LMFDB - Embedded newform 177.6.a.a.1.4

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 $ x^11 - 5x^10 - 238x^9 + 1067x^8 + 20782x^7 - 79077x^6 - 813818x^5 + 2364885x^4 + 13849341x^3 - 23890558x^2 - 74443300x - 14846072
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-5.62527$ 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)

$f(q)$	$=$	$q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +564.490 q^{10} +579.703 q^{11} +107.048 q^{12} +435.487 q^{13} +682.469 q^{14} -766.822 q^{15} -1263.14 q^{16} +424.138 q^{17} -536.647 q^{18} +1540.54 q^{19} -1013.42 q^{20} -927.089 q^{21} -3840.69 q^{22} -4164.00 q^{23} +1198.86 q^{24} +4134.46 q^{25} -2885.22 q^{26} +729.000 q^{27} -1225.22 q^{28} -8418.14 q^{29} +5080.41 q^{30} +7073.40 q^{31} +4106.07 q^{32} +5217.32 q^{33} -2810.03 q^{34} +8776.70 q^{35} +963.434 q^{36} +12420.5 q^{37} -10206.5 q^{38} +3919.38 q^{39} -11349.5 q^{40} -2421.33 q^{41} +6142.22 q^{42} -11711.3 q^{43} +6895.12 q^{44} -6901.40 q^{45} +27587.6 q^{46} -9436.30 q^{47} -11368.3 q^{48} -6195.96 q^{49} -27391.9 q^{50} +3817.24 q^{51} +5179.79 q^{52} -23764.2 q^{53} -4829.82 q^{54} -49392.1 q^{55} -13721.5 q^{56} +13864.8 q^{57} +55772.5 q^{58} +3481.00 q^{59} -9120.77 q^{60} +5566.88 q^{61} -46863.2 q^{62} -8343.80 q^{63} +13216.7 q^{64} -37104.6 q^{65} -34566.2 q^{66} -57888.7 q^{67} +5044.80 q^{68} -37476.0 q^{69} -58148.0 q^{70} -11960.0 q^{71} +10789.7 q^{72} +25056.7 q^{73} -82289.1 q^{74} +37210.2 q^{75} +18323.5 q^{76} -59715.1 q^{77} -25967.0 q^{78} +17801.5 q^{79} +107623. q^{80} +6561.00 q^{81} +16042.0 q^{82} -2768.37 q^{83} -11027.0 q^{84} -36137.6 q^{85} +77590.7 q^{86} -75763.3 q^{87} +77219.9 q^{88} +17994.8 q^{89} +45723.7 q^{90} -44859.5 q^{91} -49527.6 q^{92} +63660.6 q^{93} +62518.1 q^{94} -131257. q^{95} +36954.6 q^{96} -166125. q^{97} +41049.9 q^{98} +46955.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * 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 $

$2$	−6.62527	−1.17119	−0.585597	−	0.810602i	$-0.699140\pi$
$2$	−6.62527	−1.17119	−0.585597	+	0.810602i	$0.699140\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	11.8942	0.371695
$5$	−85.2025	−1.52415	−0.762074	−	0.647490i	$-0.775819\pi$
$5$	−85.2025	−1.52415	−0.762074	+	0.647490i	$0.775819\pi$
$6$	−59.6275	−0.676189
$7$	−103.010	−0.794573	−0.397287	−	0.917695i	$-0.630048\pi$
$7$	−103.010	−0.794573	−0.397287	+	0.917695i	$0.630048\pi$
$8$	133.206	0.735867
$9$	81.0000	0.333333
$10$	564.490	1.78507
$11$	579.703	1.44452	0.722260	−	0.691622i	$-0.243103\pi$
$11$	579.703	1.44452	0.722260	+	0.691622i	$0.243103\pi$
$12$	107.048	0.214598
$13$	435.487	0.714689	0.357344	−	0.933973i	$-0.383682\pi$
$13$	435.487	0.714689	0.357344	+	0.933973i	$0.383682\pi$
$14$	682.469	0.930599
$15$	−766.822	−0.879967
$16$	−1263.14	−1.23354
$17$	424.138	0.355946	0.177973	−	0.984035i	$-0.443046\pi$
$17$	424.138	0.355946	0.177973	+	0.984035i	$0.443046\pi$
$18$	−536.647	−0.390398
$19$	1540.54	0.979012	0.489506	−	0.872000i	$-0.337177\pi$
$19$	1540.54	0.979012	0.489506	+	0.872000i	$0.337177\pi$
$20$	−1013.42	−0.566518
$21$	−927.089	−0.458747
$22$	−3840.69	−1.69181
$23$	−4164.00	−1.64131	−0.820656	−	0.571423i	$-0.806391\pi$
$23$	−4164.00	−1.64131	−0.820656	+	0.571423i	$0.806391\pi$
$24$	1198.86	0.424853
$25$	4134.46	1.32303
$26$	−2885.22	−0.837039
$27$	729.000	0.192450
$28$	−1225.22	−0.295339
$29$	−8418.14	−1.85875	−0.929376	−	0.369135i	$-0.879654\pi$
$29$	−8418.14	−1.85875	−0.929376	+	0.369135i	$0.879654\pi$
$30$	5080.41	1.03061
$31$	7073.40	1.32198	0.660989	−	0.750396i	$-0.270137\pi$
$31$	7073.40	1.32198	0.660989	+	0.750396i	$0.270137\pi$
$32$	4106.07	0.708845
$33$	5217.32	0.833994
$34$	−2810.03	−0.416882
$35$	8776.70	1.21105
$36$	963.434	0.123898
$37$	12420.5	1.49154	0.745769	−	0.666205i	$-0.232082\pi$
$37$	12420.5	1.49154	0.745769	+	0.666205i	$0.232082\pi$
$38$	−10206.5	−1.14661
$39$	3919.38	0.412626
$40$	−11349.5	−1.12157
$41$	−2421.33	−0.224954	−0.112477	−	0.993654i	$-0.535878\pi$
$41$	−2421.33	−0.224954	−0.112477	+	0.993654i	$0.535878\pi$
$42$	6142.22	0.537282
$43$	−11711.3	−0.965905	−0.482953	−	0.875646i	$-0.660436\pi$
$43$	−11711.3	−0.965905	−0.482953	+	0.875646i	$0.660436\pi$
$44$	6895.12	0.536921
$45$	−6901.40	−0.508049
$46$	27587.6	1.92229
$47$	−9436.30	−0.623099	−0.311550	−	0.950230i	$-0.600848\pi$
$47$	−9436.30	−0.623099	−0.311550	+	0.950230i	$0.600848\pi$
$48$	−11368.3	−0.712183
$49$	−6195.96	−0.368654
$50$	−27391.9	−1.54952
$51$	3817.24	0.205506
$52$	5179.79	0.265646
$53$	−23764.2	−1.16207	−0.581037	−	0.813877i	$-0.697353\pi$
$53$	−23764.2	−1.16207	−0.581037	+	0.813877i	$0.697353\pi$
$54$	−4829.82	−0.225396
$55$	−49392.1	−2.20166
$56$	−13721.5	−0.584700
$57$	13864.8	0.565233
$58$	55772.5	2.17696
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−9120.77	−0.327080
$61$	5566.88	0.191552	0.0957761	−	0.995403i	$-0.469467\pi$
$61$	5566.88	0.191552	0.0957761	+	0.995403i	$0.469467\pi$
$62$	−46863.2	−1.54829
$63$	−8343.80	−0.264858
$64$	13216.7	0.403343
$65$	−37104.6	−1.08929
$66$	−34566.2	−0.976769
$67$	−57888.7	−1.57546	−0.787729	−	0.616022i	$-0.788743\pi$
$67$	−57888.7	−1.57546	−0.787729	+	0.616022i	$0.788743\pi$
$68$	5044.80	0.132304
$69$	−37476.0	−0.947611
$70$	−58148.0	−1.41837
$71$	−11960.0	−0.281569	−0.140784	−	0.990040i	$-0.544962\pi$
$71$	−11960.0	−0.281569	−0.140784	+	0.990040i	$0.544962\pi$
$72$	10789.7	0.245289
$73$	25056.7	0.550322	0.275161	−	0.961398i	$-0.411269\pi$
$73$	25056.7	0.550322	0.275161	+	0.961398i	$0.411269\pi$
$74$	−82289.1	−1.74688
$75$	37210.2	0.763850
$76$	18323.5	0.363894
$77$	−59715.1	−1.14778
$78$	−25967.0	−0.483265
$79$	17801.5	0.320914	0.160457	−	0.987043i	$-0.448703\pi$
$79$	17801.5	0.320914	0.160457	+	0.987043i	$0.448703\pi$
$80$	107623.	1.88009
$81$	6561.00	0.111111
$82$	16042.0	0.263465
$83$	−2768.37	−0.0441092	−0.0220546	−	0.999757i	$-0.507021\pi$
$83$	−2768.37	−0.0441092	−0.0220546	+	0.999757i	$0.507021\pi$
$84$	−11027.0	−0.170514
$85$	−36137.6	−0.542515
$86$	77590.7	1.13126
$87$	−75763.3	−1.07315
$88$	77219.9	1.06297
$89$	17994.8	0.240809	0.120404	−	0.992725i	$-0.461581\pi$
$89$	17994.8	0.240809	0.120404	+	0.992725i	$0.461581\pi$
$90$	45723.7	0.595024
$91$	−44859.5	−0.567872
$92$	−49527.6	−0.610067
$93$	63660.6	0.763244
$94$	62518.1	0.729770
$95$	−131257.	−1.49216
$96$	36954.6	0.409252
$97$	−166125.	−1.79269	−0.896346	−	0.443355i	$-0.853788\pi$
$97$	−166125.	−1.79269	−0.896346	+	0.443355i	$0.853788\pi$
$98$	41049.9	0.431765
$99$	46955.9	0.481507
$100$	49176.3	0.491763
$101$	−38127.7	−0.371909	−0.185954	−	0.982558i	$-0.559538\pi$
$101$	−38127.7	−0.371909	−0.185954	+	0.982558i	$0.559538\pi$
$102$	−25290.2	−0.240687
$103$	81615.4	0.758018	0.379009	−	0.925393i	$-0.376265\pi$
$103$	81615.4	0.758018	0.379009	+	0.925393i	$0.376265\pi$
$104$	58009.5	0.525916
$105$	78990.3	0.699198
$106$	157444.	1.36101
$107$	121265.	1.02395	0.511973	−	0.859002i	$-0.328915\pi$
$107$	121265.	1.02395	0.511973	+	0.859002i	$0.328915\pi$
$108$	8670.90	0.0715328
$109$	−153096.	−1.23424	−0.617118	−	0.786870i	$-0.711700\pi$
$109$	−153096.	−1.23424	−0.617118	+	0.786870i	$0.711700\pi$
$110$	327236.	2.57857
$111$	111784.	0.861140
$112$	130116.	0.980136
$113$	−54428.5	−0.400987	−0.200494	−	0.979695i	$-0.564255\pi$
$113$	−54428.5	−0.400987	−0.200494	+	0.979695i	$0.564255\pi$
$114$	−91858.3	−0.661997
$115$	354783.	2.50160
$116$	−100127.	−0.690889
$117$	35274.4	0.238230
$118$	−23062.6	−0.152476
$119$	−43690.4	−0.282825
$120$	−102145.	−0.647539
$121$	175004.	1.08664
$122$	−36882.1	−0.224345
$123$	−21791.9	−0.129877
$124$	84132.8	0.491373
$125$	−86008.6	−0.492342
$126$	55280.0	0.310200
$127$	−203111.	−1.11744	−0.558721	−	0.829356i	$-0.688708\pi$
$127$	−203111.	−1.11744	−0.558721	+	0.829356i	$0.688708\pi$
$128$	−218959.	−1.18124
$129$	−105402.	−0.557666
$130$	245828.	1.27577
$131$	−282282.	−1.43716	−0.718579	−	0.695445i	$-0.755207\pi$
$131$	−282282.	−1.43716	−0.718579	+	0.695445i	$0.755207\pi$
$132$	62056.1	0.309992
$133$	−158690.	−0.777896
$134$	383529.	1.84517
$135$	−62112.6	−0.293322
$136$	56497.7	0.261929
$137$	−290437.	−1.32206	−0.661029	−	0.750360i	$-0.729880\pi$
$137$	−290437.	−1.32206	−0.661029	+	0.750360i	$0.729880\pi$
$138$	248289.	1.10984
$139$	429789.	1.88677	0.943383	−	0.331705i	$-0.107624\pi$
$139$	429789.	1.88677	0.943383	+	0.331705i	$0.107624\pi$
$140$	104392.	0.450140
$141$	−84926.7	−0.359746
$142$	79238.2	0.329772
$143$	252453.	1.03238
$144$	−102315.	−0.411179
$145$	717247.	2.83301
$146$	−166008.	−0.644534
$147$	−55763.7	−0.212842
$148$	147732.	0.554397
$149$	−383936.	−1.41675	−0.708376	−	0.705835i	$-0.750572\pi$
$149$	−383936.	−1.41675	−0.708376	+	0.705835i	$0.750572\pi$
$150$	−246527.	−0.894617
$151$	−91551.4	−0.326755	−0.163378	−	0.986564i	$-0.552239\pi$
$151$	−91551.4	−0.326755	−0.163378	+	0.986564i	$0.552239\pi$
$152$	205209.	0.720422
$153$	34355.1	0.118649
$154$	395629.	1.34427
$155$	−602671.	−2.01489
$156$	46618.1	0.153371
$157$	−18734.2	−0.0606578	−0.0303289	−	0.999540i	$-0.509655\pi$
$157$	−18734.2	−0.0606578	−0.0303289	+	0.999540i	$0.509655\pi$
$158$	−117940.	−0.375852
$159$	−213878.	−0.670923
$160$	−349847.	−1.08039
$161$	428933.	1.30414
$162$	−43468.4	−0.130133
$163$	85172.5	0.251091	0.125545	−	0.992088i	$-0.459932\pi$
$163$	85172.5	0.251091	0.125545	+	0.992088i	$0.459932\pi$
$164$	−28799.9	−0.0836143
$165$	−444529.	−1.27113
$166$	18341.2	0.0516604
$167$	541622.	1.50281	0.751407	−	0.659839i	$-0.229375\pi$
$167$	541622.	1.50281	0.751407	+	0.659839i	$0.229375\pi$
$168$	−123494.	−0.337577
$169$	−181644.	−0.489220
$170$	239421.	0.635390
$171$	124783.	0.326337
$172$	−139297.	−0.359022
$173$	238752.	0.606502	0.303251	−	0.952911i	$-0.401928\pi$
$173$	238752.	0.606502	0.303251	+	0.952911i	$0.401928\pi$
$174$	501953.	1.25687
$175$	−425890.	−1.05124
$176$	−732247.	−1.78187
$177$	31329.0	0.0751646
$178$	−119221.	−0.282034
$179$	284533.	0.663744	0.331872	−	0.943324i	$-0.392320\pi$
$179$	284533.	0.663744	0.331872	+	0.943324i	$0.392320\pi$
$180$	−82086.9	−0.188839
$181$	−402281.	−0.912711	−0.456355	−	0.889798i	$-0.650845\pi$
$181$	−402281.	−0.912711	−0.456355	+	0.889798i	$0.650845\pi$
$182$	297206.	0.665089
$183$	50101.9	0.110593
$184$	−554670.	−1.20779
$185$	−1.05826e6	−2.27332
$186$	−421769.	−0.893907
$187$	245874.	0.514172
$188$	−112238.	−0.231603
$189$	−75094.2	−0.152916
$190$	869617.	1.74761
$191$	−624305.	−1.23826	−0.619132	−	0.785287i	$-0.712515\pi$
$191$	−624305.	−1.23826	−0.619132	+	0.785287i	$0.712515\pi$
$192$	118951.	0.232870
$193$	835697.	1.61494	0.807469	−	0.589910i	$-0.200837\pi$
$193$	835697.	1.61494	0.807469	+	0.589910i	$0.200837\pi$
$194$	1.10062e6	2.09959
$195$	−333941.	−0.628903
$196$	−73696.3	−0.137027
$197$	−724552.	−1.33016	−0.665080	−	0.746772i	$-0.731603\pi$
$197$	−724552.	−1.33016	−0.665080	+	0.746772i	$0.731603\pi$
$198$	−311096.	−0.563938
$199$	−691882.	−1.23851	−0.619255	−	0.785190i	$-0.712565\pi$
$199$	−691882.	−1.23851	−0.619255	+	0.785190i	$0.712565\pi$
$200$	550736.	0.973572
$201$	−520999.	−0.909591
$202$	252606.	0.435577
$203$	867152.	1.47691
$204$	45403.2	0.0763855
$205$	206303.	0.342863
$206$	−540725.	−0.887786
$207$	−337284.	−0.547104
$208$	−550082.	−0.881595
$209$	893053.	1.41420
$210$	−523332.	−0.818897
$211$	249343.	0.385559	0.192779	−	0.981242i	$-0.438250\pi$
$211$	249343.	0.385559	0.192779	+	0.981242i	$0.438250\pi$
$212$	−282657.	−0.431937
$213$	−107640.	−0.162564
$214$	−803416.	−1.19924
$215$	997833.	1.47218
$216$	97107.3	0.141618
$217$	−728630.	−1.05041
$218$	1.01430e6	1.44553
$219$	225510.	0.317729
$220$	−587482.	−0.818347
$221$	184706.	0.254391
$222$	−740602.	−1.00856
$223$	−542135.	−0.730038	−0.365019	−	0.931000i	$-0.618938\pi$
$223$	−542135.	−0.730038	−0.365019	+	0.931000i	$0.618938\pi$
$224$	−422966.	−0.563229
$225$	334891.	0.441009
$226$	360604.	0.469634
$227$	−480667.	−0.619127	−0.309563	−	0.950879i	$-0.600183\pi$
$227$	−480667.	−0.619127	−0.309563	+	0.950879i	$0.600183\pi$
$228$	164912.	0.210094
$229$	−623840.	−0.786112	−0.393056	−	0.919514i	$-0.628582\pi$
$229$	−623840.	−0.786112	−0.393056	+	0.919514i	$0.628582\pi$
$230$	−2.35053e6	−2.92986
$231$	−537436.	−0.662669
$232$	−1.12135e6	−1.36779
$233$	645676.	0.779157	0.389579	−	0.920993i	$-0.372621\pi$
$233$	645676.	0.779157	0.389579	+	0.920993i	$0.372621\pi$
$234$	−233703.	−0.279013
$235$	803996.	0.949695
$236$	41403.9	0.0483906
$237$	160213.	0.185280
$238$	289461.	0.331243
$239$	1.10502e6	1.25134	0.625669	−	0.780089i	$-0.284826\pi$
$239$	1.10502e6	1.25134	0.625669	+	0.780089i	$0.284826\pi$
$240$	968606.	1.08547
$241$	1.44502e6	1.60262	0.801309	−	0.598250i	$-0.204137\pi$
$241$	1.44502e6	1.60262	0.801309	+	0.598250i	$0.204137\pi$
$242$	−1.15945e6	−1.27266
$243$	59049.0	0.0641500
$244$	66213.8	0.0711990
$245$	527911.	0.561883
$246$	144378.	0.152112
$247$	670883.	0.699688
$248$	942220.	0.972799
$249$	−24915.3	−0.0254664
$250$	569830.	0.576628
$251$	528809.	0.529803	0.264902	−	0.964275i	$-0.414660\pi$
$251$	528809.	0.529803	0.264902	+	0.964275i	$0.414660\pi$
$252$	−99243.2	−0.0984463
$253$	−2.41388e6	−2.37091
$254$	1.34567e6	1.30874
$255$	−325238.	−0.313221
$256$	1.02773e6	0.980116
$257$	−1.15172e6	−1.08771	−0.543856	−	0.839179i	$-0.683036\pi$
$257$	−1.15172e6	−1.08771	−0.543856	+	0.839179i	$0.683036\pi$
$258$	698316.	0.653135
$259$	−1.27943e6	−1.18514
$260$	−441331.	−0.404884
$261$	−681870.	−0.619584
$262$	1.87019e6	1.68319
$263$	452277.	0.403195	0.201598	−	0.979468i	$-0.435387\pi$
$263$	452277.	0.403195	0.201598	+	0.979468i	$0.435387\pi$
$264$	694979.	0.613709
$265$	2.02477e6	1.77117
$266$	1.05137e6	0.911067
$267$	161953.	0.139031
$268$	−688543.	−0.585590
$269$	−1.71384e6	−1.44407	−0.722036	−	0.691856i	$-0.756793\pi$
$269$	−1.71384e6	−1.44407	−0.722036	+	0.691856i	$0.756793\pi$
$270$	411513.	0.343537
$271$	1.32879e6	1.09909	0.549546	−	0.835463i	$-0.314801\pi$
$271$	1.32879e6	1.09909	0.549546	+	0.835463i	$0.314801\pi$
$272$	−535746.	−0.439073
$273$	−403735.	−0.327861
$274$	1.92422e6	1.54839
$275$	2.39676e6	1.91114
$276$	−445748.	−0.352223
$277$	−1.54297e6	−1.20825	−0.604126	−	0.796889i	$-0.706478\pi$
$277$	−1.54297e6	−1.20825	−0.604126	+	0.796889i	$0.706478\pi$
$278$	−2.84747e6	−2.20977
$279$	572946.	0.440659
$280$	1.16911e6	0.891169
$281$	−5515.62	−0.00416705	−0.00208352	−	0.999998i	$-0.500663\pi$
$281$	−5515.62	−0.00416705	−0.00208352	+	0.999998i	$0.500663\pi$
$282$	562663.	0.421333
$283$	−944988.	−0.701391	−0.350696	−	0.936489i	$-0.614055\pi$
$283$	−944988.	−0.701391	−0.350696	+	0.936489i	$0.614055\pi$
$284$	−142255.	−0.104658
$285$	−1.18132e6	−0.861498
$286$	−1.67257e6	−1.20912
$287$	249421.	0.178742
$288$	332592.	0.236282
$289$	−1.23996e6	−0.873302
$290$	−4.75196e6	−3.31801
$291$	−1.49513e6	−1.03501
$292$	298031.	0.204552
$293$	−1.52734e6	−1.03936	−0.519681	−	0.854361i	$-0.673949\pi$
$293$	−1.52734e6	−1.03936	−0.519681	+	0.854361i	$0.673949\pi$
$294$	369449.	0.249280
$295$	−296590.	−0.198427
$296$	1.65448e6	1.09757
$297$	422603.	0.277998
$298$	2.54368e6	1.65929
$299$	−1.81337e6	−1.17303
$300$	442587.	0.283919
$301$	1.20638e6	0.767482
$302$	606553.	0.382694
$303$	−343149.	−0.214722
$304$	−1.94592e6	−1.20765
$305$	−474312.	−0.291954
$306$	−227612.	−0.138961
$307$	−2.82858e6	−1.71286	−0.856431	−	0.516261i	$-0.827323\pi$
$307$	−2.82858e6	−1.71286	−0.856431	+	0.516261i	$0.827323\pi$
$308$	−710266.	−0.426623
$309$	734539.	0.437642
$310$	3.99286e6	2.35983
$311$	490910.	0.287806	0.143903	−	0.989592i	$-0.454035\pi$
$311$	490910.	0.287806	0.143903	+	0.989592i	$0.454035\pi$
$312$	522086.	0.303638
$313$	3.05776e6	1.76418	0.882089	−	0.471083i	$-0.156137\pi$
$313$	3.05776e6	1.76418	0.882089	+	0.471083i	$0.156137\pi$
$314$	124119.	0.0710420
$315$	710912.	0.403682
$316$	211735.	0.119282
$317$	−3.44305e6	−1.92440	−0.962199	−	0.272348i	$-0.912200\pi$
$317$	−3.44305e6	−1.92440	−0.962199	+	0.272348i	$0.912200\pi$
$318$	1.41700e6	0.785781
$319$	−4.88002e6	−2.68500
$320$	−1.12610e6	−0.614754
$321$	1.09139e6	0.591176
$322$	−2.84180e6	−1.52740
$323$	653399.	0.348476
$324$	78038.1	0.0412995
$325$	1.80050e6	0.945553
$326$	−564291.	−0.294076
$327$	−1.37787e6	−0.712587
$328$	−322536.	−0.165536
$329$	972032.	0.495098
$330$	2.94513e6	1.48874
$331$	−2.53352e6	−1.27102	−0.635512	−	0.772091i	$-0.719211\pi$
$331$	−2.53352e6	−1.27102	−0.635512	+	0.772091i	$0.719211\pi$
$332$	−32927.7	−0.0163952
$333$	1.00606e6	0.497179
$334$	−3.58840e6	−1.76009
$335$	4.93226e6	2.40123
$336$	1.17105e6	0.565882
$337$	−2.44618e6	−1.17331	−0.586657	−	0.809835i	$-0.699556\pi$
$337$	−2.44618e6	−1.17331	−0.586657	+	0.809835i	$0.699556\pi$
$338$	1.20344e6	0.572972
$339$	−489857.	−0.231510
$340$	−429829.	−0.201650
$341$	4.10047e6	1.90962
$342$	−826724.	−0.382204
$343$	2.36953e6	1.08750
$344$	−1.56002e6	−0.710778
$345$	3.19305e6	1.44430
$346$	−1.58180e6	−0.710332
$347$	92368.8	0.0411815	0.0205907	−	0.999788i	$-0.493445\pi$
$347$	92368.8	0.0411815	0.0205907	+	0.999788i	$0.493445\pi$
$348$	−901147.	−0.398885
$349$	519444.	0.228284	0.114142	−	0.993464i	$-0.463588\pi$
$349$	519444.	0.228284	0.114142	+	0.993464i	$0.463588\pi$
$350$	2.82164e6	1.23121
$351$	317470.	0.137542
$352$	2.38030e6	1.02394
$353$	−1.65548e6	−0.707109	−0.353555	−	0.935414i	$-0.615027\pi$
$353$	−1.65548e6	−0.707109	−0.353555	+	0.935414i	$0.615027\pi$
$354$	−207563.	−0.0880323
$355$	1.01902e6	0.429153
$356$	214035.	0.0895074
$357$	−393213.	−0.163289
$358$	−1.88511e6	−0.777373
$359$	2.51488e6	1.02987	0.514934	−	0.857230i	$-0.327816\pi$
$359$	2.51488e6	1.02987	0.514934	+	0.857230i	$0.327816\pi$
$360$	−919309.	−0.373857
$361$	−102848.	−0.0415361
$362$	2.66522e6	1.06896
$363$	1.57504e6	0.627371
$364$	−533570.	−0.211075
$365$	−2.13489e6	−0.838773
$366$	−331939.	−0.129525
$367$	−792348.	−0.307080	−0.153540	−	0.988142i	$-0.549067\pi$
$367$	−792348.	−0.307080	−0.153540	+	0.988142i	$0.549067\pi$
$368$	5.25972e6	2.02462
$369$	−196128.	−0.0749847
$370$	7.01124e6	2.66250
$371$	2.44795e6	0.923352
$372$	757195.	0.283694
$373$	846687.	0.315102	0.157551	−	0.987511i	$-0.449640\pi$
$373$	846687.	0.315102	0.157551	+	0.987511i	$0.449640\pi$
$374$	−1.62898e6	−0.602195
$375$	−774077.	−0.284254
$376$	−1.25697e6	−0.458518
$377$	−3.66599e6	−1.32843
$378$	497520.	0.179094
$379$	1.63333e6	0.584085	0.292043	−	0.956405i	$-0.405665\pi$
$379$	1.63333e6	0.584085	0.292043	+	0.956405i	$0.405665\pi$
$380$	−1.56121e6	−0.554628
$381$	−1.82800e6	−0.645155
$382$	4.13619e6	1.45025
$383$	−4.23461e6	−1.47508	−0.737541	−	0.675302i	$-0.764013\pi$
$383$	−4.23461e6	−1.47508	−0.737541	+	0.675302i	$0.764013\pi$
$384$	−1.97063e6	−0.681988
$385$	5.08787e6	1.74938
$386$	−5.53672e6	−1.89141
$387$	−948617.	−0.321968
$388$	−1.97593e6	−0.666335
$389$	4.32595e6	1.44946	0.724732	−	0.689031i	$-0.241963\pi$
$389$	4.32595e6	1.44946	0.724732	+	0.689031i	$0.241963\pi$
$390$	2.21245e6	0.736567
$391$	−1.76611e6	−0.584219
$392$	−825340.	−0.271280
$393$	−2.54054e6	−0.829744
$394$	4.80035e6	1.55787
$395$	−1.51673e6	−0.489120
$396$	558505.	0.178974
$397$	3.34065e6	1.06379	0.531894	−	0.846811i	$-0.321480\pi$
$397$	3.34065e6	1.06379	0.531894	+	0.846811i	$0.321480\pi$
$398$	4.58391e6	1.45054
$399$	−1.42821e6	−0.449119
$400$	−5.22241e6	−1.63200
$401$	−600538.	−0.186500	−0.0932502	−	0.995643i	$-0.529726\pi$
$401$	−600538.	−0.186500	−0.0932502	+	0.995643i	$0.529726\pi$
$402$	3.45176e6	1.06531
$403$	3.08037e6	0.944802
$404$	−453500.	−0.138237
$405$	−559013.	−0.169350
$406$	−5.74512e6	−1.72975
$407$	7.20019e6	2.15456
$408$	508480.	0.151225
$409$	−1.87846e6	−0.555256	−0.277628	−	0.960689i	$-0.589548\pi$
$409$	−1.87846e6	−0.555256	−0.277628	+	0.960689i	$0.589548\pi$
$410$	−1.36681e6	−0.401559
$411$	−2.61393e6	−0.763291
$412$	970754.	0.281751
$413$	−358577.	−0.103445
$414$	2.23460e6	0.640765
$415$	235872.	0.0672289
$416$	1.78814e6	0.506604
$417$	3.86810e6	1.08932
$418$	−5.91672e6	−1.65630
$419$	−4.65041e6	−1.29407	−0.647033	−	0.762462i	$-0.723990\pi$
$419$	−4.65041e6	−1.29407	−0.647033	+	0.762462i	$0.723990\pi$
$420$	939530.	0.259889
$421$	−1.24723e6	−0.342959	−0.171479	−	0.985188i	$-0.554855\pi$
$421$	−1.24723e6	−0.342959	−0.171479	+	0.985188i	$0.554855\pi$
$422$	−1.65196e6	−0.451564
$423$	−764340.	−0.207700
$424$	−3.16554e6	−0.855131
$425$	1.75358e6	0.470927
$426$	713144.	0.190394
$427$	−573443.	−0.152202
$428$	1.44236e6	0.380596
$429$	2.27208e6	0.596046
$430$	−6.61092e6	−1.72421
$431$	975574.	0.252969	0.126484	−	0.991969i	$-0.459631\pi$
$431$	975574.	0.252969	0.126484	+	0.991969i	$0.459631\pi$
$432$	−920831.	−0.237394
$433$	2.56758e6	0.658119	0.329060	−	0.944309i	$-0.393268\pi$
$433$	2.56758e6	0.658119	0.329060	+	0.944309i	$0.393268\pi$
$434$	4.82737e6	1.23023
$435$	6.45522e6	1.63564
$436$	−1.82096e6	−0.458760
$437$	−6.41479e6	−1.60686
$438$	−1.49407e6	−0.372122
$439$	875156.	0.216733	0.108366	−	0.994111i	$-0.465438\pi$
$439$	875156.	0.216733	0.108366	+	0.994111i	$0.465438\pi$
$440$	−6.57933e6	−1.62013
$441$	−501873.	−0.122885
$442$	−1.22373e6	−0.297941
$443$	4.39426e6	1.06384	0.531920	−	0.846795i	$-0.321471\pi$
$443$	4.39426e6	1.06384	0.531920	+	0.846795i	$0.321471\pi$
$444$	1.32959e6	0.320081
$445$	−1.53320e6	−0.367028
$446$	3.59180e6	0.855016
$447$	−3.45543e6	−0.817962
$448$	−1.36145e6	−0.320485
$449$	2.22268e6	0.520308	0.260154	−	0.965567i	$-0.416227\pi$
$449$	2.22268e6	0.520308	0.260154	+	0.965567i	$0.416227\pi$
$450$	−2.21875e6	−0.516507
$451$	−1.40365e6	−0.324951
$452$	−647386.	−0.149045
$453$	−823962.	−0.188652
$454$	3.18455e6	0.725118
$455$	3.82214e6	0.865521
$456$	1.84688e6	0.415936
$457$	−3.49053e6	−0.781810	−0.390905	−	0.920431i	$-0.627838\pi$
$457$	−3.49053e6	−0.781810	−0.390905	+	0.920431i	$0.627838\pi$
$458$	4.13311e6	0.920690
$459$	309196.	0.0685019
$460$	4.21987e6	0.929833
$461$	341191.	0.0747732	0.0373866	−	0.999301i	$-0.488097\pi$
$461$	341191.	0.0747732	0.0373866	+	0.999301i	$0.488097\pi$
$462$	3.56066e6	0.776114
$463$	−6.72986e6	−1.45899	−0.729497	−	0.683984i	$-0.760246\pi$
$463$	−6.72986e6	−1.45899	−0.729497	+	0.683984i	$0.760246\pi$
$464$	1.06333e7	2.29284
$465$	−5.42404e6	−1.16330
$466$	−4.27778e6	−0.912544
$467$	−2.11594e6	−0.448964	−0.224482	−	0.974478i	$-0.572069\pi$
$467$	−2.11594e6	−0.448964	−0.224482	+	0.974478i	$0.572069\pi$
$468$	419563.	0.0885488
$469$	5.96311e6	1.25182
$470$	−5.32669e6	−1.11228
$471$	−168608.	−0.0350208
$472$	463691.	0.0958017
$473$	−6.78908e6	−1.39527
$474$	−1.06146e6	−0.216998
$475$	6.36929e6	1.29526
$476$	−519664.	−0.105125
$477$	−1.92490e6	−0.387358
$478$	−7.32105e6	−1.46556
$479$	−8.71672e6	−1.73586	−0.867929	−	0.496688i	$-0.834549\pi$
$479$	−8.71672e6	−1.73586	−0.867929	+	0.496688i	$0.834549\pi$
$480$	−3.14863e6	−0.623761
$481$	5.40896e6	1.06599
$482$	−9.57363e6	−1.87698
$483$	3.86040e6	0.752946
$484$	2.08154e6	0.403898
$485$	1.41543e7	2.73233
$486$	−391216.	−0.0751321
$487$	−8.19716e6	−1.56618	−0.783089	−	0.621910i	$-0.786357\pi$
$487$	−8.19716e6	−1.56618	−0.783089	+	0.621910i	$0.786357\pi$
$488$	741542.	0.140957
$489$	766553.	0.144967
$490$	−3.49756e6	−0.658074
$491$	−6.65738e6	−1.24623	−0.623117	−	0.782128i	$-0.714134\pi$
$491$	−6.65738e6	−1.24623	−0.623117	+	0.782128i	$0.714134\pi$
$492$	−259199.	−0.0482748
$493$	−3.57045e6	−0.661616
$494$	−4.44479e6	−0.819471
$495$	−4.00076e6	−0.733887
$496$	−8.93472e6	−1.63071
$497$	1.23200e6	0.223727
$498$	165071.	0.0298261
$499$	−2.16723e6	−0.389630	−0.194815	−	0.980840i	$-0.562411\pi$
$499$	−2.16723e6	−0.389630	−0.194815	+	0.980840i	$0.562411\pi$
$500$	−1.02301e6	−0.183001
$501$	4.87460e6	0.867650
$502$	−3.50351e6	−0.620503
$503$	−3.01053e6	−0.530547	−0.265273	−	0.964173i	$-0.585462\pi$
$503$	−3.01053e6	−0.530547	−0.265273	+	0.964173i	$0.585462\pi$
$504$	−1.11145e6	−0.194900
$505$	3.24857e6	0.566844
$506$	1.59926e7	2.77679
$507$	−1.63480e6	−0.282451
$508$	−2.41586e6	−0.415348
$509$	8.34439e6	1.42758	0.713790	−	0.700360i	$-0.246977\pi$
$509$	8.34439e6	1.42758	0.713790	+	0.700360i	$0.246977\pi$
$510$	2.15479e6	0.366843
$511$	−2.58109e6	−0.437271
$512$	197715.	0.0333322
$513$	1.12305e6	0.188411
$514$	7.63045e6	1.27392
$515$	−6.95384e6	−1.15533
$516$	−1.25368e6	−0.207282
$517$	−5.47025e6	−0.900079
$518$	8.47659e6	1.38802
$519$	2.14877e6	0.350164
$520$	−4.94256e6	−0.801573
$521$	7.03207e6	1.13498	0.567491	−	0.823380i	$-0.307914\pi$
$521$	7.03207e6	1.13498	0.567491	+	0.823380i	$0.307914\pi$
$522$	4.51757e6	0.725653
$523$	4.76023e6	0.760982	0.380491	−	0.924785i	$-0.375755\pi$
$523$	4.76023e6	0.760982	0.380491	+	0.924785i	$0.375755\pi$
$524$	−3.35753e6	−0.534185
$525$	−3.83301e6	−0.606935
$526$	−2.99646e6	−0.472220
$527$	3.00010e6	0.470553
$528$	−6.59022e6	−1.02876
$529$	1.09025e7	1.69390
$530$	−1.34146e7	−2.07439
$531$	281961.	0.0433963
$532$	−1.88750e6	−0.289140
$533$	−1.05446e6	−0.160772
$534$	−1.07298e6	−0.162832
$535$	−1.03321e7	−1.56065
$536$	−7.71113e6	−1.15933
$537$	2.56080e6	0.383213
$538$	1.13546e7	1.69129
$539$	−3.59182e6	−0.532528
$540$	−738782.	−0.109027
$541$	1.92671e6	0.283024	0.141512	−	0.989937i	$-0.454804\pi$
$541$	1.92671e6	0.283024	0.141512	+	0.989937i	$0.454804\pi$
$542$	−8.80362e6	−1.28725
$543$	−3.62053e6	−0.526954
$544$	1.74154e6	0.252311
$545$	1.30442e7	1.88116
$546$	2.67486e6	0.383989
$547$	2.45466e6	0.350771	0.175385	−	0.984500i	$-0.443883\pi$
$547$	2.45466e6	0.350771	0.175385	+	0.984500i	$0.443883\pi$
$548$	−3.45453e6	−0.491403
$549$	450917.	0.0638507
$550$	−1.58792e7	−2.23832
$551$	−1.29685e7	−1.81974
$552$	−4.99203e6	−0.697316
$553$	−1.83373e6	−0.254989
$554$	1.02226e7	1.41510
$555$	−9.52431e6	−1.31250
$556$	5.11201e6	0.701302
$557$	7.38777e6	1.00896	0.504482	−	0.863422i	$-0.331684\pi$
$557$	7.38777e6	1.00896	0.504482	+	0.863422i	$0.331684\pi$
$558$	−3.79592e6	−0.516097
$559$	−5.10013e6	−0.690322
$560$	−1.10862e7	−1.49387
$561$	2.21286e6	0.296857
$562$	36542.5	0.00488042
$563$	2.38312e6	0.316866	0.158433	−	0.987370i	$-0.449356\pi$
$563$	2.38312e6	0.316866	0.158433	+	0.987370i	$0.449356\pi$
$564$	−1.01014e6	−0.133716
$565$	4.63745e6	0.611164
$566$	6.26081e6	0.821465
$567$	−675848.	−0.0882859
$568$	−1.59314e6	−0.207197
$569$	−7.30870e6	−0.946367	−0.473184	−	0.880964i	$-0.656895\pi$
$569$	−7.30870e6	−0.946367	−0.473184	+	0.880964i	$0.656895\pi$
$570$	7.82655e6	1.00898
$571$	2.52181e6	0.323684	0.161842	−	0.986817i	$-0.448256\pi$
$571$	2.52181e6	0.323684	0.161842	+	0.986817i	$0.448256\pi$
$572$	3.00274e6	0.383731
$573$	−5.61874e6	−0.714912
$574$	−1.65248e6	−0.209342
$575$	−1.72159e7	−2.17150
$576$	1.07056e6	0.134448
$577$	−758503.	−0.0948457	−0.0474229	−	0.998875i	$-0.515101\pi$
$577$	−758503.	−0.0948457	−0.0474229	+	0.998875i	$0.515101\pi$
$578$	8.21510e6	1.02281
$579$	7.52128e6	0.932385
$580$	8.53111e6	1.05302
$581$	285169.	0.0350480
$582$	9.90561e6	1.21220
$583$	−1.37762e7	−1.67864
$584$	3.33771e6	0.404964
$585$	−3.00547e6	−0.363097
$586$	1.01190e7	1.21729
$587$	4.83844e6	0.579576	0.289788	−	0.957091i	$-0.406415\pi$
$587$	4.83844e6	0.579576	0.289788	+	0.957091i	$0.406415\pi$
$588$	−663267.	−0.0791124
$589$	1.08968e7	1.29423
$590$	1.96499e6	0.232397
$591$	−6.52096e6	−0.767968
$592$	−1.56888e7	−1.83987
$593$	−3.38920e6	−0.395785	−0.197893	−	0.980224i	$-0.563410\pi$
$593$	−3.38920e6	−0.395785	−0.197893	+	0.980224i	$0.563410\pi$
$594$	−2.79986e6	−0.325590
$595$	3.72253e6	0.431068
$596$	−4.56663e6	−0.526600
$597$	−6.22694e6	−0.715054
$598$	1.20141e7	1.37384
$599$	7.50330e6	0.854447	0.427224	−	0.904146i	$-0.359492\pi$
$599$	7.50330e6	0.854447	0.427224	+	0.904146i	$0.359492\pi$
$600$	4.95662e6	0.562092
$601$	1.43644e7	1.62219	0.811095	−	0.584915i	$-0.198872\pi$
$601$	1.43644e7	1.62219	0.811095	+	0.584915i	$0.198872\pi$
$602$	−7.99261e6	−0.898871
$603$	−4.68899e6	−0.525153
$604$	−1.08893e6	−0.121453
$605$	−1.49108e7	−1.65620
$606$	2.27345e6	0.251481
$607$	−7.75401e6	−0.854191	−0.427095	−	0.904207i	$-0.640463\pi$
$607$	−7.75401e6	−0.854191	−0.427095	+	0.904207i	$0.640463\pi$
$608$	6.32555e6	0.693968
$609$	7.80437e6	0.852697
$610$	3.14244e6	0.341935
$611$	−4.10939e6	−0.445322
$612$	408628.	0.0441012
$613$	2.52805e6	0.271728	0.135864	−	0.990727i	$-0.456619\pi$
$613$	2.52805e6	0.271728	0.135864	+	0.990727i	$0.456619\pi$
$614$	1.87401e7	2.00609
$615$	1.85673e6	0.197952
$616$	−7.95442e6	−0.844611
$617$	8.69599e6	0.919615	0.459808	−	0.888018i	$-0.347918\pi$
$617$	8.69599e6	0.919615	0.459808	+	0.888018i	$0.347918\pi$
$618$	−4.86652e6	−0.512563
$619$	−1.01187e6	−0.106145	−0.0530723	−	0.998591i	$-0.516901\pi$
$619$	−1.01187e6	−0.106145	−0.0530723	+	0.998591i	$0.516901\pi$
$620$	−7.16832e6	−0.748925
$621$	−3.03555e6	−0.315870
$622$	−3.25241e6	−0.337077
$623$	−1.85364e6	−0.191340
$624$	−4.95074e6	−0.508989
$625$	−5.59205e6	−0.572626
$626$	−2.02585e7	−2.06619
$627$	8.03748e6	0.816490
$628$	−222829.	−0.0225462
$629$	5.26800e6	0.530907
$630$	−4.70999e6	−0.472790
$631$	1.14790e7	1.14771	0.573854	−	0.818958i	$-0.305448\pi$
$631$	1.14790e7	1.14771	0.573854	+	0.818958i	$0.305448\pi$
$632$	2.37126e6	0.236150
$633$	2.24408e6	0.222602
$634$	2.28111e7	2.25384
$635$	1.73056e7	1.70315
$636$	−2.54391e6	−0.249379
$637$	−2.69826e6	−0.263473
$638$	3.23315e7	3.14466
$639$	−968759.	−0.0938563
$640$	1.86558e7	1.80038
$641$	1.67427e7	1.60946	0.804728	−	0.593643i	$-0.202311\pi$
$641$	1.67427e7	1.60946	0.804728	+	0.593643i	$0.202311\pi$
$642$	−7.23074e6	−0.692381
$643$	−8.05866e6	−0.768662	−0.384331	−	0.923195i	$-0.625568\pi$
$643$	−8.05866e6	−0.768662	−0.384331	+	0.923195i	$0.625568\pi$
$644$	5.10183e6	0.484743
$645$	8.98050e6	0.849965
$646$	−4.32895e6	−0.408132
$647$	3.80079e6	0.356955	0.178477	−	0.983944i	$-0.442883\pi$
$647$	3.80079e6	0.356955	0.178477	+	0.983944i	$0.442883\pi$
$648$	873965.	0.0817630
$649$	2.01794e6	0.188060
$650$	−1.19288e7	−1.10743
$651$	−6.55767e6	−0.606453
$652$	1.01306e6	0.0933291
$653$	−7.58623e6	−0.696215	−0.348107	−	0.937455i	$-0.613176\pi$
$653$	−7.58623e6	−0.696215	−0.348107	+	0.937455i	$0.613176\pi$
$654$	9.12874e6	0.834577
$655$	2.40511e7	2.19044
$656$	3.05848e6	0.277489
$657$	2.02959e6	0.183441
$658$	−6.43998e6	−0.579856
$659$	1.09734e7	0.984299	0.492149	−	0.870511i	$-0.336211\pi$
$659$	1.09734e7	0.984299	0.492149	+	0.870511i	$0.336211\pi$
$660$	−5.28734e6	−0.472473
$661$	−5.85236e6	−0.520988	−0.260494	−	0.965476i	$-0.583885\pi$
$661$	−5.85236e6	−0.520988	−0.260494	+	0.965476i	$0.583885\pi$
$662$	1.67852e7	1.48862
$663$	1.66236e6	0.146873
$664$	−368764.	−0.0324585
$665$	1.35208e7	1.18563
$666$	−6.66542e6	−0.582293
$667$	3.50531e7	3.05079
$668$	6.44219e6	0.558589
$669$	−4.87922e6	−0.421488
$670$	−3.26776e7	−2.81231
$671$	3.22713e6	0.276701
$672$	−3.80669e6	−0.325181
$673$	6.43218e6	0.547420	0.273710	−	0.961812i	$-0.411749\pi$
$673$	6.43218e6	0.547420	0.273710	+	0.961812i	$0.411749\pi$
$674$	1.62066e7	1.37418
$675$	3.01402e6	0.254617
$676$	−2.16052e6	−0.181841
$677$	−2.35723e7	−1.97665	−0.988325	−	0.152363i	$-0.951312\pi$
$677$	−2.35723e7	−1.97665	−0.988325	+	0.152363i	$0.951312\pi$
$678$	3.24544e6	0.271143
$679$	1.71125e7	1.42442
$680$	−4.81375e6	−0.399219
$681$	−4.32600e6	−0.357453
$682$	−2.71667e7	−2.23654
$683$	2.00530e7	1.64486	0.822428	−	0.568870i	$-0.192619\pi$
$683$	2.00530e7	1.64486	0.822428	+	0.568870i	$0.192619\pi$
$684$	1.48420e6	0.121298
$685$	2.47460e7	2.01501
$686$	−1.56988e7	−1.27367
$687$	−5.61456e6	−0.453862
$688$	1.47931e7	1.19148
$689$	−1.03490e7	−0.830520
$690$	−2.11548e7	−1.69156
$691$	2.03136e7	1.61842	0.809211	−	0.587518i	$-0.199895\pi$
$691$	2.03136e7	1.61842	0.809211	+	0.587518i	$0.199895\pi$
$692$	2.83978e6	0.225434
$693$	−4.83692e6	−0.382592
$694$	−611969.	−0.0482315
$695$	−3.66191e7	−2.87571
$696$	−1.00921e7	−0.789696
$697$	−1.02698e6	−0.0800716
$698$	−3.44146e6	−0.267365
$699$	5.81109e6	0.449847
$700$	−5.06564e6	−0.390742
$701$	1.59318e7	1.22453	0.612265	−	0.790653i	$-0.290259\pi$
$701$	1.59318e7	1.22453	0.612265	+	0.790653i	$0.290259\pi$
$702$	−2.10333e6	−0.161088
$703$	1.91342e7	1.46023
$704$	7.66178e6	0.582637
$705$	7.23597e6	0.548307
$706$	1.09680e7	0.828162
$707$	3.92753e6	0.295509
$708$	372635.	0.0279383
$709$	2.13021e7	1.59150	0.795749	−	0.605626i	$-0.207077\pi$
$709$	2.13021e7	1.59150	0.795749	+	0.605626i	$0.207077\pi$
$710$	−6.75129e6	−0.502621
$711$	1.44192e6	0.106971
$712$	2.39702e6	0.177203
$713$	−2.94536e7	−2.16978
$714$	2.60515e6	0.191243
$715$	−2.15096e7	−1.57350
$716$	3.38431e6	0.246710
$717$	9.94517e6	0.722461
$718$	−1.66618e7	−1.20618
$719$	−1.46154e7	−1.05436	−0.527180	−	0.849753i	$-0.676751\pi$
$719$	−1.46154e7	−1.05436	−0.527180	+	0.849753i	$0.676751\pi$
$720$	8.71745e6	0.626698
$721$	−8.40720e6	−0.602300
$722$	681393.	0.0486469
$723$	1.30051e7	0.925272
$724$	−4.78483e6	−0.339250
$725$	−3.48045e7	−2.45918
$726$	−1.04351e7	−0.734773
$727$	−6.13626e6	−0.430594	−0.215297	−	0.976549i	$-0.569072\pi$
$727$	−6.13626e6	−0.430594	−0.215297	+	0.976549i	$0.569072\pi$
$728$	−5.97556e6	−0.417878
$729$	531441.	0.0370370
$730$	1.41443e7	0.982365
$731$	−4.96721e6	−0.343810
$732$	595924.	0.0411068
$733$	1.06072e7	0.729190	0.364595	−	0.931166i	$-0.381207\pi$
$733$	1.06072e7	0.729190	0.364595	+	0.931166i	$0.381207\pi$
$734$	5.24953e6	0.359650
$735$	4.75120e6	0.324403
$736$	−1.70977e7	−1.16344
$737$	−3.35582e7	−2.27578
$738$	1.29940e6	0.0878216
$739$	−75441.2	−0.00508156	−0.00254078	−	0.999997i	$-0.500809\pi$
$739$	−75441.2	−0.00508156	−0.00254078	+	0.999997i	$0.500809\pi$
$740$	−1.25872e7	−0.844984
$741$	6.03795e6	0.403965
$742$	−1.62183e7	−1.08142
$743$	−3.43706e6	−0.228410	−0.114205	−	0.993457i	$-0.536432\pi$
$743$	−3.43706e6	−0.228410	−0.114205	+	0.993457i	$0.536432\pi$
$744$	8.47998e6	0.561646
$745$	3.27123e7	2.15934
$746$	−5.60953e6	−0.369045
$747$	−224238.	−0.0147031
$748$	2.92448e6	0.191115
$749$	−1.24915e7	−0.813600
$750$	5.12847e6	0.332916
$751$	8.47000e6	0.548004	0.274002	−	0.961729i	$-0.411653\pi$
$751$	8.47000e6	0.548004	0.274002	+	0.961729i	$0.411653\pi$
$752$	1.19194e7	0.768616
$753$	4.75928e6	0.305882
$754$	2.42882e7	1.55585
$755$	7.80040e6	0.498023
$756$	−893189.	−0.0568380
$757$	−9.70756e6	−0.615702	−0.307851	−	0.951435i	$-0.599610\pi$
$757$	−9.70756e6	−0.615702	−0.307851	+	0.951435i	$0.599610\pi$
$758$	−1.08213e7	−0.684077
$759$	−2.17249e7	−1.36884
$760$	−1.74843e7	−1.09803
$761$	−4.60781e6	−0.288425	−0.144212	−	0.989547i	$-0.546065\pi$
$761$	−4.60781e6	−0.288425	−0.144212	+	0.989547i	$0.546065\pi$
$762$	1.21110e7	0.755602
$763$	1.57704e7	0.980691
$764$	−7.42564e6	−0.460257
$765$	−2.92714e6	−0.180838
$766$	2.80554e7	1.72761
$767$	1.51593e6	0.0930445
$768$	9.24953e6	0.565870
$769$	−1.09236e7	−0.666114	−0.333057	−	0.942907i	$-0.608080\pi$
$769$	−1.09236e7	−0.666114	−0.333057	+	0.942907i	$0.608080\pi$
$770$	−3.37086e7	−2.04887
$771$	−1.03655e7	−0.627990
$772$	9.93999e6	0.600265
$773$	6.36770e6	0.383295	0.191648	−	0.981464i	$-0.438617\pi$
$773$	6.36770e6	0.383295	0.191648	+	0.981464i	$0.438617\pi$
$774$	6.28484e6	0.377088
$775$	2.92447e7	1.74901
$776$	−2.21289e7	−1.31918
$777$	−1.15149e7	−0.684238
$778$	−2.86606e7	−1.69760
$779$	−3.73014e6	−0.220233
$780$	−3.97198e6	−0.233760
$781$	−6.93323e6	−0.406732
$782$	1.17009e7	0.684233
$783$	−6.13683e6	−0.357717
$784$	7.82638e6	0.454748
$785$	1.59620e6	0.0924514
$786$	1.68317e7	0.971791
$787$	−2.17413e7	−1.25126	−0.625631	−	0.780119i	$-0.715159\pi$
$787$	−2.17413e7	−1.25126	−0.625631	+	0.780119i	$0.715159\pi$
$788$	−8.61799e6	−0.494414
$789$	4.07050e6	0.232785
$790$	1.00487e7	0.572854
$791$	5.60668e6	0.318614
$792$	6.25482e6	0.354325
$793$	2.42430e6	0.136900
$794$	−2.21328e7	−1.24590
$795$	1.82229e7	1.02259
$796$	−8.22942e6	−0.460348
$797$	−1.29730e7	−0.723424	−0.361712	−	0.932290i	$-0.617808\pi$
$797$	−1.29730e7	−0.723424	−0.361712	+	0.932290i	$0.617808\pi$
$798$	9.46231e6	0.526005
$799$	−4.00229e6	−0.221790
$800$	1.69764e7	0.937822
$801$	1.45758e6	0.0802696
$802$	3.97873e6	0.218428
$803$	1.45254e7	0.794951
$804$	−6.19688e6	−0.338091
$805$	−3.65461e7	−1.98770
$806$	−2.04083e7	−1.10655
$807$	−1.54245e7	−0.833735
$808$	−5.07884e6	−0.273675
$809$	−1.50725e7	−0.809682	−0.404841	−	0.914387i	$-0.632673\pi$
$809$	−1.50725e7	−0.809682	−0.404841	+	0.914387i	$0.632673\pi$
$810$	3.70362e6	0.198341
$811$	−9.99366e6	−0.533547	−0.266773	−	0.963759i	$-0.585958\pi$
$811$	−9.99366e6	−0.533547	−0.266773	+	0.963759i	$0.585958\pi$
$812$	1.03141e7	0.548962
$813$	1.19591e7	0.634561
$814$	−4.77032e7	−2.52340
$815$	−7.25691e6	−0.382699
$816$	−4.82172e6	−0.253499
$817$	−1.80417e7	−0.945633
$818$	1.24453e7	0.650312
$819$	−3.63362e6	−0.189291
$820$	2.45382e6	0.127441
$821$	2.35975e7	1.22182	0.610912	−	0.791698i	$-0.290803\pi$
$821$	2.35975e7	1.22182	0.610912	+	0.791698i	$0.290803\pi$
$822$	1.73180e7	0.893962
$823$	−7.42657e6	−0.382198	−0.191099	−	0.981571i	$-0.561205\pi$
$823$	−7.42657e6	−0.382198	−0.191099	+	0.981571i	$0.561205\pi$
$824$	1.08717e7	0.557800
$825$	2.15708e7	1.10340
$826$	2.37567e6	0.121154
$827$	−2.03546e7	−1.03490	−0.517451	−	0.855713i	$-0.673119\pi$
$827$	−2.03546e7	−1.03490	−0.517451	+	0.855713i	$0.673119\pi$
$828$	−4.01174e6	−0.203356
$829$	1.84957e7	0.934725	0.467362	−	0.884066i	$-0.345204\pi$
$829$	1.84957e7	0.934725	0.467362	+	0.884066i	$0.345204\pi$
$830$	−1.56272e6	−0.0787381
$831$	−1.38867e7	−0.697584
$832$	5.75572e6	0.288264
$833$	−2.62794e6	−0.131221
$834$	−2.56272e7	−1.27581
$835$	−4.61476e7	−2.29051
$836$	1.06222e7	0.525652
$837$	5.15651e6	0.254415
$838$	3.08103e7	1.51560
$839$	4.89142e6	0.239900	0.119950	−	0.992780i	$-0.461727\pi$
$839$	4.89142e6	0.239900	0.119950	+	0.992780i	$0.461727\pi$
$840$	1.05220e7	0.514517
$841$	5.03540e7	2.45496
$842$	8.26325e6	0.401671
$843$	−49640.6	−0.00240585
$844$	2.96574e6	0.143310
$845$	1.54765e7	0.745644
$846$	5.06396e6	0.243257
$847$	−1.80272e7	−0.863413
$848$	3.00176e7	1.43346
$849$	−8.50490e6	−0.404948
$850$	−1.16179e7	−0.551547
$851$	−5.17189e7	−2.44808
$852$	−1.28029e6	−0.0604242
$853$	−2.49648e7	−1.17478	−0.587389	−	0.809305i	$-0.699844\pi$
$853$	−2.49648e7	−1.17478	−0.587389	+	0.809305i	$0.699844\pi$
$854$	3.79922e6	0.178258
$855$	−1.06319e7	−0.497386
$856$	1.61533e7	0.753488
$857$	−4.44419e6	−0.206700	−0.103350	−	0.994645i	$-0.532956\pi$
$857$	−4.44419e6	−0.206700	−0.103350	+	0.994645i	$0.532956\pi$
$858$	−1.50531e7	−0.698085
$859$	−2.83513e7	−1.31096	−0.655480	−	0.755212i	$-0.727534\pi$
$859$	−2.83513e7	−1.31096	−0.655480	+	0.755212i	$0.727534\pi$
$860$	1.18685e7	0.547203
$861$	2.24479e6	0.103197
$862$	−6.46345e6	−0.296276
$863$	1.98739e7	0.908358	0.454179	−	0.890911i	$-0.349933\pi$
$863$	1.98739e7	0.908358	0.454179	+	0.890911i	$0.349933\pi$
$864$	2.99332e6	0.136417
$865$	−2.03423e7	−0.924400
$866$	−1.70109e7	−0.770785
$867$	−1.11597e7	−0.504201
$868$	−8.66651e6	−0.390431
$869$	1.03196e7	0.463566
$870$	−4.27676e7	−1.91565
$871$	−2.52098e7	−1.12596
$872$	−2.03934e7	−0.908234
$873$	−1.34561e7	−0.597564
$874$	4.24997e7	1.88195
$875$	8.85973e6	0.391202
$876$	2.68228e6	0.118098
$877$	2.39535e7	1.05165	0.525823	−	0.850594i	$-0.323757\pi$
$877$	2.39535e7	1.05165	0.525823	+	0.850594i	$0.323757\pi$
$878$	−5.79815e6	−0.253836
$879$	−1.37461e7	−0.600076
$880$	6.23893e7	2.71583
$881$	1.44336e7	0.626522	0.313261	−	0.949667i	$-0.398579\pi$
$881$	1.44336e7	0.626522	0.313261	+	0.949667i	$0.398579\pi$
$882$	3.32505e6	0.143922
$883$	−1.96597e7	−0.848547	−0.424274	−	0.905534i	$-0.639471\pi$
$883$	−1.96597e7	−0.848547	−0.424274	+	0.905534i	$0.639471\pi$
$884$	2.19694e6	0.0945558
$885$	−2.66931e6	−0.114562
$886$	−2.91131e7	−1.24596
$887$	430936.	0.0183909	0.00919547	−	0.999958i	$-0.497073\pi$
$887$	430936.	0.0183909	0.00919547	+	0.999958i	$0.497073\pi$
$888$	1.48904e7	0.633684
$889$	2.09225e7	0.887889
$890$	1.01579e7	0.429861
$891$	3.80343e6	0.160502
$892$	−6.44829e6	−0.271352
$893$	−1.45370e7	−0.610021
$894$	2.28932e7	0.957992
$895$	−2.42430e7	−1.01164
$896$	2.25549e7	0.938580
$897$	−1.63203e7	−0.677247
$898$	−1.47258e7	−0.609381
$899$	−5.95449e7	−2.45723
$900$	3.98328e6	0.163921
$901$	−1.00793e7	−0.413636
$902$	9.29956e6	0.380580
$903$	1.08574e7	0.443106
$904$	−7.25021e6	−0.295073
$905$	3.42753e7	1.39111
$906$	5.45898e6	0.220948
$907$	−1.15056e7	−0.464398	−0.232199	−	0.972668i	$-0.574592\pi$
$907$	−1.15056e7	−0.464398	−0.232199	+	0.972668i	$0.574592\pi$
$908$	−5.71717e6	−0.230126
$909$	−3.08834e6	−0.123970
$910$	−2.53227e7	−1.01369
$911$	3.19861e7	1.27693	0.638463	−	0.769653i	$-0.279571\pi$
$911$	3.19861e7	1.27693	0.638463	+	0.769653i	$0.279571\pi$
$912$	−1.75133e7	−0.697236
$913$	−1.60483e6	−0.0637166
$914$	2.31257e7	0.915652
$915$	−4.26881e6	−0.168560
$916$	−7.42011e6	−0.292194
$917$	2.90778e7	1.14193
$918$	−2.04851e6	−0.0802290
$919$	3.83417e7	1.49756	0.748778	−	0.662821i	$-0.230641\pi$
$919$	3.83417e7	1.49756	0.748778	+	0.662821i	$0.230641\pi$
$920$	4.72593e7	1.84085
$921$	−2.54572e7	−0.988922
$922$	−2.26049e6	−0.0875739
$923$	−5.20842e6	−0.201234
$924$	−6.39239e6	−0.246311
$925$	5.13520e7	1.97335
$926$	4.45872e7	1.70877
$927$	6.61085e6	0.252673
$928$	−3.45655e7	−1.31757
$929$	3.81222e7	1.44923	0.724617	−	0.689151i	$-0.242016\pi$
$929$	3.81222e7	1.44923	0.724617	+	0.689151i	$0.242016\pi$
$930$	3.59358e7	1.36245
$931$	−9.54510e6	−0.360916
$932$	7.67983e6	0.289609
$933$	4.41819e6	0.166165
$934$	1.40187e7	0.525824
$935$	−2.09490e7	−0.783674
$936$	4.69877e6	0.175305
$937$	−1.63559e7	−0.608591	−0.304295	−	0.952578i	$-0.598421\pi$
$937$	−1.63559e7	−0.608591	−0.304295	+	0.952578i	$0.598421\pi$
$938$	−3.95072e7	−1.46612
$939$	2.75198e7	1.01855
$940$	9.56293e6	0.352997
$941$	1.57758e7	0.580789	0.290395	−	0.956907i	$-0.406213\pi$
$941$	1.57758e7	0.580789	0.290395	+	0.956907i	$0.406213\pi$
$942$	1.11707e6	0.0410161
$943$	1.00824e7	0.369220
$944$	−4.39700e6	−0.160593
$945$	6.39821e6	0.233066
$946$	4.49795e7	1.63413
$947$	−2.76570e7	−1.00214	−0.501072	−	0.865405i	$-0.667061\pi$
$947$	−2.76570e7	−1.00214	−0.501072	+	0.865405i	$0.667061\pi$
$948$	1.90562e6	0.0688675
$949$	1.09119e7	0.393309
$950$	−4.21983e7	−1.51700
$951$	−3.09874e7	−1.11105
$952$	−5.81982e6	−0.208122
$953$	1.15464e6	0.0411825	0.0205912	−	0.999788i	$-0.493445\pi$
$953$	1.15464e6	0.0411825	0.0205912	+	0.999788i	$0.493445\pi$
$954$	1.27530e7	0.453671
$955$	5.31923e7	1.88730
$956$	1.31434e7	0.465116
$957$	−4.39202e7	−1.55019
$958$	5.77507e7	2.03303
$959$	2.99179e7	1.05047
$960$	−1.01349e7	−0.354928
$961$	2.14039e7	0.747625
$962$	−3.58358e7	−1.24848
$963$	9.82249e6	0.341315
$964$	1.71874e7	0.595686
$965$	−7.12035e7	−2.46140
$966$	−2.55762e7	−0.881846
$967$	−4.77090e7	−1.64072	−0.820360	−	0.571848i	$-0.806227\pi$
$967$	−4.77090e7	−1.64072	−0.820360	+	0.571848i	$0.806227\pi$
$968$	2.33116e7	0.799621
$969$	5.88059e6	0.201192
$970$	−9.37759e7	−3.20009
$971$	3.61364e7	1.22998	0.614988	−	0.788537i	$-0.289161\pi$
$971$	3.61364e7	1.22998	0.614988	+	0.788537i	$0.289161\pi$
$972$	702343.	0.0238443
$973$	−4.42725e7	−1.49917
$974$	5.43084e7	1.83430
$975$	1.62045e7	0.545915
$976$	−7.03176e6	−0.236287
$977$	2.58953e7	0.867930	0.433965	−	0.900930i	$-0.357114\pi$
$977$	2.58953e7	0.867930	0.433965	+	0.900930i	$0.357114\pi$
$978$	−5.07862e6	−0.169785
$979$	1.04316e7	0.347853
$980$	6.27911e6	0.208849
$981$	−1.24008e7	−0.411412
$982$	4.41070e7	1.45958
$983$	−3.78204e7	−1.24837	−0.624183	−	0.781278i	$-0.714568\pi$
$983$	−3.78204e7	−1.24837	−0.624183	+	0.781278i	$0.714568\pi$
$984$	−2.90282e6	−0.0955724
$985$	6.17336e7	2.02736
$986$	2.36552e7	0.774880
$987$	8.74829e6	0.285845
$988$	7.97965e6	0.260071
$989$	4.87659e7	1.58535
$990$	2.65061e7	0.859525
$991$	−3.64574e7	−1.17924	−0.589619	−	0.807681i	$-0.700722\pi$
$991$	−3.64574e7	−1.17924	−0.589619	+	0.807681i	$0.700722\pi$
$992$	2.90439e7	0.937077
$993$	−2.28017e7	−0.733826
$994$	−8.16232e6	−0.262028
$995$	5.89501e7	1.88767
$996$	−296349.	−0.00946575
$997$	1.17735e6	0.0375119	0.0187559	−	0.999824i	$-0.494029\pi$
$997$	1.17735e6	0.0375119	0.0187559	+	0.999824i	$0.494029\pi$
$998$	1.43585e7	0.456333
$999$	9.05453e6	0.287047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.4	✓	11
3.2	odd	2		531.6.a.b.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.4	✓	11	1.1	even	1	trivial
531.6.a.b.1.8		11	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)

\(f(q)\)	\(=\)	\(q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +564.490 q^{10} +579.703 q^{11} +107.048 q^{12} +435.487 q^{13} +682.469 q^{14} -766.822 q^{15} -1263.14 q^{16} +424.138 q^{17} -536.647 q^{18} +1540.54 q^{19} -1013.42 q^{20} -927.089 q^{21} -3840.69 q^{22} -4164.00 q^{23} +1198.86 q^{24} +4134.46 q^{25} -2885.22 q^{26} +729.000 q^{27} -1225.22 q^{28} -8418.14 q^{29} +5080.41 q^{30} +7073.40 q^{31} +4106.07 q^{32} +5217.32 q^{33} -2810.03 q^{34} +8776.70 q^{35} +963.434 q^{36} +12420.5 q^{37} -10206.5 q^{38} +3919.38 q^{39} -11349.5 q^{40} -2421.33 q^{41} +6142.22 q^{42} -11711.3 q^{43} +6895.12 q^{44} -6901.40 q^{45} +27587.6 q^{46} -9436.30 q^{47} -11368.3 q^{48} -6195.96 q^{49} -27391.9 q^{50} +3817.24 q^{51} +5179.79 q^{52} -23764.2 q^{53} -4829.82 q^{54} -49392.1 q^{55} -13721.5 q^{56} +13864.8 q^{57} +55772.5 q^{58} +3481.00 q^{59} -9120.77 q^{60} +5566.88 q^{61} -46863.2 q^{62} -8343.80 q^{63} +13216.7 q^{64} -37104.6 q^{65} -34566.2 q^{66} -57888.7 q^{67} +5044.80 q^{68} -37476.0 q^{69} -58148.0 q^{70} -11960.0 q^{71} +10789.7 q^{72} +25056.7 q^{73} -82289.1 q^{74} +37210.2 q^{75} +18323.5 q^{76} -59715.1 q^{77} -25967.0 q^{78} +17801.5 q^{79} +107623. q^{80} +6561.00 q^{81} +16042.0 q^{82} -2768.37 q^{83} -11027.0 q^{84} -36137.6 q^{85} +77590.7 q^{86} -75763.3 q^{87} +77219.9 q^{88} +17994.8 q^{89} +45723.7 q^{90} -44859.5 q^{91} -49527.6 q^{92} +63660.6 q^{93} +62518.1 q^{94} -131257. q^{95} +36954.6 q^{96} -166125. q^{97} +41049.9 q^{98} +46955.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9} - 399 q^{10} - 698 q^{11} + 1350 q^{12} - 1556 q^{13} - 1679 q^{14} - 1728 q^{15} - 2662 q^{16} - 4793 q^{17} - 486 q^{18} - 3753 q^{19} - 11023 q^{20} - 3339 q^{21} - 9534 q^{22} - 7323 q^{23} - 5589 q^{24} + 7867 q^{25} - 4844 q^{26} + 8019 q^{27} + 3650 q^{28} - 15467 q^{29} - 3591 q^{30} - 5151 q^{31} - 15368 q^{32} - 6282 q^{33} + 8452 q^{34} - 23285 q^{35} + 12150 q^{36} + 8623 q^{37} + 15205 q^{38} - 14004 q^{39} + 41530 q^{40} - 6369 q^{41} - 15111 q^{42} - 20506 q^{43} - 55632 q^{44} - 15552 q^{45} - 45191 q^{46} - 47899 q^{47} - 23958 q^{48} - 10322 q^{49} - 102147 q^{50} - 43137 q^{51} - 292 q^{52} - 80048 q^{53} - 4374 q^{54} - 2114 q^{55} - 108126 q^{56} - 33777 q^{57} - 58294 q^{58} + 38291 q^{59} - 99207 q^{60} - 82527 q^{61} - 67438 q^{62} - 30051 q^{63} - 51411 q^{64} - 167646 q^{65} - 85806 q^{66} - 166976 q^{67} - 136533 q^{68} - 65907 q^{69} + 76140 q^{70} - 183560 q^{71} - 50301 q^{72} - 36809 q^{73} - 116686 q^{74} + 70803 q^{75} + 55580 q^{76} - 164885 q^{77} - 43596 q^{78} - 281518 q^{79} - 32683 q^{80} + 72171 q^{81} + 178815 q^{82} - 254691 q^{83} + 32850 q^{84} + 4763 q^{85} + 349324 q^{86} - 139203 q^{87} + 251285 q^{88} - 89687 q^{89} - 32319 q^{90} + 34897 q^{91} - 20240 q^{92} - 46359 q^{93} + 96548 q^{94} - 155113 q^{95} - 138312 q^{96} - 45828 q^{97} + 465864 q^{98} - 56538 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 99 * q^3 + 150 * q^4 - 192 * q^5 - 54 * q^6 - 371 * q^7 - 621 * q^8 + 891 * q^9 - 399 * q^10 - 698 * q^11 + 1350 * q^12 - 1556 * q^13 - 1679 * q^14 - 1728 * q^15 - 2662 * q^16 - 4793 * q^17 - 486 * q^18 - 3753 * q^19 - 11023 * q^20 - 3339 * q^21 - 9534 * q^22 - 7323 * q^23 - 5589 * q^24 + 7867 * q^25 - 4844 * q^26 + 8019 * q^27 + 3650 * q^28 - 15467 * q^29 - 3591 * q^30 - 5151 * q^31 - 15368 * q^32 - 6282 * q^33 + 8452 * q^34 - 23285 * q^35 + 12150 * q^36 + 8623 * q^37 + 15205 * q^38 - 14004 * q^39 + 41530 * q^40 - 6369 * q^41 - 15111 * q^42 - 20506 * q^43 - 55632 * q^44 - 15552 * q^45 - 45191 * q^46 - 47899 * q^47 - 23958 * q^48 - 10322 * q^49 - 102147 * q^50 - 43137 * q^51 - 292 * q^52 - 80048 * q^53 - 4374 * q^54 - 2114 * q^55 - 108126 * q^56 - 33777 * q^57 - 58294 * q^58 + 38291 * q^59 - 99207 * q^60 - 82527 * q^61 - 67438 * q^62 - 30051 * q^63 - 51411 * q^64 - 167646 * q^65 - 85806 * q^66 - 166976 * q^67 - 136533 * q^68 - 65907 * q^69 + 76140 * q^70 - 183560 * q^71 - 50301 * q^72 - 36809 * q^73 - 116686 * q^74 + 70803 * q^75 + 55580 * q^76 - 164885 * q^77 - 43596 * q^78 - 281518 * q^79 - 32683 * q^80 + 72171 * q^81 + 178815 * q^82 - 254691 * q^83 + 32850 * q^84 + 4763 * q^85 + 349324 * q^86 - 139203 * q^87 + 251285 * q^88 - 89687 * q^89 - 32319 * q^90 + 34897 * q^91 - 20240 * q^92 - 46359 * q^93 + 96548 * q^94 - 155113 * q^95 - 138312 * q^96 - 45828 * q^97 + 465864 * q^98 - 56538 * q^99

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