LMFDB - Embedded newform 309.6.a.d.1.6

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			1.6
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)

$f(q)$	$=$	$q-7.82591 q^{2} +9.00000 q^{3} +29.2448 q^{4} +102.916 q^{5} -70.4332 q^{6} -33.8830 q^{7} +21.5617 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-7.82591 q^{2} +9.00000 q^{3} +29.2448 q^{4} +102.916 q^{5} -70.4332 q^{6} -33.8830 q^{7} +21.5617 q^{8} +81.0000 q^{9} -805.408 q^{10} +683.094 q^{11} +263.204 q^{12} +98.4797 q^{13} +265.165 q^{14} +926.241 q^{15} -1104.57 q^{16} +603.601 q^{17} -633.899 q^{18} +219.902 q^{19} +3009.75 q^{20} -304.947 q^{21} -5345.83 q^{22} +3733.22 q^{23} +194.055 q^{24} +7466.63 q^{25} -770.693 q^{26} +729.000 q^{27} -990.903 q^{28} +4289.71 q^{29} -7248.67 q^{30} +2670.00 q^{31} +7954.32 q^{32} +6147.85 q^{33} -4723.73 q^{34} -3487.09 q^{35} +2368.83 q^{36} -9299.17 q^{37} -1720.93 q^{38} +886.317 q^{39} +2219.03 q^{40} -14913.0 q^{41} +2386.49 q^{42} -5164.18 q^{43} +19977.0 q^{44} +8336.17 q^{45} -29215.8 q^{46} -24442.0 q^{47} -9941.17 q^{48} -15658.9 q^{49} -58433.1 q^{50} +5432.41 q^{51} +2880.02 q^{52} +14933.3 q^{53} -5705.09 q^{54} +70301.1 q^{55} -730.574 q^{56} +1979.12 q^{57} -33570.8 q^{58} +1221.66 q^{59} +27087.8 q^{60} -14836.1 q^{61} -20895.2 q^{62} -2744.52 q^{63} -26903.4 q^{64} +10135.1 q^{65} -48112.5 q^{66} -37331.8 q^{67} +17652.2 q^{68} +33599.0 q^{69} +27289.7 q^{70} -1672.71 q^{71} +1746.50 q^{72} +78123.8 q^{73} +72774.5 q^{74} +67199.7 q^{75} +6431.00 q^{76} -23145.3 q^{77} -6936.24 q^{78} +22282.1 q^{79} -113678. q^{80} +6561.00 q^{81} +116708. q^{82} -105312. q^{83} -8918.13 q^{84} +62120.0 q^{85} +40414.4 q^{86} +38607.4 q^{87} +14728.6 q^{88} -114535. q^{89} -65238.1 q^{90} -3336.79 q^{91} +109177. q^{92} +24030.0 q^{93} +191281. q^{94} +22631.4 q^{95} +71588.9 q^{96} -103800. q^{97} +122545. q^{98} +55330.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.82591	−1.38344	−0.691719	−	0.722167i	$-0.743146\pi$
$2$	−7.82591	−1.38344	−0.691719	+	0.722167i	$0.743146\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	29.2448	0.913901
$5$	102.916	1.84101	0.920505	−	0.390730i	$-0.127777\pi$
$5$	102.916	1.84101	0.920505	+	0.390730i	$0.127777\pi$
$6$	−70.4332	−0.798728
$7$	−33.8830	−0.261359	−0.130679	−	0.991425i	$-0.541716\pi$
$7$	−33.8830	−0.261359	−0.130679	+	0.991425i	$0.541716\pi$
$8$	21.5617	0.119113
$9$	81.0000	0.333333
$10$	−805.408	−2.54692
$11$	683.094	1.70215	0.851077	−	0.525041i	$-0.175950\pi$
$11$	683.094	1.70215	0.851077	+	0.525041i	$0.175950\pi$
$12$	263.204	0.527641
$13$	98.4797	0.161618	0.0808088	−	0.996730i	$-0.474250\pi$
$13$	98.4797	0.161618	0.0808088	+	0.996730i	$0.474250\pi$
$14$	265.165	0.361574
$15$	926.241	1.06291
$16$	−1104.57	−1.07869
$17$	603.601	0.506556	0.253278	−	0.967393i	$-0.418491\pi$
$17$	603.601	0.506556	0.253278	+	0.967393i	$0.418491\pi$
$18$	−633.899	−0.461146
$19$	219.902	0.139748	0.0698740	−	0.997556i	$-0.477740\pi$
$19$	219.902	0.139748	0.0698740	+	0.997556i	$0.477740\pi$
$20$	3009.75	1.68250
$21$	−304.947	−0.150896
$22$	−5345.83	−2.35482
$23$	3733.22	1.47151	0.735756	−	0.677246i	$-0.236827\pi$
$23$	3733.22	1.47151	0.735756	+	0.677246i	$0.236827\pi$
$24$	194.055	0.0687696
$25$	7466.63	2.38932
$26$	−770.693	−0.223588
$27$	729.000	0.192450
$28$	−990.903	−0.238856
$29$	4289.71	0.947180	0.473590	−	0.880745i	$-0.342958\pi$
$29$	4289.71	0.947180	0.473590	+	0.880745i	$0.342958\pi$
$30$	−7248.67	−1.47047
$31$	2670.00	0.499007	0.249503	−	0.968374i	$-0.419733\pi$
$31$	2670.00	0.499007	0.249503	+	0.968374i	$0.419733\pi$
$32$	7954.32	1.37318
$33$	6147.85	0.982739
$34$	−4723.73	−0.700789
$35$	−3487.09	−0.481164
$36$	2368.83	0.304634
$37$	−9299.17	−1.11671	−0.558354	−	0.829602i	$-0.688567\pi$
$37$	−9299.17	−1.11671	−0.558354	+	0.829602i	$0.688567\pi$
$38$	−1720.93	−0.193333
$39$	886.317	0.0933099
$40$	2219.03	0.219287
$41$	−14913.0	−1.38550	−0.692750	−	0.721178i	$-0.743601\pi$
$41$	−14913.0	−1.38550	−0.692750	+	0.721178i	$0.743601\pi$
$42$	2386.49	0.208755
$43$	−5164.18	−0.425922	−0.212961	−	0.977061i	$-0.568311\pi$
$43$	−5164.18	−0.425922	−0.212961	+	0.977061i	$0.568311\pi$
$44$	19977.0	1.55560
$45$	8336.17	0.613670
$46$	−29215.8	−2.03575
$47$	−24442.0	−1.61396	−0.806978	−	0.590581i	$-0.798899\pi$
$47$	−24442.0	−1.61396	−0.806978	+	0.590581i	$0.798899\pi$
$48$	−9941.17	−0.622780
$49$	−15658.9	−0.931692
$50$	−58433.1	−3.30548
$51$	5432.41	0.292460
$52$	2880.02	0.147702
$53$	14933.3	0.730241	0.365120	−	0.930960i	$-0.381028\pi$
$53$	14933.3	0.730241	0.365120	+	0.930960i	$0.381028\pi$
$54$	−5705.09	−0.266243
$55$	70301.1	3.13368
$56$	−730.574	−0.0311311
$57$	1979.12	0.0806835
$58$	−33570.8	−1.31037
$59$	1221.66	0.0456898	0.0228449	−	0.999739i	$-0.492728\pi$
$59$	1221.66	0.0456898	0.0228449	+	0.999739i	$0.492728\pi$
$60$	27087.8	0.971393
$61$	−14836.1	−0.510499	−0.255250	−	0.966875i	$-0.582158\pi$
$61$	−14836.1	−0.510499	−0.255250	+	0.966875i	$0.582158\pi$
$62$	−20895.2	−0.690345
$63$	−2744.52	−0.0871196
$64$	−26903.4	−0.821027
$65$	10135.1	0.297540
$66$	−48112.5	−1.35956
$67$	−37331.8	−1.01600	−0.507998	−	0.861358i	$-0.669614\pi$
$67$	−37331.8	−1.01600	−0.507998	+	0.861358i	$0.669614\pi$
$68$	17652.2	0.462942
$69$	33599.0	0.849578
$70$	27289.7	0.665661
$71$	−1672.71	−0.0393800	−0.0196900	−	0.999806i	$-0.506268\pi$
$71$	−1672.71	−0.0393800	−0.0196900	+	0.999806i	$0.506268\pi$
$72$	1746.50	0.0397042
$73$	78123.8	1.71584	0.857919	−	0.513785i	$-0.171757\pi$
$73$	78123.8	1.71584	0.857919	+	0.513785i	$0.171757\pi$
$74$	72774.5	1.54490
$75$	67199.7	1.37948
$76$	6431.00	0.127716
$77$	−23145.3	−0.444873
$78$	−6936.24	−0.129088
$79$	22282.1	0.401687	0.200843	−	0.979623i	$-0.435632\pi$
$79$	22282.1	0.401687	0.200843	+	0.979623i	$0.435632\pi$
$80$	−113678.	−1.98587
$81$	6561.00	0.111111
$82$	116708.	1.91675
$83$	−105312.	−1.67796	−0.838982	−	0.544160i	$-0.816849\pi$
$83$	−105312.	−1.67796	−0.838982	+	0.544160i	$0.816849\pi$
$84$	−8918.13	−0.137904
$85$	62120.0	0.932576
$86$	40414.4	0.589237
$87$	38607.4	0.546855
$88$	14728.6	0.202748
$89$	−114535.	−1.53272	−0.766358	−	0.642414i	$-0.777933\pi$
$89$	−114535.	−1.53272	−0.766358	+	0.642414i	$0.777933\pi$
$90$	−65238.1	−0.848975
$91$	−3336.79	−0.0422401
$92$	109177.	1.34482
$93$	24030.0	0.288102
$94$	191281.	2.23281
$95$	22631.4	0.257277
$96$	71588.9	0.792807
$97$	−103800.	−1.12013	−0.560065	−	0.828449i	$-0.689224\pi$
$97$	−103800.	−1.12013	−0.560065	+	0.828449i	$0.689224\pi$
$98$	122545.	1.28894
$99$	55330.6	0.567385
$100$	218360.	2.18360
$101$	155194.	1.51381	0.756907	−	0.653523i	$-0.226710\pi$
$101$	155194.	1.51381	0.756907	+	0.653523i	$0.226710\pi$
$102$	−42513.5	−0.404601
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	2123.39	0.0192507
$105$	−31383.8	−0.277800
$106$	−116867.	−1.01024
$107$	176050.	1.48654	0.743269	−	0.668993i	$-0.233274\pi$
$107$	176050.	1.48654	0.743269	+	0.668993i	$0.233274\pi$
$108$	21319.5	0.175880
$109$	84335.4	0.679898	0.339949	−	0.940444i	$-0.389590\pi$
$109$	84335.4	0.679898	0.339949	+	0.940444i	$0.389590\pi$
$110$	−550170.	−4.33526
$111$	−83692.6	−0.644732
$112$	37426.3	0.281924
$113$	221437.	1.63137	0.815687	−	0.578493i	$-0.196359\pi$
$113$	221437.	1.63137	0.815687	+	0.578493i	$0.196359\pi$
$114$	−15488.4	−0.111621
$115$	384207.	2.70907
$116$	125452.	0.865629
$117$	7976.86	0.0538725
$118$	−9560.57	−0.0632090
$119$	−20451.8	−0.132393
$120$	19971.3	0.126606
$121$	305567.	1.89733
$122$	116106.	0.706244
$123$	−134217.	−0.799919
$124$	78083.6	0.456043
$125$	446821.	2.55775
$126$	21478.4	0.120525
$127$	−99184.7	−0.545677	−0.272838	−	0.962060i	$-0.587962\pi$
$127$	−99184.7	−0.545677	−0.272838	+	0.962060i	$0.587962\pi$
$128$	−43994.6	−0.237342
$129$	−46477.6	−0.245906
$130$	−79316.4	−0.411628
$131$	−199956.	−1.01802	−0.509009	−	0.860761i	$-0.669988\pi$
$131$	−199956.	−1.01802	−0.509009	+	0.860761i	$0.669988\pi$
$132$	179793.	0.898126
$133$	−7450.95	−0.0365243
$134$	292155.	1.40557
$135$	75025.5	0.354303
$136$	13014.6	0.0603372
$137$	−339296.	−1.54446	−0.772231	−	0.635341i	$-0.780859\pi$
$137$	−339296.	−1.54446	−0.772231	+	0.635341i	$0.780859\pi$
$138$	−262943.	−1.17534
$139$	−182391.	−0.800694	−0.400347	−	0.916364i	$-0.631110\pi$
$139$	−182391.	−0.800694	−0.400347	+	0.916364i	$0.631110\pi$
$140$	−101979.	−0.439736
$141$	−219978.	−0.931818
$142$	13090.5	0.0544798
$143$	67270.9	0.275098
$144$	−89470.5	−0.359562
$145$	441478.	1.74377
$146$	−611390.	−2.37376
$147$	−140930.	−0.537912
$148$	−271953.	−1.02056
$149$	67279.4	0.248266	0.124133	−	0.992266i	$-0.460385\pi$
$149$	67279.4	0.248266	0.124133	+	0.992266i	$0.460385\pi$
$150$	−525898.	−1.90842
$151$	50070.8	0.178707	0.0893536	−	0.996000i	$-0.471520\pi$
$151$	50070.8	0.178707	0.0893536	+	0.996000i	$0.471520\pi$
$152$	4741.46	0.0166457
$153$	48891.7	0.168852
$154$	181133.	0.615454
$155$	274784.	0.918677
$156$	25920.2	0.0852760
$157$	−59023.5	−0.191107	−0.0955533	−	0.995424i	$-0.530462\pi$
$157$	−59023.5	−0.191107	−0.0955533	+	0.995424i	$0.530462\pi$
$158$	−174377.	−0.555709
$159$	134400.	0.421605
$160$	818624.	2.52804
$161$	−126493.	−0.384593
$162$	−51345.8	−0.153715
$163$	241896.	0.713116	0.356558	−	0.934273i	$-0.383950\pi$
$163$	241896.	0.713116	0.356558	+	0.934273i	$0.383950\pi$
$164$	−436130.	−1.26621
$165$	632710.	1.80923
$166$	824162.	2.32136
$167$	−82784.0	−0.229697	−0.114848	−	0.993383i	$-0.536638\pi$
$167$	−82784.0	−0.229697	−0.114848	+	0.993383i	$0.536638\pi$
$168$	−6575.17	−0.0179735
$169$	−361595.	−0.973880
$170$	−486145.	−1.29016
$171$	17812.1	0.0465826
$172$	−151026.	−0.389251
$173$	16440.5	0.0417637	0.0208819	−	0.999782i	$-0.493353\pi$
$173$	16440.5	0.0417637	0.0208819	+	0.999782i	$0.493353\pi$
$174$	−302138.	−0.756540
$175$	−252992.	−0.624470
$176$	−754528.	−1.83609
$177$	10994.9	0.0263790
$178$	896337.	2.12042
$179$	338665.	0.790020	0.395010	−	0.918677i	$-0.370741\pi$
$179$	338665.	0.790020	0.395010	+	0.918677i	$0.370741\pi$
$180$	243790.	0.560834
$181$	623259.	1.41407	0.707037	−	0.707177i	$-0.250032\pi$
$181$	623259.	1.41407	0.707037	+	0.707177i	$0.250032\pi$
$182$	26113.4	0.0584366
$183$	−133525.	−0.294737
$184$	80494.4	0.175276
$185$	−957030.	−2.05587
$186$	−188056.	−0.398571
$187$	412316.	0.862237
$188$	−714802.	−1.47500
$189$	−24700.7	−0.0502985
$190$	−177111.	−0.355927
$191$	577862.	1.14615	0.573074	−	0.819504i	$-0.305751\pi$
$191$	577862.	1.14615	0.573074	+	0.819504i	$0.305751\pi$
$192$	−242131.	−0.474020
$193$	198426.	0.383448	0.191724	−	0.981449i	$-0.438592\pi$
$193$	198426.	0.383448	0.191724	+	0.981449i	$0.438592\pi$
$194$	812330.	1.54963
$195$	91215.9	0.171785
$196$	−457943.	−0.851474
$197$	−739285.	−1.35721	−0.678604	−	0.734504i	$-0.737415\pi$
$197$	−739285.	−1.35721	−0.678604	+	0.734504i	$0.737415\pi$
$198$	−433012.	−0.784942
$199$	145359.	0.260202	0.130101	−	0.991501i	$-0.458470\pi$
$199$	145359.	0.260202	0.130101	+	0.991501i	$0.458470\pi$
$200$	160993.	0.284598
$201$	−335986.	−0.586585
$202$	−1.21454e6	−2.09427
$203$	−145348.	−0.247554
$204$	158870.	0.267280
$205$	−1.53479e6	−2.55072
$206$	83025.1	0.136314
$207$	302391.	0.490504
$208$	−108778.	−0.174335
$209$	150214.	0.237872
$210$	245607.	0.384320
$211$	172947.	0.267427	0.133714	−	0.991020i	$-0.457310\pi$
$211$	172947.	0.267427	0.133714	+	0.991020i	$0.457310\pi$
$212$	436722.	0.667368
$213$	−15054.4	−0.0227360
$214$	−1.37775e6	−2.05653
$215$	−531475.	−0.784128
$216$	15718.5	0.0229232
$217$	−90467.6	−0.130420
$218$	−660001.	−0.940597
$219$	703114.	0.990640
$220$	2.05594e6	2.86388
$221$	59442.5	0.0818684
$222$	654970.	0.891947
$223$	−682572.	−0.919150	−0.459575	−	0.888139i	$-0.651998\pi$
$223$	−682572.	−0.919150	−0.459575	+	0.888139i	$0.651998\pi$
$224$	−269516.	−0.358893
$225$	604797.	0.796440
$226$	−1.73294e6	−2.25691
$227$	1.29347e6	1.66606	0.833032	−	0.553225i	$-0.186603\pi$
$227$	1.29347e6	1.66606	0.833032	+	0.553225i	$0.186603\pi$
$228$	57879.0	0.0737367
$229$	−1.30971e6	−1.65038	−0.825192	−	0.564852i	$-0.808933\pi$
$229$	−1.30971e6	−1.65038	−0.825192	+	0.564852i	$0.808933\pi$
$230$	−3.00677e6	−3.74783
$231$	−208308.	−0.256847
$232$	92493.2	0.112821
$233$	117636.	0.141955	0.0709775	−	0.997478i	$-0.477388\pi$
$233$	117636.	0.141955	0.0709775	+	0.997478i	$0.477388\pi$
$234$	−62426.2	−0.0745293
$235$	−2.51546e6	−2.97131
$236$	35727.1	0.0417559
$237$	200539.	0.231914
$238$	160054.	0.183157
$239$	−544042.	−0.616081	−0.308040	−	0.951373i	$-0.599673\pi$
$239$	−544042.	−0.616081	−0.308040	+	0.951373i	$0.599673\pi$
$240$	−1.02310e6	−1.14654
$241$	484729.	0.537597	0.268798	−	0.963196i	$-0.413373\pi$
$241$	484729.	0.537597	0.268798	+	0.963196i	$0.413373\pi$
$242$	−2.39134e6	−2.62484
$243$	59049.0	0.0641500
$244$	−433879.	−0.466546
$245$	−1.61155e6	−1.71525
$246$	1.05037e6	1.10664
$247$	21655.9	0.0225857
$248$	57569.6	0.0594380
$249$	−947808.	−0.968773
$250$	−3.49678e6	−3.53850
$251$	1.30279e6	1.30524	0.652620	−	0.757685i	$-0.273670\pi$
$251$	1.30279e6	1.30524	0.652620	+	0.757685i	$0.273670\pi$
$252$	−80263.2	−0.0796187
$253$	2.55014e6	2.50474
$254$	776210.	0.754910
$255$	559080.	0.538423
$256$	1.20521e6	1.14938
$257$	−1.85224e6	−1.74930	−0.874649	−	0.484757i	$-0.838908\pi$
$257$	−1.85224e6	−1.74930	−0.874649	+	0.484757i	$0.838908\pi$
$258$	363730.	0.340196
$259$	315084.	0.291862
$260$	296399.	0.271922
$261$	347466.	0.315727
$262$	1.56483e6	1.40837
$263$	1.00619e6	0.896995	0.448497	−	0.893784i	$-0.351959\pi$
$263$	1.00619e6	0.896995	0.448497	+	0.893784i	$0.351959\pi$
$264$	132558.	0.117057
$265$	1.53687e6	1.34438
$266$	58310.4	0.0505292
$267$	−1.03081e6	−0.884914
$268$	−1.09176e6	−0.928520
$269$	479227.	0.403795	0.201897	−	0.979407i	$-0.435289\pi$
$269$	479227.	0.403795	0.201897	+	0.979407i	$0.435289\pi$
$270$	−587143.	−0.490156
$271$	−546590.	−0.452104	−0.226052	−	0.974115i	$-0.572582\pi$
$271$	−546590.	−0.452104	−0.226052	+	0.974115i	$0.572582\pi$
$272$	−666722.	−0.546415
$273$	−30031.1	−0.0243874
$274$	2.65530e6	2.13667
$275$	5.10041e6	4.06699
$276$	982597.	0.776430
$277$	−1.79716e6	−1.40730	−0.703652	−	0.710545i	$-0.748449\pi$
$277$	−1.79716e6	−1.40730	−0.703652	+	0.710545i	$0.748449\pi$
$278$	1.42738e6	1.10771
$279$	216270.	0.166336
$280$	−75187.5	−0.0573127
$281$	1.44250e6	1.08981	0.544903	−	0.838499i	$-0.316566\pi$
$281$	1.44250e6	1.08981	0.544903	+	0.838499i	$0.316566\pi$
$282$	1.72153e6	1.28911
$283$	328985.	0.244180	0.122090	−	0.992519i	$-0.461040\pi$
$283$	328985.	0.244180	0.122090	+	0.992519i	$0.461040\pi$
$284$	−48918.2	−0.0359894
$285$	203682.	0.148539
$286$	−526456.	−0.380581
$287$	505299.	0.362113
$288$	644300.	0.457728
$289$	−1.05552e6	−0.743401
$290$	−3.45496e6	−2.41240
$291$	−934201.	−0.646707
$292$	2.28472e6	1.56811
$293$	319369.	0.217332	0.108666	−	0.994078i	$-0.465342\pi$
$293$	319369.	0.217332	0.108666	+	0.994078i	$0.465342\pi$
$294$	1.10291e6	0.744169
$295$	125728.	0.0841154
$296$	−200506.	−0.133014
$297$	497976.	0.327580
$298$	−526523.	−0.343460
$299$	367646.	0.237822
$300$	1.96524e6	1.26070
$301$	174978.	0.111318
$302$	−391849.	−0.247230
$303$	1.39675e6	0.874001
$304$	−242898.	−0.150744
$305$	−1.52687e6	−0.939835
$306$	−382622.	−0.233596
$307$	3.27895e6	1.98559	0.992793	−	0.119838i	$-0.0382376\pi$
$307$	3.27895e6	1.98559	0.992793	+	0.119838i	$0.0382376\pi$
$308$	−676880.	−0.406570
$309$	−95481.0	−0.0568880
$310$	−2.15044e6	−1.27093
$311$	1.51067e6	0.885664	0.442832	−	0.896605i	$-0.353974\pi$
$311$	1.51067e6	0.885664	0.442832	+	0.896605i	$0.353974\pi$
$312$	19110.5	0.0111144
$313$	−3.10601e6	−1.79202	−0.896010	−	0.444035i	$-0.853547\pi$
$313$	−3.10601e6	−1.79202	−0.896010	+	0.444035i	$0.853547\pi$
$314$	461912.	0.264384
$315$	−282454.	−0.160388
$316$	651635.	0.367102
$317$	−553571.	−0.309404	−0.154702	−	0.987961i	$-0.549442\pi$
$317$	−553571.	−0.309404	−0.154702	+	0.987961i	$0.549442\pi$
$318$	−1.05180e6	−0.583264
$319$	2.93027e6	1.61225
$320$	−2.76878e6	−1.51152
$321$	1.58445e6	0.858253
$322$	989921.	0.532060
$323$	132733.	0.0707902
$324$	191875.	0.101545
$325$	735311.	0.386156
$326$	−1.89306e6	−0.986552
$327$	759019.	0.392539
$328$	−321550.	−0.165030
$329$	828168.	0.421822
$330$	−4.95153e6	−2.50296
$331$	−1.43955e6	−0.722200	−0.361100	−	0.932527i	$-0.617599\pi$
$331$	−1.43955e6	−0.722200	−0.361100	+	0.932527i	$0.617599\pi$
$332$	−3.07983e6	−1.53349
$333$	−753233.	−0.372236
$334$	647860.	0.317772
$335$	−3.84203e6	−1.87046
$336$	336837.	0.162769
$337$	2.12673e6	1.02009	0.510044	−	0.860148i	$-0.329629\pi$
$337$	2.12673e6	1.02009	0.510044	+	0.860148i	$0.329629\pi$
$338$	2.82981e6	1.34730
$339$	1.99293e6	0.941875
$340$	1.81669e6	0.852282
$341$	1.82386e6	0.849387
$342$	−139396.	−0.0644442
$343$	1.10004e6	0.504864
$344$	−111348.	−0.0507327
$345$	3.45786e6	1.56408
$346$	−128662.	−0.0577775
$347$	1.33615e6	0.595705	0.297853	−	0.954612i	$-0.403730\pi$
$347$	1.33615e6	0.595705	0.297853	+	0.954612i	$0.403730\pi$
$348$	1.12907e6	0.499771
$349$	−977300.	−0.429501	−0.214751	−	0.976669i	$-0.568894\pi$
$349$	−977300.	−0.429501	−0.214751	+	0.976669i	$0.568894\pi$
$350$	1.97989e6	0.863915
$351$	71791.7	0.0311033
$352$	5.43355e6	2.33737
$353$	−527197.	−0.225184	−0.112592	−	0.993641i	$-0.535915\pi$
$353$	−527197.	−0.225184	−0.112592	+	0.993641i	$0.535915\pi$
$354$	−86045.1	−0.0364937
$355$	−172148.	−0.0724990
$356$	−3.34955e6	−1.40075
$357$	−184066.	−0.0764371
$358$	−2.65036e6	−1.09294
$359$	−2.33578e6	−0.956525	−0.478263	−	0.878217i	$-0.658733\pi$
$359$	−2.33578e6	−0.956525	−0.478263	+	0.878217i	$0.658733\pi$
$360$	179742.	0.0730958
$361$	−2.42774e6	−0.980471
$362$	−4.87757e6	−1.95628
$363$	2.75010e6	1.09542
$364$	−97583.9	−0.0386033
$365$	8.04016e6	3.15888
$366$	1.04495e6	0.407750
$367$	1.92504e6	0.746061	0.373031	−	0.927819i	$-0.378319\pi$
$367$	1.92504e6	0.746061	0.373031	+	0.927819i	$0.378319\pi$
$368$	−4.12362e6	−1.58730
$369$	−1.20796e6	−0.461833
$370$	7.48963e6	2.84417
$371$	−505985.	−0.190855
$372$	702753.	0.263297
$373$	2.72081e6	1.01257	0.506285	−	0.862366i	$-0.331018\pi$
$373$	2.72081e6	1.01257	0.506285	+	0.862366i	$0.331018\pi$
$374$	−3.22675e6	−1.19285
$375$	4.02139e6	1.47672
$376$	−527010.	−0.192242
$377$	422449.	0.153081
$378$	193306.	0.0695849
$379$	−16688.8	−0.00596799	−0.00298400	−	0.999996i	$-0.500950\pi$
$379$	−16688.8	−0.00596799	−0.00298400	+	0.999996i	$0.500950\pi$
$380$	661850.	0.235126
$381$	−892662.	−0.315047
$382$	−4.52229e6	−1.58562
$383$	−832988.	−0.290163	−0.145081	−	0.989420i	$-0.546344\pi$
$383$	−832988.	−0.290163	−0.145081	+	0.989420i	$0.546344\pi$
$384$	−395952.	−0.137029
$385$	−2.38201e6	−0.819016
$386$	−1.55287e6	−0.530476
$387$	−418299.	−0.141974
$388$	−3.03562e6	−1.02369
$389$	−853583.	−0.286004	−0.143002	−	0.989722i	$-0.545675\pi$
$389$	−853583.	−0.286004	−0.143002	+	0.989722i	$0.545675\pi$
$390$	−713847.	−0.237653
$391$	2.25338e6	0.745404
$392$	−337633.	−0.110976
$393$	−1.79960e6	−0.587753
$394$	5.78558e6	1.87761
$395$	2.29317e6	0.739510
$396$	1.61813e6	0.518533
$397$	−4.18815e6	−1.33366	−0.666832	−	0.745208i	$-0.732350\pi$
$397$	−4.18815e6	−1.33366	−0.666832	+	0.745208i	$0.732350\pi$
$398$	−1.13757e6	−0.359973
$399$	−67058.5	−0.0210873
$400$	−8.24745e6	−2.57733
$401$	−4.99805e6	−1.55217	−0.776086	−	0.630627i	$-0.782798\pi$
$401$	−4.99805e6	−1.55217	−0.776086	+	0.630627i	$0.782798\pi$
$402$	2.62940e6	0.811505
$403$	262941.	0.0806483
$404$	4.53863e6	1.38348
$405$	675229.	0.204557
$406$	1.13748e6	0.342475
$407$	−6.35221e6	−1.90081
$408$	117132.	0.0348357
$409$	5.25510e6	1.55336	0.776681	−	0.629894i	$-0.216902\pi$
$409$	5.25510e6	1.55336	0.776681	+	0.629894i	$0.216902\pi$
$410$	1.20111e7	3.52877
$411$	−3.05366e6	−0.891696
$412$	−310258.	−0.0900494
$413$	−41393.4	−0.0119414
$414$	−2.36648e6	−0.678582
$415$	−1.08382e7	−3.08915
$416$	783340.	0.221930
$417$	−1.64152e6	−0.462281
$418$	−1.17556e6	−0.329082
$419$	6.39992e6	1.78090	0.890449	−	0.455083i	$-0.150390\pi$
$419$	6.39992e6	1.78090	0.890449	+	0.455083i	$0.150390\pi$
$420$	−917815.	−0.253882
$421$	−631609.	−0.173677	−0.0868386	−	0.996222i	$-0.527676\pi$
$421$	−631609.	−0.173677	−0.0868386	+	0.996222i	$0.527676\pi$
$422$	−1.35346e6	−0.369969
$423$	−1.97980e6	−0.537986
$424$	321987.	0.0869808
$425$	4.50686e6	1.21033
$426$	117814.	0.0314539
$427$	502692.	0.133423
$428$	5.14855e6	1.35855
$429$	605438.	0.158828
$430$	4.15927e6	1.08479
$431$	−1.85285e6	−0.480450	−0.240225	−	0.970717i	$-0.577221\pi$
$431$	−1.85285e6	−0.480450	−0.240225	+	0.970717i	$0.577221\pi$
$432$	−805235.	−0.207593
$433$	331158.	0.0848820	0.0424410	−	0.999099i	$-0.486487\pi$
$433$	331158.	0.0848820	0.0424410	+	0.999099i	$0.486487\pi$
$434$	707991.	0.180428
$435$	3.97330e6	1.00677
$436$	2.46638e6	0.621360
$437$	820943.	0.205641
$438$	−5.50251e6	−1.37049
$439$	498693.	0.123501	0.0617507	−	0.998092i	$-0.480332\pi$
$439$	498693.	0.123501	0.0617507	+	0.998092i	$0.480332\pi$
$440$	1.51581e6	0.373261
$441$	−1.26837e6	−0.310564
$442$	−465191.	−0.113260
$443$	−7.42325e6	−1.79715	−0.898576	−	0.438818i	$-0.855397\pi$
$443$	−7.42325e6	−1.79715	−0.898576	+	0.438818i	$0.855397\pi$
$444$	−2.44757e6	−0.589221
$445$	−1.17874e7	−2.82175
$446$	5.34175e6	1.27159
$447$	605515.	0.143336
$448$	911569.	0.214583
$449$	−2.07982e6	−0.486867	−0.243434	−	0.969918i	$-0.578274\pi$
$449$	−2.07982e6	−0.486867	−0.243434	+	0.969918i	$0.578274\pi$
$450$	−4.73308e6	−1.10183
$451$	−1.01870e7	−2.35834
$452$	6.47588e6	1.49092
$453$	450637.	0.103177
$454$	−1.01226e7	−2.30490
$455$	−343408.	−0.0777646
$456$	42673.1	0.00961041
$457$	−4.91643e6	−1.10118	−0.550592	−	0.834775i	$-0.685598\pi$
$457$	−4.91643e6	−1.10118	−0.550592	+	0.834775i	$0.685598\pi$
$458$	1.02496e7	2.28321
$459$	440025.	0.0974868
$460$	1.12361e7	2.47582
$461$	−122874.	−0.0269283	−0.0134641	−	0.999909i	$-0.504286\pi$
$461$	−122874.	−0.0269283	−0.0134641	+	0.999909i	$0.504286\pi$
$462$	1.63020e6	0.355332
$463$	−1.28368e6	−0.278294	−0.139147	−	0.990272i	$-0.544436\pi$
$463$	−1.28368e6	−0.278294	−0.139147	+	0.990272i	$0.544436\pi$
$464$	−4.73830e6	−1.02171
$465$	2.47306e6	0.530398
$466$	−920609.	−0.196386
$467$	820297.	0.174052	0.0870259	−	0.996206i	$-0.472264\pi$
$467$	820297.	0.174052	0.0870259	+	0.996206i	$0.472264\pi$
$468$	233282.	0.0492341
$469$	1.26491e6	0.265539
$470$	1.96858e7	4.11063
$471$	−531211.	−0.110335
$472$	26341.0	0.00544222
$473$	−3.52762e6	−0.724985
$474$	−1.56940e6	−0.320839
$475$	1.64193e6	0.333903
$476$	−598110.	−0.120994
$477$	1.20960e6	0.243414
$478$	4.25762e6	0.852309
$479$	1.67124e6	0.332813	0.166406	−	0.986057i	$-0.446784\pi$
$479$	1.67124e6	0.332813	0.166406	+	0.986057i	$0.446784\pi$
$480$	7.36762e6	1.45957
$481$	−915780.	−0.180480
$482$	−3.79345e6	−0.743732
$483$	−1.13843e6	−0.222045
$484$	8.93624e6	1.73397
$485$	−1.06827e7	−2.06217
$486$	−462112.	−0.0887476
$487$	5.22186e6	0.997707	0.498854	−	0.866686i	$-0.333755\pi$
$487$	5.22186e6	0.997707	0.498854	+	0.866686i	$0.333755\pi$
$488$	−319891.	−0.0608068
$489$	2.17707e6	0.411718
$490$	1.26118e7	2.37295
$491$	−5.16133e6	−0.966180	−0.483090	−	0.875571i	$-0.660486\pi$
$491$	−5.16133e6	−0.966180	−0.483090	+	0.875571i	$0.660486\pi$
$492$	−3.92517e6	−0.731047
$493$	2.58927e6	0.479800
$494$	−169477.	−0.0312459
$495$	5.69439e6	1.04456
$496$	−2.94921e6	−0.538272
$497$	56676.6	0.0102923
$498$	7.41746e6	1.34024
$499$	6.00642e6	1.07985	0.539926	−	0.841713i	$-0.318452\pi$
$499$	6.00642e6	1.07985	0.539926	+	0.841713i	$0.318452\pi$
$500$	1.30672e7	2.33754
$501$	−745056.	−0.132616
$502$	−1.01955e7	−1.80572
$503$	2.76710e6	0.487647	0.243823	−	0.969820i	$-0.421598\pi$
$503$	2.76710e6	0.487647	0.243823	+	0.969820i	$0.421598\pi$
$504$	−59176.5	−0.0103770
$505$	1.59719e7	2.78695
$506$	−1.99572e7	−3.46515
$507$	−3.25435e6	−0.562270
$508$	−2.90064e6	−0.498695
$509$	6.19789e6	1.06035	0.530175	−	0.847888i	$-0.322126\pi$
$509$	6.19789e6	1.06035	0.530175	+	0.847888i	$0.322126\pi$
$510$	−4.37531e6	−0.744875
$511$	−2.64707e6	−0.448449
$512$	−8.02402e6	−1.35275
$513$	160309.	0.0268945
$514$	1.44954e7	2.42004
$515$	−1.09183e6	−0.181400
$516$	−1.35923e6	−0.224734
$517$	−1.66962e7	−2.74720
$518$	−2.46582e6	−0.403772
$519$	147964.	0.0241123
$520$	218530.	0.0354407
$521$	−3.80902e6	−0.614780	−0.307390	−	0.951584i	$-0.599456\pi$
$521$	−3.80902e6	−0.614780	−0.307390	+	0.951584i	$0.599456\pi$
$522$	−2.71924e6	−0.436788
$523$	−3.85803e6	−0.616753	−0.308377	−	0.951264i	$-0.599786\pi$
$523$	−3.85803e6	−0.616753	−0.308377	+	0.951264i	$0.599786\pi$
$524$	−5.84767e6	−0.930368
$525$	−2.27693e6	−0.360538
$526$	−7.87434e6	−1.24094
$527$	1.61161e6	0.252775
$528$	−6.79075e6	−1.06007
$529$	7.50059e6	1.16535
$530$	−1.20274e7	−1.85987
$531$	98954.2	0.0152299
$532$	−217902.	−0.0333796
$533$	−1.46863e6	−0.223921
$534$	8.06703e6	1.22422
$535$	1.81183e7	2.73673
$536$	−804936.	−0.121018
$537$	3.04799e6	0.456118
$538$	−3.75039e6	−0.558625
$539$	−1.06965e7	−1.58588
$540$	2.19411e6	0.323798
$541$	−1.05599e7	−1.55120	−0.775601	−	0.631224i	$-0.782553\pi$
$541$	−1.05599e7	−1.55120	−0.775601	+	0.631224i	$0.782553\pi$
$542$	4.27756e6	0.625458
$543$	5.60933e6	0.816416
$544$	4.80124e6	0.695594
$545$	8.67944e6	1.25170
$546$	235021.	0.0337384
$547$	−7.98331e6	−1.14081	−0.570407	−	0.821362i	$-0.693215\pi$
$547$	−7.98331e6	−1.14081	−0.570407	+	0.821362i	$0.693215\pi$
$548$	−9.92266e6	−1.41149
$549$	−1.20172e6	−0.170166
$550$	−3.99153e7	−5.62643
$551$	943315.	0.132366
$552$	724450.	0.101195
$553$	−754984.	−0.104984
$554$	1.40644e7	1.94692
$555$	−8.61327e6	−1.18696
$556$	−5.33400e6	−0.731755
$557$	−1.11083e7	−1.51709	−0.758545	−	0.651620i	$-0.774090\pi$
$557$	−1.11083e7	−1.51709	−0.758545	+	0.651620i	$0.774090\pi$
$558$	−1.69251e6	−0.230115
$559$	−508567.	−0.0688365
$560$	3.85175e6	0.519025
$561$	3.71085e6	0.497813
$562$	−1.12889e7	−1.50768
$563$	4.77414e6	0.634781	0.317391	−	0.948295i	$-0.397193\pi$
$563$	4.77414e6	0.634781	0.317391	+	0.948295i	$0.397193\pi$
$564$	−6.43322e6	−0.851590
$565$	2.27893e7	3.00338
$566$	−2.57461e6	−0.337808
$567$	−222306.	−0.0290399
$568$	−36066.5	−0.00469065
$569$	−5.39583e6	−0.698679	−0.349340	−	0.936996i	$-0.613594\pi$
$569$	−5.39583e6	−0.698679	−0.349340	+	0.936996i	$0.613594\pi$
$570$	−1.59400e6	−0.205495
$571$	−6.32795e6	−0.812218	−0.406109	−	0.913825i	$-0.633115\pi$
$571$	−6.32795e6	−0.812218	−0.406109	+	0.913825i	$0.633115\pi$
$572$	1.96733e6	0.251412
$573$	5.20075e6	0.661728
$574$	−3.95442e6	−0.500960
$575$	2.78746e7	3.51592
$576$	−2.17918e6	−0.273676
$577$	1.15393e7	1.44291	0.721454	−	0.692462i	$-0.243474\pi$
$577$	1.15393e7	1.44291	0.721454	+	0.692462i	$0.243474\pi$
$578$	8.26042e6	1.02845
$579$	1.78584e6	0.221384
$580$	1.29109e7	1.59363
$581$	3.56829e6	0.438550
$582$	7.31097e6	0.894680
$583$	1.02009e7	1.24298
$584$	1.68448e6	0.204378
$585$	820943.	0.0991799
$586$	−2.49936e6	−0.300666
$587$	−9.73075e6	−1.16560	−0.582802	−	0.812614i	$-0.698044\pi$
$587$	−9.73075e6	−1.16560	−0.582802	+	0.812614i	$0.698044\pi$
$588$	−4.12149e6	−0.491599
$589$	587138.	0.0697352
$590$	−983932.	−0.116368
$591$	−6.65357e6	−0.783584
$592$	1.02716e7	1.20458
$593$	8.62091e6	1.00674	0.503369	−	0.864072i	$-0.332094\pi$
$593$	8.62091e6	1.00674	0.503369	+	0.864072i	$0.332094\pi$
$594$	−3.89711e6	−0.453186
$595$	−2.10481e6	−0.243737
$596$	1.96758e6	0.226890
$597$	1.30823e6	0.150228
$598$	−2.87717e6	−0.329012
$599$	−1.61364e6	−0.183755	−0.0918775	−	0.995770i	$-0.529287\pi$
$599$	−1.61364e6	−0.183755	−0.0918775	+	0.995770i	$0.529287\pi$
$600$	1.44894e6	0.164313
$601$	6.67329e6	0.753623	0.376811	−	0.926290i	$-0.377020\pi$
$601$	6.67329e6	0.753623	0.376811	+	0.926290i	$0.377020\pi$
$602$	−1.36936e6	−0.154002
$603$	−3.02388e6	−0.338665
$604$	1.46431e6	0.163321
$605$	3.14476e7	3.49300
$606$	−1.09308e7	−1.20913
$607$	5.78517e6	0.637301	0.318650	−	0.947872i	$-0.396770\pi$
$607$	5.78517e6	0.637301	0.318650	+	0.947872i	$0.396770\pi$
$608$	1.74917e6	0.191899
$609$	−1.30813e6	−0.142925
$610$	1.19491e7	1.30020
$611$	−2.40704e6	−0.260844
$612$	1.42983e6	0.154314
$613$	−7.38642e6	−0.793931	−0.396966	−	0.917833i	$-0.629937\pi$
$613$	−7.38642e6	−0.793931	−0.396966	+	0.917833i	$0.629937\pi$
$614$	−2.56608e7	−2.74694
$615$	−1.38131e7	−1.47266
$616$	−499051.	−0.0529899
$617$	−1.65776e6	−0.175311	−0.0876553	−	0.996151i	$-0.527937\pi$
$617$	−1.65776e6	−0.175311	−0.0876553	+	0.996151i	$0.527937\pi$
$618$	747226.	0.0787010
$619$	2.03696e6	0.213676	0.106838	−	0.994276i	$-0.465927\pi$
$619$	2.03696e6	0.213676	0.106838	+	0.994276i	$0.465927\pi$
$620$	8.03603e6	0.839580
$621$	2.72152e6	0.283193
$622$	−1.18224e7	−1.22526
$623$	3.88078e6	0.400589
$624$	−979004.	−0.100652
$625$	2.26517e7	2.31953
$626$	2.43074e7	2.47915
$627$	1.35192e6	0.137336
$628$	−1.72613e6	−0.174652
$629$	−5.61299e6	−0.565676
$630$	2.21046e6	0.221887
$631$	−3.76775e6	−0.376711	−0.188356	−	0.982101i	$-0.560316\pi$
$631$	−3.76775e6	−0.376711	−0.188356	+	0.982101i	$0.560316\pi$
$632$	480439.	0.0478459
$633$	1.55652e6	0.154399
$634$	4.33220e6	0.428041
$635$	−1.02077e7	−1.00460
$636$	3.93050e6	0.385305
$637$	−1.54209e6	−0.150578
$638$	−2.29320e7	−2.23044
$639$	−135490.	−0.0131267
$640$	−4.52773e6	−0.436949
$641$	−3.40168e6	−0.327001	−0.163500	−	0.986543i	$-0.552278\pi$
$641$	−3.40168e6	−0.327001	−0.163500	+	0.986543i	$0.552278\pi$
$642$	−1.23997e7	−1.18734
$643$	−5.15667e6	−0.491861	−0.245930	−	0.969287i	$-0.579093\pi$
$643$	−5.15667e6	−0.491861	−0.245930	+	0.969287i	$0.579093\pi$
$644$	−3.69926e6	−0.351480
$645$	−4.78328e6	−0.452716
$646$	−1.03876e6	−0.0979338
$647$	−1.02748e7	−0.964972	−0.482486	−	0.875904i	$-0.660266\pi$
$647$	−1.02748e7	−0.964972	−0.482486	+	0.875904i	$0.660266\pi$
$648$	141466.	0.0132347
$649$	834506.	0.0777710
$650$	−5.75448e6	−0.534223
$651$	−814208.	−0.0752979
$652$	7.07422e6	0.651718
$653$	−2.18278e6	−0.200321	−0.100160	−	0.994971i	$-0.531936\pi$
$653$	−2.18278e6	−0.200321	−0.100160	+	0.994971i	$0.531936\pi$
$654$	−5.94001e6	−0.543054
$655$	−2.05786e7	−1.87418
$656$	1.64726e7	1.49452
$657$	6.32803e6	0.571946
$658$	−6.48117e6	−0.583564
$659$	−1.95440e7	−1.75308	−0.876538	−	0.481333i	$-0.840153\pi$
$659$	−1.95440e7	−1.75308	−0.876538	+	0.481333i	$0.840153\pi$
$660$	1.85035e7	1.65346
$661$	1.54507e7	1.37544	0.687722	−	0.725974i	$-0.258611\pi$
$661$	1.54507e7	1.37544	0.687722	+	0.725974i	$0.258611\pi$
$662$	1.12658e7	0.999119
$663$	534982.	0.0472667
$664$	−2.27070e6	−0.199866
$665$	−766819.	−0.0672417
$666$	5.89473e6	0.514966
$667$	1.60144e7	1.39379
$668$	−2.42100e6	−0.209920
$669$	−6.14315e6	−0.530671
$670$	3.00673e7	2.58766
$671$	−1.01344e7	−0.868948
$672$	−2.42565e6	−0.207207
$673$	−9.87103e6	−0.840088	−0.420044	−	0.907504i	$-0.637985\pi$
$673$	−9.87103e6	−0.840088	−0.420044	+	0.907504i	$0.637985\pi$
$674$	−1.66436e7	−1.41123
$675$	5.44317e6	0.459825
$676$	−1.05748e7	−0.890030
$677$	5.76266e6	0.483227	0.241614	−	0.970373i	$-0.422323\pi$
$677$	5.76266e6	0.483227	0.241614	+	0.970373i	$0.422323\pi$
$678$	−1.55965e7	−1.30303
$679$	3.51706e6	0.292756
$680$	1.33941e6	0.111081
$681$	1.16412e7	0.961902
$682$	−1.42734e7	−1.17507
$683$	−4.29021e6	−0.351906	−0.175953	−	0.984399i	$-0.556301\pi$
$683$	−4.29021e6	−0.351906	−0.175953	+	0.984399i	$0.556301\pi$
$684$	520911.	0.0425719
$685$	−3.49189e7	−2.84337
$686$	−8.60884e6	−0.698449
$687$	−1.17874e7	−0.952850
$688$	5.70422e6	0.459436
$689$	1.47063e6	0.118020
$690$	−2.70609e7	−2.16381
$691$	−7.17940e6	−0.571996	−0.285998	−	0.958230i	$-0.592325\pi$
$691$	−7.17940e6	−0.571996	−0.285998	+	0.958230i	$0.592325\pi$
$692$	480799.	0.0381679
$693$	−1.87477e6	−0.148291
$694$	−1.04566e7	−0.824121
$695$	−1.87709e7	−1.47409
$696$	832439.	0.0651372
$697$	−9.00153e6	−0.701834
$698$	7.64826e6	0.594189
$699$	1.05872e6	0.0819578
$700$	−7.39871e6	−0.570704
$701$	−4.67951e6	−0.359671	−0.179835	−	0.983697i	$-0.557557\pi$
$701$	−4.67951e6	−0.359671	−0.179835	+	0.983697i	$0.557557\pi$
$702$	−561835.	−0.0430295
$703$	−2.04491e6	−0.156058
$704$	−1.83776e7	−1.39752
$705$	−2.26392e7	−1.71549
$706$	4.12580e6	0.311527
$707$	−5.25845e6	−0.395648
$708$	321544.	0.0241078
$709$	1.55105e7	1.15881	0.579403	−	0.815041i	$-0.303286\pi$
$709$	1.55105e7	1.15881	0.579403	+	0.815041i	$0.303286\pi$
$710$	1.34722e6	0.100298
$711$	1.80485e6	0.133896
$712$	−2.46956e6	−0.182566
$713$	9.96769e6	0.734295
$714$	1.44049e6	0.105746
$715$	6.92323e6	0.506458
$716$	9.90421e6	0.722000
$717$	−4.89638e6	−0.355694
$718$	1.82796e7	1.32329
$719$	1.24964e7	0.901494	0.450747	−	0.892652i	$-0.351158\pi$
$719$	1.24964e7	0.901494	0.450747	+	0.892652i	$0.351158\pi$
$720$	−9.20792e6	−0.661957
$721$	359465.	0.0257524
$722$	1.89993e7	1.35642
$723$	4.36256e6	0.310382
$724$	1.82271e7	1.29232
$725$	3.20296e7	2.26312
$726$	−2.15220e7	−1.51545
$727$	2.21053e7	1.55117	0.775585	−	0.631243i	$-0.217455\pi$
$727$	2.21053e7	1.55117	0.775585	+	0.631243i	$0.217455\pi$
$728$	−71946.8	−0.00503133
$729$	531441.	0.0370370
$730$	−6.29216e7	−4.37011
$731$	−3.11711e6	−0.215754
$732$	−3.90491e6	−0.269360
$733$	−1.70419e7	−1.17154	−0.585770	−	0.810477i	$-0.699208\pi$
$733$	−1.70419e7	−1.17154	−0.585770	+	0.810477i	$0.699208\pi$
$734$	−1.50652e7	−1.03213
$735$	−1.45039e7	−0.990303
$736$	2.96952e7	2.02066
$737$	−2.55011e7	−1.72938
$738$	9.45336e6	0.638918
$739$	1.19822e7	0.807098	0.403549	−	0.914958i	$-0.367776\pi$
$739$	1.19822e7	0.807098	0.403549	+	0.914958i	$0.367776\pi$
$740$	−2.79882e7	−1.87886
$741$	194903.	0.0130399
$742$	3.95979e6	0.264036
$743$	2.51894e7	1.67396	0.836980	−	0.547233i	$-0.184319\pi$
$743$	2.51894e7	1.67396	0.836980	+	0.547233i	$0.184319\pi$
$744$	518126.	0.0343165
$745$	6.92411e6	0.457060
$746$	−2.12928e7	−1.40083
$747$	−8.53027e6	−0.559321
$748$	1.20581e7	0.787999
$749$	−5.96510e6	−0.388520
$750$	−3.14710e7	−2.04295
$751$	−1.21500e7	−0.786101	−0.393050	−	0.919517i	$-0.628580\pi$
$751$	−1.21500e7	−0.786101	−0.393050	+	0.919517i	$0.628580\pi$
$752$	2.69980e7	1.74095
$753$	1.17251e7	0.753581
$754$	−3.30605e6	−0.211778
$755$	5.15307e6	0.329002
$756$	−722368.	−0.0459679
$757$	−2.71359e7	−1.72110	−0.860548	−	0.509370i	$-0.829879\pi$
$757$	−2.71359e7	−1.72110	−0.860548	+	0.509370i	$0.829879\pi$
$758$	130605.	0.00825635
$759$	2.29513e7	1.44611
$760$	487970.	0.0306450
$761$	1.14417e7	0.716193	0.358096	−	0.933685i	$-0.383426\pi$
$761$	1.14417e7	0.716193	0.358096	+	0.933685i	$0.383426\pi$
$762$	6.98589e6	0.435847
$763$	−2.85754e6	−0.177697
$764$	1.68995e7	1.04747
$765$	5.03172e6	0.310859
$766$	6.51889e6	0.401422
$767$	120308.	0.00738427
$768$	1.08469e7	0.663592
$769$	−533449.	−0.0325295	−0.0162647	−	0.999868i	$-0.505177\pi$
$769$	−533449.	−0.0325295	−0.0162647	+	0.999868i	$0.505177\pi$
$770$	1.86414e7	1.13306
$771$	−1.66701e7	−1.00996
$772$	5.80295e6	0.350433
$773$	−2.97332e7	−1.78975	−0.894876	−	0.446315i	$-0.852736\pi$
$773$	−2.97332e7	−1.78975	−0.894876	+	0.446315i	$0.852736\pi$
$774$	3.27357e6	0.196412
$775$	1.99359e7	1.19229
$776$	−2.23810e6	−0.133422
$777$	2.83576e6	0.168506
$778$	6.68006e6	0.395669
$779$	−3.27941e6	−0.193621
$780$	2.66759e6	0.156994
$781$	−1.14262e6	−0.0670308
$782$	−1.76347e7	−1.03122
$783$	3.12720e6	0.182285
$784$	1.72965e7	1.00500
$785$	−6.07444e6	−0.351829
$786$	1.40835e7	0.813120
$787$	−1.43452e7	−0.825600	−0.412800	−	0.910822i	$-0.635449\pi$
$787$	−1.43452e7	−0.825600	−0.412800	+	0.910822i	$0.635449\pi$
$788$	−2.16203e7	−1.24035
$789$	9.05569e6	0.517880
$790$	−1.79462e7	−1.02307
$791$	−7.50295e6	−0.426374
$792$	1.19302e6	0.0675826
$793$	−1.46105e6	−0.0825056
$794$	3.27761e7	1.84504
$795$	1.38318e7	0.776179
$796$	4.25101e6	0.237799
$797$	−508354.	−0.0283479	−0.0141739	−	0.999900i	$-0.504512\pi$
$797$	−508354.	−0.0283479	−0.0141739	+	0.999900i	$0.504512\pi$
$798$	524794.	0.0291730
$799$	−1.47532e7	−0.817560
$800$	5.93920e7	3.28097
$801$	−9.27730e6	−0.510905
$802$	3.91143e7	2.14733
$803$	5.33659e7	2.92062
$804$	−9.82586e6	−0.536081
$805$	−1.30181e7	−0.708039
$806$	−2.05775e6	−0.111572
$807$	4.31304e6	0.233131
$808$	3.34625e6	0.180314
$809$	3.12790e7	1.68028	0.840139	−	0.542371i	$-0.182473\pi$
$809$	3.12790e7	1.68028	0.840139	+	0.542371i	$0.182473\pi$
$810$	−5.28428e6	−0.282992
$811$	3.12860e7	1.67031	0.835157	−	0.550011i	$-0.185377\pi$
$811$	3.12860e7	1.67031	0.835157	+	0.550011i	$0.185377\pi$
$812$	−4.25068e6	−0.226240
$813$	−4.91931e6	−0.261022
$814$	4.97118e7	2.62965
$815$	2.48949e7	1.31285
$816$	−6.00050e6	−0.315473
$817$	−1.13561e6	−0.0595218
$818$	−4.11259e7	−2.14898
$819$	−270280.	−0.0140800
$820$	−4.48845e7	−2.33111
$821$	−4.33740e6	−0.224580	−0.112290	−	0.993675i	$-0.535819\pi$
$821$	−4.33740e6	−0.224580	−0.112290	+	0.993675i	$0.535819\pi$
$822$	2.38977e7	1.23361
$823$	−3.53989e7	−1.82175	−0.910877	−	0.412678i	$-0.864594\pi$
$823$	−3.53989e7	−1.82175	−0.910877	+	0.412678i	$0.864594\pi$
$824$	−228748.	−0.0117365
$825$	4.59037e7	2.34808
$826$	323941.	0.0165202
$827$	−1.40962e7	−0.716701	−0.358351	−	0.933587i	$-0.616661\pi$
$827$	−1.40962e7	−0.716701	−0.358351	+	0.933587i	$0.616661\pi$
$828$	8.84337e6	0.448272
$829$	3.87149e6	0.195655	0.0978277	−	0.995203i	$-0.468811\pi$
$829$	3.87149e6	0.195655	0.0978277	+	0.995203i	$0.468811\pi$
$830$	8.48191e7	4.27365
$831$	−1.61745e7	−0.812508
$832$	−2.64944e6	−0.132692
$833$	−9.45175e6	−0.471954
$834$	1.28464e7	0.639537
$835$	−8.51977e6	−0.422875
$836$	4.39298e6	0.217392
$837$	1.94643e6	0.0960339
$838$	−5.00851e7	−2.46376
$839$	1.15325e7	0.565610	0.282805	−	0.959177i	$-0.408735\pi$
$839$	1.15325e7	0.565610	0.282805	+	0.959177i	$0.408735\pi$
$840$	−676688.	−0.0330895
$841$	−2.10957e6	−0.102850
$842$	4.94291e6	0.240272
$843$	1.29825e7	0.629200
$844$	5.05779e6	0.244402
$845$	−3.72138e7	−1.79292
$846$	1.54937e7	0.744270
$847$	−1.03535e7	−0.495883
$848$	−1.64949e7	−0.787701
$849$	2.96087e6	0.140977
$850$	−3.52703e7	−1.67441
$851$	−3.47159e7	−1.64325
$852$	−440264.	−0.0207785
$853$	−1.97514e7	−0.929449	−0.464725	−	0.885455i	$-0.653847\pi$
$853$	−1.97514e7	−0.929449	−0.464725	+	0.885455i	$0.653847\pi$
$854$	−3.93402e6	−0.184583
$855$	1.83314e6	0.0857591
$856$	3.79593e6	0.177065
$857$	−3.81924e6	−0.177634	−0.0888168	−	0.996048i	$-0.528309\pi$
$857$	−3.81924e6	−0.177634	−0.0888168	+	0.996048i	$0.528309\pi$
$858$	−4.73810e6	−0.219729
$859$	2.26191e7	1.04591	0.522953	−	0.852362i	$-0.324830\pi$
$859$	2.26191e7	1.04591	0.522953	+	0.852362i	$0.324830\pi$
$860$	−1.55429e7	−0.716615
$861$	4.54769e6	0.209066
$862$	1.45003e7	0.664672
$863$	1.56828e6	0.0716798	0.0358399	−	0.999358i	$-0.488589\pi$
$863$	1.56828e6	0.0716798	0.0358399	+	0.999358i	$0.488589\pi$
$864$	5.79870e6	0.264269
$865$	1.69198e6	0.0768874
$866$	−2.59161e6	−0.117429
$867$	−9.49970e6	−0.429203
$868$	−2.64571e6	−0.119191
$869$	1.52207e7	0.683733
$870$	−3.10947e7	−1.39280
$871$	−3.67643e6	−0.164203
$872$	1.81841e6	0.0809844
$873$	−8.40781e6	−0.373377
$874$	−6.42462e6	−0.284491
$875$	−1.51397e7	−0.668492
$876$	2.05625e7	0.905347
$877$	−1.10885e7	−0.486827	−0.243414	−	0.969923i	$-0.578267\pi$
$877$	−1.10885e7	−0.486827	−0.243414	+	0.969923i	$0.578267\pi$
$878$	−3.90273e6	−0.170857
$879$	2.87433e6	0.125477
$880$	−7.76528e7	−3.38026
$881$	−1.32952e7	−0.577104	−0.288552	−	0.957464i	$-0.593174\pi$
$881$	−1.32952e7	−0.577104	−0.288552	+	0.957464i	$0.593174\pi$
$882$	9.92618e6	0.429646
$883$	3.18262e7	1.37367	0.686836	−	0.726812i	$-0.258999\pi$
$883$	3.18262e7	1.37367	0.686836	+	0.726812i	$0.258999\pi$
$884$	1.73839e6	0.0748196
$885$	1.13155e6	0.0485640
$886$	5.80937e7	2.48625
$887$	5.14270e6	0.219473	0.109737	−	0.993961i	$-0.464999\pi$
$887$	5.14270e6	0.219473	0.109737	+	0.993961i	$0.464999\pi$
$888$	−1.80455e6	−0.0767957
$889$	3.36068e6	0.142617
$890$	9.22471e7	3.90371
$891$	4.48178e6	0.189128
$892$	−1.99617e7	−0.840012
$893$	−5.37484e6	−0.225547
$894$	−4.73870e6	−0.198297
$895$	3.48540e7	1.45444
$896$	1.49067e6	0.0620314
$897$	3.30882e6	0.137307
$898$	1.62765e7	0.673551
$899$	1.14535e7	0.472649
$900$	1.76872e7	0.727868
$901$	9.01376e6	0.369908
$902$	7.97226e7	3.26261
$903$	1.57480e6	0.0642698
$904$	4.77455e6	0.194317
$905$	6.41431e7	2.60332
$906$	−3.52664e6	−0.142738
$907$	−1.42585e7	−0.575515	−0.287757	−	0.957703i	$-0.592910\pi$
$907$	−1.42585e7	−0.575515	−0.287757	+	0.957703i	$0.592910\pi$
$908$	3.78273e7	1.52262
$909$	1.25707e7	0.504604
$910$	2.68748e6	0.107582
$911$	1.34389e7	0.536499	0.268250	−	0.963349i	$-0.413555\pi$
$911$	1.34389e7	0.536499	0.268250	+	0.963349i	$0.413555\pi$
$912$	−2.18608e6	−0.0870321
$913$	−7.19380e7	−2.85615
$914$	3.84755e7	1.52342
$915$	−1.37418e7	−0.542614
$916$	−3.83021e7	−1.50829
$917$	6.77510e6	0.266068
$918$	−3.44360e6	−0.134867
$919$	1.00642e7	0.393089	0.196545	−	0.980495i	$-0.437028\pi$
$919$	1.00642e7	0.393089	0.196545	+	0.980495i	$0.437028\pi$
$920$	8.28414e6	0.322684
$921$	2.95106e7	1.14638
$922$	961603.	0.0372536
$923$	−164728.	−0.00636450
$924$	−6.09192e6	−0.234733
$925$	−6.94335e7	−2.66818
$926$	1.00459e7	0.385002
$927$	−859329.	−0.0328443
$928$	3.41217e7	1.30065
$929$	3.57287e7	1.35824	0.679122	−	0.734025i	$-0.262361\pi$
$929$	3.57287e7	1.35824	0.679122	+	0.734025i	$0.262361\pi$
$930$	−1.93539e7	−0.733773
$931$	−3.44343e6	−0.130202
$932$	3.44025e6	0.129733
$933$	1.35960e7	0.511338
$934$	−6.41957e6	−0.240790
$935$	4.24338e7	1.58739
$936$	171994.	0.00641689
$937$	7.87788e6	0.293130	0.146565	−	0.989201i	$-0.453178\pi$
$937$	7.87788e6	0.293130	0.146565	+	0.989201i	$0.453178\pi$
$938$	−9.89910e6	−0.367357
$939$	−2.79541e7	−1.03462
$940$	−7.35643e7	−2.71549
$941$	3.02922e7	1.11521	0.557605	−	0.830106i	$-0.311720\pi$
$941$	3.02922e7	1.11521	0.557605	+	0.830106i	$0.311720\pi$
$942$	4.15721e6	0.152642
$943$	−5.56737e7	−2.03878
$944$	−1.34941e6	−0.0492849
$945$	−2.54209e6	−0.0926001
$946$	2.76068e7	1.00297
$947$	−3.12659e7	−1.13291	−0.566455	−	0.824093i	$-0.691686\pi$
$947$	−3.12659e7	−1.13291	−0.566455	+	0.824093i	$0.691686\pi$
$948$	5.86472e6	0.211947
$949$	7.69361e6	0.277310
$950$	−1.28496e7	−0.461934
$951$	−4.98214e6	−0.178634
$952$	−440975.	−0.0157697
$953$	−2.75341e7	−0.982060	−0.491030	−	0.871143i	$-0.663379\pi$
$953$	−2.75341e7	−0.982060	−0.491030	+	0.871143i	$0.663379\pi$
$954$	−9.46620e6	−0.336748
$955$	5.94710e7	2.11007
$956$	−1.59104e7	−0.563037
$957$	2.63725e7	0.930831
$958$	−1.30790e7	−0.460426
$959$	1.14964e7	0.403659
$960$	−2.49190e7	−0.872677
$961$	−2.15003e7	−0.750992
$962$	7.16681e6	0.249683
$963$	1.42600e7	0.495513
$964$	1.41758e7	0.491310
$965$	2.04212e7	0.705932
$966$	8.90929e6	0.307185
$967$	−3.59120e7	−1.23502	−0.617509	−	0.786564i	$-0.711858\pi$
$967$	−3.59120e7	−1.23502	−0.617509	+	0.786564i	$0.711858\pi$
$968$	6.58853e6	0.225996
$969$	1.19460e6	0.0408707
$970$	8.36015e7	2.85289
$971$	−1.55620e7	−0.529684	−0.264842	−	0.964292i	$-0.585320\pi$
$971$	−1.55620e7	−0.529684	−0.264842	+	0.964292i	$0.585320\pi$
$972$	1.72688e6	0.0586268
$973$	6.17996e6	0.209268
$974$	−4.08658e7	−1.38027
$975$	6.61780e6	0.222947
$976$	1.63876e7	0.550668
$977$	−2.43514e7	−0.816184	−0.408092	−	0.912941i	$-0.633806\pi$
$977$	−2.43514e7	−0.816184	−0.408092	+	0.912941i	$0.633806\pi$
$978$	−1.70375e7	−0.569586
$979$	−7.82379e7	−2.60892
$980$	−4.71295e7	−1.56757
$981$	6.83117e6	0.226633
$982$	4.03921e7	1.33665
$983$	−2.74918e7	−0.907442	−0.453721	−	0.891144i	$-0.649904\pi$
$983$	−2.74918e7	−0.907442	−0.453721	+	0.891144i	$0.649904\pi$
$984$	−2.89395e6	−0.0952804
$985$	−7.60840e7	−2.49863
$986$	−2.02634e7	−0.663774
$987$	7.45351e6	0.243539
$988$	633323.	0.0206411
$989$	−1.92790e7	−0.626750
$990$	−4.45637e7	−1.44509
$991$	2.10770e7	0.681751	0.340875	−	0.940109i	$-0.389277\pi$
$991$	2.10770e7	0.681751	0.340875	+	0.940109i	$0.389277\pi$
$992$	2.12380e7	0.685228
$993$	−1.29560e7	−0.416963
$994$	−443546.	−0.0142388
$995$	1.49597e7	0.479034
$996$	−2.77185e7	−0.885362
$997$	5.82751e7	1.85671	0.928357	−	0.371690i	$-0.121221\pi$
$997$	5.82751e7	1.85671	0.928357	+	0.371690i	$0.121221\pi$
$998$	−4.70057e7	−1.49391
$999$	−6.77910e6	−0.214911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.d.1.6	✓	25
3.2	odd	2		927.6.a.f.1.20		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.d.1.6	✓	25	1.1	even	1	trivial
927.6.a.f.1.20		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)

\(f(q)\)	\(=\)	\(q-7.82591 q^{2} +9.00000 q^{3} +29.2448 q^{4} +102.916 q^{5} -70.4332 q^{6} -33.8830 q^{7} +21.5617 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-7.82591 q^{2} +9.00000 q^{3} +29.2448 q^{4} +102.916 q^{5} -70.4332 q^{6} -33.8830 q^{7} +21.5617 q^{8} +81.0000 q^{9} -805.408 q^{10} +683.094 q^{11} +263.204 q^{12} +98.4797 q^{13} +265.165 q^{14} +926.241 q^{15} -1104.57 q^{16} +603.601 q^{17} -633.899 q^{18} +219.902 q^{19} +3009.75 q^{20} -304.947 q^{21} -5345.83 q^{22} +3733.22 q^{23} +194.055 q^{24} +7466.63 q^{25} -770.693 q^{26} +729.000 q^{27} -990.903 q^{28} +4289.71 q^{29} -7248.67 q^{30} +2670.00 q^{31} +7954.32 q^{32} +6147.85 q^{33} -4723.73 q^{34} -3487.09 q^{35} +2368.83 q^{36} -9299.17 q^{37} -1720.93 q^{38} +886.317 q^{39} +2219.03 q^{40} -14913.0 q^{41} +2386.49 q^{42} -5164.18 q^{43} +19977.0 q^{44} +8336.17 q^{45} -29215.8 q^{46} -24442.0 q^{47} -9941.17 q^{48} -15658.9 q^{49} -58433.1 q^{50} +5432.41 q^{51} +2880.02 q^{52} +14933.3 q^{53} -5705.09 q^{54} +70301.1 q^{55} -730.574 q^{56} +1979.12 q^{57} -33570.8 q^{58} +1221.66 q^{59} +27087.8 q^{60} -14836.1 q^{61} -20895.2 q^{62} -2744.52 q^{63} -26903.4 q^{64} +10135.1 q^{65} -48112.5 q^{66} -37331.8 q^{67} +17652.2 q^{68} +33599.0 q^{69} +27289.7 q^{70} -1672.71 q^{71} +1746.50 q^{72} +78123.8 q^{73} +72774.5 q^{74} +67199.7 q^{75} +6431.00 q^{76} -23145.3 q^{77} -6936.24 q^{78} +22282.1 q^{79} -113678. q^{80} +6561.00 q^{81} +116708. q^{82} -105312. q^{83} -8918.13 q^{84} +62120.0 q^{85} +40414.4 q^{86} +38607.4 q^{87} +14728.6 q^{88} -114535. q^{89} -65238.1 q^{90} -3336.79 q^{91} +109177. q^{92} +24030.0 q^{93} +191281. q^{94} +22631.4 q^{95} +71588.9 q^{96} -103800. q^{97} +122545. q^{98} +55330.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 14 q^{2} + 225 q^{3} + 486 q^{4} + 47 q^{5} + 126 q^{6} + 402 q^{7} + 342 q^{8} + 2025 q^{9}+O(q^{10}) \) 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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