LMFDB - Embedded newform 959.6.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [959,6,Mod(1,959)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(959, 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("959.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 959 = 7 \cdot 137 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	959.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:	$153.808083201$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	959.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.19852 q^{2} +12.7141 q^{3} +6.42163 q^{4} +82.2940 q^{5} -78.8085 q^{6} +49.0000 q^{7} +158.548 q^{8} -81.3521 q^{9} +O(q^{10})$	\(q-6.19852 q^{2} +12.7141 q^{3} +6.42163 q^{4} +82.2940 q^{5} -78.8085 q^{6} +49.0000 q^{7} +158.548 q^{8} -81.3521 q^{9} -510.101 q^{10} -122.384 q^{11} +81.6452 q^{12} -406.832 q^{13} -303.727 q^{14} +1046.29 q^{15} -1188.25 q^{16} -1176.10 q^{17} +504.262 q^{18} +1307.58 q^{19} +528.462 q^{20} +622.990 q^{21} +758.602 q^{22} +746.885 q^{23} +2015.79 q^{24} +3647.30 q^{25} +2521.75 q^{26} -4123.84 q^{27} +314.660 q^{28} +4381.92 q^{29} -6485.47 q^{30} +54.4113 q^{31} +2291.89 q^{32} -1556.01 q^{33} +7290.07 q^{34} +4032.41 q^{35} -522.413 q^{36} +468.249 q^{37} -8105.07 q^{38} -5172.49 q^{39} +13047.5 q^{40} +1421.79 q^{41} -3861.62 q^{42} -16709.4 q^{43} -785.908 q^{44} -6694.79 q^{45} -4629.58 q^{46} -9431.87 q^{47} -15107.6 q^{48} +2401.00 q^{49} -22607.9 q^{50} -14953.0 q^{51} -2612.53 q^{52} +16707.4 q^{53} +25561.7 q^{54} -10071.5 q^{55} +7768.85 q^{56} +16624.7 q^{57} -27161.4 q^{58} -33823.9 q^{59} +6718.91 q^{60} -49446.1 q^{61} -337.269 q^{62} -3986.25 q^{63} +23817.9 q^{64} -33479.8 q^{65} +9644.93 q^{66} +33309.5 q^{67} -7552.47 q^{68} +9495.96 q^{69} -24994.9 q^{70} -28005.0 q^{71} -12898.2 q^{72} -46621.1 q^{73} -2902.45 q^{74} +46372.1 q^{75} +8396.81 q^{76} -5996.83 q^{77} +32061.8 q^{78} -34176.6 q^{79} -97786.3 q^{80} -32662.3 q^{81} -8812.98 q^{82} +39873.0 q^{83} +4000.61 q^{84} -96785.8 q^{85} +103574. q^{86} +55712.1 q^{87} -19403.8 q^{88} +39902.7 q^{89} +41497.8 q^{90} -19934.8 q^{91} +4796.22 q^{92} +691.790 q^{93} +58463.6 q^{94} +107606. q^{95} +29139.2 q^{96} -4112.61 q^{97} -14882.6 q^{98} +9956.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) $ 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−6.19852	−1.09575	−0.547877	−	0.836559i	$-0.684564\pi$
$2$	−6.19852	−1.09575	−0.547877	+	0.836559i	$0.684564\pi$
$3$	12.7141	0.815609	0.407804	−	0.913069i	$-0.366295\pi$
$3$	12.7141	0.815609	0.407804	+	0.913069i	$0.366295\pi$
$4$	6.42163	0.200676
$5$	82.2940	1.47212	0.736060	−	0.676916i	$-0.236684\pi$
$5$	82.2940	1.47212	0.736060	+	0.676916i	$0.236684\pi$
$6$	−78.8085	−0.893706
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	158.548	0.875862
$9$	−81.3521	−0.334782
$10$	−510.101	−1.61308
$11$	−122.384	−0.304961	−0.152480	−	0.988306i	$-0.548726\pi$
$11$	−122.384	−0.304961	−0.152480	+	0.988306i	$0.548726\pi$
$12$	81.6452	0.163673
$13$	−406.832	−0.667662	−0.333831	−	0.942633i	$-0.608341\pi$
$13$	−406.832	−0.667662	−0.333831	+	0.942633i	$0.608341\pi$
$14$	−303.727	−0.414156
$15$	1046.29	1.20067
$16$	−1188.25	−1.16041
$17$	−1176.10	−0.987009	−0.493505	−	0.869743i	$-0.664284\pi$
$17$	−1176.10	−0.987009	−0.493505	+	0.869743i	$0.664284\pi$
$18$	504.262	0.366839
$19$	1307.58	0.830969	0.415485	−	0.909600i	$-0.363612\pi$
$19$	1307.58	0.830969	0.415485	+	0.909600i	$0.363612\pi$
$20$	528.462	0.295419
$21$	622.990	0.308271
$22$	758.602	0.334162
$23$	746.885	0.294398	0.147199	−	0.989107i	$-0.452974\pi$
$23$	746.885	0.294398	0.147199	+	0.989107i	$0.452974\pi$
$24$	2015.79	0.714361
$25$	3647.30	1.16714
$26$	2521.75	0.731593
$27$	−4123.84	−1.08866
$28$	314.660	0.0758484
$29$	4381.92	0.967541	0.483770	−	0.875195i	$-0.339267\pi$
$29$	4381.92	0.967541	0.483770	+	0.875195i	$0.339267\pi$
$30$	−6485.47	−1.31564
$31$	54.4113	0.0101692	0.00508458	−	0.999987i	$-0.498382\pi$
$31$	54.4113	0.0101692	0.00508458	+	0.999987i	$0.498382\pi$
$32$	2291.89	0.395656
$33$	−1556.01	−0.248729
$34$	7290.07	1.08152
$35$	4032.41	0.556409
$36$	−522.413	−0.0671828
$37$	468.249	0.0562306	0.0281153	−	0.999605i	$-0.491049\pi$
$37$	468.249	0.0562306	0.0281153	+	0.999605i	$0.491049\pi$
$38$	−8105.07	−0.910538
$39$	−5172.49	−0.544551
$40$	13047.5	1.28937
$41$	1421.79	0.132092	0.0660458	−	0.997817i	$-0.478962\pi$
$41$	1421.79	0.132092	0.0660458	+	0.997817i	$0.478962\pi$
$42$	−3861.62	−0.337789
$43$	−16709.4	−1.37813	−0.689064	−	0.724700i	$-0.741978\pi$
$43$	−16709.4	−1.37813	−0.689064	+	0.724700i	$0.741978\pi$
$44$	−785.908	−0.0611984
$45$	−6694.79	−0.492839
$46$	−4629.58	−0.322587
$47$	−9431.87	−0.622807	−0.311403	−	0.950278i	$-0.600799\pi$
$47$	−9431.87	−0.622807	−0.311403	+	0.950278i	$0.600799\pi$
$48$	−15107.6	−0.946437
$49$	2401.00	0.142857
$50$	−22607.9	−1.27890
$51$	−14953.0	−0.805014
$52$	−2612.53	−0.133984
$53$	16707.4	0.816993	0.408497	−	0.912760i	$-0.366053\pi$
$53$	16707.4	0.816993	0.408497	+	0.912760i	$0.366053\pi$
$54$	25561.7	1.19290
$55$	−10071.5	−0.448939
$56$	7768.85	0.331045
$57$	16624.7	0.677746
$58$	−27161.4	−1.06019
$59$	−33823.9	−1.26501	−0.632505	−	0.774556i	$-0.717973\pi$
$59$	−33823.9	−1.26501	−0.632505	+	0.774556i	$0.717973\pi$
$60$	6718.91	0.240947
$61$	−49446.1	−1.70140	−0.850702	−	0.525649i	$-0.823823\pi$
$61$	−49446.1	−1.70140	−0.850702	+	0.525649i	$0.823823\pi$
$62$	−337.269	−0.0111429
$63$	−3986.25	−0.126536
$64$	23817.9	0.726864
$65$	−33479.8	−0.982878
$66$	9644.93	0.272546
$67$	33309.5	0.906527	0.453263	−	0.891377i	$-0.350260\pi$
$67$	33309.5	0.906527	0.453263	+	0.891377i	$0.350260\pi$
$68$	−7552.47	−0.198069
$69$	9495.96	0.240113
$70$	−24994.9	−0.609687
$71$	−28005.0	−0.659311	−0.329655	−	0.944101i	$-0.606933\pi$
$71$	−28005.0	−0.659311	−0.329655	+	0.944101i	$0.606933\pi$
$72$	−12898.2	−0.293223
$73$	−46621.1	−1.02394	−0.511971	−	0.859003i	$-0.671084\pi$
$73$	−46621.1	−1.02394	−0.511971	+	0.859003i	$0.671084\pi$
$74$	−2902.45	−0.0616149
$75$	46372.1	0.951928
$76$	8396.81	0.166756
$77$	−5996.83	−0.115264
$78$	32061.8	0.596694
$79$	−34176.6	−0.616115	−0.308057	−	0.951368i	$-0.599679\pi$
$79$	−34176.6	−0.616115	−0.308057	+	0.951368i	$0.599679\pi$
$80$	−97786.3	−1.70826
$81$	−32662.3	−0.553139
$82$	−8812.98	−0.144740
$83$	39873.0	0.635307	0.317653	−	0.948207i	$-0.397105\pi$
$83$	39873.0	0.635307	0.317653	+	0.948207i	$0.397105\pi$
$84$	4000.61	0.0618627
$85$	−96785.8	−1.45300
$86$	103574.	1.51009
$87$	55712.1	0.789135
$88$	−19403.8	−0.267104
$89$	39902.7	0.533983	0.266991	−	0.963699i	$-0.413971\pi$
$89$	39902.7	0.533983	0.266991	+	0.963699i	$0.413971\pi$
$90$	41497.8	0.540031
$91$	−19934.8	−0.252352
$92$	4796.22	0.0590786
$93$	691.790	0.00829405
$94$	58463.6	0.682443
$95$	107606.	1.22329
$96$	29139.2	0.322701
$97$	−4112.61	−0.0443801	−0.0221900	−	0.999754i	$-0.507064\pi$
$97$	−4112.61	−0.0443801	−0.0221900	+	0.999754i	$0.507064\pi$
$98$	−14882.6	−0.156536
$99$	9956.22	0.102095
$100$	23421.7	0.234217
$101$	−17069.3	−0.166499	−0.0832494	−	0.996529i	$-0.526530\pi$
$101$	−17069.3	−0.166499	−0.0832494	+	0.996529i	$0.526530\pi$
$102$	92686.5	0.882097
$103$	−5495.98	−0.0510449	−0.0255224	−	0.999674i	$-0.508125\pi$
$103$	−5495.98	−0.0510449	−0.0255224	+	0.999674i	$0.508125\pi$
$104$	−64502.4	−0.584780
$105$	51268.4	0.453812
$106$	−103561.	−0.895223
$107$	−93729.5	−0.791438	−0.395719	−	0.918372i	$-0.629505\pi$
$107$	−93729.5	−0.791438	−0.395719	+	0.918372i	$0.629505\pi$
$108$	−26481.8	−0.218468
$109$	25408.5	0.204839	0.102420	−	0.994741i	$-0.467342\pi$
$109$	25408.5	0.204839	0.102420	+	0.994741i	$0.467342\pi$
$110$	62428.4	0.491927
$111$	5953.36	0.0458622
$112$	−58224.5	−0.438592
$113$	−218519.	−1.60988	−0.804938	−	0.593359i	$-0.797801\pi$
$113$	−218519.	−1.60988	−0.804938	+	0.593359i	$0.797801\pi$
$114$	−103049.	−0.742643
$115$	61464.2	0.433389
$116$	28139.1	0.194162
$117$	33096.6	0.223521
$118$	209658.	1.38614
$119$	−57628.8	−0.373055
$120$	165888.	1.05163
$121$	−146073.	−0.906999
$122$	306492.	1.86432
$123$	18076.7	0.107735
$124$	349.409	0.00204071
$125$	42982.5	0.246046
$126$	24708.8	0.138652
$127$	185476.	1.02042	0.510209	−	0.860050i	$-0.329568\pi$
$127$	185476.	1.02042	0.510209	+	0.860050i	$0.329568\pi$
$128$	−220976.	−1.19212
$129$	−212445.	−1.12401
$130$	207525.	1.07699
$131$	−118428.	−0.602945	−0.301472	−	0.953475i	$-0.597478\pi$
$131$	−118428.	−0.602945	−0.301472	+	0.953475i	$0.597478\pi$
$132$	−9992.10	−0.0499139
$133$	64071.5	0.314077
$134$	−206469.	−0.993330
$135$	−339367.	−1.60264
$136$	−186468.	−0.864484
$137$	18769.0	0.0854358
$137$	18769.0	0.0854358
$138$	−58860.9	−0.263105
$139$	234725.	1.03044	0.515220	−	0.857058i	$-0.327710\pi$
$139$	234725.	1.03044	0.515220	+	0.857058i	$0.327710\pi$
$140$	25894.6	0.111658
$141$	−119918.	−0.507967
$142$	173590.	0.722442
$143$	49789.9	0.203611
$144$	96667.0	0.388483
$145$	360606.	1.42434
$146$	288982.	1.12199
$147$	30526.5	0.116516
$148$	3006.92	0.0112841
$149$	−256951.	−0.948167	−0.474084	−	0.880480i	$-0.657221\pi$
$149$	−256951.	−0.948167	−0.474084	+	0.880480i	$0.657221\pi$
$150$	−287439.	−1.04308
$151$	345159.	1.23191	0.615953	−	0.787783i	$-0.288771\pi$
$151$	345159.	1.23191	0.615953	+	0.787783i	$0.288771\pi$
$152$	207314.	0.727814
$153$	95678.0	0.330433
$154$	37171.5	0.126301
$155$	4477.72	0.0149702
$156$	−33215.9	−0.109278
$157$	144932.	0.469261	0.234630	−	0.972085i	$-0.424612\pi$
$157$	144932.	0.469261	0.234630	+	0.972085i	$0.424612\pi$
$158$	211845.	0.675110
$159$	212419.	0.666347
$160$	188608.	0.582453
$161$	36597.4	0.111272
$162$	202458.	0.606104
$163$	77003.8	0.227009	0.113505	−	0.993537i	$-0.463792\pi$
$163$	77003.8	0.227009	0.113505	+	0.993537i	$0.463792\pi$
$164$	9130.20	0.0265076
$165$	−128050.	−0.366159
$166$	−247154.	−0.696140
$167$	109203.	0.303000	0.151500	−	0.988457i	$-0.451590\pi$
$167$	109203.	0.303000	0.151500	+	0.988457i	$0.451590\pi$
$168$	98773.8	0.270003
$169$	−205781.	−0.554228
$170$	599929.	1.59213
$171$	−106374.	−0.278194
$172$	−107302.	−0.276557
$173$	16353.1	0.0415417	0.0207709	−	0.999784i	$-0.493388\pi$
$173$	16353.1	0.0415417	0.0207709	+	0.999784i	$0.493388\pi$
$174$	−345332.	−0.864698
$175$	178718.	0.441136
$176$	145424.	0.353878
$177$	−430040.	−1.03175
$178$	−247338.	−0.585113
$179$	−376783.	−0.878939	−0.439469	−	0.898258i	$-0.644833\pi$
$179$	−376783.	−0.878939	−0.439469	+	0.898258i	$0.644833\pi$
$180$	−42991.5	−0.0989011
$181$	−402528.	−0.913272	−0.456636	−	0.889654i	$-0.650946\pi$
$181$	−402528.	−0.913272	−0.456636	+	0.889654i	$0.650946\pi$
$182$	123566.	0.276516
$183$	−628662.	−1.38768
$184$	118417.	0.257852
$185$	38534.1	0.0827782
$186$	−4288.07	−0.00908824
$187$	143936.	0.300999
$188$	−60568.0	−0.124982
$189$	−202068.	−0.411475
$190$	−666999.	−1.34042
$191$	−317224.	−0.629192	−0.314596	−	0.949226i	$-0.601869\pi$
$191$	−317224.	−0.629192	−0.314596	+	0.949226i	$0.601869\pi$
$192$	302822.	0.592836
$193$	367310.	0.709806	0.354903	−	0.934903i	$-0.384514\pi$
$193$	367310.	0.709806	0.354903	+	0.934903i	$0.384514\pi$
$194$	25492.1	0.0486296
$195$	−425665.	−0.801644
$196$	15418.3	0.0286680
$197$	−112383.	−0.206317	−0.103159	−	0.994665i	$-0.532895\pi$
$197$	−112383.	−0.206317	−0.103159	+	0.994665i	$0.532895\pi$
$198$	−61713.8	−0.111871
$199$	463857.	0.830331	0.415165	−	0.909746i	$-0.363724\pi$
$199$	463857.	0.830331	0.415165	+	0.909746i	$0.363724\pi$
$200$	578273.	1.02225
$201$	423499.	0.739371
$202$	105804.	0.182442
$203$	214714.	0.365696
$204$	−96022.8	−0.161547
$205$	117005.	0.194455
$206$	34066.9	0.0559326
$207$	−60760.7	−0.0985591
$208$	483420.	0.774758
$209$	−160028.	−0.253413
$210$	−317788.	−0.497266
$211$	−295790.	−0.457381	−0.228690	−	0.973499i	$-0.573444\pi$
$211$	−295790.	−0.457381	−0.228690	+	0.973499i	$0.573444\pi$
$212$	107289.	0.163951
$213$	−356058.	−0.537740
$214$	580984.	0.867221
$215$	−1.37508e6	−2.02877
$216$	−653826.	−0.953516
$217$	2666.15	0.00384358
$218$	−157495.	−0.224453
$219$	−592744.	−0.835136
$220$	−64675.5	−0.0900914
$221$	478474.	0.658989
$222$	−36902.0	−0.0502536
$223$	−181197.	−0.243999	−0.122000	−	0.992530i	$-0.538931\pi$
$223$	−181197.	−0.243999	−0.122000	+	0.992530i	$0.538931\pi$
$224$	112302.	0.149544
$225$	−296716.	−0.390737
$226$	1.35449e6	1.76403
$227$	1.02136e6	1.31557	0.657786	−	0.753205i	$-0.271493\pi$
$227$	1.02136e6	1.31557	0.657786	+	0.753205i	$0.271493\pi$
$228$	106758.	0.136007
$229$	1.04556e6	1.31753	0.658766	−	0.752348i	$-0.271079\pi$
$229$	1.04556e6	1.31753	0.658766	+	0.752348i	$0.271079\pi$
$230$	−380987.	−0.474887
$231$	−76244.3	−0.0940107
$232$	694744.	0.847432
$233$	222159.	0.268086	0.134043	−	0.990976i	$-0.457204\pi$
$233$	222159.	0.268086	0.134043	+	0.990976i	$0.457204\pi$
$234$	−205150.	−0.244924
$235$	−776187.	−0.916846
$236$	−217205.	−0.253857
$237$	−434525.	−0.502509
$238$	357213.	0.408776
$239$	−465565.	−0.527212	−0.263606	−	0.964630i	$-0.584912\pi$
$239$	−465565.	−0.527212	−0.263606	+	0.964630i	$0.584912\pi$
$240$	−1.24326e6	−1.39327
$241$	649088.	0.719881	0.359941	−	0.932975i	$-0.382797\pi$
$241$	649088.	0.719881	0.359941	+	0.932975i	$0.382797\pi$
$242$	905437.	0.993847
$243$	586822.	0.637515
$244$	−317525.	−0.341431
$245$	197588.	0.210303
$246$	−112049.	−0.118051
$247$	−531966.	−0.554806
$248$	8626.80	0.00890678
$249$	506949.	0.518162
$250$	−266428.	−0.269606
$251$	−852653.	−0.854256	−0.427128	−	0.904191i	$-0.640475\pi$
$251$	−852653.	−0.854256	−0.427128	+	0.904191i	$0.640475\pi$
$252$	−25598.2	−0.0253927
$253$	−91407.1	−0.0897798
$254$	−1.14968e6	−1.11813
$255$	−1.23054e6	−1.18508
$256$	607551.	0.579406
$257$	−1.15547e6	−1.09125	−0.545627	−	0.838028i	$-0.683709\pi$
$257$	−1.15547e6	−1.09125	−0.545627	+	0.838028i	$0.683709\pi$
$258$	1.31684e6	1.23164
$259$	22944.2	0.0212532
$260$	−214995.	−0.197240
$261$	−356478.	−0.323915
$262$	734080.	0.660679
$263$	−1.23872e6	−1.10429	−0.552145	−	0.833748i	$-0.686190\pi$
$263$	−1.23872e6	−1.10429	−0.552145	+	0.833748i	$0.686190\pi$
$264$	−246702.	−0.217852
$265$	1.37492e6	1.20271
$266$	−397149.	−0.344151
$267$	507326.	0.435521
$268$	213901.	0.181918
$269$	−129918.	−0.109468	−0.0547340	−	0.998501i	$-0.517431\pi$
$269$	−129918.	−0.109468	−0.0547340	+	0.998501i	$0.517431\pi$
$270$	2.10357e6	1.75610
$271$	−569504.	−0.471057	−0.235528	−	0.971867i	$-0.575682\pi$
$271$	−569504.	−0.471057	−0.235528	+	0.971867i	$0.575682\pi$
$272$	1.39750e6	1.14533
$273$	−253452.	−0.205821
$274$	−116340.	−0.0936166
$275$	−446373.	−0.355931
$276$	60979.6	0.0481850
$277$	−346792.	−0.271562	−0.135781	−	0.990739i	$-0.543354\pi$
$277$	−346792.	−0.271562	−0.135781	+	0.990739i	$0.543354\pi$
$278$	−1.45495e6	−1.12911
$279$	−4426.47	−0.00340445
$280$	639330.	0.487338
$281$	457717.	0.345805	0.172902	−	0.984939i	$-0.444685\pi$
$281$	457717.	0.345805	0.172902	+	0.984939i	$0.444685\pi$
$282$	743312.	0.556606
$283$	−2.25632e6	−1.67469	−0.837344	−	0.546676i	$-0.815893\pi$
$283$	−2.25632e6	−1.67469	−0.837344	+	0.546676i	$0.815893\pi$
$284$	−179838.	−0.132308
$285$	1.36811e6	0.997723
$286$	−308623.	−0.223107
$287$	69667.6	0.0499259
$288$	−186450.	−0.132459
$289$	−36649.8	−0.0258123
$290$	−2.23522e6	−1.56072
$291$	−52288.1	−0.0361968
$292$	−299384.	−0.205481
$293$	1.49158e6	1.01503	0.507515	−	0.861643i	$-0.330564\pi$
$293$	1.49158e6	1.01503	0.507515	+	0.861643i	$0.330564\pi$
$294$	−189219.	−0.127672
$295$	−2.78351e6	−1.86225
$296$	74240.0	0.0492502
$297$	504694.	0.331999
$298$	1.59272e6	1.03896
$299$	−303857.	−0.196558
$300$	297785.	0.191029
$301$	−818760.	−0.520883
$302$	−2.13948e6	−1.34986
$303$	−217020.	−0.135798
$304$	−1.55374e6	−0.964261
$305$	−4.06912e6	−2.50467
$306$	−593062.	−0.362073
$307$	−900949.	−0.545575	−0.272787	−	0.962074i	$-0.587946\pi$
$307$	−900949.	−0.545575	−0.272787	+	0.962074i	$0.587946\pi$
$308$	−38509.5	−0.0231308
$309$	−69876.4	−0.0416327
$310$	−27755.3	−0.0164037
$311$	1.04892e6	0.614955	0.307477	−	0.951555i	$-0.400515\pi$
$311$	1.04892e6	0.614955	0.307477	+	0.951555i	$0.400515\pi$
$312$	−820089.	−0.476952
$313$	1.46980e6	0.848001	0.424001	−	0.905662i	$-0.360625\pi$
$313$	1.46980e6	0.848001	0.424001	+	0.905662i	$0.360625\pi$
$314$	−898362.	−0.514194
$315$	−328045.	−0.186276
$316$	−219470.	−0.123640
$317$	−1.83665e6	−1.02654	−0.513272	−	0.858226i	$-0.671567\pi$
$317$	−1.83665e6	−1.02654	−0.513272	+	0.858226i	$0.671567\pi$
$318$	−1.31668e6	−0.730152
$319$	−536278.	−0.295062
$320$	1.96007e6	1.07003
$321$	−1.19168e6	−0.645504
$322$	−226850.	−0.121927
$323$	−1.53784e6	−0.820174
$324$	−209745.	−0.111002
$325$	−1.48384e6	−0.779253
$326$	−477310.	−0.248746
$327$	323046.	0.167069
$328$	225422.	0.115694
$329$	−462162.	−0.235399
$330$	793720.	0.401220
$331$	−1.63705e6	−0.821279	−0.410640	−	0.911798i	$-0.634695\pi$
$331$	−1.63705e6	−0.821279	−0.410640	+	0.911798i	$0.634695\pi$
$332$	256050.	0.127491
$333$	−38093.0	−0.0188250
$334$	−676895.	−0.332013
$335$	2.74117e6	1.33452
$336$	−740271.	−0.357719
$337$	971470.	0.465967	0.232983	−	0.972481i	$-0.425151\pi$
$337$	971470.	0.465967	0.232983	+	0.972481i	$0.425151\pi$
$338$	1.27554e6	0.607297
$339$	−2.77826e6	−1.31303
$340$	−621523.	−0.291582
$341$	−6659.09	−0.00310120
$342$	659364.	0.304832
$343$	117649.	0.0539949
$344$	−2.64924e6	−1.20705
$345$	781461.	0.353476
$346$	−101365.	−0.0455195
$347$	−2.66852e6	−1.18973	−0.594863	−	0.803827i	$-0.702794\pi$
$347$	−2.66852e6	−1.18973	−0.594863	+	0.803827i	$0.702794\pi$
$348$	357763.	0.158361
$349$	−445053.	−0.195591	−0.0977953	−	0.995207i	$-0.531179\pi$
$349$	−445053.	−0.195591	−0.0977953	+	0.995207i	$0.531179\pi$
$350$	−1.10779e6	−0.483377
$351$	1.67771e6	0.726857
$352$	−280491.	−0.120660
$353$	−3.86473e6	−1.65075	−0.825377	−	0.564582i	$-0.809037\pi$
$353$	−3.86473e6	−1.65075	−0.825377	+	0.564582i	$0.809037\pi$
$354$	2.66561e6	1.13055
$355$	−2.30465e6	−0.970585
$356$	256240.	0.107158
$357$	−732698.	−0.304267
$358$	2.33550e6	0.963100
$359$	−2.85835e6	−1.17052	−0.585261	−	0.810845i	$-0.699008\pi$
$359$	−2.85835e6	−1.17052	−0.585261	+	0.810845i	$0.699008\pi$
$360$	−1.06144e6	−0.431659
$361$	−766328.	−0.309490
$362$	2.49508e6	1.00072
$363$	−1.85719e6	−0.739756
$364$	−128014.	−0.0506411
$365$	−3.83664e6	−1.50737
$366$	3.89677e6	1.52056
$367$	−3.29660e6	−1.27762	−0.638809	−	0.769366i	$-0.720572\pi$
$367$	−3.29660e6	−1.27762	−0.638809	+	0.769366i	$0.720572\pi$
$368$	−887490.	−0.341621
$369$	−115665.	−0.0442219
$370$	−238854.	−0.0907045
$371$	818661.	0.308794
$372$	4442.42	0.00166442
$373$	3.28837e6	1.22380	0.611898	−	0.790937i	$-0.290406\pi$
$373$	3.28837e6	1.22380	0.611898	+	0.790937i	$0.290406\pi$
$374$	−892190.	−0.329821
$375$	546484.	0.200678
$376$	−1.49540e6	−0.545493
$377$	−1.78270e6	−0.645990
$378$	1.25252e6	0.450875
$379$	−2.89887e6	−1.03665	−0.518323	−	0.855185i	$-0.673443\pi$
$379$	−2.89887e6	−1.03665	−0.518323	+	0.855185i	$0.673443\pi$
$380$	691007.	0.245484
$381$	2.35816e6	0.832262
$382$	1.96632e6	0.689439
$383$	−1.45223e6	−0.505870	−0.252935	−	0.967483i	$-0.581396\pi$
$383$	−1.45223e6	−0.505870	−0.252935	+	0.967483i	$0.581396\pi$
$384$	−2.80951e6	−0.972303
$385$	−493504.	−0.169683
$386$	−2.27678e6	−0.777772
$387$	1.35934e6	0.461373
$388$	−26409.7	−0.00890602
$389$	−3.24895e6	−1.08860	−0.544301	−	0.838890i	$-0.683205\pi$
$389$	−3.24895e6	−1.08860	−0.544301	+	0.838890i	$0.683205\pi$
$390$	2.63849e6	0.878405
$391$	−878411.	−0.290573
$392$	380674.	0.125123
$393$	−1.50571e6	−0.491767
$394$	696608.	0.226073
$395$	−2.81253e6	−0.906995
$396$	63935.2	0.0204881
$397$	−1.12398e6	−0.357916	−0.178958	−	0.983857i	$-0.557273\pi$
$397$	−1.12398e6	−0.357916	−0.178958	+	0.983857i	$0.557273\pi$
$398$	−2.87522e6	−0.909838
$399$	814611.	0.256164
$400$	−4.33393e6	−1.35435
$401$	3.69149e6	1.14641	0.573207	−	0.819411i	$-0.305699\pi$
$401$	3.69149e6	1.14641	0.573207	+	0.819411i	$0.305699\pi$
$402$	−2.62507e6	−0.810169
$403$	−22136.3	−0.00678956
$404$	−109613.	−0.0334123
$405$	−2.68791e6	−0.814287
$406$	−1.33091e6	−0.400713
$407$	−57306.4	−0.0171481
$408$	−2.37077e6	−0.705081
$409$	−2.89342e6	−0.855269	−0.427635	−	0.903952i	$-0.640653\pi$
$409$	−2.89342e6	−0.855269	−0.427635	+	0.903952i	$0.640653\pi$
$410$	−725255.	−0.213074
$411$	238631.	0.0696822
$412$	−35293.2	−0.0102435
$413$	−1.65737e6	−0.478129
$414$	376626.	0.107996
$415$	3.28131e6	0.935248
$416$	−932412.	−0.264165
$417$	2.98432e6	0.840436
$418$	991934.	0.277678
$419$	6.64782e6	1.84988	0.924941	−	0.380111i	$-0.124114\pi$
$419$	6.64782e6	1.84988	0.924941	+	0.380111i	$0.124114\pi$
$420$	329227.	0.0910693
$421$	4.41377e6	1.21368	0.606840	−	0.794824i	$-0.292437\pi$
$421$	4.41377e6	1.21368	0.606840	+	0.794824i	$0.292437\pi$
$422$	1.83346e6	0.501176
$423$	767302.	0.208505
$424$	2.64892e6	0.715573
$425$	−4.28959e6	−1.15198
$426$	2.20703e6	0.589230
$427$	−2.42286e6	−0.643070
$428$	−601896.	−0.158823
$429$	633033.	0.166067
$430$	8.52348e6	2.22303
$431$	−1.74015e6	−0.451226	−0.225613	−	0.974217i	$-0.572438\pi$
$431$	−1.74015e6	−0.451226	−0.225613	+	0.974217i	$0.572438\pi$
$432$	4.90017e6	1.26329
$433$	−3.06055e6	−0.784475	−0.392238	−	0.919864i	$-0.628299\pi$
$433$	−3.06055e6	−0.784475	−0.392238	+	0.919864i	$0.628299\pi$
$434$	−16526.2	−0.00421162
$435$	4.58477e6	1.16170
$436$	163164.	0.0411063
$437$	976614.	0.244635
$438$	3.67414e6	0.915103
$439$	573489.	0.142025	0.0710123	−	0.997475i	$-0.477377\pi$
$439$	573489.	0.142025	0.0710123	+	0.997475i	$0.477377\pi$
$440$	−1.59682e6	−0.393209
$441$	−195326.	−0.0478260
$442$	−2.96583e6	−0.722089
$443$	1.47615e6	0.357371	0.178686	−	0.983906i	$-0.442815\pi$
$443$	1.47615e6	0.357371	0.178686	+	0.983906i	$0.442815\pi$
$444$	38230.3	0.00920344
$445$	3.28375e6	0.786086
$446$	1.12315e6	0.267363
$447$	−3.26690e6	−0.773334
$448$	1.16708e6	0.274729
$449$	5.88084e6	1.37665	0.688325	−	0.725402i	$-0.258346\pi$
$449$	5.88084e6	1.37665	0.688325	+	0.725402i	$0.258346\pi$
$450$	1.83920e6	0.428151
$451$	−174005.	−0.0402828
$452$	−1.40325e6	−0.323064
$453$	4.38839e6	1.00475
$454$	−6.33092e6	−1.44154
$455$	−1.64051e6	−0.371493
$456$	2.63581e6	0.593612
$457$	1.08046e6	0.242001	0.121000	−	0.992652i	$-0.461390\pi$
$457$	1.08046e6	0.242001	0.121000	+	0.992652i	$0.461390\pi$
$458$	−6.48094e6	−1.44369
$459$	4.85004e6	1.07452
$460$	394701.	0.0869707
$461$	1.07101e6	0.234716	0.117358	−	0.993090i	$-0.462557\pi$
$461$	1.07101e6	0.234716	0.117358	+	0.993090i	$0.462557\pi$
$462$	472601.	0.103013
$463$	−324758.	−0.0704057	−0.0352029	−	0.999380i	$-0.511208\pi$
$463$	−324758.	−0.0704057	−0.0352029	+	0.999380i	$0.511208\pi$
$464$	−5.20684e6	−1.12274
$465$	56930.2	0.0122098
$466$	−1.37706e6	−0.293756
$467$	−144677.	−0.0306978	−0.0153489	−	0.999882i	$-0.504886\pi$
$467$	−144677.	−0.0306978	−0.0153489	+	0.999882i	$0.504886\pi$
$468$	212534.	0.0448554
$469$	1.63216e6	0.342635
$470$	4.81121e6	1.00464
$471$	1.84267e6	0.382733
$472$	−5.36272e6	−1.10797
$473$	2.04497e6	0.420275
$474$	2.69341e6	0.550626
$475$	4.76915e6	0.969855
$476$	−370071.	−0.0748631
$477$	−1.35918e6	−0.273515
$478$	2.88581e6	0.577695
$479$	−6.25858e6	−1.24634	−0.623171	−	0.782086i	$-0.714156\pi$
$479$	−6.25858e6	−1.24634	−0.623171	+	0.782086i	$0.714156\pi$
$480$	2.39798e6	0.475054
$481$	−190499.	−0.0375430
$482$	−4.02338e6	−0.788812
$483$	465302.	0.0907543
$484$	−938028.	−0.182013
$485$	−338443.	−0.0653328
$486$	−3.63743e6	−0.698560
$487$	−8.23452e6	−1.57332	−0.786658	−	0.617389i	$-0.788190\pi$
$487$	−8.23452e6	−1.57332	−0.786658	+	0.617389i	$0.788190\pi$
$488$	−7.83958e6	−1.49019
$489$	979033.	0.185151
$490$	−1.22475e6	−0.230440
$491$	−4.27314e6	−0.799914	−0.399957	−	0.916534i	$-0.630975\pi$
$491$	−4.27314e6	−0.799914	−0.399957	+	0.916534i	$0.630975\pi$
$492$	116082.	0.0216199
$493$	−5.15357e6	−0.954972
$494$	3.29740e6	0.607931
$495$	819337.	0.150297
$496$	−64654.5	−0.0118003
$497$	−1.37225e6	−0.249196
$498$	−3.14233e6	−0.567778
$499$	5.01349e6	0.901340	0.450670	−	0.892691i	$-0.351185\pi$
$499$	5.01349e6	0.901340	0.450670	+	0.892691i	$0.351185\pi$
$500$	276018.	0.0493756
$501$	1.38841e6	0.247129
$502$	5.28519e6	0.936054
$503$	−3.04642e6	−0.536871	−0.268436	−	0.963298i	$-0.586507\pi$
$503$	−3.04642e6	−0.536871	−0.268436	+	0.963298i	$0.586507\pi$
$504$	−632012.	−0.110828
$505$	−1.40470e6	−0.245106
$506$	566589.	0.0983765
$507$	−2.61632e6	−0.452033
$508$	1.19106e6	0.204774
$509$	−2.27020e6	−0.388391	−0.194196	−	0.980963i	$-0.562210\pi$
$509$	−2.27020e6	−0.388391	−0.194196	+	0.980963i	$0.562210\pi$
$510$	7.62755e6	1.29855
$511$	−2.28443e6	−0.387014
$512$	3.30531e6	0.557234
$513$	−5.39226e6	−0.904643
$514$	7.16221e6	1.19575
$515$	−452286.	−0.0751442
$516$	−1.36424e6	−0.225563
$517$	1.15431e6	0.189932
$518$	−142220.	−0.0232882
$519$	207914.	0.0338818
$520$	−5.30816e6	−0.860866
$521$	7.74423e6	1.24993	0.624963	−	0.780655i	$-0.285114\pi$
$521$	7.74423e6	1.24993	0.624963	+	0.780655i	$0.285114\pi$
$522$	2.20964e6	0.354931
$523$	−1.43517e6	−0.229429	−0.114714	−	0.993399i	$-0.536595\pi$
$523$	−1.43517e6	−0.229429	−0.114714	+	0.993399i	$0.536595\pi$
$524$	−760504.	−0.120997
$525$	2.27223e6	0.359795
$526$	7.67821e6	1.21003
$527$	−63993.0	−0.0100371
$528$	1.84893e6	0.288626
$529$	−5.87851e6	−0.913330
$530$	−8.52245e6	−1.31788
$531$	2.75165e6	0.423503
$532$	411444.	0.0630277
$533$	−578429.	−0.0881925
$534$	−3.14467e6	−0.477224
$535$	−7.71338e6	−1.16509
$536$	5.28115e6	0.793992
$537$	−4.79045e6	−0.716870
$538$	805297.	0.119950
$539$	−293845.	−0.0435659
$540$	−2.17929e6	−0.321611
$541$	−887689.	−0.130397	−0.0651985	−	0.997872i	$-0.520768\pi$
$541$	−887689.	−0.130397	−0.0651985	+	0.997872i	$0.520768\pi$
$542$	3.53008e6	0.516162
$543$	−5.11778e6	−0.744873
$544$	−2.69548e6	−0.390516
$545$	2.09097e6	0.301548
$546$	1.57103e6	0.225529
$547$	3.73868e6	0.534257	0.267129	−	0.963661i	$-0.413925\pi$
$547$	3.73868e6	0.534257	0.267129	+	0.963661i	$0.413925\pi$
$548$	120528.	0.0171449
$549$	4.02254e6	0.569599
$550$	2.76685e6	0.390013
$551$	5.72972e6	0.803997
$552$	1.50557e6	0.210306
$553$	−1.67466e6	−0.232870
$554$	2.14959e6	0.297565
$555$	489926.	0.0675146
$556$	1.50732e6	0.206785
$557$	8.48681e6	1.15906	0.579530	−	0.814951i	$-0.303236\pi$
$557$	8.48681e6	1.15906	0.579530	+	0.814951i	$0.303236\pi$
$558$	27437.6	0.00373044
$559$	6.79791e6	0.920124
$560$	−4.79153e6	−0.645660
$561$	1.83002e6	0.245498
$562$	−2.83716e6	−0.378917
$563$	−8.16279e6	−1.08534	−0.542672	−	0.839944i	$-0.682587\pi$
$563$	−8.16279e6	−1.08534	−0.542672	+	0.839944i	$0.682587\pi$
$564$	−770067.	−0.101937
$565$	−1.79828e7	−2.36993
$566$	1.39858e7	1.83505
$567$	−1.60045e6	−0.209067
$568$	−4.44014e6	−0.577465
$569$	−2.02127e6	−0.261724	−0.130862	−	0.991401i	$-0.541775\pi$
$569$	−2.02127e6	−0.261724	−0.130862	+	0.991401i	$0.541775\pi$
$570$	−8.48028e6	−1.09326
$571$	1.09831e6	0.140973	0.0704865	−	0.997513i	$-0.477545\pi$
$571$	1.09831e6	0.140973	0.0704865	+	0.997513i	$0.477545\pi$
$572$	319732.	0.0408598
$573$	−4.03322e6	−0.513174
$574$	−431836.	−0.0547065
$575$	2.72412e6	0.343603
$576$	−1.93763e6	−0.243341
$577$	−6.60638e6	−0.826084	−0.413042	−	0.910712i	$-0.635534\pi$
$577$	−6.60638e6	−0.826084	−0.413042	+	0.910712i	$0.635534\pi$
$578$	227175.	0.0282839
$579$	4.67001e6	0.578924
$580$	2.31568e6	0.285830
$581$	1.95378e6	0.240123
$582$	324109.	0.0396628
$583$	−2.04472e6	−0.249151
$584$	−7.39168e6	−0.896832
$585$	2.72365e6	0.329050
$586$	−9.24561e6	−1.11222
$587$	2.37224e6	0.284160	0.142080	−	0.989855i	$-0.454621\pi$
$587$	2.37224e6	0.284160	0.142080	+	0.989855i	$0.454621\pi$
$588$	196030.	0.0233819
$589$	71147.2	0.00845026
$590$	1.72536e7	2.04056
$591$	−1.42885e6	−0.168274
$592$	−556399.	−0.0652503
$593$	1.26500e7	1.47725	0.738626	−	0.674116i	$-0.235475\pi$
$593$	1.26500e7	1.47725	0.738626	+	0.674116i	$0.235475\pi$
$594$	−3.12835e6	−0.363789
$595$	−4.74251e6	−0.549181
$596$	−1.65005e6	−0.190274
$597$	5.89751e6	0.677225
$598$	1.88346e6	0.215379
$599$	1.03778e7	1.18178	0.590891	−	0.806751i	$-0.298776\pi$
$599$	1.03778e7	1.18178	0.590891	+	0.806751i	$0.298776\pi$
$600$	7.35221e6	0.833757
$601$	1.99209e6	0.224969	0.112485	−	0.993653i	$-0.464119\pi$
$601$	1.99209e6	0.224969	0.112485	+	0.993653i	$0.464119\pi$
$602$	5.07510e6	0.570760
$603$	−2.70979e6	−0.303489
$604$	2.21649e6	0.247214
$605$	−1.20209e7	−1.33521
$606$	1.34520e6	0.148801
$607$	−7.03909e6	−0.775434	−0.387717	−	0.921778i	$-0.626736\pi$
$607$	−7.03909e6	−0.775434	−0.387717	+	0.921778i	$0.626736\pi$
$608$	2.99683e6	0.328778
$609$	2.72989e6	0.298265
$610$	2.52225e7	2.74450
$611$	3.83719e6	0.415824
$612$	614409.	0.0663100
$613$	9.17016e6	0.985657	0.492828	−	0.870127i	$-0.335963\pi$
$613$	9.17016e6	0.985657	0.492828	+	0.870127i	$0.335963\pi$
$614$	5.58455e6	0.597816
$615$	1.48761e6	0.158599
$616$	−950786.	−0.100956
$617$	1.16423e7	1.23120	0.615598	−	0.788060i	$-0.288914\pi$
$617$	1.16423e7	1.23120	0.615598	+	0.788060i	$0.288914\pi$
$618$	433130.	0.0456191
$619$	1.18289e7	1.24085	0.620423	−	0.784268i	$-0.286961\pi$
$619$	1.18289e7	1.24085	0.620423	+	0.784268i	$0.286961\pi$
$620$	28754.3	0.00300416
$621$	−3.08004e6	−0.320499
$622$	−6.50178e6	−0.673839
$623$	1.95523e6	0.201826
$624$	6.14624e6	0.631900
$625$	−7.86062e6	−0.804928
$626$	−9.11056e6	−0.929200
$627$	−2.03460e6	−0.206686
$628$	930698.	0.0941694
$629$	−550707.	−0.0555001
$630$	2.03339e6	0.204112
$631$	−1.40936e7	−1.40913	−0.704563	−	0.709641i	$-0.748857\pi$
$631$	−1.40936e7	−1.40913	−0.704563	+	0.709641i	$0.748857\pi$
$632$	−5.41864e6	−0.539632
$633$	−3.76070e6	−0.373044
$634$	1.13845e7	1.12484
$635$	1.52636e7	1.50218
$636$	1.36408e6	0.133720
$637$	−976803.	−0.0953803
$638$	3.32413e6	0.323316
$639$	2.27827e6	0.220725
$640$	−1.81850e7	−1.75494
$641$	7.78081e6	0.747962	0.373981	−	0.927436i	$-0.377992\pi$
$641$	7.78081e6	0.747962	0.373981	+	0.927436i	$0.377992\pi$
$642$	7.38668e6	0.707313
$643$	−9.14404e6	−0.872189	−0.436095	−	0.899901i	$-0.643639\pi$
$643$	−9.14404e6	−0.872189	−0.436095	+	0.899901i	$0.643639\pi$
$644$	235015.	0.0223296
$645$	−1.74829e7	−1.65468
$646$	9.53236e6	0.898709
$647$	5.79462e6	0.544207	0.272104	−	0.962268i	$-0.412281\pi$
$647$	5.79462e6	0.544207	0.272104	+	0.962268i	$0.412281\pi$
$648$	−5.17854e6	−0.484473
$649$	4.13952e6	0.385779
$650$	9.19761e6	0.853869
$651$	33897.7	0.00313486
$652$	494490.	0.0455553
$653$	−2.22882e6	−0.204546	−0.102273	−	0.994756i	$-0.532612\pi$
$653$	−2.22882e6	−0.204546	−0.102273	+	0.994756i	$0.532612\pi$
$654$	−2.00241e6	−0.183066
$655$	−9.74594e6	−0.887607
$656$	−1.68945e6	−0.153280
$657$	3.79272e6	0.342797
$658$	2.86472e6	0.257939
$659$	2.66584e6	0.239123	0.119561	−	0.992827i	$-0.461851\pi$
$659$	2.66584e6	0.239123	0.119561	+	0.992827i	$0.461851\pi$
$660$	−822290.	−0.0734793
$661$	8.63157e6	0.768398	0.384199	−	0.923250i	$-0.374478\pi$
$661$	8.63157e6	0.768398	0.384199	+	0.923250i	$0.374478\pi$
$662$	1.01473e7	0.899920
$663$	6.08336e6	0.537477
$664$	6.32178e6	0.556441
$665$	5.27270e6	0.462359
$666$	236120.	0.0206276
$667$	3.27279e6	0.284842
$668$	701260.	0.0608048
$669$	−2.30375e6	−0.199008
$670$	−1.69912e7	−1.46230
$671$	6.05143e6	0.518862
$672$	1.42782e6	0.121969
$673$	1.89018e6	0.160866	0.0804331	−	0.996760i	$-0.474370\pi$
$673$	1.89018e6	0.160866	0.0804331	+	0.996760i	$0.474370\pi$
$674$	−6.02168e6	−0.510585
$675$	−1.50409e7	−1.27062
$676$	−1.32145e6	−0.111220
$677$	−2.34802e6	−0.196893	−0.0984463	−	0.995142i	$-0.531387\pi$
$677$	−2.34802e6	−0.196893	−0.0984463	+	0.995142i	$0.531387\pi$
$678$	1.72211e7	1.43876
$679$	−201518.	−0.0167741
$680$	−1.53452e7	−1.27262
$681$	1.29857e7	1.07299
$682$	41276.5	0.00339815
$683$	−1.61043e7	−1.32097	−0.660483	−	0.750841i	$-0.729648\pi$
$683$	−1.61043e7	−1.32097	−0.660483	+	0.750841i	$0.729648\pi$
$684$	−683098.	−0.0558268
$685$	1.54458e6	0.125772
$686$	−729250.	−0.0591651
$687$	1.32934e7	1.07459
$688$	1.98550e7	1.59919
$689$	−6.79709e6	−0.545475
$690$	−4.84390e6	−0.387322
$691$	2.36773e7	1.88642	0.943208	−	0.332202i	$-0.107791\pi$
$691$	2.36773e7	1.88642	0.943208	+	0.332202i	$0.107791\pi$
$692$	105014.	0.00833643
$693$	487855.	0.0385885
$694$	1.65409e7	1.30365
$695$	1.93165e7	1.51693
$696$	8.83304e6	0.691173
$697$	−1.67216e6	−0.130376
$698$	2.75867e6	0.214319
$699$	2.82455e6	0.218653
$700$	1.14766e6	0.0885255
$701$	7.69692e6	0.591591	0.295796	−	0.955251i	$-0.404415\pi$
$701$	7.69692e6	0.591591	0.295796	+	0.955251i	$0.404415\pi$
$702$	−1.03993e7	−0.796456
$703$	612274.	0.0467259
$704$	−2.91493e6	−0.221665
$705$	−9.86850e6	−0.747788
$706$	2.39556e7	1.80882
$707$	−836394.	−0.0629307
$708$	−2.76156e6	−0.207048
$709$	−8.28439e6	−0.618935	−0.309468	−	0.950910i	$-0.600151\pi$
$709$	−8.28439e6	−0.618935	−0.309468	+	0.950910i	$0.600151\pi$
$710$	1.42854e7	1.06352
$711$	2.78034e6	0.206264
$712$	6.32649e6	0.467695
$713$	40639.0	0.00299378
$714$	4.54164e6	0.333401
$715$	4.09741e6	0.299740
$716$	−2.41956e6	−0.176382
$717$	−5.91923e6	−0.429999
$718$	1.77176e7	1.28260
$719$	8.17284e6	0.589591	0.294795	−	0.955560i	$-0.404749\pi$
$719$	8.17284e6	0.589591	0.294795	+	0.955560i	$0.404749\pi$
$720$	7.95511e6	0.571893
$721$	−269303.	−0.0192932
$722$	4.75010e6	0.339125
$723$	8.25256e6	0.587142
$724$	−2.58489e6	−0.183272
$725$	1.59822e7	1.12925
$726$	1.15118e7	0.810591
$727$	1.64950e7	1.15748	0.578742	−	0.815511i	$-0.303544\pi$
$727$	1.64950e7	1.15748	0.578742	+	0.815511i	$0.303544\pi$
$728$	−3.16062e6	−0.221026
$729$	1.53978e7	1.07310
$730$	2.37815e7	1.65170
$731$	1.96519e7	1.36023
$732$	−4.03704e6	−0.278474
$733$	−1.16278e7	−0.799352	−0.399676	−	0.916657i	$-0.630877\pi$
$733$	−1.16278e7	−0.799352	−0.399676	+	0.916657i	$0.630877\pi$
$734$	2.04340e7	1.39995
$735$	2.51215e6	0.171525
$736$	1.71178e6	0.116480
$737$	−4.07656e6	−0.276455
$738$	716954.	0.0484563
$739$	−2.22721e6	−0.150020	−0.0750100	−	0.997183i	$-0.523899\pi$
$739$	−2.22721e6	−0.150020	−0.0750100	+	0.997183i	$0.523899\pi$
$740$	247452.	0.0166116
$741$	−6.76346e6	−0.452505
$742$	−5.07449e6	−0.338363
$743$	1.85943e7	1.23568	0.617842	−	0.786302i	$-0.288007\pi$
$743$	1.85943e7	1.23568	0.617842	+	0.786302i	$0.288007\pi$
$744$	109682.	0.00726445
$745$	−2.11455e7	−1.39582
$746$	−2.03830e7	−1.34098
$747$	−3.24375e6	−0.212689
$748$	924305.	0.0604034
$749$	−4.59274e6	−0.299135
$750$	−3.38739e6	−0.219893
$751$	−8.21379e6	−0.531427	−0.265714	−	0.964052i	$-0.585608\pi$
$751$	−8.21379e6	−0.531427	−0.265714	+	0.964052i	$0.585608\pi$
$752$	1.12075e7	0.722708
$753$	−1.08407e7	−0.696739
$754$	1.10501e7	0.707846
$755$	2.84046e7	1.81351
$756$	−1.29761e6	−0.0825732
$757$	−4.57296e6	−0.290040	−0.145020	−	0.989429i	$-0.546325\pi$
$757$	−4.57296e6	−0.290040	−0.145020	+	0.989429i	$0.546325\pi$
$758$	1.79687e7	1.13591
$759$	−1.16216e6	−0.0732252
$760$	1.70607e7	1.07143
$761$	−3.06785e7	−1.92032	−0.960159	−	0.279455i	$-0.909846\pi$
$761$	−3.06785e7	−1.92032	−0.960159	+	0.279455i	$0.909846\pi$
$762$	−1.46171e7	−0.911954
$763$	1.24502e6	0.0774219
$764$	−2.03710e6	−0.126264
$765$	7.87373e6	0.486437
$766$	9.00169e6	0.554309
$767$	1.37607e7	0.844599
$768$	7.72445e6	0.472569
$769$	−7.45921e6	−0.454859	−0.227430	−	0.973794i	$-0.573032\pi$
$769$	−7.45921e6	−0.454859	−0.227430	+	0.973794i	$0.573032\pi$
$770$	3.05899e6	0.185931
$771$	−1.46907e7	−0.890037
$772$	2.35873e6	0.142441
$773$	−1.29822e7	−0.781448	−0.390724	−	0.920508i	$-0.627775\pi$
$773$	−1.29822e7	−0.781448	−0.390724	+	0.920508i	$0.627775\pi$
$774$	−8.42592e6	−0.505551
$775$	198455.	0.0118688
$776$	−652046.	−0.0388708
$777$	291715.	0.0173343
$778$	2.01387e7	1.19284
$779$	1.85910e6	0.109764
$780$	−2.73347e6	−0.160871
$781$	3.42738e6	0.201064
$782$	5.44484e6	0.318397
$783$	−1.80703e7	−1.05332
$784$	−2.85300e6	−0.165772
$785$	1.19270e7	0.690808
$786$	9.33316e6	0.538856
$787$	9.79577e6	0.563770	0.281885	−	0.959448i	$-0.409040\pi$
$787$	9.79577e6	0.563770	0.281885	+	0.959448i	$0.409040\pi$
$788$	−721683.	−0.0414029
$789$	−1.57492e7	−0.900668
$790$	1.74335e7	0.993843
$791$	−1.07074e7	−0.608476
$792$	1.57854e6	0.0894216
$793$	2.01162e7	1.13596
$794$	6.96700e6	0.392188
$795$	1.74808e7	0.980943
$796$	2.97872e6	0.166627
$797$	−1.70809e7	−0.952499	−0.476250	−	0.879310i	$-0.658004\pi$
$797$	−1.70809e7	−0.952499	−0.476250	+	0.879310i	$0.658004\pi$
$798$	−5.04938e6	−0.280692
$799$	1.10928e7	0.614716
$800$	8.35920e6	0.461785
$801$	−3.24617e6	−0.178768
$802$	−2.28818e7	−1.25619
$803$	5.70569e6	0.312262
$804$	2.71956e6	0.148374
$805$	3.01175e6	0.163806
$806$	137212.	0.00743968
$807$	−1.65178e6	−0.0892831
$808$	−2.70630e6	−0.145830
$809$	1.79030e7	0.961732	0.480866	−	0.876794i	$-0.340322\pi$
$809$	1.79030e7	0.961732	0.480866	+	0.876794i	$0.340322\pi$
$810$	1.66611e7	0.892258
$811$	−1.12946e7	−0.603000	−0.301500	−	0.953466i	$-0.597487\pi$
$811$	−1.12946e7	−0.603000	−0.301500	+	0.953466i	$0.597487\pi$
$812$	1.37882e6	0.0733865
$813$	−7.24072e6	−0.384198
$814$	355215.	0.0187901
$815$	6.33695e6	0.334185
$816$	1.77680e7	0.934142
$817$	−2.18489e7	−1.14518
$818$	1.79349e7	0.937164
$819$	1.62173e6	0.0844831
$820$	751361.	0.0390224
$821$	−1.18345e7	−0.612764	−0.306382	−	0.951909i	$-0.599118\pi$
$821$	−1.18345e7	−0.612764	−0.306382	+	0.951909i	$0.599118\pi$
$822$	−1.47916e6	−0.0763545
$823$	−1.57484e7	−0.810468	−0.405234	−	0.914213i	$-0.632810\pi$
$823$	−1.57484e7	−0.810468	−0.405234	+	0.914213i	$0.632810\pi$
$824$	−871377.	−0.0447083
$825$	−5.67523e6	−0.290301
$826$	1.02733e7	0.523912
$827$	2.95820e7	1.50406	0.752028	−	0.659131i	$-0.229076\pi$
$827$	2.95820e7	1.50406	0.752028	+	0.659131i	$0.229076\pi$
$828$	−390183.	−0.0197784
$829$	2.09920e7	1.06088	0.530442	−	0.847721i	$-0.322026\pi$
$829$	2.09920e7	1.06088	0.530442	+	0.847721i	$0.322026\pi$
$830$	−2.03393e7	−1.02480
$831$	−4.40914e6	−0.221488
$832$	−9.68987e6	−0.485299
$833$	−2.82381e6	−0.141001
$834$	−1.84983e7	−0.920911
$835$	8.98673e6	0.446052
$836$	−1.02764e6	−0.0508540
$837$	−224383.	−0.0110708
$838$	−4.12066e7	−2.02701
$839$	−1.84234e7	−0.903577	−0.451789	−	0.892125i	$-0.649214\pi$
$839$	−1.84234e7	−0.903577	−0.451789	+	0.892125i	$0.649214\pi$
$840$	8.12849e6	0.397477
$841$	−1.30993e6	−0.0638645
$842$	−2.73588e7	−1.32990
$843$	5.81945e6	0.282041
$844$	−1.89946e6	−0.0917853
$845$	−1.69345e7	−0.815890
$846$	−4.75614e6	−0.228470
$847$	−7.15758e6	−0.342813
$848$	−1.98526e7	−0.948043
$849$	−2.86870e7	−1.36589
$850$	2.65891e7	1.26228
$851$	349728.	0.0165542
$852$	−2.28648e6	−0.107912
$853$	−4.14291e7	−1.94954	−0.974772	−	0.223204i	$-0.928348\pi$
$853$	−4.14291e7	−1.94954	−0.974772	+	0.223204i	$0.928348\pi$
$854$	1.50181e7	0.704646
$855$	−8.75398e6	−0.409534
$856$	−1.48606e7	−0.693190
$857$	1.70077e7	0.791032	0.395516	−	0.918459i	$-0.370566\pi$
$857$	1.70077e7	0.791032	0.395516	+	0.918459i	$0.370566\pi$
$858$	−3.92386e6	−0.181968
$859$	−2.04622e7	−0.946169	−0.473085	−	0.881017i	$-0.656860\pi$
$859$	−2.04622e7	−0.946169	−0.473085	+	0.881017i	$0.656860\pi$
$860$	−8.83028e6	−0.407126
$861$	885760.	0.0407200
$862$	1.07864e7	0.494432
$863$	−1.69595e7	−0.775152	−0.387576	−	0.921838i	$-0.626687\pi$
$863$	−1.69595e7	−0.775152	−0.387576	+	0.921838i	$0.626687\pi$
$864$	−9.45137e6	−0.430735
$865$	1.34576e6	0.0611544
$866$	1.89709e7	0.859592
$867$	−465969.	−0.0210528
$868$	17121.1	0.000771314 0
$869$	4.18269e6	0.187891
$870$	−2.84188e7	−1.27294
$871$	−1.35513e7	−0.605253
$872$	4.02847e6	0.179411
$873$	334569.	0.0148577
$874$	−6.05356e6	−0.268060
$875$	2.10614e6	0.0929968
$876$	−3.80639e6	−0.167592
$877$	−1.45129e7	−0.637171	−0.318586	−	0.947894i	$-0.603208\pi$
$877$	−1.45129e7	−0.637171	−0.318586	+	0.947894i	$0.603208\pi$
$878$	−3.55478e6	−0.155624
$879$	1.89641e7	0.827867
$880$	1.19675e7	0.520951
$881$	4.33071e6	0.187983	0.0939916	−	0.995573i	$-0.470037\pi$
$881$	4.33071e6	0.187983	0.0939916	+	0.995573i	$0.470037\pi$
$882$	1.21073e6	0.0524055
$883$	2.28581e7	0.986592	0.493296	−	0.869862i	$-0.335792\pi$
$883$	2.28581e7	0.986592	0.493296	+	0.869862i	$0.335792\pi$
$884$	3.07259e6	0.132243
$885$	−3.53897e7	−1.51887
$886$	−9.14992e6	−0.391591
$887$	−1.00810e7	−0.430225	−0.215113	−	0.976589i	$-0.569012\pi$
$887$	−1.00810e7	−0.430225	−0.215113	+	0.976589i	$0.569012\pi$
$888$	943893.	0.0401689
$889$	9.08832e6	0.385682
$890$	−2.03544e7	−0.861357
$891$	3.99735e6	0.168686
$892$	−1.16358e6	−0.0489648
$893$	−1.23329e7	−0.517533
$894$	2.02499e7	0.847383
$895$	−3.10070e7	−1.29390
$896$	−1.08278e7	−0.450579
$897$	−3.86326e6	−0.160315
$898$	−3.64525e7	−1.50847
$899$	238426.	0.00983907
$900$	−1.90540e6	−0.0784115
$901$	−1.96495e7	−0.806380
$902$	1.07857e6	0.0441400
$903$	−1.04098e7	−0.424837
$904$	−3.46457e7	−1.41003
$905$	−3.31257e7	−1.34445
$906$	−2.72015e7	−1.10096
$907$	−2.25398e7	−0.909771	−0.454885	−	0.890550i	$-0.650320\pi$
$907$	−2.25398e7	−0.909771	−0.454885	+	0.890550i	$0.650320\pi$
$908$	6.55880e6	0.264004
$909$	1.38862e6	0.0557408
$910$	1.01687e7	0.407065
$911$	3.36249e7	1.34235	0.671174	−	0.741300i	$-0.265790\pi$
$911$	3.36249e7	1.34235	0.671174	+	0.741300i	$0.265790\pi$
$912$	−1.97544e7	−0.786460
$913$	−4.87983e6	−0.193744
$914$	−6.69723e6	−0.265173
$915$	−5.17351e7	−2.04283
$916$	6.71422e6	0.264397
$917$	−5.80299e6	−0.227892
$918$	−3.00631e7	−1.17741
$919$	−1.04261e7	−0.407225	−0.203613	−	0.979052i	$-0.565268\pi$
$919$	−1.04261e7	−0.407225	−0.203613	+	0.979052i	$0.565268\pi$
$920$	9.74502e6	0.379589
$921$	−1.14547e7	−0.444976
$922$	−6.63870e6	−0.257191
$923$	1.13933e7	0.440197
$924$	−489613.	−0.0188657
$925$	1.70785e6	0.0656288
$926$	2.01302e6	0.0771473
$927$	447109.	0.0170889
$928$	1.00429e7	0.382813
$929$	−1.90164e7	−0.722920	−0.361460	−	0.932388i	$-0.617722\pi$
$929$	−1.90164e7	−0.722920	−0.361460	+	0.932388i	$0.617722\pi$
$930$	−352883.	−0.0133790
$931$	3.13950e6	0.118710
$932$	1.42662e6	0.0537984
$933$	1.33361e7	0.501563
$934$	896784.	0.0336373
$935$	1.18451e7	0.443107
$936$	5.24740e6	0.195774
$937$	−1.95492e7	−0.727410	−0.363705	−	0.931514i	$-0.618488\pi$
$937$	−1.95492e7	−0.727410	−0.363705	+	0.931514i	$0.618488\pi$
$938$	−1.01170e7	−0.375443
$939$	1.86871e7	0.691637
$940$	−4.98439e6	−0.183989
$941$	−1.44190e7	−0.530836	−0.265418	−	0.964133i	$-0.585510\pi$
$941$	−1.44190e7	−0.530836	−0.265418	+	0.964133i	$0.585510\pi$
$942$	−1.14218e7	−0.419381
$943$	1.06191e6	0.0388875
$944$	4.01915e7	1.46792
$945$	−1.66290e7	−0.605740
$946$	−1.26758e7	−0.460518
$947$	−2.10426e7	−0.762473	−0.381237	−	0.924477i	$-0.624502\pi$
$947$	−2.10426e7	−0.762473	−0.381237	+	0.924477i	$0.624502\pi$
$948$	−2.79036e6	−0.100841
$949$	1.89669e7	0.683647
$950$	−2.95617e7	−1.06272
$951$	−2.33513e7	−0.837259
$952$	−9.13693e6	−0.326744
$953$	3.00978e7	1.07350	0.536750	−	0.843741i	$-0.319652\pi$
$953$	3.00978e7	1.07350	0.536750	+	0.843741i	$0.319652\pi$
$954$	8.42490e6	0.299705
$955$	−2.61057e7	−0.926246
$956$	−2.98969e6	−0.105799
$957$	−6.81829e6	−0.240655
$958$	3.87939e7	1.36568
$959$	919681.	0.0322917
$960$	2.49205e7	0.872726
$961$	−2.86262e7	−0.999897
$962$	1.18081e6	0.0411379
$963$	7.62509e6	0.264959
$964$	4.16820e6	0.144463
$965$	3.02274e7	1.04492
$966$	−2.88418e6	−0.0994444
$967$	−6.83561e6	−0.235078	−0.117539	−	0.993068i	$-0.537500\pi$
$967$	−6.83561e6	−0.235078	−0.117539	+	0.993068i	$0.537500\pi$
$968$	−2.31596e7	−0.794406
$969$	−1.95523e7	−0.668942
$970$	2.09785e6	0.0715887
$971$	−1.55221e6	−0.0528327	−0.0264164	−	0.999651i	$-0.508410\pi$
$971$	−1.55221e6	−0.0528327	−0.0264164	+	0.999651i	$0.508410\pi$
$972$	3.76836e6	0.127934
$973$	1.15015e7	0.389470
$974$	5.10418e7	1.72397
$975$	−1.88657e7	−0.635566
$976$	5.87545e7	1.97432
$977$	1.11606e7	0.374069	0.187034	−	0.982353i	$-0.440112\pi$
$977$	1.11606e7	0.374069	0.187034	+	0.982353i	$0.440112\pi$
$978$	−6.06856e6	−0.202880
$979$	−4.88347e6	−0.162844
$980$	1.26884e6	0.0422028
$981$	−2.06704e6	−0.0685765
$982$	2.64871e7	0.876509
$983$	−3.76835e7	−1.24385	−0.621924	−	0.783078i	$-0.713649\pi$
$983$	−3.76835e7	−1.24385	−0.621924	+	0.783078i	$0.713649\pi$
$984$	2.86603e6	0.0943611
$985$	−9.24845e6	−0.303724
$986$	3.19445e7	1.04641
$987$	−5.87596e6	−0.191993
$988$	−3.41609e6	−0.111336
$989$	−1.24800e7	−0.405718
$990$	−5.07868e6	−0.164688
$991$	2.40894e7	0.779188	0.389594	−	0.920987i	$-0.372615\pi$
$991$	2.40894e7	0.779188	0.389594	+	0.920987i	$0.372615\pi$
$992$	124704.	0.00402349
$993$	−2.08135e7	−0.669843
$994$	8.50590e6	0.273058
$995$	3.81726e7	1.22235
$996$	3.25544e6	0.103983
$997$	1.14787e7	0.365726	0.182863	−	0.983138i	$-0.441464\pi$
$997$	1.14787e7	0.365726	0.182863	+	0.983138i	$0.441464\pi$
$998$	−3.10762e7	−0.987647
$999$	−1.93098e6	−0.0612160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.6.a.a.1.19	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.6.a.a.1.19	✓	74	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 959 = 7 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	959.a (trivial)

\(f(q)\)	\(=\)	\(q-6.19852 q^{2} +12.7141 q^{3} +6.42163 q^{4} +82.2940 q^{5} -78.8085 q^{6} +49.0000 q^{7} +158.548 q^{8} -81.3521 q^{9} +O(q^{10})\)	\(q-6.19852 q^{2} +12.7141 q^{3} +6.42163 q^{4} +82.2940 q^{5} -78.8085 q^{6} +49.0000 q^{7} +158.548 q^{8} -81.3521 q^{9} -510.101 q^{10} -122.384 q^{11} +81.6452 q^{12} -406.832 q^{13} -303.727 q^{14} +1046.29 q^{15} -1188.25 q^{16} -1176.10 q^{17} +504.262 q^{18} +1307.58 q^{19} +528.462 q^{20} +622.990 q^{21} +758.602 q^{22} +746.885 q^{23} +2015.79 q^{24} +3647.30 q^{25} +2521.75 q^{26} -4123.84 q^{27} +314.660 q^{28} +4381.92 q^{29} -6485.47 q^{30} +54.4113 q^{31} +2291.89 q^{32} -1556.01 q^{33} +7290.07 q^{34} +4032.41 q^{35} -522.413 q^{36} +468.249 q^{37} -8105.07 q^{38} -5172.49 q^{39} +13047.5 q^{40} +1421.79 q^{41} -3861.62 q^{42} -16709.4 q^{43} -785.908 q^{44} -6694.79 q^{45} -4629.58 q^{46} -9431.87 q^{47} -15107.6 q^{48} +2401.00 q^{49} -22607.9 q^{50} -14953.0 q^{51} -2612.53 q^{52} +16707.4 q^{53} +25561.7 q^{54} -10071.5 q^{55} +7768.85 q^{56} +16624.7 q^{57} -27161.4 q^{58} -33823.9 q^{59} +6718.91 q^{60} -49446.1 q^{61} -337.269 q^{62} -3986.25 q^{63} +23817.9 q^{64} -33479.8 q^{65} +9644.93 q^{66} +33309.5 q^{67} -7552.47 q^{68} +9495.96 q^{69} -24994.9 q^{70} -28005.0 q^{71} -12898.2 q^{72} -46621.1 q^{73} -2902.45 q^{74} +46372.1 q^{75} +8396.81 q^{76} -5996.83 q^{77} +32061.8 q^{78} -34176.6 q^{79} -97786.3 q^{80} -32662.3 q^{81} -8812.98 q^{82} +39873.0 q^{83} +4000.61 q^{84} -96785.8 q^{85} +103574. q^{86} +55712.1 q^{87} -19403.8 q^{88} +39902.7 q^{89} +41497.8 q^{90} -19934.8 q^{91} +4796.22 q^{92} +691.790 q^{93} +58463.6 q^{94} +107606. q^{95} +29139.2 q^{96} -4112.61 q^{97} -14882.6 q^{98} +9956.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9} - 1322 q^{10} - 1446 q^{11} - 1466 q^{12} - 1746 q^{13} - 980 q^{14} - 4313 q^{15} + 9208 q^{16} - 3681 q^{17} - 10234 q^{18} - 2860 q^{19} - 7308 q^{20} - 2401 q^{21} - 13879 q^{22} - 13685 q^{23} - 13424 q^{24} + 18155 q^{25} - 9144 q^{26} - 6865 q^{27} + 47824 q^{28} - 19489 q^{29} + 2307 q^{30} - 33560 q^{31} - 27274 q^{32} - 40132 q^{33} - 35811 q^{34} - 8281 q^{35} - 27689 q^{36} - 70663 q^{37} - 37203 q^{38} - 51201 q^{39} - 86817 q^{40} - 67917 q^{41} - 13377 q^{42} - 104475 q^{43} - 45827 q^{44} - 93598 q^{45} - 137776 q^{46} - 43192 q^{47} - 135425 q^{48} + 177674 q^{49} - 73802 q^{50} - 110795 q^{51} - 107131 q^{52} - 99015 q^{53} - 46226 q^{54} - 71678 q^{55} - 36603 q^{56} - 146490 q^{57} - 143069 q^{58} - 12512 q^{59} - 177875 q^{60} - 125581 q^{61} - 75283 q^{62} + 209475 q^{63} - 8449 q^{64} - 95447 q^{65} + 213311 q^{66} - 282713 q^{67} + 191684 q^{68} - 171171 q^{69} - 64778 q^{70} - 189029 q^{71} + 20181 q^{72} - 96401 q^{73} - 96089 q^{74} - 21522 q^{75} - 276776 q^{76} - 70854 q^{77} + 106155 q^{78} - 454125 q^{79} + 253095 q^{80} + 12226 q^{81} + 107086 q^{82} - 168146 q^{83} - 71834 q^{84} - 329524 q^{85} + 191853 q^{86} + 61244 q^{87} - 505209 q^{88} - 325374 q^{89} - 277645 q^{90} - 85554 q^{91} - 189827 q^{92} - 347054 q^{93} - 125581 q^{94} - 343566 q^{95} + 289017 q^{96} - 844266 q^{97} - 48020 q^{98} - 490575 q^{99}+O(q^{100}) \) 74 * q - 20 * q^2 - 49 * q^3 + 976 * q^4 - 169 * q^5 - 273 * q^6 + 3626 * q^7 - 747 * q^8 + 4275 * q^9 - 1322 * q^10 - 1446 * q^11 - 1466 * q^12 - 1746 * q^13 - 980 * q^14 - 4313 * q^15 + 9208 * q^16 - 3681 * q^17 - 10234 * q^18 - 2860 * q^19 - 7308 * q^20 - 2401 * q^21 - 13879 * q^22 - 13685 * q^23 - 13424 * q^24 + 18155 * q^25 - 9144 * q^26 - 6865 * q^27 + 47824 * q^28 - 19489 * q^29 + 2307 * q^30 - 33560 * q^31 - 27274 * q^32 - 40132 * q^33 - 35811 * q^34 - 8281 * q^35 - 27689 * q^36 - 70663 * q^37 - 37203 * q^38 - 51201 * q^39 - 86817 * q^40 - 67917 * q^41 - 13377 * q^42 - 104475 * q^43 - 45827 * q^44 - 93598 * q^45 - 137776 * q^46 - 43192 * q^47 - 135425 * q^48 + 177674 * q^49 - 73802 * q^50 - 110795 * q^51 - 107131 * q^52 - 99015 * q^53 - 46226 * q^54 - 71678 * q^55 - 36603 * q^56 - 146490 * q^57 - 143069 * q^58 - 12512 * q^59 - 177875 * q^60 - 125581 * q^61 - 75283 * q^62 + 209475 * q^63 - 8449 * q^64 - 95447 * q^65 + 213311 * q^66 - 282713 * q^67 + 191684 * q^68 - 171171 * q^69 - 64778 * q^70 - 189029 * q^71 + 20181 * q^72 - 96401 * q^73 - 96089 * q^74 - 21522 * q^75 - 276776 * q^76 - 70854 * q^77 + 106155 * q^78 - 454125 * q^79 + 253095 * q^80 + 12226 * q^81 + 107086 * q^82 - 168146 * q^83 - 71834 * q^84 - 329524 * q^85 + 191853 * q^86 + 61244 * q^87 - 505209 * q^88 - 325374 * q^89 - 277645 * q^90 - 85554 * q^91 - 189827 * q^92 - 347054 * q^93 - 125581 * q^94 - 343566 * q^95 + 289017 * q^96 - 844266 * q^97 - 48020 * q^98 - 490575 * q^99

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