LMFDB - Embedded newform 309.6.a.b.1.13

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			1.13
Root			$5.13523$ 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)

$f(q)$	$=$	$q+5.13523 q^{2} -9.00000 q^{3} -5.62942 q^{4} +59.3296 q^{5} -46.2171 q^{6} +179.902 q^{7} -193.236 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+5.13523 q^{2} -9.00000 q^{3} -5.62942 q^{4} +59.3296 q^{5} -46.2171 q^{6} +179.902 q^{7} -193.236 q^{8} +81.0000 q^{9} +304.671 q^{10} -138.657 q^{11} +50.6648 q^{12} +488.676 q^{13} +923.839 q^{14} -533.967 q^{15} -812.168 q^{16} +573.258 q^{17} +415.954 q^{18} -562.328 q^{19} -333.991 q^{20} -1619.12 q^{21} -712.037 q^{22} +124.752 q^{23} +1739.12 q^{24} +395.003 q^{25} +2509.46 q^{26} -729.000 q^{27} -1012.74 q^{28} +2787.64 q^{29} -2742.04 q^{30} +3526.61 q^{31} +2012.87 q^{32} +1247.92 q^{33} +2943.81 q^{34} +10673.5 q^{35} -455.983 q^{36} -6774.31 q^{37} -2887.69 q^{38} -4398.08 q^{39} -11464.6 q^{40} +3871.24 q^{41} -8314.55 q^{42} +7002.56 q^{43} +780.560 q^{44} +4805.70 q^{45} +640.629 q^{46} +17572.4 q^{47} +7309.51 q^{48} +15557.8 q^{49} +2028.43 q^{50} -5159.32 q^{51} -2750.96 q^{52} +8408.66 q^{53} -3743.58 q^{54} -8226.49 q^{55} -34763.5 q^{56} +5060.96 q^{57} +14315.2 q^{58} +3218.20 q^{59} +3005.92 q^{60} +33075.0 q^{61} +18110.0 q^{62} +14572.1 q^{63} +36325.9 q^{64} +28992.9 q^{65} +6408.34 q^{66} +41443.9 q^{67} -3227.11 q^{68} -1122.77 q^{69} +54811.0 q^{70} +5494.37 q^{71} -15652.1 q^{72} +20168.3 q^{73} -34787.7 q^{74} -3555.03 q^{75} +3165.58 q^{76} -24944.8 q^{77} -22585.2 q^{78} +74307.1 q^{79} -48185.6 q^{80} +6561.00 q^{81} +19879.7 q^{82} +38574.8 q^{83} +9114.70 q^{84} +34011.2 q^{85} +35959.7 q^{86} -25088.7 q^{87} +26793.5 q^{88} +34248.1 q^{89} +24678.4 q^{90} +87913.8 q^{91} -702.280 q^{92} -31739.5 q^{93} +90238.4 q^{94} -33362.7 q^{95} -18115.8 q^{96} -92755.4 q^{97} +79893.0 q^{98} -11231.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.13523	0.907789	0.453894	−	0.891055i	$-0.350034\pi$
$2$	5.13523	0.907789	0.453894	+	0.891055i	$0.350034\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−5.62942	−0.175919
$5$	59.3296	1.06132	0.530660	−	0.847585i	$-0.321944\pi$
$5$	59.3296	1.06132	0.530660	+	0.847585i	$0.321944\pi$
$6$	−46.2171	−0.524112
$7$	179.902	1.38769	0.693843	−	0.720126i	$-0.255916\pi$
$7$	179.902	1.38769	0.693843	+	0.720126i	$0.255916\pi$
$8$	−193.236	−1.06749
$9$	81.0000	0.333333
$10$	304.671	0.963455
$11$	−138.657	−0.345510	−0.172755	−	0.984965i	$-0.555267\pi$
$11$	−138.657	−0.345510	−0.172755	+	0.984965i	$0.555267\pi$
$12$	50.6648	0.101567
$13$	488.676	0.801978	0.400989	−	0.916083i	$-0.368667\pi$
$13$	488.676	0.801978	0.400989	+	0.916083i	$0.368667\pi$
$14$	923.839	1.25973
$15$	−533.967	−0.612754
$16$	−812.168	−0.793133
$17$	573.258	0.481091	0.240546	−	0.970638i	$-0.422674\pi$
$17$	573.258	0.481091	0.240546	+	0.970638i	$0.422674\pi$
$18$	415.954	0.302596
$19$	−562.328	−0.357360	−0.178680	−	0.983907i	$-0.557183\pi$
$19$	−562.328	−0.357360	−0.178680	+	0.983907i	$0.557183\pi$
$20$	−333.991	−0.186707
$21$	−1619.12	−0.801181
$22$	−712.037	−0.313651
$23$	124.752	0.0491730	0.0245865	−	0.999698i	$-0.492173\pi$
$23$	124.752	0.0491730	0.0245865	+	0.999698i	$0.492173\pi$
$24$	1739.12	0.616314
$25$	395.003	0.126401
$26$	2509.46	0.728026
$27$	−729.000	−0.192450
$28$	−1012.74	−0.244121
$29$	2787.64	0.615519	0.307759	−	0.951464i	$-0.400421\pi$
$29$	2787.64	0.615519	0.307759	+	0.951464i	$0.400421\pi$
$30$	−2742.04	−0.556251
$31$	3526.61	0.659103	0.329552	−	0.944138i	$-0.393102\pi$
$31$	3526.61	0.659103	0.329552	+	0.944138i	$0.393102\pi$
$32$	2012.87	0.347489
$33$	1247.92	0.199481
$34$	2943.81	0.436729
$35$	10673.5	1.47278
$36$	−455.983	−0.0586398
$37$	−6774.31	−0.813507	−0.406753	−	0.913538i	$-0.633339\pi$
$37$	−6774.31	−0.813507	−0.406753	+	0.913538i	$0.633339\pi$
$38$	−2887.69	−0.324408
$39$	−4398.08	−0.463022
$40$	−11464.6	−1.13295
$41$	3871.24	0.359659	0.179829	−	0.983698i	$-0.442445\pi$
$41$	3871.24	0.359659	0.179829	+	0.983698i	$0.442445\pi$
$42$	−8314.55	−0.727304
$43$	7002.56	0.577545	0.288772	−	0.957398i	$-0.406753\pi$
$43$	7002.56	0.577545	0.288772	+	0.957398i	$0.406753\pi$
$44$	780.560	0.0607820
$45$	4805.70	0.353773
$46$	640.629	0.0446387
$47$	17572.4	1.16034	0.580172	−	0.814494i	$-0.302985\pi$
$47$	17572.4	1.16034	0.580172	+	0.814494i	$0.302985\pi$
$48$	7309.51	0.457916
$49$	15557.8	0.925675
$50$	2028.43	0.114745
$51$	−5159.32	−0.277758
$52$	−2750.96	−0.141083
$53$	8408.66	0.411185	0.205592	−	0.978638i	$-0.434088\pi$
$53$	8408.66	0.411185	0.205592	+	0.978638i	$0.434088\pi$
$54$	−3743.58	−0.174704
$55$	−8226.49	−0.366697
$56$	−34763.5	−1.48134
$57$	5060.96	0.206322
$58$	14315.2	0.558761
$59$	3218.20	0.120360	0.0601801	−	0.998188i	$-0.480833\pi$
$59$	3218.20	0.120360	0.0601801	+	0.998188i	$0.480833\pi$
$60$	3005.92	0.107795
$61$	33075.0	1.13809	0.569043	−	0.822308i	$-0.307314\pi$
$61$	33075.0	1.13809	0.569043	+	0.822308i	$0.307314\pi$
$62$	18110.0	0.598326
$63$	14572.1	0.462562
$64$	36325.9	1.10858
$65$	28992.9	0.851155
$66$	6408.34	0.181086
$67$	41443.9	1.12791	0.563954	−	0.825807i	$-0.309280\pi$
$67$	41443.9	1.12791	0.563954	+	0.825807i	$0.309280\pi$
$68$	−3227.11	−0.0846332
$69$	−1122.77	−0.0283901
$70$	54811.0	1.33697
$71$	5494.37	0.129352	0.0646758	−	0.997906i	$-0.479399\pi$
$71$	5494.37	0.129352	0.0646758	+	0.997906i	$0.479399\pi$
$72$	−15652.1	−0.355829
$73$	20168.3	0.442958	0.221479	−	0.975165i	$-0.428912\pi$
$73$	20168.3	0.442958	0.221479	+	0.975165i	$0.428912\pi$
$74$	−34787.7	−0.738492
$75$	−3555.03	−0.0729777
$76$	3165.58	0.0628665
$77$	−24944.8	−0.479460
$78$	−22585.2	−0.420326
$79$	74307.1	1.33956	0.669781	−	0.742559i	$-0.266388\pi$
$79$	74307.1	1.33956	0.669781	+	0.742559i	$0.266388\pi$
$80$	−48185.6	−0.841768
$81$	6561.00	0.111111
$82$	19879.7	0.326494
$83$	38574.8	0.614623	0.307311	−	0.951609i	$-0.400571\pi$
$83$	38574.8	0.614623	0.307311	+	0.951609i	$0.400571\pi$
$84$	9114.70	0.140943
$85$	34011.2	0.510592
$86$	35959.7	0.524289
$87$	−25088.7	−0.355370
$88$	26793.5	0.368828
$89$	34248.1	0.458312	0.229156	−	0.973390i	$-0.426403\pi$
$89$	34248.1	0.458312	0.229156	+	0.973390i	$0.426403\pi$
$90$	24678.4	0.321152
$91$	87913.8	1.11289
$92$	−702.280	−0.00865049
$93$	−31739.5	−0.380533
$94$	90238.4	1.05335
$95$	−33362.7	−0.379274
$96$	−18115.8	−0.200623
$97$	−92755.4	−1.00094	−0.500472	−	0.865753i	$-0.666840\pi$
$97$	−92755.4	−1.00094	−0.500472	+	0.865753i	$0.666840\pi$
$98$	79893.0	0.840317
$99$	−11231.2	−0.115170
$100$	−2223.64	−0.0222364
$101$	−63029.4	−0.614808	−0.307404	−	0.951579i	$-0.599460\pi$
$101$	−63029.4	−0.614808	−0.307404	+	0.951579i	$0.599460\pi$
$102$	−26494.3	−0.252146
$103$	10609.0	0.0985329
$103$	10609.0	0.0985329
$104$	−94429.6	−0.856100
$105$	−96061.8	−0.850310
$106$	43180.4	0.373269
$107$	66384.6	0.560542	0.280271	−	0.959921i	$-0.409576\pi$
$107$	66384.6	0.560542	0.280271	+	0.959921i	$0.409576\pi$
$108$	4103.85	0.0338557
$109$	11247.8	0.0906779	0.0453390	−	0.998972i	$-0.485563\pi$
$109$	11247.8	0.0906779	0.0453390	+	0.998972i	$0.485563\pi$
$110$	−42244.9	−0.332884
$111$	60968.8	0.469678
$112$	−146111.	−1.10062
$113$	−30612.8	−0.225532	−0.112766	−	0.993622i	$-0.535971\pi$
$113$	−30612.8	−0.225532	−0.112766	+	0.993622i	$0.535971\pi$
$114$	25989.2	0.187297
$115$	7401.47	0.0521883
$116$	−15692.8	−0.108282
$117$	39582.7	0.267326
$118$	16526.2	0.109262
$119$	103130.	0.667604
$120$	103181.	0.654106
$121$	−141825.	−0.880623
$122$	169848.	1.03314
$123$	−34841.2	−0.207649
$124$	−19852.8	−0.115949
$125$	−161970.	−0.927168
$126$	74831.0	0.419909
$127$	−126546.	−0.696209	−0.348104	−	0.937456i	$-0.613174\pi$
$127$	−126546.	−0.696209	−0.348104	+	0.937456i	$0.613174\pi$
$128$	122130.	0.658867
$129$	−63023.0	−0.333445
$130$	148885.	0.772669
$131$	−72525.7	−0.369244	−0.184622	−	0.982810i	$-0.559106\pi$
$131$	−72525.7	−0.369244	−0.184622	+	0.982810i	$0.559106\pi$
$132$	−7025.04	−0.0350925
$133$	−101164.	−0.495904
$134$	212824.	1.02390
$135$	−43251.3	−0.204251
$136$	−110774.	−0.513558
$137$	−46395.8	−0.211192	−0.105596	−	0.994409i	$-0.533675\pi$
$137$	−46395.8	−0.211192	−0.105596	+	0.994409i	$0.533675\pi$
$138$	−5765.66	−0.0257722
$139$	−205573.	−0.902461	−0.451230	−	0.892408i	$-0.649015\pi$
$139$	−205573.	−0.902461	−0.451230	+	0.892408i	$0.649015\pi$
$140$	−60085.8	−0.259091
$141$	−158152.	−0.669925
$142$	28214.8	0.117424
$143$	−67758.5	−0.277092
$144$	−65785.6	−0.264378
$145$	165389.	0.653263
$146$	103569.	0.402112
$147$	−140020.	−0.534439
$148$	38135.4	0.143112
$149$	−85245.0	−0.314560	−0.157280	−	0.987554i	$-0.550273\pi$
$149$	−85245.0	−0.314560	−0.157280	+	0.987554i	$0.550273\pi$
$150$	−18255.9	−0.0662483
$151$	−194308.	−0.693503	−0.346752	−	0.937957i	$-0.612715\pi$
$151$	−194308.	−0.693503	−0.346752	+	0.937957i	$0.612715\pi$
$152$	108662.	0.381477
$153$	46433.9	0.160364
$154$	−128097.	−0.435249
$155$	209232.	0.699520
$156$	24758.6	0.0814545
$157$	−314171.	−1.01722	−0.508612	−	0.860996i	$-0.669841\pi$
$157$	−314171.	−1.01722	−0.508612	+	0.860996i	$0.669841\pi$
$158$	381584.	1.21604
$159$	−75677.9	−0.237398
$160$	119423.	0.368797
$161$	22443.1	0.0682368
$162$	33692.2	0.100865
$163$	619768.	1.82709	0.913545	−	0.406737i	$-0.133334\pi$
$163$	619768.	1.82709	0.913545	+	0.406737i	$0.133334\pi$
$164$	−21792.8	−0.0632709
$165$	74038.4	0.211713
$166$	198091.	0.557948
$167$	−573006.	−1.58989	−0.794947	−	0.606679i	$-0.792501\pi$
$167$	−573006.	−1.58989	−0.794947	+	0.606679i	$0.792501\pi$
$168$	312872.	0.855250
$169$	−132489.	−0.356832
$170$	174655.	0.463510
$171$	−45548.6	−0.119120
$172$	−39420.3	−0.101601
$173$	510059.	1.29570	0.647852	−	0.761767i	$-0.275668\pi$
$173$	510059.	1.29570	0.647852	+	0.761767i	$0.275668\pi$
$174$	−128836.	−0.322601
$175$	71062.0	0.175405
$176$	112613.	0.274036
$177$	−28963.8	−0.0694900
$178$	175872.	0.416051
$179$	−142744.	−0.332985	−0.166492	−	0.986043i	$-0.553244\pi$
$179$	−142744.	−0.332985	−0.166492	+	0.986043i	$0.553244\pi$
$180$	−27053.3	−0.0622356
$181$	−217911.	−0.494405	−0.247203	−	0.968964i	$-0.579511\pi$
$181$	−217911.	−0.494405	−0.247203	+	0.968964i	$0.579511\pi$
$182$	451458.	1.01027
$183$	−297675.	−0.657074
$184$	−24106.5	−0.0524915
$185$	−401917.	−0.863391
$186$	−162990.	−0.345444
$187$	−79486.4	−0.166222
$188$	−98922.5	−0.204127
$189$	−131149.	−0.267060
$190$	−171325.	−0.344300
$191$	361385.	0.716781	0.358390	−	0.933572i	$-0.383326\pi$
$191$	361385.	0.716781	0.358390	+	0.933572i	$0.383326\pi$
$192$	−326933.	−0.640039
$193$	916181.	1.77047	0.885234	−	0.465147i	$-0.153998\pi$
$193$	916181.	1.77047	0.885234	+	0.465147i	$0.153998\pi$
$194$	−476320.	−0.908646
$195$	−260936.	−0.491415
$196$	−87581.4	−0.162844
$197$	443302.	0.813831	0.406915	−	0.913466i	$-0.366604\pi$
$197$	443302.	0.813831	0.406915	+	0.913466i	$0.366604\pi$
$198$	−57675.0	−0.104550
$199$	184113.	0.329573	0.164787	−	0.986329i	$-0.447306\pi$
$199$	184113.	0.329573	0.164787	+	0.986329i	$0.447306\pi$
$200$	−76328.7	−0.134931
$201$	−372995.	−0.651197
$202$	−323670.	−0.558116
$203$	501502.	0.854147
$204$	29044.0	0.0488630
$205$	229679.	0.381713
$206$	54479.6	0.0894471
$207$	10104.9	0.0163910
$208$	−396887.	−0.636075
$209$	77971.0	0.123472
$210$	−493299.	−0.771902
$211$	−1.14118e6	−1.76461	−0.882303	−	0.470681i	$-0.844008\pi$
$211$	−1.14118e6	−1.76461	−0.882303	+	0.470681i	$0.844008\pi$
$212$	−47335.9	−0.0723354
$213$	−49449.3	−0.0746812
$214$	340900.	0.508853
$215$	415459.	0.612960
$216$	140869.	0.205438
$217$	634445.	0.914629
$218$	57760.1	0.0823164
$219$	−181515.	−0.255742
$220$	46310.3	0.0645091
$221$	280137.	0.385824
$222$	313089.	0.426369
$223$	−54437.1	−0.0733048	−0.0366524	−	0.999328i	$-0.511669\pi$
$223$	−54437.1	−0.0733048	−0.0366524	+	0.999328i	$0.511669\pi$
$224$	362120.	0.482206
$225$	31995.3	0.0421337
$226$	−157204.	−0.204735
$227$	602381.	0.775902	0.387951	−	0.921680i	$-0.373183\pi$
$227$	602381.	0.775902	0.387951	+	0.921680i	$0.373183\pi$
$228$	−28490.2	−0.0362960
$229$	−65029.1	−0.0819444	−0.0409722	−	0.999160i	$-0.513046\pi$
$229$	−65029.1	−0.0819444	−0.0409722	+	0.999160i	$0.513046\pi$
$230$	38008.3	0.0473760
$231$	224503.	0.276817
$232$	−538671.	−0.657058
$233$	−584841.	−0.705745	−0.352872	−	0.935671i	$-0.614795\pi$
$233$	−584841.	−0.705745	−0.352872	+	0.935671i	$0.614795\pi$
$234$	203266.	0.242675
$235$	1.04256e6	1.23150
$236$	−18116.6	−0.0211737
$237$	−668764.	−0.773396
$238$	529598.	0.606044
$239$	−171355.	−0.194045	−0.0970227	−	0.995282i	$-0.530932\pi$
$239$	−171355.	−0.194045	−0.0970227	+	0.995282i	$0.530932\pi$
$240$	433671.	0.485995
$241$	287295.	0.318629	0.159315	−	0.987228i	$-0.449072\pi$
$241$	287295.	0.318629	0.159315	+	0.987228i	$0.449072\pi$
$242$	−728305.	−0.799419
$243$	−59049.0	−0.0641500
$244$	−186193.	−0.200211
$245$	923039.	0.982438
$246$	−178917.	−0.188502
$247$	−274796.	−0.286595
$248$	−681467.	−0.703584
$249$	−347173.	−0.354853
$250$	−831751.	−0.841673
$251$	49964.4	0.0500583	0.0250291	−	0.999687i	$-0.492032\pi$
$251$	49964.4	0.0500583	0.0250291	+	0.999687i	$0.492032\pi$
$252$	−82032.3	−0.0813736
$253$	−17297.7	−0.0169898
$254$	−649843.	−0.632010
$255$	−306100.	−0.294790
$256$	−535264.	−0.510467
$257$	−1.86314e6	−1.75959	−0.879796	−	0.475352i	$-0.842321\pi$
$257$	−1.86314e6	−1.75959	−0.879796	+	0.475352i	$0.842321\pi$
$258$	−323638.	−0.302698
$259$	−1.21871e6	−1.12889
$260$	−163213.	−0.149735
$261$	225799.	0.205173
$262$	−372436.	−0.335196
$263$	123175.	0.109808	0.0549039	−	0.998492i	$-0.482515\pi$
$263$	123175.	0.109808	0.0549039	+	0.998492i	$0.482515\pi$
$264$	−241142.	−0.212943
$265$	498883.	0.436399
$266$	−519501.	−0.450176
$267$	−308233.	−0.264607
$268$	−233305.	−0.198421
$269$	−1.50910e6	−1.27157	−0.635783	−	0.771868i	$-0.719323\pi$
$269$	−1.50910e6	−1.27157	−0.635783	+	0.771868i	$0.719323\pi$
$270$	−222105.	−0.185417
$271$	−327004.	−0.270477	−0.135238	−	0.990813i	$-0.543180\pi$
$271$	−327004.	−0.270477	−0.135238	+	0.990813i	$0.543180\pi$
$272$	−465582.	−0.381569
$273$	−791224.	−0.642530
$274$	−238253.	−0.191718
$275$	−54770.1	−0.0436729
$276$	6320.52	0.00499436
$277$	−827108.	−0.647684	−0.323842	−	0.946111i	$-0.604975\pi$
$277$	−827108.	−0.647684	−0.323842	+	0.946111i	$0.604975\pi$
$278$	−1.05566e6	−0.819244
$279$	285656.	0.219701
$280$	−2.06251e6	−1.57217
$281$	1.35248e6	1.02180	0.510899	−	0.859641i	$-0.329313\pi$
$281$	1.35248e6	1.02180	0.510899	+	0.859641i	$0.329313\pi$
$282$	−812146.	−0.608151
$283$	526277.	0.390614	0.195307	−	0.980742i	$-0.437430\pi$
$283$	526277.	0.390614	0.195307	+	0.980742i	$0.437430\pi$
$284$	−30930.1	−0.0227554
$285$	300265.	0.218974
$286$	−347955.	−0.251541
$287$	696445.	0.499094
$288$	163043.	0.115830
$289$	−1.09123e6	−0.768551
$290$	849313.	0.593025
$291$	834798.	0.577895
$292$	−113536.	−0.0779248
$293$	788988.	0.536910	0.268455	−	0.963292i	$-0.413487\pi$
$293$	788988.	0.536910	0.268455	+	0.963292i	$0.413487\pi$
$294$	−719037.	−0.485157
$295$	190934.	0.127741
$296$	1.30904e6	0.868407
$297$	101081.	0.0664935
$298$	−437753.	−0.285554
$299$	60963.1	0.0394357
$300$	20012.7	0.0128382
$301$	1.25978e6	0.801451
$302$	−997817.	−0.629555
$303$	567265.	0.354960
$304$	456705.	0.283434
$305$	1.96232e6	1.20787
$306$	238449.	0.145576
$307$	−1.02878e6	−0.622985	−0.311492	−	0.950249i	$-0.600829\pi$
$307$	−1.02878e6	−0.622985	−0.311492	+	0.950249i	$0.600829\pi$
$308$	140425.	0.0843463
$309$	−95481.0	−0.0568880
$310$	1.07446e6	0.635016
$311$	−808322.	−0.473897	−0.236948	−	0.971522i	$-0.576147\pi$
$311$	−808322.	−0.473897	−0.236948	+	0.971522i	$0.576147\pi$
$312$	849866.	0.494270
$313$	73070.3	0.0421580	0.0210790	−	0.999778i	$-0.493290\pi$
$313$	73070.3	0.0421580	0.0210790	+	0.999778i	$0.493290\pi$
$314$	−1.61334e6	−0.923425
$315$	864556.	0.490927
$316$	−418306.	−0.235655
$317$	2.17223e6	1.21411	0.607056	−	0.794659i	$-0.292351\pi$
$317$	2.17223e6	1.21411	0.607056	+	0.794659i	$0.292351\pi$
$318$	−388624.	−0.215507
$319$	−386526.	−0.212668
$320$	2.15520e6	1.17656
$321$	−597461.	−0.323629
$322$	115251.	0.0619446
$323$	−322359.	−0.171923
$324$	−36934.6	−0.0195466
$325$	193028.	0.101371
$326$	3.18265e6	1.65861
$327$	−101230.	−0.0523529
$328$	−748062.	−0.383931
$329$	3.16132e6	1.61019
$330$	380204.	0.192191
$331$	478984.	0.240298	0.120149	−	0.992756i	$-0.461663\pi$
$331$	478984.	0.240298	0.120149	+	0.992756i	$0.461663\pi$
$332$	−217154.	−0.108124
$333$	−548719.	−0.271169
$334$	−2.94252e6	−1.44329
$335$	2.45885e6	1.19707
$336$	1.31500e6	0.635443
$337$	−1.37495e6	−0.659494	−0.329747	−	0.944069i	$-0.606964\pi$
$337$	−1.37495e6	−0.659494	−0.329747	+	0.944069i	$0.606964\pi$
$338$	−680362.	−0.323928
$339$	275516.	0.130211
$340$	−191463.	−0.0898230
$341$	−488991.	−0.227727
$342$	−233903.	−0.108136
$343$	−224731.	−0.103140
$344$	−1.35314e6	−0.616521
$345$	−66613.2	−0.0301310
$346$	2.61927e6	1.17623
$347$	654413.	0.291762	0.145881	−	0.989302i	$-0.453398\pi$
$347$	654413.	0.291762	0.145881	+	0.989302i	$0.453398\pi$
$348$	141235.	0.0625164
$349$	−2.49845e6	−1.09801	−0.549006	−	0.835819i	$-0.684994\pi$
$349$	−2.49845e6	−1.09801	−0.549006	+	0.835819i	$0.684994\pi$
$350$	364920.	0.159231
$351$	−356244.	−0.154341
$352$	−279099.	−0.120061
$353$	861840.	0.368120	0.184060	−	0.982915i	$-0.441076\pi$
$353$	861840.	0.368120	0.184060	+	0.982915i	$0.441076\pi$
$354$	−148736.	−0.0630822
$355$	325979.	0.137284
$356$	−192797.	−0.0806260
$357$	−928173.	−0.385441
$358$	−733021.	−0.302280
$359$	102442.	0.0419511	0.0209755	−	0.999780i	$-0.493323\pi$
$359$	102442.	0.0419511	0.0209755	+	0.999780i	$0.493323\pi$
$360$	−928633.	−0.377648
$361$	−2.15989e6	−0.872294
$362$	−1.11902e6	−0.448815
$363$	1.27643e6	0.508428
$364$	−494904.	−0.195779
$365$	1.19658e6	0.470120
$366$	−1.52863e6	−0.596484
$367$	−2.82164e6	−1.09354	−0.546772	−	0.837282i	$-0.684144\pi$
$367$	−2.82164e6	−1.09354	−0.546772	+	0.837282i	$0.684144\pi$
$368$	−101319.	−0.0390008
$369$	313571.	0.119886
$370$	−2.06394e6	−0.783777
$371$	1.51274e6	0.570596
$372$	178675.	0.0669432
$373$	−41297.0	−0.0153690	−0.00768452	−	0.999970i	$-0.502446\pi$
$373$	−41297.0	−0.0153690	−0.00768452	+	0.999970i	$0.502446\pi$
$374$	−408181.	−0.150895
$375$	1.45773e6	0.535301
$376$	−3.39562e6	−1.23865
$377$	1.36225e6	0.493632
$378$	−673479.	−0.242435
$379$	−3.38483e6	−1.21043	−0.605214	−	0.796063i	$-0.706912\pi$
$379$	−3.38483e6	−1.21043	−0.605214	+	0.796063i	$0.706912\pi$
$380$	187813.	0.0667215
$381$	1.13891e6	0.401956
$382$	1.85579e6	0.650686
$383$	2.57245e6	0.896085	0.448043	−	0.894012i	$-0.352121\pi$
$383$	2.57245e6	0.896085	0.448043	+	0.894012i	$0.352121\pi$
$384$	−1.09917e6	−0.380397
$385$	−1.47996e6	−0.508861
$386$	4.70480e6	1.60721
$387$	567207.	0.192515
$388$	522159.	0.176085
$389$	338599.	0.113452	0.0567260	−	0.998390i	$-0.481934\pi$
$389$	338599.	0.113452	0.0567260	+	0.998390i	$0.481934\pi$
$390$	−1.33997e6	−0.446101
$391$	71514.9	0.0236567
$392$	−3.00633e6	−0.988145
$393$	652732.	0.213183
$394$	2.27646e6	0.738787
$395$	4.40861e6	1.42170
$396$	63225.4	0.0202607
$397$	2.15097e6	0.684948	0.342474	−	0.939527i	$-0.388735\pi$
$397$	2.15097e6	0.684948	0.342474	+	0.939527i	$0.388735\pi$
$398$	945463.	0.299183
$399$	910477.	0.286310
$400$	−320809.	−0.100253
$401$	488506.	0.151708	0.0758541	−	0.997119i	$-0.475832\pi$
$401$	488506.	0.151708	0.0758541	+	0.997119i	$0.475832\pi$
$402$	−1.91541e6	−0.591150
$403$	1.72337e6	0.528586
$404$	354819.	0.108157
$405$	389262.	0.117924
$406$	2.57533e6	0.775385
$407$	939308.	0.281075
$408$	996964.	0.296503
$409$	−4.94635e6	−1.46210	−0.731050	−	0.682324i	$-0.760969\pi$
$409$	−4.94635e6	−1.46210	−0.731050	+	0.682324i	$0.760969\pi$
$410$	1.17946e6	0.346515
$411$	417562.	0.121932
$412$	−59722.5	−0.0173338
$413$	578961.	0.167022
$414$	51890.9	0.0148796
$415$	2.28863e6	0.652312
$416$	983641.	0.278678
$417$	1.85015e6	0.521036
$418$	400399.	0.112086
$419$	4.83045e6	1.34416	0.672082	−	0.740477i	$-0.265400\pi$
$419$	4.83045e6	1.34416	0.672082	+	0.740477i	$0.265400\pi$
$420$	540772.	0.149586
$421$	3.86927e6	1.06396	0.531979	−	0.846758i	$-0.321449\pi$
$421$	3.86927e6	1.06396	0.531979	+	0.846758i	$0.321449\pi$
$422$	−5.86022e6	−1.60189
$423$	1.42337e6	0.386781
$424$	−1.62485e6	−0.438934
$425$	226439.	0.0608104
$426$	−253934.	−0.0677948
$427$	5.95026e6	1.57931
$428$	−373707.	−0.0986101
$429$	609826.	0.159979
$430$	2.13348e6	0.556438
$431$	6.07881e6	1.57625	0.788125	−	0.615515i	$-0.211052\pi$
$431$	6.07881e6	1.57625	0.788125	+	0.615515i	$0.211052\pi$
$432$	592071.	0.152639
$433$	−1.79582e6	−0.460301	−0.230151	−	0.973155i	$-0.573922\pi$
$433$	−1.79582e6	−0.460301	−0.230151	+	0.973155i	$0.573922\pi$
$434$	3.25802e6	0.830290
$435$	−1.48851e6	−0.377161
$436$	−63318.6	−0.0159520
$437$	−70151.4	−0.0175725
$438$	−932120.	−0.232160
$439$	−1.60523e6	−0.397536	−0.198768	−	0.980047i	$-0.563694\pi$
$439$	−1.60523e6	−0.397536	−0.198768	+	0.980047i	$0.563694\pi$
$440$	1.58965e6	0.391444
$441$	1.26018e6	0.308558
$442$	1.43857e6	0.350247
$443$	3.72310e6	0.901355	0.450678	−	0.892687i	$-0.351182\pi$
$443$	3.72310e6	0.901355	0.450678	+	0.892687i	$0.351182\pi$
$444$	−343219.	−0.0826255
$445$	2.03193e6	0.486416
$446$	−279547.	−0.0665453
$447$	767205.	0.181611
$448$	6.53512e6	1.53836
$449$	−5.42638e6	−1.27027	−0.635133	−	0.772403i	$-0.719055\pi$
$449$	−5.42638e6	−1.27027	−0.635133	+	0.772403i	$0.719055\pi$
$450$	164303.	0.0382485
$451$	−536776.	−0.124266
$452$	172333.	0.0396754
$453$	1.74877e6	0.400394
$454$	3.09337e6	0.704355
$455$	5.21589e6	1.18114
$456$	−977957.	−0.220246
$457$	3.65841e6	0.819412	0.409706	−	0.912218i	$-0.365631\pi$
$457$	3.65841e6	0.819412	0.409706	+	0.912218i	$0.365631\pi$
$458$	−333939.	−0.0743882
$459$	−417905.	−0.0925861
$460$	−41666.0	−0.00918094
$461$	172819.	0.0378739	0.0189370	−	0.999821i	$-0.493972\pi$
$461$	172819.	0.0378739	0.0189370	+	0.999821i	$0.493972\pi$
$462$	1.15287e6	0.251291
$463$	5.67014e6	1.22925	0.614627	−	0.788818i	$-0.289307\pi$
$463$	5.67014e6	1.22925	0.614627	+	0.788818i	$0.289307\pi$
$464$	−2.26403e6	−0.488188
$465$	−1.88309e6	−0.403868
$466$	−3.00329e6	−0.640667
$467$	−4.49603e6	−0.953975	−0.476987	−	0.878910i	$-0.658271\pi$
$467$	−4.49603e6	−0.953975	−0.476987	+	0.878910i	$0.658271\pi$
$468$	−222828.	−0.0470278
$469$	7.45585e6	1.56518
$470$	5.35381e6	1.11794
$471$	2.82754e6	0.587295
$472$	−621871.	−0.128483
$473$	−970956.	−0.199548
$474$	−3.43426e6	−0.702080
$475$	−222122.	−0.0451707
$476$	−580564.	−0.117444
$477$	681101.	0.137062
$478$	−879950.	−0.176152
$479$	2.08938e6	0.416081	0.208041	−	0.978120i	$-0.433291\pi$
$479$	2.08938e6	0.416081	0.208041	+	0.978120i	$0.433291\pi$
$480$	−1.07481e6	−0.212925
$481$	−3.31044e6	−0.652414
$482$	1.47533e6	0.289248
$483$	−201988.	−0.0393965
$484$	798393.	0.154919
$485$	−5.50314e6	−1.06232
$486$	−303230.	−0.0582347
$487$	2.74031e6	0.523573	0.261787	−	0.965126i	$-0.415688\pi$
$487$	2.74031e6	0.523573	0.261787	+	0.965126i	$0.415688\pi$
$488$	−6.39126e6	−1.21489
$489$	−5.57791e6	−1.05487
$490$	4.74002e6	0.891846
$491$	2.52691e6	0.473026	0.236513	−	0.971628i	$-0.423995\pi$
$491$	2.52691e6	0.473026	0.236513	+	0.971628i	$0.423995\pi$
$492$	196136.	0.0365295
$493$	1.59803e6	0.296121
$494$	−1.41114e6	−0.260168
$495$	−666345.	−0.122232
$496$	−2.86420e6	−0.522756
$497$	988449.	0.179500
$498$	−1.78282e6	−0.322131
$499$	4.88877e6	0.878917	0.439459	−	0.898263i	$-0.355170\pi$
$499$	4.88877e6	0.878917	0.439459	+	0.898263i	$0.355170\pi$
$500$	911795.	0.163107
$501$	5.15705e6	0.917925
$502$	256578.	0.0454424
$503$	−1.94547e6	−0.342850	−0.171425	−	0.985197i	$-0.554837\pi$
$503$	−1.94547e6	−0.342850	−0.171425	+	0.985197i	$0.554837\pi$
$504$	−2.81585e6	−0.493779
$505$	−3.73951e6	−0.652509
$506$	−88827.9	−0.0154231
$507$	1.19240e6	0.206017
$508$	712381.	0.122477
$509$	−9.98842e6	−1.70884	−0.854422	−	0.519580i	$-0.826088\pi$
$509$	−9.98842e6	−1.70884	−0.854422	+	0.519580i	$0.826088\pi$
$510$	−1.57190e6	−0.267607
$511$	3.62832e6	0.614687
$512$	−6.65687e6	−1.12226
$513$	409937.	0.0687740
$514$	−9.56763e6	−1.59734
$515$	629428.	0.104575
$516$	354783.	0.0586595
$517$	−2.43654e6	−0.400911
$518$	−6.25838e6	−1.02480
$519$	−4.59054e6	−0.748075
$520$	−5.60247e6	−0.908597
$521$	−8.01513e6	−1.29365	−0.646824	−	0.762639i	$-0.723903\pi$
$521$	−8.01513e6	−1.29365	−0.646824	+	0.762639i	$0.723903\pi$
$522$	1.15953e6	0.186254
$523$	−3.02310e6	−0.483279	−0.241639	−	0.970366i	$-0.577685\pi$
$523$	−3.02310e6	−0.483279	−0.241639	+	0.970366i	$0.577685\pi$
$524$	408278.	0.0649572
$525$	−639558.	−0.101270
$526$	632532.	0.0996823
$527$	2.02166e6	0.317089
$528$	−1.01352e6	−0.158215
$529$	−6.42078e6	−0.997582
$530$	2.56188e6	0.396158
$531$	260674.	0.0401201
$532$	569495.	0.0872391
$533$	1.89178e6	0.288438
$534$	−1.58285e6	−0.240207
$535$	3.93857e6	0.594914
$536$	−8.00844e6	−1.20403
$537$	1.28469e6	0.192249
$538$	−7.74960e6	−1.15431
$539$	−2.15721e6	−0.319830
$540$	243480.	0.0359317
$541$	−1.12892e7	−1.65832	−0.829162	−	0.559008i	$-0.811182\pi$
$541$	−1.12892e7	−1.65832	−0.829162	+	0.559008i	$0.811182\pi$
$542$	−1.67924e6	−0.245536
$543$	1.96120e6	0.285445
$544$	1.15389e6	0.167174
$545$	667328.	0.0962383
$546$	−4.06312e6	−0.583281
$547$	−8.45511e6	−1.20823	−0.604117	−	0.796896i	$-0.706474\pi$
$547$	−8.45511e6	−1.20823	−0.604117	+	0.796896i	$0.706474\pi$
$548$	261181.	0.0371527
$549$	2.67907e6	0.379362
$550$	−281257.	−0.0396458
$551$	−1.56757e6	−0.219962
$552$	216958.	0.0303060
$553$	1.33680e7	1.85889
$554$	−4.24739e6	−0.587960
$555$	3.61726e6	0.498479
$556$	1.15725e6	0.158760
$557$	−1.12285e7	−1.53350	−0.766752	−	0.641943i	$-0.778129\pi$
$557$	−1.12285e7	−1.53350	−0.766752	+	0.641943i	$0.778129\pi$
$558$	1.46691e6	0.199442
$559$	3.42198e6	0.463178
$560$	−8.66870e6	−1.16811
$561$	715377.	0.0959684
$562$	6.94529e6	0.927577
$563$	−1.31796e7	−1.75239	−0.876197	−	0.481952i	$-0.839928\pi$
$563$	−1.31796e7	−1.75239	−0.876197	+	0.481952i	$0.839928\pi$
$564$	890302.	0.117853
$565$	−1.81625e6	−0.239361
$566$	2.70255e6	0.354595
$567$	1.18034e6	0.154187
$568$	−1.06171e6	−0.138081
$569$	−1.08558e7	−1.40567	−0.702833	−	0.711355i	$-0.748082\pi$
$569$	−1.08558e7	−1.40567	−0.702833	+	0.711355i	$0.748082\pi$
$570$	1.54193e6	0.198782
$571$	−2.18219e6	−0.280093	−0.140046	−	0.990145i	$-0.544725\pi$
$571$	−2.18219e6	−0.280093	−0.140046	+	0.990145i	$0.544725\pi$
$572$	381441.	0.0487458
$573$	−3.25246e6	−0.413834
$574$	3.57641e6	0.453072
$575$	49277.3	0.00621552
$576$	2.94240e6	0.369527
$577$	−485790.	−0.0607448	−0.0303724	−	0.999539i	$-0.509669\pi$
$577$	−485790.	−0.0607448	−0.0303724	+	0.999539i	$0.509669\pi$
$578$	−5.60373e6	−0.697682
$579$	−8.24563e6	−1.02218
$580$	−931046.	−0.114922
$581$	6.93970e6	0.852904
$582$	4.28688e6	0.524607
$583$	−1.16592e6	−0.142069
$584$	−3.89724e6	−0.472851
$585$	2.34843e6	0.283718
$586$	4.05164e6	0.487401
$587$	1.20222e7	1.44008	0.720041	−	0.693932i	$-0.244123\pi$
$587$	1.20222e7	1.44008	0.720041	+	0.693932i	$0.244123\pi$
$588$	788233.	0.0940181
$589$	−1.98311e6	−0.235537
$590$	980492.	0.115962
$591$	−3.98972e6	−0.469865
$592$	5.50188e6	0.645219
$593$	6.71939e6	0.784680	0.392340	−	0.919820i	$-0.371666\pi$
$593$	6.71939e6	0.784680	0.392340	+	0.919820i	$0.371666\pi$
$594$	519075.	0.0603621
$595$	6.11868e6	0.708542
$596$	479880.	0.0553372
$597$	−1.65702e6	−0.190279
$598$	313060.	0.0357993
$599$	1.29102e7	1.47016	0.735082	−	0.677978i	$-0.237144\pi$
$599$	1.29102e7	1.47016	0.735082	+	0.677978i	$0.237144\pi$
$600$	686959.	0.0779027
$601$	−336511.	−0.0380026	−0.0190013	−	0.999819i	$-0.506049\pi$
$601$	−336511.	−0.0380026	−0.0190013	+	0.999819i	$0.506049\pi$
$602$	6.46924e6	0.727548
$603$	3.35695e6	0.375969
$604$	1.09384e6	0.122001
$605$	−8.41443e6	−0.934623
$606$	2.91303e6	0.322229
$607$	−1.13566e7	−1.25105	−0.625526	−	0.780203i	$-0.715116\pi$
$607$	−1.13566e7	−1.25105	−0.625526	+	0.780203i	$0.715116\pi$
$608$	−1.13190e6	−0.124179
$609$	−4.51352e6	−0.493142
$610$	1.00770e7	1.09649
$611$	8.58721e6	0.930570
$612$	−261396.	−0.0282111
$613$	5.01291e6	0.538814	0.269407	−	0.963026i	$-0.413172\pi$
$613$	5.01291e6	0.538814	0.269407	+	0.963026i	$0.413172\pi$
$614$	−5.28303e6	−0.565539
$615$	−2.06711e6	−0.220382
$616$	4.82022e6	0.511817
$617$	−4.57664e6	−0.483988	−0.241994	−	0.970278i	$-0.577801\pi$
$617$	−4.57664e6	−0.483988	−0.241994	+	0.970278i	$0.577801\pi$
$618$	−490317.	−0.0516423
$619$	7.12453e6	0.747359	0.373680	−	0.927558i	$-0.378096\pi$
$619$	7.12453e6	0.747359	0.373680	+	0.927558i	$0.378096\pi$
$620$	−1.17786e6	−0.123059
$621$	−90944.0	−0.00946335
$622$	−4.15092e6	−0.430198
$623$	6.16131e6	0.635994
$624$	3.57198e6	0.367238
$625$	−1.08440e7	−1.11042
$626$	375233.	0.0382706
$627$	−701739.	−0.0712864
$628$	1.76860e6	0.178949
$629$	−3.88343e6	−0.391371
$630$	4.43969e6	0.445658
$631$	−1.47542e7	−1.47517	−0.737586	−	0.675253i	$-0.764034\pi$
$631$	−1.47542e7	−1.47517	−0.737586	+	0.675253i	$0.764034\pi$
$632$	−1.43588e7	−1.42996
$633$	1.02706e7	1.01880
$634$	1.11549e7	1.10216
$635$	−7.50793e6	−0.738900
$636$	426023.	0.0417628
$637$	7.60272e6	0.742370
$638$	−1.98490e6	−0.193058
$639$	445044.	0.0431172
$640$	7.24594e6	0.699269
$641$	−6.95239e6	−0.668328	−0.334164	−	0.942515i	$-0.608454\pi$
$641$	−6.95239e6	−0.668328	−0.334164	+	0.942515i	$0.608454\pi$
$642$	−3.06810e6	−0.293787
$643$	−1.61008e7	−1.53575	−0.767873	−	0.640602i	$-0.778685\pi$
$643$	−1.61008e7	−1.53575	−0.767873	+	0.640602i	$0.778685\pi$
$644$	−126342.	−0.0120042
$645$	−3.73913e6	−0.353893
$646$	−1.65539e6	−0.156070
$647$	5.97116e6	0.560787	0.280394	−	0.959885i	$-0.409535\pi$
$647$	5.97116e6	0.560787	0.280394	+	0.959885i	$0.409535\pi$
$648$	−1.26782e6	−0.118610
$649$	−446227.	−0.0415857
$650$	991245.	0.0920233
$651$	−5.71001e6	−0.528061
$652$	−3.48893e6	−0.321420
$653$	−1.11255e7	−1.02103	−0.510513	−	0.859870i	$-0.670545\pi$
$653$	−1.11255e7	−1.02103	−0.510513	+	0.859870i	$0.670545\pi$
$654$	−519841.	−0.0475254
$655$	−4.30292e6	−0.391887
$656$	−3.14410e6	−0.285257
$657$	1.63363e6	0.147653
$658$	1.62341e7	1.46172
$659$	1.05309e7	0.944606	0.472303	−	0.881436i	$-0.343423\pi$
$659$	1.05309e7	0.944606	0.472303	+	0.881436i	$0.343423\pi$
$660$	−416793.	−0.0372444
$661$	3.45165e6	0.307273	0.153636	−	0.988127i	$-0.450902\pi$
$661$	3.45165e6	0.307273	0.153636	+	0.988127i	$0.450902\pi$
$662$	2.45969e6	0.218140
$663$	−2.52123e6	−0.222756
$664$	−7.45403e6	−0.656102
$665$	−6.00203e6	−0.526313
$666$	−2.81780e6	−0.246164
$667$	347763.	0.0302669
$668$	3.22569e6	0.279693
$669$	489934.	0.0423226
$670$	1.26268e7	1.08669
$671$	−4.58609e6	−0.393220
$672$	−3.25908e6	−0.278402
$673$	9.42726e6	0.802320	0.401160	−	0.916008i	$-0.368607\pi$
$673$	9.42726e6	0.802320	0.401160	+	0.916008i	$0.368607\pi$
$674$	−7.06067e6	−0.598682
$675$	−287957.	−0.0243259
$676$	745837.	0.0627736
$677$	1.57042e7	1.31687	0.658435	−	0.752637i	$-0.271219\pi$
$677$	1.57042e7	1.31687	0.658435	+	0.752637i	$0.271219\pi$
$678$	1.41484e6	0.118204
$679$	−1.66869e7	−1.38900
$680$	−6.57217e6	−0.545050
$681$	−5.42143e6	−0.447967
$682$	−2.51108e6	−0.206728
$683$	5.81451e6	0.476937	0.238469	−	0.971150i	$-0.423355\pi$
$683$	5.81451e6	0.476937	0.238469	+	0.971150i	$0.423355\pi$
$684$	256412.	0.0209555
$685$	−2.75264e6	−0.224142
$686$	−1.15404e6	−0.0936294
$687$	585262.	0.0473106
$688$	−5.68725e6	−0.458070
$689$	4.10911e6	0.329761
$690$	−342074.	−0.0273525
$691$	−1.42807e7	−1.13777	−0.568886	−	0.822416i	$-0.692625\pi$
$691$	−1.42807e7	−1.13777	−0.568886	+	0.822416i	$0.692625\pi$
$692$	−2.87134e6	−0.227939
$693$	−2.02053e6	−0.159820
$694$	3.36056e6	0.264858
$695$	−1.21965e7	−0.957800
$696$	4.84804e6	0.379353
$697$	2.21922e6	0.173029
$698$	−1.28301e7	−0.996763
$699$	5.26357e6	0.407462
$700$	−400038.	−0.0308571
$701$	1.33396e7	1.02529	0.512647	−	0.858600i	$-0.328665\pi$
$701$	1.33396e7	1.02529	0.512647	+	0.858600i	$0.328665\pi$
$702$	−1.82940e6	−0.140109
$703$	3.80939e6	0.290715
$704$	−5.03686e6	−0.383026
$705$	−9.38308e6	−0.711005
$706$	4.42574e6	0.334175
$707$	−1.13391e7	−0.853162
$708$	163049.	0.0122246
$709$	1.11838e7	0.835552	0.417776	−	0.908550i	$-0.362810\pi$
$709$	1.11838e7	0.835552	0.417776	+	0.908550i	$0.362810\pi$
$710$	1.67398e6	0.124624
$711$	6.01888e6	0.446520
$712$	−6.61796e6	−0.489242
$713$	439951.	0.0324101
$714$	−4.76638e6	−0.349899
$715$	−4.02008e6	−0.294083
$716$	803563.	0.0585784
$717$	1.54220e6	0.112032
$718$	526064.	0.0380827
$719$	5.15926e6	0.372191	0.186095	−	0.982532i	$-0.440417\pi$
$719$	5.15926e6	0.372191	0.186095	+	0.982532i	$0.440417\pi$
$720$	−3.90304e6	−0.280589
$721$	1.90858e6	0.136733
$722$	−1.10915e7	−0.791859
$723$	−2.58566e6	−0.183961
$724$	1.22671e6	0.0869754
$725$	1.10113e6	0.0778022
$726$	6.55474e6	0.461545
$727$	1.60159e7	1.12387	0.561934	−	0.827182i	$-0.310057\pi$
$727$	1.60159e7	1.12387	0.561934	+	0.827182i	$0.310057\pi$
$728$	−1.69881e7	−1.18800
$729$	531441.	0.0370370
$730$	6.14470e6	0.426770
$731$	4.01427e6	0.277852
$732$	1.67573e6	0.115592
$733$	−115898.	−0.00796736	−0.00398368	−	0.999992i	$-0.501268\pi$
$733$	−115898.	−0.00796736	−0.00398368	+	0.999992i	$0.501268\pi$
$734$	−1.44898e7	−0.992707
$735$	−8.30735e6	−0.567211
$736$	251109.	0.0170871
$737$	−5.74650e6	−0.389704
$738$	1.61026e6	0.108831
$739$	1.13762e7	0.766278	0.383139	−	0.923691i	$-0.374843\pi$
$739$	1.13762e7	0.766278	0.383139	+	0.923691i	$0.374843\pi$
$740$	2.26256e6	0.151887
$741$	2.47317e6	0.165466
$742$	7.76825e6	0.517981
$743$	2.60121e7	1.72863	0.864316	−	0.502949i	$-0.167752\pi$
$743$	2.60121e7	1.72863	0.864316	+	0.502949i	$0.167752\pi$
$744$	6.13320e6	0.406214
$745$	−5.05755e6	−0.333849
$746$	−212070.	−0.0139518
$747$	3.12456e6	0.204874
$748$	447462.	0.0292417
$749$	1.19427e7	0.777856
$750$	7.48576e6	0.485940
$751$	−1.47952e7	−0.957239	−0.478620	−	0.878022i	$-0.658863\pi$
$751$	−1.47952e7	−0.957239	−0.478620	+	0.878022i	$0.658863\pi$
$752$	−1.42718e7	−0.920308
$753$	−449679.	−0.0289012
$754$	6.99547e6	0.448114
$755$	−1.15282e7	−0.736029
$756$	738291.	0.0469811
$757$	8.14734e6	0.516745	0.258372	−	0.966045i	$-0.416814\pi$
$757$	8.14734e6	0.516745	0.258372	+	0.966045i	$0.416814\pi$
$758$	−1.73819e7	−1.09881
$759$	155680.	0.00980906
$760$	6.44687e6	0.404869
$761$	−6.61106e6	−0.413818	−0.206909	−	0.978360i	$-0.566340\pi$
$761$	−6.61106e6	−0.413818	−0.206909	+	0.978360i	$0.566340\pi$
$762$	5.84859e6	0.364891
$763$	2.02351e6	0.125833
$764$	−2.03439e6	−0.126096
$765$	2.75490e6	0.170197
$766$	1.32101e7	0.813456
$767$	1.57265e6	0.0965262
$768$	4.81737e6	0.294718
$769$	−2.80960e7	−1.71328	−0.856641	−	0.515913i	$-0.827453\pi$
$769$	−2.80960e7	−1.71328	−0.856641	+	0.515913i	$0.827453\pi$
$770$	−7.59995e6	−0.461938
$771$	1.67682e7	1.01590
$772$	−5.15756e6	−0.311459
$773$	1.42306e7	0.856591	0.428296	−	0.903639i	$-0.359114\pi$
$773$	1.42306e7	0.856591	0.428296	+	0.903639i	$0.359114\pi$
$774$	2.91274e6	0.174763
$775$	1.39302e6	0.0833113
$776$	1.79237e7	1.06849
$777$	1.09684e7	0.651766
$778$	1.73879e6	0.102990
$779$	−2.17691e6	−0.128528
$780$	1.46892e6	0.0864493
$781$	−761834.	−0.0446923
$782$	367245.	0.0214753
$783$	−2.03219e6	−0.118457
$784$	−1.26356e7	−0.734183
$785$	−1.86396e7	−1.07960
$786$	3.35193e6	0.193525
$787$	4.62128e6	0.265966	0.132983	−	0.991118i	$-0.457544\pi$
$787$	4.62128e6	0.265966	0.132983	+	0.991118i	$0.457544\pi$
$788$	−2.49553e6	−0.143169
$789$	−1.10858e6	−0.0633976
$790$	2.26392e7	1.29061
$791$	−5.50732e6	−0.312967
$792$	2.17028e6	0.122943
$793$	1.61629e7	0.912719
$794$	1.10457e7	0.621788
$795$	−4.48994e6	−0.251955
$796$	−1.03645e6	−0.0579783
$797$	3.64089e6	0.203030	0.101515	−	0.994834i	$-0.467631\pi$
$797$	3.64089e6	0.203030	0.101515	+	0.994834i	$0.467631\pi$
$798$	4.67551e6	0.259909
$799$	1.00735e7	0.558232
$800$	795091.	0.0439230
$801$	2.77410e6	0.152771
$802$	2.50859e6	0.137719
$803$	−2.79648e6	−0.153047
$804$	2.09974e6	0.114558
$805$	1.33154e6	0.0724211
$806$	8.84989e6	0.479844
$807$	1.35819e7	0.734139
$808$	1.21795e7	0.656300
$809$	1.64743e7	0.884987	0.442493	−	0.896772i	$-0.354094\pi$
$809$	1.64743e7	0.884987	0.442493	+	0.896772i	$0.354094\pi$
$810$	1.99895e6	0.107051
$811$	1.23806e7	0.660980	0.330490	−	0.943810i	$-0.392786\pi$
$811$	1.23806e7	0.660980	0.330490	+	0.943810i	$0.392786\pi$
$812$	−2.82317e6	−0.150261
$813$	2.94304e6	0.156160
$814$	4.82356e6	0.255157
$815$	3.67706e7	1.93913
$816$	4.19023e6	0.220299
$817$	−3.93774e6	−0.206391
$818$	−2.54007e7	−1.32728
$819$	7.12102e6	0.370965
$820$	−1.29296e6	−0.0671507
$821$	−1.61768e7	−0.837597	−0.418799	−	0.908079i	$-0.637549\pi$
$821$	−1.61768e7	−0.837597	−0.418799	+	0.908079i	$0.637549\pi$
$822$	2.14428e6	0.110688
$823$	−2.17184e7	−1.11771	−0.558853	−	0.829267i	$-0.688758\pi$
$823$	−2.17184e7	−1.11771	−0.558853	+	0.829267i	$0.688758\pi$
$824$	−2.05004e6	−0.105183
$825$	492931.	0.0252145
$826$	2.97310e6	0.151621
$827$	−2.32540e7	−1.18232	−0.591158	−	0.806556i	$-0.701329\pi$
$827$	−2.32540e7	−1.18232	−0.591158	+	0.806556i	$0.701329\pi$
$828$	−56884.6	−0.00288350
$829$	1.94461e7	0.982756	0.491378	−	0.870946i	$-0.336493\pi$
$829$	1.94461e7	0.982756	0.491378	+	0.870946i	$0.336493\pi$
$830$	1.17526e7	0.592161
$831$	7.44397e6	0.373940
$832$	1.77516e7	0.889056
$833$	8.91864e6	0.445334
$834$	9.50096e6	0.472991
$835$	−3.39962e7	−1.68739
$836$	−438931.	−0.0217210
$837$	−2.57090e6	−0.126844
$838$	2.48054e7	1.22022
$839$	3.28773e7	1.61247	0.806233	−	0.591598i	$-0.201503\pi$
$839$	3.28773e7	1.61247	0.806233	+	0.591598i	$0.201503\pi$
$840$	1.85626e7	0.907695
$841$	−1.27402e7	−0.621137
$842$	1.98696e7	0.965848
$843$	−1.21723e7	−0.589935
$844$	6.42418e6	0.310428
$845$	−7.86053e6	−0.378713
$846$	7.30931e6	0.351116
$847$	−2.55147e7	−1.22203
$848$	−6.82925e6	−0.326124
$849$	−4.73649e6	−0.225521
$850$	1.16281e6	0.0552030
$851$	−845107.	−0.0400026
$852$	278371.	0.0131379
$853$	−2.05600e7	−0.967500	−0.483750	−	0.875206i	$-0.660726\pi$
$853$	−2.05600e7	−0.967500	−0.483750	+	0.875206i	$0.660726\pi$
$854$	3.05559e7	1.43368
$855$	−2.70238e6	−0.126425
$856$	−1.28279e7	−0.598371
$857$	2.19695e6	0.102181	0.0510904	−	0.998694i	$-0.483730\pi$
$857$	2.19695e6	0.102181	0.0510904	+	0.998694i	$0.483730\pi$
$858$	3.13160e6	0.145227
$859$	−2.64705e7	−1.22399	−0.611996	−	0.790861i	$-0.709633\pi$
$859$	−2.64705e7	−1.22399	−0.611996	+	0.790861i	$0.709633\pi$
$860$	−2.33879e6	−0.107831
$861$	−6.26801e6	−0.288152
$862$	3.12161e7	1.43090
$863$	−1.54368e7	−0.705553	−0.352777	−	0.935708i	$-0.614762\pi$
$863$	−1.54368e7	−0.705553	−0.352777	+	0.935708i	$0.614762\pi$
$864$	−1.46738e6	−0.0668743
$865$	3.02616e7	1.37516
$866$	−9.22193e6	−0.417856
$867$	9.82109e6	0.443723
$868$	−3.57156e6	−0.160901
$869$	−1.03032e7	−0.462832
$870$	−7.64382e6	−0.342383
$871$	2.02526e7	0.904556
$872$	−2.17348e6	−0.0967975
$873$	−7.51319e6	−0.333648
$874$	−360244.	−0.0159521
$875$	−2.91387e7	−1.28662
$876$	1.02182e6	0.0449899
$877$	−1.59208e7	−0.698984	−0.349492	−	0.936939i	$-0.613646\pi$
$877$	−1.59208e7	−0.698984	−0.349492	+	0.936939i	$0.613646\pi$
$878$	−8.24323e6	−0.360879
$879$	−7.10090e6	−0.309985
$880$	6.68129e6	0.290840
$881$	−1.83573e7	−0.796836	−0.398418	−	0.917204i	$-0.630441\pi$
$881$	−1.83573e7	−0.796836	−0.398418	+	0.917204i	$0.630441\pi$
$882$	6.47133e6	0.280106
$883$	1.46620e7	0.632838	0.316419	−	0.948619i	$-0.397519\pi$
$883$	1.46620e7	0.632838	0.316419	+	0.948619i	$0.397519\pi$
$884$	−1.57701e6	−0.0678740
$885$	−1.71841e6	−0.0737511
$886$	1.91190e7	0.818240
$887$	3.31086e6	0.141297	0.0706483	−	0.997501i	$-0.477493\pi$
$887$	3.31086e6	0.141297	0.0706483	+	0.997501i	$0.477493\pi$
$888$	−1.17814e7	−0.501375
$889$	−2.27659e7	−0.966120
$890$	1.04344e7	0.441563
$891$	−909731.	−0.0383900
$892$	306449.	0.0128957
$893$	−9.88147e6	−0.414661
$894$	3.93978e6	0.164865
$895$	−8.46892e6	−0.353403
$896$	2.19715e7	0.914302
$897$	−548668.	−0.0227682
$898$	−2.78657e7	−1.15313
$899$	9.83091e6	0.405690
$900$	−180115.	−0.00741213
$901$	4.82033e6	0.197817
$902$	−2.75647e6	−0.112807
$903$	−1.13380e7	−0.462718
$904$	5.91549e6	0.240752
$905$	−1.29286e7	−0.524722
$906$	8.98035e6	0.363474
$907$	−2.14890e7	−0.867355	−0.433678	−	0.901068i	$-0.642784\pi$
$907$	−2.14890e7	−0.867355	−0.433678	+	0.901068i	$0.642784\pi$
$908$	−3.39106e6	−0.136496
$909$	−5.10538e6	−0.204936
$910$	2.67848e7	1.07222
$911$	3.64007e7	1.45316	0.726581	−	0.687081i	$-0.241108\pi$
$911$	3.64007e7	1.45316	0.726581	+	0.687081i	$0.241108\pi$
$912$	−4.11035e6	−0.163641
$913$	−5.34868e6	−0.212359
$914$	1.87868e7	0.743853
$915$	−1.76609e7	−0.697366
$916$	366076.	0.0144156
$917$	−1.30475e7	−0.512396
$918$	−2.14604e6	−0.0840486
$919$	5.33041e6	0.208196	0.104098	−	0.994567i	$-0.466804\pi$
$919$	5.33041e6	0.208196	0.104098	+	0.994567i	$0.466804\pi$
$920$	−1.43023e6	−0.0557103
$921$	9.25904e6	0.359681
$922$	887467.	0.0343815
$923$	2.68496e6	0.103737
$924$	−1.26382e6	−0.0486974
$925$	−2.67588e6	−0.102828
$926$	2.91175e7	1.11590
$927$	859329.	0.0328443
$928$	5.61116e6	0.213886
$929$	−3.20825e7	−1.21963	−0.609817	−	0.792542i	$-0.708757\pi$
$929$	−3.20825e7	−1.21963	−0.609817	+	0.792542i	$0.708757\pi$
$930$	−9.67011e6	−0.366627
$931$	−8.74860e6	−0.330799
$932$	3.29231e6	0.124154
$933$	7.27490e6	0.273604
$934$	−2.30881e7	−0.866008
$935$	−4.71590e6	−0.176415
$936$	−7.64879e6	−0.285367
$937$	8.18884e6	0.304701	0.152350	−	0.988327i	$-0.451316\pi$
$937$	8.18884e6	0.304701	0.152350	+	0.988327i	$0.451316\pi$
$938$	3.82875e7	1.42085
$939$	−657633.	−0.0243399
$940$	−5.86903e6	−0.216644
$941$	4.00779e7	1.47547	0.737735	−	0.675090i	$-0.235895\pi$
$941$	4.00779e7	1.47547	0.737735	+	0.675090i	$0.235895\pi$
$942$	1.45201e7	0.533140
$943$	482944.	0.0176855
$944$	−2.61372e6	−0.0954616
$945$	−7.78100e6	−0.283437
$946$	−4.98608e6	−0.181147
$947$	1.04558e7	0.378865	0.189432	−	0.981894i	$-0.439335\pi$
$947$	1.04558e7	0.378865	0.189432	+	0.981894i	$0.439335\pi$
$948$	3.76475e6	0.136055
$949$	9.85576e6	0.355242
$950$	−1.14065e6	−0.0410055
$951$	−1.95501e7	−0.700967
$952$	−1.99285e7	−0.712658
$953$	−3.67139e7	−1.30948	−0.654740	−	0.755855i	$-0.727222\pi$
$953$	−3.67139e7	−1.30948	−0.654740	+	0.755855i	$0.727222\pi$
$954$	3.49761e6	0.124423
$955$	2.14408e7	0.760734
$956$	964631.	0.0341363
$957$	3.47874e6	0.122784
$958$	1.07294e7	0.377714
$959$	−8.34671e6	−0.293068
$960$	−1.93968e7	−0.679286
$961$	−1.61922e7	−0.565583
$962$	−1.69999e7	−0.592254
$963$	5.37715e6	0.186847
$964$	−1.61730e6	−0.0560531
$965$	5.43566e7	1.87903
$966$	−1.03725e6	−0.0357637
$967$	−3.05716e6	−0.105136	−0.0525681	−	0.998617i	$-0.516741\pi$
$967$	−3.05716e6	−0.105136	−0.0525681	+	0.998617i	$0.516741\pi$
$968$	2.74057e7	0.940053
$969$	2.90123e6	0.0992597
$970$	−2.82599e7	−0.964364
$971$	1.06966e7	0.364080	0.182040	−	0.983291i	$-0.441730\pi$
$971$	1.06966e7	0.364080	0.182040	+	0.983291i	$0.441730\pi$
$972$	332411.	0.0112852
$973$	−3.69830e7	−1.25233
$974$	1.40721e7	0.475294
$975$	−1.73726e6	−0.0585265
$976$	−2.68624e7	−0.902653
$977$	−7.42638e6	−0.248909	−0.124455	−	0.992225i	$-0.539718\pi$
$977$	−7.42638e6	−0.248909	−0.124455	+	0.992225i	$0.539718\pi$
$978$	−2.86438e7	−0.957600
$979$	−4.74875e6	−0.158352
$980$	−5.19617e6	−0.172830
$981$	911072.	0.0302260
$982$	1.29762e7	0.429408
$983$	2.13383e7	0.704329	0.352165	−	0.935938i	$-0.385446\pi$
$983$	2.13383e7	0.704329	0.352165	+	0.935938i	$0.385446\pi$
$984$	6.73256e6	0.221663
$985$	2.63009e7	0.863735
$986$	8.20627e6	0.268815
$987$	−2.84519e7	−0.929646
$988$	1.54694e6	0.0504176
$989$	873581.	0.0283996
$990$	−3.42184e6	−0.110961
$991$	−3.09832e7	−1.00217	−0.501086	−	0.865398i	$-0.667066\pi$
$991$	−3.09832e7	−1.00217	−0.501086	+	0.865398i	$0.667066\pi$
$992$	7.09862e6	0.229031
$993$	−4.31085e6	−0.138736
$994$	5.07591e6	0.162948
$995$	1.09234e7	0.349783
$996$	1.95438e6	0.0624254
$997$	2.03756e7	0.649190	0.324595	−	0.945853i	$-0.394772\pi$
$997$	2.03756e7	0.649190	0.324595	+	0.945853i	$0.394772\pi$
$998$	2.51049e7	0.797871
$999$	4.93848e6	0.156559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.b.1.13	✓	20
3.2	odd	2		927.6.a.c.1.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.b.1.13	✓	20	1.1	even	1	trivial
927.6.a.c.1.8		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)

\(f(q)\)	\(=\)	\(q+5.13523 q^{2} -9.00000 q^{3} -5.62942 q^{4} +59.3296 q^{5} -46.2171 q^{6} +179.902 q^{7} -193.236 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+5.13523 q^{2} -9.00000 q^{3} -5.62942 q^{4} +59.3296 q^{5} -46.2171 q^{6} +179.902 q^{7} -193.236 q^{8} +81.0000 q^{9} +304.671 q^{10} -138.657 q^{11} +50.6648 q^{12} +488.676 q^{13} +923.839 q^{14} -533.967 q^{15} -812.168 q^{16} +573.258 q^{17} +415.954 q^{18} -562.328 q^{19} -333.991 q^{20} -1619.12 q^{21} -712.037 q^{22} +124.752 q^{23} +1739.12 q^{24} +395.003 q^{25} +2509.46 q^{26} -729.000 q^{27} -1012.74 q^{28} +2787.64 q^{29} -2742.04 q^{30} +3526.61 q^{31} +2012.87 q^{32} +1247.92 q^{33} +2943.81 q^{34} +10673.5 q^{35} -455.983 q^{36} -6774.31 q^{37} -2887.69 q^{38} -4398.08 q^{39} -11464.6 q^{40} +3871.24 q^{41} -8314.55 q^{42} +7002.56 q^{43} +780.560 q^{44} +4805.70 q^{45} +640.629 q^{46} +17572.4 q^{47} +7309.51 q^{48} +15557.8 q^{49} +2028.43 q^{50} -5159.32 q^{51} -2750.96 q^{52} +8408.66 q^{53} -3743.58 q^{54} -8226.49 q^{55} -34763.5 q^{56} +5060.96 q^{57} +14315.2 q^{58} +3218.20 q^{59} +3005.92 q^{60} +33075.0 q^{61} +18110.0 q^{62} +14572.1 q^{63} +36325.9 q^{64} +28992.9 q^{65} +6408.34 q^{66} +41443.9 q^{67} -3227.11 q^{68} -1122.77 q^{69} +54811.0 q^{70} +5494.37 q^{71} -15652.1 q^{72} +20168.3 q^{73} -34787.7 q^{74} -3555.03 q^{75} +3165.58 q^{76} -24944.8 q^{77} -22585.2 q^{78} +74307.1 q^{79} -48185.6 q^{80} +6561.00 q^{81} +19879.7 q^{82} +38574.8 q^{83} +9114.70 q^{84} +34011.2 q^{85} +35959.7 q^{86} -25088.7 q^{87} +26793.5 q^{88} +34248.1 q^{89} +24678.4 q^{90} +87913.8 q^{91} -702.280 q^{92} -31739.5 q^{93} +90238.4 q^{94} -33362.7 q^{95} -18115.8 q^{96} -92755.4 q^{97} +79893.0 q^{98} -11231.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 180 q^{3} + 326 q^{4} + 97 q^{5} - 36 q^{6} + 10 q^{7} + 312 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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