LMFDB - Embedded newform 177.6.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$12$
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} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 $ x^12 - 4x^11 - 283x^10 + 1045x^9 + 27968x^8 - 94393x^7 - 1130486x^6 + 3566264x^5 + 15496192x^4 - 53008480x^3 - 16576192x^2 + 120303168*x - 50564480
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			1.9
Root			$-5.27208$ 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)

$f(q)$	$=$	$q+5.27208 q^{2} -9.00000 q^{3} -4.20512 q^{4} -17.5332 q^{5} -47.4488 q^{6} +172.711 q^{7} -190.876 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+5.27208 q^{2} -9.00000 q^{3} -4.20512 q^{4} -17.5332 q^{5} -47.4488 q^{6} +172.711 q^{7} -190.876 q^{8} +81.0000 q^{9} -92.4366 q^{10} +249.532 q^{11} +37.8461 q^{12} +282.746 q^{13} +910.545 q^{14} +157.799 q^{15} -871.753 q^{16} -1347.49 q^{17} +427.039 q^{18} -2886.53 q^{19} +73.7293 q^{20} -1554.40 q^{21} +1315.55 q^{22} +692.702 q^{23} +1717.89 q^{24} -2817.59 q^{25} +1490.66 q^{26} -729.000 q^{27} -726.269 q^{28} -2778.00 q^{29} +831.930 q^{30} -4109.10 q^{31} +1512.09 q^{32} -2245.79 q^{33} -7104.11 q^{34} -3028.17 q^{35} -340.615 q^{36} -10616.6 q^{37} -15218.0 q^{38} -2544.72 q^{39} +3346.68 q^{40} -828.466 q^{41} -8194.91 q^{42} +8995.66 q^{43} -1049.31 q^{44} -1420.19 q^{45} +3651.98 q^{46} -4346.77 q^{47} +7845.78 q^{48} +13022.0 q^{49} -14854.6 q^{50} +12127.5 q^{51} -1188.98 q^{52} -1799.96 q^{53} -3843.35 q^{54} -4375.10 q^{55} -32966.4 q^{56} +25978.8 q^{57} -14645.9 q^{58} -3481.00 q^{59} -663.564 q^{60} -28023.9 q^{61} -21663.5 q^{62} +13989.6 q^{63} +35868.0 q^{64} -4957.46 q^{65} -11840.0 q^{66} +30957.2 q^{67} +5666.38 q^{68} -6234.32 q^{69} -15964.8 q^{70} +3945.44 q^{71} -15461.0 q^{72} +17740.6 q^{73} -55971.8 q^{74} +25358.3 q^{75} +12138.2 q^{76} +43096.8 q^{77} -13416.0 q^{78} -57063.7 q^{79} +15284.6 q^{80} +6561.00 q^{81} -4367.74 q^{82} +17500.9 q^{83} +6536.42 q^{84} +23625.9 q^{85} +47425.9 q^{86} +25002.0 q^{87} -47629.8 q^{88} -53616.7 q^{89} -7487.37 q^{90} +48833.3 q^{91} -2912.89 q^{92} +36981.9 q^{93} -22916.6 q^{94} +50610.2 q^{95} -13608.8 q^{96} -115705. q^{97} +68653.0 q^{98} +20212.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * 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 $

$2$	5.27208	0.931982	0.465991	−	0.884790i	$-0.345698\pi$
$2$	5.27208	0.931982	0.465991	+	0.884790i	$0.345698\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−4.20512	−0.131410
$5$	−17.5332	−0.313644	−0.156822	−	0.987627i	$-0.550125\pi$
$5$	−17.5332	−0.313644	−0.156822	+	0.987627i	$0.550125\pi$
$6$	−47.4488	−0.538080
$7$	172.711	1.33221	0.666107	−	0.745856i	$-0.267959\pi$
$7$	172.711	1.33221	0.666107	+	0.745856i	$0.267959\pi$
$8$	−190.876	−1.05445
$9$	81.0000	0.333333
$10$	−92.4366	−0.292310
$11$	249.532	0.621791	0.310895	−	0.950444i	$-0.399371\pi$
$11$	249.532	0.621791	0.310895	+	0.950444i	$0.399371\pi$
$12$	37.8461	0.0758696
$13$	282.746	0.464022	0.232011	−	0.972713i	$-0.425469\pi$
$13$	282.746	0.464022	0.232011	+	0.972713i	$0.425469\pi$
$14$	910.545	1.24160
$15$	157.799	0.181082
$16$	−871.753	−0.851321
$17$	−1347.49	−1.13085	−0.565425	−	0.824800i	$-0.691288\pi$
$17$	−1347.49	−1.13085	−0.565425	+	0.824800i	$0.691288\pi$
$18$	427.039	0.310661
$19$	−2886.53	−1.83439	−0.917196	−	0.398436i	$-0.869553\pi$
$19$	−2886.53	−1.83439	−0.917196	+	0.398436i	$0.869553\pi$
$20$	73.7293	0.0412159
$21$	−1554.40	−0.769154
$22$	1315.55	0.579498
$23$	692.702	0.273040	0.136520	−	0.990637i	$-0.456408\pi$
$23$	692.702	0.273040	0.136520	+	0.990637i	$0.456408\pi$
$24$	1717.89	0.608789
$25$	−2817.59	−0.901628
$26$	1490.66	0.432460
$27$	−729.000	−0.192450
$28$	−726.269	−0.175066
$29$	−2778.00	−0.613391	−0.306695	−	0.951808i	$-0.599223\pi$
$29$	−2778.00	−0.613391	−0.306695	+	0.951808i	$0.599223\pi$
$30$	831.930	0.168765
$31$	−4109.10	−0.767967	−0.383983	−	0.923340i	$-0.625448\pi$
$31$	−4109.10	−0.767967	−0.383983	+	0.923340i	$0.625448\pi$
$32$	1512.09	0.261038
$33$	−2245.79	−0.358991
$34$	−7104.11	−1.05393
$35$	−3028.17	−0.417841
$36$	−340.615	−0.0438033
$37$	−10616.6	−1.27492	−0.637459	−	0.770484i	$-0.720015\pi$
$37$	−10616.6	−1.27492	−0.637459	+	0.770484i	$0.720015\pi$
$38$	−15218.0	−1.70962
$39$	−2544.72	−0.267903
$40$	3346.68	0.330723
$41$	−828.466	−0.0769688	−0.0384844	−	0.999259i	$-0.512253\pi$
$41$	−828.466	−0.0769688	−0.0384844	+	0.999259i	$0.512253\pi$
$42$	−8194.91	−0.716838
$43$	8995.66	0.741929	0.370964	−	0.928647i	$-0.379027\pi$
$43$	8995.66	0.741929	0.370964	+	0.928647i	$0.379027\pi$
$44$	−1049.31	−0.0817096
$45$	−1420.19	−0.104548
$46$	3651.98	0.254469
$47$	−4346.77	−0.287027	−0.143513	−	0.989648i	$-0.545840\pi$
$47$	−4346.77	−0.287027	−0.143513	+	0.989648i	$0.545840\pi$
$48$	7845.78	0.491511
$49$	13022.0	0.774795
$50$	−14854.6	−0.840300
$51$	12127.5	0.652896
$52$	−1188.98	−0.0609772
$53$	−1799.96	−0.0880185	−0.0440092	−	0.999031i	$-0.514013\pi$
$53$	−1799.96	−0.0880185	−0.0440092	+	0.999031i	$0.514013\pi$
$54$	−3843.35	−0.179360
$55$	−4375.10	−0.195021
$56$	−32966.4	−1.40476
$57$	25978.8	1.05909
$58$	−14645.9	−0.571669
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−663.564	−0.0237960
$61$	−28023.9	−0.964283	−0.482142	−	0.876093i	$-0.660141\pi$
$61$	−28023.9	−0.964283	−0.482142	+	0.876093i	$0.660141\pi$
$62$	−21663.5	−0.715731
$63$	13989.6	0.444071
$64$	35868.0	1.09460
$65$	−4957.46	−0.145538
$66$	−11840.0	−0.334573
$67$	30957.2	0.842509	0.421254	−	0.906943i	$-0.361590\pi$
$67$	30957.2	0.842509	0.421254	+	0.906943i	$0.361590\pi$
$68$	5666.38	0.148605
$69$	−6234.32	−0.157640
$70$	−15964.8	−0.389420
$71$	3945.44	0.0928858	0.0464429	−	0.998921i	$-0.485211\pi$
$71$	3945.44	0.0928858	0.0464429	+	0.998921i	$0.485211\pi$
$72$	−15461.0	−0.351484
$73$	17740.6	0.389637	0.194819	−	0.980839i	$-0.437588\pi$
$73$	17740.6	0.389637	0.194819	+	0.980839i	$0.437588\pi$
$74$	−55971.8	−1.18820
$75$	25358.3	0.520555
$76$	12138.2	0.241058
$77$	43096.8	0.828359
$78$	−13416.0	−0.249681
$79$	−57063.7	−1.02871	−0.514354	−	0.857578i	$-0.671968\pi$
$79$	−57063.7	−1.02871	−0.514354	+	0.857578i	$0.671968\pi$
$80$	15284.6	0.267012
$81$	6561.00	0.111111
$82$	−4367.74	−0.0717335
$83$	17500.9	0.278846	0.139423	−	0.990233i	$-0.455475\pi$
$83$	17500.9	0.278846	0.139423	+	0.990233i	$0.455475\pi$
$84$	6536.42	0.101075
$85$	23625.9	0.354684
$86$	47425.9	0.691464
$87$	25002.0	0.354141
$88$	−47629.8	−0.655650
$89$	−53616.7	−0.717505	−0.358753	−	0.933433i	$-0.616798\pi$
$89$	−53616.7	−0.717505	−0.358753	+	0.933433i	$0.616798\pi$
$90$	−7487.37	−0.0974368
$91$	48833.3	0.618177
$92$	−2912.89	−0.0358802
$93$	36981.9	0.443386
$94$	−22916.6	−0.267504
$95$	50610.2	0.575346
$96$	−13608.8	−0.150710
$97$	−115705.	−1.24859	−0.624297	−	0.781187i	$-0.714615\pi$
$97$	−115705.	−1.24859	−0.624297	+	0.781187i	$0.714615\pi$
$98$	68653.0	0.722094
$99$	20212.1	0.207264
$100$	11848.3	0.118483
$101$	28439.9	0.277412	0.138706	−	0.990334i	$-0.455706\pi$
$101$	28439.9	0.277412	0.138706	+	0.990334i	$0.455706\pi$
$102$	63936.9	0.608487
$103$	−25331.5	−0.235271	−0.117636	−	0.993057i	$-0.537531\pi$
$103$	−25331.5	−0.235271	−0.117636	+	0.993057i	$0.537531\pi$
$104$	−53969.6	−0.489290
$105$	27253.6	0.241240
$106$	−9489.56	−0.0820316
$107$	10368.8	0.0875529	0.0437764	−	0.999041i	$-0.486061\pi$
$107$	10368.8	0.0875529	0.0437764	+	0.999041i	$0.486061\pi$
$108$	3065.53	0.0252899
$109$	−37934.4	−0.305820	−0.152910	−	0.988240i	$-0.548865\pi$
$109$	−37934.4	−0.305820	−0.152910	+	0.988240i	$0.548865\pi$
$110$	−23065.9	−0.181756
$111$	95549.7	0.736075
$112$	−150561.	−1.13414
$113$	2314.90	0.0170544	0.00852719	−	0.999964i	$-0.497286\pi$
$113$	2314.90	0.0170544	0.00852719	+	0.999964i	$0.497286\pi$
$114$	136962.	0.987050
$115$	−12145.3	−0.0856374
$116$	11681.8	0.0806057
$117$	22902.5	0.154674
$118$	−18352.1	−0.121334
$119$	−232727.	−1.50653
$120$	−30120.1	−0.190943
$121$	−98784.8	−0.613376
$122$	−147745.	−0.898694
$123$	7456.19	0.0444380
$124$	17279.3	0.100919
$125$	104193.	0.596434
$126$	73754.2	0.413866
$127$	123281.	0.678245	0.339122	−	0.940742i	$-0.389870\pi$
$127$	123281.	0.678245	0.339122	+	0.940742i	$0.389870\pi$
$128$	140712.	0.759113
$129$	−80961.0	−0.428353
$130$	−26136.1	−0.135638
$131$	−114697.	−0.583947	−0.291973	−	0.956426i	$-0.594312\pi$
$131$	−114697.	−0.583947	−0.291973	+	0.956426i	$0.594312\pi$
$132$	9443.81	0.0471750
$133$	−498535.	−2.44380
$134$	163209.	0.785203
$135$	12781.7	0.0603608
$136$	257205.	1.19243
$137$	−26527.5	−0.120752	−0.0603760	−	0.998176i	$-0.519230\pi$
$137$	−26527.5	−0.120752	−0.0603760	+	0.998176i	$0.519230\pi$
$138$	−32867.8	−0.146917
$139$	178087.	0.781799	0.390900	−	0.920433i	$-0.372164\pi$
$139$	178087.	0.781799	0.390900	+	0.920433i	$0.372164\pi$
$140$	12733.8	0.0549085
$141$	39121.0	0.165715
$142$	20800.7	0.0865679
$143$	70554.2	0.288525
$144$	−70612.0	−0.283774
$145$	48707.3	0.192386
$146$	93529.8	0.363135
$147$	−117198.	−0.447328
$148$	44644.2	0.167537
$149$	387487.	1.42985	0.714926	−	0.699200i	$-0.246460\pi$
$149$	387487.	1.42985	0.714926	+	0.699200i	$0.246460\pi$
$150$	133691.	0.485148
$151$	428825.	1.53052	0.765258	−	0.643724i	$-0.222611\pi$
$151$	428825.	1.53052	0.765258	+	0.643724i	$0.222611\pi$
$152$	550971.	1.93428
$153$	−109147.	−0.376950
$154$	227210.	0.772015
$155$	72045.7	0.240868
$156$	10700.8	0.0352052
$157$	255345.	0.826759	0.413380	−	0.910559i	$-0.364348\pi$
$157$	255345.	0.826759	0.413380	+	0.910559i	$0.364348\pi$
$158$	−300845.	−0.958737
$159$	16199.7	0.0508175
$160$	−26511.8	−0.0818728
$161$	119637.	0.363748
$162$	34590.1	0.103554
$163$	−344110.	−1.01444	−0.507222	−	0.861816i	$-0.669328\pi$
$163$	−344110.	−1.01444	−0.507222	+	0.861816i	$0.669328\pi$
$164$	3483.80	0.0101145
$165$	39375.9	0.112595
$166$	92266.1	0.259880
$167$	489467.	1.35810	0.679051	−	0.734091i	$-0.262391\pi$
$167$	489467.	1.35810	0.679051	+	0.734091i	$0.262391\pi$
$168$	296698.	0.811037
$169$	−291347.	−0.784683
$170$	124558.	0.330559
$171$	−233809.	−0.611464
$172$	−37827.9	−0.0974969
$173$	154041.	0.391310	0.195655	−	0.980673i	$-0.437317\pi$
$173$	154041.	0.391310	0.195655	+	0.980673i	$0.437317\pi$
$174$	131813.	0.330053
$175$	−486627.	−1.20116
$176$	−217530.	−0.529344
$177$	31329.0	0.0751646
$178$	−282672.	−0.668702
$179$	−309320.	−0.721565	−0.360782	−	0.932650i	$-0.617490\pi$
$179$	−309320.	−0.721565	−0.360782	+	0.932650i	$0.617490\pi$
$180$	5972.08	0.0137386
$181$	−120297.	−0.272935	−0.136467	−	0.990645i	$-0.543575\pi$
$181$	−120297.	−0.272935	−0.136467	+	0.990645i	$0.543575\pi$
$182$	257453.	0.576130
$183$	252215.	0.556729
$184$	−132220.	−0.287908
$185$	186144.	0.399870
$186$	194972.	0.413227
$187$	−336243.	−0.703152
$188$	18278.7	0.0377182
$189$	−125906.	−0.256385
$190$	266821.	0.536212
$191$	868356.	1.72232	0.861161	−	0.508332i	$-0.169738\pi$
$191$	868356.	1.72232	0.861161	+	0.508332i	$0.169738\pi$
$192$	−322812.	−0.631970
$193$	−865143.	−1.67184	−0.835920	−	0.548851i	$-0.815065\pi$
$193$	−865143.	−1.67184	−0.835920	+	0.548851i	$0.815065\pi$
$194$	−610004.	−1.16367
$195$	44617.1	0.0840262
$196$	−54759.0	−0.101816
$197$	1.03866e6	1.90682	0.953410	−	0.301677i	$-0.0975464\pi$
$197$	1.03866e6	1.90682	0.953410	+	0.301677i	$0.0975464\pi$
$198$	106560.	0.193166
$199$	−518573.	−0.928277	−0.464138	−	0.885763i	$-0.653636\pi$
$199$	−518573.	−0.928277	−0.464138	+	0.885763i	$0.653636\pi$
$200$	537811.	0.950724
$201$	−278615.	−0.486423
$202$	149938.	0.258542
$203$	−479790.	−0.817168
$204$	−50997.4	−0.0857971
$205$	14525.7	0.0241408
$206$	−133550.	−0.219268
$207$	56108.8	0.0910134
$208$	−246485.	−0.395032
$209$	−720282.	−1.14061
$210$	143683.	0.224832
$211$	268913.	0.415820	0.207910	−	0.978148i	$-0.433334\pi$
$211$	268913.	0.415820	0.207910	+	0.978148i	$0.433334\pi$
$212$	7569.06	0.0115665
$213$	−35508.9	−0.0536276
$214$	54665.4	0.0815977
$215$	−157723.	−0.232701
$216$	139149.	0.202930
$217$	−709685.	−1.02310
$218$	−199993.	−0.285019
$219$	−159665.	−0.224957
$220$	18397.8	0.0256277
$221$	−380999.	−0.524739
$222$	503746.	0.686008
$223$	−1.29991e6	−1.75046	−0.875231	−	0.483705i	$-0.839291\pi$
$223$	−1.29991e6	−1.75046	−0.875231	+	0.483705i	$0.839291\pi$
$224$	261154.	0.347758
$225$	−228224.	−0.300543
$226$	12204.3	0.0158944
$227$	648463.	0.835257	0.417629	−	0.908618i	$-0.362861\pi$
$227$	648463.	0.835257	0.417629	+	0.908618i	$0.362861\pi$
$228$	−109244.	−0.139175
$229$	−1.20958e6	−1.52421	−0.762106	−	0.647452i	$-0.775835\pi$
$229$	−1.20958e6	−1.52421	−0.762106	+	0.647452i	$0.775835\pi$
$230$	−64031.0	−0.0798125
$231$	−387871.	−0.478253
$232$	530255.	0.646792
$233$	766201.	0.924598	0.462299	−	0.886724i	$-0.347025\pi$
$233$	766201.	0.924598	0.462299	+	0.886724i	$0.347025\pi$
$234$	120744.	0.144153
$235$	76213.0	0.0900242
$236$	14638.0	0.0171081
$237$	513573.	0.593925
$238$	−1.22695e6	−1.40406
$239$	−764937.	−0.866226	−0.433113	−	0.901340i	$-0.642585\pi$
$239$	−764937.	−0.866226	−0.433113	+	0.901340i	$0.642585\pi$
$240$	−137562.	−0.154159
$241$	982809.	1.09000	0.545000	−	0.838436i	$-0.316530\pi$
$241$	982809.	1.09000	0.545000	+	0.838436i	$0.316530\pi$
$242$	−520802.	−0.571655
$243$	−59049.0	−0.0641500
$244$	117844.	0.126717
$245$	−228317.	−0.243010
$246$	39309.7	0.0414154
$247$	−816156.	−0.851199
$248$	784330.	0.809785
$249$	−157508.	−0.160992
$250$	549313.	0.555865
$251$	−1.96682e6	−1.97052	−0.985258	−	0.171077i	$-0.945275\pi$
$251$	−1.96682e6	−1.97052	−0.985258	+	0.171077i	$0.945275\pi$
$252$	−58827.8	−0.0583554
$253$	172851.	0.169774
$254$	649947.	0.632112
$255$	−212633.	−0.204777
$256$	−405929.	−0.387124
$257$	80164.1	0.0757089	0.0378545	−	0.999283i	$-0.487948\pi$
$257$	80164.1	0.0757089	0.0378545	+	0.999283i	$0.487948\pi$
$258$	−426833.	−0.399217
$259$	−1.83361e6	−1.69847
$260$	20846.7	0.0191251
$261$	−225018.	−0.204464
$262$	−604692.	−0.544228
$263$	−1.67260e6	−1.49108	−0.745542	−	0.666459i	$-0.767809\pi$
$263$	−1.67260e6	−1.49108	−0.745542	+	0.666459i	$0.767809\pi$
$264$	428668.	0.378539
$265$	31559.1	0.0276065
$266$	−2.62832e6	−2.27758
$267$	482550.	0.414252
$268$	−130179.	−0.110714
$269$	218494.	0.184102	0.0920512	−	0.995754i	$-0.470658\pi$
$269$	218494.	0.184102	0.0920512	+	0.995754i	$0.470658\pi$
$270$	67386.3	0.0562551
$271$	1.22825e6	1.01593	0.507966	−	0.861377i	$-0.330397\pi$
$271$	1.22825e6	1.01593	0.507966	+	0.861377i	$0.330397\pi$
$272$	1.17468e6	0.962716
$273$	−439500.	−0.356905
$274$	−139855.	−0.112539
$275$	−703078.	−0.560624
$276$	26216.1	0.0207155
$277$	1.66772e6	1.30594	0.652969	−	0.757384i	$-0.273523\pi$
$277$	1.66772e6	1.30594	0.652969	+	0.757384i	$0.273523\pi$
$278$	938890.	0.728623
$279$	−332837.	−0.255989
$280$	578007.	0.440594
$281$	−2.37484e6	−1.79419	−0.897095	−	0.441837i	$-0.854327\pi$
$281$	−2.37484e6	−1.79419	−0.897095	+	0.441837i	$0.854327\pi$
$282$	206249.	0.154443
$283$	573803.	0.425889	0.212945	−	0.977064i	$-0.431695\pi$
$283$	573803.	0.425889	0.212945	+	0.977064i	$0.431695\pi$
$284$	−16591.0	−0.0122061
$285$	−455492.	−0.332176
$286$	371968.	0.268900
$287$	−143085.	−0.102539
$288$	122479.	0.0870125
$289$	395884.	0.278820
$290$	256789.	0.179300
$291$	1.04134e6	0.720876
$292$	−74601.3	−0.0512023
$293$	−196310.	−0.133590	−0.0667949	−	0.997767i	$-0.521277\pi$
$293$	−196310.	−0.133590	−0.0667949	+	0.997767i	$0.521277\pi$
$294$	−617877.	−0.416901
$295$	61033.1	0.0408329
$296$	2.02647e6	1.34434
$297$	−181909.	−0.119664
$298$	2.04286e6	1.33260
$299$	195859.	0.126697
$300$	−106635.	−0.0684061
$301$	1.55365e6	0.988408
$302$	2.26080e6	1.42641
$303$	−255959.	−0.160164
$304$	2.51634e6	1.56166
$305$	491350.	0.302441
$306$	−575433.	−0.351310
$307$	−2.15114e6	−1.30263	−0.651317	−	0.758806i	$-0.725783\pi$
$307$	−2.15114e6	−1.30263	−0.651317	+	0.758806i	$0.725783\pi$
$308$	−181227.	−0.108855
$309$	227984.	0.135834
$310$	379831.	0.224485
$311$	2.39479e6	1.40400	0.701998	−	0.712179i	$-0.252291\pi$
$311$	2.39479e6	1.40400	0.701998	+	0.712179i	$0.252291\pi$
$312$	485727.	0.282492
$313$	1.14808e6	0.662388	0.331194	−	0.943563i	$-0.392549\pi$
$313$	1.14808e6	0.662388	0.331194	+	0.943563i	$0.392549\pi$
$314$	1.34620e6	0.770524
$315$	−245282.	−0.139280
$316$	239960.	0.135183
$317$	1.27600e6	0.713188	0.356594	−	0.934259i	$-0.383938\pi$
$317$	1.27600e6	0.713188	0.356594	+	0.934259i	$0.383938\pi$
$318$	85406.0	0.0473610
$319$	−693200.	−0.381401
$320$	−628881.	−0.343316
$321$	−93319.5	−0.0505487
$322$	630736.	0.339007
$323$	3.88958e6	2.07442
$324$	−27589.8	−0.0146011
$325$	−796662.	−0.418375
$326$	−1.81418e6	−0.945443
$327$	341409.	0.176565
$328$	158135.	0.0811600
$329$	−750734.	−0.382381
$330$	207593.	0.104937
$331$	−2.54695e6	−1.27777	−0.638883	−	0.769304i	$-0.720603\pi$
$331$	−2.54695e6	−1.27777	−0.638883	+	0.769304i	$0.720603\pi$
$332$	−73593.3	−0.0366432
$333$	−859947.	−0.424973
$334$	2.58051e6	1.26573
$335$	−542779.	−0.264248
$336$	1.35505e6	0.654797
$337$	−569867.	−0.273337	−0.136669	−	0.990617i	$-0.543640\pi$
$337$	−569867.	−0.273337	−0.136669	+	0.990617i	$0.543640\pi$
$338$	−1.53601e6	−0.731311
$339$	−20834.1	−0.00984635
$340$	−99349.9	−0.0466090
$341$	−1.02535e6	−0.477515
$342$	−1.23266e6	−0.569873
$343$	−653714.	−0.300022
$344$	−1.71706e6	−0.782329
$345$	109308.	0.0494428
$346$	812117.	0.364694
$347$	49490.3	0.0220646	0.0110323	−	0.999939i	$-0.496488\pi$
$347$	49490.3	0.0220646	0.0110323	+	0.999939i	$0.496488\pi$
$348$	−105136.	−0.0465377
$349$	291186.	0.127970	0.0639849	−	0.997951i	$-0.479619\pi$
$349$	291186.	0.127970	0.0639849	+	0.997951i	$0.479619\pi$
$350$	−2.56554e6	−1.11946
$351$	−206122.	−0.0893011
$352$	377315.	0.162311
$353$	2.92278e6	1.24842	0.624208	−	0.781258i	$-0.285422\pi$
$353$	2.92278e6	1.24842	0.624208	+	0.781258i	$0.285422\pi$
$354$	165169.	0.0700520
$355$	−69176.2	−0.0291331
$356$	225465.	0.0942874
$357$	2.09454e6	0.869797
$358$	−1.63076e6	−0.672485
$359$	−3.89236e6	−1.59396	−0.796978	−	0.604008i	$-0.793570\pi$
$359$	−3.89236e6	−1.59396	−0.796978	+	0.604008i	$0.793570\pi$
$360$	271081.	0.110241
$361$	5.85596e6	2.36500
$362$	−634217.	−0.254370
$363$	889064.	0.354133
$364$	−205350.	−0.0812346
$365$	−311049.	−0.122207
$366$	1.32970e6	0.518861
$367$	2.27009e6	0.879787	0.439893	−	0.898050i	$-0.355016\pi$
$367$	2.27009e6	0.879787	0.439893	+	0.898050i	$0.355016\pi$
$368$	−603865.	−0.232445
$369$	−67105.7	−0.0256563
$370$	981366.	0.372672
$371$	−310873.	−0.117259
$372$	−155513.	−0.0582653
$373$	2.65018e6	0.986287	0.493143	−	0.869948i	$-0.335848\pi$
$373$	2.65018e6	0.986287	0.493143	+	0.869948i	$0.335848\pi$
$374$	−1.77270e6	−0.655325
$375$	−937734.	−0.344351
$376$	829697.	0.302656
$377$	−785470.	−0.284627
$378$	−663788.	−0.238946
$379$	−870790.	−0.311398	−0.155699	−	0.987805i	$-0.549763\pi$
$379$	−870790.	−0.311398	−0.155699	+	0.987805i	$0.549763\pi$
$380$	−212822.	−0.0756062
$381$	−1.10953e6	−0.391585
$382$	4.57805e6	1.60517
$383$	2.50857e6	0.873834	0.436917	−	0.899502i	$-0.356070\pi$
$383$	2.50857e6	0.873834	0.436917	+	0.899502i	$0.356070\pi$
$384$	−1.26641e6	−0.438274
$385$	−755626.	−0.259810
$386$	−4.56111e6	−1.55812
$387$	728649.	0.247310
$388$	486552.	0.164078
$389$	2.35346e6	0.788555	0.394278	−	0.918991i	$-0.370995\pi$
$389$	2.35346e6	0.788555	0.394278	+	0.918991i	$0.370995\pi$
$390$	235225.	0.0783109
$391$	−933412.	−0.308767
$392$	−2.48559e6	−0.816985
$393$	1.03227e6	0.337142
$394$	5.47593e6	1.77712
$395$	1.00051e6	0.322648
$396$	−84994.3	−0.0272365
$397$	3.69134e6	1.17546	0.587730	−	0.809057i	$-0.300022\pi$
$397$	3.69134e6	1.17546	0.587730	+	0.809057i	$0.300022\pi$
$398$	−2.73396e6	−0.865137
$399$	4.48681e6	1.41093
$400$	2.45624e6	0.767575
$401$	4.26272e6	1.32381	0.661905	−	0.749588i	$-0.269748\pi$
$401$	4.26272e6	1.32381	0.661905	+	0.749588i	$0.269748\pi$
$402$	−1.46888e6	−0.453337
$403$	−1.16183e6	−0.356353
$404$	−119593.	−0.0364547
$405$	−115035.	−0.0348493
$406$	−2.52949e6	−0.761586
$407$	−2.64919e6	−0.792733
$408$	−2.31484e6	−0.688449
$409$	2.90876e6	0.859806	0.429903	−	0.902875i	$-0.358548\pi$
$409$	2.90876e6	0.859806	0.429903	+	0.902875i	$0.358548\pi$
$410$	76580.6	0.0224988
$411$	238747.	0.0697162
$412$	106522.	0.0309170
$413$	−601206.	−0.173440
$414$	295811.	0.0848228
$415$	−306847.	−0.0874584
$416$	427538.	0.121127
$417$	−1.60278e6	−0.451372
$418$	−3.79739e6	−1.06303
$419$	−2.77871e6	−0.773230	−0.386615	−	0.922241i	$-0.626356\pi$
$419$	−2.77871e6	−0.773230	−0.386615	+	0.922241i	$0.626356\pi$
$420$	−114605.	−0.0317014
$421$	−2.25028e6	−0.618774	−0.309387	−	0.950936i	$-0.600124\pi$
$421$	−2.25028e6	−0.618774	−0.309387	+	0.950936i	$0.600124\pi$
$422$	1.41773e6	0.387536
$423$	−352089.	−0.0956756
$424$	343571.	0.0928114
$425$	3.79668e6	1.01960
$426$	−187206.	−0.0499800
$427$	−4.84003e6	−1.28463
$428$	−43602.2	−0.0115053
$429$	−634988.	−0.166580
$430$	−831529.	−0.216873
$431$	1.51833e6	0.393708	0.196854	−	0.980433i	$-0.436928\pi$
$431$	1.51833e6	0.393708	0.196854	+	0.980433i	$0.436928\pi$
$432$	635508.	0.163837
$433$	−1.99352e6	−0.510975	−0.255488	−	0.966812i	$-0.582236\pi$
$433$	−1.99352e6	−0.510975	−0.255488	+	0.966812i	$0.582236\pi$
$434$	−3.74152e6	−0.953507
$435$	−438366.	−0.111074
$436$	159519.	0.0401879
$437$	−1.99951e6	−0.500863
$438$	−841768.	−0.209656
$439$	−5.57781e6	−1.38134	−0.690672	−	0.723168i	$-0.742685\pi$
$439$	−5.57781e6	−1.38134	−0.690672	+	0.723168i	$0.742685\pi$
$440$	835103.	0.205640
$441$	1.05478e6	0.258265
$442$	−2.00866e6	−0.489047
$443$	6.89006e6	1.66807	0.834034	−	0.551713i	$-0.186026\pi$
$443$	6.89006e6	1.66807	0.834034	+	0.551713i	$0.186026\pi$
$444$	−401798.	−0.0967276
$445$	940074.	0.225041
$446$	−6.85326e6	−1.63140
$447$	−3.48738e6	−0.825525
$448$	6.19478e6	1.45825
$449$	−6.32514e6	−1.48066	−0.740328	−	0.672246i	$-0.765330\pi$
$449$	−6.32514e6	−1.48066	−0.740328	+	0.672246i	$0.765330\pi$
$450$	−1.20322e6	−0.280100
$451$	−206729.	−0.0478585
$452$	−9734.43	−0.00224112
$453$	−3.85943e6	−0.883644
$454$	3.41875e6	0.778445
$455$	−856205.	−0.193887
$456$	−4.95874e6	−1.11676
$457$	−3.82920e6	−0.857664	−0.428832	−	0.903384i	$-0.641075\pi$
$457$	−3.82920e6	−0.857664	−0.428832	+	0.903384i	$0.641075\pi$
$458$	−6.37700e6	−1.42054
$459$	982323.	0.217632
$460$	51072.4	0.0112536
$461$	1.78400e6	0.390969	0.195484	−	0.980707i	$-0.437372\pi$
$461$	1.78400e6	0.390969	0.195484	+	0.980707i	$0.437372\pi$
$462$	−2.04489e6	−0.445723
$463$	−5.66499e6	−1.22814	−0.614068	−	0.789253i	$-0.710468\pi$
$463$	−5.66499e6	−1.22814	−0.614068	+	0.789253i	$0.710468\pi$
$464$	2.42173e6	0.522193
$465$	−648412.	−0.139065
$466$	4.03948e6	0.861709
$467$	−5.63789e6	−1.19626	−0.598128	−	0.801400i	$-0.704089\pi$
$467$	−5.63789e6	−1.19626	−0.598128	+	0.801400i	$0.704089\pi$
$468$	−96307.6	−0.0203257
$469$	5.34663e6	1.12240
$470$	401801.	0.0839009
$471$	−2.29811e6	−0.477330
$472$	664441.	0.137278
$473$	2.24470e6	0.461324
$474$	2.70760e6	0.553527
$475$	8.13305e6	1.65394
$476$	978644.	0.197974
$477$	−145797.	−0.0293395
$478$	−4.03281e6	−0.807306
$479$	−548448.	−0.109219	−0.0546094	−	0.998508i	$-0.517391\pi$
$479$	−548448.	−0.109219	−0.0546094	+	0.998508i	$0.517391\pi$
$480$	238606.	0.0472693
$481$	−3.00182e6	−0.591591
$482$	5.18145e6	1.01586
$483$	−1.07673e6	−0.210010
$484$	415402.	0.0806038
$485$	2.02867e6	0.391614
$486$	−311311.	−0.0597867
$487$	3.97227e6	0.758956	0.379478	−	0.925201i	$-0.376104\pi$
$487$	3.97227e6	0.758956	0.379478	+	0.925201i	$0.376104\pi$
$488$	5.34911e6	1.01679
$489$	3.09699e6	0.585689
$490$	−1.20371e6	−0.226480
$491$	1.01781e7	1.90530	0.952648	−	0.304077i	$-0.0983480\pi$
$491$	1.01781e7	1.90530	0.952648	+	0.304077i	$0.0983480\pi$
$492$	−31354.2	−0.00583960
$493$	3.74334e6	0.693652
$494$	−4.30285e6	−0.793302
$495$	−354383.	−0.0650069
$496$	3.58212e6	0.653786
$497$	681419.	0.123744
$498$	−830395.	−0.150042
$499$	1.92114e6	0.345389	0.172694	−	0.984975i	$-0.444753\pi$
$499$	1.92114e6	0.345389	0.172694	+	0.984975i	$0.444753\pi$
$500$	−438143.	−0.0783774
$501$	−4.40521e6	−0.784101
$502$	−1.03692e7	−1.83648
$503$	−7.27930e6	−1.28283	−0.641416	−	0.767193i	$-0.721653\pi$
$503$	−7.27930e6	−1.28283	−0.641416	+	0.767193i	$0.721653\pi$
$504$	−2.67028e6	−0.468253
$505$	−498643.	−0.0870084
$506$	911286.	0.158226
$507$	2.62213e6	0.453037
$508$	−518411.	−0.0891281
$509$	4.24954e6	0.727021	0.363511	−	0.931590i	$-0.381578\pi$
$509$	4.24954e6	0.727021	0.363511	+	0.931590i	$0.381578\pi$
$510$	−1.12102e6	−0.190848
$511$	3.06399e6	0.519080
$512$	−6.64288e6	−1.11991
$513$	2.10428e6	0.353029
$514$	422632.	0.0705593
$515$	444144.	0.0737913
$516$	340451.	0.0562898
$517$	−1.08466e6	−0.178471
$518$	−9.66693e6	−1.58294
$519$	−1.38637e6	−0.225923
$520$	946262.	0.153463
$521$	4.44795e6	0.717903	0.358951	−	0.933356i	$-0.383134\pi$
$521$	4.44795e6	0.717903	0.358951	+	0.933356i	$0.383134\pi$
$522$	−1.18631e6	−0.190556
$523$	−8.10718e6	−1.29603	−0.648016	−	0.761627i	$-0.724401\pi$
$523$	−8.10718e6	−1.29603	−0.648016	+	0.761627i	$0.724401\pi$
$524$	482314.	0.0767365
$525$	4.37964e6	0.693491
$526$	−8.81808e6	−1.38966
$527$	5.53699e6	0.868454
$528$	1.95777e6	0.305617
$529$	−5.95651e6	−0.925449
$530$	166383.	0.0257287
$531$	−281961.	−0.0433963
$532$	2.09640e6	0.321140
$533$	−234246.	−0.0357152
$534$	2.54405e6	0.386075
$535$	−181799.	−0.0274604
$536$	−5.90900e6	−0.888386
$537$	2.78388e6	0.416596
$538$	1.15192e6	0.171580
$539$	3.24940e6	0.481760
$540$	−53748.7	−0.00793201
$541$	−2.00354e6	−0.294310	−0.147155	−	0.989113i	$-0.547012\pi$
$541$	−2.00354e6	−0.294310	−0.147155	+	0.989113i	$0.547012\pi$
$542$	6.47546e6	0.946830
$543$	1.08268e6	0.157579
$544$	−2.03753e6	−0.295194
$545$	665111.	0.0959187
$546$	−2.31708e6	−0.332629
$547$	−1.34714e6	−0.192506	−0.0962529	−	0.995357i	$-0.530686\pi$
$547$	−1.34714e6	−0.192506	−0.0962529	+	0.995357i	$0.530686\pi$
$548$	111551.	0.0158680
$549$	−2.26994e6	−0.321428
$550$	−3.70668e6	−0.522491
$551$	8.01878e6	1.12520
$552$	1.18998e6	0.166224
$553$	−9.85551e6	−1.37046
$554$	8.79234e6	1.21711
$555$	−1.67529e6	−0.230865
$556$	−748878.	−0.102736
$557$	3.66674e6	0.500774	0.250387	−	0.968146i	$-0.419442\pi$
$557$	3.66674e6	0.500774	0.250387	+	0.968146i	$0.419442\pi$
$558$	−1.75474e6	−0.238577
$559$	2.54349e6	0.344271
$560$	2.63982e6	0.355717
$561$	3.02619e6	0.405965
$562$	−1.25204e7	−1.67215
$563$	−5.44490e6	−0.723967	−0.361983	−	0.932185i	$-0.617900\pi$
$563$	−5.44490e6	−0.723967	−0.361983	+	0.932185i	$0.617900\pi$
$564$	−164508.	−0.0217766
$565$	−40587.6	−0.00534900
$566$	3.02514e6	0.396921
$567$	1.13315e6	0.148024
$568$	−753091.	−0.0979438
$569$	−1.26085e7	−1.63261	−0.816304	−	0.577623i	$-0.803981\pi$
$569$	−1.26085e7	−1.63261	−0.816304	+	0.577623i	$0.803981\pi$
$570$	−2.40139e6	−0.309582
$571$	4.88397e6	0.626878	0.313439	−	0.949608i	$-0.398519\pi$
$571$	4.88397e6	0.626878	0.313439	+	0.949608i	$0.398519\pi$
$572$	−296689.	−0.0379150
$573$	−7.81521e6	−0.994383
$574$	−754355.	−0.0955644
$575$	−1.95175e6	−0.246181
$576$	2.90531e6	0.364868
$577$	1.67375e6	0.209291	0.104646	−	0.994510i	$-0.466629\pi$
$577$	1.67375e6	0.209291	0.104646	+	0.994510i	$0.466629\pi$
$578$	2.08714e6	0.259855
$579$	7.78629e6	0.965237
$580$	−204820.	−0.0252815
$581$	3.02259e6	0.371483
$582$	5.49004e6	0.671843
$583$	−449148.	−0.0547291
$584$	−3.38626e6	−0.410854
$585$	−401554.	−0.0485126
$586$	−1.03496e6	−0.124503
$587$	1.02763e7	1.23095	0.615477	−	0.788155i	$-0.288963\pi$
$587$	1.02763e7	1.23095	0.615477	+	0.788155i	$0.288963\pi$
$588$	492831.	0.0587834
$589$	1.18610e7	1.40875
$590$	321772.	0.0380556
$591$	−9.34798e6	−1.10090
$592$	9.25508e6	1.08537
$593$	−3.79932e6	−0.443679	−0.221839	−	0.975083i	$-0.571206\pi$
$593$	−3.79932e6	−0.443679	−0.221839	+	0.975083i	$0.571206\pi$
$594$	−959038.	−0.111524
$595$	4.08045e6	0.472515
$596$	−1.62943e6	−0.187897
$597$	4.66716e6	0.535941
$598$	1.03258e6	0.118079
$599$	8.22274e6	0.936375	0.468187	−	0.883629i	$-0.344907\pi$
$599$	8.22274e6	0.936375	0.468187	+	0.883629i	$0.344907\pi$
$600$	−4.84030e6	−0.548901
$601$	−1.05611e7	−1.19268	−0.596339	−	0.802733i	$-0.703378\pi$
$601$	−1.05611e7	−1.19268	−0.596339	+	0.802733i	$0.703378\pi$
$602$	8.19096e6	0.921178
$603$	2.50753e6	0.280836
$604$	−1.80326e6	−0.201125
$605$	1.73202e6	0.192382
$606$	−1.34944e6	−0.149270
$607$	4.34859e6	0.479045	0.239523	−	0.970891i	$-0.423009\pi$
$607$	4.34859e6	0.479045	0.239523	+	0.970891i	$0.423009\pi$
$608$	−4.36470e6	−0.478845
$609$	4.31811e6	0.471792
$610$	2.59044e6	0.281870
$611$	−1.22903e6	−0.133187
$612$	458977.	0.0495350
$613$	1.02071e7	1.09712	0.548558	−	0.836113i	$-0.315177\pi$
$613$	1.02071e7	1.09712	0.548558	+	0.836113i	$0.315177\pi$
$614$	−1.13410e7	−1.21403
$615$	−130731.	−0.0139377
$616$	−8.22617e6	−0.873466
$617$	1.49495e7	1.58093	0.790465	−	0.612507i	$-0.209839\pi$
$617$	1.49495e7	1.58093	0.790465	+	0.612507i	$0.209839\pi$
$618$	1.20195e6	0.126595
$619$	−1.32070e7	−1.38541	−0.692703	−	0.721223i	$-0.743580\pi$
$619$	−1.32070e7	−1.38541	−0.692703	+	0.721223i	$0.743580\pi$
$620$	−302961.	−0.0316525
$621$	−504980.	−0.0525466
$622$	1.26255e7	1.30850
$623$	−9.26018e6	−0.955871
$624$	2.21837e6	0.228072
$625$	6.97812e6	0.714560
$626$	6.05279e6	0.617333
$627$	6.48253e6	0.658531
$628$	−1.07376e6	−0.108644
$629$	1.43059e7	1.44174
$630$	−1.29315e6	−0.129807
$631$	1.29466e6	0.129444	0.0647220	−	0.997903i	$-0.479384\pi$
$631$	1.29466e6	0.129444	0.0647220	+	0.997903i	$0.479384\pi$
$632$	1.08921e7	1.08472
$633$	−2.42021e6	−0.240074
$634$	6.72721e6	0.664678
$635$	−2.16151e6	−0.212727
$636$	−68121.6	−0.00667793
$637$	3.68192e6	0.359522
$638$	−3.65461e6	−0.355459
$639$	319581.	0.0309619
$640$	−2.46714e6	−0.238091
$641$	−1.26928e7	−1.22015	−0.610076	−	0.792343i	$-0.708861\pi$
$641$	−1.26928e7	−1.22015	−0.610076	+	0.792343i	$0.708861\pi$
$642$	−491988.	−0.0471104
$643$	−1.44334e7	−1.37671	−0.688353	−	0.725375i	$-0.741666\pi$
$643$	−1.44334e7	−1.37671	−0.688353	+	0.725375i	$0.741666\pi$
$644$	−503088.	−0.0478002
$645$	1.41951e6	0.134350
$646$	2.05062e7	1.93332
$647$	−1.82857e7	−1.71731	−0.858657	−	0.512551i	$-0.828701\pi$
$647$	−1.82857e7	−1.71731	−0.858657	+	0.512551i	$0.828701\pi$
$648$	−1.25234e6	−0.117161
$649$	−868620.	−0.0809503
$650$	−4.20007e6	−0.389918
$651$	6.38717e6	0.590685
$652$	1.44702e6	0.133308
$653$	3.51962e6	0.323008	0.161504	−	0.986872i	$-0.448366\pi$
$653$	3.51962e6	0.323008	0.161504	+	0.986872i	$0.448366\pi$
$654$	1.79994e6	0.164556
$655$	2.01101e6	0.183151
$656$	722217.	0.0655252
$657$	1.43699e6	0.129879
$658$	−3.95794e6	−0.356372
$659$	1.63394e7	1.46562	0.732811	−	0.680432i	$-0.238208\pi$
$659$	1.63394e7	1.46562	0.732811	+	0.680432i	$0.238208\pi$
$660$	−165580.	−0.0147962
$661$	−1.96074e7	−1.74549	−0.872743	−	0.488179i	$-0.837661\pi$
$661$	−1.96074e7	−1.74549	−0.872743	+	0.488179i	$0.837661\pi$
$662$	−1.34278e7	−1.19085
$663$	3.42899e6	0.302958
$664$	−3.34051e6	−0.294030
$665$	8.74092e6	0.766484
$666$	−4.53372e6	−0.396067
$667$	−1.92433e6	−0.167480
$668$	−2.05827e6	−0.178468
$669$	1.16992e7	1.01063
$670$	−2.86158e6	−0.246274
$671$	−6.99287e6	−0.599583
$672$	−2.35039e6	−0.200778
$673$	1.03079e7	0.877268	0.438634	−	0.898666i	$-0.355462\pi$
$673$	1.03079e7	0.877268	0.438634	+	0.898666i	$0.355462\pi$
$674$	−3.00439e6	−0.254745
$675$	2.05402e6	0.173518
$676$	1.22515e6	0.103115
$677$	−5.71024e6	−0.478832	−0.239416	−	0.970917i	$-0.576956\pi$
$677$	−5.71024e6	−0.478832	−0.239416	+	0.970917i	$0.576956\pi$
$678$	−109839.	−0.00917662
$679$	−1.99834e7	−1.66339
$680$	−4.50963e6	−0.373998
$681$	−5.83616e6	−0.482236
$682$	−5.40574e6	−0.445035
$683$	1.66857e6	0.136865	0.0684325	−	0.997656i	$-0.478200\pi$
$683$	1.66857e6	0.136865	0.0684325	+	0.997656i	$0.478200\pi$
$684$	983195.	0.0803525
$685$	465112.	0.0378731
$686$	−3.44644e6	−0.279615
$687$	1.08862e7	0.880004
$688$	−7.84200e6	−0.631620
$689$	−508933.	−0.0408425
$690$	576279.	0.0460798
$691$	−8.48113e6	−0.675707	−0.337854	−	0.941199i	$-0.609701\pi$
$691$	−8.48113e6	−0.675707	−0.337854	+	0.941199i	$0.609701\pi$
$692$	−647761.	−0.0514221
$693$	3.49084e6	0.276120
$694$	260917.	0.0205638
$695$	−3.12244e6	−0.245207
$696$	−4.77229e6	−0.373426
$697$	1.11635e6	0.0870401
$698$	1.53516e6	0.119265
$699$	−6.89581e6	−0.533817
$700$	2.04633e6	0.157845
$701$	2.15565e7	1.65685	0.828426	−	0.560099i	$-0.189237\pi$
$701$	2.15565e7	1.65685	0.828426	+	0.560099i	$0.189237\pi$
$702$	−1.08669e6	−0.0832270
$703$	3.06452e7	2.33870
$704$	8.95020e6	0.680614
$705$	−685917.	−0.0519755
$706$	1.54092e7	1.16350
$707$	4.91187e6	0.369572
$708$	−131742.	−0.00987738
$709$	−1.62242e7	−1.21213	−0.606063	−	0.795417i	$-0.707252\pi$
$709$	−1.62242e7	−1.21213	−0.606063	+	0.795417i	$0.707252\pi$
$710$	−364703.	−0.0271515
$711$	−4.62216e6	−0.342903
$712$	1.02342e7	0.756576
$713$	−2.84638e6	−0.209686
$714$	1.10426e7	0.810635
$715$	−1.23704e6	−0.0904940
$716$	1.30073e6	0.0948208
$717$	6.88443e6	0.500116
$718$	−2.05208e7	−1.48554
$719$	−6.26793e6	−0.452170	−0.226085	−	0.974108i	$-0.572593\pi$
$719$	−6.26793e6	−0.452170	−0.226085	+	0.974108i	$0.572593\pi$
$720$	1.23806e6	0.0890039
$721$	−4.37503e6	−0.313432
$722$	3.08731e7	2.20413
$723$	−8.84528e6	−0.629312
$724$	505864.	0.0358664
$725$	7.82725e6	0.553050
$726$	4.68722e6	0.330045
$727$	−1.51303e7	−1.06172	−0.530862	−	0.847458i	$-0.678132\pi$
$727$	−1.51303e7	−1.06172	−0.530862	+	0.847458i	$0.678132\pi$
$728$	−9.32113e6	−0.651839
$729$	531441.	0.0370370
$730$	−1.63988e6	−0.113895
$731$	−1.21216e7	−0.839009
$732$	−1.06060e6	−0.0731598
$733$	−1.09692e7	−0.754073	−0.377037	−	0.926198i	$-0.623057\pi$
$733$	−1.09692e7	−0.754073	−0.377037	+	0.926198i	$0.623057\pi$
$734$	1.19681e7	0.819945
$735$	2.05485e6	0.140302
$736$	1.04743e6	0.0712738
$737$	7.72480e6	0.523864
$738$	−353787.	−0.0239112
$739$	8.31352e6	0.559982	0.279991	−	0.960003i	$-0.409669\pi$
$739$	8.31352e6	0.559982	0.279991	+	0.960003i	$0.409669\pi$
$740$	−782757.	−0.0525470
$741$	7.34541e6	0.491440
$742$	−1.63895e6	−0.109284
$743$	−2.57946e7	−1.71418	−0.857091	−	0.515165i	$-0.827731\pi$
$743$	−2.57946e7	−1.71418	−0.857091	+	0.515165i	$0.827731\pi$
$744$	−7.05897e6	−0.467530
$745$	−6.79389e6	−0.448464
$746$	1.39720e7	0.919201
$747$	1.41757e6	0.0929487
$748$	1.41394e6	0.0924012
$749$	1.79081e6	0.116639
$750$	−4.94381e6	−0.320929
$751$	2.42931e7	1.57175	0.785874	−	0.618387i	$-0.212214\pi$
$751$	2.42931e7	1.57175	0.785874	+	0.618387i	$0.212214\pi$
$752$	3.78931e6	0.244352
$753$	1.77014e7	1.13768
$754$	−4.14106e6	−0.265267
$755$	−7.51869e6	−0.480037
$756$	529450.	0.0336915
$757$	2.12215e7	1.34597	0.672987	−	0.739654i	$-0.265011\pi$
$757$	2.12215e7	1.34597	0.672987	+	0.739654i	$0.265011\pi$
$758$	−4.59088e6	−0.290217
$759$	−1.55566e6	−0.0980190
$760$	−9.66029e6	−0.606675
$761$	−2.57870e7	−1.61414	−0.807068	−	0.590459i	$-0.798947\pi$
$761$	−2.57870e7	−1.61414	−0.807068	+	0.590459i	$0.798947\pi$
$762$	−5.84952e6	−0.364950
$763$	−6.55167e6	−0.407418
$764$	−3.65154e6	−0.226330
$765$	1.91370e6	0.118228
$766$	1.32254e7	0.814397
$767$	−984240.	−0.0604105
$768$	3.65336e6	0.223506
$769$	−2.71632e7	−1.65640	−0.828200	−	0.560433i	$-0.810635\pi$
$769$	−2.71632e7	−1.65640	−0.828200	+	0.560433i	$0.810635\pi$
$770$	−3.98372e6	−0.242138
$771$	−721477.	−0.0437106
$772$	3.63803e6	0.219697
$773$	6.81267e6	0.410080	0.205040	−	0.978754i	$-0.434268\pi$
$773$	6.81267e6	0.410080	0.205040	+	0.978754i	$0.434268\pi$
$774$	3.84150e6	0.230488
$775$	1.15777e7	0.692420
$776$	2.20853e7	1.31658
$777$	1.65025e7	0.980609
$778$	1.24076e7	0.734919
$779$	2.39139e6	0.141191
$780$	−187620.	−0.0110419
$781$	984513.	0.0577555
$782$	−4.92103e6	−0.287766
$783$	2.02516e6	0.118047
$784$	−1.13519e7	−0.659599
$785$	−4.47703e6	−0.259308
$786$	5.44222e6	0.314210
$787$	−1.38930e7	−0.799575	−0.399788	−	0.916608i	$-0.630916\pi$
$787$	−1.38930e7	−0.799575	−0.399788	+	0.916608i	$0.630916\pi$
$788$	−4.36771e6	−0.250575
$789$	1.50534e7	0.860878
$790$	5.27477e6	0.300702
$791$	399808.	0.0227201
$792$	−3.85801e6	−0.218550
$793$	−7.92367e6	−0.447449
$794$	1.94611e7	1.09551
$795$	−284032.	−0.0159386
$796$	2.18066e6	0.121985
$797$	5.90905e6	0.329512	0.164756	−	0.986334i	$-0.447316\pi$
$797$	5.90905e6	0.329512	0.164756	+	0.986334i	$0.447316\pi$
$798$	2.36549e7	1.31496
$799$	5.85726e6	0.324584
$800$	−4.26045e6	−0.235359
$801$	−4.34295e6	−0.239168
$802$	2.24734e7	1.23377
$803$	4.42684e6	0.242273
$804$	1.17161e6	0.0639208
$805$	−2.09762e6	−0.114087
$806$	−6.12528e6	−0.332115
$807$	−1.96645e6	−0.106292
$808$	−5.42851e6	−0.292518
$809$	−1.34744e7	−0.723832	−0.361916	−	0.932211i	$-0.617877\pi$
$809$	−1.34744e7	−0.723832	−0.361916	+	0.932211i	$0.617877\pi$
$810$	−606477.	−0.0324789
$811$	1.21144e6	0.0646770	0.0323385	−	0.999477i	$-0.489705\pi$
$811$	1.21144e6	0.0646770	0.0323385	+	0.999477i	$0.489705\pi$
$812$	2.01758e6	0.107384
$813$	−1.10543e7	−0.586549
$814$	−1.39667e7	−0.738813
$815$	6.03335e6	0.318174
$816$	−1.05721e7	−0.555824
$817$	−2.59663e7	−1.36099
$818$	1.53353e7	0.801323
$819$	3.95550e6	0.206059
$820$	−61082.2	−0.00317234
$821$	1.88231e7	0.974615	0.487308	−	0.873230i	$-0.337979\pi$
$821$	1.88231e7	0.974615	0.487308	+	0.873230i	$0.337979\pi$
$822$	1.25870e6	0.0649743
$823$	−2.94279e7	−1.51446	−0.757232	−	0.653146i	$-0.773449\pi$
$823$	−2.94279e7	−1.51446	−0.757232	+	0.653146i	$0.773449\pi$
$824$	4.83520e6	0.248082
$825$	6.32770e6	0.323676
$826$	−3.16961e6	−0.161642
$827$	−2.79462e7	−1.42089	−0.710443	−	0.703755i	$-0.751505\pi$
$827$	−2.79462e7	−1.42089	−0.710443	+	0.703755i	$0.751505\pi$
$828$	−235944.	−0.0119601
$829$	2.14227e6	0.108265	0.0541324	−	0.998534i	$-0.482761\pi$
$829$	2.14227e6	0.108265	0.0541324	+	0.998534i	$0.482761\pi$
$830$	−1.61772e6	−0.0815096
$831$	−1.50095e7	−0.753984
$832$	1.01415e7	0.507920
$833$	−1.75470e7	−0.876176
$834$	−8.45001e6	−0.420671
$835$	−8.58194e6	−0.425960
$836$	3.02887e6	0.149887
$837$	2.99553e6	0.147795
$838$	−1.46496e7	−0.720636
$839$	−3.02878e7	−1.48547	−0.742733	−	0.669588i	$-0.766471\pi$
$839$	−3.02878e7	−1.48547	−0.742733	+	0.669588i	$0.766471\pi$
$840$	−5.20207e6	−0.254377
$841$	−1.27939e7	−0.623752
$842$	−1.18637e7	−0.576686
$843$	2.13736e7	1.03588
$844$	−1.13081e6	−0.0546429
$845$	5.10826e6	0.246111
$846$	−1.85624e6	−0.0891679
$847$	−1.70612e7	−0.817148
$848$	1.56912e6	0.0749320
$849$	−5.16422e6	−0.245887
$850$	2.00164e7	0.950253
$851$	−7.35416e6	−0.348104
$852$	149319.	0.00704721
$853$	−2.43537e7	−1.14602	−0.573011	−	0.819548i	$-0.694225\pi$
$853$	−2.43537e7	−1.14602	−0.573011	+	0.819548i	$0.694225\pi$
$854$	−2.55171e7	−1.19725
$855$	4.09943e6	0.191782
$856$	−1.97917e6	−0.0923204
$857$	8.50412e6	0.395528	0.197764	−	0.980250i	$-0.436632\pi$
$857$	8.50412e6	0.395528	0.197764	+	0.980250i	$0.436632\pi$
$858$	−3.34771e6	−0.155249
$859$	2.11370e7	0.977372	0.488686	−	0.872460i	$-0.337476\pi$
$859$	2.11370e7	0.977372	0.488686	+	0.872460i	$0.337476\pi$
$860$	663244.	0.0305793
$861$	1.28776e6	0.0592009
$862$	8.00478e6	0.366928
$863$	−2.26285e7	−1.03426	−0.517128	−	0.855908i	$-0.672999\pi$
$863$	−2.26285e7	−1.03426	−0.517128	+	0.855908i	$0.672999\pi$
$864$	−1.10231e6	−0.0502367
$865$	−2.70084e6	−0.122732
$866$	−1.05100e7	−0.476220
$867$	−3.56296e6	−0.160977
$868$	2.98431e6	0.134445
$869$	−1.42392e7	−0.639641
$870$	−2.31110e6	−0.103519
$871$	8.75303e6	0.390943
$872$	7.24077e6	0.322473
$873$	−9.37207e6	−0.416198
$874$	−1.05416e7	−0.466795
$875$	1.79952e7	0.794577
$876$	671411.	0.0295616
$877$	1.62481e7	0.713351	0.356675	−	0.934228i	$-0.383910\pi$
$877$	1.62481e7	0.713351	0.356675	+	0.934228i	$0.383910\pi$
$878$	−2.94067e7	−1.28739
$879$	1.76679e6	0.0771281
$880$	3.81400e6	0.166025
$881$	1.94120e7	0.842617	0.421308	−	0.906917i	$-0.361571\pi$
$881$	1.94120e7	0.842617	0.421308	+	0.906917i	$0.361571\pi$
$882$	5.56089e6	0.240698
$883$	−2.20769e7	−0.952875	−0.476437	−	0.879208i	$-0.658072\pi$
$883$	−2.20769e7	−0.952875	−0.476437	+	0.879208i	$0.658072\pi$
$884$	1.60215e6	0.0689560
$885$	−549298.	−0.0235749
$886$	3.63250e7	1.55461
$887$	−1.75467e7	−0.748834	−0.374417	−	0.927260i	$-0.622157\pi$
$887$	−1.75467e7	−0.748834	−0.374417	+	0.927260i	$0.622157\pi$
$888$	−1.82382e7	−0.776157
$889$	2.12919e7	0.903567
$890$	4.95615e6	0.209734
$891$	1.63718e6	0.0690879
$892$	5.46630e6	0.230028
$893$	1.25471e7	0.526520
$894$	−1.83858e7	−0.769374
$895$	5.42337e6	0.226314
$896$	2.43025e7	1.01130
$897$	−1.76273e6	−0.0731484
$898$	−3.33467e7	−1.37994
$899$	1.14151e7	0.471064
$900$	959712.	0.0394943
$901$	2.42544e6	0.0995356
$902$	−1.08989e6	−0.0446033
$903$	−1.39828e7	−0.570657
$904$	−441860.	−0.0179831
$905$	2.10920e6	0.0856044
$906$	−2.03472e7	−0.823540
$907$	−2.33262e7	−0.941514	−0.470757	−	0.882263i	$-0.656019\pi$
$907$	−2.33262e7	−0.941514	−0.470757	+	0.882263i	$0.656019\pi$
$908$	−2.72686e6	−0.109761
$909$	2.30363e6	0.0924705
$910$	−4.51399e6	−0.180699
$911$	−1.17853e7	−0.470483	−0.235242	−	0.971937i	$-0.575588\pi$
$911$	−1.17853e7	−0.470483	−0.235242	+	0.971937i	$0.575588\pi$
$912$	−2.26471e7	−0.901623
$913$	4.36703e6	0.173384
$914$	−2.01879e7	−0.799327
$915$	−4.42215e6	−0.174615
$916$	5.08643e6	0.200297
$917$	−1.98094e7	−0.777942
$918$	5.17889e6	0.202829
$919$	1.39182e7	0.543619	0.271810	−	0.962351i	$-0.412378\pi$
$919$	1.39182e7	0.543619	0.271810	+	0.962351i	$0.412378\pi$
$920$	2.31825e6	0.0903006
$921$	1.93602e7	0.752076
$922$	9.40539e6	0.364376
$923$	1.11556e6	0.0431011
$924$	1.63105e6	0.0628473
$925$	2.99133e7	1.14950
$926$	−2.98663e7	−1.14460
$927$	−2.05186e6	−0.0784237
$928$	−4.20059e6	−0.160118
$929$	−3.32567e7	−1.26427	−0.632136	−	0.774857i	$-0.717822\pi$
$929$	−3.32567e7	−1.26427	−0.632136	+	0.774857i	$0.717822\pi$
$930$	−3.41848e6	−0.129606
$931$	−3.75883e7	−1.42128
$932$	−3.22197e6	−0.121501
$933$	−2.15531e7	−0.810598
$934$	−2.97234e7	−1.11489
$935$	5.89542e6	0.220539
$936$	−4.37154e6	−0.163097
$937$	−1.26083e7	−0.469144	−0.234572	−	0.972099i	$-0.575369\pi$
$937$	−1.26083e7	−0.469144	−0.234572	+	0.972099i	$0.575369\pi$
$938$	2.81879e7	1.04606
$939$	−1.03327e7	−0.382430
$940$	−320485.	−0.0118301
$941$	2.76092e6	0.101644	0.0508218	−	0.998708i	$-0.483816\pi$
$941$	2.76092e6	0.101644	0.0508218	+	0.998708i	$0.483816\pi$
$942$	−1.21158e7	−0.444862
$943$	−573880.	−0.0210156
$944$	3.03457e6	0.110833
$945$	2.20754e6	0.0804135
$946$	1.18343e7	0.429946
$947$	2.29370e6	0.0831117	0.0415559	−	0.999136i	$-0.486769\pi$
$947$	2.29370e6	0.0831117	0.0415559	+	0.999136i	$0.486769\pi$
$948$	−2.15964e6	−0.0780477
$949$	5.01608e6	0.180800
$950$	4.28781e7	1.54144
$951$	−1.14840e7	−0.411759
$952$	4.44220e7	1.58857
$953$	−3.80168e6	−0.135595	−0.0677975	−	0.997699i	$-0.521597\pi$
$953$	−3.80168e6	−0.135595	−0.0677975	+	0.997699i	$0.521597\pi$
$954$	−768654.	−0.0273439
$955$	−1.52251e7	−0.540196
$956$	3.21665e6	0.113831
$957$	6.23880e6	0.220202
$958$	−2.89147e6	−0.101790
$959$	−4.58158e6	−0.160868
$960$	5.65993e6	0.198213
$961$	−1.17445e7	−0.410227
$962$	−1.58258e7	−0.551352
$963$	839875.	0.0291843
$964$	−4.13283e6	−0.143237
$965$	1.51687e7	0.524362
$966$	−5.67663e6	−0.195726
$967$	−1.18301e7	−0.406838	−0.203419	−	0.979092i	$-0.565205\pi$
$967$	−1.18301e7	−0.406838	−0.203419	+	0.979092i	$0.565205\pi$
$968$	1.88557e7	0.646777
$969$	−3.50063e7	−1.19767
$970$	1.06953e7	0.364977
$971$	−4.88523e7	−1.66279	−0.831394	−	0.555683i	$-0.812457\pi$
$971$	−4.88523e7	−1.66279	−0.831394	+	0.555683i	$0.812457\pi$
$972$	248308.	0.00842996
$973$	3.07575e7	1.04152
$974$	2.09421e7	0.707333
$975$	7.16996e6	0.241549
$976$	2.44300e7	0.820915
$977$	4.77067e7	1.59898	0.799489	−	0.600681i	$-0.205104\pi$
$977$	4.77067e7	1.59898	0.799489	+	0.600681i	$0.205104\pi$
$978$	1.63276e7	0.545852
$979$	−1.33791e7	−0.446138
$980$	960101.	0.0319339
$981$	−3.07268e6	−0.101940
$982$	5.36597e7	1.77570
$983$	4.35421e7	1.43723	0.718613	−	0.695410i	$-0.244777\pi$
$983$	4.35421e7	1.43723	0.718613	+	0.695410i	$0.244777\pi$
$984$	−1.42321e6	−0.0468578
$985$	−1.82111e7	−0.598062
$986$	1.97352e7	0.646471
$987$	6.75661e6	0.220768
$988$	3.43204e6	0.111856
$989$	6.23131e6	0.202576
$990$	−1.86834e6	−0.0605853
$991$	1.39948e7	0.452672	0.226336	−	0.974049i	$-0.427325\pi$
$991$	1.39948e7	0.452672	0.226336	+	0.974049i	$0.427325\pi$
$992$	−6.21333e6	−0.200468
$993$	2.29226e7	0.737718
$994$	3.59250e6	0.115327
$995$	9.09226e6	0.291148
$996$	662340.	0.0211560
$997$	1.81460e7	0.578152	0.289076	−	0.957306i	$-0.406652\pi$
$997$	1.81460e7	0.578152	0.289076	+	0.957306i	$0.406652\pi$
$998$	1.01284e7	0.321896
$999$	7.73953e6	0.245358

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.9	✓	12	1.1	even	1	trivial
531.6.a.d.1.4		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)

\(f(q)\)	\(=\)	\(q+5.27208 q^{2} -9.00000 q^{3} -4.20512 q^{4} -17.5332 q^{5} -47.4488 q^{6} +172.711 q^{7} -190.876 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+5.27208 q^{2} -9.00000 q^{3} -4.20512 q^{4} -17.5332 q^{5} -47.4488 q^{6} +172.711 q^{7} -190.876 q^{8} +81.0000 q^{9} -92.4366 q^{10} +249.532 q^{11} +37.8461 q^{12} +282.746 q^{13} +910.545 q^{14} +157.799 q^{15} -871.753 q^{16} -1347.49 q^{17} +427.039 q^{18} -2886.53 q^{19} +73.7293 q^{20} -1554.40 q^{21} +1315.55 q^{22} +692.702 q^{23} +1717.89 q^{24} -2817.59 q^{25} +1490.66 q^{26} -729.000 q^{27} -726.269 q^{28} -2778.00 q^{29} +831.930 q^{30} -4109.10 q^{31} +1512.09 q^{32} -2245.79 q^{33} -7104.11 q^{34} -3028.17 q^{35} -340.615 q^{36} -10616.6 q^{37} -15218.0 q^{38} -2544.72 q^{39} +3346.68 q^{40} -828.466 q^{41} -8194.91 q^{42} +8995.66 q^{43} -1049.31 q^{44} -1420.19 q^{45} +3651.98 q^{46} -4346.77 q^{47} +7845.78 q^{48} +13022.0 q^{49} -14854.6 q^{50} +12127.5 q^{51} -1188.98 q^{52} -1799.96 q^{53} -3843.35 q^{54} -4375.10 q^{55} -32966.4 q^{56} +25978.8 q^{57} -14645.9 q^{58} -3481.00 q^{59} -663.564 q^{60} -28023.9 q^{61} -21663.5 q^{62} +13989.6 q^{63} +35868.0 q^{64} -4957.46 q^{65} -11840.0 q^{66} +30957.2 q^{67} +5666.38 q^{68} -6234.32 q^{69} -15964.8 q^{70} +3945.44 q^{71} -15461.0 q^{72} +17740.6 q^{73} -55971.8 q^{74} +25358.3 q^{75} +12138.2 q^{76} +43096.8 q^{77} -13416.0 q^{78} -57063.7 q^{79} +15284.6 q^{80} +6561.00 q^{81} -4367.74 q^{82} +17500.9 q^{83} +6536.42 q^{84} +23625.9 q^{85} +47425.9 q^{86} +25002.0 q^{87} -47629.8 q^{88} -53616.7 q^{89} -7487.37 q^{90} +48833.3 q^{91} -2912.89 q^{92} +36981.9 q^{93} -22916.6 q^{94} +50610.2 q^{95} -13608.8 q^{96} -115705. q^{97} +68653.0 q^{98} +20212.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * q^99

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