LMFDB - Embedded newform 177.6.a.c.1.8

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			1.8
Root			$-3.21799$ 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)

$f(q)$	$=$	$q+5.21799 q^{2} +9.00000 q^{3} -4.77260 q^{4} -21.6600 q^{5} +46.9619 q^{6} +150.168 q^{7} -191.879 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+5.21799 q^{2} +9.00000 q^{3} -4.77260 q^{4} -21.6600 q^{5} +46.9619 q^{6} +150.168 q^{7} -191.879 q^{8} +81.0000 q^{9} -113.022 q^{10} +527.794 q^{11} -42.9534 q^{12} +51.3772 q^{13} +783.574 q^{14} -194.940 q^{15} -848.499 q^{16} -968.342 q^{17} +422.657 q^{18} +2271.01 q^{19} +103.375 q^{20} +1351.51 q^{21} +2754.02 q^{22} +3803.24 q^{23} -1726.91 q^{24} -2655.84 q^{25} +268.086 q^{26} +729.000 q^{27} -716.691 q^{28} +7264.82 q^{29} -1017.20 q^{30} -513.041 q^{31} +1712.67 q^{32} +4750.15 q^{33} -5052.79 q^{34} -3252.64 q^{35} -386.581 q^{36} +11311.7 q^{37} +11850.1 q^{38} +462.395 q^{39} +4156.10 q^{40} +17019.0 q^{41} +7052.17 q^{42} -7359.17 q^{43} -2518.95 q^{44} -1754.46 q^{45} +19845.3 q^{46} -15367.8 q^{47} -7636.49 q^{48} +5743.39 q^{49} -13858.2 q^{50} -8715.07 q^{51} -245.203 q^{52} -32078.1 q^{53} +3803.91 q^{54} -11432.0 q^{55} -28814.1 q^{56} +20439.1 q^{57} +37907.7 q^{58} -3481.00 q^{59} +930.371 q^{60} +13858.8 q^{61} -2677.04 q^{62} +12163.6 q^{63} +36088.7 q^{64} -1112.83 q^{65} +24786.2 q^{66} -26206.8 q^{67} +4621.51 q^{68} +34229.2 q^{69} -16972.2 q^{70} -49223.6 q^{71} -15542.2 q^{72} -5312.00 q^{73} +59024.5 q^{74} -23902.6 q^{75} -10838.6 q^{76} +79257.7 q^{77} +2412.77 q^{78} -41133.2 q^{79} +18378.5 q^{80} +6561.00 q^{81} +88805.2 q^{82} +60927.7 q^{83} -6450.22 q^{84} +20974.3 q^{85} -38400.0 q^{86} +65383.3 q^{87} -101273. q^{88} +4240.18 q^{89} -9154.76 q^{90} +7715.21 q^{91} -18151.3 q^{92} -4617.37 q^{93} -80188.8 q^{94} -49190.1 q^{95} +15414.0 q^{96} -4918.71 q^{97} +29968.9 q^{98} +42751.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.21799	0.922419	0.461209	−	0.887291i	$-0.347416\pi$
$2$	5.21799	0.922419	0.461209	+	0.887291i	$0.347416\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−4.77260	−0.149144
$5$	−21.6600	−0.387466	−0.193733	−	0.981054i	$-0.562060\pi$
$5$	−21.6600	−0.387466	−0.193733	+	0.981054i	$0.562060\pi$
$6$	46.9619	0.532559
$7$	150.168	1.15833	0.579164	−	0.815211i	$-0.303379\pi$
$7$	150.168	1.15833	0.579164	+	0.815211i	$0.303379\pi$
$8$	−191.879	−1.05999
$9$	81.0000	0.333333
$10$	−113.022	−0.357406
$11$	527.794	1.31517	0.657587	−	0.753379i	$-0.271577\pi$
$11$	527.794	1.31517	0.657587	+	0.753379i	$0.271577\pi$
$12$	−42.9534	−0.0861082
$13$	51.3772	0.0843165	0.0421582	−	0.999111i	$-0.486577\pi$
$13$	51.3772	0.0843165	0.0421582	+	0.999111i	$0.486577\pi$
$14$	783.574	1.06846
$15$	−194.940	−0.223704
$16$	−848.499	−0.828612
$17$	−968.342	−0.812655	−0.406328	−	0.913727i	$-0.633191\pi$
$17$	−968.342	−0.812655	−0.406328	+	0.913727i	$0.633191\pi$
$18$	422.657	0.307473
$19$	2271.01	1.44323	0.721614	−	0.692296i	$-0.243401\pi$
$19$	2271.01	1.44323	0.721614	+	0.692296i	$0.243401\pi$
$20$	103.375	0.0577881
$21$	1351.51	0.668762
$22$	2754.02	1.21314
$23$	3803.24	1.49911	0.749556	−	0.661941i	$-0.230267\pi$
$23$	3803.24	1.49911	0.749556	+	0.661941i	$0.230267\pi$
$24$	−1726.91	−0.611986
$25$	−2655.84	−0.849870
$26$	268.086	0.0777751
$27$	729.000	0.192450
$28$	−716.691	−0.172757
$29$	7264.82	1.60409	0.802047	−	0.597261i	$-0.203744\pi$
$29$	7264.82	1.60409	0.802047	+	0.597261i	$0.203744\pi$
$30$	−1017.20	−0.206348
$31$	−513.041	−0.0958843	−0.0479422	−	0.998850i	$-0.515266\pi$
$31$	−513.041	−0.0958843	−0.0479422	+	0.998850i	$0.515266\pi$
$32$	1712.67	0.295664
$33$	4750.15	0.759316
$34$	−5052.79	−0.749608
$35$	−3252.64	−0.448813
$36$	−386.581	−0.0497146
$37$	11311.7	1.35839	0.679196	−	0.733957i	$-0.262329\pi$
$37$	11311.7	1.35839	0.679196	+	0.733957i	$0.262329\pi$
$38$	11850.1	1.33126
$39$	462.395	0.0486801
$40$	4156.10	0.410711
$41$	17019.0	1.58116	0.790579	−	0.612360i	$-0.209780\pi$
$41$	17019.0	1.58116	0.790579	+	0.612360i	$0.209780\pi$
$42$	7052.17	0.616878
$43$	−7359.17	−0.606956	−0.303478	−	0.952838i	$-0.598148\pi$
$43$	−7359.17	−0.606956	−0.303478	+	0.952838i	$0.598148\pi$
$44$	−2518.95	−0.196150
$45$	−1754.46	−0.129155
$46$	19845.3	1.38281
$47$	−15367.8	−1.01477	−0.507383	−	0.861720i	$-0.669387\pi$
$47$	−15367.8	−1.01477	−0.507383	+	0.861720i	$0.669387\pi$
$48$	−7636.49	−0.478400
$49$	5743.39	0.341726
$50$	−13858.2	−0.783936
$51$	−8715.07	−0.469187
$52$	−245.203	−0.0125753
$53$	−32078.1	−1.56862	−0.784312	−	0.620367i	$-0.786984\pi$
$53$	−32078.1	−1.56862	−0.784312	+	0.620367i	$0.786984\pi$
$54$	3803.91	0.177520
$55$	−11432.0	−0.509585
$56$	−28814.1	−1.22782
$57$	20439.1	0.833248
$58$	37907.7	1.47965
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	930.371	0.0333640
$61$	13858.8	0.476872	0.238436	−	0.971158i	$-0.423365\pi$
$61$	13858.8	0.476872	0.238436	+	0.971158i	$0.423365\pi$
$62$	−2677.04	−0.0884455
$63$	12163.6	0.386110
$64$	36088.7	1.10134
$65$	−1112.83	−0.0326698
$66$	24786.2	0.700407
$67$	−26206.8	−0.713224	−0.356612	−	0.934252i	$-0.616068\pi$
$67$	−26206.8	−0.713224	−0.356612	+	0.934252i	$0.616068\pi$
$68$	4621.51	0.121202
$69$	34229.2	0.865513
$70$	−16972.2	−0.413994
$71$	−49223.6	−1.15885	−0.579426	−	0.815025i	$-0.696723\pi$
$71$	−49223.6	−1.15885	−0.579426	+	0.815025i	$0.696723\pi$
$72$	−15542.2	−0.353331
$73$	−5312.00	−0.116668	−0.0583339	−	0.998297i	$-0.518579\pi$
$73$	−5312.00	−0.116668	−0.0583339	+	0.998297i	$0.518579\pi$
$74$	59024.5	1.25301
$75$	−23902.6	−0.490673
$76$	−10838.6	−0.215248
$77$	79257.7	1.52340
$78$	2412.77	0.0449035
$79$	−41133.2	−0.741524	−0.370762	−	0.928728i	$-0.620903\pi$
$79$	−41133.2	−0.741524	−0.370762	+	0.928728i	$0.620903\pi$
$80$	18378.5	0.321059
$81$	6561.00	0.111111
$82$	88805.2	1.45849
$83$	60927.7	0.970777	0.485388	−	0.874299i	$-0.338678\pi$
$83$	60927.7	0.970777	0.485388	+	0.874299i	$0.338678\pi$
$84$	−6450.22	−0.0997416
$85$	20974.3	0.314876
$86$	−38400.0	−0.559868
$87$	65383.3	0.926124
$88$	−101273.	−1.39407
$89$	4240.18	0.0567426	0.0283713	−	0.999597i	$-0.490968\pi$
$89$	4240.18	0.0567426	0.0283713	+	0.999597i	$0.490968\pi$
$90$	−9154.76	−0.119135
$91$	7715.21	0.0976662
$92$	−18151.3	−0.223583
$93$	−4617.37	−0.0553588
$94$	−80188.8	−0.936040
$95$	−49190.1	−0.559202
$96$	15414.0	0.170702
$97$	−4918.71	−0.0530789	−0.0265395	−	0.999648i	$-0.508449\pi$
$97$	−4918.71	−0.0530789	−0.0265395	+	0.999648i	$0.508449\pi$
$98$	29968.9	0.315214
$99$	42751.3	0.438391
$100$	12675.3	0.126753
$101$	−152708.	−1.48956	−0.744780	−	0.667310i	$-0.767446\pi$
$101$	−152708.	−1.48956	−0.744780	+	0.667310i	$0.767446\pi$
$102$	−45475.2	−0.432787
$103$	104142.	0.967237	0.483619	−	0.875279i	$-0.339322\pi$
$103$	104142.	0.967237	0.483619	+	0.875279i	$0.339322\pi$
$104$	−9858.21	−0.0893747
$105$	−29273.7	−0.259122
$106$	−167383.	−1.44693
$107$	148892.	1.25722	0.628611	−	0.777720i	$-0.283624\pi$
$107$	148892.	1.25722	0.628611	+	0.777720i	$0.283624\pi$
$108$	−3479.22	−0.0287027
$109$	−115623.	−0.932135	−0.466067	−	0.884749i	$-0.654330\pi$
$109$	−115623.	−0.932135	−0.466067	+	0.884749i	$0.654330\pi$
$110$	−59652.2	−0.470051
$111$	101806.	0.784268
$112$	−127417.	−0.959806
$113$	−6712.64	−0.0494535	−0.0247268	−	0.999694i	$-0.507872\pi$
$113$	−6712.64	−0.0494535	−0.0247268	+	0.999694i	$0.507872\pi$
$114$	106651.	0.768603
$115$	−82378.2	−0.580855
$116$	−34672.1	−0.239240
$117$	4161.56	0.0281055
$118$	−18163.8	−0.120089
$119$	−145414.	−0.941322
$120$	37404.9	0.237124
$121$	117516.	0.729680
$122$	72315.2	0.439876
$123$	153171.	0.912882
$124$	2448.54	0.0143005
$125$	125213.	0.716762
$126$	63469.5	0.356155
$127$	−254609.	−1.40076	−0.700381	−	0.713769i	$-0.746986\pi$
$127$	−254609.	−1.40076	−0.700381	+	0.713769i	$0.746986\pi$
$128$	133505.	0.720231
$129$	−66232.5	−0.350426
$130$	−5806.74	−0.0301352
$131$	−246062.	−1.25276	−0.626379	−	0.779519i	$-0.715464\pi$
$131$	−246062.	−1.25276	−0.626379	+	0.779519i	$0.715464\pi$
$132$	−22670.6	−0.113247
$133$	341032.	1.67173
$134$	−136747.	−0.657892
$135$	−15790.2	−0.0745679
$136$	185804.	0.861408
$137$	171097.	0.778827	0.389413	−	0.921063i	$-0.372678\pi$
$137$	171097.	0.778827	0.389413	+	0.921063i	$0.372678\pi$
$138$	178607.	0.798365
$139$	−256672.	−1.12678	−0.563392	−	0.826189i	$-0.690504\pi$
$139$	−256672.	−1.12678	−0.563392	+	0.826189i	$0.690504\pi$
$140$	15523.5	0.0669377
$141$	−138310.	−0.585876
$142$	−256848.	−1.06895
$143$	27116.6	0.110891
$144$	−68728.4	−0.276204
$145$	−157356.	−0.621532
$146$	−27718.0	−0.107617
$147$	51690.5	0.197296
$148$	−53986.4	−0.202596
$149$	122191.	0.450894	0.225447	−	0.974255i	$-0.427616\pi$
$149$	122191.	0.450894	0.225447	+	0.974255i	$0.427616\pi$
$150$	−124723.	−0.452606
$151$	−485698.	−1.73350	−0.866750	−	0.498743i	$-0.833795\pi$
$151$	−485698.	−1.73350	−0.866750	+	0.498743i	$0.833795\pi$
$152$	−435759.	−1.52981
$153$	−78435.7	−0.270885
$154$	413566.	1.40522
$155$	11112.5	0.0371519
$156$	−2206.83	−0.00726034
$157$	−472070.	−1.52847	−0.764235	−	0.644938i	$-0.776883\pi$
$157$	−472070.	−1.52847	−0.764235	+	0.644938i	$0.776883\pi$
$158$	−214633.	−0.683995
$159$	−288703.	−0.905645
$160$	−37096.4	−0.114560
$161$	571124.	1.73646
$162$	34235.2	0.102491
$163$	253916.	0.748549	0.374275	−	0.927318i	$-0.377892\pi$
$163$	253916.	0.748549	0.374275	+	0.927318i	$0.377892\pi$
$164$	−81225.1	−0.235820
$165$	−102888.	−0.294209
$166$	317920.	0.895463
$167$	−79311.3	−0.220061	−0.110031	−	0.993928i	$-0.535095\pi$
$167$	−79311.3	−0.220061	−0.110031	+	0.993928i	$0.535095\pi$
$168$	−259327.	−0.708882
$169$	−368653.	−0.992891
$170$	109444.	0.290448
$171$	183952.	0.481076
$172$	35122.3	0.0905237
$173$	551760.	1.40163	0.700817	−	0.713341i	$-0.252819\pi$
$173$	551760.	1.40163	0.700817	+	0.713341i	$0.252819\pi$
$174$	341170.	0.854274
$175$	−398822.	−0.984429
$176$	−447833.	−1.08977
$177$	−31329.0	−0.0751646
$178$	22125.2	0.0523405
$179$	738237.	1.72212	0.861060	−	0.508504i	$-0.169801\pi$
$179$	738237.	1.72212	0.861060	+	0.508504i	$0.169801\pi$
$180$	8373.34	0.0192627
$181$	663540.	1.50546	0.752732	−	0.658327i	$-0.228736\pi$
$181$	663540.	1.50546	0.752732	+	0.658327i	$0.228736\pi$
$182$	40257.9	0.0900891
$183$	124729.	0.275322
$184$	−729762.	−1.58905
$185$	−245013.	−0.526331
$186$	−24093.4	−0.0510640
$187$	−511085.	−1.06878
$188$	73344.2	0.151346
$189$	109472.	0.222921
$190$	−256673.	−0.515818
$191$	−825937.	−1.63819	−0.819093	−	0.573660i	$-0.805523\pi$
$191$	−825937.	−1.63819	−0.819093	+	0.573660i	$0.805523\pi$
$192$	324798.	0.635858
$193$	−596260.	−1.15224	−0.576120	−	0.817365i	$-0.695434\pi$
$193$	−596260.	−1.15224	−0.576120	+	0.817365i	$0.695434\pi$
$194$	−25665.8	−0.0489610
$195$	−10015.5	−0.0188619
$196$	−27410.9	−0.0509663
$197$	847138.	1.55521	0.777604	−	0.628754i	$-0.216435\pi$
$197$	847138.	1.55521	0.777604	+	0.628754i	$0.216435\pi$
$198$	223076.	0.404380
$199$	−481833.	−0.862509	−0.431254	−	0.902230i	$-0.641929\pi$
$199$	−481833.	−0.862509	−0.431254	+	0.902230i	$0.641929\pi$
$200$	509601.	0.900855
$201$	−235861.	−0.411780
$202$	−796828.	−1.37400
$203$	1.09094e6	1.85807
$204$	41593.6	0.0699762
$205$	−368633.	−0.612645
$206$	543412.	0.892198
$207$	308062.	0.499704
$208$	−43593.5	−0.0698657
$209$	1.19863e6	1.89809
$210$	−152750.	−0.239019
$211$	612379.	0.946922	0.473461	−	0.880815i	$-0.343005\pi$
$211$	612379.	0.946922	0.473461	+	0.880815i	$0.343005\pi$
$212$	153096.	0.233950
$213$	−443013.	−0.669063
$214$	776917.	1.15969
$215$	159400.	0.235175
$216$	−139880.	−0.203995
$217$	−77042.2	−0.111066
$218$	−603320.	−0.859818
$219$	−47808.0	−0.0673582
$220$	54560.5	0.0760014
$221$	−49750.7	−0.0685202
$222$	531221.	0.723424
$223$	1.24590e6	1.67773	0.838865	−	0.544340i	$-0.183220\pi$
$223$	1.24590e6	1.67773	0.838865	+	0.544340i	$0.183220\pi$
$224$	257188.	0.342476
$225$	−215123.	−0.283290
$226$	−35026.5	−0.0456169
$227$	−1.24352e6	−1.60173	−0.800864	−	0.598846i	$-0.795626\pi$
$227$	−1.24352e6	−1.60173	−0.800864	+	0.598846i	$0.795626\pi$
$228$	−97547.5	−0.124274
$229$	524991.	0.661550	0.330775	−	0.943710i	$-0.392690\pi$
$229$	524991.	0.661550	0.330775	+	0.943710i	$0.392690\pi$
$230$	−429849.	−0.535792
$231$	713320.	0.879537
$232$	−1.39397e6	−1.70033
$233$	529442.	0.638894	0.319447	−	0.947604i	$-0.396503\pi$
$233$	529442.	0.638894	0.319447	+	0.947604i	$0.396503\pi$
$234$	21714.9	0.0259250
$235$	332866.	0.393188
$236$	16613.4	0.0194169
$237$	−370199.	−0.428119
$238$	−758767.	−0.868293
$239$	−443263.	−0.501958	−0.250979	−	0.967993i	$-0.580752\pi$
$239$	−443263.	−0.501958	−0.250979	+	0.967993i	$0.580752\pi$
$240$	165407.	0.185364
$241$	−54132.2	−0.0600362	−0.0300181	−	0.999549i	$-0.509556\pi$
$241$	−54132.2	−0.0600362	−0.0300181	+	0.999549i	$0.509556\pi$
$242$	613196.	0.673071
$243$	59049.0	0.0641500
$244$	−66142.6	−0.0711225
$245$	−124402.	−0.132407
$246$	799246.	0.842060
$247$	116678.	0.121688
$248$	98441.7	0.101637
$249$	548349.	0.560478
$250$	653361.	0.661155
$251$	841171.	0.842753	0.421376	−	0.906886i	$-0.361547\pi$
$251$	841171.	0.842753	0.421376	+	0.906886i	$0.361547\pi$
$252$	−58052.0	−0.0575858
$253$	2.00733e6	1.97159
$254$	−1.32855e6	−1.29209
$255$	188769.	0.181794
$256$	−458211.	−0.436984
$257$	−338918.	−0.320083	−0.160041	−	0.987110i	$-0.551163\pi$
$257$	−338918.	−0.320083	−0.160041	+	0.987110i	$0.551163\pi$
$258$	−345600.	−0.323240
$259$	1.69866e6	1.57347
$260$	5311.10	0.00487249
$261$	588450.	0.534698
$262$	−1.28395e6	−1.15557
$263$	2.18386e6	1.94686	0.973431	−	0.228981i	$-0.0735395\pi$
$263$	2.18386e6	1.94686	0.973431	+	0.228981i	$0.0735395\pi$
$264$	−911454.	−0.804868
$265$	694812.	0.607789
$266$	1.77950e6	1.54204
$267$	38161.6	0.0327604
$268$	125074.	0.106373
$269$	−104452.	−0.0880108	−0.0440054	−	0.999031i	$-0.514012\pi$
$269$	−104452.	−0.0880108	−0.0440054	+	0.999031i	$0.514012\pi$
$270$	−82392.8	−0.0687828
$271$	−263637.	−0.218063	−0.109032	−	0.994038i	$-0.534775\pi$
$271$	−263637.	−0.218063	−0.109032	+	0.994038i	$0.534775\pi$
$272$	821637.	0.673376
$273$	69436.9	0.0563876
$274$	892782.	0.718405
$275$	−1.40174e6	−1.11773
$276$	−163362.	−0.129086
$277$	677687.	0.530677	0.265338	−	0.964155i	$-0.414516\pi$
$277$	677687.	0.530677	0.265338	+	0.964155i	$0.414516\pi$
$278$	−1.33931e6	−1.03937
$279$	−41556.3	−0.0319614
$280$	624113.	0.475738
$281$	31956.5	0.0241431	0.0120716	−	0.999927i	$-0.496157\pi$
$281$	31956.5	0.0241431	0.0120716	+	0.999927i	$0.496157\pi$
$282$	−721700.	−0.540423
$283$	395858.	0.293815	0.146907	−	0.989150i	$-0.453068\pi$
$283$	395858.	0.293815	0.146907	+	0.989150i	$0.453068\pi$
$284$	234925.	0.172835
$285$	−442711.	−0.322855
$286$	141494.	0.102288
$287$	2.55571e6	1.83150
$288$	138726.	0.0985547
$289$	−482172.	−0.339592
$290$	−821082.	−0.573313
$291$	−44268.4	−0.0306451
$292$	25352.0	0.0174003
$293$	1.30735e6	0.889658	0.444829	−	0.895616i	$-0.353264\pi$
$293$	1.30735e6	0.889658	0.444829	+	0.895616i	$0.353264\pi$
$294$	269720.	0.181989
$295$	75398.5	0.0504438
$296$	−2.17049e6	−1.43988
$297$	384762.	0.253105
$298$	637593.	0.415913
$299$	195400.	0.126400
$300$	114077.	0.0731807
$301$	−1.10511e6	−0.703055
$302$	−2.53437e6	−1.59901
$303$	−1.37437e6	−0.859998
$304$	−1.92695e6	−1.19588
$305$	−300182.	−0.184772
$306$	−409276.	−0.249869
$307$	−2.11977e6	−1.28364	−0.641820	−	0.766856i	$-0.721820\pi$
$307$	−2.11977e6	−1.28364	−0.641820	+	0.766856i	$0.721820\pi$
$308$	−378265.	−0.227206
$309$	937278.	0.558435
$310$	57984.7	0.0342696
$311$	2.50058e6	1.46602	0.733009	−	0.680219i	$-0.238115\pi$
$311$	2.50058e6	1.46602	0.733009	+	0.680219i	$0.238115\pi$
$312$	−88723.9	−0.0516005
$313$	−3.29921e6	−1.90349	−0.951743	−	0.306897i	$-0.900709\pi$
$313$	−3.29921e6	−1.90349	−0.951743	+	0.306897i	$0.900709\pi$
$314$	−2.46325e6	−1.40989
$315$	−263464.	−0.149604
$316$	196312.	0.110594
$317$	−275609.	−0.154044	−0.0770220	−	0.997029i	$-0.524541\pi$
$317$	−275609.	−0.154044	−0.0770220	+	0.997029i	$0.524541\pi$
$318$	−1.50645e6	−0.835384
$319$	3.83433e6	2.10966
$320$	−781681.	−0.426731
$321$	1.34003e6	0.725858
$322$	2.98012e6	1.60175
$323$	−2.19911e6	−1.17285
$324$	−31313.0	−0.0165715
$325$	−136450.	−0.0716580
$326$	1.32493e6	0.690476
$327$	−1.04061e6	−0.538168
$328$	−3.26560e6	−1.67601
$329$	−2.30775e6	−1.17543
$330$	−536870.	−0.271384
$331$	−2.58017e6	−1.29443	−0.647215	−	0.762307i	$-0.724067\pi$
$331$	−2.58017e6	−1.29443	−0.647215	+	0.762307i	$0.724067\pi$
$332$	−290783.	−0.144785
$333$	916251.	0.452797
$334$	−413846.	−0.202989
$335$	567639.	0.276350
$336$	−1.14676e6	−0.554144
$337$	223512.	0.107208	0.0536039	−	0.998562i	$-0.482929\pi$
$337$	223512.	0.107208	0.0536039	+	0.998562i	$0.482929\pi$
$338$	−1.92363e6	−0.915861
$339$	−60413.8	−0.0285520
$340$	−100102.	−0.0469618
$341$	−270780.	−0.126104
$342$	959858.	0.443753
$343$	−1.66140e6	−0.762498
$344$	1.41207e6	0.643369
$345$	−741404.	−0.335357
$346$	2.87908e6	1.29289
$347$	−2.39743e6	−1.06886	−0.534431	−	0.845212i	$-0.679474\pi$
$347$	−2.39743e6	−1.06886	−0.534431	+	0.845212i	$0.679474\pi$
$348$	−312049.	−0.138126
$349$	1.79102e6	0.787113	0.393557	−	0.919300i	$-0.371245\pi$
$349$	1.79102e6	0.787113	0.393557	+	0.919300i	$0.371245\pi$
$350$	−2.08105e6	−0.908056
$351$	37454.0	0.0162267
$352$	903937.	0.388849
$353$	−883662.	−0.377441	−0.188721	−	0.982031i	$-0.560434\pi$
$353$	−883662.	−0.377441	−0.188721	+	0.982031i	$0.560434\pi$
$354$	−163474.	−0.0693332
$355$	1.06618e6	0.449016
$356$	−20236.7	−0.00846281
$357$	−1.30872e6	−0.543472
$358$	3.85211e6	1.58851
$359$	−597411.	−0.244645	−0.122323	−	0.992490i	$-0.539034\pi$
$359$	−597411.	−0.244645	−0.122323	+	0.992490i	$0.539034\pi$
$360$	336644.	0.136904
$361$	2.68138e6	1.08291
$362$	3.46234e6	1.38867
$363$	1.05764e6	0.421281
$364$	−36821.6	−0.0145663
$365$	115058.	0.0452048
$366$	650837.	0.253962
$367$	−2.44464e6	−0.947437	−0.473719	−	0.880676i	$-0.657089\pi$
$367$	−2.44464e6	−0.947437	−0.473719	+	0.880676i	$0.657089\pi$
$368$	−3.22705e6	−1.24218
$369$	1.37854e6	0.527053
$370$	−1.27847e6	−0.485498
$371$	−4.81710e6	−1.81698
$372$	22036.8	0.00825642
$373$	−3.44062e6	−1.28045	−0.640227	−	0.768186i	$-0.721160\pi$
$373$	−3.44062e6	−1.28045	−0.640227	+	0.768186i	$0.721160\pi$
$374$	−2.66684e6	−0.985865
$375$	1.12692e6	0.413823
$376$	2.94875e6	1.07564
$377$	373246.	0.135251
$378$	571226.	0.205626
$379$	−695527.	−0.248723	−0.124361	−	0.992237i	$-0.539688\pi$
$379$	−695527.	−0.248723	−0.124361	+	0.992237i	$0.539688\pi$
$380$	234765.	0.0834014
$381$	−2.29148e6	−0.808730
$382$	−4.30973e6	−1.51109
$383$	453295.	0.157901	0.0789503	−	0.996879i	$-0.474843\pi$
$383$	453295.	0.157901	0.0789503	+	0.996879i	$0.474843\pi$
$384$	1.20154e6	0.415826
$385$	−1.71672e6	−0.590267
$386$	−3.11128e6	−1.06285
$387$	−596092.	−0.202319
$388$	23475.1	0.00791639
$389$	−5.66314e6	−1.89751	−0.948753	−	0.316017i	$-0.897654\pi$
$389$	−5.66314e6	−1.89751	−0.948753	+	0.316017i	$0.897654\pi$
$390$	−52260.7	−0.0173986
$391$	−3.68283e6	−1.21826
$392$	−1.10204e6	−0.362227
$393$	−2.21456e6	−0.723280
$394$	4.42036e6	1.43455
$395$	890946.	0.287315
$396$	−204035.	−0.0653833
$397$	2.54465e6	0.810312	0.405156	−	0.914248i	$-0.367217\pi$
$397$	2.54465e6	0.810312	0.405156	+	0.914248i	$0.367217\pi$
$398$	−2.51420e6	−0.795594
$399$	3.06929e6	0.965175
$400$	2.25348e6	0.704213
$401$	−168328.	−0.0522753	−0.0261376	−	0.999658i	$-0.508321\pi$
$401$	−168328.	−0.0522753	−0.0261376	+	0.999658i	$0.508321\pi$
$402$	−1.23072e6	−0.379834
$403$	−26358.6	−0.00808462
$404$	728814.	0.222159
$405$	−142111.	−0.0430518
$406$	5.69252e6	1.71392
$407$	5.97027e6	1.78652
$408$	1.67224e6	0.497334
$409$	2.01773e6	0.596423	0.298212	−	0.954500i	$-0.403610\pi$
$409$	2.01773e6	0.596423	0.298212	+	0.954500i	$0.403610\pi$
$410$	−1.92352e6	−0.565116
$411$	1.53987e6	0.449656
$412$	−497028.	−0.144257
$413$	−522734.	−0.150802
$414$	1.60747e6	0.460936
$415$	−1.31969e6	−0.376143
$416$	87992.2	0.0249293
$417$	−2.31005e6	−0.650550
$418$	6.25441e6	1.75084
$419$	3.20396e6	0.891563	0.445782	−	0.895142i	$-0.352926\pi$
$419$	3.20396e6	0.891563	0.445782	+	0.895142i	$0.352926\pi$
$420$	139712.	0.0386465
$421$	993569.	0.273208	0.136604	−	0.990626i	$-0.456381\pi$
$421$	993569.	0.273208	0.136604	+	0.990626i	$0.456381\pi$
$422$	3.19539e6	0.873458
$423$	−1.24479e6	−0.338256
$424$	6.15511e6	1.66273
$425$	2.57176e6	0.690651
$426$	−2.31163e6	−0.617156
$427$	2.08115e6	0.552375
$428$	−710602.	−0.187507
$429$	244049.	0.0640228
$430$	831746.	0.216930
$431$	−7.34140e6	−1.90365	−0.951823	−	0.306649i	$-0.900792\pi$
$431$	−7.34140e6	−1.90365	−0.951823	+	0.306649i	$0.900792\pi$
$432$	−618556.	−0.159467
$433$	−5.16376e6	−1.32357	−0.661784	−	0.749695i	$-0.730200\pi$
$433$	−5.16376e6	−1.32357	−0.661784	+	0.749695i	$0.730200\pi$
$434$	−402005.	−0.102449
$435$	−1.41620e6	−0.358842
$436$	551823.	0.139022
$437$	8.63719e6	2.16356
$438$	−249462.	−0.0621324
$439$	335620.	0.0831163	0.0415582	−	0.999136i	$-0.486768\pi$
$439$	335620.	0.0831163	0.0415582	+	0.999136i	$0.486768\pi$
$440$	2.19357e6	0.540156
$441$	465214.	0.113909
$442$	−259599.	−0.0632043
$443$	6.81650e6	1.65026	0.825129	−	0.564944i	$-0.191102\pi$
$443$	6.81650e6	1.65026	0.825129	+	0.564944i	$0.191102\pi$
$444$	−485878.	−0.116969
$445$	−91842.4	−0.0219859
$446$	6.50111e6	1.54757
$447$	1.09972e6	0.260324
$448$	5.41936e6	1.27571
$449$	1.94054e6	0.454263	0.227132	−	0.973864i	$-0.427065\pi$
$449$	1.94054e6	0.454263	0.227132	+	0.973864i	$0.427065\pi$
$450$	−1.12251e6	−0.261312
$451$	8.98255e6	2.07950
$452$	32036.7	0.00737568
$453$	−4.37128e6	−1.00084
$454$	−6.48868e6	−1.47746
$455$	−167112.	−0.0378423
$456$	−3.92183e6	−0.883236
$457$	4.70547e6	1.05393	0.526966	−	0.849887i	$-0.323330\pi$
$457$	4.70547e6	1.05393	0.526966	+	0.849887i	$0.323330\pi$
$458$	2.73939e6	0.610226
$459$	−705921.	−0.156396
$460$	393158.	0.0866309
$461$	1.04225e6	0.228413	0.114206	−	0.993457i	$-0.463567\pi$
$461$	1.04225e6	0.228413	0.114206	+	0.993457i	$0.463567\pi$
$462$	3.72209e6	0.811302
$463$	670929.	0.145454	0.0727268	−	0.997352i	$-0.476830\pi$
$463$	670929.	0.145454	0.0727268	+	0.997352i	$0.476830\pi$
$464$	−6.16419e6	−1.32917
$465$	100012.	0.0214497
$466$	2.76262e6	0.589328
$467$	−2.18853e6	−0.464367	−0.232183	−	0.972672i	$-0.574587\pi$
$467$	−2.18853e6	−0.464367	−0.232183	+	0.972672i	$0.574587\pi$
$468$	−19861.4	−0.00419176
$469$	−3.93541e6	−0.826149
$470$	1.73689e6	0.362684
$471$	−4.24863e6	−0.882463
$472$	667931.	0.137999
$473$	−3.88413e6	−0.798253
$474$	−1.93169e6	−0.394905
$475$	−6.03144e6	−1.22656
$476$	694002.	0.140392
$477$	−2.59832e6	−0.522875
$478$	−2.31294e6	−0.463015
$479$	−4.83496e6	−0.962840	−0.481420	−	0.876490i	$-0.659879\pi$
$479$	−4.83496e6	−0.962840	−0.481420	+	0.876490i	$0.659879\pi$
$480$	−333868.	−0.0661411
$481$	581166.	0.114535
$482$	−282461.	−0.0553785
$483$	5.14012e6	1.00255
$484$	−560855.	−0.108827
$485$	106539.	0.0205663
$486$	308117.	0.0591732
$487$	7.05912e6	1.34874	0.674370	−	0.738394i	$-0.264415\pi$
$487$	7.05912e6	1.34874	0.674370	+	0.738394i	$0.264415\pi$
$488$	−2.65922e6	−0.505480
$489$	2.28524e6	0.432175
$490$	−649128.	−0.122135
$491$	2.74825e6	0.514462	0.257231	−	0.966350i	$-0.417190\pi$
$491$	2.74825e6	0.514462	0.257231	+	0.966350i	$0.417190\pi$
$492$	−731025.	−0.136151
$493$	−7.03482e6	−1.30357
$494$	608825.	0.112247
$495$	−925995.	−0.169862
$496$	435315.	0.0794509
$497$	−7.39181e6	−1.34233
$498$	2.86128e6	0.516996
$499$	−1.00805e7	−1.81230	−0.906149	−	0.422958i	$-0.860992\pi$
$499$	−1.00805e7	−1.81230	−0.906149	+	0.422958i	$0.860992\pi$
$500$	−597592.	−0.106901
$501$	−713802.	−0.127053
$502$	4.38922e6	0.777371
$503$	8.49561e6	1.49718	0.748591	−	0.663032i	$-0.230731\pi$
$503$	8.49561e6	1.49718	0.748591	+	0.663032i	$0.230731\pi$
$504$	−2.33394e6	−0.409273
$505$	3.30766e6	0.577154
$506$	1.04742e7	1.81863
$507$	−3.31788e6	−0.573246
$508$	1.21515e6	0.208915
$509$	−6.16900e6	−1.05541	−0.527704	−	0.849428i	$-0.676947\pi$
$509$	−6.16900e6	−1.05541	−0.527704	+	0.849428i	$0.676947\pi$
$510$	984993.	0.167690
$511$	−797692.	−0.135140
$512$	−6.66309e6	−1.12331
$513$	1.65557e6	0.277749
$514$	−1.76847e6	−0.295250
$515$	−2.25572e6	−0.374772
$516$	316101.	0.0522639
$517$	−8.11102e6	−1.33459
$518$	8.86359e6	1.45139
$519$	4.96584e6	0.809234
$520$	213529.	0.0346297
$521$	−4.98898e6	−0.805225	−0.402612	−	0.915371i	$-0.631898\pi$
$521$	−4.98898e6	−0.805225	−0.402612	+	0.915371i	$0.631898\pi$
$522$	3.07053e6	0.493215
$523$	−2.82384e6	−0.451425	−0.225712	−	0.974194i	$-0.572471\pi$
$523$	−2.82384e6	−0.451425	−0.225712	+	0.974194i	$0.572471\pi$
$524$	1.17436e6	0.186841
$525$	−3.58940e6	−0.568360
$526$	1.13953e7	1.79582
$527$	496799.	0.0779209
$528$	−4.03050e6	−0.629178
$529$	8.02829e6	1.24734
$530$	3.62552e6	0.560636
$531$	−281961.	−0.0433963
$532$	−1.62761e6	−0.249328
$533$	874391.	0.133318
$534$	199127.	0.0302188
$535$	−3.22501e6	−0.487131
$536$	5.02853e6	0.756012
$537$	6.64413e6	0.994266
$538$	−545029.	−0.0811829
$539$	3.03133e6	0.449429
$540$	75360.1	0.0111213
$541$	−1.48508e6	−0.218151	−0.109075	−	0.994033i	$-0.534789\pi$
$541$	−1.48508e6	−0.218151	−0.109075	+	0.994033i	$0.534789\pi$
$542$	−1.37565e6	−0.201146
$543$	5.97186e6	0.869180
$544$	−1.65845e6	−0.240273
$545$	2.50440e6	0.361171
$546$	362321.	0.0520130
$547$	−1.20672e7	−1.72440	−0.862198	−	0.506571i	$-0.830913\pi$
$547$	−1.20672e7	−1.72440	−0.862198	+	0.506571i	$0.830913\pi$
$548$	−816577.	−0.116157
$549$	1.12256e6	0.158957
$550$	−7.31426e6	−1.03101
$551$	1.64985e7	2.31507
$552$	−6.56786e6	−0.917436
$553$	−6.17689e6	−0.858928
$554$	3.53616e6	0.489506
$555$	−2.20511e6	−0.303877
$556$	1.22499e6	0.168053
$557$	−1.54643e6	−0.211199	−0.105600	−	0.994409i	$-0.533676\pi$
$557$	−1.54643e6	−0.211199	−0.105600	+	0.994409i	$0.533676\pi$
$558$	−216840.	−0.0294818
$559$	−378094.	−0.0511764
$560$	2.75986e6	0.371892
$561$	−4.59977e6	−0.617062
$562$	166749.	0.0222701
$563$	1.88354e6	0.250439	0.125220	−	0.992129i	$-0.460036\pi$
$563$	1.88354e6	0.250439	0.125220	+	0.992129i	$0.460036\pi$
$564$	660098.	0.0873797
$565$	145396.	0.0191616
$566$	2.06558e6	0.271020
$567$	985251.	0.128703
$568$	9.44498e6	1.22837
$569$	1.00339e6	0.129924	0.0649622	−	0.997888i	$-0.479307\pi$
$569$	1.00339e6	0.129924	0.0649622	+	0.997888i	$0.479307\pi$
$570$	−2.31006e6	−0.297808
$571$	7.14637e6	0.917266	0.458633	−	0.888626i	$-0.348339\pi$
$571$	7.14637e6	0.917266	0.458633	+	0.888626i	$0.348339\pi$
$572$	−129417.	−0.0165387
$573$	−7.43343e6	−0.945808
$574$	1.33357e7	1.68941
$575$	−1.01008e7	−1.27405
$576$	2.92318e6	0.367113
$577$	−4.39566e6	−0.549649	−0.274824	−	0.961494i	$-0.588620\pi$
$577$	−4.39566e6	−0.549649	−0.274824	+	0.961494i	$0.588620\pi$
$578$	−2.51597e6	−0.313246
$579$	−5.36634e6	−0.665246
$580$	750997.	0.0926976
$581$	9.14938e6	1.12448
$582$	−230992.	−0.0282677
$583$	−1.69306e7	−2.06301
$584$	1.01926e6	0.123667
$585$	−90139.4	−0.0108899
$586$	6.82174e6	0.820637
$587$	−9.07708e6	−1.08730	−0.543652	−	0.839311i	$-0.682959\pi$
$587$	−9.07708e6	−1.08730	−0.543652	+	0.839311i	$0.682959\pi$
$588$	−246698.	−0.0294254
$589$	−1.16512e6	−0.138383
$590$	393429.	0.0465303
$591$	7.62424e6	0.897900
$592$	−9.59800e6	−1.12558
$593$	−2.24665e6	−0.262360	−0.131180	−	0.991359i	$-0.541877\pi$
$593$	−2.24665e6	−0.262360	−0.131180	+	0.991359i	$0.541877\pi$
$594$	2.00768e6	0.233469
$595$	3.14967e6	0.364730
$596$	−583170.	−0.0672481
$597$	−4.33649e6	−0.497970
$598$	1.01959e6	0.116594
$599$	2.81454e6	0.320509	0.160255	−	0.987076i	$-0.448768\pi$
$599$	2.81454e6	0.320509	0.160255	+	0.987076i	$0.448768\pi$
$600$	4.58641e6	0.520109
$601$	−7.44310e6	−0.840557	−0.420279	−	0.907395i	$-0.638068\pi$
$601$	−7.44310e6	−0.840557	−0.420279	+	0.907395i	$0.638068\pi$
$602$	−5.76645e6	−0.648511
$603$	−2.12275e6	−0.237741
$604$	2.31804e6	0.258541
$605$	−2.54539e6	−0.282726
$606$	−7.17145e6	−0.793278
$607$	−1.48571e7	−1.63667	−0.818335	−	0.574742i	$-0.805102\pi$
$607$	−1.48571e7	−1.63667	−0.818335	+	0.574742i	$0.805102\pi$
$608$	3.88949e6	0.426710
$609$	9.81848e6	1.07276
$610$	−1.56635e6	−0.170437
$611$	−789554.	−0.0855615
$612$	374342.	0.0404008
$613$	−8.75960e6	−0.941528	−0.470764	−	0.882259i	$-0.656022\pi$
$613$	−8.75960e6	−0.941528	−0.470764	+	0.882259i	$0.656022\pi$
$614$	−1.10609e7	−1.18405
$615$	−3.31769e6	−0.353711
$616$	−1.52079e7	−1.61479
$617$	1.22453e6	0.129496	0.0647478	−	0.997902i	$-0.479376\pi$
$617$	1.22453e6	0.129496	0.0647478	+	0.997902i	$0.479376\pi$
$618$	4.89071e6	0.515111
$619$	1.13512e7	1.19074	0.595369	−	0.803452i	$-0.297006\pi$
$619$	1.13512e7	1.19074	0.595369	+	0.803452i	$0.297006\pi$
$620$	−53035.4	−0.00554098
$621$	2.77256e6	0.288504
$622$	1.30480e7	1.35228
$623$	636739.	0.0657266
$624$	−392342.	−0.0403370
$625$	5.58739e6	0.572149
$626$	−1.72153e7	−1.75581
$627$	1.07876e7	1.09586
$628$	2.25300e6	0.227962
$629$	−1.09536e7	−1.10390
$630$	−1.37475e6	−0.137998
$631$	8.37476e6	0.837334	0.418667	−	0.908140i	$-0.362497\pi$
$631$	8.37476e6	0.837334	0.418667	+	0.908140i	$0.362497\pi$
$632$	7.89260e6	0.786009
$633$	5.51141e6	0.546706
$634$	−1.43812e6	−0.142093
$635$	5.51483e6	0.542748
$636$	1.37786e6	0.135071
$637$	295079.	0.0288131
$638$	2.00075e7	1.94599
$639$	−3.98711e6	−0.386284
$640$	−2.89172e6	−0.279065
$641$	3.09372e6	0.297396	0.148698	−	0.988883i	$-0.452492\pi$
$641$	3.09372e6	0.297396	0.148698	+	0.988883i	$0.452492\pi$
$642$	6.99225e6	0.669545
$643$	3.68773e6	0.351748	0.175874	−	0.984413i	$-0.443725\pi$
$643$	3.68773e6	0.351748	0.175874	+	0.984413i	$0.443725\pi$
$644$	−2.72575e6	−0.258983
$645$	1.43460e6	0.135778
$646$	−1.14749e7	−1.08186
$647$	1.12690e7	1.05834	0.529171	−	0.848516i	$-0.322503\pi$
$647$	1.12690e7	1.05834	0.529171	+	0.848516i	$0.322503\pi$
$648$	−1.25892e6	−0.117777
$649$	−1.83725e6	−0.171221
$650$	−711994.	−0.0660987
$651$	−693380.	−0.0641237
$652$	−1.21184e6	−0.111641
$653$	9.48265e6	0.870255	0.435128	−	0.900369i	$-0.356703\pi$
$653$	9.48265e6	0.870255	0.435128	+	0.900369i	$0.356703\pi$
$654$	−5.42988e6	−0.496416
$655$	5.32972e6	0.485401
$656$	−1.44406e7	−1.31017
$657$	−430272.	−0.0388893
$658$	−1.20418e7	−1.08424
$659$	1.67506e6	0.150251	0.0751255	−	0.997174i	$-0.476064\pi$
$659$	1.67506e6	0.150251	0.0751255	+	0.997174i	$0.476064\pi$
$660$	491045.	0.0438794
$661$	−1.47650e7	−1.31441	−0.657203	−	0.753714i	$-0.728260\pi$
$661$	−1.47650e7	−1.31441	−0.657203	+	0.753714i	$0.728260\pi$
$662$	−1.34633e7	−1.19401
$663$	−447756.	−0.0395602
$664$	−1.16907e7	−1.02902
$665$	−7.38677e6	−0.647740
$666$	4.78099e6	0.417669
$667$	2.76298e7	2.40472
$668$	378521.	0.0328208
$669$	1.12131e7	0.968638
$670$	2.96193e6	0.254911
$671$	7.31461e6	0.627169
$672$	2.31469e6	0.197729
$673$	4.22348e6	0.359445	0.179723	−	0.983717i	$-0.442480\pi$
$673$	4.22348e6	0.359445	0.179723	+	0.983717i	$0.442480\pi$
$674$	1.16628e6	0.0988904
$675$	−1.93611e6	−0.163558
$676$	1.75943e6	0.148083
$677$	−5.35812e6	−0.449304	−0.224652	−	0.974439i	$-0.572125\pi$
$677$	−5.35812e6	−0.449304	−0.224652	+	0.974439i	$0.572125\pi$
$678$	−315238.	−0.0263369
$679$	−738633.	−0.0614829
$680$	−4.02453e6	−0.333766
$681$	−1.11917e7	−0.924758
$682$	−1.41293e6	−0.116321
$683$	−3.41248e6	−0.279910	−0.139955	−	0.990158i	$-0.544696\pi$
$683$	−3.41248e6	−0.279910	−0.139955	+	0.990158i	$0.544696\pi$
$684$	−877928.	−0.0717494
$685$	−3.70596e6	−0.301769
$686$	−8.66916e6	−0.703342
$687$	4.72492e6	0.381946
$688$	6.24425e6	0.502932
$689$	−1.64808e6	−0.132261
$690$	−3.86864e6	−0.309339
$691$	−1.38499e7	−1.10345	−0.551724	−	0.834027i	$-0.686030\pi$
$691$	−1.38499e7	−1.10345	−0.551724	+	0.834027i	$0.686030\pi$
$692$	−2.63333e6	−0.209045
$693$	6.41988e6	0.507801
$694$	−1.25097e7	−0.985938
$695$	5.55951e6	0.436591
$696$	−1.25457e7	−0.981683
$697$	−1.64802e7	−1.28494
$698$	9.34553e6	0.726048
$699$	4.76498e6	0.368866
$700$	1.90342e6	0.146821
$701$	−232405.	−0.0178628	−0.00893142	−	0.999960i	$-0.502843\pi$
$701$	−232405.	−0.0178628	−0.00893142	+	0.999960i	$0.502843\pi$
$702$	195435.	0.0149678
$703$	2.56891e7	1.96047
$704$	1.90474e7	1.44845
$705$	2.99580e6	0.227007
$706$	−4.61094e6	−0.348159
$707$	−2.29318e7	−1.72540
$708$	149521.	0.0112103
$709$	−3.14519e6	−0.234981	−0.117490	−	0.993074i	$-0.537485\pi$
$709$	−3.14519e6	−0.234981	−0.117490	+	0.993074i	$0.537485\pi$
$710$	5.56334e6	0.414181
$711$	−3.33179e6	−0.247175
$712$	−813602.	−0.0601467
$713$	−1.95122e6	−0.143741
$714$	−6.82891e6	−0.501309
$715$	−587346.	−0.0429664
$716$	−3.52331e6	−0.256843
$717$	−3.98937e6	−0.289805
$718$	−3.11728e6	−0.225665
$719$	−8.47359e6	−0.611287	−0.305644	−	0.952146i	$-0.598872\pi$
$719$	−8.47359e6	−0.611287	−0.305644	+	0.952146i	$0.598872\pi$
$720$	1.48866e6	0.107020
$721$	1.56388e7	1.12038
$722$	1.39914e7	0.998892
$723$	−487190.	−0.0346619
$724$	−3.16681e6	−0.224531
$725$	−1.92942e7	−1.36327
$726$	5.51876e6	0.388598
$727$	−5.10460e6	−0.358200	−0.179100	−	0.983831i	$-0.557319\pi$
$727$	−5.10460e6	−0.358200	−0.179100	+	0.983831i	$0.557319\pi$
$728$	−1.48039e6	−0.103525
$729$	531441.	0.0370370
$730$	600371.	0.0416978
$731$	7.12619e6	0.493246
$732$	−595284.	−0.0410626
$733$	−3.23461e6	−0.222363	−0.111181	−	0.993800i	$-0.535463\pi$
$733$	−3.23461e6	−0.222363	−0.111181	+	0.993800i	$0.535463\pi$
$734$	−1.27561e7	−0.873934
$735$	−1.11962e6	−0.0764454
$736$	6.51369e6	0.443234
$737$	−1.38318e7	−0.938014
$738$	7.19322e6	0.486163
$739$	−2.43694e7	−1.64147	−0.820735	−	0.571309i	$-0.806436\pi$
$739$	−2.43694e7	−1.64147	−0.820735	+	0.571309i	$0.806436\pi$
$740$	1.16935e6	0.0784990
$741$	1.05010e6	0.0702565
$742$	−2.51356e7	−1.67602
$743$	−1.35628e7	−0.901315	−0.450657	−	0.892697i	$-0.648810\pi$
$743$	−1.35628e7	−0.901315	−0.450657	+	0.892697i	$0.648810\pi$
$744$	885975.	0.0586799
$745$	−2.64667e6	−0.174706
$746$	−1.79531e7	−1.18112
$747$	4.93514e6	0.323592
$748$	2.43920e6	0.159402
$749$	2.23588e7	1.45628
$750$	5.88025e6	0.381718
$751$	−3.68893e6	−0.238671	−0.119336	−	0.992854i	$-0.538076\pi$
$751$	−3.68893e6	−0.238671	−0.119336	+	0.992854i	$0.538076\pi$
$752$	1.30395e7	0.840848
$753$	7.57054e6	0.486564
$754$	1.94759e6	0.124758
$755$	1.05202e7	0.671673
$756$	−522468.	−0.0332472
$757$	4.79135e6	0.303892	0.151946	−	0.988389i	$-0.451446\pi$
$757$	4.79135e6	0.303892	0.151946	+	0.988389i	$0.451446\pi$
$758$	−3.62925e6	−0.229427
$759$	1.80660e7	1.13830
$760$	9.43854e6	0.592749
$761$	7.35535e6	0.460407	0.230203	−	0.973143i	$-0.426061\pi$
$761$	7.35535e6	0.460407	0.230203	+	0.973143i	$0.426061\pi$
$762$	−1.19569e7	−0.745988
$763$	−1.73629e7	−1.07972
$764$	3.94187e6	0.244325
$765$	1.69892e6	0.104959
$766$	2.36529e6	0.145650
$767$	−178844.	−0.0109771
$768$	−4.12390e6	−0.252293
$769$	−2.77997e7	−1.69521	−0.847607	−	0.530625i	$-0.821957\pi$
$769$	−2.77997e7	−1.69521	−0.847607	+	0.530625i	$0.821957\pi$
$770$	−8.95784e6	−0.544473
$771$	−3.05026e6	−0.184800
$772$	2.84571e6	0.171849
$773$	9.35408e6	0.563057	0.281529	−	0.959553i	$-0.409159\pi$
$773$	9.35408e6	0.563057	0.281529	+	0.959553i	$0.409159\pi$
$774$	−3.11040e6	−0.186623
$775$	1.36256e6	0.0814892
$776$	943798.	0.0562632
$777$	1.52879e7	0.908441
$778$	−2.95502e7	−1.75030
$779$	3.86504e7	2.28197
$780$	47799.9	0.00281313
$781$	−2.59799e7	−1.52409
$782$	−1.92170e7	−1.12375
$783$	5.29605e6	0.308708
$784$	−4.87326e6	−0.283158
$785$	1.02250e7	0.592231
$786$	−1.15556e7	−0.667167
$787$	8.96042e6	0.515693	0.257847	−	0.966186i	$-0.416987\pi$
$787$	8.96042e6	0.515693	0.257847	+	0.966186i	$0.416987\pi$
$788$	−4.04305e6	−0.231950
$789$	1.96547e7	1.12402
$790$	4.64895e6	0.265025
$791$	−1.00802e6	−0.0572835
$792$	−8.20308e6	−0.464691
$793$	712028.	0.0402082
$794$	1.32780e7	0.747447
$795$	6.25331e6	0.350907
$796$	2.29959e6	0.128638
$797$	−1.17914e7	−0.657536	−0.328768	−	0.944411i	$-0.606633\pi$
$797$	−1.17914e7	−0.657536	−0.328768	+	0.944411i	$0.606633\pi$
$798$	1.60155e7	0.890295
$799$	1.48812e7	0.824655
$800$	−4.54858e6	−0.251276
$801$	343455.	0.0189142
$802$	−878336.	−0.0482197
$803$	−2.80364e6	−0.153438
$804$	1.12567e6	0.0614145
$805$	−1.23706e7	−0.672821
$806$	−137539.	−0.00745741
$807$	−940068.	−0.0508131
$808$	2.93014e7	1.57892
$809$	2.15179e7	1.15592	0.577960	−	0.816065i	$-0.303849\pi$
$809$	2.15179e7	1.15592	0.577960	+	0.816065i	$0.303849\pi$
$810$	−741535.	−0.0397118
$811$	1.33906e7	0.714906	0.357453	−	0.933931i	$-0.383645\pi$
$811$	1.33906e7	0.714906	0.357453	+	0.933931i	$0.383645\pi$
$812$	−5.20663e6	−0.277119
$813$	−2.37273e6	−0.125899
$814$	3.11528e7	1.64792
$815$	−5.49982e6	−0.290038
$816$	7.39473e6	0.388774
$817$	−1.67127e7	−0.875976
$818$	1.05285e7	0.550152
$819$	624932.	0.0325554
$820$	1.75934e6	0.0913722
$821$	−8.26050e6	−0.427709	−0.213854	−	0.976866i	$-0.568602\pi$
$821$	−8.26050e6	−0.427709	−0.213854	+	0.976866i	$0.568602\pi$
$822$	8.03504e6	0.414771
$823$	3.28873e7	1.69250	0.846251	−	0.532784i	$-0.178854\pi$
$823$	3.28873e7	1.69250	0.846251	+	0.532784i	$0.178854\pi$
$824$	−1.99827e7	−1.02526
$825$	−1.26156e7	−0.645319
$826$	−2.72762e6	−0.139102
$827$	−2.91579e6	−0.148249	−0.0741247	−	0.997249i	$-0.523616\pi$
$827$	−2.91579e6	−0.148249	−0.0741247	+	0.997249i	$0.523616\pi$
$828$	−1.47026e6	−0.0745277
$829$	1.16799e6	0.0590274	0.0295137	−	0.999564i	$-0.490604\pi$
$829$	1.16799e6	0.0590274	0.0295137	+	0.999564i	$0.490604\pi$
$830$	−6.88615e6	−0.346961
$831$	6.09919e6	0.306386
$832$	1.85414e6	0.0928610
$833$	−5.56156e6	−0.277705
$834$	−1.20538e7	−0.600079
$835$	1.71788e6	0.0852664
$836$	−5.72056e6	−0.283089
$837$	−374007.	−0.0184529
$838$	1.67182e7	0.822395
$839$	4.82533e6	0.236659	0.118329	−	0.992974i	$-0.462246\pi$
$839$	4.82533e6	0.236659	0.118329	+	0.992974i	$0.462246\pi$
$840$	5.61702e6	0.274668
$841$	3.22664e7	1.57312
$842$	5.18443e6	0.252012
$843$	287609.	0.0139391
$844$	−2.92264e6	−0.141227
$845$	7.98504e6	0.384712
$846$	−6.49530e6	−0.312013
$847$	1.76471e7	0.845210
$848$	2.72182e7	1.29978
$849$	3.56273e6	0.169634
$850$	1.34194e7	0.637070
$851$	4.30213e7	2.03638
$852$	2.11432e6	0.0997866
$853$	2.55798e7	1.20372	0.601859	−	0.798603i	$-0.294427\pi$
$853$	2.55798e7	1.20372	0.601859	+	0.798603i	$0.294427\pi$
$854$	1.08594e7	0.509521
$855$	−3.98440e6	−0.186401
$856$	−2.85693e7	−1.33265
$857$	−1.16798e7	−0.543232	−0.271616	−	0.962406i	$-0.587558\pi$
$857$	−1.16798e7	−0.543232	−0.271616	+	0.962406i	$0.587558\pi$
$858$	1.27345e6	0.0590558
$859$	1.36617e6	0.0631717	0.0315858	−	0.999501i	$-0.489944\pi$
$859$	1.36617e6	0.0631717	0.0315858	+	0.999501i	$0.489944\pi$
$860$	−760751.	−0.0350749
$861$	2.30014e7	1.05742
$862$	−3.83074e7	−1.75596
$863$	−2.59879e7	−1.18780	−0.593901	−	0.804538i	$-0.702413\pi$
$863$	−2.59879e7	−1.18780	−0.593901	+	0.804538i	$0.702413\pi$
$864$	1.24854e6	0.0569006
$865$	−1.19511e7	−0.543086
$866$	−2.69444e7	−1.22088
$867$	−4.33955e6	−0.196063
$868$	367692.	0.0165647
$869$	−2.17099e7	−0.975232
$870$	−7.38974e6	−0.331002
$871$	−1.34643e6	−0.0601366
$872$	2.21857e7	0.988055
$873$	−398416.	−0.0176930
$874$	4.50688e7	1.99571
$875$	1.88030e7	0.830246
$876$	228168.	0.0100460
$877$	−3.18973e7	−1.40041	−0.700204	−	0.713943i	$-0.746907\pi$
$877$	−3.18973e7	−1.40041	−0.700204	+	0.713943i	$0.746907\pi$
$878$	1.75126e6	0.0766681
$879$	1.17662e7	0.513644
$880$	9.70007e6	0.422249
$881$	1.48478e7	0.644497	0.322249	−	0.946655i	$-0.395561\pi$
$881$	1.48478e7	0.644497	0.322249	+	0.946655i	$0.395561\pi$
$882$	2.42748e6	0.105071
$883$	2.11125e7	0.911249	0.455625	−	0.890172i	$-0.349416\pi$
$883$	2.11125e7	0.911249	0.455625	+	0.890172i	$0.349416\pi$
$884$	237440.	0.0102194
$885$	678587.	0.0291237
$886$	3.55684e7	1.52223
$887$	−1.01713e7	−0.434076	−0.217038	−	0.976163i	$-0.569640\pi$
$887$	−1.01713e7	−0.434076	−0.217038	+	0.976163i	$0.569640\pi$
$888$	−1.95344e7	−0.831318
$889$	−3.82341e7	−1.62254
$890$	−479233.	−0.0202802
$891$	3.46286e6	0.146130
$892$	−5.94619e6	−0.250223
$893$	−3.49003e7	−1.46454
$894$	5.73834e6	0.240128
$895$	−1.59902e7	−0.667263
$896$	2.00481e7	0.834265
$897$	1.75860e6	0.0729770
$898$	1.01257e7	0.419021
$899$	−3.72715e6	−0.153807
$900$	1.02670e6	0.0422509
$901$	3.10625e7	1.27475
$902$	4.68708e7	1.91817
$903$	−9.94599e6	−0.405909
$904$	1.28801e6	0.0524203
$905$	−1.43723e7	−0.583316
$906$	−2.28093e7	−0.923191
$907$	−3.32335e7	−1.34140	−0.670700	−	0.741729i	$-0.734006\pi$
$907$	−3.32335e7	−1.34140	−0.670700	+	0.741729i	$0.734006\pi$
$908$	5.93483e6	0.238888
$909$	−1.23693e7	−0.496520
$910$	−871986.	−0.0349065
$911$	701228.	0.0279939	0.0139970	−	0.999902i	$-0.495544\pi$
$911$	701228.	0.0279939	0.0139970	+	0.999902i	$0.495544\pi$
$912$	−1.73425e7	−0.690439
$913$	3.21573e7	1.27674
$914$	2.45531e7	0.972166
$915$	−2.70164e6	−0.106678
$916$	−2.50557e6	−0.0986661
$917$	−3.69507e7	−1.45111
$918$	−3.68349e6	−0.144262
$919$	1.45028e7	0.566451	0.283226	−	0.959053i	$-0.408595\pi$
$919$	1.45028e7	0.566451	0.283226	+	0.959053i	$0.408595\pi$
$920$	1.58067e7	0.615702
$921$	−1.90779e7	−0.741109
$922$	5.43846e6	0.210692
$923$	−2.52897e6	−0.0977102
$924$	−3.40439e6	−0.131177
$925$	−3.00422e7	−1.15446
$926$	3.50090e6	0.134169
$927$	8.43550e6	0.322412
$928$	1.24422e7	0.474273
$929$	−1.70226e7	−0.647124	−0.323562	−	0.946207i	$-0.604880\pi$
$929$	−1.70226e7	−0.647124	−0.323562	+	0.946207i	$0.604880\pi$
$930$	521863.	0.0197856
$931$	1.30433e7	0.493188
$932$	−2.52682e6	−0.0952870
$933$	2.25052e7	0.846406
$934$	−1.14197e7	−0.428340
$935$	1.10701e7	0.414117
$936$	−798515.	−0.0297916
$937$	−2.02964e7	−0.755214	−0.377607	−	0.925966i	$-0.623253\pi$
$937$	−2.02964e7	−0.755214	−0.377607	+	0.925966i	$0.623253\pi$
$938$	−2.05349e7	−0.762055
$939$	−2.96929e7	−1.09898
$940$	−1.58864e6	−0.0586415
$941$	4.68227e7	1.72378	0.861891	−	0.507093i	$-0.169280\pi$
$941$	4.68227e7	1.72378	0.861891	+	0.507093i	$0.169280\pi$
$942$	−2.21693e7	−0.814000
$943$	6.47275e7	2.37033
$944$	2.95363e6	0.107876
$945$	−2.37117e6	−0.0863742
$946$	−2.02673e7	−0.736323
$947$	1.05919e7	0.383793	0.191897	−	0.981415i	$-0.438536\pi$
$947$	1.05919e7	0.383793	0.191897	+	0.981415i	$0.438536\pi$
$948$	1.76681e6	0.0638512
$949$	−272916.	−0.00983701
$950$	−3.14720e7	−1.13140
$951$	−2.48048e6	−0.0889373
$952$	2.79018e7	0.997793
$953$	2.94030e7	1.04872	0.524360	−	0.851497i	$-0.324305\pi$
$953$	2.94030e7	1.04872	0.524360	+	0.851497i	$0.324305\pi$
$954$	−1.35580e7	−0.482309
$955$	1.78898e7	0.634742
$956$	2.11552e6	0.0748638
$957$	3.45090e7	1.21801
$958$	−2.52288e7	−0.888141
$959$	2.56933e7	0.902138
$960$	−7.03513e6	−0.246373
$961$	−2.83659e7	−0.990806
$962$	3.03252e6	0.105649
$963$	1.20603e7	0.419074
$964$	258351.	0.00895402
$965$	1.29150e7	0.446454
$966$	2.68211e7	0.924770
$967$	4.00215e7	1.37635	0.688173	−	0.725547i	$-0.258413\pi$
$967$	4.00215e7	1.37635	0.688173	+	0.725547i	$0.258413\pi$
$968$	−2.25488e7	−0.773455
$969$	−1.97920e7	−0.677143
$970$	555922.	0.0189707
$971$	3.43019e7	1.16753	0.583767	−	0.811921i	$-0.301578\pi$
$971$	3.43019e7	1.16753	0.583767	+	0.811921i	$0.301578\pi$
$972$	−281817.	−0.00956757
$973$	−3.85438e7	−1.30519
$974$	3.68344e7	1.24410
$975$	−1.22805e6	−0.0413718
$976$	−1.17592e7	−0.395142
$977$	−5.48788e7	−1.83937	−0.919684	−	0.392660i	$-0.871555\pi$
$977$	−5.48788e7	−1.83937	−0.919684	+	0.392660i	$0.871555\pi$
$978$	1.19244e7	0.398646
$979$	2.23794e6	0.0746264
$980$	593720.	0.0197477
$981$	−9.36548e6	−0.310712
$982$	1.43404e7	0.474549
$983$	4.78986e7	1.58102	0.790512	−	0.612446i	$-0.209814\pi$
$983$	4.78986e7	1.58102	0.790512	+	0.612446i	$0.209814\pi$
$984$	−2.93904e7	−0.967648
$985$	−1.83490e7	−0.602591
$986$	−3.67076e7	−1.20244
$987$	−2.07697e7	−0.678637
$988$	−556858.	−0.0181490
$989$	−2.79887e7	−0.909896
$990$	−4.83183e6	−0.156684
$991$	3.75136e7	1.21340	0.606702	−	0.794930i	$-0.292492\pi$
$991$	3.75136e7	1.21340	0.606702	+	0.794930i	$0.292492\pi$
$992$	−878669.	−0.0283495
$993$	−2.32216e7	−0.747340
$994$	−3.85704e7	−1.23819
$995$	1.04365e7	0.334193
$996$	−2.61705e6	−0.0835918
$997$	3.98840e7	1.27075	0.635375	−	0.772203i	$-0.280845\pi$
$997$	3.98840e7	1.27075	0.635375	+	0.772203i	$0.280845\pi$
$998$	−5.25998e7	−1.67170
$999$	8.24626e6	0.261423

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.8	✓	12	1.1	even	1	trivial
531.6.a.c.1.5		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)

\(f(q)\)	\(=\)	\(q+5.21799 q^{2} +9.00000 q^{3} -4.77260 q^{4} -21.6600 q^{5} +46.9619 q^{6} +150.168 q^{7} -191.879 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+5.21799 q^{2} +9.00000 q^{3} -4.77260 q^{4} -21.6600 q^{5} +46.9619 q^{6} +150.168 q^{7} -191.879 q^{8} +81.0000 q^{9} -113.022 q^{10} +527.794 q^{11} -42.9534 q^{12} +51.3772 q^{13} +783.574 q^{14} -194.940 q^{15} -848.499 q^{16} -968.342 q^{17} +422.657 q^{18} +2271.01 q^{19} +103.375 q^{20} +1351.51 q^{21} +2754.02 q^{22} +3803.24 q^{23} -1726.91 q^{24} -2655.84 q^{25} +268.086 q^{26} +729.000 q^{27} -716.691 q^{28} +7264.82 q^{29} -1017.20 q^{30} -513.041 q^{31} +1712.67 q^{32} +4750.15 q^{33} -5052.79 q^{34} -3252.64 q^{35} -386.581 q^{36} +11311.7 q^{37} +11850.1 q^{38} +462.395 q^{39} +4156.10 q^{40} +17019.0 q^{41} +7052.17 q^{42} -7359.17 q^{43} -2518.95 q^{44} -1754.46 q^{45} +19845.3 q^{46} -15367.8 q^{47} -7636.49 q^{48} +5743.39 q^{49} -13858.2 q^{50} -8715.07 q^{51} -245.203 q^{52} -32078.1 q^{53} +3803.91 q^{54} -11432.0 q^{55} -28814.1 q^{56} +20439.1 q^{57} +37907.7 q^{58} -3481.00 q^{59} +930.371 q^{60} +13858.8 q^{61} -2677.04 q^{62} +12163.6 q^{63} +36088.7 q^{64} -1112.83 q^{65} +24786.2 q^{66} -26206.8 q^{67} +4621.51 q^{68} +34229.2 q^{69} -16972.2 q^{70} -49223.6 q^{71} -15542.2 q^{72} -5312.00 q^{73} +59024.5 q^{74} -23902.6 q^{75} -10838.6 q^{76} +79257.7 q^{77} +2412.77 q^{78} -41133.2 q^{79} +18378.5 q^{80} +6561.00 q^{81} +88805.2 q^{82} +60927.7 q^{83} -6450.22 q^{84} +20974.3 q^{85} -38400.0 q^{86} +65383.3 q^{87} -101273. q^{88} +4240.18 q^{89} -9154.76 q^{90} +7715.21 q^{91} -18151.3 q^{92} -4617.37 q^{93} -80188.8 q^{94} -49190.1 q^{95} +15414.0 q^{96} -4918.71 q^{97} +29968.9 q^{98} +42751.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 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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