LMFDB - Embedded newform 959.6.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-10.4384 q^{2} +13.3623 q^{3} +76.9593 q^{4} -73.3008 q^{5} -139.480 q^{6} +49.0000 q^{7} -469.301 q^{8} -64.4491 q^{9} +O(q^{10})$	\(q-10.4384 q^{2} +13.3623 q^{3} +76.9593 q^{4} -73.3008 q^{5} -139.480 q^{6} +49.0000 q^{7} -469.301 q^{8} -64.4491 q^{9} +765.139 q^{10} +533.867 q^{11} +1028.35 q^{12} +443.332 q^{13} -511.479 q^{14} -979.466 q^{15} +2436.03 q^{16} +1801.51 q^{17} +672.743 q^{18} -313.510 q^{19} -5641.17 q^{20} +654.752 q^{21} -5572.69 q^{22} -3155.14 q^{23} -6270.93 q^{24} +2248.00 q^{25} -4627.65 q^{26} -4108.23 q^{27} +3771.00 q^{28} +2114.96 q^{29} +10224.0 q^{30} -8706.93 q^{31} -10410.5 q^{32} +7133.69 q^{33} -18804.8 q^{34} -3591.74 q^{35} -4959.96 q^{36} +1209.20 q^{37} +3272.53 q^{38} +5923.93 q^{39} +34400.1 q^{40} -9281.62 q^{41} -6834.54 q^{42} -13686.5 q^{43} +41086.0 q^{44} +4724.17 q^{45} +32934.5 q^{46} +7853.98 q^{47} +32551.0 q^{48} +2401.00 q^{49} -23465.4 q^{50} +24072.3 q^{51} +34118.5 q^{52} +19127.9 q^{53} +42883.1 q^{54} -39132.9 q^{55} -22995.7 q^{56} -4189.21 q^{57} -22076.7 q^{58} +32968.2 q^{59} -75379.0 q^{60} -24104.6 q^{61} +90886.0 q^{62} -3158.01 q^{63} +30715.9 q^{64} -32496.6 q^{65} -74464.0 q^{66} -39511.5 q^{67} +138643. q^{68} -42160.0 q^{69} +37491.8 q^{70} +50007.4 q^{71} +30246.0 q^{72} +38025.8 q^{73} -12622.1 q^{74} +30038.5 q^{75} -24127.5 q^{76} +26159.5 q^{77} -61836.1 q^{78} +21063.0 q^{79} -178563. q^{80} -39234.2 q^{81} +96884.9 q^{82} -40097.3 q^{83} +50389.3 q^{84} -132052. q^{85} +142865. q^{86} +28260.8 q^{87} -250544. q^{88} -49632.3 q^{89} -49312.6 q^{90} +21723.3 q^{91} -242818. q^{92} -116345. q^{93} -81982.6 q^{94} +22980.5 q^{95} -139109. q^{96} -35035.9 q^{97} -25062.5 q^{98} -34407.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.4384	−1.84526	−0.922629	−	0.385689i	$-0.873964\pi$
$2$	−10.4384	−1.84526	−0.922629	+	0.385689i	$0.873964\pi$
$3$	13.3623	0.857192	0.428596	−	0.903496i	$-0.359008\pi$
$3$	13.3623	0.857192	0.428596	+	0.903496i	$0.359008\pi$
$4$	76.9593	2.40498
$5$	−73.3008	−1.31124	−0.655622	−	0.755089i	$-0.727593\pi$
$5$	−73.3008	−1.31124	−0.655622	+	0.755089i	$0.727593\pi$
$6$	−139.480	−1.58174
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−469.301	−2.59254
$9$	−64.4491	−0.265223
$10$	765.139	2.41958
$11$	533.867	1.33031	0.665153	−	0.746707i	$-0.268366\pi$
$11$	533.867	1.33031	0.665153	+	0.746707i	$0.268366\pi$
$12$	1028.35	2.06153
$13$	443.332	0.727563	0.363781	−	0.931484i	$-0.381486\pi$
$13$	443.332	0.727563	0.363781	+	0.931484i	$0.381486\pi$
$14$	−511.479	−0.697442
$15$	−979.466	−1.12399
$16$	2436.03	2.37894
$17$	1801.51	1.51187	0.755934	−	0.654648i	$-0.227183\pi$
$17$	1801.51	1.51187	0.755934	+	0.654648i	$0.227183\pi$
$18$	672.743	0.489404
$19$	−313.510	−0.199236	−0.0996180	−	0.995026i	$-0.531762\pi$
$19$	−313.510	−0.199236	−0.0996180	+	0.995026i	$0.531762\pi$
$20$	−5641.17	−3.15351
$21$	654.752	0.323988
$22$	−5572.69	−2.45476
$23$	−3155.14	−1.24365	−0.621827	−	0.783155i	$-0.713609\pi$
$23$	−3155.14	−1.24365	−0.621827	+	0.783155i	$0.713609\pi$
$24$	−6270.93	−2.22231
$25$	2248.00	0.719361
$26$	−4627.65	−1.34254
$27$	−4108.23	−1.08454
$28$	3771.00	0.908996
$29$	2114.96	0.466990	0.233495	−	0.972358i	$-0.424984\pi$
$29$	2114.96	0.466990	0.233495	+	0.972358i	$0.424984\pi$
$30$	10224.0	2.07405
$31$	−8706.93	−1.62727	−0.813637	−	0.581373i	$-0.802516\pi$
$31$	−8706.93	−1.62727	−0.813637	+	0.581373i	$0.802516\pi$
$32$	−10410.5	−1.79721
$33$	7133.69	1.14033
$34$	−18804.8	−2.78979
$35$	−3591.74	−0.495604
$36$	−4959.96	−0.637854
$37$	1209.20	0.145210	0.0726048	−	0.997361i	$-0.476869\pi$
$37$	1209.20	0.145210	0.0726048	+	0.997361i	$0.476869\pi$
$38$	3272.53	0.367642
$39$	5923.93	0.623661
$40$	34400.1	3.39946
$41$	−9281.62	−0.862312	−0.431156	−	0.902277i	$-0.641894\pi$
$41$	−9281.62	−0.862312	−0.431156	+	0.902277i	$0.641894\pi$
$42$	−6834.54	−0.597841
$43$	−13686.5	−1.12881	−0.564405	−	0.825498i	$-0.690895\pi$
$43$	−13686.5	−1.12881	−0.564405	+	0.825498i	$0.690895\pi$
$44$	41086.0	3.19935
$45$	4724.17	0.347772
$46$	32934.5	2.29486
$47$	7853.98	0.518615	0.259307	−	0.965795i	$-0.416506\pi$
$47$	7853.98	0.518615	0.259307	+	0.965795i	$0.416506\pi$
$48$	32551.0	2.03920
$49$	2401.00	0.142857
$50$	−23465.4	−1.32741
$51$	24072.3	1.29596
$52$	34118.5	1.74977
$53$	19127.9	0.935359	0.467679	−	0.883898i	$-0.345090\pi$
$53$	19127.9	0.935359	0.467679	+	0.883898i	$0.345090\pi$
$54$	42883.1	2.00125
$55$	−39132.9	−1.74435
$56$	−22995.7	−0.979890
$57$	−4189.21	−0.170783
$58$	−22076.7	−0.861718
$59$	32968.2	1.23301	0.616504	−	0.787352i	$-0.288549\pi$
$59$	32968.2	1.23301	0.616504	+	0.787352i	$0.288549\pi$
$60$	−75379.0	−2.70316
$61$	−24104.6	−0.829420	−0.414710	−	0.909954i	$-0.636117\pi$
$61$	−24104.6	−0.829420	−0.414710	+	0.909954i	$0.636117\pi$
$62$	90886.0	3.00274
$63$	−3158.01	−0.100245
$64$	30715.9	0.937375
$65$	−32496.6	−0.954012
$66$	−74464.0	−2.10420
$67$	−39511.5	−1.07532	−0.537659	−	0.843163i	$-0.680691\pi$
$67$	−39511.5	−1.07532	−0.537659	+	0.843163i	$0.680691\pi$
$68$	138643.	3.63601
$69$	−42160.0	−1.06605
$70$	37491.8	0.914516
$71$	50007.4	1.17730	0.588652	−	0.808387i	$-0.299659\pi$
$71$	50007.4	1.17730	0.588652	+	0.808387i	$0.299659\pi$
$72$	30246.0	0.687602
$73$	38025.8	0.835164	0.417582	−	0.908639i	$-0.362878\pi$
$73$	38025.8	0.835164	0.417582	+	0.908639i	$0.362878\pi$
$74$	−12622.1	−0.267949
$75$	30038.5	0.616630
$76$	−24127.5	−0.479158
$77$	26159.5	0.502808
$78$	−61836.1	−1.15081
$79$	21063.0	0.379710	0.189855	−	0.981812i	$-0.439198\pi$
$79$	21063.0	0.379710	0.189855	+	0.981812i	$0.439198\pi$
$80$	−178563.	−3.11937
$81$	−39234.2	−0.664434
$82$	96884.9	1.59119
$83$	−40097.3	−0.638880	−0.319440	−	0.947606i	$-0.603495\pi$
$83$	−40097.3	−0.638880	−0.319440	+	0.947606i	$0.603495\pi$
$84$	50389.3	0.779184
$85$	−132052.	−1.98243
$86$	142865.	2.08295
$87$	28260.8	0.400300
$88$	−250544.	−3.44888
$89$	−49632.3	−0.664185	−0.332092	−	0.943247i	$-0.607755\pi$
$89$	−49632.3	−0.664185	−0.332092	+	0.943247i	$0.607755\pi$
$90$	−49312.6	−0.641728
$91$	21723.3	0.274993
$92$	−242818.	−2.99096
$93$	−116345.	−1.39489
$94$	−81982.6	−0.956978
$95$	22980.5	0.261247
$96$	−139109.	−1.54055
$97$	−35035.9	−0.378080	−0.189040	−	0.981969i	$-0.560538\pi$
$97$	−35035.9	−0.378080	−0.189040	+	0.981969i	$0.560538\pi$
$98$	−25062.5	−0.263608
$99$	−34407.3	−0.352827
$100$	173005.	1.73005
$101$	143017.	1.39504	0.697518	−	0.716567i	$-0.254288\pi$
$101$	143017.	1.39504	0.697518	+	0.716567i	$0.254288\pi$
$102$	−251275.	−2.39138
$103$	−23898.2	−0.221958	−0.110979	−	0.993823i	$-0.535399\pi$
$103$	−23898.2	−0.221958	−0.110979	+	0.993823i	$0.535399\pi$
$104$	−208056.	−1.88624
$105$	−47993.8	−0.424827
$106$	−199664.	−1.72598
$107$	−124685.	−1.05282	−0.526412	−	0.850230i	$-0.676463\pi$
$107$	−124685.	−1.05282	−0.526412	+	0.850230i	$0.676463\pi$
$108$	−316166.	−2.60829
$109$	−13768.2	−0.110997	−0.0554985	−	0.998459i	$-0.517675\pi$
$109$	−13768.2	−0.110997	−0.0554985	+	0.998459i	$0.517675\pi$
$110$	408483.	3.21878
$111$	16157.7	0.124472
$112$	119366.	0.899154
$113$	116697.	0.859735	0.429867	−	0.902892i	$-0.358560\pi$
$113$	116697.	0.859735	0.429867	+	0.902892i	$0.358560\pi$
$114$	43728.5	0.315139
$115$	231274.	1.63073
$116$	162766.	1.12310
$117$	−28572.3	−0.192966
$118$	−344134.	−2.27522
$119$	88273.9	0.571432
$120$	459664.	2.91399
$121$	123963.	0.769712
$122$	251612.	1.53049
$123$	−124024.	−0.739166
$124$	−670079.	−3.91356
$125$	64284.6	0.367987
$126$	32964.4	0.184977
$127$	−211478.	−1.16347	−0.581736	−	0.813377i	$-0.697626\pi$
$127$	−211478.	−1.16347	−0.581736	+	0.813377i	$0.697626\pi$
$128$	12513.9	0.0675097
$129$	−182883.	−0.967607
$130$	339211.	1.76040
$131$	124617.	0.634454	0.317227	−	0.948350i	$-0.397248\pi$
$131$	124617.	0.634454	0.317227	+	0.948350i	$0.397248\pi$
$132$	549003.	2.74246
$133$	−15362.0	−0.0753041
$134$	412435.	1.98424
$135$	301136.	1.42209
$136$	−845449.	−3.91958
$137$	18769.0	0.0854358
$137$	18769.0	0.0854358
$138$	440081.	1.96714
$139$	236696.	1.03909	0.519546	−	0.854442i	$-0.326101\pi$
$139$	236696.	1.03909	0.519546	+	0.854442i	$0.326101\pi$
$140$	−276417.	−1.19192
$141$	104947.	0.444552
$142$	−521995.	−2.17243
$143$	236680.	0.967881
$144$	−157000.	−0.630948
$145$	−155028.	−0.612338
$146$	−396927.	−1.54109
$147$	32082.9	0.122456
$148$	93059.4	0.349226
$149$	−232725.	−0.858771	−0.429385	−	0.903121i	$-0.641270\pi$
$149$	−232725.	−0.858771	−0.429385	+	0.903121i	$0.641270\pi$
$150$	−313552.	−1.13784
$151$	117896.	0.420783	0.210392	−	0.977617i	$-0.432526\pi$
$151$	117896.	0.420783	0.210392	+	0.977617i	$0.432526\pi$
$152$	147131.	0.516528
$153$	−116106.	−0.400982
$154$	−273062.	−0.927811
$155$	638225.	2.13375
$156$	455901.	1.49989
$157$	−45688.4	−0.147930	−0.0739650	−	0.997261i	$-0.523565\pi$
$157$	−45688.4	−0.147930	−0.0739650	+	0.997261i	$0.523565\pi$
$158$	−219863.	−0.700663
$159$	255593.	0.801782
$160$	763100.	2.35658
$161$	−154602.	−0.470057
$162$	409540.	1.22605
$163$	456867.	1.34686	0.673428	−	0.739253i	$-0.264821\pi$
$163$	456867.	1.34686	0.673428	+	0.739253i	$0.264821\pi$
$164$	−714307.	−2.07384
$165$	−522905.	−1.49525
$166$	418549.	1.17890
$167$	226753.	0.629160	0.314580	−	0.949231i	$-0.398136\pi$
$167$	226753.	0.629160	0.314580	+	0.949231i	$0.398136\pi$
$168$	−307276.	−0.839953
$169$	−174750.	−0.470652
$170$	1.37840e6	3.65809
$171$	20205.5	0.0528419
$172$	−1.05330e6	−2.71476
$173$	−538339.	−1.36754	−0.683770	−	0.729697i	$-0.739661\pi$
$173$	−538339.	−1.36754	−0.683770	+	0.729697i	$0.739661\pi$
$174$	−294996.	−0.738657
$175$	110152.	0.271893
$176$	1.30052e6	3.16471
$177$	440531.	1.05692
$178$	518079.	1.22559
$179$	−299663.	−0.699038	−0.349519	−	0.936929i	$-0.613655\pi$
$179$	−299663.	−0.699038	−0.349519	+	0.936929i	$0.613655\pi$
$180$	363569.	0.836383
$181$	−474485.	−1.07653	−0.538265	−	0.842775i	$-0.680920\pi$
$181$	−474485.	−1.07653	−0.538265	+	0.842775i	$0.680920\pi$
$182$	−226755.	−0.507433
$183$	−322092.	−0.710972
$184$	1.48071e6	3.22423
$185$	−88635.6	−0.190405
$186$	1.21445e6	2.57392
$187$	961765.	2.01125
$188$	604436.	1.24726
$189$	−201303.	−0.409917
$190$	−239879.	−0.482068
$191$	903678.	1.79238	0.896191	−	0.443669i	$-0.146324\pi$
$191$	903678.	1.79238	0.896191	+	0.443669i	$0.146324\pi$
$192$	410435.	0.803510
$193$	−317827.	−0.614182	−0.307091	−	0.951680i	$-0.599356\pi$
$193$	−317827.	−0.614182	−0.307091	+	0.951680i	$0.599356\pi$
$194$	365717.	0.697655
$195$	−434229.	−0.817771
$196$	184779.	0.343568
$197$	421931.	0.774598	0.387299	−	0.921954i	$-0.373408\pi$
$197$	421931.	0.774598	0.387299	+	0.921954i	$0.373408\pi$
$198$	359155.	0.651057
$199$	−202300.	−0.362128	−0.181064	−	0.983471i	$-0.557954\pi$
$199$	−202300.	−0.362128	−0.181064	+	0.983471i	$0.557954\pi$
$200$	−1.05499e6	−1.86497
$201$	−527964.	−0.921753
$202$	−1.49287e6	−2.57420
$203$	103633.	0.176506
$204$	1.85258e6	3.11675
$205$	680350.	1.13070
$206$	249457.	0.409570
$207$	203346.	0.329845
$208$	1.07997e6	1.73083
$209$	−167373.	−0.265045
$210$	500977.	0.783916
$211$	656905.	1.01577	0.507886	−	0.861424i	$-0.330427\pi$
$211$	656905.	1.01577	0.507886	+	0.861424i	$0.330427\pi$
$212$	1.47207e6	2.24952
$213$	668214.	1.00917
$214$	1.30151e6	1.94273
$215$	1.00323e6	1.48015
$216$	1.92799e6	2.81171
$217$	−426640.	−0.615052
$218$	143718.	0.204818
$219$	508112.	0.715895
$220$	−3.01164e6	−4.19513
$221$	798665.	1.09998
$222$	−168660.	−0.229684
$223$	220957.	0.297540	0.148770	−	0.988872i	$-0.452469\pi$
$223$	220957.	0.297540	0.148770	+	0.988872i	$0.452469\pi$
$224$	−510116.	−0.679281
$225$	−144882.	−0.190791
$226$	−1.21813e6	−1.58643
$227$	−1.16087e6	−1.49526	−0.747632	−	0.664113i	$-0.768809\pi$
$227$	−1.16087e6	−1.49526	−0.747632	+	0.664113i	$0.768809\pi$
$228$	−322399.	−0.410730
$229$	114889.	0.144773	0.0723866	−	0.997377i	$-0.476938\pi$
$229$	114889.	0.144773	0.0723866	+	0.997377i	$0.476938\pi$
$230$	−2.41413e6	−3.00913
$231$	349551.	0.431003
$232$	−992554.	−1.21069
$233$	−1.65362e6	−1.99547	−0.997737	−	0.0672347i	$-0.978582\pi$
$233$	−1.65362e6	−1.99547	−0.997737	+	0.0672347i	$0.978582\pi$
$234$	298248.	0.356072
$235$	−575702.	−0.680030
$236$	2.53721e6	2.96535
$237$	281450.	0.325484
$238$	−921434.	−1.05444
$239$	−1.24253e6	−1.40705	−0.703527	−	0.710669i	$-0.748393\pi$
$239$	−1.24253e6	−1.40705	−0.703527	+	0.710669i	$0.748393\pi$
$240$	−2.38601e6	−2.67389
$241$	−794594.	−0.881257	−0.440628	−	0.897690i	$-0.645244\pi$
$241$	−794594.	−0.881257	−0.440628	+	0.897690i	$0.645244\pi$
$242$	−1.29397e6	−1.42032
$243$	474040.	0.514991
$244$	−1.85507e6	−1.99474
$245$	−175995.	−0.187321
$246$	1.29460e6	1.36395
$247$	−138989.	−0.144957
$248$	4.08617e6	4.21878
$249$	−535791.	−0.547643
$250$	−671026.	−0.679031
$251$	−872805.	−0.874446	−0.437223	−	0.899353i	$-0.644038\pi$
$251$	−872805.	−0.874446	−0.437223	+	0.899353i	$0.644038\pi$
$252$	−243038.	−0.241086
$253$	−1.68443e6	−1.65444
$254$	2.20748e6	2.14691
$255$	−1.76452e6	−1.69932
$256$	−1.11353e6	−1.06195
$257$	−451485.	−0.426393	−0.213197	−	0.977009i	$-0.568387\pi$
$257$	−451485.	−0.426393	−0.213197	+	0.977009i	$0.568387\pi$
$258$	1.90900e6	1.78548
$259$	59251.0	0.0548841
$260$	−2.50091e6	−2.29438
$261$	−136308.	−0.123856
$262$	−1.30080e6	−1.17073
$263$	190506.	0.169832	0.0849158	−	0.996388i	$-0.472938\pi$
$263$	190506.	0.169832	0.0849158	+	0.996388i	$0.472938\pi$
$264$	−3.34784e6	−2.95635
$265$	−1.40209e6	−1.22648
$266$	160354.	0.138955
$267$	−663201.	−0.569334
$268$	−3.04078e6	−2.58611
$269$	−1.61560e6	−1.36130	−0.680650	−	0.732609i	$-0.738303\pi$
$269$	−1.61560e6	−1.36130	−0.680650	+	0.732609i	$0.738303\pi$
$270$	−3.14336e6	−2.62413
$271$	−1.80403e6	−1.49218	−0.746089	−	0.665846i	$-0.768071\pi$
$271$	−1.80403e6	−1.49218	−0.746089	+	0.665846i	$0.768071\pi$
$272$	4.38853e6	3.59664
$273$	290273.	0.235722
$274$	−195917.	−0.157651
$275$	1.20013e6	0.956969
$276$	−3.24460e6	−2.56383
$277$	642333.	0.502992	0.251496	−	0.967858i	$-0.419078\pi$
$277$	642333.	0.502992	0.251496	+	0.967858i	$0.419078\pi$
$278$	−2.47072e6	−1.91739
$279$	561154.	0.431590
$280$	1.68560e6	1.28487
$281$	1.46244e6	1.10488	0.552438	−	0.833554i	$-0.313698\pi$
$281$	1.46244e6	1.10488	0.552438	+	0.833554i	$0.313698\pi$
$282$	−1.09548e6	−0.820313
$283$	267859.	0.198811	0.0994053	−	0.995047i	$-0.468306\pi$
$283$	267859.	0.198811	0.0994053	+	0.995047i	$0.468306\pi$
$284$	3.84853e6	2.83139
$285$	307073.	0.223939
$286$	−2.47055e6	−1.78599
$287$	−454799.	−0.325923
$288$	670950.	0.476660
$289$	1.82557e6	1.28574
$290$	1.61824e6	1.12992
$291$	−468160.	−0.324087
$292$	2.92644e6	2.00855
$293$	2.34086e6	1.59297	0.796484	−	0.604660i	$-0.206691\pi$
$293$	2.34086e6	1.59297	0.796484	+	0.604660i	$0.206691\pi$
$294$	−334892.	−0.225963
$295$	−2.41660e6	−1.61677
$296$	−567480.	−0.376462
$297$	−2.19325e6	−1.44277
$298$	2.42926e6	1.58465
$299$	−1.39878e6	−0.904837
$300$	2.31174e6	1.48298
$301$	−670638.	−0.426650
$302$	−1.23064e6	−0.776453
$303$	1.91104e6	1.19581
$304$	−763721.	−0.473970
$305$	1.76688e6	1.08757
$306$	1.21195e6	0.739914
$307$	−2.97262e6	−1.80008	−0.900042	−	0.435803i	$-0.856464\pi$
$307$	−2.97262e6	−1.80008	−0.900042	+	0.435803i	$0.856464\pi$
$308$	2.01321e6	1.20924
$309$	−319334.	−0.190261
$310$	−6.66202e6	−3.93733
$311$	−679164.	−0.398175	−0.199087	−	0.979982i	$-0.563798\pi$
$311$	−679164.	−0.398175	−0.199087	+	0.979982i	$0.563798\pi$
$312$	−2.78010e6	−1.61687
$313$	3.29520e6	1.90117	0.950585	−	0.310466i	$-0.100485\pi$
$313$	3.29520e6	1.90117	0.950585	+	0.310466i	$0.100485\pi$
$314$	476911.	0.272969
$315$	231484.	0.131445
$316$	1.62099e6	0.913194
$317$	−1.69254e6	−0.946002	−0.473001	−	0.881062i	$-0.656829\pi$
$317$	−1.69254e6	−0.946002	−0.473001	+	0.881062i	$0.656829\pi$
$318$	−2.66797e6	−1.47949
$319$	1.12911e6	0.621240
$320$	−2.25150e6	−1.22913
$321$	−1.66608e6	−0.902471
$322$	1.61379e6	0.867377
$323$	−564791.	−0.301218
$324$	−3.01943e6	−1.59795
$325$	996611.	0.523380
$326$	−4.76894e6	−2.48530
$327$	−183975.	−0.0951457
$328$	4.35587e6	2.23558
$329$	384845.	0.196018
$330$	5.45826e6	2.75911
$331$	−899882.	−0.451456	−0.225728	−	0.974190i	$-0.572476\pi$
$331$	−899882.	−0.451456	−0.225728	+	0.974190i	$0.572476\pi$
$332$	−3.08586e6	−1.53649
$333$	−77932.1	−0.0385129
$334$	−2.36693e6	−1.16096
$335$	2.89622e6	1.41000
$336$	1.59500e6	0.770747
$337$	−10394.8	−0.00498586	−0.00249293	−	0.999997i	$-0.500794\pi$
$337$	−10394.8	−0.00498586	−0.00249293	+	0.999997i	$0.500794\pi$
$338$	1.82410e6	0.868475
$339$	1.55934e6	0.736957
$340$	−1.01626e7	−4.76769
$341$	−4.64834e6	−2.16477
$342$	−210912.	−0.0975069
$343$	117649.	0.0539949
$344$	6.42308e6	2.92649
$345$	3.09036e6	1.39785
$346$	5.61937e6	2.52347
$347$	1.78916e6	0.797672	0.398836	−	0.917022i	$-0.369414\pi$
$347$	1.78916e6	0.797672	0.398836	+	0.917022i	$0.369414\pi$
$348$	2.17493e6	0.962713
$349$	−1.88584e6	−0.828782	−0.414391	−	0.910099i	$-0.636005\pi$
$349$	−1.88584e6	−0.828782	−0.414391	+	0.910099i	$0.636005\pi$
$350$	−1.14981e6	−0.501712
$351$	−1.82131e6	−0.789070
$352$	−5.55784e6	−2.39083
$353$	−1.91818e6	−0.819319	−0.409660	−	0.912238i	$-0.634353\pi$
$353$	−1.91818e6	−0.819319	−0.409660	+	0.912238i	$0.634353\pi$
$354$	−4.59842e6	−1.95030
$355$	−3.66558e6	−1.54373
$356$	−3.81966e6	−1.59735
$357$	1.17954e6	0.489827
$358$	3.12799e6	1.28991
$359$	−2.52932e6	−1.03578	−0.517890	−	0.855447i	$-0.673283\pi$
$359$	−2.52932e6	−1.03578	−0.517890	+	0.855447i	$0.673283\pi$
$360$	−2.21706e6	−0.901614
$361$	−2.37781e6	−0.960305
$362$	4.95285e6	1.98648
$363$	1.65643e6	0.659790
$364$	1.67181e6	0.661352
$365$	−2.78732e6	−1.09510
$366$	3.36211e6	1.31193
$367$	1.28382e6	0.497553	0.248776	−	0.968561i	$-0.419972\pi$
$367$	1.28382e6	0.497553	0.248776	+	0.968561i	$0.419972\pi$
$368$	−7.68603e6	−2.95858
$369$	598192.	0.228705
$370$	925209.	0.351347
$371$	937269.	0.353532
$372$	−8.95379e6	−3.35467
$373$	−1.85632e6	−0.690846	−0.345423	−	0.938447i	$-0.612265\pi$
$373$	−1.85632e6	−0.690846	−0.345423	+	0.938447i	$0.612265\pi$
$374$	−1.00392e7	−3.71127
$375$	858990.	0.315435
$376$	−3.68588e6	−1.34453
$377$	937631.	0.339765
$378$	2.10127e6	0.756402
$379$	1.74189e6	0.622906	0.311453	−	0.950262i	$-0.399184\pi$
$379$	1.74189e6	0.622906	0.311453	+	0.950262i	$0.399184\pi$
$380$	1.76856e6	0.628293
$381$	−2.82583e6	−0.997319
$382$	−9.43291e6	−3.30741
$383$	3.53718e6	1.23214	0.616070	−	0.787691i	$-0.288724\pi$
$383$	3.53718e6	1.23214	0.616070	+	0.787691i	$0.288724\pi$
$384$	167214.	0.0578687
$385$	−1.91751e6	−0.659304
$386$	3.31759e6	1.13332
$387$	882083.	0.299386
$388$	−2.69634e6	−0.909274
$389$	727009.	0.243593	0.121797	−	0.992555i	$-0.461134\pi$
$389$	727009.	0.243593	0.121797	+	0.992555i	$0.461134\pi$
$390$	4.53263e6	1.50900
$391$	−5.68402e6	−1.88024
$392$	−1.12679e6	−0.370364
$393$	1.66517e6	0.543849
$394$	−4.40427e6	−1.42933
$395$	−1.54393e6	−0.497893
$396$	−2.64796e6	−0.848541
$397$	35372.4	0.0112639	0.00563195	−	0.999984i	$-0.498207\pi$
$397$	35372.4	0.0112639	0.00563195	+	0.999984i	$0.498207\pi$
$398$	2.11167e6	0.668220
$399$	−205272.	−0.0645500
$400$	5.47620e6	1.71131
$401$	−771600.	−0.239624	−0.119812	−	0.992797i	$-0.538229\pi$
$401$	−771600.	−0.239624	−0.119812	+	0.992797i	$0.538229\pi$
$402$	5.51108e6	1.70087
$403$	−3.86006e6	−1.18394
$404$	1.10065e7	3.35503
$405$	2.87589e6	0.871235
$406$	−1.08176e6	−0.325699
$407$	645554.	0.193173
$408$	−1.12971e7	−3.35983
$409$	4.79113e6	1.41622	0.708109	−	0.706104i	$-0.249549\pi$
$409$	4.79113e6	1.41622	0.708109	+	0.706104i	$0.249549\pi$
$410$	−7.10173e6	−2.08643
$411$	250797.	0.0732348
$412$	−1.83918e6	−0.533804
$413$	1.61544e6	0.466033
$414$	−2.12260e6	−0.608650
$415$	2.93916e6	0.837728
$416$	−4.61532e6	−1.30758
$417$	3.16280e6	0.890701
$418$	1.74710e6	0.489076
$419$	32510.1	0.00904656	0.00452328	−	0.999990i	$-0.498560\pi$
$419$	32510.1	0.00904656	0.00452328	+	0.999990i	$0.498560\pi$
$420$	−3.69357e6	−1.02170
$421$	−3.02892e6	−0.832880	−0.416440	−	0.909163i	$-0.636722\pi$
$421$	−3.02892e6	−0.832880	−0.416440	+	0.909163i	$0.636722\pi$
$422$	−6.85701e6	−1.87436
$423$	−506182.	−0.137548
$424$	−8.97675e6	−2.42496
$425$	4.04979e6	1.08758
$426$	−6.97505e6	−1.86219
$427$	−1.18112e6	−0.313491
$428$	−9.59568e6	−2.53202
$429$	3.16259e6	0.829659
$430$	−1.04721e7	−2.73125
$431$	−4.65585e6	−1.20727	−0.603637	−	0.797260i	$-0.706282\pi$
$431$	−4.65585e6	−1.20727	−0.603637	+	0.797260i	$0.706282\pi$
$432$	−1.00078e7	−2.58005
$433$	−6.65962e6	−1.70698	−0.853492	−	0.521106i	$-0.825520\pi$
$433$	−6.65962e6	−1.70698	−0.853492	+	0.521106i	$0.825520\pi$
$434$	4.45342e6	1.13493
$435$	−2.07154e6	−0.524891
$436$	−1.05959e6	−0.266945
$437$	989170.	0.247781
$438$	−5.30386e6	−1.32101
$439$	−693648.	−0.171782	−0.0858911	−	0.996305i	$-0.527374\pi$
$439$	−693648.	−0.171782	−0.0858911	+	0.996305i	$0.527374\pi$
$440$	1.83651e7	4.52232
$441$	−154742.	−0.0378890
$442$	−8.33675e6	−2.02974
$443$	−5.82129e6	−1.40932	−0.704661	−	0.709544i	$-0.748901\pi$
$443$	−5.82129e6	−1.40932	−0.704661	+	0.709544i	$0.748901\pi$
$444$	1.24349e6	0.299353
$445$	3.63808e6	0.870908
$446$	−2.30643e6	−0.549038
$447$	−3.10974e6	−0.736131
$448$	1.50508e6	0.354294
$449$	2.77126e6	0.648727	0.324363	−	0.945933i	$-0.394850\pi$
$449$	2.77126e6	0.648727	0.324363	+	0.945933i	$0.394850\pi$
$450$	1.51233e6	0.352058
$451$	−4.95515e6	−1.14714
$452$	8.98093e6	2.06764
$453$	1.57537e6	0.360692
$454$	1.21175e7	2.75915
$455$	−1.59233e6	−0.360583
$456$	1.96600e6	0.442763
$457$	−6.34190e6	−1.42046	−0.710230	−	0.703970i	$-0.751409\pi$
$457$	−6.34190e6	−1.42046	−0.710230	+	0.703970i	$0.751409\pi$
$458$	−1.19925e6	−0.267144
$459$	−7.40100e6	−1.63968
$460$	1.77987e7	3.92188
$461$	8.15629e6	1.78748	0.893738	−	0.448589i	$-0.148073\pi$
$461$	8.15629e6	1.78748	0.893738	+	0.448589i	$0.148073\pi$
$462$	−3.64873e6	−0.795311
$463$	−2.41401e6	−0.523343	−0.261672	−	0.965157i	$-0.584274\pi$
$463$	−2.41401e6	−0.523343	−0.261672	+	0.965157i	$0.584274\pi$
$464$	5.15212e6	1.11094
$465$	8.52815e6	1.82904
$466$	1.72611e7	3.68216
$467$	−318123.	−0.0674998	−0.0337499	−	0.999430i	$-0.510745\pi$
$467$	−318123.	−0.0674998	−0.0337499	+	0.999430i	$0.510745\pi$
$468$	−2.19891e6	−0.464079
$469$	−1.93606e6	−0.406432
$470$	6.00939e6	1.25483
$471$	−610501.	−0.126804
$472$	−1.54720e7	−3.19663
$473$	−7.30677e6	−1.50166
$474$	−2.93787e6	−0.600602
$475$	−704771.	−0.143322
$476$	6.79349e6	1.37428
$477$	−1.23278e6	−0.248078
$478$	1.29699e7	2.59638
$479$	−1.94293e6	−0.386918	−0.193459	−	0.981108i	$-0.561971\pi$
$479$	−1.94293e6	−0.386918	−0.193459	+	0.981108i	$0.561971\pi$
$480$	1.01968e7	2.02004
$481$	536078.	0.105649
$482$	8.29425e6	1.62615
$483$	−2.06584e6	−0.402929
$484$	9.54009e6	1.85114
$485$	2.56816e6	0.495755
$486$	−4.94820e6	−0.950291
$487$	6.04995e6	1.15593	0.577963	−	0.816063i	$-0.303848\pi$
$487$	6.04995e6	1.15593	0.577963	+	0.816063i	$0.303848\pi$
$488$	1.13123e7	2.15031
$489$	6.10479e6	1.15451
$490$	1.83710e6	0.345655
$491$	3.03623e6	0.568369	0.284184	−	0.958770i	$-0.408277\pi$
$491$	3.03623e6	0.568369	0.284184	+	0.958770i	$0.408277\pi$
$492$	−9.54478e6	−1.77768
$493$	3.81012e6	0.706028
$494$	1.45082e6	0.267482
$495$	2.52208e6	0.462642
$496$	−2.12104e7	−3.87118
$497$	2.45036e6	0.444979
$498$	5.59278e6	1.01054
$499$	1.37368e6	0.246964	0.123482	−	0.992347i	$-0.460594\pi$
$499$	1.37368e6	0.246964	0.123482	+	0.992347i	$0.460594\pi$
$500$	4.94730e6	0.885000
$501$	3.02994e6	0.539311
$502$	9.11065e6	1.61358
$503$	1.19942e6	0.211373	0.105687	−	0.994399i	$-0.466296\pi$
$503$	1.19942e6	0.211373	0.105687	+	0.994399i	$0.466296\pi$
$504$	1.48205e6	0.259889
$505$	−1.04833e7	−1.82923
$506$	1.75826e7	3.05287
$507$	−2.33506e6	−0.403439
$508$	−1.62752e7	−2.79812
$509$	6.82160e6	1.16706	0.583528	−	0.812093i	$-0.301672\pi$
$509$	6.82160e6	1.16706	0.583528	+	0.812093i	$0.301672\pi$
$510$	1.84186e7	3.13568
$511$	1.86327e6	0.315662
$512$	1.12230e7	1.89206
$513$	1.28797e6	0.216079
$514$	4.71276e6	0.786805
$515$	1.75175e6	0.291041
$516$	−1.40745e7	−2.32707
$517$	4.19298e6	0.689916
$518$	−618483.	−0.101275
$519$	−7.19344e6	−1.17224
$520$	1.52507e7	2.47332
$521$	−1.06838e7	−1.72437	−0.862184	−	0.506596i	$-0.830904\pi$
$521$	−1.06838e7	−1.72437	−0.862184	+	0.506596i	$0.830904\pi$
$522$	1.42283e6	0.228547
$523$	−1.15560e7	−1.84737	−0.923686	−	0.383151i	$-0.874839\pi$
$523$	−1.15560e7	−1.84737	−0.923686	+	0.383151i	$0.874839\pi$
$524$	9.59046e6	1.52585
$525$	1.47188e6	0.233064
$526$	−1.98857e6	−0.313383
$527$	−1.56856e7	−2.46022
$528$	1.73779e7	2.71276
$529$	3.51859e6	0.546676
$530$	1.46355e7	2.26318
$531$	−2.12477e6	−0.327022
$532$	−1.18225e6	−0.181105
$533$	−4.11484e6	−0.627386
$534$	6.92273e6	1.05057
$535$	9.13952e6	1.38051
$536$	1.85428e7	2.78781
$537$	−4.00419e6	−0.599210
$538$	1.68642e7	2.51195
$539$	1.28181e6	0.190044
$540$	2.31752e7	3.42010
$541$	−8.46577e6	−1.24358	−0.621790	−	0.783184i	$-0.713594\pi$
$541$	−8.46577e6	−1.24358	−0.621790	+	0.783184i	$0.713594\pi$
$542$	1.88311e7	2.75345
$543$	−6.34021e6	−0.922793
$544$	−1.87547e7	−2.71714
$545$	1.00922e6	0.145544
$546$	−3.02997e6	−0.434967
$547$	7.24502e6	1.03531	0.517656	−	0.855589i	$-0.326805\pi$
$547$	7.24502e6	1.03531	0.517656	+	0.855589i	$0.326805\pi$
$548$	1.44445e6	0.205471
$549$	1.55352e6	0.219981
$550$	−1.25274e7	−1.76585
$551$	−663063.	−0.0930413
$552$	1.97857e7	2.76378
$553$	1.03209e6	0.143517
$554$	−6.70490e6	−0.928150
$555$	−1.18437e6	−0.163214
$556$	1.82160e7	2.49899
$557$	6.81050e6	0.930124	0.465062	−	0.885278i	$-0.346032\pi$
$557$	6.81050e6	0.930124	0.465062	+	0.885278i	$0.346032\pi$
$558$	−5.85753e6	−0.796395
$559$	−6.06766e6	−0.821281
$560$	−8.74959e6	−1.17901
$561$	1.28514e7	1.72402
$562$	−1.52655e7	−2.03878
$563$	−7.91667e6	−1.05262	−0.526310	−	0.850293i	$-0.676425\pi$
$563$	−7.91667e6	−1.05262	−0.526310	+	0.850293i	$0.676425\pi$
$564$	8.07665e6	1.06914
$565$	−8.55400e6	−1.12732
$566$	−2.79600e6	−0.366857
$567$	−1.92247e6	−0.251133
$568$	−2.34685e7	−3.05221
$569$	−8.82740e6	−1.14302	−0.571508	−	0.820597i	$-0.693641\pi$
$569$	−8.82740e6	−1.14302	−0.571508	+	0.820597i	$0.693641\pi$
$570$	−3.20533e6	−0.413224
$571$	−1.07568e7	−1.38068	−0.690338	−	0.723487i	$-0.742538\pi$
$571$	−1.07568e7	−1.38068	−0.690338	+	0.723487i	$0.742538\pi$
$572$	1.82147e7	2.32773
$573$	1.20752e7	1.53641
$574$	4.74736e6	0.601412
$575$	−7.09277e6	−0.894636
$576$	−1.97961e6	−0.248613
$577$	1.42030e6	0.177600	0.0887998	−	0.996049i	$-0.471697\pi$
$577$	1.42030e6	0.177600	0.0887998	+	0.996049i	$0.471697\pi$
$578$	−1.90560e7	−2.37253
$579$	−4.24689e6	−0.526472
$580$	−1.19309e7	−1.47266
$581$	−1.96477e6	−0.241474
$582$	4.88682e6	0.598024
$583$	1.02118e7	1.24431
$584$	−1.78456e7	−2.16520
$585$	2.09437e6	0.253026
$586$	−2.44348e7	−2.93944
$587$	−1.07076e7	−1.28261	−0.641307	−	0.767285i	$-0.721607\pi$
$587$	−1.07076e7	−1.28261	−0.641307	+	0.767285i	$0.721607\pi$
$588$	2.46907e6	0.294504
$589$	2.72971e6	0.324212
$590$	2.52253e7	2.98336
$591$	5.63797e6	0.663979
$592$	2.94566e6	0.345444
$593$	9.45617e6	1.10428	0.552139	−	0.833752i	$-0.313812\pi$
$593$	9.45617e6	1.10428	0.552139	+	0.833752i	$0.313812\pi$
$594$	2.28939e7	2.66228
$595$	−6.47054e6	−0.749287
$596$	−1.79103e7	−2.06532
$597$	−2.70319e6	−0.310413
$598$	1.46009e7	1.66966
$599$	7.70013e6	0.876861	0.438431	−	0.898765i	$-0.355534\pi$
$599$	7.70013e6	0.876861	0.438431	+	0.898765i	$0.355534\pi$
$600$	−1.40971e7	−1.59864
$601$	−7.28136e6	−0.822293	−0.411146	−	0.911569i	$-0.634872\pi$
$601$	−7.28136e6	−0.822293	−0.411146	+	0.911569i	$0.634872\pi$
$602$	7.00036e6	0.787280
$603$	2.54648e6	0.285199
$604$	9.07322e6	1.01197
$605$	−9.08657e6	−1.00928
$606$	−1.99481e7	−2.20658
$607$	7.86596e6	0.866523	0.433261	−	0.901268i	$-0.357363\pi$
$607$	7.86596e6	0.866523	0.433261	+	0.901268i	$0.357363\pi$
$608$	3.26381e6	0.358068
$609$	1.38478e6	0.151299
$610$	−1.84433e7	−2.00685
$611$	3.48192e6	0.377325
$612$	−8.93540e6	−0.964351
$613$	−1.32524e7	−1.42444	−0.712218	−	0.701958i	$-0.752309\pi$
$613$	−1.32524e7	−1.42444	−0.712218	+	0.701958i	$0.752309\pi$
$614$	3.10292e7	3.32162
$615$	9.09104e6	0.969227
$616$	−1.22767e7	−1.30355
$617$	9.38633e6	0.992620	0.496310	−	0.868145i	$-0.334688\pi$
$617$	9.38633e6	0.992620	0.496310	+	0.868145i	$0.334688\pi$
$618$	3.33332e6	0.351080
$619$	−4.91957e6	−0.516060	−0.258030	−	0.966137i	$-0.583073\pi$
$619$	−4.91957e6	−0.516060	−0.258030	+	0.966137i	$0.583073\pi$
$620$	4.91173e7	5.13163
$621$	1.29620e7	1.34879
$622$	7.08936e6	0.734735
$623$	−2.43198e6	−0.251038
$624$	1.44309e7	1.48365
$625$	−1.17371e7	−1.20188
$626$	−3.43965e7	−3.50815
$627$	−2.23648e6	−0.227194
$628$	−3.51614e6	−0.355768
$629$	2.17839e6	0.219538
$630$	−2.41632e6	−0.242551
$631$	699204.	0.0699086	0.0349543	−	0.999389i	$-0.488871\pi$
$631$	699204.	0.0699086	0.0349543	+	0.999389i	$0.488871\pi$
$632$	−9.88487e6	−0.984416
$633$	8.77776e6	0.870711
$634$	1.76674e7	1.74562
$635$	1.55015e7	1.52560
$636$	1.96702e7	1.92827
$637$	1.06444e6	0.103938
$638$	−1.17860e7	−1.14635
$639$	−3.22293e6	−0.312248
$640$	−917275.	−0.0885217
$641$	−1.02792e7	−0.988127	−0.494063	−	0.869426i	$-0.664489\pi$
$641$	−1.02792e7	−0.988127	−0.494063	+	0.869426i	$0.664489\pi$
$642$	1.73911e7	1.66529
$643$	1.02669e7	0.979292	0.489646	−	0.871921i	$-0.337126\pi$
$643$	1.02669e7	0.979292	0.489646	+	0.871921i	$0.337126\pi$
$644$	−1.18981e7	−1.13048
$645$	1.34055e7	1.26877
$646$	5.89549e6	0.555825
$647$	−2.97689e6	−0.279577	−0.139789	−	0.990181i	$-0.544642\pi$
$647$	−2.97689e6	−0.279577	−0.139789	+	0.990181i	$0.544642\pi$
$648$	1.84126e7	1.72258
$649$	1.76006e7	1.64028
$650$	−1.04030e7	−0.965771
$651$	−5.70088e6	−0.527217
$652$	3.51602e7	3.23916
$653$	−1.02458e7	−0.940296	−0.470148	−	0.882588i	$-0.655800\pi$
$653$	−1.02458e7	−0.940296	−0.470148	+	0.882588i	$0.655800\pi$
$654$	1.92040e6	0.175568
$655$	−9.13454e6	−0.831924
$656$	−2.26103e7	−2.05138
$657$	−2.45073e6	−0.221504
$658$	−4.01715e6	−0.361704
$659$	−1.85607e7	−1.66487	−0.832434	−	0.554124i	$-0.813053\pi$
$659$	−1.85607e7	−1.66487	−0.832434	+	0.554124i	$0.813053\pi$
$660$	−4.02424e7	−3.59603
$661$	1.48475e7	1.32175	0.660874	−	0.750497i	$-0.270186\pi$
$661$	1.48475e7	1.32175	0.660874	+	0.750497i	$0.270186\pi$
$662$	9.39329e6	0.833053
$663$	1.06720e7	0.942892
$664$	1.88177e7	1.65633
$665$	1.12605e6	0.0987420
$666$	813483.	0.0710662
$667$	−6.67302e6	−0.580775
$668$	1.74507e7	1.51312
$669$	2.95249e6	0.255049
$670$	−3.02318e7	−2.60182
$671$	−1.28686e7	−1.10338
$672$	−6.81632e6	−0.582274
$673$	1.12992e6	0.0961633	0.0480817	−	0.998843i	$-0.484689\pi$
$673$	1.12992e6	0.0961633	0.0480817	+	0.998843i	$0.484689\pi$
$674$	108504.	0.00920020
$675$	−9.23530e6	−0.780174
$676$	−1.34486e7	−1.13191
$677$	−1.72693e7	−1.44811	−0.724057	−	0.689740i	$-0.757725\pi$
$677$	−1.72693e7	−1.44811	−0.724057	+	0.689740i	$0.757725\pi$
$678$	−1.62770e7	−1.35988
$679$	−1.71676e6	−0.142901
$680$	6.19720e7	5.13953
$681$	−1.55118e7	−1.28173
$682$	4.85211e7	3.99456
$683$	1.59858e7	1.31124	0.655620	−	0.755091i	$-0.272407\pi$
$683$	1.59858e7	1.31124	0.655620	+	0.755091i	$0.272407\pi$
$684$	1.55500e6	0.127084
$685$	−1.37578e6	−0.112027
$686$	−1.22806e6	−0.0996346
$687$	1.53518e6	0.124098
$688$	−3.33407e7	−2.68537
$689$	8.48002e6	0.680532
$690$	−3.22583e7	−2.57940
$691$	3.87055e6	0.308374	0.154187	−	0.988042i	$-0.450724\pi$
$691$	3.87055e6	0.308374	0.154187	+	0.988042i	$0.450724\pi$
$692$	−4.14301e7	−3.28890
$693$	−1.68596e6	−0.133356
$694$	−1.86758e7	−1.47191
$695$	−1.73500e7	−1.36250
$696$	−1.32628e7	−1.03780
$697$	−1.67209e7	−1.30370
$698$	1.96850e7	1.52932
$699$	−2.20962e7	−1.71050
$700$	8.47722e6	0.653896
$701$	−1.25695e7	−0.966103	−0.483051	−	0.875592i	$-0.660472\pi$
$701$	−1.25695e7	−0.966103	−0.483051	+	0.875592i	$0.660472\pi$
$702$	1.90114e7	1.45604
$703$	−379098.	−0.0289310
$704$	1.63982e7	1.24699
$705$	−7.69270e6	−0.582916
$706$	2.00227e7	1.51186
$707$	7.00785e6	0.527274
$708$	3.39030e7	2.54188
$709$	−1.84398e7	−1.37766	−0.688828	−	0.724925i	$-0.741874\pi$
$709$	−1.84398e7	−1.37766	−0.688828	+	0.724925i	$0.741874\pi$
$710$	3.82626e7	2.84858
$711$	−1.35749e6	−0.100708
$712$	2.32925e7	1.72193
$713$	2.74716e7	2.02377
$714$	−1.23125e7	−0.903857
$715$	−1.73488e7	−1.26913
$716$	−2.30619e7	−1.68117
$717$	−1.66030e7	−1.20611
$718$	2.64020e7	1.91128
$719$	−1.02656e7	−0.740560	−0.370280	−	0.928920i	$-0.620738\pi$
$719$	−1.02656e7	−0.740560	−0.370280	+	0.928920i	$0.620738\pi$
$720$	1.15082e7	0.827327
$721$	−1.17101e6	−0.0838923
$722$	2.48204e7	1.77201
$723$	−1.06176e7	−0.755406
$724$	−3.65160e7	−2.58903
$725$	4.75444e6	0.335935
$726$	−1.72904e7	−1.21748
$727$	3.35717e6	0.235579	0.117790	−	0.993039i	$-0.462419\pi$
$727$	3.35717e6	0.235579	0.117790	+	0.993039i	$0.462419\pi$
$728$	−1.01947e7	−0.712931
$729$	1.58682e7	1.10588
$730$	2.90951e7	2.02075
$731$	−2.46563e7	−1.70661
$732$	−2.47880e7	−1.70987
$733$	−1.58601e7	−1.09030	−0.545149	−	0.838339i	$-0.683527\pi$
$733$	−1.58601e7	−1.09030	−0.545149	+	0.838339i	$0.683527\pi$
$734$	−1.34010e7	−0.918113
$735$	−2.35170e6	−0.160570
$736$	3.28468e7	2.23510
$737$	−2.10939e7	−1.43050
$738$	−6.24414e6	−0.422019
$739$	2.43515e7	1.64026	0.820132	−	0.572174i	$-0.193900\pi$
$739$	2.43515e7	1.64026	0.820132	+	0.572174i	$0.193900\pi$
$740$	−6.82133e6	−0.457920
$741$	−1.85721e6	−0.124256
$742$	−9.78354e6	−0.652359
$743$	−1.28886e7	−0.856509	−0.428255	−	0.903658i	$-0.640871\pi$
$743$	−1.28886e7	−0.856509	−0.428255	+	0.903658i	$0.640871\pi$
$744$	5.46006e7	3.61630
$745$	1.70589e7	1.12606
$746$	1.93770e7	1.27479
$747$	2.58423e6	0.169446
$748$	7.40167e7	4.83700
$749$	−6.10958e6	−0.397930
$750$	−8.96645e6	−0.582059
$751$	1.41933e6	0.0918296	0.0459148	−	0.998945i	$-0.485380\pi$
$751$	1.41933e6	0.0918296	0.0459148	+	0.998945i	$0.485380\pi$
$752$	1.91325e7	1.23375
$753$	−1.16627e7	−0.749568
$754$	−9.78732e6	−0.626954
$755$	−8.64190e6	−0.551749
$756$	−1.54921e7	−0.985841
$757$	−615499.	−0.0390380	−0.0195190	−	0.999809i	$-0.506213\pi$
$757$	−615499.	−0.0390380	−0.0195190	+	0.999809i	$0.506213\pi$
$758$	−1.81825e7	−1.14942
$759$	−2.25078e7	−1.41817
$760$	−1.07848e7	−0.677294
$761$	−2.21306e7	−1.38526	−0.692631	−	0.721292i	$-0.743548\pi$
$761$	−2.21306e7	−1.38526	−0.692631	+	0.721292i	$0.743548\pi$
$762$	2.94970e7	1.84031
$763$	−674643.	−0.0419529
$764$	6.95464e7	4.31064
$765$	8.51063e6	0.525785
$766$	−3.69223e7	−2.27362
$767$	1.46159e7	0.897090
$768$	−1.48793e7	−0.910292
$769$	−1.99500e7	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$769$	−1.99500e7	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$770$	2.00156e7	1.21659
$771$	−6.03287e6	−0.365501
$772$	−2.44597e7	−1.47709
$773$	8.18346e6	0.492593	0.246296	−	0.969195i	$-0.420786\pi$
$773$	8.18346e6	0.492593	0.246296	+	0.969195i	$0.420786\pi$
$774$	−9.20749e6	−0.552445
$775$	−1.95732e7	−1.17060
$776$	1.64424e7	0.980189
$777$	791729.	0.0470461
$778$	−7.58878e6	−0.449493
$779$	2.90988e6	0.171803
$780$	−3.34179e7	−1.96672
$781$	2.66973e7	1.56617
$782$	5.93318e7	3.46953
$783$	−8.68875e6	−0.506469
$784$	5.84891e6	0.339848
$785$	3.34899e6	0.193972
$786$	−1.73817e7	−1.00354
$787$	−2.35289e7	−1.35414	−0.677071	−	0.735918i	$-0.736751\pi$
$787$	−2.35289e7	−1.35414	−0.677071	+	0.735918i	$0.736751\pi$
$788$	3.24715e7	1.86289
$789$	2.54559e6	0.145578
$790$	1.61161e7	0.918740
$791$	5.71817e6	0.324949
$792$	1.61473e7	0.914720
$793$	−1.06863e7	−0.603455
$794$	−369230.	−0.0207848
$795$	−1.87352e7	−1.05133
$796$	−1.55688e7	−0.870910
$797$	715702.	0.0399104	0.0199552	−	0.999801i	$-0.493648\pi$
$797$	715702.	0.0399104	0.0199552	+	0.999801i	$0.493648\pi$
$798$	2.14270e6	0.119111
$799$	1.41490e7	0.784077
$800$	−2.34029e7	−1.29284
$801$	3.19876e6	0.176157
$802$	8.05423e6	0.442169
$803$	2.03007e7	1.11102
$804$	−4.06317e7	−2.21679
$805$	1.13325e7	0.616360
$806$	4.02927e7	2.18468
$807$	−2.15882e7	−1.16689
$808$	−6.71182e7	−3.61669
$809$	2.41661e7	1.29818	0.649091	−	0.760711i	$-0.275149\pi$
$809$	2.41661e7	1.29818	0.649091	+	0.760711i	$0.275149\pi$
$810$	−3.00196e7	−1.60765
$811$	4.44605e6	0.237368	0.118684	−	0.992932i	$-0.462132\pi$
$811$	4.44605e6	0.237368	0.118684	+	0.992932i	$0.462132\pi$
$812$	7.97554e6	0.424492
$813$	−2.41060e7	−1.27908
$814$	−6.73852e6	−0.356454
$815$	−3.34887e7	−1.76606
$816$	5.86408e7	3.08301
$817$	4.29086e6	0.224900
$818$	−5.00115e7	−2.61329
$819$	−1.40004e6	−0.0729344
$820$	5.23592e7	2.71931
$821$	−1.95894e6	−0.101429	−0.0507146	−	0.998713i	$-0.516150\pi$
$821$	−1.95894e6	−0.101429	−0.0507146	+	0.998713i	$0.516150\pi$
$822$	−2.61791e6	−0.135137
$823$	1.67108e6	0.0859997	0.0429998	−	0.999075i	$-0.486309\pi$
$823$	1.67108e6	0.0859997	0.0429998	+	0.999075i	$0.486309\pi$
$824$	1.12154e7	0.575437
$825$	1.60365e7	0.820306
$826$	−1.68626e7	−0.859951
$827$	−2.27600e7	−1.15720	−0.578599	−	0.815612i	$-0.696400\pi$
$827$	−2.27600e7	−1.15720	−0.578599	+	0.815612i	$0.696400\pi$
$828$	1.56494e7	0.793270
$829$	−3.84847e7	−1.94492	−0.972460	−	0.233069i	$-0.925123\pi$
$829$	−3.84847e7	−1.94492	−0.972460	+	0.233069i	$0.925123\pi$
$830$	−3.06800e7	−1.54582
$831$	8.58304e6	0.431160
$832$	1.36173e7	0.681999
$833$	4.32542e6	0.215981
$834$	−3.30145e7	−1.64357
$835$	−1.66211e7	−0.824983
$836$	−1.28809e7	−0.637426
$837$	3.57700e7	1.76484
$838$	−339352.	−0.0166932
$839$	−7.38960e6	−0.362423	−0.181212	−	0.983444i	$-0.558002\pi$
$839$	−7.38960e6	−0.362423	−0.181212	+	0.983444i	$0.558002\pi$
$840$	2.25235e7	1.10138
$841$	−1.60381e7	−0.781920
$842$	3.16169e7	1.53688
$843$	1.95416e7	0.947090
$844$	5.05549e7	2.44291
$845$	1.28093e7	0.617140
$846$	5.28371e6	0.253812
$847$	6.07418e6	0.290924
$848$	4.65962e7	2.22516
$849$	3.57921e6	0.170419
$850$	−4.22732e7	−2.00686
$851$	−3.81521e6	−0.180590
$852$	5.14252e7	2.42704
$853$	−3.47855e6	−0.163691	−0.0818456	−	0.996645i	$-0.526081\pi$
$853$	−3.47855e6	−0.163691	−0.0818456	+	0.996645i	$0.526081\pi$
$854$	1.23290e7	0.578472
$855$	−1.48108e6	−0.0692886
$856$	5.85149e7	2.72949
$857$	−4.04135e7	−1.87964	−0.939818	−	0.341674i	$-0.889006\pi$
$857$	−4.04135e7	−1.87964	−0.939818	+	0.341674i	$0.889006\pi$
$858$	−3.30122e7	−1.53093
$859$	−2.55554e7	−1.18168	−0.590841	−	0.806788i	$-0.701204\pi$
$859$	−2.55554e7	−1.18168	−0.590841	+	0.806788i	$0.701204\pi$
$860$	7.72079e7	3.55972
$861$	−6.07716e6	−0.279379
$862$	4.85994e7	2.22773
$863$	−1.67134e7	−0.763902	−0.381951	−	0.924182i	$-0.624748\pi$
$863$	−1.67134e7	−0.763902	−0.381951	+	0.924182i	$0.624748\pi$
$864$	4.27688e7	1.94914
$865$	3.94606e7	1.79318
$866$	6.95154e7	3.14983
$867$	2.43938e7	1.10213
$868$	−3.28339e7	−1.47919
$869$	1.12448e7	0.505130
$870$	2.16234e7	0.968560
$871$	−1.75167e7	−0.782361
$872$	6.46144e6	0.287765
$873$	2.25803e6	0.100275
$874$	−1.03253e7	−0.457219
$875$	3.14995e6	0.139086
$876$	3.91040e7	1.72171
$877$	3.77285e7	1.65642	0.828210	−	0.560418i	$-0.189359\pi$
$877$	3.77285e7	1.65642	0.828210	+	0.560418i	$0.189359\pi$
$878$	7.24055e6	0.316982
$879$	3.12793e7	1.36548
$880$	−9.53289e7	−4.14971
$881$	−3.70411e7	−1.60784	−0.803922	−	0.594735i	$-0.797257\pi$
$881$	−3.70411e7	−1.60784	−0.803922	+	0.594735i	$0.797257\pi$
$882$	1.61526e6	0.0699149
$883$	−8.44444e6	−0.364476	−0.182238	−	0.983254i	$-0.558334\pi$
$883$	−8.44444e6	−0.364476	−0.182238	+	0.983254i	$0.558334\pi$
$884$	6.14647e7	2.64542
$885$	−3.22913e7	−1.38588
$886$	6.07647e7	2.60056
$887$	2.28816e7	0.976512	0.488256	−	0.872700i	$-0.337633\pi$
$887$	2.28816e7	0.976512	0.488256	+	0.872700i	$0.337633\pi$
$888$	−7.58284e6	−0.322700
$889$	−1.03624e7	−0.439751
$890$	−3.79756e7	−1.60705
$891$	−2.09458e7	−0.883900
$892$	1.70047e7	0.715576
$893$	−2.46230e6	−0.103327
$894$	3.24606e7	1.35835
$895$	2.19656e7	0.916610
$896$	613179.	0.0255163
$897$	−1.86909e7	−0.775618
$898$	−2.89274e7	−1.19707
$899$	−1.84148e7	−0.759922
$900$	−1.11500e7	−0.458847
$901$	3.44591e7	1.41414
$902$	5.17236e7	2.11676
$903$	−8.96127e6	−0.365721
$904$	−5.47661e7	−2.22890
$905$	3.47801e7	1.41159
$906$	−1.64442e7	−0.665569
$907$	1.37313e7	0.554235	0.277117	−	0.960836i	$-0.410621\pi$
$907$	1.37313e7	0.554235	0.277117	+	0.960836i	$0.410621\pi$
$908$	−8.93394e7	−3.59607
$909$	−9.21734e6	−0.369995
$910$	1.66213e7	0.665368
$911$	−1.04574e7	−0.417474	−0.208737	−	0.977972i	$-0.566935\pi$
$911$	−1.04574e7	−0.417474	−0.208737	+	0.977972i	$0.566935\pi$
$912$	−1.02051e7	−0.406283
$913$	−2.14066e7	−0.849906
$914$	6.61990e7	2.62112
$915$	2.36096e7	0.932257
$916$	8.84175e6	0.348176
$917$	6.10625e6	0.239801
$918$	7.72542e7	3.02563
$919$	−477140.	−0.0186362	−0.00931809	−	0.999957i	$-0.502966\pi$
$919$	−477140.	−0.0186362	−0.00931809	+	0.999957i	$0.502966\pi$
$920$	−1.08537e8	−4.22775
$921$	−3.97210e7	−1.54302
$922$	−8.51383e7	−3.29836
$923$	2.21699e7	0.856562
$924$	2.69012e7	1.03655
$925$	2.71829e6	0.104458
$926$	2.51983e7	0.965704
$927$	1.54021e6	0.0588684
$928$	−2.20179e7	−0.839279
$929$	1.96605e7	0.747403	0.373701	−	0.927549i	$-0.378088\pi$
$929$	1.96605e7	0.747403	0.373701	+	0.927549i	$0.378088\pi$
$930$	−8.90198e7	−3.37504
$931$	−752738.	−0.0284623
$932$	−1.27261e8	−4.79907
$933$	−9.07519e6	−0.341312
$934$	3.32068e6	0.124554
$935$	−7.04981e7	−2.63723
$936$	1.34090e7	0.500273
$937$	1.02547e7	0.381568	0.190784	−	0.981632i	$-0.438897\pi$
$937$	1.02547e7	0.381568	0.190784	+	0.981632i	$0.438897\pi$
$938$	2.02093e7	0.749971
$939$	4.40314e7	1.62967
$940$	−4.43056e7	−1.63546
$941$	−1.03352e6	−0.0380490	−0.0190245	−	0.999819i	$-0.506056\pi$
$941$	−1.03352e6	−0.0380490	−0.0190245	+	0.999819i	$0.506056\pi$
$942$	6.37263e6	0.233987
$943$	2.92849e7	1.07242
$944$	8.03117e7	2.93325
$945$	1.47557e7	0.537501
$946$	7.62706e7	2.77096
$947$	1.31414e7	0.476176	0.238088	−	0.971244i	$-0.423479\pi$
$947$	1.31414e7	0.476176	0.238088	+	0.971244i	$0.423479\pi$
$948$	2.16602e7	0.782782
$949$	1.68581e7	0.607634
$950$	7.35665e6	0.264467
$951$	−2.26163e7	−0.810905
$952$	−4.14270e7	−1.48146
$953$	2.84796e7	1.01579	0.507893	−	0.861420i	$-0.330425\pi$
$953$	2.84796e7	1.01579	0.507893	+	0.861420i	$0.330425\pi$
$954$	1.28682e7	0.457769
$955$	−6.62403e7	−2.35025
$956$	−9.56239e7	−3.38393
$957$	1.50875e7	0.532522
$958$	2.02810e7	0.713963
$959$	919681.	0.0322917
$960$	−3.00852e7	−1.05360
$961$	4.71815e7	1.64802
$962$	−5.59578e6	−0.194950
$963$	8.03585e6	0.279233
$964$	−6.11513e7	−2.11940
$965$	2.32969e7	0.805342
$966$	2.15640e7	0.743508
$967$	4.78545e7	1.64572	0.822862	−	0.568241i	$-0.192376\pi$
$967$	4.78545e7	1.64572	0.822862	+	0.568241i	$0.192376\pi$
$968$	−5.81759e7	−1.99551
$969$	−7.54690e6	−0.258202
$970$	−2.68073e7	−0.914796
$971$	−1.60036e7	−0.544715	−0.272358	−	0.962196i	$-0.587803\pi$
$971$	−1.60036e7	−0.544715	−0.272358	+	0.962196i	$0.587803\pi$
$972$	3.64818e7	1.23854
$973$	1.15981e7	0.392740
$974$	−6.31516e7	−2.13298
$975$	1.33170e7	0.448637
$976$	−5.87194e7	−1.97314
$977$	−3.67928e7	−1.23318	−0.616590	−	0.787285i	$-0.711486\pi$
$977$	−3.67928e7	−1.23318	−0.616590	+	0.787285i	$0.711486\pi$
$978$	−6.37240e7	−2.13037
$979$	−2.64970e7	−0.883569
$980$	−1.35445e7	−0.450502
$981$	887350.	0.0294389
$982$	−3.16932e7	−1.04879
$983$	−2.35711e7	−0.778031	−0.389015	−	0.921231i	$-0.627185\pi$
$983$	−2.35711e7	−0.778031	−0.389015	+	0.921231i	$0.627185\pi$
$984$	5.82044e7	1.91632
$985$	−3.09279e7	−1.01569
$986$	−3.97714e7	−1.30280
$987$	5.14241e6	0.168025
$988$	−1.06965e7	−0.348617
$989$	4.31829e7	1.40385
$990$	−2.63263e7	−0.853695
$991$	5.63912e7	1.82401	0.912005	−	0.410179i	$-0.134534\pi$
$991$	5.63912e7	1.82401	0.912005	+	0.410179i	$0.134534\pi$
$992$	9.06438e7	2.92455
$993$	−1.20245e7	−0.386984
$994$	−2.55778e7	−0.821101
$995$	1.48287e7	0.474838
$996$	−4.12341e7	−1.31707
$997$	3.34509e7	1.06579	0.532893	−	0.846182i	$-0.321105\pi$
$997$	3.34509e7	1.06579	0.532893	+	0.846182i	$0.321105\pi$
$998$	−1.43390e7	−0.455713
$999$	−4.96768e6	−0.157485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	959.6.a.a.1.3	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.6.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-10.4384 q^{2} +13.3623 q^{3} +76.9593 q^{4} -73.3008 q^{5} -139.480 q^{6} +49.0000 q^{7} -469.301 q^{8} -64.4491 q^{9} +O(q^{10})\)	\(q-10.4384 q^{2} +13.3623 q^{3} +76.9593 q^{4} -73.3008 q^{5} -139.480 q^{6} +49.0000 q^{7} -469.301 q^{8} -64.4491 q^{9} +765.139 q^{10} +533.867 q^{11} +1028.35 q^{12} +443.332 q^{13} -511.479 q^{14} -979.466 q^{15} +2436.03 q^{16} +1801.51 q^{17} +672.743 q^{18} -313.510 q^{19} -5641.17 q^{20} +654.752 q^{21} -5572.69 q^{22} -3155.14 q^{23} -6270.93 q^{24} +2248.00 q^{25} -4627.65 q^{26} -4108.23 q^{27} +3771.00 q^{28} +2114.96 q^{29} +10224.0 q^{30} -8706.93 q^{31} -10410.5 q^{32} +7133.69 q^{33} -18804.8 q^{34} -3591.74 q^{35} -4959.96 q^{36} +1209.20 q^{37} +3272.53 q^{38} +5923.93 q^{39} +34400.1 q^{40} -9281.62 q^{41} -6834.54 q^{42} -13686.5 q^{43} +41086.0 q^{44} +4724.17 q^{45} +32934.5 q^{46} +7853.98 q^{47} +32551.0 q^{48} +2401.00 q^{49} -23465.4 q^{50} +24072.3 q^{51} +34118.5 q^{52} +19127.9 q^{53} +42883.1 q^{54} -39132.9 q^{55} -22995.7 q^{56} -4189.21 q^{57} -22076.7 q^{58} +32968.2 q^{59} -75379.0 q^{60} -24104.6 q^{61} +90886.0 q^{62} -3158.01 q^{63} +30715.9 q^{64} -32496.6 q^{65} -74464.0 q^{66} -39511.5 q^{67} +138643. q^{68} -42160.0 q^{69} +37491.8 q^{70} +50007.4 q^{71} +30246.0 q^{72} +38025.8 q^{73} -12622.1 q^{74} +30038.5 q^{75} -24127.5 q^{76} +26159.5 q^{77} -61836.1 q^{78} +21063.0 q^{79} -178563. q^{80} -39234.2 q^{81} +96884.9 q^{82} -40097.3 q^{83} +50389.3 q^{84} -132052. q^{85} +142865. q^{86} +28260.8 q^{87} -250544. q^{88} -49632.3 q^{89} -49312.6 q^{90} +21723.3 q^{91} -242818. q^{92} -116345. q^{93} -81982.6 q^{94} +22980.5 q^{95} -139109. q^{96} -35035.9 q^{97} -25062.5 q^{98} -34407.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 20 q^{2} - 49 q^{3} + 976 q^{4} - 169 q^{5} - 273 q^{6} + 3626 q^{7} - 747 q^{8} + 4275 q^{9}+O(q^{10}) \) 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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