LMFDB - Embedded newform 1500.2.o.b.649.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			649.3
Root			$-0.462894 + 1.33631i$ of defining polynomial
Character	$\chi$	$=$	1500.649
Dual form			1500.2.o.b.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{3} -0.0883282i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{3} -0.0883282i q^{7} +(-0.309017 - 0.951057i) q^{9} +(0.701409 - 2.15871i) q^{11} +(2.52199 - 0.819443i) q^{13} +(-1.22749 - 1.68949i) q^{17} +(1.42464 - 1.03506i) q^{19} +(-0.0714590 - 0.0519180i) q^{21} +(-4.50810 - 1.46477i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(2.99851 + 2.17855i) q^{29} +(3.32199 - 2.41356i) q^{31} +(-1.33416 - 1.83631i) q^{33} +(-6.77065 + 2.19992i) q^{37} +(0.819443 - 2.52199i) q^{39} +(-2.03623 - 6.26687i) q^{41} -1.79469i q^{43} +(5.94311 - 8.17999i) q^{47} +6.99220 q^{49} -2.08833 q^{51} +(0.565120 - 0.777821i) q^{53} -1.76095i q^{57} +(2.77436 + 8.53860i) q^{59} +(2.92521 - 9.00287i) q^{61} +(-0.0840051 + 0.0272949i) q^{63} +(-8.17249 - 11.2485i) q^{67} +(-3.83482 + 2.78616i) q^{69} +(-4.97363 - 3.61355i) q^{71} +(3.00310 + 0.975766i) q^{73} +(-0.190675 - 0.0619542i) q^{77} +(10.8021 + 7.84821i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-9.29846 - 12.7982i) q^{83} +(3.52496 - 1.14533i) q^{87} +(3.16767 - 9.74909i) q^{89} +(-0.0723799 - 0.222762i) q^{91} -4.10620i q^{93} +(-7.52820 + 10.3617i) q^{97} -2.26981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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			0
$2$		0			0
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	0.0883282i		−	0.0333849i	−0.999861	−	0.0166925i	$-0.994686\pi$
$7$		−	0.0883282i		−	0.0333849i	0.999861	−	0.0166925i	$-0.00531362\pi$
$8$		0			0
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	0.701409	−	2.15871i	0.211483	−	0.650877i	−0.787902	−	0.615801i	$-0.788833\pi$
$11$	0.701409	−	2.15871i	0.211483	−	0.650877i	0.999385	−	0.0350761i	$-0.0111674\pi$
$12$		0			0
$13$	2.52199	−	0.819443i	0.699473	−	0.227273i	0.0623720	−	0.998053i	$-0.480133\pi$
$13$	2.52199	−	0.819443i	0.699473	−	0.227273i	0.637101	+	0.770780i	$0.280133\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.22749	−	1.68949i	−0.297710	−	0.409762i	0.633790	−	0.773506i	$-0.281499\pi$
$17$	−1.22749	−	1.68949i	−0.297710	−	0.409762i	−0.931499	+	0.363743i	$0.881499\pi$
$18$		0			0
$19$	1.42464	−	1.03506i	0.326835	−	0.237459i	−0.412252	−	0.911070i	$-0.635258\pi$
$19$	1.42464	−	1.03506i	0.326835	−	0.237459i	0.739086	+	0.673611i	$0.235258\pi$
$20$		0			0
$21$	−0.0714590	−	0.0519180i	−0.0155936	−	0.0113294i
$22$		0			0
$23$	−4.50810	−	1.46477i	−0.940005	−	0.305426i	−0.201357	−	0.979518i	$-0.564535\pi$
$23$	−4.50810	−	1.46477i	−0.940005	−	0.305426i	−0.738647	+	0.674092i	$0.764535\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$		0			0
$29$	2.99851	+	2.17855i	0.556809	+	0.404546i	0.830290	−	0.557332i	$-0.188175\pi$
$29$	2.99851	+	2.17855i	0.556809	+	0.404546i	−0.273480	+	0.961878i	$0.588175\pi$
$30$		0			0
$31$	3.32199	−	2.41356i	0.596646	−	0.433489i	−0.248041	−	0.968750i	$-0.579787\pi$
$31$	3.32199	−	2.41356i	0.596646	−	0.433489i	0.844687	+	0.535261i	$0.179787\pi$
$32$		0			0
$33$	−1.33416	−	1.83631i	−0.232247	−	0.319661i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.77065	+	2.19992i	−1.11309	+	0.361664i	−0.807126	−	0.590379i	$-0.798978\pi$
$37$	−6.77065	+	2.19992i	−1.11309	+	0.361664i	−0.305963	+	0.952044i	$0.598978\pi$
$38$		0			0
$39$	0.819443	−	2.52199i	0.131216	−	0.403841i
$40$		0			0
$41$	−2.03623	−	6.26687i	−0.318006	−	0.978721i	−0.974499	−	0.224390i	$-0.927961\pi$
$41$	−2.03623	−	6.26687i	−0.318006	−	0.978721i	0.656494	−	0.754332i	$-0.272039\pi$
$42$		0			0
$43$		−	1.79469i		−	0.273688i	−0.990593	−	0.136844i	$-0.956304\pi$
$43$		−	1.79469i		−	0.273688i	0.990593	−	0.136844i	$-0.0436959\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.94311	−	8.17999i	0.866892	−	1.19317i	−0.112990	−	0.993596i	$-0.536043\pi$
$47$	5.94311	−	8.17999i	0.866892	−	1.19317i	0.979882	−	0.199578i	$-0.0639571\pi$
$48$		0			0
$49$	6.99220			0.998885
$50$		0			0
$51$	−2.08833			−0.292424
$52$		0			0
$53$	0.565120	−	0.777821i	0.0776252	−	0.106842i	−0.768439	−	0.639923i	$-0.778966\pi$
$53$	0.565120	−	0.777821i	0.0776252	−	0.106842i	0.846064	+	0.533081i	$0.178966\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1.76095i		−	0.233244i
$58$		0			0
$59$	2.77436	+	8.53860i	0.361191	+	1.11163i	0.952332	+	0.305063i	$0.0986774\pi$
$59$	2.77436	+	8.53860i	0.361191	+	1.11163i	−0.591142	+	0.806568i	$0.701323\pi$
$60$		0			0
$61$	2.92521	−	9.00287i	0.374535	−	1.15270i	−0.569257	−	0.822159i	$-0.692769\pi$
$61$	2.92521	−	9.00287i	0.374535	−	1.15270i	0.943792	−	0.330540i	$-0.107231\pi$
$62$		0			0
$63$	−0.0840051	+	0.0272949i	−0.0105836	+	0.00343883i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.17249	−	11.2485i	−0.998429	−	1.37422i	−0.926285	−	0.376825i	$-0.877016\pi$
$67$	−8.17249	−	11.2485i	−0.998429	−	1.37422i	−0.0721440	−	0.997394i	$-0.522984\pi$
$68$		0			0
$69$	−3.83482	+	2.78616i	−0.461658	+	0.335414i
$70$		0			0
$71$	−4.97363	−	3.61355i	−0.590261	−	0.428850i	0.252148	−	0.967689i	$-0.418863\pi$
$71$	−4.97363	−	3.61355i	−0.590261	−	0.428850i	−0.842409	+	0.538839i	$0.818863\pi$
$72$		0			0
$73$	3.00310	+	0.975766i	0.351486	+	0.114205i	0.479438	−	0.877576i	$-0.340840\pi$
$73$	3.00310	+	0.975766i	0.351486	+	0.114205i	−0.127952	+	0.991780i	$0.540840\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.190675	−	0.0619542i	−0.0217295	−	0.00706033i
$78$		0			0
$79$	10.8021	+	7.84821i	1.21534	+	0.882993i	0.995704	−	0.0925903i	$-0.0295147\pi$
$79$	10.8021	+	7.84821i	1.21534	+	0.882993i	0.219631	+	0.975583i	$0.429515\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−9.29846	−	12.7982i	−1.02064	−	1.40479i	−0.911755	−	0.410734i	$-0.865272\pi$
$83$	−9.29846	−	12.7982i	−1.02064	−	1.40479i	−0.108884	−	0.994054i	$-0.534728\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.52496	−	1.14533i	0.377915	−	0.122792i
$88$		0			0
$89$	3.16767	−	9.74909i	0.335772	−	1.03340i	−0.630568	−	0.776134i	$-0.717178\pi$
$89$	3.16767	−	9.74909i	0.335772	−	1.03340i	0.966340	−	0.257267i	$-0.0828220\pi$
$90$		0			0
$91$	−0.0723799	−	0.222762i	−0.00758747	−	0.0233518i
$92$		0			0
$93$		−	4.10620i		−	0.425793i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.52820	+	10.3617i	−0.764373	+	1.05207i	0.232465	+	0.972605i	$0.425321\pi$
$97$	−7.52820	+	10.3617i	−0.764373	+	1.05207i	−0.996838	+	0.0794643i	$0.974679\pi$
$98$		0			0
$99$	−2.26981			−0.228124
$100$		0			0
$101$	−2.72537			−0.271185			−0.135592	−	0.990765i	$-0.543294\pi$
$101$	−2.72537			−0.271185			−0.135592	+	0.990765i	$0.543294\pi$
$102$		0			0
$103$	0.211589	−	0.291227i	0.0208485	−	0.0286954i	−0.798466	−	0.602041i	$-0.794355\pi$
$103$	0.211589	−	0.291227i	0.0208485	−	0.0286954i	0.819314	+	0.573345i	$0.194355\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			0.0286533i			0.00277002i	0.999999	+	0.00138501i	$0.000440863\pi$
$107$			0.0286533i			0.00277002i	−0.999999	+	0.00138501i	$0.999559\pi$
$108$		0			0
$109$	5.84714	+	17.9956i	0.560054	+	1.72367i	0.682207	+	0.731159i	$0.261020\pi$
$109$	5.84714	+	17.9956i	0.560054	+	1.72367i	−0.122153	+	0.992511i	$0.538980\pi$
$110$		0			0
$111$	−2.19992	+	6.77065i	−0.208807	+	0.642642i
$112$		0			0
$113$	4.65428	−	1.51227i	0.437838	−	0.142262i	−0.0818000	−	0.996649i	$-0.526067\pi$
$113$	4.65428	−	1.51227i	0.437838	−	0.142262i	0.519638	+	0.854387i	$0.326067\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.55867	−	2.14533i	−0.144099	−	0.198336i
$118$		0			0
$119$	−0.149230	+	0.108422i	−0.0136799	+	0.00993901i
$120$		0			0
$121$	4.73111	+	3.43736i	0.430101	+	0.312487i
$122$		0			0
$123$	−6.26687	−	2.03623i	−0.565065	−	0.183601i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.10993	−	1.01048i	−0.275961	−	0.0896652i	0.167767	−	0.985827i	$-0.446344\pi$
$127$	−3.10993	−	1.01048i	−0.275961	−	0.0896652i	−0.443728	+	0.896161i	$0.646344\pi$
$128$		0			0
$129$	−1.45193	−	1.05489i	−0.127836	−	0.0928781i
$130$		0			0
$131$	−2.90882	+	2.11338i	−0.254145	+	0.184647i	−0.707562	−	0.706651i	$-0.750205\pi$
$131$	−2.90882	+	2.11338i	−0.254145	+	0.184647i	0.453417	+	0.891299i	$0.350205\pi$
$132$		0			0
$133$	−0.0914251	−	0.125836i	−0.00792756	−	0.0109114i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.1867	+	5.25938i	−1.38292	+	0.449339i	−0.903629	−	0.428315i	$-0.859107\pi$
$137$	−16.1867	+	5.25938i	−1.38292	+	0.449339i	−0.479294	+	0.877654i	$0.659107\pi$
$138$		0			0
$139$	5.86699	−	18.0567i	0.497632	−	1.53155i	−0.315184	−	0.949031i	$-0.602066\pi$
$139$	5.86699	−	18.0567i	0.497632	−	1.53155i	0.812815	−	0.582522i	$-0.197934\pi$
$140$		0			0
$141$	−3.12448	−	9.61615i	−0.263128	−	0.809826i
$142$		0			0
$143$		−	6.01901i		−	0.503335i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.10991	−	5.65681i	0.338980	−	0.466566i
$148$		0			0
$149$	−20.3441			−1.66665			−0.833327	−	0.552780i	$-0.813567\pi$
$149$	−20.3441			−1.66665			−0.833327	+	0.552780i	$0.813567\pi$
$150$		0			0
$151$	13.2609			1.07915			0.539577	−	0.841936i	$-0.318584\pi$
$151$	13.2609			1.07915			0.539577	+	0.841936i	$0.318584\pi$
$152$		0			0
$153$	−1.22749	+	1.68949i	−0.0992366	+	0.136587i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			12.8066i			1.02208i	0.859558	+	0.511039i	$0.170739\pi$
$157$			12.8066i			1.02208i	−0.859558	+	0.511039i	$0.829261\pi$
$158$		0			0
$159$	−0.297101	−	0.914384i	−0.0235617	−	0.0725153i
$160$		0			0
$161$	−0.129381	+	0.398193i	−0.0101966	+	0.0313820i
$162$		0			0
$163$	14.3273	−	4.65524i	1.12220	−	0.364626i	0.311596	−	0.950215i	$-0.399137\pi$
$163$	14.3273	−	4.65524i	1.12220	−	0.364626i	0.810608	+	0.585589i	$0.199137\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.02861	+	2.79215i	0.156979	+	0.216063i	0.880261	−	0.474490i	$-0.157367\pi$
$167$	2.02861	+	2.79215i	0.156979	+	0.216063i	−0.723282	+	0.690553i	$0.757367\pi$
$168$		0			0
$169$	−4.82830	+	3.50796i	−0.371407	+	0.269843i
$170$		0			0
$171$	−1.42464	−	1.03506i	−0.108945	−	0.0791531i
$172$		0			0
$173$	2.29639	+	0.746142i	0.174591	+	0.0567281i	0.395008	−	0.918678i	$-0.370742\pi$
$173$	2.29639	+	0.746142i	0.174591	+	0.0567281i	−0.220417	+	0.975406i	$0.570742\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.53860	+	2.77436i	0.641800	+	0.208533i
$178$		0			0
$179$	−3.29228	−	2.39198i	−0.246077	−	0.178785i	0.457910	−	0.888999i	$-0.348598\pi$
$179$	−3.29228	−	2.39198i	−0.246077	−	0.178785i	−0.703986	+	0.710214i	$0.748598\pi$
$180$		0			0
$181$	10.7893	−	7.83888i	0.801962	−	0.582660i	−0.109527	−	0.993984i	$-0.534934\pi$
$181$	10.7893	−	7.83888i	0.801962	−	0.582660i	0.911489	+	0.411324i	$0.134934\pi$
$182$		0			0
$183$	−5.56408	−	7.65830i	−0.411309	−	0.566118i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.50810	+	1.46477i	−0.329665	+	0.107115i
$188$		0			0
$189$	−0.0272949	+	0.0840051i	−0.00198541	+	0.00611047i
$190$		0			0
$191$	7.80358	+	24.0169i	0.564647	+	1.73780i	0.668998	+	0.743264i	$0.266723\pi$
$191$	7.80358	+	24.0169i	0.564647	+	1.73780i	−0.104351	+	0.994541i	$0.533277\pi$
$192$		0			0
$193$			24.6399i			1.77362i	0.462139	+	0.886808i	$0.347082\pi$
$193$			24.6399i			1.77362i	−0.462139	+	0.886808i	$0.652918\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.9446	−	15.0640i	0.779774	−	1.07327i	−0.215533	−	0.976496i	$-0.569149\pi$
$197$	10.9446	−	15.0640i	0.779774	−	1.07327i	0.995307	−	0.0967697i	$-0.0308510\pi$
$198$		0			0
$199$	−9.85708			−0.698750			−0.349375	−	0.936983i	$-0.613606\pi$
$199$	−9.85708			−0.698750			−0.349375	+	0.936983i	$0.613606\pi$
$200$		0			0
$201$	−13.9039			−0.980703
$202$		0			0
$203$	0.192427	−	0.264853i	0.0135057	−	0.0185890i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			4.74010i			0.329460i
$208$		0			0
$209$	−1.23515	−	3.80139i	−0.0854369	−	0.262948i
$210$		0			0
$211$	−2.44086	+	7.51219i	−0.168036	+	0.517161i	−0.999247	−	0.0387958i	$-0.987648\pi$
$211$	−2.44086	+	7.51219i	−0.168036	+	0.517161i	0.831212	+	0.555956i	$0.187648\pi$
$212$		0			0
$213$	−5.84685	+	1.89976i	−0.400619	+	0.130169i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.213186	−	0.293425i	−0.0144720	−	0.0199190i
$218$		0			0
$219$	2.55459	−	1.85602i	0.172623	−	0.125418i
$220$		0			0
$221$	−4.48015	−	3.25502i	−0.301368	−	0.218956i
$222$		0			0
$223$	8.73235	+	2.83731i	0.584762	+	0.190001i	0.586433	−	0.809998i	$-0.300532\pi$
$223$	8.73235	+	2.83731i	0.584762	+	0.190001i	−0.00167090	+	0.999999i	$0.500532\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.9994	+	3.57392i	0.730056	+	0.237209i	0.650377	−	0.759611i	$-0.274611\pi$
$227$	10.9994	+	3.57392i	0.730056	+	0.237209i	0.0796781	+	0.996821i	$0.474611\pi$
$228$		0			0
$229$	20.1820	+	14.6631i	1.33366	+	0.968962i	0.999652	+	0.0263923i	$0.00840190\pi$
$229$	20.1820	+	14.6631i	1.33366	+	0.968962i	0.334010	+	0.942570i	$0.391598\pi$
$230$		0			0
$231$	−0.162198	+	0.117844i	−0.0106718	+	0.00775355i
$232$		0			0
$233$	7.65295	+	10.5334i	0.501361	+	0.690065i	0.982433	−	0.186617i	$-0.0597522\pi$
$233$	7.65295	+	10.5334i	0.501361	+	0.690065i	−0.481071	+	0.876681i	$0.659752\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	12.6987	−	4.12605i	0.824867	−	0.268016i
$238$		0			0
$239$	8.16071	−	25.1161i	0.527872	−	1.62462i	−0.230693	−	0.973027i	$-0.574099\pi$
$239$	8.16071	−	25.1161i	0.527872	−	1.62462i	0.758565	−	0.651597i	$-0.225901\pi$
$240$		0			0
$241$	−1.92700	−	5.93070i	−0.124129	−	0.382030i	0.869612	−	0.493735i	$-0.164369\pi$
$241$	−1.92700	−	5.93070i	−0.124129	−	0.382030i	−0.993741	+	0.111705i	$0.964369\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.74475	−	3.77782i	0.174644	−	0.240377i
$248$		0			0
$249$	−15.8195			−1.00252
$250$		0			0
$251$	7.46802			0.471377			0.235689	−	0.971829i	$-0.424265\pi$
$251$	7.46802			0.471377			0.235689	+	0.971829i	$0.424265\pi$
$252$		0			0
$253$	−6.32405	+	8.70430i	−0.397589	+	0.547235i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			8.39880i			0.523903i	0.965081	+	0.261951i	$0.0843660\pi$
$257$			8.39880i			0.523903i	−0.965081	+	0.261951i	$0.915634\pi$
$258$		0			0
$259$	0.194315	+	0.598039i	0.0120741	+	0.0371604i
$260$		0			0
$261$	1.14533	−	3.52496i	0.0708941	−	0.218190i
$262$		0			0
$263$	−9.53415	+	3.09783i	−0.587901	+	0.191021i	−0.587837	−	0.808979i	$-0.700020\pi$
$263$	−9.53415	+	3.09783i	−0.587901	+	0.191021i	−6.39037e−5		1.00000i	$0.500020\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.02527	−	8.29307i	−0.368740	−	0.507528i
$268$		0			0
$269$	−14.2542	+	10.3563i	−0.869094	+	0.631434i	−0.930344	−	0.366689i	$-0.880491\pi$
$269$	−14.2542	+	10.3563i	−0.869094	+	0.631434i	0.0612496	+	0.998122i	$0.480491\pi$
$270$		0			0
$271$	3.92718	+	2.85327i	0.238559	+	0.173324i	0.700641	−	0.713514i	$-0.252897\pi$
$271$	3.92718	+	2.85327i	0.238559	+	0.173324i	−0.462082	+	0.886837i	$0.652897\pi$
$272$		0			0
$273$	−0.222762	−	0.0723799i	−0.0134822	−	0.00438063i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	21.5053	+	6.98748i	1.29213	+	0.419837i	0.872835	−	0.488015i	$-0.162279\pi$
$277$	21.5053	+	6.98748i	1.29213	+	0.419837i	0.419291	+	0.907852i	$0.362279\pi$
$278$		0			0
$279$	−3.32199	−	2.41356i	−0.198882	−	0.144496i
$280$		0			0
$281$	−23.6671	+	17.1952i	−1.41186	+	1.02578i	−0.418815	+	0.908071i	$0.637555\pi$
$281$	−23.6671	+	17.1952i	−1.41186	+	1.02578i	−0.993048	+	0.117708i	$0.962445\pi$
$282$		0			0
$283$	17.1944	+	23.6661i	1.02210	+	1.40680i	0.910719	+	0.413026i	$0.135528\pi$
$283$	17.1944	+	23.6661i	1.02210	+	1.40680i	0.111383	+	0.993778i	$0.464472\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.553541	+	0.179857i	−0.0326745	+	0.0106166i
$288$		0			0
$289$	3.90563	−	12.0203i	0.229743	−	0.707076i
$290$		0			0
$291$	3.95781	+	12.1809i	0.232011	+	0.714056i
$292$		0			0
$293$			13.4104i			0.783447i	0.920083	+	0.391723i	$0.128121\pi$
$293$			13.4104i			0.783447i	−0.920083	+	0.391723i	$0.871879\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.33416	+	1.83631i	−0.0774157	+	0.106554i
$298$		0			0
$299$	−12.5697			−0.726923
$300$		0			0
$301$	−0.158522			−0.00913704
$302$		0			0
$303$	−1.60193	+	2.20487i	−0.0920287	+	0.126667i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			13.5444i			0.773022i	0.922285	+	0.386511i	$0.126320\pi$
$307$			13.5444i			0.773022i	−0.922285	+	0.386511i	$0.873680\pi$
$308$		0			0
$309$	−0.111239	−	0.342358i	−0.00632815	−	0.0194761i
$310$		0			0
$311$	−0.630031	+	1.93904i	−0.0357258	+	0.109953i	−0.967329	−	0.253524i	$-0.918410\pi$
$311$	−0.630031	+	1.93904i	−0.0357258	+	0.109953i	0.931603	+	0.363477i	$0.118410\pi$
$312$		0			0
$313$	−17.3840	+	5.64839i	−0.982599	+	0.319266i	−0.755892	−	0.654697i	$-0.772796\pi$
$313$	−17.3840	+	5.64839i	−0.982599	+	0.319266i	−0.226708	+	0.973963i	$0.572796\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0491	+	15.2078i	0.620579	+	0.854153i	0.997395	−	0.0721348i	$-0.0229812\pi$
$317$	11.0491	+	15.2078i	0.620579	+	0.854153i	−0.376816	+	0.926288i	$0.622981\pi$
$318$		0			0
$319$	6.80604	−	4.94488i	0.381065	−	0.276860i
$320$		0			0
$321$	0.0231810	+	0.0168420i	0.00129384	+	0.000940029i
$322$		0			0
$323$	−3.49746	−	1.13639i	−0.194604	−	0.0632306i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	17.9956	+	5.84714i	0.995161	+	0.323348i
$328$		0			0
$329$	−0.722523	−	0.524944i	−0.0398340	−	0.0289411i
$330$		0			0
$331$	6.73111	−	4.89044i	0.369976	−	0.268803i	−0.387225	−	0.921985i	$-0.626566\pi$
$331$	6.73111	−	4.89044i	0.369976	−	0.268803i	0.757201	+	0.653182i	$0.226566\pi$
$332$		0			0
$333$	4.18449	+	5.75946i	0.229309	+	0.315617i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−16.7331	+	5.43691i	−0.911509	+	0.296167i	−0.726979	−	0.686660i	$-0.759076\pi$
$337$	−16.7331	+	5.43691i	−0.911509	+	0.296167i	−0.184530	+	0.982827i	$0.559076\pi$
$338$		0			0
$339$	1.51227	−	4.65428i	0.0821351	−	0.252786i
$340$		0			0
$341$	−2.88012	−	8.86411i	−0.155967	−	0.480019i
$342$		0			0
$343$		−	1.23591i		−	0.0667326i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.1151	−	24.9333i	0.972469	−	1.33849i	0.0316789	−	0.999498i	$-0.489915\pi$
$347$	18.1151	−	24.9333i	0.972469	−	1.33849i	0.940790	−	0.338990i	$-0.110085\pi$
$348$		0			0
$349$	−22.0376			−1.17964			−0.589822	−	0.807533i	$-0.700802\pi$
$349$	−22.0376			−1.17964			−0.589822	+	0.807533i	$0.700802\pi$
$350$		0			0
$351$	−2.65177			−0.141541
$352$		0			0
$353$	−3.59496	+	4.94803i	−0.191340	+	0.263357i	−0.893899	−	0.448269i	$-0.852041\pi$
$353$	−3.59496	+	4.94803i	−0.191340	+	0.263357i	0.702559	+	0.711626i	$0.252041\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			0.184458i			0.00976256i
$358$		0			0
$359$	−4.57676	−	14.0858i	−0.241552	−	0.743422i	−0.996184	−	0.0872735i	$-0.972185\pi$
$359$	−4.57676	−	14.0858i	−0.241552	−	0.743422i	0.754632	−	0.656148i	$-0.227815\pi$
$360$		0			0
$361$	−4.91308	+	15.1209i	−0.258583	+	0.795836i
$362$		0			0
$363$	5.56176	−	1.80712i	0.291917	−	0.0948495i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.82431	−	10.7692i	−0.408426	−	0.562150i	0.554408	−	0.832245i	$-0.312945\pi$
$367$	−7.82431	−	10.7692i	−0.408426	−	0.562150i	−0.962834	+	0.270095i	$0.912945\pi$
$368$		0			0
$369$	−5.33092	+	3.87314i	−0.277517	+	0.201628i
$370$		0			0
$371$	−0.0687035	−	0.0499160i	−0.00356691	−	0.00259151i
$372$		0			0
$373$	16.1897	+	5.26035i	0.838271	+	0.272371i	0.696525	−	0.717532i	$-0.254728\pi$
$373$	16.1897	+	5.26035i	0.838271	+	0.272371i	0.141746	+	0.989903i	$0.454728\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.34739	+	3.03715i	0.481415	+	0.156421i
$378$		0			0
$379$	−2.29328	−	1.66617i	−0.117798	−	0.0855852i	0.527326	−	0.849663i	$-0.323194\pi$
$379$	−2.29328	−	1.66617i	−0.117798	−	0.0855852i	−0.645124	+	0.764078i	$0.723194\pi$
$380$		0			0
$381$	−2.64546	+	1.92204i	−0.135531	+	0.0984691i
$382$		0			0
$383$	5.90634	+	8.12938i	0.301800	+	0.415392i	0.932802	−	0.360389i	$-0.117356\pi$
$383$	5.90634	+	8.12938i	0.301800	+	0.415392i	−0.631002	+	0.775781i	$0.717356\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.70685	+	0.554590i	−0.0867642	+	0.0281914i
$388$		0			0
$389$	−2.58687	+	7.96156i	−0.131159	+	0.403667i	−0.994973	−	0.100144i	$-0.968070\pi$
$389$	−2.58687	+	7.96156i	−0.131159	+	0.403667i	0.863813	+	0.503812i	$0.168070\pi$
$390$		0			0
$391$	3.05892	+	9.41440i	0.154696	+	0.476107i
$392$		0			0
$393$			3.59550i			0.181369i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.92797	+	6.78277i	−0.247328	+	0.340418i	−0.914573	−	0.404420i	$-0.867473\pi$
$397$	−4.92797	+	6.78277i	−0.247328	+	0.340418i	0.667245	+	0.744838i	$0.267473\pi$
$398$		0			0
$399$	−0.155542			−0.00778682
$400$		0			0
$401$	2.14450			0.107091			0.0535455	−	0.998565i	$-0.482948\pi$
$401$	2.14450			0.107091			0.0535455	+	0.998565i	$0.482948\pi$
$402$		0			0
$403$	6.40022	−	8.80915i	0.318818	−	0.438815i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			16.1589i			0.800969i
$408$		0			0
$409$	1.10861	+	3.41195i	0.0548173	+	0.168710i	0.974717	−	0.223444i	$-0.0717300\pi$
$409$	1.10861	+	3.41195i	0.0548173	+	0.168710i	−0.919900	+	0.392154i	$0.871730\pi$
$410$		0			0
$411$	−5.25938	+	16.1867i	−0.259426	+	0.798431i
$412$		0			0
$413$	0.754199	−	0.245054i	0.0371117	−	0.0120583i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.1597	−	15.3600i	−0.546492	−	0.752181i
$418$		0			0
$419$	−7.44874	+	5.41183i	−0.363895	+	0.264385i	−0.754675	−	0.656099i	$-0.772205\pi$
$419$	−7.44874	+	5.41183i	−0.363895	+	0.264385i	0.390780	+	0.920484i	$0.372205\pi$
$420$		0			0
$421$	33.0957	+	24.0454i	1.61299	+	1.17190i	0.852890	+	0.522090i	$0.174848\pi$
$421$	33.0957	+	24.0454i	1.61299	+	1.17190i	0.760095	+	0.649812i	$0.225152\pi$
$422$		0			0
$423$	−9.61615	−	3.12448i	−0.467553	−	0.151917i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.795207	−	0.258378i	−0.0384828	−	0.0125038i
$428$		0			0
$429$	−4.86948	−	3.53789i	−0.235101	−	0.170811i
$430$		0			0
$431$	−1.83058	+	1.32999i	−0.0881758	+	0.0640634i	−0.631000	−	0.775783i	$-0.717355\pi$
$431$	−1.83058	+	1.32999i	−0.0881758	+	0.0640634i	0.542824	+	0.839847i	$0.317355\pi$
$432$		0			0
$433$	−2.68923	−	3.70141i	−0.129236	−	0.177878i	0.739495	−	0.673162i	$-0.235064\pi$
$433$	−2.68923	−	3.70141i	−0.129236	−	0.177878i	−0.868731	+	0.495283i	$0.835064\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.93855	+	2.57939i	−0.379753	+	0.123389i
$438$		0			0
$439$	0.541703	−	1.66719i	0.0258541	−	0.0795706i	−0.937297	−	0.348532i	$-0.886680\pi$
$439$	0.541703	−	1.66719i	0.0258541	−	0.0795706i	0.963151	+	0.268961i	$0.0866803\pi$
$440$		0			0
$441$	−2.16071	−	6.64998i	−0.102891	−	0.316666i
$442$		0			0
$443$		−	20.8364i		−	0.989967i	−0.868902	−	0.494983i	$-0.835174\pi$
$443$		−	20.8364i		−	0.989967i	0.868902	−	0.494983i	$-0.164826\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−11.9580	+	16.4587i	−0.565592	+	0.778471i
$448$		0			0
$449$	−25.1952			−1.18904			−0.594518	−	0.804082i	$-0.702657\pi$
$449$	−25.1952			−1.18904			−0.594518	+	0.804082i	$0.702657\pi$
$450$		0			0
$451$	−14.9566			−0.704280
$452$		0			0
$453$	7.79454	−	10.7283i	0.366220	−	0.504058i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			39.5166i			1.84851i	0.381775	+	0.924255i	$0.375313\pi$
$457$			39.5166i			1.84851i	−0.381775	+	0.924255i	$0.624687\pi$
$458$		0			0
$459$	0.645329	+	1.98612i	0.0301214	+	0.0927041i
$460$		0			0
$461$	4.50731	−	13.8721i	0.209927	−	0.646087i	−0.789548	−	0.613688i	$-0.789685\pi$
$461$	4.50731	−	13.8721i	0.209927	−	0.646087i	0.999475	−	0.0323993i	$-0.0103148\pi$
$462$		0			0
$463$	9.38989	−	3.05096i	0.436385	−	0.141790i	−0.0825821	−	0.996584i	$-0.526317\pi$
$463$	9.38989	−	3.05096i	0.436385	−	0.141790i	0.518967	+	0.854794i	$0.326317\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.4268	+	17.1041i	0.575045	+	0.791481i	0.993141	−	0.116921i	$-0.0373025\pi$
$467$	12.4268	+	17.1041i	0.575045	+	0.791481i	−0.418096	+	0.908403i	$0.637303\pi$
$468$		0			0
$469$	−0.993557	+	0.721861i	−0.0458782	+	0.0333324i
$470$		0			0
$471$	10.3608	+	7.52753i	0.477399	+	0.346850i
$472$		0			0
$473$	−3.87422	−	1.25881i	−0.178137	−	0.0578802i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.914384	−	0.297101i	−0.0418667	−	0.0136033i
$478$		0			0
$479$	33.5317	+	24.3622i	1.53210	+	1.11314i	0.955055	+	0.296429i	$0.0957957\pi$
$479$	33.5317	+	24.3622i	1.53210	+	1.11314i	0.577049	+	0.816710i	$0.304204\pi$
$480$		0			0
$481$	−15.2728	+	11.0963i	−0.696379	+	0.505949i
$482$		0			0
$483$	0.246097	+	0.338723i	0.0111978	+	0.0154124i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	3.84198	−	1.24834i	0.174097	−	0.0565675i	−0.220671	−	0.975348i	$-0.570825\pi$
$487$	3.84198	−	1.24834i	0.174097	−	0.0565675i	0.394768	+	0.918781i	$0.370825\pi$
$488$		0			0
$489$	4.65524	−	14.3273i	0.210517	−	0.647905i
$490$		0			0
$491$	8.95383	+	27.5570i	0.404081	+	1.24363i	0.921661	+	0.387997i	$0.126833\pi$
$491$	8.95383	+	27.5570i	0.404081	+	1.24363i	−0.517580	+	0.855635i	$0.673167\pi$
$492$		0			0
$493$		−	7.74010i		−	0.348597i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.319178	+	0.439311i	−0.0143171	+	0.0197058i
$498$		0			0
$499$	−23.6824			−1.06017			−0.530086	−	0.847944i	$-0.677840\pi$
$499$	−23.6824			−1.06017			−0.530086	+	0.847944i	$0.677840\pi$
$500$		0			0
$501$	3.45128			0.154192
$502$		0			0
$503$	−7.84233	+	10.7940i	−0.349672	+	0.481282i	−0.947235	−	0.320540i	$-0.896136\pi$
$503$	−7.84233	+	10.7940i	−0.349672	+	0.481282i	0.597563	+	0.801822i	$0.296136\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			5.96810i			0.265053i
$508$		0			0
$509$	3.20479	+	9.86333i	0.142050	+	0.437184i	0.996620	−	0.0821518i	$-0.0261792\pi$
$509$	3.20479	+	9.86333i	0.142050	+	0.437184i	−0.854570	+	0.519336i	$0.826179\pi$
$510$		0			0
$511$	0.0861877	−	0.265258i	0.00381272	−	0.0117343i
$512$		0			0
$513$	−1.67476	+	0.544164i	−0.0739427	+	0.0240254i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−13.4897	−	18.5670i	−0.593277	−	0.816575i
$518$		0			0
$519$	1.95343	−	1.41925i	0.0857458	−	0.0622980i
$520$		0			0
$521$	−23.9450	−	17.3970i	−1.04905	−	0.762178i	−0.0770169	−	0.997030i	$-0.524540\pi$
$521$	−23.9450	−	17.3970i	−1.04905	−	0.762178i	−0.972031	+	0.234852i	$0.924540\pi$
$522$		0			0
$523$	−2.03505	−	0.661227i	−0.0889864	−	0.0289134i	0.264185	−	0.964472i	$-0.414897\pi$
$523$	−2.03505	−	0.661227i	−0.0889864	−	0.0289134i	−0.353172	+	0.935558i	$0.614897\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.15540	−	2.64985i	−0.355255	−	0.115429i
$528$		0			0
$529$	−0.429950	−	0.312377i	−0.0186935	−	0.0135816i
$530$		0			0
$531$	7.26336	−	5.27714i	0.315203	−	0.229008i
$532$		0			0
$533$	−10.2707	−	14.1364i	−0.444873	−	0.612315i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.87031	+	1.25754i	−0.167016	+	0.0542668i
$538$		0			0
$539$	4.90439	−	15.0942i	0.211247	−	0.650151i
$540$		0			0
$541$	−2.66128	−	8.19057i	−0.114417	−	0.352140i	0.877408	−	0.479745i	$-0.159271\pi$
$541$	−2.66128	−	8.19057i	−0.114417	−	0.352140i	−0.991825	+	0.127605i	$0.959271\pi$
$542$		0			0
$543$		−	13.3363i		−	0.572316i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.7004	−	18.8570i	0.585787	−	0.806267i	−0.408528	−	0.912746i	$-0.633958\pi$
$547$	13.7004	−	18.8570i	0.585787	−	0.806267i	0.994315	+	0.106479i	$0.0339577\pi$
$548$		0			0
$549$	−9.46618			−0.404007
$550$		0			0
$551$	6.52673			0.278048
$552$		0			0
$553$	0.693218	−	0.954133i	0.0294786	−	0.0405739i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	37.2790i		−	1.57956i	−0.613389	−	0.789781i	$-0.710194\pi$
$557$		−	37.2790i		−	1.57956i	0.613389	−	0.789781i	$-0.289806\pi$
$558$		0			0
$559$	−1.47065	−	4.52618i	−0.0622017	−	0.191437i
$560$		0			0
$561$	−1.46477	+	4.50810i	−0.0618427	+	0.190332i
$562$		0			0
$563$	−10.2225	+	3.32150i	−0.430828	+	0.139985i	−0.516400	−	0.856347i	$-0.672728\pi$
$563$	−10.2225	+	3.32150i	−0.430828	+	0.139985i	0.0855718	+	0.996332i	$0.472728\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0519180	+	0.0714590i	0.00218035	+	0.00300100i
$568$		0			0
$569$	6.10555	−	4.43594i	0.255958	−	0.185964i	−0.452405	−	0.891812i	$-0.649434\pi$
$569$	6.10555	−	4.43594i	0.255958	−	0.185964i	0.708363	+	0.705848i	$0.249434\pi$
$570$		0			0
$571$	−23.9648	−	17.4115i	−1.00290	−	0.728647i	−0.0401891	−	0.999192i	$-0.512796\pi$
$571$	−23.9648	−	17.4115i	−1.00290	−	0.728647i	−0.962707	+	0.270545i	$0.912796\pi$
$572$		0			0
$573$	24.0169	+	7.80358i	1.00332	+	0.325999i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.8124	+	4.81283i	0.616647	+	0.200361i	0.600651	−	0.799511i	$-0.294908\pi$
$577$	14.8124	+	4.81283i	0.616647	+	0.200361i	0.0159961	+	0.999872i	$0.494908\pi$
$578$		0			0
$579$	19.9341	+	14.4829i	0.828431	+	0.601891i
$580$		0			0
$581$	−1.13044	+	0.821316i	−0.0468987	+	0.0340739i
$582$		0			0
$583$	−1.28271	−	1.76550i	−0.0531246	−	0.0731197i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−37.1780	+	12.0799i	−1.53450	+	0.498590i	−0.949853	−	0.312697i	$-0.898768\pi$
$587$	−37.1780	+	12.0799i	−1.53450	+	0.498590i	−0.584649	+	0.811287i	$0.698768\pi$
$588$		0			0
$589$	2.23445	−	6.87692i	0.0920688	−	0.283358i
$590$		0			0
$591$	−5.75394	−	17.7088i	−0.236685	−	0.728443i
$592$		0			0
$593$			18.6722i			0.766775i	0.923588	+	0.383387i	$0.125243\pi$
$593$			18.6722i			0.766775i	−0.923588	+	0.383387i	$0.874757\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.79385	+	7.97455i	−0.237126	+	0.326376i
$598$		0			0
$599$	14.0186			0.572783			0.286392	−	0.958113i	$-0.407544\pi$
$599$	14.0186			0.572783			0.286392	+	0.958113i	$0.407544\pi$
$600$		0			0
$601$	−9.89791			−0.403744			−0.201872	−	0.979412i	$-0.564703\pi$
$601$	−9.89791			−0.403744			−0.201872	+	0.979412i	$0.564703\pi$
$602$		0			0
$603$	−8.17249	+	11.2485i	−0.332810	+	0.458073i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	22.2953i		−	0.904939i	−0.891780	−	0.452469i	$-0.850543\pi$
$607$		−	22.2953i		−	0.904939i	0.891780	−	0.452469i	$-0.149457\pi$
$608$		0			0
$609$	−0.101165	−	0.311353i	−0.00409940	−	0.0126167i
$610$		0			0
$611$	8.28540	−	25.4998i	0.335192	−	1.03161i
$612$		0			0
$613$	−15.6247	+	5.07676i	−0.631075	+	0.205049i	−0.607051	−	0.794663i	$-0.707648\pi$
$613$	−15.6247	+	5.07676i	−0.631075	+	0.205049i	−0.0240235	+	0.999711i	$0.507648\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.22486	+	3.06226i	0.0895696	+	0.123282i	0.851450	−	0.524436i	$-0.175724\pi$
$617$	2.22486	+	3.06226i	0.0895696	+	0.123282i	−0.761880	+	0.647718i	$0.775724\pi$
$618$		0			0
$619$	−0.341478	+	0.248098i	−0.0137252	+	0.00997192i	−0.594627	−	0.804002i	$-0.702700\pi$
$619$	−0.341478	+	0.248098i	−0.0137252	+	0.00997192i	0.580902	+	0.813974i	$0.302700\pi$
$620$		0			0
$621$	3.83482	+	2.78616i	0.153886	+	0.111805i
$622$		0			0
$623$	−0.861119	−	0.279795i	−0.0345000	−	0.0112097i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.80139	−	1.23515i	−0.151813	−	0.0493270i
$628$		0			0
$629$	12.0276	+	8.73860i	0.479574	+	0.348431i
$630$		0			0
$631$	28.2527	−	20.5268i	1.12472	−	0.817159i	0.139805	−	0.990179i	$-0.455353\pi$
$631$	28.2527	−	20.5268i	1.12472	−	0.817159i	0.984918	+	0.173020i	$0.0553525\pi$
$632$		0			0
$633$	4.64279	+	6.39025i	0.184534	+	0.253990i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	17.6342	−	5.72971i	0.698693	−	0.227019i
$638$		0			0
$639$	−1.89976	+	5.84685i	−0.0751532	+	0.231298i
$640$		0			0
$641$	1.12876	+	3.47396i	0.0445833	+	0.137213i	0.970870	−	0.239605i	$-0.0770180\pi$
$641$	1.12876	+	3.47396i	0.0445833	+	0.137213i	−0.926287	+	0.376819i	$0.877018\pi$
$642$		0			0
$643$		−	34.3967i		−	1.35647i	−0.734844	−	0.678236i	$-0.762745\pi$
$643$		−	34.3967i		−	1.35647i	0.734844	−	0.678236i	$-0.237255\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.4817	−	25.4378i	0.726589	−	1.00006i	−0.272690	−	0.962102i	$-0.587913\pi$
$647$	18.4817	−	25.4378i	0.726589	−	1.00006i	0.999279	−	0.0379623i	$-0.0120867\pi$
$648$		0			0
$649$	20.3783			0.799920
$650$		0			0
$651$	−0.362693			−0.0142151
$652$		0			0
$653$	20.5020	−	28.2185i	0.802304	−	1.10428i	−0.190161	−	0.981753i	$-0.560901\pi$
$653$	20.5020	−	28.2185i	0.802304	−	1.10428i	0.992466	−	0.122524i	$-0.0390989\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	3.15765i		−	0.123192i
$658$		0			0
$659$	13.3549	+	41.1021i	0.520232	+	1.60111i	0.773555	+	0.633729i	$0.218477\pi$
$659$	13.3549	+	41.1021i	0.520232	+	1.60111i	−0.253323	+	0.967382i	$0.581523\pi$
$660$		0			0
$661$	−3.10111	+	9.54425i	−0.120619	+	0.371228i	−0.993078	−	0.117461i	$-0.962525\pi$
$661$	−3.10111	+	9.54425i	−0.120619	+	0.371228i	0.872458	+	0.488689i	$0.162525\pi$
$662$		0			0
$663$	−5.26673	+	1.71127i	−0.204543	+	0.0664600i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.3265	−	14.2132i	−0.399845	−	0.550339i
$668$		0			0
$669$	7.42818	−	5.39689i	0.287190	−	0.208656i
$670$		0			0
$671$	−17.3829	−	12.6294i	−0.671058	−	0.487552i
$672$		0			0
$673$	−28.4237	−	9.23541i	−1.09565	−	0.355999i	−0.295224	−	0.955428i	$-0.595394\pi$
$673$	−28.4237	−	9.23541i	−1.09565	−	0.355999i	−0.800428	+	0.599429i	$0.795394\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.5205	−	6.99242i	−0.827098	−	0.268740i	−0.135276	−	0.990808i	$-0.543192\pi$
$677$	−21.5205	−	6.99242i	−0.827098	−	0.268740i	−0.691823	+	0.722068i	$0.743192\pi$
$678$		0			0
$679$	0.915228	+	0.664952i	0.0351232	+	0.0255185i
$680$		0			0
$681$	9.35664	−	6.79800i	0.358547	−	0.260500i
$682$		0			0
$683$	15.0830	+	20.7599i	0.577134	+	0.794357i	0.993378	−	0.114896i	$-0.0366535\pi$
$683$	15.0830	+	20.7599i	0.577134	+	0.794357i	−0.416243	+	0.909253i	$0.636654\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	23.7253	−	7.70882i	0.905177	−	0.294110i
$688$		0			0
$689$	0.787845	−	2.42474i	0.0300145	−	0.0923751i
$690$		0			0
$691$	−10.5879	−	32.5862i	−0.402782	−	1.23964i	−0.922733	−	0.385440i	$-0.874050\pi$
$691$	−10.5879	−	32.5862i	−0.402782	−	1.23964i	0.519950	−	0.854196i	$-0.325950\pi$
$692$		0			0
$693$			0.200488i			0.00761590i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.08839	+	11.1327i	−0.306370	+	0.421682i
$698$		0			0
$699$	13.0200			0.492461
$700$		0			0
$701$	42.0813			1.58939			0.794695	−	0.607009i	$-0.207631\pi$
$701$	42.0813			1.58939			0.794695	+	0.607009i	$0.207631\pi$
$702$		0			0
$703$	−7.36869	+	10.1421i	−0.277916	+	0.382518i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			0.240727i			0.00905347i
$708$		0			0
$709$	6.41915	+	19.7561i	0.241076	+	0.741956i	0.996257	+	0.0864398i	$0.0275490\pi$
$709$	6.41915	+	19.7561i	0.241076	+	0.741956i	−0.755181	+	0.655516i	$0.772451\pi$
$710$		0			0
$711$	4.12605	−	12.6987i	0.154739	−	0.476237i
$712$		0			0
$713$	−18.5112	+	6.01464i	−0.693249	+	0.225250i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−15.5226	−	21.3650i	−0.579702	−	0.797891i
$718$		0			0
$719$	20.8627	−	15.1577i	0.778049	−	0.565285i	−0.126344	−	0.991986i	$-0.540324\pi$
$719$	20.8627	−	15.1577i	0.778049	−	0.565285i	0.904393	+	0.426701i	$0.140324\pi$
$720$		0			0
$721$	−0.0257235	−	0.0186892i	−0.000957995	−	0.000696024i
$722$		0			0
$723$	−5.93070	−	1.92700i	−0.220565	−	0.0716659i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.81476	−	2.86409i	−0.326921	−	0.106223i	0.140958	−	0.990016i	$-0.454982\pi$
$727$	−8.81476	−	2.86409i	−0.326921	−	0.106223i	−0.467879	+	0.883792i	$0.654982\pi$
$728$		0			0
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	−3.03212	+	2.20296i	−0.112147	+	0.0814795i
$732$		0			0
$733$	−12.3663	−	17.0208i	−0.456760	−	0.628676i	0.517073	−	0.855941i	$-0.327022\pi$
$733$	−12.3663	−	17.0208i	−0.456760	−	0.628676i	−0.973833	+	0.227265i	$0.927022\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−30.0145	+	9.75230i	−1.10560	+	0.359230i
$738$		0			0
$739$	2.73729	−	8.42450i	0.100693	−	0.309900i	−0.888003	−	0.459838i	$-0.847907\pi$
$739$	2.73729	−	8.42450i	0.100693	−	0.309900i	0.988695	+	0.149938i	$0.0479074\pi$
$740$		0			0
$741$	−1.44300	−	4.44110i	−0.0530099	−	0.163148i
$742$		0			0
$743$		−	13.9773i		−	0.512778i	−0.966574	−	0.256389i	$-0.917467\pi$
$743$		−	13.9773i		−	0.512778i	0.966574	−	0.256389i	$-0.0825328\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.29846	+	12.7982i	−0.340213	+	0.468263i
$748$		0			0
$749$	0.00253090			9.24769e−5
$750$		0			0
$751$	−32.8762			−1.19967			−0.599834	−	0.800124i	$-0.704767\pi$
$751$	−32.8762			−1.19967			−0.599834	+	0.800124i	$0.704767\pi$
$752$		0			0
$753$	4.38959	−	6.04175i	0.159966	−	0.220174i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	31.4556i		−	1.14327i	−0.820507	−	0.571636i	$-0.806309\pi$
$757$		−	31.4556i		−	1.14327i	0.820507	−	0.571636i	$-0.193691\pi$
$758$		0			0
$759$	3.32475	+	10.2325i	0.120681	+	0.371417i
$760$		0			0
$761$	11.7053	−	36.0252i	0.424317	−	1.30591i	−0.479330	−	0.877635i	$-0.659120\pi$
$761$	11.7053	−	36.0252i	0.424317	−	1.30591i	0.903647	−	0.428279i	$-0.140880\pi$
$762$		0			0
$763$	1.58952	−	0.516467i	0.0575446	−	0.0186974i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.9938	+	19.2608i	0.505286	+	0.695467i
$768$		0			0
$769$	11.4835	−	8.34323i	0.414105	−	0.300865i	−0.361157	−	0.932505i	$-0.617618\pi$
$769$	11.4835	−	8.34323i	0.414105	−	0.300865i	0.775261	+	0.631640i	$0.217618\pi$
$770$		0			0
$771$	6.79477	+	4.93669i	0.244708	+	0.177791i
$772$		0			0
$773$	34.5978	+	11.2415i	1.24440	+	0.404329i	0.855910	−	0.517126i	$-0.172998\pi$
$773$	34.5978	+	11.2415i	1.24440	+	0.404329i	0.388487	+	0.921454i	$0.372998\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.598039	+	0.194315i	0.0214545	+	0.00697100i
$778$		0			0
$779$	−9.38750	−	6.82041i	−0.336342	−	0.244367i
$780$		0			0
$781$	−11.2892	+	8.20206i	−0.403958	+	0.293493i
$782$		0			0
$783$	−2.17855	−	2.99851i	−0.0778548	−	0.107158i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	32.7612	−	10.6448i	1.16781	−	0.379445i	0.339985	−	0.940431i	$-0.389578\pi$
$787$	32.7612	−	10.6448i	1.16781	−	0.379445i	0.827825	+	0.560986i	$0.189578\pi$
$788$		0			0
$789$	−3.09783	+	9.53415i	−0.110286	+	0.339425i
$790$		0			0
$791$	−0.133576	−	0.411104i	−0.00474941	−	0.0146172i
$792$		0			0
$793$		−	25.1021i		−	0.891403i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.6903	−	29.8541i	0.768310	−	1.05749i	−0.228167	−	0.973622i	$-0.573273\pi$
$797$	21.6903	−	29.8541i	0.768310	−	1.05749i	0.996477	−	0.0838661i	$-0.0267268\pi$
$798$		0			0
$799$	−21.1151			−0.747000
$800$		0			0
$801$	−10.2508			−0.362194
$802$		0			0
$803$	4.21280	−	5.79842i	0.148667	−	0.204622i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			17.6192i			0.620224i
$808$		0			0
$809$	−11.1567	−	34.3367i	−0.392248	−	1.20721i	−0.931084	−	0.364804i	$-0.881136\pi$
$809$	−11.1567	−	34.3367i	−0.392248	−	1.20721i	0.538837	−	0.842410i	$-0.318864\pi$
$810$		0			0
$811$	4.03780	−	12.4271i	0.141786	−	0.436374i	−0.854797	−	0.518962i	$-0.826319\pi$
$811$	4.03780	−	12.4271i	0.141786	−	0.436374i	0.996584	+	0.0825883i	$0.0263186\pi$
$812$		0			0
$813$	4.61668	−	1.50005i	0.161914	−	0.0526091i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.85762	−	2.55679i	−0.0649897	−	0.0894507i
$818$		0			0
$819$	−0.189493	+	0.137675i	−0.00662142	+	0.00481074i
$820$		0			0
$821$	20.9421	+	15.2153i	0.730885	+	0.531019i	0.889843	−	0.456266i	$-0.150813\pi$
$821$	20.9421	+	15.2153i	0.730885	+	0.531019i	−0.158958	+	0.987285i	$0.550813\pi$
$822$		0			0
$823$	−37.2583	−	12.1060i	−1.29874	−	0.421987i	−0.423599	−	0.905850i	$-0.639233\pi$
$823$	−37.2583	−	12.1060i	−1.29874	−	0.421987i	−0.875144	+	0.483863i	$0.839233\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−43.2012	−	14.0369i	−1.50225	−	0.488112i	−0.561580	−	0.827423i	$-0.689806\pi$
$827$	−43.2012	−	14.0369i	−1.50225	−	0.488112i	−0.940674	+	0.339311i	$0.889806\pi$
$828$		0			0
$829$	13.0692	+	9.49531i	0.453911	+	0.329786i	0.791138	−	0.611638i	$-0.209489\pi$
$829$	13.0692	+	9.49531i	0.453911	+	0.329786i	−0.337227	+	0.941423i	$0.609489\pi$
$830$		0			0
$831$	18.2935	−	13.2910i	0.634593	−	0.461059i
$832$		0			0
$833$	−8.58284	−	11.8133i	−0.297378	−	0.409306i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.90523	+	1.26889i	−0.134984	+	0.0438591i
$838$		0			0
$839$	−3.23891	+	9.96835i	−0.111820	+	0.344146i	−0.991270	−	0.131844i	$-0.957910\pi$
$839$	−3.23891	+	9.96835i	−0.111820	+	0.344146i	0.879451	+	0.475990i	$0.157910\pi$
$840$		0			0
$841$	−4.71649	−	14.5159i	−0.162638	−	0.500547i
$842$		0			0
$843$			29.2542i			1.00757i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.303615	−	0.417891i	0.0104323	−	0.0143589i
$848$		0			0
$849$	29.2529			1.00396
$850$		0			0
$851$	33.7452			1.15677
$852$		0			0
$853$	22.4658	−	30.9215i	0.769214	−	1.05873i	−0.227177	−	0.973854i	$-0.572950\pi$
$853$	22.4658	−	30.9215i	0.769214	−	1.05873i	0.996391	−	0.0848793i	$-0.0270505\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			25.3637i			0.866408i	0.901296	+	0.433204i	$0.142617\pi$
$857$			25.3637i			0.866408i	−0.901296	+	0.433204i	$0.857383\pi$
$858$		0			0
$859$	−11.0541	−	34.0209i	−0.377159	−	1.16078i	−0.942010	−	0.335584i	$-0.891066\pi$
$859$	−11.0541	−	34.0209i	−0.377159	−	1.16078i	0.564851	−	0.825193i	$-0.308934\pi$
$860$		0			0
$861$	−0.179857	+	0.553541i	−0.00612949	+	0.0188646i
$862$		0			0
$863$	42.1228	−	13.6865i	1.43388	−	0.465894i	0.513893	−	0.857854i	$-0.328203\pi$
$863$	42.1228	−	13.6865i	1.43388	−	0.465894i	0.919982	+	0.391960i	$0.128203\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−7.42895	−	10.2251i	−0.252300	−	0.347262i
$868$		0			0
$869$	24.5188	−	17.8139i	0.831742	−	0.604296i
$870$		0			0
$871$	−29.8284	−	21.6716i	−1.01070	−	0.734314i
$872$		0			0
$873$	12.1809	+	3.95781i	0.412260	+	0.133952i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.32715	+	3.03057i	0.314955	+	0.102335i	0.462229	−	0.886761i	$-0.347050\pi$
$877$	9.32715	+	3.03057i	0.314955	+	0.102335i	−0.147274	+	0.989096i	$0.547050\pi$
$878$		0			0
$879$	10.8493	+	7.88246i	0.365937	+	0.265869i
$880$		0			0
$881$	0.794690	−	0.577376i	0.0267738	−	0.0194523i	−0.574318	−	0.818632i	$-0.694733\pi$
$881$	0.794690	−	0.577376i	0.0267738	−	0.0194523i	0.601092	+	0.799180i	$0.294733\pi$
$882$		0			0
$883$	−9.48223	−	13.0512i	−0.319103	−	0.439207i	0.619090	−	0.785320i	$-0.287501\pi$
$883$	−9.48223	−	13.0512i	−0.319103	−	0.439207i	−0.938193	+	0.346113i	$0.887501\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−47.9395	+	15.5765i	−1.60965	+	0.523008i	−0.969469	−	0.245215i	$-0.921141\pi$
$887$	−47.9395	+	15.5765i	−1.60965	+	0.523008i	−0.640183	+	0.768222i	$0.721141\pi$
$888$		0			0
$889$	−0.0892535	+	0.274694i	−0.00299347	+	0.00921294i
$890$		0			0
$891$	0.701409	+	2.15871i	0.0234981	+	0.0723196i
$892$		0			0
$893$		−	17.8050i		−	0.595822i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−7.38827	+	10.1691i	−0.246687	+	0.339536i
$898$		0			0
$899$	15.2191			0.507584
$900$		0			0
$901$	−2.00780			−0.0668896
$902$		0			0
$903$	−0.0931767	+	0.128247i	−0.00310073	+	0.00426779i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	26.1281i		−	0.867570i	−0.901016	−	0.433785i	$-0.857178\pi$
$907$		−	26.1281i		−	0.867570i	0.901016	−	0.433785i	$-0.142822\pi$
$908$		0			0
$909$	0.842186	+	2.59198i	0.0279336	+	0.0859706i
$910$		0			0
$911$	−9.71659	+	29.9046i	−0.321925	+	0.990783i	0.650885	+	0.759177i	$0.274398\pi$
$911$	−9.71659	+	29.9046i	−0.321925	+	0.990783i	−0.972810	+	0.231607i	$0.925602\pi$
$912$		0			0
$913$	−34.1498	+	11.0959i	−1.13019	+	0.367222i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.186671	+	0.256931i	0.00616443	+	0.00848461i
$918$		0			0
$919$	−39.7376	+	28.8711i	−1.31082	+	0.952368i	−0.310824	+	0.950467i	$0.600605\pi$
$919$	−39.7376	+	28.8711i	−1.31082	+	0.952368i	−0.999998	+	0.00190086i	$0.999395\pi$
$920$		0			0
$921$	10.9577	+	7.96122i	0.361068	+	0.262331i
$922$		0			0
$923$	−15.5045	−	5.03772i	−0.510337	−	0.165819i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.342358	−	0.111239i	−0.0112445	−	0.00365356i
$928$		0			0
$929$	12.9520	+	9.41016i	0.424941	+	0.308737i	0.779623	−	0.626249i	$-0.215411\pi$
$929$	12.9520	+	9.41016i	0.424941	+	0.308737i	−0.354682	+	0.934987i	$0.615411\pi$
$930$		0			0
$931$	9.96137	−	7.23736i	0.326471	−	0.237195i
$932$		0			0
$933$	1.19839	+	1.64944i	0.0392335	+	0.0540003i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	28.7856	−	9.35301i	0.940385	−	0.305550i	0.201583	−	0.979472i	$-0.435392\pi$
$937$	28.7856	−	9.35301i	0.940385	−	0.305550i	0.738803	+	0.673922i	$0.235392\pi$
$938$		0			0
$939$	−5.64839	+	17.3840i	−0.184328	+	0.567304i
$940$		0			0
$941$	−3.80436	−	11.7086i	−0.124019	−	0.381690i	0.869702	−	0.493577i	$-0.164311\pi$
$941$	−3.80436	−	11.7086i	−0.124019	−	0.381690i	−0.993721	+	0.111886i	$0.964311\pi$
$942$		0			0
$943$			31.2343i			1.01713i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.8549	+	32.8335i	−0.775181	+	1.06695i	0.220616	+	0.975361i	$0.429193\pi$
$947$	−23.8549	+	32.8335i	−0.775181	+	1.06695i	−0.995797	+	0.0915849i	$0.970807\pi$
$948$		0			0
$949$	8.37336			0.271811
$950$		0			0
$951$	18.7978			0.609562
$952$		0			0
$953$	4.72082	−	6.49765i	0.152922	−	0.210479i	−0.725682	−	0.688031i	$-0.758475\pi$
$953$	4.72082	−	6.49765i	0.152922	−	0.210479i	0.878604	+	0.477551i	$0.158475\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	8.41272i		−	0.271945i
$958$		0			0
$959$	0.464551	+	1.42974i	0.0150011	+	0.0461688i
$960$		0			0
$961$	−4.36923	+	13.4471i	−0.140943	+	0.433778i
$962$		0			0
$963$	0.0272509	−	0.00885436i	0.000878149	−	0.000285328i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−15.8530	−	21.8198i	−0.509798	−	0.701677i	0.474087	−	0.880478i	$-0.342778\pi$
$967$	−15.8530	−	21.8198i	−0.509798	−	0.701677i	−0.983885	+	0.178801i	$0.942778\pi$
$968$		0			0
$969$	−2.97512	+	2.16155i	−0.0955745	+	0.0694389i
$970$		0			0
$971$	−24.0715	−	17.4889i	−0.772490	−	0.561247i	0.130226	−	0.991484i	$-0.458430\pi$
$971$	−24.0715	−	17.4889i	−0.772490	−	0.561247i	−0.902716	+	0.430238i	$0.858430\pi$
$972$		0			0
$973$	−1.59492	−	0.518220i	−0.0511307	−	0.0166134i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.35239	−	0.439419i	−0.0432669	−	0.0140583i	0.287304	−	0.957840i	$-0.407241\pi$
$977$	−1.35239	−	0.439419i	−0.0432669	−	0.0140583i	−0.330570	+	0.943781i	$0.607241\pi$
$978$		0			0
$979$	−18.8237	−	13.6762i	−0.601607	−	0.437093i
$980$		0			0
$981$	15.3080	−	11.1219i	0.488747	−	0.355096i
$982$		0			0
$983$	1.19298	+	1.64200i	0.0380502	+	0.0523716i	0.827618	−	0.561291i	$-0.189695\pi$
$983$	1.19298	+	1.64200i	0.0380502	+	0.0523716i	−0.789568	+	0.613663i	$0.789695\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.849377	+	0.275979i	−0.0270360	+	0.00878452i
$988$		0			0
$989$	−2.62881	+	8.09065i	−0.0835913	+	0.257268i
$990$		0			0
$991$	6.25185	+	19.2412i	0.198597	+	0.611217i	0.999916	+	0.0129803i	$0.00413187\pi$
$991$	6.25185	+	19.2412i	0.198597	+	0.611217i	−0.801319	+	0.598237i	$0.795868\pi$
$992$		0			0
$993$		−	8.32012i		−	0.264031i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.7566	+	14.8051i	−0.340663	+	0.468883i	−0.944635	−	0.328123i	$-0.893584\pi$
$997$	−10.7566	+	14.8051i	−0.340663	+	0.468883i	0.603972	+	0.797006i	$0.293584\pi$
$998$		0			0
$999$	7.11909			0.225238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.b.649.3		16
5.2	odd	4		1500.2.m.a.601.2		8
5.3	odd	4		300.2.m.b.121.2	✓	8
5.4	even	2	inner	1500.2.o.b.649.2		16
15.8	even	4		900.2.n.b.721.1		8
25.6	even	5	inner	1500.2.o.b.349.1		16
25.8	odd	20		300.2.m.b.181.2	yes	8
25.9	even	10		7500.2.d.c.1249.3		8
25.12	odd	20		7500.2.a.f.1.3		4
25.13	odd	20		7500.2.a.e.1.2		4
25.16	even	5		7500.2.d.c.1249.6		8
25.17	odd	20		1500.2.m.a.901.2		8
25.19	even	10	inner	1500.2.o.b.349.4		16
75.8	even	20		900.2.n.b.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.121.2	✓	8	5.3	odd	4
300.2.m.b.181.2	yes	8	25.8	odd	20
900.2.n.b.181.1		8	75.8	even	20
900.2.n.b.721.1		8	15.8	even	4
1500.2.m.a.601.2		8	5.2	odd	4
1500.2.m.a.901.2		8	25.17	odd	20
1500.2.o.b.349.1		16	25.6	even	5	inner
1500.2.o.b.349.4		16	25.19	even	10	inner
1500.2.o.b.649.2		16	5.4	even	2	inner
1500.2.o.b.649.3		16	1.1	even	1	trivial
7500.2.a.e.1.2		4	25.13	odd	20
7500.2.a.f.1.3		4	25.12	odd	20
7500.2.d.c.1249.3		8	25.9	even	10
7500.2.d.c.1249.6		8	25.16	even	5

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{3} -0.0883282i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{3} -0.0883282i q^{7} +(-0.309017 - 0.951057i) q^{9} +(0.701409 - 2.15871i) q^{11} +(2.52199 - 0.819443i) q^{13} +(-1.22749 - 1.68949i) q^{17} +(1.42464 - 1.03506i) q^{19} +(-0.0714590 - 0.0519180i) q^{21} +(-4.50810 - 1.46477i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(2.99851 + 2.17855i) q^{29} +(3.32199 - 2.41356i) q^{31} +(-1.33416 - 1.83631i) q^{33} +(-6.77065 + 2.19992i) q^{37} +(0.819443 - 2.52199i) q^{39} +(-2.03623 - 6.26687i) q^{41} -1.79469i q^{43} +(5.94311 - 8.17999i) q^{47} +6.99220 q^{49} -2.08833 q^{51} +(0.565120 - 0.777821i) q^{53} -1.76095i q^{57} +(2.77436 + 8.53860i) q^{59} +(2.92521 - 9.00287i) q^{61} +(-0.0840051 + 0.0272949i) q^{63} +(-8.17249 - 11.2485i) q^{67} +(-3.83482 + 2.78616i) q^{69} +(-4.97363 - 3.61355i) q^{71} +(3.00310 + 0.975766i) q^{73} +(-0.190675 - 0.0619542i) q^{77} +(10.8021 + 7.84821i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-9.29846 - 12.7982i) q^{83} +(3.52496 - 1.14533i) q^{87} +(3.16767 - 9.74909i) q^{89} +(-0.0723799 - 0.222762i) q^{91} -4.10620i q^{93} +(-7.52820 + 10.3617i) q^{97} -2.26981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Introduction

L-functions

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