LMFDB - Embedded newform 309.6.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$49.5586003222$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.31841 q^{2} -9.00000 q^{3} -3.71447 q^{4} +65.7440 q^{5} +47.8657 q^{6} -27.6535 q^{7} +189.944 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-5.31841 q^{2} -9.00000 q^{3} -3.71447 q^{4} +65.7440 q^{5} +47.8657 q^{6} -27.6535 q^{7} +189.944 q^{8} +81.0000 q^{9} -349.654 q^{10} +204.624 q^{11} +33.4302 q^{12} -1181.33 q^{13} +147.073 q^{14} -591.696 q^{15} -891.340 q^{16} -1062.83 q^{17} -430.792 q^{18} +660.803 q^{19} -244.204 q^{20} +248.882 q^{21} -1088.28 q^{22} +3860.18 q^{23} -1709.50 q^{24} +1197.27 q^{25} +6282.80 q^{26} -729.000 q^{27} +102.718 q^{28} +7773.91 q^{29} +3146.88 q^{30} -5898.33 q^{31} -1337.71 q^{32} -1841.62 q^{33} +5652.56 q^{34} -1818.05 q^{35} -300.872 q^{36} -1566.36 q^{37} -3514.42 q^{38} +10632.0 q^{39} +12487.7 q^{40} +6670.60 q^{41} -1323.66 q^{42} -7947.40 q^{43} -760.070 q^{44} +5325.26 q^{45} -20530.0 q^{46} +26534.4 q^{47} +8022.06 q^{48} -16042.3 q^{49} -6367.58 q^{50} +9565.44 q^{51} +4388.01 q^{52} +13200.7 q^{53} +3877.12 q^{54} +13452.8 q^{55} -5252.63 q^{56} -5947.23 q^{57} -41344.9 q^{58} -50984.3 q^{59} +2197.84 q^{60} +9260.60 q^{61} +31369.8 q^{62} -2239.94 q^{63} +35637.3 q^{64} -77665.3 q^{65} +9794.48 q^{66} +59911.8 q^{67} +3947.84 q^{68} -34741.6 q^{69} +9669.16 q^{70} -81703.8 q^{71} +15385.5 q^{72} +24006.4 q^{73} +8330.53 q^{74} -10775.4 q^{75} -2454.53 q^{76} -5658.58 q^{77} -56545.2 q^{78} -80413.7 q^{79} -58600.2 q^{80} +6561.00 q^{81} -35477.0 q^{82} -12703.1 q^{83} -924.464 q^{84} -69874.5 q^{85} +42267.6 q^{86} -69965.2 q^{87} +38867.2 q^{88} -8508.98 q^{89} -28321.9 q^{90} +32667.9 q^{91} -14338.5 q^{92} +53085.0 q^{93} -141121. q^{94} +43443.8 q^{95} +12039.4 q^{96} +1196.73 q^{97} +85319.5 q^{98} +16574.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) $ 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.31841	−0.940172	−0.470086	−	0.882621i	$-0.655777\pi$
$2$	−5.31841	−0.940172	−0.470086	+	0.882621i	$0.655777\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−3.71447	−0.116077
$5$	65.7440	1.17606	0.588032	−	0.808838i	$-0.299903\pi$
$5$	65.7440	1.17606	0.588032	+	0.808838i	$0.299903\pi$
$6$	47.8657	0.542808
$7$	−27.6535	−0.213307	−0.106654	−	0.994296i	$-0.534014\pi$
$7$	−27.6535	−0.213307	−0.106654	+	0.994296i	$0.534014\pi$
$8$	189.944	1.04930
$9$	81.0000	0.333333
$10$	−349.654	−1.10570
$11$	204.624	0.509888	0.254944	−	0.966956i	$-0.417943\pi$
$11$	204.624	0.509888	0.254944	+	0.966956i	$0.417943\pi$
$12$	33.4302	0.0670172
$13$	−1181.33	−1.93871	−0.969355	−	0.245665i	$-0.920994\pi$
$13$	−1181.33	−1.93871	−0.969355	+	0.245665i	$0.920994\pi$
$14$	147.073	0.200545
$15$	−591.696	−0.679001
$16$	−891.340	−0.870449
$17$	−1062.83	−0.891950	−0.445975	−	0.895045i	$-0.647143\pi$
$17$	−1062.83	−0.891950	−0.445975	+	0.895045i	$0.647143\pi$
$18$	−430.792	−0.313391
$19$	660.803	0.419941	0.209970	−	0.977708i	$-0.432663\pi$
$19$	660.803	0.419941	0.209970	+	0.977708i	$0.432663\pi$
$20$	−244.204	−0.136514
$21$	248.882	0.123153
$22$	−1088.28	−0.479382
$23$	3860.18	1.52156	0.760778	−	0.649012i	$-0.224817\pi$
$23$	3860.18	1.52156	0.760778	+	0.649012i	$0.224817\pi$
$24$	−1709.50	−0.605816
$25$	1197.27	0.383126
$26$	6282.80	1.82272
$27$	−729.000	−0.192450
$28$	102.718	0.0247601
$29$	7773.91	1.71650	0.858251	−	0.513229i	$-0.171551\pi$
$29$	7773.91	1.71650	0.858251	+	0.513229i	$0.171551\pi$
$30$	3146.88	0.638377
$31$	−5898.33	−1.10236	−0.551182	−	0.834385i	$-0.685823\pi$
$31$	−5898.33	−1.10236	−0.551182	+	0.834385i	$0.685823\pi$
$32$	−1337.71	−0.230933
$33$	−1841.62	−0.294384
$34$	5652.56	0.838586
$35$	−1818.05	−0.250863
$36$	−300.872	−0.0386924
$37$	−1566.36	−0.188099	−0.0940494	−	0.995568i	$-0.529981\pi$
$37$	−1566.36	−0.188099	−0.0940494	+	0.995568i	$0.529981\pi$
$38$	−3514.42	−0.394816
$39$	10632.0	1.11931
$40$	12487.7	1.23405
$41$	6670.60	0.619734	0.309867	−	0.950780i	$-0.399716\pi$
$41$	6670.60	0.619734	0.309867	+	0.950780i	$0.399716\pi$
$42$	−1323.66	−0.115785
$43$	−7947.40	−0.655472	−0.327736	−	0.944769i	$-0.606286\pi$
$43$	−7947.40	−0.655472	−0.327736	+	0.944769i	$0.606286\pi$
$44$	−760.070	−0.0591864
$45$	5325.26	0.392021
$46$	−20530.0	−1.43052
$47$	26534.4	1.75212	0.876060	−	0.482202i	$-0.160163\pi$
$47$	26534.4	1.75212	0.876060	+	0.482202i	$0.160163\pi$
$48$	8022.06	0.502554
$49$	−16042.3	−0.954500
$50$	−6367.58	−0.360205
$51$	9565.44	0.514967
$52$	4388.01	0.225040
$53$	13200.7	0.645518	0.322759	−	0.946481i	$-0.395390\pi$
$53$	13200.7	0.645518	0.322759	+	0.946481i	$0.395390\pi$
$54$	3877.12	0.180936
$55$	13452.8	0.599661
$56$	−5252.63	−0.223824
$57$	−5947.23	−0.242453
$58$	−41344.9	−1.61381
$59$	−50984.3	−1.90681	−0.953403	−	0.301700i	$-0.902446\pi$
$59$	−50984.3	−1.90681	−0.953403	+	0.301700i	$0.902446\pi$
$60$	2197.84	0.0788165
$61$	9260.60	0.318650	0.159325	−	0.987226i	$-0.449068\pi$
$61$	9260.60	0.318650	0.159325	+	0.987226i	$0.449068\pi$
$62$	31369.8	1.03641
$63$	−2239.94	−0.0711024
$64$	35637.3	1.08757
$65$	−77665.3	−2.28005
$66$	9794.48	0.276772
$67$	59911.8	1.63052	0.815259	−	0.579097i	$-0.196595\pi$
$67$	59911.8	1.63052	0.815259	+	0.579097i	$0.196595\pi$
$68$	3947.84	0.103535
$69$	−34741.6	−0.878471
$70$	9669.16	0.235854
$71$	−81703.8	−1.92352	−0.961760	−	0.273895i	$-0.911688\pi$
$71$	−81703.8	−1.92352	−0.961760	+	0.273895i	$0.911688\pi$
$72$	15385.5	0.349768
$73$	24006.4	0.527255	0.263627	−	0.964625i	$-0.415081\pi$
$73$	24006.4	0.527255	0.263627	+	0.964625i	$0.415081\pi$
$74$	8330.53	0.176845
$75$	−10775.4	−0.221198
$76$	−2454.53	−0.0487455
$77$	−5658.58	−0.108763
$78$	−56545.2	−1.05235
$79$	−80413.7	−1.44965	−0.724824	−	0.688934i	$-0.758079\pi$
$79$	−80413.7	−1.44965	−0.724824	+	0.688934i	$0.758079\pi$
$80$	−58600.2	−1.02370
$81$	6561.00	0.111111
$82$	−35477.0	−0.582656
$83$	−12703.1	−0.202402	−0.101201	−	0.994866i	$-0.532269\pi$
$83$	−12703.1	−0.202402	−0.101201	+	0.994866i	$0.532269\pi$
$84$	−924.464	−0.0142953
$85$	−69874.5	−1.04899
$86$	42267.6	0.616256
$87$	−69965.2	−0.991023
$88$	38867.2	0.535028
$89$	−8508.98	−0.113868	−0.0569341	−	0.998378i	$-0.518133\pi$
$89$	−8508.98	−0.113868	−0.0569341	+	0.998378i	$0.518133\pi$
$90$	−28321.9	−0.368567
$91$	32667.9	0.413541
$92$	−14338.5	−0.176618
$93$	53085.0	0.636450
$94$	−141121.	−1.64729
$95$	43443.8	0.493877
$96$	12039.4	0.133329
$97$	1196.73	0.0129142	0.00645710	−	0.999979i	$-0.497945\pi$
$97$	1196.73	0.0129142	0.00645710	+	0.999979i	$0.497945\pi$
$98$	85319.5	0.897394
$99$	16574.5	0.169963
$100$	−4447.22	−0.0444722
$101$	−57099.1	−0.556962	−0.278481	−	0.960442i	$-0.589831\pi$
$101$	−57099.1	−0.556962	−0.278481	+	0.960442i	$0.589831\pi$
$102$	−50873.0	−0.484158
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	−224387.	−2.03430
$105$	16362.5	0.144836
$106$	−70207.0	−0.606898
$107$	56675.6	0.478560	0.239280	−	0.970951i	$-0.423089\pi$
$107$	56675.6	0.478560	0.239280	+	0.970951i	$0.423089\pi$
$108$	2707.85	0.0223391
$109$	−189744.	−1.52968	−0.764841	−	0.644220i	$-0.777182\pi$
$109$	−189744.	−1.52968	−0.764841	+	0.644220i	$0.777182\pi$
$110$	−71547.5	−0.563784
$111$	14097.2	0.108599
$112$	24648.7	0.185673
$113$	−136835.	−1.00809	−0.504046	−	0.863677i	$-0.668156\pi$
$113$	−136835.	−1.00809	−0.504046	+	0.863677i	$0.668156\pi$
$114$	31629.8	0.227947
$115$	253784.	1.78945
$116$	−28876.0	−0.199247
$117$	−95687.7	−0.646236
$118$	271156.	1.79272
$119$	29390.9	0.190259
$120$	−112389.	−0.712478
$121$	−119180.	−0.740014
$122$	−49251.7	−0.299586
$123$	−60035.4	−0.357803
$124$	21909.2	0.127959
$125$	−126737.	−0.725483
$126$	11912.9	0.0668485
$127$	−47200.1	−0.259677	−0.129839	−	0.991535i	$-0.541446\pi$
$127$	−47200.1	−0.259677	−0.129839	+	0.991535i	$0.541446\pi$
$128$	−146728.	−0.791565
$129$	71526.6	0.378437
$130$	413056.	2.14363
$131$	309958.	1.57807	0.789033	−	0.614351i	$-0.210582\pi$
$131$	309958.	1.57807	0.789033	+	0.614351i	$0.210582\pi$
$132$	6840.63	0.0341713
$133$	−18273.5	−0.0895764
$134$	−318636.	−1.53297
$135$	−47927.4	−0.226334
$136$	−201878.	−0.935927
$137$	−163573.	−0.744578	−0.372289	−	0.928117i	$-0.621427\pi$
$137$	−163573.	−0.744578	−0.372289	+	0.928117i	$0.621427\pi$
$138$	184770.	0.825914
$139$	−95131.0	−0.417624	−0.208812	−	0.977956i	$-0.566960\pi$
$139$	−95131.0	−0.417624	−0.208812	+	0.977956i	$0.566960\pi$
$140$	6753.11	0.0291195
$141$	−238809.	−1.01159
$142$	434535.	1.80844
$143$	−241728.	−0.988525
$144$	−72198.5	−0.290150
$145$	511088.	2.01872
$146$	−127676.	−0.495710
$147$	144381.	0.551081
$148$	5818.18	0.0218340
$149$	157967.	0.582909	0.291455	−	0.956585i	$-0.405861\pi$
$149$	157967.	0.582909	0.291455	+	0.956585i	$0.405861\pi$
$150$	57308.2	0.207964
$151$	−18287.2	−0.0652686	−0.0326343	−	0.999467i	$-0.510390\pi$
$151$	−18287.2	−0.0652686	−0.0326343	+	0.999467i	$0.510390\pi$
$152$	125516.	0.440645
$153$	−86089.0	−0.297317
$154$	30094.7	0.102256
$155$	−387780.	−1.29645
$156$	−39492.1	−0.129927
$157$	−457063.	−1.47988	−0.739941	−	0.672672i	$-0.765147\pi$
$157$	−457063.	−1.47988	−0.739941	+	0.672672i	$0.765147\pi$
$158$	427674.	1.36292
$159$	−118807.	−0.372690
$160$	−87946.1	−0.271592
$161$	−106748.	−0.324559
$162$	−34894.1	−0.104464
$163$	−278889.	−0.822173	−0.411086	−	0.911596i	$-0.634851\pi$
$163$	−278889.	−0.822173	−0.411086	+	0.911596i	$0.634851\pi$
$164$	−24777.7	−0.0719370
$165$	−121075.	−0.346214
$166$	67560.5	0.190293
$167$	−492699.	−1.36707	−0.683534	−	0.729919i	$-0.739558\pi$
$167$	−492699.	−1.36707	−0.683534	+	0.729919i	$0.739558\pi$
$168$	47273.7	0.129225
$169$	1.02425e6	2.75859
$170$	371621.	0.986231
$171$	53525.0	0.139980
$172$	29520.4	0.0760854
$173$	−327095.	−0.830919	−0.415459	−	0.909612i	$-0.636379\pi$
$173$	−327095.	−0.830919	−0.415459	+	0.909612i	$0.636379\pi$
$174$	372104.	0.931732
$175$	−33108.7	−0.0817236
$176$	−182389.	−0.443832
$177$	458859.	1.10089
$178$	45254.3	0.107056
$179$	−673931.	−1.57211	−0.786055	−	0.618156i	$-0.787880\pi$
$179$	−673931.	−1.57211	−0.786055	+	0.618156i	$0.787880\pi$
$180$	−19780.5	−0.0455047
$181$	−271808.	−0.616689	−0.308344	−	0.951275i	$-0.599775\pi$
$181$	−271808.	−0.616689	−0.308344	+	0.951275i	$0.599775\pi$
$182$	−173742.	−0.388799
$183$	−83345.4	−0.183973
$184$	733220.	1.59658
$185$	−102978.	−0.221216
$186$	−282328.	−0.598372
$187$	−217480.	−0.454795
$188$	−98561.1	−0.203381
$189$	20159.4	0.0410510
$190$	−231052.	−0.464329
$191$	885587.	1.75650	0.878249	−	0.478203i	$-0.158712\pi$
$191$	885587.	1.75650	0.878249	+	0.478203i	$0.158712\pi$
$192$	−320736.	−0.627906
$193$	69644.1	0.134583	0.0672917	−	0.997733i	$-0.478564\pi$
$193$	69644.1	0.134583	0.0672917	+	0.997733i	$0.478564\pi$
$194$	−6364.71	−0.0121416
$195$	698988.	1.31639
$196$	59588.6	0.110796
$197$	390961.	0.717741	0.358871	−	0.933387i	$-0.383162\pi$
$197$	390961.	0.717741	0.358871	+	0.933387i	$0.383162\pi$
$198$	−88150.3	−0.159794
$199$	11193.9	0.0200377	0.0100189	−	0.999950i	$-0.496811\pi$
$199$	11193.9	0.0200377	0.0100189	+	0.999950i	$0.496811\pi$
$200$	227415.	0.402016
$201$	−539206.	−0.941380
$202$	303677.	0.523640
$203$	−214976.	−0.366142
$204$	−35530.6	−0.0597760
$205$	438552.	0.728846
$206$	56423.1	0.0926379
$207$	312675.	0.507186
$208$	1.05297e6	1.68755
$209$	135216.	0.214123
$210$	−87022.4	−0.136171
$211$	−537378.	−0.830948	−0.415474	−	0.909605i	$-0.636384\pi$
$211$	−537378.	−0.830948	−0.415474	+	0.909605i	$0.636384\pi$
$212$	−49033.8	−0.0749300
$213$	735334.	1.11054
$214$	−301424.	−0.449928
$215$	−522494.	−0.770877
$216$	−138469.	−0.201939
$217$	163110.	0.235142
$218$	1.00914e6	1.43816
$219$	−216058.	−0.304411
$220$	−49970.0	−0.0696070
$221$	1.25555e6	1.72923
$222$	−74974.7	−0.102102
$223$	−966200.	−1.30108	−0.650541	−	0.759471i	$-0.725458\pi$
$223$	−966200.	−1.30108	−0.650541	+	0.759471i	$0.725458\pi$
$224$	36992.3	0.0492596
$225$	96978.9	0.127709
$226$	727744.	0.947780
$227$	−82440.5	−0.106188	−0.0530941	−	0.998590i	$-0.516908\pi$
$227$	−82440.5	−0.106188	−0.0530941	+	0.998590i	$0.516908\pi$
$228$	22090.8	0.0281432
$229$	1.00195e6	1.26257	0.631285	−	0.775551i	$-0.282528\pi$
$229$	1.00195e6	1.26257	0.631285	+	0.775551i	$0.282528\pi$
$230$	−1.34973e6	−1.68239
$231$	50927.2	0.0627942
$232$	1.47661e6	1.80113
$233$	992954.	1.19823	0.599114	−	0.800664i	$-0.295520\pi$
$233$	992954.	1.19823	0.599114	+	0.800664i	$0.295520\pi$
$234$	508907.	0.607573
$235$	1.74447e6	2.06061
$236$	189380.	0.221337
$237$	723724.	0.836955
$238$	−156313.	−0.178876
$239$	−264755.	−0.299812	−0.149906	−	0.988700i	$-0.547897\pi$
$239$	−264755.	−0.299812	−0.149906	+	0.988700i	$0.547897\pi$
$240$	527402.	0.591036
$241$	−253581.	−0.281238	−0.140619	−	0.990064i	$-0.544909\pi$
$241$	−253581.	−0.281238	−0.140619	+	0.990064i	$0.544909\pi$
$242$	633849.	0.695740
$243$	−59049.0	−0.0641500
$244$	−34398.2	−0.0369881
$245$	−1.05468e6	−1.12255
$246$	319293.	0.336397
$247$	−780626.	−0.814143
$248$	−1.12035e6	−1.15671
$249$	114328.	0.116857
$250$	674038.	0.682078
$251$	−1.38989e6	−1.39250	−0.696249	−	0.717800i	$-0.745149\pi$
$251$	−1.38989e6	−1.39250	−0.696249	+	0.717800i	$0.745149\pi$
$252$	8320.18	0.00825337
$253$	789886.	0.775824
$254$	251030.	0.244141
$255$	628870.	0.605635
$256$	−360037.	−0.343358
$257$	837474.	0.790931	0.395466	−	0.918481i	$-0.370583\pi$
$257$	837474.	0.790931	0.395466	+	0.918481i	$0.370583\pi$
$258$	−380408.	−0.355796
$259$	43315.3	0.0401228
$260$	288485.	0.264661
$261$	629687.	0.572168
$262$	−1.64849e6	−1.48365
$263$	257330.	0.229404	0.114702	−	0.993400i	$-0.463409\pi$
$263$	257330.	0.229404	0.114702	+	0.993400i	$0.463409\pi$
$264$	−349805.	−0.308898
$265$	867869.	0.759171
$266$	97186.2	0.0842172
$267$	76580.9	0.0657419
$268$	−222541.	−0.189266
$269$	−1.22522e6	−1.03236	−0.516181	−	0.856479i	$-0.672647\pi$
$269$	−1.22522e6	−1.03236	−0.516181	+	0.856479i	$0.672647\pi$
$270$	254898.	0.212792
$271$	−817105.	−0.675857	−0.337928	−	0.941172i	$-0.609726\pi$
$271$	−817105.	−0.675857	−0.337928	+	0.941172i	$0.609726\pi$
$272$	947340.	0.776397
$273$	−294011.	−0.238758
$274$	869949.	0.700031
$275$	244990.	0.195352
$276$	129047.	0.101970
$277$	−1.30515e6	−1.02202	−0.511012	−	0.859573i	$-0.670729\pi$
$277$	−1.30515e6	−1.02202	−0.511012	+	0.859573i	$0.670729\pi$
$278$	505946.	0.392638
$279$	−477765.	−0.367454
$280$	−345329.	−0.263232
$281$	−2.14154e6	−1.61793	−0.808966	−	0.587855i	$-0.799973\pi$
$281$	−2.14154e6	−1.61793	−0.808966	+	0.587855i	$0.799973\pi$
$282$	1.27009e6	0.951066
$283$	−1.66914e6	−1.23888	−0.619438	−	0.785046i	$-0.712639\pi$
$283$	−1.66914e6	−1.23888	−0.619438	+	0.785046i	$0.712639\pi$
$284$	303486.	0.223277
$285$	−390994.	−0.285140
$286$	1.28561e6	0.929383
$287$	−184466.	−0.132194
$288$	−108354.	−0.0769776
$289$	−290255.	−0.204426
$290$	−2.71818e6	−1.89794
$291$	−10770.6	−0.00745601
$292$	−89171.2	−0.0612022
$293$	2.38731e6	1.62457	0.812286	−	0.583259i	$-0.198223\pi$
$293$	2.38731e6	1.62457	0.812286	+	0.583259i	$0.198223\pi$
$294$	−767875.	−0.518111
$295$	−3.35191e6	−2.24253
$296$	−297520.	−0.197373
$297$	−149171.	−0.0981280
$298$	−840135.	−0.548035
$299$	−4.56015e6	−2.94986
$300$	40025.0	0.0256761
$301$	219774.	0.139817
$302$	97258.8	0.0613637
$303$	513892.	0.321562
$304$	−589000.	−0.365537
$305$	608829.	0.374753
$306$	457857.	0.279529
$307$	1.93139e6	1.16956	0.584781	−	0.811191i	$-0.301180\pi$
$307$	1.93139e6	1.16956	0.584781	+	0.811191i	$0.301180\pi$
$308$	21018.6	0.0126249
$309$	95481.0	0.0568880
$310$	2.06237e6	1.21889
$311$	−552412.	−0.323864	−0.161932	−	0.986802i	$-0.551772\pi$
$311$	−552412.	−0.323864	−0.161932	+	0.986802i	$0.551772\pi$
$312$	2.01948e6	1.17450
$313$	−1.25927e6	−0.726539	−0.363270	−	0.931684i	$-0.618340\pi$
$313$	−1.25927e6	−0.726539	−0.363270	+	0.931684i	$0.618340\pi$
$314$	2.43085e6	1.39134
$315$	−147262.	−0.0836210
$316$	298694.	0.168271
$317$	1.21842e6	0.681000	0.340500	−	0.940244i	$-0.389404\pi$
$317$	1.21842e6	0.681000	0.340500	+	0.940244i	$0.389404\pi$
$318$	631863.	0.350393
$319$	1.59073e6	0.875224
$320$	2.34294e6	1.27905
$321$	−510080.	−0.276297
$322$	567728.	0.305141
$323$	−702319.	−0.374566
$324$	−24370.6	−0.0128975
$325$	−1.41437e6	−0.742771
$326$	1.48325e6	0.772984
$327$	1.70769e6	0.883162
$328$	1.26704e6	0.650289
$329$	−733769.	−0.373740
$330$	643928.	0.325501
$331$	−2.82021e6	−1.41486	−0.707428	−	0.706786i	$-0.750145\pi$
$331$	−2.82021e6	−1.41486	−0.707428	+	0.706786i	$0.750145\pi$
$332$	47185.4	0.0234943
$333$	−126875.	−0.0626996
$334$	2.62038e6	1.28528
$335$	3.93884e6	1.91759
$336$	−221838.	−0.107198
$337$	−2.82180e6	−1.35348	−0.676738	−	0.736224i	$-0.736607\pi$
$337$	−2.82180e6	−1.35348	−0.676738	+	0.736224i	$0.736607\pi$
$338$	−5.44737e6	−2.59355
$339$	1.23151e6	0.582022
$340$	259547.	0.121764
$341$	−1.20694e6	−0.562082
$342$	−284668.	−0.131605
$343$	908399.	0.416909
$344$	−1.50956e6	−0.687790
$345$	−2.28405e6	−1.03314
$346$	1.73963e6	0.781206
$347$	−2.92866e6	−1.30570	−0.652852	−	0.757486i	$-0.726428\pi$
$347$	−2.92866e6	−1.30570	−0.652852	+	0.757486i	$0.726428\pi$
$348$	259884.	0.115035
$349$	−1.89812e6	−0.834180	−0.417090	−	0.908865i	$-0.636950\pi$
$349$	−1.89812e6	−0.834180	−0.417090	+	0.908865i	$0.636950\pi$
$350$	176086.	0.0768342
$351$	861189.	0.373105
$352$	−273727.	−0.117750
$353$	2.94544e6	1.25809	0.629047	−	0.777368i	$-0.283445\pi$
$353$	2.94544e6	1.25809	0.629047	+	0.777368i	$0.283445\pi$
$354$	−2.44040e6	−1.03503
$355$	−5.37153e6	−2.26218
$356$	31606.4	0.0132175
$357$	−264518.	−0.109846
$358$	3.58425e6	1.47805
$359$	−3.71976e6	−1.52328	−0.761639	−	0.648002i	$-0.775605\pi$
$359$	−3.71976e6	−1.52328	−0.761639	+	0.648002i	$0.775605\pi$
$360$	1.01150e6	0.411350
$361$	−2.03944e6	−0.823650
$362$	1.44559e6	0.579793
$363$	1.07262e6	0.427247
$364$	−121344.	−0.0480027
$365$	1.57828e6	0.620085
$366$	443265.	0.172966
$367$	−3.65672e6	−1.41719	−0.708593	−	0.705617i	$-0.750670\pi$
$367$	−3.65672e6	−1.41719	−0.708593	+	0.705617i	$0.750670\pi$
$368$	−3.44073e6	−1.32444
$369$	540318.	0.206578
$370$	547682.	0.207981
$371$	−365047.	−0.137694
$372$	−197182.	−0.0738773
$373$	4.83186e6	1.79822	0.899109	−	0.437724i	$-0.144215\pi$
$373$	4.83186e6	1.79822	0.899109	+	0.437724i	$0.144215\pi$
$374$	1.15665e6	0.427585
$375$	1.14063e6	0.418858
$376$	5.04005e6	1.83851
$377$	−9.18355e6	−3.32780
$378$	−107216.	−0.0385950
$379$	577587.	0.206547	0.103274	−	0.994653i	$-0.467068\pi$
$379$	577587.	0.206547	0.103274	+	0.994653i	$0.467068\pi$
$380$	−161371.	−0.0573279
$381$	424801.	0.149925
$382$	−4.70992e6	−1.65141
$383$	−2.46053e6	−0.857102	−0.428551	−	0.903518i	$-0.640976\pi$
$383$	−2.46053e6	−0.857102	−0.428551	+	0.903518i	$0.640976\pi$
$384$	1.32055e6	0.457010
$385$	−372017.	−0.127912
$386$	−370396.	−0.126531
$387$	−643740.	−0.218491
$388$	−4445.22	−0.00149904
$389$	3.13808e6	1.05145	0.525727	−	0.850653i	$-0.323793\pi$
$389$	3.13808e6	1.05145	0.525727	+	0.850653i	$0.323793\pi$
$390$	−3.71751e6	−1.23763
$391$	−4.10271e6	−1.35715
$392$	−3.04714e6	−1.00156
$393$	−2.78963e6	−0.911097
$394$	−2.07929e6	−0.674800
$395$	−5.28672e6	−1.70488
$396$	−61565.7	−0.0197288
$397$	−450800.	−0.143552	−0.0717758	−	0.997421i	$-0.522867\pi$
$397$	−450800.	−0.143552	−0.0717758	+	0.997421i	$0.522867\pi$
$398$	−59533.7	−0.0188389
$399$	164462.	0.0517169
$400$	−1.06717e6	−0.333492
$401$	5.77051e6	1.79206	0.896032	−	0.443989i	$-0.146437\pi$
$401$	5.77051e6	1.79206	0.896032	+	0.443989i	$0.146437\pi$
$402$	2.86772e6	0.885059
$403$	6.96787e6	2.13716
$404$	212093.	0.0646506
$405$	431346.	0.130674
$406$	1.14333e6	0.344237
$407$	−320514.	−0.0959093
$408$	1.81690e6	0.540357
$409$	76756.5	0.0226886	0.0113443	−	0.999936i	$-0.496389\pi$
$409$	76756.5	0.0226886	0.0113443	+	0.999936i	$0.496389\pi$
$410$	−2.33240e6	−0.685241
$411$	1.47216e6	0.429882
$412$	39406.8	0.0114374
$413$	1.40990e6	0.406735
$414$	−1.66293e6	−0.476842
$415$	−835154.	−0.238038
$416$	1.58027e6	0.447712
$417$	856179.	0.241115
$418$	−719135.	−0.201312
$419$	−866932.	−0.241240	−0.120620	−	0.992699i	$-0.538488\pi$
$419$	−866932.	−0.241240	−0.120620	+	0.992699i	$0.538488\pi$
$420$	−60778.0	−0.0168121
$421$	−527969.	−0.145179	−0.0725894	−	0.997362i	$-0.523126\pi$
$421$	−527969.	−0.145179	−0.0725894	+	0.997362i	$0.523126\pi$
$422$	2.85800e6	0.781234
$423$	2.14928e6	0.584040
$424$	2.50741e6	0.677345
$425$	−1.27249e6	−0.341729
$426$	−3.91081e6	−1.04410
$427$	−256088.	−0.0679704
$428$	−210520.	−0.0555499
$429$	2.17556e6	0.570725
$430$	2.77884e6	0.724757
$431$	163581.	0.0424169	0.0212084	−	0.999775i	$-0.493249\pi$
$431$	163581.	0.0424169	0.0212084	+	0.999775i	$0.493249\pi$
$432$	649787.	0.167518
$433$	4.88091e6	1.25107	0.625535	−	0.780196i	$-0.284881\pi$
$433$	4.88091e6	1.25107	0.625535	+	0.780196i	$0.284881\pi$
$434$	−867485.	−0.221074
$435$	−4.59979e6	−1.16551
$436$	704797.	0.177561
$437$	2.55082e6	0.638964
$438$	1.14909e6	0.286198
$439$	−5.15478e6	−1.27658	−0.638292	−	0.769795i	$-0.720359\pi$
$439$	−5.15478e6	−1.27658	−0.638292	+	0.769795i	$0.720359\pi$
$440$	2.55528e6	0.629227
$441$	−1.29942e6	−0.318167
$442$	−6.67753e6	−1.62577
$443$	6.35529e6	1.53860	0.769301	−	0.638887i	$-0.220605\pi$
$443$	6.35529e6	1.53860	0.769301	+	0.638887i	$0.220605\pi$
$444$	−52363.6	−0.0126059
$445$	−559414.	−0.133916
$446$	5.13865e6	1.22324
$447$	−1.42170e6	−0.336543
$448$	−985499.	−0.231986
$449$	4.01827e6	0.940639	0.470319	−	0.882496i	$-0.344139\pi$
$449$	4.01827e6	0.940639	0.470319	+	0.882496i	$0.344139\pi$
$450$	−515774.	−0.120068
$451$	1.36496e6	0.315995
$452$	508269.	0.117017
$453$	164585.	0.0376829
$454$	438453.	0.0998351
$455$	2.14772e6	0.486350
$456$	−1.12964e6	−0.254407
$457$	3.15587e6	0.706853	0.353427	−	0.935462i	$-0.385016\pi$
$457$	3.15587e6	0.706853	0.353427	+	0.935462i	$0.385016\pi$
$458$	−5.32876e6	−1.18703
$459$	774801.	0.171656
$460$	−942672.	−0.207714
$461$	−1.11864e6	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$461$	−1.11864e6	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$462$	−270852.	−0.0590374
$463$	7.31045e6	1.58486	0.792432	−	0.609961i	$-0.208815\pi$
$463$	7.31045e6	1.58486	0.792432	+	0.609961i	$0.208815\pi$
$464$	−6.92919e6	−1.49413
$465$	3.49002e6	0.748505
$466$	−5.28094e6	−1.12654
$467$	−6.28233e6	−1.33299	−0.666497	−	0.745507i	$-0.732207\pi$
$467$	−6.28233e6	−1.33299	−0.666497	+	0.745507i	$0.732207\pi$
$468$	355429.	0.0750133
$469$	−1.65677e6	−0.347801
$470$	−9.27783e6	−1.93732
$471$	4.11357e6	0.854410
$472$	−9.68418e6	−2.00082
$473$	−1.62623e6	−0.334217
$474$	−3.84906e6	−0.786881
$475$	791159.	0.160890
$476$	−109172.	−0.0220848
$477$	1.06926e6	0.215173
$478$	1.40808e6	0.281875
$479$	−8.91350e6	−1.77505	−0.887523	−	0.460763i	$-0.847576\pi$
$479$	−8.91350e6	−1.77505	−0.887523	+	0.460763i	$0.847576\pi$
$480$	791515.	0.156804
$481$	1.85038e6	0.364669
$482$	1.34865e6	0.264412
$483$	960729.	0.187384
$484$	442691.	0.0858988
$485$	78677.9	0.0151879
$486$	314047.	0.0603120
$487$	−2.95222e6	−0.564060	−0.282030	−	0.959406i	$-0.591008\pi$
$487$	−2.95222e6	−0.564060	−0.282030	+	0.959406i	$0.591008\pi$
$488$	1.75900e6	0.334361
$489$	2.51001e6	0.474682
$490$	5.60924e6	1.05539
$491$	1.00898e7	1.88878	0.944389	−	0.328831i	$-0.106655\pi$
$491$	1.00898e7	1.88878	0.944389	+	0.328831i	$0.106655\pi$
$492$	223000.	0.0415328
$493$	−8.26232e6	−1.53103
$494$	4.15169e6	0.765434
$495$	1.08968e6	0.199887
$496$	5.25741e6	0.959551
$497$	2.25940e6	0.410301
$498$	−608045.	−0.109866
$499$	4.34867e6	0.781817	0.390909	−	0.920429i	$-0.372161\pi$
$499$	4.34867e6	0.781817	0.390909	+	0.920429i	$0.372161\pi$
$500$	470760.	0.0842120
$501$	4.43429e6	0.789277
$502$	7.39199e6	1.30919
$503$	−2.38041e6	−0.419499	−0.209750	−	0.977755i	$-0.567265\pi$
$503$	−2.38041e6	−0.419499	−0.209750	+	0.977755i	$0.567265\pi$
$504$	−425463.	−0.0746081
$505$	−3.75392e6	−0.655023
$506$	−4.20094e6	−0.729408
$507$	−9.21822e6	−1.59268
$508$	175323.	0.0301426
$509$	9.79178e6	1.67520	0.837601	−	0.546282i	$-0.183957\pi$
$509$	9.79178e6	1.67520	0.837601	+	0.546282i	$0.183957\pi$
$510$	−3.34459e6	−0.569400
$511$	−663863.	−0.112467
$512$	6.61011e6	1.11438
$513$	−481725.	−0.0808176
$514$	−4.45403e6	−0.743611
$515$	−697478.	−0.115881
$516$	−265684.	−0.0439279
$517$	5.42957e6	0.893385
$518$	−230368.	−0.0377223
$519$	2.94385e6	0.479731
$520$	−1.47521e7	−2.39246
$521$	1.28762e6	0.207822	0.103911	−	0.994587i	$-0.466864\pi$
$521$	1.28762e6	0.207822	0.103911	+	0.994587i	$0.466864\pi$
$522$	−3.34893e6	−0.537936
$523$	1.32779e6	0.212263	0.106132	−	0.994352i	$-0.466153\pi$
$523$	1.32779e6	0.212263	0.106132	+	0.994352i	$0.466153\pi$
$524$	−1.15133e6	−0.183178
$525$	297979.	0.0471832
$526$	−1.36859e6	−0.215679
$527$	6.26890e6	0.983252
$528$	1.64151e6	0.256246
$529$	8.46466e6	1.31514
$530$	−4.61569e6	−0.713751
$531$	−4.12973e6	−0.635602
$532$	67876.5	0.0103978
$533$	−7.88017e6	−1.20148
$534$	−407289.	−0.0618086
$535$	3.72608e6	0.562817
$536$	1.13799e7	1.71091
$537$	6.06538e6	0.907658
$538$	6.51621e6	0.970598
$539$	−3.28264e6	−0.486688
$540$	178025.	0.0262722
$541$	−1.05492e7	−1.54963	−0.774816	−	0.632187i	$-0.782157\pi$
$541$	−1.05492e7	−1.54963	−0.774816	+	0.632187i	$0.782157\pi$
$542$	4.34570e6	0.635421
$543$	2.44627e6	0.356045
$544$	1.42175e6	0.205980
$545$	−1.24745e7	−1.79900
$546$	1.56367e6	0.224473
$547$	−5.13844e6	−0.734283	−0.367141	−	0.930165i	$-0.619663\pi$
$547$	−5.13844e6	−0.734283	−0.367141	+	0.930165i	$0.619663\pi$
$548$	607587.	0.0864285
$549$	750109.	0.106217
$550$	−1.30296e6	−0.183664
$551$	5.13702e6	0.720829
$552$	−6.59898e6	−0.921784
$553$	2.22372e6	0.309220
$554$	6.94134e6	0.960879
$555$	926806.	0.127719
$556$	353361.	0.0484766
$557$	1.02995e6	0.140663	0.0703313	−	0.997524i	$-0.477594\pi$
$557$	1.02995e6	0.140663	0.0703313	+	0.997524i	$0.477594\pi$
$558$	2.54095e6	0.345470
$559$	9.38850e6	1.27077
$560$	1.62050e6	0.218363
$561$	1.95732e6	0.262576
$562$	1.13896e7	1.52113
$563$	6.24587e6	0.830467	0.415233	−	0.909715i	$-0.363700\pi$
$563$	6.24587e6	0.830467	0.415233	+	0.909715i	$0.363700\pi$
$564$	887050.	0.117422
$565$	−8.99606e6	−1.18558
$566$	8.87720e6	1.16476
$567$	−181435.	−0.0237008
$568$	−1.55192e7	−2.01836
$569$	−7.19476e6	−0.931613	−0.465806	−	0.884887i	$-0.654236\pi$
$569$	−7.19476e6	−0.931613	−0.465806	+	0.884887i	$0.654236\pi$
$570$	2.07947e6	0.268081
$571$	−4.87648e6	−0.625916	−0.312958	−	0.949767i	$-0.601320\pi$
$571$	−4.87648e6	−0.625916	−0.312958	+	0.949767i	$0.601320\pi$
$572$	897893.	0.114745
$573$	−7.97028e6	−1.01411
$574$	981065.	0.124285
$575$	4.62168e6	0.582949
$576$	2.88662e6	0.362522
$577$	5.59013e6	0.699008	0.349504	−	0.936935i	$-0.386350\pi$
$577$	5.59013e6	0.699008	0.349504	+	0.936935i	$0.386350\pi$
$578$	1.54370e6	0.192195
$579$	−626797.	−0.0777017
$580$	−1.89842e6	−0.234327
$581$	351286.	0.0431739
$582$	57282.4	0.00700993
$583$	2.70119e6	0.329142
$584$	4.55989e6	0.553250
$585$	−6.29089e6	−0.760015
$586$	−1.26967e7	−1.52738
$587$	−4.56130e6	−0.546379	−0.273189	−	0.961960i	$-0.588079\pi$
$587$	−4.56130e6	−0.546379	−0.273189	+	0.961960i	$0.588079\pi$
$588$	−536297.	−0.0639679
$589$	−3.89763e6	−0.462927
$590$	1.78268e7	2.10836
$591$	−3.51865e6	−0.414388
$592$	1.39615e6	0.163730
$593$	−1.04456e7	−1.21982	−0.609910	−	0.792471i	$-0.708794\pi$
$593$	−1.04456e7	−1.21982	−0.609910	+	0.792471i	$0.708794\pi$
$594$	793353.	0.0922572
$595$	1.93228e6	0.223757
$596$	−586764.	−0.0676625
$597$	−100745.	−0.0115688
$598$	2.42528e7	2.77337
$599$	−90977.3	−0.0103601	−0.00518007	−	0.999987i	$-0.501649\pi$
$599$	−90977.3	−0.0103601	−0.00518007	+	0.999987i	$0.501649\pi$
$600$	−2.04673e6	−0.232104
$601$	2.57567e6	0.290874	0.145437	−	0.989368i	$-0.453541\pi$
$601$	2.57567e6	0.290874	0.145437	+	0.989368i	$0.453541\pi$
$602$	−1.16885e6	−0.131452
$603$	4.85286e6	0.543506
$604$	67927.2	0.00757620
$605$	−7.83537e6	−0.870304
$606$	−2.73309e6	−0.302324
$607$	8.97396e6	0.988581	0.494291	−	0.869297i	$-0.335428\pi$
$607$	8.97396e6	0.988581	0.494291	+	0.869297i	$0.335428\pi$
$608$	−883960.	−0.0969781
$609$	1.93479e6	0.211392
$610$	−3.23800e6	−0.352332
$611$	−3.13458e7	−3.39685
$612$	319775.	0.0345117
$613$	2.52871e6	0.271799	0.135899	−	0.990723i	$-0.456608\pi$
$613$	2.52871e6	0.271799	0.135899	+	0.990723i	$0.456608\pi$
$614$	−1.02719e7	−1.09959
$615$	−3.94696e6	−0.420800
$616$	−1.07481e6	−0.114125
$617$	1.31406e7	1.38964	0.694820	−	0.719184i	$-0.255484\pi$
$617$	1.31406e7	1.38964	0.694820	+	0.719184i	$0.255484\pi$
$618$	−507808.	−0.0534845
$619$	−1.06586e7	−1.11808	−0.559041	−	0.829140i	$-0.688831\pi$
$619$	−1.06586e7	−1.11808	−0.559041	+	0.829140i	$0.688831\pi$
$620$	1.44040e6	0.150488
$621$	−2.81407e6	−0.292824
$622$	2.93796e6	0.304488
$623$	235304.	0.0242889
$624$	−9.47669e6	−0.974306
$625$	−1.20736e7	−1.23634
$626$	6.69734e6	0.683072
$627$	−1.21695e6	−0.123624
$628$	1.69775e6	0.171781
$629$	1.66476e6	0.167775
$630$	783202.	0.0786181
$631$	−5.83008e6	−0.582910	−0.291455	−	0.956585i	$-0.594139\pi$
$631$	−5.83008e6	−0.582910	−0.291455	+	0.956585i	$0.594139\pi$
$632$	−1.52741e7	−1.52112
$633$	4.83640e6	0.479748
$634$	−6.48004e6	−0.640257
$635$	−3.10312e6	−0.305397
$636$	441304.	0.0432608
$637$	1.89512e7	1.85050
$638$	−8.46015e6	−0.822861
$639$	−6.61801e6	−0.641173
$640$	−9.64645e6	−0.930931
$641$	1.91052e7	1.83657	0.918285	−	0.395920i	$-0.129574\pi$
$641$	1.91052e7	1.83657	0.918285	+	0.395920i	$0.129574\pi$
$642$	2.71282e6	0.259766
$643$	1.47045e7	1.40256	0.701280	−	0.712886i	$-0.252612\pi$
$643$	1.47045e7	1.40256	0.701280	+	0.712886i	$0.252612\pi$
$644$	396511.	0.0376739
$645$	4.70245e6	0.445066
$646$	3.73522e6	0.352156
$647$	1.20631e7	1.13291	0.566457	−	0.824091i	$-0.308314\pi$
$647$	1.20631e7	1.13291	0.566457	+	0.824091i	$0.308314\pi$
$648$	1.24622e6	0.116589
$649$	−1.04326e7	−0.972258
$650$	7.52221e6	0.698332
$651$	−1.46799e6	−0.135759
$652$	1.03593e6	0.0954355
$653$	1.83653e7	1.68545	0.842723	−	0.538347i	$-0.180951\pi$
$653$	1.83653e7	1.68545	0.842723	+	0.538347i	$0.180951\pi$
$654$	−9.08222e6	−0.830324
$655$	2.03779e7	1.85591
$656$	−5.94577e6	−0.539446
$657$	1.94452e6	0.175752
$658$	3.90249e6	0.351380
$659$	4.20737e6	0.377396	0.188698	−	0.982035i	$-0.439573\pi$
$659$	4.20737e6	0.377396	0.188698	+	0.982035i	$0.439573\pi$
$660$	449730.	0.0401876
$661$	974878.	0.0867854	0.0433927	−	0.999058i	$-0.486183\pi$
$661$	974878.	0.0867854	0.0433927	+	0.999058i	$0.486183\pi$
$662$	1.49991e7	1.33021
$663$	−1.12999e7	−0.998372
$664$	−2.41289e6	−0.212382
$665$	−1.20137e6	−0.105348
$666$	674773.	0.0589484
$667$	3.00087e7	2.61176
$668$	1.83011e6	0.158685
$669$	8.69580e6	0.751181
$670$	−2.09484e7	−1.80287
$671$	1.89494e6	0.162476
$672$	−332931.	−0.0284401
$673$	−1.54699e6	−0.131659	−0.0658293	−	0.997831i	$-0.520969\pi$
$673$	−1.54699e6	−0.131659	−0.0658293	+	0.997831i	$0.520969\pi$
$674$	1.50075e7	1.27250
$675$	−872810.	−0.0737327
$676$	−3.80453e6	−0.320210
$677$	−104382.	−0.00875291	−0.00437645	−	0.999990i	$-0.501393\pi$
$677$	−104382.	−0.00875291	−0.00437645	+	0.999990i	$0.501393\pi$
$678$	−6.54970e6	−0.547201
$679$	−33093.9	−0.00275469
$680$	−1.32723e7	−1.10071
$681$	741965.	0.0613078
$682$	6.41900e6	0.528453
$683$	1.23040e6	0.100924	0.0504618	−	0.998726i	$-0.483931\pi$
$683$	1.23040e6	0.100924	0.0504618	+	0.998726i	$0.483931\pi$
$684$	−198817.	−0.0162485
$685$	−1.07539e7	−0.875671
$686$	−4.83124e6	−0.391966
$687$	−9.01751e6	−0.728945
$688$	7.08384e6	0.570555
$689$	−1.55944e7	−1.25147
$690$	1.21475e7	0.971328
$691$	1.77167e7	1.41152	0.705761	−	0.708450i	$-0.250605\pi$
$691$	1.77167e7	1.41152	0.705761	+	0.708450i	$0.250605\pi$
$692$	1.21498e6	0.0964507
$693$	−458345.	−0.0362543
$694$	1.55758e7	1.22759
$695$	−6.25429e6	−0.491152
$696$	−1.32895e7	−1.03988
$697$	−7.08969e6	−0.552771
$698$	1.00950e7	0.784272
$699$	−8.93659e6	−0.691797
$700$	122981.	0.00948625
$701$	−3.82851e6	−0.294262	−0.147131	−	0.989117i	$-0.547004\pi$
$701$	−3.82851e6	−0.294262	−0.147131	+	0.989117i	$0.547004\pi$
$702$	−4.58016e6	−0.350783
$703$	−1.03505e6	−0.0789903
$704$	7.29226e6	0.554537
$705$	−1.57003e7	−1.18969
$706$	−1.56650e7	−1.18282
$707$	1.57899e6	0.118804
$708$	−1.70442e6	−0.127789
$709$	1.84161e7	1.37588	0.687941	−	0.725766i	$-0.258515\pi$
$709$	1.84161e7	1.37588	0.687941	+	0.725766i	$0.258515\pi$
$710$	2.85680e7	2.12684
$711$	−6.51351e6	−0.483216
$712$	−1.61623e6	−0.119482
$713$	−2.27686e7	−1.67731
$714$	1.40682e6	0.103274
$715$	−1.58922e7	−1.16257
$716$	2.50330e6	0.182486
$717$	2.38280e6	0.173097
$718$	1.97832e7	1.43214
$719$	1.15573e7	0.833745	0.416873	−	0.908965i	$-0.363126\pi$
$719$	1.15573e7	0.833745	0.416873	+	0.908965i	$0.363126\pi$
$720$	−4.74662e6	−0.341235
$721$	293376.	0.0210178
$722$	1.08466e7	0.774372
$723$	2.28223e6	0.162373
$724$	1.00962e6	0.0715835
$725$	9.30747e6	0.657638
$726$	−5.70464e6	−0.401686
$727$	−1.41273e7	−0.991342	−0.495671	−	0.868510i	$-0.665078\pi$
$727$	−1.41273e7	−0.991342	−0.495671	+	0.868510i	$0.665078\pi$
$728$	6.20509e6	0.433930
$729$	531441.	0.0370370
$730$	−8.39394e6	−0.582987
$731$	8.44672e6	0.584648
$732$	309584.	0.0213551
$733$	−1.00715e7	−0.692365	−0.346183	−	0.938167i	$-0.612522\pi$
$733$	−1.00715e7	−0.692365	−0.346183	+	0.938167i	$0.612522\pi$
$734$	1.94480e7	1.33240
$735$	9.49215e6	0.648106
$736$	−5.16379e6	−0.351377
$737$	1.22594e7	0.831381
$738$	−2.87364e6	−0.194219
$739$	−1.40694e7	−0.947685	−0.473842	−	0.880610i	$-0.657133\pi$
$739$	−1.40694e7	−0.947685	−0.473842	+	0.880610i	$0.657133\pi$
$740$	382510.	0.0256782
$741$	7.02563e6	0.470046
$742$	1.94147e6	0.129456
$743$	−2.02196e7	−1.34369	−0.671846	−	0.740691i	$-0.734498\pi$
$743$	−2.02196e7	−1.34369	−0.671846	+	0.740691i	$0.734498\pi$
$744$	1.00832e7	0.667829
$745$	1.03854e7	0.685539
$746$	−2.56978e7	−1.69063
$747$	−1.02895e6	−0.0674674
$748$	807823.	0.0527913
$749$	−1.56728e6	−0.102080
$750$	−6.06634e6	−0.393798
$751$	3.34049e6	0.216128	0.108064	−	0.994144i	$-0.465535\pi$
$751$	3.34049e6	0.216128	0.108064	+	0.994144i	$0.465535\pi$
$752$	−2.36511e7	−1.52513
$753$	1.25090e7	0.803959
$754$	4.88419e7	3.12870
$755$	−1.20227e6	−0.0767601
$756$	−74881.6	−0.00476509
$757$	2.35619e7	1.49441	0.747206	−	0.664593i	$-0.231395\pi$
$757$	2.35619e7	1.49441	0.747206	+	0.664593i	$0.231395\pi$
$758$	−3.07184e6	−0.194190
$759$	−7.10897e6	−0.447922
$760$	8.25190e6	0.518227
$761$	1.87040e7	1.17077	0.585387	−	0.810754i	$-0.300943\pi$
$761$	1.87040e7	1.17077	0.585387	+	0.810754i	$0.300943\pi$
$762$	−2.25927e6	−0.140955
$763$	5.24708e6	0.326292
$764$	−3.28949e6	−0.203889
$765$	−5.65983e6	−0.349663
$766$	1.30861e7	0.805823
$767$	6.02293e7	3.69674
$768$	3.24033e6	0.198238
$769$	−8.46446e6	−0.516159	−0.258079	−	0.966124i	$-0.583090\pi$
$769$	−8.46446e6	−0.516159	−0.258079	+	0.966124i	$0.583090\pi$
$770$	1.97854e6	0.120259
$771$	−7.53727e6	−0.456644
$772$	−258691.	−0.0156221
$773$	2.11047e7	1.27037	0.635185	−	0.772360i	$-0.280924\pi$
$773$	2.11047e7	1.27037	0.635185	+	0.772360i	$0.280924\pi$
$774$	3.42367e6	0.205419
$775$	−7.06189e6	−0.422344
$776$	227312.	0.0135509
$777$	−389837.	−0.0231649
$778$	−1.66896e7	−0.988548
$779$	4.40795e6	0.260251
$780$	−2.59637e6	−0.152802
$781$	−1.67186e7	−0.980780
$782$	2.18199e7	1.27596
$783$	−5.66718e6	−0.330341
$784$	1.42991e7	0.830843
$785$	−3.00491e7	−1.74044
$786$	1.48364e7	0.856588
$787$	−1.37411e7	−0.790830	−0.395415	−	0.918502i	$-0.629399\pi$
$787$	−1.37411e7	−0.790830	−0.395415	+	0.918502i	$0.629399\pi$
$788$	−1.45221e6	−0.0833134
$789$	−2.31597e6	−0.132446
$790$	2.81170e7	1.60288
$791$	3.78397e6	0.215033
$792$	3.14824e6	0.178343
$793$	−1.09398e7	−0.617771
$794$	2.39754e6	0.134963
$795$	−7.81082e6	−0.438307
$796$	−41579.4	−0.00232592
$797$	−2.11657e6	−0.118028	−0.0590142	−	0.998257i	$-0.518796\pi$
$797$	−2.11657e6	−0.118028	−0.0590142	+	0.998257i	$0.518796\pi$
$798$	−874676.	−0.0486228
$799$	−2.82014e7	−1.56280
$800$	−1.60159e6	−0.0884765
$801$	−689228.	−0.0379561
$802$	−3.06900e7	−1.68485
$803$	4.91229e6	0.268841
$804$	2.00287e6	0.109273
$805$	−7.01802e6	−0.381702
$806$	−3.70580e7	−2.00930
$807$	1.10269e7	0.596035
$808$	−1.08457e7	−0.584423
$809$	1.37283e7	0.737474	0.368737	−	0.929534i	$-0.379790\pi$
$809$	1.37283e7	0.737474	0.368737	+	0.929534i	$0.379790\pi$
$810$	−2.29408e6	−0.122856
$811$	−3.91813e6	−0.209183	−0.104591	−	0.994515i	$-0.533354\pi$
$811$	−3.91813e6	−0.209183	−0.104591	+	0.994515i	$0.533354\pi$
$812$	798522.	0.0425008
$813$	7.35394e6	0.390206
$814$	1.70463e6	0.0901712
$815$	−1.83353e7	−0.966928
$816$	−8.52606e6	−0.448253
$817$	−5.25167e6	−0.275259
$818$	−408223.	−0.0213311
$819$	2.64610e6	0.137847
$820$	−1.62899e6	−0.0846025
$821$	−1.65269e7	−0.855726	−0.427863	−	0.903844i	$-0.640733\pi$
$821$	−1.65269e7	−0.855726	−0.427863	+	0.903844i	$0.640733\pi$
$822$	−7.82954e6	−0.404163
$823$	1.01573e7	0.522732	0.261366	−	0.965240i	$-0.415827\pi$
$823$	1.01573e7	0.522732	0.261366	+	0.965240i	$0.415827\pi$
$824$	−2.01512e6	−0.103391
$825$	−2.20491e6	−0.112786
$826$	−7.49841e6	−0.382401
$827$	−2.21663e7	−1.12701	−0.563507	−	0.826111i	$-0.690548\pi$
$827$	−2.21663e7	−1.12701	−0.563507	+	0.826111i	$0.690548\pi$
$828$	−1.16142e6	−0.0588727
$829$	−1.07583e7	−0.543698	−0.271849	−	0.962340i	$-0.587635\pi$
$829$	−1.07583e7	−0.543698	−0.271849	+	0.962340i	$0.587635\pi$
$830$	4.44170e6	0.223797
$831$	1.17464e7	0.590066
$832$	−4.20994e7	−2.10847
$833$	1.70502e7	0.851366
$834$	−4.55351e6	−0.226690
$835$	−3.23920e7	−1.60776
$836$	−502256.	−0.0248548
$837$	4.29988e6	0.212150
$838$	4.61070e6	0.226807
$839$	−2.23949e7	−1.09836	−0.549180	−	0.835704i	$-0.685060\pi$
$839$	−2.23949e7	−1.09836	−0.549180	+	0.835704i	$0.685060\pi$
$840$	3.10796e6	0.151977
$841$	3.99225e7	1.94638
$842$	2.80796e6	0.136493
$843$	1.92739e7	0.934114
$844$	1.99607e6	0.0964541
$845$	6.73380e7	3.24428
$846$	−1.14308e7	−0.549098
$847$	3.29575e6	0.157850
$848$	−1.17663e7	−0.561891
$849$	1.50223e7	0.715265
$850$	6.76763e6	0.321284
$851$	−6.04642e6	−0.286203
$852$	−2.73138e6	−0.128909
$853$	−9.00267e6	−0.423642	−0.211821	−	0.977308i	$-0.567939\pi$
$853$	−9.00267e6	−0.423642	−0.211821	+	0.977308i	$0.567939\pi$
$854$	1.36198e6	0.0639039
$855$	3.51895e6	0.164626
$856$	1.07652e7	0.502155
$857$	−2.39504e7	−1.11394	−0.556968	−	0.830534i	$-0.688035\pi$
$857$	−2.39504e7	−1.11394	−0.556968	+	0.830534i	$0.688035\pi$
$858$	−1.15705e7	−0.536580
$859$	−1.53707e7	−0.710740	−0.355370	−	0.934726i	$-0.615645\pi$
$859$	−1.53707e7	−0.710740	−0.355370	+	0.934726i	$0.615645\pi$
$860$	1.94079e6	0.0894813
$861$	1.66019e6	0.0763221
$862$	−869989.	−0.0398791
$863$	−1.60111e7	−0.731804	−0.365902	−	0.930653i	$-0.619239\pi$
$863$	−1.60111e7	−0.731804	−0.365902	+	0.930653i	$0.619239\pi$
$864$	975187.	0.0444430
$865$	−2.15045e7	−0.977214
$866$	−2.59587e7	−1.17622
$867$	2.61230e6	0.118025
$868$	−605866.	−0.0272946
$869$	−1.64546e7	−0.739158
$870$	2.44636e7	1.09578
$871$	−7.07756e7	−3.16110
$872$	−3.60407e7	−1.60510
$873$	96935.2	0.00430473
$874$	−1.35663e7	−0.600735
$875$	3.50472e6	0.154751
$876$	802541.	0.0353351
$877$	−6.66288e6	−0.292525	−0.146262	−	0.989246i	$-0.546724\pi$
$877$	−6.66288e6	−0.292525	−0.146262	+	0.989246i	$0.546724\pi$
$878$	2.74153e7	1.20021
$879$	−2.14858e7	−0.937947
$880$	−1.19910e7	−0.521974
$881$	−3.10528e7	−1.34791	−0.673955	−	0.738772i	$-0.735406\pi$
$881$	−3.10528e7	−1.34791	−0.673955	+	0.738772i	$0.735406\pi$
$882$	6.91088e6	0.299131
$883$	−2.11474e7	−0.912757	−0.456379	−	0.889786i	$-0.650854\pi$
$883$	−2.11474e7	−0.912757	−0.456379	+	0.889786i	$0.650854\pi$
$884$	−4.66370e6	−0.200724
$885$	3.01672e7	1.29472
$886$	−3.38001e7	−1.44655
$887$	−6.36747e6	−0.271743	−0.135871	−	0.990726i	$-0.543383\pi$
$887$	−6.36747e6	−0.271743	−0.135871	+	0.990726i	$0.543383\pi$
$888$	2.67768e6	0.113953
$889$	1.30525e6	0.0553910
$890$	2.97520e6	0.125904
$891$	1.34254e6	0.0566542
$892$	3.58892e6	0.151026
$893$	1.75340e7	0.735786
$894$	7.56121e6	0.316408
$895$	−4.43069e7	−1.84890
$896$	4.05754e6	0.168847
$897$	4.10413e7	1.70310
$898$	−2.13708e7	−0.884362
$899$	−4.58531e7	−1.89221
$900$	−360225.	−0.0148241
$901$	−1.40301e7	−0.575770
$902$	−7.25945e6	−0.297089
$903$	−1.97796e6	−0.0807233
$904$	−2.59910e7	−1.05780
$905$	−1.78697e7	−0.725265
$906$	−875329.	−0.0354284
$907$	1.54561e7	0.623851	0.311926	−	0.950107i	$-0.399026\pi$
$907$	1.54561e7	0.623851	0.311926	+	0.950107i	$0.399026\pi$
$908$	306223.	0.0123260
$909$	−4.62503e6	−0.185654
$910$	−1.14225e7	−0.457253
$911$	−1.45974e7	−0.582746	−0.291373	−	0.956610i	$-0.594112\pi$
$911$	−1.45974e7	−0.582746	−0.291373	+	0.956610i	$0.594112\pi$
$912$	5.30100e6	0.211043
$913$	−2.59937e6	−0.103203
$914$	−1.67842e7	−0.664563
$915$	−5.47946e6	−0.216364
$916$	−3.72170e6	−0.146556
$917$	−8.57145e6	−0.336613
$918$	−4.12071e6	−0.161386
$919$	−2.23731e7	−0.873851	−0.436925	−	0.899498i	$-0.643933\pi$
$919$	−2.23731e7	−0.873851	−0.436925	+	0.899498i	$0.643933\pi$
$920$	4.82048e7	1.87768
$921$	−1.73825e7	−0.675247
$922$	5.94938e6	0.230486
$923$	9.65192e7	3.72915
$924$	−189168.	−0.00728898
$925$	−1.87535e6	−0.0720656
$926$	−3.88800e7	−1.49004
$927$	−859329.	−0.0328443
$928$	−1.03992e7	−0.396397
$929$	1.56270e7	0.594069	0.297035	−	0.954867i	$-0.404002\pi$
$929$	1.56270e7	0.594069	0.297035	+	0.954867i	$0.404002\pi$
$930$	−1.85613e7	−0.703724
$931$	−1.06008e7	−0.400833
$932$	−3.68830e6	−0.139087
$933$	4.97171e6	0.186983
$934$	3.34120e7	1.25324
$935$	−1.42980e7	−0.534867
$936$	−1.81753e7	−0.678099
$937$	1.76177e7	0.655540	0.327770	−	0.944757i	$-0.393703\pi$
$937$	1.76177e7	0.655540	0.327770	+	0.944757i	$0.393703\pi$
$938$	8.81141e6	0.326993
$939$	1.13335e7	0.419468
$940$	−6.47980e6	−0.239189
$941$	3.59532e7	1.32362	0.661810	−	0.749672i	$-0.269789\pi$
$941$	3.59532e7	1.32362	0.661810	+	0.749672i	$0.269789\pi$
$942$	−2.18777e7	−0.803292
$943$	2.57497e7	0.942960
$944$	4.54443e7	1.65978
$945$	1.32536e6	0.0482786
$946$	8.64896e6	0.314222
$947$	6.73917e6	0.244192	0.122096	−	0.992518i	$-0.461038\pi$
$947$	6.73917e6	0.244192	0.122096	+	0.992518i	$0.461038\pi$
$948$	−2.68825e6	−0.0971514
$949$	−2.83595e7	−1.02219
$950$	−4.20771e6	−0.151265
$951$	−1.09657e7	−0.393176
$952$	5.58264e6	0.199640
$953$	−2.54080e7	−0.906231	−0.453115	−	0.891452i	$-0.649687\pi$
$953$	−2.54080e7	−0.906231	−0.453115	+	0.891452i	$0.649687\pi$
$954$	−5.68677e6	−0.202299
$955$	5.82220e7	2.06575
$956$	983425.	0.0348014
$957$	−1.43166e7	−0.505311
$958$	4.74057e7	1.66885
$959$	4.52337e6	0.158824
$960$	−2.10865e7	−0.738458
$961$	6.16112e6	0.215204
$962$	−9.84110e6	−0.342851
$963$	4.59072e6	0.159520
$964$	941920.	0.0326454
$965$	4.57868e6	0.158279
$966$	−5.10956e6	−0.176173
$967$	−1.25153e7	−0.430402	−0.215201	−	0.976570i	$-0.569041\pi$
$967$	−1.25153e7	−0.430402	−0.215201	+	0.976570i	$0.569041\pi$
$968$	−2.26376e7	−0.776500
$969$	6.32087e6	0.216256
$970$	−418441.	−0.0142793
$971$	1.84110e7	0.626656	0.313328	−	0.949645i	$-0.398556\pi$
$971$	1.84110e7	0.626656	0.313328	+	0.949645i	$0.398556\pi$
$972$	219336.	0.00744636
$973$	2.63071e6	0.0890821
$974$	1.57011e7	0.530314
$975$	1.27293e7	0.428839
$976$	−8.25434e6	−0.277369
$977$	−1.53347e7	−0.513971	−0.256986	−	0.966415i	$-0.582729\pi$
$977$	−1.53347e7	−0.513971	−0.256986	+	0.966415i	$0.582729\pi$
$978$	−1.33492e7	−0.446282
$979$	−1.74114e6	−0.0580601
$980$	3.91759e6	0.130303
$981$	−1.53692e7	−0.509894
$982$	−5.36620e7	−1.77578
$983$	3.00945e7	0.993352	0.496676	−	0.867936i	$-0.334554\pi$
$983$	3.00945e7	0.993352	0.496676	+	0.867936i	$0.334554\pi$
$984$	−1.14034e7	−0.375445
$985$	2.57033e7	0.844110
$986$	4.39425e7	1.43943
$987$	6.60392e6	0.215779
$988$	2.89961e6	0.0945034
$989$	−3.06784e7	−0.997338
$990$	−5.79535e6	−0.187928
$991$	1.04793e7	0.338959	0.169479	−	0.985534i	$-0.445791\pi$
$991$	1.04793e7	0.338959	0.169479	+	0.985534i	$0.445791\pi$
$992$	7.89023e6	0.254572
$993$	2.53819e7	0.816867
$994$	−1.20164e7	−0.385753
$995$	735931.	0.0235656
$996$	−424669.	−0.0135644
$997$	−3.56721e7	−1.13656	−0.568278	−	0.822836i	$-0.692390\pi$
$997$	−3.56721e7	−1.13656	−0.568278	+	0.822836i	$0.692390\pi$
$998$	−2.31280e7	−0.735043
$999$	1.14187e6	0.0361996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.c.1.8	✓	22
3.2	odd	2		927.6.a.d.1.15		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.c.1.8	✓	22	1.1	even	1	trivial
927.6.a.d.1.15		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.31841 q^{2} -9.00000 q^{3} -3.71447 q^{4} +65.7440 q^{5} +47.8657 q^{6} -27.6535 q^{7} +189.944 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-5.31841 q^{2} -9.00000 q^{3} -3.71447 q^{4} +65.7440 q^{5} +47.8657 q^{6} -27.6535 q^{7} +189.944 q^{8} +81.0000 q^{9} -349.654 q^{10} +204.624 q^{11} +33.4302 q^{12} -1181.33 q^{13} +147.073 q^{14} -591.696 q^{15} -891.340 q^{16} -1062.83 q^{17} -430.792 q^{18} +660.803 q^{19} -244.204 q^{20} +248.882 q^{21} -1088.28 q^{22} +3860.18 q^{23} -1709.50 q^{24} +1197.27 q^{25} +6282.80 q^{26} -729.000 q^{27} +102.718 q^{28} +7773.91 q^{29} +3146.88 q^{30} -5898.33 q^{31} -1337.71 q^{32} -1841.62 q^{33} +5652.56 q^{34} -1818.05 q^{35} -300.872 q^{36} -1566.36 q^{37} -3514.42 q^{38} +10632.0 q^{39} +12487.7 q^{40} +6670.60 q^{41} -1323.66 q^{42} -7947.40 q^{43} -760.070 q^{44} +5325.26 q^{45} -20530.0 q^{46} +26534.4 q^{47} +8022.06 q^{48} -16042.3 q^{49} -6367.58 q^{50} +9565.44 q^{51} +4388.01 q^{52} +13200.7 q^{53} +3877.12 q^{54} +13452.8 q^{55} -5252.63 q^{56} -5947.23 q^{57} -41344.9 q^{58} -50984.3 q^{59} +2197.84 q^{60} +9260.60 q^{61} +31369.8 q^{62} -2239.94 q^{63} +35637.3 q^{64} -77665.3 q^{65} +9794.48 q^{66} +59911.8 q^{67} +3947.84 q^{68} -34741.6 q^{69} +9669.16 q^{70} -81703.8 q^{71} +15385.5 q^{72} +24006.4 q^{73} +8330.53 q^{74} -10775.4 q^{75} -2454.53 q^{76} -5658.58 q^{77} -56545.2 q^{78} -80413.7 q^{79} -58600.2 q^{80} +6561.00 q^{81} -35477.0 q^{82} -12703.1 q^{83} -924.464 q^{84} -69874.5 q^{85} +42267.6 q^{86} -69965.2 q^{87} +38867.2 q^{88} -8508.98 q^{89} -28321.9 q^{90} +32667.9 q^{91} -14338.5 q^{92} +53085.0 q^{93} -141121. q^{94} +43443.8 q^{95} +12039.4 q^{96} +1196.73 q^{97} +85319.5 q^{98} +16574.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

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