LMFDB - Embedded newform 3150.2.m.g.2843.4

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2843.4
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.2843
Dual form			3150.2.m.g.1457.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.585786i q^{11} +(0.0249440 + 0.0249440i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-1.92152 - 1.92152i) q^{17} -4.87832i q^{19} +(0.414214 - 0.414214i) q^{22} +(5.15660 - 5.15660i) q^{23} +0.0352762i q^{26} +(-0.707107 - 0.707107i) q^{28} +4.58114 q^{29} +9.83839 q^{31} +(-0.707107 - 0.707107i) q^{32} -2.71744i q^{34} +(-2.87832 + 2.87832i) q^{37} +(3.44949 - 3.44949i) q^{38} -0.979336i q^{41} +(4.27463 + 4.27463i) q^{43} +0.585786 q^{44} +7.29253 q^{46} +(6.32780 + 6.32780i) q^{47} -1.00000i q^{49} +(-0.0249440 + 0.0249440i) q^{52} +(1.56084 - 1.56084i) q^{53} -1.00000i q^{56} +(3.23936 + 3.23936i) q^{58} +0.670951 q^{59} +2.35363 q^{61} +(6.95680 + 6.95680i) q^{62} -1.00000i q^{64} +(-5.08516 + 5.08516i) q^{67} +(1.92152 - 1.92152i) q^{68} +2.92820i q^{71} +(-2.51059 - 2.51059i) q^{73} -4.07055 q^{74} +4.87832 q^{76} +(0.414214 + 0.414214i) q^{77} +8.71279i q^{79} +(0.692495 - 0.692495i) q^{82} +(2.99207 - 2.99207i) q^{83} +6.04524i q^{86} +(0.414214 + 0.414214i) q^{88} +9.72741 q^{89} -0.0352762 q^{91} +(5.15660 + 5.15660i) q^{92} +8.94887i q^{94} +(-4.74666 + 4.74666i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$		−	0.585786i		−	0.176621i	−0.996093	−	0.0883106i	$-0.971853\pi$
$11$		−	0.585786i		−	0.176621i	0.996093	−	0.0883106i	$-0.0281468\pi$
$12$		0			0
$13$	0.0249440	+	0.0249440i	0.00691823	+	0.00691823i	0.710557	−	0.703639i	$-0.248443\pi$
$13$	0.0249440	+	0.0249440i	0.00691823	+	0.00691823i	−0.703639	+	0.710557i	$0.748443\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.92152	−	1.92152i	−0.466037	−	0.466037i	0.434591	−	0.900628i	$-0.356893\pi$
$17$	−1.92152	−	1.92152i	−0.466037	−	0.466037i	−0.900628	+	0.434591i	$0.856893\pi$
$18$		0			0
$19$		−	4.87832i		−	1.11916i	−0.828776	−	0.559581i	$-0.810962\pi$
$19$		−	4.87832i		−	1.11916i	0.828776	−	0.559581i	$-0.189038\pi$
$20$		0			0
$21$		0			0
$22$	0.414214	−	0.414214i	0.0883106	−	0.0883106i
$23$	5.15660	−	5.15660i	1.07522	−	1.07522i	0.0782944	−	0.996930i	$-0.475053\pi$
$23$	5.15660	−	5.15660i	1.07522	−	1.07522i	0.996930	−	0.0782944i	$-0.0249474\pi$
$24$		0			0
$25$		0			0
$26$			0.0352762i			0.00691823i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	4.58114			0.850697			0.425348	−	0.905030i	$-0.360152\pi$
$29$	4.58114			0.850697			0.425348	+	0.905030i	$0.360152\pi$
$30$		0			0
$31$	9.83839			1.76703			0.883514	−	0.468405i	$-0.155171\pi$
$31$	9.83839			1.76703			0.883514	+	0.468405i	$0.155171\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	2.71744i		−	0.466037i
$35$		0			0
$36$		0			0
$37$	−2.87832	+	2.87832i	−0.473192	+	0.473192i	−0.902946	−	0.429754i	$-0.858600\pi$
$37$	−2.87832	+	2.87832i	−0.473192	+	0.473192i	0.429754	+	0.902946i	$0.358600\pi$
$38$	3.44949	−	3.44949i	0.559581	−	0.559581i
$39$		0			0
$40$		0			0
$41$		−	0.979336i		−	0.152947i	−0.997072	−	0.0764733i	$-0.975634\pi$
$41$		−	0.979336i		−	0.152947i	0.997072	−	0.0764733i	$-0.0243660\pi$
$42$		0			0
$43$	4.27463	+	4.27463i	0.651875	+	0.651875i	0.953444	−	0.301569i	$-0.0975103\pi$
$43$	4.27463	+	4.27463i	0.651875	+	0.651875i	−0.301569	+	0.953444i	$0.597510\pi$
$44$	0.585786			0.0883106
$45$		0			0
$46$	7.29253			1.07522
$47$	6.32780	+	6.32780i	0.923005	+	0.923005i	0.997241	−	0.0742355i	$-0.0236517\pi$
$47$	6.32780	+	6.32780i	0.923005	+	0.923005i	−0.0742355	+	0.997241i	$0.523652\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	−0.0249440	+	0.0249440i	−0.00345911	+	0.00345911i
$53$	1.56084	−	1.56084i	0.214398	−	0.214398i	−0.591735	−	0.806133i	$-0.701557\pi$
$53$	1.56084	−	1.56084i	0.214398	−	0.214398i	0.806133	+	0.591735i	$0.201557\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	3.23936	+	3.23936i	0.425348	+	0.425348i
$59$	0.670951			0.0873503			0.0436752	−	0.999046i	$-0.486093\pi$
$59$	0.670951			0.0873503			0.0436752	+	0.999046i	$0.486093\pi$
$60$		0			0
$61$	2.35363			0.301351			0.150676	−	0.988583i	$-0.451855\pi$
$61$	2.35363			0.301351			0.150676	+	0.988583i	$0.451855\pi$
$62$	6.95680	+	6.95680i	0.883514	+	0.883514i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−5.08516	+	5.08516i	−0.621252	+	0.621252i	−0.945851	−	0.324600i	$-0.894770\pi$
$67$	−5.08516	+	5.08516i	−0.621252	+	0.621252i	0.324600	+	0.945851i	$0.394770\pi$
$68$	1.92152	−	1.92152i	0.233018	−	0.233018i
$69$		0			0
$70$		0			0
$71$			2.92820i			0.347514i	0.984789	+	0.173757i	$0.0555907\pi$
$71$			2.92820i			0.347514i	−0.984789	+	0.173757i	$0.944409\pi$
$72$		0			0
$73$	−2.51059	−	2.51059i	−0.293842	−	0.293842i	0.544754	−	0.838596i	$-0.316623\pi$
$73$	−2.51059	−	2.51059i	−0.293842	−	0.293842i	−0.838596	+	0.544754i	$0.816623\pi$
$74$	−4.07055			−0.473192
$75$		0			0
$76$	4.87832			0.559581
$77$	0.414214	+	0.414214i	0.0472040	+	0.0472040i
$78$		0			0
$79$			8.71279i			0.980266i	0.871648	+	0.490133i	$0.163052\pi$
$79$			8.71279i			0.980266i	−0.871648	+	0.490133i	$0.836948\pi$
$80$		0			0
$81$		0			0
$82$	0.692495	−	0.692495i	0.0764733	−	0.0764733i
$83$	2.99207	−	2.99207i	0.328423	−	0.328423i	−0.523564	−	0.851986i	$-0.675398\pi$
$83$	2.99207	−	2.99207i	0.328423	−	0.328423i	0.851986	+	0.523564i	$0.175398\pi$
$84$		0			0
$85$		0			0
$86$			6.04524i			0.651875i
$87$		0			0
$88$	0.414214	+	0.414214i	0.0441553	+	0.0441553i
$89$	9.72741			1.03110			0.515552	−	0.856859i	$-0.327587\pi$
$89$	9.72741			1.03110			0.515552	+	0.856859i	$0.327587\pi$
$90$		0			0
$91$	−0.0352762			−0.00369795
$92$	5.15660	+	5.15660i	0.537612	+	0.537612i
$93$		0			0
$94$			8.94887i			0.923005i
$95$		0			0
$96$		0			0
$97$	−4.74666	+	4.74666i	−0.481951	+	0.481951i	−0.905754	−	0.423804i	$-0.860695\pi$
$97$	−4.74666	+	4.74666i	−0.481951	+	0.481951i	0.423804	+	0.905754i	$0.360695\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	6.18618i		−	0.615548i	−0.951459	−	0.307774i	$-0.900416\pi$
$101$		−	6.18618i		−	0.615548i	0.951459	−	0.307774i	$-0.0995841\pi$
$102$		0			0
$103$	0.272229	+	0.272229i	0.0268235	+	0.0268235i	0.720391	−	0.693568i	$-0.243962\pi$
$103$	0.272229	+	0.272229i	0.0268235	+	0.0268235i	−0.693568	+	0.720391i	$0.743962\pi$
$104$	−0.0352762			−0.00345911
$105$		0			0
$106$	2.20736			0.214398
$107$	−3.97934	−	3.97934i	−0.384697	−	0.384697i	0.488094	−	0.872791i	$-0.337692\pi$
$107$	−3.97934	−	3.97934i	−0.384697	−	0.384697i	−0.872791	+	0.488094i	$0.837692\pi$
$108$		0			0
$109$		−	8.61982i		−	0.825629i	−0.910815	−	0.412814i	$-0.864546\pi$
$109$		−	8.61982i		−	0.825629i	0.910815	−	0.412814i	$-0.135454\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	6.13165	−	6.13165i	0.576817	−	0.576817i	−0.357208	−	0.934025i	$-0.616271\pi$
$113$	6.13165	−	6.13165i	0.576817	−	0.576817i	0.934025	+	0.357208i	$0.116271\pi$
$114$		0			0
$115$		0			0
$116$			4.58114i			0.425348i
$117$		0			0
$118$	0.474434	+	0.474434i	0.0436752	+	0.0436752i
$119$	2.71744			0.249107
$120$		0			0
$121$	10.6569			0.968805
$122$	1.66427	+	1.66427i	0.150676	+	0.150676i
$123$		0			0
$124$			9.83839i			0.883514i
$125$		0			0
$126$		0			0
$127$	−14.1356	+	14.1356i	−1.25433	+	1.25433i	−0.300569	+	0.953760i	$0.597176\pi$
$127$	−14.1356	+	14.1356i	−1.25433	+	1.25433i	−0.953760	+	0.300569i	$0.902824\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	19.3843i		−	1.69361i	−0.531903	−	0.846805i	$-0.678523\pi$
$131$		−	19.3843i		−	1.69361i	0.531903	−	0.846805i	$-0.321477\pi$
$132$		0			0
$133$	3.44949	+	3.44949i	0.299109	+	0.299109i
$134$	−7.19151			−0.621252
$135$		0			0
$136$	2.71744			0.233018
$137$	5.29858	+	5.29858i	0.452688	+	0.452688i	0.896246	−	0.443558i	$-0.146284\pi$
$137$	5.29858	+	5.29858i	0.452688	+	0.452688i	−0.443558	+	0.896246i	$0.646284\pi$
$138$		0			0
$139$		−	4.33386i		−	0.367593i	−0.982964	−	0.183796i	$-0.941161\pi$
$139$		−	4.33386i		−	0.367593i	0.982964	−	0.183796i	$-0.0588387\pi$
$140$		0			0
$141$		0			0
$142$	−2.07055	+	2.07055i	−0.173757	+	0.173757i
$143$	0.0146119	−	0.0146119i	0.00122191	−	0.00122191i
$144$		0			0
$145$		0			0
$146$		−	3.55051i		−	0.293842i
$147$		0			0
$148$	−2.87832	−	2.87832i	−0.236596	−	0.236596i
$149$	16.4083			1.34422			0.672111	−	0.740450i	$-0.265388\pi$
$149$	16.4083			1.34422			0.672111	+	0.740450i	$0.265388\pi$
$150$		0			0
$151$	6.19275			0.503959			0.251980	−	0.967733i	$-0.418918\pi$
$151$	6.19275			0.503959			0.251980	+	0.967733i	$0.418918\pi$
$152$	3.44949	+	3.44949i	0.279791	+	0.279791i
$153$		0			0
$154$			0.585786i			0.0472040i
$155$		0			0
$156$		0			0
$157$	−6.65561	+	6.65561i	−0.531175	+	0.531175i	−0.920922	−	0.389747i	$-0.872563\pi$
$157$	−6.65561	+	6.65561i	−0.531175	+	0.531175i	0.389747	+	0.920922i	$0.372563\pi$
$158$	−6.16088	+	6.16088i	−0.490133	+	0.490133i
$159$		0			0
$160$		0			0
$161$			7.29253i			0.574732i
$162$		0			0
$163$	7.26002	+	7.26002i	0.568649	+	0.568649i	0.931750	−	0.363101i	$-0.118282\pi$
$163$	7.26002	+	7.26002i	0.568649	+	0.568649i	−0.363101	+	0.931750i	$0.618282\pi$
$164$	0.979336			0.0764733
$165$		0			0
$166$	4.23143			0.328423
$167$	0.484766	+	0.484766i	0.0375123	+	0.0375123i	0.725614	−	0.688102i	$-0.241556\pi$
$167$	0.484766	+	0.484766i	0.0375123	+	0.0375123i	−0.688102	+	0.725614i	$0.741556\pi$
$168$		0			0
$169$		−	12.9988i		−	0.999904i
$170$		0			0
$171$		0			0
$172$	−4.27463	+	4.27463i	−0.325938	+	0.325938i
$173$	15.8126	−	15.8126i	1.20221	−	1.20221i	0.228714	−	0.973494i	$-0.426548\pi$
$173$	15.8126	−	15.8126i	1.20221	−	1.20221i	0.973494	−	0.228714i	$-0.0734520\pi$
$174$		0			0
$175$		0			0
$176$			0.585786i			0.0441553i
$177$		0			0
$178$	6.87832	+	6.87832i	0.515552	+	0.515552i
$179$	5.14235			0.384357			0.192179	−	0.981360i	$-0.438445\pi$
$179$	5.14235			0.384357			0.192179	+	0.981360i	$0.438445\pi$
$180$		0			0
$181$	15.0411			1.11800			0.558999	−	0.829169i	$-0.311186\pi$
$181$	15.0411			1.11800			0.558999	+	0.829169i	$0.311186\pi$
$182$	−0.0249440	−	0.0249440i	−0.00184897	−	0.00184897i
$183$		0			0
$184$			7.29253i			0.537612i
$185$		0			0
$186$		0			0
$187$	−1.12560	+	1.12560i	−0.0823120	+	0.0823120i
$188$	−6.32780	+	6.32780i	−0.461503	+	0.461503i
$189$		0			0
$190$		0			0
$191$		−	11.8732i		−	0.859111i	−0.903040	−	0.429556i	$-0.858670\pi$
$191$		−	11.8732i		−	0.859111i	0.903040	−	0.429556i	$-0.141330\pi$
$192$		0			0
$193$	−0.0864086	−	0.0864086i	−0.00621983	−	0.00621983i	0.703990	−	0.710210i	$-0.251400\pi$
$193$	−0.0864086	−	0.0864086i	−0.00621983	−	0.00621983i	−0.710210	+	0.703990i	$0.751400\pi$
$194$	−6.71279			−0.481951
$195$		0			0
$196$	1.00000			0.0714286
$197$	15.3374	+	15.3374i	1.09275	+	1.09275i	0.995234	+	0.0975106i	$0.0310880\pi$
$197$	15.3374	+	15.3374i	1.09275	+	1.09275i	0.0975106	+	0.995234i	$0.468912\pi$
$198$		0			0
$199$			13.4256i			0.951715i	0.879522	+	0.475857i	$0.157862\pi$
$199$			13.4256i			0.951715i	−0.879522	+	0.475857i	$0.842138\pi$
$200$		0			0
$201$		0			0
$202$	4.37429	−	4.37429i	0.307774	−	0.307774i
$203$	−3.23936	+	3.23936i	−0.227358	+	0.227358i
$204$		0			0
$205$		0			0
$206$			0.384990i			0.0268235i
$207$		0			0
$208$	−0.0249440	−	0.0249440i	−0.00172956	−	0.00172956i
$209$	−2.85765			−0.197668
$210$		0			0
$211$	−16.2263			−1.11706			−0.558531	−	0.829484i	$-0.688635\pi$
$211$	−16.2263			−1.11706			−0.558531	+	0.829484i	$0.688635\pi$
$212$	1.56084	+	1.56084i	0.107199	+	0.107199i
$213$		0			0
$214$		−	5.62763i		−	0.384697i
$215$		0			0
$216$		0			0
$217$	−6.95680	+	6.95680i	−0.472258	+	0.472258i
$218$	6.09513	−	6.09513i	0.412814	−	0.412814i
$219$		0			0
$220$		0			0
$221$		−	0.0958609i		−	0.00644830i
$222$		0			0
$223$	−11.1919	−	11.1919i	−0.749463	−	0.749463i	0.224915	−	0.974378i	$-0.427790\pi$
$223$	−11.1919	−	11.1919i	−0.749463	−	0.749463i	−0.974378	+	0.224915i	$0.927790\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	8.67147			0.576817
$227$	−14.5784	−	14.5784i	−0.967601	−	0.967601i	0.0318907	−	0.999491i	$-0.489847\pi$
$227$	−14.5784	−	14.5784i	−0.967601	−	0.967601i	−0.999491	+	0.0318907i	$0.989847\pi$
$228$		0			0
$229$			16.0905i			1.06329i	0.846967	+	0.531645i	$0.178426\pi$
$229$			16.0905i			1.06329i	−0.846967	+	0.531645i	$0.821574\pi$
$230$		0			0
$231$		0			0
$232$	−3.23936	+	3.23936i	−0.212674	+	0.212674i
$233$	−13.7162	+	13.7162i	−0.898578	+	0.898578i	−0.995310	−	0.0967326i	$-0.969161\pi$
$233$	−13.7162	+	13.7162i	−0.898578	+	0.898578i	0.0967326	+	0.995310i	$0.469161\pi$
$234$		0			0
$235$		0			0
$236$			0.670951i			0.0436752i
$237$		0			0
$238$	1.92152	+	1.92152i	0.124554	+	0.124554i
$239$	0.485281			0.0313902			0.0156951	−	0.999877i	$-0.495004\pi$
$239$	0.485281			0.0313902			0.0156951	+	0.999877i	$0.495004\pi$
$240$		0			0
$241$	9.57598			0.616843			0.308422	−	0.951250i	$-0.400199\pi$
$241$	9.57598			0.616843			0.308422	+	0.951250i	$0.400199\pi$
$242$	7.53553	+	7.53553i	0.484402	+	0.484402i
$243$		0			0
$244$			2.35363i			0.150676i
$245$		0			0
$246$		0			0
$247$	0.121685	−	0.121685i	0.00774262	−	0.00774262i
$248$	−6.95680	+	6.95680i	−0.441757	+	0.441757i
$249$		0			0
$250$		0			0
$251$		−	23.8532i		−	1.50560i	−0.658250	−	0.752799i	$-0.728703\pi$
$251$		−	23.8532i		−	1.50560i	0.658250	−	0.752799i	$-0.271297\pi$
$252$		0			0
$253$	−3.02066	−	3.02066i	−0.189908	−	0.189908i
$254$	−19.9907			−1.25433
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.62095	−	4.62095i	−0.288247	−	0.288247i	0.548140	−	0.836387i	$-0.315336\pi$
$257$	−4.62095	−	4.62095i	−0.288247	−	0.288247i	−0.836387	+	0.548140i	$0.815336\pi$
$258$		0			0
$259$		−	4.07055i		−	0.252932i
$260$		0			0
$261$		0			0
$262$	13.7067	−	13.7067i	0.846805	−	0.846805i
$263$	−7.67183	+	7.67183i	−0.473065	+	0.473065i	−0.902905	−	0.429840i	$-0.858570\pi$
$263$	−7.67183	+	7.67183i	−0.473065	+	0.473065i	0.429840	+	0.902905i	$0.358570\pi$
$264$		0			0
$265$		0			0
$266$			4.87832i			0.299109i
$267$		0			0
$268$	−5.08516	−	5.08516i	−0.310626	−	0.310626i
$269$	20.4629			1.24764			0.623821	−	0.781567i	$-0.285579\pi$
$269$	20.4629			1.24764			0.623821	+	0.781567i	$0.285579\pi$
$270$		0			0
$271$	−23.2500			−1.41233			−0.706167	−	0.708045i	$-0.749577\pi$
$271$	−23.2500			−1.41233			−0.706167	+	0.708045i	$0.749577\pi$
$272$	1.92152	+	1.92152i	0.116509	+	0.116509i
$273$		0			0
$274$			7.49333i			0.452688i
$275$		0			0
$276$		0			0
$277$	−20.3636	+	20.3636i	−1.22353	+	1.22353i	−0.257161	+	0.966368i	$0.582787\pi$
$277$	−20.3636	+	20.3636i	−1.22353	+	1.22353i	−0.966368	+	0.257161i	$0.917213\pi$
$278$	3.06450	−	3.06450i	0.183796	−	0.183796i
$279$		0			0
$280$		0			0
$281$		−	22.1421i		−	1.32089i	−0.750875	−	0.660445i	$-0.770368\pi$
$281$		−	22.1421i		−	1.32089i	0.750875	−	0.660445i	$-0.229632\pi$
$282$		0			0
$283$	14.4600	+	14.4600i	0.859556	+	0.859556i	0.991286	−	0.131730i	$-0.0420530\pi$
$283$	14.4600	+	14.4600i	0.859556	+	0.859556i	−0.131730	+	0.991286i	$0.542053\pi$
$284$	−2.92820			−0.173757
$285$		0			0
$286$	0.0206643			0.00122191
$287$	0.692495	+	0.692495i	0.0408767	+	0.0408767i
$288$		0			0
$289$		−	9.61553i		−	0.565619i
$290$		0			0
$291$		0			0
$292$	2.51059	−	2.51059i	0.146921	−	0.146921i
$293$	0.442922	−	0.442922i	0.0258758	−	0.0258758i	−0.694051	−	0.719926i	$-0.744176\pi$
$293$	0.442922	−	0.442922i	0.0258758	−	0.0258758i	0.719926	+	0.694051i	$0.244176\pi$
$294$		0			0
$295$		0			0
$296$		−	4.07055i		−	0.236596i
$297$		0			0
$298$	11.6024	+	11.6024i	0.672111	+	0.672111i
$299$	0.257253			0.0148773
$300$		0			0
$301$	−6.04524			−0.348442
$302$	4.37894	+	4.37894i	0.251980	+	0.251980i
$303$		0			0
$304$			4.87832i			0.279791i
$305$		0			0
$306$		0			0
$307$	−14.3696	+	14.3696i	−0.820119	+	0.820119i	−0.986125	−	0.166006i	$-0.946913\pi$
$307$	−14.3696	+	14.3696i	−0.820119	+	0.820119i	0.166006	+	0.986125i	$0.446913\pi$
$308$	−0.414214	+	0.414214i	−0.0236020	+	0.0236020i
$309$		0			0
$310$		0			0
$311$		−	17.0892i		−	0.969042i	−0.874780	−	0.484521i	$-0.838994\pi$
$311$		−	17.0892i		−	0.969042i	0.874780	−	0.484521i	$-0.161006\pi$
$312$		0			0
$313$	2.66098	+	2.66098i	0.150408	+	0.150408i	0.778300	−	0.627892i	$-0.216082\pi$
$313$	2.66098	+	2.66098i	0.150408	+	0.150408i	−0.627892	+	0.778300i	$0.716082\pi$
$314$	−9.41245			−0.531175
$315$		0			0
$316$	−8.71279			−0.490133
$317$	−9.56011	−	9.56011i	−0.536949	−	0.536949i	0.385682	−	0.922632i	$-0.373966\pi$
$317$	−9.56011	−	9.56011i	−0.536949	−	0.536949i	−0.922632	+	0.385682i	$0.873966\pi$
$318$		0			0
$319$		−	2.68357i		−	0.150251i
$320$		0			0
$321$		0			0
$322$	−5.15660	+	5.15660i	−0.287366	+	0.287366i
$323$	−9.37378	+	9.37378i	−0.521571	+	0.521571i
$324$		0			0
$325$		0			0
$326$			10.2672i			0.568649i
$327$		0			0
$328$	0.692495	+	0.692495i	0.0382366	+	0.0382366i
$329$	−8.94887			−0.493367
$330$		0			0
$331$	2.71404			0.149177			0.0745885	−	0.997214i	$-0.476236\pi$
$331$	2.71404			0.149177			0.0745885	+	0.997214i	$0.476236\pi$
$332$	2.99207	+	2.99207i	0.164211	+	0.164211i
$333$		0			0
$334$			0.685563i			0.0375123i
$335$		0			0
$336$		0			0
$337$	15.9867	−	15.9867i	0.870851	−	0.870851i	−0.121714	−	0.992565i	$-0.538839\pi$
$337$	15.9867	−	15.9867i	0.870851	−	0.870851i	0.992565	+	0.121714i	$0.0388391\pi$
$338$	9.19151	−	9.19151i	0.499952	−	0.499952i
$339$		0			0
$340$		0			0
$341$		−	5.76320i		−	0.312095i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−6.04524			−0.325938
$345$		0			0
$346$	22.3624			1.20221
$347$	−18.0228	−	18.0228i	−0.967516	−	0.967516i	0.0319731	−	0.999489i	$-0.489821\pi$
$347$	−18.0228	−	18.0228i	−0.967516	−	0.967516i	−0.999489	+	0.0319731i	$0.989821\pi$
$348$		0			0
$349$		−	22.6437i		−	1.21209i	−0.795431	−	0.606044i	$-0.792756\pi$
$349$		−	22.6437i		−	1.21209i	0.795431	−	0.606044i	$-0.207244\pi$
$350$		0			0
$351$		0			0
$352$	−0.414214	+	0.414214i	−0.0220777	+	0.0220777i
$353$	14.5266	−	14.5266i	0.773173	−	0.773173i	−0.205487	−	0.978660i	$-0.565878\pi$
$353$	14.5266	−	14.5266i	0.773173	−	0.773173i	0.978660	+	0.205487i	$0.0658777\pi$
$354$		0			0
$355$		0			0
$356$			9.72741i			0.515552i
$357$		0			0
$358$	3.63619	+	3.63619i	0.192179	+	0.192179i
$359$	12.3264			0.650562			0.325281	−	0.945617i	$-0.394541\pi$
$359$	12.3264			0.650562			0.325281	+	0.945617i	$0.394541\pi$
$360$		0			0
$361$	−4.79796			−0.252524
$362$	10.6357	+	10.6357i	0.558999	+	0.558999i
$363$		0			0
$364$		−	0.0352762i		−	0.00184897i
$365$		0			0
$366$		0			0
$367$	20.3428	−	20.3428i	1.06188	−	1.06188i	0.0639302	−	0.997954i	$-0.479637\pi$
$367$	20.3428	−	20.3428i	1.06188	−	1.06188i	0.997954	−	0.0639302i	$-0.0203635\pi$
$368$	−5.15660	+	5.15660i	−0.268806	+	0.268806i
$369$		0			0
$370$		0			0
$371$			2.20736i			0.114601i
$372$		0			0
$373$	16.7980	+	16.7980i	0.869765	+	0.869765i	0.992446	−	0.122681i	$-0.0391491\pi$
$373$	16.7980	+	16.7980i	0.869765	+	0.869765i	−0.122681	+	0.992446i	$0.539149\pi$
$374$	−1.59184			−0.0823120
$375$		0			0
$376$	−8.94887			−0.461503
$377$	0.114272	+	0.114272i	0.00588531	+	0.00588531i
$378$		0			0
$379$		−	13.5108i		−	0.694001i	−0.937865	−	0.347000i	$-0.887200\pi$
$379$		−	13.5108i		−	0.694001i	0.937865	−	0.347000i	$-0.112800\pi$
$380$		0			0
$381$		0			0
$382$	8.39559	−	8.39559i	0.429556	−	0.429556i
$383$	−3.84377	+	3.84377i	−0.196407	+	0.196407i	−0.798458	−	0.602051i	$-0.794351\pi$
$383$	−3.84377	+	3.84377i	−0.196407	+	0.196407i	0.602051	+	0.798458i	$0.294351\pi$
$384$		0			0
$385$		0			0
$386$		−	0.122200i		−	0.00621983i
$387$		0			0
$388$	−4.74666	−	4.74666i	−0.240975	−	0.240975i
$389$	−35.9081			−1.82061			−0.910305	−	0.413937i	$-0.864153\pi$
$389$	−35.9081			−1.82061			−0.910305	+	0.413937i	$0.864153\pi$
$390$		0			0
$391$	−19.8170			−1.00219
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$		0			0
$394$			21.6904i			1.09275i
$395$		0			0
$396$		0			0
$397$	17.9227	−	17.9227i	0.899513	−	0.899513i	−0.0958795	−	0.995393i	$-0.530566\pi$
$397$	17.9227	−	17.9227i	0.899513	−	0.899513i	0.995393	+	0.0958795i	$0.0305663\pi$
$398$	−9.49333	+	9.49333i	−0.475857	+	0.475857i
$399$		0			0
$400$		0			0
$401$			33.4042i			1.66813i	0.551669	+	0.834063i	$0.313991\pi$
$401$			33.4042i			1.66813i	−0.551669	+	0.834063i	$0.686009\pi$
$402$		0			0
$403$	0.245409	+	0.245409i	0.0122247	+	0.0122247i
$404$	6.18618			0.307774
$405$		0			0
$406$	−4.58114			−0.227358
$407$	1.68608	+	1.68608i	0.0835758	+	0.0835758i
$408$		0			0
$409$			39.4438i			1.95037i	0.221395	+	0.975184i	$0.428939\pi$
$409$			39.4438i			1.95037i	−0.221395	+	0.975184i	$0.571061\pi$
$410$		0			0
$411$		0			0
$412$	−0.272229	+	0.272229i	−0.0134118	+	0.0134118i
$413$	−0.474434	+	0.474434i	−0.0233454	+	0.0233454i
$414$		0			0
$415$		0			0
$416$		−	0.0352762i		−	0.00172956i
$417$		0			0
$418$	−2.02066	−	2.02066i	−0.0988339	−	0.0988339i
$419$	−32.5989			−1.59256			−0.796281	−	0.604927i	$-0.793202\pi$
$419$	−32.5989			−1.59256			−0.796281	+	0.604927i	$0.793202\pi$
$420$		0			0
$421$	−14.6330			−0.713167			−0.356583	−	0.934264i	$-0.616058\pi$
$421$	−14.6330			−0.713167			−0.356583	+	0.934264i	$0.616058\pi$
$422$	−11.4737	−	11.4737i	−0.558531	−	0.558531i
$423$		0			0
$424$			2.20736i			0.107199i
$425$		0			0
$426$		0			0
$427$	−1.66427	+	1.66427i	−0.0805395	+	0.0805395i
$428$	3.97934	−	3.97934i	0.192348	−	0.192348i
$429$		0			0
$430$		0			0
$431$			5.88347i			0.283397i	0.989910	+	0.141699i	$0.0452564\pi$
$431$			5.88347i			0.283397i	−0.989910	+	0.141699i	$0.954744\pi$
$432$		0			0
$433$	−7.55532	−	7.55532i	−0.363085	−	0.363085i	0.501862	−	0.864948i	$-0.332648\pi$
$433$	−7.55532	−	7.55532i	−0.363085	−	0.363085i	−0.864948	+	0.501862i	$0.832648\pi$
$434$	−9.83839			−0.472258
$435$		0			0
$436$	8.61982			0.412814
$437$	−25.1555	−	25.1555i	−1.20335	−	1.20335i
$438$		0			0
$439$		−	21.1614i		−	1.00998i	−0.863126	−	0.504989i	$-0.831497\pi$
$439$		−	21.1614i		−	1.00998i	0.863126	−	0.504989i	$-0.168503\pi$
$440$		0			0
$441$		0			0
$442$	0.0677839	−	0.0677839i	0.00322415	−	0.00322415i
$443$	−4.32640	+	4.32640i	−0.205553	+	0.205553i	−0.802374	−	0.596821i	$-0.796430\pi$
$443$	−4.32640	+	4.32640i	−0.205553	+	0.205553i	0.596821	+	0.802374i	$0.296430\pi$
$444$		0			0
$445$		0			0
$446$		−	15.8277i		−	0.749463i
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	4.38623			0.206999			0.103500	−	0.994629i	$-0.466996\pi$
$449$	4.38623			0.206999			0.103500	+	0.994629i	$0.466996\pi$
$450$		0			0
$451$	−0.573682			−0.0270136
$452$	6.13165	+	6.13165i	0.288409	+	0.288409i
$453$		0			0
$454$		−	20.6169i		−	0.967601i
$455$		0			0
$456$		0			0
$457$	1.36960	−	1.36960i	0.0640672	−	0.0640672i	−0.674347	−	0.738414i	$-0.735575\pi$
$457$	1.36960	−	1.36960i	0.0640672	−	0.0640672i	0.738414	+	0.674347i	$0.235575\pi$
$458$	−11.3777	+	11.3777i	−0.531645	+	0.531645i
$459$		0			0
$460$		0			0
$461$		−	0.856388i		−	0.0398860i	−0.999801	−	0.0199430i	$-0.993652\pi$
$461$		−	0.856388i		−	0.0398860i	0.999801	−	0.0199430i	$-0.00634847\pi$
$462$		0			0
$463$	3.76393	+	3.76393i	0.174925	+	0.174925i	0.789139	−	0.614215i	$-0.210527\pi$
$463$	3.76393	+	3.76393i	0.174925	+	0.174925i	−0.614215	+	0.789139i	$0.710527\pi$
$464$	−4.58114			−0.212674
$465$		0			0
$466$	−19.3976			−0.898578
$467$	19.3844	+	19.3844i	0.897002	+	0.897002i	0.995170	−	0.0981679i	$-0.0312982\pi$
$467$	19.3844	+	19.3844i	0.897002	+	0.897002i	−0.0981679	+	0.995170i	$0.531298\pi$
$468$		0			0
$469$		−	7.19151i		−	0.332073i
$470$		0			0
$471$		0			0
$472$	−0.474434	+	0.474434i	−0.0218376	+	0.0218376i
$473$	2.50402	−	2.50402i	0.115135	−	0.115135i
$474$		0			0
$475$		0			0
$476$			2.71744i			0.124554i
$477$		0			0
$478$	0.343146	+	0.343146i	0.0156951	+	0.0156951i
$479$	27.8192			1.27109			0.635545	−	0.772064i	$-0.280776\pi$
$479$	27.8192			1.27109			0.635545	+	0.772064i	$0.280776\pi$
$480$		0			0
$481$	−0.143594			−0.00654730
$482$	6.77124	+	6.77124i	0.308422	+	0.308422i
$483$		0			0
$484$			10.6569i			0.484402i
$485$		0			0
$486$		0			0
$487$	−19.7899	+	19.7899i	−0.896767	+	0.896767i	−0.995149	−	0.0983821i	$-0.968633\pi$
$487$	−19.7899	+	19.7899i	−0.896767	+	0.896767i	0.0983821	+	0.995149i	$0.468633\pi$
$488$	−1.66427	+	1.66427i	−0.0753378	+	0.0753378i
$489$		0			0
$490$		0			0
$491$			11.2817i			0.509135i	0.967055	+	0.254567i	$0.0819330\pi$
$491$			11.2817i			0.509135i	−0.967055	+	0.254567i	$0.918067\pi$
$492$		0			0
$493$	−8.80275	−	8.80275i	−0.396456	−	0.396456i
$494$	0.172088			0.00774262
$495$		0			0
$496$	−9.83839			−0.441757
$497$	−2.07055	−	2.07055i	−0.0928770	−	0.0928770i
$498$		0			0
$499$			25.0825i			1.12285i	0.827529	+	0.561423i	$0.189746\pi$
$499$			25.0825i			1.12285i	−0.827529	+	0.561423i	$0.810254\pi$
$500$		0			0
$501$		0			0
$502$	16.8667	−	16.8667i	0.752799	−	0.752799i
$503$	−3.68357	+	3.68357i	−0.164242	+	0.164242i	−0.784443	−	0.620201i	$-0.787051\pi$
$503$	−3.68357	+	3.68357i	−0.164242	+	0.164242i	0.620201	+	0.784443i	$0.287051\pi$
$504$		0			0
$505$		0			0
$506$		−	4.27186i		−	0.189908i
$507$		0			0
$508$	−14.1356	−	14.1356i	−0.627164	−	0.627164i
$509$	41.1742			1.82501			0.912507	−	0.409061i	$-0.134144\pi$
$509$	41.1742			1.82501			0.912507	+	0.409061i	$0.134144\pi$
$510$		0			0
$511$	3.55051			0.157065
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	6.53501i		−	0.288247i
$515$		0			0
$516$		0			0
$517$	3.70674	−	3.70674i	0.163022	−	0.163022i
$518$	2.87832	−	2.87832i	0.126466	−	0.126466i
$519$		0			0
$520$		0			0
$521$			7.30639i			0.320099i	0.987109	+	0.160049i	$0.0511654\pi$
$521$			7.30639i			0.320099i	−0.987109	+	0.160049i	$0.948835\pi$
$522$		0			0
$523$	1.96060	+	1.96060i	0.0857308	+	0.0857308i	0.748672	−	0.662941i	$-0.230692\pi$
$523$	1.96060	+	1.96060i	0.0857308	+	0.0857308i	−0.662941	+	0.748672i	$0.730692\pi$
$524$	19.3843			0.846805
$525$		0			0
$526$	−10.8496			−0.473065
$527$	−18.9047	−	18.9047i	−0.823500	−	0.823500i
$528$		0			0
$529$		−	30.1810i		−	1.31222i
$530$		0			0
$531$		0			0
$532$	−3.44949	+	3.44949i	−0.149554	+	0.149554i
$533$	0.0244286	−	0.0244286i	0.00105812	−	0.00105812i
$534$		0			0
$535$		0			0
$536$		−	7.19151i		−	0.310626i
$537$		0			0
$538$	14.4694	+	14.4694i	0.623821	+	0.623821i
$539$	−0.585786			−0.0252316
$540$		0			0
$541$	−13.5423			−0.582227			−0.291113	−	0.956689i	$-0.594026\pi$
$541$	−13.5423			−0.582227			−0.291113	+	0.956689i	$0.594026\pi$
$542$	−16.4402	−	16.4402i	−0.706167	−	0.706167i
$543$		0			0
$544$			2.71744i			0.116509i
$545$		0			0
$546$		0			0
$547$	−17.5392	+	17.5392i	−0.749921	+	0.749921i	−0.974464	−	0.224543i	$-0.927911\pi$
$547$	−17.5392	+	17.5392i	−0.749921	+	0.749921i	0.224543	+	0.974464i	$0.427911\pi$
$548$	−5.29858	+	5.29858i	−0.226344	+	0.226344i
$549$		0			0
$550$		0			0
$551$		−	22.3483i		−	0.952068i
$552$		0			0
$553$	−6.16088	−	6.16088i	−0.261987	−	0.261987i
$554$	−28.7985			−1.22353
$555$		0			0
$556$	4.33386			0.183796
$557$	−19.5639	−	19.5639i	−0.828948	−	0.828948i	0.158423	−	0.987371i	$-0.449359\pi$
$557$	−19.5639	−	19.5639i	−0.828948	−	0.828948i	−0.987371	+	0.158423i	$0.949359\pi$
$558$		0			0
$559$			0.213253i			0.00901965i
$560$		0			0
$561$		0			0
$562$	15.6569	−	15.6569i	0.660445	−	0.660445i
$563$	−9.44156	+	9.44156i	−0.397914	+	0.397914i	−0.877497	−	0.479582i	$-0.840788\pi$
$563$	−9.44156	+	9.44156i	−0.397914	+	0.397914i	0.479582	+	0.877497i	$0.340788\pi$
$564$		0			0
$565$		0			0
$566$			20.4495i			0.859556i
$567$		0			0
$568$	−2.07055	−	2.07055i	−0.0868784	−	0.0868784i
$569$	17.2613			0.723633			0.361816	−	0.932249i	$-0.382157\pi$
$569$	17.2613			0.723633			0.361816	+	0.932249i	$0.382157\pi$
$570$		0			0
$571$	−9.88415			−0.413639			−0.206819	−	0.978379i	$-0.566311\pi$
$571$	−9.88415			−0.413639			−0.206819	+	0.978379i	$0.566311\pi$
$572$	0.0146119	+	0.0146119i	0.000610953	+	0.000610953i
$573$		0			0
$574$			0.979336i			0.0408767i
$575$		0			0
$576$		0			0
$577$	27.5140	−	27.5140i	1.14542	−	1.14542i	0.157980	−	0.987442i	$-0.449502\pi$
$577$	27.5140	−	27.5140i	1.14542	−	1.14542i	0.987442	−	0.157980i	$-0.0504982\pi$
$578$	6.79920	−	6.79920i	0.282810	−	0.282810i
$579$		0			0
$580$		0			0
$581$			4.23143i			0.175549i
$582$		0			0
$583$	−0.914320	−	0.914320i	−0.0378673	−	0.0378673i
$584$	3.55051			0.146921
$585$		0			0
$586$	0.626386			0.0258758
$587$	−7.47632	−	7.47632i	−0.308581	−	0.308581i	0.535778	−	0.844359i	$-0.320018\pi$
$587$	−7.47632	−	7.47632i	−0.308581	−	0.308581i	−0.844359	+	0.535778i	$0.820018\pi$
$588$		0			0
$589$		−	47.9948i		−	1.97759i
$590$		0			0
$591$		0			0
$592$	2.87832	−	2.87832i	0.118298	−	0.118298i
$593$	−10.2024	+	10.2024i	−0.418961	+	0.418961i	−0.884846	−	0.465884i	$-0.845736\pi$
$593$	−10.2024	+	10.2024i	−0.418961	+	0.418961i	0.465884	+	0.884846i	$0.345736\pi$
$594$		0			0
$595$		0			0
$596$			16.4083i			0.672111i
$597$		0			0
$598$	0.181905	+	0.181905i	0.00743865	+	0.00743865i
$599$	−32.7293			−1.33728			−0.668642	−	0.743584i	$-0.733124\pi$
$599$	−32.7293			−1.33728			−0.668642	+	0.743584i	$0.733124\pi$
$600$		0			0
$601$	−37.5685			−1.53245			−0.766225	−	0.642573i	$-0.777867\pi$
$601$	−37.5685			−1.53245			−0.766225	+	0.642573i	$0.777867\pi$
$602$	−4.27463	−	4.27463i	−0.174221	−	0.174221i
$603$		0			0
$604$			6.19275i			0.251980i
$605$		0			0
$606$		0			0
$607$	28.4243	−	28.4243i	1.15371	−	1.15371i	0.167905	−	0.985803i	$-0.446300\pi$
$607$	28.4243	−	28.4243i	1.15371	−	1.15371i	0.985803	−	0.167905i	$-0.0537003\pi$
$608$	−3.44949	+	3.44949i	−0.139895	+	0.139895i
$609$		0			0
$610$		0			0
$611$			0.315682i			0.0127711i
$612$		0			0
$613$	−32.4894	−	32.4894i	−1.31223	−	1.31223i	−0.919766	−	0.392467i	$-0.871622\pi$
$613$	−32.4894	−	32.4894i	−1.31223	−	1.31223i	−0.392467	−	0.919766i	$-0.628378\pi$
$614$	−20.3218			−0.820119
$615$		0			0
$616$	−0.585786			−0.0236020
$617$	14.0451	+	14.0451i	0.565434	+	0.565434i	0.930846	−	0.365412i	$-0.119072\pi$
$617$	14.0451	+	14.0451i	0.565434	+	0.565434i	−0.365412	+	0.930846i	$0.619072\pi$
$618$		0			0
$619$			29.1719i			1.17252i	0.810124	+	0.586259i	$0.199400\pi$
$619$			29.1719i			1.17252i	−0.810124	+	0.586259i	$0.800600\pi$
$620$		0			0
$621$		0			0
$622$	12.0839	−	12.0839i	0.484521	−	0.484521i
$623$	−6.87832	+	6.87832i	−0.275574	+	0.275574i
$624$		0			0
$625$		0			0
$626$			3.76320i			0.150408i
$627$		0			0
$628$	−6.65561	−	6.65561i	−0.265588	−	0.265588i
$629$	11.0615			0.441050
$630$		0			0
$631$	−36.5826			−1.45633			−0.728165	−	0.685402i	$-0.759626\pi$
$631$	−36.5826			−1.45633			−0.728165	+	0.685402i	$0.759626\pi$
$632$	−6.16088	−	6.16088i	−0.245066	−	0.245066i
$633$		0			0
$634$		−	13.5200i		−	0.536949i
$635$		0			0
$636$		0			0
$637$	0.0249440	−	0.0249440i	0.000988318	−	0.000988318i
$638$	1.89757	−	1.89757i	0.0751256	−	0.0751256i
$639$		0			0
$640$		0			0
$641$			45.6957i			1.80487i	0.430825	+	0.902436i	$0.358223\pi$
$641$			45.6957i			1.80487i	−0.430825	+	0.902436i	$0.641777\pi$
$642$		0			0
$643$	−18.3877	−	18.3877i	−0.725139	−	0.725139i	0.244509	−	0.969647i	$-0.421373\pi$
$643$	−18.3877	−	18.3877i	−0.725139	−	0.725139i	−0.969647	+	0.244509i	$0.921373\pi$
$644$	−7.29253			−0.287366
$645$		0			0
$646$	−13.2565			−0.521571
$647$	−16.5423	−	16.5423i	−0.650343	−	0.650343i	0.302733	−	0.953076i	$-0.402101\pi$
$647$	−16.5423	−	16.5423i	−0.650343	−	0.650343i	−0.953076	+	0.302733i	$0.902101\pi$
$648$		0			0
$649$		−	0.393034i		−	0.0154279i
$650$		0			0
$651$		0			0
$652$	−7.26002	+	7.26002i	−0.284324	+	0.284324i
$653$	6.67876	−	6.67876i	0.261360	−	0.261360i	−0.564246	−	0.825607i	$-0.690833\pi$
$653$	6.67876	−	6.67876i	0.261360	−	0.261360i	0.825607	+	0.564246i	$0.190833\pi$
$654$		0			0
$655$		0			0
$656$			0.979336i			0.0382366i
$657$		0			0
$658$	−6.32780	−	6.32780i	−0.246684	−	0.246684i
$659$	−31.7335			−1.23616			−0.618080	−	0.786115i	$-0.712089\pi$
$659$	−31.7335			−1.23616			−0.618080	+	0.786115i	$0.712089\pi$
$660$		0			0
$661$	42.4019			1.64924			0.824622	−	0.565684i	$-0.191388\pi$
$661$	42.4019			1.64924			0.824622	+	0.565684i	$0.191388\pi$
$662$	1.91912	+	1.91912i	0.0745885	+	0.0745885i
$663$		0			0
$664$			4.23143i			0.164211i
$665$		0			0
$666$		0			0
$667$	23.6231	−	23.6231i	0.914690	−	0.914690i
$668$	−0.484766	+	0.484766i	−0.0187562	+	0.0187562i
$669$		0			0
$670$		0			0
$671$		−	1.37872i		−	0.0532250i
$672$		0			0
$673$	−27.8748	−	27.8748i	−1.07450	−	1.07450i	−0.996992	−	0.0775032i	$-0.975305\pi$
$673$	−27.8748	−	27.8748i	−1.07450	−	1.07450i	−0.0775032	−	0.996992i	$-0.524695\pi$
$674$	22.6086			0.870851
$675$		0			0
$676$	12.9988			0.499952
$677$	−1.95616	−	1.95616i	−0.0751815	−	0.0751815i	0.668516	−	0.743698i	$-0.266930\pi$
$677$	−1.95616	−	1.95616i	−0.0751815	−	0.0751815i	−0.743698	+	0.668516i	$0.766930\pi$
$678$		0			0
$679$		−	6.71279i		−	0.257613i
$680$		0			0
$681$		0			0
$682$	4.07520	−	4.07520i	0.156047	−	0.156047i
$683$	−24.5400	+	24.5400i	−0.938996	+	0.938996i	−0.998243	−	0.0592472i	$-0.981130\pi$
$683$	−24.5400	+	24.5400i	−0.938996	+	0.938996i	0.0592472	+	0.998243i	$0.481130\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	−4.27463	−	4.27463i	−0.162969	−	0.162969i
$689$	0.0778674			0.00296651
$690$		0			0
$691$	−0.993716			−0.0378027			−0.0189014	−	0.999821i	$-0.506017\pi$
$691$	−0.993716			−0.0378027			−0.0189014	+	0.999821i	$0.506017\pi$
$692$	15.8126	+	15.8126i	0.601104	+	0.601104i
$693$		0			0
$694$		−	25.4881i		−	0.967516i
$695$		0			0
$696$		0			0
$697$	−1.88181	+	1.88181i	−0.0712787	+	0.0712787i
$698$	16.0115	−	16.0115i	0.606044	−	0.606044i
$699$		0			0
$700$		0			0
$701$			46.4565i			1.75464i	0.479909	+	0.877318i	$0.340669\pi$
$701$			46.4565i			1.75464i	−0.479909	+	0.877318i	$0.659331\pi$
$702$		0			0
$703$	14.0413	+	14.0413i	0.529579	+	0.529579i
$704$	−0.585786			−0.0220777
$705$		0			0
$706$	20.5437			0.773173
$707$	4.37429	+	4.37429i	0.164512	+	0.164512i
$708$		0			0
$709$			10.5904i			0.397729i	0.980027	+	0.198865i	$0.0637254\pi$
$709$			10.5904i			0.397729i	−0.980027	+	0.198865i	$0.936275\pi$
$710$		0			0
$711$		0			0
$712$	−6.87832	+	6.87832i	−0.257776	+	0.257776i
$713$	50.7326	−	50.7326i	1.89995	−	1.89995i
$714$		0			0
$715$		0			0
$716$			5.14235i			0.192179i
$717$		0			0
$718$	8.71608	+	8.71608i	0.325281	+	0.325281i
$719$	16.2086			0.604479			0.302240	−	0.953232i	$-0.402266\pi$
$719$	16.2086			0.604479			0.302240	+	0.953232i	$0.402266\pi$
$720$		0			0
$721$	−0.384990			−0.0143378
$722$	−3.39267	−	3.39267i	−0.126262	−	0.126262i
$723$		0			0
$724$			15.0411i			0.558999i
$725$		0			0
$726$		0			0
$727$	4.44183	−	4.44183i	0.164738	−	0.164738i	−0.619924	−	0.784662i	$-0.712836\pi$
$727$	4.44183	−	4.44183i	0.164738	−	0.164738i	0.784662	+	0.619924i	$0.212836\pi$
$728$	0.0249440	−	0.0249440i	0.000924487	−	0.000924487i
$729$		0			0
$730$		0			0
$731$		−	16.4276i		−	0.607596i
$732$		0			0
$733$	−22.9524	−	22.9524i	−0.847767	−	0.847767i	0.142087	−	0.989854i	$-0.454619\pi$
$733$	−22.9524	−	22.9524i	−0.847767	−	0.847767i	−0.989854	+	0.142087i	$0.954619\pi$
$734$	28.7690			1.06188
$735$		0			0
$736$	−7.29253			−0.268806
$737$	2.97882	+	2.97882i	0.109726	+	0.109726i
$738$		0			0
$739$			2.01607i			0.0741623i	0.999312	+	0.0370812i	$0.0118060\pi$
$739$			2.01607i			0.0741623i	−0.999312	+	0.0370812i	$0.988194\pi$
$740$		0			0
$741$		0			0
$742$	−1.56084	+	1.56084i	−0.0573003	+	0.0573003i
$743$	−4.57937	+	4.57937i	−0.168001	+	0.168001i	−0.786100	−	0.618099i	$-0.787903\pi$
$743$	−4.57937	+	4.57937i	−0.168001	+	0.168001i	0.618099	+	0.786100i	$0.287903\pi$
$744$		0			0
$745$		0			0
$746$			23.7559i			0.869765i
$747$		0			0
$748$	−1.12560	−	1.12560i	−0.0411560	−	0.0411560i
$749$	5.62763			0.205629
$750$		0			0
$751$	13.5894			0.495882			0.247941	−	0.968775i	$-0.420246\pi$
$751$	13.5894			0.495882			0.247941	+	0.968775i	$0.420246\pi$
$752$	−6.32780	−	6.32780i	−0.230751	−	0.230751i
$753$		0			0
$754$			0.161605i			0.00588531i
$755$		0			0
$756$		0			0
$757$	−19.4354	+	19.4354i	−0.706391	+	0.706391i	−0.965775	−	0.259383i	$-0.916481\pi$
$757$	−19.4354	+	19.4354i	−0.706391	+	0.706391i	0.259383	+	0.965775i	$0.416481\pi$
$758$	9.55355	−	9.55355i	0.347000	−	0.347000i
$759$		0			0
$760$		0			0
$761$			4.32354i			0.156728i	0.996925	+	0.0783641i	$0.0249697\pi$
$761$			4.32354i			0.156728i	−0.996925	+	0.0783641i	$0.975030\pi$
$762$		0			0
$763$	6.09513	+	6.09513i	0.220659	+	0.220659i
$764$	11.8732			0.429556
$765$		0			0
$766$	−5.43591			−0.196407
$767$	0.0167362	+	0.0167362i	0.000604310	+	0.000604310i
$768$		0			0
$769$			23.5218i			0.848219i	0.905611	+	0.424109i	$0.139413\pi$
$769$			23.5218i			0.848219i	−0.905611	+	0.424109i	$0.860587\pi$
$770$		0			0
$771$		0			0
$772$	0.0864086	−	0.0864086i	0.00310992	−	0.00310992i
$773$	−20.3027	+	20.3027i	−0.730236	+	0.730236i	−0.970666	−	0.240430i	$-0.922711\pi$
$773$	−20.3027	+	20.3027i	−0.730236	+	0.730236i	0.240430	+	0.970666i	$0.422711\pi$
$774$		0			0
$775$		0			0
$776$		−	6.71279i		−	0.240975i
$777$		0			0
$778$	−25.3908	−	25.3908i	−0.910305	−	0.910305i
$779$	−4.77751			−0.171172
$780$		0			0
$781$	1.71530			0.0613783
$782$	−14.0127	−	14.0127i	−0.501094	−	0.501094i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$		0			0
$786$		0			0
$787$	36.8569	−	36.8569i	1.31381	−	1.31381i	0.395222	−	0.918586i	$-0.370668\pi$
$787$	36.8569	−	36.8569i	1.31381	−	1.31381i	0.918586	−	0.395222i	$-0.129332\pi$
$788$	−15.3374	+	15.3374i	−0.546373	+	0.546373i
$789$		0			0
$790$		0			0
$791$			8.67147i			0.308322i
$792$		0			0
$793$	0.0587090	+	0.0587090i	0.00208482	+	0.00208482i
$794$	25.3465			0.899513
$795$		0			0
$796$	−13.4256			−0.475857
$797$	5.72865	+	5.72865i	0.202919	+	0.202919i	0.801250	−	0.598330i	$-0.204169\pi$
$797$	5.72865	+	5.72865i	0.202919	+	0.202919i	−0.598330	+	0.801250i	$0.704169\pi$
$798$		0			0
$799$		−	24.3180i		−	0.860309i
$800$		0			0
$801$		0			0
$802$	−23.6203	+	23.6203i	−0.834063	+	0.834063i
$803$	−1.47067	+	1.47067i	−0.0518988	+	0.0518988i
$804$		0			0
$805$		0			0
$806$			0.347061i			0.0122247i
$807$		0			0
$808$	4.37429	+	4.37429i	0.153887	+	0.153887i
$809$	27.2215			0.957056			0.478528	−	0.878072i	$-0.341171\pi$
$809$	27.2215			0.957056			0.478528	+	0.878072i	$0.341171\pi$
$810$		0			0
$811$	−33.2813			−1.16866			−0.584332	−	0.811515i	$-0.698643\pi$
$811$	−33.2813			−1.16866			−0.584332	+	0.811515i	$0.698643\pi$
$812$	−3.23936	−	3.23936i	−0.113679	−	0.113679i
$813$		0			0
$814$			2.38447i			0.0835758i
$815$		0			0
$816$		0			0
$817$	20.8530	−	20.8530i	0.729554	−	0.729554i
$818$	−27.8910	+	27.8910i	−0.975184	+	0.975184i
$819$		0			0
$820$		0			0
$821$			12.0545i			0.420704i	0.977626	+	0.210352i	$0.0674610\pi$
$821$			12.0545i			0.420704i	−0.977626	+	0.210352i	$0.932539\pi$
$822$		0			0
$823$	19.1280	+	19.1280i	0.666762	+	0.666762i	0.956965	−	0.290203i	$-0.0937230\pi$
$823$	19.1280	+	19.1280i	0.666762	+	0.666762i	−0.290203	+	0.956965i	$0.593723\pi$
$824$	−0.384990			−0.0134118
$825$		0			0
$826$	−0.670951			−0.0233454
$827$	26.4601	+	26.4601i	0.920109	+	0.920109i	0.997037	−	0.0769276i	$-0.0245110\pi$
$827$	26.4601	+	26.4601i	0.920109	+	0.920109i	−0.0769276	+	0.997037i	$0.524511\pi$
$828$		0			0
$829$			2.18260i			0.0758047i	0.999281	+	0.0379024i	$0.0120676\pi$
$829$			2.18260i			0.0758047i	−0.999281	+	0.0379024i	$0.987932\pi$
$830$		0			0
$831$		0			0
$832$	0.0249440	−	0.0249440i	0.000864779	−	0.000864779i
$833$	−1.92152	+	1.92152i	−0.0665767	+	0.0665767i
$834$		0			0
$835$		0			0
$836$		−	2.85765i		−	0.0988339i
$837$		0			0
$838$	−23.0509	−	23.0509i	−0.796281	−	0.796281i
$839$	−52.0744			−1.79781			−0.898904	−	0.438146i	$-0.855635\pi$
$839$	−52.0744			−1.79781			−0.898904	+	0.438146i	$0.855635\pi$
$840$		0			0
$841$	−8.01314			−0.276315
$842$	−10.3471	−	10.3471i	−0.356583	−	0.356583i
$843$		0			0
$844$		−	16.2263i		−	0.558531i
$845$		0			0
$846$		0			0
$847$	−7.53553	+	7.53553i	−0.258924	+	0.258924i
$848$	−1.56084	+	1.56084i	−0.0535995	+	0.0535995i
$849$		0			0
$850$		0			0
$851$			29.6846i			1.01758i
$852$		0			0
$853$	−33.9351	−	33.9351i	−1.16192	−	1.16192i	−0.984056	−	0.177859i	$-0.943083\pi$
$853$	−33.9351	−	33.9351i	−1.16192	−	1.16192i	−0.177859	−	0.984056i	$-0.556917\pi$
$854$	−2.35363			−0.0805395
$855$		0			0
$856$	5.62763			0.192348
$857$	−25.7965	−	25.7965i	−0.881192	−	0.881192i	0.112464	−	0.993656i	$-0.464126\pi$
$857$	−25.7965	−	25.7965i	−0.881192	−	0.881192i	−0.993656	+	0.112464i	$0.964126\pi$
$858$		0			0
$859$			28.1396i			0.960112i	0.877238	+	0.480056i	$0.159384\pi$
$859$			28.1396i			0.960112i	−0.877238	+	0.480056i	$0.840616\pi$
$860$		0			0
$861$		0			0
$862$	−4.16024	+	4.16024i	−0.141699	+	0.141699i
$863$	−26.5740	+	26.5740i	−0.904590	+	0.904590i	−0.995829	−	0.0912392i	$-0.970917\pi$
$863$	−26.5740	+	26.5740i	−0.904590	+	0.904590i	0.0912392	+	0.995829i	$0.470917\pi$
$864$		0			0
$865$		0			0
$866$		−	10.6848i		−	0.363085i
$867$		0			0
$868$	−6.95680	−	6.95680i	−0.236129	−	0.236129i
$869$	5.10384			0.173136
$870$		0			0
$871$	−0.253689			−0.00859592
$872$	6.09513	+	6.09513i	0.206407	+	0.206407i
$873$		0			0
$874$		−	35.5753i		−	1.20335i
$875$		0			0
$876$		0			0
$877$	22.9574	−	22.9574i	0.775217	−	0.775217i	−0.203796	−	0.979013i	$-0.565328\pi$
$877$	22.9574	−	22.9574i	0.775217	−	0.775217i	0.979013	+	0.203796i	$0.0653280\pi$
$878$	14.9634	−	14.9634i	0.504989	−	0.504989i
$879$		0			0
$880$		0			0
$881$			48.8268i			1.64502i	0.568753	+	0.822508i	$0.307426\pi$
$881$			48.8268i			1.64502i	−0.568753	+	0.822508i	$0.692574\pi$
$882$		0			0
$883$	−1.18290	−	1.18290i	−0.0398078	−	0.0398078i	0.686923	−	0.726730i	$-0.258961\pi$
$883$	−1.18290	−	1.18290i	−0.0398078	−	0.0398078i	−0.726730	+	0.686923i	$0.758961\pi$
$884$	0.0958609			0.00322415
$885$		0			0
$886$	−6.11845			−0.205553
$887$	−7.01262	−	7.01262i	−0.235461	−	0.235461i	0.579507	−	0.814967i	$-0.303245\pi$
$887$	−7.01262	−	7.01262i	−0.235461	−	0.235461i	−0.814967	+	0.579507i	$0.803245\pi$
$888$		0			0
$889$		−	19.9907i		−	0.670467i
$890$		0			0
$891$		0			0
$892$	11.1919	−	11.1919i	0.374732	−	0.374732i
$893$	30.8690	−	30.8690i	1.03299	−	1.03299i
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	3.10154	+	3.10154i	0.103500	+	0.103500i
$899$	45.0711			1.50320
$900$		0			0
$901$	−5.99838			−0.199835
$902$	−0.405654	−	0.405654i	−0.0135068	−	0.0135068i
$903$		0			0
$904$			8.67147i			0.288409i
$905$		0			0
$906$		0			0
$907$	6.95267	−	6.95267i	0.230860	−	0.230860i	−0.582192	−	0.813051i	$-0.697805\pi$
$907$	6.95267	−	6.95267i	0.230860	−	0.230860i	0.813051	+	0.582192i	$0.197805\pi$
$908$	14.5784	−	14.5784i	0.483800	−	0.483800i
$909$		0			0
$910$		0			0
$911$		−	6.43828i		−	0.213310i	−0.994296	−	0.106655i	$-0.965986\pi$
$911$		−	6.43828i		−	0.213310i	0.994296	−	0.106655i	$-0.0340140\pi$
$912$		0			0
$913$	−1.75272	−	1.75272i	−0.0580064	−	0.0580064i
$914$	1.93691			0.0640672
$915$		0			0
$916$	−16.0905			−0.531645
$917$	13.7067	+	13.7067i	0.452637	+	0.452637i
$918$		0			0
$919$		−	16.4598i		−	0.542959i	−0.962444	−	0.271480i	$-0.912487\pi$
$919$		−	16.4598i		−	0.542959i	0.962444	−	0.271480i	$-0.0875129\pi$
$920$		0			0
$921$		0			0
$922$	0.605558	−	0.605558i	0.0199430	−	0.0199430i
$923$	−0.0730412	+	0.0730412i	−0.00240418	+	0.00240418i
$924$		0			0
$925$		0			0
$926$			5.32300i			0.174925i
$927$		0			0
$928$	−3.23936	−	3.23936i	−0.106337	−	0.106337i
$929$	−35.6763			−1.17050			−0.585250	−	0.810853i	$-0.699004\pi$
$929$	−35.6763			−1.17050			−0.585250	+	0.810853i	$0.699004\pi$
$930$		0			0
$931$	−4.87832			−0.159880
$932$	−13.7162	−	13.7162i	−0.449289	−	0.449289i
$933$		0			0
$934$			27.4136i			0.897002i
$935$		0			0
$936$		0			0
$937$	−22.6490	+	22.6490i	−0.739912	+	0.739912i	−0.972561	−	0.232649i	$-0.925261\pi$
$937$	−22.6490	+	22.6490i	−0.739912	+	0.739912i	0.232649	+	0.972561i	$0.425261\pi$
$938$	5.08516	−	5.08516i	0.166036	−	0.166036i
$939$		0			0
$940$		0			0
$941$			31.3964i			1.02349i	0.859137	+	0.511746i	$0.171001\pi$
$941$			31.3964i			1.02349i	−0.859137	+	0.511746i	$0.828999\pi$
$942$		0			0
$943$	−5.05004	−	5.05004i	−0.164452	−	0.164452i
$944$	−0.670951			−0.0218376
$945$		0			0
$946$	3.54122			0.115135
$947$	−13.7087	−	13.7087i	−0.445472	−	0.445472i	0.448374	−	0.893846i	$-0.352003\pi$
$947$	−13.7087	−	13.7087i	−0.445472	−	0.445472i	−0.893846	+	0.448374i	$0.852003\pi$
$948$		0			0
$949$		−	0.125248i		−	0.00406574i
$950$		0			0
$951$		0			0
$952$	−1.92152	+	1.92152i	−0.0622768	+	0.0622768i
$953$	−8.88969	+	8.88969i	−0.287965	+	0.287965i	−0.836275	−	0.548310i	$-0.815271\pi$
$953$	−8.88969	+	8.88969i	−0.287965	+	0.287965i	0.548310	+	0.836275i	$0.315271\pi$
$954$		0			0
$955$		0			0
$956$			0.485281i			0.0156951i
$957$		0			0
$958$	19.6711	+	19.6711i	0.635545	+	0.635545i
$959$	−7.49333			−0.241972
$960$		0			0
$961$	65.7940			2.12239
$962$	−0.101536	−	0.101536i	−0.00327365	−	0.00327365i
$963$		0			0
$964$			9.57598i			0.308422i
$965$		0			0
$966$		0			0
$967$	21.8890	−	21.8890i	0.703902	−	0.703902i	−0.261344	−	0.965246i	$-0.584166\pi$
$967$	21.8890	−	21.8890i	0.703902	−	0.703902i	0.965246	+	0.261344i	$0.0841657\pi$
$968$	−7.53553	+	7.53553i	−0.242201	+	0.242201i
$969$		0			0
$970$		0			0
$971$			1.40284i			0.0450192i	0.999747	+	0.0225096i	$0.00716563\pi$
$971$			1.40284i			0.0450192i	−0.999747	+	0.0225096i	$0.992834\pi$
$972$		0			0
$973$	3.06450	+	3.06450i	0.0982434	+	0.0982434i
$974$	−27.9872			−0.896767
$975$		0			0
$976$	−2.35363			−0.0753378
$977$	34.6622	+	34.6622i	1.10894	+	1.10894i	0.993290	+	0.115651i	$0.0368956\pi$
$977$	34.6622	+	34.6622i	1.10894	+	1.10894i	0.115651	+	0.993290i	$0.463104\pi$
$978$		0			0
$979$		−	5.69818i		−	0.182115i
$980$		0			0
$981$		0			0
$982$	−7.97734	+	7.97734i	−0.254567	+	0.254567i
$983$	16.6955	−	16.6955i	0.532503	−	0.532503i	−0.388813	−	0.921317i	$-0.627115\pi$
$983$	16.6955	−	16.6955i	0.532503	−	0.532503i	0.921317	+	0.388813i	$0.127115\pi$
$984$		0			0
$985$		0			0
$986$		−	12.4490i		−	0.396456i
$987$		0			0
$988$	0.121685	+	0.121685i	0.00387131	+	0.00387131i
$989$	44.0851			1.40183
$990$		0			0
$991$	−56.8845			−1.80700			−0.903498	−	0.428593i	$-0.859009\pi$
$991$	−56.8845			−1.80700			−0.903498	+	0.428593i	$0.859009\pi$
$992$	−6.95680	−	6.95680i	−0.220878	−	0.220878i
$993$		0			0
$994$		−	2.92820i		−	0.0928770i
$995$		0			0
$996$		0			0
$997$	19.0305	−	19.0305i	0.602701	−	0.602701i	−0.338327	−	0.941028i	$-0.609861\pi$
$997$	19.0305	−	19.0305i	0.602701	−	0.602701i	0.941028	+	0.338327i	$0.109861\pi$
$998$	−17.7360	+	17.7360i	−0.561423	+	0.561423i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.g.2843.4	yes	8
3.2	odd	2		3150.2.m.h.2843.2	yes	8
5.2	odd	4		3150.2.m.h.1457.2	yes	8
5.3	odd	4		3150.2.m.l.1457.3	yes	8
5.4	even	2		3150.2.m.k.2843.1	yes	8
15.2	even	4	inner	3150.2.m.g.1457.4	✓	8
15.8	even	4		3150.2.m.k.1457.1	yes	8
15.14	odd	2		3150.2.m.l.2843.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.g.1457.4	✓	8	15.2	even	4	inner
3150.2.m.g.2843.4	yes	8	1.1	even	1	trivial
3150.2.m.h.1457.2	yes	8	5.2	odd	4
3150.2.m.h.2843.2	yes	8	3.2	odd	2
3150.2.m.k.1457.1	yes	8	15.8	even	4
3150.2.m.k.2843.1	yes	8	5.4	even	2
3150.2.m.l.1457.3	yes	8	5.3	odd	4
3150.2.m.l.2843.3	yes	8	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.585786i q^{11} +(0.0249440 + 0.0249440i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-1.92152 - 1.92152i) q^{17} -4.87832i q^{19} +(0.414214 - 0.414214i) q^{22} +(5.15660 - 5.15660i) q^{23} +0.0352762i q^{26} +(-0.707107 - 0.707107i) q^{28} +4.58114 q^{29} +9.83839 q^{31} +(-0.707107 - 0.707107i) q^{32} -2.71744i q^{34} +(-2.87832 + 2.87832i) q^{37} +(3.44949 - 3.44949i) q^{38} -0.979336i q^{41} +(4.27463 + 4.27463i) q^{43} +0.585786 q^{44} +7.29253 q^{46} +(6.32780 + 6.32780i) q^{47} -1.00000i q^{49} +(-0.0249440 + 0.0249440i) q^{52} +(1.56084 - 1.56084i) q^{53} -1.00000i q^{56} +(3.23936 + 3.23936i) q^{58} +0.670951 q^{59} +2.35363 q^{61} +(6.95680 + 6.95680i) q^{62} -1.00000i q^{64} +(-5.08516 + 5.08516i) q^{67} +(1.92152 - 1.92152i) q^{68} +2.92820i q^{71} +(-2.51059 - 2.51059i) q^{73} -4.07055 q^{74} +4.87832 q^{76} +(0.414214 + 0.414214i) q^{77} +8.71279i q^{79} +(0.692495 - 0.692495i) q^{82} +(2.99207 - 2.99207i) q^{83} +6.04524i q^{86} +(0.414214 + 0.414214i) q^{88} +9.72741 q^{89} -0.0352762 q^{91} +(5.15660 + 5.15660i) q^{92} +8.94887i q^{94} +(-4.74666 + 4.74666i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Introduction

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