LMFDB - Embedded newform 309.6.a.d.1.19

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			1.19
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)

$f(q)$	$=$	$q+6.30173 q^{2} +9.00000 q^{3} +7.71183 q^{4} -103.382 q^{5} +56.7156 q^{6} +116.004 q^{7} -153.058 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+6.30173 q^{2} +9.00000 q^{3} +7.71183 q^{4} -103.382 q^{5} +56.7156 q^{6} +116.004 q^{7} -153.058 q^{8} +81.0000 q^{9} -651.483 q^{10} -558.207 q^{11} +69.4065 q^{12} +269.871 q^{13} +731.028 q^{14} -930.434 q^{15} -1211.31 q^{16} +2244.57 q^{17} +510.440 q^{18} +2636.69 q^{19} -797.261 q^{20} +1044.04 q^{21} -3517.67 q^{22} +1792.86 q^{23} -1377.52 q^{24} +7562.75 q^{25} +1700.65 q^{26} +729.000 q^{27} +894.605 q^{28} +3144.99 q^{29} -5863.35 q^{30} +867.512 q^{31} -2735.49 q^{32} -5023.86 q^{33} +14144.7 q^{34} -11992.7 q^{35} +624.658 q^{36} -994.784 q^{37} +16615.7 q^{38} +2428.84 q^{39} +15823.3 q^{40} -16088.9 q^{41} +6579.25 q^{42} +10233.9 q^{43} -4304.79 q^{44} -8373.91 q^{45} +11298.1 q^{46} -17669.6 q^{47} -10901.8 q^{48} -3350.00 q^{49} +47658.4 q^{50} +20201.1 q^{51} +2081.20 q^{52} +10580.8 q^{53} +4593.96 q^{54} +57708.3 q^{55} -17755.3 q^{56} +23730.2 q^{57} +19818.9 q^{58} +38030.1 q^{59} -7175.35 q^{60} +1978.21 q^{61} +5466.83 q^{62} +9396.35 q^{63} +21523.5 q^{64} -27899.6 q^{65} -31659.0 q^{66} +38875.8 q^{67} +17309.7 q^{68} +16135.8 q^{69} -75574.8 q^{70} -58523.3 q^{71} -12397.7 q^{72} -5034.93 q^{73} -6268.86 q^{74} +68064.7 q^{75} +20333.7 q^{76} -64754.4 q^{77} +15305.9 q^{78} +64703.6 q^{79} +125227. q^{80} +6561.00 q^{81} -101388. q^{82} -52140.3 q^{83} +8051.45 q^{84} -232047. q^{85} +64491.6 q^{86} +28304.9 q^{87} +85437.7 q^{88} +75368.8 q^{89} -52770.1 q^{90} +31306.2 q^{91} +13826.3 q^{92} +7807.61 q^{93} -111349. q^{94} -272585. q^{95} -24619.4 q^{96} -39391.1 q^{97} -21110.8 q^{98} -45214.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.30173	1.11400	0.557000	−	0.830513i	$-0.311952\pi$
$2$	6.30173	1.11400	0.557000	+	0.830513i	$0.311952\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	7.71183	0.240995
$5$	−103.382	−1.84935	−0.924673	−	0.380763i	$-0.875661\pi$
$5$	−103.382	−1.84935	−0.924673	+	0.380763i	$0.875661\pi$
$6$	56.7156	0.643168
$7$	116.004	0.894806	0.447403	−	0.894332i	$-0.352349\pi$
$7$	116.004	0.894806	0.447403	+	0.894332i	$0.352349\pi$
$8$	−153.058	−0.845532
$9$	81.0000	0.333333
$10$	−651.483	−2.06017
$11$	−558.207	−1.39096	−0.695478	−	0.718548i	$-0.744807\pi$
$11$	−558.207	−1.39096	−0.695478	+	0.718548i	$0.744807\pi$
$12$	69.4065	0.139138
$13$	269.871	0.442891	0.221446	−	0.975173i	$-0.428922\pi$
$13$	269.871	0.442891	0.221446	+	0.975173i	$0.428922\pi$
$14$	731.028	0.996814
$15$	−930.434	−1.06772
$16$	−1211.31	−1.18292
$17$	2244.57	1.88370	0.941848	−	0.336040i	$-0.109088\pi$
$17$	2244.57	1.88370	0.941848	+	0.336040i	$0.109088\pi$
$18$	510.440	0.371333
$19$	2636.69	1.67562	0.837810	−	0.545961i	$-0.183836\pi$
$19$	2636.69	1.67562	0.837810	+	0.545961i	$0.183836\pi$
$20$	−797.261	−0.445682
$21$	1044.04	0.516617
$22$	−3517.67	−1.54952
$23$	1792.86	0.706688	0.353344	−	0.935493i	$-0.385045\pi$
$23$	1792.86	0.706688	0.353344	+	0.935493i	$0.385045\pi$
$24$	−1377.52	−0.488168
$25$	7562.75	2.42008
$26$	1700.65	0.493381
$27$	729.000	0.192450
$28$	894.605	0.215643
$29$	3144.99	0.694422	0.347211	−	0.937787i	$-0.387129\pi$
$29$	3144.99	0.694422	0.347211	+	0.937787i	$0.387129\pi$
$30$	−5863.35	−1.18944
$31$	867.512	0.162133	0.0810665	−	0.996709i	$-0.474167\pi$
$31$	867.512	0.162133	0.0810665	+	0.996709i	$0.474167\pi$
$32$	−2735.49	−0.472236
$33$	−5023.86	−0.803069
$34$	14144.7	2.09844
$35$	−11992.7	−1.65481
$36$	624.658	0.0803315
$37$	−994.784	−0.119461	−0.0597303	−	0.998215i	$-0.519024\pi$
$37$	−994.784	−0.119461	−0.0597303	+	0.998215i	$0.519024\pi$
$38$	16615.7	1.86664
$39$	2428.84	0.255703
$40$	15823.3	1.56368
$41$	−16088.9	−1.49474	−0.747371	−	0.664407i	$-0.768684\pi$
$41$	−16088.9	−1.49474	−0.747371	+	0.664407i	$0.768684\pi$
$42$	6579.25	0.575511
$43$	10233.9	0.844057	0.422029	−	0.906583i	$-0.361318\pi$
$43$	10233.9	0.844057	0.422029	+	0.906583i	$0.361318\pi$
$44$	−4304.79	−0.335213
$45$	−8373.91	−0.616448
$46$	11298.1	0.787250
$47$	−17669.6	−1.16676	−0.583382	−	0.812198i	$-0.698271\pi$
$47$	−17669.6	−1.16676	−0.583382	+	0.812198i	$0.698271\pi$
$48$	−10901.8	−0.682957
$49$	−3350.00	−0.199322
$50$	47658.4	2.69597
$51$	20201.1	1.08755
$52$	2081.20	0.106734
$53$	10580.8	0.517403	0.258701	−	0.965957i	$-0.416705\pi$
$53$	10580.8	0.517403	0.258701	+	0.965957i	$0.416705\pi$
$54$	4593.96	0.214389
$55$	57708.3	2.57236
$56$	−17755.3	−0.756587
$57$	23730.2	0.967420
$58$	19818.9	0.773586
$59$	38030.1	1.42232	0.711160	−	0.703030i	$-0.248170\pi$
$59$	38030.1	1.42232	0.711160	+	0.703030i	$0.248170\pi$
$60$	−7175.35	−0.257315
$61$	1978.21	0.0680687	0.0340343	−	0.999421i	$-0.489164\pi$
$61$	1978.21	0.0680687	0.0340343	+	0.999421i	$0.489164\pi$
$62$	5466.83	0.180616
$63$	9396.35	0.298269
$64$	21523.5	0.656845
$65$	−27899.6	−0.819059
$66$	−31659.0	−0.894618
$67$	38875.8	1.05802	0.529008	−	0.848617i	$-0.322564\pi$
$67$	38875.8	1.05802	0.529008	+	0.848617i	$0.322564\pi$
$68$	17309.7	0.453961
$69$	16135.8	0.408006
$70$	−75574.8	−1.84345
$71$	−58523.3	−1.37779	−0.688895	−	0.724861i	$-0.741904\pi$
$71$	−58523.3	−1.37779	−0.688895	+	0.724861i	$0.741904\pi$
$72$	−12397.7	−0.281844
$73$	−5034.93	−0.110582	−0.0552912	−	0.998470i	$-0.517609\pi$
$73$	−5034.93	−0.110582	−0.0552912	+	0.998470i	$0.517609\pi$
$74$	−6268.86	−0.133079
$75$	68064.7	1.39723
$76$	20333.7	0.403816
$77$	−64754.4	−1.24464
$78$	15305.9	0.284853
$79$	64703.6	1.16643	0.583217	−	0.812316i	$-0.301794\pi$
$79$	64703.6	1.16643	0.583217	+	0.812316i	$0.301794\pi$
$80$	125227.	2.18762
$81$	6561.00	0.111111
$82$	−101388.	−1.66514
$83$	−52140.3	−0.830766	−0.415383	−	0.909647i	$-0.636352\pi$
$83$	−52140.3	−0.830766	−0.415383	+	0.909647i	$0.636352\pi$
$84$	8051.45	0.124502
$85$	−232047.	−3.48360
$86$	64491.6	0.940279
$87$	28304.9	0.400925
$88$	85437.7	1.17610
$89$	75368.8	1.00859	0.504297	−	0.863530i	$-0.331752\pi$
$89$	75368.8	1.00859	0.504297	+	0.863530i	$0.331752\pi$
$90$	−52770.1	−0.686723
$91$	31306.2	0.396302
$92$	13826.3	0.170308
$93$	7807.61	0.0936075
$94$	−111349.	−1.29977
$95$	−272585.	−3.09880
$96$	−24619.4	−0.272646
$97$	−39391.1	−0.425078	−0.212539	−	0.977153i	$-0.568173\pi$
$97$	−39391.1	−0.425078	−0.212539	+	0.977153i	$0.568173\pi$
$98$	−21110.8	−0.222044
$99$	−45214.7	−0.463652
$100$	58322.6	0.583226
$101$	21820.6	0.212845	0.106422	−	0.994321i	$-0.466060\pi$
$101$	21820.6	0.212845	0.106422	+	0.994321i	$0.466060\pi$
$102$	127302.	1.21153
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	−41305.7	−0.374479
$105$	−107934.	−0.955403
$106$	66677.4	0.576386
$107$	85318.3	0.720415	0.360208	−	0.932872i	$-0.382706\pi$
$107$	85318.3	0.720415	0.360208	+	0.932872i	$0.382706\pi$
$108$	5621.92	0.0463794
$109$	98738.4	0.796012	0.398006	−	0.917383i	$-0.369702\pi$
$109$	98738.4	0.796012	0.398006	+	0.917383i	$0.369702\pi$
$110$	363662.	2.86560
$111$	−8953.06	−0.0689706
$112$	−140517.	−1.05848
$113$	114958.	0.846918	0.423459	−	0.905915i	$-0.360816\pi$
$113$	114958.	0.846918	0.423459	+	0.905915i	$0.360816\pi$
$114$	149542.	1.07771
$115$	−185349.	−1.30691
$116$	24253.6	0.167352
$117$	21859.5	0.147630
$118$	239656.	1.58446
$119$	260380.	1.68554
$120$	142410.	0.902791
$121$	150544.	0.934757
$122$	12466.1	0.0758285
$123$	−144800.	−0.862990
$124$	6690.10	0.0390732
$125$	−458781.	−2.62622
$126$	59213.3	0.332271
$127$	330124.	1.81622	0.908109	−	0.418734i	$-0.137526\pi$
$127$	330124.	1.81622	0.908109	+	0.418734i	$0.137526\pi$
$128$	223171.	1.20396
$129$	92105.5	0.487317
$130$	−175816.	−0.912431
$131$	346039.	1.76176	0.880880	−	0.473339i	$-0.156951\pi$
$131$	346039.	1.76176	0.880880	+	0.473339i	$0.156951\pi$
$132$	−38743.1	−0.193535
$133$	305868.	1.49936
$134$	244985.	1.17863
$135$	−75365.2	−0.355907
$136$	−343548.	−1.59272
$137$	−233444.	−1.06263	−0.531313	−	0.847176i	$-0.678301\pi$
$137$	−233444.	−1.06263	−0.531313	+	0.847176i	$0.678301\pi$
$138$	101683.	0.454519
$139$	−256507.	−1.12606	−0.563031	−	0.826436i	$-0.690365\pi$
$139$	−256507.	−1.12606	−0.563031	+	0.826436i	$0.690365\pi$
$140$	−92485.7	−0.398799
$141$	−159027.	−0.673632
$142$	−368798.	−1.53486
$143$	−150644.	−0.616042
$144$	−98115.8	−0.394305
$145$	−325134.	−1.28423
$146$	−31728.8	−0.123189
$147$	−30150.0	−0.115078
$148$	−7671.60	−0.0287894
$149$	184024.	0.679061	0.339531	−	0.940595i	$-0.389732\pi$
$149$	184024.	0.679061	0.339531	+	0.940595i	$0.389732\pi$
$150$	428926.	1.55652
$151$	−386946.	−1.38105	−0.690523	−	0.723310i	$-0.742620\pi$
$151$	−386946.	−1.38105	−0.690523	+	0.723310i	$0.742620\pi$
$152$	−403566.	−1.41679
$153$	181810.	0.627899
$154$	−408065.	−1.38652
$155$	−89684.8	−0.299840
$156$	18730.8	0.0616232
$157$	172060.	0.557097	0.278549	−	0.960422i	$-0.410147\pi$
$157$	172060.	0.557097	0.278549	+	0.960422i	$0.410147\pi$
$158$	407745.	1.29941
$159$	95227.2	0.298723
$160$	282799.	0.873328
$161$	207980.	0.632349
$162$	41345.7	0.123778
$163$	203270.	0.599244	0.299622	−	0.954058i	$-0.403139\pi$
$163$	203270.	0.599244	0.299622	+	0.954058i	$0.403139\pi$
$164$	−124075.	−0.360225
$165$	519374.	1.48515
$166$	−328574.	−0.925472
$167$	6896.14	0.0191344	0.00956720	−	0.999954i	$-0.496955\pi$
$167$	6896.14	0.0191344	0.00956720	+	0.999954i	$0.496955\pi$
$168$	−159798.	−0.436816
$169$	−298463.	−0.803847
$170$	−1.46230e6	−3.88073
$171$	213572.	0.558540
$172$	78922.4	0.203413
$173$	443784.	1.12734	0.563671	−	0.825999i	$-0.309388\pi$
$173$	443784.	1.12734	0.563671	+	0.825999i	$0.309388\pi$
$174$	178370.	0.446630
$175$	877311.	2.16550
$176$	676159.	1.64538
$177$	342271.	0.821177
$178$	474954.	1.12357
$179$	−179499.	−0.418726	−0.209363	−	0.977838i	$-0.567139\pi$
$179$	−179499.	−0.418726	−0.209363	+	0.977838i	$0.567139\pi$
$180$	−64578.1	−0.148561
$181$	−417026.	−0.946165	−0.473082	−	0.881018i	$-0.656859\pi$
$181$	−417026.	−0.946165	−0.473082	+	0.881018i	$0.656859\pi$
$182$	197283.	0.441480
$183$	17803.9	0.0392995
$184$	−274411.	−0.597527
$185$	102842.	0.220924
$186$	49201.5	0.104279
$187$	−1.25293e6	−2.62014
$188$	−136265.	−0.281184
$189$	84567.1	0.172206
$190$	−1.71776e6	−3.45206
$191$	−599025.	−1.18812	−0.594061	−	0.804420i	$-0.702476\pi$
$191$	−599025.	−1.18812	−0.594061	+	0.804420i	$0.702476\pi$
$192$	193712.	0.379230
$193$	601412.	1.16219	0.581097	−	0.813834i	$-0.302624\pi$
$193$	601412.	1.16219	0.581097	+	0.813834i	$0.302624\pi$
$194$	−248232.	−0.473536
$195$	−251097.	−0.472884
$196$	−25834.6	−0.0480355
$197$	−181318.	−0.332871	−0.166435	−	0.986052i	$-0.553226\pi$
$197$	−181318.	−0.332871	−0.166435	+	0.986052i	$0.553226\pi$
$198$	−284931.	−0.516508
$199$	475979.	0.852030	0.426015	−	0.904716i	$-0.359917\pi$
$199$	475979.	0.852030	0.426015	+	0.904716i	$0.359917\pi$
$200$	−1.15754e6	−2.04625
$201$	349882.	0.610846
$202$	137507.	0.237109
$203$	364832.	0.621373
$204$	155788.	0.262094
$205$	1.66329e6	2.76429
$206$	−66855.1	−0.109766
$207$	145222.	0.235563
$208$	−326896.	−0.523903
$209$	−1.47182e6	−2.33071
$210$	−680173.	−1.06432
$211$	780645.	1.20711	0.603556	−	0.797321i	$-0.293750\pi$
$211$	780645.	1.20711	0.603556	+	0.797321i	$0.293750\pi$
$212$	81597.3	0.124691
$213$	−526710.	−0.795467
$214$	537653.	0.802542
$215$	−1.05800e6	−1.56095
$216$	−111579.	−0.162723
$217$	100635.	0.145078
$218$	622223.	0.886757
$219$	−45314.4	−0.0638448
$220$	445036.	0.619924
$221$	605743.	0.834272
$222$	−56419.8	−0.0768332
$223$	191775.	0.258243	0.129122	−	0.991629i	$-0.458784\pi$
$223$	191775.	0.258243	0.129122	+	0.991629i	$0.458784\pi$
$224$	−317328.	−0.422560
$225$	612582.	0.806693
$226$	724431.	0.943466
$227$	619000.	0.797308	0.398654	−	0.917102i	$-0.369478\pi$
$227$	619000.	0.797308	0.398654	+	0.917102i	$0.369478\pi$
$228$	183004.	0.233143
$229$	−705382.	−0.888865	−0.444433	−	0.895812i	$-0.646595\pi$
$229$	−705382.	−0.888865	−0.444433	+	0.895812i	$0.646595\pi$
$230$	−1.16802e6	−1.45590
$231$	−582789.	−0.718591
$232$	−481364.	−0.587156
$233$	1.12175e6	1.35365	0.676826	−	0.736143i	$-0.263355\pi$
$233$	1.12175e6	1.35365	0.676826	+	0.736143i	$0.263355\pi$
$234$	137753.	0.164460
$235$	1.82671e6	2.15775
$236$	293282.	0.342772
$237$	582332.	0.673442
$238$	1.64084e6	1.87769
$239$	−888097.	−1.00569	−0.502847	−	0.864376i	$-0.667714\pi$
$239$	−888097.	−1.00569	−0.502847	+	0.864376i	$0.667714\pi$
$240$	1.12704e6	1.26302
$241$	−57744.1	−0.0640420	−0.0320210	−	0.999487i	$-0.510194\pi$
$241$	−57744.1	−0.0640420	−0.0320210	+	0.999487i	$0.510194\pi$
$242$	948685.	1.04132
$243$	59049.0	0.0641500
$244$	15255.6	0.0164042
$245$	346328.	0.368615
$246$	−912491.	−0.961370
$247$	711566.	0.742118
$248$	−132779.	−0.137089
$249$	−469263.	−0.479643
$250$	−2.89112e6	−2.92560
$251$	−1.61551e6	−1.61854	−0.809271	−	0.587435i	$-0.800138\pi$
$251$	−1.61551e6	−1.61854	−0.809271	+	0.587435i	$0.800138\pi$
$252$	72463.0	0.0718812
$253$	−1.00079e6	−0.982971
$254$	2.08035e6	2.02327
$255$	−2.08842e6	−2.01126
$256$	717611.	0.684367
$257$	−1.15956e6	−1.09511	−0.547557	−	0.836768i	$-0.684442\pi$
$257$	−1.15956e6	−1.09511	−0.547557	+	0.836768i	$0.684442\pi$
$258$	580424.	0.542870
$259$	−115399.	−0.106894
$260$	−215157.	−0.197389
$261$	254744.	0.231474
$262$	2.18065e6	1.96260
$263$	−766621.	−0.683426	−0.341713	−	0.939804i	$-0.611007\pi$
$263$	−766621.	−0.683426	−0.341713	+	0.939804i	$0.611007\pi$
$264$	768940.	0.679020
$265$	−1.09386e6	−0.956857
$266$	1.92750e6	1.67028
$267$	678319.	0.582312
$268$	299803.	0.254976
$269$	1.78793e6	1.50650	0.753250	−	0.657734i	$-0.228485\pi$
$269$	1.78793e6	1.50650	0.753250	+	0.657734i	$0.228485\pi$
$270$	−474931.	−0.396480
$271$	−1.21947e6	−1.00867	−0.504333	−	0.863509i	$-0.668262\pi$
$271$	−1.21947e6	−1.00867	−0.504333	+	0.863509i	$0.668262\pi$
$272$	−2.71886e6	−2.22825
$273$	281755.	0.228805
$274$	−1.47110e6	−1.18376
$275$	−4.22157e6	−3.36622
$276$	124436.	0.0983274
$277$	−864257.	−0.676774	−0.338387	−	0.941007i	$-0.609881\pi$
$277$	−864257.	−0.676774	−0.338387	+	0.941007i	$0.609881\pi$
$278$	−1.61644e6	−1.25443
$279$	70268.5	0.0540443
$280$	1.83557e6	1.39919
$281$	1.77830e6	1.34350	0.671752	−	0.740776i	$-0.265542\pi$
$281$	1.77830e6	1.34350	0.671752	+	0.740776i	$0.265542\pi$
$282$	−1.00214e6	−0.750425
$283$	−1.17394e6	−0.871327	−0.435663	−	0.900110i	$-0.643486\pi$
$283$	−1.17394e6	−0.871327	−0.435663	+	0.900110i	$0.643486\pi$
$284$	−451322.	−0.332040
$285$	−2.45327e6	−1.78909
$286$	−949315.	−0.686271
$287$	−1.86638e6	−1.33750
$288$	−221574.	−0.157412
$289$	3.61823e6	2.54831
$290$	−2.04890e6	−1.43063
$291$	−354520.	−0.245419
$292$	−38828.5	−0.0266498
$293$	1.63258e6	1.11098	0.555489	−	0.831524i	$-0.312531\pi$
$293$	1.63258e6	1.11098	0.555489	+	0.831524i	$0.312531\pi$
$294$	−189997.	−0.128197
$295$	−3.93161e6	−2.63036
$296$	152259.	0.101008
$297$	−406933.	−0.267690
$298$	1.15967e6	0.756474
$299$	483841.	0.312986
$300$	524903.	0.336726
$301$	1.18718e6	0.755268
$302$	−2.43843e6	−1.53848
$303$	196385.	0.122886
$304$	−3.19384e6	−1.98212
$305$	−204510.	−0.125883
$306$	1.14572e6	0.699479
$307$	1.27949e6	0.774801	0.387401	−	0.921911i	$-0.373373\pi$
$307$	1.27949e6	0.774801	0.387401	+	0.921911i	$0.373373\pi$
$308$	−499375.	−0.299950
$309$	−95481.0	−0.0568880
$310$	−565169.	−0.334021
$311$	−385118.	−0.225784	−0.112892	−	0.993607i	$-0.536011\pi$
$311$	−385118.	−0.225784	−0.112892	+	0.993607i	$0.536011\pi$
$312$	−371752.	−0.216205
$313$	452183.	0.260888	0.130444	−	0.991456i	$-0.458360\pi$
$313$	452183.	0.260888	0.130444	+	0.991456i	$0.458360\pi$
$314$	1.08428e6	0.620606
$315$	−971409.	−0.551602
$316$	498983.	0.281105
$317$	−1.02167e6	−0.571032	−0.285516	−	0.958374i	$-0.592165\pi$
$317$	−1.02167e6	−0.571032	−0.285516	+	0.958374i	$0.592165\pi$
$318$	600096.	0.332777
$319$	−1.75555e6	−0.965911
$320$	−2.22513e6	−1.21473
$321$	767865.	0.415932
$322$	1.31063e6	0.704436
$323$	5.91824e6	3.15636
$324$	50597.3	0.0267772
$325$	2.04096e6	1.07183
$326$	1.28095e6	0.667558
$327$	888646.	0.459578
$328$	2.46253e6	1.26385
$329$	−2.04975e6	−1.04403
$330$	3.27296e6	1.65446
$331$	−3.73031e6	−1.87143	−0.935717	−	0.352751i	$-0.885246\pi$
$331$	−3.73031e6	−1.87143	−0.935717	+	0.352751i	$0.885246\pi$
$332$	−402097.	−0.200210
$333$	−80577.5	−0.0398202
$334$	43457.6	0.0213157
$335$	−4.01904e6	−1.95664
$336$	−1.26465e6	−0.611114
$337$	3.94187e6	1.89072	0.945362	−	0.326024i	$-0.105709\pi$
$337$	3.94187e6	1.89072	0.945362	+	0.326024i	$0.105709\pi$
$338$	−1.88083e6	−0.895485
$339$	1.03462e6	0.488968
$340$	−1.78951e6	−0.839530
$341$	−484251.	−0.225520
$342$	1.34587e6	0.622213
$343$	−2.33830e6	−1.07316
$344$	−1.56638e6	−0.713677
$345$	−1.66814e6	−0.754545
$346$	2.79661e6	1.25586
$347$	−2.71003e6	−1.20823	−0.604115	−	0.796897i	$-0.706473\pi$
$347$	−2.71003e6	−1.20823	−0.604115	+	0.796897i	$0.706473\pi$
$348$	218282.	0.0966208
$349$	1.21757e6	0.535094	0.267547	−	0.963545i	$-0.413787\pi$
$349$	1.21757e6	0.535094	0.267547	+	0.963545i	$0.413787\pi$
$350$	5.52858e6	2.41237
$351$	196736.	0.0852345
$352$	1.52697e6	0.656860
$353$	−1.95357e6	−0.834434	−0.417217	−	0.908807i	$-0.636994\pi$
$353$	−1.95357e6	−0.834434	−0.417217	+	0.908807i	$0.636994\pi$
$354$	2.15690e6	0.914791
$355$	6.05023e6	2.54801
$356$	581231.	0.243066
$357$	2.34342e6	0.973148
$358$	−1.13115e6	−0.466460
$359$	1.40052e6	0.573525	0.286762	−	0.958002i	$-0.407421\pi$
$359$	1.40052e6	0.573525	0.286762	+	0.958002i	$0.407421\pi$
$360$	1.28169e6	0.521227
$361$	4.47605e6	1.80770
$362$	−2.62799e6	−1.05403
$363$	1.35489e6	0.539682
$364$	241428.	0.0955066
$365$	520519.	0.204505
$366$	112195.	0.0437796
$367$	4.41079e6	1.70943	0.854715	−	0.519098i	$-0.173732\pi$
$367$	4.41079e6	1.70943	0.854715	+	0.519098i	$0.173732\pi$
$368$	−2.17171e6	−0.835953
$369$	−1.30320e6	−0.498247
$370$	648085.	0.246109
$371$	1.22742e6	0.462975
$372$	60210.9	0.0225589
$373$	−2.15700e6	−0.802745	−0.401372	−	0.915915i	$-0.631467\pi$
$373$	−2.15700e6	−0.802745	−0.401372	+	0.915915i	$0.631467\pi$
$374$	−7.89565e6	−2.91883
$375$	−4.12903e6	−1.51625
$376$	2.70447e6	0.986536
$377$	848739.	0.307554
$378$	532919.	0.191837
$379$	2.52758e6	0.903873	0.451937	−	0.892050i	$-0.350733\pi$
$379$	2.52758e6	0.903873	0.451937	+	0.892050i	$0.350733\pi$
$380$	−2.10213e6	−0.746794
$381$	2.97112e6	1.04859
$382$	−3.77489e6	−1.32357
$383$	−4.09496e6	−1.42644	−0.713219	−	0.700941i	$-0.752764\pi$
$383$	−4.09496e6	−1.42644	−0.713219	+	0.700941i	$0.752764\pi$
$384$	2.00854e6	0.695107
$385$	6.69441e6	2.30176
$386$	3.78994e6	1.29468
$387$	828949.	0.281352
$388$	−303777.	−0.102441
$389$	475571.	0.159346	0.0796731	−	0.996821i	$-0.474612\pi$
$389$	475571.	0.159346	0.0796731	+	0.996821i	$0.474612\pi$
$390$	−1.58234e6	−0.526792
$391$	4.02421e6	1.33118
$392$	512743.	0.168533
$393$	3.11435e6	1.01715
$394$	−1.14262e6	−0.370818
$395$	−6.68916e6	−2.15714
$396$	−348688.	−0.111738
$397$	1.01263e6	0.322460	0.161230	−	0.986917i	$-0.448454\pi$
$397$	1.01263e6	0.322460	0.161230	+	0.986917i	$0.448454\pi$
$398$	2.99949e6	0.949161
$399$	2.75281e6	0.865653
$400$	−9.16080e6	−2.86275
$401$	753052.	0.233864	0.116932	−	0.993140i	$-0.462694\pi$
$401$	753052.	0.233864	0.116932	+	0.993140i	$0.462694\pi$
$402$	2.20486e6	0.680482
$403$	234116.	0.0718073
$404$	168276.	0.0512944
$405$	−678286.	−0.205483
$406$	2.29907e6	0.692210
$407$	555295.	0.166164
$408$	−3.09193e6	−0.919560
$409$	−1.02074e6	−0.301721	−0.150861	−	0.988555i	$-0.548204\pi$
$409$	−1.02074e6	−0.301721	−0.150861	+	0.988555i	$0.548204\pi$
$410$	1.04816e7	3.07942
$411$	−2.10099e6	−0.613507
$412$	−81814.8	−0.0237459
$413$	4.41166e6	1.27270
$414$	915150.	0.262417
$415$	5.39035e6	1.53637
$416$	−738227.	−0.209149
$417$	−2.30856e6	−0.650132
$418$	−9.27501e6	−2.59641
$419$	5.15830e6	1.43539	0.717697	−	0.696355i	$-0.245196\pi$
$419$	5.15830e6	1.43539	0.717697	+	0.696355i	$0.245196\pi$
$420$	−832371.	−0.230247
$421$	−3.92452e6	−1.07915	−0.539574	−	0.841938i	$-0.681415\pi$
$421$	−3.92452e6	−1.07915	−0.539574	+	0.841938i	$0.681415\pi$
$422$	4.91942e6	1.34472
$423$	−1.43124e6	−0.388921
$424$	−1.61947e6	−0.437480
$425$	1.69751e7	4.55869
$426$	−3.31918e6	−0.886150
$427$	229481.	0.0609083
$428$	657960.	0.173616
$429$	−1.35579e6	−0.355672
$430$	−6.66724e6	−1.73890
$431$	−493934.	−0.128078	−0.0640391	−	0.997947i	$-0.520398\pi$
$431$	−493934.	−0.128078	−0.0640391	+	0.997947i	$0.520398\pi$
$432$	−883042.	−0.227652
$433$	−5.87148e6	−1.50497	−0.752485	−	0.658610i	$-0.771145\pi$
$433$	−5.87148e6	−1.50497	−0.752485	+	0.658610i	$0.771145\pi$
$434$	634176.	0.161616
$435$	−2.92620e6	−0.741449
$436$	761454.	0.191835
$437$	4.72723e6	1.18414
$438$	−285559.	−0.0711231
$439$	−2.41517e6	−0.598118	−0.299059	−	0.954235i	$-0.596673\pi$
$439$	−2.41517e6	−0.598118	−0.299059	+	0.954235i	$0.596673\pi$
$440$	−8.83269e6	−2.17501
$441$	−271350.	−0.0664406
$442$	3.81723e6	0.929379
$443$	−3.66851e6	−0.888137	−0.444069	−	0.895993i	$-0.646465\pi$
$443$	−3.66851e6	−0.888137	−0.444069	+	0.895993i	$0.646465\pi$
$444$	−69044.4	−0.0166215
$445$	−7.79174e6	−1.86524
$446$	1.20851e6	0.287683
$447$	1.65622e6	0.392056
$448$	2.49682e6	0.587749
$449$	−3.74039e6	−0.875591	−0.437795	−	0.899075i	$-0.644241\pi$
$449$	−3.74039e6	−0.875591	−0.437795	+	0.899075i	$0.644241\pi$
$450$	3.86033e6	0.898655
$451$	8.98092e6	2.07912
$452$	886533.	0.204103
$453$	−3.48252e6	−0.797347
$454$	3.90077e6	0.888200
$455$	−3.23648e6	−0.732899
$456$	−3.63209e6	−0.817984
$457$	4.29721e6	0.962490	0.481245	−	0.876586i	$-0.340185\pi$
$457$	4.29721e6	0.962490	0.481245	+	0.876586i	$0.340185\pi$
$458$	−4.44513e6	−0.990195
$459$	1.63629e6	0.362517
$460$	−1.42938e6	−0.314958
$461$	2.17799e6	0.477313	0.238656	−	0.971104i	$-0.423293\pi$
$461$	2.17799e6	0.477313	0.238656	+	0.971104i	$0.423293\pi$
$462$	−3.67258e6	−0.800510
$463$	−3.09281e6	−0.670504	−0.335252	−	0.942128i	$-0.608821\pi$
$463$	−3.09281e6	−0.670504	−0.335252	+	0.942128i	$0.608821\pi$
$464$	−3.80954e6	−0.821444
$465$	−807163.	−0.173113
$466$	7.06898e6	1.50797
$467$	7.54363e6	1.60062	0.800310	−	0.599586i	$-0.204668\pi$
$467$	7.54363e6	1.60062	0.800310	+	0.599586i	$0.204668\pi$
$468$	168577.	0.0355781
$469$	4.50976e6	0.946719
$470$	1.15115e7	2.40373
$471$	1.54854e6	0.321640
$472$	−5.82080e6	−1.20262
$473$	−5.71265e6	−1.17405
$474$	3.66970e6	0.750213
$475$	1.99406e7	4.05513
$476$	2.00800e6	0.406207
$477$	857045.	0.172468
$478$	−5.59655e6	−1.12034
$479$	−982890.	−0.195734	−0.0978670	−	0.995200i	$-0.531202\pi$
$479$	−982890.	−0.195734	−0.0978670	+	0.995200i	$0.531202\pi$
$480$	2.54519e6	0.504216
$481$	−268463.	−0.0529081
$482$	−363888.	−0.0713427
$483$	1.87182e6	0.365087
$484$	1.16097e6	0.225271
$485$	4.07231e6	0.786116
$486$	372111.	0.0714631
$487$	9.43659e6	1.80299	0.901494	−	0.432792i	$-0.142472\pi$
$487$	9.43659e6	1.80299	0.901494	+	0.432792i	$0.142472\pi$
$488$	−302780.	−0.0575542
$489$	1.82943e6	0.345974
$490$	2.18247e6	0.410637
$491$	−5.01452e6	−0.938697	−0.469348	−	0.883013i	$-0.655511\pi$
$491$	−5.01452e6	−0.938697	−0.469348	+	0.883013i	$0.655511\pi$
$492$	−1.11667e6	−0.207976
$493$	7.05914e6	1.30808
$494$	4.48410e6	0.826719
$495$	4.67437e6	0.857452
$496$	−1.05082e6	−0.191790
$497$	−6.78896e6	−1.23286
$498$	−2.95717e6	−0.534322
$499$	−6.38635e6	−1.14816	−0.574078	−	0.818800i	$-0.694639\pi$
$499$	−6.38635e6	−1.14816	−0.574078	+	0.818800i	$0.694639\pi$
$500$	−3.53804e6	−0.632904
$501$	62065.3	0.0110473
$502$	−1.01805e7	−1.80306
$503$	7.12379e6	1.25543	0.627713	−	0.778445i	$-0.283991\pi$
$503$	7.12379e6	1.25543	0.627713	+	0.778445i	$0.283991\pi$
$504$	−1.43818e6	−0.252196
$505$	−2.25584e6	−0.393623
$506$	−6.30670e6	−1.09503
$507$	−2.68617e6	−0.464101
$508$	2.54586e6	0.437699
$509$	−4.03653e6	−0.690580	−0.345290	−	0.938496i	$-0.612219\pi$
$509$	−4.03653e6	−0.690580	−0.345290	+	0.938496i	$0.612219\pi$
$510$	−1.31607e7	−2.24054
$511$	−584073.	−0.0989499
$512$	−2.61928e6	−0.441577
$513$	1.92215e6	0.322473
$514$	−7.30722e6	−1.21996
$515$	1.09677e6	0.182221
$516$	710302.	0.117441
$517$	9.86331e6	1.62292
$518$	−727215.	−0.119080
$519$	3.99405e6	0.650872
$520$	4.27025e6	0.692540
$521$	−422052.	−0.0681196	−0.0340598	−	0.999420i	$-0.510844\pi$
$521$	−422052.	−0.0681196	−0.0340598	+	0.999420i	$0.510844\pi$
$522$	1.60533e6	0.257862
$523$	−3.33896e6	−0.533773	−0.266887	−	0.963728i	$-0.585995\pi$
$523$	−3.33896e6	−0.533773	−0.266887	+	0.963728i	$0.585995\pi$
$524$	2.66859e6	0.424575
$525$	7.89580e6	1.25025
$526$	−4.83104e6	−0.761336
$527$	1.94719e6	0.305409
$528$	6.08543e6	0.949963
$529$	−3.22198e6	−0.500592
$530$	−6.89321e6	−1.06594
$531$	3.08044e6	0.474107
$532$	2.35880e6	0.361337
$533$	−4.34192e6	−0.662008
$534$	4.27459e6	0.648695
$535$	−8.82034e6	−1.33230
$536$	−5.95023e6	−0.894586
$537$	−1.61549e6	−0.241751
$538$	1.12670e7	1.67824
$539$	1.86999e6	0.277248
$540$	−581203.	−0.0857716
$541$	−4.88056e6	−0.716929	−0.358464	−	0.933543i	$-0.616700\pi$
$541$	−4.88056e6	−0.716929	−0.358464	+	0.933543i	$0.616700\pi$
$542$	−7.68477e6	−1.12365
$543$	−3.75323e6	−0.546268
$544$	−6.13999e6	−0.889550
$545$	−1.02077e7	−1.47210
$546$	1.77555e6	0.254889
$547$	3.01327e6	0.430596	0.215298	−	0.976548i	$-0.430928\pi$
$547$	3.01327e6	0.430596	0.215298	+	0.976548i	$0.430928\pi$
$548$	−1.80028e6	−0.256087
$549$	160235.	0.0226896
$550$	−2.66032e7	−3.74997
$551$	8.29236e6	1.16359
$552$	−2.46970e6	−0.344982
$553$	7.50589e6	1.04373
$554$	−5.44632e6	−0.753925
$555$	925581.	0.127550
$556$	−1.97814e6	−0.271375
$557$	4.00845e6	0.547443	0.273722	−	0.961809i	$-0.411745\pi$
$557$	4.00845e6	0.547443	0.273722	+	0.961809i	$0.411745\pi$
$558$	442813.	0.0602053
$559$	2.76184e6	0.373826
$560$	1.45268e7	1.95750
$561$	−1.12764e7	−1.51274
$562$	1.12064e7	1.49666
$563$	3.69525e6	0.491329	0.245665	−	0.969355i	$-0.420994\pi$
$563$	3.69525e6	0.491329	0.245665	+	0.969355i	$0.420994\pi$
$564$	−1.22639e6	−0.162342
$565$	−1.18845e7	−1.56624
$566$	−7.39788e6	−0.970657
$567$	761104.	0.0994229
$568$	8.95744e6	1.16496
$569$	891414.	0.115425	0.0577124	−	0.998333i	$-0.481619\pi$
$569$	891414.	0.115425	0.0577124	+	0.998333i	$0.481619\pi$
$570$	−1.54598e7	−1.99305
$571$	4.29472e6	0.551245	0.275623	−	0.961266i	$-0.411116\pi$
$571$	4.29472e6	0.551245	0.275623	+	0.961266i	$0.411116\pi$
$572$	−1.16174e6	−0.148463
$573$	−5.39122e6	−0.685963
$574$	−1.17614e7	−1.48998
$575$	1.35590e7	1.71024
$576$	1.74340e6	0.218948
$577$	−5.71859e6	−0.715072	−0.357536	−	0.933899i	$-0.616383\pi$
$577$	−5.71859e6	−0.715072	−0.357536	+	0.933899i	$0.616383\pi$
$578$	2.28011e7	2.83881
$579$	5.41271e6	0.670993
$580$	−2.50737e6	−0.309492
$581$	−6.04850e6	−0.743374
$582$	−2.23409e6	−0.273396
$583$	−5.90627e6	−0.719684
$584$	770634.	0.0935009
$585$	−2.25987e6	−0.273020
$586$	1.02881e7	1.23763
$587$	7.50389e6	0.898859	0.449429	−	0.893316i	$-0.351627\pi$
$587$	7.50389e6	0.898859	0.449429	+	0.893316i	$0.351627\pi$
$588$	−232512.	−0.0277333
$589$	2.28736e6	0.271673
$590$	−2.47760e7	−2.93022
$591$	−1.63186e6	−0.192183
$592$	1.20499e6	0.141312
$593$	1.64427e7	1.92016	0.960079	−	0.279728i	$-0.0902443\pi$
$593$	1.64427e7	1.92016	0.960079	+	0.279728i	$0.0902443\pi$
$594$	−2.56438e6	−0.298206
$595$	−2.69185e7	−3.11715
$596$	1.41916e6	0.163650
$597$	4.28381e6	0.491920
$598$	3.04904e6	0.348666
$599$	−4.16887e6	−0.474735	−0.237367	−	0.971420i	$-0.576285\pi$
$599$	−4.16887e6	−0.474735	−0.237367	+	0.971420i	$0.576285\pi$
$600$	−1.04178e7	−1.18140
$601$	−3.61110e6	−0.407805	−0.203903	−	0.978991i	$-0.565363\pi$
$601$	−3.61110e6	−0.407805	−0.203903	+	0.978991i	$0.565363\pi$
$602$	7.48130e6	0.841368
$603$	3.14894e6	0.352672
$604$	−2.98406e6	−0.332825
$605$	−1.55634e7	−1.72869
$606$	1.23757e6	0.136895
$607$	−1.62756e7	−1.79294	−0.896469	−	0.443106i	$-0.853876\pi$
$607$	−1.62756e7	−1.79294	−0.896469	+	0.443106i	$0.853876\pi$
$608$	−7.21264e6	−0.791289
$609$	3.28349e6	0.358750
$610$	−1.28877e6	−0.140233
$611$	−4.76852e6	−0.516750
$612$	1.40209e6	0.151320
$613$	−2.91754e6	−0.313592	−0.156796	−	0.987631i	$-0.550117\pi$
$613$	−2.91754e6	−0.313592	−0.156796	+	0.987631i	$0.550117\pi$
$614$	8.06299e6	0.863128
$615$	1.49696e7	1.59597
$616$	9.91114e6	1.05238
$617$	4.51384e6	0.477345	0.238673	−	0.971100i	$-0.423288\pi$
$617$	4.51384e6	0.477345	0.238673	+	0.971100i	$0.423288\pi$
$618$	−601696.	−0.0633732
$619$	1.01636e7	1.06615	0.533076	−	0.846067i	$-0.321036\pi$
$619$	1.01636e7	1.06615	0.533076	+	0.846067i	$0.321036\pi$
$620$	−691633.	−0.0722598
$621$	1.30700e6	0.136002
$622$	−2.42691e6	−0.251523
$623$	8.74310e6	0.902496
$624$	−2.94206e6	−0.302476
$625$	2.37959e7	2.43670
$626$	2.84954e6	0.290629
$627$	−1.32464e7	−1.34564
$628$	1.32690e6	0.134257
$629$	−2.23286e6	−0.225027
$630$	−6.12156e6	−0.614484
$631$	−1.86727e7	−1.86695	−0.933475	−	0.358642i	$-0.883240\pi$
$631$	−1.86727e7	−1.86695	−0.933475	+	0.358642i	$0.883240\pi$
$632$	−9.90337e6	−0.986258
$633$	7.02581e6	0.696927
$634$	−6.43826e6	−0.636130
$635$	−3.41287e7	−3.35881
$636$	734376.	0.0719906
$637$	−904067.	−0.0882779
$638$	−1.10630e7	−1.07602
$639$	−4.74039e6	−0.459263
$640$	−2.30718e7	−2.22654
$641$	−1.24164e7	−1.19358	−0.596788	−	0.802399i	$-0.703557\pi$
$641$	−1.24164e7	−1.19358	−0.596788	+	0.802399i	$0.703557\pi$
$642$	4.83888e6	0.463348
$643$	8.12431e6	0.774924	0.387462	−	0.921886i	$-0.373352\pi$
$643$	8.12431e6	0.774924	0.387462	+	0.921886i	$0.373352\pi$
$644$	1.60391e6	0.152393
$645$	−9.52201e6	−0.901217
$646$	3.72952e7	3.51618
$647$	5.09873e6	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$647$	5.09873e6	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$648$	−1.00421e6	−0.0939479
$649$	−2.12287e7	−1.97838
$650$	1.28616e7	1.19402
$651$	905716.	0.0837606
$652$	1.56758e6	0.144415
$653$	−7.51734e6	−0.689892	−0.344946	−	0.938623i	$-0.612103\pi$
$653$	−7.51734e6	−0.689892	−0.344946	+	0.938623i	$0.612103\pi$
$654$	5.60001e6	0.511970
$655$	−3.57741e7	−3.25810
$656$	1.94886e7	1.76815
$657$	−407829.	−0.0368608
$658$	−1.29170e7	−1.16305
$659$	−7.35962e6	−0.660149	−0.330075	−	0.943955i	$-0.607074\pi$
$659$	−7.35962e6	−0.660149	−0.330075	+	0.943955i	$0.607074\pi$
$660$	4.00533e6	0.357913
$661$	−1.43428e7	−1.27682	−0.638411	−	0.769695i	$-0.720408\pi$
$661$	−1.43428e7	−1.27682	−0.638411	+	0.769695i	$0.720408\pi$
$662$	−2.35074e7	−2.08478
$663$	5.45169e6	0.481667
$664$	7.98047e6	0.702439
$665$	−3.16211e7	−2.77283
$666$	−507778.	−0.0443597
$667$	5.63853e6	0.490740
$668$	53181.9	0.00461129
$669$	1.72597e6	0.149097
$670$	−2.53269e7	−2.17969
$671$	−1.10425e6	−0.0946805
$672$	−2.85595e6	−0.243965
$673$	−1.08610e7	−0.924339	−0.462169	−	0.886792i	$-0.652929\pi$
$673$	−1.08610e7	−0.924339	−0.462169	+	0.886792i	$0.652929\pi$
$674$	2.48406e7	2.10626
$675$	5.51324e6	0.465744
$676$	−2.30169e6	−0.193723
$677$	1.49264e7	1.25165	0.625826	−	0.779963i	$-0.284762\pi$
$677$	1.49264e7	1.25165	0.625826	+	0.779963i	$0.284762\pi$
$678$	6.51988e6	0.544710
$679$	−4.56953e6	−0.380362
$680$	3.55166e7	2.94550
$681$	5.57100e6	0.460326
$682$	−3.05162e6	−0.251229
$683$	1.79368e7	1.47127	0.735636	−	0.677377i	$-0.236883\pi$
$683$	1.79368e7	1.47127	0.735636	+	0.677377i	$0.236883\pi$
$684$	1.64703e6	0.134605
$685$	2.41338e7	1.96516
$686$	−1.47353e7	−1.19550
$687$	−6.34844e6	−0.513186
$688$	−1.23964e7	−0.998449
$689$	2.85545e6	0.229153
$690$	−1.05122e7	−0.840563
$691$	−3.98389e6	−0.317404	−0.158702	−	0.987327i	$-0.550731\pi$
$691$	−3.98389e6	−0.317404	−0.158702	+	0.987327i	$0.550731\pi$
$692$	3.42238e6	0.271684
$693$	−5.24510e6	−0.414879
$694$	−1.70779e7	−1.34597
$695$	2.65181e7	2.08248
$696$	−4.33227e6	−0.338995
$697$	−3.61126e7	−2.81564
$698$	7.67280e6	0.596095
$699$	1.00958e7	0.781531
$700$	6.76567e6	0.521874
$701$	−4.17558e6	−0.320938	−0.160469	−	0.987041i	$-0.551301\pi$
$701$	−4.17558e6	−0.320938	−0.160469	+	0.987041i	$0.551301\pi$
$702$	1.23978e6	0.0949512
$703$	−2.62294e6	−0.200171
$704$	−1.20146e7	−0.913642
$705$	1.64404e7	1.24578
$706$	−1.23109e7	−0.929559
$707$	2.53128e6	0.190455
$708$	2.63953e6	0.197899
$709$	9.86426e6	0.736968	0.368484	−	0.929634i	$-0.379877\pi$
$709$	9.86426e6	0.736968	0.368484	+	0.929634i	$0.379877\pi$
$710$	3.81269e7	2.83848
$711$	5.24099e6	0.388812
$712$	−1.15358e7	−0.852798
$713$	1.55533e6	0.114577
$714$	1.47676e7	1.08409
$715$	1.55738e7	1.13927
$716$	−1.38427e6	−0.100911
$717$	−7.99287e6	−0.580637
$718$	8.82568e6	0.638906
$719$	841184.	0.0606833	0.0303416	−	0.999540i	$-0.490340\pi$
$719$	841184.	0.0606833	0.0303416	+	0.999540i	$0.490340\pi$
$720$	1.01434e7	0.729207
$721$	−1.23069e6	−0.0881679
$722$	2.82069e7	2.01378
$723$	−519697.	−0.0369747
$724$	−3.21603e6	−0.228021
$725$	2.37847e7	1.68056
$726$	8.53817e6	0.601206
$727$	1.08837e7	0.763733	0.381866	−	0.924218i	$-0.375281\pi$
$727$	1.08837e7	0.763733	0.381866	+	0.924218i	$0.375281\pi$
$728$	−4.79164e6	−0.335086
$729$	531441.	0.0370370
$730$	3.28017e6	0.227819
$731$	2.29708e7	1.58995
$732$	137300.	0.00947096
$733$	2.30371e7	1.58368	0.791839	−	0.610730i	$-0.209124\pi$
$733$	2.30371e7	1.58368	0.791839	+	0.610730i	$0.209124\pi$
$734$	2.77956e7	1.90430
$735$	3.11696e6	0.212820
$736$	−4.90435e6	−0.333724
$737$	−2.17007e7	−1.47165
$738$	−8.21241e6	−0.555047
$739$	−5.15501e6	−0.347231	−0.173615	−	0.984814i	$-0.555545\pi$
$739$	−5.15501e6	−0.347231	−0.173615	+	0.984814i	$0.555545\pi$
$740$	793102.	0.0532415
$741$	6.40410e6	0.428462
$742$	7.73486e6	0.515754
$743$	−1.49636e7	−0.994408	−0.497204	−	0.867634i	$-0.665640\pi$
$743$	−1.49636e7	−0.994408	−0.497204	+	0.867634i	$0.665640\pi$
$744$	−1.19501e6	−0.0791481
$745$	−1.90247e7	−1.25582
$746$	−1.35928e7	−0.894257
$747$	−4.22337e6	−0.276922
$748$	−9.66241e6	−0.631439
$749$	9.89729e6	0.644632
$750$	−2.60200e7	−1.68910
$751$	2.13063e7	1.37850	0.689251	−	0.724522i	$-0.257940\pi$
$751$	2.13063e7	1.37850	0.689251	+	0.724522i	$0.257940\pi$
$752$	2.14033e7	1.38018
$753$	−1.45396e7	−0.934466
$754$	5.34853e6	0.342615
$755$	4.00031e7	2.55403
$756$	652167.	0.0415006
$757$	−866811.	−0.0549775	−0.0274887	−	0.999622i	$-0.508751\pi$
$757$	−866811.	−0.0549775	−0.0274887	+	0.999622i	$0.508751\pi$
$758$	1.59282e7	1.00691
$759$	−9.00709e6	−0.567519
$760$	4.17213e7	2.62013
$761$	−2.04242e7	−1.27845	−0.639223	−	0.769021i	$-0.720744\pi$
$761$	−2.04242e7	−1.27845	−0.639223	+	0.769021i	$0.720744\pi$
$762$	1.87232e7	1.16813
$763$	1.14541e7	0.712277
$764$	−4.61958e6	−0.286331
$765$	−1.87958e7	−1.16120
$766$	−2.58054e7	−1.58905
$767$	1.02632e7	0.629934
$768$	6.45850e6	0.395120
$769$	1.93545e7	1.18023	0.590115	−	0.807319i	$-0.299082\pi$
$769$	1.93545e7	1.18023	0.590115	+	0.807319i	$0.299082\pi$
$770$	4.21864e7	2.56416
$771$	−1.04360e7	−0.632265
$772$	4.63798e6	0.280083
$773$	−8.93938e6	−0.538095	−0.269047	−	0.963127i	$-0.586709\pi$
$773$	−8.93938e6	−0.538095	−0.269047	+	0.963127i	$0.586709\pi$
$774$	5.22382e6	0.313426
$775$	6.56077e6	0.392375
$776$	6.02910e6	0.359417
$777$	−1.03859e6	−0.0617153
$778$	2.99692e6	0.177512
$779$	−4.24215e7	−2.50462
$780$	−1.93642e6	−0.113963
$781$	3.26681e7	1.91644
$782$	2.53595e7	1.48294
$783$	2.29269e6	0.133642
$784$	4.05788e6	0.235781
$785$	−1.77878e7	−1.03027
$786$	1.96258e7	1.13311
$787$	4.33335e6	0.249395	0.124697	−	0.992195i	$-0.460204\pi$
$787$	4.33335e6	0.249395	0.124697	+	0.992195i	$0.460204\pi$
$788$	−1.39829e6	−0.0802200
$789$	−6.89959e6	−0.394576
$790$	−4.21533e7	−2.40305
$791$	1.33356e7	0.757827
$792$	6.92046e6	0.392032
$793$	533860.	0.0301470
$794$	6.38135e6	0.359221
$795$	−9.84474e6	−0.552441
$796$	3.67067e6	0.205335
$797$	3.27360e7	1.82549	0.912745	−	0.408530i	$-0.133958\pi$
$797$	3.27360e7	1.82549	0.912745	+	0.408530i	$0.133958\pi$
$798$	1.73475e7	0.964337
$799$	−3.96607e7	−2.19783
$800$	−2.06878e7	−1.14285
$801$	6.10487e6	0.336198
$802$	4.74553e6	0.260525
$803$	2.81053e6	0.153815
$804$	2.69823e6	0.147211
$805$	−2.15013e7	−1.16943
$806$	1.47534e6	0.0799933
$807$	1.60914e7	0.869779
$808$	−3.33980e6	−0.179967
$809$	−2.65560e7	−1.42657	−0.713283	−	0.700876i	$-0.752793\pi$
$809$	−2.65560e7	−1.42657	−0.713283	+	0.700876i	$0.752793\pi$
$810$	−4.27438e6	−0.228908
$811$	−9.21095e6	−0.491759	−0.245879	−	0.969300i	$-0.579077\pi$
$811$	−9.21095e6	−0.491759	−0.245879	+	0.969300i	$0.579077\pi$
$812$	2.81352e6	0.149748
$813$	−1.09752e7	−0.582354
$814$	3.49932e6	0.185107
$815$	−2.10144e7	−1.10821
$816$	−2.44697e7	−1.28648
$817$	2.69838e7	1.41432
$818$	−6.43242e6	−0.336117
$819$	2.53580e6	0.132101
$820$	1.28270e7	0.666180
$821$	−5.64917e6	−0.292500	−0.146250	−	0.989248i	$-0.546720\pi$
$821$	−5.64917e6	−0.292500	−0.146250	+	0.989248i	$0.546720\pi$
$822$	−1.32399e7	−0.683447
$823$	−7.03718e6	−0.362159	−0.181080	−	0.983468i	$-0.557959\pi$
$823$	−7.03718e6	−0.362159	−0.181080	+	0.983468i	$0.557959\pi$
$824$	1.62379e6	0.0833127
$825$	−3.79942e7	−1.94349
$826$	2.78011e7	1.41779
$827$	−1.69465e7	−0.861619	−0.430810	−	0.902443i	$-0.641772\pi$
$827$	−1.69465e7	−0.861619	−0.430810	+	0.902443i	$0.641772\pi$
$828$	1.11993e6	0.0567693
$829$	3.21051e7	1.62251	0.811256	−	0.584691i	$-0.198784\pi$
$829$	3.21051e7	1.62251	0.811256	+	0.584691i	$0.198784\pi$
$830$	3.39685e7	1.71152
$831$	−7.77831e6	−0.390735
$832$	5.80856e6	0.290911
$833$	−7.51931e6	−0.375462
$834$	−1.45479e7	−0.724247
$835$	−712934.	−0.0353861
$836$	−1.13504e7	−0.561689
$837$	632416.	0.0312025
$838$	3.25062e7	1.59903
$839$	−2.43643e7	−1.19495	−0.597474	−	0.801888i	$-0.703829\pi$
$839$	−2.43643e7	−1.19495	−0.597474	+	0.801888i	$0.703829\pi$
$840$	1.65202e7	0.807823
$841$	−1.06202e7	−0.517778
$842$	−2.47313e7	−1.20217
$843$	1.60047e7	0.775673
$844$	6.02020e6	0.290908
$845$	3.08556e7	1.48659
$846$	−9.01930e6	−0.433258
$847$	1.74637e7	0.836427
$848$	−1.28166e7	−0.612044
$849$	−1.05655e7	−0.503061
$850$	1.06973e8	5.07838
$851$	−1.78351e6	−0.0844213
$852$	−4.06190e6	−0.191703
$853$	2.34900e7	1.10538	0.552690	−	0.833387i	$-0.313602\pi$
$853$	2.34900e7	1.10538	0.552690	+	0.833387i	$0.313602\pi$
$854$	1.44613e6	0.0678518
$855$	−2.20794e7	−1.03293
$856$	−1.30586e7	−0.609134
$857$	−2.48954e7	−1.15789	−0.578946	−	0.815366i	$-0.696536\pi$
$857$	−2.48954e7	−1.15789	−0.578946	+	0.815366i	$0.696536\pi$
$858$	−8.54384e6	−0.396219
$859$	−3.03375e7	−1.40280	−0.701401	−	0.712767i	$-0.747442\pi$
$859$	−3.03375e7	−1.40280	−0.701401	+	0.712767i	$0.747442\pi$
$860$	−8.15912e6	−0.376181
$861$	−1.67974e7	−0.772209
$862$	−3.11264e6	−0.142679
$863$	2.22788e7	1.01827	0.509136	−	0.860686i	$-0.329965\pi$
$863$	2.22788e7	1.01827	0.509136	+	0.860686i	$0.329965\pi$
$864$	−1.99417e6	−0.0908819
$865$	−4.58790e7	−2.08485
$866$	−3.70005e7	−1.67653
$867$	3.25641e7	1.47127
$868$	776081.	0.0349629
$869$	−3.61180e7	−1.62246
$870$	−1.84401e7	−0.825973
$871$	1.04914e7	0.468586
$872$	−1.51127e7	−0.673054
$873$	−3.19068e6	−0.141693
$874$	2.97898e7	1.31913
$875$	−5.32206e7	−2.34995
$876$	−349457.	−0.0153863
$877$	1.33252e7	0.585027	0.292514	−	0.956261i	$-0.405508\pi$
$877$	1.33252e7	0.585027	0.292514	+	0.956261i	$0.405508\pi$
$878$	−1.52198e7	−0.666303
$879$	1.46932e7	0.641423
$880$	−6.99024e7	−3.04288
$881$	−3.21627e7	−1.39609	−0.698044	−	0.716055i	$-0.745946\pi$
$881$	−3.21627e7	−1.39609	−0.698044	+	0.716055i	$0.745946\pi$
$882$	−1.70998e6	−0.0740148
$883$	3.35792e7	1.44933	0.724667	−	0.689099i	$-0.241994\pi$
$883$	3.35792e7	1.44933	0.724667	+	0.689099i	$0.241994\pi$
$884$	4.67139e6	0.201055
$885$	−3.53845e7	−1.51864
$886$	−2.31179e7	−0.989384
$887$	−1.07017e7	−0.456713	−0.228356	−	0.973578i	$-0.573335\pi$
$887$	−1.07017e7	−0.456713	−0.228356	+	0.973578i	$0.573335\pi$
$888$	1.37033e6	0.0583168
$889$	3.82958e7	1.62516
$890$	−4.91015e7	−2.07788
$891$	−3.66239e6	−0.154551
$892$	1.47893e6	0.0622352
$893$	−4.65894e7	−1.95505
$894$	1.04370e7	0.436750
$895$	1.85569e7	0.774368
$896$	2.58888e7	1.07731
$897$	4.35457e6	0.180703
$898$	−2.35709e7	−0.975407
$899$	2.72831e6	0.112589
$900$	4.72413e6	0.194409
$901$	2.37493e7	0.974629
$902$	5.65954e7	2.31614
$903$	1.06846e7	0.436054
$904$	−1.75951e7	−0.716096
$905$	4.31128e7	1.74979
$906$	−2.19459e7	−0.888245
$907$	1.81514e7	0.732642	0.366321	−	0.930489i	$-0.380617\pi$
$907$	1.81514e7	0.732642	0.366321	+	0.930489i	$0.380617\pi$
$908$	4.77362e6	0.192147
$909$	1.76747e6	0.0709482
$910$	−2.03954e7	−0.816449
$911$	−3.63531e7	−1.45126	−0.725631	−	0.688084i	$-0.758452\pi$
$911$	−3.63531e7	−1.45126	−0.725631	+	0.688084i	$0.758452\pi$
$912$	−2.87446e7	−1.14438
$913$	2.91051e7	1.15556
$914$	2.70799e7	1.07221
$915$	−1.84059e6	−0.0726783
$916$	−5.43979e6	−0.214212
$917$	4.01420e7	1.57643
$918$	1.03115e7	0.403844
$919$	2.65642e6	0.103755	0.0518773	−	0.998653i	$-0.483480\pi$
$919$	2.65642e6	0.103755	0.0518773	+	0.998653i	$0.483480\pi$
$920$	2.83691e7	1.10503
$921$	1.15154e7	0.447332
$922$	1.37251e7	0.531726
$923$	−1.57937e7	−0.610211
$924$	−4.49437e6	−0.173177
$925$	−7.52330e6	−0.289104
$926$	−1.94901e7	−0.746941
$927$	−859329.	−0.0328443
$928$	−8.60306e6	−0.327932
$929$	1.55567e7	0.591397	0.295698	−	0.955281i	$-0.404448\pi$
$929$	1.55567e7	0.591397	0.295698	+	0.955281i	$0.404448\pi$
$930$	−5.08652e6	−0.192847
$931$	−8.83293e6	−0.333988
$932$	8.65076e6	0.326223
$933$	−3.46606e6	−0.130356
$934$	4.75379e7	1.78309
$935$	1.29530e8	4.84554
$936$	−3.34576e6	−0.124826
$937$	−2.29611e7	−0.854366	−0.427183	−	0.904165i	$-0.640494\pi$
$937$	−2.29611e7	−0.854366	−0.427183	+	0.904165i	$0.640494\pi$
$938$	2.84193e7	1.05464
$939$	4.06965e6	0.150624
$940$	1.40873e7	0.520006
$941$	−3.52803e7	−1.29885	−0.649424	−	0.760426i	$-0.724990\pi$
$941$	−3.52803e7	−1.29885	−0.649424	+	0.760426i	$0.724990\pi$
$942$	9.75849e6	0.358307
$943$	−2.88452e7	−1.05632
$944$	−4.60661e7	−1.68249
$945$	−8.74268e6	−0.318468
$946$	−3.59996e7	−1.30789
$947$	2.80427e7	1.01612	0.508059	−	0.861322i	$-0.330363\pi$
$947$	2.80427e7	1.01612	0.508059	+	0.861322i	$0.330363\pi$
$948$	4.49085e6	0.162296
$949$	−1.35878e6	−0.0489760
$950$	1.25661e8	4.51742
$951$	−9.19499e6	−0.329686
$952$	−3.98531e7	−1.42518
$953$	−5.24495e6	−0.187072	−0.0935360	−	0.995616i	$-0.529817\pi$
$953$	−5.24495e6	−0.187072	−0.0935360	+	0.995616i	$0.529817\pi$
$954$	5.40087e6	0.192129
$955$	6.19281e7	2.19725
$956$	−6.84885e6	−0.242367
$957$	−1.58000e7	−0.557669
$958$	−6.19391e6	−0.218048
$959$	−2.70805e7	−0.950844
$960$	−2.00262e7	−0.701327
$961$	−2.78766e7	−0.973713
$962$	−1.69178e6	−0.0589395
$963$	6.91079e6	0.240138
$964$	−445312.	−0.0154338
$965$	−6.21749e7	−2.14930
$966$	1.17957e7	0.406706
$967$	−3.40447e7	−1.17080	−0.585401	−	0.810744i	$-0.699063\pi$
$967$	−3.40447e7	−1.17080	−0.585401	+	0.810744i	$0.699063\pi$
$968$	−2.30418e7	−0.790367
$969$	5.32642e7	1.82232
$970$	2.56626e7	0.875733
$971$	5.70328e7	1.94123	0.970614	−	0.240643i	$-0.0773584\pi$
$971$	5.70328e7	1.94123	0.970614	+	0.240643i	$0.0773584\pi$
$972$	455376.	0.0154598
$973$	−2.97559e7	−1.00761
$974$	5.94669e7	2.00853
$975$	1.83687e7	0.618822
$976$	−2.39622e6	−0.0805196
$977$	−4.24122e7	−1.42153	−0.710763	−	0.703432i	$-0.751650\pi$
$977$	−4.24122e7	−1.42153	−0.710763	+	0.703432i	$0.751650\pi$
$978$	1.15286e7	0.385415
$979$	−4.20714e7	−1.40291
$980$	2.67082e6	0.0888342
$981$	7.99781e6	0.265337
$982$	−3.16001e7	−1.04571
$983$	3.06318e7	1.01109	0.505544	−	0.862801i	$-0.331292\pi$
$983$	3.06318e7	1.01109	0.505544	+	0.862801i	$0.331292\pi$
$984$	2.21627e7	0.729685
$985$	1.87449e7	0.615593
$986$	4.44848e7	1.45720
$987$	−1.84478e7	−0.602770
$988$	5.48748e6	0.178846
$989$	1.83481e7	0.596485
$990$	2.94566e7	0.955201
$991$	3.45027e7	1.11601	0.558007	−	0.829836i	$-0.311566\pi$
$991$	3.45027e7	1.11601	0.558007	+	0.829836i	$0.311566\pi$
$992$	−2.37307e6	−0.0765651
$993$	−3.35728e7	−1.08047
$994$	−4.27822e7	−1.37340
$995$	−4.92074e7	−1.57570
$996$	−3.61888e6	−0.115591
$997$	4.19439e7	1.33638	0.668192	−	0.743989i	$-0.267068\pi$
$997$	4.19439e7	1.33638	0.668192	+	0.743989i	$0.267068\pi$
$998$	−4.02450e7	−1.27905
$999$	−725198.	−0.0229902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.19	✓	25
3.2	odd	2		927.6.a.f.1.7		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.19	✓	25	1.1	even	1	trivial
927.6.a.f.1.7		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)

\(f(q)\)	\(=\)	\(q+6.30173 q^{2} +9.00000 q^{3} +7.71183 q^{4} -103.382 q^{5} +56.7156 q^{6} +116.004 q^{7} -153.058 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+6.30173 q^{2} +9.00000 q^{3} +7.71183 q^{4} -103.382 q^{5} +56.7156 q^{6} +116.004 q^{7} -153.058 q^{8} +81.0000 q^{9} -651.483 q^{10} -558.207 q^{11} +69.4065 q^{12} +269.871 q^{13} +731.028 q^{14} -930.434 q^{15} -1211.31 q^{16} +2244.57 q^{17} +510.440 q^{18} +2636.69 q^{19} -797.261 q^{20} +1044.04 q^{21} -3517.67 q^{22} +1792.86 q^{23} -1377.52 q^{24} +7562.75 q^{25} +1700.65 q^{26} +729.000 q^{27} +894.605 q^{28} +3144.99 q^{29} -5863.35 q^{30} +867.512 q^{31} -2735.49 q^{32} -5023.86 q^{33} +14144.7 q^{34} -11992.7 q^{35} +624.658 q^{36} -994.784 q^{37} +16615.7 q^{38} +2428.84 q^{39} +15823.3 q^{40} -16088.9 q^{41} +6579.25 q^{42} +10233.9 q^{43} -4304.79 q^{44} -8373.91 q^{45} +11298.1 q^{46} -17669.6 q^{47} -10901.8 q^{48} -3350.00 q^{49} +47658.4 q^{50} +20201.1 q^{51} +2081.20 q^{52} +10580.8 q^{53} +4593.96 q^{54} +57708.3 q^{55} -17755.3 q^{56} +23730.2 q^{57} +19818.9 q^{58} +38030.1 q^{59} -7175.35 q^{60} +1978.21 q^{61} +5466.83 q^{62} +9396.35 q^{63} +21523.5 q^{64} -27899.6 q^{65} -31659.0 q^{66} +38875.8 q^{67} +17309.7 q^{68} +16135.8 q^{69} -75574.8 q^{70} -58523.3 q^{71} -12397.7 q^{72} -5034.93 q^{73} -6268.86 q^{74} +68064.7 q^{75} +20333.7 q^{76} -64754.4 q^{77} +15305.9 q^{78} +64703.6 q^{79} +125227. q^{80} +6561.00 q^{81} -101388. q^{82} -52140.3 q^{83} +8051.45 q^{84} -232047. q^{85} +64491.6 q^{86} +28304.9 q^{87} +85437.7 q^{88} +75368.8 q^{89} -52770.1 q^{90} +31306.2 q^{91} +13826.3 q^{92} +7807.61 q^{93} -111349. q^{94} -272585. q^{95} -24619.4 q^{96} -39391.1 q^{97} -21110.8 q^{98} -45214.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 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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