LMFDB - Embedded newform 177.6.a.a.1.11

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			1.11
Root			$9.42442$ 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)

$f(q)$	$=$	$q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} -255.921 q^{10} -604.600 q^{11} +350.738 q^{12} -893.648 q^{13} -1665.11 q^{14} -273.406 q^{15} -752.340 q^{16} +1088.04 q^{17} +682.378 q^{18} +2022.78 q^{19} -1183.87 q^{20} -1778.88 q^{21} -5093.40 q^{22} +1324.04 q^{23} +528.528 q^{24} -2202.15 q^{25} -7528.47 q^{26} +729.000 q^{27} -7702.70 q^{28} +2519.29 q^{29} -2303.29 q^{30} +8782.14 q^{31} -8217.24 q^{32} -5441.40 q^{33} +9166.09 q^{34} +6004.38 q^{35} +3156.64 q^{36} -13007.9 q^{37} +17040.7 q^{38} -8042.83 q^{39} -1783.98 q^{40} +10648.4 q^{41} -14986.0 q^{42} +7396.68 q^{43} -23561.8 q^{44} -2460.65 q^{45} +11154.3 q^{46} -23429.3 q^{47} -6771.06 q^{48} +22259.6 q^{49} -18551.9 q^{50} +9792.34 q^{51} -34826.2 q^{52} -17464.3 q^{53} +6141.40 q^{54} +18366.8 q^{55} -11607.2 q^{56} +18205.0 q^{57} +21223.6 q^{58} +3481.00 q^{59} -10654.9 q^{60} -11795.1 q^{61} +73984.4 q^{62} -16009.9 q^{63} -45150.6 q^{64} +27147.6 q^{65} -45840.6 q^{66} -46995.6 q^{67} +42401.8 q^{68} +11916.4 q^{69} +50583.4 q^{70} -34625.3 q^{71} +4756.76 q^{72} -31175.2 q^{73} -109584. q^{74} -19819.4 q^{75} +78829.3 q^{76} +119501. q^{77} -67756.2 q^{78} -72100.3 q^{79} +22854.9 q^{80} +6561.00 q^{81} +89706.8 q^{82} +31482.3 q^{83} -69324.3 q^{84} -33052.9 q^{85} +62312.7 q^{86} +22673.7 q^{87} -35505.4 q^{88} +101434. q^{89} -20729.6 q^{90} +176632. q^{91} +51599.0 q^{92} +79039.2 q^{93} -197378. q^{94} -61448.7 q^{95} -73955.2 q^{96} -182378. q^{97} +187525. q^{98} -48972.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.42442	1.48924	0.744621	−	0.667488i	$-0.232630\pi$
$2$	8.42442	1.48924	0.744621	+	0.667488i	$0.232630\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	38.9709	1.21784
$5$	−30.3784	−0.543426	−0.271713	−	0.962378i	$-0.587590\pi$
$5$	−30.3784	−0.543426	−0.271713	+	0.962378i	$0.587590\pi$
$6$	75.8198	0.859814
$7$	−197.653	−1.52461	−0.762304	−	0.647220i	$-0.775932\pi$
$7$	−197.653	−1.52461	−0.762304	+	0.647220i	$0.775932\pi$
$8$	58.7254	0.324415
$9$	81.0000	0.333333
$10$	−255.921	−0.809292
$11$	−604.600	−1.50656	−0.753280	−	0.657700i	$-0.771529\pi$
$11$	−604.600	−1.50656	−0.753280	+	0.657700i	$0.771529\pi$
$12$	350.738	0.703120
$13$	−893.648	−1.46659	−0.733294	−	0.679912i	$-0.762018\pi$
$13$	−893.648	−1.46659	−0.733294	+	0.679912i	$0.762018\pi$
$14$	−1665.11	−2.27051
$15$	−273.406	−0.313747
$16$	−752.340	−0.734707
$17$	1088.04	0.913107	0.456553	−	0.889696i	$-0.349084\pi$
$17$	1088.04	0.913107	0.456553	+	0.889696i	$0.349084\pi$
$18$	682.378	0.496414
$19$	2022.78	1.28548	0.642738	−	0.766086i	$-0.277799\pi$
$19$	2022.78	1.28548	0.642738	+	0.766086i	$0.277799\pi$
$20$	−1183.87	−0.661805
$21$	−1778.88	−0.880232
$22$	−5093.40	−2.24363
$23$	1324.04	0.521894	0.260947	−	0.965353i	$-0.415965\pi$
$23$	1324.04	0.521894	0.260947	+	0.965353i	$0.415965\pi$
$24$	528.528	0.187301
$25$	−2202.15	−0.704689
$26$	−7528.47	−2.18410
$27$	729.000	0.192450
$28$	−7702.70	−1.85673
$29$	2519.29	0.556268	0.278134	−	0.960542i	$-0.410284\pi$
$29$	2519.29	0.556268	0.278134	+	0.960542i	$0.410284\pi$
$30$	−2303.29	−0.467245
$31$	8782.14	1.64133	0.820665	−	0.571409i	$-0.193603\pi$
$31$	8782.14	1.64133	0.820665	+	0.571409i	$0.193603\pi$
$32$	−8217.24	−1.41857
$33$	−5441.40	−0.869813
$34$	9166.09	1.35984
$35$	6004.38	0.828511
$36$	3156.64	0.405946
$37$	−13007.9	−1.56208	−0.781038	−	0.624484i	$-0.785309\pi$
$37$	−13007.9	−1.56208	−0.781038	+	0.624484i	$0.785309\pi$
$38$	17040.7	1.91438
$39$	−8042.83	−0.846735
$40$	−1783.98	−0.176295
$41$	10648.4	0.989295	0.494648	−	0.869094i	$-0.335297\pi$
$41$	10648.4	0.989295	0.494648	+	0.869094i	$0.335297\pi$
$42$	−14986.0	−1.31088
$43$	7396.68	0.610050	0.305025	−	0.952344i	$-0.401335\pi$
$43$	7396.68	0.610050	0.305025	+	0.952344i	$0.401335\pi$
$44$	−23561.8	−1.83475
$45$	−2460.65	−0.181142
$46$	11154.3	0.777226
$47$	−23429.3	−1.54709	−0.773543	−	0.633744i	$-0.781517\pi$
$47$	−23429.3	−1.54709	−0.773543	+	0.633744i	$0.781517\pi$
$48$	−6771.06	−0.424183
$49$	22259.6	1.32443
$50$	−18551.9	−1.04945
$51$	9792.34	0.527183
$52$	−34826.2	−1.78607
$53$	−17464.3	−0.854006	−0.427003	−	0.904250i	$-0.640431\pi$
$53$	−17464.3	−0.854006	−0.427003	+	0.904250i	$0.640431\pi$
$54$	6141.40	0.286605
$55$	18366.8	0.818703
$56$	−11607.2	−0.494605
$57$	18205.0	0.742169
$58$	21223.6	0.828417
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−10654.9	−0.382093
$61$	−11795.1	−0.405861	−0.202930	−	0.979193i	$-0.565047\pi$
$61$	−11795.1	−0.405861	−0.202930	+	0.979193i	$0.565047\pi$
$62$	73984.4	2.44434
$63$	−16009.9	−0.508202
$64$	−45150.6	−1.37789
$65$	27147.6	0.796981
$66$	−45840.6	−1.29536
$67$	−46995.6	−1.27900	−0.639499	−	0.768792i	$-0.720858\pi$
$67$	−46995.6	−1.27900	−0.639499	+	0.768792i	$0.720858\pi$
$68$	42401.8	1.11202
$69$	11916.4	0.301316
$70$	50583.4	1.23385
$71$	−34625.3	−0.815170	−0.407585	−	0.913167i	$-0.633629\pi$
$71$	−34625.3	−0.815170	−0.407585	+	0.913167i	$0.633629\pi$
$72$	4756.76	0.108138
$73$	−31175.2	−0.684703	−0.342351	−	0.939572i	$-0.611223\pi$
$73$	−31175.2	−0.684703	−0.342351	+	0.939572i	$0.611223\pi$
$74$	−109584.	−2.32631
$75$	−19819.4	−0.406852
$76$	78829.3	1.56550
$77$	119501.	2.29691
$78$	−67756.2	−1.26099
$79$	−72100.3	−1.29978	−0.649889	−	0.760029i	$-0.725185\pi$
$79$	−72100.3	−1.29978	−0.649889	+	0.760029i	$0.725185\pi$
$80$	22854.9	0.399259
$81$	6561.00	0.111111
$82$	89706.8	1.47330
$83$	31482.3	0.501616	0.250808	−	0.968037i	$-0.419304\pi$
$83$	31482.3	0.501616	0.250808	+	0.968037i	$0.419304\pi$
$84$	−69324.3	−1.07198
$85$	−33052.9	−0.496206
$86$	62312.7	0.908512
$87$	22673.7	0.321161
$88$	−35505.4	−0.488751
$89$	101434.	1.35740	0.678702	−	0.734414i	$-0.262543\pi$
$89$	101434.	1.35740	0.678702	+	0.734414i	$0.262543\pi$
$90$	−20729.6	−0.269764
$91$	176632.	2.23597
$92$	51599.0	0.635583
$93$	79039.2	0.947622
$94$	−197378.	−2.30398
$95$	−61448.7	−0.698560
$96$	−73955.2	−0.819012
$97$	−182378.	−1.96808	−0.984042	−	0.177938i	$-0.943057\pi$
$97$	−182378.	−1.96808	−0.984042	+	0.177938i	$0.943057\pi$
$98$	187525.	1.97239
$99$	−48972.6	−0.502187
$100$	−85819.7	−0.858197
$101$	−103804.	−1.01253	−0.506267	−	0.862377i	$-0.668975\pi$
$101$	−103804.	−1.01253	−0.506267	+	0.862377i	$0.668975\pi$
$102$	82494.8	0.785102
$103$	−106395.	−0.988166	−0.494083	−	0.869415i	$-0.664496\pi$
$103$	−106395.	−0.988166	−0.494083	+	0.869415i	$0.664496\pi$
$104$	−52479.8	−0.475783
$105$	54039.4	0.478341
$106$	−147126.	−1.27182
$107$	−53771.6	−0.454039	−0.227020	−	0.973890i	$-0.572898\pi$
$107$	−53771.6	−0.454039	−0.227020	+	0.973890i	$0.572898\pi$
$108$	28409.8	0.234373
$109$	114408.	0.922336	0.461168	−	0.887313i	$-0.347431\pi$
$109$	114408.	0.922336	0.461168	+	0.887313i	$0.347431\pi$
$110$	154730.	1.21925
$111$	−117071.	−0.901864
$112$	148702.	1.12014
$113$	53614.8	0.394992	0.197496	−	0.980304i	$-0.436719\pi$
$113$	53614.8	0.394992	0.197496	+	0.980304i	$0.436719\pi$
$114$	153366.	1.10527
$115$	−40222.3	−0.283610
$116$	98179.1	0.677445
$117$	−72385.5	−0.488863
$118$	29325.4	0.193883
$119$	−215054.	−1.39213
$120$	−16055.9	−0.101784
$121$	204490.	1.26972
$122$	−99366.9	−0.604425
$123$	95835.8	0.571170
$124$	342247.	1.99888
$125$	161830.	0.926372
$126$	−134874.	−0.756836
$127$	109149.	0.600496	0.300248	−	0.953861i	$-0.402931\pi$
$127$	109149.	0.600496	0.300248	+	0.953861i	$0.402931\pi$
$128$	−117416.	−0.633435
$129$	66570.1	0.352213
$130$	228703.	1.18690
$131$	−236500.	−1.20407	−0.602037	−	0.798468i	$-0.705644\pi$
$131$	−236500.	−1.20407	−0.602037	+	0.798468i	$0.705644\pi$
$132$	−212056.	−1.05929
$133$	−399807.	−1.95984
$134$	−395910.	−1.90474
$135$	−22145.9	−0.104582
$136$	63895.4	0.296226
$137$	−106227.	−0.483542	−0.241771	−	0.970333i	$-0.577728\pi$
$137$	−106227.	−0.483542	−0.241771	+	0.970333i	$0.577728\pi$
$138$	100389.	0.448731
$139$	422871.	1.85640	0.928199	−	0.372084i	$-0.121357\pi$
$139$	422871.	1.85640	0.928199	+	0.372084i	$0.121357\pi$
$140$	233996.	1.00899
$141$	−210864.	−0.893210
$142$	−291698.	−1.21398
$143$	540300.	2.20950
$144$	−60939.5	−0.244902
$145$	−76532.2	−0.302290
$146$	−262633.	−1.01969
$147$	200337.	0.764658
$148$	−506928.	−1.90236
$149$	15495.1	0.0571781	0.0285891	−	0.999591i	$-0.490899\pi$
$149$	15495.1	0.0571781	0.0285891	+	0.999591i	$0.490899\pi$
$150$	−166967.	−0.605901
$151$	309025.	1.10294	0.551469	−	0.834195i	$-0.314067\pi$
$151$	309025.	1.10294	0.551469	+	0.834195i	$0.314067\pi$
$152$	118788.	0.417027
$153$	88131.1	0.304369
$154$	1.00673e6	3.42066
$155$	−266787.	−0.891941
$156$	−313436.	−1.03119
$157$	505383.	1.63633	0.818166	−	0.574982i	$-0.194991\pi$
$157$	505383.	1.63633	0.818166	+	0.574982i	$0.194991\pi$
$158$	−607403.	−1.93568
$159$	−157178.	−0.493061
$160$	249627.	0.770888
$161$	−261701.	−0.795683
$162$	55272.6	0.165471
$163$	48063.9	0.141694	0.0708468	−	0.997487i	$-0.477430\pi$
$163$	48063.9	0.141694	0.0708468	+	0.997487i	$0.477430\pi$
$164$	414978.	1.20480
$165$	165301.	0.472679
$166$	265220.	0.747028
$167$	−609677.	−1.69164	−0.845821	−	0.533467i	$-0.820889\pi$
$167$	−609677.	−1.69164	−0.845821	+	0.533467i	$0.820889\pi$
$168$	−104465.	−0.285561
$169$	427314.	1.15088
$170$	−278451.	−0.738970
$171$	163845.	0.428492
$172$	288255.	0.742943
$173$	679574.	1.72632	0.863160	−	0.504930i	$-0.168482\pi$
$173$	679574.	1.72632	0.863160	+	0.504930i	$0.168482\pi$
$174$	191012.	0.478287
$175$	435262.	1.07437
$176$	454865.	1.10688
$177$	31329.0	0.0751646
$178$	854524.	2.02150
$179$	−47499.1	−0.110803	−0.0554017	−	0.998464i	$-0.517644\pi$
$179$	−47499.1	−0.110803	−0.0554017	+	0.998464i	$0.517644\pi$
$180$	−95893.7	−0.220602
$181$	−520.636	−0.00118124	−0.000590619	−	1.00000i	$-0.500188\pi$
$181$	−520.636	−0.00118124	−0.000590619		1.00000i	$0.500188\pi$
$182$	1.48802e6	3.32990
$183$	−106156.	−0.234324
$184$	77754.9	0.169310
$185$	395159.	0.848872
$186$	665860.	1.41124
$187$	−657828.	−1.37565
$188$	−913059.	−1.88410
$189$	−144089.	−0.293411
$190$	−517670.	−1.04032
$191$	630499.	1.25055	0.625275	−	0.780405i	$-0.284987\pi$
$191$	630499.	1.25055	0.625275	+	0.780405i	$0.284987\pi$
$192$	−406355.	−0.795523
$193$	338210.	0.653572	0.326786	−	0.945098i	$-0.394034\pi$
$193$	338210.	0.653572	0.326786	+	0.945098i	$0.394034\pi$
$194$	−1.53643e6	−2.93095
$195$	244328.	0.460137
$196$	867477.	1.61294
$197$	−968902.	−1.77875	−0.889373	−	0.457181i	$-0.848859\pi$
$197$	−968902.	−1.77875	−0.889373	+	0.457181i	$0.848859\pi$
$198$	−412566.	−0.747877
$199$	−287993.	−0.515525	−0.257763	−	0.966208i	$-0.582985\pi$
$199$	−287993.	−0.515525	−0.257763	+	0.966208i	$0.582985\pi$
$200$	−129322.	−0.228611
$201$	−422960.	−0.738430
$202$	−874486.	−1.50791
$203$	−497946.	−0.848090
$204$	381616.	0.642024
$205$	−323482.	−0.537608
$206$	−896320.	−1.47162
$207$	107247.	0.173965
$208$	672327.	1.07751
$209$	−1.22297e6	−1.93665
$210$	455251.	0.712365
$211$	881159.	1.36254	0.681268	−	0.732034i	$-0.261429\pi$
$211$	881159.	1.36254	0.681268	+	0.732034i	$0.261429\pi$
$212$	−680598.	−1.04004
$213$	−311628.	−0.470638
$214$	−452994.	−0.676174
$215$	−224699.	−0.331517
$216$	42810.8	0.0624337
$217$	−1.73581e6	−2.50238
$218$	963819.	1.37358
$219$	−280577.	−0.395313
$220$	715770.	0.997049
$221$	−972323.	−1.33915
$222$	−986254.	−1.34309
$223$	−1.14135e6	−1.53694	−0.768468	−	0.639889i	$-0.778980\pi$
$223$	−1.14135e6	−1.53694	−0.768468	+	0.639889i	$0.778980\pi$
$224$	1.62416e6	2.16276
$225$	−178374.	−0.234896
$226$	451673.	0.588238
$227$	−640098.	−0.824483	−0.412242	−	0.911075i	$-0.635254\pi$
$227$	−640098.	−0.824483	−0.412242	+	0.911075i	$0.635254\pi$
$228$	709464.	0.903843
$229$	711235.	0.896241	0.448120	−	0.893973i	$-0.352094\pi$
$229$	711235.	0.896241	0.448120	+	0.893973i	$0.352094\pi$
$230$	−338850.	−0.422364
$231$	1.07551e6	1.32612
$232$	147947.	0.180462
$233$	−309299.	−0.373240	−0.186620	−	0.982432i	$-0.559753\pi$
$233$	−309299.	−0.373240	−0.186620	+	0.982432i	$0.559753\pi$
$234$	−609806.	−0.728034
$235$	711744.	0.840726
$236$	135658.	0.158549
$237$	−648903.	−0.750428
$238$	−1.81170e6	−2.07322
$239$	−826348.	−0.935768	−0.467884	−	0.883790i	$-0.654983\pi$
$239$	−826348.	−0.935768	−0.467884	+	0.883790i	$0.654983\pi$
$240$	205694.	0.230512
$241$	−1.26956e6	−1.40802	−0.704011	−	0.710189i	$-0.748609\pi$
$241$	−1.26956e6	−1.40802	−0.704011	+	0.710189i	$0.748609\pi$
$242$	1.72271e6	1.89092
$243$	59049.0	0.0641500
$244$	−459665.	−0.494273
$245$	−676213.	−0.719728
$246$	807361.	0.850609
$247$	−1.80765e6	−1.88526
$248$	515734.	0.532472
$249$	283341.	0.289608
$250$	1.36333e6	1.37959
$251$	147810.	0.148088	0.0740441	−	0.997255i	$-0.476409\pi$
$251$	147810.	0.148088	0.0740441	+	0.997255i	$0.476409\pi$
$252$	−623919.	−0.618909
$253$	−800516.	−0.786264
$254$	919516.	0.894283
$255$	−297476.	−0.286485
$256$	455658.	0.434549
$257$	−855931.	−0.808362	−0.404181	−	0.914679i	$-0.632443\pi$
$257$	−855931.	−0.808362	−0.404181	+	0.914679i	$0.632443\pi$
$258$	560815.	0.524530
$259$	2.57104e6	2.38155
$260$	1.05797e6	0.970595
$261$	204063.	0.185423
$262$	−1.99238e6	−1.79316
$263$	−1.75000e6	−1.56009	−0.780044	−	0.625725i	$-0.784803\pi$
$263$	−1.75000e6	−1.56009	−0.780044	+	0.625725i	$0.784803\pi$
$264$	−319548.	−0.282180
$265$	530537.	0.464089
$266$	−3.36814e6	−2.91868
$267$	912907.	0.783698
$268$	−1.83146e6	−1.55761
$269$	193488.	0.163032	0.0815161	−	0.996672i	$-0.474024\pi$
$269$	193488.	0.163032	0.0815161	+	0.996672i	$0.474024\pi$
$270$	−186566.	−0.155748
$271$	−106308.	−0.0879308	−0.0439654	−	0.999033i	$-0.513999\pi$
$271$	−106308.	−0.0879308	−0.0439654	+	0.999033i	$0.513999\pi$
$272$	−818574.	−0.670866
$273$	1.58969e6	1.29094
$274$	−894903.	−0.720111
$275$	1.33142e6	1.06166
$276$	464391.	0.366954
$277$	1.54305e6	1.20832	0.604159	−	0.796864i	$-0.293509\pi$
$277$	1.54305e6	1.20832	0.604159	+	0.796864i	$0.293509\pi$
$278$	3.56244e6	2.76462
$279$	711353.	0.547110
$280$	352610.	0.268781
$281$	−527848.	−0.398789	−0.199394	−	0.979919i	$-0.563897\pi$
$281$	−527848.	−0.398789	−0.199394	+	0.979919i	$0.563897\pi$
$282$	−1.77640e6	−1.33021
$283$	1.29156e6	0.958628	0.479314	−	0.877644i	$-0.340886\pi$
$283$	1.29156e6	0.958628	0.479314	+	0.877644i	$0.340886\pi$
$284$	−1.34938e6	−0.992745
$285$	−553039.	−0.403314
$286$	4.55171e6	3.29048
$287$	−2.10469e6	−1.50829
$288$	−665596.	−0.472857
$289$	−236031.	−0.166236
$290$	−644739.	−0.450183
$291$	−1.64140e6	−1.13627
$292$	−1.21492e6	−0.833858
$293$	−1.09687e6	−0.746422	−0.373211	−	0.927746i	$-0.621743\pi$
$293$	−1.09687e6	−0.746422	−0.373211	+	0.927746i	$0.621743\pi$
$294$	1.68772e6	1.13876
$295$	−105747.	−0.0707480
$296$	−763892.	−0.506760
$297$	−440753.	−0.289938
$298$	130538.	0.0851520
$299$	−1.18323e6	−0.765403
$300$	−772378.	−0.495480
$301$	−1.46197e6	−0.930087
$302$	2.60336e6	1.64254
$303$	−934233.	−0.584586
$304$	−1.52182e6	−0.944448
$305$	358317.	0.220555
$306$	742453.	0.453279
$307$	813798.	0.492800	0.246400	−	0.969168i	$-0.420752\pi$
$307$	813798.	0.492800	0.246400	+	0.969168i	$0.420752\pi$
$308$	4.65705e6	2.79727
$309$	−957559.	−0.570518
$310$	−2.24753e6	−1.32832
$311$	−1.55418e6	−0.911169	−0.455585	−	0.890192i	$-0.650570\pi$
$311$	−1.55418e6	−0.911169	−0.455585	+	0.890192i	$0.650570\pi$
$312$	−472318.	−0.274693
$313$	1.15183e6	0.664548	0.332274	−	0.943183i	$-0.392184\pi$
$313$	1.15183e6	0.664548	0.332274	+	0.943183i	$0.392184\pi$
$314$	4.25756e6	2.43689
$315$	486355.	0.276170
$316$	−2.80981e6	−1.58292
$317$	−159930.	−0.0893888	−0.0446944	−	0.999001i	$-0.514231\pi$
$317$	−159930.	−0.0893888	−0.0446944	+	0.999001i	$0.514231\pi$
$318$	−1.32414e6	−0.734286
$319$	−1.52317e6	−0.838051
$320$	1.37160e6	0.748779
$321$	−483944.	−0.262140
$322$	−2.20468e6	−1.18496
$323$	2.20086e6	1.17378
$324$	255688.	0.135315
$325$	1.96795e6	1.03349
$326$	404911.	0.211016
$327$	1.02967e6	0.532511
$328$	625333.	0.320942
$329$	4.63086e6	2.35870
$330$	1.39257e6	0.703932
$331$	−547660.	−0.274752	−0.137376	−	0.990519i	$-0.543867\pi$
$331$	−547660.	−0.274752	−0.137376	+	0.990519i	$0.543867\pi$
$332$	1.22689e6	0.610888
$333$	−1.05364e6	−0.520692
$334$	−5.13617e6	−2.51926
$335$	1.42765e6	0.695041
$336$	1.33832e6	0.646713
$337$	1.00634e6	0.482693	0.241347	−	0.970439i	$-0.422411\pi$
$337$	1.00634e6	0.482693	0.241347	+	0.970439i	$0.422411\pi$
$338$	3.59987e6	1.71394
$339$	482533.	0.228049
$340$	−1.28810e6	−0.604299
$341$	−5.30968e6	−2.47276
$342$	1.38030e6	0.638128
$343$	−1.07773e6	−0.494624
$344$	434373.	0.197909
$345$	−362001.	−0.163743
$346$	5.72502e6	2.57091
$347$	−306742.	−0.136757	−0.0683786	−	0.997659i	$-0.521783\pi$
$347$	−306742.	−0.136757	−0.0683786	+	0.997659i	$0.521783\pi$
$348$	883612.	0.391123
$349$	570494.	0.250719	0.125360	−	0.992111i	$-0.459992\pi$
$349$	570494.	0.250719	0.125360	+	0.992111i	$0.459992\pi$
$350$	3.66683e6	1.60000
$351$	−651469.	−0.282245
$352$	4.96814e6	2.13716
$353$	−906528.	−0.387208	−0.193604	−	0.981080i	$-0.562018\pi$
$353$	−906528.	−0.387208	−0.193604	+	0.981080i	$0.562018\pi$
$354$	263929.	0.111938
$355$	1.05186e6	0.442984
$356$	3.95298e6	1.65310
$357$	−1.93548e6	−0.803746
$358$	−400153.	−0.165013
$359$	3.49718e6	1.43213	0.716065	−	0.698034i	$-0.245942\pi$
$359$	3.49718e6	1.43213	0.716065	+	0.698034i	$0.245942\pi$
$360$	−144503.	−0.0587651
$361$	1.61552e6	0.652447
$362$	−4386.05	−0.00175915
$363$	1.84041e6	0.733075
$364$	6.88350e6	2.72305
$365$	947053.	0.372085
$366$	−894302.	−0.348965
$367$	848113.	0.328692	0.164346	−	0.986403i	$-0.447449\pi$
$367$	848113.	0.328692	0.164346	+	0.986403i	$0.447449\pi$
$368$	−996130.	−0.383439
$369$	862523.	0.329765
$370$	3.32898e6	1.26417
$371$	3.45186e6	1.30202
$372$	3.08023e6	1.15405
$373$	269484.	0.100291	0.0501455	−	0.998742i	$-0.484032\pi$
$373$	269484.	0.100291	0.0501455	+	0.998742i	$0.484032\pi$
$374$	−5.54182e6	−2.04868
$375$	1.45647e6	0.534841
$376$	−1.37589e6	−0.501898
$377$	−2.25136e6	−0.815816
$378$	−1.21387e6	−0.436959
$379$	−4.75548e6	−1.70058	−0.850289	−	0.526316i	$-0.823573\pi$
$379$	−4.75548e6	−1.70058	−0.850289	+	0.526316i	$0.823573\pi$
$380$	−2.39471e6	−0.850734
$381$	982340.	0.346696
$382$	5.31159e6	1.86237
$383$	−5.52910e6	−1.92600	−0.963002	−	0.269493i	$-0.913144\pi$
$383$	−5.52910e6	−1.92600	−0.963002	+	0.269493i	$0.913144\pi$
$384$	−1.05674e6	−0.365714
$385$	−3.63025e6	−1.24820
$386$	2.84922e6	0.973326
$387$	599131.	0.203350
$388$	−7.10743e6	−2.39681
$389$	1.57117e6	0.526440	0.263220	−	0.964736i	$-0.415215\pi$
$389$	1.57117e6	0.526440	0.263220	+	0.964736i	$0.415215\pi$
$390$	2.05833e6	0.685256
$391$	1.44061e6	0.476545
$392$	1.30721e6	0.429664
$393$	−2.12850e6	−0.695172
$394$	−8.16243e6	−2.64898
$395$	2.19029e6	0.706333
$396$	−1.90850e6	−0.611583
$397$	1.51249e6	0.481632	0.240816	−	0.970571i	$-0.422585\pi$
$397$	1.51249e6	0.481632	0.240816	+	0.970571i	$0.422585\pi$
$398$	−2.42618e6	−0.767741
$399$	−3.59827e6	−1.13152
$400$	1.65677e6	0.517740
$401$	533958.	0.165824	0.0829118	−	0.996557i	$-0.473578\pi$
$401$	533958.	0.165824	0.0829118	+	0.996557i	$0.473578\pi$
$402$	−3.56319e6	−1.09970
$403$	−7.84814e6	−2.40715
$404$	−4.04532e6	−1.23310
$405$	−199313.	−0.0603806
$406$	−4.19490e6	−1.26301
$407$	7.86456e6	2.35336
$408$	575059.	0.171026
$409$	5.73488e6	1.69518	0.847591	−	0.530650i	$-0.178052\pi$
$409$	5.73488e6	1.69518	0.847591	+	0.530650i	$0.178052\pi$
$410$	−2.72515e6	−0.800628
$411$	−956045.	−0.279173
$412$	−4.14632e6	−1.20343
$413$	−688030.	−0.198487
$414$	903497.	0.259075
$415$	−956384.	−0.272591
$416$	7.34332e6	2.08046
$417$	3.80584e6	1.07179
$418$	−1.03028e7	−2.88413
$419$	3.45104e6	0.960318	0.480159	−	0.877182i	$-0.340579\pi$
$419$	3.45104e6	0.960318	0.480159	+	0.877182i	$0.340579\pi$
$420$	2.10596e6	0.582542
$421$	−1.93686e6	−0.532590	−0.266295	−	0.963892i	$-0.585800\pi$
$421$	−1.93686e6	−0.532590	−0.266295	+	0.963892i	$0.585800\pi$
$422$	7.42325e6	2.02914
$423$	−1.89777e6	−0.515695
$424$	−1.02560e6	−0.277052
$425$	−2.39602e6	−0.643456
$426$	−2.62528e6	−0.700894
$427$	2.33134e6	0.618778
$428$	−2.09552e6	−0.552947
$429$	4.86270e6	1.27566
$430$	−1.89296e6	−0.493709
$431$	−727579.	−0.188663	−0.0943315	−	0.995541i	$-0.530071\pi$
$431$	−727579.	−0.188663	−0.0943315	+	0.995541i	$0.530071\pi$
$432$	−548456.	−0.141394
$433$	108435.	0.0277938	0.0138969	−	0.999903i	$-0.495576\pi$
$433$	108435.	0.0277938	0.0138969	+	0.999903i	$0.495576\pi$
$434$	−1.46232e7	−3.72665
$435$	−688790.	−0.174527
$436$	4.45857e6	1.12326
$437$	2.67824e6	0.670882
$438$	−2.36370e6	−0.588717
$439$	−1.97340e6	−0.488712	−0.244356	−	0.969686i	$-0.578577\pi$
$439$	−1.97340e6	−0.488712	−0.244356	+	0.969686i	$0.578577\pi$
$440$	1.07860e6	0.265600
$441$	1.80303e6	0.441476
$442$	−8.19125e6	−1.99432
$443$	6.75043e6	1.63426	0.817131	−	0.576452i	$-0.195563\pi$
$443$	6.75043e6	1.63426	0.817131	+	0.576452i	$0.195563\pi$
$444$	−4.56235e6	−1.09833
$445$	−3.08141e6	−0.737648
$446$	−9.61519e6	−2.28887
$447$	139456.	0.0330118
$448$	8.92414e6	2.10074
$449$	−2.44220e6	−0.571697	−0.285849	−	0.958275i	$-0.592275\pi$
$449$	−2.44220e6	−0.571697	−0.285849	+	0.958275i	$0.592275\pi$
$450$	−1.50270e6	−0.349817
$451$	−6.43804e6	−1.49043
$452$	2.08941e6	0.481037
$453$	2.78122e6	0.636782
$454$	−5.39245e6	−1.22785
$455$	−5.36580e6	−1.21508
$456$	1.06909e6	0.240771
$457$	7.55416e6	1.69198	0.845991	−	0.533197i	$-0.179010\pi$
$457$	7.55416e6	1.69198	0.845991	+	0.533197i	$0.179010\pi$
$458$	5.99175e6	1.33472
$459$	793180.	0.175728
$460$	−1.56750e6	−0.345392
$461$	4.16445e6	0.912652	0.456326	−	0.889813i	$-0.349165\pi$
$461$	4.16445e6	0.912652	0.456326	+	0.889813i	$0.349165\pi$
$462$	9.06053e6	1.97492
$463$	1.76553e6	0.382757	0.191378	−	0.981516i	$-0.438704\pi$
$463$	1.76553e6	0.382757	0.191378	+	0.981516i	$0.438704\pi$
$464$	−1.89537e6	−0.408694
$465$	−2.40109e6	−0.514962
$466$	−2.60566e6	−0.555845
$467$	−7.17957e6	−1.52337	−0.761686	−	0.647946i	$-0.775628\pi$
$467$	−7.17957e6	−1.52337	−0.761686	+	0.647946i	$0.775628\pi$
$468$	−2.82092e6	−0.595356
$469$	9.28881e6	1.94997
$470$	5.99603e6	1.25204
$471$	4.54845e6	0.944737
$472$	204423.	0.0422352
$473$	−4.47203e6	−0.919078
$474$	−5.46663e6	−1.11757
$475$	−4.45446e6	−0.905860
$476$	−8.38083e6	−1.69539
$477$	−1.41461e6	−0.284669
$478$	−6.96150e6	−1.39358
$479$	−3.33708e6	−0.664549	−0.332275	−	0.943183i	$-0.607816\pi$
$479$	−3.33708e6	−0.664549	−0.332275	+	0.943183i	$0.607816\pi$
$480$	2.24664e6	0.445072
$481$	1.16245e7	2.29092
$482$	−1.06953e7	−2.09688
$483$	−2.35531e6	−0.459388
$484$	7.96916e6	1.54632
$485$	5.54036e6	1.06951
$486$	497454.	0.0955349
$487$	5.15101e6	0.984170	0.492085	−	0.870547i	$-0.336235\pi$
$487$	5.15101e6	0.984170	0.492085	+	0.870547i	$0.336235\pi$
$488$	−692672.	−0.131667
$489$	432575.	0.0818068
$490$	−5.69670e6	−1.07185
$491$	−2.53964e6	−0.475410	−0.237705	−	0.971337i	$-0.576395\pi$
$491$	−2.53964e6	−0.475410	−0.237705	+	0.971337i	$0.576395\pi$
$492$	3.73480e6	0.695593
$493$	2.74109e6	0.507932
$494$	−1.52284e7	−2.80761
$495$	1.48771e6	0.272901
$496$	−6.60715e6	−1.20590
$497$	6.84379e6	1.24281
$498$	2.38698e6	0.431297
$499$	−2.87671e6	−0.517184	−0.258592	−	0.965987i	$-0.583259\pi$
$499$	−2.87671e6	−0.517184	−0.258592	+	0.965987i	$0.583259\pi$
$500$	6.30667e6	1.12817
$501$	−5.48709e6	−0.976670
$502$	1.24522e6	0.220539
$503$	−7.87525e6	−1.38786	−0.693928	−	0.720044i	$-0.744122\pi$
$503$	−7.87525e6	−1.38786	−0.693928	+	0.720044i	$0.744122\pi$
$504$	−940186.	−0.164868
$505$	3.15339e6	0.550237
$506$	−6.74388e6	−1.17094
$507$	3.84582e6	0.664461
$508$	4.25362e6	0.731307
$509$	5.21697e6	0.892532	0.446266	−	0.894900i	$-0.352753\pi$
$509$	5.21697e6	0.892532	0.446266	+	0.894900i	$0.352753\pi$
$510$	−2.50606e6	−0.426645
$511$	6.16187e6	1.04390
$512$	7.59596e6	1.28058
$513$	1.47460e6	0.247390
$514$	−7.21072e6	−1.20385
$515$	3.23213e6	0.536995
$516$	2.59429e6	0.428938
$517$	1.41653e7	2.33078
$518$	2.16595e7	3.54670
$519$	6.11617e6	0.996692
$520$	1.59425e6	0.258553
$521$	−5.77782e6	−0.932544	−0.466272	−	0.884641i	$-0.654403\pi$
$521$	−5.77782e6	−0.932544	−0.466272	+	0.884641i	$0.654403\pi$
$522$	1.71911e6	0.276139
$523$	−4.06016e6	−0.649067	−0.324533	−	0.945874i	$-0.605207\pi$
$523$	−4.06016e6	−0.649067	−0.324533	+	0.945874i	$0.605207\pi$
$524$	−9.21661e6	−1.46637
$525$	3.91735e6	0.620290
$526$	−1.47427e7	−2.32335
$527$	9.55530e6	1.49871
$528$	4.09378e6	0.639058
$529$	−4.68326e6	−0.727627
$530$	4.46947e6	0.691140
$531$	281961.	0.0433963
$532$	−1.55808e7	−2.38678
$533$	−9.51594e6	−1.45089
$534$	7.69072e6	1.16711
$535$	1.63350e6	0.246737
$536$	−2.75983e6	−0.414926
$537$	−427492.	−0.0639724
$538$	1.63002e6	0.242794
$539$	−1.34582e7	−1.99533
$540$	−863043.	−0.127364
$541$	4.55205e6	0.668672	0.334336	−	0.942454i	$-0.391488\pi$
$541$	4.55205e6	0.668672	0.334336	+	0.942454i	$0.391488\pi$
$542$	−895580.	−0.130950
$543$	−4685.72	−0.000681988 0
$544$	−8.94067e6	−1.29531
$545$	−3.47553e6	−0.501221
$546$	1.33922e7	1.92252
$547$	1.31265e6	0.187578	0.0937889	−	0.995592i	$-0.470102\pi$
$547$	1.31265e6	0.187578	0.0937889	+	0.995592i	$0.470102\pi$
$548$	−4.13977e6	−0.588877
$549$	−955404.	−0.135287
$550$	1.12164e7	1.58106
$551$	5.09597e6	0.715069
$552$	699794.	0.0977513
$553$	1.42508e7	1.98165
$554$	1.29993e7	1.79948
$555$	3.55643e6	0.490096
$556$	1.64796e7	2.26079
$557$	−8.08811e6	−1.10461	−0.552305	−	0.833642i	$-0.686252\pi$
$557$	−8.08811e6	−1.10461	−0.552305	+	0.833642i	$0.686252\pi$
$558$	5.99274e6	0.814779
$559$	−6.61003e6	−0.894692
$560$	−4.51734e6	−0.608713
$561$	−5.92045e6	−0.794232
$562$	−4.44681e6	−0.593893
$563$	606847.	0.0806878	0.0403439	−	0.999186i	$-0.487155\pi$
$563$	606847.	0.0806878	0.0403439	+	0.999186i	$0.487155\pi$
$564$	−8.21753e6	−1.08779
$565$	−1.62873e6	−0.214649
$566$	1.08807e7	1.42763
$567$	−1.29680e6	−0.169401
$568$	−2.03339e6	−0.264453
$569$	−5.04180e6	−0.652837	−0.326418	−	0.945225i	$-0.605842\pi$
$569$	−5.04180e6	−0.652837	−0.326418	+	0.945225i	$0.605842\pi$
$570$	−4.65903e6	−0.600632
$571$	−9.40238e6	−1.20683	−0.603417	−	0.797426i	$-0.706194\pi$
$571$	−9.40238e6	−1.20683	−0.603417	+	0.797426i	$0.706194\pi$
$572$	2.10559e7	2.69082
$573$	5.67449e6	0.722005
$574$	−1.77308e7	−2.24620
$575$	−2.91574e6	−0.367773
$576$	−3.65720e6	−0.459296
$577$	−430213.	−0.0537953	−0.0268977	−	0.999638i	$-0.508563\pi$
$577$	−430213.	−0.0537953	−0.0268977	+	0.999638i	$0.508563\pi$
$578$	−1.98842e6	−0.247565
$579$	3.04389e6	0.377340
$580$	−2.98252e6	−0.368141
$581$	−6.22257e6	−0.764768
$582$	−1.38279e7	−1.69219
$583$	1.05589e7	1.28661
$584$	−1.83077e6	−0.222128
$585$	2.19896e6	0.265660
$586$	−9.24046e6	−1.11160
$587$	6.88680e6	0.824940	0.412470	−	0.910971i	$-0.364666\pi$
$587$	6.88680e6	0.824940	0.412470	+	0.910971i	$0.364666\pi$
$588$	7.80730e6	0.931231
$589$	1.77643e7	2.10989
$590$	−890859.	−0.105361
$591$	−8.72012e6	−1.02696
$592$	9.78634e6	1.14767
$593$	1.50380e7	1.75612	0.878059	−	0.478552i	$-0.158838\pi$
$593$	1.50380e7	1.75612	0.878059	+	0.478552i	$0.158838\pi$
$594$	−3.71309e6	−0.431787
$595$	6.53299e6	0.756519
$596$	603859.	0.0696337
$597$	−2.59194e6	−0.297639
$598$	−9.96800e6	−1.13987
$599$	−9.04381e6	−1.02987	−0.514937	−	0.857228i	$-0.672185\pi$
$599$	−9.04381e6	−1.02987	−0.514937	+	0.857228i	$0.672185\pi$
$600$	−1.16390e6	−0.131989
$601$	4.79275e6	0.541250	0.270625	−	0.962685i	$-0.412770\pi$
$601$	4.79275e6	0.541250	0.270625	+	0.962685i	$0.412770\pi$
$602$	−1.23163e7	−1.38512
$603$	−3.80664e6	−0.426333
$604$	1.20430e7	1.34320
$605$	−6.21209e6	−0.690000
$606$	−7.87037e6	−0.870590
$607$	−8.02372e6	−0.883902	−0.441951	−	0.897039i	$-0.645713\pi$
$607$	−8.02372e6	−0.883902	−0.441951	+	0.897039i	$0.645713\pi$
$608$	−1.66216e7	−1.82354
$609$	−4.48151e6	−0.489645
$610$	3.01861e6	0.328460
$611$	2.09375e7	2.26894
$612$	3.43454e6	0.370672
$613$	−1.08600e7	−1.16729	−0.583645	−	0.812009i	$-0.698374\pi$
$613$	−1.08600e7	−1.16729	−0.583645	+	0.812009i	$0.698374\pi$
$614$	6.85577e6	0.733898
$615$	−2.91134e6	−0.310388
$616$	7.01774e6	0.745153
$617$	328233.	0.0347112	0.0173556	−	0.999849i	$-0.494475\pi$
$617$	328233.	0.0347112	0.0173556	+	0.999849i	$0.494475\pi$
$618$	−8.06688e6	−0.849639
$619$	1.10733e7	1.16159	0.580793	−	0.814051i	$-0.302742\pi$
$619$	1.10733e7	1.16159	0.580793	+	0.814051i	$0.302742\pi$
$620$	−1.03969e7	−1.08624
$621$	965227.	0.100439
$622$	−1.30930e7	−1.35695
$623$	−2.00487e7	−2.06951
$624$	6.05094e6	0.622102
$625$	1.96557e6	0.201274
$626$	9.70348e6	0.989673
$627$	−1.10067e7	−1.11812
$628$	1.96952e7	1.99279
$629$	−1.41531e7	−1.42634
$630$	4.09726e6	0.411284
$631$	8.11446e6	0.811309	0.405654	−	0.914027i	$-0.367044\pi$
$631$	8.11446e6	0.811309	0.405654	+	0.914027i	$0.367044\pi$
$632$	−4.23412e6	−0.421668
$633$	7.93043e6	0.786661
$634$	−1.34732e6	−0.133121
$635$	−3.31577e6	−0.326325
$636$	−6.12538e6	−0.600468
$637$	−1.98923e7	−1.94239
$638$	−1.28318e7	−1.24806
$639$	−2.80465e6	−0.271723
$640$	3.56691e6	0.344225
$641$	−3.81722e6	−0.366946	−0.183473	−	0.983025i	$-0.558734\pi$
$641$	−3.81722e6	−0.366946	−0.183473	+	0.983025i	$0.558734\pi$
$642$	−4.07695e6	−0.390389
$643$	−7.74644e6	−0.738881	−0.369441	−	0.929254i	$-0.620451\pi$
$643$	−7.74644e6	−0.738881	−0.369441	+	0.929254i	$0.620451\pi$
$644$	−1.01987e7	−0.969014
$645$	−2.02230e6	−0.191401
$646$	1.85409e7	1.74804
$647$	60872.6	0.00571691	0.00285845	−	0.999996i	$-0.499090\pi$
$647$	60872.6	0.00571691	0.00285845	+	0.999996i	$0.499090\pi$
$648$	385297.	0.0360461
$649$	−2.10461e6	−0.196137
$650$	1.65788e7	1.53911
$651$	−1.56223e7	−1.44475
$652$	1.87309e6	0.172560
$653$	263078.	0.0241436	0.0120718	−	0.999927i	$-0.496157\pi$
$653$	263078.	0.0241436	0.0120718	+	0.999927i	$0.496157\pi$
$654$	8.67437e6	0.793037
$655$	7.18450e6	0.654324
$656$	−8.01124e6	−0.726842
$657$	−2.52519e6	−0.228234
$658$	3.90123e7	3.51267
$659$	−6.13618e6	−0.550408	−0.275204	−	0.961386i	$-0.588745\pi$
$659$	−6.13618e6	−0.550408	−0.275204	+	0.961386i	$0.588745\pi$
$660$	6.44193e6	0.575647
$661$	5.91533e6	0.526593	0.263297	−	0.964715i	$-0.415190\pi$
$661$	5.91533e6	0.526593	0.263297	+	0.964715i	$0.415190\pi$
$662$	−4.61372e6	−0.409172
$663$	−8.75090e6	−0.773160
$664$	1.84881e6	0.162732
$665$	1.21455e7	1.06503
$666$	−8.87628e6	−0.775435
$667$	3.33565e6	0.290313
$668$	−2.37596e7	−2.06015
$669$	−1.02721e7	−0.887350
$670$	1.20271e7	1.03508
$671$	7.13132e6	0.611454
$672$	1.46174e7	1.24867
$673$	−351835.	−0.0299434	−0.0149717	−	0.999888i	$-0.504766\pi$
$673$	−351835.	−0.0299434	−0.0149717	+	0.999888i	$0.504766\pi$
$674$	8.47785e6	0.718847
$675$	−1.60537e6	−0.135617
$676$	1.66528e7	1.40159
$677$	7.74491e6	0.649449	0.324724	−	0.945809i	$-0.394728\pi$
$677$	7.74491e6	0.649449	0.324724	+	0.945809i	$0.394728\pi$
$678$	4.06506e6	0.339620
$679$	3.60476e7	3.00055
$680$	−1.94104e6	−0.160977
$681$	−5.76088e6	−0.476016
$682$	−4.47310e7	−3.68254
$683$	33771.4	0.00277011	0.00138506	−	0.999999i	$-0.499559\pi$
$683$	33771.4	0.00277011	0.00138506	+	0.999999i	$0.499559\pi$
$684$	6.38517e6	0.521834
$685$	3.22702e6	0.262769
$686$	−9.07925e6	−0.736614
$687$	6.40112e6	0.517445
$688$	−5.56482e6	−0.448208
$689$	1.56069e7	1.25247
$690$	−3.04965e6	−0.243852
$691$	1.03899e6	0.0827782	0.0413891	−	0.999143i	$-0.486822\pi$
$691$	1.03899e6	0.0827782	0.0413891	+	0.999143i	$0.486822\pi$
$692$	2.64836e7	2.10238
$693$	9.67957e6	0.765637
$694$	−2.58413e6	−0.203664
$695$	−1.28462e7	−1.00881
$696$	1.33152e6	0.104190
$697$	1.15859e7	0.903332
$698$	4.80608e6	0.373381
$699$	−2.78369e6	−0.215490
$700$	1.69625e7	1.30841
$701$	−1.05020e7	−0.807194	−0.403597	−	0.914937i	$-0.632240\pi$
$701$	−1.05020e7	−0.807194	−0.403597	+	0.914937i	$0.632240\pi$
$702$	−5.48825e6	−0.420331
$703$	−2.63120e7	−2.00801
$704$	2.72981e7	2.07587
$705$	6.40570e6	0.485393
$706$	−7.63697e6	−0.576646
$707$	2.05171e7	1.54372
$708$	1.22092e6	0.0915384
$709$	−2.35801e7	−1.76169	−0.880847	−	0.473402i	$-0.843026\pi$
$709$	−2.35801e7	−1.76169	−0.880847	+	0.473402i	$0.843026\pi$
$710$	8.86133e6	0.659710
$711$	−5.84013e6	−0.433260
$712$	5.95676e6	0.440362
$713$	1.16279e7	0.856600
$714$	−1.63053e7	−1.19697
$715$	−1.64134e7	−1.20070
$716$	−1.85108e6	−0.134941
$717$	−7.43713e6	−0.540266
$718$	2.94617e7	2.13279
$719$	−1.21771e7	−0.878459	−0.439230	−	0.898375i	$-0.644749\pi$
$719$	−1.21771e7	−0.878459	−0.439230	+	0.898375i	$0.644749\pi$
$720$	1.85125e6	0.133086
$721$	2.10294e7	1.50657
$722$	1.36098e7	0.971650
$723$	−1.14260e7	−0.812922
$724$	−20289.6	−0.00143856
$725$	−5.54787e6	−0.391996
$726$	1.55044e7	1.09173
$727$	1.11269e7	0.780794	0.390397	−	0.920647i	$-0.372338\pi$
$727$	1.11269e7	0.780794	0.390397	+	0.920647i	$0.372338\pi$
$728$	1.03728e7	0.725382
$729$	531441.	0.0370370
$730$	7.97837e6	0.554124
$731$	8.04787e6	0.557041
$732$	−4.13699e6	−0.285369
$733$	−2.36514e7	−1.62591	−0.812955	−	0.582327i	$-0.802143\pi$
$733$	−2.36514e7	−1.62591	−0.812955	+	0.582327i	$0.802143\pi$
$734$	7.14486e6	0.489501
$735$	−6.08592e6	−0.415535
$736$	−1.08800e7	−0.740343
$737$	2.84135e7	1.92689
$738$	7.26625e6	0.491100
$739$	−1.88274e7	−1.26817	−0.634087	−	0.773262i	$-0.718624\pi$
$739$	−1.88274e7	−1.26817	−0.634087	+	0.773262i	$0.718624\pi$
$740$	1.53997e7	1.03379
$741$	−1.62688e7	−1.08846
$742$	2.90800e7	1.93903
$743$	4.04511e6	0.268818	0.134409	−	0.990926i	$-0.457086\pi$
$743$	4.04511e6	0.268818	0.134409	+	0.990926i	$0.457086\pi$
$744$	4.64161e6	0.307423
$745$	−470718.	−0.0310721
$746$	2.27025e6	0.149357
$747$	2.55007e6	0.167205
$748$	−2.56361e7	−1.67532
$749$	1.06281e7	0.692232
$750$	1.22699e7	0.796507
$751$	8.38036e6	0.542204	0.271102	−	0.962551i	$-0.412612\pi$
$751$	8.38036e6	0.542204	0.271102	+	0.962551i	$0.412612\pi$
$752$	1.76268e7	1.13665
$753$	1.33029e6	0.0854987
$754$	−1.89664e7	−1.21495
$755$	−9.38769e6	−0.599365
$756$	−5.61527e6	−0.357327
$757$	1.50776e7	0.956296	0.478148	−	0.878279i	$-0.341308\pi$
$757$	1.50776e7	0.956296	0.478148	+	0.878279i	$0.341308\pi$
$758$	−4.00622e7	−2.53257
$759$	−7.20464e6	−0.453950
$760$	−3.60860e6	−0.226623
$761$	2.51452e6	0.157396	0.0786981	−	0.996898i	$-0.474924\pi$
$761$	2.51452e6	0.157396	0.0786981	+	0.996898i	$0.474924\pi$
$762$	8.27564e6	0.516315
$763$	−2.26130e7	−1.40620
$764$	2.45711e7	1.52297
$765$	−2.67728e6	−0.165402
$766$	−4.65794e7	−2.86829
$767$	−3.11079e6	−0.190933
$768$	4.10092e6	0.250887
$769$	−2.14386e7	−1.30732	−0.653659	−	0.756790i	$-0.726767\pi$
$769$	−2.14386e7	−1.30732	−0.653659	+	0.756790i	$0.726767\pi$
$770$	−3.05827e7	−1.85887
$771$	−7.70338e6	−0.466708
$772$	1.31803e7	0.795945
$773$	8.22664e6	0.495192	0.247596	−	0.968863i	$-0.420359\pi$
$773$	8.22664e6	0.495192	0.247596	+	0.968863i	$0.420359\pi$
$774$	5.04733e6	0.302837
$775$	−1.93396e7	−1.15663
$776$	−1.07102e7	−0.638476
$777$	2.31394e7	1.37499
$778$	1.32362e7	0.783996
$779$	2.15394e7	1.27171
$780$	9.52169e6	0.560373
$781$	2.09345e7	1.22810
$782$	1.21363e7	0.709690
$783$	1.83657e6	0.107054
$784$	−1.67468e7	−0.973066
$785$	−1.53527e7	−0.889225
$786$	−1.79314e7	−1.03528
$787$	8.31927e6	0.478793	0.239397	−	0.970922i	$-0.423050\pi$
$787$	8.31927e6	0.478793	0.239397	+	0.970922i	$0.423050\pi$
$788$	−3.77589e7	−2.16623
$789$	−1.57500e7	−0.900717
$790$	1.84520e7	1.05190
$791$	−1.05971e7	−0.602208
$792$	−2.87593e6	−0.162917
$793$	1.05407e7	0.595231
$794$	1.27418e7	0.717266
$795$	4.77483e6	0.267942
$796$	−1.12234e7	−0.627827
$797$	−648589.	−0.0361679	−0.0180840	−	0.999836i	$-0.505757\pi$
$797$	−648589.	−0.0361679	−0.0180840	+	0.999836i	$0.505757\pi$
$798$	−3.03133e7	−1.68510
$799$	−2.54919e7	−1.41265
$800$	1.80956e7	0.999651
$801$	8.21617e6	0.452468
$802$	4.49829e6	0.246951
$803$	1.88485e7	1.03155
$804$	−1.64831e7	−0.899289
$805$	7.95005e6	0.432395
$806$	−6.61160e7	−3.58483
$807$	1.74139e6	0.0941267
$808$	−6.09591e6	−0.328481
$809$	6.42299e6	0.345037	0.172519	−	0.985006i	$-0.444810\pi$
$809$	6.42299e6	0.345037	0.172519	+	0.985006i	$0.444810\pi$
$810$	−1.67909e6	−0.0899213
$811$	−3.00650e7	−1.60513	−0.802564	−	0.596566i	$-0.796531\pi$
$811$	−3.00650e7	−1.60513	−0.802564	+	0.596566i	$0.796531\pi$
$812$	−1.94054e7	−1.03284
$813$	−956768.	−0.0507669
$814$	6.62543e7	3.50472
$815$	−1.46011e6	−0.0769999
$816$	−7.36717e6	−0.387325
$817$	1.49618e7	0.784205
$818$	4.83131e7	2.52453
$819$	1.43072e7	0.745323
$820$	−1.26064e7	−0.654720
$821$	2.26374e7	1.17211	0.586056	−	0.810271i	$-0.300680\pi$
$821$	2.26374e7	1.17211	0.586056	+	0.810271i	$0.300680\pi$
$822$	−8.05413e6	−0.415756
$823$	−1.72791e7	−0.889245	−0.444622	−	0.895718i	$-0.646662\pi$
$823$	−1.72791e7	−0.889245	−0.444622	+	0.895718i	$0.646662\pi$
$824$	−6.24811e6	−0.320576
$825$	1.19828e7	0.612947
$826$	−5.79625e6	−0.295595
$827$	2.43809e6	0.123961	0.0619805	−	0.998077i	$-0.480258\pi$
$827$	2.43809e6	0.123961	0.0619805	+	0.998077i	$0.480258\pi$
$828$	4.17952e6	0.211861
$829$	−2.40502e7	−1.21544	−0.607718	−	0.794153i	$-0.707915\pi$
$829$	−2.40502e7	−1.21544	−0.607718	+	0.794153i	$0.707915\pi$
$830$	−8.05698e6	−0.405954
$831$	1.38875e7	0.697622
$832$	4.03487e7	2.02079
$833$	2.42193e7	1.20934
$834$	3.20620e7	1.59616
$835$	1.85210e7	0.919281
$836$	−4.76602e7	−2.35852
$837$	6.40218e6	0.315874
$838$	2.90730e7	1.43014
$839$	−2.36128e7	−1.15809	−0.579046	−	0.815295i	$-0.696575\pi$
$839$	−2.36128e7	−1.15809	−0.579046	+	0.815295i	$0.696575\pi$
$840$	3.17349e6	0.155181
$841$	−1.41643e7	−0.690566
$842$	−1.63169e7	−0.793155
$843$	−4.75063e6	−0.230241
$844$	3.43395e7	1.65935
$845$	−1.29811e7	−0.625418
$846$	−1.59876e7	−0.767994
$847$	−4.04181e7	−1.93583
$848$	1.31391e7	0.627444
$849$	1.16241e7	0.553464
$850$	−2.01851e7	−0.958261
$851$	−1.72230e7	−0.815237
$852$	−1.21444e7	−0.573162
$853$	−2.14660e7	−1.01013	−0.505067	−	0.863080i	$-0.668532\pi$
$853$	−2.14660e7	−1.01013	−0.505067	+	0.863080i	$0.668532\pi$
$854$	1.96402e7	0.921510
$855$	−4.97735e6	−0.232853
$856$	−3.15776e6	−0.147297
$857$	1.36770e7	0.636121	0.318060	−	0.948071i	$-0.396969\pi$
$857$	1.36770e7	0.636121	0.318060	+	0.948071i	$0.396969\pi$
$858$	4.09654e7	1.89976
$859$	6.29314e6	0.290994	0.145497	−	0.989359i	$-0.453522\pi$
$859$	6.29314e6	0.290994	0.145497	+	0.989359i	$0.453522\pi$
$860$	−8.75673e6	−0.403734
$861$	−1.89422e7	−0.870809
$862$	−6.12943e6	−0.280965
$863$	5.79993e6	0.265092	0.132546	−	0.991177i	$-0.457685\pi$
$863$	5.79993e6	0.265092	0.132546	+	0.991177i	$0.457685\pi$
$864$	−5.99037e6	−0.273004
$865$	−2.06444e7	−0.938127
$866$	913499.	0.0413917
$867$	−2.12428e6	−0.0959762
$868$	−6.76462e7	−3.04750
$869$	4.35919e7	1.95819
$870$	−5.80265e6	−0.259913
$871$	4.19975e7	1.87576
$872$	6.71864e6	0.299219
$873$	−1.47726e7	−0.656028
$874$	2.25626e7	0.999104
$875$	−3.19862e7	−1.41235
$876$	−1.09343e7	−0.481428
$877$	−1.16101e6	−0.0509728	−0.0254864	−	0.999675i	$-0.508113\pi$
$877$	−1.16101e6	−0.0509728	−0.0254864	+	0.999675i	$0.508113\pi$
$878$	−1.66247e7	−0.727810
$879$	−9.87180e6	−0.430947
$880$	−1.38181e7	−0.601507
$881$	−2.13517e7	−0.926813	−0.463407	−	0.886146i	$-0.653373\pi$
$881$	−2.13517e7	−0.926813	−0.463407	+	0.886146i	$0.653373\pi$
$882$	1.51895e7	0.657464
$883$	2.62499e7	1.13299	0.566495	−	0.824065i	$-0.308299\pi$
$883$	2.62499e7	1.13299	0.566495	+	0.824065i	$0.308299\pi$
$884$	−3.78922e7	−1.63087
$885$	−951725.	−0.0408464
$886$	5.68684e7	2.43381
$887$	−4.59171e7	−1.95959	−0.979795	−	0.200006i	$-0.935904\pi$
$887$	−4.59171e7	−1.95959	−0.979795	+	0.200006i	$0.935904\pi$
$888$	−6.87503e6	−0.292578
$889$	−2.15736e7	−0.915520
$890$	−2.59591e7	−1.09854
$891$	−3.96678e6	−0.167396
$892$	−4.44793e7	−1.87174
$893$	−4.73922e7	−1.98874
$894$	1.17484e6	0.0491625
$895$	1.44295e6	0.0602134
$896$	2.32076e7	0.965740
$897$	−1.06490e7	−0.441906
$898$	−2.05742e7	−0.851395
$899$	2.21248e7	0.913019
$900$	−6.95140e6	−0.286066
$901$	−1.90018e7	−0.779799
$902$	−5.42367e7	−2.21961
$903$	−1.31578e7	−0.536986
$904$	3.14855e6	0.128141
$905$	15816.1	0.000641915 0
$906$	2.34302e7	0.948321
$907$	1.22694e7	0.495229	0.247614	−	0.968859i	$-0.420353\pi$
$907$	1.22694e7	0.495229	0.247614	+	0.968859i	$0.420353\pi$
$908$	−2.49452e7	−1.00409
$909$	−8.40810e6	−0.337511
$910$	−4.52038e7	−1.80955
$911$	−3.04688e7	−1.21635	−0.608175	−	0.793803i	$-0.708098\pi$
$911$	−3.04688e7	−1.21635	−0.608175	+	0.793803i	$0.708098\pi$
$912$	−1.36963e7	−0.545277
$913$	−1.90342e7	−0.755715
$914$	6.36394e7	2.51977
$915$	3.22485e6	0.127338
$916$	2.77174e7	1.09148
$917$	4.67449e7	1.83574
$918$	6.68208e6	0.261701
$919$	1.89310e7	0.739407	0.369704	−	0.929150i	$-0.379459\pi$
$919$	1.89310e7	0.739407	0.369704	+	0.929150i	$0.379459\pi$
$920$	−2.36207e6	−0.0920075
$921$	7.32418e6	0.284518
$922$	3.50831e7	1.35916
$923$	3.09428e7	1.19552
$924$	4.19135e7	1.61500
$925$	2.86453e7	1.10078
$926$	1.48736e7	0.570017
$927$	−8.61803e6	−0.329389
$928$	−2.07016e7	−0.789105
$929$	7.49000e6	0.284736	0.142368	−	0.989814i	$-0.454528\pi$
$929$	7.49000e6	0.284736	0.142368	+	0.989814i	$0.454528\pi$
$930$	−2.02278e7	−0.766903
$931$	4.50263e7	1.70252
$932$	−1.20536e7	−0.454547
$933$	−1.39876e7	−0.526064
$934$	−6.04837e7	−2.26867
$935$	1.99838e7	0.747564
$936$	−4.25086e6	−0.158594
$937$	2.44259e7	0.908871	0.454436	−	0.890780i	$-0.349841\pi$
$937$	2.44259e7	0.908871	0.454436	+	0.890780i	$0.349841\pi$
$938$	7.82528e7	2.90398
$939$	1.03664e7	0.383677
$940$	2.77373e7	1.02387
$941$	−2.74938e7	−1.01219	−0.506094	−	0.862478i	$-0.668911\pi$
$941$	−2.74938e7	−1.01219	−0.506094	+	0.862478i	$0.668911\pi$
$942$	3.83180e7	1.40694
$943$	1.40990e7	0.516307
$944$	−2.61890e6	−0.0956507
$945$	4.37719e6	0.159447
$946$	−3.76743e7	−1.36873
$947$	−2.86619e7	−1.03855	−0.519277	−	0.854606i	$-0.673799\pi$
$947$	−2.86619e7	−1.03855	−0.519277	+	0.854606i	$0.673799\pi$
$948$	−2.52883e7	−0.913900
$949$	2.78596e7	1.00418
$950$	−3.75262e7	−1.34904
$951$	−1.43937e6	−0.0516086
$952$	−1.26291e7	−0.451628
$953$	1.44834e7	0.516580	0.258290	−	0.966067i	$-0.416841\pi$
$953$	1.44834e7	0.516580	0.258290	+	0.966067i	$0.416841\pi$
$954$	−1.19172e7	−0.423940
$955$	−1.91536e7	−0.679581
$956$	−3.22035e7	−1.13961
$957$	−1.37085e7	−0.483849
$958$	−2.81129e7	−0.989674
$959$	2.09961e7	0.737212
$960$	1.23444e7	0.432308
$961$	4.84968e7	1.69397
$962$	9.79293e7	3.41173
$963$	−4.35550e6	−0.151346
$964$	−4.94757e7	−1.71474
$965$	−1.02743e7	−0.355168
$966$	−1.98421e7	−0.684139
$967$	2.23539e7	0.768753	0.384376	−	0.923177i	$-0.374417\pi$
$967$	2.23539e7	0.768753	0.384376	+	0.923177i	$0.374417\pi$
$968$	1.20088e7	0.411917
$969$	1.98077e7	0.677680
$970$	4.66743e7	1.59275
$971$	−5.00533e7	−1.70367	−0.851833	−	0.523814i	$-0.824509\pi$
$971$	−5.00533e7	−1.70367	−0.851833	+	0.523814i	$0.824509\pi$
$972$	2.30119e6	0.0781244
$973$	−8.35817e7	−2.83028
$974$	4.33943e7	1.46567
$975$	1.77115e7	0.596684
$976$	8.87393e6	0.298189
$977$	4.82166e7	1.61607	0.808035	−	0.589134i	$-0.200531\pi$
$977$	4.82166e7	1.61607	0.808035	+	0.589134i	$0.200531\pi$
$978$	3.64419e6	0.121830
$979$	−6.13271e7	−2.04501
$980$	−2.63526e7	−0.876512
$981$	9.26702e6	0.307445
$982$	−2.13950e7	−0.708000
$983$	−3.21582e7	−1.06147	−0.530735	−	0.847538i	$-0.678084\pi$
$983$	−3.21582e7	−1.06147	−0.530735	+	0.847538i	$0.678084\pi$
$984$	5.62800e6	0.185296
$985$	2.94337e7	0.966617
$986$	2.30921e7	0.756433
$987$	4.16778e7	1.36179
$988$	−7.04456e7	−2.29595
$989$	9.79351e6	0.318382
$990$	1.25331e7	0.406416
$991$	−1.12835e7	−0.364972	−0.182486	−	0.983208i	$-0.558414\pi$
$991$	−1.12835e7	−0.364972	−0.182486	+	0.983208i	$0.558414\pi$
$992$	−7.21649e7	−2.32834
$993$	−4.92894e6	−0.158628
$994$	5.76550e7	1.85085
$995$	8.74879e6	0.280150
$996$	1.10420e7	0.352696
$997$	5.30973e7	1.69174	0.845872	−	0.533387i	$-0.179081\pi$
$997$	5.30973e7	1.69174	0.845872	+	0.533387i	$0.179081\pi$
$998$	−2.42346e7	−0.770212
$999$	−9.48274e6	−0.300621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.a.1.11	✓	11
3.2	odd	2		531.6.a.b.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.a.1.11	✓	11	1.1	even	1	trivial
531.6.a.b.1.1		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)

\(f(q)\)	\(=\)	\(q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+8.42442 q^{2} +9.00000 q^{3} +38.9709 q^{4} -30.3784 q^{5} +75.8198 q^{6} -197.653 q^{7} +58.7254 q^{8} +81.0000 q^{9} -255.921 q^{10} -604.600 q^{11} +350.738 q^{12} -893.648 q^{13} -1665.11 q^{14} -273.406 q^{15} -752.340 q^{16} +1088.04 q^{17} +682.378 q^{18} +2022.78 q^{19} -1183.87 q^{20} -1778.88 q^{21} -5093.40 q^{22} +1324.04 q^{23} +528.528 q^{24} -2202.15 q^{25} -7528.47 q^{26} +729.000 q^{27} -7702.70 q^{28} +2519.29 q^{29} -2303.29 q^{30} +8782.14 q^{31} -8217.24 q^{32} -5441.40 q^{33} +9166.09 q^{34} +6004.38 q^{35} +3156.64 q^{36} -13007.9 q^{37} +17040.7 q^{38} -8042.83 q^{39} -1783.98 q^{40} +10648.4 q^{41} -14986.0 q^{42} +7396.68 q^{43} -23561.8 q^{44} -2460.65 q^{45} +11154.3 q^{46} -23429.3 q^{47} -6771.06 q^{48} +22259.6 q^{49} -18551.9 q^{50} +9792.34 q^{51} -34826.2 q^{52} -17464.3 q^{53} +6141.40 q^{54} +18366.8 q^{55} -11607.2 q^{56} +18205.0 q^{57} +21223.6 q^{58} +3481.00 q^{59} -10654.9 q^{60} -11795.1 q^{61} +73984.4 q^{62} -16009.9 q^{63} -45150.6 q^{64} +27147.6 q^{65} -45840.6 q^{66} -46995.6 q^{67} +42401.8 q^{68} +11916.4 q^{69} +50583.4 q^{70} -34625.3 q^{71} +4756.76 q^{72} -31175.2 q^{73} -109584. q^{74} -19819.4 q^{75} +78829.3 q^{76} +119501. q^{77} -67756.2 q^{78} -72100.3 q^{79} +22854.9 q^{80} +6561.00 q^{81} +89706.8 q^{82} +31482.3 q^{83} -69324.3 q^{84} -33052.9 q^{85} +62312.7 q^{86} +22673.7 q^{87} -35505.4 q^{88} +101434. q^{89} -20729.6 q^{90} +176632. q^{91} +51599.0 q^{92} +79039.2 q^{93} -197378. q^{94} -61448.7 q^{95} -73955.2 q^{96} -182378. q^{97} +187525. q^{98} -48972.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 99 q^{3} + 150 q^{4} - 192 q^{5} - 54 q^{6} - 371 q^{7} - 621 q^{8} + 891 q^{9}+O(q^{10}) \) 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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