LMFDB - Embedded newform 177.6.a.b.1.1

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			1.1
Root			$10.9029$ 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)

$f(q)$	$=$	$q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} -960.699 q^{10} +423.027 q^{11} -781.856 q^{12} -1047.72 q^{13} -672.832 q^{14} -793.028 q^{15} +3742.96 q^{16} -2034.81 q^{17} -883.133 q^{18} -1532.11 q^{19} +7654.74 q^{20} -555.403 q^{21} -4612.21 q^{22} +2986.67 q^{23} +5384.45 q^{24} +4639.12 q^{25} +11423.2 q^{26} -729.000 q^{27} +5361.05 q^{28} +115.477 q^{29} +8646.29 q^{30} -3626.28 q^{31} -21664.3 q^{32} -3807.24 q^{33} +22185.3 q^{34} +5437.66 q^{35} +7036.70 q^{36} -15040.3 q^{37} +16704.4 q^{38} +9429.51 q^{39} -52716.3 q^{40} -829.256 q^{41} +6055.49 q^{42} -12294.1 q^{43} +36749.5 q^{44} +7137.25 q^{45} -32563.3 q^{46} -16104.8 q^{47} -33686.6 q^{48} -12998.7 q^{49} -50579.8 q^{50} +18313.3 q^{51} -91018.7 q^{52} +34428.4 q^{53} +7948.20 q^{54} +37274.7 q^{55} -36920.2 q^{56} +13788.9 q^{57} -1259.04 q^{58} -3481.00 q^{59} -68892.6 q^{60} +16418.9 q^{61} +39536.9 q^{62} +4998.63 q^{63} +116429. q^{64} -92319.3 q^{65} +41509.9 q^{66} +9818.25 q^{67} -176770. q^{68} -26880.0 q^{69} -59286.1 q^{70} +3381.64 q^{71} -48460.0 q^{72} +27012.0 q^{73} +163982. q^{74} -41752.1 q^{75} -133098. q^{76} +26105.6 q^{77} -102809. q^{78} +20426.3 q^{79} +329808. q^{80} +6561.00 q^{81} +9041.29 q^{82} -54511.3 q^{83} -48249.4 q^{84} -179296. q^{85} +134041. q^{86} -1039.30 q^{87} -253085. q^{88} -69700.2 q^{89} -77816.6 q^{90} -64656.5 q^{91} +259460. q^{92} +32636.5 q^{93} +175589. q^{94} -135000. q^{95} +194979. q^{96} +48526.4 q^{97} +141723. q^{98} +34265.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.9029	−1.92738	−0.963688	−	0.267032i	$-0.913957\pi$
$2$	−10.9029	−1.92738	−0.963688	+	0.267032i	$0.913957\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	86.8728	2.71478
$5$	88.1143	1.57624	0.788118	−	0.615524i	$-0.211056\pi$
$5$	88.1143	1.57624	0.788118	+	0.615524i	$0.211056\pi$
$6$	98.1259	1.11277
$7$	61.7114	0.476015	0.238007	−	0.971263i	$-0.423506\pi$
$7$	61.7114	0.476015	0.238007	+	0.971263i	$0.423506\pi$
$8$	−598.272	−3.30502
$9$	81.0000	0.333333
$10$	−960.699	−3.03800
$11$	423.027	1.05411	0.527055	−	0.849831i	$-0.323296\pi$
$11$	423.027	1.05411	0.527055	+	0.849831i	$0.323296\pi$
$12$	−781.856	−1.56738
$13$	−1047.72	−1.71944	−0.859722	−	0.510762i	$-0.829363\pi$
$13$	−1047.72	−1.71944	−0.859722	+	0.510762i	$0.829363\pi$
$14$	−672.832	−0.917459
$15$	−793.028	−0.910040
$16$	3742.96	3.65523
$17$	−2034.81	−1.70766	−0.853831	−	0.520550i	$-0.825727\pi$
$17$	−2034.81	−1.70766	−0.853831	+	0.520550i	$0.825727\pi$
$18$	−883.133	−0.642458
$19$	−1532.11	−0.973654	−0.486827	−	0.873498i	$-0.661846\pi$
$19$	−1532.11	−0.973654	−0.486827	+	0.873498i	$0.661846\pi$
$20$	7654.74	4.27913
$21$	−555.403	−0.274827
$22$	−4612.21	−2.03167
$23$	2986.67	1.17725	0.588623	−	0.808408i	$-0.299670\pi$
$23$	2986.67	1.17725	0.588623	+	0.808408i	$0.299670\pi$
$24$	5384.45	1.90815
$25$	4639.12	1.48452
$26$	11423.2	3.31402
$27$	−729.000	−0.192450
$28$	5361.05	1.29227
$29$	115.477	0.0254978	0.0127489	−	0.999919i	$-0.495942\pi$
$29$	115.477	0.0254978	0.0127489	+	0.999919i	$0.495942\pi$
$30$	8646.29	1.75399
$31$	−3626.28	−0.677730	−0.338865	−	0.940835i	$-0.610043\pi$
$31$	−3626.28	−0.677730	−0.338865	+	0.940835i	$0.610043\pi$
$32$	−21664.3	−3.73999
$33$	−3807.24	−0.608591
$34$	22185.3	3.29131
$35$	5437.66	0.750312
$36$	7036.70	0.904925
$37$	−15040.3	−1.80614	−0.903070	−	0.429493i	$-0.858692\pi$
$37$	−15040.3	−1.80614	−0.903070	+	0.429493i	$0.858692\pi$
$38$	16704.4	1.87660
$39$	9429.51	0.992722
$40$	−52716.3	−5.20949
$41$	−829.256	−0.0770423	−0.0385211	−	0.999258i	$-0.512265\pi$
$41$	−829.256	−0.0770423	−0.0385211	+	0.999258i	$0.512265\pi$
$42$	6055.49	0.529695
$43$	−12294.1	−1.01397	−0.506985	−	0.861955i	$-0.669240\pi$
$43$	−12294.1	−1.01397	−0.506985	+	0.861955i	$0.669240\pi$
$44$	36749.5	2.86167
$45$	7137.25	0.525412
$46$	−32563.3	−2.26900
$47$	−16104.8	−1.06343	−0.531717	−	0.846922i	$-0.678453\pi$
$47$	−16104.8	−1.06343	−0.531717	+	0.846922i	$0.678453\pi$
$48$	−33686.6	−2.11035
$49$	−12998.7	−0.773410
$50$	−50579.8	−2.86123
$51$	18313.3	0.985919
$52$	−91018.7	−4.66791
$53$	34428.4	1.68356	0.841778	−	0.539824i	$-0.181509\pi$
$53$	34428.4	1.68356	0.841778	+	0.539824i	$0.181509\pi$
$54$	7948.20	0.370924
$55$	37274.7	1.66153
$56$	−36920.2	−1.57324
$57$	13788.9	0.562139
$58$	−1259.04	−0.0491438
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−68892.6	−2.47056
$61$	16418.9	0.564961	0.282481	−	0.959273i	$-0.408843\pi$
$61$	16418.9	0.564961	0.282481	+	0.959273i	$0.408843\pi$
$62$	39536.9	1.30624
$63$	4998.63	0.158672
$64$	116429.	3.55313
$65$	−92319.3	−2.71025
$66$	41509.9	1.17298
$67$	9818.25	0.267206	0.133603	−	0.991035i	$-0.457345\pi$
$67$	9818.25	0.267206	0.133603	+	0.991035i	$0.457345\pi$
$68$	−176770.	−4.63592
$69$	−26880.0	−0.679683
$70$	−59286.1	−1.44613
$71$	3381.64	0.0796125	0.0398062	−	0.999207i	$-0.487326\pi$
$71$	3381.64	0.0796125	0.0398062	+	0.999207i	$0.487326\pi$
$72$	−48460.0	−1.10167
$73$	27012.0	0.593267	0.296634	−	0.954991i	$-0.404136\pi$
$73$	27012.0	0.593267	0.296634	+	0.954991i	$0.404136\pi$
$74$	163982.	3.48111
$75$	−41752.1	−0.857087
$76$	−133098.	−2.64325
$77$	26105.6	0.501772
$78$	−102809.	−1.91335
$79$	20426.3	0.368233	0.184117	−	0.982904i	$-0.441058\pi$
$79$	20426.3	0.368233	0.184117	+	0.982904i	$0.441058\pi$
$80$	329808.	5.76151
$81$	6561.00	0.111111
$82$	9041.29	0.148489
$83$	−54511.3	−0.868543	−0.434272	−	0.900782i	$-0.642994\pi$
$83$	−54511.3	−0.868543	−0.434272	+	0.900782i	$0.642994\pi$
$84$	−48249.4	−0.746095
$85$	−179296.	−2.69168
$86$	134041.	1.95430
$87$	−1039.30	−0.0147211
$88$	−253085.	−3.48385
$89$	−69700.2	−0.932736	−0.466368	−	0.884591i	$-0.654438\pi$
$89$	−69700.2	−0.932736	−0.466368	+	0.884591i	$0.654438\pi$
$90$	−77816.6	−1.01267
$91$	−64656.5	−0.818481
$92$	259460.	3.19596
$93$	32636.5	0.391287
$94$	175589.	2.04964
$95$	−135000.	−1.53471
$96$	194979.	2.15928
$97$	48526.4	0.523660	0.261830	−	0.965114i	$-0.415674\pi$
$97$	48526.4	0.523660	0.261830	+	0.965114i	$0.415674\pi$
$98$	141723.	1.49065
$99$	34265.1	0.351370
$100$	403014.	4.03014
$101$	107128.	1.04496	0.522478	−	0.852653i	$-0.325008\pi$
$101$	107128.	1.04496	0.522478	+	0.852653i	$0.325008\pi$
$102$	−199668.	−1.90024
$103$	−93523.6	−0.868617	−0.434308	−	0.900764i	$-0.643007\pi$
$103$	−93523.6	−0.868617	−0.434308	+	0.900764i	$0.643007\pi$
$104$	626823.	5.68279
$105$	−48938.9	−0.433193
$106$	−375369.	−3.24484
$107$	51795.7	0.437356	0.218678	−	0.975797i	$-0.429826\pi$
$107$	51795.7	0.437356	0.218678	+	0.975797i	$0.429826\pi$
$108$	−63330.3	−0.522459
$109$	−147885.	−1.19223	−0.596113	−	0.802901i	$-0.703289\pi$
$109$	−147885.	−1.19223	−0.596113	+	0.802901i	$0.703289\pi$
$110$	−406401.	−3.20238
$111$	135363.	1.04278
$112$	230983.	1.73995
$113$	−83662.7	−0.616362	−0.308181	−	0.951328i	$-0.599720\pi$
$113$	−83662.7	−0.616362	−0.308181	+	0.951328i	$0.599720\pi$
$114$	−150339.	−1.08345
$115$	263168.	1.85562
$116$	10031.9	0.0692208
$117$	−84865.6	−0.573148
$118$	37952.9	0.250923
$119$	−125571.	−0.812873
$120$	474447.	3.00770
$121$	17900.5	0.111148
$122$	−179013.	−1.08889
$123$	7463.31	0.0444804
$124$	−315025.	−1.83988
$125$	133416.	0.763716
$126$	−54499.4	−0.305820
$127$	−155048.	−0.853016	−0.426508	−	0.904484i	$-0.640256\pi$
$127$	−155048.	−0.853016	−0.426508	+	0.904484i	$0.640256\pi$
$128$	−576153.	−3.10823
$129$	110647.	0.585416
$130$	1.00655e6	5.22367
$131$	−370672.	−1.88717	−0.943587	−	0.331124i	$-0.892572\pi$
$131$	−370672.	−1.88717	−0.943587	+	0.331124i	$0.892572\pi$
$132$	−330746.	−1.65219
$133$	−94548.4	−0.463474
$134$	−107047.	−0.515007
$135$	−64235.3	−0.303347
$136$	1.21737e6	5.64385
$137$	194058.	0.883345	0.441673	−	0.897176i	$-0.354385\pi$
$137$	194058.	0.883345	0.441673	+	0.897176i	$0.354385\pi$
$138$	293070.	1.31001
$139$	−80499.1	−0.353390	−0.176695	−	0.984266i	$-0.556541\pi$
$139$	−80499.1	−0.353390	−0.176695	+	0.984266i	$0.556541\pi$
$140$	472385.	2.03693
$141$	144943.	0.613973
$142$	−36869.6	−0.153443
$143$	−443215.	−1.81248
$144$	303180.	1.21841
$145$	10175.2	0.0401905
$146$	−294509.	−1.14345
$147$	116988.	0.446528
$148$	−1.30659e6	−4.90327
$149$	229972.	0.848611	0.424305	−	0.905519i	$-0.360518\pi$
$149$	229972.	0.848611	0.424305	+	0.905519i	$0.360518\pi$
$150$	455218.	1.65193
$151$	−103481.	−0.369333	−0.184667	−	0.982801i	$-0.559121\pi$
$151$	−103481.	−0.369333	−0.184667	+	0.982801i	$0.559121\pi$
$152$	916616.	3.21794
$153$	−164820.	−0.569221
$154$	−284626.	−0.967103
$155$	−319527.	−1.06826
$156$	819168.	2.69502
$157$	222025.	0.718875	0.359438	−	0.933169i	$-0.382969\pi$
$157$	222025.	0.718875	0.359438	+	0.933169i	$0.382969\pi$
$158$	−222706.	−0.709723
$159$	−309856.	−0.972001
$160$	−1.90894e6	−5.89510
$161$	184312.	0.560387
$162$	−71533.8	−0.214153
$163$	−1674.56	−0.00493664	−0.00246832	−	0.999997i	$-0.500786\pi$
$163$	−1674.56	−0.00493664	−0.00246832	+	0.999997i	$0.500786\pi$
$164$	−72039.9	−0.209153
$165$	−335472.	−0.959282
$166$	594331.	1.67401
$167$	−633831.	−1.75866	−0.879330	−	0.476212i	$-0.842009\pi$
$167$	−633831.	−1.75866	−0.879330	+	0.476212i	$0.842009\pi$
$168$	332282.	0.908309
$169$	726431.	1.95649
$170$	1.95484e6	5.18788
$171$	−124101.	−0.324551
$172$	−1.06802e6	−2.75270
$173$	304757.	0.774175	0.387087	−	0.922043i	$-0.373481\pi$
$173$	304757.	0.774175	0.387087	+	0.922043i	$0.373481\pi$
$174$	11331.3	0.0283732
$175$	286287.	0.706653
$176$	1.58337e6	3.85302
$177$	31329.0	0.0751646
$178$	759933.	1.79773
$179$	67132.3	0.156603	0.0783013	−	0.996930i	$-0.475050\pi$
$179$	67132.3	0.156603	0.0783013	+	0.996930i	$0.475050\pi$
$180$	620034.	1.42638
$181$	111781.	0.253613	0.126807	−	0.991927i	$-0.459527\pi$
$181$	111781.	0.253613	0.126807	+	0.991927i	$0.459527\pi$
$182$	704942.	1.57752
$183$	−147770.	−0.326180
$184$	−1.78684e6	−3.89082
$185$	−1.32526e6	−2.84690
$186$	−355832.	−0.754158
$187$	−860780.	−1.80006
$188$	−1.39907e6	−2.88698
$189$	−44987.6	−0.0916091
$190$	1.47189e6	2.95796
$191$	−731353.	−1.45059	−0.725294	−	0.688440i	$-0.758296\pi$
$191$	−731353.	−1.45059	−0.725294	+	0.688440i	$0.758296\pi$
$192$	−1.04786e6	−2.05140
$193$	685155.	1.32402	0.662011	−	0.749494i	$-0.269703\pi$
$193$	685155.	1.32402	0.662011	+	0.749494i	$0.269703\pi$
$194$	−529078.	−1.00929
$195$	830874.	1.56476
$196$	−1.12923e6	−2.09963
$197$	−723750.	−1.32869	−0.664344	−	0.747427i	$-0.731289\pi$
$197$	−723750.	−1.32869	−0.664344	+	0.747427i	$0.731289\pi$
$198$	−373589.	−0.677222
$199$	−186876.	−0.334519	−0.167260	−	0.985913i	$-0.553492\pi$
$199$	−186876.	−0.334519	−0.167260	+	0.985913i	$0.553492\pi$
$200$	−2.77546e6	−4.90636
$201$	−88364.2	−0.154272
$202$	−1.16800e6	−2.01402
$203$	7126.28	0.0121373
$204$	1.59093e6	2.67655
$205$	−73069.3	−0.121437
$206$	1.01968e6	1.67415
$207$	241920.	0.392415
$208$	−3.92158e6	−6.28497
$209$	−648121.	−1.02634
$210$	533575.	0.834925
$211$	−143708.	−0.222216	−0.111108	−	0.993808i	$-0.535440\pi$
$211$	−143708.	−0.222216	−0.111108	+	0.993808i	$0.535440\pi$
$212$	2.99089e6	4.57048
$213$	−30434.7	−0.0459643
$214$	−564723.	−0.842948
$215$	−1.08329e6	−1.59826
$216$	436140.	0.636051
$217$	−223783.	−0.322609
$218$	1.61237e6	2.29787
$219$	−243108.	−0.342523
$220$	3.23816e6	4.51067
$221$	2.13192e6	2.93623
$222$	−1.47584e6	−2.00982
$223$	299009.	0.402645	0.201322	−	0.979525i	$-0.435476\pi$
$223$	299009.	0.402645	0.201322	+	0.979525i	$0.435476\pi$
$224$	−1.33694e6	−1.78029
$225$	375769.	0.494840
$226$	912164.	1.18796
$227$	106091.	0.136651	0.0683255	−	0.997663i	$-0.478234\pi$
$227$	106091.	0.136651	0.0683255	+	0.997663i	$0.478234\pi$
$228$	1.19789e6	1.52608
$229$	−222769.	−0.280715	−0.140358	−	0.990101i	$-0.544825\pi$
$229$	−222769.	−0.280715	−0.140358	+	0.990101i	$0.544825\pi$
$230$	−2.86929e6	−3.57647
$231$	−234950.	−0.289698
$232$	−69086.9	−0.0842706
$233$	−877575.	−1.05900	−0.529498	−	0.848311i	$-0.677620\pi$
$233$	−877575.	−1.05900	−0.529498	+	0.848311i	$0.677620\pi$
$234$	925279.	1.10467
$235$	−1.41906e6	−1.67622
$236$	−302404.	−0.353434
$237$	−183837.	−0.212599
$238$	1.36909e6	1.56671
$239$	1.55403e6	1.75980	0.879902	−	0.475156i	$-0.157608\pi$
$239$	1.55403e6	1.75980	0.879902	+	0.475156i	$0.157608\pi$
$240$	−2.96827e6	−3.32641
$241$	−65896.5	−0.0730836	−0.0365418	−	0.999332i	$-0.511634\pi$
$241$	−65896.5	−0.0730836	−0.0365418	+	0.999332i	$0.511634\pi$
$242$	−195167.	−0.214223
$243$	−59049.0	−0.0641500
$244$	1.42635e6	1.53374
$245$	−1.14537e6	−1.21908
$246$	−81371.6	−0.0857304
$247$	1.60522e6	1.67414
$248$	2.16950e6	2.23991
$249$	490602.	0.501454
$250$	−1.45462e6	−1.47197
$251$	−24842.7	−0.0248894	−0.0124447	−	0.999923i	$-0.503961\pi$
$251$	−24842.7	−0.0248894	−0.0124447	+	0.999923i	$0.503961\pi$
$252$	434245.	0.430758
$253$	1.26344e6	1.24095
$254$	1.69047e6	1.64408
$255$	1.61366e6	1.55404
$256$	2.55600e6	2.43759
$257$	501967.	0.474070	0.237035	−	0.971501i	$-0.423824\pi$
$257$	501967.	0.474070	0.237035	+	0.971501i	$0.423824\pi$
$258$	−1.20637e6	−1.12832
$259$	−928157.	−0.859750
$260$	−8.02004e6	−7.35772
$261$	9353.68	0.00849926
$262$	4.04140e6	3.63729
$263$	1.26902e6	1.13130	0.565652	−	0.824644i	$-0.308624\pi$
$263$	1.26902e6	1.13130	0.565652	+	0.824644i	$0.308624\pi$
$264$	2.27776e6	2.01140
$265$	3.03363e6	2.65368
$266$	1.03085e6	0.893288
$267$	627302.	0.538516
$268$	852939.	0.725406
$269$	−1.04097e6	−0.877121	−0.438560	−	0.898702i	$-0.644511\pi$
$269$	−1.04097e6	−0.877121	−0.438560	+	0.898702i	$0.644511\pi$
$270$	700350.	0.584663
$271$	−2.07017e6	−1.71231	−0.856155	−	0.516718i	$-0.827153\pi$
$271$	−2.07017e6	−1.71231	−0.856155	+	0.516718i	$0.827153\pi$
$272$	−7.61622e6	−6.24191
$273$	581908.	0.472550
$274$	−2.11579e6	−1.70254
$275$	1.96247e6	1.56485
$276$	−2.33514e6	−1.84519
$277$	1.93149e6	1.51249	0.756247	−	0.654287i	$-0.227031\pi$
$277$	1.93149e6	1.51249	0.756247	+	0.654287i	$0.227031\pi$
$278$	877672.	0.681115
$279$	−293728.	−0.225910
$280$	−3.25320e6	−2.47979
$281$	859707.	0.649508	0.324754	−	0.945799i	$-0.394718\pi$
$281$	859707.	0.649508	0.324754	+	0.945799i	$0.394718\pi$
$282$	−1.58030e6	−1.18336
$283$	−789427.	−0.585930	−0.292965	−	0.956123i	$-0.594642\pi$
$283$	−789427.	−0.585930	−0.292965	+	0.956123i	$0.594642\pi$
$284$	293772.	0.216130
$285$	1.21500e6	0.886064
$286$	4.83232e6	3.49334
$287$	−51174.6	−0.0366733
$288$	−1.75481e6	−1.24666
$289$	2.72060e6	1.91611
$290$	−110939.	−0.0774622
$291$	−436738.	−0.302335
$292$	2.34661e6	1.61059
$293$	−1.83732e6	−1.25030	−0.625152	−	0.780503i	$-0.714963\pi$
$293$	−1.83732e6	−1.25030	−0.625152	+	0.780503i	$0.714963\pi$
$294$	−1.27551e6	−0.860628
$295$	−306726.	−0.205208
$296$	8.99818e6	5.96933
$297$	−308386.	−0.202864
$298$	−2.50735e6	−1.63559
$299$	−3.12920e6	−2.02421
$300$	−3.62712e6	−2.32680
$301$	−758686.	−0.482665
$302$	1.12824e6	0.711843
$303$	−964148.	−0.603305
$304$	−5.73461e6	−3.55893
$305$	1.44674e6	0.890512
$306$	1.79701e6	1.09710
$307$	−443750.	−0.268715	−0.134358	−	0.990933i	$-0.542897\pi$
$307$	−443750.	−0.268715	−0.134358	+	0.990933i	$0.542897\pi$
$308$	2.26787e6	1.36220
$309$	841713.	0.501496
$310$	3.48376e6	2.05894
$311$	−651682.	−0.382063	−0.191031	−	0.981584i	$-0.561183\pi$
$311$	−651682.	−0.382063	−0.191031	+	0.981584i	$0.561183\pi$
$312$	−5.64141e6	−3.28096
$313$	−1.28063e6	−0.738859	−0.369430	−	0.929259i	$-0.620447\pi$
$313$	−1.28063e6	−0.738859	−0.369430	+	0.929259i	$0.620447\pi$
$314$	−2.42072e6	−1.38554
$315$	440450.	0.250104
$316$	1.77449e6	0.999670
$317$	1.85275e6	1.03554	0.517772	−	0.855518i	$-0.326761\pi$
$317$	1.85275e6	1.03554	0.517772	+	0.855518i	$0.326761\pi$
$318$	3.37832e6	1.87341
$319$	48850.0	0.0268775
$320$	1.02591e7	5.60057
$321$	−466162.	−0.252507
$322$	−2.00953e6	−1.08008
$323$	3.11755e6	1.66267
$324$	569973.	0.301642
$325$	−4.86052e6	−2.55255
$326$	18257.5	0.00951475
$327$	1.33097e6	0.688332
$328$	496121.	0.254626
$329$	−993849.	−0.506210
$330$	3.65761e6	1.84890
$331$	−646915.	−0.324547	−0.162273	−	0.986746i	$-0.551883\pi$
$331$	−646915.	−0.324547	−0.162273	+	0.986746i	$0.551883\pi$
$332$	−4.73555e6	−2.35790
$333$	−1.21826e6	−0.602047
$334$	6.91058e6	3.38960
$335$	865128.	0.421180
$336$	−2.07885e6	−1.00456
$337$	−1.93315e6	−0.927235	−0.463618	−	0.886035i	$-0.653449\pi$
$337$	−1.93315e6	−0.927235	−0.463618	+	0.886035i	$0.653449\pi$
$338$	−7.92019e6	−3.77089
$339$	752964.	0.355857
$340$	−1.55759e7	−7.30731
$341$	−1.53401e6	−0.714402
$342$	1.35305e6	0.625532
$343$	−1.83935e6	−0.844169
$344$	7.35521e6	3.35119
$345$	−2.36851e6	−1.07134
$346$	−3.32273e6	−1.49213
$347$	−2.55520e6	−1.13920	−0.569601	−	0.821921i	$-0.692902\pi$
$347$	−2.55520e6	−1.13920	−0.569601	+	0.821921i	$0.692902\pi$
$348$	−90286.7	−0.0399646
$349$	−106267.	−0.0467019	−0.0233509	−	0.999727i	$-0.507434\pi$
$349$	−106267.	−0.0467019	−0.0233509	+	0.999727i	$0.507434\pi$
$350$	−3.12135e6	−1.36199
$351$	763790.	0.330907
$352$	−9.16459e6	−3.94236
$353$	421809.	0.180169	0.0900844	−	0.995934i	$-0.471286\pi$
$353$	421809.	0.180169	0.0900844	+	0.995934i	$0.471286\pi$
$354$	−341576.	−0.144870
$355$	297970.	0.125488
$356$	−6.05505e6	−2.53217
$357$	1.13014e6	0.469312
$358$	−731936.	−0.301832
$359$	2.33843e6	0.957607	0.478804	−	0.877922i	$-0.341071\pi$
$359$	2.33843e6	0.957607	0.478804	+	0.877922i	$0.341071\pi$
$360$	−4.27002e6	−1.73650
$361$	−128752.	−0.0519980
$362$	−1.21874e6	−0.488808
$363$	−161104.	−0.0641712
$364$	−5.61689e6	−2.22199
$365$	2.38015e6	0.935129
$366$	1.61112e6	0.628672
$367$	1.76169e6	0.682755	0.341377	−	0.939926i	$-0.389107\pi$
$367$	1.76169e6	0.682755	0.341377	+	0.939926i	$0.389107\pi$
$368$	1.11790e7	4.30311
$369$	−67169.8	−0.0256808
$370$	1.44492e7	5.48705
$371$	2.12463e6	0.801397
$372$	2.83522e6	1.06226
$373$	555814.	0.206851	0.103425	−	0.994637i	$-0.467020\pi$
$373$	555814.	0.206851	0.103425	+	0.994637i	$0.467020\pi$
$374$	9.38498e6	3.46940
$375$	−1.20074e6	−0.440932
$376$	9.63504e6	3.51467
$377$	−120988.	−0.0438420
$378$	490495.	0.176565
$379$	1.23190e6	0.440532	0.220266	−	0.975440i	$-0.429307\pi$
$379$	1.23190e6	0.440532	0.220266	+	0.975440i	$0.429307\pi$
$380$	−1.17279e7	−4.16639
$381$	1.39543e6	0.492489
$382$	7.97386e6	2.79583
$383$	2.07159e6	0.721617	0.360808	−	0.932640i	$-0.382501\pi$
$383$	2.07159e6	0.721617	0.360808	+	0.932640i	$0.382501\pi$
$384$	5.18538e6	1.79454
$385$	2.30027e6	0.790911
$386$	−7.47016e6	−2.55189
$387$	−995822.	−0.337990
$388$	4.21563e6	1.42162
$389$	−4.06653e6	−1.36254	−0.681271	−	0.732031i	$-0.738573\pi$
$389$	−4.06653e6	−1.36254	−0.681271	+	0.732031i	$0.738573\pi$
$390$	−9.05892e6	−3.01589
$391$	−6.07731e6	−2.01034
$392$	7.77676e6	2.55613
$393$	3.33605e6	1.08956
$394$	7.89096e6	2.56088
$395$	1.79985e6	0.580422
$396$	2.97671e6	0.953891
$397$	−4.63853e6	−1.47708	−0.738541	−	0.674209i	$-0.764485\pi$
$397$	−4.63853e6	−1.47708	−0.738541	+	0.674209i	$0.764485\pi$
$398$	2.03749e6	0.644744
$399$	850936.	0.267587
$400$	1.73640e7	5.42626
$401$	2.63194e6	0.817363	0.408681	−	0.912677i	$-0.365989\pi$
$401$	2.63194e6	0.817363	0.408681	+	0.912677i	$0.365989\pi$
$402$	963425.	0.297340
$403$	3.79933e6	1.16532
$404$	9.30647e6	2.83682
$405$	578118.	0.175137
$406$	−77697.0	−0.0233932
$407$	−6.36244e6	−1.90387
$408$	−1.09563e7	−3.25848
$409$	3.04976e6	0.901482	0.450741	−	0.892655i	$-0.351160\pi$
$409$	3.04976e6	0.901482	0.450741	+	0.892655i	$0.351160\pi$
$410$	796666.	0.234054
$411$	−1.74652e6	−0.510000
$412$	−8.12466e6	−2.35810
$413$	−214817.	−0.0619719
$414$	−2.63763e6	−0.756332
$415$	−4.80322e6	−1.36903
$416$	2.26982e7	6.43070
$417$	724492.	0.204030
$418$	7.06639e6	1.97814
$419$	1.34161e6	0.373329	0.186664	−	0.982424i	$-0.440232\pi$
$419$	1.34161e6	0.373329	0.186664	+	0.982424i	$0.440232\pi$
$420$	−4.25146e6	−1.17602
$421$	2.54019e6	0.698492	0.349246	−	0.937031i	$-0.386438\pi$
$421$	2.54019e6	0.698492	0.349246	+	0.937031i	$0.386438\pi$
$422$	1.56683e6	0.428293
$423$	−1.30449e6	−0.354478
$424$	−2.05976e7	−5.56418
$425$	−9.43974e6	−2.53506
$426$	331826.	0.0885904
$427$	1.01323e6	0.268930
$428$	4.49964e6	1.18732
$429$	3.98893e6	1.04644
$430$	1.18109e7	3.08044
$431$	4.17832e6	1.08345	0.541725	−	0.840556i	$-0.317772\pi$
$431$	4.17832e6	1.08345	0.541725	+	0.840556i	$0.317772\pi$
$432$	−2.72862e6	−0.703450
$433$	−74580.5	−0.0191164	−0.00955819	−	0.999954i	$-0.503043\pi$
$433$	−74580.5	−0.0191164	−0.00955819	+	0.999954i	$0.503043\pi$
$434$	2.43988e6	0.621790
$435$	−91576.9	−0.0232040
$436$	−1.28472e7	−3.23663
$437$	−4.57589e6	−1.14623
$438$	2.65058e6	0.660170
$439$	7.12201e6	1.76377	0.881884	−	0.471466i	$-0.156275\pi$
$439$	7.12201e6	1.76377	0.881884	+	0.471466i	$0.156275\pi$
$440$	−2.23004e7	−5.49137
$441$	−1.05289e6	−0.257803
$442$	−2.32441e7	−5.65922
$443$	−7.36242e6	−1.78243	−0.891213	−	0.453585i	$-0.850145\pi$
$443$	−7.36242e6	−1.78243	−0.891213	+	0.453585i	$0.850145\pi$
$444$	1.17593e7	2.83090
$445$	−6.14158e6	−1.47021
$446$	−3.26006e6	−0.776047
$447$	−2.06974e6	−0.489946
$448$	7.18500e6	1.69134
$449$	−5.60487e6	−1.31205	−0.656023	−	0.754741i	$-0.727763\pi$
$449$	−5.60487e6	−1.31205	−0.656023	+	0.754741i	$0.727763\pi$
$450$	−4.09696e6	−0.953742
$451$	−350798.	−0.0812111
$452$	−7.26801e6	−1.67328
$453$	931329.	0.213235
$454$	−1.15669e6	−0.263378
$455$	−5.69716e6	−1.29012
$456$	−8.24954e6	−1.85788
$457$	−2.27985e6	−0.510641	−0.255320	−	0.966856i	$-0.582181\pi$
$457$	−2.27985e6	−0.510641	−0.255320	+	0.966856i	$0.582181\pi$
$458$	2.42883e6	0.541044
$459$	1.48338e6	0.328640
$460$	2.28621e7	5.03759
$461$	5.70375e6	1.24999	0.624997	−	0.780627i	$-0.285100\pi$
$461$	5.70375e6	1.24999	0.624997	+	0.780627i	$0.285100\pi$
$462$	2.56163e6	0.558357
$463$	3.15681e6	0.684378	0.342189	−	0.939631i	$-0.388832\pi$
$463$	3.15681e6	0.684378	0.342189	+	0.939631i	$0.388832\pi$
$464$	432227.	0.0932003
$465$	2.87574e6	0.616761
$466$	9.56810e6	2.04108
$467$	4.10668e6	0.871362	0.435681	−	0.900101i	$-0.356508\pi$
$467$	4.10668e6	0.871362	0.435681	+	0.900101i	$0.356508\pi$
$468$	−7.37251e6	−1.55597
$469$	605898.	0.127194
$470$	1.54719e7	3.23071
$471$	−1.99823e6	−0.415043
$472$	2.08259e6	0.430277
$473$	−5.20073e6	−1.06884
$474$	2.00435e6	0.409759
$475$	−7.10762e6	−1.44541
$476$	−1.09087e7	−2.20677
$477$	2.78870e6	0.561185
$478$	−1.69434e7	−3.39180
$479$	−3.96139e6	−0.788876	−0.394438	−	0.918923i	$-0.629061\pi$
$479$	−3.96139e6	−0.788876	−0.394438	+	0.918923i	$0.629061\pi$
$480$	1.71804e7	3.40354
$481$	1.57580e7	3.10556
$482$	718462.	0.140860
$483$	−1.65880e6	−0.323539
$484$	1.55506e6	0.301741
$485$	4.27587e6	0.825411
$486$	643804.	0.123641
$487$	−9.18635e6	−1.75517	−0.877587	−	0.479417i	$-0.840848\pi$
$487$	−9.18635e6	−1.75517	−0.877587	+	0.479417i	$0.840848\pi$
$488$	−9.82295e6	−1.86721
$489$	15071.0	0.00285017
$490$	1.24878e7	2.34962
$491$	3.85969e6	0.722518	0.361259	−	0.932465i	$-0.382347\pi$
$491$	3.85969e6	0.722518	0.361259	+	0.932465i	$0.382347\pi$
$492$	648359.	0.120754
$493$	−234975.	−0.0435416
$494$	−1.75015e7	−3.22670
$495$	3.01925e6	0.553842
$496$	−1.35730e7	−2.47726
$497$	208686.	0.0378967
$498$	−5.34897e6	−0.966490
$499$	−3.44774e6	−0.619845	−0.309922	−	0.950762i	$-0.600303\pi$
$499$	−3.44774e6	−0.619845	−0.309922	+	0.950762i	$0.600303\pi$
$500$	1.15902e7	2.07332
$501$	5.70448e6	1.01536
$502$	270857.	0.0479712
$503$	5.17527e6	0.912038	0.456019	−	0.889970i	$-0.349275\pi$
$503$	5.17527e6	0.912038	0.456019	+	0.889970i	$0.349275\pi$
$504$	−2.99054e6	−0.524412
$505$	9.43946e6	1.64710
$506$	−1.37751e7	−2.39177
$507$	−6.53788e6	−1.12958
$508$	−1.34695e7	−2.31575
$509$	−86953.7	−0.0148763	−0.00743813	−	0.999972i	$-0.502368\pi$
$509$	−86953.7	−0.0148763	−0.00743813	+	0.999972i	$0.502368\pi$
$510$	−1.75936e7	−2.99522
$511$	1.66695e6	0.282404
$512$	−9.43086e6	−1.58992
$513$	1.11690e6	0.187380
$514$	−5.47289e6	−0.913710
$515$	−8.24077e6	−1.36915
$516$	9.61221e6	1.58927
$517$	−6.81275e6	−1.12098
$518$	1.01196e7	1.65706
$519$	−2.74282e6	−0.446970
$520$	5.52321e7	8.95742
$521$	−6.15153e6	−0.992861	−0.496431	−	0.868076i	$-0.665356\pi$
$521$	−6.15153e6	−0.992861	−0.496431	+	0.868076i	$0.665356\pi$
$522$	−101982.	−0.0163813
$523$	1.72407e6	0.275613	0.137807	−	0.990459i	$-0.455995\pi$
$523$	1.72407e6	0.275613	0.137807	+	0.990459i	$0.455995\pi$
$524$	−3.22014e7	−5.12326
$525$	−2.57658e6	−0.407986
$526$	−1.38360e7	−2.18045
$527$	7.37879e6	1.15733
$528$	−1.42503e7	−2.22454
$529$	2.48384e6	0.385909
$530$	−3.30754e7	−5.11464
$531$	−281961.	−0.0433963
$532$	−8.21369e6	−1.25823
$533$	868831.	0.132470
$534$	−6.83940e6	−1.03792
$535$	4.56394e6	0.689375
$536$	−5.87398e6	−0.883122
$537$	−604191.	−0.0904146
$538$	1.13496e7	1.69054
$539$	−5.49879e6	−0.815259
$540$	−5.58030e6	−0.823518
$541$	−8.39290e6	−1.23287	−0.616437	−	0.787404i	$-0.711425\pi$
$541$	−8.39290e6	−1.23287	−0.616437	+	0.787404i	$0.711425\pi$
$542$	2.25708e7	3.30027
$543$	−1.00603e6	−0.146424
$544$	4.40829e7	6.38664
$545$	−1.30308e7	−1.87923
$546$	−6.34448e6	−0.910782
$547$	−1.01323e7	−1.44790	−0.723952	−	0.689850i	$-0.757676\pi$
$547$	−1.01323e7	−1.44790	−0.723952	+	0.689850i	$0.757676\pi$
$548$	1.68584e7	2.39808
$549$	1.32993e6	0.188320
$550$	−2.13966e7	−3.01605
$551$	−176924.	−0.0248260
$552$	1.60816e7	2.24637
$553$	1.26054e6	0.175284
$554$	−2.10588e7	−2.91514
$555$	1.19274e7	1.64366
$556$	−6.99318e6	−0.959374
$557$	9.82722e6	1.34212	0.671062	−	0.741401i	$-0.265838\pi$
$557$	9.82722e6	1.34212	0.671062	+	0.741401i	$0.265838\pi$
$558$	3.20249e6	0.435413
$559$	1.28808e7	1.74347
$560$	2.03529e7	2.74256
$561$	7.74702e6	1.03927
$562$	−9.37328e6	−1.25185
$563$	9.96382e6	1.32481	0.662407	−	0.749144i	$-0.269535\pi$
$563$	9.96382e6	1.32481	0.662407	+	0.749144i	$0.269535\pi$
$564$	1.25916e7	1.66680
$565$	−7.37187e6	−0.971531
$566$	8.60703e6	1.12931
$567$	404889.	0.0528905
$568$	−2.02314e6	−0.263121
$569$	1.30624e7	1.69138	0.845692	−	0.533672i	$-0.179188\pi$
$569$	1.30624e7	1.69138	0.845692	+	0.533672i	$0.179188\pi$
$570$	−1.32470e7	−1.70778
$571$	1.30362e7	1.67325	0.836625	−	0.547776i	$-0.184525\pi$
$571$	1.30362e7	1.67325	0.836625	+	0.547776i	$0.184525\pi$
$572$	−3.85033e7	−4.92049
$573$	6.58218e6	0.837497
$574$	557951.	0.0706832
$575$	1.38555e7	1.74764
$576$	9.43075e6	1.18438
$577$	−1.37814e7	−1.72327	−0.861637	−	0.507524i	$-0.830561\pi$
$577$	−1.37814e7	−1.72327	−0.861637	+	0.507524i	$0.830561\pi$
$578$	−2.96624e7	−3.69307
$579$	−6.16639e6	−0.764425
$580$	883949.	0.109108
$581$	−3.36397e6	−0.413440
$582$	4.76170e6	0.582713
$583$	1.45641e7	1.77465
$584$	−1.61606e7	−1.96076
$585$	−7.47787e6	−0.903417
$586$	2.00321e7	2.40981
$587$	−4.70405e6	−0.563478	−0.281739	−	0.959491i	$-0.590911\pi$
$587$	−4.70405e6	−0.563478	−0.281739	+	0.959491i	$0.590911\pi$
$588$	1.01631e7	1.21222
$589$	5.55584e6	0.659874
$590$	3.34419e6	0.395514
$591$	6.51375e6	0.767118
$592$	−5.62951e7	−6.60187
$593$	4.77416e6	0.557519	0.278760	−	0.960361i	$-0.410077\pi$
$593$	4.77416e6	0.557519	0.278760	+	0.960361i	$0.410077\pi$
$594$	3.36230e6	0.390994
$595$	−1.10646e7	−1.28128
$596$	1.99783e7	2.30379
$597$	1.68188e6	0.193135
$598$	3.41173e7	3.90141
$599$	−1.34470e6	−0.153129	−0.0765645	−	0.997065i	$-0.524395\pi$
$599$	−1.34470e6	−0.153129	−0.0765645	+	0.997065i	$0.524395\pi$
$600$	2.49791e7	2.83269
$601$	−1.25261e7	−1.41458	−0.707292	−	0.706921i	$-0.750084\pi$
$601$	−1.25261e7	−1.41458	−0.707292	+	0.706921i	$0.750084\pi$
$602$	8.27187e6	0.930277
$603$	795278.	0.0890688
$604$	−8.98969e6	−1.00266
$605$	1.57728e6	0.175195
$606$	1.05120e7	1.16280
$607$	−1.01433e7	−1.11740	−0.558698	−	0.829371i	$-0.688699\pi$
$607$	−1.01433e7	−1.11740	−0.558698	+	0.829371i	$0.688699\pi$
$608$	3.31920e7	3.64146
$609$	−64136.5	−0.00700749
$610$	−1.57736e7	−1.71635
$611$	1.68734e7	1.82851
$612$	−1.43184e7	−1.54531
$613$	5.39122e6	0.579476	0.289738	−	0.957106i	$-0.406432\pi$
$613$	5.39122e6	0.579476	0.289738	+	0.957106i	$0.406432\pi$
$614$	4.83815e6	0.517915
$615$	657624.	0.0701116
$616$	−1.56182e7	−1.65837
$617$	1.83062e6	0.193591	0.0967957	−	0.995304i	$-0.469141\pi$
$617$	1.83062e6	0.193591	0.0967957	+	0.995304i	$0.469141\pi$
$618$	−9.17709e6	−0.966572
$619$	1.04088e7	1.09188	0.545939	−	0.837825i	$-0.316173\pi$
$619$	1.04088e7	1.09188	0.545939	+	0.837825i	$0.316173\pi$
$620$	−2.77582e7	−2.90009
$621$	−2.17728e6	−0.226561
$622$	7.10521e6	0.736378
$623$	−4.30130e6	−0.443996
$624$	3.52943e7	3.62863
$625$	−2.74143e6	−0.280722
$626$	1.39625e7	1.42406
$627$	5.83309e6	0.592557
$628$	1.92880e7	1.95159
$629$	3.06041e7	3.08428
$630$	−4.80218e6	−0.482044
$631$	4.99395e6	0.499310	0.249655	−	0.968335i	$-0.419683\pi$
$631$	4.99395e6	0.499310	0.249655	+	0.968335i	$0.419683\pi$
$632$	−1.22205e7	−1.21702
$633$	1.29337e6	0.128296
$634$	−2.02003e7	−1.99588
$635$	−1.36620e7	−1.34455
$636$	−2.69181e7	−2.63877
$637$	1.36190e7	1.32984
$638$	−532606.	−0.0518030
$639$	273913.	0.0265375
$640$	−5.07673e7	−4.89930
$641$	6.06889e6	0.583397	0.291699	−	0.956510i	$-0.405780\pi$
$641$	6.06889e6	0.583397	0.291699	+	0.956510i	$0.405780\pi$
$642$	5.08251e6	0.486676
$643$	−1.56458e7	−1.49235	−0.746176	−	0.665748i	$-0.768112\pi$
$643$	−1.56458e7	−1.49235	−0.746176	+	0.665748i	$0.768112\pi$
$644$	1.60117e7	1.52132
$645$	9.74957e6	0.922754
$646$	−3.39902e7	−3.20459
$647$	1.46905e7	1.37967	0.689837	−	0.723964i	$-0.257682\pi$
$647$	1.46905e7	1.37967	0.689837	+	0.723964i	$0.257682\pi$
$648$	−3.92526e6	−0.367224
$649$	−1.47256e6	−0.137233
$650$	5.29936e7	4.91972
$651$	2.01404e6	0.186259
$652$	−145474.	−0.0134019
$653$	1.07967e7	0.990852	0.495426	−	0.868650i	$-0.335012\pi$
$653$	1.07967e7	0.990852	0.495426	+	0.868650i	$0.335012\pi$
$654$	−1.45114e7	−1.32667
$655$	−3.26615e7	−2.97463
$656$	−3.10387e6	−0.281608
$657$	2.18798e6	0.197756
$658$	1.08358e7	0.975657
$659$	−1.33499e7	−1.19747	−0.598734	−	0.800948i	$-0.704329\pi$
$659$	−1.33499e7	−1.19747	−0.598734	+	0.800948i	$0.704329\pi$
$660$	−2.91434e7	−2.60424
$661$	−1.52627e7	−1.35871	−0.679354	−	0.733810i	$-0.737740\pi$
$661$	−1.52627e7	−1.35871	−0.679354	+	0.733810i	$0.737740\pi$
$662$	7.05324e6	0.625524
$663$	−1.91873e7	−1.69523
$664$	3.26126e7	2.87055
$665$	−8.33106e6	−0.730544
$666$	1.32826e7	1.16037
$667$	344893.	0.0300172
$668$	−5.50627e7	−4.77437
$669$	−2.69108e6	−0.232467
$670$	−9.43238e6	−0.811773
$671$	6.94562e6	0.595531
$672$	1.20324e7	1.02785
$673$	700630.	0.0596281	0.0298141	−	0.999555i	$-0.490508\pi$
$673$	700630.	0.0596281	0.0298141	+	0.999555i	$0.490508\pi$
$674$	2.10769e7	1.78713
$675$	−3.38192e6	−0.285696
$676$	6.31071e7	5.31143
$677$	1.76900e7	1.48339	0.741697	−	0.670735i	$-0.234021\pi$
$677$	1.76900e7	1.48339	0.741697	+	0.670735i	$0.234021\pi$
$678$	−8.20948e6	−0.685869
$679$	2.99464e6	0.249270
$680$	1.07268e8	8.89605
$681$	−954816.	−0.0788954
$682$	1.67251e7	1.37692
$683$	−1.72148e7	−1.41205	−0.706024	−	0.708187i	$-0.749513\pi$
$683$	−1.72148e7	−1.41205	−0.706024	+	0.708187i	$0.749513\pi$
$684$	−1.07810e7	−0.881084
$685$	1.70993e7	1.39236
$686$	2.00542e7	1.62703
$687$	2.00492e6	0.162071
$688$	−4.60163e7	−3.70630
$689$	−3.60715e7	−2.89478
$690$	2.58236e7	2.06488
$691$	−1.54571e7	−1.23149	−0.615746	−	0.787944i	$-0.711145\pi$
$691$	−1.54571e7	−1.23149	−0.615746	+	0.787944i	$0.711145\pi$
$692$	2.64751e7	2.10171
$693$	2.11455e6	0.167257
$694$	2.78590e7	2.19567
$695$	−7.09312e6	−0.557025
$696$	621783.	0.0486536
$697$	1.68738e6	0.131562
$698$	1.15862e6	0.0900120
$699$	7.89818e6	0.611412
$700$	2.48706e7	1.91841
$701$	90599.9	0.00696358	0.00348179	−	0.999994i	$-0.498892\pi$
$701$	90599.9	0.00696358	0.00348179	+	0.999994i	$0.498892\pi$
$702$	−8.32751e6	−0.637783
$703$	2.30433e7	1.75856
$704$	4.92526e7	3.74539
$705$	1.27715e7	0.967767
$706$	−4.59894e6	−0.347253
$707$	6.61099e6	0.497414
$708$	2.72164e6	0.204055
$709$	7.81917e6	0.584178	0.292089	−	0.956391i	$-0.405650\pi$
$709$	7.81917e6	0.584178	0.292089	+	0.956391i	$0.405650\pi$
$710$	−3.24874e6	−0.241863
$711$	1.65453e6	0.122744
$712$	4.16997e7	3.08271
$713$	−1.08305e7	−0.797855
$714$	−1.23218e7	−0.904541
$715$	−3.90535e7	−2.85690
$716$	5.83197e6	0.425141
$717$	−1.39863e7	−1.01602
$718$	−2.54956e7	−1.84567
$719$	2.06917e7	1.49270	0.746352	−	0.665552i	$-0.231804\pi$
$719$	2.06917e7	1.49270	0.746352	+	0.665552i	$0.231804\pi$
$720$	2.67145e7	1.92050
$721$	−5.77148e6	−0.413475
$722$	1.40377e6	0.100220
$723$	593069.	0.0421948
$724$	9.71073e6	0.688503
$725$	535714.	0.0378519
$726$	1.75650e6	0.123682
$727$	−1.54163e7	−1.08179	−0.540896	−	0.841089i	$-0.681915\pi$
$727$	−1.54163e7	−1.08179	−0.540896	+	0.841089i	$0.681915\pi$
$728$	3.86822e7	2.70509
$729$	531441.	0.0370370
$730$	−2.59505e7	−1.80234
$731$	2.50162e7	1.73152
$732$	−1.28372e7	−0.885507
$733$	1.32653e7	0.911924	0.455962	−	0.889999i	$-0.349295\pi$
$733$	1.32653e7	0.911924	0.455962	+	0.889999i	$0.349295\pi$
$734$	−1.92075e7	−1.31592
$735$	1.03083e7	0.703834
$736$	−6.47042e7	−4.40289
$737$	4.15338e6	0.281665
$738$	732344.	0.0494965
$739$	1.43430e7	0.966114	0.483057	−	0.875589i	$-0.339526\pi$
$739$	1.43430e7	0.966114	0.483057	+	0.875589i	$0.339526\pi$
$740$	−1.15129e8	−7.72871
$741$	−1.44470e7	−0.966567
$742$	−2.31646e7	−1.54459
$743$	6.61514e6	0.439609	0.219805	−	0.975544i	$-0.429458\pi$
$743$	6.61514e6	0.439609	0.219805	+	0.975544i	$0.429458\pi$
$744$	−1.95255e7	−1.29321
$745$	2.02638e7	1.33761
$746$	−6.05998e6	−0.398679
$747$	−4.41542e6	−0.289514
$748$	−7.47784e7	−4.88677
$749$	3.19639e6	0.208188
$750$	1.30915e7	0.849841
$751$	5.45848e6	0.353160	0.176580	−	0.984286i	$-0.443497\pi$
$751$	5.45848e6	0.353160	0.176580	+	0.984286i	$0.443497\pi$
$752$	−6.02795e7	−3.88710
$753$	223584.	0.0143699
$754$	1.31912e6	0.0845000
$755$	−9.11815e6	−0.582156
$756$	−3.90820e6	−0.248698
$757$	1.40547e7	0.891416	0.445708	−	0.895178i	$-0.352952\pi$
$757$	1.40547e7	0.891416	0.445708	+	0.895178i	$0.352952\pi$
$758$	−1.34313e7	−0.849070
$759$	−1.13710e7	−0.716461
$760$	8.07669e7	5.07224
$761$	−7.51836e6	−0.470610	−0.235305	−	0.971922i	$-0.575609\pi$
$761$	−7.51836e6	−0.470610	−0.235305	+	0.971922i	$0.575609\pi$
$762$	−1.52142e7	−0.949212
$763$	−9.12621e6	−0.567517
$764$	−6.35347e7	−3.93802
$765$	−1.45230e7	−0.897226
$766$	−2.25863e7	−1.39083
$767$	3.64712e6	0.223853
$768$	−2.30040e7	−1.40734
$769$	1.72875e7	1.05418	0.527091	−	0.849809i	$-0.323283\pi$
$769$	1.72875e7	1.05418	0.527091	+	0.849809i	$0.323283\pi$
$770$	−2.50796e7	−1.52438
$771$	−4.51770e6	−0.273704
$772$	5.95213e7	3.59442
$773$	7.13686e6	0.429594	0.214797	−	0.976659i	$-0.431091\pi$
$773$	7.13686e6	0.429594	0.214797	+	0.976659i	$0.431091\pi$
$774$	1.08573e7	0.651434
$775$	−1.68227e7	−1.00610
$776$	−2.90320e7	−1.73070
$777$	8.35342e6	0.496377
$778$	4.43369e7	2.62613
$779$	1.27051e6	0.0750125
$780$	7.21804e7	4.24798
$781$	1.43052e6	0.0839203
$782$	6.62602e7	3.87468
$783$	−84183.1	−0.00490705
$784$	−4.86536e7	−2.82699
$785$	1.95636e7	1.13312
$786$	−3.63726e7	−2.09999
$787$	−5.86391e6	−0.337482	−0.168741	−	0.985660i	$-0.553970\pi$
$787$	−5.86391e6	−0.337482	−0.168741	+	0.985660i	$0.553970\pi$
$788$	−6.28742e7	−3.60709
$789$	−1.14212e7	−0.653159
$790$	−1.96236e7	−1.11869
$791$	−5.16294e6	−0.293397
$792$	−2.04999e7	−1.16128
$793$	−1.72024e7	−0.971419
$794$	5.05734e7	2.84689
$795$	−2.73027e7	−1.53210
$796$	−1.62344e7	−0.908144
$797$	1.96169e7	1.09392	0.546958	−	0.837160i	$-0.315786\pi$
$797$	1.96169e7	1.09392	0.546958	+	0.837160i	$0.315786\pi$
$798$	−9.27765e6	−0.515740
$799$	3.27702e7	1.81599
$800$	−1.00503e8	−5.55209
$801$	−5.64571e6	−0.310912
$802$	−2.86957e7	−1.57536
$803$	1.14268e7	0.625369
$804$	−7.67645e6	−0.418813
$805$	1.62405e7	0.883302
$806$	−4.14237e7	−2.24601
$807$	9.36877e6	0.506406
$808$	−6.40914e7	−3.45360
$809$	−2.49811e7	−1.34196	−0.670982	−	0.741474i	$-0.734127\pi$
$809$	−2.49811e7	−1.34196	−0.670982	+	0.741474i	$0.734127\pi$
$810$	−6.30315e6	−0.337555
$811$	−1.44411e7	−0.770987	−0.385493	−	0.922711i	$-0.625969\pi$
$811$	−1.44411e7	−0.770987	−0.385493	+	0.922711i	$0.625969\pi$
$812$	619080.	0.0329501
$813$	1.86315e7	0.988603
$814$	6.93689e7	3.66947
$815$	−147552.	−0.00778130
$816$	6.85460e7	3.60377
$817$	1.88359e7	0.987257
$818$	−3.32512e7	−1.73749
$819$	−5.23718e6	−0.272827
$820$	−6.34774e6	−0.329674
$821$	−625911.	−0.0324082	−0.0162041	−	0.999869i	$-0.505158\pi$
$821$	−625911.	−0.0324082	−0.0162041	+	0.999869i	$0.505158\pi$
$822$	1.90421e7	0.982961
$823$	2.15073e7	1.10684	0.553422	−	0.832901i	$-0.313322\pi$
$823$	2.15073e7	1.10684	0.553422	+	0.832901i	$0.313322\pi$
$824$	5.59526e7	2.87079
$825$	−1.76622e7	−0.903464
$826$	2.34213e6	0.119443
$827$	2.06626e7	1.05056	0.525280	−	0.850929i	$-0.323960\pi$
$827$	2.06626e7	1.05056	0.525280	+	0.850929i	$0.323960\pi$
$828$	2.10163e7	1.06532
$829$	−5.93386e6	−0.299882	−0.149941	−	0.988695i	$-0.547908\pi$
$829$	−5.93386e6	−0.299882	−0.149941	+	0.988695i	$0.547908\pi$
$830$	5.23690e7	2.63863
$831$	−1.73834e7	−0.873238
$832$	−1.21985e8	−6.10941
$833$	2.64499e7	1.32072
$834$	−7.89905e6	−0.393242
$835$	−5.58495e7	−2.77206
$836$	−5.63041e7	−2.78628
$837$	2.64355e6	0.130429
$838$	−1.46274e7	−0.719544
$839$	−925271.	−0.0453800	−0.0226900	−	0.999743i	$-0.507223\pi$
$839$	−925271.	−0.0453800	−0.0226900	+	0.999743i	$0.507223\pi$
$840$	2.92788e7	1.43171
$841$	−2.04978e7	−0.999350
$842$	−2.76954e7	−1.34626
$843$	−7.73736e6	−0.374994
$844$	−1.24843e7	−0.603265
$845$	6.40089e7	3.08389
$846$	1.42227e7	0.683212
$847$	1.10466e6	0.0529080
$848$	1.28864e8	6.15379
$849$	7.10485e6	0.338287
$850$	1.02920e8	4.88601
$851$	−4.49203e7	−2.12627
$852$	−2.64395e6	−0.124783
$853$	1.48698e7	0.699732	0.349866	−	0.936800i	$-0.386227\pi$
$853$	1.48698e7	0.699732	0.349866	+	0.936800i	$0.386227\pi$
$854$	−1.10471e7	−0.518329
$855$	−1.09350e7	−0.511569
$856$	−3.09879e7	−1.44547
$857$	−4.11203e7	−1.91251	−0.956256	−	0.292531i	$-0.905503\pi$
$857$	−4.11203e7	−1.91251	−0.956256	+	0.292531i	$0.905503\pi$
$858$	−4.34909e7	−2.01688
$859$	1.38706e7	0.641378	0.320689	−	0.947185i	$-0.396086\pi$
$859$	1.38706e7	0.641378	0.320689	+	0.947185i	$0.396086\pi$
$860$	−9.41081e7	−4.33891
$861$	460571.	0.0211733
$862$	−4.55557e7	−2.08821
$863$	1.87918e7	0.858898	0.429449	−	0.903091i	$-0.358708\pi$
$863$	1.87918e7	0.858898	0.429449	+	0.903091i	$0.358708\pi$
$864$	1.57933e7	0.719761
$865$	2.68535e7	1.22028
$866$	813143.	0.0368445
$867$	−2.44854e7	−1.10627
$868$	−1.94406e7	−0.875812
$869$	8.64088e6	0.388158
$870$	998452.	0.0447228
$871$	−1.02868e7	−0.459447
$872$	8.84756e7	3.94033
$873$	3.93064e6	0.174553
$874$	4.98904e7	2.20922
$875$	8.23327e6	0.363540
$876$	−2.11195e7	−0.929873
$877$	4.12113e7	1.80933	0.904665	−	0.426124i	$-0.140121\pi$
$877$	4.12113e7	1.80933	0.904665	+	0.426124i	$0.140121\pi$
$878$	−7.76505e7	−3.39944
$879$	1.65359e7	0.721863
$880$	1.39518e8	6.07326
$881$	3.73000e7	1.61908	0.809542	−	0.587062i	$-0.199716\pi$
$881$	3.73000e7	1.61908	0.809542	+	0.587062i	$0.199716\pi$
$882$	1.14796e7	0.496884
$883$	−3.73701e7	−1.61295	−0.806477	−	0.591265i	$-0.798629\pi$
$883$	−3.73701e7	−1.61295	−0.806477	+	0.591265i	$0.798629\pi$
$884$	1.85206e8	7.97121
$885$	2.76053e6	0.118477
$886$	8.02716e7	3.43540
$887$	−2.39606e6	−0.102256	−0.0511280	−	0.998692i	$-0.516282\pi$
$887$	−2.39606e6	−0.102256	−0.0511280	+	0.998692i	$0.516282\pi$
$888$	−8.09836e7	−3.44639
$889$	−9.56824e6	−0.406048
$890$	6.69609e7	2.83365
$891$	2.77548e6	0.117123
$892$	2.59758e7	1.09309
$893$	2.46742e7	1.03542
$894$	2.25662e7	0.944309
$895$	5.91531e6	0.246843
$896$	−3.55552e7	−1.47956
$897$	2.81628e7	1.16868
$898$	6.11092e7	2.52881
$899$	−418753.	−0.0172806
$900$	3.26441e7	1.34338
$901$	−7.00554e7	−2.87494
$902$	3.82470e6	0.156524
$903$	6.82818e6	0.278667
$904$	5.00530e7	2.03709
$905$	9.84950e6	0.399754
$906$	−1.01542e7	−0.410983
$907$	−6.32877e6	−0.255447	−0.127724	−	0.991810i	$-0.540767\pi$
$907$	−6.32877e6	−0.255447	−0.127724	+	0.991810i	$0.540767\pi$
$908$	9.21640e6	0.370977
$909$	8.67733e6	0.348318
$910$	6.21155e7	2.48654
$911$	−1.22155e6	−0.0487659	−0.0243830	−	0.999703i	$-0.507762\pi$
$911$	−1.22155e6	−0.0487659	−0.0243830	+	0.999703i	$0.507762\pi$
$912$	5.16115e7	2.05475
$913$	−2.30597e7	−0.915540
$914$	2.48569e7	0.984197
$915$	−1.30206e7	−0.514137
$916$	−1.93526e7	−0.762080
$917$	−2.28747e7	−0.898323
$918$	−1.61731e7	−0.633412
$919$	−2.44744e7	−0.955924	−0.477962	−	0.878381i	$-0.658624\pi$
$919$	−2.44744e7	−0.955924	−0.477962	+	0.878381i	$0.658624\pi$
$920$	−1.57446e8	−6.13285
$921$	3.99375e6	0.155143
$922$	−6.21873e7	−2.40921
$923$	−3.54302e6	−0.136889
$924$	−2.04108e7	−0.786466
$925$	−6.97737e7	−2.68125
$926$	−3.44184e7	−1.31905
$927$	−7.57541e6	−0.289539
$928$	−2.50174e6	−0.0953614
$929$	471008.	0.0179056	0.00895280	−	0.999960i	$-0.497150\pi$
$929$	471008.	0.0179056	0.00895280	+	0.999960i	$0.497150\pi$
$930$	−3.13538e7	−1.18873
$931$	1.99154e7	0.753034
$932$	−7.62374e7	−2.87494
$933$	5.86513e6	0.220584
$934$	−4.47746e7	−1.67944
$935$	−7.58470e7	−2.83733
$936$	5.07727e7	1.89426
$937$	9.92896e6	0.369449	0.184725	−	0.982790i	$-0.440861\pi$
$937$	9.92896e6	0.369449	0.184725	+	0.982790i	$0.440861\pi$
$938$	−6.60604e6	−0.245151
$939$	1.15256e7	0.426581
$940$	−1.23278e8	−4.55057
$941$	−2.51107e7	−0.924452	−0.462226	−	0.886762i	$-0.652949\pi$
$941$	−2.51107e7	−0.924452	−0.462226	+	0.886762i	$0.652949\pi$
$942$	2.17865e7	0.799943
$943$	−2.47671e6	−0.0906978
$944$	−1.30292e7	−0.475871
$945$	−3.96405e6	−0.144398
$946$	5.67029e7	2.06005
$947$	1.98803e7	0.720356	0.360178	−	0.932884i	$-0.382716\pi$
$947$	1.98803e7	0.720356	0.360178	+	0.932884i	$0.382716\pi$
$948$	−1.59704e7	−0.577160
$949$	−2.83011e7	−1.02009
$950$	7.74936e7	2.78584
$951$	−1.66748e7	−0.597872
$952$	7.51257e7	2.68656
$953$	3.07521e7	1.09684	0.548418	−	0.836204i	$-0.315230\pi$
$953$	3.07521e7	1.09684	0.548418	+	0.836204i	$0.315230\pi$
$954$	−3.04049e7	−1.08161
$955$	−6.44427e7	−2.28647
$956$	1.35003e8	4.77747
$957$	−439650.	−0.0155177
$958$	4.31905e7	1.52046
$959$	1.19756e7	0.420486
$960$	−9.23315e7	−3.23349
$961$	−1.54793e7	−0.540682
$962$	−1.71808e8	−5.98558
$963$	4.19546e6	0.145785
$964$	−5.72462e6	−0.198406
$965$	6.03719e7	2.08697
$966$	1.80857e7	0.623582
$967$	3.47128e7	1.19378	0.596888	−	0.802324i	$-0.296404\pi$
$967$	3.47128e7	1.19378	0.596888	+	0.802324i	$0.296404\pi$
$968$	−1.07093e7	−0.367345
$969$	−2.80579e7	−0.959944
$970$	−4.66193e7	−1.59088
$971$	6.63760e6	0.225924	0.112962	−	0.993599i	$-0.463966\pi$
$971$	6.63760e6	0.225924	0.112962	+	0.993599i	$0.463966\pi$
$972$	−5.12975e6	−0.174153
$973$	−4.96771e6	−0.168219
$974$	1.00158e8	3.38288
$975$	4.37446e7	1.47371
$976$	6.14551e7	2.06506
$977$	2.24812e7	0.753500	0.376750	−	0.926315i	$-0.377042\pi$
$977$	2.24812e7	0.753500	0.376750	+	0.926315i	$0.377042\pi$
$978$	−164318.	−0.00549334
$979$	−2.94850e7	−0.983207
$980$	−9.95016e7	−3.30952
$981$	−1.19787e7	−0.397409
$982$	−4.20818e7	−1.39256
$983$	−4.47702e7	−1.47776	−0.738882	−	0.673835i	$-0.764646\pi$
$983$	−4.47702e7	−1.47776	−0.738882	+	0.673835i	$0.764646\pi$
$984$	−4.46509e6	−0.147008
$985$	−6.37727e7	−2.09432
$986$	2.56190e6	0.0839210
$987$	8.94464e6	0.292260
$988$	1.39450e8	4.54493
$989$	−3.67184e7	−1.19369
$990$	−3.29185e7	−1.06746
$991$	−173229.	−0.00560320	−0.00280160	−	0.999996i	$-0.500892\pi$
$991$	−173229.	−0.00560320	−0.00280160	+	0.999996i	$0.500892\pi$
$992$	7.85608e7	2.53470
$993$	5.82224e6	0.187377
$994$	−2.27528e6	−0.0730412
$995$	−1.64664e7	−0.527281
$996$	4.26200e7	1.36133
$997$	1.72883e7	0.550825	0.275413	−	0.961326i	$-0.411186\pi$
$997$	1.72883e7	0.550825	0.275413	+	0.961326i	$0.411186\pi$
$998$	3.75903e7	1.19467
$999$	1.09644e7	0.347592

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.1	✓	12
3.2	odd	2		531.6.a.d.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.1	✓	12	1.1	even	1	trivial
531.6.a.d.1.12		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)

\(f(q)\)	\(=\)	\(q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} -960.699 q^{10} +423.027 q^{11} -781.856 q^{12} -1047.72 q^{13} -672.832 q^{14} -793.028 q^{15} +3742.96 q^{16} -2034.81 q^{17} -883.133 q^{18} -1532.11 q^{19} +7654.74 q^{20} -555.403 q^{21} -4612.21 q^{22} +2986.67 q^{23} +5384.45 q^{24} +4639.12 q^{25} +11423.2 q^{26} -729.000 q^{27} +5361.05 q^{28} +115.477 q^{29} +8646.29 q^{30} -3626.28 q^{31} -21664.3 q^{32} -3807.24 q^{33} +22185.3 q^{34} +5437.66 q^{35} +7036.70 q^{36} -15040.3 q^{37} +16704.4 q^{38} +9429.51 q^{39} -52716.3 q^{40} -829.256 q^{41} +6055.49 q^{42} -12294.1 q^{43} +36749.5 q^{44} +7137.25 q^{45} -32563.3 q^{46} -16104.8 q^{47} -33686.6 q^{48} -12998.7 q^{49} -50579.8 q^{50} +18313.3 q^{51} -91018.7 q^{52} +34428.4 q^{53} +7948.20 q^{54} +37274.7 q^{55} -36920.2 q^{56} +13788.9 q^{57} -1259.04 q^{58} -3481.00 q^{59} -68892.6 q^{60} +16418.9 q^{61} +39536.9 q^{62} +4998.63 q^{63} +116429. q^{64} -92319.3 q^{65} +41509.9 q^{66} +9818.25 q^{67} -176770. q^{68} -26880.0 q^{69} -59286.1 q^{70} +3381.64 q^{71} -48460.0 q^{72} +27012.0 q^{73} +163982. q^{74} -41752.1 q^{75} -133098. q^{76} +26105.6 q^{77} -102809. q^{78} +20426.3 q^{79} +329808. q^{80} +6561.00 q^{81} +9041.29 q^{82} -54511.3 q^{83} -48249.4 q^{84} -179296. q^{85} +134041. q^{86} -1039.30 q^{87} -253085. q^{88} -69700.2 q^{89} -77816.6 q^{90} -64656.5 q^{91} +259460. q^{92} +32636.5 q^{93} +175589. q^{94} -135000. q^{95} +194979. q^{96} +48526.4 q^{97} +141723. q^{98} +34265.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 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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