LMFDB - Embedded newform 1950.2.bc.g.901.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.4
Root			$-1.80668 + 1.80668i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.g.751.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.62926 + 2.67270i) q^{11} +1.00000 q^{12} +(3.60194 - 0.161290i) q^{13} +2.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(-3.48387 + 2.01141i) q^{19} -2.32258i q^{21} +(2.67270 + 4.62926i) q^{22} +(2.46797 - 4.27464i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.20002 + 1.66129i) q^{26} -1.00000 q^{27} +(2.01141 + 1.16129i) q^{28} +(-2.14539 + 3.71592i) q^{29} +3.47183i q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.62926 - 2.67270i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(2.72733 + 1.57463i) q^{37} -4.02283 q^{38} +(1.66129 - 3.20002i) q^{39} +(2.29078 + 1.32258i) q^{41} +(1.16129 - 2.01141i) q^{42} +(-6.12539 - 10.6095i) q^{43} +5.34541i q^{44} +(4.27464 - 2.46797i) q^{46} +1.81894i q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.802812 + 1.39051i) q^{49} -4.00000 q^{51} +(1.94065 + 3.03873i) q^{52} +5.48693 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.16129 + 2.01141i) q^{56} +4.02283i q^{57} +(-3.71592 + 2.14539i) q^{58} +(5.87744 - 3.39334i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(-1.73592 + 3.00670i) q^{62} +(-2.01141 - 1.16129i) q^{63} -1.00000 q^{64} +5.34541 q^{66} +(-3.55872 - 2.05463i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-2.46797 - 4.27464i) q^{69} +(13.7454 - 7.93593i) q^{71} +(0.866025 - 0.500000i) q^{72} +13.5734i q^{73} +(1.57463 + 2.72733i) q^{74} +(-3.48387 - 2.01141i) q^{76} +12.4151 q^{77} +(3.03873 - 1.94065i) q^{78} -7.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.32258 + 2.29078i) q^{82} +11.3360i q^{83} +(2.01141 - 1.16129i) q^{84} -12.2508i q^{86} +(2.14539 + 3.71592i) q^{87} +(-2.67270 + 4.62926i) q^{88} +(-1.50670 - 0.869891i) q^{89} +(7.05769 - 4.50732i) q^{91} +4.93593 q^{92} +(3.00670 + 1.73592i) q^{93} +(-0.909471 + 1.57525i) q^{94} +1.00000i q^{96} +(13.9510 - 8.05463i) q^{97} +(-1.39051 + 0.802812i) q^{98} -5.34541i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	2.01141	−	1.16129i	0.760243	−	0.438926i	−0.0691402	−	0.997607i	$-0.522026\pi$
$7$	2.01141	−	1.16129i	0.760243	−	0.438926i	0.829383	+	0.558681i	$0.188692\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.62926	+	2.67270i	1.39577	+	0.805850i	0.993946	−	0.109865i	$-0.0350420\pi$
$11$	4.62926	+	2.67270i	1.39577	+	0.805850i	0.401827	+	0.915716i	$0.368375\pi$
$12$	1.00000			0.288675
$13$	3.60194	−	0.161290i	0.998999	−	0.0447338i
$13$	3.60194	−	0.161290i	0.998999	−	0.0447338i
$14$	2.32258			0.620736
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.48387	+	2.01141i	−0.799254	+	0.461450i	−0.843210	−	0.537584i	$-0.819337\pi$
$19$	−3.48387	+	2.01141i	−0.799254	+	0.461450i	0.0439559	+	0.999033i	$0.486004\pi$
$20$		0			0
$21$		−	2.32258i		−	0.506828i
$22$	2.67270	+	4.62926i	0.569822	+	0.986961i
$23$	2.46797	−	4.27464i	0.514607	−	0.891325i	−0.485250	−	0.874376i	$-0.661271\pi$
$23$	2.46797	−	4.27464i	0.514607	−	0.891325i	0.999856	−	0.0169494i	$-0.00539541\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	3.20002	+	1.66129i	0.627575	+	0.325806i
$27$	−1.00000			−0.192450
$28$	2.01141	+	1.16129i	0.380121	+	0.219463i
$29$	−2.14539	+	3.71592i	−0.398388	+	0.690029i	−0.993527	−	0.113594i	$-0.963764\pi$
$29$	−2.14539	+	3.71592i	−0.398388	+	0.690029i	0.595139	+	0.803623i	$0.297097\pi$
$30$		0			0
$31$			3.47183i			0.623560i	0.950154	+	0.311780i	$0.100925\pi$
$31$			3.47183i			0.623560i	−0.950154	+	0.311780i	$0.899075\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	4.62926	−	2.67270i	0.805850	−	0.465258i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	2.72733	+	1.57463i	0.448371	+	0.258867i	0.707142	−	0.707072i	$-0.249984\pi$
$37$	2.72733	+	1.57463i	0.448371	+	0.258867i	−0.258771	+	0.965939i	$0.583318\pi$
$38$	−4.02283			−0.652589
$39$	1.66129	−	3.20002i	0.266019	−	0.512413i
$40$		0			0
$41$	2.29078	+	1.32258i	0.357759	+	0.206552i	0.668097	−	0.744074i	$-0.267109\pi$
$41$	2.29078	+	1.32258i	0.357759	+	0.206552i	−0.310338	+	0.950626i	$0.600442\pi$
$42$	1.16129	−	2.01141i	0.179191	−	0.310368i
$43$	−6.12539	−	10.6095i	−0.934113	−	1.61793i	−0.776207	−	0.630478i	$-0.782859\pi$
$43$	−6.12539	−	10.6095i	−0.934113	−	1.61793i	−0.157906	−	0.987454i	$-0.550474\pi$
$44$			5.34541i			0.805850i
$45$		0			0
$46$	4.27464	−	2.46797i	0.630262	−	0.363882i
$47$			1.81894i			0.265320i	0.991162	+	0.132660i	$0.0423518\pi$
$47$			1.81894i			0.265320i	−0.991162	+	0.132660i	$0.957648\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−0.802812	+	1.39051i	−0.114687	+	0.198644i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	1.94065	+	3.03873i	0.269120	+	0.421396i
$53$	5.48693			0.753687			0.376844	−	0.926277i	$-0.377009\pi$
$53$	5.48693			0.753687			0.376844	+	0.926277i	$0.377009\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	1.16129	+	2.01141i	0.155184	+	0.268786i
$57$			4.02283i			0.532836i
$58$	−3.71592	+	2.14539i	−0.487924	+	0.281703i
$59$	5.87744	−	3.39334i	0.765177	−	0.441775i	−0.0659742	−	0.997821i	$-0.521016\pi$
$59$	5.87744	−	3.39334i	0.765177	−	0.441775i	0.831152	+	0.556046i	$0.187682\pi$
$60$		0			0
$61$	−0.267949	−	0.464102i	−0.0343074	−	0.0594221i	0.848362	−	0.529417i	$-0.177589\pi$
$61$	−0.267949	−	0.464102i	−0.0343074	−	0.0594221i	−0.882669	+	0.469995i	$0.844256\pi$
$62$	−1.73592	+	3.00670i	−0.220462	+	0.381851i
$63$	−2.01141	−	1.16129i	−0.253414	−	0.146309i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.34541			0.657974
$67$	−3.55872	−	2.05463i	−0.434767	−	0.251013i	0.266608	−	0.963805i	$-0.414097\pi$
$67$	−3.55872	−	2.05463i	−0.434767	−	0.251013i	−0.701376	+	0.712792i	$0.747430\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	−2.46797	−	4.27464i	−0.297108	−	0.514607i
$70$		0			0
$71$	13.7454	−	7.93593i	1.63128	−	0.941822i	0.647586	−	0.761992i	$-0.275779\pi$
$71$	13.7454	−	7.93593i	1.63128	−	0.941822i	0.983698	−	0.179830i	$-0.0575547\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			13.5734i			1.58864i	0.607498	+	0.794321i	$0.292173\pi$
$73$			13.5734i			1.58864i	−0.607498	+	0.794321i	$0.707827\pi$
$74$	1.57463	+	2.72733i	0.183047	+	0.317046i
$75$		0			0
$76$	−3.48387	−	2.01141i	−0.399627	−	0.230725i
$77$	12.4151			1.41484
$78$	3.03873	−	1.94065i	0.344068	−	0.219736i
$79$	−7.96774			−0.896441			−0.448220	−	0.893923i	$-0.647942\pi$
$79$	−7.96774			−0.896441			−0.448220	+	0.893923i	$0.647942\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.32258	+	2.29078i	0.146054	+	0.252974i
$83$			11.3360i			1.24428i	0.782904	+	0.622142i	$0.213737\pi$
$83$			11.3360i			1.24428i	−0.782904	+	0.622142i	$0.786263\pi$
$84$	2.01141	−	1.16129i	0.219463	−	0.126707i
$85$		0			0
$86$		−	12.2508i		−	1.32104i
$87$	2.14539	+	3.71592i	0.230010	+	0.398388i
$88$	−2.67270	+	4.62926i	−0.284911	+	0.493480i
$89$	−1.50670	−	0.869891i	−0.159709	−	0.0922083i	0.418015	−	0.908440i	$-0.362726\pi$
$89$	−1.50670	−	0.869891i	−0.159709	−	0.0922083i	−0.577725	+	0.816232i	$0.696059\pi$
$90$		0			0
$91$	7.05769	−	4.50732i	0.739847	−	0.472495i
$92$	4.93593			0.514607
$93$	3.00670	+	1.73592i	0.311780	+	0.180006i
$94$	−0.909471	+	1.57525i	−0.0938048	+	0.162475i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	13.9510	−	8.05463i	1.41651	−	0.817824i	0.420522	−	0.907282i	$-0.361847\pi$
$97$	13.9510	−	8.05463i	1.41651	−	0.817824i	0.995991	+	0.0894586i	$0.0285137\pi$
$98$	−1.39051	+	0.802812i	−0.140463	+	0.0810962i
$99$		−	5.34541i		−	0.537233i
$100$		0			0
$101$	6.34541	−	10.9906i	0.631391	−	1.09360i	−0.355876	−	0.934533i	$-0.615817\pi$
$101$	6.34541	−	10.9906i	0.631391	−	1.09360i	0.987267	−	0.159069i	$-0.0508492\pi$
$102$	−3.46410	−	2.00000i	−0.342997	−	0.198030i
$103$	4.79612			0.472575			0.236288	−	0.971683i	$-0.424069\pi$
$103$	4.79612			0.472575			0.236288	+	0.971683i	$0.424069\pi$
$104$	0.161290	+	3.60194i	0.0158158	+	0.353199i
$105$		0			0
$106$	4.75182	+	2.74346i	0.461537	+	0.266469i
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	−0.782185	−	0.623046i	$-0.785895\pi$
$107$	1.53590	−	2.66025i	0.148481	−	0.257176i	0.930666	+	0.365869i	$0.119228\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	6.69081i		−	0.640864i	−0.947272	−	0.320432i	$-0.896172\pi$
$109$		−	6.69081i		−	0.640864i	0.947272	−	0.320432i	$-0.103828\pi$
$110$		0			0
$111$	2.72733	−	1.57463i	0.258867	−	0.149457i
$112$			2.32258i			0.219463i
$113$	−3.55486	−	6.15720i	−0.334413	−	0.579220i	0.648959	−	0.760823i	$-0.275205\pi$
$113$	−3.55486	−	6.15720i	−0.334413	−	0.579220i	−0.983372	+	0.181603i	$0.941871\pi$
$114$	−2.01141	+	3.48387i	−0.188386	+	0.326294i
$115$		0			0
$116$	−4.29078			−0.398388
$117$	−1.94065	−	3.03873i	−0.179413	−	0.280931i
$118$	6.78668			0.624765
$119$	−8.04565	−	4.64516i	−0.737544	−	0.425821i
$120$		0			0
$121$	8.78668	+	15.2190i	0.798789	+	1.38354i
$122$		−	0.535898i		−	0.0485180i
$123$	2.29078	−	1.32258i	0.206552	−	0.119253i
$124$	−3.00670	+	1.73592i	−0.270009	+	0.155890i
$125$		0			0
$126$	−1.16129	−	2.01141i	−0.103456	−	0.179191i
$127$	1.06604	−	1.84644i	0.0945961	−	0.163845i	−0.814844	−	0.579680i	$-0.803177\pi$
$127$	1.06604	−	1.84644i	0.0945961	−	0.163845i	0.909440	+	0.415835i	$0.136511\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−12.2508			−1.07862
$130$		0			0
$131$	1.25851			0.109957			0.0549785	−	0.998488i	$-0.482491\pi$
$131$	1.25851			0.109957			0.0549785	+	0.998488i	$0.482491\pi$
$132$	4.62926	+	2.67270i	0.402925	+	0.232629i
$133$	−4.67167	+	8.09156i	−0.405085	+	0.701628i
$134$	−2.05463	−	3.55872i	−0.177493	−	0.307427i
$135$		0			0
$136$	3.46410	−	2.00000i	0.297044	−	0.171499i
$137$	−17.0736	+	9.85744i	−1.45870	+	0.842178i	−0.998947	−	0.0458713i	$-0.985394\pi$
$137$	−17.0736	+	9.85744i	−1.45870	+	0.842178i	−0.459748	+	0.888049i	$0.652060\pi$
$138$		−	4.93593i		−	0.420175i
$139$	−2.83871	−	4.91679i	−0.240776	−	0.417037i	0.720159	−	0.693809i	$-0.244069\pi$
$139$	−2.83871	−	4.91679i	−0.240776	−	0.417037i	−0.960936	+	0.276772i	$0.910735\pi$
$140$		0			0
$141$	1.57525	+	0.909471i	0.132660	+	0.0765913i
$142$	15.8719			1.33194
$143$	17.1054	+	8.88027i	1.43043	+	0.742605i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−6.78668	+	11.7549i	−0.561670	+	0.972841i
$147$	0.802812	+	1.39051i	0.0662148	+	0.114687i
$148$			3.14925i			0.258867i
$149$	−16.8680	+	9.73875i	−1.38188	+	0.797829i	−0.992382	−	0.123198i	$-0.960685\pi$
$149$	−16.8680	+	9.73875i	−1.38188	+	0.797829i	−0.389499	+	0.921027i	$0.627352\pi$
$150$		0			0
$151$			14.5170i			1.18138i	0.806899	+	0.590690i	$0.201144\pi$
$151$			14.5170i			1.18138i	−0.806899	+	0.590690i	$0.798856\pi$
$152$	−2.01141	−	3.48387i	−0.163147	−	0.282579i
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	10.7518	+	6.20757i	0.866406	+	0.500220i
$155$		0			0
$156$	3.60194	−	0.161290i	0.288386	−	0.0129135i
$157$	−24.3829			−1.94596			−0.972982	−	0.230879i	$-0.925840\pi$
$157$	−24.3829			−1.94596			−0.972982	+	0.230879i	$0.925840\pi$
$158$	−6.90026	−	3.98387i	−0.548956	−	0.316940i
$159$	2.74346	−	4.75182i	0.217571	−	0.376844i
$160$		0			0
$161$		−	11.4641i		−	0.903498i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−20.4614	+	11.8134i	−1.60266	+	0.925295i	−0.611704	+	0.791086i	$0.709516\pi$
$163$	−20.4614	+	11.8134i	−1.60266	+	0.925295i	−0.990953	+	0.134208i	$0.957151\pi$
$164$			2.64516i			0.206552i
$165$		0			0
$166$	−5.66799	+	9.81724i	−0.439921	+	0.761966i
$167$	−14.5035	−	8.37357i	−1.12231	−	0.647967i	−0.180321	−	0.983608i	$-0.557714\pi$
$167$	−14.5035	−	8.37357i	−1.12231	−	0.647967i	−0.941990	+	0.335641i	$0.891047\pi$
$168$	2.32258			0.179191
$169$	12.9480	−	1.16191i	0.995998	−	0.0893780i
$170$		0			0
$171$	3.48387	+	2.01141i	0.266418	+	0.153817i
$172$	6.12539	−	10.6095i	0.467057	−	0.808966i
$173$	−8.06604	−	13.9708i	−0.613250	−	1.06218i	−0.990689	−	0.136146i	$-0.956529\pi$
$173$	−8.06604	−	13.9708i	−0.613250	−	1.06218i	0.377439	−	0.926034i	$-0.376805\pi$
$174$			4.29078i			0.325283i
$175$		0			0
$176$	−4.62926	+	2.67270i	−0.348943	+	0.201463i
$177$		−	6.78668i		−	0.510118i
$178$	−0.869891	−	1.50670i	−0.0652011	−	0.112932i
$179$	3.66412	−	6.34644i	0.273869	−	0.474355i	−0.695980	−	0.718061i	$-0.745030\pi$
$179$	3.66412	−	6.34644i	0.273869	−	0.474355i	0.969849	+	0.243706i	$0.0783631\pi$
$180$		0			0
$181$	−19.5734			−1.45488			−0.727438	−	0.686173i	$-0.759289\pi$
$181$	−19.5734			−1.45488			−0.727438	+	0.686173i	$0.759289\pi$
$182$	8.36580	−	0.374609i	0.620114	−	0.0277678i
$183$	−0.535898			−0.0396147
$184$	4.27464	+	2.46797i	0.315131	+	0.181941i
$185$		0			0
$186$	1.73592	+	3.00670i	0.127284	+	0.220462i
$187$		−	21.3816i		−	1.56358i
$188$	−1.57525	+	0.909471i	−0.114887	+	0.0663300i
$189$	−2.01141	+	1.16129i	−0.146309	+	0.0844714i
$190$		0			0
$191$	8.51873	+	14.7549i	0.616394	+	1.06763i	0.990138	+	0.140094i	$0.0447404\pi$
$191$	8.51873	+	14.7549i	0.616394	+	1.06763i	−0.373744	+	0.927532i	$0.621926\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−5.33031	−	3.07746i	−0.383684	−	0.221520i	0.295736	−	0.955270i	$-0.404435\pi$
$193$	−5.33031	−	3.07746i	−0.383684	−	0.221520i	−0.679420	+	0.733750i	$0.737769\pi$
$194$	16.1093			1.15658
$195$		0			0
$196$	−1.60562			−0.114687
$197$	11.9396	+	6.89334i	0.850662	+	0.491130i	0.860874	−	0.508818i	$-0.169917\pi$
$197$	11.9396	+	6.89334i	0.850662	+	0.491130i	−0.0102119	+	0.999948i	$0.503251\pi$
$198$	2.67270	−	4.62926i	0.189941	−	0.328987i
$199$	1.14152	+	1.97717i	0.0809203	+	0.140158i	0.903646	−	0.428281i	$-0.140881\pi$
$199$	1.14152	+	1.97717i	0.0809203	+	0.140158i	−0.822725	+	0.568439i	$0.807547\pi$
$200$		0			0
$201$	−3.55872	+	2.05463i	−0.251013	+	0.144922i
$202$	10.9906	−	6.34541i	0.773293	−	0.446461i
$203$			9.96567i			0.699453i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	4.15356	+	2.39806i	0.289392	+	0.167081i
$207$	−4.93593			−0.343071
$208$	−1.66129	+	3.20002i	−0.115190	+	0.221881i
$209$	−21.5036			−1.48744
$210$		0			0
$211$	−11.2387	+	19.4661i	−0.773707	+	1.34010i	0.161811	+	0.986822i	$0.448267\pi$
$211$	−11.2387	+	19.4661i	−0.773707	+	1.34010i	−0.935518	+	0.353278i	$0.885067\pi$
$212$	2.74346	+	4.75182i	0.188422	+	0.326356i
$213$		−	15.8719i		−	1.08752i
$214$	2.66025	−	1.53590i	0.181851	−	0.104992i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	4.03180	+	6.98329i	0.273697	+	0.474057i
$218$	3.34541	−	5.79441i	0.226579	−	0.392447i
$219$	11.7549	+	6.78668i	0.794321	+	0.458601i
$220$		0			0
$221$	−7.76261	−	12.1549i	−0.522170	−	0.817628i
$222$	3.14925			0.211364
$223$	−1.19417	−	0.689457i	−0.0799678	−	0.0461694i	0.459483	−	0.888187i	$-0.348035\pi$
$223$	−1.19417	−	0.689457i	−0.0799678	−	0.0461694i	−0.539451	+	0.842017i	$0.681368\pi$
$224$	−1.16129	+	2.01141i	−0.0775919	+	0.134393i
$225$		0			0
$226$		−	7.10972i		−	0.472931i
$227$	16.7321	−	9.66025i	1.11055	−	0.641174i	0.171575	−	0.985171i	$-0.445115\pi$
$227$	16.7321	−	9.66025i	1.11055	−	0.641174i	0.938971	+	0.343998i	$0.111781\pi$
$228$	−3.48387	+	2.01141i	−0.230725	+	0.133209i
$229$		−	15.7626i		−	1.04162i	−0.853672	−	0.520811i	$-0.825630\pi$
$229$		−	15.7626i		−	1.04162i	0.853672	−	0.520811i	$-0.174370\pi$
$230$		0			0
$231$	6.20757	−	10.7518i	0.408428	−	0.707418i
$232$	−3.71592	−	2.14539i	−0.243962	−	0.140852i
$233$	16.5549			1.08455			0.542275	−	0.840201i	$-0.317563\pi$
$233$	16.5549			1.08455			0.542275	+	0.840201i	$0.317563\pi$
$234$	−0.161290	−	3.60194i	−0.0105438	−	0.235466i
$235$		0			0
$236$	5.87744	+	3.39334i	0.382589	+	0.220888i
$237$	−3.98387	+	6.90026i	−0.258780	+	0.448220i
$238$	−4.64516	−	8.04565i	−0.301101	−	0.521522i
$239$			26.2006i			1.69477i	0.530976	+	0.847387i	$0.321825\pi$
$239$			26.2006i			1.69477i	−0.530976	+	0.847387i	$0.678175\pi$
$240$		0			0
$241$	−13.5529	+	7.82479i	−0.873021	+	0.504039i	−0.868351	−	0.495950i	$-0.834820\pi$
$241$	−13.5529	+	7.82479i	−0.873021	+	0.504039i	−0.00466988	+	0.999989i	$0.501486\pi$
$242$			17.5734i			1.12966i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.267949	−	0.464102i	0.0171537	−	0.0297111i
$245$		0			0
$246$	2.64516			0.168649
$247$	−12.2243	+	7.80691i	−0.777812	+	0.496742i
$248$	−3.47183			−0.220462
$249$	9.81724	+	5.66799i	0.622142	+	0.359194i
$250$		0			0
$251$	−14.1708	−	24.5446i	−0.894454	−	1.54924i	−0.834479	−	0.551040i	$-0.814231\pi$
$251$	−14.1708	−	24.5446i	−0.894454	−	1.54924i	−0.0599750	−	0.998200i	$-0.519102\pi$
$252$		−	2.32258i		−	0.146309i
$253$	22.8497	−	13.1923i	1.43655	−	0.829392i
$254$	1.84644	−	1.06604i	0.115856	−	0.0668895i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.25465	−	10.8334i	0.390154	−	0.675767i	−0.602315	−	0.798258i	$-0.705755\pi$
$257$	6.25465	−	10.8334i	0.390154	−	0.675767i	0.992470	+	0.122491i	$0.0390883\pi$
$258$	−10.6095	−	6.12539i	−0.660518	−	0.381350i
$259$	7.31439			0.454494
$260$		0			0
$261$	4.29078			0.265592
$262$	1.08991	+	0.629257i	0.0673346	+	0.0388756i
$263$	−5.35295	+	9.27159i	−0.330077	+	0.571711i	−0.982527	−	0.186122i	$-0.940408\pi$
$263$	−5.35295	+	9.27159i	−0.330077	+	0.571711i	0.652449	+	0.757832i	$0.273741\pi$
$264$	2.67270	+	4.62926i	0.164493	+	0.284911i
$265$		0			0
$266$	−8.09156	+	4.67167i	−0.496126	+	0.286438i
$267$	−1.50670	+	0.869891i	−0.0922083	+	0.0532365i
$268$		−	4.10926i		−	0.251013i
$269$	−3.76261	−	6.51703i	−0.229410	−	0.397350i	0.728223	−	0.685340i	$-0.240346\pi$
$269$	−3.76261	−	6.51703i	−0.229410	−	0.397350i	−0.957633	+	0.287990i	$0.907013\pi$
$270$		0			0
$271$	8.52920	+	4.92434i	0.518112	+	0.299132i	0.736162	−	0.676805i	$-0.236636\pi$
$271$	8.52920	+	4.92434i	0.518112	+	0.299132i	−0.218050	+	0.975938i	$0.569970\pi$
$272$	4.00000			0.242536
$273$	−0.374609	−	8.36580i	−0.0226723	−	0.506321i
$274$	−19.7149			−1.19102
$275$		0			0
$276$	2.46797	−	4.27464i	0.148554	−	0.257303i
$277$	−0.476550	−	0.825410i	−0.0286331	−	0.0495941i	0.851354	−	0.524592i	$-0.175782\pi$
$277$	−0.476550	−	0.825410i	−0.0286331	−	0.0495941i	−0.879987	+	0.474998i	$0.842449\pi$
$278$		−	5.67742i		−	0.340509i
$279$	3.00670	−	1.73592i	0.180006	−	0.103927i
$280$		0			0
$281$		−	5.57336i		−	0.332479i	−0.986085	−	0.166239i	$-0.946838\pi$
$281$		−	5.57336i		−	0.332479i	0.986085	−	0.166239i	$-0.0531625\pi$
$282$	0.909471	+	1.57525i	0.0541582	+	0.0938048i
$283$	−11.0067	+	19.0642i	−0.654280	+	1.13325i	0.327794	+	0.944749i	$0.393695\pi$
$283$	−11.0067	+	19.0642i	−0.654280	+	1.13325i	−0.982074	+	0.188497i	$0.939638\pi$
$284$	13.7454	+	7.93593i	0.815642	+	0.470911i
$285$		0			0
$286$	10.3736	+	16.2432i	0.613402	+	0.960483i
$287$	6.14359			0.362645
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		−	16.1093i		−	0.944342i
$292$	−11.7549	+	6.78668i	−0.687902	+	0.397160i
$293$	−5.92623	+	3.42151i	−0.346214	+	0.199887i	−0.663016	−	0.748605i	$-0.730724\pi$
$293$	−5.92623	+	3.42151i	−0.346214	+	0.199887i	0.316803	+	0.948491i	$0.397391\pi$
$294$			1.60562i			0.0936419i
$295$		0			0
$296$	−1.57463	+	2.72733i	−0.0915233	+	0.158523i
$297$	−4.62926	−	2.67270i	−0.268617	−	0.155086i
$298$	−19.4775			−1.12830
$299$	8.20002	−	15.7951i	0.474219	−	0.913453i
$300$		0			0
$301$	−24.6414	−	14.2267i	−1.42031	−	0.820014i
$302$	−7.25851	+	12.5721i	−0.417681	+	0.723444i
$303$	−6.34541	−	10.9906i	−0.364534	−	0.631391i
$304$		−	4.02283i		−	0.230725i
$305$		0			0
$306$	−3.46410	+	2.00000i	−0.198030	+	0.114332i
$307$			4.75442i			0.271349i	0.990753	+	0.135675i	$0.0433202\pi$
$307$			4.75442i			0.271349i	−0.990753	+	0.135675i	$0.956680\pi$
$308$	6.20757	+	10.7518i	0.353709	+	0.612642i
$309$	2.39806	−	4.15356i	0.136421	−	0.236288i
$310$		0			0
$311$	1.93639			0.109803			0.0549013	−	0.998492i	$-0.482516\pi$
$311$	1.93639			0.109803			0.0549013	+	0.998492i	$0.482516\pi$
$312$	3.20002	+	1.66129i	0.181165	+	0.0940520i
$313$	−25.5545			−1.44443			−0.722213	−	0.691671i	$-0.756875\pi$
$313$	−25.5545			−1.44443			−0.722213	+	0.691671i	$0.756875\pi$
$314$	−21.1162	−	12.1914i	−1.19166	−	0.688002i
$315$		0			0
$316$	−3.98387	−	6.90026i	−0.224110	−	0.388170i
$317$			12.6667i			0.711435i	0.934594	+	0.355717i	$0.115763\pi$
$317$			12.6667i			0.711435i	−0.934594	+	0.355717i	$0.884237\pi$
$318$	4.75182	−	2.74346i	0.266469	−	0.153846i
$319$	−19.8631	+	11.4680i	−1.11212	+	0.642083i
$320$		0			0
$321$	−1.53590	−	2.66025i	−0.0857255	−	0.148481i
$322$	5.73205	−	9.92820i	0.319435	−	0.553277i
$323$	13.9355	+	8.04565i	0.775391	+	0.447672i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−23.6267			−1.30856
$327$	−5.79441	−	3.34541i	−0.320432	−	0.185001i
$328$	−1.32258	+	2.29078i	−0.0730272	+	0.126487i
$329$	2.11232	+	3.65864i	0.116456	+	0.201708i
$330$		0			0
$331$	−20.5231	+	11.8490i	−1.12805	+	0.651282i	−0.943445	−	0.331530i	$-0.892435\pi$
$331$	−20.5231	+	11.8490i	−1.12805	+	0.651282i	−0.184609	+	0.982812i	$0.559102\pi$
$332$	−9.81724	+	5.66799i	−0.538791	+	0.311071i
$333$		−	3.14925i		−	0.172578i
$334$	−8.37357	−	14.5035i	−0.458182	−	0.793594i
$335$		0			0
$336$	2.01141	+	1.16129i	0.109732	+	0.0633536i
$337$	−19.5554			−1.06525			−0.532625	−	0.846351i	$-0.678795\pi$
$337$	−19.5554			−1.06525			−0.532625	+	0.846351i	$0.678795\pi$
$338$	11.7942	+	5.46774i	0.641521	+	0.297406i
$339$	−7.10972			−0.386147
$340$		0			0
$341$	−9.27918	+	16.0720i	−0.502496	+	0.870348i
$342$	2.01141	+	3.48387i	0.108765	+	0.188386i
$343$			19.9872i			1.07921i
$344$	10.6095	−	6.12539i	0.572025	−	0.330259i
$345$		0			0
$346$		−	16.1321i		−	0.867266i
$347$	−11.5187	−	19.9510i	−0.618358	−	1.07103i	−0.989785	−	0.142565i	$-0.954465\pi$
$347$	−11.5187	−	19.9510i	−0.618358	−	1.07103i	0.371427	−	0.928462i	$-0.378868\pi$
$348$	−2.14539	+	3.71592i	−0.115005	+	0.199194i
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$		0			0
$351$	−3.60194	+	0.161290i	−0.192257	+	0.00860902i
$352$	−5.34541			−0.284911
$353$	−24.6018	−	14.2039i	−1.30942	−	0.755996i	−0.327424	−	0.944877i	$-0.606181\pi$
$353$	−24.6018	−	14.2039i	−1.30942	−	0.755996i	−0.982000	+	0.188881i	$0.939514\pi$
$354$	3.39334	−	5.87744i	0.180354	−	0.312382i
$355$		0			0
$356$		−	1.73978i		−	0.0922083i
$357$	−8.04565	+	4.64516i	−0.425821	+	0.245848i
$358$	6.34644	−	3.66412i	0.335420	−	0.193655i
$359$			23.5734i			1.24415i	0.782956	+	0.622077i	$0.213711\pi$
$359$			23.5734i			1.24415i	−0.782956	+	0.622077i	$0.786289\pi$
$360$		0			0
$361$	−1.40844	+	2.43948i	−0.0741282	+	0.128394i
$362$	−16.9510	−	9.78668i	−0.890926	−	0.514377i
$363$	17.5734			0.922362
$364$	7.43230	+	3.85848i	0.389558	+	0.202239i
$365$		0			0
$366$	−0.464102	−	0.267949i	−0.0242590	−	0.0140059i
$367$	13.7454	−	23.8078i	0.717506	−	1.24276i	−0.244479	−	0.969655i	$-0.578617\pi$
$367$	13.7454	−	23.8078i	0.717506	−	1.24276i	0.961985	−	0.273103i	$-0.0880498\pi$
$368$	2.46797	+	4.27464i	0.128652	+	0.222831i
$369$		−	2.64516i		−	0.137701i
$370$		0			0
$371$	11.0365	−	6.37191i	0.572985	−	0.330813i
$372$			3.47183i			0.180006i
$373$	13.1710	+	22.8129i	0.681971	+	1.18121i	0.974379	+	0.224914i	$0.0722102\pi$
$373$	13.1710	+	22.8129i	0.681971	+	1.18121i	−0.292408	+	0.956294i	$0.594456\pi$
$374$	10.6908	−	18.5170i	0.552809	−	0.957493i
$375$		0			0
$376$	−1.81894			−0.0938048
$377$	−7.12822	+	13.7306i	−0.367122	+	0.707160i
$378$	−2.32258			−0.119461
$379$	0.388456	+	0.224275i	0.0199537	+	0.0115202i	0.509944	−	0.860208i	$-0.329666\pi$
$379$	0.388456	+	0.224275i	0.0199537	+	0.0115202i	−0.489990	+	0.871728i	$0.663000\pi$
$380$		0			0
$381$	−1.06604	−	1.84644i	−0.0546151	−	0.0945961i
$382$			17.0375i			0.871713i
$383$	−10.4985	+	6.06133i	−0.536450	+	0.309719i	−0.743639	−	0.668582i	$-0.766902\pi$
$383$	−10.4985	+	6.06133i	−0.536450	+	0.309719i	0.207189	+	0.978301i	$0.433568\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−3.07746	−	5.33031i	−0.156638	−	0.271306i
$387$	−6.12539	+	10.6095i	−0.311371	+	0.539311i
$388$	13.9510	+	8.05463i	0.708256	+	0.408912i
$389$	18.6195			0.944045			0.472022	−	0.881587i	$-0.343524\pi$
$389$	18.6195			0.944045			0.472022	+	0.881587i	$0.343524\pi$
$390$		0			0
$391$	−19.7437			−0.998484
$392$	−1.39051	−	0.802812i	−0.0702314	−	0.0405481i
$393$	0.629257	−	1.08991i	0.0317418	−	0.0549785i
$394$	6.89334	+	11.9396i	0.347281	+	0.601509i
$395$		0			0
$396$	4.62926	−	2.67270i	0.232629	−	0.134308i
$397$	−9.78970	+	5.65208i	−0.491331	+	0.283670i	−0.725126	−	0.688616i	$-0.758219\pi$
$397$	−9.78970	+	5.65208i	−0.491331	+	0.283670i	0.233796	+	0.972286i	$0.424885\pi$
$398$			2.28304i			0.114439i
$399$	4.67167	+	8.09156i	0.233876	+	0.405085i
$400$		0			0
$401$	−1.30406	−	0.752899i	−0.0651216	−	0.0375980i	0.467086	−	0.884212i	$-0.345304\pi$
$401$	−1.30406	−	0.752899i	−0.0651216	−	0.0375980i	−0.532207	+	0.846614i	$0.678637\pi$
$402$	−4.10926			−0.204951
$403$	0.559971	+	12.5053i	0.0278942	+	0.622935i
$404$	12.6908			0.631391
$405$		0			0
$406$	−4.98283	+	8.63052i	−0.247294	+	0.428326i
$407$	8.41702	+	14.5787i	0.417216	+	0.722640i
$408$		−	4.00000i		−	0.198030i
$409$	9.64697	−	5.56968i	0.477012	−	0.275403i	−0.242158	−	0.970237i	$-0.577855\pi$
$409$	9.64697	−	5.56968i	0.477012	−	0.275403i	0.719170	+	0.694834i	$0.244522\pi$
$410$		0			0
$411$			19.7149i			0.972464i
$412$	2.39806	+	4.15356i	0.118144	+	0.204631i
$413$	7.88130	−	13.6508i	0.387814	−	0.671713i
$414$	−4.27464	−	2.46797i	−0.210087	−	0.121294i
$415$		0			0
$416$	−3.03873	+	1.94065i	−0.148986	+	0.0951483i
$417$	−5.67742			−0.278024
$418$	−18.6227	−	10.7518i	−0.910866	−	0.525889i
$419$	7.75488	−	13.4318i	0.378851	−	0.656188i	−0.612045	−	0.790823i	$-0.709653\pi$
$419$	7.75488	−	13.4318i	0.378851	−	0.656188i	0.990895	+	0.134635i	$0.0429861\pi$
$420$		0			0
$421$		−	39.4452i		−	1.92244i	−0.275778	−	0.961221i	$-0.588935\pi$
$421$		−	39.4452i		−	1.92244i	0.275778	−	0.961221i	$-0.411065\pi$
$422$	−19.4661	+	11.2387i	−0.947594	+	0.547094i
$423$	1.57525	−	0.909471i	0.0765913	−	0.0442200i
$424$			5.48693i			0.266469i
$425$		0			0
$426$	7.93593	−	13.7454i	0.384497	−	0.665969i
$427$	−1.07791	−	0.622333i	−0.0521639	−	0.0301168i
$428$	3.07180			0.148481
$429$	16.2432	−	10.3736i	0.784231	−	0.500841i
$430$		0			0
$431$	1.86621	+	1.07746i	0.0898921	+	0.0518993i	0.544272	−	0.838909i	$-0.316806\pi$
$431$	1.86621	+	1.07746i	0.0898921	+	0.0518993i	−0.454380	+	0.890808i	$0.650139\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−0.669689	−	1.15994i	−0.0321832	−	0.0557429i	0.849485	−	0.527612i	$-0.176913\pi$
$433$	−0.669689	−	1.15994i	−0.0321832	−	0.0557429i	−0.881668	+	0.471870i	$0.843579\pi$
$434$			8.06361i			0.387066i
$435$		0			0
$436$	5.79441	−	3.34541i	0.277502	−	0.160216i
$437$			19.8564i			0.949861i
$438$	6.78668	+	11.7549i	0.324280	+	0.561670i
$439$	−15.8490	+	27.4513i	−0.756434	+	1.31018i	0.188225	+	0.982126i	$0.439727\pi$
$439$	−15.8490	+	27.4513i	−0.756434	+	1.31018i	−0.944658	+	0.328055i	$0.893607\pi$
$440$		0			0
$441$	1.60562			0.0764583
$442$	−0.645159	−	14.4078i	−0.0306871	−	0.685308i
$443$	28.0904			1.33461			0.667307	−	0.744782i	$-0.267447\pi$
$443$	28.0904			1.33461			0.667307	+	0.744782i	$0.267447\pi$
$444$	2.72733	+	1.57463i	0.129434	+	0.0747285i
$445$		0			0
$446$	−0.689457	−	1.19417i	−0.0326467	−	0.0565458i
$447$			19.4775i			0.921254i
$448$	−2.01141	+	1.16129i	−0.0950303	+	0.0548658i
$449$	25.0426	−	14.4583i	1.18183	−	0.682332i	0.225395	−	0.974267i	$-0.427633\pi$
$449$	25.0426	−	14.4583i	1.18183	−	0.682332i	0.956438	+	0.291936i	$0.0942994\pi$
$450$		0			0
$451$	7.06973	+	12.2451i	0.332900	+	0.576600i
$452$	3.55486	−	6.15720i	0.167206	−	0.289610i
$453$	12.5721	+	7.25851i	0.590690	+	0.341035i
$454$	19.3205			0.906756
$455$		0			0
$456$	−4.02283			−0.188386
$457$	−8.39958	−	4.84950i	−0.392916	−	0.226850i	0.290507	−	0.956873i	$-0.406176\pi$
$457$	−8.39958	−	4.84950i	−0.392916	−	0.226850i	−0.683423	+	0.730023i	$0.739509\pi$
$458$	7.88130	−	13.6508i	0.368269	−	0.637861i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	10.3905	−	5.99896i	0.483934	−	0.279400i	−0.238120	−	0.971236i	$-0.576531\pi$
$461$	10.3905	−	5.99896i	0.483934	−	0.279400i	0.722055	+	0.691836i	$0.243198\pi$
$462$	10.7518	−	6.20757i	0.500220	−	0.288802i
$463$		−	6.42664i		−	0.298671i	−0.988787	−	0.149336i	$-0.952287\pi$
$463$		−	6.42664i		−	0.298671i	0.988787	−	0.149336i	$-0.0477135\pi$
$464$	−2.14539	−	3.71592i	−0.0995971	−	0.172507i
$465$		0			0
$466$	14.3370	+	8.27747i	0.664149	+	0.383447i
$467$	−26.2642			−1.21536			−0.607681	−	0.794182i	$-0.707900\pi$
$467$	−26.2642			−1.21536			−0.607681	+	0.794182i	$0.707900\pi$
$468$	1.66129	−	3.20002i	0.0767932	−	0.147921i
$469$	−9.54409			−0.440705
$470$		0			0
$471$	−12.1914	+	21.1162i	−0.561752	+	0.972982i
$472$	3.39334	+	5.87744i	0.156191	+	0.270531i
$473$		−	65.4854i		−	3.01102i
$474$	−6.90026	+	3.98387i	−0.316940	+	0.182985i
$475$		0			0
$476$		−	9.29032i		−	0.425821i
$477$	−2.74346	−	4.75182i	−0.125615	−	0.217571i
$478$	−13.1003	+	22.6904i	−0.599193	+	1.03783i
$479$	−22.2418	−	12.8413i	−1.01625	−	0.586735i	−0.103237	−	0.994657i	$-0.532920\pi$
$479$	−22.2418	−	12.8413i	−1.01625	−	0.586735i	−0.913017	+	0.407922i	$0.866253\pi$
$480$		0			0
$481$	10.0777	+	5.23182i	0.459502	+	0.238551i
$482$	−15.6496			−0.712818
$483$	−9.92820	−	5.73205i	−0.451749	−	0.260817i
$484$	−8.78668	+	15.2190i	−0.399395	+	0.691772i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	8.12238	−	4.68946i	0.368060	−	0.212500i	−0.304551	−	0.952496i	$-0.598506\pi$
$487$	8.12238	−	4.68946i	0.368060	−	0.212500i	0.672611	+	0.739997i	$0.265173\pi$
$488$	0.464102	−	0.267949i	0.0210089	−	0.0121295i
$489$			23.6267i			1.06844i
$490$		0			0
$491$	−3.86927	+	6.70177i	−0.174618	+	0.302447i	−0.940029	−	0.341095i	$-0.889202\pi$
$491$	−3.86927	+	6.70177i	−0.174618	+	0.302447i	0.765411	+	0.643541i	$0.222536\pi$
$492$	2.29078	+	1.32258i	0.103276	+	0.0596265i
$493$	17.1631			0.772987
$494$	−14.4900	+	0.648841i	−0.651935	+	0.0291927i
$495$		0			0
$496$	−3.00670	−	1.73592i	−0.135005	−	0.0779450i
$497$	18.4318	−	31.9249i	0.826781	−	1.43203i
$498$	5.66799	+	9.81724i	0.253989	+	0.439921i
$499$			3.18106i			0.142404i	0.997462	+	0.0712019i	$0.0226834\pi$
$499$			3.18106i			0.142404i	−0.997462	+	0.0712019i	$0.977317\pi$
$500$		0			0
$501$	−14.5035	+	8.37357i	−0.647967	+	0.374104i
$502$		−	28.3416i		−	1.26495i
$503$	−17.5379	−	30.3765i	−0.781975	−	1.35442i	−0.930789	−	0.365556i	$-0.880879\pi$
$503$	−17.5379	−	30.3765i	−0.781975	−	1.35442i	0.148814	−	0.988865i	$-0.452454\pi$
$504$	1.16129	−	2.01141i	0.0517280	−	0.0895955i
$505$		0			0
$506$	26.3846			1.17294
$507$	5.46774	−	11.7942i	0.242831	−	0.523800i
$508$	2.13209			0.0945961
$509$	−16.2697	−	9.39334i	−0.721144	−	0.416353i	0.0940298	−	0.995569i	$-0.470025\pi$
$509$	−16.2697	−	9.39334i	−0.721144	−	0.416353i	−0.815173	+	0.579217i	$0.803358\pi$
$510$		0			0
$511$	15.7626	+	27.3016i	0.697297	+	1.20775i
$512$		−	1.00000i		−	0.0441942i
$513$	3.48387	−	2.01141i	0.153817	−	0.0888061i
$514$	10.8334	−	6.25465i	0.477839	−	0.275881i
$515$		0			0
$516$	−6.12539	−	10.6095i	−0.269655	−	0.467057i
$517$	−4.86149	+	8.42035i	−0.213808	+	0.370327i
$518$	6.33445	+	3.65720i	0.278320	+	0.160688i
$519$	−16.1321			−0.708120
$520$		0			0
$521$	5.28512			0.231545			0.115773	−	0.993276i	$-0.463066\pi$
$521$	5.28512			0.231545			0.115773	+	0.993276i	$0.463066\pi$
$522$	3.71592	+	2.14539i	0.162641	+	0.0939011i
$523$	−10.3762	+	17.9721i	−0.453718	+	0.785863i	−0.998614	−	0.0526409i	$-0.983236\pi$
$523$	−10.3762	+	17.9721i	−0.453718	+	0.785863i	0.544895	+	0.838504i	$0.316569\pi$
$524$	0.629257	+	1.08991i	0.0274892	+	0.0476127i
$525$		0			0
$526$	−9.27159	+	5.35295i	−0.404260	+	0.233400i
$527$	12.0268	−	6.94367i	0.523895	−	0.302471i
$528$			5.34541i			0.232629i
$529$	−0.681725	−	1.18078i	−0.0296402	−	0.0513384i
$530$		0			0
$531$	−5.87744	−	3.39334i	−0.255059	−	0.147258i
$532$	−9.34333			−0.405085
$533$	8.46456	+	4.39438i	0.366641	+	0.190342i
$534$	−1.73978			−0.0752877
$535$		0			0
$536$	2.05463	−	3.55872i	0.0887465	−	0.153713i
$537$	−3.66412	−	6.34644i	−0.158118	−	0.273869i
$538$		−	7.52522i		−	0.324435i
$539$	−7.43284	+	4.29135i	−0.320155	+	0.184842i
$540$		0			0
$541$		−	28.7365i		−	1.23548i	−0.786384	−	0.617739i	$-0.788049\pi$
$541$		−	28.7365i		−	1.23548i	0.786384	−	0.617739i	$-0.211951\pi$
$542$	4.92434	+	8.52920i	0.211518	+	0.366361i
$543$	−9.78668	+	16.9510i	−0.419987	+	0.727438i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$		0			0
$546$	3.85848	−	7.43230i	0.165128	−	0.318073i
$547$	−18.3768			−0.785737			−0.392869	−	0.919595i	$-0.628517\pi$
$547$	−18.3768			−0.785737			−0.392869	+	0.919595i	$0.628517\pi$
$548$	−17.0736	−	9.85744i	−0.729348	−	0.421089i
$549$	−0.267949	+	0.464102i	−0.0114358	+	0.0198074i
$550$		0			0
$551$		−	17.2610i		−	0.735345i
$552$	4.27464	−	2.46797i	0.181941	−	0.105044i
$553$	−16.0264	+	9.25285i	−0.681512	+	0.393471i
$554$		−	0.953101i		−	0.0404934i
$555$		0			0
$556$	2.83871	−	4.91679i	0.120388	−	0.208518i
$557$	−22.9831	−	13.2693i	−0.973826	−	0.562238i	−0.0734252	−	0.997301i	$-0.523393\pi$
$557$	−22.9831	−	13.2693i	−0.973826	−	0.562238i	−0.900400	+	0.435062i	$0.856726\pi$
$558$	3.47183			0.146974
$559$	−23.7745	−	37.2268i	−1.00555	−	1.57453i
$560$		0			0
$561$	−18.5170	−	10.6908i	−0.781790	−	0.451366i
$562$	2.78668	−	4.82667i	0.117549	−	0.203601i
$563$	3.03056	+	5.24908i	0.127723	+	0.221222i	0.922794	−	0.385294i	$-0.125900\pi$
$563$	3.03056	+	5.24908i	0.127723	+	0.221222i	−0.795071	+	0.606516i	$0.792567\pi$
$564$			1.81894i			0.0765913i
$565$		0			0
$566$	−19.0642	+	11.0067i	−0.801326	+	0.462646i
$567$			2.32258i			0.0975392i
$568$	7.93593	+	13.7454i	0.332984	+	0.576746i
$569$	−7.24818	+	12.5542i	−0.303860	+	0.526300i	−0.977007	−	0.213208i	$-0.931609\pi$
$569$	−7.24818	+	12.5542i	−0.303860	+	0.526300i	0.673147	+	0.739509i	$0.264942\pi$
$570$		0			0
$571$	−2.90413			−0.121534			−0.0607670	−	0.998152i	$-0.519355\pi$
$571$	−2.90413			−0.121534			−0.0607670	+	0.998152i	$0.519355\pi$
$572$	0.862160	+	19.2538i	0.0360487	+	0.805044i
$573$	17.0375			0.711750
$574$	5.32051	+	3.07180i	0.222074	+	0.128214i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			18.8180i			0.783405i	0.920092	+	0.391702i	$0.128114\pi$
$577$			18.8180i			0.783405i	−0.920092	+	0.391702i	$0.871886\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	−5.33031	+	3.07746i	−0.221520	+	0.127895i
$580$		0			0
$581$	13.1643	+	22.8013i	0.546149	+	0.945958i
$582$	8.05463	−	13.9510i	0.333875	−	0.578289i
$583$	25.4004	+	14.6649i	1.05198	+	0.607359i
$584$	−13.5734			−0.561670
$585$		0			0
$586$	−6.84302			−0.282682
$587$	3.40901	+	1.96820i	0.140705	+	0.0812361i	0.568700	−	0.822545i	$-0.307447\pi$
$587$	3.40901	+	1.96820i	0.140705	+	0.0812361i	−0.427995	+	0.903781i	$0.640780\pi$
$588$	−0.802812	+	1.39051i	−0.0331074	+	0.0573437i
$589$	−6.98329	−	12.0954i	−0.287741	−	0.498383i
$590$		0			0
$591$	11.9396	−	6.89334i	0.491130	−	0.283554i
$592$	−2.72733	+	1.57463i	−0.112093	+	0.0647168i
$593$		−	20.1227i		−	0.826338i	−0.910654	−	0.413169i	$-0.864422\pi$
$593$		−	20.1227i		−	0.826338i	0.910654	−	0.413169i	$-0.135578\pi$
$594$	−2.67270	−	4.62926i	−0.109662	−	0.189941i
$595$		0			0
$596$	−16.8680	−	9.73875i	−0.690940	−	0.398915i
$597$	2.28304			0.0934388
$598$	14.9990	−	9.57893i	0.613353	−	0.391712i
$599$	48.1172			1.96601			0.983007	−	0.183567i	$-0.0587644\pi$
$599$	48.1172			1.96601			0.983007	+	0.183567i	$0.0587644\pi$
$600$		0			0
$601$	2.12109	−	3.67383i	0.0865209	−	0.149859i	−0.819517	−	0.573054i	$-0.805758\pi$
$601$	2.12109	−	3.67383i	0.0865209	−	0.149859i	0.906038	+	0.423196i	$0.139092\pi$
$602$	−14.2267	−	24.6414i	−0.579837	−	1.00431i
$603$			4.10926i			0.167342i
$604$	−12.5721	+	7.25851i	−0.511552	+	0.295345i
$605$		0			0
$606$		−	12.6908i		−	0.515529i
$607$	6.03424	+	10.4516i	0.244922	+	0.424218i	0.962110	−	0.272663i	$-0.0879042\pi$
$607$	6.03424	+	10.4516i	0.244922	+	0.424218i	−0.717188	+	0.696880i	$0.754571\pi$
$608$	2.01141	−	3.48387i	0.0815736	−	0.141290i
$609$	8.63052	+	4.98283i	0.349726	+	0.201915i
$610$		0			0
$611$	0.293377	+	6.55172i	0.0118688	+	0.265054i
$612$	−4.00000			−0.161690
$613$	−36.1497	−	20.8711i	−1.46007	−	0.842974i	−0.461060	−	0.887369i	$-0.652531\pi$
$613$	−36.1497	−	20.8711i	−1.46007	−	0.842974i	−0.999014	+	0.0443946i	$0.985864\pi$
$614$	−2.37721	+	4.11745i	−0.0959364	+	0.166167i
$615$		0			0
$616$			12.4151i			0.500220i
$617$	28.9760	−	16.7293i	1.16653	−	0.673497i	0.213670	−	0.976906i	$-0.431458\pi$
$617$	28.9760	−	16.7293i	1.16653	−	0.673497i	0.952860	+	0.303409i	$0.0981249\pi$
$618$	4.15356	−	2.39806i	0.167081	−	0.0964640i
$619$			38.0978i			1.53128i	0.643270	+	0.765639i	$0.277577\pi$
$619$			38.0978i			1.53128i	−0.643270	+	0.765639i	$0.722423\pi$
$620$		0			0
$621$	−2.46797	+	4.27464i	−0.0990361	+	0.171536i
$622$	1.67696	+	0.968196i	0.0672401	+	0.0388211i
$623$	−4.04078			−0.161891
$624$	1.94065	+	3.03873i	0.0776883	+	0.121646i
$625$		0			0
$626$	−22.1308	−	12.7772i	−0.884526	−	0.510681i
$627$	−10.7518	+	18.6227i	−0.429386	+	0.743719i
$628$	−12.1914	−	21.1162i	−0.486491	−	0.842628i
$629$		−	12.5970i		−	0.502276i
$630$		0			0
$631$	−21.4775	+	12.4000i	−0.855005	+	0.493638i	−0.862337	−	0.506335i	$-0.831000\pi$
$631$	−21.4775	+	12.4000i	−0.855005	+	0.493638i	0.00733109	+	0.999973i	$0.497666\pi$
$632$		−	7.96774i		−	0.316940i
$633$	11.2387	+	19.4661i	0.446700	+	0.773707i
$634$	−6.33337	+	10.9697i	−0.251530	+	0.435663i
$635$		0			0
$636$	5.48693			0.217571
$637$	−2.66741	+	5.13802i	−0.105686	+	0.203576i
$638$	−22.9359			−0.908042
$639$	−13.7454	−	7.93593i	−0.543761	−	0.313941i
$640$		0			0
$641$	2.04259	+	3.53788i	0.0806776	+	0.139738i	0.903541	−	0.428501i	$-0.140958\pi$
$641$	2.04259	+	3.53788i	0.0806776	+	0.139738i	−0.822864	+	0.568239i	$0.807625\pi$
$642$		−	3.07180i		−	0.121234i
$643$	31.6806	−	18.2908i	1.24936	−	0.721318i	0.278377	−	0.960472i	$-0.410203\pi$
$643$	31.6806	−	18.2908i	1.24936	−	0.721318i	0.970982	+	0.239154i	$0.0768701\pi$
$644$	9.92820	−	5.73205i	0.391226	−	0.225874i
$645$		0			0
$646$	8.04565	+	13.9355i	0.316552	+	0.548284i
$647$	−8.61704	+	14.9251i	−0.338771	+	0.586768i	−0.984202	−	0.177050i	$-0.943344\pi$
$647$	−8.61704	+	14.9251i	−0.338771	+	0.586768i	0.645431	+	0.763818i	$0.276678\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	36.2776			1.42402
$650$		0			0
$651$	8.06361			0.316038
$652$	−20.4614	−	11.8134i	−0.801329	−	0.462647i
$653$	−10.9637	+	18.9897i	−0.429042	+	0.743123i	−0.996788	−	0.0800806i	$-0.974482\pi$
$653$	−10.9637	+	18.9897i	−0.429042	+	0.743123i	0.567746	+	0.823204i	$0.307816\pi$
$654$	−3.34541	−	5.79441i	−0.130816	−	0.226579i
$655$		0			0
$656$	−2.29078	+	1.32258i	−0.0894397	+	0.0516381i
$657$	11.7549	−	6.78668i	0.458601	−	0.264774i
$658$			4.22464i			0.164694i
$659$	24.2379	+	41.9813i	0.944176	+	1.63536i	0.757393	+	0.652960i	$0.226473\pi$
$659$	24.2379	+	41.9813i	0.944176	+	1.63536i	0.186783	+	0.982401i	$0.440194\pi$
$660$		0			0
$661$	−25.8267	−	14.9110i	−1.00454	−	0.579972i	−0.0949524	−	0.995482i	$-0.530270\pi$
$661$	−25.8267	−	14.9110i	−1.00454	−	0.579972i	−0.909589	+	0.415510i	$0.863603\pi$
$662$	−23.6981			−0.921052
$663$	−14.4078	+	0.645159i	−0.559551	+	0.0250559i
$664$	−11.3360			−0.439921
$665$		0			0
$666$	1.57463	−	2.72733i	0.0610155	−	0.105682i
$667$	10.5895	+	18.3415i	0.410027	+	0.710187i
$668$		−	16.7471i		−	0.647967i
$669$	−1.19417	+	0.689457i	−0.0461694	+	0.0266559i
$670$		0			0
$671$		−	2.86459i		−	0.110586i
$672$	1.16129	+	2.01141i	0.0447977	+	0.0775919i
$673$	15.3360	−	26.5627i	0.591158	−	1.02392i	−0.402919	−	0.915236i	$-0.632004\pi$
$673$	15.3360	−	26.5627i	0.591158	−	1.02392i	0.994077	−	0.108680i	$-0.0346625\pi$
$674$	−16.9355	−	9.77770i	−0.652330	−	0.376623i
$675$		0			0
$676$	7.48023	+	10.6323i	0.287701	+	0.408935i
$677$	−21.0831			−0.810290			−0.405145	−	0.914252i	$-0.632779\pi$
$677$	−21.0831			−0.810290			−0.405145	+	0.914252i	$0.632779\pi$
$678$	−6.15720	−	3.55486i	−0.236466	−	0.136524i
$679$	18.7075	−	32.4024i	0.717929	−	1.24349i
$680$		0			0
$681$		−	19.3205i		−	0.740363i
$682$	−16.0720	+	9.27918i	−0.615429	+	0.355318i
$683$	11.5493	−	6.66799i	0.441921	−	0.255143i	−0.262491	−	0.964934i	$-0.584544\pi$
$683$	11.5493	−	6.66799i	0.441921	−	0.255143i	0.704412	+	0.709791i	$0.251211\pi$
$684$			4.02283i			0.153817i
$685$		0			0
$686$	−9.99362	+	17.3095i	−0.381558	+	0.660878i
$687$	−13.6508	−	7.88130i	−0.520811	−	0.300691i
$688$	12.2508			0.467057
$689$	19.7636	−	0.884986i	0.752933	−	0.0337153i
$690$		0			0
$691$	−30.2289	−	17.4527i	−1.14996	−	0.663932i	−0.201085	−	0.979574i	$-0.564447\pi$
$691$	−30.2289	−	17.4527i	−1.14996	−	0.663932i	−0.948878	+	0.315642i	$0.897780\pi$
$692$	8.06604	−	13.9708i	0.306625	−	0.531090i
$693$	−6.20757	−	10.7518i	−0.235806	−	0.408428i
$694$		−	23.0375i		−	0.874490i
$695$		0			0
$696$	−3.71592	+	2.14539i	−0.140852	+	0.0813207i
$697$		−	10.5806i		−	0.400770i
$698$	7.66025	+	13.2679i	0.289945	+	0.502199i
$699$	8.27747	−	14.3370i	0.313083	−	0.542275i
$700$		0			0
$701$	39.6715			1.49837			0.749186	−	0.662360i	$-0.230445\pi$
$701$	39.6715			1.49837			0.749186	+	0.662360i	$0.230445\pi$
$702$	−3.20002	−	1.66129i	−0.120777	−	0.0627013i
$703$	−12.6689			−0.477817
$704$	−4.62926	−	2.67270i	−0.174472	−	0.100731i
$705$		0			0
$706$	−14.2039	−	24.6018i	−0.534570	−	0.925903i
$707$		−	29.4754i		−	1.10854i
$708$	5.87744	−	3.39334i	0.220888	−	0.127530i
$709$	2.45467	−	1.41720i	0.0921869	−	0.0532242i	−0.453198	−	0.891410i	$-0.649717\pi$
$709$	2.45467	−	1.41720i	0.0921869	−	0.0532242i	0.545385	+	0.838186i	$0.316384\pi$
$710$		0			0
$711$	3.98387	+	6.90026i	0.149407	+	0.258780i
$712$	0.869891	−	1.50670i	0.0326005	−	0.0564658i
$713$	14.8409	+	8.56837i	0.555794	+	0.320888i
$714$	−9.29032			−0.347681
$715$		0			0
$716$	7.32824			0.273869
$717$	22.6904	+	13.1003i	0.847387	+	0.489239i
$718$	−11.7867	+	20.4151i	−0.439875	+	0.761886i
$719$	−21.8564	−	37.8564i	−0.815106	−	1.41181i	−0.909251	−	0.416247i	$-0.863345\pi$
$719$	−21.8564	−	37.8564i	−0.815106	−	1.41181i	0.0941451	−	0.995558i	$-0.469988\pi$
$720$		0			0
$721$	9.64697	−	5.56968i	0.359272	−	0.207426i
$722$	−2.43948	+	1.40844i	−0.0907881	+	0.0524165i
$723$			15.6496i			0.582014i
$724$	−9.78668	−	16.9510i	−0.363719	−	0.629980i
$725$		0			0
$726$	15.2190	+	8.78668i	0.564829	+	0.326104i
$727$	16.2568			0.602932			0.301466	−	0.953477i	$-0.402524\pi$
$727$	16.2568			0.602932			0.301466	+	0.953477i	$0.402524\pi$
$728$	4.50732	+	7.05769i	0.167052	+	0.261575i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−24.5016	+	42.4380i	−0.906223	+	1.56962i
$732$	−0.267949	−	0.464102i	−0.00990369	−	0.0171537i
$733$		−	4.96774i		−	0.183488i	−0.995783	−	0.0917438i	$-0.970756\pi$
$733$		−	4.96774i		−	0.183488i	0.995783	−	0.0917438i	$-0.0292441\pi$
$734$	23.8078	−	13.7454i	0.878762	−	0.507354i
$735$		0			0
$736$			4.93593i			0.181941i
$737$	−10.9828	−	19.0228i	−0.404558	−	0.700715i
$738$	1.32258	−	2.29078i	0.0486848	−	0.0843246i
$739$	43.0306	+	24.8437i	1.58291	+	0.913892i	0.994432	+	0.105377i	$0.0336048\pi$
$739$	43.0306	+	24.8437i	1.58291	+	0.913892i	0.588475	+	0.808515i	$0.299729\pi$
$740$		0			0
$741$	0.648841	+	14.4900i	0.0238358	+	0.532303i
$742$	12.7438			0.467841
$743$	−18.6559	−	10.7710i	−0.684420	−	0.395150i	0.117098	−	0.993120i	$-0.462641\pi$
$743$	−18.6559	−	10.7710i	−0.684420	−	0.395150i	−0.801518	+	0.597970i	$0.795974\pi$
$744$	−1.73592	+	3.00670i	−0.0636418	+	0.110231i
$745$		0			0
$746$			26.3421i			0.964452i
$747$	9.81724	−	5.66799i	0.359194	−	0.207381i
$748$	18.5170	−	10.6908i	0.677050	−	0.390895i
$749$		−	7.13449i		−	0.260689i
$750$		0			0
$751$	−3.17436	+	5.49816i	−0.115834	+	0.200631i	−0.918113	−	0.396319i	$-0.870287\pi$
$751$	−3.17436	+	5.49816i	−0.115834	+	0.200631i	0.802279	+	0.596950i	$0.203621\pi$
$752$	−1.57525	−	0.909471i	−0.0574435	−	0.0331650i
$753$	−28.3416			−1.03283
$754$	−13.0385	+	8.32690i	−0.474834	+	0.303248i
$755$		0			0
$756$	−2.01141	−	1.16129i	−0.0731544	−	0.0422357i
$757$	−24.0554	+	41.6651i	−0.874307	+	1.51434i	−0.0168078	+	0.999859i	$0.505350\pi$
$757$	−24.0554	+	41.6651i	−0.874307	+	1.51434i	−0.857499	+	0.514485i	$0.827983\pi$
$758$	0.224275	+	0.388456i	0.00814604	+	0.0141094i
$759$		−	26.3846i		−	0.957699i
$760$		0			0
$761$	29.1734	−	16.8433i	1.05754	−	0.610569i	0.132786	−	0.991145i	$-0.457608\pi$
$761$	29.1734	−	16.8433i	1.05754	−	0.610569i	0.924750	+	0.380576i	$0.124274\pi$
$762$		−	2.13209i		−	0.0772374i
$763$	−7.76997	−	13.4580i	−0.281292	−	0.487212i
$764$	−8.51873	+	14.7549i	−0.308197	+	0.533813i
$765$		0			0
$766$	−12.1227			−0.438009
$767$	20.6229	−	13.1706i	0.744649	−	0.475562i
$768$	−1.00000			−0.0360844
$769$	−5.18651	−	2.99443i	−0.187030	−	0.107982i	0.403561	−	0.914953i	$-0.367772\pi$
$769$	−5.18651	−	2.99443i	−0.187030	−	0.107982i	−0.590592	+	0.806971i	$0.701106\pi$
$770$		0			0
$771$	−6.25465	−	10.8334i	−0.225256	−	0.390154i
$772$		−	6.15491i		−	0.221520i
$773$	−11.6811	+	6.74409i	−0.420140	+	0.242568i	−0.695137	−	0.718877i	$-0.744656\pi$
$773$	−11.6811	+	6.74409i	−0.420140	+	0.242568i	0.274997	+	0.961445i	$0.411323\pi$
$774$	−10.6095	+	6.12539i	−0.381350	+	0.220173i
$775$		0			0
$776$	8.05463	+	13.9510i	0.289144	+	0.500813i
$777$	3.65720	−	6.33445i	0.131201	−	0.227247i
$778$	16.1249	+	9.30974i	0.578107	+	0.333770i
$779$	−10.6410			−0.381254
$780$		0			0
$781$	84.8416			3.03587
$782$	−17.0986	−	9.87187i	−0.611444	−	0.353017i
$783$	2.14539	−	3.71592i	0.0766699	−	0.132796i
$784$	−0.802812	−	1.39051i	−0.0286718	−	0.0496611i
$785$		0			0
$786$	1.08991	−	0.629257i	0.0388756	−	0.0224449i
$787$	47.3272	−	27.3244i	1.68703	−	0.974009i	0.730261	−	0.683168i	$-0.239398\pi$
$787$	47.3272	−	27.3244i	1.68703	−	0.974009i	0.956772	−	0.290841i	$-0.0939349\pi$
$788$			13.7867i			0.491130i
$789$	5.35295	+	9.27159i	0.190570	+	0.330077i
$790$		0			0
$791$	−14.3006	−	8.25644i	−0.508470	−	0.293565i
$792$	5.34541			0.189941
$793$	−1.03999	−	1.62845i	−0.0369312	−	0.0578279i
$794$	−11.3042			−0.401170
$795$		0			0
$796$	−1.14152	+	1.97717i	−0.0404602	+	0.0700791i
$797$	19.1622	+	33.1899i	0.678760	+	1.17565i	0.975355	+	0.220643i	$0.0708155\pi$
$797$	19.1622	+	33.1899i	0.678760	+	1.17565i	−0.296595	+	0.955003i	$0.595851\pi$
$798$			9.34333i			0.330750i
$799$	6.30100	−	3.63788i	0.222913	−	0.128699i
$800$		0			0
$801$			1.73978i			0.0614722i
$802$	−0.752899	−	1.30406i	−0.0265858	−	0.0460479i
$803$	−36.2776	+	62.8346i	−1.28021	+	2.21738i
$804$	−3.55872	−	2.05463i	−0.125507	−	0.0724612i
$805$		0			0
$806$	−5.76772	+	11.1099i	−0.203159	+	0.391331i
$807$	−7.52522			−0.264900
$808$	10.9906	+	6.34541i	0.386647	+	0.223231i
$809$	−5.69081	+	9.85677i	−0.200078	+	0.346546i	−0.948553	−	0.316617i	$-0.897453\pi$
$809$	−5.69081	+	9.85677i	−0.200078	+	0.346546i	0.748475	+	0.663163i	$0.230786\pi$
$810$		0			0
$811$		−	10.8899i		−	0.382397i	−0.981551	−	0.191198i	$-0.938763\pi$
$811$		−	10.8899i		−	0.382397i	0.981551	−	0.191198i	$-0.0612374\pi$
$812$	−8.63052	+	4.98283i	−0.302872	+	0.174863i
$813$	8.52920	−	4.92434i	0.299132	−	0.172704i
$814$			16.8340i			0.590033i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	42.6801	+	24.6414i	1.49319	+	0.862093i
$818$	11.1394			0.389479
$819$	−7.43230	−	3.85848i	−0.259705	−	0.134826i
$820$		0			0
$821$	−1.46194	−	0.844051i	−0.0510220	−	0.0294576i	0.474272	−	0.880378i	$-0.342711\pi$
$821$	−1.46194	−	0.844051i	−0.0510220	−	0.0294576i	−0.525294	+	0.850921i	$0.676045\pi$
$822$	−9.85744	+	17.0736i	−0.343818	+	0.595510i
$823$	−3.38908	−	5.87006i	−0.118136	−	0.204617i	0.800893	−	0.598807i	$-0.204359\pi$
$823$	−3.38908	−	5.87006i	−0.118136	−	0.204617i	−0.919029	+	0.394190i	$0.871025\pi$
$824$			4.79612i			0.167081i
$825$		0			0
$826$	13.6508	−	7.88130i	0.474973	−	0.274226i
$827$			30.2298i			1.05119i	0.850733	+	0.525597i	$0.176158\pi$
$827$			30.2298i			1.05119i	−0.850733	+	0.525597i	$0.823842\pi$
$828$	−2.46797	−	4.27464i	−0.0857678	−	0.148554i
$829$	−5.22023	+	9.04170i	−0.181306	+	0.314031i	−0.942326	−	0.334698i	$-0.891366\pi$
$829$	−5.22023	+	9.04170i	−0.181306	+	0.314031i	0.761020	+	0.648729i	$0.224699\pi$
$830$		0			0
$831$	−0.953101			−0.0330627
$832$	−3.60194	+	0.161290i	−0.124875	+	0.00559172i
$833$	6.42249			0.222526
$834$	−4.91679	−	2.83871i	−0.170255	−	0.0982965i
$835$		0			0
$836$	−10.7518	−	18.6227i	−0.371859	−	0.644079i
$837$		−	3.47183i		−	0.120004i
$838$	13.4318	−	7.75488i	0.463995	−	0.267888i
$839$	9.69647	−	5.59826i	0.334759	−	0.193273i	−0.323193	−	0.946333i	$-0.604756\pi$
$839$	9.69647	−	5.59826i	0.334759	−	0.193273i	0.657952	+	0.753060i	$0.271423\pi$
$840$		0			0
$841$	5.29462	+	9.17056i	0.182573	+	0.316226i
$842$	19.7226	−	34.1606i	0.679686	−	1.17725i
$843$	−4.82667	−	2.78668i	−0.166239	−	0.0959784i
$844$	−22.4775			−0.773707
$845$		0			0
$846$	1.81894			0.0625365
$847$	35.3473	+	20.4078i	1.21455	+	0.701219i
$848$	−2.74346	+	4.75182i	−0.0942109	+	0.163178i
$849$	11.0067	+	19.0642i	0.377749	+	0.654280i
$850$		0			0
$851$	13.4619	−	7.77225i	0.461469	−	0.266429i
$852$	13.7454	−	7.93593i	0.470911	−	0.271881i
$853$		−	21.8185i		−	0.747051i	−0.927620	−	0.373525i	$-0.878149\pi$
$853$		−	21.8185i		−	0.747051i	0.927620	−	0.373525i	$-0.121851\pi$
$854$	−0.622333	−	1.07791i	−0.0212958	−	0.0368854i
$855$		0			0
$856$	2.66025	+	1.53590i	0.0909256	+	0.0524959i
$857$	9.42369			0.321907			0.160954	−	0.986962i	$-0.448543\pi$
$857$	9.42369			0.321907			0.160954	+	0.986962i	$0.448543\pi$
$858$	19.2538	−	0.862160i	0.657315	−	0.0294336i
$859$	24.4775			0.835161			0.417581	−	0.908640i	$-0.362878\pi$
$859$	24.4775			0.835161			0.417581	+	0.908640i	$0.362878\pi$
$860$		0			0
$861$	3.07180	−	5.32051i	0.104687	−	0.181322i
$862$	1.07746	+	1.86621i	0.0366983	+	0.0635633i
$863$			29.7873i			1.01397i	0.861954	+	0.506986i	$0.169240\pi$
$863$			29.7873i			1.01397i	−0.861954	+	0.506986i	$0.830760\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	1.33938i		−	0.0455139i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	−4.03180	+	6.98329i	−0.136848	+	0.237028i
$869$	−36.8847	−	21.2954i	−1.25123	−	0.722397i
$870$		0			0
$871$	−13.1497	−	6.82667i	−0.445561	−	0.231313i
$872$	6.69081			0.226579
$873$	−13.9510	−	8.05463i	−0.472171	−	0.272608i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$		0			0
$876$			13.5734i			0.458601i
$877$	−1.65393	+	0.954895i	−0.0558491	+	0.0322445i	−0.527665	−	0.849453i	$-0.676932\pi$
$877$	−1.65393	+	0.954895i	−0.0558491	+	0.0322445i	0.471815	+	0.881697i	$0.343599\pi$
$878$	−27.4513	+	15.8490i	−0.926438	+	0.534879i
$879$			6.84302i			0.230809i
$880$		0			0
$881$	3.18412	−	5.51505i	0.107276	−	0.185807i	−0.807390	−	0.590018i	$-0.799121\pi$
$881$	3.18412	−	5.51505i	0.107276	−	0.185807i	0.914666	+	0.404211i	$0.132454\pi$
$882$	1.39051	+	0.802812i	0.0468209	+	0.0270321i
$883$	34.9897			1.17750			0.588749	−	0.808316i	$-0.299621\pi$
$883$	34.9897			1.17750			0.588749	+	0.808316i	$0.299621\pi$
$884$	6.64516	−	12.8001i	0.223501	−	0.430513i
$885$		0			0
$886$	24.3270	+	14.0452i	0.817281	+	0.471858i
$887$	10.7001	−	18.5331i	0.359273	−	0.622279i	−0.628567	−	0.777756i	$-0.716358\pi$
$887$	10.7001	−	18.5331i	0.359273	−	0.622279i	0.987840	+	0.155477i	$0.0496914\pi$
$888$	1.57463	+	2.72733i	0.0528410	+	0.0915233i
$889$		−	4.95194i		−	0.166083i
$890$		0			0
$891$	−4.62926	+	2.67270i	−0.155086	+	0.0895389i
$892$		−	1.37891i		−	0.0461694i
$893$	−3.65864	−	6.33696i	−0.122432	−	0.212058i
$894$	−9.73875	+	16.8680i	−0.325712	+	0.564150i
$895$		0			0
$896$	−2.32258			−0.0775919
$897$	−9.57893	−	14.9990i	−0.319831	−	0.500801i
$898$	28.9167			0.964963
$899$	−12.9011	−	7.44843i	−0.430274	−	0.248419i
$900$		0			0
$901$	−10.9739	−	19.0073i	−0.365592	−	0.633224i
$902$			14.1395i			0.470792i
$903$	−24.6414	+	14.2267i	−0.820014	+	0.473435i
$904$	6.15720	−	3.55486i	0.204785	−	0.118233i
$905$		0			0
$906$	7.25851	+	12.5721i	0.241148	+	0.417681i
$907$	−16.2347	+	28.1192i	−0.539063	+	0.933684i	0.459892	+	0.887975i	$0.347888\pi$
$907$	−16.2347	+	28.1192i	−0.539063	+	0.933684i	−0.998955	+	0.0457093i	$0.985445\pi$
$908$	16.7321	+	9.66025i	0.555273	+	0.320587i
$909$	−12.6908			−0.420928
$910$		0			0
$911$	34.4380			1.14098			0.570490	−	0.821304i	$-0.306753\pi$
$911$	34.4380			1.14098			0.570490	+	0.821304i	$0.306753\pi$
$912$	−3.48387	−	2.01141i	−0.115362	−	0.0666045i
$913$	−30.2977	+	52.4771i	−1.00271	+	1.73674i
$914$	−4.84950	−	8.39958i	−0.160407	−	0.277833i
$915$		0			0
$916$	13.6508	−	7.88130i	0.451036	−	0.260406i
$917$	2.53139	−	1.46150i	0.0835939	−	0.0482630i
$918$			4.00000i			0.132020i
$919$	−18.2413	−	31.5949i	−0.601727	−	1.04222i	−0.992560	−	0.121759i	$-0.961146\pi$
$919$	−18.2413	−	31.5949i	−0.601727	−	1.04222i	0.390833	−	0.920462i	$-0.372187\pi$
$920$		0			0
$921$	4.11745	+	2.37721i	0.135675	+	0.0783317i
$922$	11.9979			0.395131
$923$	48.2303	−	30.8018i	1.58752	−	1.01385i
$924$	12.4151			0.408428
$925$		0			0
$926$	3.21332	−	5.56563i	0.105596	−	0.182898i
$927$	−2.39806	−	4.15356i	−0.0787626	−	0.136421i
$928$		−	4.29078i		−	0.140852i
$929$	43.2233	−	24.9550i	1.41811	−	0.818747i	0.421978	−	0.906606i	$-0.361336\pi$
$929$	43.2233	−	24.9550i	1.41811	−	0.818747i	0.996133	+	0.0878597i	$0.0280027\pi$
$930$		0			0
$931$		−	6.45914i		−	0.211690i
$932$	8.27747	+	14.3370i	0.271138	+	0.469624i
$933$	0.968196	−	1.67696i	0.0316973	−	0.0549013i
$934$	−22.7454	−	13.1321i	−0.744254	−	0.429695i
$935$		0			0
$936$	3.03873	−	1.94065i	0.0993239	−	0.0634322i
$937$	15.8873			0.519017			0.259508	−	0.965741i	$-0.416440\pi$
$937$	15.8873			0.519017			0.259508	+	0.965741i	$0.416440\pi$
$938$	−8.26542	−	4.77204i	−0.269876	−	0.155813i
$939$	−12.7772	+	22.1308i	−0.416970	+	0.722213i
$940$		0			0
$941$			6.99273i			0.227956i	0.993483	+	0.113978i	$0.0363594\pi$
$941$			6.99273i			0.227956i	−0.993483	+	0.113978i	$0.963641\pi$
$942$	−21.1162	+	12.1914i	−0.688002	+	0.397218i
$943$	11.3071	−	6.52817i	0.368210	−	0.212586i
$944$			6.78668i			0.220888i
$945$		0			0
$946$	32.7427	−	56.7120i	1.06456	−	1.84387i
$947$	45.2987	+	26.1532i	1.47201	+	0.849865i	0.999505	−	0.0314631i	$-0.0100167\pi$
$947$	45.2987	+	26.1532i	1.47201	+	0.849865i	0.472505	+	0.881328i	$0.343350\pi$
$948$	−7.96774			−0.258780
$949$	2.18925	+	48.8905i	0.0710659	+	1.58705i
$950$		0			0
$951$	10.9697	+	6.33337i	0.355717	+	0.205374i
$952$	4.64516	−	8.04565i	0.150550	−	0.260761i
$953$	−14.4414	−	25.0132i	−0.467802	−	0.810256i	0.531521	−	0.847045i	$-0.321621\pi$
$953$	−14.4414	−	25.0132i	−0.467802	−	0.810256i	−0.999323	+	0.0367885i	$0.988287\pi$
$954$		−	5.48693i		−	0.177646i
$955$		0			0
$956$	−22.6904	+	13.1003i	−0.733859	+	0.423693i
$957$			22.9359i			0.741413i
$958$	−12.8413	−	22.2418i	−0.414884	−	0.718600i
$959$	−22.8947	+	39.6548i	−0.739308	+	1.28052i
$960$		0			0
$961$	18.9464			0.611173
$962$	6.11160	+	9.56973i	0.197046	+	0.308540i
$963$	−3.07180			−0.0989873
$964$	−13.5529	−	7.82479i	−0.436510	−	0.252019i
$965$		0			0
$966$	−5.73205	−	9.92820i	−0.184426	−	0.319435i
$967$		−	10.8610i		−	0.349265i	−0.984634	−	0.174633i	$-0.944126\pi$
$967$		−	10.8610i		−	0.349265i	0.984634	−	0.174633i	$-0.0558738\pi$
$968$	−15.2190	+	8.78668i	−0.489156	+	0.282415i
$969$	13.9355	−	8.04565i	0.447672	−	0.258464i
$970$		0			0
$971$	12.4990	+	21.6488i	0.401111	+	0.694744i	0.993860	−	0.110643i	$-0.0352909\pi$
$971$	12.4990	+	21.6488i	0.401111	+	0.694744i	−0.592749	+	0.805387i	$0.701958\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−11.4196	−	6.59313i	−0.366097	−	0.211366i
$974$	9.37891			0.300520
$975$		0			0
$976$	0.535898			0.0171537
$977$	37.0359	+	21.3827i	1.18488	+	0.684092i	0.957139	−	0.289629i	$-0.0935321\pi$
$977$	37.0359	+	21.3827i	1.18488	+	0.684092i	0.227743	+	0.973721i	$0.426865\pi$
$978$	−11.8134	+	20.4614i	−0.377750	+	0.654282i
$979$	−4.64992	−	8.05390i	−0.148612	−	0.257404i
$980$		0			0
$981$	−5.79441	+	3.34541i	−0.185001	+	0.106811i
$982$	−6.70177	+	3.86927i	−0.213862	+	0.123473i
$983$			10.1288i			0.323058i	0.986868	+	0.161529i	$0.0516425\pi$
$983$			10.1288i			0.323058i	−0.986868	+	0.161529i	$0.948358\pi$
$984$	1.32258	+	2.29078i	0.0421623	+	0.0730272i
$985$		0			0
$986$	14.8637	+	8.58155i	0.473356	+	0.273292i
$987$	4.22464			0.134472
$988$	−12.8731	−	6.68308i	−0.409548	−	0.212617i
$989$	−60.4691			−1.92280
$990$		0			0
$991$	−10.1241	+	17.5355i	−0.321604	+	0.557035i	−0.980819	−	0.194920i	$-0.937555\pi$
$991$	−10.1241	+	17.5355i	−0.321604	+	0.557035i	0.659215	+	0.751954i	$0.270889\pi$
$992$	−1.73592	−	3.00670i	−0.0551154	−	0.0954627i
$993$			23.6981i			0.752036i
$994$	31.9249	−	18.4318i	1.01260	−	0.584622i
$995$		0			0
$996$			11.3360i			0.359194i
$997$	−10.3981	−	18.0100i	−0.329310	−	0.570381i	0.653065	−	0.757302i	$-0.273483\pi$
$997$	−10.3981	−	18.0100i	−0.329310	−	0.570381i	−0.982375	+	0.186920i	$0.940149\pi$
$998$	−1.59053	+	2.75488i	−0.0503473	+	0.0872041i
$999$	−2.72733	−	1.57463i	−0.0862890	−	0.0498190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.g.901.4		8
5.2	odd	4		1950.2.y.j.199.2		8
5.3	odd	4		1950.2.y.k.199.3		8
5.4	even	2		390.2.bb.c.121.1	✓	8
13.10	even	6	inner	1950.2.bc.g.751.4		8
15.14	odd	2		1170.2.bs.f.901.3		8
65.4	even	6		5070.2.b.ba.1351.3		8
65.9	even	6		5070.2.b.ba.1351.6		8
65.19	odd	12		5070.2.a.ca.1.3		4
65.23	odd	12		1950.2.y.j.49.2		8
65.49	even	6		390.2.bb.c.361.1	yes	8
65.59	odd	12		5070.2.a.bz.1.2		4
65.62	odd	12		1950.2.y.k.49.3		8
195.179	odd	6		1170.2.bs.f.361.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.1	✓	8	5.4	even	2
390.2.bb.c.361.1	yes	8	65.49	even	6
1170.2.bs.f.361.3		8	195.179	odd	6
1170.2.bs.f.901.3		8	15.14	odd	2
1950.2.y.j.49.2		8	65.23	odd	12
1950.2.y.j.199.2		8	5.2	odd	4
1950.2.y.k.49.3		8	65.62	odd	12
1950.2.y.k.199.3		8	5.3	odd	4
1950.2.bc.g.751.4		8	13.10	even	6	inner
1950.2.bc.g.901.4		8	1.1	even	1	trivial
5070.2.a.bz.1.2		4	65.59	odd	12
5070.2.a.ca.1.3		4	65.19	odd	12
5070.2.b.ba.1351.3		8	65.4	even	6
5070.2.b.ba.1351.6		8	65.9	even	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.62926 + 2.67270i) q^{11} +1.00000 q^{12} +(3.60194 - 0.161290i) q^{13} +2.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(-3.48387 + 2.01141i) q^{19} -2.32258i q^{21} +(2.67270 + 4.62926i) q^{22} +(2.46797 - 4.27464i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.20002 + 1.66129i) q^{26} -1.00000 q^{27} +(2.01141 + 1.16129i) q^{28} +(-2.14539 + 3.71592i) q^{29} +3.47183i q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.62926 - 2.67270i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(2.72733 + 1.57463i) q^{37} -4.02283 q^{38} +(1.66129 - 3.20002i) q^{39} +(2.29078 + 1.32258i) q^{41} +(1.16129 - 2.01141i) q^{42} +(-6.12539 - 10.6095i) q^{43} +5.34541i q^{44} +(4.27464 - 2.46797i) q^{46} +1.81894i q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.802812 + 1.39051i) q^{49} -4.00000 q^{51} +(1.94065 + 3.03873i) q^{52} +5.48693 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.16129 + 2.01141i) q^{56} +4.02283i q^{57} +(-3.71592 + 2.14539i) q^{58} +(5.87744 - 3.39334i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(-1.73592 + 3.00670i) q^{62} +(-2.01141 - 1.16129i) q^{63} -1.00000 q^{64} +5.34541 q^{66} +(-3.55872 - 2.05463i) q^{67} +(2.00000 - 3.46410i) q^{68} +(-2.46797 - 4.27464i) q^{69} +(13.7454 - 7.93593i) q^{71} +(0.866025 - 0.500000i) q^{72} +13.5734i q^{73} +(1.57463 + 2.72733i) q^{74} +(-3.48387 - 2.01141i) q^{76} +12.4151 q^{77} +(3.03873 - 1.94065i) q^{78} -7.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.32258 + 2.29078i) q^{82} +11.3360i q^{83} +(2.01141 - 1.16129i) q^{84} -12.2508i q^{86} +(2.14539 + 3.71592i) q^{87} +(-2.67270 + 4.62926i) q^{88} +(-1.50670 - 0.869891i) q^{89} +(7.05769 - 4.50732i) q^{91} +4.93593 q^{92} +(3.00670 + 1.73592i) q^{93} +(-0.909471 + 1.57525i) q^{94} +1.00000i q^{96} +(13.9510 - 8.05463i) q^{97} +(-1.39051 + 0.802812i) q^{98} -5.34541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} - 2 q^{22} - 4 q^{23} - 12 q^{26} - 8 q^{27} - 8 q^{29} + 6 q^{33} + 4 q^{36} - 30 q^{37} + 6 q^{39} + 2 q^{42} - 14 q^{43} - 6 q^{46} + 4 q^{48} + 14 q^{49} - 32 q^{51} + 6 q^{52} - 16 q^{53} + 2 q^{56} + 6 q^{58} + 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} - 4 q^{66} - 24 q^{67} + 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} - 6 q^{76} - 16 q^{77} - 6 q^{78} - 20 q^{79} - 4 q^{81} - 4 q^{82} + 8 q^{87} + 2 q^{88} + 42 q^{89} - 10 q^{91} - 8 q^{92} - 30 q^{93} - 8 q^{94} + 24 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^9 + 6 * q^11 + 8 * q^12 + 12 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 - 2 * q^22 - 4 * q^23 - 12 * q^26 - 8 * q^27 - 8 * q^29 + 6 * q^33 + 4 * q^36 - 30 * q^37 + 6 * q^39 + 2 * q^42 - 14 * q^43 - 6 * q^46 + 4 * q^48 + 14 * q^49 - 32 * q^51 + 6 * q^52 - 16 * q^53 + 2 * q^56 + 6 * q^58 + 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 - 4 * q^66 - 24 * q^67 + 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 - 6 * q^76 - 16 * q^77 - 6 * q^78 - 20 * q^79 - 4 * q^81 - 4 * q^82 + 8 * q^87 + 2 * q^88 + 42 * q^89 - 10 * q^91 - 8 * q^92 - 30 * q^93 - 8 * q^94 + 24 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

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