LMFDB - Embedded newform 309.6.a.b.1.18

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			1.18
Root			$9.02016$ 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)

$f(q)$	$=$	$q+9.02016 q^{2} -9.00000 q^{3} +49.3633 q^{4} -67.0257 q^{5} -81.1814 q^{6} +0.186737 q^{7} +156.620 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.02016 q^{2} -9.00000 q^{3} +49.3633 q^{4} -67.0257 q^{5} -81.1814 q^{6} +0.186737 q^{7} +156.620 q^{8} +81.0000 q^{9} -604.583 q^{10} -59.2116 q^{11} -444.270 q^{12} +1059.24 q^{13} +1.68440 q^{14} +603.232 q^{15} -166.891 q^{16} +184.344 q^{17} +730.633 q^{18} -522.627 q^{19} -3308.61 q^{20} -1.68063 q^{21} -534.098 q^{22} +637.671 q^{23} -1409.58 q^{24} +1367.45 q^{25} +9554.52 q^{26} -729.000 q^{27} +9.21795 q^{28} +7419.26 q^{29} +5441.25 q^{30} +5976.36 q^{31} -6517.21 q^{32} +532.904 q^{33} +1662.81 q^{34} -12.5162 q^{35} +3998.43 q^{36} +10713.8 q^{37} -4714.18 q^{38} -9533.17 q^{39} -10497.5 q^{40} +7435.37 q^{41} -15.1596 q^{42} +10231.9 q^{43} -2922.88 q^{44} -5429.08 q^{45} +5751.90 q^{46} +26105.1 q^{47} +1502.02 q^{48} -16807.0 q^{49} +12334.6 q^{50} -1659.09 q^{51} +52287.6 q^{52} +7891.36 q^{53} -6575.70 q^{54} +3968.70 q^{55} +29.2467 q^{56} +4703.65 q^{57} +66922.9 q^{58} +42368.4 q^{59} +29777.5 q^{60} -56441.5 q^{61} +53907.7 q^{62} +15.1257 q^{63} -53445.8 q^{64} -70996.4 q^{65} +4806.88 q^{66} -12611.0 q^{67} +9099.82 q^{68} -5739.04 q^{69} -112.898 q^{70} +58411.9 q^{71} +12686.2 q^{72} -82465.6 q^{73} +96640.2 q^{74} -12307.0 q^{75} -25798.6 q^{76} -11.0570 q^{77} -85990.7 q^{78} -44561.2 q^{79} +11186.0 q^{80} +6561.00 q^{81} +67068.3 q^{82} -58712.8 q^{83} -82.9615 q^{84} -12355.8 q^{85} +92293.3 q^{86} -66773.3 q^{87} -9273.69 q^{88} +105385. q^{89} -48971.2 q^{90} +197.799 q^{91} +31477.6 q^{92} -53787.2 q^{93} +235472. q^{94} +35029.5 q^{95} +58654.9 q^{96} +106868. q^{97} -151602. q^{98} -4796.14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.02016	1.59455	0.797277	−	0.603614i	$-0.206273\pi$
$2$	9.02016	1.59455	0.797277	+	0.603614i	$0.206273\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	49.3633	1.54260
$5$	−67.0257	−1.19899	−0.599496	−	0.800378i	$-0.704632\pi$
$5$	−67.0257	−1.19899	−0.599496	+	0.800378i	$0.704632\pi$
$6$	−81.1814	−0.920616
$7$	0.186737	0.00144041	0.000720203	−	1.00000i	$-0.499771\pi$
$7$	0.186737	0.00144041	0.000720203		1.00000i	$0.499771\pi$
$8$	156.620	0.865210
$9$	81.0000	0.333333
$10$	−604.583	−1.91186
$11$	−59.2116	−0.147545	−0.0737725	−	0.997275i	$-0.523504\pi$
$11$	−59.2116	−0.147545	−0.0737725	+	0.997275i	$0.523504\pi$
$12$	−444.270	−0.890622
$13$	1059.24	1.73835	0.869173	−	0.494508i	$-0.164652\pi$
$13$	1059.24	1.73835	0.869173	+	0.494508i	$0.164652\pi$
$14$	1.68440	0.00229681
$15$	603.232	0.692239
$16$	−166.891	−0.162979
$17$	184.344	0.154706	0.0773528	−	0.997004i	$-0.475353\pi$
$17$	184.344	0.154706	0.0773528	+	0.997004i	$0.475353\pi$
$18$	730.633	0.531518
$19$	−522.627	−0.332130	−0.166065	−	0.986115i	$-0.553106\pi$
$19$	−522.627	−0.332130	−0.166065	+	0.986115i	$0.553106\pi$
$20$	−3308.61	−1.84957
$21$	−1.68063	−0.000831619 0
$22$	−534.098	−0.235269
$23$	637.671	0.251349	0.125675	−	0.992072i	$-0.459890\pi$
$23$	637.671	0.251349	0.125675	+	0.992072i	$0.459890\pi$
$24$	−1409.58	−0.499529
$25$	1367.45	0.437583
$26$	9554.52	2.77189
$27$	−729.000	−0.192450
$28$	9.21795	0.00222197
$29$	7419.26	1.63820	0.819098	−	0.573654i	$-0.194475\pi$
$29$	7419.26	1.63820	0.819098	+	0.573654i	$0.194475\pi$
$30$	5441.25	1.10381
$31$	5976.36	1.11695	0.558473	−	0.829523i	$-0.311387\pi$
$31$	5976.36	1.11695	0.558473	+	0.829523i	$0.311387\pi$
$32$	−6517.21	−1.12509
$33$	532.904	0.0851852
$34$	1662.81	0.246687
$35$	−12.5162	−0.00172704
$36$	3998.43	0.514201
$37$	10713.8	1.28659	0.643294	−	0.765620i	$-0.277567\pi$
$37$	10713.8	1.28659	0.643294	+	0.765620i	$0.277567\pi$
$38$	−4714.18	−0.529599
$39$	−9533.17	−1.00363
$40$	−10497.5	−1.03738
$41$	7435.37	0.690786	0.345393	−	0.938458i	$-0.387746\pi$
$41$	7435.37	0.690786	0.345393	+	0.938458i	$0.387746\pi$
$42$	−15.1596	−0.00132606
$43$	10231.9	0.843888	0.421944	−	0.906622i	$-0.361348\pi$
$43$	10231.9	0.843888	0.421944	+	0.906622i	$0.361348\pi$
$44$	−2922.88	−0.227603
$45$	−5429.08	−0.399664
$46$	5751.90	0.400790
$47$	26105.1	1.72377	0.861887	−	0.507100i	$-0.169283\pi$
$47$	26105.1	1.72377	0.861887	+	0.507100i	$0.169283\pi$
$48$	1502.02	0.0940962
$49$	−16807.0	−0.999998
$50$	12334.6	0.697750
$51$	−1659.09	−0.0893194
$52$	52287.6	2.68158
$53$	7891.36	0.385889	0.192945	−	0.981210i	$-0.438196\pi$
$53$	7891.36	0.385889	0.192945	+	0.981210i	$0.438196\pi$
$54$	−6575.70	−0.306872
$55$	3968.70	0.176905
$56$	29.2467	0.00124625
$57$	4703.65	0.191755
$58$	66922.9	2.61219
$59$	42368.4	1.58457	0.792286	−	0.610150i	$-0.208891\pi$
$59$	42368.4	1.58457	0.792286	+	0.610150i	$0.208891\pi$
$60$	29777.5	1.06785
$61$	−56441.5	−1.94211	−0.971055	−	0.238855i	$-0.923228\pi$
$61$	−56441.5	−1.94211	−0.971055	+	0.238855i	$0.923228\pi$
$62$	53907.7	1.78103
$63$	15.1257	0.000480135 0
$64$	−53445.8	−1.63104
$65$	−70996.4	−2.08426
$66$	4806.88	0.135832
$67$	−12611.0	−0.343212	−0.171606	−	0.985166i	$-0.554896\pi$
$67$	−12611.0	−0.343212	−0.171606	+	0.985166i	$0.554896\pi$
$68$	9099.82	0.238649
$69$	−5739.04	−0.145116
$70$	−112.898	−0.00275385
$71$	58411.9	1.37517	0.687583	−	0.726105i	$-0.258672\pi$
$71$	58411.9	1.37517	0.687583	+	0.726105i	$0.258672\pi$
$72$	12686.2	0.288403
$73$	−82465.6	−1.81120	−0.905598	−	0.424137i	$-0.860577\pi$
$73$	−82465.6	−1.81120	−0.905598	+	0.424137i	$0.860577\pi$
$74$	96640.2	2.05153
$75$	−12307.0	−0.252639
$76$	−25798.6	−0.512345
$77$	−11.0570	−0.000212525 0
$78$	−85990.7	−1.60035
$79$	−44561.2	−0.803320	−0.401660	−	0.915789i	$-0.631567\pi$
$79$	−44561.2	−0.803320	−0.401660	+	0.915789i	$0.631567\pi$
$80$	11186.0	0.195411
$81$	6561.00	0.111111
$82$	67068.3	1.10149
$83$	−58712.8	−0.935487	−0.467744	−	0.883864i	$-0.654933\pi$
$83$	−58712.8	−0.935487	−0.467744	+	0.883864i	$0.654933\pi$
$84$	−82.9615	−0.00128286
$85$	−12355.8	−0.185491
$86$	92293.3	1.34562
$87$	−66773.3	−0.945812
$88$	−9273.69	−0.127657
$89$	105385.	1.41027	0.705136	−	0.709073i	$-0.250886\pi$
$89$	105385.	1.41027	0.705136	+	0.709073i	$0.250886\pi$
$90$	−48971.2	−0.637286
$91$	197.799	0.00250392
$92$	31477.6	0.387732
$93$	−53787.2	−0.644869
$94$	235472.	2.74865
$95$	35029.5	0.398221
$96$	58654.9	0.649570
$97$	106868.	1.15323	0.576616	−	0.817016i	$-0.304373\pi$
$97$	106868.	1.15323	0.576616	+	0.817016i	$0.304373\pi$
$98$	−151602.	−1.59455
$99$	−4796.14	−0.0491817
$100$	67501.7	0.675017
$101$	−61079.2	−0.595785	−0.297893	−	0.954599i	$-0.596284\pi$
$101$	−61079.2	−0.595785	−0.297893	+	0.954599i	$0.596284\pi$
$102$	−14965.3	−0.142425
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	165898.	1.50403
$105$	112.646	0.000997105 0
$106$	71181.4	0.615321
$107$	−97521.4	−0.823456	−0.411728	−	0.911307i	$-0.635075\pi$
$107$	−97521.4	−0.823456	−0.411728	+	0.911307i	$0.635075\pi$
$108$	−35985.8	−0.296874
$109$	108944.	0.878291	0.439145	−	0.898416i	$-0.355281\pi$
$109$	108944.	0.878291	0.439145	+	0.898416i	$0.355281\pi$
$110$	35798.3	0.282085
$111$	−96424.2	−0.742811
$112$	−31.1647	−0.000234757 0
$113$	41451.4	0.305381	0.152691	−	0.988274i	$-0.451206\pi$
$113$	41451.4	0.305381	0.152691	+	0.988274i	$0.451206\pi$
$114$	42427.6	0.305764
$115$	−42740.4	−0.301366
$116$	366239.	2.52708
$117$	85798.5	0.579449
$118$	382170.	2.52668
$119$	34.4238	0.000222839 0
$120$	94477.9	0.598932
$121$	−157545.	−0.978230
$122$	−509111.	−3.09680
$123$	−66918.4	−0.398825
$124$	295013.	1.72300
$125$	117801.	0.674333
$126$	136.436	0.000765602 0
$127$	−28857.8	−0.158765	−0.0793823	−	0.996844i	$-0.525295\pi$
$127$	−28857.8	−0.158765	−0.0793823	+	0.996844i	$0.525295\pi$
$128$	−273539.	−1.47569
$129$	−92087.0	−0.487219
$130$	−640399.	−3.32347
$131$	50095.7	0.255048	0.127524	−	0.991835i	$-0.459297\pi$
$131$	50095.7	0.255048	0.127524	+	0.991835i	$0.459297\pi$
$132$	26305.9	0.131407
$133$	−97.5938	−0.000478402 0
$134$	−113753.	−0.547270
$135$	48861.8	0.230746
$136$	28871.9	0.133853
$137$	−159252.	−0.724911	−0.362455	−	0.932001i	$-0.618061\pi$
$137$	−159252.	−0.724911	−0.362455	+	0.932001i	$0.618061\pi$
$138$	−51767.1	−0.231396
$139$	−131290.	−0.576362	−0.288181	−	0.957576i	$-0.593051\pi$
$139$	−131290.	−0.576362	−0.288181	+	0.957576i	$0.593051\pi$
$140$	−617.840	−0.00266413
$141$	−234946.	−0.995221
$142$	526885.	2.19278
$143$	−62719.3	−0.256485
$144$	−13518.2	−0.0543265
$145$	−497281.	−1.96418
$146$	−743853.	−2.88805
$147$	151263.	0.577349
$148$	528868.	1.98469
$149$	−518375.	−1.91284	−0.956419	−	0.291998i	$-0.905680\pi$
$149$	−518375.	−1.91284	−0.956419	+	0.291998i	$0.905680\pi$
$150$	−111011.	−0.402846
$151$	335953.	1.19905	0.599523	−	0.800358i	$-0.295357\pi$
$151$	335953.	1.19905	0.599523	+	0.800358i	$0.295357\pi$
$152$	−81853.7	−0.287362
$153$	14931.8	0.0515686
$154$	−99.7357	−0.000338882 0
$155$	−400570.	−1.33921
$156$	−470589.	−1.54821
$157$	182021.	0.589350	0.294675	−	0.955598i	$-0.404789\pi$
$157$	182021.	0.589350	0.294675	+	0.955598i	$0.404789\pi$
$158$	−401949.	−1.28094
$159$	−71022.3	−0.222793
$160$	436821.	1.34897
$161$	119.077	0.000362045 0
$162$	59181.3	0.177173
$163$	−406535.	−1.19847	−0.599237	−	0.800572i	$-0.704529\pi$
$163$	−406535.	−1.19847	−0.599237	+	0.800572i	$0.704529\pi$
$164$	367035.	1.06561
$165$	−35718.3	−0.102136
$166$	−529599.	−1.49168
$167$	541123.	1.50143	0.750715	−	0.660626i	$-0.229709\pi$
$167$	541123.	1.50143	0.750715	+	0.660626i	$0.229709\pi$
$168$	−263.220	−0.000719525 0
$169$	750698.	2.02185
$170$	−111451.	−0.295775
$171$	−42332.8	−0.110710
$172$	505080.	1.30178
$173$	409428.	1.04007	0.520034	−	0.854145i	$-0.325919\pi$
$173$	409428.	1.04007	0.520034	+	0.854145i	$0.325919\pi$
$174$	−602306.	−1.50815
$175$	255.353	0.000630298 0
$176$	9881.87	0.0240468
$177$	−381315.	−0.914853
$178$	950587.	2.24875
$179$	220244.	0.513772	0.256886	−	0.966442i	$-0.417303\pi$
$179$	220244.	0.513772	0.256886	+	0.966442i	$0.417303\pi$
$180$	−267997.	−0.616523
$181$	−63164.8	−0.143311	−0.0716553	−	0.997429i	$-0.522828\pi$
$181$	−63164.8	−0.143311	−0.0716553	+	0.997429i	$0.522828\pi$
$182$	1784.18	0.00399264
$183$	507973.	1.12128
$184$	99871.9	0.217470
$185$	−718100.	−1.54261
$186$	−485169.	−1.02828
$187$	−10915.3	−0.0228261
$188$	1.28863e6	2.65910
$189$	−136.131	−0.000277206 0
$190$	315971.	0.634986
$191$	−610079.	−1.21005	−0.605024	−	0.796207i	$-0.706837\pi$
$191$	−610079.	−1.21005	−0.605024	+	0.796207i	$0.706837\pi$
$192$	481012.	0.941679
$193$	240453.	0.464662	0.232331	−	0.972637i	$-0.425365\pi$
$193$	240453.	0.464662	0.232331	+	0.972637i	$0.425365\pi$
$194$	963962.	1.83889
$195$	638968.	1.20335
$196$	−829647.	−1.54260
$197$	1.04148e6	1.91198	0.955992	−	0.293392i	$-0.0947841\pi$
$197$	1.04148e6	1.91198	0.955992	+	0.293392i	$0.0947841\pi$
$198$	−43261.9	−0.0784229
$199$	225088.	0.402921	0.201461	−	0.979497i	$-0.435431\pi$
$199$	225088.	0.402921	0.201461	+	0.979497i	$0.435431\pi$
$200$	214169.	0.378601
$201$	113499.	0.198154
$202$	−550944.	−0.950012
$203$	1385.45	0.00235967
$204$	−81898.4	−0.137784
$205$	−498361.	−0.828247
$206$	95694.9	0.157116
$207$	51651.4	0.0837830
$208$	−176778.	−0.283315
$209$	30945.6	0.0490042
$210$	1016.08	0.00158994
$211$	−796584.	−1.23176	−0.615879	−	0.787840i	$-0.711199\pi$
$211$	−796584.	−1.23176	−0.615879	+	0.787840i	$0.711199\pi$
$212$	389544.	0.595273
$213$	−525707.	−0.793953
$214$	−879659.	−1.31305
$215$	−685800.	−1.01182
$216$	−114176.	−0.166510
$217$	1116.01	0.00160886
$218$	982695.	1.40048
$219$	742190.	1.04569
$220$	195908.	0.272895
$221$	195264.	0.268932
$222$	−869762.	−1.18445
$223$	1.13620e6	1.53000	0.765000	−	0.644031i	$-0.222739\pi$
$223$	1.13620e6	1.53000	0.765000	+	0.644031i	$0.222739\pi$
$224$	−1217.00	−0.00162059
$225$	110763.	0.145861
$226$	373898.	0.486947
$227$	332623.	0.428437	0.214219	−	0.976786i	$-0.431280\pi$
$227$	332623.	0.428437	0.214219	+	0.976786i	$0.431280\pi$
$228$	232187.	0.295802
$229$	42272.4	0.0532682	0.0266341	−	0.999645i	$-0.491521\pi$
$229$	42272.4	0.0532682	0.0266341	+	0.999645i	$0.491521\pi$
$230$	−385525.	−0.480544
$231$	99.5128	0.000122701 0
$232$	1.16200e6	1.41738
$233$	194144.	0.234279	0.117140	−	0.993115i	$-0.462627\pi$
$233$	194144.	0.234279	0.117140	+	0.993115i	$0.462627\pi$
$234$	773916.	0.923963
$235$	−1.74971e6	−2.06679
$236$	2.09144e6	2.44436
$237$	401050.	0.463797
$238$	310.508	0.000355329 0
$239$	−486200.	−0.550580	−0.275290	−	0.961361i	$-0.588774\pi$
$239$	−486200.	−0.550580	−0.275290	+	0.961361i	$0.588774\pi$
$240$	−100674.	−0.112821
$241$	202577.	0.224672	0.112336	−	0.993670i	$-0.464167\pi$
$241$	202577.	0.224672	0.112336	+	0.993670i	$0.464167\pi$
$242$	−1.42108e6	−1.55984
$243$	−59049.0	−0.0641500
$244$	−2.78614e6	−2.99590
$245$	1.12650e6	1.19899
$246$	−603614.	−0.635948
$247$	−553588.	−0.577357
$248$	936015.	0.966393
$249$	528415.	0.540104
$250$	1.06259e6	1.07526
$251$	−669193.	−0.670452	−0.335226	−	0.942138i	$-0.608813\pi$
$251$	−669193.	−0.670452	−0.335226	+	0.942138i	$0.608813\pi$
$252$	746.654	0.000740658 0
$253$	−37757.5	−0.0370853
$254$	−260302.	−0.253159
$255$	111202.	0.107093
$256$	−757098.	−0.722025
$257$	−515879.	−0.487208	−0.243604	−	0.969875i	$-0.578330\pi$
$257$	−515879.	−0.487208	−0.243604	+	0.969875i	$0.578330\pi$
$258$	−830639.	−0.776897
$259$	2000.66	0.00185321
$260$	−3.50462e6	−3.21519
$261$	600960.	0.546065
$262$	451871.	0.406688
$263$	−195449.	−0.174239	−0.0871194	−	0.996198i	$-0.527766\pi$
$263$	−195449.	−0.174239	−0.0871194	+	0.996198i	$0.527766\pi$
$264$	83463.2	0.0737030
$265$	−528924.	−0.462678
$266$	−880.312	−0.000762838 0
$267$	−948462.	−0.814220
$268$	−622521.	−0.529440
$269$	1.05755e6	0.891087	0.445543	−	0.895260i	$-0.353011\pi$
$269$	1.05755e6	0.891087	0.445543	+	0.895260i	$0.353011\pi$
$270$	440741.	0.367937
$271$	837423.	0.692663	0.346331	−	0.938112i	$-0.387427\pi$
$271$	837423.	0.692663	0.346331	+	0.938112i	$0.387427\pi$
$272$	−30765.3	−0.0252138
$273$	−1780.19	−0.00144564
$274$	−1.43648e6	−1.15591
$275$	−80968.7	−0.0645633
$276$	−283298.	−0.223857
$277$	−619139.	−0.484829	−0.242414	−	0.970173i	$-0.577939\pi$
$277$	−619139.	−0.484829	−0.242414	+	0.970173i	$0.577939\pi$
$278$	−1.18426e6	−0.919041
$279$	484085.	0.372315
$280$	−1960.28	−0.00149425
$281$	−90188.8	−0.0681376	−0.0340688	−	0.999419i	$-0.510847\pi$
$281$	−90188.8	−0.0681376	−0.0340688	+	0.999419i	$0.510847\pi$
$282$	−2.11925e6	−1.58693
$283$	2.18071e6	1.61857	0.809285	−	0.587417i	$-0.199855\pi$
$283$	2.18071e6	1.61857	0.809285	+	0.587417i	$0.199855\pi$
$284$	2.88340e6	2.12134
$285$	−315265.	−0.229913
$286$	−565738.	−0.408978
$287$	1388.46	0.000995012 0
$288$	−527894.	−0.375030
$289$	−1.38587e6	−0.976066
$290$	−4.48556e6	−3.13200
$291$	−961808.	−0.665818
$292$	−4.07077e6	−2.79396
$293$	−1.47035e6	−1.00058	−0.500289	−	0.865859i	$-0.666773\pi$
$293$	−1.47035e6	−1.00058	−0.500289	+	0.865859i	$0.666773\pi$
$294$	1.36441e6	0.920614
$295$	−2.83977e6	−1.89989
$296$	1.67799e6	1.11317
$297$	43165.2	0.0283951
$298$	−4.67582e6	−3.05012
$299$	675448.	0.436932
$300$	−607516.	−0.389721
$301$	1910.67	0.00121554
$302$	3.03035e6	1.91194
$303$	549713.	0.343977
$304$	87221.7	0.0541303
$305$	3.78303e6	2.32858
$306$	134688.	0.0822289
$307$	1.37164e6	0.830606	0.415303	−	0.909683i	$-0.363675\pi$
$307$	1.37164e6	0.830606	0.415303	+	0.909683i	$0.363675\pi$
$308$	−545.809	−0.000327841 0
$309$	−95481.0	−0.0568880
$310$	−3.61320e6	−2.13544
$311$	−1.42178e6	−0.833552	−0.416776	−	0.909009i	$-0.636840\pi$
$311$	−1.42178e6	−0.833552	−0.416776	+	0.909009i	$0.636840\pi$
$312$	−1.49308e6	−0.868354
$313$	−1.65100e6	−0.952548	−0.476274	−	0.879297i	$-0.658013\pi$
$313$	−1.65100e6	−0.952548	−0.476274	+	0.879297i	$0.658013\pi$
$314$	1.64186e6	0.939750
$315$	−1013.81	−0.000575679 0
$316$	−2.19969e6	−1.23920
$317$	1.15570e6	0.645948	0.322974	−	0.946408i	$-0.395317\pi$
$317$	1.15570e6	0.645948	0.322974	+	0.946408i	$0.395317\pi$
$318$	−640632.	−0.355256
$319$	−439306.	−0.241708
$320$	3.58224e6	1.95560
$321$	877693.	0.475423
$322$	1074.09	0.000577300 0
$323$	−96343.1	−0.0513824
$324$	323873.	0.171400
$325$	1.44846e6	0.760672
$326$	−3.66701e6	−1.91103
$327$	−980499.	−0.507081
$328$	1.16453e6	0.597674
$329$	4874.78	0.00248293
$330$	−322185.	−0.162862
$331$	−1.46043e6	−0.732673	−0.366336	−	0.930482i	$-0.619388\pi$
$331$	−1.46043e6	−0.732673	−0.366336	+	0.930482i	$0.619388\pi$
$332$	−2.89826e6	−1.44308
$333$	867818.	0.428862
$334$	4.88102e6	2.39411
$335$	845262.	0.411509
$336$	280.482	0.000135537 0
$337$	−2.77710e6	−1.33204	−0.666018	−	0.745936i	$-0.732003\pi$
$337$	−2.77710e6	−1.33204	−0.666018	+	0.745936i	$0.732003\pi$
$338$	6.77142e6	3.22395
$339$	−373062.	−0.176312
$340$	−609922.	−0.286139
$341$	−353869.	−0.164800
$342$	−381849.	−0.176533
$343$	−6276.97	−0.00288081
$344$	1.60251e6	0.730140
$345$	384664.	0.173994
$346$	3.69310e6	1.65845
$347$	−813719.	−0.362786	−0.181393	−	0.983411i	$-0.558061\pi$
$347$	−813719.	−0.362786	−0.181393	+	0.983411i	$0.558061\pi$
$348$	−3.29615e6	−1.45901
$349$	1.25783e6	0.552787	0.276393	−	0.961045i	$-0.410861\pi$
$349$	1.25783e6	0.552787	0.276393	+	0.961045i	$0.410861\pi$
$350$	2303.32	0.00100504
$351$	−772187.	−0.334545
$352$	385894.	0.166001
$353$	−996323.	−0.425563	−0.212781	−	0.977100i	$-0.568252\pi$
$353$	−996323.	−0.425563	−0.212781	+	0.977100i	$0.568252\pi$
$354$	−3.43953e6	−1.45878
$355$	−3.91510e6	−1.64882
$356$	5.20214e6	2.17549
$357$	−309.814	−0.000128656 0
$358$	1.98663e6	0.819238
$359$	863127.	0.353459	0.176729	−	0.984259i	$-0.443448\pi$
$359$	863127.	0.353459	0.176729	+	0.984259i	$0.443448\pi$
$360$	−850301.	−0.345793
$361$	−2.20296e6	−0.889690
$362$	−569756.	−0.228517
$363$	1.41790e6	0.564782
$364$	9764.02	0.00386256
$365$	5.52731e6	2.17161
$366$	4.58200e6	1.78794
$367$	3.89972e6	1.51136	0.755681	−	0.654940i	$-0.227306\pi$
$367$	3.89972e6	1.51136	0.755681	+	0.654940i	$0.227306\pi$
$368$	−106422.	−0.0409647
$369$	602265.	0.230262
$370$	−6.47738e6	−2.45977
$371$	1473.61	0.000555837 0
$372$	−2.65511e6	−0.994777
$373$	2.00658e6	0.746766	0.373383	−	0.927677i	$-0.378198\pi$
$373$	2.00658e6	0.746766	0.373383	+	0.927677i	$0.378198\pi$
$374$	−98457.6	−0.0363974
$375$	−1.06021e6	−0.389327
$376$	4.08857e6	1.49143
$377$	7.85878e6	2.84775
$378$	−1227.92	−0.000442020 0
$379$	−1.57020e6	−0.561509	−0.280754	−	0.959780i	$-0.590585\pi$
$379$	−1.57020e6	−0.561509	−0.280754	+	0.959780i	$0.590585\pi$
$380$	1.72917e6	0.614297
$381$	259720.	0.0916628
$382$	−5.50301e6	−1.92949
$383$	5.01329e6	1.74633	0.873165	−	0.487425i	$-0.162064\pi$
$383$	5.01329e6	1.74633	0.873165	+	0.487425i	$0.162064\pi$
$384$	2.46185e6	0.851988
$385$	741.102	0.000254816 0
$386$	2.16893e6	0.740929
$387$	828783.	0.281296
$388$	5.27533e6	1.77898
$389$	1.40192e6	0.469732	0.234866	−	0.972028i	$-0.424535\pi$
$389$	1.40192e6	0.469732	0.234866	+	0.972028i	$0.424535\pi$
$390$	5.76359e6	1.91881
$391$	117551.	0.0388851
$392$	−2.63230e6	−0.865208
$393$	−450861.	−0.147252
$394$	9.39429e6	3.04876
$395$	2.98674e6	0.963175
$396$	−236753.	−0.0758678
$397$	3.09670e6	0.986104	0.493052	−	0.870000i	$-0.335881\pi$
$397$	3.09670e6	0.986104	0.493052	+	0.870000i	$0.335881\pi$
$398$	2.03033e6	0.642480
$399$	878.344	0.000276206 0
$400$	−228215.	−0.0713171
$401$	256741.	0.0797323	0.0398662	−	0.999205i	$-0.487307\pi$
$401$	256741.	0.0797323	0.0398662	+	0.999205i	$0.487307\pi$
$402$	1.02378e6	0.315967
$403$	6.33040e6	1.94164
$404$	−3.01507e6	−0.919060
$405$	−439756.	−0.133221
$406$	12497.0	0.00376262
$407$	−634381.	−0.189830
$408$	−259847.	−0.0772800
$409$	−5.15669e6	−1.52427	−0.762136	−	0.647417i	$-0.775849\pi$
$409$	−5.15669e6	−1.52427	−0.762136	+	0.647417i	$0.775849\pi$
$410$	−4.49530e6	−1.32068
$411$	1.43327e6	0.418527
$412$	523695.	0.151997
$413$	7911.74	0.00228243
$414$	465904.	0.133597
$415$	3.93527e6	1.12164
$416$	−6.90330e6	−1.95579
$417$	1.18161e6	0.332763
$418$	279134.	0.0781398
$419$	−2.20013e6	−0.612229	−0.306115	−	0.951995i	$-0.599029\pi$
$419$	−2.20013e6	−0.612229	−0.306115	+	0.951995i	$0.599029\pi$
$420$	5560.56	0.00153814
$421$	−1.12463e6	−0.309246	−0.154623	−	0.987974i	$-0.549416\pi$
$421$	−1.12463e6	−0.309246	−0.154623	+	0.987974i	$0.549416\pi$
$422$	−7.18532e6	−1.96411
$423$	2.11451e6	0.574591
$424$	1.23594e6	0.333875
$425$	252081.	0.0676966
$426$	−4.74196e6	−1.26600
$427$	−10539.7	−0.00279743
$428$	−4.81398e6	−1.27027
$429$	564474.	0.148081
$430$	−6.18602e6	−1.61339
$431$	5.24879e6	1.36102	0.680512	−	0.732737i	$-0.261757\pi$
$431$	5.24879e6	1.36102	0.680512	+	0.732737i	$0.261757\pi$
$432$	121663.	0.0313654
$433$	−2.07798e6	−0.532625	−0.266312	−	0.963887i	$-0.585805\pi$
$433$	−2.07798e6	−0.532625	−0.266312	+	0.963887i	$0.585805\pi$
$434$	10066.6	0.00256541
$435$	4.47553e6	1.13402
$436$	5.37785e6	1.35485
$437$	−333264.	−0.0834806
$438$	6.69467e6	1.66742
$439$	−907297.	−0.224692	−0.112346	−	0.993669i	$-0.535837\pi$
$439$	−907297.	−0.224692	−0.112346	+	0.993669i	$0.535837\pi$
$440$	621576.	0.153060
$441$	−1.36136e6	−0.333333
$442$	1.76132e6	0.428827
$443$	−2.62937e6	−0.636563	−0.318282	−	0.947996i	$-0.603106\pi$
$443$	−2.62937e6	−0.636563	−0.318282	+	0.947996i	$0.603106\pi$
$444$	−4.75982e6	−1.14586
$445$	−7.06349e6	−1.69090
$446$	1.02487e7	2.43967
$447$	4.66537e6	1.10438
$448$	−9980.30	−0.00234935
$449$	2.01141e6	0.470851	0.235426	−	0.971892i	$-0.424352\pi$
$449$	2.01141e6	0.470851	0.235426	+	0.971892i	$0.424352\pi$
$450$	999103.	0.232583
$451$	−440260.	−0.101922
$452$	2.04618e6	0.471082
$453$	−3.02357e6	−0.692269
$454$	3.00031e6	0.683166
$455$	−13257.6	−0.00300219
$456$	736683.	0.165909
$457$	−2.05313e6	−0.459861	−0.229930	−	0.973207i	$-0.573850\pi$
$457$	−2.05313e6	−0.459861	−0.229930	+	0.973207i	$0.573850\pi$
$458$	381304.	0.0849390
$459$	−134387.	−0.0297731
$460$	−2.10981e6	−0.464888
$461$	6.46103e6	1.41595	0.707977	−	0.706235i	$-0.249608\pi$
$461$	6.46103e6	1.41595	0.707977	+	0.706235i	$0.249608\pi$
$462$	897.622	0.000195654 0
$463$	−138144.	−0.0299489	−0.0149745	−	0.999888i	$-0.504767\pi$
$463$	−138144.	−0.0299489	−0.0149745	+	0.999888i	$0.504767\pi$
$464$	−1.23821e6	−0.266992
$465$	3.60513e6	0.773194
$466$	1.75121e6	0.373571
$467$	−4.78776e6	−1.01587	−0.507937	−	0.861394i	$-0.669592\pi$
$467$	−4.78776e6	−1.01587	−0.507937	+	0.861394i	$0.669592\pi$
$468$	4.23530e6	0.893859
$469$	−2354.94	−0.000494365 0
$470$	−1.57827e7	−3.29561
$471$	−1.63819e6	−0.340261
$472$	6.63572e6	1.37099
$473$	−605846.	−0.124511
$474$	3.61754e6	0.739550
$475$	−714666.	−0.145335
$476$	1699.27	0.000343752 0
$477$	639200.	0.128630
$478$	−4.38560e6	−0.877929
$479$	−1.89722e6	−0.377814	−0.188907	−	0.981995i	$-0.560494\pi$
$479$	−1.89722e6	−0.377814	−0.188907	+	0.981995i	$0.560494\pi$
$480$	−3.93139e6	−0.778830
$481$	1.13485e7	2.23653
$482$	1.82728e6	0.358251
$483$	−1071.69	−0.000209027 0
$484$	−7.77694e6	−1.50902
$485$	−7.16287e6	−1.38272
$486$	−532631.	−0.102291
$487$	−8.83111e6	−1.68730	−0.843651	−	0.536892i	$-0.819598\pi$
$487$	−8.83111e6	−1.68730	−0.843651	+	0.536892i	$0.819598\pi$
$488$	−8.83985e6	−1.68033
$489$	3.65881e6	0.691939
$490$	1.01612e7	1.91185
$491$	6.98810e6	1.30814	0.654072	−	0.756432i	$-0.273059\pi$
$491$	6.98810e6	1.30814	0.654072	+	0.756432i	$0.273059\pi$
$492$	−3.30331e6	−0.615229
$493$	1.36769e6	0.253438
$494$	−4.99345e6	−0.920627
$495$	321465.	0.0589685
$496$	−997400.	−0.182039
$497$	10907.7	0.00198080
$498$	4.76639e6	0.861225
$499$	1.39712e6	0.251178	0.125589	−	0.992082i	$-0.459918\pi$
$499$	1.39712e6	0.251178	0.125589	+	0.992082i	$0.459918\pi$
$500$	5.81505e6	1.04023
$501$	−4.87011e6	−0.866851
$502$	−6.03623e6	−1.06907
$503$	6.58524e6	1.16052	0.580259	−	0.814432i	$-0.302951\pi$
$503$	6.58524e6	1.16052	0.580259	+	0.814432i	$0.302951\pi$
$504$	2368.98	0.000415418 0
$505$	4.09388e6	0.714342
$506$	−340579.	−0.0591346
$507$	−6.75628e6	−1.16731
$508$	−1.42452e6	−0.244911
$509$	3.21803e6	0.550549	0.275274	−	0.961366i	$-0.411231\pi$
$509$	3.21803e6	0.550549	0.275274	+	0.961366i	$0.411231\pi$
$510$	1.00306e6	0.170766
$511$	−15399.4	−0.00260886
$512$	1.92409e6	0.324378
$513$	380995.	0.0639184
$514$	−4.65331e6	−0.776880
$515$	−711076.	−0.118140
$516$	−4.54572e6	−0.751585
$517$	−1.54572e6	−0.254334
$518$	18046.3	0.00295504
$519$	−3.68485e6	−0.600484
$520$	−1.11194e7	−1.80333
$521$	−5.77366e6	−0.931874	−0.465937	−	0.884818i	$-0.654283\pi$
$521$	−5.77366e6	−0.931874	−0.465937	+	0.884818i	$0.654283\pi$
$522$	5.42076e6	0.870730
$523$	9.71976e6	1.55382	0.776911	−	0.629610i	$-0.216785\pi$
$523$	9.71976e6	1.55382	0.776911	+	0.629610i	$0.216785\pi$
$524$	2.47289e6	0.393438
$525$	−2298.18	−0.000363903 0
$526$	−1.76298e6	−0.277833
$527$	1.10170e6	0.172798
$528$	−88936.8	−0.0138834
$529$	−6.02972e6	−0.936824
$530$	−4.77098e6	−0.737765
$531$	3.43184e6	0.528190
$532$	−4817.55	−0.000737984 0
$533$	7.87585e6	1.20082
$534$	−8.55528e6	−1.29832
$535$	6.53644e6	0.987318
$536$	−1.97513e6	−0.296950
$537$	−1.98219e6	−0.296627
$538$	9.53926e6	1.42089
$539$	995167.	0.147545
$540$	2.41198e6	0.355950
$541$	8.28467e6	1.21698	0.608488	−	0.793563i	$-0.291776\pi$
$541$	8.28467e6	1.21698	0.608488	+	0.793563i	$0.291776\pi$
$542$	7.55369e6	1.10449
$543$	568483.	0.0827405
$544$	−1.20141e6	−0.174058
$545$	−7.30207e6	−1.05306
$546$	−16057.6	−0.00230515
$547$	−4.42737e6	−0.632671	−0.316336	−	0.948647i	$-0.602453\pi$
$547$	−4.42737e6	−0.632671	−0.316336	+	0.948647i	$0.602453\pi$
$548$	−7.86122e6	−1.11825
$549$	−4.57176e6	−0.647370
$550$	−730351.	−0.102950
$551$	−3.87751e6	−0.544094
$552$	−898847.	−0.125556
$553$	−8321.21	−0.00115711
$554$	−5.58473e6	−0.773086
$555$	6.46290e6	0.890625
$556$	−6.48092e6	−0.889098
$557$	−4.76534e6	−0.650812	−0.325406	−	0.945574i	$-0.605501\pi$
$557$	−4.76534e6	−0.650812	−0.325406	+	0.945574i	$0.605501\pi$
$558$	4.36652e6	0.593677
$559$	1.08380e7	1.46697
$560$	2088.84	0.000281471 0
$561$	98237.6	0.0131786
$562$	−813517.	−0.108649
$563$	1.00683e7	1.33871	0.669354	−	0.742944i	$-0.266571\pi$
$563$	1.00683e7	1.33871	0.669354	+	0.742944i	$0.266571\pi$
$564$	−1.15977e7	−1.53523
$565$	−2.77831e6	−0.366150
$566$	1.96703e7	2.58090
$567$	1225.18	0.000160045 0
$568$	9.14845e6	1.18981
$569$	5.75672e6	0.745409	0.372704	−	0.927950i	$-0.378431\pi$
$569$	5.75672e6	0.745409	0.372704	+	0.927950i	$0.378431\pi$
$570$	−2.84374e6	−0.366609
$571$	3.56589e6	0.457697	0.228848	−	0.973462i	$-0.426504\pi$
$571$	3.56589e6	0.457697	0.228848	+	0.973462i	$0.426504\pi$
$572$	−3.09603e6	−0.395654
$573$	5.49071e6	0.698622
$574$	12524.1	0.00158660
$575$	871983.	0.109986
$576$	−4.32911e6	−0.543679
$577$	260014.	0.0325130	0.0162565	−	0.999868i	$-0.494825\pi$
$577$	260014.	0.0325130	0.0162565	+	0.999868i	$0.494825\pi$
$578$	−1.25008e7	−1.55639
$579$	−2.16408e6	−0.268273
$580$	−2.45474e7	−3.02996
$581$	−10963.8	−0.00134748
$582$	−8.67566e6	−1.06168
$583$	−467260.	−0.0569360
$584$	−1.29157e7	−1.56706
$585$	−5.75071e6	−0.694755
$586$	−1.32628e7	−1.59548
$587$	205259.	0.0245870	0.0122935	−	0.999924i	$-0.496087\pi$
$587$	205259.	0.0245870	0.0122935	+	0.999924i	$0.496087\pi$
$588$	7.46682e6	0.890620
$589$	−3.12341e6	−0.370971
$590$	−2.56152e7	−3.02948
$591$	−9.37330e6	−1.10388
$592$	−1.78804e6	−0.209687
$593$	−1.57214e7	−1.83593	−0.917964	−	0.396664i	$-0.870168\pi$
$593$	−1.57214e7	−1.83593	−0.917964	+	0.396664i	$0.870168\pi$
$594$	389357.	0.0452775
$595$	−2307.28	−0.000267182 0
$596$	−2.55887e7	−2.95075
$597$	−2.02579e6	−0.232627
$598$	6.09265e6	0.696711
$599$	−8.13785e6	−0.926708	−0.463354	−	0.886173i	$-0.653354\pi$
$599$	−8.13785e6	−0.926708	−0.463354	+	0.886173i	$0.653354\pi$
$600$	−1.92752e6	−0.218586
$601$	6.68724e6	0.755198	0.377599	−	0.925969i	$-0.376750\pi$
$601$	6.68724e6	0.755198	0.377599	+	0.925969i	$0.376750\pi$
$602$	17234.6	0.00193825
$603$	−1.02149e6	−0.114404
$604$	1.65837e7	1.84965
$605$	1.05596e7	1.17289
$606$	4.95850e6	0.548490
$607$	658726.	0.0725660	0.0362830	−	0.999342i	$-0.488448\pi$
$607$	658726.	0.0725660	0.0362830	+	0.999342i	$0.488448\pi$
$608$	3.40607e6	0.373676
$609$	−12469.0	−0.00136235
$610$	3.41236e7	3.71304
$611$	2.76516e7	2.99652
$612$	737085.	0.0795498
$613$	−7.94130e6	−0.853572	−0.426786	−	0.904353i	$-0.640354\pi$
$613$	−7.94130e6	−0.853572	−0.426786	+	0.904353i	$0.640354\pi$
$614$	1.23724e7	1.32445
$615$	4.48525e6	0.478188
$616$	−1731.74	−0.000183879 0
$617$	3.35102e6	0.354376	0.177188	−	0.984177i	$-0.443300\pi$
$617$	3.35102e6	0.354376	0.177188	+	0.984177i	$0.443300\pi$
$618$	−861254.	−0.0907110
$619$	1.12186e7	1.17682	0.588410	−	0.808563i	$-0.299754\pi$
$619$	1.12186e7	1.17682	0.588410	+	0.808563i	$0.299754\pi$
$620$	−1.97734e7	−2.06587
$621$	−464862.	−0.0483722
$622$	−1.28247e7	−1.32914
$623$	19679.2	0.00203136
$624$	1.59100e6	0.163572
$625$	−1.21690e7	−1.24610
$626$	−1.48923e7	−1.51889
$627$	−278510.	−0.0282926
$628$	8.98517e6	0.909132
$629$	1.97502e6	0.199042
$630$	−9144.73	−0.000917951 0
$631$	5.59799e6	0.559705	0.279852	−	0.960043i	$-0.409714\pi$
$631$	5.59799e6	0.559705	0.279852	+	0.960043i	$0.409714\pi$
$632$	−6.97915e6	−0.695040
$633$	7.16926e6	0.711156
$634$	1.04246e7	1.03000
$635$	1.93421e6	0.190358
$636$	−3.50589e6	−0.343681
$637$	−1.78026e7	−1.73834
$638$	−3.96261e6	−0.385416
$639$	4.73136e6	0.458389
$640$	1.83341e7	1.76934
$641$	−1.64631e7	−1.58259	−0.791293	−	0.611437i	$-0.790592\pi$
$641$	−1.64631e7	−1.58259	−0.791293	+	0.611437i	$0.790592\pi$
$642$	7.91693e6	0.758087
$643$	−1.48931e6	−0.142055	−0.0710276	−	0.997474i	$-0.522628\pi$
$643$	−1.48931e6	−0.142055	−0.0710276	+	0.997474i	$0.522628\pi$
$644$	5878.02	0.000558491 0
$645$	6.17220e6	0.584172
$646$	−869030.	−0.0819320
$647$	−7.20206e6	−0.676388	−0.338194	−	0.941076i	$-0.609816\pi$
$647$	−7.20206e6	−0.676388	−0.338194	+	0.941076i	$0.609816\pi$
$648$	1.02758e6	0.0961344
$649$	−2.50870e6	−0.233796
$650$	1.30653e7	1.21293
$651$	−10044.1	−0.000928874 0
$652$	−2.00679e7	−1.84877
$653$	275765.	0.0253079	0.0126540	−	0.999920i	$-0.495972\pi$
$653$	275765.	0.0253079	0.0126540	+	0.999920i	$0.495972\pi$
$654$	−8.84426e6	−0.808569
$655$	−3.35770e6	−0.305801
$656$	−1.24090e6	−0.112584
$657$	−6.67971e6	−0.603732
$658$	43971.3	0.00395917
$659$	−1.14045e7	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$659$	−1.14045e7	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$660$	−1.76317e6	−0.157556
$661$	−2.11732e7	−1.88488	−0.942439	−	0.334377i	$-0.891474\pi$
$661$	−2.11732e7	−1.88488	−0.942439	+	0.334377i	$0.891474\pi$
$662$	−1.31733e7	−1.16829
$663$	−1.75738e6	−0.155268
$664$	−9.19558e6	−0.809392
$665$	6541.29	0.000573601 0
$666$	7.82786e6	0.683844
$667$	4.73105e6	0.411759
$668$	2.67116e7	2.31611
$669$	−1.02258e7	−0.883346
$670$	7.62440e6	0.656173
$671$	3.34199e6	0.286549
$672$	10953.0	0.000935645 0
$673$	−1.27484e7	−1.08497	−0.542486	−	0.840065i	$-0.682517\pi$
$673$	−1.27484e7	−1.08497	−0.542486	+	0.840065i	$0.682517\pi$
$674$	−2.50498e7	−2.12400
$675$	−996870.	−0.0842130
$676$	3.70569e7	3.11891
$677$	−2.05103e7	−1.71989	−0.859944	−	0.510389i	$-0.829502\pi$
$677$	−2.05103e7	−1.71989	−0.859944	+	0.510389i	$0.829502\pi$
$678$	−3.36508e6	−0.281139
$679$	19956.1	0.00166112
$680$	−1.93516e6	−0.160489
$681$	−2.99360e6	−0.247358
$682$	−3.19196e6	−0.262782
$683$	−1.65105e7	−1.35428	−0.677139	−	0.735855i	$-0.736780\pi$
$683$	−1.65105e7	−1.35428	−0.677139	+	0.735855i	$0.736780\pi$
$684$	−2.08969e6	−0.170782
$685$	1.06740e7	0.869163
$686$	−56619.2	−0.00459361
$687$	−380451.	−0.0307544
$688$	−1.70761e6	−0.137536
$689$	8.35886e6	0.670809
$690$	3.46973e6	0.277442
$691$	9.01291e6	0.718076	0.359038	−	0.933323i	$-0.383105\pi$
$691$	9.01291e6	0.718076	0.359038	+	0.933323i	$0.383105\pi$
$692$	2.02107e7	1.60441
$693$	−895.615	−7.08416e−5 0
$694$	−7.33988e6	−0.578482
$695$	8.79983e6	0.691054
$696$	−1.04580e7	−0.818326
$697$	1.37067e6	0.106868
$698$	1.13458e7	0.881448
$699$	−1.74730e6	−0.135261
$700$	12605.1	0.000972299 0
$701$	−1.46160e7	−1.12339	−0.561697	−	0.827343i	$-0.689851\pi$
$701$	−1.46160e7	−1.12339	−0.561697	+	0.827343i	$0.689851\pi$
$702$	−6.96525e6	−0.533450
$703$	−5.59932e6	−0.427314
$704$	3.16461e6	0.240651
$705$	1.57474e7	1.19326
$706$	−8.98699e6	−0.678583
$707$	−11405.7	−0.000858173 0
$708$	−1.88230e7	−1.41125
$709$	−3.18662e6	−0.238075	−0.119038	−	0.992890i	$-0.537981\pi$
$709$	−3.18662e6	−0.238075	−0.119038	+	0.992890i	$0.537981\pi$
$710$	−3.53148e7	−2.62912
$711$	−3.60945e6	−0.267773
$712$	1.65053e7	1.22018
$713$	3.81095e6	0.280743
$714$	−2794.57	−0.000205149 0
$715$	4.20381e6	0.307523
$716$	1.08720e7	0.792547
$717$	4.37580e6	0.317877
$718$	7.78554e6	0.563609
$719$	9.44430e6	0.681315	0.340657	−	0.940188i	$-0.389350\pi$
$719$	9.44430e6	0.681315	0.340657	+	0.940188i	$0.389350\pi$
$720$	906065.	0.0651370
$721$	1981.09	0.000141927 0
$722$	−1.98710e7	−1.41866
$723$	−1.82320e6	−0.129714
$724$	−3.11802e6	−0.221071
$725$	1.01455e7	0.716847
$726$	1.27897e7	0.900575
$727$	−2.44941e7	−1.71880	−0.859401	−	0.511302i	$-0.829163\pi$
$727$	−2.44941e7	−1.71880	−0.859401	+	0.511302i	$0.829163\pi$
$728$	30979.3	0.00216642
$729$	531441.	0.0370370
$730$	4.98573e7	3.46275
$731$	1.88619e6	0.130554
$732$	2.50752e7	1.72969
$733$	−9.68378e6	−0.665710	−0.332855	−	0.942978i	$-0.608012\pi$
$733$	−9.68378e6	−0.665710	−0.332855	+	0.942978i	$0.608012\pi$
$734$	3.51761e7	2.40995
$735$	−1.01385e7	−0.692237
$736$	−4.15584e6	−0.282790
$737$	746717.	0.0506393
$738$	5.43253e6	0.367165
$739$	−2.55371e7	−1.72013	−0.860064	−	0.510187i	$-0.829576\pi$
$739$	−2.55371e7	−1.72013	−0.860064	+	0.510187i	$0.829576\pi$
$740$	−3.54478e7	−2.37963
$741$	4.98229e6	0.333337
$742$	13292.2	0.000886312 0
$743$	1.57860e7	1.04906	0.524530	−	0.851392i	$-0.324241\pi$
$743$	1.57860e7	1.04906	0.524530	+	0.851392i	$0.324241\pi$
$744$	−8.42413e6	−0.557947
$745$	3.47444e7	2.29348
$746$	1.80997e7	1.19076
$747$	−4.75574e6	−0.311829
$748$	−538814.	−0.0352116
$749$	−18210.8	−0.00118611
$750$	−9.56327e6	−0.620802
$751$	−6.43744e6	−0.416498	−0.208249	−	0.978076i	$-0.566777\pi$
$751$	−6.43744e6	−0.416498	−0.208249	+	0.978076i	$0.566777\pi$
$752$	−4.35670e6	−0.280940
$753$	6.02274e6	0.387085
$754$	7.08875e7	4.54089
$755$	−2.25175e7	−1.43765
$756$	−6719.88	−0.000427619 0
$757$	2.51699e6	0.159640	0.0798200	−	0.996809i	$-0.474565\pi$
$757$	2.51699e6	0.159640	0.0798200	+	0.996809i	$0.474565\pi$
$758$	−1.41634e7	−0.895356
$759$	339818.	0.0214112
$760$	5.48630e6	0.344545
$761$	−5.65249e6	−0.353817	−0.176908	−	0.984227i	$-0.556610\pi$
$761$	−5.65249e6	−0.353817	−0.176908	+	0.984227i	$0.556610\pi$
$762$	2.34272e6	0.146161
$763$	20343.9	0.00126510
$764$	−3.01155e7	−1.86662
$765$	−1.00082e6	−0.0618303
$766$	4.52207e7	2.78462
$767$	4.48783e7	2.75453
$768$	6.81388e6	0.416861
$769$	−1.28871e7	−0.785847	−0.392924	−	0.919571i	$-0.628536\pi$
$769$	−1.28871e7	−0.785847	−0.392924	+	0.919571i	$0.628536\pi$
$770$	6684.86	0.000406317 0
$771$	4.64291e6	0.281290
$772$	1.18696e7	0.716789
$773$	2.61437e7	1.57368	0.786842	−	0.617154i	$-0.211714\pi$
$773$	2.61437e7	1.57368	0.786842	+	0.617154i	$0.211714\pi$
$774$	7.47575e6	0.448542
$775$	8.17236e6	0.488757
$776$	1.67376e7	0.997787
$777$	−18006.0	−0.00106995
$778$	1.26456e7	0.749014
$779$	−3.88593e6	−0.229431
$780$	3.15415e7	1.85629
$781$	−3.45866e6	−0.202899
$782$	1.06033e6	0.0620045
$783$	−5.40864e6	−0.315271
$784$	2.80493e6	0.162979
$785$	−1.22001e7	−0.706626
$786$	−4.06684e6	−0.234801
$787$	−2.81981e7	−1.62287	−0.811434	−	0.584443i	$-0.801313\pi$
$787$	−2.81981e7	−1.62287	−0.811434	+	0.584443i	$0.801313\pi$
$788$	5.14108e7	2.94943
$789$	1.75904e6	0.100597
$790$	2.69409e7	1.53583
$791$	7740.50	0.000439873 0
$792$	−751169.	−0.0425525
$793$	−5.97851e7	−3.37606
$794$	2.79327e7	1.57240
$795$	4.76032e6	0.267127
$796$	1.11111e7	0.621548
$797$	−1.94976e6	−0.108726	−0.0543632	−	0.998521i	$-0.517313\pi$
$797$	−1.94976e6	−0.108726	−0.0543632	+	0.998521i	$0.517313\pi$
$798$	7922.80	0.000440425 0
$799$	4.81231e6	0.266678
$800$	−8.91195e6	−0.492320
$801$	8.53616e6	0.470090
$802$	2.31585e6	0.127137
$803$	4.88291e6	0.267233
$804$	5.60269e6	0.305672
$805$	−7981.21	−0.000434089 0
$806$	5.71012e7	3.09605
$807$	−9.51794e6	−0.514469
$808$	−9.56620e6	−0.515479
$809$	−1.98855e7	−1.06823	−0.534116	−	0.845411i	$-0.679356\pi$
$809$	−1.98855e7	−1.06823	−0.534116	+	0.845411i	$0.679356\pi$
$810$	−3.96667e6	−0.212429
$811$	1.74446e7	0.931343	0.465672	−	0.884958i	$-0.345813\pi$
$811$	1.74446e7	0.931343	0.465672	+	0.884958i	$0.345813\pi$
$812$	68390.3	0.00364003
$813$	−7.53681e6	−0.399909
$814$	−5.72222e6	−0.302694
$815$	2.72483e7	1.43696
$816$	276888.	0.0145572
$817$	−5.34746e6	−0.280280
$818$	−4.65141e7	−2.43053
$819$	16021.7	0.000834642 0
$820$	−2.46008e7	−1.27766
$821$	9.63248e6	0.498747	0.249373	−	0.968407i	$-0.419775\pi$
$821$	9.63248e6	0.498747	0.249373	+	0.968407i	$0.419775\pi$
$822$	1.29283e7	0.667365
$823$	3.05877e7	1.57415	0.787076	−	0.616856i	$-0.211594\pi$
$823$	3.05877e7	1.57415	0.787076	+	0.616856i	$0.211594\pi$
$824$	1.66158e6	0.0852516
$825$	728719.	0.0372756
$826$	71365.1	0.00363945
$827$	−2.29189e7	−1.16528	−0.582639	−	0.812731i	$-0.697980\pi$
$827$	−2.29189e7	−1.16528	−0.582639	+	0.812731i	$0.697980\pi$
$828$	2.54968e6	0.129244
$829$	−6.82054e6	−0.344693	−0.172346	−	0.985036i	$-0.555135\pi$
$829$	−6.82054e6	−0.344693	−0.172346	+	0.985036i	$0.555135\pi$
$830$	3.54968e7	1.78852
$831$	5.57225e6	0.279916
$832$	−5.66120e7	−2.83531
$833$	−3.09826e6	−0.154705
$834$	1.06583e7	0.530609
$835$	−3.62692e7	−1.80020
$836$	1.52758e6	0.0755939
$837$	−4.35676e6	−0.214956
$838$	−1.98456e7	−0.976233
$839$	−2.58202e7	−1.26635	−0.633177	−	0.774007i	$-0.718250\pi$
$839$	−2.58202e7	−1.26635	−0.633177	+	0.774007i	$0.718250\pi$
$840$	17642.5	0.000862705 0
$841$	3.45343e7	1.68368
$842$	−1.01443e7	−0.493110
$843$	811699.	0.0393393
$844$	−3.93220e7	−1.90011
$845$	−5.03161e7	−2.42418
$846$	1.90732e7	0.916217
$847$	−29419.5	−0.00140905
$848$	−1.31700e6	−0.0628920
$849$	−1.96264e7	−0.934481
$850$	2.27381e6	0.107946
$851$	6.83188e6	0.323383
$852$	−2.59506e7	−1.22475
$853$	5.07448e6	0.238792	0.119396	−	0.992847i	$-0.461904\pi$
$853$	5.07448e6	0.238792	0.119396	+	0.992847i	$0.461904\pi$
$854$	−95069.8	−0.00446065
$855$	2.83739e6	0.132740
$856$	−1.52738e7	−0.712462
$857$	2.27591e7	1.05853	0.529265	−	0.848457i	$-0.322468\pi$
$857$	2.27591e7	1.05853	0.529265	+	0.848457i	$0.322468\pi$
$858$	5.09164e6	0.236124
$859$	2.78099e7	1.28593	0.642963	−	0.765897i	$-0.277705\pi$
$859$	2.78099e7	1.28593	0.642963	+	0.765897i	$0.277705\pi$
$860$	−3.38533e7	−1.56083
$861$	−12496.1	−0.000574470 0
$862$	4.73449e7	2.17023
$863$	−3.64508e7	−1.66602	−0.833010	−	0.553259i	$-0.813384\pi$
$863$	−3.64508e7	−1.66602	−0.833010	+	0.553259i	$0.813384\pi$
$864$	4.75105e6	0.216523
$865$	−2.74422e7	−1.24703
$866$	−1.87437e7	−0.849299
$867$	1.24729e7	0.563532
$868$	55089.7	0.00248183
$869$	2.63854e6	0.118526
$870$	4.03700e7	1.80826
$871$	−1.33581e7	−0.596622
$872$	1.70628e7	0.759906
$873$	8.65627e6	0.384410
$874$	−3.00610e6	−0.133114
$875$	21997.8	0.000971314 0
$876$	3.66369e7	1.61309
$877$	−1.62858e7	−0.715007	−0.357503	−	0.933912i	$-0.616372\pi$
$877$	−1.62858e7	−0.715007	−0.357503	+	0.933912i	$0.616372\pi$
$878$	−8.18397e6	−0.358284
$879$	1.32331e7	0.577684
$880$	−662340.	−0.0288320
$881$	−2.68491e7	−1.16544	−0.582719	−	0.812673i	$-0.698011\pi$
$881$	−2.68491e7	−1.16544	−0.582719	+	0.812673i	$0.698011\pi$
$882$	−1.22797e7	−0.531517
$883$	−3.91728e6	−0.169076	−0.0845381	−	0.996420i	$-0.526941\pi$
$883$	−3.91728e6	−0.169076	−0.0845381	+	0.996420i	$0.526941\pi$
$884$	9.63890e6	0.414855
$885$	2.55579e7	1.09690
$886$	−2.37173e7	−1.01503
$887$	−9.84265e6	−0.420052	−0.210026	−	0.977696i	$-0.567355\pi$
$887$	−9.84265e6	−0.420052	−0.210026	+	0.977696i	$0.567355\pi$
$888$	−1.51019e7	−0.642688
$889$	−5388.81	−0.000228685 0
$890$	−6.37138e7	−2.69624
$891$	−388487.	−0.0163939
$892$	5.60864e7	2.36018
$893$	−1.36432e7	−0.572517
$894$	4.20824e7	1.76099
$895$	−1.47620e7	−0.616009
$896$	−51079.8	−0.00212559
$897$	−6.07903e6	−0.252263
$898$	1.81432e7	0.750798
$899$	4.43402e7	1.82978
$900$	5.46764e6	0.225006
$901$	1.45472e6	0.0596992
$902$	−3.97122e6	−0.162520
$903$	−17196.0	−0.000701793 0
$904$	6.49210e6	0.264219
$905$	4.23367e6	0.171828
$906$	−2.72731e7	−1.10386
$907$	3.98049e7	1.60664	0.803320	−	0.595548i	$-0.203065\pi$
$907$	3.98049e7	1.60664	0.803320	+	0.595548i	$0.203065\pi$
$908$	1.64193e7	0.660908
$909$	−4.94741e6	−0.198595
$910$	−119586.	−0.00478715
$911$	−4.43869e7	−1.77198	−0.885990	−	0.463704i	$-0.846520\pi$
$911$	−4.43869e7	−1.77198	−0.885990	+	0.463704i	$0.846520\pi$
$912$	−784996.	−0.0312522
$913$	3.47648e6	0.138027
$914$	−1.85196e7	−0.733273
$915$	−3.40473e7	−1.34440
$916$	2.08670e6	0.0821717
$917$	9354.71	0.000367373 0
$918$	−1.21219e6	−0.0474749
$919$	−2.70034e7	−1.05470	−0.527351	−	0.849648i	$-0.676815\pi$
$919$	−2.70034e7	−1.05470	−0.527351	+	0.849648i	$0.676815\pi$
$920$	−6.69399e6	−0.260745
$921$	−1.23448e7	−0.479551
$922$	5.82795e7	2.25782
$923$	6.18723e7	2.39052
$924$	4912.28	0.000189279 0
$925$	1.46506e7	0.562989
$926$	−1.24609e6	−0.0477552
$927$	859329.	0.0328443
$928$	−4.83529e7	−1.84312
$929$	3.24253e7	1.23266	0.616331	−	0.787487i	$-0.288618\pi$
$929$	3.24253e7	1.23266	0.616331	+	0.787487i	$0.288618\pi$
$930$	3.25188e7	1.23290
$931$	8.78378e6	0.332129
$932$	9.58358e6	0.361400
$933$	1.27961e7	0.481251
$934$	−4.31863e7	−1.61987
$935$	731605.	0.0273683
$936$	1.34377e7	0.501345
$937$	−3.40448e7	−1.26678	−0.633392	−	0.773831i	$-0.718338\pi$
$937$	−3.40448e7	−1.26678	−0.633392	+	0.773831i	$0.718338\pi$
$938$	−21241.9	−0.000788292 0
$939$	1.48590e7	0.549954
$940$	−8.63715e7	−3.18824
$941$	2.41019e7	0.887315	0.443658	−	0.896196i	$-0.353681\pi$
$941$	2.41019e7	0.887315	0.443658	+	0.896196i	$0.353681\pi$
$942$	−1.47768e7	−0.542565
$943$	4.74133e6	0.173628
$944$	−7.07090e6	−0.258252
$945$	9124.29	0.000332368 0
$946$	−5.46483e6	−0.198540
$947$	3.34592e7	1.21239	0.606193	−	0.795317i	$-0.292696\pi$
$947$	3.34592e7	1.21239	0.606193	+	0.795317i	$0.292696\pi$
$948$	1.97972e7	0.715455
$949$	−8.73509e7	−3.14849
$950$	−6.44640e6	−0.231744
$951$	−1.04013e7	−0.372938
$952$	5391.44	0.000192802 0
$953$	2.78231e6	0.0992370	0.0496185	−	0.998768i	$-0.484199\pi$
$953$	2.78231e6	0.0992370	0.0496185	+	0.998768i	$0.484199\pi$
$954$	5.76569e6	0.205107
$955$	4.08910e7	1.45084
$956$	−2.40004e7	−0.849326
$957$	3.95375e6	0.139550
$958$	−1.71132e7	−0.602445
$959$	−29738.3	−0.00104417
$960$	−3.22402e7	−1.12907
$961$	7.08769e6	0.247569
$962$	1.02365e8	3.56627
$963$	−7.89923e6	−0.274485
$964$	9.99989e6	0.346579
$965$	−1.61166e7	−0.557127
$966$	−9666.82	−0.000333304 0
$967$	−6.60893e6	−0.227282	−0.113641	−	0.993522i	$-0.536251\pi$
$967$	−6.60893e6	−0.227282	−0.113641	+	0.993522i	$0.536251\pi$
$968$	−2.46746e7	−0.846374
$969$	867088.	0.0296656
$970$	−6.46103e7	−2.20482
$971$	7.75931e6	0.264104	0.132052	−	0.991243i	$-0.457843\pi$
$971$	7.75931e6	0.264104	0.132052	+	0.991243i	$0.457843\pi$
$972$	−2.91485e6	−0.0989580
$973$	−24516.7	−0.000830196 0
$974$	−7.96580e7	−2.69049
$975$	−1.30361e7	−0.439174
$976$	9.41957e6	0.316524
$977$	−4.39703e7	−1.47375	−0.736873	−	0.676031i	$-0.763698\pi$
$977$	−4.39703e7	−1.47375	−0.736873	+	0.676031i	$0.763698\pi$
$978$	3.30031e7	1.10333
$979$	−6.23999e6	−0.208079
$980$	5.56077e7	1.84957
$981$	8.82449e6	0.292764
$982$	6.30338e7	2.08591
$983$	2.87370e7	0.948545	0.474273	−	0.880378i	$-0.342711\pi$
$983$	2.87370e7	0.948545	0.474273	+	0.880378i	$0.342711\pi$
$984$	−1.04807e7	−0.345067
$985$	−6.98058e7	−2.29246
$986$	1.23368e7	0.404121
$987$	−43873.0	−0.00143352
$988$	−2.73269e7	−0.890633
$989$	6.52458e6	0.212110
$990$	2.89966e6	0.0940285
$991$	8.24841e6	0.266800	0.133400	−	0.991062i	$-0.457410\pi$
$991$	8.24841e6	0.266800	0.133400	+	0.991062i	$0.457410\pi$
$992$	−3.89492e7	−1.25666
$993$	1.31439e7	0.423009
$994$	98388.8	0.00315849
$995$	−1.50867e7	−0.483100
$996$	2.60843e7	0.833165
$997$	−1.70409e6	−0.0542945	−0.0271472	−	0.999631i	$-0.508642\pi$
$997$	−1.70409e6	−0.0542945	−0.0271472	+	0.999631i	$0.508642\pi$
$998$	1.26022e7	0.400517
$999$	−7.81036e6	−0.247604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.18	✓	20
3.2	odd	2		927.6.a.c.1.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.18	✓	20	1.1	even	1	trivial
927.6.a.c.1.3		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)

\(f(q)\)	\(=\)	\(q+9.02016 q^{2} -9.00000 q^{3} +49.3633 q^{4} -67.0257 q^{5} -81.1814 q^{6} +0.186737 q^{7} +156.620 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.02016 q^{2} -9.00000 q^{3} +49.3633 q^{4} -67.0257 q^{5} -81.1814 q^{6} +0.186737 q^{7} +156.620 q^{8} +81.0000 q^{9} -604.583 q^{10} -59.2116 q^{11} -444.270 q^{12} +1059.24 q^{13} +1.68440 q^{14} +603.232 q^{15} -166.891 q^{16} +184.344 q^{17} +730.633 q^{18} -522.627 q^{19} -3308.61 q^{20} -1.68063 q^{21} -534.098 q^{22} +637.671 q^{23} -1409.58 q^{24} +1367.45 q^{25} +9554.52 q^{26} -729.000 q^{27} +9.21795 q^{28} +7419.26 q^{29} +5441.25 q^{30} +5976.36 q^{31} -6517.21 q^{32} +532.904 q^{33} +1662.81 q^{34} -12.5162 q^{35} +3998.43 q^{36} +10713.8 q^{37} -4714.18 q^{38} -9533.17 q^{39} -10497.5 q^{40} +7435.37 q^{41} -15.1596 q^{42} +10231.9 q^{43} -2922.88 q^{44} -5429.08 q^{45} +5751.90 q^{46} +26105.1 q^{47} +1502.02 q^{48} -16807.0 q^{49} +12334.6 q^{50} -1659.09 q^{51} +52287.6 q^{52} +7891.36 q^{53} -6575.70 q^{54} +3968.70 q^{55} +29.2467 q^{56} +4703.65 q^{57} +66922.9 q^{58} +42368.4 q^{59} +29777.5 q^{60} -56441.5 q^{61} +53907.7 q^{62} +15.1257 q^{63} -53445.8 q^{64} -70996.4 q^{65} +4806.88 q^{66} -12611.0 q^{67} +9099.82 q^{68} -5739.04 q^{69} -112.898 q^{70} +58411.9 q^{71} +12686.2 q^{72} -82465.6 q^{73} +96640.2 q^{74} -12307.0 q^{75} -25798.6 q^{76} -11.0570 q^{77} -85990.7 q^{78} -44561.2 q^{79} +11186.0 q^{80} +6561.00 q^{81} +67068.3 q^{82} -58712.8 q^{83} -82.9615 q^{84} -12355.8 q^{85} +92293.3 q^{86} -66773.3 q^{87} -9273.69 q^{88} +105385. q^{89} -48971.2 q^{90} +197.799 q^{91} +31477.6 q^{92} -53787.2 q^{93} +235472. q^{94} +35029.5 q^{95} +58654.9 q^{96} +106868. q^{97} -151602. q^{98} -4796.14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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