LMFDB - Embedded newform 390.2.bb.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(121,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("390.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bb (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:	$3.11416567883$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$3.17270 - 3.17270i$ of defining polynomial
Character	$\chi$	$=$	390.361
Dual form			390.2.bb.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(4.62926 - 2.67270i) q^{11} -1.00000 q^{12} +(-3.60194 - 0.161290i) q^{13} +2.32258 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(-3.48387 - 2.01141i) q^{19} +(0.866025 + 0.500000i) q^{20} +2.32258i q^{21} +(-2.67270 + 4.62926i) q^{22} +(-2.46797 - 4.27464i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(3.20002 - 1.66129i) q^{26} +1.00000 q^{27} +(-2.01141 + 1.16129i) q^{28} +(-2.14539 - 3.71592i) q^{29} +(-0.500000 + 0.866025i) q^{30} -3.47183i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.62926 - 2.67270i) q^{33} +4.00000i q^{34} +(1.16129 - 2.01141i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.72733 + 1.57463i) q^{37} +4.02283 q^{38} +(1.66129 + 3.20002i) q^{39} -1.00000 q^{40} +(2.29078 - 1.32258i) q^{41} +(-1.16129 - 2.01141i) q^{42} +(6.12539 - 10.6095i) q^{43} -5.34541i q^{44} +(-0.866025 - 0.500000i) q^{45} +(4.27464 + 2.46797i) q^{46} +1.81894i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.802812 - 1.39051i) q^{49} +(0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(-1.94065 + 3.03873i) q^{52} -5.48693 q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.67270 + 4.62926i) q^{55} +(1.16129 - 2.01141i) q^{56} +4.02283i q^{57} +(3.71592 + 2.14539i) q^{58} +(5.87744 + 3.39334i) q^{59} -1.00000i q^{60} +(-0.267949 + 0.464102i) q^{61} +(1.73592 + 3.00670i) q^{62} +(2.01141 - 1.16129i) q^{63} -1.00000 q^{64} +(0.161290 - 3.60194i) q^{65} +5.34541 q^{66} +(3.55872 - 2.05463i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.46797 + 4.27464i) q^{69} +2.32258i q^{70} +(13.7454 + 7.93593i) q^{71} +(-0.866025 - 0.500000i) q^{72} +13.5734i q^{73} +(1.57463 - 2.72733i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-3.48387 + 2.01141i) q^{76} -12.4151 q^{77} +(-3.03873 - 1.94065i) q^{78} -7.96774 q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.32258 + 2.29078i) q^{82} +11.3360i q^{83} +(2.01141 + 1.16129i) q^{84} +(3.46410 + 2.00000i) q^{85} +12.2508i q^{86} +(-2.14539 + 3.71592i) q^{87} +(2.67270 + 4.62926i) q^{88} +(-1.50670 + 0.869891i) q^{89} +1.00000 q^{90} +(7.05769 + 4.50732i) q^{91} -4.93593 q^{92} +(-3.00670 + 1.73592i) q^{93} +(-0.909471 - 1.57525i) q^{94} +(2.01141 - 3.48387i) q^{95} -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} - 4 q^{10} + 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} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 4 q^{36} + 30 q^{37} + 6 q^{39} - 8 q^{40} - 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^{55} + 2 q^{56} - 6 q^{58} + 24 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 6 q^{65} - 4 q^{66} + 24 q^{67} - 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} + 4 q^{75} - 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} + 8 q^{90} - 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 - 4 * q^10 + 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 - 8 * q^25 - 12 * q^26 + 8 * q^27 - 8 * q^29 - 4 * q^30 - 6 * q^33 + 2 * q^35 + 4 * q^36 + 30 * q^37 + 6 * q^39 - 8 * q^40 - 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^55 + 2 * q^56 - 6 * q^58 + 24 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 6 * q^65 - 4 * q^66 + 24 * q^67 - 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 + 4 * q^75 - 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 + 8 * q^90 - 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	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
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−2.01141	−	1.16129i	−0.760243	−	0.438926i	0.0691402	−	0.997607i	$-0.477974\pi$
$7$	−2.01141	−	1.16129i	−0.760243	−	0.438926i	−0.829383	+	0.558681i	$0.811308\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	4.62926	−	2.67270i	1.39577	−	0.805850i	0.401827	−	0.915716i	$-0.368375\pi$
$11$	4.62926	−	2.67270i	1.39577	−	0.805850i	0.993946	+	0.109865i	$0.0350420\pi$
$12$	−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
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.48387	−	2.01141i	−0.799254	−	0.461450i	0.0439559	−	0.999033i	$-0.486004\pi$
$19$	−3.48387	−	2.01141i	−0.799254	−	0.461450i	−0.843210	+	0.537584i	$0.819337\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$			2.32258i			0.506828i
$22$	−2.67270	+	4.62926i	−0.569822	+	0.986961i
$23$	−2.46797	−	4.27464i	−0.514607	−	0.891325i	−0.999856	−	0.0169494i	$-0.994605\pi$
$23$	−2.46797	−	4.27464i	−0.514607	−	0.891325i	0.485250	−	0.874376i	$-0.338729\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−1.00000			−0.200000
$26$	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	0.595139	−	0.803623i	$-0.297097\pi$
$29$	−2.14539	−	3.71592i	−0.398388	−	0.690029i	−0.993527	+	0.113594i	$0.963764\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$		−	3.47183i		−	0.623560i	−0.950154	−	0.311780i	$-0.899075\pi$
$31$		−	3.47183i		−	0.623560i	0.950154	−	0.311780i	$-0.100925\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.62926	−	2.67270i	−0.805850	−	0.465258i
$34$			4.00000i			0.685994i
$35$	1.16129	−	2.01141i	0.196294	−	0.339991i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−2.72733	+	1.57463i	−0.448371	+	0.258867i	−0.707142	−	0.707072i	$-0.750016\pi$
$37$	−2.72733	+	1.57463i	−0.448371	+	0.258867i	0.258771	+	0.965939i	$0.416682\pi$
$38$	4.02283			0.652589
$39$	1.66129	+	3.20002i	0.266019	+	0.512413i
$40$	−1.00000			−0.158114
$41$	2.29078	−	1.32258i	0.357759	−	0.206552i	−0.310338	−	0.950626i	$-0.600442\pi$
$41$	2.29078	−	1.32258i	0.357759	−	0.206552i	0.668097	+	0.744074i	$0.267109\pi$
$42$	−1.16129	−	2.01141i	−0.179191	−	0.310368i
$43$	6.12539	−	10.6095i	0.934113	−	1.61793i	0.157906	−	0.987454i	$-0.449526\pi$
$43$	6.12539	−	10.6095i	0.934113	−	1.61793i	0.776207	−	0.630478i	$-0.217141\pi$
$44$		−	5.34541i		−	0.805850i
$45$	−0.866025	−	0.500000i	−0.129099	−	0.0745356i
$46$	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
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−4.00000			−0.560112
$52$	−1.94065	+	3.03873i	−0.269120	+	0.421396i
$53$	−5.48693			−0.753687			−0.376844	−	0.926277i	$-0.622991\pi$
$53$	−5.48693			−0.753687			−0.376844	+	0.926277i	$0.622991\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	2.67270	+	4.62926i	0.360387	+	0.624209i
$56$	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	0.831152	−	0.556046i	$-0.187682\pi$
$59$	5.87744	+	3.39334i	0.765177	+	0.441775i	−0.0659742	+	0.997821i	$0.521016\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	−0.882669	−	0.469995i	$-0.844256\pi$
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	0.848362	+	0.529417i	$0.177589\pi$
$62$	1.73592	+	3.00670i	0.220462	+	0.381851i
$63$	2.01141	−	1.16129i	0.253414	−	0.146309i
$64$	−1.00000			−0.125000
$65$	0.161290	−	3.60194i	0.0200055	−	0.446766i
$66$	5.34541			0.657974
$67$	3.55872	−	2.05463i	0.434767	−	0.251013i	−0.266608	−	0.963805i	$-0.585903\pi$
$67$	3.55872	−	2.05463i	0.434767	−	0.251013i	0.701376	+	0.712792i	$0.252570\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−2.46797	+	4.27464i	−0.297108	+	0.514607i
$70$			2.32258i			0.277601i
$71$	13.7454	+	7.93593i	1.63128	+	0.941822i	0.983698	+	0.179830i	$0.0575547\pi$
$71$	13.7454	+	7.93593i	1.63128	+	0.941822i	0.647586	+	0.761992i	$0.275779\pi$
$72$	−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
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−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	$0.647942\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−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
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$			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	−0.577725	−	0.816232i	$-0.696059\pi$
$89$	−1.50670	+	0.869891i	−0.159709	+	0.0922083i	0.418015	+	0.908440i	$0.362726\pi$
$90$	1.00000			0.105409
$91$	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
$95$	2.01141	−	3.48387i	0.206367	−	0.357437i
$96$		−	1.00000i		−	0.102062i
$97$	−13.9510	−	8.05463i	−1.41651	−	0.817824i	−0.420522	−	0.907282i	$-0.638153\pi$
$97$	−13.9510	−	8.05463i	−1.41651	−	0.817824i	−0.995991	+	0.0894586i	$0.971486\pi$
$98$	1.39051	+	0.802812i	0.140463	+	0.0810962i
$99$			5.34541i			0.537233i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.34541	+	10.9906i	0.631391	+	1.09360i	0.987267	+	0.159069i	$0.0508492\pi$
$101$	6.34541	+	10.9906i	0.631391	+	1.09360i	−0.355876	+	0.934533i	$0.615817\pi$
$102$	3.46410	−	2.00000i	0.342997	−	0.198030i
$103$	−4.79612			−0.472575			−0.236288	−	0.971683i	$-0.575931\pi$
$103$	−4.79612			−0.472575			−0.236288	+	0.971683i	$0.575931\pi$
$104$	0.161290	−	3.60194i	0.0158158	−	0.353199i
$105$	−2.32258			−0.226661
$106$	4.75182	−	2.74346i	0.461537	−	0.266469i
$107$	−1.53590	−	2.66025i	−0.148481	−	0.257176i	0.782185	−	0.623046i	$-0.214105\pi$
$107$	−1.53590	−	2.66025i	−0.148481	−	0.257176i	−0.930666	+	0.365869i	$0.880772\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			6.69081i			0.640864i	0.947272	+	0.320432i	$0.103828\pi$
$109$			6.69081i			0.640864i	−0.947272	+	0.320432i	$0.896172\pi$
$110$	−4.62926	−	2.67270i	−0.441382	−	0.254832i
$111$	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	$-0.724795\pi$
$113$	3.55486	−	6.15720i	0.334413	−	0.579220i	0.983372	+	0.181603i	$0.0581286\pi$
$114$	−2.01141	−	3.48387i	−0.188386	−	0.326294i
$115$	4.27464	−	2.46797i	0.398613	−	0.230139i
$116$	−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
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	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
$125$		−	1.00000i		−	0.0894427i
$126$	−1.16129	+	2.01141i	−0.103456	+	0.179191i
$127$	−1.06604	−	1.84644i	−0.0945961	−	0.163845i	0.814844	−	0.579680i	$-0.196823\pi$
$127$	−1.06604	−	1.84644i	−0.0945961	−	0.163845i	−0.909440	+	0.415835i	$0.863489\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−12.2508			−1.07862
$130$	1.66129	+	3.20002i	0.145705	+	0.280660i
$131$	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
$135$			1.00000i			0.0860663i
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	17.0736	+	9.85744i	1.45870	+	0.842178i	0.998947	−	0.0458713i	$-0.0146064\pi$
$137$	17.0736	+	9.85744i	1.45870	+	0.842178i	0.459748	+	0.888049i	$0.347940\pi$
$138$		−	4.93593i		−	0.420175i
$139$	−2.83871	+	4.91679i	−0.240776	+	0.417037i	−0.960936	−	0.276772i	$-0.910735\pi$
$139$	−2.83871	+	4.91679i	−0.240776	+	0.417037i	0.720159	+	0.693809i	$0.244069\pi$
$140$	−1.16129	−	2.01141i	−0.0981469	−	0.169995i
$141$	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
$145$	3.71592	−	2.14539i	0.308590	−	0.178165i
$146$	−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	−0.389499	−	0.921027i	$-0.627352\pi$
$149$	−16.8680	−	9.73875i	−1.38188	−	0.797829i	−0.992382	+	0.123198i	$0.960685\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$		−	14.5170i		−	1.18138i	−0.806899	−	0.590690i	$-0.798856\pi$
$151$		−	14.5170i		−	1.18138i	0.806899	−	0.590690i	$-0.201144\pi$
$152$	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
$155$	3.47183			0.278864
$156$	3.60194	+	0.161290i	0.288386	+	0.0129135i
$157$	24.3829			1.94596			0.972982	−	0.230879i	$-0.0741602\pi$
$157$	24.3829			1.94596			0.972982	+	0.230879i	$0.0741602\pi$
$158$	6.90026	−	3.98387i	0.548956	−	0.316940i
$159$	2.74346	+	4.75182i	0.217571	+	0.376844i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$			11.4641i			0.903498i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	20.4614	+	11.8134i	1.60266	+	0.925295i	0.990953	+	0.134208i	$0.0428492\pi$
$163$	20.4614	+	11.8134i	1.60266	+	0.925295i	0.611704	+	0.791086i	$0.290484\pi$
$164$		−	2.64516i		−	0.206552i
$165$	2.67270	−	4.62926i	0.208070	−	0.360387i
$166$	−5.66799	−	9.81724i	−0.439921	−	0.761966i
$167$	14.5035	−	8.37357i	1.12231	−	0.647967i	0.180321	−	0.983608i	$-0.442286\pi$
$167$	14.5035	−	8.37357i	1.12231	−	0.647967i	0.941990	+	0.335641i	$0.108953\pi$
$168$	−2.32258			−0.179191
$169$	12.9480	+	1.16191i	0.995998	+	0.0893780i
$170$	−4.00000			−0.306786
$171$	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	−0.377439	−	0.926034i	$-0.623195\pi$
$173$	8.06604	−	13.9708i	0.613250	−	1.06218i	0.990689	−	0.136146i	$-0.0434715\pi$
$174$		−	4.29078i		−	0.325283i
$175$	2.01141	+	1.16129i	0.152049	+	0.0877853i
$176$	−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	0.969849	−	0.243706i	$-0.0783631\pi$
$179$	3.66412	+	6.34644i	0.273869	+	0.474355i	−0.695980	+	0.718061i	$0.745030\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	−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
$185$	−1.57463	−	2.72733i	−0.115769	−	0.200518i
$186$	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
$190$			4.02283i			0.291846i
$191$	8.51873	−	14.7549i	0.616394	−	1.06763i	−0.373744	−	0.927532i	$-0.621926\pi$
$191$	8.51873	−	14.7549i	0.616394	−	1.06763i	0.990138	−	0.140094i	$-0.0447404\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	5.33031	−	3.07746i	0.383684	−	0.221520i	−0.295736	−	0.955270i	$-0.595565\pi$
$193$	5.33031	−	3.07746i	0.383684	−	0.221520i	0.679420	+	0.733750i	$0.262231\pi$
$194$	16.1093			1.15658
$195$	−3.20002	+	1.66129i	−0.229158	+	0.118967i
$196$	−1.60562			−0.114687
$197$	−11.9396	+	6.89334i	−0.850662	+	0.491130i	−0.860874	−	0.508818i	$-0.830083\pi$
$197$	−11.9396	+	6.89334i	−0.850662	+	0.491130i	0.0102119	+	0.999948i	$0.496749\pi$
$198$	−2.67270	−	4.62926i	−0.189941	−	0.328987i
$199$	1.14152	−	1.97717i	0.0809203	−	0.140158i	−0.822725	−	0.568439i	$-0.807547\pi$
$199$	1.14152	−	1.97717i	0.0809203	−	0.140158i	0.903646	+	0.428281i	$0.140881\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−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
$205$	1.32258	+	2.29078i	0.0923730	+	0.159995i
$206$	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
$210$	2.01141	−	1.16129i	0.138801	−	0.0801366i
$211$	−11.2387	−	19.4661i	−0.773707	−	1.34010i	−0.935518	−	0.353278i	$-0.885067\pi$
$211$	−11.2387	−	19.4661i	−0.773707	−	1.34010i	0.161811	−	0.986822i	$-0.448267\pi$
$212$	−2.74346	+	4.75182i	−0.188422	+	0.326356i
$213$		−	15.8719i		−	1.08752i
$214$	2.66025	+	1.53590i	0.181851	+	0.104992i
$215$	10.6095	+	6.12539i	0.723561	+	0.417748i
$216$			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
$220$	5.34541			0.360387
$221$	−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	$-0.651965\pi$
$223$	1.19417	−	0.689457i	0.0799678	−	0.0461694i	0.539451	+	0.842017i	$0.318632\pi$
$224$	−1.16129	−	2.01141i	−0.0775919	−	0.134393i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$			7.10972i			0.472931i
$227$	−16.7321	−	9.66025i	−1.11055	−	0.641174i	−0.171575	−	0.985171i	$-0.554885\pi$
$227$	−16.7321	−	9.66025i	−1.11055	−	0.641174i	−0.938971	+	0.343998i	$0.888219\pi$
$228$	3.48387	+	2.01141i	0.230725	+	0.133209i
$229$			15.7626i			1.04162i	0.853672	+	0.520811i	$0.174370\pi$
$229$			15.7626i			1.04162i	−0.853672	+	0.520811i	$0.825630\pi$
$230$	−2.46797	+	4.27464i	−0.162733	+	0.281862i
$231$	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	$-0.682437\pi$
$233$	−16.5549			−1.08455			−0.542275	+	0.840201i	$0.682437\pi$
$234$	−0.161290	+	3.60194i	−0.0105438	+	0.235466i
$235$	−1.81894			−0.118655
$236$	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	$-0.678175\pi$
$239$		−	26.2006i		−	1.69477i	0.530976	−	0.847387i	$-0.321825\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	−13.5529	−	7.82479i	−0.873021	−	0.504039i	−0.00466988	−	0.999989i	$-0.501486\pi$
$241$	−13.5529	−	7.82479i	−0.873021	−	0.504039i	−0.868351	+	0.495950i	$0.834820\pi$
$242$			17.5734i			1.12966i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.267949	+	0.464102i	0.0171537	+	0.0297111i
$245$	1.39051	−	0.802812i	0.0888365	−	0.0512898i
$246$	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
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−14.1708	+	24.5446i	−0.894454	+	1.54924i	−0.0599750	+	0.998200i	$0.519102\pi$
$251$	−14.1708	+	24.5446i	−0.894454	+	1.54924i	−0.834479	+	0.551040i	$0.814231\pi$
$252$		−	2.32258i		−	0.146309i
$253$	−22.8497	−	13.1923i	−1.43655	−	0.829392i
$254$	1.84644	+	1.06604i	0.115856	+	0.0668895i
$255$		−	4.00000i		−	0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.25465	−	10.8334i	−0.390154	−	0.675767i	0.602315	−	0.798258i	$-0.294245\pi$
$257$	−6.25465	−	10.8334i	−0.390154	−	0.675767i	−0.992470	+	0.122491i	$0.960912\pi$
$258$	10.6095	−	6.12539i	0.660518	−	0.381350i
$259$	7.31439			0.454494
$260$	−3.03873	−	1.94065i	−0.188454	−	0.120354i
$261$	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	$-0.0595919\pi$
$263$	5.35295	+	9.27159i	0.330077	+	0.571711i	−0.652449	+	0.757832i	$0.726259\pi$
$264$	2.67270	−	4.62926i	0.164493	−	0.284911i
$265$		−	5.48693i		−	0.337059i
$266$	−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	−0.957633	−	0.287990i	$-0.907013\pi$
$269$	−3.76261	+	6.51703i	−0.229410	+	0.397350i	0.728223	+	0.685340i	$0.240346\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	8.52920	−	4.92434i	0.518112	−	0.299132i	−0.218050	−	0.975938i	$-0.569970\pi$
$271$	8.52920	−	4.92434i	0.518112	−	0.299132i	0.736162	+	0.676805i	$0.236636\pi$
$272$	−4.00000			−0.242536
$273$	0.374609	−	8.36580i	0.0226723	−	0.506321i
$274$	−19.7149			−1.19102
$275$	−4.62926	+	2.67270i	−0.279155	+	0.161170i
$276$	2.46797	+	4.27464i	0.148554	+	0.257303i
$277$	0.476550	−	0.825410i	0.0286331	−	0.0495941i	−0.851354	−	0.524592i	$-0.824218\pi$
$277$	0.476550	−	0.825410i	0.0286331	−	0.0495941i	0.879987	+	0.474998i	$0.157551\pi$
$278$		−	5.67742i		−	0.340509i
$279$	3.00670	+	1.73592i	0.180006	+	0.103927i
$280$	2.01141	+	1.16129i	0.120205	+	0.0694003i
$281$			5.57336i			0.332479i	0.986085	+	0.166239i	$0.0531625\pi$
$281$			5.57336i			0.332479i	−0.986085	+	0.166239i	$0.946838\pi$
$282$	−0.909471	+	1.57525i	−0.0541582	+	0.0938048i
$283$	11.0067	+	19.0642i	0.654280	+	1.13325i	0.982074	+	0.188497i	$0.0603616\pi$
$283$	11.0067	+	19.0642i	0.654280	+	1.13325i	−0.327794	+	0.944749i	$0.606305\pi$
$284$	13.7454	−	7.93593i	0.815642	−	0.470911i
$285$	−4.02283			−0.238292
$286$	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
$290$	−2.14539	+	3.71592i	−0.125981	+	0.218206i
$291$			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	$-0.269276\pi$
$293$	5.92623	+	3.42151i	0.346214	+	0.199887i	−0.316803	+	0.948491i	$0.602609\pi$
$294$		−	1.60562i		−	0.0936419i
$295$	−3.39334	+	5.87744i	−0.197568	+	0.342198i
$296$	−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
$300$	1.00000			0.0577350
$301$	−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
$305$	−0.464102	−	0.267949i	−0.0265744	−	0.0153427i
$306$	−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
$310$	−3.00670	+	1.73592i	−0.170769	+	0.0985934i
$311$	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	$-0.243125\pi$
$313$	25.5545			1.44443			0.722213	+	0.691671i	$0.243125\pi$
$314$	−21.1162	+	12.1914i	−1.19166	+	0.688002i
$315$	1.16129	+	2.01141i	0.0654313	+	0.113330i
$316$	−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
$320$		−	1.00000i		−	0.0559017i
$321$	−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
$325$	3.60194	+	0.161290i	0.199800	+	0.00894675i
$326$	−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
$330$			5.34541i			0.294255i
$331$	−20.5231	−	11.8490i	−1.12805	−	0.651282i	−0.184609	−	0.982812i	$-0.559102\pi$
$331$	−20.5231	−	11.8490i	−1.12805	−	0.651282i	−0.943445	+	0.331530i	$0.892435\pi$
$332$	9.81724	+	5.66799i	0.538791	+	0.311071i
$333$		−	3.14925i		−	0.172578i
$334$	−8.37357	+	14.5035i	−0.458182	+	0.793594i
$335$	2.05463	+	3.55872i	0.112256	+	0.194434i
$336$	2.01141	−	1.16129i	0.109732	−	0.0633536i
$337$	19.5554			1.06525			0.532625	−	0.846351i	$-0.321205\pi$
$337$	19.5554			1.06525			0.532625	+	0.846351i	$0.321205\pi$
$338$	−11.7942	+	5.46774i	−0.641521	+	0.297406i
$339$	−7.10972			−0.386147
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	−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
$345$	−4.27464	−	2.46797i	−0.230139	−	0.132871i
$346$			16.1321i			0.867266i
$347$	11.5187	−	19.9510i	0.618358	−	1.07103i	−0.371427	−	0.928462i	$-0.621132\pi$
$347$	11.5187	−	19.9510i	0.618358	−	1.07103i	0.989785	−	0.142565i	$-0.0455351\pi$
$348$	2.14539	+	3.71592i	0.115005	+	0.199194i
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	−0.100924	−	0.994894i	$-0.532180\pi$
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	0.811141	+	0.584850i	$0.198847\pi$
$350$	−2.32258			−0.124147
$351$	−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	$-0.393819\pi$
$353$	24.6018	−	14.2039i	1.30942	−	0.755996i	0.982000	+	0.188881i	$0.0604860\pi$
$354$	3.39334	+	5.87744i	0.180354	+	0.312382i
$355$	−7.93593	+	13.7454i	−0.421196	+	0.729532i
$356$			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	$-0.786289\pi$
$359$		−	23.5734i		−	1.24415i	0.782956	−	0.622077i	$-0.213711\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	−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
$365$	−13.5734			−0.710462
$366$	−0.464102	+	0.267949i	−0.0242590	+	0.0140059i
$367$	−13.7454	−	23.8078i	−0.717506	−	1.24276i	−0.961985	−	0.273103i	$-0.911950\pi$
$367$	−13.7454	−	23.8078i	−0.717506	−	1.24276i	0.244479	−	0.969655i	$-0.421383\pi$
$368$	−2.46797	+	4.27464i	−0.128652	+	0.222831i
$369$			2.64516i			0.137701i
$370$	2.72733	+	1.57463i	0.141787	+	0.0818609i
$371$	11.0365	+	6.37191i	0.572985	+	0.330813i
$372$			3.47183i			0.180006i
$373$	−13.1710	+	22.8129i	−0.681971	+	1.18121i	0.292408	+	0.956294i	$0.405544\pi$
$373$	−13.1710	+	22.8129i	−0.681971	+	1.18121i	−0.974379	+	0.224914i	$0.927790\pi$
$374$	10.6908	+	18.5170i	0.552809	+	0.957493i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$	−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	−0.489990	−	0.871728i	$-0.663000\pi$
$379$	0.388456	−	0.224275i	0.0199537	−	0.0115202i	0.509944	+	0.860208i	$0.329666\pi$
$380$	−2.01141	−	3.48387i	−0.103183	−	0.178719i
$381$	−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	$-0.233098\pi$
$383$	10.4985	+	6.06133i	0.536450	+	0.309719i	−0.207189	+	0.978301i	$0.566432\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		−	12.4151i		−	0.632734i
$386$	−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	$0.343524\pi$
$390$	1.94065	−	3.03873i	0.0982687	−	0.153872i
$391$	−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
$395$		−	7.96774i		−	0.400900i
$396$	4.62926	+	2.67270i	0.232629	+	0.134308i
$397$	9.78970	+	5.65208i	0.491331	+	0.283670i	0.725126	−	0.688616i	$-0.241781\pi$
$397$	9.78970	+	5.65208i	0.491331	+	0.283670i	−0.233796	+	0.972286i	$0.575115\pi$
$398$			2.28304i			0.114439i
$399$	4.67167	−	8.09156i	0.233876	−	0.405085i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−1.30406	+	0.752899i	−0.0651216	+	0.0375980i	−0.532207	−	0.846614i	$-0.678637\pi$
$401$	−1.30406	+	0.752899i	−0.0651216	+	0.0375980i	0.467086	+	0.884212i	$0.345304\pi$
$402$	4.10926			0.204951
$403$	−0.559971	+	12.5053i	−0.0278942	+	0.622935i
$404$	12.6908			0.631391
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−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	0.719170	−	0.694834i	$-0.244522\pi$
$409$	9.64697	+	5.56968i	0.477012	+	0.275403i	−0.242158	+	0.970237i	$0.577855\pi$
$410$	−2.29078	−	1.32258i	−0.113133	−	0.0653176i
$411$		−	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
$415$	−11.3360			−0.556461
$416$	−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	0.990895	−	0.134635i	$-0.0429861\pi$
$419$	7.75488	+	13.4318i	0.378851	+	0.656188i	−0.612045	+	0.790823i	$0.709653\pi$
$420$	−1.16129	+	2.01141i	−0.0566651	+	0.0981469i
$421$			39.4452i			1.92244i	0.275778	+	0.961221i	$0.411065\pi$
$421$			39.4452i			1.92244i	−0.275778	+	0.961221i	$0.588935\pi$
$422$	19.4661	+	11.2387i	0.947594	+	0.547094i
$423$	−1.57525	−	0.909471i	−0.0765913	−	0.0442200i
$424$		−	5.48693i		−	0.266469i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	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
$430$	−12.2508			−0.590785
$431$	1.86621	−	1.07746i	0.0898921	−	0.0518993i	−0.454380	−	0.890808i	$-0.650139\pi$
$431$	1.86621	−	1.07746i	0.0898921	−	0.0518993i	0.544272	+	0.838909i	$0.316806\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	0.669689	−	1.15994i	0.0321832	−	0.0557429i	−0.849485	−	0.527612i	$-0.823087\pi$
$433$	0.669689	−	1.15994i	0.0321832	−	0.0557429i	0.881668	+	0.471870i	$0.156421\pi$
$434$		−	8.06361i		−	0.387066i
$435$	−3.71592	−	2.14539i	−0.178165	−	0.102863i
$436$	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	−0.944658	−	0.328055i	$-0.893607\pi$
$439$	−15.8490	−	27.4513i	−0.756434	−	1.31018i	0.188225	−	0.982126i	$-0.439727\pi$
$440$	−4.62926	+	2.67270i	−0.220691	+	0.127416i
$441$	1.60562			0.0764583
$442$	0.645159	−	14.4078i	0.0306871	−	0.685308i
$443$	−28.0904			−1.33461			−0.667307	−	0.744782i	$-0.732553\pi$
$443$	−28.0904			−1.33461			−0.667307	+	0.744782i	$0.732553\pi$
$444$	2.72733	−	1.57463i	0.129434	−	0.0747285i
$445$	−0.869891	−	1.50670i	−0.0412368	−	0.0714242i
$446$	−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	0.956438	−	0.291936i	$-0.0942994\pi$
$449$	25.0426	+	14.4583i	1.18183	+	0.682332i	0.225395	+	0.974267i	$0.427633\pi$
$450$			1.00000i			0.0471405i
$451$	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
$455$	−4.50732	+	7.05769i	−0.211306	+	0.330870i
$456$	−4.02283			−0.188386
$457$	8.39958	−	4.84950i	0.392916	−	0.226850i	−0.290507	−	0.956873i	$-0.593824\pi$
$457$	8.39958	−	4.84950i	0.392916	−	0.226850i	0.683423	+	0.730023i	$0.260491\pi$
$458$	−7.88130	−	13.6508i	−0.368269	−	0.637861i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		−	4.93593i		−	0.230139i
$461$	10.3905	+	5.99896i	0.483934	+	0.279400i	0.722055	−	0.691836i	$-0.243198\pi$
$461$	10.3905	+	5.99896i	0.483934	+	0.279400i	−0.238120	+	0.971236i	$0.576531\pi$
$462$	−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
$465$	−1.73592	−	3.00670i	−0.0805012	−	0.139432i
$466$	14.3370	−	8.27747i	0.664149	−	0.383447i
$467$	26.2642			1.21536			0.607681	−	0.794182i	$-0.292100\pi$
$467$	26.2642			1.21536			0.607681	+	0.794182i	$0.292100\pi$
$468$	−1.66129	−	3.20002i	−0.0767932	−	0.147921i
$469$	−9.54409			−0.440705
$470$	1.57525	−	0.909471i	0.0726609	−	0.0419508i
$471$	−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
$475$	3.48387	+	2.01141i	0.159851	+	0.0922900i
$476$			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	−0.913017	−	0.407922i	$-0.866253\pi$
$479$	−22.2418	+	12.8413i	−1.01625	+	0.586735i	−0.103237	+	0.994657i	$0.532920\pi$
$480$	1.00000			0.0456435
$481$	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
$485$	8.05463	−	13.9510i	0.365742	−	0.633484i
$486$		−	1.00000i		−	0.0453609i
$487$	−8.12238	−	4.68946i	−0.368060	−	0.212500i	0.304551	−	0.952496i	$-0.401494\pi$
$487$	−8.12238	−	4.68946i	−0.368060	−	0.212500i	−0.672611	+	0.739997i	$0.734827\pi$
$488$	−0.464102	−	0.267949i	−0.0210089	−	0.0121295i
$489$		−	23.6267i		−	1.06844i
$490$	−0.802812	+	1.39051i	−0.0362673	+	0.0628169i
$491$	−3.86927	−	6.70177i	−0.174618	−	0.302447i	0.765411	−	0.643541i	$-0.222536\pi$
$491$	−3.86927	−	6.70177i	−0.174618	−	0.302447i	−0.940029	+	0.341095i	$0.889202\pi$
$492$	−2.29078	+	1.32258i	−0.103276	+	0.0596265i
$493$	−17.1631			−0.772987
$494$	−14.4900	−	0.648841i	−0.651935	−	0.0291927i
$495$	−5.34541			−0.240258
$496$	−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	$-0.977317\pi$
$499$		−	3.18106i		−	0.142404i	0.997462	−	0.0712019i	$-0.0226834\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−14.5035	−	8.37357i	−0.647967	−	0.374104i
$502$		−	28.3416i		−	1.26495i
$503$	17.5379	−	30.3765i	0.781975	−	1.35442i	−0.148814	−	0.988865i	$-0.547546\pi$
$503$	17.5379	−	30.3765i	0.781975	−	1.35442i	0.930789	−	0.365556i	$-0.119121\pi$
$504$	1.16129	+	2.01141i	0.0517280	+	0.0895955i
$505$	−10.9906	+	6.34541i	−0.489074	+	0.282367i
$506$	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	−0.815173	−	0.579217i	$-0.803358\pi$
$509$	−16.2697	+	9.39334i	−0.721144	+	0.416353i	0.0940298	+	0.995569i	$0.470025\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	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
$515$		−	4.79612i		−	0.211342i
$516$	−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
$520$	3.60194	+	0.161290i	0.157956	+	0.00707303i
$521$	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	$-0.0167639\pi$
$523$	10.3762	+	17.9721i	0.453718	+	0.785863i	−0.544895	+	0.838504i	$0.683431\pi$
$524$	0.629257	−	1.08991i	0.0274892	−	0.0476127i
$525$		−	2.32258i		−	0.101366i
$526$	−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
$530$	2.74346	+	4.75182i	0.119168	+	0.206406i
$531$	−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
$535$	2.66025	−	1.53590i	0.115013	−	0.0664027i
$536$	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
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$			28.7365i			1.23548i	0.786384	+	0.617739i	$0.211951\pi$
$541$			28.7365i			1.23548i	−0.786384	+	0.617739i	$0.788049\pi$
$542$	−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
$545$	−6.69081			−0.286603
$546$	3.85848	+	7.43230i	0.165128	+	0.318073i
$547$	18.3768			0.785737			0.392869	−	0.919595i	$-0.371483\pi$
$547$	18.3768			0.785737			0.392869	+	0.919595i	$0.371483\pi$
$548$	17.0736	−	9.85744i	0.729348	−	0.421089i
$549$	−0.267949	−	0.464102i	−0.0114358	−	0.0198074i
$550$	2.67270	−	4.62926i	0.113964	−	0.197392i
$551$			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
$555$	−1.57463	+	2.72733i	−0.0668392	+	0.115769i
$556$	2.83871	+	4.91679i	0.120388	+	0.208518i
$557$	22.9831	−	13.2693i	0.973826	−	0.562238i	0.0734252	−	0.997301i	$-0.476607\pi$
$557$	22.9831	−	13.2693i	0.973826	−	0.562238i	0.900400	+	0.435062i	$0.143274\pi$
$558$	−3.47183			−0.146974
$559$	−23.7745	+	37.2268i	−1.00555	+	1.57453i
$560$	−2.32258			−0.0981469
$561$	−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	$-0.874100\pi$
$563$	−3.03056	+	5.24908i	−0.127723	+	0.221222i	0.795071	+	0.606516i	$0.207433\pi$
$564$		−	1.81894i		−	0.0765913i
$565$	6.15720	+	3.55486i	0.259035	+	0.149554i
$566$	−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	0.673147	−	0.739509i	$-0.264942\pi$
$569$	−7.24818	−	12.5542i	−0.303860	−	0.526300i	−0.977007	+	0.213208i	$0.931609\pi$
$570$	3.48387	−	2.01141i	0.145923	−	0.0842488i
$571$	−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
$575$	2.46797	+	4.27464i	0.102921	+	0.178265i
$576$	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
$580$		−	4.29078i		−	0.178165i
$581$	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
$585$	3.03873	+	1.94065i	0.125636	+	0.0802361i
$586$	−6.84302			−0.282682
$587$	−3.40901	+	1.96820i	−0.140705	+	0.0812361i	−0.568700	−	0.822545i	$-0.692553\pi$
$587$	−3.40901	+	1.96820i	−0.140705	+	0.0812361i	0.427995	+	0.903781i	$0.359220\pi$
$588$	0.802812	+	1.39051i	0.0331074	+	0.0573437i
$589$	−6.98329	+	12.0954i	−0.287741	+	0.498383i
$590$		−	6.78668i		−	0.279403i
$591$	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
$595$	−4.64516	−	8.04565i	−0.190433	−	0.329840i
$596$	−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	$0.0587644\pi$
$600$	−0.866025	+	0.500000i	−0.0353553	+	0.0204124i
$601$	2.12109	+	3.67383i	0.0865209	+	0.149859i	0.906038	−	0.423196i	$-0.139092\pi$
$601$	2.12109	+	3.67383i	0.0865209	+	0.149859i	−0.819517	+	0.573054i	$0.805758\pi$
$602$	14.2267	−	24.6414i	0.579837	−	1.00431i
$603$			4.10926i			0.167342i
$604$	−12.5721	−	7.25851i	−0.511552	−	0.295345i
$605$	15.2190	+	8.78668i	0.618739	+	0.357229i
$606$			12.6908i			0.515529i
$607$	−6.03424	+	10.4516i	−0.244922	+	0.424218i	−0.962110	−	0.272663i	$-0.912096\pi$
$607$	−6.03424	+	10.4516i	−0.244922	+	0.424218i	0.717188	+	0.696880i	$0.245429\pi$
$608$	−2.01141	−	3.48387i	−0.0815736	−	0.141290i
$609$	8.63052	−	4.98283i	0.349726	−	0.201915i
$610$	0.535898			0.0216979
$611$	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	$-0.347469\pi$
$613$	36.1497	−	20.8711i	1.46007	−	0.842974i	0.999014	+	0.0443946i	$0.0141359\pi$
$614$	−2.37721	−	4.11745i	−0.0959364	−	0.166167i
$615$	1.32258	−	2.29078i	0.0533316	−	0.0923730i
$616$		−	12.4151i		−	0.500220i
$617$	−28.9760	−	16.7293i	−1.16653	−	0.673497i	−0.213670	−	0.976906i	$-0.568542\pi$
$617$	−28.9760	−	16.7293i	−1.16653	−	0.673497i	−0.952860	+	0.303409i	$0.901875\pi$
$618$	−4.15356	−	2.39806i	−0.167081	−	0.0964640i
$619$		−	38.0978i		−	1.53128i	−0.643270	−	0.765639i	$-0.722423\pi$
$619$		−	38.0978i		−	1.53128i	0.643270	−	0.765639i	$-0.277577\pi$
$620$	1.73592	−	3.00670i	0.0697161	−	0.120752i
$621$	−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
$625$	1.00000			0.0400000
$626$	−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
$630$	−2.01141	−	1.16129i	−0.0801366	−	0.0462669i
$631$	−21.4775	−	12.4000i	−0.855005	−	0.493638i	0.00733109	−	0.999973i	$-0.497666\pi$
$631$	−21.4775	−	12.4000i	−0.855005	−	0.493638i	−0.862337	+	0.506335i	$0.831000\pi$
$632$		−	7.96774i		−	0.316940i
$633$	−11.2387	+	19.4661i	−0.446700	+	0.773707i
$634$	−6.33337	−	10.9697i	−0.251530	−	0.435663i
$635$	1.84644	−	1.06604i	0.0732738	−	0.0423046i
$636$	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
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	2.04259	−	3.53788i	0.0806776	−	0.139738i	−0.822864	−	0.568239i	$-0.807625\pi$
$641$	2.04259	−	3.53788i	0.0806776	−	0.139738i	0.903541	+	0.428501i	$0.140958\pi$
$642$		−	3.07180i		−	0.121234i
$643$	−31.6806	−	18.2908i	−1.24936	−	0.721318i	−0.278377	−	0.960472i	$-0.589797\pi$
$643$	−31.6806	−	18.2908i	−1.24936	−	0.721318i	−0.970982	+	0.239154i	$0.923130\pi$
$644$	9.92820	+	5.73205i	0.391226	+	0.225874i
$645$		−	12.2508i		−	0.482374i
$646$	8.04565	−	13.9355i	0.316552	−	0.548284i
$647$	8.61704	+	14.9251i	0.338771	+	0.586768i	0.984202	−	0.177050i	$-0.0566556\pi$
$647$	8.61704	+	14.9251i	0.338771	+	0.586768i	−0.645431	+	0.763818i	$0.723322\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	36.2776			1.42402
$650$	−3.20002	+	1.66129i	−0.125515	+	0.0651611i
$651$	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	$-0.0255178\pi$
$653$	10.9637	+	18.9897i	0.429042	+	0.743123i	−0.567746	+	0.823204i	$0.692184\pi$
$654$	−3.34541	+	5.79441i	−0.130816	+	0.226579i
$655$			1.25851i			0.0491742i
$656$	−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	0.186783	−	0.982401i	$-0.440194\pi$
$659$	24.2379	−	41.9813i	0.944176	−	1.63536i	0.757393	−	0.652960i	$-0.226473\pi$
$660$	−2.67270	−	4.62926i	−0.104035	−	0.180194i
$661$	−25.8267	+	14.9110i	−1.00454	+	0.579972i	−0.909589	−	0.415510i	$-0.863603\pi$
$661$	−25.8267	+	14.9110i	−1.00454	+	0.579972i	−0.0949524	+	0.995482i	$0.530270\pi$
$662$	23.6981			0.921052
$663$	14.4078	+	0.645159i	0.559551	+	0.0250559i
$664$	−11.3360			−0.439921
$665$	−8.09156	+	4.67167i	−0.313777	+	0.181159i
$666$	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
$670$	−3.55872	−	2.05463i	−0.137486	−	0.0793773i
$671$			2.86459i			0.110586i
$672$	−1.16129	+	2.01141i	−0.0447977	+	0.0775919i
$673$	−15.3360	−	26.5627i	−0.591158	−	1.02392i	−0.994077	−	0.108680i	$-0.965338\pi$
$673$	−15.3360	−	26.5627i	−0.591158	−	1.02392i	0.402919	−	0.915236i	$-0.367996\pi$
$674$	−16.9355	+	9.77770i	−0.652330	+	0.376623i
$675$	−1.00000			−0.0384900
$676$	7.48023	−	10.6323i	0.287701	−	0.408935i
$677$	21.0831			0.810290			0.405145	−	0.914252i	$-0.367221\pi$
$677$	21.0831			0.810290			0.405145	+	0.914252i	$0.367221\pi$
$678$	6.15720	−	3.55486i	0.236466	−	0.136524i
$679$	18.7075	+	32.4024i	0.717929	+	1.24349i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$			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	$-0.415456\pi$
$683$	−11.5493	−	6.66799i	−0.441921	−	0.255143i	−0.704412	+	0.709791i	$0.748789\pi$
$684$		−	4.02283i		−	0.153817i
$685$	−9.85744	+	17.0736i	−0.376634	+	0.652348i
$686$	−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
$690$	4.93593			0.187908
$691$	−30.2289	+	17.4527i	−1.14996	+	0.663932i	−0.948878	−	0.315642i	$-0.897780\pi$
$691$	−30.2289	+	17.4527i	−1.14996	+	0.663932i	−0.201085	+	0.979574i	$0.564447\pi$
$692$	−8.06604	−	13.9708i	−0.306625	−	0.531090i
$693$	6.20757	−	10.7518i	0.235806	−	0.408428i
$694$			23.0375i			0.874490i
$695$	−4.91679	−	2.83871i	−0.186504	−	0.107678i
$696$	−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
$700$	2.01141	−	1.16129i	0.0760243	−	0.0438926i
$701$	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
$705$	0.909471	+	1.57525i	0.0342527	+	0.0593274i
$706$	−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	0.545385	−	0.838186i	$-0.316384\pi$
$709$	2.45467	+	1.41720i	0.0921869	+	0.0532242i	−0.453198	+	0.891410i	$0.649717\pi$
$710$		−	15.8719i		−	0.595661i
$711$	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
$715$	−8.88027	−	17.1054i	−0.332103	−	0.639706i
$716$	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	0.0941451	+	0.995558i	$0.469988\pi$
$719$	−21.8564	+	37.8564i	−0.815106	+	1.41181i	−0.909251	+	0.416247i	$0.863345\pi$
$720$			1.00000i			0.0372678i
$721$	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
$725$	2.14539	+	3.71592i	0.0796777	+	0.138006i
$726$	15.2190	−	8.78668i	0.564829	−	0.326104i
$727$	−16.2568			−0.602932			−0.301466	−	0.953477i	$-0.597476\pi$
$727$	−16.2568			−0.602932			−0.301466	+	0.953477i	$0.597476\pi$
$728$	−4.50732	+	7.05769i	−0.167052	+	0.261575i
$729$	1.00000			0.0370370
$730$	11.7549	−	6.78668i	0.435068	−	0.251186i
$731$	−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
$735$	−1.39051	−	0.802812i	−0.0512898	−	0.0296122i
$736$		−	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	0.588475	−	0.808515i	$-0.299729\pi$
$739$	43.0306	−	24.8437i	1.58291	−	0.913892i	0.994432	−	0.105377i	$-0.0336048\pi$
$740$	−3.14925			−0.115769
$741$	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	$-0.537359\pi$
$743$	18.6559	−	10.7710i	0.684420	−	0.395150i	0.801518	+	0.597970i	$0.204026\pi$
$744$	−1.73592	−	3.00670i	−0.0636418	−	0.110231i
$745$	9.73875	−	16.8680i	0.356800	−	0.617996i
$746$		−	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
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−3.17436	−	5.49816i	−0.115834	−	0.200631i	0.802279	−	0.596950i	$-0.203621\pi$
$751$	−3.17436	−	5.49816i	−0.115834	−	0.200631i	−0.918113	+	0.396319i	$0.870287\pi$
$752$	1.57525	−	0.909471i	0.0574435	−	0.0331650i
$753$	28.3416			1.03283
$754$	−13.0385	−	8.32690i	−0.474834	−	0.303248i
$755$	14.5170			0.528329
$756$	−2.01141	+	1.16129i	−0.0731544	+	0.0422357i
$757$	24.0554	+	41.6651i	0.874307	+	1.51434i	0.857499	+	0.514485i	$0.172017\pi$
$757$	24.0554	+	41.6651i	0.874307	+	1.51434i	0.0168078	+	0.999859i	$0.494650\pi$
$758$	−0.224275	+	0.388456i	−0.00814604	+	0.0141094i
$759$			26.3846i			0.957699i
$760$	3.48387	+	2.01141i	0.126373	+	0.0729616i
$761$	29.1734	+	16.8433i	1.05754	+	0.610569i	0.924750	−	0.380576i	$-0.124274\pi$
$761$	29.1734	+	16.8433i	1.05754	+	0.610569i	0.132786	+	0.991145i	$0.457608\pi$
$762$		−	2.13209i		−	0.0772374i
$763$	7.76997	−	13.4580i	0.281292	−	0.487212i
$764$	−8.51873	−	14.7549i	−0.308197	−	0.533813i
$765$	−3.46410	+	2.00000i	−0.125245	+	0.0723102i
$766$	−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	−0.590592	−	0.806971i	$-0.701106\pi$
$769$	−5.18651	+	2.99443i	−0.187030	+	0.107982i	0.403561	+	0.914953i	$0.367772\pi$
$770$	6.20757	+	10.7518i	0.223705	+	0.387469i

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.866025 + 0.500000i) q^{6} +(-2.01141 - 1.16129i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(4.62926 - 2.67270i) q^{11} -1.00000 q^{12} +(-3.60194 - 0.161290i) q^{13} +2.32258 q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} -1.00000i q^{18} +(-3.48387 - 2.01141i) q^{19} +(0.866025 + 0.500000i) q^{20} +2.32258i q^{21} +(-2.67270 + 4.62926i) q^{22} +(-2.46797 - 4.27464i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000 q^{25} +(3.20002 - 1.66129i) q^{26} +1.00000 q^{27} +(-2.01141 + 1.16129i) q^{28} +(-2.14539 - 3.71592i) q^{29} +(-0.500000 + 0.866025i) q^{30} -3.47183i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.62926 - 2.67270i) q^{33} +4.00000i q^{34} +(1.16129 - 2.01141i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.72733 + 1.57463i) q^{37} +4.02283 q^{38} +(1.66129 + 3.20002i) q^{39} -1.00000 q^{40} +(2.29078 - 1.32258i) q^{41} +(-1.16129 - 2.01141i) q^{42} +(6.12539 - 10.6095i) q^{43} -5.34541i q^{44} +(-0.866025 - 0.500000i) q^{45} +(4.27464 + 2.46797i) q^{46} +1.81894i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.802812 - 1.39051i) q^{49} +(0.866025 - 0.500000i) q^{50} -4.00000 q^{51} +(-1.94065 + 3.03873i) q^{52} -5.48693 q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.67270 + 4.62926i) q^{55} +(1.16129 - 2.01141i) q^{56} +4.02283i q^{57} +(3.71592 + 2.14539i) q^{58} +(5.87744 + 3.39334i) q^{59} -1.00000i q^{60} +(-0.267949 + 0.464102i) q^{61} +(1.73592 + 3.00670i) q^{62} +(2.01141 - 1.16129i) q^{63} -1.00000 q^{64} +(0.161290 - 3.60194i) q^{65} +5.34541 q^{66} +(3.55872 - 2.05463i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.46797 + 4.27464i) q^{69} +2.32258i q^{70} +(13.7454 + 7.93593i) q^{71} +(-0.866025 - 0.500000i) q^{72} +13.5734i q^{73} +(1.57463 - 2.72733i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-3.48387 + 2.01141i) q^{76} -12.4151 q^{77} +(-3.03873 - 1.94065i) q^{78} -7.96774 q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.32258 + 2.29078i) q^{82} +11.3360i q^{83} +(2.01141 + 1.16129i) q^{84} +(3.46410 + 2.00000i) q^{85} +12.2508i q^{86} +(-2.14539 + 3.71592i) q^{87} +(2.67270 + 4.62926i) q^{88} +(-1.50670 + 0.869891i) q^{89} +1.00000 q^{90} +(7.05769 + 4.50732i) q^{91} -4.93593 q^{92} +(-3.00670 + 1.73592i) q^{93} +(-0.909471 - 1.57525i) q^{94} +(2.01141 - 3.48387i) q^{95} -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	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{14} - 4 q^{16} + 16 q^{17} - 6 q^{19} + 2 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 4 q^{36} + 30 q^{37} + 6 q^{39} - 8 q^{40} - 2 q^{42} + 14 q^{43} - 6 q^{46} - 4 q^{48} + 14 q^{49} - 32 q^{51} - 6 q^{52} + 16 q^{53} - 2 q^{55} + 2 q^{56} - 6 q^{58} + 24 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 6 q^{65} - 4 q^{66} + 24 q^{67} - 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} + 4 q^{75} - 6 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} - 4 q^{81} + 4 q^{82} - 8 q^{87} - 2 q^{88} + 42 q^{89} + 8 q^{90} - 10 q^{91} + 8 q^{92} + 30 q^{93} - 8 q^{94} - 24 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^10 + 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 - 8 * q^25 - 12 * q^26 + 8 * q^27 - 8 * q^29 - 4 * q^30 - 6 * q^33 + 2 * q^35 + 4 * q^36 + 30 * q^37 + 6 * q^39 - 8 * q^40 - 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^55 + 2 * q^56 - 6 * q^58 + 24 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 6 * q^65 - 4 * q^66 + 24 * q^67 - 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 + 4 * q^75 - 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 + 8 * q^90 - 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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