LMFDB - Embedded newform 354.6.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 17196 x^{6} - 154000 x^{5} + 98085975 x^{4} + 1816612536 x^{3} - 184506058580 x^{2} + \cdots - 7060184373200 $ x^8 - 17196x^6 - 154000x^5 + 98085975x^4 + 1816612536x^3 - 184506058580x^2 - 5340414471536x - 7060184373200
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-36.8040$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -31.8040 q^{5} -36.0000 q^{6} +191.018 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -31.8040 q^{5} -36.0000 q^{6} +191.018 q^{7} -64.0000 q^{8} +81.0000 q^{9} +127.216 q^{10} -698.120 q^{11} +144.000 q^{12} +600.249 q^{13} -764.071 q^{14} -286.236 q^{15} +256.000 q^{16} +131.534 q^{17} -324.000 q^{18} +2571.85 q^{19} -508.864 q^{20} +1719.16 q^{21} +2792.48 q^{22} -1399.62 q^{23} -576.000 q^{24} -2113.51 q^{25} -2401.00 q^{26} +729.000 q^{27} +3056.29 q^{28} -221.640 q^{29} +1144.94 q^{30} +5166.10 q^{31} -1024.00 q^{32} -6283.08 q^{33} -526.136 q^{34} -6075.13 q^{35} +1296.00 q^{36} +4304.98 q^{37} -10287.4 q^{38} +5402.24 q^{39} +2035.46 q^{40} +3940.02 q^{41} -6876.64 q^{42} -7965.07 q^{43} -11169.9 q^{44} -2576.12 q^{45} +5598.48 q^{46} +9063.39 q^{47} +2304.00 q^{48} +19680.8 q^{49} +8454.02 q^{50} +1183.81 q^{51} +9603.99 q^{52} +9905.13 q^{53} -2916.00 q^{54} +22203.0 q^{55} -12225.1 q^{56} +23146.6 q^{57} +886.562 q^{58} -3481.00 q^{59} -4579.78 q^{60} -48440.1 q^{61} -20664.4 q^{62} +15472.4 q^{63} +4096.00 q^{64} -19090.3 q^{65} +25132.3 q^{66} -21511.1 q^{67} +2104.54 q^{68} -12596.6 q^{69} +24300.5 q^{70} +77074.8 q^{71} -5184.00 q^{72} +53070.6 q^{73} -17219.9 q^{74} -19021.6 q^{75} +41149.5 q^{76} -133353. q^{77} -21609.0 q^{78} -79750.5 q^{79} -8141.82 q^{80} +6561.00 q^{81} -15760.1 q^{82} +109874. q^{83} +27506.6 q^{84} -4183.31 q^{85} +31860.3 q^{86} -1994.76 q^{87} +44679.7 q^{88} +19800.5 q^{89} +10304.5 q^{90} +114658. q^{91} -22393.9 q^{92} +46494.9 q^{93} -36253.6 q^{94} -81795.0 q^{95} -9216.00 q^{96} +10978.1 q^{97} -78723.2 q^{98} -56547.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9}+O(q^{10}) $ 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9} - 160 q^{10} - 349 q^{11} + 1152 q^{12} + 121 q^{13} - 724 q^{14} + 360 q^{15} + 2048 q^{16} + 437 q^{17} - 2592 q^{18} + 1314 q^{19} + 640 q^{20} + 1629 q^{21} + 1396 q^{22} + 1224 q^{23} - 4608 q^{24} + 9592 q^{25} - 484 q^{26} + 5832 q^{27} + 2896 q^{28} + 5276 q^{29} - 1440 q^{30} + 18332 q^{31} - 8192 q^{32} - 3141 q^{33} - 1748 q^{34} + 19518 q^{35} + 10368 q^{36} + 30331 q^{37} - 5256 q^{38} + 1089 q^{39} - 2560 q^{40} + 8323 q^{41} - 6516 q^{42} + 30851 q^{43} - 5584 q^{44} + 3240 q^{45} - 4896 q^{46} - 5730 q^{47} + 18432 q^{48} + 32295 q^{49} - 38368 q^{50} + 3933 q^{51} + 1936 q^{52} - 33524 q^{53} - 23328 q^{54} + 23660 q^{55} - 11584 q^{56} + 11826 q^{57} - 21104 q^{58} - 27848 q^{59} + 5760 q^{60} + 2692 q^{61} - 73328 q^{62} + 14661 q^{63} + 32768 q^{64} - 59892 q^{65} + 12564 q^{66} + 56244 q^{67} + 6992 q^{68} + 11016 q^{69} - 78072 q^{70} - 48473 q^{71} - 41472 q^{72} - 30796 q^{73} - 121324 q^{74} + 86328 q^{75} + 21024 q^{76} + 59683 q^{77} - 4356 q^{78} + 135513 q^{79} + 10240 q^{80} + 52488 q^{81} - 33292 q^{82} - 88111 q^{83} + 26064 q^{84} + 114418 q^{85} - 123404 q^{86} + 47484 q^{87} + 22336 q^{88} - 112196 q^{89} - 12960 q^{90} + 377433 q^{91} + 19584 q^{92} + 164988 q^{93} + 22920 q^{94} + 328146 q^{95} - 73728 q^{96} + 551378 q^{97} - 129180 q^{98} - 28269 q^{99}+O(q^{100}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9 - 160 * q^10 - 349 * q^11 + 1152 * q^12 + 121 * q^13 - 724 * q^14 + 360 * q^15 + 2048 * q^16 + 437 * q^17 - 2592 * q^18 + 1314 * q^19 + 640 * q^20 + 1629 * q^21 + 1396 * q^22 + 1224 * q^23 - 4608 * q^24 + 9592 * q^25 - 484 * q^26 + 5832 * q^27 + 2896 * q^28 + 5276 * q^29 - 1440 * q^30 + 18332 * q^31 - 8192 * q^32 - 3141 * q^33 - 1748 * q^34 + 19518 * q^35 + 10368 * q^36 + 30331 * q^37 - 5256 * q^38 + 1089 * q^39 - 2560 * q^40 + 8323 * q^41 - 6516 * q^42 + 30851 * q^43 - 5584 * q^44 + 3240 * q^45 - 4896 * q^46 - 5730 * q^47 + 18432 * q^48 + 32295 * q^49 - 38368 * q^50 + 3933 * q^51 + 1936 * q^52 - 33524 * q^53 - 23328 * q^54 + 23660 * q^55 - 11584 * q^56 + 11826 * q^57 - 21104 * q^58 - 27848 * q^59 + 5760 * q^60 + 2692 * q^61 - 73328 * q^62 + 14661 * q^63 + 32768 * q^64 - 59892 * q^65 + 12564 * q^66 + 56244 * q^67 + 6992 * q^68 + 11016 * q^69 - 78072 * q^70 - 48473 * q^71 - 41472 * q^72 - 30796 * q^73 - 121324 * q^74 + 86328 * q^75 + 21024 * q^76 + 59683 * q^77 - 4356 * q^78 + 135513 * q^79 + 10240 * q^80 + 52488 * q^81 - 33292 * q^82 - 88111 * q^83 + 26064 * q^84 + 114418 * q^85 - 123404 * q^86 + 47484 * q^87 + 22336 * q^88 - 112196 * q^89 - 12960 * q^90 + 377433 * q^91 + 19584 * q^92 + 164988 * q^93 + 22920 * q^94 + 328146 * q^95 - 73728 * q^96 + 551378 * q^97 - 129180 * q^98 - 28269 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−31.8040	−0.568927	−0.284464	−	0.958687i	$-0.591815\pi$
$5$	−31.8040	−0.568927	−0.284464	+	0.958687i	$0.591815\pi$
$6$	−36.0000	−0.408248
$7$	191.018	1.47343	0.736714	−	0.676205i	$-0.236377\pi$
$7$	191.018	1.47343	0.736714	+	0.676205i	$0.236377\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	127.216	0.402292
$11$	−698.120	−1.73960	−0.869798	−	0.493409i	$-0.835751\pi$
$11$	−698.120	−1.73960	−0.869798	+	0.493409i	$0.835751\pi$
$12$	144.000	0.288675
$13$	600.249	0.985084	0.492542	−	0.870289i	$-0.336068\pi$
$13$	600.249	0.985084	0.492542	+	0.870289i	$0.336068\pi$
$14$	−764.071	−1.04187
$15$	−286.236	−0.328470
$16$	256.000	0.250000
$17$	131.534	0.110386	0.0551932	−	0.998476i	$-0.482423\pi$
$17$	131.534	0.110386	0.0551932	+	0.998476i	$0.482423\pi$
$18$	−324.000	−0.235702
$19$	2571.85	1.63441	0.817205	−	0.576347i	$-0.195522\pi$
$19$	2571.85	1.63441	0.817205	+	0.576347i	$0.195522\pi$
$20$	−508.864	−0.284464
$21$	1719.16	0.850684
$22$	2792.48	1.23008
$23$	−1399.62	−0.551685	−0.275842	−	0.961203i	$-0.588957\pi$
$23$	−1399.62	−0.551685	−0.275842	+	0.961203i	$0.588957\pi$
$24$	−576.000	−0.204124
$25$	−2113.51	−0.676322
$26$	−2401.00	−0.696560
$27$	729.000	0.192450
$28$	3056.29	0.736714
$29$	−221.640	−0.0489389	−0.0244694	−	0.999701i	$-0.507790\pi$
$29$	−221.640	−0.0489389	−0.0244694	+	0.999701i	$0.507790\pi$
$30$	1144.94	0.232264
$31$	5166.10	0.965513	0.482757	−	0.875755i	$-0.339636\pi$
$31$	5166.10	0.965513	0.482757	+	0.875755i	$0.339636\pi$
$32$	−1024.00	−0.176777
$33$	−6283.08	−1.00436
$34$	−526.136	−0.0780550
$35$	−6075.13	−0.838273
$36$	1296.00	0.166667
$37$	4304.98	0.516972	0.258486	−	0.966015i	$-0.416776\pi$
$37$	4304.98	0.516972	0.258486	+	0.966015i	$0.416776\pi$
$38$	−10287.4	−1.15570
$39$	5402.24	0.568738
$40$	2035.46	0.201146
$41$	3940.02	0.366049	0.183024	−	0.983108i	$-0.441411\pi$
$41$	3940.02	0.366049	0.183024	+	0.983108i	$0.441411\pi$
$42$	−6876.64	−0.601524
$43$	−7965.07	−0.656929	−0.328464	−	0.944516i	$-0.606531\pi$
$43$	−7965.07	−0.656929	−0.328464	+	0.944516i	$0.606531\pi$
$44$	−11169.9	−0.869798
$45$	−2576.12	−0.189642
$46$	5598.48	0.390100
$47$	9063.39	0.598475	0.299238	−	0.954179i	$-0.403268\pi$
$47$	9063.39	0.598475	0.299238	+	0.954179i	$0.403268\pi$
$48$	2304.00	0.144338
$49$	19680.8	1.17099
$50$	8454.02	0.478232
$51$	1183.81	0.0637316
$52$	9603.99	0.492542
$53$	9905.13	0.484362	0.242181	−	0.970231i	$-0.422137\pi$
$53$	9905.13	0.484362	0.242181	+	0.970231i	$0.422137\pi$
$54$	−2916.00	−0.136083
$55$	22203.0	0.989703
$56$	−12225.1	−0.520935
$57$	23146.6	0.943627
$58$	886.562	0.0346050
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−4579.78	−0.164235
$61$	−48440.1	−1.66679	−0.833394	−	0.552680i	$-0.813605\pi$
$61$	−48440.1	−1.66679	−0.833394	+	0.552680i	$0.813605\pi$
$62$	−20664.4	−0.682721
$63$	15472.4	0.491143
$64$	4096.00	0.125000
$65$	−19090.3	−0.560441
$66$	25132.3	0.710187
$67$	−21511.1	−0.585431	−0.292716	−	0.956200i	$-0.594559\pi$
$67$	−21511.1	−0.585431	−0.292716	+	0.956200i	$0.594559\pi$
$68$	2104.54	0.0551932
$69$	−12596.6	−0.318515
$70$	24300.5	0.592749
$71$	77074.8	1.81454	0.907269	−	0.420550i	$-0.138163\pi$
$71$	77074.8	1.81454	0.907269	+	0.420550i	$0.138163\pi$
$72$	−5184.00	−0.117851
$73$	53070.6	1.16559	0.582796	−	0.812618i	$-0.301959\pi$
$73$	53070.6	1.16559	0.582796	+	0.812618i	$0.301959\pi$
$74$	−17219.9	−0.365554
$75$	−19021.6	−0.390475
$76$	41149.5	0.817205
$77$	−133353.	−2.56317
$78$	−21609.0	−0.402159
$79$	−79750.5	−1.43769	−0.718845	−	0.695170i	$-0.755329\pi$
$79$	−79750.5	−1.43769	−0.718845	+	0.695170i	$0.755329\pi$
$80$	−8141.82	−0.142232
$81$	6561.00	0.111111
$82$	−15760.1	−0.258835
$83$	109874.	1.75066	0.875328	−	0.483529i	$-0.160645\pi$
$83$	109874.	1.75066	0.875328	+	0.483529i	$0.160645\pi$
$84$	27506.6	0.425342
$85$	−4183.31	−0.0628018
$86$	31860.3	0.464519
$87$	−1994.76	−0.0282549
$88$	44679.7	0.615040
$89$	19800.5	0.264972	0.132486	−	0.991185i	$-0.457704\pi$
$89$	19800.5	0.264972	0.132486	+	0.991185i	$0.457704\pi$
$90$	10304.5	0.134097
$91$	114658.	1.45145
$92$	−22393.9	−0.275842
$93$	46494.9	0.557439
$94$	−36253.6	−0.423186
$95$	−81795.0	−0.929860
$96$	−9216.00	−0.102062
$97$	10978.1	0.118468	0.0592338	−	0.998244i	$-0.481134\pi$
$97$	10978.1	0.118468	0.0592338	+	0.998244i	$0.481134\pi$
$98$	−78723.2	−0.828014
$99$	−56547.7	−0.579865
$100$	−33816.1	−0.338161
$101$	−3970.56	−0.0387301	−0.0193651	−	0.999812i	$-0.506164\pi$
$101$	−3970.56	−0.0387301	−0.0193651	+	0.999812i	$0.506164\pi$
$102$	−4735.22	−0.0450651
$103$	−80935.4	−0.751701	−0.375851	−	0.926680i	$-0.622649\pi$
$103$	−80935.4	−0.751701	−0.375851	+	0.926680i	$0.622649\pi$
$104$	−38416.0	−0.348280
$105$	−54676.2	−0.483977
$106$	−39620.5	−0.342496
$107$	167803.	1.41691	0.708454	−	0.705757i	$-0.249393\pi$
$107$	167803.	1.41691	0.708454	+	0.705757i	$0.249393\pi$
$108$	11664.0	0.0962250
$109$	176963.	1.42665	0.713324	−	0.700835i	$-0.247189\pi$
$109$	176963.	1.42665	0.713324	+	0.700835i	$0.247189\pi$
$110$	−88812.0	−0.699826
$111$	38744.8	0.298474
$112$	48900.6	0.368357
$113$	159408.	1.17440	0.587198	−	0.809443i	$-0.300231\pi$
$113$	159408.	1.17440	0.587198	+	0.809443i	$0.300231\pi$
$114$	−92586.5	−0.667245
$115$	44513.5	0.313868
$116$	−3546.25	−0.0244694
$117$	48620.2	0.328361
$118$	13924.0	0.0920575
$119$	25125.3	0.162646
$120$	18319.1	0.116132
$121$	326320.	2.02619
$122$	193760.	1.17860
$123$	35460.2	0.211338
$124$	82657.5	0.482757
$125$	166605.	0.953705
$126$	−61889.8	−0.347290
$127$	118263.	0.650640	0.325320	−	0.945604i	$-0.394528\pi$
$127$	118263.	0.650640	0.325320	+	0.945604i	$0.394528\pi$
$128$	−16384.0	−0.0883883
$129$	−71685.6	−0.379278
$130$	76361.3	0.396292
$131$	241960.	1.23187	0.615936	−	0.787796i	$-0.288778\pi$
$131$	241960.	1.23187	0.615936	+	0.787796i	$0.288778\pi$
$132$	−100529.	−0.502178
$133$	491269.	2.40818
$134$	86044.4	0.413962
$135$	−23185.1	−0.109490
$136$	−8418.17	−0.0390275
$137$	286571.	1.30446	0.652231	−	0.758020i	$-0.273833\pi$
$137$	286571.	1.30446	0.652231	+	0.758020i	$0.273833\pi$
$138$	50386.3	0.225224
$139$	194021.	0.851748	0.425874	−	0.904782i	$-0.359967\pi$
$139$	194021.	0.851748	0.425874	+	0.904782i	$0.359967\pi$
$140$	−97202.1	−0.419137
$141$	81570.5	0.345530
$142$	−308299.	−1.28307
$143$	−419046.	−1.71365
$144$	20736.0	0.0833333
$145$	7049.05	0.0278427
$146$	−212282.	−0.824199
$147$	177127.	0.676071
$148$	68879.7	0.258486
$149$	−73664.2	−0.271826	−0.135913	−	0.990721i	$-0.543397\pi$
$149$	−73664.2	−0.271826	−0.135913	+	0.990721i	$0.543397\pi$
$150$	76086.2	0.276107
$151$	−239602.	−0.855163	−0.427581	−	0.903977i	$-0.640634\pi$
$151$	−239602.	−0.855163	−0.427581	+	0.903977i	$0.640634\pi$
$152$	−164598.	−0.577851
$153$	10654.3	0.0367955
$154$	533413.	1.81243
$155$	−164303.	−0.549307
$156$	86435.9	0.284369
$157$	378138.	1.22434	0.612170	−	0.790726i	$-0.290297\pi$
$157$	378138.	1.22434	0.612170	+	0.790726i	$0.290297\pi$
$158$	319002.	1.01660
$159$	89146.1	0.279647
$160$	32567.3	0.100573
$161$	−267353.	−0.812867
$162$	−26244.0	−0.0785674
$163$	−108352.	−0.319425	−0.159712	−	0.987164i	$-0.551057\pi$
$163$	−108352.	−0.319425	−0.159712	+	0.987164i	$0.551057\pi$
$164$	63040.3	0.183024
$165$	199827.	0.571405
$166$	−439497.	−1.23790
$167$	364815.	1.01223	0.506117	−	0.862465i	$-0.331080\pi$
$167$	364815.	1.01223	0.506117	+	0.862465i	$0.331080\pi$
$168$	−110026.	−0.300762
$169$	−10993.9	−0.0296097
$170$	16733.2	0.0444076
$171$	208320.	0.544803
$172$	−127441.	−0.328464
$173$	639057.	1.62340	0.811698	−	0.584077i	$-0.198544\pi$
$173$	639057.	1.62340	0.811698	+	0.584077i	$0.198544\pi$
$174$	7979.06	0.0199792
$175$	−403717.	−0.996511
$176$	−178719.	−0.434899
$177$	−31329.0	−0.0751646
$178$	−79201.8	−0.187364
$179$	−477384.	−1.11361	−0.556807	−	0.830642i	$-0.687974\pi$
$179$	−477384.	−1.11361	−0.556807	+	0.830642i	$0.687974\pi$
$180$	−41218.0	−0.0948212
$181$	−326378.	−0.740498	−0.370249	−	0.928933i	$-0.620728\pi$
$181$	−326378.	−0.740498	−0.370249	+	0.928933i	$0.620728\pi$
$182$	−458633.	−1.02633
$183$	−435961.	−0.962320
$184$	89575.7	0.195050
$185$	−136916.	−0.294119
$186$	−185979.	−0.394169
$187$	−91826.5	−0.192028
$188$	145014.	0.299238
$189$	139252.	0.283561
$190$	327180.	0.657511
$191$	−461752.	−0.915851	−0.457926	−	0.888990i	$-0.651407\pi$
$191$	−461752.	−0.915851	−0.457926	+	0.888990i	$0.651407\pi$
$192$	36864.0	0.0721688
$193$	606981.	1.17296	0.586478	−	0.809965i	$-0.300514\pi$
$193$	606981.	1.17296	0.586478	+	0.809965i	$0.300514\pi$
$194$	−43912.6	−0.0837693
$195$	−171813.	−0.323571
$196$	314893.	0.585494
$197$	−287126.	−0.527116	−0.263558	−	0.964644i	$-0.584896\pi$
$197$	−287126.	−0.527116	−0.263558	+	0.964644i	$0.584896\pi$
$198$	226191.	0.410026
$199$	−421426.	−0.754377	−0.377188	−	0.926137i	$-0.623109\pi$
$199$	−421426.	−0.754377	−0.377188	+	0.926137i	$0.623109\pi$
$200$	135264.	0.239116
$201$	−193600.	−0.337999
$202$	15882.3	0.0273863
$203$	−42337.3	−0.0721079
$204$	18940.9	0.0318658
$205$	−125308.	−0.208255
$206$	323741.	0.531533
$207$	−113369.	−0.183895
$208$	153664.	0.246271
$209$	−1.79546e6	−2.84321
$210$	218705.	0.342224
$211$	−812832.	−1.25688	−0.628441	−	0.777857i	$-0.716307\pi$
$211$	−812832.	−1.25688	−0.628441	+	0.777857i	$0.716307\pi$
$212$	158482.	0.242181
$213$	693673.	1.04762
$214$	−671214.	−1.00190
$215$	253321.	0.373745
$216$	−46656.0	−0.0680414
$217$	986816.	1.42261
$218$	−707853.	−1.00879
$219$	477635.	0.672955
$220$	355248.	0.494851
$221$	78953.2	0.108740
$222$	−154979.	−0.211053
$223$	645838.	0.869684	0.434842	−	0.900507i	$-0.356804\pi$
$223$	645838.	0.869684	0.434842	+	0.900507i	$0.356804\pi$
$224$	−195602.	−0.260468
$225$	−171194.	−0.225441
$226$	−637633.	−0.830423
$227$	−1.41475e6	−1.82228	−0.911142	−	0.412092i	$-0.864798\pi$
$227$	−1.41475e6	−1.82228	−0.911142	+	0.412092i	$0.864798\pi$
$228$	370346.	0.471814
$229$	−871665.	−1.09840	−0.549201	−	0.835691i	$-0.685068\pi$
$229$	−871665.	−1.09840	−0.549201	+	0.835691i	$0.685068\pi$
$230$	−178054.	−0.221938
$231$	−1.20018e6	−1.47985
$232$	14185.0	0.0173025
$233$	1.05827e6	1.27705	0.638523	−	0.769602i	$-0.279546\pi$
$233$	1.05827e6	1.27705	0.638523	+	0.769602i	$0.279546\pi$
$234$	−194481.	−0.232187
$235$	−288252.	−0.340489
$236$	−55696.0	−0.0650945
$237$	−717754.	−0.830051
$238$	−100501.	−0.115008
$239$	21894.2	0.0247933	0.0123967	−	0.999923i	$-0.496054\pi$
$239$	21894.2	0.0247933	0.0123967	+	0.999923i	$0.496054\pi$
$240$	−73276.4	−0.0821176
$241$	1.59612e6	1.77020	0.885099	−	0.465403i	$-0.154091\pi$
$241$	1.59612e6	1.77020	0.885099	+	0.465403i	$0.154091\pi$
$242$	−1.30528e6	−1.43273
$243$	59049.0	0.0641500
$244$	−775041.	−0.833394
$245$	−625928.	−0.666207
$246$	−141841.	−0.149439
$247$	1.54375e6	1.61003
$248$	−330630.	−0.341360
$249$	988869.	1.01074
$250$	−666422.	−0.674371
$251$	−435596.	−0.436415	−0.218208	−	0.975902i	$-0.570021\pi$
$251$	−435596.	−0.436415	−0.218208	+	0.975902i	$0.570021\pi$
$252$	247559.	0.245571
$253$	977103.	0.959708
$254$	−473053.	−0.460072
$255$	−37649.8	−0.0362587
$256$	65536.0	0.0625000
$257$	−1.88077e6	−1.77624	−0.888121	−	0.459610i	$-0.847989\pi$
$257$	−1.88077e6	−1.77624	−0.888121	+	0.459610i	$0.847989\pi$
$258$	286742.	0.268190
$259$	822328.	0.761720
$260$	−305445.	−0.280221
$261$	−17952.9	−0.0163130
$262$	−967841.	−0.871065
$263$	974253.	0.868525	0.434262	−	0.900786i	$-0.357009\pi$
$263$	974253.	0.868525	0.434262	+	0.900786i	$0.357009\pi$
$264$	402117.	0.355093
$265$	−315023.	−0.275567
$266$	−1.96507e6	−1.70284
$267$	178204.	0.152982
$268$	−344178.	−0.292716
$269$	−140928.	−0.118745	−0.0593727	−	0.998236i	$-0.518910\pi$
$269$	−140928.	−0.118745	−0.0593727	+	0.998236i	$0.518910\pi$
$270$	92740.5	0.0774212
$271$	−285272.	−0.235959	−0.117979	−	0.993016i	$-0.537642\pi$
$271$	−285272.	−0.235959	−0.117979	+	0.993016i	$0.537642\pi$
$272$	33672.7	0.0275966
$273$	1.03192e6	0.837995
$274$	−1.14629e6	−0.922394
$275$	1.47548e6	1.17653
$276$	−201545.	−0.159258
$277$	118936.	0.0931352	0.0465676	−	0.998915i	$-0.485172\pi$
$277$	118936.	0.0931352	0.0465676	+	0.998915i	$0.485172\pi$
$278$	−776083.	−0.602277
$279$	418454.	0.321838
$280$	388808.	0.296374
$281$	1.40209e6	1.05928	0.529638	−	0.848224i	$-0.322328\pi$
$281$	1.40209e6	1.05928	0.529638	+	0.848224i	$0.322328\pi$
$282$	−326282.	−0.244326
$283$	552571.	0.410130	0.205065	−	0.978748i	$-0.434259\pi$
$283$	552571.	0.410130	0.205065	+	0.978748i	$0.434259\pi$
$284$	1.23320e6	0.907269
$285$	−736155.	−0.536855
$286$	1.67618e6	1.21173
$287$	752614.	0.539346
$288$	−82944.0	−0.0589256
$289$	−1.40256e6	−0.987815
$290$	−28196.2	−0.0196877
$291$	98803.3	0.0683973
$292$	849130.	0.582796
$293$	−1.47250e6	−1.00204	−0.501021	−	0.865435i	$-0.667042\pi$
$293$	−1.47250e6	−1.00204	−0.501021	+	0.865435i	$0.667042\pi$
$294$	−708509.	−0.478054
$295$	110710.	0.0740680
$296$	−275519.	−0.182777
$297$	−508929.	−0.334785
$298$	294657.	0.192210
$299$	−840121.	−0.543456
$300$	−304345.	−0.195237
$301$	−1.52147e6	−0.967937
$302$	958410.	0.604691
$303$	−35735.1	−0.0223608
$304$	658393.	0.408603
$305$	1.54059e6	0.948281
$306$	−42617.0	−0.0260183
$307$	336814.	0.203960	0.101980	−	0.994786i	$-0.467482\pi$
$307$	336814.	0.203960	0.101980	+	0.994786i	$0.467482\pi$
$308$	−2.13365e6	−1.28158
$309$	−728418.	−0.433995
$310$	657210.	0.388419
$311$	−2.02331e6	−1.18621	−0.593104	−	0.805126i	$-0.702098\pi$
$311$	−2.02331e6	−1.18621	−0.593104	+	0.805126i	$0.702098\pi$
$312$	−345744.	−0.201079
$313$	−3.36131e6	−1.93931	−0.969656	−	0.244475i	$-0.921384\pi$
$313$	−3.36131e6	−1.93931	−0.969656	+	0.244475i	$0.921384\pi$
$314$	−1.51255e6	−0.865739
$315$	−492086.	−0.279424
$316$	−1.27601e6	−0.718845
$317$	−1.91686e6	−1.07138	−0.535688	−	0.844416i	$-0.679948\pi$
$317$	−1.91686e6	−1.07138	−0.535688	+	0.844416i	$0.679948\pi$
$318$	−356585.	−0.197740
$319$	154732.	0.0851338
$320$	−130269.	−0.0711159
$321$	1.51023e6	0.818052
$322$	1.06941e6	0.574784
$323$	338285.	0.180417
$324$	104976.	0.0555556
$325$	−1.26863e6	−0.666234
$326$	433408.	0.225867
$327$	1.59267e6	0.823675
$328$	−252161.	−0.129418
$329$	1.73127e6	0.881810
$330$	−799308.	−0.404045
$331$	1.87859e6	0.942458	0.471229	−	0.882011i	$-0.343811\pi$
$331$	1.87859e6	0.942458	0.471229	+	0.882011i	$0.343811\pi$
$332$	1.75799e6	0.875328
$333$	348703.	0.172324
$334$	−1.45926e6	−0.715758
$335$	684139.	0.333068
$336$	440105.	0.212671
$337$	−2.75890e6	−1.32331	−0.661654	−	0.749810i	$-0.730145\pi$
$337$	−2.75890e6	−1.32331	−0.661654	+	0.749810i	$0.730145\pi$
$338$	43975.4	0.0209372
$339$	1.43467e6	0.678038
$340$	−66932.9	−0.0314009
$341$	−3.60655e6	−1.67960
$342$	−833278.	−0.385234
$343$	548949.	0.251940
$344$	509764.	0.232259
$345$	400622.	0.181212
$346$	−2.55623e6	−1.14791
$347$	−287073.	−0.127988	−0.0639938	−	0.997950i	$-0.520384\pi$
$347$	−287073.	−0.127988	−0.0639938	+	0.997950i	$0.520384\pi$
$348$	−31916.2	−0.0141274
$349$	541387.	0.237927	0.118964	−	0.992899i	$-0.462043\pi$
$349$	541387.	0.237927	0.118964	+	0.992899i	$0.462043\pi$
$350$	1.61487e6	0.704640
$351$	437582.	0.189579
$352$	714875.	0.307520
$353$	−1.70022e6	−0.726219	−0.363109	−	0.931746i	$-0.618285\pi$
$353$	−1.70022e6	−0.726219	−0.363109	+	0.931746i	$0.618285\pi$
$354$	125316.	0.0531494
$355$	−2.45129e6	−1.03234
$356$	316807.	0.132486
$357$	226128.	0.0939039
$358$	1.90953e6	0.787444
$359$	227841.	0.0933029	0.0466514	−	0.998911i	$-0.485145\pi$
$359$	227841.	0.0933029	0.0466514	+	0.998911i	$0.485145\pi$
$360$	164872.	0.0670487
$361$	4.13830e6	1.67130
$362$	1.30551e6	0.523611
$363$	2.93688e6	1.16982
$364$	1.83453e6	0.725725
$365$	−1.68786e6	−0.663137
$366$	1.74384e6	0.680463
$367$	3.14524e6	1.21896	0.609478	−	0.792803i	$-0.291379\pi$
$367$	3.14524e6	1.21896	0.609478	+	0.792803i	$0.291379\pi$
$368$	−358303.	−0.137921
$369$	319142.	0.122016
$370$	547662.	0.207974
$371$	1.89206e6	0.713673
$372$	743918.	0.278720
$373$	4.26550e6	1.58744	0.793720	−	0.608283i	$-0.208141\pi$
$373$	4.26550e6	1.58744	0.793720	+	0.608283i	$0.208141\pi$
$374$	367306.	0.135784
$375$	1.49945e6	0.550622
$376$	−580057.	−0.211593
$377$	−133040.	−0.0482089
$378$	−557008.	−0.200508
$379$	−1.00918e6	−0.360888	−0.180444	−	0.983585i	$-0.557753\pi$
$379$	−1.00918e6	−0.360888	−0.180444	+	0.983585i	$0.557753\pi$
$380$	−1.30872e6	−0.464930
$381$	1.06437e6	0.375647
$382$	1.84701e6	0.647605
$383$	3.37960e6	1.17725	0.588625	−	0.808407i	$-0.299670\pi$
$383$	3.37960e6	1.17725	0.588625	+	0.808407i	$0.299670\pi$
$384$	−147456.	−0.0510310
$385$	4.24117e6	1.45826
$386$	−2.42793e6	−0.829406
$387$	−645170.	−0.218976
$388$	175650.	0.0592338
$389$	−3.60447e6	−1.20772	−0.603862	−	0.797089i	$-0.706372\pi$
$389$	−3.60447e6	−1.20772	−0.603862	+	0.797089i	$0.706372\pi$
$390$	687252.	0.228799
$391$	−184098.	−0.0608985
$392$	−1.25957e6	−0.414007
$393$	2.17764e6	0.711222
$394$	1.14850e6	0.372727
$395$	2.53638e6	0.817941
$396$	−904763.	−0.289933
$397$	−1.96862e6	−0.626881	−0.313440	−	0.949608i	$-0.601482\pi$
$397$	−1.96862e6	−0.626881	−0.313440	+	0.949608i	$0.601482\pi$
$398$	1.68570e6	0.533425
$399$	4.42142e6	1.39037
$400$	−541057.	−0.169080
$401$	997738.	0.309853	0.154926	−	0.987926i	$-0.450486\pi$
$401$	997738.	0.309853	0.154926	+	0.987926i	$0.450486\pi$
$402$	774400.	0.239001
$403$	3.10095e6	0.951112
$404$	−63529.0	−0.0193651
$405$	−208666.	−0.0632141
$406$	169349.	0.0509880
$407$	−3.00539e6	−0.899321
$408$	−75763.6	−0.0225325
$409$	−3.04608e6	−0.900394	−0.450197	−	0.892929i	$-0.648646\pi$
$409$	−3.04608e6	−0.900394	−0.450197	+	0.892929i	$0.648646\pi$
$410$	501234.	0.147259
$411$	2.57914e6	0.753131
$412$	−1.29497e6	−0.375851
$413$	−664933.	−0.191824
$414$	453477.	0.130033
$415$	−3.49444e6	−0.995996
$416$	−614655.	−0.174140
$417$	1.74619e6	0.491757
$418$	7.18183e6	2.01045
$419$	−4.39144e6	−1.22200	−0.611002	−	0.791629i	$-0.709233\pi$
$419$	−4.39144e6	−1.22200	−0.611002	+	0.791629i	$0.709233\pi$
$420$	−874819.	−0.241989
$421$	−1.07934e6	−0.296794	−0.148397	−	0.988928i	$-0.547411\pi$
$421$	−1.07934e6	−0.296794	−0.148397	+	0.988928i	$0.547411\pi$
$422$	3.25133e6	0.888750
$423$	734135.	0.199492
$424$	−633928.	−0.171248
$425$	−277998.	−0.0746567
$426$	−2.77469e6	−0.740782
$427$	−9.25292e6	−2.45589
$428$	2.68485e6	0.708454
$429$	−3.77141e6	−0.989375
$430$	−1.01328e6	−0.264277
$431$	2.04276e6	0.529692	0.264846	−	0.964291i	$-0.414679\pi$
$431$	2.04276e6	0.529692	0.264846	+	0.964291i	$0.414679\pi$
$432$	186624.	0.0481125
$433$	3.74104e6	0.958900	0.479450	−	0.877569i	$-0.340836\pi$
$433$	3.74104e6	0.958900	0.479450	+	0.877569i	$0.340836\pi$
$434$	−3.94727e6	−1.00594
$435$	63441.5	0.0160750
$436$	2.83141e6	0.713324
$437$	−3.59961e6	−0.901679
$438$	−1.91054e6	−0.475851
$439$	−4.96235e6	−1.22893	−0.614464	−	0.788945i	$-0.710628\pi$
$439$	−4.96235e6	−1.22893	−0.614464	+	0.788945i	$0.710628\pi$
$440$	−1.42099e6	−0.349913
$441$	1.59415e6	0.390330
$442$	−315813.	−0.0768907
$443$	−850593.	−0.205927	−0.102963	−	0.994685i	$-0.532832\pi$
$443$	−850593.	−0.205927	−0.102963	+	0.994685i	$0.532832\pi$
$444$	619917.	0.149237
$445$	−629734.	−0.150750
$446$	−2.58335e6	−0.614960
$447$	−662978.	−0.156939
$448$	782409.	0.184178
$449$	3.02258e6	0.707559	0.353779	−	0.935329i	$-0.384896\pi$
$449$	3.02258e6	0.707559	0.353779	+	0.935329i	$0.384896\pi$
$450$	684776.	0.159411
$451$	−2.75061e6	−0.636776
$452$	2.55053e6	0.587198
$453$	−2.15642e6	−0.493729
$454$	5.65902e6	1.28855
$455$	−3.64659e6	−0.825769
$456$	−1.48138e6	−0.333623
$457$	4.80048e6	1.07521	0.537606	−	0.843196i	$-0.319329\pi$
$457$	4.80048e6	1.07521	0.537606	+	0.843196i	$0.319329\pi$
$458$	3.48666e6	0.776687
$459$	95888.3	0.0212439
$460$	712217.	0.156934
$461$	−6.46411e6	−1.41663	−0.708315	−	0.705896i	$-0.750545\pi$
$461$	−6.46411e6	−1.41663	−0.708315	+	0.705896i	$0.750545\pi$
$462$	4.80072e6	1.04641
$463$	−5.15601e6	−1.11779	−0.558896	−	0.829238i	$-0.688775\pi$
$463$	−5.15601e6	−1.11779	−0.558896	+	0.829238i	$0.688775\pi$
$464$	−56740.0	−0.0122347
$465$	−1.47872e6	−0.317142
$466$	−4.23308e6	−0.903008
$467$	−6.08581e6	−1.29130	−0.645649	−	0.763634i	$-0.723413\pi$
$467$	−6.08581e6	−1.29130	−0.645649	+	0.763634i	$0.723413\pi$
$468$	777923.	0.164181
$469$	−4.10900e6	−0.862590
$470$	1.15301e6	0.240762
$471$	3.40325e6	0.706873
$472$	222784.	0.0460287
$473$	5.56057e6	1.14279
$474$	2.87102e6	0.586935
$475$	−5.43561e6	−1.10539
$476$	402005.	0.0813232
$477$	802315.	0.161454
$478$	−87576.8	−0.0175315
$479$	7.43491e6	1.48060	0.740298	−	0.672279i	$-0.234684\pi$
$479$	7.43491e6	1.48060	0.740298	+	0.672279i	$0.234684\pi$
$480$	293106.	0.0580659
$481$	2.58406e6	0.509261
$482$	−6.38446e6	−1.25172
$483$	−2.40617e6	−0.469309
$484$	5.22112e6	1.01310
$485$	−349149.	−0.0673995
$486$	−236196.	−0.0453609
$487$	−5.80546e6	−1.10921	−0.554605	−	0.832114i	$-0.687131\pi$
$487$	−5.80546e6	−1.10921	−0.554605	+	0.832114i	$0.687131\pi$
$488$	3.10017e6	0.589298
$489$	−975169.	−0.184420
$490$	2.50371e6	0.471080
$491$	6.75064e6	1.26369	0.631846	−	0.775094i	$-0.282298\pi$
$491$	6.75064e6	1.26369	0.631846	+	0.775094i	$0.282298\pi$
$492$	567363.	0.105669
$493$	−29153.3	−0.00540219
$494$	−6.17500e6	−1.13846
$495$	1.79844e6	0.329901
$496$	1.32252e6	0.241378
$497$	1.47227e7	2.67359
$498$	−3.95548e6	−0.714703
$499$	5.27690e6	0.948696	0.474348	−	0.880337i	$-0.342684\pi$
$499$	5.27690e6	0.948696	0.474348	+	0.880337i	$0.342684\pi$
$500$	2.66569e6	0.476853
$501$	3.28333e6	0.584414
$502$	1.74238e6	0.308592
$503$	−2.43718e6	−0.429505	−0.214753	−	0.976668i	$-0.568894\pi$
$503$	−2.43718e6	−0.429505	−0.214753	+	0.976668i	$0.568894\pi$
$504$	−990236.	−0.173645
$505$	126280.	0.0220346
$506$	−3.90841e6	−0.678616
$507$	−98944.7	−0.0170951
$508$	1.89221e6	0.325320
$509$	601758.	0.102950	0.0514751	−	0.998674i	$-0.483608\pi$
$509$	601758.	0.102950	0.0514751	+	0.998674i	$0.483608\pi$
$510$	150599.	0.0256387
$511$	1.01374e7	1.71742
$512$	−262144.	−0.0441942
$513$	1.87488e6	0.314542
$514$	7.52306e6	1.25599
$515$	2.57407e6	0.427663
$516$	−1.14697e6	−0.189639
$517$	−6.32733e6	−1.04110
$518$	−3.28931e6	−0.538618
$519$	5.75152e6	0.937268
$520$	1.22178e6	0.198146
$521$	8.15533e6	1.31628	0.658139	−	0.752897i	$-0.271344\pi$
$521$	8.15533e6	1.31628	0.658139	+	0.752897i	$0.271344\pi$
$522$	71811.5	0.0115350
$523$	7.79498e6	1.24612	0.623061	−	0.782173i	$-0.285889\pi$
$523$	7.79498e6	1.24612	0.623061	+	0.782173i	$0.285889\pi$
$524$	3.87136e6	0.615936
$525$	−3.63346e6	−0.575336
$526$	−3.89701e6	−0.614140
$527$	679517.	0.106580
$528$	−1.60847e6	−0.251089
$529$	−4.47740e6	−0.695644
$530$	1.26009e6	0.194855
$531$	−281961.	−0.0433963
$532$	7.86030e6	1.20409
$533$	2.36499e6	0.360589
$534$	−712816.	−0.108174
$535$	−5.33682e6	−0.806117
$536$	1.37671e6	0.206981
$537$	−4.29645e6	−0.642946
$538$	563712.	0.0839656
$539$	−1.37396e7	−2.03705
$540$	−370962.	−0.0547450
$541$	−3.09743e6	−0.454996	−0.227498	−	0.973779i	$-0.573055\pi$
$541$	−3.09743e6	−0.454996	−0.227498	+	0.973779i	$0.573055\pi$
$542$	1.14109e6	0.166848
$543$	−2.93740e6	−0.427527
$544$	−134691.	−0.0195137
$545$	−5.62814e6	−0.811659
$546$	−4.12770e6	−0.592552
$547$	1.14481e7	1.63593	0.817963	−	0.575271i	$-0.195103\pi$
$547$	1.14481e7	1.63593	0.817963	+	0.575271i	$0.195103\pi$
$548$	4.58514e6	0.652231
$549$	−3.92365e6	−0.555596
$550$	−5.90192e6	−0.831930
$551$	−570025.	−0.0799862
$552$	806182.	0.112612
$553$	−1.52338e7	−2.11833
$554$	−475744.	−0.0658565
$555$	−1.23224e6	−0.169810
$556$	3.10433e6	0.425874
$557$	−2.08019e6	−0.284097	−0.142048	−	0.989860i	$-0.545369\pi$
$557$	−2.08019e6	−0.284097	−0.142048	+	0.989860i	$0.545369\pi$
$558$	−1.67382e6	−0.227574
$559$	−4.78103e6	−0.647130
$560$	−1.55523e6	−0.209568
$561$	−826438.	−0.110867
$562$	−5.60835e6	−0.749022
$563$	−1.14375e6	−0.152075	−0.0760377	−	0.997105i	$-0.524227\pi$
$563$	−1.14375e6	−0.152075	−0.0760377	+	0.997105i	$0.524227\pi$
$564$	1.30513e6	0.172765
$565$	−5.06982e6	−0.668146
$566$	−2.21028e6	−0.290006
$567$	1.25327e6	0.163714
$568$	−4.93278e6	−0.641536
$569$	9.39507e6	1.21652	0.608260	−	0.793738i	$-0.291868\pi$
$569$	9.39507e6	1.21652	0.608260	+	0.793738i	$0.291868\pi$
$570$	2.94462e6	0.379614
$571$	3.85904e6	0.495323	0.247662	−	0.968847i	$-0.420338\pi$
$571$	3.85904e6	0.495323	0.247662	+	0.968847i	$0.420338\pi$
$572$	−6.70473e6	−0.856824
$573$	−4.15576e6	−0.528767
$574$	−3.01046e6	−0.381375
$575$	2.95811e6	0.373116
$576$	331776.	0.0416667
$577$	−1.10359e7	−1.37997	−0.689986	−	0.723823i	$-0.742383\pi$
$577$	−1.10359e7	−1.37997	−0.689986	+	0.723823i	$0.742383\pi$
$578$	5.61022e6	0.698491
$579$	5.46283e6	0.677207
$580$	112785.	0.0139213
$581$	2.09880e7	2.57947
$582$	−395213.	−0.0483642
$583$	−6.91496e6	−0.842594
$584$	−3.39652e6	−0.412099
$585$	−1.54632e6	−0.186814
$586$	5.89000e6	0.708551
$587$	−4.89158e6	−0.585941	−0.292971	−	0.956121i	$-0.594644\pi$
$587$	−4.89158e6	−0.585941	−0.292971	+	0.956121i	$0.594644\pi$
$588$	2.83404e6	0.338035
$589$	1.32864e7	1.57804
$590$	−442839.	−0.0523740
$591$	−2.58413e6	−0.304331
$592$	1.10207e6	0.129243
$593$	−3.33340e6	−0.389270	−0.194635	−	0.980876i	$-0.562352\pi$
$593$	−3.33340e6	−0.389270	−0.194635	+	0.980876i	$0.562352\pi$
$594$	2.03572e6	0.236729
$595$	−799086.	−0.0925340
$596$	−1.17863e6	−0.135913
$597$	−3.79283e6	−0.435540
$598$	3.36049e6	0.384281
$599$	1.16107e7	1.32218	0.661092	−	0.750305i	$-0.270093\pi$
$599$	1.16107e7	1.32218	0.661092	+	0.750305i	$0.270093\pi$
$600$	1.21738e6	0.138054
$601$	−8.99435e6	−1.01574	−0.507871	−	0.861433i	$-0.669567\pi$
$601$	−8.99435e6	−1.01574	−0.507871	+	0.861433i	$0.669567\pi$
$602$	6.08588e6	0.684435
$603$	−1.74240e6	−0.195144
$604$	−3.83364e6	−0.427581
$605$	−1.03783e7	−1.15276
$606$	142940.	0.0158115
$607$	2.53774e6	0.279561	0.139780	−	0.990183i	$-0.455360\pi$
$607$	2.53774e6	0.279561	0.139780	+	0.990183i	$0.455360\pi$
$608$	−2.63357e6	−0.288926
$609$	−381036.	−0.0416315
$610$	−6.16235e6	−0.670536
$611$	5.44029e6	0.589548
$612$	170468.	0.0183977
$613$	5.29411e6	0.569039	0.284519	−	0.958670i	$-0.408166\pi$
$613$	5.29411e6	0.569039	0.284519	+	0.958670i	$0.408166\pi$
$614$	−1.34726e6	−0.144221
$615$	−1.12778e6	−0.120236
$616$	8.53461e6	0.906217
$617$	−1.45007e7	−1.53347	−0.766735	−	0.641964i	$-0.778120\pi$
$617$	−1.45007e7	−1.53347	−0.766735	+	0.641964i	$0.778120\pi$
$618$	2.91367e6	0.306881
$619$	−136154.	−0.0142825	−0.00714123	−	0.999975i	$-0.502273\pi$
$619$	−136154.	−0.0142825	−0.00714123	+	0.999975i	$0.502273\pi$
$620$	−2.62884e6	−0.274653
$621$	−1.02032e6	−0.106172
$622$	8.09322e6	0.838775
$623$	3.78224e6	0.390417
$624$	1.38297e6	0.142185
$625$	1.30599e6	0.133733
$626$	1.34452e7	1.37130
$627$	−1.61591e7	−1.64153
$628$	6.05022e6	0.612170
$629$	566251.	0.0570667
$630$	1.96834e6	0.197583
$631$	1.14638e7	1.14619	0.573094	−	0.819490i	$-0.305743\pi$
$631$	1.14638e7	1.14619	0.573094	+	0.819490i	$0.305743\pi$
$632$	5.10403e6	0.508300
$633$	−7.31549e6	−0.725662
$634$	7.66744e6	0.757578
$635$	−3.76124e6	−0.370167
$636$	1.42634e6	0.139823
$637$	1.18134e7	1.15352
$638$	−618926.	−0.0601987
$639$	6.24305e6	0.604846
$640$	521077.	0.0502865
$641$	−8.85877e6	−0.851586	−0.425793	−	0.904821i	$-0.640005\pi$
$641$	−8.85877e6	−0.851586	−0.425793	+	0.904821i	$0.640005\pi$
$642$	−6.04092e6	−0.578450
$643$	−6.08004e6	−0.579934	−0.289967	−	0.957037i	$-0.593644\pi$
$643$	−6.08004e6	−0.579934	−0.289967	+	0.957037i	$0.593644\pi$
$644$	−4.27764e6	−0.406434
$645$	2.27989e6	0.215782
$646$	−1.35314e6	−0.127574
$647$	1.28667e6	0.120839	0.0604195	−	0.998173i	$-0.480756\pi$
$647$	1.28667e6	0.120839	0.0604195	+	0.998173i	$0.480756\pi$
$648$	−419904.	−0.0392837
$649$	2.43015e6	0.226476
$650$	5.07452e6	0.471098
$651$	8.88135e6	0.821346
$652$	−1.73363e6	−0.159712
$653$	−6.78685e6	−0.622852	−0.311426	−	0.950270i	$-0.600807\pi$
$653$	−6.78685e6	−0.622852	−0.311426	+	0.950270i	$0.600807\pi$
$654$	−6.37068e6	−0.582426
$655$	−7.69530e6	−0.700846
$656$	1.00865e6	0.0915122
$657$	4.29872e6	0.388531
$658$	−6.92508e6	−0.623534
$659$	4.63861e6	0.416078	0.208039	−	0.978121i	$-0.433292\pi$
$659$	4.63861e6	0.416078	0.208039	+	0.978121i	$0.433292\pi$
$660$	3.19723e6	0.285703
$661$	−4.36764e6	−0.388815	−0.194408	−	0.980921i	$-0.562278\pi$
$661$	−4.36764e6	−0.388815	−0.194408	+	0.980921i	$0.562278\pi$
$662$	−7.51436e6	−0.666418
$663$	710579.	0.0627810
$664$	−7.03196e6	−0.618951
$665$	−1.56243e7	−1.37008
$666$	−1.39481e6	−0.121851
$667$	310213.	0.0269988
$668$	5.83703e6	0.506117
$669$	5.81254e6	0.502112
$670$	−2.73656e6	−0.235514
$671$	3.38170e7	2.89954
$672$	−1.76042e6	−0.150381
$673$	4.33840e6	0.369225	0.184613	−	0.982811i	$-0.440897\pi$
$673$	4.33840e6	0.369225	0.184613	+	0.982811i	$0.440897\pi$
$674$	1.10356e7	0.935720
$675$	−1.54075e6	−0.130158
$676$	−175902.	−0.0148048
$677$	−7.41245e6	−0.621570	−0.310785	−	0.950480i	$-0.600592\pi$
$677$	−7.41245e6	−0.621570	−0.310785	+	0.950480i	$0.600592\pi$
$678$	−5.73869e6	−0.479445
$679$	2.09702e6	0.174553
$680$	267732.	0.0222038
$681$	−1.27328e7	−1.05210
$682$	1.44262e7	1.18766
$683$	−2.06811e7	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$683$	−2.06811e7	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$684$	3.33311e6	0.272402
$685$	−9.11411e6	−0.742144
$686$	−2.19580e6	−0.178148
$687$	−7.84499e6	−0.634162
$688$	−2.03906e6	−0.164232
$689$	5.94554e6	0.477137
$690$	−1.60249e6	−0.128136
$691$	−2.24238e7	−1.78655	−0.893274	−	0.449512i	$-0.851598\pi$
$691$	−2.24238e7	−1.78655	−0.893274	+	0.449512i	$0.851598\pi$
$692$	1.02249e7	0.811698
$693$	−1.08016e7	−0.854389
$694$	1.14829e6	0.0905010
$695$	−6.17064e6	−0.484583
$696$	127665.	0.00998961
$697$	518247.	0.0404068
$698$	−2.16555e6	−0.168240
$699$	9.52443e6	0.737303
$700$	−6.45948e6	−0.498256
$701$	−3.79052e6	−0.291342	−0.145671	−	0.989333i	$-0.546534\pi$
$701$	−3.79052e6	−0.291342	−0.145671	+	0.989333i	$0.546534\pi$
$702$	−1.75033e6	−0.134053
$703$	1.10717e7	0.844944
$704$	−2.85950e6	−0.217449
$705$	−2.59427e6	−0.196581
$706$	6.80087e6	0.513514
$707$	−758448.	−0.0570660
$708$	−501264.	−0.0375823
$709$	1.00795e6	0.0753047	0.0376523	−	0.999291i	$-0.488012\pi$
$709$	1.00795e6	0.0753047	0.0376523	+	0.999291i	$0.488012\pi$
$710$	9.80514e6	0.729975
$711$	−6.45979e6	−0.479230
$712$	−1.26723e6	−0.0936818
$713$	−7.23058e6	−0.532659
$714$	−904512.	−0.0664001
$715$	1.33273e7	0.974941
$716$	−7.63814e6	−0.556807
$717$	197048.	0.0143144
$718$	−911363.	−0.0659751
$719$	−1.24851e7	−0.900677	−0.450339	−	0.892858i	$-0.648697\pi$
$719$	−1.24851e7	−0.900677	−0.450339	+	0.892858i	$0.648697\pi$
$720$	−659488.	−0.0474106
$721$	−1.54601e7	−1.10758
$722$	−1.65532e7	−1.18179
$723$	1.43650e7	1.02202
$724$	−5.22204e6	−0.370249
$725$	468438.	0.0330984
$726$	−1.17475e7	−0.827189
$727$	2.29639e7	1.61142	0.805712	−	0.592307i	$-0.201783\pi$
$727$	2.29639e7	1.61142	0.805712	+	0.592307i	$0.201783\pi$
$728$	−7.33813e6	−0.513165
$729$	531441.	0.0370370
$730$	6.75143e6	0.468909
$731$	−1.04768e6	−0.0725160
$732$	−6.97537e6	−0.481160
$733$	−390477.	−0.0268433	−0.0134216	−	0.999910i	$-0.504272\pi$
$733$	−390477.	−0.0268433	−0.0134216	+	0.999910i	$0.504272\pi$
$734$	−1.25810e7	−0.861933
$735$	−5.63336e6	−0.384635
$736$	1.43321e6	0.0975250
$737$	1.50173e7	1.01841
$738$	−1.27657e6	−0.0862785
$739$	−1.13289e7	−0.763090	−0.381545	−	0.924350i	$-0.624608\pi$
$739$	−1.13289e7	−0.763090	−0.381545	+	0.924350i	$0.624608\pi$
$740$	−2.19065e6	−0.147060
$741$	1.38937e7	0.929552
$742$	−7.56822e6	−0.504643
$743$	−9.55349e6	−0.634878	−0.317439	−	0.948279i	$-0.602823\pi$
$743$	−9.55349e6	−0.634878	−0.317439	+	0.948279i	$0.602823\pi$
$744$	−2.97567e6	−0.197085
$745$	2.34282e6	0.154649
$746$	−1.70620e7	−1.12249
$747$	8.89982e6	0.583552
$748$	−1.46922e6	−0.0960138
$749$	3.20534e7	2.08771
$750$	−5.99780e6	−0.389348
$751$	1.40168e7	0.906879	0.453440	−	0.891287i	$-0.350197\pi$
$751$	1.40168e7	0.906879	0.453440	+	0.891287i	$0.350197\pi$
$752$	2.32023e6	0.149619
$753$	−3.92037e6	−0.251964
$754$	532158.	0.0340888
$755$	7.62032e6	0.486525
$756$	2.22803e6	0.141781
$757$	−7.98177e6	−0.506244	−0.253122	−	0.967434i	$-0.581457\pi$
$757$	−7.98177e6	−0.506244	−0.253122	+	0.967434i	$0.581457\pi$
$758$	4.03674e6	0.255186
$759$	8.79393e6	0.554087
$760$	5.23488e6	0.328755
$761$	−1.31367e7	−0.822288	−0.411144	−	0.911570i	$-0.634871\pi$
$761$	−1.31367e7	−0.822288	−0.411144	+	0.911570i	$0.634871\pi$
$762$	−4.25748e6	−0.265622
$763$	3.38031e7	2.10206
$764$	−7.38803e6	−0.457926
$765$	−338848.	−0.0209339
$766$	−1.35184e7	−0.832441
$767$	−2.08947e6	−0.128247
$768$	589824.	0.0360844
$769$	−2.24963e7	−1.37182	−0.685908	−	0.727689i	$-0.740595\pi$
$769$	−2.24963e7	−1.37182	−0.685908	+	0.727689i	$0.740595\pi$
$770$	−1.69647e7	−1.03114
$771$	−1.69269e7	−1.02551
$772$	9.71170e6	0.586478
$773$	−2.25029e7	−1.35453	−0.677266	−	0.735738i	$-0.736835\pi$
$773$	−2.25029e7	−1.35453	−0.677266	+	0.735738i	$0.736835\pi$
$774$	2.58068e6	0.154840
$775$	−1.09186e7	−0.652998
$776$	−702601.	−0.0418846
$777$	7.40095e6	0.439779
$778$	1.44179e7	0.853989
$779$	1.01331e7	0.598274
$780$	−2.74901e6	−0.161785
$781$	−5.38074e7	−3.15656
$782$	736391.	0.0430617
$783$	−161576.	−0.00941829
$784$	5.03829e6	0.292747
$785$	−1.20263e7	−0.696560
$786$	−8.71057e6	−0.502910
$787$	−2.54685e7	−1.46577	−0.732887	−	0.680350i	$-0.761828\pi$
$787$	−2.54685e7	−1.46577	−0.732887	+	0.680350i	$0.761828\pi$
$788$	−4.59401e6	−0.263558
$789$	8.76827e6	0.501443
$790$	−1.01455e7	−0.578372
$791$	3.04498e7	1.73039
$792$	3.61905e6	0.205013
$793$	−2.90761e7	−1.64193
$794$	7.87446e6	0.443271
$795$	−2.83520e6	−0.159099
$796$	−6.74281e6	−0.377188
$797$	3.35253e7	1.86951	0.934754	−	0.355296i	$-0.115620\pi$
$797$	3.35253e7	1.86951	0.934754	+	0.355296i	$0.115620\pi$
$798$	−1.76857e7	−0.983137
$799$	1.19214e6	0.0660635
$800$	2.16423e6	0.119558
$801$	1.60384e6	0.0883240
$802$	−3.99095e6	−0.219099
$803$	−3.70496e7	−2.02766
$804$	−3.09760e6	−0.168999
$805$	8.50288e6	0.462462
$806$	−1.24038e7	−0.672537
$807$	−1.26835e6	−0.0685576
$808$	254116.	0.0136932
$809$	−1.96768e7	−1.05702	−0.528510	−	0.848927i	$-0.677249\pi$
$809$	−1.96768e7	−1.05702	−0.528510	+	0.848927i	$0.677249\pi$
$810$	834664.	0.0446991
$811$	3.16290e7	1.68862	0.844312	−	0.535852i	$-0.180010\pi$
$811$	3.16290e7	1.68862	0.844312	+	0.535852i	$0.180010\pi$
$812$	−677396.	−0.0360540
$813$	−2.56745e6	−0.136231
$814$	1.20216e7	0.635916
$815$	3.44603e6	0.181729
$816$	303054.	0.0159329
$817$	−2.04849e7	−1.07369
$818$	1.21843e7	0.636675
$819$	9.28732e6	0.483817
$820$	−2.00493e6	−0.104128
$821$	−5.43290e6	−0.281302	−0.140651	−	0.990059i	$-0.544920\pi$
$821$	−5.43290e6	−0.281302	−0.140651	+	0.990059i	$0.544920\pi$
$822$	−1.03166e7	−0.532544
$823$	−2.85473e7	−1.46915	−0.734574	−	0.678529i	$-0.762618\pi$
$823$	−2.85473e7	−1.46915	−0.734574	+	0.678529i	$0.762618\pi$
$824$	5.17986e6	0.265767
$825$	1.32793e7	0.679268
$826$	2.65973e6	0.135640
$827$	2.02716e7	1.03068	0.515340	−	0.856986i	$-0.327666\pi$
$827$	2.02716e7	1.03068	0.515340	+	0.856986i	$0.327666\pi$
$828$	−1.81391e6	−0.0919474
$829$	1.87907e7	0.949634	0.474817	−	0.880084i	$-0.342514\pi$
$829$	1.87907e7	0.949634	0.474817	+	0.880084i	$0.342514\pi$
$830$	1.39778e7	0.704276
$831$	1.07042e6	0.0537716
$832$	2.45862e6	0.123135
$833$	2.58870e6	0.129261
$834$	−6.98475e6	−0.347725
$835$	−1.16026e7	−0.575888
$836$	−2.87273e7	−1.42161
$837$	3.76608e6	0.185813
$838$	1.75658e7	0.864087
$839$	5.41243e6	0.265453	0.132726	−	0.991153i	$-0.457627\pi$
$839$	5.41243e6	0.265453	0.132726	+	0.991153i	$0.457627\pi$
$840$	3.49928e6	0.171112
$841$	−2.04620e7	−0.997605
$842$	4.31738e6	0.209865
$843$	1.26188e7	0.611574
$844$	−1.30053e7	−0.628441
$845$	349649.	0.0168457
$846$	−2.93654e6	−0.141062
$847$	6.23330e7	2.98545
$848$	2.53571e6	0.121091
$849$	4.97314e6	0.236789
$850$	1.11199e6	0.0527903
$851$	−6.02534e6	−0.285205
$852$	1.10988e7	0.523812
$853$	−3.51045e7	−1.65192	−0.825962	−	0.563726i	$-0.809367\pi$
$853$	−3.51045e7	−1.65192	−0.825962	+	0.563726i	$0.809367\pi$
$854$	3.70117e7	1.73658
$855$	−6.62540e6	−0.309953
$856$	−1.07394e7	−0.500952
$857$	2.65649e7	1.23554	0.617768	−	0.786360i	$-0.288037\pi$
$857$	2.65649e7	1.23554	0.617768	+	0.786360i	$0.288037\pi$
$858$	1.50856e7	0.699594
$859$	−360703.	−0.0166789	−0.00833943	−	0.999965i	$-0.502655\pi$
$859$	−360703.	−0.0166789	−0.00833943	+	0.999965i	$0.502655\pi$
$860$	4.05314e6	0.186872
$861$	6.77353e6	0.311392
$862$	−8.17103e6	−0.374549
$863$	1.43581e6	0.0656250	0.0328125	−	0.999462i	$-0.489554\pi$
$863$	1.43581e6	0.0656250	0.0328125	+	0.999462i	$0.489554\pi$
$864$	−746496.	−0.0340207
$865$	−2.03246e7	−0.923594
$866$	−1.49642e7	−0.678044
$867$	−1.26230e7	−0.570315
$868$	1.57891e7	0.711307
$869$	5.56754e7	2.50100
$870$	−253766.	−0.0113667
$871$	−1.29120e7	−0.576699
$872$	−1.13256e7	−0.504396
$873$	889230.	0.0394892
$874$	1.43984e7	0.637583
$875$	3.18246e7	1.40522
$876$	7.64217e6	0.336478
$877$	−4.22038e7	−1.85290	−0.926450	−	0.376417i	$-0.877156\pi$
$877$	−4.22038e7	−1.85290	−0.926450	+	0.376417i	$0.877156\pi$
$878$	1.98494e7	0.868983
$879$	−1.32525e7	−0.578530
$880$	5.68397e6	0.247426
$881$	−7.62184e6	−0.330841	−0.165421	−	0.986223i	$-0.552898\pi$
$881$	−7.62184e6	−0.330841	−0.165421	+	0.986223i	$0.552898\pi$
$882$	−6.37658e6	−0.276005
$883$	−1.07486e7	−0.463926	−0.231963	−	0.972725i	$-0.574515\pi$
$883$	−1.07486e7	−0.463926	−0.231963	+	0.972725i	$0.574515\pi$
$884$	1.26325e6	0.0543699
$885$	996387.	0.0427632
$886$	3.40237e6	0.145612
$887$	3.50823e7	1.49720	0.748599	−	0.663023i	$-0.230727\pi$
$887$	3.50823e7	1.49720	0.748599	+	0.663023i	$0.230727\pi$
$888$	−2.47967e6	−0.105526
$889$	2.25904e7	0.958670
$890$	2.51893e6	0.106596
$891$	−4.58036e6	−0.193288
$892$	1.03334e7	0.434842
$893$	2.33097e7	0.978154
$894$	2.65191e6	0.110972
$895$	1.51827e7	0.633566
$896$	−3.12964e6	−0.130234
$897$	−7.56109e6	−0.313764
$898$	−1.20903e7	−0.500320
$899$	−1.14502e6	−0.0472511
$900$	−2.73910e6	−0.112720
$901$	1.30286e6	0.0534670
$902$	1.10024e7	0.450269
$903$	−1.36932e7	−0.558839
$904$	−1.02021e7	−0.415212
$905$	1.03801e7	0.421289
$906$	8.62569e6	0.349119
$907$	2.91937e7	1.17834	0.589171	−	0.808008i	$-0.299454\pi$
$907$	2.91937e7	1.17834	0.589171	+	0.808008i	$0.299454\pi$
$908$	−2.26361e7	−0.911142
$909$	−321616.	−0.0129100
$910$	1.45864e7	0.583907
$911$	−1.09436e7	−0.436882	−0.218441	−	0.975850i	$-0.570097\pi$
$911$	−1.09436e7	−0.436882	−0.218441	+	0.975850i	$0.570097\pi$
$912$	5.92553e6	0.235907
$913$	−7.67054e7	−3.04543
$914$	−1.92019e7	−0.760290
$915$	1.38653e7	0.547490
$916$	−1.39466e7	−0.549201
$917$	4.62187e7	1.81508
$918$	−383553.	−0.0150217
$919$	−1.67487e7	−0.654174	−0.327087	−	0.944994i	$-0.606067\pi$
$919$	−1.67487e7	−0.654174	−0.327087	+	0.944994i	$0.606067\pi$
$920$	−2.84887e6	−0.110969
$921$	3.03133e6	0.117756
$922$	2.58565e7	1.00171
$923$	4.62641e7	1.78747
$924$	−1.92029e7	−0.739923
$925$	−9.09860e6	−0.349639
$926$	2.06240e7	0.790398
$927$	−6.55576e6	−0.250567
$928$	226960.	0.00865125
$929$	−6.78387e6	−0.257892	−0.128946	−	0.991652i	$-0.541159\pi$
$929$	−6.78387e6	−0.257892	−0.128946	+	0.991652i	$0.541159\pi$
$930$	5.91489e6	0.224254
$931$	5.06160e7	1.91388
$932$	1.69323e7	0.638523
$933$	−1.82098e7	−0.684857
$934$	2.43433e7	0.913086
$935$	2.92045e6	0.109250
$936$	−3.11169e6	−0.116093
$937$	2.10816e7	0.784430	0.392215	−	0.919874i	$-0.371709\pi$
$937$	2.10816e7	0.784430	0.392215	+	0.919874i	$0.371709\pi$
$938$	1.64360e7	0.609943
$939$	−3.02518e7	−1.11966
$940$	−4.61203e6	−0.170244
$941$	−3.43880e7	−1.26600	−0.632999	−	0.774153i	$-0.718176\pi$
$941$	−3.43880e7	−1.26600	−0.632999	+	0.774153i	$0.718176\pi$
$942$	−1.36130e7	−0.499834
$943$	−5.51453e6	−0.201943
$944$	−891136.	−0.0325472
$945$	−4.42877e6	−0.161326
$946$	−2.22423e7	−0.808075
$947$	6.23561e6	0.225946	0.112973	−	0.993598i	$-0.463963\pi$
$947$	6.23561e6	0.225946	0.112973	+	0.993598i	$0.463963\pi$
$948$	−1.14841e7	−0.415026
$949$	3.18556e7	1.14821
$950$	2.17424e7	0.781627
$951$	−1.72517e7	−0.618560
$952$	−1.60802e6	−0.0575042
$953$	5.47898e6	0.195419	0.0977096	−	0.995215i	$-0.468848\pi$
$953$	5.47898e6	0.195419	0.0977096	+	0.995215i	$0.468848\pi$
$954$	−3.20926e6	−0.114165
$955$	1.46855e7	0.521053
$956$	350307.	0.0123967
$957$	1.39258e6	0.0491520
$958$	−2.97396e7	−1.04694
$959$	5.47402e7	1.92203
$960$	−1.17242e6	−0.0410588
$961$	−1.94060e6	−0.0677842
$962$	−1.03362e7	−0.360102
$963$	1.35921e7	0.472302
$964$	2.55378e7	0.885099
$965$	−1.93044e7	−0.667327
$966$	9.62469e6	0.331852
$967$	2.33320e7	0.802391	0.401195	−	0.915993i	$-0.368595\pi$
$967$	2.33320e7	0.802391	0.401195	+	0.915993i	$0.368595\pi$
$968$	−2.08845e7	−0.716367
$969$	3.04457e6	0.104164
$970$	1.39660e6	0.0476586
$971$	−7.62846e6	−0.259650	−0.129825	−	0.991537i	$-0.541442\pi$
$971$	−7.62846e6	−0.259650	−0.129825	+	0.991537i	$0.541442\pi$
$972$	944784.	0.0320750
$973$	3.70614e7	1.25499
$974$	2.32218e7	0.784330
$975$	−1.14177e7	−0.384650
$976$	−1.24007e7	−0.416697
$977$	3.81744e7	1.27949	0.639744	−	0.768588i	$-0.279040\pi$
$977$	3.81744e7	1.27949	0.639744	+	0.768588i	$0.279040\pi$
$978$	3.90068e6	0.130405
$979$	−1.38231e7	−0.460944
$980$	−1.00149e7	−0.333104
$981$	1.43340e7	0.475549
$982$	−2.70026e7	−0.893565
$983$	3.28124e7	1.08306	0.541532	−	0.840680i	$-0.317845\pi$
$983$	3.28124e7	1.08306	0.541532	+	0.840680i	$0.317845\pi$
$984$	−2.26945e6	−0.0747194
$985$	9.13174e6	0.299891
$986$	116613.	0.00381992
$987$	1.55814e7	0.509113
$988$	2.47000e7	0.805016
$989$	1.11481e7	0.362417
$990$	−7.19377e6	−0.233275
$991$	1.16714e6	0.0377519	0.0188759	−	0.999822i	$-0.493991\pi$
$991$	1.16714e6	0.0377519	0.0188759	+	0.999822i	$0.493991\pi$
$992$	−5.29008e6	−0.170680
$993$	1.69073e7	0.544128
$994$	−5.88906e7	−1.89051
$995$	1.34030e7	0.429186
$996$	1.58219e7	0.505371
$997$	−2.29765e7	−0.732060	−0.366030	−	0.930603i	$-0.619283\pi$
$997$	−2.29765e7	−0.732060	−0.366030	+	0.930603i	$0.619283\pi$
$998$	−2.11076e7	−0.670829
$999$	3.13833e6	0.0994913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.h.1.4	✓	8
3.2	odd	2		1062.6.a.m.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.h.1.4	✓	8	1.1	even	1	trivial
1062.6.a.m.1.5		8	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -31.8040 q^{5} -36.0000 q^{6} +191.018 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -31.8040 q^{5} -36.0000 q^{6} +191.018 q^{7} -64.0000 q^{8} +81.0000 q^{9} +127.216 q^{10} -698.120 q^{11} +144.000 q^{12} +600.249 q^{13} -764.071 q^{14} -286.236 q^{15} +256.000 q^{16} +131.534 q^{17} -324.000 q^{18} +2571.85 q^{19} -508.864 q^{20} +1719.16 q^{21} +2792.48 q^{22} -1399.62 q^{23} -576.000 q^{24} -2113.51 q^{25} -2401.00 q^{26} +729.000 q^{27} +3056.29 q^{28} -221.640 q^{29} +1144.94 q^{30} +5166.10 q^{31} -1024.00 q^{32} -6283.08 q^{33} -526.136 q^{34} -6075.13 q^{35} +1296.00 q^{36} +4304.98 q^{37} -10287.4 q^{38} +5402.24 q^{39} +2035.46 q^{40} +3940.02 q^{41} -6876.64 q^{42} -7965.07 q^{43} -11169.9 q^{44} -2576.12 q^{45} +5598.48 q^{46} +9063.39 q^{47} +2304.00 q^{48} +19680.8 q^{49} +8454.02 q^{50} +1183.81 q^{51} +9603.99 q^{52} +9905.13 q^{53} -2916.00 q^{54} +22203.0 q^{55} -12225.1 q^{56} +23146.6 q^{57} +886.562 q^{58} -3481.00 q^{59} -4579.78 q^{60} -48440.1 q^{61} -20664.4 q^{62} +15472.4 q^{63} +4096.00 q^{64} -19090.3 q^{65} +25132.3 q^{66} -21511.1 q^{67} +2104.54 q^{68} -12596.6 q^{69} +24300.5 q^{70} +77074.8 q^{71} -5184.00 q^{72} +53070.6 q^{73} -17219.9 q^{74} -19021.6 q^{75} +41149.5 q^{76} -133353. q^{77} -21609.0 q^{78} -79750.5 q^{79} -8141.82 q^{80} +6561.00 q^{81} -15760.1 q^{82} +109874. q^{83} +27506.6 q^{84} -4183.31 q^{85} +31860.3 q^{86} -1994.76 q^{87} +44679.7 q^{88} +19800.5 q^{89} +10304.5 q^{90} +114658. q^{91} -22393.9 q^{92} +46494.9 q^{93} -36253.6 q^{94} -81795.0 q^{95} -9216.00 q^{96} +10978.1 q^{97} -78723.2 q^{98} -56547.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9} - 160 q^{10} - 349 q^{11} + 1152 q^{12} + 121 q^{13} - 724 q^{14} + 360 q^{15} + 2048 q^{16} + 437 q^{17} - 2592 q^{18} + 1314 q^{19} + 640 q^{20} + 1629 q^{21} + 1396 q^{22} + 1224 q^{23} - 4608 q^{24} + 9592 q^{25} - 484 q^{26} + 5832 q^{27} + 2896 q^{28} + 5276 q^{29} - 1440 q^{30} + 18332 q^{31} - 8192 q^{32} - 3141 q^{33} - 1748 q^{34} + 19518 q^{35} + 10368 q^{36} + 30331 q^{37} - 5256 q^{38} + 1089 q^{39} - 2560 q^{40} + 8323 q^{41} - 6516 q^{42} + 30851 q^{43} - 5584 q^{44} + 3240 q^{45} - 4896 q^{46} - 5730 q^{47} + 18432 q^{48} + 32295 q^{49} - 38368 q^{50} + 3933 q^{51} + 1936 q^{52} - 33524 q^{53} - 23328 q^{54} + 23660 q^{55} - 11584 q^{56} + 11826 q^{57} - 21104 q^{58} - 27848 q^{59} + 5760 q^{60} + 2692 q^{61} - 73328 q^{62} + 14661 q^{63} + 32768 q^{64} - 59892 q^{65} + 12564 q^{66} + 56244 q^{67} + 6992 q^{68} + 11016 q^{69} - 78072 q^{70} - 48473 q^{71} - 41472 q^{72} - 30796 q^{73} - 121324 q^{74} + 86328 q^{75} + 21024 q^{76} + 59683 q^{77} - 4356 q^{78} + 135513 q^{79} + 10240 q^{80} + 52488 q^{81} - 33292 q^{82} - 88111 q^{83} + 26064 q^{84} + 114418 q^{85} - 123404 q^{86} + 47484 q^{87} + 22336 q^{88} - 112196 q^{89} - 12960 q^{90} + 377433 q^{91} + 19584 q^{92} + 164988 q^{93} + 22920 q^{94} + 328146 q^{95} - 73728 q^{96} + 551378 q^{97} - 129180 q^{98} - 28269 q^{99}+O(q^{100}) \) 8 * q - 32 * q^2 + 72 * q^3 + 128 * q^4 + 40 * q^5 - 288 * q^6 + 181 * q^7 - 512 * q^8 + 648 * q^9 - 160 * q^10 - 349 * q^11 + 1152 * q^12 + 121 * q^13 - 724 * q^14 + 360 * q^15 + 2048 * q^16 + 437 * q^17 - 2592 * q^18 + 1314 * q^19 + 640 * q^20 + 1629 * q^21 + 1396 * q^22 + 1224 * q^23 - 4608 * q^24 + 9592 * q^25 - 484 * q^26 + 5832 * q^27 + 2896 * q^28 + 5276 * q^29 - 1440 * q^30 + 18332 * q^31 - 8192 * q^32 - 3141 * q^33 - 1748 * q^34 + 19518 * q^35 + 10368 * q^36 + 30331 * q^37 - 5256 * q^38 + 1089 * q^39 - 2560 * q^40 + 8323 * q^41 - 6516 * q^42 + 30851 * q^43 - 5584 * q^44 + 3240 * q^45 - 4896 * q^46 - 5730 * q^47 + 18432 * q^48 + 32295 * q^49 - 38368 * q^50 + 3933 * q^51 + 1936 * q^52 - 33524 * q^53 - 23328 * q^54 + 23660 * q^55 - 11584 * q^56 + 11826 * q^57 - 21104 * q^58 - 27848 * q^59 + 5760 * q^60 + 2692 * q^61 - 73328 * q^62 + 14661 * q^63 + 32768 * q^64 - 59892 * q^65 + 12564 * q^66 + 56244 * q^67 + 6992 * q^68 + 11016 * q^69 - 78072 * q^70 - 48473 * q^71 - 41472 * q^72 - 30796 * q^73 - 121324 * q^74 + 86328 * q^75 + 21024 * q^76 + 59683 * q^77 - 4356 * q^78 + 135513 * q^79 + 10240 * q^80 + 52488 * q^81 - 33292 * q^82 - 88111 * q^83 + 26064 * q^84 + 114418 * q^85 - 123404 * q^86 + 47484 * q^87 + 22336 * q^88 - 112196 * q^89 - 12960 * q^90 + 377433 * q^91 + 19584 * q^92 + 164988 * q^93 + 22920 * q^94 + 328146 * q^95 - 73728 * q^96 + 551378 * q^97 - 129180 * q^98 - 28269 * q^99

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