LMFDB - Embedded newform 309.6.a.d.1.3

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			1.3
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)

$f(q)$	$=$	$q-9.32103 q^{2} +9.00000 q^{3} +54.8817 q^{4} -99.7771 q^{5} -83.8893 q^{6} -63.0953 q^{7} -213.281 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.32103 q^{2} +9.00000 q^{3} +54.8817 q^{4} -99.7771 q^{5} -83.8893 q^{6} -63.0953 q^{7} -213.281 q^{8} +81.0000 q^{9} +930.026 q^{10} -579.785 q^{11} +493.935 q^{12} +47.4327 q^{13} +588.114 q^{14} -897.994 q^{15} +231.785 q^{16} -1039.45 q^{17} -755.004 q^{18} -2271.45 q^{19} -5475.94 q^{20} -567.858 q^{21} +5404.20 q^{22} -1823.24 q^{23} -1919.53 q^{24} +6830.47 q^{25} -442.121 q^{26} +729.000 q^{27} -3462.78 q^{28} -5486.01 q^{29} +8370.23 q^{30} -2786.83 q^{31} +4664.51 q^{32} -5218.07 q^{33} +9688.72 q^{34} +6295.47 q^{35} +4445.42 q^{36} +3873.55 q^{37} +21172.3 q^{38} +426.894 q^{39} +21280.6 q^{40} -7358.70 q^{41} +5293.02 q^{42} -11655.5 q^{43} -31819.6 q^{44} -8081.95 q^{45} +16994.5 q^{46} -16075.5 q^{47} +2086.06 q^{48} -12826.0 q^{49} -63667.1 q^{50} -9355.02 q^{51} +2603.18 q^{52} -10787.3 q^{53} -6795.03 q^{54} +57849.3 q^{55} +13457.0 q^{56} -20443.1 q^{57} +51135.3 q^{58} -19801.7 q^{59} -49283.4 q^{60} -23723.1 q^{61} +25976.2 q^{62} -5110.72 q^{63} -50895.2 q^{64} -4732.69 q^{65} +48637.8 q^{66} +28434.1 q^{67} -57046.6 q^{68} -16409.2 q^{69} -58680.3 q^{70} +12148.0 q^{71} -17275.8 q^{72} -35515.4 q^{73} -36105.4 q^{74} +61474.2 q^{75} -124661. q^{76} +36581.7 q^{77} -3979.09 q^{78} +43499.1 q^{79} -23126.8 q^{80} +6561.00 q^{81} +68590.7 q^{82} +44725.5 q^{83} -31165.0 q^{84} +103713. q^{85} +108642. q^{86} -49374.1 q^{87} +123657. q^{88} -77518.2 q^{89} +75332.1 q^{90} -2992.78 q^{91} -100062. q^{92} -25081.5 q^{93} +149840. q^{94} +226639. q^{95} +41980.6 q^{96} -82213.2 q^{97} +119551. q^{98} -46962.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.32103	−1.64774	−0.823871	−	0.566778i	$-0.808190\pi$
$2$	−9.32103	−1.64774	−0.823871	+	0.566778i	$0.808190\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	54.8817	1.71505
$5$	−99.7771	−1.78487	−0.892434	−	0.451179i	$-0.851004\pi$
$5$	−99.7771	−1.78487	−0.892434	+	0.451179i	$0.851004\pi$
$6$	−83.8893	−0.951324
$7$	−63.0953	−0.486690	−0.243345	−	0.969940i	$-0.578245\pi$
$7$	−63.0953	−0.486690	−0.243345	+	0.969940i	$0.578245\pi$
$8$	−213.281	−1.17822
$9$	81.0000	0.333333
$10$	930.026	2.94100
$11$	−579.785	−1.44473	−0.722363	−	0.691514i	$-0.756944\pi$
$11$	−579.785	−1.44473	−0.722363	+	0.691514i	$0.756944\pi$
$12$	493.935	0.990186
$13$	47.4327	0.0778429	0.0389215	−	0.999242i	$-0.487608\pi$
$13$	47.4327	0.0778429	0.0389215	+	0.999242i	$0.487608\pi$
$14$	588.114	0.801939
$15$	−897.994	−1.03049
$16$	231.785	0.226353
$17$	−1039.45	−0.872329	−0.436164	−	0.899867i	$-0.643663\pi$
$17$	−1039.45	−0.872329	−0.436164	+	0.899867i	$0.643663\pi$
$18$	−755.004	−0.549247
$19$	−2271.45	−1.44351	−0.721755	−	0.692149i	$-0.756664\pi$
$19$	−2271.45	−1.44351	−0.721755	+	0.692149i	$0.756664\pi$
$20$	−5475.94	−3.06114
$21$	−567.858	−0.280990
$22$	5404.20	2.38054
$23$	−1823.24	−0.718661	−0.359330	−	0.933210i	$-0.616995\pi$
$23$	−1823.24	−0.718661	−0.359330	+	0.933210i	$0.616995\pi$
$24$	−1919.53	−0.680247
$25$	6830.47	2.18575
$26$	−442.121	−0.128265
$27$	729.000	0.192450
$28$	−3462.78	−0.834698
$29$	−5486.01	−1.21133	−0.605664	−	0.795721i	$-0.707092\pi$
$29$	−5486.01	−1.21133	−0.605664	+	0.795721i	$0.707092\pi$
$30$	8370.23	1.69799
$31$	−2786.83	−0.520843	−0.260421	−	0.965495i	$-0.583861\pi$
$31$	−2786.83	−0.520843	−0.260421	+	0.965495i	$0.583861\pi$
$32$	4664.51	0.805251
$33$	−5218.07	−0.834113
$34$	9688.72	1.43737
$35$	6295.47	0.868676
$36$	4445.42	0.571684
$37$	3873.55	0.465162	0.232581	−	0.972577i	$-0.425283\pi$
$37$	3873.55	0.465162	0.232581	+	0.972577i	$0.425283\pi$
$38$	21172.3	2.37853
$39$	426.894	0.0449426
$40$	21280.6	2.10297
$41$	−7358.70	−0.683662	−0.341831	−	0.939761i	$-0.611047\pi$
$41$	−7358.70	−0.683662	−0.341831	+	0.939761i	$0.611047\pi$
$42$	5293.02	0.463000
$43$	−11655.5	−0.961304	−0.480652	−	0.876912i	$-0.659600\pi$
$43$	−11655.5	−0.961304	−0.480652	+	0.876912i	$0.659600\pi$
$44$	−31819.6	−2.47778
$45$	−8081.95	−0.594956
$46$	16994.5	1.18417
$47$	−16075.5	−1.06150	−0.530749	−	0.847529i	$-0.678089\pi$
$47$	−16075.5	−1.06150	−0.530749	+	0.847529i	$0.678089\pi$
$48$	2086.06	0.130685
$49$	−12826.0	−0.763133
$50$	−63667.1	−3.60155
$51$	−9355.02	−0.503639
$52$	2603.18	0.133505
$53$	−10787.3	−0.527503	−0.263751	−	0.964591i	$-0.584960\pi$
$53$	−10787.3	−0.527503	−0.263751	+	0.964591i	$0.584960\pi$
$54$	−6795.03	−0.317108
$55$	57849.3	2.57864
$56$	13457.0	0.573428
$57$	−20443.1	−0.833411
$58$	51135.3	1.99595
$59$	−19801.7	−0.740580	−0.370290	−	0.928916i	$-0.620742\pi$
$59$	−19801.7	−0.740580	−0.370290	+	0.928916i	$0.620742\pi$
$60$	−49283.4	−1.76735
$61$	−23723.1	−0.816295	−0.408148	−	0.912916i	$-0.633825\pi$
$61$	−23723.1	−0.816295	−0.408148	+	0.912916i	$0.633825\pi$
$62$	25976.2	0.858214
$63$	−5110.72	−0.162230
$64$	−50895.2	−1.55320
$65$	−4732.69	−0.138939
$66$	48637.8	1.37440
$67$	28434.1	0.773842	0.386921	−	0.922113i	$-0.373539\pi$
$67$	28434.1	0.773842	0.386921	+	0.922113i	$0.373539\pi$
$68$	−57046.6	−1.49609
$69$	−16409.2	−0.414919
$70$	−58680.3	−1.43135
$71$	12148.0	0.285995	0.142998	−	0.989723i	$-0.454326\pi$
$71$	12148.0	0.285995	0.142998	+	0.989723i	$0.454326\pi$
$72$	−17275.8	−0.392741
$73$	−35515.4	−0.780027	−0.390013	−	0.920809i	$-0.627530\pi$
$73$	−35515.4	−0.780027	−0.390013	+	0.920809i	$0.627530\pi$
$74$	−36105.4	−0.766467
$75$	61474.2	1.26194
$76$	−124661.	−2.47569
$77$	36581.7	0.703133
$78$	−3979.09	−0.0740538
$79$	43499.1	0.784174	0.392087	−	0.919928i	$-0.371753\pi$
$79$	43499.1	0.784174	0.392087	+	0.919928i	$0.371753\pi$
$80$	−23126.8	−0.404009
$81$	6561.00	0.111111
$82$	68590.7	1.12650
$83$	44725.5	0.712623	0.356311	−	0.934367i	$-0.384034\pi$
$83$	44725.5	0.712623	0.356311	+	0.934367i	$0.384034\pi$
$84$	−31165.0	−0.481913
$85$	103713.	1.55699
$86$	108642.	1.58398
$87$	−49374.1	−0.699360
$88$	123657.	1.70221
$89$	−77518.2	−1.03736	−0.518679	−	0.854969i	$-0.673576\pi$
$89$	−77518.2	−1.03736	−0.518679	+	0.854969i	$0.673576\pi$
$90$	75332.1	0.980333
$91$	−2992.78	−0.0378853
$92$	−100062.	−1.23254
$93$	−25081.5	−0.300709
$94$	149840.	1.74907
$95$	226639.	2.57647
$96$	41980.6	0.464912
$97$	−82213.2	−0.887181	−0.443591	−	0.896230i	$-0.646296\pi$
$97$	−82213.2	−0.887181	−0.443591	+	0.896230i	$0.646296\pi$
$98$	119551.	1.25745
$99$	−46962.6	−0.481575
$100$	374868.	3.74868
$101$	101841.	0.993393	0.496696	−	0.867924i	$-0.334546\pi$
$101$	101841.	0.993393	0.496696	+	0.867924i	$0.334546\pi$
$102$	87198.5	0.829867
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	−10116.5	−0.0917162
$105$	56659.2	0.501530
$106$	100549.	0.869188
$107$	−121030.	−1.02196	−0.510982	−	0.859592i	$-0.670718\pi$
$107$	−121030.	−1.02196	−0.510982	+	0.859592i	$0.670718\pi$
$108$	40008.7	0.330062
$109$	122169.	0.984906	0.492453	−	0.870339i	$-0.336100\pi$
$109$	122169.	0.984906	0.492453	+	0.870339i	$0.336100\pi$
$110$	−539215.	−4.24894
$111$	34861.9	0.268561
$112$	−14624.5	−0.110163
$113$	157443.	1.15992	0.579959	−	0.814645i	$-0.303068\pi$
$113$	157443.	1.15992	0.579959	+	0.814645i	$0.303068\pi$
$114$	190551.	1.37325
$115$	181918.	1.28271
$116$	−301081.	−2.07749
$117$	3842.05	0.0259476
$118$	184572.	1.22029
$119$	65584.3	0.424553
$120$	191525.	1.21415
$121$	175100.	1.08723
$122$	221124.	1.34504
$123$	−66228.3	−0.394713
$124$	−152946.	−0.893272
$125$	−369721.	−2.11641
$126$	47637.2	0.267313
$127$	161149.	0.886578	0.443289	−	0.896379i	$-0.353812\pi$
$127$	161149.	0.886578	0.443289	+	0.896379i	$0.353812\pi$
$128$	325132.	1.75402
$129$	−104900.	−0.555009
$130$	44113.6	0.228936
$131$	384602.	1.95809	0.979047	−	0.203636i	$-0.0652758\pi$
$131$	384602.	1.95809	0.979047	+	0.203636i	$0.0652758\pi$
$132$	−286376.	−1.43055
$133$	143318.	0.702541
$134$	−265035.	−1.27509
$135$	−72737.5	−0.343498
$136$	221694.	1.02780
$137$	−138571.	−0.630768	−0.315384	−	0.948964i	$-0.602133\pi$
$137$	−138571.	−0.630768	−0.315384	+	0.948964i	$0.602133\pi$
$138$	152950.	0.683679
$139$	192458.	0.844888	0.422444	−	0.906389i	$-0.361172\pi$
$139$	192458.	0.844888	0.422444	+	0.906389i	$0.361172\pi$
$140$	345506.	1.48983
$141$	−144679.	−0.612856
$142$	−113232.	−0.471246
$143$	−27500.8	−0.112462
$144$	18774.6	0.0754508
$145$	547378.	2.16206
$146$	331040.	1.28528
$147$	−115434.	−0.440595
$148$	212587.	0.797777
$149$	−366647.	−1.35295	−0.676477	−	0.736464i	$-0.736494\pi$
$149$	−366647.	−1.35295	−0.676477	+	0.736464i	$0.736494\pi$
$150$	−573004.	−2.07936
$151$	−125209.	−0.446884	−0.223442	−	0.974717i	$-0.571729\pi$
$151$	−125209.	−0.446884	−0.223442	+	0.974717i	$0.571729\pi$
$152$	484457.	1.70077
$153$	−84195.2	−0.290776
$154$	−340980.	−1.15858
$155$	278062.	0.929635
$156$	23428.7	0.0770790
$157$	85501.9	0.276839	0.138419	−	0.990374i	$-0.455798\pi$
$157$	85501.9	0.276839	0.138419	+	0.990374i	$0.455798\pi$
$158$	−405457.	−1.29212
$159$	−97086.0	−0.304554
$160$	−465412.	−1.43727
$161$	115038.	0.349765
$162$	−61155.3	−0.183082
$163$	−670179.	−1.97570	−0.987852	−	0.155398i	$-0.950334\pi$
$163$	−670179.	−1.97570	−0.987852	+	0.155398i	$0.950334\pi$
$164$	−403858.	−1.17252
$165$	520644.	1.48878
$166$	−416888.	−1.17422
$167$	282623.	0.784180	0.392090	−	0.919927i	$-0.371752\pi$
$167$	282623.	0.784180	0.392090	+	0.919927i	$0.371752\pi$
$168$	121113.	0.331069
$169$	−369043.	−0.993940
$170$	−966713.	−2.56552
$171$	−183988.	−0.481170
$172$	−639675.	−1.64869
$173$	386846.	0.982705	0.491353	−	0.870961i	$-0.336503\pi$
$173$	386846.	0.982705	0.491353	+	0.870961i	$0.336503\pi$
$174$	460218.	1.15237
$175$	−430971.	−1.06378
$176$	−134386.	−0.327017
$177$	−178215.	−0.427574
$178$	722550.	1.70930
$179$	756424.	1.76455	0.882273	−	0.470738i	$-0.156012\pi$
$179$	756424.	1.76455	0.882273	+	0.470738i	$0.156012\pi$
$180$	−443551.	−1.02038
$181$	275939.	0.626062	0.313031	−	0.949743i	$-0.398656\pi$
$181$	275939.	0.626062	0.313031	+	0.949743i	$0.398656\pi$
$182$	27895.8	0.0624252
$183$	−213508.	−0.471288
$184$	388862.	0.846742
$185$	−386491.	−0.830253
$186$	233785.	0.495490
$187$	602656.	1.26028
$188$	−882249.	−1.82052
$189$	−45996.5	−0.0936635
$190$	−2.11251e6	−4.24536
$191$	−907738.	−1.80043	−0.900217	−	0.435442i	$-0.856592\pi$
$191$	−907738.	−1.80043	−0.900217	+	0.435442i	$0.856592\pi$
$192$	−458057.	−0.896740
$193$	624823.	1.20743	0.603717	−	0.797198i	$-0.293686\pi$
$193$	624823.	1.20743	0.603717	+	0.797198i	$0.293686\pi$
$194$	766312.	1.46185
$195$	−42594.2	−0.0802166
$196$	−703911.	−1.30881
$197$	−659175.	−1.21014	−0.605069	−	0.796173i	$-0.706855\pi$
$197$	−659175.	−1.21014	−0.605069	+	0.796173i	$0.706855\pi$
$198$	437740.	0.793512
$199$	−228121.	−0.408349	−0.204175	−	0.978934i	$-0.565451\pi$
$199$	−228121.	−0.408349	−0.204175	+	0.978934i	$0.565451\pi$
$200$	−1.45681e6	−2.57530
$201$	255907.	0.446778
$202$	−949267.	−1.63685
$203$	346142.	0.589541
$204$	−513419.	−0.863768
$205$	734230.	1.22025
$206$	98886.9	0.162357
$207$	−147682.	−0.239554
$208$	10994.2	0.0176199
$209$	1.31695e6	2.08548
$210$	−528123.	−0.826393
$211$	−465422.	−0.719682	−0.359841	−	0.933014i	$-0.617169\pi$
$211$	−465422.	−0.719682	−0.359841	+	0.933014i	$0.617169\pi$
$212$	−592027.	−0.904694
$213$	109332.	0.165120
$214$	1.12813e6	1.68393
$215$	1.16295e6	1.71580
$216$	−155482.	−0.226749
$217$	175836.	0.253489
$218$	−1.13874e6	−1.62287
$219$	−319639.	−0.450349
$220$	3.17487e6	4.42251
$221$	−49303.7	−0.0679046
$222$	−324949.	−0.442520
$223$	−257398.	−0.346611	−0.173306	−	0.984868i	$-0.555445\pi$
$223$	−257398.	−0.346611	−0.173306	+	0.984868i	$0.555445\pi$
$224$	−294309.	−0.391907
$225$	553268.	0.728584
$226$	−1.46753e6	−1.91125
$227$	862416.	1.11084	0.555421	−	0.831569i	$-0.312557\pi$
$227$	862416.	1.11084	0.555421	+	0.831569i	$0.312557\pi$
$228$	−1.12195e6	−1.42934
$229$	98191.6	0.123733	0.0618665	−	0.998084i	$-0.480295\pi$
$229$	98191.6	0.123733	0.0618665	+	0.998084i	$0.480295\pi$
$230$	−1.69566e6	−2.11358
$231$	329236.	0.405954
$232$	1.17006e6	1.42721
$233$	−107933.	−0.130246	−0.0651230	−	0.997877i	$-0.520744\pi$
$233$	−107933.	−0.130246	−0.0651230	+	0.997877i	$0.520744\pi$
$234$	−35811.8	−0.0427550
$235$	1.60396e6	1.89463
$236$	−1.08675e6	−1.27013
$237$	391492.	0.452743
$238$	−611313.	−0.699554
$239$	101713.	0.115182	0.0575909	−	0.998340i	$-0.481658\pi$
$239$	101713.	0.115182	0.0575909	+	0.998340i	$0.481658\pi$
$240$	−208142.	−0.233255
$241$	1.15338e6	1.27917	0.639585	−	0.768720i	$-0.279106\pi$
$241$	1.15338e6	1.27917	0.639585	+	0.768720i	$0.279106\pi$
$242$	−1.63211e6	−1.79148
$243$	59049.0	0.0641500
$244$	−1.30196e6	−1.39999
$245$	1.27974e6	1.36209
$246$	617317.	0.650385
$247$	−107741.	−0.112367
$248$	594378.	0.613668
$249$	402529.	0.411433
$250$	3.44618e6	3.48729
$251$	1.73177e6	1.73503	0.867515	−	0.497412i	$-0.165716\pi$
$251$	1.73177e6	1.73503	0.867515	+	0.497412i	$0.165716\pi$
$252$	−280485.	−0.278233
$253$	1.05709e6	1.03827
$254$	−1.50207e6	−1.46085
$255$	933417.	0.898929
$256$	−1.40192e6	−1.33697
$257$	−1.22906e6	−1.16075	−0.580377	−	0.814348i	$-0.697095\pi$
$257$	−1.22906e6	−1.16075	−0.580377	+	0.814348i	$0.697095\pi$
$258$	977774.	0.914511
$259$	−244403.	−0.226390
$260$	−259738.	−0.238288
$261$	−444367.	−0.403776
$262$	−3.58489e6	−3.22643
$263$	−2.11756e6	−1.88776	−0.943878	−	0.330294i	$-0.892852\pi$
$263$	−2.11756e6	−1.88776	−0.943878	+	0.330294i	$0.892852\pi$
$264$	1.11291e6	0.982770
$265$	1.07633e6	0.941522
$266$	−1.33587e6	−1.15761
$267$	−697664.	−0.598919
$268$	1.56051e6	1.32718
$269$	197002.	0.165993	0.0829967	−	0.996550i	$-0.473551\pi$
$269$	197002.	0.165993	0.0829967	+	0.996550i	$0.473551\pi$
$270$	677989.	0.565996
$271$	−2.36630e6	−1.95725	−0.978624	−	0.205655i	$-0.934067\pi$
$271$	−2.36630e6	−1.95725	−0.978624	+	0.205655i	$0.934067\pi$
$272$	−240928.	−0.197454
$273$	−26935.0	−0.0218731
$274$	1.29162e6	1.03934
$275$	−3.96021e6	−3.15781
$276$	−900562.	−0.711608
$277$	−2.00594e6	−1.57079	−0.785394	−	0.618996i	$-0.787540\pi$
$277$	−2.00594e6	−1.57079	−0.785394	+	0.618996i	$0.787540\pi$
$278$	−1.79391e6	−1.39216
$279$	−225733.	−0.173614
$280$	−1.34270e6	−1.02349
$281$	−903800.	−0.682821	−0.341410	−	0.939914i	$-0.610905\pi$
$281$	−903800.	−0.682821	−0.341410	+	0.939914i	$0.610905\pi$
$282$	1.34856e6	1.00983
$283$	501540.	0.372254	0.186127	−	0.982526i	$-0.440406\pi$
$283$	501540.	0.372254	0.186127	+	0.982526i	$0.440406\pi$
$284$	666703.	0.490497
$285$	2.03975e6	1.48753
$286$	256336.	0.185308
$287$	464300.	0.332731
$288$	377826.	0.268417
$289$	−339407.	−0.239043
$290$	−5.10213e6	−3.56251
$291$	−739919.	−0.512214
$292$	−1.94915e6	−1.33779
$293$	−1.96063e6	−1.33422	−0.667109	−	0.744960i	$-0.732469\pi$
$293$	−1.96063e6	−1.33422	−0.667109	+	0.744960i	$0.732469\pi$
$294$	1.07596e6	0.725987
$295$	1.97576e6	1.32184
$296$	−826153.	−0.548064
$297$	−422664.	−0.278038
$298$	3.41753e6	2.22932
$299$	−86481.1	−0.0559427
$300$	3.37381e6	2.16430
$301$	735409.	0.467856
$302$	1.16708e6	0.736349
$303$	916573.	0.573536
$304$	−526489.	−0.326742
$305$	2.36702e6	1.45698
$306$	784787.	0.479124
$307$	−1.68085e6	−1.01785	−0.508926	−	0.860811i	$-0.669957\pi$
$307$	−1.68085e6	−1.01785	−0.508926	+	0.860811i	$0.669957\pi$
$308$	2.00767e6	1.20591
$309$	−95481.0	−0.0568880
$310$	−2.59183e6	−1.53180
$311$	−683477.	−0.400703	−0.200352	−	0.979724i	$-0.564208\pi$
$311$	−683477.	−0.400703	−0.200352	+	0.979724i	$0.564208\pi$
$312$	−91048.3	−0.0529524
$313$	334516.	0.192999	0.0964996	−	0.995333i	$-0.469235\pi$
$313$	334516.	0.192999	0.0964996	+	0.995333i	$0.469235\pi$
$314$	−796966.	−0.456158
$315$	509933.	0.289559
$316$	2.38730e6	1.34490
$317$	−1.57827e6	−0.882133	−0.441067	−	0.897474i	$-0.645400\pi$
$317$	−1.57827e6	−0.882133	−0.441067	+	0.897474i	$0.645400\pi$
$318$	904942.	0.501826
$319$	3.18071e6	1.75004
$320$	5.07818e6	2.77225
$321$	−1.08927e6	−0.590031
$322$	−1.07227e6	−0.576322
$323$	2.36105e6	1.25921
$324$	360079.	0.190561
$325$	323987.	0.170145
$326$	6.24676e6	3.25545
$327$	1.09952e6	0.568636
$328$	1.56947e6	0.805506
$329$	1.01429e6	0.516620
$330$	−4.85294e6	−2.45313
$331$	806446.	0.404581	0.202291	−	0.979326i	$-0.435161\pi$
$331$	806446.	0.404581	0.202291	+	0.979326i	$0.435161\pi$
$332$	2.45461e6	1.22219
$333$	313757.	0.155054
$334$	−2.63434e6	−1.29213
$335$	−2.83707e6	−1.38120
$336$	−131621.	−0.0636029
$337$	−2.60457e6	−1.24928	−0.624641	−	0.780912i	$-0.714755\pi$
$337$	−2.60457e6	−1.24928	−0.624641	+	0.780912i	$0.714755\pi$
$338$	3.43986e6	1.63776
$339$	1.41699e6	0.669679
$340$	5.69195e6	2.67032
$341$	1.61576e6	0.752475
$342$	1.71496e6	0.792844
$343$	1.86970e6	0.858099
$344$	2.48590e6	1.13263
$345$	1.63726e6	0.740575
$346$	−3.60581e6	−1.61924
$347$	−2.14038e6	−0.954260	−0.477130	−	0.878833i	$-0.658323\pi$
$347$	−2.14038e6	−0.954260	−0.477130	+	0.878833i	$0.658323\pi$
$348$	−2.70973e6	−1.19944
$349$	208751.	0.0917413	0.0458707	−	0.998947i	$-0.485394\pi$
$349$	208751.	0.0917413	0.0458707	+	0.998947i	$0.485394\pi$
$350$	4.01709e6	1.75284
$351$	34578.4	0.0149809
$352$	−2.70442e6	−1.16337
$353$	2.96949e6	1.26837	0.634183	−	0.773183i	$-0.281337\pi$
$353$	2.96949e6	1.26837	0.634183	+	0.773183i	$0.281337\pi$
$354$	1.66115e6	0.704532
$355$	−1.21209e6	−0.510464
$356$	−4.25433e6	−1.77912
$357$	590258.	0.245116
$358$	−7.05066e6	−2.90752
$359$	−4.16560e6	−1.70585	−0.852925	−	0.522033i	$-0.825174\pi$
$359$	−4.16560e6	−1.70585	−0.852925	+	0.522033i	$0.825174\pi$
$360$	1.72372e6	0.700990
$361$	2.68340e6	1.08372
$362$	−2.57204e6	−1.03159
$363$	1.57590e6	0.627715
$364$	−164249.	−0.0649753
$365$	3.54362e6	1.39224
$366$	1.99012e6	0.776561
$367$	−3.84920e6	−1.49178	−0.745891	−	0.666068i	$-0.767976\pi$
$367$	−3.84920e6	−1.49178	−0.745891	+	0.666068i	$0.767976\pi$
$368$	−422599.	−0.162671
$369$	−596055.	−0.227887
$370$	3.60250e6	1.36804
$371$	680630.	0.256730
$372$	−1.37651e6	−0.515731
$373$	−2.46989e6	−0.919189	−0.459595	−	0.888129i	$-0.652005\pi$
$373$	−2.46989e6	−0.919189	−0.459595	+	0.888129i	$0.652005\pi$
$374$	−5.61738e6	−2.07661
$375$	−3.32749e6	−1.22191
$376$	3.42859e6	1.25068
$377$	−260216.	−0.0942933
$378$	428735.	0.154333
$379$	−5.36770e6	−1.91951	−0.959755	−	0.280839i	$-0.909387\pi$
$379$	−5.36770e6	−1.91951	−0.959755	+	0.280839i	$0.909387\pi$
$380$	1.24383e7	4.41879
$381$	1.45034e6	0.511866
$382$	8.46106e6	2.96665
$383$	−1.09218e6	−0.380450	−0.190225	−	0.981741i	$-0.560922\pi$
$383$	−1.09218e6	−0.380450	−0.190225	+	0.981741i	$0.560922\pi$
$384$	2.92618e6	1.01268
$385$	−3.65002e6	−1.25500
$386$	−5.82400e6	−1.98954
$387$	−944097.	−0.320435
$388$	−4.51200e6	−1.52156
$389$	5.06954e6	1.69861	0.849307	−	0.527899i	$-0.177020\pi$
$389$	5.06954e6	1.69861	0.849307	+	0.527899i	$0.177020\pi$
$390$	397022.	0.132176
$391$	1.89516e6	0.626908
$392$	2.73554e6	0.899140
$393$	3.46142e6	1.13051
$394$	6.14419e6	1.99400
$395$	−4.34022e6	−1.39965
$396$	−2.57739e6	−0.825927
$397$	−3.15219e6	−1.00377	−0.501887	−	0.864933i	$-0.667361\pi$
$397$	−3.15219e6	−1.00377	−0.501887	+	0.864933i	$0.667361\pi$
$398$	2.12632e6	0.672854
$399$	1.28986e6	0.405612
$400$	1.58320e6	0.494750
$401$	273429.	0.0849150	0.0424575	−	0.999098i	$-0.486481\pi$
$401$	273429.	0.0849150	0.0424575	+	0.999098i	$0.486481\pi$
$402$	−2.38531e6	−0.736174
$403$	−132187.	−0.0405439
$404$	5.58923e6	1.70372
$405$	−654638.	−0.198319
$406$	−3.22640e6	−0.971410
$407$	−2.24582e6	−0.672032
$408$	1.99525e6	0.593399
$409$	4.39710e6	1.29975	0.649873	−	0.760043i	$-0.274822\pi$
$409$	4.39710e6	1.29975	0.649873	+	0.760043i	$0.274822\pi$
$410$	−6.84379e6	−2.01065
$411$	−1.24713e6	−0.364174
$412$	−582240.	−0.168989
$413$	1.24939e6	0.360433
$414$	1.37655e6	0.394722
$415$	−4.46258e6	−1.27194
$416$	221250.	0.0626831
$417$	1.73212e6	0.487796
$418$	−1.22754e7	−3.43633
$419$	−1.15750e6	−0.322096	−0.161048	−	0.986947i	$-0.551487\pi$
$419$	−1.15750e6	−0.322096	−0.161048	+	0.986947i	$0.551487\pi$
$420$	3.10955e6	0.860151
$421$	−633206.	−0.174117	−0.0870583	−	0.996203i	$-0.527747\pi$
$421$	−633206.	−0.174117	−0.0870583	+	0.996203i	$0.527747\pi$
$422$	4.33821e6	1.18585
$423$	−1.30211e6	−0.353833
$424$	2.30073e6	0.621515
$425$	−7.09991e6	−1.90669
$426$	−1.01909e6	−0.272074
$427$	1.49682e6	0.397282
$428$	−6.64236e6	−1.75272
$429$	−247507.	−0.0649298
$430$	−1.08399e7	−2.82719
$431$	−5.83157e6	−1.51214	−0.756070	−	0.654490i	$-0.772883\pi$
$431$	−5.83157e6	−1.51214	−0.756070	+	0.654490i	$0.772883\pi$
$432$	168971.	0.0435616
$433$	715356.	0.183359	0.0916796	−	0.995789i	$-0.470776\pi$
$433$	715356.	0.183359	0.0916796	+	0.995789i	$0.470776\pi$
$434$	−1.63897e6	−0.417684
$435$	4.92640e6	1.24827
$436$	6.70484e6	1.68917
$437$	4.14140e6	1.03739
$438$	2.97936e6	0.742058
$439$	−1.43976e6	−0.356558	−0.178279	−	0.983980i	$-0.557053\pi$
$439$	−1.43976e6	−0.356558	−0.178279	+	0.983980i	$0.557053\pi$
$440$	−1.23382e7	−3.03821
$441$	−1.03890e6	−0.254378
$442$	459562.	0.111889
$443$	7.75531e6	1.87754	0.938771	−	0.344541i	$-0.111965\pi$
$443$	7.75531e6	1.87754	0.938771	+	0.344541i	$0.111965\pi$
$444$	1.91328e6	0.460597
$445$	7.73454e6	1.85155
$446$	2.39921e6	0.571126
$447$	−3.29983e6	−0.781128
$448$	3.21125e6	0.755926
$449$	1.05975e6	0.248077	0.124039	−	0.992277i	$-0.460415\pi$
$449$	1.05975e6	0.248077	0.124039	+	0.992277i	$0.460415\pi$
$450$	−5.15703e6	−1.20052
$451$	4.26647e6	0.987705
$452$	8.64074e6	1.98932
$453$	−1.12688e6	−0.258008
$454$	−8.03861e6	−1.83038
$455$	298611.	0.0676203
$456$	4.36012e6	0.981942
$457$	−3.40134e6	−0.761832	−0.380916	−	0.924610i	$-0.624391\pi$
$457$	−3.40134e6	−0.761832	−0.380916	+	0.924610i	$0.624391\pi$
$458$	−915247.	−0.203880
$459$	−757757.	−0.167880
$460$	9.98394e6	2.19992
$461$	−4.33158e6	−0.949279	−0.474640	−	0.880180i	$-0.657422\pi$
$461$	−4.33158e6	−0.949279	−0.474640	+	0.880180i	$0.657422\pi$
$462$	−3.06882e6	−0.668908
$463$	−508342.	−0.110206	−0.0551028	−	0.998481i	$-0.517549\pi$
$463$	−508342.	−0.110206	−0.0551028	+	0.998481i	$0.517549\pi$
$464$	−1.27157e6	−0.274187
$465$	2.50256e6	0.536725
$466$	1.00605e6	0.214612
$467$	8.84164e6	1.87603	0.938017	−	0.346589i	$-0.112660\pi$
$467$	8.84164e6	1.87603	0.938017	+	0.346589i	$0.112660\pi$
$468$	210858.	0.0445016
$469$	−1.79406e6	−0.376621
$470$	−1.49506e7	−3.12187
$471$	769517.	0.159833
$472$	4.22332e6	0.872568
$473$	6.75770e6	1.38882
$474$	−3.64911e6	−0.746004
$475$	−1.55151e7	−3.15515
$476$	3.59937e6	0.728131
$477$	−873774.	−0.175834
$478$	−948075.	−0.189790
$479$	−3.49053e6	−0.695108	−0.347554	−	0.937660i	$-0.612988\pi$
$479$	−3.49053e6	−0.695108	−0.347554	+	0.937660i	$0.612988\pi$
$480$	−4.18871e6	−0.829806
$481$	183733.	0.0362096
$482$	−1.07507e7	−2.10774
$483$	1.03534e6	0.201937
$484$	9.60979e6	1.86466
$485$	8.20300e6	1.58350
$486$	−550398.	−0.105703
$487$	−2.46331e6	−0.470648	−0.235324	−	0.971917i	$-0.575615\pi$
$487$	−2.46331e6	−0.470648	−0.235324	+	0.971917i	$0.575615\pi$
$488$	5.05969e6	0.961777
$489$	−6.03161e6	−1.14067
$490$	−1.19285e7	−2.24437
$491$	9.57771e6	1.79291	0.896454	−	0.443137i	$-0.146134\pi$
$491$	9.57771e6	1.79291	0.896454	+	0.443137i	$0.146134\pi$
$492$	−3.63472e6	−0.676953
$493$	5.70242e6	1.05668
$494$	1.00426e6	0.185152
$495$	4.68579e6	0.859548
$496$	−645946.	−0.117894
$497$	−766482.	−0.139191
$498$	−3.75199e6	−0.677935
$499$	−1.19111e6	−0.214141	−0.107070	−	0.994251i	$-0.534147\pi$
$499$	−1.19111e6	−0.214141	−0.107070	+	0.994251i	$0.534147\pi$
$500$	−2.02909e7	−3.62975
$501$	2.54361e6	0.452747
$502$	−1.61419e7	−2.85888
$503$	6.89989e6	1.21597	0.607984	−	0.793949i	$-0.291978\pi$
$503$	6.89989e6	1.21597	0.607984	+	0.793949i	$0.291978\pi$
$504$	1.09002e6	0.191143
$505$	−1.01614e7	−1.77307
$506$	−9.85315e6	−1.71080
$507$	−3.32139e6	−0.573852
$508$	8.84410e6	1.52053
$509$	4.28456e6	0.733014	0.366507	−	0.930415i	$-0.380554\pi$
$509$	4.28456e6	0.733014	0.366507	+	0.930415i	$0.380554\pi$
$510$	−8.70041e6	−1.48120
$511$	2.24086e6	0.379631
$512$	2.66309e6	0.448964
$513$	−1.65589e6	−0.277804
$514$	1.14561e7	1.91262
$515$	1.05854e6	0.175868
$516$	−5.75707e6	−0.951869
$517$	9.32032e6	1.53357
$518$	2.27808e6	0.373031
$519$	3.48162e6	0.567365
$520$	1.00939e6	0.163701
$521$	−5.04502e6	−0.814270	−0.407135	−	0.913368i	$-0.633472\pi$
$521$	−5.04502e6	−0.814270	−0.407135	+	0.913368i	$0.633472\pi$
$522$	4.14196e6	0.665318
$523$	−1.13686e7	−1.81741	−0.908707	−	0.417435i	$-0.862929\pi$
$523$	−1.13686e7	−1.81741	−0.908707	+	0.417435i	$0.862929\pi$
$524$	2.11076e7	3.35823
$525$	−3.87874e6	−0.614175
$526$	1.97378e7	3.11053
$527$	2.89676e6	0.454346
$528$	−1.20947e6	−0.188804
$529$	−3.11214e6	−0.483527
$530$	−1.00325e7	−1.55138
$531$	−1.60394e6	−0.246860
$532$	7.86553e6	1.20489
$533$	−349043.	−0.0532183
$534$	6.50295e6	0.986863
$535$	1.20761e7	1.82407
$536$	−6.06445e6	−0.911757
$537$	6.80782e6	1.01876
$538$	−1.83627e6	−0.273514
$539$	7.43632e6	1.10252
$540$	−3.99196e6	−0.589117
$541$	3.49451e6	0.513326	0.256663	−	0.966501i	$-0.417377\pi$
$541$	3.49451e6	0.513326	0.256663	+	0.966501i	$0.417377\pi$
$542$	2.20563e7	3.22504
$543$	2.48345e6	0.361457
$544$	−4.84852e6	−0.702444
$545$	−1.21897e7	−1.75793
$546$	251062.	0.0360412
$547$	−9.21155e6	−1.31633	−0.658165	−	0.752874i	$-0.728667\pi$
$547$	−9.21155e6	−1.31633	−0.658165	+	0.752874i	$0.728667\pi$
$548$	−7.60498e6	−1.08180
$549$	−1.92157e6	−0.272098
$550$	3.69132e7	5.20326
$551$	1.24612e7	1.74856
$552$	3.49976e6	0.488867
$553$	−2.74459e6	−0.381649
$554$	1.86974e7	2.58825
$555$	−3.47842e6	−0.479347
$556$	1.05624e7	1.44903
$557$	1.13874e7	1.55521	0.777603	−	0.628755i	$-0.216435\pi$
$557$	1.13874e7	1.55521	0.777603	+	0.628755i	$0.216435\pi$
$558$	2.10407e6	0.286071
$559$	−552852.	−0.0748307
$560$	1.45920e6	0.196627
$561$	5.42391e6	0.727621
$562$	8.42435e6	1.12511
$563$	8.37939e6	1.11414	0.557072	−	0.830464i	$-0.311925\pi$
$563$	8.37939e6	1.11414	0.557072	+	0.830464i	$0.311925\pi$
$564$	−7.94024e6	−1.05108
$565$	−1.57092e7	−2.07030
$566$	−4.67487e6	−0.613379
$567$	−413968.	−0.0540766
$568$	−2.59094e6	−0.336966
$569$	1.15426e7	1.49459	0.747296	−	0.664491i	$-0.231351\pi$
$569$	1.15426e7	1.49459	0.747296	+	0.664491i	$0.231351\pi$
$570$	−1.90126e7	−2.45106
$571$	−121476.	−0.0155919	−0.00779596	−	0.999970i	$-0.502482\pi$
$571$	−121476.	−0.0155919	−0.00779596	+	0.999970i	$0.502482\pi$
$572$	−1.50929e6	−0.192878
$573$	−8.16964e6	−1.03948
$574$	−4.32775e6	−0.548255
$575$	−1.24536e7	−1.57081
$576$	−4.12251e6	−0.517733
$577$	−1.43523e7	−1.79466	−0.897329	−	0.441362i	$-0.854496\pi$
$577$	−1.43523e7	−1.79466	−0.897329	+	0.441362i	$0.854496\pi$
$578$	3.16362e6	0.393881
$579$	5.62341e6	0.697113
$580$	3.00410e7	3.70804
$581$	−2.82197e6	−0.346826
$582$	6.89681e6	0.843997
$583$	6.25434e6	0.762097
$584$	7.57476e6	0.919045
$585$	−383348.	−0.0463131
$586$	1.82751e7	2.19845
$587$	−1.18223e7	−1.41614	−0.708068	−	0.706144i	$-0.750433\pi$
$587$	−1.18223e7	−1.41614	−0.708068	+	0.706144i	$0.750433\pi$
$588$	−6.33520e6	−0.755644
$589$	6.33016e6	0.751841
$590$	−1.84161e7	−2.17805
$591$	−5.93257e6	−0.698674
$592$	897830.	0.105291
$593$	−5.28251e6	−0.616884	−0.308442	−	0.951243i	$-0.599807\pi$
$593$	−5.28251e6	−0.616884	−0.308442	+	0.951243i	$0.599807\pi$
$594$	3.93966e6	0.458134
$595$	−6.54381e6	−0.757771
$596$	−2.01222e7	−2.32039
$597$	−2.05308e6	−0.235760
$598$	806093.	0.0921790
$599$	1.20026e7	1.36681	0.683407	−	0.730038i	$-0.260498\pi$
$599$	1.20026e7	1.36681	0.683407	+	0.730038i	$0.260498\pi$
$600$	−1.31113e7	−1.48685
$601$	−3.69881e6	−0.417711	−0.208855	−	0.977947i	$-0.566974\pi$
$601$	−3.69881e6	−0.417711	−0.208855	+	0.977947i	$0.566974\pi$
$602$	−6.85477e6	−0.770907
$603$	2.30316e6	0.257947
$604$	−6.87170e6	−0.766429
$605$	−1.74710e7	−1.94057
$606$	−8.54341e6	−0.945038
$607$	1.43592e7	1.58183	0.790913	−	0.611929i	$-0.209606\pi$
$607$	1.43592e7	1.58183	0.790913	+	0.611929i	$0.209606\pi$
$608$	−1.05952e7	−1.16239
$609$	3.11527e6	0.340371
$610$	−2.20631e7	−2.40072
$611$	−762502.	−0.0826301
$612$	−4.62078e6	−0.498696
$613$	−3.01624e6	−0.324201	−0.162101	−	0.986774i	$-0.551827\pi$
$613$	−3.01624e6	−0.324201	−0.162101	+	0.986774i	$0.551827\pi$
$614$	1.56673e7	1.67716
$615$	6.60807e6	0.704510
$616$	−7.80219e6	−0.828447
$617$	−1.60753e7	−1.69999	−0.849994	−	0.526792i	$-0.823395\pi$
$617$	−1.60753e7	−1.69999	−0.849994	+	0.526792i	$0.823395\pi$
$618$	889982.	0.0937367
$619$	6.51841e6	0.683778	0.341889	−	0.939740i	$-0.388933\pi$
$619$	6.51841e6	0.683778	0.341889	+	0.939740i	$0.388933\pi$
$620$	1.52605e7	1.59437
$621$	−1.32914e6	−0.138306
$622$	6.37071e6	0.660255
$623$	4.89103e6	0.504871
$624$	98947.6	0.0101729
$625$	1.55445e7	1.59176
$626$	−3.11803e6	−0.318013
$627$	1.18526e7	1.20405
$628$	4.69249e6	0.474793
$629$	−4.02635e6	−0.405774
$630$	−4.75310e6	−0.477118
$631$	1.13220e7	1.13201	0.566003	−	0.824403i	$-0.308489\pi$
$631$	1.13220e7	1.13201	0.566003	+	0.824403i	$0.308489\pi$
$632$	−9.27753e6	−0.923931
$633$	−4.18880e6	−0.415509
$634$	1.47111e7	1.45353
$635$	−1.60789e7	−1.58242
$636$	−5.32824e6	−0.522326
$637$	−608370.	−0.0594045
$638$	−2.96475e7	−2.88361
$639$	983988.	0.0953318
$640$	−3.24407e7	−3.13069
$641$	−3.25176e6	−0.312589	−0.156295	−	0.987710i	$-0.549955\pi$
$641$	−3.25176e6	−0.312589	−0.156295	+	0.987710i	$0.549955\pi$
$642$	1.01532e7	0.972218
$643$	1.68098e7	1.60338	0.801688	−	0.597743i	$-0.203936\pi$
$643$	1.68098e7	1.60338	0.801688	+	0.597743i	$0.203936\pi$
$644$	6.31347e6	0.599865
$645$	1.04666e7	0.990617
$646$	−2.20075e7	−2.07486
$647$	100670.	0.00945451	0.00472725	−	0.999989i	$-0.498495\pi$
$647$	100670.	0.00945451	0.00472725	+	0.999989i	$0.498495\pi$
$648$	−1.39934e6	−0.130914
$649$	1.14807e7	1.06994
$650$	−3.01990e6	−0.280355
$651$	1.58252e6	0.146352
$652$	−3.67806e7	−3.38844
$653$	1.46587e7	1.34528	0.672639	−	0.739971i	$-0.265161\pi$
$653$	1.46587e7	1.34528	0.672639	+	0.739971i	$0.265161\pi$
$654$	−1.02487e7	−0.936965
$655$	−3.83745e7	−3.49494
$656$	−1.70564e6	−0.154749
$657$	−2.87675e6	−0.260009
$658$	−9.45421e6	−0.851256
$659$	−3.86247e6	−0.346459	−0.173230	−	0.984881i	$-0.555420\pi$
$659$	−3.86247e6	−0.346459	−0.173230	+	0.984881i	$0.555420\pi$
$660$	2.85738e7	2.55334
$661$	−1.97173e7	−1.75527	−0.877637	−	0.479327i	$-0.840881\pi$
$661$	−1.97173e7	−1.75527	−0.877637	+	0.479327i	$0.840881\pi$
$662$	−7.51691e6	−0.666645
$663$	−443734.	−0.0392047
$664$	−9.53909e6	−0.839628
$665$	−1.42999e7	−1.25394
$666$	−2.92454e6	−0.255489
$667$	1.00023e7	0.870534
$668$	1.55108e7	1.34491
$669$	−2.31658e6	−0.200116
$670$	2.64444e7	2.27587
$671$	1.37543e7	1.17932
$672$	−2.64878e6	−0.226268
$673$	−8.63278e6	−0.734705	−0.367353	−	0.930082i	$-0.619736\pi$
$673$	−8.63278e6	−0.734705	−0.367353	+	0.930082i	$0.619736\pi$
$674$	2.42773e7	2.05849
$675$	4.97941e6	0.420648
$676$	−2.02537e7	−1.70466
$677$	7.78646e6	0.652933	0.326466	−	0.945209i	$-0.394142\pi$
$677$	7.78646e6	0.652933	0.326466	+	0.945209i	$0.394142\pi$
$678$	−1.32078e7	−1.10346
$679$	5.18727e6	0.431782
$680$	−2.21200e7	−1.83448
$681$	7.76174e6	0.641345
$682$	−1.50606e7	−1.23988
$683$	−1.57311e7	−1.29035	−0.645176	−	0.764034i	$-0.723216\pi$
$683$	−1.57311e7	−1.29035	−0.645176	+	0.764034i	$0.723216\pi$
$684$	−1.00976e7	−0.825231
$685$	1.38262e7	1.12584
$686$	−1.74276e7	−1.41392
$687$	883725.	0.0714373
$688$	−2.70157e6	−0.217593
$689$	−511672.	−0.0410623
$690$	−1.52609e7	−1.22028
$691$	−1.13184e6	−0.0901756	−0.0450878	−	0.998983i	$-0.514357\pi$
$691$	−1.13184e6	−0.0901756	−0.0450878	+	0.998983i	$0.514357\pi$
$692$	2.12308e7	1.68539
$693$	2.96312e6	0.234378
$694$	1.99505e7	1.57237
$695$	−1.92029e7	−1.50801
$696$	1.05306e7	0.824001
$697$	7.64898e6	0.596378
$698$	−1.94578e6	−0.151166
$699$	−971397.	−0.0751975
$700$	−2.36524e7	−1.82444
$701$	−2.68515e6	−0.206383	−0.103191	−	0.994662i	$-0.532905\pi$
$701$	−2.68515e6	−0.206383	−0.103191	+	0.994662i	$0.532905\pi$
$702$	−322307.	−0.0246846
$703$	−8.79857e6	−0.671466
$704$	2.95083e7	2.24395
$705$	1.44357e7	1.09387
$706$	−2.76787e7	−2.08994
$707$	−6.42572e6	−0.483474
$708$	−9.78075e6	−0.733312
$709$	−5.39658e6	−0.403184	−0.201592	−	0.979470i	$-0.564612\pi$
$709$	−5.39658e6	−0.403184	−0.201592	+	0.979470i	$0.564612\pi$
$710$	1.12980e7	0.841112
$711$	3.52343e6	0.261391
$712$	1.65331e7	1.22224
$713$	5.08106e6	0.374309
$714$	−5.50182e6	−0.403888
$715$	2.74395e6	0.200729
$716$	4.15138e7	3.02629
$717$	915421.	0.0665002
$718$	3.88277e7	2.81080
$719$	−7.42248e6	−0.535460	−0.267730	−	0.963494i	$-0.586274\pi$
$719$	−7.42248e6	−0.535460	−0.267730	+	0.963494i	$0.586274\pi$
$720$	−1.87327e6	−0.134670
$721$	669378.	0.0479550
$722$	−2.50120e7	−1.78569
$723$	1.03804e7	0.738529
$724$	1.51440e7	1.07373
$725$	−3.74720e7	−2.64766
$726$	−1.46890e7	−1.03431
$727$	−2.19212e7	−1.53826	−0.769129	−	0.639094i	$-0.779309\pi$
$727$	−2.19212e7	−1.53826	−0.769129	+	0.639094i	$0.779309\pi$
$728$	638303.	0.0446373
$729$	531441.	0.0370370
$730$	−3.30302e7	−2.29406
$731$	1.21153e7	0.838573
$732$	−1.17177e7	−0.808284
$733$	−1.73498e7	−1.19271	−0.596355	−	0.802721i	$-0.703385\pi$
$733$	−1.73498e7	−1.19271	−0.596355	+	0.802721i	$0.703385\pi$
$734$	3.58785e7	2.45807
$735$	1.15177e7	0.786404
$736$	−8.50452e6	−0.578703
$737$	−1.64857e7	−1.11799
$738$	5.55585e6	0.375500
$739$	3.93770e6	0.265236	0.132618	−	0.991167i	$-0.457662\pi$
$739$	3.93770e6	0.265236	0.132618	+	0.991167i	$0.457662\pi$
$740$	−2.12113e7	−1.42393
$741$	−969669.	−0.0648751
$742$	−6.34418e6	−0.423025
$743$	−479555.	−0.0318689	−0.0159344	−	0.999873i	$-0.505072\pi$
$743$	−479555.	−0.0318689	−0.0159344	+	0.999873i	$0.505072\pi$
$744$	5.34940e6	0.354301
$745$	3.65830e7	2.41484
$746$	2.30219e7	1.51459
$747$	3.62276e6	0.237541
$748$	3.30748e7	2.16144
$749$	7.63646e6	0.497379
$750$	3.10157e7	2.01339
$751$	−1.44420e6	−0.0934388	−0.0467194	−	0.998908i	$-0.514877\pi$
$751$	−1.44420e6	−0.0934388	−0.0467194	+	0.998908i	$0.514877\pi$
$752$	−3.72605e6	−0.240273
$753$	1.55860e7	1.00172
$754$	2.42548e6	0.155371
$755$	1.24930e7	0.797628
$756$	−2.52436e6	−0.160638
$757$	−1.29389e7	−0.820651	−0.410325	−	0.911939i	$-0.634585\pi$
$757$	−1.29389e7	−0.820651	−0.410325	+	0.911939i	$0.634585\pi$
$758$	5.00325e7	3.16286
$759$	9.51379e6	0.599444
$760$	−4.83378e7	−3.03566
$761$	2.62656e7	1.64409	0.822045	−	0.569422i	$-0.192833\pi$
$761$	2.62656e7	1.64409	0.822045	+	0.569422i	$0.192833\pi$
$762$	−1.35186e7	−0.843423
$763$	−7.70829e6	−0.479344
$764$	−4.98182e7	−3.08784
$765$	8.40076e6	0.518997
$766$	1.01802e7	0.626883
$767$	−939247.	−0.0576489
$768$	−1.26172e7	−0.771901
$769$	−1.06034e7	−0.646589	−0.323294	−	0.946298i	$-0.604790\pi$
$769$	−1.06034e7	−0.646589	−0.323294	+	0.946298i	$0.604790\pi$
$770$	3.40220e7	2.06791
$771$	−1.10615e7	−0.670162
$772$	3.42913e7	2.07081
$773$	−3.18948e7	−1.91986	−0.959932	−	0.280232i	$-0.909589\pi$
$773$	−3.18948e7	−1.91986	−0.959932	+	0.280232i	$0.909589\pi$
$774$	8.79996e6	0.527993
$775$	−1.90354e7	−1.13843
$776$	1.75345e7	1.04530
$777$	−2.19962e6	−0.130706
$778$	−4.72534e7	−2.79888
$779$	1.67149e7	0.986873
$780$	−2.33764e6	−0.137576
$781$	−7.04323e6	−0.413185
$782$	−1.76649e7	−1.03298
$783$	−3.99930e6	−0.233120
$784$	−2.97287e6	−0.172737
$785$	−8.53113e6	−0.494120
$786$	−3.22640e7	−1.86278
$787$	7.04745e6	0.405597	0.202799	−	0.979220i	$-0.434996\pi$
$787$	7.04745e6	0.405597	0.202799	+	0.979220i	$0.434996\pi$
$788$	−3.61766e7	−2.07545
$789$	−1.90580e7	−1.08990
$790$	4.04553e7	2.30626
$791$	−9.93392e6	−0.564520
$792$	1.00162e7	0.567403
$793$	−1.12525e6	−0.0635428
$794$	2.93817e7	1.65396
$795$	9.68696e6	0.543588
$796$	−1.25196e7	−0.700340
$797$	−3.22742e7	−1.79974	−0.899871	−	0.436157i	$-0.856339\pi$
$797$	−3.22742e7	−1.79974	−0.899871	+	0.436157i	$0.856339\pi$
$798$	−1.20228e7	−0.668344
$799$	1.67096e7	0.925975
$800$	3.18608e7	1.76008
$801$	−6.27897e6	−0.345786
$802$	−2.54864e6	−0.139918
$803$	2.05913e7	1.12693
$804$	1.40446e7	0.766247
$805$	−1.14781e7	−0.624284
$806$	1.23212e6	0.0668059
$807$	1.77302e6	0.0958363
$808$	−2.17208e7	−1.17044
$809$	4.91038e6	0.263781	0.131891	−	0.991264i	$-0.457895\pi$
$809$	4.91038e6	0.263781	0.131891	+	0.991264i	$0.457895\pi$
$810$	6.10190e6	0.326778
$811$	1.17660e7	0.628167	0.314084	−	0.949395i	$-0.398303\pi$
$811$	1.17660e7	0.628167	0.314084	+	0.949395i	$0.398303\pi$
$812$	1.89968e7	1.01109
$813$	−2.12967e7	−1.13002
$814$	2.09334e7	1.10733
$815$	6.68685e7	3.52637
$816$	−2.16835e6	−0.114000
$817$	2.64750e7	1.38765
$818$	−4.09855e7	−2.14164
$819$	−242415.	−0.0126284
$820$	4.02958e7	2.09279
$821$	−8.43991e6	−0.436999	−0.218499	−	0.975837i	$-0.570116\pi$
$821$	−8.43991e6	−0.436999	−0.218499	+	0.975837i	$0.570116\pi$
$822$	1.16246e7	0.600064
$823$	2.29145e6	0.117926	0.0589631	−	0.998260i	$-0.481221\pi$
$823$	2.29145e6	0.117926	0.0589631	+	0.998260i	$0.481221\pi$
$824$	2.26270e6	0.116094
$825$	−3.56419e7	−1.82316
$826$	−1.16456e7	−0.593900
$827$	2.51041e7	1.27638	0.638191	−	0.769878i	$-0.279683\pi$
$827$	2.51041e7	1.27638	0.638191	+	0.769878i	$0.279683\pi$
$828$	−8.10506e6	−0.410847
$829$	−1.03453e7	−0.522823	−0.261412	−	0.965227i	$-0.584188\pi$
$829$	−1.03453e7	−0.522823	−0.261412	+	0.965227i	$0.584188\pi$
$830$	4.15959e7	2.09582
$831$	−1.80534e7	−0.906895
$832$	−2.41410e6	−0.120906
$833$	1.33319e7	0.665703
$834$	−1.61452e7	−0.803762
$835$	−2.81993e7	−1.39966
$836$	7.22767e7	3.57670
$837$	−2.03160e6	−0.100236
$838$	1.07891e7	0.530731
$839$	−1.98536e7	−0.973719	−0.486859	−	0.873480i	$-0.661858\pi$
$839$	−1.98536e7	−0.973719	−0.486859	+	0.873480i	$0.661858\pi$
$840$	−1.20843e7	−0.590914
$841$	9.58516e6	0.467314
$842$	5.90214e6	0.286899
$843$	−8.13420e6	−0.394227
$844$	−2.55431e7	−1.23429
$845$	3.68221e7	1.77405
$846$	1.21370e7	0.583025
$847$	−1.10480e7	−0.529145
$848$	−2.50034e6	−0.119402
$849$	4.51386e6	0.214921
$850$	6.61785e7	3.14174
$851$	−7.06240e6	−0.334294
$852$	6.00033e6	0.283189
$853$	3.62686e7	1.70670	0.853352	−	0.521336i	$-0.174566\pi$
$853$	3.62686e7	1.70670	0.853352	+	0.521336i	$0.174566\pi$
$854$	−1.39519e7	−0.654619
$855$	1.83578e7	0.858824
$856$	2.58135e7	1.20410
$857$	8.81306e6	0.409897	0.204948	−	0.978773i	$-0.434297\pi$
$857$	8.81306e6	0.409897	0.204948	+	0.978773i	$0.434297\pi$
$858$	2.30702e6	0.106988
$859$	4.06691e7	1.88054	0.940268	−	0.340435i	$-0.110574\pi$
$859$	4.06691e7	1.88054	0.940268	+	0.340435i	$0.110574\pi$
$860$	6.38249e7	2.94269
$861$	4.17870e6	0.192103
$862$	5.43563e7	2.49162
$863$	−1.31720e7	−0.602037	−0.301019	−	0.953618i	$-0.597327\pi$
$863$	−1.31720e7	−0.602037	−0.301019	+	0.953618i	$0.597327\pi$
$864$	3.40043e6	0.154971
$865$	−3.85984e7	−1.75400
$866$	−6.66786e6	−0.302129
$867$	−3.05466e6	−0.138011
$868$	9.65018e6	0.434746
$869$	−2.52201e7	−1.13292
$870$	−4.59192e7	−2.05682
$871$	1.34870e6	0.0602381
$872$	−2.60563e7	−1.16044
$873$	−6.65927e6	−0.295727
$874$	−3.86021e7	−1.70936
$875$	2.33277e7	1.03003
$876$	−1.75423e7	−0.772372
$877$	1.98708e7	0.872402	0.436201	−	0.899849i	$-0.356324\pi$
$877$	1.98708e7	0.872402	0.436201	+	0.899849i	$0.356324\pi$
$878$	1.34201e7	0.587515
$879$	−1.76457e7	−0.770312
$880$	1.34086e7	0.583683
$881$	−2.38914e7	−1.03705	−0.518527	−	0.855061i	$-0.673519\pi$
$881$	−2.38914e7	−1.03705	−0.518527	+	0.855061i	$0.673519\pi$
$882$	9.68366e6	0.419149
$883$	−1.27350e7	−0.549666	−0.274833	−	0.961492i	$-0.588623\pi$
$883$	−1.27350e7	−0.549666	−0.274833	+	0.961492i	$0.588623\pi$
$884$	−2.70587e6	−0.116460
$885$	1.77818e7	0.763163
$886$	−7.22875e7	−3.09371
$887$	1.71657e7	0.732575	0.366288	−	0.930502i	$-0.380629\pi$
$887$	1.71657e7	0.732575	0.366288	+	0.930502i	$0.380629\pi$
$888$	−7.43538e6	−0.316425
$889$	−1.01677e7	−0.431488
$890$	−7.20939e7	−3.05087
$891$	−3.80397e6	−0.160525
$892$	−1.41264e7	−0.594456
$893$	3.65147e7	1.53228
$894$	3.07578e7	1.28710
$895$	−7.54738e7	−3.14948
$896$	−2.05143e7	−0.853663
$897$	−778330.	−0.0322985
$898$	−9.87795e6	−0.408767
$899$	1.52886e7	0.630911
$900$	3.03643e7	1.24956
$901$	1.12129e7	0.460156
$902$	−3.97679e7	−1.62748
$903$	6.61868e6	0.270117
$904$	−3.35796e7	−1.36664
$905$	−2.75324e7	−1.11744
$906$	1.05037e7	0.425131
$907$	−2.93680e7	−1.18538	−0.592688	−	0.805432i	$-0.701933\pi$
$907$	−2.93680e7	−1.18538	−0.592688	+	0.805432i	$0.701933\pi$
$908$	4.73308e7	1.90515
$909$	8.24915e6	0.331131
$910$	−2.78336e6	−0.111421
$911$	−1.02666e7	−0.409856	−0.204928	−	0.978777i	$-0.565696\pi$
$911$	−1.02666e7	−0.409856	−0.204928	+	0.978777i	$0.565696\pi$
$912$	−4.73840e6	−0.188645
$913$	−2.59312e7	−1.02955
$914$	3.17040e7	1.25530
$915$	2.13032e7	0.841187
$916$	5.38892e6	0.212209
$917$	−2.42666e7	−0.952984
$918$	7.06308e6	0.276622
$919$	−3.54735e7	−1.38553	−0.692764	−	0.721164i	$-0.743607\pi$
$919$	−3.54735e7	−1.38553	−0.692764	+	0.721164i	$0.743607\pi$
$920$	−3.87995e7	−1.51132
$921$	−1.51277e7	−0.587657
$922$	4.03748e7	1.56417
$923$	576212.	0.0222627
$924$	1.80690e7	0.696233
$925$	2.64581e7	1.01673
$926$	4.73827e6	0.181590
$927$	−859329.	−0.0328443
$928$	−2.55896e7	−0.975423
$929$	1.89323e6	0.0719721	0.0359860	−	0.999352i	$-0.488543\pi$
$929$	1.89323e6	0.0719721	0.0359860	+	0.999352i	$0.488543\pi$
$930$	−2.33264e7	−0.884384
$931$	2.91336e7	1.10159
$932$	−5.92354e6	−0.223379
$933$	−6.15129e6	−0.231346
$934$	−8.24133e7	−3.09122
$935$	−6.01313e7	−2.24943
$936$	−819435.	−0.0305721
$937$	1.41597e7	0.526874	0.263437	−	0.964677i	$-0.415144\pi$
$937$	1.41597e7	0.526874	0.263437	+	0.964677i	$0.415144\pi$
$938$	1.67225e7	0.620574
$939$	3.01064e6	0.111428
$940$	8.80282e7	3.24939
$941$	4.54801e6	0.167435	0.0837176	−	0.996490i	$-0.473321\pi$
$941$	4.54801e6	0.167435	0.0837176	+	0.996490i	$0.473321\pi$
$942$	−7.17269e6	−0.263363
$943$	1.34167e7	0.491321
$944$	−4.58973e6	−0.167632
$945$	4.58940e6	0.167177
$946$	−6.29888e7	−2.28842
$947$	2.81797e7	1.02108	0.510541	−	0.859853i	$-0.329445\pi$
$947$	2.81797e7	1.02108	0.510541	+	0.859853i	$0.329445\pi$
$948$	2.14857e7	0.776478
$949$	−1.68459e6	−0.0607196
$950$	1.44617e8	5.19888
$951$	−1.42045e7	−0.509300
$952$	−1.39879e7	−0.500218
$953$	−2.92142e7	−1.04198	−0.520992	−	0.853561i	$-0.674438\pi$
$953$	−2.92142e7	−1.04198	−0.520992	+	0.853561i	$0.674438\pi$
$954$	8.14448e6	0.289729
$955$	9.05715e7	3.21353
$956$	5.58220e6	0.197543
$957$	2.86264e7	1.01038
$958$	3.25353e7	1.14536
$959$	8.74315e6	0.306988
$960$	4.57036e7	1.60056
$961$	−2.08627e7	−0.728723
$962$	−1.71258e6	−0.0596640
$963$	−9.80347e6	−0.340654
$964$	6.32992e7	2.19384
$965$	−6.23430e7	−2.15511
$966$	−9.65045e6	−0.332740
$967$	4.10392e7	1.41134	0.705671	−	0.708540i	$-0.250646\pi$
$967$	4.10392e7	1.41134	0.705671	+	0.708540i	$0.250646\pi$
$968$	−3.73455e7	−1.28100
$969$	2.12495e7	0.727008
$970$	−7.64604e7	−2.60920
$971$	2.75750e7	0.938573	0.469287	−	0.883046i	$-0.344511\pi$
$971$	2.75750e7	0.938573	0.469287	+	0.883046i	$0.344511\pi$
$972$	3.24071e6	0.110021
$973$	−1.21432e7	−0.411198
$974$	2.29606e7	0.775507
$975$	2.91589e6	0.0982334
$976$	−5.49866e6	−0.184770
$977$	−2.09157e7	−0.701029	−0.350514	−	0.936557i	$-0.613993\pi$
$977$	−2.09157e7	−0.701029	−0.350514	+	0.936557i	$0.613993\pi$
$978$	5.62209e7	1.87953
$979$	4.49439e7	1.49870
$980$	7.02342e7	2.33606
$981$	9.89569e6	0.328302
$982$	−8.92742e7	−2.95425
$983$	−6.15690e6	−0.203226	−0.101613	−	0.994824i	$-0.532400\pi$
$983$	−6.15690e6	−0.203226	−0.101613	+	0.994824i	$0.532400\pi$
$984$	1.41252e7	0.465059
$985$	6.57706e7	2.15994
$986$	−5.31524e7	−1.74113
$987$	9.12858e6	0.298271
$988$	−5.91301e6	−0.192715
$989$	2.12508e7	0.690851
$990$	−4.36764e7	−1.41631
$991$	−4.95710e6	−0.160341	−0.0801704	−	0.996781i	$-0.525546\pi$
$991$	−4.95710e6	−0.160341	−0.0801704	+	0.996781i	$0.525546\pi$
$992$	−1.29992e7	−0.419409
$993$	7.25802e6	0.233585
$994$	7.14441e6	0.229351
$995$	2.27612e7	0.728849
$996$	2.20915e7	0.705629
$997$	9.81607e6	0.312752	0.156376	−	0.987698i	$-0.450019\pi$
$997$	9.81607e6	0.312752	0.156376	+	0.987698i	$0.450019\pi$
$998$	1.11023e7	0.352849
$999$	2.82381e6	0.0895205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.3	✓	25
3.2	odd	2		927.6.a.f.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.3	✓	25	1.1	even	1	trivial
927.6.a.f.1.23		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)

\(f(q)\)	\(=\)	\(q-9.32103 q^{2} +9.00000 q^{3} +54.8817 q^{4} -99.7771 q^{5} -83.8893 q^{6} -63.0953 q^{7} -213.281 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.32103 q^{2} +9.00000 q^{3} +54.8817 q^{4} -99.7771 q^{5} -83.8893 q^{6} -63.0953 q^{7} -213.281 q^{8} +81.0000 q^{9} +930.026 q^{10} -579.785 q^{11} +493.935 q^{12} +47.4327 q^{13} +588.114 q^{14} -897.994 q^{15} +231.785 q^{16} -1039.45 q^{17} -755.004 q^{18} -2271.45 q^{19} -5475.94 q^{20} -567.858 q^{21} +5404.20 q^{22} -1823.24 q^{23} -1919.53 q^{24} +6830.47 q^{25} -442.121 q^{26} +729.000 q^{27} -3462.78 q^{28} -5486.01 q^{29} +8370.23 q^{30} -2786.83 q^{31} +4664.51 q^{32} -5218.07 q^{33} +9688.72 q^{34} +6295.47 q^{35} +4445.42 q^{36} +3873.55 q^{37} +21172.3 q^{38} +426.894 q^{39} +21280.6 q^{40} -7358.70 q^{41} +5293.02 q^{42} -11655.5 q^{43} -31819.6 q^{44} -8081.95 q^{45} +16994.5 q^{46} -16075.5 q^{47} +2086.06 q^{48} -12826.0 q^{49} -63667.1 q^{50} -9355.02 q^{51} +2603.18 q^{52} -10787.3 q^{53} -6795.03 q^{54} +57849.3 q^{55} +13457.0 q^{56} -20443.1 q^{57} +51135.3 q^{58} -19801.7 q^{59} -49283.4 q^{60} -23723.1 q^{61} +25976.2 q^{62} -5110.72 q^{63} -50895.2 q^{64} -4732.69 q^{65} +48637.8 q^{66} +28434.1 q^{67} -57046.6 q^{68} -16409.2 q^{69} -58680.3 q^{70} +12148.0 q^{71} -17275.8 q^{72} -35515.4 q^{73} -36105.4 q^{74} +61474.2 q^{75} -124661. q^{76} +36581.7 q^{77} -3979.09 q^{78} +43499.1 q^{79} -23126.8 q^{80} +6561.00 q^{81} +68590.7 q^{82} +44725.5 q^{83} -31165.0 q^{84} +103713. q^{85} +108642. q^{86} -49374.1 q^{87} +123657. q^{88} -77518.2 q^{89} +75332.1 q^{90} -2992.78 q^{91} -100062. q^{92} -25081.5 q^{93} +149840. q^{94} +226639. q^{95} +41980.6 q^{96} -82213.2 q^{97} +119551. q^{98} -46962.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 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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