LMFDB - Embedded newform 675.2.q.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(143,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("675.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.q (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.2
Root			$1.60599 + 0.430324i$ of defining polynomial
Character	$\chi$	$=$	675.143
Dual form			675.2.q.a.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60599 + 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(-0.465559 - 1.73749i) q^{7} +(1.45267 - 1.45267i) q^{8} +O(q^{10})$	\(q+(-1.60599 + 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(-0.465559 - 1.73749i) q^{7} +(1.45267 - 1.45267i) q^{8} +(-3.12636 - 1.80501i) q^{11} +(-0.342574 + 1.27850i) q^{13} +(1.49537 + 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(-0.277007 - 0.277007i) q^{17} +6.25273i q^{19} +(5.79765 + 1.55348i) q^{22} +(2.16347 + 0.579699i) q^{23} -2.20068i q^{26} +(-0.972242 - 0.972242i) q^{28} +(-1.56832 + 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(1.06430 - 3.97202i) q^{32} +(0.564074 + 0.325668i) q^{34} +(-5.55242 + 5.55242i) q^{37} +(-2.69070 - 10.0418i) q^{38} +(-1.29036 + 0.744991i) q^{41} +(-4.10976 + 1.10121i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(-3.82042 + 1.02368i) q^{47} +(3.26005 - 1.88219i) q^{49} +(0.261857 + 0.977265i) q^{52} +(-7.48222 + 7.48222i) q^{53} +(-3.20031 - 1.84770i) q^{56} +(1.34977 - 5.03742i) q^{58} +(0.279377 + 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(5.70446 + 5.70446i) q^{62} -3.05196i q^{64} +(-10.8351 - 2.90325i) q^{67} +(-0.289242 - 0.0775020i) q^{68} +8.01611i q^{71} +(1.29315 + 1.29315i) q^{73} +(6.52779 - 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(-1.68068 + 6.27237i) q^{77} +(-6.96917 - 4.02365i) q^{79} +(1.75172 - 1.75172i) q^{82} +(-0.150243 - 0.560714i) q^{83} +(6.12636 - 3.53706i) q^{86} +(-7.16367 + 1.91950i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(1.65372 - 0.443112i) q^{92} +(5.69504 - 3.28804i) q^{94} +(1.37786 + 5.14224i) q^{97} +(-4.42566 + 4.42566i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 + 2 * q^7	$ 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.60599	+	0.430324i	−1.13561	+	0.304285i	−0.777183	−	0.629274i	$-0.783352\pi$
$2$	−1.60599	+	0.430324i	−1.13561	+	0.304285i	−0.358423	+	0.933559i	$0.616686\pi$
$3$		0			0
$3$		0			0
$4$	0.661975	−	0.382191i	0.330987	−	0.191096i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.465559	−	1.73749i	−0.175965	−	0.656710i	−0.996385	−	0.0849489i	$-0.972927\pi$
$7$	−0.465559	−	1.73749i	−0.175965	−	0.656710i	0.820421	−	0.571761i	$-0.193739\pi$
$8$	1.45267	−	1.45267i	0.513598	−	0.513598i
$9$		0			0
$10$		0			0
$11$	−3.12636	−	1.80501i	−0.942634	−	0.544230i	−0.0518493	−	0.998655i	$-0.516512\pi$
$11$	−3.12636	−	1.80501i	−0.942634	−	0.544230i	−0.890785	+	0.454425i	$0.849845\pi$
$12$		0			0
$13$	−0.342574	+	1.27850i	−0.0950128	+	0.354593i	−0.997021	−	0.0771255i	$-0.975426\pi$
$13$	−0.342574	+	1.27850i	−0.0950128	+	0.354593i	0.902009	+	0.431718i	$0.142092\pi$
$14$	1.49537	+	2.59005i	0.399654	+	0.692220i
$15$		0			0
$16$	−2.47224	+	4.28205i	−0.618061	+	1.07051i
$17$	−0.277007	−	0.277007i	−0.0671841	−	0.0671841i	0.672716	−	0.739900i	$-0.265127\pi$
$17$	−0.277007	−	0.277007i	−0.0671841	−	0.0671841i	−0.739900	+	0.672716i	$0.765127\pi$
$18$		0			0
$19$			6.25273i			1.43447i	0.696829	+	0.717237i	$0.254594\pi$
$19$			6.25273i			1.43447i	−0.696829	+	0.717237i	$0.745406\pi$
$20$		0			0
$21$		0			0
$22$	5.79765	+	1.55348i	1.23606	+	0.331202i
$23$	2.16347	+	0.579699i	0.451114	+	0.120876i	0.477221	−	0.878784i	$-0.341644\pi$
$23$	2.16347	+	0.579699i	0.451114	+	0.120876i	−0.0261067	+	0.999659i	$0.508311\pi$
$24$		0			0
$25$		0			0
$26$		−	2.20068i		−	0.431589i
$27$		0			0
$28$	−0.972242	−	0.972242i	−0.183737	−	0.183737i
$29$	−1.56832	+	2.71642i	−0.291230	+	0.504426i	−0.974101	−	0.226114i	$-0.927398\pi$
$29$	−1.56832	+	2.71642i	−0.291230	+	0.504426i	0.682871	+	0.730539i	$0.260731\pi$
$30$		0			0
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	0.561623	−	0.827393i	$-0.310177\pi$
$31$	−2.42605	−	4.20205i	−0.435732	−	0.754710i	−0.997355	+	0.0726832i	$0.976844\pi$
$32$	1.06430	−	3.97202i	0.188143	−	0.702160i
$33$		0			0
$34$	0.564074	+	0.325668i	0.0967378	+	0.0558516i
$35$		0			0
$36$		0			0
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	−0.996493	−	0.0836807i	$-0.973332\pi$
$37$	−5.55242	+	5.55242i	−0.912812	+	0.912812i	0.0836807	+	0.996493i	$0.473332\pi$
$38$	−2.69070	−	10.0418i	−0.436489	−	1.62900i
$39$		0			0
$40$		0			0
$41$	−1.29036	+	0.744991i	−0.201521	+	0.116348i	−0.597365	−	0.801970i	$-0.703785\pi$
$41$	−1.29036	+	0.744991i	−0.201521	+	0.116348i	0.395844	+	0.918318i	$0.370452\pi$
$42$		0			0
$43$	−4.10976	+	1.10121i	−0.626733	+	0.167933i	−0.558187	−	0.829715i	$-0.688503\pi$
$43$	−4.10976	+	1.10121i	−0.626733	+	0.167933i	−0.0685463	+	0.997648i	$0.521836\pi$
$44$	−2.75943			−0.416000
$45$		0			0
$46$	−3.72396			−0.549069
$47$	−3.82042	+	1.02368i	−0.557266	+	0.149319i	−0.526450	−	0.850206i	$-0.676477\pi$
$47$	−3.82042	+	1.02368i	−0.557266	+	0.149319i	−0.0308158	+	0.999525i	$0.509811\pi$
$48$		0			0
$49$	3.26005	−	1.88219i	0.465722	−	0.268884i
$50$		0			0
$51$		0			0
$52$	0.261857	+	0.977265i	0.0363131	+	0.135522i
$53$	−7.48222	+	7.48222i	−1.02776	+	1.02776i	−0.0281581	+	0.999603i	$0.508964\pi$
$53$	−7.48222	+	7.48222i	−1.02776	+	1.02776i	−0.999603	+	0.0281581i	$0.991036\pi$
$54$		0			0
$55$		0			0
$56$	−3.20031	−	1.84770i	−0.427660	−	0.246909i
$57$		0			0
$58$	1.34977	−	5.03742i	0.177234	−	0.661446i
$59$	0.279377	+	0.483896i	0.0363718	+	0.0629978i	0.883638	−	0.468170i	$-0.155087\pi$
$59$	0.279377	+	0.483896i	0.0363718	+	0.0629978i	−0.847266	+	0.531168i	$0.821753\pi$
$60$		0			0
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	−0.990959	−	0.134162i	$-0.957166\pi$
$61$	−2.96237	+	5.13097i	−0.379292	+	0.656953i	0.611667	+	0.791115i	$0.290499\pi$
$62$	5.70446	+	5.70446i	0.724467	+	0.724467i
$63$		0			0
$64$		−	3.05196i		−	0.381495i
$65$		0			0
$66$		0			0
$67$	−10.8351	−	2.90325i	−1.32371	−	0.354688i	−0.473346	−	0.880876i	$-0.656954\pi$
$67$	−10.8351	−	2.90325i	−1.32371	−	0.354688i	−0.850368	+	0.526188i	$0.823621\pi$
$68$	−0.289242	−	0.0775020i	−0.0350757	−	0.00939850i
$69$		0			0
$70$		0			0
$71$			8.01611i			0.951338i	0.879624	+	0.475669i	$0.157794\pi$
$71$			8.01611i			0.951338i	−0.879624	+	0.475669i	$0.842206\pi$
$72$		0			0
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	0.778721	−	0.627370i	$-0.215869\pi$
$73$	1.29315	+	1.29315i	0.151352	+	0.151352i	−0.627370	+	0.778721i	$0.715869\pi$
$74$	6.52779	−	11.3065i	0.758840	−	1.31435i
$75$		0			0
$76$	2.38974	+	4.13915i	0.274122	+	0.474793i
$77$	−1.68068	+	6.27237i	−0.191531	+	0.714802i
$78$		0			0
$79$	−6.96917	−	4.02365i	−0.784093	−	0.452696i	0.0537859	−	0.998552i	$-0.482871\pi$
$79$	−6.96917	−	4.02365i	−0.784093	−	0.452696i	−0.837879	+	0.545856i	$0.816204\pi$
$80$		0			0
$81$		0			0
$82$	1.75172	−	1.75172i	0.193445	−	0.193445i
$83$	−0.150243	−	0.560714i	−0.0164913	−	0.0615463i	0.957190	−	0.289461i	$-0.0934760\pi$
$83$	−0.150243	−	0.560714i	−0.0164913	−	0.0615463i	−0.973681	+	0.227914i	$0.926809\pi$
$84$		0			0
$85$		0			0
$86$	6.12636	−	3.53706i	0.660623	−	0.381411i
$87$		0			0
$88$	−7.16367	+	1.91950i	−0.763650	+	0.204619i
$89$	−16.4343			−1.74203			−0.871016	−	0.491255i	$-0.836538\pi$
$89$	−16.4343			−1.74203			−0.871016	+	0.491255i	$0.836538\pi$
$90$		0			0
$91$	2.38087			0.249583
$92$	1.65372	−	0.443112i	0.172412	−	0.0461976i
$93$		0			0
$94$	5.69504	−	3.28804i	0.587399	−	0.339135i
$95$		0			0
$96$		0			0
$97$	1.37786	+	5.14224i	0.139900	+	0.522116i	0.999930	+	0.0118706i	$0.00377862\pi$
$97$	1.37786	+	5.14224i	0.139900	+	0.522116i	−0.860029	+	0.510245i	$0.829555\pi$
$98$	−4.42566	+	4.42566i	−0.447059	+	0.447059i
$99$		0			0
$100$		0			0
$101$	4.73008	+	2.73092i	0.470661	+	0.271736i	0.716516	−	0.697570i	$-0.245735\pi$
$101$	4.73008	+	2.73092i	0.470661	+	0.271736i	−0.245855	+	0.969307i	$0.579069\pi$
$102$		0			0
$103$	1.34888	−	5.03410i	0.132909	−	0.496024i	−0.867088	−	0.498154i	$-0.834011\pi$
$103$	1.34888	−	5.03410i	0.132909	−	0.496024i	0.999998	+	0.00212995i	$0.000677984\pi$
$104$	1.35960	+	2.35489i	0.133320	+	0.230916i
$105$		0			0
$106$	8.79659	−	15.2361i	0.854401	−	1.47987i
$107$	−4.07498	−	4.07498i	−0.393944	−	0.393944i	0.482147	−	0.876090i	$-0.339857\pi$
$107$	−4.07498	−	4.07498i	−0.393944	−	0.393944i	−0.876090	+	0.482147i	$0.839857\pi$
$108$		0			0
$109$			1.10747i			0.106077i	0.998592	+	0.0530384i	$0.0168906\pi$
$109$			1.10747i			0.106077i	−0.998592	+	0.0530384i	$0.983109\pi$
$110$		0			0
$111$		0			0
$112$	8.59099	+	2.30195i	0.811773	+	0.217514i
$113$	8.06067	+	2.15985i	0.758284	+	0.203182i	0.617190	−	0.786815i	$-0.288271\pi$
$113$	8.06067	+	2.15985i	0.758284	+	0.203182i	0.141095	+	0.989996i	$0.454938\pi$
$114$		0			0
$115$		0			0
$116$			2.39760i			0.222611i
$117$		0			0
$118$	−0.656909	−	0.656909i	−0.0604734	−	0.0604734i
$119$	−0.352334	+	0.610260i	−0.0322984	+	0.0559425i
$120$		0			0
$121$	1.01610	+	1.75994i	0.0923731	+	0.159995i
$122$	2.54955	−	9.51507i	0.230826	−	0.861454i
$123$		0			0
$124$	−3.21197	−	1.85443i	−0.288444	−	0.166533i
$125$		0			0
$126$		0			0
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.0287470	−	0.999587i	$-0.490848\pi$
$127$	11.5887	−	11.5887i	1.02833	−	1.02833i	0.999587	−	0.0287470i	$-0.00915171\pi$
$128$	3.44193	+	12.8454i	0.304226	+	1.13539i
$129$		0			0
$130$		0			0
$131$	−4.34401	+	2.50802i	−0.379538	+	0.219126i	−0.677617	−	0.735415i	$-0.736987\pi$
$131$	−4.34401	+	2.50802i	−0.379538	+	0.219126i	0.298079	+	0.954541i	$0.403654\pi$
$132$		0			0
$133$	10.8641	−	2.91101i	0.942033	−	0.252417i
$134$	18.6504			1.61115
$135$		0			0
$136$	−0.804802			−0.0690112
$137$	−0.440837	+	0.118122i	−0.0376632	+	0.0100918i	−0.277601	−	0.960696i	$-0.589539\pi$
$137$	−0.440837	+	0.118122i	−0.0376632	+	0.0100918i	0.239938	+	0.970788i	$0.422873\pi$
$138$		0			0
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.955504	−	0.294977i	$-0.904688\pi$
$139$	−13.8860	+	8.01711i	−1.17780	+	0.680003i	−0.222295	+	0.974980i	$0.571355\pi$
$140$		0			0
$141$		0			0
$142$	−3.44952	−	12.8738i	−0.289478	−	1.08035i
$143$	3.37872	−	3.37872i	0.282542	−	0.282542i
$144$		0			0
$145$		0			0
$146$	−2.63326	−	1.52031i	−0.217930	−	0.125822i
$147$		0			0
$148$	−1.55348	+	5.79765i	−0.127695	+	0.476564i
$149$	3.44153	+	5.96090i	0.281941	+	0.488336i	0.971863	−	0.235548i	$-0.0756885\pi$
$149$	3.44153	+	5.96090i	0.281941	+	0.488336i	−0.689922	+	0.723884i	$0.742355\pi$
$150$		0			0
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	−0.635874	−	0.771793i	$-0.719360\pi$
$151$	4.30647	−	7.45902i	0.350455	−	0.607006i	0.986329	+	0.164787i	$0.0526935\pi$
$152$	9.08317	+	9.08317i	0.736743	+	0.736743i
$153$		0			0
$154$		−	10.7966i		−	0.870014i
$155$		0			0
$156$		0			0
$157$	1.60930	+	0.431209i	0.128436	+	0.0344142i	0.322464	−	0.946582i	$-0.395489\pi$
$157$	1.60930	+	0.431209i	0.128436	+	0.0344142i	−0.194029	+	0.980996i	$0.562155\pi$
$158$	12.9239	+	3.46295i	1.02817	+	0.275497i
$159$		0			0
$160$		0			0
$161$		−	4.02889i		−	0.317521i
$162$		0			0
$163$	10.5120	+	10.5120i	0.823363	+	0.823363i	0.986589	−	0.163225i	$-0.0521898\pi$
$163$	10.5120	+	10.5120i	0.823363	+	0.823363i	−0.163225	+	0.986589i	$0.552190\pi$
$164$	−0.569458	+	0.986331i	−0.0444672	+	0.0770195i
$165$		0			0
$166$	0.482577	+	0.835848i	0.0374552	+	0.0648744i
$167$	2.51657	−	9.39195i	0.194738	−	0.726771i	−0.797597	−	0.603191i	$-0.793896\pi$
$167$	2.51657	−	9.39195i	0.194738	−	0.726771i	0.992335	−	0.123580i	$-0.0394376\pi$
$168$		0			0
$169$	9.74112	+	5.62404i	0.749317	+	0.432618i
$170$		0			0
$171$		0			0
$172$	−2.29969	+	2.29969i	−0.175350	+	0.175350i
$173$	−3.88335	−	14.4929i	−0.295246	−	1.10187i	−0.941022	−	0.338346i	$-0.890133\pi$
$173$	−3.88335	−	14.4929i	−0.295246	−	1.10187i	0.645776	−	0.763527i	$-0.276534\pi$
$174$		0			0
$175$		0			0
$176$	15.4583	−	8.92483i	1.16521	−	0.672735i
$177$		0			0
$178$	26.3933	−	7.07207i	1.97826	−	0.530074i
$179$	4.21995			0.315414			0.157707	−	0.987486i	$-0.449590\pi$
$179$	4.21995			0.315414			0.157707	+	0.987486i	$0.449590\pi$
$180$		0			0
$181$	23.7930			1.76852			0.884261	−	0.466993i	$-0.154663\pi$
$181$	23.7930			1.76852			0.884261	+	0.466993i	$0.154663\pi$
$182$	−3.82366	+	1.02455i	−0.283428	+	0.0759444i
$183$		0			0
$184$	3.98492	−	2.30070i	0.293772	−	0.169610i
$185$		0			0
$186$		0			0
$187$	0.366025	+	1.36603i	0.0267664	+	0.0998937i
$188$	−2.13778	+	2.13778i	−0.155914	+	0.155914i
$189$		0			0
$190$		0			0
$191$	20.1545	+	11.6362i	1.45833	+	0.841965i	0.998929	−	0.0462661i	$-0.0147322\pi$
$191$	20.1545	+	11.6362i	1.45833	+	0.841965i	0.459397	+	0.888231i	$0.348066\pi$
$192$		0			0
$193$	−5.36663	+	20.0285i	−0.386299	+	1.44169i	0.449811	+	0.893124i	$0.351491\pi$
$193$	−5.36663	+	20.0285i	−0.386299	+	1.44169i	−0.836110	+	0.548562i	$0.815175\pi$
$194$	−4.42566	−	7.66547i	−0.317744	−	0.550348i
$195$		0			0
$196$	1.43871	−	2.49193i	0.102765	−	0.177995i
$197$	−6.52613	−	6.52613i	−0.464968	−	0.464968i	0.435312	−	0.900280i	$-0.356638\pi$
$197$	−6.52613	−	6.52613i	−0.464968	−	0.464968i	−0.900280	+	0.435312i	$0.856638\pi$
$198$		0			0
$199$		−	4.03778i		−	0.286231i	−0.989706	−	0.143115i	$-0.954288\pi$
$199$		−	4.03778i		−	0.286231i	0.989706	−	0.143115i	$-0.0457120\pi$
$200$		0			0
$201$		0			0
$202$	−8.77165	−	2.35036i	−0.617171	−	0.165370i
$203$	5.44989	+	1.46029i	0.382507	+	0.102493i
$204$		0			0
$205$		0			0
$206$			8.66517i			0.603731i
$207$		0			0
$208$	−4.62768	−	4.62768i	−0.320872	−	0.320872i
$209$	11.2862	−	19.5483i	0.780684	−	1.35219i
$210$		0			0
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	0.887631	−	0.460556i	$-0.152350\pi$
$211$	0.653114	+	1.13123i	0.0449623	+	0.0778769i	−0.842668	+	0.538433i	$0.819017\pi$
$212$	−2.09340	+	7.81268i	−0.143775	+	0.536577i
$213$		0			0
$214$	8.29795	+	4.79082i	0.567236	+	0.327494i
$215$		0			0
$216$		0			0
$217$	−6.17155	+	6.17155i	−0.418952	+	0.418952i
$218$	−0.476572	−	1.77859i	−0.0322776	−	0.120461i
$219$		0			0
$220$		0			0
$221$	0.449050	−	0.259259i	0.0302063	−	0.0174396i
$222$		0			0
$223$	−8.01142	+	2.14665i	−0.536485	+	0.143751i	−0.516881	−	0.856057i	$-0.672907\pi$
$223$	−8.01142	+	2.14665i	−0.536485	+	0.143751i	−0.0196035	+	0.999808i	$0.506240\pi$
$224$	−7.39683			−0.494222
$225$		0			0
$226$	−13.8748			−0.922937
$227$	8.90739	−	2.38673i	0.591204	−	0.158413i	0.0492007	−	0.998789i	$-0.484333\pi$
$227$	8.90739	−	2.38673i	0.591204	−	0.158413i	0.542003	+	0.840376i	$0.317666\pi$
$228$		0			0
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.945641	−	0.325211i	$-0.894565\pi$
$229$	−17.2032	+	9.93228i	−1.13682	+	0.656344i	−0.191179	+	0.981555i	$0.561231\pi$
$230$		0			0
$231$		0			0
$232$	1.66780	+	6.22433i	0.109497	+	0.408647i
$233$	−5.45304	+	5.45304i	−0.357241	+	0.357241i	−0.862795	−	0.505554i	$-0.831288\pi$
$233$	−5.45304	+	5.45304i	−0.357241	+	0.357241i	0.505554	+	0.862795i	$0.331288\pi$
$234$		0			0
$235$		0			0
$236$	0.369882	+	0.213551i	0.0240772	+	0.0139010i
$237$		0			0
$238$	0.303235	−	1.13169i	0.0196558	−	0.0733566i
$239$	−3.48185	−	6.03074i	−0.225222	−	0.390096i	0.731164	−	0.682202i	$-0.238977\pi$
$239$	−3.48185	−	6.03074i	−0.225222	−	0.390096i	−0.956386	+	0.292106i	$0.905644\pi$
$240$		0			0
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	0.185993	+	0.982551i	$0.440450\pi$
$241$	−11.7660	+	20.3794i	−0.757918	+	1.31275i	−0.943911	+	0.330201i	$0.892883\pi$
$242$	−2.38920	−	2.38920i	−0.153584	−	0.153584i
$243$		0			0
$244$			4.52877i			0.289925i
$245$		0			0
$246$		0			0
$247$	−7.99413	−	2.14202i	−0.508654	−	0.136293i
$248$	−9.62847	−	2.57994i	−0.611408	−	0.163826i
$249$		0			0
$250$		0			0
$251$		−	20.7941i		−	1.31251i	−0.754537	−	0.656257i	$-0.772139\pi$
$251$		−	20.7941i		−	1.31251i	0.754537	−	0.656257i	$-0.227861\pi$
$252$		0			0
$253$	−5.71742	−	5.71742i	−0.359451	−	0.359451i
$254$	−13.6245	+	23.5983i	−0.854876	+	1.48069i
$255$		0			0
$256$	−8.00344	−	13.8624i	−0.500215	−	0.866398i
$257$	2.72001	−	10.1512i	0.169670	−	0.633216i	−0.827729	−	0.561129i	$-0.810367\pi$
$257$	2.72001	−	10.1512i	0.169670	−	0.633216i	0.997398	−	0.0720873i	$-0.0229660\pi$
$258$		0			0
$259$	12.2323	+	7.06229i	0.760075	+	0.438830i
$260$		0			0
$261$		0			0
$262$	5.89718	−	5.89718i	0.364329	−	0.364329i
$263$	3.86662	+	14.4304i	0.238426	+	0.889818i	0.976574	+	0.215180i	$0.0690338\pi$
$263$	3.86662	+	14.4304i	0.238426	+	0.889818i	−0.738148	+	0.674638i	$0.764300\pi$
$264$		0			0
$265$		0			0
$266$	−16.1949	+	9.35012i	−0.992972	+	0.573293i
$267$		0			0
$268$	−8.28214	+	2.21919i	−0.505912	+	0.135559i
$269$	−0.781994			−0.0476790			−0.0238395	−	0.999716i	$-0.507589\pi$
$269$	−0.781994			−0.0476790			−0.0238395	+	0.999716i	$0.507589\pi$
$270$		0			0
$271$	−12.4677			−0.757357			−0.378679	−	0.925528i	$-0.623621\pi$
$271$	−12.4677			−0.757357			−0.378679	+	0.925528i	$0.623621\pi$
$272$	1.87099	−	0.501329i	0.113445	−	0.0303976i
$273$		0			0
$274$	0.657149	−	0.379405i	0.0396998	−	0.0229207i
$275$		0			0
$276$		0			0
$277$	2.43120	+	9.07336i	0.146077	+	0.545165i	0.999705	+	0.0242830i	$0.00773027\pi$
$277$	2.43120	+	9.07336i	0.146077	+	0.545165i	−0.853629	+	0.520882i	$0.825603\pi$
$278$	18.8509	−	18.8509i	1.13060	−	1.13060i
$279$		0			0
$280$		0			0
$281$	−26.6024	−	15.3589i	−1.58697	−	0.916237i	−0.993803	−	0.111156i	$-0.964545\pi$
$281$	−26.6024	−	15.3589i	−1.58697	−	0.916237i	−0.593165	−	0.805081i	$-0.702122\pi$
$282$		0			0
$283$	4.86835	−	18.1689i	0.289393	−	1.08003i	−0.656175	−	0.754609i	$-0.727827\pi$
$283$	4.86835	−	18.1689i	0.289393	−	1.08003i	0.945569	−	0.325423i	$-0.105507\pi$
$284$	3.06369	+	5.30647i	0.181797	+	0.314881i
$285$		0			0
$286$	−3.97224	+	6.88013i	−0.234884	+	0.406830i
$287$	1.89515	+	1.89515i	0.111867	+	0.111867i
$288$		0			0
$289$		−	16.8465i		−	0.990973i
$290$		0			0
$291$		0			0
$292$	1.35026	+	0.361802i	0.0790181	+	0.0211728i
$293$	−32.6486	−	8.74817i	−1.90735	−	0.511074i	−0.994765	−	0.102194i	$-0.967414\pi$
$293$	−32.6486	−	8.74817i	−1.90735	−	0.511074i	−0.912588	−	0.408880i	$-0.865919\pi$
$294$		0			0
$295$		0			0
$296$			16.1317i			0.937636i
$297$		0			0
$298$	−8.09218	−	8.09218i	−0.468767	−	0.468767i
$299$	−1.48229	+	2.56741i	−0.0857232	+	0.148477i
$300$		0			0
$301$	3.82668	+	6.62800i	0.220566	+	0.382031i
$302$	−3.70635	+	13.8323i	−0.213276	+	0.795959i
$303$		0			0
$304$	−26.7745	−	15.4583i	−1.53562	−	0.886592i
$305$		0			0
$306$		0			0
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	−0.639440	−	0.768841i	$-0.720834\pi$
$307$	2.26728	−	2.26728i	0.129400	−	0.129400i	0.768841	+	0.639440i	$0.220834\pi$
$308$	1.28468	+	4.79449i	0.0732014	+	0.273191i
$309$		0			0
$310$		0			0
$311$	1.86689	−	1.07785i	0.105862	−	0.0611193i	−0.446134	−	0.894966i	$-0.647200\pi$
$311$	1.86689	−	1.07785i	0.105862	−	0.0611193i	0.551996	+	0.833847i	$0.313866\pi$
$312$		0			0
$313$	−20.9905	+	5.62439i	−1.18645	+	0.317909i	−0.797483	−	0.603341i	$-0.793836\pi$
$313$	−20.9905	+	5.62439i	−1.18645	+	0.317909i	−0.388971	+	0.921250i	$0.627169\pi$
$314$	−2.77007			−0.156324
$315$		0			0
$316$	−6.15122			−0.346033
$317$	4.47853	−	1.20002i	0.251539	−	0.0673997i	−0.130846	−	0.991403i	$-0.541769\pi$
$317$	4.47853	−	1.20002i	0.251539	−	0.0673997i	0.382385	+	0.924003i	$0.375103\pi$
$318$		0			0
$319$	9.80630	−	5.66167i	0.549047	−	0.316993i
$320$		0			0
$321$		0			0
$322$	1.73373	+	6.47035i	0.0966167	+	0.360579i
$323$	1.73205	−	1.73205i	0.0963739	−	0.0963739i
$324$		0			0
$325$		0			0
$326$	−21.4057	−	12.3586i	−1.18555	−	0.684480i
$327$		0			0
$328$	−0.792246	+	2.95670i	−0.0437445	+	0.163257i
$329$	3.55726	+	6.16136i	0.196118	+	0.339687i
$330$		0			0
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	−0.119604	−	0.992822i	$-0.538162\pi$
$331$	14.5549	−	25.2097i	0.800007	−	1.38565i	0.919611	−	0.392831i	$-0.128504\pi$
$332$	−0.313757	−	0.313757i	−0.0172197	−	0.0172197i
$333$		0			0
$334$			16.1663i			0.884582i
$335$		0			0
$336$		0			0
$337$	24.1823	+	6.47963i	1.31729	+	0.352968i	0.847963	−	0.530055i	$-0.177829\pi$
$337$	24.1823	+	6.47963i	1.31729	+	0.352968i	0.469330	+	0.883023i	$0.344495\pi$
$338$	−18.0643	−	4.84031i	−0.982568	−	0.263278i
$339$		0			0
$340$		0			0
$341$			17.5162i			0.948554i
$342$		0			0
$343$	−13.6916	−	13.6916i	−0.739274	−	0.739274i
$344$	−4.37045	+	7.56984i	−0.235639	+	0.408138i
$345$		0			0
$346$	12.4733	+	21.6043i	0.670566	+	1.16145i
$347$	−9.05260	+	33.7848i	−0.485969	+	1.81366i	0.0896885	+	0.995970i	$0.471413\pi$
$347$	−9.05260	+	33.7848i	−0.485969	+	1.81366i	−0.575657	+	0.817691i	$0.695254\pi$
$348$		0			0
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.882029	−	0.471194i	$-0.156177\pi$
$349$	17.0932	+	9.86876i	0.914978	+	0.528263i	0.0329483	+	0.999457i	$0.489510\pi$
$350$		0			0
$351$		0			0
$352$	−10.4969	+	10.4969i	−0.559487	+	0.559487i
$353$	−1.95875	−	7.31017i	−0.104254	−	0.389081i	0.894006	−	0.448056i	$-0.147883\pi$
$353$	−1.95875	−	7.31017i	−0.104254	−	0.389081i	−0.998259	+	0.0589749i	$0.981217\pi$
$354$		0			0
$355$		0			0
$356$	−10.8791	+	6.28105i	−0.576591	+	0.332895i
$357$		0			0
$358$	−6.77720	+	1.81594i	−0.358186	+	0.0959756i
$359$	−8.47760			−0.447430			−0.223715	−	0.974655i	$-0.571819\pi$
$359$	−8.47760			−0.447430			−0.223715	+	0.974655i	$0.571819\pi$
$360$		0			0
$361$	−20.0966			−1.05772
$362$	−38.2114	+	10.2387i	−2.00835	+	0.538135i
$363$		0			0
$364$	1.57608	−	0.909949i	0.0826089	−	0.0476943i
$365$		0			0
$366$		0			0
$367$	2.12506	+	7.93083i	0.110927	+	0.413986i	0.998950	−	0.0458135i	$-0.0145880\pi$
$367$	2.12506	+	7.93083i	0.110927	+	0.413986i	−0.888023	+	0.459799i	$0.847921\pi$
$368$	−7.83091	+	7.83091i	−0.408215	+	0.408215i
$369$		0			0
$370$		0			0
$371$	16.4837	+	9.51686i	0.855791	+	0.494091i
$372$		0			0
$373$	5.56939	−	20.7853i	0.288372	−	1.07622i	−0.657967	−	0.753046i	$-0.728584\pi$
$373$	5.56939	−	20.7853i	0.288372	−	1.07622i	0.946340	−	0.323174i	$-0.104750\pi$
$374$	−1.17567	−	2.03631i	−0.0607923	−	0.105295i
$375$		0			0
$376$	−4.06275	+	7.03689i	−0.209520	+	0.362900i
$377$	−2.93568	−	2.93568i	−0.151195	−	0.151195i
$378$		0			0
$379$		−	11.1614i		−	0.573325i	−0.958032	−	0.286663i	$-0.907454\pi$
$379$		−	11.1614i		−	0.573325i	0.958032	−	0.286663i	$-0.0925458\pi$
$380$		0			0
$381$		0			0
$382$	−37.3752	−	10.0147i	−1.91228	−	0.512394i
$383$	14.6977	+	3.93824i	0.751018	+	0.201235i	0.613970	−	0.789330i	$-0.289572\pi$
$383$	14.6977	+	3.93824i	0.751018	+	0.201235i	0.137049	+	0.990564i	$0.456238\pi$
$384$		0			0
$385$		0			0
$386$		−	34.4750i		−	1.75473i
$387$		0			0
$388$	2.87743	+	2.87743i	0.146079	+	0.146079i
$389$	−12.7395	+	22.0655i	−0.645920	+	1.11877i	0.338168	+	0.941086i	$0.390193\pi$
$389$	−12.7395	+	22.0655i	−0.645920	+	1.11877i	−0.984088	+	0.177681i	$0.943140\pi$
$390$		0			0
$391$	−0.438715	−	0.759876i	−0.0221868	−	0.0384286i
$392$	2.00158	−	7.47000i	0.101095	−	0.377292i
$393$		0			0
$394$	13.2893	+	7.67255i	0.669503	+	0.386538i
$395$		0			0
$396$		0			0
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	−0.541309	−	0.840824i	$-0.682071\pi$
$397$	5.96779	−	5.96779i	0.299515	−	0.299515i	0.840824	+	0.541309i	$0.182071\pi$
$398$	1.73755	+	6.48464i	0.0870957	+	0.325046i
$399$		0			0
$400$		0			0
$401$	−23.6805	+	13.6719i	−1.18255	+	0.682744i	−0.956602	−	0.291396i	$-0.905880\pi$
$401$	−23.6805	+	13.6719i	−1.18255	+	0.682744i	−0.225945	+	0.974140i	$0.572547\pi$
$402$		0			0
$403$	6.20343	−	1.66220i	0.309015	−	0.0828003i
$404$	4.17493			0.207711
$405$		0			0
$406$	−9.38087			−0.465565
$407$	27.3810	−	7.33673i	1.35723	−	0.363668i
$408$		0			0
$409$	23.5441	−	13.5932i	1.16418	−	0.672140i	0.211878	−	0.977296i	$-0.432042\pi$
$409$	23.5441	−	13.5932i	1.16418	−	0.672140i	0.952302	+	0.305157i	$0.0987088\pi$
$410$		0			0
$411$		0			0
$412$	−1.03106	−	3.84798i	−0.0507968	−	0.189576i
$413$	0.710697	−	0.710697i	0.0349711	−	0.0349711i
$414$		0			0
$415$		0			0
$416$	4.71363	+	2.72142i	0.231105	+	0.133428i
$417$		0			0
$418$	−9.71346	+	36.2511i	−0.475101	+	1.77310i
$419$	−15.7018	−	27.1964i	−0.767084	−	1.32863i	−0.939138	−	0.343541i	$-0.888373\pi$
$419$	−15.7018	−	27.1964i	−0.767084	−	1.32863i	0.172053	−	0.985088i	$-0.444960\pi$
$420$		0			0
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	0.194629	+	0.980877i	$0.437650\pi$
$421$	−15.4328	+	26.7304i	−0.752150	+	1.30276i	−0.946779	+	0.321885i	$0.895683\pi$
$422$	−1.53569	−	1.53569i	−0.0747562	−	0.0747562i
$423$		0			0
$424$			21.7384i			1.05571i
$425$		0			0
$426$		0			0
$427$	10.2942	+	2.75831i	0.498170	+	0.133484i
$428$	−4.25496	−	1.14011i	−0.205671	−	0.0551095i
$429$		0			0
$430$		0			0
$431$		−	32.6869i		−	1.57447i	−0.616652	−	0.787236i	$-0.711511\pi$
$431$		−	32.6869i		−	1.57447i	0.616652	−	0.787236i	$-0.288489\pi$
$432$		0			0
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	0.859684	−	0.510826i	$-0.170660\pi$
$433$	7.25927	+	7.25927i	0.348858	+	0.348858i	−0.510826	+	0.859684i	$0.670660\pi$
$434$	7.25568	−	12.5672i	0.348284	−	0.603245i
$435$		0			0
$436$	0.423267	+	0.733120i	0.0202708	+	0.0351101i
$437$	−3.62470	+	13.5276i	−0.173393	+	0.647111i
$438$		0			0
$439$	−19.4684	−	11.2401i	−0.929175	−	0.536459i	−0.0426241	−	0.999091i	$-0.513572\pi$
$439$	−19.4684	−	11.2401i	−0.929175	−	0.536459i	−0.886550	+	0.462632i	$0.846905\pi$
$440$		0			0
$441$		0			0
$442$	−0.609604	+	0.609604i	−0.0289959	+	0.0289959i
$443$	−2.00030	−	7.46524i	−0.0950373	−	0.354684i	0.901988	−	0.431762i	$-0.142108\pi$
$443$	−2.00030	−	7.46524i	−0.0950373	−	0.354684i	−0.997025	+	0.0770774i	$0.975441\pi$
$444$		0			0
$445$		0			0
$446$	11.9425	−	6.89501i	0.565494	−	0.326488i
$447$		0			0
$448$	−5.30275	+	1.42087i	−0.250531	+	0.0671297i
$449$	38.1502			1.80042			0.900209	−	0.435458i	$-0.143414\pi$
$449$	38.1502			1.80042			0.900209	+	0.435458i	$0.143414\pi$
$450$		0			0
$451$	5.37886			0.253280
$452$	6.16144	−	1.65095i	0.289810	−	0.0776543i
$453$		0			0
$454$	−13.2781	+	7.66612i	−0.623173	+	0.359789i
$455$		0			0
$456$		0			0
$457$	−7.20855	−	26.9027i	−0.337202	−	1.25845i	−0.901463	−	0.432857i	$-0.857505\pi$
$457$	−7.20855	−	26.9027i	−0.337202	−	1.25845i	0.564261	−	0.825596i	$-0.309161\pi$
$458$	23.3541	−	23.3541i	1.09127	−	1.09127i
$459$		0			0
$460$		0			0
$461$	21.2301	+	12.2572i	0.988784	+	0.570874i	0.904910	−	0.425602i	$-0.139938\pi$
$461$	21.2301	+	12.2572i	0.988784	+	0.570874i	0.0838731	+	0.996476i	$0.473271\pi$
$462$		0			0
$463$	4.62735	−	17.2695i	0.215051	−	0.802582i	−0.771097	−	0.636717i	$-0.780292\pi$
$463$	4.62735	−	17.2695i	0.215051	−	0.802582i	0.986149	−	0.165865i	$-0.0530415\pi$
$464$	−7.75455	−	13.4313i	−0.359996	−	0.623531i
$465$		0			0
$466$	6.41096	−	11.1041i	0.296982	−	0.514388i
$467$	−22.2894	−	22.2894i	−1.03143	−	1.03143i	−0.999490	−	0.0319412i	$-0.989831\pi$
$467$	−22.2894	−	22.2894i	−1.03143	−	1.03143i	−0.0319412	−	0.999490i	$-0.510169\pi$
$468$		0			0
$469$			20.1775i			0.931709i
$470$		0			0
$471$		0			0
$472$	1.10879	+	0.297098i	0.0510360	+	0.0136751i
$473$	14.8363	+	3.97538i	0.682174	+	0.182788i
$474$		0			0
$475$		0			0
$476$			0.538636i			0.0246883i
$477$		0			0
$478$	8.18699	+	8.18699i	0.374464	+	0.374464i
$479$	−6.76273	+	11.7134i	−0.308997	+	0.535199i	−0.978143	−	0.207932i	$-0.933327\pi$
$479$	−6.76273	+	11.7134i	−0.308997	+	0.535199i	0.669146	+	0.743131i	$0.266660\pi$
$480$		0			0
$481$	−5.19667	−	9.00089i	−0.236948	−	0.410405i
$482$	10.1264	−	37.7923i	0.461246	−	1.72139i
$483$		0			0
$484$	1.34527	+	0.776693i	0.0611487	+	0.0353042i
$485$		0			0
$486$		0			0
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	−0.984040	−	0.177946i	$-0.943055\pi$
$487$	−17.7890	+	17.7890i	−0.806094	+	0.806094i	0.177946	+	0.984040i	$0.443055\pi$
$488$	3.15027	+	11.7570i	0.142606	+	0.532213i
$489$		0			0
$490$		0			0
$491$	17.9785	−	10.3799i	0.811359	−	0.468438i	−0.0360688	−	0.999349i	$-0.511484\pi$
$491$	17.9785	−	10.3799i	0.811359	−	0.468438i	0.847427	+	0.530911i	$0.178150\pi$
$492$		0			0
$493$	1.18690	−	0.318030i	0.0534554	−	0.0143233i
$494$	13.7603			0.619103
$495$		0			0
$496$	23.9912			1.07724
$497$	13.9279	−	3.73197i	0.624752	−	0.167402i
$498$		0			0
$499$	−8.56156	+	4.94302i	−0.383268	+	0.221280i	−0.679239	−	0.733917i	$-0.737690\pi$
$499$	−8.56156	+	4.94302i	−0.383268	+	0.221280i	0.295971	+	0.955197i	$0.404357\pi$
$500$		0			0
$501$		0			0
$502$	8.94821	+	33.3952i	0.399378	+	1.49050i
$503$	16.8084	−	16.8084i	0.749450	−	0.749450i	−0.224926	−	0.974376i	$-0.572214\pi$
$503$	16.8084	−	16.8084i	0.749450	−	0.749450i	0.974376	+	0.224926i	$0.0722140\pi$
$504$		0			0
$505$		0			0
$506$	11.6425	+	6.72178i	0.517571	+	0.298820i
$507$		0			0
$508$	3.24234	−	12.1006i	0.143855	−	0.536876i
$509$	20.1795	+	34.9520i	0.894442	+	1.54922i	0.834494	+	0.551017i	$0.185760\pi$
$509$	20.1795	+	34.9520i	0.894442	+	1.54922i	0.0599475	+	0.998202i	$0.480907\pi$
$510$		0			0
$511$	1.64480	−	2.84887i	0.0727615	−	0.126027i
$512$	0.0117190	+	0.0117190i	0.000517913	+	0.000517913i
$513$		0			0
$514$			17.4733i			0.770712i
$515$		0			0
$516$		0			0
$517$	13.7918	+	3.69550i	0.606562	+	0.162528i
$518$	−22.6839	−	6.07815i	−0.996675	−	0.267058i
$519$		0			0
$520$		0			0
$521$			11.5144i			0.504456i	0.967668	+	0.252228i	$0.0811633\pi$
$521$			11.5144i			0.504456i	−0.967668	+	0.252228i	$0.918837\pi$
$522$		0			0
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.933584	+	0.358358i	$0.116663\pi$
$523$	29.5457	+	29.5457i	1.29194	+	1.29194i	0.358358	+	0.933584i	$0.383337\pi$
$524$	−1.91708	+	3.32049i	−0.0837482	+	0.145056i
$525$		0			0
$526$	−12.4195	−	21.5112i	−0.541517	−	0.937934i
$527$	−0.491963	+	1.83603i	−0.0214303	+	0.0799788i
$528$		0			0
$529$	−15.5740	−	8.99168i	−0.677133	−	0.390943i
$530$		0			0
$531$		0			0
$532$	6.07917	−	6.07917i	0.263565	−	0.263565i
$533$	−0.510428	−	1.90494i	−0.0221091	−	0.0825123i
$534$		0			0
$535$		0			0
$536$	−19.9573	+	11.5223i	−0.862024	+	0.497690i
$537$		0			0
$538$	1.25587	−	0.336511i	0.0541446	−	0.0145080i
$539$	−13.5895			−0.585340
$540$		0			0
$541$	6.30670			0.271146			0.135573	−	0.990767i	$-0.456712\pi$
$541$	6.30670			0.271146			0.135573	+	0.990767i	$0.456712\pi$
$542$	20.0230	−	5.36514i	0.860060	−	0.230452i
$543$		0			0
$544$	−1.39509	+	0.805458i	−0.0598142	+	0.0345337i
$545$		0			0
$546$		0			0
$547$	−7.99863	−	29.8513i	−0.341997	−	1.27635i	−0.896082	−	0.443889i	$-0.853599\pi$
$547$	−7.99863	−	29.8513i	−0.341997	−	1.27635i	0.554085	−	0.832460i	$-0.313068\pi$
$548$	−0.246678	+	0.246678i	−0.0105375	+	0.0105375i
$549$		0			0
$550$		0			0
$551$	−16.9850	−	9.80630i	−0.723586	−	0.417762i
$552$		0			0
$553$	−3.74650	+	13.9821i	−0.159317	+	0.594580i
$554$	−7.80896	−	13.5255i	−0.331771	−	0.574644i
$555$		0			0
$556$	−6.12814	+	10.6143i	−0.259891	+	0.450145i
$557$	6.63181	+	6.63181i	0.280999	+	0.280999i	0.833507	−	0.552509i	$-0.186329\pi$
$557$	6.63181	+	6.63181i	0.280999	+	0.280999i	−0.552509	+	0.833507i	$0.686329\pi$
$558$		0			0
$559$		−	5.63159i		−	0.238191i
$560$		0			0
$561$		0			0
$562$	49.3326	+	13.2186i	2.08097	+	0.557594i
$563$	−18.2031	−	4.87751i	−0.767170	−	0.205563i	−0.146049	−	0.989277i	$-0.546656\pi$
$563$	−18.2031	−	4.87751i	−0.767170	−	0.205563i	−0.621121	+	0.783715i	$0.713322\pi$
$564$		0			0
$565$		0			0
$566$			31.2741i			1.31455i
$567$		0			0
$568$	11.6448	+	11.6448i	0.488605	+	0.488605i
$569$	10.4878	−	18.1654i	0.439670	−	0.761531i	−0.557994	−	0.829845i	$-0.688429\pi$
$569$	10.4878	−	18.1654i	0.439670	−	0.761531i	0.997664	+	0.0683141i	$0.0217620\pi$
$570$		0			0
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	−0.999899	−	0.0142078i	$-0.995477\pi$
$571$	−12.2406	−	21.2014i	−0.512254	−	0.887250i	0.487645	−	0.873042i	$-0.337856\pi$
$572$	0.945309	−	3.52794i	0.0395254	−	0.147511i
$573$		0			0
$574$	−3.85913	−	2.22807i	−0.161077	−	0.0929978i
$575$		0			0
$576$		0			0
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	−0.399634	−	0.916675i	$-0.630863\pi$
$577$	12.4198	−	12.4198i	0.517041	−	0.517041i	0.916675	+	0.399634i	$0.130863\pi$
$578$	7.24946	+	27.0554i	0.301538	+	1.12535i
$579$		0			0
$580$		0			0
$581$	−0.904288	+	0.522091i	−0.0375162	+	0.0216600i
$582$		0			0
$583$	36.8976	−	9.88668i	1.52814	−	0.409465i
$584$	3.75705			0.155468
$585$		0			0
$586$	56.1979			2.32151
$587$	14.6173	−	3.91669i	0.603320	−	0.161659i	0.0557861	−	0.998443i	$-0.482234\pi$
$587$	14.6173	−	3.91669i	0.603320	−	0.161659i	0.547534	+	0.836784i	$0.315567\pi$
$588$		0			0
$589$	26.2743	−	15.1695i	1.08261	−	0.625047i
$590$		0			0
$591$		0			0
$592$	−10.0488	−	37.5027i	−0.413003	−	1.54135i
$593$	−12.8270	+	12.8270i	−0.526744	+	0.526744i	−0.919600	−	0.392856i	$-0.871487\pi$
$593$	−12.8270	+	12.8270i	−0.526744	+	0.526744i	0.392856	+	0.919600i	$0.371487\pi$
$594$		0			0
$595$		0			0
$596$	4.55641	+	2.63064i	0.186638	+	0.107755i
$597$		0			0
$598$	1.27573	−	4.76109i	0.0521685	−	0.194696i
$599$	3.45057	+	5.97656i	0.140987	+	0.244196i	0.927868	−	0.372908i	$-0.121639\pi$
$599$	3.45057	+	5.97656i	0.140987	+	0.244196i	−0.786882	+	0.617104i	$0.788306\pi$
$600$		0			0
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	−0.708459	−	0.705752i	$-0.750609\pi$
$601$	6.29969	−	10.9114i	0.256970	−	0.445085i	0.965429	+	0.260667i	$0.0839426\pi$
$602$	−8.99779	−	8.99779i	−0.366722	−	0.366722i
$603$		0			0
$604$		−	6.58358i		−	0.267882i
$605$		0			0
$606$		0			0
$607$	−35.9453	−	9.63152i	−1.45898	−	0.390931i	−0.559839	−	0.828601i	$-0.689137\pi$
$607$	−35.9453	−	9.63152i	−1.45898	−	0.390931i	−0.899136	+	0.437670i	$0.855804\pi$
$608$	24.8359	+	6.65477i	1.00723	+	0.269887i
$609$		0			0
$610$		0			0
$611$		−	5.23510i		−	0.211789i
$612$		0			0
$613$	−12.4072	−	12.4072i	−0.501121	−	0.501121i	0.410665	−	0.911786i	$-0.365296\pi$
$613$	−12.4072	−	12.4072i	−0.501121	−	0.501121i	−0.911786	+	0.410665i	$0.865296\pi$
$614$	−2.66556	+	4.61689i	−0.107573	+	0.186322i
$615$		0			0
$616$	6.67023	+	11.5532i	0.268751	+	0.465491i
$617$	−2.65843	+	9.92141i	−0.107025	+	0.399421i	−0.998567	−	0.0535162i	$-0.982957\pi$
$617$	−2.65843	+	9.92141i	−0.107025	+	0.399421i	0.891542	+	0.452937i	$0.149624\pi$
$618$		0			0
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	0.0627048	−	0.998032i	$-0.480027\pi$
$619$	−19.1639	−	11.0643i	−0.770264	−	0.444712i	−0.832969	+	0.553320i	$0.813361\pi$
$620$		0			0
$621$		0			0
$622$	−2.53439	+	2.53439i	−0.101620	+	0.101620i
$623$	7.65114	+	28.5544i	0.306536	+	1.14401i
$624$		0			0
$625$		0			0
$626$	31.2902	−	18.0654i	1.25061	−	0.722040i
$627$		0			0
$628$	1.23012	−	0.329609i	0.0490870	−	0.0131528i
$629$	3.07612			0.122653
$630$		0			0
$631$	8.15013			0.324451			0.162226	−	0.986754i	$-0.448133\pi$
$631$	8.15013			0.324451			0.162226	+	0.986754i	$0.448133\pi$
$632$	−15.9690	+	4.27888i	−0.635212	+	0.170205i
$633$		0			0
$634$	−6.67608	+	3.85443i	−0.265141	+	0.153079i
$635$		0			0
$636$		0			0
$637$	1.28958	+	4.81277i	0.0510949	+	0.190689i
$638$	−13.3125	+	13.3125i	−0.527046	+	0.527046i
$639$		0			0
$640$		0			0
$641$	2.49058	+	1.43794i	0.0983722	+	0.0567952i	0.548379	−	0.836230i	$-0.315245\pi$
$641$	2.49058	+	1.43794i	0.0983722	+	0.0567952i	−0.450007	+	0.893025i	$0.648578\pi$
$642$		0			0
$643$	−2.54626	+	9.50279i	−0.100415	+	0.374753i	−0.997785	−	0.0665259i	$-0.978809\pi$
$643$	−2.54626	+	9.50279i	−0.100415	+	0.374753i	0.897370	+	0.441279i	$0.145475\pi$
$644$	−1.53981	−	2.66702i	−0.0606768	−	0.105095i
$645$		0			0
$646$	−2.03631	+	3.52700i	−0.0801177	+	0.138768i
$647$	14.2662	+	14.2662i	0.560862	+	0.560862i	0.929552	−	0.368691i	$-0.120194\pi$
$647$	14.2662	+	14.2662i	0.560862	+	0.560862i	−0.368691	+	0.929552i	$0.620194\pi$
$648$		0			0
$649$		−	2.01711i		−	0.0791786i
$650$		0			0
$651$		0			0
$652$	10.9763	+	2.94108i	0.429864	+	0.115182i
$653$	38.3580	+	10.2780i	1.50106	+	0.402209i	0.913456	−	0.406937i	$-0.133403\pi$
$653$	38.3580	+	10.2780i	1.50106	+	0.402209i	0.587607	+	0.809146i	$0.300070\pi$
$654$		0			0
$655$		0			0
$656$		−	7.36719i		−	0.287641i
$657$		0			0
$658$	−8.36431	−	8.36431i	−0.326075	−	0.326075i
$659$	23.3689	−	40.4762i	0.910324	−	1.57673i	0.0967171	−	0.995312i	$-0.469166\pi$
$659$	23.3689	−	40.4762i	0.910324	−	1.57673i	0.813607	−	0.581415i	$-0.197501\pi$
$660$		0			0
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	0.806089	−	0.591794i	$-0.201580\pi$
$661$	−2.81433	−	4.87455i	−0.109465	−	0.189598i	−0.915553	+	0.402196i	$0.868247\pi$
$662$	−12.5266	+	46.7499i	−0.486860	+	1.81699i
$663$		0			0
$664$	−1.03279	−	0.596280i	−0.0400799	−	0.0231402i
$665$		0			0
$666$		0			0
$667$	−4.96772	+	4.96772i	−0.192351	+	0.192351i
$668$	−1.92362	−	7.17905i	−0.0744271	−	0.277766i
$669$		0			0
$670$		0			0
$671$	18.5229	−	10.6942i	0.715068	−	0.412845i
$672$		0			0
$673$	−28.7938	+	7.71528i	−1.10992	+	0.297402i	−0.766798	−	0.641888i	$-0.778151\pi$
$673$	−28.7938	+	7.71528i	−1.10992	+	0.297402i	−0.343122	+	0.939291i	$0.611485\pi$
$674$	−41.6249			−1.60333
$675$		0			0
$676$	8.59784			0.330686
$677$	−48.2839	+	12.9376i	−1.85570	+	0.497234i	−0.999802	−	0.0199076i	$-0.993663\pi$
$677$	−48.2839	+	12.9376i	−1.85570	+	0.497234i	−0.855900	+	0.517141i	$0.826996\pi$
$678$		0			0
$679$	8.29312	−	4.78804i	0.318261	−	0.183748i
$680$		0			0
$681$		0			0
$682$	−7.53763	−	28.1308i	−0.288631	−	1.07718i
$683$	4.38271	−	4.38271i	0.167700	−	0.167700i	−0.618268	−	0.785968i	$-0.712165\pi$
$683$	4.38271	−	4.38271i	0.167700	−	0.167700i	0.785968	+	0.618268i	$0.212165\pi$
$684$		0			0
$685$		0			0
$686$	27.8803	+	16.0967i	1.06447	+	0.614575i
$687$		0			0
$688$	5.44491	−	20.3207i	0.207585	−	0.774718i
$689$	−7.00282	−	12.1292i	−0.266786	−	0.462087i
$690$		0			0
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	−0.872544	−	0.488536i	$-0.837531\pi$
$691$	−0.346648	+	0.600412i	−0.0131871	+	0.0228407i	0.859357	+	0.511377i	$0.170864\pi$
$692$	−8.10973	−	8.10973i	−0.308286	−	0.308286i
$693$		0			0
$694$		−	58.1535i		−	2.20748i
$695$		0			0
$696$		0			0
$697$	0.563807	+	0.151072i	0.0213557	+	0.00572225i
$698$	−31.6983	−	8.49352i	−1.19980	−	0.321485i
$699$		0			0
$700$		0			0
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$		0			0
$703$	−34.7178	−	34.7178i	−1.30941	−	1.30941i
$704$	−5.50881	+	9.54154i	−0.207621	+	0.359610i
$705$		0			0
$706$	6.29148	+	10.8972i	0.236783	+	0.410120i
$707$	2.54281	−	9.48988i	0.0956320	−	0.356904i
$708$		0			0
$709$	4.59399	+	2.65234i	0.172531	+	0.0996109i	0.583779	−	0.811913i	$-0.301574\pi$
$709$	4.59399	+	2.65234i	0.172531	+	0.0996109i	−0.411248	+	0.911524i	$0.634907\pi$
$710$		0			0
$711$		0			0
$712$	−23.8737	+	23.8737i	−0.894704	+	0.894704i
$713$	−2.81276	−	10.4974i	−0.105339	−	0.393130i
$714$		0			0
$715$		0			0
$716$	2.79350	−	1.61283i	0.104398	−	0.0602742i
$717$		0			0
$718$	13.6149	−	3.64811i	0.508105	−	0.136146i
$719$	28.3121			1.05586			0.527932	−	0.849286i	$-0.322967\pi$
$719$	28.3121			1.05586			0.527932	+	0.849286i	$0.322967\pi$
$720$		0			0
$721$	−9.37468			−0.349131
$722$	32.2750	−	8.64806i	1.20115	−	0.321847i
$723$		0			0
$724$	15.7504	−	9.09349i	0.585359	−	0.337957i
$725$		0			0
$726$		0			0
$727$	11.6483	+	43.4720i	0.432011	+	1.61229i	0.748119	+	0.663565i	$0.230957\pi$
$727$	11.6483	+	43.4720i	0.432011	+	1.61229i	−0.316108	+	0.948723i	$0.602376\pi$
$728$	3.45863	−	3.45863i	0.128185	−	0.128185i
$729$		0			0
$730$		0			0
$731$	1.44348	+	0.833392i	0.0533889	+	0.0308241i
$732$		0			0
$733$	−6.25836	+	23.3565i	−0.231158	+	0.862693i	0.748685	+	0.662926i	$0.230685\pi$
$733$	−6.25836	+	23.3565i	−0.231158	+	0.862693i	−0.979843	+	0.199768i	$0.935981\pi$
$734$	−6.82565	−	11.8224i	−0.251939	−	0.436372i
$735$		0			0
$736$	4.60515	−	7.97635i	0.169748	−	0.294012i
$737$	28.6340	+	28.6340i	1.05475	+	1.05475i
$738$		0			0
$739$		−	5.60736i		−	0.206270i	−0.994667	−	0.103135i	$-0.967113\pi$
$739$		−	5.60736i		−	0.206270i	0.994667	−	0.103135i	$-0.0328874\pi$
$740$		0			0
$741$		0			0
$742$	−30.5680	−	8.19067i	−1.12219	−	0.300689i
$743$	−8.24852	−	2.21018i	−0.302609	−	0.0810838i	0.104320	−	0.994544i	$-0.466733\pi$
$743$	−8.24852	−	2.21018i	−0.302609	−	0.0810838i	−0.406928	+	0.913460i	$0.633400\pi$
$744$		0			0
$745$		0			0
$746$			35.7776i			1.30991i
$747$		0			0
$748$	0.764383	+	0.764383i	0.0279486	+	0.0279486i
$749$	−5.18310	+	8.97739i	−0.189386	+	0.328027i
$750$		0			0
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	0.905287	−	0.424800i	$-0.139656\pi$
$751$	2.32268	+	4.02301i	0.0847560	+	0.146802i	−0.820531	+	0.571602i	$0.806322\pi$
$752$	5.06156	−	18.8900i	0.184576	−	0.688848i
$753$		0			0
$754$	5.97796	+	3.45138i	0.217704	+	0.125692i
$755$		0			0
$756$		0			0
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	−0.648557	−	0.761166i	$-0.724627\pi$
$757$	3.09830	−	3.09830i	0.112609	−	0.112609i	0.761166	+	0.648557i	$0.224627\pi$
$758$	4.80304	+	17.9252i	0.174454	+	0.651072i
$759$		0			0
$760$		0			0
$761$	−38.9876	+	22.5095i	−1.41330	+	0.815968i	−0.995698	−	0.0926625i	$-0.970462\pi$
$761$	−38.9876	+	22.5095i	−1.41330	+	0.815968i	−0.417601	+	0.908631i	$0.637129\pi$
$762$		0			0
$763$	1.92422	−	0.515595i	0.0696616	−	0.0186658i
$764$	17.7890			0.643584
$765$		0			0
$766$	−25.2991			−0.914094
$767$	−0.714369	+	0.191415i	−0.0257944	+	0.00691158i
$768$		0			0
$769$	−5.40503	+	3.12060i	−0.194910	+	0.112532i	−0.594279	−	0.804259i	$-0.702563\pi$
$769$	−5.40503	+	3.12060i	−0.194910	+	0.112532i	0.399369	+	0.916790i	$0.369229\pi$
$770$		0			0
$771$		0			0
$772$	4.10216	+	15.3095i	0.147640	+	0.551000i
$773$	−19.5366	+	19.5366i	−0.702681	+	0.702681i	−0.964985	−	0.262304i	$-0.915518\pi$
$773$	−19.5366	+	19.5366i	−0.702681	+	0.702681i	0.262304	+	0.964985i	$0.415518\pi$
$774$		0			0
$775$		0			0
$776$	9.47158	+	5.46842i	0.340010	+	0.196305i
$777$		0			0
$778$	10.9643	−	40.9192i	0.393088	−	1.46702i
$779$	−4.65823	−	8.06829i	−0.166898	−	0.289076i
$780$		0			0
$781$	14.4691	−	25.0613i	0.517747	−	0.896764i
$782$	1.03156	+	1.03156i	0.0368887	+	0.0368887i
$783$		0			0
$784$			18.6129i			0.664748i
$785$		0			0
$786$		0			0
$787$	28.3409	+	7.59393i	1.01024	+	0.270694i	0.725732	−	0.687978i	$-0.241501\pi$
$787$	28.3409	+	7.59393i	1.01024	+	0.270694i	0.284513	+	0.958672i	$0.408168\pi$
$788$	−6.81437	−	1.82590i	−0.242752	−	0.0650451i
$789$		0			0
$790$		0			0
$791$		−	15.0109i		−	0.533725i
$792$		0			0
$793$	−5.54513	−	5.54513i	−0.196913	−	0.196913i
$794$	−7.01613	+	12.1523i	−0.248993	+	0.431269i
$795$		0			0
$796$	−1.54321	−	2.67291i	−0.0546975	−	0.0947388i
$797$	0.454070	−	1.69461i	0.0160840	−	0.0600263i	−0.957417	−	0.288707i	$-0.906775\pi$
$797$	0.454070	−	1.69461i	0.0160840	−	0.0600263i	0.973501	+	0.228681i	$0.0734413\pi$
$798$		0			0
$799$	1.34185	+	0.774718i	0.0474712	+	0.0274075i
$800$		0			0
$801$		0			0
$802$	32.1473	−	32.1473i	1.13516	−	1.13516i
$803$	−1.70871	−	6.37700i	−0.0602991	−	0.225039i
$804$		0			0
$805$		0			0
$806$	−9.24736	+	5.33897i	−0.325724	+	0.188057i
$807$		0			0
$808$	10.8384	−	2.90414i	0.381294	−	0.102167i
$809$	−27.5870			−0.969908			−0.484954	−	0.874540i	$-0.661164\pi$
$809$	−27.5870			−0.969908			−0.484954	+	0.874540i	$0.661164\pi$
$810$		0			0
$811$	−44.5699			−1.56506			−0.782530	−	0.622613i	$-0.786071\pi$
$811$	−44.5699			−1.56506			−0.782530	+	0.622613i	$0.786071\pi$
$812$	4.16580	−	1.11622i	0.146191	−	0.0391718i
$813$		0			0
$814$	−40.8165	+	23.5654i	−1.43062	+	0.825968i
$815$		0			0
$816$		0			0
$817$	−6.88556	−	25.6972i	−0.240895	−	0.899033i
$818$	−31.9621	+	31.9621i	−1.11753	+	1.11753i
$819$		0			0
$820$		0			0
$821$	−38.4678	−	22.2094i	−1.34254	−	0.775114i	−0.355357	−	0.934731i	$-0.615641\pi$
$821$	−38.4678	−	22.2094i	−1.34254	−	0.775114i	−0.987179	+	0.159617i	$0.948974\pi$
$822$		0			0
$823$	−8.19082	+	30.5686i	−0.285514	+	1.06555i	0.662949	+	0.748665i	$0.269305\pi$
$823$	−8.19082	+	30.5686i	−0.285514	+	1.06555i	−0.948463	+	0.316888i	$0.897362\pi$
$824$	−5.35341	−	9.27239i	−0.186495	−	0.323019i
$825$		0			0
$826$	−0.835543	+	1.44720i	−0.0290723	+	0.0503546i
$827$	−2.06846	−	2.06846i	−0.0719275	−	0.0719275i	0.670228	−	0.742155i	$-0.266196\pi$
$827$	−2.06846	−	2.06846i	−0.0719275	−	0.0719275i	−0.742155	+	0.670228i	$0.766196\pi$
$828$		0			0
$829$			12.9618i			0.450182i	0.974338	+	0.225091i	$0.0722680\pi$
$829$			12.9618i			0.450182i	−0.974338	+	0.225091i	$0.927732\pi$
$830$		0			0
$831$		0			0
$832$	3.90193	+	1.04552i	0.135275	+	0.0362469i
$833$	−1.42444	−	0.381677i	−0.0493539	−	0.0132243i
$834$		0			0
$835$		0			0
$836$		−	17.2540i		−	0.596742i
$837$		0			0
$838$	36.9202	+	36.9202i	1.27539	+	1.27539i
$839$	−9.19525	+	15.9266i	−0.317455	+	0.549849i	−0.979956	−	0.199212i	$-0.936162\pi$
$839$	−9.19525	+	15.9266i	−0.317455	+	0.549849i	0.662501	+	0.749061i	$0.269495\pi$
$840$		0			0
$841$	9.58072	+	16.5943i	0.330370	+	0.572217i
$842$	13.2822	−	49.5699i	0.457736	−	1.70829i
$843$		0			0
$844$	0.864691	+	0.499230i	0.0297639	+	0.0171842i
$845$		0			0
$846$		0			0
$847$	2.58483	−	2.58483i	0.0888158	−	0.0888158i
$848$	−13.5414	−	50.5371i	−0.465013	−	1.73545i
$849$		0			0
$850$		0			0
$851$	−15.2312	+	8.79374i	−0.522119	+	0.301445i
$852$		0			0
$853$	13.3437	−	3.57544i	0.456880	−	0.122421i	−0.0230366	−	0.999735i	$-0.507333\pi$
$853$	13.3437	−	3.57544i	0.456880	−	0.122421i	0.479917	+	0.877314i	$0.340667\pi$
$854$	−17.7193			−0.606342
$855$		0			0
$856$	−11.8392			−0.404657
$857$	5.89302	−	1.57903i	0.201302	−	0.0539387i	−0.156759	−	0.987637i	$-0.550105\pi$
$857$	5.89302	−	1.57903i	0.201302	−	0.0539387i	0.358061	+	0.933698i	$0.383438\pi$
$858$		0			0
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	−0.749558	−	0.661939i	$-0.769734\pi$
$859$	−16.1515	+	9.32505i	−0.551081	+	0.318166i	0.198477	+	0.980106i	$0.436400\pi$
$860$		0			0
$861$		0			0
$862$	14.0659	+	52.4948i	0.479088	+	1.78798i
$863$	9.43441	−	9.43441i	0.321151	−	0.321151i	−0.528058	−	0.849209i	$-0.677079\pi$
$863$	9.43441	−	9.43441i	0.321151	−	0.321151i	0.849209	+	0.528058i	$0.177079\pi$
$864$		0			0
$865$		0			0
$866$	−14.7822	−	8.53448i	−0.502318	−	0.290013i
$867$		0			0
$868$	−1.72670	+	6.44412i	−0.0586079	+	0.218728i
$869$	14.5254	+	25.1588i	0.492742	+	0.853454i
$870$		0			0
$871$	7.42362	−	12.8581i	0.251540	−	0.435680i
$872$	1.60880	+	1.60880i	0.0544808	+	0.0544808i
$873$		0			0
$874$		−	23.2849i		−	0.787625i
$875$		0			0
$876$		0			0
$877$	−47.4768	−	12.7214i	−1.60318	−	0.429570i	−0.657177	−	0.753736i	$-0.728250\pi$
$877$	−47.4768	−	12.7214i	−1.60318	−	0.429570i	−0.946000	+	0.324166i	$0.894916\pi$
$878$	36.1029	+	9.67374i	1.21841	+	0.326473i
$879$		0			0
$880$		0			0
$881$		−	17.7562i		−	0.598222i	−0.954218	−	0.299111i	$-0.903310\pi$
$881$		−	17.7562i		−	0.598222i	0.954218	−	0.299111i	$-0.0966901\pi$
$882$		0			0
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	0.557716	−	0.830032i	$-0.311678\pi$
$883$	−8.09196	−	8.09196i	−0.272316	−	0.272316i	−0.830032	+	0.557716i	$0.811678\pi$
$884$	0.198173	−	0.343246i	0.00666528	−	0.0115446i
$885$		0			0
$886$	6.42494	+	11.1283i	0.215850	+	0.373863i
$887$	2.74978	−	10.2623i	0.0923287	−	0.344575i	−0.904272	−	0.426956i	$-0.859586\pi$
$887$	2.74978	−	10.2623i	0.0923287	−	0.344575i	0.996601	+	0.0823810i	$0.0262525\pi$
$888$		0			0
$889$	−25.5305	−	14.7401i	−0.856267	−	0.494366i
$890$		0			0
$891$		0			0
$892$	−4.48293	+	4.48293i	−0.150100	+	0.150100i
$893$	−6.40079	−	23.8881i	−0.214194	−	0.799383i
$894$		0			0
$895$		0			0
$896$	20.7164	−	11.9606i	0.692087	−	0.399577i
$897$		0			0
$898$	−61.2688	+	16.4169i	−2.04457	+	0.547840i
$899$	15.2193			0.507594
$900$		0			0
$901$	4.14526			0.138098
$902$	−8.63839	+	2.31465i	−0.287627	+	0.0770694i
$903$		0			0
$904$	14.8471	−	8.57197i	0.493807	−	0.285099i
$905$		0			0
$906$		0			0
$907$	2.00855	+	7.49600i	0.0666927	+	0.248901i	0.991222	−	0.132212i	$-0.0422078\pi$
$907$	2.00855	+	7.49600i	0.0666927	+	0.248901i	−0.924529	+	0.381112i	$0.875541\pi$
$908$	4.98428	−	4.98428i	0.165409	−	0.165409i
$909$		0			0
$910$		0			0
$911$	11.1341	+	6.42830i	0.368890	+	0.212979i	0.672974	−	0.739667i	$-0.265017\pi$
$911$	11.1341	+	6.42830i	0.368890	+	0.212979i	−0.304083	+	0.952645i	$0.598350\pi$
$912$		0			0
$913$	−0.542379	+	2.02419i	−0.0179501	+	0.0669908i
$914$	23.1537	+	40.1034i	0.765857	+	1.32650i
$915$		0			0
$916$	−7.59207	+	13.1498i	−0.250849	+	0.434483i
$917$	6.38005	+	6.38005i	0.210688	+	0.210688i
$918$		0			0
$919$			30.7848i			1.01550i	0.861505	+	0.507749i	$0.169522\pi$
$919$			30.7848i			1.01550i	−0.861505	+	0.507749i	$0.830478\pi$
$920$		0			0
$921$		0			0
$922$	−39.3699	−	10.5491i	−1.29658	−	0.347417i
$923$	−10.2486	−	2.74611i	−0.337337	−	0.0903893i
$924$		0			0
$925$		0			0
$926$			29.7259i			0.976854i
$927$		0			0
$928$	9.12048	+	9.12048i	0.299394	+	0.299394i
$929$	12.1446	−	21.0351i	0.398453	−	0.690141i	−0.595082	−	0.803665i	$-0.702881\pi$
$929$	12.1446	−	21.0351i	0.398453	−	0.690141i	0.993535	+	0.113524i	$0.0362139\pi$
$930$		0			0
$931$	11.7688	+	20.3842i	0.385708	+	0.668066i
$932$	−1.52567	+	5.69388i	−0.0499750	+	0.186509i
$933$		0			0
$934$	45.3882	+	26.2049i	1.48515	+	0.857451i
$935$		0			0
$936$		0			0
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	−0.338534	−	0.940954i	$-0.609931\pi$
$937$	18.4403	−	18.4403i	0.602420	−	0.602420i	0.940954	+	0.338534i	$0.109931\pi$
$938$	−8.68284	−	32.4048i	−0.283505	−	1.05805i
$939$		0			0
$940$		0			0
$941$	34.2802	−	19.7917i	1.11750	−	0.645191i	0.176741	−	0.984257i	$-0.443444\pi$
$941$	34.2802	−	19.7917i	1.11750	−	0.645191i	0.940763	+	0.339066i	$0.110111\pi$
$942$		0			0
$943$	−3.22353	+	0.863741i	−0.104972	+	0.0281273i
$944$	−2.76275			−0.0899200
$945$		0			0
$946$	−25.5377			−0.830301
$947$	−39.9850	+	10.7139i	−1.29934	+	0.348156i	−0.841199	−	0.540725i	$-0.818150\pi$
$947$	−39.9850	+	10.7139i	−1.29934	+	0.348156i	−0.458138	+	0.888881i	$0.651483\pi$
$948$		0			0
$949$	−2.09629	+	1.21029i	−0.0680485	+	0.0392878i
$950$		0			0
$951$		0			0
$952$	0.374683	+	1.39834i	0.0121435	+	0.0453203i
$953$	17.2048	−	17.2048i	0.557319	−	0.557319i	−0.371224	−	0.928543i	$-0.621062\pi$
$953$	17.2048	−	17.2048i	0.557319	−	0.557319i	0.928543	+	0.371224i	$0.121062\pi$
$954$		0			0
$955$		0			0
$956$	−4.60979	−	2.66147i	−0.149091	−	0.0860780i
$957$		0			0
$958$	5.82033	−	21.7218i	0.188046	−	0.701798i
$959$	0.410471	+	0.710957i	0.0132548	+	0.0229580i
$960$		0			0
$961$	3.72853	−	6.45800i	0.120275	−	0.208323i
$962$	12.2191	+	12.2191i	0.393959	+	0.393959i
$963$		0			0
$964$			17.9875i			0.579339i
$965$		0			0
$966$		0			0
$967$	21.3448	+	5.71932i	0.686402	+	0.183921i	0.585132	−	0.810938i	$-0.301043\pi$
$967$	21.3448	+	5.71932i	0.686402	+	0.183921i	0.101270	+	0.994859i	$0.467709\pi$
$968$	4.03269	+	1.08056i	0.129616	+	0.0347304i
$969$		0			0
$970$		0			0
$971$			3.58038i			0.114900i	0.998348	+	0.0574499i	$0.0182969\pi$
$971$			3.58038i			0.114900i	−0.998348	+	0.0574499i	$0.981703\pi$
$972$		0			0
$973$	20.3944	+	20.3944i	0.653815	+	0.653815i
$974$	20.9139	−	36.2239i	0.670124	−	1.16069i
$975$		0			0
$976$	−14.6474	−	25.3700i	−0.468851	−	0.812074i
$977$	−5.33127	+	19.8966i	−0.170562	+	0.636548i	0.826703	+	0.562639i	$0.190214\pi$
$977$	−5.33127	+	19.8966i	−0.170562	+	0.636548i	−0.997265	+	0.0739084i	$0.976453\pi$
$978$		0			0
$979$	51.3796	+	29.6640i	1.64210	+	0.948067i
$980$		0			0
$981$		0			0
$982$	−24.4066	+	24.4066i	−0.778846	+	0.778846i
$983$	7.58120	+	28.2934i	0.241803	+	0.902420i	0.974963	+	0.222365i	$0.0713776\pi$
$983$	7.58120	+	28.2934i	0.241803	+	0.902420i	−0.733161	+	0.680055i	$0.761956\pi$
$984$		0			0
$985$		0			0
$986$	−1.76930	+	1.02151i	−0.0563460	+	0.0325314i
$987$		0			0
$988$	−6.11057	+	1.63732i	−0.194403	+	0.0520902i
$989$	−9.52971			−0.303027
$990$		0			0
$991$	−21.0816			−0.669679			−0.334840	−	0.942275i	$-0.608682\pi$
$991$	−21.0816			−0.669679			−0.334840	+	0.942275i	$0.608682\pi$
$992$	−19.2726	+	5.16409i	−0.611907	+	0.163960i
$993$		0			0
$994$	−20.7621	+	11.9870i	−0.658535	+	0.380205i
$995$		0			0
$996$		0			0
$997$	13.3859	+	49.9569i	0.423936	+	1.58215i	0.766236	+	0.642559i	$0.222127\pi$
$997$	13.3859	+	49.9569i	0.423936	+	1.58215i	−0.342300	+	0.939591i	$0.611206\pi$
$998$	11.6227	−	11.6227i	0.367909	−	0.367909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.q.a.143.2		16
3.2	odd	2		225.2.p.b.218.3		16
5.2	odd	4	inner	675.2.q.a.332.2		16
5.3	odd	4		135.2.m.a.62.3		16
5.4	even	2		135.2.m.a.8.3		16
9.4	even	3		225.2.p.b.68.3		16
9.5	odd	6	inner	675.2.q.a.368.2		16
15.2	even	4		225.2.p.b.182.3		16
15.8	even	4		45.2.l.a.2.2	✓	16
15.14	odd	2		45.2.l.a.38.2	yes	16
45.4	even	6		45.2.l.a.23.2	yes	16
45.13	odd	12		45.2.l.a.32.2	yes	16
45.14	odd	6		135.2.m.a.98.3		16
45.22	odd	12		225.2.p.b.32.3		16
45.23	even	12		135.2.m.a.17.3		16
45.29	odd	6		405.2.f.a.323.7		16
45.32	even	12	inner	675.2.q.a.557.2		16
45.34	even	6		405.2.f.a.323.2		16
45.38	even	12		405.2.f.a.242.2		16
45.43	odd	12		405.2.f.a.242.7		16
60.23	odd	4		720.2.cu.c.497.1		16
60.59	even	2		720.2.cu.c.353.3		16
180.103	even	12		720.2.cu.c.257.3		16
180.139	odd	6		720.2.cu.c.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	15.8	even	4
45.2.l.a.23.2	yes	16	45.4	even	6
45.2.l.a.32.2	yes	16	45.13	odd	12
45.2.l.a.38.2	yes	16	15.14	odd	2
135.2.m.a.8.3		16	5.4	even	2
135.2.m.a.17.3		16	45.23	even	12
135.2.m.a.62.3		16	5.3	odd	4
135.2.m.a.98.3		16	45.14	odd	6
225.2.p.b.32.3		16	45.22	odd	12
225.2.p.b.68.3		16	9.4	even	3
225.2.p.b.182.3		16	15.2	even	4
225.2.p.b.218.3		16	3.2	odd	2
405.2.f.a.242.2		16	45.38	even	12
405.2.f.a.242.7		16	45.43	odd	12
405.2.f.a.323.2		16	45.34	even	6
405.2.f.a.323.7		16	45.29	odd	6
675.2.q.a.143.2		16	1.1	even	1	trivial
675.2.q.a.332.2		16	5.2	odd	4	inner
675.2.q.a.368.2		16	9.5	odd	6	inner
675.2.q.a.557.2		16	45.32	even	12	inner
720.2.cu.c.113.1		16	180.139	odd	6
720.2.cu.c.257.3		16	180.103	even	12
720.2.cu.c.353.3		16	60.59	even	2
720.2.cu.c.497.1		16	60.23	odd	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60599 + 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(-0.465559 - 1.73749i) q^{7} +(1.45267 - 1.45267i) q^{8} +O(q^{10})\)	\(q+(-1.60599 + 0.430324i) q^{2} +(0.661975 - 0.382191i) q^{4} +(-0.465559 - 1.73749i) q^{7} +(1.45267 - 1.45267i) q^{8} +(-3.12636 - 1.80501i) q^{11} +(-0.342574 + 1.27850i) q^{13} +(1.49537 + 2.59005i) q^{14} +(-2.47224 + 4.28205i) q^{16} +(-0.277007 - 0.277007i) q^{17} +6.25273i q^{19} +(5.79765 + 1.55348i) q^{22} +(2.16347 + 0.579699i) q^{23} -2.20068i q^{26} +(-0.972242 - 0.972242i) q^{28} +(-1.56832 + 2.71642i) q^{29} +(-2.42605 - 4.20205i) q^{31} +(1.06430 - 3.97202i) q^{32} +(0.564074 + 0.325668i) q^{34} +(-5.55242 + 5.55242i) q^{37} +(-2.69070 - 10.0418i) q^{38} +(-1.29036 + 0.744991i) q^{41} +(-4.10976 + 1.10121i) q^{43} -2.75943 q^{44} -3.72396 q^{46} +(-3.82042 + 1.02368i) q^{47} +(3.26005 - 1.88219i) q^{49} +(0.261857 + 0.977265i) q^{52} +(-7.48222 + 7.48222i) q^{53} +(-3.20031 - 1.84770i) q^{56} +(1.34977 - 5.03742i) q^{58} +(0.279377 + 0.483896i) q^{59} +(-2.96237 + 5.13097i) q^{61} +(5.70446 + 5.70446i) q^{62} -3.05196i q^{64} +(-10.8351 - 2.90325i) q^{67} +(-0.289242 - 0.0775020i) q^{68} +8.01611i q^{71} +(1.29315 + 1.29315i) q^{73} +(6.52779 - 11.3065i) q^{74} +(2.38974 + 4.13915i) q^{76} +(-1.68068 + 6.27237i) q^{77} +(-6.96917 - 4.02365i) q^{79} +(1.75172 - 1.75172i) q^{82} +(-0.150243 - 0.560714i) q^{83} +(6.12636 - 3.53706i) q^{86} +(-7.16367 + 1.91950i) q^{88} -16.4343 q^{89} +2.38087 q^{91} +(1.65372 - 0.443112i) q^{92} +(5.69504 - 3.28804i) q^{94} +(1.37786 + 5.14224i) q^{97} +(-4.42566 + 4.42566i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 + 2 * q^7	\( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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