LMFDB - Embedded newform 26.5.d.b.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(5,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("26.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.d (of order $4$, degree $2$, 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:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 522x^{4} + 68121x^{2} + 54756 $ x^6 + 522x^4 + 68121x^2 + 54756
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$-15.6870i$ of defining polynomial
Character	$\chi$	$=$	26.5
Dual form			26.5.d.b.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 2.00000i) q^{2} +15.6870 q^{3} -8.00000i q^{4} +(-24.8574 + 24.8574i) q^{5} +(31.3741 - 31.3741i) q^{6} +(-19.1704 - 19.1704i) q^{7} +(-16.0000 - 16.0000i) q^{8} +165.083 q^{9} +O(q^{10})$	\(q+(2.00000 - 2.00000i) q^{2} +15.6870 q^{3} -8.00000i q^{4} +(-24.8574 + 24.8574i) q^{5} +(31.3741 - 31.3741i) q^{6} +(-19.1704 - 19.1704i) q^{7} +(-16.0000 - 16.0000i) q^{8} +165.083 q^{9} +99.4296i q^{10} +(-121.804 - 121.804i) q^{11} -125.496i q^{12} +(2.23147 + 168.985i) q^{13} -76.6814 q^{14} +(-389.939 + 389.939i) q^{15} -64.0000 q^{16} +214.028i q^{17} +(330.166 - 330.166i) q^{18} +(261.735 - 261.735i) q^{19} +(198.859 + 198.859i) q^{20} +(-300.726 - 300.726i) q^{21} -487.215 q^{22} +200.448i q^{23} +(-250.993 - 250.993i) q^{24} -610.780i q^{25} +(342.433 + 333.508i) q^{26} +1319.02 q^{27} +(-153.363 + 153.363i) q^{28} +384.896 q^{29} +1559.76i q^{30} +(525.347 - 525.347i) q^{31} +(-128.000 + 128.000i) q^{32} +(-1910.74 - 1910.74i) q^{33} +(428.055 + 428.055i) q^{34} +953.050 q^{35} -1320.67i q^{36} +(553.816 + 553.816i) q^{37} -1046.94i q^{38} +(35.0052 + 2650.88i) q^{39} +795.437 q^{40} +(-495.881 + 495.881i) q^{41} -1202.90 q^{42} -2761.02i q^{43} +(-974.429 + 974.429i) q^{44} +(-4103.54 + 4103.54i) q^{45} +(400.896 + 400.896i) q^{46} +(-861.536 - 861.536i) q^{47} -1003.97 q^{48} -1666.00i q^{49} +(-1221.56 - 1221.56i) q^{50} +3357.46i q^{51} +(1351.88 - 17.8518i) q^{52} -3729.57 q^{53} +(2638.03 - 2638.03i) q^{54} +6055.44 q^{55} +613.451i q^{56} +(4105.85 - 4105.85i) q^{57} +(769.793 - 769.793i) q^{58} +(3767.92 + 3767.92i) q^{59} +(3119.51 + 3119.51i) q^{60} +2525.59 q^{61} -2101.39i q^{62} +(-3164.70 - 3164.70i) q^{63} +512.000i q^{64} +(-4256.00 - 4145.06i) q^{65} -7642.95 q^{66} +(-1776.91 + 1776.91i) q^{67} +1712.22 q^{68} +3144.44i q^{69} +(1906.10 - 1906.10i) q^{70} +(-2831.37 + 2831.37i) q^{71} +(-2641.33 - 2641.33i) q^{72} +(4989.40 + 4989.40i) q^{73} +2215.27 q^{74} -9581.33i q^{75} +(-2093.88 - 2093.88i) q^{76} +4670.04i q^{77} +(5371.77 + 5231.75i) q^{78} -6672.68 q^{79} +(1590.87 - 1590.87i) q^{80} +7319.73 q^{81} +1983.52i q^{82} +(-3471.45 + 3471.45i) q^{83} +(-2405.81 + 2405.81i) q^{84} +(-5320.17 - 5320.17i) q^{85} +(-5522.05 - 5522.05i) q^{86} +6037.89 q^{87} +3897.72i q^{88} +(-4348.32 - 4348.32i) q^{89} +16414.2i q^{90} +(3196.73 - 3282.29i) q^{91} +1603.59 q^{92} +(8241.14 - 8241.14i) q^{93} -3446.14 q^{94} +13012.1i q^{95} +(-2007.94 + 2007.94i) q^{96} +(-5982.40 + 5982.40i) q^{97} +(-3331.99 - 3331.99i) q^{98} +(-20107.7 - 20107.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9	$ 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9} - 66 q^{11} - 294 q^{13} - 360 q^{14} - 288 q^{15} - 384 q^{16} + 1116 q^{18} - 318 q^{19} + 240 q^{20} + 756 q^{21} - 264 q^{22} + 84 q^{26} - 1404 q^{27} - 720 q^{28} - 276 q^{29} + 3282 q^{31} - 768 q^{32} - 3240 q^{33} + 2280 q^{34} + 5424 q^{35} - 3006 q^{37} + 2376 q^{39} + 960 q^{40} - 894 q^{41} + 3024 q^{42} - 528 q^{44} - 17226 q^{45} - 4848 q^{46} + 1566 q^{47} - 3300 q^{50} + 2688 q^{52} - 1356 q^{53} - 2808 q^{54} + 22212 q^{55} + 16812 q^{57} - 552 q^{58} + 5178 q^{59} + 2304 q^{60} + 2172 q^{61} - 24210 q^{63} + 1146 q^{65} - 12960 q^{66} + 1134 q^{67} + 9120 q^{68} + 10848 q^{70} - 18498 q^{71} - 8928 q^{72} - 13278 q^{73} - 12024 q^{74} + 2544 q^{76} + 25992 q^{78} - 13596 q^{79} + 1920 q^{80} + 58158 q^{81} - 11490 q^{83} + 6048 q^{84} - 10512 q^{85} - 7128 q^{86} + 30744 q^{87} - 28038 q^{89} - 6402 q^{91} - 19392 q^{92} + 23364 q^{93} + 6264 q^{94} - 27378 q^{97} - 11340 q^{98} - 61074 q^{99}+O(q^{100}) $ 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9 - 66 * q^11 - 294 * q^13 - 360 * q^14 - 288 * q^15 - 384 * q^16 + 1116 * q^18 - 318 * q^19 + 240 * q^20 + 756 * q^21 - 264 * q^22 + 84 * q^26 - 1404 * q^27 - 720 * q^28 - 276 * q^29 + 3282 * q^31 - 768 * q^32 - 3240 * q^33 + 2280 * q^34 + 5424 * q^35 - 3006 * q^37 + 2376 * q^39 + 960 * q^40 - 894 * q^41 + 3024 * q^42 - 528 * q^44 - 17226 * q^45 - 4848 * q^46 + 1566 * q^47 - 3300 * q^50 + 2688 * q^52 - 1356 * q^53 - 2808 * q^54 + 22212 * q^55 + 16812 * q^57 - 552 * q^58 + 5178 * q^59 + 2304 * q^60 + 2172 * q^61 - 24210 * q^63 + 1146 * q^65 - 12960 * q^66 + 1134 * q^67 + 9120 * q^68 + 10848 * q^70 - 18498 * q^71 - 8928 * q^72 - 13278 * q^73 - 12024 * q^74 + 2544 * q^76 + 25992 * q^78 - 13596 * q^79 + 1920 * q^80 + 58158 * q^81 - 11490 * q^83 + 6048 * q^84 - 10512 * q^85 - 7128 * q^86 + 30744 * q^87 - 28038 * q^89 - 6402 * q^91 - 19392 * q^92 + 23364 * q^93 + 6264 * q^94 - 27378 * q^97 - 11340 * q^98 - 61074 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$	15.6870			1.74300			0.871502	−	0.490392i	$-0.163146\pi$
$3$	15.6870			1.74300			0.871502	+	0.490392i	$0.163146\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−24.8574	+	24.8574i	−0.994296	+	0.994296i	−0.999984	−	0.00568817i	$-0.998189\pi$
$5$	−24.8574	+	24.8574i	−0.994296	+	0.994296i	0.00568817	+	0.999984i	$0.498189\pi$
$6$	31.3741	−	31.3741i	0.871502	−	0.871502i
$7$	−19.1704	−	19.1704i	−0.391232	−	0.391232i	0.483895	−	0.875126i	$-0.339222\pi$
$7$	−19.1704	−	19.1704i	−0.391232	−	0.391232i	−0.875126	+	0.483895i	$0.839222\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	165.083			2.03806
$10$			99.4296i			0.994296i
$11$	−121.804	−	121.804i	−1.00664	−	1.00664i	−0.999978	−	0.00666391i	$-0.997879\pi$
$11$	−121.804	−	121.804i	−1.00664	−	1.00664i	−0.00666391	−	0.999978i	$-0.502121\pi$
$12$		−	125.496i		−	0.871502i
$13$	2.23147	+	168.985i	0.0132040	+	0.999913i
$13$	2.23147	+	168.985i	0.0132040	+	0.999913i
$14$	−76.6814			−0.391232
$15$	−389.939	+	389.939i	−1.73306	+	1.73306i
$16$	−64.0000			−0.250000
$17$			214.028i			0.740580i	0.928916	+	0.370290i	$0.120742\pi$
$17$			214.028i			0.740580i	−0.928916	+	0.370290i	$0.879258\pi$
$18$	330.166	−	330.166i	1.01903	−	1.01903i
$19$	261.735	−	261.735i	0.725028	−	0.725028i	−0.244597	−	0.969625i	$-0.578656\pi$
$19$	261.735	−	261.735i	0.725028	−	0.725028i	0.969625	+	0.244597i	$0.0786556\pi$
$20$	198.859	+	198.859i	0.497148	+	0.497148i
$21$	−300.726	−	300.726i	−0.681919	−	0.681919i
$22$	−487.215			−1.00664
$23$			200.448i			0.378919i	0.981889	+	0.189460i	$0.0606736\pi$
$23$			200.448i			0.378919i	−0.981889	+	0.189460i	$0.939326\pi$
$24$	−250.993	−	250.993i	−0.435751	−	0.435751i
$25$		−	610.780i		−	0.977248i
$26$	342.433	+	333.508i	0.506558	+	0.493354i
$27$	1319.02			1.80935
$28$	−153.363	+	153.363i	−0.195616	+	0.195616i
$29$	384.896			0.457665			0.228833	−	0.973466i	$-0.426509\pi$
$29$	384.896			0.457665			0.228833	+	0.973466i	$0.426509\pi$
$30$			1559.76i			1.73306i
$31$	525.347	−	525.347i	0.546667	−	0.546667i	−0.378808	−	0.925475i	$-0.623666\pi$
$31$	525.347	−	525.347i	0.546667	−	0.546667i	0.925475	+	0.378808i	$0.123666\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	−1910.74	−	1910.74i	−1.75458	−	1.75458i
$34$	428.055	+	428.055i	0.370290	+	0.370290i
$35$	953.050			0.778000
$36$		−	1320.67i		−	1.01903i
$37$	553.816	+	553.816i	0.404541	+	0.404541i	0.879830	−	0.475289i	$-0.157656\pi$
$37$	553.816	+	553.816i	0.404541	+	0.404541i	−0.475289	+	0.879830i	$0.657656\pi$
$38$		−	1046.94i		−	0.725028i
$39$	35.0052	+	2650.88i	0.0230146	+	1.74285i
$40$	795.437			0.497148
$41$	−495.881	+	495.881i	−0.294992	+	0.294992i	−0.839048	−	0.544057i	$-0.816888\pi$
$41$	−495.881	+	495.881i	−0.294992	+	0.294992i	0.544057	+	0.839048i	$0.316888\pi$
$42$	−1202.90			−0.681919
$43$		−	2761.02i		−	1.49325i	−0.665244	−	0.746626i	$-0.731672\pi$
$43$		−	2761.02i		−	1.49325i	0.665244	−	0.746626i	$-0.268328\pi$
$44$	−974.429	+	974.429i	−0.503321	+	0.503321i
$45$	−4103.54	+	4103.54i	−2.02644	+	2.02644i
$46$	400.896	+	400.896i	0.189460	+	0.189460i
$47$	−861.536	−	861.536i	−0.390012	−	0.390012i	0.484680	−	0.874692i	$-0.338936\pi$
$47$	−861.536	−	861.536i	−0.390012	−	0.390012i	−0.874692	+	0.484680i	$0.838936\pi$
$48$	−1003.97			−0.435751
$49$		−	1666.00i		−	0.693876i
$50$	−1221.56	−	1221.56i	−0.488624	−	0.488624i
$51$			3357.46i			1.29083i
$52$	1351.88	−	17.8518i	0.499956	−	0.00660199i
$53$	−3729.57			−1.32772			−0.663860	−	0.747857i	$-0.731083\pi$
$53$	−3729.57			−1.32772			−0.663860	+	0.747857i	$0.731083\pi$
$54$	2638.03	−	2638.03i	0.904676	−	0.904676i
$55$	6055.44			2.00180
$56$			613.451i			0.195616i
$57$	4105.85	−	4105.85i	1.26373	−	1.26373i
$58$	769.793	−	769.793i	0.228833	−	0.228833i
$59$	3767.92	+	3767.92i	1.08243	+	1.08243i	0.996283	+	0.0861425i	$0.0274540\pi$
$59$	3767.92	+	3767.92i	1.08243	+	1.08243i	0.0861425	+	0.996283i	$0.472546\pi$
$60$	3119.51	+	3119.51i	0.866531	+	0.866531i
$61$	2525.59			0.678741			0.339370	−	0.940653i	$-0.389786\pi$
$61$	2525.59			0.678741			0.339370	+	0.940653i	$0.389786\pi$
$62$		−	2101.39i		−	0.546667i
$63$	−3164.70	−	3164.70i	−0.797355	−	0.797355i
$64$			512.000i			0.125000i
$65$	−4256.00	−	4145.06i	−1.00734	−	0.981080i
$66$	−7642.95			−1.75458
$67$	−1776.91	+	1776.91i	−0.395837	+	0.395837i	−0.876762	−	0.480925i	$-0.840301\pi$
$67$	−1776.91	+	1776.91i	−0.395837	+	0.395837i	0.480925	+	0.876762i	$0.340301\pi$
$68$	1712.22			0.370290
$69$			3144.44i			0.660458i
$70$	1906.10	−	1906.10i	0.389000	−	0.389000i
$71$	−2831.37	+	2831.37i	−0.561668	+	0.561668i	−0.929781	−	0.368113i	$-0.880004\pi$
$71$	−2831.37	+	2831.37i	−0.561668	+	0.561668i	0.368113	+	0.929781i	$0.380004\pi$
$72$	−2641.33	−	2641.33i	−0.509516	−	0.509516i
$73$	4989.40	+	4989.40i	0.936273	+	0.936273i	0.998088	−	0.0618144i	$-0.0196887\pi$
$73$	4989.40	+	4989.40i	0.936273	+	0.936273i	−0.0618144	+	0.998088i	$0.519689\pi$
$74$	2215.27			0.404541
$75$		−	9581.33i		−	1.70335i
$76$	−2093.88	−	2093.88i	−0.362514	−	0.362514i
$77$			4670.04i			0.787660i
$78$	5371.77	+	5231.75i	0.882934	+	0.859919i
$79$	−6672.68			−1.06917			−0.534584	−	0.845115i	$-0.679532\pi$
$79$	−6672.68			−1.06917			−0.534584	+	0.845115i	$0.679532\pi$
$80$	1590.87	−	1590.87i	0.248574	−	0.248574i
$81$	7319.73			1.11564
$82$			1983.52i			0.294992i
$83$	−3471.45	+	3471.45i	−0.503911	+	0.503911i	−0.912651	−	0.408740i	$-0.865968\pi$
$83$	−3471.45	+	3471.45i	−0.503911	+	0.503911i	0.408740	+	0.912651i	$0.365968\pi$
$84$	−2405.81	+	2405.81i	−0.340959	+	0.340959i
$85$	−5320.17	−	5320.17i	−0.736356	−	0.736356i
$86$	−5522.05	−	5522.05i	−0.746626	−	0.746626i
$87$	6037.89			0.797712
$88$			3897.72i			0.503321i
$89$	−4348.32	−	4348.32i	−0.548961	−	0.548961i	0.377179	−	0.926140i	$-0.376894\pi$
$89$	−4348.32	−	4348.32i	−0.548961	−	0.548961i	−0.926140	+	0.377179i	$0.876894\pi$
$90$			16414.2i			2.02644i
$91$	3196.73	−	3282.29i	0.386032	−	0.396363i
$92$	1603.59			0.189460
$93$	8241.14	−	8241.14i	0.952843	−	0.952843i
$94$	−3446.14			−0.390012
$95$			13012.1i			1.44178i
$96$	−2007.94	+	2007.94i	−0.217876	+	0.217876i
$97$	−5982.40	+	5982.40i	−0.635817	+	0.635817i	−0.949521	−	0.313704i	$-0.898430\pi$
$97$	−5982.40	+	5982.40i	−0.635817	+	0.635817i	0.313704	+	0.949521i	$0.398430\pi$
$98$	−3331.99	−	3331.99i	−0.346938	−	0.346938i
$99$	−20107.7	−	20107.7i	−2.05160	−	2.05160i
$100$	−4886.24			−0.488624
$101$			8321.49i			0.815753i	0.913037	+	0.407876i	$0.133731\pi$
$101$			8321.49i			0.815753i	−0.913037	+	0.407876i	$0.866269\pi$
$102$	6714.92	+	6714.92i	0.645417	+	0.645417i
$103$		−	6095.04i		−	0.574516i	−0.957853	−	0.287258i	$-0.907256\pi$
$103$		−	6095.04i		−	0.574516i	0.957853	−	0.287258i	$-0.0927438\pi$
$104$	2668.06	−	2739.47i	0.246677	−	0.253279i
$105$	14950.5			1.35606
$106$	−7459.14	+	7459.14i	−0.663860	+	0.663860i
$107$	14500.9			1.26656			0.633282	−	0.773921i	$-0.281707\pi$
$107$	14500.9			1.26656			0.633282	+	0.773921i	$0.281707\pi$
$108$		−	10552.1i		−	0.904676i
$109$	11385.4	−	11385.4i	0.958286	−	0.958286i	−0.0408778	−	0.999164i	$-0.513015\pi$
$109$	11385.4	−	11385.4i	0.958286	−	0.958286i	0.999164	+	0.0408778i	$0.0130154\pi$
$110$	12110.9	−	12110.9i	1.00090	−	1.00090i
$111$	8687.74	+	8687.74i	0.705116	+	0.705116i
$112$	1226.90	+	1226.90i	0.0978079	+	0.0978079i
$113$	−16249.4			−1.27257			−0.636284	−	0.771455i	$-0.719529\pi$
$113$	−16249.4			−1.27257			−0.636284	+	0.771455i	$0.719529\pi$
$114$		−	16423.4i		−	1.26373i
$115$	−4982.62	−	4982.62i	−0.376758	−	0.376758i
$116$		−	3079.17i		−	0.228833i
$117$	368.379	+	27896.6i	0.0269106	+	2.03789i
$118$	15071.7			1.08243
$119$	4102.99	−	4102.99i	0.289739	−	0.289739i
$120$	12478.0			0.866531
$121$			15031.3i			1.02666i
$122$	5051.19	−	5051.19i	0.339370	−	0.339370i
$123$	−7778.90	+	7778.90i	−0.514172	+	0.514172i
$124$	−4202.77	−	4202.77i	−0.273333	−	0.273333i
$125$	−353.477	−	353.477i	−0.0226225	−	0.0226225i
$126$	−12658.8			−0.797355
$127$			11260.9i			0.698177i	0.937090	+	0.349088i	$0.113509\pi$
$127$			11260.9i			0.698177i	−0.937090	+	0.349088i	$0.886491\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$		−	43312.3i		−	2.60275i
$130$	−16802.1	+	221.874i	−0.994209	+	0.0131287i
$131$	8340.38			0.486008			0.243004	−	0.970025i	$-0.421867\pi$
$131$	8340.38			0.486008			0.243004	+	0.970025i	$0.421867\pi$
$132$	−15285.9	+	15285.9i	−0.877290	+	0.877290i
$133$	−10035.1			−0.567308
$134$			7107.65i			0.395837i
$135$	−32787.3	+	32787.3i	−1.79903	+	1.79903i
$136$	3424.44	−	3424.44i	0.185145	−	0.185145i
$137$	16636.0	+	16636.0i	0.886357	+	0.886357i	0.994171	−	0.107814i	$-0.0343852\pi$
$137$	16636.0	+	16636.0i	0.886357	+	0.886357i	−0.107814	+	0.994171i	$0.534385\pi$
$138$	6288.88	+	6288.88i	0.330229	+	0.330229i
$139$	−2418.22			−0.125160			−0.0625801	−	0.998040i	$-0.519933\pi$
$139$	−2418.22			−0.125160			−0.0625801	+	0.998040i	$0.519933\pi$
$140$		−	7624.40i		−	0.389000i
$141$	−13515.0	−	13515.0i	−0.679792	−	0.679792i
$142$			11325.5i			0.561668i
$143$	20311.2	−	20854.8i	0.993262	−	1.01985i
$144$	−10565.3			−0.509516
$145$	−9567.52	+	9567.52i	−0.455055	+	0.455055i
$146$	19957.6			0.936273
$147$		−	26134.5i		−	1.20943i
$148$	4430.53	−	4430.53i	0.202270	−	0.202270i
$149$	15832.3	−	15832.3i	0.713133	−	0.713133i	−0.254056	−	0.967189i	$-0.581765\pi$
$149$	15832.3	−	15832.3i	0.713133	−	0.713133i	0.967189	+	0.254056i	$0.0817648\pi$
$150$	−19162.7	−	19162.7i	−0.851674	−	0.851674i
$151$	−8120.71	−	8120.71i	−0.356156	−	0.356156i	0.506238	−	0.862394i	$-0.331036\pi$
$151$	−8120.71	−	8120.71i	−0.356156	−	0.356156i	−0.862394	+	0.506238i	$0.831036\pi$
$152$	−8375.53			−0.362514
$153$			35332.4i			1.50935i
$154$	9340.07	+	9340.07i	0.393830	+	0.393830i
$155$			26117.5i			1.08710i
$156$	21207.0	−	280.041i	0.871426	−	0.0115073i
$157$	−14794.6			−0.600210			−0.300105	−	0.953906i	$-0.597022\pi$
$157$	−14794.6			−0.600210			−0.300105	+	0.953906i	$0.597022\pi$
$158$	−13345.4	+	13345.4i	−0.534584	+	0.534584i
$159$	−58505.9			−2.31422
$160$		−	6363.49i		−	0.248574i
$161$	3842.66	−	3842.66i	0.148245	−	0.148245i
$162$	14639.5	−	14639.5i	0.557821	−	0.557821i
$163$	1467.11	+	1467.11i	0.0552189	+	0.0552189i	0.734177	−	0.678958i	$-0.237568\pi$
$163$	1467.11	+	1467.11i	0.0552189	+	0.0552189i	−0.678958	+	0.734177i	$0.737568\pi$
$164$	3967.05	+	3967.05i	0.147496	+	0.147496i
$165$	94992.0			3.48914
$166$			13885.8i			0.503911i
$167$	−2651.48	−	2651.48i	−0.0950724	−	0.0950724i	0.657971	−	0.753043i	$-0.271415\pi$
$167$	−2651.48	−	2651.48i	−0.0950724	−	0.0950724i	−0.753043	+	0.657971i	$0.771415\pi$
$168$			9623.23i			0.340959i
$169$	−28551.0	+	754.172i	−0.999651	+	0.0264056i
$170$	−21280.7			−0.736356
$171$	43208.1	−	43208.1i	1.47765	−	1.47765i
$172$	−22088.2			−0.746626
$173$		−	33811.1i		−	1.12971i	−0.825190	−	0.564856i	$-0.808932\pi$
$173$		−	33811.1i		−	1.12971i	0.825190	−	0.564856i	$-0.191068\pi$
$174$	12075.8	−	12075.8i	0.398856	−	0.398856i
$175$	−11708.9	+	11708.9i	−0.382330	+	0.382330i
$176$	7795.43	+	7795.43i	0.251660	+	0.251660i
$177$	59107.6	+	59107.6i	1.88667	+	1.88667i
$178$	−17393.3			−0.548961
$179$		−	13403.4i		−	0.418320i	−0.977881	−	0.209160i	$-0.932927\pi$
$179$		−	13403.4i		−	0.418320i	0.977881	−	0.209160i	$-0.0670730\pi$
$180$	32828.3	+	32828.3i	1.01322	+	1.01322i
$181$		−	50105.0i		−	1.52941i	−0.644381	−	0.764705i	$-0.722885\pi$
$181$		−	50105.0i		−	1.52941i	0.644381	−	0.764705i	$-0.277115\pi$
$182$	−171.112	−	12958.0i	−0.00516581	−	0.391198i
$183$	39619.1			1.18305
$184$	3207.17	−	3207.17i	0.0947298	−	0.0947298i
$185$	−27532.9			−0.804466
$186$		−	32964.5i		−	0.952843i
$187$	26069.4	−	26069.4i	0.745499	−	0.745499i
$188$	−6892.29	+	6892.29i	−0.195006	+	0.195006i
$189$	−25286.0	−	25286.0i	−0.707875	−	0.707875i
$190$	26024.2	+	26024.2i	0.720892	+	0.720892i
$191$	−42392.9			−1.16206			−0.581028	−	0.813884i	$-0.697349\pi$
$191$	−42392.9			−1.16206			−0.581028	+	0.813884i	$0.697349\pi$
$192$			8031.76i			0.217876i
$193$	21880.0	+	21880.0i	0.587398	+	0.587398i	0.936926	−	0.349528i	$-0.113658\pi$
$193$	21880.0	+	21880.0i	0.587398	+	0.587398i	−0.349528	+	0.936926i	$0.613658\pi$
$194$			23929.6i			0.635817i
$195$	−66764.1	−	65023.8i	−1.75579	−	1.71003i
$196$	−13328.0			−0.346938
$197$	−23173.2	+	23173.2i	−0.597109	+	0.597109i	−0.939542	−	0.342433i	$-0.888749\pi$
$197$	−23173.2	+	23173.2i	−0.597109	+	0.597109i	0.342433	+	0.939542i	$0.388749\pi$
$198$	−80431.0			−2.05160
$199$			66023.4i			1.66722i	0.552357	+	0.833608i	$0.313729\pi$
$199$			66023.4i			1.66722i	−0.552357	+	0.833608i	$0.686271\pi$
$200$	−9772.48	+	9772.48i	−0.244312	+	0.244312i
$201$	−27874.5	+	27874.5i	−0.689945	+	0.689945i
$202$	16643.0	+	16643.0i	0.407876	+	0.407876i
$203$	−7378.60	−	7378.60i	−0.179053	−	0.179053i
$204$	26859.7			0.645417
$205$		−	24652.6i		−	0.586618i
$206$	−12190.1	−	12190.1i	−0.287258	−	0.287258i
$207$			33090.6i			0.772262i
$208$	−142.814	−	10815.1i	−0.00330099	−	0.249978i
$209$	−63760.6			−1.45969
$210$	29901.1	−	29901.1i	0.678029	−	0.678029i
$211$	55880.9			1.25516			0.627579	−	0.778553i	$-0.284046\pi$
$211$	55880.9			1.25516			0.627579	+	0.778553i	$0.284046\pi$
$212$			29836.5i			0.663860i
$213$	−44415.8	+	44415.8i	−0.978990	+	0.978990i
$214$	29001.8	−	29001.8i	0.633282	−	0.633282i
$215$	68631.8	+	68631.8i	1.48473	+	1.48473i
$216$	−21104.3	−	21104.3i	−0.452338	−	0.452338i
$217$	−20142.2			−0.427747
$218$		−	45541.6i		−	0.958286i
$219$	78268.9	+	78268.9i	1.63193	+	1.63193i
$220$		−	48443.5i		−	1.00090i
$221$	−36167.5	+	477.597i	−0.740516	+	0.00977860i
$222$	34751.0			0.705116
$223$	4976.75	−	4976.75i	0.100077	−	0.100077i	−0.655295	−	0.755373i	$-0.727456\pi$
$223$	4976.75	−	4976.75i	0.100077	−	0.100077i	0.755373	+	0.655295i	$0.227456\pi$
$224$	4907.61			0.0978079
$225$		−	100830.i		−	1.99169i
$226$	−32498.8	+	32498.8i	−0.636284	+	0.636284i
$227$	25079.8	−	25079.8i	0.486712	−	0.486712i	−0.420555	−	0.907267i	$-0.638165\pi$
$227$	25079.8	−	25079.8i	0.486712	−	0.486712i	0.907267	+	0.420555i	$0.138165\pi$
$228$	−32846.8	−	32846.8i	−0.631864	−	0.631864i
$229$	−9795.19	−	9795.19i	−0.186785	−	0.186785i	0.607520	−	0.794305i	$-0.292165\pi$
$229$	−9795.19	−	9795.19i	−0.186785	−	0.186785i	−0.794305	+	0.607520i	$0.792165\pi$
$230$	−19930.5			−0.376758
$231$			73259.1i			1.37290i
$232$	−6158.34	−	6158.34i	−0.114416	−	0.114416i
$233$		−	79317.3i		−	1.46102i	−0.682902	−	0.730510i	$-0.739282\pi$
$233$		−	79317.3i		−	1.46102i	0.682902	−	0.730510i	$-0.260718\pi$
$234$	56530.0	+	55056.5i	1.03240	+	1.00549i
$235$	42831.1			0.775574
$236$	30143.4	−	30143.4i	0.541213	−	0.541213i
$237$	−104675.			−1.86356
$238$		−	16411.9i		−	0.289739i
$239$	−14491.6	+	14491.6i	−0.253699	+	0.253699i	−0.822486	−	0.568786i	$-0.807413\pi$
$239$	−14491.6	+	14491.6i	−0.253699	+	0.253699i	0.568786	+	0.822486i	$0.307413\pi$
$240$	24956.1	−	24956.1i	0.433265	−	0.433265i
$241$	13605.1	+	13605.1i	0.234244	+	0.234244i	0.814462	−	0.580217i	$-0.197032\pi$
$241$	13605.1	+	13605.1i	0.234244	+	0.234244i	−0.580217	+	0.814462i	$0.697032\pi$
$242$	30062.5	+	30062.5i	0.513328	+	0.513328i
$243$	7984.53			0.135219
$244$		−	20204.8i		−	0.339370i
$245$	41412.3	+	41412.3i	0.689917	+	0.689917i
$246$			31115.6i			0.514172i
$247$	44813.4	+	43645.3i	0.734538	+	0.715392i
$248$	−16811.1			−0.273333
$249$	−54456.7	+	54456.7i	−0.878320	+	0.878320i
$250$	−1413.91			−0.0226225
$251$		−	98939.6i		−	1.57044i	−0.619214	−	0.785222i	$-0.712549\pi$
$251$		−	98939.6i		−	1.57044i	0.619214	−	0.785222i	$-0.287451\pi$
$252$	−25317.6	+	25317.6i	−0.398678	+	0.398678i
$253$	24415.3	−	24415.3i	0.381436	−	0.381436i
$254$	22521.8	+	22521.8i	0.349088	+	0.349088i
$255$	−83457.7	−	83457.7i	−1.28347	−	1.28347i
$256$	4096.00			0.0625000
$257$			30271.6i			0.458321i	0.973389	+	0.229160i	$0.0735981\pi$
$257$			30271.6i			0.458321i	−0.973389	+	0.229160i	$0.926402\pi$
$258$	−86624.6	−	86624.6i	−1.30137	−	1.30137i
$259$		−	21233.7i		−	0.316538i
$260$	−33160.5	+	34048.0i	−0.490540	+	0.503669i
$261$	63539.9			0.932751
$262$	16680.8	−	16680.8i	0.243004	−	0.243004i
$263$	125142.			1.80922			0.904609	−	0.426243i	$-0.140163\pi$
$263$	125142.			1.80922			0.904609	+	0.426243i	$0.140163\pi$
$264$			61143.6i			0.877290i
$265$	92707.3	−	92707.3i	1.32015	−	1.32015i
$266$	−20070.2	+	20070.2i	−0.283654	+	0.283654i
$267$	−68212.3	−	68212.3i	−0.956842	−	0.956842i
$268$	14215.3	+	14215.3i	0.197918	+	0.197918i
$269$	12035.1			0.166321			0.0831604	−	0.996536i	$-0.473499\pi$
$269$	12035.1			0.166321			0.0831604	+	0.996536i	$0.473499\pi$
$270$			131149.i			1.79903i
$271$	−50235.1	−	50235.1i	−0.684020	−	0.684020i	0.276883	−	0.960904i	$-0.410699\pi$
$271$	−50235.1	−	50235.1i	−0.684020	−	0.684020i	−0.960904	+	0.276883i	$0.910699\pi$
$272$		−	13697.8i		−	0.185145i
$273$	50147.2	−	51489.3i	0.672855	−	0.690863i
$274$	66544.1			0.886357
$275$	−74395.2	+	74395.2i	−0.983738	+	0.983738i
$276$	25155.5			0.330229
$277$			98029.0i			1.27760i	0.769372	+	0.638800i	$0.220569\pi$
$277$			98029.0i			1.27760i	−0.769372	+	0.638800i	$0.779431\pi$
$278$	−4836.44	+	4836.44i	−0.0625801	+	0.0625801i
$279$	86725.9	−	86725.9i	1.11414	−	1.11414i
$280$	−15248.8	−	15248.8i	−0.194500	−	0.194500i
$281$	−9669.18	−	9669.18i	−0.122455	−	0.122455i	0.643223	−	0.765679i	$-0.277597\pi$
$281$	−9669.18	−	9669.18i	−0.122455	−	0.122455i	−0.765679	+	0.643223i	$0.777597\pi$
$282$	−54059.8			−0.679792
$283$			49043.4i			0.612361i	0.951973	+	0.306181i	$0.0990511\pi$
$283$			49043.4i			0.612361i	−0.951973	+	0.306181i	$0.900949\pi$
$284$	22651.0	+	22651.0i	0.280834	+	0.280834i
$285$			204121.i			2.51304i
$286$	−1087.21	−	82332.1i	−0.0132917	−	1.00655i
$287$	19012.4			0.230820
$288$	−21130.7	+	21130.7i	−0.254758	+	0.254758i
$289$	37713.1			0.451541
$290$			38270.1i			0.455055i
$291$	−93846.2	+	93846.2i	−1.10823	+	1.10823i
$292$	39915.2	−	39915.2i	0.468137	−	0.468137i
$293$	−12448.3	−	12448.3i	−0.145002	−	0.145002i	0.630879	−	0.775881i	$-0.282694\pi$
$293$	−12448.3	−	12448.3i	−0.145002	−	0.145002i	−0.775881	+	0.630879i	$0.782694\pi$
$294$	−52269.1	−	52269.1i	−0.604714	−	0.604714i
$295$	−187321.			−2.15250
$296$		−	17722.1i		−	0.202270i
$297$	−160661.	−	160661.i	−1.82137	−	1.82137i
$298$		−	63329.1i		−	0.713133i
$299$	−33872.8	+	447.295i	−0.378886	+	0.00500324i
$300$	−76650.6			−0.851674
$301$	−52929.8	+	52929.8i	−0.584207	+	0.584207i
$302$	−32482.8			−0.356156
$303$			130540.i			1.42186i
$304$	−16751.1	+	16751.1i	−0.181257	+	0.181257i
$305$	−62779.7	+	62779.7i	−0.674869	+	0.674869i
$306$	70664.8	+	70664.8i	0.754675	+	0.754675i
$307$	−47991.9	−	47991.9i	−0.509204	−	0.509204i	0.405078	−	0.914282i	$-0.367244\pi$
$307$	−47991.9	−	47991.9i	−0.509204	−	0.509204i	−0.914282	+	0.405078i	$0.867244\pi$
$308$	37360.3			0.393830
$309$		−	95613.2i		−	1.00138i
$310$	52235.0	+	52235.0i	0.543548	+	0.543548i
$311$		−	139514.i		−	1.44244i	−0.692707	−	0.721219i	$-0.743582\pi$
$311$		−	139514.i		−	1.44244i	0.692707	−	0.721219i	$-0.256418\pi$
$312$	41854.0	−	42974.1i	0.429959	−	0.441467i
$313$	128894.			1.31566			0.657831	−	0.753166i	$-0.271474\pi$
$313$	128894.			1.31566			0.657831	+	0.753166i	$0.271474\pi$
$314$	−29589.1	+	29589.1i	−0.300105	+	0.300105i
$315$	157333.			1.58561
$316$			53381.4i			0.534584i
$317$	87302.4	−	87302.4i	0.868776	−	0.868776i	−0.123561	−	0.992337i	$-0.539432\pi$
$317$	87302.4	−	87302.4i	0.868776	−	0.868776i	0.992337	+	0.123561i	$0.0394316\pi$
$318$	−117012.	+	117012.i	−1.15711	+	1.15711i
$319$	−46881.8	−	46881.8i	−0.460705	−	0.460705i
$320$	−12727.0	−	12727.0i	−0.124287	−	0.124287i
$321$	227476.			2.20763
$322$		−	15370.7i		−	0.148245i
$323$	56018.6	+	56018.6i	0.536942	+	0.536942i
$324$		−	58557.8i		−	0.557821i
$325$	103213.	−	1362.94i	0.977163	−	0.0129036i
$326$	5868.45			0.0552189
$327$	178603.	−	178603.i	1.67030	−	1.67030i
$328$	15868.2			0.147496
$329$			33031.9i			0.305170i
$330$	189984.	−	189984.i	1.74457	−	1.74457i
$331$	−80301.0	+	80301.0i	−0.732935	+	0.732935i	−0.971200	−	0.238266i	$-0.923421\pi$
$331$	−80301.0	+	80301.0i	−0.732935	+	0.732935i	0.238266	+	0.971200i	$0.423421\pi$
$332$	27771.6	+	27771.6i	0.251956	+	0.251956i
$333$	91425.8	+	91425.8i	0.824480	+	0.824480i
$334$	−10605.9			−0.0950724
$335$		−	88338.8i		−	0.787158i
$336$	19246.5	+	19246.5i	0.170480	+	0.170480i
$337$			173490.i			1.52762i	0.645442	+	0.763809i	$0.276673\pi$
$337$			173490.i			1.52762i	−0.645442	+	0.763809i	$0.723327\pi$
$338$	−55593.7	+	58610.4i	−0.486623	+	0.513028i
$339$	−254905.			−2.21809
$340$	−42561.4	+	42561.4i	−0.368178	+	0.368178i
$341$	−127978.			−1.10060
$342$		−	172832.i		−	1.47765i
$343$	−77965.7	+	77965.7i	−0.662698	+	0.662698i
$344$	−44176.4	+	44176.4i	−0.373313	+	0.373313i
$345$	−78162.6	−	78162.6i	−0.656690	−	0.656690i
$346$	−67622.3	−	67622.3i	−0.564856	−	0.564856i
$347$	−20748.5			−0.172317			−0.0861585	−	0.996281i	$-0.527459\pi$
$347$	−20748.5			−0.172317			−0.0861585	+	0.996281i	$0.527459\pi$
$348$		−	48303.1i		−	0.398856i
$349$	8784.62	+	8784.62i	0.0721227	+	0.0721227i	0.742248	−	0.670125i	$-0.233760\pi$
$349$	8784.62	+	8784.62i	0.0721227	+	0.0721227i	−0.670125	+	0.742248i	$0.733760\pi$
$350$			46835.5i			0.382330i
$351$	2943.35	+	222894.i	0.0238906	+	1.80919i
$352$	31181.7			0.251660
$353$	139415.	−	139415.i	1.11882	−	1.11882i	0.126908	−	0.991915i	$-0.459495\pi$
$353$	139415.	−	139415.i	1.11882	−	1.11882i	0.991915	−	0.126908i	$-0.0405052\pi$
$354$	236430.			1.88667
$355$		−	140761.i		−	1.11693i
$356$	−34786.6	+	34786.6i	−0.274481	+	0.274481i
$357$	64363.7	−	64363.7i	0.505016	−	0.505016i
$358$	−26806.8	−	26806.8i	−0.209160	−	0.209160i
$359$	137098.	+	137098.i	1.06376	+	1.06376i	0.997824	+	0.0659327i	$0.0210023\pi$
$359$	137098.	+	137098.i	1.06376	+	1.06376i	0.0659327	+	0.997824i	$0.478998\pi$
$360$	131313.			1.01322
$361$		−	6689.60i		−	0.0513317i
$362$	−100210.	−	100210.i	−0.764705	−	0.764705i
$363$			235796.i			1.78946i
$364$	−26258.3	−	25573.8i	−0.198182	−	0.193016i
$365$	−248047.			−1.86186
$366$	79238.2	−	79238.2i	0.591524	−	0.591524i
$367$	−122198.			−0.907262			−0.453631	−	0.891190i	$-0.649872\pi$
$367$	−122198.			−0.907262			−0.453631	+	0.891190i	$0.649872\pi$
$368$		−	12828.7i		−	0.0947298i
$369$	−81861.6	+	81861.6i	−0.601212	+	0.601212i
$370$	−55065.7	+	55065.7i	−0.402233	+	0.402233i
$371$	71497.1	+	71497.1i	0.519446	+	0.519446i
$372$	−65929.1	−	65929.1i	−0.476421	−	0.476421i
$373$	−94789.6			−0.681307			−0.340654	−	0.940189i	$-0.610648\pi$
$373$	−94789.6			−0.681307			−0.340654	+	0.940189i	$0.610648\pi$
$374$		−	104277.i		−	0.745499i
$375$	−5545.00	−	5545.00i	−0.0394311	−	0.0394311i
$376$			27569.2i			0.195006i
$377$	858.885	+	65041.8i	0.00604300	+	0.457625i
$378$	−101144.			−0.707875
$379$	86447.4	−	86447.4i	0.601829	−	0.601829i	−0.338968	−	0.940798i	$-0.610078\pi$
$379$	86447.4	−	86447.4i	0.601829	−	0.601829i	0.940798	+	0.338968i	$0.110078\pi$
$380$	104097.			0.720892
$381$			176650.i			1.21693i
$382$	−84785.9	+	84785.9i	−0.581028	+	0.581028i
$383$	−43904.8	+	43904.8i	−0.299305	+	0.299305i	−0.840742	−	0.541437i	$-0.817881\pi$
$383$	−43904.8	+	43904.8i	−0.299305	+	0.299305i	0.541437	+	0.840742i	$0.317881\pi$
$384$	16063.5	+	16063.5i	0.108938	+	0.108938i
$385$	−116085.	−	116085.i	−0.783167	−	0.783167i
$386$	87520.0			0.587398
$387$		−	455799.i		−	3.04334i
$388$	47859.2	+	47859.2i	0.317909	+	0.317909i
$389$		−	29028.6i		−	0.191835i	−0.995389	−	0.0959173i	$-0.969422\pi$
$389$		−	29028.6i		−	0.191835i	0.995389	−	0.0959173i	$-0.0305784\pi$
$390$	−263576.	+	3480.55i	−1.73291	+	0.0228833i
$391$	−42901.5			−0.280620
$392$	−26655.9	+	26655.9i	−0.173469	+	0.173469i
$393$	130836.			0.847114
$394$			92692.8i			0.597109i
$395$	165865.	−	165865.i	1.06307	−	1.06307i
$396$	−160862.	+	160862.i	−1.02580	+	1.02580i
$397$	102962.	+	102962.i	0.653273	+	0.653273i	0.953780	−	0.300507i	$-0.0971557\pi$
$397$	102962.	+	102962.i	0.653273	+	0.653273i	−0.300507	+	0.953780i	$0.597156\pi$
$398$	132047.	+	132047.i	0.833608	+	0.833608i
$399$	−157421.			−0.988820
$400$			39089.9i			0.244312i
$401$	−16095.0	−	16095.0i	−0.100093	−	0.100093i	0.655287	−	0.755380i	$-0.272548\pi$
$401$	−16095.0	−	16095.0i	−0.100093	−	0.100093i	−0.755380	+	0.655287i	$0.772548\pi$
$402$			111498.i			0.689945i
$403$	89948.2	+	87603.6i	0.553837	+	0.539401i
$404$	66571.9			0.407876
$405$	−181949.	+	181949.i	−1.10928	+	1.10928i
$406$	−29514.4			−0.179053
$407$		−	134914.i		−	0.814455i
$408$	53719.4	−	53719.4i	0.322709	−	0.322709i
$409$	−49345.6	+	49345.6i	−0.294986	+	0.294986i	−0.839046	−	0.544060i	$-0.816886\pi$
$409$	−49345.6	+	49345.6i	−0.294986	+	0.294986i	0.544060	+	0.839046i	$0.316886\pi$
$410$	−49305.2	−	49305.2i	−0.293309	−	0.293309i
$411$	260970.	+	260970.i	1.54492	+	1.54492i
$412$	−48760.4			−0.287258
$413$		−	144465.i		−	0.846958i
$414$	66181.3	+	66181.3i	0.386131	+	0.386131i
$415$		−	172582.i		−	1.00207i
$416$	−21915.7	−	21344.5i	−0.126640	−	0.123339i
$417$	−37934.7			−0.218155
$418$	−127521.	+	127521.i	−0.729844	+	0.729844i
$419$	−125730.			−0.716162			−0.358081	−	0.933691i	$-0.616569\pi$
$419$	−125730.			−0.716162			−0.358081	+	0.933691i	$0.616569\pi$
$420$		−	119604.i		−	0.678029i
$421$	228269.	−	228269.i	1.28790	−	1.28790i	0.351843	−	0.936059i	$-0.385555\pi$
$421$	228269.	−	228269.i	1.28790	−	1.28790i	0.936059	−	0.351843i	$-0.114445\pi$
$422$	111762.	−	111762.i	0.627579	−	0.627579i
$423$	−142225.	−	142225.i	−0.794869	−	0.794869i
$424$	59673.1	+	59673.1i	0.331930	+	0.331930i
$425$	130724.			0.723731
$426$			177663.i			0.978990i
$427$	−48416.5	−	48416.5i	−0.265545	−	0.265545i
$428$		−	116007.i		−	0.633282i
$429$	318623.	−	327150.i	1.73126	−	1.77760i
$430$	274527.			1.48473
$431$	−49624.1	+	49624.1i	−0.267140	+	0.267140i	−0.827947	−	0.560807i	$-0.810491\pi$
$431$	−49624.1	+	49624.1i	−0.267140	+	0.267140i	0.560807	+	0.827947i	$0.310491\pi$
$432$	−84417.1			−0.452338
$433$			289131.i			1.54212i	0.636761	+	0.771061i	$0.280274\pi$
$433$			289131.i			1.54212i	−0.636761	+	0.771061i	$0.719726\pi$
$434$	−40284.3	+	40284.3i	−0.213873	+	0.213873i
$435$	−150086.	+	150086.i	−0.793162	+	0.793162i
$436$	−91083.2	−	91083.2i	−0.479143	−	0.479143i
$437$	52464.4	+	52464.4i	0.274727	+	0.274727i
$438$	313076.			1.63193
$439$			136036.i			0.705872i	0.935647	+	0.352936i	$0.114817\pi$
$439$			136036.i			0.705872i	−0.935647	+	0.352936i	$0.885183\pi$
$440$	−96887.1	−	96887.1i	−0.500450	−	0.500450i
$441$		−	275028.i		−	1.41416i
$442$	−71379.9	+	73290.3i	−0.365369	+	0.375147i
$443$	−70628.3			−0.359891			−0.179946	−	0.983677i	$-0.557592\pi$
$443$	−70628.3			−0.359891			−0.179946	+	0.983677i	$0.557592\pi$
$444$	69501.9	−	69501.9i	0.352558	−	0.352558i
$445$	216176.			1.09166
$446$		−	19907.0i		−	0.100077i
$447$	248362.	−	248362.i	1.24299	−	1.24299i
$448$	9815.22	−	9815.22i	0.0489040	−	0.0489040i
$449$	−31522.2	−	31522.2i	−0.156359	−	0.156359i	0.624592	−	0.780951i	$-0.285265\pi$
$449$	−31522.2	−	31522.2i	−0.156359	−	0.156359i	−0.780951	+	0.624592i	$0.785265\pi$
$450$	−201659.	−	201659.i	−0.995847	−	0.995847i
$451$	120800.			0.593902
$452$			129995.i			0.636284i
$453$	−127390.	−	127390.i	−0.620781	−	0.620781i
$454$		−	100319.i		−	0.486712i
$455$	2126.70	+	161051.i	0.0102727	+	0.777932i
$456$	−131387.			−0.631864
$457$	−161962.	+	161962.i	−0.775500	+	0.775500i	−0.979062	−	0.203562i	$-0.934748\pi$
$457$	−161962.	+	161962.i	−0.775500	+	0.775500i	0.203562	+	0.979062i	$0.434748\pi$
$458$	−39180.8			−0.186785
$459$			282306.i			1.33997i
$460$	−39861.0	+	39861.0i	−0.188379	+	0.188379i
$461$	271494.	−	271494.i	1.27749	−	1.27749i	0.335425	−	0.942067i	$-0.391120\pi$
$461$	271494.	−	271494.i	1.27749	−	1.27749i	0.942067	−	0.335425i	$-0.108880\pi$
$462$	146518.	+	146518.i	0.686448	+	0.686448i
$463$	−237950.	−	237950.i	−1.11000	−	1.11000i	−0.993149	−	0.116854i	$-0.962719\pi$
$463$	−237950.	−	237950.i	−1.11000	−	1.11000i	−0.116854	−	0.993149i	$-0.537281\pi$
$464$	−24633.4			−0.114416
$465$			409706.i			1.89481i
$466$	−158635.	−	158635.i	−0.730510	−	0.730510i
$467$			358235.i			1.64261i	0.570491	+	0.821304i	$0.306753\pi$
$467$			358235.i			1.64261i	−0.570491	+	0.821304i	$0.693247\pi$
$468$	223173.	−	2947.03i	1.01894	−	0.0134553i
$469$	68128.0			0.309728
$470$	85662.2	−	85662.2i	0.387787	−	0.387787i
$471$	−232083.			−1.04617
$472$		−	120574.i		−	0.541213i
$473$	−336303.	+	336303.i	−1.50317	+	1.50317i
$474$	−209349.	+	209349.i	−0.931782	+	0.931782i
$475$	−159863.	−	159863.i	−0.708532	−	0.708532i
$476$	−32823.9	−	32823.9i	−0.144869	−	0.144869i
$477$	−615689.			−2.70598
$478$			57966.3i			0.253699i
$479$	158178.	+	158178.i	0.689406	+	0.689406i	0.962101	−	0.272695i	$-0.0879149\pi$
$479$	158178.	+	158178.i	0.689406	+	0.689406i	−0.272695	+	0.962101i	$0.587915\pi$
$480$		−	99824.4i		−	0.433265i
$481$	−92351.0	+	94822.6i	−0.399164	+	0.409847i
$482$	54420.6			0.234244
$483$	60280.0	−	60280.0i	0.258392	−	0.258392i
$484$	120250.			0.513328
$485$		−	297414.i		−	1.26438i
$486$	15969.1	−	15969.1i	0.0676094	−	0.0676094i
$487$	161551.	−	161551.i	0.681166	−	0.681166i	−0.279097	−	0.960263i	$-0.590035\pi$
$487$	161551.	−	161551.i	0.681166	−	0.681166i	0.960263	+	0.279097i	$0.0900352\pi$
$488$	−40409.5	−	40409.5i	−0.169685	−	0.169685i
$489$	23014.6	+	23014.6i	0.0962468	+	0.0962468i
$490$	165649.			0.689917
$491$			101825.i			0.422368i	0.977446	+	0.211184i	$0.0677319\pi$
$491$			101825.i			0.422368i	−0.977446	+	0.211184i	$0.932268\pi$
$492$	62231.2	+	62231.2i	0.257086	+	0.257086i
$493$			82378.5i			0.338938i
$494$	176918.	−	2336.22i	0.724965	−	0.00957325i
$495$	999652.			4.07980
$496$	−33622.2	+	33622.2i	−0.136667	+	0.136667i
$497$	108557.			0.439485
$498$			217827.i			0.878320i
$499$	−223438.	+	223438.i	−0.897337	+	0.897337i	−0.995200	−	0.0978625i	$-0.968799\pi$
$499$	−223438.	+	223438.i	−0.897337	+	0.897337i	0.0978625	+	0.995200i	$0.468799\pi$
$500$	−2827.81	+	2827.81i	−0.0113113	+	0.0113113i
$501$	−41593.8	−	41593.8i	−0.165712	−	0.165712i
$502$	−197879.	−	197879.i	−0.785222	−	0.785222i
$503$	116980.			0.462354			0.231177	−	0.972912i	$-0.425742\pi$
$503$	116980.			0.462354			0.231177	+	0.972912i	$0.425742\pi$
$504$			101271.i			0.398678i
$505$	−206851.	−	206851.i	−0.811099	−	0.811099i
$506$		−	97661.3i		−	0.381436i
$507$	−447881.	+	11830.7i	−1.74240	+	0.0460252i
$508$	90087.2			0.349088
$509$	−213142.	+	213142.i	−0.822683	+	0.822683i	−0.986492	−	0.163809i	$-0.947622\pi$
$509$	−213142.	+	213142.i	−0.822683	+	0.822683i	0.163809	+	0.986492i	$0.447622\pi$
$510$	−333831.			−1.28347
$511$		−	191297.i		−	0.732599i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	345233.	−	345233.i	1.31183	−	1.31183i
$514$	60543.3	+	60543.3i	0.229160	+	0.229160i
$515$	151507.	+	151507.i	0.571239	+	0.571239i
$516$	−346498.			−1.30137
$517$			209877.i			0.785204i
$518$	−42467.4	−	42467.4i	−0.158269	−	0.158269i
$519$		−	530396.i		−	1.96909i
$520$	1774.99	+	134417.i	0.00656433	+	0.497104i
$521$	−427796.			−1.57602			−0.788010	−	0.615663i	$-0.788888\pi$
$521$	−427796.			−1.57602			−0.788010	+	0.615663i	$0.788888\pi$
$522$	127080.	−	127080.i	0.466376	−	0.466376i
$523$	−289897.			−1.05984			−0.529920	−	0.848047i	$-0.677778\pi$
$523$	−289897.			−1.05984			−0.529920	+	0.848047i	$0.677778\pi$
$524$		−	66723.0i		−	0.243004i
$525$	−183677.	+	183677.i	−0.666403	+	0.666403i
$526$	250284.	−	250284.i	0.904609	−	0.904609i
$527$	112439.	+	112439.i	0.404851	+	0.404851i
$528$	122287.	+	122287.i	0.438645	+	0.438645i
$529$	239662.			0.856420
$530$		−	370829.i		−	1.32015i
$531$	622021.	+	622021.i	2.20605	+	2.20605i
$532$			80280.9i			0.283654i
$533$	−84903.1	−	82690.0i	−0.298861	−	0.291071i
$534$	−272849.			−0.956842
$535$	−360454.	+	360454.i	−1.25934	+	1.25934i
$536$	56861.2			0.197918
$537$		−	210260.i		−	0.729134i
$538$	24070.3	−	24070.3i	0.0831604	−	0.0831604i
$539$	−202924.	+	202924.i	−0.698484	+	0.698484i
$540$	262299.	+	262299.i	0.899515	+	0.899515i
$541$	−216514.	−	216514.i	−0.739760	−	0.739760i	0.232772	−	0.972531i	$-0.425220\pi$
$541$	−216514.	−	216514.i	−0.739760	−	0.739760i	−0.972531	+	0.232772i	$0.925220\pi$
$542$	−200941.			−0.684020
$543$		−	785999.i		−	2.66577i
$544$	−27395.6	−	27395.6i	−0.0925726	−	0.0925726i
$545$			566023.i			1.90564i
$546$	−2684.25	−	203273.i	−0.00900403	−	0.681859i
$547$	378313.			1.26438			0.632189	−	0.774814i	$-0.282157\pi$
$547$	378313.			1.26438			0.632189	+	0.774814i	$0.282157\pi$
$548$	133088.	−	133088.i	0.443178	−	0.443178i
$549$	416933.			1.38332
$550$			297581.i			0.983738i
$551$	100741.	−	100741.i	0.331820	−	0.331820i
$552$	50311.0	−	50311.0i	0.165114	−	0.165114i
$553$	127918.	+	127918.i	0.418292	+	0.418292i
$554$	196058.	+	196058.i	0.638800	+	0.638800i
$555$	−431909.			−1.40219
$556$			19345.8i			0.0625801i
$557$	6900.16	+	6900.16i	0.0222407	+	0.0222407i	0.718140	−	0.695899i	$-0.244994\pi$
$557$	6900.16	+	6900.16i	0.0222407	+	0.0222407i	−0.695899	+	0.718140i	$0.744994\pi$
$558$		−	346904.i		−	1.11414i
$559$	466572.	−	6161.14i	1.49312	−	0.0197169i
$560$	−60995.2			−0.194500
$561$	408951.	−	408951.i	1.29941	−	1.29941i
$562$	−38676.7			−0.122455
$563$		−	285426.i		−	0.900484i	−0.892906	−	0.450242i	$-0.851338\pi$
$563$		−	285426.i		−	0.900484i	0.892906	−	0.450242i	$-0.148662\pi$
$564$	−108120.	+	108120.i	−0.339896	+	0.339896i
$565$	403918.	−	403918.i	1.26531	−	1.26531i
$566$	98086.8	+	98086.8i	0.306181	+	0.306181i
$567$	−140322.	−	140322.i	−0.436475	−	0.436475i
$568$	90603.8			0.280834
$569$			539927.i			1.66767i	0.552013	+	0.833836i	$0.313860\pi$
$569$			539927.i			1.66767i	−0.552013	+	0.833836i	$0.686140\pi$
$570$	408243.	+	408243.i	1.25652	+	1.25652i
$571$		−	383358.i		−	1.17580i	−0.808935	−	0.587899i	$-0.799955\pi$
$571$		−	383358.i		−	1.17580i	0.808935	−	0.587899i	$-0.200045\pi$
$572$	−166839.	−	162490.i	−0.509923	−	0.496631i
$573$	−665020.			−2.02547
$574$	38024.8	−	38024.8i	0.115410	−	0.115410i
$575$	122430.			0.370298
$576$			84522.6i			0.254758i
$577$	155219.	−	155219.i	0.466223	−	0.466223i	−0.434466	−	0.900688i	$-0.643063\pi$
$577$	155219.	−	155219.i	0.466223	−	0.466223i	0.900688	+	0.434466i	$0.143063\pi$
$578$	75426.3	−	75426.3i	0.225770	−	0.225770i
$579$	343233.	+	343233.i	1.02384	+	1.02384i
$580$	76540.2	+	76540.2i	0.227527	+	0.227527i
$581$	133098.			0.394292
$582$			375385.i			1.10823i
$583$	454275.	+	454275.i	1.33654	+	1.33654i
$584$		−	159661.i		−	0.468137i
$585$	−702594.	−	684281.i	−2.05302	−	1.99951i
$586$	−49793.3			−0.145002
$587$	437665.	−	437665.i	1.27018	−	1.27018i	0.324190	−	0.945992i	$-0.394908\pi$
$587$	437665.	−	437665.i	1.27018	−	1.27018i	0.945992	−	0.324190i	$-0.105092\pi$
$588$	−209076.			−0.604714
$589$		−	275003.i		−	0.792698i
$590$	−374643.	+	374643.i	−1.07625	+	1.07625i
$591$	−363519.	+	363519.i	−1.04076	+	1.04076i
$592$	−35444.2	−	35444.2i	−0.101135	−	0.101135i
$593$	−489553.	−	489553.i	−1.39216	−	1.39216i	−0.820461	−	0.571702i	$-0.806283\pi$
$593$	−489553.	−	489553.i	−1.39216	−	1.39216i	−0.571702	−	0.820461i	$-0.693717\pi$
$594$	−642644.			−1.82137
$595$			203979.i			0.576171i
$596$	−126658.	−	126658.i	−0.356567	−	0.356567i
$597$			1.03571e6i			2.90596i
$598$	−66851.0	+	68640.2i	−0.186941	+	0.191945i
$599$	−381111.			−1.06218			−0.531089	−	0.847316i	$-0.678217\pi$
$599$	−381111.			−1.06218			−0.531089	+	0.847316i	$0.678217\pi$
$600$	−153301.	+	153301.i	−0.425837	+	0.425837i
$601$	−363389.			−1.00606			−0.503029	−	0.864270i	$-0.667781\pi$
$601$	−363389.			−1.00606			−0.503029	+	0.864270i	$0.667781\pi$
$602$			211719.i			0.584207i
$603$	−293338.	+	293338.i	−0.806741	+	0.806741i
$604$	−64965.7	+	64965.7i	−0.178078	+	0.178078i
$605$	−373638.	−	373638.i	−1.02080	−	1.02080i
$606$	261079.	+	261079.i	0.710930	+	0.710930i
$607$	528109.			1.43333			0.716664	−	0.697418i	$-0.245668\pi$
$607$	528109.			1.43333			0.716664	+	0.697418i	$0.245668\pi$
$608$			67004.2i			0.181257i
$609$	−115748.	−	115748.i	−0.312090	−	0.312090i
$610$			251119.i			0.674869i
$611$	143664.	−	147509.i	0.384828	−	0.395128i
$612$	282659.			0.754675
$613$	235423.	−	235423.i	0.626509	−	0.626509i	−0.320679	−	0.947188i	$-0.603911\pi$
$613$	235423.	−	235423.i	0.626509	−	0.626509i	0.947188	+	0.320679i	$0.103911\pi$
$614$	−191968.			−0.509204
$615$		−	386726.i		−	1.02248i
$616$	74720.6	−	74720.6i	0.196915	−	0.196915i
$617$	−346330.	+	346330.i	−0.909746	+	0.909746i	−0.996251	−	0.0865055i	$-0.972430\pi$
$617$	−346330.	+	346330.i	−0.909746	+	0.909746i	0.0865055	+	0.996251i	$0.472430\pi$
$618$	−191226.	−	191226.i	−0.500692	−	0.500692i
$619$	181847.	+	181847.i	0.474596	+	0.474596i	0.903398	−	0.428802i	$-0.141064\pi$
$619$	181847.	+	181847.i	0.474596	+	0.474596i	−0.428802	+	0.903398i	$0.641064\pi$
$620$	208940.			0.543548
$621$			264395.i			0.685598i
$622$	−279028.	−	279028.i	−0.721219	−	0.721219i
$623$			166718.i			0.429542i
$624$	−2240.33	−	169656.i	−0.00575365	−	0.435713i
$625$	399310.			1.02223
$626$	257788.	−	257788.i	0.657831	−	0.657831i
$627$	−1.00022e6			−2.54424
$628$			118357.i			0.300105i
$629$	−118532.	+	118532.i	−0.299595	+	0.299595i
$630$	314665.	−	314665.i	0.792807	−	0.792807i
$631$	−407988.	−	407988.i	−1.02468	−	1.02468i	−0.999688	−	0.0249927i	$-0.992044\pi$
$631$	−407988.	−	407988.i	−1.02468	−	1.02468i	−0.0249927	−	0.999688i	$-0.507956\pi$
$632$	106763.	+	106763.i	0.267292	+	0.267292i
$633$	876605.			2.18775
$634$		−	349210.i		−	0.868776i
$635$	−279916.	−	279916.i	−0.694194	−	0.694194i
$636$			468047.i			1.15711i
$637$	281529.	−	3717.62i	0.693815	−	0.00916192i
$638$	−187527.			−0.460705
$639$	−467412.	+	467412.i	−1.14472	+	1.14472i
$640$	−50907.9			−0.124287
$641$			148496.i			0.361409i	0.983537	+	0.180705i	$0.0578378\pi$
$641$			148496.i			0.361409i	−0.983537	+	0.180705i	$0.942162\pi$
$642$	454952.	−	454952.i	1.10381	−	1.10381i
$643$	59858.1	−	59858.1i	0.144777	−	0.144777i	−0.631003	−	0.775780i	$-0.717356\pi$
$643$	59858.1	−	59858.1i	0.144777	−	0.144777i	0.775780	+	0.631003i	$0.217356\pi$
$644$	−30741.3	−	30741.3i	−0.0741226	−	0.0741226i
$645$	1.07663e6	+	1.07663e6i	2.58790	+	2.58790i
$646$	224074.			0.536942
$647$			304950.i			0.728484i	0.931304	+	0.364242i	$0.118672\pi$
$647$			304950.i			0.728484i	−0.931304	+	0.364242i	$0.881328\pi$
$648$	−117116.	−	117116.i	−0.278911	−	0.278911i
$649$		−	917893.i		−	2.17923i
$650$	203700.	−	209151.i	0.482129	−	0.495033i
$651$	−315971.			−0.745564
$652$	11736.9	−	11736.9i	0.0276095	−	0.0276095i
$653$	33622.3			0.0788499			0.0394250	−	0.999223i	$-0.487447\pi$
$653$	33622.3			0.0788499			0.0394250	+	0.999223i	$0.487447\pi$
$654$		−	714413.i		−	1.67030i
$655$	−207320.	+	207320.i	−0.483235	+	0.483235i
$656$	31736.4	−	31736.4i	0.0737479	−	0.0737479i
$657$	823666.	+	823666.i	1.90819	+	1.90819i
$658$	66063.8	+	66063.8i	0.152585	+	0.152585i
$659$	236957.			0.545631			0.272815	−	0.962066i	$-0.412045\pi$
$659$	236957.			0.545631			0.272815	+	0.962066i	$0.412045\pi$
$660$		−	759936.i		−	1.74457i
$661$	−38782.2	−	38782.2i	−0.0887626	−	0.0887626i	0.661331	−	0.750094i	$-0.269992\pi$
$661$	−38782.2	−	38782.2i	−0.0887626	−	0.0887626i	−0.750094	+	0.661331i	$0.769992\pi$
$662$			321204.i			0.732935i
$663$	−567362.	+	7492.08i	−1.29072	+	0.0170442i
$664$	111086.			0.251956
$665$	249447.	−	249447.i	0.564072	−	0.564072i
$666$	365703.			0.824480
$667$			77151.8i			0.173418i
$668$	−21211.8	+	21211.8i	−0.0475362	+	0.0475362i
$669$	78070.5	−	78070.5i	0.174436	−	0.174436i
$670$	−176678.	−	176678.i	−0.393579	−	0.393579i
$671$	−307627.	−	307627.i	−0.683249	−	0.683249i
$672$	76985.9			0.170480
$673$			829850.i			1.83218i	0.400967	+	0.916092i	$0.368674\pi$
$673$			829850.i			1.83218i	−0.400967	+	0.916092i	$0.631326\pi$
$674$	346980.	+	346980.i	0.763809	+	0.763809i
$675$		−	805629.i		−	1.76818i
$676$	6033.37	+	228408.i	0.0132028	+	0.499826i
$677$	544929.			1.18895			0.594474	−	0.804115i	$-0.297360\pi$
$677$	544929.			1.18895			0.594474	+	0.804115i	$0.297360\pi$
$678$	−509810.	+	509810.i	−1.10905	+	1.10905i
$679$	229370.			0.497504
$680$			170245.i			0.368178i
$681$	393428.	−	393428.i	0.848341	−	0.848341i
$682$	−255957.	+	255957.i	−0.550298	+	0.550298i
$683$	216539.	+	216539.i	0.464190	+	0.464190i	0.900026	−	0.435836i	$-0.143547\pi$
$683$	216539.	+	216539.i	0.464190	+	0.464190i	−0.435836	+	0.900026i	$0.643547\pi$
$684$	−345665.	−	345665.i	−0.738827	−	0.738827i
$685$	−827057.			−1.76260
$686$			311863.i			0.662698i
$687$	−153658.	−	153658.i	−0.325567	−	0.325567i
$688$			176705.i			0.373313i
$689$	−8322.42	−	630242.i	−0.0175312	−	1.32760i
$690$	−312650.			−0.656690
$691$	−158020.	+	158020.i	−0.330946	+	0.330946i	−0.852946	−	0.522000i	$-0.825186\pi$
$691$	−158020.	+	158020.i	−0.330946	+	0.330946i	0.522000	+	0.852946i	$0.325186\pi$
$692$	−270489.			−0.564856
$693$			770945.i			1.60530i
$694$	−41497.0	+	41497.0i	−0.0861585	+	0.0861585i
$695$	60110.7	−	60110.7i	0.124446	−	0.124446i
$696$	−96606.2	−	96606.2i	−0.199428	−	0.199428i
$697$	−106132.	−	106132.i	−0.218465	−	0.218465i
$698$	35138.5			0.0721227
$699$		−	1.24425e6i		−	2.54657i
$700$	93670.9	+	93670.9i	0.191165	+	0.191165i
$701$			113941.i			0.231869i	0.993257	+	0.115934i	$0.0369863\pi$
$701$			113941.i			0.231869i	−0.993257	+	0.115934i	$0.963014\pi$
$702$	451676.	+	439902.i	0.916542	+	0.892651i
$703$	289906.			0.586607
$704$	62363.5	−	62363.5i	0.125830	−	0.125830i
$705$	671893.			1.35183
$706$		−	557661.i		−	1.11882i
$707$	159526.	−	159526.i	0.319148	−	0.319148i
$708$	472860.	−	472860.i	0.943336	−	0.943336i
$709$	−553270.	−	553270.i	−1.10064	−	1.10064i	−0.994334	−	0.106305i	$-0.966098\pi$
$709$	−553270.	−	553270.i	−1.10064	−	1.10064i	−0.106305	−	0.994334i	$-0.533902\pi$
$710$	−281522.	−	281522.i	−0.558464	−	0.558464i
$711$	−1.10155e6			−2.17903
$712$			139146.i			0.274481i
$713$	105305.	+	105305.i	0.207143	+	0.207143i
$714$		−	257455.i		−	0.505016i
$715$	13512.5	+	1.02328e6i	0.0264317	+	2.00162i
$716$	−107227.			−0.209160
$717$	−227330.	+	227330.i	−0.442199	+	0.442199i
$718$	548392.			1.06376
$719$		−	32164.4i		−	0.0622182i	−0.999516	−	0.0311091i	$-0.990096\pi$
$719$		−	32164.4i		−	0.0622182i	0.999516	−	0.0311091i	$-0.00990393\pi$
$720$	262626.	−	262626.i	0.506610	−	0.506610i
$721$	−116844.	+	116844.i	−0.224769	+	0.224769i
$722$	−13379.2	−	13379.2i	−0.0256658	−	0.0256658i
$723$	213424.	+	213424.i	0.408289	+	0.408289i
$724$	−400840.			−0.764705
$725$		−	235087.i		−	0.447252i
$726$	471592.	+	471592.i	0.894732	+	0.894732i
$727$		−	517646.i		−	0.979408i	−0.871889	−	0.489704i	$-0.837105\pi$
$727$		−	517646.i		−	0.979408i	0.871889	−	0.489704i	$-0.162895\pi$
$728$	−103664.	+	1368.90i	−0.195599	+	0.00258291i
$729$	−467644.			−0.879956
$730$	−496094.	+	496094.i	−0.930932	+	0.930932i
$731$	590936.			1.10587
$732$		−	316953.i		−	0.591524i
$733$	−352588.	+	352588.i	−0.656236	+	0.656236i	−0.954487	−	0.298252i	$-0.903597\pi$
$733$	−352588.	+	352588.i	−0.656236	+	0.656236i	0.298252	+	0.954487i	$0.403597\pi$
$734$	−244396.	+	244396.i	−0.453631	+	0.453631i
$735$	649636.	+	649636.i	1.20253	+	1.20253i
$736$	−25657.4	−	25657.4i	−0.0473649	−	0.0473649i
$737$	432869.			0.796932
$738$			327446.i			0.601212i
$739$	−437052.	−	437052.i	−0.800285	−	0.800285i	0.182855	−	0.983140i	$-0.441466\pi$
$739$	−437052.	−	437052.i	−0.800285	−	0.800285i	−0.983140	+	0.182855i	$0.941466\pi$
$740$			220263.i			0.402233i
$741$	702990.	+	684666.i	1.28030	+	1.24693i
$742$	285988.			0.519446
$743$	74900.9	−	74900.9i	0.135678	−	0.135678i	−0.636006	−	0.771684i	$-0.719415\pi$
$743$	74900.9	−	74900.9i	0.135678	−	0.135678i	0.771684	+	0.636006i	$0.219415\pi$
$744$	−263716.			−0.476421
$745$			787098.i			1.41813i
$746$	−189579.	+	189579.i	−0.340654	+	0.340654i
$747$	−573077.	+	573077.i	−1.02700	+	1.02700i
$748$	−208555.	−	208555.i	−0.372750	−	0.372750i
$749$	−277987.	−	277987.i	−0.495520	−	0.495520i
$750$	−22180.0			−0.0394311
$751$			204101.i			0.361880i	0.983494	+	0.180940i	$0.0579141\pi$
$751$			204101.i			0.361880i	−0.983494	+	0.180940i	$0.942086\pi$
$752$	55138.3	+	55138.3i	0.0975030	+	0.0975030i
$753$		−	1.55207e6i		−	2.73729i
$754$	131801.	+	128366.i	0.231834	+	0.225791i
$755$	403719.			0.708249
$756$	−202288.	+	202288.i	−0.353938	+	0.353938i
$757$	−995602.			−1.73738			−0.868688	−	0.495359i	$-0.835036\pi$
$757$	−995602.			−1.73738			−0.868688	+	0.495359i	$0.835036\pi$
$758$		−	345790.i		−	0.601829i
$759$	383004.	−	383004.i	0.664844	−	0.664844i
$760$	208194.	−	208194.i	0.360446	−	0.360446i
$761$	−163045.	−	163045.i	−0.281540	−	0.281540i	0.552183	−	0.833723i	$-0.313795\pi$
$761$	−163045.	−	163045.i	−0.281540	−	0.281540i	−0.833723	+	0.552183i	$0.813795\pi$
$762$	353300.	+	353300.i	0.608463	+	0.608463i
$763$	−436524.			−0.749824
$764$			339144.i			0.581028i
$765$	−878271.	−	878271.i	−1.50074	−	1.50074i
$766$			175619.i			0.299305i
$767$	−628315.	+	645131.i	−1.06804	+	1.09662i
$768$	64254.1			0.108938
$769$	−472455.	+	472455.i	−0.798929	+	0.798929i	−0.982927	−	0.183998i	$-0.941096\pi$
$769$	−472455.	+	472455.i	−0.798929	+	0.798929i	0.183998	+	0.982927i	$0.441096\pi$
$770$	−464340.			−0.783167
$771$			474872.i			0.798855i
$772$	175040.	−	175040.i	0.293699	−	0.293699i
$773$	−116691.	+	116691.i	−0.195290	+	0.195290i	−0.797977	−	0.602688i	$-0.794097\pi$
$773$	−116691.	+	116691.i	−0.195290	+	0.195290i	0.602688	+	0.797977i	$0.294097\pi$
$774$	−911597.	−	911597.i	−1.52167	−	1.52167i
$775$	−320871.	−	320871.i	−0.534229	−	0.534229i
$776$	191437.			0.317909
$777$		−	333094.i		−	0.551728i
$778$	−58057.2	−	58057.2i	−0.0959173	−	0.0959173i
$779$			259579.i			0.427754i
$780$	−520190.	+	534113.i	−0.855014	+	0.877897i
$781$	689742.			1.13080
$782$	−85803.0	+	85803.0i	−0.140310	+	0.140310i
$783$	507685.			0.828077
$784$			106624.i			0.173469i
$785$	367754.	−	367754.i	0.596786	−	0.596786i
$786$	261672.	−	261672.i	0.423557	−	0.423557i
$787$	738537.	+	738537.i	1.19240	+	1.19240i	0.976391	+	0.216012i	$0.0693051\pi$
$787$	738537.	+	738537.i	1.19240	+	1.19240i	0.216012	+	0.976391i	$0.430695\pi$
$788$	185386.	+	185386.i	0.298555	+	0.298555i
$789$	1.96310e6			3.15347
$790$		−	663461.i		−	1.06307i
$791$	311507.	+	311507.i	0.497869	+	0.497869i
$792$			643448.i			1.02580i
$793$	5635.79	+	426788.i	0.00896208	+	0.678682i
$794$	411847.			0.653273
$795$	1.45430e6	−	1.45430e6i	2.30102	−	2.30102i
$796$	528187.			0.833608
$797$		−	150378.i		−	0.236738i	−0.992970	−	0.118369i	$-0.962234\pi$
$797$		−	150378.i		−	0.236738i	0.992970	−	0.118369i	$-0.0377665\pi$
$798$	−314842.	+	314842.i	−0.494410	+	0.494410i
$799$	184393.	−	184393.i	0.288835	−	0.288835i
$800$	78179.8	+	78179.8i	0.122156	+	0.122156i
$801$	−717835.	−	717835.i	−1.11882	−	1.11882i
$802$	−64380.0			−0.100093
$803$		−	1.21545e6i		−	1.88498i
$804$	222996.	+	222996.i	0.344973	+	0.344973i
$805$			191037.i			0.294799i
$806$	355103.	−	4689.19i	0.546619	−	0.00721817i
$807$	188796.			0.289898
$808$	133144.	−	133144.i	0.203938	−	0.203938i
$809$	−55982.0			−0.0855365			−0.0427682	−	0.999085i	$-0.513618\pi$
$809$	−55982.0			−0.0855365			−0.0427682	+	0.999085i	$0.513618\pi$
$810$			727798.i			1.10928i
$811$	−270787.	+	270787.i	−0.411705	+	0.411705i	−0.882332	−	0.470627i	$-0.844028\pi$
$811$	−270787.	+	270787.i	−0.411705	+	0.411705i	0.470627	+	0.882332i	$0.344028\pi$
$812$	−59028.8	+	59028.8i	−0.0895266	+	0.0895266i
$813$	−788041.	−	788041.i	−1.19225	−	1.19225i
$814$	−269827.	−	269827.i	−0.407228	−	0.407228i
$815$	−72937.1			−0.109808
$816$		−	214878.i		−	0.322709i
$817$	−722657.	−	722657.i	−1.08265	−	1.08265i
$818$			197382.i			0.294986i
$819$	527726.	−	541850.i	0.786758	−	0.807814i
$820$	−197221.			−0.293309
$821$	−199647.	+	199647.i	−0.296194	+	0.296194i	−0.839521	−	0.543327i	$-0.817164\pi$
$821$	−199647.	+	199647.i	−0.296194	+	0.296194i	0.543327	+	0.839521i	$0.317164\pi$
$822$	1.04388e6			1.54492
$823$		−	7704.02i		−	0.0113741i	−0.999984	−	0.00568706i	$-0.998190\pi$
$823$		−	7704.02i		−	0.0113741i	0.999984	−	0.00568706i	$-0.00181026\pi$
$824$	−97520.7	+	97520.7i	−0.143629	+	0.143629i
$825$	−1.16704e6	+	1.16704e6i	−1.71466	+	1.71466i
$826$	−288930.	−	288930.i	−0.423479	−	0.423479i
$827$	−175163.	−	175163.i	−0.256113	−	0.256113i	0.567358	−	0.823471i	$-0.307966\pi$
$827$	−175163.	−	175163.i	−0.256113	−	0.256113i	−0.823471	+	0.567358i	$0.807966\pi$
$828$	264725.			0.386131
$829$			648977.i			0.944322i	0.881512	+	0.472161i	$0.156526\pi$
$829$			648977.i			0.944322i	−0.881512	+	0.472161i	$0.843474\pi$
$830$	−345164.	−	345164.i	−0.501037	−	0.501037i
$831$			1.53779e6i			2.22686i
$832$	−86520.5	+	1142.51i	−0.124989	+	0.00165050i
$833$	356569.			0.513871
$834$	−75869.5	+	75869.5i	−0.109077	+	0.109077i
$835$	131818.			0.189060
$836$			510085.i			0.729844i
$837$	692941.	−	692941.i	0.989112	−	0.989112i
$838$	−251460.	+	251460.i	−0.358081	+	0.358081i
$839$	−275173.	−	275173.i	−0.390915	−	0.390915i	0.484098	−	0.875014i	$-0.339148\pi$
$839$	−275173.	−	275173.i	−0.390915	−	0.390915i	−0.875014	+	0.484098i	$0.839148\pi$
$840$	−239208.	−	239208.i	−0.339014	−	0.339014i
$841$	−559136.			−0.790543
$842$		−	913076.i		−	1.28790i
$843$	−151681.	−	151681.i	−0.213440	−	0.213440i
$844$		−	447047.i		−	0.627579i
$845$	690958.	−	728451.i	0.967694	−	1.02020i
$846$	−568901.			−0.794869
$847$	288154.	−	288154.i	0.401660	−	0.401660i
$848$	238692.			0.331930
$849$			769346.i			1.06735i
$850$	261448.	−	261448.i	0.361865	−	0.361865i
$851$	−111011.	+	111011.i	−0.153288	+	0.153288i
$852$	355326.	+	355326.i	0.489495	+	0.489495i
$853$	377441.	+	377441.i	0.518741	+	0.518741i	0.917190	−	0.398449i	$-0.130451\pi$
$853$	377441.	+	377441.i	0.518741	+	0.518741i	−0.398449	+	0.917190i	$0.630451\pi$
$854$	−193666.			−0.265545
$855$			2.14808e6i			2.93845i
$856$	−232014.	−	232014.i	−0.316641	−	0.316641i
$857$			182085.i			0.247920i	0.992287	+	0.123960i	$0.0395594\pi$
$857$			182085.i			0.247920i	−0.992287	+	0.123960i	$0.960441\pi$
$858$	−17055.0	−	1.29155e6i	−0.0231674	−	1.75443i
$859$	−1.16804e6			−1.58297			−0.791485	−	0.611189i	$-0.790692\pi$
$859$	−1.16804e6			−1.58297			−0.791485	+	0.611189i	$0.790692\pi$
$860$	549055.	−	549055.i	0.742367	−	0.742367i
$861$	298249.			0.402320
$862$			198497.i			0.267140i
$863$	−13379.2	+	13379.2i	−0.0179643	+	0.0179643i	−0.716032	−	0.698068i	$-0.754043\pi$
$863$	−13379.2	+	13379.2i	−0.0179643	+	0.0179643i	0.698068	+	0.716032i	$0.254043\pi$
$864$	−168834.	+	168834.i	−0.226169	+	0.226169i
$865$	840456.	+	840456.i	1.12327	+	1.12327i
$866$	578262.	+	578262.i	0.771061	+	0.771061i
$867$	591607.			0.787037
$868$			161137.i			0.213873i
$869$	812757.	+	812757.i	1.07627	+	1.07627i
$870$			600344.i			0.793162i
$871$	−304237.	−	296307.i	−0.401029	−	0.390576i
$872$	−364333.			−0.479143
$873$	−987594.	+	987594.i	−1.29584	+	1.29584i
$874$	209857.			0.274727
$875$			13552.5i			0.0177013i
$876$	626151.	−	626151.i	0.815964	−	0.815964i
$877$	666366.	−	666366.i	0.866390	−	0.866390i	−0.125680	−	0.992071i	$-0.540111\pi$
$877$	666366.	−	666366.i	0.866390	−	0.866390i	0.992071	+	0.125680i	$0.0401114\pi$
$878$	272073.	+	272073.i	0.352936	+	0.352936i
$879$	−195277.	−	195277.i	−0.252740	−	0.252740i
$880$	−387548.			−0.500450
$881$		−	548809.i		−	0.707081i	−0.935419	−	0.353541i	$-0.884978\pi$
$881$		−	548809.i		−	0.707081i	0.935419	−	0.353541i	$-0.115022\pi$
$882$	−550056.	−	550056.i	−0.707082	−	0.707082i
$883$		−	459731.i		−	0.589634i	−0.955554	−	0.294817i	$-0.904741\pi$
$883$		−	459731.i		−	0.589634i	0.955554	−	0.294817i	$-0.0952586\pi$
$884$	3820.77	+	289340.i	0.00488930	+	0.370258i
$885$	−2.93852e6			−3.75182
$886$	−141257.	+	141257.i	−0.179946	+	0.179946i
$887$	658381.			0.836817			0.418408	−	0.908259i	$-0.362588\pi$
$887$	658381.			0.836817			0.418408	+	0.908259i	$0.362588\pi$
$888$		−	278008.i		−	0.352558i
$889$	215875.	−	215875.i	0.273149	−	0.273149i
$890$	432352.	−	432352.i	0.545830	−	0.545830i
$891$	−891570.	−	891570.i	−1.12305	−	1.12305i
$892$	−39814.0	−	39814.0i	−0.0500387	−	0.0500387i
$893$	−450989.			−0.565539
$894$		−	993446.i		−	1.24299i
$895$	333174.	+	333174.i	0.415934	+	0.415934i
$896$		−	39260.9i		−	0.0489040i
$897$	−531364.	+	7016.73i	−0.660400	+	0.00872067i
$898$	−126089.			−0.156359
$899$	202204.	−	202204.i	0.250190	−	0.250190i
$900$	−806636.			−0.995847
$901$		−	798231.i		−	0.983284i
$902$	241600.	−	241600.i	0.296951	−	0.296951i
$903$	−830312.	+	830312.i	−1.01828	+	1.01828i
$904$	259991.	+	259991.i	0.318142	+	0.318142i
$905$	1.24548e6	+	1.24548e6i	1.52068	+	1.52068i
$906$	−509560.			−0.620781
$907$			39025.7i			0.0474391i	0.999719	+	0.0237195i	$0.00755087\pi$
$907$			39025.7i			0.0474391i	−0.999719	+	0.0237195i	$0.992449\pi$
$908$	−200638.	−	200638.i	−0.243356	−	0.243356i
$909$			1.37374e6i			1.66256i
$910$	326356.	+	317849.i	0.394102	+	0.383830i
$911$	−1.19426e6			−1.43901			−0.719505	−	0.694487i	$-0.755631\pi$
$911$	−1.19426e6			−1.43901			−0.719505	+	0.694487i	$0.755631\pi$
$912$	−262774.	+	262774.i	−0.315932	+	0.315932i
$913$	845669.			1.01452
$914$			647850.i			0.775500i
$915$	−984827.	+	984827.i	−1.17630	+	1.17630i
$916$	−78361.5	+	78361.5i	−0.0933925	+	0.0933925i
$917$	−159888.	−	159888.i	−0.190142	−	0.190142i
$918$	564612.	+	564612.i	0.669985	+	0.669985i
$919$	662319.			0.784217			0.392108	−	0.919919i	$-0.371746\pi$
$919$	662319.			0.784217			0.392108	+	0.919919i	$0.371746\pi$
$920$			159444.i			0.188379i
$921$	−752852.	−	752852.i	−0.887545	−	0.887545i
$922$		−	1.08598e6i		−	1.27749i
$923$	−484778.	−	472142.i	−0.569035	−	0.554203i
$924$	586073.			0.686448
$925$	338260.	−	338260.i	0.395336	−	0.395336i
$926$	−951801.			−1.11000
$927$		−	1.00619e6i		−	1.17090i
$928$	−49266.7	+	49266.7i	−0.0572081	+	0.0572081i
$929$	−965961.	+	965961.i	−1.11925	+	1.11925i	−0.127402	+	0.991851i	$0.540664\pi$
$929$	−965961.	+	965961.i	−1.11925	+	1.11925i	−0.991851	+	0.127402i	$0.959336\pi$
$930$	819413.	+	819413.i	0.947407	+	0.947407i
$931$	−436050.	−	436050.i	−0.503079	−	0.503079i
$932$	−634539.			−0.730510
$933$		−	2.18856e6i		−	2.51418i
$934$	716469.	+	716469.i	0.821304	+	0.821304i
$935$			1.29603e6i			1.48249i
$936$	440452.	−	452240.i	0.502744	−	0.516199i
$937$	1.36056e6			1.54967			0.774833	−	0.632166i	$-0.217834\pi$
$937$	1.36056e6			1.54967			0.774833	+	0.632166i	$0.217834\pi$
$938$	136256.	−	136256.i	0.154864	−	0.154864i
$939$	2.02197e6			2.29320
$940$		−	342649.i		−	0.387787i
$941$	97567.1	−	97567.1i	0.110185	−	0.110185i	−0.649865	−	0.760050i	$-0.725174\pi$
$941$	97567.1	−	97567.1i	0.110185	−	0.110185i	0.760050	+	0.649865i	$0.225174\pi$
$942$	−464166.	+	464166.i	−0.523084	+	0.523084i
$943$	−99398.4	−	99398.4i	−0.111778	−	0.111778i
$944$	−241147.	−	241147.i	−0.270606	−	0.270606i
$945$	1.25709e6			1.40767
$946$			1.34521e6i			1.50317i
$947$	−100059.	−	100059.i	−0.111572	−	0.111572i	0.649117	−	0.760689i	$-0.275139\pi$
$947$	−100059.	−	100059.i	−0.111572	−	0.111572i	−0.760689	+	0.649117i	$0.775139\pi$
$948$			837397.i			0.931782i
$949$	−832001.	+	854269.i	−0.923829	+	0.948554i
$950$	−639450.			−0.708532
$951$	1.36952e6	−	1.36952e6i	1.51428	−	1.51428i
$952$	−131296.			−0.144869
$953$		−	1.53902e6i		−	1.69456i	−0.531146	−	0.847280i	$-0.678238\pi$
$953$		−	1.53902e6i		−	1.69456i	0.531146	−	0.847280i	$-0.321762\pi$
$954$	−1.23138e6	+	1.23138e6i	−1.35299	+	1.35299i
$955$	1.05378e6	−	1.05378e6i	1.15543	−	1.15543i
$956$	115933.	+	115933.i	0.126850	+	0.126850i
$957$	−735436.	−	735436.i	−0.803011	−	0.803011i
$958$	632712.			0.689406
$959$		−	637837.i		−	0.693542i
$960$	−199649.	−	199649.i	−0.216633	−	0.216633i
$961$			371543.i			0.402311i
$962$	4943.30	+	374347.i	0.00534155	+	0.404505i
$963$	2.39385e6			2.58134
$964$	108841.	−	108841.i	0.117122	−	0.117122i
$965$	−1.08776e6			−1.16810
$966$		−	241120.i		−	0.258392i
$967$	−553053.	+	553053.i	−0.591444	+	0.591444i	−0.938021	−	0.346578i	$-0.887344\pi$
$967$	−553053.	+	553053.i	−0.591444	+	0.591444i	0.346578	+	0.938021i	$0.387344\pi$
$968$	240500.	−	240500.i	0.256664	−	0.256664i
$969$	878766.	+	878766.i	0.935892	+	0.935892i
$970$	−594828.	−	594828.i	−0.632190	−	0.632190i
$971$	−829980.			−0.880297			−0.440148	−	0.897925i	$-0.645074\pi$
$971$	−829980.			−0.880297			−0.440148	+	0.897925i	$0.645074\pi$
$972$		−	63876.3i		−	0.0676094i
$973$	46358.2	+	46358.2i	0.0489667	+	0.0489667i
$974$		−	646206.i		−	0.681166i
$975$	1.61910e6	−	21380.5i	1.70320	−	0.0224910i
$976$	−161638.			−0.169685
$977$	−465208.	+	465208.i	−0.487369	+	0.487369i	−0.907475	−	0.420106i	$-0.861993\pi$
$977$	−465208.	+	465208.i	−0.487369	+	0.487369i	0.420106	+	0.907475i	$0.361993\pi$
$978$	92058.5			0.0962468
$979$			1.05928e6i			1.10521i
$980$	331298.	−	331298.i	0.344959	−	0.344959i
$981$	1.87954e6	−	1.87954e6i	1.95305	−	1.95305i
$982$	203650.	+	203650.i	0.211184	+	0.211184i
$983$	327064.	+	327064.i	0.338474	+	0.338474i	0.855793	−	0.517319i	$-0.173070\pi$
$983$	327064.	+	327064.i	0.338474	+	0.338474i	−0.517319	+	0.855793i	$0.673070\pi$
$984$	248925.			0.257086
$985$		−	1.15205e6i		−	1.18741i
$986$	164757.	+	164757.i	0.169469	+	0.169469i
$987$			518173.i			0.531913i
$988$	349163.	−	358508.i	0.357696	−	0.367269i
$989$	553442.			0.565822
$990$	1.99930e6	−	1.99930e6i	2.03990	−	2.03990i
$991$	1.53311e6			1.56108			0.780542	−	0.625103i	$-0.214943\pi$
$991$	1.53311e6			1.56108			0.780542	+	0.625103i	$0.214943\pi$
$992$			134489.i			0.136667i
$993$	−1.25969e6	+	1.25969e6i	−1.27751	+	1.27751i
$994$	217113.	−	217113.i	0.219742	−	0.219742i
$995$	−1.64117e6	−	1.64117e6i	−1.65771	−	1.65771i
$996$	435654.	+	435654.i	0.439160	+	0.439160i
$997$	−700936.			−0.705161			−0.352580	−	0.935782i	$-0.614696\pi$
$997$	−700936.			−0.705161			−0.352580	+	0.935782i	$0.614696\pi$
$998$			893752.i			0.897337i
$999$	730493.	+	730493.i	0.731956	+	0.731956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.d.b.5.3	✓	6
3.2	odd	2		234.5.i.a.109.3		6
4.3	odd	2		208.5.t.a.161.1		6
13.5	odd	4		338.5.d.c.99.3		6
13.8	odd	4	inner	26.5.d.b.21.3	yes	6
13.12	even	2		338.5.d.c.239.3		6
39.8	even	4		234.5.i.a.73.3		6
52.47	even	4		208.5.t.a.177.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.d.b.5.3	✓	6	1.1	even	1	trivial
26.5.d.b.21.3	yes	6	13.8	odd	4	inner
208.5.t.a.161.1		6	4.3	odd	2
208.5.t.a.177.1		6	52.47	even	4
234.5.i.a.73.3		6	39.8	even	4
234.5.i.a.109.3		6	3.2	odd	2
338.5.d.c.99.3		6	13.5	odd	4
338.5.d.c.239.3		6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} +15.6870 q^{3} -8.00000i q^{4} +(-24.8574 + 24.8574i) q^{5} +(31.3741 - 31.3741i) q^{6} +(-19.1704 - 19.1704i) q^{7} +(-16.0000 - 16.0000i) q^{8} +165.083 q^{9} +O(q^{10})\)	\(q+(2.00000 - 2.00000i) q^{2} +15.6870 q^{3} -8.00000i q^{4} +(-24.8574 + 24.8574i) q^{5} +(31.3741 - 31.3741i) q^{6} +(-19.1704 - 19.1704i) q^{7} +(-16.0000 - 16.0000i) q^{8} +165.083 q^{9} +99.4296i q^{10} +(-121.804 - 121.804i) q^{11} -125.496i q^{12} +(2.23147 + 168.985i) q^{13} -76.6814 q^{14} +(-389.939 + 389.939i) q^{15} -64.0000 q^{16} +214.028i q^{17} +(330.166 - 330.166i) q^{18} +(261.735 - 261.735i) q^{19} +(198.859 + 198.859i) q^{20} +(-300.726 - 300.726i) q^{21} -487.215 q^{22} +200.448i q^{23} +(-250.993 - 250.993i) q^{24} -610.780i q^{25} +(342.433 + 333.508i) q^{26} +1319.02 q^{27} +(-153.363 + 153.363i) q^{28} +384.896 q^{29} +1559.76i q^{30} +(525.347 - 525.347i) q^{31} +(-128.000 + 128.000i) q^{32} +(-1910.74 - 1910.74i) q^{33} +(428.055 + 428.055i) q^{34} +953.050 q^{35} -1320.67i q^{36} +(553.816 + 553.816i) q^{37} -1046.94i q^{38} +(35.0052 + 2650.88i) q^{39} +795.437 q^{40} +(-495.881 + 495.881i) q^{41} -1202.90 q^{42} -2761.02i q^{43} +(-974.429 + 974.429i) q^{44} +(-4103.54 + 4103.54i) q^{45} +(400.896 + 400.896i) q^{46} +(-861.536 - 861.536i) q^{47} -1003.97 q^{48} -1666.00i q^{49} +(-1221.56 - 1221.56i) q^{50} +3357.46i q^{51} +(1351.88 - 17.8518i) q^{52} -3729.57 q^{53} +(2638.03 - 2638.03i) q^{54} +6055.44 q^{55} +613.451i q^{56} +(4105.85 - 4105.85i) q^{57} +(769.793 - 769.793i) q^{58} +(3767.92 + 3767.92i) q^{59} +(3119.51 + 3119.51i) q^{60} +2525.59 q^{61} -2101.39i q^{62} +(-3164.70 - 3164.70i) q^{63} +512.000i q^{64} +(-4256.00 - 4145.06i) q^{65} -7642.95 q^{66} +(-1776.91 + 1776.91i) q^{67} +1712.22 q^{68} +3144.44i q^{69} +(1906.10 - 1906.10i) q^{70} +(-2831.37 + 2831.37i) q^{71} +(-2641.33 - 2641.33i) q^{72} +(4989.40 + 4989.40i) q^{73} +2215.27 q^{74} -9581.33i q^{75} +(-2093.88 - 2093.88i) q^{76} +4670.04i q^{77} +(5371.77 + 5231.75i) q^{78} -6672.68 q^{79} +(1590.87 - 1590.87i) q^{80} +7319.73 q^{81} +1983.52i q^{82} +(-3471.45 + 3471.45i) q^{83} +(-2405.81 + 2405.81i) q^{84} +(-5320.17 - 5320.17i) q^{85} +(-5522.05 - 5522.05i) q^{86} +6037.89 q^{87} +3897.72i q^{88} +(-4348.32 - 4348.32i) q^{89} +16414.2i q^{90} +(3196.73 - 3282.29i) q^{91} +1603.59 q^{92} +(8241.14 - 8241.14i) q^{93} -3446.14 q^{94} +13012.1i q^{95} +(-2007.94 + 2007.94i) q^{96} +(-5982.40 + 5982.40i) q^{97} +(-3331.99 - 3331.99i) q^{98} +(-20107.7 - 20107.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9	\( 6 q + 12 q^{2} - 30 q^{5} - 90 q^{7} - 96 q^{8} + 558 q^{9} - 66 q^{11} - 294 q^{13} - 360 q^{14} - 288 q^{15} - 384 q^{16} + 1116 q^{18} - 318 q^{19} + 240 q^{20} + 756 q^{21} - 264 q^{22} + 84 q^{26} - 1404 q^{27} - 720 q^{28} - 276 q^{29} + 3282 q^{31} - 768 q^{32} - 3240 q^{33} + 2280 q^{34} + 5424 q^{35} - 3006 q^{37} + 2376 q^{39} + 960 q^{40} - 894 q^{41} + 3024 q^{42} - 528 q^{44} - 17226 q^{45} - 4848 q^{46} + 1566 q^{47} - 3300 q^{50} + 2688 q^{52} - 1356 q^{53} - 2808 q^{54} + 22212 q^{55} + 16812 q^{57} - 552 q^{58} + 5178 q^{59} + 2304 q^{60} + 2172 q^{61} - 24210 q^{63} + 1146 q^{65} - 12960 q^{66} + 1134 q^{67} + 9120 q^{68} + 10848 q^{70} - 18498 q^{71} - 8928 q^{72} - 13278 q^{73} - 12024 q^{74} + 2544 q^{76} + 25992 q^{78} - 13596 q^{79} + 1920 q^{80} + 58158 q^{81} - 11490 q^{83} + 6048 q^{84} - 10512 q^{85} - 7128 q^{86} + 30744 q^{87} - 28038 q^{89} - 6402 q^{91} - 19392 q^{92} + 23364 q^{93} + 6264 q^{94} - 27378 q^{97} - 11340 q^{98} - 61074 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 30 * q^5 - 90 * q^7 - 96 * q^8 + 558 * q^9 - 66 * q^11 - 294 * q^13 - 360 * q^14 - 288 * q^15 - 384 * q^16 + 1116 * q^18 - 318 * q^19 + 240 * q^20 + 756 * q^21 - 264 * q^22 + 84 * q^26 - 1404 * q^27 - 720 * q^28 - 276 * q^29 + 3282 * q^31 - 768 * q^32 - 3240 * q^33 + 2280 * q^34 + 5424 * q^35 - 3006 * q^37 + 2376 * q^39 + 960 * q^40 - 894 * q^41 + 3024 * q^42 - 528 * q^44 - 17226 * q^45 - 4848 * q^46 + 1566 * q^47 - 3300 * q^50 + 2688 * q^52 - 1356 * q^53 - 2808 * q^54 + 22212 * q^55 + 16812 * q^57 - 552 * q^58 + 5178 * q^59 + 2304 * q^60 + 2172 * q^61 - 24210 * q^63 + 1146 * q^65 - 12960 * q^66 + 1134 * q^67 + 9120 * q^68 + 10848 * q^70 - 18498 * q^71 - 8928 * q^72 - 13278 * q^73 - 12024 * q^74 + 2544 * q^76 + 25992 * q^78 - 13596 * q^79 + 1920 * q^80 + 58158 * q^81 - 11490 * q^83 + 6048 * q^84 - 10512 * q^85 - 7128 * q^86 + 30744 * q^87 - 28038 * q^89 - 6402 * q^91 - 19392 * q^92 + 23364 * q^93 + 6264 * q^94 - 27378 * q^97 - 11340 * q^98 - 61074 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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