LMFDB - Embedded newform 225.2.k.b.124.4

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			124.4
Root			$-1.50511 + 0.403293i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.b.49.4

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.664805	−	0.747017i	$-0.268514\pi$
$2$	0.495361	+	0.285997i	0.350273	+	0.202230i	−0.314533	+	0.949247i	$0.601848\pi$
$3$	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	0.715161	−	0.698960i	$-0.246353\pi$
$7$	1.23669	+	0.714003i	0.467425	+	0.269868i	−0.247736	+	0.968828i	$0.579687\pi$
$8$		−	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	−0.994080	−	0.108653i	$-0.965346\pi$
$11$	−1.33641	+	2.31473i	−0.402943	+	0.697918i	0.591136	+	0.806572i	$0.298679\pi$
$12$	−1.01450	−	2.71400i	−0.292860	−	0.783465i
$13$	4.04678	−	2.33641i	1.12238	−	0.648004i	0.180370	−	0.983599i	$-0.442271\pi$
$13$	4.04678	−	2.33641i	1.12238	−	0.648004i	0.942006	+	0.335595i	$0.108937\pi$
$14$	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	$-0.894929\pi$
$17$		−	2.67282i		−	0.648255i	0.946013	−	0.324127i	$-0.105071\pi$
$18$	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	−0.927799	−	0.373081i	$-0.878301\pi$
$23$	−5.12483	+	2.95882i	−1.06860	+	0.616957i	−0.140802	+	0.990038i	$0.544968\pi$
$24$	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	−0.0309603	+	0.999521i	$0.509857\pi$
$29$	−4.74482	+	8.21826i	−0.881090	+	1.52609i	−0.850130	+	0.526573i	$0.823477\pi$
$30$		0			0
$31$	−3.48040	−	6.02823i	−0.625098	−	1.08270i	−0.988522	−	0.151078i	$-0.951726\pi$
$31$	−3.48040	−	6.02823i	−0.625098	−	1.08270i	0.363424	−	0.931624i	$-0.381608\pi$
$32$	−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	$0.0477152\pi$
$37$			1.81681i			0.298682i	−0.988786	+	0.149341i	$0.952285\pi$
$38$	−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	0.917731	−	0.397202i	$-0.130019\pi$
$41$	0.735581	+	1.27406i	0.114879	+	0.198975i	−0.802853	+	0.596177i	$0.796685\pi$
$42$	0.495361	+	1.32520i	0.0764358	+	0.204483i
$43$	−0.408039	−	0.235581i	−0.0622254	−	0.0359258i	0.468565	−	0.883429i	$-0.344771\pi$
$43$	−0.408039	−	0.235581i	−0.0622254	−	0.0359258i	−0.530790	+	0.847503i	$0.678105\pi$
$44$	4.47116			0.674053
$45$		0			0
$46$	−3.38485			−0.499069
$47$	6.02480	+	3.47842i	0.878808	+	0.507380i	0.870265	−	0.492584i	$-0.163947\pi$
$47$	6.02480	+	3.47842i	0.878808	+	0.507380i	0.00854274	+	0.999964i	$0.497281\pi$
$48$	−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	$-0.974965\pi$
$53$		−	1.14399i		−	0.157139i	0.996909	−	0.0785693i	$-0.0250352\pi$
$54$	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	0.826387	−	0.563102i	$-0.190392\pi$
$59$	−0.571993	−	0.990721i	−0.0744672	−	0.128981i	−0.900854	+	0.434121i	$0.857059\pi$
$60$		0			0
$61$	1.26442	−	2.19004i	0.161892	−	0.280406i	−0.773655	−	0.633607i	$-0.781574\pi$
$61$	1.26442	−	2.19004i	0.161892	−	0.280406i	0.935547	+	0.353201i	$0.114907\pi$
$62$		−	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	−0.109051	−	0.994036i	$-0.534781\pi$
$67$	5.70751	−	3.29523i	0.697283	−	0.402577i	0.806335	+	0.591459i	$0.201448\pi$
$68$	−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	$-0.968055\pi$
$73$		−	1.71203i		−	0.200378i	0.994968	−	0.100189i	$-0.0319447\pi$
$74$	−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	−0.874012	−	0.485905i	$-0.838490\pi$
$79$	−0.143987	+	0.249392i	−0.0161998	+	0.0280588i	0.857812	+	0.513964i	$0.171823\pi$
$80$		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	0.689600	−	0.724190i	$-0.257786\pi$
$83$	3.71007	+	2.14201i	0.407233	+	0.235116i	−0.282367	+	0.959306i	$0.591120\pi$
$84$	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	0.803225	−	0.595675i	$-0.203115\pi$
$97$	6.78555	+	3.91764i	0.688968	+	0.397776i	−0.114257	+	0.993451i	$0.536449\pi$
$98$		−	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	−0.742372	−	0.669988i	$-0.766299\pi$
$101$	2.10083	−	3.63875i	0.209040	−	0.362069i	0.951413	+	0.307919i	$0.0996326\pi$
$102$	1.68450	−	2.04316i	0.166790	−	0.202303i
$103$	−1.57340	+	0.908405i	−0.155032	+	0.0895078i	−0.575509	−	0.817795i	$-0.695196\pi$
$103$	−1.57340	+	0.908405i	−0.155032	+	0.0895078i	0.420477	+	0.907303i	$0.361863\pi$
$104$	−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	$-0.804589\pi$
$107$		−	11.9176i		−	1.15212i	0.817407	−	0.576061i	$-0.195411\pi$
$108$	−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	0.658384	−	0.752682i	$-0.271240\pi$
$113$	17.4272	−	10.0616i	1.63942	−	0.946518i	0.981034	−	0.193836i	$-0.0620929\pi$
$114$	−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	$-0.969063\pi$
$127$		−	2.18714i		−	0.194078i	0.995281	−	0.0970388i	$-0.0309371\pi$
$128$	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	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	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	0.0726153	−	0.997360i	$-0.476865\pi$
$137$	−8.83490	−	5.10083i	−0.754816	−	0.435793i	−0.827431	+	0.561567i	$0.810199\pi$
$138$	−5.78226	−	0.968056i	−0.492218	−	0.0824064i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		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	−0.903927	−	0.427687i	$-0.859329\pi$
$149$	−10.0381	−	17.3865i	−0.822351	−	1.42435i	0.0815762	−	0.996667i	$-0.474005\pi$
$150$		0			0
$151$	−1.51960	+	2.63203i	−0.123663	+	0.214191i	−0.921210	−	0.389066i	$-0.872798\pi$
$151$	−1.51960	+	2.63203i	−0.123663	+	0.214191i	0.797546	+	0.603258i	$0.206131\pi$
$152$			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	−0.506953	−	0.861974i	$-0.669228\pi$
$157$	−0.174643	+	0.100830i	−0.0139381	+	0.00804714i	0.493015	+	0.870021i	$0.335895\pi$
$158$	−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	$0.245820\pi$
$163$			17.8168i			1.39552i	−0.716331	+	0.697760i	$0.754180\pi$
$164$	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	−0.891514	−	0.452993i	$-0.850356\pi$
$167$	−12.2117	+	7.05042i	−0.944968	+	0.545578i	−0.0534538	+	0.998570i	$0.517023\pi$
$168$	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	0.349317	−	0.937005i	$-0.386414\pi$
$173$	−3.78140	−	2.18319i	−0.287494	−	0.165985i	−0.636811	+	0.771020i	$0.719747\pi$
$174$	−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	−0.810121	−	0.586263i	$-0.800598\pi$
$191$	1.41877	−	2.45738i	0.102659	−	0.177810i	0.912779	+	0.408453i	$0.133932\pi$
$192$	2.02121	+	0.338388i	0.145869	+	0.0244211i
$193$	−16.2710	+	9.39409i	−1.17121	+	0.676201i	−0.953966	−	0.299915i	$-0.903042\pi$
$193$	−16.2710	+	9.39409i	−1.17121	+	0.676201i	−0.217249	+	0.976116i	$0.569708\pi$
$194$	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	$-0.933346\pi$
$197$		−	5.83528i		−	0.415747i	0.978156	−	0.207873i	$-0.0666542\pi$
$198$	−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	0.684862	−	0.728673i	$-0.259863\pi$
$211$	−4.19243	−	7.26149i	−0.288618	−	0.499902i	−0.973480	+	0.228771i	$0.926529\pi$
$212$	−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	0.210073	−	0.977686i	$-0.432630\pi$
$223$	−7.93834	−	4.58321i	−0.531591	−	0.306914i	−0.741664	+	0.670772i	$0.765963\pi$
$224$	−7.75123			−0.517901
$225$		0			0
$226$	11.5104			0.765658
$227$	−2.31473	−	1.33641i	−0.153634	−	0.0887008i	0.421212	−	0.906962i	$-0.361605\pi$
$227$	−2.31473	−	1.33641i	−0.153634	−	0.0887008i	−0.574846	+	0.818261i	$0.694938\pi$
$228$	4.74056	+	12.6821i	0.313951	+	0.839890i
$229$	1.27365	+	2.20603i	0.0841654	+	0.145779i	0.905035	−	0.425336i	$-0.139844\pi$
$229$	1.27365	+	2.20603i	0.0841654	+	0.145779i	−0.820870	+	0.571115i	$0.806511\pi$
$230$		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	$-0.934688\pi$
$233$		−	6.22013i		−	0.407494i	0.979024	−	0.203747i	$-0.0653121\pi$
$234$	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	0.966965	−	0.254909i	$-0.0820455\pi$
$239$	4.06163	+	7.03494i	0.262725	+	0.455053i	−0.704240	+	0.709962i	$0.748712\pi$
$240$		0			0
$241$	13.1821	−	22.8320i	0.849131	−	1.47074i	−0.0328536	−	0.999460i	$-0.510460\pi$
$241$	13.1821	−	22.8320i	0.849131	−	1.47074i	0.881985	−	0.471278i	$-0.156207\pi$
$242$			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	0.0724199	−	0.997374i	$-0.476928\pi$
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.899961	+	0.435970i	$0.143595\pi$
$258$	−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	0.147550	−	0.989055i	$-0.452861\pi$
$263$	−10.3016	−	5.94761i	−0.635221	−	0.366745i	−0.782771	+	0.622309i	$0.786195\pi$
$264$	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	0.0535366	−	0.998566i	$-0.482951\pi$
$277$	−13.0563	−	7.53807i	−0.784479	−	0.452919i	−0.838015	+	0.545647i	$0.816284\pi$
$278$			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	−0.948015	−	0.318226i	$-0.896913\pi$
$281$	−3.32605	+	5.76088i	−0.198415	+	0.343665i	0.749599	+	0.661892i	$0.230246\pi$
$282$	2.41326	+	6.45600i	0.143707	+	0.384449i
$283$	23.2934	−	13.4485i	1.38465	−	0.799428i	0.391943	−	0.919989i	$-0.371803\pi$
$283$	23.2934	−	13.4485i	1.38465	−	0.799428i	0.992706	+	0.120562i	$0.0384696\pi$
$284$	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	−0.152837	−	0.988251i	$-0.548841\pi$
$293$	10.7256	−	6.19243i	0.626596	−	0.361765i	0.779433	+	0.626486i	$0.215507\pi$
$294$	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	$0.0226695\pi$
$307$			2.49359i			0.142317i	−0.997465	+	0.0711583i	$0.977330\pi$
$308$	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	0.972900	+	0.231228i	$0.0742742\pi$
$311$	12.1101	+	20.9752i	0.686699	+	1.18940i	−0.286201	+	0.958170i	$0.592392\pi$
$312$	−5.95348	−	15.9269i	−0.337049	−	0.901682i
$313$	30.3837	+	17.5420i	1.71739	+	0.991534i	0.923618	+	0.383315i	$0.125218\pi$
$313$	30.3837	+	17.5420i	1.71739	+	0.991534i	0.793770	+	0.608219i	$0.208116\pi$
$314$	−0.115349			−0.00650950
$315$		0			0
$316$	0.481728			0.0270993
$317$	−9.06829	−	5.23558i	−0.509326	−	0.294060i	0.223231	−	0.974766i	$-0.428340\pi$
$317$	−9.06829	−	5.23558i	−0.509326	−	0.294060i	−0.732557	+	0.680706i	$0.761673\pi$
$318$	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	−0.999016	−	0.0443606i	$-0.985875\pi$
$331$	−8.38880	+	14.5298i	−0.461090	+	0.798632i	0.537925	+	0.842993i	$0.319208\pi$
$332$		−	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	0.305008	−	0.952350i	$-0.401341\pi$
$337$	23.5394	−	13.5905i	1.28227	−	0.740320i	0.977263	+	0.212030i	$0.0680074\pi$
$338$	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	0.160530	−	0.987031i	$-0.448680\pi$
$347$	20.4086	−	11.7829i	1.09559	−	0.632539i	0.935059	+	0.354492i	$0.115346\pi$
$348$	27.1180	+	4.54005i	1.45368	+	0.243372i
$349$	−5.35601	+	9.27689i	−0.286701	+	0.496580i	−0.973020	−	0.230720i	$-0.925892\pi$
$349$	−5.35601	+	9.27689i	−0.286701	+	0.496580i	0.686319	+	0.727300i	$0.259225\pi$
$350$		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	−0.284392	−	0.958708i	$-0.591792\pi$
$353$	−23.6141	−	13.6336i	−1.25685	−	0.725644i	−0.972461	+	0.233064i	$0.925125\pi$
$354$	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	0.296152	−	0.955141i	$-0.404297\pi$
$367$	−7.33624	−	4.23558i	−0.382949	−	0.221096i	−0.679100	+	0.734045i	$0.737630\pi$
$368$		−	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	−0.255554	−	0.966795i	$-0.582258\pi$
$373$	8.76700	−	5.06163i	0.453938	−	0.262081i	0.709492	+	0.704714i	$0.248925\pi$
$374$	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	−0.266813	−	0.963748i	$-0.585970\pi$
$383$	8.50161	−	4.90841i	0.434412	−	0.250808i	0.701224	+	0.712941i	$0.252637\pi$
$384$	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	−0.725166	−	0.688574i	$-0.758237\pi$
$389$	4.61007	−	7.98487i	0.233740	−	0.404849i	0.958906	+	0.283725i	$0.0915703\pi$
$390$		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	$0.195640\pi$
$397$			22.9793i			1.15330i	−0.816993	+	0.576648i	$0.804360\pi$
$398$	−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	0.970461	−	0.241259i	$-0.0775602\pi$
$401$	5.53279	+	9.58307i	0.276294	+	0.478556i	−0.694167	+	0.719814i	$0.744227\pi$
$402$	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	0.561411	−	0.827537i	$-0.310259\pi$
$409$	−8.81681	−	15.2712i	−0.435963	−	0.755110i	−0.997374	+	0.0724270i	$0.976926\pi$
$410$		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	0.821411	+	0.570336i	$0.193187\pi$
$419$	18.5173	+	32.0730i	0.904631	+	1.56687i	0.0832199	+	0.996531i	$0.473480\pi$
$420$		0			0
$421$	−2.52884	+	4.38007i	−0.123248	+	0.213472i	−0.921047	−	0.389452i	$-0.872664\pi$
$421$	−2.52884	+	4.38007i	−0.123248	+	0.213472i	0.797799	+	0.602924i	$0.205998\pi$
$422$		−	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	$0.308948\pi$
$433$			34.3434i			1.65044i	−0.564813	+	0.825219i	$0.691052\pi$
$434$	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	−0.999267	−	0.0382924i	$-0.987808\pi$
$439$	−9.77365	+	16.9285i	−0.466471	+	0.807952i	0.532796	+	0.846244i	$0.321141\pi$
$440$		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	0.268081	−	0.963396i	$-0.413611\pi$
$443$	−9.09686	−	5.25208i	−0.432205	−	0.249534i	−0.700286	+	0.713863i	$0.746944\pi$
$444$	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	0.188217	−	0.982127i	$-0.439729\pi$
$457$	−12.1472	−	7.01319i	−0.568222	−	0.328063i	−0.756439	+	0.654064i	$0.773063\pi$
$458$			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	−0.436102	−	0.899897i	$-0.643641\pi$
$461$	12.0513	−	20.8734i	0.561283	−	0.972171i	0.997385	−	0.0722736i	$-0.0230255\pi$
$462$	−3.72949	−	0.624385i	−0.173512	−	0.0290490i
$463$	−29.3930	+	16.9700i	−1.36601	+	0.788664i	−0.990415	−	0.138121i	$-0.955894\pi$
$463$	−29.3930	+	16.9700i	−1.36601	+	0.788664i	−0.375591	+	0.926785i	$0.622560\pi$
$464$	−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	$0.218305\pi$
$467$			27.3720i			1.26663i	−0.773896	+	0.633313i	$0.781695\pi$
$468$	−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	−0.800076	−	0.599898i	$-0.795208\pi$
$479$	2.61515	−	4.52957i	0.119489	−	0.206961i	0.919565	+	0.392937i	$0.128541\pi$
$480$		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	$0.183163\pi$
$487$			24.0185i			1.08838i	−0.838962	+	0.544190i	$0.816837\pi$
$488$	−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	0.649734	−	0.760161i	$-0.274880\pi$
$491$	−7.38880	−	12.7978i	−0.333452	−	0.577556i	−0.983186	+	0.182606i	$0.941547\pi$
$492$	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	0.997797	+	0.0663440i	$0.0211335\pi$
$499$	12.4280	+	21.5259i	0.556354	+	0.963633i	−0.441443	+	0.897289i	$0.645533\pi$
$500$		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	$0.334323\pi$
$503$			38.9154i			1.73515i	−0.497305	+	0.867576i	$0.665677\pi$
$504$	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	0.887548	−	0.460715i	$-0.152407\pi$
$509$	1.01037	+	1.75001i	0.0447837	+	0.0775676i	−0.842765	+	0.538282i	$0.819073\pi$
$510$		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	$-0.644323\pi$
$523$		−	41.1170i		−	1.79792i	0.438028	−	0.898961i	$-0.355677\pi$
$524$	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	0.999806	−	0.0196900i	$-0.00626792\pi$
$547$	34.6764	+	20.0204i	1.48266	+	0.856013i	0.482851	+	0.875702i	$0.339601\pi$
$548$			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	$0.0987047\pi$
$557$			14.4033i			0.610288i	−0.952306	+	0.305144i	$0.901295\pi$
$558$	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	0.143196	−	0.989694i	$-0.454262\pi$
$563$	25.4335	−	14.6840i	1.07189	−	0.618858i	0.928698	+	0.370836i	$0.120929\pi$
$564$	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	0.323062	−	0.946378i	$-0.395288\pi$
$569$	23.4033	−	40.5357i	0.981118	−	1.69935i	0.658056	−	0.752969i	$-0.271379\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	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	$-0.799996\pi$
$577$		−	28.2386i		−	1.17559i	0.809010	−	0.587794i	$-0.200004\pi$
$578$	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	0.787056	−	0.616882i	$-0.211604\pi$
$587$	15.6598	+	9.04118i	0.646348	+	0.373169i	−0.140707	+	0.990051i	$0.544938\pi$
$588$	−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	$-0.949209\pi$
$593$		−	7.73840i		−	0.317778i	0.987296	−	0.158889i	$-0.0507912\pi$
$594$	−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	−0.996522	−	0.0833249i	$-0.973446\pi$
$599$	−13.9608	−	24.1808i	−0.570423	−	0.988001i	0.426100	−	0.904676i	$-0.359887\pi$
$600$		0			0
$601$	−19.2201	+	33.2902i	−0.784006	+	1.35794i	0.145586	+	0.989346i	$0.453493\pi$
$601$	−19.2201	+	33.2902i	−0.784006	+	1.35794i	−0.929591	+	0.368592i	$0.879840\pi$
$602$		−	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	−0.488712	−	0.872445i	$-0.662533\pi$
$607$	0.554113	−	0.319917i	0.0224907	−	0.0129850i	0.511203	+	0.859460i	$0.329200\pi$
$608$	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	$0.331582\pi$
$613$			42.7467i			1.72652i	−0.504757	+	0.863262i	$0.668418\pi$
$614$	−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	−0.820517	−	0.571622i	$-0.806314\pi$
$617$	−18.2753	+	10.5513i	−0.735737	+	0.424778i	0.0847805	+	0.996400i	$0.472981\pi$
$618$	−1.77525	−	0.297209i	−0.0714109	−	0.0119555i
$619$	−6.82605	+	11.8231i	−0.274362	+	0.475209i	−0.969974	−	0.243209i	$-0.921800\pi$
$619$	−6.82605	+	11.8231i	−0.274362	+	0.475209i	0.695612	+	0.718418i	$0.255133\pi$
$620$		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	0.480642	+	0.876917i	$0.340404\pi$
$641$	−13.1429	+	22.7641i	−0.519112	+	0.899128i	−0.999753	+	0.0222106i	$0.992930\pi$
$642$	7.51089	−	9.11007i	0.296431	−	0.359546i
$643$	17.8250	−	10.2913i	0.702950	−	0.405848i	−0.105495	−	0.994420i	$-0.533643\pi$
$643$	17.8250	−	10.2913i	0.702950	−	0.405848i	0.808445	+	0.588571i	$0.200309\pi$
$644$	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	$-0.848896\pi$
$647$		−	23.2527i		−	0.914159i	0.889426	−	0.457079i	$-0.151104\pi$
$648$	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	−0.147225	−	0.989103i	$-0.547034\pi$
$653$	16.2459	−	9.37957i	0.635751	−	0.367051i	0.782976	+	0.622052i	$0.213701\pi$
$654$	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	−0.868740	−	0.495268i	$-0.835070\pi$
$659$	−0.140034	+	0.242545i	−0.00545494	+	0.00944823i	0.863285	+	0.504717i	$0.168403\pi$
$660$		0			0
$661$	19.8930	+	34.4556i	0.773746	+	1.34017i	0.935496	+	0.353336i	$0.114953\pi$
$661$	19.8930	+	34.4556i	0.773746	+	1.34017i	−0.161750	+	0.986832i	$0.551714\pi$
$662$	−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	−0.178068	−	0.984018i	$-0.556985\pi$
$673$	−29.0368	−	16.7644i	−1.11929	−	0.646221i	−0.941219	+	0.337797i	$0.890318\pi$
$674$	15.5473			0.598860
$675$		0			0
$676$	−14.7799			−0.568456
$677$	23.8048	+	13.7437i	0.914891	+	0.528213i	0.882002	−	0.471246i	$-0.156196\pi$
$677$	23.8048	+	13.7437i	0.914891	+	0.528213i	0.0328897	+	0.999459i	$0.489529\pi$
$678$	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	$-0.769832\pi$
$683$		−	34.5865i		−	1.32342i	0.749762	−	0.661708i	$-0.230168\pi$
$684$	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	0.160282	+	0.987071i	$0.448760\pi$
$691$	−20.3641	+	35.2717i	−0.774688	+	1.34180i	−0.934970	+	0.354727i	$0.884574\pi$
$692$			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	−0.688904	−	0.724853i	$-0.741908\pi$
$709$	7.54316	−	13.0651i	0.283289	−	0.490671i	0.972193	+	0.234182i	$0.0752410\pi$
$710$		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	−0.200315	−	0.979732i	$-0.564197\pi$
$727$	−30.9789	−	17.8857i	−1.14895	−	0.663344i	−0.948630	+	0.316388i	$0.897530\pi$
$728$		−	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	−0.808732	−	0.588177i	$-0.799846\pi$
$733$	−19.0526	+	11.0000i	−0.703722	+	0.406294i	0.105010	+	0.994471i	$0.466513\pi$
$734$	−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	−0.847036	−	0.531536i	$-0.821615\pi$
$743$	−22.0853	+	12.7509i	−0.810231	+	0.467787i	0.0368054	+	0.999322i	$0.488282\pi$
$744$	−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	0.983596	−	0.180384i	$-0.0577342\pi$
$751$	9.19638	+	15.9286i	0.335581	+	0.581243i	−0.648016	+	0.761627i	$0.724401\pi$
$752$	−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	$0.275495\pi$
$757$			41.8986i			1.52283i	−0.648264	+	0.761415i	$0.724505\pi$
$758$	−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	0.929179	−	0.369630i	$-0.120515\pi$
$761$	3.98568	+	6.90340i	0.144481	+	0.250248i	−0.784698	+	0.619878i	$0.787182\pi$
$762$	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	0.915244	−	0.402901i	$-0.131998\pi$
$769$	3.01432	+	5.22095i	0.108699	+	0.188272i	−0.806544	+	0.591174i	$0.798665\pi$
$770$		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	$0.294393\pi$
$773$			44.4033i			1.59708i	−0.601944	+	0.798538i	$0.705607\pi$
$774$	−0.154153	−	0.793674i	−0.00554093	−	0.0285280i
$775$		0			0
$776$	8.23030	−	14.2553i	0.295451

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