LMFDB - Embedded newform 475.2.g.b.18.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(18,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("475.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 35x^{8} + 223x^{4} + 289 $ x^12 + 35x^8 + 223x^4 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.3
Root			$-0.813901 + 0.813901i$ of defining polynomial
Character	$\chi$	$=$	475.18
Dual form			475.2.g.b.132.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813901 - 0.813901i) q^{2} +(2.01945 - 2.01945i) q^{3} -0.675131i q^{4} -3.28726 q^{6} +(2.67513 - 2.67513i) q^{7} +(-2.17729 + 2.17729i) q^{8} -5.15633i q^{9} +O(q^{10})$	\(q+(-0.813901 - 0.813901i) q^{2} +(2.01945 - 2.01945i) q^{3} -0.675131i q^{4} -3.28726 q^{6} +(2.67513 - 2.67513i) q^{7} +(-2.17729 + 2.17729i) q^{8} -5.15633i q^{9} +2.15633 q^{11} +(-1.36339 - 1.36339i) q^{12} +(-2.01945 + 2.01945i) q^{13} -4.35458 q^{14} +2.19394 q^{16} +(-1.80606 + 1.80606i) q^{17} +(-4.19674 + 4.19674i) q^{18} +(4.35458 - 0.193937i) q^{19} -10.8046i q^{21} +(-1.75503 - 1.75503i) q^{22} +(2.67513 + 2.67513i) q^{23} +8.79384i q^{24} +3.28726 q^{26} +(-4.35458 - 4.35458i) q^{27} +(-1.80606 - 1.80606i) q^{28} -7.29450 q^{29} +2.09540i q^{31} +(2.56894 + 2.56894i) q^{32} +(4.35458 - 4.35458i) q^{33} +2.93991 q^{34} -3.48119 q^{36} +(0.391644 + 0.391644i) q^{37} +(-3.70204 - 3.38635i) q^{38} +8.15633i q^{39} +3.51007i q^{41} +(-8.79384 + 8.79384i) q^{42} +(5.24965 + 5.24965i) q^{43} -1.45580i q^{44} -4.35458i q^{46} +(-1.63752 + 1.63752i) q^{47} +(4.43054 - 4.43054i) q^{48} -7.31265i q^{49} +7.29450i q^{51} +(1.36339 + 1.36339i) q^{52} +(-4.43054 + 4.43054i) q^{53} +7.08840i q^{54} +11.6491i q^{56} +(8.40220 - 9.18549i) q^{57} +(5.93700 + 5.93700i) q^{58} -3.51007 q^{59} -4.93207 q^{61} +(1.70545 - 1.70545i) q^{62} +(-13.7938 - 13.7938i) q^{63} -8.56959i q^{64} -7.08840 q^{66} +(-7.68614 - 7.68614i) q^{67} +(1.21933 + 1.21933i) q^{68} +10.8046 q^{69} -10.8046i q^{71} +(11.2268 + 11.2268i) q^{72} +(-9.73084 - 9.73084i) q^{73} -0.637519i q^{74} +(-0.130933 - 2.93991i) q^{76} +(5.76845 - 5.76845i) q^{77} +(6.63844 - 6.63844i) q^{78} +5.19910 q^{79} -2.11871 q^{81} +(2.85685 - 2.85685i) q^{82} +(8.44358 + 8.44358i) q^{83} -7.29450 q^{84} -8.54538i q^{86} +(-14.7308 + 14.7308i) q^{87} +(-4.69495 + 4.69495i) q^{88} +5.60547 q^{89} +10.8046i q^{91} +(1.80606 - 1.80606i) q^{92} +(4.23155 + 4.23155i) q^{93} +2.66556 q^{94} +10.3757 q^{96} +(5.59074 + 5.59074i) q^{97} +(-5.95177 + 5.95177i) q^{98} -11.1187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{6} + 12 q^{7}+O(q^{10}) $ 12 * q - 16 * q^6 + 12 * q^7	$ 12 q - 16 q^{6} + 12 q^{7} - 16 q^{11} + 28 q^{16} - 20 q^{17} + 12 q^{23} + 16 q^{26} - 20 q^{28} - 20 q^{36} - 4 q^{38} - 4 q^{43} + 44 q^{47} + 88 q^{58} - 24 q^{61} - 8 q^{62} - 60 q^{63} - 8 q^{66} - 44 q^{68} - 28 q^{73} - 20 q^{76} + 24 q^{77} + 60 q^{81} - 88 q^{82} + 36 q^{83} - 88 q^{87} + 20 q^{92} + 96 q^{93} + 24 q^{96}+O(q^{100}) $ 12 * q - 16 * q^6 + 12 * q^7 - 16 * q^11 + 28 * q^16 - 20 * q^17 + 12 * q^23 + 16 * q^26 - 20 * q^28 - 20 * q^36 - 4 * q^38 - 4 * q^43 + 44 * q^47 + 88 * q^58 - 24 * q^61 - 8 * q^62 - 60 * q^63 - 8 * q^66 - 44 * q^68 - 28 * q^73 - 20 * q^76 + 24 * q^77 + 60 * q^81 - 88 * q^82 + 36 * q^83 - 88 * q^87 + 20 * q^92 + 96 * q^93 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.813901	−	0.813901i	−0.575515	−	0.575515i	0.358149	−	0.933664i	$-0.383408\pi$
$2$	−0.813901	−	0.813901i	−0.575515	−	0.575515i	−0.933664	+	0.358149i	$0.883408\pi$
$3$	2.01945	−	2.01945i	1.16593	−	1.16593i	0.182773	−	0.983155i	$-0.441493\pi$
$3$	2.01945	−	2.01945i	1.16593	−	1.16593i	0.983155	−	0.182773i	$-0.0585072\pi$
$4$		−	0.675131i		−	0.337565i
$5$		0			0
$5$		0			0
$6$	−3.28726			−1.34202
$7$	2.67513	−	2.67513i	1.01110	−	1.01110i	0.0111668	−	0.999938i	$-0.496445\pi$
$7$	2.67513	−	2.67513i	1.01110	−	1.01110i	0.999938	−	0.0111668i	$-0.00355457\pi$
$8$	−2.17729	+	2.17729i	−0.769789	+	0.769789i
$9$		−	5.15633i		−	1.71878i
$10$		0			0
$11$	2.15633			0.650157			0.325078	−	0.945687i	$-0.394609\pi$
$11$	2.15633			0.650157			0.325078	+	0.945687i	$0.394609\pi$
$12$	−1.36339	−	1.36339i	−0.393577	−	0.393577i
$13$	−2.01945	+	2.01945i	−0.560094	+	0.560094i	−0.929334	−	0.369240i	$-0.879618\pi$
$13$	−2.01945	+	2.01945i	−0.560094	+	0.560094i	0.369240	+	0.929334i	$0.379618\pi$
$14$	−4.35458			−1.16381
$15$		0			0
$16$	2.19394			0.548484
$17$	−1.80606	+	1.80606i	−0.438035	+	0.438035i	−0.891350	−	0.453315i	$-0.850241\pi$
$17$	−1.80606	+	1.80606i	−0.438035	+	0.438035i	0.453315	+	0.891350i	$0.350241\pi$
$18$	−4.19674	+	4.19674i	−0.989180	+	0.989180i
$19$	4.35458	−	0.193937i	0.999010	−	0.0444921i
$19$	4.35458	−	0.193937i	0.999010	−	0.0444921i
$20$		0			0
$21$		−	10.8046i		−	2.35775i
$22$	−1.75503	−	1.75503i	−0.374175	−	0.374175i
$23$	2.67513	+	2.67513i	0.557803	+	0.557803i	0.928682	−	0.370878i	$-0.120943\pi$
$23$	2.67513	+	2.67513i	0.557803	+	0.557803i	−0.370878	+	0.928682i	$0.620943\pi$
$24$			8.79384i			1.79504i
$25$		0			0
$26$	3.28726			0.644684
$27$	−4.35458	−	4.35458i	−0.838040	−	0.838040i
$28$	−1.80606	−	1.80606i	−0.341314	−	0.341314i
$29$	−7.29450			−1.35455			−0.677277	−	0.735728i	$-0.736840\pi$
$29$	−7.29450			−1.35455			−0.677277	+	0.735728i	$0.736840\pi$
$30$		0			0
$31$			2.09540i			0.376345i	0.982136	+	0.188173i	$0.0602564\pi$
$31$			2.09540i			0.376345i	−0.982136	+	0.188173i	$0.939744\pi$
$32$	2.56894	+	2.56894i	0.454128	+	0.454128i
$33$	4.35458	−	4.35458i	0.758036	−	0.758036i
$34$	2.93991			0.504191
$35$		0			0
$36$	−3.48119			−0.580199
$37$	0.391644	+	0.391644i	0.0643860	+	0.0643860i	0.738567	−	0.674181i	$-0.235503\pi$
$37$	0.391644	+	0.391644i	0.0643860	+	0.0643860i	−0.674181	+	0.738567i	$0.735503\pi$
$38$	−3.70204	−	3.38635i	−0.600551	−	0.549339i
$39$			8.15633i			1.30606i
$40$		0			0
$41$			3.51007i			0.548181i	0.961704	+	0.274090i	$0.0883768\pi$
$41$			3.51007i			0.548181i	−0.961704	+	0.274090i	$0.911623\pi$
$42$	−8.79384	+	8.79384i	−1.35692	+	1.35692i
$43$	5.24965	+	5.24965i	0.800564	+	0.800564i	0.983184	−	0.182620i	$-0.0584578\pi$
$43$	5.24965	+	5.24965i	0.800564	+	0.800564i	−0.182620	+	0.983184i	$0.558458\pi$
$44$		−	1.45580i		−	0.219470i
$45$		0			0
$46$		−	4.35458i		−	0.642048i
$47$	−1.63752	+	1.63752i	−0.238857	+	0.238857i	−0.816377	−	0.577520i	$-0.804021\pi$
$47$	−1.63752	+	1.63752i	−0.238857	+	0.238857i	0.577520	+	0.816377i	$0.304021\pi$
$48$	4.43054	−	4.43054i	0.639493	−	0.639493i
$49$		−	7.31265i		−	1.04466i
$50$		0			0
$51$			7.29450i			1.02143i
$52$	1.36339	+	1.36339i	0.189068	+	0.189068i
$53$	−4.43054	+	4.43054i	−0.608581	+	0.608581i	−0.942575	−	0.333994i	$-0.891603\pi$
$53$	−4.43054	+	4.43054i	−0.608581	+	0.608581i	0.333994	+	0.942575i	$0.391603\pi$
$54$			7.08840i			0.964609i
$55$		0			0
$56$			11.6491i			1.55667i
$57$	8.40220	−	9.18549i	1.11290	−	1.21665i
$58$	5.93700	+	5.93700i	0.779566	+	0.779566i
$59$	−3.51007			−0.456972			−0.228486	−	0.973547i	$-0.573378\pi$
$59$	−3.51007			−0.456972			−0.228486	+	0.973547i	$0.573378\pi$
$60$		0			0
$61$	−4.93207			−0.631487			−0.315744	−	0.948845i	$-0.602254\pi$
$61$	−4.93207			−0.631487			−0.315744	+	0.948845i	$0.602254\pi$
$62$	1.70545	−	1.70545i	0.216592	−	0.216592i
$63$	−13.7938	−	13.7938i	−1.73786	−	1.73786i
$64$		−	8.56959i		−	1.07120i
$65$		0			0
$66$	−7.08840			−0.872521
$67$	−7.68614	−	7.68614i	−0.939011	−	0.939011i	0.0592327	−	0.998244i	$-0.481135\pi$
$67$	−7.68614	−	7.68614i	−0.939011	−	0.939011i	−0.998244	+	0.0592327i	$0.981135\pi$
$68$	1.21933	+	1.21933i	0.147865	+	0.147865i
$69$	10.8046			1.30072
$70$		0			0
$71$		−	10.8046i		−	1.28227i	−0.767430	−	0.641133i	$-0.778465\pi$
$71$		−	10.8046i		−	1.28227i	0.767430	−	0.641133i	$-0.221535\pi$
$72$	11.2268	+	11.2268i	1.32309	+	1.32309i
$73$	−9.73084	−	9.73084i	−1.13891	−	1.13891i	−0.988646	−	0.150263i	$-0.951988\pi$
$73$	−9.73084	−	9.73084i	−1.13891	−	1.13891i	−0.150263	−	0.988646i	$-0.548012\pi$
$74$		−	0.637519i		−	0.0741101i
$75$		0			0
$76$	−0.130933	−	2.93991i	−0.0150190	−	0.337231i
$77$	5.76845	−	5.76845i	0.657376	−	0.657376i
$78$	6.63844	−	6.63844i	0.751655	−	0.751655i
$79$	5.19910			0.584944			0.292472	−	0.956274i	$-0.405522\pi$
$79$	5.19910			0.584944			0.292472	+	0.956274i	$0.405522\pi$
$80$		0			0
$81$	−2.11871			−0.235413
$82$	2.85685	−	2.85685i	0.315486	−	0.315486i
$83$	8.44358	+	8.44358i	0.926804	+	0.926804i	0.997498	−	0.0706944i	$-0.0225215\pi$
$83$	8.44358	+	8.44358i	0.926804	+	0.926804i	−0.0706944	+	0.997498i	$0.522522\pi$
$84$	−7.29450			−0.795895
$85$		0			0
$86$		−	8.54538i		−	0.921472i
$87$	−14.7308	+	14.7308i	−1.57931	+	1.57931i
$88$	−4.69495	+	4.69495i	−0.500483	+	0.500483i
$89$	5.60547			0.594179			0.297089	−	0.954850i	$-0.403984\pi$
$89$	5.60547			0.594179			0.297089	+	0.954850i	$0.403984\pi$
$90$		0			0
$91$			10.8046i			1.13263i
$92$	1.80606	−	1.80606i	0.188295	−	0.188295i
$93$	4.23155	+	4.23155i	0.438791	+	0.438791i
$94$	2.66556			0.274931
$95$		0			0
$96$	10.3757			1.05896
$97$	5.59074	+	5.59074i	0.567654	+	0.567654i	0.931470	−	0.363817i	$-0.118527\pi$
$97$	5.59074	+	5.59074i	0.567654	+	0.567654i	−0.363817	+	0.931470i	$0.618527\pi$
$98$	−5.95177	+	5.95177i	−0.601220	+	0.601220i
$99$		−	11.1187i		−	1.11747i
$100$		0			0
$101$	−5.76845			−0.573982			−0.286991	−	0.957933i	$-0.592655\pi$
$101$	−5.76845			−0.573982			−0.286991	+	0.957933i	$0.592655\pi$
$102$	5.93700	−	5.93700i	0.587850	−	0.587850i
$103$	13.1397	−	13.1397i	1.29469	−	1.29469i	0.362843	−	0.931850i	$-0.381806\pi$
$103$	13.1397	−	13.1397i	1.29469	−	1.29469i	0.931850	−	0.362843i	$-0.118194\pi$
$104$		−	8.79384i		−	0.862307i
$105$		0			0
$106$	7.21203			0.700495
$107$	10.4129	+	10.4129i	1.00666	+	1.00666i	0.999978	+	0.00667734i	$0.00212548\pi$
$107$	10.4129	+	10.4129i	1.00666	+	1.00666i	0.00667734	+	0.999978i	$0.497875\pi$
$108$	−2.93991	+	2.93991i	−0.282893	+	0.282893i
$109$	−2.09540			−0.200703			−0.100351	−	0.994952i	$-0.531997\pi$
$109$	−2.09540			−0.200703			−0.100351	+	0.994952i	$0.531997\pi$
$110$		0			0
$111$	1.58181			0.150139
$112$	5.86907	−	5.86907i	0.554575	−	0.554575i
$113$	1.49062	−	1.49062i	0.140226	−	0.140226i	−0.633509	−	0.773735i	$-0.718386\pi$
$113$	1.49062	−	1.49062i	0.140226	−	0.140226i	0.773735	+	0.633509i	$0.218386\pi$
$114$	−14.3146	+	0.637519i	−1.34069	+	0.0597092i
$115$		0			0
$116$			4.92474i			0.457251i
$117$	10.4129	+	10.4129i	0.962675	+	0.962675i
$118$	2.85685	+	2.85685i	0.262994	+	0.262994i
$119$			9.66291i			0.885798i
$120$		0			0
$121$	−6.35026			−0.577297
$122$	4.01422	+	4.01422i	0.363430	+	0.363430i
$123$	7.08840	+	7.08840i	0.639139	+	0.639139i
$124$	1.41467			0.127041
$125$		0			0
$126$			22.4536i			2.00033i
$127$	−3.96294	−	3.96294i	−0.351654	−	0.351654i	0.509071	−	0.860725i	$-0.329989\pi$
$127$	−3.96294	−	3.96294i	−0.351654	−	0.351654i	−0.860725	+	0.509071i	$0.829989\pi$
$128$	−1.83693	+	1.83693i	−0.162363	+	0.162363i
$129$	21.2028			1.86680
$130$		0			0
$131$	13.4010			1.17085			0.585427	−	0.810725i	$-0.300927\pi$
$131$	13.4010			1.17085			0.585427	+	0.810725i	$0.300927\pi$
$132$	−2.93991	−	2.93991i	−0.255887	−	0.255887i
$133$	11.1303	−	12.1679i	0.965117	−	1.05509i
$134$			12.5115i			1.08083i
$135$		0			0
$136$		−	7.86465i		−	0.674388i
$137$	−1.38787	+	1.38787i	−0.118574	+	0.118574i	−0.763904	−	0.645330i	$-0.776720\pi$
$137$	−1.38787	+	1.38787i	−0.118574	+	0.118574i	0.645330	+	0.763904i	$0.276720\pi$
$138$	−8.79384	−	8.79384i	−0.748582	−	0.748582i
$139$			1.11871i			0.0948881i	0.998874	+	0.0474440i	$0.0151076\pi$
$139$			1.11871i			0.0948881i	−0.998874	+	0.0474440i	$0.984892\pi$
$140$		0			0
$141$			6.61376i			0.556979i
$142$	−8.79384	+	8.79384i	−0.737963	+	0.737963i
$143$	−4.35458	+	4.35458i	−0.364148	+	0.364148i
$144$		−	11.3127i		−	0.942721i
$145$		0			0
$146$			15.8399i			1.31092i
$147$	−14.7675	−	14.7675i	−1.21800	−	1.21800i
$148$	0.264411	−	0.264411i	0.0217345	−	0.0217345i
$149$			2.15633i			0.176653i	0.996092	+	0.0883265i	$0.0281519\pi$
$149$			2.15633i			0.176653i	−0.996092	+	0.0883265i	$0.971848\pi$
$150$		0			0
$151$			7.29450i			0.593618i	0.954937	+	0.296809i	$0.0959224\pi$
$151$			7.29450i			0.593618i	−0.954937	+	0.296809i	$0.904078\pi$
$152$	−9.05894	+	9.90345i	−0.734777	+	0.803276i
$153$	9.31265	+	9.31265i	0.752883	+	0.752883i
$154$	−9.38990			−0.756659
$155$		0			0
$156$	5.50659			0.440880
$157$	4.58181	−	4.58181i	0.365668	−	0.365668i	−0.500226	−	0.865895i	$-0.666750\pi$
$157$	4.58181	−	4.58181i	0.365668	−	0.365668i	0.865895	+	0.500226i	$0.166750\pi$
$158$	−4.23155	−	4.23155i	−0.336644	−	0.336644i
$159$			17.8945i			1.41912i
$160$		0			0
$161$	14.3127			1.12799
$162$	1.72442	+	1.72442i	0.135483	+	0.135483i
$163$	−10.1817	−	10.1817i	−0.797494	−	0.797494i	0.185206	−	0.982700i	$-0.440705\pi$
$163$	−10.1817	−	10.1817i	−0.797494	−	0.797494i	−0.982700	+	0.185206i	$0.940705\pi$
$164$	2.36976			0.185047
$165$		0			0
$166$		−	13.7445i		−	1.06678i
$167$	−2.27391	−	2.27391i	−0.175961	−	0.175961i	0.613632	−	0.789592i	$-0.289708\pi$
$167$	−2.27391	−	2.27391i	−0.175961	−	0.175961i	−0.789592	+	0.613632i	$0.789708\pi$
$168$	23.5247	+	23.5247i	1.81497	+	1.81497i
$169$			4.84367i			0.372590i
$170$		0			0
$171$	−1.00000	−	22.4536i	−0.0764719	−	1.71707i
$172$	3.54420	−	3.54420i	0.270243	−	0.270243i
$173$	10.8805	−	10.8805i	0.827231	−	0.827231i	−0.159902	−	0.987133i	$-0.551118\pi$
$173$	10.8805	−	10.8805i	0.827231	−	0.827231i	0.987133	+	0.159902i	$0.0511179\pi$
$174$	23.9789			1.81783
$175$		0			0
$176$	4.73084			0.356601
$177$	−7.08840	+	7.08840i	−0.532797	+	0.532797i
$178$	−4.56230	−	4.56230i	−0.341959	−	0.341959i
$179$	−5.19910			−0.388599			−0.194299	−	0.980942i	$-0.562243\pi$
$179$	−5.19910			−0.388599			−0.194299	+	0.980942i	$0.562243\pi$
$180$		0			0
$181$		−	7.02014i		−	0.521803i	−0.965365	−	0.260901i	$-0.915980\pi$
$181$		−	7.02014i		−	0.521803i	0.965365	−	0.260901i	$-0.0840198\pi$
$182$	8.79384	−	8.79384i	0.651843	−	0.651843i
$183$	−9.96005	+	9.96005i	−0.736268	+	0.736268i
$184$	−11.6491			−0.858781
$185$		0			0
$186$		−	6.88812i		−	0.505062i
$187$	−3.89446	+	3.89446i	−0.284791	+	0.284791i
$188$	1.10554	+	1.10554i	0.0806298	+	0.0806298i
$189$	−23.2982			−1.69469
$190$		0			0
$191$	−4.43866			−0.321170			−0.160585	−	0.987022i	$-0.551338\pi$
$191$	−4.43866			−0.321170			−0.160585	+	0.987022i	$0.551338\pi$
$192$	−17.3058	−	17.3058i	−1.24894	−	1.24894i
$193$	4.27863	−	4.27863i	0.307982	−	0.307982i	−0.536144	−	0.844126i	$-0.680120\pi$
$193$	4.27863	−	4.27863i	0.307982	−	0.307982i	0.844126	+	0.536144i	$0.180120\pi$
$194$		−	9.10062i		−	0.653386i
$195$		0			0
$196$	−4.93700			−0.352643
$197$	−13.3430	+	13.3430i	−0.950647	+	0.950647i	−0.998838	−	0.0481911i	$-0.984654\pi$
$197$	−13.3430	+	13.3430i	−0.950647	+	0.950647i	0.0481911	+	0.998838i	$0.484654\pi$
$198$	−9.04953	+	9.04953i	−0.643122	+	0.643122i
$199$			14.6253i			1.03676i	0.855150	+	0.518380i	$0.173465\pi$
$199$			14.6253i			1.03676i	−0.855150	+	0.518380i	$0.826535\pi$
$200$		0			0
$201$	−31.0435			−2.18964
$202$	4.69495	+	4.69495i	0.330335	+	0.330335i
$203$	−19.5137	+	19.5137i	−1.36960	+	1.36960i
$204$	4.92474			0.344801
$205$		0			0
$206$	−21.3888			−1.49023
$207$	13.7938	−	13.7938i	0.958738	−	0.958738i
$208$	−4.43054	+	4.43054i	−0.307202	+	0.307202i
$209$	9.38990	−	0.418190i	0.649513	−	0.0289268i
$210$		0			0
$211$		−	16.0037i		−	1.10174i	−0.834592	−	0.550869i	$-0.814296\pi$
$211$		−	16.0037i		−	1.10174i	0.834592	−	0.550869i	$-0.185704\pi$
$212$	2.99119	+	2.99119i	0.205436	+	0.205436i
$213$	−21.8192	−	21.8192i	−1.49503	−	1.49503i
$214$		−	16.9502i		−	1.15869i
$215$		0			0
$216$	18.9624			1.29023
$217$	5.60547	+	5.60547i	0.380524	+	0.380524i
$218$	1.70545	+	1.70545i	0.115508	+	0.115508i
$219$	−39.3018			−2.65577
$220$		0			0
$221$		−	7.29450i		−	0.490681i
$222$	−1.28744	−	1.28744i	−0.0864071	−	0.0864071i
$223$	−3.17965	+	3.17965i	−0.212925	+	0.212925i	−0.805509	−	0.592584i	$-0.798108\pi$
$223$	−3.17965	+	3.17965i	−0.212925	+	0.212925i	0.592584	+	0.805509i	$0.298108\pi$
$224$	13.7445			0.918342
$225$		0			0
$226$	−2.42644			−0.161404
$227$	−3.49534	−	3.49534i	−0.231994	−	0.231994i	0.581531	−	0.813524i	$-0.302454\pi$
$227$	−3.49534	−	3.49534i	−0.231994	−	0.231994i	−0.813524	+	0.581531i	$0.802454\pi$
$228$	−6.20141	−	5.67258i	−0.410698	−	0.375676i
$229$		−	10.2170i		−	0.675156i	−0.941298	−	0.337578i	$-0.890392\pi$
$229$		−	10.2170i		−	0.675156i	0.941298	−	0.337578i	$-0.109608\pi$
$230$		0			0
$231$		−	23.2982i		−	1.53291i
$232$	15.8822	−	15.8822i	1.04272	−	1.04272i
$233$	−8.61213	−	8.61213i	−0.564199	−	0.564199i	0.366298	−	0.930497i	$-0.380625\pi$
$233$	−8.61213	−	8.61213i	−0.564199	−	0.564199i	−0.930497	+	0.366298i	$0.880625\pi$
$234$		−	16.9502i		−	1.10807i
$235$		0			0
$236$			2.36976i			0.154258i
$237$	10.4993	−	10.4993i	0.682002	−	0.682002i
$238$	7.86465	−	7.86465i	0.509790	−	0.509790i
$239$		−	14.1260i		−	0.913735i	−0.889535	−	0.456868i	$-0.848971\pi$
$239$		−	14.1260i		−	0.913735i	0.889535	−	0.456868i	$-0.151029\pi$
$240$		0			0
$241$			26.8082i			1.72687i	0.504460	+	0.863435i	$0.331691\pi$
$241$			26.8082i			1.72687i	−0.504460	+	0.863435i	$0.668309\pi$
$242$	5.16848	+	5.16848i	0.332243	+	0.332243i
$243$	8.78512	−	8.78512i	0.563566	−	0.563566i
$244$			3.32979i			0.213168i
$245$		0			0
$246$		−	11.5385i		−	0.735668i
$247$	−8.40220	+	9.18549i	−0.534619	+	0.584459i
$248$	−4.56230	−	4.56230i	−0.289706	−	0.289706i
$249$	34.1027			2.16117
$250$		0			0
$251$	7.66291			0.483679			0.241839	−	0.970316i	$-0.422249\pi$
$251$	7.66291			0.483679			0.241839	+	0.970316i	$0.422249\pi$
$252$	−9.31265	+	9.31265i	−0.586642	+	0.586642i
$253$	5.76845	+	5.76845i	0.362659	+	0.362659i
$254$			6.45088i			0.404764i
$255$		0			0
$256$	−14.1490			−0.884314
$257$	−17.7074	−	17.7074i	−1.10456	−	1.10456i	−0.993853	−	0.110705i	$-0.964689\pi$
$257$	−17.7074	−	17.7074i	−1.10456	−	1.10456i	−0.110705	−	0.993853i	$-0.535311\pi$
$258$	−17.2569	−	17.2569i	−1.07437	−	1.07437i
$259$	2.09540			0.130202
$260$		0			0
$261$			37.6128i			2.32817i
$262$	−10.9071	−	10.9071i	−0.673844	−	0.673844i
$263$	−1.21933	−	1.21933i	−0.0751871	−	0.0751871i	0.668513	−	0.743700i	$-0.266931\pi$
$263$	−1.21933	−	1.21933i	−0.0751871	−	0.0751871i	−0.743700	+	0.668513i	$0.766931\pi$
$264$			18.9624i			1.16705i
$265$		0			0
$266$	−18.9624	+	0.844513i	−1.16266	+	0.0517804i
$267$	11.3199	−	11.3199i	0.692769	−	0.692769i
$268$	−5.18915	+	5.18915i	−0.316978	+	0.316978i
$269$	−32.4137			−1.97630			−0.988149	−	0.153498i	$-0.950946\pi$
$269$	−32.4137			−1.97630			−0.988149	+	0.153498i	$0.950946\pi$
$270$		0			0
$271$	−18.0059			−1.09378			−0.546890	−	0.837205i	$-0.684188\pi$
$271$	−18.0059			−1.09378			−0.546890	+	0.837205i	$0.684188\pi$
$272$	−3.96239	+	3.96239i	−0.240255	+	0.240255i
$273$	21.8192	+	21.8192i	1.32056	+	1.32056i
$274$	2.25918			0.136482
$275$		0			0
$276$		−	7.29450i		−	0.439077i
$277$	−9.93207	+	9.93207i	−0.596760	+	0.596760i	−0.939449	−	0.342689i	$-0.888662\pi$
$277$	−9.93207	+	9.93207i	−0.596760	+	0.596760i	0.342689	+	0.939449i	$0.388662\pi$
$278$	0.910522	−	0.910522i	0.0546095	−	0.0546095i
$279$	10.8046			0.646852
$280$		0			0
$281$			0.680731i			0.0406090i	0.999794	+	0.0203045i	$0.00646357\pi$
$281$			0.680731i			0.0406090i	−0.999794	+	0.0203045i	$0.993536\pi$
$282$	5.38295	−	5.38295i	0.320550	−	0.320550i
$283$	19.5623	+	19.5623i	1.16286	+	1.16286i	0.983847	+	0.179011i	$0.0572897\pi$
$283$	19.5623	+	19.5623i	1.16286	+	1.16286i	0.179011	+	0.983847i	$0.442710\pi$
$284$	−7.29450			−0.432849
$285$		0			0
$286$	7.08840			0.419146
$287$	9.38990	+	9.38990i	0.554268	+	0.554268i
$288$	13.2463	−	13.2463i	0.780544	−	0.780544i
$289$			10.4763i			0.616251i
$290$		0			0
$291$	22.5804			1.32369
$292$	−6.56959	+	6.56959i	−0.384456	+	0.384456i
$293$	−21.8489	+	21.8489i	−1.27642	+	1.27642i	−0.333770	+	0.942655i	$0.608321\pi$
$293$	−21.8489	+	21.8489i	−1.27642	+	1.27642i	−0.942655	+	0.333770i	$0.891679\pi$
$294$			24.0386i			1.40196i
$295$		0			0
$296$	−1.70545			−0.0991272
$297$	−9.38990	−	9.38990i	−0.544857	−	0.544857i
$298$	1.75503	−	1.75503i	0.101666	−	0.101666i
$299$	−10.8046			−0.624844
$300$		0			0
$301$	28.0870			1.61891
$302$	5.93700	−	5.93700i	0.341636	−	0.341636i
$303$	−11.6491	+	11.6491i	−0.669222	+	0.669222i
$304$	9.55368	−	0.425485i	0.547941	−	0.0244032i
$305$		0			0
$306$		−	15.1591i		−	0.866591i
$307$	−11.1962	−	11.1962i	−0.639001	−	0.639001i	0.311308	−	0.950309i	$-0.399233\pi$
$307$	−11.1962	−	11.1962i	−0.639001	−	0.639001i	−0.950309	+	0.311308i	$0.899233\pi$
$308$	−3.89446	−	3.89446i	−0.221907	−	0.221907i
$309$		−	53.0698i		−	3.01904i
$310$		0			0
$311$	−18.8423			−1.06845			−0.534223	−	0.845343i	$-0.679396\pi$
$311$	−18.8423			−1.06845			−0.534223	+	0.845343i	$0.679396\pi$
$312$	−17.7587	−	17.7587i	−1.00539	−	1.00539i
$313$	3.26187	+	3.26187i	0.184372	+	0.184372i	0.793258	−	0.608886i	$-0.208383\pi$
$313$	3.26187	+	3.26187i	0.184372	+	0.184372i	−0.608886	+	0.793258i	$0.708383\pi$
$314$	−7.45828			−0.420895
$315$		0			0
$316$		−	3.51007i		−	0.197457i
$317$	5.37761	+	5.37761i	0.302037	+	0.302037i	0.841810	−	0.539774i	$-0.181490\pi$
$317$	5.37761	+	5.37761i	0.302037	+	0.302037i	−0.539774	+	0.841810i	$0.681490\pi$
$318$	14.5643	−	14.5643i	0.816726	−	0.816726i
$319$	−15.7293			−0.880672
$320$		0			0
$321$	42.0567			2.34737
$322$	−11.6491	−	11.6491i	−0.649178	−	0.649178i
$323$	−7.51439	+	8.21491i	−0.418112	+	0.457090i
$324$			1.43041i			0.0794672i
$325$		0			0
$326$			16.5738i			0.917939i
$327$	−4.23155	+	4.23155i	−0.234005	+	0.234005i
$328$	−7.64244	−	7.64244i	−0.421983	−	0.421983i
$329$			8.76116i			0.483018i
$330$		0			0
$331$		−	21.8835i		−	1.20283i	−0.798939	−	0.601413i	$-0.794605\pi$
$331$		−	21.8835i		−	1.20283i	0.798939	−	0.601413i	$-0.205395\pi$
$332$	5.70052	−	5.70052i	0.312857	−	0.312857i
$333$	2.01945	−	2.01945i	0.110665	−	0.110665i
$334$			3.70148i			0.202536i
$335$		0			0
$336$		−	23.7045i		−	1.29319i
$337$	19.9666	+	19.9666i	1.08765	+	1.08765i	0.995770	+	0.0918798i	$0.0292876\pi$
$337$	19.9666	+	19.9666i	1.08765	+	1.08765i	0.0918798	+	0.995770i	$0.470712\pi$
$338$	3.94227	−	3.94227i	0.214431	−	0.214431i
$339$		−	6.02047i		−	0.326987i
$340$		0			0
$341$			4.51836i			0.244683i
$342$	−17.4611	+	19.0889i	−0.944190	+	1.03221i
$343$	−0.836381	−	0.836381i	−0.0451603	−	0.0451603i
$344$	−22.8600			−1.23253
$345$		0			0
$346$	−17.7113			−0.952167
$347$	−8.16125	+	8.16125i	−0.438119	+	0.438119i	−0.891379	−	0.453260i	$-0.850261\pi$
$347$	−8.16125	+	8.16125i	−0.438119	+	0.438119i	0.453260	+	0.891379i	$0.350261\pi$
$348$	9.94525	+	9.94525i	0.533121	+	0.533121i
$349$			33.5877i			1.79791i	0.438043	+	0.898954i	$0.355672\pi$
$349$			33.5877i			1.79791i	−0.438043	+	0.898954i	$0.644328\pi$
$350$		0			0
$351$	17.5877			0.938761
$352$	5.53946	+	5.53946i	0.295254	+	0.295254i
$353$	−3.88129	−	3.88129i	−0.206580	−	0.206580i	0.596232	−	0.802812i	$-0.296664\pi$
$353$	−3.88129	−	3.88129i	−0.206580	−	0.206580i	−0.802812	+	0.596232i	$0.796664\pi$
$354$	11.5385			0.613265
$355$		0			0
$356$		−	3.78443i		−	0.200574i
$357$	19.5137	+	19.5137i	1.03278	+	1.03278i
$358$	4.23155	+	4.23155i	0.223644	+	0.223644i
$359$			24.1925i			1.27683i	0.769691	+	0.638416i	$0.220410\pi$
$359$			24.1925i			1.27683i	−0.769691	+	0.638416i	$0.779590\pi$
$360$		0			0
$361$	18.9248	−	1.68903i	0.996041	−	0.0888961i
$362$	−5.71370	+	5.71370i	−0.300305	+	0.300305i
$363$	−12.8240	+	12.8240i	−0.673086	+	0.673086i
$364$	7.29450			0.382335
$365$		0			0
$366$	16.2130			0.847467
$367$	−4.83146	+	4.83146i	−0.252200	+	0.252200i	−0.821872	−	0.569672i	$-0.807070\pi$
$367$	−4.83146	+	4.83146i	−0.252200	+	0.252200i	0.569672	+	0.821872i	$0.307070\pi$
$368$	5.86907	+	5.86907i	0.305946	+	0.305946i
$369$	18.0991			0.942199
$370$		0			0
$371$			23.7045i			1.23068i
$372$	2.85685	−	2.85685i	0.148121	−	0.148121i
$373$	4.95936	−	4.95936i	0.256786	−	0.256786i	−0.566960	−	0.823746i	$-0.691880\pi$
$373$	4.95936	−	4.95936i	0.256786	−	0.256786i	0.823746	+	0.566960i	$0.191880\pi$
$374$	6.33941			0.327803
$375$		0			0
$376$		−	7.13071i		−	0.367738i
$377$	14.7308	−	14.7308i	0.758677	−	0.758677i
$378$	18.9624	+	18.9624i	0.975320	+	0.975320i
$379$	25.7999			1.32525			0.662627	−	0.748950i	$-0.269442\pi$
$379$	25.7999			1.32525			0.662627	+	0.748950i	$0.269442\pi$
$380$		0			0
$381$	−16.0059			−0.820006
$382$	3.61263	+	3.61263i	0.184838	+	0.184838i
$383$	0.920467	−	0.920467i	0.0470337	−	0.0470337i	−0.683199	−	0.730232i	$-0.739412\pi$
$383$	0.920467	−	0.920467i	0.0470337	−	0.0470337i	0.730232	+	0.683199i	$0.239412\pi$
$384$			7.41915i			0.378607i
$385$		0			0
$386$	−6.96476			−0.354497
$387$	27.0689	−	27.0689i	1.37599	−	1.37599i
$388$	3.77448	−	3.77448i	0.191620	−	0.191620i
$389$			4.83638i			0.245214i	0.992455	+	0.122607i	$0.0391255\pi$
$389$			4.83638i			0.245214i	−0.992455	+	0.122607i	$0.960874\pi$
$390$		0			0
$391$	−9.66291			−0.488674
$392$	15.9218	+	15.9218i	0.804171	+	0.804171i
$393$	27.0627	−	27.0627i	1.36513	−	1.36513i
$394$	21.7197			1.09422
$395$		0			0
$396$	−7.50659			−0.377220
$397$	2.14315	−	2.14315i	0.107562	−	0.107562i	−0.651278	−	0.758839i	$-0.725767\pi$
$397$	2.14315	−	2.14315i	0.107562	−	0.107562i	0.758839	+	0.651278i	$0.225767\pi$
$398$	11.9035	−	11.9035i	0.596671	−	0.596671i
$399$	−2.09540	−	47.0494i	−0.104901	−	2.35541i
$400$		0			0
$401$			19.1074i			0.954176i	0.878856	+	0.477088i	$0.158308\pi$
$401$			19.1074i			0.954176i	−0.878856	+	0.477088i	$0.841692\pi$
$402$	25.2663	+	25.2663i	1.26017	+	1.26017i
$403$	−4.23155	−	4.23155i	−0.210788	−	0.210788i
$404$			3.89446i			0.193757i
$405$		0			0
$406$	31.7645			1.57644
$407$	0.844513	+	0.844513i	0.0418609	+	0.0418609i
$408$	−15.8822	−	15.8822i	−0.786288	−	0.786288i
$409$	15.3229			0.757670			0.378835	−	0.925464i	$-0.376325\pi$
$409$	15.3229			0.757670			0.378835	+	0.925464i	$0.376325\pi$
$410$		0			0
$411$			5.60547i			0.276497i
$412$	−8.87102	−	8.87102i	−0.437044	−	0.437044i
$413$	−9.38990	+	9.38990i	−0.462047	+	0.462047i
$414$	−22.4536			−1.10354
$415$		0			0
$416$	−10.3757			−0.508708
$417$	2.25918	+	2.25918i	0.110633	+	0.110633i
$418$	−7.98281	−	7.30208i	−0.390452	−	0.357156i
$419$		−	25.8251i		−	1.26164i	−0.775929	−	0.630820i	$-0.782719\pi$
$419$		−	25.8251i		−	1.26164i	0.775929	−	0.630820i	$-0.217281\pi$
$420$		0			0
$421$			25.1192i			1.22423i	0.790767	+	0.612117i	$0.209682\pi$
$421$			25.1192i			1.22423i	−0.790767	+	0.612117i	$0.790318\pi$
$422$	−13.0254	+	13.0254i	−0.634066	+	0.634066i
$423$	8.44358	+	8.44358i	0.410541	+	0.410541i
$424$		−	19.2931i		−	0.936958i
$425$		0			0
$426$			35.5174i			1.72082i
$427$	−13.1939	+	13.1939i	−0.638499	+	0.638499i
$428$	7.03008	−	7.03008i	0.339812	−	0.339812i
$429$			17.5877i			0.849142i
$430$		0			0
$431$		−	35.9238i		−	1.73039i	−0.501438	−	0.865193i	$-0.667196\pi$
$431$		−	35.9238i		−	1.73039i	0.501438	−	0.865193i	$-0.332804\pi$
$432$	−9.55368	−	9.55368i	−0.459652	−	0.459652i
$433$	−16.6084	+	16.6084i	−0.798151	+	0.798151i	−0.982804	−	0.184653i	$-0.940884\pi$
$433$	−16.6084	+	16.6084i	−0.798151	+	0.798151i	0.184653	+	0.982804i	$0.440884\pi$
$434$		−	9.12459i		−	0.437994i
$435$		0			0
$436$			1.41467i			0.0677504i
$437$	12.1679	+	11.1303i	0.582069	+	0.532433i
$438$	31.9878	+	31.9878i	1.52844	+	1.52844i
$439$	22.2899			1.06384			0.531919	−	0.846796i	$-0.321471\pi$
$439$	22.2899			1.06384			0.531919	+	0.846796i	$0.321471\pi$
$440$		0			0
$441$	−37.7064			−1.79554
$442$	−5.93700	+	5.93700i	−0.282394	+	0.282394i
$443$	−21.2193	−	21.2193i	−1.00816	−	1.00816i	−0.999966	−	0.00819433i	$-0.997392\pi$
$443$	−21.2193	−	21.2193i	−1.00816	−	1.00816i	−0.00819433	−	0.999966i	$-0.502608\pi$
$444$		−	1.06793i		−	0.0506816i
$445$		0			0
$446$	5.17584			0.245083
$447$	4.35458	+	4.35458i	0.205965	+	0.205965i
$448$	−22.9248	−	22.9248i	−1.08309	−	1.08309i
$449$	−7.97523			−0.376374			−0.188187	−	0.982133i	$-0.560261\pi$
$449$	−7.97523			−0.376374			−0.188187	+	0.982133i	$0.560261\pi$
$450$		0			0
$451$			7.56885i			0.356403i
$452$	−1.00637	−	1.00637i	−0.0473355	−	0.0473355i
$453$	14.7308	+	14.7308i	0.692115	+	0.692115i
$454$			5.68972i			0.267032i
$455$		0			0
$456$	1.70545	+	38.2935i	0.0798649	+	1.79326i
$457$	2.22425	−	2.22425i	0.104046	−	0.104046i	−0.653167	−	0.757214i	$-0.726560\pi$
$457$	2.22425	−	2.22425i	0.104046	−	0.104046i	0.757214	+	0.653167i	$0.226560\pi$
$458$	−8.31559	+	8.31559i	−0.388562	+	0.388562i
$459$	15.7293			0.734181
$460$		0			0
$461$	−17.1636			−0.799389			−0.399695	−	0.916648i	$-0.630884\pi$
$461$	−17.1636			−0.799389			−0.399695	+	0.916648i	$0.630884\pi$
$462$	−18.9624	+	18.9624i	−0.882210	+	0.882210i
$463$	−18.3888	−	18.3888i	−0.854601	−	0.854601i	0.136095	−	0.990696i	$-0.456545\pi$
$463$	−18.3888	−	18.3888i	−0.854601	−	0.854601i	−0.990696	+	0.136095i	$0.956545\pi$
$464$	−16.0037			−0.742951
$465$		0			0
$466$			14.0188i			0.649410i
$467$	19.2252	−	19.2252i	0.889637	−	0.889637i	−0.104851	−	0.994488i	$-0.533437\pi$
$467$	19.2252	−	19.2252i	0.889637	−	0.889637i	0.994488	+	0.104851i	$0.0334367\pi$
$468$	7.03008	−	7.03008i	0.324966	−	0.324966i
$469$	−41.1229			−1.89888
$470$		0			0
$471$		−	18.5054i		−	0.852685i
$472$	7.64244	−	7.64244i	0.351772	−	0.351772i
$473$	11.3199	+	11.3199i	0.520492	+	0.520492i
$474$	−17.0908			−0.785005
$475$		0			0
$476$	6.52373			0.299015
$477$	22.8453	+	22.8453i	1.04601	+	1.04601i
$478$	−11.4972	+	11.4972i	−0.525868	+	0.525868i
$479$		−	0.282333i		−	0.0129001i	−0.999979	−	0.00645007i	$-0.997947\pi$
$479$		−	0.282333i		−	0.0129001i	0.999979	−	0.00645007i	$-0.00205313\pi$
$480$		0			0
$481$	−1.58181			−0.0721243
$482$	21.8192	−	21.8192i	0.993839	−	0.993839i
$483$	28.9036	−	28.9036i	1.31516	−	1.31516i
$484$			4.28726i			0.194875i
$485$		0			0
$486$	−14.3004			−0.648681
$487$	−19.9054	−	19.9054i	−0.901999	−	0.901999i	0.0936103	−	0.995609i	$-0.470159\pi$
$487$	−19.9054	−	19.9054i	−0.901999	−	0.901999i	−0.995609	+	0.0936103i	$0.970159\pi$
$488$	10.7386	−	10.7386i	0.486112	−	0.486112i
$489$	−41.1229			−1.85964
$490$		0			0
$491$	14.8872			0.671848			0.335924	−	0.941889i	$-0.390951\pi$
$491$	14.8872			0.671848			0.335924	+	0.941889i	$0.390951\pi$
$492$	4.78560	−	4.78560i	0.215751	−	0.215751i
$493$	13.1743	−	13.1743i	0.593342	−	0.593342i
$494$	14.3146	−	0.637519i	0.644046	−	0.0286834i
$495$		0			0
$496$			4.59718i			0.206419i
$497$	−28.9036	−	28.9036i	−1.29650	−	1.29650i
$498$	−27.7562	−	27.7562i	−1.24379	−	1.24379i
$499$			24.5950i			1.10102i	0.834828	+	0.550511i	$0.185567\pi$
$499$			24.5950i			1.10102i	−0.834828	+	0.550511i	$0.814433\pi$
$500$		0			0
$501$	−9.18409			−0.410315
$502$	−6.23685	−	6.23685i	−0.278364	−	0.278364i
$503$	3.01222	+	3.01222i	0.134308	+	0.134308i	0.771065	−	0.636757i	$-0.219724\pi$
$503$	3.01222	+	3.01222i	0.134308	+	0.134308i	−0.636757	+	0.771065i	$0.719724\pi$
$504$	60.0664			2.67557
$505$		0			0
$506$		−	9.38990i		−	0.417432i
$507$	9.78154	+	9.78154i	0.434413	+	0.434413i
$508$	−2.67550	+	2.67550i	−0.118706	+	0.118706i
$509$	16.0037			0.709350			0.354675	−	0.934990i	$-0.384592\pi$
$509$	16.0037			0.709350			0.354675	+	0.934990i	$0.384592\pi$
$510$		0			0
$511$	−52.0625			−2.30311
$512$	15.1898	+	15.1898i	0.671299	+	0.671299i
$513$	−19.8069	−	18.1179i	−0.874496	−	0.799924i
$514$			28.8242i			1.27138i
$515$		0			0
$516$		−	14.3146i		−	0.630167i
$517$	−3.53102	+	3.53102i	−0.155294	+	0.155294i
$518$	−1.70545	−	1.70545i	−0.0749331	−	0.0749331i
$519$		−	43.9452i		−	1.92898i
$520$		0			0
$521$		−	13.2275i		−	0.579509i	−0.957101	−	0.289754i	$-0.906426\pi$
$521$		−	13.2275i		−	0.579509i	0.957101	−	0.289754i	$-0.0935736\pi$
$522$	30.6131	−	30.6131i	1.33990	−	1.33990i
$523$	−25.4695	+	25.4695i	−1.11370	+	1.11370i	−0.121059	+	0.992645i	$0.538629\pi$
$523$	−25.4695	+	25.4695i	−1.11370	+	1.11370i	−0.992645	+	0.121059i	$0.961371\pi$
$524$		−	9.04746i		−	0.395240i
$525$		0			0
$526$			1.98483i			0.0865425i
$527$	−3.78443	−	3.78443i	−0.164852	−	0.164852i
$528$	9.55368	−	9.55368i	0.415770	−	0.415770i
$529$		−	8.68735i		−	0.377711i
$530$		0			0
$531$			18.0991i			0.785432i
$532$	−8.21491	−	7.51439i	−0.356162	−	0.325790i
$533$	−7.08840	−	7.08840i	−0.307033	−	0.307033i
$534$	−18.4266			−0.797398
$535$		0			0
$536$	33.4699			1.44568
$537$	−10.4993	+	10.4993i	−0.453078	+	0.453078i
$538$	26.3815	+	26.3815i	1.13739	+	1.13739i
$539$		−	15.7685i		−	0.679195i
$540$		0			0
$541$	−15.0679			−0.647821			−0.323910	−	0.946088i	$-0.604998\pi$
$541$	−15.0679			−0.647821			−0.323910	+	0.946088i	$0.604998\pi$
$542$	14.6550	+	14.6550i	0.629486	+	0.629486i
$543$	−14.1768	−	14.1768i	−0.608384	−	0.608384i
$544$	−9.27932			−0.397848
$545$		0			0
$546$		−	35.5174i		−	1.52000i
$547$	13.4554	+	13.4554i	0.575311	+	0.575311i	0.933608	−	0.358297i	$-0.116642\pi$
$547$	13.4554	+	13.4554i	0.575311	+	0.575311i	−0.358297	+	0.933608i	$0.616642\pi$
$548$	0.936996	+	0.936996i	0.0400265	+	0.0400265i
$549$			25.4314i			1.08538i
$550$		0			0
$551$	−31.7645	+	1.41467i	−1.35321	+	0.0602669i
$552$	−23.5247	+	23.5247i	−1.00128	+	1.00128i
$553$	13.9083	−	13.9083i	0.591439	−	0.591439i
$554$	16.1674			0.686889
$555$		0			0
$556$	0.755278			0.0320309
$557$	−25.4445	+	25.4445i	−1.07812	+	1.07812i	−0.0814416	+	0.996678i	$0.525952\pi$
$557$	−25.4445	+	25.4445i	−1.07812	+	1.07812i	−0.996678	+	0.0814416i	$0.974048\pi$
$558$	−8.79384	−	8.79384i	−0.372273	−	0.372273i
$559$	−21.2028			−0.896781
$560$		0			0
$561$			15.7293i			0.664092i
$562$	0.554047	−	0.554047i	0.0233711	−	0.0233711i
$563$	23.6286	−	23.6286i	0.995826	−	0.995826i	−0.00416555	−	0.999991i	$-0.501326\pi$
$563$	23.6286	−	23.6286i	0.995826	−	0.995826i	0.999991	+	0.00416555i	$0.00132594\pi$
$564$	4.46516			0.188017
$565$		0			0
$566$		−	31.8435i		−	1.33848i
$567$	−5.66784	+	5.66784i	−0.238027	+	0.238027i
$568$	23.5247	+	23.5247i	0.987074	+	0.987074i
$569$	12.4936			0.523759			0.261879	−	0.965101i	$-0.415658\pi$
$569$	12.4936			0.523759			0.261879	+	0.965101i	$0.415658\pi$
$570$		0			0
$571$	32.4544			1.35817			0.679087	−	0.734058i	$-0.262376\pi$
$571$	32.4544			1.35817			0.679087	+	0.734058i	$0.262376\pi$
$572$	2.93991	+	2.93991i	0.122924	+	0.122924i
$573$	−8.96363	+	8.96363i	−0.374461	+	0.374461i
$574$		−	15.2849i		−	0.637979i
$575$		0			0
$576$	−44.1876			−1.84115
$577$	−12.9248	+	12.9248i	−0.538066	+	0.538066i	−0.922960	−	0.384895i	$-0.874238\pi$
$577$	−12.9248	+	12.9248i	−0.538066	+	0.538066i	0.384895	+	0.922960i	$0.374238\pi$
$578$	8.52664	−	8.52664i	0.354662	−	0.354662i
$579$		−	17.2809i		−	0.718170i
$580$		0			0
$581$	45.1754			1.87419
$582$	−18.3782	−	18.3782i	−0.761801	−	0.761801i
$583$	−9.55368	+	9.55368i	−0.395673	+	0.395673i
$584$	42.3737			1.75344
$585$		0			0
$586$	35.5656			1.46920
$587$	−17.4060	+	17.4060i	−0.718421	+	0.718421i	−0.968282	−	0.249861i	$-0.919615\pi$
$587$	−17.4060	+	17.4060i	−0.718421	+	0.718421i	0.249861	+	0.968282i	$0.419615\pi$
$588$	−9.97000	+	9.97000i	−0.411156	+	0.411156i
$589$	0.406375	+	9.12459i	0.0167444	+	0.375972i
$590$		0			0
$591$			53.8908i			2.21677i
$592$	0.859243	+	0.859243i	0.0353147	+	0.0353147i
$593$	10.6873	+	10.6873i	0.438877	+	0.438877i	0.891634	−	0.452757i	$-0.149560\pi$
$593$	10.6873	+	10.6873i	0.438877	+	0.438877i	−0.452757	+	0.891634i	$0.649560\pi$
$594$			15.2849i			0.627147i
$595$		0			0
$596$	1.45580			0.0596320
$597$	29.5350	+	29.5350i	1.20879	+	1.20879i
$598$	8.79384	+	8.79384i	0.359607	+	0.359607i
$599$	5.19910			0.212429			0.106215	−	0.994343i	$-0.466127\pi$
$599$	5.19910			0.212429			0.106215	+	0.994343i	$0.466127\pi$
$600$		0			0
$601$		−	36.8789i		−	1.50432i	−0.658981	−	0.752160i	$-0.729012\pi$
$601$		−	36.8789i		−	1.50432i	0.658981	−	0.752160i	$-0.270988\pi$
$602$	−22.8600	−	22.8600i	−0.931705	−	0.931705i
$603$	−39.6322	+	39.6322i	−1.61395	+	1.61395i
$604$	4.92474			0.200385
$605$		0			0
$606$	18.9624			0.770294
$607$	6.90285	+	6.90285i	0.280178	+	0.280178i	0.833180	−	0.553002i	$-0.186518\pi$
$607$	6.90285	+	6.90285i	0.280178	+	0.280178i	−0.553002	+	0.833180i	$0.686518\pi$
$608$	11.6849	+	10.6884i	0.473883	+	0.433473i
$609$			78.8139i			3.19370i
$610$		0			0
$611$		−	6.61376i		−	0.267564i
$612$	6.28726	−	6.28726i	0.254147	−	0.254147i
$613$	19.8119	+	19.8119i	0.800197	+	0.800197i	0.983126	−	0.182929i	$-0.0585579\pi$
$613$	19.8119	+	19.8119i	0.800197	+	0.800197i	−0.182929	+	0.983126i	$0.558558\pi$
$614$			18.2252i			0.735510i
$615$		0			0
$616$			25.1192i			1.01208i
$617$	29.2579	−	29.2579i	1.17788	−	1.17788i	0.197595	−	0.980284i	$-0.436687\pi$
$617$	29.2579	−	29.2579i	1.17788	−	1.17788i	0.980284	−	0.197595i	$-0.0633130\pi$
$618$	−43.1936	+	43.1936i	−1.73750	+	1.73750i
$619$			17.6424i			0.709110i	0.935035	+	0.354555i	$0.115368\pi$
$619$			17.6424i			0.709110i	−0.935035	+	0.354555i	$0.884632\pi$
$620$		0			0
$621$		−	23.2982i		−	0.934923i
$622$	15.3357	+	15.3357i	0.614907	+	0.614907i
$623$	14.9954	−	14.9954i	0.600777	−	0.600777i
$624$			17.8945i			0.716352i
$625$		0			0
$626$		−	5.30967i		−	0.212217i
$627$	18.1179	−	19.8069i	0.723558	−	0.791011i
$628$	−3.09332	−	3.09332i	−0.123437	−	0.123437i
$629$	−1.41467			−0.0564066
$630$		0			0
$631$	−25.6326			−1.02042			−0.510209	−	0.860051i	$-0.670432\pi$
$631$	−25.6326			−1.02042			−0.510209	+	0.860051i	$0.670432\pi$
$632$	−11.3199	+	11.3199i	−0.450283	+	0.450283i
$633$	−32.3185	−	32.3185i	−1.28455	−	1.28455i
$634$		−	8.75368i		−	0.347653i
$635$		0			0
$636$	12.0811			0.479047
$637$	14.7675	+	14.7675i	0.585110	+	0.585110i
$638$	12.8021	+	12.8021i	0.506840	+	0.506840i
$639$	−55.7119			−2.20393
$640$		0			0
$641$		−	8.02843i		−	0.317104i	−0.987351	−	0.158552i	$-0.949317\pi$
$641$		−	8.02843i		−	0.317104i	0.987351	−	0.158552i	$-0.0506826\pi$
$642$	−34.2300	−	34.2300i	−1.35095	−	1.35095i
$643$	−14.0108	−	14.0108i	−0.552532	−	0.552532i	0.374639	−	0.927171i	$-0.377767\pi$
$643$	−14.0108	−	14.0108i	−0.552532	−	0.552532i	−0.927171	+	0.374639i	$0.877767\pi$
$644$		−	9.66291i		−	0.380772i
$645$		0			0
$646$	12.8021	−	0.570157i	0.503692	−	0.0224325i
$647$	24.8315	−	24.8315i	0.976225	−	0.976225i	−0.0234986	−	0.999724i	$-0.507481\pi$
$647$	24.8315	−	24.8315i	0.976225	−	0.976225i	0.999724	+	0.0234986i	$0.00748052\pi$
$648$	4.61306	−	4.61306i	0.181218	−	0.181218i
$649$	−7.56885			−0.297103
$650$		0			0
$651$	22.6399			0.887327
$652$	−6.87399	+	6.87399i	−0.269206	+	0.269206i
$653$	27.6009	+	27.6009i	1.08011	+	1.08011i	0.996499	+	0.0836064i	$0.0266438\pi$
$653$	27.6009	+	27.6009i	1.08011	+	1.08011i	0.0836064	+	0.996499i	$0.473356\pi$
$654$	6.88812			0.269347
$655$		0			0
$656$			7.70087i			0.300668i
$657$	−50.1754	+	50.1754i	−1.95753	+	1.95753i
$658$	7.13071	−	7.13071i	0.277984	−	0.277984i
$659$	−14.7210			−0.573449			−0.286725	−	0.958013i	$-0.592566\pi$
$659$	−14.7210			−0.573449			−0.286725	+	0.958013i	$0.592566\pi$
$660$		0			0
$661$			30.1863i			1.17411i	0.809547	+	0.587055i	$0.199713\pi$
$661$			30.1863i			1.17411i	−0.809547	+	0.587055i	$0.800287\pi$
$662$	−17.8110	+	17.8110i	−0.692244	+	0.692244i
$663$	−14.7308	−	14.7308i	−0.572098	−	0.572098i
$664$	−36.7683			−1.42689
$665$		0			0
$666$	−3.28726			−0.127379
$667$	−19.5137	−	19.5137i	−0.755575	−	0.755575i
$668$	−1.53519	+	1.53519i	−0.0593982	+	0.0593982i
$669$			12.8423i			0.496510i
$670$		0			0
$671$	−10.6351			−0.410565
$672$	27.7562	−	27.7562i	1.07072	−	1.07072i
$673$	−9.72032	+	9.72032i	−0.374691	+	0.374691i	−0.869182	−	0.494492i	$-0.835354\pi$
$673$	−9.72032	+	9.72032i	−0.374691	+	0.374691i	0.494492	+	0.869182i	$0.335354\pi$
$674$		−	32.5017i		−	1.25192i
$675$		0			0
$676$	3.27011			0.125774
$677$	−13.5166	−	13.5166i	−0.519486	−	0.519486i	0.397930	−	0.917416i	$-0.369729\pi$
$677$	−13.5166	−	13.5166i	−0.519486	−	0.519486i	−0.917416	+	0.397930i	$0.869729\pi$
$678$	−4.90006	+	4.90006i	−0.188186	+	0.188186i
$679$	29.9119			1.14791
$680$		0			0
$681$	−14.1173			−0.540976
$682$	3.67750	−	3.67750i	0.140819	−	0.140819i
$683$	−1.49062	+	1.49062i	−0.0570371	+	0.0570371i	−0.735050	−	0.678013i	$-0.762841\pi$
$683$	−1.49062	+	1.49062i	−0.0570371	+	0.0570371i	0.678013	+	0.735050i	$0.262841\pi$
$684$	−15.1591	+	0.675131i	−0.579625	+	0.0258143i
$685$		0			0
$686$			1.36146i			0.0519809i
$687$	−20.6326	−	20.6326i	−0.787183	−	0.787183i
$688$	11.5174	+	11.5174i	0.439096	+	0.439096i
$689$		−	17.8945i		−	0.681725i
$690$		0			0
$691$	29.9452			1.13917			0.569585	−	0.821932i	$-0.307104\pi$
$691$	29.9452			1.13917			0.569585	+	0.821932i	$0.307104\pi$
$692$	−7.34577	−	7.34577i	−0.279244	−	0.279244i
$693$	−29.7440	−	29.7440i	−1.12988	−	1.12988i
$694$	13.2849			0.504288
$695$		0			0
$696$		−	64.1467i		−	2.43147i
$697$	−6.33941	−	6.33941i	−0.240122	−	0.240122i
$698$	27.3370	−	27.3370i	1.03472	−	1.03472i
$699$	−34.7835			−1.31563
$700$		0			0
$701$	23.6932			0.894881			0.447440	−	0.894314i	$-0.352336\pi$
$701$	23.6932			0.894881			0.447440	+	0.894314i	$0.352336\pi$
$702$	−14.3146	−	14.3146i	−0.540271	−	0.540271i
$703$	1.78140	+	1.62949i	0.0671869	+	0.0614575i
$704$		−	18.4788i		−	0.696447i
$705$		0			0
$706$			6.31796i			0.237780i
$707$	−15.4314	+	15.4314i	−0.580356	+	0.580356i
$708$	4.78560	+	4.78560i	0.179854	+	0.179854i
$709$		−	26.7367i		−	1.00412i	−0.864833	−	0.502059i	$-0.832576\pi$
$709$		−	26.7367i		−	1.00412i	0.864833	−	0.502059i	$-0.167424\pi$
$710$		0			0
$711$		−	26.8082i		−	1.00539i
$712$	−12.2047	+	12.2047i	−0.457392	+	0.457392i
$713$	−5.60547	+	5.60547i	−0.209927	+	0.209927i
$714$		−	31.7645i		−	1.18876i
$715$		0			0
$716$			3.51007i			0.131177i
$717$	−28.5267	−	28.5267i	−1.06535	−	1.06535i
$718$	19.6903	−	19.6903i	0.734836	−	0.734836i
$719$			30.1465i			1.12427i	0.827044	+	0.562137i	$0.190021\pi$
$719$			30.1465i			1.12427i	−0.827044	+	0.562137i	$0.809979\pi$
$720$		0			0
$721$		−	70.3008i		−	2.61814i
$722$	−16.7776	−	14.0282i	−0.624397	−	0.522075i
$723$	54.1378	+	54.1378i	2.01341	+	2.01341i
$724$	−4.73951			−0.176143
$725$		0			0
$726$	20.8749			0.774742
$727$	31.5174	−	31.5174i	1.16892	−	1.16892i	0.186451	−	0.982464i	$-0.440301\pi$
$727$	31.5174	−	31.5174i	1.16892	−	1.16892i	0.982464	−	0.186451i	$-0.0596986\pi$
$728$	−23.5247	−	23.5247i	−0.871883	−	0.871883i
$729$		−	41.8383i		−	1.54957i
$730$		0			0
$731$	−18.9624			−0.701349
$732$	6.72434	+	6.72434i	0.248539	+	0.248539i
$733$	10.5515	+	10.5515i	0.389728	+	0.389728i	0.874591	−	0.484862i	$-0.161130\pi$
$733$	10.5515	+	10.5515i	0.389728	+	0.389728i	−0.484862	+	0.874591i	$0.661130\pi$
$734$	7.86465			0.290290
$735$		0			0
$736$			13.7445i			0.506628i
$737$	−16.5738	−	16.5738i	−0.610504	−	0.610504i
$738$	−14.7308	−	14.7308i	−0.542250	−	0.542250i
$739$		−	30.6859i		−	1.12880i	−0.825501	−	0.564400i	$-0.809108\pi$
$739$		−	30.6859i		−	1.12880i	0.825501	−	0.564400i	$-0.190892\pi$
$740$		0			0
$741$	1.58181	+	35.5174i	0.0581092	+	1.30476i
$742$	19.2931	−	19.2931i	0.708273	−	0.708273i
$743$	−14.2586	+	14.2586i	−0.523096	+	0.523096i	−0.918505	−	0.395409i	$-0.870603\pi$
$743$	−14.2586	+	14.2586i	−0.523096	+	0.523096i	0.395409	+	0.918505i	$0.370603\pi$
$744$	−18.4266			−0.675553
$745$		0			0
$746$	−8.07285			−0.295568
$747$	43.5379	−	43.5379i	1.59297	−	1.59297i
$748$	2.62927	+	2.62927i	0.0961356	+	0.0961356i
$749$	55.7119			2.03567
$750$		0			0
$751$			41.8036i			1.52543i	0.646732	+	0.762717i	$0.276135\pi$
$751$			41.8036i			1.52543i	−0.646732	+	0.762717i	$0.723865\pi$
$752$	−3.59261	+	3.59261i	−0.131009	+	0.131009i
$753$	15.4748	−	15.4748i	0.563934	−	0.563934i
$754$	−23.9789			−0.873260
$755$		0			0
$756$			15.7293i			0.572069i
$757$	16.1187	−	16.1187i	0.585845	−	0.585845i	−0.350659	−	0.936503i	$-0.614042\pi$
$757$	16.1187	−	16.1187i	0.585845	−	0.585845i	0.936503	+	0.350659i	$0.114042\pi$
$758$	−20.9986	−	20.9986i	−0.762703	−	0.762703i
$759$	23.2982			0.845669
$760$		0			0
$761$	31.8846			1.15582			0.577908	−	0.816102i	$-0.303869\pi$
$761$	31.8846			1.15582			0.577908	+	0.816102i	$0.303869\pi$
$762$	13.0272	+	13.0272i	0.471926	+	0.471926i
$763$	−5.60547	+	5.60547i	−0.202932	+	0.202932i
$764$			2.99668i			0.108416i
$765$		0			0
$766$	−1.49834			−0.0541371
$767$	7.08840	−	7.08840i	0.255947	−	0.255947i
$768$	−28.5732	+	28.5732i	−1.03105	+	1.03105i
$769$		−	4.23155i		−	0.152594i	−0.997085	−	0.0762968i	$-0.975690\pi$
$769$		−	4.23155i		−	0.152594i	0.997085	−	0.0762968i	$-0.0243096\pi$
$770$		0			0
$771$	−71.5183			−2.57567
$772$	−2.88863	−	2.88863i	−0.103964	−	0.103964i
$773$	10.1998	−	10.1998i	0.366861	−	0.366861i	−0.499470	−	0.866331i	$-0.666472\pi$
$773$	10.1998	−	10.1998i	0.366861	−	0.366861i	0.866331	+	0.499470i	$0.166472\pi$
$774$	−44.0628			−1.58380
$775$		0			0
$776$	−24.3453			−0.873947
$777$	4.23155	−	4.23155i	0.151806	−	0.151806i
$778$	3.93633	−	3.93633i	0.141124	−	0.141124i
$779$	0.680731	+	15.2849i	0.0243897	+	0.547638i
$780$		0			0
$781$		−	23.2982i		−	0.833674i
$782$	7.86465	+	7.86465i	0.281239	+	0.281239i
$783$	31.7645	+	31.7645i	1.13517	+	1.13517i
$784$		−	16.0435i		−	0.572982i
$785$		0			0
$786$	−44.0527			−1.57131
$787$	−1.13360	−	1.13360i	−0.0404084	−	0.0404084i	0.686614	−	0.727022i	$-0.259096\pi$
$787$	−1.13360	−	1.13360i	−0.0404084	−	0.0404084i	−0.727022	+	0.686614i	$0.759096\pi$
$788$	9.00825	+	9.00825i	0.320906	+	0.320906i
$789$	−4.92474			−0.175325
$790$		0			0
$791$		−	7.97523i		−	0.283566i
$792$	24.2087	+	24.2087i	0.860218	+	0.860218i
$793$	9.96005	−	9.96005i	0.353692	−	0.353692i
$794$	−3.48863			−0.123807
$795$		0			0
$796$	9.87399			0.349974
$797$	−3.11843	−	3.11843i	−0.110460	−	0.110460i	0.649716	−	0.760177i	$-0.274888\pi$
$797$	−3.11843	−	3.11843i	−0.110460	−	0.110460i	−0.760177	+	0.649716i	$0.774888\pi$
$798$	−36.5881	+	39.9990i	−1.29520	+	1.41595i
$799$		−	5.91493i		−	0.209255i
$800$		0			0
$801$		−	28.9036i		−	1.02126i
$802$	15.5515	−	15.5515i	0.549142	−	0.549142i
$803$	−20.9829	−	20.9829i	−0.740469	−	0.740469i
$804$			20.9584i			0.739146i
$805$		0			0
$806$			6.88812i			0.242624i
$807$	−65.4577	+	65.4577i	−2.30422	+	2.30422i
$808$	12.5596	−	12.5596i	0.441845	−	0.441845i
$809$		−	30.4847i		−	1.07179i	−0.844286	−	0.535893i	$-0.819975\pi$
$809$		−	30.4847i		−	1.07179i	0.844286	−	0.535893i	$-0.180025\pi$
$810$		0			0
$811$		−	25.3936i		−	0.891688i	−0.895111	−	0.445844i	$-0.852904\pi$
$811$		−	25.3936i		−	0.891688i	0.895111	−	0.445844i	$-0.147096\pi$
$812$	13.1743	+	13.1743i	0.462328	+	0.462328i
$813$	−36.3619	+	36.3619i	−1.27527	+	1.27527i
$814$		−	1.37470i		−	0.0481832i
$815$		0			0
$816$			16.0037i			0.560240i
$817$	23.8781	+	21.8419i	0.835390	+	0.764152i
$818$	−12.4713	−	12.4713i	−0.436050	−	0.436050i
$819$	55.7119			1.94673
$820$		0			0
$821$	1.16362			0.0406106			0.0203053	−	0.999794i	$-0.493536\pi$
$821$	1.16362			0.0406106			0.0203053	+	0.999794i	$0.493536\pi$
$822$	4.56230	−	4.56230i	0.159128	−	0.159128i
$823$	−35.3307	−	35.3307i	−1.23155	−	1.23155i	−0.963367	−	0.268185i	$-0.913576\pi$
$823$	−35.3307	−	35.3307i	−1.23155	−	1.23155i	−0.268185	−	0.963367i	$-0.586424\pi$
$824$			57.2179i			1.99328i
$825$		0			0
$826$	15.2849			0.531829
$827$	−1.59318	−	1.59318i	−0.0554004	−	0.0554004i	0.678864	−	0.734264i	$-0.262473\pi$
$827$	−1.59318	−	1.59318i	−0.0554004	−	0.0554004i	−0.734264	+	0.678864i	$0.762473\pi$
$828$	−9.31265	−	9.31265i	−0.323637	−	0.323637i
$829$	−28.2229			−0.980222			−0.490111	−	0.871660i	$-0.663044\pi$
$829$	−28.2229			−0.980222			−0.490111	+	0.871660i	$0.663044\pi$
$830$		0			0
$831$			40.1146i			1.39156i
$832$	17.3058	+	17.3058i	0.599972	+	0.599972i
$833$	13.2071	+	13.2071i	0.457599	+	0.457599i
$834$		−	3.67750i		−	0.127341i
$835$		0			0
$836$	−0.282333	−	6.33941i	−0.00976470	−	0.219253i
$837$	9.12459	−	9.12459i	0.315392	−	0.315392i
$838$	−21.0191	+	21.0191i	−0.726092	+	0.726092i
$839$	−38.8954			−1.34282			−0.671410	−	0.741086i	$-0.734311\pi$
$839$	−38.8954			−1.34282			−0.671410	+	0.741086i	$0.734311\pi$
$840$		0			0
$841$	24.2097			0.834816
$842$	20.4445	−	20.4445i	0.704565	−	0.704565i
$843$	1.37470	+	1.37470i	0.0473472	+	0.0473472i
$844$	−10.8046			−0.371908
$845$		0			0
$846$		−	13.7445i		−	0.472545i
$847$	−16.9878	+	16.9878i	−0.583707	+	0.583707i
$848$	−9.72032	+	9.72032i	−0.333797	+	0.333797i
$849$	79.0100			2.71162
$850$		0			0
$851$			2.09540i			0.0718294i
$852$	−14.7308	+	14.7308i	−0.504670	+	0.504670i
$853$	−11.0508	−	11.0508i	−0.378372	−	0.378372i	0.492143	−	0.870514i	$-0.336214\pi$
$853$	−11.0508	−	11.0508i	−0.378372	−	0.378372i	−0.870514	+	0.492143i	$0.836214\pi$
$854$	21.4771			0.734932
$855$		0			0
$856$	−45.3439			−1.54982
$857$	−38.6358	−	38.6358i	−1.31977	−	1.31977i	−0.913952	−	0.405822i	$-0.866985\pi$
$857$	−38.6358	−	38.6358i	−1.31977	−	1.31977i	−0.405822	−	0.913952i	$-0.633015\pi$
$858$	14.3146	−	14.3146i	0.488694	−	0.488694i
$859$		−	24.4241i		−	0.833339i	−0.909058	−	0.416669i	$-0.863197\pi$
$859$		−	24.4241i		−	0.833339i	0.909058	−	0.416669i	$-0.136803\pi$
$860$		0			0
$861$	37.9248			1.29247
$862$	−29.2384	+	29.2384i	−0.995863	+	0.995863i
$863$	−0.809893	+	0.809893i	−0.0275691	+	0.0275691i	−0.720757	−	0.693188i	$-0.756206\pi$
$863$	−0.809893	+	0.809893i	−0.0275691	+	0.0275691i	0.693188	+	0.720757i	$0.256206\pi$
$864$		−	22.3733i		−	0.761155i
$865$		0			0
$866$	27.0352			0.918695
$867$	21.1563	+	21.1563i	0.718504	+	0.718504i
$868$	3.78443	−	3.78443i	0.128452	−	0.128452i
$869$	11.2109			0.380305
$870$		0			0
$871$	31.0435			1.05187
$872$	4.56230	−	4.56230i	0.154499	−	0.154499i
$873$	28.8277	−	28.8277i	0.975669	−	0.975669i
$874$	−0.844513	−	18.9624i	−0.0285661	−	0.641412i
$875$		0			0
$876$			26.5339i			0.896496i
$877$	35.2283	+	35.2283i	1.18958	+	1.18958i	0.977185	+	0.212390i	$0.0681249\pi$
$877$	35.2283	+	35.2283i	1.18958	+	1.18958i	0.212390	+	0.977185i	$0.431875\pi$
$878$	−18.1417	−	18.1417i	−0.612254	−	0.612254i
$879$			88.2452i			2.97644i
$880$		0			0
$881$	−12.8305			−0.432271			−0.216135	−	0.976363i	$-0.569345\pi$
$881$	−12.8305			−0.432271			−0.216135	+	0.976363i	$0.569345\pi$
$882$	30.6893	+	30.6893i	1.03336	+	1.03336i
$883$	5.53198	+	5.53198i	0.186166	+	0.186166i	0.794036	−	0.607870i	$-0.207976\pi$
$883$	5.53198	+	5.53198i	0.186166	+	0.186166i	−0.607870	+	0.794036i	$0.707976\pi$
$884$	−4.92474			−0.165637
$885$		0			0
$886$			34.5409i			1.16042i
$887$	−17.0760	−	17.0760i	−0.573357	−	0.573357i	0.359708	−	0.933065i	$-0.382876\pi$
$887$	−17.0760	−	17.0760i	−0.573357	−	0.573357i	−0.933065	+	0.359708i	$0.882876\pi$
$888$	−3.44406	+	3.44406i	−0.115575	+	0.115575i
$889$	−21.2028			−0.711118
$890$		0			0
$891$	−4.56864			−0.153055
$892$	2.14668	+	2.14668i	0.0718761	+	0.0718761i
$893$	−6.81314	+	7.44829i	−0.227993	+	0.249247i
$894$		−	7.08840i		−	0.237071i
$895$		0			0
$896$			9.82803i			0.328332i
$897$	−21.8192	+	21.8192i	−0.728523	+	0.728523i
$898$	6.49104	+	6.49104i	0.216609	+	0.216609i
$899$		−	15.2849i		−	0.509780i
$900$		0			0
$901$		−	16.0037i		−	0.533159i
$902$	6.16029	−	6.16029i	0.205115	−	0.205115i
$903$	56.7201	−	56.7201i	1.88753	−	1.88753i
$904$			6.49104i			0.215889i
$905$		0			0
$906$		−	23.9789i		−	0.796645i
$907$	8.59188	+	8.59188i	0.285289	+	0.285289i	0.835214	−	0.549925i	$-0.185344\pi$
$907$	8.59188	+	8.59188i	0.285289	+	0.285289i	−0.549925	+	0.835214i	$0.685344\pi$
$908$	−2.35981	+	2.35981i	−0.0783131	+	0.0783131i
$909$			29.7440i			0.986547i
$910$		0			0
$911$		−	36.2513i		−	1.20106i	−0.799602	−	0.600530i	$-0.794956\pi$
$911$		−	36.2513i		−	1.20106i	0.799602	−	0.600530i	$-0.205044\pi$
$912$	18.4339	−	20.1524i	0.610407	−	0.667312i
$913$	18.2071	+	18.2071i	0.602567	+	0.602567i
$914$	−3.62064			−0.119760
$915$		0			0
$916$	−6.89778			−0.227909
$917$	35.8496	−	35.8496i	1.18386	−	1.18386i
$918$	−12.8021	−	12.8021i	−0.422532	−	0.422532i
$919$			15.0640i			0.496914i	0.968643	+	0.248457i	$0.0799235\pi$
$919$			15.0640i			0.496914i	−0.968643	+	0.248457i	$0.920077\pi$
$920$		0			0
$921$	−45.2203			−1.49006
$922$	13.9695	+	13.9695i	0.460060	+	0.460060i
$923$	21.8192	+	21.8192i	0.718189	+	0.718189i
$924$	−15.7293			−0.517456
$925$		0			0
$926$			29.9334i			0.983671i
$927$	−67.7526	−	67.7526i	−2.22529	−	2.22529i
$928$	−18.7391	−	18.7391i	−0.615141	−	0.615141i
$929$		−	7.57310i		−	0.248465i	−0.992253	−	0.124233i	$-0.960353\pi$
$929$		−	7.57310i		−	0.248465i	0.992253	−	0.124233i	$-0.0396469\pi$
$930$		0			0
$931$	−1.41819	−	31.8435i	−0.0464793	−	1.04363i
$932$	−5.81431	+	5.81431i	−0.190454	+	0.190454i
$933$	−38.0509	+	38.0509i	−1.24573	+	1.24573i
$934$	−31.2948			−1.02400
$935$		0			0
$936$	−45.3439			−1.48211
$937$	15.9829	−	15.9829i	0.522137	−	0.522137i	−0.396079	−	0.918216i	$-0.629629\pi$
$937$	15.9829	−	15.9829i	0.522137	−	0.522137i	0.918216	+	0.396079i	$0.129629\pi$
$938$	33.4699	+	33.4699i	1.09283	+	1.09283i
$939$	13.1743			0.429928
$940$		0			0
$941$		−	26.6762i		−	0.869620i	−0.900522	−	0.434810i	$-0.856816\pi$
$941$		−	26.6762i		−	0.869620i	0.900522	−	0.434810i	$-0.143184\pi$
$942$	−15.0616	+	15.0616i	−0.490733	+	0.490733i
$943$	−9.38990	+	9.38990i	−0.305777	+	0.305777i
$944$	−7.70087			−0.250642
$945$		0			0
$946$		−	18.4266i		−	0.599101i
$947$	−26.2325	+	26.2325i	−0.852442	+	0.852442i	−0.990433	−	0.137992i	$-0.955935\pi$
$947$	−26.2325	+	26.2325i	−0.852442	+	0.852442i	0.137992	+	0.990433i	$0.455935\pi$
$948$	−7.08840	−	7.08840i	−0.230220	−	0.230220i
$949$	39.3018			1.27579
$950$		0			0
$951$	21.7196			0.704306
$952$	−21.0390	−	21.0390i	−0.681877	−	0.681877i
$953$	27.5768	−	27.5768i	0.893300	−	0.893300i	−0.101533	−	0.994832i	$-0.532375\pi$
$953$	27.5768	−	27.5768i	0.893300	−	0.893300i	0.994832	+	0.101533i	$0.0323746\pi$
$954$		−	37.1876i		−	1.20399i
$955$		0			0
$956$	−9.53690			−0.308446
$957$	−31.7645	+	31.7645i	−1.02680	+	1.02680i
$958$	−0.229791	+	0.229791i	−0.00742422	+	0.00742422i
$959$			7.42548i			0.239781i
$960$		0			0
$961$	26.6093			0.858364
$962$	1.28744	+	1.28744i	0.0415086	+	0.0415086i
$963$	53.6924	−	53.6924i	1.73021	−	1.73021i
$964$	18.0991			0.582931
$965$		0			0
$966$	−47.0494			−1.51379
$967$	11.3004	−	11.3004i	0.363397	−	0.363397i	−0.501665	−	0.865062i	$-0.667279\pi$
$967$	11.3004	−	11.3004i	0.363397	−	0.363397i	0.865062	+	0.501665i	$0.167279\pi$
$968$	13.8264	−	13.8264i	0.444396	−	0.444396i
$969$	1.41467	+	31.7645i	0.0454457	+	1.02042i
$970$		0			0
$971$			32.9624i			1.05781i	0.848680	+	0.528907i	$0.177398\pi$
$971$			32.9624i			1.05781i	−0.848680	+	0.528907i	$0.822602\pi$
$972$	−5.93111	−	5.93111i	−0.190240	−	0.190240i
$973$	2.99271	+	2.99271i	0.0959417	+	0.0959417i
$974$			32.4020i			1.03823i
$975$		0			0
$976$	−10.8207			−0.346361
$977$	−23.5792	−	23.5792i	−0.754366	−	0.754366i	0.220925	−	0.975291i	$-0.429093\pi$
$977$	−23.5792	−	23.5792i	−0.754366	−	0.754366i	−0.975291	+	0.220925i	$0.929093\pi$
$978$	33.4699	+	33.4699i	1.07025	+	1.07025i
$979$	12.0872			0.386309
$980$		0			0
$981$			10.8046i			0.344963i
$982$	−12.1167	−	12.1167i	−0.386659	−	0.386659i
$983$	11.3187	−	11.3187i	0.361009	−	0.361009i	−0.503175	−	0.864184i	$-0.667835\pi$
$983$	11.3187	−	11.3187i	0.361009	−	0.361009i	0.864184	+	0.503175i	$0.167835\pi$
$984$	−30.8670			−0.984004
$985$		0			0
$986$	−21.4452			−0.682954
$987$	17.6927	+	17.6927i	0.563164	+	0.563164i
$988$	6.20141	+	5.67258i	0.197293	+	0.180469i
$989$			28.0870i			0.893114i
$990$		0			0
$991$			52.2018i			1.65824i	0.559068	+	0.829122i	$0.311159\pi$
$991$			52.2018i			1.65824i	−0.559068	+	0.829122i	$0.688841\pi$
$992$	−5.38295	+	5.38295i	−0.170909	+	0.170909i
$993$	−44.1925	−	44.1925i	−1.40241	−	1.40241i
$994$			47.0494i			1.49232i
$995$		0			0
$996$		−	23.0238i		−	0.729537i
$997$	4.66291	−	4.66291i	0.147676	−	0.147676i	−0.629403	−	0.777079i	$-0.716701\pi$
$997$	4.66291	−	4.66291i	0.147676	−	0.147676i	0.777079	+	0.629403i	$0.216701\pi$
$998$	20.0179	−	20.0179i	0.633655	−	0.633655i
$999$		−	3.41090i		−	0.107916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.g.b.18.3		12
5.2	odd	4	inner	475.2.g.b.132.4		12
5.3	odd	4		95.2.g.b.37.3	yes	12
5.4	even	2		95.2.g.b.18.4	yes	12
15.8	even	4		855.2.p.f.37.4		12
15.14	odd	2		855.2.p.f.208.3		12
19.18	odd	2	inner	475.2.g.b.18.4		12
95.18	even	4		95.2.g.b.37.4	yes	12
95.37	even	4	inner	475.2.g.b.132.3		12
95.94	odd	2		95.2.g.b.18.3	✓	12
285.113	odd	4		855.2.p.f.37.3		12
285.284	even	2		855.2.p.f.208.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.3	✓	12	95.94	odd	2
95.2.g.b.18.4	yes	12	5.4	even	2
95.2.g.b.37.3	yes	12	5.3	odd	4
95.2.g.b.37.4	yes	12	95.18	even	4
475.2.g.b.18.3		12	1.1	even	1	trivial
475.2.g.b.18.4		12	19.18	odd	2	inner
475.2.g.b.132.3		12	95.37	even	4	inner
475.2.g.b.132.4		12	5.2	odd	4	inner
855.2.p.f.37.3		12	285.113	odd	4
855.2.p.f.37.4		12	15.8	even	4
855.2.p.f.208.3		12	15.14	odd	2
855.2.p.f.208.4		12	285.284	even	2

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.813901 - 0.813901i) q^{2} +(2.01945 - 2.01945i) q^{3} -0.675131i q^{4} -3.28726 q^{6} +(2.67513 - 2.67513i) q^{7} +(-2.17729 + 2.17729i) q^{8} -5.15633i q^{9} +O(q^{10})\)	\(q+(-0.813901 - 0.813901i) q^{2} +(2.01945 - 2.01945i) q^{3} -0.675131i q^{4} -3.28726 q^{6} +(2.67513 - 2.67513i) q^{7} +(-2.17729 + 2.17729i) q^{8} -5.15633i q^{9} +2.15633 q^{11} +(-1.36339 - 1.36339i) q^{12} +(-2.01945 + 2.01945i) q^{13} -4.35458 q^{14} +2.19394 q^{16} +(-1.80606 + 1.80606i) q^{17} +(-4.19674 + 4.19674i) q^{18} +(4.35458 - 0.193937i) q^{19} -10.8046i q^{21} +(-1.75503 - 1.75503i) q^{22} +(2.67513 + 2.67513i) q^{23} +8.79384i q^{24} +3.28726 q^{26} +(-4.35458 - 4.35458i) q^{27} +(-1.80606 - 1.80606i) q^{28} -7.29450 q^{29} +2.09540i q^{31} +(2.56894 + 2.56894i) q^{32} +(4.35458 - 4.35458i) q^{33} +2.93991 q^{34} -3.48119 q^{36} +(0.391644 + 0.391644i) q^{37} +(-3.70204 - 3.38635i) q^{38} +8.15633i q^{39} +3.51007i q^{41} +(-8.79384 + 8.79384i) q^{42} +(5.24965 + 5.24965i) q^{43} -1.45580i q^{44} -4.35458i q^{46} +(-1.63752 + 1.63752i) q^{47} +(4.43054 - 4.43054i) q^{48} -7.31265i q^{49} +7.29450i q^{51} +(1.36339 + 1.36339i) q^{52} +(-4.43054 + 4.43054i) q^{53} +7.08840i q^{54} +11.6491i q^{56} +(8.40220 - 9.18549i) q^{57} +(5.93700 + 5.93700i) q^{58} -3.51007 q^{59} -4.93207 q^{61} +(1.70545 - 1.70545i) q^{62} +(-13.7938 - 13.7938i) q^{63} -8.56959i q^{64} -7.08840 q^{66} +(-7.68614 - 7.68614i) q^{67} +(1.21933 + 1.21933i) q^{68} +10.8046 q^{69} -10.8046i q^{71} +(11.2268 + 11.2268i) q^{72} +(-9.73084 - 9.73084i) q^{73} -0.637519i q^{74} +(-0.130933 - 2.93991i) q^{76} +(5.76845 - 5.76845i) q^{77} +(6.63844 - 6.63844i) q^{78} +5.19910 q^{79} -2.11871 q^{81} +(2.85685 - 2.85685i) q^{82} +(8.44358 + 8.44358i) q^{83} -7.29450 q^{84} -8.54538i q^{86} +(-14.7308 + 14.7308i) q^{87} +(-4.69495 + 4.69495i) q^{88} +5.60547 q^{89} +10.8046i q^{91} +(1.80606 - 1.80606i) q^{92} +(4.23155 + 4.23155i) q^{93} +2.66556 q^{94} +10.3757 q^{96} +(5.59074 + 5.59074i) q^{97} +(-5.95177 + 5.95177i) q^{98} -11.1187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{6} + 12 q^{7}+O(q^{10}) \) 12 * q - 16 * q^6 + 12 * q^7	\( 12 q - 16 q^{6} + 12 q^{7} - 16 q^{11} + 28 q^{16} - 20 q^{17} + 12 q^{23} + 16 q^{26} - 20 q^{28} - 20 q^{36} - 4 q^{38} - 4 q^{43} + 44 q^{47} + 88 q^{58} - 24 q^{61} - 8 q^{62} - 60 q^{63} - 8 q^{66} - 44 q^{68} - 28 q^{73} - 20 q^{76} + 24 q^{77} + 60 q^{81} - 88 q^{82} + 36 q^{83} - 88 q^{87} + 20 q^{92} + 96 q^{93} + 24 q^{96}+O(q^{100}) \) 12 * q - 16 * q^6 + 12 * q^7 - 16 * q^11 + 28 * q^16 - 20 * q^17 + 12 * q^23 + 16 * q^26 - 20 * q^28 - 20 * q^36 - 4 * q^38 - 4 * q^43 + 44 * q^47 + 88 * q^58 - 24 * q^61 - 8 * q^62 - 60 * q^63 - 8 * q^66 - 44 * q^68 - 28 * q^73 - 20 * q^76 + 24 * q^77 + 60 * q^81 - 88 * q^82 + 36 * q^83 - 88 * q^87 + 20 * q^92 + 96 * q^93 + 24 * q^96

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