LMFDB - Embedded newform 27.7.d.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not 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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 75 x^{8} - 2 x^{7} + 4610 x^{6} - 2412 x^{5} + 66932 x^{4} - 174032 x^{3} + \cdots + 1982464 $ x^10 - x^9 + 75x^8 - 2x^7 + 4610x^6 - 2412x^5 + 66932x^4 - 174032x^3 + 870720x^2 - 1272832x + 1982464
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$-2.32209 + 4.02197i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.7.d.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.96626 + 4.02197i) q^{2} +(0.352523 - 0.610587i) q^{4} +(-80.3236 - 46.3749i) q^{5} +(60.0074 + 103.936i) q^{7} -509.141i q^{8} +O(q^{10})$	\(q+(-6.96626 + 4.02197i) q^{2} +(0.352523 - 0.610587i) q^{4} +(-80.3236 - 46.3749i) q^{5} +(60.0074 + 103.936i) q^{7} -509.141i q^{8} +746.074 q^{10} +(1299.95 - 750.527i) q^{11} +(2142.08 - 3710.18i) q^{13} +(-836.055 - 482.697i) q^{14} +(2070.31 + 3585.89i) q^{16} +940.477i q^{17} -8397.07 q^{19} +(-56.6318 + 32.6964i) q^{20} +(-6037.20 + 10456.7i) q^{22} +(-7822.55 - 4516.35i) q^{23} +(-3511.24 - 6081.65i) q^{25} +34461.5i q^{26} +84.6160 q^{28} +(11618.5 - 6707.92i) q^{29} +(6751.04 - 11693.1i) q^{31} +(-625.213 - 360.967i) q^{32} +(-3782.57 - 6551.61i) q^{34} -11131.3i q^{35} +39037.3 q^{37} +(58496.2 - 33772.8i) q^{38} +(-23611.4 + 40896.1i) q^{40} +(-95285.0 - 55012.8i) q^{41} +(-5770.09 - 9994.09i) q^{43} -1058.31i q^{44} +72658.5 q^{46} +(-22839.5 + 13186.4i) q^{47} +(51622.7 - 89413.2i) q^{49} +(48920.5 + 28244.2i) q^{50} +(-1510.26 - 2615.85i) q^{52} +12963.7i q^{53} -139222. q^{55} +(52918.1 - 30552.3i) q^{56} +(-53958.1 + 93458.2i) q^{58} +(160987. + 92945.8i) q^{59} +(48707.2 + 84363.3i) q^{61} +108610. i q^{62} -259193. q^{64} +(-344118. + 198677. i) q^{65} +(48333.5 - 83716.1i) q^{67} +(574.243 + 331.540i) q^{68} +(44770.0 + 77543.9i) q^{70} -264450. i q^{71} -154006. q^{73} +(-271944. + 157007. i) q^{74} +(-2960.16 + 5127.15i) q^{76} +(156013. + 90074.4i) q^{77} +(43195.7 + 74817.2i) q^{79} -384042. i q^{80} +885040. q^{82} +(543967. - 314059. i) q^{83} +(43614.5 - 75542.5i) q^{85} +(80391.9 + 46414.3i) q^{86} +(-382124. - 661858. i) q^{88} -874390. i q^{89} +514162. q^{91} +(-5515.25 + 3184.23i) q^{92} +(106070. - 183719. i) q^{94} +(674483. + 389413. i) q^{95} +(95150.6 + 164806. i) q^{97} +830500. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	$ 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) $ 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−6.96626	+	4.02197i	−0.870783	+	0.502747i	−0.867608	−	0.497248i	$-0.834344\pi$
$2$	−6.96626	+	4.02197i	−0.870783	+	0.502747i	−0.00317434	+	0.999995i	$0.501010\pi$
$3$		0			0
$3$		0			0
$4$	0.352523	−	0.610587i	0.00550817	−	0.00954043i
$5$	−80.3236	−	46.3749i	−0.642589	−	0.370999i	0.143022	−	0.989719i	$-0.454318\pi$
$5$	−80.3236	−	46.3749i	−0.642589	−	0.370999i	−0.785611	+	0.618721i	$0.787651\pi$
$6$		0			0
$7$	60.0074	+	103.936i	0.174949	+	0.303020i	0.940144	−	0.340779i	$-0.110691\pi$
$7$	60.0074	+	103.936i	0.174949	+	0.303020i	−0.765195	+	0.643799i	$0.777357\pi$
$8$		−	509.141i		−	0.994416i
$9$		0			0
$10$	746.074			0.746074
$11$	1299.95	−	750.527i	0.976672	−	0.563882i	0.0754083	−	0.997153i	$-0.475974\pi$
$11$	1299.95	−	750.527i	0.976672	−	0.563882i	0.901264	+	0.433271i	$0.142641\pi$
$12$		0			0
$13$	2142.08	−	3710.18i	0.975000	−	1.68875i	0.295065	−	0.955477i	$-0.404659\pi$
$13$	2142.08	−	3710.18i	0.975000	−	1.68875i	0.679935	−	0.733273i	$-0.262008\pi$
$14$	−836.055	−	482.697i	−0.304685	−	0.175910i
$15$		0			0
$16$	2070.31	+	3585.89i	0.505447	+	0.875461i
$17$			940.477i			0.191426i	0.995409	+	0.0957131i	$0.0305131\pi$
$17$			940.477i			0.191426i	−0.995409	+	0.0957131i	$0.969487\pi$
$18$		0			0
$19$	−8397.07			−1.22424			−0.612121	−	0.790764i	$-0.709683\pi$
$19$	−8397.07			−1.22424			−0.612121	+	0.790764i	$0.709683\pi$
$20$	−56.6318	+	32.6964i	−0.00707898	+	0.00408705i
$21$		0			0
$22$	−6037.20	+	10456.7i	−0.566979	+	0.982037i
$23$	−7822.55	−	4516.35i	−0.642932	−	0.371197i	0.142811	−	0.989750i	$-0.454386\pi$
$23$	−7822.55	−	4516.35i	−0.642932	−	0.371197i	−0.785743	+	0.618553i	$0.787719\pi$
$24$		0			0
$25$	−3511.24	−	6081.65i	−0.224720	−	0.389226i
$26$			34461.5i			1.96071i
$27$		0			0
$28$	84.6160			0.00385459
$29$	11618.5	−	6707.92i	0.476381	−	0.275039i	−0.242526	−	0.970145i	$-0.577976\pi$
$29$	11618.5	−	6707.92i	0.476381	−	0.275039i	0.718907	+	0.695106i	$0.244643\pi$
$30$		0			0
$31$	6751.04	−	11693.1i	0.226613	−	0.392506i	−0.730189	−	0.683245i	$-0.760568\pi$
$31$	6751.04	−	11693.1i	0.226613	−	0.392506i	0.956802	+	0.290740i	$0.0939013\pi$
$32$	−625.213	−	360.967i	−0.0190800	−	0.0110158i
$33$		0			0
$34$	−3782.57	−	6551.61i	−0.0962389	−	0.166691i
$35$		−	11131.3i		−	0.259623i
$36$		0			0
$37$	39037.3			0.770681			0.385341	−	0.922774i	$-0.374084\pi$
$37$	39037.3			0.770681			0.385341	+	0.922774i	$0.374084\pi$
$38$	58496.2	−	33772.8i	1.06605	−	0.615483i
$39$		0			0
$40$	−23611.4	+	40896.1i	−0.368927	+	0.639001i
$41$	−95285.0	−	55012.8i	−1.38253	−	0.798201i	−0.390067	−	0.920786i	$-0.627548\pi$
$41$	−95285.0	−	55012.8i	−1.38253	−	0.798201i	−0.992458	+	0.122585i	$0.960882\pi$
$42$		0			0
$43$	−5770.09	−	9994.09i	−0.0725734	−	0.125701i	0.827455	−	0.561532i	$-0.189788\pi$
$43$	−5770.09	−	9994.09i	−0.0725734	−	0.125701i	−0.900028	+	0.435831i	$0.856454\pi$
$44$		−	1058.31i		−	0.0124238i
$45$		0			0
$46$	72658.5			0.746471
$47$	−22839.5	+	13186.4i	−0.219985	+	0.127008i	−0.605943	−	0.795508i	$-0.707204\pi$
$47$	−22839.5	+	13186.4i	−0.219985	+	0.127008i	0.385959	+	0.922516i	$0.373871\pi$
$48$		0			0
$49$	51622.7	−	89413.2i	0.438786	−	0.759999i
$50$	48920.5	+	28244.2i	0.391364	+	0.225954i
$51$		0			0
$52$	−1510.26	−	2615.85i	−0.0107409	−	0.0186038i
$53$			12963.7i			0.0870766i	0.999052	+	0.0435383i	$0.0138631\pi$
$53$			12963.7i			0.0870766i	−0.999052	+	0.0435383i	$0.986137\pi$
$54$		0			0
$55$	−139222.			−0.836798
$56$	52918.1	−	30552.3i	0.301328	−	0.173972i
$57$		0			0
$58$	−53958.1	+	93458.2i	−0.276550	+	0.478998i
$59$	160987.	+	92945.8i	0.783853	+	0.452557i	0.837794	−	0.545987i	$-0.183845\pi$
$59$	160987.	+	92945.8i	0.783853	+	0.452557i	−0.0539413	+	0.998544i	$0.517178\pi$
$60$		0			0
$61$	48707.2	+	84363.3i	0.214587	+	0.371676i	0.953145	−	0.302515i	$-0.0978261\pi$
$61$	48707.2	+	84363.3i	0.214587	+	0.371676i	−0.738558	+	0.674190i	$0.764493\pi$
$62$			108610.i			0.455716i
$63$		0			0
$64$	−259193.			−0.988742
$65$	−344118.	+	198677.i	−1.25305	+	0.723448i
$66$		0			0
$67$	48333.5	−	83716.1i	0.160703	−	0.278346i	−0.774418	−	0.632674i	$-0.781957\pi$
$67$	48333.5	−	83716.1i	0.160703	−	0.278346i	0.935121	+	0.354329i	$0.115291\pi$
$68$	574.243	+	331.540i	0.00182629	+	0.00105441i
$69$		0			0
$70$	44770.0	+	77543.9i	0.130525	+	0.226075i
$71$		−	264450.i		−	0.738871i	−0.929256	−	0.369435i	$-0.879551\pi$
$71$		−	264450.i		−	0.738871i	0.929256	−	0.369435i	$-0.120449\pi$
$72$		0			0
$73$	−154006.			−0.395885			−0.197942	−	0.980214i	$-0.563426\pi$
$73$	−154006.			−0.395885			−0.197942	+	0.980214i	$0.563426\pi$
$74$	−271944.	+	157007.i	−0.671096	+	0.387457i
$75$		0			0
$76$	−2960.16	+	5127.15i	−0.00674333	+	0.0116798i
$77$	156013.	+	90074.4i	0.341735	+	0.197301i
$78$		0			0
$79$	43195.7	+	74817.2i	0.0876112	+	0.151747i	0.906501	−	0.422204i	$-0.138743\pi$
$79$	43195.7	+	74817.2i	0.0876112	+	0.151747i	−0.818890	+	0.573951i	$0.805410\pi$
$80$		−	384042.i		−	0.750082i
$81$		0			0
$82$	885040.			1.60517
$83$	543967.	−	314059.i	0.951345	−	0.549259i	0.0578467	−	0.998325i	$-0.481577\pi$
$83$	543967.	−	314059.i	0.951345	−	0.549259i	0.893499	+	0.449066i	$0.148243\pi$
$84$		0			0
$85$	43614.5	−	75542.5i	0.0710189	−	0.123008i
$86$	80391.9	+	46414.3i	0.126391	+	0.0729720i
$87$		0			0
$88$	−382124.	−	661858.i	−0.560733	−	0.971219i
$89$		−	874390.i		−	1.24032i	−0.784474	−	0.620162i	$-0.787067\pi$
$89$		−	874390.i		−	1.24032i	0.784474	−	0.620162i	$-0.212933\pi$
$90$		0			0
$91$	514162.			0.682300
$92$	−5515.25	+	3184.23i	−0.00708275	+	0.00408923i
$93$		0			0
$94$	106070.	−	183719.i	0.127706	−	0.221193i
$95$	674483.	+	389413.i	0.786684	+	0.454192i
$96$		0			0
$97$	95150.6	+	164806.i	0.104255	+	0.180575i	0.913434	−	0.406988i	$-0.133421\pi$
$97$	95150.6	+	164806.i	0.104255	+	0.180575i	−0.809179	+	0.587563i	$0.800088\pi$
$98$			830500.i			0.882392i
$99$		0			0
$100$	−4951.17			−0.00495117
$101$	−983657.	+	567915.i	−0.954728	+	0.551213i	−0.894547	−	0.446975i	$-0.852501\pi$
$101$	−983657.	+	567915.i	−0.954728	+	0.551213i	−0.0601817	+	0.998187i	$0.519168\pi$
$102$		0			0
$103$	−555871.	+	962798.i	−0.508701	+	0.881096i	0.491248	+	0.871020i	$0.336541\pi$
$103$	−555871.	+	962798.i	−0.508701	+	0.881096i	−0.999949	+	0.0100765i	$0.996792\pi$
$104$	−1.88901e6	−	1.09062e6i	−1.67932	−	0.969556i
$105$		0			0
$106$	−52139.6	−	90308.5i	−0.0437775	−	0.0758248i
$107$			1.27312e6i			1.03924i	0.854396	+	0.519622i	$0.173927\pi$
$107$			1.27312e6i			1.03924i	−0.854396	+	0.519622i	$0.826073\pi$
$108$		0			0
$109$	−1.87984e6			−1.45158			−0.725792	−	0.687915i	$-0.758526\pi$
$109$	−1.87984e6			−1.45158			−0.725792	+	0.687915i	$0.758526\pi$
$110$	969859.	−	559948.i	0.728669	−	0.420697i
$111$		0			0
$112$	−248468.	+	430360.i	−0.176855	+	0.306322i
$113$	1.21138e6	+	699388.i	0.839544	+	0.484711i	0.857109	−	0.515135i	$-0.172258\pi$
$113$	1.21138e6	+	699388.i	0.839544	+	0.484711i	−0.0175650	+	0.999846i	$0.505591\pi$
$114$		0			0
$115$	418890.	+	725539.i	0.275427	+	0.477054i
$116$		−	9458.78i		−	0.00605984i
$117$		0			0
$118$	−1.49530e6			−0.910087
$119$	−97749.4	+	56435.6i	−0.0580060	+	0.0334898i
$120$		0			0
$121$	240800.	−	417079.i	0.135926	−	0.235430i
$122$	−678614.	−	391798.i	−0.373717	−	0.215766i
$123$		0			0
$124$	−4759.79	−	8244.19i	−0.00249645	−	0.00432397i
$125$			2.10055e6i			1.07548i
$126$		0			0
$127$	2.84521e6			1.38900			0.694501	−	0.719491i	$-0.255625\pi$
$127$	2.84521e6			1.38900			0.694501	+	0.719491i	$0.255625\pi$
$128$	1.84562e6	−	1.06557e6i	0.880060	−	0.508103i
$129$		0			0
$130$	1.59815e6	−	2.76807e6i	0.727422	−	1.25993i
$131$	−1.24280e6	−	717533.i	−0.552827	−	0.319175i	0.197435	−	0.980316i	$-0.436739\pi$
$131$	−1.24280e6	−	717533.i	−0.552827	−	0.319175i	−0.750261	+	0.661141i	$0.770072\pi$
$132$		0			0
$133$	−503887.	−	872757.i	−0.214180	−	0.370970i
$134$			777584.i			0.323172i
$135$		0			0
$136$	478836.			0.190357
$137$	485772.	−	280461.i	0.188917	−	0.109071i	−0.402558	−	0.915394i	$-0.631879\pi$
$137$	485772.	−	280461.i	0.188917	−	0.109071i	0.591475	+	0.806323i	$0.298546\pi$
$138$		0			0
$139$	−409282.	+	708898.i	−0.152398	+	0.263961i	−0.932108	−	0.362179i	$-0.882033\pi$
$139$	−409282.	+	708898.i	−0.152398	+	0.263961i	0.779711	+	0.626140i	$0.215366\pi$
$140$	−6796.66	−	3924.05i	−0.00247692	−	0.00143005i
$141$		0			0
$142$	1.06361e6	+	1.84223e6i	0.371465	+	0.643396i
$143$		−	6.43074e6i		−	2.19914i
$144$		0			0
$145$	−1.24432e6			−0.408156
$146$	1.07284e6	−	619407.i	0.344729	−	0.199030i
$147$		0			0
$148$	13761.5	−	23835.7i	0.00424504	−	0.00735263i
$149$	−2.45815e6	−	1.41921e6i	−0.743104	−	0.429032i	0.0800926	−	0.996787i	$-0.474478\pi$
$149$	−2.45815e6	−	1.41921e6i	−0.743104	−	0.429032i	−0.823197	+	0.567756i	$0.807812\pi$
$150$		0			0
$151$	881580.	+	1.52694e6i	0.256054	+	0.443498i	0.965181	−	0.261582i	$-0.0842443\pi$
$151$	881580.	+	1.52694e6i	0.256054	+	0.443498i	−0.709127	+	0.705080i	$0.750911\pi$
$152$			4.27529e6i			1.21741i
$153$		0			0
$154$	−1.44911e6			−0.396769
$155$	−1.08454e6	+	626157.i	−0.291238	+	0.168147i
$156$		0			0
$157$	215379.	−	373048.i	0.0556551	−	0.0963974i	−0.836856	−	0.547424i	$-0.815609\pi$
$157$	215379.	−	373048.i	0.0556551	−	0.0963974i	0.892511	+	0.451026i	$0.148942\pi$
$158$	−601825.	−	347464.i	−0.152581	−	0.0880924i
$159$		0			0
$160$	33479.6	+	57988.3i	0.00817373	+	0.0141573i
$161$		−	1.08406e6i		−	0.259762i
$162$		0			0
$163$	4.87338e6			1.12530			0.562649	−	0.826696i	$-0.309782\pi$
$163$	4.87338e6			1.12530			0.562649	+	0.826696i	$0.309782\pi$
$164$	−67180.3	+	38786.6i	−0.0152304	+	0.00879325i
$165$		0			0
$166$	−2.52628e6	+	4.37564e6i	−0.552277	+	0.956571i
$167$	6.72564e6	+	3.88305e6i	1.44406	+	0.833726i	0.998117	−	0.0613369i	$-0.0195364\pi$
$167$	6.72564e6	+	3.88305e6i	1.44406	+	0.833726i	0.445939	+	0.895063i	$0.352870\pi$
$168$		0			0
$169$	−6.76357e6	−	1.17148e7i	−1.40125	−	2.42704i
$170$			701665.i			0.142818i
$171$		0			0
$172$	−8136.35			−0.00159898
$173$	−6.09924e6	+	3.52140e6i	−1.17798	+	0.680106i	−0.955546	−	0.294842i	$-0.904733\pi$
$173$	−6.09924e6	+	3.52140e6i	−1.17798	+	0.680106i	−0.222432	+	0.974948i	$0.571400\pi$
$174$		0			0
$175$	421401.	−	729889.i	0.0786289	−	0.136189i
$176$	5.38261e6	+	3.10765e6i	0.987313	+	0.570025i
$177$		0			0
$178$	3.51677e6	+	6.09123e6i	0.623568	+	1.08005i
$179$		−	352194.i		−	0.0614077i	−0.999529	−	0.0307039i	$-0.990225\pi$
$179$		−	352194.i		−	0.0614077i	0.999529	−	0.0307039i	$-0.00977488\pi$
$180$		0			0
$181$	−503263.			−0.0848710			−0.0424355	−	0.999099i	$-0.513512\pi$
$181$	−503263.			−0.0848710			−0.0424355	+	0.999099i	$0.513512\pi$
$182$	−3.58179e6	+	2.06794e6i	−0.594135	+	0.343024i
$183$		0			0
$184$	−2.29946e6	+	3.98278e6i	−0.369124	+	0.639342i
$185$	−3.13562e6	−	1.81035e6i	−0.495231	−	0.285922i
$186$		0			0
$187$	705853.	+	1.22257e6i	0.107942	+	0.186961i
$188$			18594.0i			0.00279833i
$189$		0			0
$190$	−6.26483e6			−0.913374
$191$	5.51607e6	−	3.18470e6i	0.791643	−	0.457055i	−0.0488977	−	0.998804i	$-0.515571\pi$
$191$	5.51607e6	−	3.18470e6i	0.791643	−	0.457055i	0.840541	+	0.541749i	$0.182237\pi$
$192$		0			0
$193$	−1.35056e6	+	2.33925e6i	−0.187864	+	0.325390i	−0.944538	−	0.328403i	$-0.893490\pi$
$193$	−1.35056e6	+	2.33925e6i	−0.187864	+	0.325390i	0.756674	+	0.653792i	$0.226823\pi$
$194$	−1.32569e6	−	765386.i	−0.181567	−	0.104827i
$195$		0			0
$196$	−36396.4	−	63040.3i	−0.00483381	−	0.00837241i
$197$		−	5.74167e6i		−	0.750999i	−0.926823	−	0.375499i	$-0.877471\pi$
$197$		−	5.74167e6i		−	0.750999i	0.926823	−	0.375499i	$-0.122529\pi$
$198$		0			0
$199$	−7.52739e6			−0.955180			−0.477590	−	0.878583i	$-0.658490\pi$
$199$	−7.52739e6			−0.955180			−0.477590	+	0.878583i	$0.658490\pi$
$200$	−3.09642e6	+	1.78772e6i	−0.387052	+	0.223465i
$201$		0			0
$202$	4.56828e6	−	7.91249e6i	0.554240	−	0.959973i
$203$	1.39439e6	+	805050.i	0.166685	+	0.0962354i
$204$		0			0
$205$	5.10243e6	+	8.83766e6i	0.592264	+	1.02583i
$206$		−	8.94280e6i		−	1.02299i
$207$		0			0
$208$	1.77391e7			1.97125
$209$	−1.09158e7	+	6.30223e6i	−1.19568	+	0.690328i
$210$		0			0
$211$	6.34178e6	−	1.09843e7i	0.675094	−	1.16930i	−0.301348	−	0.953514i	$-0.597437\pi$
$211$	6.34178e6	−	1.09843e7i	0.675094	−	1.16930i	0.976441	−	0.215782i	$-0.0692302\pi$
$212$	7915.47	+	4570.00i	0.000830748	+	0.000479632i
$213$		0			0
$214$	−5.12045e6	−	8.86888e6i	−0.522477	−	0.904956i
$215$			1.07035e6i			0.107699i
$216$		0			0
$217$	1.62045e6			0.158583
$218$	1.30955e7	−	7.56068e6i	1.26401	−	0.729779i
$219$		0			0
$220$	−49079.0	+	85007.4i	−0.00460923	+	0.00798341i
$221$	3.48934e6	+	2.01457e6i	0.323271	+	0.186641i
$222$		0			0
$223$	6.60263e6	+	1.14361e7i	0.595392	+	1.03125i	0.993491	+	0.113906i	$0.0363364\pi$
$223$	6.60263e6	+	1.14361e7i	0.595392	+	1.03125i	−0.398100	+	0.917342i	$0.630330\pi$
$224$		−	86642.8i		−	0.00770883i
$225$		0			0
$226$	−1.12517e7			−0.974747
$227$	1.37632e7	−	7.94620e6i	1.17664	−	0.679332i	0.221403	−	0.975182i	$-0.428936\pi$
$227$	1.37632e7	−	7.94620e6i	1.17664	−	0.679332i	0.955234	+	0.295851i	$0.0956031\pi$
$228$		0			0
$229$	1.57241e6	−	2.72350e6i	0.130936	−	0.226788i	−0.793102	−	0.609089i	$-0.791535\pi$
$229$	1.57241e6	−	2.72350e6i	0.130936	−	0.226788i	0.924038	+	0.382301i	$0.124868\pi$
$230$	−5.83620e6	−	3.36953e6i	−0.479674	−	0.276940i
$231$		0			0
$232$	−3.41528e6	−	5.91544e6i	−0.273503	−	0.473721i
$233$			6.95409e6i			0.549759i	0.961479	+	0.274880i	$0.0886380\pi$
$233$			6.95409e6i			0.549759i	−0.961479	+	0.274880i	$0.911362\pi$
$234$		0			0
$235$	2.44606e6			0.188480
$236$	113503.	−	65531.0i	0.00863518	−	0.00498553i
$237$		0			0
$238$	453965.	−	786290.i	0.0336738	−	0.0583247i
$239$	−2.35289e6	−	1.35844e6i	−0.172349	−	0.0995057i	0.411344	−	0.911480i	$-0.365059\pi$
$239$	−2.35289e6	−	1.35844e6i	−0.172349	−	0.0995057i	−0.583693	+	0.811974i	$0.698393\pi$
$240$		0			0
$241$	1.35533e6	+	2.34750e6i	0.0968266	+	0.167709i	0.910369	−	0.413796i	$-0.135797\pi$
$241$	1.35533e6	+	2.34750e6i	0.0968266	+	0.167709i	−0.813543	+	0.581505i	$0.802464\pi$
$242$			3.87397e6i			0.273344i
$243$		0			0
$244$	68681.6			0.00472793
$245$	−8.29305e6	+	4.78799e6i	−0.563918	+	0.325578i
$246$		0			0
$247$	−1.79872e7	+	3.11547e7i	−1.19364	+	2.06744i
$248$	−5.95346e6	−	3.43723e6i	−0.390314	−	0.225348i
$249$		0			0
$250$	−8.44835e6	−	1.46330e7i	−0.540694	−	0.936510i
$251$			2.84107e7i			1.79664i	0.439342	+	0.898320i	$0.355212\pi$
$251$			2.84107e7i			1.79664i	−0.439342	+	0.898320i	$0.644788\pi$
$252$		0			0
$253$	−1.35586e7			−0.837244
$254$	−1.98205e7	+	1.14434e7i	−1.20952	+	0.698316i
$255$		0			0
$256$	−277202.	+	480127.i	−0.0165225	+	0.0286178i
$257$	−9.70883e6	−	5.60539e6i	−0.571962	−	0.330223i	0.185970	−	0.982555i	$-0.440457\pi$
$257$	−9.70883e6	−	5.60539e6i	−0.571962	−	0.330223i	−0.757933	+	0.652333i	$0.773790\pi$
$258$		0			0
$259$	2.34253e6	+	4.05738e6i	0.134830	+	0.233532i
$260$			280153.i			0.0159395i
$261$		0			0
$262$	1.15436e7			0.641856
$263$	2.41287e7	−	1.39307e7i	1.32638	−	0.765784i	0.341639	−	0.939831i	$-0.389018\pi$
$263$	2.41287e7	−	1.39307e7i	1.32638	−	0.765784i	0.984737	+	0.174047i	$0.0556846\pi$
$264$		0			0
$265$	601190.	−	1.04129e6i	0.0323053	−	0.0559545i
$266$	7.02041e6	+	4.05324e6i	0.373008	+	0.215356i
$267$		0			0
$268$	−34077.3	−	59023.7i	−0.00177036	−	0.00306635i
$269$			7.85279e6i			0.403429i	0.979444	+	0.201714i	$0.0646513\pi$
$269$			7.85279e6i			0.403429i	−0.979444	+	0.201714i	$0.935349\pi$
$270$		0			0
$271$	2.02821e6			0.101907			0.0509535	−	0.998701i	$-0.483774\pi$
$271$	2.02821e6			0.101907			0.0509535	+	0.998701i	$0.483774\pi$
$272$	−3.37244e6	+	1.94708e6i	−0.167586	+	0.0967559i
$273$		0			0
$274$	−2.25601e6	+	3.90753e6i	−0.109670	+	0.189955i
$275$	−9.12889e6	−	5.27056e6i	−0.438955	−	0.253431i
$276$		0			0
$277$	−1.40017e7	−	2.42517e7i	−0.658782	−	1.14104i	−0.980931	−	0.194355i	$-0.937739\pi$
$277$	−1.40017e7	−	2.42517e7i	−0.658782	−	1.14104i	0.322149	−	0.946689i	$-0.395595\pi$
$278$		−	6.58449e6i		−	0.306470i
$279$		0			0
$280$	−5.66743e6			−0.258174
$281$	3.01460e7	−	1.74048e7i	1.35866	−	0.784423i	0.369217	−	0.929343i	$-0.379626\pi$
$281$	3.01460e7	−	1.74048e7i	1.35866	−	0.784423i	0.989443	+	0.144921i	$0.0462926\pi$
$282$		0			0
$283$	1.54784e7	−	2.68093e7i	0.682914	−	1.18284i	−0.291174	−	0.956670i	$-0.594046\pi$
$283$	1.54784e7	−	2.68093e7i	0.682914	−	1.18284i	0.974088	−	0.226171i	$-0.0726208\pi$
$284$	−161470.	−	93224.7i	−0.00704914	−	0.00406983i
$285$		0			0
$286$	2.58643e7	+	4.47982e7i	1.10561	+	1.91497i
$287$		−	1.32047e7i		−	0.558578i
$288$		0			0
$289$	2.32531e7			0.963356
$290$	8.66823e6	−	5.00460e6i	0.355415	−	0.205199i
$291$		0			0
$292$	−54290.6	+	94034.0i	−0.00218060	+	0.00377691i
$293$	2.14339e7	+	1.23749e7i	0.852116	+	0.491969i	0.861364	−	0.507988i	$-0.169611\pi$
$293$	2.14339e7	+	1.23749e7i	0.852116	+	0.491969i	−0.00924835	+	0.999957i	$0.502944\pi$
$294$		0			0
$295$	−8.62070e6	−	1.49315e7i	−0.335797	−	0.581617i
$296$		−	1.98755e7i		−	0.766378i
$297$		0			0
$298$	2.28322e7			0.862776
$299$	−3.35130e7	+	1.93487e7i	−1.25372	+	0.723834i
$300$		0			0
$301$	692497.	−	1.19944e6i	0.0253932	−	0.0439824i
$302$	−1.22826e7	−	7.09138e6i	−0.445934	−	0.257460i
$303$		0			0
$304$	−1.73846e7	−	3.01109e7i	−0.618790	−	1.07178i
$305$		−	9.03516e6i		−	0.318446i
$306$		0			0
$307$	−1.90164e7			−0.657222			−0.328611	−	0.944465i	$-0.606581\pi$
$307$	−1.90164e7			−0.657222			−0.328611	+	0.944465i	$0.606581\pi$
$308$	109997.	−	63506.5i	0.00376467	−	0.00217353i
$309$		0			0
$310$	5.03677e6	−	8.72394e6i	0.169070	−	0.292838i
$311$	−2.49630e7	−	1.44124e7i	−0.829879	−	0.479131i	0.0239322	−	0.999714i	$-0.492381\pi$
$311$	−2.49630e7	−	1.44124e7i	−0.829879	−	0.479131i	−0.853811	+	0.520583i	$0.825715\pi$
$312$		0			0
$313$	2.40307e7	+	4.16225e7i	0.783672	+	1.35736i	0.929789	+	0.368092i	$0.119989\pi$
$313$	2.40307e7	+	4.16225e7i	0.783672	+	1.35736i	−0.146118	+	0.989267i	$0.546678\pi$
$314$			3.46500e6i			0.111922i
$315$		0			0
$316$	60909.9			0.00193031
$317$	3.07478e6	−	1.77522e6i	0.0965242	−	0.0557282i	−0.450961	−	0.892544i	$-0.648919\pi$
$317$	3.07478e6	−	1.77522e6i	0.0965242	−	0.0557282i	0.547485	+	0.836815i	$0.315585\pi$
$318$		0			0
$319$	1.00689e7	−	1.74399e7i	0.310179	−	0.537245i
$320$	2.08193e7	+	1.20200e7i	0.635355	+	0.366822i
$321$		0			0
$322$	4.36005e6	+	7.55183e6i	0.130594	+	0.226196i
$323$		−	7.89725e6i		−	0.234352i
$324$		0			0
$325$	−3.00854e7			−0.876406
$326$	−3.39492e7	+	1.96006e7i	−0.979890	+	0.565740i
$327$		0			0
$328$	−2.80093e7	+	4.85135e7i	−0.793744	+	1.37481i
$329$	−2.74107e6	−	1.58256e6i	−0.0769721	−	0.0444398i
$330$		0			0
$331$	4.51963e6	+	7.82823e6i	0.124629	+	0.215864i	0.921588	−	0.388170i	$-0.126893\pi$
$331$	4.51963e6	+	7.82823e6i	0.124629	+	0.215864i	−0.796959	+	0.604034i	$0.793559\pi$
$332$		−	442852.i		−	0.0121017i
$333$		0			0
$334$	−6.24701e7			−1.67661
$335$	−7.76465e6	+	4.48292e6i	−0.206532	+	0.119241i
$336$		0			0
$337$	82154.7	−	142296.i	0.00214656	−	0.00371795i	−0.864950	−	0.501858i	$-0.832650\pi$
$337$	82154.7	−	142296.i	0.00214656	−	0.00371795i	0.867097	+	0.498140i	$0.165983\pi$
$338$	9.42335e7	+	5.44058e7i	2.44037	+	1.40895i
$339$		0			0
$340$	−30750.2	−	53260.9i	−0.000782368	−	0.00135510i
$341$		−	2.02673e7i		−	0.511132i
$342$		0			0
$343$	2.65106e7			0.656958
$344$	−5.08840e6	+	2.93779e6i	−0.124999	+	0.0721681i
$345$		0			0
$346$	2.83259e7	−	4.90619e7i	0.683842	−	1.18445i
$347$	−2.59533e7	−	1.49841e7i	−0.621160	−	0.358627i	0.156160	−	0.987732i	$-0.450088\pi$
$347$	−2.59533e7	−	1.49841e7i	−0.621160	−	0.358627i	−0.777321	+	0.629105i	$0.783422\pi$
$348$		0			0
$349$	−1.24435e7	−	2.15528e7i	−0.292729	−	0.507022i	0.681725	−	0.731609i	$-0.261230\pi$
$349$	−1.24435e7	−	2.15528e7i	−0.292729	−	0.507022i	−0.974454	+	0.224587i	$0.927897\pi$
$350$			6.77946e6i			0.158122i
$351$		0			0
$352$	−1.08366e6			−0.0248465
$353$	−1.88005e7	+	1.08545e7i	−0.427410	+	0.246765i	−0.698243	−	0.715861i	$-0.746034\pi$
$353$	−1.88005e7	+	1.08545e7i	−0.427410	+	0.246765i	0.270833	+	0.962626i	$0.412701\pi$
$354$		0			0
$355$	−1.22638e7	+	2.12416e7i	−0.274120	+	0.474790i
$356$	−533891.	−	308242.i	−0.0118332	−	0.00683191i
$357$		0			0
$358$	1.41651e6	+	2.45348e6i	0.0308725	+	0.0534728i
$359$			7.81560e7i			1.68919i	0.535404	+	0.844596i	$0.320159\pi$
$359$			7.81560e7i			1.68919i	−0.535404	+	0.844596i	$0.679841\pi$
$360$		0			0
$361$	2.34649e7			0.498767
$362$	3.50586e6	−	2.02411e6i	0.0739042	−	0.0426686i
$363$		0			0
$364$	181254.	−	313941.i	0.00375823	−	0.00650944i
$365$	1.23703e7	+	7.14200e6i	0.254391	+	0.146873i
$366$		0			0
$367$	−2.43155e7	−	4.21157e7i	−0.491910	−	0.852012i	0.508047	−	0.861329i	$-0.330368\pi$
$367$	−2.43155e7	−	4.21157e7i	−0.491910	−	0.852012i	−0.999957	+	0.00931702i	$0.997034\pi$
$368$		−	3.74010e7i		−	0.750482i
$369$		0			0
$370$	2.91247e7			0.574985
$371$	−1.34739e6	+	777919.i	−0.0263860	+	0.0152339i
$372$		0			0
$373$	−2.28561e7	+	3.95878e7i	−0.440428	+	0.762843i	−0.997721	−	0.0674723i	$-0.978507\pi$
$373$	−2.28561e7	+	3.95878e7i	−0.440428	+	0.762843i	0.557293	+	0.830316i	$0.311840\pi$
$374$	−9.83431e6	−	5.67784e6i	−0.187988	−	0.108535i
$375$		0			0
$376$	6.71372e6	+	1.16285e7i	0.126299	+	0.218756i
$377$		−	5.74755e7i		−	1.07265i
$378$		0			0
$379$	2.09916e7			0.385593			0.192796	−	0.981239i	$-0.438244\pi$
$379$	2.09916e7			0.385593			0.192796	+	0.981239i	$0.438244\pi$
$380$	475541.	−	274554.i	0.00866638	−	0.00500353i
$381$		0			0
$382$	−2.56176e7	+	4.43709e7i	−0.459566	+	0.795991i
$383$	−5.34458e7	−	3.08569e7i	−0.951299	−	0.549233i	−0.0578149	−	0.998327i	$-0.518413\pi$
$383$	−5.34458e7	−	3.08569e7i	−0.951299	−	0.549233i	−0.893484	+	0.449095i	$0.851747\pi$
$384$		0			0
$385$	−8.35438e6	−	1.44702e7i	−0.146397	−	0.253567i
$386$		−	2.17277e7i		−	0.377792i
$387$		0			0
$388$	134171.			0.00229701
$389$	1.24081e7	−	7.16380e6i	0.210793	−	0.121701i	−0.390887	−	0.920439i	$-0.627832\pi$
$389$	1.24081e7	−	7.16380e6i	0.210793	−	0.121701i	0.601680	+	0.798737i	$0.294498\pi$
$390$		0			0
$391$	4.24752e6	−	7.35693e6i	0.0710568	−	0.123074i
$392$	−4.55239e7	−	2.62832e7i	−0.755756	−	0.436336i
$393$		0			0
$394$	2.30928e7	+	3.99979e7i	0.377562	+	0.653957i
$395$		−	8.01278e6i		−	0.130015i
$396$		0			0
$397$	7.70168e7			1.23088			0.615438	−	0.788186i	$-0.288979\pi$
$397$	7.70168e7			1.23088			0.615438	+	0.788186i	$0.288979\pi$
$398$	5.24378e7	−	3.02750e7i	0.831754	−	0.480213i
$399$		0			0
$400$	1.45387e7	−	2.51818e7i	0.227168	−	0.393466i
$401$	7.57065e7	+	4.37092e7i	1.17409	+	0.677859i	0.954639	−	0.297765i	$-0.0962411\pi$
$401$	7.57065e7	+	4.37092e7i	1.17409	+	0.677859i	0.219448	+	0.975624i	$0.429574\pi$
$402$		0			0
$403$	−2.89225e7	−	5.00952e7i	−0.441896	−	0.765386i
$404$			800812.i			0.0121447i
$405$		0			0
$406$	−1.29516e7			−0.193528
$407$	5.07466e7	−	2.92985e7i	0.752703	−	0.434573i
$408$		0			0
$409$	2.56830e7	−	4.44842e7i	0.375384	−	0.650183i	−0.615001	−	0.788526i	$-0.710844\pi$
$409$	2.56830e7	−	4.44842e7i	0.375384	−	0.650183i	0.990384	+	0.138343i	$0.0441777\pi$
$410$	−7.10897e7	−	4.10436e7i	−1.03147	−	0.595517i
$411$		0			0
$412$	391915.	+	678816.i	0.00560402	+	0.00970645i
$413$			2.23098e7i			0.316698i
$414$		0			0
$415$	−5.82579e7			−0.815099
$416$	−2.67851e6	+	1.54644e6i	−0.0372060	+	0.0214809i
$417$		0			0
$418$	5.06948e7	−	8.78059e7i	0.694120	−	1.20225i
$419$	−1.15800e7	−	6.68574e6i	−0.157423	−	0.0908881i	0.419219	−	0.907885i	$-0.362304\pi$
$419$	−1.15800e7	−	6.68574e6i	−0.157423	−	0.0908881i	−0.576642	+	0.816997i	$0.695637\pi$
$420$		0			0
$421$	5.48660e7	+	9.50307e7i	0.735287	+	1.27355i	0.954597	+	0.297899i	$0.0962860\pi$
$421$	5.48660e7	+	9.50307e7i	0.735287	+	1.27355i	−0.219310	+	0.975655i	$0.570381\pi$
$422$			1.02026e8i			1.35760i
$423$		0			0
$424$	6.60035e6			0.0865904
$425$	5.71965e6	−	3.30224e6i	0.0745080	−	0.0430172i
$426$		0			0
$427$	−5.84559e6	+	1.01249e7i	−0.0750835	+	0.130048i
$428$	777350.	+	448803.i	0.00991483	+	0.00572433i
$429$		0			0
$430$	−4.30491e6	−	7.45633e6i	−0.0541451	−	0.0937820i
$431$			6.35161e7i			0.793327i	0.917964	+	0.396664i	$0.129832\pi$
$431$			6.35161e7i			0.793327i	−0.917964	+	0.396664i	$0.870168\pi$
$432$		0			0
$433$	−1.45827e7			−0.179628			−0.0898142	−	0.995959i	$-0.528627\pi$
$433$	−1.45827e7			−0.179628			−0.0898142	+	0.995959i	$0.528627\pi$
$434$	−1.12885e7	+	6.51740e6i	−0.138091	+	0.0797270i
$435$		0			0
$436$	−662687.	+	1.14781e6i	−0.00799557	+	0.0138487i
$437$	6.56865e7	+	3.79241e7i	0.787103	+	0.454434i
$438$		0			0
$439$	−2.80070e7	−	4.85095e7i	−0.331034	−	0.573367i	0.651681	−	0.758493i	$-0.274064\pi$
$439$	−2.80070e7	−	4.85095e7i	−0.331034	−	0.573367i	−0.982715	+	0.185126i	$0.940731\pi$
$440$			7.08838e7i			0.832126i
$441$		0			0
$442$	−3.24102e7			−0.375332
$443$	1.15568e7	−	6.67232e6i	0.132931	−	0.0767478i	−0.432060	−	0.901845i	$-0.642213\pi$
$443$	1.15568e7	−	6.67232e6i	0.132931	−	0.0767478i	0.564991	+	0.825097i	$0.308880\pi$
$444$		0			0
$445$	−4.05497e7	+	7.02341e7i	−0.460159	+	0.797018i
$446$	−9.19913e7	−	5.31112e7i	−1.03691	−	0.598662i
$447$		0			0
$448$	−1.55535e7	−	2.69395e7i	−0.172979	−	0.299609i
$449$		−	9.37897e7i		−	1.03613i	−0.855340	−	0.518067i	$-0.826652\pi$
$449$		−	9.37897e7i		−	1.03613i	0.855340	−	0.518067i	$-0.173348\pi$
$450$		0			0
$451$	−1.65154e8			−1.80037
$452$	854075.	−	493101.i	0.00924870	−	0.00533974i
$453$		0			0
$454$	−6.39188e7	+	1.10711e8i	−0.683063	+	1.18310i
$455$	−4.12993e7	−	2.38442e7i	−0.438439	−	0.253133i
$456$		0			0
$457$	5.76767e7	+	9.98990e7i	0.604299	+	1.04668i	0.992162	+	0.124959i	$0.0398800\pi$
$457$	5.76767e7	+	9.98990e7i	0.604299	+	1.04668i	−0.387863	+	0.921717i	$0.626787\pi$
$458$			2.52968e7i			0.263311i
$459$		0			0
$460$	590673.			0.00606840
$461$	−1.60801e7	+	9.28384e6i	−0.164129	+	0.0947600i	−0.579815	−	0.814748i	$-0.696875\pi$
$461$	−1.60801e7	+	9.28384e6i	−0.164129	+	0.0947600i	0.415686	+	0.909508i	$0.363542\pi$
$462$		0			0
$463$	−3.53162e7	+	6.11695e7i	−0.355821	+	0.616300i	−0.987258	−	0.159127i	$-0.949132\pi$
$463$	−3.53162e7	+	6.11695e7i	−0.355821	+	0.616300i	0.631437	+	0.775427i	$0.282465\pi$
$464$	4.81077e7	+	2.77750e7i	0.481571	+	0.278035i
$465$		0			0
$466$	−2.79692e7	−	4.84440e7i	−0.276390	−	0.478721i
$467$			8.13433e7i			0.798677i	0.916804	+	0.399338i	$0.130760\pi$
$467$			8.13433e7i			0.798677i	−0.916804	+	0.399338i	$0.869240\pi$
$468$		0			0
$469$	1.16015e7			0.112459
$470$	−1.70399e7	+	9.83800e6i	−0.164125	+	0.0947574i
$471$		0			0
$472$	4.73225e7	−	8.19650e7i	0.450031	−	0.779476i
$473$	−1.50017e7	−	8.66121e6i	−0.141761	−	0.0818456i
$474$		0			0
$475$	2.94842e7	+	5.10681e7i	0.275111	+	0.476506i
$476$			79579.4i			0.000737870i
$477$		0			0
$478$	2.18545e7			0.200105
$479$	−9.72480e7	+	5.61461e7i	−0.884859	+	0.510874i	−0.872257	−	0.489047i	$-0.837345\pi$
$479$	−9.72480e7	+	5.61461e7i	−0.884859	+	0.510874i	−0.0126015	+	0.999921i	$0.504011\pi$
$480$		0			0
$481$	8.36208e7	−	1.44836e8i	0.751414	−	1.30149i
$482$	−1.88832e7	−	1.09022e7i	−0.168630	−	0.0973585i
$483$		0			0
$484$	−169775.	−	294059.i	−0.00149740	−	0.00259358i
$485$		−	1.76504e7i		−	0.154714i
$486$		0			0
$487$	1.17703e8			1.01907			0.509533	−	0.860451i	$-0.329818\pi$
$487$	1.17703e8			1.01907			0.509533	+	0.860451i	$0.329818\pi$
$488$	4.29528e7	−	2.47988e7i	0.369600	−	0.213389i
$489$		0			0
$490$	3.85143e7	−	6.67088e7i	0.327367	−	0.567016i
$491$	1.17596e8	+	6.78940e7i	0.993453	+	0.573571i	0.906305	−	0.422625i	$-0.138891\pi$
$491$	1.17596e8	+	6.78940e7i	0.993453	+	0.573571i	0.0871486	+	0.996195i	$0.472225\pi$
$492$		0			0
$493$	6.30865e6	+	1.09269e7i	0.0526496	+	0.0911918i
$494$		−	2.89375e8i		−	2.40038i
$495$		0			0
$496$	5.59070e7			0.458164
$497$	2.74859e7	−	1.58690e7i	0.223893	−	0.129265i
$498$		0			0
$499$	−2.40967e7	+	4.17367e7i	−0.193935	+	0.335905i	−0.946551	−	0.322555i	$-0.895458\pi$
$499$	−2.40967e7	+	4.17367e7i	−0.193935	+	0.335905i	0.752616	+	0.658460i	$0.228792\pi$
$500$	1.28257e6	+	740491.i	0.0102605	+	0.00592393i
$501$		0			0
$502$	−1.14267e8	−	1.97916e8i	−0.903255	−	1.56448i
$503$		−	1.99031e7i		−	0.156393i	−0.996938	−	0.0781963i	$-0.975084\pi$
$503$		−	1.99031e7i		−	0.156393i	0.996938	−	0.0781963i	$-0.0249161\pi$
$504$		0			0
$505$	1.05348e8			0.817997
$506$	9.44525e7	−	5.45322e7i	0.729058	−	0.420922i
$507$		0			0
$508$	1.00300e6	−	1.73725e6i	0.00765086	−	0.0132517i
$509$	4.74516e7	+	2.73962e7i	0.359830	+	0.207748i	0.669006	−	0.743257i	$-0.266720\pi$
$509$	4.74516e7	+	2.73962e7i	0.359830	+	0.207748i	−0.309176	+	0.951005i	$0.600053\pi$
$510$		0			0
$511$	−9.24150e6	−	1.60067e7i	−0.0692595	−	0.119961i
$512$			1.31933e8i			0.982979i
$513$		0			0
$514$	9.01790e7			0.664073
$515$	8.92992e7	−	5.15569e7i	0.653772	−	0.377455i
$516$		0			0
$517$	−1.97934e7	+	3.42832e7i	−0.143235	+	0.248091i
$518$	−3.26373e7	−	1.88432e7i	−0.234815	−	0.135570i
$519$		0			0
$520$	1.01155e8	+	1.75205e8i	0.719408	+	1.24605i
$521$		−	2.09737e8i		−	1.48307i	−0.670912	−	0.741537i	$-0.734097\pi$
$521$		−	2.09737e8i		−	1.48307i	0.670912	−	0.741537i	$-0.265903\pi$
$522$		0			0
$523$	1.69217e7			0.118287			0.0591436	−	0.998249i	$-0.481163\pi$
$523$	1.69217e7			0.118287			0.0591436	+	0.998249i	$0.481163\pi$
$524$	−876234.	+	505894.i	−0.00609012	+	0.00351613i
$525$		0			0
$526$	−1.12058e8	+	1.94090e8i	−0.769990	+	1.33366i
$527$	1.09971e7	+	6.34919e6i	0.0751359	+	0.0433797i
$528$		0			0
$529$	−3.32231e7	−	5.75441e7i	−0.224426	−	0.388717i
$530$			9.67188e6i			0.0649656i
$531$		0			0
$532$	−710526.			−0.00471895
$533$	−4.08215e8	+	2.35683e8i	−2.69592	+	1.55649i
$534$		0			0
$535$	5.90407e7	−	1.02262e8i	0.385559	−	0.667807i
$536$	−4.26233e7	−	2.46086e7i	−0.276792	−	0.159806i
$537$		0			0
$538$	−3.15837e7	−	5.47046e7i	−0.202822	−	0.351299i
$539$		−	1.54977e8i		−	0.989694i
$540$		0			0
$541$	−2.96138e8			−1.87026			−0.935132	−	0.354299i	$-0.884719\pi$
$541$	−2.96138e8			−1.87026			−0.935132	+	0.354299i	$0.884719\pi$
$542$	−1.41290e7	+	8.15739e6i	−0.0887388	+	0.0512334i
$543$		0			0
$544$	339481.	−	587999.i	0.00210872	−	0.00365241i
$545$	1.50996e8	+	8.71775e7i	0.932772	+	0.538536i
$546$		0			0
$547$	2.32052e7	+	4.01926e7i	0.141783	+	0.245575i	0.928168	−	0.372161i	$-0.121383\pi$
$547$	2.32052e7	+	4.01926e7i	0.141783	+	0.245575i	−0.786385	+	0.617736i	$0.788050\pi$
$548$		−	395475.i		−	0.00240313i
$549$		0			0
$550$	8.47923e7			0.509645
$551$	−9.75610e7	+	5.63269e7i	−0.583205	+	0.336714i
$552$		0			0
$553$	−5.18413e6	+	8.97917e6i	−0.0306549	+	0.0530959i
$554$	1.95079e8	+	1.12629e8i	1.14731	+	0.662401i
$555$		0			0
$556$	288563.	+	499805.i	0.00167886	+	0.00290788i
$557$			1.93358e8i			1.11892i	0.828859	+	0.559458i	$0.188991\pi$
$557$			1.93358e8i			1.11892i	−0.828859	+	0.559458i	$0.811009\pi$
$558$		0			0
$559$	−4.94399e7			−0.283036
$560$	3.99158e7	−	2.30454e7i	0.227290	−	0.131226i
$561$		0			0
$562$	−1.40003e8	+	2.42493e8i	−0.788732	+	1.36612i
$563$	−2.78735e8	−	1.60928e8i	−1.56195	−	0.901790i	−0.997060	−	0.0766203i	$-0.975587\pi$
$563$	−2.78735e8	−	1.60928e8i	−1.56195	−	0.901790i	−0.564885	−	0.825169i	$-0.691080\pi$
$564$		0			0
$565$	−6.48681e7	−	1.12355e8i	−0.359655	−	0.622940i
$566$			2.49014e8i			1.37333i
$567$		0			0
$568$	−1.34642e8			−0.734745
$569$	1.32578e8	−	7.65442e7i	0.719674	−	0.415504i	−0.0949586	−	0.995481i	$-0.530272\pi$
$569$	1.32578e8	−	7.65442e7i	0.719674	−	0.415504i	0.814633	+	0.579977i	$0.196939\pi$
$570$		0			0
$571$	1.23735e8	−	2.14315e8i	0.664635	−	1.15118i	−0.314749	−	0.949175i	$-0.601920\pi$
$571$	1.23735e8	−	2.14315e8i	0.664635	−	1.15118i	0.979384	−	0.202007i	$-0.0647465\pi$
$572$	−3.92653e6	−	2.26698e6i	−0.0209807	−	0.0121132i
$573$		0			0
$574$	5.31090e7	+	9.19875e7i	0.280823	+	0.486400i
$575$			6.34320e7i			0.333661i
$576$		0			0
$577$	1.55274e8			0.808296			0.404148	−	0.914694i	$-0.367568\pi$
$577$	1.55274e8			0.808296			0.404148	+	0.914694i	$0.367568\pi$
$578$	−1.61987e8	+	9.35232e7i	−0.838874	+	0.484324i
$579$		0			0
$580$	−438650.	+	759763.i	−0.00224819	+	0.00389399i
$581$	6.52841e7	+	3.76918e7i	0.332873	+	0.192185i
$582$		0			0
$583$	9.72960e6	+	1.68522e7i	0.0491009	+	0.0850453i
$584$			7.84107e7i			0.393674i
$585$		0			0
$586$	−1.99086e8			−0.989343
$587$	2.78742e8	−	1.60932e8i	1.37812	−	0.795659i	0.386189	−	0.922420i	$-0.373791\pi$
$587$	2.78742e8	−	1.60932e8i	1.37812	−	0.795659i	0.991933	+	0.126760i	$0.0404579\pi$
$588$		0			0
$589$	−5.66889e7	+	9.81881e7i	−0.277429	+	0.480522i
$590$	1.20108e8	+	6.93444e7i	0.584812	+	0.337641i
$591$		0			0
$592$	8.08194e7	+	1.39983e8i	0.389539	+	0.674701i
$593$		−	3.82156e8i		−	1.83264i	−0.400448	−	0.916319i	$-0.631146\pi$
$593$		−	3.82156e8i		−	1.83264i	0.400448	−	0.916319i	$-0.368854\pi$
$594$		0			0
$595$	1.04688e7			0.0496987
$596$	−1.73311e6	+	1.00061e6i	−0.00818629	+	0.00472636i
$597$		0			0
$598$	1.55640e8	−	2.69576e8i	0.727810	−	1.26060i
$599$	7.30381e7	+	4.21685e7i	0.339835	+	0.196204i	0.660199	−	0.751090i	$-0.270472\pi$
$599$	7.30381e7	+	4.21685e7i	0.339835	+	0.196204i	−0.320364	+	0.947295i	$0.603805\pi$
$600$		0			0
$601$	−4.80447e7	−	8.32159e7i	−0.221321	−	0.383339i	0.733889	−	0.679270i	$-0.237703\pi$
$601$	−4.80447e7	−	8.32159e7i	−0.221321	−	0.383339i	−0.955209	+	0.295931i	$0.904370\pi$
$602$			1.11408e7i			0.0510655i
$603$		0			0
$604$	1.24311e6			0.00564155
$605$	−3.86839e7	+	2.23342e7i	−0.174689	+	0.100857i
$606$		0			0
$607$	4.97861e7	−	8.62320e7i	0.222609	−	0.385569i	−0.732991	−	0.680239i	$-0.761876\pi$
$607$	4.97861e7	−	8.62320e7i	0.222609	−	0.385569i	0.955599	+	0.294669i	$0.0952095\pi$
$608$	5.24996e6	+	3.03106e6i	0.0233585	+	0.0134860i
$609$		0			0
$610$	3.63391e7	+	6.29412e7i	0.160098	+	0.277297i
$611$			1.12985e8i			0.495332i
$612$		0			0
$613$	−2.79460e8			−1.21322			−0.606609	−	0.795000i	$-0.707471\pi$
$613$	−2.79460e8			−1.21322			−0.606609	+	0.795000i	$0.707471\pi$
$614$	1.32473e8	−	7.64833e7i	0.572298	−	0.330416i
$615$		0			0
$616$	4.58606e7	−	7.94328e7i	0.196199	−	0.339827i
$617$	−3.17031e8	−	1.83038e8i	−1.34973	−	0.779265i	−0.361516	−	0.932366i	$-0.617741\pi$
$617$	−3.17031e8	−	1.83038e8i	−1.34973	−	0.779265i	−0.988211	+	0.153101i	$0.951074\pi$
$618$		0			0
$619$	1.53497e8	+	2.65865e8i	0.647186	+	1.12096i	0.983792	+	0.179313i	$0.0573875\pi$
$619$	1.53497e8	+	2.65865e8i	0.647186	+	1.12096i	−0.336606	+	0.941645i	$0.609279\pi$
$620$			882938.i			0.00370472i
$621$		0			0
$622$	2.31865e8			0.963526
$623$	9.08805e7	−	5.24699e7i	0.375843	−	0.216993i
$624$		0			0
$625$	4.25495e7	−	7.36978e7i	0.174283	−	0.301866i
$626$	−3.34809e8	−	1.93302e8i	−1.36482	−	0.787976i
$627$		0			0
$628$	−151852.	−	263016.i	−0.000613115	−	0.00106195i
$629$			3.67137e7i			0.147529i
$630$		0			0
$631$	4.69076e8			1.86705			0.933523	−	0.358518i	$-0.116718\pi$
$631$	4.69076e8			1.86705			0.933523	+	0.358518i	$0.116718\pi$
$632$	3.80925e7	−	2.19927e7i	0.150900	−	0.0871220i
$633$		0			0
$634$	−1.42798e7	+	2.47333e7i	−0.0560344	+	0.0970544i
$635$	−2.28538e8	−	1.31946e8i	−0.892558	−	0.515319i
$636$		0			0
$637$	−2.21159e8	−	3.83059e8i	−0.855632	−	1.48200i
$638$			1.61988e8i			0.623765i
$639$		0			0
$640$	−1.97662e8			−0.754022
$641$	−1.78248e8	+	1.02911e8i	−0.676784	+	0.390742i	−0.798642	−	0.601806i	$-0.794448\pi$
$641$	−1.78248e8	+	1.02911e8i	−0.676784	+	0.390742i	0.121858	+	0.992548i	$0.461115\pi$
$642$		0			0
$643$	−1.50649e8	+	2.60932e8i	−0.566676	+	0.981511i	0.430216	+	0.902726i	$0.358437\pi$
$643$	−1.50649e8	+	2.60932e8i	−0.566676	+	0.981511i	−0.996892	+	0.0787851i	$0.974896\pi$
$644$	−661912.	−	382155.i	−0.00247824	−	0.00143081i
$645$		0			0
$646$	3.17625e7	+	5.50143e7i	0.117820	+	0.204070i
$647$			1.33959e8i			0.494604i	0.968938	+	0.247302i	$0.0795440\pi$
$647$			1.33959e8i			0.494604i	−0.968938	+	0.247302i	$0.920456\pi$
$648$		0			0
$649$	2.79033e8			1.02076
$650$	2.09583e8	−	1.21003e8i	0.763159	−	0.440610i
$651$		0			0
$652$	1.71798e6	−	2.97562e6i	0.00619833	−	0.0107358i
$653$	3.13278e8	+	1.80871e8i	1.12510	+	0.649576i	0.942698	−	0.333649i	$-0.108280\pi$
$653$	3.13278e8	+	1.80871e8i	1.12510	+	0.649576i	0.182401	+	0.983224i	$0.441613\pi$
$654$		0			0
$655$	6.65510e7	+	1.15270e8i	0.236827	+	0.410196i
$656$		−	4.55575e8i		−	1.61380i
$657$		0			0
$658$	2.54601e7			0.0893679
$659$	3.64863e8	−	2.10654e8i	1.27489	−	0.736060i	0.298989	−	0.954257i	$-0.403351\pi$
$659$	3.64863e8	−	2.10654e8i	1.27489	−	0.736060i	0.975905	+	0.218196i	$0.0700173\pi$
$660$		0			0
$661$	−1.67487e8	+	2.90095e8i	−0.579930	+	1.00447i	0.415557	+	0.909567i	$0.363587\pi$
$661$	−1.67487e8	+	2.90095e8i	−0.579930	+	1.00447i	−0.995487	+	0.0949012i	$0.969746\pi$
$662$	−6.29699e7	−	3.63557e7i	−0.217049	−	0.125314i
$663$		0			0
$664$	−1.59901e8	−	2.76956e8i	−0.546193	−	0.946033i
$665$			9.34707e7i			0.317842i
$666$		0			0
$667$	−1.21181e8			−0.408374
$668$	4.74188e6	−	2.73773e6i	0.0159082	−	0.00918461i
$669$		0			0
$670$	3.60604e7	−	6.24584e7i	0.119896	−	0.207666i
$671$	1.26634e8	+	7.31121e7i	0.419162	+	0.242003i
$672$		0			0
$673$	−1.42359e8	−	2.46572e8i	−0.467024	−	0.808908i	0.532267	−	0.846577i	$-0.321340\pi$
$673$	−1.42359e8	−	2.46572e8i	−0.467024	−	0.808908i	−0.999290	+	0.0376682i	$0.988007\pi$
$674$			1.32170e6i			0.00431670i
$675$		0			0
$676$	−9.53725e6			−0.0308733
$677$	−1.29812e8	+	7.49471e7i	−0.418359	+	0.241540i	−0.694375	−	0.719613i	$-0.744319\pi$
$677$	−1.29812e8	+	7.49471e7i	−0.418359	+	0.241540i	0.276016	+	0.961153i	$0.410986\pi$
$678$		0			0
$679$	−1.14195e7	+	1.97791e7i	−0.0364785	+	0.0631826i
$680$	−3.84618e7	−	2.22059e7i	−0.122322	−	0.0706224i
$681$		0			0
$682$	8.15147e7	+	1.41188e8i	0.256970	+	0.445085i
$683$			5.60477e8i			1.75912i	0.475787	+	0.879560i	$0.342163\pi$
$683$			5.60477e8i			1.75912i	−0.475787	+	0.879560i	$0.657837\pi$
$684$		0			0
$685$	−5.20253e7			−0.161861
$686$	−1.84680e8	+	1.06625e8i	−0.572067	+	0.330283i
$687$		0			0
$688$	2.38918e7	−	4.13818e7i	0.0733640	−	0.127070i
$689$	4.80977e7	+	2.77692e7i	0.147051	+	0.0848997i
$690$		0			0
$691$	−8.08334e6	−	1.40008e7i	−0.0244995	−	0.0424343i	0.853516	−	0.521067i	$-0.174466\pi$
$691$	−8.08334e6	−	1.40008e7i	−0.0244995	−	0.0424343i	−0.878015	+	0.478633i	$0.841133\pi$
$692$			4.96549e6i			0.0149846i
$693$		0			0
$694$	2.41063e8			0.721194
$695$	6.57501e7	−	3.79608e7i	0.195858	−	0.113079i
$696$		0			0
$697$	5.17383e7	−	8.96134e7i	0.152797	−	0.264652i
$698$	1.73369e8	+	1.00095e8i	0.509807	+	0.294337i
$699$		0			0
$700$	−297107.	−	514605.i	−0.000866202	−	0.00150031i
$701$			5.37669e8i			1.56085i	0.625249	+	0.780425i	$0.284997\pi$
$701$			5.37669e8i			1.56085i	−0.625249	+	0.780425i	$0.715003\pi$
$702$		0			0
$703$	−3.27799e8			−0.943500
$704$	−3.36938e8	+	1.94531e8i	−0.965677	+	0.557534i
$705$		0			0
$706$	8.73127e7	−	1.51230e8i	0.248121	−	0.429758i
$707$	−1.18054e8	−	6.81582e7i	−0.334057	−	0.192868i
$708$		0			0
$709$	2.93468e8	+	5.08302e8i	0.823422	+	1.42621i	0.903119	+	0.429390i	$0.141271\pi$
$709$	2.93468e8	+	5.08302e8i	0.823422	+	1.42621i	−0.0796974	+	0.996819i	$0.525395\pi$
$710$		−	1.97299e8i		−	0.551252i
$711$		0			0
$712$	−4.45188e8			−1.23340
$713$	−1.05621e8	+	6.09801e7i	−0.291394	+	0.168236i
$714$		0			0
$715$	−2.98225e8	+	5.16540e8i	−0.815878	+	1.41314i
$716$	−215045.	−	124156.i	−0.000585856	−	0.000338244i
$717$		0			0
$718$	−3.14341e8	−	5.44455e8i	−0.849236	−	1.47092i
$719$		−	4.52832e8i		−	1.21829i	−0.793059	−	0.609144i	$-0.791513\pi$
$719$		−	4.52832e8i		−	1.21829i	0.793059	−	0.609144i	$-0.208487\pi$
$720$		0			0
$721$	−1.33426e8			−0.355987
$722$	−1.63463e8	+	9.43753e7i	−0.434317	+	0.250753i
$723$		0			0
$724$	−177412.	+	307286.i	−0.000467484	+	0.000809705i
$725$	−8.15905e7	−	4.71063e7i	−0.214104	−	0.123613i
$726$		0			0
$727$	8.62458e7	+	1.49382e8i	0.224458	+	0.388772i	0.956157	−	0.292856i	$-0.0946056\pi$
$727$	8.62458e7	+	1.49382e8i	0.224458	+	0.388772i	−0.731699	+	0.681628i	$0.761272\pi$
$728$		−	2.61781e8i		−	0.678491i
$729$		0			0
$730$	−1.14900e8			−0.295359
$731$	9.39921e6	−	5.42664e6i	0.0240624	−	0.0138924i
$732$		0			0
$733$	8.58050e7	−	1.48619e8i	0.217872	−	0.377365i	−0.736285	−	0.676671i	$-0.763422\pi$
$733$	8.58050e7	−	1.48619e8i	0.217872	−	0.377365i	0.954157	+	0.299306i	$0.0967552\pi$
$734$	3.38776e8	+	1.95593e8i	0.856692	+	0.494612i
$735$		0			0
$736$	3.26051e6	+	5.64736e6i	0.00817808	+	0.0141649i
$737$		−	1.45102e8i		−	0.362470i
$738$		0			0
$739$	5.61249e8			1.39066			0.695332	−	0.718688i	$-0.255257\pi$
$739$	5.61249e8			1.39066			0.695332	+	0.718688i	$0.255257\pi$
$740$	−2.21075e6	+	1.27638e6i	−0.00545563	+	0.00314981i
$741$		0			0
$742$	6.25753e6	−	1.08384e7i	0.0153176	−	0.0265309i
$743$	1.02996e8	+	5.94646e7i	0.251103	+	0.144975i	0.620269	−	0.784389i	$-0.287023\pi$
$743$	1.02996e8	+	5.94646e7i	0.251103	+	0.144975i	−0.369166	+	0.929363i	$0.620357\pi$
$744$		0			0
$745$	1.31632e8	+	2.27993e8i	0.318340	+	0.551382i
$746$		−	3.67706e8i		−	0.885694i
$747$		0			0
$748$	995317.			0.00237825
$749$	−1.32323e8	+	7.63966e7i	−0.314912	+	0.181815i
$750$		0			0
$751$	−1.22156e7	+	2.11581e7i	−0.0288400	+	0.0499524i	−0.880085	−	0.474816i	$-0.842515\pi$
$751$	−1.22156e7	+	2.11581e7i	−0.0288400	+	0.0499524i	0.851245	+	0.524768i	$0.175848\pi$
$752$	−9.45696e7	−	5.45998e7i	−0.222381	−	0.128392i
$753$		0			0
$754$	2.31165e8	+	4.00389e8i	0.539272	+	0.934046i
$755$		−	1.63533e8i		−	0.379983i
$756$		0			0
$757$	−2.95715e8			−0.681688			−0.340844	−	0.940120i	$-0.610713\pi$
$757$	−2.95715e8			−0.681688			−0.340844	+	0.940120i	$0.610713\pi$
$758$	−1.46233e8	+	8.44278e7i	−0.335767	+	0.193855i
$759$		0			0
$760$	1.98266e8	−	3.43407e8i	0.451656	−	0.782291i
$761$	−2.26182e8	−	1.30586e8i	−0.513220	−	0.296308i	0.220936	−	0.975288i	$-0.429089\pi$
$761$	−2.26182e8	−	1.30586e8i	−0.513220	−	0.296308i	−0.734156	+	0.678981i	$0.762422\pi$
$762$		0			0
$763$	−1.12805e8	−	1.95383e8i	−0.253953	−	0.439859i
$764$		−	4.49072e6i		−	0.0100701i
$765$		0			0
$766$	4.96423e8			1.10450
$767$	6.89692e8	−	3.98194e8i	1.52851	−	0.882487i
$768$		0			0
$769$	2.50506e8	−	4.33889e8i	0.550857	−	0.954112i	−0.447356	−	0.894356i	$-0.647634\pi$
$769$	2.50506e8	−	4.33889e8i	0.550857	−	0.954112i	0.998213	−	0.0597559i	$-0.0190322\pi$
$770$	1.16398e8	+	6.72021e7i	0.254960	+	0.147201i
$771$		0			0
$772$	952210.	+	1.64928e6i	0.00206957	+	0.00358460i
$773$		−	4.17209e8i		−	0.903265i	−0.892204	−	0.451633i	$-0.850842\pi$
$773$		−	4.17209e8i		−	0.903265i	0.892204	−	0.451633i	$-0.149158\pi$
$774$		0			0
$775$	−9.48181e7			−0.203698
$776$	8.39093e7	−	4.84451e7i	0.179566	−	0.103673i
$777$		0			0
$778$	−5.76252e7	+	9.98098e7i	−0.122370	+	0.211951i
$779$	8.00115e8	+	4.61947e8i	1.69254	+	0.977191i
$780$		0			0
$781$	−1.98477e8	−	3.43772e8i	−0.416636	−	0.721635i
$782$			6.83337e7i			0.142894i
$783$		0			0
$784$	4.27501e8			0.887133
$785$	−3.46001e7	+	1.99764e7i	−0.0715267	+	0.0412959i
$786$		0			0
$787$	4.21601e8	−	7.30234e8i	0.864922	−	1.49809i	−0.00220161	−	0.999998i	$-0.500701\pi$
$787$	4.21601e8	−	7.30234e8i	0.864922	−	1.49809i	0.867124	−	0.498092i	$-0.165966\pi$
$788$	−3.50579e6	−	2.02407e6i	−0.00716485	−	0.00413663i
$789$		0			0
$790$	3.22272e7	+	5.58191e7i	0.0653644	+	0.113214i
$791$			1.67874e8i			0.339199i
$792$		0			0
$793$	4.17338e8			0.836889
$794$	−5.36519e8	+	3.09759e8i	−1.07182	+	0.618818i
$795$		0			0
$796$	−2.65358e6	+	4.59613e6i	−0.00526129	+	0.00911282i
$797$	−6.47167e8	−	3.73642e8i	−1.27833	−	0.738042i	−0.301786	−	0.953376i	$-0.597583\pi$
$797$	−6.47167e8	−	3.73642e8i	−1.27833	−	0.738042i	−0.976540	+	0.215334i	$0.930916\pi$
$798$		0			0
$799$	−1.24015e7	−	2.14800e7i	−0.0243127	−	0.0421108i
$800$			5.06977e6i			0.00990190i
$801$		0			0
$802$	−7.03189e8			−1.36317
$803$	−2.00200e8	+	1.15586e8i	−0.386649	+	0.223232i
$804$		0			0
$805$	−5.02731e7	+	8.70755e7i	−0.0963713	+	0.166920i
$806$	4.02963e8	+	2.32651e8i	0.769590	+	0.444323i
$807$		0			0
$808$	2.89149e8	+	5.00820e8i	0.548135	+	0.949397i
$809$		−	4.29916e8i		−	0.811967i	−0.913880	−	0.405984i	$-0.866929\pi$
$809$		−	4.29916e8i		−	0.811967i	0.913880	−	0.405984i	$-0.133071\pi$
$810$		0			0
$811$	−2.17167e8			−0.407128			−0.203564	−	0.979062i	$-0.565252\pi$
$811$	−2.17167e8			−0.407128			−0.203564	+	0.979062i	$0.565252\pi$
$812$	983107.	−	567597.i	0.00183625	−	0.00106016i
$813$		0			0
$814$	−2.35676e8	+	4.08203e8i	−0.436960	+	0.756837i
$815$	−3.91448e8	−	2.26002e8i	−0.723104	−	0.417484i
$816$		0			0
$817$	4.84519e7	+	8.39211e7i	0.0888473	+	0.153888i
$818$			4.13185e8i			0.754891i
$819$		0			0
$820$	7.19489e6			0.0130492
$821$	−9.93226e7	+	5.73439e7i	−0.179481	+	0.103623i	−0.587049	−	0.809552i	$-0.699710\pi$
$821$	−9.93226e7	+	5.73439e7i	−0.179481	+	0.103623i	0.407568	+	0.913175i	$0.366377\pi$
$822$		0			0
$823$	−3.31550e8	+	5.74262e8i	−0.594771	+	1.03017i	0.398808	+	0.917034i	$0.369424\pi$
$823$	−3.31550e8	+	5.74262e8i	−0.594771	+	1.03017i	−0.993579	+	0.113139i	$0.963909\pi$
$824$	4.90200e8	+	2.83017e8i	0.876176	+	0.505861i
$825$		0			0
$826$	−8.97292e7	−	1.55416e8i	−0.159219	−	0.275775i
$827$			7.09882e7i			0.125508i	0.998029	+	0.0627538i	$0.0199883\pi$
$827$			7.09882e7i			0.125508i	−0.998029	+	0.0627538i	$0.980012\pi$
$828$		0			0
$829$	−9.23151e8			−1.62035			−0.810176	−	0.586187i	$-0.800629\pi$
$829$	−9.23151e8			−1.62035			−0.810176	+	0.586187i	$0.800629\pi$
$830$	4.05839e8	−	2.34311e8i	0.709774	−	0.409788i
$831$		0			0
$832$	−5.55211e8	+	9.61653e8i	−0.964024	+	1.66974i
$833$	8.40910e7	+	4.85500e7i	0.145484	+	0.0839951i
$834$		0			0
$835$	−3.60152e8	−	6.23801e8i	−0.618623	−	1.07149i
$836$			8.88671e6i			0.0152098i
$837$		0			0
$838$	1.07559e8			0.182775
$839$	−5.54532e8	+	3.20159e8i	−0.938946	+	0.542101i	−0.889630	−	0.456682i	$-0.849038\pi$
$839$	−5.54532e8	+	3.20159e8i	−0.938946	+	0.542101i	−0.0493163	+	0.998783i	$0.515704\pi$
$840$		0			0
$841$	−2.07419e8	+	3.59261e8i	−0.348707	+	0.603979i
$842$	−7.64421e8	−	4.41339e8i	−1.28055	−	0.739326i
$843$		0			0
$844$	−4.47125e6	−	7.74443e6i	−0.00743706	−	0.0128814i
$845$			1.25464e9i			2.07945i
$846$		0			0
$847$	5.77993e7			0.0951201
$848$	−4.64864e7	+	2.68389e7i	−0.0762321	+	0.0440126i
$849$		0			0
$850$	−2.65631e7	+	4.60086e7i	−0.0432535	+	0.0749173i
$851$	−3.05371e8	−	1.76306e8i	−0.495495	−	0.286074i
$852$		0			0
$853$	1.17026e8	+	2.02694e8i	0.188553	+	0.326584i	0.944768	−	0.327740i	$-0.106287\pi$
$853$	1.17026e8	+	2.02694e8i	0.188553	+	0.326584i	−0.756215	+	0.654323i	$0.772954\pi$
$854$		−	9.40432e7i		−	0.150992i
$855$		0			0
$856$	6.48197e8			1.03344
$857$	7.81860e8	−	4.51407e8i	1.24219	−	0.717177i	0.272647	−	0.962114i	$-0.412101\pi$
$857$	7.81860e8	−	4.51407e8i	1.24219	−	0.717177i	0.969539	+	0.244937i	$0.0787674\pi$
$858$		0			0
$859$	3.87666e8	−	6.71458e8i	0.611616	−	1.05935i	−0.379352	−	0.925252i	$-0.623853\pi$
$859$	3.87666e8	−	6.71458e8i	0.611616	−	1.05935i	0.990968	−	0.134097i	$-0.0428135\pi$
$860$	653541.	+	377322.i	0.00102749	+	0.000593222i
$861$		0			0
$862$	−2.55460e8	−	4.42470e8i	−0.398842	−	0.690815i
$863$			1.80225e6i			0.00280402i	0.999999	+	0.00140201i	$0.000446274\pi$
$863$			1.80225e6i			0.00280402i	−0.999999	+	0.00140201i	$0.999554\pi$
$864$		0			0
$865$	6.53217e8			1.00927
$866$	1.01587e8	−	5.86513e7i	0.156417	−	0.0903075i
$867$		0			0
$868$	571245.	−	989426.i	0.000873501	−	0.00151295i
$869$	1.12305e8	+	6.48391e7i	0.171135	+	0.0988047i
$870$		0			0
$871$	−2.07068e8	−	3.58652e8i	−0.313371	−	0.542774i
$872$			9.57105e8i			1.44348i
$873$		0			0
$874$	−6.10119e8			−0.913861
$875$	−2.18322e8	+	1.26049e8i	−0.325892	+	0.188154i
$876$		0			0
$877$	1.32637e8	−	2.29734e8i	0.196637	−	0.340585i	−0.750799	−	0.660531i	$-0.770331\pi$
$877$	1.32637e8	−	2.29734e8i	0.196637	−	0.340585i	0.947436	+	0.319945i	$0.103665\pi$
$878$	3.90208e8	+	2.25286e8i	0.576517	+	0.332852i
$879$		0			0
$880$	−2.88234e8	−	4.99236e8i	−0.422958	−	0.732584i
$881$		−	1.59497e6i		−	0.00233251i	−0.999999	−	0.00116626i	$-0.999629\pi$
$881$		−	1.59497e6i		−	0.00233251i	0.999999	−	0.00116626i	$-0.000371231\pi$
$882$		0			0
$883$	7.55655e8			1.09759			0.548796	−	0.835956i	$-0.315086\pi$
$883$	7.55655e8			1.09759			0.548796	+	0.835956i	$0.315086\pi$
$884$	2.46014e6	−	1.42037e6i	0.00356126	−	0.00205610i
$885$		0			0
$886$	−5.36718e7	+	9.29623e7i	−0.0771694	+	0.133661i
$887$	−3.65191e8	−	2.10843e8i	−0.523298	−	0.302127i	0.214985	−	0.976617i	$-0.431030\pi$
$887$	−3.65191e8	−	2.10843e8i	−0.523298	−	0.302127i	−0.738283	+	0.674491i	$0.764363\pi$
$888$		0			0
$889$	1.70734e8	+	2.95720e8i	0.243004	+	0.420896i
$890$		−	6.52359e8i		−	0.925373i
$891$		0			0
$892$	9.31032e6			0.0131181
$893$	1.91785e8	−	1.10727e8i	0.269314	−	0.155489i
$894$		0			0
$895$	−1.63330e7	+	2.82895e7i	−0.0227822	+	0.0394599i
$896$	2.21502e8	+	1.27884e8i	0.307931	+	0.177784i
$897$		0			0
$898$	3.77220e8	+	6.53364e8i	0.520913	+	0.902248i
$899$		−	1.81142e8i		−	0.249310i
$900$		0			0
$901$	−1.21921e7			−0.0166687
$902$	1.15051e9	−	6.64247e8i	1.56773	−	0.905127i
$903$		0			0
$904$	3.56087e8	−	6.16761e8i	0.482005	−	0.834857i
$905$	4.04239e7	+	2.33388e7i	0.0545372	+	0.0314870i
$906$		0			0
$907$	5.00053e8	+	8.66117e8i	0.670184	+	1.16079i	0.977852	+	0.209299i	$0.0671180\pi$
$907$	5.00053e8	+	8.66117e8i	0.670184	+	1.16079i	−0.307668	+	0.951494i	$0.599549\pi$
$908$		−	1.12049e7i		−	0.0149675i
$909$		0			0
$910$	3.83603e8			0.509046
$911$	1.24689e8	−	7.19891e7i	0.164920	−	0.0952164i	−0.415268	−	0.909699i	$-0.636312\pi$
$911$	1.24689e8	−	7.19891e7i	0.164920	−	0.0952164i	0.580188	+	0.814482i	$0.302979\pi$
$912$		0			0
$913$	4.71420e8	−	8.16523e8i	0.619435	−	1.07289i
$914$	−8.03582e8	−	4.63948e8i	−1.05243	−	0.607618i
$915$		0			0
$916$	−1.10862e6	−	1.92019e6i	−0.00144244	−	0.00249837i
$917$		−	1.72229e8i		−	0.223357i
$918$		0			0
$919$	−1.25483e9			−1.61673			−0.808365	−	0.588682i	$-0.799647\pi$
$919$	−1.25483e9			−1.61673			−0.808365	+	0.588682i	$0.799647\pi$
$920$	3.69402e8	−	2.13274e8i	0.474390	−	0.273889i
$921$		0			0
$922$	7.46787e7	−	1.29347e8i	0.0952805	−	0.165031i
$923$	−9.81158e8	−	5.66472e8i	−1.24777	−	0.720399i
$924$		0			0
$925$	−1.37069e8	−	2.37411e8i	−0.173187	−	0.299969i
$926$		−	5.68164e8i		−	0.715551i
$927$		0			0
$928$	−9.68535e6			−0.0121191
$929$	3.98994e7	−	2.30359e7i	0.0497644	−	0.0287315i	−0.474911	−	0.880034i	$-0.657520\pi$
$929$	3.98994e7	−	2.30359e7i	0.0497644	−	0.0287315i	0.524676	+	0.851302i	$0.324187\pi$
$930$		0			0
$931$	−4.33480e8	+	7.50809e8i	−0.537180	+	0.930423i
$932$	4.24608e6	+	2.45148e6i	0.00524494	+	0.00302817i
$933$		0			0
$934$	−3.27160e8	−	5.66658e8i	−0.401532	−	0.695474i
$935$		−	1.30935e8i		−	0.160185i
$936$		0			0
$937$	5.55499e8			0.675250			0.337625	−	0.941281i	$-0.390376\pi$
$937$	5.55499e8			0.675250			0.337625	+	0.941281i	$0.390376\pi$
$938$	−8.08190e7	+	4.66608e7i	−0.0979275	+	0.0565385i
$939$		0			0
$940$	862293.	−	1.49354e6i	0.00103818	−	0.00179818i
$941$	7.36911e8	+	4.25456e8i	0.884394	+	0.510605i	0.872105	−	0.489319i	$-0.162755\pi$
$941$	7.36911e8	+	4.25456e8i	0.884394	+	0.510605i	0.0122896	+	0.999924i	$0.496088\pi$
$942$		0			0
$943$	4.96914e8	+	8.60681e8i	0.592579	+	1.02638i
$944$			7.69708e8i			0.914976i
$945$		0			0
$946$	1.39341e8			0.164590
$947$	−1.09931e9	+	6.34686e8i	−1.29440	+	0.747325i	−0.979432	−	0.201776i	$-0.935329\pi$
$947$	−1.09931e9	+	6.34686e8i	−1.29440	+	0.747325i	−0.314973	+	0.949101i	$0.601995\pi$
$948$		0			0
$949$	−3.29892e8	+	5.71390e8i	−0.385988	+	0.668550i
$950$	−4.10789e8	−	2.37169e8i	−0.479124	−	0.276622i
$951$		0			0
$952$	2.87337e7	+	4.97682e7i	0.0333028	+	0.0576821i
$953$		−	1.54351e9i		−	1.78333i	−0.452694	−	0.891666i	$-0.649537\pi$
$953$		−	1.54351e9i		−	1.78333i	0.452694	−	0.891666i	$-0.350463\pi$
$954$		0			0
$955$	−5.90761e8			−0.678268
$956$	−1.65890e6	+	957764.i	−0.00189865	+	0.00109619i
$957$		0			0
$958$	4.51636e8	−	7.82257e8i	0.513680	−	0.889720i
$959$	5.82999e7	+	3.36595e7i	0.0661016	+	0.0381638i
$960$		0			0
$961$	3.52599e8	+	6.10719e8i	0.397293	+	0.688131i
$962$			1.34528e9i			1.51108i
$963$		0			0
$964$	1.91114e6			0.00213335
$965$	2.16965e8	−	1.25265e8i	0.241439	−	0.139395i
$966$		0			0
$967$	5.94735e8	−	1.03011e9i	0.657724	−	1.13921i	−0.323479	−	0.946235i	$-0.604852\pi$
$967$	5.94735e8	−	1.03011e9i	0.657724	−	1.13921i	0.981203	−	0.192977i	$-0.0618142\pi$
$968$	−2.12352e8	−	1.22601e8i	−0.234115	−	0.135167i
$969$		0			0
$970$	7.09893e7	+	1.22957e8i	0.0777818	+	0.134722i
$971$			8.11000e8i			0.885856i	0.896557	+	0.442928i	$0.146060\pi$
$971$			8.11000e8i			0.885856i	−0.896557	+	0.442928i	$0.853940\pi$
$972$		0			0
$973$	−9.82399e7			−0.106647
$974$	−8.19952e8	+	4.73400e8i	−0.887384	+	0.512331i
$975$		0			0
$976$	−2.01678e8	+	3.49317e8i	−0.216925	+	0.375725i
$977$	1.17951e9	+	6.80992e8i	1.26479	+	0.730228i	0.973998	−	0.226558i	$-0.0727474\pi$
$977$	1.17951e9	+	6.80992e8i	1.26479	+	0.730228i	0.290794	+	0.956786i	$0.406081\pi$
$978$		0			0
$979$	−6.56253e8	−	1.13666e9i	−0.699396	−	1.21139i
$980$			6.75151e6i			0.00717336i
$981$		0			0
$982$	−1.09227e9			−1.15344
$983$	1.09347e8	−	6.31316e7i	0.115119	−	0.0664640i	−0.441335	−	0.897342i	$-0.645495\pi$
$983$	1.09347e8	−	6.31316e7i	0.115119	−	0.0664640i	0.556454	+	0.830878i	$0.312162\pi$
$984$		0			0
$985$	−2.66269e8	+	4.61191e8i	−0.278620	+	0.482584i
$986$	−8.78953e7	−	5.07464e7i	−0.0916928	−	0.0529388i
$987$		0			0
$988$	1.26818e7	+	2.19655e7i	0.0131495	+	0.0227756i
$989$			1.04239e8i			0.107756i
$990$		0			0
$991$	−1.97170e8			−0.202590			−0.101295	−	0.994856i	$-0.532299\pi$
$991$	−1.97170e8			−0.202590			−0.101295	+	0.994856i	$0.532299\pi$
$992$	−8.44167e6	+	4.87380e6i	−0.00864756	+	0.00499267i
$993$		0			0
$994$	−1.27649e8	+	2.21095e8i	−0.129975	+	0.225123i
$995$	6.04627e8	+	3.49082e8i	0.613788	+	0.354371i
$996$		0			0
$997$	−4.53174e7	−	7.84920e7i	−0.0457277	−	0.0792026i	0.842256	−	0.539078i	$-0.181227\pi$
$997$	−4.53174e7	−	7.84920e7i	−0.0457277	−	0.0792026i	−0.887983	+	0.459876i	$0.847894\pi$
$998$		−	3.87665e8i		−	0.390000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.7.d.a.17.2		10
3.2	odd	2		9.7.d.a.5.4	yes	10
4.3	odd	2		432.7.q.a.17.2		10
9.2	odd	6	inner	27.7.d.a.8.2		10
9.4	even	3		81.7.b.a.80.3		10
9.5	odd	6		81.7.b.a.80.8		10
9.7	even	3		9.7.d.a.2.4	✓	10
12.11	even	2		144.7.q.a.113.4		10
36.7	odd	6		144.7.q.a.65.4		10
36.11	even	6		432.7.q.a.305.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.d.a.2.4	✓	10	9.7	even	3
9.7.d.a.5.4	yes	10	3.2	odd	2
27.7.d.a.8.2		10	9.2	odd	6	inner
27.7.d.a.17.2		10	1.1	even	1	trivial
81.7.b.a.80.3		10	9.4	even	3
81.7.b.a.80.8		10	9.5	odd	6
144.7.q.a.65.4		10	36.7	odd	6
144.7.q.a.113.4		10	12.11	even	2
432.7.q.a.17.2		10	4.3	odd	2
432.7.q.a.305.2		10	36.11	even	6

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.96626 + 4.02197i) q^{2} +(0.352523 - 0.610587i) q^{4} +(-80.3236 - 46.3749i) q^{5} +(60.0074 + 103.936i) q^{7} -509.141i q^{8} +O(q^{10})\)	\(q+(-6.96626 + 4.02197i) q^{2} +(0.352523 - 0.610587i) q^{4} +(-80.3236 - 46.3749i) q^{5} +(60.0074 + 103.936i) q^{7} -509.141i q^{8} +746.074 q^{10} +(1299.95 - 750.527i) q^{11} +(2142.08 - 3710.18i) q^{13} +(-836.055 - 482.697i) q^{14} +(2070.31 + 3585.89i) q^{16} +940.477i q^{17} -8397.07 q^{19} +(-56.6318 + 32.6964i) q^{20} +(-6037.20 + 10456.7i) q^{22} +(-7822.55 - 4516.35i) q^{23} +(-3511.24 - 6081.65i) q^{25} +34461.5i q^{26} +84.6160 q^{28} +(11618.5 - 6707.92i) q^{29} +(6751.04 - 11693.1i) q^{31} +(-625.213 - 360.967i) q^{32} +(-3782.57 - 6551.61i) q^{34} -11131.3i q^{35} +39037.3 q^{37} +(58496.2 - 33772.8i) q^{38} +(-23611.4 + 40896.1i) q^{40} +(-95285.0 - 55012.8i) q^{41} +(-5770.09 - 9994.09i) q^{43} -1058.31i q^{44} +72658.5 q^{46} +(-22839.5 + 13186.4i) q^{47} +(51622.7 - 89413.2i) q^{49} +(48920.5 + 28244.2i) q^{50} +(-1510.26 - 2615.85i) q^{52} +12963.7i q^{53} -139222. q^{55} +(52918.1 - 30552.3i) q^{56} +(-53958.1 + 93458.2i) q^{58} +(160987. + 92945.8i) q^{59} +(48707.2 + 84363.3i) q^{61} +108610. i q^{62} -259193. q^{64} +(-344118. + 198677. i) q^{65} +(48333.5 - 83716.1i) q^{67} +(574.243 + 331.540i) q^{68} +(44770.0 + 77543.9i) q^{70} -264450. i q^{71} -154006. q^{73} +(-271944. + 157007. i) q^{74} +(-2960.16 + 5127.15i) q^{76} +(156013. + 90074.4i) q^{77} +(43195.7 + 74817.2i) q^{79} -384042. i q^{80} +885040. q^{82} +(543967. - 314059. i) q^{83} +(43614.5 - 75542.5i) q^{85} +(80391.9 + 46414.3i) q^{86} +(-382124. - 661858. i) q^{88} -874390. i q^{89} +514162. q^{91} +(-5515.25 + 3184.23i) q^{92} +(106070. - 183719. i) q^{94} +(674483. + 389413. i) q^{95} +(95150.6 + 164806. i) q^{97} +830500. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7}+O(q^{10}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7	\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} - 132 q^{10} - 483 q^{11} - 841 q^{13} - 12174 q^{14} - 1985 q^{16} + 6176 q^{19} + 63186 q^{20} + 3471 q^{22} - 53565 q^{23} + 8452 q^{25} - 22660 q^{28} + 80679 q^{29} - 24601 q^{31} - 218295 q^{32} + 7425 q^{34} + 12764 q^{37} + 371877 q^{38} + 54150 q^{40} - 232251 q^{41} - 93271 q^{43} + 112512 q^{46} + 142887 q^{47} + 86238 q^{49} - 318459 q^{50} + 186920 q^{52} - 419982 q^{55} - 342546 q^{56} - 380658 q^{58} + 995061 q^{59} - 59305 q^{61} + 403066 q^{64} - 1642029 q^{65} + 158513 q^{67} + 1693791 q^{68} - 304788 q^{70} + 933896 q^{73} - 595182 q^{74} + 666641 q^{76} + 2198883 q^{77} + 468707 q^{79} - 2038470 q^{82} - 3008337 q^{83} - 1189944 q^{85} - 1905549 q^{86} - 349773 q^{88} - 211778 q^{91} + 973788 q^{92} + 809124 q^{94} + 2562954 q^{95} + 336029 q^{97}+O(q^{100}) \) 10 * q + 3 * q^2 + 127 * q^4 + 219 * q^5 - 121 * q^7 - 132 * q^10 - 483 * q^11 - 841 * q^13 - 12174 * q^14 - 1985 * q^16 + 6176 * q^19 + 63186 * q^20 + 3471 * q^22 - 53565 * q^23 + 8452 * q^25 - 22660 * q^28 + 80679 * q^29 - 24601 * q^31 - 218295 * q^32 + 7425 * q^34 + 12764 * q^37 + 371877 * q^38 + 54150 * q^40 - 232251 * q^41 - 93271 * q^43 + 112512 * q^46 + 142887 * q^47 + 86238 * q^49 - 318459 * q^50 + 186920 * q^52 - 419982 * q^55 - 342546 * q^56 - 380658 * q^58 + 995061 * q^59 - 59305 * q^61 + 403066 * q^64 - 1642029 * q^65 + 158513 * q^67 + 1693791 * q^68 - 304788 * q^70 + 933896 * q^73 - 595182 * q^74 + 666641 * q^76 + 2198883 * q^77 + 468707 * q^79 - 2038470 * q^82 - 3008337 * q^83 - 1189944 * q^85 - 1905549 * q^86 - 349773 * q^88 - 211778 * q^91 + 973788 * q^92 + 809124 * q^94 + 2562954 * q^95 + 336029 * q^97

Introduction

L-functions

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