LMFDB - Embedded newform 1500.2.o.b.649.2

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			649.2
Root			$0.462894 - 1.33631i$ of defining polynomial
Character	$\chi$	$=$	1500.649
Dual form			1500.2.o.b.349.1

$q$-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	$0.00531362\pi$
$7$			0.0883282i			0.0333849i	−0.999861	+	0.0166925i	$0.994686\pi$
$8$		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	−0.637101	−	0.770780i	$-0.719867\pi$
$13$	−2.52199	+	0.819443i	−0.699473	+	0.227273i	−0.0623720	+	0.998053i	$0.519867\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.22749	+	1.68949i	0.297710	+	0.409762i	0.931499	−	0.363743i	$-0.118501\pi$
$17$	1.22749	+	1.68949i	0.297710	+	0.409762i	−0.633790	+	0.773506i	$0.718501\pi$
$18$		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	0.738647	−	0.674092i	$-0.235465\pi$
$23$	4.50810	+	1.46477i	0.940005	+	0.305426i	0.201357	+	0.979518i	$0.435465\pi$
$24$		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	0.305963	−	0.952044i	$-0.401022\pi$
$37$	6.77065	−	2.19992i	1.11309	−	0.361664i	0.807126	+	0.590379i	$0.201022\pi$
$38$		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	$0.0436959\pi$
$43$			1.79469i			0.273688i	−0.990593	+	0.136844i	$0.956304\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.94311	+	8.17999i	−0.866892	+	1.19317i	0.112990	+	0.993596i	$0.463957\pi$
$47$	−5.94311	+	8.17999i	−0.866892	+	1.19317i	−0.979882	+	0.199578i	$0.936043\pi$
$48$		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	−0.846064	−	0.533081i	$-0.821034\pi$
$53$	−0.565120	+	0.777821i	−0.0776252	+	0.106842i	0.768439	+	0.639923i	$0.221034\pi$
$54$		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	$0.122984\pi$
$67$	8.17249	+	11.2485i	0.998429	+	1.37422i	0.0721440	+	0.997394i	$0.477016\pi$
$68$		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	0.127952	−	0.991780i	$-0.459160\pi$
$73$	−3.00310	−	0.975766i	−0.351486	−	0.114205i	−0.479438	+	0.877576i	$0.659160\pi$
$74$		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	$0.134728\pi$
$83$	9.29846	+	12.7982i	1.02064	+	1.40479i	0.108884	+	0.994054i	$0.465272\pi$
$84$		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	$-0.574679\pi$
$97$	7.52820	−	10.3617i	0.764373	−	1.05207i	0.996838	−	0.0794643i	$-0.0253210\pi$
$98$		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	−0.819314	−	0.573345i	$-0.805645\pi$
$103$	−0.211589	+	0.291227i	−0.0208485	+	0.0286954i	0.798466	+	0.602041i	$0.205645\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	0.0286533i		−	0.00277002i	−0.999999	−	0.00138501i	$-0.999559\pi$
$107$		−	0.0286533i		−	0.00277002i	0.999999	−	0.00138501i	$-0.000440863\pi$
$108$		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	−0.519638	−	0.854387i	$-0.673933\pi$
$113$	−4.65428	+	1.51227i	−0.437838	+	0.142262i	0.0818000	+	0.996649i	$0.473933\pi$
$114$		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	0.443728	−	0.896161i	$-0.353656\pi$
$127$	3.10993	+	1.01048i	0.275961	+	0.0896652i	−0.167767	+	0.985827i	$0.553656\pi$
$128$		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	0.479294	−	0.877654i	$-0.340893\pi$
$137$	16.1867	−	5.25938i	1.38292	−	0.449339i	0.903629	+	0.428315i	$0.140893\pi$
$138$		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	$-0.829261\pi$
$157$		−	12.8066i		−	1.02208i	0.859558	−	0.511039i	$-0.170739\pi$
$158$		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	−0.810608	−	0.585589i	$-0.800863\pi$
$163$	−14.3273	+	4.65524i	−1.12220	+	0.364626i	−0.311596	+	0.950215i	$0.600863\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.02861	−	2.79215i	−0.156979	−	0.216063i	0.723282	−	0.690553i	$-0.242633\pi$
$167$	−2.02861	−	2.79215i	−0.156979	−	0.216063i	−0.880261	+	0.474490i	$0.842633\pi$
$168$		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	0.220417	−	0.975406i	$-0.429258\pi$
$173$	−2.29639	−	0.746142i	−0.174591	−	0.0567281i	−0.395008	+	0.918678i	$0.629258\pi$
$174$		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	$-0.652918\pi$
$193$		−	24.6399i		−	1.77362i	0.462139	−	0.886808i	$-0.347082\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.9446	+	15.0640i	−0.779774	+	1.07327i	0.215533	+	0.976496i	$0.430851\pi$
$197$	−10.9446	+	15.0640i	−0.779774	+	1.07327i	−0.995307	+	0.0967697i	$0.969149\pi$
$198$		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	0.00167090	−	0.999999i	$-0.499468\pi$
$223$	−8.73235	−	2.83731i	−0.584762	−	0.190001i	−0.586433	+	0.809998i	$0.699468\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.9994	−	3.57392i	−0.730056	−	0.237209i	−0.0796781	−	0.996821i	$-0.525389\pi$
$227$	−10.9994	−	3.57392i	−0.730056	−	0.237209i	−0.650377	+	0.759611i	$0.725389\pi$
$228$		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	0.481071	−	0.876681i	$-0.340248\pi$
$233$	−7.65295	−	10.5334i	−0.501361	−	0.690065i	−0.982433	+	0.186617i	$0.940248\pi$
$234$		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	$-0.915634\pi$
$257$		−	8.39880i		−	0.523903i	0.965081	−	0.261951i	$-0.0843660\pi$
$258$		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	6.39037e−5	−	1.00000i	$-0.499980\pi$
$263$	9.53415	−	3.09783i	0.587901	−	0.191021i	0.587837	+	0.808979i	$0.299980\pi$
$264$		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	−0.419291	−	0.907852i	$-0.637721\pi$
$277$	−21.5053	−	6.98748i	−1.29213	−	0.419837i	−0.872835	+	0.488015i	$0.837721\pi$
$278$		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	$-0.864472\pi$
$283$	−17.1944	−	23.6661i	−1.02210	−	1.40680i	−0.111383	−	0.993778i	$-0.535528\pi$
$284$		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	$-0.871879\pi$
$293$		−	13.4104i		−	0.783447i	0.920083	−	0.391723i	$-0.128121\pi$
$294$		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	$-0.873680\pi$
$307$		−	13.5444i		−	0.773022i	0.922285	−	0.386511i	$-0.126320\pi$
$308$		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	0.226708	−	0.973963i	$-0.427204\pi$
$313$	17.3840	−	5.64839i	0.982599	−	0.319266i	0.755892	+	0.654697i	$0.227204\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.0491	−	15.2078i	−0.620579	−	0.854153i	0.376816	−	0.926288i	$-0.377019\pi$
$317$	−11.0491	−	15.2078i	−0.620579	−	0.854153i	−0.997395	+	0.0721348i	$0.977019\pi$
$318$		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	0.184530	−	0.982827i	$-0.440924\pi$
$337$	16.7331	−	5.43691i	0.911509	−	0.296167i	0.726979	+	0.686660i	$0.240924\pi$
$338$		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	$0.510085\pi$
$347$	−18.1151	+	24.9333i	−0.972469	+	1.33849i	−0.940790	+	0.338990i	$0.889915\pi$
$348$		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	−0.702559	−	0.711626i	$-0.747959\pi$
$353$	3.59496	−	4.94803i	0.191340	−	0.263357i	0.893899	+	0.448269i	$0.147959\pi$
$354$		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	0.962834	−	0.270095i	$-0.0870553\pi$
$367$	7.82431	+	10.7692i	0.408426	+	0.562150i	−0.554408	+	0.832245i	$0.687055\pi$
$368$		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	−0.141746	−	0.989903i	$-0.545272\pi$
$373$	−16.1897	−	5.26035i	−0.838271	−	0.272371i	−0.696525	+	0.717532i	$0.745272\pi$
$374$		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	0.631002	−	0.775781i	$-0.282644\pi$
$383$	−5.90634	−	8.12938i	−0.301800	−	0.415392i	−0.932802	+	0.360389i	$0.882644\pi$
$384$		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	−0.667245	−	0.744838i	$-0.732527\pi$
$397$	4.92797	−	6.78277i	0.247328	−	0.340418i	0.914573	+	0.404420i	$0.132527\pi$
$398$		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	0.868731	−	0.495283i	$-0.164936\pi$
$433$	2.68923	+	3.70141i	0.129236	+	0.177878i	−0.739495	+	0.673162i	$0.764936\pi$
$434$		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	$0.164826\pi$
$443$			20.8364i			0.989967i	−0.868902	+	0.494983i	$0.835174\pi$
$444$		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	$-0.624687\pi$
$457$		−	39.5166i		−	1.84851i	0.381775	−	0.924255i	$-0.375313\pi$
$458$		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	−0.518967	−	0.854794i	$-0.673683\pi$
$463$	−9.38989	+	3.05096i	−0.436385	+	0.141790i	0.0825821	+	0.996584i	$0.473683\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.4268	−	17.1041i	−0.575045	−	0.791481i	0.418096	−	0.908403i	$-0.362697\pi$
$467$	−12.4268	−	17.1041i	−0.575045	−	0.791481i	−0.993141	+	0.116921i	$0.962697\pi$
$468$		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	−0.394768	−	0.918781i	$-0.629175\pi$
$487$	−3.84198	+	1.24834i	−0.174097	+	0.0565675i	0.220671	+	0.975348i	$0.429175\pi$
$488$		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	−0.597563	−	0.801822i	$-0.703864\pi$
$503$	7.84233	−	10.7940i	0.349672	−	0.481282i	0.947235	+	0.320540i	$0.103864\pi$
$504$		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	0.353172	−	0.935558i	$-0.385103\pi$
$523$	2.03505	+	0.661227i	0.0889864	+	0.0289134i	−0.264185	+	0.964472i	$0.585103\pi$
$524$		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	−0.994315	−	0.106479i	$-0.966042\pi$
$547$	−13.7004	+	18.8570i	−0.585787	+	0.806267i	0.408528	+	0.912746i	$0.366042\pi$
$548$		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	$0.289806\pi$
$557$			37.2790i			1.57956i	−0.613389	+	0.789781i	$0.710194\pi$
$558$		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	−0.0855718	−	0.996332i	$-0.527272\pi$
$563$	10.2225	−	3.32150i	0.430828	−	0.139985i	0.516400	+	0.856347i	$0.327272\pi$
$564$		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	−0.0159961	−	0.999872i	$-0.505092\pi$
$577$	−14.8124	−	4.81283i	−0.616647	−	0.200361i	−0.600651	+	0.799511i	$0.705092\pi$
$578$		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	0.584649	−	0.811287i	$-0.301232\pi$
$587$	37.1780	−	12.0799i	1.53450	−	0.498590i	0.949853	+	0.312697i	$0.101232\pi$
$588$		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	$-0.874757\pi$
$593$		−	18.6722i		−	0.766775i	0.923588	−	0.383387i	$-0.125243\pi$
$594$		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	$0.149457\pi$
$607$			22.2953i			0.904939i	−0.891780	+	0.452469i	$0.850543\pi$
$608$		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	0.0240235	−	0.999711i	$-0.492352\pi$
$613$	15.6247	−	5.07676i	0.631075	−	0.205049i	0.607051	+	0.794663i	$0.292352\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.22486	−	3.06226i	−0.0895696	−	0.123282i	0.761880	−	0.647718i	$-0.224276\pi$
$617$	−2.22486	−	3.06226i	−0.0895696	−	0.123282i	−0.851450	+	0.524436i	$0.824276\pi$
$618$		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	$0.237255\pi$
$643$			34.3967i			1.35647i	−0.734844	+	0.678236i	$0.762745\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.4817	+	25.4378i	−0.726589	+	1.00006i	0.272690	+	0.962102i	$0.412087\pi$
$647$	−18.4817	+	25.4378i	−0.726589	+	1.00006i	−0.999279	+	0.0379623i	$0.987913\pi$
$648$		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	$0.439099\pi$
$653$	−20.5020	+	28.2185i	−0.802304	+	1.10428i	−0.992466	+	0.122524i	$0.960901\pi$
$654$		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	0.800428	−	0.599429i	$-0.204606\pi$
$673$	28.4237	+	9.23541i	1.09565	+	0.355999i	0.295224	+	0.955428i	$0.404606\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.5205	+	6.99242i	0.827098	+	0.268740i	0.691823	−	0.722068i	$-0.256808\pi$
$677$	21.5205	+	6.99242i	0.827098	+	0.268740i	0.135276	+	0.990808i	$0.456808\pi$
$678$		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	0.416243	−	0.909253i	$-0.363346\pi$
$683$	−15.0830	−	20.7599i	−0.577134	−	0.794357i	−0.993378	+	0.114896i	$0.963346\pi$
$684$		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	0.467879	−	0.883792i	$-0.345018\pi$
$727$	8.81476	+	2.86409i	0.326921	+	0.106223i	−0.140958	+	0.990016i	$0.545018\pi$
$728$		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	0.973833	−	0.227265i	$-0.0729784\pi$
$733$	12.3663	+	17.0208i	0.456760	+	0.628676i	−0.517073	+	0.855941i	$0.672978\pi$
$734$		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	$0.0825328\pi$
$743$			13.9773i			0.512778i	−0.966574	+	0.256389i	$0.917467\pi$
$744$		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	$0.193691\pi$
$757$			31.4556i			1.14327i	−0.820507	+	0.571636i	$0.806309\pi$
$758$		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	−0.388487	−	0.921454i	$-0.627002\pi$
$773$	−34.5978	−	11.2415i	−1.24440	−	0.404329i	−0.855910	+	0.517126i	$0.827002\pi$
$774$		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	−0.827825	−	0.560986i	$-0.810422\pi$
$787$	−32.7612	+	10.6448i	−1.16781	+	0.379445i	−0.339985	+	0.940431i	$0.610422\pi$
$788$		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	$0.426727\pi$
$797$	−21.6903	+	29.8541i	−0.768310	+	1.05749i	−0.996477	+	0.0838661i	$0.973273\pi$
$798$		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	0.875144	−	0.483863i	$-0.160767\pi$
$823$	37.2583	+	12.1060i	1.29874	+	0.421987i	0.423599	+	0.905850i	$0.360767\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	43.2012	+	14.0369i	1.50225	+	0.488112i	0.940674	−	0.339311i	$-0.110194\pi$
$827$	43.2012	+	14.0369i	1.50225	+	0.488112i	0.561580	+	0.827423i	$0.310194\pi$
$828$		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	$0.427050\pi$
$853$	−22.4658	+	30.9215i	−0.769214	+	1.05873i	−0.996391	+	0.0848793i	$0.972950\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	25.3637i		−	0.866408i	−0.901296	−	0.433204i	$-0.857383\pi$
$857$		−	25.3637i		−	0.866408i	0.901296	−	0.433204i	$-0.142617\pi$
$858$		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	−0.919982	−	0.391960i	$-0.871797\pi$
$863$	−42.1228	+	13.6865i	−1.43388	+	0.465894i	−0.513893	+	0.857854i	$0.671797\pi$
$864$		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	0.147274	−	0.989096i	$-0.452950\pi$
$877$	−9.32715	−	3.03057i	−0.314955	−	0.102335i	−0.462229	+	0.886761i	$0.652950\pi$
$878$		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	0.938193	−	0.346113i	$-0.112499\pi$
$883$	9.48223	+	13.0512i	0.319103	+	0.439207i	−0.619090	+	0.785320i	$0.712499\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	47.9395	−	15.5765i	1.60965	−	0.523008i	0.640183	−	0.768222i	$-0.278859\pi$
$887$	47.9395	−	15.5765i	1.60965	−	0.523008i	0.969469	+	0.245215i	$0.0788585\pi$
$888$		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	$0.142822\pi$
$907$			26.1281i			0.867570i	−0.901016	+	0.433785i	$0.857178\pi$
$908$		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	−0.738803	−	0.673922i	$-0.764608\pi$
$937$	−28.7856	+	9.35301i	−0.940385	+	0.305550i	−0.201583	+	0.979472i	$0.564608\pi$
$938$		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	$-0.570807\pi$
$947$	23.8549	−	32.8335i	0.775181	−	1.06695i	0.995797	−	0.0915849i	$-0.0291933\pi$
$948$		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	−0.878604	−	0.477551i	$-0.841525\pi$
$953$	−4.72082	+	6.49765i	−0.152922	+	0.210479i	0.725682	+	0.688031i	$0.241525\pi$
$954$		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	0.983885	−	0.178801i	$-0.0572218\pi$
$967$	15.8530	+	21.8198i	0.509798	+	0.701677i	−0.474087	+	0.880478i	$0.657222\pi$
$968$		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	0.330570	−	0.943781i	$-0.392759\pi$
$977$	1.35239	+	0.439419i	0.0432669	+	0.0140583i	−0.287304	+	0.957840i	$0.592759\pi$
$978$		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	0.789568	−	0.613663i	$-0.210305\pi$
$983$	−1.19298	−	1.64200i	−0.0380502	−	0.0523716i	−0.827618	+	0.561291i	$0.810305\pi$
$984$		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	−0.603972	−	0.797006i	$-0.706416\pi$
$997$	10.7566	−	14.8051i	0.340663	−	0.468883i	0.944635	+	0.328123i	$0.106416\pi$
$998$		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.649.2		16
5.2	odd	4		300.2.m.b.121.2	✓	8
5.3	odd	4		1500.2.m.a.601.2		8
5.4	even	2	inner	1500.2.o.b.649.3		16
15.2	even	4		900.2.n.b.721.1		8
25.6	even	5	inner	1500.2.o.b.349.4		16
25.8	odd	20		1500.2.m.a.901.2		8
25.9	even	10		7500.2.d.c.1249.6		8
25.12	odd	20		7500.2.a.e.1.2		4
25.13	odd	20		7500.2.a.f.1.3		4
25.16	even	5		7500.2.d.c.1249.3		8
25.17	odd	20		300.2.m.b.181.2	yes	8
25.19	even	10	inner	1500.2.o.b.349.1		16
75.17	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	5.2	odd	4
300.2.m.b.181.2	yes	8	25.17	odd	20
900.2.n.b.181.1		8	75.17	even	20
900.2.n.b.721.1		8	15.2	even	4
1500.2.m.a.601.2		8	5.3	odd	4
1500.2.m.a.901.2		8	25.8	odd	20
1500.2.o.b.349.1		16	25.19	even	10	inner
1500.2.o.b.349.4		16	25.6	even	5	inner
1500.2.o.b.649.2		16	1.1	even	1	trivial
1500.2.o.b.649.3		16	5.4	even	2	inner
7500.2.a.e.1.2		4	25.12	odd	20
7500.2.a.f.1.3		4	25.13	odd	20
7500.2.d.c.1249.3		8	25.16	even	5
7500.2.d.c.1249.6		8	25.9	even	10

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

Modular forms

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Database

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