LMFDB - Embedded newform 354.6.a.h.1.8

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			1.8
Root			$85.8007$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +90.8007 q^{5} -36.0000 q^{6} +19.2910 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +90.8007 q^{5} -36.0000 q^{6} +19.2910 q^{7} -64.0000 q^{8} +81.0000 q^{9} -363.203 q^{10} -68.0658 q^{11} +144.000 q^{12} +977.925 q^{13} -77.1641 q^{14} +817.206 q^{15} +256.000 q^{16} -635.634 q^{17} -324.000 q^{18} -2266.32 q^{19} +1452.81 q^{20} +173.619 q^{21} +272.263 q^{22} +4987.84 q^{23} -576.000 q^{24} +5119.77 q^{25} -3911.70 q^{26} +729.000 q^{27} +308.657 q^{28} +2939.63 q^{29} -3268.83 q^{30} +4390.90 q^{31} -1024.00 q^{32} -612.592 q^{33} +2542.54 q^{34} +1751.64 q^{35} +1296.00 q^{36} +792.231 q^{37} +9065.29 q^{38} +8801.33 q^{39} -5811.24 q^{40} -85.1653 q^{41} -694.477 q^{42} +5645.02 q^{43} -1089.05 q^{44} +7354.86 q^{45} -19951.4 q^{46} -4447.34 q^{47} +2304.00 q^{48} -16434.9 q^{49} -20479.1 q^{50} -5720.71 q^{51} +15646.8 q^{52} -27302.3 q^{53} -2916.00 q^{54} -6180.42 q^{55} -1234.63 q^{56} -20396.9 q^{57} -11758.5 q^{58} -3481.00 q^{59} +13075.3 q^{60} -54081.5 q^{61} -17563.6 q^{62} +1562.57 q^{63} +4096.00 q^{64} +88796.3 q^{65} +2450.37 q^{66} +1863.86 q^{67} -10170.1 q^{68} +44890.6 q^{69} -7006.56 q^{70} +54813.8 q^{71} -5184.00 q^{72} +17689.4 q^{73} -3168.92 q^{74} +46077.9 q^{75} -36261.2 q^{76} -1313.06 q^{77} -35205.3 q^{78} +69708.2 q^{79} +23245.0 q^{80} +6561.00 q^{81} +340.661 q^{82} +22722.8 q^{83} +2777.91 q^{84} -57716.0 q^{85} -22580.1 q^{86} +26456.6 q^{87} +4356.21 q^{88} -51172.2 q^{89} -29419.4 q^{90} +18865.2 q^{91} +79805.5 q^{92} +39518.1 q^{93} +17789.4 q^{94} -205784. q^{95} -9216.00 q^{96} +166854. q^{97} +65739.4 q^{98} -5513.33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	90.8007	1.62429	0.812146	−	0.583454i	$-0.198299\pi$
$5$	90.8007	1.62429	0.812146	+	0.583454i	$0.198299\pi$
$6$	−36.0000	−0.408248
$7$	19.2910	0.148803	0.0744013	−	0.997228i	$-0.476295\pi$
$7$	19.2910	0.148803	0.0744013	+	0.997228i	$0.476295\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−363.203	−1.14855
$11$	−68.0658	−0.169608	−0.0848041	−	0.996398i	$-0.527026\pi$
$11$	−68.0658	−0.169608	−0.0848041	+	0.996398i	$0.527026\pi$
$12$	144.000	0.288675
$13$	977.925	1.60490	0.802449	−	0.596721i	$-0.203530\pi$
$13$	977.925	1.60490	0.802449	+	0.596721i	$0.203530\pi$
$14$	−77.1641	−0.105219
$15$	817.206	0.937786
$16$	256.000	0.250000
$17$	−635.634	−0.533439	−0.266720	−	0.963774i	$-0.585940\pi$
$17$	−635.634	−0.533439	−0.266720	+	0.963774i	$0.585940\pi$
$18$	−324.000	−0.235702
$19$	−2266.32	−1.44025	−0.720125	−	0.693845i	$-0.755915\pi$
$19$	−2266.32	−1.44025	−0.720125	+	0.693845i	$0.755915\pi$
$20$	1452.81	0.812146
$21$	173.619	0.0859112
$22$	272.263	0.119931
$23$	4987.84	1.96604	0.983022	−	0.183490i	$-0.0587394\pi$
$23$	4987.84	1.96604	0.983022	+	0.183490i	$0.0587394\pi$
$24$	−576.000	−0.204124
$25$	5119.77	1.63833
$26$	−3911.70	−1.13483
$27$	729.000	0.192450
$28$	308.657	0.0744013
$29$	2939.63	0.649078	0.324539	−	0.945872i	$-0.394791\pi$
$29$	2939.63	0.649078	0.324539	+	0.945872i	$0.394791\pi$
$30$	−3268.83	−0.663115
$31$	4390.90	0.820634	0.410317	−	0.911943i	$-0.365418\pi$
$31$	4390.90	0.820634	0.410317	+	0.911943i	$0.365418\pi$
$32$	−1024.00	−0.176777
$33$	−612.592	−0.0979234
$34$	2542.54	0.377198
$35$	1751.64	0.241699
$36$	1296.00	0.166667
$37$	792.231	0.0951365	0.0475683	−	0.998868i	$-0.484853\pi$
$37$	792.231	0.0951365	0.0475683	+	0.998868i	$0.484853\pi$
$38$	9065.29	1.01841
$39$	8801.33	0.926588
$40$	−5811.24	−0.574274
$41$	−85.1653	−0.00791231	−0.00395615	−	0.999992i	$-0.501259\pi$
$41$	−85.1653	−0.00791231	−0.00395615	+	0.999992i	$0.501259\pi$
$42$	−694.477	−0.0607484
$43$	5645.02	0.465580	0.232790	−	0.972527i	$-0.425215\pi$
$43$	5645.02	0.465580	0.232790	+	0.972527i	$0.425215\pi$
$44$	−1089.05	−0.0848041
$45$	7354.86	0.541431
$46$	−19951.4	−1.39020
$47$	−4447.34	−0.293668	−0.146834	−	0.989161i	$-0.546908\pi$
$47$	−4447.34	−0.293668	−0.146834	+	0.989161i	$0.546908\pi$
$48$	2304.00	0.144338
$49$	−16434.9	−0.977858
$50$	−20479.1	−1.15847
$51$	−5720.71	−0.307981
$52$	15646.8	0.802449
$53$	−27302.3	−1.33508	−0.667542	−	0.744572i	$-0.732654\pi$
$53$	−27302.3	−1.33508	−0.667542	+	0.744572i	$0.732654\pi$
$54$	−2916.00	−0.136083
$55$	−6180.42	−0.275493
$56$	−1234.63	−0.0526096
$57$	−20396.9	−0.831529
$58$	−11758.5	−0.458968
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	13075.3	0.468893
$61$	−54081.5	−1.86090	−0.930452	−	0.366413i	$-0.880586\pi$
$61$	−54081.5	−1.86090	−0.930452	+	0.366413i	$0.880586\pi$
$62$	−17563.6	−0.580276
$63$	1562.57	0.0496008
$64$	4096.00	0.125000
$65$	88796.3	2.60682
$66$	2450.37	0.0692423
$67$	1863.86	0.0507255	0.0253627	−	0.999678i	$-0.491926\pi$
$67$	1863.86	0.0507255	0.0253627	+	0.999678i	$0.491926\pi$
$68$	−10170.1	−0.266720
$69$	44890.6	1.13510
$70$	−7006.56	−0.170907
$71$	54813.8	1.29046	0.645229	−	0.763989i	$-0.276762\pi$
$71$	54813.8	1.29046	0.645229	+	0.763989i	$0.276762\pi$
$72$	−5184.00	−0.117851
$73$	17689.4	0.388512	0.194256	−	0.980951i	$-0.437771\pi$
$73$	17689.4	0.388512	0.194256	+	0.980951i	$0.437771\pi$
$74$	−3168.92	−0.0672717
$75$	46077.9	0.945888
$76$	−36261.2	−0.720125
$77$	−1313.06	−0.0252381
$78$	−35205.3	−0.655197
$79$	69708.2	1.25665	0.628327	−	0.777949i	$-0.283740\pi$
$79$	69708.2	1.25665	0.628327	+	0.777949i	$0.283740\pi$
$80$	23245.0	0.406073
$81$	6561.00	0.111111
$82$	340.661	0.00559485
$83$	22722.8	0.362048	0.181024	−	0.983479i	$-0.442059\pi$
$83$	22722.8	0.362048	0.181024	+	0.983479i	$0.442059\pi$
$84$	2777.91	0.0429556
$85$	−57716.0	−0.866461
$86$	−22580.1	−0.329215
$87$	26456.6	0.374745
$88$	4356.21	0.0599656
$89$	−51172.2	−0.684792	−0.342396	−	0.939556i	$-0.611238\pi$
$89$	−51172.2	−0.684792	−0.342396	+	0.939556i	$0.611238\pi$
$90$	−29419.4	−0.382849
$91$	18865.2	0.238813
$92$	79805.5	0.983022
$93$	39518.1	0.473793
$94$	17789.4	0.207654
$95$	−205784.	−2.33939
$96$	−9216.00	−0.102062
$97$	166854.	1.80056	0.900278	−	0.435315i	$-0.143363\pi$
$97$	166854.	1.80056	0.900278	+	0.435315i	$0.143363\pi$
$98$	65739.4	0.691450
$99$	−5513.33	−0.0565361
$100$	81916.3	0.819163
$101$	−175489.	−1.71177	−0.855886	−	0.517164i	$-0.826988\pi$
$101$	−175489.	−1.71177	−0.855886	+	0.517164i	$0.826988\pi$
$102$	22882.8	0.217776
$103$	94644.9	0.879031	0.439516	−	0.898235i	$-0.355150\pi$
$103$	94644.9	0.879031	0.439516	+	0.898235i	$0.355150\pi$
$104$	−62587.2	−0.567417
$105$	15764.8	0.139545
$106$	109209.	0.944048
$107$	45332.0	0.382777	0.191388	−	0.981514i	$-0.438701\pi$
$107$	45332.0	0.382777	0.191388	+	0.981514i	$0.438701\pi$
$108$	11664.0	0.0962250
$109$	−55813.1	−0.449955	−0.224978	−	0.974364i	$-0.572231\pi$
$109$	−55813.1	−0.449955	−0.224978	+	0.974364i	$0.572231\pi$
$110$	24721.7	0.194803
$111$	7130.08	0.0549271
$112$	4938.50	0.0372006
$113$	131430.	0.968271	0.484136	−	0.874993i	$-0.339134\pi$
$113$	131430.	0.968271	0.484136	+	0.874993i	$0.339134\pi$
$114$	81587.6	0.587979
$115$	452900.	3.19343
$116$	47034.0	0.324539
$117$	79211.9	0.534966
$118$	13924.0	0.0920575
$119$	−12262.0	−0.0793771
$120$	−52301.2	−0.331557
$121$	−156418.	−0.971233
$122$	216326.	1.31586
$123$	−766.488	−0.00456817
$124$	70254.4	0.410317
$125$	181126.	1.03683
$126$	−6250.29	−0.0350731
$127$	230101.	1.26593	0.632965	−	0.774180i	$-0.281838\pi$
$127$	230101.	1.26593	0.632965	+	0.774180i	$0.281838\pi$
$128$	−16384.0	−0.0883883
$129$	50805.1	0.268803
$130$	−355185.	−1.84330
$131$	−274638.	−1.39824	−0.699122	−	0.715002i	$-0.746426\pi$
$131$	−274638.	−1.39824	−0.699122	+	0.715002i	$0.746426\pi$
$132$	−9801.47	−0.0489617
$133$	−43719.7	−0.214313
$134$	−7455.44	−0.0358683
$135$	66193.7	0.312595
$136$	40680.6	0.188599
$137$	260740.	1.18688	0.593439	−	0.804879i	$-0.297770\pi$
$137$	260740.	1.18688	0.593439	+	0.804879i	$0.297770\pi$
$138$	−179562.	−0.802634
$139$	426230.	1.87114	0.935572	−	0.353136i	$-0.114885\pi$
$139$	426230.	1.87114	0.935572	+	0.353136i	$0.114885\pi$
$140$	28026.2	0.120849
$141$	−40026.1	−0.169549
$142$	−219255.	−0.912492
$143$	−66563.2	−0.272204
$144$	20736.0	0.0833333
$145$	266920.	1.05429
$146$	−70757.4	−0.274720
$147$	−147914.	−0.564566
$148$	12675.7	0.0475683
$149$	−260830.	−0.962479	−0.481240	−	0.876589i	$-0.659813\pi$
$149$	−260830.	−0.962479	−0.481240	+	0.876589i	$0.659813\pi$
$150$	−184312.	−0.668844
$151$	306281.	1.09314	0.546572	−	0.837412i	$-0.315933\pi$
$151$	306281.	1.09314	0.546572	+	0.837412i	$0.315933\pi$
$152$	145045.	0.509205
$153$	−51486.4	−0.177813
$154$	5252.24	0.0178461
$155$	398697.	1.33295
$156$	140821.	0.463294
$157$	−251309.	−0.813691	−0.406846	−	0.913497i	$-0.633371\pi$
$157$	−251309.	−0.813691	−0.406846	+	0.913497i	$0.633371\pi$
$158$	−278833.	−0.888589
$159$	−245720.	−0.770812
$160$	−92979.9	−0.287137
$161$	96220.6	0.292552
$162$	−26244.0	−0.0785674
$163$	141358.	0.416726	0.208363	−	0.978052i	$-0.433186\pi$
$163$	141358.	0.416726	0.208363	+	0.978052i	$0.433186\pi$
$164$	−1362.65	−0.00395615
$165$	−55623.8	−0.159056
$166$	−90891.1	−0.256007
$167$	40603.1	0.112659	0.0563297	−	0.998412i	$-0.482060\pi$
$167$	40603.1	0.112659	0.0563297	+	0.998412i	$0.482060\pi$
$168$	−11111.6	−0.0303742
$169$	585045.	1.57569
$170$	230864.	0.612681
$171$	−183572.	−0.480083
$172$	90320.3	0.232790
$173$	−109803.	−0.278933	−0.139466	−	0.990227i	$-0.544539\pi$
$173$	−109803.	−0.278933	−0.139466	+	0.990227i	$0.544539\pi$
$174$	−105827.	−0.264985
$175$	98765.6	0.243787
$176$	−17424.8	−0.0424021
$177$	−31329.0	−0.0751646
$178$	204689.	0.484221
$179$	−298219.	−0.695669	−0.347834	−	0.937556i	$-0.613083\pi$
$179$	−298219.	−0.695669	−0.347834	+	0.937556i	$0.613083\pi$
$180$	117678.	0.270715
$181$	292093.	0.662713	0.331356	−	0.943506i	$-0.392494\pi$
$181$	292093.	0.662713	0.331356	+	0.943506i	$0.392494\pi$
$182$	−75460.7	−0.168866
$183$	−486733.	−1.07439
$184$	−319222.	−0.695101
$185$	71935.1	0.154530
$186$	−158072.	−0.335022
$187$	43264.9	0.0904757
$188$	−71157.5	−0.146834
$189$	14063.2	0.0286371
$190$	823135.	1.65420
$191$	−433269.	−0.859359	−0.429679	−	0.902982i	$-0.641373\pi$
$191$	−433269.	−0.859359	−0.429679	+	0.902982i	$0.641373\pi$
$192$	36864.0	0.0721688
$193$	96493.8	0.186469	0.0932344	−	0.995644i	$-0.470279\pi$
$193$	96493.8	0.186469	0.0932344	+	0.995644i	$0.470279\pi$
$194$	−667415.	−1.27319
$195$	799167.	1.50505
$196$	−262958.	−0.488929
$197$	−842541.	−1.54677	−0.773385	−	0.633937i	$-0.781438\pi$
$197$	−842541.	−1.54677	−0.773385	+	0.633937i	$0.781438\pi$
$198$	22053.3	0.0399771
$199$	860765.	1.54082	0.770410	−	0.637549i	$-0.220051\pi$
$199$	860765.	1.54082	0.770410	+	0.637549i	$0.220051\pi$
$200$	−327665.	−0.579236
$201$	16774.7	0.0292864
$202$	701955.	1.21041
$203$	56708.4	0.0965845
$204$	−91531.3	−0.153991
$205$	−7733.07	−0.0128519
$206$	−378580.	−0.621569
$207$	404015.	0.655348
$208$	250349.	0.401224
$209$	154259.	0.244278
$210$	−63059.0	−0.0986731
$211$	−233993.	−0.361824	−0.180912	−	0.983499i	$-0.557905\pi$
$211$	−233993.	−0.361824	−0.180912	+	0.983499i	$0.557905\pi$
$212$	−436836.	−0.667542
$213$	493324.	0.745047
$214$	−181328.	−0.270664
$215$	512571.	0.756237
$216$	−46656.0	−0.0680414
$217$	84705.0	0.122112
$218$	223252.	0.318167
$219$	159204.	0.224308
$220$	−98886.7	−0.137747
$221$	−621603.	−0.856115
$222$	−28520.3	−0.0388393
$223$	33977.9	0.0457545	0.0228773	−	0.999738i	$-0.492717\pi$
$223$	33977.9	0.0457545	0.0228773	+	0.999738i	$0.492717\pi$
$224$	−19754.0	−0.0263048
$225$	414701.	0.546109
$226$	−525718.	−0.684671
$227$	28003.6	0.0360703	0.0180351	−	0.999837i	$-0.494259\pi$
$227$	28003.6	0.0360703	0.0180351	+	0.999837i	$0.494259\pi$
$228$	−326350.	−0.415764
$229$	−1.38721e6	−1.74805	−0.874026	−	0.485879i	$-0.838500\pi$
$229$	−1.38721e6	−1.74805	−0.874026	+	0.485879i	$0.838500\pi$
$230$	−1.81160e6	−2.25810
$231$	−11817.5	−0.0145712
$232$	−188136.	−0.229484
$233$	−49808.4	−0.0601052	−0.0300526	−	0.999548i	$-0.509567\pi$
$233$	−49808.4	−0.0601052	−0.0300526	+	0.999548i	$0.509567\pi$
$234$	−316848.	−0.378278
$235$	−403822.	−0.477002
$236$	−55696.0	−0.0650945
$237$	627373.	0.725530
$238$	49048.2	0.0561281
$239$	−266589.	−0.301889	−0.150945	−	0.988542i	$-0.548232\pi$
$239$	−266589.	−0.301889	−0.150945	+	0.988542i	$0.548232\pi$
$240$	209205.	0.234446
$241$	1.05040e6	1.16496	0.582482	−	0.812844i	$-0.302082\pi$
$241$	1.05040e6	1.16496	0.582482	+	0.812844i	$0.302082\pi$
$242$	625672.	0.686765
$243$	59049.0	0.0641500
$244$	−865304.	−0.930452
$245$	−1.49230e6	−1.58833
$246$	3065.95	0.00323019
$247$	−2.21629e6	−2.31145
$248$	−281018.	−0.290138
$249$	204505.	0.209029
$250$	−724505.	−0.733148
$251$	−1.18382e6	−1.18605	−0.593025	−	0.805184i	$-0.702066\pi$
$251$	−1.18382e6	−1.18605	−0.593025	+	0.805184i	$0.702066\pi$
$252$	25001.2	0.0248004
$253$	−339501.	−0.333457
$254$	−920405.	−0.895148
$255$	−519444.	−0.500252
$256$	65536.0	0.0625000
$257$	1.28679e6	1.21527	0.607636	−	0.794215i	$-0.292118\pi$
$257$	1.28679e6	1.21527	0.607636	+	0.794215i	$0.292118\pi$
$258$	−203221.	−0.190072
$259$	15282.9	0.0141566
$260$	1.42074e6	1.30341
$261$	238110.	0.216359
$262$	1.09855e6	0.988708
$263$	−959903.	−0.855733	−0.427866	−	0.903842i	$-0.640735\pi$
$263$	−959903.	−0.855733	−0.427866	+	0.903842i	$0.640735\pi$
$264$	39205.9	0.0346211
$265$	−2.47906e6	−2.16857
$266$	174879.	0.151542
$267$	−460549.	−0.395365
$268$	29821.7	0.0253627
$269$	923814.	0.778402	0.389201	−	0.921153i	$-0.372751\pi$
$269$	923814.	0.778402	0.389201	+	0.921153i	$0.372751\pi$
$270$	−264775.	−0.221038
$271$	−790352.	−0.653728	−0.326864	−	0.945071i	$-0.605992\pi$
$271$	−790352.	−0.653728	−0.326864	+	0.945071i	$0.605992\pi$
$272$	−162722.	−0.133360
$273$	169787.	0.137879
$274$	−1.04296e6	−0.839250
$275$	−348481.	−0.277874
$276$	718249.	0.567548
$277$	−106488.	−0.0833875	−0.0416937	−	0.999130i	$-0.513275\pi$
$277$	−106488.	−0.0833875	−0.0416937	+	0.999130i	$0.513275\pi$
$278$	−1.70492e6	−1.32310
$279$	355663.	0.273545
$280$	−112105.	−0.0854534
$281$	−1.78226e6	−1.34649	−0.673247	−	0.739418i	$-0.735101\pi$
$281$	−1.78226e6	−1.34649	−0.673247	+	0.739418i	$0.735101\pi$
$282$	160104.	0.119889
$283$	1.85517e6	1.37695	0.688476	−	0.725259i	$-0.258280\pi$
$283$	1.85517e6	1.37695	0.688476	+	0.725259i	$0.258280\pi$
$284$	877021.	0.645229
$285$	−1.85205e6	−1.35065
$286$	266253.	0.192477
$287$	−1642.93	−0.00117737
$288$	−82944.0	−0.0589256
$289$	−1.01583e6	−0.715443
$290$	−1.06768e6	−0.745497
$291$	1.50168e6	1.03955
$292$	283030.	0.194256
$293$	1.24918e6	0.850074	0.425037	−	0.905176i	$-0.360261\pi$
$293$	1.24918e6	0.850074	0.425037	+	0.905176i	$0.360261\pi$
$294$	591655.	0.399209
$295$	−316077.	−0.211465
$296$	−50702.8	−0.0336358
$297$	−49619.9	−0.0326411
$298$	1.04332e6	0.680576
$299$	4.87774e6	3.15530
$300$	737247.	0.472944
$301$	108898.	0.0692794
$302$	−1.22512e6	−0.772969
$303$	−1.57940e6	−0.988292
$304$	−580179.	−0.360062
$305$	−4.91064e6	−3.02265
$306$	205945.	0.125733
$307$	−2.08103e6	−1.26018	−0.630091	−	0.776521i	$-0.716982\pi$
$307$	−2.08103e6	−1.26018	−0.630091	+	0.776521i	$0.716982\pi$
$308$	−21008.9	−0.0126191
$309$	851804.	0.507509
$310$	−1.59479e6	−0.942537
$311$	2.44568e6	1.43383	0.716916	−	0.697159i	$-0.245553\pi$
$311$	2.44568e6	1.43383	0.716916	+	0.697159i	$0.245553\pi$
$312$	−563285.	−0.327598
$313$	3.14454e6	1.81425	0.907124	−	0.420864i	$-0.138273\pi$
$313$	3.14454e6	1.81425	0.907124	+	0.420864i	$0.138273\pi$
$314$	1.00524e6	0.575367
$315$	141883.	0.0805663
$316$	1.11533e6	0.628327
$317$	−1.47321e6	−0.823409	−0.411705	−	0.911317i	$-0.635066\pi$
$317$	−1.47321e6	−0.823409	−0.411705	+	0.911317i	$0.635066\pi$
$318$	982881.	0.545046
$319$	−200088.	−0.110089
$320$	371920.	0.203037
$321$	407988.	0.220996
$322$	−384882.	−0.206866
$323$	1.44055e6	0.768286
$324$	104976.	0.0555556
$325$	5.00675e6	2.62934
$326$	−565431.	−0.294670
$327$	−502317.	−0.259782
$328$	5450.58	0.00279742
$329$	−85793.8	−0.0436985
$330$	222495.	0.112470
$331$	−2.61555e6	−1.31218	−0.656089	−	0.754684i	$-0.727790\pi$
$331$	−2.61555e6	−1.31218	−0.656089	+	0.754684i	$0.727790\pi$
$332$	363565.	0.181024
$333$	64170.7	0.0317122
$334$	−162412.	−0.0796623
$335$	169240.	0.0823930
$336$	44446.5	0.0214778
$337$	−1.31382e6	−0.630174	−0.315087	−	0.949063i	$-0.602034\pi$
$337$	−1.31382e6	−0.630174	−0.315087	+	0.949063i	$0.602034\pi$
$338$	−2.34018e6	−1.11418
$339$	1.18287e6	0.559032
$340$	−923456.	−0.433231
$341$	−298870.	−0.139186
$342$	734289.	0.339470
$343$	−641270.	−0.294310
$344$	−361281.	−0.164607
$345$	4.07610e6	1.84373
$346$	439212.	0.197235
$347$	−2.15457e6	−0.960587	−0.480294	−	0.877108i	$-0.659470\pi$
$347$	−2.15457e6	−0.960587	−0.480294	+	0.877108i	$0.659470\pi$
$348$	423306.	0.187373
$349$	−122315.	−0.0537545	−0.0268773	−	0.999639i	$-0.508556\pi$
$349$	−122315.	−0.0537545	−0.0268773	+	0.999639i	$0.508556\pi$
$350$	−395062.	−0.172383
$351$	712907.	0.308863
$352$	69699.3	0.0299828
$353$	−1.52821e6	−0.652750	−0.326375	−	0.945240i	$-0.605827\pi$
$353$	−1.52821e6	−0.652750	−0.326375	+	0.945240i	$0.605827\pi$
$354$	125316.	0.0531494
$355$	4.97713e6	2.09608
$356$	−818755.	−0.342396
$357$	−110358.	−0.0458284
$358$	1.19288e6	0.491912
$359$	571327.	0.233964	0.116982	−	0.993134i	$-0.462678\pi$
$359$	571327.	0.233964	0.116982	+	0.993134i	$0.462678\pi$
$360$	−470711.	−0.191425
$361$	2.66012e6	1.07432
$362$	−1.16837e6	−0.468609
$363$	−1.40776e6	−0.560742
$364$	301843.	0.119406
$365$	1.60621e6	0.631058
$366$	1.94693e6	0.759711
$367$	−4.74418e6	−1.83864	−0.919319	−	0.393514i	$-0.871259\pi$
$367$	−4.74418e6	−1.83864	−0.919319	+	0.393514i	$0.871259\pi$
$368$	1.27689e6	0.491511
$369$	−6898.39	−0.00263744
$370$	−287740.	−0.109269
$371$	−526689.	−0.198664
$372$	632290.	0.236897
$373$	2.62099e6	0.975424	0.487712	−	0.873005i	$-0.337832\pi$
$373$	2.62099e6	0.975424	0.487712	+	0.873005i	$0.337832\pi$
$374$	−173060.	−0.0639760
$375$	1.63014e6	0.598613
$376$	284630.	0.103827
$377$	2.87473e6	1.04170
$378$	−56252.6	−0.0202495
$379$	40496.3	0.0144816	0.00724081	−	0.999974i	$-0.497695\pi$
$379$	40496.3	0.0144816	0.00724081	+	0.999974i	$0.497695\pi$
$380$	−3.29254e6	−1.16969
$381$	2.07091e6	0.730885
$382$	1.73308e6	0.607658
$383$	−1.86409e6	−0.649335	−0.324668	−	0.945828i	$-0.605252\pi$
$383$	−1.86409e6	−0.649335	−0.324668	+	0.945828i	$0.605252\pi$
$384$	−147456.	−0.0510310
$385$	−119227.	−0.0409941
$386$	−385975.	−0.131853
$387$	457246.	0.155193
$388$	2.66966e6	0.900278
$389$	3.75948e6	1.25966	0.629830	−	0.776733i	$-0.283124\pi$
$389$	3.75948e6	1.25966	0.629830	+	0.776733i	$0.283124\pi$
$390$	−3.19667e6	−1.06423
$391$	−3.17044e6	−1.04876
$392$	1.05183e6	0.345725
$393$	−2.47175e6	−0.807277
$394$	3.37016e6	1.09373
$395$	6.32955e6	2.04117
$396$	−88213.2	−0.0282680
$397$	−4.67416e6	−1.48843	−0.744214	−	0.667942i	$-0.767175\pi$
$397$	−4.67416e6	−1.48843	−0.744214	+	0.667942i	$0.767175\pi$
$398$	−3.44306e6	−1.08952
$399$	−393477.	−0.123734
$400$	1.31066e6	0.409581
$401$	−2.81671e6	−0.874745	−0.437372	−	0.899280i	$-0.644091\pi$
$401$	−2.81671e6	−0.874745	−0.437372	+	0.899280i	$0.644091\pi$
$402$	−67098.9	−0.0207086
$403$	4.29397e6	1.31703
$404$	−2.80782e6	−0.855886
$405$	595743.	0.180477
$406$	−226834.	−0.0682955
$407$	−53923.8	−0.0161359
$408$	366125.	0.108888
$409$	3.61326e6	1.06805	0.534024	−	0.845469i	$-0.320679\pi$
$409$	3.61326e6	1.06805	0.534024	+	0.845469i	$0.320679\pi$
$410$	30932.3	0.00908767
$411$	2.34666e6	0.685245
$412$	1.51432e6	0.439516
$413$	−67152.1	−0.0193724
$414$	−1.61606e6	−0.463401
$415$	2.06324e6	0.588072
$416$	−1.00140e6	−0.283708
$417$	3.83607e6	1.08031
$418$	−617036.	−0.172731
$419$	−2.23385e6	−0.621610	−0.310805	−	0.950474i	$-0.600599\pi$
$419$	−2.23385e6	−0.621610	−0.310805	+	0.950474i	$0.600599\pi$
$420$	252236.	0.0697724
$421$	6.08814e6	1.67409	0.837047	−	0.547132i	$-0.184280\pi$
$421$	6.08814e6	1.67409	0.837047	+	0.547132i	$0.184280\pi$
$422$	935973.	0.255848
$423$	−360235.	−0.0978892
$424$	1.74734e6	0.472024
$425$	−3.25430e6	−0.873947
$426$	−1.97330e6	−0.526827
$427$	−1.04329e6	−0.276907
$428$	725312.	0.191388
$429$	−599069.	−0.157157
$430$	−2.05029e6	−0.534741
$431$	−6.26855e6	−1.62545	−0.812726	−	0.582646i	$-0.802018\pi$
$431$	−6.26855e6	−1.62545	−0.812726	+	0.582646i	$0.802018\pi$
$432$	186624.	0.0481125
$433$	−1.47296e6	−0.377546	−0.188773	−	0.982021i	$-0.560451\pi$
$433$	−1.47296e6	−0.377546	−0.188773	+	0.982021i	$0.560451\pi$
$434$	−338820.	−0.0863465
$435$	2.40228e6	0.608696
$436$	−893009.	−0.224978
$437$	−1.13041e7	−2.83159
$438$	−636817.	−0.158609
$439$	−2.88487e6	−0.714439	−0.357219	−	0.934021i	$-0.616275\pi$
$439$	−2.88487e6	−0.714439	−0.357219	+	0.934021i	$0.616275\pi$
$440$	395547.	0.0974016
$441$	−1.33122e6	−0.325953
$442$	2.48641e6	0.605365
$443$	628814.	0.152234	0.0761172	−	0.997099i	$-0.475748\pi$
$443$	628814.	0.152234	0.0761172	+	0.997099i	$0.475748\pi$
$444$	114081.	0.0274635
$445$	−4.64647e6	−1.11230
$446$	−135911.	−0.0323533
$447$	−2.34747e6	−0.555688
$448$	79016.1	0.0186003
$449$	−6.14446e6	−1.43836	−0.719180	−	0.694823i	$-0.755482\pi$
$449$	−6.14446e6	−1.43836	−0.719180	+	0.694823i	$0.755482\pi$
$450$	−1.65880e6	−0.386157
$451$	5796.84	0.00134199
$452$	2.10287e6	0.484136
$453$	2.75653e6	0.631127
$454$	−112014.	−0.0255055
$455$	1.71297e6	0.387902
$456$	1.30540e6	0.293990
$457$	20719.4	0.00464072	0.00232036	−	0.999997i	$-0.499261\pi$
$457$	20719.4	0.00464072	0.00232036	+	0.999997i	$0.499261\pi$
$458$	5.54885e6	1.23606
$459$	−463377.	−0.102660
$460$	7.24639e6	1.59671
$461$	4.21856e6	0.924510	0.462255	−	0.886747i	$-0.347040\pi$
$461$	4.21856e6	0.924510	0.462255	+	0.886747i	$0.347040\pi$
$462$	47270.1	0.0103034
$463$	1.38091e6	0.299373	0.149687	−	0.988733i	$-0.452174\pi$
$463$	1.38091e6	0.299373	0.149687	+	0.988733i	$0.452174\pi$
$464$	752544.	0.162270
$465$	3.58827e6	0.769579
$466$	199233.	0.0425008
$467$	−3.72868e6	−0.791157	−0.395579	−	0.918432i	$-0.629456\pi$
$467$	−3.72868e6	−0.791157	−0.395579	+	0.918432i	$0.629456\pi$
$468$	1.26739e6	0.267483
$469$	35955.8	0.00754808
$470$	1.61529e6	0.337291
$471$	−2.26179e6	−0.469785
$472$	222784.	0.0460287
$473$	−384232.	−0.0789662
$474$	−2.50949e6	−0.513027
$475$	−1.16030e7	−2.35960
$476$	−196193.	−0.0396886
$477$	−2.21148e6	−0.445028
$478$	1.06636e6	0.213468
$479$	−894333.	−0.178099	−0.0890493	−	0.996027i	$-0.528383\pi$
$479$	−894333.	−0.178099	−0.0890493	+	0.996027i	$0.528383\pi$
$480$	−836819.	−0.165779
$481$	774742.	0.152684
$482$	−4.20160e6	−0.823754
$483$	865985.	0.168905
$484$	−2.50269e6	−0.485617
$485$	1.51504e7	2.92463
$486$	−236196.	−0.0453609
$487$	7.04968e6	1.34694	0.673468	−	0.739216i	$-0.264804\pi$
$487$	7.04968e6	1.34694	0.673468	+	0.739216i	$0.264804\pi$
$488$	3.46122e6	0.657929
$489$	1.27222e6	0.240597
$490$	5.96919e6	1.12312
$491$	−1.95206e6	−0.365418	−0.182709	−	0.983167i	$-0.558487\pi$
$491$	−1.95206e6	−0.365418	−0.182709	+	0.983167i	$0.558487\pi$
$492$	−12263.8	−0.00228409
$493$	−1.86853e6	−0.346244
$494$	8.86518e6	1.63444
$495$	−500614.	−0.0918311
$496$	1.12407e6	0.205158
$497$	1.05741e6	0.192023
$498$	−818020.	−0.147806
$499$	−8.63432e6	−1.55230	−0.776152	−	0.630546i	$-0.782831\pi$
$499$	−8.63432e6	−1.55230	−0.776152	+	0.630546i	$0.782831\pi$
$500$	2.89802e6	0.518414
$501$	365428.	0.0650440
$502$	4.73529e6	0.838663
$503$	7.38812e6	1.30201	0.651005	−	0.759074i	$-0.274348\pi$
$503$	7.38812e6	1.30201	0.651005	+	0.759074i	$0.274348\pi$
$504$	−100005.	−0.0175365
$505$	−1.59345e7	−2.78042
$506$	1.35801e6	0.235790
$507$	5.26540e6	0.909728
$508$	3.68162e6	0.632965
$509$	540033.	0.0923902	0.0461951	−	0.998932i	$-0.485290\pi$
$509$	540033.	0.0923902	0.0461951	+	0.998932i	$0.485290\pi$
$510$	2.07778e6	0.353731
$511$	341246.	0.0578116
$512$	−262144.	−0.0441942
$513$	−1.65215e6	−0.277176
$514$	−5.14715e6	−0.859328
$515$	8.59382e6	1.42780
$516$	812882.	0.134401
$517$	302712.	0.0498084
$518$	−61131.8	−0.0100102
$519$	−988228.	−0.161042
$520$	−5.68296e6	−0.921651
$521$	−1.12129e6	−0.180978	−0.0904889	−	0.995897i	$-0.528843\pi$
$521$	−1.12129e6	−0.180978	−0.0904889	+	0.995897i	$0.528843\pi$
$522$	−952439.	−0.152989
$523$	−6.91762e6	−1.10587	−0.552933	−	0.833226i	$-0.686491\pi$
$523$	−6.91762e6	−1.10587	−0.552933	+	0.833226i	$0.686491\pi$
$524$	−4.39421e6	−0.699122
$525$	888890.	0.140750
$526$	3.83961e6	0.605094
$527$	−2.79101e6	−0.437758
$528$	−156824.	−0.0244808
$529$	1.84422e7	2.86533
$530$	9.91626e6	1.53341
$531$	−281961.	−0.0433963
$532$	−699515.	−0.107156
$533$	−83285.3	−0.0126984
$534$	1.84220e6	0.279565
$535$	4.11618e6	0.621741
$536$	−119287.	−0.0179342
$537$	−2.68397e6	−0.401645
$538$	−3.69526e6	−0.550413
$539$	1.11865e6	0.165853
$540$	1.05910e6	0.156298
$541$	−8.25073e6	−1.21199	−0.605995	−	0.795468i	$-0.707225\pi$
$541$	−8.25073e6	−1.21199	−0.605995	+	0.795468i	$0.707225\pi$
$542$	3.16141e6	0.462256
$543$	2.62884e6	0.382617
$544$	650889.	0.0942996
$545$	−5.06786e6	−0.730859
$546$	−679147.	−0.0974949
$547$	−1.85242e6	−0.264710	−0.132355	−	0.991202i	$-0.542254\pi$
$547$	−1.85242e6	−0.264710	−0.132355	+	0.991202i	$0.542254\pi$
$548$	4.17184e6	0.593439
$549$	−4.38060e6	−0.620301
$550$	1.39392e6	0.196486
$551$	−6.66214e6	−0.934834
$552$	−2.87300e6	−0.401317
$553$	1.34474e6	0.186993
$554$	425951.	0.0589638
$555$	647416.	0.0892177
$556$	6.81968e6	0.935572
$557$	6.80130e6	0.928868	0.464434	−	0.885608i	$-0.346258\pi$
$557$	6.80130e6	0.928868	0.464434	+	0.885608i	$0.346258\pi$
$558$	−1.42265e6	−0.193425
$559$	5.52040e6	0.747208
$560$	448420.	0.0604247
$561$	389384.	0.0522362
$562$	7.12902e6	0.952115
$563$	−1.09352e7	−1.45397	−0.726983	−	0.686655i	$-0.759078\pi$
$563$	−1.09352e7	−1.45397	−0.726983	+	0.686655i	$0.759078\pi$
$564$	−640417.	−0.0847745
$565$	1.19339e7	1.57276
$566$	−7.42070e6	−0.973652
$567$	126568.	0.0165336
$568$	−3.50808e6	−0.456246
$569$	−8.01933e6	−1.03838	−0.519191	−	0.854658i	$-0.673767\pi$
$569$	−8.01933e6	−1.03838	−0.519191	+	0.854658i	$0.673767\pi$
$570$	7.40821e6	0.955051
$571$	−3.02983e6	−0.388891	−0.194445	−	0.980913i	$-0.562291\pi$
$571$	−3.02983e6	−0.388891	−0.194445	+	0.980913i	$0.562291\pi$
$572$	−1.06501e6	−0.136102
$573$	−3.89942e6	−0.496151
$574$	6571.71	0.000832527 0
$575$	2.55366e7	3.22102
$576$	331776.	0.0416667
$577$	−1.40643e7	−1.75864	−0.879321	−	0.476230i	$-0.842003\pi$
$577$	−1.40643e7	−1.75864	−0.879321	+	0.476230i	$0.842003\pi$
$578$	4.06330e6	0.505894
$579$	868444.	0.107658
$580$	4.27072e6	0.527146
$581$	438346.	0.0538737
$582$	−6.00674e6	−0.735074
$583$	1.85835e6	0.226441
$584$	−1.13212e6	−0.137360
$585$	7.19250e6	0.868941
$586$	−4.99673e6	−0.601093
$587$	3.16272e6	0.378848	0.189424	−	0.981895i	$-0.439338\pi$
$587$	3.16272e6	0.378848	0.189424	+	0.981895i	$0.439338\pi$
$588$	−2.36662e6	−0.282283
$589$	−9.95120e6	−1.18192
$590$	1.26431e6	0.149528
$591$	−7.58287e6	−0.893028
$592$	202811.	0.0237841
$593$	−5.09693e6	−0.595213	−0.297606	−	0.954689i	$-0.596188\pi$
$593$	−5.09693e6	−0.595213	−0.297606	+	0.954689i	$0.596188\pi$
$594$	198480.	0.0230808
$595$	−1.11340e6	−0.128932
$596$	−4.17328e6	−0.481240
$597$	7.74689e6	0.889593
$598$	−1.95109e7	−2.23113
$599$	−1.57513e7	−1.79370	−0.896851	−	0.442334i	$-0.854151\pi$
$599$	−1.57513e7	−1.79370	−0.896851	+	0.442334i	$0.854151\pi$
$600$	−2.94899e6	−0.334422
$601$	−6.38437e6	−0.720994	−0.360497	−	0.932760i	$-0.617393\pi$
$601$	−6.38437e6	−0.720994	−0.360497	+	0.932760i	$0.617393\pi$
$602$	−435593.	−0.0489880
$603$	150973.	0.0169085
$604$	4.90049e6	0.546572
$605$	−1.42029e7	−1.57757
$606$	6.31760e6	0.698828
$607$	−1.45247e6	−0.160006	−0.0800028	−	0.996795i	$-0.525493\pi$
$607$	−1.45247e6	−0.160006	−0.0800028	+	0.996795i	$0.525493\pi$
$608$	2.32071e6	0.254603
$609$	510376.	0.0557631
$610$	1.96425e7	2.13734
$611$	−4.34917e6	−0.471306
$612$	−823782.	−0.0889065
$613$	−1.11755e7	−1.20121	−0.600603	−	0.799547i	$-0.705073\pi$
$613$	−1.11755e7	−1.20121	−0.600603	+	0.799547i	$0.705073\pi$
$614$	8.32413e6	0.891083
$615$	−69597.6	−0.00742005
$616$	84035.8	0.00892303
$617$	3.29875e6	0.348848	0.174424	−	0.984671i	$-0.444194\pi$
$617$	3.29875e6	0.348848	0.174424	+	0.984671i	$0.444194\pi$
$618$	−3.40722e6	−0.358863
$619$	1.13187e7	1.18732	0.593661	−	0.804715i	$-0.297682\pi$
$619$	1.13187e7	1.18732	0.593661	+	0.804715i	$0.297682\pi$
$620$	6.37915e6	0.666475
$621$	3.63614e6	0.378365
$622$	−9.78271e6	−1.01387
$623$	−987164.	−0.101899
$624$	2.25314e6	0.231647
$625$	447120.	0.0457851
$626$	−1.25782e7	−1.28287
$627$	1.38833e6	0.141034
$628$	−4.02095e6	−0.406846
$629$	−503569.	−0.0507496
$630$	−567531.	−0.0569690
$631$	1.14284e6	0.114264	0.0571322	−	0.998367i	$-0.481804\pi$
$631$	1.14284e6	0.114264	0.0571322	+	0.998367i	$0.481804\pi$
$632$	−4.46132e6	−0.444294
$633$	−2.10594e6	−0.208899
$634$	5.89283e6	0.582238
$635$	2.08934e7	2.05624
$636$	−3.93153e6	−0.385406
$637$	−1.60721e7	−1.56936
$638$	800351.	0.0778447
$639$	4.43992e6	0.430153
$640$	−1.48768e6	−0.143569
$641$	−2.76850e6	−0.266133	−0.133067	−	0.991107i	$-0.542482\pi$
$641$	−2.76850e6	−0.266133	−0.133067	+	0.991107i	$0.542482\pi$
$642$	−1.63195e6	−0.156268
$643$	2.93152e6	0.279618	0.139809	−	0.990178i	$-0.455351\pi$
$643$	2.93152e6	0.279618	0.139809	+	0.990178i	$0.455351\pi$
$644$	1.53953e6	0.146276
$645$	4.61314e6	0.436614
$646$	−5.76221e6	−0.543260
$647$	1.24967e7	1.17364	0.586822	−	0.809716i	$-0.300379\pi$
$647$	1.24967e7	1.17364	0.586822	+	0.809716i	$0.300379\pi$
$648$	−419904.	−0.0392837
$649$	236937.	0.0220811
$650$	−2.00270e7	−1.85923
$651$	762345.	0.0705016
$652$	2.26172e6	0.208363
$653$	−1.51758e7	−1.39273	−0.696367	−	0.717686i	$-0.745202\pi$
$653$	−1.51758e7	−1.39273	−0.696367	+	0.717686i	$0.745202\pi$
$654$	2.00927e6	0.183694
$655$	−2.49374e7	−2.27116
$656$	−21802.3	−0.00197808
$657$	1.43284e6	0.129504
$658$	343175.	0.0308995
$659$	−5.13325e6	−0.460446	−0.230223	−	0.973138i	$-0.573946\pi$
$659$	−5.13325e6	−0.460446	−0.230223	+	0.973138i	$0.573946\pi$
$660$	−889980.	−0.0795281
$661$	3.04537e6	0.271104	0.135552	−	0.990770i	$-0.456719\pi$
$661$	3.04537e6	0.271104	0.135552	+	0.990770i	$0.456719\pi$
$662$	1.04622e7	0.927850
$663$	−5.59442e6	−0.494278
$664$	−1.45426e6	−0.128003
$665$	−3.96978e6	−0.348107
$666$	−256683.	−0.0224239
$667$	1.46624e7	1.27612
$668$	649649.	0.0563297
$669$	305801.	0.0264164
$670$	−676959.	−0.0582606
$671$	3.68110e6	0.315625
$672$	−177786.	−0.0151871
$673$	−7.81158e6	−0.664815	−0.332408	−	0.943136i	$-0.607861\pi$
$673$	−7.81158e6	−0.664815	−0.332408	+	0.943136i	$0.607861\pi$
$674$	5.25527e6	0.445600
$675$	3.73231e6	0.315296
$676$	9.36071e6	0.787847
$677$	−6.52434e6	−0.547097	−0.273549	−	0.961858i	$-0.588197\pi$
$677$	−6.52434e6	−0.547097	−0.273549	+	0.961858i	$0.588197\pi$
$678$	−4.73147e6	−0.395295
$679$	3.21878e6	0.267927
$680$	3.69383e6	0.306340
$681$	252032.	0.0208252
$682$	1.19548e6	0.0984196
$683$	1.98593e7	1.62896	0.814482	−	0.580189i	$-0.197021\pi$
$683$	1.98593e7	1.62896	0.814482	+	0.580189i	$0.197021\pi$
$684$	−2.93715e6	−0.240042
$685$	2.36754e7	1.92784
$686$	2.56508e6	0.208109
$687$	−1.24849e7	−1.00924
$688$	1.44512e6	0.116395
$689$	−2.66996e7	−2.14267
$690$	−1.63044e7	−1.30371
$691$	1.73704e7	1.38393	0.691965	−	0.721931i	$-0.256745\pi$
$691$	1.73704e7	1.38393	0.691965	+	0.721931i	$0.256745\pi$
$692$	−1.75685e6	−0.139466
$693$	−106358.	−0.00841271
$694$	8.61828e6	0.679238
$695$	3.87020e7	3.03928
$696$	−1.69322e6	−0.132493
$697$	54134.0	0.00422073
$698$	489259.	0.0380102
$699$	−448275.	−0.0347018
$700$	1.58025e6	0.121894
$701$	−2.35091e7	−1.80693	−0.903466	−	0.428660i	$-0.858986\pi$
$701$	−2.35091e7	−1.80693	−0.903466	+	0.428660i	$0.858986\pi$
$702$	−2.85163e6	−0.218399
$703$	−1.79545e6	−0.137020
$704$	−278797.	−0.0212010
$705$	−3.63440e6	−0.275397
$706$	6.11285e6	0.461564
$707$	−3.38536e6	−0.254716
$708$	−501264.	−0.0375823
$709$	−1.57935e7	−1.17995	−0.589975	−	0.807421i	$-0.700863\pi$
$709$	−1.57935e7	−1.17995	−0.589975	+	0.807421i	$0.700863\pi$
$710$	−1.99085e7	−1.48215
$711$	5.64636e6	0.418885
$712$	3.27502e6	0.242111
$713$	2.19011e7	1.61340
$714$	441433.	0.0324056
$715$	−6.04399e6	−0.442139
$716$	−4.77150e6	−0.347834
$717$	−2.39930e6	−0.174296
$718$	−2.28531e6	−0.165437
$719$	9.21582e6	0.664832	0.332416	−	0.943133i	$-0.392136\pi$
$719$	9.21582e6	0.664832	0.332416	+	0.943133i	$0.392136\pi$
$720$	1.88284e6	0.135358
$721$	1.82580e6	0.130802
$722$	−1.06405e7	−0.759658
$723$	9.45361e6	0.672592
$724$	4.67350e6	0.331356
$725$	1.50502e7	1.06340
$726$	5.63105e6	0.396504
$727$	−915909.	−0.0642712	−0.0321356	−	0.999484i	$-0.510231\pi$
$727$	−915909.	−0.0642712	−0.0321356	+	0.999484i	$0.510231\pi$
$728$	−1.20737e6	−0.0844331
$729$	531441.	0.0370370
$730$	−6.42482e6	−0.446225
$731$	−3.58816e6	−0.248358
$732$	−7.78773e6	−0.537197
$733$	−7.75153e6	−0.532878	−0.266439	−	0.963852i	$-0.585847\pi$
$733$	−7.75153e6	−0.532878	−0.266439	+	0.963852i	$0.585847\pi$
$734$	1.89767e7	1.30011
$735$	−1.34307e7	−0.917021
$736$	−5.10755e6	−0.347551
$737$	−126865.	−0.00860346
$738$	27593.6	0.00186495
$739$	1.76153e7	1.18653	0.593267	−	0.805006i	$-0.297838\pi$
$739$	1.76153e7	1.18653	0.593267	+	0.805006i	$0.297838\pi$
$740$	1.15096e6	0.0772648
$741$	−1.99466e7	−1.33452
$742$	2.10675e6	0.140477
$743$	−4.18084e6	−0.277838	−0.138919	−	0.990304i	$-0.544363\pi$
$743$	−4.18084e6	−0.277838	−0.138919	+	0.990304i	$0.544363\pi$
$744$	−2.52916e6	−0.167511
$745$	−2.36835e7	−1.56335
$746$	−1.04840e7	−0.689729
$747$	1.84055e6	0.120683
$748$	692239.	0.0452379
$749$	874501.	0.0569581
$750$	−6.52055e6	−0.423283
$751$	−201977.	−0.0130678	−0.00653389	−	0.999979i	$-0.502080\pi$
$751$	−201977.	−0.0130678	−0.00653389	+	0.999979i	$0.502080\pi$
$752$	−1.13852e6	−0.0734169
$753$	−1.06544e7	−0.684766
$754$	−1.14989e7	−0.736596
$755$	2.78105e7	1.77558
$756$	225011.	0.0143185
$757$	8.26507e6	0.524212	0.262106	−	0.965039i	$-0.415583\pi$
$757$	8.26507e6	0.524212	0.262106	+	0.965039i	$0.415583\pi$
$758$	−161985.	−0.0102401
$759$	−3.05551e6	−0.192522
$760$	1.31702e7	0.827098
$761$	2.87626e7	1.80039	0.900195	−	0.435487i	$-0.143424\pi$
$761$	2.87626e7	1.80039	0.900195	+	0.435487i	$0.143424\pi$
$762$	−8.28365e6	−0.516814
$763$	−1.07669e6	−0.0669545
$764$	−6.93231e6	−0.429679
$765$	−4.67500e6	−0.288820
$766$	7.45634e6	0.459149
$767$	−3.40416e6	−0.208940
$768$	589824.	0.0360844
$769$	4.49101e6	0.273860	0.136930	−	0.990581i	$-0.456276\pi$
$769$	4.49101e6	0.273860	0.136930	+	0.990581i	$0.456276\pi$
$770$	476907.	0.0289872
$771$	1.15811e7	0.701638
$772$	1.54390e6	0.0932344
$773$	−2.82516e7	−1.70057	−0.850286	−	0.526322i	$-0.823571\pi$
$773$	−2.82516e7	−1.70057	−0.850286	+	0.526322i	$0.823571\pi$
$774$	−1.82899e6	−0.109738
$775$	2.24804e7	1.34447
$776$	−1.06786e7	−0.636593
$777$	137547.	0.00817329
$778$	−1.50379e7	−0.890715
$779$	193012.	0.0113957
$780$	1.27867e7	0.752525
$781$	−3.73094e6	−0.218872
$782$	1.26818e7	0.741589
$783$	2.14299e6	0.124915
$784$	−4.20732e6	−0.244464
$785$	−2.28191e7	−1.32167
$786$	9.88698e6	0.570831
$787$	−1.40642e6	−0.0809428	−0.0404714	−	0.999181i	$-0.512886\pi$
$787$	−1.40642e6	−0.0809428	−0.0404714	+	0.999181i	$0.512886\pi$
$788$	−1.34807e7	−0.773385
$789$	−8.63913e6	−0.494058
$790$	−2.53182e7	−1.44333
$791$	2.53541e6	0.144081
$792$	352853.	0.0199885
$793$	−5.28876e7	−2.98656
$794$	1.86967e7	1.05248
$795$	−2.23116e7	−1.25202
$796$	1.37722e7	0.770410
$797$	−2.68656e7	−1.49814	−0.749068	−	0.662494i	$-0.769498\pi$
$797$	−2.68656e7	−1.49814	−0.749068	+	0.662494i	$0.769498\pi$
$798$	1.57391e6	0.0874928
$799$	2.82688e6	0.156654
$800$	−5.24264e6	−0.289618
$801$	−4.14494e6	−0.228264
$802$	1.12668e7	0.618538
$803$	−1.20404e6	−0.0658949
$804$	268396.	0.0146432
$805$	8.73690e6	0.475190
$806$	−1.71759e7	−0.931283
$807$	8.31433e6	0.449411
$808$	1.12313e7	0.605203
$809$	5.91282e6	0.317632	0.158816	−	0.987308i	$-0.449232\pi$
$809$	5.91282e6	0.317632	0.158816	+	0.987308i	$0.449232\pi$
$810$	−2.38297e6	−0.127616
$811$	−3.14466e7	−1.67889	−0.839443	−	0.543448i	$-0.817119\pi$
$811$	−3.14466e7	−1.67889	−0.839443	+	0.543448i	$0.817119\pi$
$812$	907334.	0.0482922
$813$	−7.11317e6	−0.377430
$814$	215695.	0.0114098
$815$	1.28354e7	0.676885
$816$	−1.46450e6	−0.0769953
$817$	−1.27934e7	−0.670551
$818$	−1.44530e7	−0.755224
$819$	1.52808e6	0.0796043
$820$	−123729.	−0.00642595
$821$	−1.26936e6	−0.0657246	−0.0328623	−	0.999460i	$-0.510462\pi$
$821$	−1.26936e6	−0.0657246	−0.0328623	+	0.999460i	$0.510462\pi$
$822$	−9.38664e6	−0.484541
$823$	−1.45973e7	−0.751228	−0.375614	−	0.926776i	$-0.622568\pi$
$823$	−1.45973e7	−0.751228	−0.375614	+	0.926776i	$0.622568\pi$
$824$	−6.05727e6	−0.310784
$825$	−3.13633e6	−0.160430
$826$	268608.	0.0136984
$827$	−857506.	−0.0435987	−0.0217993	−	0.999762i	$-0.506939\pi$
$827$	−857506.	−0.0435987	−0.0217993	+	0.999762i	$0.506939\pi$
$828$	6.46424e6	0.327674
$829$	−3.05043e6	−0.154161	−0.0770804	−	0.997025i	$-0.524560\pi$
$829$	−3.05043e6	−0.154161	−0.0770804	+	0.997025i	$0.524560\pi$
$830$	−8.25298e6	−0.415830
$831$	−958391.	−0.0481438
$832$	4.00558e6	0.200612
$833$	1.04466e7	0.521628
$834$	−1.53443e7	−0.763891
$835$	3.68679e6	0.182992
$836$	2.46814e6	0.122139
$837$	3.20097e6	0.157931
$838$	8.93538e6	0.439545
$839$	−107056.	−0.00525059	−0.00262529	−	0.999997i	$-0.500836\pi$
$839$	−107056.	−0.00525059	−0.00262529	+	0.999997i	$0.500836\pi$
$840$	−1.00894e6	−0.0493366
$841$	−1.18698e7	−0.578698
$842$	−2.43526e7	−1.18376
$843$	−1.60403e7	−0.777398
$844$	−3.74389e6	−0.180912
$845$	5.31225e7	2.55939
$846$	1.44094e6	0.0692181
$847$	−3.01747e6	−0.144522
$848$	−6.98938e6	−0.333771
$849$	1.66966e7	0.794983
$850$	1.30172e7	0.617974
$851$	3.95152e6	0.187043
$852$	7.89319e6	0.372523
$853$	−2.31261e7	−1.08825	−0.544126	−	0.839003i	$-0.683139\pi$
$853$	−2.31261e7	−1.08825	−0.544126	+	0.839003i	$0.683139\pi$
$854$	4.17315e6	0.195803
$855$	−1.66685e7	−0.779795
$856$	−2.90125e6	−0.135332
$857$	−1.12261e7	−0.522129	−0.261064	−	0.965321i	$-0.584073\pi$
$857$	−1.12261e7	−0.522129	−0.261064	+	0.965321i	$0.584073\pi$
$858$	2.39628e6	0.111127
$859$	−8.10257e6	−0.374662	−0.187331	−	0.982297i	$-0.559984\pi$
$859$	−8.10257e6	−0.374662	−0.187331	+	0.982297i	$0.559984\pi$
$860$	8.20114e6	0.378119
$861$	−14786.3	−0.000679756 0
$862$	2.50742e7	1.14937
$863$	−1.98271e6	−0.0906217	−0.0453109	−	0.998973i	$-0.514428\pi$
$863$	−1.98271e6	−0.0906217	−0.0453109	+	0.998973i	$0.514428\pi$
$864$	−746496.	−0.0340207
$865$	−9.97020e6	−0.453068
$866$	5.89183e6	0.266966
$867$	−9.14244e6	−0.413061
$868$	1.35528e6	0.0610562
$869$	−4.74474e6	−0.213139
$870$	−9.60912e6	−0.430413
$871$	1.82271e6	0.0814092
$872$	3.57204e6	0.159083
$873$	1.35152e7	0.600185
$874$	4.52162e7	2.00224
$875$	3.49411e6	0.154283
$876$	2.54727e6	0.112154
$877$	7.19813e6	0.316025	0.158012	−	0.987437i	$-0.449491\pi$
$877$	7.19813e6	0.316025	0.158012	+	0.987437i	$0.449491\pi$
$878$	1.15395e7	0.505184
$879$	1.12426e7	0.490790
$880$	−1.58219e6	−0.0688734
$881$	3.75441e6	0.162968	0.0814840	−	0.996675i	$-0.474034\pi$
$881$	3.75441e6	0.162968	0.0814840	+	0.996675i	$0.474034\pi$
$882$	5.32489e6	0.230483
$883$	4.48940e7	1.93770	0.968850	−	0.247649i	$-0.0796581\pi$
$883$	4.48940e7	1.93770	0.968850	+	0.247649i	$0.0796581\pi$
$884$	−9.94564e6	−0.428058
$885$	−2.84470e6	−0.122089
$886$	−2.51526e6	−0.107646
$887$	−4.95164e6	−0.211320	−0.105660	−	0.994402i	$-0.533695\pi$
$887$	−4.95164e6	−0.211320	−0.105660	+	0.994402i	$0.533695\pi$
$888$	−456325.	−0.0194197
$889$	4.43889e6	0.188374
$890$	1.85859e7	0.786517
$891$	−446580.	−0.0188454
$892$	543646.	0.0228773
$893$	1.00791e7	0.422955
$894$	9.38987e6	0.392931
$895$	−2.70785e7	−1.12997
$896$	−316064.	−0.0131524
$897$	4.38996e7	1.82171
$898$	2.45778e7	1.01707
$899$	1.29076e7	0.532655
$900$	6.63522e6	0.273054
$901$	1.73542e7	0.712187
$902$	−23187.4	−0.000948932 0
$903$	980084.	0.0399985
$904$	−8.41149e6	−0.342336
$905$	2.65223e7	1.07644
$906$	−1.10261e7	−0.446274
$907$	3.76360e7	1.51910	0.759549	−	0.650451i	$-0.225420\pi$
$907$	3.76360e7	1.51910	0.759549	+	0.650451i	$0.225420\pi$
$908$	448058.	0.0180351
$909$	−1.42146e7	−0.570591
$910$	−6.85189e6	−0.274288
$911$	−2.13988e7	−0.854267	−0.427134	−	0.904189i	$-0.640477\pi$
$911$	−2.13988e7	−0.854267	−0.427134	+	0.904189i	$0.640477\pi$
$912$	−5.22161e6	−0.207882
$913$	−1.54664e6	−0.0614064
$914$	−82877.4	−0.00328149
$915$	−4.41957e7	−1.74513
$916$	−2.21954e7	−0.874026
$917$	−5.29806e6	−0.208062
$918$	1.85351e6	0.0725919
$919$	1.55931e7	0.609038	0.304519	−	0.952506i	$-0.401504\pi$
$919$	1.55931e7	0.609038	0.304519	+	0.952506i	$0.401504\pi$
$920$	−2.89856e7	−1.12905
$921$	−1.87293e7	−0.727566
$922$	−1.68742e7	−0.653727
$923$	5.36038e7	2.07105
$924$	−189080.	−0.00728562
$925$	4.05604e6	0.155865
$926$	−5.52364e6	−0.211689
$927$	7.66624e6	0.293010
$928$	−3.01018e6	−0.114742
$929$	2.51446e7	0.955884	0.477942	−	0.878392i	$-0.341383\pi$
$929$	2.51446e7	0.955884	0.477942	+	0.878392i	$0.341383\pi$
$930$	−1.43531e7	−0.544174
$931$	3.72467e7	1.40836
$932$	−796934.	−0.0300526
$933$	2.20111e7	0.827824
$934$	1.49147e7	0.559433
$935$	3.92849e6	0.146959
$936$	−5.06956e6	−0.189139
$937$	8.15147e6	0.303310	0.151655	−	0.988433i	$-0.451540\pi$
$937$	8.15147e6	0.303310	0.151655	+	0.988433i	$0.451540\pi$
$938$	−143823.	−0.00533730
$939$	2.83009e7	1.04746
$940$	−6.46115e6	−0.238501
$941$	−1.00929e7	−0.371570	−0.185785	−	0.982590i	$-0.559483\pi$
$941$	−1.00929e7	−0.371570	−0.185785	+	0.982590i	$0.559483\pi$
$942$	9.04714e6	0.332188
$943$	−424791.	−0.0155559
$944$	−891136.	−0.0325472
$945$	1.27694e6	0.0465150
$946$	1.53693e6	0.0558375
$947$	2.02114e7	0.732356	0.366178	−	0.930545i	$-0.380666\pi$
$947$	2.02114e7	0.732356	0.366178	+	0.930545i	$0.380666\pi$
$948$	1.00380e7	0.362765
$949$	1.72989e7	0.623522
$950$	4.64122e7	1.66849
$951$	−1.32589e7	−0.475396
$952$	784770.	0.0280640
$953$	2.40883e7	0.859159	0.429580	−	0.903029i	$-0.358662\pi$
$953$	2.40883e7	0.859159	0.429580	+	0.903029i	$0.358662\pi$
$954$	8.84593e6	0.314683
$955$	−3.93412e7	−1.39585
$956$	−4.26543e6	−0.150945
$957$	−1.80079e6	−0.0635599
$958$	3.57733e6	0.125935
$959$	5.02995e6	0.176611
$960$	3.34728e6	0.117223
$961$	−9.34914e6	−0.326560
$962$	−3.09897e6	−0.107964
$963$	3.67189e6	0.127592
$964$	1.68064e7	0.582482
$965$	8.76170e6	0.302880
$966$	−3.46394e6	−0.119434
$967$	3.45319e6	0.118756	0.0593778	−	0.998236i	$-0.481088\pi$
$967$	3.45319e6	0.118756	0.0593778	+	0.998236i	$0.481088\pi$
$968$	1.00108e7	0.343383
$969$	1.29650e7	0.443570
$970$	−6.06018e7	−2.06803
$971$	2.59394e7	0.882901	0.441451	−	0.897286i	$-0.354464\pi$
$971$	2.59394e7	0.882901	0.441451	+	0.897286i	$0.354464\pi$
$972$	944784.	0.0320750
$973$	8.22242e6	0.278431
$974$	−2.81987e7	−0.952428
$975$	4.50607e7	1.51805
$976$	−1.38449e7	−0.465226
$977$	−1.13153e7	−0.379253	−0.189626	−	0.981856i	$-0.560728\pi$
$977$	−1.13153e7	−0.379253	−0.189626	+	0.981856i	$0.560728\pi$
$978$	−5.08888e6	−0.170128
$979$	3.48307e6	0.116146
$980$	−2.38767e7	−0.794163
$981$	−4.52086e6	−0.149985
$982$	7.80824e6	0.258389
$983$	−5.59419e7	−1.84652	−0.923259	−	0.384179i	$-0.874484\pi$
$983$	−5.59419e7	−1.84652	−0.923259	+	0.384179i	$0.874484\pi$
$984$	49055.2	0.00161509
$985$	−7.65033e7	−2.51241
$986$	7.47410e6	0.244831
$987$	−772144.	−0.0252293
$988$	−3.54607e7	−1.15573
$989$	2.81564e7	0.915350
$990$	2.00246e6	0.0649344
$991$	−6.00724e7	−1.94308	−0.971540	−	0.236875i	$-0.923877\pi$
$991$	−6.00724e7	−1.94308	−0.971540	+	0.236875i	$0.923877\pi$
$992$	−4.49628e6	−0.145069
$993$	−2.35399e7	−0.757586
$994$	−4.22966e6	−0.135781
$995$	7.81581e7	2.50274
$996$	3.27208e6	0.104514
$997$	−1.94667e7	−0.620232	−0.310116	−	0.950699i	$-0.600368\pi$
$997$	−1.94667e7	−0.620232	−0.310116	+	0.950699i	$0.600368\pi$
$998$	3.45373e7	1.09765
$999$	577536.	0.0183090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.h.1.8	✓	8
3.2	odd	2		1062.6.a.m.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.h.1.8	✓	8	1.1	even	1	trivial
1062.6.a.m.1.1		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +90.8007 q^{5} -36.0000 q^{6} +19.2910 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +90.8007 q^{5} -36.0000 q^{6} +19.2910 q^{7} -64.0000 q^{8} +81.0000 q^{9} -363.203 q^{10} -68.0658 q^{11} +144.000 q^{12} +977.925 q^{13} -77.1641 q^{14} +817.206 q^{15} +256.000 q^{16} -635.634 q^{17} -324.000 q^{18} -2266.32 q^{19} +1452.81 q^{20} +173.619 q^{21} +272.263 q^{22} +4987.84 q^{23} -576.000 q^{24} +5119.77 q^{25} -3911.70 q^{26} +729.000 q^{27} +308.657 q^{28} +2939.63 q^{29} -3268.83 q^{30} +4390.90 q^{31} -1024.00 q^{32} -612.592 q^{33} +2542.54 q^{34} +1751.64 q^{35} +1296.00 q^{36} +792.231 q^{37} +9065.29 q^{38} +8801.33 q^{39} -5811.24 q^{40} -85.1653 q^{41} -694.477 q^{42} +5645.02 q^{43} -1089.05 q^{44} +7354.86 q^{45} -19951.4 q^{46} -4447.34 q^{47} +2304.00 q^{48} -16434.9 q^{49} -20479.1 q^{50} -5720.71 q^{51} +15646.8 q^{52} -27302.3 q^{53} -2916.00 q^{54} -6180.42 q^{55} -1234.63 q^{56} -20396.9 q^{57} -11758.5 q^{58} -3481.00 q^{59} +13075.3 q^{60} -54081.5 q^{61} -17563.6 q^{62} +1562.57 q^{63} +4096.00 q^{64} +88796.3 q^{65} +2450.37 q^{66} +1863.86 q^{67} -10170.1 q^{68} +44890.6 q^{69} -7006.56 q^{70} +54813.8 q^{71} -5184.00 q^{72} +17689.4 q^{73} -3168.92 q^{74} +46077.9 q^{75} -36261.2 q^{76} -1313.06 q^{77} -35205.3 q^{78} +69708.2 q^{79} +23245.0 q^{80} +6561.00 q^{81} +340.661 q^{82} +22722.8 q^{83} +2777.91 q^{84} -57716.0 q^{85} -22580.1 q^{86} +26456.6 q^{87} +4356.21 q^{88} -51172.2 q^{89} -29419.4 q^{90} +18865.2 q^{91} +79805.5 q^{92} +39518.1 q^{93} +17789.4 q^{94} -205784. q^{95} -9216.00 q^{96} +166854. q^{97} +65739.4 q^{98} -5513.33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} + 72 q^{3} + 128 q^{4} + 40 q^{5} - 288 q^{6} + 181 q^{7} - 512 q^{8} + 648 q^{9}+O(q^{10}) \) 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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