LMFDB - Embedded newform 275.2.z.a.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(49,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("275.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.11316496000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.1
Root			$-1.28932 - 0.418926i$ of defining polynomial
Character	$\chi$	$=$	275.124
Dual form			275.2.z.a.224.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.796845 - 1.09676i) q^{2} +(0.547326 - 0.177837i) q^{3} +(0.0501062 - 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(-3.47080 - 1.12773i) q^{7} +(-2.78771 + 0.905781i) q^{8} +(-2.15911 + 1.56869i) q^{9} +(0.490303 - 3.28018i) q^{11} -0.0933146i q^{12} +(-1.66399 - 2.29029i) q^{13} +(1.52884 + 4.70527i) q^{14} +(2.95244 + 2.14507i) q^{16} +(2.17008 - 2.98685i) q^{17} +(3.44095 + 1.11803i) q^{18} +(0.0293950 + 0.0904686i) q^{19} -2.10021 q^{21} +(-3.98828 + 2.07605i) q^{22} -1.16215i q^{23} +(-1.36470 + 0.991515i) q^{24} +(-1.18596 + 3.65001i) q^{26} +(-1.91757 + 2.63930i) q^{27} +(-0.347817 + 0.478730i) q^{28} +(2.08707 - 6.42333i) q^{29} +(-5.48382 + 3.98423i) q^{31} +0.914918i q^{32} +(-0.314983 - 1.88253i) q^{33} -5.00509 q^{34} +(0.133724 + 0.411560i) q^{36} +(9.35820 + 3.04066i) q^{37} +(0.0757994 - 0.104329i) q^{38} +(-1.31805 - 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +(1.67354 + 2.30344i) q^{42} +2.96862i q^{43} +(-0.481274 - 0.239968i) q^{44} +(-1.27460 + 0.926052i) q^{46} +(2.11601 - 0.687534i) q^{47} +(1.99742 + 0.649001i) q^{48} +(5.11155 + 3.71376i) q^{49} +(0.656567 - 2.02070i) q^{51} +(-0.436565 + 0.141849i) q^{52} +(1.75979 + 2.42214i) q^{53} +4.42270 q^{54} +10.6970 q^{56} +(0.0321774 + 0.0442883i) q^{57} +(-8.70794 + 2.82938i) q^{58} +(2.62930 - 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(8.73951 + 2.83964i) q^{62} +(9.26289 - 3.00970i) q^{63} +(6.90832 - 5.01919i) q^{64} +(-1.81369 + 1.84554i) q^{66} -13.4153i q^{67} +(-0.351872 - 0.484310i) q^{68} +(-0.206673 - 0.636074i) q^{69} +(-6.71734 - 4.88043i) q^{71} +(4.59808 - 6.32872i) q^{72} +(1.25542 + 0.407912i) q^{73} +(-4.12215 - 12.6867i) q^{74} +0.0154241 q^{76} +(-5.40091 + 10.8319i) q^{77} +2.20866i q^{78} +(-11.2179 + 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-6.62834 + 9.12312i) q^{82} +(6.25666 - 8.61155i) q^{83} +(-0.105234 + 0.323876i) q^{84} +(3.25587 - 2.36553i) q^{86} -3.88682i q^{87} +(1.60431 + 9.58829i) q^{88} +12.1612 q^{89} +(3.19256 + 9.82567i) q^{91} +(-0.179216 - 0.0582308i) q^{92} +(-2.29290 + 3.15590i) q^{93} +(-2.44020 - 1.77291i) q^{94} +(0.162706 + 0.500759i) q^{96} +(2.54589 + 3.50412i) q^{97} -8.56545i q^{98} +(4.08696 + 7.85141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44}+ \cdots + 40 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.796845	−	1.09676i	−0.563455	−	0.775529i	0.428306	−	0.903634i	$-0.359111\pi$
$2$	−0.796845	−	1.09676i	−0.563455	−	0.775529i	−0.991761	+	0.128105i	$0.959111\pi$
$3$	0.547326	−	0.177837i	0.315999	−	0.102674i	−0.146723	−	0.989178i	$-0.546873\pi$
$3$	0.547326	−	0.177837i	0.315999	−	0.102674i	0.462722	+	0.886503i	$0.346873\pi$
$4$	0.0501062	−	0.154211i	0.0250531	−	0.0771056i
$5$		0			0
$5$		0			0
$6$	−0.631180	−	0.458579i	−0.257678	−	0.187214i
$7$	−3.47080	−	1.12773i	−1.31184	−	0.426242i	−0.432154	−	0.901800i	$-0.642246\pi$
$7$	−3.47080	−	1.12773i	−1.31184	−	0.426242i	−0.879685	+	0.475558i	$0.842246\pi$
$8$	−2.78771	+	0.905781i	−0.985603	+	0.320242i
$9$	−2.15911	+	1.56869i	−0.719704	+	0.522895i
$10$		0			0
$11$	0.490303	−	3.28018i	0.147832	−	0.989012i
$11$	0.490303	−	3.28018i	0.147832	−	0.989012i
$12$		−	0.0933146i		−	0.0269376i
$13$	−1.66399	−	2.29029i	−0.461509	−	0.635212i	0.513312	−	0.858202i	$-0.328418\pi$
$13$	−1.66399	−	2.29029i	−0.461509	−	0.635212i	−0.974821	+	0.222990i	$0.928418\pi$
$14$	1.52884	+	4.70527i	0.408599	+	1.25754i
$15$		0			0
$16$	2.95244	+	2.14507i	0.738109	+	0.536268i
$17$	2.17008	−	2.98685i	0.526321	−	0.724419i	−0.460243	−	0.887793i	$-0.652238\pi$
$17$	2.17008	−	2.98685i	0.526321	−	0.724419i	0.986564	+	0.163374i	$0.0522378\pi$
$18$	3.44095	+	1.11803i	0.811041	+	0.263523i
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	0.954372	−	0.298621i	$-0.0965267\pi$
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	−0.947628	+	0.319376i	$0.896527\pi$
$20$		0			0
$21$	−2.10021			−0.458304
$22$	−3.98828	+	2.07605i	−0.850304	+	0.442616i
$23$		−	1.16215i		−	0.242324i	−0.992633	−	0.121162i	$-0.961338\pi$
$23$		−	1.16215i		−	0.242324i	0.992633	−	0.121162i	$-0.0386621\pi$
$24$	−1.36470	+	0.991515i	−0.278569	+	0.202392i
$25$		0			0
$26$	−1.18596	+	3.65001i	−0.232586	+	0.715827i
$27$	−1.91757	+	2.63930i	−0.369036	+	0.507934i
$28$	−0.347817	+	0.478730i	−0.0657313	+	0.0904714i
$29$	2.08707	−	6.42333i	0.387559	−	1.19278i	−0.547049	−	0.837101i	$-0.684249\pi$
$29$	2.08707	−	6.42333i	0.387559	−	1.19278i	0.934607	−	0.355682i	$-0.115751\pi$
$30$		0			0
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.958803	−	0.284071i	$-0.908315\pi$
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.0261194	+	0.999659i	$0.508315\pi$
$32$			0.914918i			0.161736i
$33$	−0.314983	−	1.88253i	−0.0548314	−	0.327706i
$34$	−5.00509			−0.858366
$35$		0			0
$36$	0.133724	+	0.411560i	0.0222873	+	0.0685933i
$37$	9.35820	+	3.04066i	1.53848	+	0.499882i	0.950956	−	0.309326i	$-0.100103\pi$
$37$	9.35820	+	3.04066i	1.53848	+	0.499882i	0.587523	+	0.809208i	$0.300103\pi$
$38$	0.0757994	−	0.104329i	0.0122963	−	0.0169244i
$39$	−1.31805	−	0.957617i	−0.211056	−	0.153341i
$40$		0			0
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	−0.923831	−	0.382800i	$-0.874960\pi$
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	0.522391	−	0.852706i	$-0.325040\pi$
$42$	1.67354	+	2.30344i	0.258234	+	0.355428i
$43$			2.96862i			0.452710i	0.974045	+	0.226355i	$0.0726810\pi$
$43$			2.96862i			0.452710i	−0.974045	+	0.226355i	$0.927319\pi$
$44$	−0.481274	−	0.239968i	−0.0725547	−	0.0361765i
$45$		0			0
$46$	−1.27460	+	0.926052i	−0.187930	+	0.136539i
$47$	2.11601	−	0.687534i	0.308652	−	0.100287i	−0.150595	−	0.988595i	$-0.548119\pi$
$47$	2.11601	−	0.687534i	0.308652	−	0.100287i	0.459248	+	0.888308i	$0.348119\pi$
$48$	1.99742	+	0.649001i	0.288303	+	0.0936753i
$49$	5.11155	+	3.71376i	0.730221	+	0.530537i
$50$		0			0
$51$	0.656567	−	2.02070i	0.0919377	−	0.282955i
$52$	−0.436565	+	0.141849i	−0.0605407	+	0.0196708i
$53$	1.75979	+	2.42214i	0.241725	+	0.332706i	0.912592	−	0.408872i	$-0.134078\pi$
$53$	1.75979	+	2.42214i	0.241725	+	0.332706i	−0.670867	+	0.741578i	$0.734078\pi$
$54$	4.42270			0.601853
$55$		0			0
$56$	10.6970			1.42945
$57$	0.0321774	+	0.0442883i	0.00426200	+	0.00586613i
$58$	−8.70794	+	2.82938i	−1.14341	+	0.371516i
$59$	2.62930	−	8.09216i	0.342306	−	1.05351i	−0.620704	−	0.784045i	$-0.713153\pi$
$59$	2.62930	−	8.09216i	0.342306	−	1.05351i	0.963010	−	0.269465i	$-0.0868468\pi$
$60$		0			0
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	0.932836	−	0.360302i	$-0.117326\pi$
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	−0.0544052	+	0.998519i	$0.517326\pi$
$62$	8.73951	+	2.83964i	1.10992	+	0.360634i
$63$	9.26289	−	3.00970i	1.16702	−	0.379186i
$64$	6.90832	−	5.01919i	0.863541	−	0.627399i
$65$		0			0
$66$	−1.81369	+	1.84554i	−0.223250	+	0.227171i
$67$		−	13.4153i		−	1.63894i	−0.573123	−	0.819469i	$-0.694268\pi$
$67$		−	13.4153i		−	1.63894i	0.573123	−	0.819469i	$-0.305732\pi$
$68$	−0.351872	−	0.484310i	−0.0426707	−	0.0587312i
$69$	−0.206673	−	0.636074i	−0.0248805	−	0.0765743i
$70$		0			0
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	0.112890	−	0.993607i	$-0.463989\pi$
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	−0.910092	+	0.414406i	$0.863989\pi$
$72$	4.59808	−	6.32872i	0.541889	−	0.745846i
$73$	1.25542	+	0.407912i	0.146936	+	0.0477425i	0.381562	−	0.924343i	$-0.375386\pi$
$73$	1.25542	+	0.407912i	0.146936	+	0.0477425i	−0.234625	+	0.972086i	$0.575386\pi$
$74$	−4.12215	−	12.6867i	−0.479190	−	1.47480i
$75$		0			0
$76$	0.0154241			0.00176927
$77$	−5.40091	+	10.8319i	−0.615491	+	1.23441i
$78$			2.20866i			0.250081i
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.998859	−	0.0477484i	$-0.984795\pi$
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.263253	+	0.964727i	$0.584795\pi$
$80$		0			0
$81$	1.89395	−	5.82899i	0.210439	−	0.647665i
$82$	−6.62834	+	9.12312i	−0.731977	+	1.00748i
$83$	6.25666	−	8.61155i	0.686757	−	0.945240i	−0.313233	−	0.949676i	$-0.601412\pi$
$83$	6.25666	−	8.61155i	0.686757	−	0.945240i	0.999990	+	0.00443607i	$0.00141205\pi$
$84$	−0.105234	+	0.323876i	−0.0114819	+	0.0353378i
$85$		0			0
$86$	3.25587	−	2.36553i	0.351090	−	0.255082i
$87$		−	3.88682i		−	0.416710i
$88$	1.60431	+	9.58829i	0.171020	+	1.02212i
$89$	12.1612			1.28908			0.644540	−	0.764570i	$-0.277049\pi$
$89$	12.1612			1.28908			0.644540	+	0.764570i	$0.277049\pi$
$90$		0			0
$91$	3.19256	+	9.82567i	0.334671	+	1.03001i
$92$	−0.179216	−	0.0582308i	−0.0186846	−	0.00607098i
$93$	−2.29290	+	3.15590i	−0.237762	+	0.327252i
$94$	−2.44020	−	1.77291i	−0.251687	−	0.182861i
$95$		0			0
$96$	0.162706	+	0.500759i	0.0166062	+	0.0511085i
$97$	2.54589	+	3.50412i	0.258496	+	0.355789i	0.918464	−	0.395504i	$-0.129430\pi$
$97$	2.54589	+	3.50412i	0.258496	+	0.355789i	−0.659968	+	0.751294i	$0.729430\pi$
$98$		−	8.56545i		−	0.865241i
$99$	4.08696	+	7.85141i	0.410755	+	0.789096i
$100$		0			0
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	−0.910153	−	0.414271i	$-0.864036\pi$
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	0.112743	+	0.993624i	$0.464036\pi$
$102$	−2.73942	+	0.890091i	−0.271243	+	0.0881321i
$103$	−3.86690	−	1.25643i	−0.381017	−	0.123800i	0.112245	−	0.993681i	$-0.464196\pi$
$103$	−3.86690	−	1.25643i	−0.381017	−	0.123800i	−0.493263	+	0.869880i	$0.664196\pi$
$104$	6.71323	+	4.87744i	0.658286	+	0.478273i
$105$		0			0
$106$	1.25424	−	3.86014i	0.121822	−	0.374930i
$107$	−1.84369	+	0.599053i	−0.178237	+	0.0579126i	−0.396776	−	0.917916i	$-0.629871\pi$
$107$	−1.84369	+	0.599053i	−0.178237	+	0.0579126i	0.218539	+	0.975828i	$0.429871\pi$
$108$	0.310928	+	0.427956i	0.0299191	+	0.0411801i
$109$	−6.12664			−0.586825			−0.293413	−	0.955986i	$-0.594791\pi$
$109$	−6.12664			−0.586825			−0.293413	+	0.955986i	$0.594791\pi$
$110$		0			0
$111$	5.66273			0.537483
$112$	−7.82825	−	10.7747i	−0.739700	−	1.01811i
$113$	5.50212	−	1.78775i	0.517596	−	0.168177i	−0.0385582	−	0.999256i	$-0.512276\pi$
$113$	5.50212	−	1.78775i	0.517596	−	0.168177i	0.556154	+	0.831079i	$0.312276\pi$
$114$	0.0229335	−	0.0705819i	0.00214791	−	0.00661060i
$115$		0			0
$116$	−0.885974	−	0.643698i	−0.0822606	−	0.0597659i
$117$	7.18549	+	2.33471i	0.664299	+	0.215844i
$118$	−10.9703	+	3.56448i	−1.00990	+	0.328137i
$119$	−10.9003	+	7.91951i	−0.999226	+	0.725980i
$120$		0			0
$121$	−10.5192	−	3.21657i	−0.956291	−	0.292415i
$122$		−	11.4966i		−	1.04085i
$123$	−2.81377	−	3.87283i	−0.253710	−	0.349201i
$124$	0.339639	+	1.04530i	0.0305005	+	0.0938708i
$125$		0			0
$126$	−10.6820	−	7.76094i	−0.951630	−	0.691400i
$127$	1.43292	−	1.97224i	0.127151	−	0.175008i	−0.740695	−	0.671841i	$-0.765504\pi$
$127$	1.43292	−	1.97224i	0.127151	−	0.175008i	0.867846	+	0.496833i	$0.165504\pi$
$128$	−9.26945	−	3.01183i	−0.819312	−	0.266211i
$129$	0.527931	+	1.62480i	0.0464817	+	0.143056i
$130$		0			0
$131$	7.04156			0.615224			0.307612	−	0.951512i	$-0.400470\pi$
$131$	7.04156			0.615224			0.307612	+	0.951512i	$0.400470\pi$
$132$	−0.306089	−	0.0457524i	−0.0266416	−	0.00398224i
$133$		−	0.347148i		−	0.0301016i
$134$	−14.7134	+	10.6899i	−1.27104	+	0.923468i
$135$		0			0
$136$	−3.34410	+	10.2921i	−0.286754	+	0.882539i
$137$	−5.62678	+	7.74461i	−0.480729	+	0.661666i	−0.978645	−	0.205559i	$-0.934099\pi$
$137$	−5.62678	+	7.74461i	−0.480729	+	0.661666i	0.497916	+	0.867225i	$0.334099\pi$
$138$	−0.532936	+	0.733524i	−0.0453666	+	0.0624417i
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	−0.957585	−	0.288151i	$-0.906959\pi$
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	0.944073	+	0.329735i	$0.106959\pi$
$140$		0			0
$141$	1.03588	−	0.752611i	0.0872369	−	0.0633813i
$142$			11.2563i			0.944607i
$143$	−8.32843	+	4.33527i	−0.696459	+	0.362533i
$144$	−9.73958			−0.811632
$145$		0			0
$146$	−0.552996	−	1.70195i	−0.0457663	−	0.140854i
$147$	3.45813	+	1.12361i	0.285222	+	0.0926742i
$148$	0.937809	−	1.29078i	0.0770874	−	0.106102i
$149$	−6.60144	−	4.79623i	−0.540811	−	0.392922i	0.283575	−	0.958950i	$-0.408479\pi$
$149$	−6.60144	−	4.79623i	−0.540811	−	0.392922i	−0.824386	+	0.566028i	$0.808479\pi$
$150$		0			0
$151$	0.599563	+	1.84526i	0.0487917	+	0.150165i	0.972484	−	0.232970i	$-0.0748443\pi$
$151$	0.599563	+	1.84526i	0.0487917	+	0.150165i	−0.923692	+	0.383135i	$0.874844\pi$
$152$	−0.163889	−	0.225574i	−0.0132932	−	0.0182965i
$153$			9.85312i			0.796577i
$154$	16.1838	−	2.70785i	1.30412	−	0.218205i
$155$		0			0
$156$	−0.213718	+	0.155275i	−0.0171111	+	0.0124319i
$157$	−20.2332	+	6.57418i	−1.61479	+	0.524676i	−0.970704	−	0.240279i	$-0.922761\pi$
$157$	−20.2332	+	6.57418i	−1.61479	+	0.524676i	−0.644084	+	0.764955i	$0.722761\pi$
$158$	17.8779	+	5.80887i	1.42229	+	0.462129i
$159$	1.39392	+	1.01274i	0.110545	+	0.0803159i
$160$		0			0
$161$	−1.31059	+	4.03358i	−0.103289	+	0.317891i
$162$	−7.90221	+	2.56758i	−0.620856	+	0.201728i
$163$	−9.39337	−	12.9289i	−0.735746	−	1.01267i	−0.998852	−	0.0479001i	$-0.984747\pi$
$163$	−9.39337	−	12.9289i	−0.735746	−	1.01267i	0.263107	−	0.964767i	$-0.415253\pi$
$164$	−1.34878			−0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	−10.4091	−	14.3269i	−0.805481	−	1.10865i	−0.992005	−	0.126199i	$-0.959722\pi$
$167$	−10.4091	−	14.3269i	−0.805481	−	1.10865i	0.186524	−	0.982450i	$-0.440278\pi$
$168$	5.85477	−	1.90233i	0.451706	−	0.146768i
$169$	1.54066	−	4.74168i	0.118513	−	0.364744i
$170$		0			0
$171$	−0.205384	−	0.149220i	−0.0157061	−	0.0114112i
$172$	0.457794	+	0.148746i	0.0349065	+	0.0113418i
$173$	15.1080	−	4.90888i	1.14864	−	0.373216i	0.328009	−	0.944675i	$-0.393622\pi$
$173$	15.1080	−	4.90888i	1.14864	−	0.373216i	0.820631	+	0.571459i	$0.193622\pi$
$174$	−4.26292	+	3.09719i	−0.323171	+	0.234798i
$175$		0			0
$176$	8.48382	−	8.63280i	0.639492	−	0.650722i
$177$		−	4.89664i		−	0.368054i
$178$	−9.69057	−	13.3379i	−0.726339	−	0.999719i
$179$	5.21653	+	16.0548i	0.389902	+	1.19999i	0.932862	+	0.360235i	$0.117304\pi$
$179$	5.21653	+	16.0548i	0.389902	+	1.19999i	−0.542960	+	0.839759i	$0.682696\pi$
$180$		0			0
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.986187	+	0.165636i	$0.0529676\pi$
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.462277	+	0.886735i	$0.347032\pi$
$182$	8.23247	−	11.3310i	0.610231	−	0.839911i
$183$	4.64153	+	1.50812i	0.343112	+	0.111484i
$184$	1.05265	+	3.23972i	0.0776024	+	0.238836i
$185$		0			0
$186$	5.28836			0.387761
$187$	−8.73343	−	8.58271i	−0.638652	−	0.627630i
$188$		−	0.360762i		−	0.0263113i
$189$	9.63191	−	6.99800i	0.700619	−	0.509029i
$190$		0			0
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	−0.872669	−	0.488312i	$-0.837613\pi$
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	0.993027	+	0.117890i	$0.0376129\pi$
$192$	2.88851	−	3.97569i	0.208460	−	0.286921i
$193$	−10.7471	+	14.7921i	−0.773593	+	1.06476i	0.222367	+	0.974963i	$0.428622\pi$
$193$	−10.7471	+	14.7921i	−0.773593	+	1.06476i	−0.995960	+	0.0897961i	$0.971378\pi$
$194$	1.81451	−	5.58448i	0.130274	−	0.400942i
$195$		0			0
$196$	0.828823	−	0.602175i	0.0592017	−	0.0430125i
$197$			2.64566i			0.188496i	0.995549	+	0.0942478i	$0.0300446\pi$
$197$			2.64566i			0.188496i	−0.995549	+	0.0942478i	$0.969955\pi$
$198$	5.35447	−	10.7388i	0.380525	−	0.763172i
$199$	−6.52800			−0.462757			−0.231379	−	0.972864i	$-0.574324\pi$
$199$	−6.52800			−0.462757			−0.231379	+	0.972864i	$0.574324\pi$
$200$		0			0
$201$	−2.38574	−	7.34254i	−0.168277	−	0.517903i
$202$	12.7716	+	4.14976i	0.898610	+	0.291976i
$203$	−14.4876	+	19.9404i	−1.01683	+	1.39954i
$204$	−0.278717	−	0.202500i	−0.0195141	−	0.0141778i
$205$		0			0
$206$	1.70331	+	5.24226i	0.118676	+	0.365246i
$207$	1.82304	+	2.50920i	0.126710	+	0.174402i
$208$		−	10.3313i		−	0.716349i
$209$	0.311166	−	0.0520641i	0.0215238	−	0.00360135i
$210$		0			0
$211$	22.2057	−	16.1334i	1.52871	−	1.11067i	0.571752	−	0.820426i	$-0.306264\pi$
$211$	22.2057	−	16.1334i	1.52871	−	1.11067i	0.956953	−	0.290243i	$-0.0937362\pi$
$212$	0.461697	−	0.150014i	0.0317095	−	0.0103030i
$213$	−4.54450	−	1.47660i	−0.311384	−	0.101175i
$214$	2.12616	+	1.54474i	0.145341	+	0.105597i
$215$		0			0
$216$	2.95498	−	9.09450i	0.201061	−	0.618802i
$217$	23.5264	−	7.64418i	1.59707	−	0.518921i
$218$	4.88198	+	6.71947i	0.330650	+	0.455100i
$219$	0.759669			0.0513337
$220$		0			0
$221$	−10.4518			−0.703061
$222$	−4.51232	−	6.21068i	−0.302847	−	0.416834i
$223$	−4.83321	+	1.57040i	−0.323656	+	0.105162i	−0.466338	−	0.884606i	$-0.654427\pi$
$223$	−4.83321	+	1.57040i	−0.323656	+	0.105162i	0.142683	+	0.989768i	$0.454427\pi$
$224$	1.03178	−	3.17550i	0.0689388	−	0.212172i
$225$		0			0
$226$	−6.34507	−	4.60997i	−0.422068	−	0.306650i
$227$	3.55676	+	1.15566i	0.236071	+	0.0767040i	0.424663	−	0.905351i	$-0.360393\pi$
$227$	3.55676	+	1.15566i	0.236071	+	0.0767040i	−0.188593	+	0.982055i	$0.560393\pi$
$228$	0.00844204	−	0.00274299i	0.000559088	−	0.000181659i
$229$	21.7821	−	15.8256i	1.43940	−	1.04578i	0.451232	−	0.892407i	$-0.350985\pi$
$229$	21.7821	−	15.8256i	1.43940	−	1.04578i	0.988168	−	0.153378i	$-0.0490152\pi$
$230$		0			0
$231$	−1.02974	+	6.88908i	−0.0677520	+	0.453268i
$232$			19.7968i			1.29972i
$233$	10.7663	+	14.8185i	0.705323	+	0.970794i	0.999885	+	0.0151615i	$0.00482625\pi$
$233$	10.7663	+	14.8185i	0.705323	+	0.970794i	−0.294562	+	0.955632i	$0.595174\pi$
$234$	−3.16510	−	9.74119i	−0.206909	−	0.636801i
$235$		0			0
$236$	−1.11616	−	0.810936i	−0.0726557	−	0.0527874i
$237$	−4.69043	+	6.45582i	−0.304676	+	0.419351i
$238$	17.3717	+	5.64439i	1.12604	+	0.365872i
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	0.998846	+	0.0480283i	$0.0152938\pi$
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	−0.779853	+	0.625963i	$0.784706\pi$
$240$		0			0
$241$	−9.99444			−0.643798			−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444			−0.643798			−0.321899	+	0.946774i	$0.604321\pi$
$242$	4.85437	+	14.1002i	0.312050	+	0.906394i
$243$		−	13.3143i		−	0.854110i
$244$	1.11245	−	0.808245i	0.0712175	−	0.0517426i
$245$		0			0
$246$	−2.00543	+	6.17209i	−0.127862	+	0.393518i
$247$	0.158286	−	0.217862i	0.0100715	−	0.0138622i
$248$	11.6784	−	16.0740i	0.741581	−	1.02070i
$249$	1.89298	−	5.82599i	0.119963	−	0.369207i
$250$		0			0
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	−0.806396	−	0.591376i	$-0.798585\pi$
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	0.313242	+	0.949673i	$0.398585\pi$
$252$		−	1.57925i		−	0.0994832i
$253$	−3.81206	−	0.569804i	−0.239662	−	0.0358233i
$254$	−3.30490			−0.207368
$255$		0			0
$256$	−1.19443	−	3.67608i	−0.0746520	−	0.229755i
$257$	9.91721	+	3.22230i	0.618618	+	0.201001i	0.601527	−	0.798853i	$-0.294559\pi$
$257$	9.91721	+	3.22230i	0.618618	+	0.201001i	0.0170916	+	0.999854i	$0.494559\pi$
$258$	1.36135	−	1.87373i	0.0847538	−	0.116654i
$259$	−29.0514	−	21.1071i	−1.80517	−	1.31153i
$260$		0			0
$261$	5.56998	+	17.1426i	0.344773	+	1.06110i
$262$	−5.61103	−	7.72292i	−0.346651	−	0.477124i
$263$			10.9619i			0.675937i	0.941157	+	0.337968i	$0.109740\pi$
$263$			10.9619i			0.675937i	−0.941157	+	0.337968i	$0.890260\pi$
$264$	2.58323	+	4.96262i	0.158987	+	0.305428i
$265$		0			0
$266$	−0.380739	+	0.276623i	−0.0233446	+	0.0169609i
$267$	6.65613	−	2.16271i	0.407348	−	0.132355i
$268$	−2.06879	−	0.672190i	−0.126371	−	0.0410605i
$269$	−0.0722816	−	0.0525156i	−0.00440708	−	0.00320193i	0.585580	−	0.810615i	$-0.300867\pi$
$269$	−0.0722816	−	0.0525156i	−0.00440708	−	0.00320193i	−0.589987	+	0.807413i	$0.700867\pi$
$270$		0			0
$271$	−4.14069	+	12.7437i	−0.251529	+	0.774126i	0.742965	+	0.669330i	$0.233419\pi$
$271$	−4.14069	+	12.7437i	−0.251529	+	0.774126i	−0.994494	+	0.104796i	$0.966581\pi$
$272$	12.8140	−	4.16353i	0.776965	−	0.252451i
$273$	3.49474	+	4.81010i	0.211511	+	0.291120i
$274$	12.9777			0.784010
$275$		0			0
$276$	−0.108445			−0.00652764
$277$	2.29629	+	3.16057i	0.137971	+	0.189901i	0.872411	−	0.488773i	$-0.162555\pi$
$277$	2.29629	+	3.16057i	0.137971	+	0.189901i	−0.734440	+	0.678673i	$0.762555\pi$
$278$	0.664648	−	0.215957i	0.0398630	−	0.0129523i
$279$	5.59017	−	17.2048i	0.334675	−	1.03002i
$280$		0			0
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	0.624267	−	0.781211i	$-0.285398\pi$
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	−0.550067	+	0.835120i	$0.685398\pi$
$282$	−1.65087	−	0.536401i	−0.0983081	−	0.0319422i
$283$	−5.14683	+	1.67231i	−0.305947	+	0.0994083i	−0.457967	−	0.888969i	$-0.651422\pi$
$283$	−5.14683	+	1.67231i	−0.305947	+	0.0994083i	0.152020	+	0.988377i	$0.451422\pi$
$284$	−1.08920	+	0.791349i	−0.0646320	+	0.0469579i
$285$		0			0
$286$	11.3912	+	5.67979i	0.673578	+	0.335853i
$287$			30.3566i			1.79190i
$288$	−1.43522	−	1.97541i	−0.0845711	−	0.116402i
$289$	1.04122	+	3.20456i	0.0612484	+	0.188503i
$290$		0			0
$291$	2.01659	+	1.46514i	0.118215	+	0.0858881i
$292$	0.125809	−	0.173162i	0.00736243	−	0.0101335i
$293$	−10.8577	−	3.52789i	−0.634315	−	0.206102i	−0.0258295	−	0.999666i	$-0.508223\pi$
$293$	−10.8577	−	3.52789i	−0.634315	−	0.206102i	−0.608486	+	0.793565i	$0.708223\pi$
$294$	−1.52326	−	4.68810i	−0.0888381	−	0.273415i
$295$		0			0
$296$	−28.8421			−1.67641
$297$	7.71721	+	7.58403i	0.447798	+	0.440070i
$298$			11.0621i			0.640808i
$299$	−2.66165	+	1.93381i	−0.153927	+	0.111835i
$300$		0			0
$301$	3.34780	−	10.3035i	0.192964	−	0.593883i
$302$	1.54606	−	2.12797i	0.0889657	−	0.122451i
$303$	−3.35077	+	4.61193i	−0.192496	+	0.264949i
$304$	−0.107275	+	0.330157i	−0.00615262	+	0.0189358i
$305$		0			0
$306$	10.8065	−	7.85141i	0.617769	−	0.448835i
$307$		−	4.25008i		−	0.242565i	−0.992618	−	0.121282i	$-0.961299\pi$
$307$		−	4.25008i		−	0.242565i	0.992618	−	0.121282i	$-0.0387007\pi$
$308$	1.39978	+	1.37563i	0.0797601	+	0.0783836i
$309$	−2.33990			−0.133112
$310$		0			0
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	−0.984465	−	0.175579i	$-0.943820\pi$
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	0.693247	−	0.720700i	$-0.256180\pi$
$312$	4.54172	+	1.47569i	0.257124	+	0.0835447i
$313$	15.6215	−	21.5012i	0.882982	−	1.21532i	−0.0926041	−	0.995703i	$-0.529519\pi$
$313$	15.6215	−	21.5012i	0.882982	−	1.21532i	0.975586	−	0.219617i	$-0.0704809\pi$
$314$	23.3331	+	16.9525i	1.31676	+	0.956683i
$315$		0			0
$316$	0.694778	+	2.13831i	0.0390843	+	0.120289i
$317$	−3.40736	−	4.68982i	−0.191376	−	0.263407i	0.702537	−	0.711648i	$-0.252051\pi$
$317$	−3.40736	−	4.68982i	−0.191376	−	0.263407i	−0.893913	+	0.448241i	$0.852051\pi$
$318$		−	2.33581i		−	0.130985i
$319$	−20.0464	−	9.99534i	−1.12238	−	0.559632i
$320$		0			0
$321$	−0.902569	+	0.655755i	−0.0503765	+	0.0366007i
$322$	5.46822	−	1.77673i	0.304732	−	0.0990134i
$323$	0.334006	+	0.108525i	0.0185846	+	0.00603850i
$324$	−0.803996	−	0.584137i	−0.0446664	−	0.0324521i
$325$		0			0
$326$	−6.69484	+	20.6046i	−0.370793	+	1.14118i
$327$	−3.35327	+	1.08954i	−0.185436	+	0.0602519i
$328$	14.3314	+	19.7255i	0.791321	+	1.08916i
$329$	−8.11961			−0.447648
$330$		0			0
$331$	−12.9230			−0.710311			−0.355155	−	0.934807i	$-0.615572\pi$
$331$	−12.9230			−0.710311			−0.355155	+	0.934807i	$0.615572\pi$
$332$	−1.01450	−	1.39634i	−0.0556779	−	0.0766340i
$333$	−24.9752	+	8.11495i	−1.36863	+	0.444696i
$334$	−7.41878	+	22.8327i	−0.405938	+	1.24935i
$335$		0			0
$336$	−6.20075	−	4.50511i	−0.338278	−	0.245774i
$337$	12.7303	+	4.13631i	0.693461	+	0.225319i	0.634479	−	0.772940i	$-0.281215\pi$
$337$	12.7303	+	4.13631i	0.693461	+	0.225319i	0.0589818	+	0.998259i	$0.481215\pi$
$338$	−6.42817	+	2.08864i	−0.349646	+	0.113607i
$339$	2.69353	−	1.95696i	0.146292	−	0.106288i
$340$		0			0
$341$	10.3803	+	19.9414i	0.562123	+	1.07989i
$342$			0.344163i			0.0186102i
$343$	1.46246	+	2.01291i	0.0789656	+	0.108687i
$344$	−2.68892	−	8.27564i	−0.144977	−	0.446193i
$345$		0			0
$346$	−17.4226	−	12.6583i	−0.936646	−	0.680513i
$347$	−4.96619	+	6.83538i	−0.266599	+	0.366942i	−0.921238	−	0.389000i	$-0.872821\pi$
$347$	−4.96619	+	6.83538i	−0.266599	+	0.366942i	0.654639	+	0.755942i	$0.272821\pi$
$348$	−0.599391	−	0.194754i	−0.0321307	−	0.0104399i
$349$	3.21341	+	9.88987i	0.172010	+	0.529393i	0.999484	−	0.0321111i	$-0.0102230\pi$
$349$	3.21341	+	9.88987i	0.172010	+	0.529393i	−0.827474	+	0.561504i	$0.810223\pi$
$350$		0			0
$351$	9.23559			0.492959
$352$	3.00110	+	0.448587i	0.159959	+	0.0239098i
$353$		−	19.1073i		−	1.01698i	−0.861069	−	0.508489i	$-0.830204\pi$
$353$		−	19.1073i		−	1.01698i	0.861069	−	0.508489i	$-0.169796\pi$
$354$	−5.37046	+	3.90187i	−0.285437	+	0.207382i
$355$		0			0
$356$	0.609350	−	1.87539i	0.0322955	−	0.0993953i
$357$	−4.55762	+	6.27303i	−0.241215	+	0.332004i
$358$	13.4516	−	18.5145i	0.710938	−	0.978522i
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	−0.908586	−	0.417698i	$-0.862837\pi$
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	0.980578	+	0.196129i	$0.0628371\pi$
$360$		0			0
$361$	15.3640	−	11.1626i	0.808632	−	0.587505i
$362$		−	32.6546i		−	1.71629i
$363$	−6.32946	+	0.110193i	−0.332211	+	0.00578362i
$364$	1.67520			0.0878041
$365$		0			0
$366$	−2.04453	−	6.29240i	−0.106869	−	0.328909i
$367$	−27.9247	−	9.07327i	−1.45766	−	0.473621i	−0.530302	−	0.847809i	$-0.677922\pi$
$367$	−27.9247	−	9.07327i	−1.45766	−	0.473621i	−0.927353	+	0.374188i	$0.877922\pi$
$368$	2.49289	−	3.43117i	0.129951	−	0.178862i
$369$	17.9600	+	13.0487i	0.934958	+	0.679287i
$370$		0			0
$371$	−3.37634	−	10.3913i	−0.175291	−	0.539490i
$372$	0.371787	+	0.511720i	0.0192762	+	0.0265315i
$373$			4.96478i			0.257067i	0.991705	+	0.128533i	$0.0410269\pi$
$373$			4.96478i			0.257067i	−0.991705	+	0.128533i	$0.958973\pi$
$374$	−2.45401	+	16.4176i	−0.126894	+	0.848934i
$375$		0			0
$376$	−5.27606	+	3.83329i	−0.272092	+	0.197687i
$377$	−18.1842	+	5.90839i	−0.936532	+	0.304298i
$378$	−15.3503	−	4.98761i	−0.789534	−	0.256535i
$379$	6.40996	+	4.65711i	0.329258	+	0.239220i	0.740116	−	0.672480i	$-0.234771\pi$
$379$	6.40996	+	4.65711i	0.329258	+	0.239220i	−0.410858	+	0.911699i	$0.634771\pi$
$380$		0			0
$381$	0.433536	−	1.33429i	0.0222107	−	0.0683576i
$382$	−6.94016	+	2.25499i	−0.355089	+	0.115375i
$383$	−14.4099	−	19.8335i	−0.736309	−	1.01344i	−0.998823	−	0.0485140i	$-0.984551\pi$
$383$	−14.4099	−	19.8335i	−0.736309	−	1.01344i	0.262514	−	0.964928i	$-0.415449\pi$
$384$	−5.60903			−0.286235
$385$		0			0
$386$	24.7872			1.26164
$387$	−4.65683	−	6.40958i	−0.236720	−	0.325817i
$388$	0.667939	−	0.217026i	0.0339095	−	0.0110179i
$389$	−1.68752	+	5.19366i	−0.0855608	+	0.263329i	−0.984679	−	0.174377i	$-0.944209\pi$
$389$	−1.68752	+	5.19366i	−0.0855608	+	0.263329i	0.899118	+	0.437706i	$0.144209\pi$
$390$		0			0
$391$	−3.47116	−	2.52195i	−0.175544	−	0.127540i
$392$	−17.6133	−	5.72292i	−0.889608	−	0.289051i
$393$	3.85403	−	1.25225i	0.194410	−	0.0631677i
$394$	2.90166	−	2.10818i	0.146184	−	0.106209i
$395$		0			0
$396$	1.41556	−	0.236850i	0.0711344	−	0.0119022i
$397$		−	6.43455i		−	0.322941i	−0.986878	−	0.161470i	$-0.948376\pi$
$397$		−	6.43455i		−	0.322941i	0.986878	−	0.161470i	$-0.0516236\pi$
$398$	5.20180	+	7.15967i	0.260743	+	0.358882i
$399$	−0.0617358	−	0.190003i	−0.00309066	−	0.00951206i
$400$		0			0
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	0.843741	−	0.536751i	$-0.180348\pi$
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	−0.249750	+	0.968310i	$0.580348\pi$
$402$	−6.15197	+	8.46746i	−0.306832	+	0.422319i
$403$	18.2501	+	5.92981i	0.909101	+	0.295385i
$404$	0.496337	+	1.52757i	0.0246937	+	0.0759994i
$405$		0			0
$406$	33.4143			1.65832
$407$	14.5623	−	29.2058i	0.721826	−	1.44768i
$408$			6.22784i			0.308324i
$409$	3.55625	−	2.58376i	0.175845	−	0.127759i	−0.496381	−	0.868105i	$-0.665338\pi$
$409$	3.55625	−	2.58376i	0.175845	−	0.127759i	0.672226	+	0.740346i	$0.265338\pi$
$410$		0			0
$411$	−1.70241	+	5.23948i	−0.0839737	+	0.258444i
$412$	−0.387512	+	0.533365i	−0.0190914	+	0.0262770i
$413$	−18.2516	+	25.1211i	−0.898101	+	1.23613i
$414$	1.29932	−	3.99890i	0.0638581	−	0.196535i
$415$		0			0
$416$	2.09543	−	1.52242i	0.102737	−	0.0746427i
$417$			0.296668i			0.0145279i
$418$	−0.305053	−	0.299789i	−0.0149206	−	0.0146631i
$419$	−17.8526			−0.872159			−0.436079	−	0.899908i	$-0.643633\pi$
$419$	−17.8526			−0.872159			−0.436079	+	0.899908i	$0.643633\pi$
$420$		0			0
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	0.908090	−	0.418776i	$-0.137541\pi$
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	−0.980810	+	0.194965i	$0.937541\pi$
$422$	−35.3891	−	11.4986i	−1.72271	−	0.559743i
$423$	−3.49018	+	4.80382i	−0.169698	+	0.233570i
$424$	−7.09969	−	5.15823i	−0.344792	−	0.250506i
$425$		0			0
$426$	2.00179	+	6.16086i	0.0969868	+	0.298495i
$427$	−18.1910	−	25.0378i	−0.880324	−	1.21166i
$428$			0.314335i			0.0151939i
$429$	−3.78740	+	3.85391i	−0.182857	+	0.186069i
$430$		0			0
$431$	20.1234	−	14.6205i	0.969312	−	0.704247i	0.0140175	−	0.999902i	$-0.495538\pi$
$431$	20.1234	−	14.6205i	0.969312	−	0.704247i	0.955295	+	0.295655i	$0.0955380\pi$
$432$	−11.3230	+	3.67906i	−0.544778	+	0.177009i
$433$	20.2102	+	6.56669i	0.971240	+	0.315575i	0.751316	−	0.659942i	$-0.229419\pi$
$433$	20.2102	+	6.56669i	0.971240	+	0.315575i	0.219923	+	0.975517i	$0.429419\pi$
$434$	−27.1307	−	19.7116i	−1.30232	−	0.946188i
$435$		0			0
$436$	−0.306983	+	0.944796i	−0.0147018	+	0.0452475i
$437$	0.105138	−	0.0341614i	0.00502943	−	0.00163416i
$438$	−0.605339	−	0.833177i	−0.0289242	−	0.0398107i
$439$	15.9119			0.759434			0.379717	−	0.925103i	$-0.376021\pi$
$439$	15.9119			0.759434			0.379717	+	0.925103i	$0.376021\pi$
$440$		0			0
$441$	−16.8621			−0.802958
$442$	8.32843	+	11.4631i	0.396143	+	0.545244i
$443$	25.0010	−	8.12332i	1.18783	−	0.385951i	0.352562	−	0.935788i	$-0.385310\pi$
$443$	25.0010	−	8.12332i	1.18783	−	0.385951i	0.835272	+	0.549838i	$0.185310\pi$
$444$	0.283738	−	0.873257i	0.0134656	−	0.0414429i
$445$		0			0
$446$	5.57368	+	4.04952i	0.263922	+	0.191750i
$447$	−4.46609	−	1.45112i	−0.211239	−	0.0686356i
$448$	−29.6377	+	9.62987i	−1.40025	+	0.454969i
$449$	−6.62554	+	4.81373i	−0.312678	+	0.227174i	−0.733045	−	0.680180i	$-0.761902\pi$
$449$	−6.62554	+	4.81373i	−0.312678	+	0.227174i	0.420366	+	0.907354i	$0.361902\pi$
$450$		0			0
$451$	−27.2102	+	4.55278i	−1.28128	+	0.214382i
$452$		−	0.938065i		−	0.0441229i
$453$	0.656313	+	0.903337i	0.0308363	+	0.0424425i
$454$	−1.56670	−	4.82181i	−0.0735289	−	0.226299i
$455$		0			0
$456$	−0.129817	−	0.0943172i	−0.00607922	−	0.00441681i
$457$	7.00428	−	9.64056i	0.327646	−	0.450966i	−0.613136	−	0.789977i	$-0.710092\pi$
$457$	7.00428	−	9.64056i	0.327646	−	0.450966i	0.940782	+	0.339011i	$0.110092\pi$
$458$	−34.7139	−	11.2792i	−1.62207	−	0.527043i
$459$	3.72195	+	11.4550i	0.173726	+	0.534673i
$460$		0			0
$461$	6.96172			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$462$	8.37624	−	4.36015i	0.389698	−	0.202853i
$463$		−	12.4762i		−	0.579817i	−0.957054	−	0.289909i	$-0.906375\pi$
$463$		−	12.4762i		−	0.579817i	0.957054	−	0.289909i	$-0.0936249\pi$
$464$	19.9404	−	14.4876i	0.925712	−	0.672569i
$465$		0			0
$466$	7.67335	−	23.6161i	0.355461	−	1.09400i
$467$	−3.61263	+	4.97235i	−0.167172	+	0.230093i	−0.884381	−	0.466765i	$-0.845419\pi$
$467$	−3.61263	+	4.97235i	−0.167172	+	0.230093i	0.717209	+	0.696858i	$0.245419\pi$
$468$	0.720076	−	0.991100i	0.0332855	−	0.0458136i
$469$	−15.1288	+	46.5618i	−0.698585	+	2.15002i
$470$		0			0
$471$	−9.90505	+	7.19644i	−0.456401	+	0.331594i
$472$			24.9401i			1.14796i
$473$	9.73762	+	1.45552i	0.447736	+	0.0669250i
$474$	10.8181			0.496890
$475$		0			0
$476$	0.675105	+	2.07776i	0.0309434	+	0.0952340i
$477$	−7.59915	−	2.46911i	−0.347941	−	0.113053i
$478$	8.73013	−	12.0160i	0.399307	−	0.549599i
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	0.916829	−	0.399281i	$-0.130740\pi$
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	−0.0964228	+	0.995340i	$0.530740\pi$
$480$		0			0
$481$	−8.60798	−	26.4926i	−0.392490	−	1.20796i
$482$	7.96402	+	10.9615i	0.362751	+	0.499284i
$483$			2.44076i			0.111058i
$484$	−1.02311	+	1.46101i	−0.0465049	+	0.0664095i
$485$		0			0
$486$	−14.6026	+	10.6094i	−0.662387	+	0.481252i
$487$	32.5553	−	10.5778i	1.47522	−	0.479328i	0.542539	−	0.840030i	$-0.317463\pi$
$487$	32.5553	−	10.5778i	1.47522	−	0.479328i	0.932681	+	0.360702i	$0.117463\pi$
$488$	−23.6408	−	7.68135i	−1.07017	−	0.347719i
$489$	−7.44047	−	5.40582i	−0.336470	−	0.244460i
$490$		0			0
$491$	−5.25197	+	16.1639i	−0.237018	+	0.729467i	0.759829	+	0.650123i	$0.225283\pi$
$491$	−5.25197	+	16.1639i	−0.237018	+	0.729467i	−0.996847	+	0.0793441i	$0.974717\pi$
$492$	−0.738221	+	0.239863i	−0.0332816	+	0.0108138i
$493$	−14.6565	−	20.1729i	−0.660094	−	0.908541i
$494$	−0.365073			−0.0164254
$495$		0			0
$496$	−24.7371			−1.11073
$497$	17.8107	+	24.5144i	0.798920	+	1.09962i
$498$	−7.89815	+	2.56626i	−0.353925	+	0.114997i
$499$	−1.61599	+	4.97352i	−0.0723418	+	0.222645i	−0.980690	−	0.195570i	$-0.937344\pi$
$499$	−1.61599	+	4.97352i	−0.0723418	+	0.222645i	0.908348	+	0.418215i	$0.137344\pi$
$500$		0			0
$501$	−8.24504	−	5.99037i	−0.368361	−	0.267630i
$502$	12.4515	+	4.04575i	0.555740	+	0.180571i
$503$	39.8919	−	12.9617i	1.77869	−	0.577931i	0.779845	−	0.625973i	$-0.215298\pi$
$503$	39.8919	−	12.9617i	1.77869	−	0.577931i	0.998845	+	0.0480416i	$0.0152980\pi$
$504$	−23.0961	+	16.7803i	−1.02878	+	0.747454i
$505$		0			0
$506$	2.41268	+	4.63497i	0.107257	+	0.206050i
$507$		−	2.86923i		−	0.127427i
$508$	−0.232344	−	0.319794i	−0.0103086	−	0.0141886i
$509$	−6.29399	−	19.3709i	−0.278976	−	0.858601i	−0.988140	−	0.153557i	$-0.950927\pi$
$509$	−6.29399	−	19.3709i	−0.278976	−	0.858601i	0.709163	−	0.705044i	$-0.249073\pi$
$510$		0			0
$511$	−3.89731	−	2.83156i	−0.172407	−	0.125261i
$512$	−14.5377	+	20.0094i	−0.642481	+	0.884300i
$513$	−0.295141	−	0.0958972i	−0.0130308	−	0.00423396i
$514$	−4.36838	−	13.4445i	−0.192681	−	0.593012i
$515$		0			0
$516$	0.277016			0.0121949
$517$	−1.21775	−	7.27801i	−0.0535566	−	0.320086i
$518$			48.6816i			2.13895i
$519$	7.39602	−	5.37352i	0.324649	−	0.235872i
$520$		0			0
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	−0.803958	−	0.594686i	$-0.797276\pi$
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	0.999963	−	0.00855656i	$-0.00272367\pi$
$522$	14.3630	−	19.7690i	0.628652	−	0.865265i
$523$	−6.55975	+	9.02873i	−0.286838	+	0.394799i	−0.927984	−	0.372620i	$-0.878459\pi$
$523$	−6.55975	+	9.02873i	−0.286838	+	0.394799i	0.641146	+	0.767419i	$0.278459\pi$
$524$	0.352826	−	1.08589i	0.0154133	−	0.0474372i
$525$		0			0
$526$	12.0226	−	8.73490i	0.524209	−	0.380860i
$527$			25.0254i			1.09013i
$528$	3.10818	−	6.23370i	0.135266	−	0.271287i
$529$	21.6494			0.941279
$530$		0			0
$531$	7.01710	+	21.5964i	0.304516	+	0.937205i
$532$	−0.0535341	−	0.0173943i	−0.00232100	−	0.000754138i
$533$	−13.8415	+	19.0511i	−0.599540	+	0.825197i
$534$	−7.67588	−	5.57685i	−0.332168	−	0.241334i
$535$		0			0
$536$	12.1513	+	37.3979i	0.524857	+	1.61534i
$537$	5.71029	+	7.85954i	0.246417	+	0.339164i
$538$			0.121123i			0.00522197i
$539$	14.6880	−	14.9459i	0.632658	−	0.643768i
$540$		0			0
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	−0.757834	−	0.652447i	$-0.773742\pi$
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	0.386331	+	0.922360i	$0.373742\pi$
$542$	17.2763	−	5.61343i	0.742083	−	0.241117i
$543$	13.1837	+	4.28363i	0.565765	+	0.183828i
$544$	2.73273	+	1.98544i	0.117165	+	0.0851251i
$545$		0			0
$546$	2.49077	−	7.66581i	0.106595	−	0.328066i
$547$	−1.66207	+	0.540038i	−0.0710648	+	0.0230904i	−0.344334	−	0.938847i	$-0.611895\pi$
$547$	−1.66207	+	0.540038i	−0.0710648	+	0.0230904i	0.273269	+	0.961938i	$0.411895\pi$
$548$	0.912367	+	1.25577i	0.0389744	+	0.0536437i
$549$	−22.6325			−0.965930
$550$		0			0
$551$	0.642459			0.0273697
$552$	1.15229	+	1.58599i	0.0490446	+	0.0675041i
$553$	48.1264	−	15.6372i	2.04654	−	0.664962i
$554$	1.63661	−	5.03698i	0.0695331	−	0.214001i
$555$		0			0
$556$	0.0676235	+	0.0491313i	0.00286787	+	0.00208363i
$557$	−18.5307	−	6.02100i	−0.785173	−	0.255118i	−0.111126	−	0.993806i	$-0.535446\pi$
$557$	−18.5307	−	6.02100i	−0.785173	−	0.255118i	−0.674047	+	0.738688i	$0.735446\pi$
$558$	−23.3241	+	7.57845i	−0.987387	+	0.320821i
$559$	6.79900	−	4.93976i	0.287567	−	0.208930i
$560$		0			0
$561$	−6.30636	−	3.14442i	−0.266255	−	0.132757i
$562$		−	2.08426i		−	0.0879191i
$563$	−8.63407	−	11.8838i	−0.363883	−	0.500842i	0.587343	−	0.809338i	$-0.300174\pi$
$563$	−8.63407	−	11.8838i	−0.363883	−	0.500842i	−0.951225	+	0.308497i	$0.900174\pi$
$564$	−0.0641570	−	0.197455i	−0.00270150	−	0.00831435i
$565$		0			0
$566$	5.93535	+	4.31228i	0.249481	+	0.181259i
$567$	−13.1471	+	18.0954i	−0.552124	+	0.759934i
$568$	23.1466	+	7.52078i	0.971209	+	0.315565i
$569$	−6.15980	−	18.9579i	−0.258232	−	0.794758i	−0.993176	−	0.116629i	$-0.962791\pi$
$569$	−6.15980	−	18.9579i	−0.258232	−	0.794758i	0.734943	−	0.678129i	$-0.237209\pi$
$570$		0			0
$571$	5.24422			0.219464			0.109732	−	0.993961i	$-0.465001\pi$
$571$	5.24422			0.219464			0.109732	+	0.993961i	$0.465001\pi$
$572$	0.251240	+	1.50156i	0.0105049	+	0.0627834i
$573$		−	3.09776i		−	0.129411i
$574$	33.2940	−	24.1895i	1.38967	−	1.00965i
$575$		0			0
$576$	−7.04230	+	21.6740i	−0.293429	+	0.903083i
$577$	22.1010	−	30.4194i	0.920075	−	1.26637i	−0.0435320	−	0.999052i	$-0.513861\pi$
$577$	22.1010	−	30.4194i	0.920075	−	1.26637i	0.963607	−	0.267323i	$-0.0861390\pi$
$578$	2.68495	−	3.69551i	0.111679	−	0.153713i
$579$	−3.25158	+	10.0073i	−0.135131	+	0.415891i
$580$		0			0
$581$	−31.4271	+	22.8331i	−1.30382	+	0.947278i
$582$		−	3.37922i		−	0.140073i
$583$	8.80789	−	4.58484i	0.364785	−	0.189885i
$584$	−3.86923			−0.160110
$585$		0			0
$586$	4.78267	+	14.7195i	0.197570	+	0.608059i
$587$	24.3196	+	7.90191i	1.00378	+	0.326147i	0.764373	−	0.644774i	$-0.223048\pi$
$587$	24.3196	+	7.90191i	1.00378	+	0.326147i	0.239403	+	0.970920i	$0.423048\pi$
$588$	0.346548	−	0.476982i	0.0142914	−	0.0196704i
$589$	−0.521644	−	0.378997i	−0.0214940	−	0.0156163i
$590$		0			0
$591$	0.470497	+	1.44804i	0.0193536	+	0.0595644i
$592$	21.1071	+	29.0514i	0.867495	+	1.19400i
$593$		−	40.2260i		−	1.65188i	−0.563754	−	0.825942i	$-0.690644\pi$
$593$		−	40.2260i		−	1.65188i	0.563754	−	0.825942i	$-0.309356\pi$
$594$	2.16846	−	14.5073i	0.0889731	−	0.595240i
$595$		0			0
$596$	−1.07040	+	0.777695i	−0.0438455	+	0.0318556i
$597$	−3.57295	+	1.16092i	−0.146231	+	0.0475133i
$598$	4.24185	+	1.37826i	0.173462	+	0.0563613i
$599$	3.98843	+	2.89776i	0.162963	+	0.118399i	0.666278	−	0.745704i	$-0.267886\pi$
$599$	3.98843	+	2.89776i	0.162963	+	0.118399i	−0.503315	+	0.864103i	$0.667886\pi$
$600$		0			0
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	−0.0339497	−	0.999424i	$-0.510809\pi$
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	0.614912	−	0.788596i	$-0.289191\pi$
$602$	−13.9682	+	4.53853i	−0.569300	+	0.184977i
$603$	21.0444	+	28.9651i	0.856993	+	1.17955i
$604$	0.314602			0.0128010
$605$		0			0
$606$	7.72824			0.313938
$607$	26.5306	+	36.5162i	1.07684	+	1.48215i	0.862951	+	0.505288i	$0.168614\pi$
$607$	26.5306	+	36.5162i	1.07684	+	1.48215i	0.213891	+	0.976857i	$0.431386\pi$
$608$	−0.0827714	+	0.0268941i	−0.00335682	+	0.00109070i
$609$	−4.38328	+	13.4904i	−0.177620	+	0.546657i
$610$		0			0
$611$	−5.09568	−	3.70223i	−0.206149	−	0.149776i
$612$	1.51946	+	0.493703i	0.0614206	+	0.0199567i
$613$	4.50247	−	1.46294i	0.181853	−	0.0590877i	−0.216675	−	0.976244i	$-0.569521\pi$
$613$	4.50247	−	1.46294i	0.181853	−	0.0590877i	0.398528	+	0.917156i	$0.369521\pi$
$614$	−4.66133	+	3.38666i	−0.188116	+	0.136674i
$615$		0			0
$616$	5.24479	−	35.0883i	0.211319	−	1.41375i
$617$			17.8468i			0.718486i	0.933244	+	0.359243i	$0.116965\pi$
$617$			17.8468i			0.718486i	−0.933244	+	0.359243i	$0.883035\pi$
$618$	1.86454	+	2.56632i	0.0750027	+	0.103232i
$619$	−0.110304	−	0.339482i	−0.00443351	−	0.0136449i	0.948815	−	0.315832i	$-0.102283\pi$
$619$	−0.110304	−	0.339482i	−0.00443351	−	0.0136449i	−0.953249	+	0.302187i	$0.902283\pi$
$620$		0			0
$621$	3.06726	+	2.22850i	0.123085	+	0.0894264i
$622$	−13.2431	+	18.2276i	−0.531002	+	0.730861i
$623$	−42.2089	−	13.7145i	−1.69107	−	0.549461i
$624$	−1.83729	−	5.65461i	−0.0735506	−	0.226365i
$625$		0			0
$626$	−36.0297			−1.44004
$627$	0.161051	−	0.0838329i	0.00643174	−	0.00334796i
$628$			3.44960i			0.137654i
$629$	29.3900	−	21.3531i	1.17186	−	0.851404i
$630$		0			0
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	0.536516	+	0.843890i	$0.319740\pi$
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	−0.930077	+	0.367366i	$0.880260\pi$
$632$	23.8898	−	32.8815i	0.950287	−	1.30796i
$633$	9.28466	−	12.7792i	0.369032	−	0.507929i
$634$	−2.42849	+	7.47413i	−0.0964477	+	0.296836i
$635$		0			0
$636$	0.226021	−	0.164214i	0.00896231	−	0.00651150i
$637$		−	17.8866i		−	0.708693i
$638$	5.01136	+	29.9509i	0.198402	+	1.18577i
$639$	22.1594			0.876610
$640$		0			0
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	0.957047	−	0.289932i	$-0.0936326\pi$
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	−0.944685	+	0.327979i	$0.893633\pi$
$642$	1.43842	+	0.467370i	0.0567697	+	0.0184456i
$643$	8.80057	−	12.1130i	0.347061	−	0.477688i	−0.599426	−	0.800430i	$-0.704605\pi$
$643$	8.80057	−	12.1130i	0.347061	−	0.477688i	0.946487	+	0.322742i	$0.104605\pi$
$644$	0.556354	+	0.404215i	0.0219234	+	0.0159283i
$645$		0			0
$646$	−0.147125	−	0.452803i	−0.00578855	−	0.0178153i
$647$	−10.5139	−	14.4712i	−0.413345	−	0.568920i	0.550686	−	0.834713i	$-0.314366\pi$
$647$	−10.5139	−	14.4712i	−0.413345	−	0.568920i	−0.964030	+	0.265793i	$0.914366\pi$
$648$			17.9650i			0.705732i
$649$	−25.2546	−	12.5922i	−0.991331	−	0.494287i
$650$		0			0
$651$	11.5172	−	8.36772i	0.451394	−	0.327957i
$652$	−2.46444	+	0.800746i	−0.0965150	+	0.0313596i
$653$	−43.5244	−	14.1419i	−1.70324	−	0.553416i	−0.714055	−	0.700089i	$-0.753144\pi$
$653$	−43.5244	−	14.1419i	−1.70324	−	0.553416i	−0.989185	+	0.146673i	$0.953144\pi$
$654$	3.86701	+	2.80955i	0.151212	+	0.109862i
$655$		0			0
$656$	9.38072	−	28.8709i	0.366255	−	1.12722i
$657$	−3.35049	+	1.08864i	−0.130715	+	0.0424719i
$658$	6.47007	+	8.90529i	0.252230	+	0.347164i
$659$	9.54036			0.371640			0.185820	−	0.982584i	$-0.440506\pi$
$659$	9.54036			0.371640			0.185820	+	0.982584i	$0.440506\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$	10.2976	+	14.1734i	0.400228	+	0.550866i
$663$	−5.72052	+	1.85871i	−0.222167	+	0.0721863i
$664$	−9.64154	+	29.6736i	−0.374164	+	1.15156i
$665$		0			0
$666$	28.8016	+	20.9256i	1.11604	+	0.810850i
$667$	−7.46486	−	2.42548i	−0.289040	−	0.0939149i
$668$	−2.73093	+	0.887333i	−0.105663	+	0.0343319i
$669$	−2.36607	+	1.71905i	−0.0914774	+	0.0664622i
$670$		0			0
$671$	19.7144	−	20.0606i	0.761065	−	0.774430i
$672$		−	1.92152i		−	0.0741243i
$673$	27.8041	+	38.2690i	1.07177	+	1.47516i	0.868273	+	0.496086i	$0.165230\pi$
$673$	27.8041	+	38.2690i	1.07177	+	1.47516i	0.203494	+	0.979076i	$0.434770\pi$
$674$	−5.60749	−	17.2581i	−0.215992	−	0.664756i
$675$		0			0
$676$	−0.654023	−	0.475175i	−0.0251547	−	0.0182760i
$677$	16.1894	−	22.2828i	0.622210	−	0.856399i	−0.375301	−	0.926903i	$-0.622461\pi$
$677$	16.1894	−	22.2828i	0.622210	−	0.856399i	0.997512	+	0.0705039i	$0.0224607\pi$
$678$	−4.29265	−	1.39477i	−0.164858	−	0.0535657i
$679$	−4.88457	−	15.0332i	−0.187453	−	0.576920i
$680$		0			0
$681$	2.15223			0.0824736
$682$	13.5995	−	27.2749i	0.520753	−	1.04441i
$683$			27.1617i			1.03931i	0.854375	+	0.519656i	$0.173940\pi$
$683$			27.1617i			1.03931i	−0.854375	+	0.519656i	$0.826060\pi$
$684$	−0.0333024	+	0.0241956i	−0.00127335	+	0.000925143i
$685$		0			0
$686$	1.04233	−	3.20795i	0.0397962	−	0.122480i
$687$	9.10752	−	12.5354i	0.347474	−	0.478256i
$688$	−6.36790	+	8.76467i	−0.242774	+	0.334150i
$689$	2.61913	−	8.06084i	0.0997808	−	0.307094i
$690$		0			0
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	−0.465906	−	0.884834i	$-0.654272\pi$
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	0.697554	+	0.716532i	$0.254272\pi$
$692$		−	2.57579i		−	0.0979167i
$693$	−5.33073	−	31.8597i	−0.202498	−	1.21025i
$694$	11.4541			0.434791
$695$		0			0
$696$	3.52060	+	10.8353i	0.133448	+	0.410711i
$697$	−29.2074	−	9.49007i	−1.10631	−	0.359462i
$698$	8.28625	−	11.4051i	0.313639	−	0.431688i
$699$	8.52796	+	6.19593i	0.322557	+	0.234351i
$700$		0			0
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	−0.945880	−	0.324516i	$-0.894799\pi$
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	0.574487	−	0.818513i	$-0.305201\pi$
$702$	−7.35934	−	10.1293i	−0.277760	−	0.382304i
$703$			0.936004i			0.0353021i
$704$	−13.0767	−	25.1215i	−0.492847	−	0.946802i
$705$		0			0
$706$	−20.9562	+	15.2255i	−0.788696	+	0.573021i
$707$	34.3807	−	11.1710i	1.29302	−	0.420127i
$708$	−0.755117	−	0.245352i	−0.0283790	−	0.00922091i
$709$	−11.6807	−	8.48651i	−0.438677	−	0.318718i	0.346432	−	0.938075i	$-0.387393\pi$
$709$	−11.6807	−	8.48651i	−0.438677	−	0.318718i	−0.785109	+	0.619357i	$0.787393\pi$
$710$		0			0
$711$	11.4355	−	35.1947i	0.428863	−	1.31991i
$712$	−33.9017	+	11.0153i	−1.27052	+	0.412817i
$713$	4.63026	+	6.37300i	0.173405	+	0.238671i
$714$	10.5117			0.393392
$715$		0			0
$716$	2.73721			0.102294
$717$	3.70600	+	5.10087i	0.138403	+	0.190496i
$718$	−5.69129	+	1.84921i	−0.212397	+	0.0690120i
$719$	−1.67179	+	5.14526i	−0.0623474	+	0.191886i	−0.977378	−	0.211498i	$-0.932166\pi$
$719$	−1.67179	+	5.14526i	−0.0623474	+	0.191886i	0.915031	+	0.403383i	$0.132166\pi$
$720$		0			0
$721$	12.0043	+	8.72166i	0.447065	+	0.324811i
$722$	−24.4855	−	7.95581i	−0.911255	−	0.296085i
$723$	−5.47022	+	1.77738i	−0.203440	+	0.0661016i
$724$	3.15978	−	2.29571i	0.117432	−	0.0853195i
$725$		0			0
$726$	5.16446	+	6.85412i	0.191671	+	0.254380i
$727$		−	16.7753i		−	0.622161i	−0.950384	−	0.311080i	$-0.899309\pi$
$727$		−	16.7753i		−	0.622161i	0.950384	−	0.311080i	$-0.100691\pi$
$728$	−17.7998	−	24.4993i	−0.659705	−	0.908006i
$729$	3.31409	+	10.1997i	0.122744	+	0.377767i
$730$		0			0
$731$	8.86684	+	6.44213i	0.327952	+	0.238271i
$732$	0.465139	−	0.640209i	0.0171920	−	0.0236628i
$733$	13.3957	+	4.35252i	0.494781	+	0.160764i	0.545770	−	0.837935i	$-0.316237\pi$
$733$	13.3957	+	4.35252i	0.494781	+	0.160764i	−0.0509889	+	0.998699i	$0.516237\pi$
$734$	12.3004	+	37.8567i	0.454016	+	1.39732i
$735$		0			0
$736$	1.06327			0.0391926
$737$	−44.0046	−	6.57756i	−1.62093	−	0.242287i
$738$		−	30.0956i		−	1.10783i
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.977971	−	0.208743i	$-0.933063\pi$
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.103683	+	0.994610i	$0.533063\pi$
$740$		0			0
$741$	0.0478902	−	0.147391i	0.00175929	−	0.00541454i
$742$	−8.70640	+	11.9833i	−0.319622	+	0.439922i
$743$	1.15039	−	1.58338i	0.0422037	−	0.0580884i	−0.787394	−	0.616451i	$-0.788570\pi$
$743$	1.15039	−	1.58338i	0.0422037	−	0.0580884i	0.829597	+	0.558362i	$0.188570\pi$
$744$	3.53336	−	10.8746i	0.129539	−	0.398681i
$745$		0			0
$746$	5.44519	−	3.95617i	0.199363	−	0.144846i
$747$			28.4080i			1.03939i
$748$	−1.76115	+	0.916745i	−0.0643940	+	0.0335195i
$749$	7.07466			0.258503
$750$		0			0
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	0.999414	+	0.0342181i	$0.0108941\pi$
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	−0.788430	+	0.615124i	$0.789106\pi$
$752$	7.72220	+	2.50910i	0.281600	+	0.0914973i
$753$	−3.26678	+	4.49634i	−0.119048	+	0.163856i
$754$	20.9701	+	15.2356i	0.763685	+	0.554850i
$755$		0			0
$756$	−0.596550	−	1.83599i	−0.0216963	−	0.0667744i
$757$	8.55054	+	11.7688i	0.310775	+	0.427744i	0.935623	−	0.353002i	$-0.114839\pi$
$757$	8.55054	+	11.7688i	0.310775	+	0.427744i	−0.624848	+	0.780746i	$0.714839\pi$
$758$		−	10.7412i		−	0.390138i
$759$	−2.18777	+	0.366056i	−0.0794111	+	0.0132870i
$760$		0			0
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	−0.763556	−	0.645741i	$-0.776548\pi$
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	0.378185	+	0.925730i	$0.376548\pi$
$762$	−1.80886	+	0.587734i	−0.0655281	+	0.0212914i
$763$	21.2643	+	6.90920i	0.769820	+	0.250130i
$764$	−0.706114	−	0.513022i	−0.0255463	−	0.0185605i
$765$		0			0
$766$	−10.2702	+	31.6084i	−0.371077	+	1.14206i
$767$	−22.9085	+	7.44344i	−0.827180	+	0.268767i
$768$	−1.30749	−	1.79960i	−0.0471799	−	0.0649376i
$769$	−38.9767			−1.40554			−0.702768	−	0.711419i	$-0.748053\pi$
$769$	−38.9767			−1.40554			−0.702768	+	0.711419i	$0.748053\pi$
$770$		0			0
$771$	6.00099			0.216121
$772$	1.74261	+	2.39850i	0.0627179	+	0.0863239i
$773$	−36.8571	+	11.9756i	−1.32566	+	0.430733i	−0.884435	−	0.466664i	$-0.845456\pi$
$773$	−36.8571	+	11.9756i	−1.32566	+	0.430733i	−0.441225	+	0.897397i	$0.645456\pi$
$774$	−3.31902	+	10.2149i	−0.119300	+	0.367167i
$775$		0			0
$776$	−10.2712	−	7.46243i	−0.368713	−	0.267886i
$777$	−19.6542	−	6.38604i	−0.705091	−	0.229098i
$778$	7.04091	−	2.28773i	0.252429	−	0.0820192i
$779$	0.640147	−	0.465094i	0.0229356	−	0.0166637i
$780$		0			0
$781$	−19.3023	+	19.6412i	−0.690689	+	0.702818i
$782$			5.81665i			0.208003i
$783$	12.9510	+	17.8256i	0.462832	+	0.637034i
$784$	7.12525	+	21.9293i	0.254473	+	0.783188i
$785$		0			0
$786$	−4.44449	−	3.22911i	−0.158530	−	0.115179i
$787$	−12.5693	+	17.3002i	−0.448048	+	0.616685i	−0.971977	−	0.235077i	$-0.924466\pi$
$787$	−12.5693	+	17.3002i	−0.448048	+	0.616685i	0.523929	+	0.851762i	$0.324466\pi$
$788$	0.407990	+	0.132564i	0.0145341	+	0.00472240i
$789$	1.94943	+	5.99971i	0.0694014	+	0.213595i
$790$		0			0
$791$	−21.1128			−0.750686
$792$	−18.5049	−	18.1855i	−0.657543	−	0.646195i
$793$		−	24.0075i		−	0.852533i
$794$	−7.05718	+	5.12734i	−0.250450	+	0.181963i
$795$		0			0
$796$	−0.327093	+	1.00669i	−0.0115935	+	0.0356812i
$797$	−1.30756	+	1.79970i	−0.0463162	+	0.0637488i	−0.831547	−	0.555454i	$-0.812544\pi$
$797$	−1.30756	+	1.79970i	−0.0463162	+	0.0637488i	0.785231	+	0.619203i	$0.212544\pi$
$798$	−0.159195	+	0.219113i	−0.00563543	+	0.00775651i
$799$	2.53834	−	7.81222i	0.0898002	−	0.276377i
$800$		0			0
$801$	−26.2573	+	19.0770i	−0.927756	+	0.674054i
$802$		−	19.9319i		−	0.703821i
$803$	1.95356	−	3.91802i	0.0689398	−	0.138264i
$804$	−1.25184			−0.0441491
$805$		0			0
$806$	−8.03889	−	24.7412i	−0.283158	−	0.871470i
$807$	−0.0489008	−	0.0158888i	−0.00172139	−	0.000559314i
$808$	17.0665	−	23.4900i	0.600397	−	0.826376i
$809$	17.1254	+	12.4424i	0.602098	+	0.437450i	0.846623	−	0.532193i	$-0.178632\pi$
$809$	17.1254	+	12.4424i	0.602098	+	0.437450i	−0.244525	+	0.969643i	$0.578632\pi$
$810$		0			0
$811$	−11.3462	−	34.9201i	−0.398420	−	1.22621i	−0.926266	−	0.376871i	$-0.877000\pi$
$811$	−11.3462	−	34.9201i	−0.398420	−	1.22621i	0.527845	−	0.849341i	$-0.323000\pi$
$812$	2.34912	+	3.23329i	0.0824380	+	0.113466i
$813$			7.71135i			0.270449i
$814$	−43.6357	+	7.30109i	−1.52943	+	0.255903i
$815$		0			0
$816$	6.27303	−	4.55762i	0.219600	−	0.159549i
$817$	−0.268567	+	0.0872627i	−0.00939597	+	0.00305294i
$818$	−5.66756	−	1.84150i	−0.198161	−	0.0643866i
$819$	−22.3065	−	16.2066i	−0.779451	−	0.566305i
$820$		0			0
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	0.472439	+	0.881363i	$0.343374\pi$
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	−0.900264	+	0.435345i	$0.856626\pi$
$822$	7.10303	−	2.30791i	0.247747	−	0.0804977i
$823$	−26.9960	−	37.1568i	−0.941021	−	1.29520i	−0.955402	−	0.295308i	$-0.904578\pi$
$823$	−26.9960	−	37.1568i	−0.941021	−	1.29520i	0.0143810	−	0.999897i	$-0.495422\pi$
$824$	11.9178			0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	23.3321	+	32.1139i	0.811337	+	1.11671i	0.991116	+	0.133002i	$0.0424616\pi$
$827$	23.3321	+	32.1139i	0.811337	+	1.11671i	−0.179779	+	0.983707i	$0.557538\pi$
$828$	0.478293	−	0.155407i	0.0166218	−	0.00540076i
$829$	−2.36578	+	7.28113i	−0.0821671	+	0.252884i	−0.983697	−	0.179832i	$-0.942445\pi$
$829$	−2.36578	+	7.28113i	−0.0821671	+	0.252884i	0.901530	+	0.432716i	$0.142445\pi$
$830$		0			0
$831$	1.81889	+	1.32150i	0.0630966	+	0.0458423i
$832$	−22.9908	−	7.47017i	−0.797063	−	0.258982i
$833$	22.1849	−	7.20831i	0.768661	−	0.249753i
$834$	0.325374	−	0.236398i	0.0112668	−	0.00818580i
$835$		0			0
$836$	0.00756251	−	0.0505940i	0.000261555	−	0.00174983i
$837$		−	22.1135i		−	0.764354i
$838$	14.2258	+	19.5801i	0.491422	+	0.676384i
$839$	−8.52536	−	26.2383i	−0.294328	−	0.905848i	−0.983446	−	0.181200i	$-0.942002\pi$
$839$	−8.52536	−	26.2383i	−0.294328	−	0.905848i	0.689118	−	0.724649i	$-0.257998\pi$
$840$		0			0
$841$	−13.4418	−	9.76607i	−0.463512	−	0.336761i
$842$	−3.84760	+	5.29576i	−0.132597	+	0.182504i
$843$	0.841477	+	0.273412i	0.0289820	+	0.00941683i
$844$	−1.37531	−	4.23276i	−0.0473400	−	0.145697i
$845$		0			0
$846$	8.04979			0.276757
$847$	32.8826	+	23.0269i	1.12986	+	0.791213i
$848$			10.9261i			0.375203i
$849$	−2.51960	+	1.83059i	−0.0864724	+	0.0628258i
$850$		0			0
$851$	3.53370	−	10.8756i	0.121134	−	0.372811i
$852$	−0.455416	+	0.626826i	−0.0156023	+	0.0214747i
$853$	−24.7749	+	34.0998i	−0.848277	+	1.16755i	0.135962	+	0.990714i	$0.456587\pi$
$853$	−24.7749	+	34.0998i	−0.848277	+	1.16755i	−0.984240	+	0.176840i	$0.943413\pi$
$854$	−12.9651	+	39.9024i	−0.443656	+	1.36543i
$855$		0			0
$856$	4.59707	−	3.33997i	0.157125	−	0.114158i
$857$		−	45.0850i		−	1.54008i	−0.637998	−	0.770038i	$-0.720237\pi$
$857$		−	45.0850i		−	1.54008i	0.637998	−	0.770038i	$-0.279763\pi$
$858$	7.24480	+	1.08291i	0.247333	+	0.0369700i
$859$	11.8257			0.403488			0.201744	−	0.979438i	$-0.435339\pi$
$859$	11.8257			0.403488			0.201744	+	0.979438i	$0.435339\pi$
$860$		0			0
$861$	5.39854	+	16.6150i	0.183982	+	0.566237i
$862$	−32.0705	−	10.4204i	−1.09233	−	0.354919i
$863$	−16.3823	+	22.5484i	−0.557662	+	0.767555i	−0.991027	−	0.133663i	$-0.957326\pi$
$863$	−16.3823	+	22.5484i	−0.557662	+	0.767555i	0.433365	+	0.901218i	$0.357326\pi$
$864$	−2.41475	−	1.75442i	−0.0821514	−	0.0596865i
$865$		0			0
$866$	−8.90229	−	27.3984i	−0.302512	−	0.931037i
$867$	1.13978	+	1.56877i	0.0387089	+	0.0532782i
$868$		−	4.01105i		−	0.136144i
$869$	21.2342	+	40.7929i	0.720323	+	1.38380i
$870$		0			0
$871$	−30.7249	+	22.3230i	−1.04107	+	0.756384i
$872$	17.0793	−	5.54939i	0.578377	−	0.187926i
$873$	−10.9937	−	3.57207i	−0.372081	−	0.120896i
$874$	−0.121246	−	0.0880900i	−0.00410119	−	0.00297969i
$875$		0			0
$876$	0.0380642	−	0.117149i	0.00128607	−	0.00395811i
$877$	10.8869	−	3.53736i	0.367624	−	0.119448i	−0.119379	−	0.992849i	$-0.538090\pi$
$877$	10.8869	−	3.53736i	0.367624	−	0.119448i	0.487003	+	0.873401i	$0.338090\pi$
$878$	−12.6793	−	17.4516i	−0.427907	−	0.588963i
$879$	−6.57011			−0.221604
$880$		0			0
$881$	47.0037			1.58360			0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037			1.58360			0.791798	+	0.610783i	$0.209145\pi$
$882$	13.4365	+	18.4938i	0.452431	+	0.622717i
$883$	−44.6185	+	14.4974i	−1.50153	+	0.487877i	−0.940464	−	0.339894i	$-0.889609\pi$
$883$	−44.6185	+	14.4974i	−1.50153	+	0.487877i	−0.561067	+	0.827770i	$0.689609\pi$
$884$	−0.523698	+	1.61178i	−0.0176139	+	0.0542099i
$885$		0			0
$886$	−28.8313	−	20.9472i	−0.968607	−	0.703734i
$887$	−26.4800	−	8.60386i	−0.889110	−	0.288889i	−0.171375	−	0.985206i	$-0.554821\pi$
$887$	−26.4800	−	8.60386i	−0.889110	−	0.288889i	−0.717735	+	0.696316i	$0.754821\pi$
$888$	−15.7860	+	5.12920i	−0.529745	+	0.172125i
$889$	−7.19754	+	5.22932i	−0.241398	+	0.175386i
$890$		0			0
$891$	−18.1915	−	9.07048i	−0.609439	−	0.303872i
$892$			0.824022i			0.0275903i
$893$	0.124401	+	0.171223i	0.00416290	+	0.00572975i
$894$	1.96725	+	6.05456i	0.0657946	+	0.202495i
$895$		0			0
$896$	28.7759	+	20.9069i	0.961335	+	0.698451i
$897$	−1.11289	+	1.53176i	−0.0371584	+	0.0511441i
$898$	10.5591	+	3.43085i	0.352360	+	0.114489i
$899$	14.1469	+	43.5397i	0.471826	+	1.45213i
$900$		0			0
$901$	11.0534			0.368244
$902$	26.6756	+	26.2153i	0.888201	+	0.872872i
$903$		−	6.23473i		−	0.207479i
$904$	−13.7190	+	9.96742i	−0.456287	+	0.331512i
$905$		0			0
$906$	0.467767	−	1.43964i	0.0155405	−	0.0478288i
$907$	−16.8243	+	23.1567i	−0.558643	+	0.768907i	−0.991153	−	0.132723i	$-0.957628\pi$
$907$	−16.8243	+	23.1567i	−0.558643	+	0.768907i	0.432510	+	0.901629i	$0.357628\pi$
$908$	0.356432	−	0.490586i	0.0118286	−	0.0162807i
$909$	8.16930	−	25.1425i	0.270959	−	0.833925i
$910$		0			0
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	−0.654389	−	0.756158i	$-0.727074\pi$
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	0.516932	+	0.856026i	$0.327074\pi$
$912$			0.199781i			0.00661542i
$913$	−25.1798	−	24.7452i	−0.833330	−	0.818948i
$914$	−16.1547			−0.534351
$915$		0			0
$916$	−1.34907	−	4.15200i	−0.0445744	−	0.137186i
$917$	−24.4398	−	7.94098i	−0.807074	−	0.262234i
$918$	9.59759	−	13.2100i	0.316768	−	0.435993i
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	0.948792	−	0.315902i	$-0.102307\pi$
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	−0.00724799	+	0.999974i	$0.502307\pi$
$920$		0			0
$921$	−0.755822	−	2.32618i	−0.0249052	−	0.0766503i
$922$	−5.54742	−	7.63536i	−0.182694	−	0.251457i
$923$			23.5057i			0.773699i
$924$	1.01078	+	0.503984i	0.0332521	+	0.0165798i
$925$		0			0
$926$	−13.6834	+	9.94159i	−0.449665	+	0.326701i
$927$	10.3200	−	3.35318i	0.338954	−	0.110133i
$928$	5.87682	+	1.90950i	0.192916	+	0.0626823i
$929$	−47.8474	−	34.7632i	−1.56982	−	1.14054i	−0.927325	−	0.374256i	$-0.877898\pi$
$929$	−47.8474	−	34.7632i	−1.56982	−	1.14054i	−0.642498	−	0.766287i	$-0.722102\pi$
$930$		0			0
$931$	−0.185724	+	0.571601i	−0.00608687	+	0.0187335i
$932$	2.82464	−	0.917781i	0.0925242	−	0.0300629i
$933$	−5.62181	−	7.73775i	−0.184050	−	0.253323i
$934$	8.33220			0.272638
$935$		0			0
$936$	−22.1458			−0.723857
$937$	−8.48911	−	11.6843i	−0.277327	−	0.381708i	0.647519	−	0.762049i	$-0.275807\pi$
$937$	−8.48911	−	11.6843i	−0.277327	−	0.381708i	−0.924846	+	0.380341i	$0.875807\pi$
$938$	63.1226	−	20.5098i	2.06103	−	0.669668i
$939$	4.72637	−	14.5463i	0.154239	−	0.474700i
$940$		0			0
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	0.805991	−	0.591927i	$-0.201633\pi$
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	−0.313891	+	0.949459i	$0.601633\pi$
$942$	15.7856	+	5.12905i	0.514322	+	0.167113i
$943$	−9.19386	+	2.98727i	−0.299393	+	0.0972788i
$944$	25.1211	−	18.2516i	0.817623	−	0.594038i
$945$		0			0
$946$	−6.16301	−	11.8397i	−0.200377	−	0.384942i
$947$		−	0.991391i		−	0.0322159i	−0.999870	−	0.0161079i	$-0.994872\pi$
$947$		−	0.991391i		−	0.0322159i	0.999870	−	0.0161079i	$-0.00512754\pi$
$948$	0.760540	+	1.04679i	0.0247012	+	0.0339983i
$949$	−1.15478	−	3.55405i	−0.0374858	−	0.115369i
$950$		0			0
$951$	−2.69896	−	1.96091i	−0.0875198	−	0.0635869i
$952$	23.2134	−	31.9505i	0.752351	−	1.03552i
$953$	7.85957	+	2.55373i	0.254597	+	0.0827234i	0.433535	−	0.901137i	$-0.357266\pi$
$953$	7.85957	+	2.55373i	0.254597	+	0.0827234i	−0.178938	+	0.983860i	$0.557266\pi$
$954$	3.34731	+	10.3020i	0.108373	+	0.333539i
$955$		0			0
$956$	1.77646			0.0574549
$957$	−12.7495	−	1.90572i	−0.412132	−	0.0616031i
$958$		−	30.0881i		−	0.972101i
$959$	28.2633	−	20.5345i	0.912669	−	0.663093i
$960$		0			0
$961$	4.61867	−	14.2148i	0.148989	−	0.458542i
$962$	−22.1969	+	30.5515i	−0.715658	+	0.985019i
$963$	3.04102	−	4.18560i	0.0979954	−	0.134879i
$964$	−0.500784	+	1.54125i	−0.0161292	+	0.0496404i
$965$		0			0
$966$	2.67693	−	1.94491i	0.0861289	−	0.0625763i
$967$			7.36029i			0.236691i	0.992972	+	0.118345i	$0.0377590\pi$
$967$			7.36029i			0.236691i	−0.992972	+	0.118345i	$0.962241\pi$
$968$	32.2380	−	0.561246i	1.03617	−	0.0180391i
$969$	0.202110			0.00649271
$970$		0			0
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	0.923339	−	0.383986i	$-0.125449\pi$
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	−0.972698	+	0.232074i	$0.925449\pi$
$972$	−2.05321	−	0.667127i	−0.0658566	−	0.0213981i
$973$	1.10579	−	1.52199i	0.0354500	−	0.0487927i
$974$	−37.5429	−	27.2765i	−1.20295	−	0.873996i
$975$		0			0
$976$	9.56357	+	29.4337i	0.306123	+	0.942148i
$977$	−6.07583	−	8.36266i	−0.194383	−	0.267545i	0.700689	−	0.713467i	$-0.252876\pi$
$977$	−6.07583	−	8.36266i	−0.194383	−	0.267545i	−0.895072	+	0.445922i	$0.852876\pi$
$978$			12.4680i			0.398684i
$979$	5.96266	−	39.8908i	0.190567	−	1.27492i
$980$		0			0
$981$	13.2281	−	9.61077i	0.422340	−	0.306848i
$982$	21.9130	−	7.11996i	0.699272	−	0.227207i
$983$	27.6390	+	8.98045i	0.881547	+	0.286432i	0.714599	−	0.699534i	$-0.246609\pi$
$983$	27.6390	+	8.98045i	0.881547	+	0.286432i	0.166947	+	0.985966i	$0.446609\pi$
$984$	11.3519	+	8.24764i	0.361886	+	0.262925i
$985$		0			0
$986$	−10.4460	+	32.1493i	−0.332667	+	1.02384i
$987$	−4.44408	+	1.44397i	−0.141456	+	0.0459620i
$988$	−0.0256657	−	0.0353258i	−0.000816534	−	0.00112386i
$989$	3.44997			0.109703
$990$		0			0
$991$	7.70381			0.244719			0.122360	−	0.992486i	$-0.460954\pi$
$991$	7.70381			0.244719			0.122360	+	0.992486i	$0.460954\pi$
$992$	−3.64524	−	5.01724i	−0.115737	−	0.159298i
$993$	−7.07308	+	2.29818i	−0.224458	+	0.0729307i
$994$	12.6941	−	39.0683i	0.402631	−	1.23917i
$995$		0			0
$996$	−0.803583	−	0.583837i	−0.0254625	−	0.0184996i
$997$	−2.72400	−	0.885080i	−0.0862698	−	0.0280308i	0.265564	−	0.964093i	$-0.414442\pi$
$997$	−2.72400	−	0.885080i	−0.0862698	−	0.0280308i	−0.351834	+	0.936062i	$0.614442\pi$
$998$	6.74247	−	2.19076i	0.213429	−	0.0693473i
$999$	−25.9702	+	18.8685i	−0.821661	+	0.596972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.z.a.124.1		16
5.2	odd	4		275.2.h.a.201.2		8
5.3	odd	4		55.2.g.b.36.1	yes	8
5.4	even	2	inner	275.2.z.a.124.4		16
11.4	even	5	inner	275.2.z.a.224.4		16
15.8	even	4		495.2.n.e.91.2		8
20.3	even	4		880.2.bo.h.641.1		8
55.2	even	20		3025.2.a.w.1.4		4
55.3	odd	20		605.2.g.m.511.2		8
55.4	even	10	inner	275.2.z.a.224.1		16
55.8	even	20		605.2.g.e.511.1		8
55.13	even	20		605.2.a.k.1.1		4
55.18	even	20		605.2.g.k.81.2		8
55.28	even	20		605.2.g.e.251.1		8
55.37	odd	20		275.2.h.a.26.2		8
55.38	odd	20		605.2.g.m.251.2		8
55.42	odd	20		3025.2.a.bd.1.1		4
55.43	even	4		605.2.g.k.366.2		8
55.48	odd	20		55.2.g.b.26.1	✓	8
55.53	odd	20		605.2.a.j.1.4		4
165.53	even	20		5445.2.a.bp.1.1		4
165.68	odd	20		5445.2.a.bi.1.4		4
165.158	even	20		495.2.n.e.136.2		8
220.103	even	20		880.2.bo.h.81.1		8
220.123	odd	20		9680.2.a.cm.1.2		4
220.163	even	20		9680.2.a.cn.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	55.48	odd	20
55.2.g.b.36.1	yes	8	5.3	odd	4
275.2.h.a.26.2		8	55.37	odd	20
275.2.h.a.201.2		8	5.2	odd	4
275.2.z.a.124.1		16	1.1	even	1	trivial
275.2.z.a.124.4		16	5.4	even	2	inner
275.2.z.a.224.1		16	55.4	even	10	inner
275.2.z.a.224.4		16	11.4	even	5	inner
495.2.n.e.91.2		8	15.8	even	4
495.2.n.e.136.2		8	165.158	even	20
605.2.a.j.1.4		4	55.53	odd	20
605.2.a.k.1.1		4	55.13	even	20
605.2.g.e.251.1		8	55.28	even	20
605.2.g.e.511.1		8	55.8	even	20
605.2.g.k.81.2		8	55.18	even	20
605.2.g.k.366.2		8	55.43	even	4
605.2.g.m.251.2		8	55.38	odd	20
605.2.g.m.511.2		8	55.3	odd	20
880.2.bo.h.81.1		8	220.103	even	20
880.2.bo.h.641.1		8	20.3	even	4
3025.2.a.w.1.4		4	55.2	even	20
3025.2.a.bd.1.1		4	55.42	odd	20
5445.2.a.bi.1.4		4	165.68	odd	20
5445.2.a.bp.1.1		4	165.53	even	20
9680.2.a.cm.1.2		4	220.123	odd	20
9680.2.a.cn.1.2		4	220.163	even	20

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.796845 - 1.09676i) q^{2} +(0.547326 - 0.177837i) q^{3} +(0.0501062 - 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(-3.47080 - 1.12773i) q^{7} +(-2.78771 + 0.905781i) q^{8} +(-2.15911 + 1.56869i) q^{9} +(0.490303 - 3.28018i) q^{11} -0.0933146i q^{12} +(-1.66399 - 2.29029i) q^{13} +(1.52884 + 4.70527i) q^{14} +(2.95244 + 2.14507i) q^{16} +(2.17008 - 2.98685i) q^{17} +(3.44095 + 1.11803i) q^{18} +(0.0293950 + 0.0904686i) q^{19} -2.10021 q^{21} +(-3.98828 + 2.07605i) q^{22} -1.16215i q^{23} +(-1.36470 + 0.991515i) q^{24} +(-1.18596 + 3.65001i) q^{26} +(-1.91757 + 2.63930i) q^{27} +(-0.347817 + 0.478730i) q^{28} +(2.08707 - 6.42333i) q^{29} +(-5.48382 + 3.98423i) q^{31} +0.914918i q^{32} +(-0.314983 - 1.88253i) q^{33} -5.00509 q^{34} +(0.133724 + 0.411560i) q^{36} +(9.35820 + 3.04066i) q^{37} +(0.0757994 - 0.104329i) q^{38} +(-1.31805 - 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +(1.67354 + 2.30344i) q^{42} +2.96862i q^{43} +(-0.481274 - 0.239968i) q^{44} +(-1.27460 + 0.926052i) q^{46} +(2.11601 - 0.687534i) q^{47} +(1.99742 + 0.649001i) q^{48} +(5.11155 + 3.71376i) q^{49} +(0.656567 - 2.02070i) q^{51} +(-0.436565 + 0.141849i) q^{52} +(1.75979 + 2.42214i) q^{53} +4.42270 q^{54} +10.6970 q^{56} +(0.0321774 + 0.0442883i) q^{57} +(-8.70794 + 2.82938i) q^{58} +(2.62930 - 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(8.73951 + 2.83964i) q^{62} +(9.26289 - 3.00970i) q^{63} +(6.90832 - 5.01919i) q^{64} +(-1.81369 + 1.84554i) q^{66} -13.4153i q^{67} +(-0.351872 - 0.484310i) q^{68} +(-0.206673 - 0.636074i) q^{69} +(-6.71734 - 4.88043i) q^{71} +(4.59808 - 6.32872i) q^{72} +(1.25542 + 0.407912i) q^{73} +(-4.12215 - 12.6867i) q^{74} +0.0154241 q^{76} +(-5.40091 + 10.8319i) q^{77} +2.20866i q^{78} +(-11.2179 + 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-6.62834 + 9.12312i) q^{82} +(6.25666 - 8.61155i) q^{83} +(-0.105234 + 0.323876i) q^{84} +(3.25587 - 2.36553i) q^{86} -3.88682i q^{87} +(1.60431 + 9.58829i) q^{88} +12.1612 q^{89} +(3.19256 + 9.82567i) q^{91} +(-0.179216 - 0.0582308i) q^{92} +(-2.29290 + 3.15590i) q^{93} +(-2.44020 - 1.77291i) q^{94} +(0.162706 + 0.500759i) q^{96} +(2.54589 + 3.50412i) q^{97} -8.56545i q^{98} +(4.08696 + 7.85141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 14 q^{6} + 10 q^{9} + 6 q^{11} + 32 q^{14} + 8 q^{16} - 30 q^{19} - 40 q^{21} - 26 q^{24} + 20 q^{26} + 18 q^{29} - 20 q^{31} - 8 q^{34} - 30 q^{36} - 42 q^{39} + 16 q^{41} + 24 q^{44}+ \cdots + 40 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 14 * q^6 + 10 * q^9 + 6 * q^11 + 32 * q^14 + 8 * q^16 - 30 * q^19 - 40 * q^21 - 26 * q^24 + 20 * q^26 + 18 * q^29 - 20 * q^31 - 8 * q^34 - 30 * q^36 - 42 * q^39 + 16 * q^41 + 24 * q^44 + 6 * q^46 - 2 * q^49 + 2 * q^51 - 32 * q^54 + 44 * q^56 + 54 * q^59 + 12 * q^61 + 52 * q^64 + 26 * q^66 + 2 * q^69 - 40 * q^71 - 40 * q^74 - 74 * q^79 + 16 * q^81 - 56 * q^84 - 6 * q^86 + 32 * q^89 + 88 * q^91 - 34 * q^94 - 34 * q^96 + 40 * q^99

Introduction

L-functions

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