LMFDB - Embedded newform 3150.2.m.b.1457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.b.2843.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.585786i q^{11} +(-4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-0.585786 + 0.585786i) q^{17} +2.82843i q^{19} +(-0.414214 - 0.414214i) q^{22} +(-4.82843 - 4.82843i) q^{23} +5.65685i q^{26} +(0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(-0.707107 + 0.707107i) q^{32} +0.828427i q^{34} +(-6.24264 - 6.24264i) q^{37} +(2.00000 + 2.00000i) q^{38} +3.17157i q^{41} +(-6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(-9.24264 + 9.24264i) q^{47} +1.00000i q^{49} +(4.00000 + 4.00000i) q^{52} +(2.58579 + 2.58579i) q^{53} -1.00000i q^{56} +(0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(1.24264 - 1.24264i) q^{62} +1.00000i q^{64} +(-8.41421 - 8.41421i) q^{67} +(0.585786 + 0.585786i) q^{68} -1.17157i q^{71} +(-7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(0.414214 - 0.414214i) q^{77} +5.65685i q^{79} +(2.24264 + 2.24264i) q^{82} +(0.828427 + 0.828427i) q^{83} +8.58579i q^{86} +(-0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(-4.82843 + 4.82843i) q^{92} +13.0711i q^{94} +(4.58579 + 4.58579i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q - 16 q^{13} + 4 q^{14} - 4 q^{16} - 8 q^{17} + 4 q^{22} - 8 q^{23} - 8 q^{29} + 24 q^{31} - 8 q^{37} + 8 q^{38} + 4 q^{43} - 8 q^{44} - 16 q^{46} - 20 q^{47} + 16 q^{52} + 16 q^{53} + 8 q^{58} - 12 q^{62} - 28 q^{67} + 8 q^{68} - 24 q^{74} - 4 q^{77} - 8 q^{82} - 8 q^{83} + 4 q^{88} + 24 q^{89} - 8 q^{92} + 24 q^{97}+O(q^{100}) $ 4 * q - 16 * q^13 + 4 * q^14 - 4 * q^16 - 8 * q^17 + 4 * q^22 - 8 * q^23 - 8 * q^29 + 24 * q^31 - 8 * q^37 + 8 * q^38 + 4 * q^43 - 8 * q^44 - 16 * q^46 - 20 * q^47 + 16 * q^52 + 16 * q^53 + 8 * q^58 - 12 * q^62 - 28 * q^67 + 8 * q^68 - 24 * q^74 - 4 * q^77 - 8 * q^82 - 8 * q^83 + 4 * q^88 + 24 * q^89 - 8 * q^92 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	0.585786i		−	0.176621i	−0.996093	−	0.0883106i	$-0.971853\pi$
$11$		−	0.585786i		−	0.176621i	0.996093	−	0.0883106i	$-0.0281468\pi$
$12$		0			0
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.585786	+	0.585786i	−0.142074	+	0.142074i	−0.774567	−	0.632492i	$-0.782032\pi$
$17$	−0.585786	+	0.585786i	−0.142074	+	0.142074i	0.632492	+	0.774567i	$0.282032\pi$
$18$		0			0
$19$			2.82843i			0.648886i	0.945905	+	0.324443i	$0.105177\pi$
$19$			2.82843i			0.648886i	−0.945905	+	0.324443i	$0.894823\pi$
$20$		0			0
$21$		0			0
$22$	−0.414214	−	0.414214i	−0.0883106	−	0.0883106i
$23$	−4.82843	−	4.82843i	−1.00680	−	1.00680i	−0.999977	−	0.00681991i	$-0.997829\pi$
$23$	−4.82843	−	4.82843i	−1.00680	−	1.00680i	−0.00681991	−	0.999977i	$-0.502171\pi$
$24$		0			0
$25$		0			0
$26$			5.65685i			1.10940i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	0.828427			0.153835			0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427			0.153835			0.0769175	+	0.997037i	$0.475492\pi$
$30$		0			0
$31$	1.75736			0.315631			0.157816	−	0.987469i	$-0.449555\pi$
$31$	1.75736			0.315631			0.157816	+	0.987469i	$0.449555\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			0.828427i			0.142074i
$35$		0			0
$36$		0			0
$37$	−6.24264	−	6.24264i	−1.02628	−	1.02628i	−0.999645	−	0.0266387i	$-0.991520\pi$
$37$	−6.24264	−	6.24264i	−1.02628	−	1.02628i	−0.0266387	−	0.999645i	$-0.508480\pi$
$38$	2.00000	+	2.00000i	0.324443	+	0.324443i
$39$		0			0
$40$		0			0
$41$			3.17157i			0.495316i	0.968847	+	0.247658i	$0.0796610\pi$
$41$			3.17157i			0.495316i	−0.968847	+	0.247658i	$0.920339\pi$
$42$		0			0
$43$	−6.07107	+	6.07107i	−0.925829	+	0.925829i	−0.997433	−	0.0716040i	$-0.977188\pi$
$43$	−6.07107	+	6.07107i	−0.925829	+	0.925829i	0.0716040	+	0.997433i	$0.477188\pi$
$44$	−0.585786			−0.0883106
$45$		0			0
$46$	−6.82843			−1.00680
$47$	−9.24264	+	9.24264i	−1.34818	+	1.34818i	−0.460537	+	0.887640i	$0.652343\pi$
$47$	−9.24264	+	9.24264i	−1.34818	+	1.34818i	−0.887640	+	0.460537i	$0.847657\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	2.58579	+	2.58579i	0.355185	+	0.355185i	0.862035	−	0.506849i	$-0.169190\pi$
$53$	2.58579	+	2.58579i	0.355185	+	0.355185i	−0.506849	+	0.862035i	$0.669190\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	0.585786	−	0.585786i	0.0769175	−	0.0769175i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	−9.89949			−1.26750			−0.633750	−	0.773538i	$-0.718485\pi$
$61$	−9.89949			−1.26750			−0.633750	+	0.773538i	$0.718485\pi$
$62$	1.24264	−	1.24264i	0.157816	−	0.157816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−8.41421	−	8.41421i	−1.02796	−	1.02796i	−0.999598	−	0.0283621i	$-0.990971\pi$
$67$	−8.41421	−	8.41421i	−1.02796	−	1.02796i	−0.0283621	−	0.999598i	$-0.509029\pi$
$68$	0.585786	+	0.585786i	0.0710370	+	0.0710370i
$69$		0			0
$70$		0			0
$71$		−	1.17157i		−	0.139040i	−0.997581	−	0.0695201i	$-0.977853\pi$
$71$		−	1.17157i		−	0.139040i	0.997581	−	0.0695201i	$-0.0221468\pi$
$72$		0			0
$73$	−7.07107	+	7.07107i	−0.827606	+	0.827606i	−0.987185	−	0.159579i	$-0.948986\pi$
$73$	−7.07107	+	7.07107i	−0.827606	+	0.827606i	0.159579	+	0.987185i	$0.448986\pi$
$74$	−8.82843			−1.02628
$75$		0			0
$76$	2.82843			0.324443
$77$	0.414214	−	0.414214i	0.0472040	−	0.0472040i
$78$		0			0
$79$			5.65685i			0.636446i	0.948016	+	0.318223i	$0.103086\pi$
$79$			5.65685i			0.636446i	−0.948016	+	0.318223i	$0.896914\pi$
$80$		0			0
$81$		0			0
$82$	2.24264	+	2.24264i	0.247658	+	0.247658i
$83$	0.828427	+	0.828427i	0.0909317	+	0.0909317i	0.751109	−	0.660178i	$-0.229519\pi$
$83$	0.828427	+	0.828427i	0.0909317	+	0.0909317i	−0.660178	+	0.751109i	$0.729519\pi$
$84$		0			0
$85$		0			0
$86$			8.58579i			0.925829i
$87$		0			0
$88$	−0.414214	+	0.414214i	−0.0441553	+	0.0441553i
$89$	3.17157			0.336186			0.168093	−	0.985771i	$-0.446239\pi$
$89$	3.17157			0.336186			0.168093	+	0.985771i	$0.446239\pi$
$90$		0			0
$91$	−5.65685			−0.592999
$92$	−4.82843	+	4.82843i	−0.503398	+	0.503398i
$93$		0			0
$94$			13.0711i			1.34818i
$95$		0			0
$96$		0			0
$97$	4.58579	+	4.58579i	0.465616	+	0.465616i	0.900491	−	0.434875i	$-0.143207\pi$
$97$	4.58579	+	4.58579i	0.465616	+	0.465616i	−0.434875	+	0.900491i	$0.643207\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	17.6569i		−	1.75692i	−0.477813	−	0.878461i	$-0.658571\pi$
$101$		−	17.6569i		−	1.75692i	0.477813	−	0.878461i	$-0.341429\pi$
$102$		0			0
$103$	7.41421	−	7.41421i	0.730544	−	0.730544i	−0.240183	−	0.970728i	$-0.577208\pi$
$103$	7.41421	−	7.41421i	0.730544	−	0.730544i	0.970728	+	0.240183i	$0.0772076\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	3.65685			0.355185
$107$	5.17157	−	5.17157i	0.499955	−	0.499955i	−0.411469	−	0.911424i	$-0.634984\pi$
$107$	5.17157	−	5.17157i	0.499955	−	0.499955i	0.911424	+	0.411469i	$0.134984\pi$
$108$		0			0
$109$			9.31371i			0.892091i	0.895010	+	0.446046i	$0.147168\pi$
$109$			9.31371i			0.892091i	−0.895010	+	0.446046i	$0.852832\pi$
$110$		0			0
$111$		0			0
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	11.3137	+	11.3137i	1.06430	+	1.06430i	0.997785	+	0.0665190i	$0.0211893\pi$
$113$	11.3137	+	11.3137i	1.06430	+	1.06430i	0.0665190	+	0.997785i	$0.478811\pi$
$114$		0			0
$115$		0			0
$116$		−	0.828427i		−	0.0769175i
$117$		0			0
$118$	2.00000	−	2.00000i	0.184115	−	0.184115i
$119$	−0.828427			−0.0759418
$120$		0			0
$121$	10.6569			0.968805
$122$	−7.00000	+	7.00000i	−0.633750	+	0.633750i
$123$		0			0
$124$		−	1.75736i		−	0.157816i
$125$		0			0
$126$		0			0
$127$	−7.65685	−	7.65685i	−0.679436	−	0.679436i	0.280437	−	0.959873i	$-0.409521\pi$
$127$	−7.65685	−	7.65685i	−0.679436	−	0.679436i	−0.959873	+	0.280437i	$0.909521\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	16.4853i		−	1.44033i	−0.693805	−	0.720163i	$-0.744067\pi$
$131$		−	16.4853i		−	1.44033i	0.693805	−	0.720163i	$-0.255933\pi$
$132$		0			0
$133$	−2.00000	+	2.00000i	−0.173422	+	0.173422i
$134$	−11.8995			−1.02796
$135$		0			0
$136$	0.828427			0.0710370
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.0255558	+	0.999673i	$0.508136\pi$
$137$	−12.0000	+	12.0000i	−1.02523	+	1.02523i	−0.999673	+	0.0255558i	$0.991864\pi$
$138$		0			0
$139$			17.6569i			1.49763i	0.662776	+	0.748817i	$0.269378\pi$
$139$			17.6569i			1.49763i	−0.662776	+	0.748817i	$0.730622\pi$
$140$		0			0
$141$		0			0
$142$	−0.828427	−	0.828427i	−0.0695201	−	0.0695201i
$143$	2.34315	+	2.34315i	0.195944	+	0.195944i
$144$		0			0
$145$		0			0
$146$			10.0000i			0.827606i
$147$		0			0
$148$	−6.24264	+	6.24264i	−0.513142	+	0.513142i
$149$	−8.14214			−0.667030			−0.333515	−	0.942745i	$-0.608235\pi$
$149$	−8.14214			−0.667030			−0.333515	+	0.942745i	$0.608235\pi$
$150$		0			0
$151$	−18.8284			−1.53224			−0.766118	−	0.642700i	$-0.777814\pi$
$151$	−18.8284			−1.53224			−0.766118	+	0.642700i	$0.777814\pi$
$152$	2.00000	−	2.00000i	0.162221	−	0.162221i
$153$		0			0
$154$		−	0.585786i		−	0.0472040i
$155$		0			0
$156$		0			0
$157$	9.65685	+	9.65685i	0.770701	+	0.770701i	0.978229	−	0.207528i	$-0.0665419\pi$
$157$	9.65685	+	9.65685i	0.770701	+	0.770701i	−0.207528	+	0.978229i	$0.566542\pi$
$158$	4.00000	+	4.00000i	0.318223	+	0.318223i
$159$		0			0
$160$		0			0
$161$		−	6.82843i		−	0.538155i
$162$		0			0
$163$	−11.7279	+	11.7279i	−0.918602	+	0.918602i	−0.996928	−	0.0783260i	$-0.975042\pi$
$163$	−11.7279	+	11.7279i	−0.918602	+	0.918602i	0.0783260	+	0.996928i	$0.475042\pi$
$164$	3.17157			0.247658
$165$		0			0
$166$	1.17157			0.0909317
$167$	7.58579	−	7.58579i	0.587006	−	0.587006i	−0.349814	−	0.936819i	$-0.613755\pi$
$167$	7.58579	−	7.58579i	0.587006	−	0.587006i	0.936819	+	0.349814i	$0.113755\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$		0			0
$171$		0			0
$172$	6.07107	+	6.07107i	0.462915	+	0.462915i
$173$	11.4853	+	11.4853i	0.873210	+	0.873210i	0.992821	−	0.119611i	$-0.0381648\pi$
$173$	11.4853	+	11.4853i	0.873210	+	0.873210i	−0.119611	+	0.992821i	$0.538165\pi$
$174$		0			0
$175$		0			0
$176$			0.585786i			0.0441553i
$177$		0			0
$178$	2.24264	−	2.24264i	0.168093	−	0.168093i
$179$	16.5858			1.23968			0.619840	−	0.784728i	$-0.287198\pi$
$179$	16.5858			1.23968			0.619840	+	0.784728i	$0.287198\pi$
$180$		0			0
$181$	−19.0711			−1.41754			−0.708771	−	0.705439i	$-0.750750\pi$
$181$	−19.0711			−1.41754			−0.708771	+	0.705439i	$0.750750\pi$
$182$	−4.00000	+	4.00000i	−0.296500	+	0.296500i
$183$		0			0
$184$			6.82843i			0.503398i
$185$		0			0
$186$		0			0
$187$	0.343146	+	0.343146i	0.0250933	+	0.0250933i
$188$	9.24264	+	9.24264i	0.674089	+	0.674089i
$189$		0			0
$190$		0			0
$191$			14.3431i			1.03783i	0.854825	+	0.518917i	$0.173665\pi$
$191$			14.3431i			1.03783i	−0.854825	+	0.518917i	$0.826335\pi$
$192$		0			0
$193$	−13.4853	+	13.4853i	−0.970692	+	0.970692i	−0.999583	−	0.0288908i	$-0.990802\pi$
$193$	−13.4853	+	13.4853i	−0.970692	+	0.970692i	0.0288908	+	0.999583i	$0.490802\pi$
$194$	6.48528			0.465616
$195$		0			0
$196$	1.00000			0.0714286
$197$	10.2426	−	10.2426i	0.729758	−	0.729758i	−0.240813	−	0.970571i	$-0.577414\pi$
$197$	10.2426	−	10.2426i	0.729758	−	0.729758i	0.970571	+	0.240813i	$0.0774142\pi$
$198$		0			0
$199$			4.10051i			0.290677i	0.989382	+	0.145339i	$0.0464271\pi$
$199$			4.10051i			0.290677i	−0.989382	+	0.145339i	$0.953573\pi$
$200$		0			0
$201$		0			0
$202$	−12.4853	−	12.4853i	−0.878461	−	0.878461i
$203$	0.585786	+	0.585786i	0.0411141	+	0.0411141i
$204$		0			0
$205$		0			0
$206$		−	10.4853i		−	0.730544i
$207$		0			0
$208$	4.00000	−	4.00000i	0.277350	−	0.277350i
$209$	1.65685			0.114607
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.58579	−	2.58579i	0.177593	−	0.177593i
$213$		0			0
$214$		−	7.31371i		−	0.499955i
$215$		0			0
$216$		0			0
$217$	1.24264	+	1.24264i	0.0843559	+	0.0843559i
$218$	6.58579	+	6.58579i	0.446046	+	0.446046i
$219$		0			0
$220$		0			0
$221$		−	4.68629i		−	0.315234i
$222$		0			0
$223$	−7.31371	+	7.31371i	−0.489762	+	0.489762i	−0.908231	−	0.418469i	$-0.862567\pi$
$223$	−7.31371	+	7.31371i	−0.489762	+	0.489762i	0.418469	+	0.908231i	$0.362567\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	16.0000			1.06430
$227$	−1.17157	+	1.17157i	−0.0777600	+	0.0777600i	−0.744917	−	0.667157i	$-0.767511\pi$
$227$	−1.17157	+	1.17157i	−0.0777600	+	0.0777600i	0.667157	+	0.744917i	$0.267511\pi$
$228$		0			0
$229$		−	8.24264i		−	0.544689i	−0.962200	−	0.272345i	$-0.912201\pi$
$229$		−	8.24264i		−	0.544689i	0.962200	−	0.272345i	$-0.0877990\pi$
$230$		0			0
$231$		0			0
$232$	−0.585786	−	0.585786i	−0.0384588	−	0.0384588i
$233$	−14.8284	−	14.8284i	−0.971443	−	0.971443i	0.0281608	−	0.999603i	$-0.491035\pi$
$233$	−14.8284	−	14.8284i	−0.971443	−	0.971443i	−0.999603	+	0.0281608i	$0.991035\pi$
$234$		0			0
$235$		0			0
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$	−0.585786	+	0.585786i	−0.0379709	+	0.0379709i
$239$	13.6569			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$239$	13.6569			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$240$		0			0
$241$	−4.14214			−0.266818			−0.133409	−	0.991061i	$-0.542592\pi$
$241$	−4.14214			−0.266818			−0.133409	+	0.991061i	$0.542592\pi$
$242$	7.53553	−	7.53553i	0.484402	−	0.484402i
$243$		0			0
$244$			9.89949i			0.633750i
$245$		0			0
$246$		0			0
$247$	−11.3137	−	11.3137i	−0.719874	−	0.719874i
$248$	−1.24264	−	1.24264i	−0.0789078	−	0.0789078i
$249$		0			0
$250$		0			0
$251$			26.6274i			1.68071i	0.542038	+	0.840354i	$0.317653\pi$
$251$			26.6274i			1.68071i	−0.542038	+	0.840354i	$0.682347\pi$
$252$		0			0
$253$	−2.82843	+	2.82843i	−0.177822	+	0.177822i
$254$	−10.8284			−0.679436
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.58579	+	8.58579i	−0.535567	+	0.535567i	−0.922224	−	0.386657i	$-0.873630\pi$
$257$	−8.58579	+	8.58579i	−0.535567	+	0.535567i	0.386657	+	0.922224i	$0.373630\pi$
$258$		0			0
$259$		−	8.82843i		−	0.548572i
$260$		0			0
$261$		0			0
$262$	−11.6569	−	11.6569i	−0.720163	−	0.720163i
$263$	−7.65685	−	7.65685i	−0.472142	−	0.472142i	0.430465	−	0.902607i	$-0.358349\pi$
$263$	−7.65685	−	7.65685i	−0.472142	−	0.472142i	−0.902607	+	0.430465i	$0.858349\pi$
$264$		0			0
$265$		0			0
$266$			2.82843i			0.173422i
$267$		0			0
$268$	−8.41421	+	8.41421i	−0.513980	+	0.513980i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$		0			0
$271$	4.10051			0.249088			0.124544	−	0.992214i	$-0.460253\pi$
$271$	4.10051			0.249088			0.124544	+	0.992214i	$0.460253\pi$
$272$	0.585786	−	0.585786i	0.0355185	−	0.0355185i
$273$		0			0
$274$			16.9706i			1.02523i
$275$		0			0
$276$		0			0
$277$	2.10051	+	2.10051i	0.126207	+	0.126207i	0.767389	−	0.641182i	$-0.221556\pi$
$277$	2.10051	+	2.10051i	0.126207	+	0.126207i	−0.641182	+	0.767389i	$0.721556\pi$
$278$	12.4853	+	12.4853i	0.748817	+	0.748817i
$279$		0			0
$280$		0			0
$281$			19.0711i			1.13768i	0.822447	+	0.568842i	$0.192609\pi$
$281$			19.0711i			1.13768i	−0.822447	+	0.568842i	$0.807391\pi$
$282$		0			0
$283$	21.3137	−	21.3137i	1.26697	−	1.26697i	0.319322	−	0.947646i	$-0.396545\pi$
$283$	21.3137	−	21.3137i	1.26697	−	1.26697i	0.947646	−	0.319322i	$-0.103455\pi$
$284$	−1.17157			−0.0695201
$285$		0			0
$286$	3.31371			0.195944
$287$	−2.24264	+	2.24264i	−0.132379	+	0.132379i
$288$		0			0
$289$			16.3137i			0.959630i
$290$		0			0
$291$		0			0
$292$	7.07107	+	7.07107i	0.413803	+	0.413803i
$293$	−8.65685	−	8.65685i	−0.505739	−	0.505739i	0.407477	−	0.913216i	$-0.366409\pi$
$293$	−8.65685	−	8.65685i	−0.505739	−	0.505739i	−0.913216	+	0.407477i	$0.866409\pi$
$294$		0			0
$295$		0			0
$296$			8.82843i			0.513142i
$297$		0			0
$298$	−5.75736	+	5.75736i	−0.333515	+	0.333515i
$299$	38.6274			2.23388
$300$		0			0
$301$	−8.58579			−0.494877
$302$	−13.3137	+	13.3137i	−0.766118	+	0.766118i
$303$		0			0
$304$		−	2.82843i		−	0.162221i
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−0.414214	−	0.414214i	−0.0236020	−	0.0236020i
$309$		0			0
$310$		0			0
$311$			4.82843i			0.273795i	0.990585	+	0.136897i	$0.0437131\pi$
$311$			4.82843i			0.273795i	−0.990585	+	0.136897i	$0.956287\pi$
$312$		0			0
$313$	−2.24264	+	2.24264i	−0.126762	+	0.126762i	−0.767641	−	0.640880i	$-0.778570\pi$
$313$	−2.24264	+	2.24264i	−0.126762	+	0.126762i	0.640880	+	0.767641i	$0.278570\pi$
$314$	13.6569			0.770701
$315$		0			0
$316$	5.65685			0.318223
$317$	24.7279	−	24.7279i	1.38886	−	1.38886i	0.561132	−	0.827726i	$-0.310366\pi$
$317$	24.7279	−	24.7279i	1.38886	−	1.38886i	0.827726	−	0.561132i	$-0.189634\pi$
$318$		0			0
$319$		−	0.485281i		−	0.0271705i
$320$		0			0
$321$		0			0
$322$	−4.82843	−	4.82843i	−0.269078	−	0.269078i
$323$	−1.65685	−	1.65685i	−0.0921898	−	0.0921898i
$324$		0			0
$325$		0			0
$326$			16.5858i			0.918602i
$327$		0			0
$328$	2.24264	−	2.24264i	0.123829	−	0.123829i
$329$	−13.0711			−0.720631
$330$		0			0
$331$	18.6274			1.02386			0.511928	−	0.859029i	$-0.328932\pi$
$331$	18.6274			1.02386			0.511928	+	0.859029i	$0.328932\pi$
$332$	0.828427	−	0.828427i	0.0454658	−	0.0454658i
$333$		0			0
$334$		−	10.7279i		−	0.587006i
$335$		0			0
$336$		0			0
$337$	−10.1716	−	10.1716i	−0.554081	−	0.554081i	0.373535	−	0.927616i	$-0.378146\pi$
$337$	−10.1716	−	10.1716i	−0.554081	−	0.554081i	−0.927616	+	0.373535i	$0.878146\pi$
$338$	−13.4350	−	13.4350i	−0.730769	−	0.730769i
$339$		0			0
$340$		0			0
$341$		−	1.02944i		−	0.0557472i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	8.58579			0.462915
$345$		0			0
$346$	16.2426			0.873210
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	−0.441666	−	0.897180i	$-0.645612\pi$
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	0.897180	+	0.441666i	$0.145612\pi$
$348$		0			0
$349$		−	32.7279i		−	1.75189i	−0.482415	−	0.875943i	$-0.660240\pi$
$349$		−	32.7279i		−	1.75189i	0.482415	−	0.875943i	$-0.339760\pi$
$350$		0			0
$351$		0			0
$352$	0.414214	+	0.414214i	0.0220777	+	0.0220777i
$353$	−18.3848	−	18.3848i	−0.978523	−	0.978523i	0.0212513	−	0.999774i	$-0.493235\pi$
$353$	−18.3848	−	18.3848i	−0.978523	−	0.978523i	−0.999774	+	0.0212513i	$0.993235\pi$
$354$		0			0
$355$		0			0
$356$		−	3.17157i		−	0.168093i
$357$		0			0
$358$	11.7279	−	11.7279i	0.619840	−	0.619840i
$359$	23.7990			1.25606			0.628031	−	0.778188i	$-0.283861\pi$
$359$	23.7990			1.25606			0.628031	+	0.778188i	$0.283861\pi$
$360$		0			0
$361$	11.0000			0.578947
$362$	−13.4853	+	13.4853i	−0.708771	+	0.708771i
$363$		0			0
$364$			5.65685i			0.296500i
$365$		0			0
$366$		0			0
$367$	10.2426	+	10.2426i	0.534661	+	0.534661i	0.921956	−	0.387295i	$-0.126590\pi$
$367$	10.2426	+	10.2426i	0.534661	+	0.534661i	−0.387295	+	0.921956i	$0.626590\pi$
$368$	4.82843	+	4.82843i	0.251699	+	0.251699i
$369$		0			0
$370$		0			0
$371$			3.65685i			0.189854i
$372$		0			0
$373$	11.0711	−	11.0711i	0.573238	−	0.573238i	−0.359794	−	0.933032i	$-0.617153\pi$
$373$	11.0711	−	11.0711i	0.573238	−	0.573238i	0.933032	+	0.359794i	$0.117153\pi$
$374$	0.485281			0.0250933
$375$		0			0
$376$	13.0711			0.674089
$377$	−3.31371	+	3.31371i	−0.170665	+	0.170665i
$378$		0			0
$379$		−	25.7990i		−	1.32521i	−0.748971	−	0.662603i	$-0.769452\pi$
$379$		−	25.7990i		−	1.32521i	0.748971	−	0.662603i	$-0.230548\pi$
$380$		0			0
$381$		0			0
$382$	10.1421	+	10.1421i	0.518917	+	0.518917i
$383$	−4.41421	−	4.41421i	−0.225556	−	0.225556i	0.585277	−	0.810833i	$-0.300986\pi$
$383$	−4.41421	−	4.41421i	−0.225556	−	0.225556i	−0.810833	+	0.585277i	$0.800986\pi$
$384$		0			0
$385$		0			0
$386$			19.0711i			0.970692i
$387$		0			0
$388$	4.58579	−	4.58579i	0.232808	−	0.232808i
$389$	−9.79899			−0.496829			−0.248414	−	0.968654i	$-0.579909\pi$
$389$	−9.79899			−0.496829			−0.248414	+	0.968654i	$0.579909\pi$
$390$		0			0
$391$	5.65685			0.286079
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	14.4853i		−	0.729758i
$395$		0			0
$396$		0			0
$397$	0.928932	+	0.928932i	0.0466218	+	0.0466218i	0.730033	−	0.683412i	$-0.239505\pi$
$397$	0.928932	+	0.928932i	0.0466218	+	0.0466218i	−0.683412	+	0.730033i	$0.739505\pi$
$398$	2.89949	+	2.89949i	0.145339	+	0.145339i
$399$		0			0
$400$		0			0
$401$		−	26.8701i		−	1.34183i	−0.741536	−	0.670913i	$-0.765902\pi$
$401$		−	26.8701i		−	1.34183i	0.741536	−	0.670913i	$-0.234098\pi$
$402$		0			0
$403$	−7.02944	+	7.02944i	−0.350161	+	0.350161i
$404$	−17.6569			−0.878461
$405$		0			0
$406$	0.828427			0.0411141
$407$	−3.65685	+	3.65685i	−0.181264	+	0.181264i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$		0			0
$411$		0			0
$412$	−7.41421	−	7.41421i	−0.365272	−	0.365272i
$413$	2.00000	+	2.00000i	0.0984136	+	0.0984136i
$414$		0			0
$415$		0			0
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$	1.17157	−	1.17157i	0.0573035	−	0.0573035i
$419$	−18.6274			−0.910009			−0.455004	−	0.890489i	$-0.650362\pi$
$419$	−18.6274			−0.910009			−0.455004	+	0.890489i	$0.650362\pi$
$420$		0			0
$421$	−40.6274			−1.98006			−0.990030	−	0.140860i	$-0.955013\pi$
$421$	−40.6274			−1.98006			−0.990030	+	0.140860i	$0.955013\pi$
$422$	−2.82843	+	2.82843i	−0.137686	+	0.137686i
$423$		0			0
$424$		−	3.65685i		−	0.177593i
$425$		0			0
$426$		0			0
$427$	−7.00000	−	7.00000i	−0.338754	−	0.338754i
$428$	−5.17157	−	5.17157i	−0.249977	−	0.249977i
$429$		0			0
$430$		0			0
$431$		−	26.1421i		−	1.25922i	−0.776910	−	0.629611i	$-0.783214\pi$
$431$		−	26.1421i		−	1.25922i	0.776910	−	0.629611i	$-0.216786\pi$
$432$		0			0
$433$	−18.2426	+	18.2426i	−0.876685	+	0.876685i	−0.993190	−	0.116505i	$-0.962831\pi$
$433$	−18.2426	+	18.2426i	−0.876685	+	0.876685i	0.116505	+	0.993190i	$0.462831\pi$
$434$	1.75736			0.0843559
$435$		0			0
$436$	9.31371			0.446046
$437$	13.6569	−	13.6569i	0.653296	−	0.653296i
$438$		0			0
$439$			3.89949i			0.186113i	0.995661	+	0.0930564i	$0.0296637\pi$
$439$			3.89949i			0.186113i	−0.995661	+	0.0930564i	$0.970336\pi$
$440$		0			0
$441$		0			0
$442$	−3.31371	−	3.31371i	−0.157617	−	0.157617i
$443$	3.51472	+	3.51472i	0.166989	+	0.166989i	0.785655	−	0.618665i	$-0.212326\pi$
$443$	3.51472	+	3.51472i	0.166989	+	0.166989i	−0.618665	+	0.785655i	$0.712326\pi$
$444$		0			0
$445$		0			0
$446$			10.3431i			0.489762i
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	−16.7279			−0.789439			−0.394720	−	0.918802i	$-0.629158\pi$
$449$	−16.7279			−0.789439			−0.394720	+	0.918802i	$0.629158\pi$
$450$		0			0
$451$	1.85786			0.0874834
$452$	11.3137	−	11.3137i	0.532152	−	0.532152i
$453$		0			0
$454$			1.65685i			0.0777600i
$455$		0			0
$456$		0			0
$457$	−2.17157	−	2.17157i	−0.101582	−	0.101582i	0.654489	−	0.756071i	$-0.272884\pi$
$457$	−2.17157	−	2.17157i	−0.101582	−	0.101582i	−0.756071	+	0.654489i	$0.772884\pi$
$458$	−5.82843	−	5.82843i	−0.272345	−	0.272345i
$459$		0			0
$460$		0			0
$461$			5.31371i			0.247484i	0.992314	+	0.123742i	$0.0394895\pi$
$461$			5.31371i			0.247484i	−0.992314	+	0.123742i	$0.960510\pi$
$462$		0			0
$463$	19.7990	−	19.7990i	0.920137	−	0.920137i	−0.0769016	−	0.997039i	$-0.524503\pi$
$463$	19.7990	−	19.7990i	0.920137	−	0.920137i	0.997039	+	0.0769016i	$0.0245027\pi$
$464$	−0.828427			−0.0384588
$465$		0			0
$466$	−20.9706			−0.971443
$467$	14.0000	−	14.0000i	0.647843	−	0.647843i	−0.304629	−	0.952471i	$-0.598532\pi$
$467$	14.0000	−	14.0000i	0.647843	−	0.647843i	0.952471	+	0.304629i	$0.0985323\pi$
$468$		0			0
$469$		−	11.8995i		−	0.549468i
$470$		0			0
$471$		0			0
$472$	−2.00000	−	2.00000i	−0.0920575	−	0.0920575i
$473$	3.55635	+	3.55635i	0.163521	+	0.163521i
$474$		0			0
$475$		0			0
$476$			0.828427i			0.0379709i
$477$		0			0
$478$	9.65685	−	9.65685i	0.441694	−	0.441694i
$479$	19.1716			0.875972			0.437986	−	0.898982i	$-0.355692\pi$
$479$	19.1716			0.875972			0.437986	+	0.898982i	$0.355692\pi$
$480$		0			0
$481$	49.9411			2.27712
$482$	−2.92893	+	2.92893i	−0.133409	+	0.133409i
$483$		0			0
$484$		−	10.6569i		−	0.484402i
$485$		0			0
$486$		0			0
$487$	−18.9706	−	18.9706i	−0.859638	−	0.859638i	0.131657	−	0.991295i	$-0.457970\pi$
$487$	−18.9706	−	18.9706i	−0.859638	−	0.859638i	−0.991295	+	0.131657i	$0.957970\pi$
$488$	7.00000	+	7.00000i	0.316875	+	0.316875i
$489$		0			0
$490$		0			0
$491$			26.7279i			1.20621i	0.797660	+	0.603107i	$0.206071\pi$
$491$			26.7279i			1.20621i	−0.797660	+	0.603107i	$0.793929\pi$
$492$		0			0
$493$	−0.485281	+	0.485281i	−0.0218560	+	0.0218560i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	−1.75736			−0.0789078
$497$	0.828427	−	0.828427i	0.0371600	−	0.0371600i
$498$		0			0
$499$		−	23.4558i		−	1.05003i	−0.851094	−	0.525014i	$-0.824060\pi$
$499$		−	23.4558i		−	1.05003i	0.851094	−	0.525014i	$-0.175940\pi$
$500$		0			0
$501$		0			0
$502$	18.8284	+	18.8284i	0.840354	+	0.840354i
$503$	16.5563	+	16.5563i	0.738211	+	0.738211i	0.972232	−	0.234021i	$-0.0751883\pi$
$503$	16.5563	+	16.5563i	0.738211	+	0.738211i	−0.234021	+	0.972232i	$0.575188\pi$
$504$		0			0
$505$		0			0
$506$			4.00000i			0.177822i
$507$		0			0
$508$	−7.65685	+	7.65685i	−0.339718	+	0.339718i
$509$	−18.3431			−0.813046			−0.406523	−	0.913641i	$-0.633259\pi$
$509$	−18.3431			−0.813046			−0.406523	+	0.913641i	$0.633259\pi$
$510$		0			0
$511$	−10.0000			−0.442374
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			12.1421i			0.535567i
$515$		0			0
$516$		0			0
$517$	5.41421	+	5.41421i	0.238117	+	0.238117i
$518$	−6.24264	−	6.24264i	−0.274286	−	0.274286i
$519$		0			0
$520$		0			0
$521$		−	42.7696i		−	1.87377i	−0.349640	−	0.936884i	$-0.613696\pi$
$521$		−	42.7696i		−	1.87377i	0.349640	−	0.936884i	$-0.386304\pi$
$522$		0			0
$523$	25.3137	−	25.3137i	1.10689	−	1.10689i	0.113334	−	0.993557i	$-0.463847\pi$
$523$	25.3137	−	25.3137i	1.10689	−	1.10689i	0.993557	−	0.113334i	$-0.0361531\pi$
$524$	−16.4853			−0.720163
$525$		0			0
$526$	−10.8284			−0.472142
$527$	−1.02944	+	1.02944i	−0.0448430	+	0.0448430i
$528$		0			0
$529$			23.6274i			1.02728i
$530$		0			0
$531$		0			0
$532$	2.00000	+	2.00000i	0.0867110	+	0.0867110i
$533$	−12.6863	−	12.6863i	−0.549504	−	0.549504i
$534$		0			0
$535$		0			0
$536$			11.8995i			0.513980i
$537$		0			0
$538$	4.00000	−	4.00000i	0.172452	−	0.172452i
$539$	0.585786			0.0252316
$540$		0			0
$541$	−29.1127			−1.25165			−0.625826	−	0.779962i	$-0.715238\pi$
$541$	−29.1127			−1.25165			−0.625826	+	0.779962i	$0.715238\pi$
$542$	2.89949	−	2.89949i	0.124544	−	0.124544i
$543$		0			0
$544$		−	0.828427i		−	0.0355185i
$545$		0			0
$546$		0			0
$547$	12.5563	+	12.5563i	0.536871	+	0.536871i	0.922608	−	0.385738i	$-0.126053\pi$
$547$	12.5563	+	12.5563i	0.536871	+	0.536871i	−0.385738	+	0.922608i	$0.626053\pi$
$548$	12.0000	+	12.0000i	0.512615	+	0.512615i
$549$		0			0
$550$		0			0
$551$			2.34315i			0.0998214i
$552$		0			0
$553$	−4.00000	+	4.00000i	−0.170097	+	0.170097i
$554$	2.97056			0.126207
$555$		0			0
$556$	17.6569			0.748817
$557$	−7.55635	+	7.55635i	−0.320173	+	0.320173i	−0.848833	−	0.528661i	$-0.822694\pi$
$557$	−7.55635	+	7.55635i	−0.320173	+	0.320173i	0.528661	+	0.848833i	$0.322694\pi$
$558$		0			0
$559$		−	48.5685i		−	2.05423i
$560$		0			0
$561$		0			0
$562$	13.4853	+	13.4853i	0.568842	+	0.568842i
$563$	−6.68629	−	6.68629i	−0.281794	−	0.281794i	0.552030	−	0.833824i	$-0.313853\pi$
$563$	−6.68629	−	6.68629i	−0.281794	−	0.281794i	−0.833824	+	0.552030i	$0.813853\pi$
$564$		0			0
$565$		0			0
$566$		−	30.1421i		−	1.26697i
$567$		0			0
$568$	−0.828427	+	0.828427i	−0.0347600	+	0.0347600i
$569$	−14.1005			−0.591124			−0.295562	−	0.955324i	$-0.595507\pi$
$569$	−14.1005			−0.591124			−0.295562	+	0.955324i	$0.595507\pi$
$570$		0			0
$571$	−11.0294			−0.461568			−0.230784	−	0.973005i	$-0.574129\pi$
$571$	−11.0294			−0.461568			−0.230784	+	0.973005i	$0.574129\pi$
$572$	2.34315	−	2.34315i	0.0979718	−	0.0979718i
$573$		0			0
$574$			3.17157i			0.132379i
$575$		0			0
$576$		0			0
$577$	10.7279	+	10.7279i	0.446609	+	0.446609i	0.894226	−	0.447616i	$-0.147727\pi$
$577$	10.7279	+	10.7279i	0.446609	+	0.446609i	−0.447616	+	0.894226i	$0.647727\pi$
$578$	11.5355	+	11.5355i	0.479815	+	0.479815i
$579$		0			0
$580$		0			0
$581$			1.17157i			0.0486050i
$582$		0			0
$583$	1.51472	−	1.51472i	0.0627332	−	0.0627332i
$584$	10.0000			0.413803
$585$		0			0
$586$	−12.2426			−0.505739
$587$	−17.7990	+	17.7990i	−0.734643	+	0.734643i	−0.971536	−	0.236893i	$-0.923871\pi$
$587$	−17.7990	+	17.7990i	−0.734643	+	0.734643i	0.236893	+	0.971536i	$0.423871\pi$
$588$		0			0
$589$			4.97056i			0.204808i
$590$		0			0
$591$		0			0
$592$	6.24264	+	6.24264i	0.256571	+	0.256571i
$593$	16.3848	+	16.3848i	0.672842	+	0.672842i	0.958370	−	0.285528i	$-0.0921690\pi$
$593$	16.3848	+	16.3848i	0.672842	+	0.672842i	−0.285528	+	0.958370i	$0.592169\pi$
$594$		0			0
$595$		0			0
$596$			8.14214i			0.333515i
$597$		0			0
$598$	27.3137	−	27.3137i	1.11694	−	1.11694i
$599$	−15.3137			−0.625701			−0.312851	−	0.949802i	$-0.601284\pi$
$599$	−15.3137			−0.625701			−0.312851	+	0.949802i	$0.601284\pi$
$600$		0			0
$601$	−4.14214			−0.168961			−0.0844806	−	0.996425i	$-0.526923\pi$
$601$	−4.14214			−0.168961			−0.0844806	+	0.996425i	$0.526923\pi$
$602$	−6.07107	+	6.07107i	−0.247438	+	0.247438i
$603$		0			0
$604$			18.8284i			0.766118i
$605$		0			0
$606$		0			0
$607$	7.31371	+	7.31371i	0.296854	+	0.296854i	0.839780	−	0.542926i	$-0.182684\pi$
$607$	7.31371	+	7.31371i	0.296854	+	0.296854i	−0.542926	+	0.839780i	$0.682684\pi$
$608$	−2.00000	−	2.00000i	−0.0811107	−	0.0811107i
$609$		0			0
$610$		0			0
$611$		−	73.9411i		−	2.99134i
$612$		0			0
$613$	9.07107	−	9.07107i	0.366377	−	0.366377i	−0.499777	−	0.866154i	$-0.666585\pi$
$613$	9.07107	−	9.07107i	0.366377	−	0.366377i	0.866154	+	0.499777i	$0.166585\pi$
$614$		0			0
$615$		0			0
$616$	−0.585786			−0.0236020
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	−0.999500	−	0.0316203i	$-0.989933\pi$
$617$	−24.0416	+	24.0416i	−0.967880	+	0.967880i	0.0316203	+	0.999500i	$0.489933\pi$
$618$		0			0
$619$			17.8579i			0.717768i	0.933382	+	0.358884i	$0.116843\pi$
$619$			17.8579i			0.717768i	−0.933382	+	0.358884i	$0.883157\pi$
$620$		0			0
$621$		0			0
$622$	3.41421	+	3.41421i	0.136897	+	0.136897i
$623$	2.24264	+	2.24264i	0.0898495	+	0.0898495i
$624$		0			0
$625$		0			0
$626$			3.17157i			0.126762i
$627$		0			0
$628$	9.65685	−	9.65685i	0.385350	−	0.385350i
$629$	7.31371			0.291617
$630$		0			0
$631$	−0.201010			−0.00800209			−0.00400104	−	0.999992i	$-0.501274\pi$
$631$	−0.201010			−0.00800209			−0.00400104	+	0.999992i	$0.501274\pi$
$632$	4.00000	−	4.00000i	0.159111	−	0.159111i
$633$		0			0
$634$		−	34.9706i		−	1.38886i
$635$		0			0
$636$		0			0
$637$	−4.00000	−	4.00000i	−0.158486	−	0.158486i
$638$	−0.343146	−	0.343146i	−0.0135853	−	0.0135853i
$639$		0			0
$640$		0			0
$641$			21.2132i			0.837871i	0.908016	+	0.418936i	$0.137597\pi$
$641$			21.2132i			0.837871i	−0.908016	+	0.418936i	$0.862403\pi$
$642$		0			0
$643$	10.9706	−	10.9706i	0.432637	−	0.432637i	−0.456888	−	0.889524i	$-0.651036\pi$
$643$	10.9706	−	10.9706i	0.432637	−	0.432637i	0.889524	+	0.456888i	$0.151036\pi$
$644$	−6.82843			−0.269078
$645$		0			0
$646$	−2.34315			−0.0921898
$647$	33.2426	−	33.2426i	1.30690	−	1.30690i	0.383264	−	0.923639i	$-0.374800\pi$
$647$	33.2426	−	33.2426i	1.30690	−	1.30690i	0.923639	−	0.383264i	$-0.125200\pi$
$648$		0			0
$649$		−	1.65685i		−	0.0650372i
$650$		0			0
$651$		0			0
$652$	11.7279	+	11.7279i	0.459301	+	0.459301i
$653$	−14.2426	−	14.2426i	−0.557358	−	0.557358i	0.371197	−	0.928554i	$-0.378948\pi$
$653$	−14.2426	−	14.2426i	−0.557358	−	0.557358i	−0.928554	+	0.371197i	$0.878948\pi$
$654$		0			0
$655$		0			0
$656$		−	3.17157i		−	0.123829i
$657$		0			0
$658$	−9.24264	+	9.24264i	−0.360316	+	0.360316i
$659$	−26.7279			−1.04117			−0.520586	−	0.853809i	$-0.674286\pi$
$659$	−26.7279			−1.04117			−0.520586	+	0.853809i	$0.674286\pi$
$660$		0			0
$661$	40.0416			1.55744			0.778719	−	0.627372i	$-0.215870\pi$
$661$	40.0416			1.55744			0.778719	+	0.627372i	$0.215870\pi$
$662$	13.1716	−	13.1716i	0.511928	−	0.511928i
$663$		0			0
$664$		−	1.17157i		−	0.0454658i
$665$		0			0
$666$		0			0
$667$	−4.00000	−	4.00000i	−0.154881	−	0.154881i
$668$	−7.58579	−	7.58579i	−0.293503	−	0.293503i
$669$		0			0
$670$		0			0
$671$			5.79899i			0.223868i
$672$		0			0
$673$	−3.34315	+	3.34315i	−0.128869	+	0.128869i	−0.768599	−	0.639731i	$-0.779046\pi$
$673$	−3.34315	+	3.34315i	−0.128869	+	0.128869i	0.639731	+	0.768599i	$0.279046\pi$
$674$	−14.3848			−0.554081
$675$		0			0
$676$	−19.0000			−0.730769
$677$	−15.8284	+	15.8284i	−0.608336	+	0.608336i	−0.942511	−	0.334175i	$-0.891542\pi$
$677$	−15.8284	+	15.8284i	−0.608336	+	0.608336i	0.334175	+	0.942511i	$0.391542\pi$
$678$		0			0
$679$			6.48528i			0.248882i
$680$		0			0
$681$		0			0
$682$	−0.727922	−	0.727922i	−0.0278736	−	0.0278736i
$683$	−24.3848	−	24.3848i	−0.933058	−	0.933058i	0.0648383	−	0.997896i	$-0.479347\pi$
$683$	−24.3848	−	24.3848i	−0.933058	−	0.933058i	−0.997896	+	0.0648383i	$0.979347\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	6.07107	−	6.07107i	0.231457	−	0.231457i
$689$	−20.6863			−0.788085
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	11.4853	−	11.4853i	0.436605	−	0.436605i
$693$		0			0
$694$		−	12.0000i		−	0.455514i
$695$		0			0
$696$		0			0
$697$	−1.85786	−	1.85786i	−0.0703716	−	0.0703716i
$698$	−23.1421	−	23.1421i	−0.875943	−	0.875943i
$699$		0			0
$700$		0			0
$701$		−	40.8284i		−	1.54207i	−0.636794	−	0.771034i	$-0.719740\pi$
$701$		−	40.8284i		−	1.54207i	0.636794	−	0.771034i	$-0.280260\pi$
$702$		0			0
$703$	17.6569	−	17.6569i	0.665941	−	0.665941i
$704$	0.585786			0.0220777
$705$		0			0
$706$	−26.0000			−0.978523
$707$	12.4853	−	12.4853i	0.469557	−	0.469557i
$708$		0			0
$709$			40.8284i			1.53334i	0.642039	+	0.766672i	$0.278089\pi$
$709$			40.8284i			1.53334i	−0.642039	+	0.766672i	$0.721911\pi$
$710$		0			0
$711$		0			0
$712$	−2.24264	−	2.24264i	−0.0840465	−	0.0840465i
$713$	−8.48528	−	8.48528i	−0.317776	−	0.317776i
$714$		0			0
$715$		0			0
$716$		−	16.5858i		−	0.619840i
$717$		0			0
$718$	16.8284	−	16.8284i	0.628031	−	0.628031i
$719$	38.6274			1.44056			0.720280	−	0.693684i	$-0.244013\pi$
$719$	38.6274			1.44056			0.720280	+	0.693684i	$0.244013\pi$
$720$		0			0
$721$	10.4853			0.390492
$722$	7.77817	−	7.77817i	0.289474	−	0.289474i
$723$		0			0
$724$			19.0711i			0.708771i
$725$		0			0
$726$		0			0
$727$	22.6274	+	22.6274i	0.839204	+	0.839204i	0.988754	−	0.149550i	$-0.0477824\pi$
$727$	22.6274	+	22.6274i	0.839204	+	0.839204i	−0.149550	+	0.988754i	$0.547782\pi$
$728$	4.00000	+	4.00000i	0.148250	+	0.148250i
$729$		0			0
$730$		0			0
$731$		−	7.11270i		−	0.263073i
$732$		0			0
$733$	0.443651	−	0.443651i	0.0163866	−	0.0163866i	−0.698866	−	0.715253i	$-0.746312\pi$
$733$	0.443651	−	0.443651i	0.0163866	−	0.0163866i	0.715253	+	0.698866i	$0.246312\pi$
$734$	14.4853			0.534661
$735$		0			0
$736$	6.82843			0.251699
$737$	−4.92893	+	4.92893i	−0.181560	+	0.181560i
$738$		0			0
$739$			7.45584i			0.274268i	0.990553	+	0.137134i	$0.0437890\pi$
$739$			7.45584i			0.274268i	−0.990553	+	0.137134i	$0.956211\pi$
$740$		0			0
$741$		0			0
$742$	2.58579	+	2.58579i	0.0949272	+	0.0949272i
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.988192	+	0.153222i	$0.0489651\pi$
$743$	31.1127	+	31.1127i	1.14141	+	1.14141i	0.153222	+	0.988192i	$0.451035\pi$
$744$		0			0
$745$		0			0
$746$		−	15.6569i		−	0.573238i
$747$		0			0
$748$	0.343146	−	0.343146i	0.0125467	−	0.0125467i
$749$	7.31371			0.267237
$750$		0			0
$751$	48.4853			1.76925			0.884627	−	0.466300i	$-0.154413\pi$
$751$	48.4853			1.76925			0.884627	+	0.466300i	$0.154413\pi$
$752$	9.24264	−	9.24264i	0.337044	−	0.337044i
$753$		0			0
$754$			4.68629i			0.170665i
$755$		0			0
$756$		0			0
$757$	23.5563	+	23.5563i	0.856170	+	0.856170i	0.990884	−	0.134714i	$-0.0430117\pi$
$757$	23.5563	+	23.5563i	0.856170	+	0.856170i	−0.134714	+	0.990884i	$0.543012\pi$
$758$	−18.2426	−	18.2426i	−0.662603	−	0.662603i
$759$		0			0
$760$		0			0
$761$		−	18.9706i		−	0.687682i	−0.939028	−	0.343841i	$-0.888272\pi$
$761$		−	18.9706i		−	0.687682i	0.939028	−	0.343841i	$-0.111728\pi$
$762$		0			0
$763$	−6.58579	+	6.58579i	−0.238421	+	0.238421i
$764$	14.3431			0.518917
$765$		0			0
$766$	−6.24264			−0.225556
$767$	−11.3137	+	11.3137i	−0.408514	+	0.408514i
$768$		0			0
$769$			41.5980i			1.50006i	0.661403	+	0.750031i	$0.269961\pi$
$769$			41.5980i			1.50006i	−0.661403	+	0.750031i	$0.730039\pi$
$770$		0			0
$771$		0			0
$772$	13.4853	+	13.4853i	0.485346	+	0.485346i
$773$	−34.9411	−	34.9411i	−1.25674	−	1.25674i	−0.952638	−	0.304107i	$-0.901642\pi$
$773$	−34.9411	−	34.9411i	−1.25674	−	1.25674i	−0.304107	−	0.952638i	$-0.598358\pi$
$774$		0			0
$775$		0			0
$776$		−	6.48528i		−	0.232808i
$777$		0			0
$778$	−6.92893	+	6.92893i	−0.248414	+	0.248414i
$779$	−8.97056			−0.321404
$780$		0			0
$781$	−0.686292			−0.0245574
$782$	4.00000	−	4.00000i	0.143040	−	0.143040i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	15.5147	+	15.5147i	0.553040	+	0.553040i	0.927317	−	0.374277i	$-0.122109\pi$
$787$	15.5147	+	15.5147i	0.553040	+	0.553040i	−0.374277	+	0.927317i	$0.622109\pi$
$788$	−10.2426	−	10.2426i	−0.364879	−	0.364879i
$789$		0			0
$790$		0			0
$791$			16.0000i			0.568895i
$792$		0			0
$793$	39.5980	−	39.5980i	1.40617	−	1.40617i
$794$	1.31371			0.0466218
$795$		0			0
$796$	4.10051			0.145339
$797$	−20.1716	+	20.1716i	−0.714514	+	0.714514i	−0.967476	−	0.252962i	$-0.918595\pi$
$797$	−20.1716	+	20.1716i	−0.714514	+	0.714514i	0.252962	+	0.967476i	$0.418595\pi$
$798$		0			0
$799$		−	10.8284i		−	0.383082i
$800$		0			0
$801$		0			0
$802$	−19.0000	−	19.0000i	−0.670913	−	0.670913i
$803$	4.14214	+	4.14214i	0.146173	+	0.146173i
$804$		0			0
$805$		0			0
$806$			9.94113i			0.350161i
$807$		0			0
$808$	−12.4853	+	12.4853i	−0.439231	+	0.439231i
$809$	−46.3848			−1.63080			−0.815401	−	0.578897i	$-0.803483\pi$
$809$	−46.3848			−1.63080			−0.815401	+	0.578897i	$0.803483\pi$
$810$		0			0
$811$	28.9706			1.01729			0.508647	−	0.860975i	$-0.330146\pi$
$811$	28.9706			1.01729			0.508647	+	0.860975i	$0.330146\pi$
$812$	0.585786	−	0.585786i	0.0205571	−	0.0205571i
$813$		0			0
$814$			5.17157i			0.181264i
$815$		0			0
$816$		0			0
$817$	−17.1716	−	17.1716i	−0.600757	−	0.600757i
$818$	7.07107	+	7.07107i	0.247234	+	0.247234i
$819$		0			0
$820$		0			0
$821$			9.79899i			0.341987i	0.985272	+	0.170994i	$0.0546977\pi$
$821$			9.79899i			0.341987i	−0.985272	+	0.170994i	$0.945302\pi$
$822$		0			0
$823$	−28.4853	+	28.4853i	−0.992934	+	0.992934i	−0.999975	−	0.00704072i	$-0.997759\pi$
$823$	−28.4853	+	28.4853i	−0.992934	+	0.992934i	0.00704072	+	0.999975i	$0.497759\pi$
$824$	−10.4853			−0.365272
$825$		0			0
$826$	2.82843			0.0984136
$827$	14.2426	−	14.2426i	0.495265	−	0.495265i	−0.414695	−	0.909960i	$-0.636112\pi$
$827$	14.2426	−	14.2426i	0.495265	−	0.495265i	0.909960	+	0.414695i	$0.136112\pi$
$828$		0			0
$829$			11.7574i			0.408350i	0.978934	+	0.204175i	$0.0654512\pi$
$829$			11.7574i			0.408350i	−0.978934	+	0.204175i	$0.934549\pi$
$830$		0			0
$831$		0			0
$832$	−4.00000	−	4.00000i	−0.138675	−	0.138675i
$833$	−0.585786	−	0.585786i	−0.0202963	−	0.0202963i
$834$		0			0
$835$		0			0
$836$		−	1.65685i		−	0.0573035i
$837$		0			0
$838$	−13.1716	+	13.1716i	−0.455004	+	0.455004i
$839$	−30.4853			−1.05247			−0.526234	−	0.850340i	$-0.676397\pi$
$839$	−30.4853			−1.05247			−0.526234	+	0.850340i	$0.676397\pi$
$840$		0			0
$841$	−28.3137			−0.976335
$842$	−28.7279	+	28.7279i	−0.990030	+	0.990030i
$843$		0			0
$844$			4.00000i			0.137686i
$845$		0			0
$846$		0			0
$847$	7.53553	+	7.53553i	0.258924	+	0.258924i
$848$	−2.58579	−	2.58579i	−0.0887963	−	0.0887963i
$849$		0			0
$850$		0			0
$851$			60.2843i			2.06652i
$852$		0			0
$853$	15.0711	−	15.0711i	0.516024	−	0.516024i	−0.400342	−	0.916366i	$-0.631109\pi$
$853$	15.0711	−	15.0711i	0.516024	−	0.516024i	0.916366	+	0.400342i	$0.131109\pi$
$854$	−9.89949			−0.338754
$855$		0			0
$856$	−7.31371			−0.249977
$857$	−6.44365	+	6.44365i	−0.220111	+	0.220111i	−0.808545	−	0.588434i	$-0.799745\pi$
$857$	−6.44365	+	6.44365i	−0.220111	+	0.220111i	0.588434	+	0.808545i	$0.299745\pi$
$858$		0			0
$859$		−	40.0000i		−	1.36478i	−0.730987	−	0.682391i	$-0.760940\pi$
$859$		−	40.0000i		−	1.36478i	0.730987	−	0.682391i	$-0.239060\pi$
$860$		0			0
$861$		0			0
$862$	−18.4853	−	18.4853i	−0.629611	−	0.629611i
$863$	21.1716	+	21.1716i	0.720689	+	0.720689i	0.968745	−	0.248057i	$-0.0797920\pi$
$863$	21.1716	+	21.1716i	0.720689	+	0.720689i	−0.248057	+	0.968745i	$0.579792\pi$
$864$		0			0
$865$		0			0
$866$			25.7990i			0.876685i
$867$		0			0
$868$	1.24264	−	1.24264i	0.0421780	−	0.0421780i
$869$	3.31371			0.112410
$870$		0			0
$871$	67.3137			2.28084
$872$	6.58579	−	6.58579i	0.223023	−	0.223023i
$873$		0			0
$874$		−	19.3137i		−	0.653296i
$875$		0			0
$876$		0			0
$877$	37.6985	+	37.6985i	1.27299	+	1.27299i	0.944513	+	0.328475i	$0.106535\pi$
$877$	37.6985	+	37.6985i	1.27299	+	1.27299i	0.328475	+	0.944513i	$0.393465\pi$
$878$	2.75736	+	2.75736i	0.0930564	+	0.0930564i
$879$		0			0
$880$		0			0
$881$			8.62742i			0.290665i	0.989383	+	0.145333i	$0.0464252\pi$
$881$			8.62742i			0.290665i	−0.989383	+	0.145333i	$0.953575\pi$
$882$		0			0
$883$	−37.3848	+	37.3848i	−1.25810	+	1.25810i	−0.306098	+	0.952000i	$0.599023\pi$
$883$	−37.3848	+	37.3848i	−1.25810	+	1.25810i	−0.952000	+	0.306098i	$0.900977\pi$
$884$	−4.68629			−0.157617
$885$		0			0
$886$	4.97056			0.166989
$887$	39.7279	−	39.7279i	1.33393	−	1.33393i	0.432114	−	0.901819i	$-0.357768\pi$
$887$	39.7279	−	39.7279i	1.33393	−	1.33393i	0.901819	−	0.432114i	$-0.142232\pi$
$888$		0			0
$889$		−	10.8284i		−	0.363174i
$890$		0			0
$891$		0			0
$892$	7.31371	+	7.31371i	0.244881	+	0.244881i
$893$	−26.1421	−	26.1421i	−0.874813	−	0.874813i
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−11.8284	+	11.8284i	−0.394720	+	0.394720i
$899$	1.45584			0.0485551
$900$		0			0
$901$	−3.02944			−0.100925
$902$	1.31371	−	1.31371i	0.0437417	−	0.0437417i
$903$		0			0
$904$		−	16.0000i		−	0.532152i
$905$		0			0
$906$		0			0
$907$	−19.5858	−	19.5858i	−0.650335	−	0.650335i	0.302738	−	0.953074i	$-0.402099\pi$
$907$	−19.5858	−	19.5858i	−0.650335	−	0.650335i	−0.953074	+	0.302738i	$0.902099\pi$
$908$	1.17157	+	1.17157i	0.0388800	+	0.0388800i
$909$		0			0
$910$		0			0
$911$		−	4.00000i		−	0.132526i	−0.997802	−	0.0662630i	$-0.978892\pi$
$911$		−	4.00000i		−	0.132526i	0.997802	−	0.0662630i	$-0.0211076\pi$
$912$		0			0
$913$	0.485281	−	0.485281i	0.0160605	−	0.0160605i
$914$	−3.07107			−0.101582
$915$		0			0
$916$	−8.24264			−0.272345
$917$	11.6569	−	11.6569i	0.384943	−	0.384943i
$918$		0			0
$919$		−	55.7990i		−	1.84064i	−0.391168	−	0.920319i	$-0.627929\pi$
$919$		−	55.7990i		−	1.84064i	0.391168	−	0.920319i	$-0.372071\pi$
$920$		0			0
$921$		0			0
$922$	3.75736	+	3.75736i	0.123742	+	0.123742i
$923$	4.68629	+	4.68629i	0.154251	+	0.154251i
$924$		0			0
$925$		0			0
$926$		−	28.0000i		−	0.920137i
$927$		0			0
$928$	−0.585786	+	0.585786i	−0.0192294	+	0.0192294i
$929$	−13.0294			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$929$	−13.0294			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$930$		0			0
$931$	−2.82843			−0.0926980
$932$	−14.8284	+	14.8284i	−0.485721	+	0.485721i
$933$		0			0
$934$		−	19.7990i		−	0.647843i
$935$		0			0
$936$		0			0
$937$	29.2132	+	29.2132i	0.954354	+	0.954354i	0.999003	−	0.0446490i	$-0.0142169\pi$
$937$	29.2132	+	29.2132i	0.954354	+	0.954354i	−0.0446490	+	0.999003i	$0.514217\pi$
$938$	−8.41421	−	8.41421i	−0.274734	−	0.274734i
$939$		0			0
$940$		0			0
$941$		−	10.2843i		−	0.335258i	−0.985850	−	0.167629i	$-0.946389\pi$
$941$		−	10.2843i		−	0.335258i	0.985850	−	0.167629i	$-0.0536110\pi$
$942$		0			0
$943$	15.3137	−	15.3137i	0.498683	−	0.498683i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	5.02944			0.163521
$947$	−9.75736	+	9.75736i	−0.317072	+	0.317072i	−0.847641	−	0.530570i	$-0.821978\pi$
$947$	−9.75736	+	9.75736i	−0.317072	+	0.317072i	0.530570	+	0.847641i	$0.321978\pi$
$948$		0			0
$949$		−	56.5685i		−	1.83629i
$950$		0			0
$951$		0			0
$952$	0.585786	+	0.585786i	0.0189854	+	0.0189854i
$953$	27.7574	+	27.7574i	0.899149	+	0.899149i	0.995361	−	0.0962118i	$-0.0306726\pi$
$953$	27.7574	+	27.7574i	0.899149	+	0.899149i	−0.0962118	+	0.995361i	$0.530673\pi$
$954$		0			0
$955$		0			0
$956$		−	13.6569i		−	0.441694i
$957$		0			0
$958$	13.5563	−	13.5563i	0.437986	−	0.437986i
$959$	−16.9706			−0.548008
$960$		0			0
$961$	−27.9117			−0.900377
$962$	35.3137	−	35.3137i	1.13856	−	1.13856i
$963$		0			0
$964$			4.14214i			0.133409i
$965$		0			0
$966$		0			0
$967$	−20.2843	−	20.2843i	−0.652298	−	0.652298i	0.301248	−	0.953546i	$-0.402597\pi$
$967$	−20.2843	−	20.2843i	−0.652298	−	0.652298i	−0.953546	+	0.301248i	$0.902597\pi$
$968$	−7.53553	−	7.53553i	−0.242201	−	0.242201i
$969$		0			0
$970$		0			0
$971$			36.0000i			1.15529i	0.816286	+	0.577647i	$0.196029\pi$
$971$			36.0000i			1.15529i	−0.816286	+	0.577647i	$0.803971\pi$
$972$		0			0
$973$	−12.4853	+	12.4853i	−0.400260	+	0.400260i
$974$	−26.8284			−0.859638
$975$		0			0
$976$	9.89949			0.316875
$977$	−32.9706	+	32.9706i	−1.05482	+	1.05482i	−0.0564143	+	0.998407i	$0.517967\pi$
$977$	−32.9706	+	32.9706i	−1.05482	+	1.05482i	−0.998407	+	0.0564143i	$0.982033\pi$
$978$		0			0
$979$		−	1.85786i		−	0.0593776i
$980$		0			0
$981$		0			0
$982$	18.8995	+	18.8995i	0.603107	+	0.603107i
$983$	−40.5563	−	40.5563i	−1.29355	−	1.29355i	−0.932578	−	0.360969i	$-0.882446\pi$
$983$	−40.5563	−	40.5563i	−1.29355	−	1.29355i	−0.360969	−	0.932578i	$-0.617554\pi$
$984$		0			0
$985$		0			0
$986$			0.686292i			0.0218560i
$987$		0			0
$988$	−11.3137	+	11.3137i	−0.359937	+	0.359937i
$989$	58.6274			1.86424
$990$		0			0
$991$	−30.1421			−0.957496			−0.478748	−	0.877952i	$-0.658909\pi$
$991$	−30.1421			−0.957496			−0.478748	+	0.877952i	$0.658909\pi$
$992$	−1.24264	+	1.24264i	−0.0394539	+	0.0394539i
$993$		0			0
$994$		−	1.17157i		−	0.0371600i
$995$		0			0
$996$		0			0
$997$	−1.89949	−	1.89949i	−0.0601576	−	0.0601576i	0.676388	−	0.736546i	$-0.263544\pi$
$997$	−1.89949	−	1.89949i	−0.0601576	−	0.0601576i	−0.736546	+	0.676388i	$0.763544\pi$
$998$	−16.5858	−	16.5858i	−0.525014	−	0.525014i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.b.1457.2		4
3.2	odd	2		3150.2.m.a.1457.1		4
5.2	odd	4		630.2.m.b.323.2	yes	4
5.3	odd	4		3150.2.m.a.2843.1		4
5.4	even	2		630.2.m.a.197.1	✓	4
15.2	even	4		630.2.m.a.323.1	yes	4
15.8	even	4	inner	3150.2.m.b.2843.2		4
15.14	odd	2		630.2.m.b.197.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.a.197.1	✓	4	5.4	even	2
630.2.m.a.323.1	yes	4	15.2	even	4
630.2.m.b.197.2	yes	4	15.14	odd	2
630.2.m.b.323.2	yes	4	5.2	odd	4
3150.2.m.a.1457.1		4	3.2	odd	2
3150.2.m.a.2843.1		4	5.3	odd	4
3150.2.m.b.1457.2		4	1.1	even	1	trivial
3150.2.m.b.2843.2		4	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -0.585786i q^{11} +(-4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-0.585786 + 0.585786i) q^{17} +2.82843i q^{19} +(-0.414214 - 0.414214i) q^{22} +(-4.82843 - 4.82843i) q^{23} +5.65685i q^{26} +(0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(-0.707107 + 0.707107i) q^{32} +0.828427i q^{34} +(-6.24264 - 6.24264i) q^{37} +(2.00000 + 2.00000i) q^{38} +3.17157i q^{41} +(-6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(-9.24264 + 9.24264i) q^{47} +1.00000i q^{49} +(4.00000 + 4.00000i) q^{52} +(2.58579 + 2.58579i) q^{53} -1.00000i q^{56} +(0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(1.24264 - 1.24264i) q^{62} +1.00000i q^{64} +(-8.41421 - 8.41421i) q^{67} +(0.585786 + 0.585786i) q^{68} -1.17157i q^{71} +(-7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(0.414214 - 0.414214i) q^{77} +5.65685i q^{79} +(2.24264 + 2.24264i) q^{82} +(0.828427 + 0.828427i) q^{83} +8.58579i q^{86} +(-0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(-4.82843 + 4.82843i) q^{92} +13.0711i q^{94} +(4.58579 + 4.58579i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q - 16 q^{13} + 4 q^{14} - 4 q^{16} - 8 q^{17} + 4 q^{22} - 8 q^{23} - 8 q^{29} + 24 q^{31} - 8 q^{37} + 8 q^{38} + 4 q^{43} - 8 q^{44} - 16 q^{46} - 20 q^{47} + 16 q^{52} + 16 q^{53} + 8 q^{58} - 12 q^{62} - 28 q^{67} + 8 q^{68} - 24 q^{74} - 4 q^{77} - 8 q^{82} - 8 q^{83} + 4 q^{88} + 24 q^{89} - 8 q^{92} + 24 q^{97}+O(q^{100}) \) 4 * q - 16 * q^13 + 4 * q^14 - 4 * q^16 - 8 * q^17 + 4 * q^22 - 8 * q^23 - 8 * q^29 + 24 * q^31 - 8 * q^37 + 8 * q^38 + 4 * q^43 - 8 * q^44 - 16 * q^46 - 20 * q^47 + 16 * q^52 + 16 * q^53 + 8 * q^58 - 12 * q^62 - 28 * q^67 + 8 * q^68 - 24 * q^74 - 4 * q^77 - 8 * q^82 - 8 * q^83 + 4 * q^88 + 24 * q^89 - 8 * q^92 + 24 * q^97

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