LMFDB - Embedded newform 225.2.k.b.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-1.50511 - 0.403293i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.2.k.b.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +O(q^{10})$	\(q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +(-1.33641 - 2.31473i) q^{11} +(-1.01450 + 2.71400i) q^{12} +(4.04678 + 2.33641i) q^{13} +(0.408405 - 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} +2.67282i q^{17} +(1.12559 - 1.29523i) q^{18} -4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(-1.32401 - 0.764419i) q^{22} +(-5.12483 - 2.95882i) q^{23} +(0.600830 + 3.58880i) q^{24} +2.67282 q^{26} +(4.56592 - 2.48040i) q^{27} +2.38880i q^{28} +(-4.74482 - 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(-4.70079 - 2.71400i) q^{32} +(-2.94497 - 3.57199i) q^{33} +(0.764419 + 1.32401i) q^{34} +(-0.956844 + 4.92641i) q^{36} -1.81681i q^{37} +(-2.31473 + 1.33641i) q^{38} +(7.58123 + 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(0.495361 - 1.32520i) q^{42} +(-0.408039 + 0.235581i) q^{43} +4.47116 q^{44} -3.38485 q^{46} +(6.02480 - 3.47842i) q^{47} +(-2.36228 - 2.86525i) q^{48} +(-2.48040 + 4.29618i) q^{49} +(0.764419 + 4.56592i) q^{51} +(-6.76956 + 3.90841i) q^{52} +1.14399i q^{53} +(1.55239 - 2.53453i) q^{54} +(1.50000 + 2.59808i) q^{56} +(-7.98247 + 1.33641i) q^{57} +(-4.70079 - 2.71400i) q^{58} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +3.98153i q^{62} +(2.81009 - 3.23360i) q^{63} +1.18319 q^{64} +(-2.48040 - 0.927175i) q^{66} +(5.70751 + 3.29523i) q^{67} +(-3.87214 - 2.23558i) q^{68} +(-9.60083 - 3.58880i) q^{69} -12.8745 q^{71} +(2.05277 + 5.95882i) q^{72} +1.71203i q^{73} +(-0.519602 - 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(-3.30545 - 1.90841i) q^{77} +(4.56592 - 0.764419i) q^{78} +(-0.143987 - 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} -0.841495i q^{82} +(3.71007 - 2.14201i) q^{83} +(0.683190 + 4.08074i) q^{84} +(-0.134751 + 0.233396i) q^{86} +(-10.4559 - 12.6821i) q^{87} +(4.86286 - 2.80757i) q^{88} +3.00000 q^{89} +6.67282 q^{91} +(8.57293 - 4.94958i) q^{92} +(-4.22143 + 11.2933i) q^{93} +(1.98963 - 3.44615i) q^{94} +(-8.80644 - 3.29186i) q^{96} +(6.78555 - 3.91764i) q^{97} +2.83754i q^{98} +(-6.05239 - 5.25970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9	$ 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.495361	−	0.285997i	0.350273	−	0.202230i	−0.314533	−	0.949247i	$-0.601848\pi$
$2$	0.495361	−	0.285997i	0.350273	−	0.202230i	0.664805	+	0.747017i	$0.268514\pi$
$3$	1.70828	−	0.285997i	0.986273	−	0.165120i
$3$	1.70828	−	0.285997i	0.986273	−	0.165120i
$4$	−0.836412	+	1.44871i	−0.418206	+	0.724354i
$5$		0			0
$5$		0			0
$6$	0.764419	−	0.630233i	0.312073	−	0.257291i
$7$	1.23669	−	0.714003i	0.467425	−	0.269868i	−0.247736	−	0.968828i	$-0.579687\pi$
$7$	1.23669	−	0.714003i	0.467425	−	0.269868i	0.715161	+	0.698960i	$0.246353\pi$
$8$			2.10083i			0.742756i
$9$	2.83641	−	0.977122i	0.945471	−	0.325707i
$10$		0			0
$11$	−1.33641	−	2.31473i	−0.402943	−	0.697918i	0.591136	−	0.806572i	$-0.298679\pi$
$11$	−1.33641	−	2.31473i	−0.402943	−	0.697918i	−0.994080	+	0.108653i	$0.965346\pi$
$12$	−1.01450	+	2.71400i	−0.292860	+	0.783465i
$13$	4.04678	+	2.33641i	1.12238	+	0.648004i	0.942006	−	0.335595i	$-0.108937\pi$
$13$	4.04678	+	2.33641i	1.12238	+	0.648004i	0.180370	+	0.983599i	$0.442271\pi$
$14$	0.408405	−	0.707378i	0.109151	−	0.189055i
$15$		0			0
$16$	−1.07199	−	1.85675i	−0.267998	−	0.464187i
$17$			2.67282i			0.648255i	0.946013	+	0.324127i	$0.105071\pi$
$17$			2.67282i			0.648255i	−0.946013	+	0.324127i	$0.894929\pi$
$18$	1.12559	−	1.29523i	0.265305	−	0.305289i
$19$	−4.67282			−1.07202			−0.536010	−	0.844212i	$-0.680069\pi$
$19$	−4.67282			−1.07202			−0.536010	+	0.844212i	$0.680069\pi$
$20$		0			0
$21$	1.90841	−	1.57340i	0.416448	−	0.343345i
$22$	−1.32401	−	0.764419i	−0.282280	−	0.162975i
$23$	−5.12483	−	2.95882i	−1.06860	−	0.616957i	−0.140802	−	0.990038i	$-0.544968\pi$
$23$	−5.12483	−	2.95882i	−1.06860	−	0.616957i	−0.927799	+	0.373081i	$0.878301\pi$
$24$	0.600830	+	3.58880i	0.122644	+	0.732560i
$25$		0			0
$26$	2.67282			0.524184
$27$	4.56592	−	2.48040i	0.878712	−	0.477353i
$28$			2.38880i			0.451441i
$29$	−4.74482	−	8.21826i	−0.881090	−	1.52609i	−0.850130	−	0.526573i	$-0.823477\pi$
$29$	−4.74482	−	8.21826i	−0.881090	−	1.52609i	−0.0309603	−	0.999521i	$-0.509857\pi$
$30$		0			0
$31$	−3.48040	+	6.02823i	−0.625098	+	1.08270i	0.363424	+	0.931624i	$0.381608\pi$
$31$	−3.48040	+	6.02823i	−0.625098	+	1.08270i	−0.988522	+	0.151078i	$0.951726\pi$
$32$	−4.70079	−	2.71400i	−0.830990	−	0.479773i
$33$	−2.94497	−	3.57199i	−0.512653	−	0.621804i
$34$	0.764419	+	1.32401i	0.131097	+	0.227066i
$35$		0			0
$36$	−0.956844	+	4.92641i	−0.159474	+	0.821068i
$37$		−	1.81681i		−	0.298682i	−0.988786	−	0.149341i	$-0.952285\pi$
$37$		−	1.81681i		−	0.298682i	0.988786	−	0.149341i	$-0.0477152\pi$
$38$	−2.31473	+	1.33641i	−0.375499	+	0.216795i
$39$	7.58123	+	2.83387i	1.21397	+	0.453782i
$40$		0			0
$41$	0.735581	−	1.27406i	0.114879	−	0.198975i	−0.802853	−	0.596177i	$-0.796685\pi$
$41$	0.735581	−	1.27406i	0.114879	−	0.198975i	0.917731	+	0.397202i	$0.130019\pi$
$42$	0.495361	−	1.32520i	0.0764358	−	0.204483i
$43$	−0.408039	+	0.235581i	−0.0622254	+	0.0359258i	−0.530790	−	0.847503i	$-0.678105\pi$
$43$	−0.408039	+	0.235581i	−0.0622254	+	0.0359258i	0.468565	+	0.883429i	$0.344771\pi$
$44$	4.47116			0.674053
$45$		0			0
$46$	−3.38485			−0.499069
$47$	6.02480	−	3.47842i	0.878808	−	0.507380i	0.00854274	−	0.999964i	$-0.497281\pi$
$47$	6.02480	−	3.47842i	0.878808	−	0.507380i	0.870265	+	0.492584i	$0.163947\pi$
$48$	−2.36228	−	2.86525i	−0.340966	−	0.413563i
$49$	−2.48040	+	4.29618i	−0.354343	+	0.613739i
$50$		0			0
$51$	0.764419	+	4.56592i	0.107040	+	0.639357i
$52$	−6.76956	+	3.90841i	−0.938769	+	0.541998i
$53$			1.14399i			0.157139i	0.996909	+	0.0785693i	$0.0250352\pi$
$53$			1.14399i			0.157139i	−0.996909	+	0.0785693i	$0.974965\pi$
$54$	1.55239	−	2.53453i	0.211254	−	0.344906i
$55$		0			0
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	−7.98247	+	1.33641i	−1.05730	+	0.177012i
$58$	−4.70079	−	2.71400i	−0.617244	−	0.356366i
$59$	−0.571993	+	0.990721i	−0.0744672	+	0.128981i	−0.900854	−	0.434121i	$-0.857059\pi$
$59$	−0.571993	+	0.990721i	−0.0744672	+	0.128981i	0.826387	+	0.563102i	$0.190392\pi$
$60$		0			0
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	0.935547	−	0.353201i	$-0.114907\pi$
$61$	1.26442	+	2.19004i	0.161892	+	0.280406i	−0.773655	+	0.633607i	$0.781574\pi$
$62$			3.98153i			0.505655i
$63$	2.81009	−	3.23360i	0.354039	−	0.407396i
$64$	1.18319			0.147899
$65$		0			0
$66$	−2.48040	−	0.927175i	−0.305316	−	0.114127i
$67$	5.70751	+	3.29523i	0.697283	+	0.402577i	0.806335	−	0.591459i	$-0.201448\pi$
$67$	5.70751	+	3.29523i	0.697283	+	0.402577i	−0.109051	+	0.994036i	$0.534781\pi$
$68$	−3.87214	−	2.23558i	−0.469566	−	0.271104i
$69$	−9.60083	−	3.58880i	−1.15580	−	0.432040i
$70$		0			0
$71$	−12.8745			−1.52792			−0.763960	−	0.645263i	$-0.776748\pi$
$71$	−12.8745			−1.52792			−0.763960	+	0.645263i	$0.776748\pi$
$72$	2.05277	+	5.95882i	0.241921	+	0.702254i
$73$			1.71203i			0.200378i	0.994968	+	0.100189i	$0.0319447\pi$
$73$			1.71203i			0.200378i	−0.994968	+	0.100189i	$0.968055\pi$
$74$	−0.519602	−	0.899976i	−0.0604025	−	0.104620i
$75$		0			0
$76$	3.90841	−	6.76956i	0.448325	−	0.776521i
$77$	−3.30545	−	1.90841i	−0.376692	−	0.217483i
$78$	4.56592	−	0.764419i	0.516989	−	0.0865534i
$79$	−0.143987	−	0.249392i	−0.0161998	−	0.0280588i	0.857812	−	0.513964i	$-0.171823\pi$
$79$	−0.143987	−	0.249392i	−0.0161998	−	0.0280588i	−0.874012	+	0.485905i	$0.838490\pi$
$80$		0			0
$81$	7.09046	−	5.54304i	0.787829	−	0.615894i
$82$		−	0.841495i		−	0.0929276i
$83$	3.71007	−	2.14201i	0.407233	−	0.235116i	−0.282367	−	0.959306i	$-0.591120\pi$
$83$	3.71007	−	2.14201i	0.407233	−	0.235116i	0.689600	+	0.724190i	$0.257786\pi$
$84$	0.683190	+	4.08074i	0.0745421	+	0.445245i
$85$		0			0
$86$	−0.134751	+	0.233396i	−0.0145306	+	0.0251677i
$87$	−10.4559	−	12.6821i	−1.12098	−	1.35966i
$88$	4.86286	−	2.80757i	0.518383	−	0.299288i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	6.67282			0.699502
$92$	8.57293	−	4.94958i	0.893790	−	0.516030i
$93$	−4.22143	+	11.2933i	−0.437742	+	1.17106i
$94$	1.98963	−	3.44615i	0.205215	−	0.355443i
$95$		0			0
$96$	−8.80644	−	3.29186i	−0.898804	−	0.335974i
$97$	6.78555	−	3.91764i	0.688968	−	0.397776i	−0.114257	−	0.993451i	$-0.536449\pi$
$97$	6.78555	−	3.91764i	0.688968	−	0.397776i	0.803225	+	0.595675i	$0.203115\pi$
$98$			2.83754i			0.286635i
$99$	−6.05239	−	5.25970i	−0.608288	−	0.528620i
$100$		0			0
$101$	2.10083	+	3.63875i	0.209040	+	0.362069i	0.951413	−	0.307919i	$-0.0996326\pi$
$101$	2.10083	+	3.63875i	0.209040	+	0.362069i	−0.742372	+	0.669988i	$0.766299\pi$
$102$	1.68450	+	2.04316i	0.166790	+	0.202303i
$103$	−1.57340	−	0.908405i	−0.155032	−	0.0895078i	0.420477	−	0.907303i	$-0.361863\pi$
$103$	−1.57340	−	0.908405i	−0.155032	−	0.0895078i	−0.575509	+	0.817795i	$0.695196\pi$
$104$	−4.90841	+	8.50161i	−0.481309	+	0.833651i
$105$		0			0
$106$	0.327176	+	0.566686i	0.0317782	+	0.0550414i
$107$			11.9176i			1.15212i	0.817407	+	0.576061i	$0.195411\pi$
$107$			11.9176i			1.15212i	−0.817407	+	0.576061i	$0.804589\pi$
$108$	−0.225617	+	8.68932i	−0.0217100	+	0.836130i
$109$	16.6521			1.59498			0.797491	−	0.603331i	$-0.206160\pi$
$109$	16.6521			1.59498			0.797491	+	0.603331i	$0.206160\pi$
$110$		0			0
$111$	−0.519602	−	3.10361i	−0.0493184	−	0.294582i
$112$	−2.65145	−	1.53081i	−0.250538	−	0.144648i
$113$	17.4272	+	10.0616i	1.63942	+	0.946518i	0.981034	+	0.193836i	$0.0620929\pi$
$113$	17.4272	+	10.0616i	1.63942	+	0.946518i	0.658384	+	0.752682i	$0.271240\pi$
$114$	−3.57199	+	2.94497i	−0.334548	+	0.275821i
$115$		0			0
$116$	15.8745			1.47391
$117$	13.7613	+	2.67282i	1.27223	+	0.247103i
$118$			0.654353i			0.0602380i
$119$	1.90841	+	3.30545i	0.174943	+	0.303011i
$120$		0			0
$121$	1.92801	−	3.33941i	0.175273	−	0.303582i
$122$	1.25269	+	0.723239i	0.113413	+	0.0654790i
$123$	0.892198	−	2.38683i	0.0804468	−	0.215213i
$124$	−5.82209	−	10.0842i	−0.522839	−	0.905584i
$125$		0			0
$126$	0.467210	−	2.40548i	0.0416224	−	0.214297i
$127$			2.18714i			0.194078i	0.995281	+	0.0970388i	$0.0309371\pi$
$127$			2.18714i			0.194078i	−0.995281	+	0.0970388i	$0.969063\pi$
$128$	9.98769	−	5.76640i	0.882795	−	0.509682i
$129$	−0.629668	+	0.519136i	−0.0554391	+	0.0457074i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	7.63798	−	1.27874i	0.664801	−	0.111300i
$133$	−5.77883	+	3.33641i	−0.501089	+	0.289304i
$134$	3.76970			0.325653
$135$		0			0
$136$	−5.61515			−0.481495
$137$	−8.83490	+	5.10083i	−0.754816	+	0.435793i	−0.827431	−	0.561567i	$-0.810199\pi$
$137$	−8.83490	+	5.10083i	−0.754816	+	0.435793i	0.0726153	+	0.997360i	$0.476865\pi$
$138$	−5.78226	+	0.968056i	−0.492218	+	0.0824064i
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		0			0
$141$	9.29721	−	7.66518i	0.782966	−	0.645524i
$142$	−6.37751	+	3.68206i	−0.535189	+	0.308992i
$143$		−	12.4896i		−	1.04444i
$144$	−4.85488	−	4.21903i	−0.404574	−	0.351586i
$145$		0			0
$146$	0.489634	+	0.848071i	0.0405224	+	0.0701868i
$147$	−3.00851	+	8.04844i	−0.248138	+	0.663824i
$148$	2.63203	+	1.51960i	0.216351	+	0.124910i
$149$	−10.0381	+	17.3865i	−0.822351	+	1.42435i	0.0815762	+	0.996667i	$0.474005\pi$
$149$	−10.0381	+	17.3865i	−0.822351	+	1.42435i	−0.903927	+	0.427687i	$0.859329\pi$
$150$		0			0
$151$	−1.51960	−	2.63203i	−0.123663	−	0.214191i	0.797546	−	0.603258i	$-0.206131\pi$
$151$	−1.51960	−	2.63203i	−0.123663	−	0.214191i	−0.921210	+	0.389066i	$0.872798\pi$
$152$		−	9.81681i		−	0.796248i
$153$	2.61168	+	7.58123i	0.211141	+	0.612906i
$154$	−2.18319			−0.175926
$155$		0			0
$156$	−10.4465	+	8.61270i	−0.836388	+	0.689568i
$157$	−0.174643	−	0.100830i	−0.0139381	−	0.00804714i	0.493015	−	0.870021i	$-0.335895\pi$
$157$	−0.174643	−	0.100830i	−0.0139381	−	0.00804714i	−0.506953	+	0.861974i	$0.669228\pi$
$158$	−0.142651	−	0.0823593i	−0.0113487	−	0.00655216i
$159$	0.327176	+	1.95424i	0.0259468	+	0.154982i
$160$		0			0
$161$	−8.45043			−0.665987
$162$	1.92705	−	4.77365i	0.151403	−	0.375054i
$163$		−	17.8168i		−	1.39552i	−0.716331	−	0.697760i	$-0.754180\pi$
$163$		−	17.8168i		−	1.39552i	0.716331	−	0.697760i	$-0.245820\pi$
$164$	1.23050	+	2.13129i	0.0960858	+	0.166425i
$165$		0			0
$166$	1.22522	−	2.12214i	0.0950952	−	0.164710i
$167$	−12.2117	−	7.05042i	−0.944968	−	0.545578i	−0.0534538	−	0.998570i	$-0.517023\pi$
$167$	−12.2117	−	7.05042i	−0.944968	−	0.545578i	−0.891514	+	0.452993i	$0.850356\pi$
$168$	3.30545	+	4.00924i	0.255021	+	0.309319i
$169$	4.41764	+	7.65158i	0.339819	+	0.588583i
$170$		0			0
$171$	−13.2541	+	4.56592i	−1.01356	+	0.349165i
$172$		−	0.788172i		−	0.0600976i
$173$	−3.78140	+	2.18319i	−0.287494	+	0.165985i	−0.636811	−	0.771020i	$-0.719747\pi$
$173$	−3.78140	+	2.18319i	−0.287494	+	0.165985i	0.349317	+	0.937005i	$0.386414\pi$
$174$	−8.80644	−	3.29186i	−0.667615	−	0.249555i
$175$		0			0
$176$	−2.86525	+	4.96276i	−0.215976	+	0.374082i
$177$	−0.693779	+	1.85601i	−0.0521476	+	0.139507i
$178$	1.48608	−	0.857990i	0.111387	−	0.0643091i
$179$	15.1625			1.13330			0.566648	−	0.823960i	$-0.308240\pi$
$179$	15.1625			1.13330			0.566648	+	0.823960i	$0.308240\pi$
$180$		0			0
$181$	3.20166			0.237978			0.118989	−	0.992896i	$-0.462035\pi$
$181$	3.20166			0.237978			0.118989	+	0.992896i	$0.462035\pi$
$182$	3.30545	−	1.90841i	0.245017	−	0.141460i
$183$	2.78632	+	3.37957i	0.205971	+	0.249825i
$184$	6.21598	−	10.7664i	0.458248	−	0.793709i
$185$		0			0
$186$	1.13870	+	6.80155i	0.0834938	+	0.498714i
$187$	6.18687	−	3.57199i	0.452429	−	0.261210i
$188$			11.6376i			0.848757i
$189$	3.87562	−	6.32757i	0.281910	−	0.460263i
$190$		0			0
$191$	1.41877	+	2.45738i	0.102659	+	0.177810i	0.912779	−	0.408453i	$-0.133932\pi$
$191$	1.41877	+	2.45738i	0.102659	+	0.177810i	−0.810121	+	0.586263i	$0.800598\pi$
$192$	2.02121	−	0.338388i	0.145869	−	0.0244211i
$193$	−16.2710	−	9.39409i	−1.17121	−	0.676201i	−0.217249	−	0.976116i	$-0.569708\pi$
$193$	−16.2710	−	9.39409i	−1.17121	−	0.676201i	−0.953966	+	0.299915i	$0.903042\pi$
$194$	2.24086	−	3.88129i	0.160885	−	0.278660i
$195$		0			0
$196$	−4.14927	−	7.18675i	−0.296376	−	0.513339i
$197$			5.83528i			0.415747i	0.978156	+	0.207873i	$0.0666542\pi$
$197$			5.83528i			0.415747i	−0.978156	+	0.207873i	$0.933346\pi$
$198$	−4.50237	−	0.874485i	−0.319970	−	0.0621469i
$199$	−13.0761			−0.926943			−0.463472	−	0.886112i	$-0.653396\pi$
$199$	−13.0761			−0.926943			−0.463472	+	0.886112i	$0.653396\pi$
$200$		0			0
$201$	10.6924	+	3.99684i	0.754186	+	0.281915i
$202$	2.08134	+	1.20166i	0.146442	+	0.0845486i
$203$	−11.7357	−	6.77563i	−0.823687	−	0.475556i
$204$	−7.25405	−	2.71157i	−0.507885	−	0.189848i
$205$		0			0
$206$	−1.03920			−0.0724047
$207$	−17.4272	−	3.38485i	−1.21128	−	0.235263i
$208$		−	10.0185i		−	0.694656i
$209$	6.24482	+	10.8163i	0.431963	+	0.748182i
$210$		0			0
$211$	−4.19243	+	7.26149i	−0.288618	+	0.499902i	−0.973480	−	0.228771i	$-0.926529\pi$
$211$	−4.19243	+	7.26149i	−0.288618	+	0.499902i	0.684862	+	0.728673i	$0.259863\pi$
$212$	−1.65730	−	0.956844i	−0.113824	−	0.0657163i
$213$	−21.9932	+	3.68206i	−1.50695	+	0.252291i
$214$	3.40841	+	5.90353i	0.232994	+	0.403557i
$215$		0			0
$216$	5.21090	+	9.59222i	0.354557	+	0.652668i
$217$			9.94006i			0.674776i
$218$	8.24879	−	4.76244i	0.558679	−	0.322553i
$219$	0.489634	+	2.92461i	0.0330864	+	0.197627i
$220$		0			0
$221$	−6.24482	+	10.8163i	−0.420072	+	0.727586i
$222$	−1.14501	−	1.38880i	−0.0768482	−	0.0932104i
$223$	−7.93834	+	4.58321i	−0.531591	+	0.306914i	−0.741664	−	0.670772i	$-0.765963\pi$
$223$	−7.93834	+	4.58321i	−0.531591	+	0.306914i	0.210073	+	0.977686i	$0.432630\pi$
$224$	−7.75123			−0.517901
$225$		0			0
$226$	11.5104			0.765658
$227$	−2.31473	+	1.33641i	−0.153634	+	0.0887008i	−0.574846	−	0.818261i	$-0.694938\pi$
$227$	−2.31473	+	1.33641i	−0.153634	+	0.0887008i	0.421212	+	0.906962i	$0.361605\pi$
$228$	4.74056	−	12.6821i	0.313951	−	0.839890i
$229$	1.27365	−	2.20603i	0.0841654	−	0.145779i	−0.820870	−	0.571115i	$-0.806511\pi$
$229$	1.27365	−	2.20603i	0.0841654	−	0.145779i	0.905035	+	0.425336i	$0.139844\pi$
$230$		0			0
$231$	−6.19243	−	2.31473i	−0.407432	−	0.152298i
$232$	17.2652	−	9.96806i	1.13351	−	0.654435i
$233$			6.22013i			0.407494i	0.979024	+	0.203747i	$0.0653121\pi$
$233$			6.22013i			0.407494i	−0.979024	+	0.203747i	$0.934688\pi$
$234$	7.58123	−	2.61168i	0.495600	−	0.170731i
$235$		0			0
$236$	−0.956844	−	1.65730i	−0.0622852	−	0.107881i
$237$	−0.317294	−	0.384851i	−0.0206105	−	0.0249987i
$238$	1.89070	+	1.09159i	0.122556	+	0.0707576i
$239$	4.06163	−	7.03494i	0.262725	−	0.455053i	−0.704240	−	0.709962i	$-0.748712\pi$
$239$	4.06163	−	7.03494i	0.262725	−	0.455053i	0.966965	+	0.254909i	$0.0820455\pi$
$240$		0			0
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	0.881985	+	0.471278i	$0.156207\pi$
$241$	13.1821	+	22.8320i	0.849131	+	1.47074i	−0.0328536	+	0.999460i	$0.510460\pi$
$242$		−	2.20561i		−	0.141782i
$243$	10.5272	−	11.4969i	0.675319	−	0.737526i
$244$	−4.23030			−0.270817
$245$		0			0
$246$	−0.240665	−	1.43751i	−0.0153442	−	0.0916520i
$247$	−18.9099	−	10.9176i	−1.20321	−	0.694673i
$248$	−12.6643	−	7.31173i	−0.804183	−	0.464295i
$249$	5.72522	−	4.72021i	0.362821	−	0.299131i
$250$		0			0
$251$	−0.549569			−0.0346885			−0.0173443	−	0.999850i	$-0.505521\pi$
$251$	−0.549569			−0.0346885			−0.0173443	+	0.999850i	$0.505521\pi$
$252$	2.33415	+	6.77563i	0.147038	+	0.426825i
$253$			15.8168i			0.994394i
$254$	0.625515	+	1.08342i	0.0392483	+	0.0679801i
$255$		0			0
$256$	2.11515	−	3.66355i	0.132197	−	0.228972i
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.899961	−	0.435970i	$-0.143595\pi$
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.0724199	+	0.997374i	$0.476928\pi$
$258$	−0.163441	+	0.437242i	−0.0101754	+	0.0272215i
$259$	−1.29721	−	2.24683i	−0.0806046	−	0.139611i
$260$		0			0
$261$	−21.4885	−	18.6741i	−1.33010	−	1.15590i
$262$		−	3.43196i		−	0.212027i
$263$	−10.3016	+	5.94761i	−0.635221	+	0.366745i	−0.782771	−	0.622309i	$-0.786195\pi$
$263$	−10.3016	+	5.94761i	−0.635221	+	0.366745i	0.147550	+	0.989055i	$0.452861\pi$
$264$	7.50415	−	6.18687i	0.461849	−	0.380776i
$265$		0			0
$266$	−1.90841	+	3.30545i	−0.117012	+	0.202670i
$267$	5.12483	−	0.857990i	0.313634	−	0.0525081i
$268$	−9.54766	+	5.51234i	−0.583216	+	0.336720i
$269$	−28.5737			−1.74217			−0.871084	−	0.491134i	$-0.836583\pi$
$269$	−28.5737			−1.74217			−0.871084	+	0.491134i	$0.836583\pi$
$270$		0			0
$271$	−23.3641			−1.41927			−0.709635	−	0.704570i	$-0.751140\pi$
$271$	−23.3641			−1.41927			−0.709635	+	0.704570i	$0.751140\pi$
$272$	4.96276	−	2.86525i	0.300911	−	0.173731i
$273$	11.3990	−	1.90841i	0.689900	−	0.115502i
$274$	−2.91764	+	5.05350i	−0.176261	+	0.305293i
$275$		0			0
$276$	13.2294	−	10.9071i	0.796314	−	0.656529i
$277$	−13.0563	+	7.53807i	−0.784479	+	0.452919i	−0.838015	−	0.545647i	$-0.816284\pi$
$277$	−13.0563	+	7.53807i	−0.784479	+	0.452919i	0.0535366	+	0.998566i	$0.482951\pi$
$278$		−	4.57595i		−	0.274447i
$279$	−3.98153	+	20.4993i	−0.238368	+	1.22726i
$280$		0			0
$281$	−3.32605	−	5.76088i	−0.198415	−	0.343665i	0.749599	−	0.661892i	$-0.230246\pi$
$281$	−3.32605	−	5.76088i	−0.198415	−	0.343665i	−0.948015	+	0.318226i	$0.896913\pi$
$282$	2.41326	−	6.45600i	0.143707	−	0.384449i
$283$	23.2934	+	13.4485i	1.38465	+	0.799428i	0.992706	−	0.120562i	$-0.0384696\pi$
$283$	23.2934	+	13.4485i	1.38465	+	0.799428i	0.391943	+	0.919989i	$0.371803\pi$
$284$	10.7684	−	18.6514i	0.638985	−	1.10675i
$285$		0			0
$286$	−3.57199	−	6.18687i	−0.211216	−	0.365838i
$287$		−	2.10083i		−	0.124008i
$288$	−15.9853	−	3.10478i	−0.941943	−	0.182951i
$289$	9.85601			0.579765
$290$		0			0
$291$	10.4712	−	8.63306i	0.613830	−	0.506079i
$292$	−2.48023	−	1.43196i	−0.145144	−	0.0837991i
$293$	10.7256	+	6.19243i	0.626596	+	0.361765i	0.779433	−	0.626486i	$-0.215507\pi$
$293$	10.7256	+	6.19243i	0.626596	+	0.361765i	−0.152837	+	0.988251i	$0.548841\pi$
$294$	0.811528	+	4.84730i	0.0473292	+	0.282701i
$295$		0			0
$296$	3.81681			0.221848
$297$	−11.8434	−	7.25405i	−0.687224	−	0.420923i
$298$			11.4834i			0.665217i
$299$	−13.8260	−	23.9474i	−0.799581	−	1.38491i
$300$		0			0
$301$	−0.336412	+	0.582682i	−0.0193905	+	0.0335853i
$302$	−1.50550	−	0.869202i	−0.0866319	−	0.0500169i
$303$	4.62947	+	5.61515i	0.265956	+	0.322582i
$304$	5.00924	+	8.67625i	0.287299	+	0.497617i
$305$		0			0
$306$	3.46193	+	3.00851i	0.197905	+	0.171985i
$307$		−	2.49359i		−	0.142317i	−0.997465	−	0.0711583i	$-0.977330\pi$
$307$		−	2.49359i		−	0.142317i	0.997465	−	0.0711583i	$-0.0226695\pi$
$308$	5.52944	−	3.19243i	0.315069	−	0.181905i
$309$	−2.94761	−	1.10182i	−0.167684	−	0.0626802i
$310$		0			0
$311$	12.1101	−	20.9752i	0.686699	−	1.18940i	−0.286201	−	0.958170i	$-0.592392\pi$
$311$	12.1101	−	20.9752i	0.686699	−	1.18940i	0.972900	−	0.231228i	$-0.0742742\pi$
$312$	−5.95348	+	15.9269i	−0.337049	+	0.901682i
$313$	30.3837	−	17.5420i	1.71739	−	0.991534i	0.793770	−	0.608219i	$-0.208116\pi$
$313$	30.3837	−	17.5420i	1.71739	−	0.991534i	0.923618	−	0.383315i	$-0.125218\pi$
$314$	−0.115349			−0.00650950
$315$		0			0
$316$	0.481728			0.0270993
$317$	−9.06829	+	5.23558i	−0.509326	+	0.294060i	−0.732557	−	0.680706i	$-0.761673\pi$
$317$	−9.06829	+	5.23558i	−0.509326	+	0.294060i	0.223231	+	0.974766i	$0.428340\pi$
$318$	0.720978	+	0.874485i	0.0404304	+	0.0490387i
$319$	−12.6821	+	21.9660i	−0.710059	+	1.22986i
$320$		0			0
$321$	3.40841	+	20.3586i	0.190239	+	1.13631i
$322$	−4.18601	+	2.41679i	−0.233277	+	0.134683i
$323$		−	12.4896i		−	0.694942i
$324$	2.09970	+	14.9083i	0.116650	+	0.828238i
$325$		0			0
$326$	−5.09555	−	8.82575i	−0.282216	−	0.488813i
$327$	28.4464	−	4.76244i	1.57309	−	0.263364i
$328$	2.67659	+	1.54533i	0.147790	+	0.0853267i
$329$	4.96721	−	8.60346i	0.273851	−	0.474324i
$330$		0			0
$331$	−8.38880	−	14.5298i	−0.461090	−	0.798632i	0.537925	−	0.842993i	$-0.319208\pi$
$331$	−8.38880	−	14.5298i	−0.461090	−	0.798632i	−0.999016	+	0.0443606i	$0.985875\pi$
$332$			7.16641i			0.393308i
$333$	−1.77525	−	5.15322i	−0.0972829	−	0.282395i
$334$	−8.06558			−0.441329
$335$		0			0
$336$	−4.96721	−	1.85675i	−0.270984	−	0.101294i
$337$	23.5394	+	13.5905i	1.28227	+	0.740320i	0.977263	−	0.212030i	$-0.0680074\pi$
$337$	23.5394	+	13.5905i	1.28227	+	0.740320i	0.305008	+	0.952350i	$0.401341\pi$
$338$	4.37665	+	2.52686i	0.238058	+	0.137443i
$339$	32.6481	+	12.2039i	1.77320	+	0.662825i
$340$		0			0
$341$	18.6050			1.00752
$342$	−5.25970	+	6.05239i	−0.284412	+	0.327276i
$343$			17.0801i			0.922239i
$344$	−0.494917	−	0.857221i	−0.0266841	−	0.0462182i
$345$		0			0
$346$	−1.24877	+	2.16293i	−0.0671343	+	0.116280i
$347$	20.4086	+	11.7829i	1.09559	+	0.632539i	0.935059	−	0.354492i	$-0.115346\pi$
$347$	20.4086	+	11.7829i	1.09559	+	0.632539i	0.160530	+	0.987031i	$0.448680\pi$
$348$	27.1180	−	4.54005i	1.45368	−	0.243372i
$349$	−5.35601	−	9.27689i	−0.286701	−	0.496580i	0.686319	−	0.727300i	$-0.259225\pi$
$349$	−5.35601	−	9.27689i	−0.286701	−	0.496580i	−0.973020	+	0.230720i	$0.925892\pi$
$350$		0			0
$351$	24.2725	+	0.630233i	1.29557	+	0.0336393i
$352$			14.5081i			0.773285i
$353$	−23.6141	+	13.6336i	−1.25685	+	0.725644i	−0.972461	−	0.233064i	$-0.925125\pi$
$353$	−23.6141	+	13.6336i	−1.25685	+	0.725644i	−0.284392	+	0.958708i	$0.591792\pi$
$354$	0.187143	+	1.11781i	0.00994652	+	0.0594112i
$355$		0			0
$356$	−2.50924	+	4.34612i	−0.132989	+	0.230344i
$357$	4.20543	+	5.10083i	0.222575	+	0.269965i
$358$	7.51089	−	4.33641i	0.396963	−	0.229186i
$359$	10.6807			0.563707			0.281854	−	0.959457i	$-0.409051\pi$
$359$	10.6807			0.563707			0.281854	+	0.959457i	$0.409051\pi$
$360$		0			0
$361$	2.83528			0.149225
$362$	1.58598	−	0.915664i	0.0833571	−	0.0481262i
$363$	2.33851	−	6.25603i	0.122740	−	0.328356i
$364$	−5.58123	+	9.66697i	−0.292536	+	0.506687i
$365$		0			0
$366$	2.34678	+	0.877227i	0.122668	+	0.0458534i
$367$	−7.33624	+	4.23558i	−0.382949	+	0.221096i	−0.679100	−	0.734045i	$-0.737630\pi$
$367$	−7.33624	+	4.23558i	−0.382949	+	0.221096i	0.296152	+	0.955141i	$0.404297\pi$
$368$			12.6873i			0.661373i
$369$	0.841495	−	4.33252i	0.0438065	−	0.225542i
$370$		0			0
$371$	0.816810	+	1.41476i	0.0424067	+	0.0734505i
$372$	−12.8298	−	15.5614i	−0.665193	−	0.806822i
$373$	8.76700	+	5.06163i	0.453938	+	0.262081i	0.709492	−	0.704714i	$-0.248925\pi$
$373$	8.76700	+	5.06163i	0.453938	+	0.262081i	−0.255554	+	0.966795i	$0.582258\pi$
$374$	2.04316	−	3.53885i	0.105649	−	0.182990i
$375$		0			0
$376$	7.30757	+	12.6571i	0.376859	+	0.652740i
$377$		−	44.3434i		−	2.28380i
$378$	0.110165	−	4.24284i	0.00566626	−	0.218228i
$379$	−11.9216			−0.612371			−0.306186	−	0.951972i	$-0.599053\pi$
$379$	−11.9216			−0.612371			−0.306186	+	0.951972i	$0.599053\pi$
$380$		0			0
$381$	0.625515	+	3.73624i	0.0320461	+	0.191414i
$382$	1.40561	+	0.811528i	0.0719171	+	0.0415214i
$383$	8.50161	+	4.90841i	0.434412	+	0.250808i	0.701224	−	0.712941i	$-0.252637\pi$
$383$	8.50161	+	4.90841i	0.434412	+	0.250808i	−0.266813	+	0.963748i	$0.585970\pi$
$384$	15.4126	−	12.7070i	0.786519	−	0.648453i
$385$		0			0
$386$	−10.7467			−0.546993
$387$	−0.927175	+	1.06691i	−0.0471309	+	0.0542341i
$388$			13.1070i			0.665409i
$389$	4.61007	+	7.98487i	0.233740	+	0.404849i	0.958906	−	0.283725i	$-0.0915703\pi$
$389$	4.61007	+	7.98487i	0.233740	+	0.404849i	−0.725166	+	0.688574i	$0.758237\pi$
$390$		0			0
$391$	7.90841	−	13.6978i	0.399945	−	0.692725i
$392$	−9.02554	−	5.21090i	−0.455858	−	0.263190i
$393$	3.63875	−	9.73445i	0.183550	−	0.491038i
$394$	1.66887	+	2.89057i	0.0840765	+	0.145625i
$395$		0			0
$396$	12.6821	−	4.36887i	0.637297	−	0.219544i
$397$		−	22.9793i		−	1.15330i	−0.816993	−	0.576648i	$-0.804360\pi$
$397$		−	22.9793i		−	1.15330i	0.816993	−	0.576648i	$-0.195640\pi$
$398$	−6.47741	+	3.73973i	−0.324683	+	0.187456i
$399$	−8.91764	+	7.35224i	−0.446440	+	0.368072i
$400$		0			0
$401$	5.53279	−	9.58307i	0.276294	−	0.478556i	−0.694167	−	0.719814i	$-0.744227\pi$
$401$	5.53279	−	9.58307i	0.276294	−	0.478556i	0.970461	+	0.241259i	$0.0775602\pi$
$402$	6.43969	−	1.07812i	0.321183	−	0.0537718i
$403$	−28.1688	+	16.2633i	−1.40319	+	0.810132i
$404$	−7.02864			−0.349688
$405$		0			0
$406$	−7.75123			−0.384687
$407$	−4.20543	+	2.42801i	−0.208455	+	0.120352i
$408$	−9.59222	+	1.60591i	−0.474886	+	0.0795046i
$409$	−8.81681	+	15.2712i	−0.435963	+	0.755110i	−0.997374	−	0.0724270i	$-0.976926\pi$
$409$	−8.81681	+	15.2712i	−0.435963	+	0.755110i	0.561411	+	0.827537i	$0.310259\pi$
$410$		0			0
$411$	−13.6336	+	11.2404i	−0.672497	+	0.554447i
$412$	2.63203	−	1.51960i	0.129671	−	0.0748654i
$413$			1.63362i			0.0803852i
$414$	−9.60083	+	3.30741i	−0.471855	+	0.162550i
$415$		0			0
$416$	−12.6821	−	21.9660i	−0.621789	−	1.07697i
$417$	4.85166	−	12.9793i	0.237587	−	0.635597i
$418$	6.18687	+	3.57199i	0.302610	+	0.174712i
$419$	18.5173	−	32.0730i	0.904631	−	1.56687i	0.0832199	−	0.996531i	$-0.473480\pi$
$419$	18.5173	−	32.0730i	0.904631	−	1.56687i	0.821411	−	0.570336i	$-0.193187\pi$
$420$		0			0
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	0.797799	−	0.602924i	$-0.205998\pi$
$421$	−2.52884	−	4.38007i	−0.123248	−	0.213472i	−0.921047	+	0.389452i	$0.872664\pi$
$422$			4.79608i			0.233469i
$423$	13.6900	−	15.7532i	0.665630	−	0.765947i
$424$	−2.40332			−0.116716
$425$		0			0
$426$	−9.84150	+	8.11392i	−0.476822	+	0.393121i
$427$	3.12739	+	1.80560i	0.151345	+	0.0873790i
$428$	−17.2652	−	9.96806i	−0.834544	−	0.481824i
$429$	−3.57199	−	21.3357i	−0.172457	−	1.03010i
$430$		0			0
$431$	−5.23030			−0.251935			−0.125967	−	0.992034i	$-0.540203\pi$
$431$	−5.23030			−0.251935			−0.125967	+	0.992034i	$0.540203\pi$
$432$	−9.50011	−	5.81879i	−0.457074	−	0.279957i
$433$		−	34.3434i		−	1.65044i	−0.564813	−	0.825219i	$-0.691052\pi$
$433$		−	34.3434i		−	1.65044i	0.564813	−	0.825219i	$-0.308948\pi$
$434$	2.84283	+	4.92392i	0.136460	+	0.236356i
$435$		0			0
$436$	−13.9280	+	24.1240i	−0.667031	+	1.15533i
$437$	23.9474	+	13.8260i	1.14556	+	0.661389i
$438$	1.07898	+	1.30871i	0.0515554	+	0.0625324i
$439$	−9.77365	−	16.9285i	−0.466471	−	0.807952i	0.532796	−	0.846244i	$-0.321141\pi$
$439$	−9.77365	−	16.9285i	−0.466471	−	0.807952i	−0.999267	+	0.0382924i	$0.987808\pi$
$440$		0			0
$441$	−2.83754	+	14.6094i	−0.135121	+	0.695685i
$442$			7.14399i			0.339805i
$443$	−9.09686	+	5.25208i	−0.432205	+	0.249534i	−0.700286	−	0.713863i	$-0.746944\pi$
$443$	−9.09686	+	5.25208i	−0.432205	+	0.249534i	0.268081	+	0.963396i	$0.413611\pi$
$444$	4.93083	+	1.84315i	0.234007	+	0.0874719i
$445$		0			0
$446$	−2.62156	+	4.54068i	−0.124135	+	0.215007i
$447$	−12.1753	+	32.5717i	−0.575873	+	1.54059i
$448$	1.46324	−	0.844801i	0.0691315	−	0.0399131i
$449$	−22.8560			−1.07864			−0.539321	−	0.842100i	$-0.681319\pi$
$449$	−22.8560			−1.07864			−0.539321	+	0.842100i	$0.681319\pi$
$450$		0			0
$451$	−3.93216			−0.185158
$452$	−29.1527	+	16.8313i	−1.37123	+	0.791679i
$453$	−3.34865	−	4.06163i	−0.157333	−	0.190832i
$454$	−0.764419	+	1.32401i	−0.0358759	+	0.0621390i
$455$		0			0
$456$	−2.80757	−	16.7698i	−0.131477	−	0.785319i
$457$	−12.1472	+	7.01319i	−0.568222	+	0.328063i	−0.756439	−	0.654064i	$-0.773063\pi$
$457$	−12.1472	+	7.01319i	−0.568222	+	0.328063i	0.188217	+	0.982127i	$0.439729\pi$
$458$		−	1.45704i		−	0.0680832i
$459$	6.62967	+	12.2039i	0.309446	+	0.569629i
$460$		0			0
$461$	12.0513	+	20.8734i	0.561283	+	0.972171i	0.997385	+	0.0722736i	$0.0230255\pi$
$461$	12.0513	+	20.8734i	0.561283	+	0.972171i	−0.436102	+	0.899897i	$0.643641\pi$
$462$	−3.72949	+	0.624385i	−0.173512	+	0.0290490i
$463$	−29.3930	−	16.9700i	−1.36601	−	0.788664i	−0.375591	−	0.926785i	$-0.622560\pi$
$463$	−29.3930	−	16.9700i	−1.36601	−	0.788664i	−0.990415	+	0.138121i	$0.955894\pi$
$464$	−10.1728	+	17.6198i	−0.472261	+	0.817981i
$465$		0			0
$466$	1.77894	+	3.08121i	0.0824077	+	0.142734i
$467$		−	27.3720i		−	1.26663i	−0.773896	−	0.633313i	$-0.781695\pi$
$467$		−	27.3720i		−	1.26663i	0.773896	−	0.633313i	$-0.218305\pi$
$468$	−15.3823	+	17.7005i	−0.711045	+	0.818207i
$469$	9.41123			0.434570
$470$		0			0
$471$	−0.327176	−	0.122299i	−0.0150755	−	0.00563523i
$472$	−2.08134	−	1.20166i	−0.0958013	−	0.0553109i
$473$	1.09062	+	0.629668i	0.0501466	+	0.0289521i
$474$	−0.267241	−	0.0998949i	−0.0122748	−	0.00458832i
$475$		0			0
$476$	−6.38485			−0.292649
$477$	1.11781	+	3.24482i	0.0511812	+	0.148570i
$478$		−	4.64645i		−	0.212524i
$479$	2.61515	+	4.52957i	0.119489	+	0.206961i	0.919565	−	0.392937i	$-0.128541\pi$
$479$	2.61515	+	4.52957i	0.119489	+	0.206961i	−0.800076	+	0.599898i	$0.795208\pi$
$480$		0			0
$481$	4.24482	−	7.35224i	0.193547	−	0.335233i
$482$	13.0597	+	7.54005i	0.594855	+	0.343440i
$483$	−14.4357	+	2.41679i	−0.656846	+	0.109968i
$484$	3.22522	+	5.58624i	0.146601	+	0.253920i
$485$		0			0
$486$	1.92668	−	8.70585i	0.0873958	−	0.394905i
$487$		−	24.0185i		−	1.08838i	−0.838962	−	0.544190i	$-0.816837\pi$
$487$		−	24.0185i		−	1.08838i	0.838962	−	0.544190i	$-0.183163\pi$
$488$	−4.60090	+	2.65633i	−0.208273	+	0.120246i
$489$	−5.09555	−	30.4360i	−0.230429	−	1.37636i
$490$		0			0
$491$	−7.38880	+	12.7978i	−0.333452	+	0.577556i	−0.983186	−	0.182606i	$-0.941547\pi$
$491$	−7.38880	+	12.7978i	−0.333452	+	0.577556i	0.649734	+	0.760161i	$0.274880\pi$
$492$	2.71157	+	3.28890i	0.122247	+	0.148275i
$493$	21.9660	−	12.6821i	0.989298	−	0.571171i
$494$	−12.4896			−0.561935
$495$		0			0
$496$	14.9239			0.670101
$497$	−15.9217	+	9.19243i	−0.714188	+	0.412337i
$498$	1.48608	−	3.97560i	0.0665929	−	0.178151i
$499$	12.4280	−	21.5259i	0.556354	−	0.963633i	−0.441443	−	0.897289i	$-0.645533\pi$
$499$	12.4280	−	21.5259i	0.556354	−	0.963633i	0.997797	−	0.0663440i	$-0.0211335\pi$
$500$		0			0
$501$	−22.8773	−	8.55155i	−1.02208	−	0.382055i
$502$	−0.272235	+	0.157175i	−0.0121504	+	0.00701506i
$503$		−	38.9154i		−	1.73515i	−0.497305	−	0.867576i	$-0.665677\pi$
$503$		−	38.9154i		−	1.73515i	0.497305	−	0.867576i	$-0.334323\pi$
$504$	6.79326	+	5.90353i	0.302596	+	0.262964i
$505$		0			0
$506$	4.52355	+	7.83503i	0.201097	+	0.348309i
$507$	9.73487	+	11.8076i	0.432341	+	0.524393i
$508$	−3.16853	−	1.82935i	−0.140581	−	0.0811644i
$509$	1.01037	−	1.75001i	0.0447837	−	0.0775676i	−0.842765	−	0.538282i	$-0.819073\pi$
$509$	1.01037	−	1.75001i	0.0447837	−	0.0775676i	0.887548	+	0.460715i	$0.152407\pi$
$510$		0			0
$511$	1.22239	+	2.11725i	0.0540755	+	0.0936615i
$512$			20.6459i			0.912428i
$513$	−21.3357	+	11.5905i	−0.941996	+	0.511732i
$514$	10.2959			0.454132
$515$		0			0
$516$	−0.225415	−	1.34642i	−0.00992333	−	0.0592726i
$517$	−16.1032	−	9.29721i	−0.708220	−	0.408891i
$518$	−1.28517	−	0.741995i	−0.0564672	−	0.0326014i
$519$	−5.83528	+	4.81096i	−0.256140	+	0.211178i
$520$		0			0
$521$	−23.0290			−1.00892			−0.504460	−	0.863435i	$-0.668308\pi$
$521$	−23.0290			−1.00892			−0.504460	+	0.863435i	$0.668308\pi$
$522$	−15.9853	−	3.10478i	−0.699657	−	0.135893i
$523$			41.1170i			1.79792i	0.438028	+	0.898961i	$0.355677\pi$
$523$			41.1170i			1.79792i	−0.438028	+	0.898961i	$0.644323\pi$
$524$	5.01847	+	8.69225i	0.219233	+	0.379723i
$525$		0			0
$526$	−3.40199	+	5.89242i	−0.148334	+	0.256922i
$527$	−16.1124	−	9.30249i	−0.701867	−	0.405223i
$528$	−3.47530	+	9.29721i	−0.151243	+	0.404609i
$529$	6.00924	+	10.4083i	0.261271	+	0.452535i
$530$		0			0
$531$	−0.654353	+	3.36900i	−0.0283965	+	0.146202i
$532$		−	11.1625i		−	0.483954i
$533$	5.95348	−	3.43724i	0.257874	−	0.148883i
$534$	2.29326	−	1.89070i	0.0992389	−	0.0818185i
$535$		0			0
$536$	−6.92272	+	11.9905i	−0.299016	+	0.517911i
$537$	25.9017	−	4.33641i	1.11774	−	0.187130i
$538$	−14.1543	+	8.17198i	−0.610234	+	0.352319i
$539$	13.2593			0.571120
$540$		0			0
$541$	5.20957			0.223977			0.111988	−	0.993710i	$-0.464278\pi$
$541$	5.20957			0.223977			0.111988	+	0.993710i	$0.464278\pi$
$542$	−11.5737	+	6.68206i	−0.497132	+	0.287019i
$543$	5.46932	−	0.915664i	0.234711	−	0.0392949i
$544$	7.25405	−	12.5644i	0.311015	−	0.538694i
$545$		0			0
$546$	5.10083	−	4.20543i	0.218295	−	0.179976i
$547$	34.6764	−	20.0204i	1.48266	−	0.856013i	0.482851	−	0.875702i	$-0.339601\pi$
$547$	34.6764	−	20.0204i	1.48266	−	0.856013i	0.999806	+	0.0196900i	$0.00626792\pi$
$548$		−	17.0656i		−	0.729005i
$549$	5.72635	+	4.97636i	0.244394	+	0.212386i
$550$		0			0
$551$	22.1717	+	38.4025i	0.944546	+	1.63600i
$552$	7.53946	−	20.1697i	0.320901	−	0.858480i
$553$	−0.356133	−	0.205614i	−0.0151443	−	0.00874359i
$554$	−4.31173	+	7.46813i	−0.183188	+	0.317290i
$555$		0			0
$556$	6.69129	+	11.5897i	0.283774	+	0.491511i
$557$		−	14.4033i		−	0.610288i	−0.952306	−	0.305144i	$-0.901295\pi$
$557$		−	14.4033i		−	0.610288i	0.952306	−	0.305144i	$-0.0987047\pi$
$558$	3.89044	+	11.2933i	0.164695	+	0.478082i
$559$	−2.20166			−0.0931203
$560$		0			0
$561$	9.54731	−	7.87137i	0.403088	−	0.332330i
$562$	−3.29518	−	1.90248i	−0.138999	−	0.0802511i
$563$	25.4335	+	14.6840i	1.07189	+	0.618858i	0.928698	−	0.370836i	$-0.120929\pi$
$563$	25.4335	+	14.6840i	1.07189	+	0.618858i	0.143196	+	0.989694i	$0.454262\pi$
$564$	3.32831	+	19.8802i	0.140147	+	0.837107i
$565$		0			0
$566$	15.3849			0.646674
$567$	4.81096	−	11.9176i	0.202041	−	0.500494i
$568$		−	27.0471i		−	1.13487i
$569$	23.4033	+	40.5357i	0.981118	+	1.69935i	0.658056	+	0.752969i	$0.271379\pi$
$569$	23.4033	+	40.5357i	0.981118	+	1.69935i	0.323062	+	0.946378i	$0.395288\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	18.0938	+	10.4465i	0.756541	+	0.436789i
$573$	3.12646	+	3.79213i	0.130610	+	0.158418i
$574$	−0.600830	−	1.04067i	−0.0250782	−	0.0434367i
$575$		0			0
$576$	3.35601	−	1.15612i	0.139834	−	0.0481717i
$577$			28.2386i			1.17559i	0.809010	+	0.587794i	$0.200004\pi$
$577$			28.2386i			1.17559i	−0.809010	+	0.587794i	$0.799996\pi$
$578$	4.88228	−	2.81879i	0.203076	−	0.117246i
$579$	−30.4821	−	11.3942i	−1.26679	−	0.473528i
$580$		0			0
$581$	3.05880	−	5.29801i	0.126901	−	0.219798i
$582$	2.71798	−	7.27119i	0.112664	−	0.301401i
$583$	2.64802	−	1.52884i	0.109670	−	0.0633180i
$584$	−3.59668			−0.148832
$585$		0			0
$586$	7.08405			0.292639
$587$	15.6598	−	9.04118i	0.646348	−	0.373169i	−0.140707	−	0.990051i	$-0.544938\pi$
$587$	15.6598	−	9.04118i	0.646348	−	0.373169i	0.787056	+	0.616882i	$0.211604\pi$
$588$	−9.14348	−	11.0903i	−0.377071	−	0.457355i
$589$	16.2633	−	28.1688i	0.670117	−	1.16068i
$590$		0			0
$591$	1.66887	+	9.96827i	0.0686482	+	0.410040i
$592$	−3.37336	+	1.94761i	−0.138644	+	0.0800462i
$593$			7.73840i			0.317778i	0.987296	+	0.158889i	$0.0507912\pi$
$593$			7.73840i			0.317778i	−0.987296	+	0.158889i	$0.949209\pi$
$594$	−7.94139	−	0.206197i	−0.325839	−	0.00846037i
$595$		0			0
$596$	−16.7919	−	29.0845i	−0.687824	−	1.19135i
$597$	−22.3377	+	3.73973i	−0.914220	+	0.153057i
$598$	−13.6978	−	7.90841i	−0.560143	−	0.323399i
$599$	−13.9608	+	24.1808i	−0.570423	+	0.988001i	0.426100	+	0.904676i	$0.359887\pi$
$599$	−13.9608	+	24.1808i	−0.570423	+	0.988001i	−0.996522	+	0.0833249i	$0.973446\pi$
$600$		0			0
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	−0.929591	−	0.368592i	$-0.879840\pi$
$601$	−19.2201	−	33.2902i	−0.784006	−	1.35794i	0.145586	−	0.989346i	$-0.453493\pi$
$602$			0.384851i			0.0156853i
$603$	19.4087	+	3.76970i	0.790383	+	0.153514i
$604$	5.08405			0.206867
$605$		0			0
$606$	3.89917	+	1.45751i	0.158393	+	0.0592074i
$607$	0.554113	+	0.319917i	0.0224907	+	0.0129850i	0.511203	−	0.859460i	$-0.329200\pi$
$607$	0.554113	+	0.319917i	0.0224907	+	0.0129850i	−0.488712	+	0.872445i	$0.662533\pi$
$608$	21.9660	+	12.6821i	0.890838	+	0.514325i
$609$	−21.9857	−	8.21826i	−0.890905	−	0.333021i
$610$		0			0
$611$	32.5081			1.31514
$612$	−13.1674	−	2.55748i	−0.532261	−	0.103380i
$613$		−	42.7467i		−	1.72652i	−0.504757	−	0.863262i	$-0.668418\pi$
$613$		−	42.7467i		−	1.72652i	0.504757	−	0.863262i	$-0.331582\pi$
$614$	−0.713157	−	1.23522i	−0.0287807	−	0.0498496i
$615$		0			0
$616$	4.00924	−	6.94420i	0.161537	−	0.279790i
$617$	−18.2753	−	10.5513i	−0.735737	−	0.424778i	0.0847805	−	0.996400i	$-0.472981\pi$
$617$	−18.2753	−	10.5513i	−0.735737	−	0.424778i	−0.820517	+	0.571622i	$0.806314\pi$
$618$	−1.77525	+	0.297209i	−0.0714109	+	0.0119555i
$619$	−6.82605	−	11.8231i	−0.274362	−	0.475209i	0.695612	−	0.718418i	$-0.255133\pi$
$619$	−6.82605	−	11.8231i	−0.274362	−	0.475209i	−0.969974	+	0.243209i	$0.921800\pi$
$620$		0			0
$621$	−30.7386	−	0.798123i	−1.23350	−	0.0320276i
$622$		−	13.8538i		−	0.555485i
$623$	3.71007	−	2.14201i	0.148641	−	0.0858178i
$624$	−2.86525	−	17.1143i	−0.114702	−	0.685121i
$625$		0			0
$626$	10.0339	−	17.3793i	0.401036	−	0.694615i
$627$	13.7613	+	16.6913i	0.549574	+	0.666586i
$628$	0.292148	−	0.168672i	0.0116580	−	0.00673073i
$629$	4.85601			0.193622
$630$		0			0
$631$	33.2593			1.32403			0.662017	−	0.749489i	$-0.269701\pi$
$631$	33.2593			1.32403			0.662017	+	0.749489i	$0.269701\pi$
$632$	0.523930	−	0.302491i	0.0208408	−	0.0120325i
$633$	−5.08506	+	13.6037i	−0.202113	+	0.540697i
$634$	−2.99472	+	5.18700i	−0.118935	+	0.206002i
$635$		0			0
$636$	−3.10478	−	1.16057i	−0.123113	−	0.0460196i
$637$	−20.0753	+	11.5905i	−0.795411	+	0.459231i
$638$			14.5081i			0.574381i
$639$	−36.5173	+	12.5799i	−1.44460	+	0.497655i
$640$		0			0
$641$	−13.1429	−	22.7641i	−0.519112	−	0.899128i	−0.999753	−	0.0222106i	$-0.992930\pi$
$641$	−13.1429	−	22.7641i	−0.519112	−	0.899128i	0.480642	−	0.876917i	$-0.340404\pi$
$642$	7.51089	+	9.11007i	0.296431	+	0.359546i
$643$	17.8250	+	10.2913i	0.702950	+	0.405848i	0.808445	−	0.588571i	$-0.200309\pi$
$643$	17.8250	+	10.2913i	0.702950	+	0.405848i	−0.105495	+	0.994420i	$0.533643\pi$
$644$	7.06804	−	12.2422i	0.278520	−	0.482410i
$645$		0			0
$646$	−3.57199	−	6.18687i	−0.140538	−	0.243419i
$647$			23.2527i			0.914159i	0.889426	+	0.457079i	$0.151104\pi$
$647$			23.2527i			0.914159i	−0.889426	+	0.457079i	$0.848896\pi$
$648$	11.6450	+	14.8959i	0.457458	+	0.585165i
$649$	3.05767			0.120024
$650$		0			0
$651$	2.84283	+	16.9804i	0.111419	+	0.665513i
$652$	25.8114	+	14.9022i	1.01085	+	0.583615i
$653$	16.2459	+	9.37957i	0.635751	+	0.367051i	0.782976	−	0.622052i	$-0.213701\pi$
$653$	16.2459	+	9.37957i	0.635751	+	0.367051i	−0.147225	+	0.989103i	$0.547034\pi$
$654$	12.7292	−	10.4947i	0.497750	−	0.410375i
$655$		0			0
$656$	−3.15415			−0.123149
$657$	1.67286	+	4.85601i	0.0652645	+	0.189451i
$658$		−	5.68242i		−	0.221524i
$659$	−0.140034	−	0.242545i	−0.00545494	−	0.00944823i	0.863285	−	0.504717i	$-0.168403\pi$
$659$	−0.140034	−	0.242545i	−0.00545494	−	0.00944823i	−0.868740	+	0.495268i	$0.835070\pi$
$660$		0			0
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	−0.161750	−	0.986832i	$-0.551714\pi$
$661$	19.8930	−	34.4556i	0.773746	−	1.34017i	0.935496	−	0.353336i	$-0.114953\pi$
$662$	−8.31097	−	4.79834i	−0.323015	−	0.186493i
$663$	−7.57443	+	20.2633i	−0.294167	+	0.786961i
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$		0			0
$666$	−2.35319	−	2.04499i	−0.0911843	−	0.0792417i
$667$			56.1562i			2.17438i
$668$	20.4280	−	11.7941i	0.790382	−	0.456327i
$669$	−12.2501	+	10.0997i	−0.473616	+	0.390478i
$670$		0			0
$671$	3.37957	−	5.85358i	0.130467	−	0.225975i
$672$	−13.2412	+	2.21683i	−0.510792	+	0.0855159i
$673$	−29.0368	+	16.7644i	−1.11929	+	0.646221i	−0.941219	−	0.337797i	$-0.890318\pi$
$673$	−29.0368	+	16.7644i	−1.11929	+	0.646221i	−0.178068	+	0.984018i	$0.556985\pi$
$674$	15.5473			0.598860
$675$		0			0
$676$	−14.7799			−0.568456
$677$	23.8048	−	13.7437i	0.914891	−	0.528213i	0.0328897	−	0.999459i	$-0.489529\pi$
$677$	23.8048	−	13.7437i	0.914891	−	0.528213i	0.882002	+	0.471246i	$0.156196\pi$
$678$	19.6629	−	3.29193i	0.755148	−	0.126426i
$679$	5.59442	−	9.68981i	0.214694	−	0.371861i
$680$		0			0
$681$	−3.57199	+	2.94497i	−0.136879	+	0.112851i
$682$	9.21618	−	5.32096i	0.352906	−	0.203750i
$683$			34.5865i			1.32342i	0.749762	+	0.661708i	$0.230168\pi$
$683$			34.5865i			1.32342i	−0.749762	+	0.661708i	$0.769832\pi$
$684$	4.47116	−	23.0202i	0.170959	−	0.880201i
$685$		0			0
$686$	4.88485	+	8.46081i	0.186504	+	0.323035i
$687$	1.54483	−	4.13277i	0.0589391	−	0.157675i
$688$	0.874830	+	0.505083i	0.0333526	+	0.0192561i
$689$	−2.67282	+	4.62947i	−0.101826	+	0.176369i
$690$		0			0
$691$	−20.3641	−	35.2717i	−0.774688	−	1.34180i	−0.934970	−	0.354727i	$-0.884574\pi$
$691$	−20.3641	−	35.2717i	−0.774688	−	1.34180i	0.160282	−	0.987071i	$-0.448760\pi$
$692$		−	7.30418i		−	0.277663i
$693$	−11.2404	−	2.18319i	−0.426987	−	0.0829325i
$694$	13.4795			0.511674
$695$		0			0
$696$	26.6429	−	21.9660i	1.00989	−	0.832618i
$697$	3.40535	+	1.96608i	0.128987	+	0.0744706i
$698$	−5.30632	−	3.06360i	−0.200847	−	0.115959i
$699$	1.77894	+	10.6257i	0.0672856	+	0.401901i
$700$		0			0
$701$	−19.4712			−0.735416			−0.367708	−	0.929941i	$-0.619857\pi$
$701$	−19.4712			−0.735416			−0.367708	+	0.929941i	$0.619857\pi$
$702$	12.2039	−	6.62967i	0.460606	−	0.250221i
$703$			8.48963i			0.320193i
$704$	−1.58123	−	2.73877i	−0.0595948	−	0.103221i
$705$		0			0
$706$	−7.79834	+	13.5071i	−0.293494	+	0.508347i
$707$	5.19615	+	3.00000i	0.195421	+	0.112827i
$708$	−2.10854	−	2.55748i	−0.0792436	−	0.0961158i
$709$	7.54316	+	13.0651i	0.283289	+	0.490671i	0.972193	−	0.234182i	$-0.0752410\pi$
$709$	7.54316	+	13.0651i	0.283289	+	0.490671i	−0.688904	+	0.724853i	$0.741908\pi$
$710$		0			0
$711$	−0.652092	−	0.566686i	−0.0244553	−	0.0212524i
$712$			6.30249i			0.236196i
$713$	35.6729	−	20.5957i	1.33596	−	0.771317i
$714$	3.54203	+	1.32401i	0.132557	+	0.0495499i
$715$		0			0
$716$	−12.6821	+	21.9660i	−0.473951	+	0.820907i
$717$	4.92641	−	13.1792i	0.183980	−	0.492188i
$718$	5.29081	−	3.05465i	0.197451	−	0.113999i
$719$	3.43196			0.127990			0.0639952	−	0.997950i	$-0.479616\pi$
$719$	3.43196			0.127990			0.0639952	+	0.997950i	$0.479616\pi$
$720$		0			0
$721$	−2.59442			−0.0966211
$722$	1.40449	−	0.810881i	0.0522696	−	0.0301779i
$723$	29.0485	+	35.2333i	1.08032	+	1.31034i
$724$	−2.67791	+	4.63827i	−0.0995236	+	0.172380i
$725$		0			0
$726$	−0.630798	−	3.76780i	−0.0234111	−	0.139836i
$727$	−30.9789	+	17.8857i	−1.14895	+	0.663344i	−0.948630	−	0.316388i	$-0.897530\pi$
$727$	−30.9789	+	17.8857i	−1.14895	+	0.663344i	−0.200315	+	0.979732i	$0.564197\pi$
$728$			14.0185i			0.519559i
$729$	14.6952	−	22.6506i	0.544268	−	0.838911i
$730$		0			0
$731$	−0.629668	−	1.09062i	−0.0232891	−	0.0403379i
$732$	−7.22652	+	1.20985i	−0.267100	+	0.0447174i
$733$	−19.0526	−	11.0000i	−0.703722	−	0.406294i	0.105010	−	0.994471i	$-0.466513\pi$
$733$	−19.0526	−	11.0000i	−0.703722	−	0.406294i	−0.808732	+	0.588177i	$0.799846\pi$
$734$	−2.42272	+	4.19628i	−0.0894244	+	0.154888i
$735$		0			0
$736$	16.0605	+	27.8176i	0.591998	+	1.02537i
$737$		−	17.6151i		−	0.648862i
$738$	−0.822244	−	2.38683i	−0.0302672	−	0.0878603i
$739$	−6.08631			−0.223889			−0.111944	−	0.993714i	$-0.535708\pi$
$739$	−6.08631			−0.223889			−0.111944	+	0.993714i	$0.535708\pi$
$740$		0			0
$741$	−35.4257	−	13.2422i	−1.30140	−	0.486463i
$742$	0.809231	+	0.467210i	0.0297078	+	0.0171518i
$743$	−22.0853	−	12.7509i	−0.810231	−	0.467787i	0.0368054	−	0.999322i	$-0.488282\pi$
$743$	−22.0853	−	12.7509i	−0.810231	−	0.467787i	−0.847036	+	0.531536i	$0.821615\pi$
$744$	−23.7252	−	8.86850i	−0.869809	−	0.325135i
$745$		0			0
$746$	5.79043			0.212003
$747$	8.43028	−	9.70081i	0.308448	−	0.354934i
$748$			11.9506i			0.436958i
$749$	8.50924	+	14.7384i	0.310921	+	0.538530i
$750$		0			0
$751$	9.19638	−	15.9286i	0.335581	−	0.581243i	−0.648016	−	0.761627i	$-0.724401\pi$
$751$	9.19638	−	15.9286i	0.335581	−	0.581243i	0.983596	+	0.180384i	$0.0577342\pi$
$752$	−12.9171	−	7.45769i	−0.471038	−	0.271954i
$753$	−0.938816	+	0.157175i	−0.0342124	+	0.00572777i
$754$	−12.6821	−	21.9660i	−0.461853	−	0.799953i
$755$		0			0
$756$	5.92518	+	10.9071i	0.215497	+	0.396687i
$757$		−	41.8986i		−	1.52283i	−0.648264	−	0.761415i	$-0.724505\pi$
$757$		−	41.8986i		−	1.52283i	0.648264	−	0.761415i	$-0.275495\pi$
$758$	−5.90549	+	3.40954i	−0.214497	+	0.123840i
$759$	4.52355	+	27.0195i	0.164195	+	0.980745i
$760$		0			0
$761$	3.98568	−	6.90340i	0.144481	−	0.250248i	−0.784698	−	0.619878i	$-0.787182\pi$
$761$	3.98568	−	6.90340i	0.144481	−	0.250248i	0.929179	+	0.369630i	$0.120515\pi$
$762$	1.37841	+	1.67189i	0.0499345	+	0.0605663i
$763$	20.5935	−	11.8896i	0.745534	−	0.430434i
$764$	−4.74671			−0.171730
$765$		0			0
$766$	5.61515			0.202884
$767$	−4.62947	+	2.67282i	−0.167160	+	0.0965101i
$768$	2.56550	−	6.86327i	0.0925744	−	0.247657i
$769$	3.01432	−	5.22095i	0.108699	−	0.188272i	−0.806544	−	0.591174i	$-0.798665\pi$
$769$	3.01432	−	5.22095i	0.108699	−	0.188272i	0.915244	+	0.402901i	$0.131998\pi$
$770$		0			0
$771$	29.2034	+	10.9162i	1.05173	+	0.393139i
$772$	27.2186	−	15.7147i	0.979618	−	0.565583i
$773$		−	44.4033i		−	1.59708i	−0.601944	−	0.798538i	$-0.705607\pi$
$773$		−	44.4033i		−	1.59708i	0.601944	−	0.798538i	$-0.294393\pi$
$774$	−0.154153	+	0.793674i	−0.00554093	+	0.0285280i
$775$		0			0
$776$	8.23030	+	14.2553i	0.295451	+	0.511735i
$777$	−2.85858	−	3.46721i	−0.102551	−	0.124385i
$778$	4.56729	+	2.63693i	0.163745	+	0.0945384i
$779$	−3.43724	+	5.95348i	−0.123152	+	0.213305i
$780$		0			0
$781$	17.2056	+	29.8010i	0.615665	+	1.06636i
$782$		−	9.04711i		−	0.323524i
$783$	−42.0490	−	25.7549i	−1.50271	−	0.920405i
$784$	10.6359			0.379853
$785$		0			0
$786$	−0.981529	−	5.86273i	−0.0350100	−	0.209117i
$787$	−14.5817	−	8.41877i	−0.519783	−	0.300097i	0.217063	−	0.976158i	$-0.430352\pi$
$787$	−14.5817	−	8.41877i	−0.519783	−	0.300097i	−0.736846	+	0.676061i	$0.763686\pi$
$788$	−8.45362	−	4.88070i	−0.301148	−	0.173868i
$789$	−15.8969	+	13.1064i	−0.565945	+	0.466599i
$790$		0			0
$791$	28.7361			1.02174
$792$	11.0497	−	12.7150i	0.392635	−	0.451810i
$793$			11.8168i			0.419627i
$794$	−6.57199	−	11.3830i	−0.233231	−	0.403968i
$795$		0			0
$796$	10.9370	−	18.9435i	0.387653	−	0.671435i
$797$	28.9010	+	16.6860i	1.02373	+	0.591049i	0.915181	−	0.403043i	$-0.132047\pi$
$797$	28.9010	+	16.6860i	1.02373	+	0.591049i	0.108545	+	0.994091i	$0.465381\pi$
$798$	−2.31473	+	6.19243i	−0.0819407	+	0.219209i
$799$	9.29721	+	16.1032i	0.328912	+	0.569692i
$800$		0			0
$801$	8.50924	−	2.93137i	0.300659	−	0.103575i
$802$		−	6.32944i		−	0.223500i
$803$	3.96289	−	2.28797i	0.139847	−	0.0807408i
$804$	−14.7335	+	12.1472i	−0.519611	+	0.428399i
$805$		0			0
$806$	−9.30249	+	16.1124i	−0.327666	+	0.567535i
$807$	−48.8117	+	8.17198i	−1.71825	+	0.287667i
$808$	−7.64439	+	4.41349i	−0.268929	+	0.155266i
$809$	−29.1809			−1.02595			−0.512973	−	0.858404i	$-0.671456\pi$
$809$	−29.1809			−1.02595			−0.512973	+	0.858404i	$0.671456\pi$
$810$		0			0
$811$	−15.5552			−0.546217			−0.273109	−	0.961983i	$-0.588052\pi$
$811$	−15.5552			−0.546217			−0.273109	+	0.961983i	$0.588052\pi$
$812$	19.6318	−	11.3344i	0.688942	−	0.397761i
$813$	−39.9124	+	6.68206i	−1.39979	+	0.234350i
$814$	−1.38880	+	2.40548i	−0.0486775	+	0.0843120i
$815$		0			0
$816$	7.65831	−	6.31397i	0.268094	−	0.221033i
$817$	1.90669	−	1.10083i	0.0667068	−	0.0385132i
$818$			10.0863i			0.352660i
$819$	18.9269	−	6.52016i	0.661359	−	0.227833i
$820$		0			0
$821$	11.8588	+	20.5401i	0.413876	+	0.716855i	0.995310	−	0.0967393i	$-0.0308413\pi$
$821$	11.8588	+	20.5401i	0.413876	+	0.716855i	−0.581434	+	0.813594i	$0.697508\pi$
$822$	−3.53885	+	9.46721i	−0.123432	+	0.330207i
$823$	16.7732	+	9.68404i	0.584678	+	0.337564i	0.762990	−	0.646410i	$-0.223730\pi$
$823$	16.7732	+	9.68404i	0.584678	+	0.337564i	−0.178312	+	0.983974i	$0.557064\pi$
$824$	1.90841	−	3.30545i	0.0664824	−	0.115151i
$825$		0			0
$826$	0.467210	+	0.809231i	0.0162563	+	0.0281568i
$827$			52.2241i			1.81601i	0.418960	+	0.908005i	$0.362395\pi$
$827$			52.2241i			1.81601i	−0.418960	+	0.908005i	$0.637605\pi$
$828$	19.4800	−	22.4159i	0.676977	−	0.779005i
$829$	26.6442			0.925391			0.462695	−	0.886517i	$-0.346882\pi$
$829$	26.6442			0.925391			0.462695	+	0.886517i	$0.346882\pi$
$830$		0			0
$831$	−20.1479	+	16.6112i	−0.698924	+	0.576235i
$832$	4.78811	+	2.76442i	0.165998	+	0.0958390i
$833$	−11.4829	−	6.62967i	−0.397860	−	0.229704i
$834$	−1.30871	−	7.81698i	−0.0453168	−	0.270680i
$835$		0			0
$836$	−20.8930			−0.722598
$837$	−0.938816	+	36.1572i	−0.0324502	+	1.24977i
$838$		−	21.1836i		−	0.731775i
$839$	−12.5196	−	21.6846i	−0.432225	−	0.748635i	0.564840	−	0.825201i	$-0.308938\pi$
$839$	−12.5196	−	21.6846i	−0.432225	−	0.748635i	−0.997065	+	0.0765655i	$0.975605\pi$
$840$		0			0
$841$	−30.5266	+	52.8736i	−1.05264	+	1.82323i
$842$	−2.50537	−	1.44648i	−0.0863409	−	0.0498489i
$843$	−7.32940	−	8.88993i	−0.252438	−	0.306186i
$844$	−7.01319	−	12.1472i	−0.241404	−	0.418124i
$845$		0			0
$846$	2.27611	−	11.7188i	0.0782544	−	0.402901i
$847$		−	5.50641i		−	0.189203i
$848$	2.12409	−	1.22635i	0.0729417	−	0.0421129i
$849$	43.6378	+	16.3118i	1.49764	+	0.559821i
$850$		0			0
$851$	−5.37562	+	9.31084i	−0.184274	+	0.319171i
$852$	13.0611	−	34.9414i	0.447467	−	1.19707i
$853$	9.41758	−	5.43724i	0.322452	−	0.186168i	−0.330033	−	0.943969i	$-0.607060\pi$
$853$	9.41758	−	5.43724i	0.322452	−	0.186168i	0.652485	+	0.757802i	$0.273727\pi$
$854$	2.06558			0.0706827
$855$		0			0
$856$	−25.0369			−0.855745
$857$	−16.1032	+	9.29721i	−0.550076	+	0.317587i	−0.749153	−	0.662397i	$-0.769539\pi$
$857$	−16.1032	+	9.29721i	−0.550076	+	0.317587i	0.199077	+	0.979984i	$0.436206\pi$
$858$	−7.87137	−	9.54731i	−0.268724	−	0.325940i
$859$	−2.33246	+	4.03994i	−0.0795825	+	0.137841i	−0.903070	−	0.429494i	$-0.858692\pi$
$859$	−2.33246	+	4.03994i	−0.0795825	+	0.137841i	0.823487	+	0.567335i	$0.192025\pi$
$860$		0			0
$861$	−0.600830	−	3.58880i	−0.0204762	−	0.122306i
$862$	−2.59088	+	1.49585i	−0.0882459	+	0.0509488i
$863$			28.0594i			0.955152i	0.878590	+	0.477576i	$0.158484\pi$
$863$			28.0594i			0.955152i	−0.878590	+	0.477576i	$0.841516\pi$
$864$	−28.1952	−	0.732086i	−0.959222	−	0.0249061i
$865$		0			0
$866$	−9.82209	−	17.0124i	−0.333768	−	0.578104i
$867$	16.8368	−	2.81879i	0.571807	−	0.0957310i
$868$	−14.4002	−	8.31399i	−0.488776	−	0.282195i
$869$	−0.384851	+	0.666581i	−0.0130552	+	0.0226122i
$870$		0			0
$871$	15.3980	+	26.6702i	0.521743	+	0.903685i
$872$			34.9832i			1.18468i
$873$	15.4186	−	17.7424i	0.521841	−	0.600488i
$874$	15.8168			0.535012
$875$		0			0
$876$	−4.64645	−	1.73685i	−0.156989	−	0.0586826i
$877$	−30.0236	−	17.3342i	−1.01383	−	0.585333i	−0.101516	−	0.994834i	$-0.532369\pi$
$877$	−30.0236	−	17.3342i	−1.01383	−	0.585333i	−0.912310	+	0.409501i	$0.865703\pi$
$878$	−9.68297	−	5.59046i	−0.326784	−	0.188669i
$879$	20.0933	+	7.51089i	0.677730	+	0.253336i
$880$		0			0
$881$	−5.29854			−0.178512			−0.0892561	−	0.996009i	$-0.528449\pi$
$881$	−5.29854			−0.178512			−0.0892561	+	0.996009i	$0.528449\pi$
$882$	2.77263	+	8.04844i	0.0933592	+	0.271005i
$883$			10.3025i			0.346706i	0.984860	+	0.173353i	$0.0554602\pi$
$883$			10.3025i			0.346706i	−0.984860	+	0.173353i	$0.944540\pi$
$884$	−10.4465	−	18.0938i	−0.351353	−	0.608561i
$885$		0			0
$886$	−3.00415	+	5.20334i	−0.100926	+	0.174810i
$887$	−35.8971	−	20.7252i	−1.20531	−	0.695885i	−0.243577	−	0.969882i	$-0.578321\pi$
$887$	−35.8971	−	20.7252i	−1.20531	−	0.695885i	−0.961731	+	0.273997i	$0.911654\pi$
$888$	6.52016	−	1.09159i	0.218802	−	0.0366315i
$889$	1.56163	+	2.70482i	0.0523753	+	0.0907167i
$890$		0			0
$891$	−22.3064	−	9.00475i	−0.747294	−	0.301670i
$892$		−	15.3338i		−	0.513413i
$893$	−28.1528	+	16.2541i	−0.942099	+	0.543921i
$894$	3.28422	+	19.6168i	0.109841	+	0.656086i
$895$		0			0
$896$	8.23445	−	14.2625i	0.275094	−	0.476476i
$897$	−30.4676	−	36.9546i	−1.01728	−	1.23388i
$898$	−11.3220	+	6.53674i	−0.377819	+	0.218134i
$899$	66.0554			2.20307
$900$		0			0
$901$	−3.05767			−0.101866
$902$	−1.94784	+	1.12458i	−0.0648559	+	0.0374446i
$903$	−0.408039	+	1.09159i	−0.0135787	+	0.0363260i
$904$	−21.1378	+	36.6117i	−0.703032	+	1.21769i
$905$		0			0
$906$	−2.82040	−	1.05427i	−0.0937015	−	0.0350257i
$907$	−14.5424	+	8.39606i	−0.482873	+	0.278787i	−0.721613	−	0.692297i	$-0.756599\pi$
$907$	−14.5424	+	8.39606i	−0.482873	+	0.278787i	0.238740	+	0.971083i	$0.423266\pi$
$908$		−	4.47116i		−	0.148381i
$909$	9.51432	+	8.26821i	0.315570	+	0.274239i
$910$		0			0
$911$	−18.6768	−	32.3491i	−0.618789	−	1.07177i	−0.989707	−	0.143109i	$-0.954290\pi$
$911$	−18.6768	−	32.3491i	−0.618789	−	1.07177i	0.370918	−	0.928666i	$-0.379043\pi$
$912$	11.0385	+	13.3888i	0.365522	+	0.443348i
$913$	−9.91636	−	5.72522i	−0.328184	−	0.189477i
$914$	−4.01150	+	6.94812i	−0.132689	+	0.229823i
$915$		0			0
$916$	2.13060	+	3.69031i	0.0703970	+	0.121931i
$917$		−	8.56804i		−	0.282942i
$918$	6.77435	+	4.14927i	0.223587	+	0.136946i
$919$	−37.1316			−1.22486			−0.612429	−	0.790526i	$-0.709807\pi$
$919$	−37.1316			−1.22486			−0.612429	+	0.790526i	$0.709807\pi$
$920$		0			0
$921$	−0.713157	−	4.25973i	−0.0234993	−	0.140363i
$922$	11.9394	+	6.89324i	0.393205	+	0.227017i
$923$	−52.1003	−	30.0801i	−1.71490	−	0.990098i
$924$	8.53279	−	7.03494i	0.280708	−	0.231433i
$925$		0			0
$926$	−19.4135			−0.637967
$927$	−5.35044	−	1.03920i	−0.175732	−	0.0341319i
$928$			51.5098i			1.69089i
$929$	−23.9977	−	41.5653i	−0.787340	−	1.36371i	−0.927591	−	0.373597i	$-0.878124\pi$
$929$	−23.9977	−	41.5653i	−0.787340	−	1.36371i	0.140251	−	0.990116i	$-0.455209\pi$
$930$		0			0
$931$	11.5905	−	20.0753i	0.379862	−	0.657941i
$932$	−9.01115	−	5.20259i	−0.295170	−	0.170417i
$933$	14.6885	−	39.2949i	0.480879	−	1.28646i
$934$	−7.82831	−	13.5590i	−0.256150	−	0.443665i
$935$		0			0
$936$	−5.61515	+	28.9102i	−0.183537	+	0.944958i
$937$			22.0079i			0.718967i	0.933151	+	0.359483i	$0.117047\pi$
$937$			22.0079i			0.718967i	−0.933151	+	0.359483i	$0.882953\pi$
$938$	4.66195	−	2.69158i	0.152218	−	0.0878832i
$939$	46.8867	−	38.6562i	1.53009	−	1.26150i
$940$		0			0
$941$	−20.2921	+	35.1470i	−0.661504	+	1.14576i	0.318716	+	0.947850i	$0.396748\pi$
$941$	−20.2921	+	35.1470i	−0.661504	+	1.14576i	−0.980220	+	0.197909i	$0.936585\pi$
$942$	−0.197047	+	0.0329893i	−0.00642015	+	0.00107485i
$943$	−7.53946	+	4.35291i	−0.245518	+	0.141750i
$944$	2.45269			0.0798283
$945$		0			0
$946$	0.720331			0.0234200
$947$	26.1817	−	15.1160i	0.850790	−	0.491204i	−0.0101273	−	0.999949i	$-0.503224\pi$
$947$	26.1817	−	15.1160i	0.850790	−	0.491204i	0.860917	+	0.508745i	$0.169890\pi$
$948$	0.822925	−	0.137773i	0.0267273	−	0.00447465i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$	−13.9938	+	11.5373i	−0.453780	+	0.374123i
$952$	−6.94420	+	4.00924i	−0.225063	+	0.129940i
$953$		−	2.50811i		−	0.0812455i	−0.999175	−	0.0406227i	$-0.987066\pi$
$953$		−	2.50811i		−	0.0812455i	0.999175	−	0.0406227i	$-0.0129342\pi$
$954$	1.48173	+	1.28766i	0.0479727	+	0.0416896i
$955$		0			0
$956$	6.79439	+	11.7682i	0.219746	+	0.380612i
$957$	−15.3823	+	41.1510i	−0.497238	+	1.33022i
$958$	2.59088	+	1.49585i	0.0837077	+	0.0483286i
$959$	−7.28402	+	12.6163i	−0.235213	+	0.407401i
$960$		0			0
$961$	−8.72635	−	15.1145i	−0.281495	−	0.487564i
$962$		−	4.85601i		−	0.156564i
$963$	11.6450	+	33.8033i	0.375255	+	1.08930i
$964$	−44.1025			−1.42045
$965$		0			0
$966$	−6.45967	+	5.32574i	−0.207836	+	0.171353i
$967$	18.8386	+	10.8765i	0.605808	+	0.349763i	0.771323	−	0.636444i	$-0.219595\pi$
$967$	18.8386	+	10.8765i	0.605808	+	0.349763i	−0.165515	+	0.986207i	$0.552929\pi$
$968$	7.01552	+	4.05042i	0.225488	+	0.130185i
$969$	−3.57199	−	21.3357i	−0.114749	−	0.685403i
$970$		0			0
$971$	22.7512			0.730122			0.365061	−	0.930984i	$-0.381048\pi$
$971$	22.7512			0.730122			0.365061	+	0.930984i	$0.381048\pi$
$972$	7.85058	+	24.8669i	0.251808	+	0.797608i
$973$		−	11.4241i		−	0.366238i
$974$	−6.86920	−	11.8978i	−0.220103	−	0.381230i
$975$		0			0
$976$	2.71090	−	4.69541i	0.0867737	−	0.150296i
$977$	−34.0156	−	19.6389i	−1.08825	−	0.628304i	−0.155143	−	0.987892i	$-0.549584\pi$
$977$	−34.0156	−	19.6389i	−1.08825	−	0.628304i	−0.933111	+	0.359588i	$0.882917\pi$
$978$	−11.2287	−	13.6195i	−0.359055	−	0.435504i
$979$	−4.00924	−	6.94420i	−0.128136	−	0.221938i
$980$		0			0
$981$	47.2322	−	16.2711i	1.50801	−	0.519497i
$982$			8.45269i			0.269736i
$983$	−29.2629	+	16.8949i	−0.933341	+	0.538865i	−0.887867	−	0.460101i	$-0.847813\pi$
$983$	−29.2629	+	16.8949i	−0.933341	+	0.538865i	−0.0454743	+	0.998966i	$0.514480\pi$
$984$	5.01432	+	1.87436i	0.159851	+	0.0597523i
$985$		0			0
$986$	7.25405	−	12.5644i	0.231016	−	0.400132i
$987$	6.02480	−	16.1177i	0.191772	−	0.513032i
$988$	31.6329	−	18.2633i	1.00638	−	0.581033i
$989$	2.78817			0.0886587
$990$		0			0
$991$	−23.7983			−0.755979			−0.377990	−	0.925810i	$-0.623384\pi$
$991$	−23.7983			−0.755979			−0.377990	+	0.925810i	$0.623384\pi$
$992$	32.7213	−	18.8916i	1.03890	−	0.599810i
$993$	−18.4859	−	22.4218i	−0.586631	−	0.711534i
$994$	−5.25801	+	9.10713i	−0.166774	+	0.288861i
$995$		0			0
$996$	2.04957	+	12.2422i	0.0649431	+	0.387909i
$997$	44.7549	−	25.8392i	1.41740	−	0.818337i	0.421331	−	0.906907i	$-0.361563\pi$
$997$	44.7549	−	25.8392i	1.41740	−	0.818337i	0.996070	+	0.0885702i	$0.0282298\pi$
$998$		−	14.2175i		−	0.450046i
$999$	−4.50641	−	8.29541i	−0.142577	−	0.262455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.b.49.4		12
3.2	odd	2		675.2.k.b.199.3		12
5.2	odd	4		225.2.e.b.76.2		6
5.3	odd	4		45.2.e.b.31.2	yes	6
5.4	even	2	inner	225.2.k.b.49.3		12
9.2	odd	6		675.2.k.b.424.4		12
9.4	even	3		2025.2.b.l.649.4		6
9.5	odd	6		2025.2.b.m.649.3		6
9.7	even	3	inner	225.2.k.b.124.3		12
15.2	even	4		675.2.e.b.226.2		6
15.8	even	4		135.2.e.b.91.2		6
15.14	odd	2		675.2.k.b.199.4		12
20.3	even	4		720.2.q.i.481.2		6
45.2	even	12		675.2.e.b.451.2		6
45.4	even	6		2025.2.b.l.649.3		6
45.7	odd	12		225.2.e.b.151.2		6
45.13	odd	12		405.2.a.j.1.2		3
45.14	odd	6		2025.2.b.m.649.4		6
45.22	odd	12		2025.2.a.n.1.2		3
45.23	even	12		405.2.a.i.1.2		3
45.29	odd	6		675.2.k.b.424.3		12
45.32	even	12		2025.2.a.o.1.2		3
45.34	even	6	inner	225.2.k.b.124.4		12
45.38	even	12		135.2.e.b.46.2		6
45.43	odd	12		45.2.e.b.16.2	✓	6
60.23	odd	4		2160.2.q.k.1441.2		6
180.23	odd	12		6480.2.a.bs.1.2		3
180.43	even	12		720.2.q.i.241.2		6
180.83	odd	12		2160.2.q.k.721.2		6
180.103	even	12		6480.2.a.bv.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.2	✓	6	45.43	odd	12
45.2.e.b.31.2	yes	6	5.3	odd	4
135.2.e.b.46.2		6	45.38	even	12
135.2.e.b.91.2		6	15.8	even	4
225.2.e.b.76.2		6	5.2	odd	4
225.2.e.b.151.2		6	45.7	odd	12
225.2.k.b.49.3		12	5.4	even	2	inner
225.2.k.b.49.4		12	1.1	even	1	trivial
225.2.k.b.124.3		12	9.7	even	3	inner
225.2.k.b.124.4		12	45.34	even	6	inner
405.2.a.i.1.2		3	45.23	even	12
405.2.a.j.1.2		3	45.13	odd	12
675.2.e.b.226.2		6	15.2	even	4
675.2.e.b.451.2		6	45.2	even	12
675.2.k.b.199.3		12	3.2	odd	2
675.2.k.b.199.4		12	15.14	odd	2
675.2.k.b.424.3		12	45.29	odd	6
675.2.k.b.424.4		12	9.2	odd	6
720.2.q.i.241.2		6	180.43	even	12
720.2.q.i.481.2		6	20.3	even	4
2025.2.a.n.1.2		3	45.22	odd	12
2025.2.a.o.1.2		3	45.32	even	12
2025.2.b.l.649.3		6	45.4	even	6
2025.2.b.l.649.4		6	9.4	even	3
2025.2.b.m.649.3		6	9.5	odd	6
2025.2.b.m.649.4		6	45.14	odd	6
2160.2.q.k.721.2		6	180.83	odd	12
2160.2.q.k.1441.2		6	60.23	odd	4
6480.2.a.bs.1.2		3	180.23	odd	12
6480.2.a.bv.1.2		3	180.103	even	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +O(q^{10})\)	\(q+(0.495361 - 0.285997i) q^{2} +(1.70828 - 0.285997i) q^{3} +(-0.836412 + 1.44871i) q^{4} +(0.764419 - 0.630233i) q^{6} +(1.23669 - 0.714003i) q^{7} +2.10083i q^{8} +(2.83641 - 0.977122i) q^{9} +(-1.33641 - 2.31473i) q^{11} +(-1.01450 + 2.71400i) q^{12} +(4.04678 + 2.33641i) q^{13} +(0.408405 - 0.707378i) q^{14} +(-1.07199 - 1.85675i) q^{16} +2.67282i q^{17} +(1.12559 - 1.29523i) q^{18} -4.67282 q^{19} +(1.90841 - 1.57340i) q^{21} +(-1.32401 - 0.764419i) q^{22} +(-5.12483 - 2.95882i) q^{23} +(0.600830 + 3.58880i) q^{24} +2.67282 q^{26} +(4.56592 - 2.48040i) q^{27} +2.38880i q^{28} +(-4.74482 - 8.21826i) q^{29} +(-3.48040 + 6.02823i) q^{31} +(-4.70079 - 2.71400i) q^{32} +(-2.94497 - 3.57199i) q^{33} +(0.764419 + 1.32401i) q^{34} +(-0.956844 + 4.92641i) q^{36} -1.81681i q^{37} +(-2.31473 + 1.33641i) q^{38} +(7.58123 + 2.83387i) q^{39} +(0.735581 - 1.27406i) q^{41} +(0.495361 - 1.32520i) q^{42} +(-0.408039 + 0.235581i) q^{43} +4.47116 q^{44} -3.38485 q^{46} +(6.02480 - 3.47842i) q^{47} +(-2.36228 - 2.86525i) q^{48} +(-2.48040 + 4.29618i) q^{49} +(0.764419 + 4.56592i) q^{51} +(-6.76956 + 3.90841i) q^{52} +1.14399i q^{53} +(1.55239 - 2.53453i) q^{54} +(1.50000 + 2.59808i) q^{56} +(-7.98247 + 1.33641i) q^{57} +(-4.70079 - 2.71400i) q^{58} +(-0.571993 + 0.990721i) q^{59} +(1.26442 + 2.19004i) q^{61} +3.98153i q^{62} +(2.81009 - 3.23360i) q^{63} +1.18319 q^{64} +(-2.48040 - 0.927175i) q^{66} +(5.70751 + 3.29523i) q^{67} +(-3.87214 - 2.23558i) q^{68} +(-9.60083 - 3.58880i) q^{69} -12.8745 q^{71} +(2.05277 + 5.95882i) q^{72} +1.71203i q^{73} +(-0.519602 - 0.899976i) q^{74} +(3.90841 - 6.76956i) q^{76} +(-3.30545 - 1.90841i) q^{77} +(4.56592 - 0.764419i) q^{78} +(-0.143987 - 0.249392i) q^{79} +(7.09046 - 5.54304i) q^{81} -0.841495i q^{82} +(3.71007 - 2.14201i) q^{83} +(0.683190 + 4.08074i) q^{84} +(-0.134751 + 0.233396i) q^{86} +(-10.4559 - 12.6821i) q^{87} +(4.86286 - 2.80757i) q^{88} +3.00000 q^{89} +6.67282 q^{91} +(8.57293 - 4.94958i) q^{92} +(-4.22143 + 11.2933i) q^{93} +(1.98963 - 3.44615i) q^{94} +(-8.80644 - 3.29186i) q^{96} +(6.78555 - 3.91764i) q^{97} +2.83754i q^{98} +(-6.05239 - 5.25970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9	\( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more