LMFDB - Embedded newform 825.2.n.l.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.819390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 10x^{6} - 13x^{5} + 29x^{4} - 7x^{3} + 80x^{2} + 143x + 121 $ x^8 - 3x^7 + 10x^6 - 13x^5 + 29x^4 - 7x^3 + 80x^2 + 143*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.2
Root			$2.06426 - 1.49977i$ of defining polynomial
Character	$\chi$	$=$	825.751
Dual form			825.2.n.l.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.06426 - 1.49977i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.39382 - 4.28973i) q^{4} +(2.06426 + 1.49977i) q^{6} +(1.44623 - 4.45102i) q^{7} +(-1.97946 - 6.09215i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.54508 - 2.12663i) q^{11} +4.51049 q^{12} +(-2.89382 + 2.10248i) q^{13} +(-3.69014 - 11.3571i) q^{14} +(-5.92484 - 4.30465i) q^{16} +(1.02054 + 0.741466i) q^{17} +(-0.788477 + 2.42668i) q^{18} +(2.18229 + 6.71641i) q^{19} +4.68008 q^{21} +(-8.44317 - 0.572862i) q^{22} +3.08744 q^{23} +(5.18229 - 3.76516i) q^{24} +(-2.82035 + 8.68013i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-17.0779 - 12.4078i) q^{28} +(1.91436 - 5.89178i) q^{29} +(0.0537743 - 0.0390693i) q^{31} -5.87507 q^{32} +(1.23607 - 3.07768i) q^{33} +3.21869 q^{34} +(1.39382 + 4.28973i) q^{36} +(-1.22422 + 3.76775i) q^{37} +(14.5779 + 10.5915i) q^{38} +(-2.89382 - 2.10248i) q^{39} +(1.62204 + 4.99212i) q^{41} +(9.66091 - 7.01906i) q^{42} +9.77194 q^{43} +(-12.6700 + 7.95359i) q^{44} +(6.37328 - 4.63046i) q^{46} +(1.67044 + 5.14110i) q^{47} +(2.26309 - 6.96507i) q^{48} +(-12.0569 - 8.75988i) q^{49} +(-0.389812 + 1.19972i) q^{51} +(4.98562 + 15.3442i) q^{52} +(10.6404 - 7.73068i) q^{53} -2.55157 q^{54} -29.9791 q^{56} +(-5.71332 + 4.15097i) q^{57} +(-4.88461 - 15.0333i) q^{58} +(-0.163963 + 0.504625i) q^{59} +(-4.96165 - 3.60485i) q^{61} +(0.0524091 - 0.161298i) q^{62} +(1.44623 + 4.45102i) q^{63} +(-0.277992 + 0.201973i) q^{64} +(-2.06426 - 8.20696i) q^{66} +3.10841 q^{67} +(4.60313 - 3.34437i) q^{68} +(0.954071 + 2.93633i) q^{69} +(-6.73650 - 4.89435i) q^{71} +(5.18229 + 3.76516i) q^{72} +(-5.15554 + 15.8671i) q^{73} +(3.12367 + 9.61367i) q^{74} +31.8533 q^{76} +(-13.1464 + 8.25265i) q^{77} -9.12683 q^{78} +(-6.10150 + 4.43300i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.8354 + 7.87235i) q^{82} +(3.90209 + 2.83504i) q^{83} +(6.52318 - 20.0763i) q^{84} +(20.1718 - 14.6557i) q^{86} +6.19499 q^{87} +(-7.91784 + 19.7146i) q^{88} -6.05763 q^{89} +(5.17308 + 15.9211i) q^{91} +(4.30332 - 13.2443i) q^{92} +(0.0537743 + 0.0390693i) q^{93} +(11.1587 + 8.10727i) q^{94} +(-1.81550 - 5.58753i) q^{96} +(-2.46029 + 1.78750i) q^{97} -38.0265 q^{98} +(3.30902 + 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + 3 q^{6} + 7 q^{7} - 16 q^{8} - 2 q^{9} + 2 q^{11} + 18 q^{12} - 5 q^{13} - 2 q^{14} - 11 q^{16} + 8 q^{17} - 2 q^{18} - 5 q^{19} - 8 q^{21} - 8 q^{22} - 2 q^{23} + 19 q^{24}+ \cdots + 22 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + 3 * q^6 + 7 * q^7 - 16 * q^8 - 2 * q^9 + 2 * q^11 + 18 * q^12 - 5 * q^13 - 2 * q^14 - 11 * q^16 + 8 * q^17 - 2 * q^18 - 5 * q^19 - 8 * q^21 - 8 * q^22 - 2 * q^23 + 19 * q^24 - 32 * q^26 - 2 * q^27 - 51 * q^28 - 3 * q^29 + 5 * q^31 + 16 * q^32 - 8 * q^33 - 46 * q^34 - 7 * q^36 - 19 * q^37 + 31 * q^38 - 5 * q^39 - 18 * q^41 + 23 * q^42 + 52 * q^43 - 38 * q^44 + 33 * q^46 + 18 * q^47 + 4 * q^48 - 47 * q^49 - 7 * q^51 - 29 * q^52 + 31 * q^53 - 2 * q^54 - 68 * q^56 - 5 * q^57 - 35 * q^58 - 2 * q^59 - 22 * q^61 + 14 * q^62 + 7 * q^63 - 16 * q^64 - 3 * q^66 - 38 * q^67 - 2 * q^69 + 19 * q^72 - 18 * q^73 - 12 * q^74 + 92 * q^76 + 13 * q^77 + 18 * q^78 - 18 * q^79 - 2 * q^81 + 15 * q^82 - 28 * q^83 + 39 * q^84 + 53 * q^86 + 32 * q^87 - 64 * q^88 + 34 * q^89 + 33 * q^91 - 12 * q^92 + 5 * q^93 + 12 * q^94 - 14 * q^96 - 11 * q^97 - 24 * q^98 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	2.06426	−	1.49977i	1.45965	−	1.06050i	0.476199	−	0.879338i	$-0.342014\pi$
$2$	2.06426	−	1.49977i	1.45965	−	1.06050i	0.983453	−	0.181162i	$-0.0579857\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.39382	−	4.28973i	0.696908	−	2.14486i
$5$		0			0
$5$		0			0
$6$	2.06426	+	1.49977i	0.842730	+	0.612280i
$7$	1.44623	−	4.45102i	0.546622	−	1.68233i	−0.170480	−	0.985361i	$-0.554532\pi$
$7$	1.44623	−	4.45102i	0.546622	−	1.68233i	0.717102	−	0.696968i	$-0.245468\pi$
$8$	−1.97946	−	6.09215i	−0.699845	−	2.15390i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$12$	4.51049			1.30206
$13$	−2.89382	+	2.10248i	−0.802600	+	0.583123i	−0.911676	−	0.410910i	$-0.865211\pi$
$13$	−2.89382	+	2.10248i	−0.802600	+	0.583123i	0.109075	+	0.994033i	$0.465211\pi$
$14$	−3.69014	−	11.3571i	−0.986231	−	3.03531i
$15$		0			0
$16$	−5.92484	−	4.30465i	−1.48121	−	1.07616i
$17$	1.02054	+	0.741466i	0.247517	+	0.179832i	0.704626	−	0.709579i	$-0.251115\pi$
$17$	1.02054	+	0.741466i	0.247517	+	0.179832i	−0.457108	+	0.889411i	$0.651115\pi$
$18$	−0.788477	+	2.42668i	−0.185846	+	0.571975i
$19$	2.18229	+	6.71641i	0.500653	+	1.54085i	0.807959	+	0.589239i	$0.200572\pi$
$19$	2.18229	+	6.71641i	0.500653	+	1.54085i	−0.307306	+	0.951611i	$0.599428\pi$
$20$		0			0
$21$	4.68008			1.02128
$22$	−8.44317	−	0.572862i	−1.80009	−	0.122135i
$23$	3.08744			0.643776			0.321888	−	0.946778i	$-0.395683\pi$
$23$	3.08744			0.643776			0.321888	+	0.946778i	$0.395683\pi$
$24$	5.18229	−	3.76516i	1.05783	−	0.768559i
$25$		0			0
$26$	−2.82035	+	8.68013i	−0.553115	+	1.70231i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−17.0779	−	12.4078i	−3.22742	−	2.34486i
$29$	1.91436	−	5.89178i	0.355487	−	1.09408i	−0.600239	−	0.799820i	$-0.704928\pi$
$29$	1.91436	−	5.89178i	0.355487	−	1.09408i	0.955727	−	0.294256i	$-0.0950720\pi$
$30$		0			0
$31$	0.0537743	−	0.0390693i	0.00965815	−	0.00701706i	−0.582946	−	0.812511i	$-0.698100\pi$
$31$	0.0537743	−	0.0390693i	0.00965815	−	0.00701706i	0.592604	+	0.805494i	$0.298100\pi$
$32$	−5.87507			−1.03858
$33$	1.23607	−	3.07768i	0.215172	−	0.535756i
$34$	3.21869			0.552001
$35$		0			0
$36$	1.39382	+	4.28973i	0.232303	+	0.714954i
$37$	−1.22422	+	3.76775i	−0.201260	+	0.619415i	0.798586	+	0.601880i	$0.205582\pi$
$37$	−1.22422	+	3.76775i	−0.201260	+	0.619415i	−0.999846	+	0.0175344i	$0.994418\pi$
$38$	14.5779	+	10.5915i	2.36485	+	1.71816i
$39$	−2.89382	−	2.10248i	−0.463382	−	0.336666i
$40$		0			0
$41$	1.62204	+	4.99212i	0.253320	+	0.779639i	0.994156	+	0.107953i	$0.0344295\pi$
$41$	1.62204	+	4.99212i	0.253320	+	0.779639i	−0.740836	+	0.671686i	$0.765570\pi$
$42$	9.66091	−	7.01906i	1.49071	−	1.08306i
$43$	9.77194			1.49021			0.745104	−	0.666949i	$-0.232400\pi$
$43$	9.77194			1.49021			0.745104	+	0.666949i	$0.232400\pi$
$44$	−12.6700	+	7.95359i	−1.91008	+	1.19905i
$45$		0			0
$46$	6.37328	−	4.63046i	0.939688	−	0.682724i
$47$	1.67044	+	5.14110i	0.243659	+	0.749906i	0.995854	+	0.0909651i	$0.0289952\pi$
$47$	1.67044	+	5.14110i	0.243659	+	0.749906i	−0.752195	+	0.658941i	$0.771005\pi$
$48$	2.26309	−	6.96507i	0.326649	−	1.00532i
$49$	−12.0569	−	8.75988i	−1.72242	−	1.25141i
$50$		0			0
$51$	−0.389812	+	1.19972i	−0.0545845	+	0.167994i
$52$	4.98562	+	15.3442i	0.691381	+	2.12785i
$53$	10.6404	−	7.73068i	1.46157	−	1.06189i	0.478616	−	0.878024i	$-0.341139\pi$
$53$	10.6404	−	7.73068i	1.46157	−	1.06189i	0.982951	−	0.183866i	$-0.0588614\pi$
$54$	−2.55157			−0.347224
$55$		0			0
$56$	−29.9791			−4.00612
$57$	−5.71332	+	4.15097i	−0.756748	+	0.549809i
$58$	−4.88461	−	15.0333i	−0.641380	−	1.97397i
$59$	−0.163963	+	0.504625i	−0.0213461	+	0.0656966i	−0.961162	−	0.275984i	$-0.910996\pi$
$59$	−0.163963	+	0.504625i	−0.0213461	+	0.0656966i	0.939816	+	0.341681i	$0.110996\pi$
$60$		0			0
$61$	−4.96165	−	3.60485i	−0.635274	−	0.461554i	0.222949	−	0.974830i	$-0.428432\pi$
$61$	−4.96165	−	3.60485i	−0.635274	−	0.461554i	−0.858223	+	0.513276i	$0.828432\pi$
$62$	0.0524091	−	0.161298i	0.00665596	−	0.0204849i
$63$	1.44623	+	4.45102i	0.182207	+	0.560776i
$64$	−0.277992	+	0.201973i	−0.0347490	+	0.0252466i
$65$		0			0
$66$	−2.06426	−	8.20696i	−0.254093	−	1.01021i
$67$	3.10841			0.379753			0.189876	−	0.981808i	$-0.439191\pi$
$67$	3.10841			0.379753			0.189876	+	0.981808i	$0.439191\pi$
$68$	4.60313	−	3.34437i	0.558212	−	0.405564i
$69$	0.954071	+	2.93633i	0.114857	+	0.353493i
$70$		0			0
$71$	−6.73650	−	4.89435i	−0.799475	−	0.580853i	0.111285	−	0.993789i	$-0.464503\pi$
$71$	−6.73650	−	4.89435i	−0.799475	−	0.580853i	−0.910760	+	0.412936i	$0.864503\pi$
$72$	5.18229	+	3.76516i	0.610739	+	0.443728i
$73$	−5.15554	+	15.8671i	−0.603410	+	1.85711i	−0.0960405	+	0.995377i	$0.530618\pi$
$73$	−5.15554	+	15.8671i	−0.603410	+	1.85711i	−0.507370	+	0.861728i	$0.669382\pi$
$74$	3.12367	+	9.61367i	0.363119	+	1.11757i
$75$		0			0
$76$	31.8533			3.65382
$77$	−13.1464	+	8.25265i	−1.49818	+	0.940477i
$78$	−9.12683			−1.03341
$79$	−6.10150	+	4.43300i	−0.686472	+	0.498751i	−0.875499	−	0.483221i	$-0.839467\pi$
$79$	−6.10150	+	4.43300i	−0.686472	+	0.498751i	0.189026	+	0.981972i	$0.439467\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	10.8354	+	7.87235i	1.19657	+	0.869355i
$83$	3.90209	+	2.83504i	0.428310	+	0.311186i	0.780973	−	0.624565i	$-0.214724\pi$
$83$	3.90209	+	2.83504i	0.428310	+	0.311186i	−0.352663	+	0.935751i	$0.614724\pi$
$84$	6.52318	−	20.0763i	0.711737	−	2.19050i
$85$		0			0
$86$	20.1718	−	14.6557i	2.17518	−	1.58036i
$87$	6.19499			0.664172
$88$	−7.91784	+	19.7146i	−0.844045	+	2.10159i
$89$	−6.05763			−0.642108			−0.321054	−	0.947061i	$-0.604037\pi$
$89$	−6.05763			−0.642108			−0.321054	+	0.947061i	$0.604037\pi$
$90$		0			0
$91$	5.17308	+	15.9211i	0.542286	+	1.66899i
$92$	4.30332	−	13.2443i	0.448653	−	1.38081i
$93$	0.0537743	+	0.0390693i	0.00557614	+	0.00405130i
$94$	11.1587	+	8.10727i	1.15093	+	0.836201i
$95$		0			0
$96$	−1.81550	−	5.58753i	−0.185293	−	0.570274i
$97$	−2.46029	+	1.78750i	−0.249804	+	0.181493i	−0.705640	−	0.708571i	$-0.749340\pi$
$97$	−2.46029	+	1.78750i	−0.249804	+	0.181493i	0.455836	+	0.890064i	$0.349340\pi$
$98$	−38.0265			−3.84125
$99$	3.30902	+	0.224514i	0.332569	+	0.0225645i
$100$		0			0
$101$	0.815928	−	0.592806i	0.0811879	−	0.0589864i	−0.546451	−	0.837491i	$-0.684021\pi$
$101$	0.815928	−	0.592806i	0.0811879	−	0.0589864i	0.627639	+	0.778505i	$0.284021\pi$
$102$	0.994630	+	3.06116i	0.0984830	+	0.303100i
$103$	−2.07047	+	6.37226i	−0.204010	+	0.627878i	0.795743	+	0.605635i	$0.207081\pi$
$103$	−2.07047	+	6.37226i	−0.204010	+	0.627878i	−0.999753	+	0.0222430i	$0.992919\pi$
$104$	18.5368	+	13.4678i	1.81769	+	1.32063i
$105$		0			0
$106$	10.3702	−	31.9163i	1.00725	−	3.09998i
$107$	−2.40488	−	7.40146i	−0.232488	−	0.715526i	−0.997445	−	0.0714436i	$-0.977239\pi$
$107$	−2.40488	−	7.40146i	−0.232488	−	0.715526i	0.764956	−	0.644082i	$-0.222761\pi$
$108$	−3.64906	+	2.65120i	−0.351131	+	0.255112i
$109$	−8.65028			−0.828546			−0.414273	−	0.910153i	$-0.635964\pi$
$109$	−8.65028			−0.828546			−0.414273	+	0.910153i	$0.635964\pi$
$110$		0			0
$111$	−3.96165			−0.376023
$112$	−27.7288	+	20.1461i	−2.62012	+	1.90363i
$113$	2.32487	+	7.15522i	0.218706	+	0.673107i	0.998870	+	0.0475318i	$0.0151355\pi$
$113$	2.32487	+	7.15522i	0.218706	+	0.673107i	−0.780164	+	0.625575i	$0.784864\pi$
$114$	−5.56826	+	17.1374i	−0.521516	+	1.60506i
$115$		0			0
$116$	−22.6059	−	16.4241i	−2.09890	−	1.52494i
$117$	1.10534	−	3.40189i	0.102189	−	0.314504i
$118$	0.418362	+	1.28758i	0.0385133	+	0.118532i
$119$	4.77621	−	3.47012i	0.437835	−	0.318106i
$120$		0			0
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	−15.6486			−1.41676
$123$	−4.24655	+	3.08530i	−0.382899	+	0.278192i
$124$	−0.0926452	−	0.285133i	−0.00831978	−	0.0256057i
$125$		0			0
$126$	9.66091	+	7.01906i	0.860662	+	0.625308i
$127$	10.9523	+	7.95731i	0.971859	+	0.706097i	0.955874	−	0.293775i	$-0.0949118\pi$
$127$	10.9523	+	7.95731i	0.971859	+	0.706097i	0.0159844	+	0.999872i	$0.494912\pi$
$128$	3.36006	−	10.3412i	0.296990	−	0.914042i
$129$	3.01970	+	9.29367i	0.265869	+	0.818262i
$130$		0			0
$131$	−1.96165			−0.171390			−0.0856951	−	0.996321i	$-0.527311\pi$
$131$	−1.96165			−0.171390			−0.0856951	+	0.996321i	$0.527311\pi$
$132$	−11.4796	−	9.59212i	−0.999168	−	0.834887i
$133$	33.0510			2.86588
$134$	6.41657	−	4.66191i	0.554307	−	0.402727i
$135$		0			0
$136$	2.49700	−	7.68499i	0.214116	−	0.658982i
$137$	10.2483	+	7.44586i	0.875576	+	0.636143i	0.932077	−	0.362260i	$-0.117995\pi$
$137$	10.2483	+	7.44586i	0.875576	+	0.636143i	−0.0565017	+	0.998403i	$0.517995\pi$
$138$	6.37328	+	4.63046i	0.542529	+	0.394171i
$139$	−1.10371	+	3.39686i	−0.0936153	+	0.288118i	−0.986890	−	0.161392i	$-0.948402\pi$
$139$	−1.10371	+	3.39686i	−0.0936153	+	0.288118i	0.893275	+	0.449511i	$0.148402\pi$
$140$		0			0
$141$	−4.37328	+	3.17737i	−0.368296	+	0.267583i
$142$	−21.2463			−1.78295
$143$	11.8362	+	0.803076i	0.989793	+	0.0671566i
$144$	7.32351			0.610292
$145$		0			0
$146$	13.1547	+	40.4860i	1.08869	+	3.35064i
$147$	4.60534	−	14.1738i	0.379842	−	1.16903i
$148$	14.4563	+	10.5031i	1.18830	+	0.863351i
$149$	−16.1266	−	11.7166i	−1.32114	−	0.959864i	−0.999917	−	0.0128604i	$-0.995906\pi$
$149$	−16.1266	−	11.7166i	−1.32114	−	0.959864i	−0.321222	−	0.947004i	$-0.604094\pi$
$150$		0			0
$151$	0.926207	+	2.85057i	0.0753737	+	0.231976i	0.981644	−	0.190722i	$-0.0610829\pi$
$151$	0.926207	+	2.85057i	0.0753737	+	0.231976i	−0.906270	+	0.422698i	$0.861083\pi$
$152$	36.5976	−	26.5897i	2.96846	−	2.15671i
$153$	−1.26146			−0.101983
$154$	−14.7606	+	36.7523i	−1.18944	+	2.96158i
$155$		0			0
$156$	−13.0525	+	9.48321i	−1.04504	+	0.759264i
$157$	−2.05320	−	6.31909i	−0.163863	−	0.504318i	0.835088	−	0.550117i	$-0.185417\pi$
$157$	−2.05320	−	6.31909i	−0.163863	−	0.504318i	−0.998951	+	0.0457985i	$0.985417\pi$
$158$	−5.94659	+	18.3017i	−0.473085	+	1.45601i
$159$	10.6404	+	7.73068i	0.843836	+	0.613083i
$160$		0			0
$161$	4.46513	−	13.7423i	0.351902	−	1.08304i
$162$	−0.788477	−	2.42668i	−0.0619486	−	0.190658i
$163$	−5.30475	+	3.85412i	−0.415500	+	0.301878i	−0.775825	−	0.630949i	$-0.782666\pi$
$163$	−5.30475	+	3.85412i	−0.415500	+	0.301878i	0.360325	+	0.932827i	$0.382666\pi$
$164$	23.6757			1.84876
$165$		0			0
$166$	12.3068			0.955196
$167$	−17.6509	+	12.8241i	−1.36586	+	0.992358i	−0.367817	+	0.929898i	$0.619895\pi$
$167$	−17.6509	+	12.8241i	−1.36586	+	0.992358i	−0.998047	+	0.0624601i	$0.980105\pi$
$168$	−9.26404	−	28.5118i	−0.714736	−	2.19973i
$169$	−0.0634720	+	0.195347i	−0.00488246	+	0.0150267i
$170$		0			0
$171$	−5.71332	−	4.15097i	−0.436908	−	0.317433i
$172$	13.6203	−	41.9190i	1.03854	−	3.19629i
$173$	−7.72296	−	23.7688i	−0.587166	−	1.80711i	−0.590393	−	0.807116i	$-0.701027\pi$
$173$	−7.72296	−	23.7688i	−0.587166	−	1.80711i	0.00322738	−	0.999995i	$-0.498973\pi$
$174$	12.7881	−	9.29107i	0.969461	−	0.704354i
$175$		0			0
$176$	5.92484	+	23.5556i	0.446602	+	1.77557i
$177$	−0.530595			−0.0398819
$178$	−12.5045	+	9.08507i	−0.937254	+	0.680955i
$179$	−4.37107	−	13.4528i	−0.326709	−	1.00551i	−0.970663	−	0.240443i	$-0.922707\pi$
$179$	−4.37107	−	13.4528i	−0.326709	−	1.00551i	0.643954	−	0.765064i	$-0.277293\pi$
$180$		0			0
$181$	−8.71154	−	6.32930i	−0.647524	−	0.470454i	0.214903	−	0.976635i	$-0.431056\pi$
$181$	−8.71154	−	6.32930i	−0.647524	−	0.470454i	−0.862427	+	0.506182i	$0.831056\pi$
$182$	34.5566	+	25.1069i	2.56151	+	1.86104i
$183$	1.89518	−	5.83277i	0.140096	−	0.431171i
$184$	−6.11146	−	18.8091i	−0.450543	−	1.38663i
$185$		0			0
$186$	0.169599			0.0124356
$187$	−1.02054	−	4.05740i	−0.0746293	−	0.296707i
$188$	24.3822			1.77825
$189$	−3.78627	+	2.75088i	−0.275410	+	0.200097i
$190$		0			0
$191$	0.739552	−	2.27611i	0.0535121	−	0.164693i	−0.920729	−	0.390203i	$-0.872405\pi$
$191$	0.739552	−	2.27611i	0.0535121	−	0.164693i	0.974241	+	0.225510i	$0.0724048\pi$
$192$	−0.277992	−	0.201973i	−0.0200623	−	0.0145761i
$193$	10.1469	+	7.37212i	0.730386	+	0.530657i	0.889686	−	0.456574i	$-0.150924\pi$
$193$	10.1469	+	7.37212i	0.730386	+	0.530657i	−0.159299	+	0.987230i	$0.550924\pi$
$194$	−2.39782	+	7.37974i	−0.172154	+	0.529834i
$195$		0			0
$196$	−54.3826	+	39.5113i	−3.88447	+	2.82224i
$197$	−16.3419			−1.16431			−0.582157	−	0.813076i	$-0.697791\pi$
$197$	−16.3419			−1.16431			−0.582157	+	0.813076i	$0.697791\pi$
$198$	7.16739	−	4.49932i	0.509364	−	0.319753i
$199$	3.55103			0.251726			0.125863	−	0.992048i	$-0.459830\pi$
$199$	3.55103			0.251726			0.125863	+	0.992048i	$0.459830\pi$
$200$		0			0
$201$	0.960552	+	2.95627i	0.0677521	+	0.208519i
$202$	0.795213	−	2.44741i	0.0559510	−	0.172199i
$203$	−23.4559	−	17.0417i	−1.64628	−	1.19609i
$204$	4.60313	+	3.34437i	0.322284	+	0.234153i
$205$		0			0
$206$	5.28295	+	16.2592i	0.368080	+	1.13284i
$207$	−2.49779	+	1.81475i	−0.173608	+	0.126134i
$208$	26.1958			1.81636
$209$	8.72917	−	21.7348i	0.603810	−	1.50342i
$210$		0			0
$211$	−21.4425	+	15.5789i	−1.47616	+	1.07249i	−0.497394	+	0.867525i	$0.665710\pi$
$211$	−21.4425	+	15.5789i	−1.47616	+	1.07249i	−0.978768	+	0.204970i	$0.934290\pi$
$212$	−18.3318	−	56.4194i	−1.25903	−	3.87490i
$213$	2.57311	−	7.91923i	0.176307	−	0.542617i
$214$	−16.0648	−	11.6718i	−1.09817	−	0.797865i
$215$		0			0
$216$	−1.97946	+	6.09215i	−0.134685	+	0.414518i
$217$	−0.0961288	−	0.295854i	−0.00652565	−	0.0200839i
$218$	−17.8564	+	12.9734i	−1.20939	+	0.878673i
$219$	−16.6837			−1.12738
$220$		0			0
$221$	−4.51217			−0.303522
$222$	−8.17788	+	5.94157i	−0.548863	+	0.398772i
$223$	−5.01902	−	15.4469i	−0.336098	−	1.03440i	−0.966179	−	0.257874i	$-0.916978\pi$
$223$	−5.01902	−	15.4469i	−0.336098	−	1.03440i	0.630080	−	0.776530i	$-0.283022\pi$
$224$	−8.49668	+	26.1501i	−0.567708	+	1.74723i
$225$		0			0
$226$	15.5303	+	11.2835i	1.03306	+	0.750564i
$227$	1.45023	−	4.46335i	0.0962552	−	0.296243i	−0.891324	−	0.453368i	$-0.850222\pi$
$227$	1.45023	−	4.46335i	0.0962552	−	0.296243i	0.987579	+	0.157125i	$0.0502225\pi$
$228$	9.84320	+	30.2943i	0.651882	+	2.00629i
$229$	16.8388	−	12.2341i	1.11274	−	0.808452i	0.129646	−	0.991560i	$-0.458616\pi$
$229$	16.8388	−	12.2341i	1.11274	−	0.808452i	0.983093	+	0.183109i	$0.0586160\pi$
$230$		0			0
$231$	−11.9112	−	9.95279i	−0.783700	−	0.654846i
$232$	−39.6830			−2.60532
$233$	−4.23540	+	3.07720i	−0.277470	+	0.201594i	−0.717813	−	0.696236i	$-0.754857\pi$
$233$	−4.23540	+	3.07720i	−0.277470	+	0.201594i	0.440343	+	0.897830i	$0.354857\pi$
$234$	−2.82035	−	8.68013i	−0.184372	−	0.567438i
$235$		0			0
$236$	1.93617	+	1.40671i	0.126034	+	0.0915691i
$237$	−6.10150	−	4.43300i	−0.396335	−	0.287954i
$238$	4.65495	−	14.3265i	0.301736	−	0.928647i
$239$	3.93438	+	12.1088i	0.254494	+	0.783251i	0.993929	+	0.110023i	$0.0350925\pi$
$239$	3.93438	+	12.1088i	0.254494	+	0.783251i	−0.739435	+	0.673227i	$0.764907\pi$
$240$		0			0
$241$	−7.26505			−0.467983			−0.233991	−	0.972239i	$-0.575179\pi$
$241$	−7.26505			−0.467983			−0.233991	+	0.972239i	$0.575179\pi$
$242$	20.2703	+	19.4135i	1.30303	+	1.24794i
$243$	1.00000			0.0641500
$244$	−22.3795	+	16.2596i	−1.43270	+	1.04092i
$245$		0			0
$246$	−4.13874	+	12.7377i	−0.263876	+	0.812128i
$247$	−20.4363	−	14.8478i	−1.30033	−	0.944745i
$248$	−0.344460	−	0.250265i	−0.0218733	−	0.0158919i
$249$	−1.49047	+	4.58719i	−0.0944545	+	0.290701i
$250$		0			0
$251$	−0.630031	+	0.457745i	−0.0397672	+	0.0288926i	−0.607491	−	0.794326i	$-0.707824\pi$
$251$	−0.630031	+	0.457745i	−0.0397672	+	0.0288926i	0.567724	+	0.823219i	$0.307824\pi$
$252$	21.1095			1.32977
$253$	−7.85780	−	6.56583i	−0.494015	−	0.412790i
$254$	34.5425			2.16739
$255$		0			0
$256$	−8.78578	−	27.0399i	−0.549111	−	1.68999i
$257$	1.16380	−	3.58180i	0.0725957	−	0.223427i	−0.908175	−	0.418591i	$-0.862524\pi$
$257$	1.16380	−	3.58180i	0.0725957	−	0.223427i	0.980771	+	0.195164i	$0.0625240\pi$
$258$	20.1718	+	14.6557i	1.25584	+	0.912423i
$259$	14.9999	+	10.8980i	0.932047	+	0.677172i
$260$		0			0
$261$	1.91436	+	5.89178i	0.118496	+	0.364692i
$262$	−4.04936	+	2.94203i	−0.250170	+	0.181759i
$263$	−4.75625			−0.293283			−0.146641	−	0.989190i	$-0.546846\pi$
$263$	−4.75625			−0.293283			−0.146641	+	0.989190i	$0.546846\pi$
$264$	−21.1965	−	1.43816i	−1.30455	−	0.0885127i
$265$		0			0
$266$	68.2258	−	49.5690i	4.18319	−	3.03927i
$267$	−1.87191	−	5.76115i	−0.114559	−	0.352577i
$268$	4.33255	−	13.3342i	0.264653	−	0.814518i
$269$	20.7208	+	15.0545i	1.26337	+	0.917890i	0.998918	−	0.0465103i	$-0.0148100\pi$
$269$	20.7208	+	15.0545i	1.26337	+	0.917890i	0.264449	+	0.964400i	$0.414810\pi$
$270$		0			0
$271$	−2.52155	+	7.76053i	−0.153173	+	0.471418i	−0.997971	−	0.0636668i	$-0.979721\pi$
$271$	−2.52155	+	7.76053i	−0.153173	+	0.471418i	0.844798	+	0.535085i	$0.179721\pi$
$272$	−2.85479	−	8.78613i	−0.173097	−	0.532738i
$273$	−13.5433	+	9.83979i	−0.819678	+	0.595531i
$274$	32.3224			1.95266
$275$		0			0
$276$	13.9259			0.838238
$277$	13.2479	−	9.62518i	0.795990	−	0.578321i	−0.113745	−	0.993510i	$-0.536285\pi$
$277$	13.2479	−	9.62518i	0.795990	−	0.578321i	0.909735	+	0.415189i	$0.136285\pi$
$278$	2.81618	+	8.66732i	0.168903	+	0.519831i
$279$	−0.0205400	+	0.0632155i	−0.00122970	+	0.00378461i
$280$		0			0
$281$	6.97214	+	5.06555i	0.415923	+	0.302186i	0.775995	−	0.630739i	$-0.217248\pi$
$281$	6.97214	+	5.06555i	0.415923	+	0.302186i	−0.360072	+	0.932924i	$0.617248\pi$
$282$	−4.26224	+	13.1178i	−0.253813	+	0.781156i
$283$	1.42689	+	4.39150i	0.0848196	+	0.261048i	0.984467	−	0.175569i	$-0.0561765\pi$
$283$	1.42689	+	4.39150i	0.0848196	+	0.261048i	−0.899648	+	0.436617i	$0.856177\pi$
$284$	−30.3849	+	22.0759i	−1.80301	+	1.30996i
$285$		0			0
$286$	25.6374	−	16.0939i	1.51597	−	0.951649i
$287$	24.5659			1.45008
$288$	4.75303	−	3.45328i	0.280075	−	0.203487i
$289$	−4.76156	−	14.6546i	−0.280092	−	0.862034i
$290$		0			0
$291$	−2.46029	−	1.78750i	−0.144224	−	0.104785i
$292$	60.8797	+	44.2317i	3.56272	+	2.58847i
$293$	8.87006	−	27.2992i	0.518194	−	1.59484i	−0.259199	−	0.965824i	$-0.583459\pi$
$293$	8.87006	−	27.2992i	0.518194	−	1.59484i	0.777394	−	0.629014i	$-0.216541\pi$
$294$	−11.7508	−	36.1653i	−0.685322	−	2.10920i
$295$		0			0
$296$	25.3770			1.47501
$297$	0.809017	+	3.21644i	0.0469439	+	0.186637i
$298$	−50.8617			−2.94634
$299$	−8.93448	+	6.49128i	−0.516695	+	0.375401i
$300$		0			0
$301$	14.1324	−	43.4952i	0.814580	−	2.50702i
$302$	6.18714	+	4.49522i	0.356030	+	0.258671i
$303$	0.815928	+	0.592806i	0.0468738	+	0.0340558i
$304$	15.9820	−	49.1877i	0.916633	−	2.82111i
$305$		0			0
$306$	−2.60397	+	1.89190i	−0.148859	+	0.108153i
$307$	−16.0240			−0.914540			−0.457270	−	0.889328i	$-0.651173\pi$
$307$	−16.0240			−0.914540			−0.457270	+	0.889328i	$0.651173\pi$
$308$	17.0779	+	67.8973i	0.973104	+	3.86881i
$309$	−6.70019			−0.381161
$310$		0			0
$311$	2.62367	+	8.07483i	0.148775	+	0.457881i	0.997477	−	0.0709893i	$-0.0226156\pi$
$311$	2.62367	+	8.07483i	0.148775	+	0.457881i	−0.848702	+	0.528871i	$0.822616\pi$
$312$	−7.08044	+	21.7913i	−0.400851	+	1.23369i
$313$	−6.73522	−	4.89343i	−0.380697	−	0.276593i	0.380935	−	0.924602i	$-0.375602\pi$
$313$	−6.73522	−	4.89343i	−0.380697	−	0.276593i	−0.761633	+	0.648009i	$0.775602\pi$
$314$	−13.7155	−	9.96491i	−0.774012	−	0.562353i
$315$		0			0
$316$	10.5120	+	32.3525i	0.591345	+	1.81997i
$317$	23.9680	−	17.4138i	1.34618	−	0.978055i	0.346985	−	0.937871i	$-0.387206\pi$
$317$	23.9680	−	17.4138i	1.34618	−	0.978055i	0.999192	−	0.0401842i	$-0.0127945\pi$
$318$	33.5587			1.88188
$319$	−17.4018	+	10.9240i	−0.974315	+	0.611625i
$320$		0			0
$321$	6.29606	−	4.57435i	0.351412	−	0.255315i
$322$	−11.3931	−	35.0643i	−0.634912	−	1.95406i
$323$	−2.75287	+	8.47246i	−0.153174	+	0.471420i
$324$	−3.64906	−	2.65120i	−0.202726	−	0.147289i
$325$		0			0
$326$	−5.17006	+	15.9118i	−0.286343	+	0.881274i
$327$	−2.67308	−	8.22690i	−0.147822	−	0.454949i
$328$	27.2020	−	19.7634i	1.50198	−	1.09125i
$329$	25.2990			1.39478
$330$		0			0
$331$	15.5731			0.855973			0.427987	−	0.903785i	$-0.359223\pi$
$331$	15.5731			0.855973			0.427987	+	0.903785i	$0.359223\pi$
$332$	17.6003	−	12.7874i	0.965944	−	0.701799i
$333$	−1.22422	−	3.76775i	−0.0670867	−	0.206472i
$334$	−17.2027	+	52.9445i	−0.941291	+	2.89700i
$335$		0			0
$336$	−27.7288	−	20.1461i	−1.51273	−	1.09906i
$337$	−6.85189	+	21.0880i	−0.373246	+	1.14873i	0.571408	+	0.820666i	$0.306398\pi$
$337$	−6.85189	+	21.0880i	−0.373246	+	1.14873i	−0.944654	+	0.328068i	$0.893602\pi$
$338$	0.161953	+	0.498440i	0.00880908	+	0.0271115i
$339$	−6.08660	+	4.42217i	−0.330578	+	0.240179i
$340$		0			0
$341$	−0.219946	−	0.0149232i	−0.0119107	−	0.000808134i
$342$	−18.0193			−0.974371
$343$	−29.9236	+	21.7408i	−1.61572	+	1.17389i
$344$	−19.3432	−	59.5322i	−1.04291	−	3.20976i
$345$		0			0
$346$	−51.5900	−	37.4824i	−2.77350	−	2.01506i
$347$	−21.2348	−	15.4280i	−1.13994	−	0.828218i	−0.152833	−	0.988252i	$-0.548840\pi$
$347$	−21.2348	−	15.4280i	−1.13994	−	0.828218i	−0.987112	+	0.160034i	$0.948840\pi$
$348$	8.63468	−	26.5748i	0.462867	−	1.42456i
$349$	2.83135	+	8.71401i	0.151559	+	0.466450i	0.997796	−	0.0663563i	$-0.0211374\pi$
$349$	2.83135	+	8.71401i	0.151559	+	0.466450i	−0.846237	+	0.532806i	$0.821137\pi$
$350$		0			0
$351$	3.57695			0.190924
$352$	14.9526	+	12.4941i	0.796974	+	0.665937i
$353$	8.20404			0.436657			0.218329	−	0.975875i	$-0.429940\pi$
$353$	8.20404			0.436657			0.218329	+	0.975875i	$0.429940\pi$
$354$	−1.09528	+	0.795771i	−0.0582137	+	0.0422948i
$355$		0			0
$356$	−8.44323	+	25.9856i	−0.447490	+	1.37723i
$357$	4.77621	+	3.47012i	0.252784	+	0.183658i
$358$	−29.1991	−	21.2144i	−1.54322	−	1.12122i
$359$	1.51338	−	4.65771i	0.0798732	−	0.245824i	−0.903144	−	0.429338i	$-0.858747\pi$
$359$	1.51338	−	4.65771i	0.0798732	−	0.245824i	0.983017	+	0.183513i	$0.0587470\pi$
$360$		0			0
$361$	−24.9764	+	18.1464i	−1.31455	+	0.955076i
$362$	−27.4754			−1.44407
$363$	−9.69098	+	5.20431i	−0.508645	+	0.273155i
$364$	75.5075			3.95767
$365$		0			0
$366$	−4.83568	−	14.8827i	−0.252765	−	0.777931i
$367$	−2.53803	+	7.81124i	−0.132484	+	0.407744i	−0.995190	−	0.0979618i	$-0.968768\pi$
$367$	−2.53803	+	7.81124i	−0.132484	+	0.407744i	0.862706	+	0.505705i	$0.168768\pi$
$368$	−18.2926	−	13.2903i	−0.953567	−	0.692807i
$369$	−4.24655	−	3.08530i	−0.221067	−	0.160614i
$370$		0			0
$371$	−19.0211	−	58.5409i	−0.987525	−	3.03929i
$372$	0.242548	−	0.176222i	0.0125755	−	0.00913667i
$373$	2.37553			0.123000			0.0615002	−	0.998107i	$-0.480412\pi$
$373$	2.37553			0.123000			0.0615002	+	0.998107i	$0.480412\pi$
$374$	−8.19184	−	6.84495i	−0.423590	−	0.353944i
$375$		0			0
$376$	28.0138	−	20.3532i	1.44470	−	1.04964i
$377$	6.84757	+	21.0746i	0.352668	+	1.08540i
$378$	−3.69014	+	11.3571i	−0.189800	+	0.584145i
$379$	12.9398	+	9.40129i	0.664671	+	0.482912i	0.868237	−	0.496149i	$-0.165253\pi$
$379$	12.9398	+	9.40129i	0.664671	+	0.482912i	−0.203566	+	0.979061i	$0.565253\pi$
$380$		0			0
$381$	−4.18340	+	12.8752i	−0.214322	+	0.659616i
$382$	−1.88701	−	5.80763i	−0.0965480	−	0.297144i
$383$	−9.25413	+	6.72352i	−0.472864	+	0.343556i	−0.798556	−	0.601920i	$-0.794403\pi$
$383$	−9.25413	+	6.72352i	−0.472864	+	0.343556i	0.325692	+	0.945476i	$0.394403\pi$
$384$	10.8734			0.554880
$385$		0			0
$386$	32.0022			1.62887
$387$	−7.90567	+	5.74380i	−0.401868	+	0.291974i
$388$	4.23871	+	13.0454i	0.215188	+	0.662280i
$389$	−1.46609	+	4.51215i	−0.0743335	+	0.228775i	−0.981319	−	0.192386i	$-0.938377\pi$
$389$	−1.46609	+	4.51215i	−0.0743335	+	0.228775i	0.906986	+	0.421161i	$0.138377\pi$
$390$		0			0
$391$	3.15086	+	2.28923i	0.159346	+	0.115771i
$392$	−29.5003	+	90.7925i	−1.48999	+	4.58571i
$393$	−0.606183	−	1.86564i	−0.0305779	−	0.0941091i
$394$	−33.7340	+	24.5092i	−1.69949	+	1.23475i
$395$		0			0
$396$	5.57527	−	13.8818i	0.280168	−	0.697589i
$397$	14.5521			0.730349			0.365174	−	0.930939i	$-0.381009\pi$
$397$	14.5521			0.730349			0.365174	+	0.930939i	$0.381009\pi$
$398$	7.33025	−	5.32574i	0.367432	−	0.266955i
$399$	10.2133	+	31.4334i	0.511305	+	1.57364i
$400$		0			0
$401$	3.28406	+	2.38601i	0.163998	+	0.119152i	0.666757	−	0.745275i	$-0.267682\pi$
$401$	3.28406	+	2.38601i	0.163998	+	0.119152i	−0.502759	+	0.864426i	$0.667682\pi$
$402$	6.41657	+	4.66191i	0.320029	+	0.232515i
$403$	−0.0734705	+	0.226119i	−0.00365983	+	0.0112638i
$404$	−1.40572	−	4.32637i	−0.0699373	−	0.215245i
$405$		0			0
$406$	−73.9777			−3.67145
$407$	11.1283	−	6.98580i	0.551612	−	0.346273i
$408$	8.08047			0.400043
$409$	30.5098	−	22.1666i	1.50861	−	1.09607i	0.541821	−	0.840494i	$-0.317735\pi$
$409$	30.5098	−	22.1666i	1.50861	−	1.09607i	0.966789	−	0.255575i	$-0.0822649\pi$
$410$		0			0
$411$	−3.91452	+	12.0477i	−0.193089	+	0.594267i
$412$	24.4494	+	17.7635i	1.20454	+	0.875146i
$413$	2.00897	+	1.45960i	0.0988551	+	0.0718224i
$414$	−2.43438	+	7.49224i	−0.119643	+	0.368223i
$415$		0			0
$416$	17.0014	−	12.3522i	0.833561	−	0.605618i
$417$	−3.57167			−0.174906
$418$	−14.5779	−	57.9580i	−0.713029	−	2.83482i
$419$	−22.2849			−1.08869			−0.544343	−	0.838862i	$-0.683221\pi$
$419$	−22.2849			−1.08869			−0.544343	+	0.838862i	$0.683221\pi$
$420$		0			0
$421$	3.05146	+	9.39144i	0.148719	+	0.457711i	0.997471	−	0.0710815i	$-0.0226451\pi$
$421$	3.05146	+	9.39144i	0.148719	+	0.457711i	−0.848751	+	0.528792i	$0.822645\pi$
$422$	−20.8981	+	64.3177i	−1.01730	+	3.13094i
$423$	−4.37328	−	3.17737i	−0.212636	−	0.154489i
$424$	−68.1587	−	49.5202i	−3.31008	−	2.40491i
$425$		0			0
$426$	−6.56547	−	20.2064i	−0.318098	−	0.979005i
$427$	−23.2209	+	16.8710i	−1.12374	+	0.816445i
$428$	−35.1022			−1.69673
$429$	2.89382	+	11.5051i	0.139715	+	0.555470i
$430$		0			0
$431$	−17.1940	+	12.4922i	−0.828206	+	0.601727i	−0.919051	−	0.394138i	$-0.871043\pi$
$431$	−17.1940	+	12.4922i	−0.828206	+	0.601727i	0.0908454	+	0.995865i	$0.471043\pi$
$432$	2.26309	+	6.96507i	0.108883	+	0.335107i
$433$	−3.50401	+	10.7842i	−0.168392	+	0.518256i	−0.999270	−	0.0381974i	$-0.987838\pi$
$433$	−3.50401	+	10.7842i	−0.168392	+	0.518256i	0.830878	+	0.556454i	$0.187838\pi$
$434$	−0.642148	−	0.466548i	−0.0308241	−	0.0223950i
$435$		0			0
$436$	−12.0569	+	37.1073i	−0.577421	+	1.77712i
$437$	6.73770	+	20.7365i	0.322308	+	0.991962i
$438$	−34.4394	+	25.0217i	−1.64558	+	1.19558i
$439$	−35.1241			−1.67638			−0.838192	−	0.545376i	$-0.816387\pi$
$439$	−35.1241			−1.67638			−0.838192	+	0.545376i	$0.816387\pi$
$440$		0			0
$441$	14.9032			0.709676
$442$	−9.31430	+	6.76723i	−0.443036	+	0.321884i
$443$	3.39408	+	10.4459i	0.161258	+	0.496300i	0.998741	−	0.0501626i	$-0.0159740\pi$
$443$	3.39408	+	10.4459i	0.161258	+	0.496300i	−0.837483	+	0.546463i	$0.815974\pi$
$444$	−5.52181	+	16.9944i	−0.262054	+	0.806518i
$445$		0			0
$446$	−33.5275	−	24.3591i	−1.58757	−	1.15344i
$447$	6.15980	−	18.9579i	0.291349	−	0.896679i
$448$	0.496947	+	1.52945i	0.0234785	+	0.0722595i
$449$	17.0288	−	12.3722i	0.803640	−	0.583879i	−0.108339	−	0.994114i	$-0.534553\pi$
$449$	17.0288	−	12.3722i	0.803640	−	0.583879i	0.911980	+	0.410235i	$0.134553\pi$
$450$		0			0
$451$	6.48816	−	16.1548i	0.305515	−	0.760702i
$452$	33.9344			1.59614
$453$	−2.42484	+	1.76175i	−0.113929	+	0.0827743i
$454$	−3.70036	−	11.3885i	−0.173666	−	0.534490i
$455$		0			0
$456$	36.5976	+	26.5897i	1.71384	+	1.24518i
$457$	1.86346	+	1.35388i	0.0871690	+	0.0633320i	0.630516	−	0.776176i	$-0.282843\pi$
$457$	1.86346	+	1.35388i	0.0871690	+	0.0633320i	−0.543347	+	0.839508i	$0.682843\pi$
$458$	16.4113	−	50.5087i	0.766848	−	2.36012i
$459$	−0.389812	−	1.19972i	−0.0181948	−	0.0559980i
$460$		0			0
$461$	−26.4118			−1.23012			−0.615060	−	0.788480i	$-0.710868\pi$
$461$	−26.4118			−1.23012			−0.615060	+	0.788480i	$0.710868\pi$
$462$	−39.5148	−	2.68104i	−1.83839	−	0.124733i
$463$	3.54115			0.164571			0.0822857	−	0.996609i	$-0.473778\pi$
$463$	3.54115			0.164571			0.0822857	+	0.996609i	$0.473778\pi$
$464$	−36.7043	+	26.6673i	−1.70396	+	1.23800i
$465$		0			0
$466$	−4.12787	+	12.7043i	−0.191220	+	0.588514i
$467$	−4.90157	−	3.56120i	−0.226818	−	0.164793i	0.468573	−	0.883425i	$-0.344768\pi$
$467$	−4.90157	−	3.56120i	−0.226818	−	0.164793i	−0.695390	+	0.718632i	$0.744768\pi$
$468$	−13.0525	−	9.48321i	−0.603353	−	0.438361i
$469$	4.49546	−	13.8356i	0.207581	−	0.638869i
$470$		0			0
$471$	5.37534	−	3.90541i	0.247683	−	0.179952i
$472$	3.39881			0.156443
$473$	−24.8704	−	20.7813i	−1.14354	−	0.955524i
$474$	−19.2436			−0.883886
$475$		0			0
$476$	−8.22871	−	25.3254i	−0.377162	−	1.16079i
$477$	−4.06426	+	12.5085i	−0.186090	+	0.572725i
$478$	26.2820	+	19.0950i	1.20211	+	0.873383i
$479$	20.8807	+	15.1707i	0.954065	+	0.693169i	0.951765	−	0.306829i	$-0.0992679\pi$
$479$	20.8807	+	15.1707i	0.954065	+	0.693169i	0.00230002	+	0.999997i	$0.499268\pi$
$480$		0			0
$481$	−4.37897	−	13.4771i	−0.199664	−	0.614502i
$482$	−14.9969	+	10.8959i	−0.683092	+	0.496296i
$483$	14.4495			0.657474
$484$	49.1606	+	6.70186i	2.23457	+	0.304630i
$485$		0			0
$486$	2.06426	−	1.49977i	0.0936367	−	0.0680311i
$487$	−3.13584	−	9.65113i	−0.142099	−	0.437335i	0.854528	−	0.519406i	$-0.173847\pi$
$487$	−3.13584	−	9.65113i	−0.142099	−	0.437335i	−0.996626	+	0.0820709i	$0.973847\pi$
$488$	−12.1399	+	37.3628i	−0.549548	+	1.69133i
$489$	−5.30475	−	3.85412i	−0.239889	−	0.174289i
$490$		0			0
$491$	−8.23976	+	25.3594i	−0.371855	+	1.14445i	0.573721	+	0.819051i	$0.305500\pi$
$491$	−8.23976	+	25.3594i	−0.371855	+	1.14445i	−0.945576	+	0.325402i	$0.894500\pi$
$492$	7.31618	+	22.5169i	0.329839	+	1.01514i
$493$	6.32223	−	4.59337i	0.284739	−	0.206875i
$494$	−64.4541			−2.89993
$495$		0			0
$496$	−0.486784			−0.0218573
$497$	−31.5274	+	22.9060i	−1.41420	+	1.02747i
$498$	3.80302	+	11.7045i	0.170418	+	0.524491i
$499$	4.12879	−	12.7071i	0.184830	−	0.568848i	−0.815116	−	0.579298i	$-0.803327\pi$
$499$	4.12879	−	12.7071i	0.184830	−	0.568848i	0.999945	+	0.0104507i	$0.00332661\pi$
$500$		0			0
$501$	−17.6509	−	12.8241i	−0.788582	−	0.572938i
$502$	−0.614036	+	1.88981i	−0.0274058	+	0.0843462i
$503$	−9.94239	−	30.5995i	−0.443309	−	1.36436i	−0.884328	−	0.466867i	$-0.845383\pi$
$503$	−9.94239	−	30.5995i	−0.443309	−	1.36436i	0.441019	−	0.897498i	$-0.354617\pi$
$504$	24.2536	−	17.6213i	1.08034	−	0.784913i
$505$		0			0
$506$	−26.0678	−	1.76868i	−1.15885	−	0.0786273i
$507$	−0.205400			−0.00912212
$508$	49.4002	−	35.8913i	2.19178	−	1.59242i
$509$	−8.13704	−	25.0432i	−0.360668	−	1.11002i	−0.952649	−	0.304071i	$-0.901654\pi$
$509$	−8.13704	−	25.0432i	−0.360668	−	1.11002i	0.591981	−	0.805952i	$-0.298346\pi$
$510$		0			0
$511$	63.1689	+	45.8949i	2.79443	+	2.03027i
$512$	−41.0963	−	29.8582i	−1.81622	−	1.31956i
$513$	2.18229	−	6.71641i	0.0963506	−	0.296537i
$514$	−2.96951	−	9.13920i	−0.130979	−	0.403113i
$515$		0			0
$516$	44.0762			1.94035
$517$	6.68177	−	16.6369i	0.293864	−	0.731691i
$518$	47.3082			2.07860
$519$	20.2190	−	14.6899i	0.887514	−	0.644817i
$520$		0			0
$521$	2.60439	−	8.01548i	0.114100	−	0.351165i	−0.877658	−	0.479287i	$-0.840895\pi$
$521$	2.60439	−	8.01548i	0.114100	−	0.351165i	0.991758	+	0.128123i	$0.0408952\pi$
$522$	12.7881	+	9.29107i	0.559718	+	0.406659i
$523$	35.8647	+	26.0572i	1.56825	+	1.13940i	0.928805	+	0.370569i	$0.120837\pi$
$523$	35.8647	+	26.0572i	1.56825	+	1.13940i	0.639449	+	0.768834i	$0.279163\pi$
$524$	−2.73418	+	8.41494i	−0.119443	+	0.367609i
$525$		0			0
$526$	−9.81814	+	7.13329i	−0.428091	+	0.311026i
$527$	0.0838474			0.00365245
$528$	−20.5719	+	12.9139i	−0.895275	+	0.562007i
$529$	−13.4677			−0.585553
$530$		0			0
$531$	−0.163963	−	0.504625i	−0.00711538	−	0.0218989i
$532$	46.0670	−	141.780i	1.99726	−	6.14693i
$533$	−15.1897	−	11.0360i	−0.657940	−	0.478021i
$534$	−12.5045	−	9.08507i	−0.541124	−	0.393149i
$535$		0			0
$536$	−6.15297	−	18.9369i	−0.265768	−	0.817950i
$537$	11.4436	−	8.31426i	0.493828	−	0.358787i
$538$	65.3513			2.81750
$539$	12.0569	+	47.9352i	0.519329	+	2.06472i
$540$		0			0
$541$	−15.7376	+	11.4340i	−0.676612	+	0.491588i	−0.872232	−	0.489092i	$-0.837328\pi$
$541$	−15.7376	+	11.4340i	−0.676612	+	0.491588i	0.195620	+	0.980680i	$0.437328\pi$
$542$	6.43390	+	19.8015i	0.276359	+	0.850547i
$543$	3.32751	−	10.2410i	0.142797	−	0.439485i
$544$	−5.99575	−	4.35616i	−0.257066	−	0.186769i
$545$		0			0
$546$	−13.1995	+	40.6238i	−0.564885	+	1.73854i
$547$	9.65655	+	29.7198i	0.412884	+	1.27073i	0.914130	+	0.405422i	$0.132875\pi$
$547$	9.65655	+	29.7198i	0.412884	+	1.27073i	−0.501246	+	0.865305i	$0.667125\pi$
$548$	46.2250	−	33.5844i	1.97464	−	1.43466i
$549$	6.13294			0.261747
$550$		0			0
$551$	43.7493			1.86378
$552$	16.0000	−	11.6247i	0.681006	−	0.494780i
$553$	10.9072	+	33.5690i	0.463823	+	1.42750i
$554$	12.9116	−	39.7377i	0.548560	−	1.68829i
$555$		0			0
$556$	13.0333	+	9.46921i	0.552733	+	0.401584i
$557$	0.0834344	−	0.256785i	0.00353523	−	0.0108803i	−0.949273	−	0.314452i	$-0.898179\pi$
$557$	0.0834344	−	0.256785i	0.00353523	−	0.0108803i	0.952809	+	0.303572i	$0.0981792\pi$
$558$	0.0524091	+	0.161298i	0.00221865	+	0.00682831i
$559$	−28.2782	+	20.5453i	−1.19604	+	0.868974i
$560$		0			0
$561$	3.54345	−	2.22440i	0.149605	−	0.0939141i
$562$	21.9895			0.927570
$563$	7.85538	−	5.70727i	0.331065	−	0.240533i	−0.409818	−	0.912167i	$-0.634408\pi$
$563$	7.85538	−	5.70727i	0.331065	−	0.240533i	0.740882	+	0.671635i	$0.234408\pi$
$564$	7.53451	+	23.1888i	0.317260	+	0.976426i
$565$		0			0
$566$	9.53172	+	6.92520i	0.400648	+	0.291088i
$567$	−3.78627	−	2.75088i	−0.159008	−	0.115526i
$568$	−16.4825	+	50.7279i	−0.691591	+	2.12850i
$569$	−8.23881	−	25.3564i	−0.345389	−	1.06300i	−0.961375	−	0.275241i	$-0.911242\pi$
$569$	−8.23881	−	25.3564i	−0.345389	−	1.06300i	0.615986	−	0.787757i	$-0.288758\pi$
$570$		0			0
$571$	13.1870			0.551858			0.275929	−	0.961178i	$-0.411015\pi$
$571$	13.1870			0.551858			0.275929	+	0.961178i	$0.411015\pi$
$572$	19.9425	−	49.6547i	0.833837	−	2.07617i
$573$	2.39324			0.0999790
$574$	50.7104	−	36.8433i	2.11661	−	1.53781i
$575$		0			0
$576$	0.106183	−	0.326799i	0.00442431	−	0.0136166i
$577$	1.04024	+	0.755776i	0.0433056	+	0.0314634i	0.609227	−	0.792996i	$-0.291480\pi$
$577$	1.04024	+	0.755776i	0.0433056	+	0.0314634i	−0.565922	+	0.824459i	$0.691480\pi$
$578$	−31.8076	−	23.1096i	−1.32302	−	0.961232i
$579$	−3.87575	+	11.9283i	−0.161071	+	0.495725i
$580$		0			0
$581$	18.2621	−	13.2682i	0.757641	−	0.550458i
$582$	−7.75951			−0.321642
$583$	−43.5209	−	2.95286i	−1.80245	−	0.122295i
$584$	106.870			4.42232
$585$		0			0
$586$	−22.6325	−	69.6558i	−0.934941	−	2.87745i
$587$	8.64897	−	26.6188i	0.356981	−	1.09867i	−0.597871	−	0.801593i	$-0.703986\pi$
$587$	8.64897	−	26.6188i	0.356981	−	1.09867i	0.954852	−	0.297082i	$-0.0960136\pi$
$588$	−54.3826	−	39.5113i	−2.24270	−	1.62942i
$589$	0.379757	+	0.275910i	0.0156476	+	0.0113687i
$590$		0			0
$591$	−5.04993	−	15.5421i	−0.207727	−	0.639316i
$592$	23.4722	−	17.0535i	0.964700	−	0.700895i
$593$	−0.0168463			−0.000691794			−0.000345897	−	1.00000i	$-0.500110\pi$
$593$	−0.0168463			−0.000691794			−0.000345897		1.00000i	$0.500110\pi$
$594$	6.49395	+	5.42623i	0.266450	+	0.222641i
$595$		0			0
$596$	−72.7386	+	52.8477i	−2.97949	+	2.16473i
$597$	1.09733	+	3.37723i	0.0449107	+	0.138221i
$598$	−8.70765	+	26.7994i	−0.356082	+	1.09591i
$599$	−2.73720	−	1.98869i	−0.111839	−	0.0812556i	0.530460	−	0.847710i	$-0.322019\pi$
$599$	−2.73720	−	1.98869i	−0.111839	−	0.0812556i	−0.642299	+	0.766454i	$0.722019\pi$
$600$		0			0
$601$	10.1001	−	31.0848i	0.411991	−	1.26798i	−0.502924	−	0.864331i	$-0.667743\pi$
$601$	10.1001	−	31.0848i	0.411991	−	1.26798i	0.914915	−	0.403647i	$-0.132257\pi$
$602$	−36.0598	−	110.981i	−1.46969	−	4.52324i
$603$	−2.51476	+	1.82708i	−0.102409	+	0.0744044i
$604$	13.5191			0.550086
$605$		0			0
$606$	2.57336			0.104536
$607$	2.99601	−	2.17673i	0.121604	−	0.0883508i	−0.525321	−	0.850904i	$-0.676055\pi$
$607$	2.99601	−	2.17673i	0.121604	−	0.0883508i	0.646925	+	0.762554i	$0.276055\pi$
$608$	−12.8211	−	39.4594i	−0.519966	−	1.60029i
$609$	8.95935	−	27.5740i	0.363051	−	1.11736i
$610$		0			0
$611$	−15.6430	−	11.3653i	−0.632848	−	0.459791i
$612$	−1.75824	+	5.41130i	−0.0710726	+	0.218739i
$613$	−5.19689	−	15.9944i	−0.209900	−	0.646007i	−0.999476	−	0.0323540i	$-0.989700\pi$
$613$	−5.19689	−	15.9944i	−0.209900	−	0.646007i	0.789576	−	0.613652i	$-0.210300\pi$
$614$	−33.0778	+	24.0324i	−1.33491	+	0.969869i
$615$		0			0
$616$	76.2993	+	63.7543i	3.07419	+	2.56873i
$617$	−21.3317			−0.858782			−0.429391	−	0.903119i	$-0.641272\pi$
$617$	−21.3317			−0.858782			−0.429391	+	0.903119i	$0.641272\pi$
$618$	−13.8309	+	10.0488i	−0.556362	+	0.404221i
$619$	−8.06437	−	24.8196i	−0.324134	−	0.997583i	−0.971830	−	0.235684i	$-0.924267\pi$
$619$	−8.06437	−	24.8196i	−0.324134	−	0.997583i	0.647696	−	0.761899i	$-0.275733\pi$
$620$		0			0
$621$	−2.49779	−	1.81475i	−0.100233	−	0.0728235i
$622$	17.5263	+	12.7336i	0.702742	+	0.510572i
$623$	−8.76070	+	26.9627i	−0.350990	+	1.08024i
$624$	8.09496	+	24.9137i	0.324058	+	0.997348i
$625$		0			0
$626$	−21.2423			−0.849012
$627$	23.3684	+	1.58553i	0.933246	+	0.0633199i
$628$	−29.9689			−1.19589
$629$	−4.04302	+	2.93743i	−0.161206	+	0.117123i
$630$		0			0
$631$	−1.89929	+	5.84541i	−0.0756095	+	0.232702i	−0.981717	−	0.190345i	$-0.939039\pi$
$631$	−1.89929	+	5.84541i	−0.0756095	+	0.232702i	0.906108	+	0.423047i	$0.139039\pi$
$632$	39.0842	+	28.3963i	1.55468	+	1.12954i
$633$	−21.4425	−	15.5789i	−0.852263	−	0.619205i
$634$	23.3595	−	71.8931i	0.927724	−	2.85524i
$635$		0			0
$636$	47.9932	−	34.8691i	1.90306	−	1.38265i
$637$	53.3080			2.11214
$638$	−19.5384	+	48.6487i	−0.773534	+	1.92602i
$639$	8.32677			0.329402
$640$		0			0
$641$	5.02090	+	15.4527i	0.198314	+	0.610346i	0.999922	+	0.0124968i	$0.00397795\pi$
$641$	5.02090	+	15.4527i	0.198314	+	0.610346i	−0.801608	+	0.597849i	$0.796022\pi$
$642$	6.13621	−	18.8853i	0.242177	−	0.745343i
$643$	24.2596	+	17.6256i	0.956706	+	0.695088i	0.952383	−	0.304903i	$-0.0986240\pi$
$643$	24.2596	+	17.6256i	0.956706	+	0.695088i	0.00432270	+	0.999991i	$0.498624\pi$
$644$	−52.7270	−	38.3084i	−2.07773	−	1.50956i
$645$		0			0
$646$	7.02413	+	21.6180i	0.276361	+	0.850550i
$647$	6.02094	−	4.37447i	0.236708	−	0.171978i	−0.463108	−	0.886302i	$-0.653266\pi$
$647$	6.02094	−	4.37447i	0.236708	−	0.171978i	0.699815	+	0.714324i	$0.253266\pi$
$648$	−6.40567			−0.251638
$649$	1.49045	−	0.935627i	0.0585052	−	0.0367266i
$650$		0			0
$651$	0.251668	−	0.182848i	0.00986366	−	0.00716637i
$652$	9.13929	+	28.1278i	0.357922	+	1.10157i
$653$	−4.74939	+	14.6171i	−0.185858	+	0.572012i	−0.999962	−	0.00870717i	$-0.997228\pi$
$653$	−4.74939	+	14.6171i	−0.185858	+	0.572012i	0.814104	+	0.580719i	$0.197228\pi$
$654$	−17.8564	−	12.9734i	−0.698241	−	0.507302i
$655$		0			0
$656$	11.8790	−	36.5598i	0.463798	−	1.42742i
$657$	−5.15554	−	15.8671i	−0.201137	−	0.619035i
$658$	52.2237	−	37.9427i	2.03589	−	1.47916i
$659$	28.5540			1.11231			0.556153	−	0.831080i	$-0.312277\pi$
$659$	28.5540			1.11231			0.556153	+	0.831080i	$0.312277\pi$
$660$		0			0
$661$	4.57096			0.177790			0.0888949	−	0.996041i	$-0.471666\pi$
$661$	4.57096			0.177790			0.0888949	+	0.996041i	$0.471666\pi$
$662$	32.1469	−	23.3561i	1.24942	−	0.907759i
$663$	−1.39434	−	4.29133i	−0.0541516	−	0.166662i
$664$	9.54743	−	29.3840i	0.370512	−	1.14032i
$665$		0			0
$666$	−8.17788	−	5.94157i	−0.316886	−	0.230231i
$667$	5.91046	−	18.1905i	0.228854	−	0.704340i
$668$	30.4098	+	93.5918i	1.17659	+	3.62117i
$669$	13.1400	−	9.54674i	0.508020	−	0.369098i
$670$		0			0
$671$	4.96165	+	19.7262i	0.191542	+	0.761523i
$672$	−27.4958			−1.06067
$673$	25.5314	−	18.5497i	0.984165	−	0.715038i	0.0255293	−	0.999674i	$-0.491873\pi$
$673$	25.5314	−	18.5497i	0.984165	−	0.715038i	0.958636	+	0.284636i	$0.0918729\pi$
$674$	17.4831	+	53.8073i	0.673422	+	2.07258i
$675$		0			0
$676$	0.749515	+	0.544555i	0.0288275	+	0.0209444i
$677$	−23.5996	−	17.1461i	−0.907005	−	0.658978i	0.0332504	−	0.999447i	$-0.489414\pi$
$677$	−23.5996	−	17.1461i	−0.907005	−	0.658978i	−0.940256	+	0.340469i	$0.889414\pi$
$678$	−5.93206	+	18.2570i	−0.227820	+	0.701157i
$679$	4.39809	+	13.5359i	0.168783	+	0.519461i
$680$		0			0
$681$	4.69305			0.179838
$682$	−0.476407	+	0.299064i	−0.0182426	+	0.0114517i
$683$	−19.1870			−0.734171			−0.367085	−	0.930187i	$-0.619644\pi$
$683$	−19.1870			−0.734171			−0.367085	+	0.930187i	$0.619644\pi$
$684$	−25.7698	+	18.7229i	−0.985335	+	0.715887i
$685$		0			0
$686$	−29.1639	+	89.7572i	−1.11348	+	3.42695i
$687$	16.8388	+	12.2341i	0.642440	+	0.466760i
$688$	−57.8972	−	42.0648i	−2.20731	−	1.60370i
$689$	−14.5377	+	44.7423i	−0.553841	+	1.70455i
$690$		0			0
$691$	−23.9225	+	17.3807i	−0.910054	+	0.661193i	−0.941028	−	0.338327i	$-0.890139\pi$
$691$	−23.9225	+	17.3807i	−0.910054	+	0.661193i	0.0309746	+	0.999520i	$0.490139\pi$
$692$	−112.726			−4.28521
$693$	5.78490	−	14.4038i	0.219750	−	0.547156i
$694$	−66.9726			−2.54225
$695$		0			0
$696$	−12.2627	−	37.7408i	−0.464818	−	1.43056i
$697$	−2.04613	+	6.29735i	−0.0775028	+	0.238529i
$698$	18.9137	+	13.7416i	0.715893	+	0.520127i
$699$	−4.23540	−	3.07720i	−0.160198	−	0.116390i
$700$		0			0
$701$	−3.99294	−	12.2890i	−0.150811	−	0.464150i	0.846901	−	0.531750i	$-0.178466\pi$
$701$	−3.99294	−	12.2890i	−0.150811	−	0.464150i	−0.997712	+	0.0676008i	$0.978466\pi$
$702$	7.38376	−	5.36462i	0.278682	−	0.202474i
$703$	−27.9774			−1.05519
$704$	1.13703	+	0.0771467i	0.0428536	+	0.00290758i
$705$		0			0
$706$	16.9353	−	12.3042i	0.637367	−	0.463074i
$707$	−1.45858	−	4.48905i	−0.0548555	−	0.168828i
$708$	−0.739552	+	2.27611i	−0.0277940	+	0.0855413i
$709$	31.5066	+	22.8909i	1.18325	+	0.859685i	0.992535	−	0.121960i	$-0.0389180\pi$
$709$	31.5066	+	22.8909i	1.18325	+	0.859685i	0.190719	+	0.981645i	$0.438918\pi$
$710$		0			0
$711$	2.33057	−	7.17274i	0.0874030	−	0.268999i
$712$	11.9908	+	36.9040i	0.449376	+	1.38304i
$713$	0.166025	−	0.120624i	0.00621768	−	0.00451741i
$714$	15.0637			0.563746
$715$		0			0
$716$	−63.8011			−2.38436
$717$	−10.3003	+	7.48363i	−0.384673	+	0.279481i
$718$	−3.86149	−	11.8844i	−0.144109	−	0.443523i
$719$	2.76283	−	8.50313i	0.103036	−	0.317113i	−0.886228	−	0.463249i	$-0.846684\pi$
$719$	2.76283	−	8.50313i	0.103036	−	0.317113i	0.989265	+	0.146136i	$0.0466836\pi$
$720$		0			0
$721$	25.3687	+	18.4315i	0.944781	+	0.686423i
$722$	−24.3423	+	74.9179i	−0.905927	+	2.78816i
$723$	−2.24502	−	6.90947i	−0.0834933	−	0.256966i
$724$	−39.2933	+	28.5482i	−1.46032	+	1.06099i
$725$		0			0
$726$	−12.1994	+	25.2773i	−0.452763	+	0.938129i
$727$	21.8843			0.811645			0.405822	−	0.913952i	$-0.366985\pi$
$727$	21.8843			0.811645			0.405822	+	0.913952i	$0.366985\pi$
$728$	86.7539	−	63.0304i	3.21531	−	2.33606i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	9.97266	+	7.24556i	0.368852	+	0.267987i
$732$	−22.3795	−	16.2596i	−0.827168	−	0.600973i
$733$	6.65654	−	20.4867i	0.245865	−	0.756695i	−0.749628	−	0.661859i	$-0.769768\pi$
$733$	6.65654	−	20.4867i	0.245865	−	0.756695i	0.995493	−	0.0948352i	$-0.0302324\pi$
$734$	6.47594	+	19.9309i	0.239031	+	0.735663i
$735$		0			0
$736$	−18.1389			−0.668610
$737$	−7.91117	−	6.61043i	−0.291412	−	0.243498i
$738$	−13.3932			−0.493012
$739$	−10.2697	+	7.46140i	−0.377778	+	0.274472i	−0.760429	−	0.649421i	$-0.775011\pi$
$739$	−10.2697	+	7.46140i	−0.377778	+	0.274472i	0.382651	+	0.923893i	$0.375011\pi$
$740$		0			0
$741$	7.80596	−	24.0243i	0.286759	−	0.882554i
$742$	−127.062	−	92.3163i	−4.66461	−	3.38904i
$743$	35.0121	+	25.4378i	1.28447	+	0.933222i	0.999678	−	0.0253671i	$-0.00807546\pi$
$743$	35.0121	+	25.4378i	1.28447	+	0.933222i	0.284792	+	0.958589i	$0.408075\pi$
$744$	0.131572	−	0.404937i	0.00482367	−	0.0148457i
$745$		0			0
$746$	4.90371	−	3.56276i	0.179538	−	0.130442i
$747$	−4.82325			−0.176474
$748$	−18.8276	−	1.27744i	−0.688405	−	0.0467077i
$749$	−36.4221			−1.33083
$750$		0			0
$751$	−3.87381	−	11.9224i	−0.141357	−	0.435053i	0.855167	−	0.518352i	$-0.173454\pi$
$751$	−3.87381	−	11.9224i	−0.141357	−	0.435053i	−0.996525	+	0.0832991i	$0.973454\pi$
$752$	12.2335	−	37.6508i	0.446110	−	1.37299i
$753$	−0.630031	−	0.457745i	−0.0229596	−	0.0166811i
$754$	45.7423	+	33.2337i	1.66584	+	1.21030i
$755$		0			0
$756$	6.52318	+	20.0763i	0.237246	+	0.730167i
$757$	5.19634	−	3.77536i	0.188864	−	0.137218i	−0.489335	−	0.872096i	$-0.662761\pi$
$757$	5.19634	−	3.77536i	0.188864	−	0.137218i	0.678199	+	0.734878i	$0.262761\pi$
$758$	40.8108			1.48232
$759$	3.81628	−	9.50216i	0.138522	−	0.344907i
$760$		0			0
$761$	9.25080	−	6.72110i	0.335341	−	0.243640i	−0.407352	−	0.913271i	$-0.633548\pi$
$761$	9.25080	−	6.72110i	0.335341	−	0.243640i	0.742694	+	0.669631i	$0.233548\pi$
$762$	10.6742	+	32.8519i	0.386686	+	1.19010i
$763$	−12.5103	+	38.5026i	−0.452902	+	1.39389i
$764$	−8.73307	−	6.34495i	−0.315951	−	0.229552i
$765$		0			0
$766$	−9.01918	+	27.7582i	−0.325876	+	1.00294i
$767$	−0.586487	−	1.80502i	−0.0211768	−	0.0651756i
$768$	23.0015	−	16.7115i	0.829994	−	0.603026i
$769$	−4.53314			−0.163469			−0.0817347	−	0.996654i	$-0.526046\pi$
$769$	−4.53314			−0.163469			−0.0817347	+	0.996654i	$0.526046\pi$
$770$		0			0
$771$	3.76613			0.135634
$772$	45.7672	−	33.2518i	1.64720	−	1.19676i
$773$	8.50349	+	26.1711i	0.305849	+	0.941307i	0.979359	+	0.202129i	$0.0647860\pi$
$773$	8.50349	+	26.1711i	0.305849	+	0.941307i	−0.673510	+	0.739178i	$0.735214\pi$
$774$	−7.70495	+	23.7134i	−0.276949	+	0.852361i
$775$		0			0
$776$	15.7598	+	11.4501i	0.565743	+	0.411036i
$777$	−5.72944	+	17.6334i	−0.205543	+	0.632595i
$778$	3.74082	+	11.5130i	0.134115	+	0.412763i
$779$	−29.9894	+	21.7886i	−1.07448	+	0.780656i
$780$		0			0
$781$	6.73650	+	26.7826i	0.241051	+	0.958355i
$782$	9.93751			0.355365
$783$	−5.01185	+	3.64132i	−0.179109	+	0.130130i
$784$	33.7272	+	103.802i	1.20454	+	3.70721i
$785$		0			0
$786$	−4.04936	−	2.94203i	−0.144436	−	0.104939i
$787$	−15.2852	−	11.1054i	−0.544860	−	0.395864i	0.281027	−	0.959700i	$-0.409325\pi$
$787$	−15.2852	−	11.1054i	−0.544860	−	0.395864i	−0.825887	+	0.563836i	$0.809325\pi$
$788$	−22.7777	+	70.1024i	−0.811420	+	2.49729i
$789$	−1.46976	−	4.52346i	−0.0523249	−	0.161040i
$790$		0			0
$791$	35.2104			1.25194
$792$	−5.18229	−	20.6034i	−0.184145	−	0.732112i
$793$	21.9372			0.779014
$794$	30.0393	−	21.8248i	1.06606	−	0.774534i
$795$		0			0
$796$	4.94949	−	15.2330i	0.175430	−	0.539918i
$797$	42.4072	+	30.8106i	1.50214	+	1.09137i	0.969520	+	0.245012i	$0.0787920\pi$
$797$	42.4072	+	30.8106i	1.50214	+	1.09137i	0.532619	+	0.846355i	$0.321208\pi$
$798$	68.2258	+	49.5690i	2.41517	+	1.75472i
$799$	−2.10719	+	6.48527i	−0.0745471	+	0.229432i
$800$		0			0
$801$	4.90073	−	3.56059i	0.173159	−	0.125807i
$802$	10.3576			0.365740
$803$	46.8647	−	29.4193i	1.65382	−	1.03818i
$804$	14.0204			0.494463
$805$		0			0
$806$	0.187465	+	0.576957i	0.00660317	+	0.0203225i
$807$	−7.91462	+	24.3587i	−0.278608	+	0.857467i
$808$	−5.22656	−	3.79732i	−0.183870	−	0.133589i
$809$	−33.7974	−	24.5552i	−1.18825	−	0.863316i	−0.195174	−	0.980769i	$-0.562527\pi$
$809$	−33.7974	−	24.5552i	−1.18825	−	0.863316i	−0.993079	+	0.117452i	$0.962527\pi$
$810$		0			0
$811$	0.863901	+	2.65881i	0.0303357	+	0.0933636i	0.965078	−	0.261963i	$-0.0843697\pi$
$811$	0.863901	+	2.65881i	0.0303357	+	0.0933636i	−0.934742	+	0.355326i	$0.884370\pi$
$812$	−105.797	+	76.8663i	−3.71276	+	2.69748i
$813$	−8.15990			−0.286180
$814$	12.4947	−	31.1105i	0.437938	−	1.09042i
$815$		0			0
$816$	7.47393	−	5.43013i	0.261640	−	0.190093i
$817$	21.3252	+	65.6324i	0.746076	+	2.29619i
$818$	29.7351	−	91.5154i	1.03966	−	3.19976i
$819$	−13.5433	−	9.83979i	−0.473241	−	0.343830i
$820$		0			0
$821$	10.6038	−	32.6350i	0.370074	−	1.13897i	−0.576669	−	0.816978i	$-0.695648\pi$
$821$	10.6038	−	32.6350i	0.370074	−	1.13897i	0.946742	−	0.321992i	$-0.104352\pi$
$822$	9.98816	+	30.7404i	0.348377	+	1.07219i
$823$	−16.5505	+	12.0246i	−0.576913	+	0.419152i	−0.837610	−	0.546269i	$-0.816048\pi$
$823$	−16.5505	+	12.0246i	−0.576913	+	0.419152i	0.260697	+	0.965421i	$0.416048\pi$
$824$	42.9192			1.49516
$825$		0			0
$826$	6.33612			0.220462
$827$	24.0909	−	17.5030i	0.837721	−	0.608640i	−0.0840120	−	0.996465i	$-0.526773\pi$
$827$	24.0909	−	17.5030i	0.837721	−	0.608640i	0.921733	+	0.387825i	$0.126773\pi$
$828$	4.30332	+	13.2443i	0.149551	+	0.460270i
$829$	7.09633	−	21.8403i	0.246466	−	0.758543i	−0.748926	−	0.662653i	$-0.769430\pi$
$829$	7.09633	−	21.8403i	0.246466	−	0.758543i	0.995392	−	0.0958900i	$-0.0305697\pi$
$830$		0			0
$831$	13.2479	+	9.62518i	0.459565	+	0.333894i
$832$	0.379813	−	1.16894i	0.0131676	−	0.0405259i
$833$	−5.80944	−	17.8796i	−0.201285	−	0.619492i
$834$	−7.37286	+	5.35670i	−0.255301	+	0.185487i
$835$		0			0
$836$	−81.0693	−	67.7400i	−2.80384	−	2.34284i
$837$	−0.0664687			−0.00229749
$838$	−46.0017	+	33.4222i	−1.58910	+	1.15455i
$839$	10.9370	+	33.6605i	0.377586	+	1.16209i	0.941718	+	0.336405i	$0.109211\pi$
$839$	10.9370	+	33.6605i	0.377586	+	1.16209i	−0.564132	+	0.825685i	$0.690789\pi$
$840$		0			0
$841$	−7.58686	−	5.51218i	−0.261616	−	0.190075i
$842$	20.3840	+	14.8099i	0.702480	+	0.510382i
$843$	−2.66312	+	8.19624i	−0.0917227	+	0.282293i
$844$	36.9422	+	113.697i	1.27160	+	3.91360i
$845$		0			0
$846$	−13.7929			−0.474210
$847$	51.0091	+	6.95386i	1.75269	+	0.238938i
$848$	−96.3204			−3.30766
$849$	−3.73564	+	2.71410i	−0.128207	+	0.0931476i
$850$		0			0
$851$	−3.77970	+	11.6327i	−0.129566	+	0.398764i
$852$	−30.3849	−	22.0759i	−1.04097	−	0.756308i
$853$	−26.3017	−	19.1093i	−0.900553	−	0.654290i	0.0380547	−	0.999276i	$-0.487884\pi$
$853$	−26.3017	−	19.1093i	−0.900553	−	0.654290i	−0.938608	+	0.344985i	$0.887884\pi$
$854$	−22.6314	+	69.6523i	−0.774430	+	2.38345i
$855$		0			0
$856$	−40.3304	+	29.3018i	−1.37847	+	1.00151i
$857$	−27.6562			−0.944717			−0.472359	−	0.881406i	$-0.656597\pi$
$857$	−27.6562			−0.944717			−0.472359	+	0.881406i	$0.656597\pi$
$858$	23.2286	+	19.4094i	0.793010	+	0.662625i
$859$	−22.5040			−0.767828			−0.383914	−	0.923369i	$-0.625424\pi$
$859$	−22.5040			−0.767828			−0.383914	+	0.923369i	$0.625424\pi$
$860$		0			0
$861$	7.59128	+	23.3636i	0.258710	+	0.796228i
$862$	−16.7575	+	51.5742i	−0.570761	+	1.75662i
$863$	16.0229	+	11.6413i	0.545425	+	0.396275i	0.826096	−	0.563529i	$-0.190557\pi$
$863$	16.0229	+	11.6413i	0.545425	+	0.396275i	−0.280671	+	0.959804i	$0.590557\pi$
$864$	4.75303	+	3.45328i	0.161701	+	0.117483i
$865$		0			0
$866$	8.94070	+	27.5166i	0.303817	+	0.935053i
$867$	12.4659	−	9.05702i	0.423365	−	0.307593i
$868$	−1.40312			−0.0476249
$869$	24.9562	+	1.69325i	0.846580	+	0.0574397i
$870$		0			0
$871$	−8.99517	+	6.53537i	−0.304790	+	0.221443i
$872$	17.1229	+	52.6988i	0.579854	+	1.78461i
$873$	0.939745	−	2.89224i	0.0318056	−	0.0978875i
$874$	45.0084	+	32.7005i	1.52243	+	1.10611i
$875$		0			0
$876$	−23.2540	+	71.5684i	−0.785679	+	2.41807i
$877$	−5.28357	−	16.2612i	−0.178414	−	0.549100i	0.821359	−	0.570411i	$-0.193216\pi$
$877$	−5.28357	−	16.2612i	−0.178414	−	0.549100i	−0.999773	+	0.0213106i	$0.993216\pi$
$878$	−72.5053	+	52.6782i	−2.44694	+	1.77780i
$879$	28.7041			0.968166
$880$		0			0
$881$	−2.50707			−0.0844655			−0.0422327	−	0.999108i	$-0.513447\pi$
$881$	−2.50707			−0.0844655			−0.0422327	+	0.999108i	$0.513447\pi$
$882$	30.7641	−	22.3514i	1.03588	−	0.752611i
$883$	4.72729	+	14.5491i	0.159086	+	0.489616i	0.998552	−	0.0537961i	$-0.0171321\pi$
$883$	4.72729	+	14.5491i	0.159086	+	0.489616i	−0.839466	+	0.543412i	$0.817132\pi$
$884$	−6.28914	+	19.3560i	−0.211527	+	0.651012i
$885$		0			0
$886$	22.6728	+	16.4727i	0.761706	+	0.553412i
$887$	11.7959	−	36.3041i	0.396068	−	1.21897i	−0.532058	−	0.846708i	$-0.678581\pi$
$887$	11.7959	−	36.3041i	0.396068	−	1.21897i	0.928127	−	0.372265i	$-0.121419\pi$
$888$	7.84193	+	24.1350i	0.263158	+	0.809917i
$889$	51.2577	−	37.2409i	1.71913	−	1.24902i
$890$		0			0
$891$	−2.80902	+	1.76336i	−0.0941056	+	0.0590746i
$892$	−73.2588			−2.45288
$893$	−30.8843	+	22.4388i	−1.03350	+	0.750884i
$894$	−15.7171	−	48.3724i	−0.525660	−	1.61781i
$895$		0			0
$896$	−41.1695	−	29.9114i	−1.37538	−	0.999271i
$897$	−8.93448	−	6.49128i	−0.298314	−	0.216738i
$898$	16.5965	−	51.0788i	0.553832	−	1.70452i
$899$	−0.127245	−	0.391619i	−0.00424385	−	0.0130612i
$900$		0			0
$901$	16.5910			0.552725
$902$	−10.8354	−	43.0786i	−0.360778	−	1.43436i
$903$	45.7335			1.52192
$904$	38.9887	−	28.3270i	1.29675	−	0.942140i
$905$		0			0
$906$	−2.36328	+	7.27342i	−0.0785147	+	0.241643i
$907$	−30.2406	−	21.9711i	−1.00412	−	0.729538i	−0.0411548	−	0.999153i	$-0.513104\pi$
$907$	−30.2406	−	21.9711i	−1.00412	−	0.729538i	−0.962968	+	0.269615i	$0.913104\pi$
$908$	−17.1252	−	12.4422i	−0.568320	−	0.412908i
$909$	−0.311657	+	0.959181i	−0.0103370	+	0.0318140i
$910$		0			0
$911$	−10.6651	+	7.74862i	−0.353349	+	0.256723i	−0.750273	−	0.661128i	$-0.770078\pi$
$911$	−10.6651	+	7.74862i	−0.353349	+	0.256723i	0.396923	+	0.917852i	$0.370078\pi$
$912$	51.7190			1.71259
$913$	−3.90209	−	15.5137i	−0.129140	−	0.513429i
$914$	5.87718			0.194400
$915$		0			0
$916$	−29.0107	−	89.2859i	−0.958542	−	2.95009i
$917$	−2.83699	+	8.73136i	−0.0936856	+	0.288335i
$918$	−2.60397	−	1.89190i	−0.0859440	−	0.0624419i
$919$	−29.4640	−	21.4069i	−0.971928	−	0.706147i	−0.0160380	−	0.999871i	$-0.505105\pi$
$919$	−29.4640	−	21.4069i	−0.971928	−	0.706147i	−0.955890	+	0.293724i	$0.905105\pi$
$920$		0			0
$921$	−4.95170	−	15.2398i	−0.163164	−	0.502167i
$922$	−54.5208	+	39.6117i	−1.79555	+	1.30454i
$923$	29.7845			0.980368
$924$	−59.2968	+	37.2235i	−1.95072	+	1.22456i
$925$		0			0
$926$	7.30986	−	5.31092i	0.240217	−	0.174528i
$927$	−2.07047	−	6.37226i	−0.0680033	−	0.209293i
$928$	−11.2470	+	34.6147i	−0.369200	+	1.13628i
$929$	−46.8900	−	34.0676i	−1.53841	−	1.11772i	−0.951321	−	0.308201i	$-0.900273\pi$
$929$	−46.8900	−	34.0676i	−1.53841	−	1.11772i	−0.587091	−	0.809521i	$-0.699727\pi$
$930$		0			0
$931$	32.5231	−	100.096i	1.06590	−	3.28051i
$932$	7.29697	+	22.4578i	0.239020	+	0.735628i
$933$	−6.86886	+	4.99052i	−0.224876	+	0.163382i
$934$	−15.4591			−0.505837
$935$		0			0
$936$	−22.9128			−0.748928
$937$	−23.2210	+	16.8710i	−0.758597	+	0.551153i	−0.898480	−	0.439015i	$-0.855328\pi$
$937$	−23.2210	+	16.8710i	−0.758597	+	0.551153i	0.139883	+	0.990168i	$0.455328\pi$
$938$	−11.4705	−	35.3025i	−0.374524	−	1.15267i
$939$	2.57263	−	7.91773i	0.0839545	−	0.258385i
$940$		0			0
$941$	35.9126	+	26.0920i	1.17072	+	0.850576i	0.991095	−	0.133160i	$-0.0425123\pi$
$941$	35.9126	+	26.0920i	1.17072	+	0.850576i	0.179623	+	0.983736i	$0.442512\pi$
$942$	5.23887	−	16.1236i	0.170691	−	0.525334i
$943$	5.00795	+	15.4129i	0.163081	+	0.501912i
$944$	3.14369	−	2.28402i	0.102318	−	0.0743386i
$945$		0			0
$946$	−82.5062	−	5.59798i	−2.68251	−	0.182006i
$947$	45.1635			1.46762			0.733808	−	0.679357i	$-0.237741\pi$
$947$	45.1635			1.46762			0.733808	+	0.679357i	$0.237741\pi$
$948$	−27.5207	+	19.9950i	−0.893832	+	0.649407i
$949$	−18.4411	−	56.7560i	−0.598624	−	1.84238i
$950$		0			0
$951$	23.9680	+	17.4138i	0.777216	+	0.564680i
$952$	−30.5948	−	22.2284i	−0.991584	−	0.720428i
$953$	−5.54050	+	17.0519i	−0.179474	+	0.552366i	−0.999810	−	0.0195176i	$-0.993787\pi$
$953$	−5.54050	+	17.0519i	−0.179474	+	0.552366i	0.820335	+	0.571883i	$0.193787\pi$
$954$	10.3702	+	31.9163i	0.335748	+	1.03333i
$955$		0			0
$956$	57.4271			1.85732
$957$	−15.7668	−	13.1744i	−0.509667	−	0.425869i
$958$	65.8559			2.12771
$959$	47.9631	−	34.8473i	1.54881	−	1.12528i
$960$		0			0
$961$	−9.57816	+	29.4786i	−0.308973	+	0.950921i
$962$	−29.2519	−	21.2527i	−0.943119	−	0.685216i
$963$	6.29606	+	4.57435i	0.202888	+	0.147406i
$964$	−10.1261	+	31.1651i	−0.326141	+	1.00376i
$965$		0			0
$966$	29.8275	−	21.6709i	0.959683	−	0.697251i
$967$	−13.2272			−0.425359			−0.212680	−	0.977122i	$-0.568219\pi$
$967$	−13.2272			−0.425359			−0.212680	+	0.977122i	$0.568219\pi$
$968$	62.0772	−	33.3371i	1.99524	−	1.07149i
$969$	−8.90847			−0.286181
$970$		0			0
$971$	7.03809	+	21.6610i	0.225863	+	0.695135i	0.998203	+	0.0599256i	$0.0190864\pi$
$971$	7.03809	+	21.6610i	0.225863	+	0.695135i	−0.772340	+	0.635210i	$0.780914\pi$
$972$	1.39382	−	4.28973i	0.0447067	−	0.137593i
$973$	13.5233	+	9.82526i	0.433538	+	0.314984i
$974$	−20.9477	−	15.2194i	−0.671208	−	0.487661i
$975$		0			0
$976$	13.8794	+	42.7163i	0.444268	+	1.36732i
$977$	−2.42978	+	1.76534i	−0.0777356	+	0.0564782i	−0.625974	−	0.779844i	$-0.715299\pi$
$977$	−2.42978	+	1.76534i	−0.0777356	+	0.0564782i	0.548239	+	0.836322i	$0.315299\pi$
$978$	−16.7307			−0.534988
$979$	15.4172	+	12.8823i	0.492736	+	0.411721i
$980$		0			0
$981$	6.99822	−	5.08451i	0.223436	−	0.162336i
$982$	21.0243	+	64.7061i	0.670912	+	2.06485i
$983$	−3.20721	+	9.87077i	−0.102294	+	0.314829i	−0.989086	−	0.147341i	$-0.952929\pi$
$983$	−3.20721	+	9.87077i	−0.102294	+	0.314829i	0.886792	+	0.462169i	$0.152929\pi$
$984$	27.2020	+	19.7634i	0.867168	+	0.630035i
$985$		0			0
$986$	6.16172	−	18.9638i	0.196229	−	0.603931i
$987$	7.81781	+	24.0608i	0.248844	+	0.765862i
$988$	−92.1775	+	66.9709i	−2.93256	+	2.13063i
$989$	30.1703			0.959359
$990$		0			0
$991$	10.8144			0.343529			0.171765	−	0.985138i	$-0.445053\pi$
$991$	10.8144			0.343529			0.171765	+	0.985138i	$0.445053\pi$
$992$	−0.315928	+	0.229535i	−0.0100307	+	0.00728775i
$993$	4.81234	+	14.8109i	0.152715	+	0.470009i
$994$	−30.7269	+	94.5678i	−0.974599	+	2.99951i
$995$		0			0
$996$	17.6003	+	12.7874i	0.557688	+	0.405184i
$997$	−1.55343	+	4.78096i	−0.0491976	+	0.151415i	−0.972637	−	0.232329i	$-0.925365\pi$
$997$	−1.55343	+	4.78096i	−0.0491976	+	0.151415i	0.923440	+	0.383744i	$0.125365\pi$
$998$	−10.5349	−	32.4230i	−0.333475	−	1.02633i
$999$	3.20504	−	2.32860i	0.101403	−	0.0736736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.l.751.2	yes	8
5.2	odd	4		825.2.bx.i.124.4		16
5.3	odd	4		825.2.bx.i.124.1		16
5.4	even	2		825.2.n.h.751.1	yes	8
11.2	odd	10		9075.2.a.dh.1.4		4
11.4	even	5	inner	825.2.n.l.301.2	yes	8
11.9	even	5		9075.2.a.cp.1.1		4
55.4	even	10		825.2.n.h.301.1	✓	8
55.9	even	10		9075.2.a.de.1.4		4
55.24	odd	10		9075.2.a.cn.1.1		4
55.37	odd	20		825.2.bx.i.499.1		16
55.48	odd	20		825.2.bx.i.499.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.h.301.1	✓	8	55.4	even	10
825.2.n.h.751.1	yes	8	5.4	even	2
825.2.n.l.301.2	yes	8	11.4	even	5	inner
825.2.n.l.751.2	yes	8	1.1	even	1	trivial
825.2.bx.i.124.1		16	5.3	odd	4
825.2.bx.i.124.4		16	5.2	odd	4
825.2.bx.i.499.1		16	55.37	odd	20
825.2.bx.i.499.4		16	55.48	odd	20
9075.2.a.cn.1.1		4	55.24	odd	10
9075.2.a.cp.1.1		4	11.9	even	5
9075.2.a.de.1.4		4	55.9	even	10
9075.2.a.dh.1.4		4	11.2	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.06426 - 1.49977i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.39382 - 4.28973i) q^{4} +(2.06426 + 1.49977i) q^{6} +(1.44623 - 4.45102i) q^{7} +(-1.97946 - 6.09215i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.54508 - 2.12663i) q^{11} +4.51049 q^{12} +(-2.89382 + 2.10248i) q^{13} +(-3.69014 - 11.3571i) q^{14} +(-5.92484 - 4.30465i) q^{16} +(1.02054 + 0.741466i) q^{17} +(-0.788477 + 2.42668i) q^{18} +(2.18229 + 6.71641i) q^{19} +4.68008 q^{21} +(-8.44317 - 0.572862i) q^{22} +3.08744 q^{23} +(5.18229 - 3.76516i) q^{24} +(-2.82035 + 8.68013i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-17.0779 - 12.4078i) q^{28} +(1.91436 - 5.89178i) q^{29} +(0.0537743 - 0.0390693i) q^{31} -5.87507 q^{32} +(1.23607 - 3.07768i) q^{33} +3.21869 q^{34} +(1.39382 + 4.28973i) q^{36} +(-1.22422 + 3.76775i) q^{37} +(14.5779 + 10.5915i) q^{38} +(-2.89382 - 2.10248i) q^{39} +(1.62204 + 4.99212i) q^{41} +(9.66091 - 7.01906i) q^{42} +9.77194 q^{43} +(-12.6700 + 7.95359i) q^{44} +(6.37328 - 4.63046i) q^{46} +(1.67044 + 5.14110i) q^{47} +(2.26309 - 6.96507i) q^{48} +(-12.0569 - 8.75988i) q^{49} +(-0.389812 + 1.19972i) q^{51} +(4.98562 + 15.3442i) q^{52} +(10.6404 - 7.73068i) q^{53} -2.55157 q^{54} -29.9791 q^{56} +(-5.71332 + 4.15097i) q^{57} +(-4.88461 - 15.0333i) q^{58} +(-0.163963 + 0.504625i) q^{59} +(-4.96165 - 3.60485i) q^{61} +(0.0524091 - 0.161298i) q^{62} +(1.44623 + 4.45102i) q^{63} +(-0.277992 + 0.201973i) q^{64} +(-2.06426 - 8.20696i) q^{66} +3.10841 q^{67} +(4.60313 - 3.34437i) q^{68} +(0.954071 + 2.93633i) q^{69} +(-6.73650 - 4.89435i) q^{71} +(5.18229 + 3.76516i) q^{72} +(-5.15554 + 15.8671i) q^{73} +(3.12367 + 9.61367i) q^{74} +31.8533 q^{76} +(-13.1464 + 8.25265i) q^{77} -9.12683 q^{78} +(-6.10150 + 4.43300i) q^{79} +(0.309017 - 0.951057i) q^{81} +(10.8354 + 7.87235i) q^{82} +(3.90209 + 2.83504i) q^{83} +(6.52318 - 20.0763i) q^{84} +(20.1718 - 14.6557i) q^{86} +6.19499 q^{87} +(-7.91784 + 19.7146i) q^{88} -6.05763 q^{89} +(5.17308 + 15.9211i) q^{91} +(4.30332 - 13.2443i) q^{92} +(0.0537743 + 0.0390693i) q^{93} +(11.1587 + 8.10727i) q^{94} +(-1.81550 - 5.58753i) q^{96} +(-2.46029 + 1.78750i) q^{97} -38.0265 q^{98} +(3.30902 + 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 2 q^{3} - 7 q^{4} + 3 q^{6} + 7 q^{7} - 16 q^{8} - 2 q^{9} + 2 q^{11} + 18 q^{12} - 5 q^{13} - 2 q^{14} - 11 q^{16} + 8 q^{17} - 2 q^{18} - 5 q^{19} - 8 q^{21} - 8 q^{22} - 2 q^{23} + 19 q^{24}+ \cdots + 22 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 2 * q^3 - 7 * q^4 + 3 * q^6 + 7 * q^7 - 16 * q^8 - 2 * q^9 + 2 * q^11 + 18 * q^12 - 5 * q^13 - 2 * q^14 - 11 * q^16 + 8 * q^17 - 2 * q^18 - 5 * q^19 - 8 * q^21 - 8 * q^22 - 2 * q^23 + 19 * q^24 - 32 * q^26 - 2 * q^27 - 51 * q^28 - 3 * q^29 + 5 * q^31 + 16 * q^32 - 8 * q^33 - 46 * q^34 - 7 * q^36 - 19 * q^37 + 31 * q^38 - 5 * q^39 - 18 * q^41 + 23 * q^42 + 52 * q^43 - 38 * q^44 + 33 * q^46 + 18 * q^47 + 4 * q^48 - 47 * q^49 - 7 * q^51 - 29 * q^52 + 31 * q^53 - 2 * q^54 - 68 * q^56 - 5 * q^57 - 35 * q^58 - 2 * q^59 - 22 * q^61 + 14 * q^62 + 7 * q^63 - 16 * q^64 - 3 * q^66 - 38 * q^67 - 2 * q^69 + 19 * q^72 - 18 * q^73 - 12 * q^74 + 92 * q^76 + 13 * q^77 + 18 * q^78 - 18 * q^79 - 2 * q^81 + 15 * q^82 - 28 * q^83 + 39 * q^84 + 53 * q^86 + 32 * q^87 - 64 * q^88 + 34 * q^89 + 33 * q^91 - 12 * q^92 + 5 * q^93 + 12 * q^94 - 14 * q^96 - 11 * q^97 - 24 * q^98 + 22 * q^99

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