LMFDB - Embedded newform 950.2.e.h.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.2
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.h.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.780776 - 1.35234i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{6} -4.56155 q^{7} +1.00000 q^{8} +(0.280776 + 0.486319i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.780776 - 1.35234i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{6} -4.56155 q^{7} +1.00000 q^{8} +(0.280776 + 0.486319i) q^{9} +1.00000 q^{11} -1.56155 q^{12} +(-1.00000 - 1.73205i) q^{13} +(2.28078 - 3.95042i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.56155 + 2.70469i) q^{17} -0.561553 q^{18} +(-2.50000 + 3.57071i) q^{19} +(-3.56155 + 6.16879i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(3.84233 + 6.65511i) q^{23} +(0.780776 - 1.35234i) q^{24} +2.00000 q^{26} +5.56155 q^{27} +(2.28078 + 3.95042i) q^{28} +(-1.00000 - 1.73205i) q^{29} -6.24621 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 - 1.35234i) q^{33} +(-1.56155 - 2.70469i) q^{34} +(0.280776 - 0.486319i) q^{36} -7.68466 q^{37} +(-1.84233 - 3.95042i) q^{38} -3.12311 q^{39} +(-1.06155 + 1.83866i) q^{41} +(-3.56155 - 6.16879i) q^{42} +(-2.56155 + 4.43674i) q^{43} +(-0.500000 - 0.866025i) q^{44} -7.68466 q^{46} +(5.56155 + 9.63289i) q^{47} +(0.780776 + 1.35234i) q^{48} +13.8078 q^{49} +(2.43845 + 4.22351i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.71922 - 2.97778i) q^{53} +(-2.78078 + 4.81645i) q^{54} -4.56155 q^{56} +(2.87689 + 6.16879i) q^{57} +2.00000 q^{58} +(-5.21922 + 9.03996i) q^{59} +(1.56155 + 2.70469i) q^{61} +(3.12311 - 5.40938i) q^{62} +(-1.28078 - 2.21837i) q^{63} +1.00000 q^{64} +(0.780776 + 1.35234i) q^{66} +(6.78078 + 11.7446i) q^{67} +3.12311 q^{68} +12.0000 q^{69} +(0.123106 - 0.213225i) q^{71} +(0.280776 + 0.486319i) q^{72} +(5.34233 - 9.25319i) q^{73} +(3.84233 - 6.65511i) q^{74} +(4.34233 + 0.379706i) q^{76} -4.56155 q^{77} +(1.56155 - 2.70469i) q^{78} +(1.43845 - 2.49146i) q^{79} +(3.50000 - 6.06218i) q^{81} +(-1.06155 - 1.83866i) q^{82} -9.80776 q^{83} +7.12311 q^{84} +(-2.56155 - 4.43674i) q^{86} -3.12311 q^{87} +1.00000 q^{88} +(-4.84233 - 8.38716i) q^{89} +(4.56155 + 7.90084i) q^{91} +(3.84233 - 6.65511i) q^{92} +(-4.87689 + 8.44703i) q^{93} -11.1231 q^{94} -1.56155 q^{96} +(-5.34233 + 9.25319i) q^{97} +(-6.90388 + 11.9579i) q^{98} +(0.280776 + 0.486319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 6 q^{21} - 2 q^{22} + 3 q^{23} - q^{24} + 8 q^{26} + 14 q^{27} + 5 q^{28} - 4 q^{29} + 8 q^{31} - 2 q^{32} - q^{33} + 2 q^{34} - 3 q^{36} - 6 q^{37} + 5 q^{38} + 4 q^{39} + 4 q^{41} - 6 q^{42} - 2 q^{43} - 2 q^{44} - 6 q^{46} + 14 q^{47} - q^{48} + 14 q^{49} + 18 q^{51} - 4 q^{52} - 11 q^{53} - 7 q^{54} - 10 q^{56} + 28 q^{57} + 8 q^{58} - 25 q^{59} - 2 q^{61} - 4 q^{62} - q^{63} + 4 q^{64} - q^{66} + 23 q^{67} - 4 q^{68} + 48 q^{69} - 16 q^{71} - 3 q^{72} + 9 q^{73} + 3 q^{74} + 5 q^{76} - 10 q^{77} - 2 q^{78} + 14 q^{79} + 14 q^{81} + 4 q^{82} + 2 q^{83} + 12 q^{84} - 2 q^{86} + 4 q^{87} + 4 q^{88} - 7 q^{89} + 10 q^{91} + 3 q^{92} - 36 q^{93} - 28 q^{94} + 2 q^{96} - 9 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9 + 4 * q^11 + 2 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 6 * q^21 - 2 * q^22 + 3 * q^23 - q^24 + 8 * q^26 + 14 * q^27 + 5 * q^28 - 4 * q^29 + 8 * q^31 - 2 * q^32 - q^33 + 2 * q^34 - 3 * q^36 - 6 * q^37 + 5 * q^38 + 4 * q^39 + 4 * q^41 - 6 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^46 + 14 * q^47 - q^48 + 14 * q^49 + 18 * q^51 - 4 * q^52 - 11 * q^53 - 7 * q^54 - 10 * q^56 + 28 * q^57 + 8 * q^58 - 25 * q^59 - 2 * q^61 - 4 * q^62 - q^63 + 4 * q^64 - q^66 + 23 * q^67 - 4 * q^68 + 48 * q^69 - 16 * q^71 - 3 * q^72 + 9 * q^73 + 3 * q^74 + 5 * q^76 - 10 * q^77 - 2 * q^78 + 14 * q^79 + 14 * q^81 + 4 * q^82 + 2 * q^83 + 12 * q^84 - 2 * q^86 + 4 * q^87 + 4 * q^88 - 7 * q^89 + 10 * q^91 + 3 * q^92 - 36 * q^93 - 28 * q^94 + 2 * q^96 - 9 * q^97 - 7 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.780776	−	1.35234i	0.450781	−	0.780776i	−0.547653	−	0.836705i	$-0.684479\pi$
$3$	0.780776	−	1.35234i	0.450781	−	0.780776i	0.998435	+	0.0559290i	$0.0178120\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.780776	+	1.35234i	0.318751	+	0.552092i
$7$	−4.56155			−1.72410			−0.862052	−	0.506819i	$-0.830821\pi$
$7$	−4.56155			−1.72410			−0.862052	+	0.506819i	$0.830821\pi$
$8$	1.00000			0.353553
$9$	0.280776	+	0.486319i	0.0935921	+	0.162106i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.56155			−0.450781
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	2.28078	−	3.95042i	0.609563	−	1.05579i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.56155	+	2.70469i	−0.378732	+	0.655983i	−0.990878	−	0.134761i	$-0.956973\pi$
$17$	−1.56155	+	2.70469i	−0.378732	+	0.655983i	0.612146	+	0.790745i	$0.290307\pi$
$18$	−0.561553			−0.132359
$19$	−2.50000	+	3.57071i	−0.573539	+	0.819178i
$19$	−2.50000	+	3.57071i	−0.573539	+	0.819178i
$20$		0			0
$21$	−3.56155	+	6.16879i	−0.777195	+	1.34614i
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	3.84233	+	6.65511i	0.801181	+	1.38769i	0.918839	+	0.394632i	$0.129128\pi$
$23$	3.84233	+	6.65511i	0.801181	+	1.38769i	−0.117658	+	0.993054i	$0.537539\pi$
$24$	0.780776	−	1.35234i	0.159375	−	0.276046i
$25$		0			0
$26$	2.00000			0.392232
$27$	5.56155			1.07032
$28$	2.28078	+	3.95042i	0.431026	+	0.746559i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$		0			0
$31$	−6.24621			−1.12185			−0.560926	−	0.827866i	$-0.689555\pi$
$31$	−6.24621			−1.12185			−0.560926	+	0.827866i	$0.689555\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.780776	−	1.35234i	0.135916	−	0.235413i
$34$	−1.56155	−	2.70469i	−0.267804	−	0.463850i
$35$		0			0
$36$	0.280776	−	0.486319i	0.0467961	−	0.0810532i
$37$	−7.68466			−1.26335			−0.631675	−	0.775233i	$-0.717632\pi$
$37$	−7.68466			−1.26335			−0.631675	+	0.775233i	$0.717632\pi$
$38$	−1.84233	−	3.95042i	−0.298865	−	0.640843i
$39$	−3.12311			−0.500097
$40$		0			0
$41$	−1.06155	+	1.83866i	−0.165787	+	0.287151i	−0.936934	−	0.349505i	$-0.886350\pi$
$41$	−1.06155	+	1.83866i	−0.165787	+	0.287151i	0.771148	+	0.636656i	$0.219683\pi$
$42$	−3.56155	−	6.16879i	−0.549560	−	0.951865i
$43$	−2.56155	+	4.43674i	−0.390633	+	0.676596i	−0.992533	−	0.121975i	$-0.961077\pi$
$43$	−2.56155	+	4.43674i	−0.390633	+	0.676596i	0.601900	+	0.798571i	$0.294411\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	−7.68466			−1.13304
$47$	5.56155	+	9.63289i	0.811236	+	1.40510i	0.911999	+	0.410191i	$0.134538\pi$
$47$	5.56155	+	9.63289i	0.811236	+	1.40510i	−0.100764	+	0.994910i	$0.532129\pi$
$48$	0.780776	+	1.35234i	0.112695	+	0.195194i
$49$	13.8078			1.97254
$50$		0			0
$51$	2.43845	+	4.22351i	0.341451	+	0.591410i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−1.71922	−	2.97778i	−0.236154	−	0.409030i	0.723454	−	0.690373i	$-0.242553\pi$
$53$	−1.71922	−	2.97778i	−0.236154	−	0.409030i	−0.959607	+	0.281343i	$0.909220\pi$
$54$	−2.78078	+	4.81645i	−0.378416	+	0.655435i
$55$		0			0
$56$	−4.56155			−0.609563
$57$	2.87689	+	6.16879i	0.381054	+	0.817076i
$58$	2.00000			0.262613
$59$	−5.21922	+	9.03996i	−0.679485	+	1.17690i	0.295651	+	0.955296i	$0.404463\pi$
$59$	−5.21922	+	9.03996i	−0.679485	+	1.17690i	−0.975136	+	0.221607i	$0.928870\pi$
$60$		0			0
$61$	1.56155	+	2.70469i	0.199936	+	0.346300i	0.948508	−	0.316754i	$-0.102593\pi$
$61$	1.56155	+	2.70469i	0.199936	+	0.346300i	−0.748571	+	0.663054i	$0.769260\pi$
$62$	3.12311	−	5.40938i	0.396635	−	0.686992i
$63$	−1.28078	−	2.21837i	−0.161363	−	0.279488i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.780776	+	1.35234i	0.0961069	+	0.166462i
$67$	6.78078	+	11.7446i	0.828404	+	1.43484i	0.899290	+	0.437353i	$0.144084\pi$
$67$	6.78078	+	11.7446i	0.828404	+	1.43484i	−0.0708863	+	0.997484i	$0.522583\pi$
$68$	3.12311			0.378732
$69$	12.0000			1.44463
$70$		0			0
$71$	0.123106	−	0.213225i	0.0146099	−	0.0253052i	−0.858628	−	0.512599i	$-0.828683\pi$
$71$	0.123106	−	0.213225i	0.0146099	−	0.0253052i	0.873238	+	0.487294i	$0.162016\pi$
$72$	0.280776	+	0.486319i	0.0330898	+	0.0573132i
$73$	5.34233	−	9.25319i	0.625272	−	1.08300i	−0.363216	−	0.931705i	$-0.618321\pi$
$73$	5.34233	−	9.25319i	0.625272	−	1.08300i	0.988488	−	0.151298i	$-0.0483454\pi$
$74$	3.84233	−	6.65511i	0.446662	−	0.773641i
$75$		0			0
$76$	4.34233	+	0.379706i	0.498099	+	0.0435553i
$77$	−4.56155			−0.519837
$78$	1.56155	−	2.70469i	0.176811	−	0.306246i
$79$	1.43845	−	2.49146i	0.161838	−	0.280312i	−0.773690	−	0.633564i	$-0.781591\pi$
$79$	1.43845	−	2.49146i	0.161838	−	0.280312i	0.935528	+	0.353253i	$0.114924\pi$
$80$		0			0
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$	−1.06155	−	1.83866i	−0.117229	−	0.203046i
$83$	−9.80776			−1.07654			−0.538271	−	0.842772i	$-0.680922\pi$
$83$	−9.80776			−1.07654			−0.538271	+	0.842772i	$0.680922\pi$
$84$	7.12311			0.777195
$85$		0			0
$86$	−2.56155	−	4.43674i	−0.276219	−	0.478426i
$87$	−3.12311			−0.334832
$88$	1.00000			0.106600
$89$	−4.84233	−	8.38716i	−0.513286	−	0.889037i	−0.999881	−	0.0154098i	$-0.995095\pi$
$89$	−4.84233	−	8.38716i	−0.513286	−	0.889037i	0.486595	−	0.873627i	$-0.338239\pi$
$90$		0			0
$91$	4.56155	+	7.90084i	0.478181	+	0.828233i
$92$	3.84233	−	6.65511i	0.400591	−	0.693843i
$93$	−4.87689	+	8.44703i	−0.505710	+	0.875916i
$94$	−11.1231			−1.14726
$95$		0			0
$96$	−1.56155			−0.159375
$97$	−5.34233	+	9.25319i	−0.542431	+	0.939519i	0.456332	+	0.889809i	$0.349163\pi$
$97$	−5.34233	+	9.25319i	−0.542431	+	0.939519i	−0.998764	+	0.0497093i	$0.984171\pi$
$98$	−6.90388	+	11.9579i	−0.697397	+	1.20793i
$99$	0.280776	+	0.486319i	0.0282191	+	0.0488769i
$100$		0			0
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	−4.87689			−0.482884
$103$	−14.8078			−1.45905			−0.729526	−	0.683953i	$-0.760259\pi$
$103$	−14.8078			−1.45905			−0.729526	+	0.683953i	$0.760259\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	3.43845			0.333972
$107$	14.2462			1.37723			0.688617	−	0.725126i	$-0.258218\pi$
$107$	14.2462			1.37723			0.688617	+	0.725126i	$0.258218\pi$
$108$	−2.78078	−	4.81645i	−0.267580	−	0.463463i
$109$	−1.12311	+	1.94528i	−0.107574	+	0.186324i	−0.914787	−	0.403937i	$-0.867642\pi$
$109$	−1.12311	+	1.94528i	−0.107574	+	0.186324i	0.807213	+	0.590260i	$0.200975\pi$
$110$		0			0
$111$	−6.00000	+	10.3923i	−0.569495	+	0.986394i
$112$	2.28078	−	3.95042i	0.215513	−	0.373280i
$113$	−3.80776			−0.358204			−0.179102	−	0.983830i	$-0.557319\pi$
$113$	−3.80776			−0.358204			−0.179102	+	0.983830i	$0.557319\pi$
$114$	−6.78078	−	0.592932i	−0.635078	−	0.0555331i
$115$		0			0
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$	0.561553	−	0.972638i	0.0519156	−	0.0899204i
$118$	−5.21922	−	9.03996i	−0.480468	−	0.832196i
$119$	7.12311	−	12.3376i	0.652974	−	1.13098i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	−3.12311			−0.282753
$123$	1.65767	+	2.87117i	0.149467	+	0.258885i
$124$	3.12311	+	5.40938i	0.280463	+	0.485776i
$125$		0			0
$126$	2.56155			0.228201
$127$	−5.71922	−	9.90599i	−0.507499	−	0.879014i	−0.999962	−	0.00868089i	$-0.997237\pi$
$127$	−5.71922	−	9.90599i	−0.507499	−	0.879014i	0.492463	−	0.870333i	$-0.336097\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	3.93845	−	6.82159i	0.344104	−	0.596005i	−0.641087	−	0.767468i	$-0.721516\pi$
$131$	3.93845	−	6.82159i	0.344104	−	0.596005i	0.985191	+	0.171463i	$0.0548495\pi$
$132$	−1.56155			−0.135916
$133$	11.4039	−	16.2880i	0.988842	−	1.41235i
$134$	−13.5616			−1.17154
$135$		0			0
$136$	−1.56155	+	2.70469i	−0.133902	+	0.231925i
$137$	−4.78078	−	8.28055i	−0.408449	−	0.707455i	0.586267	−	0.810118i	$-0.300597\pi$
$137$	−4.78078	−	8.28055i	−0.408449	−	0.707455i	−0.994716	+	0.102663i	$0.967264\pi$
$138$	−6.00000	+	10.3923i	−0.510754	+	0.884652i
$139$	5.90388	+	10.2258i	0.500761	+	0.867343i	1.00000		0.000878648i	$0.000279682\pi$
$139$	5.90388	+	10.2258i	0.500761	+	0.867343i	−0.499239	+	0.866464i	$0.666387\pi$
$140$		0			0
$141$	17.3693			1.46276
$142$	0.123106	+	0.213225i	0.0103308	+	0.0178935i
$143$	−1.00000	−	1.73205i	−0.0836242	−	0.144841i
$144$	−0.561553			−0.0467961
$145$		0			0
$146$	5.34233	+	9.25319i	0.442134	+	0.765799i
$147$	10.7808	−	18.6729i	0.889183	−	1.54011i
$148$	3.84233	+	6.65511i	0.315838	+	0.547047i
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	0.326411	+	0.945228i	$0.394160\pi$
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	−0.981797	+	0.189933i	$0.939173\pi$
$150$		0			0
$151$	−12.4924			−1.01662			−0.508309	−	0.861174i	$-0.669729\pi$
$151$	−12.4924			−1.01662			−0.508309	+	0.861174i	$0.669729\pi$
$152$	−2.50000	+	3.57071i	−0.202777	+	0.289623i
$153$	−1.75379			−0.141785
$154$	2.28078	−	3.95042i	0.183790	−	0.318334i
$155$		0			0
$156$	1.56155	+	2.70469i	0.125024	+	0.216548i
$157$	3.28078	−	5.68247i	0.261834	−	0.453511i	−0.704895	−	0.709312i	$-0.749006\pi$
$157$	3.28078	−	5.68247i	0.261834	−	0.453511i	0.966729	+	0.255801i	$0.0823392\pi$
$158$	1.43845	+	2.49146i	0.114437	+	0.198210i
$159$	−5.36932			−0.425815
$160$		0			0
$161$	−17.5270	−	30.3576i	−1.38132	−	2.39252i
$162$	3.50000	+	6.06218i	0.274986	+	0.476290i
$163$	20.0540			1.57075			0.785374	−	0.619021i	$-0.212471\pi$
$163$	20.0540			1.57075			0.785374	+	0.619021i	$0.212471\pi$
$164$	2.12311			0.165787
$165$		0			0
$166$	4.90388	−	8.49377i	0.380615	−	0.659245i
$167$	−5.84233	−	10.1192i	−0.452093	−	0.783048i	0.546423	−	0.837509i	$-0.315989\pi$
$167$	−5.84233	−	10.1192i	−0.452093	−	0.783048i	−0.998516	+	0.0544614i	$0.982656\pi$
$168$	−3.56155	+	6.16879i	−0.274780	+	0.475933i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−2.43845	−	0.213225i	−0.186473	−	0.0163057i
$172$	5.12311			0.390633
$173$	7.40388	−	12.8239i	0.562907	−	0.974983i	−0.434334	−	0.900752i	$-0.643016\pi$
$173$	7.40388	−	12.8239i	0.562907	−	0.974983i	0.997241	−	0.0742313i	$-0.0236503\pi$
$174$	1.56155	−	2.70469i	0.118381	−	0.205042i
$175$		0			0
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	8.15009	+	14.1164i	0.612599	+	1.06105i
$178$	9.68466			0.725896
$179$	−21.4924			−1.60642			−0.803210	−	0.595697i	$-0.796876\pi$
$179$	−21.4924			−1.60642			−0.803210	+	0.595697i	$0.796876\pi$
$180$		0			0
$181$	1.68466	+	2.91791i	0.125220	+	0.216887i	0.921819	−	0.387621i	$-0.126703\pi$
$181$	1.68466	+	2.91791i	0.125220	+	0.216887i	−0.796599	+	0.604508i	$0.793370\pi$
$182$	−9.12311			−0.676250
$183$	4.87689			0.360510
$184$	3.84233	+	6.65511i	0.283260	+	0.490621i
$185$		0			0
$186$	−4.87689	−	8.44703i	−0.357591	−	0.619366i
$187$	−1.56155	+	2.70469i	−0.114192	+	0.197786i
$188$	5.56155	−	9.63289i	0.405618	−	0.702551i
$189$	−25.3693			−1.84535
$190$		0			0
$191$	19.3693			1.40151			0.700757	−	0.713400i	$-0.252846\pi$
$191$	19.3693			1.40151			0.700757	+	0.713400i	$0.252846\pi$
$192$	0.780776	−	1.35234i	0.0563477	−	0.0975971i
$193$	−7.80776	+	13.5234i	−0.562015	+	0.973439i	0.435305	+	0.900283i	$0.356640\pi$
$193$	−7.80776	+	13.5234i	−0.562015	+	0.973439i	−0.997321	+	0.0731559i	$0.976693\pi$
$194$	−5.34233	−	9.25319i	−0.383557	−	0.664340i
$195$		0			0
$196$	−6.90388	−	11.9579i	−0.493134	−	0.854134i
$197$	−18.5616			−1.32246			−0.661228	−	0.750185i	$-0.729964\pi$
$197$	−18.5616			−1.32246			−0.661228	+	0.750185i	$0.729964\pi$
$198$	−0.561553			−0.0399078
$199$	5.56155	+	9.63289i	0.394248	+	0.682858i	0.993005	−	0.118073i	$-0.0376718\pi$
$199$	5.56155	+	9.63289i	0.394248	+	0.682858i	−0.598757	+	0.800931i	$0.704338\pi$
$200$		0			0
$201$	21.1771			1.49372
$202$	10.0000			0.703598
$203$	4.56155	+	7.90084i	0.320158	+	0.554530i
$204$	2.43845	−	4.22351i	0.170725	−	0.295705i
$205$		0			0
$206$	7.40388	−	12.8239i	0.515853	−	0.893483i
$207$	−2.15767	+	3.73720i	−0.149968	+	0.259753i
$208$	2.00000			0.138675
$209$	−2.50000	+	3.57071i	−0.172929	+	0.246991i
$210$		0			0
$211$	7.84233	−	13.5833i	0.539888	−	0.935114i	−0.459021	−	0.888425i	$-0.651800\pi$
$211$	7.84233	−	13.5833i	0.539888	−	0.935114i	0.998909	−	0.0466885i	$-0.0148668\pi$
$212$	−1.71922	+	2.97778i	−0.118077	+	0.204515i
$213$	−0.192236	−	0.332962i	−0.0131718	−	0.0228142i
$214$	−7.12311	+	12.3376i	−0.486925	+	0.843380i
$215$		0			0
$216$	5.56155			0.378416
$217$	28.4924			1.93419
$218$	−1.12311	−	1.94528i	−0.0760663	−	0.131751i
$219$	−8.34233	−	14.4493i	−0.563722	−	0.976396i
$220$		0			0
$221$	6.24621			0.420166
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	11.8423	−	20.5115i	0.793021	−	1.37355i	−0.131067	−	0.991373i	$-0.541840\pi$
$223$	11.8423	−	20.5115i	0.793021	−	1.37355i	0.924088	−	0.382179i	$-0.124826\pi$
$224$	2.28078	+	3.95042i	0.152391	+	0.263949i
$225$		0			0
$226$	1.90388	−	3.29762i	0.126644	−	0.219354i
$227$	8.93087			0.592763			0.296381	−	0.955070i	$-0.404220\pi$
$227$	8.93087			0.592763			0.296381	+	0.955070i	$0.404220\pi$
$228$	3.90388	−	5.57586i	0.258541	−	0.369270i
$229$	21.1231			1.39585			0.697927	−	0.716169i	$-0.254106\pi$
$229$	21.1231			1.39585			0.697927	+	0.716169i	$0.254106\pi$
$230$		0			0
$231$	−3.56155	+	6.16879i	−0.234333	+	0.405877i
$232$	−1.00000	−	1.73205i	−0.0656532	−	0.113715i
$233$	7.34233	−	12.7173i	0.481012	−	0.833137i	−0.518751	−	0.854926i	$-0.673603\pi$
$233$	7.34233	−	12.7173i	0.481012	−	0.833137i	0.999763	+	0.0217884i	$0.00693602\pi$
$234$	0.561553	+	0.972638i	0.0367099	+	0.0635833i
$235$		0			0
$236$	10.4384			0.679485
$237$	−2.24621	−	3.89055i	−0.145907	−	0.252719i
$238$	7.12311	+	12.3376i	0.461722	+	0.799727i
$239$	1.75379			0.113443			0.0567216	−	0.998390i	$-0.481935\pi$
$239$	1.75379			0.113443			0.0567216	+	0.998390i	$0.481935\pi$
$240$		0			0
$241$	2.21922	+	3.84381i	0.142953	+	0.247601i	0.928607	−	0.371064i	$-0.121007\pi$
$241$	2.21922	+	3.84381i	0.142953	+	0.247601i	−0.785655	+	0.618665i	$0.787674\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	2.87689	+	4.98293i	0.184553	+	0.319655i
$244$	1.56155	−	2.70469i	0.0999682	−	0.173150i
$245$		0			0
$246$	−3.31534			−0.211378
$247$	8.68466	+	0.759413i	0.552592	+	0.0483203i
$248$	−6.24621			−0.396635
$249$	−7.65767	+	13.2635i	−0.485285	+	0.840539i
$250$		0			0
$251$	1.46543	+	2.53821i	0.0924974	+	0.160210i	0.908561	−	0.417751i	$-0.137182\pi$
$251$	1.46543	+	2.53821i	0.0924974	+	0.160210i	−0.816064	+	0.577962i	$0.803848\pi$
$252$	−1.28078	+	2.21837i	−0.0806813	+	0.139744i
$253$	3.84233	+	6.65511i	0.241565	+	0.418403i
$254$	11.4384			0.717712
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.0270	−	20.8314i	−0.750223	−	1.29942i	−0.947714	−	0.319120i	$-0.896613\pi$
$257$	−12.0270	−	20.8314i	−0.750223	−	1.29942i	0.197492	−	0.980305i	$-0.436720\pi$
$258$	−8.00000			−0.498058
$259$	35.0540			2.17815
$260$		0			0
$261$	0.561553	−	0.972638i	0.0347592	−	0.0602048i
$262$	3.93845	+	6.82159i	0.243318	+	0.421439i
$263$	−11.4039	+	19.7521i	−0.703193	+	1.21797i	0.264146	+	0.964483i	$0.414910\pi$
$263$	−11.4039	+	19.7521i	−0.703193	+	1.21797i	−0.967340	+	0.253484i	$0.918423\pi$
$264$	0.780776	−	1.35234i	0.0480535	−	0.0832310i
$265$		0			0
$266$	8.40388	+	18.0201i	0.515275	+	1.10488i
$267$	−15.1231			−0.925519
$268$	6.78078	−	11.7446i	0.414202	−	0.717419i
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	−4.12311	+	7.14143i	−0.250461	+	0.433811i	−0.963653	−	0.267158i	$-0.913915\pi$
$271$	−4.12311	+	7.14143i	−0.250461	+	0.433811i	0.713192	+	0.700969i	$0.247249\pi$
$272$	−1.56155	−	2.70469i	−0.0946830	−	0.163996i
$273$	14.2462			0.862220
$274$	9.56155			0.577635
$275$		0			0
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	12.2462			0.735804			0.367902	−	0.929865i	$-0.380076\pi$
$277$	12.2462			0.735804			0.367902	+	0.929865i	$0.380076\pi$
$278$	−11.8078			−0.708183
$279$	−1.75379	−	3.03765i	−0.104997	−	0.181859i
$280$		0			0
$281$	8.18466	+	14.1762i	0.488256	+	0.845684i	0.999909	−	0.0135084i	$-0.00429998\pi$
$281$	8.18466	+	14.1762i	0.488256	+	0.845684i	−0.511653	+	0.859192i	$0.670967\pi$
$282$	−8.68466	+	15.0423i	−0.517164	+	0.895754i
$283$	−11.7808	+	20.4049i	−0.700294	+	1.21295i	0.268069	+	0.963400i	$0.413615\pi$
$283$	−11.7808	+	20.4049i	−0.700294	+	1.21295i	−0.968363	+	0.249546i	$0.919719\pi$
$284$	−0.246211			−0.0146099
$285$		0			0
$286$	2.00000			0.118262
$287$	4.84233	−	8.38716i	0.285834	−	0.495078i
$288$	0.280776	−	0.486319i	0.0165449	−	0.0286566i
$289$	3.62311	+	6.27540i	0.213124	+	0.369141i
$290$		0			0
$291$	8.34233	+	14.4493i	0.489036	+	0.847035i
$292$	−10.6847			−0.625272
$293$	−19.4384			−1.13561			−0.567803	−	0.823164i	$-0.692207\pi$
$293$	−19.4384			−1.13561			−0.567803	+	0.823164i	$0.692207\pi$
$294$	10.7808	+	18.6729i	0.628748	+	1.08902i
$295$		0			0
$296$	−7.68466			−0.446662
$297$	5.56155			0.322714
$298$	−8.00000	−	13.8564i	−0.463428	−	0.802680i
$299$	7.68466	−	13.3102i	0.444415	−	0.769750i
$300$		0			0
$301$	11.6847	−	20.2384i	0.673493	−	1.16652i
$302$	6.24621	−	10.8188i	0.359429	−	0.622549i
$303$	−15.6155			−0.897089
$304$	−1.84233	−	3.95042i	−0.105665	−	0.226572i
$305$		0			0
$306$	0.876894	−	1.51883i	0.0501287	−	0.0868255i
$307$	2.46543	−	4.27026i	0.140710	−	0.243717i	−0.787054	−	0.616884i	$-0.788395\pi$
$307$	2.46543	−	4.27026i	0.140710	−	0.243717i	0.927764	+	0.373167i	$0.121728\pi$
$308$	2.28078	+	3.95042i	0.129959	+	0.225096i
$309$	−11.5616	+	20.0252i	−0.657714	+	1.13919i
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$	−3.12311			−0.176811
$313$	8.34233	+	14.4493i	0.471536	+	0.816725i	0.999470	−	0.0325609i	$-0.0103663\pi$
$313$	8.34233	+	14.4493i	0.471536	+	0.816725i	−0.527933	+	0.849286i	$0.677033\pi$
$314$	3.28078	+	5.68247i	0.185145	+	0.320680i
$315$		0			0
$316$	−2.87689			−0.161838
$317$	3.15767	+	5.46925i	0.177352	+	0.307183i	0.940973	−	0.338482i	$-0.109913\pi$
$317$	3.15767	+	5.46925i	0.177352	+	0.307183i	−0.763620	+	0.645665i	$0.776580\pi$
$318$	2.68466	−	4.64996i	0.150548	−	0.260757i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$		0			0
$321$	11.1231	−	19.2658i	0.620831	−	1.07531i
$322$	35.0540			1.95348
$323$	−5.75379	−	12.3376i	−0.320149	−	0.686481i
$324$	−7.00000			−0.388889
$325$		0			0
$326$	−10.0270	+	17.3673i	−0.555343	+	0.961883i
$327$	1.75379	+	3.03765i	0.0969847	+	0.167982i
$328$	−1.06155	+	1.83866i	−0.0586144	+	0.101523i
$329$	−25.3693	−	43.9409i	−1.39866	−	2.42254i
$330$		0			0
$331$	−9.49242			−0.521751			−0.260875	−	0.965372i	$-0.584011\pi$
$331$	−9.49242			−0.521751			−0.260875	+	0.965372i	$0.584011\pi$
$332$	4.90388	+	8.49377i	0.269135	+	0.466156i
$333$	−2.15767	−	3.73720i	−0.118240	−	0.204797i
$334$	11.6847			0.639356
$335$		0			0
$336$	−3.56155	−	6.16879i	−0.194299	−	0.336535i
$337$	−8.02699	+	13.9032i	−0.437258	+	0.757353i	−0.997477	−	0.0709917i	$-0.977384\pi$
$337$	−8.02699	+	13.9032i	−0.437258	+	0.757353i	0.560219	+	0.828345i	$0.310717\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	−2.97301	+	5.14941i	−0.161472	+	0.279677i
$340$		0			0
$341$	−6.24621			−0.338251
$342$	1.40388	−	2.00514i	0.0759132	−	0.108426i
$343$	−31.0540			−1.67676
$344$	−2.56155	+	4.43674i	−0.138110	+	0.239213i
$345$		0			0
$346$	7.40388	+	12.8239i	0.398035	+	0.689417i
$347$	−5.34233	+	9.25319i	−0.286791	+	0.496737i	−0.973042	−	0.230628i	$-0.925922\pi$
$347$	−5.34233	+	9.25319i	−0.286791	+	0.496737i	0.686251	+	0.727365i	$0.259255\pi$
$348$	1.56155	+	2.70469i	0.0837080	+	0.144987i
$349$	2.24621			0.120237			0.0601185	−	0.998191i	$-0.480852\pi$
$349$	2.24621			0.120237			0.0601185	+	0.998191i	$0.480852\pi$
$350$		0			0
$351$	−5.56155	−	9.63289i	−0.296854	−	0.514166i
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	21.1771			1.12714			0.563571	−	0.826068i	$-0.309427\pi$
$353$	21.1771			1.12714			0.563571	+	0.826068i	$0.309427\pi$
$354$	−16.3002			−0.866345
$355$		0			0
$356$	−4.84233	+	8.38716i	−0.256643	+	0.444519i
$357$	−11.1231	−	19.2658i	−0.588697	−	1.01965i
$358$	10.7462	−	18.6130i	0.567955	−	0.983727i
$359$	−3.43845	+	5.95557i	−0.181474	+	0.314323i	−0.942383	−	0.334536i	$-0.891420\pi$
$359$	−3.43845	+	5.95557i	−0.181474	+	0.314323i	0.760908	+	0.648859i	$0.224754\pi$
$360$		0			0
$361$	−6.50000	−	17.8536i	−0.342105	−	0.939662i
$362$	−3.36932			−0.177087
$363$	−7.80776	+	13.5234i	−0.409801	+	0.709797i
$364$	4.56155	−	7.90084i	0.239090	−	0.414117i
$365$		0			0
$366$	−2.43845	+	4.22351i	−0.127460	+	0.220767i
$367$	−17.1231	−	29.6581i	−0.893819	−	1.54814i	−0.835260	−	0.549856i	$-0.814683\pi$
$367$	−17.1231	−	29.6581i	−0.893819	−	1.54814i	−0.0585592	−	0.998284i	$-0.518651\pi$
$368$	−7.68466			−0.400591
$369$	−1.19224			−0.0620653
$370$		0			0
$371$	7.84233	+	13.5833i	0.407153	+	0.705210i
$372$	9.75379			0.505710
$373$	15.1922			0.786624			0.393312	−	0.919405i	$-0.371329\pi$
$373$	15.1922			0.786624			0.393312	+	0.919405i	$0.371329\pi$
$374$	−1.56155	−	2.70469i	−0.0807460	−	0.139856i
$375$		0			0
$376$	5.56155	+	9.63289i	0.286815	+	0.496778i
$377$	−2.00000	+	3.46410i	−0.103005	+	0.178410i
$378$	12.6847	−	21.9705i	0.652428	−	1.13004i
$379$	32.4924			1.66902			0.834512	−	0.550990i	$-0.185750\pi$
$379$	32.4924			1.66902			0.834512	+	0.550990i	$0.185750\pi$
$380$		0			0
$381$	−17.8617			−0.915085
$382$	−9.68466	+	16.7743i	−0.495510	+	0.858249i
$383$	−1.56155	+	2.70469i	−0.0797916	+	0.138203i	−0.903160	−	0.429304i	$-0.858759\pi$
$383$	−1.56155	+	2.70469i	−0.0797916	+	0.138203i	0.823368	+	0.567507i	$0.192092\pi$
$384$	0.780776	+	1.35234i	0.0398438	+	0.0690115i
$385$		0			0
$386$	−7.80776	−	13.5234i	−0.397405	−	0.688325i
$387$	−2.87689			−0.146241
$388$	10.6847			0.542431
$389$	5.43845	+	9.41967i	0.275740	+	0.477596i	0.970322	−	0.241818i	$-0.0777437\pi$
$389$	5.43845	+	9.41967i	0.275740	+	0.477596i	−0.694581	+	0.719414i	$0.744410\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	13.8078			0.697397
$393$	−6.15009	−	10.6523i	−0.310231	−	0.537336i
$394$	9.28078	−	16.0748i	0.467559	−	0.809836i
$395$		0			0
$396$	0.280776	−	0.486319i	0.0141095	−	0.0244384i
$397$	−12.6501	+	21.9106i	−0.634890	+	1.09966i	0.351648	+	0.936132i	$0.385621\pi$
$397$	−12.6501	+	21.9106i	−0.634890	+	1.09966i	−0.986538	+	0.163530i	$0.947712\pi$
$398$	−11.1231			−0.557551
$399$	−13.1231	−	28.1393i	−0.656977	−	1.40873i
$400$		0			0
$401$	0.465435	−	0.806157i	0.0232427	−	0.0402575i	−0.854170	−	0.519994i	$-0.825934\pi$
$401$	0.465435	−	0.806157i	0.0232427	−	0.0402575i	0.877413	+	0.479736i	$0.159268\pi$
$402$	−10.5885	+	18.3399i	−0.528108	+	0.914711i
$403$	6.24621	+	10.8188i	0.311146	+	0.538921i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$		0			0
$406$	−9.12311			−0.452772
$407$	−7.68466			−0.380914
$408$	2.43845	+	4.22351i	0.120721	+	0.209095i
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	−0.999751	−	0.0223042i	$-0.992900\pi$
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	0.480560	−	0.876962i	$-0.340434\pi$
$410$		0			0
$411$	−14.9309			−0.736485
$412$	7.40388	+	12.8239i	0.364763	+	0.631788i
$413$	23.8078	−	41.2363i	1.17150	−	2.02910i
$414$	−2.15767	−	3.73720i	−0.106044	−	0.183673i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	18.4384			0.902935
$418$	−1.84233	−	3.95042i	−0.0901113	−	0.193221i
$419$	−13.4384			−0.656511			−0.328256	−	0.944589i	$-0.606461\pi$
$419$	−13.4384			−0.656511			−0.328256	+	0.944589i	$0.606461\pi$
$420$		0			0
$421$	0.246211	−	0.426450i	0.0119996	−	0.0207839i	−0.859963	−	0.510356i	$-0.829514\pi$
$421$	0.246211	−	0.426450i	0.0119996	−	0.0207839i	0.871963	+	0.489572i	$0.162847\pi$
$422$	7.84233	+	13.5833i	0.381759	+	0.661225i
$423$	−3.12311	+	5.40938i	−0.151851	+	0.263013i
$424$	−1.71922	−	2.97778i	−0.0834929	−	0.144614i
$425$		0			0
$426$	0.384472			0.0186277
$427$	−7.12311	−	12.3376i	−0.344711	−	0.597057i
$428$	−7.12311	−	12.3376i	−0.344308	−	0.596359i
$429$	−3.12311			−0.150785
$430$		0			0
$431$	−8.68466	−	15.0423i	−0.418325	−	0.724561i	0.577446	−	0.816429i	$-0.304049\pi$
$431$	−8.68466	−	15.0423i	−0.418325	−	0.724561i	−0.995771	+	0.0918683i	$0.970716\pi$
$432$	−2.78078	+	4.81645i	−0.133790	+	0.231731i
$433$	6.36932	+	11.0320i	0.306090	+	0.530163i	0.977503	−	0.210920i	$-0.0676459\pi$
$433$	6.36932	+	11.0320i	0.306090	+	0.530163i	−0.671414	+	0.741083i	$0.734313\pi$
$434$	−14.2462	+	24.6752i	−0.683840	+	1.18445i
$435$		0			0
$436$	2.24621			0.107574
$437$	−33.3693	−	2.91791i	−1.59627	−	0.139583i
$438$	16.6847			0.797224
$439$	−8.24621	+	14.2829i	−0.393570	+	0.681684i	−0.992918	−	0.118806i	$-0.962094\pi$
$439$	−8.24621	+	14.2829i	−0.393570	+	0.681684i	0.599347	+	0.800489i	$0.295427\pi$
$440$		0			0
$441$	3.87689	+	6.71498i	0.184614	+	0.319761i
$442$	−3.12311	+	5.40938i	−0.148551	+	0.257298i
$443$	2.53457	+	4.39000i	0.120421	+	0.208575i	0.919934	−	0.392074i	$-0.128242\pi$
$443$	2.53457	+	4.39000i	0.120421	+	0.208575i	−0.799513	+	0.600649i	$0.794909\pi$
$444$	12.0000			0.569495
$445$		0			0
$446$	11.8423	+	20.5115i	0.560751	+	0.971248i
$447$	12.4924	+	21.6375i	0.590871	+	1.02342i
$448$	−4.56155			−0.215513
$449$	29.0000			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$450$		0			0
$451$	−1.06155	+	1.83866i	−0.0499866	+	0.0865793i
$452$	1.90388	+	3.29762i	0.0895511	+	0.155107i
$453$	−9.75379	+	16.8941i	−0.458273	+	0.793752i
$454$	−4.46543	+	7.73436i	−0.209573	+	0.362992i
$455$		0			0
$456$	2.87689	+	6.16879i	0.134723	+	0.288880i
$457$	30.0540			1.40587			0.702933	−	0.711256i	$-0.251873\pi$
$457$	30.0540			1.40587			0.702933	+	0.711256i	$0.251873\pi$
$458$	−10.5616	+	18.2931i	−0.493509	+	0.854783i
$459$	−8.68466	+	15.0423i	−0.405365	+	0.702113i
$460$		0			0
$461$	−13.4924	+	23.3696i	−0.628405	+	1.08843i	0.359467	+	0.933158i	$0.382958\pi$
$461$	−13.4924	+	23.3696i	−0.628405	+	1.08843i	−0.987872	+	0.155271i	$0.950375\pi$
$462$	−3.56155	−	6.16879i	−0.165698	−	0.286998i
$463$	15.4384			0.717485			0.358743	−	0.933436i	$-0.383206\pi$
$463$	15.4384			0.717485			0.358743	+	0.933436i	$0.383206\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	7.34233	+	12.7173i	0.340127	+	0.589117i
$467$	−12.4384			−0.575583			−0.287791	−	0.957693i	$-0.592921\pi$
$467$	−12.4384			−0.575583			−0.287791	+	0.957693i	$0.592921\pi$
$468$	−1.12311			−0.0519156
$469$	−30.9309	−	53.5738i	−1.42825	−	2.47381i
$470$		0			0
$471$	−5.12311	−	8.87348i	−0.236060	−	0.408868i
$472$	−5.21922	+	9.03996i	−0.240234	+	0.416098i
$473$	−2.56155	+	4.43674i	−0.117780	+	0.204002i
$474$	4.49242			0.206344
$475$		0			0
$476$	−14.2462			−0.652974
$477$	0.965435	−	1.67218i	0.0442042	−	0.0765640i
$478$	−0.876894	+	1.51883i	−0.0401082	+	0.0694695i
$479$	−2.31534	−	4.01029i	−0.105791	−	0.183235i	0.808270	−	0.588812i	$-0.200404\pi$
$479$	−2.31534	−	4.01029i	−0.105791	−	0.183235i	−0.914061	+	0.405577i	$0.867071\pi$
$480$		0			0
$481$	7.68466	+	13.3102i	0.350390	+	0.606894i
$482$	−4.43845			−0.202166
$483$	−54.7386			−2.49069
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$		0			0
$486$	−5.75379			−0.260997
$487$	−21.9309			−0.993783			−0.496891	−	0.867813i	$-0.665525\pi$
$487$	−21.9309			−0.993783			−0.496891	+	0.867813i	$0.665525\pi$
$488$	1.56155	+	2.70469i	0.0706882	+	0.122436i
$489$	15.6577	−	27.1199i	0.708064	−	1.22640i
$490$		0			0
$491$	−18.0885	+	31.3303i	−0.816324	+	1.41392i	0.0920486	+	0.995755i	$0.470658\pi$
$491$	−18.0885	+	31.3303i	−0.816324	+	1.41392i	−0.908373	+	0.418161i	$0.862675\pi$
$492$	1.65767	−	2.87117i	0.0747336	−	0.129442i
$493$	6.24621			0.281315
$494$	−5.00000	+	7.14143i	−0.224961	+	0.321308i
$495$		0			0
$496$	3.12311	−	5.40938i	0.140232	−	0.242888i
$497$	−0.561553	+	0.972638i	−0.0251891	+	0.0436288i
$498$	−7.65767	−	13.2635i	−0.343148	−	0.594351i
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$		0			0
$501$	−18.2462			−0.815181
$502$	−2.93087			−0.130811
$503$	−17.2116	−	29.8114i	−0.767429	−	1.32923i	−0.938953	−	0.344047i	$-0.888202\pi$
$503$	−17.2116	−	29.8114i	−0.767429	−	1.32923i	0.171523	−	0.985180i	$-0.445131\pi$
$504$	−1.28078	−	2.21837i	−0.0570503	−	0.0988140i
$505$		0			0
$506$	−7.68466			−0.341625
$507$	−7.02699	−	12.1711i	−0.312079	−	0.540538i
$508$	−5.71922	+	9.90599i	−0.253750	+	0.439507i
$509$	4.56155	+	7.90084i	0.202187	+	0.350199i	0.949233	−	0.314574i	$-0.101862\pi$
$509$	4.56155	+	7.90084i	0.202187	+	0.350199i	−0.747046	+	0.664773i	$0.768528\pi$
$510$		0			0
$511$	−24.3693	+	42.2089i	−1.07804	+	1.86721i
$512$	1.00000			0.0441942
$513$	−13.9039	+	19.8587i	−0.613871	+	0.876784i
$514$	24.0540			1.06098
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	5.56155	+	9.63289i	0.244597	+	0.423654i
$518$	−17.5270	+	30.3576i	−0.770092	+	1.33384i
$519$	−11.5616	−	20.0252i	−0.507496	−	0.879009i
$520$		0			0
$521$	−2.19224			−0.0960436			−0.0480218	−	0.998846i	$-0.515292\pi$
$521$	−2.19224			−0.0960436			−0.0480218	+	0.998846i	$0.515292\pi$
$522$	0.561553	+	0.972638i	0.0245785	+	0.0425712i
$523$	19.6847	+	34.0948i	0.860750	+	1.49086i	0.871206	+	0.490917i	$0.163338\pi$
$523$	19.6847	+	34.0948i	0.860750	+	1.49086i	−0.0104561	+	0.999945i	$0.503328\pi$
$524$	−7.87689			−0.344104
$525$		0			0
$526$	−11.4039	−	19.7521i	−0.497233	−	0.861233i
$527$	9.75379	−	16.8941i	0.424882	−	0.735917i
$528$	0.780776	+	1.35234i	0.0339789	+	0.0588532i
$529$	−18.0270	+	31.2237i	−0.783782	+	1.35755i
$530$		0			0
$531$	−5.86174			−0.254378
$532$	−19.8078	−	1.73205i	−0.858775	−	0.0750939i
$533$	4.24621			0.183924
$534$	7.56155	−	13.0970i	0.327220	−	0.566762i
$535$		0			0
$536$	6.78078	+	11.7446i	0.292885	+	0.507292i
$537$	−16.7808	+	29.0652i	−0.724144	+	1.25425i
$538$	−2.00000	−	3.46410i	−0.0862261	−	0.149348i
$539$	13.8078			0.594743
$540$		0			0
$541$	−2.24621	−	3.89055i	−0.0965722	−	0.167268i	0.813692	−	0.581297i	$-0.197455\pi$
$541$	−2.24621	−	3.89055i	−0.0965722	−	0.167268i	−0.910264	+	0.414029i	$0.864121\pi$
$542$	−4.12311	−	7.14143i	−0.177103	−	0.306751i
$543$	5.26137			0.225787
$544$	3.12311			0.133902
$545$		0			0
$546$	−7.12311	+	12.3376i	−0.304841	+	0.528000i
$547$	−6.56155	−	11.3649i	−0.280552	−	0.485930i	0.690969	−	0.722884i	$-0.257184\pi$
$547$	−6.56155	−	11.3649i	−0.280552	−	0.485930i	−0.971521	+	0.236955i	$0.923851\pi$
$548$	−4.78078	+	8.28055i	−0.204225	+	0.353727i
$549$	−0.876894	+	1.51883i	−0.0374249	+	0.0648219i
$550$		0			0
$551$	8.68466	+	0.759413i	0.369979	+	0.0323521i
$552$	12.0000			0.510754
$553$	−6.56155	+	11.3649i	−0.279026	+	0.483287i
$554$	−6.12311	+	10.6055i	−0.260146	+	0.450586i
$555$		0			0
$556$	5.90388	−	10.2258i	0.250380	−	0.433672i
$557$	−18.3348	−	31.7567i	−0.776868	−	1.34558i	−0.933738	−	0.357956i	$-0.883474\pi$
$557$	−18.3348	−	31.7567i	−0.776868	−	1.34558i	0.156870	−	0.987619i	$-0.449860\pi$
$558$	3.50758			0.148488
$559$	10.2462			0.433369
$560$		0			0
$561$	2.43845	+	4.22351i	0.102951	+	0.178317i
$562$	−16.3693			−0.690498
$563$	32.3002			1.36129			0.680645	−	0.732613i	$-0.261700\pi$
$563$	32.3002			1.36129			0.680645	+	0.732613i	$0.261700\pi$
$564$	−8.68466	−	15.0423i	−0.365690	−	0.633394i
$565$		0			0
$566$	−11.7808	−	20.4049i	−0.495183	−	0.857682i
$567$	−15.9654	+	27.6529i	−0.670485	+	1.16131i
$568$	0.123106	−	0.213225i	0.00516540	−	0.00894673i
$569$	34.1771			1.43278			0.716389	−	0.697701i	$-0.245794\pi$
$569$	34.1771			1.43278			0.716389	+	0.697701i	$0.245794\pi$
$570$		0			0
$571$	15.8078			0.661534			0.330767	−	0.943712i	$-0.392693\pi$
$571$	15.8078			0.661534			0.330767	+	0.943712i	$0.392693\pi$
$572$	−1.00000	+	1.73205i	−0.0418121	+	0.0724207i
$573$	15.1231	−	26.1940i	0.631777	−	1.09427i
$574$	4.84233	+	8.38716i	0.202115	+	0.350073i
$575$		0			0
$576$	0.280776	+	0.486319i	0.0116990	+	0.0202633i
$577$	28.6847			1.19416			0.597079	−	0.802182i	$-0.296328\pi$
$577$	28.6847			1.19416			0.597079	+	0.802182i	$0.296328\pi$
$578$	−7.24621			−0.301403
$579$	12.1922	+	21.1176i	0.506692	+	0.877616i
$580$		0			0
$581$	44.7386			1.85607
$582$	−16.6847			−0.691601
$583$	−1.71922	−	2.97778i	−0.0712030	−	0.123327i
$584$	5.34233	−	9.25319i	0.221067	−	0.382900i
$585$		0			0
$586$	9.71922	−	16.8342i	0.401497	−	0.695414i
$587$	−11.3693	+	19.6922i	−0.469262	+	0.812786i	−0.999383	−	0.0351368i	$-0.988813\pi$
$587$	−11.3693	+	19.6922i	−0.469262	+	0.812786i	0.530121	+	0.847922i	$0.322147\pi$
$588$	−21.5616			−0.889183
$589$	15.6155	−	22.3034i	0.643427	−	0.918997i
$590$		0			0
$591$	−14.4924	+	25.1016i	−0.596139	+	1.03254i
$592$	3.84233	−	6.65511i	0.157919	−	0.273523i
$593$	−22.2732	−	38.5783i	−0.914651	−	1.58422i	−0.807412	−	0.589988i	$-0.799132\pi$
$593$	−22.2732	−	38.5783i	−0.914651	−	1.58422i	−0.107239	−	0.994233i	$-0.534201\pi$
$594$	−2.78078	+	4.81645i	−0.114097	+	0.197621i
$595$		0			0
$596$	16.0000			0.655386
$597$	17.3693			0.710879
$598$	7.68466	+	13.3102i	0.314249	+	0.544295i
$599$	−0.246211	−	0.426450i	−0.0100599	−	0.0174243i	0.860952	−	0.508687i	$-0.169869\pi$
$599$	−0.246211	−	0.426450i	−0.0100599	−	0.0174243i	−0.871012	+	0.491263i	$0.836536\pi$
$600$		0			0
$601$	−36.3693			−1.48354			−0.741768	−	0.670657i	$-0.766012\pi$
$601$	−36.3693			−1.48354			−0.741768	+	0.670657i	$0.766012\pi$
$602$	11.6847	+	20.2384i	0.476231	+	0.824857i
$603$	−3.80776	+	6.59524i	−0.155064	+	0.268579i
$604$	6.24621	+	10.8188i	0.254155	+	0.440209i
$605$		0			0
$606$	7.80776	−	13.5234i	0.317169	−	0.549352i
$607$	−30.8078			−1.25045			−0.625224	−	0.780445i	$-0.714993\pi$
$607$	−30.8078			−1.25045			−0.625224	+	0.780445i	$0.714993\pi$
$608$	4.34233	+	0.379706i	0.176105	+	0.0153991i
$609$	14.2462			0.577286
$610$		0			0
$611$	11.1231	−	19.2658i	0.449993	−	0.779410i
$612$	0.876894	+	1.51883i	0.0354464	+	0.0613949i
$613$	9.15767	−	15.8616i	0.369875	−	0.640642i	−0.619671	−	0.784862i	$-0.712734\pi$
$613$	9.15767	−	15.8616i	0.369875	−	0.640642i	0.989546	+	0.144220i	$0.0460672\pi$
$614$	2.46543	+	4.27026i	0.0994969	+	0.172334i
$615$		0			0
$616$	−4.56155			−0.183790
$617$	13.9039	+	24.0822i	0.559749	+	0.969514i	0.997517	+	0.0704260i	$0.0224359\pi$
$617$	13.9039	+	24.0822i	0.559749	+	0.969514i	−0.437768	+	0.899088i	$0.644231\pi$
$618$	−11.5616	−	20.0252i	−0.465074	−	0.805532i
$619$	−11.0540			−0.444297			−0.222148	−	0.975013i	$-0.571307\pi$
$619$	−11.0540			−0.444297			−0.222148	+	0.975013i	$0.571307\pi$
$620$		0			0
$621$	21.3693	+	37.0127i	0.857521	+	1.48527i
$622$	−2.00000	+	3.46410i	−0.0801927	+	0.138898i
$623$	22.0885	+	38.2585i	0.884959	+	1.53279i
$624$	1.56155	−	2.70469i	0.0625121	−	0.108274i
$625$		0			0
$626$	−16.6847			−0.666853
$627$	2.87689	+	6.16879i	0.114892	+	0.246358i
$628$	−6.56155			−0.261834
$629$	12.0000	−	20.7846i	0.478471	−	0.828737i
$630$		0			0
$631$	6.12311	+	10.6055i	0.243757	+	0.422199i	0.961781	−	0.273818i	$-0.0882867\pi$
$631$	6.12311	+	10.6055i	0.243757	+	0.422199i	−0.718024	+	0.696018i	$0.754953\pi$
$632$	1.43845	−	2.49146i	0.0572184	−	0.0991051i
$633$	−12.2462	−	21.2111i	−0.486743	−	0.843064i
$634$	−6.31534			−0.250814
$635$		0			0
$636$	2.68466	+	4.64996i	0.106454	+	0.184383i
$637$	−13.8078	−	23.9157i	−0.547084	−	0.947576i
$638$	2.00000			0.0791808
$639$	0.138261			0.00546951
$640$		0			0
$641$	−5.78078	+	10.0126i	−0.228327	+	0.395474i	−0.957312	−	0.289055i	$-0.906659\pi$
$641$	−5.78078	+	10.0126i	−0.228327	+	0.395474i	0.728985	+	0.684529i	$0.239992\pi$
$642$	11.1231	+	19.2658i	0.438994	+	0.760360i
$643$	−9.21922	+	15.9682i	−0.363571	+	0.629723i	−0.988546	−	0.150922i	$-0.951776\pi$
$643$	−9.21922	+	15.9682i	−0.363571	+	0.629723i	0.624975	+	0.780645i	$0.285109\pi$
$644$	−17.5270	+	30.3576i	−0.690660	+	1.19626i
$645$		0			0
$646$	13.5616	+	1.18586i	0.533572	+	0.0466572i
$647$	42.1771			1.65815			0.829076	−	0.559136i	$-0.188867\pi$
$647$	42.1771			1.65815			0.829076	+	0.559136i	$0.188867\pi$
$648$	3.50000	−	6.06218i	0.137493	−	0.238145i
$649$	−5.21922	+	9.03996i	−0.204872	+	0.354849i
$650$		0			0
$651$	22.2462	−	38.5316i	0.871898	−	1.51017i
$652$	−10.0270	−	17.3673i	−0.392687	−	0.680154i
$653$	33.9309			1.32782			0.663909	−	0.747814i	$-0.268896\pi$
$653$	33.9309			1.32782			0.663909	+	0.747814i	$0.268896\pi$
$654$	−3.50758			−0.137157
$655$		0			0
$656$	−1.06155	−	1.83866i	−0.0414467	−	0.0717877i
$657$	6.00000			0.234082
$658$	50.7386			1.97800
$659$	4.96543	+	8.60039i	0.193426	+	0.335023i	0.946383	−	0.323046i	$-0.104707\pi$
$659$	4.96543	+	8.60039i	0.193426	+	0.335023i	−0.752957	+	0.658069i	$0.771373\pi$
$660$		0			0
$661$	−8.93087	−	15.4687i	−0.347371	−	0.601663i	0.638411	−	0.769696i	$-0.279592\pi$
$661$	−8.93087	−	15.4687i	−0.347371	−	0.601663i	−0.985782	+	0.168032i	$0.946259\pi$
$662$	4.74621	−	8.22068i	0.184467	−	0.319506i
$663$	4.87689	−	8.44703i	0.189403	−	0.328055i
$664$	−9.80776			−0.380615
$665$		0			0
$666$	4.31534			0.167216
$667$	7.68466	−	13.3102i	0.297551	−	0.515374i
$668$	−5.84233	+	10.1192i	−0.226047	+	0.391524i
$669$	−18.4924	−	32.0298i	−0.714958	−	1.23834i
$670$		0			0
$671$	1.56155	+	2.70469i	0.0602831	+	0.104413i
$672$	7.12311			0.274780
$673$	28.1080			1.08348			0.541741	−	0.840546i	$-0.317765\pi$
$673$	28.1080			1.08348			0.541741	+	0.840546i	$0.317765\pi$
$674$	−8.02699	−	13.9032i	−0.309188	−	0.535529i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−22.1771			−0.852334			−0.426167	−	0.904644i	$-0.640136\pi$
$677$	−22.1771			−0.852334			−0.426167	+	0.904644i	$0.640136\pi$
$678$	−2.97301	−	5.14941i	−0.114178	−	0.197762i
$679$	24.3693	−	42.2089i	0.935209	−	1.61983i
$680$		0			0
$681$	6.97301	−	12.0776i	0.267206	−	0.462815i
$682$	3.12311	−	5.40938i	0.119590	−	0.207136i
$683$	−28.0000			−1.07139			−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000			−1.07139			−0.535695	+	0.844411i	$0.679950\pi$
$684$	1.03457	+	2.21837i	0.0395576	+	0.0848215i
$685$		0			0
$686$	15.5270	−	26.8935i	0.592823	−	1.02680i
$687$	16.4924	−	28.5657i	0.629225	−	1.08985i
$688$	−2.56155	−	4.43674i	−0.0976583	−	0.169149i
$689$	−3.43845	+	5.95557i	−0.130994	+	0.226889i
$690$		0			0
$691$	−49.9309			−1.89946			−0.949730	−	0.313070i	$-0.898642\pi$
$691$	−49.9309			−1.89946			−0.949730	+	0.313070i	$0.898642\pi$
$692$	−14.8078			−0.562907
$693$	−1.28078	−	2.21837i	−0.0486527	−	0.0842689i
$694$	−5.34233	−	9.25319i	−0.202792	−	0.351246i
$695$		0			0
$696$	−3.12311			−0.118381
$697$	−3.31534	−	5.74234i	−0.125578	−	0.217507i
$698$	−1.12311	+	1.94528i	−0.0425102	+	0.0736298i
$699$	−11.4654	−	19.8587i	−0.433663	−	0.751126i
$700$		0			0
$701$	13.2462	−	22.9431i	0.500302	−	0.866549i	−0.499697	−	0.866200i	$-0.666555\pi$
$701$	13.2462	−	22.9431i	0.500302	−	0.866549i	1.00000		0.000349325i	$-0.000111194\pi$
$702$	11.1231			0.419815
$703$	19.2116	−	27.4397i	0.724581	−	1.03491i
$704$	1.00000			0.0376889
$705$		0			0
$706$	−10.5885	+	18.3399i	−0.398505	+	0.690231i
$707$	22.8078	+	39.5042i	0.857774	+	1.48571i
$708$	8.15009	−	14.1164i	0.306299	−	0.530526i
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	0.947282	+	0.320400i	$0.103817\pi$
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	−0.196167	+	0.980571i	$0.562849\pi$
$710$		0			0
$711$	1.61553			0.0605870
$712$	−4.84233	−	8.38716i	−0.181474	−	0.314322i
$713$	−24.0000	−	41.5692i	−0.898807	−	1.55678i
$714$	22.2462			0.832544
$715$		0			0
$716$	10.7462	+	18.6130i	0.401605	+	0.695600i
$717$	1.36932	−	2.37173i	0.0511381	−	0.0885737i
$718$	−3.43845	−	5.95557i	−0.128322	−	0.222260i
$719$	−11.5616	+	20.0252i	−0.431173	+	0.746814i	−0.996975	−	0.0777277i	$-0.975234\pi$
$719$	−11.5616	+	20.0252i	−0.431173	+	0.746814i	0.565801	+	0.824542i	$0.308567\pi$
$720$		0			0
$721$	67.5464			2.51556
$722$	18.7116	+	3.29762i	0.696375	+	0.122725i
$723$	6.93087			0.257762
$724$	1.68466	−	2.91791i	0.0626098	−	0.108443i
$725$		0			0
$726$	−7.80776	−	13.5234i	−0.289773	−	0.501902i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	4.56155	+	7.90084i	0.169062	+	0.292825i
$729$	29.9848			1.11055
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−2.43845	−	4.22351i	−0.0901276	−	0.156106i
$733$	−1.93087			−0.0713183			−0.0356591	−	0.999364i	$-0.511353\pi$
$733$	−1.93087			−0.0713183			−0.0356591	+	0.999364i	$0.511353\pi$
$734$	34.2462			1.26405
$735$		0			0
$736$	3.84233	−	6.65511i	0.141630	−	0.245311i
$737$	6.78078	+	11.7446i	0.249773	+	0.432620i
$738$	0.596118	−	1.03251i	0.0219434	−	0.0380071i
$739$	−17.6231	+	30.5241i	−0.648276	+	1.12285i	0.335258	+	0.942126i	$0.391177\pi$
$739$	−17.6231	+	30.5241i	−0.648276	+	1.12285i	−0.983534	+	0.180721i	$0.942157\pi$
$740$		0			0
$741$	7.80776	−	11.1517i	0.286825	−	0.409669i
$742$	−15.6847			−0.575802
$743$	−11.2808	+	19.5389i	−0.413852	+	0.716812i	−0.995307	−	0.0967662i	$-0.969150\pi$
$743$	−11.2808	+	19.5389i	−0.413852	+	0.716812i	0.581456	+	0.813578i	$0.302483\pi$
$744$	−4.87689	+	8.44703i	−0.178796	+	0.309683i
$745$		0			0
$746$	−7.59612	+	13.1569i	−0.278114	+	0.481707i
$747$	−2.75379	−	4.76970i	−0.100756	−	0.174514i
$748$	3.12311			0.114192
$749$	−64.9848			−2.37449
$750$		0			0
$751$	21.5616	+	37.3457i	0.786792	+	1.36276i	0.927923	+	0.372773i	$0.121593\pi$
$751$	21.5616	+	37.3457i	0.786792	+	1.36276i	−0.141130	+	0.989991i	$0.545074\pi$
$752$	−11.1231			−0.405618
$753$	4.57671			0.166785
$754$	−2.00000	−	3.46410i	−0.0728357	−	0.126155i
$755$		0			0
$756$	12.6847	+	21.9705i	0.461337	+	0.799058i
$757$	−7.71922	+	13.3701i	−0.280560	+	0.485944i	−0.971523	−	0.236946i	$-0.923853\pi$
$757$	−7.71922	+	13.3701i	−0.280560	+	0.485944i	0.690963	+	0.722890i	$0.257187\pi$
$758$	−16.2462	+	28.1393i	−0.590089	+	1.02206i
$759$	12.0000			0.435572
$760$		0			0
$761$	13.9848			0.506950			0.253475	−	0.967342i	$-0.418426\pi$
$761$	13.9848			0.506950			0.253475	+	0.967342i	$0.418426\pi$
$762$	8.93087	−	15.4687i	0.323531	−	0.560373i
$763$	5.12311	−	8.87348i	0.185469	−	0.321242i
$764$	−9.68466	−	16.7743i	−0.350379	−	0.606874i
$765$		0			0
$766$	−1.56155	−	2.70469i	−0.0564212	−	0.0977244i
$767$	20.8769			0.753821
$768$	−1.56155			−0.0563477
$769$	3.24621	+	5.62260i	0.117061	+	0.202756i	0.918602	−	0.395184i	$-0.129319\pi$
$769$	3.24621	+	5.62260i	0.117061	+	0.202756i	−0.801541	+	0.597940i	$0.795986\pi$
$770$		0			0
$771$	−37.5616			−1.35275
$772$	15.6155			0.562015
$773$	19.6501	+	34.0350i	0.706765	+	1.22415i	0.966051	+	0.258352i	$0.0831794\pi$
$773$	19.6501	+	34.0350i	0.706765	+	1.22415i	−0.259286	+	0.965801i	$0.583487\pi$
$774$	1.43845	−	2.49146i	0.0517039	−	0.0895538i
$775$		0			0
$776$	−5.34233	+	9.25319i	−0.191778	+	0.332170i
$777$	27.3693	−	47.4050i	0.981869	−	1.70065i
$778$	−10.8769			−0.389956
$779$	−3.91146	−	8.38716i	−0.140143	−	0.300501i
$780$		0			0
$781$	0.123106	−	0.213225i	0.00440507	−	0.00762980i
$782$	12.0000	−	20.7846i	0.429119	−	0.743256i
$783$	−5.56155	−	9.63289i	−0.198754	−	0.344251i
$784$	−6.90388	+	11.9579i	−0.246567	+	0.427067i
$785$		0			0
$786$	12.3002			0.438733
$787$	−4.43845			−0.158214			−0.0791068	−	0.996866i	$-0.525207\pi$
$787$	−4.43845			−0.158214			−0.0791068	+	0.996866i	$0.525207\pi$
$788$	9.28078	+	16.0748i	0.330614	+	0.572640i
$789$	17.8078	+	30.8440i	0.633973	+	1.09807i
$790$		0			0
$791$	17.3693			0.617582
$792$	0.280776	+	0.486319i	0.00997696	+	0.0172806i
$793$	3.12311	−	5.40938i	0.110905	−	0.192093i
$794$	−12.6501	−	21.9106i	−0.448935	−	0.777578i
$795$		0			0
$796$	5.56155	−	9.63289i	0.197124	−	0.341429i
$797$	24.8078			0.878736			0.439368	−	0.898307i	$-0.355202\pi$
$797$	24.8078			0.878736			0.439368	+	0.898307i	$0.355202\pi$
$798$	30.9309	+	2.70469i	1.09494	+	0.0957449i
$799$	−34.7386			−1.22896
$800$		0			0
$801$	2.71922	−	4.70983i	0.0960790	−	0.166414i
$802$	0.465435	+	0.806157i	0.0164351	+	0.0284664i
$803$	5.34233	−	9.25319i	0.188527	−	0.326538i
$804$	−10.5885	−	18.3399i	−0.373429	−	0.646798i
$805$		0			0
$806$	−12.4924			−0.440027
$807$	3.12311	+	5.40938i	0.109939	+	0.190419i
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	27.5616			0.969013			0.484506	−	0.874788i	$-0.338999\pi$
$809$	27.5616			0.969013			0.484506	+	0.874788i	$0.338999\pi$
$810$		0			0
$811$	−18.0885	−	31.3303i	−0.635175	−	1.10015i	−0.986478	−	0.163893i	$-0.947595\pi$
$811$	−18.0885	−	31.3303i	−0.635175	−	1.10015i	0.351304	−	0.936262i	$-0.385739\pi$
$812$	4.56155	−	7.90084i	0.160079	−	0.277265i
$813$	6.43845	+	11.1517i	0.225806	+	0.391108i
$814$	3.84233	−	6.65511i	0.134674	−	0.233261i
$815$		0			0
$816$	−4.87689			−0.170725
$817$	−9.43845	−	20.2384i	−0.330209	−	0.708053i
$818$	21.0000			0.734248
$819$	−2.56155	+	4.43674i	−0.0895079	+	0.155032i
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	7.46543	−	12.9305i	0.260387	−	0.451003i
$823$	9.08854	+	15.7418i	0.316807	+	0.548725i	0.979820	−	0.199883i	$-0.0640560\pi$
$823$	9.08854	+	15.7418i	0.316807	+	0.548725i	−0.663013	+	0.748608i	$0.730723\pi$
$824$	−14.8078			−0.515853
$825$		0			0
$826$	23.8078	+	41.2363i	0.828378	+	1.43479i
$827$	−1.53457	−	2.65794i	−0.0533621	−	0.0924258i	0.838110	−	0.545501i	$-0.183660\pi$
$827$	−1.53457	−	2.65794i	−0.0533621	−	0.0924258i	−0.891473	+	0.453075i	$0.850327\pi$
$828$	4.31534			0.149968
$829$	−22.7386			−0.789745			−0.394873	−	0.918736i	$-0.629211\pi$
$829$	−22.7386			−0.789745			−0.394873	+	0.918736i	$0.629211\pi$
$830$		0			0
$831$	9.56155	−	16.5611i	0.331687	−	0.574498i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−21.5616	+	37.3457i	−0.747064	+	1.29395i
$834$	−9.21922	+	15.9682i	−0.319236	+	0.552932i
$835$		0			0
$836$	4.34233	+	0.379706i	0.150183	+	0.0131324i
$837$	−34.7386			−1.20074
$838$	6.71922	−	11.6380i	0.232112	−	0.402029i
$839$	15.2462	−	26.4072i	0.526358	−	0.911678i	−0.473171	−	0.880971i	$-0.656891\pi$
$839$	15.2462	−	26.4072i	0.526358	−	0.911678i	0.999528	−	0.0307075i	$-0.00977603\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	0.246211	+	0.426450i	0.00848500	+	0.0146965i
$843$	25.5616			0.880387
$844$	−15.6847			−0.539888
$845$		0			0
$846$	−3.12311	−	5.40938i	−0.107375	−	0.185978i
$847$	45.6155			1.56737
$848$	3.43845			0.118077
$849$	18.3963	+	31.8633i	0.631360	+	1.09355i
$850$		0			0
$851$	−29.5270	−	51.1422i	−1.01217	−	1.75313i
$852$	−0.192236	+	0.332962i	−0.00658589	+	0.0114071i
$853$	−24.3693	+	42.2089i	−0.834390	+	1.44521i	0.0601370	+	0.998190i	$0.480846\pi$
$853$	−24.3693	+	42.2089i	−0.834390	+	1.44521i	−0.894527	+	0.447015i	$0.852487\pi$
$854$	14.2462			0.487495
$855$		0			0
$856$	14.2462			0.486925
$857$	−28.3963	+	49.1838i	−0.969999	+	1.68009i	−0.274462	+	0.961598i	$0.588500\pi$
$857$	−28.3963	+	49.1838i	−0.969999	+	1.68009i	−0.695537	+	0.718490i	$0.744834\pi$
$858$	1.56155	−	2.70469i	0.0533105	−	0.0923366i
$859$	−7.25379	−	12.5639i	−0.247496	−	0.428676i	0.715334	−	0.698782i	$-0.246274\pi$
$859$	−7.25379	−	12.5639i	−0.247496	−	0.428676i	−0.962830	+	0.270107i	$0.912941\pi$
$860$		0			0
$861$	−7.56155	−	13.0970i	−0.257697	−	0.446344i
$862$	17.3693			0.591601
$863$	1.30019			0.0442589			0.0221294	−	0.999755i	$-0.492955\pi$
$863$	1.30019			0.0442589			0.0221294	+	0.999755i	$0.492955\pi$
$864$	−2.78078	−	4.81645i	−0.0946039	−	0.163859i
$865$		0			0
$866$	−12.7386			−0.432876
$867$	11.3153			0.384289
$868$	−14.2462	−	24.6752i	−0.483548	−	0.837530i
$869$	1.43845	−	2.49146i	0.0487960	−	0.0845171i
$870$		0			0
$871$	13.5616	−	23.4893i	0.459516	−	0.795905i
$872$	−1.12311	+	1.94528i	−0.0380332	+	0.0658754i
$873$	−6.00000			−0.203069
$874$	19.2116	−	27.4397i	0.649844	−	0.928162i
$875$		0			0
$876$	−8.34233	+	14.4493i	−0.281861	+	0.488198i
$877$	−1.40388	+	2.43160i	−0.0474057	+	0.0821091i	−0.888755	−	0.458383i	$-0.848429\pi$
$877$	−1.40388	+	2.43160i	−0.0474057	+	0.0821091i	0.841349	+	0.540492i	$0.181762\pi$
$878$	−8.24621	−	14.2829i	−0.278296	−	0.482023i
$879$	−15.1771	+	26.2875i	−0.511910	+	0.886655i
$880$		0			0
$881$	−15.8769			−0.534906			−0.267453	−	0.963571i	$-0.586182\pi$
$881$	−15.8769			−0.534906			−0.267453	+	0.963571i	$0.586182\pi$
$882$	−7.75379			−0.261084
$883$	5.90388	+	10.2258i	0.198681	+	0.344126i	0.948101	−	0.317969i	$-0.103001\pi$
$883$	5.90388	+	10.2258i	0.198681	+	0.344126i	−0.749420	+	0.662095i	$0.769667\pi$
$884$	−3.12311	−	5.40938i	−0.105041	−	0.181937i
$885$		0			0
$886$	−5.06913			−0.170301
$887$	−4.87689	−	8.44703i	−0.163750	−	0.283623i	0.772461	−	0.635063i	$-0.219026\pi$
$887$	−4.87689	−	8.44703i	−0.163750	−	0.283623i	−0.936211	+	0.351439i	$0.885692\pi$
$888$	−6.00000	+	10.3923i	−0.201347	+	0.348743i
$889$	26.0885	+	45.1867i	0.874982	+	1.51551i
$890$		0			0
$891$	3.50000	−	6.06218i	0.117254	−	0.203091i
$892$	−23.6847			−0.793021
$893$	−48.3002	−	4.22351i	−1.61630	−	0.141335i
$894$	−24.9848			−0.835618
$895$		0			0
$896$	2.28078	−	3.95042i	0.0761954	−	0.131974i
$897$	−12.0000	−	20.7846i	−0.400668	−	0.693978i
$898$	−14.5000	+	25.1147i	−0.483871	+	0.838090i
$899$	6.24621	+	10.8188i	0.208323	+	0.360826i
$900$		0			0
$901$	10.7386			0.357756
$902$	−1.06155	−	1.83866i	−0.0353458	−	0.0612208i
$903$	−18.2462	−	31.6034i	−0.607196	−	1.05169i
$904$	−3.80776			−0.126644
$905$		0			0
$906$	−9.75379	−	16.8941i	−0.324048	−	0.561267i
$907$	−2.41146	+	4.17677i	−0.0800712	+	0.138687i	−0.903280	−	0.429051i	$-0.858848\pi$
$907$	−2.41146	+	4.17677i	−0.0800712	+	0.138687i	0.823209	+	0.567738i	$0.192181\pi$
$908$	−4.46543	−	7.73436i	−0.148191	−	0.256674i
$909$	2.80776	−	4.86319i	0.0931277	−	0.161302i
$910$		0			0
$911$	53.6155			1.77636			0.888181	−	0.459494i	$-0.151969\pi$
$911$	53.6155			1.77636			0.888181	+	0.459494i	$0.151969\pi$
$912$	−6.78078	−	0.592932i	−0.224534	−	0.0196339i
$913$	−9.80776			−0.324590
$914$	−15.0270	+	26.0275i	−0.497049	+	0.860913i
$915$		0			0
$916$	−10.5616	−	18.2931i	−0.348964	−	0.604423i
$917$	−17.9654	+	31.1170i	−0.593271	+	1.02758i
$918$	−8.68466	−	15.0423i	−0.286636	−	0.496469i
$919$	3.75379			0.123826			0.0619130	−	0.998082i	$-0.480280\pi$
$919$	3.75379			0.123826			0.0619130	+	0.998082i	$0.480280\pi$
$920$		0			0
$921$	−3.84991	−	6.66823i	−0.126859	−	0.219726i
$922$	−13.4924	−	23.3696i	−0.444349	−	0.769636i
$923$	−0.492423			−0.0162083
$924$	7.12311			0.234333
$925$		0			0
$926$	−7.71922	+	13.3701i	−0.253669	+	0.439368i
$927$	−4.15767	−	7.20130i	−0.136556	−	0.236522i
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	−14.9924	+	25.9676i	−0.491885	+	0.851971i	−0.999956	−	0.00934469i	$-0.997025\pi$
$929$	−14.9924	+	25.9676i	−0.491885	+	0.851971i	0.508071	+	0.861315i	$0.330359\pi$
$930$		0			0
$931$	−34.5194	+	49.3036i	−1.13133	+	1.61586i
$932$	−14.6847			−0.481012
$933$	3.12311	−	5.40938i	0.102246	−	0.177095i
$934$	6.21922	−	10.7720i	0.203499	−	0.352471i
$935$		0			0
$936$	0.561553	−	0.972638i	0.0183549	−	0.0317917i
$937$	−2.41146	−	4.17677i	−0.0787789	−	0.136449i	0.823944	−	0.566671i	$-0.191769\pi$
$937$	−2.41146	−	4.17677i	−0.0787789	−	0.136449i	−0.902723	+	0.430221i	$0.858435\pi$
$938$	61.8617			2.01986
$939$	26.0540			0.850239
$940$		0			0
$941$	−0.123106	−	0.213225i	−0.00401313	−	0.00695094i	0.864012	−	0.503471i	$-0.167944\pi$
$941$	−0.123106	−	0.213225i	−0.00401313	−	0.00695094i	−0.868025	+	0.496521i	$0.834611\pi$
$942$	10.2462			0.333840
$943$	−16.3153			−0.531301
$944$	−5.21922	−	9.03996i	−0.169871	−	0.294226i
$945$		0			0
$946$	−2.56155	−	4.43674i	−0.0832833	−	0.144251i
$947$	11.7538	−	20.3582i	0.381947	−	0.661551i	−0.609394	−	0.792868i	$-0.708587\pi$
$947$	11.7538	−	20.3582i	0.381947	−	0.661551i	0.991340	+	0.131317i	$0.0419204\pi$
$948$	−2.24621	+	3.89055i	−0.0729535	+	0.126359i
$949$	−21.3693			−0.693677
$950$		0			0
$951$	9.86174			0.319789
$952$	7.12311	−	12.3376i	0.230861	−	0.399863i
$953$	−1.65767	+	2.87117i	−0.0536972	+	0.0930063i	−0.891625	−	0.452775i	$-0.850434\pi$
$953$	−1.65767	+	2.87117i	−0.0536972	+	0.0930063i	0.837927	+	0.545782i	$0.183767\pi$
$954$	0.965435	+	1.67218i	0.0312571	+	0.0541389i
$955$		0			0
$956$	−0.876894	−	1.51883i	−0.0283608	−	0.0491223i
$957$	−3.12311			−0.100956
$958$	4.63068			0.149611
$959$	21.8078	+	37.7722i	0.704209	+	1.21973i
$960$		0			0
$961$	8.01515			0.258553
$962$	−15.3693			−0.495527
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$	2.21922	−	3.84381i	0.0714764	−	0.123801i
$965$		0			0
$966$	27.3693	−	47.4050i	0.880593	−	1.52523i
$967$	10.4384	−	18.0799i	0.335678	−	0.581411i	−0.647937	−	0.761694i	$-0.724368\pi$
$967$	10.4384	−	18.0799i	0.335678	−	0.581411i	0.983615	+	0.180283i	$0.0577013\pi$
$968$	−10.0000			−0.321412
$969$	−21.1771	−	1.85179i	−0.680306	−	0.0594880i
$970$		0			0
$971$	5.46543	−	9.46641i	0.175394	−	0.303792i	−0.764903	−	0.644145i	$-0.777213\pi$
$971$	5.46543	−	9.46641i	0.175394	−	0.303792i	0.940298	+	0.340353i	$0.110547\pi$
$972$	2.87689	−	4.98293i	0.0922764	−	0.159827i
$973$	−26.9309	−	46.6456i	−0.863364	−	1.49539i
$974$	10.9654	−	18.9927i	0.351355	−	0.608565i
$975$		0			0
$976$	−3.12311			−0.0999682
$977$	42.6847			1.36560			0.682802	−	0.730604i	$-0.260761\pi$
$977$	42.6847			1.36560			0.682802	+	0.730604i	$0.260761\pi$
$978$	15.6577	+	27.1199i	0.500677	+	0.867198i
$979$	−4.84233	−	8.38716i	−0.154762	−	0.268055i
$980$		0			0
$981$	−1.26137			−0.0402723
$982$	−18.0885	−	31.3303i	−0.577229	−	0.999789i
$983$	18.7192	−	32.4226i	0.597051	−	1.03412i	−0.396203	−	0.918163i	$-0.629673\pi$
$983$	18.7192	−	32.4226i	0.597051	−	1.03412i	0.993254	−	0.115959i	$-0.0369941\pi$
$984$	1.65767	+	2.87117i	0.0528446	+	0.0915296i
$985$		0			0
$986$	−3.12311	+	5.40938i	−0.0994599	+	0.172270i
$987$	−79.2311			−2.52195
$988$	−3.68466	−	7.90084i	−0.117225	−	0.251359i
$989$	−39.3693			−1.25187
$990$		0			0
$991$	24.8078	−	42.9683i	0.788045	−	1.36493i	−0.139119	−	0.990276i	$-0.544427\pi$
$991$	24.8078	−	42.9683i	0.788045	−	1.36493i	0.927163	−	0.374658i	$-0.122240\pi$
$992$	3.12311	+	5.40938i	0.0991587	+	0.171748i
$993$	−7.41146	+	12.8370i	−0.235196	+	0.407371i
$994$	−0.561553	−	0.972638i	−0.0178114	−	0.0308502i
$995$		0			0
$996$	15.3153			0.485285
$997$	4.84233	+	8.38716i	0.153358	+	0.265624i	0.932460	−	0.361273i	$-0.117658\pi$
$997$	4.84233	+	8.38716i	0.153358	+	0.265624i	−0.779102	+	0.626897i	$0.784325\pi$
$998$	−14.5000	−	25.1147i	−0.458989	−	0.794993i
$999$	−42.7386			−1.35219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.h.201.2		4
5.2	odd	4		950.2.j.f.49.1		8
5.3	odd	4		950.2.j.f.49.4		8
5.4	even	2		190.2.e.c.11.1	✓	4
15.14	odd	2		1710.2.l.m.1531.2		4
19.7	even	3	inner	950.2.e.h.501.2		4
20.19	odd	2		1520.2.q.h.961.2		4
95.7	odd	12		950.2.j.f.349.4		8
95.49	even	6		3610.2.a.k.1.2		2
95.64	even	6		190.2.e.c.121.1	yes	4
95.83	odd	12		950.2.j.f.349.1		8
95.84	odd	6		3610.2.a.u.1.1		2
285.254	odd	6		1710.2.l.m.1261.2		4
380.159	odd	6		1520.2.q.h.881.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.c.11.1	✓	4	5.4	even	2
190.2.e.c.121.1	yes	4	95.64	even	6
950.2.e.h.201.2		4	1.1	even	1	trivial
950.2.e.h.501.2		4	19.7	even	3	inner
950.2.j.f.49.1		8	5.2	odd	4
950.2.j.f.49.4		8	5.3	odd	4
950.2.j.f.349.1		8	95.83	odd	12
950.2.j.f.349.4		8	95.7	odd	12
1520.2.q.h.881.2		4	380.159	odd	6
1520.2.q.h.961.2		4	20.19	odd	2
1710.2.l.m.1261.2		4	285.254	odd	6
1710.2.l.m.1531.2		4	15.14	odd	2
3610.2.a.k.1.2		2	95.49	even	6
3610.2.a.u.1.1		2	95.84	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.780776 - 1.35234i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{6} -4.56155 q^{7} +1.00000 q^{8} +(0.280776 + 0.486319i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.780776 - 1.35234i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{6} -4.56155 q^{7} +1.00000 q^{8} +(0.280776 + 0.486319i) q^{9} +1.00000 q^{11} -1.56155 q^{12} +(-1.00000 - 1.73205i) q^{13} +(2.28078 - 3.95042i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.56155 + 2.70469i) q^{17} -0.561553 q^{18} +(-2.50000 + 3.57071i) q^{19} +(-3.56155 + 6.16879i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(3.84233 + 6.65511i) q^{23} +(0.780776 - 1.35234i) q^{24} +2.00000 q^{26} +5.56155 q^{27} +(2.28078 + 3.95042i) q^{28} +(-1.00000 - 1.73205i) q^{29} -6.24621 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 - 1.35234i) q^{33} +(-1.56155 - 2.70469i) q^{34} +(0.280776 - 0.486319i) q^{36} -7.68466 q^{37} +(-1.84233 - 3.95042i) q^{38} -3.12311 q^{39} +(-1.06155 + 1.83866i) q^{41} +(-3.56155 - 6.16879i) q^{42} +(-2.56155 + 4.43674i) q^{43} +(-0.500000 - 0.866025i) q^{44} -7.68466 q^{46} +(5.56155 + 9.63289i) q^{47} +(0.780776 + 1.35234i) q^{48} +13.8078 q^{49} +(2.43845 + 4.22351i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-1.71922 - 2.97778i) q^{53} +(-2.78078 + 4.81645i) q^{54} -4.56155 q^{56} +(2.87689 + 6.16879i) q^{57} +2.00000 q^{58} +(-5.21922 + 9.03996i) q^{59} +(1.56155 + 2.70469i) q^{61} +(3.12311 - 5.40938i) q^{62} +(-1.28078 - 2.21837i) q^{63} +1.00000 q^{64} +(0.780776 + 1.35234i) q^{66} +(6.78078 + 11.7446i) q^{67} +3.12311 q^{68} +12.0000 q^{69} +(0.123106 - 0.213225i) q^{71} +(0.280776 + 0.486319i) q^{72} +(5.34233 - 9.25319i) q^{73} +(3.84233 - 6.65511i) q^{74} +(4.34233 + 0.379706i) q^{76} -4.56155 q^{77} +(1.56155 - 2.70469i) q^{78} +(1.43845 - 2.49146i) q^{79} +(3.50000 - 6.06218i) q^{81} +(-1.06155 - 1.83866i) q^{82} -9.80776 q^{83} +7.12311 q^{84} +(-2.56155 - 4.43674i) q^{86} -3.12311 q^{87} +1.00000 q^{88} +(-4.84233 - 8.38716i) q^{89} +(4.56155 + 7.90084i) q^{91} +(3.84233 - 6.65511i) q^{92} +(-4.87689 + 8.44703i) q^{93} -11.1231 q^{94} -1.56155 q^{96} +(-5.34233 + 9.25319i) q^{97} +(-6.90388 + 11.9579i) q^{98} +(0.280776 + 0.486319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 6 q^{21} - 2 q^{22} + 3 q^{23} - q^{24} + 8 q^{26} + 14 q^{27} + 5 q^{28} - 4 q^{29} + 8 q^{31} - 2 q^{32} - q^{33} + 2 q^{34} - 3 q^{36} - 6 q^{37} + 5 q^{38} + 4 q^{39} + 4 q^{41} - 6 q^{42} - 2 q^{43} - 2 q^{44} - 6 q^{46} + 14 q^{47} - q^{48} + 14 q^{49} + 18 q^{51} - 4 q^{52} - 11 q^{53} - 7 q^{54} - 10 q^{56} + 28 q^{57} + 8 q^{58} - 25 q^{59} - 2 q^{61} - 4 q^{62} - q^{63} + 4 q^{64} - q^{66} + 23 q^{67} - 4 q^{68} + 48 q^{69} - 16 q^{71} - 3 q^{72} + 9 q^{73} + 3 q^{74} + 5 q^{76} - 10 q^{77} - 2 q^{78} + 14 q^{79} + 14 q^{81} + 4 q^{82} + 2 q^{83} + 12 q^{84} - 2 q^{86} + 4 q^{87} + 4 q^{88} - 7 q^{89} + 10 q^{91} + 3 q^{92} - 36 q^{93} - 28 q^{94} + 2 q^{96} - 9 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9 + 4 * q^11 + 2 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 6 * q^21 - 2 * q^22 + 3 * q^23 - q^24 + 8 * q^26 + 14 * q^27 + 5 * q^28 - 4 * q^29 + 8 * q^31 - 2 * q^32 - q^33 + 2 * q^34 - 3 * q^36 - 6 * q^37 + 5 * q^38 + 4 * q^39 + 4 * q^41 - 6 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^46 + 14 * q^47 - q^48 + 14 * q^49 + 18 * q^51 - 4 * q^52 - 11 * q^53 - 7 * q^54 - 10 * q^56 + 28 * q^57 + 8 * q^58 - 25 * q^59 - 2 * q^61 - 4 * q^62 - q^63 + 4 * q^64 - q^66 + 23 * q^67 - 4 * q^68 + 48 * q^69 - 16 * q^71 - 3 * q^72 + 9 * q^73 + 3 * q^74 + 5 * q^76 - 10 * q^77 - 2 * q^78 + 14 * q^79 + 14 * q^81 + 4 * q^82 + 2 * q^83 + 12 * q^84 - 2 * q^86 + 4 * q^87 + 4 * q^88 - 7 * q^89 + 10 * q^91 + 3 * q^92 - 36 * q^93 - 28 * q^94 + 2 * q^96 - 9 * q^97 - 7 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more