LMFDB - Embedded newform 177.6.a.c.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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 $ x^12 - 2x^11 - 269x^10 + 143x^9 + 25384x^8 + 8539x^7 - 1009736x^6 - 720516x^5 + 15565376x^4 + 6775664x^3 - 75006848x^2 + 21512960*x + 49172480
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.10256$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10256 q^{2} +9.00000 q^{3} -27.5792 q^{4} -81.1594 q^{5} -18.9230 q^{6} -97.6213 q^{7} +125.269 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-2.10256 q^{2} +9.00000 q^{3} -27.5792 q^{4} -81.1594 q^{5} -18.9230 q^{6} -97.6213 q^{7} +125.269 q^{8} +81.0000 q^{9} +170.642 q^{10} -297.163 q^{11} -248.213 q^{12} -814.611 q^{13} +205.254 q^{14} -730.435 q^{15} +619.151 q^{16} -1275.83 q^{17} -170.307 q^{18} +801.964 q^{19} +2238.32 q^{20} -878.592 q^{21} +624.802 q^{22} +255.443 q^{23} +1127.42 q^{24} +3461.85 q^{25} +1712.77 q^{26} +729.000 q^{27} +2692.32 q^{28} +7410.46 q^{29} +1535.78 q^{30} -2821.92 q^{31} -5310.40 q^{32} -2674.46 q^{33} +2682.51 q^{34} +7922.89 q^{35} -2233.92 q^{36} +4781.71 q^{37} -1686.18 q^{38} -7331.50 q^{39} -10166.7 q^{40} -8224.42 q^{41} +1847.29 q^{42} -1932.60 q^{43} +8195.53 q^{44} -6573.91 q^{45} -537.083 q^{46} +23212.7 q^{47} +5572.36 q^{48} -7277.08 q^{49} -7278.75 q^{50} -11482.5 q^{51} +22466.3 q^{52} +15252.2 q^{53} -1532.76 q^{54} +24117.6 q^{55} -12228.9 q^{56} +7217.68 q^{57} -15580.9 q^{58} -3481.00 q^{59} +20144.8 q^{60} +9488.35 q^{61} +5933.26 q^{62} -7907.33 q^{63} -8647.40 q^{64} +66113.3 q^{65} +5623.22 q^{66} +28014.3 q^{67} +35186.5 q^{68} +2298.98 q^{69} -16658.3 q^{70} -26155.1 q^{71} +10146.8 q^{72} +7782.60 q^{73} -10053.8 q^{74} +31156.7 q^{75} -22117.6 q^{76} +29009.4 q^{77} +15414.9 q^{78} -51295.8 q^{79} -50249.9 q^{80} +6561.00 q^{81} +17292.3 q^{82} +17726.9 q^{83} +24230.9 q^{84} +103546. q^{85} +4063.40 q^{86} +66694.1 q^{87} -37225.2 q^{88} +104423. q^{89} +13822.0 q^{90} +79523.3 q^{91} -7044.92 q^{92} -25397.3 q^{93} -48806.1 q^{94} -65086.9 q^{95} -47793.6 q^{96} -144515. q^{97} +15300.5 q^{98} -24070.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.10256	−0.371683	−0.185842	−	0.982580i	$-0.559501\pi$
$2$	−2.10256	−0.371683	−0.185842	+	0.982580i	$0.559501\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−27.5792	−0.861852
$5$	−81.1594	−1.45182	−0.725912	−	0.687788i	$-0.758582\pi$
$5$	−81.1594	−1.45182	−0.725912	+	0.687788i	$0.758582\pi$
$6$	−18.9230	−0.214591
$7$	−97.6213	−0.753008	−0.376504	−	0.926415i	$-0.622874\pi$
$7$	−97.6213	−0.753008	−0.376504	+	0.926415i	$0.622874\pi$
$8$	125.269	0.692019
$9$	81.0000	0.333333
$10$	170.642	0.539619
$11$	−297.163	−0.740479	−0.370239	−	0.928936i	$-0.620724\pi$
$11$	−297.163	−0.740479	−0.370239	+	0.928936i	$0.620724\pi$
$12$	−248.213	−0.497590
$13$	−814.611	−1.33688	−0.668439	−	0.743767i	$-0.733037\pi$
$13$	−814.611	−1.33688	−0.668439	+	0.743767i	$0.733037\pi$
$14$	205.254	0.279880
$15$	−730.435	−0.838211
$16$	619.151	0.604640
$17$	−1275.83	−1.07071	−0.535355	−	0.844627i	$-0.679822\pi$
$17$	−1275.83	−1.07071	−0.535355	+	0.844627i	$0.679822\pi$
$18$	−170.307	−0.123894
$19$	801.964	0.509649	0.254824	−	0.966987i	$-0.417982\pi$
$19$	801.964	0.509649	0.254824	+	0.966987i	$0.417982\pi$
$20$	2238.32	1.25126
$21$	−878.592	−0.434749
$22$	624.802	0.275224
$23$	255.443	0.100687	0.0503436	−	0.998732i	$-0.483968\pi$
$23$	255.443	0.100687	0.0503436	+	0.998732i	$0.483968\pi$
$24$	1127.42	0.399537
$25$	3461.85	1.10779
$26$	1712.77	0.496895
$27$	729.000	0.192450
$28$	2692.32	0.648981
$29$	7410.46	1.63625	0.818125	−	0.575040i	$-0.195013\pi$
$29$	7410.46	1.63625	0.818125	+	0.575040i	$0.195013\pi$
$30$	1535.78	0.311549
$31$	−2821.92	−0.527401	−0.263700	−	0.964605i	$-0.584943\pi$
$31$	−2821.92	−0.527401	−0.263700	+	0.964605i	$0.584943\pi$
$32$	−5310.40	−0.916754
$33$	−2674.46	−0.427516
$34$	2682.51	0.397965
$35$	7922.89	1.09323
$36$	−2233.92	−0.287284
$37$	4781.71	0.574221	0.287111	−	0.957897i	$-0.407305\pi$
$37$	4781.71	0.574221	0.287111	+	0.957897i	$0.407305\pi$
$38$	−1686.18	−0.189428
$39$	−7331.50	−0.771847
$40$	−10166.7	−1.00469
$41$	−8224.42	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$41$	−8224.42	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$42$	1847.29	0.161589
$43$	−1932.60	−0.159393	−0.0796967	−	0.996819i	$-0.525395\pi$
$43$	−1932.60	−0.159393	−0.0796967	+	0.996819i	$0.525395\pi$
$44$	8195.53	0.638183
$45$	−6573.91	−0.483941
$46$	−537.083	−0.0374237
$47$	23212.7	1.53278	0.766392	−	0.642373i	$-0.222050\pi$
$47$	23212.7	1.53278	0.766392	+	0.642373i	$0.222050\pi$
$48$	5572.36	0.349089
$49$	−7277.08	−0.432979
$50$	−7278.75	−0.411748
$51$	−11482.5	−0.618175
$52$	22466.3	1.15219
$53$	15252.2	0.745836	0.372918	−	0.927864i	$-0.378357\pi$
$53$	15252.2	0.745836	0.372918	+	0.927864i	$0.378357\pi$
$54$	−1532.76	−0.0715305
$55$	24117.6	1.07505
$56$	−12228.9	−0.521096
$57$	7217.68	0.294246
$58$	−15580.9	−0.608167
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	20144.8	0.722413
$61$	9488.35	0.326487	0.163244	−	0.986586i	$-0.447804\pi$
$61$	9488.35	0.326487	0.163244	+	0.986586i	$0.447804\pi$
$62$	5933.26	0.196026
$63$	−7907.33	−0.251003
$64$	−8647.40	−0.263898
$65$	66113.3	1.94091
$66$	5623.22	0.158900
$67$	28014.3	0.762417	0.381209	−	0.924489i	$-0.375508\pi$
$67$	28014.3	0.762417	0.381209	+	0.924489i	$0.375508\pi$
$68$	35186.5	0.922793
$69$	2298.98	0.0581317
$70$	−16658.3	−0.406337
$71$	−26155.1	−0.615758	−0.307879	−	0.951425i	$-0.599619\pi$
$71$	−26155.1	−0.615758	−0.307879	+	0.951425i	$0.599619\pi$
$72$	10146.8	0.230673
$73$	7782.60	0.170930	0.0854649	−	0.996341i	$-0.472762\pi$
$73$	7782.60	0.170930	0.0854649	+	0.996341i	$0.472762\pi$
$74$	−10053.8	−0.213428
$75$	31156.7	0.639585
$76$	−22117.6	−0.439241
$77$	29009.4	0.557586
$78$	15414.9	0.286882
$79$	−51295.8	−0.924728	−0.462364	−	0.886690i	$-0.652999\pi$
$79$	−51295.8	−0.924728	−0.462364	+	0.886690i	$0.652999\pi$
$80$	−50249.9	−0.877830
$81$	6561.00	0.111111
$82$	17292.3	0.284000
$83$	17726.9	0.282447	0.141224	−	0.989978i	$-0.454896\pi$
$83$	17726.9	0.282447	0.141224	+	0.989978i	$0.454896\pi$
$84$	24230.9	0.374689
$85$	103546.	1.55448
$86$	4063.40	0.0592438
$87$	66694.1	0.944690
$88$	−37225.2	−0.512426
$89$	104423.	1.39740	0.698701	−	0.715414i	$-0.253762\pi$
$89$	104423.	1.39740	0.698701	+	0.715414i	$0.253762\pi$
$90$	13822.0	0.179873
$91$	79523.3	1.00668
$92$	−7044.92	−0.0867774
$93$	−25397.3	−0.304495
$94$	−48806.1	−0.569710
$95$	−65086.9	−0.739920
$96$	−47793.6	−0.529288
$97$	−144515.	−1.55949	−0.779746	−	0.626096i	$-0.784652\pi$
$97$	−144515.	−1.55949	−0.779746	+	0.626096i	$0.784652\pi$
$98$	15300.5	0.160931
$99$	−24070.2	−0.246826
$100$	−95475.3	−0.954753
$101$	5054.57	0.0493038	0.0246519	−	0.999696i	$-0.492152\pi$
$101$	5054.57	0.0493038	0.0246519	+	0.999696i	$0.492152\pi$
$102$	24142.6	0.229765
$103$	−12446.5	−0.115599	−0.0577997	−	0.998328i	$-0.518408\pi$
$103$	−12446.5	−0.115599	−0.0577997	+	0.998328i	$0.518408\pi$
$104$	−102045.	−0.925145
$105$	71306.0	0.631179
$106$	−32068.7	−0.277215
$107$	62239.2	0.525538	0.262769	−	0.964859i	$-0.415364\pi$
$107$	62239.2	0.525538	0.262769	+	0.964859i	$0.415364\pi$
$108$	−20105.3	−0.165863
$109$	−109466.	−0.882496	−0.441248	−	0.897385i	$-0.645464\pi$
$109$	−109466.	−0.882496	−0.441248	+	0.897385i	$0.645464\pi$
$110$	−50708.6	−0.399576
$111$	43035.4	0.331527
$112$	−60442.3	−0.455298
$113$	−132747.	−0.977977	−0.488988	−	0.872290i	$-0.662634\pi$
$113$	−132747.	−0.977977	−0.488988	+	0.872290i	$0.662634\pi$
$114$	−15175.6	−0.109366
$115$	−20731.6	−0.146180
$116$	−204375.	−1.41021
$117$	−65983.5	−0.445626
$118$	7319.00	0.0483890
$119$	124549.	0.806253
$120$	−91500.7	−0.580058
$121$	−72745.3	−0.451691
$122$	−19949.8	−0.121350
$123$	−74019.8	−0.441149
$124$	77826.5	0.454541
$125$	−27338.9	−0.156497
$126$	16625.6	0.0932935
$127$	−223789.	−1.23120	−0.615601	−	0.788058i	$-0.711087\pi$
$127$	−223789.	−1.23120	−0.615601	+	0.788058i	$0.711087\pi$
$128$	188115.	1.01484
$129$	−17393.4	−0.0920258
$130$	−139007.	−0.721404
$131$	247877.	1.26200	0.630998	−	0.775785i	$-0.282646\pi$
$131$	247877.	1.26200	0.630998	+	0.775785i	$0.282646\pi$
$132$	73759.7	0.368455
$133$	−78288.8	−0.383769
$134$	−58901.7	−0.283378
$135$	−59165.2	−0.279404
$136$	−159822.	−0.740952
$137$	202795.	0.923114	0.461557	−	0.887111i	$-0.347291\pi$
$137$	202795.	0.923114	0.461557	+	0.887111i	$0.347291\pi$
$138$	−4833.75	−0.0216066
$139$	−192882.	−0.846750	−0.423375	−	0.905955i	$-0.639155\pi$
$139$	−192882.	−0.846750	−0.423375	+	0.905955i	$0.639155\pi$
$140$	−218507.	−0.942206
$141$	208914.	0.884954
$142$	54992.6	0.228867
$143$	242072.	0.989930
$144$	50151.2	0.201547
$145$	−601428.	−2.37555
$146$	−16363.4	−0.0635317
$147$	−65493.7	−0.249981
$148$	−131876.	−0.494893
$149$	211494.	0.780429	0.390214	−	0.920724i	$-0.372401\pi$
$149$	211494.	0.780429	0.390214	+	0.920724i	$0.372401\pi$
$150$	−65508.7	−0.237723
$151$	−122664.	−0.437797	−0.218899	−	0.975748i	$-0.570246\pi$
$151$	−122664.	−0.437797	−0.218899	+	0.975748i	$0.570246\pi$
$152$	100461.	0.352687
$153$	−103343.	−0.356903
$154$	−60994.0	−0.207246
$155$	229026.	0.765693
$156$	202197.	0.665217
$157$	120555.	0.390333	0.195166	−	0.980770i	$-0.437475\pi$
$157$	120555.	0.390333	0.195166	+	0.980770i	$0.437475\pi$
$158$	107852.	0.343706
$159$	137270.	0.430609
$160$	430989.	1.33096
$161$	−24936.7	−0.0758182
$162$	−13794.9	−0.0412981
$163$	−558933.	−1.64775	−0.823875	−	0.566772i	$-0.808192\pi$
$163$	−558933.	−1.64775	−0.823875	+	0.566772i	$0.808192\pi$
$164$	226823.	0.658534
$165$	217058.	0.620678
$166$	−37271.8	−0.104981
$167$	225611.	0.625992	0.312996	−	0.949754i	$-0.398667\pi$
$167$	225611.	0.625992	0.312996	+	0.949754i	$0.398667\pi$
$168$	−110060.	−0.300855
$169$	292297.	0.787242
$170$	−217711.	−0.577775
$171$	64959.1	0.169883
$172$	53299.6	0.137373
$173$	151994.	0.386110	0.193055	−	0.981188i	$-0.438160\pi$
$173$	151994.	0.386110	0.193055	+	0.981188i	$0.438160\pi$
$174$	−140228.	−0.351125
$175$	−337951.	−0.834177
$176$	−183989.	−0.447723
$177$	−31329.0	−0.0751646
$178$	−219556.	−0.519391
$179$	−801580.	−1.86988	−0.934942	−	0.354801i	$-0.884548\pi$
$179$	−801580.	−1.86988	−0.934942	+	0.354801i	$0.884548\pi$
$180$	181304.	0.417086
$181$	678519.	1.53945	0.769725	−	0.638375i	$-0.220393\pi$
$181$	678519.	1.53945	0.769725	+	0.638375i	$0.220393\pi$
$182$	−167202.	−0.374166
$183$	85395.2	0.188498
$184$	31999.0	0.0696774
$185$	−388081.	−0.833668
$186$	53399.3	0.113176
$187$	379130.	0.792838
$188$	−640189.	−1.32103
$189$	−71165.9	−0.144916
$190$	136849.	0.275016
$191$	−564563.	−1.11977	−0.559886	−	0.828570i	$-0.689155\pi$
$191$	−564563.	−1.11977	−0.559886	+	0.828570i	$0.689155\pi$
$192$	−77826.6	−0.152361
$193$	774264.	1.49622	0.748111	−	0.663574i	$-0.230961\pi$
$193$	774264.	1.49622	0.748111	+	0.663574i	$0.230961\pi$
$194$	303851.	0.579637
$195$	595020.	1.12059
$196$	200696.	0.373164
$197$	530628.	0.974147	0.487073	−	0.873361i	$-0.338064\pi$
$197$	530628.	0.974147	0.487073	+	0.873361i	$0.338064\pi$
$198$	50609.0	0.0917412
$199$	128471.	0.229970	0.114985	−	0.993367i	$-0.463318\pi$
$199$	128471.	0.229970	0.114985	+	0.993367i	$0.463318\pi$
$200$	433662.	0.766614
$201$	252129.	0.440182
$202$	−10627.5	−0.0183254
$203$	−723418.	−1.23211
$204$	316679.	0.532775
$205$	667489.	1.10933
$206$	26169.6	0.0429664
$207$	20690.9	0.0335624
$208$	−504367.	−0.808329
$209$	−238314.	−0.377384
$210$	−149925.	−0.234599
$211$	−447265.	−0.691607	−0.345803	−	0.938307i	$-0.612394\pi$
$211$	−447265.	−0.691607	−0.345803	+	0.938307i	$0.612394\pi$
$212$	−420645.	−0.642800
$213$	−235396.	−0.355508
$214$	−130861.	−0.195334
$215$	156848.	0.231411
$216$	91321.0	0.133179
$217$	275480.	0.397137
$218$	230158.	0.328009
$219$	70043.4	0.0986864
$220$	−665144.	−0.926529
$221$	1.03931e6	1.43141
$222$	−90484.5	−0.123223
$223$	523227.	0.704576	0.352288	−	0.935892i	$-0.385404\pi$
$223$	523227.	0.704576	0.352288	+	0.935892i	$0.385404\pi$
$224$	518409.	0.690323
$225$	280410.	0.369264
$226$	279108.	0.363498
$227$	360000.	0.463700	0.231850	−	0.972752i	$-0.425522\pi$
$227$	360000.	0.463700	0.231850	+	0.972752i	$0.425522\pi$
$228$	−199058.	−0.253596
$229$	−1.17199e6	−1.47684	−0.738421	−	0.674340i	$-0.764428\pi$
$229$	−1.17199e6	−1.47684	−0.738421	+	0.674340i	$0.764428\pi$
$230$	43589.4	0.0543327
$231$	261085.	0.321923
$232$	928299.	1.13232
$233$	163113.	0.196834	0.0984170	−	0.995145i	$-0.468622\pi$
$233$	163113.	0.196834	0.0984170	+	0.995145i	$0.468622\pi$
$234$	138734.	0.165632
$235$	−1.88393e6	−2.22533
$236$	96003.4	0.112204
$237$	−461662.	−0.533892
$238$	−261871.	−0.299671
$239$	1.32642e6	1.50205	0.751026	−	0.660273i	$-0.229559\pi$
$239$	1.32642e6	1.50205	0.751026	+	0.660273i	$0.229559\pi$
$240$	−452249.	−0.506816
$241$	1.52608e6	1.69252	0.846259	−	0.532771i	$-0.178849\pi$
$241$	1.52608e6	1.69252	0.846259	+	0.532771i	$0.178849\pi$
$242$	152951.	0.167886
$243$	59049.0	0.0641500
$244$	−261682.	−0.281384
$245$	590604.	0.628610
$246$	155631.	0.163968
$247$	−653288.	−0.681338
$248$	−353499.	−0.364971
$249$	159542.	0.163071
$250$	57481.5	0.0581672
$251$	−739184.	−0.740573	−0.370287	−	0.928918i	$-0.620741\pi$
$251$	−739184.	−0.740573	−0.370287	+	0.928918i	$0.620741\pi$
$252$	218078.	0.216327
$253$	−75908.1	−0.0745567
$254$	470529.	0.457617
$255$	931914.	0.897481
$256$	−118805.	−0.113301
$257$	385343.	0.363927	0.181964	−	0.983305i	$-0.441755\pi$
$257$	385343.	0.363927	0.181964	+	0.983305i	$0.441755\pi$
$258$	36570.6	0.0342044
$259$	−466797.	−0.432393
$260$	−1.82336e6	−1.67278
$261$	600247.	0.545417
$262$	−521175.	−0.469063
$263$	−907092.	−0.808653	−0.404326	−	0.914615i	$-0.632494\pi$
$263$	−907092.	−0.808653	−0.404326	+	0.914615i	$0.632494\pi$
$264$	−335027.	−0.295849
$265$	−1.23786e6	−1.08282
$266$	164607.	0.142641
$267$	939807.	0.806790
$268$	−772613.	−0.657091
$269$	1.65731e6	1.39644	0.698220	−	0.715883i	$-0.253976\pi$
$269$	1.65731e6	1.39644	0.698220	+	0.715883i	$0.253976\pi$
$270$	124398.	0.103850
$271$	2.23356e6	1.84746	0.923730	−	0.383045i	$-0.125125\pi$
$271$	2.23356e6	1.84746	0.923730	+	0.383045i	$0.125125\pi$
$272$	−789934.	−0.647394
$273$	715710.	0.581207
$274$	−426388.	−0.343106
$275$	−1.02873e6	−0.820297
$276$	−63404.3	−0.0501009
$277$	−785622.	−0.615197	−0.307599	−	0.951516i	$-0.599525\pi$
$277$	−785622.	−0.615197	−0.307599	+	0.951516i	$0.599525\pi$
$278$	405546.	0.314723
$279$	−228576.	−0.175800
$280$	992491.	0.756539
$281$	1.77758e6	1.34296	0.671480	−	0.741023i	$-0.265659\pi$
$281$	1.77758e6	1.34296	0.671480	+	0.741023i	$0.265659\pi$
$282$	−439255.	−0.328922
$283$	797157.	0.591667	0.295834	−	0.955239i	$-0.404403\pi$
$283$	797157.	0.591667	0.295834	+	0.955239i	$0.404403\pi$
$284$	721338.	0.530692
$285$	−585782.	−0.427193
$286$	−508970.	−0.367940
$287$	802879.	0.575367
$288$	−430143.	−0.305585
$289$	207895.	0.146420
$290$	1.26454e6	0.882952
$291$	−1.30063e6	−0.900373
$292$	−214638.	−0.147316
$293$	−142245.	−0.0967986	−0.0483993	−	0.998828i	$-0.515412\pi$
$293$	−142245.	−0.0967986	−0.0483993	+	0.998828i	$0.515412\pi$
$294$	137704.	0.0929136
$295$	282516.	0.189011
$296$	599000.	0.397372
$297$	−216632.	−0.142505
$298$	−444679.	−0.290072
$299$	−208086.	−0.134606
$300$	−859278.	−0.551227
$301$	188663.	0.120024
$302$	257907.	0.162722
$303$	45491.1	0.0284656
$304$	496537.	0.308154
$305$	−770069.	−0.474002
$306$	217284.	0.132655
$307$	2.26783e6	1.37330	0.686649	−	0.726989i	$-0.259081\pi$
$307$	2.26783e6	1.37330	0.686649	+	0.726989i	$0.259081\pi$
$308$	−800058.	−0.480557
$309$	−112019.	−0.0667414
$310$	−481540.	−0.284595
$311$	2.65296e6	1.55536	0.777678	−	0.628663i	$-0.216398\pi$
$311$	2.65296e6	1.55536	0.777678	+	0.628663i	$0.216398\pi$
$312$	−918408.	−0.534133
$313$	2.58601e6	1.49200	0.746000	−	0.665946i	$-0.231972\pi$
$313$	2.58601e6	1.49200	0.746000	+	0.665946i	$0.231972\pi$
$314$	−253473.	−0.145080
$315$	641754.	0.364412
$316$	1.41470e6	0.796979
$317$	−1.84274e6	−1.02995	−0.514974	−	0.857206i	$-0.672198\pi$
$317$	−1.84274e6	−1.02995	−0.514974	+	0.857206i	$0.672198\pi$
$318$	−288618.	−0.160050
$319$	−2.20211e6	−1.21161
$320$	701818.	0.383133
$321$	560152.	0.303420
$322$	52430.8	0.0281804
$323$	−1.02317e6	−0.545686
$324$	−180947.	−0.0957613
$325$	−2.82006e6	−1.48098
$326$	1.17519e6	0.612441
$327$	−985193.	−0.509509
$328$	−1.03026e6	−0.528766
$329$	−2.26605e6	−1.15420
$330$	−456377.	−0.230695
$331$	−153074.	−0.0767949	−0.0383974	−	0.999263i	$-0.512225\pi$
$331$	−153074.	−0.0767949	−0.0383974	+	0.999263i	$0.512225\pi$
$332$	−488895.	−0.243428
$333$	387319.	0.191407
$334$	−474360.	−0.232671
$335$	−2.27362e6	−1.10690
$336$	−543981.	−0.262867
$337$	630168.	0.302260	0.151130	−	0.988514i	$-0.451709\pi$
$337$	630168.	0.302260	0.151130	+	0.988514i	$0.451709\pi$
$338$	−614572.	−0.292605
$339$	−1.19472e6	−0.564635
$340$	−2.85572e6	−1.33973
$341$	838570.	0.390529
$342$	−136580.	−0.0631426
$343$	2.35112e6	1.07904
$344$	−242094.	−0.110303
$345$	−186584.	−0.0843971
$346$	−319576.	−0.143511
$347$	−985059.	−0.439176	−0.219588	−	0.975593i	$-0.570471\pi$
$347$	−985059.	−0.439176	−0.219588	+	0.975593i	$0.570471\pi$
$348$	−1.83937e6	−0.814182
$349$	−2.32668e6	−1.02252	−0.511262	−	0.859425i	$-0.670822\pi$
$349$	−2.32668e6	−1.02252	−0.511262	+	0.859425i	$0.670822\pi$
$350$	710561.	0.310050
$351$	−593851.	−0.257282
$352$	1.57805e6	0.678837
$353$	898841.	0.383925	0.191962	−	0.981402i	$-0.438515\pi$
$353$	898841.	0.383925	0.191962	+	0.981402i	$0.438515\pi$
$354$	65871.0	0.0279374
$355$	2.12273e6	0.893973
$356$	−2.87991e6	−1.20435
$357$	1.12094e6	0.465490
$358$	1.68537e6	0.695004
$359$	−1.45729e6	−0.596774	−0.298387	−	0.954445i	$-0.596449\pi$
$359$	−1.45729e6	−0.596774	−0.298387	+	0.954445i	$0.596449\pi$
$360$	−823507.	−0.334897
$361$	−1.83295e6	−0.740258
$362$	−1.42663e6	−0.572188
$363$	−654708.	−0.260784
$364$	−2.19319e6	−0.867608
$365$	−631632.	−0.248160
$366$	−179548.	−0.0700614
$367$	4.24268e6	1.64428	0.822139	−	0.569287i	$-0.192781\pi$
$367$	4.24268e6	1.64428	0.822139	+	0.569287i	$0.192781\pi$
$368$	158158.	0.0608794
$369$	−666178.	−0.254697
$370$	815963.	0.309861
$371$	−1.48894e6	−0.561620
$372$	700439.	0.262430
$373$	−2.66753e6	−0.992742	−0.496371	−	0.868110i	$-0.665334\pi$
$373$	−2.66753e6	−0.992742	−0.496371	+	0.868110i	$0.665334\pi$
$374$	−797144.	−0.294685
$375$	−246050.	−0.0903534
$376$	2.90783e6	1.06072
$377$	−6.03664e6	−2.18747
$378$	149631.	0.0538630
$379$	−3.11327e6	−1.11332	−0.556659	−	0.830741i	$-0.687917\pi$
$379$	−3.11327e6	−1.11332	−0.556659	+	0.830741i	$0.687917\pi$
$380$	1.79505e6	0.637701
$381$	−2.01410e6	−0.710835
$382$	1.18703e6	0.416200
$383$	−1.39854e6	−0.487167	−0.243584	−	0.969880i	$-0.578323\pi$
$383$	−1.39854e6	−0.487167	−0.243584	+	0.969880i	$0.578323\pi$
$384$	1.69303e6	0.585918
$385$	−2.35439e6	−0.809517
$386$	−1.62794e6	−0.556120
$387$	−156540.	−0.0531311
$388$	3.98561e6	1.34405
$389$	5.04752e6	1.69124	0.845618	−	0.533789i	$-0.179232\pi$
$389$	5.04752e6	1.69124	0.845618	+	0.533789i	$0.179232\pi$
$390$	−1.25106e6	−0.416503
$391$	−325902.	−0.107807
$392$	−911591.	−0.299630
$393$	2.23089e6	0.728613
$394$	−1.11568e6	−0.362074
$395$	4.16314e6	1.34254
$396$	663838.	0.212728
$397$	5.24113e6	1.66897	0.834486	−	0.551030i	$-0.185765\pi$
$397$	5.24113e6	1.66897	0.834486	+	0.551030i	$0.185765\pi$
$398$	−270117.	−0.0854761
$399$	−704599.	−0.221569
$400$	2.14341e6	0.669816
$401$	−4.27332e6	−1.32710	−0.663551	−	0.748131i	$-0.730951\pi$
$401$	−4.27332e6	−1.32710	−0.663551	+	0.748131i	$0.730951\pi$
$402$	−530115.	−0.163608
$403$	2.29877e6	0.705070
$404$	−139401.	−0.0424926
$405$	−532487.	−0.161314
$406$	1.52103e6	0.457955
$407$	−1.42095e6	−0.425199
$408$	−1.43840e6	−0.427789
$409$	6.70311e6	1.98138	0.990691	−	0.136133i	$-0.0434676\pi$
$409$	6.70311e6	1.98138	0.990691	+	0.136133i	$0.0434676\pi$
$410$	−1.40344e6	−0.412318
$411$	1.82515e6	0.532960
$412$	343266.	0.0996296
$413$	339820.	0.0980333
$414$	−43503.7	−0.0124746
$415$	−1.43871e6	−0.410064
$416$	4.32591e6	1.22559
$417$	−1.73594e6	−0.488871
$418$	501069.	0.140267
$419$	−1.48858e6	−0.414225	−0.207112	−	0.978317i	$-0.566407\pi$
$419$	−1.48858e6	−0.414225	−0.207112	+	0.978317i	$0.566407\pi$
$420$	−1.96657e6	−0.543983
$421$	4.24222e6	1.16651	0.583255	−	0.812289i	$-0.301779\pi$
$421$	4.24222e6	1.16651	0.583255	+	0.812289i	$0.301779\pi$
$422$	940402.	0.257059
$423$	1.88023e6	0.510928
$424$	1.91063e6	0.516133
$425$	−4.41675e6	−1.18613
$426$	494933.	0.132136
$427$	−926266.	−0.245848
$428$	−1.71651e6	−0.452936
$429$	2.17865e6	0.571536
$430$	−329783.	−0.0860116
$431$	6.78108e6	1.75835	0.879176	−	0.476497i	$-0.158094\pi$
$431$	6.78108e6	1.75835	0.879176	+	0.476497i	$0.158094\pi$
$432$	451361.	0.116363
$433$	−2.89130e6	−0.741094	−0.370547	−	0.928814i	$-0.620830\pi$
$433$	−2.89130e6	−0.741094	−0.370547	+	0.928814i	$0.620830\pi$
$434$	−579212.	−0.147609
$435$	−5.41286e6	−1.37152
$436$	3.01899e6	0.760580
$437$	204856.	0.0513151
$438$	−147270.	−0.0366801
$439$	−1.15482e6	−0.285991	−0.142996	−	0.989723i	$-0.545674\pi$
$439$	−1.15482e6	−0.285991	−0.142996	+	0.989723i	$0.545674\pi$
$440$	3.02118e6	0.743952
$441$	−589444.	−0.144326
$442$	−2.18521e6	−0.532030
$443$	−339517.	−0.0821964	−0.0410982	−	0.999155i	$-0.513086\pi$
$443$	−339517.	−0.0821964	−0.0410982	+	0.999155i	$0.513086\pi$
$444$	−1.18688e6	−0.285727
$445$	−8.47492e6	−2.02878
$446$	−1.10011e6	−0.261879
$447$	1.90345e6	0.450581
$448$	844170.	0.198717
$449$	−7.65479e6	−1.79191	−0.895957	−	0.444141i	$-0.853509\pi$
$449$	−7.65479e6	−1.79191	−0.895957	+	0.444141i	$0.853509\pi$
$450$	−589579.	−0.137249
$451$	2.44399e6	0.565794
$452$	3.66106e6	0.842871
$453$	−1.10397e6	−0.252762
$454$	−756920.	−0.172350
$455$	−6.45407e6	−1.46152
$456$	904150.	0.203624
$457$	−4.53237e6	−1.01516	−0.507581	−	0.861604i	$-0.669460\pi$
$457$	−4.53237e6	−1.01516	−0.507581	+	0.861604i	$0.669460\pi$
$458$	2.46417e6	0.548917
$459$	−930083.	−0.206058
$460$	571762.	0.125985
$461$	−999991.	−0.219151	−0.109576	−	0.993978i	$-0.534949\pi$
$461$	−999991.	−0.219151	−0.109576	+	0.993978i	$0.534949\pi$
$462$	−548946.	−0.119653
$463$	7.61544e6	1.65098	0.825492	−	0.564414i	$-0.190898\pi$
$463$	7.61544e6	1.65098	0.825492	+	0.564414i	$0.190898\pi$
$464$	4.58819e6	0.989342
$465$	2.06123e6	0.442073
$466$	−342955.	−0.0731599
$467$	−2.99420e6	−0.635315	−0.317658	−	0.948206i	$-0.602896\pi$
$467$	−2.99420e6	−0.635315	−0.317658	+	0.948206i	$0.602896\pi$
$468$	1.81977e6	0.384063
$469$	−2.73479e6	−0.574106
$470$	3.96107e6	0.827119
$471$	1.08499e6	0.225359
$472$	−436061.	−0.0900932
$473$	574296.	0.118027
$474$	970672.	0.198439
$475$	2.77628e6	0.564585
$476$	−3.43496e6	−0.694870
$477$	1.23543e6	0.248612
$478$	−2.78887e6	−0.558288
$479$	6.42416e6	1.27932	0.639658	−	0.768660i	$-0.279076\pi$
$479$	6.42416e6	1.27932	0.639658	+	0.768660i	$0.279076\pi$
$480$	3.87890e6	0.768433
$481$	−3.89523e6	−0.767664
$482$	−3.20866e6	−0.629081
$483$	−224430.	−0.0437737
$484$	2.00626e6	0.389291
$485$	1.17287e7	2.26411
$486$	−124154.	−0.0238435
$487$	9.44440e6	1.80448	0.902240	−	0.431234i	$-0.141922\pi$
$487$	9.44440e6	1.80448	0.902240	+	0.431234i	$0.141922\pi$
$488$	1.18860e6	0.225935
$489$	−5.03040e6	−0.951328
$490$	−1.24178e6	−0.233644
$491$	−7.87399e6	−1.47398	−0.736989	−	0.675905i	$-0.763753\pi$
$491$	−7.87399e6	−1.47398	−0.736989	+	0.675905i	$0.763753\pi$
$492$	2.04141e6	0.380205
$493$	−9.45451e6	−1.75195
$494$	1.37358e6	0.253242
$495$	1.95352e6	0.358348
$496$	−1.74720e6	−0.318887
$497$	2.55329e6	0.463671
$498$	−335447.	−0.0606108
$499$	8.14323e6	1.46401	0.732007	−	0.681297i	$-0.238584\pi$
$499$	8.14323e6	1.46401	0.732007	+	0.681297i	$0.238584\pi$
$500$	753985.	0.134877
$501$	2.03050e6	0.361416
$502$	1.55418e6	0.275259
$503$	3.34061e6	0.588717	0.294358	−	0.955695i	$-0.404894\pi$
$503$	3.34061e6	0.588717	0.294358	+	0.955695i	$0.404894\pi$
$504$	−990541.	−0.173699
$505$	−410226.	−0.0715805
$506$	159601.	0.0277115
$507$	2.63068e6	0.454514
$508$	6.17193e6	1.06111
$509$	−1.19251e6	−0.204017	−0.102009	−	0.994784i	$-0.532527\pi$
$509$	−1.19251e6	−0.204017	−0.102009	+	0.994784i	$0.532527\pi$
$510$	−1.95940e6	−0.333579
$511$	−759748.	−0.128711
$512$	−5.76987e6	−0.972728
$513$	584632.	0.0980819
$514$	−810206.	−0.135266
$515$	1.01015e6	0.167830
$516$	479696.	0.0793126
$517$	−6.89795e6	−1.13499
$518$	981468.	0.160713
$519$	1.36794e6	0.222921
$520$	8.28194e6	1.34315
$521$	9.55161e6	1.54164	0.770819	−	0.637055i	$-0.219847\pi$
$521$	9.55161e6	1.54164	0.770819	+	0.637055i	$0.219847\pi$
$522$	−1.26205e6	−0.202722
$523$	1.46152e6	0.233642	0.116821	−	0.993153i	$-0.462730\pi$
$523$	1.46152e6	0.233642	0.116821	+	0.993153i	$0.462730\pi$
$524$	−6.83626e6	−1.08765
$525$	−3.04156e6	−0.481612
$526$	1.90721e6	0.300563
$527$	3.60030e6	0.564693
$528$	−1.65590e6	−0.258493
$529$	−6.37109e6	−0.989862
$530$	2.60268e6	0.402467
$531$	−281961.	−0.0433963
$532$	2.15915e6	0.330752
$533$	6.69970e6	1.02150
$534$	−1.97600e6	−0.299871
$535$	−5.05129e6	−0.762989
$536$	3.50932e6	0.527607
$537$	−7.21422e6	−1.07958
$538$	−3.48459e6	−0.519034
$539$	2.16248e6	0.320612
$540$	1.63173e6	0.240804
$541$	−1.06338e7	−1.56205	−0.781025	−	0.624500i	$-0.785303\pi$
$541$	−1.06338e7	−1.56205	−0.781025	+	0.624500i	$0.785303\pi$
$542$	−4.69619e6	−0.686670
$543$	6.10667e6	0.888802
$544$	6.77519e6	0.981577
$545$	8.88419e6	1.28123
$546$	−1.50482e6	−0.216025
$547$	1.81124e6	0.258826	0.129413	−	0.991591i	$-0.458691\pi$
$547$	1.81124e6	0.258826	0.129413	+	0.991591i	$0.458691\pi$
$548$	−5.59293e6	−0.795587
$549$	768557.	0.108829
$550$	2.16297e6	0.304891
$551$	5.94292e6	0.833913
$552$	287991.	0.0402283
$553$	5.00756e6	0.696328
$554$	1.65182e6	0.228659
$555$	−3.49273e6	−0.481319
$556$	5.31954e6	0.729772
$557$	−1.77561e6	−0.242499	−0.121250	−	0.992622i	$-0.538690\pi$
$557$	−1.77561e6	−0.242499	−0.121250	+	0.992622i	$0.538690\pi$
$558$	480594.	0.0653420
$559$	1.57431e6	0.213089
$560$	4.90546e6	0.661013
$561$	3.41217e6	0.457745
$562$	−3.73746e6	−0.499156
$563$	−7.13593e6	−0.948810	−0.474405	−	0.880307i	$-0.657337\pi$
$563$	−7.13593e6	−0.948810	−0.474405	+	0.880307i	$0.657337\pi$
$564$	−5.76170e6	−0.762699
$565$	1.07737e7	1.41985
$566$	−1.67607e6	−0.219913
$567$	−640493.	−0.0836675
$568$	−3.27642e6	−0.426117
$569$	3.82803e6	0.495672	0.247836	−	0.968802i	$-0.420281\pi$
$569$	3.82803e6	0.495672	0.247836	+	0.968802i	$0.420281\pi$
$570$	1.23164e6	0.158781
$571$	1.15161e7	1.47814	0.739070	−	0.673628i	$-0.235265\pi$
$571$	1.15161e7	1.47814	0.739070	+	0.673628i	$0.235265\pi$
$572$	−6.67616e6	−0.853172
$573$	−5.08107e6	−0.646500
$574$	−1.68810e6	−0.213854
$575$	884305.	0.111541
$576$	−700439.	−0.0879659
$577$	−1.06710e7	−1.33434	−0.667169	−	0.744906i	$-0.732494\pi$
$577$	−1.06710e7	−1.33434	−0.667169	+	0.744906i	$0.732494\pi$
$578$	−437112.	−0.0544218
$579$	6.96838e6	0.863844
$580$	1.65869e7	2.04737
$581$	−1.73052e6	−0.212685
$582$	2.73466e6	0.334654
$583$	−4.53239e6	−0.552276
$584$	974918.	0.118287
$585$	5.35518e6	0.646970
$586$	299079.	0.0359784
$587$	3.86670e6	0.463176	0.231588	−	0.972814i	$-0.425608\pi$
$587$	3.86670e6	0.463176	0.231588	+	0.972814i	$0.425608\pi$
$588$	1.80627e6	0.215446
$589$	−2.26308e6	−0.268789
$590$	−594006.	−0.0702524
$591$	4.77565e6	0.562424
$592$	2.96060e6	0.347197
$593$	−5.82698e6	−0.680467	−0.340234	−	0.940341i	$-0.610506\pi$
$593$	−5.82698e6	−0.680467	−0.340234	+	0.940341i	$0.610506\pi$
$594$	455481.	0.0529668
$595$	−1.01083e7	−1.17054
$596$	−5.83286e6	−0.672614
$597$	1.15624e6	0.132773
$598$	437514.	0.0500309
$599$	−8.74348e6	−0.995674	−0.497837	−	0.867271i	$-0.665872\pi$
$599$	−8.74348e6	−0.995674	−0.497837	+	0.867271i	$0.665872\pi$
$600$	3.90296e6	0.442605
$601$	−5.10457e6	−0.576465	−0.288233	−	0.957560i	$-0.593068\pi$
$601$	−5.10457e6	−0.576465	−0.288233	+	0.957560i	$0.593068\pi$
$602$	−396674.	−0.0446111
$603$	2.26916e6	0.254139
$604$	3.38297e6	0.377316
$605$	5.90397e6	0.655776
$606$	−95647.7	−0.0105802
$607$	1.23037e6	0.135539	0.0677697	−	0.997701i	$-0.478412\pi$
$607$	1.23037e6	0.135539	0.0677697	+	0.997701i	$0.478412\pi$
$608$	−4.25875e6	−0.467222
$609$	−6.51076e6	−0.711359
$610$	1.61912e6	0.176179
$611$	−1.89093e7	−2.04915
$612$	2.85011e6	0.307598
$613$	−1.66177e7	−1.78616	−0.893079	−	0.449900i	$-0.851460\pi$
$613$	−1.66177e7	−1.78616	−0.893079	+	0.449900i	$0.851460\pi$
$614$	−4.76824e6	−0.510432
$615$	6.00740e6	0.640470
$616$	3.63398e6	0.385860
$617$	−2.06757e6	−0.218649	−0.109324	−	0.994006i	$-0.534869\pi$
$617$	−2.06757e6	−0.218649	−0.109324	+	0.994006i	$0.534869\pi$
$618$	235526.	0.0248067
$619$	−1.03780e7	−1.08864	−0.544321	−	0.838877i	$-0.683213\pi$
$619$	−1.03780e7	−1.08864	−0.544321	+	0.838877i	$0.683213\pi$
$620$	−6.31635e6	−0.659914
$621$	186218.	0.0193772
$622$	−5.57800e6	−0.578100
$623$	−1.01939e7	−1.05225
$624$	−4.53930e6	−0.466689
$625$	−8.59949e6	−0.880587
$626$	−5.43723e6	−0.554551
$627$	−2.14482e6	−0.217883
$628$	−3.32481e6	−0.336409
$629$	−6.10067e6	−0.614824
$630$	−1.34933e6	−0.135446
$631$	−1.57468e6	−0.157441	−0.0787205	−	0.996897i	$-0.525083\pi$
$631$	−1.57468e6	−0.157441	−0.0787205	+	0.996897i	$0.525083\pi$
$632$	−6.42577e6	−0.639930
$633$	−4.02539e6	−0.399299
$634$	3.87446e6	0.382814
$635$	1.81626e7	1.78749
$636$	−3.78580e6	−0.371121
$637$	5.92799e6	0.578840
$638$	4.63007e6	0.450335
$639$	−2.11856e6	−0.205253
$640$	−1.52673e7	−1.47337
$641$	1.37514e7	1.32191	0.660954	−	0.750426i	$-0.270152\pi$
$641$	1.37514e7	1.32191	0.660954	+	0.750426i	$0.270152\pi$
$642$	−1.17775e6	−0.112776
$643$	−1.81725e7	−1.73336	−0.866678	−	0.498867i	$-0.833750\pi$
$643$	−1.81725e7	−1.73336	−0.866678	+	0.498867i	$0.833750\pi$
$644$	687734.	0.0653440
$645$	1.41164e6	0.133605
$646$	2.15128e6	0.202822
$647$	1.41770e7	1.33144	0.665721	−	0.746201i	$-0.268124\pi$
$647$	1.41770e7	1.33144	0.665721	+	0.746201i	$0.268124\pi$
$648$	821889.	0.0768910
$649$	1.03442e6	0.0964021
$650$	5.92935e6	0.550457
$651$	2.47932e6	0.229287
$652$	1.54150e7	1.42012
$653$	−7.55832e6	−0.693653	−0.346826	−	0.937929i	$-0.612741\pi$
$653$	−7.55832e6	−0.693653	−0.346826	+	0.937929i	$0.612741\pi$
$654$	2.07143e6	0.189376
$655$	−2.01175e7	−1.83220
$656$	−5.09216e6	−0.462000
$657$	630391.	0.0569766
$658$	4.76451e6	0.428996
$659$	−1.57669e7	−1.41427	−0.707134	−	0.707080i	$-0.750012\pi$
$659$	−1.57669e7	−1.41427	−0.707134	+	0.707080i	$0.750012\pi$
$660$	−5.98630e6	−0.534932
$661$	−4.61947e6	−0.411234	−0.205617	−	0.978633i	$-0.565920\pi$
$661$	−4.61947e6	−0.411234	−0.205617	+	0.978633i	$0.565920\pi$
$662$	321848.	0.0285434
$663$	9.35377e6	0.826424
$664$	2.22063e6	0.195459
$665$	6.35387e6	0.557166
$666$	−814360.	−0.0711428
$667$	1.89295e6	0.164749
$668$	−6.22217e6	−0.539512
$669$	4.70904e6	0.406787
$670$	4.78043e6	0.411415
$671$	−2.81959e6	−0.241757
$672$	4.66568e6	0.398558
$673$	−107564.	−0.00915436	−0.00457718	−	0.999990i	$-0.501457\pi$
$673$	−107564.	−0.00915436	−0.00457718	+	0.999990i	$0.501457\pi$
$674$	−1.32496e6	−0.112345
$675$	2.52369e6	0.213195
$676$	−8.06134e6	−0.678486
$677$	1.09050e7	0.914441	0.457221	−	0.889353i	$-0.348845\pi$
$677$	1.09050e7	0.914441	0.457221	+	0.889353i	$0.348845\pi$
$678$	2.51197e6	0.209865
$679$	1.41077e7	1.17431
$680$	1.29711e7	1.07573
$681$	3.24000e6	0.267718
$682$	−1.76314e6	−0.145153
$683$	−1.14750e7	−0.941237	−0.470619	−	0.882337i	$-0.655969\pi$
$683$	−1.14750e7	−0.941237	−0.470619	+	0.882337i	$0.655969\pi$
$684$	−1.79152e6	−0.146414
$685$	−1.64587e7	−1.34020
$686$	−4.94337e6	−0.401063
$687$	−1.05479e7	−0.852655
$688$	−1.19657e6	−0.0963755
$689$	−1.24246e7	−0.997092
$690$	392304.	0.0313690
$691$	−1.11344e7	−0.887101	−0.443550	−	0.896249i	$-0.646281\pi$
$691$	−1.11344e7	−0.887101	−0.443550	+	0.896249i	$0.646281\pi$
$692$	−4.19188e6	−0.332769
$693$	2.34976e6	0.185862
$694$	2.07114e6	0.163234
$695$	1.56542e7	1.22933
$696$	8.35469e6	0.653743
$697$	1.04930e7	0.818121
$698$	4.89198e6	0.380055
$699$	1.46802e6	0.113642
$700$	9.32043e6	0.718937
$701$	−1.80281e7	−1.38565	−0.692827	−	0.721104i	$-0.743635\pi$
$701$	−1.80281e7	−1.38565	−0.692827	+	0.721104i	$0.743635\pi$
$702$	1.24861e6	0.0956275
$703$	3.83476e6	0.292651
$704$	2.56969e6	0.195411
$705$	−1.69554e7	−1.28480
$706$	−1.88986e6	−0.142698
$707$	−493434.	−0.0371262
$708$	864030.	0.0647807
$709$	−2.61098e7	−1.95069	−0.975343	−	0.220694i	$-0.929168\pi$
$709$	−2.61098e7	−1.95069	−0.975343	+	0.220694i	$0.929168\pi$
$710$	−4.46317e6	−0.332275
$711$	−4.15496e6	−0.308243
$712$	1.30810e7	0.967029
$713$	−720840.	−0.0531025
$714$	−2.35684e6	−0.173015
$715$	−1.96464e7	−1.43720
$716$	2.21070e7	1.61156
$717$	1.19377e7	0.867210
$718$	3.06404e6	0.221811
$719$	−1.47690e7	−1.06544	−0.532720	−	0.846291i	$-0.678830\pi$
$719$	−1.47690e7	−1.06544	−0.532720	+	0.846291i	$0.678830\pi$
$720$	−4.07025e6	−0.292610
$721$	1.21505e6	0.0870473
$722$	3.85389e6	0.275142
$723$	1.37347e7	0.977176
$724$	−1.87131e7	−1.32678
$725$	2.56539e7	1.81263
$726$	1.37656e6	0.0969290
$727$	685611.	0.0481107	0.0240554	−	0.999711i	$-0.492342\pi$
$727$	685611.	0.0481107	0.0240554	+	0.999711i	$0.492342\pi$
$728$	9.96180e6	0.696641
$729$	531441.	0.0370370
$730$	1.32804e6	0.0922369
$731$	2.46567e6	0.170664
$732$	−2.35514e6	−0.162457
$733$	−1.49501e7	−1.02774	−0.513871	−	0.857867i	$-0.671789\pi$
$733$	−1.49501e7	−1.02774	−0.513871	+	0.857867i	$0.671789\pi$
$734$	−8.92048e6	−0.611150
$735$	5.31543e6	0.362928
$736$	−1.35650e6	−0.0923053
$737$	−8.32481e6	−0.564554
$738$	1.40068e6	0.0946667
$739$	1.74384e7	1.17461	0.587307	−	0.809365i	$-0.300188\pi$
$739$	1.74384e7	1.17461	0.587307	+	0.809365i	$0.300188\pi$
$740$	1.07030e7	0.718498
$741$	−5.87959e6	−0.393371
$742$	3.13059e6	0.208745
$743$	1.74179e7	1.15751	0.578753	−	0.815503i	$-0.303540\pi$
$743$	1.74179e7	1.15751	0.578753	+	0.815503i	$0.303540\pi$
$744$	−3.18149e6	−0.210716
$745$	−1.71648e7	−1.13304
$746$	5.60863e6	0.368986
$747$	1.43588e6	0.0941491
$748$	−1.04561e7	−0.683309
$749$	−6.07587e6	−0.395734
$750$	517334.	0.0335829
$751$	1.11888e7	0.723908	0.361954	−	0.932196i	$-0.382110\pi$
$751$	1.11888e7	0.723908	0.361954	+	0.932196i	$0.382110\pi$
$752$	1.43722e7	0.926782
$753$	−6.65265e6	−0.427570
$754$	1.26924e7	0.813045
$755$	9.95530e6	0.635605
$756$	1.96270e6	0.124896
$757$	1.99140e7	1.26305	0.631523	−	0.775357i	$-0.282430\pi$
$757$	1.99140e7	1.26305	0.631523	+	0.775357i	$0.282430\pi$
$758$	6.54583e6	0.413801
$759$	−683173.	−0.0430453
$760$	−8.15337e6	−0.512039
$761$	7.12189e6	0.445793	0.222897	−	0.974842i	$-0.428449\pi$
$761$	7.12189e6	0.445793	0.222897	+	0.974842i	$0.428449\pi$
$762$	4.23476e6	0.264205
$763$	1.06862e7	0.664526
$764$	1.55702e7	0.965076
$765$	8.38722e6	0.518161
$766$	2.94051e6	0.181072
$767$	2.83566e6	0.174047
$768$	−1.06925e6	−0.0654145
$769$	−1.73482e7	−1.05788	−0.528941	−	0.848658i	$-0.677411\pi$
$769$	−1.73482e7	−1.05788	−0.528941	+	0.848658i	$0.677411\pi$
$770$	4.95024e6	0.300884
$771$	3.46809e6	0.210114
$772$	−2.13536e7	−1.28952
$773$	1.42390e7	0.857096	0.428548	−	0.903519i	$-0.359025\pi$
$773$	1.42390e7	0.857096	0.428548	+	0.903519i	$0.359025\pi$
$774$	329135.	0.0197479
$775$	−9.76908e6	−0.584251
$776$	−1.81032e7	−1.07920
$777$	−4.20117e6	−0.249642
$778$	−1.06127e7	−0.628604
$779$	−6.59569e6	−0.389418
$780$	−1.64102e7	−0.965778
$781$	7.77232e6	0.455956
$782$	685229.	0.0400699
$783$	5.40222e6	0.314897
$784$	−4.50561e6	−0.261796
$785$	−9.78415e6	−0.566694
$786$	−4.69058e6	−0.270813
$787$	1.80722e7	1.04010	0.520049	−	0.854137i	$-0.325914\pi$
$787$	1.80722e7	1.04010	0.520049	+	0.854137i	$0.325914\pi$
$788$	−1.46343e7	−0.839570
$789$	−8.16383e6	−0.466876
$790$	−8.75324e6	−0.499001
$791$	1.29589e7	0.736424
$792$	−3.01524e6	−0.170809
$793$	−7.72931e6	−0.436474
$794$	−1.10198e7	−0.620329
$795$	−1.11408e7	−0.625168
$796$	−3.54313e6	−0.198200
$797$	1.94132e7	1.08256	0.541280	−	0.840843i	$-0.317940\pi$
$797$	1.94132e7	1.08256	0.541280	+	0.840843i	$0.317940\pi$
$798$	1.48146e6	0.0823536
$799$	−2.96156e7	−1.64117
$800$	−1.83838e7	−1.01557
$801$	8.45827e6	0.465801
$802$	8.98490e6	0.493261
$803$	−2.31270e6	−0.126570
$804$	−6.95352e6	−0.379371
$805$	2.02384e6	0.110075
$806$	−4.83329e6	−0.262063
$807$	1.49158e7	0.806235
$808$	633180.	0.0341192
$809$	−2.24002e7	−1.20332	−0.601659	−	0.798753i	$-0.705493\pi$
$809$	−2.24002e7	−1.20332	−0.601659	+	0.798753i	$0.705493\pi$
$810$	1.11958e6	0.0599576
$811$	−1.60987e7	−0.859486	−0.429743	−	0.902951i	$-0.641396\pi$
$811$	−1.60987e7	−0.859486	−0.429743	+	0.902951i	$0.641396\pi$
$812$	1.99513e7	1.06190
$813$	2.01021e7	1.06663
$814$	2.98762e6	0.158039
$815$	4.53627e7	2.39224
$816$	−7.10940e6	−0.373773
$817$	−1.54987e6	−0.0812346
$818$	−1.40937e7	−0.736446
$819$	6.44139e6	0.335560
$820$	−1.84089e7	−0.956075
$821$	3.03172e7	1.56975	0.784877	−	0.619651i	$-0.212726\pi$
$821$	3.03172e7	1.56975	0.784877	+	0.619651i	$0.212726\pi$
$822$	−3.83749e6	−0.198092
$823$	7.97674e6	0.410512	0.205256	−	0.978708i	$-0.434197\pi$
$823$	7.97674e6	0.410512	0.205256	+	0.978708i	$0.434197\pi$
$824$	−1.55916e6	−0.0799970
$825$	−9.25861e6	−0.473599
$826$	−714491.	−0.0364373
$827$	1.52413e7	0.774923	0.387461	−	0.921886i	$-0.373352\pi$
$827$	1.52413e7	0.774923	0.387461	+	0.921886i	$0.373352\pi$
$828$	−570638.	−0.0289258
$829$	1.31859e7	0.666384	0.333192	−	0.942859i	$-0.391874\pi$
$829$	1.31859e7	0.666384	0.333192	+	0.942859i	$0.391874\pi$
$830$	3.02496e6	0.152414
$831$	−7.07060e6	−0.355184
$832$	7.04426e6	0.352799
$833$	9.28435e6	0.463595
$834$	3.64991e6	0.181705
$835$	−1.83104e7	−0.908830
$836$	6.57252e6	0.325249
$837$	−2.05718e6	−0.101498
$838$	3.12982e6	0.153960
$839$	1.87408e7	0.919144	0.459572	−	0.888141i	$-0.348003\pi$
$839$	1.87408e7	0.919144	0.459572	+	0.888141i	$0.348003\pi$
$840$	8.93242e6	0.436788
$841$	3.44037e7	1.67732
$842$	−8.91952e6	−0.433572
$843$	1.59982e7	0.775358
$844$	1.23352e7	0.596062
$845$	−2.37227e7	−1.14294
$846$	−3.95329e6	−0.189903
$847$	7.10149e6	0.340127
$848$	9.44343e6	0.450962
$849$	7.17441e6	0.341599
$850$	9.28647e6	0.440863
$851$	1.22145e6	0.0578167
$852$	6.49204e6	0.306395
$853$	3.32001e7	1.56231	0.781153	−	0.624339i	$-0.214632\pi$
$853$	3.32001e7	1.56231	0.781153	+	0.624339i	$0.214632\pi$
$854$	1.94753e6	0.0913774
$855$	−5.27204e6	−0.246640
$856$	7.79663e6	0.363682
$857$	1.05094e7	0.488795	0.244397	−	0.969675i	$-0.421410\pi$
$857$	1.05094e7	0.488795	0.244397	+	0.969675i	$0.421410\pi$
$858$	−4.58073e6	−0.212430
$859$	1.47534e7	0.682198	0.341099	−	0.940027i	$-0.389201\pi$
$859$	1.47534e7	0.682198	0.341099	+	0.940027i	$0.389201\pi$
$860$	−4.32576e6	−0.199442
$861$	7.22591e6	0.332188
$862$	−1.42576e7	−0.653550
$863$	3.15055e7	1.43999	0.719994	−	0.693980i	$-0.244144\pi$
$863$	3.15055e7	1.43999	0.719994	+	0.693980i	$0.244144\pi$
$864$	−3.87128e6	−0.176429
$865$	−1.23357e7	−0.560564
$866$	6.07912e6	0.275452
$867$	1.87106e6	0.0845355
$868$	−7.59752e6	−0.342273
$869$	1.52432e7	0.684742
$870$	1.13808e7	0.509772
$871$	−2.28207e7	−1.01926
$872$	−1.37127e7	−0.610704
$873$	−1.17057e7	−0.519831
$874$	−430721.	−0.0190729
$875$	2.66885e6	0.117843
$876$	−1.93175e6	−0.0850530
$877$	1.78432e7	0.783380	0.391690	−	0.920097i	$-0.371891\pi$
$877$	1.78432e7	0.783380	0.391690	+	0.920097i	$0.371891\pi$
$878$	2.42808e6	0.106298
$879$	−1.28021e6	−0.0558867
$880$	1.49324e7	0.650015
$881$	−4.44430e6	−0.192914	−0.0964569	−	0.995337i	$-0.530751\pi$
$881$	−4.44430e6	−0.192914	−0.0964569	+	0.995337i	$0.530751\pi$
$882$	1.23934e6	0.0536437
$883$	2.25724e7	0.974264	0.487132	−	0.873328i	$-0.338043\pi$
$883$	2.25724e7	0.974264	0.487132	+	0.873328i	$0.338043\pi$
$884$	−2.86633e7	−1.23366
$885$	2.54264e6	0.109126
$886$	713855.	0.0305510
$887$	−1.77218e7	−0.756307	−0.378153	−	0.925743i	$-0.623441\pi$
$887$	−1.77218e7	−0.756307	−0.378153	+	0.925743i	$0.623441\pi$
$888$	5.39100e6	0.229423
$889$	2.18466e7	0.927104
$890$	1.78190e7	0.754064
$891$	−1.94968e6	−0.0822754
$892$	−1.44302e7	−0.607240
$893$	1.86158e7	0.781182
$894$	−4.00211e6	−0.167473
$895$	6.50558e7	2.71474
$896$	−1.83640e7	−0.764182
$897$	−1.87278e6	−0.0777150
$898$	1.60946e7	0.666025
$899$	−2.09117e7	−0.862960
$900$	−7.73350e6	−0.318251
$901$	−1.94593e7	−0.798574
$902$	−5.13863e6	−0.210296
$903$	1.69796e6	0.0692961
$904$	−1.66291e7	−0.676779
$905$	−5.50683e7	−2.23501
$906$	2.32116e6	0.0939476
$907$	−309663.	−0.0124989	−0.00624944	−	0.999980i	$-0.501989\pi$
$907$	−309663.	−0.0124989	−0.00624944	+	0.999980i	$0.501989\pi$
$908$	−9.92852e6	−0.399641
$909$	409420.	0.0164346
$910$	1.35701e7	0.543223
$911$	3.21108e7	1.28190	0.640952	−	0.767581i	$-0.278540\pi$
$911$	3.21108e7	1.28190	0.640952	+	0.767581i	$0.278540\pi$
$912$	4.46883e6	0.177913
$913$	−5.26777e6	−0.209146
$914$	9.52958e6	0.377318
$915$	−6.93063e6	−0.273665
$916$	3.23225e7	1.27282
$917$	−2.41981e7	−0.950292
$918$	1.95555e6	0.0765884
$919$	−1.92631e7	−0.752380	−0.376190	−	0.926543i	$-0.622766\pi$
$919$	−1.92631e7	−0.752380	−0.376190	+	0.926543i	$0.622766\pi$
$920$	−2.59702e6	−0.101159
$921$	2.04105e7	0.792874
$922$	2.10254e6	0.0814549
$923$	2.13062e7	0.823194
$924$	−7.20052e6	−0.277450
$925$	1.65536e7	0.636118
$926$	−1.60119e7	−0.613643
$927$	−1.00817e6	−0.0385332
$928$	−3.93525e7	−1.50004
$929$	−2.58406e7	−0.982344	−0.491172	−	0.871063i	$-0.663431\pi$
$929$	−2.58406e7	−0.982344	−0.491172	+	0.871063i	$0.663431\pi$
$930$	−4.33386e6	−0.164311
$931$	−5.83596e6	−0.220667
$932$	−4.49855e6	−0.169642
$933$	2.38766e7	0.897985
$934$	6.29549e6	0.236136
$935$	−3.07700e7	−1.15106
$936$	−8.26567e6	−0.308382
$937$	−3.94413e7	−1.46758	−0.733791	−	0.679375i	$-0.762251\pi$
$937$	−3.94413e7	−1.46758	−0.733791	+	0.679375i	$0.762251\pi$
$938$	5.75006e6	0.213386
$939$	2.32741e7	0.861406
$940$	5.19574e7	1.91791
$941$	−3.84459e7	−1.41539	−0.707695	−	0.706518i	$-0.750265\pi$
$941$	−3.84459e7	−1.41539	−0.707695	+	0.706518i	$0.750265\pi$
$942$	−2.28126e6	−0.0837621
$943$	−2.10087e6	−0.0769342
$944$	−2.15526e6	−0.0787174
$945$	5.77579e6	0.210393
$946$	−1.20749e6	−0.0438688
$947$	−1.88805e7	−0.684129	−0.342065	−	0.939676i	$-0.611126\pi$
$947$	−1.88805e7	−0.684129	−0.342065	+	0.939676i	$0.611126\pi$
$948$	1.27323e7	0.460136
$949$	−6.33979e6	−0.228512
$950$	−5.83729e6	−0.209847
$951$	−1.65846e7	−0.594640
$952$	1.56021e7	0.557942
$953$	−1.50588e7	−0.537103	−0.268552	−	0.963265i	$-0.586545\pi$
$953$	−1.50588e7	−0.537103	−0.268552	+	0.963265i	$0.586545\pi$
$954$	−2.59756e6	−0.0924049
$955$	4.58196e7	1.62571
$956$	−3.65816e7	−1.29455
$957$	−1.98190e7	−0.699523
$958$	−1.35072e7	−0.475500
$959$	−1.97971e7	−0.695112
$960$	6.31636e6	0.221202
$961$	−2.06659e7	−0.721848
$962$	8.18996e6	0.285328
$963$	5.04137e6	0.175179
$964$	−4.20880e7	−1.45870
$965$	−6.28388e7	−2.17225
$966$	471877.	0.0162699
$967$	1.72922e7	0.594681	0.297340	−	0.954772i	$-0.403900\pi$
$967$	1.72922e7	0.594681	0.297340	+	0.954772i	$0.403900\pi$
$968$	−9.11272e6	−0.312579
$969$	−9.20856e6	−0.315052
$970$	−2.46604e7	−0.841531
$971$	2.51318e7	0.855411	0.427705	−	0.903918i	$-0.359322\pi$
$971$	2.51318e7	0.855411	0.427705	+	0.903918i	$0.359322\pi$
$972$	−1.62853e6	−0.0552878
$973$	1.88294e7	0.637609
$974$	−1.98574e7	−0.670695
$975$	−2.53806e7	−0.855046
$976$	5.87472e6	0.197407
$977$	3.05606e7	1.02430	0.512148	−	0.858897i	$-0.328850\pi$
$977$	3.05606e7	1.02430	0.512148	+	0.858897i	$0.328850\pi$
$978$	1.05767e7	0.353593
$979$	−3.10306e7	−1.03475
$980$	−1.62884e7	−0.541768
$981$	−8.86674e6	−0.294165
$982$	1.65555e7	0.547853
$983$	2.31760e7	0.764989	0.382495	−	0.923958i	$-0.375065\pi$
$983$	2.31760e7	0.764989	0.382495	+	0.923958i	$0.375065\pi$
$984$	−9.27237e6	−0.305283
$985$	−4.30654e7	−1.41429
$986$	1.98787e7	0.651171
$987$	−2.03945e7	−0.666377
$988$	1.80172e7	0.587212
$989$	−493668.	−0.0160489
$990$	−4.10739e6	−0.133192
$991$	−3.50375e7	−1.13331	−0.566655	−	0.823955i	$-0.691763\pi$
$991$	−3.50375e7	−1.13331	−0.566655	+	0.823955i	$0.691763\pi$
$992$	1.49855e7	0.483497
$993$	−1.37767e6	−0.0443375
$994$	−5.36845e6	−0.172339
$995$	−1.04266e7	−0.333876
$996$	−4.40005e6	−0.140543
$997$	−5.65148e6	−0.180063	−0.0900314	−	0.995939i	$-0.528697\pi$
$997$	−5.65148e6	−0.180063	−0.0900314	+	0.995939i	$0.528697\pi$
$998$	−1.71216e7	−0.544150
$999$	3.48587e6	0.110509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.4	✓	12
3.2	odd	2		531.6.a.c.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.4	✓	12	1.1	even	1	trivial
531.6.a.c.1.9		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10256 q^{2} +9.00000 q^{3} -27.5792 q^{4} -81.1594 q^{5} -18.9230 q^{6} -97.6213 q^{7} +125.269 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-2.10256 q^{2} +9.00000 q^{3} -27.5792 q^{4} -81.1594 q^{5} -18.9230 q^{6} -97.6213 q^{7} +125.269 q^{8} +81.0000 q^{9} +170.642 q^{10} -297.163 q^{11} -248.213 q^{12} -814.611 q^{13} +205.254 q^{14} -730.435 q^{15} +619.151 q^{16} -1275.83 q^{17} -170.307 q^{18} +801.964 q^{19} +2238.32 q^{20} -878.592 q^{21} +624.802 q^{22} +255.443 q^{23} +1127.42 q^{24} +3461.85 q^{25} +1712.77 q^{26} +729.000 q^{27} +2692.32 q^{28} +7410.46 q^{29} +1535.78 q^{30} -2821.92 q^{31} -5310.40 q^{32} -2674.46 q^{33} +2682.51 q^{34} +7922.89 q^{35} -2233.92 q^{36} +4781.71 q^{37} -1686.18 q^{38} -7331.50 q^{39} -10166.7 q^{40} -8224.42 q^{41} +1847.29 q^{42} -1932.60 q^{43} +8195.53 q^{44} -6573.91 q^{45} -537.083 q^{46} +23212.7 q^{47} +5572.36 q^{48} -7277.08 q^{49} -7278.75 q^{50} -11482.5 q^{51} +22466.3 q^{52} +15252.2 q^{53} -1532.76 q^{54} +24117.6 q^{55} -12228.9 q^{56} +7217.68 q^{57} -15580.9 q^{58} -3481.00 q^{59} +20144.8 q^{60} +9488.35 q^{61} +5933.26 q^{62} -7907.33 q^{63} -8647.40 q^{64} +66113.3 q^{65} +5623.22 q^{66} +28014.3 q^{67} +35186.5 q^{68} +2298.98 q^{69} -16658.3 q^{70} -26155.1 q^{71} +10146.8 q^{72} +7782.60 q^{73} -10053.8 q^{74} +31156.7 q^{75} -22117.6 q^{76} +29009.4 q^{77} +15414.9 q^{78} -51295.8 q^{79} -50249.9 q^{80} +6561.00 q^{81} +17292.3 q^{82} +17726.9 q^{83} +24230.9 q^{84} +103546. q^{85} +4063.40 q^{86} +66694.1 q^{87} -37225.2 q^{88} +104423. q^{89} +13822.0 q^{90} +79523.3 q^{91} -7044.92 q^{92} -25397.3 q^{93} -48806.1 q^{94} -65086.9 q^{95} -47793.6 q^{96} -144515. q^{97} +15300.5 q^{98} -24070.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * q^99

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