LMFDB - Embedded newform 1950.2.z.p.1699.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1699.3
Root			$-2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.p.1849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.00656 + 0.581139i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.00656 + 0.581139i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000i q^{12} +(-3.60464 + 0.0811388i) q^{13} -1.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00656 + 0.581139i) q^{17} +1.00000i q^{18} +(2.58114 + 4.47066i) q^{19} -1.16228 q^{21} +(-0.866025 + 0.500000i) q^{22} +(1.87259 + 1.08114i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} +1.00000i q^{27} +(-1.00656 - 0.581139i) q^{28} +(-4.16228 + 7.20928i) q^{29} -0.837722 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.866025 + 0.500000i) q^{33} -1.16228 q^{34} +(-0.500000 + 0.866025i) q^{36} +(0.140537 + 0.0811388i) q^{37} +5.16228i q^{38} +(-3.16228 - 1.73205i) q^{39} +(0.581139 - 1.00656i) q^{41} +(-1.00656 - 0.581139i) q^{42} +(-2.73861 + 1.58114i) q^{43} -1.00000 q^{44} +(1.08114 + 1.87259i) q^{46} +6.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-2.82456 + 4.89227i) q^{49} -1.16228 q^{51} +(-1.87259 - 3.08114i) q^{52} -7.48683i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.581139 - 1.00656i) q^{56} +5.16228i q^{57} +(-7.20928 + 4.16228i) q^{58} +(5.00000 + 8.66025i) q^{59} +(0.0811388 + 0.140537i) q^{61} +(-0.725489 - 0.418861i) q^{62} +(-1.00656 - 0.581139i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(-1.00656 - 0.581139i) q^{68} +(1.08114 + 1.87259i) q^{69} +(-5.24342 - 9.08186i) q^{71} +(-0.866025 + 0.500000i) q^{72} -3.32456i q^{73} +(0.0811388 + 0.140537i) q^{74} +(-2.58114 + 4.47066i) q^{76} -1.16228i q^{77} +(-1.87259 - 3.08114i) q^{78} +13.4868 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.00656 - 0.581139i) q^{82} -9.00000i q^{83} +(-0.581139 - 1.00656i) q^{84} -3.16228 q^{86} +(-7.20928 + 4.16228i) q^{87} +(-0.866025 - 0.500000i) q^{88} +(-5.74342 + 9.94789i) q^{89} +(3.58114 - 2.17647i) q^{91} +2.16228i q^{92} +(-0.725489 - 0.418861i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(4.61120 - 2.66228i) q^{97} +(-4.89227 + 2.82456i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 4 q^{11} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 16 q^{21} - 4 q^{24} - 8 q^{29} - 32 q^{31} + 16 q^{34} - 4 q^{36} - 8 q^{41} - 8 q^{44} - 4 q^{46} + 28 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 40 q^{59} - 12 q^{61} - 8 q^{64} - 8 q^{66} - 4 q^{69} - 4 q^{71} - 12 q^{74} - 8 q^{76} + 32 q^{79} - 4 q^{81} + 8 q^{84} - 8 q^{89} + 16 q^{91} - 24 q^{94} - 8 q^{96} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 4 * q^11 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 16 * q^21 - 4 * q^24 - 8 * q^29 - 32 * q^31 + 16 * q^34 - 4 * q^36 - 8 * q^41 - 8 * q^44 - 4 * q^46 + 28 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 40 * q^59 - 12 * q^61 - 8 * q^64 - 8 * q^66 - 4 * q^69 - 4 * q^71 - 12 * q^74 - 8 * q^76 + 32 * q^79 - 4 * q^81 + 8 * q^84 - 8 * q^89 + 16 * q^91 - 24 * q^94 - 8 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−1.00656	+	0.581139i	−0.380445	+	0.219650i	−0.678012	−	0.735051i	$-0.737158\pi$
$7$	−1.00656	+	0.581139i	−0.380445	+	0.219650i	0.297567	+	0.954701i	$0.403825\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$			1.00000i			0.288675i
$13$	−3.60464	+	0.0811388i	−0.999747	+	0.0225039i
$13$	−3.60464	+	0.0811388i	−0.999747	+	0.0225039i
$14$	−1.16228			−0.310632
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00656	+	0.581139i	−0.244127	+	0.140947i	−0.617072	−	0.786907i	$-0.711681\pi$
$17$	−1.00656	+	0.581139i	−0.244127	+	0.140947i	0.372945	+	0.927853i	$0.378348\pi$
$18$			1.00000i			0.235702i
$19$	2.58114	+	4.47066i	0.592154	+	1.02564i	0.993942	+	0.109908i	$0.0350556\pi$
$19$	2.58114	+	4.47066i	0.592154	+	1.02564i	−0.401788	+	0.915733i	$0.631611\pi$
$20$		0			0
$21$	−1.16228			−0.253630
$22$	−0.866025	+	0.500000i	−0.184637	+	0.106600i
$23$	1.87259	+	1.08114i	0.390461	+	0.225433i	0.682360	−	0.731016i	$-0.260954\pi$
$23$	1.87259	+	1.08114i	0.390461	+	0.225433i	−0.291899	+	0.956449i	$0.594287\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−3.16228	−	1.73205i	−0.620174	−	0.339683i
$27$			1.00000i			0.192450i
$28$	−1.00656	−	0.581139i	−0.190222	−	0.109825i
$29$	−4.16228	+	7.20928i	−0.772916	+	1.33873i	0.163043	+	0.986619i	$0.447869\pi$
$29$	−4.16228	+	7.20928i	−0.772916	+	1.33873i	−0.935959	+	0.352110i	$0.885464\pi$
$30$		0			0
$31$	−0.837722			−0.150459			−0.0752297	−	0.997166i	$-0.523969\pi$
$31$	−0.837722			−0.150459			−0.0752297	+	0.997166i	$0.523969\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.866025	+	0.500000i	−0.150756	+	0.0870388i
$34$	−1.16228			−0.199329
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	0.140537	+	0.0811388i	0.0231041	+	0.0133391i	0.511508	−	0.859279i	$-0.329087\pi$
$37$	0.140537	+	0.0811388i	0.0231041	+	0.0133391i	−0.488403	+	0.872618i	$0.662421\pi$
$38$			5.16228i			0.837432i
$39$	−3.16228	−	1.73205i	−0.506370	−	0.277350i
$40$		0			0
$41$	0.581139	−	1.00656i	0.0907586	−	0.157199i	−0.817072	−	0.576536i	$-0.804404\pi$
$41$	0.581139	−	1.00656i	0.0907586	−	0.157199i	0.907831	+	0.419337i	$0.137737\pi$
$42$	−1.00656	−	0.581139i	−0.155316	−	0.0896717i
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	−0.694065	−	0.719913i	$-0.744182\pi$
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	0.276430	+	0.961034i	$0.410849\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	1.08114	+	1.87259i	0.159405	+	0.276098i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−2.82456	+	4.89227i	−0.403508	+	0.698896i
$50$		0			0
$51$	−1.16228			−0.162751
$52$	−1.87259	−	3.08114i	−0.259681	−	0.427277i
$53$		−	7.48683i		−	1.02840i	−0.857672	−	0.514198i	$-0.828090\pi$
$53$		−	7.48683i		−	1.02840i	0.857672	−	0.514198i	$-0.171910\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	−0.581139	−	1.00656i	−0.0776579	−	0.134508i
$57$			5.16228i			0.683760i
$58$	−7.20928	+	4.16228i	−0.946624	+	0.546534i
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	0.0811388	+	0.140537i	0.0103888	+	0.0179939i	0.871173	−	0.490976i	$-0.163360\pi$
$61$	0.0811388	+	0.140537i	0.0103888	+	0.0179939i	−0.860784	+	0.508970i	$0.830026\pi$
$62$	−0.725489	−	0.418861i	−0.0921372	−	0.0531954i
$63$	−1.00656	−	0.581139i	−0.126815	−	0.0732166i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.00000			−0.123091
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−1.00656	−	0.581139i	−0.122064	−	0.0704734i
$69$	1.08114	+	1.87259i	0.130154	+	0.225433i
$70$		0			0
$71$	−5.24342	−	9.08186i	−0.622279	−	1.07782i	−0.989060	−	0.147512i	$-0.952874\pi$
$71$	−5.24342	−	9.08186i	−0.622279	−	1.07782i	0.366781	−	0.930307i	$-0.380460\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$		−	3.32456i		−	0.389110i	−0.980892	−	0.194555i	$-0.937674\pi$
$73$		−	3.32456i		−	0.389110i	0.980892	−	0.194555i	$-0.0623262\pi$
$74$	0.0811388	+	0.140537i	0.00943220	+	0.0163370i
$75$		0			0
$76$	−2.58114	+	4.47066i	−0.296077	+	0.512820i
$77$		−	1.16228i		−	0.132454i
$78$	−1.87259	−	3.08114i	−0.212029	−	0.348870i
$79$	13.4868			1.51739			0.758694	−	0.651448i	$-0.225838\pi$
$79$	13.4868			1.51739			0.758694	+	0.651448i	$0.225838\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.00656	−	0.581139i	0.111156	−	0.0641760i
$83$		−	9.00000i		−	0.987878i	−0.869496	−	0.493939i	$-0.835557\pi$
$83$		−	9.00000i		−	0.987878i	0.869496	−	0.493939i	$-0.164443\pi$
$84$	−0.581139	−	1.00656i	−0.0634074	−	0.109825i
$85$		0			0
$86$	−3.16228			−0.340997
$87$	−7.20928	+	4.16228i	−0.772916	+	0.446243i
$88$	−0.866025	−	0.500000i	−0.0923186	−	0.0533002i
$89$	−5.74342	+	9.94789i	−0.608801	+	1.05447i	0.382637	+	0.923899i	$0.375016\pi$
$89$	−5.74342	+	9.94789i	−0.608801	+	1.05447i	−0.991438	+	0.130576i	$0.958317\pi$
$90$		0			0
$91$	3.58114	−	2.17647i	0.375405	−	0.228156i
$92$			2.16228i			0.225433i
$93$	−0.725489	−	0.418861i	−0.0752297	−	0.0434339i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	4.61120	−	2.66228i	0.468196	−	0.270313i	−0.247288	−	0.968942i	$-0.579539\pi$
$97$	4.61120	−	2.66228i	0.468196	−	0.270313i	0.715484	+	0.698629i	$0.246206\pi$
$98$	−4.89227	+	2.82456i	−0.494194	+	0.285323i
$99$	−1.00000			−0.100504
$100$		0			0
$101$	6.32456	−	10.9545i	0.629317	−	1.09001i	−0.358372	−	0.933579i	$-0.616668\pi$
$101$	6.32456	−	10.9545i	0.629317	−	1.09001i	0.987689	−	0.156430i	$-0.0499985\pi$
$102$	−1.00656	−	0.581139i	−0.0996645	−	0.0575413i
$103$		−	3.48683i		−	0.343568i	−0.985135	−	0.171784i	$-0.945047\pi$
$103$		−	3.48683i		−	0.343568i	0.985135	−	0.171784i	$-0.0549531\pi$
$104$	−0.0811388	−	3.60464i	−0.00795632	−	0.353464i
$105$		0			0
$106$	3.74342	−	6.48379i	0.363593	−	0.629761i
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	14.1623			1.35650			0.678250	−	0.734831i	$-0.262739\pi$
$109$	14.1623			1.35650			0.678250	+	0.734831i	$0.262739\pi$
$110$		0			0
$111$	0.0811388	+	0.140537i	0.00770136	+	0.0133391i
$112$		−	1.16228i		−	0.109825i
$113$	−4.91508	+	2.83772i	−0.462372	+	0.266950i	−0.713041	−	0.701122i	$-0.752683\pi$
$113$	−4.91508	+	2.83772i	−0.462372	+	0.266950i	0.250669	+	0.968073i	$0.419349\pi$
$114$	−2.58114	+	4.47066i	−0.241746	+	0.418716i
$115$		0			0
$116$	−8.32456			−0.772916
$117$	−1.87259	−	3.08114i	−0.173121	−	0.284851i
$118$			10.0000i			0.920575i
$119$	0.675445	−	1.16990i	0.0619179	−	0.107245i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$			0.162278i			0.0146919i
$123$	1.00656	−	0.581139i	0.0907586	−	0.0523995i
$124$	−0.418861	−	0.725489i	−0.0376148	−	0.0651508i
$125$		0			0
$126$	−0.581139	−	1.00656i	−0.0517720	−	0.0896717i
$127$	−10.6734	−	6.16228i	−0.947109	−	0.546814i	−0.0549274	−	0.998490i	$-0.517493\pi$
$127$	−10.6734	−	6.16228i	−0.947109	−	0.546814i	−0.892182	+	0.451677i	$0.850826\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−3.16228			−0.278423
$130$		0			0
$131$	−3.67544			−0.321125			−0.160563	−	0.987026i	$-0.551331\pi$
$131$	−3.67544			−0.321125			−0.160563	+	0.987026i	$0.551331\pi$
$132$	−0.866025	−	0.500000i	−0.0753778	−	0.0435194i
$133$	−5.19615	−	3.00000i	−0.450564	−	0.260133i
$134$		0			0
$135$		0			0
$136$	−0.581139	−	1.00656i	−0.0498322	−	0.0863120i
$137$	−7.49035	+	4.32456i	−0.639944	+	0.369472i	−0.784593	−	0.620011i	$-0.787128\pi$
$137$	−7.49035	+	4.32456i	−0.639944	+	0.369472i	0.144649	+	0.989483i	$0.453795\pi$
$138$			2.16228i			0.184065i
$139$	1.16228	+	2.01312i	0.0985831	+	0.170751i	0.911098	−	0.412189i	$-0.135236\pi$
$139$	1.16228	+	2.01312i	0.0985831	+	0.170751i	−0.812515	+	0.582940i	$0.801902\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		−	10.4868i		−	0.880035i
$143$	1.73205	−	3.16228i	0.144841	−	0.264443i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	1.66228	−	2.87915i	0.137571	−	0.238280i
$147$	−4.89227	+	2.82456i	−0.403508	+	0.232965i
$148$			0.162278i			0.0133391i
$149$	9.58114	+	16.5950i	0.784917	+	1.35952i	0.929048	+	0.369958i	$0.120628\pi$
$149$	9.58114	+	16.5950i	0.784917	+	1.35952i	−0.144131	+	0.989559i	$0.546039\pi$
$150$		0			0
$151$	9.48683			0.772028			0.386014	−	0.922493i	$-0.373852\pi$
$151$	9.48683			0.772028			0.386014	+	0.922493i	$0.373852\pi$
$152$	−4.47066	+	2.58114i	−0.362619	+	0.209358i
$153$	−1.00656	−	0.581139i	−0.0813757	−	0.0469823i
$154$	0.581139	−	1.00656i	0.0468295	−	0.0811111i
$155$		0			0
$156$	−0.0811388	−	3.60464i	−0.00649631	−	0.288602i
$157$		−	4.48683i		−	0.358088i	−0.983841	−	0.179044i	$-0.942700\pi$
$157$		−	4.48683i		−	0.358088i	0.983841	−	0.179044i	$-0.0573005\pi$
$158$	11.6799	+	6.74342i	0.929206	+	0.536477i
$159$	3.74342	−	6.48379i	0.296872	−	0.514198i
$160$		0			0
$161$	−2.51317			−0.198065
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−7.93477	+	4.58114i	−0.621499	+	0.358822i	−0.777452	−	0.628942i	$-0.783488\pi$
$163$	−7.93477	+	4.58114i	−0.621499	+	0.358822i	0.155954	+	0.987764i	$0.450155\pi$
$164$	1.16228			0.0907586
$165$		0			0
$166$	4.50000	−	7.79423i	0.349268	−	0.604949i
$167$	−3.88571	−	2.24342i	−0.300685	−	0.173601i	0.342065	−	0.939676i	$-0.388874\pi$
$167$	−3.88571	−	2.24342i	−0.300685	−	0.173601i	−0.642751	+	0.766075i	$0.722207\pi$
$168$		−	1.16228i		−	0.0896717i
$169$	12.9868	−	0.584952i	0.998987	−	0.0449963i
$170$		0			0
$171$	−2.58114	+	4.47066i	−0.197385	+	0.341880i
$172$	−2.73861	−	1.58114i	−0.208817	−	0.120561i
$173$	2.01312	−	1.16228i	0.153055	−	0.0883663i	−0.421517	−	0.906821i	$-0.638502\pi$
$173$	2.01312	−	1.16228i	0.153055	−	0.0883663i	0.574572	+	0.818454i	$0.305169\pi$
$174$	−8.32456			−0.631083
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$			10.0000i			0.751646i
$178$	−9.94789	+	5.74342i	−0.745626	+	0.430487i
$179$	6.82456	−	11.8205i	0.510091	−	0.883504i	−0.489840	−	0.871812i	$-0.662945\pi$
$179$	6.82456	−	11.8205i	0.510091	−	0.883504i	0.999932	−	0.0116918i	$-0.00372170\pi$
$180$		0			0
$181$	19.8377			1.47453			0.737263	−	0.675606i	$-0.236118\pi$
$181$	19.8377			1.47453			0.737263	+	0.675606i	$0.236118\pi$
$182$	4.18959	−	0.0943058i	0.310553	−	0.00699041i
$183$			0.162278i			0.0119959i
$184$	−1.08114	+	1.87259i	−0.0797026	+	0.138049i
$185$		0			0
$186$	−0.418861	−	0.725489i	−0.0307124	−	0.0531954i
$187$		−	1.16228i		−	0.0849942i
$188$	−5.19615	+	3.00000i	−0.378968	+	0.218797i
$189$	−0.581139	−	1.00656i	−0.0422716	−	0.0732166i
$190$		0			0
$191$	−6.24342	−	10.8139i	−0.451758	−	0.782467i	0.546738	−	0.837304i	$-0.315870\pi$
$191$	−6.24342	−	10.8139i	−0.451758	−	0.782467i	−0.998495	+	0.0548366i	$0.982536\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−2.87915	−	1.66228i	−0.207246	−	0.119653i	0.392785	−	0.919630i	$-0.371512\pi$
$193$	−2.87915	−	1.66228i	−0.207246	−	0.119653i	−0.600031	+	0.799977i	$0.704845\pi$
$194$	5.32456			0.382281
$195$		0			0
$196$	−5.64911			−0.403508
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$	−0.866025	−	0.500000i	−0.0615457	−	0.0355335i
$199$	−3.41886	−	5.92164i	−0.242357	−	0.419774i	0.719028	−	0.694981i	$-0.244587\pi$
$199$	−3.41886	−	5.92164i	−0.242357	−	0.419774i	−0.961385	+	0.275207i	$0.911254\pi$
$200$		0			0
$201$		0			0
$202$	10.9545	−	6.32456i	0.770752	−	0.444994i
$203$		−	9.67544i		−	0.679083i
$204$	−0.581139	−	1.00656i	−0.0406879	−	0.0704734i
$205$		0			0
$206$	1.74342	−	3.01969i	0.121470	−	0.210391i
$207$			2.16228i			0.150289i
$208$	1.73205	−	3.16228i	0.120096	−	0.219265i
$209$	−5.16228			−0.357082
$210$		0			0
$211$	9.58114	−	16.5950i	0.659593	−	1.14245i	−0.321128	−	0.947036i	$-0.604062\pi$
$211$	9.58114	−	16.5950i	0.659593	−	1.14245i	0.980721	−	0.195413i	$-0.0626046\pi$
$212$	6.48379	−	3.74342i	0.445308	−	0.257099i
$213$		−	10.4868i		−	0.718546i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	0.843219	−	0.486833i	0.0572415	−	0.0330484i
$218$	12.2649	+	7.08114i	0.830683	+	0.479595i
$219$	1.66228	−	2.87915i	0.112326	−	0.194555i
$220$		0			0
$221$	3.58114	−	2.17647i	0.240893	−	0.146405i
$222$			0.162278i			0.0108914i
$223$	12.8498	+	7.41886i	0.860489	+	0.496804i	0.864176	−	0.503190i	$-0.167840\pi$
$223$	12.8498	+	7.41886i	0.860489	+	0.496804i	−0.00368686	+	0.999993i	$0.501174\pi$
$224$	0.581139	−	1.00656i	0.0388290	−	0.0672538i
$225$		0			0
$226$	−5.67544			−0.377525
$227$	−2.87915	+	1.66228i	−0.191096	+	0.110329i	−0.592495	−	0.805574i	$-0.701857\pi$
$227$	−2.87915	+	1.66228i	−0.191096	+	0.110329i	0.401400	+	0.915903i	$0.368524\pi$
$228$	−4.47066	+	2.58114i	−0.296077	+	0.170940i
$229$	12.8114			0.846600			0.423300	−	0.905989i	$-0.360872\pi$
$229$	12.8114			0.846600			0.423300	+	0.905989i	$0.360872\pi$
$230$		0			0
$231$	0.581139	−	1.00656i	0.0382361	−	0.0662269i
$232$	−7.20928	−	4.16228i	−0.473312	−	0.273267i
$233$		−	10.3246i		−	0.676384i	−0.941077	−	0.338192i	$-0.890185\pi$
$233$		−	10.3246i		−	0.676384i	0.941077	−	0.338192i	$-0.109815\pi$
$234$	−0.0811388	−	3.60464i	−0.00530421	−	0.235643i
$235$		0			0
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$	11.6799	+	6.74342i	0.758694	+	0.438032i
$238$	1.16990	−	0.675445i	0.0758336	−	0.0437826i
$239$	−10.4868			−0.678337			−0.339168	−	0.940726i	$-0.610146\pi$
$239$	−10.4868			−0.678337			−0.339168	+	0.940726i	$0.610146\pi$
$240$		0			0
$241$	10.6491	+	18.4448i	0.685970	+	1.18813i	0.973131	+	0.230252i	$0.0739550\pi$
$241$	10.6491	+	18.4448i	0.685970	+	1.18813i	−0.287162	+	0.957882i	$0.592712\pi$
$242$			10.0000i			0.642824i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−0.0811388	+	0.140537i	−0.00519438	+	0.00899693i
$245$		0			0
$246$	1.16228			0.0741041
$247$	−9.66682	−	15.9057i	−0.615085	−	1.01206i
$248$		−	0.837722i		−	0.0531954i
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$		0			0
$251$	−0.175445	−	0.303879i	−0.0110740	−	0.0191807i	0.860435	−	0.509560i	$-0.170192\pi$
$251$	−0.175445	−	0.303879i	−0.0110740	−	0.0191807i	−0.871509	+	0.490379i	$0.836858\pi$
$252$		−	1.16228i		−	0.0732166i
$253$	−1.87259	+	1.08114i	−0.117729	+	0.0679706i
$254$	−6.16228	−	10.6734i	−0.386656	−	0.669707i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.17647	−	1.25658i	−0.135764	−	0.0783835i	0.430580	−	0.902553i	$-0.358309\pi$
$257$	−2.17647	−	1.25658i	−0.135764	−	0.0783835i	−0.566344	+	0.824169i	$0.691643\pi$
$258$	−2.73861	−	1.58114i	−0.170499	−	0.0984374i
$259$	−0.188612			−0.0117198
$260$		0			0
$261$	−8.32456			−0.515277
$262$	−3.18303	−	1.83772i	−0.196648	−	0.113535i
$263$	−3.60464	−	2.08114i	−0.222272	−	0.128329i	0.384730	−	0.923029i	$-0.374295\pi$
$263$	−3.60464	−	2.08114i	−0.222272	−	0.128329i	−0.607002	+	0.794701i	$0.707628\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$		0			0
$266$	−3.00000	−	5.19615i	−0.183942	−	0.318597i
$267$	−9.94789	+	5.74342i	−0.608801	+	0.351491i
$268$		0			0
$269$	−9.41886	−	16.3139i	−0.574278	−	0.994679i	−0.996120	−	0.0880093i	$-0.971949\pi$
$269$	−9.41886	−	16.3139i	−0.574278	−	0.994679i	0.421842	−	0.906670i	$-0.361384\pi$
$270$		0			0
$271$	−10.1623	+	17.6016i	−0.617314	+	1.06922i	0.372659	+	0.927968i	$0.378446\pi$
$271$	−10.1623	+	17.6016i	−0.617314	+	1.06922i	−0.989974	+	0.141252i	$0.954887\pi$
$272$		−	1.16228i		−	0.0704734i
$273$	4.18959	−	0.0943058i	0.253566	−	0.00570765i
$274$	−8.64911			−0.522512
$275$		0			0
$276$	−1.08114	+	1.87259i	−0.0650769	+	0.112717i
$277$	14.2780	−	8.24342i	0.857883	−	0.495299i	−0.00541989	−	0.999985i	$-0.501725\pi$
$277$	14.2780	−	8.24342i	0.857883	−	0.495299i	0.863303	+	0.504686i	$0.168392\pi$
$278$			2.32456i			0.139418i
$279$	−0.418861	−	0.725489i	−0.0250766	−	0.0434339i
$280$		0			0
$281$	17.1623			1.02382			0.511908	−	0.859040i	$-0.328939\pi$
$281$	17.1623			1.02382			0.511908	+	0.859040i	$0.328939\pi$
$282$	−5.19615	+	3.00000i	−0.309426	+	0.178647i
$283$	28.1116	+	16.2302i	1.67106	+	0.964788i	0.967045	+	0.254605i	$0.0819455\pi$
$283$	28.1116	+	16.2302i	1.67106	+	0.964788i	0.704017	+	0.710183i	$0.251388\pi$
$284$	5.24342	−	9.08186i	0.311140	−	0.538909i
$285$		0			0
$286$	3.08114	−	1.87259i	0.182192	−	0.110728i
$287$			1.35089i			0.0797405i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−7.82456	+	13.5525i	−0.460268	+	0.797207i
$290$		0			0
$291$	5.32456			0.312131
$292$	2.87915	−	1.66228i	0.168489	−	0.0972774i
$293$	−3.90852	+	2.25658i	−0.228338	+	0.131831i	−0.609805	−	0.792551i	$-0.708752\pi$
$293$	−3.90852	+	2.25658i	−0.228338	+	0.131831i	0.381467	+	0.924382i	$0.375419\pi$
$294$	−5.64911			−0.329463
$295$		0			0
$296$	−0.0811388	+	0.140537i	−0.00471610	+	0.00816852i
$297$	−0.866025	−	0.500000i	−0.0502519	−	0.0290129i
$298$			19.1623i			1.11004i
$299$	−6.83772	−	3.74517i	−0.395436	−	0.216589i
$300$		0			0
$301$	1.83772	−	3.18303i	0.105925	−	0.183467i
$302$	8.21584	+	4.74342i	0.472768	+	0.272953i
$303$	10.9545	−	6.32456i	0.629317	−	0.363336i
$304$	−5.16228			−0.296077
$305$		0			0
$306$	−0.581139	−	1.00656i	−0.0332215	−	0.0575413i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	1.00656	−	0.581139i	0.0573542	−	0.0331135i
$309$	1.74342	−	3.01969i	0.0991795	−	0.171784i
$310$		0			0
$311$	5.51317			0.312623			0.156312	−	0.987708i	$-0.450040\pi$
$311$	5.51317			0.312623			0.156312	+	0.987708i	$0.450040\pi$
$312$	1.73205	−	3.16228i	0.0980581	−	0.179029i
$313$			20.2982i			1.14732i	0.819092	+	0.573662i	$0.194478\pi$
$313$			20.2982i			1.14732i	−0.819092	+	0.573662i	$0.805522\pi$
$314$	2.24342	−	3.88571i	0.126603	−	0.219283i
$315$		0			0
$316$	6.74342	+	11.6799i	0.379347	+	0.657048i
$317$			13.8114i			0.775725i	0.921717	+	0.387862i	$0.126786\pi$
$317$			13.8114i			0.775725i	−0.921717	+	0.387862i	$0.873214\pi$
$318$	6.48379	−	3.74342i	0.363593	−	0.209920i
$319$	−4.16228	−	7.20928i	−0.233043	−	0.403642i
$320$		0			0
$321$	3.00000	+	5.19615i	0.167444	+	0.290021i
$322$	−2.17647	−	1.25658i	−0.121290	−	0.0700267i
$323$	−5.19615	−	3.00000i	−0.289122	−	0.166924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−9.16228			−0.507452
$327$	12.2649	+	7.08114i	0.678250	+	0.391588i
$328$	1.00656	+	0.581139i	0.0555781	+	0.0320880i
$329$	−3.48683	−	6.03937i	−0.192235	−	0.332961i
$330$		0			0
$331$	11.7434	+	20.3402i	0.645477	+	1.11800i	0.984191	+	0.177109i	$0.0566745\pi$
$331$	11.7434	+	20.3402i	0.645477	+	1.11800i	−0.338715	+	0.940889i	$0.609992\pi$
$332$	7.79423	−	4.50000i	0.427764	−	0.246970i
$333$			0.162278i			0.00889276i
$334$	−2.24342	−	3.88571i	−0.122754	−	0.212617i
$335$		0			0
$336$	0.581139	−	1.00656i	0.0317037	−	0.0549125i
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$	11.5394	+	5.98683i	0.627661	+	0.325641i
$339$	−5.67544			−0.308248
$340$		0			0
$341$	0.418861	−	0.725489i	0.0226826	−	0.0392874i
$342$	−4.47066	+	2.58114i	−0.241746	+	0.139572i
$343$		−	14.7018i		−	0.793821i
$344$	−1.58114	−	2.73861i	−0.0852493	−	0.147656i
$345$		0			0
$346$	2.32456			0.124969
$347$	−27.1279	+	15.6623i	−1.45630	+	0.840795i	−0.998827	−	0.0484283i	$-0.984579\pi$
$347$	−27.1279	+	15.6623i	−1.45630	+	0.840795i	−0.457473	+	0.889223i	$0.651245\pi$
$348$	−7.20928	−	4.16228i	−0.386458	−	0.223122i
$349$	−0.918861	+	1.59151i	−0.0491855	+	0.0851918i	−0.889570	−	0.456799i	$-0.848996\pi$
$349$	−0.918861	+	1.59151i	−0.0491855	+	0.0851918i	0.840384	+	0.541991i	$0.182329\pi$
$350$		0			0
$351$	−0.0811388	−	3.60464i	−0.00433087	−	0.192401i
$352$		−	1.00000i		−	0.0533002i
$353$	11.3989	+	6.58114i	0.606700	+	0.350279i	0.771673	−	0.636019i	$-0.219420\pi$
$353$	11.3989	+	6.58114i	0.606700	+	0.350279i	−0.164973	+	0.986298i	$0.552754\pi$
$354$	−5.00000	+	8.66025i	−0.265747	+	0.460287i
$355$		0			0
$356$	−11.4868			−0.608801
$357$	1.16990	−	0.675445i	0.0619179	−	0.0357483i
$358$	11.8205	−	6.82456i	0.624732	−	0.360689i
$359$	−8.64911			−0.456483			−0.228241	−	0.973605i	$-0.573298\pi$
$359$	−8.64911			−0.456483			−0.228241	+	0.973605i	$0.573298\pi$
$360$		0			0
$361$	−3.82456	+	6.62432i	−0.201292	+	0.348649i
$362$	17.1800	+	9.91886i	0.902959	+	0.521324i
$363$			10.0000i			0.524864i
$364$	3.67544	+	2.01312i	0.192646	+	0.105516i
$365$		0			0
$366$	−0.0811388	+	0.140537i	−0.00424119	+	0.00734596i
$367$	15.5885	+	9.00000i	0.813711	+	0.469796i	0.848243	−	0.529607i	$-0.177661\pi$
$367$	15.5885	+	9.00000i	0.813711	+	0.469796i	−0.0345320	+	0.999404i	$0.510994\pi$
$368$	−1.87259	+	1.08114i	−0.0976154	+	0.0563583i
$369$	1.16228			0.0605058
$370$		0			0
$371$	4.35089	+	7.53596i	0.225887	+	0.391248i
$372$		−	0.837722i		−	0.0434339i
$373$	9.08186	−	5.24342i	0.470241	−	0.271494i	−0.246100	−	0.969245i	$-0.579149\pi$
$373$	9.08186	−	5.24342i	0.470241	−	0.271494i	0.716341	+	0.697751i	$0.245816\pi$
$374$	0.581139	−	1.00656i	0.0300500	−	0.0520481i
$375$		0			0
$376$	−6.00000			−0.309426
$377$	14.4186	−	26.3246i	0.742593	−	1.35578i
$378$		−	1.16228i		−	0.0597811i
$379$	17.6491	−	30.5692i	0.906574	−	1.57023i	0.0877835	−	0.996140i	$-0.472022\pi$
$379$	17.6491	−	30.5692i	0.906574	−	1.57023i	0.818790	−	0.574093i	$-0.194645\pi$
$380$		0			0
$381$	−6.16228	−	10.6734i	−0.315703	−	0.546814i
$382$		−	12.4868i		−	0.638882i
$383$	30.9908	−	17.8925i	1.58355	−	0.914265i	0.589219	−	0.807973i	$-0.299435\pi$
$383$	30.9908	−	17.8925i	1.58355	−	0.914265i	0.994335	−	0.106292i	$-0.0338979\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−1.66228	−	2.87915i	−0.0846077	−	0.146545i
$387$	−2.73861	−	1.58114i	−0.139212	−	0.0803738i
$388$	4.61120	+	2.66228i	0.234098	+	0.135157i
$389$	−32.9737			−1.67183			−0.835916	−	0.548858i	$-0.815063\pi$
$389$	−32.9737			−1.67183			−0.835916	+	0.548858i	$0.815063\pi$
$390$		0			0
$391$	−2.51317			−0.127096
$392$	−4.89227	−	2.82456i	−0.247097	−	0.142662i
$393$	−3.18303	−	1.83772i	−0.160563	−	0.0927008i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	17.6016	−	10.1623i	0.883398	−	0.510030i	0.0116207	−	0.999932i	$-0.496301\pi$
$397$	17.6016	−	10.1623i	0.883398	−	0.510030i	0.871777	+	0.489902i	$0.162968\pi$
$398$		−	6.83772i		−	0.342744i
$399$	−3.00000	−	5.19615i	−0.150188	−	0.260133i
$400$		0			0
$401$	−16.8114	+	29.1182i	−0.839521	+	1.45409i	0.0507753	+	0.998710i	$0.483831\pi$
$401$	−16.8114	+	29.1182i	−0.839521	+	1.45409i	−0.890296	+	0.455382i	$0.849503\pi$
$402$		0			0
$403$	3.01969	−	0.0679718i	0.150421	−	0.00338592i
$404$	12.6491			0.629317
$405$		0			0
$406$	4.83772	−	8.37918i	0.240092	−	0.415852i
$407$	−0.140537	+	0.0811388i	−0.00696614	+	0.00402190i
$408$		−	1.16228i		−	0.0575413i
$409$	8.83772	+	15.3074i	0.436997	+	0.756901i	0.997456	−	0.0712807i	$-0.0227086\pi$
$409$	8.83772	+	15.3074i	0.436997	+	0.756901i	−0.560459	+	0.828182i	$0.689375\pi$
$410$		0			0
$411$	−8.64911			−0.426629
$412$	3.01969	−	1.74342i	0.148769	−	0.0858920i
$413$	−10.0656	−	5.81139i	−0.495297	−	0.285960i
$414$	−1.08114	+	1.87259i	−0.0531351	+	0.0920326i
$415$		0			0
$416$	3.08114	−	1.87259i	0.151065	−	0.0918112i
$417$			2.32456i			0.113834i
$418$	−4.47066	−	2.58114i	−0.218667	−	0.126248i
$419$	−4.17544	+	7.23208i	−0.203984	+	0.353310i	−0.949808	−	0.312832i	$-0.898722\pi$
$419$	−4.17544	+	7.23208i	−0.203984	+	0.353310i	0.745825	+	0.666142i	$0.232056\pi$
$420$		0			0
$421$	−36.8114			−1.79408			−0.897039	−	0.441952i	$-0.854286\pi$
$421$	−36.8114			−1.79408			−0.897039	+	0.441952i	$0.854286\pi$
$422$	16.5950	−	9.58114i	0.807833	−	0.466403i
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$	7.48683			0.363593
$425$		0			0
$426$	5.24342	−	9.08186i	0.254044	−	0.440018i
$427$	−0.163343	−	0.0943058i	−0.00790470	−	0.00456378i
$428$			6.00000i			0.290021i
$429$	3.08114	−	1.87259i	0.148759	−	0.0904094i
$430$		0			0
$431$	0.243416	−	0.421610i	0.0117250	−	0.0203082i	−0.860103	−	0.510120i	$-0.829601\pi$
$431$	0.243416	−	0.421610i	0.0117250	−	0.0203082i	0.871828	+	0.489812i	$0.162934\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−5.17335	+	2.98683i	−0.248615	+	0.143538i	−0.619130	−	0.785289i	$-0.712515\pi$
$433$	−5.17335	+	2.98683i	−0.248615	+	0.143538i	0.370515	+	0.928827i	$0.379181\pi$
$434$	0.973666			0.0467375
$435$		0			0
$436$	7.08114	+	12.2649i	0.339125	+	0.587382i
$437$			11.1623i			0.533964i
$438$	2.87915	−	1.66228i	0.137571	−	0.0794267i
$439$	18.3246	−	31.7391i	0.874583	−	1.51482i	0.0173773	−	0.999849i	$-0.494468\pi$
$439$	18.3246	−	31.7391i	0.874583	−	1.51482i	0.857206	−	0.514974i	$-0.172198\pi$
$440$		0			0
$441$	−5.64911			−0.269005
$442$	4.18959	−	0.0943058i	0.199278	−	0.00448567i
$443$		−	31.6491i		−	1.50369i	−0.659337	−	0.751847i	$-0.729163\pi$
$443$		−	31.6491i		−	1.50369i	0.659337	−	0.751847i	$-0.270837\pi$
$444$	−0.0811388	+	0.140537i	−0.00385068	+	0.00666957i
$445$		0			0
$446$	7.41886	+	12.8498i	0.351293	+	0.608458i
$447$			19.1623i			0.906345i
$448$	1.00656	−	0.581139i	0.0475556	−	0.0274562i
$449$	4.25658	+	7.37262i	0.200881	+	0.347935i	0.948812	−	0.315840i	$-0.102286\pi$
$449$	4.25658	+	7.37262i	0.200881	+	0.347935i	−0.747932	+	0.663776i	$0.768953\pi$
$450$		0			0
$451$	0.581139	+	1.00656i	0.0273648	+	0.0473972i
$452$	−4.91508	−	2.83772i	−0.231186	−	0.133475i
$453$	8.21584	+	4.74342i	0.386014	+	0.222865i
$454$	−3.32456			−0.156029
$455$		0			0
$456$	−5.16228			−0.241746
$457$	29.7031	+	17.1491i	1.38945	+	0.802202i	0.993254	−	0.115963i	$-0.0369953\pi$
$457$	29.7031	+	17.1491i	1.38945	+	0.802202i	0.396200	+	0.918164i	$0.370329\pi$
$458$	11.0950	+	6.40569i	0.518435	+	0.299318i
$459$	−0.581139	−	1.00656i	−0.0271252	−	0.0469823i
$460$		0			0
$461$	14.2302	+	24.6475i	0.662769	+	1.14795i	0.979885	+	0.199563i	$0.0639521\pi$
$461$	14.2302	+	24.6475i	0.662769	+	1.14795i	−0.317116	+	0.948387i	$0.602715\pi$
$462$	1.00656	−	0.581139i	0.0468295	−	0.0270370i
$463$		−	3.81139i		−	0.177130i	−0.996070	−	0.0885651i	$-0.971772\pi$
$463$		−	3.81139i		−	0.177130i	0.996070	−	0.0885651i	$-0.0282281\pi$
$464$	−4.16228	−	7.20928i	−0.193229	−	0.334682i
$465$		0			0
$466$	5.16228	−	8.94133i	0.239138	−	0.414199i
$467$		−	10.3509i		−	0.478982i	−0.970899	−	0.239491i	$-0.923019\pi$
$467$		−	10.3509i		−	0.478982i	0.970899	−	0.239491i	$-0.0769806\pi$
$468$	1.73205	−	3.16228i	0.0800641	−	0.146176i
$469$		0			0
$470$		0			0
$471$	2.24342	−	3.88571i	0.103371	−	0.179044i
$472$	−8.66025	+	5.00000i	−0.398621	+	0.230144i
$473$		−	3.16228i		−	0.145402i
$474$	6.74342	+	11.6799i	0.309735	+	0.536477i
$475$		0			0
$476$	1.35089			0.0619179
$477$	6.48379	−	3.74342i	0.296872	−	0.171399i
$478$	−9.08186	−	5.24342i	−0.415395	−	0.239828i
$479$	3.16228	−	5.47723i	0.144488	−	0.250261i	−0.784694	−	0.619884i	$-0.787180\pi$
$479$	3.16228	−	5.47723i	0.144488	−	0.250261i	0.929182	+	0.369623i	$0.120513\pi$
$480$		0			0
$481$	−0.513167	−	0.281073i	−0.0233984	−	0.0128158i
$482$			21.2982i			0.970107i
$483$	−2.17647	−	1.25658i	−0.0990327	−	0.0571765i
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	27.2684	−	15.7434i	1.23565	−	0.713402i	0.267447	−	0.963573i	$-0.413820\pi$
$487$	27.2684	−	15.7434i	1.23565	−	0.713402i	0.968202	+	0.250170i	$0.0804866\pi$
$488$	−0.140537	+	0.0811388i	−0.00636179	+	0.00367298i
$489$	−9.16228			−0.414333
$490$		0			0
$491$	9.66228	−	16.7356i	0.436052	−	0.755265i	−0.561328	−	0.827593i	$-0.689710\pi$
$491$	9.66228	−	16.7356i	0.436052	−	0.755265i	0.997381	+	0.0723281i	$0.0230429\pi$
$492$	1.00656	+	0.581139i	0.0453793	+	0.0261998i
$493$		−	9.67544i		−	0.435760i
$494$	−0.418861	−	18.6081i	−0.0188455	−	0.837220i
$495$		0			0
$496$	0.418861	−	0.725489i	0.0188074	−	0.0325754i
$497$	10.5556	+	6.09431i	0.473485	+	0.273367i
$498$	7.79423	−	4.50000i	0.349268	−	0.201650i
$499$	−11.4868			−0.514221			−0.257111	−	0.966382i	$-0.582770\pi$
$499$	−11.4868			−0.514221			−0.257111	+	0.966382i	$0.582770\pi$
$500$		0			0
$501$	−2.24342	−	3.88571i	−0.100228	−	0.173601i
$502$		−	0.350889i		−	0.0156610i
$503$	−31.8796	+	18.4057i	−1.42144	+	0.820669i	−0.996422	−	0.0845152i	$-0.973066\pi$
$503$	−31.8796	+	18.4057i	−1.42144	+	0.820669i	−0.425019	+	0.905185i	$0.639733\pi$
$504$	0.581139	−	1.00656i	0.0258860	−	0.0448358i
$505$		0			0
$506$	−2.16228			−0.0961250
$507$	11.5394	+	5.98683i	0.512483	+	0.265885i
$508$		−	12.3246i		−	0.546814i
$509$	4.25658	−	7.37262i	0.188670	−	0.326786i	−0.756137	−	0.654413i	$-0.772916\pi$
$509$	4.25658	−	7.37262i	0.188670	−	0.326786i	0.944807	+	0.327628i	$0.106249\pi$
$510$		0			0
$511$	1.93203	+	3.34637i	0.0854679	+	0.148035i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.47066	+	2.58114i	−0.197385	+	0.113960i
$514$	−1.25658	−	2.17647i	−0.0554255	−	0.0959998i
$515$		0			0
$516$	−1.58114	−	2.73861i	−0.0696058	−	0.120561i
$517$	−5.19615	−	3.00000i	−0.228527	−	0.131940i
$518$	−0.163343	−	0.0943058i	−0.00717686	−	0.00414356i
$519$	2.32456			0.102037
$520$		0			0
$521$	−4.64911			−0.203681			−0.101841	−	0.994801i	$-0.532473\pi$
$521$	−4.64911			−0.203681			−0.101841	+	0.994801i	$0.532473\pi$
$522$	−7.20928	−	4.16228i	−0.315541	−	0.182178i
$523$	21.6278	+	12.4868i	0.945719	+	0.546011i	0.891748	−	0.452531i	$-0.149479\pi$
$523$	21.6278	+	12.4868i	0.945719	+	0.546011i	0.0539705	+	0.998543i	$0.482812\pi$
$524$	−1.83772	−	3.18303i	−0.0802813	−	0.139051i
$525$		0			0
$526$	−2.08114	−	3.60464i	−0.0907420	−	0.157170i
$527$	0.843219	−	0.486833i	0.0367312	−	0.0212068i
$528$		−	1.00000i		−	0.0435194i
$529$	−9.16228	−	15.8695i	−0.398360	−	0.689980i
$530$		0			0
$531$	−5.00000	+	8.66025i	−0.216982	+	0.375823i
$532$		−	6.00000i		−	0.260133i
$533$	−2.01312	+	3.67544i	−0.0871981	+	0.159201i
$534$	−11.4868			−0.497084
$535$		0			0
$536$		0			0
$537$	11.8205	−	6.82456i	0.510091	−	0.294501i
$538$		−	18.8377i		−	0.812152i
$539$	−2.82456	−	4.89227i	−0.121662	−	0.210725i
$540$		0			0
$541$	−1.51317			−0.0650561			−0.0325281	−	0.999471i	$-0.510356\pi$
$541$	−1.51317			−0.0650561			−0.0325281	+	0.999471i	$0.510356\pi$
$542$	−17.6016	+	10.1623i	−0.756053	+	0.436507i
$543$	17.1800	+	9.91886i	0.737263	+	0.425659i
$544$	0.581139	−	1.00656i	0.0249161	−	0.0431560i
$545$		0			0
$546$	3.67544	+	2.01312i	0.157295	+	0.0861538i
$547$			35.4868i			1.51731i	0.651494	+	0.758654i	$0.274143\pi$
$547$			35.4868i			1.51731i	−0.651494	+	0.758654i	$0.725857\pi$
$548$	−7.49035	−	4.32456i	−0.319972	−	0.184736i
$549$	−0.0811388	+	0.140537i	−0.00346292	+	0.00599795i
$550$		0			0
$551$	−42.9737			−1.83074
$552$	−1.87259	+	1.08114i	−0.0797026	+	0.0460163i
$553$	−13.5753	+	7.83772i	−0.577282	+	0.333294i
$554$	16.4868			0.700458
$555$		0			0
$556$	−1.16228	+	2.01312i	−0.0492916	+	0.0853755i
$557$	20.4579	+	11.8114i	0.866830	+	0.500465i	0.866294	−	0.499535i	$-0.166496\pi$
$557$	20.4579	+	11.8114i	0.866830	+	0.500465i	0.000536539		1.00000i	$0.499829\pi$
$558$		−	0.837722i		−	0.0354636i
$559$	9.74342	−	5.92164i	0.412103	−	0.250459i
$560$		0			0
$561$	0.581139	−	1.00656i	0.0245357	−	0.0424971i
$562$	14.8630	+	8.58114i	0.626956	+	0.361973i
$563$	3.44130	−	1.98683i	0.145033	−	0.0837350i	−0.425727	−	0.904851i	$-0.639982\pi$
$563$	3.44130	−	1.98683i	0.145033	−	0.0837350i	0.570761	+	0.821116i	$0.306648\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	16.2302	+	28.1116i	0.682208	+	1.18162i
$567$		−	1.16228i		−	0.0488111i
$568$	9.08186	−	5.24342i	0.381067	−	0.220009i
$569$	−5.16228	+	8.94133i	−0.216414	+	0.374840i	−0.953709	−	0.300731i	$-0.902769\pi$
$569$	−5.16228	+	8.94133i	−0.216414	+	0.374840i	0.737295	+	0.675571i	$0.236103\pi$
$570$		0			0
$571$	16.9737			0.710326			0.355163	−	0.934804i	$-0.384425\pi$
$571$	16.9737			0.710326			0.355163	+	0.934804i	$0.384425\pi$
$572$	3.60464	−	0.0811388i	0.150717	−	0.00339258i
$573$		−	12.4868i		−	0.521645i
$574$	−0.675445	+	1.16990i	−0.0281925	+	0.0488309i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	9.00000i		−	0.374675i	−0.982296	−	0.187337i	$-0.940014\pi$
$577$		−	9.00000i		−	0.374675i	0.982296	−	0.187337i	$-0.0599858\pi$
$578$	−13.5525	+	7.82456i	−0.563711	+	0.325459i
$579$	−1.66228	−	2.87915i	−0.0690819	−	0.119653i
$580$		0			0
$581$	5.23025	+	9.05906i	0.216987	+	0.375833i
$582$	4.61120	+	2.66228i	0.191140	+	0.110355i
$583$	6.48379	+	3.74342i	0.268531	+	0.155036i
$584$	3.32456			0.137571
$585$		0			0
$586$	−4.51317			−0.186437
$587$	−12.9904	−	7.50000i	−0.536170	−	0.309558i	0.207355	−	0.978266i	$-0.433514\pi$
$587$	−12.9904	−	7.50000i	−0.536170	−	0.309558i	−0.743525	+	0.668708i	$0.766848\pi$
$588$	−4.89227	−	2.82456i	−0.201754	−	0.116483i
$589$	−2.16228	−	3.74517i	−0.0890951	−	0.154317i
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−0.140537	+	0.0811388i	−0.00577602	+	0.00333479i
$593$			25.4868i			1.04662i	0.852143	+	0.523309i	$0.175303\pi$
$593$			25.4868i			1.04662i	−0.852143	+	0.523309i	$0.824697\pi$
$594$	−0.500000	−	0.866025i	−0.0205152	−	0.0355335i
$595$		0			0
$596$	−9.58114	+	16.5950i	−0.392459	+	0.679758i
$597$		−	6.83772i		−	0.279849i
$598$	−4.04905	−	6.66228i	−0.165578	−	0.272441i
$599$	−18.4868			−0.755352			−0.377676	−	0.925938i	$-0.623277\pi$
$599$	−18.4868			−0.755352			−0.377676	+	0.925938i	$0.623277\pi$
$600$		0			0
$601$	−1.64911	+	2.85634i	−0.0672686	+	0.116513i	−0.897698	−	0.440611i	$-0.854762\pi$
$601$	−1.64911	+	2.85634i	−0.0672686	+	0.116513i	0.830429	+	0.557124i	$0.188095\pi$
$602$	3.18303	−	1.83772i	0.129731	−	0.0749000i
$603$		0			0
$604$	4.74342	+	8.21584i	0.193007	+	0.334298i
$605$		0			0
$606$	12.6491			0.513835
$607$	−21.0657	+	12.1623i	−0.855030	+	0.493652i	−0.862345	−	0.506322i	$-0.831005\pi$
$607$	−21.0657	+	12.1623i	−0.855030	+	0.493652i	0.00731503	+	0.999973i	$0.497672\pi$
$608$	−4.47066	−	2.58114i	−0.181309	−	0.104679i
$609$	4.83772	−	8.37918i	0.196034	−	0.339542i
$610$		0			0
$611$	−0.486833	−	21.6278i	−0.0196952	−	0.874968i
$612$		−	1.16228i		−	0.0469823i
$613$	−12.9676	−	7.48683i	−0.523755	−	0.302390i	0.214714	−	0.976677i	$-0.431118\pi$
$613$	−12.9676	−	7.48683i	−0.523755	−	0.302390i	−0.738470	+	0.674287i	$0.764451\pi$
$614$		0			0
$615$		0			0
$616$	1.16228			0.0468295
$617$	25.9808	−	15.0000i	1.04595	−	0.603877i	0.124434	−	0.992228i	$-0.460288\pi$
$617$	25.9808	−	15.0000i	1.04595	−	0.603877i	0.921512	+	0.388351i	$0.126955\pi$
$618$	3.01969	−	1.74342i	0.121470	−	0.0701305i
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$		0			0
$621$	−1.08114	+	1.87259i	−0.0433846	+	0.0751443i
$622$	4.77454	+	2.75658i	0.191442	+	0.110529i
$623$		−	13.3509i		−	0.534892i
$624$	3.08114	−	1.87259i	0.123344	−	0.0749635i
$625$		0			0
$626$	−10.1491	+	17.5788i	−0.405640	+	0.702589i
$627$	−4.47066	−	2.58114i	−0.178541	−	0.103081i
$628$	3.88571	−	2.24342i	0.155057	−	0.0895221i
$629$	−0.188612			−0.00752044
$630$		0			0
$631$	−17.6491	−	30.5692i	−0.702600	−	1.21694i	−0.967551	−	0.252677i	$-0.918689\pi$
$631$	−17.6491	−	30.5692i	−0.702600	−	1.21694i	0.264951	−	0.964262i	$-0.414644\pi$
$632$			13.4868i			0.536477i
$633$	16.5950	−	9.58114i	0.659593	−	0.380816i
$634$	−6.90569	+	11.9610i	−0.274260	+	0.475033i
$635$		0			0
$636$	7.48683			0.296872
$637$	9.78455	−	17.8641i	0.387678	−	0.707800i
$638$		−	8.32456i		−	0.329572i
$639$	5.24342	−	9.08186i	0.207426	−	0.359273i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$			6.00000i			0.236801i
$643$	−22.1900	+	12.8114i	−0.875087	+	0.505232i	−0.869035	−	0.494750i	$-0.835260\pi$
$643$	−22.1900	+	12.8114i	−0.875087	+	0.505232i	−0.00605178	+	0.999982i	$0.501926\pi$
$644$	−1.25658	−	2.17647i	−0.0495163	−	0.0857648i
$645$		0			0
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	−32.4417	−	18.7302i	−1.27542	−	0.736362i	−0.299414	−	0.954123i	$-0.596791\pi$
$647$	−32.4417	−	18.7302i	−1.27542	−	0.736362i	−0.976002	+	0.217761i	$0.930125\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.0000			−0.392534
$650$		0			0
$651$	0.973666			0.0381610
$652$	−7.93477	−	4.58114i	−0.310749	−	0.179411i
$653$	−11.9610	−	6.90569i	−0.468071	−	0.270241i	0.247361	−	0.968923i	$-0.420437\pi$
$653$	−11.9610	−	6.90569i	−0.468071	−	0.270241i	−0.715432	+	0.698683i	$0.753770\pi$
$654$	7.08114	+	12.2649i	0.276894	+	0.479595i
$655$		0			0
$656$	0.581139	+	1.00656i	0.0226897	+	0.0392996i
$657$	2.87915	−	1.66228i	0.112326	−	0.0648516i
$658$		−	6.97367i		−	0.271862i
$659$	−16.8246	−	29.1410i	−0.655392	−	1.13517i	−0.981795	−	0.189941i	$-0.939170\pi$
$659$	−16.8246	−	29.1410i	−0.655392	−	1.13517i	0.326404	−	0.945230i	$-0.394163\pi$
$660$		0			0
$661$	1.32456	−	2.29420i	0.0515192	−	0.0892339i	−0.839116	−	0.543953i	$-0.816927\pi$
$661$	1.32456	−	2.29420i	0.0515192	−	0.0892339i	0.890635	+	0.454719i	$0.150260\pi$
$662$			23.4868i			0.912842i
$663$	4.18959	−	0.0943058i	0.162710	−	0.00366254i
$664$	9.00000			0.349268
$665$		0			0
$666$	−0.0811388	+	0.140537i	−0.00314407	+	0.00544568i
$667$	−15.5885	+	9.00000i	−0.603587	+	0.348481i
$668$		−	4.48683i		−	0.173601i
$669$	7.41886	+	12.8498i	0.286830	+	0.496804i
$670$		0			0
$671$	−0.162278			−0.00626466
$672$	1.00656	−	0.581139i	0.0388290	−	0.0224179i
$673$	34.3371	+	19.8246i	1.32360	+	0.764180i	0.984301	−	0.176498i	$-0.0564770\pi$
$673$	34.3371	+	19.8246i	1.32360	+	0.764180i	0.339298	+	0.940679i	$0.389810\pi$
$674$	16.0000	−	27.7128i	0.616297	−	1.06746i
$675$		0			0
$676$	7.00000	+	10.9545i	0.269231	+	0.421325i
$677$			15.3509i			0.589983i	0.955500	+	0.294991i	$0.0953168\pi$
$677$			15.3509i			0.589983i	−0.955500	+	0.294991i	$0.904683\pi$
$678$	−4.91508	−	2.83772i	−0.188762	−	0.108982i
$679$	−3.09431	+	5.35949i	−0.118749	+	0.205679i
$680$		0			0
$681$	−3.32456			−0.127397
$682$	0.725489	−	0.418861i	0.0277804	−	0.0160390i
$683$	−14.7224	+	8.50000i	−0.563338	+	0.325243i	−0.754484	−	0.656318i	$-0.772113\pi$
$683$	−14.7224	+	8.50000i	−0.563338	+	0.325243i	0.191146	+	0.981562i	$0.438780\pi$
$684$	−5.16228			−0.197385
$685$		0			0
$686$	7.35089	−	12.7321i	0.280658	−	0.486114i
$687$	11.0950	+	6.40569i	0.423300	+	0.244392i
$688$		−	3.16228i		−	0.120561i
$689$	0.607473	+	26.9873i	0.0231429	+	1.02814i
$690$		0			0
$691$	23.3246	−	40.3993i	0.887308	−	1.53686i	0.0442625	−	0.999020i	$-0.485906\pi$
$691$	23.3246	−	40.3993i	0.887308	−	1.53686i	0.843045	−	0.537842i	$-0.180760\pi$
$692$	2.01312	+	1.16228i	0.0765275	+	0.0441832i
$693$	1.00656	−	0.581139i	0.0382361	−	0.0220756i
$694$	−31.3246			−1.18906
$695$		0			0
$696$	−4.16228	−	7.20928i	−0.157771	−	0.273267i
$697$			1.35089i			0.0511686i
$698$	−1.59151	+	0.918861i	−0.0602397	+	0.0347794i
$699$	5.16228	−	8.94133i	0.195255	−	0.338192i
$700$		0			0
$701$	34.7851			1.31381			0.656907	−	0.753972i	$-0.271865\pi$
$701$	34.7851			1.31381			0.656907	+	0.753972i	$0.271865\pi$
$702$	1.73205	−	3.16228i	0.0653720	−	0.119352i
$703$			0.837722i			0.0315953i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	6.58114	+	11.3989i	0.247684	+	0.429002i
$707$			14.7018i			0.552917i
$708$	−8.66025	+	5.00000i	−0.325472	+	0.187912i
$709$	9.89253	+	17.1344i	0.371522	+	0.643494i	0.989800	−	0.142465i	$-0.0455028\pi$
$709$	9.89253	+	17.1344i	0.371522	+	0.643494i	−0.618278	+	0.785959i	$0.712169\pi$
$710$		0			0
$711$	6.74342	+	11.6799i	0.252898	+	0.438032i
$712$	−9.94789	−	5.74342i	−0.372813	−	0.215244i
$713$	−1.56871	−	0.905694i	−0.0587486	−	0.0339185i
$714$	1.35089			0.0505558
$715$		0			0
$716$	13.6491			0.510091
$717$	−9.08186	−	5.24342i	−0.339168	−	0.195819i
$718$	−7.49035	−	4.32456i	−0.279537	−	0.161391i
$719$	−2.75658	−	4.77454i	−0.102803	−	0.178060i	0.810035	−	0.586381i	$-0.199448\pi$
$719$	−2.75658	−	4.77454i	−0.102803	−	0.178060i	−0.912839	+	0.408321i	$0.866115\pi$
$720$		0			0
$721$	2.02633	+	3.50971i	0.0754646	+	0.130709i
$722$	−6.62432	+	3.82456i	−0.246532	+	0.142335i
$723$			21.2982i			0.792089i
$724$	9.91886	+	17.1800i	0.368632	+	0.638489i
$725$		0			0
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$			0.324555i			0.0120371i	0.999982	+	0.00601855i	$0.00191577\pi$
$727$			0.324555i			0.0120371i	−0.999982	+	0.00601855i	$0.998084\pi$
$728$	2.17647	+	3.58114i	0.0806652	+	0.132726i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.83772	−	3.18303i	0.0679706	−	0.117729i
$732$	−0.140537	+	0.0811388i	−0.00519438	+	0.00299898i
$733$		−	50.1096i		−	1.85084i	−0.378942	−	0.925420i	$-0.623712\pi$
$733$		−	50.1096i		−	1.85084i	0.378942	−	0.925420i	$-0.376288\pi$
$734$	9.00000	+	15.5885i	0.332196	+	0.575380i
$735$		0			0
$736$	−2.16228			−0.0797026
$737$		0			0
$738$	1.00656	+	0.581139i	0.0370521	+	0.0213920i
$739$	−19.3246	+	33.4711i	−0.710865	+	1.23125i	0.253667	+	0.967291i	$0.418363\pi$
$739$	−19.3246	+	33.4711i	−0.710865	+	1.23125i	−0.964533	+	0.263963i	$0.914970\pi$
$740$		0			0
$741$	−0.418861	−	18.6081i	−0.0153872	−	0.683587i
$742$			8.70178i			0.319452i
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	0.830197	−	0.557470i	$-0.188228\pi$
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	−0.0676840	+	0.997707i	$0.521561\pi$
$744$	0.418861	−	0.725489i	0.0153562	−	0.0265977i
$745$		0			0
$746$	10.4868			0.383950
$747$	7.79423	−	4.50000i	0.285176	−	0.164646i
$748$	1.00656	−	0.581139i	0.0368036	−	0.0212485i
$749$	−6.97367			−0.254812
$750$		0			0
$751$	−1.48683	+	2.57527i	−0.0542553	+	0.0939729i	−0.891877	−	0.452277i	$-0.850612\pi$
$751$	−1.48683	+	2.57527i	−0.0542553	+	0.0939729i	0.837622	+	0.546250i	$0.183945\pi$
$752$	−5.19615	−	3.00000i	−0.189484	−	0.109399i
$753$		−	0.350889i		−	0.0127871i
$754$	25.6491	−	15.5885i	0.934086	−	0.567698i
$755$		0			0
$756$	0.581139	−	1.00656i	0.0211358	−	0.0366083i
$757$	37.2163	+	21.4868i	1.35265	+	0.780952i	0.988620	−	0.150435i	$-0.0480675\pi$
$757$	37.2163	+	21.4868i	1.35265	+	0.780952i	0.364029	+	0.931388i	$0.381401\pi$
$758$	30.5692	−	17.6491i	1.11032	−	0.641045i
$759$	−2.16228			−0.0784857
$760$		0			0
$761$	21.5811	+	37.3796i	0.782316	+	1.35501i	0.930590	+	0.366064i	$0.119295\pi$
$761$	21.5811	+	37.3796i	0.782316	+	1.35501i	−0.148274	+	0.988946i	$0.547372\pi$
$762$		−	12.3246i		−	0.446472i
$763$	−14.2552	+	8.23025i	−0.516073	+	0.297955i
$764$	6.24342	−	10.8139i	0.225879	−	0.391234i
$765$		0			0
$766$	35.7851			1.29297
$767$	−18.7259	−	30.8114i	−0.676152	−	1.11253i
$768$		−	1.00000i		−	0.0360844i
$769$	−7.48683	+	12.9676i	−0.269982	+	0.467623i	−0.968857	−	0.247621i	$-0.920351\pi$
$769$	−7.48683	+	12.9676i	−0.269982	+	0.467623i	0.698875	+	0.715244i	$0.253684\pi$
$770$		0			0
$771$	−1.25658	−	2.17647i	−0.0452547	−	0.0783835i
$772$		−	3.32456i		−	0.119653i
$773$	−41.5236	+	23.9737i	−1.49350	+	0.862273i	−0.999972	−	0.00745699i	$-0.997626\pi$
$773$	−41.5236	+	23.9737i	−1.49350	+	0.862273i	−0.493528	+	0.869730i	$0.664293\pi$
$774$	−1.58114	−	2.73861i	−0.0568329	−	0.0984374i
$775$		0			0
$776$	2.66228	+	4.61120i	0.0955702	+	0.165532i
$777$	−0.163343	−	0.0943058i	−0.00585988	−	0.00338320i
$778$	−28.5560	−	16.4868i	−1.02378	−	0.591082i
$779$	6.00000			0.214972
$780$		0			0
$781$	10.4868			0.375248
$782$	−2.17647	−	1.25658i	−0.0778303	−	0.0449353i
$783$	−7.20928	−	4.16228i	−0.257639	−	0.148748i
$784$	−2.82456	−	4.89227i	−0.100877	−	0.174724i
$785$		0			0
$786$	−1.83772	−	3.18303i	−0.0655494	−	0.113535i
$787$	−22.9155	+	13.2302i	−0.816848	+	0.471607i	−0.849328	−	0.527865i	$-0.822993\pi$
$787$	−22.9155	+	13.2302i	−0.816848	+	0.471607i	0.0324803	+	0.999472i	$0.489659\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−2.08114	−	3.60464i	−0.0740905	−	0.128329i
$790$		0			0
$791$	3.29822	−	5.71269i	0.117271	−	0.203120i
$792$		−	1.00000i		−	0.0355335i
$793$	−0.303879	−	0.500000i	−0.0107911	−	0.0177555i
$794$	20.3246			0.721291
$795$		0			0
$796$	3.41886	−	5.92164i	0.121178	−	0.209887i
$797$	−21.9089	+	12.6491i	−0.776053	+	0.448054i	−0.835030	−	0.550205i	$-0.814550\pi$
$797$	−21.9089	+	12.6491i	−0.776053	+	0.448054i	0.0589766	+	0.998259i	$0.481216\pi$
$798$		−	6.00000i		−	0.212398i
$799$	−3.48683	−	6.03937i	−0.123355	−	0.213658i
$800$		0			0
$801$	−11.4868			−0.405867
$802$	−29.1182	+	16.8114i	−1.02820	+	0.593631i
$803$	2.87915	+	1.66228i	0.101603	+	0.0586605i
$804$		0			0
$805$		0			0
$806$	2.64911	+	1.45098i	0.0933109	+	0.0511085i
$807$		−	18.8377i		−	0.663119i
$808$	10.9545	+	6.32456i	0.385376	+	0.222497i
$809$	−11.4189	+	19.7780i	−0.401466	+	0.695359i	−0.993903	−	0.110257i	$-0.964832\pi$
$809$	−11.4189	+	19.7780i	−0.401466	+	0.695359i	0.592437	+	0.805617i	$0.298166\pi$
$810$		0			0
$811$	−46.6491			−1.63807			−0.819036	−	0.573742i	$-0.805491\pi$
$811$	−46.6491			−1.63807			−0.819036	+	0.573742i	$0.805491\pi$
$812$	8.37918	−	4.83772i	0.294052	−	0.169771i
$813$	−17.6016	+	10.1623i	−0.617314	+	0.356407i
$814$	−0.162278			−0.00568783
$815$		0			0
$816$	0.581139	−	1.00656i	0.0203439	−	0.0352367i
$817$	−14.1375	−	8.16228i	−0.494608	−	0.285562i
$818$			17.6754i			0.618007i
$819$	3.67544	+	2.01312i	0.128430	+	0.0703442i
$820$		0			0
$821$	−14.8114	+	25.6541i	−0.516921	+	0.895333i	0.482886	+	0.875683i	$0.339589\pi$
$821$	−14.8114	+	25.6541i	−0.516921	+	0.895333i	−0.999807	+	0.0196502i	$0.993745\pi$
$822$	−7.49035	−	4.32456i	−0.261256	−	0.150836i
$823$	−12.2877	+	7.09431i	−0.428322	+	0.247292i	−0.698632	−	0.715482i	$-0.746207\pi$
$823$	−12.2877	+	7.09431i	−0.428322	+	0.247292i	0.270309	+	0.962774i	$0.412874\pi$
$824$	3.48683			0.121470
$825$		0			0
$826$	−5.81139	−	10.0656i	−0.202204	−	0.350228i
$827$		−	21.9737i		−	0.764099i	−0.924142	−	0.382050i	$-0.875218\pi$
$827$		−	21.9737i		−	0.764099i	0.924142	−	0.382050i	$-0.124782\pi$
$828$	−1.87259	+	1.08114i	−0.0650769	+	0.0375722i
$829$	24.1623	−	41.8503i	0.839191	−	1.45352i	−0.0513817	−	0.998679i	$-0.516363\pi$
$829$	24.1623	−	41.8503i	0.839191	−	1.45352i	0.890572	−	0.454842i	$-0.150304\pi$
$830$		0			0
$831$	16.4868			0.571922
$832$	3.60464	−	0.0811388i	0.124968	−	0.00281298i
$833$		−	6.56584i		−	0.227493i
$834$	−1.16228	+	2.01312i	−0.0402464	+	0.0697088i
$835$		0			0
$836$	−2.58114	−	4.47066i	−0.0892706	−	0.154621i
$837$		−	0.837722i		−	0.0289559i
$838$	−7.23208	+	4.17544i	−0.249828	+	0.144238i
$839$	23.0811	+	39.9777i	0.796849	+	1.38018i	0.921658	+	0.388003i	$0.126835\pi$
$839$	23.0811	+	39.9777i	0.796849	+	1.38018i	−0.124809	+	0.992181i	$0.539832\pi$
$840$		0			0
$841$	−20.1491	−	34.8993i	−0.694797	−	1.20342i
$842$	−31.8796	−	18.4057i	−1.09864	−	0.634302i
$843$	14.8630	+	8.58114i	0.511908	+	0.295550i
$844$	19.1623			0.659593
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−10.0656	−	5.81139i	−0.345859	−	0.199682i
$848$	6.48379	+	3.74342i	0.222654	+	0.128549i
$849$	16.2302	+	28.1116i	0.557021	+	0.964788i
$850$		0			0
$851$	0.175445	+	0.303879i	0.00601417	+	0.0104168i
$852$	9.08186	−	5.24342i	0.311140	−	0.179636i
$853$			34.0000i			1.16414i	0.813139	+	0.582069i	$0.197757\pi$
$853$			34.0000i			1.16414i	−0.813139	+	0.582069i	$0.802243\pi$
$854$	−0.0943058	−	0.163343i	−0.00322708	−	0.00558947i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$		−	20.3246i		−	0.694274i	−0.937815	−	0.347137i	$-0.887154\pi$
$857$		−	20.3246i		−	0.694274i	0.937815	−	0.347137i	$-0.112846\pi$
$858$	3.60464	−	0.0811388i	0.123060	−	0.00277003i
$859$	−29.1623			−0.995004			−0.497502	−	0.867463i	$-0.665749\pi$
$859$	−29.1623			−0.995004			−0.497502	+	0.867463i	$0.665749\pi$
$860$		0			0
$861$	−0.675445	+	1.16990i	−0.0230191	+	0.0398702i
$862$	0.421610	−	0.243416i	0.0143601	−	0.00829080i
$863$			17.5132i			0.596155i	0.954542	+	0.298078i	$0.0963454\pi$
$863$			17.5132i			0.596155i	−0.954542	+	0.298078i	$0.903655\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−5.97367			−0.202993
$867$	−13.5525	+	7.82456i	−0.460268	+	0.265736i
$868$	0.843219	+	0.486833i	0.0286207	+	0.0165242i
$869$	−6.74342	+	11.6799i	−0.228755	+	0.396215i
$870$		0			0
$871$		0			0
$872$			14.1623i			0.479595i
$873$	4.61120	+	2.66228i	0.156065	+	0.0901044i
$874$	−5.58114	+	9.66682i	−0.188785	+	0.326985i
$875$		0			0
$876$	3.32456			0.112326
$877$	41.4287	−	23.9189i	1.39895	−	0.807683i	0.404665	−	0.914465i	$-0.367388\pi$
$877$	41.4287	−	23.9189i	1.39895	−	0.807683i	0.994282	+	0.106783i	$0.0340549\pi$
$878$	31.7391	−	18.3246i	1.07114	−	0.618424i
$879$	−4.51317			−0.152225
$880$		0			0
$881$	17.5811	−	30.4514i	0.592324	−	1.02593i	−0.401595	−	0.915817i	$-0.631544\pi$
$881$	17.5811	−	30.4514i	0.592324	−	1.02593i	0.993919	−	0.110117i	$-0.0351226\pi$
$882$	−4.89227	−	2.82456i	−0.164731	−	0.0951077i
$883$			4.64911i			0.156455i	0.996936	+	0.0782275i	$0.0249261\pi$
$883$			4.64911i			0.156455i	−0.996936	+	0.0782275i	$0.975074\pi$
$884$	3.67544	+	2.01312i	0.123619	+	0.0677087i
$885$		0			0
$886$	15.8246	−	27.4089i	0.531636	−	0.920821i
$887$	−32.3012	−	18.6491i	−1.08457	−	0.626176i	−0.152443	−	0.988312i	$-0.548714\pi$
$887$	−32.3012	−	18.6491i	−1.08457	−	0.626176i	−0.932125	+	0.362136i	$0.882047\pi$
$888$	−0.140537	+	0.0811388i	−0.00471610	+	0.00272284i
$889$	14.3246			0.480430
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$			14.8377i			0.496804i
$893$	−26.8240	+	15.4868i	−0.897630	+	0.518247i
$894$	−9.58114	+	16.5950i	−0.320441	+	0.555020i
$895$		0			0
$896$	1.16228			0.0388290
$897$	−4.04905	−	6.66228i	−0.135194	−	0.222447i
$898$			8.51317i			0.284088i
$899$	3.48683	−	6.03937i	0.116292	−	0.201424i
$900$		0			0
$901$	4.35089	+	7.53596i	0.144949	+	0.251059i
$902$			1.16228i			0.0386996i
$903$	3.18303	−	1.83772i	0.105925	−	0.0611556i
$904$	−2.83772	−	4.91508i	−0.0943812	−	0.163473i
$905$		0			0
$906$	4.74342	+	8.21584i	0.157589	+	0.272953i
$907$	−22.6344	−	13.0680i	−0.751563	−	0.433915i	0.0746956	−	0.997206i	$-0.476201\pi$
$907$	−22.6344	−	13.0680i	−0.751563	−	0.433915i	−0.826258	+	0.563291i	$0.809535\pi$
$908$	−2.87915	−	1.66228i	−0.0955479	−	0.0551646i
$909$	12.6491			0.419545
$910$		0			0
$911$	−52.1623			−1.72821			−0.864107	−	0.503309i	$-0.832116\pi$
$911$	−52.1623			−1.72821			−0.864107	+	0.503309i	$0.832116\pi$
$912$	−4.47066	−	2.58114i	−0.148038	−	0.0854700i
$913$	7.79423	+	4.50000i	0.257951	+	0.148928i
$914$	17.1491	+	29.7031i	0.567242	+	0.982492i
$915$		0			0
$916$	6.40569	+	11.0950i	0.211650	+	0.366589i
$917$	3.69956	−	2.13594i	0.122170	−	0.0705351i
$918$		−	1.16228i		−	0.0383609i
$919$	6.74342	+	11.6799i	0.222445	+	0.385286i	0.955550	−	0.294830i	$-0.0952630\pi$
$919$	6.74342	+	11.6799i	0.222445	+	0.385286i	−0.733105	+	0.680115i	$0.761930\pi$
$920$		0			0
$921$		0			0
$922$			28.4605i			0.937297i
$923$	19.6375	+	32.3114i	0.646377	+	1.06354i
$924$	1.16228			0.0382361
$925$		0			0
$926$	1.90569	−	3.30076i	0.0626250	−	0.108470i
$927$	3.01969	−	1.74342i	0.0991795	−	0.0572613i
$928$		−	8.32456i		−	0.273267i
$929$	10.3246	+	17.8827i	0.338738	+	0.586711i	0.984196	−	0.177085i	$-0.0566668\pi$
$929$	10.3246	+	17.8827i	0.338738	+	0.586711i	−0.645458	+	0.763796i	$0.723333\pi$
$930$		0			0
$931$	−29.1623			−0.955755
$932$	8.94133	−	5.16228i	0.292883	−	0.169096i
$933$	4.77454	+	2.75658i	0.156312	+	0.0902465i
$934$	5.17544	−	8.96413i	0.169346	−	0.293315i
$935$		0			0
$936$	3.08114	−	1.87259i	0.100710	−	0.0612074i
$937$			29.6491i			0.968594i	0.874904	+	0.484297i	$0.160925\pi$
$937$			29.6491i			0.968594i	−0.874904	+	0.484297i	$0.839075\pi$
$938$		0			0
$939$	−10.1491	+	17.5788i	−0.331204	+	0.573662i
$940$		0			0
$941$	4.64911			0.151557			0.0757783	−	0.997125i	$-0.475856\pi$
$941$	4.64911			0.151557			0.0757783	+	0.997125i	$0.475856\pi$
$942$	3.88571	−	2.24342i	0.126603	−	0.0730945i
$943$	2.17647	−	1.25658i	0.0708755	−	0.0409200i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	1.58114	−	2.73861i	0.0514073	−	0.0890400i
$947$	−31.9973	−	18.4737i	−1.03977	−	0.600313i	−0.120004	−	0.992773i	$-0.538291\pi$
$947$	−31.9973	−	18.4737i	−1.03977	−	0.600313i	−0.919769	+	0.392460i	$0.871624\pi$
$948$			13.4868i			0.438032i
$949$	0.269751	+	11.9838i	0.00875647	+	0.389011i
$950$		0			0
$951$	−6.90569	+	11.9610i	−0.223932	+	0.387862i
$952$	1.16990	+	0.675445i	0.0379168	+	0.0218913i
$953$	−50.0205	+	28.8794i	−1.62032	+	0.935494i	−0.633491	+	0.773750i	$0.718379\pi$
$953$	−50.0205	+	28.8794i	−1.62032	+	0.935494i	−0.986833	+	0.161744i	$0.948288\pi$
$954$	7.48683			0.242395
$955$		0			0
$956$	−5.24342	−	9.08186i	−0.169584	−	0.293728i
$957$		−	8.32456i		−	0.269095i
$958$	5.47723	−	3.16228i	0.176961	−	0.102169i
$959$	5.02633	−	8.70587i	0.162309	−	0.281127i
$960$		0			0
$961$	−30.2982			−0.977362
$962$	−0.303879	−	0.500000i	−0.00979746	−	0.0161206i
$963$			6.00000i			0.193347i
$964$	−10.6491	+	18.4448i	−0.342985	+	0.594067i
$965$		0			0
$966$	−1.25658	−	2.17647i	−0.0404299	−	0.0700267i
$967$			19.0263i			0.611846i	0.952056	+	0.305923i	$0.0989650\pi$
$967$			19.0263i			0.611846i	−0.952056	+	0.305923i	$0.901035\pi$
$968$	−8.66025	+	5.00000i	−0.278351	+	0.160706i
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$		0			0
$971$	−11.3246	−	19.6147i	−0.363422	−	0.629466i	0.625099	−	0.780545i	$-0.285058\pi$
$971$	−11.3246	−	19.6147i	−0.363422	−	0.629466i	−0.988522	+	0.151079i	$0.951725\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−2.33981	−	1.35089i	−0.0750108	−	0.0433075i
$974$	31.4868			1.00890
$975$		0			0
$976$	−0.162278			−0.00519438
$977$	−26.8240	−	15.4868i	−0.858175	−	0.495468i	0.00522559	−	0.999986i	$-0.498337\pi$
$977$	−26.8240	−	15.4868i	−0.858175	−	0.495468i	−0.863401	+	0.504519i	$0.831670\pi$
$978$	−7.93477	−	4.58114i	−0.253726	−	0.146489i
$979$	−5.74342	−	9.94789i	−0.183560	−	0.317936i
$980$		0			0
$981$	7.08114	+	12.2649i	0.226083	+	0.391588i
$982$	16.7356	−	9.66228i	0.534053	−	0.308336i
$983$		−	4.00000i		−	0.127580i	−0.997963	−	0.0637901i	$-0.979681\pi$
$983$		−	4.00000i		−	0.127580i	0.997963	−	0.0637901i	$-0.0203188\pi$
$984$	0.581139	+	1.00656i	0.0185260	+	0.0320880i
$985$		0			0
$986$	4.83772	−	8.37918i	0.154064	−	0.266847i
$987$		−	6.97367i		−	0.221974i
$988$	8.94133	−	16.3246i	0.284462	−	0.519353i
$989$	−6.83772			−0.217427
$990$		0			0
$991$	21.5548	−	37.3340i	0.684711	−	1.18595i	−0.288817	−	0.957384i	$-0.593262\pi$
$991$	21.5548	−	37.3340i	0.684711	−	1.18595i	0.973528	−	0.228570i	$-0.0734049\pi$
$992$	0.725489	−	0.418861i	0.0230343	−	0.0132989i
$993$			23.4868i			0.745332i
$994$	6.09431	+	10.5556i	0.193300	+	0.334805i
$995$		0			0
$996$	9.00000			0.285176
$997$	−53.3669	+	30.8114i	−1.69015	+	0.975806i	−0.735755	+	0.677248i	$0.763173\pi$
$997$	−53.3669	+	30.8114i	−1.69015	+	0.975806i	−0.954391	+	0.298559i	$0.903494\pi$
$998$	−9.94789	−	5.74342i	−0.314895	−	0.181805i
$999$	−0.0811388	+	0.140537i	−0.00256712	+	0.00444638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.p.1699.3		8
5.2	odd	4		1950.2.i.bc.451.1	✓	4
5.3	odd	4		1950.2.i.bd.451.2	yes	4
5.4	even	2	inner	1950.2.z.p.1699.2		8
13.3	even	3	inner	1950.2.z.p.1849.2		8
65.3	odd	12		1950.2.i.bd.601.2	yes	4
65.29	even	6	inner	1950.2.z.p.1849.3		8
65.42	odd	12		1950.2.i.bc.601.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.bc.451.1	✓	4	5.2	odd	4
1950.2.i.bc.601.1	yes	4	65.42	odd	12
1950.2.i.bd.451.2	yes	4	5.3	odd	4
1950.2.i.bd.601.2	yes	4	65.3	odd	12
1950.2.z.p.1699.2		8	5.4	even	2	inner
1950.2.z.p.1699.3		8	1.1	even	1	trivial
1950.2.z.p.1849.2		8	13.3	even	3	inner
1950.2.z.p.1849.3		8	65.29	even	6	inner

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.00656 + 0.581139i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.00656 + 0.581139i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000i q^{12} +(-3.60464 + 0.0811388i) q^{13} -1.16228 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.00656 + 0.581139i) q^{17} +1.00000i q^{18} +(2.58114 + 4.47066i) q^{19} -1.16228 q^{21} +(-0.866025 + 0.500000i) q^{22} +(1.87259 + 1.08114i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.16228 - 1.73205i) q^{26} +1.00000i q^{27} +(-1.00656 - 0.581139i) q^{28} +(-4.16228 + 7.20928i) q^{29} -0.837722 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.866025 + 0.500000i) q^{33} -1.16228 q^{34} +(-0.500000 + 0.866025i) q^{36} +(0.140537 + 0.0811388i) q^{37} +5.16228i q^{38} +(-3.16228 - 1.73205i) q^{39} +(0.581139 - 1.00656i) q^{41} +(-1.00656 - 0.581139i) q^{42} +(-2.73861 + 1.58114i) q^{43} -1.00000 q^{44} +(1.08114 + 1.87259i) q^{46} +6.00000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-2.82456 + 4.89227i) q^{49} -1.16228 q^{51} +(-1.87259 - 3.08114i) q^{52} -7.48683i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.581139 - 1.00656i) q^{56} +5.16228i q^{57} +(-7.20928 + 4.16228i) q^{58} +(5.00000 + 8.66025i) q^{59} +(0.0811388 + 0.140537i) q^{61} +(-0.725489 - 0.418861i) q^{62} +(-1.00656 - 0.581139i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(-1.00656 - 0.581139i) q^{68} +(1.08114 + 1.87259i) q^{69} +(-5.24342 - 9.08186i) q^{71} +(-0.866025 + 0.500000i) q^{72} -3.32456i q^{73} +(0.0811388 + 0.140537i) q^{74} +(-2.58114 + 4.47066i) q^{76} -1.16228i q^{77} +(-1.87259 - 3.08114i) q^{78} +13.4868 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.00656 - 0.581139i) q^{82} -9.00000i q^{83} +(-0.581139 - 1.00656i) q^{84} -3.16228 q^{86} +(-7.20928 + 4.16228i) q^{87} +(-0.866025 - 0.500000i) q^{88} +(-5.74342 + 9.94789i) q^{89} +(3.58114 - 2.17647i) q^{91} +2.16228i q^{92} +(-0.725489 - 0.418861i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(4.61120 - 2.66228i) q^{97} +(-4.89227 + 2.82456i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} + 4 q^{6} + 4 q^{9} - 4 q^{11} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 16 q^{21} - 4 q^{24} - 8 q^{29} - 32 q^{31} + 16 q^{34} - 4 q^{36} - 8 q^{41} - 8 q^{44} - 4 q^{46} + 28 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 40 q^{59} - 12 q^{61} - 8 q^{64} - 8 q^{66} - 4 q^{69} - 4 q^{71} - 12 q^{74} - 8 q^{76} + 32 q^{79} - 4 q^{81} + 8 q^{84} - 8 q^{89} + 16 q^{91} - 24 q^{94} - 8 q^{96} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^6 + 4 * q^9 - 4 * q^11 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 16 * q^21 - 4 * q^24 - 8 * q^29 - 32 * q^31 + 16 * q^34 - 4 * q^36 - 8 * q^41 - 8 * q^44 - 4 * q^46 + 28 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 40 * q^59 - 12 * q^61 - 8 * q^64 - 8 * q^66 - 4 * q^69 - 4 * q^71 - 12 * q^74 - 8 * q^76 + 32 * q^79 - 4 * q^81 + 8 * q^84 - 8 * q^89 + 16 * q^91 - 24 * q^94 - 8 * q^96 - 8 * q^99

Introduction

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