LMFDB - Embedded newform 3150.2.m.f.1457.1

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.f.2843.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -4.82843i q^{11} +(3.41421 - 3.41421i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.58579 + 1.58579i) q^{17} -7.07107i q^{19} +(3.41421 + 3.41421i) q^{22} +(-4.82843 - 4.82843i) q^{23} +4.82843i q^{26} +(-0.707107 + 0.707107i) q^{28} -3.17157 q^{29} -8.82843 q^{31} +(0.707107 - 0.707107i) q^{32} -2.24264i q^{34} +(6.07107 + 6.07107i) q^{37} +(5.00000 + 5.00000i) q^{38} +4.82843i q^{41} +(-6.41421 + 6.41421i) q^{43} -4.82843 q^{44} +6.82843 q^{46} +(-6.41421 + 6.41421i) q^{47} +1.00000i q^{49} +(-3.41421 - 3.41421i) q^{52} +(4.82843 + 4.82843i) q^{53} -1.00000i q^{56} +(2.24264 - 2.24264i) q^{58} -8.00000 q^{59} +6.58579 q^{61} +(6.24264 - 6.24264i) q^{62} +1.00000i q^{64} +(-0.414214 - 0.414214i) q^{67} +(1.58579 + 1.58579i) q^{68} +12.2426i q^{71} +(6.00000 - 6.00000i) q^{73} -8.58579 q^{74} -7.07107 q^{76} +(-3.41421 + 3.41421i) q^{77} -13.3137i q^{79} +(-3.41421 - 3.41421i) q^{82} +(9.65685 + 9.65685i) q^{83} -9.07107i q^{86} +(3.41421 - 3.41421i) q^{88} -13.3137 q^{89} -4.82843 q^{91} +(-4.82843 + 4.82843i) q^{92} -9.07107i q^{94} +(8.24264 + 8.24264i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 8 q^{13} + 4 q^{14} - 4 q^{16} - 12 q^{17} + 8 q^{22} - 8 q^{23} - 24 q^{29} - 24 q^{31} - 4 q^{37} + 20 q^{38} - 20 q^{43} - 8 q^{44} + 16 q^{46} - 20 q^{47} - 8 q^{52} + 8 q^{53} - 8 q^{58} - 32 q^{59} + 32 q^{61} + 8 q^{62} + 4 q^{67} + 12 q^{68} + 24 q^{73} - 40 q^{74} - 8 q^{77} - 8 q^{82} + 16 q^{83} + 8 q^{88} - 8 q^{89} - 8 q^{91} - 8 q^{92} + 16 q^{97}+O(q^{100}) $ 4 * q + 8 * q^13 + 4 * q^14 - 4 * q^16 - 12 * q^17 + 8 * q^22 - 8 * q^23 - 24 * q^29 - 24 * q^31 - 4 * q^37 + 20 * q^38 - 20 * q^43 - 8 * q^44 + 16 * q^46 - 20 * q^47 - 8 * q^52 + 8 * q^53 - 8 * q^58 - 32 * q^59 + 32 * q^61 + 8 * q^62 + 4 * q^67 + 12 * q^68 + 24 * q^73 - 40 * q^74 - 8 * q^77 - 8 * q^82 + 16 * q^83 + 8 * q^88 - 8 * q^89 - 8 * q^91 - 8 * q^92 + 16 * 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
$11$		−	4.82843i		−	1.45583i	−0.685670	−	0.727913i	$-0.740491\pi$
$11$		−	4.82843i		−	1.45583i	0.685670	−	0.727913i	$-0.259509\pi$
$12$		0			0
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	−0.0517287	−	0.998661i	$-0.516473\pi$
$13$	3.41421	−	3.41421i	0.946932	−	0.946932i	0.998661	+	0.0517287i	$0.0164731\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.58579	+	1.58579i	−0.384610	+	0.384610i	−0.872760	−	0.488150i	$-0.837672\pi$
$17$	−1.58579	+	1.58579i	−0.384610	+	0.384610i	0.488150	+	0.872760i	$0.337672\pi$
$18$		0			0
$19$		−	7.07107i		−	1.62221i	−0.584898	−	0.811107i	$-0.698865\pi$
$19$		−	7.07107i		−	1.62221i	0.584898	−	0.811107i	$-0.301135\pi$
$20$		0			0
$21$		0			0
$22$	3.41421	+	3.41421i	0.727913	+	0.727913i
$23$	−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
$26$			4.82843i			0.946932i
$27$		0			0
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−3.17157			−0.588946			−0.294473	−	0.955660i	$-0.595144\pi$
$29$	−3.17157			−0.588946			−0.294473	+	0.955660i	$0.595144\pi$
$30$		0			0
$31$	−8.82843			−1.58563			−0.792816	−	0.609461i	$-0.791386\pi$
$31$	−8.82843			−1.58563			−0.792816	+	0.609461i	$0.791386\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	2.24264i		−	0.384610i
$35$		0			0
$36$		0			0
$37$	6.07107	+	6.07107i	0.998077	+	0.998077i	0.999998	−	0.00192076i	$-0.000611396\pi$
$37$	6.07107	+	6.07107i	0.998077	+	0.998077i	−0.00192076	+	0.999998i	$0.500611\pi$
$38$	5.00000	+	5.00000i	0.811107	+	0.811107i
$39$		0			0
$40$		0			0
$41$			4.82843i			0.754074i	0.926198	+	0.377037i	$0.123057\pi$
$41$			4.82843i			0.754074i	−0.926198	+	0.377037i	$0.876943\pi$
$42$		0			0
$43$	−6.41421	+	6.41421i	−0.978158	+	0.978158i	−0.999767	−	0.0216081i	$-0.993121\pi$
$43$	−6.41421	+	6.41421i	−0.978158	+	0.978158i	0.0216081	+	0.999767i	$0.493121\pi$
$44$	−4.82843			−0.727913
$45$		0			0
$46$	6.82843			1.00680
$47$	−6.41421	+	6.41421i	−0.935609	+	0.935609i	−0.998049	−	0.0624395i	$-0.980112\pi$
$47$	−6.41421	+	6.41421i	−0.935609	+	0.935609i	0.0624395	+	0.998049i	$0.480112\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−3.41421	−	3.41421i	−0.473466	−	0.473466i
$53$	4.82843	+	4.82843i	0.663235	+	0.663235i	0.956141	−	0.292906i	$-0.0946222\pi$
$53$	4.82843	+	4.82843i	0.663235	+	0.663235i	−0.292906	+	0.956141i	$0.594622\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	2.24264	−	2.24264i	0.294473	−	0.294473i
$59$	−8.00000			−1.04151			−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000			−1.04151			−0.520756	+	0.853706i	$0.674350\pi$
$60$		0			0
$61$	6.58579			0.843224			0.421612	−	0.906776i	$-0.361465\pi$
$61$	6.58579			0.843224			0.421612	+	0.906776i	$0.361465\pi$
$62$	6.24264	−	6.24264i	0.792816	−	0.792816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−0.414214	−	0.414214i	−0.0506042	−	0.0506042i	0.681352	−	0.731956i	$-0.261392\pi$
$67$	−0.414214	−	0.414214i	−0.0506042	−	0.0506042i	−0.731956	+	0.681352i	$0.761392\pi$
$68$	1.58579	+	1.58579i	0.192305	+	0.192305i
$69$		0			0
$70$		0			0
$71$			12.2426i			1.45293i	0.687201	+	0.726467i	$0.258839\pi$
$71$			12.2426i			1.45293i	−0.687201	+	0.726467i	$0.741161\pi$
$72$		0			0
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	−0.262646	−	0.964892i	$-0.584595\pi$
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	0.964892	+	0.262646i	$0.0845950\pi$
$74$	−8.58579			−0.998077
$75$		0			0
$76$	−7.07107			−0.811107
$77$	−3.41421	+	3.41421i	−0.389086	+	0.389086i
$78$		0			0
$79$		−	13.3137i		−	1.49791i	−0.662621	−	0.748955i	$-0.730556\pi$
$79$		−	13.3137i		−	1.49791i	0.662621	−	0.748955i	$-0.269444\pi$
$80$		0			0
$81$		0			0
$82$	−3.41421	−	3.41421i	−0.377037	−	0.377037i
$83$	9.65685	+	9.65685i	1.05998	+	1.05998i	0.998083	+	0.0618948i	$0.0197143\pi$
$83$	9.65685	+	9.65685i	1.05998	+	1.05998i	0.0618948	+	0.998083i	$0.480286\pi$
$84$		0			0
$85$		0			0
$86$		−	9.07107i		−	0.978158i
$87$		0			0
$88$	3.41421	−	3.41421i	0.363956	−	0.363956i
$89$	−13.3137			−1.41125			−0.705625	−	0.708585i	$-0.749334\pi$
$89$	−13.3137			−1.41125			−0.705625	+	0.708585i	$0.749334\pi$
$90$		0			0
$91$	−4.82843			−0.506157
$92$	−4.82843	+	4.82843i	−0.503398	+	0.503398i
$93$		0			0
$94$		−	9.07107i		−	0.935609i
$95$		0			0
$96$		0			0
$97$	8.24264	+	8.24264i	0.836913	+	0.836913i	0.988451	−	0.151538i	$-0.0484226\pi$
$97$	8.24264	+	8.24264i	0.836913	+	0.836913i	−0.151538	+	0.988451i	$0.548423\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$		0			0
$100$		0			0
$101$			4.34315i			0.432159i	0.976376	+	0.216080i	$0.0693271\pi$
$101$			4.34315i			0.432159i	−0.976376	+	0.216080i	$0.930673\pi$
$102$		0			0
$103$	−3.41421	+	3.41421i	−0.336412	+	0.336412i	−0.855015	−	0.518603i	$-0.826452\pi$
$103$	−3.41421	+	3.41421i	−0.336412	+	0.336412i	0.518603	+	0.855015i	$0.326452\pi$
$104$	4.82843			0.473466
$105$		0			0
$106$	−6.82843			−0.663235
$107$	−9.07107	+	9.07107i	−0.876933	+	0.876933i	−0.993216	−	0.116283i	$-0.962902\pi$
$107$	−9.07107	+	9.07107i	−0.876933	+	0.876933i	0.116283	+	0.993216i	$0.462902\pi$
$108$		0			0
$109$		−	20.1421i		−	1.92927i	−0.263595	−	0.964633i	$-0.584908\pi$
$109$		−	20.1421i		−	1.92927i	0.263595	−	0.964633i	$-0.415092\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−5.41421	−	5.41421i	−0.509326	−	0.509326i	0.404993	−	0.914320i	$-0.367274\pi$
$113$	−5.41421	−	5.41421i	−0.509326	−	0.509326i	−0.914320	+	0.404993i	$0.867274\pi$
$114$		0			0
$115$		0			0
$116$			3.17157i			0.294473i
$117$		0			0
$118$	5.65685	−	5.65685i	0.520756	−	0.520756i
$119$	2.24264			0.205583
$120$		0			0
$121$	−12.3137			−1.11943
$122$	−4.65685	+	4.65685i	−0.421612	+	0.421612i
$123$		0			0
$124$			8.82843i			0.792816i
$125$		0			0
$126$		0			0
$127$	−1.17157	−	1.17157i	−0.103960	−	0.103960i	0.653213	−	0.757174i	$-0.273420\pi$
$127$	−1.17157	−	1.17157i	−0.103960	−	0.103960i	−0.757174	+	0.653213i	$0.773420\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	6.00000i		−	0.524222i	−0.965038	−	0.262111i	$-0.915581\pi$
$131$		−	6.00000i		−	0.524222i	0.965038	−	0.262111i	$-0.0844187\pi$
$132$		0			0
$133$	−5.00000	+	5.00000i	−0.433555	+	0.433555i
$134$	0.585786			0.0506042
$135$		0			0
$136$	−2.24264			−0.192305
$137$	1.07107	−	1.07107i	0.0915075	−	0.0915075i	−0.659871	−	0.751379i	$-0.729389\pi$
$137$	1.07107	−	1.07107i	0.0915075	−	0.0915075i	0.751379	+	0.659871i	$0.229389\pi$
$138$		0			0
$139$		−	0.242641i		−	0.0205805i	−0.999947	−	0.0102903i	$-0.996724\pi$
$139$		−	0.242641i		−	0.0205805i	0.999947	−	0.0102903i	$-0.00327555\pi$
$140$		0			0
$141$		0			0
$142$	−8.65685	−	8.65685i	−0.726467	−	0.726467i
$143$	−16.4853	−	16.4853i	−1.37857	−	1.37857i
$144$		0			0
$145$		0			0
$146$			8.48528i			0.702247i
$147$		0			0
$148$	6.07107	−	6.07107i	0.499039	−	0.499039i
$149$	5.31371			0.435316			0.217658	−	0.976025i	$-0.430158\pi$
$149$	5.31371			0.435316			0.217658	+	0.976025i	$0.430158\pi$
$150$		0			0
$151$	−13.3137			−1.08345			−0.541727	−	0.840554i	$-0.682229\pi$
$151$	−13.3137			−1.08345			−0.541727	+	0.840554i	$0.682229\pi$
$152$	5.00000	−	5.00000i	0.405554	−	0.405554i
$153$		0			0
$154$		−	4.82843i		−	0.389086i
$155$		0			0
$156$		0			0
$157$	−2.58579	−	2.58579i	−0.206368	−	0.206368i	0.596354	−	0.802722i	$-0.296616\pi$
$157$	−2.58579	−	2.58579i	−0.206368	−	0.206368i	−0.802722	+	0.596354i	$0.796616\pi$
$158$	9.41421	+	9.41421i	0.748955	+	0.748955i
$159$		0			0
$160$		0			0
$161$			6.82843i			0.538155i
$162$		0			0
$163$	−4.89949	+	4.89949i	−0.383758	+	0.383758i	−0.872454	−	0.488696i	$-0.837473\pi$
$163$	−4.89949	+	4.89949i	−0.383758	+	0.383758i	0.488696	+	0.872454i	$0.337473\pi$
$164$	4.82843			0.377037
$165$		0			0
$166$	−13.6569			−1.05998
$167$	6.89949	−	6.89949i	0.533899	−	0.533899i	−0.387831	−	0.921730i	$-0.626776\pi$
$167$	6.89949	−	6.89949i	0.533899	−	0.533899i	0.921730	+	0.387831i	$0.126776\pi$
$168$		0			0
$169$		−	10.3137i		−	0.793362i
$170$		0			0
$171$		0			0
$172$	6.41421	+	6.41421i	0.489079	+	0.489079i
$173$	−8.00000	−	8.00000i	−0.608229	−	0.608229i	0.334254	−	0.942483i	$-0.391516\pi$
$173$	−8.00000	−	8.00000i	−0.608229	−	0.608229i	−0.942483	+	0.334254i	$0.891516\pi$
$174$		0			0
$175$		0			0
$176$			4.82843i			0.363956i
$177$		0			0
$178$	9.41421	−	9.41421i	0.705625	−	0.705625i
$179$	13.3137			0.995113			0.497557	−	0.867431i	$-0.334231\pi$
$179$	13.3137			0.995113			0.497557	+	0.867431i	$0.334231\pi$
$180$		0			0
$181$	−11.0711			−0.822906			−0.411453	−	0.911431i	$-0.634979\pi$
$181$	−11.0711			−0.822906			−0.411453	+	0.911431i	$0.634979\pi$
$182$	3.41421	−	3.41421i	0.253078	−	0.253078i
$183$		0			0
$184$		−	6.82843i		−	0.503398i
$185$		0			0
$186$		0			0
$187$	7.65685	+	7.65685i	0.559925	+	0.559925i
$188$	6.41421	+	6.41421i	0.467805	+	0.467805i
$189$		0			0
$190$		0			0
$191$			13.4142i			0.970618i	0.874343	+	0.485309i	$0.161293\pi$
$191$			13.4142i			0.970618i	−0.874343	+	0.485309i	$0.838707\pi$
$192$		0			0
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	−0.889271	−	0.457381i	$-0.848787\pi$
$193$	−6.00000	+	6.00000i	−0.431889	+	0.431889i	0.457381	+	0.889271i	$0.348787\pi$
$194$	−11.6569			−0.836913
$195$		0			0
$196$	1.00000			0.0714286
$197$	−3.17157	+	3.17157i	−0.225965	+	0.225965i	−0.811005	−	0.585040i	$-0.801079\pi$
$197$	−3.17157	+	3.17157i	−0.225965	+	0.225965i	0.585040	+	0.811005i	$0.301079\pi$
$198$		0			0
$199$			0.343146i			0.0243250i	0.999926	+	0.0121625i	$0.00387153\pi$
$199$			0.343146i			0.0243250i	−0.999926	+	0.0121625i	$0.996128\pi$
$200$		0			0
$201$		0			0
$202$	−3.07107	−	3.07107i	−0.216080	−	0.216080i
$203$	2.24264	+	2.24264i	0.157403	+	0.157403i
$204$		0			0
$205$		0			0
$206$		−	4.82843i		−	0.336412i
$207$		0			0
$208$	−3.41421	+	3.41421i	−0.236733	+	0.236733i
$209$	−34.1421			−2.36166
$210$		0			0
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$	4.82843	−	4.82843i	0.331618	−	0.331618i
$213$		0			0
$214$		−	12.8284i		−	0.876933i
$215$		0			0
$216$		0			0
$217$	6.24264	+	6.24264i	0.423778	+	0.423778i
$218$	14.2426	+	14.2426i	0.964633	+	0.964633i
$219$		0			0
$220$		0			0
$221$			10.8284i			0.728399i
$222$		0			0
$223$	−7.89949	+	7.89949i	−0.528989	+	0.528989i	−0.920271	−	0.391282i	$-0.872032\pi$
$223$	−7.89949	+	7.89949i	−0.528989	+	0.528989i	0.391282	+	0.920271i	$0.372032\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	7.65685			0.509326
$227$	4.34315	−	4.34315i	0.288265	−	0.288265i	−0.548129	−	0.836394i	$-0.684660\pi$
$227$	4.34315	−	4.34315i	0.288265	−	0.288265i	0.836394	+	0.548129i	$0.184660\pi$
$228$		0			0
$229$			4.92893i			0.325713i	0.986650	+	0.162857i	$0.0520708\pi$
$229$			4.92893i			0.325713i	−0.986650	+	0.162857i	$0.947929\pi$
$230$		0			0
$231$		0			0
$232$	−2.24264	−	2.24264i	−0.147237	−	0.147237i
$233$	5.41421	+	5.41421i	0.354697	+	0.354697i	0.861854	−	0.507157i	$-0.169304\pi$
$233$	5.41421	+	5.41421i	0.354697	+	0.354697i	−0.507157	+	0.861854i	$0.669304\pi$
$234$		0			0
$235$		0			0
$236$			8.00000i			0.520756i
$237$		0			0
$238$	−1.58579	+	1.58579i	−0.102791	+	0.102791i
$239$	−25.2132			−1.63091			−0.815453	−	0.578823i	$-0.803512\pi$
$239$	−25.2132			−1.63091			−0.815453	+	0.578823i	$0.803512\pi$
$240$		0			0
$241$	−7.65685			−0.493221			−0.246611	−	0.969115i	$-0.579317\pi$
$241$	−7.65685			−0.493221			−0.246611	+	0.969115i	$0.579317\pi$
$242$	8.70711	−	8.70711i	0.559714	−	0.559714i
$243$		0			0
$244$		−	6.58579i		−	0.421612i
$245$		0			0
$246$		0			0
$247$	−24.1421	−	24.1421i	−1.53613	−	1.53613i
$248$	−6.24264	−	6.24264i	−0.396408	−	0.396408i
$249$		0			0
$250$		0			0
$251$		−	6.97056i		−	0.439978i	−0.975502	−	0.219989i	$-0.929398\pi$
$251$		−	6.97056i		−	0.439978i	0.975502	−	0.219989i	$-0.0706022\pi$
$252$		0			0
$253$	−23.3137	+	23.3137i	−1.46572	+	1.46572i
$254$	1.65685			0.103960
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.89949	+	6.89949i	−0.430379	+	0.430379i	−0.888757	−	0.458378i	$-0.848430\pi$
$257$	−6.89949	+	6.89949i	−0.430379	+	0.430379i	0.458378	+	0.888757i	$0.348430\pi$
$258$		0			0
$259$		−	8.58579i		−	0.533495i
$260$		0			0
$261$		0			0
$262$	4.24264	+	4.24264i	0.262111	+	0.262111i
$263$	−22.0000	−	22.0000i	−1.35658	−	1.35658i	−0.878099	−	0.478479i	$-0.841188\pi$
$263$	−22.0000	−	22.0000i	−1.35658	−	1.35658i	−0.478479	−	0.878099i	$-0.658812\pi$
$264$		0			0
$265$		0			0
$266$		−	7.07107i		−	0.433555i
$267$		0			0
$268$	−0.414214	+	0.414214i	−0.0253021	+	0.0253021i
$269$	21.3137			1.29952			0.649760	−	0.760140i	$-0.274869\pi$
$269$	21.3137			1.29952			0.649760	+	0.760140i	$0.274869\pi$
$270$		0			0
$271$	7.17157			0.435642			0.217821	−	0.975989i	$-0.430105\pi$
$271$	7.17157			0.435642			0.217821	+	0.975989i	$0.430105\pi$
$272$	1.58579	−	1.58579i	0.0961524	−	0.0961524i
$273$		0			0
$274$			1.51472i			0.0915075i
$275$		0			0
$276$		0			0
$277$	18.0711	+	18.0711i	1.08579	+	1.08579i	0.995957	+	0.0898279i	$0.0286317\pi$
$277$	18.0711	+	18.0711i	1.08579	+	1.08579i	0.0898279	+	0.995957i	$0.471368\pi$
$278$	0.171573	+	0.171573i	0.0102903	+	0.0102903i
$279$		0			0
$280$		0			0
$281$		−	12.9289i		−	0.771275i	−0.922650	−	0.385638i	$-0.873981\pi$
$281$		−	12.9289i		−	0.771275i	0.922650	−	0.385638i	$-0.126019\pi$
$282$		0			0
$283$	18.0000	−	18.0000i	1.06999	−	1.06999i	0.0726300	−	0.997359i	$-0.476861\pi$
$283$	18.0000	−	18.0000i	1.06999	−	1.06999i	0.997359	−	0.0726300i	$-0.0231392\pi$
$284$	12.2426			0.726467
$285$		0			0
$286$	23.3137			1.37857
$287$	3.41421	−	3.41421i	0.201535	−	0.201535i
$288$		0			0
$289$			11.9706i			0.704151i
$290$		0			0
$291$		0			0
$292$	−6.00000	−	6.00000i	−0.351123	−	0.351123i
$293$	−22.4853	−	22.4853i	−1.31360	−	1.31360i	−0.918739	−	0.394865i	$-0.870791\pi$
$293$	−22.4853	−	22.4853i	−1.31360	−	1.31360i	−0.394865	−	0.918739i	$-0.629209\pi$
$294$		0			0
$295$		0			0
$296$			8.58579i			0.499039i
$297$		0			0
$298$	−3.75736	+	3.75736i	−0.217658	+	0.217658i
$299$	−32.9706			−1.90674
$300$		0			0
$301$	9.07107			0.522848
$302$	9.41421	−	9.41421i	0.541727	−	0.541727i
$303$		0			0
$304$			7.07107i			0.405554i
$305$		0			0
$306$		0			0
$307$	7.51472	+	7.51472i	0.428888	+	0.428888i	0.888249	−	0.459362i	$-0.151922\pi$
$307$	7.51472	+	7.51472i	0.428888	+	0.428888i	−0.459362	+	0.888249i	$0.651922\pi$
$308$	3.41421	+	3.41421i	0.194543	+	0.194543i
$309$		0			0
$310$		0			0
$311$		−	16.0000i		−	0.907277i	−0.891186	−	0.453638i	$-0.850126\pi$
$311$		−	16.0000i		−	0.907277i	0.891186	−	0.453638i	$-0.149874\pi$
$312$		0			0
$313$	19.6569	−	19.6569i	1.11107	−	1.11107i	0.118065	−	0.993006i	$-0.462331\pi$
$313$	19.6569	−	19.6569i	1.11107	−	1.11107i	0.993006	−	0.118065i	$-0.0376692\pi$
$314$	3.65685			0.206368
$315$		0			0
$316$	−13.3137			−0.748955
$317$	−12.2426	+	12.2426i	−0.687615	+	0.687615i	−0.961704	−	0.274089i	$-0.911624\pi$
$317$	−12.2426	+	12.2426i	−0.687615	+	0.687615i	0.274089	+	0.961704i	$0.411624\pi$
$318$		0			0
$319$			15.3137i			0.857403i
$320$		0			0
$321$		0			0
$322$	−4.82843	−	4.82843i	−0.269078	−	0.269078i
$323$	11.2132	+	11.2132i	0.623919	+	0.623919i
$324$		0			0
$325$		0			0
$326$		−	6.92893i		−	0.383758i
$327$		0			0
$328$	−3.41421	+	3.41421i	−0.188518	+	0.188518i
$329$	9.07107			0.500104
$330$		0			0
$331$	−1.85786			−0.102117			−0.0510587	−	0.998696i	$-0.516260\pi$
$331$	−1.85786			−0.102117			−0.0510587	+	0.998696i	$0.516260\pi$
$332$	9.65685	−	9.65685i	0.529989	−	0.529989i
$333$		0			0
$334$			9.75736i			0.533899i
$335$		0			0
$336$		0			0
$337$	1.51472	+	1.51472i	0.0825120	+	0.0825120i	0.747158	−	0.664646i	$-0.231418\pi$
$337$	1.51472	+	1.51472i	0.0825120	+	0.0825120i	−0.664646	+	0.747158i	$0.731418\pi$
$338$	7.29289	+	7.29289i	0.396681	+	0.396681i
$339$		0			0
$340$		0			0
$341$			42.6274i			2.30840i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−9.07107			−0.489079
$345$		0			0
$346$	11.3137			0.608229
$347$	14.8284	−	14.8284i	0.796032	−	0.796032i	−0.186436	−	0.982467i	$-0.559694\pi$
$347$	14.8284	−	14.8284i	0.796032	−	0.796032i	0.982467	+	0.186436i	$0.0596935\pi$
$348$		0			0
$349$		−	8.72792i		−	0.467195i	−0.972333	−	0.233597i	$-0.924950\pi$
$349$		−	8.72792i		−	0.467195i	0.972333	−	0.233597i	$-0.0750498\pi$
$350$		0			0
$351$		0			0
$352$	−3.41421	−	3.41421i	−0.181978	−	0.181978i
$353$	−15.3848	−	15.3848i	−0.818849	−	0.818849i	0.167092	−	0.985941i	$-0.446562\pi$
$353$	−15.3848	−	15.3848i	−0.818849	−	0.818849i	−0.985941	+	0.167092i	$0.946562\pi$
$354$		0			0
$355$		0			0
$356$			13.3137i			0.705625i
$357$		0			0
$358$	−9.41421	+	9.41421i	−0.497557	+	0.497557i
$359$	20.7279			1.09398			0.546989	−	0.837140i	$-0.315774\pi$
$359$	20.7279			1.09398			0.546989	+	0.837140i	$0.315774\pi$
$360$		0			0
$361$	−31.0000			−1.63158
$362$	7.82843	−	7.82843i	0.411453	−	0.411453i
$363$		0			0
$364$			4.82843i			0.253078i
$365$		0			0
$366$		0			0
$367$	−20.0000	−	20.0000i	−1.04399	−	1.04399i	−0.998987	−	0.0450047i	$-0.985670\pi$
$367$	−20.0000	−	20.0000i	−1.04399	−	1.04399i	−0.0450047	−	0.998987i	$-0.514330\pi$
$368$	4.82843	+	4.82843i	0.251699	+	0.251699i
$369$		0			0
$370$		0			0
$371$		−	6.82843i		−	0.354514i
$372$		0			0
$373$	11.2426	−	11.2426i	0.582122	−	0.582122i	−0.353364	−	0.935486i	$-0.614962\pi$
$373$	11.2426	−	11.2426i	0.582122	−	0.582122i	0.935486	+	0.353364i	$0.114962\pi$
$374$	−10.8284			−0.559925
$375$		0			0
$376$	−9.07107			−0.467805
$377$	−10.8284	+	10.8284i	−0.557692	+	0.557692i
$378$		0			0
$379$		−	5.65685i		−	0.290573i	−0.989390	−	0.145287i	$-0.953590\pi$
$379$		−	5.65685i		−	0.290573i	0.989390	−	0.145287i	$-0.0464104\pi$
$380$		0			0
$381$		0			0
$382$	−9.48528	−	9.48528i	−0.485309	−	0.485309i
$383$	−5.24264	−	5.24264i	−0.267886	−	0.267886i	0.560362	−	0.828248i	$-0.310662\pi$
$383$	−5.24264	−	5.24264i	−0.267886	−	0.267886i	−0.828248	+	0.560362i	$0.810662\pi$
$384$		0			0
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$		0			0
$388$	8.24264	−	8.24264i	0.418457	−	0.418457i
$389$	5.31371			0.269416			0.134708	−	0.990885i	$-0.456990\pi$
$389$	5.31371			0.269416			0.134708	+	0.990885i	$0.456990\pi$
$390$		0			0
$391$	15.3137			0.774448
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$		0			0
$394$		−	4.48528i		−	0.225965i
$395$		0			0
$396$		0			0
$397$	−25.4142	−	25.4142i	−1.27550	−	1.27550i	−0.943158	−	0.332345i	$-0.892160\pi$
$397$	−25.4142	−	25.4142i	−1.27550	−	1.27550i	−0.332345	−	0.943158i	$-0.607840\pi$
$398$	−0.242641	−	0.242641i	−0.0121625	−	0.0121625i
$399$		0			0
$400$		0			0
$401$		−	31.0711i		−	1.55162i	−0.630970	−	0.775808i	$-0.717343\pi$
$401$		−	31.0711i		−	1.55162i	0.630970	−	0.775808i	$-0.282657\pi$
$402$		0			0
$403$	−30.1421	+	30.1421i	−1.50149	+	1.50149i
$404$	4.34315			0.216080
$405$		0			0
$406$	−3.17157			−0.157403
$407$	29.3137	−	29.3137i	1.45303	−	1.45303i
$408$		0			0
$409$		−	37.3137i		−	1.84504i	−0.385944	−	0.922522i	$-0.626124\pi$
$409$		−	37.3137i		−	1.84504i	0.385944	−	0.922522i	$-0.373876\pi$
$410$		0			0
$411$		0			0
$412$	3.41421	+	3.41421i	0.168206	+	0.168206i
$413$	5.65685	+	5.65685i	0.278356	+	0.278356i
$414$		0			0
$415$		0			0
$416$		−	4.82843i		−	0.236733i
$417$		0			0
$418$	24.1421	−	24.1421i	1.18083	−	1.18083i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	28.1421			1.37156			0.685782	−	0.727807i	$-0.259460\pi$
$421$	28.1421			1.37156			0.685782	+	0.727807i	$0.259460\pi$
$422$	−2.48528	+	2.48528i	−0.120982	+	0.120982i
$423$		0			0
$424$			6.82843i			0.331618i
$425$		0			0
$426$		0			0
$427$	−4.65685	−	4.65685i	−0.225361	−	0.225361i
$428$	9.07107	+	9.07107i	0.438467	+	0.438467i
$429$		0			0
$430$		0			0
$431$		−	13.2132i		−	0.636458i	−0.948014	−	0.318229i	$-0.896912\pi$
$431$		−	13.2132i		−	0.636458i	0.948014	−	0.318229i	$-0.103088\pi$
$432$		0			0
$433$	−24.2426	+	24.2426i	−1.16503	+	1.16503i	−0.181667	+	0.983360i	$0.558149\pi$
$433$	−24.2426	+	24.2426i	−1.16503	+	1.16503i	−0.983360	+	0.181667i	$0.941851\pi$
$434$	−8.82843			−0.423778
$435$		0			0
$436$	−20.1421			−0.964633
$437$	−34.1421	+	34.1421i	−1.63324	+	1.63324i
$438$		0			0
$439$			25.7990i			1.23132i	0.788012	+	0.615659i	$0.211110\pi$
$439$			25.7990i			1.23132i	−0.788012	+	0.615659i	$0.788890\pi$
$440$		0			0
$441$		0			0
$442$	−7.65685	−	7.65685i	−0.364199	−	0.364199i
$443$	−24.4853	−	24.4853i	−1.16333	−	1.16333i	−0.983742	−	0.179589i	$-0.942523\pi$
$443$	−24.4853	−	24.4853i	−1.16333	−	1.16333i	−0.179589	−	0.983742i	$-0.557477\pi$
$444$		0			0
$445$		0			0
$446$		−	11.1716i		−	0.528989i
$447$		0			0
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	32.2426			1.52162			0.760812	−	0.648972i	$-0.224801\pi$
$449$	32.2426			1.52162			0.760812	+	0.648972i	$0.224801\pi$
$450$		0			0
$451$	23.3137			1.09780
$452$	−5.41421	+	5.41421i	−0.254663	+	0.254663i
$453$		0			0
$454$			6.14214i			0.288265i
$455$		0			0
$456$		0			0
$457$	−7.51472	−	7.51472i	−0.351524	−	0.351524i	0.509153	−	0.860676i	$-0.329959\pi$
$457$	−7.51472	−	7.51472i	−0.351524	−	0.351524i	−0.860676	+	0.509153i	$0.829959\pi$
$458$	−3.48528	−	3.48528i	−0.162857	−	0.162857i
$459$		0			0
$460$		0			0
$461$		−	37.3137i		−	1.73787i	−0.494924	−	0.868936i	$-0.664804\pi$
$461$		−	37.3137i		−	1.73787i	0.494924	−	0.868936i	$-0.335196\pi$
$462$		0			0
$463$	−5.51472	+	5.51472i	−0.256291	+	0.256291i	−0.823544	−	0.567253i	$-0.808006\pi$
$463$	−5.51472	+	5.51472i	−0.256291	+	0.256291i	0.567253	+	0.823544i	$0.308006\pi$
$464$	3.17157			0.147237
$465$		0			0
$466$	−7.65685			−0.354697
$467$	9.65685	−	9.65685i	0.446866	−	0.446866i	−0.447445	−	0.894311i	$-0.647666\pi$
$467$	9.65685	−	9.65685i	0.446866	−	0.446866i	0.894311	+	0.447445i	$0.147666\pi$
$468$		0			0
$469$			0.585786i			0.0270491i
$470$		0			0
$471$		0			0
$472$	−5.65685	−	5.65685i	−0.260378	−	0.260378i
$473$	30.9706	+	30.9706i	1.42403	+	1.42403i
$474$		0			0
$475$		0			0
$476$		−	2.24264i		−	0.102791i
$477$		0			0
$478$	17.8284	−	17.8284i	0.815453	−	0.815453i
$479$	−9.65685			−0.441233			−0.220616	−	0.975361i	$-0.570807\pi$
$479$	−9.65685			−0.441233			−0.220616	+	0.975361i	$0.570807\pi$
$480$		0			0
$481$	41.4558			1.89022
$482$	5.41421	−	5.41421i	0.246611	−	0.246611i
$483$		0			0
$484$			12.3137i			0.559714i
$485$		0			0
$486$		0			0
$487$	20.0000	+	20.0000i	0.906287	+	0.906287i	0.995970	−	0.0896838i	$-0.0285856\pi$
$487$	20.0000	+	20.0000i	0.906287	+	0.906287i	−0.0896838	+	0.995970i	$0.528586\pi$
$488$	4.65685	+	4.65685i	0.210806	+	0.210806i
$489$		0			0
$490$		0			0
$491$			22.9706i			1.03665i	0.855185	+	0.518323i	$0.173444\pi$
$491$			22.9706i			1.03665i	−0.855185	+	0.518323i	$0.826556\pi$
$492$		0			0
$493$	5.02944	−	5.02944i	0.226514	−	0.226514i
$494$	34.1421			1.53613
$495$		0			0
$496$	8.82843			0.396408
$497$	8.65685	−	8.65685i	0.388313	−	0.388313i
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$		0			0
$501$		0			0
$502$	4.92893	+	4.92893i	0.219989	+	0.219989i
$503$	−20.4142	−	20.4142i	−0.910225	−	0.910225i	0.0860648	−	0.996290i	$-0.472571\pi$
$503$	−20.4142	−	20.4142i	−0.910225	−	0.910225i	−0.996290	+	0.0860648i	$0.972571\pi$
$504$		0			0
$505$		0			0
$506$		−	32.9706i		−	1.46572i
$507$		0			0
$508$	−1.17157	+	1.17157i	−0.0519801	+	0.0519801i
$509$	18.3431			0.813046			0.406523	−	0.913641i	$-0.366741\pi$
$509$	18.3431			0.813046			0.406523	+	0.913641i	$0.366741\pi$
$510$		0			0
$511$	−8.48528			−0.375367
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	9.75736i		−	0.430379i
$515$		0			0
$516$		0			0
$517$	30.9706	+	30.9706i	1.36208	+	1.36208i
$518$	6.07107	+	6.07107i	0.266747	+	0.266747i
$519$		0			0
$520$		0			0
$521$		−	6.97056i		−	0.305386i	−0.988274	−	0.152693i	$-0.951205\pi$
$521$		−	6.97056i		−	0.305386i	0.988274	−	0.152693i	$-0.0487946\pi$
$522$		0			0
$523$	−30.2843	+	30.2843i	−1.32424	+	1.32424i	−0.413930	+	0.910309i	$0.635844\pi$
$523$	−30.2843	+	30.2843i	−1.32424	+	1.32424i	−0.910309	+	0.413930i	$0.864156\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	31.1127			1.35658
$527$	14.0000	−	14.0000i	0.609850	−	0.609850i
$528$		0			0
$529$			23.6274i			1.02728i
$530$		0			0
$531$		0			0
$532$	5.00000	+	5.00000i	0.216777	+	0.216777i
$533$	16.4853	+	16.4853i	0.714057	+	0.714057i
$534$		0			0
$535$		0			0
$536$		−	0.585786i		−	0.0253021i
$537$		0			0
$538$	−15.0711	+	15.0711i	−0.649760	+	0.649760i
$539$	4.82843			0.207975
$540$		0			0
$541$	9.51472			0.409070			0.204535	−	0.978859i	$-0.434432\pi$
$541$	9.51472			0.409070			0.204535	+	0.978859i	$0.434432\pi$
$542$	−5.07107	+	5.07107i	−0.217821	+	0.217821i
$543$		0			0
$544$			2.24264i			0.0961524i
$545$		0			0
$546$		0			0
$547$	23.7279	+	23.7279i	1.01453	+	1.01453i	0.999893	+	0.0146399i	$0.00466018\pi$
$547$	23.7279	+	23.7279i	1.01453	+	1.01453i	0.0146399	+	0.999893i	$0.495340\pi$
$548$	−1.07107	−	1.07107i	−0.0457537	−	0.0457537i
$549$		0			0
$550$		0			0
$551$			22.4264i			0.955397i
$552$		0			0
$553$	−9.41421	+	9.41421i	−0.400333	+	0.400333i
$554$	−25.5563			−1.08579
$555$		0			0
$556$	−0.242641			−0.0102903
$557$	−2.10051	+	2.10051i	−0.0890013	+	0.0890013i	−0.750206	−	0.661204i	$-0.770046\pi$
$557$	−2.10051	+	2.10051i	−0.0890013	+	0.0890013i	0.661204	+	0.750206i	$0.270046\pi$
$558$		0			0
$559$			43.7990i			1.85250i
$560$		0			0
$561$		0			0
$562$	9.14214	+	9.14214i	0.385638	+	0.385638i
$563$	−20.1421	−	20.1421i	−0.848890	−	0.848890i	0.141105	−	0.989995i	$-0.454935\pi$
$563$	−20.1421	−	20.1421i	−0.848890	−	0.848890i	−0.989995	+	0.141105i	$0.954935\pi$
$564$		0			0
$565$		0			0
$566$			25.4558i			1.06999i
$567$		0			0
$568$	−8.65685	+	8.65685i	−0.363234	+	0.363234i
$569$	10.3848			0.435352			0.217676	−	0.976021i	$-0.430152\pi$
$569$	10.3848			0.435352			0.217676	+	0.976021i	$0.430152\pi$
$570$		0			0
$571$	8.97056			0.375406			0.187703	−	0.982226i	$-0.439896\pi$
$571$	8.97056			0.375406			0.187703	+	0.982226i	$0.439896\pi$
$572$	−16.4853	+	16.4853i	−0.689284	+	0.689284i
$573$		0			0
$574$			4.82843i			0.201535i
$575$		0			0
$576$		0			0
$577$	−11.1716	−	11.1716i	−0.465079	−	0.465079i	0.435237	−	0.900316i	$-0.356665\pi$
$577$	−11.1716	−	11.1716i	−0.465079	−	0.465079i	−0.900316	+	0.435237i	$0.856665\pi$
$578$	−8.46447	−	8.46447i	−0.352075	−	0.352075i
$579$		0			0
$580$		0			0
$581$		−	13.6569i		−	0.566582i
$582$		0			0
$583$	23.3137	−	23.3137i	0.965555	−	0.965555i
$584$	8.48528			0.351123
$585$		0			0
$586$	31.7990			1.31360
$587$	14.0000	−	14.0000i	0.577842	−	0.577842i	−0.356466	−	0.934308i	$-0.616019\pi$
$587$	14.0000	−	14.0000i	0.577842	−	0.577842i	0.934308	+	0.356466i	$0.116019\pi$
$588$		0			0
$589$			62.4264i			2.57224i
$590$		0			0
$591$		0			0
$592$	−6.07107	−	6.07107i	−0.249519	−	0.249519i
$593$	14.4142	+	14.4142i	0.591921	+	0.591921i	0.938150	−	0.346229i	$-0.112538\pi$
$593$	14.4142	+	14.4142i	0.591921	+	0.591921i	−0.346229	+	0.938150i	$0.612538\pi$
$594$		0			0
$595$		0			0
$596$		−	5.31371i		−	0.217658i
$597$		0			0
$598$	23.3137	−	23.3137i	0.953368	−	0.953368i
$599$	−4.92893			−0.201391			−0.100695	−	0.994917i	$-0.532107\pi$
$599$	−4.92893			−0.201391			−0.100695	+	0.994917i	$0.532107\pi$
$600$		0			0
$601$	−18.0000			−0.734235			−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000			−0.734235			−0.367118	+	0.930175i	$0.619655\pi$
$602$	−6.41421	+	6.41421i	−0.261424	+	0.261424i
$603$		0			0
$604$			13.3137i			0.541727i
$605$		0			0
$606$		0			0
$607$	−12.3848	−	12.3848i	−0.502683	−	0.502683i	0.409588	−	0.912271i	$-0.365672\pi$
$607$	−12.3848	−	12.3848i	−0.502683	−	0.502683i	−0.912271	+	0.409588i	$0.865672\pi$
$608$	−5.00000	−	5.00000i	−0.202777	−	0.202777i
$609$		0			0
$610$		0			0
$611$			43.7990i			1.77192i
$612$		0			0
$613$	−3.58579	+	3.58579i	−0.144829	+	0.144829i	−0.775803	−	0.630975i	$-0.782655\pi$
$613$	−3.58579	+	3.58579i	−0.144829	+	0.144829i	0.630975	+	0.775803i	$0.282655\pi$
$614$	−10.6274			−0.428888
$615$		0			0
$616$	−4.82843			−0.194543
$617$	−24.5858	+	24.5858i	−0.989786	+	0.989786i	−0.999948	−	0.0101619i	$-0.996765\pi$
$617$	−24.5858	+	24.5858i	−0.989786	+	0.989786i	0.0101619	+	0.999948i	$0.496765\pi$
$618$		0			0
$619$			34.8701i			1.40155i	0.713384	+	0.700773i	$0.247161\pi$
$619$			34.8701i			1.40155i	−0.713384	+	0.700773i	$0.752839\pi$
$620$		0			0
$621$		0			0
$622$	11.3137	+	11.3137i	0.453638	+	0.453638i
$623$	9.41421	+	9.41421i	0.377173	+	0.377173i
$624$		0			0
$625$		0			0
$626$			27.7990i			1.11107i
$627$		0			0
$628$	−2.58579	+	2.58579i	−0.103184	+	0.103184i
$629$	−19.2548			−0.767741
$630$		0			0
$631$	4.97056			0.197875			0.0989375	−	0.995094i	$-0.468456\pi$
$631$	4.97056			0.197875			0.0989375	+	0.995094i	$0.468456\pi$
$632$	9.41421	−	9.41421i	0.374477	−	0.374477i
$633$		0			0
$634$		−	17.3137i		−	0.687615i
$635$		0			0
$636$		0			0
$637$	3.41421	+	3.41421i	0.135276	+	0.135276i
$638$	−10.8284	−	10.8284i	−0.428702	−	0.428702i
$639$		0			0
$640$		0			0
$641$		−	40.5269i		−	1.60072i	−0.599522	−	0.800358i	$-0.704643\pi$
$641$		−	40.5269i		−	1.60072i	0.599522	−	0.800358i	$-0.295357\pi$
$642$		0			0
$643$	0.142136	−	0.142136i	0.00560528	−	0.00560528i	−0.704299	−	0.709904i	$-0.748738\pi$
$643$	0.142136	−	0.142136i	0.00560528	−	0.00560528i	0.709904	+	0.704299i	$0.248738\pi$
$644$	6.82843			0.269078
$645$		0			0
$646$	−15.8579			−0.623919
$647$	−18.2132	+	18.2132i	−0.716035	+	0.716035i	−0.967791	−	0.251756i	$-0.918992\pi$
$647$	−18.2132	+	18.2132i	−0.716035	+	0.716035i	0.251756	+	0.967791i	$0.418992\pi$
$648$		0			0
$649$			38.6274i			1.51626i
$650$		0			0
$651$		0			0
$652$	4.89949	+	4.89949i	0.191879	+	0.191879i
$653$	−2.58579	−	2.58579i	−0.101190	−	0.101190i	0.654700	−	0.755889i	$-0.272795\pi$
$653$	−2.58579	−	2.58579i	−0.101190	−	0.101190i	−0.755889	+	0.654700i	$0.772795\pi$
$654$		0			0
$655$		0			0
$656$		−	4.82843i		−	0.188518i
$657$		0			0
$658$	−6.41421	+	6.41421i	−0.250052	+	0.250052i
$659$	17.7990			0.693350			0.346675	−	0.937985i	$-0.387311\pi$
$659$	17.7990			0.693350			0.346675	+	0.937985i	$0.387311\pi$
$660$		0			0
$661$	−27.7574			−1.07964			−0.539818	−	0.841782i	$-0.681507\pi$
$661$	−27.7574			−1.07964			−0.539818	+	0.841782i	$0.681507\pi$
$662$	1.31371	−	1.31371i	0.0510587	−	0.0510587i
$663$		0			0
$664$			13.6569i			0.529989i
$665$		0			0
$666$		0			0
$667$	15.3137	+	15.3137i	0.592949	+	0.592949i
$668$	−6.89949	−	6.89949i	−0.266949	−	0.266949i
$669$		0			0
$670$		0			0
$671$		−	31.7990i		−	1.22759i
$672$		0			0
$673$	13.7990	−	13.7990i	0.531912	−	0.531912i	−0.389229	−	0.921141i	$-0.627259\pi$
$673$	13.7990	−	13.7990i	0.531912	−	0.531912i	0.921141	+	0.389229i	$0.127259\pi$
$674$	−2.14214			−0.0825120
$675$		0			0
$676$	−10.3137			−0.396681
$677$	−7.51472	+	7.51472i	−0.288814	+	0.288814i	−0.836611	−	0.547797i	$-0.815467\pi$
$677$	−7.51472	+	7.51472i	−0.288814	+	0.288814i	0.547797	+	0.836611i	$0.315467\pi$
$678$		0			0
$679$		−	11.6569i		−	0.447349i
$680$		0			0
$681$		0			0
$682$	−30.1421	−	30.1421i	−1.15420	−	1.15420i
$683$	−3.89949	−	3.89949i	−0.149210	−	0.149210i	0.628555	−	0.777765i	$-0.283647\pi$
$683$	−3.89949	−	3.89949i	−0.149210	−	0.149210i	−0.777765	+	0.628555i	$0.783647\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	6.41421	−	6.41421i	0.244540	−	0.244540i
$689$	32.9706			1.25608
$690$		0			0
$691$	−17.2132			−0.654821			−0.327411	−	0.944882i	$-0.606176\pi$
$691$	−17.2132			−0.654821			−0.327411	+	0.944882i	$0.606176\pi$
$692$	−8.00000	+	8.00000i	−0.304114	+	0.304114i
$693$		0			0
$694$			20.9706i			0.796032i
$695$		0			0
$696$		0			0
$697$	−7.65685	−	7.65685i	−0.290024	−	0.290024i
$698$	6.17157	+	6.17157i	0.233597	+	0.233597i
$699$		0			0
$700$		0			0
$701$			26.4853i			1.00034i	0.865929	+	0.500168i	$0.166728\pi$
$701$			26.4853i			1.00034i	−0.865929	+	0.500168i	$0.833272\pi$
$702$		0			0
$703$	42.9289	−	42.9289i	1.61910	−	1.61910i
$704$	4.82843			0.181978
$705$		0			0
$706$	21.7574			0.818849
$707$	3.07107	−	3.07107i	0.115499	−	0.115499i
$708$		0			0
$709$			5.31371i			0.199561i	0.995009	+	0.0997803i	$0.0318140\pi$
$709$			5.31371i			0.199561i	−0.995009	+	0.0997803i	$0.968186\pi$
$710$		0			0
$711$		0			0
$712$	−9.41421	−	9.41421i	−0.352813	−	0.352813i
$713$	42.6274	+	42.6274i	1.59641	+	1.59641i
$714$		0			0
$715$		0			0
$716$		−	13.3137i		−	0.497557i
$717$		0			0
$718$	−14.6569	+	14.6569i	−0.546989	+	0.546989i
$719$	−5.45584			−0.203469			−0.101734	−	0.994812i	$-0.532439\pi$
$719$	−5.45584			−0.203469			−0.101734	+	0.994812i	$0.532439\pi$
$720$		0			0
$721$	4.82843			0.179820
$722$	21.9203	−	21.9203i	0.815789	−	0.815789i
$723$		0			0
$724$			11.0711i			0.411453i
$725$		0			0
$726$		0			0
$727$	−10.2426	−	10.2426i	−0.379879	−	0.379879i	0.491180	−	0.871058i	$-0.336566\pi$
$727$	−10.2426	−	10.2426i	−0.379879	−	0.379879i	−0.871058	+	0.491180i	$0.836566\pi$
$728$	−3.41421	−	3.41421i	−0.126539	−	0.126539i
$729$		0			0
$730$		0			0
$731$		−	20.3431i		−	0.752418i
$732$		0			0
$733$	20.7279	−	20.7279i	0.765603	−	0.765603i	−0.211726	−	0.977329i	$-0.567908\pi$
$733$	20.7279	−	20.7279i	0.765603	−	0.765603i	0.977329	+	0.211726i	$0.0679084\pi$
$734$	28.2843			1.04399
$735$		0			0
$736$	−6.82843			−0.251699
$737$	−2.00000	+	2.00000i	−0.0736709	+	0.0736709i
$738$		0			0
$739$			2.62742i			0.0966511i	0.998832	+	0.0483255i	$0.0153885\pi$
$739$			2.62742i			0.0966511i	−0.998832	+	0.0483255i	$0.984612\pi$
$740$		0			0
$741$		0			0
$742$	4.82843	+	4.82843i	0.177257	+	0.177257i
$743$	18.1421	+	18.1421i	0.665570	+	0.665570i	0.956687	−	0.291117i	$-0.0940269\pi$
$743$	18.1421	+	18.1421i	0.665570	+	0.665570i	−0.291117	+	0.956687i	$0.594027\pi$
$744$		0			0
$745$		0			0
$746$			15.8995i			0.582122i
$747$		0			0
$748$	7.65685	−	7.65685i	0.279962	−	0.279962i
$749$	12.8284			0.468741
$750$		0			0
$751$	44.9706			1.64100			0.820500	−	0.571647i	$-0.193695\pi$
$751$	44.9706			1.64100			0.820500	+	0.571647i	$0.193695\pi$
$752$	6.41421	−	6.41421i	0.233902	−	0.233902i
$753$		0			0
$754$		−	15.3137i		−	0.557692i
$755$		0			0
$756$		0			0
$757$	24.0711	+	24.0711i	0.874878	+	0.874878i	0.992999	−	0.118121i	$-0.0376872\pi$
$757$	24.0711	+	24.0711i	0.874878	+	0.874878i	−0.118121	+	0.992999i	$0.537687\pi$
$758$	4.00000	+	4.00000i	0.145287	+	0.145287i
$759$		0			0
$760$		0			0
$761$		−	15.6569i		−	0.567561i	−0.958889	−	0.283780i	$-0.908411\pi$
$761$		−	15.6569i		−	0.567561i	0.958889	−	0.283780i	$-0.0915886\pi$
$762$		0			0
$763$	−14.2426	+	14.2426i	−0.515618	+	0.515618i
$764$	13.4142			0.485309
$765$		0			0
$766$	7.41421			0.267886
$767$	−27.3137	+	27.3137i	−0.986241	+	0.986241i
$768$		0			0
$769$			12.1421i			0.437857i	0.975741	+	0.218928i	$0.0702561\pi$
$769$			12.1421i			0.437857i	−0.975741	+	0.218928i	$0.929744\pi$
$770$		0			0
$771$		0			0
$772$	6.00000	+	6.00000i	0.215945	+	0.215945i
$773$	−31.9411	−	31.9411i	−1.14884	−	1.14884i	−0.986781	−	0.162062i	$-0.948186\pi$
$773$	−31.9411	−	31.9411i	−1.14884	−	1.14884i	−0.162062	−	0.986781i	$-0.551814\pi$
$774$		0			0
$775$		0			0
$776$			11.6569i			0.418457i
$777$		0			0
$778$	−3.75736	+	3.75736i	−0.134708	+	0.134708i
$779$	34.1421			1.22327
$780$		0			0
$781$	59.1127			2.11522
$782$	−10.8284	+	10.8284i	−0.387224	+	0.387224i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	−35.3137	−	35.3137i	−1.25880	−	1.25880i	−0.951667	−	0.307130i	$-0.900631\pi$
$787$	−35.3137	−	35.3137i	−1.25880	−	1.25880i	−0.307130	−	0.951667i	$-0.599369\pi$
$788$	3.17157	+	3.17157i	0.112983	+	0.112983i
$789$		0			0
$790$		0			0
$791$			7.65685i			0.272246i
$792$		0			0
$793$	22.4853	−	22.4853i	0.798476	−	0.798476i
$794$	35.9411			1.27550
$795$		0			0
$796$	0.343146			0.0121625
$797$	3.79899	−	3.79899i	0.134567	−	0.134567i	−0.636615	−	0.771182i	$-0.719666\pi$
$797$	3.79899	−	3.79899i	0.134567	−	0.134567i	0.771182	+	0.636615i	$0.219666\pi$
$798$		0			0
$799$		−	20.3431i		−	0.719689i
$800$		0			0
$801$		0			0
$802$	21.9706	+	21.9706i	0.775808	+	0.775808i
$803$	−28.9706	−	28.9706i	−1.02235	−	1.02235i
$804$		0			0
$805$		0			0
$806$		−	42.6274i		−	1.50149i
$807$		0			0
$808$	−3.07107	+	3.07107i	−0.108040	+	0.108040i
$809$	−9.69848			−0.340981			−0.170490	−	0.985359i	$-0.554535\pi$
$809$	−9.69848			−0.340981			−0.170490	+	0.985359i	$0.554535\pi$
$810$		0			0
$811$	−23.7574			−0.834234			−0.417117	−	0.908853i	$-0.636959\pi$
$811$	−23.7574			−0.834234			−0.417117	+	0.908853i	$0.636959\pi$
$812$	2.24264	−	2.24264i	0.0787013	−	0.0787013i
$813$		0			0
$814$			41.4558i			1.45303i
$815$		0			0
$816$		0			0
$817$	45.3553	+	45.3553i	1.58678	+	1.58678i
$818$	26.3848	+	26.3848i	0.922522	+	0.922522i
$819$		0			0
$820$		0			0
$821$		−	11.8579i		−	0.413842i	−0.978358	−	0.206921i	$-0.933656\pi$
$821$		−	11.8579i		−	0.413842i	0.978358	−	0.206921i	$-0.0663444\pi$
$822$		0			0
$823$	−14.6863	+	14.6863i	−0.511932	+	0.511932i	−0.915118	−	0.403186i	$-0.867903\pi$
$823$	−14.6863	+	14.6863i	−0.511932	+	0.511932i	0.403186	+	0.915118i	$0.367903\pi$
$824$	−4.82843			−0.168206
$825$		0			0
$826$	−8.00000			−0.278356
$827$	5.17157	−	5.17157i	0.179833	−	0.179833i	−0.611450	−	0.791283i	$-0.709413\pi$
$827$	5.17157	−	5.17157i	0.179833	−	0.179833i	0.791283	+	0.611450i	$0.209413\pi$
$828$		0			0
$829$			18.8701i			0.655384i	0.944785	+	0.327692i	$0.106271\pi$
$829$			18.8701i			0.655384i	−0.944785	+	0.327692i	$0.893729\pi$
$830$		0			0
$831$		0			0
$832$	3.41421	+	3.41421i	0.118367	+	0.118367i
$833$	−1.58579	−	1.58579i	−0.0549442	−	0.0549442i
$834$		0			0
$835$		0			0
$836$			34.1421i			1.18083i
$837$		0			0
$838$	−14.1421	+	14.1421i	−0.488532	+	0.488532i
$839$	26.8284			0.926220			0.463110	−	0.886301i	$-0.346733\pi$
$839$	26.8284			0.926220			0.463110	+	0.886301i	$0.346733\pi$
$840$		0			0
$841$	−18.9411			−0.653142
$842$	−19.8995	+	19.8995i	−0.685782	+	0.685782i
$843$		0			0
$844$		−	3.51472i		−	0.120982i
$845$		0			0
$846$		0			0
$847$	8.70711	+	8.70711i	0.299180	+	0.299180i
$848$	−4.82843	−	4.82843i	−0.165809	−	0.165809i
$849$		0			0
$850$		0			0
$851$		−	58.6274i		−	2.00972i
$852$		0			0
$853$	3.55635	−	3.55635i	0.121767	−	0.121767i	−0.643597	−	0.765364i	$-0.722559\pi$
$853$	3.55635	−	3.55635i	0.121767	−	0.121767i	0.765364	+	0.643597i	$0.222559\pi$
$854$	6.58579			0.225361
$855$		0			0
$856$	−12.8284			−0.438467
$857$	−27.0416	+	27.0416i	−0.923725	+	0.923725i	−0.997290	−	0.0735659i	$-0.976562\pi$
$857$	−27.0416	+	27.0416i	−0.923725	+	0.923725i	0.0735659	+	0.997290i	$0.476562\pi$
$858$		0			0
$859$			15.2721i			0.521077i	0.965464	+	0.260538i	$0.0839000\pi$
$859$			15.2721i			0.521077i	−0.965464	+	0.260538i	$0.916100\pi$
$860$		0			0
$861$		0			0
$862$	9.34315	+	9.34315i	0.318229	+	0.318229i
$863$	−18.6274	−	18.6274i	−0.634085	−	0.634085i	0.315005	−	0.949090i	$-0.397994\pi$
$863$	−18.6274	−	18.6274i	−0.634085	−	0.634085i	−0.949090	+	0.315005i	$0.897994\pi$
$864$		0			0
$865$		0			0
$866$		−	34.2843i		−	1.16503i
$867$		0			0
$868$	6.24264	−	6.24264i	0.211889	−	0.211889i
$869$	−64.2843			−2.18069
$870$		0			0
$871$	−2.82843			−0.0958376
$872$	14.2426	−	14.2426i	0.482317	−	0.482317i
$873$		0			0
$874$		−	48.2843i		−	1.63324i
$875$		0			0
$876$		0			0
$877$	−19.7279	−	19.7279i	−0.666165	−	0.666165i	0.290661	−	0.956826i	$-0.406125\pi$
$877$	−19.7279	−	19.7279i	−0.666165	−	0.666165i	−0.956826	+	0.290661i	$0.906125\pi$
$878$	−18.2426	−	18.2426i	−0.615659	−	0.615659i
$879$		0			0
$880$		0			0
$881$			42.4853i			1.43137i	0.698426	+	0.715683i	$0.253884\pi$
$881$			42.4853i			1.43137i	−0.698426	+	0.715683i	$0.746116\pi$
$882$		0			0
$883$	−38.8995	+	38.8995i	−1.30907	+	1.30907i	−0.386987	+	0.922085i	$0.626484\pi$
$883$	−38.8995	+	38.8995i	−1.30907	+	1.30907i	−0.922085	+	0.386987i	$0.873516\pi$
$884$	10.8284			0.364199
$885$		0			0
$886$	34.6274			1.16333
$887$	0.615224	−	0.615224i	0.0206572	−	0.0206572i	−0.696703	−	0.717360i	$-0.745350\pi$
$887$	0.615224	−	0.615224i	0.0206572	−	0.0206572i	0.717360	+	0.696703i	$0.245350\pi$
$888$		0			0
$889$			1.65685i			0.0555691i
$890$		0			0
$891$		0			0
$892$	7.89949	+	7.89949i	0.264495	+	0.264495i
$893$	45.3553	+	45.3553i	1.51776	+	1.51776i
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−22.7990	+	22.7990i	−0.760812	+	0.760812i
$899$	28.0000			0.933852
$900$		0			0
$901$	−15.3137			−0.510174
$902$	−16.4853	+	16.4853i	−0.548900	+	0.548900i
$903$		0			0
$904$		−	7.65685i		−	0.254663i
$905$		0			0
$906$		0			0
$907$	−2.75736	−	2.75736i	−0.0915566	−	0.0915566i	0.659845	−	0.751402i	$-0.270622\pi$
$907$	−2.75736	−	2.75736i	−0.0915566	−	0.0915566i	−0.751402	+	0.659845i	$0.770622\pi$
$908$	−4.34315	−	4.34315i	−0.144132	−	0.144132i
$909$		0			0
$910$		0			0
$911$		−	10.1005i		−	0.334645i	−0.985902	−	0.167322i	$-0.946488\pi$
$911$		−	10.1005i		−	0.334645i	0.985902	−	0.167322i	$-0.0535121\pi$
$912$		0			0
$913$	46.6274	−	46.6274i	1.54314	−	1.54314i
$914$	10.6274			0.351524
$915$		0			0
$916$	4.92893			0.162857
$917$	−4.24264	+	4.24264i	−0.140104	+	0.140104i
$918$		0			0
$919$		−	31.3137i		−	1.03294i	−0.856304	−	0.516472i	$-0.827245\pi$
$919$		−	31.3137i		−	1.03294i	0.856304	−	0.516472i	$-0.172755\pi$
$920$		0			0
$921$		0			0
$922$	26.3848	+	26.3848i	0.868936	+	0.868936i
$923$	41.7990	+	41.7990i	1.37583	+	1.37583i
$924$		0			0
$925$		0			0
$926$		−	7.79899i		−	0.256291i
$927$		0			0
$928$	−2.24264	+	2.24264i	−0.0736183	+	0.0736183i
$929$	−12.3431			−0.404965			−0.202483	−	0.979286i	$-0.564901\pi$
$929$	−12.3431			−0.404965			−0.202483	+	0.979286i	$0.564901\pi$
$930$		0			0
$931$	7.07107			0.231745
$932$	5.41421	−	5.41421i	0.177348	−	0.177348i
$933$		0			0
$934$			13.6569i			0.446866i
$935$		0			0
$936$		0			0
$937$	−31.0711	−	31.0711i	−1.01505	−	1.01505i	−0.999885	−	0.0151625i	$-0.995173\pi$
$937$	−31.0711	−	31.0711i	−1.01505	−	1.01505i	−0.0151625	−	0.999885i	$-0.504827\pi$
$938$	−0.414214	−	0.414214i	−0.0135246	−	0.0135246i
$939$		0			0
$940$		0			0
$941$		−	9.31371i		−	0.303618i	−0.988410	−	0.151809i	$-0.951490\pi$
$941$		−	9.31371i		−	0.303618i	0.988410	−	0.151809i	$-0.0485099\pi$
$942$		0			0
$943$	23.3137	−	23.3137i	0.759199	−	0.759199i
$944$	8.00000			0.260378
$945$		0			0
$946$	−43.7990			−1.42403
$947$	−11.4142	+	11.4142i	−0.370912	+	0.370912i	−0.867809	−	0.496897i	$-0.834473\pi$
$947$	−11.4142	+	11.4142i	−0.370912	+	0.370912i	0.496897	+	0.867809i	$0.334473\pi$
$948$		0			0
$949$		−	40.9706i		−	1.32996i
$950$		0			0
$951$		0			0
$952$	1.58579	+	1.58579i	0.0513956	+	0.0513956i
$953$	40.3848	+	40.3848i	1.30819	+	1.30819i	0.922720	+	0.385471i	$0.125961\pi$
$953$	40.3848	+	40.3848i	1.30819	+	1.30819i	0.385471	+	0.922720i	$0.374039\pi$
$954$		0			0
$955$		0			0
$956$			25.2132i			0.815453i
$957$		0			0
$958$	6.82843	−	6.82843i	0.220616	−	0.220616i
$959$	−1.51472			−0.0489128
$960$		0			0
$961$	46.9411			1.51423
$962$	−29.3137	+	29.3137i	−0.945112	+	0.945112i
$963$		0			0
$964$			7.65685i			0.246611i
$965$		0			0
$966$		0			0
$967$	7.02944	+	7.02944i	0.226051	+	0.226051i	0.811041	−	0.584989i	$-0.198901\pi$
$967$	7.02944	+	7.02944i	0.226051	+	0.226051i	−0.584989	+	0.811041i	$0.698901\pi$
$968$	−8.70711	−	8.70711i	−0.279857	−	0.279857i
$969$		0			0
$970$		0			0
$971$			35.6569i			1.14428i	0.820155	+	0.572141i	$0.193887\pi$
$971$			35.6569i			1.14428i	−0.820155	+	0.572141i	$0.806113\pi$
$972$		0			0
$973$	−0.171573	+	0.171573i	−0.00550037	+	0.00550037i
$974$	−28.2843			−0.906287
$975$		0			0
$976$	−6.58579			−0.210806
$977$	38.3848	−	38.3848i	1.22804	−	1.22804i	0.263333	−	0.964705i	$-0.415178\pi$
$977$	38.3848	−	38.3848i	1.22804	−	1.22804i	0.964705	−	0.263333i	$-0.0848217\pi$
$978$		0			0
$979$			64.2843i			2.05453i
$980$		0			0
$981$		0			0
$982$	−16.2426	−	16.2426i	−0.518323	−	0.518323i
$983$	21.5858	+	21.5858i	0.688480	+	0.688480i	0.961896	−	0.273416i	$-0.0881536\pi$
$983$	21.5858	+	21.5858i	0.688480	+	0.688480i	−0.273416	+	0.961896i	$0.588154\pi$
$984$		0			0
$985$		0			0
$986$			7.11270i			0.226514i
$987$		0			0
$988$	−24.1421	+	24.1421i	−0.768064	+	0.768064i
$989$	61.9411			1.96961
$990$		0			0
$991$	−0.686292			−0.0218008			−0.0109004	−	0.999941i	$-0.503470\pi$
$991$	−0.686292			−0.0218008			−0.0109004	+	0.999941i	$0.503470\pi$
$992$	−6.24264	+	6.24264i	−0.198204	+	0.198204i
$993$		0			0
$994$			12.2426i			0.388313i
$995$		0			0
$996$		0			0
$997$	28.5269	+	28.5269i	0.903456	+	0.903456i	0.995733	−	0.0922770i	$-0.0294145\pi$
$997$	28.5269	+	28.5269i	0.903456	+	0.903456i	−0.0922770	+	0.995733i	$0.529415\pi$
$998$	16.9706	+	16.9706i	0.537194	+	0.537194i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.f.1457.1	yes	4
3.2	odd	2		3150.2.m.e.1457.2	yes	4
5.2	odd	4		3150.2.m.c.2843.1	yes	4
5.3	odd	4		3150.2.m.e.2843.2	yes	4
5.4	even	2		3150.2.m.d.1457.2	yes	4
15.2	even	4		3150.2.m.d.2843.2	yes	4
15.8	even	4	inner	3150.2.m.f.2843.1	yes	4
15.14	odd	2		3150.2.m.c.1457.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.c.1457.1	✓	4	15.14	odd	2
3150.2.m.c.2843.1	yes	4	5.2	odd	4
3150.2.m.d.1457.2	yes	4	5.4	even	2
3150.2.m.d.2843.2	yes	4	15.2	even	4
3150.2.m.e.1457.2	yes	4	3.2	odd	2
3150.2.m.e.2843.2	yes	4	5.3	odd	4
3150.2.m.f.1457.1	yes	4	1.1	even	1	trivial
3150.2.m.f.2843.1	yes	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -4.82843i q^{11} +(3.41421 - 3.41421i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.58579 + 1.58579i) q^{17} -7.07107i q^{19} +(3.41421 + 3.41421i) q^{22} +(-4.82843 - 4.82843i) q^{23} +4.82843i q^{26} +(-0.707107 + 0.707107i) q^{28} -3.17157 q^{29} -8.82843 q^{31} +(0.707107 - 0.707107i) q^{32} -2.24264i q^{34} +(6.07107 + 6.07107i) q^{37} +(5.00000 + 5.00000i) q^{38} +4.82843i q^{41} +(-6.41421 + 6.41421i) q^{43} -4.82843 q^{44} +6.82843 q^{46} +(-6.41421 + 6.41421i) q^{47} +1.00000i q^{49} +(-3.41421 - 3.41421i) q^{52} +(4.82843 + 4.82843i) q^{53} -1.00000i q^{56} +(2.24264 - 2.24264i) q^{58} -8.00000 q^{59} +6.58579 q^{61} +(6.24264 - 6.24264i) q^{62} +1.00000i q^{64} +(-0.414214 - 0.414214i) q^{67} +(1.58579 + 1.58579i) q^{68} +12.2426i q^{71} +(6.00000 - 6.00000i) q^{73} -8.58579 q^{74} -7.07107 q^{76} +(-3.41421 + 3.41421i) q^{77} -13.3137i q^{79} +(-3.41421 - 3.41421i) q^{82} +(9.65685 + 9.65685i) q^{83} -9.07107i q^{86} +(3.41421 - 3.41421i) q^{88} -13.3137 q^{89} -4.82843 q^{91} +(-4.82843 + 4.82843i) q^{92} -9.07107i q^{94} +(8.24264 + 8.24264i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 8 q^{13} + 4 q^{14} - 4 q^{16} - 12 q^{17} + 8 q^{22} - 8 q^{23} - 24 q^{29} - 24 q^{31} - 4 q^{37} + 20 q^{38} - 20 q^{43} - 8 q^{44} + 16 q^{46} - 20 q^{47} - 8 q^{52} + 8 q^{53} - 8 q^{58} - 32 q^{59} + 32 q^{61} + 8 q^{62} + 4 q^{67} + 12 q^{68} + 24 q^{73} - 40 q^{74} - 8 q^{77} - 8 q^{82} + 16 q^{83} + 8 q^{88} - 8 q^{89} - 8 q^{91} - 8 q^{92} + 16 q^{97}+O(q^{100}) \) 4 * q + 8 * q^13 + 4 * q^14 - 4 * q^16 - 12 * q^17 + 8 * q^22 - 8 * q^23 - 24 * q^29 - 24 * q^31 - 4 * q^37 + 20 * q^38 - 20 * q^43 - 8 * q^44 + 16 * q^46 - 20 * q^47 - 8 * q^52 + 8 * q^53 - 8 * q^58 - 32 * q^59 + 32 * q^61 + 8 * q^62 + 4 * q^67 + 12 * q^68 + 24 * q^73 - 40 * q^74 - 8 * q^77 - 8 * q^82 + 16 * q^83 + 8 * q^88 - 8 * q^89 - 8 * q^91 - 8 * q^92 + 16 * q^97

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