e16	−4.56049
$733$	−1.76691e15	−0.308420	−0.154210	−	0.988038i	$-0.549283\pi$
$733$	−1.76691e15	−0.308420	−0.154210	+	0.988038i	$0.549283\pi$
$734$	1.69758e16	2.94104
$735$	−4.87911e13	−0.00838997
$736$	−4.92703e15	−0.840925
$737$	1.62911e16	2.75982
$738$	−1.17425e16	−1.97448
$739$	−1.10711e16	−1.84777	−0.923884	−	0.382673i	$-0.875004\pi$
$739$	−1.10711e16	−1.84777	−0.923884	+	0.382673i	$0.875004\pi$
$740$	4.93236e14	0.0817110
$741$	1.55089e15	0.255023
$742$	6.89177e15	1.12489
$743$	−1.07932e15	−0.174868	−0.0874341	−	0.996170i	$-0.527867\pi$
$743$	−1.07932e15	−0.174868	−0.0874341	+	0.996170i	$0.527867\pi$
$744$	−2.05506e16	−3.30501
$745$	−4.84004e14	−0.0772662
$746$	1.13099e16	1.79224
$747$	−4.20279e15	−0.661111
$748$	4.18077e14	0.0652826
$749$	−3.07158e15	−0.476115
$750$	−2.39154e15	−0.367994
$751$	8.16253e15	1.24682	0.623412	−	0.781893i	$-0.285746\pi$
$751$	8.16253e15	1.24682	0.623412	+	0.781893i	$0.285746\pi$
$752$	3.76160e15	0.570393
$753$	1.58132e16	2.38038
$754$	5.26960e15	0.787472
$755$	7.22305e14	0.107155
$756$	−1.80215e15	−0.265412
$757$	−1.51608e15	−0.221663	−0.110832	−	0.993839i	$-0.535351\pi$
$757$	−1.51608e15	−0.221663	−0.110832	+	0.993839i	$0.535351\pi$
$758$	−2.75937e15	−0.400525
$759$	2.04042e16	2.94029
$760$	−1.75821e14	−0.0251534
$761$	−7.78799e15	−1.10614	−0.553069	−	0.833135i	$-0.686544\pi$
$761$	−7.78799e15	−1.10614	−0.553069	+	0.833135i	$0.686544\pi$
$762$	−3.06556e16	−4.32272
$763$	1.01357e16	1.41896
$764$	−2.14083e16	−2.97555
$765$	1.30228e13	0.00179707
$766$	−4.39687e15	−0.602401
$767$	2.18037e15	0.296590
$768$	1.67331e16	2.25990
$769$	−1.58020e15	−0.211893	−0.105947	−	0.994372i	$-0.533787\pi$
$769$	−1.58020e15	−0.211893	−0.105947	+	0.994372i	$0.533787\pi$
$770$	−1.37976e15	−0.183699
$771$	−5.98966e15	−0.791778
$772$	2.36407e16	3.10288
$773$	−7.85872e15	−1.02415	−0.512076	−	0.858940i	$-0.671123\pi$
$773$	−7.85872e15	−1.02415	−0.512076	+	0.858940i	$0.671123\pi$
$774$	5.65656e14	0.0731942
$775$	−1.35706e16	−1.74357
$776$	−1.34955e15	−0.172167
$777$	−5.86291e15	−0.742673
$778$	1.77133e15	0.222798
$779$	−2.42988e15	−0.303479
$780$	−1.30284e15	−0.161574
$781$	−4.38272e15	−0.539714
$782$	−5.20838e14	−0.0636892
$783$	−7.26449e14	−0.0882096
$784$	−3.05589e14	−0.0368468
$785$	−2.10875e14	−0.0252489
$786$	1.53008e13	0.00181924
$787$	8.58324e15	1.01342	0.506711	−	0.862116i	$-0.330861\pi$
$787$	8.58324e15	1.01342	0.506711	+	0.862116i	$0.330861\pi$
$788$	−1.31449e16	−1.54122
$789$	9.72904e13	0.0113278
$790$	7.79713e14	0.0901542
$791$	−1.23775e16	−1.42122
$792$	−1.52111e16	−1.73449
$793$	−1.30444e16	−1.47714
$794$	1.11489e16	1.25377
$795$	−6.86846e14	−0.0767079
$796$	1.41175e16	1.56580
$797$	−1.71049e16	−1.88408	−0.942040	−	0.335501i	$-0.891094\pi$
$797$	−1.71049e16	−1.88408	−0.942040	+	0.335501i	$0.891094\pi$
$798$	4.64967e15	0.508635
$799$	−2.74454e14	−0.0298169
$800$	5.15261e15	0.555946
$801$	3.71207e15	0.397775
$802$	1.53594e14	0.0163461
$803$	2.00858e16	2.12302
$804$	4.61191e16	4.84142
$805$	1.10860e15	0.115584
$806$	−2.29994e16	−2.38163
$807$	−4.11841e15	−0.423570
$808$	−8.69923e15	−0.888625
$809$	−1.08992e16	−1.10580	−0.552899	−	0.833248i	$-0.686479\pi$
$809$	−1.08992e16	−1.10580	−0.552899	+	0.833248i	$0.686479\pi$
$810$	1.46372e15	0.147500
$811$	7.63422e15	0.764100	0.382050	−	0.924142i	$-0.375218\pi$
$811$	7.63422e15	0.764100	0.382050	+	0.924142i	$0.375218\pi$
$812$	1.01892e16	1.01294
$813$	−2.42105e16	−2.39059
$814$	1.36913e16	1.34280
$815$	−8.00702e14	−0.0780017
$816$	1.73272e14	0.0167661
$817$	1.17051e14	0.0112500
$818$	−3.33516e15	−0.318400
$819$	7.28991e15	0.691291
$820$	2.04125e15	0.192274
$821$	−9.27585e15	−0.867893	−0.433947	−	0.900939i	$-0.642879\pi$
$821$	−9.27585e15	−0.867893	−0.433947	+	0.900939i	$0.642879\pi$
$822$	1.61926e16	1.50495
$823$	1.13215e16	1.04521	0.522606	−	0.852575i	$-0.324960\pi$
$823$	1.13215e16	1.04521	0.522606	+	0.852575i	$0.324960\pi$
$824$	3.74169e14	0.0343138
$825$	−2.13384e16	−1.94386
$826$	6.53692e15	0.591538
$827$	8.48407e15	0.762648	0.381324	−	0.924441i	$-0.375468\pi$
$827$	8.48407e15	0.762648	0.381324	+	0.924441i	$0.375468\pi$
$828$	2.71908e16	2.42804
$829$	6.02526e15	0.534473	0.267236	−	0.963631i	$-0.413890\pi$
$829$	6.02526e15	0.534473	0.267236	+	0.963631i	$0.413890\pi$
$830$	1.13279e15	0.0998206
$831$	2.51276e15	0.219961
$832$	1.32249e16	1.15004
$833$	2.22964e13	0.00192614
$834$	2.55820e16	2.19544
$835$	3.06752e14	0.0261524
$836$	−7.00286e15	−0.593118
$837$	3.17063e15	0.266781
$838$	−2.14863e16	−1.79605
$839$	−8.10476e15	−0.673053	−0.336526	−	0.941674i	$-0.609252\pi$
$839$	−8.10476e15	−0.673053	−0.336526	+	0.941674i	$0.609252\pi$
$840$	−1.75566e15	−0.144846
$841$	−8.09321e15	−0.663350
$842$	−1.57526e16	−1.28273
$843$	−1.22812e16	−0.993549
$844$	5.72659e15	0.460270
$845$	3.46702e14	0.0276850
$846$	2.22161e16	1.76251
$847$	−1.25076e16	−0.985859
$848$	−4.30186e15	−0.336883
$849$	7.47035e15	0.581231
$850$	5.44685e14	0.0421057
$851$	−1.10005e16	−0.844891
$852$	−1.24072e16	−0.946794
$853$	2.11690e15	0.160502	0.0802512	−	0.996775i	$-0.474428\pi$
$853$	2.11690e15	0.160502	0.0802512	+	0.996775i	$0.474428\pi$
$854$	−3.91080e16	−2.94610
$855$	−2.18134e14	−0.0163271
$856$	9.12704e15	0.678772
$857$	1.63925e16	1.21130	0.605648	−	0.795733i	$-0.292914\pi$
$857$	1.63925e16	1.21130	0.605648	+	0.795733i	$0.292914\pi$
$858$	−3.61644e16	−2.65522
$859$	1.09497e16	0.798801	0.399400	−	0.916777i	$-0.369218\pi$
$859$	1.09497e16	0.798801	0.399400	+	0.916777i	$0.369218\pi$
$860$	−9.83300e13	−0.00712762
$861$	−2.42635e16	−1.74758
$862$	3.64723e16	2.61020
$863$	−1.28096e16	−0.910914	−0.455457	−	0.890258i	$-0.650524\pi$
$863$	−1.28096e16	−0.910914	−0.455457	+	0.890258i	$0.650524\pi$
$864$	−1.20386e15	−0.0850646
$865$	−1.31989e15	−0.0926718
$866$	1.45110e16	1.01239
$867$	1.98148e16	1.37368
$868$	−4.44715e16	−3.06354
$869$	1.39587e16	0.955515
$870$	−1.57452e15	−0.107101
$871$	2.31996e16	1.56813
$872$	−3.01178e16	−2.02294
$873$	−1.67433e15	−0.111754
$874$	8.72414e15	0.578641
$875$	−2.32618e15	−0.153320
$876$	5.68616e16	3.72431
$877$	2.83216e16	1.84340	0.921702	−	0.387898i	$-0.126799\pi$
$877$	2.83216e16	1.84340	0.921702	+	0.387898i	$0.126799\pi$
$878$	1.66515e16	1.07704
$879$	−6.67526e15	−0.429071
$880$	8.61252e14	0.0550143
$881$	−1.34936e16	−0.856567	−0.428284	−	0.903644i	$-0.640882\pi$
$881$	−1.34936e16	−0.856567	−0.428284	+	0.903644i	$0.640882\pi$
$882$	−1.80481e15	−0.113856
$883$	5.14902e15	0.322805	0.161403	−	0.986889i	$-0.448398\pi$
$883$	5.14902e15	0.322805	0.161403	+	0.986889i	$0.448398\pi$
$884$	5.95368e14	0.0370935
$885$	−6.51481e14	−0.0403379
$886$	−3.81623e16	−2.34828
$887$	−3.44513e15	−0.210681	−0.105341	−	0.994436i	$-0.533593\pi$
$887$	−3.44513e15	−0.210681	−0.105341	+	0.994436i	$0.533593\pi$
$888$	1.74213e16	1.05879
$889$	−2.98177e16	−1.80100
$890$	−1.00053e15	−0.0600597
$891$	2.62041e16	1.56330
$892$	−2.09030e16	−1.23937
$893$	4.59716e15	0.270898
$894$	−3.80336e16	−2.22747
$895$	5.76858e14	0.0335770
$896$	3.03535e16	1.75596
$897$	2.90569e16	1.67067
$898$	−3.84793e16	−2.19891
$899$	−1.79265e16	−1.01816
$900$	−2.84357e16	−1.60520
$901$	3.13872e14	0.0176103
$902$	5.66612e16	3.15973
$903$	1.16881e15	0.0647831
$904$	3.67791e16	2.02617
$905$	−5.06790e14	−0.0277499
$906$	5.67597e16	3.08912
$907$	1.19358e16	0.645671	0.322835	−	0.946455i	$-0.395364\pi$
$907$	1.19358e16	0.645671	0.322835	+	0.946455i	$0.395364\pi$
$908$	−3.26874e16	−1.75755
$909$	−1.07928e16	−0.576809
$910$	−1.96487e15	−0.104378
$911$	2.50826e16	1.32441	0.662204	−	0.749323i	$-0.269621\pi$
$911$	2.50826e16	1.32441	0.662204	+	0.749323i	$0.269621\pi$
$912$	−2.90234e15	−0.152327
$913$	2.02797e16	1.05797
$914$	4.07504e16	2.11314
$915$	3.89757e15	0.200899
$916$	6.65664e15	0.341059
$917$	1.48826e13	0.000757963 0
$918$	−1.27260e14	−0.00644254
$919$	−2.52670e16	−1.27151	−0.635754	−	0.771892i	$-0.719311\pi$
$919$	−2.52670e16	−1.27151	−0.635754	+	0.771892i	$0.719311\pi$
$920$	−3.29414e15	−0.164781
$921$	−5.07942e16	−2.52573
$922$	−3.06277e16	−1.51389
$923$	−6.24128e15	−0.306665
$924$	−6.99271e16	−3.41546
$925$	1.15042e16	0.558568
$926$	−5.40618e16	−2.60934
$927$	4.64216e14	0.0222732
$928$	6.80652e15	0.324647
$929$	−5.68538e15	−0.269571	−0.134785	−	0.990875i	$-0.543034\pi$
$929$	−5.68538e15	−0.269571	−0.134785	+	0.990875i	$0.543034\pi$
$930$	6.87208e15	0.323916
$931$	−3.73469e14	−0.0174997
$932$	−5.55955e16	−2.58972
$933$	−3.15207e16	−1.45964
$934$	−6.36664e16	−2.93091
$935$	−6.28388e13	−0.00287583
$936$	−2.16616e16	−0.985538
$937$	3.25735e16	1.47332	0.736660	−	0.676263i	$-0.236402\pi$
$937$	3.25735e16	1.47332	0.736660	+	0.676263i	$0.236402\pi$
$938$	6.95543e16	3.12758
$939$	−6.77734e15	−0.302969
$940$	−3.86190e15	−0.171632
$941$	1.39335e16	0.615628	0.307814	−	0.951447i	$-0.400403\pi$
$941$	1.39335e16	0.615628	0.307814	+	0.951447i	$0.400403\pi$
$942$	−1.65708e16	−0.727887
$943$	−4.55254e16	−1.98811
$944$	−4.08036e15	−0.177155
$945$	2.70871e14	0.0116920
$946$	−2.72945e15	−0.117132
$947$	6.46550e15	0.275853	0.137926	−	0.990442i	$-0.455956\pi$
$947$	6.46550e15	0.275853	0.137926	+	0.990442i	$0.455956\pi$
$948$	3.95162e16	1.67621
$949$	2.86035e16	1.20630
$950$	−9.12357e15	−0.382547
$951$	2.66855e16	1.11245
$952$	8.02297e14	0.0332531
$953$	2.42277e16	0.998392	0.499196	−	0.866489i	$-0.333629\pi$
$953$	2.42277e16	0.998392	0.499196	+	0.866489i	$0.333629\pi$
$954$	−2.54068e16	−1.04096
$955$	3.21776e15	0.131079
$956$	−2.82658e16	−1.14484
$957$	−2.81877e16	−1.13513
$958$	4.35627e16	1.74423
$959$	1.57500e16	0.627016
$960$	−3.95152e15	−0.156413
$961$	5.28327e16	2.07933
$962$	1.94973e16	0.762977
$963$	1.13235e16	0.440593
$964$	−6.51912e16	−2.52212
$965$	−3.55330e15	−0.136688
$966$	8.71149e16	3.33210
$967$	1.89676e16	0.721385	0.360692	−	0.932685i	$-0.382540\pi$
$967$	1.89676e16	0.721385	0.360692	+	0.932685i	$0.382540\pi$
$968$	3.71656e16	1.40549
$969$	2.11761e14	0.00796277
$970$	4.51288e14	0.0168737
$971$	−3.65394e15	−0.135849	−0.0679243	−	0.997690i	$-0.521638\pi$
$971$	−3.65394e15	−0.135849	−0.0679243	+	0.997690i	$0.521638\pi$
$972$	6.67121e16	2.46627
$973$	2.48828e16	0.914699
$974$	3.84215e16	1.40443
$975$	−3.03873e16	−1.10450
$976$	2.44113e16	0.882301
$977$	−3.65869e15	−0.131494	−0.0657469	−	0.997836i	$-0.520943\pi$
$977$	−3.65869e15	−0.131494	−0.0657469	+	0.997836i	$0.520943\pi$
$978$	−6.29201e16	−2.24867
$979$	−1.79118e16	−0.636553
$980$	3.13738e14	0.0110872
$981$	−3.73659e16	−1.31309
$982$	5.16649e16	1.80544
$983$	−3.22084e16	−1.11925	−0.559623	−	0.828747i	$-0.689054\pi$
$983$	−3.22084e16	−1.11925	−0.559623	+	0.828747i	$0.689054\pi$
$984$	7.20978e16	2.49143
$985$	1.97574e15	0.0678938
$986$	7.19520e14	0.0245878
$987$	4.59050e16	1.55997
$988$	−9.97253e15	−0.337009
$989$	2.19303e15	0.0736995
$990$	5.08657e15	0.169993
$991$	1.65787e16	0.550991	0.275496	−	0.961302i	$-0.411158\pi$
$991$	1.65787e16	0.550991	0.275496	+	0.961302i	$0.411158\pi$
$992$	−2.97074e16	−0.981863
$993$	1.57726e15	0.0518422
$994$	−1.87118e16	−0.611634
$995$	−2.12192e15	−0.0689766
$996$	5.74104e16	1.85594
$997$	−2.48578e16	−0.799171	−0.399585	−	0.916696i	$-0.630846\pi$
$997$	−2.48578e16	−0.799171	−0.399585	+	0.916696i	$0.630846\pi$
$998$	−2.77898e15	−0.0888520
$999$	−2.68783e15	−0.0854658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.12.a.a.1.7	✓	7
3.2	odd	2		171.12.a.a.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.12.a.a.1.7	✓	7	1.1	even	1	trivial
171.12.a.a.1.1		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)

\(f(q)\)	\(=\)	\(q+75.9480 q^{2} -578.534 q^{3} +3720.10 q^{4} -559.147 q^{5} -43938.5 q^{6} -42737.5 q^{7} +126992. q^{8} +157554. q^{9} +O(q^{10})\)	\(q+75.9480 q^{2} -578.534 q^{3} +3720.10 q^{4} -559.147 q^{5} -43938.5 q^{6} -42737.5 q^{7} +126992. q^{8} +157554. q^{9} -42466.1 q^{10} -760245. q^{11} -2.15220e6 q^{12} -1.08264e6 q^{13} -3.24583e6 q^{14} +323485. q^{15} +2.02605e6 q^{16} -147825. q^{17} +1.19659e7 q^{18} +2.47610e6 q^{19} -2.08008e6 q^{20} +2.47251e7 q^{21} -5.77391e7 q^{22} +4.63915e7 q^{23} -7.34693e7 q^{24} -4.85155e7 q^{25} -8.22242e7 q^{26} +1.13352e7 q^{27} -1.58988e8 q^{28} -6.40882e7 q^{29} +2.45680e7 q^{30} +2.79716e8 q^{31} -1.06206e8 q^{32} +4.39827e8 q^{33} -1.12270e7 q^{34} +2.38966e7 q^{35} +5.86116e8 q^{36} -2.37124e8 q^{37} +1.88055e8 q^{38} +6.26342e8 q^{39} -7.10073e7 q^{40} -9.81332e8 q^{41} +1.87782e9 q^{42} +4.72722e7 q^{43} -2.82818e9 q^{44} -8.80959e7 q^{45} +3.52334e9 q^{46} +1.85661e9 q^{47} -1.17214e9 q^{48} -1.50830e8 q^{49} -3.68465e9 q^{50} +8.55218e7 q^{51} -4.02752e9 q^{52} -2.12327e9 q^{53} +8.60882e8 q^{54} +4.25088e8 q^{55} -5.42734e9 q^{56} -1.43251e9 q^{57} -4.86737e9 q^{58} -2.01394e9 q^{59} +1.20340e9 q^{60} +1.20487e10 q^{61} +2.12439e10 q^{62} -6.73347e9 q^{63} -1.22155e10 q^{64} +6.05353e8 q^{65} +3.34040e10 q^{66} -2.14288e10 q^{67} -5.49924e8 q^{68} -2.68390e10 q^{69} +1.81490e9 q^{70} +5.76489e9 q^{71} +2.00082e10 q^{72} -2.64202e10 q^{73} -1.80091e10 q^{74} +2.80678e10 q^{75} +9.21133e9 q^{76} +3.24910e10 q^{77} +4.75694e10 q^{78} -1.83608e10 q^{79} -1.13286e9 q^{80} -3.44680e10 q^{81} -7.45302e10 q^{82} -2.66752e10 q^{83} +9.19798e10 q^{84} +8.26560e7 q^{85} +3.59023e9 q^{86} +3.70772e10 q^{87} -9.65452e10 q^{88} +2.35606e10 q^{89} -6.69070e9 q^{90} +4.62693e10 q^{91} +1.72581e11 q^{92} -1.61825e11 q^{93} +1.41006e11 q^{94} -1.38450e9 q^{95} +6.14435e10 q^{96} -1.06270e10 q^{97} -1.14552e10 q^{98} -1.19780e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 9 q^{2} + 10 q^{3} + 6661 q^{4} - 14307 q^{5} - 66435 q^{6} - 2209 q^{7} - 72891 q^{8} + 346867 q^{9}+O(q^{10}) \) 7 * q - 9 * q^2 + 10 * q^3 + 6661 * q^4 - 14307 * q^5 - 66435 * q^6 - 2209 * q^7 - 72891 * q^8 + 346867 * q^9	\( 7 q - 9 q^{2} + 10 q^{3} + 6661 q^{4} - 14307 q^{5} - 66435 q^{6} - 2209 q^{7} - 72891 q^{8} + 346867 q^{9} + 610116 q^{10} - 1399461 q^{11} - 500945 q^{12} - 2639296 q^{13} - 6202863 q^{14} - 10553670 q^{15} - 11910239 q^{16} - 9760773 q^{17} - 27428622 q^{18} + 17332693 q^{19} - 60822132 q^{20} - 51652462 q^{21} - 96770562 q^{22} - 117151884 q^{23} - 129456201 q^{24} - 40644056 q^{25} - 140205807 q^{26} + 123768280 q^{27} - 95042353 q^{28} - 380102178 q^{29} + 336001500 q^{30} + 108083372 q^{31} + 639362133 q^{32} + 292307766 q^{33} + 632902677 q^{34} + 258176013 q^{35} + 1082564974 q^{36} + 470630222 q^{37} - 22284891 q^{38} + 1096564364 q^{39} + 1263596868 q^{40} - 572622810 q^{41} + 3526613691 q^{42} + 1170836039 q^{43} + 1857175194 q^{44} + 325468269 q^{45} + 6333771957 q^{46} - 3485769735 q^{47} - 3849252725 q^{48} + 2791682862 q^{49} - 6699338667 q^{50} - 3006308190 q^{51} - 4968372073 q^{52} - 9143305584 q^{53} - 8531659545 q^{54} - 18483973467 q^{55} - 11872570905 q^{56} + 24760990 q^{57} + 10101698853 q^{58} - 847227714 q^{59} - 6348541140 q^{60} - 8144938567 q^{61} + 21626318880 q^{62} - 43596471133 q^{63} - 14662293047 q^{64} - 9033654252 q^{65} + 45199579482 q^{66} - 5797397824 q^{67} - 6895758945 q^{68} - 54587710308 q^{69} + 63346638156 q^{70} - 4538589186 q^{71} + 85775462646 q^{72} - 1815379657 q^{73} + 52966894338 q^{74} + 24070734700 q^{75} + 16493295439 q^{76} + 77952325659 q^{77} + 110360547051 q^{78} - 54907201480 q^{79} + 77197994292 q^{80} + 33147767443 q^{81} + 66047089392 q^{82} - 68609936724 q^{83} + 117356373533 q^{84} + 50328221961 q^{85} + 11262589308 q^{86} - 128062398816 q^{87} - 118799781006 q^{88} - 105124973892 q^{89} + 10463980248 q^{90} - 53584340240 q^{91} + 22337690499 q^{92} - 294151780936 q^{93} + 203078543976 q^{94} - 35425548393 q^{95} + 219060245223 q^{96} - 386940894664 q^{97} - 357308952786 q^{98} - 392424818133 q^{99}+O(q^{100}) \) 7 * q - 9 * q^2 + 10 * q^3 + 6661 * q^4 - 14307 * q^5 - 66435 * q^6 - 2209 * q^7 - 72891 * q^8 + 346867 * q^9 + 610116 * q^10 - 1399461 * q^11 - 500945 * q^12 - 2639296 * q^13 - 6202863 * q^14 - 10553670 * q^15 - 11910239 * q^16 - 9760773 * q^17 - 27428622 * q^18 + 17332693 * q^19 - 60822132 * q^20 - 51652462 * q^21 - 96770562 * q^22 - 117151884 * q^23 - 129456201 * q^24 - 40644056 * q^25 - 140205807 * q^26 + 123768280 * q^27 - 95042353 * q^28 - 380102178 * q^29 + 336001500 * q^30 + 108083372 * q^31 + 639362133 * q^32 + 292307766 * q^33 + 632902677 * q^34 + 258176013 * q^35 + 1082564974 * q^36 + 470630222 * q^37 - 22284891 * q^38 + 1096564364 * q^39 + 1263596868 * q^40 - 572622810 * q^41 + 3526613691 * q^42 + 1170836039 * q^43 + 1857175194 * q^44 + 325468269 * q^45 + 6333771957 * q^46 - 3485769735 * q^47 - 3849252725 * q^48 + 2791682862 * q^49 - 6699338667 * q^50 - 3006308190 * q^51 - 4968372073 * q^52 - 9143305584 * q^53 - 8531659545 * q^54 - 18483973467 * q^55 - 11872570905 * q^56 + 24760990 * q^57 + 10101698853 * q^58 - 847227714 * q^59 - 6348541140 * q^60 - 8144938567 * q^61 + 21626318880 * q^62 - 43596471133 * q^63 - 14662293047 * q^64 - 9033654252 * q^65 + 45199579482 * q^66 - 5797397824 * q^67 - 6895758945 * q^68 - 54587710308 * q^69 + 63346638156 * q^70 - 4538589186 * q^71 + 85775462646 * q^72 - 1815379657 * q^73 + 52966894338 * q^74 + 24070734700 * q^75 + 16493295439 * q^76 + 77952325659 * q^77 + 110360547051 * q^78 - 54907201480 * q^79 + 77197994292 * q^80 + 33147767443 * q^81 + 66047089392 * q^82 - 68609936724 * q^83 + 117356373533 * q^84 + 50328221961 * q^85 + 11262589308 * q^86 - 128062398816 * q^87 - 118799781006 * q^88 - 105124973892 * q^89 + 10463980248 * q^90 - 53584340240 * q^91 + 22337690499 * q^92 - 294151780936 * q^93 + 203078543976 * q^94 - 35425548393 * q^95 + 219060245223 * q^96 - 386940894664 * q^97 - 357308952786 * q^98 - 392424818133 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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