LMFDB - Embedded newform 900.2.i.f.601.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(301,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.301"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 4x^{10} + 10x^{8} + 6x^{6} + 90x^{4} + 324x^{2} + 729 $ x^12 + 4x^10 + 10x^8 + 6x^6 + 90x^4 + 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.3
Root			$-0.602950 - 1.62372i$ of defining polynomial
Character	$\chi$	$=$	900.601
Dual form			900.2.i.f.301.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.602950 - 1.62372i) q^{3} +(-1.88482 + 3.26460i) q^{7} +(-2.27290 + 1.95804i) q^{9} +(1.77290 - 3.07076i) q^{11} +(0.501753 + 0.869061i) q^{13} -1.56023 q^{17} +7.21013 q^{19} +(6.43723 + 1.09201i) q^{21} +(3.09072 + 5.35328i) q^{23} +(4.54975 + 2.50994i) q^{27} +(1.50000 - 2.59808i) q^{29} +(2.89142 + 5.00809i) q^{31} +(-6.05500 - 1.02717i) q^{33} -0.851576 q^{37} +(1.10858 - 1.33870i) q^{39} +(1.55926 + 2.70072i) q^{41} +(-1.35333 + 2.34403i) q^{43} +(4.87434 - 8.44260i) q^{47} +(-3.60506 - 6.24415i) q^{49} +(0.940739 + 2.53336i) q^{51} +11.2494 q^{53} +(-4.34735 - 11.7072i) q^{57} +(4.83216 + 8.36955i) q^{59} +(4.10506 - 7.11018i) q^{61} +(-2.10821 - 11.1107i) q^{63} +(-1.45903 - 2.52711i) q^{67} +(6.82865 - 8.24621i) q^{69} +7.21013 q^{71} -16.7817 q^{73} +(6.68319 + 11.5756i) q^{77} +(-5.49649 + 9.52020i) q^{79} +(1.33216 - 8.90086i) q^{81} +(5.09773 - 8.82952i) q^{83} +(-5.12296 - 0.869061i) q^{87} -5.33567 q^{89} -3.78285 q^{91} +(6.38833 - 7.71448i) q^{93} +(-1.93105 + 3.34467i) q^{97} +(1.98303 + 10.4509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{9} + 2 q^{11} + 10 q^{21} + 18 q^{29} + 6 q^{31} + 42 q^{39} + 14 q^{41} + 16 q^{51} + 34 q^{59} + 6 q^{61} - 14 q^{69} + 6 q^{79} - 8 q^{81} - 112 q^{89} + 12 q^{91} - 82 q^{99}+O(q^{100}) $ 12 * q - 8 * q^9 + 2 * q^11 + 10 * q^21 + 18 * q^29 + 6 * q^31 + 42 * q^39 + 14 * q^41 + 16 * q^51 + 34 * q^59 + 6 * q^61 - 14 * q^69 + 6 * q^79 - 8 * q^81 - 112 * q^89 + 12 * q^91 - 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.602950	−	1.62372i	−0.348114	−	0.937452i
$3$	−0.602950	−	1.62372i	−0.348114	−	0.937452i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.88482	+	3.26460i	−0.712394	+	1.23390i	0.251563	+	0.967841i	$0.419056\pi$
$7$	−1.88482	+	3.26460i	−0.712394	+	1.23390i	−0.963956	+	0.266061i	$0.914278\pi$
$8$		0			0
$9$	−2.27290	+	1.95804i	−0.757634	+	0.652680i
$10$		0			0
$11$	1.77290	−	3.07076i	0.534550	−	0.925868i	−0.464635	−	0.885502i	$-0.653814\pi$
$11$	1.77290	−	3.07076i	0.534550	−	0.925868i	0.999185	−	0.0403654i	$-0.0128522\pi$
$12$		0			0
$13$	0.501753	+	0.869061i	0.139161	+	0.241034i	0.927179	−	0.374618i	$-0.122226\pi$
$13$	0.501753	+	0.869061i	0.139161	+	0.241034i	−0.788018	+	0.615652i	$0.788893\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.56023			−0.378410			−0.189205	−	0.981938i	$-0.560591\pi$
$17$	−1.56023			−0.378410			−0.189205	+	0.981938i	$0.560591\pi$
$18$		0			0
$19$	7.21013			1.65412			0.827058	−	0.562116i	$-0.190013\pi$
$19$	7.21013			1.65412			0.827058	+	0.562116i	$0.190013\pi$
$20$		0			0
$21$	6.43723	+	1.09201i	1.40472	+	0.238297i
$22$		0			0
$23$	3.09072	+	5.35328i	0.644459	+	1.11624i	0.984426	+	0.175799i	$0.0562507\pi$
$23$	3.09072	+	5.35328i	0.644459	+	1.11624i	−0.339967	+	0.940437i	$0.610416\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.54975	+	2.50994i	0.875599	+	0.483039i
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	2.89142	+	5.00809i	0.519315	+	0.899480i	0.999748	+	0.0224486i	$0.00714621\pi$
$31$	2.89142	+	5.00809i	0.519315	+	0.899480i	−0.480433	+	0.877031i	$0.659520\pi$
$32$		0			0
$33$	−6.05500	−	1.02717i	−1.05404	−	0.178808i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.851576			−0.139998			−0.0699991	−	0.997547i	$-0.522300\pi$
$37$	−0.851576			−0.139998			−0.0699991	+	0.997547i	$0.522300\pi$
$38$		0			0
$39$	1.10858	−	1.33870i	0.177514	−	0.214364i
$40$		0			0
$41$	1.55926	+	2.70072i	0.243516	+	0.421782i	0.961713	−	0.274058i	$-0.0883659\pi$
$41$	1.55926	+	2.70072i	0.243516	+	0.421782i	−0.718198	+	0.695839i	$0.755033\pi$
$42$		0			0
$43$	−1.35333	+	2.34403i	−0.206381	+	0.357462i	−0.950572	−	0.310505i	$-0.899502\pi$
$43$	−1.35333	+	2.34403i	−0.206381	+	0.357462i	0.744191	+	0.667967i	$0.232835\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.87434	−	8.44260i	0.710995	−	1.23148i	−0.253489	−	0.967338i	$-0.581578\pi$
$47$	4.87434	−	8.44260i	0.710995	−	1.23148i	0.964484	−	0.264141i	$-0.0850885\pi$
$48$		0			0
$49$	−3.60506	−	6.24415i	−0.515009	−	0.892022i
$50$		0			0
$51$	0.940739	+	2.53336i	0.131730	+	0.354742i
$52$		0			0
$53$	11.2494			1.54523			0.772614	−	0.634876i	$-0.218949\pi$
$53$	11.2494			1.54523			0.772614	+	0.634876i	$0.218949\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.34735	−	11.7072i	−0.575821	−	1.55066i
$58$		0			0
$59$	4.83216	+	8.36955i	0.629094	+	1.08962i	0.987734	+	0.156147i	$0.0499073\pi$
$59$	4.83216	+	8.36955i	0.629094	+	1.08962i	−0.358640	+	0.933476i	$0.616759\pi$
$60$		0			0
$61$	4.10506	−	7.11018i	0.525600	−	0.910365i	−0.473956	−	0.880549i	$-0.657174\pi$
$61$	4.10506	−	7.11018i	0.525600	−	0.910365i	0.999555	−	0.0298166i	$-0.00949232\pi$
$62$		0			0
$63$	−2.10821	−	11.1107i	−0.265609	−	1.39981i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.45903	−	2.52711i	−0.178249	−	0.308736i	0.763032	−	0.646361i	$-0.223710\pi$
$67$	−1.45903	−	2.52711i	−0.178249	−	0.308736i	−0.941281	+	0.337625i	$0.890376\pi$
$68$		0			0
$69$	6.82865	−	8.24621i	0.822073	−	0.992727i
$70$		0			0
$71$	7.21013			0.855685			0.427842	−	0.903853i	$-0.359274\pi$
$71$	7.21013			0.855685			0.427842	+	0.903853i	$0.359274\pi$
$72$		0			0
$73$	−16.7817			−1.96415			−0.982074	−	0.188498i	$-0.939638\pi$
$73$	−16.7817			−1.96415			−0.982074	+	0.188498i	$0.939638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.68319	+	11.5756i	0.761620	+	1.31916i
$78$		0			0
$79$	−5.49649	+	9.52020i	−0.618403	+	1.07111i	0.371374	+	0.928483i	$0.378887\pi$
$79$	−5.49649	+	9.52020i	−0.618403	+	1.07111i	−0.989777	+	0.142622i	$0.954447\pi$
$80$		0			0
$81$	1.33216	−	8.90086i	0.148018	−	0.988985i
$82$		0			0
$83$	5.09773	−	8.82952i	0.559548	−	0.969166i	−0.437986	−	0.898982i	$-0.644308\pi$
$83$	5.09773	−	8.82952i	0.559548	−	0.969166i	0.997534	−	0.0701843i	$-0.0223587\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.12296	−	0.869061i	−0.549239	−	0.0931732i
$88$		0			0
$89$	−5.33567			−0.565580			−0.282790	−	0.959182i	$-0.591260\pi$
$89$	−5.33567			−0.565580			−0.282790	+	0.959182i	$0.591260\pi$
$90$		0			0
$91$	−3.78285			−0.396550
$92$		0			0
$93$	6.38833	−	7.71448i	0.662439	−	0.799954i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.93105	+	3.34467i	−0.196068	+	0.339600i	−0.947250	−	0.320495i	$-0.896151\pi$
$97$	−1.93105	+	3.34467i	−0.196068	+	0.339600i	0.751182	+	0.660095i	$0.229484\pi$
$98$		0			0
$99$	1.98303	+	10.4509i	0.199302	+	1.05036i
$100$		0			0
$101$	−2.37797	+	4.11876i	−0.236616	+	0.409832i	−0.959741	−	0.280886i	$-0.909372\pi$
$101$	−2.37797	+	4.11876i	−0.236616	+	0.409832i	0.723125	+	0.690717i	$0.242705\pi$
$102$		0			0
$103$	9.04452	+	15.6656i	0.891183	+	1.54357i	0.838458	+	0.544966i	$0.183457\pi$
$103$	9.04452	+	15.6656i	0.891183	+	1.54357i	0.0527251	+	0.998609i	$0.483209\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.61770			0.349737			0.174868	−	0.984592i	$-0.444050\pi$
$107$	3.61770			0.349737			0.174868	+	0.984592i	$0.444050\pi$
$108$		0			0
$109$	−9.63741			−0.923096			−0.461548	−	0.887115i	$-0.652706\pi$
$109$	−9.63741			−0.923096			−0.461548	+	0.887115i	$0.652706\pi$
$110$		0			0
$111$	0.513458	+	1.38272i	0.0487353	+	0.131242i
$112$		0			0
$113$	1.77912	+	3.08152i	0.167365	+	0.289885i	0.937493	−	0.348005i	$-0.113141\pi$
$113$	1.77912	+	3.08152i	0.167365	+	0.289885i	−0.770127	+	0.637890i	$0.779807\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.84209	−	0.992839i	−0.262751	−	0.0917880i
$118$		0			0
$119$	2.94074	−	5.09351i	0.269577	−	0.466921i
$120$		0			0
$121$	−0.786360	−	1.36201i	−0.0714872	−	0.123820i
$122$		0			0
$123$	3.44504	−	4.16020i	0.310629	−	0.375112i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	6.78015			0.601641			0.300820	−	0.953681i	$-0.402739\pi$
$127$	6.78015			0.601641			0.300820	+	0.953681i	$0.402739\pi$
$128$		0			0
$129$	4.62203	+	0.784084i	0.406947	+	0.0690347i
$130$		0			0
$131$	1.71364	+	2.96811i	0.149721	+	0.259325i	0.931124	−	0.364702i	$-0.118829\pi$
$131$	1.71364	+	2.96811i	0.149721	+	0.259325i	−0.781403	+	0.624027i	$0.785496\pi$
$132$		0			0
$133$	−13.5898	+	23.5382i	−1.17838	+	2.04102i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.46330	+	12.9268i	−0.637633	+	1.10441i	0.348318	+	0.937376i	$0.386753\pi$
$137$	−7.46330	+	12.9268i	−0.637633	+	1.10441i	−0.985951	+	0.167036i	$0.946580\pi$
$138$		0			0
$139$	2.71364	+	4.70016i	0.230168	+	0.398663i	0.957857	−	0.287244i	$-0.0927391\pi$
$139$	2.71364	+	4.70016i	0.230168	+	0.398663i	−0.727689	+	0.685907i	$0.759406\pi$
$140$		0			0
$141$	−16.6474	−	2.82406i	−1.40196	−	0.237829i
$142$		0			0
$143$	3.55823			0.297554
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.96505	+	9.61851i	−0.656946	+	0.793322i
$148$		0			0
$149$	−2.76939	−	4.79672i	−0.226877	−	0.392963i	0.730004	−	0.683443i	$-0.239518\pi$
$149$	−2.76939	−	4.79672i	−0.226877	−	0.392963i	−0.956881	+	0.290480i	$0.906185\pi$
$150$		0			0
$151$	−0.108576	+	0.188059i	−0.00883580	+	0.0153041i	−0.870409	−	0.492328i	$-0.836146\pi$
$151$	−0.108576	+	0.188059i	−0.00883580	+	0.0153041i	0.861574	+	0.507633i	$0.169479\pi$
$152$		0			0
$153$	3.54624	−	3.05498i	0.286696	−	0.246981i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.07947	+	1.86970i	0.0861511	+	0.149218i	0.905881	−	0.423532i	$-0.139210\pi$
$157$	1.07947	+	1.86970i	0.0861511	+	0.149218i	−0.819730	+	0.572750i	$0.805877\pi$
$158$		0			0
$159$	−6.78285	−	18.2659i	−0.537915	−	1.44858i
$160$		0			0
$161$	−23.3017			−1.83643
$162$		0			0
$163$	−8.39084			−0.657221			−0.328611	−	0.944465i	$-0.606580\pi$
$163$	−8.39084			−0.657221			−0.328611	+	0.944465i	$0.606580\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.31060	−	4.00208i	−0.178800	−	0.309691i	0.762670	−	0.646788i	$-0.223888\pi$
$167$	−2.31060	−	4.00208i	−0.178800	−	0.309691i	−0.941470	+	0.337097i	$0.890555\pi$
$168$		0			0
$169$	5.99649	−	10.3862i	0.461268	−	0.798940i
$170$		0			0
$171$	−16.3879	+	14.1177i	−1.25321	+	1.07961i
$172$		0			0
$173$	0.725146	−	1.25599i	0.0551318	−	0.0954911i	−0.837142	−	0.546985i	$-0.815775\pi$
$173$	0.725146	−	1.25599i	0.0551318	−	0.0954911i	0.892274	+	0.451494i	$0.149109\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.6762	−	12.8925i	0.802473	−	0.969058i
$178$		0			0
$179$	−19.4472			−1.45355			−0.726775	−	0.686876i	$-0.758982\pi$
$179$	−19.4472			−1.45355			−0.726775	+	0.686876i	$0.758982\pi$
$180$		0			0
$181$	−10.4273			−0.775054			−0.387527	−	0.921858i	$-0.626671\pi$
$181$	−10.4273			−0.775054			−0.387527	+	0.921858i	$0.626671\pi$
$182$		0			0
$183$	−14.0201	−	2.37837i	−1.03639	−	0.175814i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.76613	+	4.79107i	−0.202279	+	0.350358i
$188$		0			0
$189$	−16.7694	+	10.1223i	−1.21979	+	0.736289i
$190$		0			0
$191$	1.89142	−	3.27604i	0.136859	−	0.237046i	−0.789447	−	0.613818i	$-0.789633\pi$
$191$	1.89142	−	3.27604i	0.136859	−	0.237046i	0.926306	+	0.376772i	$0.122966\pi$
$192$		0			0
$193$	−7.03751	−	12.1893i	−0.506571	−	0.877407i	−0.999971	−	0.00760445i	$-0.997579\pi$
$193$	−7.03751	−	12.1893i	−0.506571	−	0.877407i	0.493400	−	0.869803i	$-0.335754\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.5044			1.53212			0.766061	−	0.642768i	$-0.222214\pi$
$197$	21.5044			1.53212			0.766061	+	0.642768i	$0.222214\pi$
$198$		0			0
$199$	7.21013			0.511112			0.255556	−	0.966794i	$-0.417741\pi$
$199$	7.21013			0.511112			0.255556	+	0.966794i	$0.417741\pi$
$200$		0			0
$201$	−3.22359	+	3.89277i	−0.227374	+	0.274575i
$202$		0			0
$203$	5.65445	+	9.79379i	0.396864	+	0.687389i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−17.5068	−	6.11573i	−1.21681	−	0.425073i
$208$		0			0
$209$	12.7828	−	22.1405i	0.884208	−	1.53149i
$210$		0			0
$211$	−1.89142	−	3.27604i	−0.130211	−	0.225532i	0.793547	−	0.608509i	$-0.208232\pi$
$211$	−1.89142	−	3.27604i	−0.130211	−	0.225532i	−0.923758	+	0.382977i	$0.874899\pi$
$212$		0			0
$213$	−4.34735	−	11.7072i	−0.297876	−	0.802164i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−21.7992			−1.47983
$218$		0			0
$219$	10.1185	+	27.2487i	0.683746	+	1.84129i
$220$		0			0
$221$	−0.782848	−	1.35593i	−0.0526600	−	0.0912099i
$222$		0			0
$223$	1.45903	−	2.52711i	0.0977038	−	0.169228i	−0.813030	−	0.582222i	$-0.802184\pi$
$223$	1.45903	−	2.52711i	0.0977038	−	0.169228i	0.910734	+	0.412994i	$0.135517\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.55923	−	4.43272i	0.169862	−	0.294210i	−0.768509	−	0.639839i	$-0.779001\pi$
$227$	2.55923	−	4.43272i	0.169862	−	0.294210i	0.938371	+	0.345629i	$0.112334\pi$
$228$		0			0
$229$	4.71013	+	8.15818i	0.311254	+	0.539108i	0.978634	−	0.205609i	$-0.0659177\pi$
$229$	4.71013	+	8.15818i	0.311254	+	0.539108i	−0.667380	+	0.744717i	$0.732584\pi$
$230$		0			0
$231$	14.7659	−	17.8311i	0.971523	−	1.17320i
$232$		0			0
$233$	26.1850			1.71544			0.857719	−	0.514118i	$-0.171881\pi$
$233$	26.1850			1.71544			0.857719	+	0.514118i	$0.171881\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	18.7722	+	3.18452i	1.21939	+	0.206857i
$238$		0			0
$239$	11.3780	+	19.7072i	0.735979	+	1.27475i	0.954292	+	0.298875i	$0.0966113\pi$
$239$	11.3780	+	19.7072i	0.735979	+	1.27475i	−0.218313	+	0.975879i	$0.570055\pi$
$240$		0			0
$241$	−8.31519	+	14.4023i	−0.535629	+	0.927736i	0.463504	+	0.886095i	$0.346592\pi$
$241$	−8.31519	+	14.4023i	−0.535629	+	0.927736i	−0.999133	+	0.0416412i	$0.986741\pi$
$242$		0			0
$243$	−15.2557	+	3.20373i	−0.978653	+	0.205519i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.61770	+	6.26604i	0.230189	+	0.398699i
$248$		0			0
$249$	−17.4103	−	2.95349i	−1.10333	−	0.187170i
$250$		0			0
$251$	−20.7758			−1.31136			−0.655679	−	0.755040i	$-0.727618\pi$
$251$	−20.7758			−1.31136			−0.655679	+	0.755040i	$0.727618\pi$
$252$		0			0
$253$	21.9181			1.37798
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.52978	−	16.5061i	−0.594451	−	1.02962i	−0.993624	−	0.112744i	$-0.964036\pi$
$257$	−9.52978	−	16.5061i	−0.594451	−	1.02962i	0.399173	−	0.916876i	$-0.369297\pi$
$258$		0			0
$259$	1.60506	−	2.78005i	0.0997338	−	0.172744i
$260$		0			0
$261$	1.67778	+	8.84223i	0.103852	+	0.547320i
$262$		0			0
$263$	−4.06899	+	7.04770i	−0.250905	+	0.434580i	−0.963775	−	0.266716i	$-0.914061\pi$
$263$	−4.06899	+	7.04770i	−0.250905	+	0.434580i	0.712870	+	0.701296i	$0.247395\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.21715	+	8.66362i	0.196886	+	0.530205i
$268$		0			0
$269$	−25.6374			−1.56314			−0.781570	−	0.623817i	$-0.785581\pi$
$269$	−25.6374			−1.56314			−0.781570	+	0.623817i	$0.785581\pi$
$270$		0			0
$271$	−3.21013			−0.195001			−0.0975007	−	0.995235i	$-0.531085\pi$
$271$	−3.21013			−0.195001			−0.0975007	+	0.995235i	$0.531085\pi$
$272$		0			0
$273$	2.28087	+	6.14227i	0.138045	+	0.371747i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.349823	+	0.605911i	−0.0210188	+	0.0364057i	−0.876343	−	0.481687i	$-0.840024\pi$
$277$	−0.349823	+	0.605911i	−0.0210188	+	0.0364057i	0.855325	+	0.518092i	$0.173358\pi$
$278$		0			0
$279$	−16.3780	−	5.72138i	−0.980523	−	0.342530i
$280$		0			0
$281$	15.3152	−	26.5267i	0.913628	−	1.58245i	0.104730	−	0.994501i	$-0.466602\pi$
$281$	15.3152	−	26.5267i	0.913628	−	1.58245i	0.808898	−	0.587949i	$-0.200064\pi$
$282$		0			0
$283$	−4.80287	−	8.31882i	−0.285501	−	0.494502i	0.687229	−	0.726440i	$-0.258827\pi$
$283$	−4.80287	−	8.31882i	−0.285501	−	0.494502i	−0.972731	+	0.231938i	$0.925493\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.7557			−0.693916
$288$		0			0
$289$	−14.5657			−0.856806
$290$		0			0
$291$	6.59512	+	1.11880i	0.386613	+	0.0655851i
$292$		0			0
$293$	−1.50526	−	2.60718i	−0.0879381	−	0.152313i	0.818701	−	0.574220i	$-0.194694\pi$
$293$	−1.50526	−	2.60718i	−0.0879381	−	0.152313i	−0.906639	+	0.421906i	$0.861361\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	15.7737	−	9.52127i	0.915281	−	0.552480i
$298$		0			0
$299$	−3.10155	+	5.37205i	−0.179367	+	0.310673i
$300$		0			0
$301$	−5.10155	−	8.83615i	−0.294049	−	0.509307i
$302$		0			0
$303$	8.12148	+	1.37773i	0.466567	+	0.0791487i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.8671			0.848512			0.424256	−	0.905542i	$-0.360536\pi$
$307$	14.8671			0.848512			0.424256	+	0.905542i	$0.360536\pi$
$308$		0			0
$309$	19.9830	−	24.1313i	1.13679	−	1.37278i
$310$		0			0
$311$	−1.53586	−	2.66018i	−0.0870905	−	0.150845i	0.819190	−	0.573523i	$-0.194424\pi$
$311$	−1.53586	−	2.66018i	−0.0870905	−	0.150845i	−0.906280	+	0.422678i	$0.861090\pi$
$312$		0			0
$313$	11.5068	−	19.9303i	0.650402	−	1.12653i	−0.332623	−	0.943060i	$-0.607934\pi$
$313$	11.5068	−	19.9303i	0.650402	−	1.12653i	0.983025	−	0.183470i	$-0.0587330\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.00450177	−	0.00779729i	0.000252844	−	0.000437939i	−0.865899	−	0.500219i	$-0.833253\pi$
$317$	0.00450177	−	0.00779729i	0.000252844	−	0.000437939i	0.866152	+	0.499781i	$0.166586\pi$
$318$		0			0
$319$	−5.31870	−	9.21227i	−0.297790	−	0.515788i
$320$		0			0
$321$	−2.18130	−	5.87412i	−0.121748	−	0.327861i
$322$		0			0
$323$	−11.2494			−0.625935
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.81088	+	15.6484i	0.321342	+	0.865359i
$328$		0			0
$329$	18.3745	+	31.8255i	1.01302	+	1.75460i
$330$		0			0
$331$	−4.49649	+	7.78815i	−0.247149	+	0.428075i	−0.962734	−	0.270451i	$-0.912827\pi$
$331$	−4.49649	+	7.78815i	−0.247149	+	0.428075i	0.715584	+	0.698526i	$0.246160\pi$
$332$		0			0
$333$	1.93555	−	1.66742i	0.106067	−	0.0913740i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.63069	−	4.55649i	−0.143303	−	0.248208i	0.785436	−	0.618943i	$-0.212439\pi$
$337$	−2.63069	−	4.55649i	−0.143303	−	0.248208i	−0.928739	+	0.370735i	$0.879106\pi$
$338$		0			0
$339$	3.93079	−	4.74678i	0.213491	−	0.257810i
$340$		0			0
$341$	20.5048			1.11040
$342$		0			0
$343$	0.792107			0.0427698
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.7477	−	18.6155i	−0.576965	−	0.999333i	−0.995825	−	0.0912825i	$-0.970903\pi$
$347$	−10.7477	−	18.6155i	−0.576965	−	0.999333i	0.418860	−	0.908051i	$-0.362430\pi$
$348$		0			0
$349$	6.28285	−	10.8822i	0.336313	−	0.582511i	−0.647423	−	0.762131i	$-0.724153\pi$
$349$	6.28285	−	10.8822i	0.336313	−	0.582511i	0.983736	+	0.179619i	$0.0574866\pi$
$350$		0			0
$351$	0.101552	+	5.21338i	0.00542046	+	0.278270i
$352$		0			0
$353$	−12.5313	+	21.7048i	−0.666973	+	1.15523i	0.311773	+	0.950157i	$0.399077\pi$
$353$	−12.5313	+	21.7048i	−0.666973	+	1.15523i	−0.978746	+	0.205075i	$0.934256\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−10.0435	−	1.70379i	−0.531560	−	0.0901741i
$358$		0			0
$359$	23.1961			1.22424			0.612121	−	0.790764i	$-0.290316\pi$
$359$	23.1961			1.22424			0.612121	+	0.790764i	$0.290316\pi$
$360$		0			0
$361$	32.9860			1.73610
$362$		0			0
$363$	−1.73739	+	2.09805i	−0.0911892	+	0.110119i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.89259	−	15.4024i	0.464190	−	0.804000i	−0.534975	−	0.844868i	$-0.679679\pi$
$367$	8.89259	−	15.4024i	0.464190	−	0.804000i	0.999165	+	0.0408679i	$0.0130123\pi$
$368$		0			0
$369$	−8.83216	−	3.08537i	−0.459784	−	0.160618i
$370$		0			0
$371$	−21.2031	+	36.7249i	−1.10081	+	1.90666i
$372$		0			0
$373$	6.45979	+	11.1887i	0.334475	+	0.579328i	0.983384	−	0.181538i	$-0.0581075\pi$
$373$	6.45979	+	11.1887i	0.334475	+	0.579328i	−0.648908	+	0.760866i	$0.724774\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.01052			0.155050
$378$		0			0
$379$	−5.56570			−0.285891			−0.142945	−	0.989731i	$-0.545657\pi$
$379$	−5.56570			−0.285891			−0.142945	+	0.989731i	$0.545657\pi$
$380$		0			0
$381$	−4.08809	−	11.0090i	−0.209439	−	0.564010i
$382$		0			0
$383$	−14.8716	−	25.7584i	−0.759905	−	1.31619i	−0.942899	−	0.333080i	$-0.891912\pi$
$383$	−14.8716	−	25.7584i	−0.759905	−	1.31619i	0.182994	−	0.983114i	$-0.441421\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.51373	−	7.97763i	−0.0769471	−	0.405526i
$388$		0			0
$389$	3.77641	−	6.54094i	0.191472	−	0.331639i	−0.754266	−	0.656568i	$-0.772007\pi$
$389$	3.77641	−	6.54094i	0.191472	−	0.331639i	0.945738	+	0.324930i	$0.105341\pi$
$390$		0			0
$391$	−4.82222	−	8.35232i	−0.243870	−	0.422395i
$392$		0			0
$393$	3.78613	−	4.57209i	0.190985	−	0.230631i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−30.1571			−1.51354			−0.756770	−	0.653682i	$-0.773224\pi$
$397$	−30.1571			−1.51354			−0.756770	+	0.653682i	$0.773224\pi$
$398$		0			0
$399$	46.4132	+	7.87356i	2.32357	+	0.394171i
$400$		0			0
$401$	10.8322	+	18.7619i	0.540932	+	0.936922i	0.998851	+	0.0479282i	$0.0152619\pi$
$401$	10.8322	+	18.7619i	0.540932	+	0.936922i	−0.457918	+	0.888994i	$0.651405\pi$
$402$		0			0
$403$	−2.90156	+	5.02565i	−0.144537	+	0.250345i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.50976	+	2.61498i	−0.0748360	+	0.129620i
$408$		0			0
$409$	4.06921	+	7.04807i	0.201209	+	0.348505i	0.948918	−	0.315522i	$-0.102180\pi$
$409$	4.06921	+	7.04807i	0.201209	+	0.348505i	−0.747709	+	0.664027i	$0.768846\pi$
$410$		0			0
$411$	25.4895	+	4.32404i	1.25730	+	0.213289i
$412$		0			0
$413$	−36.4310			−1.79265
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.99553	−	7.24014i	0.293603	−	0.354551i
$418$		0			0
$419$	−6.64736	−	11.5136i	−0.324745	−	0.562474i	0.656716	−	0.754138i	$-0.271945\pi$
$419$	−6.64736	−	11.5136i	−0.324745	−	0.562474i	−0.981461	+	0.191664i	$0.938612\pi$
$420$		0			0
$421$	−10.0692	+	17.4404i	−0.490743	+	0.849992i	−0.999943	−	0.0106561i	$-0.996608\pi$
$421$	−10.0692	+	17.4404i	−0.490743	+	0.849992i	0.509200	+	0.860648i	$0.329941\pi$
$422$		0			0
$423$	5.45205	+	28.7333i	0.265088	+	1.39706i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.4746	+	26.8028i	0.748868	+	1.29708i
$428$		0			0
$429$	−2.14544	−	5.77756i	−0.103583	−	0.278943i
$430$		0			0
$431$	25.8027			1.24287			0.621437	−	0.783464i	$-0.286549\pi$
$431$	25.8027			1.24287			0.621437	+	0.783464i	$0.286549\pi$
$432$		0			0
$433$	6.38383			0.306787			0.153394	−	0.988165i	$-0.450980\pi$
$433$	6.38383			0.306787			0.153394	+	0.988165i	$0.450980\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.2845	+	38.5978i	1.06601	+	1.84638i
$438$		0			0
$439$	−5.49649	+	9.52020i	−0.262333	+	0.454374i	−0.966861	−	0.255302i	$-0.917825\pi$
$439$	−5.49649	+	9.52020i	−0.262333	+	0.454374i	0.704528	+	0.709676i	$0.251159\pi$
$440$		0			0
$441$	20.4203	+	7.13349i	0.972393	+	0.339690i
$442$		0			0
$443$	12.6160	−	21.8515i	0.599404	−	1.03820i	−0.393505	−	0.919322i	$-0.628738\pi$
$443$	12.6160	−	21.8515i	0.599404	−	1.03820i	0.992909	−	0.118876i	$-0.0379290\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.11871	+	7.38889i	−0.289405	+	0.349482i
$448$		0			0
$449$	−19.5657			−0.923362			−0.461681	−	0.887046i	$-0.652754\pi$
$449$	−19.5657			−0.923362			−0.461681	+	0.887046i	$0.652754\pi$
$450$		0			0
$451$	11.0577			0.520685
$452$		0			0
$453$	0.370821	+	0.0629062i	0.0174227	+	0.00295559i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.26788	−	5.66013i	0.152865	−	0.264770i	−0.779415	−	0.626508i	$-0.784483\pi$
$457$	3.26788	−	5.66013i	0.152865	−	0.264770i	0.932280	+	0.361739i	$0.117817\pi$
$458$		0			0
$459$	−7.09863	−	3.91608i	−0.331336	−	0.182787i
$460$		0			0
$461$	17.7101	−	30.6748i	0.824843	−	1.42867i	−0.0771964	−	0.997016i	$-0.524597\pi$
$461$	17.7101	−	30.6748i	0.824843	−	1.42867i	0.902039	−	0.431654i	$-0.142070\pi$
$462$		0			0
$463$	−8.13348	−	14.0876i	−0.377995	−	0.654706i	0.612776	−	0.790257i	$-0.290053\pi$
$463$	−8.13348	−	14.0876i	−0.377995	−	0.654706i	−0.990770	+	0.135551i	$0.956720\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.8112			−0.731654			−0.365827	−	0.930683i	$-0.619214\pi$
$467$	−15.8112			−0.731654			−0.365827	+	0.930683i	$0.619214\pi$
$468$		0			0
$469$	11.0000			0.507933
$470$		0			0
$471$	2.38499	−	2.88009i	0.109895	−	0.132707i
$472$		0			0
$473$	4.79864	+	8.31148i	0.220642	+	0.382162i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−25.5688	+	22.0268i	−1.17072	+	1.00854i
$478$		0			0
$479$	16.3709	−	28.3553i	0.748007	−	1.29559i	−0.200769	−	0.979639i	$-0.564344\pi$
$479$	16.3709	−	28.3553i	0.748007	−	1.29559i	0.948776	−	0.315948i	$-0.102323\pi$
$480$		0			0
$481$	−0.427281	−	0.740072i	−0.0194823	−	0.0337444i
$482$		0			0
$483$	14.0498	+	37.8354i	0.639288	+	1.72157i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	36.4220			1.65044			0.825218	−	0.564814i	$-0.191052\pi$
$487$	36.4220			1.65044			0.825218	+	0.564814i	$0.191052\pi$
$488$		0			0
$489$	5.05926	+	13.6243i	0.228788	+	0.616114i
$490$		0			0
$491$	1.71364	+	2.96811i	0.0773355	+	0.133949i	0.902100	−	0.431528i	$-0.142025\pi$
$491$	1.71364	+	2.96811i	0.0773355	+	0.133949i	−0.824764	+	0.565477i	$0.808692\pi$
$492$		0			0
$493$	−2.34034	+	4.05359i	−0.105404	+	0.182564i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.5898	+	23.5382i	−0.609584	+	1.05583i
$498$		0			0
$499$	−1.71364	−	2.96811i	−0.0767131	−	0.132871i	0.825117	−	0.564962i	$-0.191109\pi$
$499$	−1.71364	−	2.96811i	−0.0767131	−	0.132871i	−0.901830	+	0.432091i	$0.857776\pi$
$500$		0			0
$501$	−5.10506	+	6.16482i	−0.228077	+	0.275424i
$502$		0			0
$503$	−17.4219			−0.776802			−0.388401	−	0.921490i	$-0.626973\pi$
$503$	−17.4219			−0.776802			−0.388401	+	0.921490i	$0.626973\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−20.4799	−	3.47421i	−0.909542	−	0.154295i
$508$		0			0
$509$	7.07272	+	12.2503i	0.313493	+	0.542985i	0.979116	−	0.203303i	$-0.0651675\pi$
$509$	7.07272	+	12.2503i	0.313493	+	0.542985i	−0.665623	+	0.746288i	$0.731834\pi$
$510$		0			0
$511$	31.6304	−	54.7854i	1.39925	−	2.42356i
$512$		0			0
$513$	32.8042	+	18.0970i	1.44834	+	0.799003i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−17.2834	−	29.9358i	−0.760125	−	1.31657i
$518$		0			0
$519$	−2.47660	−	0.420131i	−0.108710	−	0.0184417i
$520$		0			0
$521$	−20.2300			−0.886293			−0.443147	−	0.896449i	$-0.646138\pi$
$521$	−20.2300			−0.886293			−0.443147	+	0.896449i	$0.646138\pi$
$522$		0			0
$523$	36.3295			1.58858			0.794289	−	0.607540i	$-0.207844\pi$
$523$	36.3295			1.58858			0.794289	+	0.607540i	$0.207844\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.51127	−	7.81376i	−0.196514	−	0.340373i
$528$		0			0
$529$	−7.60506	+	13.1724i	−0.330655	+	0.572711i
$530$		0			0
$531$	−27.3709	−	9.56160i	−1.18780	−	0.414938i
$532$		0			0
$533$	−1.56473	+	2.71019i	−0.0677759	+	0.117391i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.7257	+	31.5767i	0.506001	+	1.36263i
$538$		0			0
$539$	−25.5657			−1.10119
$540$		0			0
$541$	24.8475			1.06828			0.534140	−	0.845396i	$-0.320636\pi$
$541$	24.8475			1.06828			0.534140	+	0.845396i	$0.320636\pi$
$542$		0			0
$543$	6.28713	+	16.9309i	0.269807	+	0.726576i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.0523	−	27.8034i	0.686347	−	1.18879i	−0.286665	−	0.958031i	$-0.592547\pi$
$547$	16.0523	−	27.8034i	0.686347	−	1.18879i	0.973012	−	0.230757i	$-0.0741201\pi$
$548$		0			0
$549$	4.59161	+	24.1986i	0.195965	+	1.03277i
$550$		0			0
$551$	10.8152	−	18.7325i	0.460743	−	0.798030i
$552$		0			0
$553$	−20.7197	−	35.8876i	−0.881093	−	1.52610i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.3894			−0.736813			−0.368406	−	0.929665i	$-0.620096\pi$
$557$	−17.3894			−0.736813			−0.368406	+	0.929665i	$0.620096\pi$
$558$		0			0
$559$	−2.71615			−0.114881
$560$		0			0
$561$	9.44717	+	1.60262i	0.398860	+	0.0676628i
$562$		0			0
$563$	−13.6700	−	23.6771i	−0.576120	−	0.997870i	−0.995919	−	0.0902525i	$-0.971233\pi$
$563$	−13.6700	−	23.6771i	−0.576120	−	0.997870i	0.419799	−	0.907617i	$-0.362101\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	26.5468	+	21.1255i	1.11486	+	0.887186i
$568$		0			0
$569$	7.59512	−	13.1551i	0.318404	−	0.551492i	−0.661751	−	0.749723i	$-0.730187\pi$
$569$	7.59512	−	13.1551i	0.318404	−	0.551492i	0.980155	+	0.198232i	$0.0635198\pi$
$570$		0			0
$571$	19.3510	+	33.5170i	0.809816	+	1.40264i	0.912991	+	0.407980i	$0.133767\pi$
$571$	19.3510	+	33.5170i	0.809816	+	1.40264i	−0.103175	+	0.994663i	$0.532900\pi$
$572$		0			0
$573$	−6.45979	−	1.09584i	−0.269862	−	0.0457795i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.82910			0.159408			0.0797038	−	0.996819i	$-0.474603\pi$
$577$	3.82910			0.159408			0.0797038	+	0.996819i	$0.474603\pi$
$578$		0			0
$579$	−15.5487	+	18.7765i	−0.646183	+	0.780324i
$580$		0			0
$581$	19.2166	+	33.2841i	0.797237	+	1.38086i
$582$		0			0
$583$	19.9441	−	34.5442i	0.826001	−	1.43068i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.3421	−	21.3772i	0.509415	−	0.882332i	−0.490526	−	0.871427i	$-0.663195\pi$
$587$	12.3421	−	21.3772i	0.509415	−	0.882332i	0.999941	−	0.0109053i	$-0.00347133\pi$
$588$		0			0
$589$	20.8475	+	36.1090i	0.859008	+	1.48785i
$590$		0			0
$591$	−12.9661	−	34.9169i	−0.533352	−	1.43629i
$592$		0			0
$593$	−38.4290			−1.57809			−0.789044	−	0.614336i	$-0.789424\pi$
$593$	−38.4290			−1.57809			−0.789044	+	0.614336i	$0.789424\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.34735	−	11.7072i	−0.177925	−	0.479144i
$598$		0			0
$599$	−7.71364	−	13.3604i	−0.315171	−	0.545892i	0.664303	−	0.747463i	$-0.268728\pi$
$599$	−7.71364	−	13.3604i	−0.315171	−	0.545892i	−0.979474	+	0.201572i	$0.935395\pi$
$600$		0			0
$601$	0.286360	−	0.495989i	0.0116809	−	0.0202318i	−0.860126	−	0.510082i	$-0.829615\pi$
$601$	0.286360	−	0.495989i	0.0116809	−	0.0202318i	0.871807	+	0.489850i	$0.162948\pi$
$602$		0			0
$603$	8.26441	+	2.88704i	0.336553	+	0.117569i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.52901	−	7.84448i	−0.183827	−	0.318398i	0.759354	−	0.650678i	$-0.225515\pi$
$607$	−4.52901	−	7.84448i	−0.183827	−	0.318398i	−0.943181	+	0.332280i	$0.892182\pi$
$608$		0			0
$609$	12.4930	−	15.0864i	0.506241	−	0.611331i
$610$		0			0
$611$	9.78285			0.395772
$612$		0			0
$613$	−6.99155			−0.282386			−0.141193	−	0.989982i	$-0.545094\pi$
$613$	−6.99155			−0.282386			−0.141193	+	0.989982i	$0.545094\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.91710	+	17.1769i	0.399247	+	0.691517i	0.993633	−	0.112663i	$-0.0359382\pi$
$617$	9.91710	+	17.1769i	0.399247	+	0.691517i	−0.594386	+	0.804180i	$0.702605\pi$
$618$		0			0
$619$	14.1016	−	24.4246i	0.566789	−	0.981708i	−0.430092	−	0.902785i	$-0.641519\pi$
$619$	14.1016	−	24.4246i	0.566789	−	0.981708i	0.996881	−	0.0789225i	$-0.0251480\pi$
$620$		0			0
$621$	0.625546	+	32.1136i	0.0251023	+	1.28867i
$622$		0			0
$623$	10.0568	−	17.4188i	0.402916	−	0.697871i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−43.6574	−	7.40605i	−1.74351	−	0.295769i
$628$		0			0
$629$	1.32865			0.0529768
$630$		0			0
$631$	−7.27482			−0.289606			−0.144803	−	0.989461i	$-0.546255\pi$
$631$	−7.27482			−0.289606			−0.144803	+	0.989461i	$0.546255\pi$
$632$		0			0
$633$	−4.17892	+	5.04642i	−0.166097	+	0.200577i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.61770	−	6.26604i	0.143339	−	0.248270i
$638$		0			0
$639$	−16.3879	+	14.1177i	−0.648296	+	0.558488i
$640$		0			0
$641$	−6.43372	+	11.1435i	−0.254116	+	0.440143i	−0.964655	−	0.263515i	$-0.915118\pi$
$641$	−6.43372	+	11.1435i	−0.254116	+	0.440143i	0.710539	+	0.703658i	$0.248451\pi$
$642$		0			0
$643$	12.6160	+	21.8515i	0.497526	+	0.861741i	0.999996	−	0.00285403i	$-0.000908467\pi$
$643$	12.6160	+	21.8515i	0.497526	+	0.861741i	−0.502470	+	0.864595i	$0.667575\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.5618			−0.926311			−0.463156	−	0.886277i	$-0.653283\pi$
$647$	−23.5618			−0.926311			−0.463156	+	0.886277i	$0.653283\pi$
$648$		0			0
$649$	34.2678			1.34513
$650$		0			0
$651$	13.1438	+	35.3957i	0.515148	+	1.38727i
$652$		0			0
$653$	−8.69020	−	15.0519i	−0.340074	−	0.589025i	0.644372	−	0.764712i	$-0.277119\pi$
$653$	−8.69020	−	15.0519i	−0.340074	−	0.589025i	−0.984446	+	0.175687i	$0.943785\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	38.1431	−	32.8592i	1.48810	−	1.28196i
$658$		0			0
$659$	7.83216	−	13.5657i	0.305098	−	0.528445i	−0.672185	−	0.740383i	$-0.734644\pi$
$659$	7.83216	−	13.5657i	0.305098	−	0.528445i	0.977283	+	0.211938i	$0.0679775\pi$
$660$		0			0
$661$	−11.7136	−	20.2886i	−0.455608	−	0.789136i	0.543115	−	0.839658i	$-0.317245\pi$
$661$	−11.7136	−	20.2886i	−0.455608	−	0.789136i	−0.998723	+	0.0505224i	$0.983911\pi$
$662$		0			0
$663$	−1.72963	+	2.08868i	−0.0671732	+	0.0811177i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	18.5443			0.718038
$668$		0			0
$669$	−4.98303	−	0.845323i	−0.192655	−	0.0326821i
$670$		0			0
$671$	−14.5557	−	25.2113i	−0.561918	−	0.973271i
$672$		0			0
$673$	14.3654	−	24.8816i	0.553745	−	0.959114i	−0.444255	−	0.895900i	$-0.646532\pi$
$673$	14.3654	−	24.8816i	0.553745	−	0.959114i	0.998000	−	0.0632136i	$-0.0201350\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.1770	−	43.6079i	0.967632	−	1.67599i	0.265260	−	0.964177i	$-0.414542\pi$
$677$	25.1770	−	43.6079i	0.967632	−	1.67599i	0.702372	−	0.711810i	$-0.252124\pi$
$678$		0			0
$679$	−7.27934	−	12.6082i	−0.279355	−	0.483858i
$680$		0			0
$681$	−8.74056	−	1.48275i	−0.334939	−	0.0568192i
$682$		0			0
$683$	−11.5953			−0.443681			−0.221841	−	0.975083i	$-0.571206\pi$
$683$	−11.5953			−0.443681			−0.221841	+	0.975083i	$0.571206\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	10.4066	−	12.5669i	0.397036	−	0.479457i
$688$		0			0
$689$	5.64443	+	9.77644i	0.215036	+	0.372453i
$690$		0			0
$691$	−22.9238	+	39.7051i	−0.872061	+	1.51045i	−0.0122006	+	0.999926i	$0.503884\pi$
$691$	−22.9238	+	39.7051i	−0.872061	+	1.51045i	−0.859861	+	0.510529i	$0.829450\pi$
$692$		0			0
$693$	−37.8557	−	13.2243i	−1.43802	−	0.502350i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.43280	−	4.21373i	−0.0921489	−	0.159606i
$698$		0			0
$699$	−15.7883	−	42.5170i	−0.597167	−	1.60814i
$700$		0			0
$701$	−38.1115			−1.43945			−0.719726	−	0.694259i	$-0.755732\pi$
$701$	−38.1115			−1.43945			−0.719726	+	0.694259i	$0.755732\pi$
$702$		0			0
$703$	−6.13997			−0.231573
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.96406	−	15.5262i	−0.337128	−	0.583923i
$708$		0			0
$709$	1.14443	−	1.98222i	0.0429801	−	0.0744437i	−0.843735	−	0.536760i	$-0.819648\pi$
$709$	1.14443	−	1.98222i	0.0429801	−	0.0744437i	0.886715	+	0.462316i	$0.152981\pi$
$710$		0			0
$711$	−6.14794	−	32.4008i	−0.230566	−	1.21513i
$712$		0			0
$713$	−17.8731	+	30.9572i	−0.669355	+	1.15936i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	25.1386	−	30.3570i	0.938816	−	1.13370i
$718$		0			0
$719$	−16.6035			−0.619205			−0.309602	−	0.950866i	$-0.600196\pi$
$719$	−16.6035			−0.619205			−0.309602	+	0.950866i	$0.600196\pi$
$720$		0			0
$721$	−68.1891			−2.53949
$722$		0			0
$723$	28.3989	+	4.81761i	1.05617	+	0.179169i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−19.3037	+	33.4350i	−0.715934	+	1.24003i	0.246664	+	0.969101i	$0.420666\pi$
$727$	−19.3037	+	33.4350i	−0.715934	+	1.24003i	−0.962598	+	0.270933i	$0.912668\pi$
$728$		0			0
$729$	14.4004	+	22.8392i	0.533347	+	0.845897i
$730$		0			0
$731$	2.11150	−	3.65722i	0.0780966	−	0.135267i
$732$		0			0
$733$	16.9501	+	29.3584i	0.626066	+	1.08438i	0.988334	+	0.152305i	$0.0486695\pi$
$733$	16.9501	+	29.3584i	0.626066	+	1.08438i	−0.362267	+	0.932074i	$0.617997\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.3469			−0.381131
$738$		0			0
$739$	−36.8405			−1.35520			−0.677600	−	0.735431i	$-0.736980\pi$
$739$	−36.8405			−1.35520			−0.677600	+	0.735431i	$0.736980\pi$
$740$		0			0
$741$	7.99298	−	9.65223i	0.293629	−	0.354584i
$742$		0			0
$743$	5.71392	+	9.89680i	0.209623	+	0.363078i	0.951596	−	0.307352i	$-0.0994429\pi$
$743$	5.71392	+	9.89680i	0.209623	+	0.363078i	−0.741973	+	0.670430i	$0.766110\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.70192	+	30.0502i	0.208622	+	1.09948i
$748$		0			0
$749$	−6.81870	+	11.8103i	−0.249150	+	0.431541i
$750$		0			0
$751$	8.10155	+	14.0323i	0.295630	+	0.512046i	0.975131	−	0.221628i	$-0.0711372\pi$
$751$	8.10155	+	14.0323i	0.295630	+	0.512046i	−0.679501	+	0.733674i	$0.737804\pi$
$752$		0			0
$753$	12.5268	+	33.7340i	0.456502	+	1.22934i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−8.08698			−0.293926			−0.146963	−	0.989142i	$-0.546950\pi$
$757$	−8.08698			−0.293926			−0.146963	+	0.989142i	$0.546950\pi$
$758$		0			0
$759$	−13.2156	−	35.5888i	−0.479694	−	1.29179i
$760$		0			0
$761$	−10.7031	−	18.5383i	−0.387987	−	0.672014i	0.604191	−	0.796839i	$-0.293496\pi$
$761$	−10.7031	−	18.5383i	−0.387987	−	0.672014i	−0.992179	+	0.124826i	$0.960163\pi$
$762$		0			0
$763$	18.1647	−	31.4623i	0.657608	−	1.13901i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.84910	+	8.39889i	−0.175091	+	0.303266i
$768$		0			0
$769$	−25.7031	−	44.5191i	−0.926878	−	1.60540i	−0.788513	−	0.615018i	$-0.789149\pi$
$769$	−25.7031	−	44.5191i	−0.926878	−	1.60540i	−0.138364	−	0.990381i	$-0.544185\pi$
$770$		0			0
$771$	−21.0552	+	25.4260i	−0.758283	+	0.915695i
$772$		0			0
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.48179	−	0.929933i	−0.196658	−	0.0333612i
$778$		0			0
$779$	11.2425	+	19.4725i	0.402803	+	0.697676i
$780$		0			0
$781$	12.7828	−	22.1405i	0.457406	−	0.792251i
$782$		0			0
$783$	13.3456	−	8.05567i	0.476934	−	0.287886i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.35683	−	4.08216i	−0.0840121	−	0.145513i	0.820958	−	0.570989i	$-0.193440\pi$
$787$	−2.35683	−	4.08216i	−0.0840121	−	0.145513i	−0.904970	+	0.425476i	$0.860107\pi$
$788$		0			0
$789$	13.8969	+	2.35747i	0.494741	+	0.0839281i
$790$		0			0
$791$	−13.4132			−0.476920
$792$		0			0
$793$	8.23891			0.292572
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.13196	−	8.88882i	−0.181784	−	0.314858i	0.760704	−	0.649098i	$-0.224854\pi$
$797$	−5.13196	−	8.88882i	−0.181784	−	0.314858i	−0.942488	+	0.334240i	$0.891520\pi$
$798$		0			0
$799$	−7.60506	+	13.1724i	−0.269048	+	0.466005i
$800$		0			0
$801$	12.1275	−	10.4475i	0.428503	−	0.369143i
$802$		0			0
$803$	−29.7523	+	51.5324i	−1.04993	+	1.81854i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.4581	+	41.6278i	0.544150	+	1.46537i
$808$		0			0
$809$	21.9860			0.772985			0.386492	−	0.922293i	$-0.373687\pi$
$809$	21.9860			0.772985			0.386492	+	0.922293i	$0.373687\pi$
$810$		0			0
$811$	−25.6951			−0.902276			−0.451138	−	0.892454i	$-0.648982\pi$
$811$	−25.6951			−0.902276			−0.451138	+	0.892454i	$0.648982\pi$
$812$		0			0
$813$	1.93555	+	5.21233i	0.0678826	+	0.182805i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−9.75767	+	16.9008i	−0.341378	+	0.591284i
$818$		0			0
$819$	8.59804	−	7.40697i	0.300440	−	0.258820i
$820$		0			0
$821$	−12.1967	+	21.1253i	−0.425667	+	0.737276i	−0.996482	−	0.0838018i	$-0.973294\pi$
$821$	−12.1967	+	21.1253i	−0.425667	+	0.737276i	0.570816	+	0.821078i	$0.306627\pi$
$822$		0			0
$823$	−1.30710	−	2.26396i	−0.0455626	−	0.0789167i	0.842345	−	0.538939i	$-0.181175\pi$
$823$	−1.30710	−	2.26396i	−0.0455626	−	0.0789167i	−0.887907	+	0.460022i	$0.847841\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.0684725			−0.00238102			−0.00119051	−	0.999999i	$-0.500379\pi$
$827$	−0.0684725			−0.00238102			−0.00119051	+	0.999999i	$0.500379\pi$
$828$		0			0
$829$	−24.7828			−0.860744			−0.430372	−	0.902652i	$-0.641618\pi$
$829$	−24.7828			−0.860744			−0.430372	+	0.902652i	$0.641618\pi$
$830$		0			0
$831$	1.19475	+	0.202679i	0.0414455	+	0.00703084i
$832$		0			0
$833$	5.62471	+	9.74229i	0.194885	+	0.337550i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.585210	+	30.0429i	0.0202278	+	1.03843i
$838$		0			0
$839$	−22.6204	+	39.1797i	−0.780944	+	1.35264i	0.150448	+	0.988618i	$0.451928\pi$
$839$	−22.6204	+	39.1797i	−0.780944	+	1.35264i	−0.931392	+	0.364017i	$0.881405\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−52.3061	−	8.87323i	−1.80152	−	0.305610i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.92857			0.203708
$848$		0			0
$849$	−10.6115	+	12.8143i	−0.364186	+	0.439787i
$850$		0			0
$851$	−2.63198	−	4.55872i	−0.0902231	−	0.156271i
$852$		0			0
$853$	10.1075	−	17.5067i	0.346074	−	0.599418i	−0.639474	−	0.768813i	$-0.720848\pi$
$853$	10.1075	−	17.5067i	0.346074	−	0.599418i	0.985548	+	0.169395i	$0.0541812\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.4213	+	23.2464i	−0.458464	+	0.794083i	−0.998880	−	0.0473147i	$-0.984934\pi$
$857$	−13.4213	+	23.2464i	−0.458464	+	0.794083i	0.540416	+	0.841398i	$0.318267\pi$
$858$		0			0
$859$	−1.68130	−	2.91209i	−0.0573651	−	0.0993592i	0.835917	−	0.548856i	$-0.184937\pi$
$859$	−1.68130	−	2.91209i	−0.0573651	−	0.0993592i	−0.893282	+	0.449497i	$0.851603\pi$
$860$		0			0
$861$	7.08809	+	19.0879i	0.241562	+	0.650513i
$862$		0			0
$863$	18.4524			0.628126			0.314063	−	0.949402i	$-0.398310\pi$
$863$	18.4524			0.628126			0.314063	+	0.949402i	$0.398310\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	8.78239	+	23.6505i	0.298266	+	0.803214i
$868$		0			0
$869$	19.4895	+	33.7567i	0.661135	+	1.14512i
$870$		0			0
$871$	1.46414	−	2.53597i	0.0496106	−	0.0859281i
$872$		0			0
$873$	−2.15992	−	11.3832i	−0.0731022	−	0.385262i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.5993	+	20.0905i	0.391679	+	0.678408i	0.992671	−	0.120847i	$-0.0385611\pi$
$877$	11.5993	+	20.0905i	0.391679	+	0.678408i	−0.600992	+	0.799255i	$0.705228\pi$
$878$		0			0
$879$	−3.32573	+	4.01611i	−0.112174	+	0.135460i
$880$		0			0
$881$	2.34854			0.0791244			0.0395622	−	0.999217i	$-0.487404\pi$
$881$	2.34854			0.0791244			0.0395622	+	0.999217i	$0.487404\pi$
$882$		0			0
$883$	16.3264			0.549428			0.274714	−	0.961526i	$-0.411417\pi$
$883$	16.3264			0.549428			0.274714	+	0.961526i	$0.411417\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4213	−	23.2464i	−0.450645	−	0.780539i	0.547782	−	0.836621i	$-0.315472\pi$
$887$	−13.4213	−	23.2464i	−0.450645	−	0.780539i	−0.998426	+	0.0560821i	$0.982139\pi$
$888$		0			0
$889$	−12.7793	+	22.1345i	−0.428605	+	0.742366i
$890$		0			0
$891$	−24.9706	−	19.8711i	−0.836546	−	0.665707i
$892$		0			0
$893$	35.1446	−	60.8722i	1.17607	−	2.03701i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	10.5928	+	1.79696i	0.353682	+	0.0599987i
$898$		0			0
$899$	17.3485			0.578606
$900$		0			0
$901$	−17.5516			−0.584730
$902$		0			0
$903$	−11.2714	+	13.6112i	−0.375089	+	0.452953i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.92130	+	6.79188i	−0.130204	+	0.225521i	−0.923755	−	0.382983i	$-0.874897\pi$
$907$	−3.92130	+	6.79188i	−0.130204	+	0.225521i	0.793551	+	0.608504i	$0.208230\pi$
$908$		0			0
$909$	−2.65981	−	14.0177i	−0.0882203	−	0.464937i
$910$		0			0
$911$	−1.28636	+	2.22804i	−0.0426190	+	0.0738183i	−0.886548	−	0.462637i	$-0.846903\pi$
$911$	−1.28636	+	2.22804i	−0.0426190	+	0.0738183i	0.843929	+	0.536455i	$0.180237\pi$
$912$		0			0
$913$	−18.0755	−	31.3078i	−0.598213	−	1.03614i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.9196			−0.426642
$918$		0			0
$919$	42.4062			1.39885			0.699426	−	0.714705i	$-0.253439\pi$
$919$	42.4062			1.39885			0.699426	+	0.714705i	$0.253439\pi$
$920$		0			0
$921$	−8.96414	−	24.1400i	−0.295379	−	0.795440i
$922$		0			0
$923$	3.61770	+	6.26604i	0.119078	+	0.206249i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−51.2311	−	17.8968i	−1.68265	−	0.587807i
$928$		0			0
$929$	−25.9167	+	44.8891i	−0.850301	+	1.47276i	0.0306361	+	0.999531i	$0.490247\pi$
$929$	−25.9167	+	44.8891i	−0.850301	+	1.47276i	−0.880937	+	0.473234i	$0.843087\pi$
$930$		0			0
$931$	−25.9930	−	45.0212i	−0.851885	−	1.47551i
$932$		0			0
$933$	−3.39333	+	4.09775i	−0.111093	+	0.134154i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.9666			−0.554275			−0.277137	−	0.960830i	$-0.589386\pi$
$937$	−16.9666			−0.554275			−0.277137	+	0.960830i	$0.589386\pi$
$938$		0			0
$939$	−39.2992	−	6.66674i	−1.28248	−	0.217561i
$940$		0			0
$941$	−2.82865	−	4.89937i	−0.0922114	−	0.159715i	0.816230	−	0.577727i	$-0.196060\pi$
$941$	−2.82865	−	4.89937i	−0.0922114	−	0.159715i	−0.908441	+	0.418012i	$0.862727\pi$
$942$		0			0
$943$	−9.63847	+	16.6943i	−0.313872	+	0.543642i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.6930	+	30.6452i	−0.574945	+	0.995834i	0.421103	+	0.907013i	$0.361643\pi$
$947$	−17.6930	+	30.6452i	−0.574945	+	0.995834i	−0.996048	+	0.0888210i	$0.971690\pi$
$948$		0			0
$949$	−8.42026	−	14.5843i	−0.273333	−	0.473427i
$950$		0			0
$951$	−0.0153749	−	0.00260821i	−0.000498566	−	8.45770e-5i
$952$		0			0
$953$	−1.66116			−0.0538101			−0.0269051	−	0.999638i	$-0.508565\pi$
$953$	−1.66116			−0.0538101			−0.0269051	+	0.999638i	$0.508565\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−11.7512	+	14.1906i	−0.379862	+	0.458717i
$958$		0			0
$959$	−28.1339	−	48.7293i	−0.908491	−	1.57355i
$960$		0			0
$961$	−1.22066	+	2.11425i	−0.0393763	+	0.0682017i
$962$		0			0
$963$	−8.22268	+	7.08360i	−0.264972	+	0.228266i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.3681	−	17.9581i	−0.333416	−	0.577494i	0.649763	−	0.760137i	$-0.274868\pi$
$967$	−10.3681	−	17.9581i	−0.333416	−	0.577494i	−0.983179	+	0.182643i	$0.941535\pi$
$968$		0			0
$969$	6.78285	+	18.2659i	0.217896	+	0.586784i
$970$		0			0
$971$	20.9193			0.671331			0.335665	−	0.941981i	$-0.391039\pi$
$971$	20.9193			0.671331			0.335665	+	0.941981i	$0.391039\pi$
$972$		0			0
$973$	−20.4589			−0.655881
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.44579	−	2.50418i	−0.0462549	−	0.0801159i	0.841971	−	0.539523i	$-0.181395\pi$
$977$	−1.44579	−	2.50418i	−0.0462549	−	0.0801159i	−0.888226	+	0.459407i	$0.848062\pi$
$978$		0			0
$979$	−9.45963	+	16.3846i	−0.302331	+	0.523653i
$980$		0			0
$981$	21.9049	−	18.8704i	0.699369	−	0.602486i
$982$		0			0
$983$	−3.15019	+	5.45628i	−0.100475	+	0.174028i	−0.911881	−	0.410456i	$-0.865370\pi$
$983$	−3.15019	+	5.45628i	−0.100475	+	0.174028i	0.811405	+	0.584484i	$0.198703\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	40.5966	−	49.0241i	1.29221	−	1.56045i
$988$		0			0
$989$	−16.7310			−0.532016
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	15.3569	+	2.60515i	0.487336	+	0.0826719i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.78963	+	8.29589i	−0.151689	+	0.262733i	−0.931849	−	0.362847i	$-0.881805\pi$
$997$	−4.78963	+	8.29589i	−0.151689	+	0.262733i	0.780159	+	0.625581i	$0.215138\pi$
$998$		0			0
$999$	−3.87445	−	2.13741i	−0.122582	−	0.0676246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.i.f.601.3		12
3.2	odd	2		2700.2.i.f.1801.1		12
5.2	odd	4		180.2.r.a.169.1	yes	12
5.3	odd	4		180.2.r.a.169.6	yes	12
5.4	even	2	inner	900.2.i.f.601.4		12
9.2	odd	6		8100.2.a.bd.1.6		6
9.4	even	3	inner	900.2.i.f.301.3		12
9.5	odd	6		2700.2.i.f.901.1		12
9.7	even	3		8100.2.a.bc.1.6		6
15.2	even	4		540.2.r.a.289.4		12
15.8	even	4		540.2.r.a.289.6		12
15.14	odd	2		2700.2.i.f.1801.6		12
20.3	even	4		720.2.by.e.529.1		12
20.7	even	4		720.2.by.e.529.6		12
45.2	even	12		1620.2.d.d.649.1		6
45.4	even	6	inner	900.2.i.f.301.4		12
45.7	odd	12		1620.2.d.c.649.6		6
45.13	odd	12		180.2.r.a.49.1	✓	12
45.14	odd	6		2700.2.i.f.901.6		12
45.22	odd	12		180.2.r.a.49.6	yes	12
45.23	even	12		540.2.r.a.469.4		12
45.29	odd	6		8100.2.a.bd.1.1		6
45.32	even	12		540.2.r.a.469.6		12
45.34	even	6		8100.2.a.bc.1.1		6
45.38	even	12		1620.2.d.d.649.2		6
45.43	odd	12		1620.2.d.c.649.5		6
60.23	odd	4		2160.2.by.e.289.6		12
60.47	odd	4		2160.2.by.e.289.4		12
180.23	odd	12		2160.2.by.e.1009.4		12
180.67	even	12		720.2.by.e.49.1		12
180.103	even	12		720.2.by.e.49.6		12
180.167	odd	12		2160.2.by.e.1009.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.r.a.49.1	✓	12	45.13	odd	12
180.2.r.a.49.6	yes	12	45.22	odd	12
180.2.r.a.169.1	yes	12	5.2	odd	4
180.2.r.a.169.6	yes	12	5.3	odd	4
540.2.r.a.289.4		12	15.2	even	4
540.2.r.a.289.6		12	15.8	even	4
540.2.r.a.469.4		12	45.23	even	12
540.2.r.a.469.6		12	45.32	even	12
720.2.by.e.49.1		12	180.67	even	12
720.2.by.e.49.6		12	180.103	even	12
720.2.by.e.529.1		12	20.3	even	4
720.2.by.e.529.6		12	20.7	even	4
900.2.i.f.301.3		12	9.4	even	3	inner
900.2.i.f.301.4		12	45.4	even	6	inner
900.2.i.f.601.3		12	1.1	even	1	trivial
900.2.i.f.601.4		12	5.4	even	2	inner
1620.2.d.c.649.5		6	45.43	odd	12
1620.2.d.c.649.6		6	45.7	odd	12
1620.2.d.d.649.1		6	45.2	even	12
1620.2.d.d.649.2		6	45.38	even	12
2160.2.by.e.289.4		12	60.47	odd	4
2160.2.by.e.289.6		12	60.23	odd	4
2160.2.by.e.1009.4		12	180.23	odd	12
2160.2.by.e.1009.6		12	180.167	odd	12
2700.2.i.f.901.1		12	9.5	odd	6
2700.2.i.f.901.6		12	45.14	odd	6
2700.2.i.f.1801.1		12	3.2	odd	2
2700.2.i.f.1801.6		12	15.14	odd	2
8100.2.a.bc.1.1		6	45.34	even	6
8100.2.a.bc.1.6		6	9.7	even	3
8100.2.a.bd.1.1		6	45.29	odd	6
8100.2.a.bd.1.6		6	9.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.602950 - 1.62372i) q^{3} +(-1.88482 + 3.26460i) q^{7} +(-2.27290 + 1.95804i) q^{9} +(1.77290 - 3.07076i) q^{11} +(0.501753 + 0.869061i) q^{13} -1.56023 q^{17} +7.21013 q^{19} +(6.43723 + 1.09201i) q^{21} +(3.09072 + 5.35328i) q^{23} +(4.54975 + 2.50994i) q^{27} +(1.50000 - 2.59808i) q^{29} +(2.89142 + 5.00809i) q^{31} +(-6.05500 - 1.02717i) q^{33} -0.851576 q^{37} +(1.10858 - 1.33870i) q^{39} +(1.55926 + 2.70072i) q^{41} +(-1.35333 + 2.34403i) q^{43} +(4.87434 - 8.44260i) q^{47} +(-3.60506 - 6.24415i) q^{49} +(0.940739 + 2.53336i) q^{51} +11.2494 q^{53} +(-4.34735 - 11.7072i) q^{57} +(4.83216 + 8.36955i) q^{59} +(4.10506 - 7.11018i) q^{61} +(-2.10821 - 11.1107i) q^{63} +(-1.45903 - 2.52711i) q^{67} +(6.82865 - 8.24621i) q^{69} +7.21013 q^{71} -16.7817 q^{73} +(6.68319 + 11.5756i) q^{77} +(-5.49649 + 9.52020i) q^{79} +(1.33216 - 8.90086i) q^{81} +(5.09773 - 8.82952i) q^{83} +(-5.12296 - 0.869061i) q^{87} -5.33567 q^{89} -3.78285 q^{91} +(6.38833 - 7.71448i) q^{93} +(-1.93105 + 3.34467i) q^{97} +(1.98303 + 10.4509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{9} + 2 q^{11} + 10 q^{21} + 18 q^{29} + 6 q^{31} + 42 q^{39} + 14 q^{41} + 16 q^{51} + 34 q^{59} + 6 q^{61} - 14 q^{69} + 6 q^{79} - 8 q^{81} - 112 q^{89} + 12 q^{91} - 82 q^{99}+O(q^{100}) \) 12 * q - 8 * q^9 + 2 * q^11 + 10 * q^21 + 18 * q^29 + 6 * q^31 + 42 * q^39 + 14 * q^41 + 16 * q^51 + 34 * q^59 + 6 * q^61 - 14 * q^69 + 6 * q^79 - 8 * q^81 - 112 * q^89 + 12 * q^91 - 82 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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