LMFDB - Embedded newform 40.3.e.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(19,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("40.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.53824000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 36x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 36x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Root			$-0.831254 + 1.81907i$ of defining polynomial
Character	$\chi$	$=$	40.19
Dual form			40.3.e.c.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831254 + 1.81907i) q^{2} +2.24849i q^{3} +(-2.61803 + 3.02422i) q^{4} +(-1.02749 - 4.89329i) q^{5} +(-4.09017 + 1.86907i) q^{6} +6.40747 q^{7} +(-7.67752 - 2.24849i) q^{8} +3.94427 q^{9} +O(q^{10})$	\(q+(0.831254 + 1.81907i) q^{2} +2.24849i q^{3} +(-2.61803 + 3.02422i) q^{4} +(-1.02749 - 4.89329i) q^{5} +(-4.09017 + 1.86907i) q^{6} +6.40747 q^{7} +(-7.67752 - 2.24849i) q^{8} +3.94427 q^{9} +(8.04713 - 5.93663i) q^{10} +8.47214 q^{11} +(-6.79994 - 5.88664i) q^{12} -17.4100 q^{13} +(5.32624 + 11.6556i) q^{14} +(11.0025 - 2.31030i) q^{15} +(-2.29180 - 15.8350i) q^{16} -19.0496i q^{17} +(3.27869 + 7.17491i) q^{18} -18.3607 q^{19} +(17.4884 + 9.70345i) q^{20} +14.4072i q^{21} +(7.04250 + 15.4114i) q^{22} -2.29753 q^{23} +(5.05573 - 17.2629i) q^{24} +(-22.8885 + 10.0556i) q^{25} +(-14.4721 - 31.6700i) q^{26} +29.1051i q^{27} +(-16.7750 + 19.3776i) q^{28} -4.62059i q^{29} +(13.3485 + 18.0939i) q^{30} +43.7669i q^{31} +(26.8999 - 17.3319i) q^{32} +19.0496i q^{33} +(34.6525 - 15.8350i) q^{34} +(-6.58359 - 31.3536i) q^{35} +(-10.3262 + 11.9283i) q^{36} +24.5452 q^{37} +(-15.2624 - 33.3994i) q^{38} -39.1463i q^{39} +(-3.11399 + 39.8786i) q^{40} +32.9443 q^{41} +(-26.2077 + 11.9760i) q^{42} -35.8506i q^{43} +(-22.1803 + 25.6216i) q^{44} +(-4.05269 - 19.3005i) q^{45} +(-1.90983 - 4.17937i) q^{46} -76.0475 q^{47} +(35.6049 - 5.15309i) q^{48} -7.94427 q^{49} +(-37.3180 - 33.2771i) q^{50} +42.8328 q^{51} +(45.5800 - 52.6517i) q^{52} +64.5599 q^{53} +(-52.9443 + 24.1937i) q^{54} +(-8.70500 - 41.4566i) q^{55} +(-49.1935 - 14.4072i) q^{56} -41.2839i q^{57} +(8.40519 - 3.84089i) q^{58} +21.1935 q^{59} +(-21.8182 + 39.3225i) q^{60} +29.3597i q^{61} +(-79.6151 + 36.3814i) q^{62} +25.2728 q^{63} +(53.8885 + 34.5257i) q^{64} +(17.8885 + 85.1922i) q^{65} +(-34.6525 + 15.8350i) q^{66} +85.0669i q^{67} +(57.6100 + 49.8724i) q^{68} -5.16598i q^{69} +(51.5618 - 38.0388i) q^{70} -73.6720i q^{71} +(-30.2822 - 8.86867i) q^{72} +21.1727i q^{73} +(20.4033 + 44.6494i) q^{74} +(-22.6099 - 51.4648i) q^{75} +(48.0689 - 55.5267i) q^{76} +54.2850 q^{77} +(71.2099 - 32.5405i) q^{78} +112.818i q^{79} +(-75.1305 + 27.4847i) q^{80} -29.9443 q^{81} +(27.3851 + 59.9279i) q^{82} -40.3476i q^{83} +(-43.5704 - 37.7185i) q^{84} +(-93.2150 + 19.5732i) q^{85} +(65.2148 - 29.8010i) q^{86} +10.3894 q^{87} +(-65.0450 - 19.0496i) q^{88} -57.5542 q^{89} +(31.7401 - 23.4157i) q^{90} -111.554 q^{91} +(6.01501 - 6.94823i) q^{92} -98.4096 q^{93} +(-63.2148 - 138.336i) q^{94} +(18.8653 + 89.8441i) q^{95} +(38.9706 + 60.4844i) q^{96} -187.311i q^{97} +(-6.60371 - 14.4512i) q^{98} +33.4164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9	$ 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9} + 20 q^{10} + 32 q^{11} - 20 q^{14} - 72 q^{16} + 32 q^{19} + 20 q^{20} + 112 q^{24} - 40 q^{25} - 80 q^{26} + 100 q^{30} + 152 q^{34} - 160 q^{35} - 20 q^{36} - 80 q^{40} + 192 q^{41} - 88 q^{44} - 60 q^{46} + 8 q^{49} - 200 q^{50} + 128 q^{51} - 352 q^{54} - 224 q^{59} + 360 q^{60} + 288 q^{64} - 152 q^{66} + 340 q^{70} + 360 q^{74} + 320 q^{75} + 152 q^{76} - 280 q^{80} - 168 q^{81} - 760 q^{84} + 316 q^{86} + 112 q^{89} - 340 q^{90} - 320 q^{91} - 300 q^{94} - 368 q^{96} + 160 q^{99}+O(q^{100}) $ 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9 + 20 * q^10 + 32 * q^11 - 20 * q^14 - 72 * q^16 + 32 * q^19 + 20 * q^20 + 112 * q^24 - 40 * q^25 - 80 * q^26 + 100 * q^30 + 152 * q^34 - 160 * q^35 - 20 * q^36 - 80 * q^40 + 192 * q^41 - 88 * q^44 - 60 * q^46 + 8 * q^49 - 200 * q^50 + 128 * q^51 - 352 * q^54 - 224 * q^59 + 360 * q^60 + 288 * q^64 - 152 * q^66 + 340 * q^70 + 360 * q^74 + 320 * q^75 + 152 * q^76 - 280 * q^80 - 168 * q^81 - 760 * q^84 + 316 * q^86 + 112 * q^89 - 340 * q^90 - 320 * q^91 - 300 * q^94 - 368 * q^96 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.831254	+	1.81907i	0.415627	+	0.909535i
$2$	0.831254	+	1.81907i	0.415627	+	0.909535i
$3$			2.24849i			0.749498i	0.927126	+	0.374749i	$0.122271\pi$
$3$			2.24849i			0.749498i	−0.927126	+	0.374749i	$0.877729\pi$
$4$	−2.61803	+	3.02422i	−0.654508	+	0.756055i
$5$	−1.02749	−	4.89329i	−0.205497	−	0.978658i
$5$	−1.02749	−	4.89329i	−0.205497	−	0.978658i
$6$	−4.09017	+	1.86907i	−0.681695	+	0.311512i
$7$	6.40747			0.915353			0.457677	−	0.889119i	$-0.348682\pi$
$7$	6.40747			0.915353			0.457677	+	0.889119i	$0.348682\pi$
$8$	−7.67752	−	2.24849i	−0.959690	−	0.281062i
$9$	3.94427			0.438252
$10$	8.04713	−	5.93663i	0.804713	−	0.593663i
$11$	8.47214			0.770194			0.385097	−	0.922876i	$-0.374168\pi$
$11$	8.47214			0.770194			0.385097	+	0.922876i	$0.374168\pi$
$12$	−6.79994	−	5.88664i	−0.566662	−	0.490553i
$13$	−17.4100			−1.33923			−0.669616	−	0.742708i	$-0.733541\pi$
$13$	−17.4100			−1.33923			−0.669616	+	0.742708i	$0.733541\pi$
$14$	5.32624	+	11.6556i	0.380446	+	0.832546i
$15$	11.0025	−	2.31030i	0.733502	−	0.154020i
$16$	−2.29180	−	15.8350i	−0.143237	−	0.989688i
$17$		−	19.0496i		−	1.12056i	−0.828303	−	0.560281i	$-0.810693\pi$
$17$		−	19.0496i		−	1.12056i	0.828303	−	0.560281i	$-0.189307\pi$
$18$	3.27869	+	7.17491i	0.182150	+	0.398606i
$19$	−18.3607			−0.966352			−0.483176	−	0.875523i	$-0.660517\pi$
$19$	−18.3607			−0.966352			−0.483176	+	0.875523i	$0.660517\pi$
$20$	17.4884	+	9.70345i	0.874418	+	0.485173i
$21$			14.4072i			0.686056i
$22$	7.04250	+	15.4114i	0.320113	+	0.700519i
$23$	−2.29753			−0.0998926			−0.0499463	−	0.998752i	$-0.515905\pi$
$23$	−2.29753			−0.0998926			−0.0499463	+	0.998752i	$0.515905\pi$
$24$	5.05573	−	17.2629i	0.210655	−	0.719286i
$25$	−22.8885	+	10.0556i	−0.915542	+	0.402223i
$26$	−14.4721	−	31.6700i	−0.556621	−	1.21808i
$27$			29.1051i			1.07797i
$28$	−16.7750	+	19.3776i	−0.599107	+	0.692057i
$29$		−	4.62059i		−	0.159331i	−0.996822	−	0.0796654i	$-0.974615\pi$
$29$		−	4.62059i		−	0.159331i	0.996822	−	0.0796654i	$-0.0253852\pi$
$30$	13.3485	+	18.0939i	0.444950	+	0.603131i
$31$			43.7669i			1.41184i	0.708294	+	0.705918i	$0.249465\pi$
$31$			43.7669i			1.41184i	−0.708294	+	0.705918i	$0.750535\pi$
$32$	26.8999	−	17.3319i	0.840623	−	0.541620i
$33$			19.0496i			0.577259i
$34$	34.6525	−	15.8350i	1.01919	−	0.465736i
$35$	−6.58359	−	31.3536i	−0.188103	−	0.895818i
$36$	−10.3262	+	11.9283i	−0.286840	+	0.331343i
$37$	24.5452			0.663382			0.331691	−	0.943388i	$-0.392381\pi$
$37$	24.5452			0.663382			0.331691	+	0.943388i	$0.392381\pi$
$38$	−15.2624	−	33.3994i	−0.401642	−	0.878931i
$39$		−	39.1463i		−	1.00375i
$40$	−3.11399	+	39.8786i	−0.0778497	+	0.996965i
$41$	32.9443			0.803519			0.401759	−	0.915745i	$-0.368399\pi$
$41$	32.9443			0.803519			0.401759	+	0.915745i	$0.368399\pi$
$42$	−26.2077	+	11.9760i	−0.623992	+	0.285143i
$43$		−	35.8506i		−	0.833735i	−0.908967	−	0.416868i	$-0.863128\pi$
$43$		−	35.8506i		−	0.833735i	0.908967	−	0.416868i	$-0.136872\pi$
$44$	−22.1803	+	25.6216i	−0.504099	+	0.582309i
$45$	−4.05269	−	19.3005i	−0.0900597	−	0.428899i
$46$	−1.90983	−	4.17937i	−0.0415180	−	0.0908558i
$47$	−76.0475			−1.61803			−0.809016	−	0.587787i	$-0.799999\pi$
$47$	−76.0475			−1.61803			−0.809016	+	0.587787i	$0.799999\pi$
$48$	35.6049	−	5.15309i	0.741770	−	0.107356i
$49$	−7.94427			−0.162128
$50$	−37.3180	−	33.2771i	−0.746360	−	0.665543i
$51$	42.8328			0.839859
$52$	45.5800	−	52.6517i	0.876538	−	1.01253i
$53$	64.5599			1.21811			0.609055	−	0.793128i	$-0.291549\pi$
$53$	64.5599			1.21811			0.609055	+	0.793128i	$0.291549\pi$
$54$	−52.9443	+	24.1937i	−0.980449	+	0.448032i
$55$	−8.70500	−	41.4566i	−0.158273	−	0.753756i
$56$	−49.1935	−	14.4072i	−0.878455	−	0.257271i
$57$		−	41.2839i		−	0.724279i
$58$	8.40519	−	3.84089i	0.144917	−	0.0662222i
$59$	21.1935			0.359212			0.179606	−	0.983739i	$-0.442518\pi$
$59$	21.1935			0.359212			0.179606	+	0.983739i	$0.442518\pi$
$60$	−21.8182	+	39.3225i	−0.363636	+	0.655375i
$61$			29.3597i			0.481307i	0.970611	+	0.240654i	$0.0773618\pi$
$61$			29.3597i			0.481307i	−0.970611	+	0.240654i	$0.922638\pi$
$62$	−79.6151	+	36.3814i	−1.28411	+	0.586797i
$63$	25.2728			0.401156
$64$	53.8885	+	34.5257i	0.842008	+	0.539464i
$65$	17.8885	+	85.1922i	0.275208	+	1.31065i
$66$	−34.6525	+	15.8350i	−0.525038	+	0.239924i
$67$			85.0669i			1.26965i	0.772654	+	0.634827i	$0.218929\pi$
$67$			85.0669i			1.26965i	−0.772654	+	0.634827i	$0.781071\pi$
$68$	57.6100	+	49.8724i	0.847206	+	0.733417i
$69$		−	5.16598i		−	0.0748693i
$70$	51.5618	−	38.0388i	0.736597	−	0.543412i
$71$		−	73.6720i		−	1.03763i	−0.854885	−	0.518817i	$-0.826373\pi$
$71$		−	73.6720i		−	1.03763i	0.854885	−	0.518817i	$-0.173627\pi$
$72$	−30.2822	−	8.86867i	−0.420586	−	0.123176i
$73$			21.1727i			0.290038i	0.989429	+	0.145019i	$0.0463243\pi$
$73$			21.1727i			0.290038i	−0.989429	+	0.145019i	$0.953676\pi$
$74$	20.4033	+	44.6494i	0.275720	+	0.603370i
$75$	−22.6099	−	51.4648i	−0.301465	−	0.686197i
$76$	48.0689	−	55.5267i	0.632485	−	0.730615i
$77$	54.2850			0.705000
$78$	71.2099	−	32.5405i	0.912947	−	0.417186i
$79$			112.818i			1.42808i	0.700105	+	0.714040i	$0.253137\pi$
$79$			112.818i			1.42808i	−0.700105	+	0.714040i	$0.746863\pi$
$80$	−75.1305	+	27.4847i	−0.939131	+	0.343558i
$81$	−29.9443			−0.369682
$82$	27.3851	+	59.9279i	0.333964	+	0.730829i
$83$		−	40.3476i		−	0.486116i	−0.970012	−	0.243058i	$-0.921850\pi$
$83$		−	40.3476i		−	0.486116i	0.970012	−	0.243058i	$-0.0781505\pi$
$84$	−43.5704	−	37.7185i	−0.518696	−	0.449029i
$85$	−93.2150	+	19.5732i	−1.09665	+	0.230272i
$86$	65.2148	−	29.8010i	0.758311	−	0.346523i
$87$	10.3894			0.119418
$88$	−65.0450	−	19.0496i	−0.739147	−	0.216472i
$89$	−57.5542			−0.646676			−0.323338	−	0.946284i	$-0.604805\pi$
$89$	−57.5542			−0.646676			−0.323338	+	0.946284i	$0.604805\pi$
$90$	31.7401	−	23.4157i	0.352668	−	0.260174i
$91$	−111.554			−1.22587
$92$	6.01501	−	6.94823i	0.0653805	−	0.0755242i
$93$	−98.4096			−1.05817
$94$	−63.2148	−	138.336i	−0.672498	−	1.47166i
$95$	18.8653	+	89.8441i	0.198583	+	0.945727i
$96$	38.9706	+	60.4844i	0.405944	+	0.630046i
$97$		−	187.311i		−	1.93104i	−0.260332	−	0.965519i	$-0.583832\pi$
$97$		−	187.311i		−	1.93104i	0.260332	−	0.965519i	$-0.416168\pi$
$98$	−6.60371	−	14.4512i	−0.0673848	−	0.147461i
$99$	33.4164			0.337539
$100$	29.5127	−	95.5458i	0.295127	−	0.955458i
$101$		−	53.0081i		−	0.524833i	−0.964955	−	0.262416i	$-0.915481\pi$
$101$		−	53.0081i		−	0.524833i	0.964955	−	0.262416i	$-0.0845194\pi$
$102$	35.6049	+	77.9159i	0.349068	+	0.763881i
$103$	74.5922			0.724196			0.362098	−	0.932140i	$-0.382061\pi$
$103$	74.5922			0.724196			0.362098	+	0.932140i	$0.382061\pi$
$104$	133.666	+	39.1463i	1.28525	+	0.376407i
$105$	70.4984	−	14.8032i	0.671414	−	0.140983i
$106$	53.6656	+	117.439i	0.506280	+	1.10791i
$107$			64.9557i			0.607063i	0.952821	+	0.303531i	$0.0981658\pi$
$107$			64.9557i			0.607063i	−0.952821	+	0.303531i	$0.901834\pi$
$108$	−88.0203	−	76.1982i	−0.815002	−	0.705539i
$109$		−	10.8774i		−	0.0997922i	−0.998754	−	0.0498961i	$-0.984111\pi$
$109$		−	10.8774i		−	0.0997922i	0.998754	−	0.0498961i	$-0.0158890\pi$
$110$	68.1764	−	50.2960i	0.619786	−	0.457236i
$111$			55.1896i			0.497204i
$112$	−14.6846	−	101.462i	−0.131113	−	0.905915i
$113$			35.9759i			0.318371i	0.987249	+	0.159185i	$0.0508868\pi$
$113$			35.9759i			0.318371i	−0.987249	+	0.159185i	$0.949113\pi$
$114$	75.0983	−	34.3174i	0.658757	−	0.301030i
$115$	2.36068	+	11.2425i	0.0205277	+	0.0977606i
$116$	13.9737	+	12.0969i	0.120463	+	0.104283i
$117$	−68.6698			−0.586921
$118$	17.6172	+	38.5525i	0.149298	+	0.326716i
$119$		−	122.060i		−	1.02571i
$120$	−89.6668	−	7.00179i	−0.747224	−	0.0583482i
$121$	−49.2229			−0.406801
$122$	−53.4074	+	24.4054i	−0.437766	+	0.200044i
$123$			74.0750i			0.602236i
$124$	−132.361	−	114.583i	−1.06742	−	0.924058i
$125$	72.7225	+	101.668i	0.581780	+	0.813346i
$126$	21.0081	+	45.9730i	0.166731	+	0.364865i
$127$	99.5079			0.783527			0.391763	−	0.920066i	$-0.371865\pi$
$127$	99.5079			0.783527			0.391763	+	0.920066i	$0.371865\pi$
$128$	−18.0096	+	126.727i	−0.140700	+	0.990052i
$129$	80.6099			0.624883
$130$	−140.101	+	103.357i	−1.07770	+	0.795053i
$131$	−6.13777			−0.0468532			−0.0234266	−	0.999726i	$-0.507458\pi$
$131$	−6.13777			−0.0468532			−0.0234266	+	0.999726i	$0.507458\pi$
$132$	−57.6100	−	49.8724i	−0.436439	−	0.377821i
$133$	−117.646			−0.884553
$134$	−154.743	+	70.7122i	−1.15480	+	0.527703i
$135$	142.420	−	29.9051i	1.05496	−	0.221519i
$136$	−42.8328	+	146.253i	−0.314947	+	1.07539i
$137$			146.027i			1.06589i	0.846150	+	0.532945i	$0.178915\pi$
$137$			146.027i			1.06589i	−0.846150	+	0.532945i	$0.821085\pi$
$138$	9.39728	−	4.29424i	0.0680963	−	0.0311177i
$139$	70.5836			0.507796			0.253898	−	0.967231i	$-0.418287\pi$
$139$	70.5836			0.507796			0.253898	+	0.967231i	$0.418287\pi$
$140$	112.056	+	62.1746i	0.800402	+	0.444104i
$141$		−	170.992i		−	1.21271i
$142$	134.015	−	61.2402i	0.943765	−	0.431269i
$143$	−147.500			−1.03147
$144$	−9.03947	−	62.4576i	−0.0627741	−	0.433733i
$145$	−22.6099	+	4.74760i	−0.155930	+	0.0327421i
$146$	−38.5147	+	17.5999i	−0.263799	+	0.120547i
$147$		−	17.8627i		−	0.121515i
$148$	−64.2600	+	74.2299i	−0.434189	+	0.501553i
$149$			30.4505i			0.204366i	0.994766	+	0.102183i	$0.0325827\pi$
$149$			30.4505i			0.204366i	−0.994766	+	0.102183i	$0.967417\pi$
$150$	74.8235	−	83.9093i	0.498823	−	0.559395i
$151$		−	214.214i		−	1.41864i	−0.704889	−	0.709318i	$-0.749003\pi$
$151$		−	214.214i		−	1.41864i	0.704889	−	0.709318i	$-0.250997\pi$
$152$	140.964	+	41.2839i	0.927398	+	0.271605i
$153$		−	75.1366i		−	0.491089i
$154$	45.1246	+	98.7482i	0.293017	+	0.641222i
$155$	214.164	−	44.9699i	1.38170	−	0.290128i
$156$	118.387	+	102.486i	0.758891	+	0.656964i
$157$	73.6355			0.469016			0.234508	−	0.972114i	$-0.424652\pi$
$157$	73.6355			0.469016			0.234508	+	0.972114i	$0.424652\pi$
$158$	−205.224	+	93.7807i	−1.29889	+	0.593549i
$159$			145.162i			0.912972i
$160$	−112.449	−	113.821i	−0.702807	−	0.711381i
$161$	−14.7214			−0.0914370
$162$	−24.8913	−	54.4707i	−0.153650	−	0.336239i
$163$		−	37.9738i		−	0.232968i	−0.993193	−	0.116484i	$-0.962838\pi$
$163$		−	37.9738i		−	0.232968i	0.993193	−	0.116484i	$-0.0371624\pi$
$164$	−86.2492	+	99.6307i	−0.525910	+	0.607504i
$165$	93.2150	−	19.5732i	0.564939	−	0.118625i
$166$	73.3951	−	33.5391i	0.442139	−	0.202043i
$167$	−157.047			−0.940402			−0.470201	−	0.882559i	$-0.655819\pi$
$167$	−157.047			−0.940402			−0.470201	+	0.882559i	$0.655819\pi$
$168$	32.3944	−	110.611i	0.192824	−	0.658401i
$169$	134.108			0.793541
$170$	−113.090	−	153.294i	−0.665237	−	0.901731i
$171$	−72.4195			−0.423506
$172$	108.420	+	93.8581i	0.630349	+	0.545687i
$173$	196.705			1.13702			0.568511	−	0.822676i	$-0.307520\pi$
$173$	196.705			1.13702			0.568511	+	0.822676i	$0.307520\pi$
$174$	8.63621	+	18.8990i	0.0496334	+	0.108615i
$175$	−146.658	+	64.4308i	−0.838044	+	0.368176i
$176$	−19.4164	−	134.156i	−0.110320	−	0.762252i
$177$			47.6535i			0.269229i
$178$	−47.8421	−	104.695i	−0.268776	−	0.588175i
$179$	−205.193			−1.14633			−0.573166	−	0.819439i	$-0.694285\pi$
$179$	−205.193			−1.14633			−0.573166	+	0.819439i	$0.694285\pi$
$180$	68.9789	+	38.2731i	0.383216	+	0.212628i
$181$			25.2845i			0.139693i	0.997558	+	0.0698467i	$0.0222510\pi$
$181$			25.2845i			0.139693i	−0.997558	+	0.0698467i	$0.977749\pi$
$182$	−92.7298	−	202.925i	−0.509505	−	1.11497i
$183$	−66.0152			−0.360739
$184$	17.6393	+	5.16598i	0.0958659	+	0.0280760i
$185$	−25.2198	−	120.107i	−0.136323	−	0.649224i
$186$	−81.8034	−	179.014i	−0.439803	−	0.962441i
$187$		−	161.390i		−	0.863050i
$188$	199.095	−	229.984i	1.05902	−	1.22332i
$189$			186.490i			0.986721i
$190$	−147.751	+	109.001i	−0.777636	+	0.573688i
$191$			106.016i			0.555059i	0.960717	+	0.277529i	$0.0895156\pi$
$191$			106.016i			0.555059i	−0.960717	+	0.277529i	$0.910484\pi$
$192$	−77.6309	+	121.168i	−0.404327	+	0.631084i
$193$			111.113i			0.575713i	0.957674	+	0.287856i	$0.0929425\pi$
$193$			111.113i			0.575713i	−0.957674	+	0.287856i	$0.907057\pi$
$194$	340.731	−	155.703i	1.75635	−	0.802592i
$195$	−191.554	+	40.2223i	−0.982329	+	0.206268i
$196$	20.7984	−	24.0252i	0.106114	−	0.122578i
$197$	17.6390			0.0895383			0.0447692	−	0.998997i	$-0.485745\pi$
$197$	17.6390			0.0895383			0.0447692	+	0.998997i	$0.485745\pi$
$198$	27.7775	+	60.7868i	0.140290	+	0.307004i
$199$		−	55.1896i		−	0.277335i	−0.990339	−	0.138667i	$-0.955718\pi$
$199$		−	55.1896i		−	0.277335i	0.990339	−	0.138667i	$-0.0442819\pi$
$200$	198.337	−	25.7371i	0.991685	−	0.128685i
$201$	−191.272			−0.951604
$202$	96.4254	−	44.0632i	0.477354	−	0.218135i
$203$		−	29.6063i		−	0.145844i
$204$	−112.138	+	129.536i	−0.549695	+	0.634979i
$205$	−33.8498	−	161.206i	−0.165121	−	0.786370i
$206$	62.0050	+	135.688i	0.300995	+	0.658682i
$207$	−9.06208			−0.0437782
$208$	39.9002	+	275.688i	0.191828	+	1.32542i
$209$	−155.554			−0.744278
$210$	85.5301	+	115.936i	0.407286	+	0.552078i
$211$	257.416			1.21998			0.609991	−	0.792408i	$-0.291173\pi$
$211$	257.416			1.21998			0.609991	+	0.792408i	$0.291173\pi$
$212$	−169.020	+	195.243i	−0.797264	+	0.920958i
$213$	165.651			0.777705
$214$	−118.159	+	53.9947i	−0.552145	+	0.252312i
$215$	−175.427	+	36.8360i	−0.815941	+	0.171330i
$216$	65.4427	−	223.455i	0.302976	−	1.03451i
$217$			280.435i			1.29233i
$218$	19.7867	−	9.04184i	0.0907645	−	0.0414763i
$219$	−47.6068			−0.217383
$220$	148.164	+	82.2090i	0.673472	+	0.373677i
$221$			331.653i			1.50069i
$222$	−100.394	+	45.8766i	−0.452225	+	0.206651i
$223$	91.2880			0.409363			0.204682	−	0.978829i	$-0.434384\pi$
$223$	91.2880			0.409363			0.204682	+	0.978829i	$0.434384\pi$
$224$	172.361	−	111.053i	0.769467	−	0.495774i
$225$	−90.2786	+	39.6619i	−0.401238	+	0.176275i
$226$	−65.4427	+	29.9051i	−0.289570	+	0.132324i
$227$		−	306.791i		−	1.35150i	−0.737130	−	0.675750i	$-0.763820\pi$
$227$		−	306.791i		−	1.35150i	0.737130	−	0.675750i	$-0.236180\pi$
$228$	124.852	+	108.083i	0.547594	+	0.474047i
$229$		−	73.6720i		−	0.321712i	−0.986978	−	0.160856i	$-0.948575\pi$
$229$		−	73.6720i		−	0.321712i	0.986978	−	0.160856i	$-0.0514255\pi$
$230$	−18.4885	+	13.6396i	−0.0803849	+	0.0593026i
$231$			122.060i			0.528396i
$232$	−10.3894	+	35.4747i	−0.0447818	+	0.152908i
$233$		−	207.422i		−	0.890223i	−0.895475	−	0.445111i	$-0.853164\pi$
$233$		−	207.422i		−	0.890223i	0.895475	−	0.445111i	$-0.146836\pi$
$234$	−57.0820	−	124.915i	−0.243940	−	0.533826i
$235$	78.1378	+	372.122i	0.332501	+	1.58350i
$236$	−55.4853	+	64.0938i	−0.235107	+	0.271584i
$237$	−253.671			−1.07034
$238$	222.035	−	101.462i	0.932920	−	0.426313i
$239$		−	246.558i		−	1.03162i	−0.856702	−	0.515812i	$-0.827490\pi$
$239$		−	246.558i		−	1.03162i	0.856702	−	0.515812i	$-0.172510\pi$
$240$	−61.7992	−	168.931i	−0.257496	−	0.703877i
$241$	285.495			1.18463			0.592314	−	0.805707i	$-0.298215\pi$
$241$	285.495			1.18463			0.592314	+	0.805707i	$0.298215\pi$
$242$	−40.9167	−	89.5399i	−0.169077	−	0.370000i
$243$			194.617i			0.800891i
$244$	−88.7902	−	76.8648i	−0.363894	−	0.315020i
$245$	8.16263	+	38.8736i	0.0333169	+	0.158668i
$246$	−134.748	+	61.5751i	−0.547755	+	0.250305i
$247$	319.660			1.29417
$248$	98.4096	−	336.021i	0.396813	−	1.35492i
$249$	90.7214			0.364343
$250$	−124.491	+	216.799i	−0.497964	+	0.867198i
$251$	−133.639			−0.532428			−0.266214	−	0.963914i	$-0.585773\pi$
$251$	−133.639			−0.532428			−0.266214	+	0.963914i	$0.585773\pi$
$252$	−66.1651	+	76.4305i	−0.262560	+	0.303296i
$253$	−19.4650			−0.0769367
$254$	82.7163	+	181.012i	0.325655	+	0.712645i
$255$	−44.0101	−	209.593i	−0.172589	−	0.821935i
$256$	−245.495	+	72.5812i	−0.958966	+	0.283520i
$257$			68.8262i			0.267806i	0.990994	+	0.133903i	$0.0427511\pi$
$257$			68.8262i			0.267806i	−0.990994	+	0.133903i	$0.957249\pi$
$258$	67.0073	+	146.635i	0.259718	+	0.568353i
$259$	157.272			0.607229
$260$	−304.473	−	168.937i	−1.17105	−	0.649758i
$261$		−	18.2249i		−	0.0698271i
$262$	−5.10204	−	11.1650i	−0.0194734	−	0.0426146i
$263$	128.278			0.487747			0.243874	−	0.969807i	$-0.421582\pi$
$263$	128.278			0.487747			0.243874	+	0.969807i	$0.421582\pi$
$264$	42.8328	−	146.253i	0.162246	−	0.553990i
$265$	−66.3344	−	315.910i	−0.250318	−	1.19211i
$266$	−97.7933	−	214.006i	−0.367644	−	0.804532i
$267$		−	129.410i		−	0.484683i
$268$	−257.261	−	222.708i	−0.959929	−	0.831000i
$269$		−	516.507i		−	1.92010i	−0.279828	−	0.960050i	$-0.590277\pi$
$269$		−	516.507i		−	1.92010i	0.279828	−	0.960050i	$-0.409723\pi$
$270$	172.787	+	234.213i	0.639950	+	0.867455i
$271$			62.2493i			0.229702i	0.993383	+	0.114851i	$0.0366391\pi$
$271$			62.2493i			0.229702i	−0.993383	+	0.114851i	$0.963361\pi$
$272$	−301.650	+	43.6577i	−1.10901	+	0.160506i
$273$		−	250.829i		−	0.918787i
$274$	−265.633	+	121.385i	−0.969464	+	0.443012i
$275$	−193.915	+	85.1922i	−0.705145	+	0.309790i
$276$	15.6231	+	13.5247i	0.0566053	+	0.0490026i
$277$	−53.3148			−0.192472			−0.0962360	−	0.995359i	$-0.530680\pi$
$277$	−53.3148			−0.192472			−0.0962360	+	0.995359i	$0.530680\pi$
$278$	58.6729	+	128.397i	0.211054	+	0.461858i
$279$			172.629i			0.618740i
$280$	−19.9528	+	255.521i	−0.0712600	+	0.912575i
$281$	370.269			1.31768			0.658842	−	0.752281i	$-0.271046\pi$
$281$	370.269			1.31768			0.658842	+	0.752281i	$0.271046\pi$
$282$	311.047	−	142.138i	1.10300	−	0.504036i
$283$		−	5.99366i		−	0.0211790i	−0.999944	−	0.0105895i	$-0.996629\pi$
$283$		−	5.99366i		−	0.0211790i	0.999944	−	0.0105895i	$-0.00337081\pi$
$284$	222.800	+	192.876i	0.784508	+	0.679140i
$285$	−202.014	+	42.4186i	−0.708821	+	0.148837i
$286$	−122.610	−	268.313i	−0.428706	−	0.938157i
$287$	211.090			0.735504
$288$	106.101	−	68.3615i	0.368405	−	0.237366i
$289$	−73.8854			−0.255659
$290$	−27.4308	−	37.1825i	−0.0945889	−	0.128216i
$291$	421.167			1.44731
$292$	−64.0310	−	55.4310i	−0.219284	−	0.189832i
$293$	−223.534			−0.762914			−0.381457	−	0.924386i	$-0.624578\pi$
$293$	−223.534			−0.762914			−0.381457	+	0.924386i	$0.624578\pi$
$294$	32.4934	−	14.8484i	0.110522	−	0.0505048i
$295$	−21.7760	−	103.706i	−0.0738170	−	0.351545i
$296$	−188.446	−	55.1896i	−0.636641	−	0.186451i
$297$			246.583i			0.830244i
$298$	−55.3916	+	25.3121i	−0.185878	+	0.0849399i
$299$	40.0000			0.133779
$300$	214.834	+	66.3592i	0.716114	+	0.221197i
$301$		−	229.712i		−	0.763162i
$302$	389.670	−	178.066i	1.29030	−	0.589623i
$303$	119.188			0.393361
$304$	42.0789	+	290.742i	0.138418	+	0.956387i
$305$	143.666	−	30.1667i	0.471035	−	0.0989073i
$306$	136.679	−	62.4576i	0.446663	−	0.204110i
$307$			44.8446i			0.146074i	0.997329	+	0.0730368i	$0.0232691\pi$
$307$			44.8446i			0.146074i	−0.997329	+	0.0730368i	$0.976731\pi$
$308$	−142.120	+	164.170i	−0.461428	+	0.533018i
$309$			167.720i			0.542783i
$310$	259.828	+	352.198i	0.838155	+	1.13612i
$311$			476.815i			1.53317i	0.642144	+	0.766584i	$0.278045\pi$
$311$			476.815i			1.53317i	−0.642144	+	0.766584i	$0.721955\pi$
$312$	−88.0203	+	300.546i	−0.282116	+	0.963290i
$313$			158.766i			0.507240i	0.967304	+	0.253620i	$0.0816212\pi$
$313$			158.766i			0.507240i	−0.967304	+	0.253620i	$0.918379\pi$
$314$	61.2098	+	133.948i	0.194936	+	0.426586i
$315$	−25.9675	−	123.667i	−0.0824364	−	0.392594i
$316$	−341.187	−	295.362i	−1.07971	−	0.934691i
$317$	−425.319			−1.34170			−0.670850	−	0.741593i	$-0.734071\pi$
$317$	−425.319			−1.34170			−0.670850	+	0.741593i	$0.734071\pi$
$318$	−264.061	+	120.667i	−0.830380	+	0.379456i
$319$		−	39.1463i		−	0.122716i
$320$	113.575	−	299.167i	0.354920	−	0.934897i
$321$	−146.053			−0.454993
$322$	−12.2372	−	26.7792i	−0.0380037	−	0.0831652i
$323$			349.763i			1.08286i
$324$	78.3951	−	90.5580i	0.241960	−	0.279500i
$325$	398.490	−	175.068i	1.22612	−	0.538670i
$326$	69.0770	−	31.5659i	0.211893	−	0.0968278i
$327$	24.4577			0.0747941
$328$	−252.930	−	74.0750i	−0.771129	−	0.225838i
$329$	−487.272			−1.48107
$330$	113.090	+	153.294i	0.342698	+	0.464528i
$331$	−570.912			−1.72481			−0.862404	−	0.506220i	$-0.831042\pi$
$331$	−570.912			−1.72481			−0.862404	+	0.506220i	$0.831042\pi$
$332$	122.020	+	105.631i	0.367530	+	0.318167i
$333$	96.8128			0.290729
$334$	−130.546	−	285.680i	−0.390856	−	0.855329i
$335$	416.257	−	87.4051i	1.24256	−	0.260911i
$336$	228.138	−	33.0183i	0.678981	−	0.0982687i
$337$		−	53.9639i		−	0.160130i	−0.996790	−	0.0800651i	$-0.974487\pi$
$337$		−	53.9639i		−	0.160130i	0.996790	−	0.0800651i	$-0.0255128\pi$
$338$	111.478	+	243.953i	0.329817	+	0.721753i
$339$	−80.8916			−0.238618
$340$	184.846	−	333.146i	0.543666	−	0.979840i
$341$			370.799i			1.08739i
$342$	−60.1990	−	131.736i	−0.176020	−	0.385194i
$343$	−364.869			−1.06376
$344$	−80.6099	+	275.244i	−0.234331	+	0.800127i
$345$	−25.2786	+	5.30798i	−0.0732714	+	0.0153854i
$346$	163.512	+	357.820i	0.472577	+	1.03416i
$347$		−	107.802i		−	0.310670i	−0.987862	−	0.155335i	$-0.950354\pi$
$347$		−	107.802i		−	0.310670i	0.987862	−	0.155335i	$-0.0496457\pi$
$348$	−27.1998	+	31.4198i	−0.0781602	+	0.0902867i
$349$			541.246i			1.55085i	0.631441	+	0.775424i	$0.282464\pi$
$349$			541.246i			1.55085i	−0.631441	+	0.775424i	$0.717536\pi$
$350$	−239.114	−	213.222i	−0.683183	−	0.609207i
$351$		−	506.720i		−	1.44365i
$352$	227.900	−	146.838i	0.647443	−	0.417153i
$353$		−	82.5678i		−	0.233903i	−0.993138	−	0.116952i	$-0.962688\pi$
$353$		−	82.5678i		−	0.233903i	0.993138	−	0.116952i	$-0.0373122\pi$
$354$	−86.6850	+	39.6121i	−0.244873	+	0.111899i
$355$	−360.498	+	75.6970i	−1.01549	+	0.213231i
$356$	150.679	−	174.056i	0.423255	−	0.488922i
$357$	274.450			0.768768
$358$	−170.568	−	373.261i	−0.476447	−	1.04263i
$359$			306.111i			0.852676i	0.904564	+	0.426338i	$0.140197\pi$
$359$			306.111i			0.852676i	−0.904564	+	0.426338i	$0.859803\pi$
$360$	−12.2824	+	157.292i	−0.0341178	+	0.436922i
$361$	−23.8854			−0.0661646
$362$	−45.9943	+	21.0179i	−0.127056	+	0.0580604i
$363$		−	110.677i		−	0.304897i
$364$	292.053	−	337.364i	0.802342	−	0.926825i
$365$	103.604	−	21.7547i	0.283847	−	0.0596019i
$366$	−54.8754	−	120.086i	−0.149933	−	0.328105i
$367$	−415.543			−1.13227			−0.566134	−	0.824313i	$-0.691562\pi$
$367$	−415.543			−1.13227			−0.566134	+	0.824313i	$0.691562\pi$
$368$	5.26547	+	36.3814i	0.0143083	+	0.0988625i
$369$	129.941			0.352144
$370$	197.518	−	145.716i	0.533833	−	0.393826i
$371$	413.666			1.11500
$372$	257.640	−	297.612i	0.692580	−	0.800033i
$373$	−237.575			−0.636931			−0.318465	−	0.947934i	$-0.603167\pi$
$373$	−237.575			−0.636931			−0.318465	+	0.947934i	$0.603167\pi$
$374$	293.580	−	134.156i	0.784975	−	0.358707i
$375$	−228.601	+	163.516i	−0.609602	+	0.436043i
$376$	583.856	+	170.992i	1.55281	+	0.454767i
$377$			80.4446i			0.213381i
$378$	−339.239	+	155.021i	−0.897458	+	0.410108i
$379$	303.135			0.799828			0.399914	−	0.916553i	$-0.369040\pi$
$379$	303.135			0.799828			0.399914	+	0.916553i	$0.369040\pi$
$380$	−321.098	−	178.162i	−0.844996	−	0.468847i
$381$			223.743i			0.587252i
$382$	−192.851	+	88.1264i	−0.504845	+	0.230697i
$383$	−282.084			−0.736512			−0.368256	−	0.929725i	$-0.620045\pi$
$383$	−282.084			−0.736512			−0.368256	+	0.929725i	$0.620045\pi$
$384$	−284.944	−	40.4946i	−0.742042	−	0.105455i
$385$	−55.7771	−	265.632i	−0.144876	−	0.689954i
$386$	−202.122	+	92.3627i	−0.523631	+	0.239282i
$387$		−	141.405i		−	0.365386i
$388$	566.469	+	490.386i	1.45997	+	1.26388i
$389$		−	437.124i		−	1.12371i	−0.827235	−	0.561856i	$-0.810088\pi$
$389$		−	437.124i		−	1.12371i	0.827235	−	0.561856i	$-0.189912\pi$
$390$	−232.397	−	315.016i	−0.595891	−	0.807732i
$391$			43.7669i			0.111936i
$392$	60.9923	+	17.8627i	0.155593	+	0.0455680i
$393$		−	13.8007i		−	0.0351164i
$394$	14.6625	+	32.0867i	0.0372145	+	0.0814382i
$395$	552.053	−	115.919i	1.39760	−	0.293467i
$396$	−87.4853	+	101.059i	−0.220922	+	0.255198i
$397$	529.779			1.33446			0.667228	−	0.744854i	$-0.267481\pi$
$397$	529.779			1.33446			0.667228	+	0.744854i	$0.267481\pi$
$398$	100.394	−	45.8766i	0.252246	−	0.115268i
$399$		−	264.525i		−	0.662971i
$400$	211.686	+	339.395i	0.529215	+	0.848488i
$401$	−280.663			−0.699907			−0.349953	−	0.936767i	$-0.613803\pi$
$401$	−280.663			−0.699907			−0.349953	+	0.936767i	$0.613803\pi$
$402$	−158.996	−	347.938i	−0.395512	−	0.865517i
$403$		−	761.982i		−	1.89077i
$404$	160.308	+	138.777i	0.396802	+	0.343507i
$405$	30.7673	+	146.526i	0.0759687	+	0.361792i
$406$	53.8560	−	24.6104i	0.132650	−	0.0606167i
$407$	207.950			0.510933
$408$	−328.850	−	96.3094i	−0.806004	−	0.236052i
$409$	245.613			0.600521			0.300260	−	0.953857i	$-0.402926\pi$
$409$	245.613			0.600521			0.300260	+	0.953857i	$0.402926\pi$
$410$	265.107	−	195.578i	0.646602	−	0.477020i
$411$	−328.341			−0.798882
$412$	−195.285	+	225.583i	−0.473992	+	0.547532i
$413$	135.797			0.328806
$414$	−7.53289	−	16.4846i	−0.0181954	−	0.0398178i
$415$	−197.432	+	41.4566i	−0.475741	+	0.0998954i
$416$	−468.328	+	301.748i	−1.12579	+	0.725355i
$417$			158.707i			0.380592i
$418$	−129.305	−	282.964i	−0.309342	−	0.676947i
$419$	−528.184			−1.26058			−0.630291	−	0.776359i	$-0.717065\pi$
$419$	−528.184			−1.26058			−0.630291	+	0.776359i	$0.717065\pi$
$420$	−139.799	+	251.958i	−0.332855	+	0.599900i
$421$		−	377.313i		−	0.896231i	−0.893976	−	0.448116i	$-0.852095\pi$
$421$		−	377.313i		−	0.896231i	0.893976	−	0.448116i	$-0.147905\pi$
$422$	213.978	+	468.259i	0.507058	+	1.10962i
$423$	−299.952			−0.709106
$424$	−495.659	−	145.162i	−1.16901	−	0.342364i
$425$	191.554	+	436.017i	0.450716	+	1.02592i
$426$	137.698	+	301.331i	0.323235	+	0.707350i
$427$			188.122i			0.440566i
$428$	−196.440	−	170.056i	−0.458973	−	0.397328i
$429$		−	331.653i		−	0.773084i
$430$	−212.832	−	288.495i	−0.494958	−	0.670918i
$431$		−	610.298i		−	1.41600i	−0.706211	−	0.708002i	$-0.749597\pi$
$431$		−	610.298i		−	1.41600i	0.706211	−	0.708002i	$-0.250403\pi$
$432$	460.880	−	66.7030i	1.06685	−	0.154405i
$433$			753.548i			1.74030i	0.492790	+	0.870148i	$0.335977\pi$
$433$			753.548i			1.74030i	−0.492790	+	0.870148i	$0.664023\pi$
$434$	−510.132	+	233.113i	−1.17542	+	0.537127i
$435$	−10.6749	−	50.8382i	−0.0245401	−	0.116870i
$436$	32.8955	+	28.4773i	0.0754484	+	0.0653149i
$437$	42.1842			0.0965313
$438$	−39.5733	−	86.6001i	−0.0903501	−	0.197717i
$439$			182.127i			0.414868i	0.978249	+	0.207434i	$0.0665113\pi$
$439$			182.127i			0.414868i	−0.978249	+	0.207434i	$0.933489\pi$
$440$	−26.3821	+	337.857i	−0.0599594	+	0.767857i
$441$	−31.3344			−0.0710530
$442$	−603.300	+	275.688i	−1.36493	+	0.623728i
$443$			715.766i			1.61572i	0.589371	+	0.807862i	$0.299376\pi$
$443$			715.766i			1.61572i	−0.589371	+	0.807862i	$0.700624\pi$
$444$	−166.906	−	144.488i	−0.375913	−	0.325424i
$445$	59.1361	+	281.629i	0.132890	+	0.632875i
$446$	75.8835	+	166.059i	0.170142	+	0.372330i
$447$	−68.4678			−0.153172
$448$	345.289	+	221.223i	0.770735	+	0.493800i
$449$	580.158			1.29211			0.646056	−	0.763290i	$-0.276417\pi$
$449$	580.158			1.29211			0.646056	+	0.763290i	$0.276417\pi$
$450$	−147.192	−	131.254i	−0.327094	−	0.291676i
$451$	279.108			0.618866
$452$	−108.799	−	94.1862i	−0.240706	−	0.208376i
$453$	481.659			1.06326
$454$	558.074	−	255.021i	1.22924	−	0.561720i
$455$	114.620	+	545.867i	0.251913	+	1.19971i
$456$	−92.8266	+	316.958i	−0.203567	+	0.695083i
$457$		−	766.228i		−	1.67665i	−0.545172	−	0.838324i	$-0.683536\pi$
$457$		−	766.228i		−	1.67665i	0.545172	−	0.838324i	$-0.316464\pi$
$458$	134.015	−	61.2402i	0.292608	−	0.133712i
$459$	554.440			1.20793
$460$	−40.1800	−	22.2940i	−0.0873479	−	0.0484651i
$461$		−	692.953i		−	1.50315i	−0.659646	−	0.751576i	$-0.729294\pi$
$461$		−	692.953i		−	1.50315i	0.659646	−	0.751576i	$-0.270706\pi$
$462$	−222.035	+	101.462i	−0.480595	+	0.219616i
$463$	620.865			1.34096			0.670480	−	0.741927i	$-0.266088\pi$
$463$	620.865			1.34096			0.670480	+	0.741927i	$0.266088\pi$
$464$	−73.1672	+	10.5895i	−0.157688	+	0.0228221i
$465$	101.115	+	481.547i	0.217451	+	1.03558i
$466$	377.315	−	172.420i	0.809689	−	0.370001i
$467$			369.999i			0.792289i	0.918188	+	0.396145i	$0.129652\pi$
$467$			369.999i			0.792289i	−0.918188	+	0.396145i	$0.870348\pi$
$468$	179.780	−	207.672i	0.384145	−	0.443745i
$469$			545.064i			1.16218i
$470$	−611.964	+	451.466i	−1.30205	+	0.960567i
$471$			165.569i			0.351526i
$472$	−162.713	−	47.6535i	−0.344732	−	0.100961i
$473$		−	303.731i		−	0.642138i
$474$	−210.865	−	461.446i	−0.444864	−	0.973515i
$475$	420.249	−	184.627i	0.884735	−	0.388689i
$476$	369.135	+	319.556i	0.775493	+	0.671336i
$477$	254.642			0.533840
$478$	448.506	−	204.952i	0.938298	−	0.428771i
$479$		−	691.029i		−	1.44265i	−0.692597	−	0.721325i	$-0.743533\pi$
$479$		−	691.029i		−	1.44265i	0.692597	−	0.721325i	$-0.256467\pi$
$480$	255.926	−	252.841i	0.533179	−	0.526752i
$481$	−427.331			−0.888423
$482$	237.319	+	519.336i	0.492363	+	1.07746i
$483$		−	33.1009i		−	0.0685319i
$484$	128.867	−	148.861i	0.266255	−	0.307564i
$485$	−916.565	+	192.459i	−1.88983	+	0.396823i
$486$	−354.021	+	161.776i	−0.728439	+	0.332872i
$487$	−850.564			−1.74654			−0.873269	−	0.487239i	$-0.838004\pi$
$487$	−850.564			−1.74654			−0.873269	+	0.487239i	$0.838004\pi$
$488$	66.0152	−	225.410i	0.135277	−	0.461905i
$489$	85.3839			0.174609
$490$	−63.9286	+	47.1622i	−0.130467	+	0.0962495i
$491$	−666.020			−1.35646			−0.678228	−	0.734851i	$-0.737252\pi$
$491$	−666.020			−1.35646			−0.678228	+	0.734851i	$0.737252\pi$
$492$	−224.019	−	193.931i	−0.455323	−	0.394169i
$493$	−88.0203			−0.178540
$494$	265.718	+	581.483i	0.537891	+	1.17709i
$495$	−34.3349	−	163.516i	−0.0693634	−	0.330336i
$496$	693.050	−	100.305i	1.39728	−	0.202227i
$497$		−	472.052i		−	0.949802i
$498$	75.4125	+	165.029i	0.151431	+	0.331383i
$499$	−400.184			−0.801972			−0.400986	−	0.916084i	$-0.631332\pi$
$499$	−400.184			−0.801972			−0.400986	+	0.916084i	$0.631332\pi$
$500$	−497.857	−	46.2423i	−0.995714	−	0.0924846i
$501$		−	353.120i		−	0.704830i
$502$	−111.088	−	243.099i	−0.221291	−	0.484262i
$503$	655.914			1.30400			0.652002	−	0.758217i	$-0.273929\pi$
$503$	655.914			1.30400			0.652002	+	0.758217i	$0.273929\pi$
$504$	−194.033	−	56.8258i	−0.384985	−	0.112750i
$505$	−259.384	+	54.4651i	−0.513631	+	0.107852i
$506$	−16.1803	−	35.4082i	−0.0319770	−	0.0699766i
$507$			301.542i			0.594757i
$508$	−260.515	+	300.934i	−0.512825	+	0.592389i
$509$			617.357i			1.21288i	0.795128	+	0.606441i	$0.207403\pi$
$509$			617.357i			1.21288i	−0.795128	+	0.606441i	$0.792597\pi$
$510$	344.681	−	254.283i	0.675846	−	0.498594i
$511$			135.664i			0.265487i
$512$	−336.099	−	386.240i	−0.656444	−	0.754375i
$513$		−	534.390i		−	1.04170i
$514$	−125.200	+	57.2120i	−0.243579	+	0.111307i
$515$	−76.6424	−	365.001i	−0.148820	−	0.708740i
$516$	−211.039	+	243.782i	−0.408991	+	0.472446i
$517$	−644.285			−1.24620
$518$	130.733	+	286.090i	0.252381	+	0.552297i
$519$			442.290i			0.852196i
$520$	54.2146	−	694.287i	0.104259	−	1.33517i
$521$	−41.7771			−0.0801863			−0.0400932	−	0.999196i	$-0.512765\pi$
$521$	−41.7771			−0.0801863			−0.0400932	+	0.999196i	$0.512765\pi$
$522$	33.1523	−	15.1495i	0.0635102	−	0.0290220i
$523$		−	926.623i		−	1.77175i	−0.463927	−	0.885873i	$-0.653560\pi$
$523$		−	926.623i		−	1.77175i	0.463927	−	0.885873i	$-0.346440\pi$
$524$	16.0689	−	18.5620i	0.0306658	−	0.0354236i
$525$	−144.872	−	329.759i	−0.275947	−	0.628113i
$526$	106.631	+	233.346i	0.202721	+	0.443623i
$527$	833.740			1.58205
$528$	301.650	−	43.6577i	0.571307	−	0.0826850i
$529$	−523.721			−0.990021
$530$	519.522	−	383.268i	0.980230	−	0.723148i
$531$	83.5929			0.157425
$532$	308.000	−	355.786i	0.578948	−	0.668771i
$533$	−573.560			−1.07610
$534$	235.406	−	107.573i	0.440836	−	0.201447i
$535$	317.847	−	66.7411i	0.594107	−	0.124750i
$536$	191.272	−	653.102i	0.356852	−	1.21847i
$537$		−	461.376i		−	0.859174i
$538$	939.563	−	429.348i	1.74640	−	0.798045i
$539$	−67.3050			−0.124870
$540$	−282.420	+	509.001i	−0.523000	+	0.942595i
$541$			638.021i			1.17934i	0.807645	+	0.589668i	$0.200742\pi$
$541$			638.021i			1.17934i	−0.807645	+	0.589668i	$0.799258\pi$
$542$	−113.236	+	51.7450i	−0.208922	+	0.0954704i
$543$	−56.8521			−0.104700
$544$	−330.164	−	512.432i	−0.606919	−	0.941970i
$545$	−53.2260	+	11.1763i	−0.0976624	+	0.0205070i
$546$	456.276	−	208.503i	0.835669	−	0.381873i
$547$			880.150i			1.60905i	0.593919	+	0.804525i	$0.297580\pi$
$547$			880.150i			1.60905i	−0.593919	+	0.804525i	$0.702420\pi$
$548$	−441.617	−	382.303i	−0.805871	−	0.697634i
$549$			115.803i			0.210934i
$550$	−316.163	−	281.928i	−0.574842	−	0.512597i
$551$			84.8373i			0.153970i
$552$	−11.6157	+	39.6619i	−0.0210429	+	0.0718513i
$553$			722.881i			1.30720i
$554$	−44.3181	−	96.9833i	−0.0799966	−	0.175060i
$555$	270.059	−	56.7066i	0.486592	−	0.102174i
$556$	−184.790	+	213.460i	−0.332357	+	0.383921i
$557$	44.6368			0.0801379			0.0400689	−	0.999197i	$-0.487242\pi$
$557$	44.6368			0.0801379			0.0400689	+	0.999197i	$0.487242\pi$
$558$	−314.024	+	143.498i	−0.562766	+	0.257165i
$559$			624.159i			1.11656i
$560$	−481.397	+	176.107i	−0.859637	+	0.314477i
$561$	362.885			0.646855
$562$	307.788	+	673.546i	0.547665	+	1.19848i
$563$			140.402i			0.249382i	0.992196	+	0.124691i	$0.0397940\pi$
$563$			140.402i			0.249382i	−0.992196	+	0.124691i	$0.960206\pi$
$564$	517.118	+	447.664i	0.916877	+	0.793730i
$565$	176.041	−	36.9648i	0.311576	−	0.0654244i
$566$	10.9029	−	4.98225i	0.0192630	−	0.00880256i
$567$	−191.867			−0.338390
$568$	−165.651	+	565.618i	−0.291639	+	0.995807i
$569$	190.715			0.335176			0.167588	−	0.985857i	$-0.446402\pi$
$569$	190.715			0.335176			0.167588	+	0.985857i	$0.446402\pi$
$570$	−245.087	−	332.217i	−0.429978	−	0.582837i
$571$	−539.305			−0.944492			−0.472246	−	0.881467i	$-0.656557\pi$
$571$	−539.305			−0.944492			−0.472246	+	0.881467i	$0.656557\pi$
$572$	386.160	−	446.072i	0.675105	−	0.779846i
$573$	−238.377			−0.416015
$574$	175.469	+	383.987i	0.305695	+	0.668967i
$575$	52.5871	−	23.1030i	0.0914558	−	0.0401791i
$576$	212.551	+	136.179i	0.369012	+	0.236422i
$577$			205.240i			0.355701i	0.984058	+	0.177851i	$0.0569144\pi$
$577$			205.240i			0.355701i	−0.984058	+	0.177851i	$0.943086\pi$
$578$	−61.4176	−	134.403i	−0.106259	−	0.232531i
$579$	−249.836			−0.431496
$580$	44.8357	−	80.8067i	0.0773030	−	0.139322i
$581$		−	258.526i		−	0.444968i
$582$	350.097	+	766.133i	0.601541	+	1.31638i
$583$	546.960			0.938182
$584$	47.6068	−	162.554i	0.0815185	−	0.278346i
$585$	70.5573	+	336.021i	0.120611	+	0.574395i
$586$	−185.813	−	406.624i	−0.317088	−	0.693898i
$587$			547.756i			0.933144i	0.884483	+	0.466572i	$0.154511\pi$
$587$			547.756i			0.933144i	−0.884483	+	0.466572i	$0.845489\pi$
$588$	54.0206	+	46.7650i	0.0918717	+	0.0795324i
$589$		−	803.590i		−	1.36433i
$590$	170.547	−	125.818i	0.289063	−	0.213251i
$591$			39.6613i			0.0671088i
$592$	−56.2525	−	388.673i	−0.0950211	−	0.656542i
$593$		−	485.793i		−	0.819213i	−0.912262	−	0.409606i	$-0.865666\pi$
$593$		−	485.793i		−	0.819213i	0.912262	−	0.409606i	$-0.134334\pi$
$594$	−448.551	+	204.973i	−0.755136	+	0.345072i
$595$	−597.272	+	125.414i	−1.00382	+	0.210781i
$596$	−92.0890	−	79.7205i	−0.154512	−	0.133759i
$597$	124.094			0.207862
$598$	33.2502	+	72.7628i	0.0556023	+	0.121677i
$599$			151.965i			0.253697i	0.991922	+	0.126849i	$0.0404862\pi$
$599$			151.965i			0.253697i	−0.991922	+	0.126849i	$0.959514\pi$
$600$	57.8697	+	445.960i	0.0964495	+	0.743266i
$601$	−572.158			−0.952010			−0.476005	−	0.879443i	$-0.657916\pi$
$601$	−572.158			−0.952010			−0.476005	+	0.879443i	$0.657916\pi$
$602$	417.862	−	190.949i	0.694123	−	0.317191i
$603$			335.527i			0.556429i
$604$	647.830	+	560.819i	1.07257	+	0.928509i
$605$	50.5759	+	240.862i	0.0835965	+	0.398119i
$606$	99.0758	+	216.812i	0.163491	+	0.357776i
$607$	−528.708			−0.871018			−0.435509	−	0.900184i	$-0.643432\pi$
$607$	−528.708			−0.871018			−0.435509	+	0.900184i	$0.643432\pi$
$608$	−493.901	+	318.225i	−0.812337	+	0.523396i
$609$	66.5697			0.109310
$610$	174.298	+	236.262i	0.285734	+	0.387314i
$611$	1323.99			2.16692
$612$	227.230	+	196.710i	0.371290	+	0.321422i
$613$	497.586			0.811723			0.405862	−	0.913934i	$-0.366971\pi$
$613$	497.586			0.811723			0.405862	+	0.913934i	$0.366971\pi$
$614$	−81.5755	+	37.2772i	−0.132859	+	0.0607121i
$615$	362.470	−	76.1111i	0.589383	−	0.123758i
$616$	−416.774	−	122.060i	−0.676581	−	0.198149i
$617$		−	437.019i		−	0.708297i	−0.935189	−	0.354148i	$-0.884771\pi$
$617$		−	437.019i		−	0.708297i	0.935189	−	0.354148i	$-0.115229\pi$
$618$	−305.095	+	139.418i	−0.493681	+	0.225595i
$619$	145.416			0.234921			0.117461	−	0.993078i	$-0.462525\pi$
$619$	145.416			0.234921			0.117461	+	0.993078i	$0.462525\pi$
$620$	−424.690	+	765.412i	−0.684984	+	1.23453i
$621$		−	66.8699i		−	0.107681i
$622$	−867.361	+	396.355i	−1.39447	+	0.637226i
$623$	−368.777			−0.591937
$624$	−619.882	+	89.7154i	−0.993401	+	0.143775i
$625$	422.771	−	460.315i	0.676433	−	0.736504i
$626$	−288.807	+	131.975i	−0.461352	+	0.210822i
$627$		−	349.763i		−	0.557835i
$628$	−192.780	+	222.690i	−0.306975	+	0.354601i
$629$		−	467.574i		−	0.743361i
$630$	203.374	−	150.036i	0.322816	−	0.238152i
$631$		−	573.075i		−	0.908202i	−0.890950	−	0.454101i	$-0.849961\pi$
$631$		−	573.075i		−	0.908202i	0.890950	−	0.454101i	$-0.150039\pi$
$632$	253.671	−	866.165i	0.401379	−	1.37051i
$633$			578.799i			0.914375i
$634$	−353.548	−	773.685i	−0.557647	−	1.22032i
$635$	−102.243	−	486.921i	−0.161013	−	0.766805i
$636$	−439.003	−	380.040i	−0.690256	−	0.597548i
$637$	138.310			0.217127
$638$	71.2099	−	32.5405i	0.111614	−	0.0510039i
$639$		−	290.582i		−	0.454746i
$640$	638.615	−	42.0836i	0.997836	−	0.0657556i
$641$	668.158			1.04237			0.521184	−	0.853444i	$-0.325491\pi$
$641$	668.158			1.04237			0.521184	+	0.853444i	$0.325491\pi$
$642$	−121.407	−	265.680i	−0.189107	−	0.413832i
$643$		−	34.5976i		−	0.0538065i	−0.999638	−	0.0269032i	$-0.991435\pi$
$643$		−	34.5976i		−	0.0538065i	0.999638	−	0.0269032i	$-0.00856460\pi$
$644$	38.5410	−	44.5206i	0.0598463	−	0.0691314i
$645$	−82.8256	−	394.448i	−0.128412	−	0.611547i
$646$	−636.243	+	290.742i	−0.984896	+	0.450064i
$647$	−279.402			−0.431843			−0.215921	−	0.976411i	$-0.569276\pi$
$647$	−279.402			−0.431843			−0.215921	+	0.976411i	$0.569276\pi$
$648$	229.898	+	67.3295i	0.354780	+	0.103904i
$649$	179.554			0.276663
$650$	649.706	+	579.355i	0.999548	+	0.891316i
$651$	−630.557			−0.968598
$652$	114.841	+	99.4167i	0.176137	+	0.152480i
$653$	−432.852			−0.662866			−0.331433	−	0.943479i	$-0.607532\pi$
$653$	−432.852			−0.662866			−0.331433	+	0.943479i	$0.607532\pi$
$654$	20.3305	+	44.4902i	0.0310864	+	0.0680279i
$655$	6.30647	+	30.0339i	0.00962820	+	0.0458532i
$656$	−75.5016	−	521.673i	−0.115094	−	0.795233i
$657$			83.5111i			0.127110i
$658$	−405.047	−	886.383i	−0.615573	−	1.34709i
$659$	840.788			1.27585			0.637927	−	0.770097i	$-0.279792\pi$
$659$	840.788			1.27585			0.637927	+	0.770097i	$0.279792\pi$
$660$	−184.846	+	333.146i	−0.280070	+	0.504766i
$661$			1019.96i			1.54305i	0.636200	+	0.771524i	$0.280505\pi$
$661$			1019.96i			1.54305i	−0.636200	+	0.771524i	$0.719495\pi$
$662$	−474.573	−	1038.53i	−0.716877	−	1.56877i
$663$	−745.720			−1.12477
$664$	−90.7214	+	309.769i	−0.136629	+	0.466520i
$665$	120.879	+	575.674i	0.181773	+	0.865675i
$666$	80.4760	+	176.109i	0.120835	+	0.264428i
$667$			10.6160i			0.0159160i
$668$	411.155	−	474.945i	0.615501	−	0.710995i
$669$			205.261i			0.306817i
$670$	505.011	+	684.545i	0.753748	+	1.02171i
$671$			248.740i			0.370700i
$672$	249.703	+	387.552i	0.371582	+	0.576714i
$673$			574.671i			0.853895i	0.904276	+	0.426948i	$0.140411\pi$
$673$			574.671i			0.853895i	−0.904276	+	0.426948i	$0.859589\pi$
$674$	98.1641	−	44.8577i	0.145644	−	0.0665544i
$675$	−292.669	−	666.174i	−0.433583	−	0.986924i
$676$	−351.100	+	405.573i	−0.519379	+	0.599960i
$677$	794.069			1.17292			0.586461	−	0.809977i	$-0.300521\pi$
$677$	794.069			1.17292			0.586461	+	0.809977i	$0.300521\pi$
$678$	−67.2415	−	147.148i	−0.0991762	−	0.217032i
$679$		−	1200.19i		−	1.76758i
$680$	759.670	+	59.3201i	1.11716	+	0.0872354i
$681$	689.817			1.01295
$682$	−674.510	+	308.228i	−0.989017	+	0.451948i
$683$		−	758.613i		−	1.11071i	−0.831614	−	0.555353i	$-0.812583\pi$
$683$		−	758.613i		−	1.11071i	0.831614	−	0.555353i	$-0.187417\pi$
$684$	189.597	−	219.012i	0.277188	−	0.320194i
$685$	714.551	−	150.041i	1.04314	−	0.219037i
$686$	−303.299	−	663.722i	−0.442126	−	0.967525i
$687$	165.651			0.241122
$688$	−567.695	+	82.1623i	−0.825138	+	0.119422i
$689$	−1123.99			−1.63133
$690$	−30.6685	−	41.5714i	−0.0444472	−	0.0602483i
$691$	1050.96			1.52093			0.760466	−	0.649377i	$-0.224970\pi$
$691$	1050.96			1.52093			0.760466	+	0.649377i	$0.224970\pi$
$692$	−514.980	+	594.878i	−0.744190	+	0.859651i
$693$	214.115			0.308968
$694$	196.100	−	89.6112i	0.282565	−	0.129123i
$695$	−72.5237	−	345.386i	−0.104351	−	0.496958i
$696$	−79.7647	−	23.3605i	−0.114604	−	0.0335639i
$697$		−	627.574i		−	0.900393i
$698$	−984.565	+	449.913i	−1.41055	+	0.644574i
$699$	466.387			0.667220
$700$	189.102	−	612.207i	0.270146	−	0.874582i
$701$			246.846i			0.352134i	0.984378	+	0.176067i	$0.0563375\pi$
$701$			246.846i			0.352134i	−0.984378	+	0.176067i	$0.943662\pi$
$702$	921.760	−	421.213i	1.31305	−	0.600019i
$703$	−450.666			−0.641061
$704$	456.551	+	292.507i	0.648510	+	0.415492i
$705$	−836.715	+	175.692i	−1.18683	+	0.249209i
$706$	150.197	−	68.6348i	0.212743	−	0.0972164i
$707$		−	339.648i		−	0.480407i
$708$	−144.114	−	124.758i	−0.203552	−	0.176212i
$709$		−	430.352i		−	0.606984i	−0.952834	−	0.303492i	$-0.901847\pi$
$709$		−	430.352i		−	0.606984i	0.952834	−	0.303492i	$-0.0981526\pi$
$710$	−437.364	−	592.849i	−0.616005	−	0.834998i
$711$			444.986i			0.625860i
$712$	441.873	+	129.410i	0.620608	+	0.181756i
$713$		−	100.556i		−	0.141032i
$714$	228.138	+	499.244i	0.319521	+	0.699222i
$715$	151.554	+	721.760i	0.211964	+	1.00945i
$716$	537.204	−	620.550i	0.750284	−	0.866690i
$717$	554.385			0.773200
$718$	−556.837	+	254.456i	−0.775539	+	0.354395i
$719$			223.713i			0.311144i	0.987825	+	0.155572i	$0.0497221\pi$
$719$			223.713i			0.311144i	−0.987825	+	0.155572i	$0.950278\pi$
$720$	−296.335	+	108.407i	−0.411577	+	0.150565i
$721$	477.947			0.662895
$722$	−19.8549	−	43.4493i	−0.0274998	−	0.0601791i
$723$			641.935i			0.887877i
$724$	−76.4659	−	66.1957i	−0.105616	−	0.0914306i
$725$	46.4627	+	105.759i	0.0640865	+	0.145874i
$726$	201.330	−	92.0011i	0.277314	−	0.126723i
$727$	237.535			0.326733			0.163366	−	0.986565i	$-0.447765\pi$
$727$	237.535			0.326733			0.163366	+	0.986565i	$0.447765\pi$
$728$	856.459	+	250.829i	1.17645	+	0.344545i
$729$	−707.093			−0.969949
$730$	125.695	+	170.380i	0.172185	+	0.233397i
$731$	−682.938			−0.934252
$732$	172.830	−	199.644i	0.236107	−	0.272738i
$733$	−706.446			−0.963774			−0.481887	−	0.876233i	$-0.660048\pi$
$733$	−706.446			−0.963774			−0.481887	+	0.876233i	$0.660048\pi$
$734$	−345.421	−	755.901i	−0.470601	−	1.02984i
$735$	−87.4071	+	18.3536i	−0.118921	+	0.0249709i
$736$	−61.8034	+	39.8204i	−0.0839720	+	0.0541039i
$737$			720.698i			0.977881i
$738$	108.014	+	236.372i	0.146361	+	0.320287i
$739$	−769.862			−1.04176			−0.520881	−	0.853629i	$-0.674397\pi$
$739$	−769.862			−1.04176			−0.520881	+	0.853629i	$0.674397\pi$
$740$	429.255	+	238.173i	0.580074	+	0.321855i
$741$			718.753i			0.969977i
$742$	343.861	+	752.487i	0.463425	+	1.01413i
$743$	−794.965			−1.06994			−0.534970	−	0.844871i	$-0.679677\pi$
$743$	−794.965			−1.06994			−0.534970	+	0.844871i	$0.679677\pi$
$744$	755.542	+	221.274i	1.01551	+	0.297411i
$745$	149.003	−	31.2875i	0.200004	−	0.0419966i
$746$	−197.485	−	432.166i	−0.264726	−	0.579311i
$747$		−	159.142i		−	0.213041i
$748$	488.080	+	422.526i	0.652513	+	0.564874i
$749$			416.202i			0.555677i
$750$	−487.472	−	279.917i	−0.649963	−	0.373223i
$751$			1178.75i			1.56958i	0.619764	+	0.784789i	$0.287228\pi$
$751$			1178.75i			1.56958i	−0.619764	+	0.784789i	$0.712772\pi$
$752$	174.285	+	1204.21i	0.231762	+	1.60135i
$753$		−	300.487i		−	0.399054i
$754$	−146.334	+	66.8699i	−0.194077	+	0.0886868i
$755$	−1048.21	+	220.102i	−1.38836	+	0.291526i
$756$	−563.988	−	488.238i	−0.746015	−	0.645818i
$757$	268.056			0.354103			0.177052	−	0.984202i	$-0.443344\pi$
$757$	268.056			0.354103			0.177052	+	0.984202i	$0.443344\pi$
$758$	251.982	+	551.423i	0.332430	+	0.727471i
$759$		−	43.7669i		−	0.0576639i
$760$	57.1750	−	732.198i	0.0752302	−	0.963419i
$761$	−587.758			−0.772350			−0.386175	−	0.922426i	$-0.626204\pi$
$761$	−587.758			−0.772350			−0.386175	+	0.922426i	$0.626204\pi$
$762$	−407.004	+	185.987i	−0.534126	+	0.244078i
$763$		−	69.6964i		−	0.0913452i
$764$	−320.616	−	277.554i	−0.419655	−	0.363291i
$765$	−367.665	+	77.2018i	−0.480608	+	0.100917i
$766$	−234.483	−	513.131i	−0.306114	−	0.669883i
$767$	−368.979			−0.481068
$768$	−163.199	−	551.995i	−0.212498	−	0.718743i
$769$	802.210			1.04319			0.521593	−	0.853194i	$-0.325338\pi$
$769$	802.210			1.04319			0.521593	+	0.853194i	$0.325338\pi$
$770$	436.839	−	322.270i	0.567323	−	0.418533i
$771$	−154.755			−0.200720
$772$	−336.029	−	290.896i	−0.435270	−	0.376809i
$773$	1133.36			1.46619			0.733093	−	0.680128i	$-0.238076\pi$
$773$	1133.36			1.46619			0.733093	+	0.680128i	$0.238076\pi$
$774$	257.225	−	117.543i	0.332332	−	0.151864i
$775$	−440.101	−	1001.76i	−0.567873	−	1.29259i
$776$	−421.167	+	1438.08i	−0.542741	+	1.85320i
$777$			353.626i			0.455117i
$778$	795.159	−	363.361i	1.02205	−	0.467045i
$779$	−604.879			−0.776482
$780$	379.854	−	684.605i	0.486993	−	0.877699i
$781$		−	624.159i		−	0.799180i
$782$	−79.6151	+	36.3814i	−0.101810	+	0.0465235i
$783$	134.483			0.171754
$784$	18.2067	+	125.798i	0.0232228	+	0.160456i
$785$	−75.6594	−	360.320i	−0.0963814	−	0.459006i
$786$	25.1045	−	11.4719i	0.0319396	−	0.0145953i
$787$		−	200.234i		−	0.254427i	−0.991875	−	0.127214i	$-0.959397\pi$
$787$		−	200.234i		−	0.254427i	0.991875	−	0.127214i	$-0.0406034\pi$
$788$	−46.1796	+	53.3443i	−0.0586036	+	0.0676959i
$789$			288.431i			0.365566i
$790$	669.761	+	907.864i	0.847799	+	1.14920i
$791$			230.515i			0.291422i
$792$	−256.555	−	75.1366i	−0.323933	−	0.0948695i
$793$		−	511.153i		−	0.644581i
$794$	440.381	+	963.705i	0.554636	+	1.21373i
$795$	710.322	−	149.152i	0.893487	−	0.187613i
$796$	166.906	+	144.488i	0.209680	+	0.181518i
$797$	−841.219			−1.05548			−0.527741	−	0.849406i	$-0.676961\pi$
$797$	−841.219			−1.05548			−0.527741	+	0.849406i	$0.676961\pi$
$798$	481.190	−	219.888i	0.602996	−	0.275549i
$799$			1448.67i			1.81310i
$800$	−441.419	+	667.195i	−0.551773	+	0.833994i
$801$	−227.009			−0.283407
$802$	−233.302	−	510.545i	−0.290900	−	0.636590i
$803$			179.378i			0.223385i
$804$	500.758	−	578.450i	0.622833	−	0.719465i
$805$	15.1260	+	72.0359i	0.0187901	+	0.0894855i
$806$	1386.10	−	633.401i	1.71973	−	0.785857i
$807$	1161.36			1.43911
$808$	−119.188	+	406.971i	−0.147510	+	0.503676i
$809$	6.22291			0.00769210			0.00384605	−	0.999993i	$-0.498776\pi$
$809$	6.22291			0.00769210			0.00384605	+	0.999993i	$0.498776\pi$
$810$	−240.966	+	177.768i	−0.297488	+	0.219467i
$811$	711.896			0.877801			0.438900	−	0.898536i	$-0.355368\pi$
$811$	711.896			0.877801			0.438900	+	0.898536i	$0.355368\pi$
$812$	89.5361	+	77.5104i	0.110266	+	0.0954562i
$813$	−139.967			−0.172161
$814$	172.859	+	378.275i	0.212358	+	0.464712i
$815$	−185.817	+	39.0176i	−0.227996	+	0.0478743i
$816$	−98.1641	−	678.258i	−0.120299	−	0.831199i
$817$			658.242i			0.805681i
$818$	204.167	+	446.787i	0.249593	+	0.546195i
$819$	−440.000			−0.537241
$820$	576.142	+	319.673i	0.702612	+	0.389845i
$821$		−	580.680i		−	0.707284i	−0.935381	−	0.353642i	$-0.884943\pi$
$821$		−	580.680i		−	0.707284i	0.935381	−	0.353642i	$-0.115057\pi$
$822$	−272.934	−	597.275i	−0.332037	−	0.726611i
$823$	1333.37			1.62013			0.810066	−	0.586339i	$-0.199431\pi$
$823$	1333.37			1.62013			0.810066	+	0.586339i	$0.199431\pi$
$824$	−572.683	−	167.720i	−0.695003	−	0.203544i
$825$	−191.554	−	436.017i	−0.232187	−	0.528505i
$826$	112.882	+	247.024i	0.136661	+	0.299060i
$827$		−	1286.25i		−	1.55532i	−0.628685	−	0.777660i	$-0.716406\pi$
$827$		−	1286.25i		−	1.55532i	0.628685	−	0.777660i	$-0.283594\pi$
$828$	23.7248	−	27.4057i	0.0286532	−	0.0330987i
$829$		−	567.591i		−	0.684670i	−0.939578	−	0.342335i	$-0.888782\pi$
$829$		−	567.591i		−	0.684670i	0.939578	−	0.342335i	$-0.111218\pi$
$830$	−239.529	−	324.683i	−0.288589	−	0.391184i
$831$		−	119.878i		−	0.144257i
$832$	−938.200	−	601.093i	−1.12764	−	0.722467i
$833$			151.335i			0.181674i
$834$	−288.699	+	131.926i	−0.346162	+	0.158184i
$835$	161.364	+	768.477i	0.193250	+	0.920332i
$836$	407.246	−	470.430i	0.487137	−	0.562715i
$837$	−1273.84			−1.52191
$838$	−439.055	−	960.804i	−0.523932	−	1.14654i
$839$		−	200.095i		−	0.238492i	−0.992865	−	0.119246i	$-0.961952\pi$
$839$		−	200.095i		−	0.238492i	0.992865	−	0.119246i	$-0.0380477\pi$
$840$	−574.538	−	44.8638i	−0.683974	−	0.0534093i
$841$	819.650			0.974614
$842$	686.360	−	313.643i	0.815154	−	0.372498i
$843$			832.549i			0.987602i
$844$	−673.925	+	778.483i	−0.798489	+	0.922374i
$845$	−137.794	−	656.231i	−0.163070	−	0.776605i
$846$	−249.336	−	545.634i	−0.294724	−	0.644957i
$847$	−315.395			−0.372367
$848$	−147.958	−	1022.31i	−0.174479	−	1.20555i
$849$	13.4767			0.0158736
$850$	−633.915	+	710.891i	−0.745782	+	0.836342i
$851$	−56.3932			−0.0662670
$852$	−433.680	+	500.965i	−0.509014	+	0.587987i
$853$	−497.128			−0.582800			−0.291400	−	0.956601i	$-0.594121\pi$
$853$	−497.128			−0.582800			−0.291400	+	0.956601i	$0.594121\pi$
$854$	−342.207	+	156.377i	−0.400710	+	0.183111i
$855$	74.4101	+	354.370i	0.0870293	+	0.414467i
$856$	146.053	−	498.699i	0.170622	−	0.582592i
$857$			196.865i			0.229714i	0.993382	+	0.114857i	$0.0366410\pi$
$857$			196.865i			0.229714i	−0.993382	+	0.114857i	$0.963359\pi$
$858$	603.300	−	275.688i	0.703147	−	0.321314i
$859$	645.980			0.752014			0.376007	−	0.926617i	$-0.377297\pi$
$859$	645.980			0.752014			0.376007	+	0.926617i	$0.377297\pi$
$860$	347.875	−	626.969i	0.404505	−	0.729033i
$861$			474.634i			0.551259i
$862$	1110.17	−	507.312i	1.28791	−	0.588529i
$863$	908.561			1.05279			0.526397	−	0.850239i	$-0.323543\pi$
$863$	908.561			1.05279			0.526397	+	0.850239i	$0.323543\pi$
$864$	504.446	+	782.926i	0.583849	+	0.906165i
$865$	−202.111	−	962.533i	−0.233655	−	1.11276i
$866$	−1370.76	+	626.390i	−1.58286	+	0.723314i
$867$		−	166.131i		−	0.191616i
$868$	−848.098	−	734.189i	−0.977071	−	0.845840i
$869$			955.812i			1.09990i
$870$	83.6048	−	61.6780i	0.0960974	−	0.0708942i
$871$		−	1481.02i		−	1.70036i
$872$	−24.4577	+	83.5111i	−0.0280478	+	0.0957696i
$873$		−	738.804i		−	0.846282i
$874$	35.0658	+	76.7360i	0.0401210	+	0.0877987i
$875$	465.967	+	651.437i	0.532534	+	0.744499i
$876$	124.636	−	143.973i	0.142279	−	0.164353i
$877$	−1268.13			−1.44599			−0.722996	−	0.690853i	$-0.757235\pi$
$877$	−1268.13			−1.44599			−0.722996	+	0.690853i	$0.757235\pi$
$878$	−331.302	+	151.394i	−0.377337	+	0.172431i
$879$		−	502.615i		−	0.571803i
$880$	−636.516	+	232.854i	−0.723313	+	0.264607i
$881$	−580.932			−0.659401			−0.329700	−	0.944086i	$-0.606948\pi$
$881$	−580.932			−0.659401			−0.329700	+	0.944086i	$0.606948\pi$
$882$	−26.0468	−	56.9994i	−0.0295315	−	0.0646252i
$883$		−	1216.42i		−	1.37760i	−0.724951	−	0.688800i	$-0.758138\pi$
$883$		−	1216.42i		−	1.37760i	0.724951	−	0.688800i	$-0.241862\pi$
$884$	−1002.99	−	868.278i	−1.13460	−	0.982215i
$885$	233.182	−	48.9633i	0.263483	−	0.0553257i
$886$	−1302.03	+	594.983i	−1.46956	+	0.671539i
$887$	69.8221			0.0787172			0.0393586	−	0.999225i	$-0.487469\pi$
$887$	69.8221			0.0787172			0.0393586	+	0.999225i	$0.487469\pi$
$888$	124.094	−	423.719i	0.139745	−	0.477162i
$889$	637.594			0.717204
$890$	−463.146	+	341.678i	−0.520389	+	0.383908i
$891$	−253.692			−0.284727
$892$	−238.995	+	276.075i	−0.267932	+	0.309501i
$893$	1396.28			1.56359
$894$	−56.9141	−	124.548i	−0.0636623	−	0.139315i
$895$	210.834	+	1004.07i	0.235568	+	1.12187i
$896$	−115.396	+	811.998i	−0.128791	+	0.906248i
$897$			89.9398i			0.100267i
$898$	482.258	+	1055.35i	0.537036	+	1.17522i
$899$	202.229			0.224949
$900$	116.406	−	376.859i	0.129340	−	0.418732i
$901$		−	1229.84i		−	1.36497i
$902$	232.010	+	507.718i	0.257217	+	0.562880i
$903$	516.506			0.571989
$904$	80.8916	−	276.206i	0.0894819	−	0.305537i
$905$	123.724	−	25.9795i	0.136712	−	0.0287066i
$906$	400.381	+	876.171i	0.441921	+	0.967077i
$907$			962.850i			1.06158i	0.847504	+	0.530788i	$0.178104\pi$
$907$			962.850i			1.06158i	−0.847504	+	0.530788i	$0.821896\pi$
$908$	927.802	+	803.189i	1.02181	+	0.884569i
$909$		−	209.078i		−	0.230009i
$910$	−897.691	+	662.256i	−0.986474	+	0.727754i
$911$			66.6124i			0.0731201i	0.999331	+	0.0365600i	$0.0116400\pi$
$911$			66.6124i			0.0731201i	−0.999331	+	0.0365600i	$0.988360\pi$
$912$	−653.731	+	94.6143i	−0.716810	+	0.103744i
$913$		−	341.830i		−	0.374403i
$914$	1393.82	−	636.930i	1.52497	−	0.696860i
$915$	67.8297	+	323.031i	0.0741308	+	0.353040i
$916$	222.800	+	192.876i	0.243232	+	0.210563i
$917$	−39.3276			−0.0428872
$918$	460.880	+	1008.56i	0.502048	+	1.09865i
$919$		−	1745.54i		−	1.89939i	−0.313175	−	0.949696i	$-0.601392\pi$
$919$		−	1745.54i		−	1.89939i	0.313175	−	0.949696i	$-0.398608\pi$
$920$	7.15448	−	91.6223i	0.00777661	−	0.0995894i
$921$	−100.833			−0.109482
$922$	1260.53	−	576.020i	1.36717	−	0.624751i
$923$			1282.63i			1.38963i
$924$	−369.135	−	319.556i	−0.399496	−	0.345840i
$925$	−561.803	+	246.816i	−0.607354	+	0.266828i
$926$	516.096	+	1129.40i	0.557340	+	1.21965i
$927$	294.212			0.317381
$928$	−80.0835	−	124.294i	−0.0862969	−	0.133937i
$929$	1617.72			1.74135			0.870677	−	0.491855i	$-0.163681\pi$
$929$	1617.72			1.74135			0.870677	+	0.491855i	$0.163681\pi$
$930$	−791.916	+	584.222i	−0.851522	+	0.628196i
$931$	145.862			0.156673
$932$	627.289	+	543.038i	0.673057	+	0.582658i
$933$	−1072.12			−1.14911
$934$	−673.055	+	307.563i	−0.720615	+	0.329297i
$935$	−789.730	+	165.826i	−0.844631	+	0.177354i
$936$	527.214	+	154.404i	0.563262	+	0.164961i
$937$			803.266i			0.857274i	0.903477	+	0.428637i	$0.141006\pi$
$937$			803.266i			0.857274i	−0.903477	+	0.428637i	$0.858994\pi$
$938$	−991.510	+	453.086i	−1.05705	+	0.483035i
$939$	−356.984			−0.380175
$940$	−1329.95	−	737.923i	−1.41484	−	0.785025i
$941$			702.194i			0.746222i	0.927787	+	0.373111i	$0.121709\pi$
$941$			702.194i			0.746222i	−0.927787	+	0.373111i	$0.878291\pi$
$942$	−301.182	+	137.630i	−0.319726	+	0.146104i
$943$	−75.6904			−0.0802656
$944$	−48.5712	−	335.599i	−0.0514525	−	0.355508i
$945$	912.551	−	191.616i	0.965663	−	0.202769i
$946$	552.508	−	252.478i	0.584047	−	0.266890i
$947$			67.0789i			0.0708331i	0.999373	+	0.0354165i	$0.0112758\pi$
$947$			67.0789i			0.0708331i	−0.999373	+	0.0354165i	$0.988724\pi$
$948$	664.120	−	767.158i	0.700549	−	0.809238i
$949$		−	368.618i		−	0.388427i
$950$	685.184	+	610.991i	0.721246	+	0.643148i
$951$		−	956.327i		−	1.00560i
$952$	−274.450	+	937.114i	−0.288288	+	0.984364i
$953$			97.4301i			0.102235i	0.998693	+	0.0511176i	$0.0162783\pi$
$953$			97.4301i			0.102235i	−0.998693	+	0.0511176i	$0.983722\pi$
$954$	211.672	+	463.211i	0.221878	+	0.485546i
$955$	518.768	−	108.930i	0.543212	−	0.114063i
$956$	745.646	+	645.497i	0.779964	+	0.675207i
$957$	88.0203			0.0919752
$958$	1257.03	−	574.421i	1.31214	−	0.599604i
$959$			935.663i			0.975666i
$960$	672.675	+	255.372i	0.700703	+	0.266012i
$961$	−954.542			−0.993280
$962$	−355.221	−	777.346i	−0.369252	−	0.808052i
$963$			256.203i			0.266047i
$964$	−747.437	+	863.400i	−0.775349	+	0.895643i
$965$	543.706	−	114.167i	0.563426	−	0.118307i
$966$	60.2129	−	27.5152i	0.0623322	−	0.0284837i
$967$	1727.52			1.78647			0.893236	−	0.449588i	$-0.148429\pi$
$967$	1727.52			1.78647			0.893236	+	0.449588i	$0.148429\pi$
$968$	377.910	+	110.677i	0.390403	+	0.114336i
$969$	−786.440			−0.811599
$970$	−1112.00	−	1507.31i	−1.14639	−	1.55393i
$971$	−379.593			−0.390930			−0.195465	−	0.980711i	$-0.562622\pi$
$971$	−379.593			−0.390930			−0.195465	+	0.980711i	$0.562622\pi$
$972$	−588.563	−	509.513i	−0.605518	−	0.524190i
$973$	452.263			0.464812
$974$	−707.034	−	1547.24i	−0.725908	−	1.58854i
$975$	393.639	+	896.002i	0.403732	+	0.918976i
$976$	464.912	−	67.2865i	0.476344	−	0.0689411i
$977$			1676.42i			1.71589i	0.513746	+	0.857943i	$0.328258\pi$
$977$			1676.42i			1.71589i	−0.513746	+	0.857943i	$0.671742\pi$
$978$	70.9757	+	155.319i	0.0725723	+	0.158813i
$979$	−487.607			−0.498066
$980$	−138.932	−	77.0869i	−0.141768	−	0.0786601i
$981$		−	42.9032i		−	0.0437342i
$982$	−553.632	−	1211.54i	−0.563780	−	1.23374i
$983$	−1108.29			−1.12746			−0.563729	−	0.825960i	$-0.690634\pi$
$983$	−1108.29			−1.12746			−0.563729	+	0.825960i	$0.690634\pi$
$984$	166.557	−	568.712i	0.169266	−	0.577960i
$985$	−18.1239	−	86.3129i	−0.0183999	−	0.0876274i
$986$	−73.1672	−	160.115i	−0.0742061	−	0.162388i
$987$		−	1095.63i		−	1.11006i
$988$	−836.880	+	966.720i	−0.847044	+	0.978462i
$989$			82.3678i			0.0832839i
$990$	268.906	−	198.381i	0.271623	−	0.200385i
$991$			1382.06i			1.39461i	0.716775	+	0.697305i	$0.245618\pi$
$991$			1382.06i			1.39461i	−0.716775	+	0.697305i	$0.754382\pi$
$992$	758.562	+	1177.33i	0.764679	+	1.18682i
$993$		−	1283.69i		−	1.29274i
$994$	858.695	−	392.395i	0.863878	−	0.394763i
$995$	−270.059	+	56.7066i	−0.271416	+	0.0569916i
$996$	−237.512	+	274.361i	−0.238465	+	0.275463i
$997$	391.981			0.393161			0.196580	−	0.980488i	$-0.437016\pi$
$997$	391.981			0.393161			0.196580	+	0.980488i	$0.437016\pi$
$998$	−332.655	−	727.963i	−0.333321	−	0.729422i
$999$			714.390i			0.715105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.e.c.19.6	yes	8
3.2	odd	2		360.3.p.g.19.3		8
4.3	odd	2		160.3.e.c.79.3		8
5.2	odd	4		200.3.g.h.51.2		8
5.3	odd	4		200.3.g.h.51.7		8
5.4	even	2	inner	40.3.e.c.19.3	✓	8
8.3	odd	2	inner	40.3.e.c.19.4	yes	8
8.5	even	2		160.3.e.c.79.4		8
12.11	even	2		1440.3.p.g.559.6		8
15.14	odd	2		360.3.p.g.19.6		8
16.3	odd	4		1280.3.h.m.1279.10		16
16.5	even	4		1280.3.h.m.1279.11		16
16.11	odd	4		1280.3.h.m.1279.7		16
16.13	even	4		1280.3.h.m.1279.6		16
20.3	even	4		800.3.g.h.751.6		8
20.7	even	4		800.3.g.h.751.3		8
20.19	odd	2		160.3.e.c.79.6		8
24.5	odd	2		1440.3.p.g.559.3		8
24.11	even	2		360.3.p.g.19.5		8
40.3	even	4		200.3.g.h.51.8		8
40.13	odd	4		800.3.g.h.751.5		8
40.19	odd	2	inner	40.3.e.c.19.5	yes	8
40.27	even	4		200.3.g.h.51.1		8
40.29	even	2		160.3.e.c.79.5		8
40.37	odd	4		800.3.g.h.751.4		8
60.59	even	2		1440.3.p.g.559.4		8
80.19	odd	4		1280.3.h.m.1279.5		16
80.29	even	4		1280.3.h.m.1279.9		16
80.59	odd	4		1280.3.h.m.1279.12		16
80.69	even	4		1280.3.h.m.1279.8		16
120.29	odd	2		1440.3.p.g.559.5		8
120.59	even	2		360.3.p.g.19.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.e.c.19.3	✓	8	5.4	even	2	inner
40.3.e.c.19.4	yes	8	8.3	odd	2	inner
40.3.e.c.19.5	yes	8	40.19	odd	2	inner
40.3.e.c.19.6	yes	8	1.1	even	1	trivial
160.3.e.c.79.3		8	4.3	odd	2
160.3.e.c.79.4		8	8.5	even	2
160.3.e.c.79.5		8	40.29	even	2
160.3.e.c.79.6		8	20.19	odd	2
200.3.g.h.51.1		8	40.27	even	4
200.3.g.h.51.2		8	5.2	odd	4
200.3.g.h.51.7		8	5.3	odd	4
200.3.g.h.51.8		8	40.3	even	4
360.3.p.g.19.3		8	3.2	odd	2
360.3.p.g.19.4		8	120.59	even	2
360.3.p.g.19.5		8	24.11	even	2
360.3.p.g.19.6		8	15.14	odd	2
800.3.g.h.751.3		8	20.7	even	4
800.3.g.h.751.4		8	40.37	odd	4
800.3.g.h.751.5		8	40.13	odd	4
800.3.g.h.751.6		8	20.3	even	4
1280.3.h.m.1279.5		16	80.19	odd	4
1280.3.h.m.1279.6		16	16.13	even	4
1280.3.h.m.1279.7		16	16.11	odd	4
1280.3.h.m.1279.8		16	80.69	even	4
1280.3.h.m.1279.9		16	80.29	even	4
1280.3.h.m.1279.10		16	16.3	odd	4
1280.3.h.m.1279.11		16	16.5	even	4
1280.3.h.m.1279.12		16	80.59	odd	4
1440.3.p.g.559.3		8	24.5	odd	2
1440.3.p.g.559.4		8	60.59	even	2
1440.3.p.g.559.5		8	120.29	odd	2
1440.3.p.g.559.6		8	12.11	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831254 + 1.81907i) q^{2} +2.24849i q^{3} +(-2.61803 + 3.02422i) q^{4} +(-1.02749 - 4.89329i) q^{5} +(-4.09017 + 1.86907i) q^{6} +6.40747 q^{7} +(-7.67752 - 2.24849i) q^{8} +3.94427 q^{9} +O(q^{10})\)	\(q+(0.831254 + 1.81907i) q^{2} +2.24849i q^{3} +(-2.61803 + 3.02422i) q^{4} +(-1.02749 - 4.89329i) q^{5} +(-4.09017 + 1.86907i) q^{6} +6.40747 q^{7} +(-7.67752 - 2.24849i) q^{8} +3.94427 q^{9} +(8.04713 - 5.93663i) q^{10} +8.47214 q^{11} +(-6.79994 - 5.88664i) q^{12} -17.4100 q^{13} +(5.32624 + 11.6556i) q^{14} +(11.0025 - 2.31030i) q^{15} +(-2.29180 - 15.8350i) q^{16} -19.0496i q^{17} +(3.27869 + 7.17491i) q^{18} -18.3607 q^{19} +(17.4884 + 9.70345i) q^{20} +14.4072i q^{21} +(7.04250 + 15.4114i) q^{22} -2.29753 q^{23} +(5.05573 - 17.2629i) q^{24} +(-22.8885 + 10.0556i) q^{25} +(-14.4721 - 31.6700i) q^{26} +29.1051i q^{27} +(-16.7750 + 19.3776i) q^{28} -4.62059i q^{29} +(13.3485 + 18.0939i) q^{30} +43.7669i q^{31} +(26.8999 - 17.3319i) q^{32} +19.0496i q^{33} +(34.6525 - 15.8350i) q^{34} +(-6.58359 - 31.3536i) q^{35} +(-10.3262 + 11.9283i) q^{36} +24.5452 q^{37} +(-15.2624 - 33.3994i) q^{38} -39.1463i q^{39} +(-3.11399 + 39.8786i) q^{40} +32.9443 q^{41} +(-26.2077 + 11.9760i) q^{42} -35.8506i q^{43} +(-22.1803 + 25.6216i) q^{44} +(-4.05269 - 19.3005i) q^{45} +(-1.90983 - 4.17937i) q^{46} -76.0475 q^{47} +(35.6049 - 5.15309i) q^{48} -7.94427 q^{49} +(-37.3180 - 33.2771i) q^{50} +42.8328 q^{51} +(45.5800 - 52.6517i) q^{52} +64.5599 q^{53} +(-52.9443 + 24.1937i) q^{54} +(-8.70500 - 41.4566i) q^{55} +(-49.1935 - 14.4072i) q^{56} -41.2839i q^{57} +(8.40519 - 3.84089i) q^{58} +21.1935 q^{59} +(-21.8182 + 39.3225i) q^{60} +29.3597i q^{61} +(-79.6151 + 36.3814i) q^{62} +25.2728 q^{63} +(53.8885 + 34.5257i) q^{64} +(17.8885 + 85.1922i) q^{65} +(-34.6525 + 15.8350i) q^{66} +85.0669i q^{67} +(57.6100 + 49.8724i) q^{68} -5.16598i q^{69} +(51.5618 - 38.0388i) q^{70} -73.6720i q^{71} +(-30.2822 - 8.86867i) q^{72} +21.1727i q^{73} +(20.4033 + 44.6494i) q^{74} +(-22.6099 - 51.4648i) q^{75} +(48.0689 - 55.5267i) q^{76} +54.2850 q^{77} +(71.2099 - 32.5405i) q^{78} +112.818i q^{79} +(-75.1305 + 27.4847i) q^{80} -29.9443 q^{81} +(27.3851 + 59.9279i) q^{82} -40.3476i q^{83} +(-43.5704 - 37.7185i) q^{84} +(-93.2150 + 19.5732i) q^{85} +(65.2148 - 29.8010i) q^{86} +10.3894 q^{87} +(-65.0450 - 19.0496i) q^{88} -57.5542 q^{89} +(31.7401 - 23.4157i) q^{90} -111.554 q^{91} +(6.01501 - 6.94823i) q^{92} -98.4096 q^{93} +(-63.2148 - 138.336i) q^{94} +(18.8653 + 89.8441i) q^{95} +(38.9706 + 60.4844i) q^{96} -187.311i q^{97} +(-6.60371 - 14.4512i) q^{98} +33.4164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9	\( 8 q - 12 q^{4} + 12 q^{6} - 40 q^{9} + 20 q^{10} + 32 q^{11} - 20 q^{14} - 72 q^{16} + 32 q^{19} + 20 q^{20} + 112 q^{24} - 40 q^{25} - 80 q^{26} + 100 q^{30} + 152 q^{34} - 160 q^{35} - 20 q^{36} - 80 q^{40} + 192 q^{41} - 88 q^{44} - 60 q^{46} + 8 q^{49} - 200 q^{50} + 128 q^{51} - 352 q^{54} - 224 q^{59} + 360 q^{60} + 288 q^{64} - 152 q^{66} + 340 q^{70} + 360 q^{74} + 320 q^{75} + 152 q^{76} - 280 q^{80} - 168 q^{81} - 760 q^{84} + 316 q^{86} + 112 q^{89} - 340 q^{90} - 320 q^{91} - 300 q^{94} - 368 q^{96} + 160 q^{99}+O(q^{100}) \) 8 * q - 12 * q^4 + 12 * q^6 - 40 * q^9 + 20 * q^10 + 32 * q^11 - 20 * q^14 - 72 * q^16 + 32 * q^19 + 20 * q^20 + 112 * q^24 - 40 * q^25 - 80 * q^26 + 100 * q^30 + 152 * q^34 - 160 * q^35 - 20 * q^36 - 80 * q^40 + 192 * q^41 - 88 * q^44 - 60 * q^46 + 8 * q^49 - 200 * q^50 + 128 * q^51 - 352 * q^54 - 224 * q^59 + 360 * q^60 + 288 * q^64 - 152 * q^66 + 340 * q^70 + 360 * q^74 + 320 * q^75 + 152 * q^76 - 280 * q^80 - 168 * q^81 - 760 * q^84 + 316 * q^86 + 112 * q^89 - 340 * q^90 - 320 * q^91 - 300 * q^94 - 368 * q^96 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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