LMFDB - Embedded newform 961.6.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,6,Mod(1,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("961.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	961.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:	$154.128850840$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 274 x^{10} + 374 x^{9} + 27209 x^{8} - 20820 x^{7} - 1191400 x^{6} + \cdots + 377955072 $ x^12 - 2x^11 - 274x^10 + 374x^9 + 27209x^8 - 20820x^7 - 1191400x^6 + 294768x^5 + 22692928x^4 + 223040x^3 - 171229056x^2 - 28454144*x + 377955072
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.80839$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80839 q^{2} +3.52764 q^{3} -24.1129 q^{4} +84.9339 q^{5} +9.90701 q^{6} -175.554 q^{7} -157.587 q^{8} -230.556 q^{9} +O(q^{10})$	\(q+2.80839 q^{2} +3.52764 q^{3} -24.1129 q^{4} +84.9339 q^{5} +9.90701 q^{6} -175.554 q^{7} -157.587 q^{8} -230.556 q^{9} +238.528 q^{10} -97.6247 q^{11} -85.0617 q^{12} -374.388 q^{13} -493.025 q^{14} +299.616 q^{15} +329.047 q^{16} -552.994 q^{17} -647.491 q^{18} -400.152 q^{19} -2048.00 q^{20} -619.292 q^{21} -274.169 q^{22} -326.731 q^{23} -555.911 q^{24} +4088.77 q^{25} -1051.43 q^{26} -1670.53 q^{27} +4233.12 q^{28} -8220.01 q^{29} +841.441 q^{30} +5966.88 q^{32} -344.385 q^{33} -1553.02 q^{34} -14910.5 q^{35} +5559.37 q^{36} -726.307 q^{37} -1123.78 q^{38} -1320.71 q^{39} -13384.5 q^{40} +17045.4 q^{41} -1739.22 q^{42} +13370.6 q^{43} +2354.02 q^{44} -19582.0 q^{45} -917.589 q^{46} -13881.8 q^{47} +1160.76 q^{48} +14012.2 q^{49} +11482.9 q^{50} -1950.76 q^{51} +9027.59 q^{52} +25915.1 q^{53} -4691.52 q^{54} -8291.65 q^{55} +27665.1 q^{56} -1411.59 q^{57} -23085.0 q^{58} +15976.5 q^{59} -7224.62 q^{60} +4952.51 q^{61} +40475.0 q^{63} +6227.87 q^{64} -31798.3 q^{65} -967.169 q^{66} -40008.0 q^{67} +13334.3 q^{68} -1152.59 q^{69} -41874.5 q^{70} -32442.3 q^{71} +36332.6 q^{72} -85493.5 q^{73} -2039.76 q^{74} +14423.7 q^{75} +9648.83 q^{76} +17138.4 q^{77} -3709.07 q^{78} +108446. q^{79} +27947.2 q^{80} +50132.0 q^{81} +47870.3 q^{82} +104197. q^{83} +14932.9 q^{84} -46967.9 q^{85} +37550.0 q^{86} -28997.2 q^{87} +15384.4 q^{88} +106477. q^{89} -54994.0 q^{90} +65725.4 q^{91} +7878.44 q^{92} -38985.5 q^{94} -33986.4 q^{95} +21049.0 q^{96} +18007.7 q^{97} +39351.9 q^{98} +22507.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 10 q^{3} + 168 q^{4} - 28 q^{5} + 72 q^{6} + 134 q^{7} - 402 q^{8} + 668 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 10 * q^3 + 168 * q^4 - 28 * q^5 + 72 * q^6 + 134 * q^7 - 402 * q^8 + 668 * q^9	\( 12 q - 2 q^{2} + 10 q^{3} + 168 q^{4} - 28 q^{5} + 72 q^{6} + 134 q^{7} - 402 q^{8} + 668 q^{9} + 746 q^{10} + 394 q^{11} - 646 q^{12} - 664 q^{13} - 432 q^{14} + 798 q^{15} + 2020 q^{16} + 432 q^{17} - 1208 q^{18} + 694 q^{19} - 5692 q^{20} - 1712 q^{21} + 616 q^{22} + 960 q^{23} + 8432 q^{24} - 88 q^{25} + 10798 q^{26} + 1642 q^{27} + 6570 q^{28} + 10748 q^{29} - 10380 q^{30} - 12206 q^{32} - 25572 q^{33} + 16026 q^{34} + 12586 q^{35} + 3252 q^{36} - 2116 q^{37} + 14516 q^{38} + 9558 q^{39} + 43746 q^{40} - 12416 q^{41} + 32978 q^{42} + 38354 q^{43} + 28734 q^{44} - 21396 q^{45} + 22116 q^{46} + 40128 q^{47} - 32098 q^{48} - 8876 q^{49} - 14432 q^{50} - 29346 q^{51} - 64628 q^{52} + 14152 q^{53} - 18436 q^{54} - 2202 q^{55} - 13296 q^{56} - 26440 q^{57} + 20612 q^{58} + 66074 q^{59} + 126478 q^{60} + 46964 q^{61} + 43328 q^{63} - 10936 q^{64} + 103544 q^{65} + 156910 q^{66} - 8434 q^{67} - 116388 q^{68} + 3768 q^{69} + 120860 q^{70} + 46854 q^{71} - 177728 q^{72} + 105776 q^{73} + 241354 q^{74} + 2800 q^{75} - 208806 q^{76} + 168460 q^{77} + 60212 q^{78} - 42030 q^{79} - 204912 q^{80} - 63960 q^{81} - 54870 q^{82} + 7174 q^{83} - 266196 q^{84} + 158072 q^{85} - 41552 q^{86} + 13808 q^{87} - 232624 q^{88} + 142500 q^{89} + 169776 q^{90} + 43450 q^{91} + 141468 q^{92} + 68500 q^{94} - 40430 q^{95} + 317764 q^{96} + 82692 q^{97} + 192032 q^{98} - 27496 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 10 * q^3 + 168 * q^4 - 28 * q^5 + 72 * q^6 + 134 * q^7 - 402 * q^8 + 668 * q^9 + 746 * q^10 + 394 * q^11 - 646 * q^12 - 664 * q^13 - 432 * q^14 + 798 * q^15 + 2020 * q^16 + 432 * q^17 - 1208 * q^18 + 694 * q^19 - 5692 * q^20 - 1712 * q^21 + 616 * q^22 + 960 * q^23 + 8432 * q^24 - 88 * q^25 + 10798 * q^26 + 1642 * q^27 + 6570 * q^28 + 10748 * q^29 - 10380 * q^30 - 12206 * q^32 - 25572 * q^33 + 16026 * q^34 + 12586 * q^35 + 3252 * q^36 - 2116 * q^37 + 14516 * q^38 + 9558 * q^39 + 43746 * q^40 - 12416 * q^41 + 32978 * q^42 + 38354 * q^43 + 28734 * q^44 - 21396 * q^45 + 22116 * q^46 + 40128 * q^47 - 32098 * q^48 - 8876 * q^49 - 14432 * q^50 - 29346 * q^51 - 64628 * q^52 + 14152 * q^53 - 18436 * q^54 - 2202 * q^55 - 13296 * q^56 - 26440 * q^57 + 20612 * q^58 + 66074 * q^59 + 126478 * q^60 + 46964 * q^61 + 43328 * q^63 - 10936 * q^64 + 103544 * q^65 + 156910 * q^66 - 8434 * q^67 - 116388 * q^68 + 3768 * q^69 + 120860 * q^70 + 46854 * q^71 - 177728 * q^72 + 105776 * q^73 + 241354 * q^74 + 2800 * q^75 - 208806 * q^76 + 168460 * q^77 + 60212 * q^78 - 42030 * q^79 - 204912 * q^80 - 63960 * q^81 - 54870 * q^82 + 7174 * q^83 - 266196 * q^84 + 158072 * q^85 - 41552 * q^86 + 13808 * q^87 - 232624 * q^88 + 142500 * q^89 + 169776 * q^90 + 43450 * q^91 + 141468 * q^92 + 68500 * q^94 - 40430 * q^95 + 317764 * q^96 + 82692 * q^97 + 192032 * q^98 - 27496 * 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 $

$2$	2.80839	0.496459	0.248229	−	0.968701i	$-0.420151\pi$
$2$	2.80839	0.496459	0.248229	+	0.968701i	$0.420151\pi$
$3$	3.52764	0.226298	0.113149	−	0.993578i	$-0.463906\pi$
$3$	3.52764	0.226298	0.113149	+	0.993578i	$0.463906\pi$
$4$	−24.1129	−0.753529
$5$	84.9339	1.51934	0.759672	−	0.650307i	$-0.225360\pi$
$5$	84.9339	1.51934	0.759672	+	0.650307i	$0.225360\pi$
$6$	9.90701	0.112348
$7$	−175.554	−1.35415	−0.677074	−	0.735915i	$-0.736752\pi$
$7$	−175.554	−1.35415	−0.677074	+	0.735915i	$0.736752\pi$
$8$	−157.587	−0.870555
$9$	−230.556	−0.948789
$10$	238.528	0.754291
$11$	−97.6247	−0.243264	−0.121632	−	0.992575i	$-0.538813\pi$
$11$	−97.6247	−0.243264	−0.121632	+	0.992575i	$0.538813\pi$
$12$	−85.0617	−0.170522
$13$	−374.388	−0.614418	−0.307209	−	0.951642i	$-0.599395\pi$
$13$	−374.388	−0.614418	−0.307209	+	0.951642i	$0.599395\pi$
$14$	−493.025	−0.672278
$15$	299.616	0.343825
$16$	329.047	0.321335
$17$	−552.994	−0.464085	−0.232043	−	0.972706i	$-0.574541\pi$
$17$	−552.994	−0.464085	−0.232043	+	0.972706i	$0.574541\pi$
$18$	−647.491	−0.471035
$19$	−400.152	−0.254297	−0.127148	−	0.991884i	$-0.540582\pi$
$19$	−400.152	−0.254297	−0.127148	+	0.991884i	$0.540582\pi$
$20$	−2048.00	−1.14487
$21$	−619.292	−0.306441
$22$	−274.169	−0.120771
$23$	−326.731	−0.128787	−0.0643933	−	0.997925i	$-0.520511\pi$
$23$	−326.731	−0.128787	−0.0643933	+	0.997925i	$0.520511\pi$
$24$	−555.911	−0.197005
$25$	4088.77	1.30841
$26$	−1051.43	−0.305033
$27$	−1670.53	−0.441008
$28$	4233.12	1.02039
$29$	−8220.01	−1.81500	−0.907502	−	0.420049i	$-0.862013\pi$
$29$	−8220.01	−1.81500	−0.907502	+	0.420049i	$0.862013\pi$
$30$	841.441	0.170695
$31$	0	0
$31$	0	0
$32$	5966.88	1.03008
$33$	−344.385	−0.0550503
$34$	−1553.02	−0.230399
$35$	−14910.5	−2.05742
$36$	5559.37	0.714940
$37$	−726.307	−0.0872199	−0.0436100	−	0.999049i	$-0.513886\pi$
$37$	−726.307	−0.0872199	−0.0436100	+	0.999049i	$0.513886\pi$
$38$	−1123.78	−0.126248
$39$	−1320.71	−0.139042
$40$	−13384.5	−1.32267
$41$	17045.4	1.58361	0.791806	−	0.610773i	$-0.209141\pi$
$41$	17045.4	1.58361	0.791806	+	0.610773i	$0.209141\pi$
$42$	−1739.22	−0.152135
$43$	13370.6	1.10276	0.551379	−	0.834255i	$-0.314102\pi$
$43$	13370.6	1.10276	0.551379	+	0.834255i	$0.314102\pi$
$44$	2354.02	0.183307
$45$	−19582.0	−1.44154
$46$	−917.589	−0.0639372
$47$	−13881.8	−0.916644	−0.458322	−	0.888786i	$-0.651549\pi$
$47$	−13881.8	−0.916644	−0.458322	+	0.888786i	$0.651549\pi$
$48$	1160.76	0.0727174
$49$	14012.2	0.833715
$50$	11482.9	0.649569
$51$	−1950.76	−0.105022
$52$	9027.59	0.462982
$53$	25915.1	1.26725	0.633627	−	0.773639i	$-0.281565\pi$
$53$	25915.1	1.26725	0.633627	+	0.773639i	$0.281565\pi$
$54$	−4691.52	−0.218942
$55$	−8291.65	−0.369602
$56$	27665.1	1.17886
$57$	−1411.59	−0.0575469
$58$	−23085.0	−0.901074
$59$	15976.5	0.597519	0.298760	−	0.954328i	$-0.403427\pi$
$59$	15976.5	0.597519	0.298760	+	0.954328i	$0.403427\pi$
$60$	−7224.62	−0.259082
$61$	4952.51	0.170412	0.0852061	−	0.996363i	$-0.472845\pi$
$61$	4952.51	0.170412	0.0852061	+	0.996363i	$0.472845\pi$
$62$	0	0
$63$	40475.0	1.28480
$64$	6227.87	0.190059
$65$	−31798.3	−0.933512
$66$	−967.169	−0.0273302
$67$	−40008.0	−1.08883	−0.544414	−	0.838816i	$-0.683248\pi$
$67$	−40008.0	−1.08883	−0.544414	+	0.838816i	$0.683248\pi$
$68$	13334.3	0.349702
$69$	−1152.59	−0.0291442
$70$	−41874.5	−1.02142
$71$	−32442.3	−0.763776	−0.381888	−	0.924209i	$-0.624726\pi$
$71$	−32442.3	−0.763776	−0.381888	+	0.924209i	$0.624726\pi$
$72$	36332.6	0.825973
$73$	−85493.5	−1.87770	−0.938849	−	0.344328i	$-0.888107\pi$
$73$	−85493.5	−1.87770	−0.938849	+	0.344328i	$0.888107\pi$
$74$	−2039.76	−0.0433011
$75$	14423.7	0.296090
$76$	9648.83	0.191620
$77$	17138.4	0.329416
$78$	−3709.07	−0.0690284
$79$	108446.	1.95499	0.977497	−	0.210949i	$-0.0676552\pi$
$79$	108446.	1.95499	0.977497	+	0.210949i	$0.0676552\pi$
$80$	27947.2	0.488218
$81$	50132.0	0.848990
$82$	47870.3	0.786197
$83$	104197.	1.66020	0.830101	−	0.557613i	$-0.188283\pi$
$83$	104197.	1.66020	0.830101	+	0.557613i	$0.188283\pi$
$84$	14932.9	0.230912
$85$	−46967.9	−0.705105
$86$	37550.0	0.547474
$87$	−28997.2	−0.410732
$88$	15384.4	0.211775
$89$	106477.	1.42489	0.712444	−	0.701729i	$-0.247588\pi$
$89$	106477.	1.42489	0.712444	+	0.701729i	$0.247588\pi$
$90$	−54994.0	−0.715663
$91$	65725.4	0.832012
$92$	7878.44	0.0970444
$93$	0	0
$94$	−38985.5	−0.455076
$95$	−33986.4	−0.386364
$96$	21049.0	0.233106
$97$	18007.7	0.194325	0.0971625	−	0.995269i	$-0.469023\pi$
$97$	18007.7	0.194325	0.0971625	+	0.995269i	$0.469023\pi$
$98$	39351.9	0.413905
$99$	22507.9	0.230806
$100$	−98592.1	−0.985921
$101$	5879.34	0.0573489	0.0286745	−	0.999589i	$-0.490871\pi$
$101$	5879.34	0.0573489	0.0286745	+	0.999589i	$0.490871\pi$
$102$	−5478.51	−0.0521389
$103$	−143716.	−1.33479	−0.667394	−	0.744705i	$-0.732590\pi$
$103$	−143716.	−1.33479	−0.667394	+	0.744705i	$0.732590\pi$
$104$	58998.8	0.534884
$105$	−52598.9	−0.465589
$106$	72779.9	0.629139
$107$	120100.	1.01411	0.507054	−	0.861915i	$-0.330735\pi$
$107$	120100.	1.01411	0.507054	+	0.861915i	$0.330735\pi$
$108$	40281.5	0.332312
$109$	189700.	1.52933	0.764664	−	0.644429i	$-0.222905\pi$
$109$	189700.	1.52933	0.764664	+	0.644429i	$0.222905\pi$
$110$	−23286.2	−0.183492
$111$	−2562.15	−0.0197377
$112$	−57765.5	−0.435134
$113$	−5625.43	−0.0414438	−0.0207219	−	0.999785i	$-0.506596\pi$
$113$	−5625.43	−0.0414438	−0.0207219	+	0.999785i	$0.506596\pi$
$114$	−3964.31	−0.0285697
$115$	−27750.5	−0.195671
$116$	198208.	1.36766
$117$	86317.4	0.582953
$118$	44868.3	0.296644
$119$	97080.3	0.628440
$120$	−47215.7	−0.299318
$121$	−151520.	−0.940823
$122$	13908.6	0.0846026
$123$	60130.2	0.358368
$124$	0	0
$125$	81856.5	0.468574
$126$	113670.	0.637850
$127$	−195502.	−1.07558	−0.537788	−	0.843080i	$-0.680740\pi$
$127$	−195502.	−1.07558	−0.537788	+	0.843080i	$0.680740\pi$
$128$	−173450.	−0.935727
$129$	47166.7	0.249552
$130$	−89302.0	−0.463450
$131$	35750.9	0.182015	0.0910077	−	0.995850i	$-0.470991\pi$
$131$	35750.9	0.182015	0.0910077	+	0.995850i	$0.470991\pi$
$132$	8304.13	0.0414820
$133$	70248.3	0.344355
$134$	−112358.	−0.540558
$135$	−141885.	−0.670042
$136$	87144.7	0.404012
$137$	20452.4	0.0930984	0.0465492	−	0.998916i	$-0.485178\pi$
$137$	20452.4	0.0930984	0.0465492	+	0.998916i	$0.485178\pi$
$138$	−3236.92	−0.0144689
$139$	−247955.	−1.08852	−0.544258	−	0.838918i	$-0.683189\pi$
$139$	−247955.	−1.08852	−0.544258	+	0.838918i	$0.683189\pi$
$140$	359536.	1.55032
$141$	−48970.0	−0.207435
$142$	−91110.8	−0.379183
$143$	36549.6	0.149466
$144$	−75863.6	−0.304879
$145$	−698158.	−2.75761
$146$	−240099.	−0.932200
$147$	49430.2	0.188668
$148$	17513.4	0.0657227
$149$	−295692.	−1.09112	−0.545561	−	0.838071i	$-0.683684\pi$
$149$	−295692.	−1.09112	−0.545561	+	0.838071i	$0.683684\pi$
$150$	40507.4	0.146996
$151$	308716.	1.10184	0.550918	−	0.834559i	$-0.314278\pi$
$151$	308716.	1.10184	0.550918	+	0.834559i	$0.314278\pi$
$152$	63058.8	0.221379
$153$	127496.	0.440319
$154$	48131.4	0.163541
$155$	0	0
$156$	31846.1	0.104772
$157$	−290256.	−0.939792	−0.469896	−	0.882722i	$-0.655709\pi$
$157$	−290256.	−0.939792	−0.469896	+	0.882722i	$0.655709\pi$
$158$	304559.	0.970574
$159$	91419.3	0.286777
$160$	506791.	1.56505
$161$	57358.9	0.174396
$162$	140790.	0.421488
$163$	460361.	1.35716	0.678578	−	0.734528i	$-0.262597\pi$
$163$	460361.	1.35716	0.678578	+	0.734528i	$0.262597\pi$
$164$	−411015.	−1.19330
$165$	−29250.0	−0.0836403
$166$	292627.	0.824222
$167$	337946.	0.937683	0.468842	−	0.883282i	$-0.344672\pi$
$167$	337946.	0.937683	0.468842	+	0.883282i	$0.344672\pi$
$168$	97592.5	0.266774
$169$	−231126.	−0.622491
$170$	−131904.	−0.350056
$171$	92257.3	0.241274
$172$	−322405.	−0.830960
$173$	−82864.8	−0.210501	−0.105251	−	0.994446i	$-0.533564\pi$
$173$	−82864.8	−0.210501	−0.105251	+	0.994446i	$0.533564\pi$
$174$	−81435.7	−0.203911
$175$	−717800.	−1.77177
$176$	−32123.1	−0.0781692
$177$	56359.4	0.135218
$178$	299029.	0.707398
$179$	−208527.	−0.486440	−0.243220	−	0.969971i	$-0.578204\pi$
$179$	−208527.	−0.486440	−0.243220	+	0.969971i	$0.578204\pi$
$180$	472179.	1.08624
$181$	−7751.48	−0.0175869	−0.00879343	−	0.999961i	$-0.502799\pi$
$181$	−7751.48	−0.0175869	−0.00879343	+	0.999961i	$0.502799\pi$
$182$	184583.	0.413060
$183$	17470.7	0.0385640
$184$	51488.6	0.112116
$185$	−61688.1	−0.132517
$186$	0	0
$187$	53985.9	0.112895
$188$	334731.	0.690718
$189$	293269.	0.597189
$190$	−95447.3	−0.191814
$191$	−128674.	−0.255216	−0.127608	−	0.991825i	$-0.540730\pi$
$191$	−128674.	−0.255216	−0.127608	+	0.991825i	$0.540730\pi$
$192$	21969.7	0.0430101
$193$	669892.	1.29453	0.647264	−	0.762266i	$-0.275913\pi$
$193$	669892.	1.29453	0.647264	+	0.762266i	$0.275913\pi$
$194$	50572.7	0.0964743
$195$	−112173.	−0.211252
$196$	−337876.	−0.628228
$197$	−869138.	−1.59560	−0.797798	−	0.602924i	$-0.794002\pi$
$197$	−869138.	−1.59560	−0.797798	+	0.602924i	$0.794002\pi$
$198$	63211.2	0.114586
$199$	807994.	1.44636	0.723179	−	0.690661i	$-0.242680\pi$
$199$	807994.	1.44636	0.723179	+	0.690661i	$0.242680\pi$
$200$	−644337.	−1.13904
$201$	−141134.	−0.246400
$202$	16511.5	0.0284714
$203$	1.44306e6	2.45778
$204$	47038.6	0.0791369
$205$	1.44774e6	2.40605
$206$	−403611.	−0.662667
$207$	75329.7	0.122191
$208$	−123191.	−0.197434
$209$	39064.7	0.0618613
$210$	−147718.	−0.231146
$211$	−772049.	−1.19382	−0.596910	−	0.802308i	$-0.703605\pi$
$211$	−772049.	−1.19382	−0.596910	+	0.802308i	$0.703605\pi$
$212$	−624889.	−0.954912
$213$	−114445.	−0.172841
$214$	337288.	0.503462
$215$	1.13562e6	1.67547
$216$	263255.	0.383921
$217$	0	0
$218$	532752.	0.759249
$219$	−301590.	−0.424920
$220$	199936.	0.278506
$221$	207034.	0.285142
$222$	−7195.52	−0.00979896
$223$	−2281.15	−0.00307179	−0.00153589	−	0.999999i	$-0.500489\pi$
$223$	−2281.15	−0.00307179	−0.00153589	+	0.999999i	$0.500489\pi$
$224$	−1.04751e6	−1.39489
$225$	−942689.	−1.24140
$226$	−15798.4	−0.0205751
$227$	248450.	0.320018	0.160009	−	0.987116i	$-0.448848\pi$
$227$	248450.	0.320018	0.160009	+	0.987116i	$0.448848\pi$
$228$	34037.6	0.0433632
$229$	1.51546e6	1.90966	0.954830	−	0.297152i	$-0.0960370\pi$
$229$	1.51546e6	1.90966	0.954830	+	0.297152i	$0.0960370\pi$
$230$	−77934.4	−0.0971426
$231$	60458.2	0.0745462
$232$	1.29537e6	1.58006
$233$	808105.	0.975165	0.487582	−	0.873077i	$-0.337879\pi$
$233$	808105.	0.975165	0.487582	+	0.873077i	$0.337879\pi$
$234$	242413.	0.289412
$235$	−1.17903e6	−1.39270
$236$	−385240.	−0.450248
$237$	382558.	0.442412
$238$	272640.	0.311994
$239$	818639.	0.927039	0.463519	−	0.886087i	$-0.346586\pi$
$239$	818639.	0.927039	0.463519	+	0.886087i	$0.346586\pi$
$240$	98587.7	0.110483
$241$	749979.	0.831777	0.415888	−	0.909416i	$-0.363471\pi$
$241$	749979.	0.831777	0.415888	+	0.909416i	$0.363471\pi$
$242$	−425529.	−0.467079
$243$	582788.	0.633132
$244$	−119419.	−0.128410
$245$	1.19011e6	1.26670
$246$	168869.	0.177915
$247$	149812.	0.156244
$248$	0	0
$249$	367570.	0.375701
$250$	229885.	0.232627
$251$	−281706.	−0.282236	−0.141118	−	0.989993i	$-0.545070\pi$
$251$	−281706.	−0.282236	−0.141118	+	0.989993i	$0.545070\pi$
$252$	−975971.	−0.968134
$253$	31897.0	0.0313292
$254$	−549046.	−0.533979
$255$	−165686.	−0.159564
$256$	−686408.	−0.654609
$257$	−968074.	−0.914273	−0.457136	−	0.889397i	$-0.651125\pi$
$257$	−968074.	−0.914273	−0.457136	+	0.889397i	$0.651125\pi$
$258$	132463.	0.123892
$259$	127506.	0.118109
$260$	766749.	0.703428
$261$	1.89517e6	1.72206
$262$	100402.	0.0903631
$263$	1.10641e6	0.986337	0.493168	−	0.869934i	$-0.335839\pi$
$263$	1.10641e6	0.986337	0.493168	+	0.869934i	$0.335839\pi$
$264$	54270.7	0.0479242
$265$	2.20107e6	1.92539
$266$	197285.	0.170958
$267$	375612.	0.322449
$268$	964709.	0.820464
$269$	2.11134e6	1.77901	0.889504	−	0.456927i	$-0.151050\pi$
$269$	2.11134e6	1.77901	0.889504	+	0.456927i	$0.151050\pi$
$270$	−398469.	−0.332648
$271$	497048.	0.411126	0.205563	−	0.978644i	$-0.434097\pi$
$271$	497048.	0.411126	0.205563	+	0.978644i	$0.434097\pi$
$272$	−181961.	−0.149127
$273$	231856.	0.188283
$274$	57438.3	0.0462195
$275$	−399165.	−0.318288
$276$	27792.3	0.0219610
$277$	1.10874e6	0.868220	0.434110	−	0.900860i	$-0.357063\pi$
$277$	1.10874e6	0.868220	0.434110	+	0.900860i	$0.357063\pi$
$278$	−696354.	−0.540404
$279$	0	0
$280$	2.34970e6	1.79109
$281$	468121.	0.353665	0.176833	−	0.984241i	$-0.443415\pi$
$281$	468121.	0.353665	0.176833	+	0.984241i	$0.443415\pi$
$282$	−137527.	−0.102983
$283$	−818274.	−0.607341	−0.303670	−	0.952777i	$-0.598212\pi$
$283$	−818274.	−0.607341	−0.303670	+	0.952777i	$0.598212\pi$
$284$	782279.	0.575527
$285$	−119892.	−0.0874335
$286$	102646.	0.0742036
$287$	−2.99240e6	−2.14444
$288$	−1.37570e6	−0.977332
$289$	−1.11406e6	−0.784625
$290$	−1.96070e6	−1.36904
$291$	63524.6	0.0439754
$292$	2.06150e6	1.41490
$293$	620660.	0.422362	0.211181	−	0.977447i	$-0.432269\pi$
$293$	620660.	0.422362	0.211181	+	0.977447i	$0.432269\pi$
$294$	138819.	0.0936659
$295$	1.35695e6	0.907837
$296$	114457.	0.0759297
$297$	163085.	0.107281
$298$	−830419.	−0.541697
$299$	122324.	0.0791288
$300$	−347798.	−0.223112
$301$	−2.34727e6	−1.49330
$302$	866997.	0.547016
$303$	20740.2	0.0129780
$304$	−131669.	−0.0817143
$305$	420636.	0.258915
$306$	358059.	0.218600
$307$	984400.	0.596109	0.298054	−	0.954549i	$-0.403662\pi$
$307$	984400.	0.596109	0.298054	+	0.954549i	$0.403662\pi$
$308$	−413257.	−0.248224
$309$	−506979.	−0.302060
$310$	0	0
$311$	994648.	0.583134	0.291567	−	0.956550i	$-0.405823\pi$
$311$	994648.	0.583134	0.291567	+	0.956550i	$0.405823\pi$
$312$	208127.	0.121043
$313$	1.90943e6	1.10165	0.550823	−	0.834622i	$-0.314314\pi$
$313$	1.90943e6	1.10165	0.550823	+	0.834622i	$0.314314\pi$
$314$	−815153.	−0.466568
$315$	3.43770e6	1.95205
$316$	−2.61495e6	−1.47314
$317$	−319654.	−0.178662	−0.0893311	−	0.996002i	$-0.528473\pi$
$317$	−319654.	−0.178662	−0.0893311	+	0.996002i	$0.528473\pi$
$318$	256741.	0.142373
$319$	802476.	0.441525
$320$	528957.	0.288766
$321$	423670.	0.229491
$322$	161087.	0.0865804
$323$	221281.	0.118015
$324$	−1.20883e6	−0.639738
$325$	−1.53079e6	−0.803908
$326$	1.29288e6	0.673772
$327$	669193.	0.346084
$328$	−2.68614e6	−1.37862
$329$	2.43701e6	1.24127
$330$	−82145.4	−0.0415239
$331$	−2.56915e6	−1.28890	−0.644450	−	0.764647i	$-0.722913\pi$
$331$	−2.56915e6	−1.28890	−0.644450	+	0.764647i	$0.722913\pi$
$332$	−2.51250e6	−1.25101
$333$	167454.	0.0827533
$334$	949085.	0.465521
$335$	−3.39803e6	−1.65431
$336$	−203776.	−0.0984701
$337$	1.08623e6	0.521013	0.260506	−	0.965472i	$-0.416110\pi$
$337$	1.08623e6	0.521013	0.260506	+	0.965472i	$0.416110\pi$
$338$	−649094.	−0.309041
$339$	−19844.5	−0.00937866
$340$	1.13253e6	0.531317
$341$	0	0
$342$	259095.	0.119783
$343$	490631.	0.225175
$344$	−2.10704e6	−0.960011
$345$	−97893.9	−0.0442800
$346$	−232717.	−0.104505
$347$	−2.17604e6	−0.970158	−0.485079	−	0.874470i	$-0.661209\pi$
$347$	−2.17604e6	−0.970158	−0.485079	+	0.874470i	$0.661209\pi$
$348$	699208.	0.309498
$349$	−1.24421e6	−0.546802	−0.273401	−	0.961900i	$-0.588149\pi$
$349$	−1.24421e6	−0.546802	−0.273401	+	0.961900i	$0.588149\pi$
$350$	−2.01586e6	−0.879612
$351$	625428.	0.270963
$352$	−582515.	−0.250582
$353$	−174718.	−0.0746279	−0.0373140	−	0.999304i	$-0.511880\pi$
$353$	−174718.	−0.0746279	−0.0373140	+	0.999304i	$0.511880\pi$
$354$	158279.	0.0671299
$355$	−2.75545e6	−1.16044
$356$	−2.56747e6	−1.07369
$357$	342464.	0.142215
$358$	−585626.	−0.241497
$359$	−644280.	−0.263839	−0.131919	−	0.991260i	$-0.542114\pi$
$359$	−644280.	−0.263839	−0.131919	+	0.991260i	$0.542114\pi$
$360$	3.08587e6	1.25494
$361$	−2.31598e6	−0.935333
$362$	−21769.2	−0.00873115
$363$	−534510.	−0.212906
$364$	−1.58483e6	−0.626945
$365$	−7.26130e6	−2.85287
$366$	49064.5	0.0191454
$367$	1.78915e6	0.693396	0.346698	−	0.937977i	$-0.387303\pi$
$367$	1.78915e6	0.693396	0.346698	+	0.937977i	$0.387303\pi$
$368$	−107510.	−0.0413836
$369$	−3.92992e6	−1.50251
$370$	−173244.	−0.0657892
$371$	−4.54951e6	−1.71605
$372$	0	0
$373$	−1.67534e6	−0.623493	−0.311746	−	0.950165i	$-0.600914\pi$
$373$	−1.67534e6	−0.623493	−0.311746	+	0.950165i	$0.600914\pi$
$374$	151614.	0.0560479
$375$	288760.	0.106037
$376$	2.18759e6	0.797989
$377$	3.07748e6	1.11517
$378$	823615.	0.296480
$379$	2.89586e6	1.03557	0.517785	−	0.855511i	$-0.326757\pi$
$379$	2.89586e6	1.03557	0.517785	+	0.855511i	$0.326757\pi$
$380$	819513.	0.291136
$381$	−689660.	−0.243401
$382$	−361368.	−0.126704
$383$	−3.13326e6	−1.09144	−0.545719	−	0.837968i	$-0.683743\pi$
$383$	−3.13326e6	−1.09144	−0.545719	+	0.837968i	$0.683743\pi$
$384$	−611869.	−0.211753
$385$	1.45563e6	0.500495
$386$	1.88132e6	0.642680
$387$	−3.08267e6	−1.04629
$388$	−434218.	−0.146429
$389$	795099.	0.266408	0.133204	−	0.991089i	$-0.457473\pi$
$389$	795099.	0.266408	0.133204	+	0.991089i	$0.457473\pi$
$390$	−315025.	−0.104878
$391$	180680.	0.0597680
$392$	−2.20815e6	−0.725794
$393$	126116.	0.0411898
$394$	−2.44088e6	−0.792148
$395$	9.21073e6	2.97031
$396$	−542732.	−0.173919
$397$	−2.03984e6	−0.649560	−0.324780	−	0.945790i	$-0.605290\pi$
$397$	−2.03984e6	−0.649560	−0.324780	+	0.945790i	$0.605290\pi$
$398$	2.26917e6	0.718056
$399$	247811.	0.0779270
$400$	1.34539e6	0.420436
$401$	2.56139e6	0.795454	0.397727	−	0.917504i	$-0.369799\pi$
$401$	2.56139e6	0.795454	0.397727	+	0.917504i	$0.369799\pi$
$402$	−396359.	−0.122327
$403$	0	0
$404$	−141768.	−0.0432141
$405$	4.25791e6	1.28991
$406$	4.05267e6	1.22019
$407$	70905.5	0.0212175
$408$	307415.	0.0914271
$409$	662466.	0.195819	0.0979095	−	0.995195i	$-0.468784\pi$
$409$	662466.	0.195819	0.0979095	+	0.995195i	$0.468784\pi$
$410$	4.06581e6	1.19450
$411$	72148.6	0.0210680
$412$	3.46541e6	1.00580
$413$	−2.80474e6	−0.809129
$414$	211555.	0.0606629
$415$	8.84988e6	2.52242
$416$	−2.23393e6	−0.632902
$417$	−874695.	−0.246329
$418$	109709.	0.0307116
$419$	4.39971e6	1.22430	0.612151	−	0.790741i	$-0.290304\pi$
$419$	4.39971e6	1.22430	0.612151	+	0.790741i	$0.290304\pi$
$420$	1.26831e6	0.350835
$421$	−3.13442e6	−0.861890	−0.430945	−	0.902378i	$-0.641820\pi$
$421$	−3.13442e6	−0.861890	−0.430945	+	0.902378i	$0.641820\pi$
$422$	−2.16822e6	−0.592682
$423$	3.20053e6	0.869702
$424$	−4.08389e6	−1.10321
$425$	−2.26106e6	−0.607212
$426$	−321406.	−0.0858085
$427$	−869433.	−0.230763
$428$	−2.89596e6	−0.764159
$429$	128934.	0.0338239
$430$	3.18926e6	0.831801
$431$	3.43679e6	0.891169	0.445585	−	0.895240i	$-0.352996\pi$
$431$	3.43679e6	0.891169	0.445585	+	0.895240i	$0.352996\pi$
$432$	−549684.	−0.141711
$433$	5.32586e6	1.36512	0.682559	−	0.730830i	$-0.260867\pi$
$433$	5.32586e6	1.36512	0.682559	+	0.730830i	$0.260867\pi$
$434$	0	0
$435$	−2.46285e6	−0.624043
$436$	−4.57422e6	−1.15239
$437$	130742.	0.0327500
$438$	−846984.	−0.210955
$439$	737296.	0.182591	0.0912957	−	0.995824i	$-0.470899\pi$
$439$	737296.	0.182591	0.0912957	+	0.995824i	$0.470899\pi$
$440$	1.30666e6	0.321759
$441$	−3.23060e6	−0.791019
$442$	581434.	0.141561
$443$	−1.50600e6	−0.364600	−0.182300	−	0.983243i	$-0.558354\pi$
$443$	−1.50600e6	−0.364600	−0.182300	+	0.983243i	$0.558354\pi$
$444$	61780.9	0.0148729
$445$	9.04350e6	2.16489
$446$	−6406.37	−0.00152502
$447$	−1.04309e6	−0.246919
$448$	−1.09333e6	−0.257369
$449$	1.64888e6	0.385986	0.192993	−	0.981200i	$-0.438180\pi$
$449$	1.64888e6	0.385986	0.192993	+	0.981200i	$0.438180\pi$
$450$	−2.64744e6	−0.616304
$451$	−1.66406e6	−0.385236
$452$	135645.	0.0312291
$453$	1.08904e6	0.249344
$454$	697745.	0.158876
$455$	5.58231e6	1.26411
$456$	222449.	0.0500977
$457$	−4.71036e6	−1.05503	−0.527514	−	0.849547i	$-0.676876\pi$
$457$	−4.71036e6	−1.05503	−0.527514	+	0.849547i	$0.676876\pi$
$458$	4.25601e6	0.948067
$459$	923795.	0.204665
$460$	669146.	0.147444
$461$	−2.24696e6	−0.492429	−0.246215	−	0.969215i	$-0.579187\pi$
$461$	−2.24696e6	−0.492429	−0.246215	+	0.969215i	$0.579187\pi$
$462$	169790.	0.0370091
$463$	2.31382e6	0.501623	0.250811	−	0.968036i	$-0.419303\pi$
$463$	2.31382e6	0.501623	0.250811	+	0.968036i	$0.419303\pi$
$464$	−2.70477e6	−0.583223
$465$	0	0
$466$	2.26948e6	0.484129
$467$	1.10058e6	0.233524	0.116762	−	0.993160i	$-0.462749\pi$
$467$	1.10058e6	0.233524	0.116762	+	0.993160i	$0.462749\pi$
$468$	−2.08136e6	−0.439272
$469$	7.02356e6	1.47443
$470$	−3.31119e6	−0.691417
$471$	−1.02392e6	−0.212673
$472$	−2.51769e6	−0.520173
$473$	−1.30530e6	−0.268262
$474$	1.07437e6	0.219639
$475$	−1.63613e6	−0.332723
$476$	−2.34089e6	−0.473548
$477$	−5.97488e6	−1.20236
$478$	2.29906e6	0.460236
$479$	3.92286e6	0.781203	0.390602	−	0.920560i	$-0.372267\pi$
$479$	3.92286e6	0.781203	0.390602	+	0.920560i	$0.372267\pi$
$480$	1.78778e6	0.354168
$481$	271921.	0.0535895
$482$	2.10624e6	0.412943
$483$	202342.	0.0394655
$484$	3.65360e6	0.708937
$485$	1.52946e6	0.295246
$486$	1.63670e6	0.314324
$487$	5.53306e6	1.05717	0.528583	−	0.848882i	$-0.322724\pi$
$487$	5.53306e6	1.05717	0.528583	+	0.848882i	$0.322724\pi$
$488$	−780452.	−0.148353
$489$	1.62399e6	0.307122
$490$	3.34231e6	0.628864
$491$	−7.29383e6	−1.36538	−0.682688	−	0.730710i	$-0.739189\pi$
$491$	−7.29383e6	−1.36538	−0.682688	+	0.730710i	$0.739189\pi$
$492$	−1.44991e6	−0.270041
$493$	4.54561e6	0.842316
$494$	420731.	0.0775689
$495$	1.91169e6	0.350674
$496$	0	0
$497$	5.69538e6	1.03426
$498$	1.03228e6	0.186520
$499$	−2.15872e6	−0.388101	−0.194051	−	0.980992i	$-0.562163\pi$
$499$	−2.15872e6	−0.388101	−0.194051	+	0.980992i	$0.562163\pi$
$500$	−1.97380e6	−0.353084
$501$	1.19215e6	0.212196
$502$	−791142.	−0.140118
$503$	−6.84043e6	−1.20549	−0.602745	−	0.797934i	$-0.705926\pi$
$503$	−6.84043e6	−1.20549	−0.602745	+	0.797934i	$0.705926\pi$
$504$	−6.37834e6	−1.11849
$505$	499356.	0.0871328
$506$	89579.4	0.0155536
$507$	−815331.	−0.140869
$508$	4.71412e6	0.810478
$509$	2.27706e6	0.389566	0.194783	−	0.980846i	$-0.437600\pi$
$509$	2.27706e6	0.389566	0.194783	+	0.980846i	$0.437600\pi$
$510$	−465311.	−0.0792170
$511$	1.50087e7	2.54268
$512$	3.62269e6	0.610741
$513$	668467.	0.112147
$514$	−2.71873e6	−0.453899
$515$	−1.22064e7	−2.02800
$516$	−1.13733e6	−0.188045
$517$	1.35521e6	0.222987
$518$	358087.	0.0586360
$519$	−292317.	−0.0476361
$520$	5.01100e6	0.812673
$521$	9.73529e6	1.57128	0.785642	−	0.618682i	$-0.212333\pi$
$521$	9.73529e6	1.57128	0.785642	+	0.618682i	$0.212333\pi$
$522$	5.32239e6	0.854929
$523$	−5.39663e6	−0.862717	−0.431359	−	0.902181i	$-0.641966\pi$
$523$	−5.39663e6	−0.862717	−0.431359	+	0.902181i	$0.641966\pi$
$524$	−862057.	−0.137154
$525$	−2.53214e6	−0.400949
$526$	3.10722e6	0.489675
$527$	0	0
$528$	−113319.	−0.0176895
$529$	−6.32959e6	−0.983414
$530$	6.18148e6	0.955879
$531$	−3.68348e6	−0.566920
$532$	−1.69389e6	−0.259482
$533$	−6.38161e6	−0.972999
$534$	1.05487e6	0.160083
$535$	1.02006e7	1.54078
$536$	6.30475e6	0.947885
$537$	−735608.	−0.110081
$538$	5.92948e6	0.883204
$539$	−1.36794e6	−0.202813
$540$	3.42126e6	0.504896
$541$	−8.32698e6	−1.22319	−0.611596	−	0.791170i	$-0.709472\pi$
$541$	−8.32698e6	−1.22319	−0.611596	+	0.791170i	$0.709472\pi$
$542$	1.39591e6	0.204107
$543$	−27344.4	−0.00397988
$544$	−3.29965e6	−0.478047
$545$	1.61120e7	2.32358
$546$	651142.	0.0934747
$547$	1.93513e6	0.276530	0.138265	−	0.990395i	$-0.455847\pi$
$547$	1.93513e6	0.276530	0.138265	+	0.990395i	$0.455847\pi$
$548$	−493166.	−0.0701523
$549$	−1.14183e6	−0.161685
$550$	−1.12101e6	−0.158017
$551$	3.28925e6	0.461549
$552$	181633.	0.0253716
$553$	−1.90381e7	−2.64735
$554$	3.11378e6	0.431036
$555$	−217613.	−0.0299884
$556$	5.97891e6	0.820229
$557$	−3.33985e6	−0.456130	−0.228065	−	0.973646i	$-0.573240\pi$
$557$	−3.33985e6	−0.456130	−0.228065	+	0.973646i	$0.573240\pi$
$558$	0	0
$559$	−5.00580e6	−0.677554
$560$	−4.90625e6	−0.661118
$561$	190443.	0.0255480
$562$	1.31467e6	0.175580
$563$	−1.30154e7	−1.73056	−0.865282	−	0.501286i	$-0.832861\pi$
$563$	−1.30154e7	−1.73056	−0.865282	+	0.501286i	$0.832861\pi$
$564$	1.18081e6	0.156308
$565$	−477789.	−0.0629674
$566$	−2.29803e6	−0.301520
$567$	−8.80088e6	−1.14966
$568$	5.11249e6	0.664908
$569$	−1.23941e7	−1.60485	−0.802423	−	0.596756i	$-0.796456\pi$
$569$	−1.23941e7	−1.60485	−0.802423	+	0.596756i	$0.796456\pi$
$570$	−336704.	−0.0434071
$571$	−2.59799e6	−0.333463	−0.166732	−	0.986002i	$-0.553321\pi$
$571$	−2.59799e6	−0.333463	−0.166732	+	0.986002i	$0.553321\pi$
$572$	−881317.	−0.112627
$573$	−453917.	−0.0577550
$574$	−8.40383e6	−1.06463
$575$	−1.33593e6	−0.168505
$576$	−1.43587e6	−0.180326
$577$	1.62056e6	0.202640	0.101320	−	0.994854i	$-0.467693\pi$
$577$	1.62056e6	0.202640	0.101320	+	0.994854i	$0.467693\pi$
$578$	−3.12871e6	−0.389534
$579$	2.36314e6	0.292950
$580$	1.68346e7	2.07794
$581$	−1.82923e7	−2.24816
$582$	178402.	0.0218320
$583$	−2.52996e6	−0.308277
$584$	1.34727e7	1.63464
$585$	7.33127e6	0.885706
$586$	1.74306e6	0.209685
$587$	−1.31134e7	−1.57080	−0.785398	−	0.618991i	$-0.787542\pi$
$587$	−1.31134e7	−1.57080	−0.785398	+	0.618991i	$0.787542\pi$
$588$	−1.19191e6	−0.142167
$589$	0	0
$590$	3.81084e6	0.450703
$591$	−3.06601e6	−0.361081
$592$	−238989.	−0.0280268
$593$	−8.92880e6	−1.04269	−0.521346	−	0.853345i	$-0.674570\pi$
$593$	−8.92880e6	−1.04269	−0.521346	+	0.853345i	$0.674570\pi$
$594$	458008.	0.0532607
$595$	8.24541e6	0.954816
$596$	7.12999e6	0.822193
$597$	2.85031e6	0.327308
$598$	343535.	0.0392842
$599$	7.93328e6	0.903412	0.451706	−	0.892167i	$-0.350816\pi$
$599$	7.93328e6	0.903412	0.451706	+	0.892167i	$0.350816\pi$
$600$	−2.27299e6	−0.257762
$601$	−2.75234e6	−0.310825	−0.155412	−	0.987850i	$-0.549671\pi$
$601$	−2.75234e6	−0.310825	−0.155412	+	0.987850i	$0.549671\pi$
$602$	−6.59205e6	−0.741360
$603$	9.22407e6	1.03307
$604$	−7.44405e6	−0.830265
$605$	−1.28692e7	−1.42943
$606$	58246.7	0.00644302
$607$	1.32163e6	0.145592	0.0727960	−	0.997347i	$-0.476808\pi$
$607$	1.32163e6	0.145592	0.0727960	+	0.997347i	$0.476808\pi$
$608$	−2.38766e6	−0.261947
$609$	5.09058e6	0.556192
$610$	1.18131e6	0.128540
$611$	5.19718e6	0.563203
$612$	−3.07430e6	−0.331793
$613$	300673.	0.0323179	0.0161589	−	0.999869i	$-0.494856\pi$
$613$	300673.	0.0323179	0.0161589	+	0.999869i	$0.494856\pi$
$614$	2.76458e6	0.295943
$615$	5.10709e6	0.544485
$616$	−2.70080e6	−0.286774
$617$	−8.91954e6	−0.943256	−0.471628	−	0.881798i	$-0.656333\pi$
$617$	−8.91954e6	−0.943256	−0.471628	+	0.881798i	$0.656333\pi$
$618$	−1.42380e6	−0.149960
$619$	1.01769e7	1.06755	0.533777	−	0.845625i	$-0.320772\pi$
$619$	1.01769e7	1.06755	0.533777	+	0.845625i	$0.320772\pi$
$620$	0	0
$621$	545815.	0.0567958
$622$	2.79336e6	0.289502
$623$	−1.86925e7	−1.92951
$624$	−434574.	−0.0446789
$625$	−5.82501e6	−0.596481
$626$	5.36242e6	0.546922
$627$	137806.	0.0139991
$628$	6.99891e6	0.708160
$629$	401643.	0.0404775
$630$	9.65442e6	0.969114
$631$	1.35733e7	1.35710	0.678550	−	0.734555i	$-0.262609\pi$
$631$	1.35733e7	1.35710	0.678550	+	0.734555i	$0.262609\pi$
$632$	−1.70897e7	−1.70193
$633$	−2.72351e6	−0.270159
$634$	−897716.	−0.0886984
$635$	−1.66047e7	−1.63417
$636$	−2.20439e6	−0.216095
$637$	−5.24602e6	−0.512249
$638$	2.25367e6	0.219199
$639$	7.47976e6	0.724662
$640$	−1.47318e7	−1.42169
$641$	−1.41650e7	−1.36167	−0.680835	−	0.732437i	$-0.738383\pi$
$641$	−1.41650e7	−1.36167	−0.680835	+	0.732437i	$0.738383\pi$
$642$	1.18983e6	0.113933
$643$	1.82858e7	1.74416	0.872081	−	0.489361i	$-0.162770\pi$
$643$	1.82858e7	1.74416	0.872081	+	0.489361i	$0.162770\pi$
$644$	−1.38309e6	−0.131412
$645$	4.00605e6	0.379156
$646$	621445.	0.0585898
$647$	−1.25091e7	−1.17480	−0.587401	−	0.809296i	$-0.699849\pi$
$647$	−1.25091e7	−1.17480	−0.587401	+	0.809296i	$0.699849\pi$
$648$	−7.90016e6	−0.739092
$649$	−1.55970e6	−0.145355
$650$	−4.29905e6	−0.399107
$651$	0	0
$652$	−1.11007e7	−1.02266
$653$	1.51626e7	1.39153	0.695763	−	0.718272i	$-0.255066\pi$
$653$	1.51626e7	1.39153	0.695763	+	0.718272i	$0.255066\pi$
$654$	1.87936e6	0.171817
$655$	3.03646e6	0.276544
$656$	5.60874e6	0.508869
$657$	1.97110e7	1.78154
$658$	6.84407e6	0.616240
$659$	5.20858e6	0.467204	0.233602	−	0.972332i	$-0.424949\pi$
$659$	5.20858e6	0.467204	0.233602	+	0.972332i	$0.424949\pi$
$660$	705302.	0.0630253
$661$	−1.60411e7	−1.42801	−0.714003	−	0.700142i	$-0.753120\pi$
$661$	−1.60411e7	−1.42801	−0.714003	+	0.700142i	$0.753120\pi$
$662$	−7.21518e6	−0.639885
$663$	730343.	0.0645272
$664$	−1.64202e7	−1.44530
$665$	5.96646e6	0.523194
$666$	470277.	0.0410836
$667$	2.68573e6	0.233748
$668$	−8.14886e6	−0.706571
$669$	−8047.07	−0.000695141 0
$670$	−9.54302e6	−0.821294
$671$	−483487.	−0.0414552
$672$	−3.69524e6	−0.315660
$673$	−1.29875e6	−0.110532	−0.0552660	−	0.998472i	$-0.517601\pi$
$673$	−1.29875e6	−0.110532	−0.0552660	+	0.998472i	$0.517601\pi$
$674$	3.05057e6	0.258661
$675$	−6.83043e6	−0.577017
$676$	5.57313e6	0.469065
$677$	−1.14169e7	−0.957363	−0.478681	−	0.877989i	$-0.658885\pi$
$677$	−1.14169e7	−0.957363	−0.478681	+	0.877989i	$0.658885\pi$
$678$	−55731.1	−0.00465611
$679$	−3.16132e6	−0.263145
$680$	7.40154e6	0.613832
$681$	876442.	0.0724194
$682$	0	0
$683$	−1.65959e7	−1.36129	−0.680644	−	0.732614i	$-0.738300\pi$
$683$	−1.65959e7	−1.36129	−0.680644	+	0.732614i	$0.738300\pi$
$684$	−2.22459e6	−0.181807
$685$	1.73710e6	0.141448
$686$	1.37789e6	0.111790
$687$	5.34600e6	0.432153
$688$	4.39956e6	0.354354
$689$	−9.70232e6	−0.778623
$690$	−274925.	−0.0219832
$691$	9.89988e6	0.788742	0.394371	−	0.918951i	$-0.370963\pi$
$691$	9.89988e6	0.788742	0.394371	+	0.918951i	$0.370963\pi$
$692$	1.99811e6	0.158619
$693$	−3.95136e6	−0.312546
$694$	−6.11117e6	−0.481643
$695$	−2.10597e7	−1.65383
$696$	4.56959e6	0.357565
$697$	−9.42602e6	−0.734931
$698$	−3.49423e6	−0.271465
$699$	2.85070e6	0.220678
$700$	1.73082e7	1.33508
$701$	4.89525e6	0.376253	0.188127	−	0.982145i	$-0.439758\pi$
$701$	4.89525e6	0.376253	0.188127	+	0.982145i	$0.439758\pi$
$702$	1.75645e6	0.134522
$703$	290633.	0.0221797
$704$	−607994.	−0.0462347
$705$	−4.15921e6	−0.315165
$706$	−490678.	−0.0370497
$707$	−1.03214e6	−0.0776589
$708$	−1.35899e6	−0.101890
$709$	9.90219e6	0.739803	0.369901	−	0.929071i	$-0.379391\pi$
$709$	9.90219e6	0.739803	0.369901	+	0.929071i	$0.379391\pi$
$710$	−7.73839e6	−0.576109
$711$	−2.50028e7	−1.85488
$712$	−1.67794e7	−1.24044
$713$	0	0
$714$	961775.	0.0706038
$715$	3.10430e6	0.227090
$716$	5.02819e6	0.366547
$717$	2.88787e6	0.209787
$718$	−1.80939e6	−0.130985
$719$	7.45761e6	0.537994	0.268997	−	0.963141i	$-0.413308\pi$
$719$	7.45761e6	0.537994	0.268997	+	0.963141i	$0.413308\pi$
$720$	−6.44339e6	−0.463216
$721$	2.52299e7	1.80750
$722$	−6.50418e6	−0.464354
$723$	2.64566e6	0.188230
$724$	186911.	0.0132522
$725$	−3.36097e7	−2.37476
$726$	−1.50111e6	−0.105699
$727$	2.65813e7	1.86526	0.932631	−	0.360831i	$-0.117507\pi$
$727$	2.65813e7	1.86526	0.932631	+	0.360831i	$0.117507\pi$
$728$	−1.03575e7	−0.724312
$729$	−1.01262e7	−0.705713
$730$	−2.03926e7	−1.41633
$731$	−7.39387e6	−0.511774
$732$	−421269.	−0.0290591
$733$	1.83057e7	1.25842	0.629210	−	0.777236i	$-0.283379\pi$
$733$	1.83057e7	1.25842	0.629210	+	0.777236i	$0.283379\pi$
$734$	5.02463e6	0.344242
$735$	4.19830e6	0.286652
$736$	−1.94956e6	−0.132661
$737$	3.90577e6	0.264873
$738$	−1.10368e7	−0.745935
$739$	1.43079e7	0.963748	0.481874	−	0.876240i	$-0.339956\pi$
$739$	1.43079e7	0.963748	0.481874	+	0.876240i	$0.339956\pi$
$740$	1.48748e6	0.0998554
$741$	528483.	0.0353578
$742$	−1.27768e7	−0.851947
$743$	2.53840e7	1.68689	0.843446	−	0.537213i	$-0.180523\pi$
$743$	2.53840e7	1.68689	0.843446	+	0.537213i	$0.180523\pi$
$744$	0	0
$745$	−2.51143e7	−1.65779
$746$	−4.70502e6	−0.309538
$747$	−2.40233e7	−1.57518
$748$	−1.30176e6	−0.0850699
$749$	−2.10841e7	−1.37325
$750$	810952.	0.0526432
$751$	−9.28006e6	−0.600414	−0.300207	−	0.953874i	$-0.597056\pi$
$751$	−9.28006e6	−0.600414	−0.300207	+	0.953874i	$0.597056\pi$
$752$	−4.56776e6	−0.294550
$753$	−993759.	−0.0638695
$754$	8.64276e6	0.553636
$755$	2.62205e7	1.67407
$756$	−7.07158e6	−0.449999
$757$	−2.31724e6	−0.146971	−0.0734855	−	0.997296i	$-0.523412\pi$
$757$	−2.31724e6	−0.146971	−0.0734855	+	0.997296i	$0.523412\pi$
$758$	8.13272e6	0.514118
$759$	112521.	0.00708973
$760$	5.35583e6	0.336351
$761$	−4.61780e6	−0.289050	−0.144525	−	0.989501i	$-0.546165\pi$
$761$	−4.61780e6	−0.289050	−0.144525	+	0.989501i	$0.546165\pi$
$762$	−1.93684e6	−0.120839
$763$	−3.33026e7	−2.07094
$764$	3.10272e6	0.192313
$765$	1.08287e7	0.668996
$766$	−8.79942e6	−0.541854
$767$	−5.98142e6	−0.367126
$768$	−2.42140e6	−0.148137
$769$	−3.96638e6	−0.241868	−0.120934	−	0.992661i	$-0.538589\pi$
$769$	−3.96638e6	−0.241868	−0.120934	+	0.992661i	$0.538589\pi$
$770$	4.08799e6	0.248475
$771$	−3.41502e6	−0.206898
$772$	−1.61531e7	−0.975465
$773$	−9.33285e6	−0.561779	−0.280890	−	0.959740i	$-0.590629\pi$
$773$	−9.33285e6	−0.561779	−0.280890	+	0.959740i	$0.590629\pi$
$774$	−8.65736e6	−0.519437
$775$	0	0
$776$	−2.83778e6	−0.169170
$777$	449796.	0.0267278
$778$	2.23295e6	0.132261
$779$	−6.82076e6	−0.402707
$780$	2.70481e6	0.159185
$781$	3.16717e6	0.185799
$782$	507421.	0.0296723
$783$	1.37318e7	0.800430
$784$	4.61068e6	0.267901
$785$	−2.46526e7	−1.42787
$786$	354184.	0.0204490
$787$	4.21127e6	0.242369	0.121184	−	0.992630i	$-0.461331\pi$
$787$	4.21127e6	0.242369	0.121184	+	0.992630i	$0.461331\pi$
$788$	2.09575e7	1.20233
$789$	3.90300e6	0.223206
$790$	2.58674e7	1.47464
$791$	987567.	0.0561210
$792$	−3.54696e6	−0.200930
$793$	−1.85416e6	−0.104704
$794$	−5.72867e6	−0.322480
$795$	7.76459e6	0.435713
$796$	−1.94831e7	−1.08987
$797$	−1.03689e7	−0.578212	−0.289106	−	0.957297i	$-0.593358\pi$
$797$	−1.03689e7	−0.578212	−0.289106	+	0.957297i	$0.593358\pi$
$798$	695950.	0.0386875
$799$	7.67654e6	0.425401
$800$	2.43972e7	1.34777
$801$	−2.45489e7	−1.35192
$802$	7.19340e6	0.394910
$803$	8.34628e6	0.456777
$804$	3.40315e6	0.185670
$805$	4.87172e6	0.264967
$806$	0	0
$807$	7.44806e6	0.402586
$808$	−926509.	−0.0499254
$809$	1.57715e6	0.0847230	0.0423615	−	0.999102i	$-0.486512\pi$
$809$	1.57715e6	0.0847230	0.0423615	+	0.999102i	$0.486512\pi$
$810$	1.19579e7	0.640386
$811$	−1.43732e7	−0.767363	−0.383681	−	0.923465i	$-0.625344\pi$
$811$	−1.43732e7	−0.767363	−0.383681	+	0.923465i	$0.625344\pi$
$812$	−3.47963e7	−1.85201
$813$	1.75341e6	0.0930371
$814$	199131.	0.0105336
$815$	3.91003e7	2.06199
$816$	−641892.	−0.0337471
$817$	−5.35028e6	−0.280428
$818$	1.86046e6	0.0972161
$819$	−1.51534e7	−0.789404
$820$	−3.49091e7	−1.81303
$821$	8.51716e6	0.440998	0.220499	−	0.975387i	$-0.429231\pi$
$821$	8.51716e6	0.440998	0.220499	+	0.975387i	$0.429231\pi$
$822$	202622.	0.0104594
$823$	−1.33607e7	−0.687592	−0.343796	−	0.939044i	$-0.611713\pi$
$823$	−1.33607e7	−0.687592	−0.343796	+	0.939044i	$0.611713\pi$
$824$	2.26478e7	1.16201
$825$	−1.40811e6	−0.0720280
$826$	−7.87682e6	−0.401699
$827$	7.44678e6	0.378621	0.189311	−	0.981917i	$-0.439375\pi$
$827$	7.44678e6	0.378621	0.189311	+	0.981917i	$0.439375\pi$
$828$	−1.81642e6	−0.0920747
$829$	−1.57553e7	−0.796234	−0.398117	−	0.917335i	$-0.630336\pi$
$829$	−1.57553e7	−0.796234	−0.398117	+	0.917335i	$0.630336\pi$
$830$	2.48539e7	1.25228
$831$	3.91123e6	0.196477
$832$	−2.33164e6	−0.116776
$833$	−7.74868e6	−0.386915
$834$	−2.45649e6	−0.122292
$835$	2.87031e7	1.42466
$836$	−941964.	−0.0466143
$837$	0	0
$838$	1.23561e7	0.607815
$839$	−5.41751e6	−0.265702	−0.132851	−	0.991136i	$-0.542413\pi$
$839$	−5.41751e6	−0.265702	−0.132851	+	0.991136i	$0.542413\pi$
$840$	8.28891e6	0.405321
$841$	4.70574e7	2.29424
$842$	−8.80268e6	−0.427893
$843$	1.65136e6	0.0800338
$844$	1.86164e7	0.899578
$845$	−1.96305e7	−0.945777
$846$	8.98834e6	0.431771
$847$	2.66000e7	1.27401
$848$	8.52728e6	0.407212
$849$	−2.88658e6	−0.137440
$850$	−6.34995e6	−0.301455
$851$	237307.	0.0112328
$852$	2.75960e6	0.130241
$853$	−2.85425e7	−1.34314	−0.671568	−	0.740943i	$-0.734379\pi$
$853$	−2.85425e7	−1.34314	−0.671568	+	0.740943i	$0.734379\pi$
$854$	−2.44171e6	−0.114564
$855$	7.83577e6	0.366578
$856$	−1.89262e7	−0.882836
$857$	2.49605e7	1.16092	0.580458	−	0.814290i	$-0.302874\pi$
$857$	2.49605e7	1.16092	0.580458	+	0.814290i	$0.302874\pi$
$858$	362097.	0.0167921
$859$	3.29728e7	1.52466	0.762331	−	0.647188i	$-0.224055\pi$
$859$	3.29728e7	1.52466	0.762331	+	0.647188i	$0.224055\pi$
$860$	−2.73831e7	−1.26251
$861$	−1.05561e7	−0.485284
$862$	9.65187e6	0.442429
$863$	1.53779e7	0.702860	0.351430	−	0.936214i	$-0.385695\pi$
$863$	1.53779e7	0.702860	0.351430	+	0.936214i	$0.385695\pi$
$864$	−9.96788e6	−0.454275
$865$	−7.03803e6	−0.319824
$866$	1.49571e7	0.677725
$867$	−3.92999e6	−0.177559
$868$	0	0
$869$	−1.05870e7	−0.475580
$870$	−6.91665e6	−0.309812
$871$	1.49785e7	0.668996
$872$	−2.98943e7	−1.33136
$873$	−4.15178e6	−0.184373
$874$	367175.	0.0162590
$875$	−1.43702e7	−0.634518
$876$	7.27222e6	0.320189
$877$	−4.69140e6	−0.205970	−0.102985	−	0.994683i	$-0.532839\pi$
$877$	−4.69140e6	−0.205970	−0.102985	+	0.994683i	$0.532839\pi$
$878$	2.07062e6	0.0906491
$879$	2.18947e6	0.0955798
$880$	−2.72834e6	−0.118766
$881$	−1.28946e7	−0.559715	−0.279857	−	0.960042i	$-0.590287\pi$
$881$	−1.28946e7	−0.559715	−0.279857	+	0.960042i	$0.590287\pi$
$882$	−9.07281e6	−0.392708
$883$	1.28876e7	0.556252	0.278126	−	0.960545i	$-0.410287\pi$
$883$	1.28876e7	0.556252	0.278126	+	0.960545i	$0.410287\pi$
$884$	−4.99220e6	−0.214863
$885$	4.78682e6	0.205442
$886$	−4.22945e6	−0.181009
$887$	1.96789e7	0.839830	0.419915	−	0.907563i	$-0.362060\pi$
$887$	1.96789e7	0.839830	0.419915	+	0.907563i	$0.362060\pi$
$888$	403762.	0.0171828
$889$	3.43211e7	1.45649
$890$	2.53977e7	1.07478
$891$	−4.89412e6	−0.206529
$892$	55005.2	0.00231468
$893$	5.55482e6	0.233100
$894$	−2.92942e6	−0.122585
$895$	−1.77110e7	−0.739070
$896$	3.04498e7	1.26711
$897$	431516.	0.0179067
$898$	4.63069e6	0.191626
$899$	0	0
$900$	2.27310e7	0.935431
$901$	−1.43309e7	−0.588114
$902$	−4.67333e6	−0.191254
$903$	−8.28031e6	−0.337931
$904$	886495.	0.0360791
$905$	−658364.	−0.0267205
$906$	3.05845e6	0.123789
$907$	−3.23622e7	−1.30623	−0.653116	−	0.757258i	$-0.726538\pi$
$907$	−3.23622e7	−1.30623	−0.653116	+	0.757258i	$0.726538\pi$
$908$	−5.99085e6	−0.241143
$909$	−1.35552e6	−0.0544121
$910$	1.56773e7	0.627580
$911$	3.51264e7	1.40229	0.701145	−	0.713019i	$-0.252673\pi$
$911$	3.51264e7	1.40229	0.701145	+	0.713019i	$0.252673\pi$
$912$	−464479.	−0.0184918
$913$	−1.01722e7	−0.403868
$914$	−1.32285e7	−0.523777
$915$	1.48385e6	0.0585919
$916$	−3.65422e7	−1.43898
$917$	−6.27621e6	−0.246476
$918$	2.59438e6	0.101608
$919$	−1.58695e7	−0.619834	−0.309917	−	0.950764i	$-0.600301\pi$
$919$	−1.58695e7	−0.619834	−0.309917	+	0.950764i	$0.600301\pi$
$920$	4.37313e6	0.170342
$921$	3.47261e6	0.134898
$922$	−6.31036e6	−0.244471
$923$	1.21460e7	0.469277
$924$	−1.45782e6	−0.0561727
$925$	−2.96970e6	−0.114119
$926$	6.49812e6	0.249035
$927$	3.31346e7	1.26643
$928$	−4.90478e7	−1.86961
$929$	−3.23917e7	−1.23139	−0.615694	−	0.787986i	$-0.711124\pi$
$929$	−3.23917e7	−1.23139	−0.615694	+	0.787986i	$0.711124\pi$
$930$	0	0
$931$	−5.60702e6	−0.212011
$932$	−1.94858e7	−0.734815
$933$	3.50876e6	0.131962
$934$	3.09087e6	0.115935
$935$	4.58523e6	0.171527
$936$	−1.36025e7	−0.507492
$937$	8.45137e6	0.314469	0.157235	−	0.987561i	$-0.449742\pi$
$937$	8.45137e6	0.314469	0.157235	+	0.987561i	$0.449742\pi$
$938$	1.97249e7	0.731996
$939$	6.73577e6	0.249301
$940$	2.84300e7	1.04944
$941$	1.88350e7	0.693411	0.346706	−	0.937974i	$-0.387300\pi$
$941$	1.88350e7	0.693411	0.346706	+	0.937974i	$0.387300\pi$
$942$	−2.87557e6	−0.105583
$943$	−5.56927e6	−0.203948
$944$	5.25701e6	0.192004
$945$	2.49085e7	0.907336
$946$	−3.66581e6	−0.133181
$947$	3.93826e7	1.42702	0.713510	−	0.700645i	$-0.247104\pi$
$947$	3.93826e7	1.42702	0.713510	+	0.700645i	$0.247104\pi$
$948$	−9.22460e6	−0.333370
$949$	3.20078e7	1.15369
$950$	−4.59489e6	−0.165183
$951$	−1.12763e6	−0.0404309
$952$	−1.52986e7	−0.547091
$953$	−9.83652e6	−0.350840	−0.175420	−	0.984494i	$-0.556128\pi$
$953$	−9.83652e6	−0.350840	−0.175420	+	0.984494i	$0.556128\pi$
$954$	−1.67798e7	−0.596920
$955$	−1.09288e7	−0.387762
$956$	−1.97398e7	−0.698550
$957$	2.83085e6	0.0999164
$958$	1.10169e7	0.387835
$959$	−3.59050e6	−0.126069
$960$	1.86597e6	0.0653472
$961$	0	0
$962$	763660.	0.0266050
$963$	−2.76898e7	−0.962174
$964$	−1.80842e7	−0.626768
$965$	5.68966e7	1.96683
$966$	568255.	0.0195930
$967$	3.44726e7	1.18552	0.592759	−	0.805380i	$-0.298039\pi$
$967$	3.44726e7	1.18552	0.592759	+	0.805380i	$0.298039\pi$
$968$	2.38777e7	0.819037
$969$	780601.	0.0267067
$970$	4.29533e6	0.146578
$971$	−3.08248e7	−1.04919	−0.524593	−	0.851353i	$-0.675782\pi$
$971$	−3.08248e7	−1.04919	−0.524593	+	0.851353i	$0.675782\pi$
$972$	−1.40527e7	−0.477084
$973$	4.35294e7	1.47401
$974$	1.55390e7	0.524839
$975$	−5.40006e6	−0.181923
$976$	1.62961e6	0.0547593
$977$	−4.07909e7	−1.36718	−0.683592	−	0.729865i	$-0.739583\pi$
$977$	−4.07909e7	−1.36718	−0.683592	+	0.729865i	$0.739583\pi$
$978$	4.56080e6	0.152473
$979$	−1.03948e7	−0.346624
$980$	−2.86971e7	−0.954494
$981$	−4.37364e7	−1.45101
$982$	−2.04840e7	−0.677852
$983$	−1.30660e7	−0.431280	−0.215640	−	0.976473i	$-0.569184\pi$
$983$	−1.30660e7	−0.431280	−0.215640	+	0.976473i	$0.569184\pi$
$984$	−9.47575e6	−0.311979
$985$	−7.38193e7	−2.42426
$986$	1.27659e7	0.418175
$987$	8.59688e6	0.280898
$988$	−3.61241e6	−0.117735
$989$	−4.36859e6	−0.142020
$990$	5.36877e6	0.174095
$991$	7.14733e6	0.231185	0.115593	−	0.993297i	$-0.463123\pi$
$991$	7.14733e6	0.231185	0.115593	+	0.993297i	$0.463123\pi$
$992$	0	0
$993$	−9.06303e6	−0.291676
$994$	1.59949e7	0.513470
$995$	6.86261e7	2.19751
$996$	−8.86320e6	−0.283101
$997$	−9.04256e6	−0.288107	−0.144053	−	0.989570i	$-0.546014\pi$
$997$	−9.04256e6	−0.288107	−0.144053	+	0.989570i	$0.546014\pi$
$998$	−6.06254e6	−0.192676
$999$	1.21332e6	0.0384646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.6.a.f.1.8		12
31.6	odd	6		31.6.c.a.5.8	✓	24
31.26	odd	6		31.6.c.a.25.8	yes	24
31.30	odd	2		961.6.a.e.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.c.a.5.8	✓	24	31.6	odd	6
31.6.c.a.25.8	yes	24	31.26	odd	6
961.6.a.e.1.8		12	31.30	odd	2
961.6.a.f.1.8		12	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q+2.80839 q^{2} +3.52764 q^{3} -24.1129 q^{4} +84.9339 q^{5} +9.90701 q^{6} -175.554 q^{7} -157.587 q^{8} -230.556 q^{9} +O(q^{10})\)	\(q+2.80839 q^{2} +3.52764 q^{3} -24.1129 q^{4} +84.9339 q^{5} +9.90701 q^{6} -175.554 q^{7} -157.587 q^{8} -230.556 q^{9} +238.528 q^{10} -97.6247 q^{11} -85.0617 q^{12} -374.388 q^{13} -493.025 q^{14} +299.616 q^{15} +329.047 q^{16} -552.994 q^{17} -647.491 q^{18} -400.152 q^{19} -2048.00 q^{20} -619.292 q^{21} -274.169 q^{22} -326.731 q^{23} -555.911 q^{24} +4088.77 q^{25} -1051.43 q^{26} -1670.53 q^{27} +4233.12 q^{28} -8220.01 q^{29} +841.441 q^{30} +5966.88 q^{32} -344.385 q^{33} -1553.02 q^{34} -14910.5 q^{35} +5559.37 q^{36} -726.307 q^{37} -1123.78 q^{38} -1320.71 q^{39} -13384.5 q^{40} +17045.4 q^{41} -1739.22 q^{42} +13370.6 q^{43} +2354.02 q^{44} -19582.0 q^{45} -917.589 q^{46} -13881.8 q^{47} +1160.76 q^{48} +14012.2 q^{49} +11482.9 q^{50} -1950.76 q^{51} +9027.59 q^{52} +25915.1 q^{53} -4691.52 q^{54} -8291.65 q^{55} +27665.1 q^{56} -1411.59 q^{57} -23085.0 q^{58} +15976.5 q^{59} -7224.62 q^{60} +4952.51 q^{61} +40475.0 q^{63} +6227.87 q^{64} -31798.3 q^{65} -967.169 q^{66} -40008.0 q^{67} +13334.3 q^{68} -1152.59 q^{69} -41874.5 q^{70} -32442.3 q^{71} +36332.6 q^{72} -85493.5 q^{73} -2039.76 q^{74} +14423.7 q^{75} +9648.83 q^{76} +17138.4 q^{77} -3709.07 q^{78} +108446. q^{79} +27947.2 q^{80} +50132.0 q^{81} +47870.3 q^{82} +104197. q^{83} +14932.9 q^{84} -46967.9 q^{85} +37550.0 q^{86} -28997.2 q^{87} +15384.4 q^{88} +106477. q^{89} -54994.0 q^{90} +65725.4 q^{91} +7878.44 q^{92} -38985.5 q^{94} -33986.4 q^{95} +21049.0 q^{96} +18007.7 q^{97} +39351.9 q^{98} +22507.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 10 q^{3} + 168 q^{4} - 28 q^{5} + 72 q^{6} + 134 q^{7} - 402 q^{8} + 668 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 10 * q^3 + 168 * q^4 - 28 * q^5 + 72 * q^6 + 134 * q^7 - 402 * q^8 + 668 * q^9	\( 12 q - 2 q^{2} + 10 q^{3} + 168 q^{4} - 28 q^{5} + 72 q^{6} + 134 q^{7} - 402 q^{8} + 668 q^{9} + 746 q^{10} + 394 q^{11} - 646 q^{12} - 664 q^{13} - 432 q^{14} + 798 q^{15} + 2020 q^{16} + 432 q^{17} - 1208 q^{18} + 694 q^{19} - 5692 q^{20} - 1712 q^{21} + 616 q^{22} + 960 q^{23} + 8432 q^{24} - 88 q^{25} + 10798 q^{26} + 1642 q^{27} + 6570 q^{28} + 10748 q^{29} - 10380 q^{30} - 12206 q^{32} - 25572 q^{33} + 16026 q^{34} + 12586 q^{35} + 3252 q^{36} - 2116 q^{37} + 14516 q^{38} + 9558 q^{39} + 43746 q^{40} - 12416 q^{41} + 32978 q^{42} + 38354 q^{43} + 28734 q^{44} - 21396 q^{45} + 22116 q^{46} + 40128 q^{47} - 32098 q^{48} - 8876 q^{49} - 14432 q^{50} - 29346 q^{51} - 64628 q^{52} + 14152 q^{53} - 18436 q^{54} - 2202 q^{55} - 13296 q^{56} - 26440 q^{57} + 20612 q^{58} + 66074 q^{59} + 126478 q^{60} + 46964 q^{61} + 43328 q^{63} - 10936 q^{64} + 103544 q^{65} + 156910 q^{66} - 8434 q^{67} - 116388 q^{68} + 3768 q^{69} + 120860 q^{70} + 46854 q^{71} - 177728 q^{72} + 105776 q^{73} + 241354 q^{74} + 2800 q^{75} - 208806 q^{76} + 168460 q^{77} + 60212 q^{78} - 42030 q^{79} - 204912 q^{80} - 63960 q^{81} - 54870 q^{82} + 7174 q^{83} - 266196 q^{84} + 158072 q^{85} - 41552 q^{86} + 13808 q^{87} - 232624 q^{88} + 142500 q^{89} + 169776 q^{90} + 43450 q^{91} + 141468 q^{92} + 68500 q^{94} - 40430 q^{95} + 317764 q^{96} + 82692 q^{97} + 192032 q^{98} - 27496 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 10 * q^3 + 168 * q^4 - 28 * q^5 + 72 * q^6 + 134 * q^7 - 402 * q^8 + 668 * q^9 + 746 * q^10 + 394 * q^11 - 646 * q^12 - 664 * q^13 - 432 * q^14 + 798 * q^15 + 2020 * q^16 + 432 * q^17 - 1208 * q^18 + 694 * q^19 - 5692 * q^20 - 1712 * q^21 + 616 * q^22 + 960 * q^23 + 8432 * q^24 - 88 * q^25 + 10798 * q^26 + 1642 * q^27 + 6570 * q^28 + 10748 * q^29 - 10380 * q^30 - 12206 * q^32 - 25572 * q^33 + 16026 * q^34 + 12586 * q^35 + 3252 * q^36 - 2116 * q^37 + 14516 * q^38 + 9558 * q^39 + 43746 * q^40 - 12416 * q^41 + 32978 * q^42 + 38354 * q^43 + 28734 * q^44 - 21396 * q^45 + 22116 * q^46 + 40128 * q^47 - 32098 * q^48 - 8876 * q^49 - 14432 * q^50 - 29346 * q^51 - 64628 * q^52 + 14152 * q^53 - 18436 * q^54 - 2202 * q^55 - 13296 * q^56 - 26440 * q^57 + 20612 * q^58 + 66074 * q^59 + 126478 * q^60 + 46964 * q^61 + 43328 * q^63 - 10936 * q^64 + 103544 * q^65 + 156910 * q^66 - 8434 * q^67 - 116388 * q^68 + 3768 * q^69 + 120860 * q^70 + 46854 * q^71 - 177728 * q^72 + 105776 * q^73 + 241354 * q^74 + 2800 * q^75 - 208806 * q^76 + 168460 * q^77 + 60212 * q^78 - 42030 * q^79 - 204912 * q^80 - 63960 * q^81 - 54870 * q^82 + 7174 * q^83 - 266196 * q^84 + 158072 * q^85 - 41552 * q^86 + 13808 * q^87 - 232624 * q^88 + 142500 * q^89 + 169776 * q^90 + 43450 * q^91 + 141468 * q^92 + 68500 * q^94 - 40430 * q^95 + 317764 * q^96 + 82692 * q^97 + 192032 * q^98 - 27496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more