LMFDB - Embedded newform 3150.2.m.c.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.c.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	$0.259509\pi$
$11$			4.82843i			1.45583i	−0.685670	+	0.727913i	$0.740491\pi$
$12$		0			0
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	−0.998661	−	0.0517287i	$-0.983527\pi$
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	0.0517287	+	0.998661i	$0.483527\pi$
$14$	−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	$-0.404856\pi$
$29$	3.17157			0.588946			0.294473	+	0.955660i	$0.404856\pi$
$30$		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	0.00192076	−	0.999998i	$-0.499389\pi$
$37$	−6.07107	−	6.07107i	−0.998077	−	0.998077i	−0.999998	+	0.00192076i	$0.999389\pi$
$38$	5.00000	+	5.00000i	0.811107	+	0.811107i
$39$		0			0
$40$		0			0
$41$		−	4.82843i		−	0.754074i	−0.926198	−	0.377037i	$-0.876943\pi$
$41$		−	4.82843i		−	0.754074i	0.926198	−	0.377037i	$-0.123057\pi$
$42$		0			0
$43$	6.41421	−	6.41421i	0.978158	−	0.978158i	−0.0216081	−	0.999767i	$-0.506879\pi$
$43$	6.41421	−	6.41421i	0.978158	−	0.978158i	0.999767	+	0.0216081i	$0.00687861\pi$
$44$	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	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$		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	0.731956	−	0.681352i	$-0.238608\pi$
$67$	0.414214	+	0.414214i	0.0506042	+	0.0506042i	−0.681352	+	0.731956i	$0.738608\pi$
$68$	1.58579	+	1.58579i	0.192305	+	0.192305i
$69$		0			0
$70$		0			0
$71$		−	12.2426i		−	1.45293i	−0.687201	−	0.726467i	$-0.741161\pi$
$71$		−	12.2426i		−	1.45293i	0.687201	−	0.726467i	$-0.258839\pi$
$72$		0			0
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	−0.964892	−	0.262646i	$-0.915405\pi$
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	0.262646	+	0.964892i	$0.415405\pi$
$74$	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	$-0.250666\pi$
$89$	13.3137			1.41125			0.705625	+	0.708585i	$0.250666\pi$
$90$		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	0.151538	−	0.988451i	$-0.451577\pi$
$97$	−8.24264	−	8.24264i	−0.836913	−	0.836913i	−0.988451	+	0.151538i	$0.951577\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	4.34315i		−	0.432159i	−0.976376	−	0.216080i	$-0.930673\pi$
$101$		−	4.34315i		−	0.432159i	0.976376	−	0.216080i	$-0.0693271\pi$
$102$		0			0
$103$	3.41421	−	3.41421i	0.336412	−	0.336412i	−0.518603	−	0.855015i	$-0.673548\pi$
$103$	3.41421	−	3.41421i	0.336412	−	0.336412i	0.855015	+	0.518603i	$0.173548\pi$
$104$	−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	0.757174	−	0.653213i	$-0.226580\pi$
$127$	1.17157	+	1.17157i	0.103960	+	0.103960i	−0.653213	+	0.757174i	$0.726580\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			6.00000i			0.524222i	0.965038	+	0.262111i	$0.0844187\pi$
$131$			6.00000i			0.524222i	−0.965038	+	0.262111i	$0.915581\pi$
$132$		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	$-0.569842\pi$
$149$	−5.31371			−0.435316			−0.217658	+	0.976025i	$0.569842\pi$
$150$		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	0.802722	−	0.596354i	$-0.203384\pi$
$157$	2.58579	+	2.58579i	0.206368	+	0.206368i	−0.596354	+	0.802722i	$0.703384\pi$
$158$	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	−0.488696	−	0.872454i	$-0.662527\pi$
$163$	4.89949	−	4.89949i	0.383758	−	0.383758i	0.872454	+	0.488696i	$0.162527\pi$
$164$	−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	$-0.665769\pi$
$179$	−13.3137			−0.995113			−0.497557	+	0.867431i	$0.665769\pi$
$180$		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	$-0.838707\pi$
$191$		−	13.4142i		−	0.970618i	0.874343	−	0.485309i	$-0.161293\pi$
$192$		0			0
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	0.889271	+	0.457381i	$0.151213\pi$
$194$	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	−0.391282	−	0.920271i	$-0.627968\pi$
$223$	7.89949	−	7.89949i	0.528989	−	0.528989i	0.920271	+	0.391282i	$0.127968\pi$
$224$	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	$-0.196488\pi$
$239$	25.2132			1.63091			0.815453	+	0.578823i	$0.196488\pi$
$240$		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	$0.0706022\pi$
$251$			6.97056i			0.439978i	−0.975502	+	0.219989i	$0.929398\pi$
$252$		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	$-0.725131\pi$
$269$	−21.3137			−1.29952			−0.649760	+	0.760140i	$0.725131\pi$
$270$		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	$-0.971368\pi$
$277$	−18.0711	−	18.0711i	−1.08579	−	1.08579i	−0.0898279	−	0.995957i	$-0.528632\pi$
$278$	0.171573	+	0.171573i	0.0102903	+	0.0102903i
$279$		0			0
$280$		0			0
$281$			12.9289i			0.771275i	0.922650	+	0.385638i	$0.126019\pi$
$281$			12.9289i			0.771275i	−0.922650	+	0.385638i	$0.873981\pi$
$282$		0			0
$283$	−18.0000	+	18.0000i	−1.06999	+	1.06999i	−0.0726300	+	0.997359i	$0.523139\pi$
$283$	−18.0000	+	18.0000i	−1.06999	+	1.06999i	−0.997359	+	0.0726300i	$0.976861\pi$
$284$	−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	0.459362	−	0.888249i	$-0.348078\pi$
$307$	−7.51472	−	7.51472i	−0.428888	−	0.428888i	−0.888249	+	0.459362i	$0.848078\pi$
$308$	3.41421	+	3.41421i	0.194543	+	0.194543i
$309$		0			0
$310$		0			0
$311$			16.0000i			0.907277i	0.891186	+	0.453638i	$0.149874\pi$
$311$			16.0000i			0.907277i	−0.891186	+	0.453638i	$0.850126\pi$
$312$		0			0
$313$	−19.6569	+	19.6569i	−1.11107	+	1.11107i	−0.118065	+	0.993006i	$0.537669\pi$
$313$	−19.6569	+	19.6569i	−1.11107	+	1.11107i	−0.993006	+	0.118065i	$0.962331\pi$
$314$	−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	0.664646	−	0.747158i	$-0.268582\pi$
$337$	−1.51472	−	1.51472i	−0.0825120	−	0.0825120i	−0.747158	+	0.664646i	$0.768582\pi$
$338$	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	$-0.684226\pi$
$359$	−20.7279			−1.09398			−0.546989	+	0.837140i	$0.684226\pi$
$360$		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	$0.0143303\pi$
$367$	20.0000	+	20.0000i	1.04399	+	1.04399i	0.0450047	+	0.998987i	$0.485670\pi$
$368$	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	−0.935486	−	0.353364i	$-0.885038\pi$
$373$	−11.2426	+	11.2426i	−0.582122	+	0.582122i	0.353364	+	0.935486i	$0.385038\pi$
$374$	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	$-0.543010\pi$
$389$	−5.31371			−0.269416			−0.134708	+	0.990885i	$0.543010\pi$
$390$		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	$0.107840\pi$
$397$	25.4142	+	25.4142i	1.27550	+	1.27550i	0.332345	+	0.943158i	$0.392160\pi$
$398$	−0.242641	−	0.242641i	−0.0121625	−	0.0121625i
$399$		0			0
$400$		0			0
$401$			31.0711i			1.55162i	0.630970	+	0.775808i	$0.282657\pi$
$401$			31.0711i			1.55162i	−0.630970	+	0.775808i	$0.717343\pi$
$402$		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	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$		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	$0.103088\pi$
$431$			13.2132i			0.636458i	−0.948014	+	0.318229i	$0.896912\pi$
$432$		0			0
$433$	24.2426	−	24.2426i	1.16503	−	1.16503i	0.181667	−	0.983360i	$-0.441851\pi$
$433$	24.2426	−	24.2426i	1.16503	−	1.16503i	0.983360	−	0.181667i	$-0.0581492\pi$
$434$	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	$-0.775199\pi$
$449$	−32.2426			−1.52162			−0.760812	+	0.648972i	$0.775199\pi$
$450$		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	0.860676	−	0.509153i	$-0.170041\pi$
$457$	7.51472	+	7.51472i	0.351524	+	0.351524i	−0.509153	+	0.860676i	$0.670041\pi$
$458$	−3.48528	−	3.48528i	−0.162857	−	0.162857i
$459$		0			0
$460$		0			0
$461$			37.3137i			1.73787i	0.494924	+	0.868936i	$0.335196\pi$
$461$			37.3137i			1.73787i	−0.494924	+	0.868936i	$0.664804\pi$
$462$		0			0
$463$	5.51472	−	5.51472i	0.256291	−	0.256291i	−0.567253	−	0.823544i	$-0.691994\pi$
$463$	5.51472	−	5.51472i	0.256291	−	0.256291i	0.823544	+	0.567253i	$0.191994\pi$
$464$	−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	$-0.429193\pi$
$479$	9.65685			0.441233			0.220616	+	0.975361i	$0.429193\pi$
$480$		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	0.0896838	−	0.995970i	$-0.471414\pi$
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	−0.995970	+	0.0896838i	$0.971414\pi$
$488$	4.65685	+	4.65685i	0.210806	+	0.210806i
$489$		0			0
$490$		0			0
$491$		−	22.9706i		−	1.03665i	−0.855185	−	0.518323i	$-0.826556\pi$
$491$		−	22.9706i		−	1.03665i	0.855185	−	0.518323i	$-0.173444\pi$
$492$		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	$-0.633259\pi$
$509$	−18.3431			−0.813046			−0.406523	+	0.913641i	$0.633259\pi$
$510$		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	$0.0487946\pi$
$521$			6.97056i			0.305386i	−0.988274	+	0.152693i	$0.951205\pi$
$522$		0			0
$523$	30.2843	−	30.2843i	1.32424	−	1.32424i	0.413930	−	0.910309i	$-0.364156\pi$
$523$	30.2843	−	30.2843i	1.32424	−	1.32424i	0.910309	−	0.413930i	$-0.135844\pi$
$524$	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	$-0.995340\pi$
$547$	−23.7279	−	23.7279i	−1.01453	−	1.01453i	−0.0146399	−	0.999893i	$-0.504660\pi$
$548$	−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	$-0.569848\pi$
$569$	−10.3848			−0.435352			−0.217676	+	0.976021i	$0.569848\pi$
$570$		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	0.900316	−	0.435237i	$-0.143335\pi$
$577$	11.1716	+	11.1716i	0.465079	+	0.465079i	−0.435237	+	0.900316i	$0.643335\pi$
$578$	−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	$-0.467893\pi$
$599$	4.92893			0.201391			0.100695	+	0.994917i	$0.467893\pi$
$600$		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	0.912271	−	0.409588i	$-0.134328\pi$
$607$	12.3848	+	12.3848i	0.502683	+	0.502683i	−0.409588	+	0.912271i	$0.634328\pi$
$608$	−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	−0.630975	−	0.775803i	$-0.717345\pi$
$613$	3.58579	−	3.58579i	0.144829	−	0.144829i	0.775803	+	0.630975i	$0.217345\pi$
$614$	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	$0.295357\pi$
$641$			40.5269i			1.60072i	−0.599522	+	0.800358i	$0.704643\pi$
$642$		0			0
$643$	−0.142136	+	0.142136i	−0.00560528	+	0.00560528i	−0.709904	−	0.704299i	$-0.751262\pi$
$643$	−0.142136	+	0.142136i	−0.00560528	+	0.00560528i	0.704299	+	0.709904i	$0.251262\pi$
$644$	−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	$-0.612689\pi$
$659$	−17.7990			−0.693350			−0.346675	+	0.937985i	$0.612689\pi$
$660$		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	−0.921141	−	0.389229i	$-0.872741\pi$
$673$	−13.7990	+	13.7990i	−0.531912	+	0.531912i	0.389229	+	0.921141i	$0.372741\pi$
$674$	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	$-0.833272\pi$
$701$		−	26.4853i		−	1.00034i	0.865929	−	0.500168i	$-0.166728\pi$
$702$		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	$-0.467561\pi$
$719$	5.45584			0.203469			0.101734	+	0.994812i	$0.467561\pi$
$720$		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	0.871058	−	0.491180i	$-0.163434\pi$
$727$	10.2426	+	10.2426i	0.379879	+	0.379879i	−0.491180	+	0.871058i	$0.663434\pi$
$728$	−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	−0.977329	−	0.211726i	$-0.932092\pi$
$733$	−20.7279	+	20.7279i	−0.765603	+	0.765603i	0.211726	+	0.977329i	$0.432092\pi$
$734$	−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	0.118121	−	0.992999i	$-0.462313\pi$
$757$	−24.0711	−	24.0711i	−0.874878	−	0.874878i	−0.992999	+	0.118121i	$0.962313\pi$
$758$	4.00000	+	4.00000i	0.145287	+	0.145287i
$759$		0			0
$760$		0			0
$761$			15.6569i			0.567561i	0.958889	+	0.283780i	$0.0915886\pi$
$761$			15.6569i			0.567561i	−0.958889	+	0.283780i	$0.908411\pi$
$762$		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	$0.0993687\pi$
$787$	35.3137	+	35.3137i	1.25880	+	1.25880i	0.307130	+	0.951667i	$0.400631\pi$
$788$	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	$-0.445465\pi$
$809$	9.69848			0.340981			0.170490	+	0.985359i	$0.445465\pi$
$810$		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	$0.0663444\pi$
$821$			11.8579i			0.413842i	−0.978358	+	0.206921i	$0.933656\pi$
$822$		0			0
$823$	14.6863	−	14.6863i	0.511932	−	0.511932i	−0.403186	−	0.915118i	$-0.632097\pi$
$823$	14.6863	−	14.6863i	0.511932	−	0.511932i	0.915118	+	0.403186i	$0.132097\pi$
$824$	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	$-0.653267\pi$
$839$	−26.8284			−0.926220			−0.463110	+	0.886301i	$0.653267\pi$
$840$		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	−0.765364	−	0.643597i	$-0.777441\pi$
$853$	−3.55635	+	3.55635i	−0.121767	+	0.121767i	0.643597	+	0.765364i	$0.277441\pi$
$854$	−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	0.956826	−	0.290661i	$-0.0938753\pi$
$877$	19.7279	+	19.7279i	0.666165	+	0.666165i	−0.290661	+	0.956826i	$0.593875\pi$
$878$	−18.2426	−	18.2426i	−0.615659	−	0.615659i
$879$		0			0
$880$		0			0
$881$		−	42.4853i		−	1.43137i	−0.698426	−	0.715683i	$-0.746116\pi$
$881$		−	42.4853i		−	1.43137i	0.698426	−	0.715683i	$-0.253884\pi$
$882$		0			0
$883$	38.8995	−	38.8995i	1.30907	−	1.30907i	0.386987	−	0.922085i	$-0.373516\pi$
$883$	38.8995	−	38.8995i	1.30907	−	1.30907i	0.922085	−	0.386987i	$-0.126484\pi$
$884$	−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	0.751402	−	0.659845i	$-0.229378\pi$
$907$	2.75736	+	2.75736i	0.0915566	+	0.0915566i	−0.659845	+	0.751402i	$0.729378\pi$
$908$	−4.34315	−	4.34315i	−0.144132	−	0.144132i
$909$		0			0
$910$		0			0
$911$			10.1005i			0.334645i	0.985902	+	0.167322i	$0.0535121\pi$
$911$			10.1005i			0.334645i	−0.985902	+	0.167322i	$0.946488\pi$
$912$		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	$-0.435099\pi$
$929$	12.3431			0.404965			0.202483	+	0.979286i	$0.435099\pi$
$930$		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	$0.00482656\pi$
$937$	31.0711	+	31.0711i	1.01505	+	1.01505i	0.0151625	+	0.999885i	$0.495173\pi$
$938$	−0.414214	−	0.414214i	−0.0135246	−	0.0135246i
$939$		0			0
$940$		0			0
$941$			9.31371i			0.303618i	0.988410	+	0.151809i	$0.0485099\pi$
$941$			9.31371i			0.303618i	−0.988410	+	0.151809i	$0.951490\pi$
$942$		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	0.584989	−	0.811041i	$-0.301099\pi$
$967$	−7.02944	−	7.02944i	−0.226051	−	0.226051i	−0.811041	+	0.584989i	$0.801099\pi$
$968$	−8.70711	−	8.70711i	−0.279857	−	0.279857i
$969$		0			0
$970$		0			0
$971$		−	35.6569i		−	1.14428i	−0.820155	−	0.572141i	$-0.806113\pi$
$971$		−	35.6569i		−	1.14428i	0.820155	−	0.572141i	$-0.193887\pi$
$972$		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	0.0922770	−	0.995733i	$-0.470585\pi$
$997$	−28.5269	−	28.5269i	−0.903456	−	0.903456i	−0.995733	+	0.0922770i	$0.970585\pi$
$998$	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.c.1457.1	✓	4
3.2	odd	2		3150.2.m.d.1457.2	yes	4
5.2	odd	4		3150.2.m.f.2843.1	yes	4
5.3	odd	4		3150.2.m.d.2843.2	yes	4
5.4	even	2		3150.2.m.e.1457.2	yes	4
15.2	even	4		3150.2.m.e.2843.2	yes	4
15.8	even	4	inner	3150.2.m.c.2843.1	yes	4
15.14	odd	2		3150.2.m.f.1457.1	yes	4

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

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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