LMFDB - Embedded newform 309.6.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,6,Mod(1,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	309.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:	$49.5586003222$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.24523 q^{2} +9.00000 q^{3} -4.48757 q^{4} -21.2020 q^{5} -47.2071 q^{6} -27.3773 q^{7} +191.386 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-5.24523 q^{2} +9.00000 q^{3} -4.48757 q^{4} -21.2020 q^{5} -47.2071 q^{6} -27.3773 q^{7} +191.386 q^{8} +81.0000 q^{9} +111.209 q^{10} +480.603 q^{11} -40.3881 q^{12} +727.571 q^{13} +143.600 q^{14} -190.818 q^{15} -860.259 q^{16} -1864.91 q^{17} -424.864 q^{18} -1065.71 q^{19} +95.1455 q^{20} -246.395 q^{21} -2520.87 q^{22} +3503.95 q^{23} +1722.47 q^{24} -2675.47 q^{25} -3816.28 q^{26} +729.000 q^{27} +122.857 q^{28} -3693.74 q^{29} +1000.88 q^{30} -5147.57 q^{31} -1612.08 q^{32} +4325.42 q^{33} +9781.86 q^{34} +580.453 q^{35} -363.493 q^{36} +16233.9 q^{37} +5589.89 q^{38} +6548.14 q^{39} -4057.76 q^{40} +7121.13 q^{41} +1292.40 q^{42} +5367.26 q^{43} -2156.74 q^{44} -1717.36 q^{45} -18379.0 q^{46} -1587.11 q^{47} -7742.34 q^{48} -16057.5 q^{49} +14033.5 q^{50} -16784.1 q^{51} -3265.02 q^{52} +9236.79 q^{53} -3823.77 q^{54} -10189.7 q^{55} -5239.62 q^{56} -9591.38 q^{57} +19374.5 q^{58} +2270.96 q^{59} +856.310 q^{60} +5257.36 q^{61} +27000.2 q^{62} -2217.56 q^{63} +35984.0 q^{64} -15426.0 q^{65} -22687.8 q^{66} +10009.9 q^{67} +8368.89 q^{68} +31535.5 q^{69} -3044.61 q^{70} -26822.0 q^{71} +15502.2 q^{72} +42832.9 q^{73} -85150.4 q^{74} -24079.3 q^{75} +4782.44 q^{76} -13157.6 q^{77} -34346.5 q^{78} +80781.8 q^{79} +18239.2 q^{80} +6561.00 q^{81} -37351.9 q^{82} -23096.5 q^{83} +1105.72 q^{84} +39539.8 q^{85} -28152.5 q^{86} -33243.6 q^{87} +91980.4 q^{88} +42174.4 q^{89} +9007.96 q^{90} -19918.9 q^{91} -15724.2 q^{92} -46328.1 q^{93} +8324.77 q^{94} +22595.2 q^{95} -14508.8 q^{96} +161882. q^{97} +84225.2 q^{98} +38928.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) $ 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * 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 $

$2$	−5.24523	−0.927234	−0.463617	−	0.886036i	$-0.653449\pi$
$2$	−5.24523	−0.927234	−0.463617	+	0.886036i	$0.653449\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−4.48757	−0.140237
$5$	−21.2020	−0.379273	−0.189637	−	0.981854i	$-0.560731\pi$
$5$	−21.2020	−0.379273	−0.189637	+	0.981854i	$0.560731\pi$
$6$	−47.2071	−0.535339
$7$	−27.3773	−0.211176	−0.105588	−	0.994410i	$-0.533673\pi$
$7$	−27.3773	−0.211176	−0.105588	+	0.994410i	$0.533673\pi$
$8$	191.386	1.05727
$9$	81.0000	0.333333
$10$	111.209	0.351675
$11$	480.603	1.19758	0.598790	−	0.800906i	$-0.295649\pi$
$11$	480.603	1.19758	0.598790	+	0.800906i	$0.295649\pi$
$12$	−40.3881	−0.0809656
$13$	727.571	1.19403	0.597017	−	0.802228i	$-0.296352\pi$
$13$	727.571	1.19403	0.597017	+	0.802228i	$0.296352\pi$
$14$	143.600	0.195810
$15$	−190.818	−0.218973
$16$	−860.259	−0.840097
$17$	−1864.91	−1.56507	−0.782536	−	0.622605i	$-0.786074\pi$
$17$	−1864.91	−1.56507	−0.782536	+	0.622605i	$0.786074\pi$
$18$	−424.864	−0.309078
$19$	−1065.71	−0.677258	−0.338629	−	0.940920i	$-0.609963\pi$
$19$	−1065.71	−0.677258	−0.338629	+	0.940920i	$0.609963\pi$
$20$	95.1455	0.0531880
$21$	−246.395	−0.121923
$22$	−2520.87	−1.11044
$23$	3503.95	1.38114	0.690570	−	0.723265i	$-0.257360\pi$
$23$	3503.95	1.38114	0.690570	+	0.723265i	$0.257360\pi$
$24$	1722.47	0.610413
$25$	−2675.47	−0.856152
$26$	−3816.28	−1.10715
$27$	729.000	0.192450
$28$	122.857	0.0296146
$29$	−3693.74	−0.815588	−0.407794	−	0.913074i	$-0.633702\pi$
$29$	−3693.74	−0.815588	−0.407794	+	0.913074i	$0.633702\pi$
$30$	1000.88	0.203040
$31$	−5147.57	−0.962051	−0.481026	−	0.876707i	$-0.659736\pi$
$31$	−5147.57	−0.962051	−0.481026	+	0.876707i	$0.659736\pi$
$32$	−1612.08	−0.278300
$33$	4325.42	0.691423
$34$	9781.86	1.45119
$35$	580.453	0.0800935
$36$	−363.493	−0.0467455
$37$	16233.9	1.94948	0.974738	−	0.223350i	$-0.0716994\pi$
$37$	16233.9	1.94948	0.974738	+	0.223350i	$0.0716994\pi$
$38$	5589.89	0.627977
$39$	6548.14	0.689376
$40$	−4057.76	−0.400993
$41$	7121.13	0.661590	0.330795	−	0.943703i	$-0.392683\pi$
$41$	7121.13	0.661590	0.330795	+	0.943703i	$0.392683\pi$
$42$	1292.40	0.113051
$43$	5367.26	0.442671	0.221336	−	0.975198i	$-0.428958\pi$
$43$	5367.26	0.442671	0.221336	+	0.975198i	$0.428958\pi$
$44$	−2156.74	−0.167944
$45$	−1717.36	−0.126424
$46$	−18379.0	−1.28064
$47$	−1587.11	−0.104800	−0.0524002	−	0.998626i	$-0.516687\pi$
$47$	−1587.11	−0.104800	−0.0524002	+	0.998626i	$0.516687\pi$
$48$	−7742.34	−0.485030
$49$	−16057.5	−0.955405
$50$	14033.5	0.793853
$51$	−16784.1	−0.903595
$52$	−3265.02	−0.167447
$53$	9236.79	0.451680	0.225840	−	0.974164i	$-0.427487\pi$
$53$	9236.79	0.451680	0.225840	+	0.974164i	$0.427487\pi$
$54$	−3823.77	−0.178446
$55$	−10189.7	−0.454210
$56$	−5239.62	−0.223270
$57$	−9591.38	−0.391015
$58$	19374.5	0.756242
$59$	2270.96	0.0849336	0.0424668	−	0.999098i	$-0.486478\pi$
$59$	2270.96	0.0849336	0.0424668	+	0.999098i	$0.486478\pi$
$60$	856.310	0.0307081
$61$	5257.36	0.180902	0.0904509	−	0.995901i	$-0.471169\pi$
$61$	5257.36	0.180902	0.0904509	+	0.995901i	$0.471169\pi$
$62$	27000.2	0.892047
$63$	−2217.56	−0.0703921
$64$	35984.0	1.09815
$65$	−15426.0	−0.452865
$66$	−22687.8	−0.641111
$67$	10009.9	0.272421	0.136211	−	0.990680i	$-0.456508\pi$
$67$	10009.9	0.272421	0.136211	+	0.990680i	$0.456508\pi$
$68$	8368.89	0.219480
$69$	31535.5	0.797402
$70$	−3044.61	−0.0742654
$71$	−26822.0	−0.631459	−0.315729	−	0.948849i	$-0.602249\pi$
$71$	−26822.0	−0.631459	−0.315729	+	0.948849i	$0.602249\pi$
$72$	15502.2	0.352422
$73$	42832.9	0.940742	0.470371	−	0.882469i	$-0.344120\pi$
$73$	42832.9	0.940742	0.470371	+	0.882469i	$0.344120\pi$
$74$	−85150.4	−1.80762
$75$	−24079.3	−0.494299
$76$	4782.44	0.0949764
$77$	−13157.6	−0.252900
$78$	−34346.5	−0.639213
$79$	80781.8	1.45628	0.728141	−	0.685427i	$-0.240384\pi$
$79$	80781.8	1.45628	0.728141	+	0.685427i	$0.240384\pi$
$80$	18239.2	0.318626
$81$	6561.00	0.111111
$82$	−37351.9	−0.613449
$83$	−23096.5	−0.368003	−0.184001	−	0.982926i	$-0.558905\pi$
$83$	−23096.5	−0.368003	−0.184001	+	0.982926i	$0.558905\pi$
$84$	1105.72	0.0170980
$85$	39539.8	0.593590
$86$	−28152.5	−0.410460
$87$	−33243.6	−0.470880
$88$	91980.4	1.26616
$89$	42174.4	0.564383	0.282192	−	0.959358i	$-0.408939\pi$
$89$	42174.4	0.564383	0.282192	+	0.959358i	$0.408939\pi$
$90$	9007.96	0.117225
$91$	−19918.9	−0.252152
$92$	−15724.2	−0.193686
$93$	−46328.1	−0.555440
$94$	8324.77	0.0971746
$95$	22595.2	0.256866
$96$	−14508.8	−0.160676
$97$	161882.	1.74691	0.873455	−	0.486905i	$-0.161874\pi$
$97$	161882.	1.74691	0.873455	+	0.486905i	$0.161874\pi$
$98$	84225.2	0.885884
$99$	38928.8	0.399193
$100$	12006.4	0.120064
$101$	−70643.8	−0.689081	−0.344541	−	0.938771i	$-0.611965\pi$
$101$	−70643.8	−0.689081	−0.344541	+	0.938771i	$0.611965\pi$
$102$	88036.7	0.837844
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	139247.	1.26241
$105$	5224.08	0.0462420
$106$	−48449.1	−0.418814
$107$	15144.5	0.127878	0.0639391	−	0.997954i	$-0.479634\pi$
$107$	15144.5	0.127878	0.0639391	+	0.997954i	$0.479634\pi$
$108$	−3271.44	−0.0269885
$109$	218053.	1.75790	0.878952	−	0.476910i	$-0.158243\pi$
$109$	218053.	1.75790	0.878952	+	0.476910i	$0.158243\pi$
$110$	53447.5	0.421159
$111$	146105.	1.12553
$112$	23551.6	0.177409
$113$	6684.65	0.0492473	0.0246237	−	0.999697i	$-0.492161\pi$
$113$	6684.65	0.0492473	0.0246237	+	0.999697i	$0.492161\pi$
$114$	50309.0	0.362563
$115$	−74290.7	−0.523830
$116$	16575.9	0.114375
$117$	58933.2	0.398011
$118$	−11911.7	−0.0787534
$119$	51056.0	0.330506
$120$	−36519.9	−0.231513
$121$	69927.8	0.434196
$122$	−27576.1	−0.167738
$123$	64090.1	0.381969
$124$	23100.1	0.134915
$125$	122982.	0.703989
$126$	11631.6	0.0652699
$127$	161626.	0.889207	0.444604	−	0.895727i	$-0.353345\pi$
$127$	161626.	0.889207	0.444604	+	0.895727i	$0.353345\pi$
$128$	−137158.	−0.739939
$129$	48305.3	0.255576
$130$	80912.7	0.419912
$131$	56506.2	0.287686	0.143843	−	0.989601i	$-0.454054\pi$
$131$	56506.2	0.287686	0.143843	+	0.989601i	$0.454054\pi$
$132$	−19410.6	−0.0969628
$133$	29176.2	0.143021
$134$	−52504.0	−0.252598
$135$	−15456.3	−0.0729912
$136$	−356916.	−1.65470
$137$	−52870.2	−0.240663	−0.120332	−	0.992734i	$-0.538396\pi$
$137$	−52870.2	−0.240663	−0.120332	+	0.992734i	$0.538396\pi$
$138$	−165411.	−0.739378
$139$	330252.	1.44980	0.724901	−	0.688853i	$-0.241885\pi$
$139$	330252.	1.44980	0.724901	+	0.688853i	$0.241885\pi$
$140$	−2604.82	−0.0112320
$141$	−14284.0	−0.0605066
$142$	140687.	0.585510
$143$	349672.	1.42995
$144$	−69681.0	−0.280032
$145$	78314.7	0.309331
$146$	−224669.	−0.872289
$147$	−144517.	−0.551603
$148$	−72850.7	−0.273388
$149$	108208.	0.399293	0.199647	−	0.979868i	$-0.436021\pi$
$149$	108208.	0.399293	0.199647	+	0.979868i	$0.436021\pi$
$150$	126301.	0.458331
$151$	−101748.	−0.363148	−0.181574	−	0.983377i	$-0.558119\pi$
$151$	−101748.	−0.363148	−0.181574	+	0.983377i	$0.558119\pi$
$152$	−203961.	−0.716043
$153$	−151057.	−0.521691
$154$	69014.5	0.234498
$155$	109139.	0.364880
$156$	−29385.2	−0.0966757
$157$	469864.	1.52133	0.760664	−	0.649146i	$-0.224874\pi$
$157$	469864.	1.52133	0.760664	+	0.649146i	$0.224874\pi$
$158$	−423719.	−1.35032
$159$	83131.1	0.260778
$160$	34179.4	0.105552
$161$	−95928.5	−0.291664
$162$	−34413.9	−0.103026
$163$	85668.2	0.252552	0.126276	−	0.991995i	$-0.459698\pi$
$163$	85668.2	0.252552	0.126276	+	0.991995i	$0.459698\pi$
$164$	−31956.6	−0.0927791
$165$	−91707.7	−0.262238
$166$	121147.	0.341225
$167$	492478.	1.36646	0.683228	−	0.730205i	$-0.260576\pi$
$167$	492478.	1.36646	0.683228	+	0.730205i	$0.260576\pi$
$168$	−47156.5	−0.128905
$169$	158066.	0.425718
$170$	−207395.	−0.550397
$171$	−86322.4	−0.225753
$172$	−24085.9	−0.0620787
$173$	−565635.	−1.43688	−0.718441	−	0.695588i	$-0.755144\pi$
$173$	−565635.	−1.43688	−0.718441	+	0.695588i	$0.755144\pi$
$174$	174371.	0.436616
$175$	73247.2	0.180799
$176$	−413443.	−1.00608
$177$	20438.6	0.0490364
$178$	−221215.	−0.523315
$179$	−200057.	−0.466683	−0.233341	−	0.972395i	$-0.574966\pi$
$179$	−200057.	−0.466683	−0.233341	+	0.972395i	$0.574966\pi$
$180$	7706.79	0.0177293
$181$	−334455.	−0.758824	−0.379412	−	0.925228i	$-0.623874\pi$
$181$	−334455.	−0.758824	−0.379412	+	0.925228i	$0.623874\pi$
$182$	104479.	0.233804
$183$	47316.2	0.104444
$184$	670605.	1.46023
$185$	−344191.	−0.739384
$186$	243002.	0.515023
$187$	−896278.	−1.87430
$188$	7122.28	0.0146969
$189$	−19958.0	−0.0406409
$190$	−118517.	−0.238175
$191$	490887.	0.973639	0.486820	−	0.873503i	$-0.338157\pi$
$191$	490887.	0.973639	0.486820	+	0.873503i	$0.338157\pi$
$192$	323856.	0.634015
$193$	181254.	0.350263	0.175132	−	0.984545i	$-0.443965\pi$
$193$	181254.	0.350263	0.175132	+	0.984545i	$0.443965\pi$
$194$	−849111.	−1.61979
$195$	−138834.	−0.261462
$196$	72059.1	0.133983
$197$	−361960.	−0.664500	−0.332250	−	0.943191i	$-0.607808\pi$
$197$	−361960.	−0.664500	−0.332250	+	0.943191i	$0.607808\pi$
$198$	−204190.	−0.370146
$199$	−536264.	−0.959944	−0.479972	−	0.877284i	$-0.659353\pi$
$199$	−536264.	−0.959944	−0.479972	+	0.877284i	$0.659353\pi$
$200$	−512047.	−0.905181
$201$	90088.8	0.157283
$202$	370543.	0.638940
$203$	101124.	0.172233
$204$	75320.0	0.126717
$205$	−150982.	−0.250923
$206$	55646.6	0.0913631
$207$	283820.	0.460380
$208$	−625900.	−1.00310
$209$	−512182.	−0.811071
$210$	−27401.5	−0.0428772
$211$	−681774.	−1.05423	−0.527114	−	0.849795i	$-0.676726\pi$
$211$	−681774.	−1.05423	−0.527114	+	0.849795i	$0.676726\pi$
$212$	−41450.7	−0.0633421
$213$	−241398.	−0.364573
$214$	−79436.5	−0.118573
$215$	−113797.	−0.167893
$216$	139520.	0.203471
$217$	140926.	0.203162
$218$	−1.14374e6	−1.62999
$219$	385496.	0.543138
$220$	45727.2	0.0636968
$221$	−1.35685e6	−1.86875
$222$	−766354.	−1.04363
$223$	516592.	0.695641	0.347821	−	0.937561i	$-0.386922\pi$
$223$	516592.	0.695641	0.347821	+	0.937561i	$0.386922\pi$
$224$	44134.4	0.0587702
$225$	−216713.	−0.285384
$226$	−35062.5	−0.0456638
$227$	279631.	0.360181	0.180091	−	0.983650i	$-0.442361\pi$
$227$	279631.	0.360181	0.180091	+	0.983650i	$0.442361\pi$
$228$	43042.0	0.0548347
$229$	1.39382e6	1.75638	0.878192	−	0.478309i	$-0.158750\pi$
$229$	1.39382e6	1.75638	0.878192	+	0.478309i	$0.158750\pi$
$230$	389672.	0.485713
$231$	−118418.	−0.146012
$232$	−706929.	−0.862294
$233$	266800.	0.321956	0.160978	−	0.986958i	$-0.448535\pi$
$233$	266800.	0.321956	0.160978	+	0.986958i	$0.448535\pi$
$234$	−309118.	−0.369050
$235$	33650.0	0.0397480
$236$	−10191.1	−0.0119108
$237$	727036.	0.840785
$238$	−267800.	−0.306457
$239$	−1.27485e6	−1.44365	−0.721827	−	0.692073i	$-0.756697\pi$
$239$	−1.27485e6	−1.44365	−0.721827	+	0.692073i	$0.756697\pi$
$240$	164153.	0.183959
$241$	659237.	0.731137	0.365569	−	0.930784i	$-0.380875\pi$
$241$	659237.	0.731137	0.365569	+	0.930784i	$0.380875\pi$
$242$	−366787.	−0.402602
$243$	59049.0	0.0641500
$244$	−23592.8	−0.0253691
$245$	340451.	0.362359
$246$	−336167.	−0.354175
$247$	−775378.	−0.808670
$248$	−985171.	−1.01714
$249$	−207869.	−0.212467
$250$	−645068.	−0.652762
$251$	−715199.	−0.716543	−0.358272	−	0.933617i	$-0.616634\pi$
$251$	−715199.	−0.716543	−0.358272	+	0.933617i	$0.616634\pi$
$252$	9951.45	0.00987154
$253$	1.68401e6	1.65403
$254$	−847768.	−0.824503
$255$	355858.	0.342709
$256$	−432065.	−0.412049
$257$	−505396.	−0.477308	−0.238654	−	0.971105i	$-0.576706\pi$
$257$	−505396.	−0.477308	−0.238654	+	0.971105i	$0.576706\pi$
$258$	−253372.	−0.236979
$259$	−444439.	−0.411683
$260$	69225.1	0.0635083
$261$	−299193.	−0.271863
$262$	−296388.	−0.266752
$263$	660298.	0.588641	0.294321	−	0.955707i	$-0.404907\pi$
$263$	660298.	0.588641	0.294321	+	0.955707i	$0.404907\pi$
$264$	827824.	0.731018
$265$	−195839.	−0.171310
$266$	−153036.	−0.132614
$267$	379570.	0.325847
$268$	−44920.0	−0.0382034
$269$	−565775.	−0.476720	−0.238360	−	0.971177i	$-0.576610\pi$
$269$	−565775.	−0.476720	−0.238360	+	0.971177i	$0.576610\pi$
$270$	81071.7	0.0676799
$271$	1.11439e6	0.921752	0.460876	−	0.887464i	$-0.347535\pi$
$271$	1.11439e6	0.921752	0.460876	+	0.887464i	$0.347535\pi$
$272$	1.60430e6	1.31481
$273$	−179270.	−0.145580
$274$	277316.	0.223151
$275$	−1.28584e6	−1.02531
$276$	−141518.	−0.111825
$277$	1.57665e6	1.23463	0.617313	−	0.786718i	$-0.288221\pi$
$277$	1.57665e6	1.23463	0.617313	+	0.786718i	$0.288221\pi$
$278$	−1.73225e6	−1.34431
$279$	−416953.	−0.320684
$280$	111090.	0.0846801
$281$	1.05399e6	0.796292	0.398146	−	0.917322i	$-0.369654\pi$
$281$	1.05399e6	0.796292	0.398146	+	0.917322i	$0.369654\pi$
$282$	74922.9	0.0561038
$283$	481908.	0.357683	0.178841	−	0.983878i	$-0.442765\pi$
$283$	481908.	0.357683	0.178841	+	0.983878i	$0.442765\pi$
$284$	120366.	0.0885536
$285$	203357.	0.148302
$286$	−1.83411e6	−1.32590
$287$	−194957.	−0.139712
$288$	−130579.	−0.0927665
$289$	2.05801e6	1.44945
$290$	−410779.	−0.286822
$291$	1.45694e6	1.00858
$292$	−192216.	−0.131927
$293$	1.90520e6	1.29649	0.648247	−	0.761430i	$-0.275502\pi$
$293$	1.90520e6	1.29649	0.648247	+	0.761430i	$0.275502\pi$
$294$	758027.	0.511465
$295$	−48148.9	−0.0322130
$296$	3.10693e6	2.06112
$297$	350359.	0.230474
$298$	−567573.	−0.370238
$299$	2.54937e6	1.64913
$300$	108057.	0.0693189
$301$	−146941.	−0.0934816
$302$	533691.	0.336723
$303$	−635794.	−0.397841
$304$	916786.	0.568963
$305$	−111467.	−0.0686112
$306$	792330.	0.483730
$307$	−1.87825e6	−1.13739	−0.568693	−	0.822550i	$-0.692551\pi$
$307$	−1.87825e6	−1.13739	−0.568693	+	0.822550i	$0.692551\pi$
$308$	59045.6	0.0354659
$309$	−95481.0	−0.0568880
$310$	−572459.	−0.338329
$311$	−1.94521e6	−1.14042	−0.570209	−	0.821499i	$-0.693138\pi$
$311$	−1.94521e6	−1.14042	−0.570209	+	0.821499i	$0.693138\pi$
$312$	1.25322e6	0.728854
$313$	1.38577e6	0.799525	0.399762	−	0.916619i	$-0.369093\pi$
$313$	1.38577e6	0.799525	0.399762	+	0.916619i	$0.369093\pi$
$314$	−2.46454e6	−1.41063
$315$	47016.7	0.0266978
$316$	−362514.	−0.204224
$317$	906144.	0.506465	0.253232	−	0.967405i	$-0.418506\pi$
$317$	906144.	0.506465	0.253232	+	0.967405i	$0.418506\pi$
$318$	−436042.	−0.241802
$319$	−1.77522e6	−0.976732
$320$	−762934.	−0.416497
$321$	136301.	0.0738305
$322$	503167.	0.270441
$323$	1.98745e6	1.05996
$324$	−29443.0	−0.0155818
$325$	−1.94660e6	−1.02227
$326$	−449350.	−0.234175
$327$	1.96247e6	1.01493
$328$	1.36288e6	0.699477
$329$	43450.8	0.0221314
$330$	481028.	0.243156
$331$	−4850.79	−0.00243356	−0.00121678	−	0.999999i	$-0.500387\pi$
$331$	−4850.79	−0.00243356	−0.00121678	+	0.999999i	$0.500387\pi$
$332$	103647.	0.0516075
$333$	1.31494e6	0.649826
$334$	−2.58316e6	−1.26702
$335$	−212229.	−0.103322
$336$	211964.	0.102427
$337$	−1.96980e6	−0.944818	−0.472409	−	0.881380i	$-0.656615\pi$
$337$	−1.96980e6	−0.944818	−0.472409	+	0.881380i	$0.656615\pi$
$338$	−829093.	−0.394740
$339$	60161.9	0.0284330
$340$	−177437.	−0.0832430
$341$	−2.47394e6	−1.15213
$342$	452781.	0.209326
$343$	899740.	0.412935
$344$	1.02722e6	0.468021
$345$	−668617.	−0.302433
$346$	2.96689e6	1.33233
$347$	−4.46686e6	−1.99149	−0.995745	−	0.0921465i	$-0.970627\pi$
$347$	−4.46686e6	−1.99149	−0.995745	+	0.0921465i	$0.970627\pi$
$348$	149183.	0.0660346
$349$	2.99325e6	1.31547	0.657733	−	0.753251i	$-0.271515\pi$
$349$	2.99325e6	1.31547	0.657733	+	0.753251i	$0.271515\pi$
$350$	−384198.	−0.167643
$351$	530399.	0.229792
$352$	−774771.	−0.333286
$353$	2.11922e6	0.905189	0.452594	−	0.891716i	$-0.350499\pi$
$353$	2.11922e6	0.905189	0.452594	+	0.891716i	$0.350499\pi$
$354$	−107205.	−0.0454683
$355$	568680.	0.239495
$356$	−189261.	−0.0791472
$357$	459504.	0.190818
$358$	1.04935e6	0.432724
$359$	1.92339e6	0.787647	0.393823	−	0.919186i	$-0.371152\pi$
$359$	1.92339e6	0.787647	0.393823	+	0.919186i	$0.371152\pi$
$360$	−328679.	−0.133664
$361$	−1.34036e6	−0.541321
$362$	1.75429e6	0.703608
$363$	629350.	0.250683
$364$	89387.4	0.0353609
$365$	−908145.	−0.356798
$366$	−248184.	−0.0968438
$367$	4.06433e6	1.57516	0.787578	−	0.616215i	$-0.211335\pi$
$367$	4.06433e6	1.57516	0.787578	+	0.616215i	$0.211335\pi$
$368$	−3.01430e6	−1.16029
$369$	576811.	0.220530
$370$	1.80536e6	0.685582
$371$	−252878.	−0.0953841
$372$	207901.	0.0778931
$373$	513191.	0.190988	0.0954942	−	0.995430i	$-0.469557\pi$
$373$	513191.	0.190988	0.0954942	+	0.995430i	$0.469557\pi$
$374$	4.70118e6	1.73791
$375$	1.10684e6	0.406448
$376$	−303751.	−0.110802
$377$	−2.68746e6	−0.973841
$378$	104684.	0.0376836
$379$	−3.13179e6	−1.11994	−0.559971	−	0.828513i	$-0.689188\pi$
$379$	−3.13179e6	−1.11994	−0.559971	+	0.828513i	$0.689188\pi$
$380$	−101397.	−0.0360220
$381$	1.45464e6	0.513384
$382$	−2.57481e6	−0.902792
$383$	5.29543e6	1.84461	0.922305	−	0.386464i	$-0.126304\pi$
$383$	5.29543e6	1.84461	0.922305	+	0.386464i	$0.126304\pi$
$384$	−1.23442e6	−0.427204
$385$	278967.	0.0959183
$386$	−950720.	−0.324776
$387$	434748.	0.147557
$388$	−726459.	−0.244981
$389$	−5.44589e6	−1.82471	−0.912357	−	0.409396i	$-0.865740\pi$
$389$	−5.44589e6	−1.82471	−0.912357	+	0.409396i	$0.865740\pi$
$390$	728215.	0.242436
$391$	−6.53453e6	−2.16159
$392$	−3.07317e6	−1.01012
$393$	508556.	0.166095
$394$	1.89856e6	0.616147
$395$	−1.71274e6	−0.552329
$396$	−174696.	−0.0559815
$397$	3.35399e6	1.06803	0.534017	−	0.845474i	$-0.320682\pi$
$397$	3.35399e6	1.06803	0.534017	+	0.845474i	$0.320682\pi$
$398$	2.81283e6	0.890093
$399$	262586.	0.0825731
$400$	2.30160e6	0.719251
$401$	1.84253e6	0.572208	0.286104	−	0.958199i	$-0.407640\pi$
$401$	1.84253e6	0.572208	0.286104	+	0.958199i	$0.407640\pi$
$402$	−472536.	−0.145838
$403$	−3.74522e6	−1.14872
$404$	317019.	0.0966344
$405$	−139106.	−0.0421415
$406$	−530421.	−0.159700
$407$	7.80204e6	2.33465
$408$	−3.21225e6	−0.955341
$409$	65532.2	0.0193708	0.00968538	−	0.999953i	$-0.496917\pi$
$409$	65532.2	0.0193708	0.00968538	+	0.999953i	$0.496917\pi$
$410$	791936.	0.232665
$411$	−475832.	−0.138947
$412$	47608.6	0.0138179
$413$	−62172.7	−0.0179360
$414$	−1.48870e6	−0.426880
$415$	489693.	0.139574
$416$	−1.17290e6	−0.332299
$417$	2.97227e6	0.837044
$418$	2.68651e6	0.752053
$419$	1.46501e6	0.407667	0.203834	−	0.979006i	$-0.434660\pi$
$419$	1.46501e6	0.407667	0.203834	+	0.979006i	$0.434660\pi$
$420$	−23443.4	−0.00648482
$421$	−5.72879e6	−1.57528	−0.787640	−	0.616136i	$-0.788697\pi$
$421$	−5.72879e6	−1.57528	−0.787640	+	0.616136i	$0.788697\pi$
$422$	3.57606e6	0.977516
$423$	−128556.	−0.0349335
$424$	1.76779e6	0.477547
$425$	4.98951e6	1.33994
$426$	1.26619e6	0.338045
$427$	−143932.	−0.0382022
$428$	−67962.1	−0.0179332
$429$	3.14705e6	0.825583
$430$	596889.	0.155676
$431$	−1.37206e6	−0.355779	−0.177890	−	0.984050i	$-0.556927\pi$
$431$	−1.37206e6	−0.355779	−0.177890	+	0.984050i	$0.556927\pi$
$432$	−627129.	−0.161677
$433$	−3.86812e6	−0.991471	−0.495736	−	0.868473i	$-0.665102\pi$
$433$	−3.86812e6	−0.991471	−0.495736	+	0.868473i	$0.665102\pi$
$434$	−739191.	−0.188379
$435$	704832.	0.178592
$436$	−978527.	−0.246523
$437$	−3.73419e6	−0.935389
$438$	−2.02202e6	−0.503616
$439$	4.54278e6	1.12502	0.562511	−	0.826790i	$-0.309835\pi$
$439$	4.54278e6	1.12502	0.562511	+	0.826790i	$0.309835\pi$
$440$	−1.95017e6	−0.480221
$441$	−1.30066e6	−0.318468
$442$	7.11699e6	1.73277
$443$	−858747.	−0.207901	−0.103950	−	0.994582i	$-0.533148\pi$
$443$	−858747.	−0.207901	−0.103950	+	0.994582i	$0.533148\pi$
$444$	−655656.	−0.157841
$445$	−894183.	−0.214055
$446$	−2.70964e6	−0.645022
$447$	973868.	0.230532
$448$	−985145.	−0.231902
$449$	957805.	0.224213	0.112107	−	0.993696i	$-0.464240\pi$
$449$	957805.	0.224213	0.112107	+	0.993696i	$0.464240\pi$
$450$	1.13671e6	0.264618
$451$	3.42243e6	0.792307
$452$	−29997.9	−0.00690628
$453$	−915731.	−0.209663
$454$	−1.46673e6	−0.333972
$455$	422321.	0.0956344
$456$	−1.83565e6	−0.413407
$457$	−8.12810e6	−1.82053	−0.910267	−	0.414022i	$-0.864124\pi$
$457$	−8.12810e6	−1.82053	−0.910267	+	0.414022i	$0.864124\pi$
$458$	−7.31093e6	−1.62858
$459$	−1.35952e6	−0.301198
$460$	333385.	0.0734601
$461$	−3.28693e6	−0.720340	−0.360170	−	0.932887i	$-0.617281\pi$
$461$	−3.28693e6	−0.720340	−0.360170	+	0.932887i	$0.617281\pi$
$462$	621131.	0.135387
$463$	−3.55219e6	−0.770093	−0.385047	−	0.922897i	$-0.625815\pi$
$463$	−3.55219e6	−0.770093	−0.385047	+	0.922897i	$0.625815\pi$
$464$	3.17757e6	0.685174
$465$	982250.	0.210664
$466$	−1.39943e6	−0.298529
$467$	−5.64080e6	−1.19687	−0.598437	−	0.801170i	$-0.704212\pi$
$467$	−5.64080e6	−1.19687	−0.598437	+	0.801170i	$0.704212\pi$
$468$	−264467.	−0.0558158
$469$	−274043.	−0.0575289
$470$	−176502.	−0.0368557
$471$	4.22877e6	0.878339
$472$	434629.	0.0897975
$473$	2.57952e6	0.530134
$474$	−3.81347e6	−0.779605
$475$	2.85128e6	0.579836
$476$	−229117.	−0.0463490
$477$	748180.	0.150560
$478$	6.68686e6	1.33861
$479$	−749342.	−0.149225	−0.0746125	−	0.997213i	$-0.523772\pi$
$479$	−749342.	−0.149225	−0.0746125	+	0.997213i	$0.523772\pi$
$480$	307615.	0.0609402
$481$	1.18113e7	2.32774
$482$	−3.45785e6	−0.677935
$483$	−863356.	−0.168392
$484$	−313806.	−0.0608902
$485$	−3.43224e6	−0.662556
$486$	−309726.	−0.0594821
$487$	−3.02077e6	−0.577160	−0.288580	−	0.957456i	$-0.593183\pi$
$487$	−3.02077e6	−0.577160	−0.288580	+	0.957456i	$0.593183\pi$
$488$	1.00618e6	0.191261
$489$	771014.	0.145811
$490$	−1.78574e6	−0.335992
$491$	163084.	0.0305287	0.0152643	−	0.999883i	$-0.495141\pi$
$491$	163084.	0.0305287	0.0152643	+	0.999883i	$0.495141\pi$
$492$	−287609.	−0.0535661
$493$	6.88847e6	1.27646
$494$	4.06704e6	0.749826
$495$	−825369.	−0.151403
$496$	4.42825e6	0.808216
$497$	734313.	0.133349
$498$	1.09032e6	0.197006
$499$	−1.36035e6	−0.244569	−0.122284	−	0.992495i	$-0.539022\pi$
$499$	−1.36035e6	−0.244569	−0.122284	+	0.992495i	$0.539022\pi$
$500$	−551889.	−0.0987250
$501$	4.43230e6	0.788924
$502$	3.75138e6	0.664403
$503$	1.34423e6	0.236894	0.118447	−	0.992960i	$-0.462208\pi$
$503$	1.34423e6	0.236894	0.118447	+	0.992960i	$0.462208\pi$
$504$	−424409.	−0.0744232
$505$	1.49779e6	0.261350
$506$	−8.83300e6	−1.53367
$507$	1.42260e6	0.245788
$508$	−725310.	−0.124699
$509$	6.96501e6	1.19159	0.595796	−	0.803136i	$-0.296837\pi$
$509$	6.96501e6	1.19159	0.595796	+	0.803136i	$0.296837\pi$
$510$	−1.86656e6	−0.317772
$511$	−1.17265e6	−0.198662
$512$	6.65533e6	1.12201
$513$	−776901.	−0.130338
$514$	2.65092e6	0.442577
$515$	224932.	0.0373709
$516$	−216773.	−0.0358411
$517$	−762770.	−0.125507
$518$	2.33119e6	0.381727
$519$	−5.09071e6	−0.829584
$520$	−2.95231e6	−0.478799
$521$	2.38115e6	0.384320	0.192160	−	0.981364i	$-0.438451\pi$
$521$	2.38115e6	0.384320	0.192160	+	0.981364i	$0.438451\pi$
$522$	1.56933e6	0.252081
$523$	−7.53515e6	−1.20458	−0.602292	−	0.798276i	$-0.705746\pi$
$523$	−7.53515e6	−1.20458	−0.602292	+	0.798276i	$0.705746\pi$
$524$	−253576.	−0.0403440
$525$	659225.	0.104384
$526$	−3.46341e6	−0.545808
$527$	9.59973e6	1.50568
$528$	−3.72099e6	−0.580862
$529$	5.84130e6	0.907550
$530$	1.02722e6	0.158845
$531$	183948.	0.0283112
$532$	−130930.	−0.0200568
$533$	5.18112e6	0.789961
$534$	−1.99093e6	−0.302136
$535$	−321094.	−0.0485007
$536$	1.91574e6	0.288022
$537$	−1.80052e6	−0.269440
$538$	2.96762e6	0.442031
$539$	−7.71727e6	−1.14417
$540$	69361.1	0.0102360
$541$	−8.19487e6	−1.20378	−0.601892	−	0.798577i	$-0.705586\pi$
$541$	−8.19487e6	−1.20378	−0.601892	+	0.798577i	$0.705586\pi$
$542$	−5.84523e6	−0.854680
$543$	−3.01009e6	−0.438107
$544$	3.00638e6	0.435559
$545$	−4.62316e6	−0.666726
$546$	940313.	0.134987
$547$	6.82722e6	0.975608	0.487804	−	0.872953i	$-0.337798\pi$
$547$	6.82722e6	0.975608	0.487804	+	0.872953i	$0.337798\pi$
$548$	237259.	0.0337498
$549$	425846.	0.0603006
$550$	6.74452e6	0.950702
$551$	3.93645e6	0.552364
$552$	6.03545e6	0.843066
$553$	−2.21158e6	−0.307532
$554$	−8.26988e6	−1.14479
$555$	−3.09772e6	−0.426884
$556$	−1.48203e6	−0.203315
$557$	−174721.	−0.0238621	−0.0119310	−	0.999929i	$-0.503798\pi$
$557$	−174721.	−0.0238621	−0.0119310	+	0.999929i	$0.503798\pi$
$558$	2.18702e6	0.297349
$559$	3.90506e6	0.528564
$560$	−499340.	−0.0672863
$561$	−8.06650e6	−1.08213
$562$	−5.52844e6	−0.738350
$563$	8.75086e6	1.16354	0.581768	−	0.813355i	$-0.302361\pi$
$563$	8.75086e6	1.16354	0.581768	+	0.813355i	$0.302361\pi$
$564$	64100.5	0.00848523
$565$	−141728.	−0.0186782
$566$	−2.52772e6	−0.331656
$567$	−179622.	−0.0234640
$568$	−5.13334e6	−0.667620
$569$	2.27506e6	0.294586	0.147293	−	0.989093i	$-0.452944\pi$
$569$	2.27506e6	0.294586	0.147293	+	0.989093i	$0.452944\pi$
$570$	−1.06665e6	−0.137510
$571$	2.50510e6	0.321540	0.160770	−	0.986992i	$-0.448602\pi$
$571$	2.50510e6	0.321540	0.160770	+	0.986992i	$0.448602\pi$
$572$	−1.56918e6	−0.200531
$573$	4.41798e6	0.562131
$574$	1.02259e6	0.129546
$575$	−9.37472e6	−1.18247
$576$	2.91471e6	0.366049
$577$	−5.55253e6	−0.694307	−0.347153	−	0.937808i	$-0.612852\pi$
$577$	−5.55253e6	−0.694307	−0.347153	+	0.937808i	$0.612852\pi$
$578$	−1.07948e7	−1.34398
$579$	1.63129e6	0.202225
$580$	−351443.	−0.0433795
$581$	632319.	0.0777135
$582$	−7.64200e6	−0.935189
$583$	4.43922e6	0.540923
$584$	8.19761e6	0.994615
$585$	−1.24950e6	−0.150955
$586$	−9.99319e6	−1.20215
$587$	−7.07102e6	−0.847007	−0.423504	−	0.905894i	$-0.639200\pi$
$587$	−7.07102e6	−0.847007	−0.423504	+	0.905894i	$0.639200\pi$
$588$	648532.	0.0773549
$589$	5.48581e6	0.651557
$590$	252552.	0.0298690
$591$	−3.25764e6	−0.383649
$592$	−1.39653e7	−1.63775
$593$	1.66775e7	1.94757	0.973787	−	0.227461i	$-0.0730424\pi$
$593$	1.66775e7	1.94757	0.973787	+	0.227461i	$0.0730424\pi$
$594$	−1.83771e6	−0.213704
$595$	−1.08249e6	−0.125352
$596$	−485589.	−0.0559955
$597$	−4.82638e6	−0.554224
$598$	−1.33720e7	−1.52913
$599$	6.41430e6	0.730436	0.365218	−	0.930922i	$-0.380994\pi$
$599$	6.41430e6	0.730436	0.365218	+	0.930922i	$0.380994\pi$
$600$	−4.60843e6	−0.522606
$601$	1.42910e7	1.61390	0.806951	−	0.590619i	$-0.201116\pi$
$601$	1.42910e7	1.61390	0.806951	+	0.590619i	$0.201116\pi$
$602$	770738.	0.0866793
$603$	810799.	0.0908071
$604$	456601.	0.0509266
$605$	−1.48261e6	−0.164679
$606$	3.33488e6	0.368892
$607$	−9.09785e6	−1.00223	−0.501114	−	0.865381i	$-0.667076\pi$
$607$	−9.09785e6	−1.00223	−0.501114	+	0.865381i	$0.667076\pi$
$608$	1.71801e6	0.188481
$609$	910120.	0.0994387
$610$	584668.	0.0636187
$611$	−1.15474e6	−0.125135
$612$	677880.	0.0731601
$613$	−4.39452e6	−0.472346	−0.236173	−	0.971711i	$-0.575893\pi$
$613$	−4.39452e6	−0.472346	−0.236173	+	0.971711i	$0.575893\pi$
$614$	9.85185e6	1.05462
$615$	−1.35884e6	−0.144871
$616$	−2.51817e6	−0.267383
$617$	1.08259e7	1.14486	0.572431	−	0.819953i	$-0.306001\pi$
$617$	1.08259e7	1.14486	0.572431	+	0.819953i	$0.306001\pi$
$618$	500820.	0.0527485
$619$	275094.	0.0288572	0.0144286	−	0.999896i	$-0.495407\pi$
$619$	275094.	0.0288572	0.0144286	+	0.999896i	$0.495407\pi$
$620$	−489768.	−0.0511696
$621$	2.55438e6	0.265801
$622$	1.02030e7	1.05744
$623$	−1.15462e6	−0.119184
$624$	−5.63310e6	−0.579143
$625$	5.75340e6	0.589148
$626$	−7.26871e6	−0.741347
$627$	−4.60964e6	−0.468272
$628$	−2.10855e6	−0.213346
$629$	−3.02746e7	−3.05107
$630$	−246613.	−0.0247551
$631$	−4.57308e6	−0.457231	−0.228615	−	0.973517i	$-0.573420\pi$
$631$	−4.57308e6	−0.457231	−0.228615	+	0.973517i	$0.573420\pi$
$632$	1.54605e7	1.53968
$633$	−6.13597e6	−0.608658
$634$	−4.75293e6	−0.469611
$635$	−3.42681e6	−0.337252
$636$	−373057.	−0.0365706
$637$	−1.16830e7	−1.14079
$638$	9.31143e6	0.905659
$639$	−2.17258e6	−0.210486
$640$	2.90802e6	0.280639
$641$	2.06375e6	0.198386	0.0991930	−	0.995068i	$-0.468374\pi$
$641$	2.06375e6	0.198386	0.0991930	+	0.995068i	$0.468374\pi$
$642$	−714929.	−0.0684581
$643$	3.24502e6	0.309521	0.154761	−	0.987952i	$-0.450539\pi$
$643$	3.24502e6	0.309521	0.154761	+	0.987952i	$0.450539\pi$
$644$	430486.	0.0409020
$645$	−1.02417e6	−0.0969332
$646$	−1.04246e7	−0.982830
$647$	9.21175e6	0.865130	0.432565	−	0.901603i	$-0.357609\pi$
$647$	9.21175e6	0.865130	0.432565	+	0.901603i	$0.357609\pi$
$648$	1.25568e6	0.117474
$649$	1.09143e6	0.101715
$650$	1.02103e7	0.947888
$651$	1.26834e6	0.117296
$652$	−384442.	−0.0354170
$653$	−1.20635e7	−1.10711	−0.553557	−	0.832811i	$-0.686730\pi$
$653$	−1.20635e7	−1.10711	−0.553557	+	0.832811i	$0.686730\pi$
$654$	−1.02936e7	−0.941075
$655$	−1.19805e6	−0.109111
$656$	−6.12602e6	−0.555800
$657$	3.46947e6	0.313581
$658$	−227909.	−0.0205210
$659$	4.74208e6	0.425358	0.212679	−	0.977122i	$-0.431781\pi$
$659$	4.74208e6	0.425358	0.212679	+	0.977122i	$0.431781\pi$
$660$	411545.	0.0367754
$661$	1.95380e7	1.73931	0.869656	−	0.493658i	$-0.164341\pi$
$661$	1.95380e7	1.73931	0.869656	+	0.493658i	$0.164341\pi$
$662$	25443.5	0.00225648
$663$	−1.22117e7	−1.07892
$664$	−4.42034e6	−0.389077
$665$	−618594.	−0.0542440
$666$	−6.89718e6	−0.602540
$667$	−1.29427e7	−1.12644
$668$	−2.21003e6	−0.191627
$669$	4.64933e6	0.401629
$670$	1.11319e6	0.0958038
$671$	2.52670e6	0.216644
$672$	397210.	0.0339310
$673$	−1.36469e7	−1.16144	−0.580721	−	0.814103i	$-0.697229\pi$
$673$	−1.36469e7	−1.16144	−0.580721	+	0.814103i	$0.697229\pi$
$674$	1.03321e7	0.876067
$675$	−1.95042e6	−0.164766
$676$	−709333.	−0.0597012
$677$	−1.35851e7	−1.13917	−0.569586	−	0.821931i	$-0.692897\pi$
$677$	−1.35851e7	−1.13917	−0.569586	+	0.821931i	$0.692897\pi$
$678$	−315563.	−0.0263640
$679$	−4.43190e6	−0.368906
$680$	7.56734e6	0.627583
$681$	2.51668e6	0.207951
$682$	1.29764e7	1.06830
$683$	2.13384e7	1.75029	0.875147	−	0.483857i	$-0.160765\pi$
$683$	2.13384e7	1.75029	0.875147	+	0.483857i	$0.160765\pi$
$684$	387378.	0.0316588
$685$	1.12096e6	0.0912771
$686$	−4.71934e6	−0.382887
$687$	1.25444e7	1.01405
$688$	−4.61723e6	−0.371887
$689$	6.72042e6	0.539322
$690$	3.50705e6	0.280426
$691$	2.10458e7	1.67676	0.838380	−	0.545086i	$-0.183503\pi$
$691$	2.10458e7	1.67676	0.838380	+	0.545086i	$0.183503\pi$
$692$	2.53833e6	0.201503
$693$	−1.06576e6	−0.0843001
$694$	2.34297e7	1.84658
$695$	−7.00202e6	−0.549871
$696$	−6.36236e6	−0.497846
$697$	−1.32802e7	−1.03544
$698$	−1.57003e7	−1.21975
$699$	2.40120e6	0.185881
$700$	−328702.	−0.0253546
$701$	−2.51195e7	−1.93070	−0.965351	−	0.260954i	$-0.915963\pi$
$701$	−2.51195e7	−1.93070	−0.965351	+	0.260954i	$0.915963\pi$
$702$	−2.78206e6	−0.213071
$703$	−1.73006e7	−1.32030
$704$	1.72940e7	1.31512
$705$	302850.	0.0229485
$706$	−1.11158e7	−0.839322
$707$	1.93403e6	0.145518
$708$	−91719.9	−0.00687670
$709$	−8.84274e6	−0.660649	−0.330325	−	0.943867i	$-0.607158\pi$
$709$	−8.84274e6	−0.660649	−0.330325	+	0.943867i	$0.607158\pi$
$710$	−2.98286e6	−0.222068
$711$	6.54332e6	0.485427
$712$	8.07158e6	0.596703
$713$	−1.80368e7	−1.32873
$714$	−2.41020e6	−0.176933
$715$	−7.41376e6	−0.542342
$716$	897771.	0.0654460
$717$	−1.14736e7	−0.833494
$718$	−1.00886e7	−0.730333
$719$	−1.70074e7	−1.22692	−0.613460	−	0.789725i	$-0.710223\pi$
$719$	−1.70074e7	−1.22692	−0.613460	+	0.789725i	$0.710223\pi$
$720$	1.47738e6	0.106209
$721$	290445.	0.0208078
$722$	7.03052e6	0.501931
$723$	5.93313e6	0.422122
$724$	1.50089e6	0.106415
$725$	9.88250e6	0.698268
$726$	−3.30108e6	−0.232442
$727$	6.73324e6	0.472485	0.236242	−	0.971694i	$-0.424084\pi$
$727$	6.73324e6	0.472485	0.236242	+	0.971694i	$0.424084\pi$
$728$	−3.81219e6	−0.266591
$729$	531441.	0.0370370
$730$	4.76343e6	0.330836
$731$	−1.00094e7	−0.692812
$732$	−212335.	−0.0146468
$733$	1.76907e7	1.21615	0.608073	−	0.793881i	$-0.291943\pi$
$733$	1.76907e7	1.21615	0.608073	+	0.793881i	$0.291943\pi$
$734$	−2.13183e7	−1.46054
$735$	3.06406e6	0.209208
$736$	−5.64866e6	−0.384371
$737$	4.81077e6	0.326246
$738$	−3.02551e6	−0.204483
$739$	1.96265e7	1.32200	0.660999	−	0.750386i	$-0.270133\pi$
$739$	1.96265e7	1.32200	0.660999	+	0.750386i	$0.270133\pi$
$740$	1.54458e6	0.103689
$741$	−6.97840e6	−0.466886
$742$	1.32640e6	0.0884434
$743$	−1.21308e7	−0.806154	−0.403077	−	0.915166i	$-0.632059\pi$
$743$	−1.21308e7	−0.806154	−0.403077	+	0.915166i	$0.632059\pi$
$744$	−8.86654e6	−0.587249
$745$	−2.29422e6	−0.151441
$746$	−2.69180e6	−0.177091
$747$	−1.87082e6	−0.122668
$748$	4.02211e6	0.262845
$749$	−414616.	−0.0270048
$750$	−5.80561e6	−0.376873
$751$	2.32111e6	0.150175	0.0750873	−	0.997177i	$-0.476076\pi$
$751$	2.32111e6	0.150175	0.0750873	+	0.997177i	$0.476076\pi$
$752$	1.36533e6	0.0880426
$753$	−6.43679e6	−0.413696
$754$	1.40963e7	0.902978
$755$	2.15726e6	0.137732
$756$	89563.1	0.00569934
$757$	−2.67796e7	−1.69850	−0.849248	−	0.527994i	$-0.822944\pi$
$757$	−2.67796e7	−1.69850	−0.849248	+	0.527994i	$0.822944\pi$
$758$	1.64270e7	1.03845
$759$	1.51561e7	0.954952
$760$	4.32439e6	0.271576
$761$	2.78262e7	1.74178	0.870889	−	0.491480i	$-0.163544\pi$
$761$	2.78262e7	1.74178	0.870889	+	0.491480i	$0.163544\pi$
$762$	−7.62991e6	−0.476027
$763$	−5.96969e6	−0.371228
$764$	−2.20289e6	−0.136540
$765$	3.20272e6	0.197863
$766$	−2.77757e7	−1.71038
$767$	1.65228e6	0.101414
$768$	−3.88858e6	−0.237897
$769$	3.53967e6	0.215847	0.107924	−	0.994159i	$-0.465580\pi$
$769$	3.53967e6	0.215847	0.107924	+	0.994159i	$0.465580\pi$
$770$	−1.46325e6	−0.0889387
$771$	−4.54856e6	−0.275574
$772$	−813391.	−0.0491197
$773$	3.14412e7	1.89256	0.946281	−	0.323347i	$-0.104808\pi$
$773$	3.14412e7	1.89256	0.946281	+	0.323347i	$0.104808\pi$
$774$	−2.28035e6	−0.136820
$775$	1.37722e7	0.823662
$776$	3.09820e7	1.84695
$777$	−3.99995e6	−0.237685
$778$	2.85649e7	1.69194
$779$	−7.58904e6	−0.448068
$780$	623026.	0.0366665
$781$	−1.28907e7	−0.756222
$782$	3.42751e7	2.00430
$783$	−2.69273e6	−0.156960
$784$	1.38136e7	0.802633
$785$	−9.96206e6	−0.576999
$786$	−2.66749e6	−0.154009
$787$	2.73524e7	1.57419	0.787096	−	0.616830i	$-0.211583\pi$
$787$	2.73524e7	1.57419	0.787096	+	0.616830i	$0.211583\pi$
$788$	1.62432e6	0.0931873
$789$	5.94268e6	0.339852
$790$	8.98369e6	0.512138
$791$	−183008.	−0.0103999
$792$	7.45042e6	0.422054
$793$	3.82510e6	0.216003
$794$	−1.75924e7	−0.990318
$795$	−1.76255e6	−0.0989060
$796$	2.40652e6	0.134619
$797$	5.65646e6	0.315427	0.157713	−	0.987485i	$-0.449588\pi$
$797$	5.65646e6	0.315427	0.157713	+	0.987485i	$0.449588\pi$
$798$	−1.37732e6	−0.0765646
$799$	2.95981e6	0.164020
$800$	4.31309e6	0.238267
$801$	3.41613e6	0.188128
$802$	−9.66450e6	−0.530571
$803$	2.05856e7	1.12661
$804$	−404280.	−0.0220568
$805$	2.03388e6	0.110620
$806$	1.96445e7	1.06513
$807$	−5.09198e6	−0.275234
$808$	−1.35202e7	−0.728542
$809$	−1.07405e7	−0.576970	−0.288485	−	0.957484i	$-0.593151\pi$
$809$	−1.07405e7	−0.576970	−0.288485	+	0.957484i	$0.593151\pi$
$810$	729645.	0.0390750
$811$	−3.57666e7	−1.90952	−0.954762	−	0.297370i	$-0.903891\pi$
$811$	−3.57666e7	−1.90952	−0.954762	+	0.297370i	$0.903891\pi$
$812$	−453803.	−0.0241533
$813$	1.00295e7	0.532174
$814$	−4.09235e7	−2.16477
$815$	−1.81634e6	−0.0957862
$816$	1.44387e7	0.759108
$817$	−5.71993e6	−0.299803
$818$	−343732.	−0.0179612
$819$	−1.61343e6	−0.0840505
$820$	677543.	0.0351886
$821$	−2.96133e7	−1.53331	−0.766654	−	0.642061i	$-0.778080\pi$
$821$	−2.96133e7	−1.53331	−0.766654	+	0.642061i	$0.778080\pi$
$822$	2.49585e6	0.128836
$823$	−2.56517e7	−1.32013	−0.660065	−	0.751208i	$-0.729471\pi$
$823$	−2.56517e7	−1.32013	−0.660065	+	0.751208i	$0.729471\pi$
$824$	−2.03041e6	−0.104176
$825$	−1.15726e7	−0.591963
$826$	326110.	0.0166308
$827$	−3.34961e7	−1.70306	−0.851530	−	0.524305i	$-0.824325\pi$
$827$	−3.34961e7	−1.70306	−0.851530	+	0.524305i	$0.824325\pi$
$828$	−1.27366e6	−0.0645622
$829$	1.00404e7	0.507415	0.253707	−	0.967281i	$-0.418350\pi$
$829$	1.00404e7	0.507415	0.253707	+	0.967281i	$0.418350\pi$
$830$	−2.56855e6	−0.129417
$831$	1.41898e7	0.712812
$832$	2.61809e7	1.31122
$833$	2.99457e7	1.49528
$834$	−1.55902e7	−0.776136
$835$	−1.04415e7	−0.518260
$836$	2.29845e6	0.113742
$837$	−3.75258e6	−0.185147
$838$	−7.68432e6	−0.378003
$839$	−8.14254e6	−0.399351	−0.199676	−	0.979862i	$-0.563989\pi$
$839$	−8.14254e6	−0.399351	−0.199676	+	0.979862i	$0.563989\pi$
$840$	999814.	0.0488901
$841$	−6.86745e6	−0.334815
$842$	3.00488e7	1.46065
$843$	9.48595e6	0.459740
$844$	3.05951e6	0.147841
$845$	−3.35132e6	−0.161463
$846$	674306.	0.0323915
$847$	−1.91443e6	−0.0916919
$848$	−7.94603e6	−0.379455
$849$	4.33717e6	0.206508
$850$	−2.61711e7	−1.24244
$851$	5.68827e7	2.69250
$852$	1.08329e6	0.0511265
$853$	−3.37756e7	−1.58939	−0.794696	−	0.607008i	$-0.792370\pi$
$853$	−3.37756e7	−1.58939	−0.794696	+	0.607008i	$0.792370\pi$
$854$	754957.	0.0354224
$855$	1.83021e6	0.0856220
$856$	2.89845e6	0.135201
$857$	2.75847e7	1.28297	0.641485	−	0.767136i	$-0.278319\pi$
$857$	2.75847e7	1.28297	0.641485	+	0.767136i	$0.278319\pi$
$858$	−1.65070e7	−0.765508
$859$	2.55757e7	1.18262	0.591310	−	0.806444i	$-0.298611\pi$
$859$	2.55757e7	1.18262	0.591310	+	0.806444i	$0.298611\pi$
$860$	510670.	0.0235448
$861$	−1.75461e6	−0.0806628
$862$	7.19678e6	0.329891
$863$	−3.13939e7	−1.43489	−0.717445	−	0.696615i	$-0.754689\pi$
$863$	−3.13939e7	−1.43489	−0.717445	+	0.696615i	$0.754689\pi$
$864$	−1.17521e6	−0.0535588
$865$	1.19926e7	0.544971
$866$	2.02892e7	0.919326
$867$	1.85221e7	0.836841
$868$	−632417.	−0.0284908
$869$	3.88239e7	1.74401
$870$	−3.69701e6	−0.165597
$871$	7.28288e6	0.325281
$872$	4.17322e7	1.85857
$873$	1.31125e7	0.582303
$874$	1.95867e7	0.867325
$875$	−3.36690e6	−0.148666
$876$	−1.72994e6	−0.0761678
$877$	−3.10351e7	−1.36256	−0.681278	−	0.732025i	$-0.738576\pi$
$877$	−3.10351e7	−1.36256	−0.681278	+	0.732025i	$0.738576\pi$
$878$	−2.38279e7	−1.04316
$879$	1.71468e7	0.748531
$880$	8.76582e6	0.381580
$881$	9.66970e6	0.419733	0.209867	−	0.977730i	$-0.432697\pi$
$881$	9.66970e6	0.419733	0.209867	+	0.977730i	$0.432697\pi$
$882$	6.82224e6	0.295295
$883$	−1.69845e7	−0.733078	−0.366539	−	0.930403i	$-0.619457\pi$
$883$	−1.69845e7	−0.733078	−0.366539	+	0.930403i	$0.619457\pi$
$884$	6.08896e6	0.262067
$885$	−433341.	−0.0185982
$886$	4.50433e6	0.192773
$887$	−1.92538e7	−0.821689	−0.410844	−	0.911706i	$-0.634766\pi$
$887$	−1.92538e7	−0.821689	−0.410844	+	0.911706i	$0.634766\pi$
$888$	2.79624e7	1.18999
$889$	−4.42489e6	−0.187779
$890$	4.69019e6	0.198480
$891$	3.15323e6	0.133064
$892$	−2.31824e6	−0.0975543
$893$	1.69140e6	0.0709770
$894$	−5.10816e6	−0.213757
$895$	4.24162e6	0.177000
$896$	3.75501e6	0.156258
$897$	2.29443e7	0.952125
$898$	−5.02391e6	−0.207898
$899$	1.90138e7	0.784638
$900$	972517.	0.0400213
$901$	−1.72257e7	−0.706913
$902$	−1.79514e7	−0.734654
$903$	−1.32247e6	−0.0539716
$904$	1.27935e6	0.0520676
$905$	7.09112e6	0.287802
$906$	4.80322e6	0.194407
$907$	3.54947e7	1.43267	0.716333	−	0.697758i	$-0.245819\pi$
$907$	3.54947e7	1.43267	0.716333	+	0.697758i	$0.245819\pi$
$908$	−1.25486e6	−0.0505106
$909$	−5.72215e6	−0.229694
$910$	−2.21517e6	−0.0886755
$911$	7.06074e6	0.281874	0.140937	−	0.990019i	$-0.454989\pi$
$911$	7.06074e6	0.281874	0.140937	+	0.990019i	$0.454989\pi$
$912$	8.25107e6	0.328491
$913$	−1.11002e7	−0.440713
$914$	4.26338e7	1.68806
$915$	−1.00320e6	−0.0396127
$916$	−6.25488e6	−0.246309
$917$	−1.54699e6	−0.0607523
$918$	7.13097e6	0.279281
$919$	−1.16926e7	−0.456692	−0.228346	−	0.973580i	$-0.573332\pi$
$919$	−1.16926e7	−0.456692	−0.228346	+	0.973580i	$0.573332\pi$
$920$	−1.42182e7	−0.553828
$921$	−1.69043e7	−0.656670
$922$	1.72407e7	0.667924
$923$	−1.95149e7	−0.753983
$924$	531410.	0.0204762
$925$	−4.34333e7	−1.66905
$926$	1.86320e7	0.714057
$927$	−859329.	−0.0328443
$928$	5.95461e6	0.226978
$929$	541270.	0.0205766	0.0102883	−	0.999947i	$-0.496725\pi$
$929$	541270.	0.0205766	0.0102883	+	0.999947i	$0.496725\pi$
$930$	−5.15213e6	−0.195335
$931$	1.71126e7	0.647056
$932$	−1.19729e6	−0.0451500
$933$	−1.75068e7	−0.658421
$934$	2.95873e7	1.10978
$935$	1.90029e7	0.710871
$936$	1.12790e7	0.420804
$937$	2.14397e7	0.797754	0.398877	−	0.917004i	$-0.369400\pi$
$937$	2.14397e7	0.797754	0.398877	+	0.917004i	$0.369400\pi$
$938$	1.43742e6	0.0533428
$939$	1.24720e7	0.461606
$940$	−151007.	−0.00557412
$941$	−2.10257e7	−0.774065	−0.387032	−	0.922066i	$-0.626500\pi$
$941$	−2.10257e7	−0.774065	−0.387032	+	0.922066i	$0.626500\pi$
$942$	−2.21809e7	−0.814426
$943$	2.49520e7	0.913749
$944$	−1.95362e6	−0.0713525
$945$	423150.	0.0154140
$946$	−1.35302e7	−0.491558
$947$	−7.36023e6	−0.266696	−0.133348	−	0.991069i	$-0.542573\pi$
$947$	−7.36023e6	−0.266696	−0.133348	+	0.991069i	$0.542573\pi$
$948$	−3.26262e6	−0.117909
$949$	3.11640e7	1.12328
$950$	−1.49556e7	−0.537644
$951$	8.15530e6	0.292407
$952$	9.77139e6	0.349433
$953$	−4.24311e7	−1.51339	−0.756697	−	0.653765i	$-0.773188\pi$
$953$	−4.24311e7	−1.51339	−0.756697	+	0.653765i	$0.773188\pi$
$954$	−3.92437e6	−0.139605
$955$	−1.04078e7	−0.369275
$956$	5.72096e6	0.202453
$957$	−1.59770e7	−0.563916
$958$	3.93047e6	0.138366
$959$	1.44744e6	0.0508223
$960$	−6.86641e6	−0.240465
$961$	−2.13166e6	−0.0744577
$962$	−6.19529e7	−2.15836
$963$	1.22671e6	0.0426260
$964$	−2.95837e6	−0.102532
$965$	−3.84295e6	−0.132846
$966$	4.52850e6	0.156139
$967$	4.08431e7	1.40460	0.702300	−	0.711881i	$-0.252157\pi$
$967$	4.08431e7	1.40460	0.702300	+	0.711881i	$0.252157\pi$
$968$	1.33832e7	0.459061
$969$	1.78870e7	0.611967
$970$	1.80029e7	0.614345
$971$	3.92116e7	1.33465	0.667324	−	0.744767i	$-0.267439\pi$
$971$	3.92116e7	1.33465	0.667324	+	0.744767i	$0.267439\pi$
$972$	−264987.	−0.00899618
$973$	−9.04141e6	−0.306164
$974$	1.58447e7	0.535162
$975$	−1.75194e7	−0.590211
$976$	−4.52269e6	−0.151975
$977$	−4.62673e7	−1.55073	−0.775367	−	0.631511i	$-0.782435\pi$
$977$	−4.62673e7	−1.55073	−0.775367	+	0.631511i	$0.782435\pi$
$978$	−4.04415e6	−0.135201
$979$	2.02691e7	0.675894
$980$	−1.52780e6	−0.0508160
$981$	1.76623e7	0.585968
$982$	−855414.	−0.0283073
$983$	−4.25853e7	−1.40564	−0.702822	−	0.711365i	$-0.748077\pi$
$983$	−4.25853e7	−1.40564	−0.702822	+	0.711365i	$0.748077\pi$
$984$	1.22659e7	0.403843
$985$	7.67429e6	0.252027
$986$	−3.61316e7	−1.18357
$987$	391057.	0.0127775
$988$	3.47956e6	0.113405
$989$	1.88066e7	0.611391
$990$	4.32925e6	0.140386
$991$	−9.21624e6	−0.298105	−0.149053	−	0.988829i	$-0.547622\pi$
$991$	−9.21624e6	−0.298105	−0.149053	+	0.988829i	$0.547622\pi$
$992$	8.29831e6	0.267738
$993$	−43657.1	−0.00140502
$994$	−3.85164e6	−0.123646
$995$	1.13699e7	0.364081
$996$	932825.	0.0297956
$997$	2.37289e7	0.756030	0.378015	−	0.925799i	$-0.376607\pi$
$997$	2.37289e7	0.756030	0.378015	+	0.925799i	$0.376607\pi$
$998$	7.13537e6	0.226772
$999$	1.18345e7	0.375177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.8	✓	25
3.2	odd	2		927.6.a.f.1.18		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.8	✓	25	1.1	even	1	trivial
927.6.a.f.1.18		25	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	309.a (trivial)

\(f(q)\)	\(=\)	\(q-5.24523 q^{2} +9.00000 q^{3} -4.48757 q^{4} -21.2020 q^{5} -47.2071 q^{6} -27.3773 q^{7} +191.386 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-5.24523 q^{2} +9.00000 q^{3} -4.48757 q^{4} -21.2020 q^{5} -47.2071 q^{6} -27.3773 q^{7} +191.386 q^{8} +81.0000 q^{9} +111.209 q^{10} +480.603 q^{11} -40.3881 q^{12} +727.571 q^{13} +143.600 q^{14} -190.818 q^{15} -860.259 q^{16} -1864.91 q^{17} -424.864 q^{18} -1065.71 q^{19} +95.1455 q^{20} -246.395 q^{21} -2520.87 q^{22} +3503.95 q^{23} +1722.47 q^{24} -2675.47 q^{25} -3816.28 q^{26} +729.000 q^{27} +122.857 q^{28} -3693.74 q^{29} +1000.88 q^{30} -5147.57 q^{31} -1612.08 q^{32} +4325.42 q^{33} +9781.86 q^{34} +580.453 q^{35} -363.493 q^{36} +16233.9 q^{37} +5589.89 q^{38} +6548.14 q^{39} -4057.76 q^{40} +7121.13 q^{41} +1292.40 q^{42} +5367.26 q^{43} -2156.74 q^{44} -1717.36 q^{45} -18379.0 q^{46} -1587.11 q^{47} -7742.34 q^{48} -16057.5 q^{49} +14033.5 q^{50} -16784.1 q^{51} -3265.02 q^{52} +9236.79 q^{53} -3823.77 q^{54} -10189.7 q^{55} -5239.62 q^{56} -9591.38 q^{57} +19374.5 q^{58} +2270.96 q^{59} +856.310 q^{60} +5257.36 q^{61} +27000.2 q^{62} -2217.56 q^{63} +35984.0 q^{64} -15426.0 q^{65} -22687.8 q^{66} +10009.9 q^{67} +8368.89 q^{68} +31535.5 q^{69} -3044.61 q^{70} -26822.0 q^{71} +15502.2 q^{72} +42832.9 q^{73} -85150.4 q^{74} -24079.3 q^{75} +4782.44 q^{76} -13157.6 q^{77} -34346.5 q^{78} +80781.8 q^{79} +18239.2 q^{80} +6561.00 q^{81} -37351.9 q^{82} -23096.5 q^{83} +1105.72 q^{84} +39539.8 q^{85} -28152.5 q^{86} -33243.6 q^{87} +91980.4 q^{88} +42174.4 q^{89} +9007.96 q^{90} -19918.9 q^{91} -15724.2 q^{92} -46328.1 q^{93} +8324.77 q^{94} +22595.2 q^{95} -14508.8 q^{96} +161882. q^{97} +84225.2 q^{98} +38928.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9} + 693 q^{10} + 1470 q^{11} + 4374 q^{12} + 2515 q^{13} + 254 q^{14} + 423 q^{15} + 11542 q^{16} + 880 q^{17} + 1134 q^{18} + 7412 q^{19} + 1927 q^{20} + 3618 q^{21} + 5461 q^{22} + 5567 q^{23} + 3078 q^{24} + 31584 q^{25} + 18502 q^{26} + 18225 q^{27} + 25011 q^{28} + 17230 q^{29} + 6237 q^{30} + 22821 q^{31} + 50233 q^{32} + 13230 q^{33} + 38342 q^{34} + 30664 q^{35} + 39366 q^{36} + 13342 q^{37} + 25860 q^{38} + 22635 q^{39} + 40701 q^{40} + 36374 q^{41} + 2286 q^{42} + 48371 q^{43} - 4133 q^{44} + 3807 q^{45} + 30489 q^{46} + 17740 q^{47} + 103878 q^{48} + 119201 q^{49} - 9505 q^{50} + 7920 q^{51} + 50699 q^{52} - 52204 q^{53} + 10206 q^{54} + 90638 q^{55} - 80285 q^{56} + 66708 q^{57} + 15313 q^{58} + 34099 q^{59} + 17343 q^{60} + 71175 q^{61} - 92130 q^{62} + 32562 q^{63} + 289374 q^{64} - 32899 q^{65} + 49149 q^{66} + 85201 q^{67} - 41169 q^{68} + 50103 q^{69} - 92312 q^{70} + 102652 q^{71} + 27702 q^{72} + 186396 q^{73} - 258113 q^{74} + 284256 q^{75} + 148369 q^{76} - 109016 q^{77} + 166518 q^{78} + 210994 q^{79} + 17955 q^{80} + 164025 q^{81} + 635103 q^{82} + 68429 q^{83} + 225099 q^{84} + 375692 q^{85} + 360833 q^{86} + 155070 q^{87} + 556985 q^{88} + 163508 q^{89} + 56133 q^{90} + 591882 q^{91} + 388500 q^{92} + 205389 q^{93} + 205288 q^{94} + 87988 q^{95} + 452097 q^{96} + 385683 q^{97} - 61147 q^{98} + 119070 q^{99}+O(q^{100}) \) 25 * q + 14 * q^2 + 225 * q^3 + 486 * q^4 + 47 * q^5 + 126 * q^6 + 402 * q^7 + 342 * q^8 + 2025 * q^9 + 693 * q^10 + 1470 * q^11 + 4374 * q^12 + 2515 * q^13 + 254 * q^14 + 423 * q^15 + 11542 * q^16 + 880 * q^17 + 1134 * q^18 + 7412 * q^19 + 1927 * q^20 + 3618 * q^21 + 5461 * q^22 + 5567 * q^23 + 3078 * q^24 + 31584 * q^25 + 18502 * q^26 + 18225 * q^27 + 25011 * q^28 + 17230 * q^29 + 6237 * q^30 + 22821 * q^31 + 50233 * q^32 + 13230 * q^33 + 38342 * q^34 + 30664 * q^35 + 39366 * q^36 + 13342 * q^37 + 25860 * q^38 + 22635 * q^39 + 40701 * q^40 + 36374 * q^41 + 2286 * q^42 + 48371 * q^43 - 4133 * q^44 + 3807 * q^45 + 30489 * q^46 + 17740 * q^47 + 103878 * q^48 + 119201 * q^49 - 9505 * q^50 + 7920 * q^51 + 50699 * q^52 - 52204 * q^53 + 10206 * q^54 + 90638 * q^55 - 80285 * q^56 + 66708 * q^57 + 15313 * q^58 + 34099 * q^59 + 17343 * q^60 + 71175 * q^61 - 92130 * q^62 + 32562 * q^63 + 289374 * q^64 - 32899 * q^65 + 49149 * q^66 + 85201 * q^67 - 41169 * q^68 + 50103 * q^69 - 92312 * q^70 + 102652 * q^71 + 27702 * q^72 + 186396 * q^73 - 258113 * q^74 + 284256 * q^75 + 148369 * q^76 - 109016 * q^77 + 166518 * q^78 + 210994 * q^79 + 17955 * q^80 + 164025 * q^81 + 635103 * q^82 + 68429 * q^83 + 225099 * q^84 + 375692 * q^85 + 360833 * q^86 + 155070 * q^87 + 556985 * q^88 + 163508 * q^89 + 56133 * q^90 + 591882 * q^91 + 388500 * q^92 + 205389 * q^93 + 205288 * q^94 + 87988 * q^95 + 452097 * q^96 + 385683 * q^97 - 61147 * q^98 + 119070 * q^99

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