LMFDB - Embedded newform 1300.2.bs.d.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(193,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("1300.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bs (of order $12$, degree $4$, 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			457.1
Root			$-0.402430i$ of defining polynomial
Character	$\chi$	$=$	1300.457
Dual form			1300.2.bs.d.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.49316 - 0.668040i) q^{3} +(0.749297 + 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +O(q^{10})$	\(q+(-2.49316 - 0.668040i) q^{3} +(0.749297 + 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(-1.32514 - 3.35321i) q^{13} +(1.33873 + 4.99621i) q^{17} +(-1.16619 + 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(-0.704305 + 2.62850i) q^{23} +(-1.20845 - 1.20845i) q^{27} +(5.94138 - 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(-2.08243 + 3.60687i) q^{33} +(8.22242 - 4.74722i) q^{37} +(1.06370 + 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(-11.5499 + 3.09480i) q^{43} -1.52128i q^{47} +(-3.12570 - 5.41387i) q^{49} -13.3507i q^{51} +(4.88398 - 4.88398i) q^{53} +3.11625 q^{57} +(-3.05172 - 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(1.58426 + 2.74402i) q^{63} +(-6.76168 - 11.7116i) q^{67} +(3.51189 - 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} +10.9921 q^{73} +(0.987192 - 0.987192i) q^{77} +3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} -6.25583i q^{83} +(-17.1044 + 4.58310i) q^{87} +(-9.80805 - 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(-0.605885 + 0.349808i) q^{93} +(0.728593 - 1.26196i) q^{97} +(4.17841 - 4.17841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.49316	−	0.668040i	−1.43943	−	0.385693i	−0.547094	−	0.837071i	$-0.684266\pi$
$3$	−2.49316	−	0.668040i	−1.43943	−	0.385693i	−0.892333	+	0.451378i	$0.850933\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.749297	+	0.432607i	0.283208	+	0.163510i	0.634875	−	0.772615i	$-0.281052\pi$
$7$	0.749297	+	0.432607i	0.283208	+	0.163510i	−0.351667	+	0.936125i	$0.614385\pi$
$8$		0			0
$9$	3.17149	+	1.83106i	1.05716	+	0.610354i
$10$		0			0
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	−0.873951	−	0.486014i	$-0.838451\pi$
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	0.999871	+	0.0160756i	$0.00511723\pi$
$12$		0			0
$13$	−1.32514	−	3.35321i	−0.367527	−	0.930013i
$13$	−1.32514	−	3.35321i	−0.367527	−	0.930013i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.33873	+	4.99621i	0.324690	+	1.21176i	0.914623	+	0.404308i	$0.132487\pi$
$17$	1.33873	+	4.99621i	0.324690	+	1.21176i	−0.589933	+	0.807452i	$0.700846\pi$
$18$		0			0
$19$	−1.16619	+	0.312480i	−0.267543	+	0.0716878i	−0.390096	−	0.920774i	$-0.627558\pi$
$19$	−1.16619	+	0.312480i	−0.267543	+	0.0716878i	0.122554	+	0.992462i	$0.460892\pi$
$20$		0			0
$21$	−1.57912	−	1.57912i	−0.344592	−	0.344592i
$22$		0			0
$23$	−0.704305	+	2.62850i	−0.146858	+	0.548080i	0.852808	+	0.522225i	$0.174898\pi$
$23$	−0.704305	+	2.62850i	−0.146858	+	0.548080i	−0.999666	+	0.0258557i	$0.991769\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.20845	−	1.20845i	−0.232567	−	0.232567i
$28$		0			0
$29$	5.94138	−	3.43026i	1.10329	−	0.636983i	0.166204	−	0.986091i	$-0.446849\pi$
$29$	5.94138	−	3.43026i	1.10329	−	0.636983i	0.937082	+	0.349109i	$0.113516\pi$
$30$		0			0
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	−0.689685	−	0.724109i	$-0.742251\pi$
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	0.724109	+	0.689685i	$0.242251\pi$
$32$		0			0
$33$	−2.08243	+	3.60687i	−0.362504	+	0.627875i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.22242	−	4.74722i	1.35176	−	0.780438i	0.363262	−	0.931687i	$-0.381663\pi$
$37$	8.22242	−	4.74722i	1.35176	−	0.780438i	0.988496	+	0.151249i	$0.0483296\pi$
$38$		0			0
$39$	1.06370	+	9.24533i	0.170328	+	1.48044i
$40$		0			0
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	0.291257	−	0.956645i	$-0.405926\pi$
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	−0.226086	+	0.974107i	$0.572593\pi$
$42$		0			0
$43$	−11.5499	+	3.09480i	−1.76135	+	0.471952i	−0.986989	−	0.160791i	$-0.948596\pi$
$43$	−11.5499	+	3.09480i	−1.76135	+	0.471952i	−0.774362	+	0.632743i	$0.781929\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.52128i		−	0.221902i	−0.993826	−	0.110951i	$-0.964610\pi$
$47$		−	1.52128i		−	0.221902i	0.993826	−	0.110951i	$-0.0353897\pi$
$48$		0			0
$49$	−3.12570	−	5.41387i	−0.446529	−	0.773411i
$50$		0			0
$51$		−	13.3507i		−	1.86947i
$52$		0			0
$53$	4.88398	−	4.88398i	0.670867	−	0.670867i	−0.287049	−	0.957916i	$-0.592674\pi$
$53$	4.88398	−	4.88398i	0.670867	−	0.670867i	0.957916	+	0.287049i	$0.0926743\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.11625			0.412757
$58$		0			0
$59$	−3.05172	−	11.3892i	−0.397300	−	1.48274i	−0.817828	−	0.575463i	$-0.804822\pi$
$59$	−3.05172	−	11.3892i	−0.397300	−	1.48274i	0.420528	−	0.907279i	$-0.361845\pi$
$60$		0			0
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	−0.990569	−	0.137018i	$-0.956248\pi$
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	0.613946	+	0.789348i	$0.289581\pi$
$62$		0			0
$63$	1.58426	+	2.74402i	0.199598	+	0.345714i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.76168	−	11.7116i	−0.826070	−	1.43080i	−0.901099	−	0.433614i	$-0.857238\pi$
$67$	−6.76168	−	11.7116i	−0.826070	−	1.43080i	0.0750284	−	0.997181i	$-0.476095\pi$
$68$		0			0
$69$	3.51189	−	6.08277i	0.422782	−	0.732279i
$70$		0			0
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	−0.682046	−	0.731309i	$-0.738910\pi$
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	0.225015	−	0.974355i	$-0.427757\pi$
$72$		0			0
$73$	10.9921			1.28653			0.643266	−	0.765643i	$-0.277579\pi$
$73$	10.9921			1.28653			0.643266	+	0.765643i	$0.277579\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.987192	−	0.987192i	0.112501	−	0.112501i
$78$		0			0
$79$			3.98168i			0.447974i	0.974592	+	0.223987i	$0.0719074\pi$
$79$			3.98168i			0.447974i	−0.974592	+	0.223987i	$0.928093\pi$
$80$		0			0
$81$	−3.28761	−	5.69431i	−0.365290	−	0.632701i
$82$		0			0
$83$		−	6.25583i		−	0.686667i	−0.939214	−	0.343333i	$-0.888444\pi$
$83$		−	6.25583i		−	0.686667i	0.939214	−	0.343333i	$-0.111556\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−17.1044	+	4.58310i	−1.83378	+	0.491360i
$88$		0			0
$89$	−9.80805	−	2.62806i	−1.03965	−	0.278574i	−0.301683	−	0.953408i	$-0.597548\pi$
$89$	−9.80805	−	2.62806i	−1.03965	−	0.278574i	−0.737969	+	0.674835i	$0.764215\pi$
$90$		0			0
$91$	0.457701	−	3.08581i	0.0479801	−	0.323481i
$92$		0			0
$93$	−0.605885	+	0.349808i	−0.0628274	+	0.0362734i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.728593	−	1.26196i	0.0739774	−	0.128133i	−0.826664	−	0.562696i	$-0.809764\pi$
$97$	0.728593	−	1.26196i	0.0739774	−	0.128133i	0.900641	+	0.434564i	$0.143097\pi$
$98$		0			0
$99$	4.17841	−	4.17841i	0.419946	−	0.419946i
$100$		0			0
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.908337	−	0.418240i	$-0.862647\pi$
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.0919621	+	0.995763i	$0.529314\pi$
$102$		0			0
$103$	−10.8660	−	10.8660i	−1.07066	−	1.07066i	−0.997306	−	0.0733504i	$-0.976631\pi$
$103$	−10.8660	−	10.8660i	−1.07066	−	1.07066i	−0.0733504	−	0.997306i	$-0.523369\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.84601	−	6.88942i	0.178461	−	0.666025i	−0.817475	−	0.575964i	$-0.804627\pi$
$107$	1.84601	−	6.88942i	0.178461	−	0.666025i	0.995936	−	0.0900615i	$-0.0287064\pi$
$108$		0			0
$109$	4.56805	+	4.56805i	0.437540	+	0.437540i	0.891183	−	0.453643i	$-0.149876\pi$
$109$	4.56805	+	4.56805i	0.437540	+	0.437540i	−0.453643	+	0.891183i	$0.649876\pi$
$110$		0			0
$111$	−23.6711	+	6.34266i	−2.24677	+	0.602019i
$112$		0			0
$113$	−2.23652	−	8.34679i	−0.210394	−	0.785200i	−0.987737	−	0.156124i	$-0.950100\pi$
$113$	−2.23652	−	8.34679i	−0.210394	−	0.785200i	0.777344	−	0.629076i	$-0.216567\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.93727	−	13.0611i	0.179101	−	1.20750i
$118$		0			0
$119$	−1.15829	+	4.32280i	−0.106180	+	0.396270i
$120$		0			0
$121$	7.27143	+	4.19816i	0.661039	+	0.381651i
$122$		0			0
$123$	−0.965692	−	0.557543i	−0.0870735	−	0.0502719i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.54494	+	1.21781i	0.403299	+	0.108064i	0.454766	−	0.890611i	$-0.349723\pi$
$127$	4.54494	+	1.21781i	0.403299	+	0.108064i	−0.0514670	+	0.998675i	$0.516390\pi$
$128$		0			0
$129$	30.8633			2.71736
$130$		0			0
$131$	15.3255			1.33900			0.669498	−	0.742814i	$-0.266509\pi$
$131$	15.3255			1.33900			0.669498	+	0.742814i	$0.266509\pi$
$132$		0			0
$133$	−1.00900	−	0.270362i	−0.0874918	−	0.0234434i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.6738	−	8.47191i	−1.25367	−	0.723804i	−0.281830	−	0.959464i	$-0.590941\pi$
$137$	−14.6738	−	8.47191i	−1.25367	−	0.723804i	−0.971835	+	0.235661i	$0.924275\pi$
$138$		0			0
$139$	−2.69425	−	1.55553i	−0.228524	−	0.131938i	0.381367	−	0.924424i	$-0.375453\pi$
$139$	−2.69425	−	1.55553i	−0.228524	−	0.131938i	−0.609891	+	0.792485i	$0.708787\pi$
$140$		0			0
$141$	−1.01628	+	3.79280i	−0.0855861	+	0.319412i
$142$		0			0
$143$	−5.77975	+	0.664975i	−0.483327	+	0.0556080i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.17619	+	15.5857i	0.344446	+	1.28549i
$148$		0			0
$149$	15.9563	−	4.27549i	1.30719	−	0.350262i	0.463029	−	0.886343i	$-0.346763\pi$
$149$	15.9563	−	4.27549i	1.30719	−	0.350262i	0.844166	+	0.536082i	$0.180096\pi$
$150$		0			0
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.999999	+	0.00150662i	$0.000479574\pi$
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.00150662	+	0.999999i	$0.499520\pi$
$152$		0			0
$153$	−4.90260	+	18.2968i	−0.396352	+	1.47920i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.83463	+	5.83463i	0.465654	+	0.465654i	0.900503	−	0.434849i	$-0.143198\pi$
$157$	5.83463	+	5.83463i	0.465654	+	0.465654i	−0.434849	+	0.900503i	$0.643198\pi$
$158$		0			0
$159$	−15.4392	+	8.91385i	−1.22441	+	0.706914i
$160$		0			0
$161$	−1.66484	+	1.66484i	−0.131208	+	0.131208i
$162$		0			0
$163$	2.64140	−	4.57504i	0.206890	−	0.358344i	−0.743843	−	0.668354i	$-0.766999\pi$
$163$	2.64140	−	4.57504i	0.206890	−	0.358344i	0.950733	+	0.310010i	$0.100332\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.81358	−	3.93382i	0.527251	−	0.304408i	−0.212645	−	0.977129i	$-0.568208\pi$
$167$	6.81358	−	3.93382i	0.527251	−	0.304408i	0.739896	+	0.672721i	$0.234875\pi$
$168$		0			0
$169$	−9.48803	+	8.88692i	−0.729848	+	0.683609i
$170$		0			0
$171$	−4.27073	−	1.14434i	−0.326591	−	0.0875098i
$172$		0			0
$173$	19.2622	−	5.16129i	1.46448	−	0.392406i	0.563444	−	0.826154i	$-0.309476\pi$
$173$	19.2622	−	5.16129i	1.46448	−	0.392406i	0.901034	+	0.433749i	$0.142809\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			30.4337i			2.28753i
$178$		0			0
$179$	−1.53139	−	2.65244i	−0.114461	−	0.198253i	0.803103	−	0.595840i	$-0.203181\pi$
$179$	−1.53139	−	2.65244i	−0.114461	−	0.198253i	−0.917564	+	0.397588i	$0.869847\pi$
$180$		0			0
$181$		−	23.3657i		−	1.73676i	−0.495901	−	0.868379i	$-0.665162\pi$
$181$		−	23.3657i		−	1.73676i	0.495901	−	0.868379i	$-0.334838\pi$
$182$		0			0
$183$	10.7372	−	10.7372i	0.793720	−	0.793720i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	8.34623			0.610337
$188$		0			0
$189$	−0.382706	−	1.42828i	−0.0278377	−	0.103892i
$190$		0			0
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	−0.698541	−	0.715570i	$-0.746167\pi$
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	0.968972	+	0.247170i	$0.0795006\pi$
$192$		0			0
$193$	1.00100	+	1.73378i	0.0720536	+	0.124800i	0.899801	−	0.436300i	$-0.143711\pi$
$193$	1.00100	+	1.73378i	0.0720536	+	0.124800i	−0.827748	+	0.561101i	$0.810378\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.59042	−	2.75469i	−0.113313	−	0.196264i	0.803791	−	0.594912i	$-0.202813\pi$
$197$	−1.59042	−	2.75469i	−0.113313	−	0.196264i	−0.917104	+	0.398648i	$0.869480\pi$
$198$		0			0
$199$	−8.20225	+	14.2067i	−0.581442	+	1.00709i	0.413867	+	0.910337i	$0.364178\pi$
$199$	−8.20225	+	14.2067i	−0.581442	+	1.00709i	−0.995309	+	0.0967496i	$0.969155\pi$
$200$		0			0
$201$	9.03414	+	33.7159i	0.637219	+	2.37813i
$202$		0			0
$203$	5.93581			0.416612
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.04664	+	7.04664i	−0.489775	+	0.489775i
$208$		0			0
$209$			1.94813i			0.134755i
$210$		0			0
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	0.992422	−	0.122876i	$-0.0392117\pi$
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	−0.602625	+	0.798025i	$0.705878\pi$
$212$		0			0
$213$			38.4048i			2.63145i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.226527	−	0.0606978i	0.0153777	−	0.00412044i
$218$		0			0
$219$	−27.4051	−	7.34318i	−1.85187	−	0.496206i
$220$		0			0
$221$	14.9794	−	11.1097i	1.00762	−	0.747320i
$222$		0			0
$223$	−8.74357	+	5.04810i	−0.585513	+	0.338046i	−0.763321	−	0.646019i	$-0.776433\pi$
$223$	−8.74357	+	5.04810i	−0.585513	+	0.338046i	0.177808	+	0.984065i	$0.443099\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.86958	+	11.8985i	−0.455950	+	0.789728i	−0.998742	−	0.0501387i	$-0.984034\pi$
$227$	−6.86958	+	11.8985i	−0.455950	+	0.789728i	0.542792	+	0.839867i	$0.317367\pi$
$228$		0			0
$229$	−3.36743	+	3.36743i	−0.222526	+	0.222526i	−0.809561	−	0.587035i	$-0.800295\pi$
$229$	−3.36743	+	3.36743i	−0.222526	+	0.222526i	0.587035	+	0.809561i	$0.300295\pi$
$230$		0			0
$231$	−3.12071	+	1.80174i	−0.205328	+	0.118546i
$232$		0			0
$233$	−19.1541	−	19.1541i	−1.25482	−	1.25482i	−0.953532	−	0.301293i	$-0.902582\pi$
$233$	−19.1541	−	19.1541i	−1.25482	−	1.25482i	−0.301293	−	0.953532i	$-0.597418\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.65992	−	9.92697i	0.172781	−	0.644826i
$238$		0			0
$239$	−18.4667	−	18.4667i	−1.19451	−	1.19451i	−0.975786	−	0.218727i	$-0.929810\pi$
$239$	−18.4667	−	18.4667i	−1.19451	−	1.19451i	−0.218727	−	0.975786i	$-0.570190\pi$
$240$		0			0
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	−0.231313	−	0.972879i	$-0.574302\pi$
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	0.286117	+	0.958195i	$0.407635\pi$
$242$		0			0
$243$	5.71949	+	21.3454i	0.366905	+	1.36931i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.59317	+	3.49640i	0.165000	+	0.222471i
$248$		0			0
$249$	−4.17915	+	15.5968i	−0.264843	+	0.988406i
$250$		0			0
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	0.666844	−	0.745198i	$-0.267645\pi$
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	−0.311938	+	0.950102i	$0.600978\pi$
$252$		0			0
$253$	3.80266	+	2.19547i	0.239071	+	0.138028i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.3489	+	2.77298i	0.645547	+	0.172974i	0.566715	−	0.823914i	$-0.308214\pi$
$257$	10.3489	+	2.77298i	0.645547	+	0.172974i	0.0788324	+	0.996888i	$0.474881\pi$
$258$		0			0
$259$	8.21472			0.510438
$260$		0			0
$261$	25.1240			1.55514
$262$		0			0
$263$	9.80873	+	2.62824i	0.604832	+	0.162064i	0.548223	−	0.836332i	$-0.315304\pi$
$263$	9.80873	+	2.62824i	0.604832	+	0.162064i	0.0566092	+	0.998396i	$0.481971\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	22.6974	+	13.1043i	1.38906	+	0.801973i
$268$		0			0
$269$	−16.1943	−	9.34977i	−0.987383	−	0.570066i	−0.0828917	−	0.996559i	$-0.526416\pi$
$269$	−16.1943	−	9.34977i	−0.987383	−	0.570066i	−0.904491	+	0.426493i	$0.859749\pi$
$270$		0			0
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	0.658220	+	0.752826i	$0.271310\pi$
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	−0.946448	+	0.322856i	$0.895357\pi$
$272$		0			0
$273$	−3.20257	+	7.38767i	−0.193828	+	0.447122i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.50958	−	13.0979i	−0.210870	−	0.786979i	−0.987580	−	0.157120i	$-0.949779\pi$
$277$	−3.50958	−	13.0979i	−0.210870	−	0.786979i	0.776709	−	0.629859i	$-0.216887\pi$
$278$		0			0
$279$	0.958804	−	0.256911i	0.0574021	−	0.0153809i
$280$		0			0
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.999730	+	0.0232200i	$0.00739181\pi$
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.0232200	+	0.999730i	$0.492608\pi$
$282$		0			0
$283$	−2.37015	+	8.84554i	−0.140891	+	0.525813i	0.859013	+	0.511954i	$0.171078\pi$
$283$	−2.37015	+	8.84554i	−0.140891	+	0.525813i	−0.999904	+	0.0138586i	$0.995589\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.264308	+	0.264308i	0.0156016	+	0.0156016i
$288$		0			0
$289$	−8.44752	+	4.87718i	−0.496913	+	0.286893i
$290$		0			0
$291$	−2.65954	+	2.65954i	−0.155905	+	0.155905i
$292$		0			0
$293$	−9.09083	+	15.7458i	−0.531092	+	0.919878i	0.468250	+	0.883596i	$0.344885\pi$
$293$	−9.09083	+	15.7458i	−0.531092	+	0.919878i	−0.999342	+	0.0362820i	$0.988449\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.38819	+	1.37882i	−0.138577	+	0.0800073i
$298$		0			0
$299$	9.74721	−	1.12144i	0.563696	−	0.0648546i
$300$		0			0
$301$	−9.99318	−	2.67766i	−0.575997	−	0.154338i
$302$		0			0
$303$	28.9408	−	7.75465i	1.66260	−	0.445493i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			28.0356i			1.60008i	0.599948	+	0.800039i	$0.295188\pi$
$307$			28.0356i			1.60008i	−0.599948	+	0.800039i	$0.704812\pi$
$308$		0			0
$309$	19.8317	+	34.3495i	1.12819	+	1.95408i
$310$		0			0
$311$			11.5168i			0.653060i	0.945187	+	0.326530i	$0.105879\pi$
$311$			11.5168i			0.653060i	−0.945187	+	0.326530i	$0.894121\pi$
$312$		0			0
$313$	10.3376	−	10.3376i	0.584316	−	0.584316i	−0.351771	−	0.936086i	$-0.614420\pi$
$313$	10.3376	−	10.3376i	0.584316	−	0.584316i	0.936086	+	0.351771i	$0.114420\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.31106			−0.129802			−0.0649010	−	0.997892i	$-0.520673\pi$
$317$	−2.31106			−0.129802			−0.0649010	+	0.997892i	$0.520673\pi$
$318$		0			0
$319$	−2.86514	−	10.6928i	−0.160417	−	0.598685i
$320$		0			0
$321$	−9.20481	+	15.9432i	−0.513763	+	0.889863i
$322$		0			0
$323$	−3.12243	−	5.40821i	−0.173737	−	0.300921i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.33724	−	14.4405i	−0.461050	−	0.798563i
$328$		0			0
$329$	0.658118	−	1.13989i	0.0362832	−	0.0628444i
$330$		0			0
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.498370	−	0.866965i	$-0.666068\pi$
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.00188163	−	0.999998i	$-0.500599\pi$
$332$		0			0
$333$	34.7698			1.90537
$334$		0			0
$335$		0			0
$336$		0			0
$337$	4.04414	−	4.04414i	0.220298	−	0.220298i	−0.588326	−	0.808624i	$-0.700213\pi$
$337$	4.04414	−	4.04414i	0.220298	−	0.220298i	0.808624	+	0.588326i	$0.200213\pi$
$338$		0			0
$339$			22.3040i			1.21139i
$340$		0			0
$341$	−0.218684	−	0.378771i	−0.0118424	−	0.0205116i
$342$		0			0
$343$		−	11.4653i		−	0.619068i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.216132	−	0.0579124i	0.0116026	−	0.00310890i	−0.253013	−	0.967463i	$-0.581422\pi$
$347$	0.216132	−	0.0579124i	0.0116026	−	0.00310890i	0.264616	+	0.964354i	$0.414755\pi$
$348$		0			0
$349$	−11.9175	−	3.19329i	−0.637930	−	0.170933i	−0.0746643	−	0.997209i	$-0.523789\pi$
$349$	−11.9175	−	3.19329i	−0.637930	−	0.170933i	−0.563266	+	0.826276i	$0.690455\pi$
$350$		0			0
$351$	−2.45083	+	5.65356i	−0.130816	+	0.301765i
$352$		0			0
$353$	11.0318	−	6.36920i	0.587162	−	0.338998i	−0.176812	−	0.984245i	$-0.556579\pi$
$353$	11.0318	−	6.36920i	0.587162	−	0.338998i	0.763975	+	0.645246i	$0.223245\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.77560	−	10.0036i	0.305677	−	0.529449i
$358$		0			0
$359$	18.8285	−	18.8285i	0.993730	−	0.993730i	−0.00625094	−	0.999980i	$-0.501990\pi$
$359$	18.8285	−	18.8285i	0.993730	−	0.993730i	0.999980	+	0.00625094i	$0.00198975\pi$
$360$		0			0
$361$	−15.1921	+	8.77118i	−0.799586	+	0.461641i
$362$		0			0
$363$	−15.3243	−	15.3243i	−0.804317	−	0.804317i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−5.35985	+	20.0032i	−0.279782	+	1.04416i	0.672787	+	0.739837i	$0.265097\pi$
$367$	−5.35985	+	20.0032i	−0.279782	+	1.04416i	−0.952569	+	0.304324i	$0.901569\pi$
$368$		0			0
$369$	1.11872	+	1.11872i	0.0582380	+	0.0582380i
$370$		0			0
$371$	5.77240	−	1.54671i	0.299688	−	0.0803012i
$372$		0			0
$373$	−1.10162	−	4.11130i	−0.0570397	−	0.212875i	0.931524	−	0.363680i	$-0.118480\pi$
$373$	−1.10162	−	4.11130i	−0.0570397	−	0.212875i	−0.988563	+	0.150805i	$0.951813\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.3755	−	15.3771i	−0.997889	−	0.791962i
$378$		0			0
$379$	2.81310	−	10.4986i	0.144499	−	0.539278i	−0.855278	−	0.518169i	$-0.826614\pi$
$379$	2.81310	−	10.4986i	0.144499	−	0.539278i	0.999777	−	0.0211086i	$-0.00671957\pi$
$380$		0			0
$381$	−10.5177	−	6.07241i	−0.538839	−	0.311099i
$382$		0			0
$383$	11.6937	+	6.75134i	0.597518	+	0.344977i	0.768065	−	0.640372i	$-0.221220\pi$
$383$	11.6937	+	6.75134i	0.597518	+	0.344977i	−0.170546	+	0.985350i	$0.554553\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−42.2973	−	11.3335i	−2.15009	−	0.576116i
$388$		0			0
$389$	−7.82344			−0.396664			−0.198332	−	0.980135i	$-0.563552\pi$
$389$	−7.82344			−0.396664			−0.198332	+	0.980135i	$0.563552\pi$
$390$		0			0
$391$	−14.0754			−0.711825
$392$		0			0
$393$	−38.2090	−	10.2381i	−1.92739	−	0.516442i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.4670	−	6.04313i	−0.525324	−	0.303296i	0.213786	−	0.976881i	$-0.431421\pi$
$397$	−10.4670	−	6.04313i	−0.525324	−	0.303296i	−0.739110	+	0.673584i	$0.764754\pi$
$398$		0			0
$399$	2.33500	+	1.34811i	0.116896	+	0.0674900i
$400$		0			0
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	0.836658	+	0.547725i	$0.184506\pi$
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	−0.998430	+	0.0560149i	$0.982161\pi$
$402$		0			0
$403$	−0.896666	−	0.388707i	−0.0446661	−	0.0193629i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.96514	−	14.7981i	−0.196545	−	0.733515i
$408$		0			0
$409$	12.0227	−	3.22147i	0.594484	−	0.159292i	0.0509825	−	0.998700i	$-0.483765\pi$
$409$	12.0227	−	3.22147i	0.594484	−	0.159292i	0.543502	+	0.839408i	$0.317098\pi$
$410$		0			0
$411$	30.9245	+	30.9245i	1.52539	+	1.52539i
$412$		0			0
$413$	2.64039	−	9.85406i	0.129925	−	0.484887i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.67805	+	5.67805i	0.278055	+	0.278055i
$418$		0			0
$419$	−6.12710	+	3.53748i	−0.299328	+	0.172817i	−0.642141	−	0.766586i	$-0.721954\pi$
$419$	−6.12710	+	3.53748i	−0.299328	+	0.172817i	0.342813	+	0.939404i	$0.388620\pi$
$420$		0			0
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	−0.944485	−	0.328555i	$-0.893438\pi$
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	0.328555	+	0.944485i	$0.393438\pi$
$422$		0			0
$423$	2.78557	−	4.82474i	0.135439	−	0.234587i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.40815	+	2.54504i	−0.213325	+	0.123163i
$428$		0			0
$429$	14.8541	+	2.20322i	0.717162	+	0.106372i
$430$		0			0
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	0.298660	−	0.954359i	$-0.403460\pi$
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	−0.218532	+	0.975830i	$0.570127\pi$
$432$		0			0
$433$	−15.5451	+	4.16531i	−0.747052	+	0.200172i	−0.612210	−	0.790695i	$-0.709719\pi$
$433$	−15.5451	+	4.16531i	−0.747052	+	0.200172i	−0.134842	+	0.990867i	$0.543053\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	3.28541i		−	0.157163i
$438$		0			0
$439$	−7.54892	−	13.0751i	−0.360290	−	0.624041i	0.627718	−	0.778441i	$-0.283989\pi$
$439$	−7.54892	−	13.0751i	−0.360290	−	0.624041i	−0.988008	+	0.154400i	$0.950656\pi$
$440$		0			0
$441$		−	22.8934i		−	1.09016i
$442$		0			0
$443$	13.3798	−	13.3798i	0.635694	−	0.635694i	−0.313797	−	0.949490i	$-0.601601\pi$
$443$	13.3798	−	13.3798i	0.635694	−	0.635694i	0.949490	+	0.313797i	$0.101601\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−42.6379			−2.01670
$448$		0			0
$449$	−4.77864	−	17.8341i	−0.225518	−	0.841645i	−0.982196	−	0.187858i	$-0.939846\pi$
$449$	−4.77864	−	17.8341i	−0.225518	−	0.841645i	0.756678	−	0.653788i	$-0.226821\pi$
$450$		0			0
$451$	0.348550	−	0.603706i	0.0164126	−	0.0284274i
$452$		0			0
$453$	−22.4612	−	38.9040i	−1.05532	−	1.82787i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.52390	+	13.0318i	0.351953	+	0.609601i	0.986592	−	0.163208i	$-0.0521843\pi$
$457$	7.52390	+	13.0318i	0.351953	+	0.609601i	−0.634638	+	0.772809i	$0.718851\pi$
$458$		0			0
$459$	4.41990	−	7.65549i	0.206303	−	0.357328i
$460$		0			0
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	0.999736	+	0.0229718i	$0.00731278\pi$
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	−0.854311	+	0.519762i	$0.826021\pi$
$462$		0			0
$463$	32.5516			1.51280			0.756400	−	0.654109i	$-0.226956\pi$
$463$	32.5516			1.51280			0.756400	+	0.654109i	$0.226956\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.4091	−	19.4091i	0.898145	−	0.898145i	−0.0971268	−	0.995272i	$-0.530965\pi$
$467$	19.4091	−	19.4091i	0.898145	−	0.898145i	0.995272	+	0.0971268i	$0.0309652\pi$
$468$		0			0
$469$		−	11.7006i		−	0.540283i
$470$		0			0
$471$	−10.6489	−	18.4444i	−0.490675	−	0.849874i
$472$		0			0
$473$			19.2943i			0.887153i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	24.4324	−	6.54664i	1.11868	−	0.299750i
$478$		0			0
$479$	5.16289	+	1.38339i	0.235899	+	0.0632088i	0.374831	−	0.927093i	$-0.377701\pi$
$479$	5.16289	+	1.38339i	0.235899	+	0.0632088i	−0.138933	+	0.990302i	$0.544367\pi$
$480$		0			0
$481$	−26.8142	−	21.2808i	−1.22262	−	0.970321i
$482$		0			0
$483$	5.26290	−	3.03853i	0.239470	−	0.138258i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.93242	+	10.2752i	−0.268823	+	0.465616i	−0.968558	−	0.248787i	$-0.919968\pi$
$487$	−5.93242	+	10.2752i	−0.268823	+	0.465616i	0.699735	+	0.714403i	$0.253301\pi$
$488$		0			0
$489$	−9.64173	+	9.64173i	−0.436014	+	0.436014i
$490$		0			0
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	−0.0649209	−	0.997890i	$-0.520680\pi$
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	0.831738	+	0.555168i	$0.187346\pi$
$492$		0			0
$493$	25.0922	+	25.0922i	1.13010	+	1.13010i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.33195	−	12.4350i	0.149459	−	0.557787i
$498$		0			0
$499$	25.2879	+	25.2879i	1.13204	+	1.13204i	0.989837	+	0.142203i	$0.0454187\pi$
$499$	25.2879	+	25.2879i	1.13204	+	1.13204i	0.142203	+	0.989837i	$0.454581\pi$
$500$		0			0
$501$	−19.6153	+	5.25591i	−0.876347	+	0.234817i
$502$		0			0
$503$	3.69726	+	13.7984i	0.164853	+	0.615239i	0.998059	+	0.0622762i	$0.0198360\pi$
$503$	3.69726	+	13.7984i	0.164853	+	0.615239i	−0.833206	+	0.552962i	$0.813497\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	29.5920	−	15.8181i	1.31423	−	0.702508i
$508$		0			0
$509$	9.01986	−	33.6626i	0.399798	−	1.49207i	−0.413653	−	0.910435i	$-0.635747\pi$
$509$	9.01986	−	33.6626i	0.399798	−	1.49207i	0.813451	−	0.581633i	$-0.197586\pi$
$510$		0			0
$511$	8.23637	+	4.75527i	0.364356	+	0.210361i
$512$		0			0
$513$	1.78690	+	1.03167i	0.0788938	+	0.0455493i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.37109	−	0.635331i	−0.104280	−	0.0279418i
$518$		0			0
$519$	−51.4717			−2.25936
$520$		0			0
$521$	20.2982			0.889281			0.444641	−	0.895709i	$-0.353331\pi$
$521$	20.2982			0.889281			0.444641	+	0.895709i	$0.353331\pi$
$522$		0			0
$523$	−18.2457	−	4.88891i	−0.797827	−	0.213777i	−0.163197	−	0.986593i	$-0.552181\pi$
$523$	−18.2457	−	4.88891i	−0.797827	−	0.213777i	−0.634630	+	0.772816i	$0.718847\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.21417	+	0.701004i	0.0528903	+	0.0305362i
$528$		0			0
$529$	13.5056	+	7.79747i	0.587201	+	0.339020i
$530$		0			0
$531$	11.1758	−	41.7085i	0.484987	−	1.80999i
$532$		0			0
$533$	−0.178038	−	1.54745i	−0.00771170	−	0.0670277i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.04605	+	7.63598i	0.0882938	+	0.329517i
$538$		0			0
$539$	−9.74349	+	2.61076i	−0.419682	+	0.112453i
$540$		0			0
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	0.111700	−	0.993742i	$-0.464371\pi$
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	−0.993742	+	0.111700i	$0.964371\pi$
$542$		0			0
$543$	−15.6092	+	58.2544i	−0.669856	+	2.49993i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.8176	+	28.8176i	1.23215	+	1.23215i	0.963135	+	0.269018i	$0.0866990\pi$
$547$	28.8176	+	28.8176i	1.23215	+	1.23215i	0.269018	+	0.963135i	$0.413301\pi$
$548$		0			0
$549$	−18.6580	+	10.7722i	−0.796304	+	0.459747i
$550$		0			0
$551$	−5.85689	+	5.85689i	−0.249512	+	0.249512i
$552$		0			0
$553$	−1.72250	+	2.98347i	−0.0732484	+	0.126870i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.50881	+	3.75786i	−0.275787	+	0.159226i	−0.631515	−	0.775364i	$-0.717566\pi$
$557$	−6.50881	+	3.75786i	−0.275787	+	0.159226i	0.355727	+	0.934590i	$0.384233\pi$
$558$		0			0
$559$	25.6828	+	34.6284i	1.08627	+	1.46462i
$560$		0			0
$561$	−20.8085	−	5.57562i	−0.878535	−	0.235403i
$562$		0			0
$563$	−23.0668	+	6.18074i	−0.972151	+	0.260487i	−0.709736	−	0.704468i	$-0.751186\pi$
$563$	−23.0668	+	6.18074i	−0.972151	+	0.260487i	−0.262415	+	0.964955i	$0.584519\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	5.68898i		−	0.238915i
$568$		0			0
$569$	1.39258	+	2.41202i	0.0583801	+	0.101117i	0.893738	−	0.448589i	$-0.148073\pi$
$569$	1.39258	+	2.41202i	0.0583801	+	0.101117i	−0.835358	+	0.549706i	$0.814740\pi$
$570$		0			0
$571$		−	28.8794i		−	1.20857i	−0.796769	−	0.604284i	$-0.793459\pi$
$571$		−	28.8794i		−	1.20857i	0.796769	−	0.604284i	$-0.206541\pi$
$572$		0			0
$573$	−13.6425	+	13.6425i	−0.569924	+	0.569924i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.20458			−0.175039			−0.0875196	−	0.996163i	$-0.527894\pi$
$577$	−4.20458			−0.175039			−0.0875196	+	0.996163i	$0.527894\pi$
$578$		0			0
$579$	−1.33742	−	4.99131i	−0.0555811	−	0.207432i
$580$		0			0
$581$	2.70632	−	4.68748i	0.112277	−	0.194469i
$582$		0			0
$583$	−5.57253	−	9.65190i	−0.230790	−	0.399741i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.71072	−	4.69510i	−0.111883	−	0.193787i	0.804646	−	0.593754i	$-0.202355\pi$
$587$	−2.71072	−	4.69510i	−0.111883	−	0.193787i	−0.916530	+	0.399967i	$0.869022\pi$
$588$		0			0
$589$	−0.163625	+	0.283406i	−0.00674204	+	0.0116776i
$590$		0			0
$591$	2.12493	+	7.93036i	0.0874081	+	0.326211i
$592$		0			0
$593$	15.8446			0.650660			0.325330	−	0.945601i	$-0.394525\pi$
$593$	15.8446			0.650660			0.325330	+	0.945601i	$0.394525\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	29.9402	−	29.9402i	1.22537	−	1.22537i
$598$		0			0
$599$		−	34.8884i		−	1.42550i	−0.701418	−	0.712750i	$-0.747450\pi$
$599$		−	34.8884i		−	1.42550i	0.701418	−	0.712750i	$-0.252550\pi$
$600$		0			0
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	0.999644	−	0.0266875i	$-0.00849591\pi$
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	−0.522934	+	0.852373i	$0.675163\pi$
$602$		0			0
$603$		−	49.5242i		−	2.01678i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	31.2836	−	8.38242i	1.26976	−	0.340232i	0.439823	−	0.898085i	$-0.355041\pi$
$607$	31.2836	−	8.38242i	1.26976	−	0.340232i	0.829940	+	0.557853i	$0.188375\pi$
$608$		0			0
$609$	−14.7989	−	3.96536i	−0.599683	−	0.160685i
$610$		0			0
$611$	−5.10118	+	2.01591i	−0.206372	+	0.0815549i
$612$		0			0
$613$	−33.8649	+	19.5519i	−1.36779	+	0.789695i	−0.990646	−	0.136458i	$-0.956428\pi$
$613$	−33.8649	+	19.5519i	−1.36779	+	0.789695i	−0.377146	+	0.926154i	$0.623095\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.14533	+	12.3761i	−0.287660	+	0.498242i	−0.973251	−	0.229745i	$-0.926211\pi$
$617$	−7.14533	+	12.3761i	−0.287660	+	0.498242i	0.685591	+	0.727987i	$0.259544\pi$
$618$		0			0
$619$	−6.85038	+	6.85038i	−0.275340	+	0.275340i	−0.831245	−	0.555906i	$-0.812372\pi$
$619$	−6.85038	+	6.85038i	−0.275340	+	0.275340i	0.555906	+	0.831245i	$0.312372\pi$
$620$		0			0
$621$	4.02754	−	2.32530i	0.161620	−	0.0933111i
$622$		0			0
$623$	−6.21223	−	6.21223i	−0.248888	−	0.248888i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.30143	−	4.85701i	0.0519742	−	0.193970i
$628$		0			0
$629$	34.7257	+	34.7257i	1.38461	+	1.38461i
$630$		0			0
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.574921	−	0.818209i	$-0.305033\pi$
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.907000	+	0.421130i	$0.138366\pi$
$632$		0			0
$633$	−7.56506	−	28.2332i	−0.300684	−	1.12217i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−14.0119	+	17.6553i	−0.555171	+	0.699527i
$638$		0			0
$639$	14.1029	−	52.6327i	0.557902	−	2.08212i
$640$		0			0
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	0.622503	−	0.782617i	$-0.286116\pi$
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	−0.366515	+	0.930412i	$0.619449\pi$
$642$		0			0
$643$	20.7800	+	11.9973i	0.819482	+	0.473128i	0.850238	−	0.526399i	$-0.176458\pi$
$643$	20.7800	+	11.9973i	0.819482	+	0.473128i	−0.0307558	+	0.999527i	$0.509791\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.5414	−	6.03995i	−0.886195	−	0.237455i	−0.213117	−	0.977027i	$-0.568361\pi$
$647$	−22.5414	−	6.03995i	−0.886195	−	0.237455i	−0.673078	+	0.739572i	$0.735028\pi$
$648$		0			0
$649$	−19.0257			−0.746825
$650$		0			0
$651$	−0.605318			−0.0237243
$652$		0			0
$653$	−20.3843	−	5.46196i	−0.797700	−	0.213743i	−0.163126	−	0.986605i	$-0.552158\pi$
$653$	−20.3843	−	5.46196i	−0.797700	−	0.213743i	−0.634574	+	0.772862i	$0.718824\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	34.8614	+	20.1273i	1.36007	+	0.785239i
$658$		0			0
$659$	13.0042	+	7.50797i	0.506571	+	0.292469i	0.731423	−	0.681924i	$-0.238856\pi$
$659$	13.0042	+	7.50797i	0.506571	+	0.292469i	−0.224852	+	0.974393i	$0.572190\pi$
$660$		0			0
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	−0.932420	−	0.361377i	$-0.882307\pi$
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	0.988188	+	0.153249i	$0.0489735\pi$
$662$		0			0
$663$	−44.7676	+	17.6915i	−1.73863	+	0.687080i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.83189	+	18.0329i	0.187092	+	0.698235i
$668$		0			0
$669$	25.1715	−	6.74467i	0.973185	−	0.260764i
$670$		0			0
$671$	6.71243	+	6.71243i	0.259130	+	0.259130i
$672$		0			0
$673$	−8.14271	+	30.3890i	−0.313878	+	1.17141i	0.611151	+	0.791514i	$0.290707\pi$
$673$	−8.14271	+	30.3890i	−0.313878	+	1.17141i	−0.925029	+	0.379896i	$0.875960\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.4080	−	19.4080i	−0.745910	−	0.745910i	0.227798	−	0.973708i	$-0.426847\pi$
$677$	−19.4080	−	19.4080i	−0.745910	−	0.745910i	−0.973708	+	0.227798i	$0.926847\pi$
$678$		0			0
$679$	1.09187	−	0.630389i	0.0419019	−	0.0241921i
$680$		0			0
$681$	25.0756	−	25.0756i	0.960899	−	0.960899i
$682$		0			0
$683$	12.1706	−	21.0802i	0.465697	−	0.806610i	−0.533536	−	0.845777i	$-0.679137\pi$
$683$	12.1706	−	21.0802i	0.465697	−	0.806610i	0.999233	+	0.0391672i	$0.0124705\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	10.6451	−	6.14597i	0.406137	−	0.234483i
$688$		0			0
$689$	−22.8490	−	9.90507i	−0.870476	−	0.377353i
$690$		0			0
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	0.0327325	−	0.999464i	$-0.489579\pi$
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	−0.471385	+	0.881928i	$0.656246\pi$
$692$		0			0
$693$	4.93848	−	1.32326i	0.187597	−	0.0502666i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			2.23460i			0.0846413i
$698$		0			0
$699$	34.9585	+	60.5498i	1.32225	+	2.29020i
$700$		0			0
$701$			21.2613i			0.803029i	0.915853	+	0.401515i	$0.131516\pi$
$701$			21.2613i			0.803029i	−0.915853	+	0.401515i	$0.868484\pi$
$702$		0			0
$703$	−8.10550	+	8.10550i	−0.305705	+	0.305705i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.0435			−0.377723
$708$		0			0
$709$	−5.58329	−	20.8371i	−0.209685	−	0.782555i	−0.987970	−	0.154644i	$-0.950577\pi$
$709$	−5.58329	−	20.8371i	−0.209685	−	0.782555i	0.778285	−	0.627911i	$-0.216090\pi$
$710$		0			0
$711$	−7.29071	+	12.6279i	−0.273423	+	0.473582i
$712$		0			0
$713$	0.368797	+	0.638775i	0.0138116	+	0.0239223i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	33.7040	+	58.3770i	1.25870	+	2.18013i
$718$		0			0
$719$	−4.13804	+	7.16730i	−0.154323	+	0.267295i	−0.932812	−	0.360363i	$-0.882653\pi$
$719$	−4.13804	+	7.16730i	−0.154323	+	0.267295i	0.778489	+	0.627658i	$0.215986\pi$
$720$		0			0
$721$	−3.44115	−	12.8425i	−0.128155	−	0.478282i
$722$		0			0
$723$	−2.27344			−0.0845500
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.41639	−	2.41639i	0.0896190	−	0.0896190i	−0.660876	−	0.750495i	$-0.729815\pi$
$727$	2.41639	−	2.41639i	0.0896190	−	0.0896190i	0.750495	+	0.660876i	$0.229815\pi$
$728$		0			0
$729$		−	37.3127i		−	1.38195i
$730$		0			0
$731$	−30.9246	−	53.5629i	−1.14379	−	1.98110i
$732$		0			0
$733$		−	32.4183i		−	1.19740i	−0.800974	−	0.598699i	$-0.795685\pi$
$733$		−	32.4183i		−	1.19740i	0.800974	−	0.598699i	$-0.204315\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.0776	+	5.64773i	−0.776404	+	0.208037i
$738$		0			0
$739$	43.7773	+	11.7301i	1.61038	+	0.431499i	0.948154	−	0.317810i	$-0.102947\pi$
$739$	43.7773	+	11.7301i	1.61038	+	0.431499i	0.662221	+	0.749309i	$0.269614\pi$
$740$		0			0
$741$	−4.12945	−	10.4494i	−0.151699	−	0.383870i
$742$		0			0
$743$	−13.1203	+	7.57500i	−0.481336	+	0.277900i	−0.720973	−	0.692963i	$-0.756305\pi$
$743$	−13.1203	+	7.57500i	−0.481336	+	0.277900i	0.239637	+	0.970863i	$0.422972\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.4548	−	19.8403i	0.419110	−	0.725919i
$748$		0			0
$749$	4.36362	−	4.36362i	0.159443	−	0.159443i
$750$		0			0
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	−0.597185	−	0.802103i	$-0.703714\pi$
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	0.396049	+	0.918229i	$0.370381\pi$
$752$		0			0
$753$	−11.8498	−	11.8498i	−0.431830	−	0.431830i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	7.31666	−	27.3061i	0.265928	−	0.992459i	−0.695751	−	0.718283i	$-0.744928\pi$
$757$	7.31666	−	27.3061i	0.265928	−	0.992459i	0.961680	−	0.274176i	$-0.0884050\pi$
$758$		0			0
$759$	−8.01399	−	8.01399i	−0.290889	−	0.290889i
$760$		0			0
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.361828	−	0.932245i	$-0.382153\pi$
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.779475	+	0.626434i	$0.215486\pi$
$762$		0			0
$763$	1.44666	+	5.39900i	0.0523725	+	0.195457i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−34.1463	+	25.3252i	−1.23295	+	0.914441i
$768$		0			0
$769$	−10.7440	+	40.0972i	−0.387439	+	1.44594i	0.446848	+	0.894610i	$0.352547\pi$
$769$	−10.7440	+	40.0972i	−0.387439	+	1.44594i	−0.834286	+	0.551331i	$0.814120\pi$
$770$		0			0
$771$	−23.9490	−	13.8270i	−0.862503	−	0.497966i
$772$		0			0
$773$	1.93793	+	1.11886i	0.0697025	+	0.0402427i	0.534446	−	0.845202i	$-0.320520\pi$
$773$	1.93793	+	1.11886i	0.0697025	+	0.0402427i	−0.464744	+	0.885445i	$0.653854\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−20.4806	−	5.48776i	−0.734738	−	0.196872i
$778$		0			0
$779$	−0.521588			−0.0186878
$780$		0			0
$781$	−24.0089			−0.859106
$782$		0			0
$783$	−11.3252	−	3.03457i	−0.404729	−	0.108447i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−37.4425	−	21.6174i	−1.33468	−	0.770577i	−0.348666	−	0.937247i	$-0.613365\pi$
$787$	−37.4425	−	21.6174i	−1.33468	−	0.770577i	−0.986013	+	0.166669i	$0.946699\pi$
$788$		0			0
$789$	−22.6990	−	13.1053i	−0.808105	−	0.466559i
$790$		0			0
$791$	1.93507	−	7.22176i	0.0688030	−	0.256776i
$792$		0			0
$793$	20.9820	+	3.11215i	0.745094	+	0.110516i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.89049	−	21.9836i	−0.208652	−	0.778699i	−0.988305	−	0.152488i	$-0.951271\pi$
$797$	−5.89049	−	21.9836i	−0.208652	−	0.778699i	0.779653	−	0.626211i	$-0.215395\pi$
$798$		0			0
$799$	7.60066	−	2.03659i	0.268892	−	0.0720494i
$800$		0			0
$801$	−26.2940	−	26.2940i	−0.929053	−	0.929053i
$802$		0			0
$803$	4.59062	−	17.1324i	0.161999	−	0.604590i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	34.1289	+	34.1289i	1.20139	+	1.20139i
$808$		0			0
$809$	25.3301	−	14.6243i	0.890558	−	0.514164i	0.0164333	−	0.999865i	$-0.494769\pi$
$809$	25.3301	−	14.6243i	0.890558	−	0.514164i	0.874125	+	0.485701i	$0.161436\pi$
$810$		0			0
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	−0.931379	−	0.364052i	$-0.881393\pi$
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	0.364052	+	0.931379i	$0.381393\pi$
$812$		0			0
$813$	23.6593	−	40.9790i	0.829767	−	1.43720i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	12.5024	−	7.21825i	0.437403	−	0.252535i
$818$		0			0
$819$	7.10191	−	8.94856i	0.248161	−	0.312688i
$820$		0			0
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.677159	−	0.735837i	$-0.263211\pi$
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.218518	+	0.975833i	$0.429878\pi$
$822$		0			0
$823$	−40.5702	+	10.8708i	−1.41419	+	0.378931i	−0.883418	−	0.468585i	$-0.844764\pi$
$823$	−40.5702	+	10.8708i	−1.41419	+	0.378931i	−0.530770	+	0.847516i	$0.678097\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	48.4948i		−	1.68633i	−0.537655	−	0.843165i	$-0.680690\pi$
$827$		−	48.4948i		−	1.68633i	0.537655	−	0.843165i	$-0.319310\pi$
$828$		0			0
$829$	20.4336	+	35.3921i	0.709689	+	1.22922i	0.964973	+	0.262351i	$0.0844978\pi$
$829$	20.4336	+	35.3921i	0.709689	+	1.22922i	−0.255284	+	0.966866i	$0.582169\pi$
$830$		0			0
$831$			34.9998i			1.21413i
$832$		0			0
$833$	22.8644	−	22.8644i	0.792205	−	0.792205i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.463232			−0.0160116
$838$		0			0
$839$	7.70239	+	28.7457i	0.265916	+	0.992412i	0.961687	+	0.274149i	$0.0883960\pi$
$839$	7.70239	+	28.7457i	0.265916	+	0.992412i	−0.695771	+	0.718263i	$0.744937\pi$
$840$		0			0
$841$	9.03332	−	15.6462i	0.311494	−	0.539523i
$842$		0			0
$843$	−31.2967	−	54.2075i	−1.07792	−	1.86701i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.63231	+	6.29135i	0.124808	+	0.216173i
$848$		0			0
$849$	11.8183	−	20.4700i	0.405605	−	0.702528i
$850$		0			0
$851$	6.68697	+	24.9561i	0.229227	+	0.855485i
$852$		0			0
$853$	8.67930			0.297174			0.148587	−	0.988899i	$-0.452528\pi$
$853$	8.67930			0.297174			0.148587	+	0.988899i	$0.452528\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.38807	−	2.38807i	0.0815751	−	0.0815751i	−0.665142	−	0.746717i	$-0.731629\pi$
$857$	2.38807	−	2.38807i	0.0815751	−	0.0815751i	0.746717	+	0.665142i	$0.231629\pi$
$858$		0			0
$859$			0.237935i			0.00811823i	0.999992	+	0.00405912i	$0.00129206\pi$
$859$			0.237935i			0.00811823i	−0.999992	+	0.00405912i	$0.998708\pi$
$860$		0			0
$861$	−0.482394	−	0.835530i	−0.0164399	−	0.0284748i
$862$		0			0
$863$			48.8736i			1.66368i	0.555017	+	0.831839i	$0.312712\pi$
$863$			48.8736i			1.66368i	−0.555017	+	0.831839i	$0.687288\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	24.3192	−	6.51630i	0.825922	−	0.221305i
$868$		0			0
$869$	6.20588	+	1.66286i	0.210520	+	0.0564087i
$870$		0			0
$871$	−30.3112	+	38.1927i	−1.02706	+	1.29411i
$872$		0			0
$873$	4.62145	−	2.66820i	0.156412	−	0.0903048i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17.4333	+	30.1953i	−0.588680	+	1.01962i	0.405725	+	0.913995i	$0.367019\pi$
$877$	−17.4333	+	30.1953i	−0.588680	+	1.01962i	−0.994406	+	0.105629i	$0.966314\pi$
$878$		0			0
$879$	33.1837	−	33.1837i	1.11926	−	1.11926i
$880$		0			0
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	−0.854361	−	0.519680i	$-0.826051\pi$
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	0.0228755	+	0.999738i	$0.492718\pi$
$882$		0			0
$883$	10.7320	+	10.7320i	0.361160	+	0.361160i	0.864240	−	0.503080i	$-0.167800\pi$
$883$	10.7320	+	10.7320i	0.361160	+	0.361160i	−0.503080	+	0.864240i	$0.667800\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.36490	−	12.5580i	0.112982	−	0.421655i	−0.886146	−	0.463406i	$-0.846627\pi$
$887$	3.36490	−	12.5580i	0.112982	−	0.421655i	0.999128	+	0.0417512i	$0.0132937\pi$
$888$		0			0
$889$	2.87868	+	2.87868i	0.0965478	+	0.0965478i
$890$		0			0
$891$	−10.2482	+	2.74600i	−0.343328	+	0.0919943i
$892$		0			0
$893$	0.475371	+	1.77411i	0.0159077	+	0.0593683i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−25.0505	−	3.71560i	−0.836413	−	0.124060i
$898$		0			0
$899$	0.481289	−	1.79620i	0.0160519	−	0.0599065i
$900$		0			0
$901$	30.9398	+	17.8631i	1.03075	+	0.595105i
$902$		0			0
$903$	23.1258	+	13.3517i	0.769578	+	0.444316i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−49.3926	−	13.2347i	−1.64006	−	0.439451i	−0.683251	−	0.730184i	$-0.739434\pi$
$907$	−49.3926	−	13.2347i	−1.64006	−	0.439451i	−0.956804	+	0.290732i	$0.906101\pi$
$908$		0			0
$909$	−42.5102			−1.40997
$910$		0			0
$911$	−45.3842			−1.50365			−0.751823	−	0.659365i	$-0.770825\pi$
$911$	−45.3842			−1.50365			−0.751823	+	0.659365i	$0.770825\pi$
$912$		0			0
$913$	−9.75039	−	2.61261i	−0.322691	−	0.0864647i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.4834	+	6.62993i	0.379214	+	0.218940i
$918$		0			0
$919$	−26.3431	−	15.2092i	−0.868977	−	0.501704i	−0.00196918	−	0.999998i	$-0.500627\pi$
$919$	−26.3431	−	15.2092i	−0.868977	−	0.501704i	−0.867008	+	0.498294i	$0.833960\pi$
$920$		0			0
$921$	18.7289	−	69.8973i	0.617139	−	2.30319i
$922$		0			0
$923$	−43.0898	+	31.9584i	−1.41832	+	1.05192i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−14.5651	−	54.3576i	−0.478380	−	1.78534i
$928$		0			0
$929$	23.9374	−	6.41401i	0.785361	−	0.210437i	0.156214	−	0.987723i	$-0.450071\pi$
$929$	23.9374	−	6.41401i	0.785361	−	0.210437i	0.629147	+	0.777286i	$0.283404\pi$
$930$		0			0
$931$	5.33689	+	5.33689i	0.174910	+	0.174910i
$932$		0			0
$933$	7.69371	−	28.7133i	0.251881	−	0.940031i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−25.3459	−	25.3459i	−0.828014	−	0.828014i	0.159228	−	0.987242i	$-0.449099\pi$
$937$	−25.3459	−	25.3459i	−0.828014	−	0.828014i	−0.987242	+	0.159228i	$0.949099\pi$
$938$		0			0
$939$	−32.6792	+	18.8674i	−1.06645	+	0.615713i
$940$		0			0
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	−0.0957715	−	0.995403i	$-0.530532\pi$
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	0.995403	+	0.0957715i	$0.0305318\pi$
$942$		0			0
$943$	−0.587809	+	1.01811i	−0.0191417	+	0.0331544i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	45.7982	−	26.4416i	1.48824	−	0.859237i	0.488332	−	0.872658i	$-0.337606\pi$
$947$	45.7982	−	26.4416i	1.48824	−	0.859237i	0.999910	+	0.0134210i	$0.00427218\pi$
$948$		0			0
$949$	−14.5661	−	36.8589i	−0.472835	−	1.19649i
$950$		0			0
$951$	5.76184	+	1.54388i	0.186840	+	0.0500637i
$952$		0			0
$953$	45.8852	−	12.2949i	1.48637	−	0.398271i	0.577860	−	0.816136i	$-0.303888\pi$
$953$	45.8852	−	12.2949i	1.48637	−	0.398271i	0.908509	+	0.417865i	$0.137221\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			28.5730i			0.923634i
$958$		0			0
$959$	−7.33001	−	12.6960i	−0.236699	−	0.409974i
$960$		0			0
$961$			30.9265i			0.997630i
$962$		0			0
$963$	18.4696	−	18.4696i	0.595173	−	0.595173i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	39.7754			1.27909			0.639546	−	0.768753i	$-0.279122\pi$
$967$	39.7754			1.27909			0.639546	+	0.768753i	$0.279122\pi$
$968$		0			0
$969$	4.17182	+	15.5694i	0.134018	+	0.500163i
$970$		0			0
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	−0.875457	−	0.483296i	$-0.839440\pi$
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	0.856275	+	0.516520i	$0.172773\pi$
$972$		0			0
$973$	−1.34586	−	2.33111i	−0.0431464	−	0.0747318i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.23433	+	14.2623i	0.263439	+	0.456291i	0.967154	−	0.254193i	$-0.0818097\pi$
$977$	8.23433	+	14.2623i	0.263439	+	0.456291i	−0.703714	+	0.710483i	$0.748476\pi$
$978$		0			0
$979$	−8.19223	+	14.1894i	−0.261825	+	0.453494i
$980$		0			0
$981$	6.12315	+	22.8519i	0.195497	+	0.729605i
$982$		0			0
$983$	1.80446			0.0575534			0.0287767	−	0.999586i	$-0.490839\pi$
$983$	1.80446			0.0575534			0.0287767	+	0.999586i	$0.490839\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.40229	+	2.40229i	−0.0764657	+	0.0764657i
$988$		0			0
$989$		−	32.5387i		−	1.03467i
$990$		0			0
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	0.876342	−	0.481690i	$-0.159977\pi$
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	−0.855327	+	0.518089i	$0.826643\pi$
$992$		0			0
$993$			90.7637i			2.88030i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−45.5416	+	12.2028i	−1.44232	+	0.386467i	−0.893344	−	0.449373i	$-0.851647\pi$
$997$	−45.5416	+	12.2028i	−1.44232	+	0.386467i	−0.548972	+	0.835841i	$0.684981\pi$
$998$		0			0
$999$	−15.6732	−	4.19962i	−0.495878	−	0.132870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bs.d.457.1		20
5.2	odd	4		260.2.bf.c.93.1	✓	20
5.3	odd	4		1300.2.bn.d.93.5		20
5.4	even	2		260.2.bk.c.197.5	yes	20
13.7	odd	12		1300.2.bn.d.657.5		20
65.7	even	12		260.2.bk.c.33.5	yes	20
65.33	even	12	inner	1300.2.bs.d.293.1		20
65.59	odd	12		260.2.bf.c.137.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.1	✓	20	5.2	odd	4
260.2.bf.c.137.1	yes	20	65.59	odd	12
260.2.bk.c.33.5	yes	20	65.7	even	12
260.2.bk.c.197.5	yes	20	5.4	even	2
1300.2.bn.d.93.5		20	5.3	odd	4
1300.2.bn.d.657.5		20	13.7	odd	12
1300.2.bs.d.293.1		20	65.33	even	12	inner
1300.2.bs.d.457.1		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.49316 - 0.668040i) q^{3} +(0.749297 + 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +O(q^{10})\)	\(q+(-2.49316 - 0.668040i) q^{3} +(0.749297 + 0.432607i) q^{7} +(3.17149 + 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(-1.32514 - 3.35321i) q^{13} +(1.33873 + 4.99621i) q^{17} +(-1.16619 + 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(-0.704305 + 2.62850i) q^{23} +(-1.20845 - 1.20845i) q^{27} +(5.94138 - 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(-2.08243 + 3.60687i) q^{33} +(8.22242 - 4.74722i) q^{37} +(1.06370 + 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(-11.5499 + 3.09480i) q^{43} -1.52128i q^{47} +(-3.12570 - 5.41387i) q^{49} -13.3507i q^{51} +(4.88398 - 4.88398i) q^{53} +3.11625 q^{57} +(-3.05172 - 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(1.58426 + 2.74402i) q^{63} +(-6.76168 - 11.7116i) q^{67} +(3.51189 - 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} +10.9921 q^{73} +(0.987192 - 0.987192i) q^{77} +3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} -6.25583i q^{83} +(-17.1044 + 4.58310i) q^{87} +(-9.80805 - 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(-0.605885 + 0.349808i) q^{93} +(0.728593 - 1.26196i) q^{97} +(4.17841 - 4.17841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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