LMFDB - Embedded newform 460.2.m.b.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.5
Character	$\chi$	$=$	460.121
Dual form			460.2.m.b.441.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.60088 + 0.763688i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.742558 - 5.16460i) q^{7} +(3.65762 + 2.35061i) q^{9} +O(q^{10})$	\(q+(2.60088 + 0.763688i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.742558 - 5.16460i) q^{7} +(3.65762 + 2.35061i) q^{9} +(2.19921 + 4.81559i) q^{11} +(-0.380417 - 2.64586i) q^{13} +(-2.60088 + 0.763688i) q^{15} +(2.62212 - 3.02609i) q^{17} +(3.33112 + 3.84432i) q^{19} +(5.87546 - 12.8655i) q^{21} +(-4.55543 + 1.49936i) q^{23} +(0.415415 - 0.909632i) q^{25} +(2.39254 + 2.76114i) q^{27} +(-5.18549 + 5.98437i) q^{29} +(-0.294321 + 0.0864204i) q^{31} +(2.04227 + 14.2043i) q^{33} +(2.16752 + 4.74620i) q^{35} +(-0.239677 - 0.154031i) q^{37} +(1.03119 - 7.17210i) q^{39} +(-2.42746 + 1.56003i) q^{41} +(-1.15730 - 0.339815i) q^{43} -4.34782 q^{45} -8.10495 q^{47} +(-19.4053 - 5.69791i) q^{49} +(9.13082 - 5.86802i) q^{51} +(-0.852155 + 5.92687i) q^{53} +(-4.45359 - 2.86215i) q^{55} +(5.72800 + 12.5426i) q^{57} +(-1.14099 - 7.93574i) q^{59} +(8.37646 - 2.45955i) q^{61} +(14.8560 - 17.1447i) q^{63} +(1.75049 + 2.02017i) q^{65} +(1.58522 - 3.47115i) q^{67} +(-12.9932 + 0.420736i) q^{69} +(0.519116 - 1.13670i) q^{71} +(-2.65089 - 3.05929i) q^{73} +(1.77512 - 2.04860i) q^{75} +(26.5037 - 7.78218i) q^{77} +(0.818854 + 5.69526i) q^{79} +(-1.30438 - 2.85618i) q^{81} +(-1.06047 - 0.681525i) q^{83} +(-0.569841 + 3.96333i) q^{85} +(-18.0571 + 11.6046i) q^{87} +(14.0701 + 4.13136i) q^{89} -13.9473 q^{91} -0.831492 q^{93} +(-4.88072 - 1.43311i) q^{95} +(-8.72775 + 5.60899i) q^{97} +(-3.27571 + 22.7831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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			0
$2$		0			0
$3$	2.60088	+	0.763688i	1.50162	+	0.440916i	0.926229	−	0.376962i	$-0.123031\pi$
$3$	2.60088	+	0.763688i	1.50162	+	0.440916i	0.575392	+	0.817878i	$0.304849\pi$
$4$		0			0
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$		0			0
$7$	0.742558	−	5.16460i	0.280661	−	1.95204i	−0.0243947	−	0.999702i	$-0.507766\pi$
$7$	0.742558	−	5.16460i	0.280661	−	1.95204i	0.305055	−	0.952335i	$-0.401325\pi$
$8$		0			0
$9$	3.65762	+	2.35061i	1.21921	+	0.783536i
$10$		0			0
$11$	2.19921	+	4.81559i	0.663086	+	1.45196i	0.879619	+	0.475680i	$0.157798\pi$
$11$	2.19921	+	4.81559i	0.663086	+	1.45196i	−0.216533	+	0.976275i	$0.569475\pi$
$12$		0			0
$13$	−0.380417	−	2.64586i	−0.105509	−	0.733830i	−0.972058	−	0.234739i	$-0.924576\pi$
$13$	−0.380417	−	2.64586i	−0.105509	−	0.733830i	0.866550	−	0.499091i	$-0.166333\pi$
$14$		0			0
$15$	−2.60088	+	0.763688i	−0.671545	+	0.197184i
$16$		0			0
$17$	2.62212	−	3.02609i	0.635958	−	0.733934i	−0.342697	−	0.939446i	$-0.611340\pi$
$17$	2.62212	−	3.02609i	0.635958	−	0.733934i	0.978655	+	0.205512i	$0.0658859\pi$
$18$		0			0
$19$	3.33112	+	3.84432i	0.764212	+	0.881948i	0.995865	−	0.0908509i	$-0.0289587\pi$
$19$	3.33112	+	3.84432i	0.764212	+	0.881948i	−0.231652	+	0.972799i	$0.574413\pi$
$20$		0			0
$21$	5.87546	−	12.8655i	1.28213	−	2.80747i
$22$		0			0
$23$	−4.55543	+	1.49936i	−0.949872	+	0.312638i
$23$	−4.55543	+	1.49936i	−0.949872	+	0.312638i
$24$		0			0
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$		0			0
$27$	2.39254	+	2.76114i	0.460445	+	0.531381i
$28$		0			0
$29$	−5.18549	+	5.98437i	−0.962921	+	1.11127i	0.0308156	+	0.999525i	$0.490190\pi$
$29$	−5.18549	+	5.98437i	−0.962921	+	1.11127i	−0.993737	+	0.111745i	$0.964356\pi$
$30$		0			0
$31$	−0.294321	+	0.0864204i	−0.0528616	+	0.0155216i	−0.308056	−	0.951368i	$-0.599679\pi$
$31$	−0.294321	+	0.0864204i	−0.0528616	+	0.0155216i	0.255195	+	0.966890i	$0.417860\pi$
$32$		0			0
$33$	2.04227	+	14.2043i	0.355514	+	2.47265i
$34$		0			0
$35$	2.16752	+	4.74620i	0.366377	+	0.802254i
$36$		0			0
$37$	−0.239677	−	0.154031i	−0.0394027	−	0.0253226i	0.520791	−	0.853684i	$-0.325637\pi$
$37$	−0.239677	−	0.154031i	−0.0394027	−	0.0253226i	−0.560194	+	0.828362i	$0.689273\pi$
$38$		0			0
$39$	1.03119	−	7.17210i	0.165123	−	1.14846i
$40$		0			0
$41$	−2.42746	+	1.56003i	−0.379105	+	0.243636i	−0.716291	−	0.697802i	$-0.754162\pi$
$41$	−2.42746	+	1.56003i	−0.379105	+	0.243636i	0.337185	+	0.941438i	$0.390525\pi$
$42$		0			0
$43$	−1.15730	−	0.339815i	−0.176487	−	0.0518213i	0.192295	−	0.981337i	$-0.438407\pi$
$43$	−1.15730	−	0.339815i	−0.176487	−	0.0518213i	−0.368782	+	0.929516i	$0.620225\pi$
$44$		0			0
$45$	−4.34782			−0.648134
$46$		0			0
$47$	−8.10495			−1.18223			−0.591114	−	0.806588i	$-0.701312\pi$
$47$	−8.10495			−1.18223			−0.591114	+	0.806588i	$0.701312\pi$
$48$		0			0
$49$	−19.4053	−	5.69791i	−2.77219	−	0.813987i
$50$		0			0
$51$	9.13082	−	5.86802i	1.27857	−	0.821687i
$52$		0			0
$53$	−0.852155	+	5.92687i	−0.117053	+	0.814118i	0.843721	+	0.536783i	$0.180360\pi$
$53$	−0.852155	+	5.92687i	−0.117053	+	0.814118i	−0.960773	+	0.277336i	$0.910549\pi$
$54$		0			0
$55$	−4.45359	−	2.86215i	−0.600523	−	0.385932i
$56$		0			0
$57$	5.72800	+	12.5426i	0.758692	+	1.66130i
$58$		0			0
$59$	−1.14099	−	7.93574i	−0.148544	−	1.03315i	−0.918605	−	0.395176i	$-0.870684\pi$
$59$	−1.14099	−	7.93574i	−0.148544	−	1.03315i	0.770062	−	0.637970i	$-0.220225\pi$
$60$		0			0
$61$	8.37646	−	2.45955i	1.07250	−	0.314913i	0.302623	−	0.953110i	$-0.402138\pi$
$61$	8.37646	−	2.45955i	1.07250	−	0.314913i	0.769873	+	0.638197i	$0.220319\pi$
$62$		0			0
$63$	14.8560	−	17.1447i	1.87167	−	2.16003i
$64$		0			0
$65$	1.75049	+	2.02017i	0.217121	+	0.250571i
$66$		0			0
$67$	1.58522	−	3.47115i	0.193665	−	0.424068i	−0.787742	−	0.616006i	$-0.788750\pi$
$67$	1.58522	−	3.47115i	0.193665	−	0.424068i	0.981407	+	0.191938i	$0.0614771\pi$
$68$		0			0
$69$	−12.9932	+	0.420736i	−1.56420	+	0.0506507i
$70$		0			0
$71$	0.519116	−	1.13670i	0.0616077	−	0.134902i	−0.876324	−	0.481722i	$-0.840011\pi$
$71$	0.519116	−	1.13670i	0.0616077	−	0.134902i	0.937932	+	0.346820i	$0.112739\pi$
$72$		0			0
$73$	−2.65089	−	3.05929i	−0.310263	−	0.358063i	0.579106	−	0.815252i	$-0.303402\pi$
$73$	−2.65089	−	3.05929i	−0.310263	−	0.358063i	−0.889369	+	0.457189i	$0.848856\pi$
$74$		0			0
$75$	1.77512	−	2.04860i	0.204973	−	0.236552i
$76$		0			0
$77$	26.5037	−	7.78218i	3.02037	−	0.886861i
$78$		0			0
$79$	0.818854	+	5.69526i	0.0921283	+	0.640766i	0.982601	+	0.185730i	$0.0594648\pi$
$79$	0.818854	+	5.69526i	0.0921283	+	0.640766i	−0.890473	+	0.455037i	$0.849626\pi$
$80$		0			0
$81$	−1.30438	−	2.85618i	−0.144931	−	0.317354i
$82$		0			0
$83$	−1.06047	−	0.681525i	−0.116402	−	0.0748071i	0.481144	−	0.876641i	$-0.340221\pi$
$83$	−1.06047	−	0.681525i	−0.116402	−	0.0748071i	−0.597546	+	0.801834i	$0.703858\pi$
$84$		0			0
$85$	−0.569841	+	3.96333i	−0.0618080	+	0.429884i
$86$		0			0
$87$	−18.0571	+	11.6046i	−1.93592	+	1.24414i
$88$		0			0
$89$	14.0701	+	4.13136i	1.49143	+	0.437923i	0.922997	−	0.384806i	$-0.125732\pi$
$89$	14.0701	+	4.13136i	1.49143	+	0.437923i	0.568433	+	0.822730i	$0.307550\pi$
$90$		0			0
$91$	−13.9473			−1.46208
$92$		0			0
$93$	−0.831492			−0.0862218
$94$		0			0
$95$	−4.88072	−	1.43311i	−0.500751	−	0.147034i
$96$		0			0
$97$	−8.72775	+	5.60899i	−0.886169	+	0.569506i	−0.902658	−	0.430358i	$-0.858387\pi$
$97$	−8.72775	+	5.60899i	−0.886169	+	0.569506i	0.0164893	+	0.999864i	$0.494751\pi$
$98$		0			0
$99$	−3.27571	+	22.7831i	−0.329221	+	2.28978i
$100$		0			0
$101$	5.61092	+	3.60592i	0.558307	+	0.358802i	0.789161	−	0.614186i	$-0.210516\pi$
$101$	5.61092	+	3.60592i	0.558307	+	0.358802i	−0.230854	+	0.972988i	$0.574152\pi$
$102$		0			0
$103$	−8.13120	−	17.8049i	−0.801191	−	1.75436i	−0.641390	−	0.767215i	$-0.721642\pi$
$103$	−8.13120	−	17.8049i	−0.801191	−	1.75436i	−0.159801	−	0.987149i	$-0.551085\pi$
$104$		0			0
$105$	2.01284	+	13.9996i	0.196433	+	1.36622i
$106$		0			0
$107$	−0.146224	+	0.0429352i	−0.0141360	+	0.00415071i	−0.288793	−	0.957392i	$-0.593254\pi$
$107$	−0.146224	+	0.0429352i	−0.0141360	+	0.00415071i	0.274657	+	0.961542i	$0.411436\pi$
$108$		0			0
$109$	−11.5488	+	13.3281i	−1.10618	+	1.27660i	−0.148450	+	0.988920i	$0.547429\pi$
$109$	−11.5488	+	13.3281i	−1.10618	+	1.27660i	−0.957727	+	0.287677i	$0.907117\pi$
$110$		0			0
$111$	−0.505741	−	0.583656i	−0.0480028	−	0.0553982i
$112$		0			0
$113$	3.19026	−	6.98569i	0.300114	−	0.657159i	−0.698156	−	0.715945i	$-0.745996\pi$
$113$	3.19026	−	6.98569i	0.300114	−	0.657159i	0.998271	+	0.0587867i	$0.0187232\pi$
$114$		0			0
$115$	3.02165	−	3.72419i	0.281771	−	0.347283i
$116$		0			0
$117$	4.82796	−	10.5718i	0.446345	−	0.977360i
$118$		0			0
$119$	−13.6815	−	15.7893i	−1.25418	−	1.44740i
$120$		0			0
$121$	−11.1499	+	12.8677i	−1.01363	+	1.16979i
$122$		0			0
$123$	−7.50492	+	2.20364i	−0.676696	+	0.198696i
$124$		0			0
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$		0			0
$127$	1.09741	+	2.40298i	0.0973791	+	0.213230i	0.952052	−	0.305937i	$-0.0989695\pi$
$127$	1.09741	+	2.40298i	0.0973791	+	0.213230i	−0.854673	+	0.519167i	$0.826242\pi$
$128$		0			0
$129$	−2.75050	−	1.76764i	−0.242168	−	0.155632i
$130$		0			0
$131$	1.47933	−	10.2890i	0.129250	−	0.898953i	−0.817258	−	0.576272i	$-0.804507\pi$
$131$	1.47933	−	10.2890i	0.129250	−	0.898953i	0.946508	−	0.322681i	$-0.104584\pi$
$132$		0			0
$133$	22.3279	−	14.3493i	1.93608	−	1.24424i
$134$		0			0
$135$	−3.50552	−	1.02931i	−0.301707	−	0.0885891i
$136$		0			0
$137$	−2.11836			−0.180984			−0.0904921	−	0.995897i	$-0.528844\pi$
$137$	−2.11836			−0.180984			−0.0904921	+	0.995897i	$0.528844\pi$
$138$		0			0
$139$	−13.1375			−1.11431			−0.557156	−	0.830408i	$-0.688107\pi$
$139$	−13.1375			−1.11431			−0.557156	+	0.830408i	$0.688107\pi$
$140$		0			0
$141$	−21.0800	−	6.18966i	−1.77526	−	0.521263i
$142$		0			0
$143$	11.9048	−	7.65073i	0.995527	−	0.639786i
$144$		0			0
$145$	1.12691	−	7.83786i	0.0935852	−	0.650899i
$146$		0			0
$147$	−46.1195	−	29.6392i	−3.80387	−	2.44460i
$148$		0			0
$149$	−0.273929	−	0.599821i	−0.0224412	−	0.0491393i	0.898080	−	0.439833i	$-0.144962\pi$
$149$	−0.273929	−	0.599821i	−0.0224412	−	0.0491393i	−0.920521	+	0.390694i	$0.872235\pi$
$150$		0			0
$151$	1.83971	+	12.7954i	0.149713	+	1.04128i	0.916689	+	0.399602i	$0.130852\pi$
$151$	1.83971	+	12.7954i	0.149713	+	1.04128i	−0.766976	+	0.641676i	$0.778239\pi$
$152$		0			0
$153$	16.7039	−	4.90470i	1.35043	−	0.396521i
$154$		0			0
$155$	0.200876	−	0.231823i	0.0161347	−	0.0186205i
$156$		0			0
$157$	15.8801	+	18.3266i	1.26737	+	1.46262i	0.824317	+	0.566129i	$0.191560\pi$
$157$	15.8801	+	18.3266i	1.26737	+	1.46262i	0.443054	+	0.896495i	$0.353895\pi$
$158$		0			0
$159$	−6.74264	+	14.7643i	−0.534726	+	1.17089i
$160$		0			0
$161$	4.36094	+	24.6403i	0.343690	+	1.94193i
$162$		0			0
$163$	−5.70251	+	12.4868i	−0.446655	+	0.978039i	0.543673	+	0.839297i	$0.317033\pi$
$163$	−5.70251	+	12.4868i	−0.446655	+	0.978039i	−0.990329	+	0.138742i	$0.955694\pi$
$164$		0			0
$165$	−9.39749	−	10.8453i	−0.731594	−	0.844304i
$166$		0			0
$167$	1.06070	−	1.22411i	0.0820792	−	0.0947245i	−0.713224	−	0.700936i	$-0.752766\pi$
$167$	1.06070	−	1.22411i	0.0820792	−	0.0947245i	0.795304	+	0.606211i	$0.207311\pi$
$168$		0			0
$169$	5.61754	−	1.64946i	0.432119	−	0.126882i
$170$		0			0
$171$	3.14748	+	21.8912i	0.240694	+	1.67406i
$172$		0			0
$173$	5.30415	+	11.6145i	0.403267	+	0.883032i	0.996929	+	0.0783169i	$0.0249546\pi$
$173$	5.30415	+	11.6145i	0.403267	+	0.883032i	−0.593661	+	0.804715i	$0.702318\pi$
$174$		0			0
$175$	−4.38942	−	2.82091i	−0.331809	−	0.213241i
$176$		0			0
$177$	3.09286	−	21.5113i	0.232473	−	1.61689i
$178$		0			0
$179$	−5.58601	+	3.58991i	−0.417518	+	0.268323i	−0.732489	−	0.680779i	$-0.761642\pi$
$179$	−5.58601	+	3.58991i	−0.417518	+	0.268323i	0.314971	+	0.949101i	$0.398005\pi$
$180$		0			0
$181$	−15.5205	−	4.55724i	−1.15363	−	0.338737i	−0.351677	−	0.936121i	$-0.614388\pi$
$181$	−15.5205	−	4.55724i	−1.15363	−	0.338737i	−0.801955	+	0.597385i	$0.796207\pi$
$182$		0			0
$183$	23.6645			1.74933
$184$		0			0
$185$	0.284905			0.0209466
$186$		0			0
$187$	20.3390	+	5.97207i	1.48733	+	0.436721i
$188$		0			0
$189$	16.0368	−	10.3062i	1.16650	−	0.749667i
$190$		0			0
$191$	0.943658	−	6.56329i	0.0682807	−	0.474903i	−0.926778	−	0.375611i	$-0.877433\pi$
$191$	0.943658	−	6.56329i	0.0682807	−	0.474903i	0.995058	−	0.0992923i	$-0.0316579\pi$
$192$		0			0
$193$	−9.20190	−	5.91370i	−0.662367	−	0.425677i	0.165800	−	0.986159i	$-0.446980\pi$
$193$	−9.20190	−	5.91370i	−0.662367	−	0.425677i	−0.828167	+	0.560482i	$0.810616\pi$
$194$		0			0
$195$	3.01004	+	6.59106i	0.215553	+	0.471995i
$196$		0			0
$197$	1.93039	+	13.4262i	0.137535	+	0.956574i	0.935363	+	0.353690i	$0.115073\pi$
$197$	1.93039	+	13.4262i	0.137535	+	0.956574i	−0.797828	+	0.602885i	$0.794018\pi$
$198$		0			0
$199$	24.6531	−	7.23880i	1.74761	−	0.513145i	0.757427	−	0.652920i	$-0.226456\pi$
$199$	24.6531	−	7.23880i	1.74761	−	0.513145i	0.990183	+	0.139775i	$0.0446381\pi$
$200$		0			0
$201$	6.77385	−	7.81743i	0.477790	−	0.551399i
$202$		0			0
$203$	27.0564	+	31.2247i	1.89899	+	2.19155i
$204$		0			0
$205$	1.19869	−	2.62477i	0.0837202	−	0.183322i
$206$		0			0
$207$	−20.1864	−	5.22394i	−1.40305	−	0.363089i
$208$		0			0
$209$	−11.1868	+	24.4958i	−0.773810	+	1.69441i
$210$		0			0
$211$	0.549900	+	0.634619i	0.0378567	+	0.0436890i	0.774362	−	0.632743i	$-0.218071\pi$
$211$	0.549900	+	0.634619i	0.0378567	+	0.0436890i	−0.736505	+	0.676432i	$0.763525\pi$
$212$		0			0
$213$	2.21825	−	2.55999i	0.151992	−	0.175408i
$214$		0			0
$215$	1.15730	−	0.339815i	0.0789274	−	0.0231752i
$216$		0			0
$217$	0.227777	+	1.58422i	0.0154625	+	0.107544i
$218$		0			0
$219$	−4.55832	−	9.98132i	−0.308022	−	0.674475i
$220$		0			0
$221$	−9.00411	−	5.78659i	−0.605682	−	0.389248i
$222$		0			0
$223$	1.68262	−	11.7029i	0.112676	−	0.783681i	−0.852621	−	0.522529i	$-0.824989\pi$
$223$	1.68262	−	11.7029i	0.112676	−	0.783681i	0.965298	−	0.261152i	$-0.0841024\pi$
$224$		0			0
$225$	3.65762	−	2.35061i	0.243841	−	0.156707i
$226$		0			0
$227$	−16.0310	−	4.70712i	−1.06401	−	0.312423i	−0.297547	−	0.954707i	$-0.596169\pi$
$227$	−16.0310	−	4.70712i	−1.06401	−	0.312423i	−0.766466	+	0.642285i	$0.777987\pi$
$228$		0			0
$229$	24.6196			1.62691			0.813453	−	0.581630i	$-0.197585\pi$
$229$	24.6196			1.62691			0.813453	+	0.581630i	$0.197585\pi$
$230$		0			0
$231$	74.8761			4.92649
$232$		0			0
$233$	5.61038	+	1.64736i	0.367548	+	0.107922i	0.460291	−	0.887768i	$-0.347745\pi$
$233$	5.61038	+	1.64736i	0.367548	+	0.107922i	−0.0927426	+	0.995690i	$0.529563\pi$
$234$		0			0
$235$	6.81832	−	4.38187i	0.444778	−	0.285842i
$236$		0			0
$237$	−2.21966	+	15.4381i	−0.144182	+	1.00281i
$238$		0			0
$239$	9.99722	+	6.42482i	0.646666	+	0.415587i	0.822447	−	0.568842i	$-0.192608\pi$
$239$	9.99722	+	6.42482i	0.646666	+	0.415587i	−0.175780	+	0.984429i	$0.556245\pi$
$240$		0			0
$241$	−3.44618	−	7.54608i	−0.221988	−	0.486086i	0.765568	−	0.643355i	$-0.222458\pi$
$241$	−3.44618	−	7.54608i	−0.221988	−	0.486086i	−0.987556	+	0.157269i	$0.949731\pi$
$242$		0			0
$243$	−2.77114	−	19.2737i	−0.177769	−	1.23641i
$244$		0			0
$245$	19.4053	−	5.69791i	1.23976	−	0.364026i
$246$		0			0
$247$	8.90432	−	10.2761i	0.566569	−	0.653855i
$248$		0			0
$249$	−2.23770	−	2.58244i	−0.141808	−	0.163655i
$250$		0			0
$251$	10.8004	−	23.6495i	0.681713	−	1.49274i	−0.179104	−	0.983830i	$-0.557320\pi$
$251$	10.8004	−	23.6495i	0.681713	−	1.49274i	0.860817	−	0.508914i	$-0.169953\pi$
$252$		0			0
$253$	−17.2386	−	18.6397i	−1.08378	−	1.17187i
$254$		0			0
$255$	−4.50884	+	9.87299i	−0.282355	+	0.618271i
$256$		0			0
$257$	10.2828	+	11.8670i	0.641424	+	0.740242i	0.979626	−	0.200831i	$-0.0643642\pi$
$257$	10.2828	+	11.8670i	0.641424	+	0.740242i	−0.338202	+	0.941073i	$0.609819\pi$
$258$		0			0
$259$	−0.973484	+	1.12346i	−0.0604894	+	0.0698085i
$260$		0			0
$261$	−33.0335	+	9.69950i	−2.04472	+	0.600384i
$262$		0			0
$263$	−1.61283	−	11.2175i	−0.0994514	−	0.691700i	−0.977160	−	0.212505i	$-0.931838\pi$
$263$	−1.61283	−	11.2175i	−0.0994514	−	0.691700i	0.877709	−	0.479195i	$-0.159071\pi$
$264$		0			0
$265$	−2.48743	−	5.44671i	−0.152802	−	0.334589i
$266$		0			0
$267$	33.4397	+	21.4904i	2.04648	+	1.31519i
$268$		0			0
$269$	0.453970	−	3.15743i	0.0276790	−	0.192512i	−0.971291	−	0.237896i	$-0.923542\pi$
$269$	0.453970	−	3.15743i	0.0276790	−	0.192512i	0.998970	+	0.0453844i	$0.0144513\pi$
$270$		0			0
$271$	4.00592	−	2.57445i	0.243343	−	0.156387i	−0.413285	−	0.910602i	$-0.635619\pi$
$271$	4.00592	−	2.57445i	0.243343	−	0.156387i	0.656628	+	0.754215i	$0.271982\pi$
$272$		0			0
$273$	−36.2753	−	10.6514i	−2.19548	−	0.644652i
$274$		0			0
$275$	5.29400			0.319240
$276$		0			0
$277$	14.5771			0.875855			0.437928	−	0.899010i	$-0.355713\pi$
$277$	14.5771			0.875855			0.437928	+	0.899010i	$0.355713\pi$
$278$		0			0
$279$	−1.27965	−	0.375740i	−0.0766108	−	0.0224950i
$280$		0			0
$281$	12.4539	−	8.00364i	0.742938	−	0.477457i	−0.113610	−	0.993525i	$-0.536241\pi$
$281$	12.4539	−	8.00364i	0.742938	−	0.477457i	0.856547	+	0.516068i	$0.172605\pi$
$282$		0			0
$283$	0.0943187	−	0.656001i	0.00560666	−	0.0389952i	−0.986826	−	0.161785i	$-0.948275\pi$
$283$	0.0943187	−	0.656001i	0.00560666	−	0.0389952i	0.992433	+	0.122790i	$0.0391840\pi$
$284$		0			0
$285$	−11.5997	−	7.45469i	−0.687109	−	0.441578i
$286$		0			0
$287$	6.25443	+	13.6953i	0.369187	+	0.808407i
$288$		0			0
$289$	0.137657	+	0.957425i	0.00809746	+	0.0563191i
$290$		0			0
$291$	−26.9834	+	7.92304i	−1.58179	+	0.464457i
$292$		0			0
$293$	−6.04386	+	6.97499i	−0.353086	+	0.407483i	−0.904312	−	0.426873i	$-0.859615\pi$
$293$	−6.04386	+	6.97499i	−0.353086	+	0.407483i	0.551225	+	0.834357i	$0.314161\pi$
$294$		0			0
$295$	5.25025	+	6.05911i	0.305681	+	0.352775i
$296$		0			0
$297$	−8.03482	+	17.5938i	−0.466228	+	1.02090i
$298$		0			0
$299$	5.70006	+	11.4826i	0.329643	+	0.664059i
$300$		0			0
$301$	−2.61437	+	5.72468i	−0.150690	+	0.329965i
$302$		0			0
$303$	11.8396	+	13.6636i	0.680165	+	0.784952i
$304$		0			0
$305$	−5.71699	+	6.59776i	−0.327354	+	0.377787i
$306$		0			0
$307$	1.56987	−	0.460955i	0.0895971	−	0.0263081i	−0.236627	−	0.971601i	$-0.576042\pi$
$307$	1.56987	−	0.460955i	0.0895971	−	0.0263081i	0.326224	+	0.945293i	$0.394224\pi$
$308$		0			0
$309$	−7.55096	−	52.5181i	−0.429559	−	2.98765i
$310$		0			0
$311$	−0.351129	−	0.768866i	−0.0199107	−	0.0435984i	0.899415	−	0.437095i	$-0.143993\pi$
$311$	−0.351129	−	0.768866i	−0.0199107	−	0.0435984i	−0.919326	+	0.393497i	$0.871265\pi$
$312$		0			0
$313$	3.44878	+	2.21640i	0.194937	+	0.125278i	0.634468	−	0.772949i	$-0.281219\pi$
$313$	3.44878	+	2.21640i	0.194937	+	0.125278i	−0.439531	+	0.898227i	$0.644856\pi$
$314$		0			0
$315$	−3.22851	+	22.4548i	−0.181906	+	1.26518i
$316$		0			0
$317$	11.6721	−	7.50118i	0.655569	−	0.421308i	−0.170129	−	0.985422i	$-0.554418\pi$
$317$	11.6721	−	7.50118i	0.655569	−	0.421308i	0.825697	+	0.564114i	$0.190782\pi$
$318$		0			0
$319$	−40.2223	−	11.8103i	−2.25201	−	0.661251i
$320$		0			0
$321$	−0.413101			−0.0230570
$322$		0			0
$323$	20.3679			1.13330
$324$		0			0
$325$	−2.56479	−	0.753091i	−0.142269	−	0.0417740i
$326$		0			0
$327$	−40.2157	+	25.8450i	−2.22393	+	1.42923i
$328$		0			0
$329$	−6.01840	+	41.8589i	−0.331805	+	2.30775i
$330$		0			0
$331$	−21.3542	−	13.7235i	−1.17373	−	0.754313i	−0.199510	−	0.979896i	$-0.563935\pi$
$331$	−21.3542	−	13.7235i	−1.17373	−	0.754313i	−0.974224	+	0.225582i	$0.927572\pi$
$332$		0			0
$333$	−0.514581	−	1.12677i	−0.0281988	−	0.0617469i
$334$		0			0
$335$	0.543072	+	3.77715i	0.0296712	+	0.206368i
$336$		0			0
$337$	19.5575	−	5.74260i	1.06536	−	0.312819i	0.298355	−	0.954455i	$-0.403562\pi$
$337$	19.5575	−	5.74260i	1.06536	−	0.312819i	0.767010	+	0.641636i	$0.221744\pi$
$338$		0			0
$339$	13.6324	−	15.7326i	0.740410	−	0.854478i
$340$		0			0
$341$	−1.06344	−	1.22727i	−0.0575884	−	0.0664605i
$342$		0			0
$343$	−28.6644	+	62.7663i	−1.54773	+	3.38906i
$344$		0			0
$345$	10.7031	−	7.37859i	0.576235	−	0.397250i
$346$		0			0
$347$	12.4432	−	27.2467i	0.667984	−	1.46268i	−0.206907	−	0.978361i	$-0.566340\pi$
$347$	12.4432	−	27.2467i	0.667984	−	1.46268i	0.874891	−	0.484320i	$-0.160933\pi$
$348$		0			0
$349$	−7.59244	−	8.76214i	−0.406414	−	0.469026i	0.515237	−	0.857048i	$-0.327704\pi$
$349$	−7.59244	−	8.76214i	−0.406414	−	0.469026i	−0.921650	+	0.388022i	$0.873159\pi$
$350$		0			0
$351$	6.39543	−	7.38072i	0.341363	−	0.393954i
$352$		0			0
$353$	−32.6427	+	9.58476i	−1.73740	+	0.510145i	−0.988327	−	0.152348i	$-0.951317\pi$
$353$	−32.6427	+	9.58476i	−1.73740	+	0.510145i	−0.749068	+	0.662493i	$0.769498\pi$
$354$		0			0
$355$	0.177841	+	1.23691i	0.00943883	+	0.0656485i
$356$		0			0
$357$	−23.5259	−	51.5144i	−1.24512	−	2.72643i
$358$		0			0
$359$	−6.00381	−	3.85842i	−0.316869	−	0.203639i	0.372532	−	0.928019i	$-0.378490\pi$
$359$	−6.00381	−	3.85842i	−0.316869	−	0.203639i	−0.689401	+	0.724380i	$0.742126\pi$
$360$		0			0
$361$	−0.978441	+	6.80520i	−0.0514969	+	0.358169i
$362$		0			0
$363$	−38.8266	+	24.9523i	−2.03787	+	1.30966i
$364$		0			0
$365$	3.88405	+	1.14046i	0.203300	+	0.0596944i
$366$		0			0
$367$	15.7600			0.822663			0.411332	−	0.911486i	$-0.365064\pi$
$367$	15.7600			0.822663			0.411332	+	0.911486i	$0.365064\pi$
$368$		0			0
$369$	−12.5457			−0.653105
$370$		0			0
$371$	29.9772	+	8.80209i	1.55634	+	0.456982i
$372$		0			0
$373$	17.8966	−	11.5014i	0.926649	−	0.595521i	0.0120697	−	0.999927i	$-0.496158\pi$
$373$	17.8966	−	11.5014i	0.926649	−	0.595521i	0.914580	+	0.404406i	$0.132522\pi$
$374$		0			0
$375$	−0.385771	+	2.68309i	−0.0199211	+	0.138554i
$376$		0			0
$377$	17.8065	+	11.4435i	0.917080	+	0.589372i
$378$		0			0
$379$	6.75225	+	14.7854i	0.346840	+	0.759473i	0.999997	+	0.00225109i	$0.000716545\pi$
$379$	6.75225	+	14.7854i	0.346840	+	0.759473i	−0.653158	+	0.757222i	$0.726556\pi$
$380$		0			0
$381$	1.01909	+	7.08796i	0.0522098	+	0.363127i
$382$		0			0
$383$	−35.2253	+	10.3431i	−1.79993	+	0.528507i	−0.997655	−	0.0684501i	$-0.978195\pi$
$383$	−35.2253	+	10.3431i	−1.79993	+	0.528507i	−0.802274	+	0.596957i	$0.796376\pi$
$384$		0			0
$385$	−18.0889	+	20.8757i	−0.921897	+	1.06393i
$386$		0			0
$387$	−3.43420	−	3.96328i	−0.174570	−	0.201465i
$388$		0			0
$389$	11.0849	−	24.2726i	0.562028	−	1.23067i	−0.388906	−	0.921277i	$-0.627147\pi$
$389$	11.0849	−	24.2726i	0.562028	−	1.23067i	0.950934	−	0.309393i	$-0.100126\pi$
$390$		0			0
$391$	−7.40768	+	17.7166i	−0.374623	+	0.895969i
$392$		0			0
$393$	11.7052	−	25.6307i	0.590447	−	1.29290i
$394$		0			0
$395$	−3.76795	−	4.34845i	−0.189586	−	0.218794i
$396$		0			0
$397$	−7.29053	+	8.41372i	−0.365901	+	0.422273i	−0.908608	−	0.417650i	$-0.862854\pi$
$397$	−7.29053	+	8.41372i	−0.365901	+	0.422273i	0.542707	+	0.839922i	$0.317399\pi$
$398$		0			0
$399$	69.0308	−	20.2693i	3.45586	−	1.01473i
$400$		0			0
$401$	0.747521	+	5.19912i	0.0373294	+	0.259632i	0.999936	−	0.0112697i	$-0.00358734\pi$
$401$	0.747521	+	5.19912i	0.0373294	+	0.259632i	−0.962607	+	0.270901i	$0.912678\pi$
$402$		0			0
$403$	0.340621	+	0.745856i	0.0169675	+	0.0371537i
$404$		0			0
$405$	2.64148	+	1.69758i	0.131256	+	0.0843532i
$406$		0			0
$407$	0.214651	−	1.49293i	0.0106399	−	0.0740020i
$408$		0			0
$409$	22.9619	−	14.7567i	1.13539	−	0.729673i	0.168714	−	0.985665i	$-0.446038\pi$
$409$	22.9619	−	14.7567i	1.13539	−	0.729673i	0.966679	+	0.255992i	$0.0824021\pi$
$410$		0			0
$411$	−5.50962	−	1.61777i	−0.271770	−	0.0797987i
$412$		0			0
$413$	−41.8322			−2.05843
$414$		0			0
$415$	1.26059			0.0618798
$416$		0			0
$417$	−34.1692	−	10.0330i	−1.67327	−	0.491318i
$418$		0			0
$419$	−11.9234	+	7.66268i	−0.582495	+	0.374347i	−0.798454	−	0.602056i	$-0.794348\pi$
$419$	−11.9234	+	7.66268i	−0.582495	+	0.374347i	0.215959	+	0.976402i	$0.430712\pi$
$420$		0			0
$421$	1.65048	−	11.4794i	0.0804396	−	0.559469i	−0.909251	−	0.416248i	$-0.863345\pi$
$421$	1.65048	−	11.4794i	0.0804396	−	0.559469i	0.989691	−	0.143221i	$-0.0457461\pi$
$422$		0			0
$423$	−29.6448	−	19.0516i	−1.44138	−	0.926319i
$424$		0			0
$425$	−1.66336	−	3.64225i	−0.0806848	−	0.176675i
$426$		0			0
$427$	−6.48260	−	45.0875i	−0.313715	−	2.18194i
$428$		0			0
$429$	36.8057	−	10.8071i	1.77700	−	0.521773i
$430$		0			0
$431$	−3.58634	+	4.13885i	−0.172748	+	0.199362i	−0.835521	−	0.549459i	$-0.814834\pi$
$431$	−3.58634	+	4.13885i	−0.172748	+	0.199362i	0.662773	+	0.748820i	$0.269379\pi$
$432$		0			0
$433$	14.7580	+	17.0316i	0.709224	+	0.818489i	0.989968	−	0.141294i	$-0.0451264\pi$
$433$	14.7580	+	17.0316i	0.709224	+	0.818489i	−0.280743	+	0.959783i	$0.590581\pi$
$434$		0			0
$435$	8.91666	−	19.5248i	0.427521	−	0.936141i
$436$		0			0
$437$	−20.9387	−	12.5180i	−1.00163	−	0.598816i
$438$		0			0
$439$	7.86032	−	17.2117i	0.375152	−	0.821469i	−0.624044	−	0.781389i	$-0.714511\pi$
$439$	7.86032	−	17.2117i	0.375152	−	0.821469i	0.999196	−	0.0400801i	$-0.0127613\pi$
$440$		0			0
$441$	−57.5836	−	66.4550i	−2.74208	−	3.16452i
$442$		0			0
$443$	−0.0337812	+	0.0389856i	−0.00160500	+	0.00185226i	−0.756552	−	0.653934i	$-0.773117\pi$
$443$	−0.0337812	+	0.0389856i	−0.00160500	+	0.00185226i	0.754947	+	0.655786i	$0.227663\pi$
$444$		0			0
$445$	−14.0701	+	4.13136i	−0.666988	+	0.195845i
$446$		0			0
$447$	−0.254382	−	1.76926i	−0.0120318	−	0.0836832i
$448$		0			0
$449$	5.12079	+	11.2130i	0.241665	+	0.529173i	0.991134	−	0.132867i	$-0.0424183\pi$
$449$	5.12079	+	11.2130i	0.241665	+	0.529173i	−0.749469	+	0.662040i	$0.769691\pi$
$450$		0			0
$451$	−12.8510	−	8.25881i	−0.605128	−	0.388892i
$452$		0			0
$453$	−4.98687	+	34.6844i	−0.234303	+	1.62962i
$454$		0			0
$455$	11.7332	−	7.54049i	0.550062	−	0.353503i
$456$		0			0
$457$	32.6443	+	9.58523i	1.52704	+	0.448378i	0.934142	−	0.356902i	$-0.116167\pi$
$457$	32.6443	+	9.58523i	1.52704	+	0.448378i	0.592894	+	0.805281i	$0.297985\pi$
$458$		0			0
$459$	14.6290			0.682822
$460$		0			0
$461$	23.3737			1.08862			0.544311	−	0.838884i	$-0.316791\pi$
$461$	23.3737			1.08862			0.544311	+	0.838884i	$0.316791\pi$
$462$		0			0
$463$	−7.85595	−	2.30672i	−0.365097	−	0.107202i	0.0940381	−	0.995569i	$-0.470022\pi$
$463$	−7.85595	−	2.30672i	−0.365097	−	0.107202i	−0.459135	+	0.888366i	$0.651841\pi$
$464$		0			0
$465$	0.699496	−	0.449539i	0.0324383	−	0.0208469i
$466$		0			0
$467$	−4.71812	+	32.8152i	−0.218328	+	1.51851i	0.525879	+	0.850559i	$0.323736\pi$
$467$	−4.71812	+	32.8152i	−0.218328	+	1.51851i	−0.744208	+	0.667948i	$0.767173\pi$
$468$		0			0
$469$	−16.7500	−	10.7646i	−0.773442	−	0.497061i
$470$		0			0
$471$	27.3065	+	59.7929i	1.25822	+	2.75511i
$472$		0			0
$473$	−0.908739	−	6.32042i	−0.0417839	−	0.290613i
$474$		0			0
$475$	4.88072	−	1.43311i	0.223943	−	0.0657555i
$476$		0			0
$477$	−17.0486	+	19.6751i	−0.780602	+	0.900863i
$478$		0			0
$479$	14.4003	+	16.6188i	0.657964	+	0.759332i	0.982443	−	0.186561i	$-0.0597343\pi$
$479$	14.4003	+	16.6188i	0.657964	+	0.759332i	−0.324479	+	0.945893i	$0.605189\pi$
$480$		0			0
$481$	−0.316368	+	0.692749i	−0.0144251	+	0.0315866i
$482$		0			0
$483$	−7.47526	+	67.4171i	−0.340136	+	3.06758i
$484$		0			0
$485$	4.30981	−	9.43716i	0.195698	−	0.428519i
$486$		0			0
$487$	2.33483	+	2.69454i	0.105801	+	0.122101i	0.806180	−	0.591670i	$-0.201531\pi$
$487$	2.33483	+	2.69454i	0.105801	+	0.122101i	−0.700379	+	0.713771i	$0.746986\pi$
$488$		0			0
$489$	−24.3676	+	28.1217i	−1.10194	+	1.27171i
$490$		0			0
$491$	31.7575	−	9.32484i	1.43320	−	0.420824i	0.529248	−	0.848467i	$-0.322474\pi$
$491$	31.7575	−	9.32484i	1.43320	−	0.420824i	0.903948	+	0.427643i	$0.140656\pi$
$492$		0			0
$493$	4.51227	+	31.3835i	0.203222	+	1.41344i
$494$		0			0
$495$	−9.56175	−	20.9373i	−0.429769	−	0.941062i
$496$		0			0
$497$	−5.48516	−	3.52510i	−0.246043	−	0.158122i
$498$		0			0
$499$	−4.29971	+	29.9052i	−0.192482	+	1.33874i	0.632931	+	0.774208i	$0.281852\pi$
$499$	−4.29971	+	29.9052i	−0.192482	+	1.33874i	−0.825412	+	0.564530i	$0.809057\pi$
$500$		0			0
$501$	3.69359	−	2.37373i	0.165017	−	0.106050i
$502$		0			0
$503$	2.89791	+	0.850904i	0.129212	+	0.0379399i	0.345699	−	0.938345i	$-0.387642\pi$
$503$	2.89791	+	0.850904i	0.129212	+	0.0379399i	−0.216487	+	0.976285i	$0.569460\pi$
$504$		0			0
$505$	−6.66971			−0.296798
$506$		0			0
$507$	15.8703			0.704823
$508$		0			0
$509$	−10.8684	−	3.19124i	−0.481733	−	0.141449i	0.0318446	−	0.999493i	$-0.489862\pi$
$509$	−10.8684	−	3.19124i	−0.481733	−	0.141449i	−0.513577	+	0.858043i	$0.671680\pi$
$510$		0			0
$511$	−17.7685	+	11.4191i	−0.786031	+	0.505151i
$512$		0			0
$513$	−2.64486	+	18.3954i	−0.116773	+	0.812176i
$514$		0			0
$515$	16.4664	+	10.5823i	0.725598	+	0.466313i
$516$		0			0
$517$	−17.8245	−	39.0301i	−0.783919	−	1.71654i
$518$		0			0
$519$	4.92564	+	34.2586i	0.216212	+	1.50379i
$520$		0			0
$521$	−12.0554	+	3.53977i	−0.528155	+	0.155080i	−0.534929	−	0.844897i	$-0.679662\pi$
$521$	−12.0554	+	3.53977i	−0.528155	+	0.155080i	0.00677465	+	0.999977i	$0.497844\pi$
$522$		0			0
$523$	23.7773	−	27.4405i	1.03971	−	1.19989i	0.0602643	−	0.998182i	$-0.480806\pi$
$523$	23.7773	−	27.4405i	1.03971	−	1.19989i	0.979446	−	0.201707i	$-0.0646489\pi$
$524$		0			0
$525$	−9.26208	−	10.6890i	−0.404230	−	0.466506i
$526$		0			0
$527$	−0.510229	+	1.11725i	−0.0222259	+	0.0486680i
$528$		0			0
$529$	18.5038	−	13.6605i	0.804515	−	0.593933i
$530$		0			0
$531$	14.4805	−	31.7079i	0.628401	−	1.37601i
$532$		0			0
$533$	5.05108	+	5.82926i	0.218787	+	0.252493i
$534$		0			0
$535$	0.0997989	−	0.115174i	0.00431468	−	0.00497941i
$536$		0			0
$537$	−17.2701	+	5.07097i	−0.745262	+	0.218829i
$538$		0			0
$539$	−15.2375	−	105.979i	−0.656324	−	4.56483i
$540$		0			0
$541$	−6.02965	−	13.2031i	−0.259235	−	0.567645i	0.734602	−	0.678498i	$-0.237369\pi$
$541$	−6.02965	−	13.2031i	−0.259235	−	0.567645i	−0.993837	+	0.110853i	$0.964642\pi$
$542$		0			0
$543$	−36.8868	−	23.7057i	−1.58296	−	1.01731i
$544$		0			0
$545$	2.50980	−	17.4561i	0.107508	−	0.747735i
$546$		0			0
$547$	17.4532	−	11.2165i	0.746244	−	0.479582i	−0.111432	−	0.993772i	$-0.535544\pi$
$547$	17.4532	−	11.2165i	0.746244	−	0.479582i	0.857676	+	0.514190i	$0.171907\pi$
$548$		0			0
$549$	36.4193	+	10.6937i	1.55434	+	0.456395i
$550$		0			0
$551$	−40.2794			−1.71596
$552$		0			0
$553$	30.0218			1.27666
$554$		0			0
$555$	0.741005	+	0.217579i	0.0314539	+	0.00923570i
$556$		0			0
$557$	−26.9110	+	17.2946i	−1.14025	+	0.732797i	−0.967675	−	0.252199i	$-0.918846\pi$
$557$	−26.9110	+	17.2946i	−1.14025	+	0.732797i	−0.172579	+	0.984996i	$0.555210\pi$
$558$		0			0
$559$	−0.458844	+	3.19133i	−0.0194071	+	0.134979i
$560$		0			0
$561$	48.3386	+	31.0653i	2.04086	+	1.31158i
$562$		0			0
$563$	−4.93762	−	10.8119i	−0.208096	−	0.455667i	0.776589	−	0.630007i	$-0.216948\pi$
$563$	−4.93762	−	10.8119i	−0.208096	−	0.455667i	−0.984685	+	0.174340i	$0.944221\pi$
$564$		0			0
$565$	1.09293	+	7.60152i	0.0459801	+	0.319798i
$566$		0			0
$567$	−15.7196	+	4.61570i	−0.660163	+	0.193841i
$568$		0			0
$569$	5.09576	−	5.88083i	0.213626	−	0.246537i	−0.638816	−	0.769360i	$-0.720575\pi$
$569$	5.09576	−	5.88083i	0.213626	−	0.246537i	0.852442	+	0.522823i	$0.175121\pi$
$570$		0			0
$571$	−20.6551	−	23.8373i	−0.864389	−	0.997558i	−0.999977	−	0.00679302i	$-0.997838\pi$
$571$	−20.6551	−	23.8373i	−0.864389	−	0.997558i	0.135588	−	0.990765i	$-0.456708\pi$
$572$		0			0
$573$	7.46665	−	16.3497i	0.311924	−	0.683018i
$574$		0			0
$575$	−0.528526	+	4.76662i	−0.0220411	+	0.198782i
$576$		0			0
$577$	−2.49592	+	5.46530i	−0.103906	+	0.227523i	−0.954443	−	0.298392i	$-0.903550\pi$
$577$	−2.49592	+	5.46530i	−0.103906	+	0.227523i	0.850537	+	0.525915i	$0.176277\pi$
$578$		0			0
$579$	−19.4168	−	22.4082i	−0.806936	−	0.931254i
$580$		0			0
$581$	−4.30727	+	4.97085i	−0.178696	+	0.206226i
$582$		0			0
$583$	−30.4154	+	8.93078i	−1.25968	+	0.369875i
$584$		0			0
$585$	1.65399	+	11.5037i	0.0683839	+	0.475620i
$586$		0			0
$587$	−3.69712	−	8.09557i	−0.152597	−	0.334140i	0.817859	−	0.575418i	$-0.195161\pi$
$587$	−3.69712	−	8.09557i	−0.152597	−	0.334140i	−0.970456	+	0.241278i	$0.922433\pi$
$588$		0			0
$589$	−1.31265	−	0.843587i	−0.0540867	−	0.0347594i
$590$		0			0
$591$	−5.23268	+	36.3941i	−0.215244	+	1.49705i
$592$		0			0
$593$	4.99587	−	3.21065i	0.205156	−	0.131846i	−0.434029	−	0.900899i	$-0.642908\pi$
$593$	4.99587	−	3.21065i	0.205156	−	0.131846i	0.639185	+	0.769053i	$0.279272\pi$
$594$		0			0
$595$	20.0459	+	5.88601i	0.821802	+	0.241303i
$596$		0			0
$597$	69.6480			2.85050
$598$		0			0
$599$	−41.9786			−1.71520			−0.857599	−	0.514319i	$-0.828045\pi$
$599$	−41.9786			−1.71520			−0.857599	+	0.514319i	$0.828045\pi$
$600$		0			0
$601$	−1.55032	−	0.455216i	−0.0632390	−	0.0185686i	0.249960	−	0.968256i	$-0.419583\pi$
$601$	−1.55032	−	0.455216i	−0.0632390	−	0.0185686i	−0.313199	+	0.949688i	$0.601401\pi$
$602$		0			0
$603$	13.9574	−	8.96989i	0.568390	−	0.365282i
$604$		0			0
$605$	2.42311	−	16.8531i	0.0985135	−	0.685177i
$606$		0			0
$607$	8.32238	+	5.34847i	0.337795	+	0.217088i	0.698530	−	0.715581i	$-0.253838\pi$
$607$	8.32238	+	5.34847i	0.337795	+	0.217088i	−0.360735	+	0.932668i	$0.617474\pi$
$608$		0			0
$609$	46.5246	+	101.875i	1.88527	+	4.12817i
$610$		0			0
$611$	3.08327	+	21.4446i	0.124736	+	0.867555i
$612$		0			0
$613$	−39.6345	+	11.6377i	−1.60082	+	0.470044i	−0.955775	−	0.294100i	$-0.904980\pi$
$613$	−39.6345	+	11.6377i	−1.60082	+	0.470044i	−0.645047	+	0.764143i	$0.723162\pi$
$614$		0			0
$615$	5.12216	−	5.91129i	0.206545	−	0.238366i
$616$		0			0
$617$	−23.9101	−	27.5937i	−0.962585	−	1.11088i	−0.993779	−	0.111369i	$-0.964477\pi$
$617$	−23.9101	−	27.5937i	−0.962585	−	1.11088i	0.0311945	−	0.999513i	$-0.490069\pi$
$618$		0			0
$619$	−0.477573	+	1.04574i	−0.0191953	+	0.0420318i	−0.918987	−	0.394288i	$-0.870991\pi$
$619$	−0.477573	+	1.04574i	−0.0191953	+	0.0420318i	0.899792	+	0.436320i	$0.143718\pi$
$620$		0			0
$621$	−15.0390	−	8.99089i	−0.603494	−	0.360792i
$622$		0			0
$623$	31.7847	−	69.5988i	1.27343	−	2.78842i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$		0			0
$627$	−47.8028	+	55.1674i	−1.90906	+	2.20317i
$628$		0			0
$629$	−1.09457	+	0.321396i	−0.0436436	+	0.0128149i
$630$		0			0
$631$	−0.160642	−	1.11729i	−0.00639505	−	0.0444785i	0.986374	−	0.164518i	$-0.0526069\pi$
$631$	−0.160642	−	1.11729i	−0.00639505	−	0.0444785i	−0.992769	+	0.120040i	$0.961698\pi$
$632$		0			0
$633$	0.945576	+	2.07052i	0.0375833	+	0.0822959i
$634$		0			0
$635$	−2.22235	−	1.42822i	−0.0881912	−	0.0566771i
$636$		0			0
$637$	−7.69377	+	53.5113i	−0.304838	+	2.12020i
$638$		0			0
$639$	4.57067	−	2.93739i	0.180813	−	0.116201i
$640$		0			0
$641$	3.22965	+	0.948311i	0.127563	+	0.0374560i	0.344891	−	0.938643i	$-0.387916\pi$
$641$	3.22965	+	0.948311i	0.127563	+	0.0374560i	−0.217328	+	0.976099i	$0.569734\pi$
$642$		0			0
$643$	−12.1135			−0.477709			−0.238855	−	0.971055i	$-0.576772\pi$
$643$	−12.1135			−0.477709			−0.238855	+	0.971055i	$0.576772\pi$
$644$		0			0
$645$	3.26952			0.128737
$646$		0			0
$647$	−23.1183	−	6.78815i	−0.908875	−	0.266870i	−0.206308	−	0.978487i	$-0.566145\pi$
$647$	−23.1183	−	6.78815i	−0.908875	−	0.266870i	−0.702567	+	0.711617i	$0.747963\pi$
$648$		0			0
$649$	35.7060	−	22.9469i	1.40158	−	0.900743i
$650$		0			0
$651$	−0.617431	+	4.29433i	−0.0241990	+	0.168308i
$652$		0			0
$653$	−25.2494	−	16.2268i	−0.988084	−	0.635003i	−0.0564516	−	0.998405i	$-0.517979\pi$
$653$	−25.2494	−	16.2268i	−0.988084	−	0.635003i	−0.931632	+	0.363402i	$0.881615\pi$
$654$		0			0
$655$	4.31815	+	9.45543i	0.168724	+	0.369454i
$656$		0			0
$657$	−2.50475	−	17.4209i	−0.0977196	−	0.679655i
$658$		0			0
$659$	−18.4969	+	5.43118i	−0.720538	+	0.211569i	−0.621387	−	0.783504i	$-0.713431\pi$
$659$	−18.4969	+	5.43118i	−0.720538	+	0.211569i	−0.0991502	+	0.995072i	$0.531612\pi$
$660$		0			0
$661$	19.8533	−	22.9119i	0.772203	−	0.891169i	−0.224318	−	0.974516i	$-0.572015\pi$
$661$	19.8533	−	22.9119i	0.772203	−	0.891169i	0.996521	+	0.0833467i	$0.0265609\pi$
$662$		0			0
$663$	−18.9995	−	21.9266i	−0.737879	−	0.851558i
$664$		0			0
$665$	−11.0256	+	24.1428i	−0.427556	+	0.936218i
$666$		0			0
$667$	14.6494	−	35.0363i	0.567226	−	1.35661i
$668$		0			0
$669$	13.3136	−	29.1528i	0.514735	−	1.12711i
$670$		0			0
$671$	30.2658	+	34.9286i	1.16840	+	1.34840i
$672$		0			0
$673$	−18.4258	+	21.2645i	−0.710263	+	0.819687i	−0.990100	−	0.140361i	$-0.955174\pi$
$673$	−18.4258	+	21.2645i	−0.710263	+	0.819687i	0.279838	+	0.960047i	$0.409719\pi$
$674$		0			0
$675$	3.50552	−	1.02931i	0.134927	−	0.0396183i
$676$		0			0
$677$	5.88043	+	40.8993i	0.226003	+	1.57189i	0.714698	+	0.699433i	$0.246564\pi$
$677$	5.88043	+	40.8993i	0.226003	+	1.57189i	−0.488695	+	0.872455i	$0.662527\pi$
$678$		0			0
$679$	22.4873	+	49.2404i	0.862985	+	1.88967i
$680$		0			0
$681$	−38.0999	−	24.4853i	−1.45999	−	0.938281i
$682$		0			0
$683$	4.60669	−	32.0402i	0.176270	−	1.22599i	−0.689031	−	0.724732i	$-0.741964\pi$
$683$	4.60669	−	32.0402i	0.176270	−	1.22599i	0.865301	−	0.501253i	$-0.167127\pi$
$684$		0			0
$685$	1.78208	−	1.14527i	0.0680898	−	0.0437587i
$686$		0			0
$687$	64.0326	+	18.8017i	2.44300	+	0.717329i
$688$		0			0
$689$	16.0059			0.609775
$690$		0			0
$691$	−32.5204			−1.23713			−0.618567	−	0.785732i	$-0.712286\pi$
$691$	−32.5204			−1.23713			−0.618567	+	0.785732i	$0.712286\pi$
$692$		0			0
$693$	115.233	+	33.8355i	4.37734	+	1.28530i
$694$		0			0
$695$	11.0520	−	7.10269i	0.419227	−	0.269421i
$696$		0			0
$697$	−1.64429	+	11.4363i	−0.0622820	+	0.433181i
$698$		0			0
$699$	13.3339	+	8.56916i	0.504334	+	0.324115i
$700$		0			0
$701$	−2.03278	−	4.45116i	−0.0767769	−	0.168118i	0.867351	−	0.497696i	$-0.165821\pi$
$701$	−2.03278	−	4.45116i	−0.0767769	−	0.168118i	−0.944128	+	0.329578i	$0.893093\pi$
$702$		0			0
$703$	−0.206249	−	1.43449i	−0.00777883	−	0.0541029i
$704$		0			0
$705$	21.0800	−	6.18966i	0.793920	−	0.233116i
$706$		0			0
$707$	22.7896	−	26.3006i	0.857090	−	0.989135i
$708$		0			0
$709$	−9.63250	−	11.1165i	−0.361756	−	0.417489i	0.545471	−	0.838130i	$-0.316351\pi$
$709$	−9.63250	−	11.1165i	−0.361756	−	0.417489i	−0.907227	+	0.420641i	$0.861805\pi$
$710$		0			0
$711$	−10.3923	+	22.7559i	−0.389740	+	0.853412i
$712$		0			0
$713$	1.21118	−	0.834975i	0.0453591	−	0.0312701i
$714$		0			0
$715$	−5.87863	+	12.8724i	−0.219848	+	0.481401i
$716$		0			0
$717$	21.0950	+	24.3450i	0.787809	+	0.909180i
$718$		0			0
$719$	9.86913	−	11.3896i	0.368057	−	0.424760i	−0.541266	−	0.840851i	$-0.682055\pi$
$719$	9.86913	−	11.3896i	0.368057	−	0.424760i	0.909323	+	0.416091i	$0.136600\pi$
$720$		0			0
$721$	−97.9929	+	28.7733i	−3.64945	+	1.07157i
$722$		0			0
$723$	−3.20026	−	22.2583i	−0.119019	−	0.827795i
$724$		0			0
$725$	3.28945	+	7.20289i	0.122167	+	0.267508i
$726$		0			0
$727$	12.3747	+	7.95275i	0.458953	+	0.294951i	0.749614	−	0.661875i	$-0.230239\pi$
$727$	12.3747	+	7.95275i	0.458953	+	0.294951i	−0.290661	+	0.956826i	$0.593875\pi$
$728$		0			0
$729$	6.17112	−	42.9211i	0.228560	−	1.58967i
$730$		0			0
$731$	−4.06290	+	2.61106i	−0.150272	+	0.0965737i
$732$		0			0
$733$	22.0807	+	6.48348i	0.815569	+	0.239473i	0.662807	−	0.748790i	$-0.269365\pi$
$733$	22.0807	+	6.48348i	0.815569	+	0.239473i	0.152762	+	0.988263i	$0.451183\pi$
$734$		0			0
$735$	54.8224			2.02215
$736$		0			0
$737$	20.2018			0.744144
$738$		0			0
$739$	21.3702	+	6.27485i	0.786115	+	0.230824i	0.650066	−	0.759878i	$-0.274741\pi$
$739$	21.3702	+	6.27485i	0.786115	+	0.230824i	0.136049	+	0.990702i	$0.456559\pi$
$740$		0			0
$741$	31.0069	−	19.9269i	1.13907	−	0.732033i
$742$		0			0
$743$	1.36998	−	9.52839i	0.0502595	−	0.349563i	−0.949138	−	0.314860i	$-0.898042\pi$
$743$	1.36998	−	9.52839i	0.0502595	−	0.349563i	0.999398	−	0.0347027i	$-0.0110484\pi$
$744$		0			0
$745$	0.554732	+	0.356504i	0.0203238	+	0.0130613i
$746$		0			0
$747$	−2.27681	−	4.98551i	−0.0833040	−	0.182410i
$748$		0			0
$749$	0.113164	+	0.787071i	0.00413491	+	0.0287589i
$750$		0			0
$751$	42.5508	−	12.4940i	1.55270	−	0.455914i	0.610794	−	0.791789i	$-0.290850\pi$
$751$	42.5508	−	12.4940i	1.55270	−	0.455914i	0.941906	+	0.335875i	$0.109032\pi$
$752$		0			0
$753$	46.1514	−	53.2615i	1.68185	−	1.94096i
$754$		0			0
$755$	−8.46539	−	9.76959i	−0.308087	−	0.355552i
$756$		0			0
$757$	16.9063	−	37.0197i	0.614471	−	1.34550i	−0.305003	−	0.952352i	$-0.598657\pi$
$757$	16.9063	−	37.0197i	0.614471	−	1.34550i	0.919473	−	0.393152i	$-0.128615\pi$
$758$		0			0
$759$	−30.6008	−	61.6446i	−1.11074	−	2.23756i
$760$		0			0
$761$	5.46852	−	11.9744i	0.198234	−	0.434071i	−0.784244	−	0.620453i	$-0.786949\pi$
$761$	5.46852	−	11.9744i	0.198234	−	0.434071i	0.982477	+	0.186382i	$0.0596761\pi$
$762$		0			0
$763$	60.2585	+	69.5420i	2.18150	+	2.51759i
$764$		0			0
$765$	−11.4005	+	13.1569i	−0.412186	+	0.475688i
$766$		0			0
$767$	−20.5628	+	6.03779i	−0.742481	+	0.218012i
$768$		0			0
$769$	−2.32998	−	16.2054i	−0.0840214	−	0.584381i	−0.987723	−	0.156218i	$-0.950070\pi$
$769$	−2.32998	−	16.2054i	−0.0840214	−	0.584381i	0.903701	−	0.428164i	$-0.140839\pi$
$770$		0			0
$771$	17.6817	+	38.7175i	0.636791	+	1.39438i
$772$		0			0
$773$	11.4564	+	7.36261i	0.412060	+	0.264815i	0.730206	−	0.683227i	$-0.239424\pi$
$773$	11.4564	+	7.36261i	0.412060	+	0.264815i	−0.318146	+	0.948042i	$0.603060\pi$
$774$		0			0
$775$	−0.0436545	+	0.303624i	−0.00156812	+	0.0109065i
$776$		0			0
$777$	−3.38989	+	2.17855i	−0.121612	+	0.0781551i
$778$		0			0
$779$	−14.0834	−	4.13527i	−0.504591	−	0.148161i
$780$		0			0
$781$	6.61555			0.236723
$782$		0			0
$783$	−28.9302			−1.03388
$784$		0			0
$785$	−23.2673	−	6.83190i	−0.830446	−	0.243841i
$786$		0			0
$787$	−3.84227	+	2.46928i	−0.136962	+	0.0880203i	−0.607328	−	0.794451i	$-0.707758\pi$
$787$	−3.84227	+	2.46928i	−0.136962	+	0.0880203i	0.470365	+	0.882472i	$0.344122\pi$
$788$		0			0
$789$	4.37188	−	30.4071i	0.155643	−	1.08252i
$790$		0			0
$791$	−33.7094	−	21.6637i	−1.19857	−	0.770273i
$792$		0			0
$793$	−9.69418	−	21.2273i	−0.344251	−	0.753804i
$794$		0			0
$795$	−2.30993	−	16.0659i	−0.0819246	−	0.569798i
$796$		0			0
$797$	11.5982	−	3.40555i	0.410831	−	0.120631i	−0.0697850	−	0.997562i	$-0.522231\pi$
$797$	11.5982	−	3.40555i	0.410831	−	0.120631i	0.480616	+	0.876931i	$0.340413\pi$
$798$		0			0
$799$	−21.2522	+	24.5263i	−0.751848	+	0.867678i
$800$		0			0
$801$	41.7519	+	48.1843i	1.47523	+	1.70251i
$802$		0			0
$803$	8.90244	−	19.4936i	0.314160	−	0.687915i
$804$		0			0
$805$	−16.9902	−	18.3711i	−0.598827	−	0.647495i
$806$		0			0
$807$	3.59201	−	7.86542i	0.126445	−	0.276876i
$808$		0			0
$809$	−14.0975	−	16.2694i	−0.495642	−	0.572002i	0.451722	−	0.892159i	$-0.350810\pi$
$809$	−14.0975	−	16.2694i	−0.495642	−	0.572002i	−0.947365	+	0.320157i	$0.896264\pi$
$810$		0			0
$811$	−13.1467	+	15.1721i	−0.461644	+	0.532765i	−0.938068	−	0.346450i	$-0.887387\pi$
$811$	−13.1467	+	15.1721i	−0.461644	+	0.532765i	0.476425	+	0.879215i	$0.341932\pi$
$812$		0			0
$813$	12.3850	−	3.63657i	0.434362	−	0.127540i
$814$		0			0
$815$	−1.95359	−	13.5875i	−0.0684314	−	0.475951i
$816$		0			0
$817$	−2.54876	−	5.58101i	−0.0891698	−	0.195255i
$818$		0			0
$819$	−51.0139	−	32.7847i	−1.78257	−	1.14559i
$820$		0			0
$821$	−6.54386	+	45.5136i	−0.228382	+	1.58843i	0.476542	+	0.879152i	$0.341890\pi$
$821$	−6.54386	+	45.5136i	−0.228382	+	1.58843i	−0.704924	+	0.709282i	$0.749019\pi$
$822$		0			0
$823$	18.2701	−	11.7415i	0.636857	−	0.409283i	−0.181986	−	0.983301i	$-0.558252\pi$
$823$	18.2701	−	11.7415i	0.636857	−	0.409283i	0.818843	+	0.574018i	$0.194616\pi$
$824$		0			0
$825$	13.7691	+	4.04297i	0.479378	+	0.140758i
$826$		0			0
$827$	−41.7983			−1.45347			−0.726734	−	0.686919i	$-0.758963\pi$
$827$	−41.7983			−1.45347			−0.726734	+	0.686919i	$0.758963\pi$
$828$		0			0
$829$	1.49130			0.0517949			0.0258975	−	0.999665i	$-0.491756\pi$
$829$	1.49130			0.0517949			0.0258975	+	0.999665i	$0.491756\pi$
$830$		0			0
$831$	37.9134	+	11.1324i	1.31520	+	0.386178i
$832$		0			0
$833$	−68.1254	+	43.7815i	−2.36041	+	1.51694i
$834$		0			0
$835$	−0.230512	+	1.60324i	−0.00797718	+	0.0554825i
$836$		0			0
$837$	−0.942793	−	0.605896i	−0.0325877	−	0.0209428i
$838$		0			0
$839$	14.6514	+	32.0821i	0.505823	+	1.10760i	0.974533	+	0.224246i	$0.0719918\pi$
$839$	14.6514	+	32.0821i	0.505823	+	1.10760i	−0.468710	+	0.883352i	$0.655281\pi$
$840$		0			0
$841$	−4.79630	−	33.3590i	−0.165390	−	1.15031i
$842$		0			0
$843$	38.5035	−	11.3056i	1.32613	−	0.389387i
$844$		0			0
$845$	−3.83401	+	4.42469i	−0.131894	+	0.152214i
$846$		0			0
$847$	58.1772	+	67.1400i	1.99899	+	2.30696i
$848$		0			0
$849$	0.746292	−	1.63415i	0.0256127	−	0.0560840i
$850$		0			0
$851$	1.32278	+	0.342315i	0.0453443	+	0.0117344i
$852$		0			0
$853$	9.87295	−	21.6187i	0.338043	−	0.740211i	−0.661913	−	0.749581i	$-0.730255\pi$
$853$	9.87295	−	21.6187i	0.338043	−	0.740211i	0.999956	+	0.00936933i	$0.00298239\pi$
$854$		0			0
$855$	−14.4831	−	16.7144i	−0.495312	−	0.571621i
$856$		0			0
$857$	−13.4532	+	15.5258i	−0.459552	+	0.530352i	−0.937476	−	0.348050i	$-0.886844\pi$
$857$	−13.4532	+	15.5258i	−0.459552	+	0.530352i	0.477924	+	0.878401i	$0.341390\pi$
$858$		0			0
$859$	−38.6651	+	11.3531i	−1.31924	+	0.387363i	−0.864217	−	0.503119i	$-0.832186\pi$
$859$	−38.6651	+	11.3531i	−1.31924	+	0.387363i	−0.455019	+	0.890482i	$0.650367\pi$
$860$		0			0
$861$	5.80811	+	40.3963i	0.197940	+	1.37670i
$862$		0			0
$863$	4.21737	+	9.23476i	0.143561	+	0.314355i	0.967730	−	0.251989i	$-0.0810847\pi$
$863$	4.21737	+	9.23476i	0.143561	+	0.314355i	−0.824169	+	0.566344i	$0.808357\pi$
$864$		0			0
$865$	−10.7414	−	6.90307i	−0.365218	−	0.234712i
$866$		0			0
$867$	−0.373145	+	2.59528i	−0.0126727	+	0.0881402i
$868$		0			0
$869$	−25.6252	+	16.4683i	−0.869275	+	0.558649i
$870$		0			0
$871$	−9.78722	−	2.87379i	−0.331627	−	0.0973745i
$872$		0			0
$873$	−45.1073			−1.52665
$874$		0			0
$875$	5.21771			0.176391
$876$		0			0
$877$	−14.9075	−	4.37724i	−0.503391	−	0.147809i	0.0201707	−	0.999797i	$-0.493579\pi$
$877$	−14.9075	−	4.37724i	−0.503391	−	0.147809i	−0.523562	+	0.851987i	$0.675397\pi$
$878$		0			0
$879$	−21.0461	+	13.5255i	−0.709868	+	0.456204i
$880$		0			0
$881$	−3.89926	+	27.1200i	−0.131370	+	0.913695i	0.812402	+	0.583097i	$0.198159\pi$
$881$	−3.89926	+	27.1200i	−0.131370	+	0.913695i	−0.943772	+	0.330598i	$0.892750\pi$
$882$		0			0
$883$	16.0737	+	10.3300i	0.540924	+	0.347631i	0.782400	−	0.622776i	$-0.213995\pi$
$883$	16.0737	+	10.3300i	0.540924	+	0.347631i	−0.241476	+	0.970407i	$0.577631\pi$
$884$		0			0
$885$	9.02801	+	19.7686i	0.303473	+	0.664514i
$886$		0			0
$887$	−1.79736	−	12.5009i	−0.0603496	−	0.419741i	−0.997491	−	0.0707912i	$-0.977448\pi$
$887$	−1.79736	−	12.5009i	−0.0603496	−	0.419741i	0.937142	−	0.348949i	$-0.113461\pi$
$888$		0			0
$889$	13.2254	−	3.88331i	0.443564	−	0.130242i
$890$		0			0
$891$	10.8856	−	12.5627i	0.364682	−	0.420866i
$892$		0			0
$893$	−26.9986	−	31.1580i	−0.903474	−	1.04266i
$894$		0			0
$895$	2.75840	−	6.04005i	0.0922031	−	0.201897i
$896$		0			0
$897$	6.05604	+	34.2181i	0.202205	+	1.14251i
$898$		0			0
$899$	1.00903	−	2.20946i	0.0336529	−	0.0736895i
$900$		0			0
$901$	15.7008	+	18.1197i	0.523069	+	0.603654i
$902$		0			0
$903$	−11.1716	+	12.8927i	−0.371766	+	0.429041i
$904$		0			0
$905$	15.5205	−	4.55724i	0.515920	−	0.151488i
$906$		0			0
$907$	−1.53424	−	10.6709i	−0.0509435	−	0.354320i	−0.999310	−	0.0371433i	$-0.988174\pi$
$907$	−1.53424	−	10.6709i	−0.0509435	−	0.354320i	0.948366	−	0.317177i	$-0.102735\pi$
$908$		0			0
$909$	12.0465	+	26.3781i	0.399557	+	0.874908i
$910$		0			0
$911$	−28.4198	−	18.2643i	−0.941589	−	0.605122i	−0.0227440	−	0.999741i	$-0.507240\pi$
$911$	−28.4198	−	18.2643i	−0.941589	−	0.605122i	−0.918845	+	0.394619i	$0.870877\pi$
$912$		0			0
$913$	0.949745	−	6.60562i	0.0314320	−	0.218614i
$914$		0			0
$915$	−19.9079	+	12.7940i	−0.658134	+	0.422957i
$916$		0			0
$917$	−52.0401	−	15.2803i	−1.71851	−	0.504601i
$918$		0			0
$919$	−18.8711			−0.622500			−0.311250	−	0.950328i	$-0.600748\pi$
$919$	−18.8711			−0.622500			−0.311250	+	0.950328i	$0.600748\pi$
$920$		0			0
$921$	4.43507			0.146140
$922$		0			0
$923$	−3.20504	−	0.941086i	−0.105495	−	0.0309762i
$924$		0			0
$925$	−0.239677	+	0.154031i	−0.00788054	+	0.00506451i
$926$		0			0
$927$	12.1114	−	84.2366i	0.397790	−	2.76669i
$928$		0			0
$929$	21.0201	+	13.5088i	0.689646	+	0.443208i	0.837960	−	0.545732i	$-0.183748\pi$
$929$	21.0201	+	13.5088i	0.689646	+	0.443208i	−0.148314	+	0.988940i	$0.547385\pi$
$930$		0			0
$931$	−42.7368	−	93.5806i	−1.40064	−	3.06698i
$932$		0			0
$933$	−0.326073	−	2.26789i	−0.0106751	−	0.0742472i
$934$		0			0
$935$	−20.3390	+	5.97207i	−0.665156	+	0.195307i
$936$		0			0
$937$	19.9085	−	22.9757i	0.650384	−	0.750583i	−0.330791	−	0.943704i	$-0.607316\pi$
$937$	19.9085	−	22.9757i	0.650384	−	0.750583i	0.981175	+	0.193121i	$0.0618611\pi$
$938$		0			0
$939$	7.27725	+	8.39839i	0.237484	+	0.274071i
$940$		0			0
$941$	−3.87201	+	8.47852i	−0.126224	+	0.276392i	−0.962185	−	0.272397i	$-0.912184\pi$
$941$	−3.87201	+	8.47852i	−0.126224	+	0.276392i	0.835961	+	0.548789i	$0.184911\pi$
$942$		0			0
$943$	8.71906	−	10.7463i	0.283932	−	0.349946i
$944$		0			0
$945$	−7.91904	+	17.3403i	−0.257607	+	0.564080i
$946$		0			0
$947$	−11.0829	−	12.7904i	−0.360146	−	0.415631i	0.546542	−	0.837431i	$-0.315944\pi$
$947$	−11.0829	−	12.7904i	−0.360146	−	0.415631i	−0.906689	+	0.421800i	$0.861398\pi$
$948$		0			0
$949$	−7.08602	+	8.17770i	−0.230022	+	0.265459i
$950$		0			0
$951$	36.0863	−	10.5959i	1.17018	−	0.343595i
$952$		0			0
$953$	2.64529	+	18.3984i	0.0856893	+	0.595982i	0.986745	+	0.162279i	$0.0518844\pi$
$953$	2.64529	+	18.3984i	0.0856893	+	0.595982i	−0.901056	+	0.433704i	$0.857206\pi$
$954$		0			0
$955$	2.75453	+	6.03157i	0.0891343	+	0.195177i
$956$		0			0
$957$	−95.5940	−	61.4345i	−3.09012	−	1.98590i
$958$		0			0
$959$	−1.57301	+	10.9405i	−0.0507951	+	0.353288i
$960$		0			0
$961$	−25.9997	+	16.7090i	−0.838700	+	0.539000i
$962$		0			0
$963$	−0.635755	−	0.186675i	−0.0204869	−	0.00601550i
$964$		0			0
$965$	10.9383			0.352117
$966$		0			0
$967$	−13.8278			−0.444671			−0.222336	−	0.974970i	$-0.571368\pi$
$967$	−13.8278			−0.444671			−0.222336	+	0.974970i	$0.571368\pi$
$968$		0			0
$969$	52.9744	+	15.5547i	1.70178	+	0.499689i
$970$		0			0
$971$	−1.25221	+	0.804746i	−0.0401853	+	0.0258255i	−0.560579	−	0.828101i	$-0.689421\pi$
$971$	−1.25221	+	0.804746i	−0.0401853	+	0.0258255i	0.520394	+	0.853926i	$0.325785\pi$
$972$		0			0
$973$	−9.75539	+	67.8502i	−0.312743	+	2.17518i
$974$		0			0
$975$	−6.09560	−	3.91740i	−0.195215	−	0.125457i
$976$		0			0
$977$	−11.1549	−	24.4259i	−0.356878	−	0.781454i	−0.999878	−	0.0155880i	$-0.995038\pi$
$977$	−11.1549	−	24.4259i	−0.356878	−	0.781454i	0.643001	−	0.765866i	$-0.277689\pi$
$978$		0			0
$979$	11.0482	+	76.8417i	0.353101	+	2.45587i
$980$		0			0
$981$	−73.5703	+	21.6022i	−2.34892	+	0.689705i
$982$		0			0
$983$	−22.3443	+	25.7867i	−0.712672	+	0.822467i	−0.990406	−	0.138191i	$-0.955871\pi$
$983$	−22.3443	+	25.7867i	−0.712672	+	0.822467i	0.277734	+	0.960658i	$0.410417\pi$
$984$		0			0
$985$	−8.88268	−	10.2512i	−0.283026	−	0.326629i
$986$		0			0
$987$	−47.6203	+	104.274i	−1.51577	+	3.31907i
$988$		0			0
$989$	5.78151	−	0.187213i	0.183841	−	0.00595303i
$990$		0			0
$991$	22.0422	−	48.2656i	0.700192	−	1.53321i	−0.139546	−	0.990216i	$-0.544564\pi$
$991$	22.0422	−	48.2656i	0.700192	−	1.53321i	0.839738	−	0.542991i	$-0.182708\pi$
$992$		0			0
$993$	−45.0594	−	52.0013i	−1.42992	−	1.65021i
$994$		0			0
$995$	−16.8259	+	19.4181i	−0.533417	+	0.615596i
$996$		0			0
$997$	−25.5113	+	7.49080i	−0.807951	+	0.237236i	−0.659520	−	0.751687i	$-0.729240\pi$
$997$	−25.5113	+	7.49080i	−0.807951	+	0.237236i	−0.148431	+	0.988923i	$0.547422\pi$
$998$		0			0
$999$	−0.148136	−	1.03031i	−0.00468681	−	0.0325975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.121.5	✓	50
23.4	even	11	inner	460.2.m.b.441.5	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.121.5	✓	50	1.1	even	1	trivial
460.2.m.b.441.5	yes	50	23.4	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.60088 + 0.763688i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.742558 - 5.16460i) q^{7} +(3.65762 + 2.35061i) q^{9} +O(q^{10})\)	\(q+(2.60088 + 0.763688i) q^{3} +(-0.841254 + 0.540641i) q^{5} +(0.742558 - 5.16460i) q^{7} +(3.65762 + 2.35061i) q^{9} +(2.19921 + 4.81559i) q^{11} +(-0.380417 - 2.64586i) q^{13} +(-2.60088 + 0.763688i) q^{15} +(2.62212 - 3.02609i) q^{17} +(3.33112 + 3.84432i) q^{19} +(5.87546 - 12.8655i) q^{21} +(-4.55543 + 1.49936i) q^{23} +(0.415415 - 0.909632i) q^{25} +(2.39254 + 2.76114i) q^{27} +(-5.18549 + 5.98437i) q^{29} +(-0.294321 + 0.0864204i) q^{31} +(2.04227 + 14.2043i) q^{33} +(2.16752 + 4.74620i) q^{35} +(-0.239677 - 0.154031i) q^{37} +(1.03119 - 7.17210i) q^{39} +(-2.42746 + 1.56003i) q^{41} +(-1.15730 - 0.339815i) q^{43} -4.34782 q^{45} -8.10495 q^{47} +(-19.4053 - 5.69791i) q^{49} +(9.13082 - 5.86802i) q^{51} +(-0.852155 + 5.92687i) q^{53} +(-4.45359 - 2.86215i) q^{55} +(5.72800 + 12.5426i) q^{57} +(-1.14099 - 7.93574i) q^{59} +(8.37646 - 2.45955i) q^{61} +(14.8560 - 17.1447i) q^{63} +(1.75049 + 2.02017i) q^{65} +(1.58522 - 3.47115i) q^{67} +(-12.9932 + 0.420736i) q^{69} +(0.519116 - 1.13670i) q^{71} +(-2.65089 - 3.05929i) q^{73} +(1.77512 - 2.04860i) q^{75} +(26.5037 - 7.78218i) q^{77} +(0.818854 + 5.69526i) q^{79} +(-1.30438 - 2.85618i) q^{81} +(-1.06047 - 0.681525i) q^{83} +(-0.569841 + 3.96333i) q^{85} +(-18.0571 + 11.6046i) q^{87} +(14.0701 + 4.13136i) q^{89} -13.9473 q^{91} -0.831492 q^{93} +(-4.88072 - 1.43311i) q^{95} +(-8.72775 + 5.60899i) q^{97} +(-3.27571 + 22.7831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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