LMFDB - Embedded newform 40.3.e.c.19.4

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			19.4
Root			$0.831254 + 1.81907i$ of defining polynomial
Character	$\chi$	$=$	40.19
Dual form			40.3.e.c.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831254 + 1.81907i) q^{2} +2.24849i q^{3} +(-2.61803 - 3.02422i) q^{4} +(1.02749 + 4.89329i) q^{5} +(-4.09017 - 1.86907i) q^{6} -6.40747 q^{7} +(7.67752 - 2.24849i) q^{8} +3.94427 q^{9} +O(q^{10})$	\(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} +(-9.75534 - 2.19850i) 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} +(12.1084 - 15.9181i) 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} +(4.94330 - 21.9348i) 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} +(18.8911 + 35.2580i) 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} +(0.734395 - 49.9946i) 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} +(35.7918 + 27.2256i) 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} +(62.5071 + 14.0868i) 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} +(-79.8401 + 5.05584i) 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} +(-38.4777 - 8.67146i) 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	$-0.651318\pi$
$7$	−6.40747			−0.915353			−0.457677	+	0.889119i	$0.651318\pi$
$8$	7.67752	−	2.24849i	0.959690	−	0.281062i
$9$	3.94427			0.438252
$10$	−9.75534	−	2.19850i	−0.975534	−	0.219850i
$11$	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	$-0.266459\pi$
$13$	17.4100			1.33923			0.669616	+	0.742708i	$0.266459\pi$
$14$	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	$0.660517\pi$
$20$	12.1084	−	15.9181i	0.605419	−	0.795907i
$21$		−	14.4072i		−	0.686056i
$22$	−7.04250	+	15.4114i	−0.320113	+	0.700519i
$23$	2.29753			0.0998926			0.0499463	−	0.998752i	$-0.484095\pi$
$23$	2.29753			0.0998926			0.0499463	+	0.998752i	$0.484095\pi$
$24$	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	$0.0253852\pi$
$29$			4.62059i			0.159331i	−0.996822	+	0.0796654i	$0.974615\pi$
$30$	4.94330	−	21.9348i	0.164777	−	0.731161i
$31$		−	43.7669i		−	1.41184i	−0.708294	−	0.705918i	$-0.750535\pi$
$31$		−	43.7669i		−	1.41184i	0.708294	−	0.705918i	$-0.249465\pi$
$32$	−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	$-0.607619\pi$
$37$	−24.5452			−0.663382			−0.331691	+	0.943388i	$0.607619\pi$
$38$	15.2624	−	33.3994i	0.401642	−	0.878931i
$39$			39.1463i			1.00375i
$40$	18.8911	+	35.2580i	0.472277	+	0.881450i
$41$	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	$-0.200001\pi$
$47$	76.0475			1.61803			0.809016	+	0.587787i	$0.200001\pi$
$48$	−35.6049	−	5.15309i	−0.741770	−	0.107356i
$49$	−7.94427			−0.162128
$50$	0.734395	−	49.9946i	0.0146879	−	0.999892i
$51$	42.8328			0.839859
$52$	−45.5800	−	52.6517i	−0.876538	−	1.01253i
$53$	−64.5599			−1.21811			−0.609055	−	0.793128i	$-0.708451\pi$
$53$	−64.5599			−1.21811			−0.609055	+	0.793128i	$0.708451\pi$
$54$	−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	$0.442518\pi$
$60$	35.7918	+	27.2256i	0.596531	+	0.453760i
$61$		−	29.3597i		−	0.481307i	−0.970611	−	0.240654i	$-0.922638\pi$
$61$		−	29.3597i		−	0.481307i	0.970611	−	0.240654i	$-0.0773618\pi$
$62$	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
$70$	62.5071	+	14.0868i	0.892958	+	0.201240i
$71$			73.6720i			1.03763i	0.854885	+	0.518817i	$0.173627\pi$
$71$			73.6720i			1.03763i	−0.854885	+	0.518817i	$0.826373\pi$
$72$	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	$-0.746863\pi$
$79$		−	112.818i		−	1.42808i	0.700105	−	0.714040i	$-0.253137\pi$
$80$	−79.8401	+	5.05584i	−0.998001	+	0.0631980i
$81$	−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	$0.604805\pi$
$90$	−38.4777	−	8.67146i	−0.427530	−	0.0963496i
$91$	−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
$100$	90.3332	+	42.8941i	0.903332	+	0.428941i
$101$			53.0081i			0.524833i	0.964955	+	0.262416i	$0.0845194\pi$
$101$			53.0081i			0.524833i	−0.964955	+	0.262416i	$0.915481\pi$
$102$	−35.6049	+	77.9159i	−0.349068	+	0.763881i
$103$	−74.5922			−0.724196			−0.362098	−	0.932140i	$-0.617939\pi$
$103$	−74.5922			−0.724196			−0.362098	+	0.932140i	$0.617939\pi$
$104$	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	$0.0158890\pi$
$109$			10.8774i			0.0997922i	−0.998754	+	0.0498961i	$0.984111\pi$
$110$	−82.6485	−	18.6259i	−0.751350	−	0.169327i
$111$		−	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
$120$	−79.2774	+	42.4765i	−0.660645	+	0.353971i
$121$	−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	$-0.628135\pi$
$127$	−99.5079			−0.783527			−0.391763	+	0.920066i	$0.628135\pi$
$128$	18.0096	+	126.727i	0.140700	+	0.990052i
$129$	80.6099			0.624883
$130$	−169.841	−	38.2758i	−1.30647	−	0.294429i
$131$	−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	$0.418287\pi$
$140$	−77.5841	+	101.995i	−0.554172	+	0.728536i
$141$			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	$-0.967417\pi$
$149$		−	30.4505i		−	0.204366i	0.994766	−	0.102183i	$-0.0325827\pi$
$150$	112.413	+	1.65128i	0.749417	+	0.0110086i
$151$			214.214i			1.41864i	0.704889	+	0.709318i	$0.250997\pi$
$151$			214.214i			1.41864i	−0.704889	+	0.709318i	$0.749003\pi$
$152$	−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	$-0.575348\pi$
$157$	−73.6355			−0.469016			−0.234508	+	0.972114i	$0.575348\pi$
$158$	205.224	+	93.7807i	1.29889	+	0.593549i
$159$		−	145.162i		−	0.912972i
$160$	57.1704	−	149.437i	0.357315	−	0.933984i
$161$	−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	$-0.344181\pi$
$167$	157.047			0.940402			0.470201	+	0.882559i	$0.344181\pi$
$168$	−32.3944	−	110.611i	−0.192824	−	0.658401i
$169$	134.108			0.793541
$170$	−41.8803	+	185.835i	−0.246355	+	1.09315i
$171$	−72.4195			−0.423506
$172$	−108.420	+	93.8581i	−0.630349	+	0.545687i
$173$	−196.705			−1.13702			−0.568511	−	0.822676i	$-0.692480\pi$
$173$	−196.705			−1.13702			−0.568511	+	0.822676i	$0.692480\pi$
$174$	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	$0.694285\pi$
$180$	47.7587	−	62.7855i	0.265326	−	0.348808i
$181$		−	25.2845i		−	0.139693i	−0.997558	−	0.0698467i	$-0.977749\pi$
$181$		−	25.2845i		−	0.139693i	0.997558	−	0.0698467i	$-0.0222510\pi$
$182$	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
$190$	179.115	+	40.3659i	0.942709	+	0.212452i
$191$		−	106.016i		−	0.555059i	−0.960717	−	0.277529i	$-0.910484\pi$
$191$		−	106.016i		−	0.555059i	0.960717	−	0.277529i	$-0.0895156\pi$
$192$	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	$-0.514255\pi$
$197$	−17.6390			−0.0895383			−0.0447692	+	0.998997i	$0.514255\pi$
$198$	−27.7775	+	60.7868i	−0.140290	+	0.307004i
$199$			55.1896i			0.277335i	0.990339	+	0.138667i	$0.0442819\pi$
$199$			55.1896i			0.277335i	−0.990339	+	0.138667i	$0.955718\pi$
$200$	−153.117	+	128.667i	−0.765586	+	0.643333i
$201$	−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
$210$	−31.6741	+	140.547i	−0.150829	+	0.669271i
$211$	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
$220$	102.584	−	134.861i	0.466290	−	0.613003i
$221$		−	331.653i		−	1.50069i
$222$	100.394	+	45.8766i	0.452225	+	0.206651i
$223$	−91.2880			−0.409363			−0.204682	−	0.978829i	$-0.565616\pi$
$223$	−91.2880			−0.409363			−0.204682	+	0.978829i	$0.565616\pi$
$224$	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	$0.0514255\pi$
$229$			73.6720i			0.321712i	−0.986978	+	0.160856i	$0.948575\pi$
$230$	−22.4132	−	5.05111i	−0.0974486	−	0.0219613i
$231$		−	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	$0.172510\pi$
$239$			246.558i			1.03162i	−0.856702	+	0.515812i	$0.827490\pi$
$240$	−11.3680	−	179.520i	−0.0473668	−	0.748000i
$241$	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
$250$	245.393	−	47.7752i	0.981570	−	0.191101i
$251$	−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
$260$	210.807	−	277.135i	0.810796	−	1.06590i
$261$			18.2249i			0.0698271i
$262$	5.10204	−	11.1650i	0.0194734	−	0.0426146i
$263$	−128.278			−0.487747			−0.243874	−	0.969807i	$-0.578418\pi$
$263$	−128.278			−0.487747			−0.243874	+	0.969807i	$0.578418\pi$
$264$	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	$0.409723\pi$
$269$			516.507i			1.92010i	−0.279828	+	0.960050i	$0.590277\pi$
$270$	63.9875	−	283.930i	0.236991	−	1.05159i
$271$		−	62.2493i		−	0.229702i	−0.993383	−	0.114851i	$-0.963361\pi$
$271$		−	62.2493i		−	0.229702i	0.993383	−	0.114851i	$-0.0366391\pi$
$272$	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	$-0.469320\pi$
$277$	53.3148			0.192472			0.0962360	+	0.995359i	$0.469320\pi$
$278$	−58.6729	+	128.397i	−0.211054	+	0.461858i
$279$		−	172.629i		−	0.618740i
$280$	−121.044	−	225.915i	−0.432300	−	0.806839i
$281$	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
$290$	10.1584	−	45.0755i	0.0350288	−	0.155433i
$291$	421.167			1.44731
$292$	64.0310	−	55.4310i	0.219284	−	0.189832i
$293$	223.534			0.762914			0.381457	−	0.924386i	$-0.375422\pi$
$293$	223.534			0.762914			0.381457	+	0.924386i	$0.375422\pi$
$294$	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
$300$	−96.4472	+	203.114i	−0.321491	+	0.677046i
$301$			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
$310$	−96.2213	+	426.961i	−0.310391	+	1.37729i
$311$		−	476.815i		−	1.53317i	−0.642144	−	0.766584i	$-0.721955\pi$
$311$		−	476.815i		−	1.53317i	0.642144	−	0.766584i	$-0.278045\pi$
$312$	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	$-0.265929\pi$
$317$	425.319			1.34170			0.670850	+	0.741593i	$0.265929\pi$
$318$	264.061	+	120.667i	0.830380	+	0.379456i
$319$			39.1463i			0.122716i
$320$	224.314	+	228.217i	0.700981	+	0.713180i
$321$	−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
$330$	41.8803	−	185.835i	0.126910	−	0.563136i
$331$	−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
$340$	−303.233	−	230.659i	−0.891863	−	0.678409i
$341$		−	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	$-0.717536\pi$
$349$		−	541.246i		−	1.55085i	0.631441	−	0.775424i	$-0.282464\pi$
$350$	−4.70562	+	320.339i	−0.0134446	+	0.915255i
$351$			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	$-0.859803\pi$
$359$		−	306.111i		−	0.852676i	0.904564	−	0.426338i	$-0.140197\pi$
$360$	74.5115	+	139.067i	0.206977	+	0.386298i
$361$	−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	$-0.308438\pi$
$367$	415.543			1.13227			0.566134	+	0.824313i	$0.308438\pi$
$368$	−5.26547	+	36.3814i	−0.0143083	+	0.0988625i
$369$	129.941			0.352144
$370$	239.446	+	53.9624i	0.647152	+	0.145844i
$371$	413.666			1.11500
$372$	−257.640	−	297.612i	−0.692580	−	0.800033i
$373$	237.575			0.636931			0.318465	−	0.947934i	$-0.396833\pi$
$373$	237.575			0.636931			0.318465	+	0.947934i	$0.396833\pi$
$374$	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	$0.369040\pi$
$380$	−222.318	+	292.268i	−0.585048	+	0.769126i
$381$		−	223.743i		−	0.587252i
$382$	192.851	+	88.1264i	0.504845	+	0.230697i
$383$	282.084			0.736512			0.368256	−	0.929725i	$-0.379955\pi$
$383$	282.084			0.736512			0.368256	+	0.929725i	$0.379955\pi$
$384$	−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	$0.189912\pi$
$389$			437.124i			1.12371i	−0.827235	+	0.561856i	$0.810088\pi$
$390$	86.0630	−	381.885i	0.220674	−	0.979193i
$391$		−	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	$-0.732519\pi$
$397$	−529.779			−1.33446			−0.667228	+	0.744854i	$0.732519\pi$
$398$	−100.394	−	45.8766i	−0.252246	−	0.115268i
$399$			264.525i			0.662971i
$400$	−106.774	−	385.486i	−0.266936	−	0.963714i
$401$	−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	$0.402926\pi$
$410$	−321.383	−	72.4278i	−0.783860	−	0.176653i
$411$	−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	$0.717065\pi$
$420$	−229.335	−	174.448i	−0.546037	−	0.415351i
$421$			377.313i			0.896231i	0.893976	+	0.448116i	$0.147905\pi$
$421$			377.313i			0.896231i	−0.893976	+	0.448116i	$0.852095\pi$
$422$	−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
$430$	−78.8174	+	349.735i	−0.183296	+	0.813337i
$431$			610.298i			1.41600i	0.706211	+	0.708002i	$0.250403\pi$
$431$			610.298i			1.41600i	−0.706211	+	0.708002i	$0.749597\pi$
$432$	−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	$-0.933489\pi$
$439$		−	182.127i		−	0.414868i	0.978249	−	0.207434i	$-0.0665113\pi$
$440$	160.048	+	298.711i	0.363745	+	0.678888i
$441$	−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	$0.276417\pi$
$450$	2.89665	−	197.192i	0.00643701	−	0.438205i
$451$	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
$460$	27.8194	−	36.5724i	0.0604769	−	0.0795052i
$461$			692.953i			1.50315i	0.659646	+	0.751576i	$0.270706\pi$
$461$			692.953i			1.50315i	−0.659646	+	0.751576i	$0.729294\pi$
$462$	222.035	+	101.462i	0.480595	+	0.219616i
$463$	−620.865			−1.34096			−0.670480	−	0.741927i	$-0.733912\pi$
$463$	−620.865			−1.34096			−0.670480	+	0.741927i	$0.733912\pi$
$464$	−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
$470$	−741.869	−	167.190i	−1.57844	−	0.355724i
$471$		−	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	$0.256467\pi$
$479$			691.029i			1.44265i	−0.692597	+	0.721325i	$0.743533\pi$
$480$	336.009	+	128.547i	0.700019	+	0.267807i
$481$	−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	$-0.161996\pi$
$487$	850.564			1.74654			0.873269	+	0.487239i	$0.161996\pi$
$488$	−66.0152	−	225.410i	−0.135277	−	0.461905i
$489$	85.3839			0.174609
$490$	77.4991	+	17.4654i	0.158161	+	0.0356438i
$491$	−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	$0.631332\pi$
$500$	−117.077	+	486.100i	−0.234154	+	0.972199i
$501$			353.120i			0.704830i
$502$	111.088	−	243.099i	0.221291	−	0.484262i
$503$	−655.914			−1.30400			−0.652002	−	0.758217i	$-0.726071\pi$
$503$	−655.914			−1.30400			−0.652002	+	0.758217i	$0.726071\pi$
$504$	−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	$-0.792597\pi$
$509$		−	617.357i		−	1.21288i	0.795128	−	0.606441i	$-0.207403\pi$
$510$	−417.849	−	94.1677i	−0.819311	−	0.184643i
$511$		−	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
$520$	328.894	+	613.842i	0.632488	+	1.18047i
$521$	−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
$530$	629.803	+	141.935i	1.18831	+	0.267801i
$531$	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
$540$	463.299	+	352.416i	0.857962	+	0.652622i
$541$		−	638.021i		−	1.17934i	−0.807645	−	0.589668i	$-0.799258\pi$
$541$		−	638.021i		−	1.17934i	0.807645	−	0.589668i	$-0.200742\pi$
$542$	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
$550$	6.22189	−	423.561i	0.0113125	−	0.770111i
$551$		−	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	$-0.512758\pi$
$557$	−44.6368			−0.0801379			−0.0400689	+	0.999197i	$0.512758\pi$
$558$	314.024	+	143.498i	0.562766	+	0.257165i
$559$		−	624.159i		−	1.11656i
$560$	511.573	−	32.3952i	0.913524	−	0.0578485i
$561$	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	$0.446402\pi$
$570$	−90.7624	+	402.738i	−0.159232	+	0.706558i
$571$	−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
$580$	73.5513	+	55.9479i	0.126813	+	0.0964619i
$581$			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
$590$	−206.750	−	46.5938i	−0.350423	−	0.0789725i
$591$		−	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	$-0.959514\pi$
$599$		−	151.965i		−	0.253697i	0.991922	−	0.126849i	$-0.0404862\pi$
$600$	−289.306	−	344.283i	−0.482177	−	0.573806i
$601$	−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	$-0.356568\pi$
$607$	528.708			0.871018			0.435509	+	0.900184i	$0.356568\pi$
$608$	493.901	+	318.225i	0.812337	+	0.523396i
$609$	66.5697			0.109310
$610$	−64.5472	+	286.414i	−0.105815	+	0.469531i
$611$	1323.99			2.16692
$612$	−227.230	+	196.710i	−0.371290	+	0.321422i
$613$	−497.586			−0.811723			−0.405862	−	0.913934i	$-0.633029\pi$
$613$	−497.586			−0.811723			−0.405862	+	0.913934i	$0.633029\pi$
$614$	−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	$0.462525\pi$
$620$	−696.688	−	529.946i	−1.12369	−	0.854752i
$621$			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
$630$	246.545	+	55.5622i	0.391341	+	0.0881939i
$631$			573.075i			0.908202i	0.890950	+	0.454101i	$0.150039\pi$
$631$			573.075i			0.908202i	−0.890950	+	0.454101i	$0.849961\pi$
$632$	−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
$640$	−601.606	+	218.336i	−0.940009	+	0.341150i
$641$	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	$-0.430724\pi$
$647$	279.402			0.431843			0.215921	+	0.976411i	$0.430724\pi$
$648$	−229.898	+	67.3295i	−0.354780	+	0.103904i
$649$	179.554			0.276663
$650$	12.7858	−	870.406i	0.0196705	−	1.33909i
$651$	−630.557			−0.968598
$652$	−114.841	+	99.4167i	−0.176137	+	0.152480i
$653$	432.852			0.662866			0.331433	−	0.943479i	$-0.392468\pi$
$653$	432.852			0.662866			0.331433	+	0.943479i	$0.392468\pi$
$654$	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	$0.279792\pi$
$660$	303.233	+	230.659i	0.459445	+	0.349484i
$661$		−	1019.96i		−	1.54305i	−0.636200	−	0.771524i	$-0.719495\pi$
$661$		−	1019.96i		−	1.54305i	0.636200	−	0.771524i	$-0.280505\pi$
$662$	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
$670$	187.019	−	829.856i	0.279133	−	1.23859i
$671$		−	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	$-0.699479\pi$
$677$	−794.069			−1.17292			−0.586461	+	0.809977i	$0.699479\pi$
$678$	67.2415	−	147.148i	0.0991762	−	0.217032i
$679$			1200.19i			1.76758i
$680$	671.649	−	359.867i	0.987720	−	0.529216i
$681$	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
$690$	11.3574	−	50.3959i	0.0164600	−	0.0730375i
$691$	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
$700$	−578.808	−	274.843i	−0.826868	−	0.392633i
$701$		−	246.846i		−	0.352134i	−0.984378	−	0.176067i	$-0.943662\pi$
$701$		−	246.846i		−	0.352134i	0.984378	−	0.176067i	$-0.0563375\pi$
$702$	−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	$0.0981526\pi$
$709$			430.352i			0.606984i	−0.952834	+	0.303492i	$0.901847\pi$
$710$	161.968	−	718.695i	0.228123	−	1.01225i
$711$		−	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	$-0.950278\pi$
$719$		−	223.713i		−	0.311144i	0.987825	−	0.155572i	$-0.0497221\pi$
$720$	−314.911	+	19.9416i	−0.437376	+	0.0276967i
$721$	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	$-0.552235\pi$
$727$	−237.535			−0.326733			−0.163366	+	0.986565i	$0.552235\pi$
$728$	−856.459	+	250.829i	−1.17645	+	0.344545i
$729$	−707.093			−0.969949
$730$	46.5482	−	206.547i	0.0637646	−	0.282941i
$731$	−682.938			−0.934252
$732$	−172.830	−	199.644i	−0.236107	−	0.272738i
$733$	706.446			0.963774			0.481887	−	0.876233i	$-0.339952\pi$
$733$	706.446			0.963774			0.481887	+	0.876233i	$0.339952\pi$
$734$	−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	$0.674397\pi$
$740$	−297.202	+	390.713i	−0.401624	+	0.527991i
$741$		−	718.753i		−	0.969977i
$742$	−343.861	+	752.487i	−0.463425	+	1.01413i
$743$	794.965			1.06994			0.534970	−	0.844871i	$-0.320323\pi$
$743$	794.965			1.06994			0.534970	+	0.844871i	$0.320323\pi$
$744$	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
$750$	107.422	+	551.764i	0.143230	+	0.735685i
$751$		−	1178.75i		−	1.56958i	−0.619764	−	0.784789i	$-0.712772\pi$
$751$		−	1178.75i		−	1.56958i	0.619764	−	0.784789i	$-0.287228\pi$
$752$	−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	$-0.556656\pi$
$757$	−268.056			−0.354103			−0.177052	+	0.984202i	$0.556656\pi$
$758$	−251.982	+	551.423i	−0.332430	+	0.727471i
$759$			43.7669i			0.0576639i
$760$	−346.853	−	647.361i	−0.456386	−	0.851791i
$761$	−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	$0.325338\pi$
$770$	529.568	+	119.345i	0.687751	+	0.154994i
$771$	−154.755			−0.200720
$772$	336.029	−	290.896i	0.435270	−	0.376809i
$773$	−1133.36			−1.46619			−0.733093	−	0.680128i	$-0.761924\pi$
$773$	−1133.36			−1.46619			−0.733093	+	0.680128i	$0.761924\pi$
$774$	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
$780$	623.136	+	473.998i	0.798893	+	0.607690i
$781$			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
$790$	−248.031	+	1100.58i	−0.313963	+	1.39314i
$791$		−	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	$-0.323039\pi$
$797$	841.219			1.05548			0.527741	+	0.849406i	$0.323039\pi$
$798$	−481.190	−	219.888i	−0.602996	−	0.275549i
$799$		−	1448.67i		−	1.81310i
$800$	789.982	+	126.207i	0.987478	+	0.157758i
$801$	−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	$0.498776\pi$
$810$	292.116	+	65.8323i	0.360638	+	0.0812745i
$811$	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
$820$	398.902	−	524.411i	0.486466	−	0.639526i
$821$			580.680i			0.707284i	0.935381	+	0.353642i	$0.115057\pi$
$821$			580.680i			0.707284i	−0.935381	+	0.353642i	$0.884943\pi$
$822$	272.934	−	597.275i	0.332037	−	0.726611i
$823$	−1333.37			−1.62013			−0.810066	−	0.586339i	$-0.800569\pi$
$823$	−1333.37			−1.62013			−0.810066	+	0.586339i	$0.800569\pi$
$824$	−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	$0.111218\pi$
$829$			567.591i			0.684670i	−0.939578	+	0.342335i	$0.888782\pi$
$830$	−88.7040	+	393.604i	−0.106872	+	0.474222i
$831$			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	$0.0380477\pi$
$839$			200.095i			0.238492i	−0.992865	+	0.119246i	$0.961952\pi$
$840$	507.968	−	272.167i	0.604724	−	0.324008i
$841$	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
$850$	−952.375	−	13.9899i	−1.12044	−	0.0164587i
$851$	−56.3932			−0.0662670
$852$	433.680	+	500.965i	0.509014	+	0.587987i
$853$	497.128			0.582800			0.291400	−	0.956601i	$-0.405879\pi$
$853$	497.128			0.582800			0.291400	+	0.956601i	$0.405879\pi$
$854$	−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	$0.377297\pi$
$860$	−570.675	−	434.093i	−0.663576	−	0.504759i
$861$		−	474.634i		−	0.551259i
$862$	−1110.17	−	507.312i	−1.28791	−	0.588529i
$863$	−908.561			−1.05279			−0.526397	−	0.850239i	$-0.676457\pi$
$863$	−908.561			−1.05279			−0.526397	+	0.850239i	$0.676457\pi$
$864$	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
$870$	101.352	+	22.8410i	0.116496	+	0.0262540i
$871$			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	$-0.242765\pi$
$877$	1268.13			1.44599			0.722996	+	0.690853i	$0.242765\pi$
$878$	331.302	+	151.394i	0.377337	+	0.172431i
$879$			502.615i			0.571803i
$880$	−676.416	+	42.8338i	−0.768655	+	0.0486747i
$881$	−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	$-0.512531\pi$
$887$	−69.8221			−0.0787172			−0.0393586	+	0.999225i	$0.512531\pi$
$888$	−124.094	−	423.719i	−0.139745	−	0.477162i
$889$	637.594			0.717204
$890$	561.460	+	126.533i	0.630854	+	0.142171i
$891$	−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
$900$	356.299	+	169.186i	0.395888	+	0.187985i
$901$			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
$910$	1088.25	+	245.251i	1.19588	+	0.269507i
$911$		−	66.6124i		−	0.0731201i	−0.999331	−	0.0365600i	$-0.988360\pi$
$911$		−	66.6124i		−	0.0731201i	0.999331	−	0.0365600i	$-0.0116400\pi$
$912$	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	$0.398608\pi$
$919$			1745.54i			1.89939i	−0.313175	+	0.949696i	$0.601392\pi$
$920$	43.4028	+	81.0063i	0.0471770	+	0.0880503i
$921$	−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	$0.163681\pi$
$930$	−960.019	−	216.353i	−1.03228	−	0.232638i
$931$	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
$940$	920.812	−	1210.53i	0.979587	−	1.28780i
$941$		−	702.194i		−	0.746222i	−0.927787	−	0.373111i	$-0.878291\pi$
$941$		−	702.194i		−	0.746222i	0.927787	−	0.373111i	$-0.121709\pi$
$942$	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
$950$	−13.4840	+	917.935i	−0.0141937	+	0.966247i
$951$			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
$960$	−513.146	+	504.369i	−0.534527	+	0.525384i
$961$	−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	$-0.851571\pi$
$967$	−1727.52			−1.78647			−0.893236	+	0.449588i	$0.851571\pi$
$968$	−377.910	+	110.677i	−0.390403	+	0.114336i
$969$	−786.440			−0.811599
$970$	−411.802	+	1827.28i	−0.424538	+	1.88379i
$971$	−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
$980$	−96.1923	+	126.458i	−0.0981554	+	0.129039i
$981$			42.9032i			0.0437342i
$982$	553.632	−	1211.54i	0.563780	−	1.23374i
$983$	1108.29			1.12746			0.563729	−	0.825960i	$-0.309366\pi$
$983$	1108.29			1.12746			0.563729	+	0.825960i	$0.309366\pi$
$984$	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
$990$	−325.988	−	73.4658i	−0.329281	−	0.0742079i
$991$		−	1382.06i		−	1.39461i	−0.716775	−	0.697305i	$-0.754382\pi$
$991$		−	1382.06i		−	1.39461i	0.716775	−	0.697305i	$-0.245618\pi$
$992$	−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	$-0.562984\pi$
$997$	−391.981			−0.393161			−0.196580	+	0.980488i	$0.562984\pi$
$998$	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.19.4	yes	8
3.2	odd	2		360.3.p.g.19.5		8
4.3	odd	2		160.3.e.c.79.4		8
5.2	odd	4		200.3.g.h.51.1		8
5.3	odd	4		200.3.g.h.51.8		8
5.4	even	2	inner	40.3.e.c.19.5	yes	8
8.3	odd	2	inner	40.3.e.c.19.6	yes	8
8.5	even	2		160.3.e.c.79.3		8
12.11	even	2		1440.3.p.g.559.3		8
15.14	odd	2		360.3.p.g.19.4		8
16.3	odd	4		1280.3.h.m.1279.11		16
16.5	even	4		1280.3.h.m.1279.10		16
16.11	odd	4		1280.3.h.m.1279.6		16
16.13	even	4		1280.3.h.m.1279.7		16
20.3	even	4		800.3.g.h.751.5		8
20.7	even	4		800.3.g.h.751.4		8
20.19	odd	2		160.3.e.c.79.5		8
24.5	odd	2		1440.3.p.g.559.6		8
24.11	even	2		360.3.p.g.19.3		8
40.3	even	4		200.3.g.h.51.7		8
40.13	odd	4		800.3.g.h.751.6		8
40.19	odd	2	inner	40.3.e.c.19.3	✓	8
40.27	even	4		200.3.g.h.51.2		8
40.29	even	2		160.3.e.c.79.6		8
40.37	odd	4		800.3.g.h.751.3		8
60.59	even	2		1440.3.p.g.559.5		8
80.19	odd	4		1280.3.h.m.1279.8		16
80.29	even	4		1280.3.h.m.1279.12		16
80.59	odd	4		1280.3.h.m.1279.9		16
80.69	even	4		1280.3.h.m.1279.5		16
120.29	odd	2		1440.3.p.g.559.4		8
120.59	even	2		360.3.p.g.19.6		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
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} +(-9.75534 - 2.19850i) 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} +(12.1084 - 15.9181i) 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} +(4.94330 - 21.9348i) 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} +(18.8911 + 35.2580i) 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} +(0.734395 - 49.9946i) 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} +(35.7918 + 27.2256i) 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} +(62.5071 + 14.0868i) 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} +(-79.8401 + 5.05584i) 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} +(-38.4777 - 8.67146i) 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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