LMFDB - Embedded newform 177.6.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 $ x^12 - 4x^11 - 283x^10 + 1045x^9 + 27968x^8 - 94393x^7 - 1130486x^6 + 3566264x^5 + 15496192x^4 - 53008480x^3 - 16576192x^2 + 120303168*x - 50564480
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.87969$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.87969 q^{2} -9.00000 q^{3} -23.7074 q^{4} -77.5334 q^{5} +25.9172 q^{6} +45.2937 q^{7} +160.420 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-2.87969 q^{2} -9.00000 q^{3} -23.7074 q^{4} -77.5334 q^{5} +25.9172 q^{6} +45.2937 q^{7} +160.420 q^{8} +81.0000 q^{9} +223.272 q^{10} +155.365 q^{11} +213.367 q^{12} +523.303 q^{13} -130.432 q^{14} +697.801 q^{15} +296.678 q^{16} +1585.45 q^{17} -233.255 q^{18} -2043.33 q^{19} +1838.12 q^{20} -407.643 q^{21} -447.403 q^{22} -1063.14 q^{23} -1443.78 q^{24} +2886.43 q^{25} -1506.95 q^{26} -729.000 q^{27} -1073.80 q^{28} +2231.64 q^{29} -2009.45 q^{30} -8697.85 q^{31} -5987.78 q^{32} -1398.29 q^{33} -4565.61 q^{34} -3511.78 q^{35} -1920.30 q^{36} +15093.5 q^{37} +5884.16 q^{38} -4709.73 q^{39} -12437.9 q^{40} -864.137 q^{41} +1173.88 q^{42} +11392.8 q^{43} -3683.30 q^{44} -6280.21 q^{45} +3061.51 q^{46} +5535.68 q^{47} -2670.11 q^{48} -14755.5 q^{49} -8312.01 q^{50} -14269.1 q^{51} -12406.2 q^{52} +18099.6 q^{53} +2099.29 q^{54} -12046.0 q^{55} +7266.01 q^{56} +18390.0 q^{57} -6426.42 q^{58} -3481.00 q^{59} -16543.0 q^{60} -44361.9 q^{61} +25047.1 q^{62} +3668.79 q^{63} +7749.20 q^{64} -40573.5 q^{65} +4026.62 q^{66} -33357.0 q^{67} -37587.0 q^{68} +9568.25 q^{69} +10112.8 q^{70} +2860.19 q^{71} +12994.0 q^{72} -63785.8 q^{73} -43464.5 q^{74} -25977.9 q^{75} +48442.2 q^{76} +7037.06 q^{77} +13562.5 q^{78} +82957.4 q^{79} -23002.5 q^{80} +6561.00 q^{81} +2488.44 q^{82} -67941.5 q^{83} +9664.17 q^{84} -122926. q^{85} -32807.6 q^{86} -20084.8 q^{87} +24923.6 q^{88} +22542.4 q^{89} +18085.0 q^{90} +23702.3 q^{91} +25204.3 q^{92} +78280.6 q^{93} -15941.0 q^{94} +158427. q^{95} +53890.0 q^{96} +26284.2 q^{97} +42491.1 q^{98} +12584.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * 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 $

$2$	−2.87969	−0.509061	−0.254531	−	0.967065i	$-0.581921\pi$
$2$	−2.87969	−0.509061	−0.254531	+	0.967065i	$0.581921\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−23.7074	−0.740857
$5$	−77.5334	−1.38696	−0.693480	−	0.720476i	$-0.743923\pi$
$5$	−77.5334	−1.38696	−0.693480	+	0.720476i	$0.743923\pi$
$6$	25.9172	0.293907
$7$	45.2937	0.349376	0.174688	−	0.984624i	$-0.444108\pi$
$7$	45.2937	0.349376	0.174688	+	0.984624i	$0.444108\pi$
$8$	160.420	0.886203
$9$	81.0000	0.333333
$10$	223.272	0.706048
$11$	155.365	0.387143	0.193572	−	0.981086i	$-0.437993\pi$
$11$	155.365	0.387143	0.193572	+	0.981086i	$0.437993\pi$
$12$	213.367	0.427734
$13$	523.303	0.858806	0.429403	−	0.903113i	$-0.358724\pi$
$13$	523.303	0.858806	0.429403	+	0.903113i	$0.358724\pi$
$14$	−130.432	−0.177854
$15$	697.801	0.800762
$16$	296.678	0.289725
$17$	1585.45	1.33055	0.665275	−	0.746598i	$-0.268314\pi$
$17$	1585.45	1.33055	0.665275	+	0.746598i	$0.268314\pi$
$18$	−233.255	−0.169687
$19$	−2043.33	−1.29854	−0.649270	−	0.760558i	$-0.724926\pi$
$19$	−2043.33	−1.29854	−0.649270	+	0.760558i	$0.724926\pi$
$20$	1838.12	1.02754
$21$	−407.643	−0.201712
$22$	−447.403	−0.197080
$23$	−1063.14	−0.419055	−0.209527	−	0.977803i	$-0.567193\pi$
$23$	−1063.14	−0.419055	−0.209527	+	0.977803i	$0.567193\pi$
$24$	−1443.78	−0.511649
$25$	2886.43	0.923657
$26$	−1506.95	−0.437185
$27$	−729.000	−0.192450
$28$	−1073.80	−0.258837
$29$	2231.64	0.492753	0.246376	−	0.969174i	$-0.420760\pi$
$29$	2231.64	0.492753	0.246376	+	0.969174i	$0.420760\pi$
$30$	−2009.45	−0.407637
$31$	−8697.85	−1.62558	−0.812788	−	0.582559i	$-0.802051\pi$
$31$	−8697.85	−1.62558	−0.812788	+	0.582559i	$0.802051\pi$
$32$	−5987.78	−1.03369
$33$	−1398.29	−0.223517
$34$	−4565.61	−0.677332
$35$	−3511.78	−0.484570
$36$	−1920.30	−0.246952
$37$	15093.5	1.81253	0.906265	−	0.422711i	$-0.138921\pi$
$37$	15093.5	1.81253	0.906265	+	0.422711i	$0.138921\pi$
$38$	5884.16	0.661037
$39$	−4709.73	−0.495832
$40$	−12437.9	−1.22913
$41$	−864.137	−0.0802829	−0.0401414	−	0.999194i	$-0.512781\pi$
$41$	−864.137	−0.0802829	−0.0401414	+	0.999194i	$0.512781\pi$
$42$	1173.88	0.102684
$43$	11392.8	0.939633	0.469817	−	0.882764i	$-0.344320\pi$
$43$	11392.8	0.939633	0.469817	+	0.882764i	$0.344320\pi$
$44$	−3683.30	−0.286818
$45$	−6280.21	−0.462320
$46$	3061.51	0.213324
$47$	5535.68	0.365533	0.182767	−	0.983156i	$-0.441495\pi$
$47$	5535.68	0.365533	0.182767	+	0.983156i	$0.441495\pi$
$48$	−2670.11	−0.167273
$49$	−14755.5	−0.877937
$50$	−8312.01	−0.470198
$51$	−14269.1	−0.768194
$52$	−12406.2	−0.636252
$53$	18099.6	0.885071	0.442536	−	0.896751i	$-0.354079\pi$
$53$	18099.6	0.885071	0.442536	+	0.896751i	$0.354079\pi$
$54$	2099.29	0.0979689
$55$	−12046.0	−0.536952
$56$	7266.01	0.309618
$57$	18390.0	0.749713
$58$	−6426.42	−0.250841
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−16543.0	−0.593249
$61$	−44361.9	−1.52646	−0.763230	−	0.646127i	$-0.776387\pi$
$61$	−44361.9	−1.52646	−0.763230	+	0.646127i	$0.776387\pi$
$62$	25047.1	0.827518
$63$	3668.79	0.116459
$64$	7749.20	0.236487
$65$	−40573.5	−1.19113
$66$	4026.62	0.113784
$67$	−33357.0	−0.907821	−0.453910	−	0.891047i	$-0.649971\pi$
$67$	−33357.0	−0.907821	−0.453910	+	0.891047i	$0.649971\pi$
$68$	−37587.0	−0.985747
$69$	9568.25	0.241941
$70$	10112.8	0.246676
$71$	2860.19	0.0673363	0.0336681	−	0.999433i	$-0.489281\pi$
$71$	2860.19	0.0673363	0.0336681	+	0.999433i	$0.489281\pi$
$72$	12994.0	0.295401
$73$	−63785.8	−1.40093	−0.700466	−	0.713686i	$-0.747024\pi$
$73$	−63785.8	−1.40093	−0.700466	+	0.713686i	$0.747024\pi$
$74$	−43464.5	−0.922689
$75$	−25977.9	−0.533274
$76$	48442.2	0.962032
$77$	7037.06	0.135258
$78$	13562.5	0.252409
$79$	82957.4	1.49550	0.747751	−	0.663979i	$-0.231133\pi$
$79$	82957.4	1.49550	0.747751	+	0.663979i	$0.231133\pi$
$80$	−23002.5	−0.401837
$81$	6561.00	0.111111
$82$	2488.44	0.0408689
$83$	−67941.5	−1.08253	−0.541265	−	0.840852i	$-0.682054\pi$
$83$	−67941.5	−1.08253	−0.541265	+	0.840852i	$0.682054\pi$
$84$	9664.17	0.149440
$85$	−122926.	−1.84542
$86$	−32807.6	−0.478331
$87$	−20084.8	−0.284491
$88$	24923.6	0.343087
$89$	22542.4	0.301665	0.150833	−	0.988559i	$-0.451805\pi$
$89$	22542.4	0.301665	0.150833	+	0.988559i	$0.451805\pi$
$90$	18085.0	0.235349
$91$	23702.3	0.300046
$92$	25204.3	0.310459
$93$	78280.6	0.938527
$94$	−15941.0	−0.186079
$95$	158427.	1.80102
$96$	53890.0	0.596802
$97$	26284.2	0.283639	0.141820	−	0.989893i	$-0.454705\pi$
$97$	26284.2	0.283639	0.141820	+	0.989893i	$0.454705\pi$
$98$	42491.1	0.446924
$99$	12584.6	0.129048
$100$	−68429.7	−0.684297
$101$	−61695.6	−0.601798	−0.300899	−	0.953656i	$-0.597287\pi$
$101$	−61695.6	−0.601798	−0.300899	+	0.953656i	$0.597287\pi$
$102$	41090.5	0.391058
$103$	−65169.6	−0.605274	−0.302637	−	0.953106i	$-0.597867\pi$
$103$	−65169.6	−0.605274	−0.302637	+	0.953106i	$0.597867\pi$
$104$	83948.2	0.761076
$105$	31606.0	0.279767
$106$	−52121.0	−0.450556
$107$	153050.	1.29233	0.646167	−	0.763196i	$-0.276371\pi$
$107$	153050.	1.29233	0.646167	+	0.763196i	$0.276371\pi$
$108$	17282.7	0.142578
$109$	−203743.	−1.64254	−0.821271	−	0.570539i	$-0.806734\pi$
$109$	−203743.	−1.64254	−0.821271	+	0.570539i	$0.806734\pi$
$110$	34688.6	0.273342
$111$	−135841.	−1.04646
$112$	13437.7	0.101223
$113$	240950.	1.77514	0.887568	−	0.460678i	$-0.152394\pi$
$113$	240950.	1.77514	0.887568	+	0.460678i	$0.152394\pi$
$114$	−52957.5	−0.381650
$115$	82428.8	0.581212
$116$	−52906.4	−0.365059
$117$	42387.5	0.286269
$118$	10024.2	0.0662741
$119$	71811.1	0.464862
$120$	111941.	0.709637
$121$	−136913.	−0.850120
$122$	127748.	0.777061
$123$	7777.23	0.0463513
$124$	206203.	1.20432
$125$	18497.3	0.105885
$126$	−10565.0	−0.0592846
$127$	−150990.	−0.830689	−0.415344	−	0.909664i	$-0.636339\pi$
$127$	−150990.	−0.830689	−0.415344	+	0.909664i	$0.636339\pi$
$128$	169294.	0.913304
$129$	−102535.	−0.542498
$130$	116839.	0.606358
$131$	−250601.	−1.27586	−0.637932	−	0.770092i	$-0.720210\pi$
$131$	−250601.	−1.27586	−0.637932	+	0.770092i	$0.720210\pi$
$132$	33149.7	0.165594
$133$	−92550.2	−0.453679
$134$	96057.7	0.462136
$135$	56521.8	0.266921
$136$	254338.	1.17914
$137$	−15685.5	−0.0713996	−0.0356998	−	0.999363i	$-0.511366\pi$
$137$	−15685.5	−0.0713996	−0.0356998	+	0.999363i	$0.511366\pi$
$138$	−27553.6	−0.123163
$139$	67099.0	0.294563	0.147282	−	0.989095i	$-0.452948\pi$
$139$	67099.0	0.294563	0.147282	+	0.989095i	$0.452948\pi$
$140$	83255.1	0.358997
$141$	−49821.2	−0.211041
$142$	−8236.45	−0.0342783
$143$	81303.0	0.332481
$144$	24030.9	0.0965750
$145$	−173027.	−0.683428
$146$	183683.	0.713160
$147$	132799.	0.506877
$148$	−357827.	−1.34282
$149$	109381.	0.403623	0.201811	−	0.979424i	$-0.435317\pi$
$149$	109381.	0.403623	0.201811	+	0.979424i	$0.435317\pi$
$150$	74808.1	0.271469
$151$	−325298.	−1.16102	−0.580509	−	0.814254i	$-0.697146\pi$
$151$	−325298.	−1.16102	−0.580509	+	0.814254i	$0.697146\pi$
$152$	−327791.	−1.15077
$153$	128422.	0.443517
$154$	−20264.5	−0.0688549
$155$	674374.	2.25461
$156$	111655.	0.367340
$157$	−244345.	−0.791142	−0.395571	−	0.918435i	$-0.629453\pi$
$157$	−244345.	−0.791142	−0.395571	+	0.918435i	$0.629453\pi$
$158$	−238891.	−0.761303
$159$	−162896.	−0.510996
$160$	464253.	1.43369
$161$	−48153.5	−0.146408
$162$	−18893.6	−0.0565624
$163$	86224.9	0.254193	0.127097	−	0.991890i	$-0.459434\pi$
$163$	86224.9	0.254193	0.127097	+	0.991890i	$0.459434\pi$
$164$	20486.5	0.0594781
$165$	108414.	0.310009
$166$	195650.	0.551074
$167$	161244.	0.447396	0.223698	−	0.974659i	$-0.428187\pi$
$167$	161244.	0.447396	0.223698	+	0.974659i	$0.428187\pi$
$168$	−65394.1	−0.178758
$169$	−97447.0	−0.262453
$170$	353987.	0.939432
$171$	−165510.	−0.432847
$172$	−270093.	−0.696133
$173$	348734.	0.885887	0.442944	−	0.896549i	$-0.353934\pi$
$173$	348734.	0.885887	0.442944	+	0.896549i	$0.353934\pi$
$174$	57837.8	0.144823
$175$	130737.	0.322703
$176$	46093.5	0.112165
$177$	31329.0	0.0751646
$178$	−64915.0	−0.153566
$179$	−306324.	−0.714577	−0.357288	−	0.933994i	$-0.616299\pi$
$179$	−306324.	−0.714577	−0.357288	+	0.933994i	$0.616299\pi$
$180$	148887.	0.342513
$181$	525696.	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$181$	525696.	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$182$	−68255.3	−0.152742
$183$	399257.	0.881302
$184$	−170549.	−0.371367
$185$	−1.17025e6	−2.51391
$186$	−225424.	−0.477768
$187$	246324.	0.515114
$188$	−131237.	−0.270808
$189$	−33019.1	−0.0672374
$190$	−456219.	−0.916831
$191$	−540574.	−1.07219	−0.536095	−	0.844158i	$-0.680101\pi$
$191$	−540574.	−1.07219	−0.536095	+	0.844158i	$0.680101\pi$
$192$	−69742.8	−0.136536
$193$	−646535.	−1.24939	−0.624696	−	0.780868i	$-0.714777\pi$
$193$	−646535.	−1.24939	−0.624696	+	0.780868i	$0.714777\pi$
$194$	−75690.4	−0.144390
$195$	365161.	0.687698
$196$	349814.	0.650425
$197$	−628338.	−1.15353	−0.576764	−	0.816911i	$-0.695685\pi$
$197$	−628338.	−1.15353	−0.576764	+	0.816911i	$0.695685\pi$
$198$	−36239.6	−0.0656932
$199$	−196577.	−0.351884	−0.175942	−	0.984401i	$-0.556297\pi$
$199$	−196577.	−0.351884	−0.175942	+	0.984401i	$0.556297\pi$
$200$	463040.	0.818547
$201$	300213.	0.524130
$202$	177664.	0.306352
$203$	101079.	0.172156
$204$	338283.	0.569121
$205$	66999.5	0.111349
$206$	187668.	0.308121
$207$	−86114.3	−0.139685
$208$	155253.	0.248817
$209$	−317463.	−0.502721
$210$	−91015.3	−0.142418
$211$	−869514.	−1.34453	−0.672265	−	0.740310i	$-0.734679\pi$
$211$	−869514.	−1.34453	−0.672265	+	0.740310i	$0.734679\pi$
$212$	−429094.	−0.655711
$213$	−25741.7	−0.0388766
$214$	−440737.	−0.657877
$215$	−883321.	−1.30323
$216$	−116946.	−0.170550
$217$	−393958.	−0.567937
$218$	586716.	0.836154
$219$	574072.	0.808828
$220$	285579.	0.397804
$221$	829673.	1.14268
$222$	391180.	0.532715
$223$	−108640.	−0.146294	−0.0731472	−	0.997321i	$-0.523304\pi$
$223$	−108640.	−0.146294	−0.0731472	+	0.997321i	$0.523304\pi$
$224$	−271209.	−0.361146
$225$	233801.	0.307886
$226$	−693861.	−0.903653
$227$	−1.10451e6	−1.42268	−0.711338	−	0.702850i	$-0.751910\pi$
$227$	−1.10451e6	−1.42268	−0.711338	+	0.702850i	$0.751910\pi$
$228$	−435980.	−0.555430
$229$	113945.	0.143584	0.0717920	−	0.997420i	$-0.477128\pi$
$229$	113945.	0.143584	0.0717920	+	0.997420i	$0.477128\pi$
$230$	−237369.	−0.295872
$231$	−63333.5	−0.0780915
$232$	357999.	0.436679
$233$	−374241.	−0.451608	−0.225804	−	0.974173i	$-0.572501\pi$
$233$	−374241.	−0.451608	−0.225804	+	0.974173i	$0.572501\pi$
$234$	−122063.	−0.145728
$235$	−429200.	−0.506980
$236$	82525.5	0.0964513
$237$	−746616.	−0.863429
$238$	−206793.	−0.236643
$239$	−1.06804e6	−1.20946	−0.604731	−	0.796430i	$-0.706719\pi$
$239$	−1.06804e6	−1.20946	−0.604731	+	0.796430i	$0.706719\pi$
$240$	207022.	0.232001
$241$	−330951.	−0.367046	−0.183523	−	0.983015i	$-0.558750\pi$
$241$	−330951.	−0.367046	−0.183523	+	0.983015i	$0.558750\pi$
$242$	394266.	0.432763
$243$	−59049.0	−0.0641500
$244$	1.05170e6	1.13089
$245$	1.14404e6	1.21766
$246$	−22396.0	−0.0235957
$247$	−1.06928e6	−1.11519
$248$	−1.39531e6	−1.44059
$249$	611474.	0.624999
$250$	−53266.3	−0.0539017
$251$	903692.	0.905391	0.452695	−	0.891665i	$-0.350463\pi$
$251$	903692.	0.905391	0.452695	+	0.891665i	$0.350463\pi$
$252$	−86977.5	−0.0862791
$253$	−165175.	−0.162234
$254$	434803.	0.422872
$255$	1.10633e6	1.06545
$256$	−735487.	−0.701415
$257$	721353.	0.681264	0.340632	−	0.940197i	$-0.389359\pi$
$257$	721353.	0.681264	0.340632	+	0.940197i	$0.389359\pi$
$258$	295269.	0.276165
$259$	683640.	0.633254
$260$	961892.	0.882455
$261$	180763.	0.164251
$262$	721652.	0.649493
$263$	601446.	0.536176	0.268088	−	0.963394i	$-0.413608\pi$
$263$	601446.	0.536176	0.268088	+	0.963394i	$0.413608\pi$
$264$	−224313.	−0.198082
$265$	−1.40332e6	−1.22756
$266$	266516.	0.230950
$267$	−202882.	−0.174166
$268$	790808.	0.672565
$269$	1.22319e6	1.03065	0.515326	−	0.856994i	$-0.327671\pi$
$269$	1.22319e6	1.03065	0.515326	+	0.856994i	$0.327671\pi$
$270$	−162765.	−0.135879
$271$	−1.75129e6	−1.44855	−0.724277	−	0.689509i	$-0.757826\pi$
$271$	−1.75129e6	−1.44855	−0.724277	+	0.689509i	$0.757826\pi$
$272$	470370.	0.385494
$273$	−213321.	−0.173232
$274$	45169.2	0.0363468
$275$	448450.	0.357588
$276$	−226838.	−0.179244
$277$	638822.	0.500243	0.250121	−	0.968214i	$-0.419529\pi$
$277$	638822.	0.500243	0.250121	+	0.968214i	$0.419529\pi$
$278$	−193224.	−0.149951
$279$	−704526.	−0.541859
$280$	−563358.	−0.429427
$281$	−1.72109e6	−1.30028	−0.650141	−	0.759814i	$-0.725290\pi$
$281$	−1.72109e6	−1.30028	−0.650141	+	0.759814i	$0.725290\pi$
$282$	143469.	0.107433
$283$	−480652.	−0.356750	−0.178375	−	0.983963i	$-0.557084\pi$
$283$	−480652.	−0.356750	−0.178375	+	0.983963i	$0.557084\pi$
$284$	−67807.7	−0.0498865
$285$	−1.42584e6	−1.03982
$286$	−234127.	−0.169253
$287$	−39140.0	−0.0280489
$288$	−485010.	−0.344564
$289$	1.09381e6	0.770364
$290$	498262.	0.347907
$291$	−236558.	−0.163759
$292$	1.51220e6	1.03789
$293$	−2.08942e6	−1.42186	−0.710931	−	0.703261i	$-0.751726\pi$
$293$	−2.08942e6	−1.42186	−0.710931	+	0.703261i	$0.751726\pi$
$294$	−382420.	−0.258031
$295$	269894.	0.180567
$296$	2.42129e6	1.60627
$297$	−113261.	−0.0745057
$298$	−314982.	−0.205469
$299$	−556344.	−0.359886
$300$	615868.	0.395079
$301$	516021.	0.328285
$302$	936756.	0.591029
$303$	555260.	0.347448
$304$	−606213.	−0.376220
$305$	3.43953e6	2.11714
$306$	−369814.	−0.225777
$307$	2.82729e6	1.71208	0.856040	−	0.516910i	$-0.172918\pi$
$307$	2.82729e6	1.71208	0.856040	+	0.516910i	$0.172918\pi$
$308$	−166830.	−0.100207
$309$	586526.	0.349455
$310$	−1.94198e6	−1.14773
$311$	−1.90959e6	−1.11954	−0.559769	−	0.828648i	$-0.689110\pi$
$311$	−1.90959e6	−1.11954	−0.559769	+	0.828648i	$0.689110\pi$
$312$	−755534.	−0.439407
$313$	−2.15361e6	−1.24253	−0.621264	−	0.783602i	$-0.713380\pi$
$313$	−2.15361e6	−1.24253	−0.621264	+	0.783602i	$0.713380\pi$
$314$	703637.	0.402740
$315$	−284454.	−0.161523
$316$	−1.96670e6	−1.10795
$317$	−2.27397e6	−1.27097	−0.635486	−	0.772113i	$-0.719200\pi$
$317$	−2.27397e6	−1.27097	−0.635486	+	0.772113i	$0.719200\pi$
$318$	469089.	0.260128
$319$	346719.	0.190766
$320$	−600822.	−0.327998
$321$	−1.37745e6	−0.746129
$322$	138667.	0.0745304
$323$	−3.23961e6	−1.72777
$324$	−155544.	−0.0823174
$325$	1.51048e6	0.793242
$326$	−248301.	−0.129400
$327$	1.83369e6	0.948322
$328$	−138625.	−0.0711469
$329$	250732.	0.127708
$330$	−312198.	−0.157814
$331$	3.45401e6	1.73282	0.866410	−	0.499334i	$-0.166422\pi$
$331$	3.45401e6	1.73282	0.866410	+	0.499334i	$0.166422\pi$
$332$	1.61072e6	0.801999
$333$	1.22257e6	0.604176
$334$	−464332.	−0.227752
$335$	2.58628e6	1.25911
$336$	−120939.	−0.0584411
$337$	2.83240e6	1.35856	0.679281	−	0.733878i	$-0.262292\pi$
$337$	2.83240e6	1.35856	0.679281	+	0.733878i	$0.262292\pi$
$338$	280617.	0.133605
$339$	−2.16855e6	−1.02487
$340$	2.91425e6	1.36719
$341$	−1.35134e6	−0.629331
$342$	476617.	0.220346
$343$	−1.42958e6	−0.656106
$344$	1.82763e6	0.832706
$345$	−741859.	−0.335563
$346$	−1.00424e6	−0.450971
$347$	−152475.	−0.0679791	−0.0339895	−	0.999422i	$-0.510821\pi$
$347$	−152475.	−0.0679791	−0.0339895	+	0.999422i	$0.510821\pi$
$348$	476158.	0.210767
$349$	3.07524e6	1.35150	0.675748	−	0.737132i	$-0.263821\pi$
$349$	3.07524e6	1.35150	0.675748	+	0.737132i	$0.263821\pi$
$350$	−376482.	−0.164276
$351$	−381488.	−0.165277
$352$	−930291.	−0.400186
$353$	2.89392e6	1.23609	0.618045	−	0.786142i	$-0.287925\pi$
$353$	2.89392e6	1.23609	0.618045	+	0.786142i	$0.287925\pi$
$354$	−90217.7	−0.0382634
$355$	−221760.	−0.0933927
$356$	−534422.	−0.223491
$357$	−646300.	−0.268388
$358$	882118.	0.363764
$359$	−3.98179e6	−1.63058	−0.815291	−	0.579052i	$-0.803423\pi$
$359$	−3.98179e6	−1.63058	−0.815291	+	0.579052i	$0.803423\pi$
$360$	−1.00747e6	−0.409709
$361$	1.69912e6	0.686207
$362$	−1.51384e6	−0.607167
$363$	1.23221e6	0.490817
$364$	−561921.	−0.222291
$365$	4.94553e6	1.94304
$366$	−1.14973e6	−0.448637
$367$	1.99313e6	0.772451	0.386225	−	0.922404i	$-0.373779\pi$
$367$	1.99313e6	0.772451	0.386225	+	0.922404i	$0.373779\pi$
$368$	−315410.	−0.121411
$369$	−69995.1	−0.0267610
$370$	3.36995e6	1.27973
$371$	819796.	0.309223
$372$	−1.85583e6	−0.695314
$373$	1.35506e6	0.504298	0.252149	−	0.967688i	$-0.418863\pi$
$373$	1.35506e6	0.504298	0.252149	+	0.967688i	$0.418863\pi$
$374$	−709336.	−0.262224
$375$	−166475.	−0.0611325
$376$	888034.	0.323936
$377$	1.16782e6	0.423179
$378$	95084.7	0.0342280
$379$	54757.5	0.0195815	0.00979074	−	0.999952i	$-0.496883\pi$
$379$	54757.5	0.0195815	0.00979074	+	0.999952i	$0.496883\pi$
$380$	−3.75589e6	−1.33430
$381$	1.35891e6	0.479598
$382$	1.55668e6	0.545810
$383$	−2.22595e6	−0.775388	−0.387694	−	0.921788i	$-0.626728\pi$
$383$	−2.22595e6	−0.775388	−0.387694	+	0.921788i	$0.626728\pi$
$384$	−1.52364e6	−0.527296
$385$	−545607.	−0.187598
$386$	1.86182e6	0.636017
$387$	922815.	0.313211
$388$	−623131.	−0.210136
$389$	3.54979e6	1.18940	0.594702	−	0.803947i	$-0.297270\pi$
$389$	3.54979e6	1.18940	0.594702	+	0.803947i	$0.297270\pi$
$390$	−1.05155e6	−0.350081
$391$	−1.68556e6	−0.557573
$392$	−2.36707e6	−0.778030
$393$	2.25541e6	0.736621
$394$	1.80942e6	0.587216
$395$	−6.43197e6	−2.07420
$396$	−298348.	−0.0956059
$397$	−3.38798e6	−1.07886	−0.539430	−	0.842031i	$-0.681360\pi$
$397$	−3.38798e6	−1.07886	−0.539430	+	0.842031i	$0.681360\pi$
$398$	566079.	0.179130
$399$	832952.	0.261931
$400$	856341.	0.267607
$401$	1.54937e6	0.481165	0.240583	−	0.970629i	$-0.422661\pi$
$401$	1.54937e6	0.481165	0.240583	+	0.970629i	$0.422661\pi$
$402$	−864519.	−0.266815
$403$	−4.55161e6	−1.39605
$404$	1.46264e6	0.445846
$405$	−508697.	−0.154107
$406$	−291077.	−0.0876379
$407$	2.34500e6	0.701708
$408$	−2.28904e6	−0.680775
$409$	−1.40903e6	−0.416497	−0.208248	−	0.978076i	$-0.566776\pi$
$409$	−1.40903e6	−0.416497	−0.208248	+	0.978076i	$0.566776\pi$
$410$	−192937.	−0.0566835
$411$	141169.	0.0412226
$412$	1.54500e6	0.448421
$413$	−157667.	−0.0454849
$414$	247982.	0.0711082
$415$	5.26774e6	1.50143
$416$	−3.13342e6	−0.887739
$417$	−603891.	−0.170066
$418$	914193.	0.255916
$419$	−1.78943e6	−0.497942	−0.248971	−	0.968511i	$-0.580092\pi$
$419$	−1.78943e6	−0.497942	−0.248971	+	0.968511i	$0.580092\pi$
$420$	−749296.	−0.207267
$421$	4.50624e6	1.23911	0.619554	−	0.784954i	$-0.287314\pi$
$421$	4.50624e6	1.23911	0.619554	+	0.784954i	$0.287314\pi$
$422$	2.50393e6	0.684449
$423$	448390.	0.121844
$424$	2.90353e6	0.784353
$425$	4.57630e6	1.22897
$426$	74128.0	0.0197906
$427$	−2.00931e6	−0.533308
$428$	−3.62843e6	−0.957434
$429$	−731727.	−0.191958
$430$	2.54369e6	0.663426
$431$	−2.68824e6	−0.697067	−0.348534	−	0.937296i	$-0.613320\pi$
$431$	−2.68824e6	−0.697067	−0.348534	+	0.937296i	$0.613320\pi$
$432$	−216279.	−0.0557576
$433$	1.53010e6	0.392194	0.196097	−	0.980584i	$-0.437173\pi$
$433$	1.53010e6	0.392194	0.196097	+	0.980584i	$0.437173\pi$
$434$	1.13447e6	0.289115
$435$	1.55724e6	0.394578
$436$	4.83022e6	1.21689
$437$	2.17235e6	0.544159
$438$	−1.65315e6	−0.411743
$439$	−698534.	−0.172992	−0.0864960	−	0.996252i	$-0.527567\pi$
$439$	−698534.	−0.172992	−0.0864960	+	0.996252i	$0.527567\pi$
$440$	−1.93241e6	−0.475848
$441$	−1.19519e6	−0.292646
$442$	−2.38920e6	−0.581696
$443$	−1.73221e6	−0.419365	−0.209682	−	0.977770i	$-0.567243\pi$
$443$	−1.73221e6	−0.419365	−0.209682	+	0.977770i	$0.567243\pi$
$444$	3.22045e6	0.775280
$445$	−1.74779e6	−0.418397
$446$	312849.	0.0744728
$447$	−984427.	−0.233032
$448$	350990.	0.0826228
$449$	2.98288e6	0.698265	0.349133	−	0.937073i	$-0.386476\pi$
$449$	2.98288e6	0.698265	0.349133	+	0.937073i	$0.386476\pi$
$450$	−673273.	−0.156733
$451$	−134257.	−0.0310810
$452$	−5.71231e6	−1.31512
$453$	2.92768e6	0.670314
$454$	3.18065e6	0.724229
$455$	−1.83772e6	−0.416152
$456$	2.95012e6	0.664397
$457$	−3.19426e6	−0.715451	−0.357725	−	0.933827i	$-0.616448\pi$
$457$	−3.19426e6	−0.715451	−0.357725	+	0.933827i	$0.616448\pi$
$458$	−328125.	−0.0730931
$459$	−1.15580e6	−0.256065
$460$	−1.95417e6	−0.430595
$461$	−7.83598e6	−1.71728	−0.858640	−	0.512580i	$-0.828690\pi$
$461$	−7.83598e6	−1.71728	−0.858640	+	0.512580i	$0.828690\pi$
$462$	182381.	0.0397534
$463$	−763425.	−0.165506	−0.0827530	−	0.996570i	$-0.526371\pi$
$463$	−763425.	−0.165506	−0.0827530	+	0.996570i	$0.526371\pi$
$464$	662079.	0.142763
$465$	−6.06936e6	−1.30170
$466$	1.07770e6	0.229896
$467$	2.85947e6	0.606727	0.303363	−	0.952875i	$-0.401890\pi$
$467$	2.85947e6	0.606727	0.303363	+	0.952875i	$0.401890\pi$
$468$	−1.00490e6	−0.212084
$469$	−1.51086e6	−0.317171
$470$	1.23596e6	0.258084
$471$	2.19911e6	0.456766
$472$	−558421.	−0.115374
$473$	1.77004e6	0.363773
$474$	2.15002e6	0.439538
$475$	−5.89794e6	−1.19941
$476$	−1.70246e6	−0.344396
$477$	1.46606e6	0.295024
$478$	3.07562e6	0.615690
$479$	5.27842e6	1.05115	0.525575	−	0.850747i	$-0.323850\pi$
$479$	5.27842e6	1.05115	0.525575	+	0.850747i	$0.323850\pi$
$480$	−4.17827e6	−0.827740
$481$	7.89846e6	1.55661
$482$	953034.	0.186849
$483$	433382.	0.0845284
$484$	3.24585e6	0.629817
$485$	−2.03791e6	−0.393396
$486$	170043.	0.0326563
$487$	−5.59895e6	−1.06975	−0.534877	−	0.844930i	$-0.679642\pi$
$487$	−5.59895e6	−1.06975	−0.534877	+	0.844930i	$0.679642\pi$
$488$	−7.11652e6	−1.35275
$489$	−776024.	−0.146758
$490$	−3.29448e6	−0.619865
$491$	4.25242e6	0.796035	0.398018	−	0.917378i	$-0.369698\pi$
$491$	4.25242e6	0.796035	0.398018	+	0.917378i	$0.369698\pi$
$492$	−184378.	−0.0343397
$493$	3.53816e6	0.655633
$494$	3.07920e6	0.567702
$495$	−975725.	−0.178984
$496$	−2.58046e6	−0.470970
$497$	129549.	0.0235257
$498$	−1.76085e6	−0.318163
$499$	−45082.1	−0.00810500	−0.00405250	−	0.999992i	$-0.501290\pi$
$499$	−45082.1	−0.00810500	−0.00405250	+	0.999992i	$0.501290\pi$
$500$	−438522.	−0.0784453
$501$	−1.45119e6	−0.258304
$502$	−2.60235e6	−0.460899
$503$	−5.54321e6	−0.976881	−0.488440	−	0.872597i	$-0.662434\pi$
$503$	−5.54321e6	−0.976881	−0.488440	+	0.872597i	$0.662434\pi$
$504$	588547.	0.103206
$505$	4.78347e6	0.834669
$506$	475651.	0.0825871
$507$	877023.	0.151527
$508$	3.57958e6	0.615421
$509$	−8.38202e6	−1.43402	−0.717008	−	0.697065i	$-0.754489\pi$
$509$	−8.38202e6	−1.43402	−0.717008	+	0.697065i	$0.754489\pi$
$510$	−3.18588e6	−0.542381
$511$	−2.88910e6	−0.489452
$512$	−3.29942e6	−0.556241
$513$	1.48959e6	0.249904
$514$	−2.07727e6	−0.346805
$515$	5.05282e6	0.839490
$516$	2.43084e6	0.401913
$517$	860052.	0.141514
$518$	−1.96867e6	−0.322365
$519$	−3.13860e6	−0.511467
$520$	−6.50879e6	−1.05558
$521$	−6.69577e6	−1.08070	−0.540351	−	0.841440i	$-0.681709\pi$
$521$	−6.69577e6	−1.08070	−0.540351	+	0.841440i	$0.681709\pi$
$522$	−520540.	−0.0836138
$523$	−4.06164e6	−0.649303	−0.324651	−	0.945834i	$-0.605247\pi$
$523$	−4.06164e6	−0.649303	−0.324651	+	0.945834i	$0.605247\pi$
$524$	5.94110e6	0.945233
$525$	−1.17663e6	−0.186313
$526$	−1.73198e6	−0.272946
$527$	−1.37900e7	−2.16291
$528$	−414841.	−0.0647585
$529$	−5.30608e6	−0.824393
$530$	4.04112e6	0.624903
$531$	−281961.	−0.0433963
$532$	2.19413e6	0.336111
$533$	−452205.	−0.0689474
$534$	584235.	0.0886614
$535$	−1.18665e7	−1.79242
$536$	−5.35113e6	−0.804513
$537$	2.75692e6	0.412561
$538$	−3.52239e6	−0.524665
$539$	−2.29249e6	−0.339887
$540$	−1.33999e6	−0.197750
$541$	−2.10875e6	−0.309765	−0.154883	−	0.987933i	$-0.549500\pi$
$541$	−2.10875e6	−0.309765	−0.154883	+	0.987933i	$0.549500\pi$
$542$	5.04317e6	0.737403
$543$	−4.73127e6	−0.688617
$544$	−9.49334e6	−1.37538
$545$	1.57969e7	2.27814
$546$	614298.	0.0881855
$547$	−7.48493e6	−1.06960	−0.534798	−	0.844980i	$-0.679612\pi$
$547$	−7.48493e6	−1.06960	−0.534798	+	0.844980i	$0.679612\pi$
$548$	371862.	0.0528969
$549$	−3.59331e6	−0.508820
$550$	−1.29140e6	−0.182034
$551$	−4.55999e6	−0.639860
$552$	1.53494e6	0.214409
$553$	3.75745e6	0.522493
$554$	−1.83961e6	−0.254654
$555$	1.05322e7	1.45140
$556$	−1.59074e6	−0.218229
$557$	7.42234e6	1.01368	0.506842	−	0.862039i	$-0.330813\pi$
$557$	7.42234e6	1.01368	0.506842	+	0.862039i	$0.330813\pi$
$558$	2.02881e6	0.275839
$559$	5.96187e6	0.806962
$560$	−1.04187e6	−0.140392
$561$	−2.21692e6	−0.297401
$562$	4.95619e6	0.661923
$563$	−818283.	−0.108801	−0.0544005	−	0.998519i	$-0.517325\pi$
$563$	−818283.	−0.108801	−0.0544005	+	0.998519i	$0.517325\pi$
$564$	1.18113e6	0.156351
$565$	−1.86817e7	−2.46204
$566$	1.38413e6	0.181608
$567$	297172.	0.0388195
$568$	458831.	0.0596736
$569$	1.44362e7	1.86928	0.934638	−	0.355599i	$-0.115723\pi$
$569$	1.44362e7	1.86928	0.934638	+	0.355599i	$0.115723\pi$
$570$	4.10597e6	0.529333
$571$	7.48418e6	0.960625	0.480312	−	0.877098i	$-0.340523\pi$
$571$	7.48418e6	0.960625	0.480312	+	0.877098i	$0.340523\pi$
$572$	−1.92748e6	−0.246321
$573$	4.86516e6	0.619029
$574$	112711.	0.0142786
$575$	−3.06868e6	−0.387063
$576$	627686.	0.0788290
$577$	−1.08673e7	−1.35888	−0.679441	−	0.733730i	$-0.737778\pi$
$577$	−1.08673e7	−1.35888	−0.679441	+	0.733730i	$0.737778\pi$
$578$	−3.14982e6	−0.392163
$579$	5.81881e6	0.721336
$580$	4.10201e6	0.506322
$581$	−3.07732e6	−0.378210
$582$	681213.	0.0833634
$583$	2.81204e6	0.342649
$584$	−1.02325e7	−1.24151
$585$	−3.28645e6	−0.397043
$586$	6.01689e6	0.723815
$587$	1.25762e7	1.50644	0.753222	−	0.657766i	$-0.228499\pi$
$587$	1.25762e7	1.50644	0.753222	+	0.657766i	$0.228499\pi$
$588$	−3.14833e6	−0.375523
$589$	1.77726e7	2.11088
$590$	−777209.	−0.0919196
$591$	5.65504e6	0.665989
$592$	4.47791e6	0.525135
$593$	−1.44755e7	−1.69042	−0.845212	−	0.534430i	$-0.820526\pi$
$593$	−1.44755e7	−1.69042	−0.845212	+	0.534430i	$0.820526\pi$
$594$	326156.	0.0379280
$595$	−5.56776e6	−0.644745
$596$	−2.59314e6	−0.299026
$597$	1.76919e6	0.203160
$598$	1.60210e6	0.183204
$599$	898434.	0.102310	0.0511551	−	0.998691i	$-0.483710\pi$
$599$	898434.	0.102310	0.0511551	+	0.998691i	$0.483710\pi$
$600$	−4.16736e6	−0.472589
$601$	1.02932e7	1.16242	0.581210	−	0.813754i	$-0.302580\pi$
$601$	1.02932e7	1.16242	0.581210	+	0.813754i	$0.302580\pi$
$602$	−1.48598e6	−0.167117
$603$	−2.70192e6	−0.302607
$604$	7.71197e6	0.860148
$605$	1.06153e7	1.17908
$606$	−1.59898e6	−0.176872
$607$	1.82491e6	0.201034	0.100517	−	0.994935i	$-0.467950\pi$
$607$	1.82491e6	0.201034	0.100517	+	0.994935i	$0.467950\pi$
$608$	1.22350e7	1.34229
$609$	−909714.	−0.0993943
$610$	−9.90476e6	−1.07775
$611$	2.89684e6	0.313922
$612$	−3.04455e6	−0.328582
$613$	−621392.	−0.0667905	−0.0333953	−	0.999442i	$-0.510632\pi$
$613$	−621392.	−0.0667905	−0.0333953	+	0.999442i	$0.510632\pi$
$614$	−8.14170e6	−0.871554
$615$	−602995.	−0.0642874
$616$	1.12888e6	0.119866
$617$	5.04840e6	0.533877	0.266938	−	0.963714i	$-0.413988\pi$
$617$	5.04840e6	0.533877	0.266938	+	0.963714i	$0.413988\pi$
$618$	−1.68901e6	−0.177894
$619$	1.49642e7	1.56974	0.784869	−	0.619662i	$-0.212730\pi$
$619$	1.49642e7	1.56974	0.784869	+	0.619662i	$0.212730\pi$
$620$	−1.59877e7	−1.67034
$621$	775028.	0.0806471
$622$	5.49902e6	0.569914
$623$	1.02103e6	0.105395
$624$	−1.39727e6	−0.143655
$625$	−1.04542e7	−1.07051
$626$	6.20172e6	0.632523
$627$	2.85717e6	0.290246
$628$	5.79279e6	0.586123
$629$	2.39300e7	2.41166
$630$	819138.	0.0822253
$631$	1.72533e7	1.72504	0.862519	−	0.506024i	$-0.168885\pi$
$631$	1.72533e7	1.72504	0.862519	+	0.506024i	$0.168885\pi$
$632$	1.33080e7	1.32532
$633$	7.82563e6	0.776265
$634$	6.54831e6	0.647002
$635$	1.17068e7	1.15213
$636$	3.86184e6	0.378575
$637$	−7.72159e6	−0.753977
$638$	−998442.	−0.0971116
$639$	231675.	0.0224454
$640$	−1.31259e7	−1.26672
$641$	−1.83730e7	−1.76618	−0.883092	−	0.469200i	$-0.844543\pi$
$641$	−1.83730e7	−1.76618	−0.883092	+	0.469200i	$0.844543\pi$
$642$	3.96663e6	0.379826
$643$	1.64115e7	1.56538	0.782690	−	0.622411i	$-0.213847\pi$
$643$	1.64115e7	1.56538	0.782690	+	0.622411i	$0.213847\pi$
$644$	1.14160e6	0.108467
$645$	7.94989e6	0.752422
$646$	9.32907e6	0.879543
$647$	−6.16024e6	−0.578545	−0.289272	−	0.957247i	$-0.593413\pi$
$647$	−6.16024e6	−0.578545	−0.289272	+	0.957247i	$0.593413\pi$
$648$	1.05251e6	0.0984670
$649$	−540826.	−0.0504018
$650$	−4.34970e6	−0.403809
$651$	3.54562e6	0.327899
$652$	−2.04417e6	−0.188321
$653$	1.38748e7	1.27334	0.636671	−	0.771135i	$-0.280311\pi$
$653$	1.38748e7	1.27334	0.636671	+	0.771135i	$0.280311\pi$
$654$	−5.28044e6	−0.482754
$655$	1.94300e7	1.76957
$656$	−256371.	−0.0232600
$657$	−5.16665e6	−0.466977
$658$	−722029.	−0.0650114
$659$	1.76364e7	1.58196	0.790982	−	0.611839i	$-0.209570\pi$
$659$	1.76364e7	1.58196	0.790982	+	0.611839i	$0.209570\pi$
$660$	−2.57021e6	−0.229672
$661$	6.64665e6	0.591697	0.295849	−	0.955235i	$-0.404398\pi$
$661$	6.64665e6	0.591697	0.295849	+	0.955235i	$0.404398\pi$
$662$	−9.94646e6	−0.882111
$663$	−7.46706e6	−0.659729
$664$	−1.08992e7	−0.959341
$665$	7.17573e6	0.629234
$666$	−3.52062e6	−0.307563
$667$	−2.37254e6	−0.206490
$668$	−3.82267e6	−0.331456
$669$	977760.	0.0844631
$670$	−7.44768e6	−0.640965
$671$	−6.89228e6	−0.590958
$672$	2.44088e6	0.208508
$673$	−1.52418e7	−1.29717	−0.648586	−	0.761141i	$-0.724639\pi$
$673$	−1.52418e7	−1.29717	−0.648586	+	0.761141i	$0.724639\pi$
$674$	−8.15642e6	−0.691591
$675$	−2.10421e6	−0.177758
$676$	2.31022e6	0.194440
$677$	−4.32639e6	−0.362789	−0.181394	−	0.983410i	$-0.558061\pi$
$677$	−4.32639e6	−0.362789	−0.181394	+	0.983410i	$0.558061\pi$
$678$	6.24475e6	0.521724
$679$	1.19051e6	0.0990967
$680$	−1.97197e7	−1.63542
$681$	9.94061e6	0.821382
$682$	3.89144e6	0.320368
$683$	6.89334e6	0.565428	0.282714	−	0.959204i	$-0.408765\pi$
$683$	6.89334e6	0.565428	0.282714	+	0.959204i	$0.408765\pi$
$684$	3.92382e6	0.320677
$685$	1.21615e6	0.0990284
$686$	4.11675e6	0.333998
$687$	−1.02550e6	−0.0828983
$688$	3.37999e6	0.272235
$689$	9.47155e6	0.760104
$690$	2.13632e6	0.170822
$691$	−1.77702e7	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$691$	−1.77702e7	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$692$	−8.26757e6	−0.656315
$693$	570002.	0.0450862
$694$	439080.	0.0346055
$695$	−5.20241e6	−0.408548
$696$	−3.22199e6	−0.252117
$697$	−1.37005e6	−0.106820
$698$	−8.85571e6	−0.687995
$699$	3.36817e6	0.260736
$700$	−3.09944e6	−0.239077
$701$	−2.94835e6	−0.226613	−0.113306	−	0.993560i	$-0.536144\pi$
$701$	−2.94835e6	−0.226613	−0.113306	+	0.993560i	$0.536144\pi$
$702$	1.09857e6	0.0841362
$703$	−3.08410e7	−2.35364
$704$	1.20396e6	0.0915543
$705$	3.86280e6	0.292705
$706$	−8.33359e6	−0.629246
$707$	−2.79442e6	−0.210254
$708$	−742729.	−0.0556862
$709$	−1.10740e7	−0.827346	−0.413673	−	0.910425i	$-0.635754\pi$
$709$	−1.10740e7	−0.827346	−0.413673	+	0.910425i	$0.635754\pi$
$710$	638600.	0.0475426
$711$	6.71955e6	0.498501
$712$	3.61625e6	0.267336
$713$	9.24702e6	0.681205
$714$	1.86114e6	0.136626
$715$	−6.30370e6	−0.461137
$716$	7.26216e6	0.529399
$717$	9.61235e6	0.698283
$718$	1.14663e7	0.830066
$719$	−5.21161e6	−0.375967	−0.187984	−	0.982172i	$-0.560195\pi$
$719$	−5.21161e6	−0.375967	−0.187984	+	0.982172i	$0.560195\pi$
$720$	−1.86320e6	−0.133946
$721$	−2.95177e6	−0.211468
$722$	−4.89292e6	−0.349322
$723$	2.97856e6	0.211914
$724$	−1.24629e7	−0.883634
$725$	6.44147e6	0.455135
$726$	−3.54839e6	−0.249856
$727$	−6.91096e6	−0.484956	−0.242478	−	0.970157i	$-0.577960\pi$
$727$	−6.91096e6	−0.484956	−0.242478	+	0.970157i	$0.577960\pi$
$728$	3.80232e6	0.265901
$729$	531441.	0.0370370
$730$	−1.42416e7	−0.989124
$731$	1.80627e7	1.25023
$732$	−9.46534e6	−0.652918
$733$	9.42723e6	0.648073	0.324037	−	0.946045i	$-0.394960\pi$
$733$	9.42723e6	0.648073	0.324037	+	0.946045i	$0.394960\pi$
$734$	−5.73959e6	−0.393225
$735$	−1.02964e7	−0.703018
$736$	6.36584e6	0.433173
$737$	−5.18251e6	−0.351457
$738$	201564.	0.0136230
$739$	−1.88305e7	−1.26839	−0.634193	−	0.773175i	$-0.718668\pi$
$739$	−1.88305e7	−1.26839	−0.634193	+	0.773175i	$0.718668\pi$
$740$	2.77436e7	1.86244
$741$	9.62355e6	0.643857
$742$	−2.36076e6	−0.157413
$743$	2.36519e6	0.157179	0.0785893	−	0.996907i	$-0.474958\pi$
$743$	2.36519e6	0.157179	0.0785893	+	0.996907i	$0.474958\pi$
$744$	1.25578e7	0.831725
$745$	−8.48067e6	−0.559808
$746$	−3.90216e6	−0.256719
$747$	−5.50326e6	−0.360843
$748$	−5.83971e6	−0.381625
$749$	6.93222e6	0.451510
$750$	479397.	0.0311202
$751$	−1.67747e7	−1.08531	−0.542657	−	0.839955i	$-0.682581\pi$
$751$	−1.67747e7	−1.08531	−0.542657	+	0.839955i	$0.682581\pi$
$752$	1.64232e6	0.105904
$753$	−8.13323e6	−0.522728
$754$	−3.36297e6	−0.215424
$755$	2.52215e7	1.61029
$756$	782798.	0.0498133
$757$	−9.79306e6	−0.621124	−0.310562	−	0.950553i	$-0.600517\pi$
$757$	−9.79306e6	−0.621124	−0.310562	+	0.950553i	$0.600517\pi$
$758$	−157684.	−0.00996817
$759$	1.48657e6	0.0936659
$760$	2.54148e7	1.59607
$761$	1.83642e7	1.14950	0.574751	−	0.818328i	$-0.305099\pi$
$761$	1.83642e7	1.14950	0.574751	+	0.818328i	$0.305099\pi$
$762$	−3.91323e6	−0.244145
$763$	−9.22827e6	−0.573864
$764$	1.28156e7	0.794338
$765$	−9.95698e6	−0.615140
$766$	6.41005e6	0.394720
$767$	−1.82162e6	−0.111807
$768$	6.61938e6	0.404962
$769$	−1.44796e6	−0.0882962	−0.0441481	−	0.999025i	$-0.514057\pi$
$769$	−1.44796e6	−0.0882962	−0.0441481	+	0.999025i	$0.514057\pi$
$770$	1.57118e6	0.0954989
$771$	−6.49218e6	−0.393328
$772$	1.53277e7	0.925620
$773$	−136665.	−0.00822637	−0.00411318	−	0.999992i	$-0.501309\pi$
$773$	−136665.	−0.00822637	−0.00411318	+	0.999992i	$0.501309\pi$
$774$	−2.65742e6	−0.159444
$775$	−2.51057e7	−1.50148
$776$	4.21651e6	0.251362
$777$	−6.15276e6	−0.365609
$778$	−1.02223e7	−0.605479
$779$	1.76572e6	0.104251
$780$	−8.65702e6	−0.509486
$781$	444374.	0.0260688
$782$	4.85388e6	0.283839
$783$	−1.62687e6	−0.0948303
$784$	−4.37763e6	−0.254360
$785$	1.89449e7	1.09728
$786$	−6.49487e6	−0.374985
$787$	2.64152e7	1.52026	0.760129	−	0.649772i	$-0.225136\pi$
$787$	2.64152e7	1.52026	0.760129	+	0.649772i	$0.225136\pi$
$788$	1.48963e7	0.854598
$789$	−5.41301e6	−0.309561
$790$	1.85220e7	1.05590
$791$	1.09135e7	0.620189
$792$	2.01881e6	0.114362
$793$	−2.32147e7	−1.31093
$794$	9.75633e6	0.549206
$795$	1.26299e7	0.708731
$796$	4.66032e6	0.260695
$797$	−1.25477e7	−0.699708	−0.349854	−	0.936804i	$-0.613769\pi$
$797$	−1.25477e7	−0.699708	−0.349854	+	0.936804i	$0.613769\pi$
$798$	−2.39864e6	−0.133339
$799$	8.77657e6	0.486360
$800$	−1.72833e7	−0.954776
$801$	1.82593e6	0.100555
$802$	−4.46170e6	−0.244943
$803$	−9.91009e6	−0.542361
$804$	−7.11727e6	−0.388305
$805$	3.73351e6	0.203061
$806$	1.31072e7	0.710677
$807$	−1.10087e7	−0.595047
$808$	−9.89720e6	−0.533315
$809$	2.17849e7	1.17027	0.585134	−	0.810937i	$-0.301042\pi$
$809$	2.17849e7	1.17027	0.585134	+	0.810937i	$0.301042\pi$
$810$	1.46489e6	0.0784497
$811$	−2.63202e7	−1.40520	−0.702599	−	0.711586i	$-0.747977\pi$
$811$	−2.63202e7	−1.40520	−0.702599	+	0.711586i	$0.747977\pi$
$812$	−2.39633e6	−0.127543
$813$	1.57616e7	0.836323
$814$	−6.75286e6	−0.357213
$815$	−6.68531e6	−0.352556
$816$	−4.23333e6	−0.222565
$817$	−2.32793e7	−1.22015
$818$	4.05756e6	0.212022
$819$	1.91989e6	0.100015
$820$	−1.58838e6	−0.0824937
$821$	−3.00385e7	−1.55532	−0.777661	−	0.628684i	$-0.783594\pi$
$821$	−3.00385e7	−1.55532	−0.777661	+	0.628684i	$0.783594\pi$
$822$	−406523.	−0.0209848
$823$	8.67425e6	0.446408	0.223204	−	0.974772i	$-0.428348\pi$
$823$	8.67425e6	0.446408	0.223204	+	0.974772i	$0.428348\pi$
$824$	−1.04545e7	−0.536395
$825$	−4.03605e6	−0.206453
$826$	454033.	0.0231546
$827$	−5.30575e6	−0.269763	−0.134882	−	0.990862i	$-0.543065\pi$
$827$	−5.30575e6	−0.269763	−0.134882	+	0.990862i	$0.543065\pi$
$828$	2.04155e6	0.103486
$829$	−3221.11	−0.000162787 0	−8.13934e−5	−	1.00000i	$-0.500026\pi$
$829$	−3221.11	−0.000162787 0	−8.13934e−5		1.00000i	$0.500026\pi$
$830$	−1.51694e7	−0.764318
$831$	−5.74940e6	−0.288815
$832$	4.05518e6	0.203096
$833$	−2.33941e7	−1.16814
$834$	1.73902e6	0.0865742
$835$	−1.25018e7	−0.620520
$836$	7.52622e6	0.372444
$837$	6.34073e6	0.312842
$838$	5.15298e6	0.253483
$839$	−1.48233e7	−0.727008	−0.363504	−	0.931593i	$-0.618420\pi$
$839$	−1.48233e7	−0.727008	−0.363504	+	0.931593i	$0.618420\pi$
$840$	5.07023e6	0.247930
$841$	−1.55309e7	−0.757195
$842$	−1.29766e7	−0.630782
$843$	1.54898e7	0.750718
$844$	2.06139e7	0.996104
$845$	7.55540e6	0.364012
$846$	−1.29122e6	−0.0620263
$847$	−6.20128e6	−0.297011
$848$	5.36975e6	0.256427
$849$	4.32586e6	0.205970
$850$	−1.31783e7	−0.625622
$851$	−1.60465e7	−0.759549
$852$	610269.	0.0288020
$853$	−1.50069e7	−0.706183	−0.353092	−	0.935589i	$-0.614870\pi$
$853$	−1.50069e7	−0.706183	−0.353092	+	0.935589i	$0.614870\pi$
$854$	5.78619e6	0.271486
$855$	1.28326e7	0.600341
$856$	2.45523e7	1.14527
$857$	9.04584e6	0.420724	0.210362	−	0.977624i	$-0.432536\pi$
$857$	9.04584e6	0.420724	0.210362	+	0.977624i	$0.432536\pi$
$858$	2.10714e6	0.0977183
$859$	5.42003e6	0.250622	0.125311	−	0.992118i	$-0.460007\pi$
$859$	5.42003e6	0.250622	0.125311	+	0.992118i	$0.460007\pi$
$860$	2.09412e7	0.965509
$861$	352260.	0.0161940
$862$	7.74129e6	0.354850
$863$	−2.45589e7	−1.12249	−0.561245	−	0.827650i	$-0.689678\pi$
$863$	−2.45589e7	−1.12249	−0.561245	+	0.827650i	$0.689678\pi$
$864$	4.36509e6	0.198934
$865$	−2.70385e7	−1.22869
$866$	−4.40622e6	−0.199651
$867$	−9.84426e6	−0.444770
$868$	9.33972e6	0.420760
$869$	1.28887e7	0.578974
$870$	−4.48436e6	−0.200864
$871$	−1.74558e7	−0.779641
$872$	−3.26844e7	−1.45562
$873$	2.12902e6	0.0945464
$874$	−6.25568e6	−0.277010
$875$	837810.	0.0369935
$876$	−1.36098e7	−0.599226
$877$	1.94355e7	0.853289	0.426644	−	0.904420i	$-0.359696\pi$
$877$	1.94355e7	0.853289	0.426644	+	0.904420i	$0.359696\pi$
$878$	2.01156e6	0.0880636
$879$	1.88048e7	0.820913
$880$	−3.57378e6	−0.155568
$881$	−4.44437e7	−1.92917	−0.964584	−	0.263775i	$-0.915032\pi$
$881$	−4.44437e7	−1.92917	−0.964584	+	0.263775i	$0.915032\pi$
$882$	3.44178e6	0.148975
$883$	−1.10995e7	−0.479072	−0.239536	−	0.970888i	$-0.576995\pi$
$883$	−1.10995e7	−0.479072	−0.239536	+	0.970888i	$0.576995\pi$
$884$	−1.96694e7	−0.846565
$885$	−2.42904e6	−0.104250
$886$	4.98823e6	0.213482
$887$	−1.92347e7	−0.820872	−0.410436	−	0.911889i	$-0.634623\pi$
$887$	−1.92347e7	−0.820872	−0.410436	+	0.911889i	$0.634623\pi$
$888$	−2.17916e7	−0.927380
$889$	−6.83889e6	−0.290223
$890$	5.03308e6	0.212990
$891$	1.01935e6	0.0430159
$892$	2.57557e6	0.108383
$893$	−1.13113e7	−0.474659
$894$	2.83484e6	0.118627
$895$	2.37504e7	0.991089
$896$	7.66793e6	0.319086
$897$	5.00710e6	0.207780
$898$	−8.58977e6	−0.355460
$899$	−1.94105e7	−0.801008
$900$	−5.54281e6	−0.228099
$901$	2.86960e7	1.17763
$902$	386617.	0.0158221
$903$	−4.64419e6	−0.189536
$904$	3.86532e7	1.57313
$905$	−4.07590e7	−1.65425
$906$	−8.43080e6	−0.341231
$907$	−1.01314e6	−0.0408931	−0.0204466	−	0.999791i	$-0.506509\pi$
$907$	−1.01314e6	−0.0408931	−0.0204466	+	0.999791i	$0.506509\pi$
$908$	2.61851e7	1.05400
$909$	−4.99734e6	−0.200599
$910$	5.29206e6	0.211847
$911$	−3.28323e7	−1.31071	−0.655354	−	0.755322i	$-0.727480\pi$
$911$	−3.28323e7	−1.31071	−0.655354	+	0.755322i	$0.727480\pi$
$912$	5.45592e6	0.217210
$913$	−1.05557e7	−0.419094
$914$	9.19846e6	0.364208
$915$	−3.09557e7	−1.22233
$916$	−2.70134e6	−0.106375
$917$	−1.13507e7	−0.445756
$918$	3.32833e6	0.130353
$919$	6.66545e6	0.260340	0.130170	−	0.991492i	$-0.458448\pi$
$919$	6.66545e6	0.260340	0.130170	+	0.991492i	$0.458448\pi$
$920$	1.32232e7	0.515071
$921$	−2.54456e7	−0.988470
$922$	2.25652e7	0.874201
$923$	1.49675e6	0.0578288
$924$	1.50147e6	0.0578546
$925$	4.35662e7	1.67416
$926$	2.19842e6	0.0842528
$927$	−5.27873e6	−0.201758
$928$	−1.33626e7	−0.509354
$929$	1.25443e7	0.476877	0.238439	−	0.971158i	$-0.423364\pi$
$929$	1.25443e7	0.476877	0.238439	+	0.971158i	$0.423364\pi$
$930$	1.74779e7	0.662645
$931$	3.01504e7	1.14004
$932$	8.87229e6	0.334577
$933$	1.71863e7	0.646366
$934$	−8.23437e6	−0.308861
$935$	−1.90983e7	−0.714442
$936$	6.79980e6	0.253692
$937$	−3.57395e7	−1.32984	−0.664921	−	0.746914i	$-0.731535\pi$
$937$	−3.57395e7	−1.32984	−0.664921	+	0.746914i	$0.731535\pi$
$938$	4.35081e6	0.161459
$939$	1.93825e7	0.717373
$940$	1.01752e7	0.375599
$941$	2.36120e7	0.869277	0.434639	−	0.900605i	$-0.356876\pi$
$941$	2.36120e7	0.869277	0.434639	+	0.900605i	$0.356876\pi$
$942$	−6.33274e6	−0.232522
$943$	918698.	0.0336429
$944$	−1.03274e6	−0.0377190
$945$	2.56008e6	0.0932556
$946$	−5.09716e6	−0.185183
$947$	−5.01198e7	−1.81608	−0.908038	−	0.418887i	$-0.862420\pi$
$947$	−5.01198e7	−1.81608	−0.908038	+	0.418887i	$0.862420\pi$
$948$	1.77003e7	0.639677
$949$	−3.33793e7	−1.20313
$950$	1.69842e7	0.610571
$951$	2.04657e7	0.733795
$952$	1.15199e7	0.411962
$953$	3.11140e7	1.10975	0.554874	−	0.831935i	$-0.312767\pi$
$953$	3.11140e7	1.10975	0.554874	+	0.831935i	$0.312767\pi$
$954$	−4.22180e6	−0.150185
$955$	4.19125e7	1.48708
$956$	2.53204e7	0.896038
$957$	−3.12047e6	−0.110139
$958$	−1.52002e7	−0.535100
$959$	−710453.	−0.0249453
$960$	5.40740e6	0.189370
$961$	4.70234e7	1.64250
$962$	−2.27451e7	−0.792410
$963$	1.23971e7	0.430778
$964$	7.84598e6	0.271928
$965$	5.01280e7	1.73286
$966$	−1.24800e6	−0.0430302
$967$	−1.64097e7	−0.564331	−0.282166	−	0.959366i	$-0.591053\pi$
$967$	−1.64097e7	−0.564331	−0.282166	+	0.959366i	$0.591053\pi$
$968$	−2.19635e7	−0.753379
$969$	2.91565e7	0.997531
$970$	5.86853e6	0.200263
$971$	−2.88792e7	−0.982962	−0.491481	−	0.870888i	$-0.663544\pi$
$971$	−2.88792e7	−0.982962	−0.491481	+	0.870888i	$0.663544\pi$
$972$	1.39990e6	0.0475260
$973$	3.03916e6	0.102913
$974$	1.61232e7	0.544571
$975$	−1.35943e7	−0.457978
$976$	−1.31612e7	−0.442253
$977$	2.68826e7	0.901021	0.450510	−	0.892771i	$-0.351242\pi$
$977$	2.68826e7	0.901021	0.450510	+	0.892771i	$0.351242\pi$
$978$	2.23471e6	0.0747091
$979$	3.50230e6	0.116788
$980$	−2.71223e7	−0.902113
$981$	−1.65032e7	−0.547514
$982$	−1.22456e7	−0.405231
$983$	−1.32072e7	−0.435942	−0.217971	−	0.975955i	$-0.569944\pi$
$983$	−1.32072e7	−0.435942	−0.217971	+	0.975955i	$0.569944\pi$
$984$	1.24762e6	0.0410767
$985$	4.87172e7	1.59990
$986$	−1.01888e7	−0.333757
$987$	−2.25659e6	−0.0737325
$988$	2.53499e7	0.826199
$989$	−1.21121e7	−0.393758
$990$	2.80978e6	0.0911138
$991$	2.08572e6	0.0674639	0.0337320	−	0.999431i	$-0.489261\pi$
$991$	2.08572e6	0.0674639	0.0337320	+	0.999431i	$0.489261\pi$
$992$	5.20807e7	1.68034
$993$	−3.10861e7	−1.00044
$994$	−373059.	−0.0119760
$995$	1.52413e7	0.488048
$996$	−1.44965e7	−0.463035
$997$	3.49916e6	0.111487	0.0557437	−	0.998445i	$-0.482247\pi$
$997$	3.49916e6	0.111487	0.0557437	+	0.998445i	$0.482247\pi$
$998$	129822.	0.00412594
$999$	−1.10031e7	−0.348821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.5	✓	12
3.2	odd	2		531.6.a.d.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.5	✓	12	1.1	even	1	trivial
531.6.a.d.1.8		12	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-2.87969 q^{2} -9.00000 q^{3} -23.7074 q^{4} -77.5334 q^{5} +25.9172 q^{6} +45.2937 q^{7} +160.420 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-2.87969 q^{2} -9.00000 q^{3} -23.7074 q^{4} -77.5334 q^{5} +25.9172 q^{6} +45.2937 q^{7} +160.420 q^{8} +81.0000 q^{9} +223.272 q^{10} +155.365 q^{11} +213.367 q^{12} +523.303 q^{13} -130.432 q^{14} +697.801 q^{15} +296.678 q^{16} +1585.45 q^{17} -233.255 q^{18} -2043.33 q^{19} +1838.12 q^{20} -407.643 q^{21} -447.403 q^{22} -1063.14 q^{23} -1443.78 q^{24} +2886.43 q^{25} -1506.95 q^{26} -729.000 q^{27} -1073.80 q^{28} +2231.64 q^{29} -2009.45 q^{30} -8697.85 q^{31} -5987.78 q^{32} -1398.29 q^{33} -4565.61 q^{34} -3511.78 q^{35} -1920.30 q^{36} +15093.5 q^{37} +5884.16 q^{38} -4709.73 q^{39} -12437.9 q^{40} -864.137 q^{41} +1173.88 q^{42} +11392.8 q^{43} -3683.30 q^{44} -6280.21 q^{45} +3061.51 q^{46} +5535.68 q^{47} -2670.11 q^{48} -14755.5 q^{49} -8312.01 q^{50} -14269.1 q^{51} -12406.2 q^{52} +18099.6 q^{53} +2099.29 q^{54} -12046.0 q^{55} +7266.01 q^{56} +18390.0 q^{57} -6426.42 q^{58} -3481.00 q^{59} -16543.0 q^{60} -44361.9 q^{61} +25047.1 q^{62} +3668.79 q^{63} +7749.20 q^{64} -40573.5 q^{65} +4026.62 q^{66} -33357.0 q^{67} -37587.0 q^{68} +9568.25 q^{69} +10112.8 q^{70} +2860.19 q^{71} +12994.0 q^{72} -63785.8 q^{73} -43464.5 q^{74} -25977.9 q^{75} +48442.2 q^{76} +7037.06 q^{77} +13562.5 q^{78} +82957.4 q^{79} -23002.5 q^{80} +6561.00 q^{81} +2488.44 q^{82} -67941.5 q^{83} +9664.17 q^{84} -122926. q^{85} -32807.6 q^{86} -20084.8 q^{87} +24923.6 q^{88} +22542.4 q^{89} +18085.0 q^{90} +23702.3 q^{91} +25204.3 q^{92} +78280.6 q^{93} -15941.0 q^{94} +158427. q^{95} +53890.0 q^{96} +26284.2 q^{97} +42491.1 q^{98} +12584.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * q^99

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