LMFDB - Embedded newform 177.5.b.a.119.58

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.58
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.13595i q^{2} +(7.24492 - 5.33959i) q^{3} -1.10604 q^{4} +17.6191i q^{5} +(22.0842 + 29.9646i) q^{6} -12.5141 q^{7} +61.6006i q^{8} +(23.9776 - 77.3697i) q^{9} +O(q^{10})$	\(q+4.13595i q^{2} +(7.24492 - 5.33959i) q^{3} -1.10604 q^{4} +17.6191i q^{5} +(22.0842 + 29.9646i) q^{6} -12.5141 q^{7} +61.6006i q^{8} +(23.9776 - 77.3697i) q^{9} -72.8715 q^{10} +184.300i q^{11} +(-8.01318 + 5.90581i) q^{12} -57.8222 q^{13} -51.7575i q^{14} +(94.0786 + 127.649i) q^{15} -272.473 q^{16} -104.178i q^{17} +(319.997 + 99.1702i) q^{18} +125.420 q^{19} -19.4874i q^{20} +(-90.6634 + 66.8200i) q^{21} -762.253 q^{22} +604.424i q^{23} +(328.922 + 446.291i) q^{24} +314.568 q^{25} -239.150i q^{26} +(-239.406 - 688.568i) q^{27} +13.8411 q^{28} +1279.45i q^{29} +(-527.948 + 389.104i) q^{30} +427.306 q^{31} -141.325i q^{32} +(984.084 + 1335.24i) q^{33} +430.875 q^{34} -220.486i q^{35} +(-26.5203 + 85.5741i) q^{36} +860.739 q^{37} +518.729i q^{38} +(-418.917 + 308.747i) q^{39} -1085.35 q^{40} +709.453i q^{41} +(-276.364 - 374.979i) q^{42} -1128.04 q^{43} -203.843i q^{44} +(1363.18 + 422.464i) q^{45} -2499.86 q^{46} -3473.39i q^{47} +(-1974.05 + 1454.90i) q^{48} -2244.40 q^{49} +1301.04i q^{50} +(-556.268 - 754.762i) q^{51} +63.9538 q^{52} -189.891i q^{53} +(2847.88 - 990.172i) q^{54} -3247.19 q^{55} -770.875i q^{56} +(908.655 - 669.689i) q^{57} -5291.74 q^{58} -453.188i q^{59} +(-104.055 - 141.185i) q^{60} +372.499 q^{61} +1767.32i q^{62} +(-300.058 + 968.211i) q^{63} -3775.06 q^{64} -1018.77i q^{65} +(-5522.46 + 4070.12i) q^{66} -1674.77 q^{67} +115.225i q^{68} +(3227.37 + 4379.00i) q^{69} +911.920 q^{70} -3593.77i q^{71} +(4766.02 + 1477.04i) q^{72} +6503.08 q^{73} +3559.97i q^{74} +(2279.02 - 1679.66i) q^{75} -138.719 q^{76} -2306.34i q^{77} +(-1276.96 - 1732.62i) q^{78} +7252.73 q^{79} -4800.73i q^{80} +(-5411.15 - 3710.28i) q^{81} -2934.26 q^{82} -875.956i q^{83} +(100.278 - 73.9057i) q^{84} +1835.52 q^{85} -4665.53i q^{86} +(6831.74 + 9269.52i) q^{87} -11353.0 q^{88} +454.594i q^{89} +(-1747.29 + 5638.05i) q^{90} +723.592 q^{91} -668.518i q^{92} +(3095.80 - 2281.64i) q^{93} +14365.8 q^{94} +2209.78i q^{95} +(-754.618 - 1023.89i) q^{96} +15117.5 q^{97} -9282.71i q^{98} +(14259.2 + 4419.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$			4.13595i			1.03399i	0.855990	+	0.516993i	$0.172949\pi$
$2$			4.13595i			1.03399i	−0.855990	+	0.516993i	$0.827051\pi$
$3$	7.24492	−	5.33959i	0.804991	−	0.593287i
$3$	7.24492	−	5.33959i	0.804991	−	0.593287i
$4$	−1.10604			−0.0691276
$5$			17.6191i			0.704763i	0.935856	+	0.352381i	$0.114628\pi$
$5$			17.6191i			0.704763i	−0.935856	+	0.352381i	$0.885372\pi$
$6$	22.0842	+	29.9646i	0.613451	+	0.832349i
$7$	−12.5141			−0.255389			−0.127695	−	0.991814i	$-0.540758\pi$
$7$	−12.5141			−0.255389			−0.127695	+	0.991814i	$0.540758\pi$
$8$			61.6006i			0.962509i
$9$	23.9776	−	77.3697i	0.296020	−	0.955182i
$10$	−72.8715			−0.728715
$11$			184.300i			1.52314i	0.648084	+	0.761569i	$0.275571\pi$
$11$			184.300i			1.52314i	−0.648084	+	0.761569i	$0.724429\pi$
$12$	−8.01318	+	5.90581i	−0.0556471	+	0.0410125i
$13$	−57.8222			−0.342143			−0.171072	−	0.985259i	$-0.554723\pi$
$13$	−57.8222			−0.342143			−0.171072	+	0.985259i	$0.554723\pi$
$14$		−	51.7575i		−	0.264069i
$15$	94.0786	+	127.649i	0.418127	+	0.567328i
$16$	−272.473			−1.06435
$17$		−	104.178i		−	0.360478i	−0.983623	−	0.180239i	$-0.942313\pi$
$17$		−	104.178i		−	0.360478i	0.983623	−	0.180239i	$-0.0576871\pi$
$18$	319.997	+	99.1702i	0.987645	+	0.306081i
$19$	125.420			0.347423			0.173711	−	0.984797i	$-0.444424\pi$
$19$	125.420			0.347423			0.173711	+	0.984797i	$0.444424\pi$
$20$		−	19.4874i		−	0.0487186i
$21$	−90.6634	+	66.8200i	−0.205586	+	0.151519i
$22$	−762.253			−1.57490
$23$			604.424i			1.14258i	0.820749	+	0.571289i	$0.193556\pi$
$23$			604.424i			1.14258i	−0.820749	+	0.571289i	$0.806444\pi$
$24$	328.922	+	446.291i	0.571045	+	0.774811i
$25$	314.568			0.503309
$26$		−	239.150i		−	0.353772i
$27$	−239.406	−	688.568i	−0.328404	−	0.944537i
$28$	13.8411			0.0176545
$29$			1279.45i			1.52135i	0.649136	+	0.760673i	$0.275131\pi$
$29$			1279.45i			1.52135i	−0.649136	+	0.760673i	$0.724869\pi$
$30$	−527.948	+	389.104i	−0.586609	+	0.432338i
$31$	427.306			0.444648			0.222324	−	0.974973i	$-0.428636\pi$
$31$	427.306			0.444648			0.222324	+	0.974973i	$0.428636\pi$
$32$		−	141.325i		−	0.138013i
$33$	984.084	+	1335.24i	0.903659	+	1.22611i
$34$	430.875			0.372729
$35$		−	220.486i		−	0.179989i
$36$	−26.5203	+	85.5741i	−0.0204632	+	0.0660294i
$37$	860.739			0.628736			0.314368	−	0.949301i	$-0.398207\pi$
$37$	860.739			0.628736			0.314368	+	0.949301i	$0.398207\pi$
$38$			518.729i			0.359230i
$39$	−418.917	+	308.747i	−0.275422	+	0.202989i
$40$	−1085.35			−0.678341
$41$			709.453i			0.422042i	0.977482	+	0.211021i	$0.0676788\pi$
$41$			709.453i			0.422042i	−0.977482	+	0.211021i	$0.932321\pi$
$42$	−276.364	−	374.979i	−0.156669	−	0.212573i
$43$	−1128.04			−0.610083			−0.305041	−	0.952339i	$-0.598670\pi$
$43$	−1128.04			−0.610083			−0.305041	+	0.952339i	$0.598670\pi$
$44$		−	203.843i		−	0.105291i
$45$	1363.18	+	422.464i	0.673177	+	0.208624i
$46$	−2499.86			−1.18141
$47$		−	3473.39i		−	1.57238i	−0.617983	−	0.786192i	$-0.712050\pi$
$47$		−	3473.39i		−	1.57238i	0.617983	−	0.786192i	$-0.287950\pi$
$48$	−1974.05	+	1454.90i	−0.856791	+	0.631465i
$49$	−2244.40			−0.934776
$50$			1301.04i			0.520415i
$51$	−556.268	−	754.762i	−0.213867	−	0.290181i
$52$	63.9538			0.0236516
$53$		−	189.891i		−	0.0676008i	−0.999429	−	0.0338004i	$-0.989239\pi$
$53$		−	189.891i		−	0.0676008i	0.999429	−	0.0338004i	$-0.0107611\pi$
$54$	2847.88	−	990.172i	0.976639	−	0.339565i
$55$	−3247.19			−1.07345
$56$		−	770.875i		−	0.245815i
$57$	908.655	−	669.689i	0.279672	−	0.206122i
$58$	−5291.74			−1.57305
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	−104.055	−	141.185i	−0.0289041	−	0.0392180i
$61$	372.499			0.100107			0.0500536	−	0.998747i	$-0.484061\pi$
$61$	372.499			0.100107			0.0500536	+	0.998747i	$0.484061\pi$
$62$			1767.32i			0.459759i
$63$	−300.058	+	968.211i	−0.0756004	+	0.243943i
$64$	−3775.06			−0.921645
$65$		−	1018.77i		−	0.241130i
$66$	−5522.46	+	4070.12i	−1.26778	+	0.934370i
$67$	−1674.77			−0.373083			−0.186542	−	0.982447i	$-0.559728\pi$
$67$	−1674.77			−0.373083			−0.186542	+	0.982447i	$0.559728\pi$
$68$			115.225i			0.0249190i
$69$	3227.37	+	4379.00i	0.677877	+	0.919765i
$70$	911.920			0.186106
$71$		−	3593.77i		−	0.712909i	−0.934313	−	0.356454i	$-0.883986\pi$
$71$		−	3593.77i		−	0.712909i	0.934313	−	0.356454i	$-0.116014\pi$
$72$	4766.02	+	1477.04i	0.919371	+	0.284922i
$73$	6503.08			1.22032			0.610159	−	0.792279i	$-0.291105\pi$
$73$	6503.08			1.22032			0.610159	+	0.792279i	$0.291105\pi$
$74$			3559.97i			0.650104i
$75$	2279.02	−	1679.66i	0.405159	−	0.298607i
$76$	−138.719			−0.0240165
$77$		−	2306.34i		−	0.388993i
$78$	−1276.96	−	1732.62i	−0.209888	−	0.284783i
$79$	7252.73			1.16211			0.581055	−	0.813864i	$-0.302640\pi$
$79$	7252.73			1.16211			0.581055	+	0.813864i	$0.302640\pi$
$80$		−	4800.73i		−	0.750114i
$81$	−5411.15	−	3710.28i	−0.824744	−	0.565506i
$82$	−2934.26			−0.436386
$83$		−	875.956i		−	0.127153i	−0.997977	−	0.0635764i	$-0.979749\pi$
$83$		−	875.956i		−	0.127153i	0.997977	−	0.0635764i	$-0.0202507\pi$
$84$	100.278	−	73.9057i	0.0142117	−	0.0104742i
$85$	1835.52			0.254051
$86$		−	4665.53i		−	0.630817i
$87$	6831.74	+	9269.52i	0.902595	+	1.22467i
$88$	−11353.0			−1.46603
$89$			454.594i			0.0573910i	0.999588	+	0.0286955i	$0.00913531\pi$
$89$			454.594i			0.0573910i	−0.999588	+	0.0286955i	$0.990865\pi$
$90$	−1747.29	+	5638.05i	−0.215714	+	0.696055i
$91$	723.592			0.0873798
$92$		−	668.518i		−	0.0789837i
$93$	3095.80	−	2281.64i	0.357937	−	0.263804i
$94$	14365.8			1.62582
$95$			2209.78i			0.244851i
$96$	−754.618	−	1023.89i	−0.0818813	−	0.111099i
$97$	15117.5			1.60670			0.803351	−	0.595506i	$-0.203048\pi$
$97$	15117.5			1.60670			0.803351	+	0.595506i	$0.203048\pi$
$98$		−	9282.71i		−	0.966546i
$99$	14259.2	+	4419.07i	1.45487	+	0.450879i
$100$	−347.926			−0.0347926
$101$		−	9729.30i		−	0.953760i	−0.878968	−	0.476880i	$-0.841768\pi$
$101$		−	9729.30i		−	0.953760i	0.878968	−	0.476880i	$-0.158232\pi$
$102$	3121.65	−	2300.69i	0.300044	−	0.221136i
$103$	17344.1			1.63485			0.817424	−	0.576036i	$-0.195401\pi$
$103$	17344.1			1.63485			0.817424	+	0.576036i	$0.195401\pi$
$104$		−	3561.88i		−	0.329316i
$105$	−1177.31	−	1597.41i	−0.106785	−	0.144889i
$106$	785.377			0.0698983
$107$			9437.06i			0.824269i	0.911123	+	0.412135i	$0.135217\pi$
$107$			9437.06i			0.824269i	−0.911123	+	0.412135i	$0.864783\pi$
$108$	264.793	+	761.585i	0.0227018	+	0.0652936i
$109$	5428.71			0.456924			0.228462	−	0.973553i	$-0.426630\pi$
$109$	5428.71			0.456924			0.228462	+	0.973553i	$0.426630\pi$
$110$		−	13430.2i		−	1.10993i
$111$	6235.99	−	4595.99i	0.506127	−	0.373021i
$112$	3409.75			0.271823
$113$		−	19985.3i		−	1.56515i	−0.622559	−	0.782573i	$-0.713907\pi$
$113$		−	19985.3i		−	1.56515i	0.622559	−	0.782573i	$-0.286093\pi$
$114$	2769.80	+	3758.15i	0.213127	+	0.289177i
$115$	−10649.4			−0.805247
$116$		−	1415.13i		−	0.105167i
$117$	−1386.44	+	4473.69i	−0.101281	+	0.326809i
$118$	1874.36			0.134614
$119$			1303.69i			0.0920622i
$120$	−7863.24	+	5795.30i	−0.546058	+	0.402451i
$121$	−19325.4			−1.31995
$122$			1540.63i			0.103509i
$123$	3788.18	+	5139.92i	0.250392	+	0.339740i
$124$	−472.619			−0.0307374
$125$			16554.3i			1.05948i
$126$	−4004.47	−	1241.02i	−0.252234	−	0.0781698i
$127$	−12448.8			−0.771824			−0.385912	−	0.922536i	$-0.626113\pi$
$127$	−12448.8			−0.771824			−0.385912	+	0.922536i	$0.626113\pi$
$128$		−	17874.6i		−	1.09098i
$129$	−8172.58	+	6023.29i	−0.491111	+	0.361955i
$130$	4213.59			0.249325
$131$		−	16297.2i		−	0.949667i	−0.880076	−	0.474833i	$-0.842508\pi$
$131$		−	16297.2i		−	0.949667i	0.880076	−	0.474833i	$-0.157492\pi$
$132$	−1088.44	−	1476.83i	−0.0624677	−	0.0847582i
$133$	−1569.51			−0.0887281
$134$		−	6926.76i		−	0.385763i
$135$	12131.9	−	4218.12i	0.665675	−	0.231447i
$136$	6417.43			0.346963
$137$		−	15218.8i		−	0.810847i	−0.914129	−	0.405423i	$-0.867124\pi$
$137$		−	15218.8i		−	0.810847i	0.914129	−	0.405423i	$-0.132876\pi$
$138$	−18111.3	+	13348.2i	−0.951024	+	0.700916i
$139$	−10113.3			−0.523434			−0.261717	−	0.965145i	$-0.584289\pi$
$139$	−10113.3			−0.523434			−0.261717	+	0.965145i	$0.584289\pi$
$140$			243.867i			0.0124422i
$141$	−18546.5	−	25164.5i	−0.932875	−	1.26575i
$142$	14863.6			0.737138
$143$		−	10656.6i		−	0.521132i
$144$	−6533.26	+	21081.2i	−0.315069	+	1.01665i
$145$	−22542.7			−1.07219
$146$			26896.4i			1.26179i
$147$	−16260.5	+	11984.2i	−0.752486	+	0.554591i
$148$	−952.014			−0.0434630
$149$			3959.95i			0.178368i	0.996015	+	0.0891841i	$0.0284259\pi$
$149$			3959.95i			0.178368i	−0.996015	+	0.0891841i	$0.971574\pi$
$150$	6947.00	+	9425.91i	0.308756	+	0.418929i
$151$	38089.7			1.67053			0.835265	−	0.549848i	$-0.185314\pi$
$151$	38089.7			1.67053			0.835265	+	0.549848i	$0.185314\pi$
$152$			7725.92i			0.334398i
$153$	−8060.23	−	2497.94i	−0.344322	−	0.106709i
$154$	9538.90			0.402214
$155$			7528.74i			0.313371i
$156$	463.340	−	341.487i	0.0190393	−	0.0140322i
$157$	−5262.12			−0.213482			−0.106741	−	0.994287i	$-0.534042\pi$
$157$	−5262.12			−0.213482			−0.106741	+	0.994287i	$0.534042\pi$
$158$			29996.9i			1.20161i
$159$	−1013.94	−	1375.74i	−0.0401067	−	0.0544180i
$160$	2490.02			0.0972664
$161$		−	7563.81i		−	0.291802i
$162$	15345.5	−	22380.2i	0.584725	−	0.852774i
$163$	−14655.4			−0.551597			−0.275798	−	0.961215i	$-0.588942\pi$
$163$	−14655.4			−0.551597			−0.275798	+	0.961215i	$0.588942\pi$
$164$		−	784.684i		−	0.0291747i
$165$	−23525.6	+	17338.6i	−0.864118	+	0.636865i
$166$	3622.91			0.131474
$167$		−	20878.3i		−	0.748621i	−0.927303	−	0.374311i	$-0.877879\pi$
$167$		−	20878.3i		−	0.748621i	0.927303	−	0.374311i	$-0.122121\pi$
$168$	−4116.15	−	5584.92i	−0.145839	−	0.197878i
$169$	−25217.6			−0.882938
$170$			7591.62i			0.262686i
$171$	3007.26	−	9703.68i	0.102844	−	0.331852i
$172$	1247.66			0.0421736
$173$		−	39920.9i		−	1.33385i	−0.745123	−	0.666927i	$-0.767609\pi$
$173$		−	39920.9i		−	1.33385i	0.745123	−	0.666927i	$-0.232391\pi$
$174$	−38338.2	+	28255.7i	−1.26629	+	0.933271i
$175$	−3936.53			−0.128540
$176$		−	50216.7i		−	1.62115i
$177$	−2419.83	−	3283.31i	−0.0772394	−	0.104801i
$178$	−1880.17			−0.0593415
$179$		−	22574.3i		−	0.704545i	−0.935898	−	0.352272i	$-0.885409\pi$
$179$		−	22574.3i		−	0.704545i	0.935898	−	0.352272i	$-0.114591\pi$
$180$	−1507.74	−	467.262i	−0.0465351	−	0.0144217i
$181$	493.442			0.0150619			0.00753094	−	0.999972i	$-0.497603\pi$
$181$	493.442			0.0150619			0.00753094	+	0.999972i	$0.497603\pi$
$182$			2992.74i			0.0903495i
$183$	2698.72	−	1988.99i	0.0805853	−	0.0593923i
$184$	−37232.9			−1.09974
$185$			15165.4i			0.443110i
$186$	9436.73	+	12804.1i	0.272770	+	0.370102i
$187$	19200.0			0.549058
$188$			3841.72i			0.108695i
$189$	2995.95	+	8616.79i	0.0838708	+	0.241225i
$190$	−9139.52			−0.253172
$191$			59111.5i			1.62034i	0.586198	+	0.810168i	$0.300624\pi$
$191$			59111.5i			1.62034i	−0.586198	+	0.810168i	$0.699376\pi$
$192$	−27350.0	+	20157.3i	−0.741916	+	0.546801i
$193$	61619.9			1.65427			0.827135	−	0.562004i	$-0.189969\pi$
$193$	61619.9			1.65427			0.827135	+	0.562004i	$0.189969\pi$
$194$			62525.0i			1.66131i
$195$	−5439.83	−	7380.93i	−0.143059	−	0.194107i
$196$	2482.40			0.0646188
$197$		−	23922.3i		−	0.616411i	−0.951320	−	0.308205i	$-0.900272\pi$
$197$		−	23922.3i		−	0.616411i	0.951320	−	0.308205i	$-0.0997284\pi$
$198$	−18277.0	+	58975.3i	−0.466203	+	1.50432i
$199$	43950.5			1.10983			0.554917	−	0.831906i	$-0.312750\pi$
$199$	43950.5			1.10983			0.554917	+	0.831906i	$0.312750\pi$
$200$			19377.6i			0.484440i
$201$	−12133.6	+	8942.58i	−0.300329	+	0.221346i
$202$	40239.9			0.986175
$203$		−	16011.2i		−	0.388535i
$204$	615.256	+	834.798i	0.0147841	+	0.0200595i
$205$	−12499.9			−0.297440
$206$			71734.3i			1.69041i
$207$	46764.1	+	14492.7i	1.09137	+	0.338226i
$208$	15755.0			0.364160
$209$			23114.8i			0.529173i
$210$	6606.78	−	4869.27i	0.149814	−	0.110414i
$211$	−26113.1			−0.586535			−0.293267	−	0.956030i	$-0.594743\pi$
$211$	−26113.1			−0.586535			−0.293267	+	0.956030i	$0.594743\pi$
$212$			210.027i			0.00467308i
$213$	−19189.3	−	26036.6i	−0.422960	−	0.573885i
$214$	−39031.1			−0.852283
$215$		−	19875.1i		−	0.429964i
$216$	42416.2	−	14747.6i	0.909126	−	0.316092i
$217$	−5347.34			−0.113558
$218$			22452.8i			0.472453i
$219$	47114.3	−	34723.7i	0.982345	−	0.724000i
$220$	3591.53			0.0742051
$221$			6023.81i			0.123335i
$222$	19008.8	+	25791.7i	0.385699	+	0.523328i
$223$	22563.4			0.453728			0.226864	−	0.973926i	$-0.427153\pi$
$223$	22563.4			0.453728			0.226864	+	0.973926i	$0.427153\pi$
$224$			1768.56i			0.0352470i
$225$	7542.60	−	24338.1i	0.148990	−	0.480752i
$226$	82658.3			1.61834
$227$			34262.6i			0.664918i	0.943118	+	0.332459i	$0.107878\pi$
$227$			34262.6i			0.664918i	−0.943118	+	0.332459i	$0.892122\pi$
$228$	−1005.01	+	740.704i	−0.0193331	+	0.0142487i
$229$	−67529.1			−1.28772			−0.643858	−	0.765145i	$-0.722667\pi$
$229$	−67529.1			−1.28772			−0.643858	+	0.765145i	$0.722667\pi$
$230$		−	44045.3i		−	0.832614i
$231$	−12314.9	−	16709.2i	−0.230785	−	0.313136i
$232$	−78815.0			−1.46431
$233$			89920.6i			1.65633i	0.560482	+	0.828166i	$0.310616\pi$
$233$			89920.6i			1.65633i	−0.560482	+	0.828166i	$0.689384\pi$
$234$	−18502.9	−	5734.24i	−0.337916	−	0.104724i
$235$	61198.0			1.10816
$236$			501.244i			0.00899965i
$237$	52545.5	−	38726.6i	0.935489	−	0.689466i
$238$	−5392.00			−0.0951911
$239$			40579.9i			0.710419i	0.934787	+	0.355210i	$0.115591\pi$
$239$			40579.9i			0.710419i	−0.934787	+	0.355210i	$0.884409\pi$
$240$	−25633.9	−	34780.9i	−0.445033	−	0.603835i
$241$	−9139.37			−0.157356			−0.0786778	−	0.996900i	$-0.525070\pi$
$241$	−9139.37			−0.157356			−0.0786778	+	0.996900i	$0.525070\pi$
$242$		−	79928.7i		−	1.36481i
$243$	−59014.7	+	2012.58i	−0.999419	+	0.0340833i
$244$	−411.999			−0.00692016
$245$		−	39544.2i		−	0.658796i
$246$	−21258.4	+	15667.7i	−0.351286	+	0.258902i
$247$	−7252.04			−0.118868
$248$			26322.3i			0.427977i
$249$	−4677.24	−	6346.23i	−0.0754382	−	0.102357i
$250$	−68467.8			−1.09548
$251$		−	60989.8i		−	0.968077i	−0.875047	−	0.484038i	$-0.839169\pi$
$251$		−	60989.8i		−	0.968077i	0.875047	−	0.484038i	$-0.160831\pi$
$252$	331.877	−	1070.88i	0.00522607	−	0.0168632i
$253$	−111395.			−1.74030
$254$		−	51487.4i		−	0.798056i
$255$	13298.2	−	9800.93i	0.204509	−	0.150726i
$256$	13527.6			0.206415
$257$			108053.i			1.63595i	0.575253	+	0.817976i	$0.304904\pi$
$257$			108053.i			1.63595i	−0.575253	+	0.817976i	$0.695096\pi$
$258$	−24912.0	−	33801.3i	−0.374256	−	0.507802i
$259$	−10771.4			−0.160572
$260$			1126.81i			0.0166687i
$261$	98990.8	+	30678.2i	1.45316	+	0.450349i
$262$	67404.5			0.981942
$263$			54855.7i			0.793068i	0.918020	+	0.396534i	$0.129787\pi$
$263$			54855.7i			0.793068i	−0.918020	+	0.396534i	$0.870213\pi$
$264$	−82251.3	+	60620.2i	−1.18014	+	0.869780i
$265$	3345.70			0.0476425
$266$		−	6491.41i		−	0.0917436i
$267$	2427.34	+	3293.49i	0.0340493	+	0.0461992i
$268$	1852.37			0.0257903
$269$		−	97294.4i		−	1.34457i	−0.740293	−	0.672285i	$-0.765313\pi$
$269$		−	97294.4i		−	1.34457i	0.740293	−	0.672285i	$-0.234687\pi$
$270$	17445.9	+	50177.0i	0.239313	+	0.688299i
$271$	−37108.8			−0.505287			−0.252643	−	0.967559i	$-0.581300\pi$
$271$	−37108.8			−0.505287			−0.252643	+	0.967559i	$0.581300\pi$
$272$			28385.8i			0.383674i
$273$	5242.36	−	3863.68i	0.0703399	−	0.0518413i
$274$	62944.0			0.838404
$275$			57974.8i			0.766609i
$276$	−3569.61	−	4843.36i	−0.0468600	−	0.0635811i
$277$	−85978.1			−1.12054			−0.560271	−	0.828309i	$-0.689303\pi$
$277$	−85978.1			−1.12054			−0.560271	+	0.828309i	$0.689303\pi$
$278$		−	41827.9i		−	0.541223i
$279$	10245.8	−	33060.6i	0.131625	−	0.424719i
$280$	13582.1			0.173241
$281$		−	96603.7i		−	1.22344i	−0.791076	−	0.611718i	$-0.790479\pi$
$281$		−	96603.7i		−	1.22344i	0.791076	−	0.611718i	$-0.209521\pi$
$282$	104079.	−	76707.3i	1.30877	−	0.964580i
$283$	−128691.			−1.60685			−0.803426	−	0.595405i	$-0.796991\pi$
$283$	−128691.			−1.60685			−0.803426	+	0.595405i	$0.796991\pi$
$284$			3974.86i			0.0492817i
$285$	11799.3	+	16009.7i	0.145267	+	0.197102i
$286$	44075.2			0.538843
$287$		−	8878.14i		−	0.107785i
$288$	−10934.3	−	3388.64i	−0.131827	−	0.0408546i
$289$	72667.9			0.870056
$290$		−	93235.6i		−	1.10863i
$291$	109525.	−	80721.0i	1.29338	−	0.953236i
$292$	−7192.67			−0.0843577
$293$		−	28502.3i		−	0.332005i	−0.986125	−	0.166003i	$-0.946914\pi$
$293$		−	28502.3i		−	0.332005i	0.986125	−	0.166003i	$-0.0530860\pi$
$294$	−49565.8	−	67252.4i	−0.573439	−	0.778060i
$295$	7984.74			0.0917523
$296$			53022.1i			0.605164i
$297$	126903.	−	44122.5i	1.43866	−	0.500204i
$298$	−16378.1			−0.184430
$299$		−	34949.1i		−	0.390926i
$300$	−2520.69	+	1857.78i	−0.0280077	+	0.0206420i
$301$	14116.4			0.155809
$302$			157537.i			1.72730i
$303$	−51950.5	−	70488.0i	−0.565854	−	0.767768i
$304$	−34173.5			−0.369779
$305$			6563.08i			0.0705518i
$306$	10331.4	−	33336.7i	0.110335	−	0.356024i
$307$	−60674.4			−0.643767			−0.321883	−	0.946779i	$-0.604316\pi$
$307$	−60674.4			−0.643767			−0.321883	+	0.946779i	$0.604316\pi$
$308$			2550.91i			0.0268902i
$309$	125657.	−	92610.4i	1.31604	−	0.969935i
$310$	−31138.5			−0.324021
$311$		−	60595.9i		−	0.626502i	−0.949670	−	0.313251i	$-0.898582\pi$
$311$		−	60595.9i		−	0.626502i	0.949670	−	0.313251i	$-0.101418\pi$
$312$	−19019.0	−	25805.6i	−0.195379	−	0.265096i
$313$	75841.1			0.774134			0.387067	−	0.922052i	$-0.373488\pi$
$313$	75841.1			0.774134			0.387067	+	0.922052i	$0.373488\pi$
$314$		−	21763.8i		−	0.220737i
$315$	−17059.0	−	5286.74i	−0.171922	−	0.0532803i
$316$	−8021.83			−0.0803339
$317$			94645.4i			0.941848i	0.882174	+	0.470924i	$0.156079\pi$
$317$			94645.4i			0.941848i	−0.882174	+	0.470924i	$0.843921\pi$
$318$	5689.99	−	4193.59i	0.0562675	−	0.0414698i
$319$	−235802.			−2.31722
$320$		−	66513.1i		−	0.649542i
$321$	50390.0	+	68370.7i	0.489028	+	0.663529i
$322$	31283.5			0.301720
$323$		−	13066.0i		−	0.125238i
$324$	5984.95	+	4103.73i	0.0570126	+	0.0390921i
$325$	−18189.0			−0.172204
$326$		−	60613.8i		−	0.570344i
$327$	39330.6	−	28987.1i	0.367819	−	0.271087i
$328$	−43702.7			−0.406219
$329$			43466.3i			0.401570i
$330$	−71711.7	−	97300.7i	−0.658510	−	0.893486i
$331$	78362.6			0.715242			0.357621	−	0.933867i	$-0.383588\pi$
$331$	78362.6			0.715242			0.357621	+	0.933867i	$0.383588\pi$
$332$			968.844i			0.00878977i
$333$	20638.5	−	66595.2i	0.186118	−	0.600557i
$334$	86351.5			0.774064
$335$		−	29507.9i		−	0.262935i
$336$	24703.4	−	18206.7i	0.218815	−	0.161269i
$337$	123318.			1.08584			0.542922	−	0.839783i	$-0.317318\pi$
$337$	123318.			1.08584			0.542922	+	0.839783i	$0.317318\pi$
$338$		−	104299.i		−	0.912946i
$339$	−106713.	−	144792.i	−0.928581	−	1.25993i
$340$	−2030.16			−0.0175620
$341$			78752.4i			0.677260i
$342$	40133.9	+	12437.9i	0.343130	+	0.106339i
$343$	58132.9			0.494121
$344$		−	69488.1i		−	0.587211i
$345$	−77153.9	+	56863.3i	−0.648216	+	0.477743i
$346$	165111.			1.37919
$347$			221064.i			1.83594i	0.396649	+	0.917971i	$0.370173\pi$
$347$			221064.i			1.83594i	−0.396649	+	0.917971i	$0.629827\pi$
$348$	−7556.19	−	10252.5i	−0.0623942	−	0.0846584i
$349$	139547.			1.14570			0.572849	−	0.819661i	$-0.305838\pi$
$349$	139547.			1.14570			0.572849	+	0.819661i	$0.305838\pi$
$350$		−	16281.3i		−	0.132908i
$351$	13843.0	+	39814.5i	0.112361	+	0.323167i
$352$	26046.2			0.210213
$353$			38605.8i			0.309815i	0.987929	+	0.154908i	$0.0495080\pi$
$353$			38605.8i			0.309815i	−0.987929	+	0.154908i	$0.950492\pi$
$354$	13579.6	−	10008.3i	0.108363	−	0.0798645i
$355$	63318.9			0.502431
$356$		−	502.800i		−	0.00396730i
$357$	6961.18	+	9445.15i	0.0546193	+	0.0741092i
$358$	93366.1			0.728489
$359$			206155.i			1.59958i	0.600282	+	0.799789i	$0.295055\pi$
$359$			206155.i			1.59958i	−0.600282	+	0.799789i	$0.704945\pi$
$360$	−26024.0	+	83972.9i	−0.200803	+	0.647939i
$361$	−114591.			−0.879297
$362$			2040.85i			0.0155738i
$363$	−140011.	+	103190.i	−1.06255	+	0.783109i
$364$	−800.323			−0.00604035
$365$			114578.i			0.860035i
$366$	8226.35	+	11161.8i	0.0614108	+	0.0833241i
$367$	134326.			0.997306			0.498653	−	0.866802i	$-0.333828\pi$
$367$	134326.			0.997306			0.498653	+	0.866802i	$0.333828\pi$
$368$		−	164689.i		−	1.21610i
$369$	54890.1	+	17011.0i	0.403127	+	0.124933i
$370$	−62723.4			−0.458169
$371$			2376.31i			0.0172645i
$372$	−3424.08	+	2523.59i	−0.0247433	+	0.0182361i
$373$	−77475.9			−0.556864			−0.278432	−	0.960456i	$-0.589815\pi$
$373$	−77475.9			−0.556864			−0.278432	+	0.960456i	$0.589815\pi$
$374$			79410.1i			0.567718i
$375$	88393.2	+	119935.i	0.628574	+	0.852869i
$376$	213963.			1.51343
$377$		−	73980.7i		−	0.520518i
$378$	−35638.6	+	12391.1i	−0.249423	+	0.0867213i
$379$	−188651.			−1.31335			−0.656674	−	0.754175i	$-0.728037\pi$
$379$	−188651.			−1.31335			−0.656674	+	0.754175i	$0.728037\pi$
$380$		−	2444.11i		−	0.0169259i
$381$	−90190.2	+	66471.2i	−0.621311	+	0.457914i
$382$	−244482.			−1.67540
$383$			117022.i			0.797753i	0.917005	+	0.398877i	$0.130600\pi$
$383$			117022.i			0.797753i	−0.917005	+	0.398877i	$0.869400\pi$
$384$	−95443.2	−	129500.i	−0.647266	−	0.878230i
$385$	40635.6			0.274148
$386$			254856.i			1.71049i
$387$	−27047.8	+	87276.4i	−0.180597	+	0.582740i
$388$	−16720.5			−0.111067
$389$		−	4246.83i		−	0.0280650i	−0.999902	−	0.0140325i	$-0.995533\pi$
$389$		−	4246.83i		−	0.0280650i	0.999902	−	0.0140325i	$-0.00446684\pi$
$390$	30527.1	−	22498.8i	0.200704	−	0.147921i
$391$	62967.7			0.411874
$392$		−	138256.i		−	0.899731i
$393$	−87020.5	−	118072.i	−0.563425	−	0.764473i
$394$	98941.3			0.637361
$395$			127786.i			0.819013i
$396$	−15771.3	−	4887.67i	−0.100572	−	0.0311682i
$397$	62357.0			0.395643			0.197822	−	0.980238i	$-0.436613\pi$
$397$	62357.0			0.395643			0.197822	+	0.980238i	$0.436613\pi$
$398$			181777.i			1.14755i
$399$	−11371.0	+	8380.54i	−0.0714253	+	0.0526412i
$400$	−85711.5			−0.535697
$401$		−	71251.0i		−	0.443100i	−0.975149	−	0.221550i	$-0.928888\pi$
$401$		−	71251.0i		−	0.443100i	0.975149	−	0.221550i	$-0.0711117\pi$
$402$	−36986.0	−	50183.8i	−0.228868	−	0.310536i
$403$	−24707.8			−0.152133
$404$			10761.0i			0.0659311i
$405$	65371.8	−	95339.4i	0.398548	−	0.581249i
$406$	66221.3			0.401740
$407$			158634.i			0.957651i
$408$	46493.8	−	34266.4i	0.279302	−	0.205849i
$409$	−269526.			−1.61122			−0.805610	−	0.592447i	$-0.798162\pi$
$409$	−269526.			−1.61122			−0.805610	+	0.592447i	$0.798162\pi$
$410$		−	51698.9i		−	0.307548i
$411$	−81262.0	−	110259.i	−0.481065	−	0.652724i
$412$	−19183.3			−0.113013
$413$			5671.22i			0.0332489i
$414$	−59940.8	+	193414.i	−0.349721	+	1.12846i
$415$	15433.5			0.0896126
$416$			8171.74i			0.0472202i
$417$	−73269.8	+	54000.7i	−0.421359	+	0.310547i
$418$	−95601.5			−0.547157
$419$			44475.0i			0.253331i	0.991946	+	0.126665i	$0.0404274\pi$
$419$			44475.0i			0.253331i	−0.991946	+	0.126665i	$0.959573\pi$
$420$	1302.15	+	1766.80i	0.00738180	+	0.0100159i
$421$	79561.8			0.448890			0.224445	−	0.974487i	$-0.427943\pi$
$421$	79561.8			0.448890			0.224445	+	0.974487i	$0.427943\pi$
$422$		−	108002.i		−	0.606469i
$423$	−268736.	−	83283.8i	−1.50191	−	0.465457i
$424$	11697.4			0.0650664
$425$		−	32771.1i		−	0.181432i
$426$	107686.	−	79365.7i	0.593389	−	0.437334i
$427$	−4661.48			−0.0255663
$428$		−	10437.8i		−	0.0569797i
$429$	−56901.9	−	77206.3i	−0.309181	−	0.419506i
$430$	82202.2			0.444577
$431$			71390.6i			0.384314i	0.981364	+	0.192157i	$0.0615483\pi$
$431$			71390.6i			0.384314i	−0.981364	+	0.192157i	$0.938452\pi$
$432$	65231.9	+	187616.i	0.349536	+	1.00532i
$433$	−207036.			−1.10426			−0.552128	−	0.833760i	$-0.686184\pi$
$433$	−207036.			−1.10426			−0.552128	+	0.833760i	$0.686184\pi$
$434$		−	22116.3i		−	0.117418i
$435$	−163320.	+	120369.i	−0.863101	+	0.636115i
$436$	−6004.38			−0.0315860
$437$			75806.6i			0.396958i
$438$	143615.	+	194862.i	0.748606	+	1.01573i
$439$	186287.			0.966615			0.483307	−	0.875451i	$-0.339435\pi$
$439$	186287.			0.966615			0.483307	+	0.875451i	$0.339435\pi$
$440$		−	200029.i		−	1.03321i
$441$	−53815.3	+	173648.i	−0.276713	+	0.892881i
$442$	−24914.2			−0.127527
$443$			13814.9i			0.0703950i	0.999380	+	0.0351975i	$0.0112060\pi$
$443$			13814.9i			0.0703950i	−0.999380	+	0.0351975i	$0.988794\pi$
$444$	−6897.26	+	5083.36i	−0.0349873	+	0.0257861i
$445$	−8009.52			−0.0404470
$446$			93321.1i			0.469148i
$447$	21144.5	+	28689.5i	0.105824	+	0.143585i
$448$	47241.4			0.235378
$449$			90440.0i			0.448609i	0.974519	+	0.224304i	$0.0720110\pi$
$449$			90440.0i			0.448609i	−0.974519	+	0.224304i	$0.927989\pi$
$450$	100661.	+	31195.8i	0.497091	+	0.154053i
$451$	−130752.			−0.642828
$452$			22104.6i			0.108195i
$453$	275957.	−	203383.i	1.34476	−	0.991104i
$454$	−141708.			−0.687516
$455$			12749.0i			0.0615820i
$456$	41253.2	+	55973.7i	0.198394	+	0.269187i
$457$	218677.			1.04706			0.523530	−	0.852008i	$-0.324615\pi$
$457$	218677.			1.04706			0.523530	+	0.852008i	$0.324615\pi$
$458$		−	279297.i		−	1.33148i
$459$	−71733.7	+	24940.9i	−0.340485	+	0.118382i
$460$	11778.7			0.0556648
$461$		−	269465.i		−	1.26794i	−0.773356	−	0.633972i	$-0.781423\pi$
$461$		−	269465.i		−	1.26794i	0.773356	−	0.633972i	$-0.218577\pi$
$462$	69108.5	−	50933.8i	0.323778	−	0.238628i
$463$	−123071.			−0.574110			−0.287055	−	0.957914i	$-0.592676\pi$
$463$	−123071.			−0.574110			−0.287055	+	0.957914i	$0.592676\pi$
$464$		−	348616.i		−	1.61924i
$465$	40200.4	+	54545.1i	0.185919	+	0.252261i
$466$	−371907.			−1.71263
$467$		−	45609.3i		−	0.209132i	−0.994518	−	0.104566i	$-0.966655\pi$
$467$		−	45609.3i		−	0.209132i	0.994518	−	0.104566i	$-0.0333453\pi$
$468$	1533.46	−	4948.09i	0.00700134	−	0.0225915i
$469$	20958.2			0.0952815
$470$			253112.i			1.14582i
$471$	−38123.6	+	28097.5i	−0.171851	+	0.126656i
$472$	27916.6			0.125308
$473$		−	207898.i		−	0.929240i
$474$	160171.	+	217325.i	0.712898	+	0.967282i
$475$	39453.0			0.174861
$476$		−	1441.94i		−	0.00636404i
$477$	−14691.8	−	4553.13i	−0.0645710	−	0.0200112i
$478$	−167836.			−0.734564
$479$			151999.i			0.662474i	0.943548	+	0.331237i	$0.107466\pi$
$479$			151999.i			0.662474i	−0.943548	+	0.331237i	$0.892534\pi$
$480$	18040.0	−	13295.7i	0.0782986	−	0.0577069i
$481$	−49769.9			−0.215118
$482$		−	37799.9i		−	0.162704i
$483$	−40387.6	−	54799.1i	−0.173123	−	0.234898i
$484$	21374.7			0.0912449
$485$			266356.i			1.13234i
$486$	−8323.94	−	244082.i	−0.0352416	−	1.03339i
$487$	404814.			1.70686			0.853428	−	0.521210i	$-0.174519\pi$
$487$	404814.			1.70686			0.853428	+	0.521210i	$0.174519\pi$
$488$			22946.1i			0.0963540i
$489$	−106177.	+	78253.7i	−0.444030	+	0.327256i
$490$	163553.			0.681186
$491$			358801.i			1.48830i	0.668013	+	0.744150i	$0.267145\pi$
$491$			358801.i			1.48830i	−0.668013	+	0.744150i	$0.732855\pi$
$492$	−4189.89	−	5684.97i	−0.0173090	−	0.0234854i
$493$	133291.			0.548411
$494$		−	29994.0i		−	0.122908i
$495$	−77859.9	+	251234.i	−0.317763	+	1.02534i
$496$	−116430.			−0.473260
$497$			44972.7i			0.182069i
$498$	26247.7	−	19344.8i	0.105836	−	0.0780021i
$499$	−397788.			−1.59753			−0.798767	−	0.601641i	$-0.794514\pi$
$499$	−397788.			−1.59753			−0.798767	+	0.601641i	$0.794514\pi$
$500$		−	18309.8i		−	0.0732391i
$501$	−111481.	−	151262.i	−0.444148	−	0.602633i
$502$	252251.			1.00098
$503$			87283.4i			0.344981i	0.985011	+	0.172491i	$0.0551815\pi$
$503$			87283.4i			0.344981i	−0.985011	+	0.172491i	$0.944819\pi$
$504$	−59642.3	−	18483.7i	−0.234798	−	0.0727661i
$505$	171421.			0.672175
$506$		−	460724.i		−	1.79945i
$507$	−182699.	+	134652.i	−0.710757	+	0.523836i
$508$	13768.8			0.0533544
$509$			221565.i			0.855196i	0.903969	+	0.427598i	$0.140640\pi$
$509$			221565.i			0.855196i	−0.903969	+	0.427598i	$0.859360\pi$
$510$	40536.1	+	55000.6i	0.155848	+	0.211460i
$511$	−81380.0			−0.311656
$512$		−	230045.i		−	0.877552i
$513$	−30026.3	−	86359.9i	−0.114095	−	0.328154i
$514$	−446901.			−1.69155
$515$			305587.i			1.15218i
$516$	9039.21	−	6662.00i	0.0339493	−	0.0250210i
$517$	640145.			2.39496
$518$		−	44549.8i		−	0.166030i
$519$	−213161.	−	289224.i	−0.791359	−	1.07374i
$520$	62757.1			0.232090
$521$		−	493353.i		−	1.81753i	−0.417304	−	0.908767i	$-0.637025\pi$
$521$		−	493353.i		−	1.81753i	0.417304	−	0.908767i	$-0.362975\pi$
$522$	−126883.	+	409420.i	−0.465654	+	1.50255i
$523$	−43949.6			−0.160676			−0.0803380	−	0.996768i	$-0.525600\pi$
$523$	−43949.6			−0.160676			−0.0803380	+	0.996768i	$0.525600\pi$
$524$			18025.4i			0.0656482i
$525$	−28519.8	+	21019.5i	−0.103473	+	0.0762611i
$526$	−226880.			−0.820022
$527$		−	44516.0i		−	0.160286i
$528$	−268137.	−	363816.i	−0.961808	−	1.30501i
$529$	−85487.2			−0.305485
$530$			13837.6i			0.0492617i
$531$	−35063.0	−	10866.4i	−0.124354	−	0.0385385i
$532$	1735.94			0.00613356
$533$		−	41022.1i		−	0.144399i
$534$	−13621.7	+	10039.4i	−0.0477693	+	0.0352065i
$535$	−166272.			−0.580914
$536$		−	103167.i		−	0.359096i
$537$	−120538.	−	163549.i	−0.417997	−	0.567152i
$538$	402404.			1.39027
$539$		−	413642.i		−	1.42379i
$540$	−13418.4	+	4665.41i	−0.0460165	+	0.0159994i
$541$	123956.			0.423520			0.211760	−	0.977322i	$-0.432080\pi$
$541$	123956.			0.423520			0.211760	+	0.977322i	$0.432080\pi$
$542$		−	153480.i		−	0.522459i
$543$	3574.95	−	2634.78i	0.0121247	−	0.00893602i
$544$	−14723.0			−0.0497506
$545$			95648.8i			0.322023i
$546$	15980.0	+	21682.1i	0.0536032	+	0.0727305i
$547$	460410.			1.53876			0.769379	−	0.638792i	$-0.220566\pi$
$547$	460410.			1.53876			0.769379	+	0.638792i	$0.220566\pi$
$548$			16832.6i			0.0560519i
$549$	8931.63	−	28820.1i	0.0296337	−	0.0956205i
$550$	−239781.			−0.792664
$551$			160468.i			0.528550i
$552$	−269749.	+	198808.i	−0.885282	+	0.652463i
$553$	−90761.3			−0.296791
$554$		−	355601.i		−	1.15863i
$555$	80977.1	+	109872.i	0.262891	+	0.356699i
$556$	11185.7			0.0361837
$557$		−	475013.i		−	1.53107i	−0.643395	−	0.765535i	$-0.722475\pi$
$557$		−	475013.i		−	1.53107i	0.643395	−	0.765535i	$-0.277525\pi$
$558$	136737.	+	42376.0i	0.439154	+	0.136098i
$559$	65226.0			0.208736
$560$			60076.7i			0.191571i
$561$	139102.	−	102520.i	0.441986	−	0.325749i
$562$	399548.			1.26502
$563$			226053.i			0.713171i	0.934263	+	0.356585i	$0.116059\pi$
$563$			226053.i			0.713171i	−0.934263	+	0.356585i	$0.883941\pi$
$564$	20513.2	+	27832.9i	0.0644874	+	0.0874985i
$565$	352123.			1.10306
$566$		−	532259.i		−	1.66146i
$567$	67715.5	+	46430.8i	0.210631	+	0.144424i
$568$	221378.			0.686181
$569$			68991.6i			0.213094i	0.994308	+	0.106547i	$0.0339795\pi$
$569$			68991.6i			0.213094i	−0.994308	+	0.106547i	$0.966020\pi$
$570$	−66215.0	+	48801.2i	−0.203801	+	0.150204i
$571$	−62435.9			−0.191497			−0.0957485	−	0.995406i	$-0.530524\pi$
$571$	−62435.9			−0.191497			−0.0957485	+	0.995406i	$0.530524\pi$
$572$			11786.7i			0.0360246i
$573$	315631.	+	428258.i	0.961325	+	1.30435i
$574$	36719.5			0.111448
$575$			190133.i			0.575070i
$576$	−90517.0	+	292075.i	−0.272826	+	0.880339i
$577$	−568288.			−1.70694			−0.853468	−	0.521145i	$-0.825505\pi$
$577$	−568288.			−1.70694			−0.853468	+	0.521145i	$0.825505\pi$
$578$			300551.i			0.899626i
$579$	446431.	−	329025.i	1.33167	−	0.981457i
$580$	24933.2			0.0741178
$581$			10961.8i			0.0324735i
$582$	333858.	+	452988.i	0.985633	+	1.33734i
$583$	34996.8			0.102965
$584$			400593.i			1.17457i
$585$	−78822.3	−	24427.8i	−0.230323	−	0.0713793i
$586$	117884.			0.343289
$587$		−	678617.i		−	1.96947i	−0.174073	−	0.984733i	$-0.555693\pi$
$587$		−	678617.i		−	1.96947i	0.174073	−	0.984733i	$-0.444307\pi$
$588$	17984.8	−	13255.0i	0.0520176	−	0.0383375i
$589$	53592.6			0.154481
$590$			33024.5i			0.0948706i
$591$	−127735.	−	173315.i	−0.365709	−	0.496205i
$592$	−234529.			−0.669194
$593$		−	62224.1i		−	0.176949i	−0.996078	−	0.0884747i	$-0.971801\pi$
$593$		−	62224.1i		−	0.176949i	0.996078	−	0.0884747i	$-0.0281993\pi$
$594$	182488.	+	524863.i	0.517204	+	1.48756i
$595$	−22969.9			−0.0648820
$596$		−	4379.87i		−	0.0123302i
$597$	318418.	−	234678.i	0.893406	−	0.658451i
$598$	144548.			0.404212
$599$			70115.3i			0.195416i	0.995215	+	0.0977078i	$0.0311511\pi$
$599$			70115.3i			0.195416i	−0.995215	+	0.0977078i	$0.968849\pi$
$600$	103468.	+	140389.i	0.287412	+	0.389970i
$601$	71660.9			0.198396			0.0991982	−	0.995068i	$-0.468372\pi$
$601$	71660.9			0.198396			0.0991982	+	0.995068i	$0.468372\pi$
$602$			58384.7i			0.161104i
$603$	−40157.0	+	129577.i	−0.110440	+	0.356362i
$604$	−42128.8			−0.115480
$605$		−	340495.i		−	0.930251i
$606$	291534.	−	214864.i	0.793861	−	0.585085i
$607$	155836.			0.422952			0.211476	−	0.977383i	$-0.432173\pi$
$607$	155836.			0.422952			0.211476	+	0.977383i	$0.432173\pi$
$608$		−	17725.0i		−	0.0479488i
$609$	−85492.9	−	115999.i	−0.230513	−	0.312767i
$610$	−27144.5			−0.0729496
$611$			200839.i			0.537981i
$612$	8914.95	+	2762.83i	0.0238021	+	0.00737652i
$613$	−224622.			−0.597767			−0.298883	−	0.954290i	$-0.596614\pi$
$613$	−224622.			−0.597767			−0.298883	+	0.954290i	$0.596614\pi$
$614$		−	250946.i		−	0.665646i
$615$	−90560.7	+	66744.3i	−0.239436	+	0.176467i
$616$	142072.			0.374410
$617$			23349.6i			0.0613352i	0.999530	+	0.0306676i	$0.00976332\pi$
$617$			23349.6i			0.0613352i	−0.999530	+	0.0306676i	$0.990237\pi$
$618$	383031.	+	519709.i	1.00290	+	1.36077i
$619$	−463633.			−1.21002			−0.605011	−	0.796217i	$-0.706831\pi$
$619$	−463633.			−1.21002			−0.605011	+	0.796217i	$0.706831\pi$
$620$		−	8327.10i		−	0.0216626i
$621$	416187.	−	144703.i	1.07921	−	0.375227i
$622$	250621.			0.647794
$623$		−	5688.82i		−	0.0146570i
$624$	114144.	−	84125.3i	0.293145	−	0.216052i
$625$	−95066.6			−0.243370
$626$			313675.i			0.800443i
$627$	123423.	+	167465.i	0.313952	+	0.425979i
$628$	5820.12			0.0147575
$629$		−	89670.2i		−	0.226645i
$630$	21865.7	−	70555.0i	0.0550911	−	0.177765i
$631$	−302085.			−0.758701			−0.379350	−	0.925253i	$-0.623852\pi$
$631$	−302085.			−0.758701			−0.379350	+	0.925253i	$0.623852\pi$
$632$			446773.i			1.11854i
$633$	−189187.	+	139433.i	−0.472155	+	0.347984i
$634$	−391448.			−0.973858
$635$		−	219336.i		−	0.543953i
$636$	1121.46	+	1521.63i	0.00277248	+	0.00376179i
$637$	129776.			0.319828
$638$		−	975266.i		−	2.39597i
$639$	−278049.	−	86170.1i	−0.680957	−	0.211035i
$640$	314935.			0.768883
$641$		−	734120.i		−	1.78670i	−0.449364	−	0.893349i	$-0.648349\pi$
$641$		−	734120.i		−	1.78670i	0.449364	−	0.893349i	$-0.351651\pi$
$642$	−282777.	+	208410.i	−0.686080	+	0.505649i
$643$	−49511.3			−0.119752			−0.0598760	−	0.998206i	$-0.519071\pi$
$643$	−49511.3			−0.119752			−0.0598760	+	0.998206i	$0.519071\pi$
$644$			8365.89i			0.0201716i
$645$	−106125.	−	143993.i	−0.255092	−	0.346117i
$646$	54040.2			0.129495
$647$			499535.i			1.19332i	0.802494	+	0.596660i	$0.203506\pi$
$647$			499535.i			1.19332i	−0.802494	+	0.596660i	$0.796494\pi$
$648$	228556.	−	333330.i	0.544305	−	0.793824i
$649$	83522.3			0.198296
$650$		−	75228.9i		−	0.178057i
$651$	−38741.1	+	28552.6i	−0.0914133	+	0.0673727i
$652$	16209.5			0.0381306
$653$		−	364408.i		−	0.854597i	−0.904111	−	0.427298i	$-0.859465\pi$
$653$		−	364408.i		−	0.854597i	0.904111	−	0.427298i	$-0.140535\pi$
$654$	119889.	+	162669.i	0.280300	+	0.380320i
$655$	287142.			0.669290
$656$		−	193307.i		−	0.449200i
$657$	155928.	−	503141.i	0.361239	−	1.16563i
$658$	−179774.			−0.415218
$659$		−	159301.i		−	0.366815i	−0.983037	−	0.183407i	$-0.941287\pi$
$659$		−	159301.i		−	0.366815i	0.983037	−	0.183407i	$-0.0587127\pi$
$660$	26020.3	−	19177.3i	0.0597344	−	0.0440249i
$661$	−312138.			−0.714403			−0.357202	−	0.934027i	$-0.616269\pi$
$661$	−312138.			−0.714403			−0.357202	+	0.934027i	$0.616269\pi$
$662$			324103.i			0.739550i
$663$	32164.7	+	43642.0i	0.0731732	+	0.0992836i
$664$	53959.4			0.122386
$665$		−	27653.3i		−	0.0625322i
$666$	275434.	+	85359.7i	0.620968	+	0.192444i
$667$	−773331.			−1.73826
$668$			23092.3i			0.0517504i
$669$	163470.	−	120479.i	0.365247	−	0.269191i
$670$	122043.			0.271871
$671$			68651.4i			0.152477i
$672$	9443.35	+	12813.0i	0.0209116	+	0.0283735i
$673$	476279.			1.05155			0.525777	−	0.850623i	$-0.323775\pi$
$673$	476279.			1.05155			0.525777	+	0.850623i	$0.323775\pi$
$674$			510037.i			1.12275i
$675$	−75309.7	−	216602.i	−0.165289	−	0.475394i
$676$	27891.7			0.0610354
$677$		−	715816.i		−	1.56179i	−0.624659	−	0.780897i	$-0.714762\pi$
$677$		−	715816.i		−	1.56179i	0.624659	−	0.780897i	$-0.285238\pi$
$678$	598852.	−	441361.i	1.30275	−	0.960140i
$679$	−189181.			−0.410335
$680$			113069.i			0.244527i
$681$	182948.	+	248229.i	0.394488	+	0.535253i
$682$	−325716.			−0.700277
$683$		−	201471.i		−	0.431888i	−0.976406	−	0.215944i	$-0.930717\pi$
$683$		−	201471.i		−	0.431888i	0.976406	−	0.215944i	$-0.0692828\pi$
$684$	−3326.16	+	10732.7i	−0.00710937	+	0.0229401i
$685$	268141.			0.571455
$686$			240434.i			0.510915i
$687$	−489243.	+	360577.i	−1.03660	+	0.763986i
$688$	307362.			0.649341
$689$			10979.9i			0.0231292i
$690$	−235184.	−	319104.i	−0.493979	−	0.670247i
$691$	260424.			0.545412			0.272706	−	0.962097i	$-0.412081\pi$
$691$	260424.			0.545412			0.272706	+	0.962097i	$0.412081\pi$
$692$			44154.2i			0.0922061i
$693$	−178441.	−	55300.6i	−0.371559	−	0.115150i
$694$	−914308.			−1.89834
$695$		−	178186.i		−	0.368897i
$696$	−571008.	+	420839.i	−1.17876	+	0.868756i
$697$	73909.4			0.152137
$698$			577160.i			1.18464i
$699$	480139.	+	651468.i	0.982681	+	1.33333i
$700$	4353.97			0.00888565
$701$			644846.i			1.31226i	0.754648	+	0.656130i	$0.227808\pi$
$701$			644846.i			1.31226i	−0.754648	+	0.656130i	$0.772192\pi$
$702$	−164671.	+	57253.9i	−0.334150	+	0.116180i
$703$	107954.			0.218437
$704$		−	695742.i		−	1.40379i
$705$	443374.	−	326772.i	0.892056	−	0.657456i
$706$	−159671.			−0.320345
$707$			121753.i			0.243580i
$708$	2676.44	+	3631.47i	0.00533938	+	0.00724463i
$709$	−780480.			−1.55264			−0.776318	−	0.630342i	$-0.782915\pi$
$709$	−780480.			−1.55264			−0.776318	+	0.630342i	$0.782915\pi$
$710$			261884.i			0.519507i
$711$	173903.	−	561142.i	0.344008	−	1.11003i
$712$	−28003.2			−0.0552393
$713$			258274.i			0.508045i
$714$	−39064.6	+	28791.1i	−0.0766279	+	0.0564757i
$715$	187760.			0.367274
$716$			24968.1i			0.0487035i
$717$	216680.	+	293998.i	0.421483	+	0.571881i
$718$	−852646.			−1.65394
$719$			246147.i			0.476143i	0.971248	+	0.238072i	$0.0765153\pi$
$719$			246147.i			0.476143i	−0.971248	+	0.238072i	$0.923485\pi$
$720$	−371431.	−	115110.i	−0.716495	−	0.222049i
$721$	−217046.			−0.417523
$722$		−	473942.i		−	0.909181i
$723$	−66214.0	+	48800.5i	−0.126670	+	0.0933571i
$724$	−545.768			−0.00104119
$725$			402475.i			0.765707i
$726$	−426786.	−	579077.i	−0.809724	−	1.09866i
$727$	229472.			0.434170			0.217085	−	0.976153i	$-0.430345\pi$
$727$	229472.			0.434170			0.217085	+	0.976153i	$0.430345\pi$
$728$			44573.7i			0.0841038i
$729$	−416810.	+	329695.i	−0.784302	+	0.620379i
$730$	−473889.			−0.889265
$731$			117517.i			0.219921i
$732$	−2984.90	+	2199.90i	−0.00557067	+	0.00410565i
$733$	876734.			1.63177			0.815887	−	0.578212i	$-0.196249\pi$
$733$	876734.			1.63177			0.815887	+	0.578212i	$0.196249\pi$
$734$			555566.i			1.03120i
$735$	−211150.	−	286494.i	−0.390855	−	0.530324i
$736$	85420.4			0.157691
$737$		−	308660.i		−	0.568257i
$738$	−70356.5	+	227023.i	−0.129179	+	0.416828i
$739$	−854572.			−1.56480			−0.782402	−	0.622774i	$-0.786006\pi$
$739$	−854572.			−1.56480			−0.782402	+	0.622774i	$0.786006\pi$
$740$		−	16773.6i		−	0.0306311i
$741$	−52540.4	+	38722.9i	−0.0956880	+	0.0705231i
$742$	−9828.27			−0.0178513
$743$		−	865819.i		−	1.56837i	−0.620525	−	0.784186i	$-0.713081\pi$
$743$		−	865819.i		−	1.56837i	0.620525	−	0.784186i	$-0.286919\pi$
$744$	140550.	+	190703.i	0.253914	+	0.344518i
$745$	−69770.7			−0.125707
$746$		−	320436.i		−	0.575790i
$747$	−67772.5	−	21003.4i	−0.121454	−	0.0376398i
$748$	−21236.0			−0.0379550
$749$		−	118096.i		−	0.210510i
$750$	−496043.	+	365590.i	−0.881855	+	0.649937i
$751$	−872834.			−1.54757			−0.773787	−	0.633446i	$-0.781640\pi$
$751$	−872834.			−1.54757			−0.773787	+	0.633446i	$0.781640\pi$
$752$			946407.i			1.67356i
$753$	−325660.	−	441866.i	−0.574348	−	0.779293i
$754$	305980.			0.538209
$755$			671106.i			1.17733i
$756$	−3313.65	−	9530.53i	−0.00579779	−	0.0166753i
$757$	624163.			1.08920			0.544598	−	0.838697i	$-0.316682\pi$
$757$	624163.			1.08920			0.544598	+	0.838697i	$0.316682\pi$
$758$		−	780248.i		−	1.35798i
$759$	−807048.	+	594804.i	−1.40093	+	1.03250i
$760$	−136124.			−0.235671
$761$			974256.i			1.68230i	0.540801	+	0.841151i	$0.318121\pi$
$761$			974256.i			1.68230i	−0.540801	+	0.841151i	$0.681879\pi$
$762$	−274921.	−	373022.i	−0.473476	−	0.642428i
$763$	−67935.3			−0.116693
$764$		−	65379.7i		−	0.112010i
$765$	44011.5	−	142014.i	0.0752043	−	0.242665i
$766$	−483995.			−0.824866
$767$			26204.3i			0.0445433i
$768$	98006.3	−	72231.7i	0.166162	−	0.122463i
$769$	−21774.8			−0.0368216			−0.0184108	−	0.999831i	$-0.505861\pi$
$769$	−21774.8			−0.0368216			−0.0184108	+	0.999831i	$0.505861\pi$
$770$			168067.i			0.283465i
$771$	576958.	+	782834.i	0.970589	+	1.31693i
$772$	−68154.2			−0.114356
$773$		−	225670.i		−	0.377672i	−0.982009	−	0.188836i	$-0.939528\pi$
$773$		−	225670.i		−	0.377672i	0.982009	−	0.188836i	$-0.0604715\pi$
$774$	−360970.	−	111868.i	−0.602545	−	0.186735i
$775$	134417.			0.223795
$776$			931244.i			1.54647i
$777$	−78037.6	+	57514.6i	−0.129259	+	0.0952656i
$778$	17564.7			0.0290189
$779$			88979.3i			0.146627i
$780$	6016.68	+	8163.62i	0.00988935	+	0.0134182i
$781$	662331.			1.08586
$782$			260431.i			0.425872i
$783$	880989.	−	306309.i	1.43697	−	0.499616i
$784$	611539.			0.994928
$785$		−	92713.6i		−	0.150454i
$786$	488340.	−	359912.i	0.790455	−	0.582574i
$787$	−313013.			−0.505374			−0.252687	−	0.967548i	$-0.581314\pi$
$787$	−313013.			−0.505374			−0.252687	+	0.967548i	$0.581314\pi$
$788$			26459.1i			0.0426110i
$789$	292907.	+	397425.i	0.470517	+	0.638413i
$790$	−528518.			−0.846848
$791$			250098.i			0.399721i
$792$	−272217.	+	878376.i	−0.433976	+	1.40033i
$793$	−21538.7			−0.0342510
$794$			257905.i			0.409090i
$795$	24239.3	−	17864.6i	0.0383518	−	0.0282657i
$796$	−48611.1			−0.0767202
$797$			92467.9i			0.145571i	0.997348	+	0.0727854i	$0.0231888\pi$
$797$			92467.9i			0.145571i	−0.997348	+	0.0727854i	$0.976811\pi$
$798$	−34661.4	−	47029.7i	−0.0544303	−	0.0738527i
$799$	−361852.			−0.566809
$800$		−	44456.4i		−	0.0694632i
$801$	35171.8	+	10900.1i	0.0548188	+	0.0169889i
$802$	294690.			0.458160
$803$			1.19852e6i			1.85871i
$804$	13420.2	−	9890.87i	0.0207610	−	0.0153011i
$805$	133267.			0.205651
$806$		−	102190.i		−	0.157304i
$807$	−519512.	−	704890.i	−0.797716	−	1.08237i
$808$	599331.			0.918003
$809$		−	739752.i		−	1.13029i	−0.824992	−	0.565144i	$-0.808821\pi$
$809$		−	739752.i		−	1.13029i	0.824992	−	0.565144i	$-0.191179\pi$
$810$	394318.	+	270374.i	0.601004	+	0.412093i
$811$	294759.			0.448151			0.224076	−	0.974572i	$-0.428064\pi$
$811$	294759.			0.448151			0.224076	+	0.974572i	$0.428064\pi$
$812$			17709.0i			0.0268585i
$813$	−268850.	+	198145.i	−0.406751	+	0.299780i
$814$	−656102.			−0.990198
$815$		−	258214.i		−	0.388745i
$816$	151568.	+	205652.i	0.227629	+	0.308854i
$817$	−141479.			−0.211957
$818$		−	1.11475e6i		−	1.66598i
$819$	17350.0	−	55984.1i	0.0258662	−	0.0834636i
$820$	13825.4			0.0205613
$821$		−	975211.i		−	1.44681i	−0.690422	−	0.723406i	$-0.742575\pi$
$821$		−	975211.i		−	1.44681i	0.690422	−	0.723406i	$-0.257425\pi$
$822$	456024.	−	336095.i	0.674908	−	0.497415i
$823$	1.09314e6			1.61390			0.806949	−	0.590620i	$-0.201117\pi$
$823$	1.09314e6			1.61390			0.806949	+	0.590620i	$0.201117\pi$
$824$			1.06841e6i			1.57356i
$825$	309562.	+	420023.i	0.454820	+	0.617113i
$826$	−23455.9			−0.0343789
$827$			37499.5i			0.0548295i	0.999624	+	0.0274147i	$0.00872748\pi$
$827$			37499.5i			0.0548295i	−0.999624	+	0.0274147i	$0.991273\pi$
$828$	−51723.0	−	16029.5i	−0.0754438	−	0.0233808i
$829$	1.21753e6			1.77162			0.885809	−	0.464049i	$-0.153604\pi$
$829$	1.21753e6			1.77162			0.885809	+	0.464049i	$0.153604\pi$
$830$			63832.3i			0.0926582i
$831$	−622904.	+	459087.i	−0.902026	+	0.664803i
$832$	218282.			0.315335
$833$			233817.i			0.336966i
$834$	−223344.	−	303040.i	−0.321101	−	0.435680i
$835$	367856.			0.527600
$836$		−	25565.9i		−	0.0365804i
$837$	−102300.	−	294229.i	−0.146024	−	0.419986i
$838$	−183946.			−0.261940
$839$			1.28850e6i			1.83046i	0.402928	+	0.915232i	$0.367993\pi$
$839$			1.28850e6i			1.83046i	−0.402928	+	0.915232i	$0.632007\pi$
$840$	98401.1	−	72522.8i	0.139457	−	0.102782i
$841$	−929715.			−1.31449
$842$			329063.i			0.464147i
$843$	−515824.	−	699886.i	−0.725849	−	0.984854i
$844$	28882.2			0.0405457
$845$		−	444311.i		−	0.622262i
$846$	344457.	−	1.11148e6i	0.481276	−	1.55296i
$847$	241839.			0.337101
$848$			51740.1i			0.0719508i
$849$	−932356.	+	687157.i	−1.29350	+	0.953324i
$850$	135540.			0.187598
$851$			520251.i			0.718380i
$852$	21224.1	+	28797.5i	0.0292382	+	0.0396713i
$853$	377623.			0.518992			0.259496	−	0.965744i	$-0.416444\pi$
$853$	377623.			0.518992			0.259496	+	0.965744i	$0.416444\pi$
$854$		−	19279.6i		−	0.0264352i
$855$	170970.	+	52985.2i	0.233877	+	0.0724807i
$856$	−581328.			−0.793367
$857$			597599.i			0.813669i	0.913502	+	0.406835i	$0.133367\pi$
$857$			597599.i			0.813669i	−0.913502	+	0.406835i	$0.866633\pi$
$858$	319321.	−	235343.i	0.433764	−	0.319689i
$859$	−794159.			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$859$	−794159.			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$860$			21982.7i			0.0297224i
$861$	−47405.6	−	64321.4i	−0.0639475	−	0.0867659i
$862$	−295268.			−0.397376
$863$		−	862132.i		−	1.15758i	−0.815475	−	0.578792i	$-0.803524\pi$
$863$		−	862132.i		−	1.15758i	0.815475	−	0.578792i	$-0.196476\pi$
$864$	−97312.0	+	33834.2i	−0.130358	+	0.0453240i
$865$	703369.			0.940051
$866$		−	856288.i		−	1.14178i
$867$	526473.	−	388017.i	0.700387	−	0.516193i
$868$	5914.39			0.00785001
$869$			1.33668e6i			1.77006i
$870$	−497839.	−	675484.i	−0.657735	−	0.892435i
$871$	96839.0			0.127648
$872$			334412.i			0.439793i
$873$	362481.	−	1.16963e6i	0.475616	−	1.53469i
$874$	−313532.			−0.410449
$875$		−	207162.i		−	0.270579i
$876$	−52110.3	+	38405.9i	−0.0679072	+	0.0500484i
$877$	756855.			0.984042			0.492021	−	0.870583i	$-0.336258\pi$
$877$	756855.			0.984042			0.492021	+	0.870583i	$0.336258\pi$
$878$			770473.i			0.999466i
$879$	−152191.	−	206497.i	−0.196975	−	0.267261i
$880$	884773.			1.14253
$881$		−	754579.i		−	0.972194i	−0.873905	−	0.486097i	$-0.838420\pi$
$881$		−	754579.i		−	0.972194i	0.873905	−	0.486097i	$-0.161580\pi$
$882$	−718200.	−	222577.i	−0.923227	−	0.286117i
$883$	1.04573e6			1.34121			0.670607	−	0.741813i	$-0.266034\pi$
$883$	1.04573e6			1.34121			0.670607	+	0.741813i	$0.266034\pi$
$884$		−	6662.59i		−	0.00852586i
$885$	57848.8	−	42635.2i	0.0738598	−	0.0544355i
$886$	−57137.8			−0.0727874
$887$		−	13006.9i		−	0.0165320i	−0.999966	−	0.00826600i	$-0.997369\pi$
$887$		−	13006.9i		−	0.0165320i	0.999966	−	0.00826600i	$-0.00263118\pi$
$888$	283116.	+	384140.i	0.359036	+	0.487152i
$889$	155785.			0.197116
$890$		−	33126.9i		−	0.0418217i
$891$	683804.	−	997273.i	0.861344	−	1.25620i
$892$	−24956.1			−0.0313651
$893$		−	435632.i		−	0.546282i
$894$	−118658.	+	87452.5i	−0.148465	+	0.109420i
$895$	397738.			0.496537
$896$			223685.i			0.278625i
$897$	−186614.	−	253204.i	−0.231931	−	0.314691i
$898$	−374055.			−0.463855
$899$			546718.i			0.676463i
$900$	−8342.43	+	26918.9i	−0.0102993	+	0.0332332i
$901$	−19782.4			−0.0243686
$902$		−	540783.i		−	0.664675i
$903$	102272.	−	75375.9i	0.125425	−	0.0924393i
$904$	1.23111e6			1.50647
$905$			8693.99i			0.0106151i
$906$	841183.	+	1.14134e6i	1.02479	+	1.39046i
$907$	−368951.			−0.448491			−0.224246	−	0.974533i	$-0.571992\pi$
$907$	−368951.			−0.448491			−0.224246	+	0.974533i	$0.571992\pi$
$908$		−	37895.8i		−	0.0459642i
$909$	−752753.	−	233286.i	−0.911014	−	0.282332i
$910$	−52729.2			−0.0636750
$911$			180909.i			0.217984i	0.994043	+	0.108992i	$0.0347622\pi$
$911$			180909.i			0.217984i	−0.994043	+	0.108992i	$0.965238\pi$
$912$	−247584.	+	182472.i	−0.297669	+	0.219385i
$913$	161438.			0.193671
$914$			904437.i			1.08264i
$915$	35044.1	+	47549.0i	0.0418575	+	0.0567935i
$916$	74690.0			0.0890167
$917$			203945.i			0.242535i
$918$	−103154.	−	296687.i	−0.122406	−	0.352057i
$919$	1.51036e6			1.78834			0.894170	−	0.447727i	$-0.147766\pi$
$919$	1.51036e6			1.78834			0.894170	+	0.447727i	$0.147766\pi$
$920$		−	656009.i		−	0.775057i
$921$	−439581.	+	323976.i	−0.518226	+	0.381939i
$922$	1.11449e6			1.31104
$923$			207800.i			0.243917i
$924$	13620.8	+	18481.1i	0.0159536	+	0.0216463i
$925$	270761.			0.316449
$926$		−	509016.i		−	0.593621i
$927$	415871.	−	1.34191e6i	0.483948	−	1.56158i
$928$	180819.			0.209965
$929$			851777.i			0.986949i	0.869760	+	0.493474i	$0.164273\pi$
$929$			851777.i			0.986949i	−0.869760	+	0.493474i	$0.835727\pi$
$930$	−225596.	+	166266.i	−0.260834	+	0.192238i
$931$	−281492.			−0.324763
$932$		−	99456.0i		−	0.114498i
$933$	−323557.	−	439012.i	−0.371696	−	0.504328i
$934$	188638.			0.216239
$935$			338286.i			0.386955i
$936$	−275582.	−	85405.5i	−0.314557	−	0.0974842i
$937$	1.23799e6			1.41007			0.705033	−	0.709175i	$-0.250932\pi$
$937$	1.23799e6			1.41007			0.705033	+	0.709175i	$0.250932\pi$
$938$			86682.0i			0.0985197i
$939$	549462.	−	404960.i	0.623170	−	0.459284i
$940$	−67687.5			−0.0766043
$941$		−	526977.i		−	0.595131i	−0.954701	−	0.297565i	$-0.903825\pi$
$941$		−	526977.i		−	0.595131i	0.954701	−	0.297565i	$-0.0961746\pi$
$942$	−116210.	−	157677.i	−0.130961	−	0.177692i
$943$	−428810.			−0.482216
$944$			123482.i			0.138566i
$945$	−151820.	+	52785.9i	−0.170006	+	0.0591091i
$946$	859855.			0.960822
$947$		−	274192.i		−	0.305742i	−0.988246	−	0.152871i	$-0.951148\pi$
$947$		−	274192.i		−	0.305742i	0.988246	−	0.152871i	$-0.0488519\pi$
$948$	−58117.5	+	42833.2i	−0.0646681	+	0.0476611i
$949$	−376022.			−0.417524
$950$			163176.i			0.180804i
$951$	505367.	+	685698.i	0.558787	+	0.758179i
$952$	−80308.3			−0.0886107
$953$		−	1.06008e6i		−	1.16722i	−0.812034	−	0.583611i	$-0.801639\pi$
$953$		−	1.06008e6i		−	1.16722i	0.812034	−	0.583611i	$-0.198361\pi$
$954$	18831.5	−	60764.4i	0.0206913	−	0.0667656i
$955$	−1.04149e6			−1.14195
$956$		−	44883.0i		−	0.0491096i
$957$	−1.70837e6	+	1.25909e6i	−1.86534	+	1.37478i
$958$	−628658.			−0.684989
$959$			190449.i			0.207082i
$960$	−355152.	−	481881.i	−0.385365	−	0.522875i
$961$	−740930.			−0.802289
$962$		−	205845.i		−	0.222429i
$963$	730142.	+	226278.i	0.787327	+	0.244000i
$964$	10108.5			0.0108776
$965$			1.08569e6i			1.16587i
$966$	226646.	−	167041.i	0.242881	−	0.179006i
$967$	−368383.			−0.393955			−0.196978	−	0.980408i	$-0.563113\pi$
$967$	−368383.			−0.393955			−0.196978	+	0.980408i	$0.563113\pi$
$968$		−	1.19045e6i		−	1.27046i
$969$	−69766.9	−	94661.9i	−0.0743023	−	0.100816i
$970$	−1.10163e6			−1.17083
$971$		−	532568.i		−	0.564854i	−0.959289	−	0.282427i	$-0.908860\pi$
$971$		−	532568.i		−	0.564854i	0.959289	−	0.282427i	$-0.0911396\pi$
$972$	65272.7	−	2226.00i	0.0690874	−	0.00235610i
$973$	126558.			0.133679
$974$			1.67429e6i			1.76487i
$975$	−131778.	+	97122.0i	−0.138623	+	0.102166i
$976$	−101496.			−0.106549
$977$		−	1.75207e6i		−	1.83553i	−0.397120	−	0.917767i	$-0.629990\pi$
$977$		−	1.75207e6i		−	1.83553i	0.397120	−	0.917767i	$-0.370010\pi$
$978$	−323653.	−	439142.i	−0.338378	−	0.459121i
$979$	−83781.5			−0.0874143
$980$			43737.5i			0.0455410i
$981$	130168.	−	420018.i	0.135259	−	0.436445i
$982$	−1.48398e6			−1.53888
$983$		−	1.27331e6i		−	1.31773i	−0.752259	−	0.658867i	$-0.771036\pi$
$983$		−	1.27331e6i		−	1.31773i	0.752259	−	0.658867i	$-0.228964\pi$
$984$	−316622.	+	233354.i	−0.327003	+	0.241005i
$985$	421489.			0.434424
$986$			551284.i			0.567050i
$987$	232092.	+	314910.i	0.238246	+	0.323260i
$988$	8021.06			0.00821709
$989$		−	681816.i		−	0.697067i
$990$	−1.03909e6	−	322024.i	−1.06019	−	0.328563i
$991$	870743.			0.886630			0.443315	−	0.896366i	$-0.353802\pi$
$991$	870743.			0.886630			0.443315	+	0.896366i	$0.353802\pi$
$992$		−	60389.2i		−	0.0613671i
$993$	567730.	−	418424.i	0.575763	−	0.424344i
$994$	−186005.			−0.188257
$995$			774368.i			0.782170i
$996$	5173.23	+	7019.19i	0.00521486	+	0.00707569i
$997$	−776903.			−0.781585			−0.390793	−	0.920479i	$-0.627799\pi$
$997$	−776903.			−0.781585			−0.390793	+	0.920479i	$0.627799\pi$
$998$		−	1.64523e6i		−	1.65183i
$999$	−206067.	−	592677.i	−0.206479	−	0.593865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.58	yes	78
3.2	odd	2	inner	177.5.b.a.119.21	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.21	✓	78	3.2	odd	2	inner
177.5.b.a.119.58	yes	78	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.13595i q^{2} +(7.24492 - 5.33959i) q^{3} -1.10604 q^{4} +17.6191i q^{5} +(22.0842 + 29.9646i) q^{6} -12.5141 q^{7} +61.6006i q^{8} +(23.9776 - 77.3697i) q^{9} +O(q^{10})\)	\(q+4.13595i q^{2} +(7.24492 - 5.33959i) q^{3} -1.10604 q^{4} +17.6191i q^{5} +(22.0842 + 29.9646i) q^{6} -12.5141 q^{7} +61.6006i q^{8} +(23.9776 - 77.3697i) q^{9} -72.8715 q^{10} +184.300i q^{11} +(-8.01318 + 5.90581i) q^{12} -57.8222 q^{13} -51.7575i q^{14} +(94.0786 + 127.649i) q^{15} -272.473 q^{16} -104.178i q^{17} +(319.997 + 99.1702i) q^{18} +125.420 q^{19} -19.4874i q^{20} +(-90.6634 + 66.8200i) q^{21} -762.253 q^{22} +604.424i q^{23} +(328.922 + 446.291i) q^{24} +314.568 q^{25} -239.150i q^{26} +(-239.406 - 688.568i) q^{27} +13.8411 q^{28} +1279.45i q^{29} +(-527.948 + 389.104i) q^{30} +427.306 q^{31} -141.325i q^{32} +(984.084 + 1335.24i) q^{33} +430.875 q^{34} -220.486i q^{35} +(-26.5203 + 85.5741i) q^{36} +860.739 q^{37} +518.729i q^{38} +(-418.917 + 308.747i) q^{39} -1085.35 q^{40} +709.453i q^{41} +(-276.364 - 374.979i) q^{42} -1128.04 q^{43} -203.843i q^{44} +(1363.18 + 422.464i) q^{45} -2499.86 q^{46} -3473.39i q^{47} +(-1974.05 + 1454.90i) q^{48} -2244.40 q^{49} +1301.04i q^{50} +(-556.268 - 754.762i) q^{51} +63.9538 q^{52} -189.891i q^{53} +(2847.88 - 990.172i) q^{54} -3247.19 q^{55} -770.875i q^{56} +(908.655 - 669.689i) q^{57} -5291.74 q^{58} -453.188i q^{59} +(-104.055 - 141.185i) q^{60} +372.499 q^{61} +1767.32i q^{62} +(-300.058 + 968.211i) q^{63} -3775.06 q^{64} -1018.77i q^{65} +(-5522.46 + 4070.12i) q^{66} -1674.77 q^{67} +115.225i q^{68} +(3227.37 + 4379.00i) q^{69} +911.920 q^{70} -3593.77i q^{71} +(4766.02 + 1477.04i) q^{72} +6503.08 q^{73} +3559.97i q^{74} +(2279.02 - 1679.66i) q^{75} -138.719 q^{76} -2306.34i q^{77} +(-1276.96 - 1732.62i) q^{78} +7252.73 q^{79} -4800.73i q^{80} +(-5411.15 - 3710.28i) q^{81} -2934.26 q^{82} -875.956i q^{83} +(100.278 - 73.9057i) q^{84} +1835.52 q^{85} -4665.53i q^{86} +(6831.74 + 9269.52i) q^{87} -11353.0 q^{88} +454.594i q^{89} +(-1747.29 + 5638.05i) q^{90} +723.592 q^{91} -668.518i q^{92} +(3095.80 - 2281.64i) q^{93} +14365.8 q^{94} +2209.78i q^{95} +(-754.618 - 1023.89i) q^{96} +15117.5 q^{97} -9282.71i q^{98} +(14259.2 + 4419.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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