LMFDB - Embedded newform 309.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("309.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$49.5586003222$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 475 x^{18} + 1732 x^{17} + 94501 x^{16} - 304042 x^{15} - 10274267 x^{14} + \cdots - 108537388253184 $ x^20 - 4x^19 - 475x^18 + 1732x^17 + 94501x^16 - 304042x^15 - 10274267x^14 + 27738506x^13 + 668854800x^12 - 1394251104x^11 - 26886918880x^10 + 36931823776x^9 + 663067133248x^8 - 391924258816x^7 - 9543181747968x^6 - 2051078115840x^5 + 69736119883776x^4 + 68811719589888x^3 - 164566613229568x^2 - 286519559659520*x - 108537388253184
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-10.4554$ of defining polynomial
Character	$\chi$	$=$	309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.4554 q^{2} -9.00000 q^{3} +77.3144 q^{4} +79.0565 q^{5} +94.0982 q^{6} +9.50763 q^{7} -473.778 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.4554 q^{2} -9.00000 q^{3} +77.3144 q^{4} +79.0565 q^{5} +94.0982 q^{6} +9.50763 q^{7} -473.778 q^{8} +81.0000 q^{9} -826.564 q^{10} +172.418 q^{11} -695.830 q^{12} +166.178 q^{13} -99.4056 q^{14} -711.509 q^{15} +2479.46 q^{16} +1845.27 q^{17} -846.884 q^{18} +2703.01 q^{19} +6112.21 q^{20} -85.5686 q^{21} -1802.69 q^{22} -585.120 q^{23} +4264.00 q^{24} +3124.94 q^{25} -1737.45 q^{26} -729.000 q^{27} +735.076 q^{28} +2812.84 q^{29} +7439.08 q^{30} +8329.23 q^{31} -10762.7 q^{32} -1551.76 q^{33} -19292.9 q^{34} +751.640 q^{35} +6262.47 q^{36} -8616.75 q^{37} -28260.9 q^{38} -1495.60 q^{39} -37455.2 q^{40} +8779.33 q^{41} +894.650 q^{42} -22444.4 q^{43} +13330.4 q^{44} +6403.58 q^{45} +6117.63 q^{46} +16340.4 q^{47} -22315.1 q^{48} -16716.6 q^{49} -32672.3 q^{50} -16607.4 q^{51} +12848.0 q^{52} +10180.9 q^{53} +7621.95 q^{54} +13630.8 q^{55} -4504.50 q^{56} -24327.1 q^{57} -29409.3 q^{58} +32541.5 q^{59} -55009.9 q^{60} -26991.8 q^{61} -87085.0 q^{62} +770.118 q^{63} +33185.1 q^{64} +13137.5 q^{65} +16224.2 q^{66} +26845.8 q^{67} +142666. q^{68} +5266.08 q^{69} -7858.66 q^{70} -10408.3 q^{71} -38376.0 q^{72} -80254.3 q^{73} +90091.1 q^{74} -28124.4 q^{75} +208982. q^{76} +1639.29 q^{77} +15637.1 q^{78} -59600.3 q^{79} +196017. q^{80} +6561.00 q^{81} -91791.0 q^{82} +38542.8 q^{83} -6615.69 q^{84} +145880. q^{85} +234664. q^{86} -25315.6 q^{87} -81687.9 q^{88} -52412.2 q^{89} -66951.7 q^{90} +1579.96 q^{91} -45238.2 q^{92} -74963.1 q^{93} -170844. q^{94} +213691. q^{95} +96864.2 q^{96} +133085. q^{97} +174778. q^{98} +13965.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * 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 $

$2$	−10.4554	−1.84826	−0.924131	−	0.382075i	$-0.875210\pi$
$2$	−10.4554	−1.84826	−0.924131	+	0.382075i	$0.875210\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	77.3144	2.41608
$5$	79.0565	1.41421	0.707103	−	0.707110i	$-0.250002\pi$
$5$	79.0565	1.41421	0.707103	+	0.707110i	$0.250002\pi$
$6$	94.0982	1.06709
$7$	9.50763	0.0733377	0.0366688	−	0.999327i	$-0.488325\pi$
$7$	9.50763	0.0733377	0.0366688	+	0.999327i	$0.488325\pi$
$8$	−473.778	−2.61728
$9$	81.0000	0.333333
$10$	−826.564	−2.61382
$11$	172.418	0.429637	0.214818	−	0.976654i	$-0.431084\pi$
$11$	172.418	0.429637	0.214818	+	0.976654i	$0.431084\pi$
$12$	−695.830	−1.39492
$13$	166.178	0.272719	0.136360	−	0.990659i	$-0.456460\pi$
$13$	166.178	0.272719	0.136360	+	0.990659i	$0.456460\pi$
$14$	−99.4056	−0.135547
$15$	−711.509	−0.816492
$16$	2479.46	2.42134
$17$	1845.27	1.54859	0.774295	−	0.632825i	$-0.218105\pi$
$17$	1845.27	1.54859	0.774295	+	0.632825i	$0.218105\pi$
$18$	−846.884	−0.616088
$19$	2703.01	1.71776	0.858882	−	0.512174i	$-0.171160\pi$
$19$	2703.01	1.71776	0.858882	+	0.512174i	$0.171160\pi$
$20$	6112.21	3.41683
$21$	−85.5686	−0.0423415
$22$	−1802.69	−0.794081
$23$	−585.120	−0.230635	−0.115317	−	0.993329i	$-0.536789\pi$
$23$	−585.120	−0.230635	−0.115317	+	0.993329i	$0.536789\pi$
$24$	4264.00	1.51109
$25$	3124.94	0.999979
$26$	−1737.45	−0.504057
$27$	−729.000	−0.192450
$28$	735.076	0.177189
$29$	2812.84	0.621084	0.310542	−	0.950560i	$-0.399489\pi$
$29$	2812.84	0.621084	0.310542	+	0.950560i	$0.399489\pi$
$30$	7439.08	1.50909
$31$	8329.23	1.55668	0.778342	−	0.627840i	$-0.216061\pi$
$31$	8329.23	1.55668	0.778342	+	0.627840i	$0.216061\pi$
$32$	−10762.7	−1.85800
$33$	−1551.76	−0.248051
$34$	−19292.9	−2.86220
$35$	751.640	0.103715
$36$	6262.47	0.805358
$37$	−8616.75	−1.03476	−0.517379	−	0.855756i	$-0.673092\pi$
$37$	−8616.75	−1.03476	−0.517379	+	0.855756i	$0.673092\pi$
$38$	−28260.9	−3.17488
$39$	−1495.60	−0.157455
$40$	−37455.2	−3.70137
$41$	8779.33	0.815646	0.407823	−	0.913061i	$-0.366288\pi$
$41$	8779.33	0.815646	0.407823	+	0.913061i	$0.366288\pi$
$42$	894.650	0.0782582
$43$	−22444.4	−1.85113	−0.925565	−	0.378588i	$-0.876410\pi$
$43$	−22444.4	−1.85113	−0.925565	+	0.378588i	$0.876410\pi$
$44$	13330.4	1.03803
$45$	6403.58	0.471402
$46$	6117.63	0.426274
$47$	16340.4	1.07899	0.539495	−	0.841989i	$-0.318615\pi$
$47$	16340.4	1.07899	0.539495	+	0.841989i	$0.318615\pi$
$48$	−22315.1	−1.39796
$49$	−16716.6	−0.994622
$50$	−32672.3	−1.84822
$51$	−16607.4	−0.894079
$52$	12848.0	0.658910
$53$	10180.9	0.497849	0.248925	−	0.968523i	$-0.419923\pi$
$53$	10180.9	0.497849	0.248925	+	0.968523i	$0.419923\pi$
$54$	7621.95	0.355698
$55$	13630.8	0.607595
$56$	−4504.50	−0.191945
$57$	−24327.1	−0.991751
$58$	−29409.3	−1.14793
$59$	32541.5	1.21705	0.608523	−	0.793536i	$-0.291762\pi$
$59$	32541.5	1.21705	0.608523	+	0.793536i	$0.291762\pi$
$60$	−55009.9	−1.97271
$61$	−26991.8	−0.928769	−0.464384	−	0.885634i	$-0.653724\pi$
$61$	−26991.8	−0.928769	−0.464384	+	0.885634i	$0.653724\pi$
$62$	−87085.0	−2.87716
$63$	770.118	0.0244459
$64$	33185.1	1.01273
$65$	13137.5	0.385681
$66$	16224.2	0.458463
$67$	26845.8	0.730616	0.365308	−	0.930887i	$-0.380964\pi$
$67$	26845.8	0.730616	0.365308	+	0.930887i	$0.380964\pi$
$68$	142666.	3.74151
$69$	5266.08	0.133157
$70$	−7858.66	−0.191692
$71$	−10408.3	−0.245039	−0.122519	−	0.992466i	$-0.539097\pi$
$71$	−10408.3	−0.245039	−0.122519	+	0.992466i	$0.539097\pi$
$72$	−38376.0	−0.872426
$73$	−80254.3	−1.76263	−0.881315	−	0.472529i	$-0.843341\pi$
$73$	−80254.3	−1.76263	−0.881315	+	0.472529i	$0.843341\pi$
$74$	90091.1	1.91251
$75$	−28124.4	−0.577338
$76$	208982.	4.15025
$77$	1639.29	0.0315085
$78$	15637.1	0.291017
$79$	−59600.3	−1.07444	−0.537219	−	0.843443i	$-0.680525\pi$
$79$	−59600.3	−1.07444	−0.537219	+	0.843443i	$0.680525\pi$
$80$	196017.	3.42428
$81$	6561.00	0.111111
$82$	−91791.0	−1.50753
$83$	38542.8	0.614113	0.307056	−	0.951691i	$-0.400656\pi$
$83$	38542.8	0.614113	0.307056	+	0.951691i	$0.400656\pi$
$84$	−6615.69	−0.102300
$85$	145880.	2.19003
$86$	234664.	3.42138
$87$	−25315.6	−0.358583
$88$	−81687.9	−1.12448
$89$	−52412.2	−0.701387	−0.350693	−	0.936490i	$-0.614054\pi$
$89$	−52412.2	−0.701387	−0.350693	+	0.936490i	$0.614054\pi$
$90$	−66951.7	−0.871275
$91$	1579.96	0.0200006
$92$	−45238.2	−0.557231
$93$	−74963.1	−0.898752
$94$	−170844.	−1.99426
$95$	213691.	2.42927
$96$	96864.2	1.07272
$97$	133085.	1.43615	0.718076	−	0.695964i	$-0.245023\pi$
$97$	133085.	1.43615	0.718076	+	0.695964i	$0.245023\pi$
$98$	174778.	1.83832
$99$	13965.9	0.143212
$100$	241603.	2.41603
$101$	−45646.4	−0.445249	−0.222624	−	0.974904i	$-0.571462\pi$
$101$	−45646.4	−0.445249	−0.222624	+	0.974904i	$0.571462\pi$
$102$	173636.	1.65249
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	−78731.6	−0.713782
$105$	−6764.76	−0.0598796
$106$	−106445.	−0.920156
$107$	−59287.0	−0.500611	−0.250305	−	0.968167i	$-0.580531\pi$
$107$	−59287.0	−0.500611	−0.250305	+	0.968167i	$0.580531\pi$
$108$	−56362.2	−0.464974
$109$	93885.1	0.756886	0.378443	−	0.925625i	$-0.376460\pi$
$109$	93885.1	0.756886	0.378443	+	0.925625i	$0.376460\pi$
$110$	−142515.	−1.12299
$111$	77550.7	0.597418
$112$	23573.7	0.177576
$113$	−223464.	−1.64631	−0.823155	−	0.567817i	$-0.807788\pi$
$113$	−223464.	−1.64631	−0.823155	+	0.567817i	$0.807788\pi$
$114$	254348.	1.83302
$115$	−46257.5	−0.326165
$116$	217473.	1.50059
$117$	13460.4	0.0909064
$118$	−340232.	−2.24942
$119$	17544.1	0.113570
$120$	337097.	2.13699
$121$	−131323.	−0.815412
$122$	282209.	1.71661
$123$	−79014.0	−0.470914
$124$	643969.	3.76107
$125$	−5.08667	−2.91178e−5 0
$126$	−8051.85	−0.0451824
$127$	32312.9	0.177773	0.0888866	−	0.996042i	$-0.471669\pi$
$127$	32312.9	0.177773	0.0888866	+	0.996042i	$0.471669\pi$
$128$	−2555.98	−0.0137890
$129$	202000.	1.06875
$130$	−137357.	−0.712840
$131$	101288.	0.515679	0.257840	−	0.966188i	$-0.416989\pi$
$131$	101288.	0.515679	0.257840	+	0.966188i	$0.416989\pi$
$132$	−119974.	−0.599309
$133$	25699.2	0.125977
$134$	−280682.	−1.35037
$135$	−57632.2	−0.272164
$136$	−874246.	−4.05309
$137$	109532.	0.498584	0.249292	−	0.968428i	$-0.419802\pi$
$137$	109532.	0.498584	0.249292	+	0.968428i	$0.419802\pi$
$138$	−55058.7	−0.246109
$139$	46521.9	0.204231	0.102115	−	0.994773i	$-0.467439\pi$
$139$	46521.9	0.204231	0.102115	+	0.994773i	$0.467439\pi$
$140$	58112.6	0.250582
$141$	−147063.	−0.622955
$142$	108823.	0.452896
$143$	28652.1	0.117170
$144$	200836.	0.807114
$145$	222374.	0.878341
$146$	839087.	3.25780
$147$	150449.	0.574245
$148$	−666199.	−2.50005
$149$	82543.7	0.304592	0.152296	−	0.988335i	$-0.451333\pi$
$149$	82543.7	0.304592	0.152296	+	0.988335i	$0.451333\pi$
$150$	294051.	1.06707
$151$	190337.	0.679329	0.339665	−	0.940547i	$-0.389686\pi$
$151$	190337.	0.679329	0.339665	+	0.940547i	$0.389686\pi$
$152$	−1.28063e6	−4.49587
$153$	149467.	0.516197
$154$	−17139.3	−0.0582361
$155$	658480.	2.20147
$156$	−115632.	−0.380422
$157$	−64097.2	−0.207534	−0.103767	−	0.994602i	$-0.533090\pi$
$157$	−64097.2	−0.207534	−0.103767	+	0.994602i	$0.533090\pi$
$158$	623143.	1.98584
$159$	−91628.4	−0.287433
$160$	−850861.	−2.62760
$161$	−5563.10	−0.0169142
$162$	−68597.6	−0.205363
$163$	−56846.3	−0.167584	−0.0837922	−	0.996483i	$-0.526703\pi$
$163$	−56846.3	−0.167584	−0.0837922	+	0.996483i	$0.526703\pi$
$164$	678769.	1.97066
$165$	−122677.	−0.350795
$166$	−402979.	−1.13504
$167$	126840.	0.351938	0.175969	−	0.984396i	$-0.443694\pi$
$167$	126840.	0.351938	0.175969	+	0.984396i	$0.443694\pi$
$168$	40540.5	0.110820
$169$	−343678.	−0.925624
$170$	−1.52523e6	−4.04774
$171$	218944.	0.572588
$172$	−1.73528e6	−4.47247
$173$	−65137.6	−0.165469	−0.0827345	−	0.996572i	$-0.526365\pi$
$173$	−65137.6	−0.165469	−0.0827345	+	0.996572i	$0.526365\pi$
$174$	264683.	0.662756
$175$	29710.7	0.0733361
$176$	427503.	1.04030
$177$	−292873.	−0.702662
$178$	547988.	1.29635
$179$	349024.	0.814183	0.407092	−	0.913387i	$-0.366543\pi$
$179$	349024.	0.814183	0.407092	+	0.913387i	$0.366543\pi$
$180$	495089.	1.13894
$181$	232690.	0.527936	0.263968	−	0.964531i	$-0.414969\pi$
$181$	232690.	0.527936	0.263968	+	0.964531i	$0.414969\pi$
$182$	−16519.0	−0.0369663
$183$	242926.	0.536225
$184$	277217.	0.603636
$185$	−681210.	−1.46336
$186$	783765.	1.66113
$187$	318157.	0.665331
$188$	1.26335e6	2.60692
$189$	−6931.06	−0.0141138
$190$	−2.23421e6	−4.48993
$191$	295504.	0.586111	0.293056	−	0.956095i	$-0.405328\pi$
$191$	295504.	0.586111	0.293056	+	0.956095i	$0.405328\pi$
$192$	−298666.	−0.584699
$193$	489603.	0.946129	0.473065	−	0.881028i	$-0.343148\pi$
$193$	489603.	0.946129	0.473065	+	0.881028i	$0.343148\pi$
$194$	−1.39145e6	−2.65439
$195$	−118237.	−0.222673
$196$	−1.29243e6	−2.40308
$197$	893461.	1.64025	0.820125	−	0.572185i	$-0.193904\pi$
$197$	893461.	1.64025	0.820125	+	0.572185i	$0.193904\pi$
$198$	−146018.	−0.264694
$199$	−654452.	−1.17151	−0.585754	−	0.810489i	$-0.699201\pi$
$199$	−654452.	−1.17151	−0.585754	+	0.810489i	$0.699201\pi$
$200$	−1.48053e6	−2.61722
$201$	−241612.	−0.421822
$202$	477249.	0.822937
$203$	26743.5	0.0455489
$204$	−1.28399e6	−2.16016
$205$	694064.	1.15349
$206$	−110921.	−0.182115
$207$	−47394.7	−0.0768783
$208$	412032.	0.660347
$209$	466048.	0.738014
$210$	70728.0	0.110673
$211$	736596.	1.13900	0.569499	−	0.821992i	$-0.307137\pi$
$211$	736596.	1.13900	0.569499	+	0.821992i	$0.307137\pi$
$212$	787132.	1.20284
$213$	93674.9	0.141473
$214$	619867.	0.925260
$215$	−1.77438e6	−2.61788
$216$	345384.	0.503696
$217$	79191.2	0.114164
$218$	−981602.	−1.39892
$219$	722289.	1.01765
$220$	1.05386e6	1.46799
$221$	306643.	0.422330
$222$	−810820.	−1.10419
$223$	−27535.8	−0.0370796	−0.0185398	−	0.999828i	$-0.505902\pi$
$223$	−27535.8	−0.0370796	−0.0185398	+	0.999828i	$0.505902\pi$
$224$	−102328.	−0.136261
$225$	253120.	0.333326
$226$	2.33640e6	3.04281
$227$	−1.31488e6	−1.69364	−0.846821	−	0.531878i	$-0.821487\pi$
$227$	−1.31488e6	−1.69364	−0.846821	+	0.531878i	$0.821487\pi$
$228$	−1.88083e6	−2.39615
$229$	−281927.	−0.355262	−0.177631	−	0.984097i	$-0.556843\pi$
$229$	−281927.	−0.355262	−0.177631	+	0.984097i	$0.556843\pi$
$230$	483639.	0.602839
$231$	−14753.6	−0.0181915
$232$	−1.33266e6	−1.62555
$233$	−1.11095e6	−1.34062	−0.670308	−	0.742083i	$-0.733838\pi$
$233$	−1.11095e6	−1.34062	−0.670308	+	0.742083i	$0.733838\pi$
$234$	−140734.	−0.168019
$235$	1.29181e6	1.52591
$236$	2.51592e6	2.94047
$237$	536403.	0.620327
$238$	−183430.	−0.209907
$239$	525148.	0.594685	0.297342	−	0.954771i	$-0.403900\pi$
$239$	525148.	0.594685	0.297342	+	0.954771i	$0.403900\pi$
$240$	−1.76415e6	−1.97701
$241$	1.38430e6	1.53528	0.767642	−	0.640879i	$-0.221430\pi$
$241$	1.38430e6	1.53528	0.767642	+	0.640879i	$0.221430\pi$
$242$	1.37303e6	1.50710
$243$	−59049.0	−0.0641500
$244$	−2.08686e6	−2.24397
$245$	−1.32156e6	−1.40660
$246$	826119.	0.870372
$247$	449181.	0.468467
$248$	−3.94621e6	−4.07428
$249$	−346885.	−0.354558
$250$	53.1830	5.38174e−5 0
$251$	776102.	0.777561	0.388781	−	0.921330i	$-0.372896\pi$
$251$	776102.	0.777561	0.388781	+	0.921330i	$0.372896\pi$
$252$	59541.2	0.0590631
$253$	−100885.	−0.0990892
$254$	−337842.	−0.328571
$255$	−1.31292e6	−1.26441
$256$	−1.03520e6	−0.987243
$257$	−847788.	−0.800672	−0.400336	−	0.916368i	$-0.631107\pi$
$257$	−847788.	−0.800672	−0.400336	+	0.916368i	$0.631107\pi$
$258$	−2.11198e6	−1.97533
$259$	−81924.8	−0.0758868
$260$	1.01572e6	0.931835
$261$	227840.	0.207028
$262$	−1.05900e6	−0.953111
$263$	1.74562e6	1.55618	0.778091	−	0.628151i	$-0.216188\pi$
$263$	1.74562e6	1.55618	0.778091	+	0.628151i	$0.216188\pi$
$264$	735191.	0.649218
$265$	804869.	0.704061
$266$	−268694.	−0.232838
$267$	471710.	0.404946
$268$	2.07557e6	1.76522
$269$	−437050.	−0.368257	−0.184128	−	0.982902i	$-0.558946\pi$
$269$	−437050.	−0.368257	−0.184128	+	0.982902i	$0.558946\pi$
$270$	602565.	0.503031
$271$	−128411.	−0.106213	−0.0531065	−	0.998589i	$-0.516912\pi$
$271$	−128411.	−0.106213	−0.0531065	+	0.998589i	$0.516912\pi$
$272$	4.57525e6	3.74967
$273$	−14219.6	−0.0115473
$274$	−1.14519e6	−0.921514
$275$	538796.	0.429628
$276$	407144.	0.321718
$277$	−733564.	−0.574432	−0.287216	−	0.957866i	$-0.592730\pi$
$277$	−733564.	−0.574432	−0.287216	+	0.957866i	$0.592730\pi$
$278$	−486403.	−0.377472
$279$	674667.	0.518895
$280$	−356111.	−0.271450
$281$	2.03738e6	1.53924	0.769622	−	0.638500i	$-0.220445\pi$
$281$	2.03738e6	1.53924	0.769622	+	0.638500i	$0.220445\pi$
$282$	1.53760e6	1.15138
$283$	−396543.	−0.294323	−0.147162	−	0.989112i	$-0.547014\pi$
$283$	−396543.	−0.294323	−0.147162	+	0.989112i	$0.547014\pi$
$284$	−804713.	−0.592032
$285$	−1.92321e6	−1.40254
$286$	−299568.	−0.216561
$287$	83470.6	0.0598176
$288$	−871778.	−0.619333
$289$	1.98515e6	1.39813
$290$	−2.32499e6	−1.62341
$291$	−1.19777e6	−0.829163
$292$	−6.20481e6	−4.25865
$293$	−2.72832e6	−1.85663	−0.928316	−	0.371793i	$-0.878743\pi$
$293$	−2.72832e6	−1.85663	−0.928316	+	0.371793i	$0.878743\pi$
$294$	−1.57300e6	−1.06136
$295$	2.57261e6	1.72115
$296$	4.08243e6	2.70825
$297$	−125693.	−0.0826836
$298$	−863023.	−0.562966
$299$	−97234.1	−0.0628986
$300$	−2.17442e6	−1.39489
$301$	−213393.	−0.135758
$302$	−1.99004e6	−1.25558
$303$	410817.	0.257064
$304$	6.70199e6	4.15930
$305$	−2.13388e6	−1.31347
$306$	−1.56273e6	−0.954067
$307$	−782173.	−0.473649	−0.236825	−	0.971552i	$-0.576107\pi$
$307$	−782173.	−0.473649	−0.236825	+	0.971552i	$0.576107\pi$
$308$	126741.	0.0761270
$309$	−95481.0	−0.0568880
$310$	−6.88464e6	−4.06890
$311$	2.11116e6	1.23771	0.618857	−	0.785504i	$-0.287596\pi$
$311$	2.11116e6	1.23771	0.618857	+	0.785504i	$0.287596\pi$
$312$	708584.	0.412102
$313$	−593851.	−0.342623	−0.171311	−	0.985217i	$-0.554800\pi$
$313$	−593851.	−0.342623	−0.171311	+	0.985217i	$0.554800\pi$
$314$	670159.	0.383578
$315$	60882.8	0.0345715
$316$	−4.60796e6	−2.59592
$317$	−64608.6	−0.0361112	−0.0180556	−	0.999837i	$-0.505748\pi$
$317$	−64608.6	−0.0361112	−0.0180556	+	0.999837i	$0.505748\pi$
$318$	958007.	0.531252
$319$	484985.	0.266840
$320$	2.62350e6	1.43221
$321$	533583.	0.289028
$322$	58164.2	0.0312619
$323$	4.98777e6	2.66011
$324$	507260.	0.268453
$325$	519296.	0.272714
$326$	594348.	0.309740
$327$	−844966.	−0.436988
$328$	−4.15946e6	−2.13477
$329$	155358.	0.0791306
$330$	1.28263e6	0.648361
$331$	3.85634e6	1.93466	0.967331	−	0.253518i	$-0.0815876\pi$
$331$	3.85634e6	1.93466	0.967331	+	0.253518i	$0.0815876\pi$
$332$	2.97991e6	1.48374
$333$	−697956.	−0.344919
$334$	−1.32616e6	−0.650473
$335$	2.12234e6	1.03324
$336$	−212164.	−0.102523
$337$	1.34711e6	0.646141	0.323070	−	0.946375i	$-0.395285\pi$
$337$	1.34711e6	0.646141	0.323070	+	0.946375i	$0.395285\pi$
$338$	3.59327e6	1.71080
$339$	2.01118e6	0.950498
$340$	1.12786e7	5.29127
$341$	1.43611e6	0.668808
$342$	−2.28913e6	−1.05829
$343$	−318730.	−0.146281
$344$	1.06337e7	4.84492
$345$	416318.	0.188312
$346$	681036.	0.305830
$347$	2.05637e6	0.916807	0.458403	−	0.888744i	$-0.348421\pi$
$347$	2.05637e6	0.916807	0.458403	+	0.888744i	$0.348421\pi$
$348$	−1.95726e6	−0.866364
$349$	4.02494e6	1.76887	0.884436	−	0.466662i	$-0.154543\pi$
$349$	4.02494e6	1.76887	0.884436	+	0.466662i	$0.154543\pi$
$350$	−310636.	−0.135544
$351$	−121144.	−0.0524848
$352$	−1.85568e6	−0.798265
$353$	4.31470e6	1.84295	0.921476	−	0.388436i	$-0.126985\pi$
$353$	4.31470e6	1.84295	0.921476	+	0.388436i	$0.126985\pi$
$354$	3.06209e6	1.29870
$355$	−822846.	−0.346536
$356$	−4.05222e6	−1.69460
$357$	−157897.	−0.0655697
$358$	−3.64917e6	−1.50482
$359$	−2.46621e6	−1.00994	−0.504968	−	0.863138i	$-0.668496\pi$
$359$	−2.46621e6	−1.00994	−0.504968	+	0.863138i	$0.668496\pi$
$360$	−3.03388e6	−1.23379
$361$	4.83016e6	1.95071
$362$	−2.43286e6	−0.975764
$363$	1.18191e6	0.470779
$364$	122154.	0.0483229
$365$	−6.34463e6	−2.49272
$366$	−2.53988e6	−0.991084
$367$	−25197.6	−0.00976549	−0.00488275	−	0.999988i	$-0.501554\pi$
$367$	−25197.6	−0.00976549	−0.00488275	+	0.999988i	$0.501554\pi$
$368$	−1.45078e6	−0.558446
$369$	711126.	0.271882
$370$	7.12229e6	2.70468
$371$	96796.5	0.0365111
$372$	−5.79572e6	−2.17145
$373$	−2.33224e6	−0.867964	−0.433982	−	0.900922i	$-0.642892\pi$
$373$	−2.33224e6	−0.867964	−0.433982	+	0.900922i	$0.642892\pi$
$374$	−3.32645e6	−1.22971
$375$	45.7801	1.68112e−5 0
$376$	−7.74171e6	−2.82402
$377$	467433.	0.169382
$378$	72466.7	0.0260861
$379$	4.40213e6	1.57422	0.787109	−	0.616813i	$-0.211577\pi$
$379$	4.40213e6	1.57422	0.787109	+	0.616813i	$0.211577\pi$
$380$	1.65214e7	5.86930
$381$	−290816.	−0.102637
$382$	−3.08960e6	−1.08329
$383$	−2.82542e6	−0.984206	−0.492103	−	0.870537i	$-0.663772\pi$
$383$	−2.82542e6	−0.984206	−0.492103	+	0.870537i	$0.663772\pi$
$384$	23003.8	0.00796107
$385$	129596.	0.0445596
$386$	−5.11897e6	−1.74870
$387$	−1.81800e6	−0.617044
$388$	1.02894e7	3.46985
$389$	−3.80388e6	−1.27454	−0.637268	−	0.770642i	$-0.719936\pi$
$389$	−3.80388e6	−1.27454	−0.637268	+	0.770642i	$0.719936\pi$
$390$	1.23621e6	0.411559
$391$	−1.07970e6	−0.357159
$392$	7.91996e6	2.60320
$393$	−911592.	−0.297728
$394$	−9.34145e6	−3.03161
$395$	−4.71180e6	−1.51948
$396$	1.07976e6	0.346011
$397$	−5.78306e6	−1.84154	−0.920771	−	0.390104i	$-0.872439\pi$
$397$	−5.78306e6	−1.84154	−0.920771	+	0.390104i	$0.872439\pi$
$398$	6.84252e6	2.16525
$399$	−231293.	−0.0727327
$400$	7.74814e6	2.42129
$401$	3.20682e6	0.995897	0.497948	−	0.867207i	$-0.334087\pi$
$401$	3.20682e6	0.995897	0.497948	+	0.867207i	$0.334087\pi$
$402$	2.52614e6	0.779637
$403$	1.38414e6	0.424538
$404$	−3.52912e6	−1.07575
$405$	518690.	0.157134
$406$	−279612.	−0.0841862
$407$	−1.48568e6	−0.444570
$408$	7.86822e6	2.34005
$409$	375011.	0.110850	0.0554251	−	0.998463i	$-0.482349\pi$
$409$	375011.	0.110850	0.0554251	+	0.998463i	$0.482349\pi$
$410$	−7.25668e6	−2.13196
$411$	−985785.	−0.287857
$412$	820228.	0.238063
$413$	309392.	0.0892553
$414$	495528.	0.142091
$415$	3.04706e6	0.868482
$416$	−1.78852e6	−0.506712
$417$	−418697.	−0.117913
$418$	−4.87269e6	−1.36404
$419$	−3.96376e6	−1.10299	−0.551496	−	0.834177i	$-0.685943\pi$
$419$	−3.96376e6	−1.10299	−0.551496	+	0.834177i	$0.685943\pi$
$420$	−523013.	−0.144674
$421$	−5.50418e6	−1.51352	−0.756759	−	0.653694i	$-0.773218\pi$
$421$	−5.50418e6	−1.51352	−0.756759	+	0.653694i	$0.773218\pi$
$422$	−7.70137e6	−2.10517
$423$	1.32357e6	0.359663
$424$	−4.82350e6	−1.30301
$425$	5.76634e6	1.54856
$426$	−979404.	−0.261480
$427$	−256628.	−0.0681137
$428$	−4.58374e6	−1.20951
$429$	−257869.	−0.0676482
$430$	1.85517e7	4.83853
$431$	1.01708e6	0.263731	0.131865	−	0.991268i	$-0.457903\pi$
$431$	1.01708e6	0.263731	0.131865	+	0.991268i	$0.457903\pi$
$432$	−1.80752e6	−0.465988
$433$	1.15811e6	0.296844	0.148422	−	0.988924i	$-0.452581\pi$
$433$	1.15811e6	0.296844	0.148422	+	0.988924i	$0.452581\pi$
$434$	−827972.	−0.211004
$435$	−2.00136e6	−0.507110
$436$	7.25867e6	1.82869
$437$	−1.58158e6	−0.396176
$438$	−7.55178e6	−1.88089
$439$	4.99061e6	1.23592	0.617962	−	0.786208i	$-0.287958\pi$
$439$	4.99061e6	1.23592	0.617962	+	0.786208i	$0.287958\pi$
$440$	−6.45796e6	−1.59024
$441$	−1.35405e6	−0.331541
$442$	−3.20606e6	−0.780577
$443$	−3.44517e6	−0.834068	−0.417034	−	0.908891i	$-0.636930\pi$
$443$	−3.44517e6	−0.834068	−0.417034	+	0.908891i	$0.636930\pi$
$444$	5.99579e6	1.44341
$445$	−4.14353e6	−0.991906
$446$	287896.	0.0685328
$447$	−742893.	−0.175856
$448$	315512.	0.0742712
$449$	−4.28871e6	−1.00395	−0.501973	−	0.864883i	$-0.667392\pi$
$449$	−4.28871e6	−1.00395	−0.501973	+	0.864883i	$0.667392\pi$
$450$	−2.64646e6	−0.616075
$451$	1.51372e6	0.350432
$452$	−1.72770e7	−3.97761
$453$	−1.71303e6	−0.392211
$454$	1.37475e7	3.13030
$455$	124906.	0.0282850
$456$	1.15256e7	2.59569
$457$	−3.03568e6	−0.679931	−0.339966	−	0.940438i	$-0.610415\pi$
$457$	−3.03568e6	−0.679931	−0.339966	+	0.940438i	$0.610415\pi$
$458$	2.94765e6	0.656617
$459$	−1.34520e6	−0.298026
$460$	−3.57637e6	−0.788040
$461$	−7.59678e6	−1.66486	−0.832429	−	0.554131i	$-0.813051\pi$
$461$	−7.59678e6	−1.66486	−0.832429	+	0.554131i	$0.813051\pi$
$462$	154254.	0.0336226
$463$	−7.60146e6	−1.64795	−0.823976	−	0.566625i	$-0.808249\pi$
$463$	−7.60146e6	−1.64795	−0.823976	+	0.566625i	$0.808249\pi$
$464$	6.97432e6	1.50386
$465$	−5.92632e6	−1.27102
$466$	1.16154e7	2.47781
$467$	−4.93954e6	−1.04808	−0.524040	−	0.851694i	$-0.675576\pi$
$467$	−4.93954e6	−1.04808	−0.524040	+	0.851694i	$0.675576\pi$
$468$	1.04069e6	0.219637
$469$	255240.	0.0535817
$470$	−1.35064e7	−2.82029
$471$	576875.	0.119820
$472$	−1.54174e7	−3.18535
$473$	−3.86982e6	−0.795313
$474$	−5.60828e6	−1.14653
$475$	8.44673e6	1.71773
$476$	1.35641e6	0.274394
$477$	824655.	0.165950
$478$	−5.49061e6	−1.09913
$479$	7.79367e6	1.55204	0.776020	−	0.630708i	$-0.217235\pi$
$479$	7.79367e6	1.55204	0.776020	+	0.630708i	$0.217235\pi$
$480$	7.65775e6	1.51704
$481$	−1.43192e6	−0.282199
$482$	−1.44734e7	−2.83761
$483$	50067.9	0.00976543
$484$	−1.01532e7	−1.97010
$485$	1.05213e7	2.03102
$486$	617378.	0.118566
$487$	−4.81928e6	−0.920789	−0.460394	−	0.887714i	$-0.652292\pi$
$487$	−4.81928e6	−0.920789	−0.460394	+	0.887714i	$0.652292\pi$
$488$	1.27881e7	2.43085
$489$	511617.	0.0967549
$490$	1.38173e7	2.59977
$491$	−90505.5	−0.0169423	−0.00847113	−	0.999964i	$-0.502696\pi$
$491$	−90505.5	−0.0169423	−0.00847113	+	0.999964i	$0.502696\pi$
$492$	−6.10892e6	−1.13776
$493$	5.19044e6	0.961805
$494$	−4.69635e6	−0.865850
$495$	1.10409e6	0.202532
$496$	2.06520e7	3.76927
$497$	−98958.5	−0.0179706
$498$	3.62681e6	0.655316
$499$	4.05033e6	0.728180	0.364090	−	0.931364i	$-0.381380\pi$
$499$	4.05033e6	0.728180	0.364090	+	0.931364i	$0.381380\pi$
$500$	−393.273	−7.03508e−5 0
$501$	−1.14156e6	−0.203191
$502$	−8.11442e6	−1.43714
$503$	−458170.	−0.0807433	−0.0403716	−	0.999185i	$-0.512854\pi$
$503$	−458170.	−0.0807433	−0.0403716	+	0.999185i	$0.512854\pi$
$504$	−364865.	−0.0639817
$505$	−3.60864e6	−0.629674
$506$	1.05479e6	0.183143
$507$	3.09310e6	0.534409
$508$	2.49825e6	0.429513
$509$	−1.93904e6	−0.331736	−0.165868	−	0.986148i	$-0.553043\pi$
$509$	−1.93904e6	−0.331736	−0.165868	+	0.986148i	$0.553043\pi$
$510$	1.37271e7	2.33697
$511$	−763028.	−0.129267
$512$	1.09052e7	1.83847
$513$	−1.97049e6	−0.330584
$514$	8.86393e6	1.47985
$515$	838711.	0.139346
$516$	1.56175e7	2.58218
$517$	2.81738e6	0.463574
$518$	856553.	0.140259
$519$	586238.	0.0955335
$520$	−6.22425e6	−1.00944
$521$	−1.20027e7	−1.93725	−0.968623	−	0.248534i	$-0.920051\pi$
$521$	−1.20027e7	−1.93725	−0.968623	+	0.248534i	$0.920051\pi$
$522$	−2.38215e6	−0.382642
$523$	−4.86242e6	−0.777318	−0.388659	−	0.921382i	$-0.627062\pi$
$523$	−4.86242e6	−0.777318	−0.388659	+	0.921382i	$0.627062\pi$
$524$	7.83102e6	1.24592
$525$	−267397.	−0.0423406
$526$	−1.82511e7	−2.87623
$527$	1.53696e7	2.41067
$528$	−3.84753e6	−0.600616
$529$	−6.09398e6	−0.946808
$530$	−8.41519e6	−1.30129
$531$	2.63586e6	0.405682
$532$	1.98692e6	0.304369
$533$	1.45893e6	0.222442
$534$	−4.93190e6	−0.748446
$535$	−4.68703e6	−0.707967
$536$	−1.27190e7	−1.91223
$537$	−3.14121e6	−0.470069
$538$	4.56952e6	0.680635
$539$	−2.88225e6	−0.427326
$540$	−4.45580e6	−0.657569
$541$	−4.37728e6	−0.643000	−0.321500	−	0.946910i	$-0.604187\pi$
$541$	−4.37728e6	−0.643000	−0.321500	+	0.946910i	$0.604187\pi$
$542$	1.34258e6	0.196310
$543$	−2.09421e6	−0.304804
$544$	−1.98600e7	−2.87728
$545$	7.42223e6	1.07039
$546$	148671.	0.0213425
$547$	−7.36111e6	−1.05190	−0.525950	−	0.850515i	$-0.676290\pi$
$547$	−7.36111e6	−1.05190	−0.525950	+	0.850515i	$0.676290\pi$
$548$	8.46837e6	1.20462
$549$	−2.18634e6	−0.309590
$550$	−5.63330e6	−0.794065
$551$	7.60314e6	1.06688
$552$	−2.49495e6	−0.348509
$553$	−566658.	−0.0787967
$554$	7.66967e6	1.06170
$555$	6.13089e6	0.844872
$556$	3.59681e6	0.493436
$557$	7.26465e6	0.992149	0.496074	−	0.868280i	$-0.334774\pi$
$557$	7.26465e6	0.992149	0.496074	+	0.868280i	$0.334774\pi$
$558$	−7.05389e6	−0.959054
$559$	−3.72977e6	−0.504839
$560$	1.86366e6	0.251129
$561$	−2.86342e6	−0.384129
$562$	−2.13016e7	−2.84493
$563$	5.23582e6	0.696167	0.348084	−	0.937463i	$-0.386832\pi$
$563$	5.23582e6	0.696167	0.348084	+	0.937463i	$0.386832\pi$
$564$	−1.13701e7	−1.50511
$565$	−1.76663e7	−2.32822
$566$	4.14600e6	0.543986
$567$	62379.5	0.00814863
$568$	4.93124e6	0.641335
$569$	9.68154e6	1.25361	0.626807	−	0.779175i	$-0.284361\pi$
$569$	9.68154e6	1.25361	0.626807	+	0.779175i	$0.284361\pi$
$570$	2.01079e7	2.59226
$571$	−257075.	−0.0329966	−0.0164983	−	0.999864i	$-0.505252\pi$
$571$	−257075.	−0.0329966	−0.0164983	+	0.999864i	$0.505252\pi$
$572$	2.21522e6	0.283092
$573$	−2.65954e6	−0.338391
$574$	−872715.	−0.110559
$575$	−1.82846e6	−0.230630
$576$	2.68799e6	0.337576
$577$	121250.	0.0151615	0.00758077	−	0.999971i	$-0.497587\pi$
$577$	121250.	0.0151615	0.00758077	+	0.999971i	$0.497587\pi$
$578$	−2.07554e7	−2.58412
$579$	−4.40642e6	−0.546248
$580$	1.71927e7	2.12214
$581$	366451.	0.0450376
$582$	1.25231e7	1.53251
$583$	1.75538e6	0.213894
$584$	3.80227e7	4.61329
$585$	1.06414e6	0.128560
$586$	2.85255e7	3.43154
$587$	−96170.5	−0.0115198	−0.00575992	−	0.999983i	$-0.501833\pi$
$587$	−96170.5	−0.0115198	−0.00575992	+	0.999983i	$0.501833\pi$
$588$	1.16319e7	1.38742
$589$	2.25140e7	2.67402
$590$	−2.68976e7	−3.18114
$591$	−8.04115e6	−0.946998
$592$	−2.13648e7	−2.50551
$593$	−4.84002e6	−0.565211	−0.282605	−	0.959236i	$-0.591199\pi$
$593$	−4.84002e6	−0.565211	−0.282605	+	0.959236i	$0.591199\pi$
$594$	1.31416e6	0.152821
$595$	1.38698e6	0.160611
$596$	6.38182e6	0.735917
$597$	5.89007e6	0.676370
$598$	1.01662e6	0.116253
$599$	3.79174e6	0.431789	0.215895	−	0.976417i	$-0.430733\pi$
$599$	3.79174e6	0.431789	0.215895	+	0.976417i	$0.430733\pi$
$600$	1.33247e7	1.51106
$601$	−1.67870e6	−0.189578	−0.0947888	−	0.995497i	$-0.530218\pi$
$601$	−1.67870e6	−0.189578	−0.0947888	+	0.995497i	$0.530218\pi$
$602$	2.23110e6	0.250916
$603$	2.17451e6	0.243539
$604$	1.47158e7	1.64131
$605$	−1.03819e7	−1.15316
$606$	−4.29524e6	−0.475123
$607$	1.54933e7	1.70676	0.853381	−	0.521288i	$-0.174548\pi$
$607$	1.54933e7	1.70676	0.853381	+	0.521288i	$0.174548\pi$
$608$	−2.90916e7	−3.19161
$609$	−240691.	−0.0262976
$610$	2.23105e7	2.42764
$611$	2.71541e6	0.294261
$612$	1.15559e7	1.24717
$613$	1.17172e7	1.25942	0.629711	−	0.776830i	$-0.283173\pi$
$613$	1.17172e7	1.25942	0.629711	+	0.776830i	$0.283173\pi$
$614$	8.17789e6	0.875428
$615$	−6.24657e6	−0.665969
$616$	−776658.	−0.0824666
$617$	1.72728e7	1.82663	0.913315	−	0.407254i	$-0.133514\pi$
$617$	1.72728e7	1.82663	0.913315	+	0.407254i	$0.133514\pi$
$618$	998288.	0.105144
$619$	3.20170e6	0.335856	0.167928	−	0.985799i	$-0.446292\pi$
$619$	3.20170e6	0.335856	0.167928	+	0.985799i	$0.446292\pi$
$620$	5.09100e7	5.31892
$621$	426552.	0.0443857
$622$	−2.20729e7	−2.28762
$623$	−498316.	−0.0514381
$624$	−3.70828e6	−0.381251
$625$	−9.76583e6	−1.00002
$626$	6.20892e6	0.633257
$627$	−4.19443e6	−0.426093
$628$	−4.95564e6	−0.501418
$629$	−1.59002e7	−1.60242
$630$	−636552.	−0.0638973
$631$	−6.47094e6	−0.646985	−0.323492	−	0.946231i	$-0.604857\pi$
$631$	−6.47094e6	−0.646985	−0.323492	+	0.946231i	$0.604857\pi$
$632$	2.82373e7	2.81210
$633$	−6.62936e6	−0.657601
$634$	675506.	0.0667430
$635$	2.55454e6	0.251408
$636$	−7.08419e6	−0.694460
$637$	−2.77794e6	−0.271252
$638$	−5.07069e6	−0.493191
$639$	−843074.	−0.0816796
$640$	−202067.	−0.0195005
$641$	−1.38470e7	−1.33110	−0.665551	−	0.746352i	$-0.731804\pi$
$641$	−1.38470e7	−1.33110	−0.665551	+	0.746352i	$0.731804\pi$
$642$	−5.57880e6	−0.534199
$643$	−1.28662e7	−1.22722	−0.613611	−	0.789608i	$-0.710284\pi$
$643$	−1.28662e7	−1.22722	−0.613611	+	0.789608i	$0.710284\pi$
$644$	−430108.	−0.0408660
$645$	1.59694e7	1.51143
$646$	−5.21489e7	−4.91659
$647$	−3.95790e6	−0.371710	−0.185855	−	0.982577i	$-0.559505\pi$
$647$	−3.95790e6	−0.371710	−0.185855	+	0.982577i	$0.559505\pi$
$648$	−3.10846e6	−0.290809
$649$	5.61074e6	0.522887
$650$	−5.42943e6	−0.504046
$651$	−712721.	−0.0659124
$652$	−4.39504e6	−0.404896
$653$	−1.93755e6	−0.177816	−0.0889079	−	0.996040i	$-0.528338\pi$
$653$	−1.93755e6	−0.177816	−0.0889079	+	0.996040i	$0.528338\pi$
$654$	8.83442e6	0.807669
$655$	8.00748e6	0.729277
$656$	2.17680e7	1.97496
$657$	−6.50060e6	−0.587543
$658$	−1.62432e6	−0.146254
$659$	−4.30178e6	−0.385865	−0.192932	−	0.981212i	$-0.561800\pi$
$659$	−4.30178e6	−0.385865	−0.192932	+	0.981212i	$0.561800\pi$
$660$	−9.48470e6	−0.847547
$661$	1.04273e7	0.928259	0.464129	−	0.885767i	$-0.346367\pi$
$661$	1.04273e7	0.928259	0.464129	+	0.885767i	$0.346367\pi$
$662$	−4.03194e7	−3.57576
$663$	−2.75979e6	−0.243833
$664$	−1.82607e7	−1.60730
$665$	2.03169e6	0.178157
$666$	7.29738e6	0.637502
$667$	−1.64585e6	−0.143244
$668$	9.80657e6	0.850308
$669$	247822.	0.0214079
$670$	−2.21898e7	−1.90970
$671$	−4.65388e6	−0.399033
$672$	920948.	0.0786705
$673$	1.84562e7	1.57074	0.785371	−	0.619025i	$-0.212472\pi$
$673$	1.84562e7	1.57074	0.785371	+	0.619025i	$0.212472\pi$
$674$	−1.40845e7	−1.19424
$675$	−2.27808e6	−0.192446
$676$	−2.65712e7	−2.23638
$677$	469218.	0.0393462	0.0196731	−	0.999806i	$-0.493737\pi$
$677$	469218.	0.0393462	0.0196731	+	0.999806i	$0.493737\pi$
$678$	−2.10276e7	−1.75677
$679$	1.26533e6	0.105324
$680$	−6.91149e7	−5.73191
$681$	1.18339e7	0.977825
$682$	−1.50150e7	−1.23613
$683$	3.35482e6	0.275180	0.137590	−	0.990489i	$-0.456064\pi$
$683$	3.35482e6	0.275180	0.137590	+	0.990489i	$0.456064\pi$
$684$	1.69275e7	1.38342
$685$	8.65919e6	0.705100
$686$	3.33243e6	0.270365
$687$	2.53735e6	0.205110
$688$	−5.56499e7	−4.48222
$689$	1.69185e6	0.135773
$690$	−4.35275e6	−0.348049
$691$	2.73427e6	0.217845	0.108922	−	0.994050i	$-0.465260\pi$
$691$	2.73427e6	0.217845	0.108922	+	0.994050i	$0.465260\pi$
$692$	−5.03607e6	−0.399785
$693$	132782.	0.0105028
$694$	−2.15001e7	−1.69450
$695$	3.67786e6	0.288824
$696$	1.19940e7	0.938512
$697$	1.62002e7	1.26310
$698$	−4.20822e7	−3.26934
$699$	9.99855e6	0.774006
$700$	2.29707e6	0.177186
$701$	1.16273e7	0.893687	0.446844	−	0.894612i	$-0.352548\pi$
$701$	1.16273e7	0.893687	0.446844	+	0.894612i	$0.352548\pi$
$702$	1.26660e6	0.0970058
$703$	−2.32911e7	−1.77747
$704$	5.72171e6	0.435105
$705$	−1.16263e7	−0.880987
$706$	−4.51117e7	−3.40626
$707$	−433989.	−0.0326535
$708$	−2.26433e7	−1.69768
$709$	4.04012e6	0.301841	0.150921	−	0.988546i	$-0.451776\pi$
$709$	4.04012e6	0.301841	0.150921	+	0.988546i	$0.451776\pi$
$710$	8.60315e6	0.640489
$711$	−4.82763e6	−0.358146
$712$	2.48318e7	1.83573
$713$	−4.87360e6	−0.359026
$714$	1.65087e6	0.121190
$715$	2.26514e6	0.165703
$716$	2.69846e7	1.96713
$717$	−4.72633e6	−0.343341
$718$	2.57851e7	1.86663
$719$	−1.66853e7	−1.20368	−0.601840	−	0.798616i	$-0.705566\pi$
$719$	−1.66853e7	−1.20368	−0.601840	+	0.798616i	$0.705566\pi$
$720$	1.58774e7	1.14143
$721$	100866.	0.00722617
$722$	−5.05010e7	−3.60543
$723$	−1.24587e7	−0.886396
$724$	1.79903e7	1.27553
$725$	8.78995e6	0.621071
$726$	−1.23573e7	−0.870122
$727$	2.78882e7	1.95697	0.978485	−	0.206317i	$-0.0661479\pi$
$727$	2.78882e7	1.95697	0.978485	+	0.206317i	$0.0661479\pi$
$728$	−748551.	−0.0523471
$729$	531441.	0.0370370
$730$	6.63353e7	4.60721
$731$	−4.14159e7	−2.86664
$732$	1.87817e7	1.29556
$733$	1.73177e7	1.19050	0.595250	−	0.803541i	$-0.297053\pi$
$733$	1.73177e7	1.19050	0.595250	+	0.803541i	$0.297053\pi$
$734$	263450.	0.0180492
$735$	1.18940e7	0.812101
$736$	6.29746e6	0.428520
$737$	4.62870e6	0.313899
$738$	−7.43507e6	−0.502510
$739$	−2.00368e7	−1.34964	−0.674818	−	0.737985i	$-0.735778\pi$
$739$	−2.00368e7	−1.34964	−0.674818	+	0.737985i	$0.735778\pi$
$740$	−5.26673e7	−3.53559
$741$	−4.04263e6	−0.270470
$742$	−1.01204e6	−0.0674821
$743$	7.75386e6	0.515283	0.257642	−	0.966241i	$-0.417055\pi$
$743$	7.75386e6	0.515283	0.257642	+	0.966241i	$0.417055\pi$
$744$	3.55158e7	2.35228
$745$	6.52562e6	0.430756
$746$	2.43844e7	1.60423
$747$	3.12197e6	0.204704
$748$	2.45981e7	1.60749
$749$	−563679.	−0.0367136
$750$	−478.647	−3.10715e−5 0
$751$	−1.59068e7	−1.02916	−0.514581	−	0.857442i	$-0.672052\pi$
$751$	−1.59068e7	−1.02916	−0.514581	+	0.857442i	$0.672052\pi$
$752$	4.05152e7	2.61261
$753$	−6.98492e6	−0.448925
$754$	−4.88718e6	−0.313062
$755$	1.50474e7	0.960711
$756$	−535871.	−0.0341001
$757$	−2.59909e7	−1.64847	−0.824235	−	0.566248i	$-0.808394\pi$
$757$	−2.59909e7	−1.64847	−0.824235	+	0.566248i	$0.808394\pi$
$758$	−4.60258e7	−2.90957
$759$	907967.	0.0572092
$760$	−1.01242e8	−6.35808
$761$	1.98230e7	1.24082	0.620408	−	0.784280i	$-0.286967\pi$
$761$	1.98230e7	1.24082	0.620408	+	0.784280i	$0.286967\pi$
$762$	3.04058e6	0.189701
$763$	892625.	0.0555082
$764$	2.28467e7	1.41609
$765$	1.18163e7	0.730009
$766$	2.95408e7	1.81907
$767$	5.40768e6	0.331912
$768$	9.31680e6	0.569985
$769$	1.20589e7	0.735345	0.367673	−	0.929955i	$-0.380155\pi$
$769$	1.20589e7	0.735345	0.367673	+	0.929955i	$0.380155\pi$
$770$	−1.35498e6	−0.0823578
$771$	7.63010e6	0.462268
$772$	3.78533e7	2.28592
$773$	2.98282e7	1.79547	0.897735	−	0.440535i	$-0.145211\pi$
$773$	2.98282e7	1.79547	0.897735	+	0.440535i	$0.145211\pi$
$774$	1.90078e7	1.14046
$775$	2.60283e7	1.55665
$776$	−6.30529e7	−3.75881
$777$	737323.	0.0438132
$778$	3.97709e7	2.35568
$779$	2.37306e7	1.40109
$780$	−9.14144e6	−0.537995
$781$	−1.79458e6	−0.105278
$782$	1.12887e7	0.660124
$783$	−2.05056e6	−0.119528
$784$	−4.14481e7	−2.40832
$785$	−5.06730e6	−0.293496
$786$	9.53101e6	0.550279
$787$	160399.	0.00923137	0.00461568	−	0.999989i	$-0.498531\pi$
$787$	160399.	0.00923137	0.00461568	+	0.999989i	$0.498531\pi$
$788$	6.90774e7	3.96297
$789$	−1.57106e7	−0.898462
$790$	4.92635e7	2.80839
$791$	−2.12461e6	−0.120737
$792$	−6.61672e6	−0.374826
$793$	−4.48545e6	−0.253293
$794$	6.04640e7	3.40365
$795$	−7.24382e6	−0.406490
$796$	−5.05985e7	−2.83045
$797$	−1.01436e7	−0.565649	−0.282824	−	0.959172i	$-0.591271\pi$
$797$	−1.01436e7	−0.565649	−0.282824	+	0.959172i	$0.591271\pi$
$798$	2.41825e6	0.134429
$799$	3.01523e7	1.67091
$800$	−3.36327e7	−1.85796
$801$	−4.24539e6	−0.233796
$802$	−3.35285e7	−1.84068
$803$	−1.38373e7	−0.757290
$804$	−1.86801e7	−1.01915
$805$	−439799.	−0.0239202
$806$	−1.44716e7	−0.784657
$807$	3.93345e6	0.212613
$808$	2.16262e7	1.16534
$809$	2.04927e7	1.10085	0.550425	−	0.834885i	$-0.314466\pi$
$809$	2.04927e7	1.10085	0.550425	+	0.834885i	$0.314466\pi$
$810$	−5.42309e6	−0.290425
$811$	−2.99380e7	−1.59835	−0.799173	−	0.601101i	$-0.794729\pi$
$811$	−2.99380e7	−1.59835	−0.799173	+	0.601101i	$0.794729\pi$
$812$	2.06765e6	0.110049
$813$	1.15570e6	0.0613221
$814$	1.55333e7	0.821682
$815$	−4.49407e6	−0.236999
$816$	−4.11773e7	−2.16487
$817$	−6.06674e7	−3.17981
$818$	−3.92088e6	−0.204880
$819$	127977.	0.00666686
$820$	5.36611e7	2.78692
$821$	4.30811e6	0.223064	0.111532	−	0.993761i	$-0.464424\pi$
$821$	4.30811e6	0.223064	0.111532	+	0.993761i	$0.464424\pi$
$822$	1.03067e7	0.532036
$823$	2.68254e7	1.38053	0.690266	−	0.723556i	$-0.257494\pi$
$823$	2.68254e7	1.38053	0.690266	+	0.723556i	$0.257494\pi$
$824$	−5.02631e6	−0.257888
$825$	−4.84916e6	−0.248046
$826$	−3.23480e6	−0.164967
$827$	2.71607e7	1.38095	0.690474	−	0.723358i	$-0.257402\pi$
$827$	2.71607e7	1.38095	0.690474	+	0.723358i	$0.257402\pi$
$828$	−3.66429e6	−0.185744
$829$	−90134.0	−0.00455515	−0.00227757	−	0.999997i	$-0.500725\pi$
$829$	−90134.0	−0.00455515	−0.00227757	+	0.999997i	$0.500725\pi$
$830$	−3.18581e7	−1.60518
$831$	6.60208e6	0.331648
$832$	5.51464e6	0.276191
$833$	−3.08466e7	−1.54026
$834$	4.37763e6	0.217933
$835$	1.00275e7	0.497712
$836$	3.60322e7	1.78310
$837$	−6.07201e6	−0.299584
$838$	4.14425e7	2.03862
$839$	−2.00769e6	−0.0984675	−0.0492337	−	0.998787i	$-0.515678\pi$
$839$	−2.00769e6	−0.0984675	−0.0492337	+	0.998787i	$0.515678\pi$
$840$	3.20499e6	0.156722
$841$	−1.25991e7	−0.614255
$842$	5.75482e7	2.79738
$843$	−1.83365e7	−0.888682
$844$	5.69495e7	2.75191
$845$	−2.71700e7	−1.30902
$846$	−1.38384e7	−0.664752
$847$	−1.24857e6	−0.0598004
$848$	2.52432e7	1.20546
$849$	3.56889e6	0.169927
$850$	−6.02891e7	−2.86214
$851$	5.04183e6	0.238651
$852$	7.24242e6	0.341810
$853$	2.13412e7	1.00426	0.502129	−	0.864793i	$-0.332550\pi$
$853$	2.13412e7	1.00426	0.502129	+	0.864793i	$0.332550\pi$
$854$	2.68314e6	0.125892
$855$	1.73089e7	0.809757
$856$	2.80889e7	1.31024
$857$	−1.00689e7	−0.468305	−0.234152	−	0.972200i	$-0.575231\pi$
$857$	−1.00689e7	−0.468305	−0.234152	+	0.972200i	$0.575231\pi$
$858$	2.69611e6	0.125032
$859$	1.19061e7	0.550538	0.275269	−	0.961367i	$-0.411233\pi$
$859$	1.19061e7	0.550538	0.275269	+	0.961367i	$0.411233\pi$
$860$	−1.37185e8	−6.32500
$861$	−751236.	−0.0345357
$862$	−1.06339e7	−0.487444
$863$	2.40690e7	1.10010	0.550049	−	0.835132i	$-0.314609\pi$
$863$	2.40690e7	1.10010	0.550049	+	0.835132i	$0.314609\pi$
$864$	7.84600e6	0.357572
$865$	−5.14955e6	−0.234007
$866$	−1.21084e7	−0.548646
$867$	−1.78663e7	−0.807212
$868$	6.12262e6	0.275828
$869$	−1.02762e7	−0.461617
$870$	2.09249e7	0.937273
$871$	4.46119e6	0.199253
$872$	−4.44807e7	−1.98098
$873$	1.07799e7	0.478718
$874$	1.65360e7	0.732238
$875$	−48.3622	−2.13543e−6 0
$876$	5.58433e7	2.45873
$877$	1.68741e7	0.740836	0.370418	−	0.928865i	$-0.379215\pi$
$877$	1.68741e7	0.740836	0.370418	+	0.928865i	$0.379215\pi$
$878$	−5.21785e7	−2.28431
$879$	2.45548e7	1.07193
$880$	3.37969e7	1.47120
$881$	−1.90496e7	−0.826889	−0.413444	−	0.910529i	$-0.635674\pi$
$881$	−1.90496e7	−0.826889	−0.413444	+	0.910529i	$0.635674\pi$
$882$	1.41570e7	0.612774
$883$	−2.90567e7	−1.25414	−0.627068	−	0.778965i	$-0.715745\pi$
$883$	−2.90567e7	−1.25414	−0.627068	+	0.778965i	$0.715745\pi$
$884$	2.37079e7	1.02038
$885$	−2.31535e7	−0.993709
$886$	3.60205e7	1.54158
$887$	−1.04434e7	−0.445689	−0.222844	−	0.974854i	$-0.571534\pi$
$887$	−1.04434e7	−0.445689	−0.222844	+	0.974854i	$0.571534\pi$
$888$	−3.67418e7	−1.56361
$889$	307219.	0.0130375
$890$	4.33221e7	1.83330
$891$	1.13124e6	0.0477374
$892$	−2.12891e6	−0.0895870
$893$	4.41682e7	1.85345
$894$	7.76721e6	0.325028
$895$	2.75926e7	1.15142
$896$	−24301.3	−0.00101125
$897$	875107.	0.0363145
$898$	4.48399e7	1.85556
$899$	2.34288e7	0.966832
$900$	1.95698e7	0.805342
$901$	1.87865e7	0.770964
$902$	−1.58264e7	−0.647690
$903$	1.92054e6	0.0783797
$904$	1.05872e8	4.30885
$905$	1.83957e7	0.746610
$906$	1.79103e7	0.724909
$907$	2.13315e7	0.860999	0.430500	−	0.902591i	$-0.358337\pi$
$907$	2.13315e7	0.860999	0.430500	+	0.902591i	$0.358337\pi$
$908$	−1.01659e8	−4.09197
$909$	−3.69735e6	−0.148416
$910$	−1.30594e6	−0.0522780
$911$	−3.81518e7	−1.52307	−0.761534	−	0.648125i	$-0.775553\pi$
$911$	−3.81518e7	−1.52307	−0.761534	+	0.648125i	$0.775553\pi$
$912$	−6.03179e7	−2.40137
$913$	6.64548e6	0.263845
$914$	3.17391e7	1.25669
$915$	1.92049e7	0.758333
$916$	−2.17970e7	−0.858339
$917$	963008.	0.0378187
$918$	1.40645e7	0.550831
$919$	−3.28081e7	−1.28142	−0.640711	−	0.767782i	$-0.721360\pi$
$919$	−3.28081e7	−1.28142	−0.640711	+	0.767782i	$0.721360\pi$
$920$	2.19158e7	0.853666
$921$	7.03955e6	0.273461
$922$	7.94270e7	3.07710
$923$	−1.72964e6	−0.0668268
$924$	−1.14066e6	−0.0439519
$925$	−2.69268e7	−1.03474
$926$	7.94759e7	3.04585
$927$	859329.	0.0328443
$928$	−3.02737e7	−1.15397
$929$	−3.65260e7	−1.38855	−0.694277	−	0.719707i	$-0.744276\pi$
$929$	−3.65260e7	−1.38855	−0.694277	+	0.719707i	$0.744276\pi$
$930$	6.19618e7	2.34918
$931$	−4.51851e7	−1.70853
$932$	−8.58924e7	−3.23903
$933$	−1.90004e7	−0.714594
$934$	5.16446e7	1.93713
$935$	2.51524e7	0.940915
$936$	−6.37726e6	−0.237927
$937$	−1.33042e6	−0.0495040	−0.0247520	−	0.999694i	$-0.507880\pi$
$937$	−1.33042e6	−0.0495040	−0.0247520	+	0.999694i	$0.507880\pi$
$938$	−2.66862e6	−0.0990330
$939$	5.34466e6	0.197813
$940$	9.98758e7	3.68672
$941$	−4.03036e7	−1.48378	−0.741891	−	0.670521i	$-0.766071\pi$
$941$	−4.03036e7	−1.48378	−0.741891	+	0.670521i	$0.766071\pi$
$942$	−6.03143e6	−0.221459
$943$	−5.13696e6	−0.188117
$944$	8.06851e7	2.94689
$945$	−547946.	−0.0199599
$946$	4.04604e7	1.46995
$947$	3.52339e7	1.27669	0.638346	−	0.769750i	$-0.279619\pi$
$947$	3.52339e7	1.27669	0.638346	+	0.769750i	$0.279619\pi$
$948$	4.14717e7	1.49876
$949$	−1.33365e7	−0.480703
$950$	−8.83135e7	−3.17481
$951$	581477.	0.0208488
$952$	−8.31201e6	−0.297244
$953$	−3.27018e7	−1.16638	−0.583189	−	0.812337i	$-0.698195\pi$
$953$	−3.27018e7	−1.16638	−0.583189	+	0.812337i	$0.698195\pi$
$954$	−8.62206e6	−0.306719
$955$	2.33615e7	0.828882
$956$	4.06015e7	1.43680
$957$	−4.36487e6	−0.154060
$958$	−8.14856e7	−2.86858
$959$	1.04139e6	0.0365650
$960$	−2.36115e7	−0.826885
$961$	4.07469e7	1.42327
$962$	1.49712e7	0.521577
$963$	−4.80225e6	−0.166870
$964$	1.07027e8	3.70936
$965$	3.87063e7	1.33802
$966$	−523478.	−0.0180491
$967$	−4.07996e7	−1.40310	−0.701551	−	0.712619i	$-0.747509\pi$
$967$	−4.07996e7	−1.40310	−0.701551	+	0.712619i	$0.747509\pi$
$968$	6.22179e7	2.13416
$969$	−4.48899e7	−1.53582
$970$	−1.10003e8	−3.75385
$971$	4.96433e7	1.68971	0.844856	−	0.534993i	$-0.179686\pi$
$971$	4.96433e7	1.68971	0.844856	+	0.534993i	$0.179686\pi$
$972$	−4.56534e6	−0.154991
$973$	442313.	0.0149778
$974$	5.03873e7	1.70186
$975$	−4.67367e6	−0.157451
$976$	−6.69250e7	−2.24887
$977$	−5.12839e7	−1.71888	−0.859438	−	0.511240i	$-0.829186\pi$
$977$	−5.12839e7	−1.71888	−0.859438	+	0.511240i	$0.829186\pi$
$978$	−5.34914e6	−0.178828
$979$	−9.03682e6	−0.301341
$980$	−1.02175e8	−3.39845
$981$	7.60469e6	0.252295
$982$	946267.	0.0313137
$983$	1.13741e7	0.375432	0.187716	−	0.982223i	$-0.439892\pi$
$983$	1.13741e7	0.375432	0.187716	+	0.982223i	$0.439892\pi$
$984$	3.74351e7	1.23251
$985$	7.06339e7	2.31965
$986$	−5.42679e7	−1.77767
$987$	−1.39822e6	−0.0456861
$988$	3.47282e7	1.13185
$989$	1.31327e7	0.426935
$990$	−1.15437e7	−0.374332
$991$	−1.87041e7	−0.604998	−0.302499	−	0.953150i	$-0.597821\pi$
$991$	−1.87041e7	−0.604998	−0.302499	+	0.953150i	$0.597821\pi$
$992$	−8.96449e7	−2.89232
$993$	−3.47070e7	−1.11698
$994$	1.03465e6	0.0332143
$995$	−5.17387e7	−1.65675
$996$	−2.68192e7	−0.856639
$997$	1.80753e7	0.575901	0.287951	−	0.957645i	$-0.407026\pi$
$997$	1.80753e7	0.575901	0.287951	+	0.957645i	$0.407026\pi$
$998$	−4.23476e7	−1.34587
$999$	6.28161e6	0.199139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.1	✓	20
3.2	odd	2		927.6.a.c.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.1	✓	20	1.1	even	1	trivial
927.6.a.c.1.20		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-10.4554 q^{2} -9.00000 q^{3} +77.3144 q^{4} +79.0565 q^{5} +94.0982 q^{6} +9.50763 q^{7} -473.778 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.4554 q^{2} -9.00000 q^{3} +77.3144 q^{4} +79.0565 q^{5} +94.0982 q^{6} +9.50763 q^{7} -473.778 q^{8} +81.0000 q^{9} -826.564 q^{10} +172.418 q^{11} -695.830 q^{12} +166.178 q^{13} -99.4056 q^{14} -711.509 q^{15} +2479.46 q^{16} +1845.27 q^{17} -846.884 q^{18} +2703.01 q^{19} +6112.21 q^{20} -85.5686 q^{21} -1802.69 q^{22} -585.120 q^{23} +4264.00 q^{24} +3124.94 q^{25} -1737.45 q^{26} -729.000 q^{27} +735.076 q^{28} +2812.84 q^{29} +7439.08 q^{30} +8329.23 q^{31} -10762.7 q^{32} -1551.76 q^{33} -19292.9 q^{34} +751.640 q^{35} +6262.47 q^{36} -8616.75 q^{37} -28260.9 q^{38} -1495.60 q^{39} -37455.2 q^{40} +8779.33 q^{41} +894.650 q^{42} -22444.4 q^{43} +13330.4 q^{44} +6403.58 q^{45} +6117.63 q^{46} +16340.4 q^{47} -22315.1 q^{48} -16716.6 q^{49} -32672.3 q^{50} -16607.4 q^{51} +12848.0 q^{52} +10180.9 q^{53} +7621.95 q^{54} +13630.8 q^{55} -4504.50 q^{56} -24327.1 q^{57} -29409.3 q^{58} +32541.5 q^{59} -55009.9 q^{60} -26991.8 q^{61} -87085.0 q^{62} +770.118 q^{63} +33185.1 q^{64} +13137.5 q^{65} +16224.2 q^{66} +26845.8 q^{67} +142666. q^{68} +5266.08 q^{69} -7858.66 q^{70} -10408.3 q^{71} -38376.0 q^{72} -80254.3 q^{73} +90091.1 q^{74} -28124.4 q^{75} +208982. q^{76} +1639.29 q^{77} +15637.1 q^{78} -59600.3 q^{79} +196017. q^{80} +6561.00 q^{81} -91791.0 q^{82} +38542.8 q^{83} -6615.69 q^{84} +145880. q^{85} +234664. q^{86} -25315.6 q^{87} -81687.9 q^{88} -52412.2 q^{89} -66951.7 q^{90} +1579.96 q^{91} -45238.2 q^{92} -74963.1 q^{93} -170844. q^{94} +213691. q^{95} +96864.2 q^{96} +133085. q^{97} +174778. q^{98} +13965.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9} + 445 q^{10} + 1712 q^{11} - 2934 q^{12} - 809 q^{13} + 388 q^{14} - 873 q^{15} + 3934 q^{16} + 2040 q^{17} + 324 q^{18} + 5320 q^{19} + 4415 q^{20} - 90 q^{21} + 705 q^{22} + 653 q^{23} - 2808 q^{24} + 5977 q^{25} - 1655 q^{26} - 14580 q^{27} - 9206 q^{28} - 706 q^{29} - 4005 q^{30} + 9091 q^{31} - 16762 q^{32} - 15408 q^{33} - 17698 q^{34} + 15988 q^{35} + 26406 q^{36} - 50 q^{37} + 3877 q^{38} + 7281 q^{39} + 30485 q^{40} + 37084 q^{41} - 3492 q^{42} + 2533 q^{43} + 64525 q^{44} + 7857 q^{45} + 13966 q^{46} + 23282 q^{47} - 35406 q^{48} + 32910 q^{49} + 85769 q^{50} - 18360 q^{51} + 58531 q^{52} + 67436 q^{53} - 2916 q^{54} + 27254 q^{55} + 130668 q^{56} - 47880 q^{57} - 26963 q^{58} + 162695 q^{59} - 39735 q^{60} + 44895 q^{61} + 115286 q^{62} + 810 q^{63} + 44238 q^{64} + 64945 q^{65} - 6345 q^{66} - 4127 q^{67} + 231174 q^{68} - 5877 q^{69} + 290034 q^{70} + 140618 q^{71} + 25272 q^{72} - 52974 q^{73} + 558413 q^{74} - 53793 q^{75} + 224357 q^{76} + 210380 q^{77} + 14895 q^{78} + 170742 q^{79} + 760913 q^{80} + 131220 q^{81} + 576206 q^{82} + 239285 q^{83} + 82854 q^{84} + 268116 q^{85} + 776443 q^{86} + 6354 q^{87} + 381839 q^{88} + 408810 q^{89} + 36045 q^{90} + 413782 q^{91} + 645628 q^{92} - 81819 q^{93} + 447752 q^{94} + 568618 q^{95} + 150858 q^{96} + 275859 q^{97} + 768726 q^{98} + 138672 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 180 * q^3 + 326 * q^4 + 97 * q^5 - 36 * q^6 + 10 * q^7 + 312 * q^8 + 1620 * q^9 + 445 * q^10 + 1712 * q^11 - 2934 * q^12 - 809 * q^13 + 388 * q^14 - 873 * q^15 + 3934 * q^16 + 2040 * q^17 + 324 * q^18 + 5320 * q^19 + 4415 * q^20 - 90 * q^21 + 705 * q^22 + 653 * q^23 - 2808 * q^24 + 5977 * q^25 - 1655 * q^26 - 14580 * q^27 - 9206 * q^28 - 706 * q^29 - 4005 * q^30 + 9091 * q^31 - 16762 * q^32 - 15408 * q^33 - 17698 * q^34 + 15988 * q^35 + 26406 * q^36 - 50 * q^37 + 3877 * q^38 + 7281 * q^39 + 30485 * q^40 + 37084 * q^41 - 3492 * q^42 + 2533 * q^43 + 64525 * q^44 + 7857 * q^45 + 13966 * q^46 + 23282 * q^47 - 35406 * q^48 + 32910 * q^49 + 85769 * q^50 - 18360 * q^51 + 58531 * q^52 + 67436 * q^53 - 2916 * q^54 + 27254 * q^55 + 130668 * q^56 - 47880 * q^57 - 26963 * q^58 + 162695 * q^59 - 39735 * q^60 + 44895 * q^61 + 115286 * q^62 + 810 * q^63 + 44238 * q^64 + 64945 * q^65 - 6345 * q^66 - 4127 * q^67 + 231174 * q^68 - 5877 * q^69 + 290034 * q^70 + 140618 * q^71 + 25272 * q^72 - 52974 * q^73 + 558413 * q^74 - 53793 * q^75 + 224357 * q^76 + 210380 * q^77 + 14895 * q^78 + 170742 * q^79 + 760913 * q^80 + 131220 * q^81 + 576206 * q^82 + 239285 * q^83 + 82854 * q^84 + 268116 * q^85 + 776443 * q^86 + 6354 * q^87 + 381839 * q^88 + 408810 * q^89 + 36045 * q^90 + 413782 * q^91 + 645628 * q^92 - 81819 * q^93 + 447752 * q^94 + 568618 * q^95 + 150858 * q^96 + 275859 * q^97 + 768726 * q^98 + 138672 * q^99

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