LMFDB - Embedded newform 309.6.a.b.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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 475 x^{18} + 1732 x^{17} + 94501 x^{16} - 304042 x^{15} - 10274267 x^{14} + \cdots - 108537388253184 $ x^20 - 4x^19 - 475x^18 + 1732x^17 + 94501x^16 - 304042x^15 - 10274267x^14 + 27738506x^13 + 668854800x^12 - 1394251104x^11 - 26886918880x^10 + 36931823776x^9 + 663067133248x^8 - 391924258816x^7 - 9543181747968x^6 - 2051078115840x^5 + 69736119883776x^4 + 68811719589888x^3 - 164566613229568x^2 - 286519559659520*x - 108537388253184
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-4.53264$ of defining polynomial
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)

$f(q)$	$=$	$q-4.53264 q^{2} -9.00000 q^{3} -11.4552 q^{4} -46.1790 q^{5} +40.7937 q^{6} -25.4481 q^{7} +196.967 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.53264 q^{2} -9.00000 q^{3} -11.4552 q^{4} -46.1790 q^{5} +40.7937 q^{6} -25.4481 q^{7} +196.967 q^{8} +81.0000 q^{9} +209.313 q^{10} -248.271 q^{11} +103.097 q^{12} -109.465 q^{13} +115.347 q^{14} +415.611 q^{15} -526.213 q^{16} -679.458 q^{17} -367.144 q^{18} -1978.68 q^{19} +528.990 q^{20} +229.033 q^{21} +1125.32 q^{22} -2507.14 q^{23} -1772.70 q^{24} -992.497 q^{25} +496.167 q^{26} -729.000 q^{27} +291.513 q^{28} -7042.99 q^{29} -1883.82 q^{30} -3728.83 q^{31} -3917.80 q^{32} +2234.44 q^{33} +3079.74 q^{34} +1175.17 q^{35} -927.870 q^{36} +734.792 q^{37} +8968.66 q^{38} +985.189 q^{39} -9095.73 q^{40} +7773.46 q^{41} -1038.12 q^{42} -8402.92 q^{43} +2843.99 q^{44} -3740.50 q^{45} +11364.0 q^{46} +6857.97 q^{47} +4735.91 q^{48} -16159.4 q^{49} +4498.63 q^{50} +6115.12 q^{51} +1253.95 q^{52} -16335.8 q^{53} +3304.29 q^{54} +11464.9 q^{55} -5012.43 q^{56} +17808.2 q^{57} +31923.3 q^{58} +1923.32 q^{59} -4760.91 q^{60} -16080.7 q^{61} +16901.4 q^{62} -2061.30 q^{63} +34596.8 q^{64} +5055.01 q^{65} -10127.9 q^{66} +20830.1 q^{67} +7783.32 q^{68} +22564.3 q^{69} -5326.61 q^{70} -27105.6 q^{71} +15954.3 q^{72} -63787.3 q^{73} -3330.55 q^{74} +8932.47 q^{75} +22666.2 q^{76} +6318.02 q^{77} -4465.50 q^{78} -34303.5 q^{79} +24300.0 q^{80} +6561.00 q^{81} -35234.3 q^{82} +16836.7 q^{83} -2623.62 q^{84} +31376.7 q^{85} +38087.4 q^{86} +63386.9 q^{87} -48901.1 q^{88} +33819.6 q^{89} +16954.3 q^{90} +2785.69 q^{91} +28719.8 q^{92} +33559.5 q^{93} -31084.7 q^{94} +91373.7 q^{95} +35260.2 q^{96} +44262.4 q^{97} +73244.7 q^{98} -20109.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * 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 $

$2$	−4.53264	−0.801265	−0.400632	−	0.916239i	$-0.631210\pi$
$2$	−4.53264	−0.801265	−0.400632	+	0.916239i	$0.631210\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−11.4552	−0.357975
$5$	−46.1790	−0.826076	−0.413038	−	0.910714i	$-0.635532\pi$
$5$	−46.1790	−0.826076	−0.413038	+	0.910714i	$0.635532\pi$
$6$	40.7937	0.462610
$7$	−25.4481	−0.196295	−0.0981477	−	0.995172i	$-0.531292\pi$
$7$	−25.4481	−0.196295	−0.0981477	+	0.995172i	$0.531292\pi$
$8$	196.967	1.08810
$9$	81.0000	0.333333
$10$	209.313	0.661905
$11$	−248.271	−0.618649	−0.309324	−	0.950957i	$-0.600103\pi$
$11$	−248.271	−0.618649	−0.309324	+	0.950957i	$0.600103\pi$
$12$	103.097	0.206677
$13$	−109.465	−0.179646	−0.0898232	−	0.995958i	$-0.528630\pi$
$13$	−109.465	−0.179646	−0.0898232	+	0.995958i	$0.528630\pi$
$14$	115.347	0.157285
$15$	415.611	0.476935
$16$	−526.213	−0.513879
$17$	−679.458	−0.570217	−0.285108	−	0.958495i	$-0.592030\pi$
$17$	−679.458	−0.570217	−0.285108	+	0.958495i	$0.592030\pi$
$18$	−367.144	−0.267088
$19$	−1978.68	−1.25746	−0.628728	−	0.777626i	$-0.716424\pi$
$19$	−1978.68	−1.25746	−0.628728	+	0.777626i	$0.716424\pi$
$20$	528.990	0.295714
$21$	229.033	0.113331
$22$	1125.32	0.495701
$23$	−2507.14	−0.988233	−0.494117	−	0.869396i	$-0.664508\pi$
$23$	−2507.14	−0.988233	−0.494117	+	0.869396i	$0.664508\pi$
$24$	−1772.70	−0.628213
$25$	−992.497	−0.317599
$26$	496.167	0.143944
$27$	−729.000	−0.192450
$28$	291.513	0.0702688
$29$	−7042.99	−1.55511	−0.777557	−	0.628812i	$-0.783541\pi$
$29$	−7042.99	−1.55511	−0.777557	+	0.628812i	$0.783541\pi$
$30$	−1883.82	−0.382151
$31$	−3728.83	−0.696897	−0.348448	−	0.937328i	$-0.613291\pi$
$31$	−3728.83	−0.696897	−0.348448	+	0.937328i	$0.613291\pi$
$32$	−3917.80	−0.676344
$33$	2234.44	0.357177
$34$	3079.74	0.456895
$35$	1175.17	0.162155
$36$	−927.870	−0.119325
$37$	734.792	0.0882389	0.0441194	−	0.999026i	$-0.485952\pi$
$37$	734.792	0.0882389	0.0441194	+	0.999026i	$0.485952\pi$
$38$	8968.66	1.00755
$39$	985.189	0.103719
$40$	−9095.73	−0.898851
$41$	7773.46	0.722195	0.361098	−	0.932528i	$-0.382402\pi$
$41$	7773.46	0.722195	0.361098	+	0.932528i	$0.382402\pi$
$42$	−1038.12	−0.0908083
$43$	−8402.92	−0.693042	−0.346521	−	0.938042i	$-0.612637\pi$
$43$	−8402.92	−0.693042	−0.346521	+	0.938042i	$0.612637\pi$
$44$	2843.99	0.221461
$45$	−3740.50	−0.275359
$46$	11364.0	0.791837
$47$	6857.97	0.452846	0.226423	−	0.974029i	$-0.427297\pi$
$47$	6857.97	0.452846	0.226423	+	0.974029i	$0.427297\pi$
$48$	4735.91	0.296688
$49$	−16159.4	−0.961468
$50$	4498.63	0.254481
$51$	6115.12	0.329215
$52$	1253.95	0.0643089
$53$	−16335.8	−0.798825	−0.399412	−	0.916771i	$-0.630786\pi$
$53$	−16335.8	−0.798825	−0.399412	+	0.916771i	$0.630786\pi$
$54$	3304.29	0.154203
$55$	11464.9	0.511051
$56$	−5012.43	−0.213589
$57$	17808.2	0.725992
$58$	31923.3	1.24606
$59$	1923.32	0.0719320	0.0359660	−	0.999353i	$-0.488549\pi$
$59$	1923.32	0.0719320	0.0359660	+	0.999353i	$0.488549\pi$
$60$	−4760.91	−0.170731
$61$	−16080.7	−0.553326	−0.276663	−	0.960967i	$-0.589228\pi$
$61$	−16080.7	−0.553326	−0.276663	+	0.960967i	$0.589228\pi$
$62$	16901.4	0.558399
$63$	−2061.30	−0.0654318
$64$	34596.8	1.05581
$65$	5055.01	0.148402
$66$	−10127.9	−0.286193
$67$	20830.1	0.566898	0.283449	−	0.958987i	$-0.408521\pi$
$67$	20830.1	0.566898	0.283449	+	0.958987i	$0.408521\pi$
$68$	7783.32	0.204123
$69$	22564.3	0.570557
$70$	−5326.61	−0.129929
$71$	−27105.6	−0.638136	−0.319068	−	0.947732i	$-0.603370\pi$
$71$	−27105.6	−0.638136	−0.319068	+	0.947732i	$0.603370\pi$
$72$	15954.3	0.362699
$73$	−63787.3	−1.40096	−0.700482	−	0.713670i	$-0.747031\pi$
$73$	−63787.3	−1.40096	−0.700482	+	0.713670i	$0.747031\pi$
$74$	−3330.55	−0.0707027
$75$	8932.47	0.183366
$76$	22666.2	0.450137
$77$	6318.02	0.121438
$78$	−4465.50	−0.0831063
$79$	−34303.5	−0.618402	−0.309201	−	0.950997i	$-0.600062\pi$
$79$	−34303.5	−0.618402	−0.309201	+	0.950997i	$0.600062\pi$
$80$	24300.0	0.424503
$81$	6561.00	0.111111
$82$	−35234.3	−0.578670
$83$	16836.7	0.268263	0.134132	−	0.990964i	$-0.457176\pi$
$83$	16836.7	0.268263	0.134132	+	0.990964i	$0.457176\pi$
$84$	−2623.62	−0.0405697
$85$	31376.7	0.471042
$86$	38087.4	0.555310
$87$	63386.9	0.897845
$88$	−48901.1	−0.673150
$89$	33819.6	0.452579	0.226289	−	0.974060i	$-0.427341\pi$
$89$	33819.6	0.452579	0.226289	+	0.974060i	$0.427341\pi$
$90$	16954.3	0.220635
$91$	2785.69	0.0352638
$92$	28719.8	0.353763
$93$	33559.5	0.402353
$94$	−31084.7	−0.362850
$95$	91373.7	1.03875
$96$	35260.2	0.390487
$97$	44262.4	0.477646	0.238823	−	0.971063i	$-0.423239\pi$
$97$	44262.4	0.477646	0.238823	+	0.971063i	$0.423239\pi$
$98$	73244.7	0.770391
$99$	−20109.9	−0.206216
$100$	11369.2	0.113692
$101$	−15789.1	−0.154011	−0.0770057	−	0.997031i	$-0.524536\pi$
$101$	−15789.1	−0.154011	−0.0770057	+	0.997031i	$0.524536\pi$
$102$	−27717.6	−0.263788
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	−21561.0	−0.195473
$105$	−10576.5	−0.0936202
$106$	74044.4	0.640070
$107$	226312.	1.91094	0.955471	−	0.295087i	$-0.0953485\pi$
$107$	226312.	1.91094	0.955471	+	0.295087i	$0.0953485\pi$
$108$	8350.83	0.0688923
$109$	24416.3	0.196840	0.0984201	−	0.995145i	$-0.468621\pi$
$109$	24416.3	0.196840	0.0984201	+	0.995145i	$0.468621\pi$
$110$	−51966.3	−0.409487
$111$	−6613.13	−0.0509447
$112$	13391.1	0.100872
$113$	127395.	0.938547	0.469274	−	0.883053i	$-0.344516\pi$
$113$	127395.	0.938547	0.469274	+	0.883053i	$0.344516\pi$
$114$	−80717.9	−0.581712
$115$	115777.	0.816356
$116$	80678.8	0.556691
$117$	−8866.70	−0.0598821
$118$	−8717.72	−0.0576365
$119$	17290.9	0.111931
$120$	81861.6	0.518952
$121$	−99412.6	−0.617274
$122$	72888.1	0.443360
$123$	−69961.1	−0.416960
$124$	42714.5	0.249471
$125$	190142.	1.08844
$126$	9343.11	0.0524282
$127$	−146334.	−0.805075	−0.402537	−	0.915404i	$-0.631872\pi$
$127$	−146334.	−0.805075	−0.402537	+	0.915404i	$0.631872\pi$
$128$	−31445.0	−0.169640
$129$	75626.3	0.400128
$130$	−22912.5	−0.118909
$131$	−113790.	−0.579330	−0.289665	−	0.957128i	$-0.593544\pi$
$131$	−113790.	−0.579330	−0.289665	+	0.957128i	$0.593544\pi$
$132$	−25595.9	−0.127860
$133$	50353.8	0.246833
$134$	−94415.4	−0.454235
$135$	33664.5	0.158978
$136$	−133831.	−0.620452
$137$	−44522.5	−0.202665	−0.101332	−	0.994853i	$-0.532311\pi$
$137$	−44522.5	−0.202665	−0.101332	+	0.994853i	$0.532311\pi$
$138$	−102276.	−0.457167
$139$	−106782.	−0.468773	−0.234387	−	0.972143i	$-0.575308\pi$
$139$	−106782.	−0.468773	−0.234387	+	0.972143i	$0.575308\pi$
$140$	−13461.8	−0.0580474
$141$	−61721.7	−0.261451
$142$	122860.	0.511316
$143$	27177.1	0.111138
$144$	−42623.2	−0.171293
$145$	325239.	1.28464
$146$	289125.	1.12254
$147$	145435.	0.555104
$148$	−8417.18	−0.0315873
$149$	360132.	1.32891	0.664456	−	0.747327i	$-0.268663\pi$
$149$	360132.	1.32891	0.664456	+	0.747327i	$0.268663\pi$
$150$	−40487.7	−0.146925
$151$	90301.3	0.322294	0.161147	−	0.986930i	$-0.448481\pi$
$151$	90301.3	0.322294	0.161147	+	0.986930i	$0.448481\pi$
$152$	−389735.	−1.36823
$153$	−55036.1	−0.190072
$154$	−28637.3	−0.0973039
$155$	172194.	0.575689
$156$	−11285.5	−0.0371287
$157$	−351704.	−1.13875	−0.569375	−	0.822078i	$-0.692815\pi$
$157$	−351704.	−1.13875	−0.569375	+	0.822078i	$0.692815\pi$
$158$	155485.	0.495503
$159$	147022.	0.461202
$160$	180920.	0.558711
$161$	63802.0	0.193986
$162$	−29738.6	−0.0890294
$163$	396900.	1.17007	0.585035	−	0.811008i	$-0.301081\pi$
$163$	396900.	1.17007	0.585035	+	0.811008i	$0.301081\pi$
$164$	−89046.4	−0.258528
$165$	−103184.	−0.295055
$166$	−76314.5	−0.214950
$167$	−503094.	−1.39591	−0.697956	−	0.716141i	$-0.745907\pi$
$167$	−503094.	−1.39591	−0.697956	+	0.716141i	$0.745907\pi$
$168$	45111.8	0.123315
$169$	−359310.	−0.967727
$170$	−142219.	−0.377430
$171$	−160273.	−0.419152
$172$	96257.1	0.248091
$173$	42645.6	0.108333	0.0541663	−	0.998532i	$-0.482750\pi$
$173$	42645.6	0.108333	0.0541663	+	0.998532i	$0.482750\pi$
$174$	−287310.	−0.719412
$175$	25257.2	0.0623432
$176$	130643.	0.317911
$177$	−17309.9	−0.0415299
$178$	−153292.	−0.362635
$179$	283966.	0.662421	0.331210	−	0.943557i	$-0.392543\pi$
$179$	283966.	0.662421	0.331210	+	0.943557i	$0.392543\pi$
$180$	42848.2	0.0985714
$181$	−510855.	−1.15905	−0.579523	−	0.814956i	$-0.696761\pi$
$181$	−510855.	−1.15905	−0.579523	+	0.814956i	$0.696761\pi$
$182$	−12626.5	−0.0282556
$183$	144726.	0.319463
$184$	−493824.	−1.07529
$185$	−33932.0	−0.0728920
$186$	−152113.	−0.322392
$187$	168690.	0.352764
$188$	−78559.4	−0.162108
$189$	18551.7	0.0377771
$190$	−414164.	−0.832316
$191$	−399921.	−0.793214	−0.396607	−	0.917989i	$-0.629812\pi$
$191$	−399921.	−0.793214	−0.396607	+	0.917989i	$0.629812\pi$
$192$	−311371.	−0.609572
$193$	−367730.	−0.710617	−0.355308	−	0.934749i	$-0.615624\pi$
$193$	−367730.	−0.710617	−0.355308	+	0.934749i	$0.615624\pi$
$194$	−200625.	−0.382721
$195$	−45495.1	−0.0856797
$196$	185109.	0.344181
$197$	906541.	1.66426	0.832132	−	0.554578i	$-0.187120\pi$
$197$	906541.	1.66426	0.832132	+	0.554578i	$0.187120\pi$
$198$	91151.1	0.165234
$199$	−154392.	−0.276370	−0.138185	−	0.990406i	$-0.544127\pi$
$199$	−154392.	−0.276370	−0.138185	+	0.990406i	$0.544127\pi$
$200$	−195489.	−0.345579
$201$	−187471.	−0.327299
$202$	71566.1	0.123404
$203$	179231.	0.305262
$204$	−70049.9	−0.117851
$205$	−358971.	−0.596588
$206$	−48086.8	−0.0789510
$207$	−203079.	−0.329411
$208$	57602.1	0.0923166
$209$	491250.	0.777923
$210$	47939.5	0.0750146
$211$	−161322.	−0.249453	−0.124726	−	0.992191i	$-0.539805\pi$
$211$	−161322.	−0.249453	−0.124726	+	0.992191i	$0.539805\pi$
$212$	187130.	0.285959
$213$	243951.	0.368428
$214$	−1.02579e6	−1.53117
$215$	388039.	0.572505
$216$	−143589.	−0.209404
$217$	94891.7	0.136798
$218$	−110670.	−0.157721
$219$	574085.	0.808846
$220$	−131333.	−0.182943
$221$	74377.1	0.102437
$222$	29974.9	0.0408202
$223$	−1.14510e6	−1.54199	−0.770997	−	0.636838i	$-0.780242\pi$
$223$	−1.14510e6	−1.54199	−0.770997	+	0.636838i	$0.780242\pi$
$224$	99700.6	0.132763
$225$	−80392.2	−0.105866
$226$	−577435.	−0.752025
$227$	−625152.	−0.805232	−0.402616	−	0.915369i	$-0.631899\pi$
$227$	−625152.	−0.805232	−0.402616	+	0.915369i	$0.631899\pi$
$228$	−203996.	−0.259887
$229$	304768.	0.384043	0.192022	−	0.981391i	$-0.438496\pi$
$229$	304768.	0.384043	0.192022	+	0.981391i	$0.438496\pi$
$230$	−524777.	−0.654117
$231$	−56862.2	−0.0701122
$232$	−1.38723e6	−1.69212
$233$	−740347.	−0.893399	−0.446700	−	0.894684i	$-0.647401\pi$
$233$	−740347.	−0.893399	−0.446700	+	0.894684i	$0.647401\pi$
$234$	40189.5	0.0479814
$235$	−316694.	−0.374085
$236$	−22032.0	−0.0257498
$237$	308731.	0.357034
$238$	−78373.4	−0.0896864
$239$	1.40413e6	1.59006	0.795028	−	0.606572i	$-0.207456\pi$
$239$	1.40413e6	1.59006	0.795028	+	0.606572i	$0.207456\pi$
$240$	−218700.	−0.245087
$241$	402583.	0.446491	0.223245	−	0.974762i	$-0.428335\pi$
$241$	402583.	0.446491	0.223245	+	0.974762i	$0.428335\pi$
$242$	450601.	0.494600
$243$	−59049.0	−0.0641500
$244$	184208.	0.198077
$245$	746225.	0.794245
$246$	317108.	0.334095
$247$	216598.	0.225897
$248$	−734455.	−0.758291
$249$	−151530.	−0.154882
$250$	−861845.	−0.872126
$251$	395462.	0.396205	0.198103	−	0.980181i	$-0.436522\pi$
$251$	395462.	0.396205	0.198103	+	0.980181i	$0.436522\pi$
$252$	23612.5	0.0234229
$253$	622451.	0.611369
$254$	663279.	0.645078
$255$	−282390.	−0.271956
$256$	−964568.	−0.919884
$257$	60605.8	0.0572376	0.0286188	−	0.999590i	$-0.490889\pi$
$257$	60605.8	0.0572376	0.0286188	+	0.999590i	$0.490889\pi$
$258$	−342787.	−0.320608
$259$	−18699.1	−0.0173209
$260$	−57906.1	−0.0531240
$261$	−570482.	−0.518371
$262$	515769.	0.464196
$263$	652827.	0.581981	0.290991	−	0.956726i	$-0.406015\pi$
$263$	652827.	0.581981	0.290991	+	0.956726i	$0.406015\pi$
$264$	440110.	0.388643
$265$	754373.	0.659890
$266$	−228235.	−0.197778
$267$	−304377.	−0.261296
$268$	−238613.	−0.202935
$269$	168544.	0.142014	0.0710071	−	0.997476i	$-0.477379\pi$
$269$	168544.	0.142014	0.0710071	+	0.997476i	$0.477379\pi$
$270$	−152589.	−0.127384
$271$	165500.	0.136891	0.0684453	−	0.997655i	$-0.478196\pi$
$271$	165500.	0.136891	0.0684453	+	0.997655i	$0.478196\pi$
$272$	357539.	0.293023
$273$	−25071.2	−0.0203596
$274$	201805.	0.162388
$275$	246408.	0.196482
$276$	−258478.	−0.204245
$277$	−2.11084e6	−1.65293	−0.826467	−	0.562985i	$-0.809653\pi$
$277$	−2.11084e6	−1.65293	−0.826467	+	0.562985i	$0.809653\pi$
$278$	484006.	0.375612
$279$	−302035.	−0.232299
$280$	231469.	0.176440
$281$	−352282.	−0.266149	−0.133075	−	0.991106i	$-0.542485\pi$
$281$	−352282.	−0.266149	−0.133075	+	0.991106i	$0.542485\pi$
$282$	279762.	0.209492
$283$	−440538.	−0.326977	−0.163489	−	0.986545i	$-0.552275\pi$
$283$	−440538.	−0.326977	−0.163489	+	0.986545i	$0.552275\pi$
$284$	310500.	0.228437
$285$	−822364.	−0.599724
$286$	−123184.	−0.0890510
$287$	−197820.	−0.141764
$288$	−317342.	−0.225448
$289$	−958194.	−0.674853
$290$	−1.47419e6	−1.02934
$291$	−398362.	−0.275769
$292$	730695.	0.501509
$293$	1.83602e6	1.24942	0.624710	−	0.780857i	$-0.285217\pi$
$293$	1.83602e6	1.24942	0.624710	+	0.780857i	$0.285217\pi$
$294$	−659202.	−0.444785
$295$	−88817.1	−0.0594212
$296$	144729.	0.0960125
$297$	180989.	0.119059
$298$	−1.63235e6	−1.06481
$299$	274445.	0.177533
$300$	−102323.	−0.0656403
$301$	213838.	0.136041
$302$	−409303.	−0.258243
$303$	142102.	0.0889185
$304$	1.04121e6	0.646180
$305$	742592.	0.457089
$306$	249459.	0.152298
$307$	776530.	0.470232	0.235116	−	0.971967i	$-0.424453\pi$
$307$	776530.	0.470232	0.235116	+	0.971967i	$0.424453\pi$
$308$	−72374.1	−0.0434717
$309$	−95481.0	−0.0568880
$310$	−780492.	−0.461280
$311$	−390585.	−0.228989	−0.114494	−	0.993424i	$-0.536525\pi$
$311$	−390585.	−0.228989	−0.114494	+	0.993424i	$0.536525\pi$
$312$	194049.	0.112856
$313$	2.63993e6	1.52311	0.761555	−	0.648100i	$-0.224436\pi$
$313$	2.63993e6	1.52311	0.761555	+	0.648100i	$0.224436\pi$
$314$	1.59415e6	0.912440
$315$	95188.7	0.0540516
$316$	392953.	0.221372
$317$	−1.02836e6	−0.574773	−0.287386	−	0.957815i	$-0.592786\pi$
$317$	−1.02836e6	−0.574773	−0.287386	+	0.957815i	$0.592786\pi$
$318$	−666400.	−0.369545
$319$	1.74857e6	0.962069
$320$	−1.59765e6	−0.872179
$321$	−2.03680e6	−1.10328
$322$	−289192.	−0.155434
$323$	1.34443e6	0.717022
$324$	−75157.5	−0.0397750
$325$	108644.	0.0570555
$326$	−1.79900e6	−0.937535
$327$	−219747.	−0.113646
$328$	1.53111e6	0.785819
$329$	−174522.	−0.0888917
$330$	467697.	0.236417
$331$	−457762.	−0.229652	−0.114826	−	0.993386i	$-0.536631\pi$
$331$	−457762.	−0.229652	−0.114826	+	0.993386i	$0.536631\pi$
$332$	−192867.	−0.0960314
$333$	59518.1	0.0294130
$334$	2.28034e6	1.11849
$335$	−961915.	−0.468300
$336$	−120520.	−0.0582386
$337$	2.56354e6	1.22960	0.614801	−	0.788682i	$-0.289236\pi$
$337$	2.56354e6	1.22960	0.614801	+	0.788682i	$0.289236\pi$
$338$	1.62862e6	0.775406
$339$	−1.14655e6	−0.541871
$340$	−359426.	−0.168621
$341$	925760.	0.431134
$342$	726462.	0.335852
$343$	838932.	0.385027
$344$	−1.65510e6	−0.754097
$345$	−1.04200e6	−0.471323
$346$	−193297.	−0.0868031
$347$	562209.	0.250654	0.125327	−	0.992116i	$-0.460002\pi$
$347$	562209.	0.250654	0.125327	+	0.992116i	$0.460002\pi$
$348$	−726109.	−0.321406
$349$	1.43697e6	0.631517	0.315758	−	0.948840i	$-0.397741\pi$
$349$	1.43697e6	0.631517	0.315758	+	0.948840i	$0.397741\pi$
$350$	−114482.	−0.0499534
$351$	79800.3	0.0345730
$352$	972676.	0.418419
$353$	−4.25788e6	−1.81868	−0.909340	−	0.416054i	$-0.863413\pi$
$353$	−4.25788e6	−1.81868	−0.909340	+	0.416054i	$0.863413\pi$
$354$	78459.5	0.0332765
$355$	1.25171e6	0.527149
$356$	−387411.	−0.162012
$357$	−155618.	−0.0646234
$358$	−1.28712e6	−0.530774
$359$	3.77092e6	1.54423	0.772113	−	0.635485i	$-0.219200\pi$
$359$	3.77092e6	1.54423	0.772113	+	0.635485i	$0.219200\pi$
$360$	−736754.	−0.299617
$361$	1.43909e6	0.581194
$362$	2.31552e6	0.928703
$363$	894713.	0.356383
$364$	−31910.6	−0.0126235
$365$	2.94563e6	1.15730
$366$	−655992.	−0.255974
$367$	2.03970e6	0.790499	0.395250	−	0.918574i	$-0.370658\pi$
$367$	2.03970e6	0.790499	0.395250	+	0.918574i	$0.370658\pi$
$368$	1.31929e6	0.507833
$369$	629650.	0.240732
$370$	153801.	0.0584058
$371$	415716.	0.156806
$372$	−384430.	−0.144032
$373$	−1.30404e6	−0.485310	−0.242655	−	0.970113i	$-0.578018\pi$
$373$	−1.30404e6	−0.485310	−0.242655	+	0.970113i	$0.578018\pi$
$374$	−764609.	−0.282657
$375$	−1.71128e6	−0.628409
$376$	1.35079e6	0.492741
$377$	770964.	0.279371
$378$	−84088.0	−0.0302694
$379$	521939.	0.186647	0.0933236	−	0.995636i	$-0.470251\pi$
$379$	521939.	0.186647	0.0933236	+	0.995636i	$0.470251\pi$
$380$	−1.04670e6	−0.371847
$381$	1.31701e6	0.464810
$382$	1.81270e6	0.635574
$383$	2.72520e6	0.949295	0.474648	−	0.880176i	$-0.342575\pi$
$383$	2.72520e6	0.949295	0.474648	+	0.880176i	$0.342575\pi$
$384$	283005.	0.0979414
$385$	−291760.	−0.100317
$386$	1.66679e6	0.569392
$387$	−680637.	−0.231014
$388$	−507034.	−0.170985
$389$	92273.8	0.0309175	0.0154587	−	0.999881i	$-0.495079\pi$
$389$	92273.8	0.0309175	0.0154587	+	0.999881i	$0.495079\pi$
$390$	206213.	0.0686521
$391$	1.70350e6	0.563507
$392$	−3.18286e6	−1.04617
$393$	1.02411e6	0.334476
$394$	−4.10902e6	−1.33352
$395$	1.58410e6	0.510846
$396$	230363.	0.0738202
$397$	5.53976e6	1.76407	0.882033	−	0.471188i	$-0.156175\pi$
$397$	5.53976e6	1.76407	0.882033	+	0.471188i	$0.156175\pi$
$398$	699801.	0.221446
$399$	−453184.	−0.142509
$400$	522264.	0.163208
$401$	1.88892e6	0.586616	0.293308	−	0.956018i	$-0.405244\pi$
$401$	1.88892e6	0.586616	0.293308	+	0.956018i	$0.405244\pi$
$402$	849738.	0.262253
$403$	408178.	0.125195
$404$	180867.	0.0551322
$405$	−302981.	−0.0917862
$406$	−812388.	−0.244596
$407$	−182427.	−0.0545889
$408$	1.20447e6	0.358218
$409$	−2.12736e6	−0.628829	−0.314415	−	0.949286i	$-0.601808\pi$
$409$	−2.12736e6	−0.628829	−0.314415	+	0.949286i	$0.601808\pi$
$410$	1.62708e6	0.478025
$411$	400703.	0.117009
$412$	−121528.	−0.0352723
$413$	−48944.9	−0.0141199
$414$	920482.	0.263946
$415$	−777501.	−0.221606
$416$	428864.	0.121503
$417$	961042.	0.270646
$418$	−2.22666e6	−0.623322
$419$	−446933.	−0.124368	−0.0621838	−	0.998065i	$-0.519807\pi$
$419$	−446933.	−0.124368	−0.0621838	+	0.998065i	$0.519807\pi$
$420$	121156.	0.0335137
$421$	−2.46850e6	−0.678779	−0.339389	−	0.940646i	$-0.610220\pi$
$421$	−2.46850e6	−0.678779	−0.339389	+	0.940646i	$0.610220\pi$
$422$	731215.	0.199878
$423$	555496.	0.150949
$424$	−3.21761e6	−0.869199
$425$	674360.	0.181100
$426$	−1.10574e6	−0.295209
$427$	409224.	0.108615
$428$	−2.59244e6	−0.684069
$429$	−244594.	−0.0641656
$430$	−1.75884e6	−0.458728
$431$	3.55124e6	0.920846	0.460423	−	0.887700i	$-0.347698\pi$
$431$	3.55124e6	0.920846	0.460423	+	0.887700i	$0.347698\pi$
$432$	383609.	0.0988961
$433$	871845.	0.223470	0.111735	−	0.993738i	$-0.464359\pi$
$433$	871845.	0.223470	0.111735	+	0.993738i	$0.464359\pi$
$434$	−430110.	−0.109611
$435$	−2.92715e6	−0.741688
$436$	−279694.	−0.0704638
$437$	4.96085e6	1.24266
$438$	−2.60212e6	−0.648100
$439$	−1.10066e6	−0.272579	−0.136289	−	0.990669i	$-0.543518\pi$
$439$	−1.10066e6	−0.272579	−0.136289	+	0.990669i	$0.543518\pi$
$440$	2.25820e6	0.556073
$441$	−1.30891e6	−0.320489
$442$	−337125.	−0.0820795
$443$	−7.64765e6	−1.85148	−0.925739	−	0.378162i	$-0.876556\pi$
$443$	−7.64765e6	−1.85148	−0.925739	+	0.378162i	$0.876556\pi$
$444$	75754.6	0.0182369
$445$	−1.56176e6	−0.373864
$446$	5.19034e6	1.23555
$447$	−3.24119e6	−0.767248
$448$	−880422.	−0.207251
$449$	−651580.	−0.152529	−0.0762644	−	0.997088i	$-0.524299\pi$
$449$	−651580.	−0.152529	−0.0762644	+	0.997088i	$0.524299\pi$
$450$	364389.	0.0848270
$451$	−1.92992e6	−0.446785
$452$	−1.45933e6	−0.335976
$453$	−812712.	−0.186076
$454$	2.83359e6	0.645204
$455$	−128640.	−0.0291305
$456$	3.50761e6	0.789950
$457$	−279909.	−0.0626942	−0.0313471	−	0.999509i	$-0.509980\pi$
$457$	−279909.	−0.0626942	−0.0313471	+	0.999509i	$0.509980\pi$
$458$	−1.38140e6	−0.307720
$459$	495325.	0.109738
$460$	−1.32625e6	−0.292235
$461$	6.41913e6	1.40677	0.703386	−	0.710808i	$-0.251670\pi$
$461$	6.41913e6	1.40677	0.703386	+	0.710808i	$0.251670\pi$
$462$	257736.	0.0561785
$463$	−6.62280e6	−1.43578	−0.717892	−	0.696154i	$-0.754893\pi$
$463$	−6.62280e6	−1.43578	−0.717892	+	0.696154i	$0.754893\pi$
$464$	3.70611e6	0.799141
$465$	−1.54974e6	−0.332374
$466$	3.35572e6	0.715849
$467$	−1.20025e6	−0.254671	−0.127335	−	0.991860i	$-0.540642\pi$
$467$	−1.20025e6	−0.254671	−0.127335	+	0.991860i	$0.540642\pi$
$468$	101570.	0.0214363
$469$	−530087.	−0.111279
$470$	1.43546e6	0.299742
$471$	3.16534e6	0.657458
$472$	378830.	0.0782690
$473$	2.08620e6	0.428749
$474$	−1.39937e6	−0.286079
$475$	1.96384e6	0.399367
$476$	−198071.	−0.0400685
$477$	−1.32320e6	−0.266275
$478$	−6.36442e6	−1.27406
$479$	−5.77265e6	−1.14957	−0.574786	−	0.818304i	$-0.694915\pi$
$479$	−5.77265e6	−1.14957	−0.574786	+	0.818304i	$0.694915\pi$
$480$	−1.62828e6	−0.322572
$481$	−80434.3	−0.0158518
$482$	−1.82476e6	−0.357757
$483$	−574218.	−0.111998
$484$	1.13879e6	0.220968
$485$	−2.04400e6	−0.394571
$486$	267648.	0.0514012
$487$	3.18521e6	0.608577	0.304288	−	0.952580i	$-0.401581\pi$
$487$	3.18521e6	0.608577	0.304288	+	0.952580i	$0.401581\pi$
$488$	−3.16736e6	−0.602072
$489$	−3.57210e6	−0.675540
$490$	−3.38237e6	−0.636401
$491$	−1.65670e6	−0.310127	−0.155064	−	0.987904i	$-0.549558\pi$
$491$	−1.65670e6	−0.310127	−0.155064	+	0.987904i	$0.549558\pi$
$492$	801418.	0.149261
$493$	4.78542e6	0.886752
$494$	−981758.	−0.181004
$495$	928658.	0.170350
$496$	1.96216e6	0.358121
$497$	689787.	0.125263
$498$	686831.	0.124101
$499$	7.81888e6	1.40570	0.702851	−	0.711337i	$-0.251910\pi$
$499$	7.81888e6	1.40570	0.702851	+	0.711337i	$0.251910\pi$
$500$	−2.17811e6	−0.389633
$501$	4.52784e6	0.805930
$502$	−1.79249e6	−0.317465
$503$	−7.45492e6	−1.31378	−0.656890	−	0.753986i	$-0.728129\pi$
$503$	−7.45492e6	−1.31378	−0.656890	+	0.753986i	$0.728129\pi$
$504$	−406007.	−0.0711962
$505$	729124.	0.127225
$506$	−2.82134e6	−0.489869
$507$	3.23379e6	0.558718
$508$	1.67628e6	0.288196
$509$	−3.15554e6	−0.539857	−0.269928	−	0.962880i	$-0.587000\pi$
$509$	−3.15554e6	−0.539857	−0.269928	+	0.962880i	$0.587000\pi$
$510$	1.27997e6	0.217909
$511$	1.62326e6	0.275003
$512$	5.37828e6	0.906710
$513$	1.44246e6	0.241997
$514$	−274704.	−0.0458625
$515$	−489913.	−0.0813957
$516$	−866314.	−0.143236
$517$	−1.70263e6	−0.280153
$518$	84756.1	0.0138786
$519$	−383811.	−0.0625459
$520$	995668.	0.161475
$521$	−3.63063e6	−0.585986	−0.292993	−	0.956115i	$-0.594651\pi$
$521$	−3.63063e6	−0.585986	−0.292993	+	0.956115i	$0.594651\pi$
$522$	2.58579e6	0.415353
$523$	904729.	0.144632	0.0723160	−	0.997382i	$-0.476961\pi$
$523$	904729.	0.144632	0.0723160	+	0.997382i	$0.476961\pi$
$524$	1.30349e6	0.207385
$525$	−227314.	−0.0359939
$526$	−2.95903e6	−0.466321
$527$	2.53358e6	0.397382
$528$	−1.17579e6	−0.183546
$529$	−150575.	−0.0233946
$530$	−3.41930e6	−0.528746
$531$	155789.	0.0239773
$532$	−576812.	−0.0883599
$533$	−850925.	−0.129740
$534$	1.37963e6	0.209368
$535$	−1.04508e7	−1.57858
$536$	4.10284e6	0.616840
$537$	−2.55570e6	−0.382449
$538$	−763947.	−0.113791
$539$	4.01191e6	0.594811
$540$	−385633.	−0.0569102
$541$	6.83426e6	1.00392	0.501959	−	0.864891i	$-0.332613\pi$
$541$	6.83426e6	1.00392	0.501959	+	0.864891i	$0.332613\pi$
$542$	−750150.	−0.109686
$543$	4.59769e6	0.669176
$544$	2.66198e6	0.385663
$545$	−1.12752e6	−0.162605
$546$	113639.	0.0163134
$547$	−79744.4	−0.0113955	−0.00569773	−	0.999984i	$-0.501814\pi$
$547$	−79744.4	−0.0113955	−0.00569773	+	0.999984i	$0.501814\pi$
$548$	510014.	0.0725489
$549$	−1.30254e6	−0.184442
$550$	−1.11688e6	−0.157434
$551$	1.39359e7	1.95549
$552$	4.44441e6	0.620821
$553$	872959.	0.121389
$554$	9.56767e6	1.32444
$555$	305388.	0.0420842
$556$	1.22321e6	0.167809
$557$	−6.64963e6	−0.908155	−0.454077	−	0.890962i	$-0.650031\pi$
$557$	−6.64963e6	−0.908155	−0.454077	+	0.890962i	$0.650031\pi$
$558$	1.36902e6	0.186133
$559$	919829.	0.124502
$560$	−618389.	−0.0833281
$561$	−1.51821e6	−0.203668
$562$	1.59677e6	0.213256
$563$	6.43203e6	0.855218	0.427609	−	0.903964i	$-0.359356\pi$
$563$	6.43203e6	0.855218	0.427609	+	0.903964i	$0.359356\pi$
$564$	707034.	0.0935928
$565$	−5.88298e6	−0.775311
$566$	1.99680e6	0.261995
$567$	−166965.	−0.0218106
$568$	−5.33890e6	−0.694354
$569$	−6.20470e6	−0.803416	−0.401708	−	0.915768i	$-0.631583\pi$
$569$	−6.20470e6	−0.803416	−0.401708	+	0.915768i	$0.631583\pi$
$570$	3.72748e6	0.480538
$571$	4.29057e6	0.550713	0.275356	−	0.961342i	$-0.411204\pi$
$571$	4.29057e6	0.550713	0.275356	+	0.961342i	$0.411204\pi$
$572$	−311319.	−0.0397846
$573$	3.59929e6	0.457962
$574$	896645.	0.113590
$575$	2.48833e6	0.313862
$576$	2.80234e6	0.351937
$577$	−7.18357e6	−0.898257	−0.449129	−	0.893467i	$-0.648265\pi$
$577$	−7.18357e6	−0.898257	−0.449129	+	0.893467i	$0.648265\pi$
$578$	4.34315e6	0.540736
$579$	3.30957e6	0.410275
$580$	−3.72567e6	−0.459869
$581$	−428461.	−0.0526588
$582$	1.80563e6	0.220964
$583$	4.05571e6	0.494192
$584$	−1.25640e7	−1.52438
$585$	409456.	0.0494672
$586$	−8.32201e6	−1.00112
$587$	−8.09268e6	−0.969387	−0.484693	−	0.874684i	$-0.661069\pi$
$587$	−8.09268e6	−0.969387	−0.484693	+	0.874684i	$0.661069\pi$
$588$	−1.66598e6	−0.198713
$589$	7.37818e6	0.876316
$590$	402576.	0.0476121
$591$	−8.15887e6	−0.960863
$592$	−386657.	−0.0453441
$593$	−1.05155e7	−1.22798	−0.613990	−	0.789314i	$-0.710437\pi$
$593$	−1.05155e7	−1.22798	−0.613990	+	0.789314i	$0.710437\pi$
$594$	−820360.	−0.0953978
$595$	−798477.	−0.0924635
$596$	−4.12538e6	−0.475717
$597$	1.38952e6	0.159562
$598$	−1.24396e6	−0.142251
$599$	−7.70183e6	−0.877055	−0.438527	−	0.898718i	$-0.644500\pi$
$599$	−7.70183e6	−0.877055	−0.438527	+	0.898718i	$0.644500\pi$
$600$	1.75940e6	0.199520
$601$	−1.04403e7	−1.17904	−0.589519	−	0.807754i	$-0.700683\pi$
$601$	−1.04403e7	−1.17904	−0.589519	+	0.807754i	$0.700683\pi$
$602$	−969252.	−0.109005
$603$	1.68724e6	0.188966
$604$	−1.03442e6	−0.115373
$605$	4.59078e6	0.509915
$606$	−644095.	−0.0712473
$607$	2.20211e6	0.242587	0.121293	−	0.992617i	$-0.461296\pi$
$607$	2.20211e6	0.242587	0.121293	+	0.992617i	$0.461296\pi$
$608$	7.75209e6	0.850472
$609$	−1.61308e6	−0.176243
$610$	−3.36590e6	−0.366249
$611$	−750711.	−0.0813522
$612$	630449.	0.0680411
$613$	−1.39564e7	−1.50011	−0.750055	−	0.661375i	$-0.769973\pi$
$613$	−1.39564e7	−1.50011	−0.750055	+	0.661375i	$0.769973\pi$
$614$	−3.51973e6	−0.376781
$615$	3.23074e6	0.344440
$616$	1.24444e6	0.132136
$617$	−9.64093e6	−1.01954	−0.509772	−	0.860309i	$-0.670270\pi$
$617$	−9.64093e6	−1.01954	−0.509772	+	0.860309i	$0.670270\pi$
$618$	432781.	0.0455824
$619$	1.57247e7	1.64951	0.824756	−	0.565489i	$-0.191313\pi$
$619$	1.57247e7	1.64951	0.824756	+	0.565489i	$0.191313\pi$
$620$	−1.97251e6	−0.206082
$621$	1.82771e6	0.190186
$622$	1.77038e6	0.183481
$623$	−860646.	−0.0888391
$624$	−518419.	−0.0532990
$625$	−5.67902e6	−0.581532
$626$	−1.19658e7	−1.22041
$627$	−4.42125e6	−0.449134
$628$	4.02884e6	0.407644
$629$	−499260.	−0.0503153
$630$	−431456.	−0.0433097
$631$	2.76022e6	0.275976	0.137988	−	0.990434i	$-0.455937\pi$
$631$	2.76022e6	0.275976	0.137988	+	0.990434i	$0.455937\pi$
$632$	−6.75664e6	−0.672881
$633$	1.45190e6	0.144022
$634$	4.66117e6	0.460545
$635$	6.75756e6	0.665052
$636$	−1.68417e6	−0.165099
$637$	1.76889e6	0.172724
$638$	−7.92563e6	−0.770872
$639$	−2.19556e6	−0.212712
$640$	1.45210e6	0.140135
$641$	−9.36772e6	−0.900511	−0.450255	−	0.892900i	$-0.648667\pi$
$641$	−9.36772e6	−0.900511	−0.450255	+	0.892900i	$0.648667\pi$
$642$	9.23210e6	0.884021
$643$	−1.14558e7	−1.09269	−0.546344	−	0.837561i	$-0.683981\pi$
$643$	−1.14558e7	−1.09269	−0.546344	+	0.837561i	$0.683981\pi$
$644$	−730864.	−0.0694420
$645$	−3.49235e6	−0.330536
$646$	−6.09383e6	−0.574525
$647$	2.06437e6	0.193877	0.0969387	−	0.995290i	$-0.469095\pi$
$647$	2.06437e6	0.193877	0.0969387	+	0.995290i	$0.469095\pi$
$648$	1.29230e6	0.120900
$649$	−477505.	−0.0445006
$650$	−492444.	−0.0457166
$651$	−854025.	−0.0789802
$652$	−4.54656e6	−0.418855
$653$	−1.68929e7	−1.55032	−0.775159	−	0.631767i	$-0.782330\pi$
$653$	−1.68929e7	−1.55032	−0.775159	+	0.631767i	$0.782330\pi$
$654$	996033.	0.0910604
$655$	5.25471e6	0.478570
$656$	−4.09049e6	−0.371121
$657$	−5.16677e6	−0.466988
$658$	791047.	0.0712258
$659$	9.92024e6	0.889833	0.444917	−	0.895572i	$-0.353233\pi$
$659$	9.92024e6	0.889833	0.444917	+	0.895572i	$0.353233\pi$
$660$	1.18199e6	0.105622
$661$	−4.73438e6	−0.421463	−0.210732	−	0.977544i	$-0.567585\pi$
$661$	−4.73438e6	−0.421463	−0.210732	+	0.977544i	$0.567585\pi$
$662$	2.07487e6	0.184012
$663$	−669394.	−0.0591423
$664$	3.31626e6	0.291896
$665$	−2.32529e6	−0.203903
$666$	−269774.	−0.0235676
$667$	1.76578e7	1.53682
$668$	5.76304e6	0.499701
$669$	1.03059e7	0.890271
$670$	4.36001e6	0.375233
$671$	3.99237e6	0.342314
$672$	−897306.	−0.0766509
$673$	2.15201e6	0.183149	0.0915747	−	0.995798i	$-0.470810\pi$
$673$	2.15201e6	0.183149	0.0915747	+	0.995798i	$0.470810\pi$
$674$	−1.16196e7	−0.985237
$675$	723530.	0.0611220
$676$	4.11597e6	0.346422
$677$	−3.95610e6	−0.331738	−0.165869	−	0.986148i	$-0.553043\pi$
$677$	−3.95610e6	−0.331738	−0.165869	+	0.986148i	$0.553043\pi$
$678$	5.19692e6	0.434182
$679$	−1.12639e6	−0.0937596
$680$	6.18016e6	0.512540
$681$	5.62637e6	0.464901
$682$	−4.19614e6	−0.345453
$683$	2.02989e6	0.166502	0.0832511	−	0.996529i	$-0.473470\pi$
$683$	2.02989e6	0.166502	0.0832511	+	0.996529i	$0.473470\pi$
$684$	1.83596e6	0.150046
$685$	2.05601e6	0.167416
$686$	−3.80258e6	−0.308509
$687$	−2.74291e6	−0.221728
$688$	4.42172e6	0.356140
$689$	1.78821e6	0.143506
$690$	4.72300e6	0.377655
$691$	−3.44787e6	−0.274698	−0.137349	−	0.990523i	$-0.543858\pi$
$691$	−3.44787e6	−0.274698	−0.137349	+	0.990523i	$0.543858\pi$
$692$	−488514.	−0.0387803
$693$	511760.	0.0404793
$694$	−2.54829e6	−0.200840
$695$	4.93111e6	0.387242
$696$	1.24851e7	0.976943
$697$	−5.28174e6	−0.411808
$698$	−6.51328e6	−0.506012
$699$	6.66312e6	0.515804
$700$	−289326.	−0.0223173
$701$	1.39412e7	1.07153	0.535767	−	0.844366i	$-0.320022\pi$
$701$	1.39412e7	1.07153	0.535767	+	0.844366i	$0.320022\pi$
$702$	−361706.	−0.0277021
$703$	−1.45392e6	−0.110956
$704$	−8.58937e6	−0.653175
$705$	2.85025e6	0.215978
$706$	1.92994e7	1.45724
$707$	401802.	0.0302317
$708$	198288.	0.0148667
$709$	−1.70460e7	−1.27353	−0.636763	−	0.771060i	$-0.719727\pi$
$709$	−1.70460e7	−1.27353	−0.636763	+	0.771060i	$0.719727\pi$
$710$	−5.67355e6	−0.422386
$711$	−2.77858e6	−0.206134
$712$	6.66134e6	0.492450
$713$	9.34871e6	0.688697
$714$	705361.	0.0517805
$715$	−1.25501e6	−0.0918084
$716$	−3.25289e6	−0.237130
$717$	−1.26372e7	−0.918020
$718$	−1.70922e7	−1.23733
$719$	−4.94937e6	−0.357049	−0.178525	−	0.983935i	$-0.557132\pi$
$719$	−4.94937e6	−0.357049	−0.178525	+	0.983935i	$0.557132\pi$
$720$	1.96830e6	0.141501
$721$	−269979.	−0.0193416
$722$	−6.52289e6	−0.465690
$723$	−3.62324e6	−0.257782
$724$	5.85194e6	0.414909
$725$	6.99015e6	0.493903
$726$	−4.05541e6	−0.285557
$727$	2.01432e7	1.41349	0.706745	−	0.707468i	$-0.250163\pi$
$727$	2.01432e7	1.41349	0.706745	+	0.707468i	$0.250163\pi$
$728$	548687.	0.0383704
$729$	531441.	0.0370370
$730$	−1.33515e7	−0.927305
$731$	5.70943e6	0.395184
$732$	−1.65787e6	−0.114360
$733$	−1.92666e7	−1.32448	−0.662240	−	0.749291i	$-0.730394\pi$
$733$	−1.92666e7	−1.32448	−0.662240	+	0.749291i	$0.730394\pi$
$734$	−9.24523e6	−0.633399
$735$	−6.71603e6	−0.458558
$736$	9.82249e6	0.668386
$737$	−5.17151e6	−0.350710
$738$	−2.85398e6	−0.192890
$739$	−1.40825e7	−0.948571	−0.474286	−	0.880371i	$-0.657294\pi$
$739$	−1.40825e7	−0.948571	−0.474286	+	0.880371i	$0.657294\pi$
$740$	388697.	0.0260935
$741$	−1.94938e6	−0.130422
$742$	−1.88429e6	−0.125643
$743$	−1.18093e7	−0.784787	−0.392393	−	0.919798i	$-0.628353\pi$
$743$	−1.18093e7	−0.784787	−0.392393	+	0.919798i	$0.628353\pi$
$744$	6.61010e6	0.437800
$745$	−1.66306e7	−1.09778
$746$	5.91075e6	0.388862
$747$	1.36377e6	0.0894210
$748$	−1.93237e6	−0.126281
$749$	−5.75920e6	−0.375109
$750$	7.75661e6	0.503522
$751$	1.21761e7	0.787787	0.393893	−	0.919156i	$-0.371128\pi$
$751$	1.21761e7	0.787787	0.393893	+	0.919156i	$0.371128\pi$
$752$	−3.60875e6	−0.232708
$753$	−3.55916e6	−0.228749
$754$	−3.49450e6	−0.223850
$755$	−4.17003e6	−0.266239
$756$	−212513.	−0.0135232
$757$	−8.85581e6	−0.561680	−0.280840	−	0.959755i	$-0.590613\pi$
$757$	−8.85581e6	−0.561680	−0.280840	+	0.959755i	$0.590613\pi$
$758$	−2.36576e6	−0.149554
$759$	−5.60206e6	−0.352974
$760$	1.79976e7	1.13026
$761$	−1.94856e7	−1.21970	−0.609849	−	0.792518i	$-0.708770\pi$
$761$	−1.94856e7	−1.21970	−0.609849	+	0.792518i	$0.708770\pi$
$762$	−5.96951e6	−0.372436
$763$	−621349.	−0.0386388
$764$	4.58117e6	0.283951
$765$	2.54151e6	0.157014
$766$	−1.23523e7	−0.760637
$767$	−210537.	−0.0129223
$768$	8.68111e6	0.531095
$769$	1.44969e7	0.884013	0.442007	−	0.897012i	$-0.354267\pi$
$769$	1.44969e7	0.884013	0.442007	+	0.897012i	$0.354267\pi$
$770$	1.32244e6	0.0803804
$771$	−545452.	−0.0330461
$772$	4.21241e6	0.254383
$773$	6.85107e6	0.412392	0.206196	−	0.978511i	$-0.433892\pi$
$773$	6.85107e6	0.412392	0.206196	+	0.978511i	$0.433892\pi$
$774$	3.08508e6	0.185103
$775$	3.70085e6	0.221334
$776$	8.71822e6	0.519725
$777$	168291.	0.0100002
$778$	−418244.	−0.0247731
$779$	−1.53812e7	−0.908128
$780$	521155.	0.0306711
$781$	6.72954e6	0.394782
$782$	−7.72134e6	−0.451519
$783$	5.13434e6	0.299282
$784$	8.50328e6	0.494079
$785$	1.62414e7	0.940694
$786$	−4.64192e6	−0.268004
$787$	1.77353e7	1.02071	0.510354	−	0.859964i	$-0.329514\pi$
$787$	1.77353e7	1.02071	0.510354	+	0.859964i	$0.329514\pi$
$788$	−1.03846e7	−0.595764
$789$	−5.87544e6	−0.336007
$790$	−7.18016e6	−0.409323
$791$	−3.24196e6	−0.184233
$792$	−3.96099e6	−0.224383
$793$	1.76028e6	0.0994029
$794$	−2.51097e7	−1.41348
$795$	−6.78935e6	−0.380987
$796$	1.76859e6	0.0989335
$797$	−2.23832e7	−1.24818	−0.624089	−	0.781353i	$-0.714530\pi$
$797$	−2.23832e7	−1.24818	−0.624089	+	0.781353i	$0.714530\pi$
$798$	2.05412e6	0.114187
$799$	−4.65970e6	−0.258221
$800$	3.88841e6	0.214806
$801$	2.73939e6	0.150860
$802$	−8.56181e6	−0.470035
$803$	1.58365e7	0.866704
$804$	2.14752e6	0.117165
$805$	−2.94632e6	−0.160247
$806$	−1.85012e6	−0.100314
$807$	−1.51689e6	−0.0819919
$808$	−3.10992e6	−0.167579
$809$	8.37723e6	0.450017	0.225009	−	0.974357i	$-0.427759\pi$
$809$	8.37723e6	0.450017	0.225009	+	0.974357i	$0.427759\pi$
$810$	1.37330e6	0.0735450
$811$	3.43073e7	1.83162	0.915808	−	0.401617i	$-0.131552\pi$
$811$	3.43073e7	1.83162	0.915808	+	0.401617i	$0.131552\pi$
$812$	−2.05312e6	−0.109276
$813$	−1.48950e6	−0.0790338
$814$	826877.	0.0437401
$815$	−1.83284e7	−0.966566
$816$	−3.21785e6	−0.169177
$817$	1.66267e7	0.871469
$818$	9.64256e6	0.503859
$819$	225641.	0.0117546
$820$	4.11208e6	0.213563
$821$	−2.01860e7	−1.04518	−0.522592	−	0.852583i	$-0.675035\pi$
$821$	−2.01860e7	−1.04518	−0.522592	+	0.852583i	$0.675035\pi$
$822$	−1.81624e6	−0.0937549
$823$	−2.12626e7	−1.09425	−0.547125	−	0.837051i	$-0.684278\pi$
$823$	−2.12626e7	−1.09425	−0.547125	+	0.837051i	$0.684278\pi$
$824$	2.08962e6	0.107213
$825$	−2.21767e6	−0.113439
$826$	221849.	0.0113138
$827$	−6.07710e6	−0.308982	−0.154491	−	0.987994i	$-0.549374\pi$
$827$	−6.07710e6	−0.308982	−0.154491	+	0.987994i	$0.549374\pi$
$828$	2.32630e6	0.117921
$829$	1.74931e7	0.884058	0.442029	−	0.897001i	$-0.354259\pi$
$829$	1.74931e7	0.884058	0.442029	+	0.897001i	$0.354259\pi$
$830$	3.52413e6	0.177565
$831$	1.89975e7	0.954322
$832$	−3.78715e6	−0.189672
$833$	1.09796e7	0.548245
$834$	−4.35606e6	−0.216859
$835$	2.32324e7	1.15313
$836$	−5.62736e6	−0.278477
$837$	2.71832e6	0.134118
$838$	2.02579e6	0.0996514
$839$	4.73202e6	0.232082	0.116041	−	0.993244i	$-0.462980\pi$
$839$	4.73202e6	0.232082	0.116041	+	0.993244i	$0.462980\pi$
$840$	−2.08322e6	−0.101868
$841$	2.90926e7	1.41838
$842$	1.11888e7	0.543882
$843$	3.17054e6	0.153661
$844$	1.84798e6	0.0892977
$845$	1.65926e7	0.799416
$846$	−2.51786e6	−0.120950
$847$	2.52986e6	0.121168
$848$	8.59612e6	0.410500
$849$	3.96484e6	0.188780
$850$	−3.05663e6	−0.145109
$851$	−1.84223e6	−0.0872006
$852$	−2.79450e6	−0.131888
$853$	−2.48038e7	−1.16720	−0.583602	−	0.812040i	$-0.698357\pi$
$853$	−2.48038e7	−1.16720	−0.583602	+	0.812040i	$0.698357\pi$
$854$	−1.85486e6	−0.0870296
$855$	7.40127e6	0.346251
$856$	4.45758e7	2.07929
$857$	3.03772e6	0.141285	0.0706424	−	0.997502i	$-0.477495\pi$
$857$	3.03772e6	0.141285	0.0706424	+	0.997502i	$0.477495\pi$
$858$	1.10865e6	0.0514136
$859$	4.08563e7	1.88919	0.944596	−	0.328235i	$-0.106454\pi$
$859$	4.08563e7	1.88919	0.944596	+	0.328235i	$0.106454\pi$
$860$	−4.44506e6	−0.204942
$861$	1.78038e6	0.0818473
$862$	−1.60965e7	−0.737842
$863$	2.85800e7	1.30628	0.653138	−	0.757239i	$-0.273452\pi$
$863$	2.85800e7	1.30628	0.653138	+	0.757239i	$0.273452\pi$
$864$	2.85608e6	0.130162
$865$	−1.96933e6	−0.0894909
$866$	−3.95176e6	−0.179059
$867$	8.62375e6	0.389626
$868$	−1.08700e6	−0.0489701
$869$	8.51656e6	0.382573
$870$	1.32677e7	0.594289
$871$	−2.28018e6	−0.101841
$872$	4.80920e6	0.214181
$873$	3.58525e6	0.159215
$874$	−2.24857e7	−0.995699
$875$	−4.83875e6	−0.213655
$876$	−6.57626e6	−0.289547
$877$	−1.63412e7	−0.717441	−0.358720	−	0.933445i	$-0.616787\pi$
$877$	−1.63412e7	−0.717441	−0.358720	+	0.933445i	$0.616787\pi$
$878$	4.98890e6	0.218408
$879$	−1.65242e7	−0.721352
$880$	−6.03298e6	−0.262618
$881$	−3.90900e6	−0.169678	−0.0848390	−	0.996395i	$-0.527038\pi$
$881$	−3.90900e6	−0.169678	−0.0848390	+	0.996395i	$0.527038\pi$
$882$	5.93282e6	0.256797
$883$	4.42763e6	0.191104	0.0955519	−	0.995424i	$-0.469538\pi$
$883$	4.42763e6	0.191104	0.0955519	+	0.995424i	$0.469538\pi$
$884$	−852004.	−0.0366700
$885$	799354.	0.0343069
$886$	3.46640e7	1.48352
$887$	−4.07831e6	−0.174049	−0.0870244	−	0.996206i	$-0.527736\pi$
$887$	−4.07831e6	−0.174049	−0.0870244	+	0.996206i	$0.527736\pi$
$888$	−1.30257e6	−0.0554328
$889$	3.72392e6	0.158032
$890$	7.07889e6	0.299564
$891$	−1.62891e6	−0.0687387
$892$	1.31174e7	0.551995
$893$	−1.35698e7	−0.569434
$894$	1.46911e7	0.614769
$895$	−1.31133e7	−0.547210
$896$	800216.	0.0332995
$897$	−2.47001e6	−0.102498
$898$	2.95338e6	0.122216
$899$	2.62621e7	1.08375
$900$	920908.	0.0378975
$901$	1.10995e7	0.455503
$902$	8.74764e6	0.357993
$903$	−1.92455e6	−0.0785433
$904$	2.50926e7	1.02123
$905$	2.35908e7	0.957460
$906$	3.68373e6	0.149096
$907$	−2.78318e7	−1.12337	−0.561686	−	0.827351i	$-0.689847\pi$
$907$	−2.78318e7	−1.12337	−0.561686	+	0.827351i	$0.689847\pi$
$908$	7.16124e6	0.288253
$909$	−1.27891e6	−0.0513371
$910$	583080.	0.0233413
$911$	2.85745e6	0.114073	0.0570364	−	0.998372i	$-0.481835\pi$
$911$	2.85745e6	0.114073	0.0570364	+	0.998372i	$0.481835\pi$
$912$	−9.37088e6	−0.373072
$913$	−4.18005e6	−0.165961
$914$	1.26873e6	0.0502346
$915$	−6.68333e6	−0.263900
$916$	−3.49117e6	−0.137478
$917$	2.89574e6	0.113720
$918$	−2.24513e6	−0.0879294
$919$	−1.92017e7	−0.749982	−0.374991	−	0.927028i	$-0.622354\pi$
$919$	−1.92017e7	−0.749982	−0.374991	+	0.927028i	$0.622354\pi$
$920$	2.28043e7	0.888274
$921$	−6.98877e6	−0.271489
$922$	−2.90956e7	−1.12720
$923$	2.96713e6	0.114639
$924$	651367.	0.0250984
$925$	−729279.	−0.0280246
$926$	3.00188e7	1.15044
$927$	859329.	0.0328443
$928$	2.75930e7	1.05179
$929$	4.18036e7	1.58918	0.794592	−	0.607144i	$-0.207685\pi$
$929$	4.18036e7	1.58918	0.794592	+	0.607144i	$0.207685\pi$
$930$	7.02443e6	0.266320
$931$	3.19743e7	1.20900
$932$	8.48081e6	0.319814
$933$	3.51526e6	0.132207
$934$	5.44029e6	0.204059
$935$	−7.78992e6	−0.291410
$936$	−1.74644e6	−0.0651576
$937$	3.41360e7	1.27017	0.635087	−	0.772440i	$-0.280964\pi$
$937$	3.41360e7	1.27017	0.635087	+	0.772440i	$0.280964\pi$
$938$	2.40269e6	0.0891643
$939$	−2.37594e7	−0.879368
$940$	3.62780e6	0.133913
$941$	−3.26395e7	−1.20163	−0.600813	−	0.799390i	$-0.705156\pi$
$941$	−3.26395e7	−1.20163	−0.600813	+	0.799390i	$0.705156\pi$
$942$	−1.43473e7	−0.526798
$943$	−1.94892e7	−0.713697
$944$	−1.01208e6	−0.0369644
$945$	−856698.	−0.0312067
$946$	−9.45599e6	−0.343542
$947$	3.91975e7	1.42031	0.710155	−	0.704046i	$-0.248625\pi$
$947$	3.91975e7	1.42031	0.710155	+	0.704046i	$0.248625\pi$
$948$	−3.53658e6	−0.127809
$949$	6.98250e6	0.251678
$950$	−8.90137e6	−0.319998
$951$	9.25522e6	0.331845
$952$	3.40573e6	0.121792
$953$	6.31993e6	0.225414	0.112707	−	0.993628i	$-0.464048\pi$
$953$	6.31993e6	0.225414	0.112707	+	0.993628i	$0.464048\pi$
$954$	5.99760e6	0.213357
$955$	1.84679e7	0.655255
$956$	−1.60846e7	−0.569200
$957$	−1.57371e7	−0.555451
$958$	2.61653e7	0.921112
$959$	1.13301e6	0.0397822
$960$	1.43788e7	0.503553
$961$	−1.47250e7	−0.514335
$962$	364580.	0.0127015
$963$	1.83312e7	0.636980
$964$	−4.61166e6	−0.159832
$965$	1.69814e7	0.587023
$966$	2.60272e6	0.0897398
$967$	−3.43566e7	−1.18153	−0.590764	−	0.806844i	$-0.701174\pi$
$967$	−3.43566e7	−1.18153	−0.590764	+	0.806844i	$0.701174\pi$
$968$	−1.95810e7	−0.671654
$969$	−1.20999e7	−0.413973
$970$	9.26469e6	0.316156
$971$	3.94115e7	1.34145	0.670726	−	0.741705i	$-0.265983\pi$
$971$	3.94115e7	1.34145	0.670726	+	0.741705i	$0.265983\pi$
$972$	676418.	0.0229641
$973$	2.71741e6	0.0920181
$974$	−1.44374e7	−0.487631
$975$	−977797.	−0.0329410
$976$	8.46187e6	0.284343
$977$	−2.05793e7	−0.689755	−0.344877	−	0.938648i	$-0.612080\pi$
$977$	−2.05793e7	−0.689755	−0.344877	+	0.938648i	$0.612080\pi$
$978$	1.61910e7	0.541286
$979$	−8.39643e6	−0.279987
$980$	−8.54815e6	−0.284320
$981$	1.97772e6	0.0656134
$982$	7.50922e6	0.248494
$983$	−3.44597e7	−1.13744	−0.568718	−	0.822532i	$-0.692561\pi$
$983$	−3.44597e7	−1.13744	−0.568718	+	0.822532i	$0.692561\pi$
$984$	−1.37800e7	−0.453693
$985$	−4.18632e7	−1.37481
$986$	−2.16906e7	−0.710523
$987$	1.57070e6	0.0513217
$988$	−2.48117e6	−0.0808655
$989$	2.10673e7	0.684887
$990$	−4.20927e6	−0.136496
$991$	2.30855e6	0.0746716	0.0373358	−	0.999303i	$-0.488113\pi$
$991$	2.30855e6	0.0746716	0.0373358	+	0.999303i	$0.488113\pi$
$992$	1.46088e7	0.471342
$993$	4.11986e6	0.132590
$994$	−3.12655e6	−0.100369
$995$	7.12966e6	0.228303
$996$	1.73580e6	0.0554437
$997$	2.02196e7	0.644220	0.322110	−	0.946702i	$-0.395608\pi$
$997$	2.02196e7	0.644220	0.322110	+	0.946702i	$0.395608\pi$
$998$	−3.54402e7	−1.12634
$999$	−535663.	−0.0169816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.6	✓	20
3.2	odd	2		927.6.a.c.1.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.6	✓	20	1.1	even	1	trivial
927.6.a.c.1.15		20	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)

\(f(q)\)	\(=\)	\(q-4.53264 q^{2} -9.00000 q^{3} -11.4552 q^{4} -46.1790 q^{5} +40.7937 q^{6} -25.4481 q^{7} +196.967 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.53264 q^{2} -9.00000 q^{3} -11.4552 q^{4} -46.1790 q^{5} +40.7937 q^{6} -25.4481 q^{7} +196.967 q^{8} +81.0000 q^{9} +209.313 q^{10} -248.271 q^{11} +103.097 q^{12} -109.465 q^{13} +115.347 q^{14} +415.611 q^{15} -526.213 q^{16} -679.458 q^{17} -367.144 q^{18} -1978.68 q^{19} +528.990 q^{20} +229.033 q^{21} +1125.32 q^{22} -2507.14 q^{23} -1772.70 q^{24} -992.497 q^{25} +496.167 q^{26} -729.000 q^{27} +291.513 q^{28} -7042.99 q^{29} -1883.82 q^{30} -3728.83 q^{31} -3917.80 q^{32} +2234.44 q^{33} +3079.74 q^{34} +1175.17 q^{35} -927.870 q^{36} +734.792 q^{37} +8968.66 q^{38} +985.189 q^{39} -9095.73 q^{40} +7773.46 q^{41} -1038.12 q^{42} -8402.92 q^{43} +2843.99 q^{44} -3740.50 q^{45} +11364.0 q^{46} +6857.97 q^{47} +4735.91 q^{48} -16159.4 q^{49} +4498.63 q^{50} +6115.12 q^{51} +1253.95 q^{52} -16335.8 q^{53} +3304.29 q^{54} +11464.9 q^{55} -5012.43 q^{56} +17808.2 q^{57} +31923.3 q^{58} +1923.32 q^{59} -4760.91 q^{60} -16080.7 q^{61} +16901.4 q^{62} -2061.30 q^{63} +34596.8 q^{64} +5055.01 q^{65} -10127.9 q^{66} +20830.1 q^{67} +7783.32 q^{68} +22564.3 q^{69} -5326.61 q^{70} -27105.6 q^{71} +15954.3 q^{72} -63787.3 q^{73} -3330.55 q^{74} +8932.47 q^{75} +22666.2 q^{76} +6318.02 q^{77} -4465.50 q^{78} -34303.5 q^{79} +24300.0 q^{80} +6561.00 q^{81} -35234.3 q^{82} +16836.7 q^{83} -2623.62 q^{84} +31376.7 q^{85} +38087.4 q^{86} +63386.9 q^{87} -48901.1 q^{88} +33819.6 q^{89} +16954.3 q^{90} +2785.69 q^{91} +28719.8 q^{92} +33559.5 q^{93} -31084.7 q^{94} +91373.7 q^{95} +35260.2 q^{96} +44262.4 q^{97} +73244.7 q^{98} -20109.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * q^99

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