LMFDB - Embedded newform 1045.6.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72815 q^{2} +13.3084 q^{3} -24.5572 q^{4} -25.0000 q^{5} -36.3073 q^{6} -136.165 q^{7} +154.296 q^{8} -65.8862 q^{9} +O(q^{10})$	\(q-2.72815 q^{2} +13.3084 q^{3} -24.5572 q^{4} -25.0000 q^{5} -36.3073 q^{6} -136.165 q^{7} +154.296 q^{8} -65.8862 q^{9} +68.2036 q^{10} -121.000 q^{11} -326.818 q^{12} +969.892 q^{13} +371.478 q^{14} -332.710 q^{15} +364.888 q^{16} -48.1913 q^{17} +179.747 q^{18} +361.000 q^{19} +613.931 q^{20} -1812.14 q^{21} +330.106 q^{22} -4541.09 q^{23} +2053.44 q^{24} +625.000 q^{25} -2646.01 q^{26} -4110.78 q^{27} +3343.84 q^{28} +7390.49 q^{29} +907.682 q^{30} +6880.91 q^{31} -5932.95 q^{32} -1610.32 q^{33} +131.473 q^{34} +3404.13 q^{35} +1617.98 q^{36} -15325.4 q^{37} -984.861 q^{38} +12907.7 q^{39} -3857.41 q^{40} -15857.0 q^{41} +4943.79 q^{42} -16069.9 q^{43} +2971.42 q^{44} +1647.16 q^{45} +12388.8 q^{46} -3305.26 q^{47} +4856.08 q^{48} +1733.95 q^{49} -1705.09 q^{50} -641.350 q^{51} -23817.8 q^{52} -15195.7 q^{53} +11214.8 q^{54} +3025.00 q^{55} -21009.8 q^{56} +4804.34 q^{57} -20162.3 q^{58} +24532.5 q^{59} +8170.44 q^{60} -11563.7 q^{61} -18772.1 q^{62} +8971.41 q^{63} +4509.53 q^{64} -24247.3 q^{65} +4393.18 q^{66} -70725.1 q^{67} +1183.44 q^{68} -60434.7 q^{69} -9286.96 q^{70} -16382.7 q^{71} -10166.0 q^{72} +78746.3 q^{73} +41809.8 q^{74} +8317.76 q^{75} -8865.16 q^{76} +16476.0 q^{77} -35214.1 q^{78} -46928.4 q^{79} -9122.20 q^{80} -38697.7 q^{81} +43260.1 q^{82} -15035.1 q^{83} +44501.2 q^{84} +1204.78 q^{85} +43841.1 q^{86} +98355.6 q^{87} -18669.9 q^{88} +1522.41 q^{89} -4493.68 q^{90} -132065. q^{91} +111517. q^{92} +91574.0 q^{93} +9017.22 q^{94} -9025.00 q^{95} -78958.1 q^{96} -13956.3 q^{97} -4730.46 q^{98} +7972.23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−2.72815	−0.482273	−0.241136	−	0.970491i	$-0.577520\pi$
$2$	−2.72815	−0.482273	−0.241136	+	0.970491i	$0.577520\pi$
$3$	13.3084	0.853735	0.426867	−	0.904314i	$-0.359617\pi$
$3$	13.3084	0.853735	0.426867	+	0.904314i	$0.359617\pi$
$4$	−24.5572	−0.767413
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−36.3073	−0.411733
$7$	−136.165	−1.05032	−0.525159	−	0.851004i	$-0.675994\pi$
$7$	−136.165	−1.05032	−0.525159	+	0.851004i	$0.675994\pi$
$8$	154.296	0.852375
$9$	−65.8862	−0.271137
$10$	68.2036	0.215679
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−326.818	−0.655167
$13$	969.892	1.59171	0.795857	−	0.605485i	$-0.207021\pi$
$13$	969.892	1.59171	0.795857	+	0.605485i	$0.207021\pi$
$14$	371.478	0.506540
$15$	−332.710	−0.381802
$16$	364.888	0.356336
$17$	−48.1913	−0.0404433	−0.0202216	−	0.999796i	$-0.506437\pi$
$17$	−48.1913	−0.0404433	−0.0202216	+	0.999796i	$0.506437\pi$
$18$	179.747	0.130762
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	613.931	0.343198
$21$	−1812.14	−0.896693
$22$	330.106	0.145411
$23$	−4541.09	−1.78995	−0.894974	−	0.446118i	$-0.852806\pi$
$23$	−4541.09	−1.78995	−0.894974	+	0.446118i	$0.852806\pi$
$24$	2053.44	0.727702
$25$	625.000	0.200000
$26$	−2646.01	−0.767640
$27$	−4110.78	−1.08521
$28$	3343.84	0.806028
$29$	7390.49	1.63184	0.815921	−	0.578163i	$-0.196230\pi$
$29$	7390.49	1.63184	0.815921	+	0.578163i	$0.196230\pi$
$30$	907.682	0.184133
$31$	6880.91	1.28600	0.643001	−	0.765865i	$-0.277689\pi$
$31$	6880.91	1.28600	0.643001	+	0.765865i	$0.277689\pi$
$32$	−5932.95	−1.02423
$33$	−1610.32	−0.257411
$34$	131.473	0.0195047
$35$	3404.13	0.469717
$36$	1617.98	0.208074
$37$	−15325.4	−1.84038	−0.920188	−	0.391477i	$-0.871964\pi$
$37$	−15325.4	−1.84038	−0.920188	+	0.391477i	$0.871964\pi$
$38$	−984.861	−0.110641
$39$	12907.7	1.35890
$40$	−3857.41	−0.381194
$41$	−15857.0	−1.47320	−0.736598	−	0.676331i	$-0.763569\pi$
$41$	−15857.0	−1.47320	−0.736598	+	0.676331i	$0.763569\pi$
$42$	4943.79	0.432451
$43$	−16069.9	−1.32539	−0.662694	−	0.748890i	$-0.730587\pi$
$43$	−16069.9	−1.32539	−0.662694	+	0.748890i	$0.730587\pi$
$44$	2971.42	0.231384
$45$	1647.16	0.121256
$46$	12388.8	0.863243
$47$	−3305.26	−0.218253	−0.109127	−	0.994028i	$-0.534805\pi$
$47$	−3305.26	−0.218253	−0.109127	+	0.994028i	$0.534805\pi$
$48$	4856.08	0.304217
$49$	1733.95	0.103168
$50$	−1705.09	−0.0964545
$51$	−641.350	−0.0345279
$52$	−23817.8	−1.22150
$53$	−15195.7	−0.743072	−0.371536	−	0.928419i	$-0.621169\pi$
$53$	−15195.7	−0.743072	−0.371536	+	0.928419i	$0.621169\pi$
$54$	11214.8	0.523369
$55$	3025.00	0.134840
$56$	−21009.8	−0.895265
$57$	4804.34	0.195860
$58$	−20162.3	−0.786993
$59$	24532.5	0.917513	0.458757	−	0.888562i	$-0.348295\pi$
$59$	24532.5	0.917513	0.458757	+	0.888562i	$0.348295\pi$
$60$	8170.44	0.293000
$61$	−11563.7	−0.397897	−0.198949	−	0.980010i	$-0.563753\pi$
$61$	−11563.7	−0.397897	−0.198949	+	0.980010i	$0.563753\pi$
$62$	−18772.1	−0.620204
$63$	8971.41	0.284780
$64$	4509.53	0.137620
$65$	−24247.3	−0.711836
$66$	4393.18	0.124142
$67$	−70725.1	−1.92480	−0.962402	−	0.271630i	$-0.912437\pi$
$67$	−70725.1	−1.92480	−0.962402	+	0.271630i	$0.912437\pi$
$68$	1183.44	0.0310367
$69$	−60434.7	−1.52814
$70$	−9286.96	−0.226531
$71$	−16382.7	−0.385691	−0.192845	−	0.981229i	$-0.561772\pi$
$71$	−16382.7	−0.385691	−0.192845	+	0.981229i	$0.561772\pi$
$72$	−10166.0	−0.231110
$73$	78746.3	1.72951	0.864755	−	0.502194i	$-0.167474\pi$
$73$	78746.3	1.72951	0.864755	+	0.502194i	$0.167474\pi$
$74$	41809.8	0.887563
$75$	8317.76	0.170747
$76$	−8865.16	−0.176057
$77$	16476.0	0.316683
$78$	−35214.1	−0.655361
$79$	−46928.4	−0.845995	−0.422997	−	0.906131i	$-0.639022\pi$
$79$	−46928.4	−0.845995	−0.422997	+	0.906131i	$0.639022\pi$
$80$	−9122.20	−0.159358
$81$	−38697.7	−0.655348
$82$	43260.1	0.710482
$83$	−15035.1	−0.239558	−0.119779	−	0.992801i	$-0.538219\pi$
$83$	−15035.1	−0.239558	−0.119779	+	0.992801i	$0.538219\pi$
$84$	44501.2	0.688134
$85$	1204.78	0.0180868
$86$	43841.1	0.639198
$87$	98355.6	1.39316
$88$	−18669.9	−0.257001
$89$	1522.41	0.0203730	0.0101865	−	0.999948i	$-0.496757\pi$
$89$	1522.41	0.0203730	0.0101865	+	0.999948i	$0.496757\pi$
$90$	−4493.68	−0.0584784
$91$	−132065.	−1.67181
$92$	111517.	1.37363
$93$	91574.0	1.09791
$94$	9017.22	0.105258
$95$	−9025.00	−0.102598
$96$	−78958.1	−0.874418
$97$	−13956.3	−0.150605	−0.0753026	−	0.997161i	$-0.523992\pi$
$97$	−13956.3	−0.150605	−0.0753026	+	0.997161i	$0.523992\pi$
$98$	−4730.46	−0.0497552
$99$	7972.23	0.0817508
$100$	−15348.3	−0.153483
$101$	198292.	1.93420	0.967099	−	0.254401i	$-0.0818783\pi$
$101$	198292.	1.93420	0.967099	+	0.254401i	$0.0818783\pi$
$102$	1749.70	0.0166518
$103$	9239.04	0.0858092	0.0429046	−	0.999079i	$-0.486339\pi$
$103$	9239.04	0.0858092	0.0429046	+	0.999079i	$0.486339\pi$
$104$	149651.	1.35674
$105$	45303.5	0.401013
$106$	41456.1	0.358363
$107$	108463.	0.915849	0.457925	−	0.888991i	$-0.348593\pi$
$107$	108463.	0.915849	0.457925	+	0.888991i	$0.348593\pi$
$108$	100949.	0.832807
$109$	100797.	0.812612	0.406306	−	0.913737i	$-0.366817\pi$
$109$	100797.	0.812612	0.406306	+	0.913737i	$0.366817\pi$
$110$	−8252.64	−0.0650296
$111$	−203956.	−1.57119
$112$	−49685.1	−0.374266
$113$	−57535.1	−0.423874	−0.211937	−	0.977283i	$-0.567977\pi$
$113$	−57535.1	−0.423874	−0.211937	+	0.977283i	$0.567977\pi$
$114$	−13106.9	−0.0944580
$115$	113527.	0.800489
$116$	−181490.	−1.25230
$117$	−63902.5	−0.431572
$118$	−66928.3	−0.442491
$119$	6561.98	0.0424783
$120$	−51336.0	−0.325438
$121$	14641.0	0.0909091
$122$	31547.4	0.191895
$123$	−211031.	−1.25772
$124$	−168976.	−0.986895
$125$	−15625.0	−0.0894427
$126$	−24475.3	−0.137341
$127$	165374.	0.909824	0.454912	−	0.890536i	$-0.349671\pi$
$127$	165374.	0.909824	0.454912	+	0.890536i	$0.349671\pi$
$128$	177552.	0.957856
$129$	−213865.	−1.13153
$130$	66150.2	0.343299
$131$	14132.2	0.0719502	0.0359751	−	0.999353i	$-0.488546\pi$
$131$	14132.2	0.0719502	0.0359751	+	0.999353i	$0.488546\pi$
$132$	39544.9	0.197540
$133$	−49155.6	−0.240960
$134$	192948.	0.928280
$135$	102770.	0.485322
$136$	−7435.74	−0.0344728
$137$	53828.0	0.245023	0.122512	−	0.992467i	$-0.460905\pi$
$137$	53828.0	0.245023	0.122512	+	0.992467i	$0.460905\pi$
$138$	164875.	0.736981
$139$	311831.	1.36893	0.684467	−	0.729044i	$-0.260035\pi$
$139$	311831.	1.36893	0.684467	+	0.729044i	$0.260035\pi$
$140$	−83595.9	−0.360467
$141$	−43987.7	−0.186330
$142$	44694.3	0.186008
$143$	−117357.	−0.479920
$144$	−24041.1	−0.0966158
$145$	−184762.	−0.729782
$146$	−214831.	−0.834095
$147$	23076.1	0.0880783
$148$	376348.	1.41233
$149$	−20040.6	−0.0739512	−0.0369756	−	0.999316i	$-0.511772\pi$
$149$	−20040.6	−0.0739512	−0.0369756	+	0.999316i	$0.511772\pi$
$150$	−22692.1	−0.0823466
$151$	57256.6	0.204354	0.102177	−	0.994766i	$-0.467419\pi$
$151$	57256.6	0.204354	0.102177	+	0.994766i	$0.467419\pi$
$152$	55701.0	0.195548
$153$	3175.14	0.0109657
$154$	−44948.9	−0.152727
$155$	−172023.	−0.575118
$156$	−316978.	−1.04284
$157$	−201751.	−0.653229	−0.326615	−	0.945158i	$-0.605908\pi$
$157$	−201751.	−0.653229	−0.326615	+	0.945158i	$0.605908\pi$
$158$	128027.	0.408000
$159$	−202231.	−0.634386
$160$	148324.	0.458048
$161$	618338.	1.88002
$162$	105573.	0.316056
$163$	−231552.	−0.682622	−0.341311	−	0.939950i	$-0.610871\pi$
$163$	−231552.	−0.682622	−0.341311	+	0.939950i	$0.610871\pi$
$164$	389403.	1.13055
$165$	40257.9	0.115118
$166$	41017.9	0.115532
$167$	678907.	1.88373	0.941867	−	0.335987i	$-0.109070\pi$
$167$	678907.	1.88373	0.941867	+	0.335987i	$0.109070\pi$
$168$	−279607.	−0.764319
$169$	569397.	1.53355
$170$	−3286.82	−0.00872276
$171$	−23784.9	−0.0622030
$172$	394633.	1.01712
$173$	315576.	0.801656	0.400828	−	0.916153i	$-0.368722\pi$
$173$	315576.	0.801656	0.400828	+	0.916153i	$0.368722\pi$
$174$	−268329.	−0.671883
$175$	−85103.2	−0.210064
$176$	−44151.5	−0.107439
$177$	326489.	0.783313
$178$	−4153.35	−0.00982536
$179$	402640.	0.939258	0.469629	−	0.882864i	$-0.344388\pi$
$179$	402640.	0.939258	0.469629	+	0.882864i	$0.344388\pi$
$180$	−40449.6	−0.0930534
$181$	−180662.	−0.409892	−0.204946	−	0.978773i	$-0.565702\pi$
$181$	−180662.	−0.409892	−0.204946	+	0.978773i	$0.565702\pi$
$182$	360294.	0.806266
$183$	−153894.	−0.339699
$184$	−700674.	−1.52571
$185$	383134.	0.823041
$186$	−249827.	−0.529490
$187$	5831.15	0.0121941
$188$	81167.9	0.167490
$189$	559746.	1.13982
$190$	24621.5	0.0494801
$191$	−818060.	−1.62256	−0.811282	−	0.584655i	$-0.801230\pi$
$191$	−818060.	−1.62256	−0.811282	+	0.584655i	$0.801230\pi$
$192$	60014.7	0.117491
$193$	−45136.7	−0.0872241	−0.0436120	−	0.999049i	$-0.513887\pi$
$193$	−45136.7	−0.0872241	−0.0436120	+	0.999049i	$0.513887\pi$
$194$	38074.7	0.0726328
$195$	−322693.	−0.607719
$196$	−42581.0	−0.0791727
$197$	209749.	0.385065	0.192533	−	0.981291i	$-0.438330\pi$
$197$	209749.	0.385065	0.192533	+	0.981291i	$0.438330\pi$
$198$	−21749.4	−0.0394262
$199$	528040.	0.945222	0.472611	−	0.881271i	$-0.343312\pi$
$199$	528040.	0.945222	0.472611	+	0.881271i	$0.343312\pi$
$200$	96435.2	0.170475
$201$	−941238.	−1.64327
$202$	−540968.	−0.932810
$203$	−1.00633e6	−1.71395
$204$	15749.8	0.0264971
$205$	396424.	0.658833
$206$	−25205.5	−0.0413834
$207$	299195.	0.485321
$208$	353902.	0.567185
$209$	−43681.0	−0.0691714
$210$	−123595.	−0.193398
$211$	649685.	1.00461	0.502304	−	0.864691i	$-0.332486\pi$
$211$	649685.	1.00461	0.502304	+	0.864691i	$0.332486\pi$
$212$	373164.	0.570243
$213$	−218027.	−0.329278
$214$	−295904.	−0.441689
$215$	401748.	0.592732
$216$	−634279.	−0.925009
$217$	−936941.	−1.35071
$218$	−274990.	−0.391900
$219$	1.04799e6	1.47654
$220$	−74285.6	−0.103478
$221$	−46740.4	−0.0643741
$222$	556422.	0.757743
$223$	−712392.	−0.959305	−0.479652	−	0.877459i	$-0.659237\pi$
$223$	−712392.	−0.959305	−0.479652	+	0.877459i	$0.659237\pi$
$224$	807861.	1.07576
$225$	−41178.9	−0.0542273
$226$	156964.	0.204423
$227$	492858.	0.634830	0.317415	−	0.948287i	$-0.397185\pi$
$227$	492858.	0.634830	0.317415	+	0.948287i	$0.397185\pi$
$228$	−117981.	−0.150306
$229$	−537560.	−0.677389	−0.338694	−	0.940896i	$-0.609985\pi$
$229$	−537560.	−0.677389	−0.338694	+	0.940896i	$0.609985\pi$
$230$	−309719.	−0.386054
$231$	219269.	0.270363
$232$	1.14033e6	1.39094
$233$	−1.43967e6	−1.73729	−0.868646	−	0.495434i	$-0.835009\pi$
$233$	−1.43967e6	−1.73729	−0.868646	+	0.495434i	$0.835009\pi$
$234$	174335.	0.208135
$235$	82631.4	0.0976058
$236$	−602451.	−0.704112
$237$	−624542.	−0.722255
$238$	−17902.0	−0.0204861
$239$	1.22421e6	1.38632	0.693158	−	0.720785i	$-0.256219\pi$
$239$	1.22421e6	1.38632	0.693158	+	0.720785i	$0.256219\pi$
$240$	−121402.	−0.136050
$241$	−972690.	−1.07878	−0.539389	−	0.842057i	$-0.681345\pi$
$241$	−972690.	−1.07878	−0.539389	+	0.842057i	$0.681345\pi$
$242$	−39942.8	−0.0438430
$243$	483916.	0.525720
$244$	283972.	0.305352
$245$	−43348.7	−0.0461382
$246$	575723.	0.606563
$247$	350131.	0.365164
$248$	1.06170e6	1.09616
$249$	−200093.	−0.204519
$250$	42627.3	0.0431358
$251$	968782.	0.970603	0.485302	−	0.874347i	$-0.338710\pi$
$251$	968782.	0.970603	0.485302	+	0.874347i	$0.338710\pi$
$252$	−220313.	−0.218544
$253$	549472.	0.539690
$254$	−451164.	−0.438783
$255$	16033.7	0.0154413
$256$	−628692.	−0.599568
$257$	−1.64295e6	−1.55164	−0.775821	−	0.630953i	$-0.782664\pi$
$257$	−1.64295e6	−1.55164	−0.775821	+	0.630953i	$0.782664\pi$
$258$	583456.	0.545706
$259$	2.08678e6	1.93298
$260$	595446.	0.546272
$261$	−486931.	−0.442452
$262$	−38554.8	−0.0346996
$263$	−1.55514e6	−1.38637	−0.693185	−	0.720760i	$-0.743793\pi$
$263$	−1.55514e6	−1.38637	−0.693185	+	0.720760i	$0.743793\pi$
$264$	−248466.	−0.219410
$265$	379892.	0.332312
$266$	134104.	0.116208
$267$	20260.8	0.0173932
$268$	1.73681e6	1.47712
$269$	−1.63321e6	−1.37614	−0.688070	−	0.725645i	$-0.741542\pi$
$269$	−1.63321e6	−1.37614	−0.688070	+	0.725645i	$0.741542\pi$
$270$	−280370.	−0.234058
$271$	−139015.	−0.114984	−0.0574920	−	0.998346i	$-0.518310\pi$
$271$	−139015.	−0.114984	−0.0574920	+	0.998346i	$0.518310\pi$
$272$	−17584.4	−0.0144114
$273$	−1.75758e6	−1.42728
$274$	−146851.	−0.118168
$275$	−75625.0	−0.0603023
$276$	1.48411e6	1.17272
$277$	−96923.2	−0.0758977	−0.0379488	−	0.999280i	$-0.512082\pi$
$277$	−96923.2	−0.0758977	−0.0379488	+	0.999280i	$0.512082\pi$
$278$	−850721.	−0.660199
$279$	−453357.	−0.348682
$280$	525245.	0.400375
$281$	−1.32516e6	−1.00116	−0.500580	−	0.865691i	$-0.666880\pi$
$281$	−1.32516e6	−1.00116	−0.500580	+	0.865691i	$0.666880\pi$
$282$	120005.	0.0898620
$283$	1.97130e6	1.46314	0.731572	−	0.681764i	$-0.238787\pi$
$283$	1.97130e6	1.46314	0.731572	+	0.681764i	$0.238787\pi$
$284$	402313.	0.295984
$285$	−120108.	−0.0875914
$286$	320167.	0.231452
$287$	2.15917e6	1.54732
$288$	390900.	0.277705
$289$	−1.41753e6	−0.998364
$290$	504058.	0.351954
$291$	−185736.	−0.128577
$292$	−1.93379e6	−1.32725
$293$	176723.	0.120261	0.0601305	−	0.998191i	$-0.480848\pi$
$293$	176723.	0.120261	0.0601305	+	0.998191i	$0.480848\pi$
$294$	−62955.0	−0.0424778
$295$	−613313.	−0.410324
$296$	−2.36465e6	−1.56869
$297$	497405.	0.327204
$298$	54673.7	0.0356646
$299$	−4.40437e6	−2.84908
$300$	−204261.	−0.131033
$301$	2.18817e6	1.39208
$302$	−156204.	−0.0985543
$303$	2.63895e6	1.65129
$304$	131725.	0.0817491
$305$	289092.	0.177945
$306$	−8662.25	−0.00528844
$307$	−1.24691e6	−0.755072	−0.377536	−	0.925995i	$-0.623228\pi$
$307$	−1.24691e6	−0.755072	−0.377536	+	0.925995i	$0.623228\pi$
$308$	−404604.	−0.243027
$309$	122957.	0.0732583
$310$	469303.	0.277364
$311$	2.40481e6	1.40988	0.704938	−	0.709269i	$-0.250975\pi$
$311$	2.40481e6	1.40988	0.704938	+	0.709269i	$0.250975\pi$
$312$	1.99161e6	1.15829
$313$	1.82312e6	1.05185	0.525926	−	0.850530i	$-0.323719\pi$
$313$	1.82312e6	1.05185	0.525926	+	0.850530i	$0.323719\pi$
$314$	550405.	0.315035
$315$	−224285.	−0.127357
$316$	1.15243e6	0.649228
$317$	159313.	0.0890438	0.0445219	−	0.999008i	$-0.485824\pi$
$317$	159313.	0.0890438	0.0445219	+	0.999008i	$0.485824\pi$
$318$	551714.	0.305947
$319$	−894249.	−0.492019
$320$	−112738.	−0.0615455
$321$	1.44348e6	0.781892
$322$	−1.68692e6	−0.906680
$323$	−17397.1	−0.00927833
$324$	950307.	0.502923
$325$	606182.	0.318343
$326$	631709.	0.329210
$327$	1.34145e6	0.693755
$328$	−2.44667e6	−1.25572
$329$	450061.	0.229235
$330$	−109830.	−0.0555181
$331$	1.55459e6	0.779915	0.389957	−	0.920833i	$-0.372490\pi$
$331$	1.55459e6	0.779915	0.389957	+	0.920833i	$0.372490\pi$
$332$	369220.	0.183840
$333$	1.00973e6	0.498993
$334$	−1.85216e6	−0.908473
$335$	1.76813e6	0.860798
$336$	−661229.	−0.319524
$337$	−912399.	−0.437633	−0.218817	−	0.975766i	$-0.570220\pi$
$337$	−912399.	−0.437633	−0.218817	+	0.975766i	$0.570220\pi$
$338$	−1.55340e6	−0.739590
$339$	−765701.	−0.361876
$340$	−29586.1	−0.0138800
$341$	−832591.	−0.387744
$342$	64888.7	0.0299988
$343$	2.05242e6	0.941959
$344$	−2.47953e6	−1.12973
$345$	1.51087e6	0.683406
$346$	−860936.	−0.386617
$347$	2.33455e6	1.04083	0.520416	−	0.853913i	$-0.325777\pi$
$347$	2.33455e6	1.04083	0.520416	+	0.853913i	$0.325777\pi$
$348$	−2.41534e6	−1.06913
$349$	3.88149e6	1.70583	0.852913	−	0.522053i	$-0.174834\pi$
$349$	3.88149e6	1.70583	0.852913	+	0.522053i	$0.174834\pi$
$350$	232174.	0.101308
$351$	−3.98702e6	−1.72735
$352$	717887.	0.308816
$353$	1.71077e6	0.730727	0.365363	−	0.930865i	$-0.380945\pi$
$353$	1.71077e6	0.730727	0.365363	+	0.930865i	$0.380945\pi$
$354$	−890710.	−0.377770
$355$	409567.	0.172486
$356$	−37386.1	−0.0156345
$357$	87329.5	0.0362652
$358$	−1.09846e6	−0.452978
$359$	1.67587e6	0.686283	0.343142	−	0.939284i	$-0.388509\pi$
$359$	1.67587e6	0.686283	0.343142	+	0.939284i	$0.388509\pi$
$360$	254150.	0.103356
$361$	130321.	0.0526316
$362$	492871.	0.197680
$363$	194848.	0.0776123
$364$	3.24316e6	1.28297
$365$	−1.96866e6	−0.773461
$366$	419845.	0.163827
$367$	1.55219e6	0.601560	0.300780	−	0.953694i	$-0.402753\pi$
$367$	1.55219e6	0.601560	0.300780	+	0.953694i	$0.402753\pi$
$368$	−1.65699e6	−0.637823
$369$	1.04476e6	0.399437
$370$	−1.04525e6	−0.396930
$371$	2.06912e6	0.780462
$372$	−2.24880e6	−0.842547
$373$	3.53992e6	1.31741	0.658705	−	0.752401i	$-0.271104\pi$
$373$	3.53992e6	1.31741	0.658705	+	0.752401i	$0.271104\pi$
$374$	−15908.2	−0.00588089
$375$	−207944.	−0.0763604
$376$	−509989.	−0.186034
$377$	7.16797e6	2.59743
$378$	−1.52707e6	−0.549704
$379$	5.45715e6	1.95150	0.975749	−	0.218894i	$-0.0702450\pi$
$379$	5.45715e6	1.95150	0.975749	+	0.218894i	$0.0702450\pi$
$380$	221629.	0.0787349
$381$	2.20086e6	0.776748
$382$	2.23179e6	0.782518
$383$	3.85604e6	1.34321	0.671605	−	0.740909i	$-0.265605\pi$
$383$	3.85604e6	1.34321	0.671605	+	0.740909i	$0.265605\pi$
$384$	2.36293e6	0.817755
$385$	−411900.	−0.141625
$386$	123139.	0.0420658
$387$	1.05879e6	0.359361
$388$	342727.	0.115576
$389$	2.84097e6	0.951902	0.475951	−	0.879472i	$-0.342104\pi$
$389$	2.84097e6	0.951902	0.475951	+	0.879472i	$0.342104\pi$
$390$	880353.	0.293086
$391$	218841.	0.0723914
$392$	267542.	0.0879380
$393$	188077.	0.0614264
$394$	−572226.	−0.185706
$395$	1.17321e6	0.378340
$396$	−195776.	−0.0627366
$397$	−4.11599e6	−1.31069	−0.655343	−	0.755332i	$-0.727476\pi$
$397$	−4.11599e6	−1.31069	−0.655343	+	0.755332i	$0.727476\pi$
$398$	−1.44057e6	−0.455855
$399$	−654183.	−0.205716
$400$	228055.	0.0712672
$401$	421404.	0.130869	0.0654346	−	0.997857i	$-0.479157\pi$
$401$	421404.	0.130869	0.0654346	+	0.997857i	$0.479157\pi$
$402$	2.56784e6	0.792505
$403$	6.67374e6	2.04695
$404$	−4.86949e6	−1.48433
$405$	967442.	0.293081
$406$	2.74541e6	0.826593
$407$	1.85437e6	0.554894
$408$	−98957.9	−0.0294307
$409$	−4.39690e6	−1.29969	−0.649843	−	0.760068i	$-0.725165\pi$
$409$	−4.39690e6	−1.29969	−0.649843	+	0.760068i	$0.725165\pi$
$410$	−1.08150e6	−0.317737
$411$	716365.	0.209185
$412$	−226885.	−0.0658511
$413$	−3.34048e6	−0.963681
$414$	−816248.	−0.234057
$415$	375877.	0.107134
$416$	−5.75432e6	−1.63027
$417$	4.14998e6	1.16871
$418$	119168.	0.0333595
$419$	−3.15633e6	−0.878309	−0.439154	−	0.898412i	$-0.644722\pi$
$419$	−3.15633e6	−0.878309	−0.439154	+	0.898412i	$0.644722\pi$
$420$	−1.11253e6	−0.307743
$421$	4.76033e6	1.30898	0.654488	−	0.756072i	$-0.272884\pi$
$421$	4.76033e6	1.30898	0.654488	+	0.756072i	$0.272884\pi$
$422$	−1.77244e6	−0.484495
$423$	217771.	0.0591764
$424$	−2.34464e6	−0.633376
$425$	−30119.6	−0.00808866
$426$	594811.	0.158802
$427$	1.57457e6	0.417919
$428$	−2.66356e6	−0.702835
$429$	−1.56183e6	−0.409724
$430$	−1.09603e6	−0.285858
$431$	−215430.	−0.0558614	−0.0279307	−	0.999610i	$-0.508892\pi$
$431$	−215430.	−0.0558614	−0.0279307	+	0.999610i	$0.508892\pi$
$432$	−1.49998e6	−0.386701
$433$	−3.66473e6	−0.939340	−0.469670	−	0.882842i	$-0.655627\pi$
$433$	−3.66473e6	−0.939340	−0.469670	+	0.882842i	$0.655627\pi$
$434$	2.55611e6	0.651411
$435$	−2.45889e6	−0.623040
$436$	−2.47530e6	−0.623609
$437$	−1.63933e6	−0.410642
$438$	−2.85907e6	−0.712096
$439$	6.14702e6	1.52231	0.761155	−	0.648570i	$-0.224632\pi$
$439$	6.14702e6	1.52231	0.761155	+	0.648570i	$0.224632\pi$
$440$	466746.	0.114934
$441$	−114243.	−0.0279727
$442$	127515.	0.0310459
$443$	−3.34447e6	−0.809688	−0.404844	−	0.914386i	$-0.632674\pi$
$443$	−3.34447e6	−0.809688	−0.404844	+	0.914386i	$0.632674\pi$
$444$	5.00860e6	1.20575
$445$	−38060.2	−0.00911110
$446$	1.94351e6	0.462646
$447$	−266709.	−0.0631347
$448$	−614041.	−0.144545
$449$	−2.61912e6	−0.613113	−0.306556	−	0.951853i	$-0.599177\pi$
$449$	−2.61912e6	−0.613113	−0.306556	+	0.951853i	$0.599177\pi$
$450$	112342.	0.0261524
$451$	1.91869e6	0.444185
$452$	1.41290e6	0.325286
$453$	761994.	0.174464
$454$	−1.34459e6	−0.306161
$455$	3.30164e6	0.747654
$456$	741291.	0.166946
$457$	855414.	0.191596	0.0957979	−	0.995401i	$-0.469460\pi$
$457$	855414.	0.191596	0.0957979	+	0.995401i	$0.469460\pi$
$458$	1.46654e6	0.326686
$459$	198104.	0.0438896
$460$	−2.78791e6	−0.614306
$461$	1.21207e6	0.265629	0.132814	−	0.991141i	$-0.457599\pi$
$461$	1.21207e6	0.265629	0.132814	+	0.991141i	$0.457599\pi$
$462$	−598198.	−0.130389
$463$	−1.79735e6	−0.389654	−0.194827	−	0.980838i	$-0.562415\pi$
$463$	−1.79735e6	−0.389654	−0.194827	+	0.980838i	$0.562415\pi$
$464$	2.69670e6	0.581484
$465$	−2.28935e6	−0.490998
$466$	3.92763e6	0.837848
$467$	4.68729e6	0.994556	0.497278	−	0.867591i	$-0.334333\pi$
$467$	4.68729e6	0.994556	0.497278	+	0.867591i	$0.334333\pi$
$468$	1.56927e6	0.331194
$469$	9.63029e6	2.02166
$470$	−225431.	−0.0470726
$471$	−2.68498e6	−0.557685
$472$	3.78528e6	0.782065
$473$	1.94446e6	0.399620
$474$	1.70384e6	0.348324
$475$	225625.	0.0458831
$476$	−161144.	−0.0325984
$477$	1.00119e6	0.201474
$478$	−3.33983e6	−0.668582
$479$	867629.	0.172781	0.0863904	−	0.996261i	$-0.472467\pi$
$479$	867629.	0.172781	0.0863904	+	0.996261i	$0.472467\pi$
$480$	1.97395e6	0.391051
$481$	−1.48639e7	−2.92935
$482$	2.65364e6	0.520265
$483$	8.22910e6	1.60503
$484$	−359542.	−0.0697648
$485$	348907.	0.0673527
$486$	−1.32019e6	−0.253540
$487$	−279431.	−0.0533891	−0.0266946	−	0.999644i	$-0.508498\pi$
$487$	−279431.	−0.0533891	−0.0266946	+	0.999644i	$0.508498\pi$
$488$	−1.78423e6	−0.339158
$489$	−3.08159e6	−0.582778
$490$	118262.	0.0222512
$491$	−6.16660e6	−1.15436	−0.577181	−	0.816616i	$-0.695847\pi$
$491$	−6.16660e6	−1.15436	−0.577181	+	0.816616i	$0.695847\pi$
$492$	5.18234e6	0.965190
$493$	−356157.	−0.0659971
$494$	−955208.	−0.176109
$495$	−199306.	−0.0365601
$496$	2.51076e6	0.458249
$497$	2.23075e6	0.405098
$498$	545884.	0.0986340
$499$	−7.28188e6	−1.30916	−0.654580	−	0.755993i	$-0.727154\pi$
$499$	−7.28188e6	−1.30916	−0.654580	+	0.755993i	$0.727154\pi$
$500$	383707.	0.0686395
$501$	9.03518e6	1.60821
$502$	−2.64298e6	−0.468095
$503$	−2.12428e6	−0.374362	−0.187181	−	0.982325i	$-0.559935\pi$
$503$	−2.12428e6	−0.374362	−0.187181	+	0.982325i	$0.559935\pi$
$504$	1.38425e6	0.242739
$505$	−4.95729e6	−0.865000
$506$	−1.49904e6	−0.260278
$507$	7.57777e6	1.30925
$508$	−4.06112e6	−0.698211
$509$	3.23226e6	0.552984	0.276492	−	0.961016i	$-0.410828\pi$
$509$	3.23226e6	0.552984	0.276492	+	0.961016i	$0.410828\pi$
$510$	−43742.4	−0.00744693
$511$	−1.07225e7	−1.81654
$512$	−3.96649e6	−0.668701
$513$	−1.48399e6	−0.248965
$514$	4.48221e6	0.748314
$515$	−230976.	−0.0383750
$516$	5.25194e6	0.868351
$517$	399936.	0.0658058
$518$	−5.69304e6	−0.932223
$519$	4.19981e6	0.684402
$520$	−3.74127e6	−0.606751
$521$	9.44690e6	1.52474	0.762369	−	0.647143i	$-0.224036\pi$
$521$	9.44690e6	1.52474	0.762369	+	0.647143i	$0.224036\pi$
$522$	1.32842e6	0.213383
$523$	7.22171e6	1.15448	0.577239	−	0.816575i	$-0.304130\pi$
$523$	7.22171e6	1.15448	0.577239	+	0.816575i	$0.304130\pi$
$524$	−347048.	−0.0552156
$525$	−1.13259e6	−0.179339
$526$	4.24264e6	0.668608
$527$	−331600.	−0.0520102
$528$	−587586.	−0.0917248
$529$	1.41852e7	2.20391
$530$	−1.03640e6	−0.160265
$531$	−1.61636e6	−0.248771
$532$	1.20713e6	0.184916
$533$	−1.53795e7	−2.34491
$534$	−55274.5	−0.00838825
$535$	−2.71159e6	−0.409580
$536$	−1.09126e7	−1.64065
$537$	5.35850e6	0.801877
$538$	4.45564e6	0.663674
$539$	−209808.	−0.0311064
$540$	−2.52374e6	−0.372443
$541$	9.73006e6	1.42930	0.714648	−	0.699484i	$-0.246587\pi$
$541$	9.73006e6	1.42930	0.714648	+	0.699484i	$0.246587\pi$
$542$	379252.	0.0554536
$543$	−2.40432e6	−0.349939
$544$	285917.	0.0414231
$545$	−2.51994e6	−0.363411
$546$	4.79494e6	0.688337
$547$	1.15239e7	1.64676	0.823382	−	0.567487i	$-0.192084\pi$
$547$	1.15239e7	1.64676	0.823382	+	0.567487i	$0.192084\pi$
$548$	−1.32187e6	−0.188034
$549$	761886.	0.107885
$550$	206316.	0.0290821
$551$	2.66797e6	0.374370
$552$	−9.32485e6	−1.30255
$553$	6.39001e6	0.888564
$554$	264421.	0.0366034
$555$	5.09891e6	0.702659
$556$	−7.65770e6	−1.05054
$557$	3.30423e6	0.451265	0.225632	−	0.974212i	$-0.427555\pi$
$557$	3.30423e6	0.451265	0.225632	+	0.974212i	$0.427555\pi$
$558$	1.23682e6	0.168160
$559$	−1.55861e7	−2.10964
$560$	1.24213e6	0.167377
$561$	77603.3	0.0104105
$562$	3.61523e6	0.482832
$563$	5.18639e6	0.689596	0.344798	−	0.938677i	$-0.387947\pi$
$563$	5.18639e6	0.689596	0.344798	+	0.938677i	$0.387947\pi$
$564$	1.08022e6	0.142992
$565$	1.43838e6	0.189562
$566$	−5.37800e6	−0.705635
$567$	5.26927e6	0.688324
$568$	−2.52779e6	−0.328753
$569$	3.10156e6	0.401605	0.200803	−	0.979632i	$-0.435645\pi$
$569$	3.10156e6	0.401605	0.200803	+	0.979632i	$0.435645\pi$
$570$	327673.	0.0422429
$571$	−1.22897e7	−1.57744	−0.788720	−	0.614753i	$-0.789256\pi$
$571$	−1.22897e7	−1.57744	−0.788720	+	0.614753i	$0.789256\pi$
$572$	2.88196e6	0.368297
$573$	−1.08871e7	−1.38524
$574$	−5.89052e6	−0.746232
$575$	−2.83818e6	−0.357990
$576$	−297116.	−0.0373138
$577$	2.79961e6	0.350073	0.175036	−	0.984562i	$-0.443996\pi$
$577$	2.79961e6	0.350073	0.175036	+	0.984562i	$0.443996\pi$
$578$	3.86724e6	0.481484
$579$	−600697.	−0.0744662
$580$	4.53725e6	0.560044
$581$	2.04726e6	0.251612
$582$	506714.	0.0620091
$583$	1.83868e6	0.224045
$584$	1.21503e7	1.47419
$585$	1.59756e6	0.193005
$586$	−482127.	−0.0579986
$587$	5.56710e6	0.666859	0.333429	−	0.942775i	$-0.391794\pi$
$587$	5.56710e6	0.666859	0.333429	+	0.942775i	$0.391794\pi$
$588$	−566685.	−0.0675925
$589$	2.48401e6	0.295029
$590$	1.67321e6	0.197888
$591$	2.79142e6	0.328743
$592$	−5.59204e6	−0.655792
$593$	5.65238e6	0.660077	0.330038	−	0.943968i	$-0.392938\pi$
$593$	5.65238e6	0.660077	0.330038	+	0.943968i	$0.392938\pi$
$594$	−1.35699e6	−0.157802
$595$	−164049.	−0.0189969
$596$	492141.	0.0567511
$597$	7.02737e6	0.806969
$598$	1.20158e7	1.37404
$599$	−4.84239e6	−0.551432	−0.275716	−	0.961239i	$-0.588915\pi$
$599$	−4.84239e6	−0.551432	−0.275716	+	0.961239i	$0.588915\pi$
$600$	1.28340e6	0.145540
$601$	−946329.	−0.106870	−0.0534350	−	0.998571i	$-0.517017\pi$
$601$	−946329.	−0.106870	−0.0534350	+	0.998571i	$0.517017\pi$
$602$	−5.96963e6	−0.671362
$603$	4.65981e6	0.521885
$604$	−1.40606e6	−0.156824
$605$	−366025.	−0.0406558
$606$	−7.19943e6	−0.796373
$607$	−1.45373e7	−1.60144	−0.800720	−	0.599039i	$-0.795549\pi$
$607$	−1.45373e7	−1.60144	−0.800720	+	0.599039i	$0.795549\pi$
$608$	−2.14180e6	−0.234974
$609$	−1.33926e7	−1.46326
$610$	−788685.	−0.0858181
$611$	−3.20574e6	−0.347397
$612$	−77972.7	−0.00841519
$613$	4.59323e6	0.493705	0.246852	−	0.969053i	$-0.420604\pi$
$613$	4.59323e6	0.493705	0.246852	+	0.969053i	$0.420604\pi$
$614$	3.40174e6	0.364150
$615$	5.27578e6	0.562469
$616$	2.54218e6	0.269933
$617$	−1.38474e7	−1.46438	−0.732192	−	0.681098i	$-0.761503\pi$
$617$	−1.38474e7	−1.46438	−0.732192	+	0.681098i	$0.761503\pi$
$618$	−335444.	−0.0353305
$619$	−9.00147e6	−0.944250	−0.472125	−	0.881532i	$-0.656513\pi$
$619$	−9.00147e6	−0.944250	−0.472125	+	0.881532i	$0.656513\pi$
$620$	4.22440e6	0.441353
$621$	1.86674e7	1.94248
$622$	−6.56068e6	−0.679944
$623$	−207299.	−0.0213982
$624$	4.70987e6	0.484226
$625$	390625.	0.0400000
$626$	−4.97374e6	−0.507280
$627$	−581325.	−0.0590541
$628$	4.95443e6	0.501297
$629$	738550.	0.0744309
$630$	611882.	0.0614210
$631$	724171.	0.0724049	0.0362025	−	0.999344i	$-0.488474\pi$
$631$	724171.	0.0724049	0.0362025	+	0.999344i	$0.488474\pi$
$632$	−7.24088e6	−0.721105
$633$	8.64628e6	0.857669
$634$	−434630.	−0.0429434
$635$	−4.13434e6	−0.406885
$636$	4.96622e6	0.486837
$637$	1.68174e6	0.164214
$638$	2.43964e6	0.237287
$639$	1.07939e6	0.104575
$640$	−4.43879e6	−0.428366
$641$	−5.24265e6	−0.503971	−0.251986	−	0.967731i	$-0.581084\pi$
$641$	−5.24265e6	−0.503971	−0.251986	+	0.967731i	$0.581084\pi$
$642$	−3.93801e6	−0.377085
$643$	6.82944e6	0.651415	0.325707	−	0.945471i	$-0.394398\pi$
$643$	6.82944e6	0.651415	0.325707	+	0.945471i	$0.394398\pi$
$644$	−1.51847e7	−1.44275
$645$	5.34663e6	0.506036
$646$	47461.7	0.00447468
$647$	7.60849e6	0.714559	0.357279	−	0.933998i	$-0.383704\pi$
$647$	7.60849e6	0.714559	0.357279	+	0.933998i	$0.383704\pi$
$648$	−5.97091e6	−0.558602
$649$	−2.96844e6	−0.276641
$650$	−1.65375e6	−0.153528
$651$	−1.24692e7	−1.15315
$652$	5.68628e6	0.523853
$653$	−1.25516e7	−1.15190	−0.575951	−	0.817484i	$-0.695368\pi$
$653$	−1.25516e7	−1.15190	−0.575951	+	0.817484i	$0.695368\pi$
$654$	−3.65968e6	−0.334579
$655$	−353306.	−0.0321771
$656$	−5.78602e6	−0.524953
$657$	−5.18830e6	−0.468934
$658$	−1.22783e6	−0.110554
$659$	1.90448e7	1.70829	0.854146	−	0.520033i	$-0.174080\pi$
$659$	1.90448e7	1.70829	0.854146	+	0.520033i	$0.174080\pi$
$660$	−988623.	−0.0883428
$661$	−1.45891e6	−0.129875	−0.0649373	−	0.997889i	$-0.520685\pi$
$661$	−1.45891e6	−0.129875	−0.0649373	+	0.997889i	$0.520685\pi$
$662$	−4.24116e6	−0.376131
$663$	−622040.	−0.0549585
$664$	−2.31986e6	−0.204193
$665$	1.22889e6	0.107760
$666$	−2.75469e6	−0.240651
$667$	−3.35609e7	−2.92091
$668$	−1.66721e7	−1.44560
$669$	−9.48080e6	−0.818992
$670$	−4.82371e6	−0.415139
$671$	1.39920e6	0.119971
$672$	1.07513e7	0.918417
$673$	−9.51654e6	−0.809918	−0.404959	−	0.914335i	$-0.632714\pi$
$673$	−9.51654e6	−0.809918	−0.404959	+	0.914335i	$0.632714\pi$
$674$	2.48916e6	0.211058
$675$	−2.56924e6	−0.217043
$676$	−1.39828e7	−1.17687
$677$	−1.52363e7	−1.27764	−0.638819	−	0.769357i	$-0.720577\pi$
$677$	−1.52363e7	−1.27764	−0.638819	+	0.769357i	$0.720577\pi$
$678$	2.08894e6	0.174523
$679$	1.90036e6	0.158183
$680$	185894.	0.0154167
$681$	6.55916e6	0.541977
$682$	2.27143e6	0.186998
$683$	7.61197e6	0.624375	0.312187	−	0.950021i	$-0.398938\pi$
$683$	7.61197e6	0.624375	0.312187	+	0.950021i	$0.398938\pi$
$684$	584092.	0.0477354
$685$	−1.34570e6	−0.109578
$686$	−5.59931e6	−0.454281
$687$	−7.15407e6	−0.578311
$688$	−5.86373e6	−0.472284
$689$	−1.47382e7	−1.18276
$690$	−4.12187e6	−0.329588
$691$	−7.60771e6	−0.606120	−0.303060	−	0.952971i	$-0.598008\pi$
$691$	−7.60771e6	−0.606120	−0.303060	+	0.952971i	$0.598008\pi$
$692$	−7.74966e6	−0.615202
$693$	−1.08554e6	−0.0858643
$694$	−6.36900e6	−0.501964
$695$	−7.79578e6	−0.612206
$696$	1.51759e7	1.18750
$697$	764168.	0.0595809
$698$	−1.05893e7	−0.822673
$699$	−1.91597e7	−1.48319
$700$	2.08990e6	0.161206
$701$	−9.56070e6	−0.734843	−0.367421	−	0.930055i	$-0.619759\pi$
$701$	−9.56070e6	−0.734843	−0.367421	+	0.930055i	$0.619759\pi$
$702$	1.08772e7	0.833053
$703$	−5.53246e6	−0.422211
$704$	−545653.	−0.0414940
$705$	1.09969e6	0.0833295
$706$	−4.66723e6	−0.352410
$707$	−2.70004e7	−2.03152
$708$	−8.01766e6	−0.601125
$709$	−1.21081e7	−0.904606	−0.452303	−	0.891864i	$-0.649397\pi$
$709$	−1.21081e7	−0.904606	−0.452303	+	0.891864i	$0.649397\pi$
$710$	−1.11736e6	−0.0831853
$711$	3.09193e6	0.229380
$712$	234902.	0.0173655
$713$	−3.12468e7	−2.30188
$714$	−238248.	−0.0174897
$715$	2.93392e6	0.214627
$716$	−9.88773e6	−0.720799
$717$	1.62923e7	1.18355
$718$	−4.57201e6	−0.330976
$719$	8.67856e6	0.626074	0.313037	−	0.949741i	$-0.398654\pi$
$719$	8.67856e6	0.626074	0.313037	+	0.949741i	$0.398654\pi$
$720$	601027.	0.0432079
$721$	−1.25804e6	−0.0901270
$722$	−355535.	−0.0253828
$723$	−1.29450e7	−0.920990
$724$	4.43655e6	0.314556
$725$	4.61905e6	0.326368
$726$	−531575.	−0.0374303
$727$	2.45021e7	1.71936	0.859679	−	0.510834i	$-0.170663\pi$
$727$	2.45021e7	1.71936	0.859679	+	0.510834i	$0.170663\pi$
$728$	−2.03772e7	−1.42501
$729$	1.58437e7	1.10417
$730$	5.37079e6	0.373019
$731$	774432.	0.0536031
$732$	3.77921e6	0.260689
$733$	2.68228e6	0.184393	0.0921965	−	0.995741i	$-0.470611\pi$
$733$	2.68228e6	0.184393	0.0921965	+	0.995741i	$0.470611\pi$
$734$	−4.23459e6	−0.290116
$735$	−576902.	−0.0393898
$736$	2.69421e7	1.83331
$737$	8.55773e6	0.580350
$738$	−2.85025e6	−0.192638
$739$	3.65278e6	0.246044	0.123022	−	0.992404i	$-0.460741\pi$
$739$	3.65278e6	0.246044	0.123022	+	0.992404i	$0.460741\pi$
$740$	−9.40871e6	−0.631613
$741$	4.65969e6	0.311753
$742$	−5.64487e6	−0.376395
$743$	2.48267e7	1.64986	0.824930	−	0.565234i	$-0.191214\pi$
$743$	2.48267e7	1.64986	0.824930	+	0.565234i	$0.191214\pi$
$744$	1.41295e7	0.935827
$745$	501015.	0.0330720
$746$	−9.65741e6	−0.635351
$747$	990605.	0.0649530
$748$	−143197.	−0.00935792
$749$	−1.47689e7	−0.961933
$750$	567301.	0.0368265
$751$	1.79695e7	1.16262	0.581309	−	0.813683i	$-0.302541\pi$
$751$	1.79695e7	1.16262	0.581309	+	0.813683i	$0.302541\pi$
$752$	−1.20605e6	−0.0777715
$753$	1.28929e7	0.828638
$754$	−1.95553e7	−1.25267
$755$	−1.43141e6	−0.0913898
$756$	−1.37458e7	−0.874713
$757$	−623640.	−0.0395543	−0.0197772	−	0.999804i	$-0.506296\pi$
$757$	−623640.	−0.0395543	−0.0197772	+	0.999804i	$0.506296\pi$
$758$	−1.48879e7	−0.941154
$759$	7.31260e6	0.460752
$760$	−1.39252e6	−0.0874518
$761$	−8.41734e6	−0.526882	−0.263441	−	0.964676i	$-0.584857\pi$
$761$	−8.41734e6	−0.526882	−0.263441	+	0.964676i	$0.584857\pi$
$762$	−6.00427e6	−0.374604
$763$	−1.37251e7	−0.853501
$764$	2.00893e7	1.24518
$765$	−79378.6	−0.00490399
$766$	−1.05198e7	−0.647794
$767$	2.37939e7	1.46042
$768$	−8.36689e6	−0.511872
$769$	−1.41819e7	−0.864803	−0.432401	−	0.901681i	$-0.642334\pi$
$769$	−1.41819e7	−0.864803	−0.432401	+	0.901681i	$0.642334\pi$
$770$	1.12372e6	0.0683018
$771$	−2.18651e7	−1.32469
$772$	1.10843e6	0.0669369
$773$	−2.48958e7	−1.49857	−0.749287	−	0.662246i	$-0.769604\pi$
$773$	−2.48958e7	−1.49857	−0.749287	+	0.662246i	$0.769604\pi$
$774$	−2.88853e6	−0.173310
$775$	4.30057e6	0.257201
$776$	−2.15340e6	−0.128372
$777$	2.77717e7	1.65025
$778$	−7.75057e6	−0.459076
$779$	−5.72437e6	−0.337974
$780$	7.92444e6	0.466372
$781$	1.98230e6	0.116290
$782$	−597030.	−0.0349124
$783$	−3.03807e7	−1.77090
$784$	632697.	0.0367626
$785$	5.04376e6	0.292133
$786$	−513103.	−0.0296243
$787$	2.09975e7	1.20845	0.604227	−	0.796813i	$-0.293482\pi$
$787$	2.09975e7	1.20845	0.604227	+	0.796813i	$0.293482\pi$
$788$	−5.15085e6	−0.295504
$789$	−2.06964e7	−1.18359
$790$	−3.20069e6	−0.182463
$791$	7.83427e6	0.445202
$792$	1.23009e6	0.0696823
$793$	−1.12155e7	−0.633339
$794$	1.12290e7	0.632107
$795$	5.05576e6	0.283706
$796$	−1.29672e7	−0.725376
$797$	131864.	0.00735325	0.00367662	−	0.999993i	$-0.498830\pi$
$797$	131864.	0.00735325	0.00367662	+	0.999993i	$0.498830\pi$
$798$	1.78471e6	0.0992110
$799$	159285.	0.00882688
$800$	−3.70809e6	−0.204845
$801$	−100306.	−0.00552388
$802$	−1.14965e6	−0.0631146
$803$	−9.52831e6	−0.521467
$804$	2.31142e7	1.26107
$805$	−1.54585e7	−0.840768
$806$	−1.82069e7	−0.987187
$807$	−2.17355e7	−1.17486
$808$	3.05957e7	1.64866
$809$	2.36877e7	1.27248	0.636240	−	0.771491i	$-0.280489\pi$
$809$	2.36877e7	1.27248	0.636240	+	0.771491i	$0.280489\pi$
$810$	−2.63932e6	−0.141345
$811$	−2.34939e7	−1.25431	−0.627153	−	0.778896i	$-0.715780\pi$
$811$	−2.34939e7	−1.25431	−0.627153	+	0.778896i	$0.715780\pi$
$812$	2.47126e7	1.31531
$813$	−1.85006e6	−0.0981658
$814$	−5.05899e6	−0.267610
$815$	5.78881e6	0.305278
$816$	−234021.	−0.0123035
$817$	−5.80125e6	−0.304065
$818$	1.19954e7	0.626803
$819$	8.70129e6	0.453288
$820$	−9.73508e6	−0.505597
$821$	6.94064e6	0.359370	0.179685	−	0.983724i	$-0.442492\pi$
$821$	6.94064e6	0.359370	0.179685	+	0.983724i	$0.442492\pi$
$822$	−1.95435e6	−0.100884
$823$	1.23006e7	0.633035	0.316517	−	0.948587i	$-0.397486\pi$
$823$	1.23006e7	0.633035	0.316517	+	0.948587i	$0.397486\pi$
$824$	1.42555e6	0.0731416
$825$	−1.00645e6	−0.0514822
$826$	9.11330e6	0.464757
$827$	−7.75917e6	−0.394504	−0.197252	−	0.980353i	$-0.563202\pi$
$827$	−7.75917e6	−0.394504	−0.197252	+	0.980353i	$0.563202\pi$
$828$	−7.34740e6	−0.372441
$829$	−1.36547e7	−0.690076	−0.345038	−	0.938589i	$-0.612134\pi$
$829$	−1.36547e7	−0.690076	−0.345038	+	0.938589i	$0.612134\pi$
$830$	−1.02545e6	−0.0516676
$831$	−1.28989e6	−0.0647965
$832$	4.37376e6	0.219052
$833$	−83561.3	−0.00417246
$834$	−1.13217e7	−0.563635
$835$	−1.69727e7	−0.842431
$836$	1.07268e6	0.0530831
$837$	−2.82860e7	−1.39559
$838$	8.61093e6	0.423584
$839$	1.45510e7	0.713653	0.356827	−	0.934171i	$-0.383859\pi$
$839$	1.45510e7	0.713653	0.356827	+	0.934171i	$0.383859\pi$
$840$	6.99017e6	0.341814
$841$	3.41082e7	1.66291
$842$	−1.29869e7	−0.631283
$843$	−1.76358e7	−0.854725
$844$	−1.59545e7	−0.770950
$845$	−1.42349e7	−0.685825
$846$	−594111.	−0.0285392
$847$	−1.99359e6	−0.0954835
$848$	−5.54473e6	−0.264783
$849$	2.62349e7	1.24914
$850$	82170.6	0.00390094
$851$	6.95939e7	3.29418
$852$	5.35415e6	0.252692
$853$	−4.17957e7	−1.96680	−0.983398	−	0.181463i	$-0.941917\pi$
$853$	−4.17957e7	−1.96680	−0.983398	+	0.181463i	$0.941917\pi$
$854$	−4.29565e6	−0.201551
$855$	594623.	0.0278180
$856$	1.67355e7	0.780647
$857$	−3.25129e6	−0.151218	−0.0756090	−	0.997138i	$-0.524090\pi$
$857$	−3.25129e6	−0.151218	−0.0756090	+	0.997138i	$0.524090\pi$
$858$	4.26091e6	0.197599
$859$	−9.37744e6	−0.433612	−0.216806	−	0.976215i	$-0.569564\pi$
$859$	−9.37744e6	−0.433612	−0.216806	+	0.976215i	$0.569564\pi$
$860$	−9.86583e6	−0.454870
$861$	2.87351e7	1.32100
$862$	587723.	0.0269404
$863$	3.30837e7	1.51212	0.756062	−	0.654500i	$-0.227121\pi$
$863$	3.30837e7	1.51212	0.756062	+	0.654500i	$0.227121\pi$
$864$	2.43891e7	1.11150
$865$	−7.88939e6	−0.358512
$866$	9.99793e6	0.453018
$867$	−1.88651e7	−0.852339
$868$	2.30087e7	1.03655
$869$	5.67833e6	0.255077
$870$	6.70821e6	0.300475
$871$	−6.85957e7	−3.06374
$872$	1.55527e7	0.692650
$873$	919526.	0.0408346
$874$	4.47234e6	0.198042
$875$	2.12758e6	0.0939433
$876$	−2.57357e7	−1.13312
$877$	1.51378e7	0.664604	0.332302	−	0.943173i	$-0.392175\pi$
$877$	1.51378e7	0.664604	0.332302	+	0.943173i	$0.392175\pi$
$878$	−1.67700e7	−0.734169
$879$	2.35191e6	0.102671
$880$	1.10379e6	0.0480484
$881$	9.71721e6	0.421796	0.210898	−	0.977508i	$-0.432361\pi$
$881$	9.71721e6	0.421796	0.210898	+	0.977508i	$0.432361\pi$
$882$	311672.	0.0134905
$883$	−3.82841e7	−1.65241	−0.826203	−	0.563373i	$-0.809503\pi$
$883$	−3.82841e7	−1.65241	−0.826203	+	0.563373i	$0.809503\pi$
$884$	1.14781e6	0.0494016
$885$	−8.16222e6	−0.350308
$886$	9.12420e6	0.390490
$887$	−7.49724e6	−0.319958	−0.159979	−	0.987120i	$-0.551143\pi$
$887$	−7.49724e6	−0.319958	−0.159979	+	0.987120i	$0.551143\pi$
$888$	−3.14697e7	−1.33925
$889$	−2.25181e7	−0.955604
$890$	103834.	0.00439403
$891$	4.68242e6	0.197595
$892$	1.74944e7	0.736183
$893$	−1.19320e6	−0.0500707
$894$	727620.	0.0304481
$895$	−1.00660e7	−0.420049
$896$	−2.41764e7	−1.00605
$897$	−5.86151e7	−2.43236
$898$	7.14535e6	0.295687
$899$	5.08533e7	2.09855
$900$	1.01124e6	0.0416148
$901$	732301.	0.0300523
$902$	−5.23447e6	−0.214218
$903$	2.91210e7	1.18847
$904$	−8.87745e6	−0.361299
$905$	4.51654e6	0.183309
$906$	−2.07883e6	−0.0841392
$907$	−7.97441e6	−0.321870	−0.160935	−	0.986965i	$-0.551451\pi$
$907$	−7.97441e6	−0.321870	−0.160935	+	0.986965i	$0.551451\pi$
$908$	−1.21032e7	−0.487177
$909$	−1.30647e7	−0.524432
$910$	−9.00735e6	−0.360573
$911$	1.80840e7	0.721935	0.360967	−	0.932578i	$-0.382447\pi$
$911$	1.80840e7	0.721935	0.360967	+	0.932578i	$0.382447\pi$
$912$	1.75305e6	0.0697921
$913$	1.81925e6	0.0722295
$914$	−2.33369e6	−0.0924014
$915$	3.84735e6	0.151918
$916$	1.32010e7	0.519837
$917$	−1.92432e6	−0.0755707
$918$	−540457.	−0.0211668
$919$	−1.83760e7	−0.717731	−0.358865	−	0.933389i	$-0.616836\pi$
$919$	−1.83760e7	−0.717731	−0.358865	+	0.933389i	$0.616836\pi$
$920$	1.75168e7	0.682317
$921$	−1.65944e7	−0.644631
$922$	−3.30670e6	−0.128106
$923$	−1.58894e7	−0.613909
$924$	−5.38464e6	−0.207480
$925$	−9.57835e6	−0.368075
$926$	4.90342e6	0.187920
$927$	−608725.	−0.0232660
$928$	−4.38474e7	−1.67138
$929$	3.02142e7	1.14861	0.574304	−	0.818642i	$-0.305273\pi$
$929$	3.02142e7	1.14861	0.574304	+	0.818642i	$0.305273\pi$
$930$	6.24568e6	0.236795
$931$	625955.	0.0236684
$932$	3.53543e7	1.33322
$933$	3.20043e7	1.20366
$934$	−1.27876e7	−0.479647
$935$	−145779.	−0.00545337
$936$	−9.85992e6	−0.367861
$937$	6.59532e6	0.245407	0.122704	−	0.992443i	$-0.460844\pi$
$937$	6.59532e6	0.245407	0.122704	+	0.992443i	$0.460844\pi$
$938$	−2.62728e7	−0.974989
$939$	2.42629e7	0.898003
$940$	−2.02920e6	−0.0749040
$941$	3.04490e7	1.12098	0.560491	−	0.828161i	$-0.310613\pi$
$941$	3.04490e7	1.12098	0.560491	+	0.828161i	$0.310613\pi$
$942$	7.32502e6	0.268956
$943$	7.20079e7	2.63694
$944$	8.95163e6	0.326943
$945$	−1.39936e7	−0.509743
$946$	−5.30478e6	−0.192726
$947$	−1.83731e7	−0.665743	−0.332871	−	0.942972i	$-0.608018\pi$
$947$	−1.83731e7	−0.665743	−0.332871	+	0.942972i	$0.608018\pi$
$948$	1.53370e7	0.554268
$949$	7.63754e7	2.75288
$950$	−615538.	−0.0221282
$951$	2.12021e6	0.0760198
$952$	1.01249e6	0.0362075
$953$	5.07121e7	1.80875	0.904377	−	0.426735i	$-0.140336\pi$
$953$	5.07121e7	1.80875	0.904377	+	0.426735i	$0.140336\pi$
$954$	−2.73138e6	−0.0971654
$955$	2.04515e7	0.725633
$956$	−3.00633e7	−1.06388
$957$	−1.19010e7	−0.420054
$958$	−2.36702e6	−0.0833274
$959$	−7.32950e6	−0.257352
$960$	−1.50037e6	−0.0525436
$961$	1.87178e7	0.653803
$962$	4.05510e7	1.41275
$963$	−7.14624e6	−0.248320
$964$	2.38866e7	0.827868
$965$	1.12842e6	0.0390078
$966$	−2.24502e7	−0.774064
$967$	4.86282e7	1.67233	0.836165	−	0.548478i	$-0.184793\pi$
$967$	4.86282e7	1.67233	0.836165	+	0.548478i	$0.184793\pi$
$968$	2.25905e6	0.0774886
$969$	−231527.	−0.00792123
$970$	−951869.	−0.0324824
$971$	3.84775e6	0.130966	0.0654830	−	0.997854i	$-0.479141\pi$
$971$	3.84775e6	0.130966	0.0654830	+	0.997854i	$0.479141\pi$
$972$	−1.18836e7	−0.403444
$973$	−4.24605e7	−1.43782
$974$	762330.	0.0257481
$975$	8.06732e6	0.271780
$976$	−4.21945e6	−0.141785
$977$	−9.40022e6	−0.315066	−0.157533	−	0.987514i	$-0.550354\pi$
$977$	−9.40022e6	−0.315066	−0.157533	+	0.987514i	$0.550354\pi$
$978$	8.40704e6	0.281058
$979$	−184211.	−0.00614270
$980$	1.06452e6	0.0354071
$981$	−6.64116e6	−0.220329
$982$	1.68234e7	0.556717
$983$	−3.76802e7	−1.24374	−0.621870	−	0.783120i	$-0.713627\pi$
$983$	−3.76802e7	−1.24374	−0.621870	+	0.783120i	$0.713627\pi$
$984$	−3.25613e7	−1.07205
$985$	−5.24372e6	−0.172206
$986$	971649.	0.0318286
$987$	5.98959e6	0.195706
$988$	−8.59824e6	−0.280232
$989$	7.29750e7	2.37238
$990$	543735.	0.0176319
$991$	1.42572e7	0.461159	0.230580	−	0.973053i	$-0.425938\pi$
$991$	1.42572e7	0.461159	0.230580	+	0.973053i	$0.425938\pi$
$992$	−4.08241e7	−1.31716
$993$	2.06892e7	0.665840
$994$	−6.08581e6	−0.195368
$995$	−1.32010e7	−0.422716
$996$	4.91373e6	0.156951
$997$	−4.40950e7	−1.40492	−0.702460	−	0.711723i	$-0.747915\pi$
$997$	−4.40950e7	−1.40492	−0.702460	+	0.711723i	$0.747915\pi$
$998$	1.98660e7	0.631372
$999$	6.29993e7	1.99720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.15	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.15	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72815 q^{2} +13.3084 q^{3} -24.5572 q^{4} -25.0000 q^{5} -36.3073 q^{6} -136.165 q^{7} +154.296 q^{8} -65.8862 q^{9} +O(q^{10})\)	\(q-2.72815 q^{2} +13.3084 q^{3} -24.5572 q^{4} -25.0000 q^{5} -36.3073 q^{6} -136.165 q^{7} +154.296 q^{8} -65.8862 q^{9} +68.2036 q^{10} -121.000 q^{11} -326.818 q^{12} +969.892 q^{13} +371.478 q^{14} -332.710 q^{15} +364.888 q^{16} -48.1913 q^{17} +179.747 q^{18} +361.000 q^{19} +613.931 q^{20} -1812.14 q^{21} +330.106 q^{22} -4541.09 q^{23} +2053.44 q^{24} +625.000 q^{25} -2646.01 q^{26} -4110.78 q^{27} +3343.84 q^{28} +7390.49 q^{29} +907.682 q^{30} +6880.91 q^{31} -5932.95 q^{32} -1610.32 q^{33} +131.473 q^{34} +3404.13 q^{35} +1617.98 q^{36} -15325.4 q^{37} -984.861 q^{38} +12907.7 q^{39} -3857.41 q^{40} -15857.0 q^{41} +4943.79 q^{42} -16069.9 q^{43} +2971.42 q^{44} +1647.16 q^{45} +12388.8 q^{46} -3305.26 q^{47} +4856.08 q^{48} +1733.95 q^{49} -1705.09 q^{50} -641.350 q^{51} -23817.8 q^{52} -15195.7 q^{53} +11214.8 q^{54} +3025.00 q^{55} -21009.8 q^{56} +4804.34 q^{57} -20162.3 q^{58} +24532.5 q^{59} +8170.44 q^{60} -11563.7 q^{61} -18772.1 q^{62} +8971.41 q^{63} +4509.53 q^{64} -24247.3 q^{65} +4393.18 q^{66} -70725.1 q^{67} +1183.44 q^{68} -60434.7 q^{69} -9286.96 q^{70} -16382.7 q^{71} -10166.0 q^{72} +78746.3 q^{73} +41809.8 q^{74} +8317.76 q^{75} -8865.16 q^{76} +16476.0 q^{77} -35214.1 q^{78} -46928.4 q^{79} -9122.20 q^{80} -38697.7 q^{81} +43260.1 q^{82} -15035.1 q^{83} +44501.2 q^{84} +1204.78 q^{85} +43841.1 q^{86} +98355.6 q^{87} -18669.9 q^{88} +1522.41 q^{89} -4493.68 q^{90} -132065. q^{91} +111517. q^{92} +91574.0 q^{93} +9017.22 q^{94} -9025.00 q^{95} -78958.1 q^{96} -13956.3 q^{97} -4730.46 q^{98} +7972.23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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