LMFDB - Embedded newform 7.10.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,10,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	7.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:	$3.60525085315$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{193}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 48 $ x^2 - x - 48
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.44622$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +O(q^{10})$	\(q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +2187.01 q^{10} +63864.3 q^{11} +77025.5 q^{12} -164679. q^{13} -26152.8 q^{14} -39316.5 q^{15} +93981.5 q^{16} -362910. q^{17} +203267. q^{18} -436498. q^{19} -78978.6 q^{20} +470156. q^{21} +695638. q^{22} +918199. q^{23} +1.93105e6 q^{24} -1.91281e6 q^{25} -1.79375e6 q^{26} +200076. q^{27} +944445. q^{28} -3.68643e6 q^{29} -428253. q^{30} +3.47629e6 q^{31} +6.07279e6 q^{32} -1.25057e7 q^{33} -3.95298e6 q^{34} -482078. q^{35} -7.34049e6 q^{36} +1.88149e7 q^{37} -4.75453e6 q^{38} +3.22469e7 q^{39} -1.98002e6 q^{40} +2.40714e6 q^{41} +5.12115e6 q^{42} -1.25306e7 q^{43} -2.51213e7 q^{44} +3.74685e6 q^{45} +1.00014e7 q^{46} -5.54509e7 q^{47} -1.84032e7 q^{48} +5.76480e6 q^{49} -2.08352e7 q^{50} +7.10639e7 q^{51} +6.47772e7 q^{52} -9.26889e7 q^{53} +2.17931e6 q^{54} +1.28228e7 q^{55} +2.36775e7 q^{56} +8.54737e7 q^{57} -4.01542e7 q^{58} -2.52600e7 q^{59} +1.54653e7 q^{60} +6.93275e7 q^{61} +3.78653e7 q^{62} -4.48057e7 q^{63} +1.80290e7 q^{64} -3.30646e7 q^{65} -1.36218e8 q^{66} -2.33494e7 q^{67} +1.42752e8 q^{68} -1.79799e8 q^{69} -5.25101e6 q^{70} -1.06194e8 q^{71} -1.84028e8 q^{72} -2.10115e8 q^{73} +2.04940e8 q^{74} +3.74561e8 q^{75} +1.71699e8 q^{76} -1.53338e8 q^{77} +3.51247e8 q^{78} -149606. q^{79} +1.88698e7 q^{80} -4.06488e8 q^{81} +2.62197e7 q^{82} +5.21565e8 q^{83} -1.84938e8 q^{84} -7.28659e7 q^{85} -1.36489e8 q^{86} +7.21865e8 q^{87} -6.29799e8 q^{88} +2.98587e8 q^{89} +4.08123e7 q^{90} +3.95394e8 q^{91} -3.61178e8 q^{92} -6.80716e8 q^{93} -6.03996e8 q^{94} -8.76410e7 q^{95} -1.18915e9 q^{96} -8.95983e8 q^{97} +6.27928e7 q^{98} +1.19179e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9}+O(q^{10}) $ 2 * q - 6 * q^2 - 86 * q^3 - 620 * q^4 - 2238 * q^5 - 3988 * q^6 - 4802 * q^7 + 2616 * q^8 + 11038 * q^9	\( 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9} + 43384 q^{10} + 35316 q^{11} + 52136 q^{12} - 26530 q^{13} + 14406 q^{14} - 307136 q^{15} - 752 q^{16} - 463920 q^{17} + 332042 q^{18} - 925426 q^{19} + 473760 q^{20} + 206486 q^{21} + 1177888 q^{22} + 778128 q^{23} + 3301296 q^{24} + 2081722 q^{25} - 4127424 q^{26} - 2798612 q^{27} + 1488620 q^{28} - 10003584 q^{29} + 4095872 q^{30} + 2467260 q^{31} + 1284576 q^{32} - 15640784 q^{33} - 2246676 q^{34} + 5373438 q^{35} - 5612716 q^{36} + 30735552 q^{37} + 3504660 q^{38} + 47417944 q^{39} - 32409984 q^{40} - 19103448 q^{41} + 9575188 q^{42} + 4065100 q^{43} - 18650976 q^{44} + 22338298 q^{45} + 12367584 q^{46} - 82195020 q^{47} - 28806496 q^{48} + 11529602 q^{49} - 88312626 q^{50} + 59971356 q^{51} + 33466384 q^{52} - 55189812 q^{53} + 52834472 q^{54} + 82445816 q^{55} - 6281016 q^{56} + 31781116 q^{57} + 66558004 q^{58} - 7069218 q^{59} + 76165376 q^{60} + 44316386 q^{61} + 54910200 q^{62} - 26502238 q^{63} + 147417152 q^{64} - 369979260 q^{65} - 83258464 q^{66} - 241921336 q^{67} + 165645816 q^{68} - 195181152 q^{69} - 104164984 q^{70} + 206493816 q^{71} - 279147720 q^{72} - 499153188 q^{73} + 3571524 q^{74} + 813228014 q^{75} + 282511768 q^{76} - 84793716 q^{77} + 94970960 q^{78} + 468535096 q^{79} + 249904128 q^{80} - 585745634 q^{81} + 389586092 q^{82} + 444023958 q^{83} - 125178536 q^{84} + 173475060 q^{85} - 416830608 q^{86} + 28134340 q^{87} - 986010816 q^{88} + 636267396 q^{89} - 273242728 q^{90} + 63698530 q^{91} - 329431488 q^{92} - 791523960 q^{93} - 152223192 q^{94} + 1104747984 q^{95} - 1714981184 q^{96} - 1632716064 q^{97} - 34588806 q^{98} + 1409417860 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 - 86 * q^3 - 620 * q^4 - 2238 * q^5 - 3988 * q^6 - 4802 * q^7 + 2616 * q^8 + 11038 * q^9 + 43384 * q^10 + 35316 * q^11 + 52136 * q^12 - 26530 * q^13 + 14406 * q^14 - 307136 * q^15 - 752 * q^16 - 463920 * q^17 + 332042 * q^18 - 925426 * q^19 + 473760 * q^20 + 206486 * q^21 + 1177888 * q^22 + 778128 * q^23 + 3301296 * q^24 + 2081722 * q^25 - 4127424 * q^26 - 2798612 * q^27 + 1488620 * q^28 - 10003584 * q^29 + 4095872 * q^30 + 2467260 * q^31 + 1284576 * q^32 - 15640784 * q^33 - 2246676 * q^34 + 5373438 * q^35 - 5612716 * q^36 + 30735552 * q^37 + 3504660 * q^38 + 47417944 * q^39 - 32409984 * q^40 - 19103448 * q^41 + 9575188 * q^42 + 4065100 * q^43 - 18650976 * q^44 + 22338298 * q^45 + 12367584 * q^46 - 82195020 * q^47 - 28806496 * q^48 + 11529602 * q^49 - 88312626 * q^50 + 59971356 * q^51 + 33466384 * q^52 - 55189812 * q^53 + 52834472 * q^54 + 82445816 * q^55 - 6281016 * q^56 + 31781116 * q^57 + 66558004 * q^58 - 7069218 * q^59 + 76165376 * q^60 + 44316386 * q^61 + 54910200 * q^62 - 26502238 * q^63 + 147417152 * q^64 - 369979260 * q^65 - 83258464 * q^66 - 241921336 * q^67 + 165645816 * q^68 - 195181152 * q^69 - 104164984 * q^70 + 206493816 * q^71 - 279147720 * q^72 - 499153188 * q^73 + 3571524 * q^74 + 813228014 * q^75 + 282511768 * q^76 - 84793716 * q^77 + 94970960 * q^78 + 468535096 * q^79 + 249904128 * q^80 - 585745634 * q^81 + 389586092 * q^82 + 444023958 * q^83 - 125178536 * q^84 + 173475060 * q^85 - 416830608 * q^86 + 28134340 * q^87 - 986010816 * q^88 + 636267396 * q^89 - 273242728 * q^90 + 63698530 * q^91 - 329431488 * q^92 - 791523960 * q^93 - 152223192 * q^94 + 1104747984 * q^95 - 1714981184 * q^96 - 1632716064 * q^97 - 34588806 * q^98 + 1409417860 * 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 $

$2$	10.8924	0.481383	0.240691	−	0.970602i	$-0.422626\pi$
$2$	10.8924	0.481383	0.240691	+	0.970602i	$0.422626\pi$
$3$	−195.817	−1.39574	−0.697870	−	0.716225i	$-0.745869\pi$
$3$	−195.817	−1.39574	−0.697870	+	0.716225i	$0.745869\pi$
$4$	−393.355	−0.768271
$5$	200.782	0.143668	0.0718340	−	0.997417i	$-0.477115\pi$
$5$	200.782	0.143668	0.0718340	+	0.997417i	$0.477115\pi$
$6$	−2132.92	−0.671885
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−9861.52	−0.851215
$9$	18661.3	0.948090
$10$	2187.01	0.0691593
$11$	63864.3	1.31520	0.657599	−	0.753369i	$-0.271572\pi$
$11$	63864.3	1.31520	0.657599	+	0.753369i	$0.271572\pi$
$12$	77025.5	1.07231
$13$	−164679.	−1.59916	−0.799581	−	0.600558i	$-0.794945\pi$
$13$	−164679.	−1.59916	−0.799581	+	0.600558i	$0.794945\pi$
$14$	−26152.8	−0.181946
$15$	−39316.5	−0.200523
$16$	93981.5	0.358511
$17$	−362910.	−1.05385	−0.526925	−	0.849912i	$-0.676655\pi$
$17$	−362910.	−1.05385	−0.526925	+	0.849912i	$0.676655\pi$
$18$	203267.	0.456394
$19$	−436498.	−0.768406	−0.384203	−	0.923249i	$-0.625524\pi$
$19$	−436498.	−0.768406	−0.384203	+	0.923249i	$0.625524\pi$
$20$	−78978.6	−0.110376
$21$	470156.	0.527540
$22$	695638.	0.633113
$23$	918199.	0.684166	0.342083	−	0.939670i	$-0.388868\pi$
$23$	918199.	0.684166	0.342083	+	0.939670i	$0.388868\pi$
$24$	1.93105e6	1.18807
$25$	−1.91281e6	−0.979359
$26$	−1.79375e6	−0.769809
$27$	200076.	0.0724531
$28$	944445.	0.290379
$29$	−3.68643e6	−0.967865	−0.483932	−	0.875105i	$-0.660792\pi$
$29$	−3.68643e6	−0.967865	−0.483932	+	0.875105i	$0.660792\pi$
$30$	−428253.	−0.0965284
$31$	3.47629e6	0.676064	0.338032	−	0.941135i	$-0.390239\pi$
$31$	3.47629e6	0.676064	0.338032	+	0.941135i	$0.390239\pi$
$32$	6.07279e6	1.02380
$33$	−1.25057e7	−1.83567
$34$	−3.95298e6	−0.507305
$35$	−482078.	−0.0543014
$36$	−7.34049e6	−0.728390
$37$	1.88149e7	1.65042	0.825210	−	0.564826i	$-0.191057\pi$
$37$	1.88149e7	1.65042	0.825210	+	0.564826i	$0.191057\pi$
$38$	−4.75453e6	−0.369897
$39$	3.22469e7	2.23201
$40$	−1.98002e6	−0.122292
$41$	2.40714e6	0.133038	0.0665188	−	0.997785i	$-0.478811\pi$
$41$	2.40714e6	0.133038	0.0665188	+	0.997785i	$0.478811\pi$
$42$	5.12115e6	0.253949
$43$	−1.25306e7	−0.558938	−0.279469	−	0.960155i	$-0.590158\pi$
$43$	−1.25306e7	−0.558938	−0.279469	+	0.960155i	$0.590158\pi$
$44$	−2.51213e7	−1.01043
$45$	3.74685e6	0.136210
$46$	1.00014e7	0.329346
$47$	−5.54509e7	−1.65756	−0.828779	−	0.559577i	$-0.810964\pi$
$47$	−5.54509e7	−1.65756	−0.828779	+	0.559577i	$0.810964\pi$
$48$	−1.84032e7	−0.500388
$49$	5.76480e6	0.142857
$50$	−2.08352e7	−0.471447
$51$	7.10639e7	1.47090
$52$	6.47772e7	1.22859
$53$	−9.26889e7	−1.61356	−0.806782	−	0.590849i	$-0.798793\pi$
$53$	−9.26889e7	−1.61356	−0.806782	+	0.590849i	$0.798793\pi$
$54$	2.17931e6	0.0348777
$55$	1.28228e7	0.188952
$56$	2.36775e7	0.321729
$57$	8.54737e7	1.07250
$58$	−4.01542e7	−0.465913
$59$	−2.52600e7	−0.271393	−0.135696	−	0.990750i	$-0.543327\pi$
$59$	−2.52600e7	−0.271393	−0.135696	+	0.990750i	$0.543327\pi$
$60$	1.54653e7	0.154056
$61$	6.93275e7	0.641093	0.320547	−	0.947233i	$-0.396133\pi$
$61$	6.93275e7	0.641093	0.320547	+	0.947233i	$0.396133\pi$
$62$	3.78653e7	0.325446
$63$	−4.48057e7	−0.358344
$64$	1.80290e7	0.134326
$65$	−3.30646e7	−0.229748
$66$	−1.36218e8	−0.883661
$67$	−2.33494e7	−0.141559	−0.0707796	−	0.997492i	$-0.522549\pi$
$67$	−2.33494e7	−0.141559	−0.0707796	+	0.997492i	$0.522549\pi$
$68$	1.42752e8	0.809643
$69$	−1.79799e8	−0.954918
$70$	−5.25101e6	−0.0261398
$71$	−1.06194e8	−0.495950	−0.247975	−	0.968766i	$-0.579765\pi$
$71$	−1.06194e8	−0.495950	−0.247975	+	0.968766i	$0.579765\pi$
$72$	−1.84028e8	−0.807028
$73$	−2.10115e8	−0.865974	−0.432987	−	0.901400i	$-0.642540\pi$
$73$	−2.10115e8	−0.865974	−0.432987	+	0.901400i	$0.642540\pi$
$74$	2.04940e8	0.794483
$75$	3.74561e8	1.36693
$76$	1.71699e8	0.590344
$77$	−1.53338e8	−0.497098
$78$	3.51247e8	1.07445
$79$	−149606.	−0.000432144 0	−0.000216072	−	1.00000i	$-0.500069\pi$
$79$	−149606.	−0.000432144 0	−0.000216072		1.00000i	$0.500069\pi$
$80$	1.88698e7	0.0515066
$81$	−4.06488e8	−1.04922
$82$	2.62197e7	0.0640420
$83$	5.21565e8	1.20630	0.603152	−	0.797626i	$-0.293911\pi$
$83$	5.21565e8	1.20630	0.603152	+	0.797626i	$0.293911\pi$
$84$	−1.84938e8	−0.405294
$85$	−7.28659e7	−0.151405
$86$	−1.36489e8	−0.269063
$87$	7.21865e8	1.35089
$88$	−6.29799e8	−1.11952
$89$	2.98587e8	0.504448	0.252224	−	0.967669i	$-0.418838\pi$
$89$	2.98587e8	0.504448	0.252224	+	0.967669i	$0.418838\pi$
$90$	4.08123e7	0.0655692
$91$	3.95394e8	0.604426
$92$	−3.61178e8	−0.525625
$93$	−6.80716e8	−0.943610
$94$	−6.03996e8	−0.797919
$95$	−8.76410e7	−0.110395
$96$	−1.18915e9	−1.42895
$97$	−8.95983e8	−1.02761	−0.513803	−	0.857908i	$-0.671764\pi$
$97$	−8.95983e8	−1.02761	−0.513803	+	0.857908i	$0.671764\pi$
$98$	6.27928e7	0.0687689
$99$	1.19179e9	1.24693
$100$	7.52413e8	0.752413
$101$	−4.13043e7	−0.0394956	−0.0197478	−	0.999805i	$-0.506286\pi$
$101$	−4.13043e7	−0.0394956	−0.0197478	+	0.999805i	$0.506286\pi$
$102$	7.74060e8	0.708066
$103$	4.29472e8	0.375982	0.187991	−	0.982171i	$-0.439802\pi$
$103$	4.29472e8	0.375982	0.187991	+	0.982171i	$0.439802\pi$
$104$	1.62398e9	1.36123
$105$	9.43990e7	0.0757906
$106$	−1.00961e9	−0.776742
$107$	1.23287e9	0.909265	0.454632	−	0.890679i	$-0.349771\pi$
$107$	1.23287e9	0.909265	0.454632	+	0.890679i	$0.349771\pi$
$108$	−7.87006e7	−0.0556636
$109$	1.69619e9	1.15095	0.575475	−	0.817820i	$-0.304817\pi$
$109$	1.69619e9	1.15095	0.575475	+	0.817820i	$0.304817\pi$
$110$	1.39672e8	0.0909581
$111$	−3.68428e9	−2.30356
$112$	−2.25650e8	−0.135504
$113$	−1.42449e9	−0.821878	−0.410939	−	0.911663i	$-0.634799\pi$
$113$	−1.42449e9	−0.821878	−0.410939	+	0.911663i	$0.634799\pi$
$114$	9.31017e8	0.516281
$115$	1.84358e8	0.0982928
$116$	1.45007e9	0.743582
$117$	−3.07311e9	−1.51615
$118$	−2.75143e8	−0.130644
$119$	8.71347e8	0.398318
$120$	3.87721e8	0.170688
$121$	1.72070e9	0.729744
$122$	7.55146e8	0.308611
$123$	−4.71359e8	−0.185686
$124$	−1.36741e9	−0.519401
$125$	−7.76211e8	−0.284371
$126$	−4.88043e8	−0.172501
$127$	−3.12858e9	−1.06716	−0.533581	−	0.845749i	$-0.679154\pi$
$127$	−3.12858e9	−1.06716	−0.533581	+	0.845749i	$0.679154\pi$
$128$	−2.91289e9	−0.959133
$129$	2.45370e9	0.780132
$130$	−3.60154e8	−0.110597
$131$	7.03123e8	0.208598	0.104299	−	0.994546i	$-0.466740\pi$
$131$	7.03123e8	0.208598	0.104299	+	0.994546i	$0.466740\pi$
$132$	4.91918e9	1.41029
$133$	1.04803e9	0.290430
$134$	−2.54332e8	−0.0681442
$135$	4.01716e7	0.0104092
$136$	3.57885e9	0.897053
$137$	−3.07310e9	−0.745306	−0.372653	−	0.927971i	$-0.621552\pi$
$137$	−3.07310e9	−0.745306	−0.372653	+	0.927971i	$0.621552\pi$
$138$	−1.95845e9	−0.459681
$139$	5.07806e9	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$139$	5.07806e9	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$140$	1.89628e8	0.0417182
$141$	1.08582e10	2.31352
$142$	−1.15671e9	−0.238742
$143$	−1.05171e10	−2.10321
$144$	1.75381e9	0.339901
$145$	−7.40169e8	−0.139051
$146$	−2.28867e9	−0.416865
$147$	−1.12885e9	−0.199391
$148$	−7.40093e9	−1.26797
$149$	2.13455e9	0.354788	0.177394	−	0.984140i	$-0.443233\pi$
$149$	2.13455e9	0.354788	0.177394	+	0.984140i	$0.443233\pi$
$150$	4.07988e9	0.658017
$151$	−2.35298e9	−0.368318	−0.184159	−	0.982897i	$-0.558956\pi$
$151$	−2.35298e9	−0.368318	−0.184159	+	0.982897i	$0.558956\pi$
$152$	4.30454e9	0.654079
$153$	−6.77236e9	−0.999145
$154$	−1.67023e9	−0.239294
$155$	6.97977e8	0.0971288
$156$	−1.26845e10	−1.71479
$157$	−2.98482e9	−0.392075	−0.196038	−	0.980596i	$-0.562807\pi$
$157$	−2.98482e9	−0.392075	−0.196038	+	0.980596i	$0.562807\pi$
$158$	−1.62958e6	−0.000208027 0
$159$	1.81501e10	2.25212
$160$	1.21931e9	0.147087
$161$	−2.20460e9	−0.258591
$162$	−4.42764e9	−0.505074
$163$	9.20745e9	1.02163	0.510817	−	0.859690i	$-0.329343\pi$
$163$	9.20745e9	1.02163	0.510817	+	0.859690i	$0.329343\pi$
$164$	−9.46860e8	−0.102209
$165$	−2.51092e9	−0.263728
$166$	5.68111e9	0.580694
$167$	−4.95501e9	−0.492970	−0.246485	−	0.969147i	$-0.579276\pi$
$167$	−4.95501e9	−0.492970	−0.246485	+	0.969147i	$0.579276\pi$
$168$	−4.63646e9	−0.449050
$169$	1.65146e10	1.55732
$170$	−7.93688e8	−0.0728835
$171$	−8.14560e9	−0.728518
$172$	4.92897e9	0.429416
$173$	3.77546e9	0.320452	0.160226	−	0.987080i	$-0.448778\pi$
$173$	3.77546e9	0.320452	0.160226	+	0.987080i	$0.448778\pi$
$174$	7.86287e9	0.650294
$175$	4.59266e9	0.370163
$176$	6.00206e9	0.471513
$177$	4.94633e9	0.378794
$178$	3.25235e9	0.242833
$179$	−1.94362e10	−1.41505	−0.707526	−	0.706687i	$-0.750189\pi$
$179$	−1.94362e10	−1.41505	−0.707526	+	0.706687i	$0.750189\pi$
$180$	−1.47384e9	−0.104646
$181$	−9.81530e9	−0.679751	−0.339875	−	0.940470i	$-0.610385\pi$
$181$	−9.81530e9	−0.679751	−0.339875	+	0.940470i	$0.610385\pi$
$182$	4.30680e9	0.290960
$183$	−1.35755e10	−0.894799
$184$	−9.05485e9	−0.582373
$185$	3.77770e9	0.237113
$186$	−7.41466e9	−0.454237
$187$	−2.31770e10	−1.38602
$188$	2.18119e10	1.27345
$189$	−4.80381e8	−0.0273847
$190$	−9.54625e8	−0.0531424
$191$	−1.84579e10	−1.00354	−0.501768	−	0.865002i	$-0.667317\pi$
$191$	−1.84579e10	−1.00354	−0.501768	+	0.865002i	$0.667317\pi$
$192$	−3.53038e9	−0.187485
$193$	4.83605e9	0.250890	0.125445	−	0.992101i	$-0.459964\pi$
$193$	4.83605e9	0.250890	0.125445	+	0.992101i	$0.459964\pi$
$194$	−9.75944e9	−0.494672
$195$	6.47460e9	0.320669
$196$	−2.26761e9	−0.109753
$197$	2.70242e10	1.27836	0.639182	−	0.769056i	$-0.279273\pi$
$197$	2.70242e10	1.27836	0.639182	+	0.769056i	$0.279273\pi$
$198$	1.29815e10	0.600248
$199$	1.65772e10	0.749330	0.374665	−	0.927160i	$-0.377758\pi$
$199$	1.65772e10	0.749330	0.374665	+	0.927160i	$0.377758\pi$
$200$	1.88632e10	0.833645
$201$	4.57220e9	0.197580
$202$	−4.49904e8	−0.0190125
$203$	8.85111e9	0.365819
$204$	−2.79533e10	−1.13005
$205$	4.83311e8	0.0191132
$206$	4.67800e9	0.180991
$207$	1.71348e10	0.648651
$208$	−1.54768e10	−0.573317
$209$	−2.78766e10	−1.01061
$210$	1.02824e9	0.0364843
$211$	−5.44866e10	−1.89243	−0.946213	−	0.323544i	$-0.895126\pi$
$211$	−5.44866e10	−1.89243	−0.946213	+	0.323544i	$0.895126\pi$
$212$	3.64596e10	1.23965
$213$	2.07946e10	0.692218
$214$	1.34290e10	0.437704
$215$	−2.51592e9	−0.0803015
$216$	−1.97305e9	−0.0616731
$217$	−8.34657e9	−0.255528
$218$	1.84757e10	0.554047
$219$	4.11441e10	1.20867
$220$	−5.04391e9	−0.145166
$221$	5.97636e10	1.68528
$222$	−4.01308e10	−1.10889
$223$	−2.05500e10	−0.556468	−0.278234	−	0.960513i	$-0.589749\pi$
$223$	−2.05500e10	−0.556468	−0.278234	+	0.960513i	$0.589749\pi$
$224$	−1.45808e10	−0.386958
$225$	−3.56955e10	−0.928521
$226$	−1.55162e10	−0.395638
$227$	−3.94058e10	−0.985017	−0.492509	−	0.870307i	$-0.663920\pi$
$227$	−3.94058e10	−0.985017	−0.492509	+	0.870307i	$0.663920\pi$
$228$	−3.36215e10	−0.823967
$229$	−1.82516e10	−0.438572	−0.219286	−	0.975661i	$-0.570373\pi$
$229$	−1.82516e10	−0.438572	−0.219286	+	0.975661i	$0.570373\pi$
$230$	2.00811e9	0.0473165
$231$	3.00262e10	0.693819
$232$	3.63538e10	0.823861
$233$	−5.08161e10	−1.12953	−0.564767	−	0.825250i	$-0.691034\pi$
$233$	−5.08161e10	−1.12953	−0.564767	+	0.825250i	$0.691034\pi$
$234$	−3.34737e10	−0.729848
$235$	−1.11336e10	−0.238138
$236$	9.93612e9	0.208503
$237$	2.92955e7	0.000603160 0
$238$	9.49110e9	0.191743
$239$	3.80447e10	0.754230	0.377115	−	0.926166i	$-0.376916\pi$
$239$	3.80447e10	0.754230	0.377115	+	0.926166i	$0.376916\pi$
$240$	−3.69503e9	−0.0718898
$241$	9.80077e10	1.87147	0.935737	−	0.352699i	$-0.114736\pi$
$241$	9.80077e10	1.87147	0.935737	+	0.352699i	$0.114736\pi$
$242$	1.87426e10	0.351286
$243$	7.56590e10	1.39198
$244$	−2.72703e10	−0.492533
$245$	1.15747e9	0.0205240
$246$	−5.13425e9	−0.0893859
$247$	7.18819e10	1.22881
$248$	−3.42815e10	−0.575476
$249$	−1.02131e11	−1.68369
$250$	−8.45484e9	−0.136891
$251$	7.75125e10	1.23265	0.616325	−	0.787492i	$-0.288621\pi$
$251$	7.75125e10	1.23265	0.616325	+	0.787492i	$0.288621\pi$
$252$	1.76245e10	0.275305
$253$	5.86401e10	0.899814
$254$	−3.40778e10	−0.513713
$255$	1.42684e10	0.211321
$256$	−4.09593e10	−0.596036
$257$	−1.07589e11	−1.53840	−0.769199	−	0.639009i	$-0.779345\pi$
$257$	−1.07589e11	−1.53840	−0.769199	+	0.639009i	$0.779345\pi$
$258$	2.67268e10	0.375542
$259$	−4.51746e10	−0.623800
$260$	1.30061e10	0.176509
$261$	−6.87934e10	−0.917623
$262$	7.65873e9	0.100416
$263$	−1.21615e10	−0.156742	−0.0783708	−	0.996924i	$-0.524972\pi$
$263$	−1.21615e10	−0.156742	−0.0783708	+	0.996924i	$0.524972\pi$
$264$	1.23325e11	1.56255
$265$	−1.86103e10	−0.231818
$266$	1.14156e10	0.139808
$267$	−5.84685e10	−0.704078
$268$	9.18458e9	0.108756
$269$	−1.23517e11	−1.43827	−0.719134	−	0.694872i	$-0.755461\pi$
$269$	−1.23517e11	−1.43827	−0.719134	+	0.694872i	$0.755461\pi$
$270$	4.37567e8	0.00501080
$271$	1.34305e11	1.51263	0.756313	−	0.654210i	$-0.226999\pi$
$271$	1.34305e11	1.51263	0.756313	+	0.654210i	$0.226999\pi$
$272$	−3.41068e10	−0.377817
$273$	−7.74248e10	−0.843622
$274$	−3.34736e10	−0.358777
$275$	−1.22160e11	−1.28805
$276$	7.07248e10	0.733636
$277$	−2.16684e10	−0.221140	−0.110570	−	0.993868i	$-0.535268\pi$
$277$	−2.16684e10	−0.221140	−0.110570	+	0.993868i	$0.535268\pi$
$278$	5.53125e10	0.555420
$279$	6.48719e10	0.640970
$280$	4.75402e9	0.0462222
$281$	7.73283e9	0.0739878	0.0369939	−	0.999315i	$-0.488222\pi$
$281$	7.73283e9	0.0739878	0.0369939	+	0.999315i	$0.488222\pi$
$282$	1.18273e11	1.11369
$283$	−7.19601e10	−0.666888	−0.333444	−	0.942770i	$-0.608211\pi$
$283$	−7.19601e10	−0.666888	−0.333444	+	0.942770i	$0.608211\pi$
$284$	4.17720e10	0.381024
$285$	1.71616e10	0.154083
$286$	−1.14557e11	−1.01245
$287$	−5.77955e9	−0.0502835
$288$	1.13326e11	0.970650
$289$	1.31159e10	0.110601
$290$	−8.06225e9	−0.0669368
$291$	1.75449e11	1.43427
$292$	8.26498e10	0.665303
$293$	1.73674e11	1.37667	0.688335	−	0.725393i	$-0.258342\pi$
$293$	1.73674e11	1.37667	0.688335	+	0.725393i	$0.258342\pi$
$294$	−1.22959e10	−0.0959835
$295$	−5.07175e9	−0.0389905
$296$	−1.85544e11	−1.40486
$297$	1.27777e10	0.0952901
$298$	2.32505e10	0.170789
$299$	−1.51208e11	−1.09409
$300$	−1.47335e11	−1.05017
$301$	3.00860e10	0.211259
$302$	−2.56297e10	−0.177302
$303$	8.08807e9	0.0551256
$304$	−4.10227e10	−0.275482
$305$	1.39197e10	0.0921046
$306$	−7.37675e10	−0.480971
$307$	2.27108e11	1.45918	0.729591	−	0.683884i	$-0.239710\pi$
$307$	2.27108e11	1.45918	0.729591	+	0.683884i	$0.239710\pi$
$308$	6.03163e10	0.381906
$309$	−8.40978e10	−0.524773
$310$	7.60267e9	0.0467561
$311$	−8.68962e10	−0.526719	−0.263360	−	0.964698i	$-0.584831\pi$
$311$	−8.68962e10	−0.526719	−0.263360	+	0.964698i	$0.584831\pi$
$312$	−3.18003e11	−1.89992
$313$	−5.25289e10	−0.309349	−0.154674	−	0.987965i	$-0.549433\pi$
$313$	−5.25289e10	−0.309349	−0.154674	+	0.987965i	$0.549433\pi$
$314$	−3.25120e10	−0.188738
$315$	−8.99618e9	−0.0514826
$316$	5.88484e7	0.000332004 0
$317$	2.63784e11	1.46718	0.733588	−	0.679595i	$-0.237844\pi$
$317$	2.63784e11	1.46718	0.733588	+	0.679595i	$0.237844\pi$
$318$	1.97698e11	1.08413
$319$	−2.35431e11	−1.27293
$320$	3.61990e9	0.0192984
$321$	−2.41417e11	−1.26910
$322$	−2.40134e10	−0.124481
$323$	1.58410e11	0.809786
$324$	1.59894e11	0.806082
$325$	3.14999e11	1.56615
$326$	1.00292e11	0.491797
$327$	−3.32143e11	−1.60643
$328$	−2.37381e10	−0.113244
$329$	1.33138e11	0.626498
$330$	−2.73501e10	−0.126954
$331$	−2.11350e11	−0.967780	−0.483890	−	0.875129i	$-0.660776\pi$
$331$	−2.11350e11	−0.967780	−0.483890	+	0.875129i	$0.660776\pi$
$332$	−2.05160e11	−0.926768
$333$	3.51110e11	1.56475
$334$	−5.39722e10	−0.237307
$335$	−4.68813e9	−0.0203375
$336$	4.41860e10	0.189129
$337$	−3.67482e11	−1.55203	−0.776017	−	0.630712i	$-0.782763\pi$
$337$	−3.67482e11	−1.55203	−0.776017	+	0.630712i	$0.782763\pi$
$338$	1.79884e11	0.749666
$339$	2.78940e11	1.14713
$340$	2.86621e10	0.116320
$341$	2.22011e11	0.889158
$342$	−8.87255e10	−0.350696
$343$	−1.38413e10	−0.0539949
$344$	1.23571e11	0.475776
$345$	−3.61004e10	−0.137191
$346$	4.11240e10	0.154260
$347$	4.33866e11	1.60647	0.803235	−	0.595662i	$-0.203110\pi$
$347$	4.33866e11	1.60647	0.803235	+	0.595662i	$0.203110\pi$
$348$	−2.83949e11	−1.03785
$349$	1.04086e11	0.375559	0.187780	−	0.982211i	$-0.439871\pi$
$349$	1.04086e11	0.375559	0.187780	+	0.982211i	$0.439871\pi$
$350$	5.00253e10	0.178190
$351$	−3.29482e10	−0.115864
$352$	3.87834e11	1.34649
$353$	−4.46890e11	−1.53184	−0.765922	−	0.642934i	$-0.777717\pi$
$353$	−4.46890e11	−1.53184	−0.765922	+	0.642934i	$0.777717\pi$
$354$	5.38776e10	0.182345
$355$	−2.13219e10	−0.0712522
$356$	−1.17451e11	−0.387553
$357$	−1.70625e11	−0.555948
$358$	−2.11708e11	−0.681182
$359$	−1.96551e11	−0.624526	−0.312263	−	0.949996i	$-0.601087\pi$
$359$	−1.96551e11	−0.624526	−0.312263	+	0.949996i	$0.601087\pi$
$360$	−3.69496e10	−0.115944
$361$	−1.32157e11	−0.409551
$362$	−1.06913e11	−0.327220
$363$	−3.36942e11	−1.01853
$364$	−1.55530e11	−0.464363
$365$	−4.21874e10	−0.124413
$366$	−1.47870e11	−0.430741
$367$	−2.25518e11	−0.648908	−0.324454	−	0.945901i	$-0.605181\pi$
$367$	−2.25518e11	−0.648908	−0.324454	+	0.945901i	$0.605181\pi$
$368$	8.62937e10	0.245281
$369$	4.49203e10	0.126132
$370$	4.11484e10	0.114142
$371$	2.22546e11	0.609870
$372$	2.67763e11	0.724948
$373$	−2.04414e11	−0.546791	−0.273395	−	0.961902i	$-0.588147\pi$
$373$	−2.04414e11	−0.546791	−0.273395	+	0.961902i	$0.588147\pi$
$374$	−2.52454e11	−0.667206
$375$	1.51995e11	0.396908
$376$	5.46831e11	1.41094
$377$	6.07076e11	1.54777
$378$	−5.23253e9	−0.0131825
$379$	4.03306e10	0.100406	0.0502029	−	0.998739i	$-0.484013\pi$
$379$	4.03306e10	0.100406	0.0502029	+	0.998739i	$0.484013\pi$
$380$	3.44740e10	0.0848136
$381$	6.12628e11	1.48948
$382$	−2.01052e11	−0.483084
$383$	−3.98325e11	−0.945895	−0.472947	−	0.881091i	$-0.656810\pi$
$383$	−3.98325e11	−0.945895	−0.472947	+	0.881091i	$0.656810\pi$
$384$	5.70393e11	1.33870
$385$	−3.07876e10	−0.0714171
$386$	5.26764e10	0.120774
$387$	−2.33837e11	−0.529923
$388$	3.52439e11	0.789480
$389$	−4.22504e11	−0.935531	−0.467765	−	0.883853i	$-0.654941\pi$
$389$	−4.22504e11	−0.935531	−0.467765	+	0.883853i	$0.654941\pi$
$390$	7.05242e10	0.154365
$391$	−3.33224e11	−0.721009
$392$	−5.68497e10	−0.121602
$393$	−1.37683e11	−0.291149
$394$	2.94359e11	0.615382
$395$	−3.00383e7	−6.20853e−5 0
$396$	−4.68795e11	−0.957976
$397$	6.50999e11	1.31529	0.657647	−	0.753326i	$-0.271552\pi$
$397$	6.50999e11	1.31529	0.657647	+	0.753326i	$0.271552\pi$
$398$	1.80567e11	0.360714
$399$	−2.05222e11	−0.405365
$400$	−1.79769e11	−0.351111
$401$	−3.10509e11	−0.599687	−0.299843	−	0.953988i	$-0.596934\pi$
$401$	−3.10509e11	−0.599687	−0.299843	+	0.953988i	$0.596934\pi$
$402$	4.98024e10	0.0951115
$403$	−5.72471e11	−1.08114
$404$	1.62472e10	0.0303433
$405$	−8.16155e10	−0.150739
$406$	9.64102e10	0.176099
$407$	1.20160e12	2.17063
$408$	−7.00799e11	−1.25205
$409$	2.99519e11	0.529261	0.264630	−	0.964350i	$-0.414750\pi$
$409$	2.99519e11	0.529261	0.264630	+	0.964350i	$0.414750\pi$
$410$	5.26444e9	0.00920078
$411$	6.01766e11	1.04025
$412$	−1.68935e11	−0.288856
$413$	6.06492e10	0.102577
$414$	1.86639e11	0.312249
$415$	1.04721e11	0.173307
$416$	−1.00006e12	−1.63722
$417$	−9.94370e11	−1.61041
$418$	−3.03645e11	−0.486488
$419$	−4.35217e11	−0.689832	−0.344916	−	0.938634i	$-0.612093\pi$
$419$	−4.35217e11	−0.689832	−0.344916	+	0.938634i	$0.612093\pi$
$420$	−3.71323e10	−0.0582277
$421$	−2.07600e11	−0.322076	−0.161038	−	0.986948i	$-0.551484\pi$
$421$	−2.07600e11	−0.322076	−0.161038	+	0.986948i	$0.551484\pi$
$422$	−5.93493e11	−0.910981
$423$	−1.03478e12	−1.57151
$424$	9.14054e11	1.37349
$425$	6.94179e11	1.03210
$426$	2.26504e11	0.333222
$427$	−1.66455e11	−0.242310
$428$	−4.84955e11	−0.698562
$429$	2.05942e12	2.93554
$430$	−2.74045e10	−0.0386557
$431$	8.61584e11	1.20268	0.601340	−	0.798993i	$-0.294634\pi$
$431$	8.61584e11	1.20268	0.601340	+	0.798993i	$0.294634\pi$
$432$	1.88034e10	0.0259752
$433$	1.45840e11	0.199379	0.0996896	−	0.995019i	$-0.468215\pi$
$433$	1.45840e11	0.199379	0.0996896	+	0.995019i	$0.468215\pi$
$434$	−9.09145e10	−0.123007
$435$	1.44938e11	0.194079
$436$	−6.67206e11	−0.884241
$437$	−4.00792e11	−0.525718
$438$	4.48160e11	0.581835
$439$	−1.07131e11	−0.137665	−0.0688324	−	0.997628i	$-0.521927\pi$
$439$	−1.07131e11	−0.137665	−0.0688324	+	0.997628i	$0.521927\pi$
$440$	−1.26452e11	−0.160839
$441$	1.07578e11	0.135441
$442$	6.50972e11	0.811263
$443$	−1.36838e11	−0.168806	−0.0844031	−	0.996432i	$-0.526898\pi$
$443$	−1.36838e11	−0.168806	−0.0844031	+	0.996432i	$0.526898\pi$
$444$	1.44923e12	1.76976
$445$	5.99510e10	0.0724731
$446$	−2.23840e11	−0.267874
$447$	−4.17981e11	−0.495191
$448$	−4.32876e10	−0.0507706
$449$	−7.65671e11	−0.889065	−0.444532	−	0.895763i	$-0.646630\pi$
$449$	−7.65671e11	−0.889065	−0.444532	+	0.895763i	$0.646630\pi$
$450$	−3.88811e11	−0.446974
$451$	1.53730e11	0.174971
$452$	5.60331e11	0.631425
$453$	4.60754e11	0.514076
$454$	−4.29226e11	−0.474170
$455$	7.93880e10	0.0868368
$456$	−8.42901e11	−0.912924
$457$	5.41842e11	0.581099	0.290549	−	0.956860i	$-0.406162\pi$
$457$	5.41842e11	0.581099	0.290549	+	0.956860i	$0.406162\pi$
$458$	−1.98805e11	−0.211121
$459$	−7.26094e10	−0.0763547
$460$	−7.25181e10	−0.0755155
$461$	−7.10838e11	−0.733021	−0.366510	−	0.930414i	$-0.619448\pi$
$461$	−7.10838e11	−0.733021	−0.366510	+	0.930414i	$0.619448\pi$
$462$	3.27059e11	0.333992
$463$	7.96272e11	0.805280	0.402640	−	0.915358i	$-0.368093\pi$
$463$	7.96272e11	0.805280	0.402640	+	0.915358i	$0.368093\pi$
$464$	−3.46456e11	−0.346990
$465$	−1.36676e11	−0.135567
$466$	−5.53511e11	−0.543738
$467$	−1.67673e12	−1.63132	−0.815658	−	0.578535i	$-0.803625\pi$
$467$	−1.67673e12	−1.63132	−0.815658	+	0.578535i	$0.803625\pi$
$468$	1.20882e12	1.16481
$469$	5.60618e10	0.0535044
$470$	−1.21272e11	−0.114635
$471$	5.84478e11	0.547235
$472$	2.49102e11	0.231014
$473$	−8.00257e11	−0.735114
$474$	3.19099e8	0.000290351 0
$475$	8.34938e11	0.752546
$476$	−3.42749e11	−0.306016
$477$	−1.72969e12	−1.52980
$478$	4.14400e11	0.363073
$479$	1.17129e12	1.01661	0.508305	−	0.861177i	$-0.330272\pi$
$479$	1.17129e12	1.01661	0.508305	+	0.861177i	$0.330272\pi$
$480$	−2.38761e11	−0.205295
$481$	−3.09842e12	−2.63929
$482$	1.06754e12	0.900895
$483$	4.31697e11	0.360925
$484$	−6.76844e11	−0.560641
$485$	−1.79897e11	−0.147634
$486$	8.24112e11	0.670074
$487$	4.49797e11	0.362357	0.181178	−	0.983450i	$-0.442009\pi$
$487$	4.49797e11	0.362357	0.181178	+	0.983450i	$0.442009\pi$
$488$	−6.83675e11	−0.545708
$489$	−1.80297e12	−1.42594
$490$	1.26077e10	0.00987990
$491$	2.25034e12	1.74735	0.873677	−	0.486506i	$-0.161729\pi$
$491$	2.25034e12	1.74735	0.873677	+	0.486506i	$0.161729\pi$
$492$	1.85411e11	0.142657
$493$	1.33784e12	1.01998
$494$	7.82970e11	0.591526
$495$	2.39290e11	0.179143
$496$	3.26707e11	0.242376
$497$	2.54972e11	0.187452
$498$	−1.11246e12	−0.810497
$499$	1.59712e10	0.0115315	0.00576574	−	0.999983i	$-0.498165\pi$
$499$	1.59712e10	0.0115315	0.00576574	+	0.999983i	$0.498165\pi$
$500$	3.05326e11	0.218474
$501$	9.70275e11	0.688058
$502$	8.44300e11	0.593376
$503$	1.73375e12	1.20762	0.603811	−	0.797127i	$-0.293648\pi$
$503$	1.73375e12	1.20762	0.603811	+	0.797127i	$0.293648\pi$
$504$	4.41852e11	0.305028
$505$	−8.29316e9	−0.00567425
$506$	6.38734e11	0.433155
$507$	−3.23384e12	−2.17361
$508$	1.23064e12	0.819869
$509$	9.77460e11	0.645460	0.322730	−	0.946491i	$-0.395399\pi$
$509$	9.77460e11	0.645460	0.322730	+	0.946491i	$0.395399\pi$
$510$	1.55417e11	0.101726
$511$	5.04487e11	0.327307
$512$	1.04525e12	0.672212
$513$	−8.73326e10	−0.0556734
$514$	−1.17191e12	−0.740558
$515$	8.62303e10	0.0540166
$516$	−9.65175e11	−0.599353
$517$	−3.54133e12	−2.18001
$518$	−4.92062e11	−0.300286
$519$	−7.39300e11	−0.447268
$520$	3.26067e11	0.195565
$521$	5.89223e11	0.350356	0.175178	−	0.984537i	$-0.443950\pi$
$521$	5.89223e11	0.350356	0.175178	+	0.984537i	$0.443950\pi$
$522$	−7.49328e11	−0.441728
$523$	1.43218e12	0.837027	0.418513	−	0.908211i	$-0.362551\pi$
$523$	1.43218e12	0.837027	0.418513	+	0.908211i	$0.362551\pi$
$524$	−2.76577e11	−0.160260
$525$	−8.99320e11	−0.516651
$526$	−1.32468e11	−0.0754527
$527$	−1.26158e12	−0.712471
$528$	−1.17530e12	−0.658109
$529$	−9.58063e11	−0.531916
$530$	−2.02711e11	−0.111593
$531$	−4.71382e11	−0.257305
$532$	−4.12248e11	−0.223129
$533$	−3.96405e11	−0.212749
$534$	−6.36865e11	−0.338931
$535$	2.47538e11	0.130632
$536$	2.30260e11	0.120497
$537$	3.80594e12	1.97505
$538$	−1.34540e12	−0.692357
$539$	3.68165e11	0.187885
$540$	−1.58017e10	−0.00799708
$541$	1.17323e12	0.588839	0.294419	−	0.955676i	$-0.404874\pi$
$541$	1.17323e12	0.588839	0.294419	+	0.955676i	$0.404874\pi$
$542$	1.46291e12	0.728152
$543$	1.92200e12	0.948755
$544$	−2.20388e12	−1.07893
$545$	3.40565e11	0.165355
$546$	−8.43345e11	−0.406105
$547$	2.59515e11	0.123942	0.0619712	−	0.998078i	$-0.480261\pi$
$547$	2.59515e11	0.123942	0.0619712	+	0.998078i	$0.480261\pi$
$548$	1.20882e12	0.572597
$549$	1.29374e12	0.607814
$550$	−1.33062e12	−0.620045
$551$	1.60912e12	0.743714
$552$	1.77309e12	0.812841
$553$	3.59205e8	0.000163335 0
$554$	−2.36022e11	−0.106453
$555$	−7.39737e11	−0.330947
$556$	−1.99748e12	−0.886432
$557$	−2.36651e12	−1.04174	−0.520871	−	0.853635i	$-0.674393\pi$
$557$	−2.36651e12	−1.04174	−0.520871	+	0.853635i	$0.674393\pi$
$558$	7.06613e11	0.308552
$559$	2.06352e12	0.893832
$560$	−4.53064e10	−0.0194676
$561$	4.53845e12	1.93453
$562$	8.42294e10	0.0356164
$563$	−2.42400e12	−1.01682	−0.508410	−	0.861115i	$-0.669767\pi$
$563$	−2.42400e12	−1.01682	−0.508410	+	0.861115i	$0.669767\pi$
$564$	−4.27113e12	−1.77741
$565$	−2.86013e11	−0.118078
$566$	−7.83821e11	−0.321028
$567$	9.75977e11	0.396566
$568$	1.04724e12	0.422160
$569$	−2.11854e12	−0.847290	−0.423645	−	0.905828i	$-0.639250\pi$
$569$	−2.11854e12	−0.847290	−0.423645	+	0.905828i	$0.639250\pi$
$570$	1.86932e11	0.0741730
$571$	−7.50992e11	−0.295646	−0.147823	−	0.989014i	$-0.547227\pi$
$571$	−7.50992e11	−0.295646	−0.147823	+	0.989014i	$0.547227\pi$
$572$	4.13695e12	1.61584
$573$	3.61437e12	1.40067
$574$	−6.29534e10	−0.0242056
$575$	−1.75634e12	−0.670045
$576$	3.36444e11	0.127354
$577$	4.35951e12	1.63737	0.818685	−	0.574243i	$-0.194704\pi$
$577$	4.35951e12	1.63737	0.818685	+	0.574243i	$0.194704\pi$
$578$	1.42864e11	0.0532413
$579$	−9.46981e11	−0.350177
$580$	2.91149e11	0.106829
$581$	−1.25228e12	−0.455940
$582$	1.91106e12	0.690433
$583$	−5.91951e12	−2.12216
$584$	2.07206e12	0.737130
$585$	−6.17026e11	−0.217822
$586$	1.89173e12	0.662704
$587$	−2.20056e12	−0.765002	−0.382501	−	0.923955i	$-0.624937\pi$
$587$	−2.20056e12	−0.765002	−0.382501	+	0.923955i	$0.624937\pi$
$588$	4.44037e11	0.153187
$589$	−1.51739e12	−0.519492
$590$	−5.52438e10	−0.0187693
$591$	−5.29179e12	−1.78426
$592$	1.76825e12	0.591693
$593$	−2.83604e12	−0.941815	−0.470907	−	0.882183i	$-0.656073\pi$
$593$	−2.83604e12	−0.941815	−0.470907	+	0.882183i	$0.656073\pi$
$594$	1.39180e11	0.0458710
$595$	1.74951e11	0.0572256
$596$	−8.39636e11	−0.272573
$597$	−3.24610e12	−1.04587
$598$	−1.64702e12	−0.526677
$599$	−8.29286e11	−0.263199	−0.131599	−	0.991303i	$-0.542011\pi$
$599$	−8.29286e11	−0.263199	−0.131599	+	0.991303i	$0.542011\pi$
$600$	−3.69374e12	−1.16355
$601$	5.62459e12	1.75855	0.879277	−	0.476311i	$-0.158026\pi$
$601$	5.62459e12	1.75855	0.879277	+	0.476311i	$0.158026\pi$
$602$	3.27710e11	0.101696
$603$	−4.35728e11	−0.134211
$604$	9.25557e11	0.282968
$605$	3.45485e11	0.104841
$606$	8.80989e10	0.0265365
$607$	−4.68777e11	−0.140158	−0.0700789	−	0.997541i	$-0.522325\pi$
$607$	−4.68777e11	−0.140158	−0.0700789	+	0.997541i	$0.522325\pi$
$608$	−2.65076e12	−0.786691
$609$	−1.73320e12	−0.510588
$610$	1.51620e11	0.0443375
$611$	9.13159e12	2.65070
$612$	2.66394e12	0.767614
$613$	5.58394e12	1.59723	0.798617	−	0.601840i	$-0.205566\pi$
$613$	5.58394e12	1.59723	0.798617	+	0.601840i	$0.205566\pi$
$614$	2.47376e12	0.702425
$615$	−9.46405e10	−0.0266771
$616$	1.51215e12	0.423137
$617$	−3.36717e12	−0.935367	−0.467683	−	0.883896i	$-0.654911\pi$
$617$	−3.36717e12	−0.935367	−0.467683	+	0.883896i	$0.654911\pi$
$618$	−9.16031e11	−0.252617
$619$	−5.66928e12	−1.55210	−0.776051	−	0.630671i	$-0.782780\pi$
$619$	−5.66928e12	−1.55210	−0.776051	+	0.630671i	$0.782780\pi$
$620$	−2.74552e11	−0.0746212
$621$	1.83709e11	0.0495700
$622$	−9.46512e11	−0.253553
$623$	−7.16909e11	−0.190663
$624$	3.03061e12	0.800201
$625$	3.58011e12	0.938505
$626$	−5.72168e11	−0.148915
$627$	5.45871e12	1.41054
$628$	1.17409e12	0.301220
$629$	−6.82812e12	−1.73930
$630$	−9.79904e10	−0.0247828
$631$	−1.06685e12	−0.267899	−0.133950	−	0.990988i	$-0.542766\pi$
$631$	−1.06685e12	−0.267899	−0.133950	+	0.990988i	$0.542766\pi$
$632$	1.47535e9	0.000367847 0
$633$	1.06694e13	2.64133
$634$	2.87325e12	0.706273
$635$	−6.28163e11	−0.153317
$636$	−7.13941e12	−1.73024
$637$	−9.49340e11	−0.228452
$638$	−2.56442e12	−0.612768
$639$	−1.98172e12	−0.470205
$640$	−5.84856e11	−0.137797
$641$	−7.83632e12	−1.83337	−0.916686	−	0.399607i	$-0.869147\pi$
$641$	−7.83632e12	−1.83337	−0.916686	+	0.399607i	$0.869147\pi$
$642$	−2.62962e12	−0.610921
$643$	7.05971e12	1.62869	0.814343	−	0.580383i	$-0.197097\pi$
$643$	7.05971e12	1.62869	0.814343	+	0.580383i	$0.197097\pi$
$644$	8.67188e11	0.198668
$645$	4.92660e11	0.112080
$646$	1.72547e12	0.389817
$647$	2.77314e12	0.622161	0.311081	−	0.950384i	$-0.399309\pi$
$647$	2.77314e12	0.622161	0.311081	+	0.950384i	$0.399309\pi$
$648$	4.00859e12	0.893108
$649$	−1.61321e12	−0.356935
$650$	3.43111e12	0.753919
$651$	1.63440e12	0.356651
$652$	−3.62179e12	−0.784891
$653$	3.09564e12	0.666257	0.333128	−	0.942882i	$-0.391896\pi$
$653$	3.09564e12	0.666257	0.333128	+	0.942882i	$0.391896\pi$
$654$	−3.61785e12	−0.773305
$655$	1.41175e11	0.0299689
$656$	2.26227e11	0.0476954
$657$	−3.92102e12	−0.821021
$658$	1.45019e12	0.301585
$659$	−4.80261e12	−0.991958	−0.495979	−	0.868335i	$-0.665191\pi$
$659$	−4.80261e12	−0.991958	−0.495979	+	0.868335i	$0.665191\pi$
$660$	9.87683e11	0.202614
$661$	−5.13389e12	−1.04602	−0.523010	−	0.852327i	$-0.675191\pi$
$661$	−5.13389e12	−1.04602	−0.523010	+	0.852327i	$0.675191\pi$
$662$	−2.30212e12	−0.465872
$663$	−1.17027e13	−2.35221
$664$	−5.14342e12	−1.02682
$665$	2.10426e11	0.0417256
$666$	3.82444e12	0.753241
$667$	−3.38488e12	−0.662181
$668$	1.94908e12	0.378735
$669$	4.02404e12	0.776685
$670$	−5.10652e10	−0.00979014
$671$	4.42755e12	0.843164
$672$	2.85516e12	0.540093
$673$	4.43802e12	0.833915	0.416957	−	0.908926i	$-0.363096\pi$
$673$	4.43802e12	0.833915	0.416957	+	0.908926i	$0.363096\pi$
$674$	−4.00277e12	−0.747122
$675$	−3.82707e11	−0.0709576
$676$	−6.49609e12	−1.19644
$677$	−4.70675e12	−0.861136	−0.430568	−	0.902558i	$-0.641687\pi$
$677$	−4.70675e12	−0.861136	−0.430568	+	0.902558i	$0.641687\pi$
$678$	3.03834e12	0.552207
$679$	2.15126e12	0.388399
$680$	7.18569e11	0.128878
$681$	7.71632e12	1.37483
$682$	2.41824e12	0.428025
$683$	6.12667e11	0.107729	0.0538644	−	0.998548i	$-0.482846\pi$
$683$	6.12667e11	0.107729	0.0538644	+	0.998548i	$0.482846\pi$
$684$	3.20411e12	0.559699
$685$	−6.17025e11	−0.107077
$686$	−1.50765e11	−0.0259922
$687$	3.57397e12	0.612133
$688$	−1.17764e12	−0.200385
$689$	1.52639e13	2.58035
$690$	−3.93222e11	−0.0660415
$691$	2.69919e12	0.450383	0.225191	−	0.974315i	$-0.427699\pi$
$691$	2.69919e12	0.450383	0.225191	+	0.974315i	$0.427699\pi$
$692$	−1.48510e12	−0.246194
$693$	−2.86148e12	−0.471293
$694$	4.72586e12	0.773327
$695$	1.01958e12	0.165764
$696$	−7.11869e12	−1.14990
$697$	−8.73576e11	−0.140202
$698$	1.13375e12	0.180788
$699$	9.95064e12	1.57654
$700$	−1.80654e12	−0.284386
$701$	−5.78506e12	−0.904850	−0.452425	−	0.891802i	$-0.649441\pi$
$701$	−5.78506e12	−0.904850	−0.452425	+	0.891802i	$0.649441\pi$
$702$	−3.58886e11	−0.0557750
$703$	−8.21267e12	−1.26819
$704$	1.15141e12	0.176666
$705$	2.18014e12	0.332379
$706$	−4.86772e12	−0.737403
$707$	9.91715e10	0.0149279
$708$	−1.94566e12	−0.291016
$709$	−3.72656e12	−0.553860	−0.276930	−	0.960890i	$-0.589317\pi$
$709$	−3.72656e12	−0.553860	−0.276930	+	0.960890i	$0.589317\pi$
$710$	−2.32248e11	−0.0342996
$711$	−2.79184e9	−0.000409711 0
$712$	−2.94453e12	−0.429394
$713$	3.19192e12	0.462541
$714$	−1.85852e12	−0.267624
$715$	−2.11164e12	−0.302165
$716$	7.64532e12	1.08714
$717$	−7.44980e12	−1.05271
$718$	−2.14092e12	−0.300636
$719$	1.33255e13	1.85953	0.929765	−	0.368154i	$-0.120010\pi$
$719$	1.33255e13	1.85953	0.929765	+	0.368154i	$0.120010\pi$
$720$	3.52134e11	0.0488328
$721$	−1.03116e12	−0.142108
$722$	−1.43952e12	−0.197151
$723$	−1.91916e13	−2.61209
$724$	3.86089e12	0.522233
$725$	7.05144e12	0.947888
$726$	−3.67012e12	−0.490304
$727$	−2.39852e12	−0.318448	−0.159224	−	0.987242i	$-0.550899\pi$
$727$	−2.39852e12	−0.318448	−0.159224	+	0.987242i	$0.550899\pi$
$728$	−3.89918e12	−0.514497
$729$	−6.81442e12	−0.893625
$730$	−4.59524e11	−0.0598901
$731$	4.54748e12	0.589037
$732$	5.33998e12	0.687448
$733$	7.93815e12	1.01567	0.507834	−	0.861455i	$-0.330446\pi$
$733$	7.93815e12	1.01567	0.507834	+	0.861455i	$0.330446\pi$
$734$	−2.45644e12	−0.312373
$735$	−2.26652e11	−0.0286462
$736$	5.57603e12	0.700447
$737$	−1.49119e12	−0.186178
$738$	4.89292e11	0.0607175
$739$	−2.20371e12	−0.271803	−0.135902	−	0.990722i	$-0.543393\pi$
$739$	−2.20371e12	−0.271803	−0.135902	+	0.990722i	$0.543393\pi$
$740$	−1.48598e12	−0.182167
$741$	−1.40757e13	−1.71509
$742$	2.42407e12	0.293581
$743$	−1.09079e12	−0.131308	−0.0656540	−	0.997842i	$-0.520913\pi$
$743$	−1.09079e12	−0.131308	−0.0656540	+	0.997842i	$0.520913\pi$
$744$	6.71290e12	0.803215
$745$	4.28580e11	0.0509716
$746$	−2.22657e12	−0.263215
$747$	9.73305e12	1.14368
$748$	9.11678e12	1.06484
$749$	−2.96012e12	−0.343670
$750$	1.65560e12	0.191064
$751$	−3.09647e11	−0.0355212	−0.0177606	−	0.999842i	$-0.505654\pi$
$751$	−3.09647e11	−0.0355212	−0.0177606	+	0.999842i	$0.505654\pi$
$752$	−5.21136e12	−0.594252
$753$	−1.51783e13	−1.72046
$754$	6.61254e12	0.745071
$755$	−4.72437e11	−0.0529155
$756$	1.88960e11	0.0210389
$757$	1.44340e12	0.159755	0.0798777	−	0.996805i	$-0.474547\pi$
$757$	1.44340e12	0.159755	0.0798777	+	0.996805i	$0.474547\pi$
$758$	4.39299e11	0.0483336
$759$	−1.14827e13	−1.25591
$760$	8.64274e11	0.0939702
$761$	−2.27862e12	−0.246287	−0.123143	−	0.992389i	$-0.539297\pi$
$761$	−2.27862e12	−0.246287	−0.123143	+	0.992389i	$0.539297\pi$
$762$	6.67302e12	0.717010
$763$	−4.07256e12	−0.435018
$764$	7.26051e12	0.770987
$765$	−1.35977e12	−0.143545
$766$	−4.33873e12	−0.455337
$767$	4.15978e12	0.434001
$768$	8.02053e12	0.831912
$769$	1.09547e13	1.12962	0.564809	−	0.825221i	$-0.308950\pi$
$769$	1.09547e13	1.12962	0.564809	+	0.825221i	$0.308950\pi$
$770$	−3.35352e11	−0.0343789
$771$	2.10677e13	2.14720
$772$	−1.90228e12	−0.192751
$773$	7.52114e12	0.757663	0.378831	−	0.925466i	$-0.376326\pi$
$773$	7.52114e12	0.757663	0.378831	+	0.925466i	$0.376326\pi$
$774$	−2.54705e12	−0.255096
$775$	−6.64948e12	−0.662110
$776$	8.83576e12	0.874714
$777$	8.84595e12	0.870662
$778$	−4.60211e12	−0.450348
$779$	−1.05071e12	−0.102227
$780$	−2.54681e12	−0.246361
$781$	−6.78201e12	−0.652272
$782$	−3.62962e12	−0.347081
$783$	−7.37564e11	−0.0701248
$784$	5.41785e11	0.0512158
$785$	−5.99298e11	−0.0563287
$786$	−1.49971e12	−0.140154
$787$	1.85303e12	0.172185	0.0860926	−	0.996287i	$-0.472562\pi$
$787$	1.85303e12	0.172185	0.0860926	+	0.996287i	$0.472562\pi$
$788$	−1.06301e13	−0.982129
$789$	2.38142e12	0.218771
$790$	−3.27191e8	−2.98868e−5 0
$791$	3.42021e12	0.310641
$792$	−1.17528e13	−1.06140
$793$	−1.14168e13	−1.02521
$794$	7.09097e12	0.633159
$795$	3.64421e12	0.323557
$796$	−6.52073e12	−0.575688
$797$	−1.84378e13	−1.61863	−0.809314	−	0.587377i	$-0.800161\pi$
$797$	−1.84378e13	−1.61863	−0.809314	+	0.587377i	$0.800161\pi$
$798$	−2.23537e12	−0.195136
$799$	2.01237e13	1.74682
$800$	−1.16161e13	−1.00266
$801$	5.57202e12	0.478262
$802$	−3.38220e12	−0.288679
$803$	−1.34189e13	−1.13893
$804$	−1.79850e12	−0.151795
$805$	−4.42644e11	−0.0371512
$806$	−6.23560e12	−0.520440
$807$	2.41866e13	2.00745
$808$	4.07323e11	0.0336192
$809$	−1.03419e13	−0.848856	−0.424428	−	0.905462i	$-0.639525\pi$
$809$	−1.03419e13	−0.848856	−0.424428	+	0.905462i	$0.639525\pi$
$810$	−8.88992e11	−0.0725630
$811$	−2.31795e13	−1.88153	−0.940764	−	0.339062i	$-0.889890\pi$
$811$	−2.31795e13	−1.88153	−0.940764	+	0.339062i	$0.889890\pi$
$812$	−3.48163e12	−0.281048
$813$	−2.62993e13	−2.11123
$814$	1.30884e13	1.04490
$815$	1.84869e12	0.146776
$816$	6.67869e12	0.527334
$817$	5.46958e12	0.429492
$818$	3.26250e12	0.254777
$819$	7.37854e12	0.573051
$820$	−1.90113e11	−0.0146842
$821$	1.10059e13	0.845436	0.422718	−	0.906261i	$-0.361076\pi$
$821$	1.10059e13	0.845436	0.422718	+	0.906261i	$0.361076\pi$
$822$	6.55470e12	0.500760
$823$	2.30119e13	1.74845	0.874224	−	0.485523i	$-0.161371\pi$
$823$	2.30119e13	1.74845	0.874224	+	0.485523i	$0.161371\pi$
$824$	−4.23525e12	−0.320041
$825$	2.39211e13	1.79778
$826$	6.60618e11	0.0493787
$827$	6.58898e12	0.489827	0.244914	−	0.969545i	$-0.421240\pi$
$827$	6.58898e12	0.489827	0.244914	+	0.969545i	$0.421240\pi$
$828$	−6.74003e12	−0.498340
$829$	−1.32427e13	−0.973829	−0.486915	−	0.873450i	$-0.661878\pi$
$829$	−1.32427e13	−0.973829	−0.486915	+	0.873450i	$0.661878\pi$
$830$	1.14067e12	0.0834271
$831$	4.24304e12	0.308654
$832$	−2.96899e12	−0.214810
$833$	−2.09210e12	−0.150550
$834$	−1.08311e13	−0.775222
$835$	−9.94878e11	−0.0708240
$836$	1.09654e13	0.776419
$837$	6.95520e11	0.0489830
$838$	−4.74058e12	−0.332073
$839$	−5.05558e12	−0.352243	−0.176122	−	0.984368i	$-0.556355\pi$
$839$	−5.05558e12	−0.352243	−0.176122	+	0.984368i	$0.556355\pi$
$840$	−9.30918e11	−0.0645141
$841$	−9.17397e11	−0.0632376
$842$	−2.26127e12	−0.155042
$843$	−1.51422e12	−0.103268
$844$	2.14326e13	1.45390
$845$	3.31584e12	0.223737
$846$	−1.12713e13	−0.756499
$847$	−4.13139e12	−0.275817
$848$	−8.71104e12	−0.578480
$849$	1.40910e13	0.930802
$850$	7.56130e12	0.496834
$851$	1.72758e13	1.12916
$852$	−8.17966e12	−0.531811
$853$	1.03049e13	0.666456	0.333228	−	0.942846i	$-0.391862\pi$
$853$	1.03049e13	0.666456	0.333228	+	0.942846i	$0.391862\pi$
$854$	−1.81310e12	−0.116644
$855$	−1.63549e12	−0.104665
$856$	−1.21580e13	−0.773979
$857$	−1.66788e13	−1.05621	−0.528105	−	0.849179i	$-0.677097\pi$
$857$	−1.66788e13	−1.05621	−0.528105	+	0.849179i	$0.677097\pi$
$858$	2.24322e13	1.41312
$859$	−2.36677e13	−1.48316	−0.741579	−	0.670865i	$-0.765923\pi$
$859$	−2.36677e13	−1.48316	−0.741579	+	0.670865i	$0.765923\pi$
$860$	9.89649e11	0.0616933
$861$	1.13173e12	0.0701827
$862$	9.38476e12	0.578949
$863$	1.26428e13	0.775880	0.387940	−	0.921685i	$-0.373187\pi$
$863$	1.26428e13	0.775880	0.387940	+	0.921685i	$0.373187\pi$
$864$	1.21502e12	0.0741772
$865$	7.58046e11	0.0460387
$866$	1.58855e12	0.0959776
$867$	−2.56832e12	−0.154370
$868$	3.28316e12	0.196315
$869$	−9.55450e9	−0.000568354 0
$870$	1.57872e12	0.0934264
$871$	3.84514e12	0.226376
$872$	−1.67271e13	−0.979705
$873$	−1.67202e13	−0.974264
$874$	−4.36561e12	−0.253071
$875$	1.86368e12	0.107482
$876$	−1.61842e13	−0.928589
$877$	2.21629e13	1.26511	0.632555	−	0.774515i	$-0.282006\pi$
$877$	2.21629e13	1.26511	0.632555	+	0.774515i	$0.282006\pi$
$878$	−1.16691e12	−0.0662695
$879$	−3.40082e13	−1.92147
$880$	1.20511e12	0.0677413
$881$	−1.87132e13	−1.04654	−0.523272	−	0.852166i	$-0.675289\pi$
$881$	−1.87132e13	−1.04654	−0.523272	+	0.852166i	$0.675289\pi$
$882$	1.17179e12	0.0651991
$883$	−1.66483e13	−0.921611	−0.460805	−	0.887501i	$-0.652439\pi$
$883$	−1.66483e13	−0.921611	−0.460805	+	0.887501i	$0.652439\pi$
$884$	−2.35083e13	−1.29475
$885$	9.93134e11	0.0544206
$886$	−1.49050e12	−0.0812604
$887$	−1.58859e13	−0.861698	−0.430849	−	0.902424i	$-0.641786\pi$
$887$	−1.58859e13	−0.861698	−0.430849	+	0.902424i	$0.641786\pi$
$888$	3.63326e13	1.96082
$889$	7.51171e12	0.403349
$890$	6.53013e11	0.0348873
$891$	−2.59600e13	−1.37993
$892$	8.08344e12	0.427518
$893$	2.42042e13	1.27368
$894$	−4.55284e12	−0.238376
$895$	−3.90244e12	−0.203298
$896$	6.99384e12	0.362518
$897$	2.96091e13	1.52707
$898$	−8.34003e12	−0.427980
$899$	−1.28151e13	−0.654339
$900$	1.40410e13	0.713355
$901$	3.36377e13	1.70046
$902$	1.67450e12	0.0842278
$903$	−5.89134e12	−0.294862
$904$	1.40477e13	0.699595
$905$	−1.97074e12	−0.0976585
$906$	5.01873e12	0.247467
$907$	−3.65370e13	−1.79267	−0.896333	−	0.443381i	$-0.853779\pi$
$907$	−3.65370e13	−1.79267	−0.896333	+	0.443381i	$0.853779\pi$
$908$	1.55005e13	0.756760
$909$	−7.70789e11	−0.0374454
$910$	8.64729e11	0.0418017
$911$	2.09138e13	1.00600	0.503002	−	0.864286i	$-0.332229\pi$
$911$	2.09138e13	1.00600	0.503002	+	0.864286i	$0.332229\pi$
$912$	8.03294e12	0.384501
$913$	3.33093e13	1.58653
$914$	5.90199e12	0.279731
$915$	−2.72572e12	−0.128554
$916$	7.17935e12	0.336942
$917$	−1.68820e12	−0.0788427
$918$	−7.90894e11	−0.0367558
$919$	−1.22511e12	−0.0566571	−0.0283286	−	0.999599i	$-0.509018\pi$
$919$	−1.22511e12	−0.0566571	−0.0283286	+	0.999599i	$0.509018\pi$
$920$	−1.81805e12	−0.0836683
$921$	−4.44716e13	−2.03664
$922$	−7.74276e12	−0.352863
$923$	1.74879e13	0.793105
$924$	−1.18109e13	−0.533041
$925$	−3.59894e13	−1.61635
$926$	8.67335e12	0.387648
$927$	8.01448e12	0.356465
$928$	−2.23869e13	−0.990896
$929$	9.53162e12	0.419852	0.209926	−	0.977717i	$-0.432678\pi$
$929$	9.53162e12	0.419852	0.209926	+	0.977717i	$0.432678\pi$
$930$	−1.48873e12	−0.0652594
$931$	−2.51632e12	−0.109772
$932$	1.99887e13	0.867788
$933$	1.70157e13	0.735163
$934$	−1.82637e13	−0.785287
$935$	−4.65353e12	−0.199127
$936$	3.03056e13	1.29057
$937$	−9.70345e12	−0.411242	−0.205621	−	0.978632i	$-0.565921\pi$
$937$	−9.70345e12	−0.411242	−0.205621	+	0.978632i	$0.565921\pi$
$938$	6.10650e11	0.0257561
$939$	1.02860e13	0.431770
$940$	4.37944e12	0.182954
$941$	−2.29625e13	−0.954698	−0.477349	−	0.878714i	$-0.658402\pi$
$941$	−2.29625e13	−0.954698	−0.477349	+	0.878714i	$0.658402\pi$
$942$	6.36639e12	0.263429
$943$	2.21024e12	0.0910198
$944$	−2.37397e12	−0.0972973
$945$	−9.64520e10	−0.00393431
$946$	−8.71676e12	−0.353871
$947$	1.40763e13	0.568738	0.284369	−	0.958715i	$-0.408216\pi$
$947$	1.40763e13	0.568738	0.284369	+	0.958715i	$0.408216\pi$
$948$	−1.15235e10	−0.000463391 0
$949$	3.46015e13	1.38483
$950$	9.09452e12	0.362263
$951$	−5.16534e13	−2.04780
$952$	−8.59281e12	−0.339054
$953$	9.86435e12	0.387392	0.193696	−	0.981062i	$-0.437953\pi$
$953$	9.86435e12	0.387392	0.193696	+	0.981062i	$0.437953\pi$
$954$	−1.88406e13	−0.736421
$955$	−3.70602e12	−0.144176
$956$	−1.49651e13	−0.579453
$957$	4.61014e13	1.77668
$958$	1.27582e13	0.489378
$959$	7.37852e12	0.281699
$960$	−7.08838e11	−0.0269356
$961$	−1.43550e13	−0.542937
$962$	−3.37493e13	−1.27051
$963$	2.30069e13	0.862065
$964$	−3.85518e13	−1.43780
$965$	9.70993e11	0.0360449
$966$	4.70224e12	0.173743
$967$	−2.37375e12	−0.0873002	−0.0436501	−	0.999047i	$-0.513899\pi$
$967$	−2.37375e12	−0.0873002	−0.0436501	+	0.999047i	$0.513899\pi$
$968$	−1.69687e13	−0.621168
$969$	−3.10193e13	−1.13025
$970$	−1.95952e12	−0.0710686
$971$	4.45895e13	1.60970	0.804852	−	0.593476i	$-0.202245\pi$
$971$	4.45895e13	1.60970	0.804852	+	0.593476i	$0.202245\pi$
$972$	−2.97608e13	−1.06942
$973$	−1.21924e13	−0.436096
$974$	4.89939e12	0.174432
$975$	−6.16822e13	−2.18594
$976$	6.51550e12	0.229839
$977$	8.90599e11	0.0312721	0.0156360	−	0.999878i	$-0.495023\pi$
$977$	8.90599e11	0.0312721	0.0156360	+	0.999878i	$0.495023\pi$
$978$	−1.96388e13	−0.686420
$979$	1.90691e13	0.663449
$980$	−4.55296e11	−0.0157680
$981$	3.16531e13	1.09120
$982$	2.45117e13	0.841146
$983$	8.23794e12	0.281402	0.140701	−	0.990052i	$-0.455064\pi$
$983$	8.23794e12	0.281402	0.140701	+	0.990052i	$0.455064\pi$
$984$	4.64832e12	0.158059
$985$	5.42597e12	0.183660
$986$	1.45724e13	0.491003
$987$	−2.60706e13	−0.874428
$988$	−2.82751e13	−0.944056
$989$	−1.15056e13	−0.382407
$990$	2.60645e12	0.0862364
$991$	8.90224e12	0.293203	0.146601	−	0.989196i	$-0.453167\pi$
$991$	8.90224e12	0.293203	0.146601	+	0.989196i	$0.453167\pi$
$992$	2.11108e13	0.692152
$993$	4.13859e13	1.35077
$994$	2.77727e12	0.0902359
$995$	3.32841e12	0.107655
$996$	4.01738e13	1.29353
$997$	1.45450e13	0.466216	0.233108	−	0.972451i	$-0.425110\pi$
$997$	1.45450e13	0.466216	0.233108	+	0.972451i	$0.425110\pi$
$998$	1.73965e11	0.00555106
$999$	3.76440e12	0.119578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.10.a.a.1.2	✓	2
3.2	odd	2		63.10.a.d.1.1		2
4.3	odd	2		112.10.a.e.1.2		2
5.2	odd	4		175.10.b.b.99.3		4
5.3	odd	4		175.10.b.b.99.2		4
5.4	even	2		175.10.a.b.1.1		2
7.2	even	3		49.10.c.c.18.1		4
7.3	odd	6		49.10.c.b.30.1		4
7.4	even	3		49.10.c.c.30.1		4
7.5	odd	6		49.10.c.b.18.1		4
7.6	odd	2		49.10.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.a.1.2	✓	2	1.1	even	1	trivial
49.10.a.b.1.2		2	7.6	odd	2
49.10.c.b.18.1		4	7.5	odd	6
49.10.c.b.30.1		4	7.3	odd	6
49.10.c.c.18.1		4	7.2	even	3
49.10.c.c.30.1		4	7.4	even	3
63.10.a.d.1.1		2	3.2	odd	2
112.10.a.e.1.2		2	4.3	odd	2
175.10.a.b.1.1		2	5.4	even	2
175.10.b.b.99.2		4	5.3	odd	4
175.10.b.b.99.3		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +O(q^{10})\)	\(q+10.8924 q^{2} -195.817 q^{3} -393.355 q^{4} +200.782 q^{5} -2132.92 q^{6} -2401.00 q^{7} -9861.52 q^{8} +18661.3 q^{9} +2187.01 q^{10} +63864.3 q^{11} +77025.5 q^{12} -164679. q^{13} -26152.8 q^{14} -39316.5 q^{15} +93981.5 q^{16} -362910. q^{17} +203267. q^{18} -436498. q^{19} -78978.6 q^{20} +470156. q^{21} +695638. q^{22} +918199. q^{23} +1.93105e6 q^{24} -1.91281e6 q^{25} -1.79375e6 q^{26} +200076. q^{27} +944445. q^{28} -3.68643e6 q^{29} -428253. q^{30} +3.47629e6 q^{31} +6.07279e6 q^{32} -1.25057e7 q^{33} -3.95298e6 q^{34} -482078. q^{35} -7.34049e6 q^{36} +1.88149e7 q^{37} -4.75453e6 q^{38} +3.22469e7 q^{39} -1.98002e6 q^{40} +2.40714e6 q^{41} +5.12115e6 q^{42} -1.25306e7 q^{43} -2.51213e7 q^{44} +3.74685e6 q^{45} +1.00014e7 q^{46} -5.54509e7 q^{47} -1.84032e7 q^{48} +5.76480e6 q^{49} -2.08352e7 q^{50} +7.10639e7 q^{51} +6.47772e7 q^{52} -9.26889e7 q^{53} +2.17931e6 q^{54} +1.28228e7 q^{55} +2.36775e7 q^{56} +8.54737e7 q^{57} -4.01542e7 q^{58} -2.52600e7 q^{59} +1.54653e7 q^{60} +6.93275e7 q^{61} +3.78653e7 q^{62} -4.48057e7 q^{63} +1.80290e7 q^{64} -3.30646e7 q^{65} -1.36218e8 q^{66} -2.33494e7 q^{67} +1.42752e8 q^{68} -1.79799e8 q^{69} -5.25101e6 q^{70} -1.06194e8 q^{71} -1.84028e8 q^{72} -2.10115e8 q^{73} +2.04940e8 q^{74} +3.74561e8 q^{75} +1.71699e8 q^{76} -1.53338e8 q^{77} +3.51247e8 q^{78} -149606. q^{79} +1.88698e7 q^{80} -4.06488e8 q^{81} +2.62197e7 q^{82} +5.21565e8 q^{83} -1.84938e8 q^{84} -7.28659e7 q^{85} -1.36489e8 q^{86} +7.21865e8 q^{87} -6.29799e8 q^{88} +2.98587e8 q^{89} +4.08123e7 q^{90} +3.95394e8 q^{91} -3.61178e8 q^{92} -6.80716e8 q^{93} -6.03996e8 q^{94} -8.76410e7 q^{95} -1.18915e9 q^{96} -8.95983e8 q^{97} +6.27928e7 q^{98} +1.19179e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9}+O(q^{10}) \) 2 * q - 6 * q^2 - 86 * q^3 - 620 * q^4 - 2238 * q^5 - 3988 * q^6 - 4802 * q^7 + 2616 * q^8 + 11038 * q^9	\( 2 q - 6 q^{2} - 86 q^{3} - 620 q^{4} - 2238 q^{5} - 3988 q^{6} - 4802 q^{7} + 2616 q^{8} + 11038 q^{9} + 43384 q^{10} + 35316 q^{11} + 52136 q^{12} - 26530 q^{13} + 14406 q^{14} - 307136 q^{15} - 752 q^{16} - 463920 q^{17} + 332042 q^{18} - 925426 q^{19} + 473760 q^{20} + 206486 q^{21} + 1177888 q^{22} + 778128 q^{23} + 3301296 q^{24} + 2081722 q^{25} - 4127424 q^{26} - 2798612 q^{27} + 1488620 q^{28} - 10003584 q^{29} + 4095872 q^{30} + 2467260 q^{31} + 1284576 q^{32} - 15640784 q^{33} - 2246676 q^{34} + 5373438 q^{35} - 5612716 q^{36} + 30735552 q^{37} + 3504660 q^{38} + 47417944 q^{39} - 32409984 q^{40} - 19103448 q^{41} + 9575188 q^{42} + 4065100 q^{43} - 18650976 q^{44} + 22338298 q^{45} + 12367584 q^{46} - 82195020 q^{47} - 28806496 q^{48} + 11529602 q^{49} - 88312626 q^{50} + 59971356 q^{51} + 33466384 q^{52} - 55189812 q^{53} + 52834472 q^{54} + 82445816 q^{55} - 6281016 q^{56} + 31781116 q^{57} + 66558004 q^{58} - 7069218 q^{59} + 76165376 q^{60} + 44316386 q^{61} + 54910200 q^{62} - 26502238 q^{63} + 147417152 q^{64} - 369979260 q^{65} - 83258464 q^{66} - 241921336 q^{67} + 165645816 q^{68} - 195181152 q^{69} - 104164984 q^{70} + 206493816 q^{71} - 279147720 q^{72} - 499153188 q^{73} + 3571524 q^{74} + 813228014 q^{75} + 282511768 q^{76} - 84793716 q^{77} + 94970960 q^{78} + 468535096 q^{79} + 249904128 q^{80} - 585745634 q^{81} + 389586092 q^{82} + 444023958 q^{83} - 125178536 q^{84} + 173475060 q^{85} - 416830608 q^{86} + 28134340 q^{87} - 986010816 q^{88} + 636267396 q^{89} - 273242728 q^{90} + 63698530 q^{91} - 329431488 q^{92} - 791523960 q^{93} - 152223192 q^{94} + 1104747984 q^{95} - 1714981184 q^{96} - 1632716064 q^{97} - 34588806 q^{98} + 1409417860 q^{99}+O(q^{100}) \) 2 * q - 6 * q^2 - 86 * q^3 - 620 * q^4 - 2238 * q^5 - 3988 * q^6 - 4802 * q^7 + 2616 * q^8 + 11038 * q^9 + 43384 * q^10 + 35316 * q^11 + 52136 * q^12 - 26530 * q^13 + 14406 * q^14 - 307136 * q^15 - 752 * q^16 - 463920 * q^17 + 332042 * q^18 - 925426 * q^19 + 473760 * q^20 + 206486 * q^21 + 1177888 * q^22 + 778128 * q^23 + 3301296 * q^24 + 2081722 * q^25 - 4127424 * q^26 - 2798612 * q^27 + 1488620 * q^28 - 10003584 * q^29 + 4095872 * q^30 + 2467260 * q^31 + 1284576 * q^32 - 15640784 * q^33 - 2246676 * q^34 + 5373438 * q^35 - 5612716 * q^36 + 30735552 * q^37 + 3504660 * q^38 + 47417944 * q^39 - 32409984 * q^40 - 19103448 * q^41 + 9575188 * q^42 + 4065100 * q^43 - 18650976 * q^44 + 22338298 * q^45 + 12367584 * q^46 - 82195020 * q^47 - 28806496 * q^48 + 11529602 * q^49 - 88312626 * q^50 + 59971356 * q^51 + 33466384 * q^52 - 55189812 * q^53 + 52834472 * q^54 + 82445816 * q^55 - 6281016 * q^56 + 31781116 * q^57 + 66558004 * q^58 - 7069218 * q^59 + 76165376 * q^60 + 44316386 * q^61 + 54910200 * q^62 - 26502238 * q^63 + 147417152 * q^64 - 369979260 * q^65 - 83258464 * q^66 - 241921336 * q^67 + 165645816 * q^68 - 195181152 * q^69 - 104164984 * q^70 + 206493816 * q^71 - 279147720 * q^72 - 499153188 * q^73 + 3571524 * q^74 + 813228014 * q^75 + 282511768 * q^76 - 84793716 * q^77 + 94970960 * q^78 + 468535096 * q^79 + 249904128 * q^80 - 585745634 * q^81 + 389586092 * q^82 + 444023958 * q^83 - 125178536 * q^84 + 173475060 * q^85 - 416830608 * q^86 + 28134340 * q^87 - 986010816 * q^88 + 636267396 * q^89 - 273242728 * q^90 + 63698530 * q^91 - 329431488 * q^92 - 791523960 * q^93 - 152223192 * q^94 + 1104747984 * q^95 - 1714981184 * q^96 - 1632716064 * q^97 - 34588806 * q^98 + 1409417860 * q^99

Introduction

L-functions

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