LMFDB - Embedded newform 475.2.g.b.132.3

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			132.3
Root			$-0.813901 - 0.813901i$ of defining polynomial
Character	$\chi$	$=$	475.132
Dual form			475.2.g.b.18.3

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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	−0.933664	−	0.358149i	$-0.883408\pi$
$2$	−0.813901	+	0.813901i	−0.575515	+	0.575515i	0.358149	+	0.933664i	$0.383408\pi$
$3$	2.01945	+	2.01945i	1.16593	+	1.16593i	0.983155	+	0.182773i	$0.0585072\pi$
$3$	2.01945	+	2.01945i	1.16593	+	1.16593i	0.182773	+	0.983155i	$0.441493\pi$
$4$			0.675131i			0.337565i
$5$		0			0
$5$		0			0
$6$	−3.28726			−1.34202
$7$	2.67513	+	2.67513i	1.01110	+	1.01110i	0.999938	+	0.0111668i	$0.00355457\pi$
$7$	2.67513	+	2.67513i	1.01110	+	1.01110i	0.0111668	+	0.999938i	$0.496445\pi$
$8$	−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	0.369240	−	0.929334i	$-0.379618\pi$
$13$	−2.01945	−	2.01945i	−0.560094	−	0.560094i	−0.929334	+	0.369240i	$0.879618\pi$
$14$	−4.35458			−1.16381
$15$		0			0
$16$	2.19394			0.548484
$17$	−1.80606	−	1.80606i	−0.438035	−	0.438035i	0.453315	−	0.891350i	$-0.350241\pi$
$17$	−1.80606	−	1.80606i	−0.438035	−	0.438035i	−0.891350	+	0.453315i	$0.850241\pi$
$18$	−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	−0.370878	−	0.928682i	$-0.620943\pi$
$23$	2.67513	−	2.67513i	0.557803	−	0.557803i	0.928682	+	0.370878i	$0.120943\pi$
$24$		−	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	$-0.939744\pi$
$31$		−	2.09540i		−	0.376345i	0.982136	−	0.188173i	$-0.0602564\pi$
$32$	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	−0.674181	−	0.738567i	$-0.735503\pi$
$37$	0.391644	−	0.391644i	0.0643860	−	0.0643860i	0.738567	+	0.674181i	$0.235503\pi$
$38$	−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	$-0.911623\pi$
$41$		−	3.51007i		−	0.548181i	0.961704	−	0.274090i	$-0.0883768\pi$
$42$	−8.79384	−	8.79384i	−1.35692	−	1.35692i
$43$	5.24965	−	5.24965i	0.800564	−	0.800564i	−0.182620	−	0.983184i	$-0.558458\pi$
$43$	5.24965	−	5.24965i	0.800564	−	0.800564i	0.983184	+	0.182620i	$0.0584578\pi$
$44$			1.45580i			0.219470i
$45$		0			0
$46$			4.35458i			0.642048i
$47$	−1.63752	−	1.63752i	−0.238857	−	0.238857i	0.577520	−	0.816377i	$-0.304021\pi$
$47$	−1.63752	−	1.63752i	−0.238857	−	0.238857i	−0.816377	+	0.577520i	$0.804021\pi$
$48$	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	0.333994	−	0.942575i	$-0.391603\pi$
$53$	−4.43054	−	4.43054i	−0.608581	−	0.608581i	−0.942575	+	0.333994i	$0.891603\pi$
$54$		−	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	−0.998244	−	0.0592327i	$-0.981135\pi$
$67$	−7.68614	+	7.68614i	−0.939011	+	0.939011i	0.0592327	+	0.998244i	$0.481135\pi$
$68$	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	$0.221535\pi$
$71$			10.8046i			1.28227i	−0.767430	+	0.641133i	$0.778465\pi$
$72$	11.2268	−	11.2268i	1.32309	−	1.32309i
$73$	−9.73084	+	9.73084i	−1.13891	+	1.13891i	−0.150263	+	0.988646i	$0.548012\pi$
$73$	−9.73084	+	9.73084i	−1.13891	+	1.13891i	−0.988646	+	0.150263i	$0.951988\pi$
$74$			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	−0.0706944	−	0.997498i	$-0.522522\pi$
$83$	8.44358	−	8.44358i	0.926804	−	0.926804i	0.997498	+	0.0706944i	$0.0225215\pi$
$84$	−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	−0.363817	−	0.931470i	$-0.618527\pi$
$97$	5.59074	−	5.59074i	0.567654	−	0.567654i	0.931470	+	0.363817i	$0.118527\pi$
$98$	−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	0.931850	+	0.362843i	$0.118194\pi$
$103$	13.1397	+	13.1397i	1.29469	+	1.29469i	0.362843	+	0.931850i	$0.381806\pi$
$104$			8.79384i			0.862307i
$105$		0			0
$106$	7.21203			0.700495
$107$	10.4129	−	10.4129i	1.00666	−	1.00666i	0.00667734	−	0.999978i	$-0.497875\pi$
$107$	10.4129	−	10.4129i	1.00666	−	1.00666i	0.999978	−	0.00667734i	$-0.00212548\pi$
$108$	−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	0.773735	−	0.633509i	$-0.218386\pi$
$113$	1.49062	+	1.49062i	0.140226	+	0.140226i	−0.633509	+	0.773735i	$0.718386\pi$
$114$	−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	−0.860725	−	0.509071i	$-0.829989\pi$
$127$	−3.96294	+	3.96294i	−0.351654	+	0.351654i	0.509071	+	0.860725i	$0.329989\pi$
$128$	−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	0.645330	−	0.763904i	$-0.276720\pi$
$137$	−1.38787	−	1.38787i	−0.118574	−	0.118574i	−0.763904	+	0.645330i	$0.776720\pi$
$138$	−8.79384	+	8.79384i	−0.748582	+	0.748582i
$139$		−	1.11871i		−	0.0948881i	−0.998874	−	0.0474440i	$-0.984892\pi$
$139$		−	1.11871i		−	0.0948881i	0.998874	−	0.0474440i	$-0.0151076\pi$
$140$		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	$-0.971848\pi$
$149$		−	2.15633i		−	0.176653i	0.996092	−	0.0883265i	$-0.0281519\pi$
$150$		0			0
$151$		−	7.29450i		−	0.593618i	−0.954937	−	0.296809i	$-0.904078\pi$
$151$		−	7.29450i		−	0.593618i	0.954937	−	0.296809i	$-0.0959224\pi$
$152$	−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	0.865895	−	0.500226i	$-0.166750\pi$
$157$	4.58181	+	4.58181i	0.365668	+	0.365668i	−0.500226	+	0.865895i	$0.666750\pi$
$158$	−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	−0.982700	−	0.185206i	$-0.940705\pi$
$163$	−10.1817	+	10.1817i	−0.797494	+	0.797494i	0.185206	+	0.982700i	$0.440705\pi$
$164$	2.36976			0.185047
$165$		0			0
$166$			13.7445i			1.06678i
$167$	−2.27391	+	2.27391i	−0.175961	+	0.175961i	−0.789592	−	0.613632i	$-0.789708\pi$
$167$	−2.27391	+	2.27391i	−0.175961	+	0.175961i	0.613632	+	0.789592i	$0.289708\pi$
$168$	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	0.987133	−	0.159902i	$-0.0511179\pi$
$173$	10.8805	+	10.8805i	0.827231	+	0.827231i	−0.159902	+	0.987133i	$0.551118\pi$
$174$	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	$0.0840198\pi$
$181$			7.02014i			0.521803i	−0.965365	+	0.260901i	$0.915980\pi$
$182$	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	0.844126	−	0.536144i	$-0.180120\pi$
$193$	4.27863	+	4.27863i	0.307982	+	0.307982i	−0.536144	+	0.844126i	$0.680120\pi$
$194$			9.10062i			0.653386i
$195$		0			0
$196$	−4.93700			−0.352643
$197$	−13.3430	−	13.3430i	−0.950647	−	0.950647i	0.0481911	−	0.998838i	$-0.484654\pi$
$197$	−13.3430	−	13.3430i	−0.950647	−	0.950647i	−0.998838	+	0.0481911i	$0.984654\pi$
$198$	−9.04953	−	9.04953i	−0.643122	−	0.643122i
$199$		−	14.6253i		−	1.03676i	−0.855150	−	0.518380i	$-0.826535\pi$
$199$		−	14.6253i		−	1.03676i	0.855150	−	0.518380i	$-0.173465\pi$
$200$		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	$0.185704\pi$
$211$			16.0037i			1.10174i	−0.834592	+	0.550869i	$0.814296\pi$
$212$	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	0.592584	−	0.805509i	$-0.298108\pi$
$223$	−3.17965	−	3.17965i	−0.212925	−	0.212925i	−0.805509	+	0.592584i	$0.798108\pi$
$224$	13.7445			0.918342
$225$		0			0
$226$	−2.42644			−0.161404
$227$	−3.49534	+	3.49534i	−0.231994	+	0.231994i	−0.813524	−	0.581531i	$-0.802454\pi$
$227$	−3.49534	+	3.49534i	−0.231994	+	0.231994i	0.581531	+	0.813524i	$0.302454\pi$
$228$	−6.20141	+	5.67258i	−0.410698	+	0.375676i
$229$			10.2170i			0.675156i	0.941298	+	0.337578i	$0.109608\pi$
$229$			10.2170i			0.675156i	−0.941298	+	0.337578i	$0.890392\pi$
$230$		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	−0.930497	−	0.366298i	$-0.880625\pi$
$233$	−8.61213	+	8.61213i	−0.564199	+	0.564199i	0.366298	+	0.930497i	$0.380625\pi$
$234$			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	$0.151029\pi$
$239$			14.1260i			0.913735i	−0.889535	+	0.456868i	$0.848971\pi$
$240$		0			0
$241$		−	26.8082i		−	1.72687i	−0.504460	−	0.863435i	$-0.668309\pi$
$241$		−	26.8082i		−	1.72687i	0.504460	−	0.863435i	$-0.331691\pi$
$242$	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	−0.110705	+	0.993853i	$0.535311\pi$
$257$	−17.7074	+	17.7074i	−1.10456	+	1.10456i	−0.993853	+	0.110705i	$0.964689\pi$
$258$	−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	−0.743700	−	0.668513i	$-0.766931\pi$
$263$	−1.21933	+	1.21933i	−0.0751871	+	0.0751871i	0.668513	+	0.743700i	$0.266931\pi$
$264$		−	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	0.342689	−	0.939449i	$-0.388662\pi$
$277$	−9.93207	−	9.93207i	−0.596760	−	0.596760i	−0.939449	+	0.342689i	$0.888662\pi$
$278$	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	$-0.993536\pi$
$281$		−	0.680731i		−	0.0406090i	0.999794	−	0.0203045i	$-0.00646357\pi$
$282$	5.38295	+	5.38295i	0.320550	+	0.320550i
$283$	19.5623	−	19.5623i	1.16286	−	1.16286i	0.179011	−	0.983847i	$-0.442710\pi$
$283$	19.5623	−	19.5623i	1.16286	−	1.16286i	0.983847	−	0.179011i	$-0.0572897\pi$
$284$	−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	−0.942655	−	0.333770i	$-0.891679\pi$
$293$	−21.8489	−	21.8489i	−1.27642	−	1.27642i	−0.333770	−	0.942655i	$-0.608321\pi$
$294$		−	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	−0.950309	−	0.311308i	$-0.899233\pi$
$307$	−11.1962	+	11.1962i	−0.639001	+	0.639001i	0.311308	+	0.950309i	$0.399233\pi$
$308$	−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	−0.608886	−	0.793258i	$-0.708383\pi$
$313$	3.26187	−	3.26187i	0.184372	−	0.184372i	0.793258	+	0.608886i	$0.208383\pi$
$314$	−7.45828			−0.420895
$315$		0			0
$316$			3.51007i			0.197457i
$317$	5.37761	−	5.37761i	0.302037	−	0.302037i	−0.539774	−	0.841810i	$-0.681490\pi$
$317$	5.37761	−	5.37761i	0.302037	−	0.302037i	0.841810	+	0.539774i	$0.181490\pi$
$318$	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	$0.205395\pi$
$331$			21.8835i			1.20283i	−0.798939	+	0.601413i	$0.794605\pi$
$332$	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	0.0918798	−	0.995770i	$-0.470712\pi$
$337$	19.9666	−	19.9666i	1.08765	−	1.08765i	0.995770	−	0.0918798i	$-0.0292876\pi$
$338$	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	0.453260	−	0.891379i	$-0.350261\pi$
$347$	−8.16125	−	8.16125i	−0.438119	−	0.438119i	−0.891379	+	0.453260i	$0.850261\pi$
$348$	9.94525	−	9.94525i	0.533121	−	0.533121i
$349$		−	33.5877i		−	1.79791i	−0.438043	−	0.898954i	$-0.644328\pi$
$349$		−	33.5877i		−	1.79791i	0.438043	−	0.898954i	$-0.355672\pi$
$350$		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	−0.802812	−	0.596232i	$-0.796664\pi$
$353$	−3.88129	+	3.88129i	−0.206580	+	0.206580i	0.596232	+	0.802812i	$0.296664\pi$
$354$	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	$-0.779590\pi$
$359$		−	24.1925i		−	1.27683i	0.769691	−	0.638416i	$-0.220410\pi$
$360$		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	0.569672	−	0.821872i	$-0.307070\pi$
$367$	−4.83146	−	4.83146i	−0.252200	−	0.252200i	−0.821872	+	0.569672i	$0.807070\pi$
$368$	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	0.823746	−	0.566960i	$-0.191880\pi$
$373$	4.95936	+	4.95936i	0.256786	+	0.256786i	−0.566960	+	0.823746i	$0.691880\pi$
$374$	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	0.730232	−	0.683199i	$-0.239412\pi$
$383$	0.920467	+	0.920467i	0.0470337	+	0.0470337i	−0.683199	+	0.730232i	$0.739412\pi$
$384$		−	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	$-0.960874\pi$
$389$		−	4.83638i		−	0.245214i	0.992455	−	0.122607i	$-0.0391255\pi$
$390$		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	0.758839	−	0.651278i	$-0.225767\pi$
$397$	2.14315	+	2.14315i	0.107562	+	0.107562i	−0.651278	+	0.758839i	$0.725767\pi$
$398$	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	$-0.841692\pi$
$401$		−	19.1074i		−	0.954176i	0.878856	−	0.477088i	$-0.158308\pi$
$402$	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	$0.217281\pi$
$419$			25.8251i			1.26164i	−0.775929	+	0.630820i	$0.782719\pi$
$420$		0			0
$421$		−	25.1192i		−	1.22423i	−0.790767	−	0.612117i	$-0.790318\pi$
$421$		−	25.1192i		−	1.22423i	0.790767	−	0.612117i	$-0.209682\pi$
$422$	−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	$0.332804\pi$
$431$			35.9238i			1.73039i	−0.501438	+	0.865193i	$0.667196\pi$
$432$	−9.55368	+	9.55368i	−0.459652	+	0.459652i
$433$	−16.6084	−	16.6084i	−0.798151	−	0.798151i	0.184653	−	0.982804i	$-0.440884\pi$
$433$	−16.6084	−	16.6084i	−0.798151	−	0.798151i	−0.982804	+	0.184653i	$0.940884\pi$
$434$			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	−0.00819433	+	0.999966i	$0.502608\pi$
$443$	−21.2193	+	21.2193i	−1.00816	+	1.00816i	−0.999966	+	0.00819433i	$0.997392\pi$
$444$			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	0.757214	−	0.653167i	$-0.226560\pi$
$457$	2.22425	+	2.22425i	0.104046	+	0.104046i	−0.653167	+	0.757214i	$0.726560\pi$
$458$	−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	−0.990696	−	0.136095i	$-0.956545\pi$
$463$	−18.3888	+	18.3888i	−0.854601	+	0.854601i	0.136095	+	0.990696i	$0.456545\pi$
$464$	−16.0037			−0.742951
$465$		0			0
$466$		−	14.0188i		−	0.649410i
$467$	19.2252	+	19.2252i	0.889637	+	0.889637i	0.994488	−	0.104851i	$-0.0334367\pi$
$467$	19.2252	+	19.2252i	0.889637	+	0.889637i	−0.104851	+	0.994488i	$0.533437\pi$
$468$	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	$0.00205313\pi$
$479$			0.282333i			0.0129001i	−0.999979	+	0.00645007i	$0.997947\pi$
$480$		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	−0.995609	−	0.0936103i	$-0.970159\pi$
$487$	−19.9054	+	19.9054i	−0.901999	+	0.901999i	0.0936103	+	0.995609i	$0.470159\pi$
$488$	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	$-0.814433\pi$
$499$		−	24.5950i		−	1.10102i	0.834828	−	0.550511i	$-0.185567\pi$
$500$		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	−0.636757	−	0.771065i	$-0.719724\pi$
$503$	3.01222	−	3.01222i	0.134308	−	0.134308i	0.771065	+	0.636757i	$0.219724\pi$
$504$	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	$0.0935736\pi$
$521$			13.2275i			0.579509i	−0.957101	+	0.289754i	$0.906426\pi$
$522$	30.6131	+	30.6131i	1.33990	+	1.33990i
$523$	−25.4695	−	25.4695i	−1.11370	−	1.11370i	−0.992645	−	0.121059i	$-0.961371\pi$
$523$	−25.4695	−	25.4695i	−1.11370	−	1.11370i	−0.121059	−	0.992645i	$-0.538629\pi$
$524$			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	−0.358297	−	0.933608i	$-0.616642\pi$
$547$	13.4554	−	13.4554i	0.575311	−	0.575311i	0.933608	+	0.358297i	$0.116642\pi$
$548$	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	−0.996678	−	0.0814416i	$-0.974048\pi$
$557$	−25.4445	−	25.4445i	−1.07812	−	1.07812i	−0.0814416	−	0.996678i	$-0.525952\pi$
$558$	−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	0.999991	−	0.00416555i	$-0.00132594\pi$
$563$	23.6286	+	23.6286i	0.995826	+	0.995826i	−0.00416555	+	0.999991i	$0.501326\pi$
$564$	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	0.384895	−	0.922960i	$-0.374238\pi$
$577$	−12.9248	−	12.9248i	−0.538066	−	0.538066i	−0.922960	+	0.384895i	$0.874238\pi$
$578$	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	0.249861	−	0.968282i	$-0.419615\pi$
$587$	−17.4060	−	17.4060i	−0.718421	−	0.718421i	−0.968282	+	0.249861i	$0.919615\pi$
$588$	−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	−0.452757	−	0.891634i	$-0.649560\pi$
$593$	10.6873	−	10.6873i	0.438877	−	0.438877i	0.891634	+	0.452757i	$0.149560\pi$
$594$		−	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	$0.270988\pi$
$601$			36.8789i			1.50432i	−0.658981	+	0.752160i	$0.729012\pi$
$602$	−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	−0.553002	−	0.833180i	$-0.686518\pi$
$607$	6.90285	−	6.90285i	0.280178	−	0.280178i	0.833180	+	0.553002i	$0.186518\pi$
$608$	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	−0.182929	−	0.983126i	$-0.558558\pi$
$613$	19.8119	−	19.8119i	0.800197	−	0.800197i	0.983126	+	0.182929i	$0.0585579\pi$
$614$		−	18.2252i		−	0.735510i
$615$		0			0
$616$		−	25.1192i		−	1.01208i
$617$	29.2579	+	29.2579i	1.17788	+	1.17788i	0.980284	+	0.197595i	$0.0633130\pi$
$617$	29.2579	+	29.2579i	1.17788	+	1.17788i	0.197595	+	0.980284i	$0.436687\pi$
$618$	−43.1936	−	43.1936i	−1.73750	−	1.73750i
$619$		−	17.6424i		−	0.709110i	−0.935035	−	0.354555i	$-0.884632\pi$
$619$		−	17.6424i		−	0.709110i	0.935035	−	0.354555i	$-0.115368\pi$
$620$		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	$0.0506826\pi$
$641$			8.02843i			0.317104i	−0.987351	+	0.158552i	$0.949317\pi$
$642$	−34.2300	+	34.2300i	−1.35095	+	1.35095i
$643$	−14.0108	+	14.0108i	−0.552532	+	0.552532i	−0.927171	−	0.374639i	$-0.877767\pi$
$643$	−14.0108	+	14.0108i	−0.552532	+	0.552532i	0.374639	+	0.927171i	$0.377767\pi$
$644$			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	0.999724	−	0.0234986i	$-0.00748052\pi$
$647$	24.8315	+	24.8315i	0.976225	+	0.976225i	−0.0234986	+	0.999724i	$0.507481\pi$
$648$	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	0.0836064	−	0.996499i	$-0.473356\pi$
$653$	27.6009	−	27.6009i	1.08011	−	1.08011i	0.996499	−	0.0836064i	$-0.0266438\pi$
$654$	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	$-0.800287\pi$
$661$		−	30.1863i		−	1.17411i	0.809547	−	0.587055i	$-0.199713\pi$
$662$	−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	0.494492	−	0.869182i	$-0.335354\pi$
$673$	−9.72032	−	9.72032i	−0.374691	−	0.374691i	−0.869182	+	0.494492i	$0.835354\pi$
$674$			32.5017i			1.25192i
$675$		0			0
$676$	3.27011			0.125774
$677$	−13.5166	+	13.5166i	−0.519486	+	0.519486i	−0.917416	−	0.397930i	$-0.869729\pi$
$677$	−13.5166	+	13.5166i	−0.519486	+	0.519486i	0.397930	+	0.917416i	$0.369729\pi$
$678$	−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	0.678013	−	0.735050i	$-0.262841\pi$
$683$	−1.49062	−	1.49062i	−0.0570371	−	0.0570371i	−0.735050	+	0.678013i	$0.762841\pi$
$684$	−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	$0.167424\pi$
$709$			26.7367i			1.00412i	−0.864833	+	0.502059i	$0.832576\pi$
$710$		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	$-0.809979\pi$
$719$		−	30.1465i		−	1.12427i	0.827044	−	0.562137i	$-0.190021\pi$
$720$		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	0.982464	+	0.186451i	$0.0596986\pi$
$727$	31.5174	+	31.5174i	1.16892	+	1.16892i	0.186451	+	0.982464i	$0.440301\pi$
$728$	−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	−0.484862	−	0.874591i	$-0.661130\pi$
$733$	10.5515	−	10.5515i	0.389728	−	0.389728i	0.874591	+	0.484862i	$0.161130\pi$
$734$	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	$0.190892\pi$
$739$			30.6859i			1.12880i	−0.825501	+	0.564400i	$0.809108\pi$
$740$		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	0.395409	−	0.918505i	$-0.370603\pi$
$743$	−14.2586	−	14.2586i	−0.523096	−	0.523096i	−0.918505	+	0.395409i	$0.870603\pi$
$744$	−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	$-0.723865\pi$
$751$		−	41.8036i		−	1.52543i	0.646732	−	0.762717i	$-0.276135\pi$
$752$	−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	0.936503	−	0.350659i	$-0.114042\pi$
$757$	16.1187	+	16.1187i	0.585845	+	0.585845i	−0.350659	+	0.936503i	$0.614042\pi$
$758$	−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	$0.0243096\pi$
$769$			4.23155i			0.152594i	−0.997085	+	0.0762968i	$0.975690\pi$
$770$		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	0.866331	−	0.499470i	$-0.166472\pi$
$773$	10.1998	+	10.1998i	0.366861	+	0.366861i	−0.499470	+	0.866331i	$0.666472\pi$
$774$	−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	−0.727022	−	0.686614i	$-0.759096\pi$
$787$	−1.13360	+	1.13360i	−0.0404084	+	0.0404084i	0.686614	+	0.727022i	$0.259096\pi$
$788$	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	−0.760177	−	0.649716i	$-0.774888\pi$
$797$	−3.11843	+	3.11843i	−0.110460	+	0.110460i	0.649716	+	0.760177i	$0.274888\pi$
$798$	−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	$0.180025\pi$
$809$			30.4847i			1.07179i	−0.844286	+	0.535893i	$0.819975\pi$
$810$		0			0
$811$			25.3936i			0.891688i	0.895111	+	0.445844i	$0.147096\pi$
$811$			25.3936i			0.891688i	−0.895111	+	0.445844i	$0.852904\pi$
$812$	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	−0.268185	+	0.963367i	$0.586424\pi$
$823$	−35.3307	+	35.3307i	−1.23155	+	1.23155i	−0.963367	+	0.268185i	$0.913576\pi$
$824$		−	57.2179i		−	1.99328i
$825$		0			0
$826$	15.2849			0.531829
$827$	−1.59318	+	1.59318i	−0.0554004	+	0.0554004i	−0.734264	−	0.678864i	$-0.762473\pi$
$827$	−1.59318	+	1.59318i	−0.0554004	+	0.0554004i	0.678864	+	0.734264i	$0.262473\pi$
$828$	−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	−0.870514	−	0.492143i	$-0.836214\pi$
$853$	−11.0508	+	11.0508i	−0.378372	+	0.378372i	0.492143	+	0.870514i	$0.336214\pi$
$854$	21.4771			0.734932
$855$		0			0
$856$	−45.3439			−1.54982
$857$	−38.6358	+	38.6358i	−1.31977	+	1.31977i	−0.405822	+	0.913952i	$0.633015\pi$
$857$	−38.6358	+	38.6358i	−1.31977	+	1.31977i	−0.913952	+	0.405822i	$0.866985\pi$
$858$	14.3146	+	14.3146i	0.488694	+	0.488694i
$859$			24.4241i			0.833339i	0.909058	+	0.416669i	$0.136803\pi$
$859$			24.4241i			0.833339i	−0.909058	+	0.416669i	$0.863197\pi$
$860$		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	0.693188	−	0.720757i	$-0.256206\pi$
$863$	−0.809893	−	0.809893i	−0.0275691	−	0.0275691i	−0.720757	+	0.693188i	$0.756206\pi$
$864$			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	0.212390	−	0.977185i	$-0.431875\pi$
$877$	35.2283	−	35.2283i	1.18958	−	1.18958i	0.977185	−	0.212390i	$-0.0681249\pi$
$878$	−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	−0.607870	−	0.794036i	$-0.707976\pi$
$883$	5.53198	−	5.53198i	0.186166	−	0.186166i	0.794036	+	0.607870i	$0.207976\pi$
$884$	−4.92474			−0.165637
$885$		0			0
$886$		−	34.5409i		−	1.16042i
$887$	−17.0760	+	17.0760i	−0.573357	+	0.573357i	−0.933065	−	0.359708i	$-0.882876\pi$
$887$	−17.0760	+	17.0760i	−0.573357	+	0.573357i	0.359708	+	0.933065i	$0.382876\pi$
$888$	−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	−0.549925	−	0.835214i	$-0.685344\pi$
$907$	8.59188	−	8.59188i	0.285289	−	0.285289i	0.835214	+	0.549925i	$0.185344\pi$
$908$	−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	$0.205044\pi$
$911$			36.2513i			1.20106i	−0.799602	+	0.600530i	$0.794956\pi$
$912$	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	$-0.920077\pi$
$919$		−	15.0640i		−	0.496914i	0.968643	−	0.248457i	$-0.0799235\pi$
$920$		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	$0.0396469\pi$
$929$			7.57310i			0.248465i	−0.992253	+	0.124233i	$0.960353\pi$
$930$		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	0.918216	−	0.396079i	$-0.129629\pi$
$937$	15.9829	+	15.9829i	0.522137	+	0.522137i	−0.396079	+	0.918216i	$0.629629\pi$
$938$	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	$0.143184\pi$
$941$			26.6762i			0.869620i	−0.900522	+	0.434810i	$0.856816\pi$
$942$	−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	0.137992	−	0.990433i	$-0.455935\pi$
$947$	−26.2325	−	26.2325i	−0.852442	−	0.852442i	−0.990433	+	0.137992i	$0.955935\pi$
$948$	−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	0.994832	−	0.101533i	$-0.0323746\pi$
$953$	27.5768	+	27.5768i	0.893300	+	0.893300i	−0.101533	+	0.994832i	$0.532375\pi$
$954$			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	0.865062	−	0.501665i	$-0.167279\pi$
$967$	11.3004	+	11.3004i	0.363397	+	0.363397i	−0.501665	+	0.865062i	$0.667279\pi$
$968$	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	$-0.822602\pi$
$971$		−	32.9624i		−	1.05781i	0.848680	−	0.528907i	$-0.177398\pi$
$972$	−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	−0.975291	−	0.220925i	$-0.929093\pi$
$977$	−23.5792	+	23.5792i	−0.754366	+	0.754366i	0.220925	+	0.975291i	$0.429093\pi$
$978$	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	0.864184	−	0.503175i	$-0.167835\pi$
$983$	11.3187	+	11.3187i	0.361009	+	0.361009i	−0.503175	+	0.864184i	$0.667835\pi$
$984$	−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	$-0.688841\pi$
$991$		−	52.2018i		−	1.65824i	0.559068	−	0.829122i	$-0.311159\pi$
$992$	−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	0.777079	−	0.629403i	$-0.216701\pi$
$997$	4.66291	+	4.66291i	0.147676	+	0.147676i	−0.629403	+	0.777079i	$0.716701\pi$
$998$	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.132.3		12
5.2	odd	4		95.2.g.b.18.3	✓	12
5.3	odd	4	inner	475.2.g.b.18.4		12
5.4	even	2		95.2.g.b.37.4	yes	12
15.2	even	4		855.2.p.f.208.4		12
15.14	odd	2		855.2.p.f.37.3		12
19.18	odd	2	inner	475.2.g.b.132.4		12
95.18	even	4	inner	475.2.g.b.18.3		12
95.37	even	4		95.2.g.b.18.4	yes	12
95.94	odd	2		95.2.g.b.37.3	yes	12
285.227	odd	4		855.2.p.f.208.3		12
285.284	even	2		855.2.p.f.37.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.3	✓	12	5.2	odd	4
95.2.g.b.18.4	yes	12	95.37	even	4
95.2.g.b.37.3	yes	12	95.94	odd	2
95.2.g.b.37.4	yes	12	5.4	even	2
475.2.g.b.18.3		12	95.18	even	4	inner
475.2.g.b.18.4		12	5.3	odd	4	inner
475.2.g.b.132.3		12	1.1	even	1	trivial
475.2.g.b.132.4		12	19.18	odd	2	inner
855.2.p.f.37.3		12	15.14	odd	2
855.2.p.f.37.4		12	285.284	even	2
855.2.p.f.208.3		12	285.227	odd	4
855.2.p.f.208.4		12	15.2	even	4

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more