LMFDB - Embedded newform 177.6.a.c.1.2

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			1.2
Root			$8.10567$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.10567 q^{2} +9.00000 q^{3} +5.27923 q^{4} -41.8018 q^{5} -54.9510 q^{6} +208.248 q^{7} +163.148 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-6.10567 q^{2} +9.00000 q^{3} +5.27923 q^{4} -41.8018 q^{5} -54.9510 q^{6} +208.248 q^{7} +163.148 q^{8} +81.0000 q^{9} +255.228 q^{10} +149.105 q^{11} +47.5131 q^{12} -952.113 q^{13} -1271.49 q^{14} -376.216 q^{15} -1165.07 q^{16} +1073.60 q^{17} -494.559 q^{18} -486.976 q^{19} -220.681 q^{20} +1874.23 q^{21} -910.386 q^{22} +2198.23 q^{23} +1468.33 q^{24} -1377.61 q^{25} +5813.29 q^{26} +729.000 q^{27} +1099.39 q^{28} -2548.98 q^{29} +2297.05 q^{30} +1027.11 q^{31} +1892.76 q^{32} +1341.94 q^{33} -6555.08 q^{34} -8705.13 q^{35} +427.618 q^{36} -3164.40 q^{37} +2973.31 q^{38} -8569.02 q^{39} -6819.88 q^{40} +14579.4 q^{41} -11443.4 q^{42} +13357.1 q^{43} +787.159 q^{44} -3385.94 q^{45} -13421.7 q^{46} +15809.5 q^{47} -10485.6 q^{48} +26560.2 q^{49} +8411.26 q^{50} +9662.44 q^{51} -5026.42 q^{52} +746.932 q^{53} -4451.03 q^{54} -6232.85 q^{55} +33975.3 q^{56} -4382.78 q^{57} +15563.2 q^{58} -3481.00 q^{59} -1986.13 q^{60} +31646.6 q^{61} -6271.22 q^{62} +16868.1 q^{63} +25725.5 q^{64} +39800.0 q^{65} -8193.47 q^{66} -36947.6 q^{67} +5667.81 q^{68} +19784.1 q^{69} +53150.6 q^{70} +67026.7 q^{71} +13215.0 q^{72} +15479.2 q^{73} +19320.8 q^{74} -12398.5 q^{75} -2570.86 q^{76} +31050.8 q^{77} +52319.6 q^{78} +45796.7 q^{79} +48701.8 q^{80} +6561.00 q^{81} -89017.1 q^{82} +16456.1 q^{83} +9894.50 q^{84} -44878.6 q^{85} -81554.1 q^{86} -22940.8 q^{87} +24326.2 q^{88} -28480.0 q^{89} +20673.4 q^{90} -198276. q^{91} +11604.9 q^{92} +9244.02 q^{93} -96527.9 q^{94} +20356.4 q^{95} +17034.8 q^{96} +79923.6 q^{97} -162168. q^{98} +12077.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.10567	−1.07934	−0.539670	−	0.841876i	$-0.681451\pi$
$2$	−6.10567	−1.07934	−0.539670	+	0.841876i	$0.681451\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	5.27923	0.164976
$5$	−41.8018	−0.747772	−0.373886	−	0.927475i	$-0.621975\pi$
$5$	−41.8018	−0.747772	−0.373886	+	0.927475i	$0.621975\pi$
$6$	−54.9510	−0.623158
$7$	208.248	1.60633	0.803166	−	0.595755i	$-0.203147\pi$
$7$	208.248	1.60633	0.803166	+	0.595755i	$0.203147\pi$
$8$	163.148	0.901275
$9$	81.0000	0.333333
$10$	255.228	0.807101
$11$	149.105	0.371544	0.185772	−	0.982593i	$-0.440521\pi$
$11$	149.105	0.371544	0.185772	+	0.982593i	$0.440521\pi$
$12$	47.5131	0.0952489
$13$	−952.113	−1.56254	−0.781268	−	0.624196i	$-0.785427\pi$
$13$	−952.113	−1.56254	−0.781268	+	0.624196i	$0.785427\pi$
$14$	−1271.49	−1.73378
$15$	−376.216	−0.431727
$16$	−1165.07	−1.13776
$17$	1073.60	0.900994	0.450497	−	0.892778i	$-0.351247\pi$
$17$	1073.60	0.900994	0.450497	+	0.892778i	$0.351247\pi$
$18$	−494.559	−0.359780
$19$	−486.976	−0.309473	−0.154737	−	0.987956i	$-0.549453\pi$
$19$	−486.976	−0.309473	−0.154737	+	0.987956i	$0.549453\pi$
$20$	−220.681	−0.123364
$21$	1874.23	0.927417
$22$	−910.386	−0.401022
$23$	2198.23	0.866469	0.433235	−	0.901281i	$-0.357372\pi$
$23$	2198.23	0.866469	0.433235	+	0.901281i	$0.357372\pi$
$24$	1468.33	0.520352
$25$	−1377.61	−0.440836
$26$	5813.29	1.68651
$27$	729.000	0.192450
$28$	1099.39	0.265006
$29$	−2548.98	−0.562823	−0.281411	−	0.959587i	$-0.590803\pi$
$29$	−2548.98	−0.562823	−0.281411	+	0.959587i	$0.590803\pi$
$30$	2297.05	0.465980
$31$	1027.11	0.191961	0.0959807	−	0.995383i	$-0.469401\pi$
$31$	1027.11	0.191961	0.0959807	+	0.995383i	$0.469401\pi$
$32$	1892.76	0.326754
$33$	1341.94	0.214511
$34$	−6555.08	−0.972480
$35$	−8705.13	−1.20117
$36$	427.618	0.0549920
$37$	−3164.40	−0.380003	−0.190001	−	0.981784i	$-0.560849\pi$
$37$	−3164.40	−0.380003	−0.190001	+	0.981784i	$0.560849\pi$
$38$	2973.31	0.334027
$39$	−8569.02	−0.902131
$40$	−6819.88	−0.673949
$41$	14579.4	1.35450	0.677252	−	0.735751i	$-0.263171\pi$
$41$	14579.4	1.35450	0.677252	+	0.735751i	$0.263171\pi$
$42$	−11443.4	−1.00100
$43$	13357.1	1.10164	0.550822	−	0.834623i	$-0.314314\pi$
$43$	13357.1	1.10164	0.550822	+	0.834623i	$0.314314\pi$
$44$	787.159	0.0612958
$45$	−3385.94	−0.249257
$46$	−13421.7	−0.935215
$47$	15809.5	1.04394	0.521969	−	0.852965i	$-0.325198\pi$
$47$	15809.5	1.04394	0.521969	+	0.852965i	$0.325198\pi$
$48$	−10485.6	−0.656885
$49$	26560.2	1.58030
$50$	8411.26	0.475813
$51$	9662.44	0.520189
$52$	−5026.42	−0.257781
$53$	746.932	0.0365251	0.0182625	−	0.999833i	$-0.494187\pi$
$53$	746.932	0.0365251	0.0182625	+	0.999833i	$0.494187\pi$
$54$	−4451.03	−0.207719
$55$	−6232.85	−0.277830
$56$	33975.3	1.44775
$57$	−4382.78	−0.178675
$58$	15563.2	0.607478
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−1986.13	−0.0712245
$61$	31646.6	1.08894	0.544468	−	0.838782i	$-0.316732\pi$
$61$	31646.6	1.08894	0.544468	+	0.838782i	$0.316732\pi$
$62$	−6271.22	−0.207192
$63$	16868.1	0.535444
$64$	25725.5	0.785080
$65$	39800.0	1.16842
$66$	−8193.47	−0.231530
$67$	−36947.6	−1.00554	−0.502770	−	0.864420i	$-0.667686\pi$
$67$	−36947.6	−1.00554	−0.502770	+	0.864420i	$0.667686\pi$
$68$	5667.81	0.148642
$69$	19784.1	0.500256
$70$	53150.6	1.29647
$71$	67026.7	1.57798	0.788991	−	0.614405i	$-0.210604\pi$
$71$	67026.7	1.57798	0.788991	+	0.614405i	$0.210604\pi$
$72$	13215.0	0.300425
$73$	15479.2	0.339971	0.169986	−	0.985447i	$-0.445628\pi$
$73$	15479.2	0.339971	0.169986	+	0.985447i	$0.445628\pi$
$74$	19320.8	0.410153
$75$	−12398.5	−0.254517
$76$	−2570.86	−0.0510557
$77$	31050.8	0.596823
$78$	52319.6	0.973706
$79$	45796.7	0.825594	0.412797	−	0.910823i	$-0.364552\pi$
$79$	45796.7	0.825594	0.412797	+	0.910823i	$0.364552\pi$
$80$	48701.8	0.850785
$81$	6561.00	0.111111
$82$	−89017.1	−1.46197
$83$	16456.1	0.262199	0.131100	−	0.991369i	$-0.458149\pi$
$83$	16456.1	0.262199	0.131100	+	0.991369i	$0.458149\pi$
$84$	9894.50	0.153001
$85$	−44878.6	−0.673739
$86$	−81554.1	−1.18905
$87$	−22940.8	−0.324946
$88$	24326.2	0.334863
$89$	−28480.0	−0.381123	−0.190562	−	0.981675i	$-0.561031\pi$
$89$	−28480.0	−0.381123	−0.190562	+	0.981675i	$0.561031\pi$
$90$	20673.4	0.269034
$91$	−198276.	−2.50995
$92$	11604.9	0.142947
$93$	9244.02	0.110829
$94$	−96527.9	−1.12676
$95$	20356.4	0.231416
$96$	17034.8	0.188651
$97$	79923.6	0.862473	0.431237	−	0.902239i	$-0.358077\pi$
$97$	79923.6	0.862473	0.431237	+	0.902239i	$0.358077\pi$
$98$	−162168.	−1.70569
$99$	12077.5	0.123848
$100$	−7272.74	−0.0727274
$101$	134102.	1.30808	0.654038	−	0.756462i	$-0.273074\pi$
$101$	134102.	1.30808	0.654038	+	0.756462i	$0.273074\pi$
$102$	−58995.7	−0.561461
$103$	−119371.	−1.10868	−0.554339	−	0.832291i	$-0.687029\pi$
$103$	−119371.	−1.10868	−0.554339	+	0.832291i	$0.687029\pi$
$104$	−155336.	−1.40828
$105$	−78346.1	−0.693497
$106$	−4560.52	−0.0394230
$107$	61222.4	0.516953	0.258476	−	0.966018i	$-0.416780\pi$
$107$	61222.4	0.516953	0.258476	+	0.966018i	$0.416780\pi$
$108$	3848.56	0.0317496
$109$	118858.	0.958211	0.479106	−	0.877757i	$-0.340961\pi$
$109$	118858.	0.958211	0.479106	+	0.877757i	$0.340961\pi$
$110$	38055.7	0.299874
$111$	−28479.6	−0.219395
$112$	−242622.	−1.82762
$113$	248492.	1.83069	0.915347	−	0.402665i	$-0.131916\pi$
$113$	248492.	1.83069	0.915347	+	0.402665i	$0.131916\pi$
$114$	26759.8	0.192851
$115$	−91889.8	−0.647922
$116$	−13456.7	−0.0928522
$117$	−77121.1	−0.520845
$118$	21253.8	0.140518
$119$	223576.	1.44730
$120$	−61378.9	−0.389105
$121$	−138819.	−0.861955
$122$	−193224.	−1.17533
$123$	131215.	0.782023
$124$	5422.37	0.0316690
$125$	188217.	1.07742
$126$	−102991.	−0.577927
$127$	−184071.	−1.01269	−0.506343	−	0.862332i	$-0.669003\pi$
$127$	−184071.	−1.01269	−0.506343	+	0.862332i	$0.669003\pi$
$128$	−217640.	−1.17412
$129$	120214.	0.636034
$130$	−243006.	−1.26112
$131$	−256895.	−1.30791	−0.653953	−	0.756535i	$-0.726891\pi$
$131$	−256895.	−1.30791	−0.653953	+	0.756535i	$0.726891\pi$
$132$	7084.43	0.0353892
$133$	−101412.	−0.497117
$134$	225590.	1.08532
$135$	−30473.5	−0.143909
$136$	175157.	0.812044
$137$	−118936.	−0.541394	−0.270697	−	0.962665i	$-0.587254\pi$
$137$	−118936.	−0.541394	−0.270697	+	0.962665i	$0.587254\pi$
$138$	−120795.	−0.539947
$139$	−147451.	−0.647306	−0.323653	−	0.946176i	$-0.604911\pi$
$139$	−147451.	−0.647306	−0.323653	+	0.946176i	$0.604911\pi$
$140$	−45956.4	−0.198164
$141$	142286.	0.602718
$142$	−409243.	−1.70318
$143$	−141965.	−0.580551
$144$	−94370.3	−0.379253
$145$	106552.	0.420863
$146$	−94511.0	−0.366945
$147$	239042.	0.912389
$148$	−16705.6	−0.0626913
$149$	125781.	0.464139	0.232070	−	0.972699i	$-0.425450\pi$
$149$	125781.	0.464139	0.232070	+	0.972699i	$0.425450\pi$
$150$	75701.3	0.274711
$151$	181920.	0.649288	0.324644	−	0.945836i	$-0.394755\pi$
$151$	181920.	0.649288	0.324644	+	0.945836i	$0.394755\pi$
$152$	−79449.2	−0.278921
$153$	86962.0	0.300331
$154$	−189586.	−0.644176
$155$	−42935.1	−0.143543
$156$	−45237.8	−0.148830
$157$	252024.	0.816004	0.408002	−	0.912981i	$-0.366226\pi$
$157$	252024.	0.816004	0.408002	+	0.912981i	$0.366226\pi$
$158$	−279620.	−0.891097
$159$	6722.39	0.0210878
$160$	−79120.7	−0.244338
$161$	457776.	1.39184
$162$	−40059.3	−0.119927
$163$	−284724.	−0.839373	−0.419687	−	0.907669i	$-0.637860\pi$
$163$	−284724.	−0.839373	−0.419687	+	0.907669i	$0.637860\pi$
$164$	76968.1	0.223461
$165$	−56095.6	−0.160405
$166$	−100475.	−0.283002
$167$	−71081.6	−0.197227	−0.0986134	−	0.995126i	$-0.531441\pi$
$167$	−71081.6	−0.197227	−0.0986134	+	0.995126i	$0.531441\pi$
$168$	305778.	0.835858
$169$	535226.	1.44152
$170$	274014.	0.727194
$171$	−39445.0	−0.103158
$172$	70515.2	0.181745
$173$	−420683.	−1.06866	−0.534331	−	0.845276i	$-0.679436\pi$
$173$	−420683.	−1.06866	−0.534331	+	0.845276i	$0.679436\pi$
$174$	140069.	0.350727
$175$	−286885.	−0.708130
$176$	−173717.	−0.422727
$177$	−31329.0	−0.0751646
$178$	173890.	0.411362
$179$	−49547.5	−0.115582	−0.0577909	−	0.998329i	$-0.518406\pi$
$179$	−49547.5	−0.115582	−0.0577909	+	0.998329i	$0.518406\pi$
$180$	−17875.2	−0.0411215
$181$	−5910.71	−0.0134104	−0.00670522	−	0.999978i	$-0.502134\pi$
$181$	−5910.71	−0.0134104	−0.00670522	+	0.999978i	$0.502134\pi$
$182$	1.21061e6	2.70909
$183$	284819.	0.628697
$184$	358637.	0.780927
$185$	132277.	0.284156
$186$	−56440.9	−0.119622
$187$	160080.	0.334759
$188$	83462.2	0.172225
$189$	151813.	0.309139
$190$	−124290.	−0.249776
$191$	745180.	1.47801	0.739006	−	0.673699i	$-0.235296\pi$
$191$	745180.	1.47801	0.739006	+	0.673699i	$0.235296\pi$
$192$	231530.	0.453266
$193$	−29909.0	−0.0577975	−0.0288987	−	0.999582i	$-0.509200\pi$
$193$	−29909.0	−0.0577975	−0.0288987	+	0.999582i	$0.509200\pi$
$194$	−487987.	−0.930902
$195$	358200.	0.674588
$196$	140217.	0.260712
$197$	−500243.	−0.918365	−0.459183	−	0.888342i	$-0.651858\pi$
$197$	−500243.	−0.918365	−0.459183	+	0.888342i	$0.651858\pi$
$198$	−73741.2	−0.133674
$199$	−517673.	−0.926664	−0.463332	−	0.886185i	$-0.653346\pi$
$199$	−517673.	−0.926664	−0.463332	+	0.886185i	$0.653346\pi$
$200$	−224755.	−0.397315
$201$	−332528.	−0.580548
$202$	−818785.	−1.41186
$203$	−530820.	−0.904081
$204$	51010.2	0.0858187
$205$	−609445.	−1.01286
$206$	728839.	1.19664
$207$	178056.	0.288823
$208$	1.10927e6	1.77779
$209$	−72610.5	−0.114983
$210$	478356.	0.748519
$211$	1.25719e6	1.94400	0.971999	−	0.234984i	$-0.0755037\pi$
$211$	1.25719e6	1.94400	0.971999	+	0.234984i	$0.0755037\pi$
$212$	3943.23	0.00602576
$213$	603240.	0.911048
$214$	−373804.	−0.557968
$215$	−558350.	−0.823779
$216$	118935.	0.173451
$217$	213894.	0.308354
$218$	−725707.	−1.03424
$219$	139313.	0.196282
$220$	−32904.6	−0.0458353
$221$	−1.02219e6	−1.40784
$222$	173887.	0.236802
$223$	967522.	1.30286	0.651431	−	0.758708i	$-0.274169\pi$
$223$	967522.	1.30286	0.651431	+	0.758708i	$0.274169\pi$
$224$	394163.	0.524876
$225$	−111587.	−0.146945
$226$	−1.51721e6	−1.97594
$227$	−374162.	−0.481943	−0.240971	−	0.970532i	$-0.577466\pi$
$227$	−374162.	−0.481943	−0.240971	+	0.970532i	$0.577466\pi$
$228$	−23137.7	−0.0294770
$229$	65812.0	0.0829309	0.0414654	−	0.999140i	$-0.486797\pi$
$229$	65812.0	0.0829309	0.0414654	+	0.999140i	$0.486797\pi$
$230$	561049.	0.699328
$231$	279457.	0.344576
$232$	−415862.	−0.507258
$233$	−633048.	−0.763918	−0.381959	−	0.924179i	$-0.624751\pi$
$233$	−633048.	−0.763918	−0.381959	+	0.924179i	$0.624751\pi$
$234$	470876.	0.562170
$235$	−660866.	−0.780628
$236$	−18377.0	−0.0214780
$237$	412170.	0.476657
$238$	−1.36508e6	−1.56213
$239$	728479.	0.824940	0.412470	−	0.910971i	$-0.364666\pi$
$239$	728479.	0.824940	0.412470	+	0.910971i	$0.364666\pi$
$240$	438316.	0.491201
$241$	1.22438e6	1.35792	0.678960	−	0.734175i	$-0.262431\pi$
$241$	1.22438e6	1.35792	0.678960	+	0.734175i	$0.262431\pi$
$242$	847582.	0.930343
$243$	59049.0	0.0641500
$244$	167070.	0.179648
$245$	−1.11026e6	−1.18171
$246$	−801154.	−0.844070
$247$	463656.	0.483563
$248$	167572.	0.173010
$249$	148105.	0.151381
$250$	−1.14919e6	−1.16290
$251$	−388944.	−0.389675	−0.194838	−	0.980835i	$-0.562418\pi$
$251$	−388944.	−0.389675	−0.194838	+	0.980835i	$0.562418\pi$
$252$	89050.5	0.0883354
$253$	327767.	0.321931
$254$	1.12387e6	1.09303
$255$	−403907.	−0.388983
$256$	505621.	0.482198
$257$	1.35199e6	1.27685	0.638427	−	0.769683i	$-0.279585\pi$
$257$	1.35199e6	1.27685	0.638427	+	0.769683i	$0.279585\pi$
$258$	−733987.	−0.686497
$259$	−658980.	−0.610411
$260$	210113.	0.192761
$261$	−206468.	−0.187608
$262$	1.56851e6	1.41168
$263$	−685770.	−0.611348	−0.305674	−	0.952136i	$-0.598882\pi$
$263$	−685770.	−0.611348	−0.305674	+	0.952136i	$0.598882\pi$
$264$	218936.	0.193333
$265$	−31223.1	−0.0273125
$266$	619186.	0.536559
$267$	−256320.	−0.220041
$268$	−195055.	−0.165890
$269$	2.15145e6	1.81281	0.906403	−	0.422413i	$-0.138817\pi$
$269$	2.15145e6	1.81281	0.906403	+	0.422413i	$0.138817\pi$
$270$	186061.	0.155327
$271$	−2.36646e6	−1.95738	−0.978692	−	0.205336i	$-0.934171\pi$
$271$	−2.36646e6	−1.95738	−0.978692	+	0.205336i	$0.934171\pi$
$272$	−1.25082e6	−1.02511
$273$	−1.78448e6	−1.44912
$274$	726186.	0.584348
$275$	−205409.	−0.163790
$276$	104445.	0.0825302
$277$	2.37254e6	1.85786	0.928930	−	0.370254i	$-0.120729\pi$
$277$	2.37254e6	1.85786	0.928930	+	0.370254i	$0.120729\pi$
$278$	900285.	0.698663
$279$	83196.2	0.0639872
$280$	−1.42023e6	−1.08259
$281$	−386861.	−0.292273	−0.146137	−	0.989264i	$-0.546684\pi$
$281$	−386861.	−0.292273	−0.146137	+	0.989264i	$0.546684\pi$
$282$	−868751.	−0.650538
$283$	19175.2	0.0142323	0.00711613	−	0.999975i	$-0.497735\pi$
$283$	19175.2	0.0142323	0.00711613	+	0.999975i	$0.497735\pi$
$284$	353849.	0.260329
$285$	183208.	0.133608
$286$	866790.	0.626612
$287$	3.03613e6	2.17578
$288$	153314.	0.108918
$289$	−267230.	−0.188209
$290$	−650571.	−0.454255
$291$	719312.	0.497949
$292$	81718.4	0.0560870
$293$	−1.93969e6	−1.31997	−0.659985	−	0.751279i	$-0.729437\pi$
$293$	−1.93969e6	−1.31997	−0.659985	+	0.751279i	$0.729437\pi$
$294$	−1.45951e6	−0.984779
$295$	145512.	0.0973517
$296$	−516266.	−0.342487
$297$	108697.	0.0715037
$298$	−767976.	−0.500965
$299$	−2.09296e6	−1.35389
$300$	−65454.7	−0.0419892
$301$	2.78159e6	1.76961
$302$	−1.11074e6	−0.700803
$303$	1.20692e6	0.755218
$304$	567358.	0.352106
$305$	−1.32288e6	−0.814276
$306$	−530961.	−0.324160
$307$	−110640.	−0.0669988	−0.0334994	−	0.999439i	$-0.510665\pi$
$307$	−110640.	−0.0669988	−0.0334994	+	0.999439i	$0.510665\pi$
$308$	163924.	0.0984615
$309$	−1.07434e6	−0.640095
$310$	262148.	0.154932
$311$	2.13892e6	1.25399	0.626994	−	0.779024i	$-0.284285\pi$
$311$	2.13892e6	1.25399	0.626994	+	0.779024i	$0.284285\pi$
$312$	−1.39802e6	−0.813068
$313$	2.94572e6	1.69953	0.849767	−	0.527158i	$-0.176742\pi$
$313$	2.94572e6	1.69953	0.849767	+	0.527158i	$0.176742\pi$
$314$	−1.53877e6	−0.880747
$315$	−705115.	−0.400390
$316$	241771.	0.136203
$317$	1.02771e6	0.574412	0.287206	−	0.957869i	$-0.407274\pi$
$317$	1.02771e6	0.574412	0.287206	+	0.957869i	$0.407274\pi$
$318$	−41044.7	−0.0227609
$319$	−380066.	−0.209113
$320$	−1.07537e6	−0.587061
$321$	551002.	0.298463
$322$	−2.79503e6	−1.50227
$323$	−522819.	−0.278834
$324$	34637.0	0.0183307
$325$	1.31164e6	0.688823
$326$	1.73843e6	0.905970
$327$	1.06972e6	0.553224
$328$	2.37861e6	1.22078
$329$	3.29230e6	1.67691
$330$	342501.	0.173132
$331$	−1.99485e6	−1.00078	−0.500391	−	0.865799i	$-0.666811\pi$
$331$	−1.99485e6	−1.00078	−0.500391	+	0.865799i	$0.666811\pi$
$332$	86875.4	0.0432565
$333$	−256316.	−0.126668
$334$	434001.	0.212875
$335$	1.54447e6	0.751915
$336$	−2.18360e6	−1.05518
$337$	−2.56238e6	−1.22905	−0.614523	−	0.788899i	$-0.710652\pi$
$337$	−2.56238e6	−1.22905	−0.614523	+	0.788899i	$0.710652\pi$
$338$	−3.26791e6	−1.55589
$339$	2.23643e6	1.05695
$340$	−236924.	−0.111151
$341$	153148.	0.0713221
$342$	240838.	0.111342
$343$	2.03108e6	0.932162
$344$	2.17919e6	0.992884
$345$	−827008.	−0.374078
$346$	2.56855e6	1.15345
$347$	−1.22248e6	−0.545026	−0.272513	−	0.962152i	$-0.587855\pi$
$347$	−1.22248e6	−0.545026	−0.272513	+	0.962152i	$0.587855\pi$
$348$	−121110.	−0.0536083
$349$	−3.21103e6	−1.41117	−0.705587	−	0.708623i	$-0.749317\pi$
$349$	−3.21103e6	−1.41117	−0.705587	+	0.708623i	$0.749317\pi$
$350$	1.75163e6	0.764313
$351$	−694090.	−0.300710
$352$	282220.	0.121403
$353$	−4.36299e6	−1.86358	−0.931789	−	0.363001i	$-0.881752\pi$
$353$	−4.36299e6	−1.86358	−0.931789	+	0.363001i	$0.881752\pi$
$354$	191285.	0.0811282
$355$	−2.80183e6	−1.17997
$356$	−150353.	−0.0628761
$357$	2.01218e6	0.835597
$358$	302521.	0.124752
$359$	38987.2	0.0159656	0.00798281	−	0.999968i	$-0.497459\pi$
$359$	38987.2	0.0159656	0.00798281	+	0.999968i	$0.497459\pi$
$360$	−552411.	−0.224650
$361$	−2.23895e6	−0.904226
$362$	36088.9	0.0144744
$363$	−1.24937e6	−0.497650
$364$	−1.04674e6	−0.414082
$365$	−647059.	−0.254221
$366$	−1.73901e6	−0.678578
$367$	−615070.	−0.238374	−0.119187	−	0.992872i	$-0.538029\pi$
$367$	−615070.	−0.238374	−0.119187	+	0.992872i	$0.538029\pi$
$368$	−2.56108e6	−0.985833
$369$	1.18093e6	0.451501
$370$	−807643.	−0.306701
$371$	155547.	0.0586715
$372$	48801.3	0.0182841
$373$	−2.59722e6	−0.966579	−0.483289	−	0.875461i	$-0.660558\pi$
$373$	−2.59722e6	−0.966579	−0.483289	+	0.875461i	$0.660558\pi$
$374$	−977394.	−0.361319
$375$	1.69395e6	0.622047
$376$	2.57930e6	0.940875
$377$	2.42692e6	0.879431
$378$	−926919.	−0.333666
$379$	−294437.	−0.105292	−0.0526459	−	0.998613i	$-0.516765\pi$
$379$	−294437.	−0.105292	−0.0526459	+	0.998613i	$0.516765\pi$
$380$	107466.	0.0381780
$381$	−1.65663e6	−0.584675
$382$	−4.54983e6	−1.59528
$383$	2.51121e6	0.874753	0.437377	−	0.899278i	$-0.355908\pi$
$383$	2.51121e6	0.874753	0.437377	+	0.899278i	$0.355908\pi$
$384$	−1.95876e6	−0.677880
$385$	−1.29798e6	−0.446288
$386$	182615.	0.0623831
$387$	1.08193e6	0.367214
$388$	421935.	0.142287
$389$	−3.42294e6	−1.14690	−0.573449	−	0.819241i	$-0.694395\pi$
$389$	−3.42294e6	−1.14690	−0.573449	+	0.819241i	$0.694395\pi$
$390$	−2.18705e6	−0.728111
$391$	2.36003e6	0.780684
$392$	4.33325e6	1.42429
$393$	−2.31205e6	−0.755120
$394$	3.05432e6	0.991229
$395$	−1.91438e6	−0.617356
$396$	63759.9	0.0204319
$397$	−4.77198e6	−1.51957	−0.759787	−	0.650172i	$-0.774697\pi$
$397$	−4.77198e6	−1.51957	−0.759787	+	0.650172i	$0.774697\pi$
$398$	3.16074e6	1.00019
$399$	−912705.	−0.287011
$400$	1.60501e6	0.501565
$401$	1.57375e6	0.488737	0.244369	−	0.969682i	$-0.421419\pi$
$401$	1.57375e6	0.488737	0.244369	+	0.969682i	$0.421419\pi$
$402$	2.03031e6	0.626609
$403$	−977928.	−0.299947
$404$	707957.	0.215801
$405$	−274261.	−0.0830858
$406$	3.24101e6	0.975811
$407$	−471828.	−0.141188
$408$	1.57641e6	0.468834
$409$	−4.72041e6	−1.39531	−0.697657	−	0.716432i	$-0.745774\pi$
$409$	−4.72041e6	−1.39531	−0.697657	+	0.716432i	$0.745774\pi$
$410$	3.72107e6	1.09322
$411$	−1.07043e6	−0.312574
$412$	−630186.	−0.182905
$413$	−724911.	−0.209127
$414$	−1.08715e6	−0.311738
$415$	−687893.	−0.196065
$416$	−1.80212e6	−0.510565
$417$	−1.32706e6	−0.373722
$418$	443336.	0.124106
$419$	−1.33538e6	−0.371595	−0.185798	−	0.982588i	$-0.559487\pi$
$419$	−1.33538e6	−0.371595	−0.185798	+	0.982588i	$0.559487\pi$
$420$	−413607.	−0.114410
$421$	−338764.	−0.0931521	−0.0465760	−	0.998915i	$-0.514831\pi$
$421$	−338764.	−0.0931521	−0.0465760	+	0.998915i	$0.514831\pi$
$422$	−7.67601e6	−2.09824
$423$	1.28057e6	0.347979
$424$	121861.	0.0329192
$425$	−1.47901e6	−0.397191
$426$	−3.68319e6	−0.983331
$427$	6.59033e6	1.74919
$428$	323207.	0.0852848
$429$	−1.27768e6	−0.335181
$430$	3.40910e6	0.889138
$431$	−7.24422e6	−1.87844	−0.939222	−	0.343311i	$-0.888452\pi$
$431$	−7.24422e6	−1.87844	−0.939222	+	0.343311i	$0.888452\pi$
$432$	−849332.	−0.218962
$433$	6.16246e6	1.57955	0.789777	−	0.613394i	$-0.210196\pi$
$433$	6.16246e6	1.57955	0.789777	+	0.613394i	$0.210196\pi$
$434$	−1.30597e6	−0.332819
$435$	958967.	0.242986
$436$	627478.	0.158082
$437$	−1.07048e6	−0.268149
$438$	−850599.	−0.211856
$439$	4.65424e6	1.15262	0.576311	−	0.817230i	$-0.304492\pi$
$439$	4.65424e6	1.15262	0.576311	+	0.817230i	$0.304492\pi$
$440$	−1.01688e6	−0.250402
$441$	2.15137e6	0.526768
$442$	6.24117e6	1.51953
$443$	−1.25610e6	−0.304098	−0.152049	−	0.988373i	$-0.548587\pi$
$443$	−1.25610e6	−0.304098	−0.152049	+	0.988373i	$0.548587\pi$
$444$	−150350.	−0.0361949
$445$	1.19051e6	0.284993
$446$	−5.90737e6	−1.40623
$447$	1.13203e6	0.267971
$448$	5.35728e6	1.26110
$449$	−4.46355e6	−1.04488	−0.522438	−	0.852677i	$-0.674977\pi$
$449$	−4.46355e6	−1.04488	−0.522438	+	0.852677i	$0.674977\pi$
$450$	681312.	0.158604
$451$	2.17386e6	0.503258
$452$	1.31185e6	0.302021
$453$	1.63728e6	0.374867
$454$	2.28451e6	0.520180
$455$	8.28826e6	1.87687
$456$	−715043.	−0.161035
$457$	4.01815e6	0.899986	0.449993	−	0.893032i	$-0.351427\pi$
$457$	4.01815e6	0.899986	0.449993	+	0.893032i	$0.351427\pi$
$458$	−401826.	−0.0895106
$459$	782658.	0.173396
$460$	−485107.	−0.106891
$461$	1.98402e6	0.434804	0.217402	−	0.976082i	$-0.430242\pi$
$461$	1.98402e6	0.434804	0.217402	+	0.976082i	$0.430242\pi$
$462$	−1.70627e6	−0.371915
$463$	2.31083e6	0.500975	0.250488	−	0.968120i	$-0.419409\pi$
$463$	2.31083e6	0.500975	0.250488	+	0.968120i	$0.419409\pi$
$464$	2.96973e6	0.640357
$465$	−386416.	−0.0828749
$466$	3.86518e6	0.824528
$467$	2.65831e6	0.564044	0.282022	−	0.959408i	$-0.408995\pi$
$467$	2.65831e6	0.564044	0.282022	+	0.959408i	$0.408995\pi$
$468$	−407140.	−0.0859270
$469$	−7.69426e6	−1.61523
$470$	4.03503e6	0.842563
$471$	2.26821e6	0.471120
$472$	−567919.	−0.117336
$473$	1.99161e6	0.409309
$474$	−2.51658e6	−0.514475
$475$	670864.	0.136427
$476$	1.18031e6	0.238769
$477$	60501.5	0.0121750
$478$	−4.44785e6	−0.890391
$479$	−6.22698e6	−1.24005	−0.620024	−	0.784582i	$-0.712877\pi$
$479$	−6.22698e6	−1.24005	−0.620024	+	0.784582i	$0.712877\pi$
$480$	−712086.	−0.141068
$481$	3.01287e6	0.593768
$482$	−7.47567e6	−1.46566
$483$	4.11999e6	0.803578
$484$	−732856.	−0.142202
$485$	−3.34095e6	−0.644934
$486$	−360534.	−0.0692397
$487$	8.29735e6	1.58532	0.792660	−	0.609664i	$-0.208696\pi$
$487$	8.29735e6	1.58532	0.792660	+	0.609664i	$0.208696\pi$
$488$	5.16308e6	0.981431
$489$	−2.56252e6	−0.484612
$490$	6.77890e6	1.27547
$491$	−6.71368e6	−1.25677	−0.628386	−	0.777901i	$-0.716284\pi$
$491$	−6.71368e6	−1.25677	−0.628386	+	0.777901i	$0.716284\pi$
$492$	692713.	0.129015
$493$	−2.73660e6	−0.507100
$494$	−2.83093e6	−0.521930
$495$	−504861.	−0.0926101
$496$	−1.19665e6	−0.218406
$497$	1.39582e7	2.53476
$498$	−904279.	−0.163391
$499$	−1.07848e7	−1.93892	−0.969458	−	0.245258i	$-0.921127\pi$
$499$	−1.07848e7	−1.93892	−0.969458	+	0.245258i	$0.921127\pi$
$500$	993641.	0.177748
$501$	−639734.	−0.113869
$502$	2.37477e6	0.420592
$503$	−6.41855e6	−1.13114	−0.565570	−	0.824700i	$-0.691344\pi$
$503$	−6.41855e6	−1.13114	−0.565570	+	0.824700i	$0.691344\pi$
$504$	2.75200e6	0.482583
$505$	−5.60571e6	−0.978143
$506$	−2.00124e6	−0.347474
$507$	4.81703e6	0.832262
$508$	−971751.	−0.167069
$509$	2.78903e6	0.477153	0.238577	−	0.971124i	$-0.423319\pi$
$509$	2.78903e6	0.477153	0.238577	+	0.971124i	$0.423319\pi$
$510$	2.46612e6	0.419845
$511$	3.22351e6	0.546107
$512$	3.87732e6	0.653667
$513$	−355005.	−0.0595582
$514$	−8.25482e6	−1.37816
$515$	4.98991e6	0.829038
$516$	634637.	0.104930
$517$	2.35728e6	0.387869
$518$	4.02351e6	0.658842
$519$	−3.78615e6	−0.616992
$520$	6.49330e6	1.05307
$521$	6.38091e6	1.02988	0.514942	−	0.857225i	$-0.327813\pi$
$521$	6.38091e6	1.02988	0.514942	+	0.857225i	$0.327813\pi$
$522$	1.26062e6	0.202493
$523$	−2.42857e6	−0.388237	−0.194119	−	0.980978i	$-0.562185\pi$
$523$	−2.42857e6	−0.388237	−0.194119	+	0.980978i	$0.562185\pi$
$524$	−1.35621e6	−0.215773
$525$	−2.58197e6	−0.408839
$526$	4.18708e6	0.659853
$527$	1.10271e6	0.172956
$528$	−1.56345e6	−0.244062
$529$	−1.60414e6	−0.249231
$530$	190638.	0.0294794
$531$	−281961.	−0.0433963
$532$	−535375.	−0.0820124
$533$	−1.38812e7	−2.11646
$534$	1.56501e6	0.237500
$535$	−2.55920e6	−0.386563
$536$	−6.02793e6	−0.906268
$537$	−445928.	−0.0667312
$538$	−1.31361e7	−1.95664
$539$	3.96025e6	0.587153
$540$	−160876.	−0.0237415
$541$	9.78542e6	1.43743	0.718714	−	0.695305i	$-0.244731\pi$
$541$	9.78542e6	1.43743	0.718714	+	0.695305i	$0.244731\pi$
$542$	1.44488e7	2.11268
$543$	−53196.4	−0.00774253
$544$	2.03208e6	0.294403
$545$	−4.96846e6	−0.716524
$546$	1.08954e7	1.56410
$547$	1.26732e7	1.81100	0.905501	−	0.424345i	$-0.139496\pi$
$547$	1.26732e7	1.81100	0.905501	+	0.424345i	$0.139496\pi$
$548$	−627892.	−0.0893169
$549$	2.56337e6	0.362979
$550$	1.25416e6	0.176785
$551$	1.24129e6	0.174179
$552$	3.22773e6	0.450869
$553$	9.53707e6	1.32618
$554$	−1.44859e7	−2.00526
$555$	1.19050e6	0.164057
$556$	−778426.	−0.106790
$557$	9.24073e6	1.26203	0.631013	−	0.775773i	$-0.282640\pi$
$557$	9.24073e6	1.26203	0.631013	+	0.775773i	$0.282640\pi$
$558$	−507968.	−0.0690639
$559$	−1.27175e7	−1.72136
$560$	1.01420e7	1.36664
$561$	1.44072e6	0.193273
$562$	2.36205e6	0.315462
$563$	1.33652e7	1.77707	0.888535	−	0.458809i	$-0.151724\pi$
$563$	1.33652e7	1.77707	0.888535	+	0.458809i	$0.151724\pi$
$564$	751160.	0.0994339
$565$	−1.03874e7	−1.36894
$566$	−117078.	−0.0153615
$567$	1.36631e6	0.178481
$568$	1.09353e7	1.42220
$569$	−8.45895e6	−1.09531	−0.547653	−	0.836705i	$-0.684479\pi$
$569$	−8.45895e6	−1.09531	−0.547653	+	0.836705i	$0.684479\pi$
$570$	−1.11861e6	−0.144208
$571$	1.49334e6	0.191677	0.0958385	−	0.995397i	$-0.469447\pi$
$571$	1.49334e6	0.191677	0.0958385	+	0.995397i	$0.469447\pi$
$572$	−749464.	−0.0957769
$573$	6.70662e6	0.853330
$574$	−1.85376e7	−2.34841
$575$	−3.02831e6	−0.381971
$576$	2.08377e6	0.261693
$577$	2.62239e6	0.327912	0.163956	−	0.986468i	$-0.447575\pi$
$577$	2.62239e6	0.327912	0.163956	+	0.986468i	$0.447575\pi$
$578$	1.63162e6	0.203142
$579$	−269181.	−0.0333694
$580$	562512.	0.0694323
$581$	3.42694e6	0.421179
$582$	−4.39188e6	−0.537457
$583$	111371.	0.0135707
$584$	2.52541e6	0.306408
$585$	3.22380e6	0.389474
$586$	1.18431e7	1.42470
$587$	9.30156e6	1.11419	0.557097	−	0.830448i	$-0.311915\pi$
$587$	9.30156e6	1.11419	0.557097	+	0.830448i	$0.311915\pi$
$588$	1.26196e6	0.150522
$589$	−500179.	−0.0594070
$590$	−888448.	−0.105076
$591$	−4.50219e6	−0.530218
$592$	3.68673e6	0.432352
$593$	−1.04915e7	−1.22518	−0.612592	−	0.790399i	$-0.709873\pi$
$593$	−1.04915e7	−1.22518	−0.612592	+	0.790399i	$0.709873\pi$
$594$	−663671.	−0.0771768
$595$	−9.34586e6	−1.08225
$596$	664025.	0.0765718
$597$	−4.65905e6	−0.535010
$598$	1.27789e7	1.46131
$599$	−3.77401e6	−0.429770	−0.214885	−	0.976639i	$-0.568938\pi$
$599$	−3.77401e6	−0.429770	−0.214885	+	0.976639i	$0.568938\pi$
$600$	−2.02280e6	−0.229390
$601$	−7.42586e6	−0.838611	−0.419305	−	0.907845i	$-0.637726\pi$
$601$	−7.42586e6	−0.838611	−0.419305	+	0.907845i	$0.637726\pi$
$602$	−1.69835e7	−1.91001
$603$	−2.99275e6	−0.335180
$604$	960396.	0.107117
$605$	5.80287e6	0.644546
$606$	−7.36906e6	−0.815137
$607$	9.37397e6	1.03265	0.516323	−	0.856394i	$-0.327300\pi$
$607$	9.37397e6	1.03265	0.516323	+	0.856394i	$0.327300\pi$
$608$	−921729.	−0.101122
$609$	−4.77738e6	−0.521971
$610$	8.07709e6	0.878881
$611$	−1.50525e7	−1.63119
$612$	459092.	0.0495475
$613$	−1.51042e7	−1.62348	−0.811740	−	0.584019i	$-0.801479\pi$
$613$	−1.51042e7	−1.62348	−0.811740	+	0.584019i	$0.801479\pi$
$614$	675533.	0.0723145
$615$	−5.48500e6	−0.584776
$616$	5.06588e6	0.537902
$617$	1.17572e7	1.24335	0.621674	−	0.783276i	$-0.286453\pi$
$617$	1.17572e7	1.24335	0.621674	+	0.783276i	$0.286453\pi$
$618$	6.55955e6	0.690880
$619$	−1.34123e7	−1.40695	−0.703473	−	0.710722i	$-0.748368\pi$
$619$	−1.34123e7	−1.40695	−0.703473	+	0.710722i	$0.748368\pi$
$620$	−226664.	−0.0236812
$621$	1.60251e6	0.166752
$622$	−1.30595e7	−1.35348
$623$	−5.93090e6	−0.612210
$624$	9.98346e6	1.02641
$625$	−3.56276e6	−0.364827
$626$	−1.79856e7	−1.83438
$627$	−653494.	−0.0663855
$628$	1.33049e6	0.134621
$629$	−3.39731e6	−0.342381
$630$	4.30520e6	0.432158
$631$	−1.63331e7	−1.63303	−0.816516	−	0.577323i	$-0.804097\pi$
$631$	−1.63331e7	−1.63303	−0.816516	+	0.577323i	$0.804097\pi$
$632$	7.47165e6	0.744087
$633$	1.13147e7	1.12237
$634$	−6.27488e6	−0.619986
$635$	7.69447e6	0.757259
$636$	35489.0	0.00347898
$637$	−2.52883e7	−2.46928
$638$	2.32056e6	0.225705
$639$	5.42916e6	0.525994
$640$	9.09773e6	0.877977
$641$	3.02654e6	0.290938	0.145469	−	0.989363i	$-0.453531\pi$
$641$	3.02654e6	0.290938	0.145469	+	0.989363i	$0.453531\pi$
$642$	−3.36424e6	−0.322143
$643$	−1.43363e7	−1.36744	−0.683722	−	0.729743i	$-0.739640\pi$
$643$	−1.43363e7	−1.36744	−0.683722	+	0.729743i	$0.739640\pi$
$644$	2.41671e6	0.229620
$645$	−5.02515e6	−0.475609
$646$	3.19216e6	0.300957
$647$	−8.34526e6	−0.783753	−0.391876	−	0.920018i	$-0.628174\pi$
$647$	−8.34526e6	−0.783753	−0.391876	+	0.920018i	$0.628174\pi$
$648$	1.07042e6	0.100142
$649$	−519034.	−0.0483709
$650$	−8.00847e6	−0.743474
$651$	1.92505e6	0.178028
$652$	−1.50312e6	−0.138476
$653$	−1.91948e7	−1.76157	−0.880787	−	0.473513i	$-0.842986\pi$
$653$	−1.91948e7	−1.76157	−0.880787	+	0.473513i	$0.842986\pi$
$654$	−6.53136e6	−0.597117
$655$	1.07386e7	0.978016
$656$	−1.69860e7	−1.54110
$657$	1.25382e6	0.113324
$658$	−2.01017e7	−1.80996
$659$	−1.01224e7	−0.907967	−0.453984	−	0.891010i	$-0.649998\pi$
$659$	−1.01224e7	−0.907967	−0.453984	+	0.891010i	$0.649998\pi$
$660$	−296142.	−0.0264630
$661$	1.37317e7	1.22242	0.611211	−	0.791467i	$-0.290683\pi$
$661$	1.37317e7	1.22242	0.611211	+	0.791467i	$0.290683\pi$
$662$	1.21799e7	1.08019
$663$	−9.19974e6	−0.812815
$664$	2.68478e6	0.236314
$665$	4.23919e6	0.371731
$666$	1.56498e6	0.136718
$667$	−5.60324e6	−0.487669
$668$	−375256.	−0.0325377
$669$	8.70770e6	0.752208
$670$	−9.43005e6	−0.811572
$671$	4.71866e6	0.404587
$672$	3.54747e6	0.303037
$673$	−1.99795e7	−1.70038	−0.850191	−	0.526475i	$-0.823513\pi$
$673$	−1.99795e7	−1.70038	−0.850191	+	0.526475i	$0.823513\pi$
$674$	1.56450e7	1.32656
$675$	−1.00428e6	−0.0848390
$676$	2.82558e6	0.237816
$677$	−1.45995e7	−1.22424	−0.612118	−	0.790767i	$-0.709682\pi$
$677$	−1.45995e7	−1.22424	−0.612118	+	0.790767i	$0.709682\pi$
$678$	−1.36549e7	−1.14081
$679$	1.66439e7	1.38542
$680$	−7.32186e6	−0.607224
$681$	−3.36746e6	−0.278250
$682$	−935069.	−0.0769809
$683$	1.29809e7	1.06477	0.532383	−	0.846504i	$-0.321297\pi$
$683$	1.29809e7	1.06477	0.532383	+	0.846504i	$0.321297\pi$
$684$	−208239.	−0.0170186
$685$	4.97175e6	0.404839
$686$	−1.24011e7	−1.00612
$687$	592308.	0.0478802
$688$	−1.55619e7	−1.25340
$689$	−711164.	−0.0570718
$690$	5.04944e6	0.403757
$691$	−1.24354e7	−0.990753	−0.495376	−	0.868678i	$-0.664970\pi$
$691$	−1.24354e7	−0.990753	−0.495376	+	0.868678i	$0.664970\pi$
$692$	−2.22088e6	−0.176303
$693$	2.51511e6	0.198941
$694$	7.46404e6	0.588268
$695$	6.16369e6	0.484038
$696$	−3.74276e6	−0.292866
$697$	1.56525e7	1.22040
$698$	1.96055e7	1.52314
$699$	−5.69743e6	−0.441049
$700$	−1.51453e6	−0.116824
$701$	−3.72318e6	−0.286166	−0.143083	−	0.989711i	$-0.545702\pi$
$701$	−3.72318e6	−0.286166	−0.143083	+	0.989711i	$0.545702\pi$
$702$	4.23789e6	0.324569
$703$	1.54099e6	0.117601
$704$	3.83580e6	0.291692
$705$	−5.94780e6	−0.450696
$706$	2.66390e7	2.01144
$707$	2.79265e7	2.10120
$708$	−165393.	−0.0124003
$709$	−9.20964e6	−0.688061	−0.344030	−	0.938958i	$-0.611792\pi$
$709$	−9.20964e6	−0.688061	−0.344030	+	0.938958i	$0.611792\pi$
$710$	1.71071e7	1.27359
$711$	3.70953e6	0.275198
$712$	−4.64646e6	−0.343497
$713$	2.25783e6	0.166329
$714$	−1.22857e7	−0.901894
$715$	5.93437e6	0.434120
$716$	−261573.	−0.0190682
$717$	6.55631e6	0.476279
$718$	−238043.	−0.0172324
$719$	−4.15670e6	−0.299865	−0.149933	−	0.988696i	$-0.547906\pi$
$719$	−4.15670e6	−0.299865	−0.149933	+	0.988696i	$0.547906\pi$
$720$	3.94484e6	0.283595
$721$	−2.48587e7	−1.78090
$722$	1.36703e7	0.975968
$723$	1.10194e7	0.783996
$724$	−31204.0	−0.00221240
$725$	3.51151e6	0.248113
$726$	7.62823e6	0.537134
$727$	−1.87342e6	−0.131462	−0.0657309	−	0.997837i	$-0.520938\pi$
$727$	−1.87342e6	−0.131462	−0.0657309	+	0.997837i	$0.520938\pi$
$728$	−3.23483e7	−2.26216
$729$	531441.	0.0370370
$730$	3.95073e6	0.274391
$731$	1.43402e7	0.992575
$732$	1.50363e6	0.103720
$733$	−1.70190e7	−1.16997	−0.584986	−	0.811044i	$-0.698900\pi$
$733$	−1.70190e7	−1.16997	−0.584986	+	0.811044i	$0.698900\pi$
$734$	3.75542e6	0.257287
$735$	−9.99236e6	−0.682260
$736$	4.16072e6	0.283122
$737$	−5.50907e6	−0.373602
$738$	−7.21039e6	−0.487324
$739$	−1.51158e7	−1.01817	−0.509084	−	0.860717i	$-0.670016\pi$
$739$	−1.51158e7	−1.01817	−0.509084	+	0.860717i	$0.670016\pi$
$740$	698323.	0.0468789
$741$	4.17290e6	0.279185
$742$	−949719.	−0.0633265
$743$	1.88824e7	1.25483	0.627416	−	0.778684i	$-0.284112\pi$
$743$	1.88824e7	1.25483	0.627416	+	0.778684i	$0.284112\pi$
$744$	1.50815e6	0.0998874
$745$	−5.25786e6	−0.347071
$746$	1.58578e7	1.04327
$747$	1.33294e6	0.0873997
$748$	845098.	0.0552272
$749$	1.27494e7	0.830398
$750$	−1.03427e7	−0.671401
$751$	−1.00270e7	−0.648739	−0.324369	−	0.945931i	$-0.605152\pi$
$751$	−1.00270e7	−0.648739	−0.324369	+	0.945931i	$0.605152\pi$
$752$	−1.84191e7	−1.18775
$753$	−3.50050e6	−0.224979
$754$	−1.48180e7	−0.949206
$755$	−7.60456e6	−0.485520
$756$	801454.	0.0510005
$757$	−2.49293e7	−1.58114	−0.790570	−	0.612372i	$-0.790215\pi$
$757$	−2.49293e7	−1.58114	−0.790570	+	0.612372i	$0.790215\pi$
$758$	1.79774e6	0.113646
$759$	2.94990e6	0.185867
$760$	3.32112e6	0.208569
$761$	−1.02441e7	−0.641229	−0.320614	−	0.947210i	$-0.603889\pi$
$761$	−1.02441e7	−0.641229	−0.320614	+	0.947210i	$0.603889\pi$
$762$	1.01149e7	0.631063
$763$	2.47519e7	1.53921
$764$	3.93398e6	0.243836
$765$	−3.63516e6	−0.224580
$766$	−1.53326e7	−0.944157
$767$	3.31431e6	0.203425
$768$	4.55059e6	0.278397
$769$	2.17564e7	1.32670	0.663348	−	0.748311i	$-0.269135\pi$
$769$	2.17564e7	1.32670	0.663348	+	0.748311i	$0.269135\pi$
$770$	7.92502e6	0.481697
$771$	1.21679e7	0.737192
$772$	−157897.	−0.00953519
$773$	2.30398e7	1.38685	0.693425	−	0.720529i	$-0.256101\pi$
$773$	2.30398e7	1.38685	0.693425	+	0.720529i	$0.256101\pi$
$774$	−6.60588e6	−0.396349
$775$	−1.41497e6	−0.0846236
$776$	1.30394e7	0.777326
$777$	−5.93082e6	−0.352421
$778$	2.08993e7	1.23789
$779$	−7.09982e6	−0.419183
$780$	1.89102e6	0.111291
$781$	9.99401e6	0.586289
$782$	−1.44096e7	−0.842624
$783$	−1.85821e6	−0.108315
$784$	−3.09443e7	−1.79801
$785$	−1.05350e7	−0.610186
$786$	1.41166e7	0.815032
$787$	3.85957e6	0.222127	0.111064	−	0.993813i	$-0.464574\pi$
$787$	3.85957e6	0.222127	0.111064	+	0.993813i	$0.464574\pi$
$788$	−2.64090e6	−0.151508
$789$	−6.17193e6	−0.352962
$790$	1.16886e7	0.666338
$791$	5.17479e7	2.94071
$792$	1.97042e6	0.111621
$793$	−3.01311e7	−1.70150
$794$	2.91361e7	1.64014
$795$	−281008.	−0.0157689
$796$	−2.73291e6	−0.152877
$797$	1.58425e7	0.883444	0.441722	−	0.897152i	$-0.354368\pi$
$797$	1.58425e7	0.883444	0.441722	+	0.897152i	$0.354368\pi$
$798$	5.57268e6	0.309782
$799$	1.69732e7	0.940582
$800$	−2.60749e6	−0.144045
$801$	−2.30688e6	−0.127041
$802$	−9.60881e6	−0.527514
$803$	2.30803e6	0.126314
$804$	−1.75549e6	−0.0957765
$805$	−1.91359e7	−1.04078
$806$	5.97091e6	0.323745
$807$	1.93631e7	1.04662
$808$	2.18786e7	1.17894
$809$	1.45751e7	0.782961	0.391481	−	0.920186i	$-0.371963\pi$
$809$	1.45751e7	0.782961	0.391481	+	0.920186i	$0.371963\pi$
$810$	1.67455e6	0.0896779
$811$	3.03425e7	1.61994	0.809970	−	0.586472i	$-0.199484\pi$
$811$	3.03425e7	1.61994	0.809970	+	0.586472i	$0.199484\pi$
$812$	−2.80232e6	−0.149152
$813$	−2.12981e7	−1.13010
$814$	2.88082e6	0.152390
$815$	1.19020e7	0.627660
$816$	−1.12574e7	−0.591850
$817$	−6.50458e6	−0.340929
$818$	2.88213e7	1.50602
$819$	−1.60603e7	−0.836651
$820$	−3.21740e6	−0.167098
$821$	3.22288e6	0.166873	0.0834366	−	0.996513i	$-0.473410\pi$
$821$	3.22288e6	0.166873	0.0834366	+	0.996513i	$0.473410\pi$
$822$	6.53568e6	0.337373
$823$	−4.75007e6	−0.244456	−0.122228	−	0.992502i	$-0.539004\pi$
$823$	−4.75007e6	−0.244456	−0.122228	+	0.992502i	$0.539004\pi$
$824$	−1.94751e7	−0.999223
$825$	−1.84868e6	−0.0945643
$826$	4.42607e6	0.225719
$827$	1.44496e7	0.734671	0.367336	−	0.930088i	$-0.380270\pi$
$827$	1.44496e7	0.734671	0.367336	+	0.930088i	$0.380270\pi$
$828$	940001.	0.0476489
$829$	−2.10004e7	−1.06131	−0.530653	−	0.847589i	$-0.678053\pi$
$829$	−2.10004e7	−1.06131	−0.530653	+	0.847589i	$0.678053\pi$
$830$	4.20005e6	0.211621
$831$	2.13528e7	1.07264
$832$	−2.44936e7	−1.22672
$833$	2.85151e7	1.42385
$834$	8.10257e6	0.403374
$835$	2.97133e6	0.147481
$836$	−383327.	−0.0189694
$837$	748765.	0.0369430
$838$	8.15340e6	0.401078
$839$	1.45792e6	0.0715040	0.0357520	−	0.999361i	$-0.488617\pi$
$839$	1.45792e6	0.0715040	0.0357520	+	0.999361i	$0.488617\pi$
$840$	−1.27820e7	−0.625031
$841$	−1.40138e7	−0.683230
$842$	2.06838e6	0.100543
$843$	−3.48175e6	−0.168744
$844$	6.63701e6	0.320713
$845$	−2.23734e7	−1.07793
$846$	−7.81876e6	−0.375588
$847$	−2.89087e7	−1.38459
$848$	−870224.	−0.0415568
$849$	172577.	0.00821700
$850$	9.03036e6	0.428704
$851$	−6.95607e6	−0.329261
$852$	3.18464e6	0.150301
$853$	−1.47110e7	−0.692262	−0.346131	−	0.938186i	$-0.612505\pi$
$853$	−1.47110e7	−0.692262	−0.346131	+	0.938186i	$0.612505\pi$
$854$	−4.02384e7	−1.88797
$855$	1.64887e6	0.0771386
$856$	9.98833e6	0.465917
$857$	2.25591e7	1.04923	0.524615	−	0.851340i	$-0.324209\pi$
$857$	2.25591e7	1.04923	0.524615	+	0.851340i	$0.324209\pi$
$858$	7.80111e6	0.361775
$859$	3.74722e7	1.73271	0.866356	−	0.499427i	$-0.166456\pi$
$859$	3.74722e7	1.73271	0.866356	+	0.499427i	$0.166456\pi$
$860$	−2.94766e6	−0.135904
$861$	2.73252e7	1.25619
$862$	4.42308e7	2.02748
$863$	7.18311e6	0.328311	0.164156	−	0.986434i	$-0.447510\pi$
$863$	7.18311e6	0.328311	0.164156	+	0.986434i	$0.447510\pi$
$864$	1.37982e6	0.0628838
$865$	1.75853e7	0.799116
$866$	−3.76260e7	−1.70488
$867$	−2.40507e6	−0.108663
$868$	1.12920e6	0.0508710
$869$	6.82851e6	0.306744
$870$	−5.85514e6	−0.262264
$871$	3.51783e7	1.57119
$872$	1.93914e7	0.863612
$873$	6.47381e6	0.287491
$874$	6.53602e6	0.289424
$875$	3.91958e7	1.73069
$876$	735465.	0.0323819
$877$	4.17457e7	1.83279	0.916394	−	0.400277i	$-0.131086\pi$
$877$	4.17457e7	1.83279	0.916394	+	0.400277i	$0.131086\pi$
$878$	−2.84172e7	−1.24407
$879$	−1.74572e7	−0.762085
$880$	7.26167e6	0.316104
$881$	−8.72480e6	−0.378718	−0.189359	−	0.981908i	$-0.560641\pi$
$881$	−8.72480e6	−0.378718	−0.189359	+	0.981908i	$0.560641\pi$
$882$	−1.31356e7	−0.568562
$883$	2.98453e6	0.128817	0.0644087	−	0.997924i	$-0.479484\pi$
$883$	2.98453e6	0.128817	0.0644087	+	0.997924i	$0.479484\pi$
$884$	−5.39639e6	−0.232259
$885$	1.30961e6	0.0562060
$886$	7.66932e6	0.328226
$887$	−2.69623e7	−1.15066	−0.575332	−	0.817920i	$-0.695127\pi$
$887$	−2.69623e7	−1.15066	−0.575332	+	0.817920i	$0.695127\pi$
$888$	−4.64640e6	−0.197735
$889$	−3.83323e7	−1.62671
$890$	−7.26889e6	−0.307605
$891$	978277.	0.0412827
$892$	5.10777e6	0.214941
$893$	−7.69886e6	−0.323071
$894$	−6.91178e6	−0.289232
$895$	2.07117e6	0.0864288
$896$	−4.53230e7	−1.88603
$897$	−1.88367e7	−0.781668
$898$	2.72530e7	1.12778
$899$	−2.61809e6	−0.108040
$900$	−589092.	−0.0242425
$901$	801910.	0.0329089
$902$	−1.32729e7	−0.543187
$903$	2.50343e7	1.02168
$904$	4.05410e7	1.64996
$905$	247078.	0.0100280
$906$	−9.99668e6	−0.404609
$907$	−1.11838e7	−0.451409	−0.225704	−	0.974196i	$-0.572468\pi$
$907$	−1.11838e7	−0.451409	−0.225704	+	0.974196i	$0.572468\pi$
$908$	−1.97529e6	−0.0795090
$909$	1.08623e7	0.436025
$910$	−5.06054e7	−2.02579
$911$	−1.36404e7	−0.544542	−0.272271	−	0.962221i	$-0.587775\pi$
$911$	−1.36404e7	−0.544542	−0.272271	+	0.962221i	$0.587775\pi$
$912$	5.10623e6	0.203289
$913$	2.45368e6	0.0974185
$914$	−2.45335e7	−0.971391
$915$	−1.19059e7	−0.470122
$916$	347437.	0.0136816
$917$	−5.34977e7	−2.10093
$918$	−4.77865e6	−0.187154
$919$	3.56348e7	1.39183	0.695914	−	0.718125i	$-0.254999\pi$
$919$	3.56348e7	1.39183	0.695914	+	0.718125i	$0.254999\pi$
$920$	−1.49917e7	−0.583956
$921$	−995762.	−0.0386818
$922$	−1.21138e7	−0.469302
$923$	−6.38170e7	−2.46565
$924$	1.47532e6	0.0568468
$925$	4.35932e6	0.167519
$926$	−1.41092e7	−0.540723
$927$	−9.66904e6	−0.369559
$928$	−4.82461e6	−0.183905
$929$	−2.06763e7	−0.786021	−0.393011	−	0.919534i	$-0.628566\pi$
$929$	−2.06763e7	−0.786021	−0.393011	+	0.919534i	$0.628566\pi$
$930$	2.35933e6	0.0894502
$931$	−1.29342e7	−0.489062
$932$	−3.34201e6	−0.126028
$933$	1.92503e7	0.723990
$934$	−1.62307e7	−0.608795
$935$	−6.69161e6	−0.250324
$936$	−1.25822e7	−0.469425
$937$	964568.	0.0358909	0.0179454	−	0.999839i	$-0.494287\pi$
$937$	964568.	0.0358909	0.0179454	+	0.999839i	$0.494287\pi$
$938$	4.69786e7	1.74338
$939$	2.65114e7	0.981227
$940$	−3.48887e6	−0.128785
$941$	3.97475e7	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$941$	3.97475e7	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$942$	−1.38490e7	−0.508499
$943$	3.20489e7	1.17364
$944$	4.05559e6	0.148124
$945$	−6.34604e6	−0.231166
$946$	−1.21601e7	−0.441784
$947$	4.51166e6	0.163479	0.0817395	−	0.996654i	$-0.473952\pi$
$947$	4.51166e6	0.163479	0.0817395	+	0.996654i	$0.473952\pi$
$948$	2.17594e6	0.0786369
$949$	−1.47380e7	−0.531217
$950$	−4.09608e6	−0.147251
$951$	9.24942e6	0.331637
$952$	3.64760e7	1.30441
$953$	−2.78914e7	−0.994807	−0.497403	−	0.867519i	$-0.665713\pi$
$953$	−2.78914e7	−0.994807	−0.497403	+	0.867519i	$0.665713\pi$
$954$	−369402.	−0.0131410
$955$	−3.11498e7	−1.10522
$956$	3.84581e6	0.136095
$957$	−3.42059e6	−0.120732
$958$	3.80199e7	1.33843
$959$	−2.47682e7	−0.869658
$960$	−9.67834e6	−0.338940
$961$	−2.75742e7	−0.963151
$962$	−1.83956e7	−0.640878
$963$	4.95902e6	0.172318
$964$	6.46379e6	0.224024
$965$	1.25025e6	0.0432193
$966$	−2.51553e7	−0.867334
$967$	8.43317e6	0.290018	0.145009	−	0.989430i	$-0.453679\pi$
$967$	8.43317e6	0.290018	0.145009	+	0.989430i	$0.453679\pi$
$968$	−2.26480e7	−0.776859
$969$	−4.70537e6	−0.160985
$970$	2.03987e7	0.696103
$971$	−7.74992e6	−0.263784	−0.131892	−	0.991264i	$-0.542105\pi$
$971$	−7.74992e6	−0.263784	−0.131892	+	0.991264i	$0.542105\pi$
$972$	311733.	0.0105832
$973$	−3.07063e7	−1.03979
$974$	−5.06609e7	−1.71110
$975$	1.18048e7	0.397692
$976$	−3.68703e7	−1.23895
$977$	−2.03500e6	−0.0682069	−0.0341035	−	0.999418i	$-0.510858\pi$
$977$	−2.03500e6	−0.0682069	−0.0341035	+	0.999418i	$0.510858\pi$
$978$	1.56459e7	0.523062
$979$	−4.24651e6	−0.141604
$980$	−5.86133e6	−0.194953
$981$	9.62748e6	0.319404
$982$	4.09915e7	1.35649
$983$	4.87946e7	1.61060	0.805301	−	0.592866i	$-0.202004\pi$
$983$	4.87946e7	1.61060	0.805301	+	0.592866i	$0.202004\pi$
$984$	2.14075e7	0.704818
$985$	2.09110e7	0.686728
$986$	1.67088e7	0.547334
$987$	2.96307e7	0.968165
$988$	2.44775e6	0.0797763
$989$	2.93620e7	0.954540
$990$	3.08251e6	0.0999579
$991$	4.77463e7	1.54439	0.772193	−	0.635388i	$-0.219160\pi$
$991$	4.77463e7	1.54439	0.772193	+	0.635388i	$0.219160\pi$
$992$	1.94408e6	0.0627242
$993$	−1.79536e7	−0.577802
$994$	−8.52240e7	−2.73587
$995$	2.16396e7	0.692934
$996$	781879.	0.0249742
$997$	−4.32326e7	−1.37744	−0.688721	−	0.725026i	$-0.741828\pi$
$997$	−4.32326e7	−1.37744	−0.688721	+	0.725026i	$0.741828\pi$
$998$	6.58482e7	2.09275
$999$	−2.30685e6	−0.0731316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.2	✓	12
3.2	odd	2		531.6.a.c.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.2	✓	12	1.1	even	1	trivial
531.6.a.c.1.11		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)

\(f(q)\)	\(=\)	\(q-6.10567 q^{2} +9.00000 q^{3} +5.27923 q^{4} -41.8018 q^{5} -54.9510 q^{6} +208.248 q^{7} +163.148 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-6.10567 q^{2} +9.00000 q^{3} +5.27923 q^{4} -41.8018 q^{5} -54.9510 q^{6} +208.248 q^{7} +163.148 q^{8} +81.0000 q^{9} +255.228 q^{10} +149.105 q^{11} +47.5131 q^{12} -952.113 q^{13} -1271.49 q^{14} -376.216 q^{15} -1165.07 q^{16} +1073.60 q^{17} -494.559 q^{18} -486.976 q^{19} -220.681 q^{20} +1874.23 q^{21} -910.386 q^{22} +2198.23 q^{23} +1468.33 q^{24} -1377.61 q^{25} +5813.29 q^{26} +729.000 q^{27} +1099.39 q^{28} -2548.98 q^{29} +2297.05 q^{30} +1027.11 q^{31} +1892.76 q^{32} +1341.94 q^{33} -6555.08 q^{34} -8705.13 q^{35} +427.618 q^{36} -3164.40 q^{37} +2973.31 q^{38} -8569.02 q^{39} -6819.88 q^{40} +14579.4 q^{41} -11443.4 q^{42} +13357.1 q^{43} +787.159 q^{44} -3385.94 q^{45} -13421.7 q^{46} +15809.5 q^{47} -10485.6 q^{48} +26560.2 q^{49} +8411.26 q^{50} +9662.44 q^{51} -5026.42 q^{52} +746.932 q^{53} -4451.03 q^{54} -6232.85 q^{55} +33975.3 q^{56} -4382.78 q^{57} +15563.2 q^{58} -3481.00 q^{59} -1986.13 q^{60} +31646.6 q^{61} -6271.22 q^{62} +16868.1 q^{63} +25725.5 q^{64} +39800.0 q^{65} -8193.47 q^{66} -36947.6 q^{67} +5667.81 q^{68} +19784.1 q^{69} +53150.6 q^{70} +67026.7 q^{71} +13215.0 q^{72} +15479.2 q^{73} +19320.8 q^{74} -12398.5 q^{75} -2570.86 q^{76} +31050.8 q^{77} +52319.6 q^{78} +45796.7 q^{79} +48701.8 q^{80} +6561.00 q^{81} -89017.1 q^{82} +16456.1 q^{83} +9894.50 q^{84} -44878.6 q^{85} -81554.1 q^{86} -22940.8 q^{87} +24326.2 q^{88} -28480.0 q^{89} +20673.4 q^{90} -198276. q^{91} +11604.9 q^{92} +9244.02 q^{93} -96527.9 q^{94} +20356.4 q^{95} +17034.8 q^{96} +79923.6 q^{97} -162168. q^{98} +12077.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 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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