LMFDB - Embedded newform 547.6.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,6,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	547.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:	$87.7299494377$
Analytic rank:	$0$
Dimension:	$117$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.9448 q^{2} +25.7259 q^{3} +87.7879 q^{4} +30.5569 q^{5} -281.564 q^{6} -19.7130 q^{7} -610.585 q^{8} +418.824 q^{9} +O(q^{10})$	\(q-10.9448 q^{2} +25.7259 q^{3} +87.7879 q^{4} +30.5569 q^{5} -281.564 q^{6} -19.7130 q^{7} -610.585 q^{8} +418.824 q^{9} -334.438 q^{10} +667.969 q^{11} +2258.42 q^{12} +614.632 q^{13} +215.754 q^{14} +786.104 q^{15} +3873.50 q^{16} +1913.06 q^{17} -4583.93 q^{18} +2707.44 q^{19} +2682.52 q^{20} -507.136 q^{21} -7310.76 q^{22} -1277.60 q^{23} -15707.9 q^{24} -2191.28 q^{25} -6727.00 q^{26} +4523.23 q^{27} -1730.56 q^{28} +3630.40 q^{29} -8603.72 q^{30} +7697.88 q^{31} -22855.8 q^{32} +17184.1 q^{33} -20938.0 q^{34} -602.368 q^{35} +36767.6 q^{36} +1114.42 q^{37} -29632.3 q^{38} +15812.0 q^{39} -18657.6 q^{40} -13932.0 q^{41} +5550.48 q^{42} -19808.2 q^{43} +58639.5 q^{44} +12797.9 q^{45} +13983.0 q^{46} +20127.6 q^{47} +99649.3 q^{48} -16418.4 q^{49} +23983.0 q^{50} +49215.3 q^{51} +53957.2 q^{52} +11099.2 q^{53} -49505.7 q^{54} +20411.0 q^{55} +12036.5 q^{56} +69651.4 q^{57} -39733.9 q^{58} -32911.4 q^{59} +69010.4 q^{60} -31661.5 q^{61} -84251.5 q^{62} -8256.28 q^{63} +126199. q^{64} +18781.2 q^{65} -188076. q^{66} +33649.3 q^{67} +167943. q^{68} -32867.5 q^{69} +6592.77 q^{70} -2988.12 q^{71} -255727. q^{72} -30280.5 q^{73} -12197.0 q^{74} -56372.7 q^{75} +237680. q^{76} -13167.7 q^{77} -173058. q^{78} -57577.6 q^{79} +118362. q^{80} +14590.2 q^{81} +152483. q^{82} -14715.6 q^{83} -44520.4 q^{84} +58457.1 q^{85} +216796. q^{86} +93395.5 q^{87} -407851. q^{88} -54896.7 q^{89} -140070. q^{90} -12116.3 q^{91} -112158. q^{92} +198035. q^{93} -220292. q^{94} +82730.8 q^{95} -587986. q^{96} +20493.5 q^{97} +179695. q^{98} +279761. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) $ 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10.9448	−1.93478	−0.967390	−	0.253293i	$-0.918486\pi$
$2$	−10.9448	−1.93478	−0.967390	+	0.253293i	$0.918486\pi$
$3$	25.7259	1.65032	0.825160	−	0.564899i	$-0.191085\pi$
$3$	25.7259	1.65032	0.825160	+	0.564899i	$0.191085\pi$
$4$	87.7879	2.74337
$5$	30.5569	0.546618	0.273309	−	0.961926i	$-0.411882\pi$
$5$	30.5569	0.546618	0.273309	+	0.961926i	$0.411882\pi$
$6$	−281.564	−3.19300
$7$	−19.7130	−0.152058	−0.0760288	−	0.997106i	$-0.524224\pi$
$7$	−19.7130	−0.152058	−0.0760288	+	0.997106i	$0.524224\pi$
$8$	−610.585	−3.37304
$9$	418.824	1.72355
$10$	−334.438	−1.05758
$11$	667.969	1.66446	0.832232	−	0.554428i	$-0.187063\pi$
$11$	667.969	1.66446	0.832232	+	0.554428i	$0.187063\pi$
$12$	2258.42	4.52744
$13$	614.632	1.00869	0.504344	−	0.863503i	$-0.331734\pi$
$13$	614.632	1.00869	0.504344	+	0.863503i	$0.331734\pi$
$14$	215.754	0.294198
$15$	786.104	0.902094
$16$	3873.50	3.78271
$17$	1913.06	1.60549	0.802743	−	0.596326i	$-0.203373\pi$
$17$	1913.06	1.60549	0.802743	+	0.596326i	$0.203373\pi$
$18$	−4583.93	−3.33470
$19$	2707.44	1.72058	0.860289	−	0.509807i	$-0.170283\pi$
$19$	2707.44	1.72058	0.860289	+	0.509807i	$0.170283\pi$
$20$	2682.52	1.49957
$21$	−507.136	−0.250944
$22$	−7310.76	−3.22037
$23$	−1277.60	−0.503589	−0.251794	−	0.967781i	$-0.581021\pi$
$23$	−1277.60	−0.503589	−0.251794	+	0.967781i	$0.581021\pi$
$24$	−15707.9	−5.56659
$25$	−2191.28	−0.701209
$26$	−6727.00	−1.95159
$27$	4523.23	1.19410
$28$	−1730.56	−0.417150
$29$	3630.40	0.801604	0.400802	−	0.916165i	$-0.368732\pi$
$29$	3630.40	0.801604	0.400802	+	0.916165i	$0.368732\pi$
$30$	−8603.72	−1.74535
$31$	7697.88	1.43869	0.719345	−	0.694653i	$-0.244442\pi$
$31$	7697.88	1.43869	0.719345	+	0.694653i	$0.244442\pi$
$32$	−22855.8	−3.94567
$33$	17184.1	2.74690
$34$	−20938.0	−3.10626
$35$	−602.368	−0.0831173
$36$	36767.6	4.72835
$37$	1114.42	0.133827	0.0669134	−	0.997759i	$-0.478685\pi$
$37$	1114.42	0.133827	0.0669134	+	0.997759i	$0.478685\pi$
$38$	−29632.3	−3.32894
$39$	15812.0	1.66466
$40$	−18657.6	−1.84376
$41$	−13932.0	−1.29436	−0.647180	−	0.762337i	$-0.724052\pi$
$41$	−13932.0	−1.29436	−0.647180	+	0.762337i	$0.724052\pi$
$42$	5550.48	0.485520
$43$	−19808.2	−1.63371	−0.816854	−	0.576845i	$-0.804284\pi$
$43$	−19808.2	−1.63371	−0.816854	+	0.576845i	$0.804284\pi$
$44$	58639.5	4.56624
$45$	12797.9	0.942126
$46$	13983.0	0.974333
$47$	20127.6	1.32907	0.664535	−	0.747258i	$-0.268630\pi$
$47$	20127.6	1.32907	0.664535	+	0.747258i	$0.268630\pi$
$48$	99649.3	6.24268
$49$	−16418.4	−0.976879
$50$	23983.0	1.35668
$51$	49215.3	2.64956
$52$	53957.2	2.76721
$53$	11099.2	0.542754	0.271377	−	0.962473i	$-0.412521\pi$
$53$	11099.2	0.542754	0.271377	+	0.962473i	$0.412521\pi$
$54$	−49505.7	−2.31031
$55$	20411.0	0.909825
$56$	12036.5	0.512896
$57$	69651.4	2.83950
$58$	−39733.9	−1.55093
$59$	−32911.4	−1.23088	−0.615441	−	0.788183i	$-0.711022\pi$
$59$	−32911.4	−1.23088	−0.615441	+	0.788183i	$0.711022\pi$
$60$	69010.4	2.47478
$61$	−31661.5	−1.08945	−0.544725	−	0.838615i	$-0.683366\pi$
$61$	−31661.5	−1.08945	−0.544725	+	0.838615i	$0.683366\pi$
$62$	−84251.5	−2.78355
$63$	−8256.28	−0.262079
$64$	126199.	3.85130
$65$	18781.2	0.551367
$66$	−188076.	−5.31464
$67$	33649.3	0.915774	0.457887	−	0.889010i	$-0.348606\pi$
$67$	33649.3	0.915774	0.457887	+	0.889010i	$0.348606\pi$
$68$	167943.	4.40444
$69$	−32867.5	−0.831082
$70$	6592.77	0.160814
$71$	−2988.12	−0.0703480	−0.0351740	−	0.999381i	$-0.511199\pi$
$71$	−2988.12	−0.0703480	−0.0351740	+	0.999381i	$0.511199\pi$
$72$	−255727.	−5.81361
$73$	−30280.5	−0.665053	−0.332526	−	0.943094i	$-0.607901\pi$
$73$	−30280.5	−0.665053	−0.332526	+	0.943094i	$0.607901\pi$
$74$	−12197.0	−0.258925
$75$	−56372.7	−1.15722
$76$	237680.	4.72018
$77$	−13167.7	−0.253094
$78$	−173058.	−3.22075
$79$	−57577.6	−1.03797	−0.518986	−	0.854783i	$-0.673690\pi$
$79$	−57577.6	−1.03797	−0.518986	+	0.854783i	$0.673690\pi$
$80$	118362.	2.06770
$81$	14590.2	0.247086
$82$	152483.	2.50430
$83$	−14715.6	−0.234468	−0.117234	−	0.993104i	$-0.537403\pi$
$83$	−14715.6	−0.234468	−0.117234	+	0.993104i	$0.537403\pi$
$84$	−44520.4	−0.688431
$85$	58457.1	0.877587
$86$	216796.	3.16086
$87$	93395.5	1.32290
$88$	−407851.	−5.61430
$89$	−54896.7	−0.734634	−0.367317	−	0.930096i	$-0.619724\pi$
$89$	−54896.7	−0.734634	−0.367317	+	0.930096i	$0.619724\pi$
$90$	−140070.	−1.82280
$91$	−12116.3	−0.153379
$92$	−112158.	−1.38153
$93$	198035.	2.37430
$94$	−220292.	−2.57146
$95$	82730.8	0.940498
$96$	−587986.	−6.51162
$97$	20493.5	0.221150	0.110575	−	0.993868i	$-0.464731\pi$
$97$	20493.5	0.221150	0.110575	+	0.993868i	$0.464731\pi$
$98$	179695.	1.89004
$99$	279761.	2.86879
$100$	−192368.	−1.92368
$101$	−159362.	−1.55447	−0.777234	−	0.629211i	$-0.783378\pi$
$101$	−159362.	−1.55447	−0.777234	+	0.629211i	$0.783378\pi$
$102$	−538649.	−5.12632
$103$	−46065.7	−0.427843	−0.213921	−	0.976851i	$-0.568624\pi$
$103$	−46065.7	−0.427843	−0.213921	+	0.976851i	$0.568624\pi$
$104$	−375285.	−3.40234
$105$	−15496.5	−0.137170
$106$	−121479.	−1.05011
$107$	214344.	1.80989	0.904944	−	0.425530i	$-0.139912\pi$
$107$	214344.	1.80989	0.904944	+	0.425530i	$0.139912\pi$
$108$	397085.	3.27585
$109$	−200883.	−1.61949	−0.809744	−	0.586784i	$-0.800394\pi$
$109$	−200883.	−1.61949	−0.809744	+	0.586784i	$0.800394\pi$
$110$	−223394.	−1.76031
$111$	28669.4	0.220857
$112$	−76358.3	−0.575190
$113$	164321.	1.21059	0.605296	−	0.796000i	$-0.293055\pi$
$113$	164321.	1.21059	0.605296	+	0.796000i	$0.293055\pi$
$114$	−762318.	−5.49381
$115$	−39039.5	−0.275270
$116$	318705.	2.19910
$117$	257423.	1.73853
$118$	360207.	2.38148
$119$	−37712.2	−0.244126
$120$	−479983.	−3.04280
$121$	285131.	1.77044
$122$	346528.	2.10784
$123$	−358415.	−2.13611
$124$	675781.	3.94686
$125$	−162449.	−0.929911
$126$	90363.0	0.507066
$127$	−131254.	−0.722111	−0.361055	−	0.932544i	$-0.617583\pi$
$127$	−131254.	−0.722111	−0.361055	+	0.932544i	$0.617583\pi$
$128$	−649836.	−3.50573
$129$	−509585.	−2.69614
$130$	−205556.	−1.06677
$131$	96884.0	0.493258	0.246629	−	0.969110i	$-0.420677\pi$
$131$	96884.0	0.493258	0.246629	+	0.969110i	$0.420677\pi$
$132$	1.50856e6	7.53576
$133$	−53371.7	−0.261627
$134$	−368283.	−1.77182
$135$	138216.	0.652714
$136$	−1.16809e6	−5.41536
$137$	−350858.	−1.59709	−0.798546	−	0.601933i	$-0.794397\pi$
$137$	−350858.	−1.59709	−0.798546	+	0.601933i	$0.794397\pi$
$138$	359727.	1.60796
$139$	45627.1	0.200302	0.100151	−	0.994972i	$-0.468067\pi$
$139$	45627.1	0.200302	0.100151	+	0.994972i	$0.468067\pi$
$140$	−52880.6	−0.228022
$141$	517802.	2.19339
$142$	32704.2	0.136108
$143$	410555.	1.67892
$144$	1.62231e6	6.51971
$145$	110934.	0.438171
$146$	331413.	1.28673
$147$	−422379.	−1.61216
$148$	97832.2	0.367137
$149$	955.384	0.00352543	0.00176271	−	0.999998i	$-0.499439\pi$
$149$	955.384	0.00352543	0.00176271	+	0.999998i	$0.499439\pi$
$150$	616986.	2.23896
$151$	−200016.	−0.713877	−0.356938	−	0.934128i	$-0.616179\pi$
$151$	−200016.	−0.713877	−0.356938	+	0.934128i	$0.616179\pi$
$152$	−1.65312e6	−5.80357
$153$	801235.	2.76714
$154$	144117.	0.489681
$155$	235223.	0.786413
$156$	1.38810e6	4.56677
$157$	77043.7	0.249453	0.124726	−	0.992191i	$-0.460195\pi$
$157$	77043.7	0.249453	0.124726	+	0.992191i	$0.460195\pi$
$158$	630173.	2.00825
$159$	285538.	0.895718
$160$	−698401.	−2.15677
$161$	25185.4	0.0765744
$162$	−159686.	−0.478057
$163$	152696.	0.450152	0.225076	−	0.974341i	$-0.427737\pi$
$163$	152696.	0.450152	0.225076	+	0.974341i	$0.427737\pi$
$164$	−1.22306e6	−3.55091
$165$	525093.	1.50150
$166$	161059.	0.453643
$167$	−601745.	−1.66963	−0.834817	−	0.550527i	$-0.814427\pi$
$167$	−601745.	−1.66963	−0.834817	+	0.550527i	$0.814427\pi$
$168$	309649.	0.846442
$169$	6479.77	0.0174519
$170$	−639799.	−1.69794
$171$	1.13394e6	2.96551
$172$	−1.73892e6	−4.48187
$173$	612113.	1.55495	0.777475	−	0.628913i	$-0.216500\pi$
$173$	612113.	1.55495	0.777475	+	0.628913i	$0.216500\pi$
$174$	−1.02219e6	−2.55952
$175$	43196.7	0.106624
$176$	2.58737e6	6.29618
$177$	−846676.	−2.03135
$178$	600831.	1.42135
$179$	−204748.	−0.477626	−0.238813	−	0.971066i	$-0.576758\pi$
$179$	−204748.	−0.477626	−0.238813	+	0.971066i	$0.576758\pi$
$180$	1.12350e6	2.58460
$181$	−69338.8	−0.157319	−0.0786593	−	0.996902i	$-0.525064\pi$
$181$	−69338.8	−0.157319	−0.0786593	+	0.996902i	$0.525064\pi$
$182$	132610.	0.296754
$183$	−814522.	−1.79794
$184$	780084.	1.69862
$185$	34053.1	0.0731521
$186$	−2.16745e6	−4.59374
$187$	1.27786e6	2.67227
$188$	1.76696e6	3.64613
$189$	−89166.5	−0.181571
$190$	−905469.	−1.81966
$191$	350796.	0.695779	0.347890	−	0.937536i	$-0.386898\pi$
$191$	350796.	0.695779	0.347890	+	0.937536i	$0.386898\pi$
$192$	3.24659e6	6.35587
$193$	−510101.	−0.985741	−0.492870	−	0.870103i	$-0.664052\pi$
$193$	−510101.	−0.985741	−0.492870	+	0.870103i	$0.664052\pi$
$194$	−224297.	−0.427877
$195$	483165.	0.909931
$196$	−1.44134e6	−2.67994
$197$	595340.	1.09295	0.546474	−	0.837476i	$-0.315970\pi$
$197$	595340.	1.09295	0.546474	+	0.837476i	$0.315970\pi$
$198$	−3.06192e6	−5.55048
$199$	109474.	0.195964	0.0979820	−	0.995188i	$-0.468761\pi$
$199$	109474.	0.195964	0.0979820	+	0.995188i	$0.468761\pi$
$200$	1.33796e6	2.36520
$201$	865658.	1.51132
$202$	1.74418e6	3.00755
$203$	−71566.2	−0.121890
$204$	4.32050e6	7.26874
$205$	−425720.	−0.707521
$206$	504178.	0.827782
$207$	−535090.	−0.867962
$208$	2.38078e6	3.81558
$209$	1.80848e6	2.86384
$210$	169605.	0.265394
$211$	−1.20010e6	−1.85571	−0.927856	−	0.372938i	$-0.878350\pi$
$211$	−1.20010e6	−1.85571	−0.927856	+	0.372938i	$0.878350\pi$
$212$	974378.	1.48898
$213$	−76872.1	−0.116097
$214$	−2.34594e6	−3.50173
$215$	−605277.	−0.893014
$216$	−2.76182e6	−4.02773
$217$	−151748.	−0.218764
$218$	2.19862e6	3.13335
$219$	−778995.	−1.09755
$220$	1.79184e6	2.49599
$221$	1.17583e6	1.61943
$222$	−313780.	−0.427310
$223$	767151.	1.03304	0.516522	−	0.856274i	$-0.327227\pi$
$223$	767151.	1.03304	0.516522	+	0.856274i	$0.327227\pi$
$224$	450556.	0.599969
$225$	−917760.	−1.20857
$226$	−1.79846e6	−2.34223
$227$	642178.	0.827162	0.413581	−	0.910467i	$-0.364278\pi$
$227$	642178.	0.827162	0.413581	+	0.910467i	$0.364278\pi$
$228$	6.11454e6	7.78981
$229$	−1.19519e6	−1.50608	−0.753042	−	0.657973i	$-0.771414\pi$
$229$	−1.19519e6	−1.50608	−0.753042	+	0.657973i	$0.771414\pi$
$230$	427278.	0.532587
$231$	−338751.	−0.417686
$232$	−2.21667e6	−2.70384
$233$	−796090.	−0.960666	−0.480333	−	0.877086i	$-0.659484\pi$
$233$	−796090.	−0.960666	−0.480333	+	0.877086i	$0.659484\pi$
$234$	−2.81743e6	−3.36367
$235$	615037.	0.726493
$236$	−2.88922e6	−3.37676
$237$	−1.48124e6	−1.71299
$238$	412751.	0.472330
$239$	−735412.	−0.832790	−0.416395	−	0.909184i	$-0.636707\pi$
$239$	−735412.	−0.832790	−0.416395	+	0.909184i	$0.636707\pi$
$240$	3.04497e6	3.41236
$241$	−739989.	−0.820696	−0.410348	−	0.911929i	$-0.634593\pi$
$241$	−739989.	−0.820696	−0.410348	+	0.911929i	$0.634593\pi$
$242$	−3.12069e6	−3.42541
$243$	−723799.	−0.786325
$244$	−2.77950e6	−2.98876
$245$	−501695.	−0.533979
$246$	3.92277e6	4.13290
$247$	1.66408e6	1.73553
$248$	−4.70021e6	−4.85275
$249$	−378573.	−0.386947
$250$	1.77796e6	1.79917
$251$	1.33304e6	1.33555	0.667775	−	0.744363i	$-0.267247\pi$
$251$	1.33304e6	1.33555	0.667775	+	0.744363i	$0.267247\pi$
$252$	−724801.	−0.718981
$253$	−853398.	−0.838205
$254$	1.43655e6	1.39712
$255$	1.50386e6	1.44830
$256$	3.07393e6	2.93152
$257$	222753.	0.210373	0.105187	−	0.994453i	$-0.466456\pi$
$257$	222753.	0.210373	0.105187	+	0.994453i	$0.466456\pi$
$258$	5.57729e6	5.21644
$259$	−21968.5	−0.0203494
$260$	1.64876e6	1.51260
$261$	1.52050e6	1.38161
$262$	−1.06037e6	−0.954344
$263$	623118.	0.555496	0.277748	−	0.960654i	$-0.410412\pi$
$263$	623118.	0.555496	0.277748	+	0.960654i	$0.410412\pi$
$264$	−1.04924e7	−9.26538
$265$	339158.	0.296679
$266$	584141.	0.506190
$267$	−1.41227e6	−1.21238
$268$	2.95400e6	2.51231
$269$	1.47340e6	1.24148	0.620741	−	0.784015i	$-0.286832\pi$
$269$	1.47340e6	1.24148	0.620741	+	0.784015i	$0.286832\pi$
$270$	−1.51274e6	−1.26286
$271$	−1.61372e6	−1.33477	−0.667383	−	0.744715i	$-0.732586\pi$
$271$	−1.61372e6	−1.33477	−0.667383	+	0.744715i	$0.732586\pi$
$272$	7.41023e6	6.07309
$273$	−311702.	−0.253124
$274$	3.84006e6	3.09002
$275$	−1.46371e6	−1.16714
$276$	−2.88537e6	−2.27997
$277$	−546310.	−0.427799	−0.213900	−	0.976856i	$-0.568617\pi$
$277$	−546310.	−0.427799	−0.213900	+	0.976856i	$0.568617\pi$
$278$	−499378.	−0.387541
$279$	3.22406e6	2.47966
$280$	367797.	0.280358
$281$	−1.87818e6	−1.41896	−0.709482	−	0.704723i	$-0.751071\pi$
$281$	−1.87818e6	−1.41896	−0.709482	+	0.704723i	$0.751071\pi$
$282$	−5.66722e6	−4.24372
$283$	−403273.	−0.299318	−0.149659	−	0.988738i	$-0.547818\pi$
$283$	−403273.	−0.299318	−0.149659	+	0.988738i	$0.547818\pi$
$284$	−262320.	−0.192990
$285$	2.12833e6	1.55212
$286$	−4.49343e6	−3.24835
$287$	274643.	0.196817
$288$	−9.57255e6	−6.80058
$289$	2.23994e6	1.57758
$290$	−1.21414e6	−0.847764
$291$	527215.	0.364968
$292$	−2.65826e6	−1.82449
$293$	787799.	0.536101	0.268050	−	0.963405i	$-0.413621\pi$
$293$	787799.	0.536101	0.268050	+	0.963405i	$0.413621\pi$
$294$	4.62283e6	3.11918
$295$	−1.00567e6	−0.672822
$296$	−680446.	−0.451403
$297$	3.02138e6	1.98753
$298$	−10456.4	−0.00682093
$299$	−785255.	−0.507964
$300$	−4.94884e6	−3.17468
$301$	390480.	0.248418
$302$	2.18913e6	1.38119
$303$	−4.09974e6	−2.56537
$304$	1.04872e7	6.50845
$305$	−967476.	−0.595512
$306$	−8.76933e6	−5.35381
$307$	29143.3	0.0176479	0.00882395	−	0.999961i	$-0.497191\pi$
$307$	29143.3	0.0176479	0.00882395	+	0.999961i	$0.497191\pi$
$308$	−1.15596e6	−0.694331
$309$	−1.18508e6	−0.706078
$310$	−2.57446e6	−1.52154
$311$	146418.	0.0858409	0.0429205	−	0.999078i	$-0.486334\pi$
$311$	146418.	0.0858409	0.0429205	+	0.999078i	$0.486334\pi$
$312$	−9.65456e6	−5.61495
$313$	1.58144e6	0.912415	0.456208	−	0.889873i	$-0.349207\pi$
$313$	1.58144e6	0.912415	0.456208	+	0.889873i	$0.349207\pi$
$314$	−843225.	−0.482636
$315$	−252286.	−0.143257
$316$	−5.05461e6	−2.84754
$317$	2.22289e6	1.24242	0.621212	−	0.783642i	$-0.286641\pi$
$317$	2.22289e6	1.24242	0.621212	+	0.783642i	$0.286641\pi$
$318$	−3.12515e6	−1.73302
$319$	2.42499e6	1.33424
$320$	3.85625e6	2.10519
$321$	5.51420e6	2.98689
$322$	−275648.	−0.148155
$323$	5.17949e6	2.76236
$324$	1.28084e6	0.677849
$325$	−1.34683e6	−0.707301
$326$	−1.67122e6	−0.870945
$327$	−5.16791e6	−2.67267
$328$	8.50670e6	4.36593
$329$	−396776.	−0.202095
$330$	−5.74701e6	−2.90508
$331$	−3.02642e6	−1.51831	−0.759154	−	0.650911i	$-0.774387\pi$
$331$	−3.02642e6	−1.51831	−0.759154	+	0.650911i	$0.774387\pi$
$332$	−1.29185e6	−0.643232
$333$	466744.	0.230658
$334$	6.58596e6	3.23037
$335$	1.02822e6	0.500578
$336$	−1.96439e6	−0.949247
$337$	−998062.	−0.478721	−0.239361	−	0.970931i	$-0.576938\pi$
$337$	−998062.	−0.478721	−0.239361	+	0.970931i	$0.576938\pi$
$338$	−70919.5	−0.0337656
$339$	4.22732e6	1.99786
$340$	5.13182e6	2.40755
$341$	5.14194e6	2.39465
$342$	−1.24107e7	−5.73761
$343$	654973.	0.300599
$344$	1.20946e7	5.51056
$345$	−1.00433e6	−0.454284
$346$	−6.69944e6	−3.00849
$347$	1.42518e6	0.635398	0.317699	−	0.948192i	$-0.397090\pi$
$347$	1.42518e6	0.635398	0.317699	+	0.948192i	$0.397090\pi$
$348$	8.19899e6	3.62921
$349$	619354.	0.272192	0.136096	−	0.990696i	$-0.456544\pi$
$349$	619354.	0.272192	0.136096	+	0.990696i	$0.456544\pi$
$350$	−472778.	−0.206294
$351$	2.78012e6	1.20447
$352$	−1.52669e7	−6.56743
$353$	293605.	0.125408	0.0627042	−	0.998032i	$-0.480028\pi$
$353$	293605.	0.125408	0.0627042	+	0.998032i	$0.480028\pi$
$354$	9.26667e6	3.93021
$355$	−91307.4	−0.0384534
$356$	−4.81926e6	−2.01537
$357$	−970181.	−0.402886
$358$	2.24092e6	0.924101
$359$	−476814.	−0.195260	−0.0976299	−	0.995223i	$-0.531126\pi$
$359$	−476814.	−0.195260	−0.0976299	+	0.995223i	$0.531126\pi$
$360$	−7.81423e6	−3.17782
$361$	4.85412e6	1.96039
$362$	758897.	0.304377
$363$	7.33526e6	2.92179
$364$	−1.06366e6	−0.420774
$365$	−925277.	−0.363530
$366$	8.91475e6	3.47862
$367$	3.25933e6	1.26318	0.631588	−	0.775304i	$-0.282403\pi$
$367$	3.25933e6	1.26318	0.631588	+	0.775304i	$0.282403\pi$
$368$	−4.94878e6	−1.90493
$369$	−5.83507e6	−2.23090
$370$	−372703.	−0.141533
$371$	−218799.	−0.0825299
$372$	1.73851e7	6.51358
$373$	−2.24581e6	−0.835796	−0.417898	−	0.908494i	$-0.637233\pi$
$373$	−2.24581e6	−0.835796	−0.417898	+	0.908494i	$0.637233\pi$
$374$	−1.39859e7	−5.17026
$375$	−4.17915e6	−1.53465
$376$	−1.22896e7	−4.48300
$377$	2.23136e6	0.808568
$378$	975907.	0.351301
$379$	321197.	0.114861	0.0574307	−	0.998349i	$-0.481709\pi$
$379$	321197.	0.114861	0.0574307	+	0.998349i	$0.481709\pi$
$380$	7.26276e6	2.58014
$381$	−3.37664e6	−1.19171
$382$	−3.83938e6	−1.34618
$383$	−2.11279e6	−0.735969	−0.367985	−	0.929832i	$-0.619952\pi$
$383$	−2.11279e6	−0.735969	−0.367985	+	0.929832i	$0.619952\pi$
$384$	−1.67176e7	−5.78558
$385$	−402363.	−0.138346
$386$	5.58293e6	1.90719
$387$	−8.29616e6	−2.81579
$388$	1.79908e6	0.606697
$389$	4.29689e6	1.43973	0.719864	−	0.694115i	$-0.244204\pi$
$389$	4.29689e6	1.43973	0.719864	+	0.694115i	$0.244204\pi$
$390$	−5.28812e6	−1.76052
$391$	−2.44413e6	−0.808504
$392$	1.00248e7	3.29505
$393$	2.49243e6	0.814033
$394$	−6.51586e6	−2.11461
$395$	−1.75939e6	−0.567374
$396$	2.45596e7	7.87016
$397$	847721.	0.269946	0.134973	−	0.990849i	$-0.456905\pi$
$397$	847721.	0.269946	0.134973	+	0.990849i	$0.456905\pi$
$398$	−1.19816e6	−0.379147
$399$	−1.37304e6	−0.431768
$400$	−8.48791e6	−2.65247
$401$	1.86323e6	0.578637	0.289319	−	0.957233i	$-0.406571\pi$
$401$	1.86323e6	0.578637	0.289319	+	0.957233i	$0.406571\pi$
$402$	−9.47443e6	−2.92407
$403$	4.73137e6	1.45119
$404$	−1.39901e7	−4.26448
$405$	445830.	0.135062
$406$	783275.	0.235830
$407$	744395.	0.222750
$408$	−3.00501e7	−8.93708
$409$	3.55430e6	1.05062	0.525311	−	0.850910i	$-0.323949\pi$
$409$	3.55430e6	1.05062	0.525311	+	0.850910i	$0.323949\pi$
$410$	4.65940e6	1.36890
$411$	−9.02615e6	−2.63571
$412$	−4.04401e6	−1.17373
$413$	648783.	0.187165
$414$	5.85643e6	1.67932
$415$	−449663.	−0.128164
$416$	−1.40479e7	−3.97995
$417$	1.17380e6	0.330563
$418$	−1.97934e7	−5.54090
$419$	2.32671e6	0.647451	0.323726	−	0.946151i	$-0.395065\pi$
$419$	2.32671e6	0.647451	0.323726	+	0.946151i	$0.395065\pi$
$420$	−1.36040e6	−0.376309
$421$	2.22951e6	0.613062	0.306531	−	0.951861i	$-0.400832\pi$
$421$	2.22951e6	0.613062	0.306531	+	0.951861i	$0.400832\pi$
$422$	1.31348e7	3.59039
$423$	8.42992e6	2.29072
$424$	−6.77702e6	−1.83073
$425$	−4.19205e6	−1.12578
$426$	841347.	0.224621
$427$	624144.	0.165659
$428$	1.88168e7	4.96519
$429$	1.05619e7	2.77076
$430$	6.62462e6	1.72778
$431$	2.47651e6	0.642166	0.321083	−	0.947051i	$-0.395953\pi$
$431$	2.47651e6	0.642166	0.321083	+	0.947051i	$0.395953\pi$
$432$	1.75207e7	4.51692
$433$	1.77637e6	0.455318	0.227659	−	0.973741i	$-0.426893\pi$
$433$	1.77637e6	0.455318	0.227659	+	0.973741i	$0.426893\pi$
$434$	1.66085e6	0.423259
$435$	2.85387e6	0.723122
$436$	−1.76351e7	−4.44285
$437$	−3.45903e6	−0.866463
$438$	8.52591e6	2.12352
$439$	2.88674e6	0.714901	0.357450	−	0.933932i	$-0.383646\pi$
$439$	2.88674e6	0.714901	0.357450	+	0.933932i	$0.383646\pi$
$440$	−1.24627e7	−3.06887
$441$	−6.87642e6	−1.68370
$442$	−1.28692e7	−3.13325
$443$	7.28956e6	1.76479	0.882393	−	0.470514i	$-0.155931\pi$
$443$	7.28956e6	1.76479	0.882393	+	0.470514i	$0.155931\pi$
$444$	2.51683e6	0.605893
$445$	−1.67747e6	−0.401564
$446$	−8.39628e6	−1.99871
$447$	24578.1	0.00581809
$448$	−2.48777e6	−0.585619
$449$	−1.84894e6	−0.432819	−0.216410	−	0.976303i	$-0.569435\pi$
$449$	−1.84894e6	−0.432819	−0.216410	+	0.976303i	$0.569435\pi$
$450$	1.00447e7	2.33832
$451$	−9.30617e6	−2.15442
$452$	1.44254e7	3.32110
$453$	−5.14561e6	−1.17812
$454$	−7.02848e6	−1.60038
$455$	−370235.	−0.0838395
$456$	−4.25281e7	−9.57775
$457$	−3.86481e6	−0.865641	−0.432821	−	0.901480i	$-0.642482\pi$
$457$	−3.86481e6	−0.865641	−0.432821	+	0.901480i	$0.642482\pi$
$458$	1.30811e7	2.91394
$459$	8.65322e6	1.91710
$460$	−3.42719e6	−0.755169
$461$	−651986.	−0.142885	−0.0714424	−	0.997445i	$-0.522760\pi$
$461$	−651986.	−0.142885	−0.0714424	+	0.997445i	$0.522760\pi$
$462$	3.70755e6	0.808131
$463$	805899.	0.174714	0.0873570	−	0.996177i	$-0.472158\pi$
$463$	805899.	0.174714	0.0873570	+	0.996177i	$0.472158\pi$
$464$	1.40623e7	3.03224
$465$	6.05134e6	1.29783
$466$	8.71302e6	1.85868
$467$	−2.26659e6	−0.480928	−0.240464	−	0.970658i	$-0.577300\pi$
$467$	−2.26659e6	−0.480928	−0.240464	+	0.970658i	$0.577300\pi$
$468$	2.25986e7	4.76943
$469$	−663328.	−0.139250
$470$	−6.73143e6	−1.40560
$471$	1.98202e6	0.411677
$472$	2.00952e7	4.15181
$473$	−1.32313e7	−2.71925
$474$	1.62118e7	3.31425
$475$	−5.93275e6	−1.20648
$476$	−3.31067e6	−0.669728
$477$	4.64862e6	0.935467
$478$	8.04891e6	1.61127
$479$	1.73557e6	0.345624	0.172812	−	0.984955i	$-0.444715\pi$
$479$	1.73557e6	0.345624	0.172812	+	0.984955i	$0.444715\pi$
$480$	−1.79670e7	−3.55937
$481$	684956.	0.134990
$482$	8.09900e6	1.58787
$483$	647917.	0.126372
$484$	2.50310e7	4.85697
$485$	626218.	0.120885
$486$	7.92181e6	1.52137
$487$	−7.77965e6	−1.48641	−0.743203	−	0.669066i	$-0.766694\pi$
$487$	−7.77965e6	−1.48641	−0.743203	+	0.669066i	$0.766694\pi$
$488$	1.93320e7	3.67475
$489$	3.92825e6	0.742895
$490$	5.49093e6	1.03313
$491$	−140027.	−0.0262125	−0.0131063	−	0.999914i	$-0.504172\pi$
$491$	−140027.	−0.0262125	−0.0131063	+	0.999914i	$0.504172\pi$
$492$	−3.14645e7	−5.86014
$493$	6.94518e6	1.28696
$494$	−1.82129e7	−3.35786
$495$	8.54862e6	1.56813
$496$	2.98177e7	5.44215
$497$	58904.8	0.0106969
$498$	4.14339e6	0.748656
$499$	−4.60996e6	−0.828792	−0.414396	−	0.910097i	$-0.636007\pi$
$499$	−4.60996e6	−0.828792	−0.414396	+	0.910097i	$0.636007\pi$
$500$	−1.42610e7	−2.55109
$501$	−1.54805e7	−2.75543
$502$	−1.45899e7	−2.58400
$503$	6.52133e6	1.14925	0.574627	−	0.818415i	$-0.305147\pi$
$503$	6.52133e6	1.14925	0.574627	+	0.818415i	$0.305147\pi$
$504$	5.04116e6	0.884004
$505$	−4.86961e6	−0.849700
$506$	9.34023e6	1.62174
$507$	166698.	0.0288012
$508$	−1.15225e7	−1.98102
$509$	1.76686e6	0.302278	0.151139	−	0.988513i	$-0.451706\pi$
$509$	1.76686e6	0.302278	0.151139	+	0.988513i	$0.451706\pi$
$510$	−1.64594e7	−2.80214
$511$	596920.	0.101126
$512$	−1.28486e7	−2.16612
$513$	1.22464e7	2.05454
$514$	−2.43798e6	−0.407025
$515$	−1.40762e6	−0.233867
$516$	−4.47354e7	−7.39651
$517$	1.34446e7	2.21219
$518$	240440.	0.0393716
$519$	1.57472e7	2.56617
$520$	−1.14675e7	−1.85978
$521$	−7.68825e6	−1.24089	−0.620445	−	0.784250i	$-0.713048\pi$
$521$	−7.68825e6	−1.24089	−0.620445	+	0.784250i	$0.713048\pi$
$522$	−1.66415e7	−2.67311
$523$	−3.82780e6	−0.611920	−0.305960	−	0.952044i	$-0.598977\pi$
$523$	−3.82780e6	−0.611920	−0.305960	+	0.952044i	$0.598977\pi$
$524$	8.50524e6	1.35319
$525$	1.11128e6	0.175964
$526$	−6.81988e6	−1.07476
$527$	1.47265e7	2.30980
$528$	6.65626e7	10.3907
$529$	−4.80408e6	−0.746399
$530$	−3.71200e6	−0.574009
$531$	−1.37841e7	−2.12149
$532$	−4.68539e6	−0.717739
$533$	−8.56309e6	−1.30561
$534$	1.54569e7	2.34569
$535$	6.54968e6	0.989317
$536$	−2.05457e7	−3.08894
$537$	−5.26734e6	−0.788235
$538$	−1.61260e7	−2.40199
$539$	−1.09670e7	−1.62598
$540$	1.21337e7	1.79064
$541$	4.31598e6	0.633995	0.316997	−	0.948426i	$-0.397325\pi$
$541$	4.31598e6	0.633995	0.316997	+	0.948426i	$0.397325\pi$
$542$	1.76618e7	2.58248
$543$	−1.78381e6	−0.259626
$544$	−4.37245e7	−6.33472
$545$	−6.13836e6	−0.885241
$546$	3.41150e6	0.489739
$547$	299209.	0.0427569
$547$	299209.	0.0427569
$548$	−3.08011e7	−4.38142
$549$	−1.32606e7	−1.87773
$550$	1.60199e7	2.25815
$551$	9.82908e6	1.37922
$552$	2.00684e7	2.80327
$553$	1.13503e6	0.157832
$554$	5.97924e6	0.827697
$555$	876047.	0.120724
$556$	4.00551e6	0.549503
$557$	−8.22295e6	−1.12303	−0.561513	−	0.827468i	$-0.689780\pi$
$557$	−8.22295e6	−1.12303	−0.561513	+	0.827468i	$0.689780\pi$
$558$	−3.52865e7	−4.79759
$559$	−1.21748e7	−1.64790
$560$	−2.33327e6	−0.314409
$561$	3.28743e7	4.41010
$562$	2.05562e7	2.74538
$563$	2.55562e6	0.339802	0.169901	−	0.985461i	$-0.445655\pi$
$563$	2.55562e6	0.339802	0.169901	+	0.985461i	$0.445655\pi$
$564$	4.54567e7	6.01728
$565$	5.02114e6	0.661731
$566$	4.41373e6	0.579115
$567$	−287617.	−0.0375713
$568$	1.82450e6	0.237286
$569$	−1.32348e7	−1.71370	−0.856852	−	0.515562i	$-0.827583\pi$
$569$	−1.32348e7	−1.71370	−0.856852	+	0.515562i	$0.827583\pi$
$570$	−2.32940e7	−3.00302
$571$	734528.	0.0942796	0.0471398	−	0.998888i	$-0.484989\pi$
$571$	734528.	0.0942796	0.0471398	+	0.998888i	$0.484989\pi$
$572$	3.60417e7	4.60591
$573$	9.02456e6	1.14826
$574$	−3.00590e6	−0.380798
$575$	2.79958e6	0.353121
$576$	5.28553e7	6.63792
$577$	1.34130e7	1.67721	0.838603	−	0.544743i	$-0.183373\pi$
$577$	1.34130e7	1.67721	0.838603	+	0.544743i	$0.183373\pi$
$578$	−2.45156e7	−3.05228
$579$	−1.31228e7	−1.62679
$580$	9.73863e6	1.20206
$581$	290089.	0.0356526
$582$	−5.77024e6	−0.706133
$583$	7.41394e6	0.903395
$584$	1.84888e7	2.24325
$585$	7.86603e6	0.950311
$586$	−8.62228e6	−1.03724
$587$	−9.29909e6	−1.11390	−0.556949	−	0.830547i	$-0.688028\pi$
$587$	−9.29909e6	−1.11390	−0.556949	+	0.830547i	$0.688028\pi$
$588$	−3.70797e7	−4.42276
$589$	2.08415e7	2.47538
$590$	1.10068e7	1.30176
$591$	1.53157e7	1.80371
$592$	4.31669e6	0.506228
$593$	2.62381e6	0.306405	0.153203	−	0.988195i	$-0.451041\pi$
$593$	2.62381e6	0.306405	0.153203	+	0.988195i	$0.451041\pi$
$594$	−3.30683e7	−3.84543
$595$	−1.15237e6	−0.133444
$596$	83871.1	0.00967156
$597$	2.81631e6	0.323403
$598$	8.59443e6	0.982798
$599$	3.00423e6	0.342111	0.171055	−	0.985261i	$-0.445282\pi$
$599$	3.00423e6	0.342111	0.171055	+	0.985261i	$0.445282\pi$
$600$	3.44203e7	3.90334
$601$	9.54302e6	1.07770	0.538852	−	0.842400i	$-0.318858\pi$
$601$	9.54302e6	1.07770	0.538852	+	0.842400i	$0.318858\pi$
$602$	−4.27371e6	−0.480633
$603$	1.40931e7	1.57839
$604$	−1.75590e7	−1.95843
$605$	8.71271e6	0.967753
$606$	4.48707e7	4.96342
$607$	5.39364e6	0.594169	0.297085	−	0.954851i	$-0.403986\pi$
$607$	5.39364e6	0.594169	0.297085	+	0.954851i	$0.403986\pi$
$608$	−6.18806e7	−6.78884
$609$	−1.84111e6	−0.201157
$610$	1.05888e7	1.15218
$611$	1.23711e7	1.34062
$612$	7.03387e7	7.59130
$613$	−1.71495e7	−1.84332	−0.921660	−	0.387999i	$-0.873167\pi$
$613$	−1.71495e7	−1.84332	−0.921660	+	0.387999i	$0.873167\pi$
$614$	−318967.	−0.0341448
$615$	−1.09520e7	−1.16764
$616$	8.03998e6	0.853696
$617$	−1.27165e7	−1.34479	−0.672396	−	0.740191i	$-0.734735\pi$
$617$	−1.27165e7	−1.34479	−0.672396	+	0.740191i	$0.734735\pi$
$618$	1.29704e7	1.36610
$619$	−6.42419e6	−0.673894	−0.336947	−	0.941524i	$-0.609394\pi$
$619$	−6.42419e6	−0.673894	−0.336947	+	0.941524i	$0.609394\pi$
$620$	2.06497e7	2.15742
$621$	−5.77889e6	−0.601333
$622$	−1.60251e6	−0.166083
$623$	1.08218e6	0.111707
$624$	6.12477e7	6.29692
$625$	1.88382e6	0.192903
$626$	−1.73085e7	−1.76532
$627$	4.65249e7	4.72625
$628$	6.76350e6	0.684341
$629$	2.13195e6	0.214857
$630$	2.76121e6	0.277171
$631$	−5.40809e6	−0.540718	−0.270359	−	0.962760i	$-0.587142\pi$
$631$	−5.40809e6	−0.540718	−0.270359	+	0.962760i	$0.587142\pi$
$632$	3.51560e7	3.50112
$633$	−3.08737e7	−3.06252
$634$	−2.43290e7	−2.40382
$635$	−4.01072e6	−0.394719
$636$	2.50668e7	2.45729
$637$	−1.00913e7	−0.985366
$638$	−2.65410e7	−2.58146
$639$	−1.25149e6	−0.121249
$640$	−1.98569e7	−1.91630
$641$	7.46913e6	0.718001	0.359001	−	0.933337i	$-0.383118\pi$
$641$	7.46913e6	0.718001	0.359001	+	0.933337i	$0.383118\pi$
$642$	−6.03516e7	−5.77898
$643$	7.70734e6	0.735152	0.367576	−	0.929994i	$-0.380188\pi$
$643$	7.70734e6	0.735152	0.367576	+	0.929994i	$0.380188\pi$
$644$	2.21097e6	0.210072
$645$	−1.55713e7	−1.47376
$646$	−5.66883e7	−5.34456
$647$	1.01152e7	0.949979	0.474990	−	0.879991i	$-0.342452\pi$
$647$	1.01152e7	0.949979	0.474990	+	0.879991i	$0.342452\pi$
$648$	−8.90855e6	−0.833431
$649$	−2.19838e7	−2.04876
$650$	1.47407e7	1.36847
$651$	−3.90387e6	−0.361030
$652$	1.34049e7	1.23493
$653$	−1.18048e7	−1.08336	−0.541681	−	0.840584i	$-0.682212\pi$
$653$	−1.18048e7	−1.08336	−0.541681	+	0.840584i	$0.682212\pi$
$654$	5.65616e7	5.17103
$655$	2.96047e6	0.269623
$656$	−5.39657e7	−4.89619
$657$	−1.26822e7	−1.14625
$658$	4.34262e6	0.391009
$659$	1.48774e6	0.133448	0.0667241	−	0.997771i	$-0.478745\pi$
$659$	1.48774e6	0.133448	0.0667241	+	0.997771i	$0.478745\pi$
$660$	4.60968e7	4.11918
$661$	6.49819e6	0.578481	0.289240	−	0.957257i	$-0.406597\pi$
$661$	6.49819e6	0.578481	0.289240	+	0.957257i	$0.406597\pi$
$662$	3.31235e7	2.93759
$663$	3.02493e7	2.67258
$664$	8.98513e6	0.790868
$665$	−1.63087e6	−0.143010
$666$	−5.10840e6	−0.446272
$667$	−4.63821e6	−0.403678
$668$	−5.28259e7	−4.58043
$669$	1.97357e7	1.70485
$670$	−1.12536e7	−0.968509
$671$	−2.11489e7	−1.81335
$672$	1.15910e7	0.990141
$673$	−1.46772e7	−1.24912	−0.624562	−	0.780975i	$-0.714722\pi$
$673$	−1.46772e7	−1.24912	−0.624562	+	0.780975i	$0.714722\pi$
$674$	1.09235e7	0.926220
$675$	−9.91166e6	−0.837311
$676$	568845.	0.0478770
$677$	−5.64709e6	−0.473536	−0.236768	−	0.971566i	$-0.576088\pi$
$677$	−5.64709e6	−0.473536	−0.236768	+	0.971566i	$0.576088\pi$
$678$	−4.62670e7	−3.86543
$679$	−403989.	−0.0336275
$680$	−3.56930e7	−2.96013
$681$	1.65206e7	1.36508
$682$	−5.62774e7	−4.63311
$683$	−1.40297e7	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$683$	−1.40297e7	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$684$	9.95461e7	8.13549
$685$	−1.07211e7	−0.872999
$686$	−7.16852e6	−0.581593
$687$	−3.07474e7	−2.48552
$688$	−7.67271e7	−6.17984
$689$	6.82195e6	0.547470
$690$	1.09921e7	0.878939
$691$	−8.47377e6	−0.675121	−0.337560	−	0.941304i	$-0.609602\pi$
$691$	−8.47377e6	−0.675121	−0.337560	+	0.941304i	$0.609602\pi$
$692$	5.37361e7	4.26581
$693$	−5.51494e6	−0.436222
$694$	−1.55983e7	−1.22935
$695$	1.39422e6	0.109489
$696$	−5.70259e7	−4.46220
$697$	−2.66529e7	−2.07808
$698$	−6.77869e6	−0.526632
$699$	−2.04802e7	−1.58541
$700$	3.79215e6	0.292509
$701$	1.36559e7	1.04960	0.524802	−	0.851225i	$-0.324139\pi$
$701$	1.36559e7	1.04960	0.524802	+	0.851225i	$0.324139\pi$
$702$	−3.04278e7	−2.33039
$703$	3.01721e6	0.230260
$704$	8.42971e7	6.41034
$705$	1.58224e7	1.19895
$706$	−3.21344e6	−0.242638
$707$	3.14151e6	0.236369
$708$	−7.43279e7	−5.57274
$709$	2.34510e7	1.75204	0.876022	−	0.482272i	$-0.160188\pi$
$709$	2.34510e7	1.75204	0.876022	+	0.482272i	$0.160188\pi$
$710$	999338.	0.0743989
$711$	−2.41149e7	−1.78900
$712$	3.35191e7	2.47795
$713$	−9.83483e6	−0.724508
$714$	1.06184e7	0.779496
$715$	1.25453e7	0.917730
$716$	−1.79744e7	−1.31030
$717$	−1.89192e7	−1.37437
$718$	5.21862e6	0.377785
$719$	9.13374e6	0.658911	0.329455	−	0.944171i	$-0.393135\pi$
$719$	9.13374e6	0.658911	0.329455	+	0.944171i	$0.393135\pi$
$720$	4.95728e7	3.56379
$721$	908093.	0.0650567
$722$	−5.31272e7	−3.79292
$723$	−1.90369e7	−1.35441
$724$	−6.08710e6	−0.431583
$725$	−7.95522e6	−0.562092
$726$	−8.02827e7	−5.65302
$727$	−1.21170e7	−0.850276	−0.425138	−	0.905128i	$-0.639774\pi$
$727$	−1.21170e7	−0.850276	−0.425138	+	0.905128i	$0.639774\pi$
$728$	7.39800e6	0.517352
$729$	−2.21658e7	−1.54477
$730$	1.01269e7	0.703349
$731$	−3.78943e7	−2.62289
$732$	−7.15051e7	−4.93241
$733$	1.55264e7	1.06736	0.533682	−	0.845686i	$-0.320808\pi$
$733$	1.55264e7	1.06736	0.533682	+	0.845686i	$0.320808\pi$
$734$	−3.56726e7	−2.44397
$735$	−1.29066e7	−0.881236
$736$	2.92006e7	1.98700
$737$	2.24766e7	1.52427
$738$	6.38635e7	4.31630
$739$	2.19704e7	1.47988	0.739942	−	0.672671i	$-0.234853\pi$
$739$	2.19704e7	1.47988	0.739942	+	0.672671i	$0.234853\pi$
$740$	2.98945e6	0.200683
$741$	4.28100e7	2.86417
$742$	2.39471e6	0.159677
$743$	1.16780e7	0.776064	0.388032	−	0.921646i	$-0.373155\pi$
$743$	1.16780e7	0.776064	0.388032	+	0.921646i	$0.373155\pi$
$744$	−1.20917e8	−8.00859
$745$	29193.5	0.00192706
$746$	2.45798e7	1.61708
$747$	−6.16325e6	−0.404118
$748$	1.12181e8	7.33103
$749$	−4.22537e6	−0.275207
$750$	4.57398e7	2.96921
$751$	1.47704e7	0.955634	0.477817	−	0.878459i	$-0.341428\pi$
$751$	1.47704e7	0.955634	0.477817	+	0.878459i	$0.341428\pi$
$752$	7.79642e7	5.02748
$753$	3.42938e7	2.20409
$754$	−2.44217e7	−1.56440
$755$	−6.11187e6	−0.390218
$756$	−7.82774e6	−0.498118
$757$	−1.61006e7	−1.02118	−0.510589	−	0.859825i	$-0.670573\pi$
$757$	−1.61006e7	−1.02118	−0.510589	+	0.859825i	$0.670573\pi$
$758$	−3.51543e6	−0.222231
$759$	−2.19545e7	−1.38331
$760$	−5.05142e7	−3.17234
$761$	−2.51712e7	−1.57558	−0.787792	−	0.615942i	$-0.788776\pi$
$761$	−2.51712e7	−1.57558	−0.787792	+	0.615942i	$0.788776\pi$
$762$	3.69565e7	2.30570
$763$	3.96002e6	0.246255
$764$	3.07956e7	1.90878
$765$	2.44832e7	1.51257
$766$	2.31240e7	1.42394
$767$	−2.02284e7	−1.24158
$768$	7.90796e7	4.83795
$769$	−1.15656e6	−0.0705267	−0.0352633	−	0.999378i	$-0.511227\pi$
$769$	−1.15656e6	−0.0705267	−0.0352633	+	0.999378i	$0.511227\pi$
$770$	4.40377e6	0.267669
$771$	5.73052e6	0.347183
$772$	−4.47807e7	−2.70425
$773$	1.54484e6	0.0929899	0.0464949	−	0.998919i	$-0.485195\pi$
$773$	1.54484e6	0.0929899	0.0464949	+	0.998919i	$0.485195\pi$
$774$	9.07995e7	5.44792
$775$	−1.68682e7	−1.00882
$776$	−1.25130e7	−0.745948
$777$	−565160.	−0.0335830
$778$	−4.70285e7	−2.78556
$779$	−3.77201e7	−2.22705
$780$	4.24160e7	2.49628
$781$	−1.99597e6	−0.117092
$782$	2.67504e7	1.56428
$783$	1.64212e7	0.957192
$784$	−6.35966e7	−3.69525
$785$	2.35421e6	0.136355
$786$	−2.72791e7	−1.57497
$787$	−5.51495e6	−0.317398	−0.158699	−	0.987327i	$-0.550730\pi$
$787$	−5.51495e6	−0.317398	−0.158699	+	0.987327i	$0.550730\pi$
$788$	5.22636e7	2.99836
$789$	1.60303e7	0.916746
$790$	1.92561e7	1.09774
$791$	−3.23927e6	−0.184080
$792$	−1.70818e8	−9.67655
$793$	−1.94602e7	−1.09891
$794$	−9.27811e6	−0.522286
$795$	8.72515e6	0.489615
$796$	9.61045e6	0.537602
$797$	−7.15247e6	−0.398851	−0.199425	−	0.979913i	$-0.563908\pi$
$797$	−7.15247e6	−0.398851	−0.199425	+	0.979913i	$0.563908\pi$
$798$	1.50276e7	0.835376
$799$	3.85053e7	2.13380
$800$	5.00834e7	2.76674
$801$	−2.29920e7	−1.26618
$802$	−2.03927e7	−1.11954
$803$	−2.02264e7	−1.10696
$804$	7.59943e7	4.14611
$805$	769586.	0.0418569
$806$	−5.17837e7	−2.80773
$807$	3.79047e7	2.04884
$808$	9.73041e7	5.24328
$809$	7.31368e6	0.392884	0.196442	−	0.980515i	$-0.437061\pi$
$809$	7.31368e6	0.392884	0.196442	+	0.980515i	$0.437061\pi$
$810$	−4.87951e6	−0.261315
$811$	2.56173e6	0.136767	0.0683836	−	0.997659i	$-0.478216\pi$
$811$	2.56173e6	0.136767	0.0683836	+	0.997659i	$0.478216\pi$
$812$	−6.28264e6	−0.334389
$813$	−4.15145e7	−2.20279
$814$	−8.14723e6	−0.430972
$815$	4.66592e6	0.246061
$816$	1.90635e8	10.0225
$817$	−5.36295e7	−2.81092
$818$	−3.89010e7	−2.03272
$819$	−5.07458e6	−0.264356
$820$	−3.73730e7	−1.94099
$821$	−4.39755e6	−0.227695	−0.113847	−	0.993498i	$-0.536317\pi$
$821$	−4.39755e6	−0.227695	−0.113847	+	0.993498i	$0.536317\pi$
$822$	9.87891e7	5.09952
$823$	1.76942e6	0.0910608	0.0455304	−	0.998963i	$-0.485502\pi$
$823$	1.76942e6	0.0910608	0.0455304	+	0.998963i	$0.485502\pi$
$824$	2.81270e7	1.44313
$825$	−3.76552e7	−1.92615
$826$	−7.10077e6	−0.362123
$827$	2.75832e7	1.40243	0.701216	−	0.712949i	$-0.252641\pi$
$827$	2.75832e7	1.40243	0.701216	+	0.712949i	$0.252641\pi$
$828$	−4.69744e7	−2.38114
$829$	1.19999e6	0.0606444	0.0303222	−	0.999540i	$-0.490347\pi$
$829$	1.19999e6	0.0606444	0.0303222	+	0.999540i	$0.490347\pi$
$830$	4.92145e6	0.247969
$831$	−1.40543e7	−0.706005
$832$	7.75661e7	3.88476
$833$	−3.14094e7	−1.56836
$834$	−1.28470e7	−0.639566
$835$	−1.83874e7	−0.912652
$836$	1.58763e8	7.85657
$837$	3.48193e7	1.71793
$838$	−2.54653e7	−1.25267
$839$	3.89076e7	1.90823	0.954113	−	0.299445i	$-0.0968016\pi$
$839$	3.89076e7	1.90823	0.954113	+	0.299445i	$0.0968016\pi$
$840$	9.46191e6	0.462680
$841$	−7.33133e6	−0.357431
$842$	−2.44015e7	−1.18614
$843$	−4.83180e7	−2.34175
$844$	−1.05354e8	−5.09091
$845$	198001.	0.00953952
$846$	−9.22635e7	−4.43204
$847$	−5.62079e6	−0.269209
$848$	4.29928e7	2.05308
$849$	−1.03746e7	−0.493971
$850$	4.58810e7	2.17814
$851$	−1.42378e6	−0.0673937
$852$	−6.74843e6	−0.318496
$853$	−2.00493e7	−0.943468	−0.471734	−	0.881741i	$-0.656372\pi$
$853$	−2.00493e7	−0.943468	−0.471734	+	0.881741i	$0.656372\pi$
$854$	−6.83111e6	−0.320514
$855$	3.46496e7	1.62100
$856$	−1.30875e8	−6.10482
$857$	1.12572e7	0.523573	0.261786	−	0.965126i	$-0.415688\pi$
$857$	1.12572e7	0.523573	0.261786	+	0.965126i	$0.415688\pi$
$858$	−1.15598e8	−5.36081
$859$	−1.17965e7	−0.545470	−0.272735	−	0.962089i	$-0.587928\pi$
$859$	−1.17965e7	−0.545470	−0.272735	+	0.962089i	$0.587928\pi$
$860$	−5.31360e7	−2.44987
$861$	7.06544e6	0.324812
$862$	−2.71048e7	−1.24245
$863$	2.37100e7	1.08369	0.541845	−	0.840478i	$-0.317726\pi$
$863$	2.37100e7	1.08369	0.541845	+	0.840478i	$0.317726\pi$
$864$	−1.03382e8	−4.71151
$865$	1.87043e7	0.849964
$866$	−1.94420e7	−0.880939
$867$	5.76246e7	2.60352
$868$	−1.33217e7	−0.600150
$869$	−3.84600e7	−1.72767
$870$	−3.12350e7	−1.39908
$871$	2.06819e7	0.923731
$872$	1.22656e8	5.46259
$873$	8.58317e6	0.381164
$874$	3.78582e7	1.67642
$875$	3.20236e6	0.141400
$876$	−6.83863e7	−3.01098
$877$	−1.63079e7	−0.715977	−0.357988	−	0.933726i	$-0.616537\pi$
$877$	−1.63079e7	−0.715977	−0.357988	+	0.933726i	$0.616537\pi$
$878$	−3.15946e7	−1.38318
$879$	2.02669e7	0.884738
$880$	7.90620e7	3.44161
$881$	−1.57171e7	−0.682231	−0.341115	−	0.940021i	$-0.610805\pi$
$881$	−1.57171e7	−0.682231	−0.341115	+	0.940021i	$0.610805\pi$
$882$	7.52607e7	3.25759
$883$	3.29712e7	1.42309	0.711546	−	0.702640i	$-0.247995\pi$
$883$	3.29712e7	1.42309	0.711546	+	0.702640i	$0.247995\pi$
$884$	1.03223e8	4.44271
$885$	−2.58718e7	−1.11037
$886$	−7.97825e7	−3.41447
$887$	−2.66821e7	−1.13870	−0.569352	−	0.822094i	$-0.692806\pi$
$887$	−2.66821e7	−1.13870	−0.569352	+	0.822094i	$0.692806\pi$
$888$	−1.75051e7	−0.744959
$889$	2.58742e6	0.109802
$890$	1.83595e7	0.776937
$891$	9.74579e6	0.411266
$892$	6.73465e7	2.83402
$893$	5.44942e7	2.28677
$894$	−269002.	−0.0112567
$895$	−6.25647e6	−0.261079
$896$	1.28102e7	0.533073
$897$	−2.02014e7	−0.838303
$898$	2.02362e7	0.837409
$899$	2.79464e7	1.15326
$900$	−8.05681e7	−3.31556
$901$	2.12335e7	0.871384
$902$	1.01854e8	4.16832
$903$	1.00455e7	0.409968
$904$	−1.00332e8	−4.08337
$905$	−2.11878e6	−0.0859931
$906$	5.63175e7	2.27941
$907$	4.20572e7	1.69755	0.848774	−	0.528756i	$-0.177341\pi$
$907$	4.20572e7	1.69755	0.848774	+	0.528756i	$0.177341\pi$
$908$	5.63754e7	2.26921
$909$	−6.67447e7	−2.67921
$910$	4.05213e6	0.162211
$911$	−7.27303e6	−0.290349	−0.145174	−	0.989406i	$-0.546374\pi$
$911$	−7.27303e6	−0.290349	−0.145174	+	0.989406i	$0.546374\pi$
$912$	2.69794e8	10.7410
$913$	−9.82956e6	−0.390263
$914$	4.22995e7	1.67482
$915$	−2.48892e7	−0.982785
$916$	−1.04923e8	−4.13174
$917$	−1.90988e6	−0.0750035
$918$	−9.47074e7	−3.70917
$919$	127847.	0.00499345	0.00249672	−	0.999997i	$-0.499205\pi$
$919$	127847.	0.00499345	0.00249672	+	0.999997i	$0.499205\pi$
$920$	2.38369e7	0.928497
$921$	749739.	0.0291247
$922$	7.13584e6	0.276451
$923$	−1.83659e6	−0.0709591
$924$	−2.97382e7	−1.14587
$925$	−2.44200e6	−0.0938406
$926$	−8.82037e6	−0.338033
$927$	−1.92934e7	−0.737411
$928$	−8.29757e7	−3.16287
$929$	−3.39499e7	−1.29062	−0.645312	−	0.763919i	$-0.723273\pi$
$929$	−3.39499e7	−1.29062	−0.645312	+	0.763919i	$0.723273\pi$
$930$	−6.62304e7	−2.51102
$931$	−4.44518e7	−1.68080
$932$	−6.98871e7	−2.63546
$933$	3.76675e6	0.141665
$934$	2.48073e7	0.930490
$935$	3.90475e7	1.46071
$936$	−1.57178e8	−5.86412
$937$	−8.60183e6	−0.320068	−0.160034	−	0.987112i	$-0.551160\pi$
$937$	−8.60183e6	−0.320068	−0.160034	+	0.987112i	$0.551160\pi$
$938$	7.25997e6	0.269419
$939$	4.06841e7	1.50578
$940$	5.39927e7	1.99304
$941$	1.07504e7	0.395777	0.197889	−	0.980224i	$-0.436592\pi$
$941$	1.07504e7	0.395777	0.197889	+	0.980224i	$0.436592\pi$
$942$	−2.16928e7	−0.796503
$943$	1.77996e7	0.651825
$944$	−1.27482e8	−4.65607
$945$	−2.72465e6	−0.0992501
$946$	1.44813e8	5.26114
$947$	−1.53376e7	−0.555754	−0.277877	−	0.960617i	$-0.589631\pi$
$947$	−1.53376e7	−0.555754	−0.277877	+	0.960617i	$0.589631\pi$
$948$	−1.30035e8	−4.69936
$949$	−1.86114e7	−0.670831
$950$	6.49325e7	2.33428
$951$	5.71859e7	2.05040
$952$	2.30265e7	0.823447
$953$	−6.41743e6	−0.228891	−0.114446	−	0.993430i	$-0.536509\pi$
$953$	−6.41743e6	−0.228891	−0.114446	+	0.993430i	$0.536509\pi$
$954$	−5.08781e7	−1.80992
$955$	1.07192e7	0.380325
$956$	−6.45602e7	−2.28465
$957$	6.23852e7	2.20192
$958$	−1.89955e7	−0.668707
$959$	6.91647e6	0.242850
$960$	9.92057e7	3.47423
$961$	3.06283e7	1.06983
$962$	−7.49668e6	−0.261175
$963$	8.97723e7	3.11944
$964$	−6.49620e7	−2.25147
$965$	−1.55871e7	−0.538823
$966$	−7.09130e6	−0.244502
$967$	2.16903e7	0.745934	0.372967	−	0.927845i	$-0.378340\pi$
$967$	2.16903e7	0.745934	0.372967	+	0.927845i	$0.378340\pi$
$968$	−1.74097e8	−5.97176
$969$	1.33247e8	4.55878
$970$	−6.85380e6	−0.233885
$971$	6.17323e6	0.210118	0.105059	−	0.994466i	$-0.466497\pi$
$971$	6.17323e6	0.210118	0.105059	+	0.994466i	$0.466497\pi$
$972$	−6.35408e7	−2.15718
$973$	−899448.	−0.0304575
$974$	8.51464e7	2.87587
$975$	−3.46485e7	−1.16727
$976$	−1.22641e8	−4.12107
$977$	−1.31766e7	−0.441639	−0.220820	−	0.975315i	$-0.570873\pi$
$977$	−1.31766e7	−0.441639	−0.220820	+	0.975315i	$0.570873\pi$
$978$	−4.29938e7	−1.43734
$979$	−3.66692e7	−1.22277
$980$	−4.40427e7	−1.46490
$981$	−8.41347e7	−2.79128
$982$	1.53256e6	0.0507154
$983$	−2.46907e7	−0.814986	−0.407493	−	0.913208i	$-0.633597\pi$
$983$	−2.46907e7	−0.814986	−0.407493	+	0.913208i	$0.633597\pi$
$984$	2.18843e8	7.20517
$985$	1.81917e7	0.597425
$986$	−7.60133e7	−2.48999
$987$	−1.02074e7	−0.333521
$988$	1.46086e8	4.76119
$989$	2.53070e7	0.822717
$990$	−9.35626e7	−3.03399
$991$	−4.96925e7	−1.60734	−0.803669	−	0.595077i	$-0.797122\pi$
$991$	−4.96925e7	−1.60734	−0.803669	+	0.595077i	$0.797122\pi$
$992$	−1.75941e8	−5.67660
$993$	−7.78576e7	−2.50569
$994$	−644699.	−0.0206962
$995$	3.34517e6	0.107117
$996$	−3.32341e7	−1.06154
$997$	3.58410e6	0.114194	0.0570968	−	0.998369i	$-0.481816\pi$
$997$	3.58410e6	0.114194	0.0570968	+	0.998369i	$0.481816\pi$
$998$	5.04549e7	1.60353
$999$	5.04076e6	0.159802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.6.a.b.1.2	✓	117

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.6.a.b.1.2	✓	117	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-10.9448 q^{2} +25.7259 q^{3} +87.7879 q^{4} +30.5569 q^{5} -281.564 q^{6} -19.7130 q^{7} -610.585 q^{8} +418.824 q^{9} +O(q^{10})\)	\(q-10.9448 q^{2} +25.7259 q^{3} +87.7879 q^{4} +30.5569 q^{5} -281.564 q^{6} -19.7130 q^{7} -610.585 q^{8} +418.824 q^{9} -334.438 q^{10} +667.969 q^{11} +2258.42 q^{12} +614.632 q^{13} +215.754 q^{14} +786.104 q^{15} +3873.50 q^{16} +1913.06 q^{17} -4583.93 q^{18} +2707.44 q^{19} +2682.52 q^{20} -507.136 q^{21} -7310.76 q^{22} -1277.60 q^{23} -15707.9 q^{24} -2191.28 q^{25} -6727.00 q^{26} +4523.23 q^{27} -1730.56 q^{28} +3630.40 q^{29} -8603.72 q^{30} +7697.88 q^{31} -22855.8 q^{32} +17184.1 q^{33} -20938.0 q^{34} -602.368 q^{35} +36767.6 q^{36} +1114.42 q^{37} -29632.3 q^{38} +15812.0 q^{39} -18657.6 q^{40} -13932.0 q^{41} +5550.48 q^{42} -19808.2 q^{43} +58639.5 q^{44} +12797.9 q^{45} +13983.0 q^{46} +20127.6 q^{47} +99649.3 q^{48} -16418.4 q^{49} +23983.0 q^{50} +49215.3 q^{51} +53957.2 q^{52} +11099.2 q^{53} -49505.7 q^{54} +20411.0 q^{55} +12036.5 q^{56} +69651.4 q^{57} -39733.9 q^{58} -32911.4 q^{59} +69010.4 q^{60} -31661.5 q^{61} -84251.5 q^{62} -8256.28 q^{63} +126199. q^{64} +18781.2 q^{65} -188076. q^{66} +33649.3 q^{67} +167943. q^{68} -32867.5 q^{69} +6592.77 q^{70} -2988.12 q^{71} -255727. q^{72} -30280.5 q^{73} -12197.0 q^{74} -56372.7 q^{75} +237680. q^{76} -13167.7 q^{77} -173058. q^{78} -57577.6 q^{79} +118362. q^{80} +14590.2 q^{81} +152483. q^{82} -14715.6 q^{83} -44520.4 q^{84} +58457.1 q^{85} +216796. q^{86} +93395.5 q^{87} -407851. q^{88} -54896.7 q^{89} -140070. q^{90} -12116.3 q^{91} -112158. q^{92} +198035. q^{93} -220292. q^{94} +82730.8 q^{95} -587986. q^{96} +20493.5 q^{97} +179695. q^{98} +279761. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9}+O(q^{10}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9	\( 117 q + 24 q^{2} + 100 q^{3} + 1962 q^{4} + 749 q^{5} + 306 q^{6} + 393 q^{7} + 1152 q^{8} + 10671 q^{9} + 850 q^{10} + 1798 q^{11} + 5361 q^{12} + 4419 q^{13} + 3847 q^{14} + 1913 q^{15} + 34722 q^{16} + 15252 q^{17} + 2367 q^{18} + 1052 q^{19} + 23568 q^{20} + 9212 q^{21} + 9176 q^{22} + 18178 q^{23} + 15983 q^{24} + 84312 q^{25} + 21552 q^{26} + 30883 q^{27} + 23528 q^{28} + 43620 q^{29} + 23582 q^{30} + 13127 q^{31} + 49108 q^{32} + 39222 q^{33} + 32097 q^{34} + 52467 q^{35} + 217244 q^{36} + 56152 q^{37} + 76245 q^{38} + 28595 q^{39} + 20368 q^{40} + 46679 q^{41} + 78924 q^{42} + 39058 q^{43} + 78528 q^{44} + 185770 q^{45} + 41430 q^{46} + 150268 q^{47} + 180930 q^{48} + 323802 q^{49} + 91604 q^{50} + 43367 q^{51} + 136030 q^{52} + 297398 q^{53} + 116761 q^{54} + 94579 q^{55} + 173545 q^{56} + 164740 q^{57} + 87844 q^{58} + 135778 q^{59} + 114650 q^{60} + 166976 q^{61} + 229394 q^{62} + 147179 q^{63} + 630138 q^{64} + 216626 q^{65} + 82380 q^{66} + 133444 q^{67} + 634057 q^{68} + 232986 q^{69} + 30943 q^{70} + 126787 q^{71} + 78583 q^{72} + 241702 q^{73} + 242589 q^{74} + 374853 q^{75} + 90228 q^{76} + 766693 q^{77} + 82537 q^{78} + 117230 q^{79} + 730509 q^{80} + 1051409 q^{81} + 468130 q^{82} + 368467 q^{83} + 234191 q^{84} + 261997 q^{85} + 230487 q^{86} + 214239 q^{87} + 247415 q^{88} + 494902 q^{89} + 41821 q^{90} + 259647 q^{91} + 663682 q^{92} + 767344 q^{93} + 373605 q^{94} + 426186 q^{95} + 474162 q^{96} + 733038 q^{97} + 461746 q^{98} + 334651 q^{99}+O(q^{100}) \) 117 * q + 24 * q^2 + 100 * q^3 + 1962 * q^4 + 749 * q^5 + 306 * q^6 + 393 * q^7 + 1152 * q^8 + 10671 * q^9 + 850 * q^10 + 1798 * q^11 + 5361 * q^12 + 4419 * q^13 + 3847 * q^14 + 1913 * q^15 + 34722 * q^16 + 15252 * q^17 + 2367 * q^18 + 1052 * q^19 + 23568 * q^20 + 9212 * q^21 + 9176 * q^22 + 18178 * q^23 + 15983 * q^24 + 84312 * q^25 + 21552 * q^26 + 30883 * q^27 + 23528 * q^28 + 43620 * q^29 + 23582 * q^30 + 13127 * q^31 + 49108 * q^32 + 39222 * q^33 + 32097 * q^34 + 52467 * q^35 + 217244 * q^36 + 56152 * q^37 + 76245 * q^38 + 28595 * q^39 + 20368 * q^40 + 46679 * q^41 + 78924 * q^42 + 39058 * q^43 + 78528 * q^44 + 185770 * q^45 + 41430 * q^46 + 150268 * q^47 + 180930 * q^48 + 323802 * q^49 + 91604 * q^50 + 43367 * q^51 + 136030 * q^52 + 297398 * q^53 + 116761 * q^54 + 94579 * q^55 + 173545 * q^56 + 164740 * q^57 + 87844 * q^58 + 135778 * q^59 + 114650 * q^60 + 166976 * q^61 + 229394 * q^62 + 147179 * q^63 + 630138 * q^64 + 216626 * q^65 + 82380 * q^66 + 133444 * q^67 + 634057 * q^68 + 232986 * q^69 + 30943 * q^70 + 126787 * q^71 + 78583 * q^72 + 241702 * q^73 + 242589 * q^74 + 374853 * q^75 + 90228 * q^76 + 766693 * q^77 + 82537 * q^78 + 117230 * q^79 + 730509 * q^80 + 1051409 * q^81 + 468130 * q^82 + 368467 * q^83 + 234191 * q^84 + 261997 * q^85 + 230487 * q^86 + 214239 * q^87 + 247415 * q^88 + 494902 * q^89 + 41821 * q^90 + 259647 * q^91 + 663682 * q^92 + 767344 * q^93 + 373605 * q^94 + 426186 * q^95 + 474162 * q^96 + 733038 * q^97 + 461746 * q^98 + 334651 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more