LMFDB - Embedded newform 675.2.r.a.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15183 - 1.27924i) q^{2} +(-0.100677 + 0.957875i) q^{4} +(0.0644453 - 2.23514i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 + 1.04909i) q^{8} +O(q^{10})$	\(q+(-1.15183 - 1.27924i) q^{2} +(-0.100677 + 0.957875i) q^{4} +(0.0644453 - 2.23514i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 + 1.04909i) q^{8} +(-2.93350 + 2.49206i) q^{10} +(3.66270 + 4.06784i) q^{11} +(1.55472 - 1.72669i) q^{13} +(7.12222 - 1.51387i) q^{14} +(4.88941 + 1.03928i) q^{16} +(1.13466 - 0.824379i) q^{17} +(4.74872 - 3.45015i) q^{19} +(2.13449 + 0.286757i) q^{20} +(0.984923 - 9.37092i) q^{22} +(3.41812 - 0.726543i) q^{23} +(-4.99169 - 0.288088i) q^{25} -3.99961 q^{26} +(-3.29599 - 2.39468i) q^{28} +(3.94221 - 1.75518i) q^{29} +(-2.89216 - 1.28767i) q^{31} +(-2.51747 - 4.36039i) q^{32} +(-2.36151 - 0.501954i) q^{34} +(8.05154 + 4.96333i) q^{35} +(0.930443 + 2.86361i) q^{37} +(-9.88326 - 2.10075i) q^{38} +(2.25180 + 3.29502i) q^{40} +(-3.09385 + 3.43607i) q^{41} +(-2.17619 + 3.76927i) q^{43} +(-4.26523 + 3.09887i) q^{44} +(-4.86650 - 3.53572i) q^{46} +(2.62209 - 1.16743i) q^{47} +(-5.44619 - 9.43308i) q^{49} +(5.38104 + 6.71738i) q^{50} +(1.49743 + 1.66306i) q^{52} +(-4.61926 - 3.35609i) q^{53} +(9.32824 - 7.92450i) q^{55} +(-0.789153 - 7.50829i) q^{56} +(-6.78604 - 3.02134i) q^{58} +(7.75922 - 8.61749i) q^{59} +(7.25373 + 8.05609i) q^{61} +(1.68404 + 5.18293i) q^{62} +(0.411065 - 1.26513i) q^{64} +(-3.75920 - 3.58629i) q^{65} +(10.3055 + 4.58831i) q^{67} +(0.675418 + 1.16986i) q^{68} +(-2.92473 - 16.0167i) q^{70} +(5.34318 + 3.88205i) q^{71} +(1.20170 - 3.69845i) q^{73} +(2.59152 - 4.48864i) q^{74} +(2.82672 + 4.89603i) q^{76} +(-22.6480 + 4.81398i) q^{77} +(-2.62186 + 1.16733i) q^{79} +(2.63803 - 10.8615i) q^{80} +7.95913 q^{82} +(0.713599 + 6.78944i) q^{83} +(-1.76948 - 2.58925i) q^{85} +(7.32838 - 1.55770i) q^{86} +(-9.55625 - 2.03124i) q^{88} +(1.41471 - 4.35403i) q^{89} +(3.03709 + 9.34720i) q^{91} +(0.351813 + 3.34727i) q^{92} +(-4.51362 - 2.00959i) q^{94} +(-7.40552 - 10.8364i) q^{95} +(12.6316 - 5.62394i) q^{97} +(-5.79405 + 17.8322i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.15183	−	1.27924i	−0.814466	−	0.904556i	0.182436	−	0.983218i	$-0.441602\pi$
$2$	−1.15183	−	1.27924i	−0.814466	−	0.904556i	−0.996901	+	0.0786620i	$0.974935\pi$
$3$		0			0
$3$		0			0
$4$	−0.100677	+	0.957875i	−0.0503383	+	0.478937i
$5$	0.0644453	−	2.23514i	0.0288208	−	0.999585i
$5$	0.0644453	−	2.23514i	0.0288208	−	0.999585i
$6$		0			0
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	0.120635	+	0.992697i	$0.461507\pi$
$7$	−2.11497	+	3.66323i	−0.799383	+	1.38457i	−0.920018	+	0.391876i	$0.871826\pi$
$8$	−1.44394	+	1.04909i	−0.510511	+	0.370908i
$9$		0			0
$10$	−2.93350	+	2.49206i	−0.927654	+	0.788057i
$11$	3.66270	+	4.06784i	1.10435	+	1.22650i	0.971921	+	0.235308i	$0.0756100\pi$
$11$	3.66270	+	4.06784i	1.10435	+	1.22650i	0.132426	+	0.991193i	$0.457723\pi$
$12$		0			0
$13$	1.55472	−	1.72669i	0.431201	−	0.478898i	−0.487911	−	0.872893i	$-0.662241\pi$
$13$	1.55472	−	1.72669i	0.431201	−	0.478898i	0.919112	+	0.393996i	$0.128908\pi$
$14$	7.12222	−	1.51387i	1.90349	−	0.404600i
$15$		0			0
$16$	4.88941	+	1.03928i	1.22235	+	0.259819i
$17$	1.13466	−	0.824379i	0.275195	−	0.199941i	−0.441624	−	0.897200i	$-0.645597\pi$
$17$	1.13466	−	0.824379i	0.275195	−	0.199941i	0.716819	+	0.697259i	$0.245597\pi$
$18$		0			0
$19$	4.74872	−	3.45015i	1.08943	−	0.791518i	0.110128	−	0.993917i	$-0.464874\pi$
$19$	4.74872	−	3.45015i	1.08943	−	0.791518i	0.979303	+	0.202400i	$0.0648740\pi$
$20$	2.13449	+	0.286757i	0.477288	+	0.0641208i
$21$		0			0
$22$	0.984923	−	9.37092i	0.209986	−	1.99789i
$23$	3.41812	−	0.726543i	0.712727	−	0.151495i	0.162741	−	0.986669i	$-0.447966\pi$
$23$	3.41812	−	0.726543i	0.712727	−	0.151495i	0.549986	+	0.835174i	$0.314633\pi$
$24$		0			0
$25$	−4.99169	−	0.288088i	−0.998339	−	0.0576177i
$26$	−3.99961			−0.784388
$27$		0			0
$28$	−3.29599	−	2.39468i	−0.622884	−	0.452552i
$29$	3.94221	−	1.75518i	0.732050	−	0.325929i	−0.00663753	−	0.999978i	$-0.502113\pi$
$29$	3.94221	−	1.75518i	0.732050	−	0.325929i	0.738687	+	0.674049i	$0.235446\pi$
$30$		0			0
$31$	−2.89216	−	1.28767i	−0.519448	−	0.231273i	0.130229	−	0.991484i	$-0.458429\pi$
$31$	−2.89216	−	1.28767i	−0.519448	−	0.231273i	−0.649676	+	0.760211i	$0.725096\pi$
$32$	−2.51747	−	4.36039i	−0.445030	−	0.770815i
$33$		0			0
$34$	−2.36151	−	0.501954i	−0.404995	−	0.0860844i
$35$	8.05154	+	4.96333i	1.36096	+	0.838956i
$36$		0			0
$37$	0.930443	+	2.86361i	0.152964	+	0.470775i	0.997949	−	0.0640154i	$-0.0203907\pi$
$37$	0.930443	+	2.86361i	0.152964	+	0.470775i	−0.844985	+	0.534790i	$0.820391\pi$
$38$	−9.88326	−	2.10075i	−1.60328	−	0.340787i
$39$		0			0
$40$	2.25180	+	3.29502i	0.356041	+	0.520989i
$41$	−3.09385	+	3.43607i	−0.483178	+	0.536624i	−0.934606	−	0.355684i	$-0.884248\pi$
$41$	−3.09385	+	3.43607i	−0.483178	+	0.536624i	0.451428	+	0.892308i	$0.350915\pi$
$42$		0			0
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	−0.982878	−	0.184259i	$-0.941011\pi$
$43$	−2.17619	+	3.76927i	−0.331866	+	0.574809i	0.651012	+	0.759068i	$0.274345\pi$
$44$	−4.26523	+	3.09887i	−0.643008	+	0.467173i
$45$		0			0
$46$	−4.86650	−	3.53572i	−0.717527	−	0.521314i
$47$	2.62209	−	1.16743i	0.382471	−	0.170287i	−0.206489	−	0.978449i	$-0.566204\pi$
$47$	2.62209	−	1.16743i	0.382471	−	0.170287i	0.588961	+	0.808162i	$0.299537\pi$
$48$		0			0
$49$	−5.44619	−	9.43308i	−0.778027	−	1.34758i
$50$	5.38104	+	6.71738i	0.760994	+	0.949981i
$51$		0			0
$52$	1.49743	+	1.66306i	0.207656	+	0.230625i
$53$	−4.61926	−	3.35609i	−0.634504	−	0.460994i	0.223454	−	0.974715i	$-0.428267\pi$
$53$	−4.61926	−	3.35609i	−0.634504	−	0.460994i	−0.857958	+	0.513720i	$0.828267\pi$
$54$		0			0
$55$	9.32824	−	7.92450i	1.25782	−	1.06854i
$56$	−0.789153	−	7.50829i	−0.105455	−	1.00334i
$57$		0			0
$58$	−6.78604	−	3.02134i	−0.891051	−	0.396721i
$59$	7.75922	−	8.61749i	1.01016	−	1.12190i	0.0176411	−	0.999844i	$-0.494384\pi$
$59$	7.75922	−	8.61749i	1.01016	−	1.12190i	0.992523	−	0.122057i	$-0.0389490\pi$
$60$		0			0
$61$	7.25373	+	8.05609i	0.928745	+	1.03148i	0.999423	+	0.0339768i	$0.0108172\pi$
$61$	7.25373	+	8.05609i	0.928745	+	1.03148i	−0.0706774	+	0.997499i	$0.522516\pi$
$62$	1.68404	+	5.18293i	0.213873	+	0.658233i
$63$		0			0
$64$	0.411065	−	1.26513i	0.0513831	−	0.158141i
$65$	−3.75920	−	3.58629i	−0.466271	−	0.444824i
$66$		0			0
$67$	10.3055	+	4.58831i	1.25902	+	0.560551i	0.924264	−	0.381754i	$-0.124680\pi$
$67$	10.3055	+	4.58831i	1.25902	+	0.560551i	0.334754	+	0.942305i	$0.391347\pi$
$68$	0.675418	+	1.16986i	0.0819064	+	0.141866i
$69$		0			0
$70$	−2.92473	−	16.0167i	−0.349572	−	1.91436i
$71$	5.34318	+	3.88205i	0.634119	+	0.460714i	0.857825	−	0.513942i	$-0.171816\pi$
$71$	5.34318	+	3.88205i	0.634119	+	0.460714i	−0.223706	+	0.974657i	$0.571816\pi$
$72$		0			0
$73$	1.20170	−	3.69845i	0.140648	−	0.432871i	−0.855777	−	0.517344i	$-0.826921\pi$
$73$	1.20170	−	3.69845i	0.140648	−	0.432871i	0.996426	+	0.0844731i	$0.0269207\pi$
$74$	2.59152	−	4.48864i	0.301258	−	0.521794i
$75$		0			0
$76$	2.82672	+	4.89603i	0.324247	+	0.561613i
$77$	−22.6480	+	4.81398i	−2.58098	+	0.548603i
$78$		0			0
$79$	−2.62186	+	1.16733i	−0.294983	+	0.131335i	−0.548892	−	0.835893i	$-0.684950\pi$
$79$	−2.62186	+	1.16733i	−0.294983	+	0.131335i	0.253909	+	0.967228i	$0.418284\pi$
$80$	2.63803	−	10.8615i	0.294940	−	1.21436i
$81$		0			0
$82$	7.95913			0.878938
$83$	0.713599	+	6.78944i	0.0783276	+	0.745237i	0.961242	+	0.275704i	$0.0889111\pi$
$83$	0.713599	+	6.78944i	0.0783276	+	0.745237i	−0.882915	+	0.469533i	$0.844422\pi$
$84$		0			0
$85$	−1.76948	−	2.58925i	−0.191927	−	0.280844i
$86$	7.32838	−	1.55770i	0.790240	−	0.167971i
$87$		0			0
$88$	−9.55625	−	2.03124i	−1.01870	−	0.216531i
$89$	1.41471	−	4.35403i	0.149959	−	0.461526i	−0.847656	−	0.530545i	$-0.821987\pi$
$89$	1.41471	−	4.35403i	0.149959	−	0.461526i	0.997615	+	0.0690197i	$0.0219871\pi$
$90$		0			0
$91$	3.03709	+	9.34720i	0.318373	+	0.979852i
$92$	0.351813	+	3.34727i	0.0366790	+	0.348977i
$93$		0			0
$94$	−4.51362	−	2.00959i	−0.465544	−	0.207274i
$95$	−7.40552	−	10.8364i	−0.759791	−	1.11179i
$96$		0			0
$97$	12.6316	−	5.62394i	1.28254	−	0.571024i	0.351585	−	0.936156i	$-0.385643\pi$
$97$	12.6316	−	5.62394i	1.28254	−	0.571024i	0.930956	+	0.365132i	$0.118976\pi$
$98$	−5.79405	+	17.8322i	−0.585287	+	1.80133i
$99$		0			0
$100$	0.778500	−	4.75241i	0.0778500	−	0.475241i
$101$	4.29330	−	7.43621i	0.427199	−	0.739930i	−0.569424	−	0.822044i	$-0.692834\pi$
$101$	4.29330	−	7.43621i	0.427199	−	0.739930i	0.996623	+	0.0821135i	$0.0261670\pi$
$102$		0			0
$103$	−0.00184111	+	0.0175170i	−0.000181410	+	0.00172600i	−0.994612	−	0.103665i	$-0.966943\pi$
$103$	−0.00184111	+	0.0175170i	−0.000181410	+	0.00172600i	0.994431	+	0.105391i	$0.0336095\pi$
$104$	−0.433479	+	4.12428i	−0.0425061	+	0.404419i
$105$		0			0
$106$	1.02737	+	9.77475i	0.0997868	+	0.949408i
$107$	−3.33334			−0.322246			−0.161123	−	0.986934i	$-0.551512\pi$
$107$	−3.33334			−0.322246			−0.161123	+	0.986934i	$0.551512\pi$
$108$		0			0
$109$	0.885216	+	2.72442i	0.0847883	+	0.260952i	0.984458	−	0.175619i	$-0.0561928\pi$
$109$	0.885216	+	2.72442i	0.0847883	+	0.260952i	−0.899670	+	0.436571i	$0.856193\pi$
$110$	−20.8818	−	2.80535i	−1.99100	−	0.267480i
$111$		0			0
$112$	−14.1481	+	15.7130i	−1.33687	+	1.48474i
$113$	5.38746	−	5.98339i	0.506810	−	0.562870i	−0.434388	−	0.900726i	$-0.643035\pi$
$113$	5.38746	−	5.98339i	0.506810	−	0.562870i	0.941198	+	0.337856i	$0.109702\pi$
$114$		0			0
$115$	−1.40364	−	7.68679i	−0.130890	−	0.716797i
$116$	1.28436	+	3.95285i	0.119250	+	0.367013i
$117$		0			0
$118$	−19.9611			−1.83757
$119$	0.620121	+	5.90006i	0.0568464	+	0.540858i
$120$		0			0
$121$	−1.98215	+	18.8589i	−0.180195	+	1.71444i
$122$	1.95057	−	18.5585i	0.176597	−	1.68020i
$123$		0			0
$124$	1.52460	−	2.64069i	0.136913	−	0.237141i
$125$	−0.965608	+	11.1386i	−0.0863666	+	0.996263i
$126$		0			0
$127$	−1.46943	+	4.52243i	−0.130391	+	0.401301i	−0.994845	−	0.101411i	$-0.967664\pi$
$127$	−1.46943	+	4.52243i	−0.130391	+	0.401301i	0.864454	+	0.502712i	$0.167664\pi$
$128$	−11.2912	+	5.02715i	−0.998008	+	0.444342i
$129$		0			0
$130$	−0.257756	+	8.93969i	−0.0226067	+	0.784063i
$131$	16.8235	+	7.49029i	1.46987	+	0.654430i	0.976525	−	0.215402i	$-0.0691063\pi$
$131$	16.8235	+	7.49029i	1.46987	+	0.654430i	0.493348	+	0.869832i	$0.335773\pi$
$132$		0			0
$133$	2.59530	+	24.6926i	0.225041	+	2.14112i
$134$	−6.00065	−	18.4681i	−0.518377	−	1.59540i
$135$		0			0
$136$	−0.773540	+	2.38071i	−0.0663305	+	0.204144i
$137$	−16.2046	−	3.44439i	−1.38445	−	0.294274i	−0.545330	−	0.838221i	$-0.683596\pi$
$137$	−16.2046	−	3.44439i	−1.38445	−	0.294274i	−0.839119	+	0.543947i	$0.816929\pi$
$138$		0			0
$139$	10.5782	−	2.24847i	0.897232	−	0.190712i	0.263861	−	0.964561i	$-0.415004\pi$
$139$	10.5782	−	2.24847i	0.897232	−	0.190712i	0.633371	+	0.773848i	$0.281671\pi$
$140$	−5.56485	+	7.21267i	−0.470316	+	0.609582i
$141$		0			0
$142$	−1.18838	−	11.3066i	−0.0997262	−	0.948832i
$143$	12.7184			1.06356
$144$		0			0
$145$	−3.66902	−	8.92450i	−0.304696	−	0.741139i
$146$	−6.11534	+	2.72273i	−0.506109	+	0.225334i
$147$		0			0
$148$	−2.83665	+	0.602949i	−0.233172	+	0.0495621i
$149$	4.92744	+	8.53458i	0.403672	+	0.699180i	0.994166	−	0.107862i	$-0.0344004\pi$
$149$	4.92744	+	8.53458i	0.403672	+	0.699180i	−0.590494	+	0.807042i	$0.701067\pi$
$150$		0			0
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	−0.214994	−	0.976615i	$-0.568973\pi$
$151$	9.07209	−	15.7133i	0.738276	−	1.27873i	0.953271	−	0.302117i	$-0.0976934\pi$
$152$	−3.23738	+	9.96363i	−0.262586	+	0.808157i
$153$		0			0
$154$	32.2448	+	23.4272i	2.59836	+	1.88782i
$155$	−3.06452	+	6.38140i	−0.246148	+	0.512566i
$156$		0			0
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	0.808010	−	0.589169i	$-0.200545\pi$
$157$	−1.33107	−	2.30547i	−0.106231	−	0.183997i	−0.914240	+	0.405172i	$0.867212\pi$
$158$	4.51323	+	2.00942i	0.359053	+	0.159861i
$159$		0			0
$160$	−9.90831	+	5.34589i	−0.783321	+	0.422630i
$161$	−4.56772	+	14.0580i	−0.359986	+	1.10792i
$162$		0			0
$163$	1.19215	+	3.66905i	0.0933761	+	0.287382i	0.986827	−	0.161779i	$-0.0517230\pi$
$163$	1.19215	+	3.66905i	0.0933761	+	0.287382i	−0.893451	+	0.449161i	$0.851723\pi$
$164$	−2.97985	−	3.30945i	−0.232687	−	0.258425i
$165$		0			0
$166$	7.86334	−	8.73313i	0.610314	−	0.677822i
$167$	9.60407	+	4.27601i	0.743186	+	0.330888i	0.743161	−	0.669112i	$-0.233326\pi$
$167$	9.60407	+	4.27601i	0.743186	+	0.330888i	2.44112e−5		1.00000i	$0.499992\pi$
$168$		0			0
$169$	0.794562	+	7.55975i	0.0611201	+	0.581519i
$170$	−1.27412	+	5.24595i	−0.0977209	+	0.402346i
$171$		0			0
$172$	−3.39140	−	2.46399i	−0.258592	−	0.187878i
$173$	−4.11360	−	4.56862i	−0.312751	−	0.347346i	0.566191	−	0.824274i	$-0.308417\pi$
$173$	−4.11360	−	4.56862i	−0.312751	−	0.347346i	−0.878942	+	0.476929i	$0.841750\pi$
$174$		0			0
$175$	11.6126	−	17.6764i	0.877831	−	1.33621i
$176$	13.6808	+	23.6959i	1.03123	+	1.78615i
$177$		0			0
$178$	−7.19932	+	3.20534i	−0.539612	+	0.240251i
$179$	−5.82725	−	4.23375i	−0.435549	−	0.316445i	0.348315	−	0.937378i	$-0.386754\pi$
$179$	−5.82725	−	4.23375i	−0.435549	−	0.316445i	−0.783864	+	0.620933i	$0.786754\pi$
$180$		0			0
$181$	−18.3734	+	13.3490i	−1.36568	+	0.992226i	−0.367622	+	0.929975i	$0.619828\pi$
$181$	−18.3734	+	13.3490i	−1.36568	+	0.992226i	−0.998061	+	0.0622510i	$0.980172\pi$
$182$	8.45906	−	14.6515i	0.627027	−	1.08604i
$183$		0			0
$184$	−4.17336	+	4.63499i	−0.307664	+	0.341696i
$185$	6.46053	−	1.89512i	0.474988	−	0.139332i
$186$		0			0
$187$	7.50937	+	1.59617i	0.549139	+	0.116723i
$188$	0.854269	+	2.62917i	0.0623039	+	0.191752i
$189$		0			0
$190$	−5.33240	+	21.9551i	−0.386853	+	1.59279i
$191$	−10.4971	−	2.23123i	−0.759545	−	0.161446i	−0.188171	−	0.982136i	$-0.560256\pi$
$191$	−10.4971	−	2.23123i	−0.759545	−	0.161446i	−0.571374	+	0.820690i	$0.693589\pi$
$192$		0			0
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	0.998930	+	0.0462566i	$0.0147292\pi$
$193$	7.49531	+	12.9823i	0.539524	+	0.934483i	−0.459405	+	0.888227i	$0.651937\pi$
$194$	−21.7437	−	9.68093i	−1.56111	−	0.695050i
$195$		0			0
$196$	9.58401	−	4.26708i	0.684572	−	0.304791i
$197$	−6.42527	−	4.66823i	−0.457782	−	0.332598i	0.334879	−	0.942261i	$-0.391305\pi$
$197$	−6.42527	−	4.66823i	−0.457782	−	0.332598i	−0.792660	+	0.609663i	$0.791305\pi$
$198$		0			0
$199$	−14.1116			−1.00034			−0.500172	−	0.865926i	$-0.666730\pi$
$199$	−14.1116			−1.00034			−0.500172	+	0.865926i	$0.666730\pi$
$200$	7.50995	−	4.82073i	0.531034	−	0.340877i
$201$		0			0
$202$	−14.4578	+	3.07310i	−1.01725	+	0.216223i
$203$	−1.90800	+	18.1534i	−0.133915	+	1.27412i
$204$		0			0
$205$	7.48071	+	7.13663i	0.522475	+	0.498444i
$206$	0.0245290	−	0.0178214i	0.00170902	−	0.00124167i
$207$		0			0
$208$	9.39616	−	6.82671i	0.651507	−	0.473347i
$209$	31.4278	+	6.68019i	2.17391	+	0.462078i
$210$		0			0
$211$	−7.16213	+	1.52236i	−0.493062	+	0.104803i	−0.447731	−	0.894169i	$-0.647768\pi$
$211$	−7.16213	+	1.52236i	−0.493062	+	0.104803i	−0.0453311	+	0.998972i	$0.514434\pi$
$212$	3.67976	−	4.08679i	0.252727	−	0.280682i
$213$		0			0
$214$	3.83943	+	4.26412i	0.262458	+	0.291489i
$215$	8.28460	+	5.10700i	0.565005	+	0.348294i
$216$		0			0
$217$	10.8339	−	7.87128i	0.735452	−	0.534337i
$218$	2.46555	−	4.27046i	0.166988	−	0.289232i
$219$		0			0
$220$	6.65154	+	9.73310i	0.448447	+	0.656205i
$221$	0.340631	−	3.24088i	0.0229133	−	0.218005i
$222$		0			0
$223$	−13.6107	−	15.1162i	−0.911441	−	1.01226i	−0.999869	−	0.0161752i	$-0.994851\pi$
$223$	−13.6107	−	15.1162i	−0.911441	−	1.01226i	0.0884282	−	0.996083i	$-0.471816\pi$
$224$	21.2975			1.42300
$225$		0			0
$226$	−13.8596			−0.921926
$227$	14.5630	+	16.1739i	0.966582	+	1.07350i	0.997261	+	0.0739685i	$0.0235664\pi$
$227$	14.5630	+	16.1739i	0.966582	+	1.07350i	−0.0306788	+	0.999529i	$0.509767\pi$
$228$		0			0
$229$	1.96308	−	18.6775i	0.129724	−	1.23424i	−0.715032	−	0.699092i	$-0.753588\pi$
$229$	1.96308	−	18.6775i	0.129724	−	1.23424i	0.844756	−	0.535151i	$-0.179745\pi$
$230$	−8.21646	+	10.6495i	−0.541777	+	0.702204i
$231$		0			0
$232$	−3.85098	+	6.67010i	−0.252830	+	0.437914i
$233$	5.17867	−	3.76252i	0.339266	−	0.246491i	−0.405086	−	0.914279i	$-0.632758\pi$
$233$	5.17867	−	3.76252i	0.339266	−	0.246491i	0.744352	+	0.667787i	$0.232758\pi$
$234$		0			0
$235$	−2.44039	−	5.93598i	−0.159193	−	0.387220i
$236$	7.47330	+	8.29994i	0.486470	+	0.540280i
$237$		0			0
$238$	6.83329	−	7.58914i	0.442937	−	0.491931i
$239$	−17.2033	+	3.65668i	−1.11279	+	0.236531i	−0.727394	−	0.686220i	$-0.759269\pi$
$239$	−17.2033	+	3.65668i	−1.11279	+	0.236531i	−0.385397	+	0.922751i	$0.625936\pi$
$240$		0			0
$241$	−7.43150	−	1.57961i	−0.478705	−	0.101752i	−0.0377616	−	0.999287i	$-0.512023\pi$
$241$	−7.43150	−	1.57961i	−0.478705	−	0.101752i	−0.440943	+	0.897535i	$0.645356\pi$
$242$	26.4080	−	19.1866i	1.69757	−	1.23336i
$243$		0			0
$244$	−8.44700	+	6.13711i	−0.540764	+	0.392888i
$245$	−21.4352	+	11.5651i	−1.36945	+	0.738866i
$246$		0			0
$247$	1.42559	−	13.5636i	0.0907080	−	0.863029i
$248$	5.52700	−	1.17480i	0.350965	−	0.0745998i
$249$		0			0
$250$	15.3611	−	11.5945i	0.971518	−	0.733299i
$251$	−25.9812			−1.63992			−0.819959	−	0.572422i	$-0.806004\pi$
$251$	−25.9812			−1.63992			−0.819959	+	0.572422i	$0.806004\pi$
$252$		0			0
$253$	15.4750	+	11.2433i	0.972906	+	0.706858i
$254$	7.47778	−	3.32932i	0.469197	−	0.208900i
$255$		0			0
$256$	17.0059	+	7.57153i	1.06287	+	0.473221i
$257$	−0.478674	−	0.829088i	−0.0298589	−	0.0517171i	0.850710	−	0.525636i	$-0.176172\pi$
$257$	−0.478674	−	0.829088i	−0.0298589	−	0.0517171i	−0.880569	+	0.473919i	$0.842839\pi$
$258$		0			0
$259$	−12.4579	−	2.64802i	−0.774099	−	0.164540i
$260$	3.81368	−	3.23978i	0.236514	−	0.200923i
$261$		0			0
$262$	−9.79591	−	30.1487i	−0.605193	−	1.86259i
$263$	−5.16771	−	1.09843i	−0.318655	−	0.0677322i	0.0458076	−	0.998950i	$-0.485414\pi$
$263$	−5.16771	−	1.09843i	−0.318655	−	0.0677322i	−0.364462	+	0.931218i	$0.618747\pi$
$264$		0			0
$265$	−7.79901	+	10.1084i	−0.479089	+	0.620954i
$266$	28.5983	−	31.7617i	1.75348	−	1.94743i
$267$		0			0
$268$	−5.43255	+	9.40945i	−0.331846	+	0.574774i
$269$	−14.1657	+	10.2920i	−0.863699	+	0.627514i	−0.928889	−	0.370359i	$-0.879235\pi$
$269$	−14.1657	+	10.2920i	−0.863699	+	0.627514i	0.0651897	+	0.997873i	$0.479235\pi$
$270$		0			0
$271$	−10.8922	−	7.91361i	−0.661651	−	0.480718i	0.205569	−	0.978643i	$-0.434096\pi$
$271$	−10.8922	−	7.91361i	−0.661651	−	0.480718i	−0.867220	+	0.497925i	$0.834096\pi$
$272$	6.40457	−	2.85150i	0.388334	−	0.172898i
$273$		0			0
$274$	14.2587	+	24.6968i	0.861400	+	1.49199i
$275$	−17.1112	−	21.3606i	−1.03184	−	1.28809i
$276$		0			0
$277$	−17.6458	−	19.5977i	−1.06024	−	1.17751i	−0.983584	−	0.180453i	$-0.942244\pi$
$277$	−17.6458	−	19.5977i	−1.06024	−	1.17751i	−0.0766522	−	0.997058i	$-0.524423\pi$
$278$	−15.0606	−	10.9422i	−0.903274	−	0.656267i
$279$		0			0
$280$	−16.8329	+	1.27999i	−1.00596	+	0.0764942i
$281$	2.62432	+	24.9688i	0.156554	+	1.48951i	0.737377	+	0.675482i	$0.236064\pi$
$281$	2.62432	+	24.9688i	0.156554	+	1.48951i	−0.580823	+	0.814030i	$0.697269\pi$
$282$		0			0
$283$	−13.1704	−	5.86384i	−0.782899	−	0.348569i	−0.0239447	−	0.999713i	$-0.507623\pi$
$283$	−13.1704	−	5.86384i	−0.782899	−	0.348569i	−0.758954	+	0.651144i	$0.774289\pi$
$284$	−4.25645	+	4.72726i	−0.252574	+	0.280512i
$285$		0			0
$286$	−14.6494	−	16.2698i	−0.866237	−	0.962053i
$287$	−6.04373	−	18.6007i	−0.356750	−	1.09796i
$288$		0			0
$289$	−4.64544	+	14.2972i	−0.273261	+	0.841011i
$290$	−7.19044	+	14.9730i	−0.422237	+	0.879247i
$291$		0			0
$292$	3.42167	+	1.52343i	0.200238	+	0.0891518i
$293$	−3.34662	−	5.79652i	−0.195512	−	0.338636i	0.751556	−	0.659669i	$-0.229303\pi$
$293$	−3.34662	−	5.79652i	−0.195512	−	0.338636i	−0.947068	+	0.321033i	$0.895970\pi$
$294$		0			0
$295$	−18.7612	−	17.8983i	−1.09232	−	1.04208i
$296$	−4.34768	−	3.15878i	−0.252704	−	0.183600i
$297$		0			0
$298$	5.24217	−	16.1337i	0.303671	−	0.934602i
$299$	4.05970	−	7.03160i	0.234778	−	0.406648i
$300$		0			0
$301$	−9.20515	−	15.9438i	−0.530576	−	0.918985i
$302$	−30.5505	+	6.49372i	−1.75799	+	0.373671i
$303$		0			0
$304$	26.8041	−	11.9339i	1.53732	−	0.684459i
$305$	18.4739	−	15.6939i	1.05781	−	0.898631i
$306$		0			0
$307$	3.26128			0.186131			0.0930657	−	0.995660i	$-0.470333\pi$
$307$	3.26128			0.186131			0.0930657	+	0.995660i	$0.470333\pi$
$308$	−2.33106	−	22.1786i	−0.132825	−	1.26374i
$309$		0			0
$310$	11.6931	−	3.43004i	0.664124	−	0.194813i
$311$	−31.5260	+	6.70106i	−1.78768	+	0.379982i	−0.978281	−	0.207282i	$-0.933538\pi$
$311$	−31.5260	+	6.70106i	−1.78768	+	0.379982i	−0.809395	+	0.587265i	$0.800205\pi$
$312$		0			0
$313$	20.0766	+	4.26742i	1.13480	+	0.241209i	0.736756	−	0.676159i	$-0.236357\pi$
$313$	20.0766	+	4.26742i	1.13480	+	0.241209i	0.398042	+	0.917367i	$0.369690\pi$
$314$	−1.41608	+	4.35826i	−0.0799142	+	0.245951i
$315$		0			0
$316$	−0.854194	−	2.62894i	−0.0480522	−	0.147889i
$317$	−0.418108	−	3.97803i	−0.0234833	−	0.223428i	−0.999969	−	0.00784728i	$-0.997502\pi$
$317$	−0.418108	−	3.97803i	−0.0234833	−	0.223428i	0.976486	−	0.215581i	$-0.0691646\pi$
$318$		0			0
$319$	21.5790	+	9.60757i	1.20819	+	0.537921i
$320$	−2.80125	−	1.00032i	−0.156594	−	0.0559195i
$321$		0			0
$322$	23.2447	−	10.3492i	1.29538	−	0.576739i
$323$	2.54395	−	7.82948i	0.141549	−	0.435644i
$324$		0			0
$325$	−8.25812	+	8.17121i	−0.458078	+	0.453257i
$326$	3.32043	−	5.75115i	0.183902	−	0.318527i
$327$		0			0
$328$	0.862612	−	8.20721i	0.0476298	−	0.453167i
$329$	−1.26907	+	12.0744i	−0.0699662	+	0.665684i
$330$		0			0
$331$	−0.154084	−	1.46601i	−0.00846920	−	0.0805791i	0.989471	−	0.144732i	$-0.0462321\pi$
$331$	−0.154084	−	1.46601i	−0.00846920	−	0.0805791i	−0.997940	+	0.0641531i	$0.979565\pi$
$332$	−6.57527			−0.360865
$333$		0			0
$334$	−5.59222	−	17.2111i	−0.305993	−	0.941749i
$335$	10.9196	−	22.7386i	0.596604	−	1.24234i
$336$		0			0
$337$	−6.23620	+	6.92600i	−0.339707	+	0.377283i	−0.888657	−	0.458572i	$-0.848361\pi$
$337$	−6.23620	+	6.92600i	−0.339707	+	0.377283i	0.548950	+	0.835855i	$0.315028\pi$
$338$	8.75550	−	9.72397i	0.476236	−	0.528914i
$339$		0			0
$340$	2.65832	−	1.43426i	0.144168	−	0.0777837i
$341$	−5.35508	−	16.4812i	−0.289994	−	0.892509i
$342$		0			0
$343$	16.4645			0.889001
$344$	−0.811996	−	7.72562i	−0.0437799	−	0.416538i
$345$		0			0
$346$	−1.10617	+	10.5245i	−0.0594682	+	0.565802i
$347$	−0.697927	+	6.64033i	−0.0374667	+	0.356472i	0.959687	+	0.281072i	$0.0906899\pi$
$347$	−0.697927	+	6.64033i	−0.0374667	+	0.356472i	−0.997153	+	0.0753997i	$0.975977\pi$
$348$		0			0
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	−0.802019	−	0.597299i	$-0.796241\pi$
$349$	2.17204	−	3.76209i	0.116267	−	0.201380i	0.918285	+	0.395919i	$0.129574\pi$
$350$	−35.9881	+	5.50497i	−1.92364	+	0.294253i
$351$		0			0
$352$	8.51663	−	26.2115i	0.453938	−	1.39708i
$353$	4.22662	−	1.88181i	0.224960	−	0.100159i	−0.291162	−	0.956674i	$-0.594042\pi$
$353$	4.22662	−	1.88181i	0.224960	−	0.100159i	0.516122	+	0.856515i	$0.327375\pi$
$354$		0			0
$355$	9.02126	−	11.6926i	0.478799	−	0.620577i
$356$	4.02818	+	1.79346i	0.213493	+	0.0950533i
$357$		0			0
$358$	1.29604	+	12.3310i	0.0684977	+	0.651712i
$359$	2.78646	+	8.57585i	0.147064	+	0.452616i	0.997271	−	0.0738329i	$-0.0235232\pi$
$359$	2.78646	+	8.57585i	0.147064	+	0.452616i	−0.850207	+	0.526449i	$0.823523\pi$
$360$		0			0
$361$	4.77550	−	14.6975i	0.251342	−	0.773551i
$362$	38.2395	+	8.12806i	2.00983	+	0.427202i
$363$		0			0
$364$	−9.25921	+	1.96810i	−0.485314	+	0.103157i
$365$	−8.18911	−	2.92431i	−0.428638	−	0.153066i
$366$		0			0
$367$	0.967647	+	9.20654i	0.0505107	+	0.480578i	0.990312	+	0.138857i	$0.0443429\pi$
$367$	0.967647	+	9.20654i	0.0505107	+	0.480578i	−0.939802	+	0.341720i	$0.888990\pi$
$368$	17.4677			0.910565
$369$		0			0
$370$	−9.86573	−	6.08168i	−0.512895	−	0.316171i
$371$	22.0637	−	9.82340i	1.14549	−	0.510006i
$372$		0			0
$373$	5.30009	−	1.12657i	0.274428	−	0.0583315i	−0.0686418	−	0.997641i	$-0.521867\pi$
$373$	5.30009	−	1.12657i	0.274428	−	0.0583315i	0.343070	+	0.939310i	$0.388533\pi$
$374$	−6.60763	−	11.4448i	−0.341673	−	0.591794i
$375$		0			0
$376$	−2.56142	+	4.43650i	−0.132095	+	0.228795i
$377$	3.09837	−	9.53579i	0.159574	−	0.491118i
$378$		0			0
$379$	7.21488	+	5.24191i	0.370603	+	0.269259i	0.757461	−	0.652880i	$-0.226440\pi$
$379$	7.21488	+	5.24191i	0.370603	+	0.269259i	−0.386858	+	0.922139i	$0.626440\pi$
$380$	11.1255	−	6.00259i	0.570724	−	0.307926i
$381$		0			0
$382$	9.23661	+	15.9983i	0.472586	+	0.818543i
$383$	16.8558	+	7.50467i	0.861290	+	0.383471i	0.789354	−	0.613938i	$-0.210416\pi$
$383$	16.8558	+	7.50467i	0.861290	+	0.383471i	0.0719357	+	0.997409i	$0.477082\pi$
$384$		0			0
$385$	9.30035	+	50.9316i	0.473990	+	2.59572i
$386$	7.97405	−	24.5416i	0.405868	−	1.24913i
$387$		0			0
$388$	4.11532	+	12.6657i	0.208924	+	0.643001i
$389$	8.47934	+	9.41726i	0.429920	+	0.477474i	0.918713	−	0.394925i	$-0.129230\pi$
$389$	8.47934	+	9.41726i	0.429920	+	0.477474i	−0.488794	+	0.872400i	$0.662563\pi$
$390$		0			0
$391$	3.27945	−	3.64220i	0.165849	−	0.184194i
$392$	17.7601	+	7.90731i	0.897021	+	0.399379i
$393$		0			0
$394$	1.42904	+	13.5964i	0.0719941	+	0.684978i
$395$	2.44018	+	5.93546i	0.122779	+	0.298645i
$396$		0			0
$397$	5.05655	+	3.67380i	0.253781	+	0.184383i	0.707401	−	0.706813i	$-0.249868\pi$
$397$	5.05655	+	3.67380i	0.253781	+	0.184383i	−0.453620	+	0.891195i	$0.649868\pi$
$398$	16.2541	+	18.0520i	0.814745	+	0.904866i
$399$		0			0
$400$	−24.1070	−	6.59633i	−1.20535	−	0.329816i
$401$	−13.3637	−	23.1466i	−0.667352	−	1.15589i	−0.978642	−	0.205572i	$-0.934094\pi$
$401$	−13.3637	−	23.1466i	−0.667352	−	1.15589i	0.311290	−	0.950315i	$-0.399239\pi$
$402$		0			0
$403$	−6.71991	+	2.99190i	−0.334743	+	0.149037i
$404$	6.69072	+	4.86109i	0.332876	+	0.241848i
$405$		0			0
$406$	25.4201	−	18.4688i	1.26158	−	0.916592i
$407$	−8.24078	+	14.2735i	−0.408480	+	0.707509i
$408$		0			0
$409$	16.0078	−	17.7784i	0.791533	−	0.879087i	−0.203454	−	0.979084i	$-0.565217\pi$
$409$	16.0078	−	17.7784i	0.791533	−	0.879087i	0.994988	+	0.0999975i	$0.0318835\pi$
$410$	0.512928	−	17.7898i	0.0253317	−	0.878573i
$411$		0			0
$412$	−0.0165938	−	0.00352711i	−0.000817516	−	0.000173768i
$413$	15.1574	+	46.6496i	0.745845	+	2.29547i
$414$		0			0
$415$	15.2213	−	1.15744i	0.747185	−	0.0568167i
$416$	−11.4430	−	2.43228i	−0.561039	−	0.119253i
$417$		0			0
$418$	−27.6539	−	47.8980i	−1.35260	−	2.34277i
$419$	11.4619	+	5.10317i	0.559951	+	0.249306i	0.667140	−	0.744933i	$-0.267518\pi$
$419$	11.4619	+	5.10317i	0.559951	+	0.249306i	−0.107189	+	0.994239i	$0.534185\pi$
$420$		0			0
$421$	−1.07815	+	0.480023i	−0.0525458	+	0.0233949i	−0.432841	−	0.901470i	$-0.642489\pi$
$421$	−1.07815	+	0.480023i	−0.0525458	+	0.0233949i	0.380296	+	0.924865i	$0.375822\pi$
$422$	10.1970	+	7.40856i	0.496382	+	0.360643i
$423$		0			0
$424$	10.1908			0.494908
$425$	−5.90137	+	3.78816i	−0.286258	+	0.183753i
$426$		0			0
$427$	−44.8528	+	9.53375i	−2.17058	+	0.461370i
$428$	0.335589	−	3.19292i	0.0162213	−	0.154336i
$429$		0			0
$430$	−3.00939	−	16.4803i	−0.145126	−	0.794752i
$431$	20.3282	−	14.7693i	0.979174	−	0.711412i	0.0216502	−	0.999766i	$-0.493108\pi$
$431$	20.3282	−	14.7693i	0.979174	−	0.711412i	0.957524	+	0.288354i	$0.0931080\pi$
$432$		0			0
$433$	16.1875	−	11.7609i	0.777922	−	0.565193i	−0.126433	−	0.991975i	$-0.540353\pi$
$433$	16.1875	−	11.7609i	0.777922	−	0.565193i	0.904355	+	0.426782i	$0.140353\pi$
$434$	−22.5480	−	4.79272i	−1.08234	−	0.230058i
$435$		0			0
$436$	−2.69877	+	0.573641i	−0.129248	+	0.0274724i
$437$	13.7250	−	15.2432i	0.656556	−	0.729179i
$438$		0			0
$439$	−15.1706	−	16.8487i	−0.724054	−	0.804143i	0.262955	−	0.964808i	$-0.415303\pi$
$439$	−15.1706	−	16.8487i	−0.724054	−	0.804143i	−0.987009	+	0.160665i	$0.948636\pi$
$440$	−5.15597	+	21.2287i	−0.245801	+	1.01204i
$441$		0			0
$442$	−4.53820	+	3.29719i	−0.215860	+	0.156832i
$443$	−2.48298	+	4.30064i	−0.117970	+	0.204330i	−0.918963	−	0.394344i	$-0.870972\pi$
$443$	−2.48298	+	4.30064i	−0.117970	+	0.204330i	0.800993	+	0.598673i	$0.204305\pi$
$444$		0			0
$445$	−9.64068	−	3.44267i	−0.457012	−	0.163198i
$446$	−3.66000	+	34.8226i	−0.173306	+	1.64890i
$447$		0			0
$448$	3.76507	+	4.18153i	0.177883	+	0.197559i
$449$	−17.7685			−0.838548			−0.419274	−	0.907860i	$-0.637715\pi$
$449$	−17.7685			−0.838548			−0.419274	+	0.907860i	$0.637715\pi$
$450$		0			0
$451$	−25.3093			−1.19177
$452$	5.18894	+	5.76290i	0.244067	+	0.271064i
$453$		0			0
$454$	3.91608	−	37.2591i	0.183791	−	1.74865i
$455$	21.0880	−	6.18593i	0.988621	−	0.290001i
$456$		0			0
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	−0.999355	−	0.0359099i	$-0.988567\pi$
$457$	−10.0171	+	17.3501i	−0.468579	+	0.811602i	0.530776	+	0.847512i	$0.321900\pi$
$458$	−26.1540	+	19.0020i	−1.22210	+	0.887906i
$459$		0			0
$460$	7.50430	−	0.570634i	0.349890	−	0.0266060i
$461$	8.43317	+	9.36598i	0.392772	+	0.436217i	0.906803	−	0.421554i	$-0.138515\pi$
$461$	8.43317	+	9.36598i	0.392772	+	0.436217i	−0.514031	+	0.857771i	$0.671849\pi$
$462$		0			0
$463$	−16.6620	+	18.5051i	−0.774351	+	0.860004i	−0.993280	−	0.115737i	$-0.963077\pi$
$463$	−16.6620	+	18.5051i	−0.774351	+	0.860004i	0.218929	+	0.975741i	$0.429744\pi$
$464$	21.0992	−	4.48477i	0.979505	−	0.208200i
$465$		0			0
$466$	−10.7781	−	2.29095i	−0.499285	−	0.106126i
$467$	29.6418	−	21.5361i	1.37166	−	0.996570i	0.374056	−	0.927406i	$-0.377967\pi$
$467$	29.6418	−	21.5361i	1.37166	−	0.996570i	0.997605	−	0.0691640i	$-0.0220332\pi$
$468$		0			0
$469$	−38.6039	+	28.0474i	−1.78256	+	1.29511i
$470$	−4.78260	+	9.95906i	−0.220605	+	0.459377i
$471$		0			0
$472$	−2.16339	+	20.5832i	−0.0995779	+	0.947421i
$473$	−23.3035	+	4.95332i	−1.07150	+	0.227754i
$474$		0			0
$475$	−24.6981	+	15.8540i	−1.13323	+	0.727432i
$476$	−5.71395			−0.261899
$477$		0			0
$478$	24.4931	+	17.7952i	1.12029	+	0.813936i
$479$	−6.67518	+	2.97198i	−0.304997	+	0.135793i	−0.553528	−	0.832831i	$-0.686719\pi$
$479$	−6.67518	+	2.97198i	−0.304997	+	0.135793i	0.248531	+	0.968624i	$0.420052\pi$
$480$		0			0
$481$	6.39115	+	2.84552i	0.291411	+	0.129745i
$482$	6.53911	+	11.3261i	0.297849	+	0.515889i
$483$		0			0
$484$	−17.8649	−	3.79730i	−0.812040	−	0.172604i
$485$	−11.7562	−	28.5957i	−0.533823	−	1.29847i
$486$		0			0
$487$	−7.65681	−	23.5652i	−0.346963	−	1.06784i	−0.960524	−	0.278195i	$-0.910264\pi$
$487$	−7.65681	−	23.5652i	−0.346963	−	1.06784i	0.613561	−	0.789647i	$-0.289736\pi$
$488$	−18.9255	−	4.02274i	−0.856717	−	0.182101i
$489$		0			0
$490$	39.4842	+	14.0997i	1.78371	+	0.636960i
$491$	13.6528	−	15.1630i	0.616143	−	0.684296i	−0.351624	−	0.936141i	$-0.614371\pi$
$491$	13.6528	−	15.1630i	0.616143	−	0.684296i	0.967768	+	0.251845i	$0.0810373\pi$
$492$		0			0
$493$	3.02613	−	5.24141i	0.136290	−	0.236061i
$494$	−18.9930	+	13.7992i	−0.854537	+	0.620857i
$495$		0			0
$496$	−12.8027	−	9.30172i	−0.574859	−	0.417659i
$497$	−25.5215	+	11.3629i	−1.14480	+	0.509696i
$498$		0			0
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	0.519355	−	0.854559i	$-0.326172\pi$
$499$	−10.7311	−	18.5869i	−0.480392	−	0.832064i	−0.999747	+	0.0224950i	$0.992839\pi$
$500$	−10.5721	−	2.04633i	−0.472800	−	0.0915145i
$501$		0			0
$502$	29.9259	+	33.2360i	1.33566	+	1.48340i
$503$	8.58020	+	6.23388i	0.382572	+	0.277955i	0.762405	−	0.647100i	$-0.224019\pi$
$503$	8.58020	+	6.23388i	0.382572	+	0.277955i	−0.379833	+	0.925055i	$0.624019\pi$
$504$		0			0
$505$	−16.3443	−	10.0753i	−0.727311	−	0.448347i
$506$	−3.44179	−	32.7465i	−0.153006	−	1.45576i
$507$		0			0
$508$	−4.18398	−	1.86283i	−0.185634	−	0.0826497i
$509$	−3.07023	+	3.40983i	−0.136085	+	0.151138i	−0.807335	−	0.590093i	$-0.799091\pi$
$509$	−3.07023	+	3.40983i	−0.136085	+	0.151138i	0.671250	+	0.741231i	$0.265758\pi$
$510$		0			0
$511$	11.0067	+	12.2242i	0.486910	+	0.540768i
$512$	−2.26343	−	6.96611i	−0.100030	−	0.307861i
$513$		0			0
$514$	−0.509248	+	1.56730i	−0.0224620	+	0.0691308i
$515$	0.0390343	+	0.00524403i	0.00172006	+	0.000231080i
$516$		0			0
$517$	14.3529	+	6.39031i	0.631239	+	0.281046i
$518$	10.9620	+	18.9867i	0.481641	+	0.834227i
$519$		0			0
$520$	9.19040	+	1.23468i	0.403025	+	0.0541441i
$521$	−9.38013	−	6.81506i	−0.410951	−	0.298573i	0.363036	−	0.931775i	$-0.381740\pi$
$521$	−9.38013	−	6.81506i	−0.410951	−	0.298573i	−0.773987	+	0.633202i	$0.781740\pi$
$522$		0			0
$523$	−2.58596	+	7.95877i	−0.113076	+	0.348013i	−0.991541	−	0.129794i	$-0.958568\pi$
$523$	−2.58596	+	7.95877i	−0.113076	+	0.348013i	0.878465	+	0.477807i	$0.158568\pi$
$524$	−8.86849	+	15.3607i	−0.387422	+	0.671034i
$525$		0			0
$526$	4.54717	+	7.87592i	0.198266	+	0.343407i
$527$	−4.34315	+	0.923165i	−0.189191	+	0.0402137i
$528$		0			0
$529$	−9.85588	+	4.38812i	−0.428517	+	0.190788i
$530$	21.9141	−	1.66637i	0.951890	−	0.0723827i
$531$		0			0
$532$	−23.9137			−1.03679
$533$	1.12296	+	10.6842i	0.0486408	+	0.462786i
$534$		0			0
$535$	−0.214818	+	7.45047i	−0.00928738	+	0.322112i
$536$	−19.6941	+	4.18611i	−0.850656	+	0.180812i
$537$		0			0
$538$	29.4824	+	6.26667i	1.27107	+	0.270175i
$539$	18.4245	−	56.7048i	0.793600	−	2.44245i
$540$		0			0
$541$	6.73533	+	20.7292i	0.289575	+	0.891219i	0.984990	+	0.172611i	$0.0552203\pi$
$541$	6.73533	+	20.7292i	0.289575	+	0.891219i	−0.695416	+	0.718608i	$0.744780\pi$
$542$	2.42252	+	23.0487i	0.104056	+	0.990028i
$543$		0			0
$544$	−6.45108	−	2.87221i	−0.276588	−	0.123145i
$545$	6.14650	−	1.80301i	0.263287	−	0.0772323i
$546$		0			0
$547$	30.4960	−	13.5777i	1.30392	−	0.580541i	0.367041	−	0.930205i	$-0.380371\pi$
$547$	30.4960	−	13.5777i	1.30392	−	0.580541i	0.936875	+	0.349664i	$0.113704\pi$
$548$	4.93071	−	15.1752i	0.210630	−	0.648251i
$549$		0			0
$550$	−7.61609	+	46.4930i	−0.324751	+	1.98247i
$551$	12.6648	−	21.9361i	0.539538	−	0.934508i
$552$		0			0
$553$	1.26896	−	12.0734i	0.0539618	−	0.513412i
$554$	−4.74507	+	45.1464i	−0.201599	+	1.91808i
$555$		0			0
$556$	1.08877	+	10.3590i	0.0461742	+	0.439318i
$557$	−0.351013			−0.0148729			−0.00743646	−	0.999972i	$-0.502367\pi$
$557$	−0.351013			−0.0148729			−0.00743646	+	0.999972i	$0.502367\pi$
$558$		0			0
$559$	3.12500	+	9.61776i	0.132173	+	0.406788i
$560$	34.2090	+	32.6355i	1.44559	+	1.37910i
$561$		0			0
$562$	28.9182	−	32.1169i	1.21984	−	1.35477i
$563$	−4.59158	+	5.09946i	−0.193512	+	0.214917i	−0.832091	−	0.554640i	$-0.812856\pi$
$563$	−4.59158	+	5.09946i	−0.193512	+	0.214917i	0.638579	+	0.769557i	$0.279523\pi$
$564$		0			0
$565$	−13.0265	−	12.4273i	−0.548029	−	0.522822i
$566$	7.66881	+	23.6022i	0.322344	+	0.992073i
$567$		0			0
$568$	−11.7878			−0.494607
$569$	1.58415	+	15.0722i	0.0664110	+	0.631858i	0.976213	+	0.216815i	$0.0695669\pi$
$569$	1.58415	+	15.0722i	0.0664110	+	0.631858i	−0.909802	+	0.415043i	$0.863766\pi$
$570$		0			0
$571$	−4.14199	+	39.4084i	−0.173337	+	1.64919i	0.469314	+	0.883031i	$0.344501\pi$
$571$	−4.14199	+	39.4084i	−0.173337	+	1.64919i	−0.642651	+	0.766159i	$0.722166\pi$
$572$	−1.28044	+	12.1826i	−0.0535381	+	0.509381i
$573$		0			0
$574$	−16.8333	+	29.1561i	−0.702609	+	1.21695i
$575$	−17.2715	+	2.64196i	−0.720272	+	0.110177i
$576$		0			0
$577$	−3.56209	+	10.9630i	−0.148292	+	0.456396i	−0.997420	−	0.0717920i	$-0.977128\pi$
$577$	−3.56209	+	10.9630i	−0.148292	+	0.456396i	0.849128	+	0.528188i	$0.177128\pi$
$578$	23.6402	−	10.5253i	0.983303	−	0.437795i
$579$		0			0
$580$	8.91793	−	2.61598i	0.370297	−	0.108622i
$581$	−26.3805	−	11.7454i	−1.09445	−	0.487280i
$582$		0			0
$583$	−3.26693	−	31.0828i	−0.135302	−	1.28732i
$584$	2.14481	+	6.60104i	0.0887528	+	0.273153i
$585$		0			0
$586$	−3.56038	+	10.9577i	−0.147078	+	0.452659i
$587$	−38.3928	−	8.16064i	−1.58464	−	0.336825i	−0.670400	−	0.742000i	$-0.733877\pi$
$587$	−38.3928	−	8.16064i	−1.58464	−	0.336825i	−0.914239	+	0.405174i	$0.867211\pi$
$588$		0			0
$589$	−18.1767	+	3.86358i	−0.748959	+	0.159196i
$590$	−1.28640	+	44.6158i	−0.0529601	+	1.83680i
$591$		0			0
$592$	1.57324	+	14.9684i	0.0646597	+	0.615196i
$593$	2.11729			0.0869465			0.0434733	−	0.999055i	$-0.486158\pi$
$593$	2.11729			0.0869465			0.0434733	+	0.999055i	$0.486158\pi$
$594$		0			0
$595$	13.2274	−	1.00583i	0.542271	−	0.0412349i
$596$	−8.67114	+	3.86064i	−0.355184	+	0.158138i
$597$		0			0
$598$	−13.6711	+	2.90589i	−0.559055	+	0.118831i
$599$	1.13371	+	1.96364i	0.0463219	+	0.0802320i	0.888257	−	0.459347i	$-0.151917\pi$
$599$	1.13371	+	1.96364i	0.0463219	+	0.0802320i	−0.841935	+	0.539579i	$0.818583\pi$
$600$		0			0
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	−0.230985	−	0.972957i	$-0.574195\pi$
$601$	17.8254	−	30.8745i	0.727113	−	1.25940i	0.958098	−	0.286440i	$-0.0924718\pi$
$602$	−9.79310	+	30.1401i	−0.399137	+	1.22842i
$603$		0			0
$604$	14.1380	+	10.2719i	0.575269	+	0.417957i
$605$	42.0245	+	5.64574i	1.70854	+	0.229532i
$606$		0			0
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	−0.999915	−	0.0130175i	$-0.995856\pi$
$607$	−12.5954	−	21.8159i	−0.511231	−	0.885478i	0.488684	−	0.872461i	$-0.337477\pi$
$608$	−26.9987	−	12.0206i	−1.09494	−	0.487500i
$609$		0			0
$610$	−41.3550	−	5.55581i	−1.67442	−	0.224948i
$611$	2.06082	−	6.34257i	0.0833720	−	0.256593i
$612$		0			0
$613$	−13.2971	−	40.9242i	−0.537063	−	1.65291i	−0.739148	−	0.673543i	$-0.764772\pi$
$613$	−13.2971	−	40.9242i	−0.537063	−	1.65291i	0.202085	−	0.979368i	$-0.435228\pi$
$614$	−3.75644	−	4.17195i	−0.151598	−	0.168366i
$615$		0			0
$616$	27.6521	−	30.7108i	1.11414	−	1.23737i
$617$	−29.2543	−	13.0248i	−1.17773	−	0.524360i	−0.277906	−	0.960608i	$-0.589640\pi$
$617$	−29.2543	−	13.0248i	−1.17773	−	0.524360i	−0.899827	+	0.436248i	$0.856307\pi$
$618$		0			0
$619$	1.36801	+	13.0157i	0.0549849	+	0.523146i	0.986999	+	0.160725i	$0.0513832\pi$
$619$	1.36801	+	13.0157i	0.0549849	+	0.523146i	−0.932014	+	0.362421i	$0.881950\pi$
$620$	−5.80406	−	3.57788i	−0.233096	−	0.143691i
$621$		0			0
$622$	44.8848	+	32.6107i	1.79972	+	1.30757i
$623$	12.9577	+	14.3910i	0.519141	+	0.576565i
$624$		0			0
$625$	24.8340	+	2.87610i	0.993360	+	0.115044i
$626$	−17.6658	−	30.5980i	−0.706067	−	1.22294i
$627$		0			0
$628$	2.34236	−	1.04289i	0.0934704	−	0.0416157i
$629$	3.41644	+	2.48219i	0.136222	+	0.0989713i
$630$		0			0
$631$	34.4722	−	25.0455i	1.37232	−	0.997047i	0.374765	−	0.927120i	$-0.377723\pi$
$631$	34.4722	−	25.0455i	1.37232	−	0.997047i	0.997552	−	0.0699268i	$-0.0222766\pi$
$632$	2.56119	−	4.43612i	0.101879	−	0.176459i
$633$		0			0
$634$	−4.60725	+	5.11686i	−0.182977	+	0.203217i
$635$	10.0136	+	3.57582i	0.397376	+	0.141902i
$636$		0			0
$637$	−24.7553	−	5.26190i	−0.980841	−	0.208484i
$638$	−12.5649	−	38.6708i	−0.497450	−	1.53099i
$639$		0			0
$640$	10.5087	+	25.5613i	0.415394	+	1.01040i
$641$	−2.60724	−	0.554186i	−0.102980	−	0.0218890i	0.156134	−	0.987736i	$-0.450097\pi$
$641$	−2.60724	−	0.554186i	−0.102980	−	0.0218890i	−0.259113	+	0.965847i	$0.583430\pi$
$642$		0			0
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	0.945505	+	0.325607i	$0.105569\pi$
$643$	19.1382	+	33.1483i	0.754736	+	1.30724i	−0.190769	+	0.981635i	$0.561098\pi$
$644$	−13.0059	−	5.79061i	−0.512505	−	0.228182i
$645$		0			0
$646$	−12.9459	+	5.76391i	−0.509352	+	0.226778i
$647$	−29.1546	−	21.1821i	−1.14619	−	0.832753i	−0.158217	−	0.987404i	$-0.550575\pi$
$647$	−29.1546	−	21.1821i	−1.14619	−	0.832753i	−0.987969	+	0.154651i	$0.950575\pi$
$648$		0			0
$649$	63.4743			2.49158
$650$	19.9648	+	1.15224i	0.783085	+	0.0451946i
$651$		0			0
$652$	−3.63451	+	0.772539i	−0.142338	+	0.0302550i
$653$	2.97420	−	28.2976i	0.116390	−	1.10737i	−0.767944	−	0.640517i	$-0.778720\pi$
$653$	2.97420	−	28.2976i	0.116390	−	1.10737i	0.884334	−	0.466855i	$-0.154613\pi$
$654$		0			0
$655$	17.8260	−	37.1201i	0.696521	−	1.45040i
$656$	−18.6981	+	13.5850i	−0.730039	+	0.530405i
$657$		0			0
$658$	16.9078	−	12.2842i	0.659134	−	0.478889i
$659$	−31.7095	−	6.74006i	−1.23523	−	0.262555i	−0.456388	−	0.889781i	$-0.650857\pi$
$659$	−31.7095	−	6.74006i	−1.23523	−	0.262555i	−0.778838	+	0.627225i	$0.784191\pi$
$660$		0			0
$661$	−45.4288	+	9.65619i	−1.76698	+	0.375582i	−0.972717	−	0.231997i	$-0.925474\pi$
$661$	−45.4288	+	9.65619i	−1.76698	+	0.375582i	−0.794259	+	0.607579i	$0.792141\pi$
$662$	−1.69789	+	1.88570i	−0.0659904	+	0.0732898i
$663$		0			0
$664$	−8.15310	−	9.05493i	−0.316402	−	0.351400i
$665$	55.3587	−	4.20953i	2.14672	−	0.163239i
$666$		0			0
$667$	12.1997	−	8.86361i	0.472375	−	0.343200i
$668$	−5.06279	+	8.76900i	−0.195885	+	0.339283i
$669$		0			0
$670$	−41.6655	+	12.2221i	−1.60968	+	0.472181i
$671$	−6.20263	+	59.0141i	−0.239450	+	2.27821i
$672$		0			0
$673$	3.91719	+	4.35048i	0.150997	+	0.167699i	0.813898	−	0.581008i	$-0.197342\pi$
$673$	3.91719	+	4.35048i	0.150997	+	0.167699i	−0.662901	+	0.748707i	$0.730675\pi$
$674$	16.0430			0.617953
$675$		0			0
$676$	−7.32129			−0.281588
$677$	−13.3028	−	14.7742i	−0.511266	−	0.567819i	0.431142	−	0.902284i	$-0.358111\pi$
$677$	−13.3028	−	14.7742i	−0.511266	−	0.567819i	−0.942408	+	0.334465i	$0.891444\pi$
$678$		0			0
$679$	−6.11358	+	58.1668i	−0.234618	+	2.23224i
$680$	5.27137	+	1.88240i	0.202148	+	0.0721866i
$681$		0			0
$682$	−14.9152	+	25.8340i	−0.571134	+	0.989233i
$683$	36.4251	−	26.4644i	1.39377	−	1.01263i	0.398328	−	0.917243i	$-0.369591\pi$
$683$	36.4251	−	26.4644i	1.39377	−	1.01263i	0.995440	−	0.0953885i	$-0.0304093\pi$
$684$		0			0
$685$	−8.74299	+	35.9975i	−0.334053	+	1.37539i
$686$	−18.9643	−	21.0620i	−0.724061	−	0.804151i
$687$		0			0
$688$	−14.5576	+	16.1679i	−0.555003	+	0.616394i
$689$	−12.9766	+	2.75826i	−0.494368	+	0.105081i
$690$		0			0
$691$	−0.983758	−	0.209104i	−0.0374239	−	0.00795470i	0.189162	−	0.981946i	$-0.439423\pi$
$691$	−0.983758	−	0.209104i	−0.0374239	−	0.00795470i	−0.226586	+	0.973991i	$0.572756\pi$
$692$	4.79031	−	3.48036i	0.182100	−	0.132304i
$693$		0			0
$694$	9.29844	−	6.75571i	0.352964	−	0.256443i
$695$	−4.34392	−	23.7887i	−0.164774	−	0.902355i
$696$		0			0
$697$	−0.677846	+	6.44928i	−0.0256753	+	0.244284i
$698$	−7.31441	+	1.55473i	−0.276855	+	0.0588472i
$699$		0			0
$700$	15.7627	+	12.9030i	0.595774	+	0.487689i
$701$	8.14396			0.307593			0.153797	−	0.988103i	$-0.450850\pi$
$701$	8.14396			0.307593			0.153797	+	0.988103i	$0.450850\pi$
$702$		0			0
$703$	14.2983	+	10.3883i	0.539270	+	0.391803i
$704$	6.65195	−	2.96164i	0.250705	−	0.111621i
$705$		0			0
$706$	−7.27561	−	3.23931i	−0.273821	−	0.121913i
$707$	18.1604	+	31.4547i	0.682992	+	1.18298i
$708$		0			0
$709$	−40.2017	−	8.54513i	−1.50981	−	0.320919i	−0.622691	−	0.782468i	$-0.713961\pi$
$709$	−40.2017	−	8.54513i	−1.50981	−	0.320919i	−0.887115	+	0.461548i	$0.847294\pi$
$710$	−25.3485	+	1.92752i	−0.951312	+	0.0723387i
$711$		0			0
$712$	2.52499	+	7.77112i	0.0946279	+	0.291235i
$713$	−10.8213	−	2.30014i	−0.405261	−	0.0861409i
$714$		0			0
$715$	0.819639	−	28.4273i	0.0306528	−	1.06312i
$716$	4.64207	−	5.15554i	0.173482	−	0.192672i
$717$		0			0
$718$	7.76100	−	13.4424i	0.289638	−	0.501668i
$719$	−39.3653	+	28.6006i	−1.46808	+	1.06662i	−0.486915	+	0.873449i	$0.661878\pi$
$719$	−39.3653	+	28.6006i	−1.46808	+	1.06662i	−0.981165	+	0.193173i	$0.938122\pi$
$720$		0			0
$721$	−0.0602751	−	0.0437924i	−0.00224476	−	0.00163091i
$722$	−24.3021	+	10.8200i	−0.904429	+	0.402678i
$723$		0			0
$724$	−10.9369	−	18.9433i	−0.406468	−	0.704023i
$725$	−20.1839	+	7.62564i	−0.749613	+	0.283209i
$726$		0			0
$727$	26.1295	+	29.0197i	0.969089	+	1.07628i	0.997056	+	0.0766736i	$0.0244299\pi$
$727$	26.1295	+	29.0197i	0.969089	+	1.07628i	−0.0279672	+	0.999609i	$0.508903\pi$
$728$	−14.1914	−	10.3107i	−0.525968	−	0.382138i
$729$		0			0
$730$	5.69157	+	13.8441i	0.210654	+	0.512393i
$731$	0.638072	+	6.07085i	0.0235999	+	0.224538i
$732$		0			0
$733$	0.702728	+	0.312875i	0.0259559	+	0.0115563i	0.419674	−	0.907675i	$-0.362145\pi$
$733$	0.702728	+	0.312875i	0.0259559	+	0.0115563i	−0.393718	+	0.919231i	$0.628811\pi$
$734$	10.6628	−	11.8422i	0.393570	−	0.437104i
$735$		0			0
$736$	−11.7730	−	13.0753i	−0.433959	−	0.481961i
$737$	19.0815	+	58.7268i	0.702876	+	2.16323i
$738$		0			0
$739$	16.0888	−	49.5162i	0.591835	−	1.82148i	0.0219476	−	0.999759i	$-0.493013\pi$
$739$	16.0888	−	49.5162i	0.591835	−	1.82148i	0.569888	−	0.821723i	$-0.306987\pi$
$740$	1.16487	+	6.37917i	0.0428214	+	0.234503i
$741$		0			0
$742$	−37.9801	−	16.9098i	−1.39429	−	0.620779i
$743$	−19.6551	−	34.0437i	−0.721076	−	1.24894i	−0.960569	−	0.278043i	$-0.910314\pi$
$743$	−19.6551	−	34.0437i	−0.721076	−	1.24894i	0.239492	−	0.970898i	$-0.423019\pi$
$744$		0			0
$745$	19.3935	−	10.4635i	0.710524	−	0.383353i
$746$	−7.54594	−	5.48244i	−0.276276	−	0.200727i
$747$		0			0
$748$	−2.28494	+	7.03234i	−0.0835458	+	0.257128i
$749$	7.04991	−	12.2108i	0.257598	−	0.446173i
$750$		0			0
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	0.959149	+	0.282903i	$0.0912973\pi$
$751$	19.8565	+	34.3925i	0.724575	+	1.25500i	−0.234573	+	0.972098i	$0.575369\pi$
$752$	14.0338	−	2.98297i	0.511759	−	0.108778i
$753$		0			0
$754$	−15.7673	+	7.02005i	−0.574211	+	0.255655i
$755$	−34.5368	−	21.2900i	−1.25692	−	0.774824i
$756$		0			0
$757$	−30.6481			−1.11392			−0.556961	−	0.830538i	$-0.688033\pi$
$757$	−30.6481			−1.11392			−0.556961	+	0.830538i	$0.688033\pi$
$758$	−1.60466	−	15.2673i	−0.0582838	−	0.554534i
$759$		0			0
$760$	22.0615	+	7.87810i	0.800253	+	0.285769i
$761$	−18.3629	+	3.90315i	−0.665654	+	0.141489i	−0.528333	−	0.849037i	$-0.677183\pi$
$761$	−18.3629	+	3.90315i	−0.665654	+	0.141489i	−0.137321	+	0.990527i	$0.543849\pi$
$762$		0			0
$763$	−11.8524	−	2.51930i	−0.429085	−	0.0912048i
$764$	3.19405	−	9.83029i	0.115557	−	0.355647i
$765$		0			0
$766$	−9.81472	−	30.2066i	−0.354620	−	1.09141i
$767$	−2.81632	−	26.7955i	−0.101692	−	0.967531i
$768$		0			0
$769$	−34.5232	−	15.3707i	−1.24494	−	0.554282i	−0.324764	−	0.945795i	$-0.605285\pi$
$769$	−34.5232	−	15.3707i	−1.24494	−	0.554282i	−0.920172	+	0.391513i	$0.871952\pi$
$770$	54.4411	−	70.5618i	1.96192	−	2.54287i
$771$		0			0
$772$	−13.1900	+	5.87256i	−0.474718	+	0.211358i
$773$	8.44199	−	25.9818i	0.303637	−	0.934500i	−0.676545	−	0.736401i	$-0.736524\pi$
$773$	8.44199	−	25.9818i	0.303637	−	0.934500i	0.980182	−	0.198098i	$-0.0634765\pi$
$774$		0			0
$775$	14.0658	+	7.26087i	0.505259	+	0.260818i
$776$	−12.3393	+	21.3722i	−0.442954	+	0.767219i
$777$		0			0
$778$	2.28015	−	21.6941i	0.0817472	−	0.777773i
$779$	−2.83689	+	26.9912i	−0.101642	+	0.967059i
$780$		0			0
$781$	3.77892	+	35.9540i	0.135220	+	1.28654i
$782$	−8.43660			−0.301692
$783$		0			0
$784$	−16.8251	−	51.7823i	−0.600896	−	1.84937i
$785$	−5.23883	+	2.82654i	−0.186982	+	0.100884i
$786$		0			0
$787$	−10.7096	+	11.8942i	−0.381755	+	0.423982i	−0.903144	−	0.429337i	$-0.858747\pi$
$787$	−10.7096	+	11.8942i	−0.381755	+	0.423982i	0.521389	+	0.853319i	$0.325414\pi$
$788$	5.11846	−	5.68462i	0.182337	−	0.202506i
$789$		0			0
$790$	4.78218	−	9.95819i	0.170142	−	0.354296i
$791$	10.5242	+	32.3902i	0.374198	+	1.15166i
$792$		0			0
$793$	25.1879			0.894448
$794$	−1.12463	−	10.7001i	−0.0399115	−	0.379732i
$795$		0			0
$796$	1.42071	−	13.5171i	0.0503556	−	0.479102i
$797$	−1.81021	+	17.2230i	−0.0641209	+	0.610070i	0.914527	+	0.404525i	$0.132563\pi$
$797$	−1.81021	+	17.2230i	−0.0641209	+	0.610070i	−0.978648	+	0.205544i	$0.934103\pi$
$798$		0			0
$799$	2.01278	−	3.48623i	0.0712070	−	0.123334i
$800$	11.3103	+	22.4910i	0.399878	+	0.795176i
$801$		0			0
$802$	−14.2173	+	43.7563i	−0.502029	+	1.54509i
$803$	19.4462	−	8.65801i	0.686242	−	0.305534i
$804$		0			0
$805$	31.1272	+	11.1155i	1.09709	+	0.391768i
$806$	11.5675	+	5.15019i	0.407449	+	0.181408i
$807$		0			0
$808$	1.60195	+	15.2415i	0.0563563	+	0.536194i
$809$	−3.76845	−	11.5981i	−0.132492	−	0.407767i	0.862700	−	0.505716i	$-0.168772\pi$
$809$	−3.76845	−	11.5981i	−0.132492	−	0.407767i	−0.995191	+	0.0979492i	$0.968772\pi$
$810$		0			0
$811$	1.10851	−	3.41163i	0.0389249	−	0.119799i	−0.929706	−	0.368303i	$-0.879939\pi$
$811$	1.10851	−	3.41163i	0.0389249	−	0.119799i	0.968631	+	0.248504i	$0.0799390\pi$
$812$	−17.1966	−	3.65525i	−0.603482	−	0.128274i
$813$		0			0
$814$	27.7511	−	5.89867i	0.972675	−	0.206748i
$815$	8.27766	−	2.42816i	0.289954	−	0.0850548i
$816$		0			0
$817$	2.67042	+	25.4074i	0.0934263	+	0.888892i
$818$	−41.1810			−1.43986
$819$		0			0
$820$	−7.58913	+	6.44709i	−0.265024	+	0.225142i
$821$	8.52808	−	3.79695i	0.297632	−	0.132514i	−0.252488	−	0.967600i	$-0.581249\pi$
$821$	8.52808	−	3.79695i	0.297632	−	0.132514i	0.550120	+	0.835086i	$0.314582\pi$
$822$		0			0
$823$	47.0748	−	10.0061i	1.64093	−	0.348790i	0.707265	−	0.706948i	$-0.249929\pi$
$823$	47.0748	−	10.0061i	1.64093	−	0.348790i	0.933661	+	0.358159i	$0.116595\pi$
$824$	−0.0157184	−	0.0272251i	−0.000547576	−	0.000948430i
$825$		0			0
$826$	42.2171	−	73.1221i	1.46892	−	2.54424i
$827$	−8.29286	+	25.5228i	−0.288371	+	0.887515i	0.696997	+	0.717074i	$0.254519\pi$
$827$	−8.29286	+	25.5228i	−0.288371	+	0.887515i	−0.985368	+	0.170441i	$0.945481\pi$
$828$		0			0
$829$	−27.4122	−	19.9161i	−0.952065	−	0.691716i	−0.000770971	−	1.00000i	$-0.500245\pi$
$829$	−27.4122	−	19.9161i	−0.952065	−	0.691716i	−0.951294	+	0.308284i	$0.900245\pi$
$830$	−19.0130	−	18.1385i	−0.659951	−	0.629596i
$831$		0			0
$832$	−1.54539	−	2.67670i	−0.0535769	−	0.0927979i
$833$	−13.9560	−	6.21361i	−0.483547	−	0.215289i
$834$		0			0
$835$	10.1764	−	21.1909i	0.352169	−	0.733340i
$836$	−9.56283	+	29.4314i	−0.330737	+	1.01790i
$837$		0			0
$838$	−6.67399	−	20.5404i	−0.230549	−	0.709558i
$839$	12.0596	+	13.3936i	0.416344	+	0.462397i	0.914438	−	0.404726i	$-0.132633\pi$
$839$	12.0596	+	13.3936i	0.416344	+	0.462397i	−0.498094	+	0.867123i	$0.665966\pi$
$840$		0			0
$841$	−6.94446	+	7.71260i	−0.239464	+	0.265952i
$842$	1.85591	+	0.826303i	0.0639587	+	0.0284763i
$843$		0			0
$844$	−0.737169	−	7.01369i	−0.0253744	−	0.241421i
$845$	16.9483	−	1.28877i	0.583039	−	0.0443349i
$846$		0			0
$847$	−64.8923	−	47.1470i	−2.22973	−	1.61999i
$848$	−19.0975	−	21.2100i	−0.655812	−	0.728353i
$849$		0			0
$850$	11.6433	+	3.18592i	0.399362	+	0.109276i
$851$	5.26090	+	9.11215i	0.180341	+	0.312361i
$852$		0			0
$853$	37.2944	−	16.6045i	1.27694	−	0.568528i	0.347558	−	0.937659i	$-0.387011\pi$
$853$	37.2944	−	16.6045i	1.27694	−	0.568528i	0.929378	+	0.369130i	$0.120344\pi$
$854$	63.8586	+	46.3960i	2.18520	+	1.58764i
$855$		0			0
$856$	4.81315	−	3.49696i	0.164510	−	0.119524i
$857$	0.284511	−	0.492787i	0.00971870	−	0.0168333i	−0.861125	−	0.508393i	$-0.830240\pi$
$857$	0.284511	−	0.492787i	0.00971870	−	0.0168333i	0.870844	+	0.491560i	$0.163573\pi$
$858$		0			0
$859$	23.5971	−	26.2073i	0.805124	−	0.894181i	−0.191049	−	0.981580i	$-0.561189\pi$
$859$	23.5971	−	26.2073i	0.805124	−	0.894181i	0.996173	+	0.0873996i	$0.0278557\pi$
$860$	−5.72593	+	7.42145i	−0.195253	+	0.253069i
$861$		0			0
$862$	−42.3080	−	8.99284i	−1.44102	−	0.306297i
$863$	−7.48769	−	23.0447i	−0.254884	−	0.784452i	−0.993852	−	0.110712i	$-0.964687\pi$
$863$	−7.48769	−	23.0447i	−0.254884	−	0.784452i	0.738968	−	0.673740i	$-0.235313\pi$
$864$		0			0
$865$	−10.4766	+	8.90005i	−0.356215	+	0.302611i
$866$	−33.6902	−	7.16107i	−1.14484	−	0.243343i
$867$		0			0
$868$	6.44898	+	11.1700i	0.218893	+	0.379133i
$869$	−14.3516	−	6.38975i	−0.486845	−	0.216758i
$870$		0			0
$871$	23.9448	−	10.6609i	0.811337	−	0.361231i
$872$	−4.13635	−	3.00523i	−0.140074	−	0.101770i
$873$		0			0
$874$	−35.3084			−1.19433
$875$	−38.7609	−	27.0950i	−1.31036	−	0.915977i
$876$		0			0
$877$	48.0471	−	10.2127i	1.62243	−	0.344859i	0.695048	−	0.718963i	$-0.255383\pi$
$877$	48.0471	−	10.2127i	1.62243	−	0.344859i	0.927387	+	0.374104i	$0.122050\pi$
$878$	−4.07947	+	38.8135i	−0.137675	+	1.30989i
$879$		0			0
$880$	53.8453	−	29.0515i	1.81513	−	0.979326i
$881$	9.93477	−	7.21804i	0.334711	−	0.243182i	−0.407716	−	0.913109i	$-0.633675\pi$
$881$	9.93477	−	7.21804i	0.334711	−	0.243182i	0.742427	+	0.669927i	$0.233675\pi$
$882$		0			0
$883$	−40.0558	+	29.1022i	−1.34798	+	0.979367i	−0.348874	+	0.937170i	$0.613436\pi$
$883$	−40.0558	+	29.1022i	−1.34798	+	0.979367i	−0.999109	+	0.0421976i	$0.986564\pi$
$884$	3.07007	+	0.652563i	0.103257	+	0.0219481i
$885$		0			0
$886$	8.36149	−	1.77729i	0.280910	−	0.0597092i
$887$	32.1435	−	35.6990i	1.07927	−	1.19865i	0.100238	−	0.994963i	$-0.468040\pi$
$887$	32.1435	−	35.6990i	1.07927	−	1.19865i	0.979035	−	0.203691i	$-0.0652938\pi$
$888$		0			0
$889$	−13.4589	−	14.9477i	−0.451398	−	0.501328i
$890$	6.70043	+	16.2981i	0.224599	+	0.546312i
$891$		0			0
$892$	15.8497	−	11.5155i	0.530688	−	0.385568i
$893$	8.42377	−	14.5904i	0.281891	−	0.488249i
$894$		0			0
$895$	−9.83855	+	12.7519i	−0.328867	+	0.426248i
$896$	5.46484	−	51.9945i	0.182567	−	1.73701i
$897$		0			0
$898$	20.4663	+	22.7301i	0.682969	+	0.758514i
$899$	−13.6616			−0.455640
$900$		0			0
$901$	−8.00797			−0.266784
$902$	29.1519	+	32.3765i	0.970653	+	1.07802i
$903$		0			0
$904$	−1.50211	+	14.2916i	−0.0499593	+	0.475331i
$905$	28.6529	+	41.9273i	0.952454	+	1.39371i
$906$		0			0
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	−0.931553	−	0.363607i	$-0.881545\pi$
$907$	−4.54408	+	7.87058i	−0.150884	+	0.261338i	0.780669	+	0.624945i	$0.214879\pi$
$908$	−16.9587	+	12.3212i	−0.562794	+	0.408894i
$909$		0			0
$910$	−32.2030	−	19.8514i	−1.06752	−	0.658067i
$911$	−1.57331	−	1.74733i	−0.0521260	−	0.0578917i	0.716518	−	0.697569i	$-0.245735\pi$
$911$	−1.57331	−	1.74733i	−0.0521260	−	0.0578917i	−0.768644	+	0.639677i	$0.779068\pi$
$912$		0			0
$913$	−25.0047	+	27.7705i	−0.827534	+	0.919069i
$914$	33.7328	−	7.17012i	1.11578	−	0.237166i
$915$		0			0
$916$	17.6931	+	3.76077i	0.584595	+	0.124259i
$917$	−63.0198	+	45.7866i	−2.08110	+	1.51201i
$918$		0			0
$919$	−35.1878	+	25.5654i	−1.16074	+	0.843325i	−0.989871	−	0.141969i	$-0.954657\pi$
$919$	−35.1878	+	25.5654i	−1.16074	+	0.843325i	−0.170866	+	0.985294i	$0.554657\pi$
$920$	10.0909	+	9.62675i	0.332687	+	0.317384i
$921$		0			0
$922$	2.26773	−	21.5760i	0.0746837	−	0.710568i
$923$	15.0102	−	3.19052i	0.494068	−	0.105017i
$924$		0			0
$925$	−3.81952	−	14.5623i	−0.125585	−	0.478806i
$926$	42.8642			1.40860
$927$		0			0
$928$	−17.5777	−	12.7709i	−0.577015	−	0.419226i
$929$	−47.0033	+	20.9272i	−1.54213	+	0.686600i	−0.989192	−	0.146624i	$-0.953159\pi$
$929$	−47.0033	+	20.9272i	−1.54213	+	0.686600i	−0.552936	+	0.833224i	$0.686493\pi$
$930$		0			0
$931$	−58.4079	−	26.0049i	−1.91424	−	0.852276i
$932$	3.08265	+	5.33931i	0.100976	+	0.174895i
$933$		0			0
$934$	−61.6920	−	13.1130i	−2.01862	−	0.429072i
$935$	4.05159	−	16.6816i	0.132501	−	0.545547i
$936$		0			0
$937$	−1.71388	−	5.27478i	−0.0559900	−	0.172320i	0.919151	−	0.393906i	$-0.128876\pi$
$937$	−1.71388	−	5.27478i	−0.0559900	−	0.172320i	−0.975141	+	0.221587i	$0.928876\pi$
$938$	80.3442	+	17.0777i	2.62333	+	0.557606i
$939$		0			0
$940$	5.93161	−	1.73997i	0.193468	−	0.0567516i
$941$	−23.4660	+	26.0616i	−0.764970	+	0.849585i	−0.992252	−	0.124244i	$-0.960349\pi$
$941$	−23.4660	+	26.0616i	−0.764970	+	0.849585i	0.227282	+	0.973829i	$0.427016\pi$
$942$		0			0
$943$	−8.07869	+	13.9927i	−0.263078	+	0.455665i
$944$	46.8939	−	34.0704i	1.52627	−	1.10890i
$945$		0			0
$946$	33.1782	+	24.1053i	1.07871	+	0.783732i
$947$	51.1465	−	22.7719i	1.66204	−	0.739987i	0.662083	−	0.749430i	$-0.269672\pi$
$947$	51.1465	−	22.7719i	1.66204	−	0.739987i	0.999955	+	0.00944271i	$0.00300575\pi$
$948$		0			0
$949$	−4.51778	−	7.82502i	−0.146653	−	0.254011i
$950$	48.7290	+	13.3336i	1.58098	+	0.432598i
$951$		0			0
$952$	−7.08509	−	7.86879i	−0.229629	−	0.255029i
$953$	5.24619	+	3.81158i	0.169941	+	0.123469i	0.669505	−	0.742808i	$-0.266506\pi$
$953$	5.24619	+	3.81158i	0.169941	+	0.123469i	−0.499564	+	0.866277i	$0.666506\pi$
$954$		0			0
$955$	−5.66360	+	23.3187i	−0.183270	+	0.754576i
$956$	−1.77067	−	16.8468i	−0.0572675	−	0.544864i
$957$		0			0
$958$	11.4905	+	5.11591i	0.371242	+	0.165288i
$959$	46.8898	−	52.0764i	1.51415	−	1.68163i
$960$		0			0
$961$	−14.0366	−	15.5892i	−0.452792	−	0.502876i
$962$	−3.72141	−	11.4533i	−0.119983	−	0.369270i
$963$		0			0
$964$	2.26125	−	6.95941i	0.0728300	−	0.224148i
$965$	29.5002	−	15.9164i	0.949645	−	0.512367i
$966$		0			0
$967$	4.57452	+	2.03671i	0.147107	+	0.0654962i	0.478970	−	0.877832i	$-0.341010\pi$
$967$	4.57452	+	2.03671i	0.147107	+	0.0654962i	−0.331863	+	0.943328i	$0.607677\pi$
$968$	−16.9225	−	29.3106i	−0.543909	−	0.942078i
$969$		0			0
$970$	−23.0395	+	47.9764i	−0.739754	+	1.54043i
$971$	40.8653	+	29.6904i	1.31143	+	0.952810i	0.999997	+	0.00254202i	$0.000809152\pi$
$971$	40.8653	+	29.6904i	1.31143	+	0.952810i	0.311434	+	0.950268i	$0.399191\pi$
$972$		0			0
$973$	−14.1359	+	43.5059i	−0.453177	+	1.39473i
$974$	−21.3261	+	36.9380i	−0.683333	+	1.18357i
$975$		0			0
$976$	27.0940	+	46.9281i	0.867257	+	1.50213i
$977$	23.3328	−	4.95954i	0.746482	−	0.158670i	0.181061	−	0.983472i	$-0.442047\pi$
$977$	23.3328	−	4.95954i	0.746482	−	0.158670i	0.565421	+	0.824802i	$0.308714\pi$
$978$		0			0
$979$	22.8932	−	10.1927i	0.731668	−	0.325760i
$980$	−8.91987	−	21.6966i	−0.284935	−	0.693072i
$981$		0			0
$982$	−35.1227			−1.12081
$983$	0.990622	+	9.42514i	0.0315959	+	0.300615i	0.998896	+	0.0469799i	$0.0149597\pi$
$983$	0.990622	+	9.42514i	0.0315959	+	0.300615i	−0.967300	+	0.253635i	$0.918374\pi$
$984$		0			0
$985$	−10.8482	+	14.0605i	−0.345653	+	0.448006i
$986$	−10.1906	+	2.16607i	−0.324534	+	0.0689818i
$987$		0			0
$988$	12.8487	+	2.73107i	0.408771	+	0.0868869i
$989$	−4.69993	+	14.4649i	−0.149449	+	0.459957i
$990$		0			0
$991$	8.47195	+	26.0740i	0.269120	+	0.828268i	0.990715	+	0.135952i	$0.0434093\pi$
$991$	8.47195	+	26.0740i	0.269120	+	0.828268i	−0.721595	+	0.692316i	$0.756591\pi$
$992$	1.66618	+	15.8526i	0.0529012	+	0.503321i
$993$		0			0
$994$	43.9322	+	19.5599i	1.39345	+	0.620402i
$995$	−0.909425	+	31.5413i	−0.0288307	+	0.999928i
$996$		0			0
$997$	23.2314	−	10.3433i	0.735745	−	0.327575i	−0.00442921	−	0.999990i	$-0.501410\pi$
$997$	23.2314	−	10.3433i	0.735745	−	0.327575i	0.740174	+	0.672416i	$0.234743\pi$
$998$	−11.4166	+	35.1366i	−0.361385	+	1.11223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.6		224
3.2	odd	2		225.2.q.a.196.23	yes	224
9.4	even	3	inner	675.2.r.a.496.23		224
9.5	odd	6		225.2.q.a.121.6	yes	224
25.6	even	5	inner	675.2.r.a.181.23		224
75.56	odd	10		225.2.q.a.106.6	yes	224
225.31	even	15	inner	675.2.r.a.631.6		224
225.131	odd	30		225.2.q.a.31.23	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.23	✓	224	225.131	odd	30
225.2.q.a.106.6	yes	224	75.56	odd	10
225.2.q.a.121.6	yes	224	9.5	odd	6
225.2.q.a.196.23	yes	224	3.2	odd	2
675.2.r.a.46.6		224	1.1	even	1	trivial
675.2.r.a.181.23		224	25.6	even	5	inner
675.2.r.a.496.23		224	9.4	even	3	inner
675.2.r.a.631.6		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15183 - 1.27924i) q^{2} +(-0.100677 + 0.957875i) q^{4} +(0.0644453 - 2.23514i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 + 1.04909i) q^{8} +O(q^{10})\)	\(q+(-1.15183 - 1.27924i) q^{2} +(-0.100677 + 0.957875i) q^{4} +(0.0644453 - 2.23514i) q^{5} +(-2.11497 + 3.66323i) q^{7} +(-1.44394 + 1.04909i) q^{8} +(-2.93350 + 2.49206i) q^{10} +(3.66270 + 4.06784i) q^{11} +(1.55472 - 1.72669i) q^{13} +(7.12222 - 1.51387i) q^{14} +(4.88941 + 1.03928i) q^{16} +(1.13466 - 0.824379i) q^{17} +(4.74872 - 3.45015i) q^{19} +(2.13449 + 0.286757i) q^{20} +(0.984923 - 9.37092i) q^{22} +(3.41812 - 0.726543i) q^{23} +(-4.99169 - 0.288088i) q^{25} -3.99961 q^{26} +(-3.29599 - 2.39468i) q^{28} +(3.94221 - 1.75518i) q^{29} +(-2.89216 - 1.28767i) q^{31} +(-2.51747 - 4.36039i) q^{32} +(-2.36151 - 0.501954i) q^{34} +(8.05154 + 4.96333i) q^{35} +(0.930443 + 2.86361i) q^{37} +(-9.88326 - 2.10075i) q^{38} +(2.25180 + 3.29502i) q^{40} +(-3.09385 + 3.43607i) q^{41} +(-2.17619 + 3.76927i) q^{43} +(-4.26523 + 3.09887i) q^{44} +(-4.86650 - 3.53572i) q^{46} +(2.62209 - 1.16743i) q^{47} +(-5.44619 - 9.43308i) q^{49} +(5.38104 + 6.71738i) q^{50} +(1.49743 + 1.66306i) q^{52} +(-4.61926 - 3.35609i) q^{53} +(9.32824 - 7.92450i) q^{55} +(-0.789153 - 7.50829i) q^{56} +(-6.78604 - 3.02134i) q^{58} +(7.75922 - 8.61749i) q^{59} +(7.25373 + 8.05609i) q^{61} +(1.68404 + 5.18293i) q^{62} +(0.411065 - 1.26513i) q^{64} +(-3.75920 - 3.58629i) q^{65} +(10.3055 + 4.58831i) q^{67} +(0.675418 + 1.16986i) q^{68} +(-2.92473 - 16.0167i) q^{70} +(5.34318 + 3.88205i) q^{71} +(1.20170 - 3.69845i) q^{73} +(2.59152 - 4.48864i) q^{74} +(2.82672 + 4.89603i) q^{76} +(-22.6480 + 4.81398i) q^{77} +(-2.62186 + 1.16733i) q^{79} +(2.63803 - 10.8615i) q^{80} +7.95913 q^{82} +(0.713599 + 6.78944i) q^{83} +(-1.76948 - 2.58925i) q^{85} +(7.32838 - 1.55770i) q^{86} +(-9.55625 - 2.03124i) q^{88} +(1.41471 - 4.35403i) q^{89} +(3.03709 + 9.34720i) q^{91} +(0.351813 + 3.34727i) q^{92} +(-4.51362 - 2.00959i) q^{94} +(-7.40552 - 10.8364i) q^{95} +(12.6316 - 5.62394i) q^{97} +(-5.79405 + 17.8322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more