LMFDB - Embedded newform 37.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.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:	$5.93420133308$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 160x^{5} + 156x^{4} + 6495x^{3} - 2943x^{2} - 64880x + 53844 $ x^7 - x^6 - 160x^5 + 156x^4 + 6495x^3 - 2943x^2 - 64880*x + 53844
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.76658$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.7666 q^{2} -23.6672 q^{3} +83.9191 q^{4} +70.6580 q^{5} +254.814 q^{6} -64.6233 q^{7} -558.991 q^{8} +317.134 q^{9} +O(q^{10})$	\(q-10.7666 q^{2} -23.6672 q^{3} +83.9191 q^{4} +70.6580 q^{5} +254.814 q^{6} -64.6233 q^{7} -558.991 q^{8} +317.134 q^{9} -760.745 q^{10} -47.9645 q^{11} -1986.13 q^{12} +1000.68 q^{13} +695.772 q^{14} -1672.27 q^{15} +3333.01 q^{16} -1776.24 q^{17} -3414.45 q^{18} -910.892 q^{19} +5929.56 q^{20} +1529.45 q^{21} +516.413 q^{22} -4171.83 q^{23} +13229.7 q^{24} +1867.56 q^{25} -10773.9 q^{26} -1754.55 q^{27} -5423.13 q^{28} -1617.92 q^{29} +18004.7 q^{30} +2858.97 q^{31} -17997.4 q^{32} +1135.18 q^{33} +19124.1 q^{34} -4566.15 q^{35} +26613.6 q^{36} -1369.00 q^{37} +9807.19 q^{38} -23683.4 q^{39} -39497.2 q^{40} -7989.87 q^{41} -16466.9 q^{42} -11947.0 q^{43} -4025.14 q^{44} +22408.1 q^{45} +44916.4 q^{46} -8023.45 q^{47} -78882.9 q^{48} -12630.8 q^{49} -20107.2 q^{50} +42038.6 q^{51} +83976.6 q^{52} +1643.54 q^{53} +18890.5 q^{54} -3389.07 q^{55} +36123.9 q^{56} +21558.2 q^{57} +17419.5 q^{58} -13153.4 q^{59} -140336. q^{60} +9032.26 q^{61} -30781.3 q^{62} -20494.3 q^{63} +87113.8 q^{64} +70706.4 q^{65} -12222.0 q^{66} -3990.39 q^{67} -149061. q^{68} +98735.4 q^{69} +49161.8 q^{70} +278.595 q^{71} -177275. q^{72} -67206.8 q^{73} +14739.4 q^{74} -44199.8 q^{75} -76441.3 q^{76} +3099.62 q^{77} +254989. q^{78} -62175.3 q^{79} +235504. q^{80} -35538.5 q^{81} +86023.5 q^{82} +63037.5 q^{83} +128350. q^{84} -125506. q^{85} +128628. q^{86} +38291.6 q^{87} +26811.7 q^{88} +23564.3 q^{89} -241258. q^{90} -64667.5 q^{91} -350097. q^{92} -67663.7 q^{93} +86385.1 q^{94} -64361.9 q^{95} +425947. q^{96} +67383.2 q^{97} +135991. q^{98} -15211.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * 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 $

$2$	−10.7666	−1.90328	−0.951640	−	0.307216i	$-0.900603\pi$
$2$	−10.7666	−1.90328	−0.951640	+	0.307216i	$0.900603\pi$
$3$	−23.6672	−1.51825	−0.759124	−	0.650946i	$-0.774373\pi$
$3$	−23.6672	−1.51825	−0.759124	+	0.650946i	$0.774373\pi$
$4$	83.9191	2.62247
$5$	70.6580	1.26397	0.631985	−	0.774981i	$-0.282241\pi$
$5$	70.6580	1.26397	0.631985	+	0.774981i	$0.282241\pi$
$6$	254.814	2.88965
$7$	−64.6233	−0.498476	−0.249238	−	0.968442i	$-0.580180\pi$
$7$	−64.6233	−0.498476	−0.249238	+	0.968442i	$0.580180\pi$
$8$	−558.991	−3.08802
$9$	317.134	1.30508
$10$	−760.745	−2.40569
$11$	−47.9645	−0.119519	−0.0597596	−	0.998213i	$-0.519033\pi$
$11$	−47.9645	−0.119519	−0.0597596	+	0.998213i	$0.519033\pi$
$12$	−1986.13	−3.98157
$13$	1000.68	1.64225	0.821124	−	0.570750i	$-0.193347\pi$
$13$	1000.68	1.64225	0.821124	+	0.570750i	$0.193347\pi$
$14$	695.772	0.948739
$15$	−1672.27	−1.91902
$16$	3333.01	3.25489
$17$	−1776.24	−1.49067	−0.745333	−	0.666693i	$-0.767709\pi$
$17$	−1776.24	−1.49067	−0.745333	+	0.666693i	$0.767709\pi$
$18$	−3414.45	−2.48393
$19$	−910.892	−0.578873	−0.289436	−	0.957197i	$-0.593468\pi$
$19$	−910.892	−0.578873	−0.289436	+	0.957197i	$0.593468\pi$
$20$	5929.56	3.31473
$21$	1529.45	0.756810
$22$	516.413	0.227479
$23$	−4171.83	−1.64440	−0.822200	−	0.569199i	$-0.807253\pi$
$23$	−4171.83	−1.64440	−0.822200	+	0.569199i	$0.807253\pi$
$24$	13229.7	4.68838
$25$	1867.56	0.597618
$26$	−10773.9	−3.12566
$27$	−1754.55	−0.463186
$28$	−5423.13	−1.30724
$29$	−1617.92	−0.357242	−0.178621	−	0.983918i	$-0.557164\pi$
$29$	−1617.92	−0.357242	−0.178621	+	0.983918i	$0.557164\pi$
$30$	18004.7	3.65243
$31$	2858.97	0.534325	0.267163	−	0.963651i	$-0.413914\pi$
$31$	2858.97	0.534325	0.267163	+	0.963651i	$0.413914\pi$
$32$	−17997.4	−3.10695
$33$	1135.18	0.181460
$34$	19124.1	2.83715
$35$	−4566.15	−0.630058
$36$	26613.6	3.42254
$37$	−1369.00	−0.164399
$37$	−1369.00	−0.164399
$38$	9807.19	1.10176
$39$	−23683.4	−2.49334
$40$	−39497.2	−3.90316
$41$	−7989.87	−0.742301	−0.371151	−	0.928573i	$-0.621037\pi$
$41$	−7989.87	−0.742301	−0.371151	+	0.928573i	$0.621037\pi$
$42$	−16466.9	−1.44042
$43$	−11947.0	−0.985342	−0.492671	−	0.870216i	$-0.663979\pi$
$43$	−11947.0	−0.985342	−0.492671	+	0.870216i	$0.663979\pi$
$44$	−4025.14	−0.313436
$45$	22408.1	1.64958
$46$	44916.4	3.12975
$47$	−8023.45	−0.529806	−0.264903	−	0.964275i	$-0.585340\pi$
$47$	−8023.45	−0.529806	−0.264903	+	0.964275i	$0.585340\pi$
$48$	−78882.9	−4.94174
$49$	−12630.8	−0.751522
$50$	−20107.2	−1.13743
$51$	42038.6	2.26320
$52$	83976.6	4.30675
$53$	1643.54	0.0803695	0.0401847	−	0.999192i	$-0.487205\pi$
$53$	1643.54	0.0803695	0.0401847	+	0.999192i	$0.487205\pi$
$54$	18890.5	0.881573
$55$	−3389.07	−0.151069
$56$	36123.9	1.53930
$57$	21558.2	0.878873
$58$	17419.5	0.679932
$59$	−13153.4	−0.491935	−0.245968	−	0.969278i	$-0.579106\pi$
$59$	−13153.4	−0.491935	−0.245968	+	0.969278i	$0.579106\pi$
$60$	−140336.	−5.03258
$61$	9032.26	0.310793	0.155397	−	0.987852i	$-0.450334\pi$
$61$	9032.26	0.310793	0.155397	+	0.987852i	$0.450334\pi$
$62$	−30781.3	−1.01697
$63$	−20494.3	−0.650550
$64$	87113.8	2.65850
$65$	70706.4	2.07575
$66$	−12222.0	−0.345369
$67$	−3990.39	−0.108600	−0.0542998	−	0.998525i	$-0.517293\pi$
$67$	−3990.39	−0.108600	−0.0542998	+	0.998525i	$0.517293\pi$
$68$	−149061.	−3.90923
$69$	98735.4	2.49661
$70$	49161.8	1.19918
$71$	278.595	0.00655884	0.00327942	−	0.999995i	$-0.498956\pi$
$71$	278.595	0.00655884	0.00327942	+	0.999995i	$0.498956\pi$
$72$	−177275.	−4.03011
$73$	−67206.8	−1.47607	−0.738034	−	0.674764i	$-0.764245\pi$
$73$	−67206.8	−1.47607	−0.738034	+	0.674764i	$0.764245\pi$
$74$	14739.4	0.312897
$75$	−44199.8	−0.907333
$76$	−76441.3	−1.51808
$77$	3099.62	0.0595774
$78$	254989.	4.74552
$79$	−62175.3	−1.12086	−0.560429	−	0.828203i	$-0.689364\pi$
$79$	−62175.3	−1.12086	−0.560429	+	0.828203i	$0.689364\pi$
$80$	235504.	4.11408
$81$	−35538.5	−0.601847
$82$	86023.5	1.41281
$83$	63037.5	1.00439	0.502196	−	0.864754i	$-0.332525\pi$
$83$	63037.5	1.00439	0.502196	+	0.864754i	$0.332525\pi$
$84$	128350.	1.98471
$85$	−125506.	−1.88416
$86$	128628.	1.87538
$87$	38291.6	0.542382
$88$	26811.7	0.369078
$89$	23564.3	0.315340	0.157670	−	0.987492i	$-0.449602\pi$
$89$	23564.3	0.315340	0.157670	+	0.987492i	$0.449602\pi$
$90$	−241258.	−3.13961
$91$	−64667.5	−0.818621
$92$	−350097.	−4.31239
$93$	−67663.7	−0.811239
$94$	86385.1	1.00837
$95$	−64361.9	−0.731677
$96$	425947.	4.71712
$97$	67383.2	0.727148	0.363574	−	0.931565i	$-0.381556\pi$
$97$	67383.2	0.727148	0.363574	+	0.931565i	$0.381556\pi$
$98$	135991.	1.43036
$99$	−15211.2	−0.155982
$100$	156724.	1.56724
$101$	−68684.8	−0.669973	−0.334986	−	0.942223i	$-0.608732\pi$
$101$	−68684.8	−0.669973	−0.334986	+	0.942223i	$0.608732\pi$
$102$	−452612.	−4.30750
$103$	188993.	1.75531	0.877654	−	0.479294i	$-0.159107\pi$
$103$	188993.	1.75531	0.877654	+	0.479294i	$0.159107\pi$
$104$	−559374.	−5.07129
$105$	108068.	0.956585
$106$	−17695.3	−0.152966
$107$	−108748.	−0.918256	−0.459128	−	0.888370i	$-0.651838\pi$
$107$	−108748.	−0.918256	−0.459128	+	0.888370i	$0.651838\pi$
$108$	−147240.	−1.21469
$109$	−79649.6	−0.642121	−0.321061	−	0.947059i	$-0.604039\pi$
$109$	−79649.6	−0.642121	−0.321061	+	0.947059i	$0.604039\pi$
$110$	36488.7	0.287526
$111$	32400.3	0.249599
$112$	−215390.	−1.62248
$113$	150829.	1.11119	0.555594	−	0.831454i	$-0.312491\pi$
$113$	150829.	1.11119	0.555594	+	0.831454i	$0.312491\pi$
$114$	−232108.	−1.67274
$115$	−294774.	−2.07847
$116$	−135775.	−0.936858
$117$	317351.	2.14326
$118$	141617.	0.936290
$119$	114787.	0.743060
$120$	934787.	5.92597
$121$	−158750.	−0.985715
$122$	−97246.5	−0.591527
$123$	189098.	1.12700
$124$	239923.	1.40125
$125$	−88848.4	−0.508598
$126$	220653.	1.23818
$127$	42329.9	0.232883	0.116442	−	0.993198i	$-0.462851\pi$
$127$	42329.9	0.232883	0.116442	+	0.993198i	$0.462851\pi$
$128$	−362001.	−1.95292
$129$	282751.	1.49599
$130$	−761266.	−3.95073
$131$	−130113.	−0.662433	−0.331217	−	0.943555i	$-0.607459\pi$
$131$	−130113.	−0.662433	−0.331217	+	0.943555i	$0.607459\pi$
$132$	95263.5	0.475874
$133$	58864.9	0.288554
$134$	42962.8	0.206695
$135$	−123973.	−0.585453
$136$	992905.	4.60320
$137$	239673.	1.09098	0.545491	−	0.838117i	$-0.316343\pi$
$137$	239673.	1.09098	0.545491	+	0.838117i	$0.316343\pi$
$138$	−1.06304e6	−4.75174
$139$	346134.	1.51952	0.759762	−	0.650202i	$-0.225316\pi$
$139$	346134.	1.51952	0.759762	+	0.650202i	$0.225316\pi$
$140$	−383188.	−1.65231
$141$	189892.	0.804377
$142$	−2999.51	−0.0124833
$143$	−47997.3	−0.196280
$144$	1.05701e6	4.24789
$145$	−114319.	−0.451543
$146$	723587.	2.80937
$147$	298936.	1.14100
$148$	−114885.	−0.431132
$149$	−99210.8	−0.366095	−0.183047	−	0.983104i	$-0.558596\pi$
$149$	−99210.8	−0.366095	−0.183047	+	0.983104i	$0.558596\pi$
$150$	475880.	1.72691
$151$	−423923.	−1.51302	−0.756510	−	0.653982i	$-0.773097\pi$
$151$	−423923.	−1.51302	−0.756510	+	0.653982i	$0.773097\pi$
$152$	509181.	1.78757
$153$	−563308.	−1.94544
$154$	−33372.3	−0.113393
$155$	202009.	0.675371
$156$	−1.98749e6	−6.53872
$157$	−559410.	−1.81126	−0.905630	−	0.424069i	$-0.860601\pi$
$157$	−559410.	−1.81126	−0.905630	+	0.424069i	$0.860601\pi$
$158$	669415.	2.13331
$159$	−38898.0	−0.122021
$160$	−1.27166e6	−3.92709
$161$	269598.	0.819693
$162$	382628.	1.14548
$163$	488362.	1.43970	0.719851	−	0.694129i	$-0.244210\pi$
$163$	488362.	1.43970	0.719851	+	0.694129i	$0.244210\pi$
$164$	−670503.	−1.94666
$165$	80209.8	0.229360
$166$	−678698.	−1.91164
$167$	−322371.	−0.894468	−0.447234	−	0.894417i	$-0.647591\pi$
$167$	−322371.	−0.894468	−0.447234	+	0.894417i	$0.647591\pi$
$168$	−854949.	−2.33704
$169$	630076.	1.69698
$170$	1.35127e6	3.58607
$171$	−288875.	−0.755475
$172$	−1.00258e6	−2.58403
$173$	86276.2	0.219167	0.109584	−	0.993978i	$-0.465048\pi$
$173$	86276.2	0.219167	0.109584	+	0.993978i	$0.465048\pi$
$174$	−412270.	−1.03231
$175$	−120688.	−0.297898
$176$	−159866.	−0.389022
$177$	311304.	0.746880
$178$	−253707.	−0.600181
$179$	101192.	0.236055	0.118027	−	0.993010i	$-0.462343\pi$
$179$	101192.	0.236055	0.118027	+	0.993010i	$0.462343\pi$
$180$	1.88047e6	4.32598
$181$	98640.9	0.223800	0.111900	−	0.993719i	$-0.464306\pi$
$181$	98640.9	0.223800	0.111900	+	0.993719i	$0.464306\pi$
$182$	696248.	1.55806
$183$	−213768.	−0.471862
$184$	2.33202e6	5.07794
$185$	−96730.8	−0.207795
$186$	728507.	1.54401
$187$	85196.6	0.178163
$188$	−673321.	−1.38940
$189$	113385.	0.230887
$190$	692957.	1.39259
$191$	13265.8	0.0263118	0.0131559	−	0.999913i	$-0.495812\pi$
$191$	13265.8	0.0263118	0.0131559	+	0.999913i	$0.495812\pi$
$192$	−2.06174e6	−4.03627
$193$	94261.5	0.182155	0.0910775	−	0.995844i	$-0.470969\pi$
$193$	94261.5	0.182155	0.0910775	+	0.995844i	$0.470969\pi$
$194$	−725487.	−1.38397
$195$	−1.67342e6	−3.15151
$196$	−1.05997e6	−1.97085
$197$	−103935.	−0.190808	−0.0954039	−	0.995439i	$-0.530414\pi$
$197$	−103935.	−0.190808	−0.0954039	+	0.995439i	$0.530414\pi$
$198$	163772.	0.296878
$199$	−364148.	−0.651845	−0.325923	−	0.945396i	$-0.605675\pi$
$199$	−364148.	−0.651845	−0.325923	+	0.945396i	$0.605675\pi$
$200$	−1.04395e6	−1.84546
$201$	94441.1	0.164881
$202$	739500.	1.27514
$203$	104555.	0.178077
$204$	3.52785e6	5.93518
$205$	−564549.	−0.938246
$206$	−2.03481e6	−3.34084
$207$	−1.32303e6	−2.14607
$208$	3.33529e6	5.34534
$209$	43690.5	0.0691864
$210$	−1.16352e6	−1.82065
$211$	−537868.	−0.831705	−0.415853	−	0.909432i	$-0.636517\pi$
$211$	−537868.	−0.831705	−0.415853	+	0.909432i	$0.636517\pi$
$212$	137925.	0.210767
$213$	−6593.54	−0.00995794
$214$	1.17085e6	1.74770
$215$	−844150.	−1.24544
$216$	980777.	1.43033
$217$	−184756.	−0.266348
$218$	857553.	1.22214
$219$	1.59059e6	2.24104
$220$	−284408.	−0.396174
$221$	−1.77746e6	−2.44804
$222$	−348841.	−0.475056
$223$	−512280.	−0.689835	−0.344917	−	0.938633i	$-0.612093\pi$
$223$	−512280.	−0.689835	−0.344917	+	0.938633i	$0.612093\pi$
$224$	1.16305e6	1.54874
$225$	592266.	0.779939
$226$	−1.62391e6	−2.11490
$227$	−288737.	−0.371910	−0.185955	−	0.982558i	$-0.559538\pi$
$227$	−288737.	−0.371910	−0.185955	+	0.982558i	$0.559538\pi$
$228$	1.80915e6	2.30482
$229$	675142.	0.850759	0.425379	−	0.905015i	$-0.360141\pi$
$229$	675142.	0.850759	0.425379	+	0.905015i	$0.360141\pi$
$230$	3.17370e6	3.95591
$231$	−73359.2	−0.0904534
$232$	904405.	1.10317
$233$	883174.	1.06575	0.532876	−	0.846193i	$-0.321111\pi$
$233$	883174.	1.06575	0.532876	+	0.846193i	$0.321111\pi$
$234$	−3.41679e6	−4.07923
$235$	−566921.	−0.669658
$236$	−1.10382e6	−1.29009
$237$	1.47151e6	1.70174
$238$	−1.23586e6	−1.41425
$239$	1.00042e6	1.13289	0.566444	−	0.824100i	$-0.308319\pi$
$239$	1.00042e6	1.13289	0.566444	+	0.824100i	$0.308319\pi$
$240$	−5.57371e6	−6.24620
$241$	1.25323e6	1.38991	0.694956	−	0.719052i	$-0.255424\pi$
$241$	1.25323e6	1.38991	0.694956	+	0.719052i	$0.255424\pi$
$242$	1.70920e6	1.87609
$243$	1.26745e6	1.37694
$244$	757980.	0.815047
$245$	−892470.	−0.949901
$246$	−2.03593e6	−2.14499
$247$	−911516.	−0.950653
$248$	−1.59814e6	−1.65001
$249$	−1.49192e6	−1.52492
$250$	956593.	0.968004
$251$	745763.	0.747166	0.373583	−	0.927597i	$-0.378129\pi$
$251$	745763.	0.747166	0.373583	+	0.927597i	$0.378129\pi$
$252$	−1.71986e6	−1.70605
$253$	200100.	0.196537
$254$	−455749.	−0.443242
$255$	2.97037e6	2.86062
$256$	1.10987e6	1.05846
$257$	1.84294e6	1.74052	0.870260	−	0.492593i	$-0.163951\pi$
$257$	1.84294e6	1.74052	0.870260	+	0.492593i	$0.163951\pi$
$258$	−3.04426e6	−2.84730
$259$	88469.3	0.0819489
$260$	5.93362e6	5.44360
$261$	−513099.	−0.466229
$262$	1.40087e6	1.26080
$263$	68515.8	0.0610803	0.0305401	−	0.999534i	$-0.490277\pi$
$263$	68515.8	0.0610803	0.0305401	+	0.999534i	$0.490277\pi$
$264$	−634557.	−0.560352
$265$	116129.	0.101585
$266$	−633773.	−0.549199
$267$	−557700.	−0.478765
$268$	−334870.	−0.284799
$269$	−1.24301e6	−1.04736	−0.523679	−	0.851916i	$-0.675441\pi$
$269$	−1.24301e6	−1.04736	−0.523679	+	0.851916i	$0.675441\pi$
$270$	1.33476e6	1.11428
$271$	−1.16753e6	−0.965705	−0.482853	−	0.875702i	$-0.660399\pi$
$271$	−1.16753e6	−0.965705	−0.482853	+	0.875702i	$0.660399\pi$
$272$	−5.92024e6	−4.85195
$273$	1.53050e6	1.24287
$274$	−2.58045e6	−2.07644
$275$	−89576.4	−0.0714269
$276$	8.28579e6	6.54729
$277$	960377.	0.752042	0.376021	−	0.926611i	$-0.377292\pi$
$277$	960377.	0.752042	0.376021	+	0.926611i	$0.377292\pi$
$278$	−3.72668e6	−2.89208
$279$	906678.	0.697337
$280$	2.55244e6	1.94563
$281$	188325.	0.142279	0.0711396	−	0.997466i	$-0.477336\pi$
$281$	188325.	0.142279	0.0711396	+	0.997466i	$0.477336\pi$
$282$	−2.04449e6	−1.53095
$283$	−1.00210e6	−0.743779	−0.371889	−	0.928277i	$-0.621290\pi$
$283$	−1.00210e6	−0.743779	−0.371889	+	0.928277i	$0.621290\pi$
$284$	23379.4	0.0172004
$285$	1.52326e6	1.11087
$286$	516766.	0.373576
$287$	516332.	0.370019
$288$	−5.70758e6	−4.05482
$289$	1.73518e6	1.22208
$290$	1.23083e6	0.859413
$291$	−1.59477e6	−1.10399
$292$	−5.63994e6	−3.87095
$293$	1.08054e6	0.735314	0.367657	−	0.929961i	$-0.380160\pi$
$293$	1.08054e6	0.735314	0.367657	+	0.929961i	$0.380160\pi$
$294$	−3.21852e6	−2.17164
$295$	−929393.	−0.621791
$296$	765259.	0.507667
$297$	84156.0	0.0553597
$298$	1.06816e6	0.696780
$299$	−4.17469e6	−2.70051
$300$	−3.70921e6	−2.37946
$301$	772053.	0.491169
$302$	4.56420e6	2.87970
$303$	1.62557e6	1.01718
$304$	−3.03601e6	−1.88417
$305$	638202.	0.392833
$306$	6.06489e6	3.70271
$307$	−1.66355e6	−1.00737	−0.503686	−	0.863887i	$-0.668023\pi$
$307$	−1.66355e6	−1.00737	−0.503686	+	0.863887i	$0.668023\pi$
$308$	260118.	0.156240
$309$	−4.47293e6	−2.66499
$310$	−2.17495e6	−1.28542
$311$	1.16244e6	0.681504	0.340752	−	0.940153i	$-0.389318\pi$
$311$	1.16244e6	0.681504	0.340752	+	0.940153i	$0.389318\pi$
$312$	1.32388e7	7.69949
$313$	−2.14736e6	−1.23892	−0.619462	−	0.785026i	$-0.712649\pi$
$313$	−2.14736e6	−1.23892	−0.619462	+	0.785026i	$0.712649\pi$
$314$	6.02293e6	3.44733
$315$	−1.44808e6	−0.822276
$316$	−5.21770e6	−2.93942
$317$	−791177.	−0.442207	−0.221103	−	0.975250i	$-0.570966\pi$
$317$	−791177.	−0.442207	−0.221103	+	0.975250i	$0.570966\pi$
$318$	418798.	0.232240
$319$	77602.8	0.0426973
$320$	6.15529e6	3.36026
$321$	2.57377e6	1.39414
$322$	−2.90264e6	−1.56011
$323$	1.61797e6	0.862906
$324$	−2.98236e6	−1.57833
$325$	1.86884e6	0.981437
$326$	−5.25798e6	−2.74016
$327$	1.88508e6	0.974900
$328$	4.46627e6	2.29224
$329$	518502.	0.264095
$330$	−863584.	−0.436536
$331$	2.41282e6	1.21047	0.605236	−	0.796046i	$-0.293079\pi$
$331$	2.41282e6	1.21047	0.605236	+	0.796046i	$0.293079\pi$
$332$	5.29005e6	2.63399
$333$	−434157.	−0.214554
$334$	3.47083e6	1.70242
$335$	−281953.	−0.137266
$336$	5.09767e6	2.46334
$337$	−966468.	−0.463567	−0.231784	−	0.972767i	$-0.574456\pi$
$337$	−966468.	−0.463567	−0.231784	+	0.972767i	$0.574456\pi$
$338$	−6.78376e6	−3.22982
$339$	−3.56968e6	−1.68706
$340$	−1.05323e7	−4.94115
$341$	−137129.	−0.0638622
$342$	3.11020e6	1.43788
$343$	1.90237e6	0.873091
$344$	6.67826e6	3.04276
$345$	6.97645e6	3.15564
$346$	−928899.	−0.417136
$347$	−157404.	−0.0701765	−0.0350882	−	0.999384i	$-0.511171\pi$
$347$	−157404.	−0.0701765	−0.0350882	+	0.999384i	$0.511171\pi$
$348$	3.21340e6	1.42238
$349$	9591.96	0.00421545	0.00210772	−	0.999998i	$-0.499329\pi$
$349$	9591.96	0.00421545	0.00210772	+	0.999998i	$0.499329\pi$
$350$	1.29939e6	0.566983
$351$	−1.75575e6	−0.760667
$352$	863234.	0.371340
$353$	−3.35378e6	−1.43251	−0.716255	−	0.697838i	$-0.754145\pi$
$353$	−3.35378e6	−1.43251	−0.716255	+	0.697838i	$0.754145\pi$
$354$	−3.35167e6	−1.42152
$355$	19684.9	0.00829017
$356$	1.97750e6	0.826972
$357$	−2.71667e6	−1.12815
$358$	−1.08949e6	−0.449279
$359$	4.66114e6	1.90878	0.954390	−	0.298561i	$-0.0965068\pi$
$359$	4.66114e6	1.90878	0.954390	+	0.298561i	$0.0965068\pi$
$360$	−1.25259e7	−5.09394
$361$	−1.64637e6	−0.664906
$362$	−1.06202e6	−0.425954
$363$	3.75717e6	1.49656
$364$	−5.42684e6	−2.14681
$365$	−4.74870e6	−1.86570
$366$	2.30155e6	0.898085
$367$	−1.39535e6	−0.540777	−0.270389	−	0.962751i	$-0.587152\pi$
$367$	−1.39535e6	−0.540777	−0.270389	+	0.962751i	$0.587152\pi$
$368$	−1.39048e7	−5.35234
$369$	−2.53386e6	−0.968762
$370$	1.04146e6	0.395492
$371$	−106211.	−0.0400622
$372$	−5.67828e6	−2.12745
$373$	−3.21540e6	−1.19664	−0.598319	−	0.801258i	$-0.704165\pi$
$373$	−3.21540e6	−1.19664	−0.598319	+	0.801258i	$0.704165\pi$
$374$	−917275.	−0.339094
$375$	2.10279e6	0.772179
$376$	4.48504e6	1.63605
$377$	−1.61903e6	−0.586680
$378$	−1.22076e6	−0.439443
$379$	−1.59564e6	−0.570607	−0.285303	−	0.958437i	$-0.592094\pi$
$379$	−1.59564e6	−0.570607	−0.285303	+	0.958437i	$0.592094\pi$
$380$	−5.40119e6	−1.91880
$381$	−1.00183e6	−0.353575
$382$	−142828.	−0.0500787
$383$	4.00003e6	1.39337	0.696685	−	0.717378i	$-0.254658\pi$
$383$	4.00003e6	1.39337	0.696685	+	0.717378i	$0.254658\pi$
$384$	8.56754e6	2.96502
$385$	219013.	0.0753041
$386$	−1.01487e6	−0.346692
$387$	−3.78880e6	−1.28595
$388$	5.65474e6	1.90692
$389$	1.58645e6	0.531559	0.265780	−	0.964034i	$-0.414371\pi$
$389$	1.58645e6	0.531559	0.265780	+	0.964034i	$0.414371\pi$
$390$	1.80170e7	5.99820
$391$	7.41019e6	2.45125
$392$	7.06052e6	2.32071
$393$	3.07940e6	1.00574
$394$	1.11902e6	0.363160
$395$	−4.39319e6	−1.41673
$396$	−1.27651e6	−0.409059
$397$	−4.98925e6	−1.58876	−0.794382	−	0.607419i	$-0.792205\pi$
$397$	−4.98925e6	−1.58876	−0.794382	+	0.607419i	$0.792205\pi$
$398$	3.92062e6	1.24064
$399$	−1.39316e6	−0.438097
$400$	6.22459e6	1.94518
$401$	−6.10653e6	−1.89642	−0.948209	−	0.317648i	$-0.897107\pi$
$401$	−6.10653e6	−1.89642	−0.948209	+	0.317648i	$0.897107\pi$
$402$	−1.01681e6	−0.313815
$403$	2.86093e6	0.877495
$404$	−5.76397e6	−1.75698
$405$	−2.51108e6	−0.760716
$406$	−1.12570e6	−0.338929
$407$	65663.4	0.0196488
$408$	−2.34992e7	−6.98881
$409$	4.31343e6	1.27501	0.637506	−	0.770445i	$-0.279966\pi$
$409$	4.31343e6	1.27501	0.637506	+	0.770445i	$0.279966\pi$
$410$	6.07825e6	1.78574
$411$	−5.67237e6	−1.65638
$412$	1.58602e7	4.60325
$413$	850016.	0.245218
$414$	1.42445e7	4.08457
$415$	4.45410e6	1.26952
$416$	−1.80097e7	−5.10238
$417$	−8.19201e6	−2.30701
$418$	−470397.	−0.131681
$419$	3.51924e6	0.979296	0.489648	−	0.871920i	$-0.337125\pi$
$419$	3.51924e6	0.979296	0.489648	+	0.871920i	$0.337125\pi$
$420$	9.06896e6	2.50862
$421$	4.05072e6	1.11385	0.556925	−	0.830563i	$-0.311981\pi$
$421$	4.05072e6	1.11385	0.556925	+	0.830563i	$0.311981\pi$
$422$	5.79099e6	1.58297
$423$	−2.54451e6	−0.691439
$424$	−918726.	−0.248183
$425$	−3.31724e6	−0.890849
$426$	70989.8	0.0189528
$427$	−583694.	−0.154923
$428$	−9.12608e6	−2.40810
$429$	1.13596e6	0.298002
$430$	9.08860e6	2.37042
$431$	−4.27958e6	−1.10971	−0.554853	−	0.831948i	$-0.687226\pi$
$431$	−4.27958e6	−1.10971	−0.554853	+	0.831948i	$0.687226\pi$
$432$	−5.84792e6	−1.50762
$433$	−2.61024e6	−0.669052	−0.334526	−	0.942386i	$-0.608576\pi$
$433$	−2.61024e6	−0.669052	−0.334526	+	0.942386i	$0.608576\pi$
$434$	1.98919e6	0.506935
$435$	2.70561e6	0.685555
$436$	−6.68412e6	−1.68395
$437$	3.80009e6	0.951898
$438$	−1.71253e7	−4.26532
$439$	6.12333e6	1.51644	0.758222	−	0.651996i	$-0.226068\pi$
$439$	6.12333e6	1.51644	0.758222	+	0.651996i	$0.226068\pi$
$440$	1.89446e6	0.466503
$441$	−4.00567e6	−0.980796
$442$	1.91371e7	4.65931
$443$	8.15346e6	1.97393	0.986967	−	0.160922i	$-0.0514467\pi$
$443$	8.15346e6	1.97393	0.986967	+	0.160922i	$0.0514467\pi$
$444$	2.71901e6	0.654566
$445$	1.66501e6	0.398581
$446$	5.51550e6	1.31295
$447$	2.34804e6	0.555823
$448$	−5.62958e6	−1.32520
$449$	−1.35540e6	−0.317285	−0.158643	−	0.987336i	$-0.550712\pi$
$449$	−1.35540e6	−0.317285	−0.158643	+	0.987336i	$0.550712\pi$
$450$	−6.37668e6	−1.48444
$451$	383230.	0.0887193
$452$	1.26574e7	2.91406
$453$	1.00331e7	2.29714
$454$	3.10871e6	0.707848
$455$	−4.56928e6	−1.03471
$456$	−1.20509e7	−2.71398
$457$	−683177.	−0.153018	−0.0765090	−	0.997069i	$-0.524377\pi$
$457$	−683177.	−0.153018	−0.0765090	+	0.997069i	$0.524377\pi$
$458$	−7.26897e6	−1.61923
$459$	3.11650e6	0.690456
$460$	−2.47371e7	−5.45073
$461$	−8.37135e6	−1.83461	−0.917304	−	0.398188i	$-0.869639\pi$
$461$	−8.37135e6	−1.83461	−0.917304	+	0.398188i	$0.869639\pi$
$462$	789828.	0.172158
$463$	6.69663e6	1.45179	0.725895	−	0.687806i	$-0.241426\pi$
$463$	6.69663e6	1.45179	0.725895	+	0.687806i	$0.241426\pi$
$464$	−5.39255e6	−1.16278
$465$	−4.78099e6	−1.02538
$466$	−9.50875e6	−2.02842
$467$	−3.85465e6	−0.817887	−0.408943	−	0.912560i	$-0.634103\pi$
$467$	−3.85465e6	−0.817887	−0.408943	+	0.912560i	$0.634103\pi$
$468$	2.66318e7	5.62065
$469$	257872.	0.0541342
$470$	6.10380e6	1.27455
$471$	1.32396e7	2.74994
$472$	7.35264e6	1.51911
$473$	573030.	0.117767
$474$	−1.58432e7	−3.23889
$475$	−1.70114e6	−0.345945
$476$	9.63280e6	1.94866
$477$	521224.	0.104889
$478$	−1.07711e7	−2.15620
$479$	−9.16044e6	−1.82422	−0.912111	−	0.409944i	$-0.865548\pi$
$479$	−9.16044e6	−1.82422	−0.912111	+	0.409944i	$0.865548\pi$
$480$	3.00966e7	5.96230
$481$	−1.36994e6	−0.269984
$482$	−1.34930e7	−2.64539
$483$	−6.38061e6	−1.24450
$484$	−1.33222e7	−2.58501
$485$	4.76117e6	0.919092
$486$	−1.36461e7	−2.62070
$487$	−5.67280e6	−1.08387	−0.541933	−	0.840422i	$-0.682307\pi$
$487$	−5.67280e6	−1.08387	−0.541933	+	0.840422i	$0.682307\pi$
$488$	−5.04896e6	−0.959736
$489$	−1.15581e7	−2.18583
$490$	9.60884e6	1.80793
$491$	2.15610e6	0.403612	0.201806	−	0.979425i	$-0.435319\pi$
$491$	2.15610e6	0.403612	0.201806	+	0.979425i	$0.435319\pi$
$492$	1.58689e7	2.95552
$493$	2.87382e6	0.532528
$494$	9.81390e6	1.80936
$495$	−1.07479e6	−0.197157
$496$	9.52898e6	1.73917
$497$	−18003.7	−0.00326942
$498$	1.60628e7	2.90235
$499$	6.36090e6	1.14358	0.571791	−	0.820399i	$-0.306249\pi$
$499$	6.36090e6	1.14358	0.571791	+	0.820399i	$0.306249\pi$
$500$	−7.45608e6	−1.33378
$501$	7.62961e6	1.35803
$502$	−8.02932e6	−1.42206
$503$	5.73803e6	1.01121	0.505606	−	0.862764i	$-0.331269\pi$
$503$	5.73803e6	1.01121	0.505606	+	0.862764i	$0.331269\pi$
$504$	1.14561e7	2.00891
$505$	−4.85313e6	−0.846825
$506$	−2.15439e6	−0.374066
$507$	−1.49121e7	−2.57644
$508$	3.55229e6	0.610730
$509$	5.86667e6	1.00368	0.501842	−	0.864959i	$-0.332656\pi$
$509$	5.86667e6	1.00368	0.501842	+	0.864959i	$0.332656\pi$
$510$	−3.19807e7	−5.44455
$511$	4.34313e6	0.735784
$512$	−365474.	−0.0616144
$513$	1.59820e6	0.268126
$514$	−1.98422e7	−3.31270
$515$	1.33539e7	2.21866
$516$	2.37282e7	3.92320
$517$	384841.	0.0633220
$518$	−952511.	−0.155972
$519$	−2.04191e6	−0.332750
$520$	−3.95243e7	−6.40996
$521$	6.78628e6	1.09531	0.547656	−	0.836704i	$-0.315520\pi$
$521$	6.78628e6	1.09531	0.547656	+	0.836704i	$0.315520\pi$
$522$	5.52432e6	0.887365
$523$	1.91496e6	0.306130	0.153065	−	0.988216i	$-0.451086\pi$
$523$	1.91496e6	0.306130	0.153065	+	0.988216i	$0.451086\pi$
$524$	−1.09190e7	−1.73721
$525$	2.85633e6	0.452284
$526$	−737680.	−0.116253
$527$	−5.07823e6	−0.796500
$528$	3.78357e6	0.590633
$529$	1.09678e7	1.70405
$530$	−1.25032e6	−0.193344
$531$	−4.17139e6	−0.642015
$532$	4.93989e6	0.756725
$533$	−7.99534e6	−1.21904
$534$	6.00452e6	0.911224
$535$	−7.68395e6	−1.16065
$536$	2.23059e6	0.335357
$537$	−2.39492e6	−0.358390
$538$	1.33830e7	1.99341
$539$	605831.	0.0898214
$540$	−1.04037e7	−1.53534
$541$	−1.04027e7	−1.52811	−0.764053	−	0.645154i	$-0.776793\pi$
$541$	−1.04027e7	−1.52811	−0.764053	+	0.645154i	$0.776793\pi$
$542$	1.25703e7	1.83801
$543$	−2.33455e6	−0.339784
$544$	3.19677e7	4.63142
$545$	−5.62788e6	−0.811622
$546$	−1.64782e7	−2.36553
$547$	1.04608e7	1.49484	0.747421	−	0.664351i	$-0.231292\pi$
$547$	1.04608e7	1.49484	0.747421	+	0.664351i	$0.231292\pi$
$548$	2.01131e7	2.86107
$549$	2.86444e6	0.405610
$550$	964431.	0.135945
$551$	1.47375e6	0.206798
$552$	−5.51922e7	−7.70957
$553$	4.01797e6	0.558720
$554$	−1.03400e7	−1.43135
$555$	2.28934e6	0.315485
$556$	2.90473e7	3.98491
$557$	−4.38817e6	−0.599302	−0.299651	−	0.954049i	$-0.596870\pi$
$557$	−4.38817e6	−0.599302	−0.299651	+	0.954049i	$0.596870\pi$
$558$	−9.76182e6	−1.32723
$559$	−1.19552e7	−1.61818
$560$	−1.52190e7	−2.05077
$561$	−2.01636e6	−0.270496
$562$	−2.02761e6	−0.270797
$563$	−1.37531e7	−1.82865	−0.914325	−	0.404982i	$-0.867278\pi$
$563$	−1.37531e7	−1.82865	−0.914325	+	0.404982i	$0.867278\pi$
$564$	1.59356e7	2.10946
$565$	1.06573e7	1.40451
$566$	1.07892e7	1.41562
$567$	2.29661e6	0.300006
$568$	−155732.	−0.0202538
$569$	1.18191e7	1.53039	0.765197	−	0.643796i	$-0.222641\pi$
$569$	1.18191e7	1.53039	0.765197	+	0.643796i	$0.222641\pi$
$570$	−1.64003e7	−2.11429
$571$	1.71185e6	0.219723	0.109862	−	0.993947i	$-0.464959\pi$
$571$	1.71185e6	0.219723	0.109862	+	0.993947i	$0.464959\pi$
$572$	−4.02789e6	−0.514740
$573$	−313964.	−0.0399479
$574$	−5.55912e6	−0.704250
$575$	−7.79114e6	−0.982723
$576$	2.76268e7	3.46956
$577$	6.54779e6	0.818757	0.409378	−	0.912365i	$-0.365746\pi$
$577$	6.54779e6	0.818757	0.409378	+	0.912365i	$0.365746\pi$
$578$	−1.86820e7	−2.32597
$579$	−2.23090e6	−0.276557
$580$	−9.59357e6	−1.18416
$581$	−4.07369e6	−0.500665
$582$	1.71702e7	2.10120
$583$	−78831.6	−0.00960570
$584$	3.75680e7	4.55813
$585$	2.24234e7	2.70902
$586$	−1.16337e7	−1.39951
$587$	−7.71695e6	−0.924380	−0.462190	−	0.886781i	$-0.652936\pi$
$587$	−7.71695e6	−0.924380	−0.462190	+	0.886781i	$0.652936\pi$
$588$	2.50864e7	2.99223
$589$	−2.60422e6	−0.309306
$590$	1.00064e7	1.18344
$591$	2.45984e6	0.289694
$592$	−4.56289e6	−0.535101
$593$	−1.47686e7	−1.72466	−0.862329	−	0.506349i	$-0.830995\pi$
$593$	−1.47686e7	−1.72466	−0.862329	+	0.506349i	$0.830995\pi$
$594$	−906071.	−0.105365
$595$	8.11060e6	0.939206
$596$	−8.32569e6	−0.960073
$597$	8.61834e6	0.989664
$598$	4.49471e7	5.13983
$599$	−1.95718e6	−0.222876	−0.111438	−	0.993771i	$-0.535546\pi$
$599$	−1.95718e6	−0.222876	−0.111438	+	0.993771i	$0.535546\pi$
$600$	2.47073e7	2.80186
$601$	−3.87141e6	−0.437203	−0.218601	−	0.975814i	$-0.570149\pi$
$601$	−3.87141e6	−0.437203	−0.218601	+	0.975814i	$0.570149\pi$
$602$	−8.31237e6	−0.934832
$603$	−1.26549e6	−0.141731
$604$	−3.55753e7	−3.96786
$605$	−1.12170e7	−1.24591
$606$	−1.75019e7	−1.93599
$607$	6.34410e6	0.698873	0.349437	−	0.936960i	$-0.386373\pi$
$607$	6.34410e6	0.698873	0.349437	+	0.936960i	$0.386373\pi$
$608$	1.63937e7	1.79853
$609$	−2.47453e6	−0.270364
$610$	−6.87125e6	−0.747672
$611$	−8.02894e6	−0.870072
$612$	−4.72723e7	−5.10186
$613$	2.23621e6	0.240359	0.120180	−	0.992752i	$-0.461653\pi$
$613$	2.23621e6	0.240359	0.120180	+	0.992752i	$0.461653\pi$
$614$	1.79108e7	1.91731
$615$	1.33613e7	1.42449
$616$	−1.73266e6	−0.183976
$617$	−4.40553e6	−0.465892	−0.232946	−	0.972490i	$-0.574836\pi$
$617$	−4.40553e6	−0.465892	−0.232946	+	0.972490i	$0.574836\pi$
$618$	4.81582e7	5.07223
$619$	3.94728e6	0.414068	0.207034	−	0.978334i	$-0.433619\pi$
$619$	3.94728e6	0.414068	0.207034	+	0.978334i	$0.433619\pi$
$620$	1.69525e7	1.77114
$621$	7.31968e6	0.761664
$622$	−1.25155e7	−1.29709
$623$	−1.52280e6	−0.157190
$624$	−7.89368e7	−8.11556
$625$	−1.21140e7	−1.24047
$626$	2.31198e7	2.35802
$627$	−1.03403e6	−0.105042
$628$	−4.69452e7	−4.74998
$629$	2.43168e6	0.245064
$630$	1.55909e7	1.56502
$631$	5.18942e6	0.518855	0.259427	−	0.965763i	$-0.416466\pi$
$631$	5.18942e6	0.518855	0.259427	+	0.965763i	$0.416466\pi$
$632$	3.47555e7	3.46123
$633$	1.27298e7	1.26274
$634$	8.51826e6	0.841643
$635$	2.99095e6	0.294357
$636$	−3.26428e6	−0.319997
$637$	−1.26395e7	−1.23419
$638$	−835516.	−0.0812649
$639$	88351.9	0.00855980
$640$	−2.55783e7	−2.46843
$641$	−4.26536e6	−0.410025	−0.205013	−	0.978759i	$-0.565724\pi$
$641$	−4.26536e6	−0.410025	−0.205013	+	0.978759i	$0.565724\pi$
$642$	−2.77107e7	−2.65344
$643$	−1.75228e7	−1.67138	−0.835690	−	0.549201i	$-0.814932\pi$
$643$	−1.75228e7	−1.67138	−0.835690	+	0.549201i	$0.814932\pi$
$644$	2.26244e7	2.14962
$645$	1.99786e7	1.89089
$646$	−1.74200e7	−1.64235
$647$	−5.19964e6	−0.488329	−0.244164	−	0.969734i	$-0.578514\pi$
$647$	−5.19964e6	−0.488329	−0.244164	+	0.969734i	$0.578514\pi$
$648$	1.98657e7	1.85852
$649$	630896.	0.0587957
$650$	−2.01210e7	−1.86795
$651$	4.37265e6	0.404383
$652$	4.09829e7	3.77558
$653$	2.11913e7	1.94480	0.972400	−	0.233320i	$-0.0749591\pi$
$653$	2.11913e7	1.94480	0.972400	+	0.233320i	$0.0749591\pi$
$654$	−2.02958e7	−1.85551
$655$	−9.19352e6	−0.837295
$656$	−2.66303e7	−2.41611
$657$	−2.13136e7	−1.92639
$658$	−5.58249e6	−0.502647
$659$	−6.62934e6	−0.594644	−0.297322	−	0.954777i	$-0.596093\pi$
$659$	−6.62934e6	−0.594644	−0.297322	+	0.954777i	$0.596093\pi$
$660$	6.73113e6	0.601490
$661$	304352.	0.0270940	0.0135470	−	0.999908i	$-0.495688\pi$
$661$	304352.	0.0270940	0.0135470	+	0.999908i	$0.495688\pi$
$662$	−2.59778e7	−2.30387
$663$	4.20674e7	3.71674
$664$	−3.52374e7	−3.10159
$665$	4.15928e6	0.364723
$666$	4.67438e6	0.408356
$667$	6.74970e6	0.587449
$668$	−2.70531e7	−2.34572
$669$	1.21242e7	1.04734
$670$	3.03567e6	0.261256
$671$	−433228.	−0.0371458
$672$	−2.75261e7	−2.35137
$673$	−407292.	−0.0346632	−0.0173316	−	0.999850i	$-0.505517\pi$
$673$	−407292.	−0.0346632	−0.0173316	+	0.999850i	$0.505517\pi$
$674$	1.04055e7	0.882298
$675$	−3.27672e6	−0.276809
$676$	5.28754e7	4.45028
$677$	−1.15318e7	−0.966997	−0.483499	−	0.875345i	$-0.660634\pi$
$677$	−1.15318e7	−0.966997	−0.483499	+	0.875345i	$0.660634\pi$
$678$	3.84333e7	3.21095
$679$	−4.35453e6	−0.362465
$680$	7.01567e7	5.81831
$681$	6.83358e6	0.564652
$682$	1.47641e6	0.121548
$683$	−3.36938e6	−0.276375	−0.138187	−	0.990406i	$-0.544128\pi$
$683$	−3.36938e6	−0.276375	−0.138187	+	0.990406i	$0.544128\pi$
$684$	−2.42422e7	−1.98121
$685$	1.69348e7	1.37897
$686$	−2.04820e7	−1.66174
$687$	−1.59787e7	−1.29166
$688$	−3.98194e7	−3.20718
$689$	1.64467e6	0.131987
$690$	−7.51125e7	−6.00606
$691$	−7.97672e6	−0.635520	−0.317760	−	0.948171i	$-0.602931\pi$
$691$	−7.97672e6	−0.635520	−0.317760	+	0.948171i	$0.602931\pi$
$692$	7.24022e6	0.574760
$693$	982996.	0.0777533
$694$	1.69470e6	0.133565
$695$	2.44572e7	1.92063
$696$	−2.14047e7	−1.67489
$697$	1.41920e7	1.10652
$698$	−103273.	−0.00802317
$699$	−2.09022e7	−1.61808
$700$	−1.01280e7	−0.781230
$701$	3.45065e6	0.265220	0.132610	−	0.991168i	$-0.457664\pi$
$701$	3.45065e6	0.265220	0.132610	+	0.991168i	$0.457664\pi$
$702$	1.89034e7	1.44776
$703$	1.24701e6	0.0951661
$704$	−4.17837e6	−0.317742
$705$	1.34174e7	1.01671
$706$	3.61087e7	2.72647
$707$	4.43864e6	0.333965
$708$	2.61243e7	1.95867
$709$	−2.22094e7	−1.65928	−0.829641	−	0.558297i	$-0.811455\pi$
$709$	−2.22094e7	−1.65928	−0.829641	+	0.558297i	$0.811455\pi$
$710$	−211939.	−0.0157785
$711$	−1.97179e7	−1.46281
$712$	−1.31722e7	−0.973778
$713$	−1.19272e7	−0.878644
$714$	2.92493e7	2.14719
$715$	−3.39139e6	−0.248092
$716$	8.49194e6	0.619048
$717$	−2.36770e7	−1.72000
$718$	−5.01845e7	−3.63294
$719$	1.14967e7	0.829373	0.414687	−	0.909964i	$-0.363891\pi$
$719$	1.14967e7	0.829373	0.414687	+	0.909964i	$0.363891\pi$
$720$	7.46864e7	5.36921
$721$	−1.22134e7	−0.874978
$722$	1.77258e7	1.26550
$723$	−2.96603e7	−2.11023
$724$	8.27786e6	0.586910
$725$	−3.02156e6	−0.213494
$726$	−4.04519e7	−2.84837
$727$	1.16354e7	0.816481	0.408241	−	0.912874i	$-0.366142\pi$
$727$	1.16354e7	0.816481	0.408241	+	0.912874i	$0.366142\pi$
$728$	3.61486e7	2.52792
$729$	−2.13611e7	−1.48869
$730$	5.11272e7	3.55096
$731$	2.12207e7	1.46882
$732$	−1.79392e7	−1.23744
$733$	−1.57155e7	−1.08036	−0.540180	−	0.841549i	$-0.681644\pi$
$733$	−1.57155e7	−1.08036	−0.540180	+	0.841549i	$0.681644\pi$
$734$	1.50232e7	1.02925
$735$	2.11222e7	1.44219
$736$	7.50820e7	5.10907
$737$	191397.	0.0129797
$738$	2.72810e7	1.84382
$739$	8.37662e6	0.564232	0.282116	−	0.959380i	$-0.408964\pi$
$739$	8.37662e6	0.564232	0.282116	+	0.959380i	$0.408964\pi$
$740$	−8.11757e6	−0.544937
$741$	2.15730e7	1.44333
$742$	1.14353e6	0.0762496
$743$	6.01778e6	0.399912	0.199956	−	0.979805i	$-0.435920\pi$
$743$	6.01778e6	0.399912	0.199956	+	0.979805i	$0.435920\pi$
$744$	3.78234e7	2.50512
$745$	−7.01004e6	−0.462732
$746$	3.46189e7	2.27754
$747$	1.99913e7	1.31081
$748$	7.14962e6	0.467228
$749$	7.02768e6	0.457728
$750$	−2.26398e7	−1.46967
$751$	−1.39393e7	−0.901863	−0.450931	−	0.892559i	$-0.648908\pi$
$751$	−1.39393e7	−0.901863	−0.450931	+	0.892559i	$0.648908\pi$
$752$	−2.67422e7	−1.72446
$753$	−1.76501e7	−1.13438
$754$	1.74314e7	1.11662
$755$	−2.99536e7	−1.91241
$756$	9.51514e6	0.605495
$757$	−1.63595e7	−1.03760	−0.518802	−	0.854895i	$-0.673622\pi$
$757$	−1.63595e7	−1.03760	−0.518802	+	0.854895i	$0.673622\pi$
$758$	1.71796e7	1.08602
$759$	−4.73579e6	−0.298393
$760$	3.59777e7	2.25943
$761$	−1.60196e7	−1.00274	−0.501372	−	0.865232i	$-0.667171\pi$
$761$	−1.60196e7	−1.00274	−0.501372	+	0.865232i	$0.667171\pi$
$762$	1.07863e7	0.672952
$763$	5.14722e6	0.320082
$764$	1.11326e6	0.0690020
$765$	−3.98022e7	−2.45897
$766$	−4.30666e7	−2.65197
$767$	−1.31624e7	−0.807880
$768$	−2.62675e7	−1.60700
$769$	−1.46215e7	−0.891612	−0.445806	−	0.895130i	$-0.647083\pi$
$769$	−1.46215e7	−0.891612	−0.445806	+	0.895130i	$0.647083\pi$
$770$	−2.35802e6	−0.143325
$771$	−4.36172e7	−2.64254
$772$	7.91034e6	0.477696
$773$	1.91987e7	1.15564	0.577820	−	0.816164i	$-0.303903\pi$
$773$	1.91987e7	1.15564	0.577820	+	0.816164i	$0.303903\pi$
$774$	4.07924e7	2.44752
$775$	5.33929e6	0.319323
$776$	−3.76666e7	−2.24545
$777$	−2.09382e6	−0.124419
$778$	−1.70806e7	−1.01171
$779$	7.27791e6	0.429698
$780$	−1.40432e8	−8.26474
$781$	−13362.6	−0.000783907 0
$782$	−7.97824e7	−4.66541
$783$	2.83872e6	0.165470
$784$	−4.20987e7	−2.44612
$785$	−3.95268e7	−2.28938
$786$	−3.31546e7	−1.91420
$787$	−441025.	−0.0253820	−0.0126910	−	0.999919i	$-0.504040\pi$
$787$	−441025.	−0.0253820	−0.0126910	+	0.999919i	$0.504040\pi$
$788$	−8.72213e6	−0.500388
$789$	−1.62157e6	−0.0927351
$790$	4.72996e7	2.69643
$791$	−9.74704e6	−0.553900
$792$	8.50292e6	0.481676
$793$	9.03844e6	0.510400
$794$	5.37172e7	3.02386
$795$	−2.74845e6	−0.154231
$796$	−3.05589e7	−1.70945
$797$	3.11304e7	1.73596	0.867980	−	0.496600i	$-0.165418\pi$
$797$	3.11304e7	1.73596	0.867980	+	0.496600i	$0.165418\pi$
$798$	1.49996e7	0.833821
$799$	1.42516e7	0.789763
$800$	−3.36111e7	−1.85677
$801$	7.47305e6	0.411544
$802$	6.57465e7	3.60941
$803$	3.22354e6	0.176418
$804$	7.92541e6	0.432396
$805$	1.90492e7	1.03607
$806$	−3.08024e7	−1.67012
$807$	2.94186e7	1.59015
$808$	3.83942e7	2.06889
$809$	2.82647e7	1.51835	0.759176	−	0.650885i	$-0.225602\pi$
$809$	2.82647e7	1.51835	0.759176	+	0.650885i	$0.225602\pi$
$810$	2.70357e7	1.44786
$811$	−1.36201e7	−0.727155	−0.363577	−	0.931564i	$-0.618445\pi$
$811$	−1.36201e7	−0.727155	−0.363577	+	0.931564i	$0.618445\pi$
$812$	8.77420e6	0.467001
$813$	2.76321e7	1.46618
$814$	−706969.	−0.0373972
$815$	3.45067e7	1.81974
$816$	1.40115e8	7.36647
$817$	1.08824e7	0.570388
$818$	−4.64408e7	−2.42670
$819$	−2.05083e7	−1.06836
$820$	−4.73764e7	−2.46052
$821$	1.69419e7	0.877209	0.438605	−	0.898680i	$-0.355473\pi$
$821$	1.69419e7	0.877209	0.438605	+	0.898680i	$0.355473\pi$
$822$	6.10720e7	3.15256
$823$	2.09055e7	1.07587	0.537936	−	0.842985i	$-0.319204\pi$
$823$	2.09055e7	1.07587	0.537936	+	0.842985i	$0.319204\pi$
$824$	−1.05646e8	−5.42043
$825$	2.12002e6	0.108444
$826$	−9.15176e6	−0.466718
$827$	1.24093e7	0.630932	0.315466	−	0.948937i	$-0.397839\pi$
$827$	1.24093e7	0.630932	0.315466	+	0.948937i	$0.397839\pi$
$828$	−1.11028e8	−5.62802
$829$	2.86974e7	1.45029	0.725147	−	0.688594i	$-0.241772\pi$
$829$	2.86974e7	1.45029	0.725147	+	0.688594i	$0.241772\pi$
$830$	−4.79554e7	−2.41625
$831$	−2.27294e7	−1.14179
$832$	8.71734e7	4.36592
$833$	2.24354e7	1.12027
$834$	8.81999e7	4.39089
$835$	−2.27781e7	−1.13058
$836$	3.66647e6	0.181440
$837$	−5.01620e6	−0.247492
$838$	−3.78902e7	−1.86387
$839$	−2.74028e7	−1.34397	−0.671985	−	0.740565i	$-0.734558\pi$
$839$	−2.74028e7	−1.34397	−0.671985	+	0.740565i	$0.734558\pi$
$840$	−6.04090e7	−2.95395
$841$	−1.78935e7	−0.872378
$842$	−4.36123e7	−2.11997
$843$	−4.45711e6	−0.216015
$844$	−4.51374e7	−2.18112
$845$	4.45199e7	2.14493
$846$	2.73957e7	1.31600
$847$	1.02590e7	0.491355
$848$	5.47794e6	0.261594
$849$	2.37168e7	1.12924
$850$	3.57153e7	1.69553
$851$	5.71124e6	0.270338
$852$	−553324.	−0.0261144
$853$	−3.54404e7	−1.66773	−0.833865	−	0.551969i	$-0.813877\pi$
$853$	−3.54404e7	−1.66773	−0.833865	+	0.551969i	$0.813877\pi$
$854$	6.28439e6	0.294862
$855$	−2.04114e7	−0.954897
$856$	6.07894e7	2.83559
$857$	1.42824e7	0.664279	0.332139	−	0.943230i	$-0.392230\pi$
$857$	1.42824e7	0.664279	0.332139	+	0.943230i	$0.392230\pi$
$858$	−1.22304e7	−0.567182
$859$	−9.48303e6	−0.438494	−0.219247	−	0.975669i	$-0.570360\pi$
$859$	−9.48303e6	−0.438494	−0.219247	+	0.975669i	$0.570360\pi$
$860$	−7.08403e7	−3.26614
$861$	−1.22201e7	−0.561781
$862$	4.60764e7	2.11208
$863$	1.74649e7	0.798249	0.399125	−	0.916897i	$-0.369314\pi$
$863$	1.74649e7	0.798249	0.399125	+	0.916897i	$0.369314\pi$
$864$	3.15773e7	1.43910
$865$	6.09610e6	0.277021
$866$	2.81033e7	1.27339
$867$	−4.10669e7	−1.85543
$868$	−1.55046e7	−0.698491
$869$	2.98221e6	0.133964
$870$	−2.91302e7	−1.30480
$871$	−3.99312e6	−0.178347
$872$	4.45234e7	1.98288
$873$	2.13695e7	0.948985
$874$	−4.09140e7	−1.81173
$875$	5.74168e6	0.253524
$876$	1.33481e8	5.87706
$877$	−2.14974e7	−0.943815	−0.471907	−	0.881648i	$-0.656434\pi$
$877$	−2.14974e7	−0.943815	−0.471907	+	0.881648i	$0.656434\pi$
$878$	−6.59273e7	−2.88622
$879$	−2.55734e7	−1.11639
$880$	−1.12958e7	−0.491712
$881$	3.20228e7	1.39001	0.695007	−	0.719003i	$-0.255401\pi$
$881$	3.20228e7	1.39001	0.695007	+	0.719003i	$0.255401\pi$
$882$	4.31273e7	1.86673
$883$	697710.	0.0301143	0.0150572	−	0.999887i	$-0.495207\pi$
$883$	697710.	0.0301143	0.0150572	+	0.999887i	$0.495207\pi$
$884$	−1.49163e8	−6.41992
$885$	2.19961e7	0.944034
$886$	−8.77849e7	−3.75695
$887$	−1.32853e6	−0.0566971	−0.0283486	−	0.999598i	$-0.509025\pi$
$887$	−1.32853e6	−0.0566971	−0.0283486	+	0.999598i	$0.509025\pi$
$888$	−1.81115e7	−0.770765
$889$	−2.73550e6	−0.116087
$890$	−1.79264e7	−0.758610
$891$	1.70458e6	0.0719323
$892$	−4.29901e7	−1.80907
$893$	7.30850e6	0.306690
$894$	−2.52803e7	−1.05789
$895$	7.15002e6	0.298366
$896$	2.33937e7	0.973484
$897$	9.88030e7	4.10005
$898$	1.45930e7	0.603883
$899$	−4.62560e6	−0.190884
$900$	4.97025e7	2.04537
$901$	−2.91933e6	−0.119804
$902$	−4.12607e6	−0.168858
$903$	−1.82723e7	−0.745717
$904$	−8.43119e7	−3.43137
$905$	6.96977e6	0.282877
$906$	−1.08022e8	−4.37210
$907$	2.22771e7	0.899166	0.449583	−	0.893239i	$-0.351573\pi$
$907$	2.22771e7	0.899166	0.449583	+	0.893239i	$0.351573\pi$
$908$	−2.42305e7	−0.975323
$909$	−2.17823e7	−0.874367
$910$	4.91955e7	1.96934
$911$	−7.03396e6	−0.280804	−0.140402	−	0.990095i	$-0.544840\pi$
$911$	−7.03396e6	−0.280804	−0.140402	+	0.990095i	$0.544840\pi$
$912$	7.18538e7	2.86064
$913$	−3.02356e6	−0.120044
$914$	7.35547e6	0.291236
$915$	−1.51044e7	−0.596419
$916$	5.66573e7	2.23109
$917$	8.40832e6	0.330207
$918$	−3.35541e7	−1.31413
$919$	−2.65369e7	−1.03648	−0.518241	−	0.855234i	$-0.673413\pi$
$919$	−2.65369e7	−1.03648	−0.518241	+	0.855234i	$0.673413\pi$
$920$	1.64776e8	6.41836
$921$	3.93715e7	1.52944
$922$	9.01308e7	3.49177
$923$	278785.	0.0107712
$924$	−6.15624e6	−0.237212
$925$	−2.55669e6	−0.0982478
$926$	−7.20997e7	−2.76316
$927$	5.99363e7	2.29082
$928$	2.91184e7	1.10993
$929$	3.83355e6	0.145734	0.0728671	−	0.997342i	$-0.476785\pi$
$929$	3.83355e6	0.145734	0.0728671	+	0.997342i	$0.476785\pi$
$930$	5.14749e7	1.95159
$931$	1.15053e7	0.435036
$932$	7.41152e7	2.79491
$933$	−2.75116e7	−1.03469
$934$	4.15014e7	1.55667
$935$	6.01982e6	0.225193
$936$	−1.77397e8	−6.61844
$937$	5.88785e6	0.219082	0.109541	−	0.993982i	$-0.465062\pi$
$937$	5.88785e6	0.219082	0.109541	+	0.993982i	$0.465062\pi$
$938$	−2.77640e6	−0.103033
$939$	5.08220e7	1.88100
$940$	−4.75755e7	−1.75616
$941$	−2.78697e7	−1.02602	−0.513012	−	0.858381i	$-0.671470\pi$
$941$	−2.78697e7	−1.02602	−0.513012	+	0.858381i	$0.671470\pi$
$942$	−1.42546e8	−5.23391
$943$	3.33324e7	1.22064
$944$	−4.38404e7	−1.60120
$945$	8.01154e6	0.291834
$946$	−6.16958e6	−0.224144
$947$	−2.07230e7	−0.750894	−0.375447	−	0.926844i	$-0.622511\pi$
$947$	−2.07230e7	−0.750894	−0.375447	+	0.926844i	$0.622511\pi$
$948$	1.23488e8	4.46277
$949$	−6.72528e7	−2.42407
$950$	1.83155e7	0.658430
$951$	1.87249e7	0.671380
$952$	−6.41648e7	−2.29459
$953$	4.20353e7	1.49928	0.749638	−	0.661848i	$-0.230228\pi$
$953$	4.20353e7	1.49928	0.749638	+	0.661848i	$0.230228\pi$
$954$	−5.61179e6	−0.199632
$955$	937337.	0.0332573
$956$	8.39542e7	2.97097
$957$	−1.83664e6	−0.0648252
$958$	9.86266e7	3.47200
$959$	−1.54884e7	−0.543828
$960$	−1.45678e8	−5.10172
$961$	−2.04554e7	−0.714496
$962$	1.47495e7	0.513855
$963$	−3.44879e7	−1.19840
$964$	1.05170e8	3.64501
$965$	6.66033e6	0.230238
$966$	6.86973e7	2.36863
$967$	−141966.	−0.00488222	−0.00244111	−	0.999997i	$-0.500777\pi$
$967$	−141966.	−0.00488222	−0.00244111	+	0.999997i	$0.500777\pi$
$968$	8.87401e7	3.04391
$969$	−3.82927e7	−1.31011
$970$	−5.12615e7	−1.74929
$971$	−4.73654e7	−1.61218	−0.806089	−	0.591794i	$-0.798420\pi$
$971$	−4.73654e7	−1.61218	−0.806089	+	0.591794i	$0.798420\pi$
$972$	1.06363e8	3.61099
$973$	−2.23683e7	−0.757446
$974$	6.10767e7	2.06290
$975$	−4.42300e7	−1.49007
$976$	3.01046e7	1.01160
$977$	−2.77914e6	−0.0931482	−0.0465741	−	0.998915i	$-0.514830\pi$
$977$	−2.77914e6	−0.0931482	−0.0465741	+	0.998915i	$0.514830\pi$
$978$	1.24442e8	4.16024
$979$	−1.13025e6	−0.0376893
$980$	−7.48953e7	−2.49109
$981$	−2.52596e7	−0.838019
$982$	−2.32138e7	−0.768187
$983$	−1.05988e7	−0.349844	−0.174922	−	0.984582i	$-0.555967\pi$
$983$	−1.05988e7	−0.349844	−0.174922	+	0.984582i	$0.555967\pi$
$984$	−1.05704e8	−3.48019
$985$	−7.34384e6	−0.241175
$986$	−3.09412e7	−1.01355
$987$	−1.22715e7	−0.400962
$988$	−7.64936e7	−2.49306
$989$	4.98408e7	1.62030
$990$	1.15718e7	0.375244
$991$	4.93586e7	1.59654	0.798268	−	0.602303i	$-0.205750\pi$
$991$	4.93586e7	1.59654	0.798268	+	0.602303i	$0.205750\pi$
$992$	−5.14540e7	−1.66012
$993$	−5.71046e7	−1.83780
$994$	193838.	0.00622262
$995$	−2.57299e7	−0.823913
$996$	−1.25200e8	−3.99906
$997$	−3.51091e7	−1.11862	−0.559310	−	0.828959i	$-0.688934\pi$
$997$	−3.51091e7	−1.11862	−0.559310	+	0.828959i	$0.688934\pi$
$998$	−6.84851e7	−2.17656
$999$	2.40198e6	0.0761474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.a.a.1.1	✓	7
3.2	odd	2		333.6.a.c.1.7		7
4.3	odd	2		592.6.a.g.1.6		7
5.4	even	2		925.6.a.a.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.a.a.1.1	✓	7	1.1	even	1	trivial
333.6.a.c.1.7		7	3.2	odd	2
592.6.a.g.1.6		7	4.3	odd	2
925.6.a.a.1.7		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q-10.7666 q^{2} -23.6672 q^{3} +83.9191 q^{4} +70.6580 q^{5} +254.814 q^{6} -64.6233 q^{7} -558.991 q^{8} +317.134 q^{9} +O(q^{10})\)	\(q-10.7666 q^{2} -23.6672 q^{3} +83.9191 q^{4} +70.6580 q^{5} +254.814 q^{6} -64.6233 q^{7} -558.991 q^{8} +317.134 q^{9} -760.745 q^{10} -47.9645 q^{11} -1986.13 q^{12} +1000.68 q^{13} +695.772 q^{14} -1672.27 q^{15} +3333.01 q^{16} -1776.24 q^{17} -3414.45 q^{18} -910.892 q^{19} +5929.56 q^{20} +1529.45 q^{21} +516.413 q^{22} -4171.83 q^{23} +13229.7 q^{24} +1867.56 q^{25} -10773.9 q^{26} -1754.55 q^{27} -5423.13 q^{28} -1617.92 q^{29} +18004.7 q^{30} +2858.97 q^{31} -17997.4 q^{32} +1135.18 q^{33} +19124.1 q^{34} -4566.15 q^{35} +26613.6 q^{36} -1369.00 q^{37} +9807.19 q^{38} -23683.4 q^{39} -39497.2 q^{40} -7989.87 q^{41} -16466.9 q^{42} -11947.0 q^{43} -4025.14 q^{44} +22408.1 q^{45} +44916.4 q^{46} -8023.45 q^{47} -78882.9 q^{48} -12630.8 q^{49} -20107.2 q^{50} +42038.6 q^{51} +83976.6 q^{52} +1643.54 q^{53} +18890.5 q^{54} -3389.07 q^{55} +36123.9 q^{56} +21558.2 q^{57} +17419.5 q^{58} -13153.4 q^{59} -140336. q^{60} +9032.26 q^{61} -30781.3 q^{62} -20494.3 q^{63} +87113.8 q^{64} +70706.4 q^{65} -12222.0 q^{66} -3990.39 q^{67} -149061. q^{68} +98735.4 q^{69} +49161.8 q^{70} +278.595 q^{71} -177275. q^{72} -67206.8 q^{73} +14739.4 q^{74} -44199.8 q^{75} -76441.3 q^{76} +3099.62 q^{77} +254989. q^{78} -62175.3 q^{79} +235504. q^{80} -35538.5 q^{81} +86023.5 q^{82} +63037.5 q^{83} +128350. q^{84} -125506. q^{85} +128628. q^{86} +38291.6 q^{87} +26811.7 q^{88} +23564.3 q^{89} -241258. q^{90} -64667.5 q^{91} -350097. q^{92} -67663.7 q^{93} +86385.1 q^{94} -64361.9 q^{95} +425947. q^{96} +67383.2 q^{97} +135991. q^{98} -15211.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9	\( 7 q - 8 q^{2} - 47 q^{3} + 106 q^{4} - 64 q^{5} - 141 q^{6} - 293 q^{7} - 474 q^{8} + 292 q^{9} - 2017 q^{10} - 1457 q^{11} - 3917 q^{12} - 536 q^{13} - 488 q^{14} - 254 q^{15} + 2714 q^{16} - 3068 q^{17} + 4107 q^{18} - 1900 q^{19} + 1453 q^{20} + 2425 q^{21} + 4467 q^{22} - 3986 q^{23} + 11523 q^{24} + 12231 q^{25} + 911 q^{26} - 10697 q^{27} + 6486 q^{28} - 7436 q^{29} + 50276 q^{30} + 5776 q^{31} - 13366 q^{32} + 2973 q^{33} + 24128 q^{34} - 17714 q^{35} + 57889 q^{36} - 9583 q^{37} + 1248 q^{38} - 34826 q^{39} - 46751 q^{40} - 25089 q^{41} - 6232 q^{42} - 22538 q^{43} - 22817 q^{44} - 68648 q^{45} + 25485 q^{46} - 60861 q^{47} - 70825 q^{48} - 29182 q^{49} + 26797 q^{50} + 21508 q^{51} + 74493 q^{52} - 15681 q^{53} - 58620 q^{54} + 2930 q^{55} - 5542 q^{56} + 27032 q^{57} + 4979 q^{58} - 54536 q^{59} + 78104 q^{60} + 48694 q^{61} - 5601 q^{62} - 21062 q^{63} + 67074 q^{64} + 22480 q^{65} + 77598 q^{66} - 39724 q^{67} - 183104 q^{68} + 245960 q^{69} + 162468 q^{70} - 92187 q^{71} + 17685 q^{72} + 73251 q^{73} + 10952 q^{74} - 162813 q^{75} + 13504 q^{76} - 4605 q^{77} + 235693 q^{78} + 78604 q^{79} + 112473 q^{80} + 236431 q^{81} + 200777 q^{82} - 82223 q^{83} + 201198 q^{84} + 86716 q^{85} - 55686 q^{86} + 107506 q^{87} - 633 q^{88} + 181680 q^{89} - 732742 q^{90} - 14802 q^{91} - 684469 q^{92} - 37328 q^{93} + 34724 q^{94} - 222304 q^{95} + 397743 q^{96} + 39092 q^{97} - 318498 q^{98} - 29766 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 47 * q^3 + 106 * q^4 - 64 * q^5 - 141 * q^6 - 293 * q^7 - 474 * q^8 + 292 * q^9 - 2017 * q^10 - 1457 * q^11 - 3917 * q^12 - 536 * q^13 - 488 * q^14 - 254 * q^15 + 2714 * q^16 - 3068 * q^17 + 4107 * q^18 - 1900 * q^19 + 1453 * q^20 + 2425 * q^21 + 4467 * q^22 - 3986 * q^23 + 11523 * q^24 + 12231 * q^25 + 911 * q^26 - 10697 * q^27 + 6486 * q^28 - 7436 * q^29 + 50276 * q^30 + 5776 * q^31 - 13366 * q^32 + 2973 * q^33 + 24128 * q^34 - 17714 * q^35 + 57889 * q^36 - 9583 * q^37 + 1248 * q^38 - 34826 * q^39 - 46751 * q^40 - 25089 * q^41 - 6232 * q^42 - 22538 * q^43 - 22817 * q^44 - 68648 * q^45 + 25485 * q^46 - 60861 * q^47 - 70825 * q^48 - 29182 * q^49 + 26797 * q^50 + 21508 * q^51 + 74493 * q^52 - 15681 * q^53 - 58620 * q^54 + 2930 * q^55 - 5542 * q^56 + 27032 * q^57 + 4979 * q^58 - 54536 * q^59 + 78104 * q^60 + 48694 * q^61 - 5601 * q^62 - 21062 * q^63 + 67074 * q^64 + 22480 * q^65 + 77598 * q^66 - 39724 * q^67 - 183104 * q^68 + 245960 * q^69 + 162468 * q^70 - 92187 * q^71 + 17685 * q^72 + 73251 * q^73 + 10952 * q^74 - 162813 * q^75 + 13504 * q^76 - 4605 * q^77 + 235693 * q^78 + 78604 * q^79 + 112473 * q^80 + 236431 * q^81 + 200777 * q^82 - 82223 * q^83 + 201198 * q^84 + 86716 * q^85 - 55686 * q^86 + 107506 * q^87 - 633 * q^88 + 181680 * q^89 - 732742 * q^90 - 14802 * q^91 - 684469 * q^92 - 37328 * q^93 + 34724 * q^94 - 222304 * q^95 + 397743 * q^96 + 39092 * q^97 - 318498 * q^98 - 29766 * q^99

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