LMFDB - Embedded newform 1148.2.k.b.337.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.16
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +O(q^{10})$	\(q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +(-3.89109 - 3.89109i) q^{11} +(-2.36139 - 2.36139i) q^{13} +(4.22578 - 4.22578i) q^{15} +(1.41870 - 1.41870i) q^{17} +(2.77167 - 2.77167i) q^{19} -2.42015i q^{21} -6.33212 q^{23} -1.09761 q^{25} +(0.244504 - 0.244504i) q^{27} +(-1.38204 - 1.38204i) q^{29} +6.75810 q^{31} -13.3177i q^{33} +(-1.74608 + 1.74608i) q^{35} +0.731303 q^{37} -8.08211i q^{39} +(4.55889 + 4.49628i) q^{41} -7.12884i q^{43} +7.05519 q^{45} +(-5.61063 + 5.61063i) q^{47} +1.00000i q^{49} +4.85565 q^{51} +(4.60712 + 4.60712i) q^{53} +(-9.60841 + 9.60841i) q^{55} +9.48634 q^{57} -10.1934 q^{59} -9.57500i q^{61} +(2.02029 - 2.02029i) q^{63} +(-5.83106 + 5.83106i) q^{65} +(-3.13423 + 3.13423i) q^{67} +(-10.8362 - 10.8362i) q^{69} +(-2.44329 - 2.44329i) q^{71} +13.6735i q^{73} +(-1.87834 - 1.87834i) q^{75} +5.50284i q^{77} +(-1.22940 - 1.22940i) q^{79} +9.40821 q^{81} +6.98865 q^{83} +(-3.50324 - 3.50324i) q^{85} -4.73018i q^{87} +(11.5345 + 11.5345i) q^{89} +3.33951i q^{91} +(11.5652 + 11.5652i) q^{93} +(-6.84417 - 6.84417i) q^{95} +(11.0829 - 11.0829i) q^{97} +(11.1173 - 11.1173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.71130	+	1.71130i	0.988022	+	0.988022i	0.999929	−	0.0119072i	$-0.00379027\pi$
$3$	1.71130	+	1.71130i	0.988022	+	0.988022i	−0.0119072	+	0.999929i	$0.503790\pi$
$4$		0			0
$5$		−	2.46933i		−	1.10432i	−0.833738	−	0.552160i	$-0.813804\pi$
$5$		−	2.46933i		−	1.10432i	0.833738	−	0.552160i	$-0.186196\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$			2.85712i			0.952375i
$10$		0			0
$11$	−3.89109	−	3.89109i	−1.17321	−	1.17321i	−0.981440	−	0.191768i	$-0.938578\pi$
$11$	−3.89109	−	3.89109i	−1.17321	−	1.17321i	−0.191768	−	0.981440i	$-0.561422\pi$
$12$		0			0
$13$	−2.36139	−	2.36139i	−0.654932	−	0.654932i	0.299245	−	0.954176i	$-0.403265\pi$
$13$	−2.36139	−	2.36139i	−0.654932	−	0.654932i	−0.954176	+	0.299245i	$0.903265\pi$
$14$		0			0
$15$	4.22578	−	4.22578i	1.09109	−	1.09109i
$16$		0			0
$17$	1.41870	−	1.41870i	0.344085	−	0.344085i	−0.513816	−	0.857901i	$-0.671769\pi$
$17$	1.41870	−	1.41870i	0.344085	−	0.344085i	0.857901	+	0.513816i	$0.171769\pi$
$18$		0			0
$19$	2.77167	−	2.77167i	0.635864	−	0.635864i	−0.313668	−	0.949533i	$-0.601558\pi$
$19$	2.77167	−	2.77167i	0.635864	−	0.635864i	0.949533	+	0.313668i	$0.101558\pi$
$20$		0			0
$21$		−	2.42015i		−	0.528120i
$22$		0			0
$23$	−6.33212			−1.32034			−0.660169	−	0.751117i	$-0.729516\pi$
$23$	−6.33212			−1.32034			−0.660169	+	0.751117i	$0.729516\pi$
$24$		0			0
$25$	−1.09761			−0.219522
$26$		0			0
$27$	0.244504	−	0.244504i	0.0470549	−	0.0470549i
$28$		0			0
$29$	−1.38204	−	1.38204i	−0.256638	−	0.256638i	0.567047	−	0.823685i	$-0.308086\pi$
$29$	−1.38204	−	1.38204i	−0.256638	−	0.256638i	−0.823685	+	0.567047i	$0.808086\pi$
$30$		0			0
$31$	6.75810			1.21379			0.606895	−	0.794782i	$-0.292415\pi$
$31$	6.75810			1.21379			0.606895	+	0.794782i	$0.292415\pi$
$32$		0			0
$33$		−	13.3177i		−	2.31831i
$34$		0			0
$35$	−1.74608	+	1.74608i	−0.295142	+	0.295142i
$36$		0			0
$37$	0.731303			0.120225			0.0601127	−	0.998192i	$-0.480854\pi$
$37$	0.731303			0.120225			0.0601127	+	0.998192i	$0.480854\pi$
$38$		0			0
$39$		−	8.08211i		−	1.29417i
$40$		0			0
$41$	4.55889	+	4.49628i	0.711980	+	0.702200i
$41$	4.55889	+	4.49628i	0.711980	+	0.702200i
$42$		0			0
$43$		−	7.12884i		−	1.08714i	−0.839365	−	0.543569i	$-0.817073\pi$
$43$		−	7.12884i		−	1.08714i	0.839365	−	0.543569i	$-0.182927\pi$
$44$		0			0
$45$	7.05519			1.05173
$46$		0			0
$47$	−5.61063	+	5.61063i	−0.818395	+	0.818395i	−0.985875	−	0.167480i	$-0.946437\pi$
$47$	−5.61063	+	5.61063i	−0.818395	+	0.818395i	0.167480	+	0.985875i	$0.446437\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	4.85565			0.679927
$52$		0			0
$53$	4.60712	+	4.60712i	0.632836	+	0.632836i	0.948778	−	0.315942i	$-0.102321\pi$
$53$	4.60712	+	4.60712i	0.632836	+	0.632836i	−0.315942	+	0.948778i	$0.602321\pi$
$54$		0			0
$55$	−9.60841	+	9.60841i	−1.29560	+	1.29560i
$56$		0			0
$57$	9.48634			1.25650
$58$		0			0
$59$	−10.1934			−1.32707			−0.663533	−	0.748147i	$-0.730944\pi$
$59$	−10.1934			−1.32707			−0.663533	+	0.748147i	$0.730944\pi$
$60$		0			0
$61$		−	9.57500i		−	1.22595i	−0.790101	−	0.612976i	$-0.789972\pi$
$61$		−	9.57500i		−	1.22595i	0.790101	−	0.612976i	$-0.210028\pi$
$62$		0			0
$63$	2.02029	−	2.02029i	0.254533	−	0.254533i
$64$		0			0
$65$	−5.83106	+	5.83106i	−0.723254	+	0.723254i
$66$		0			0
$67$	−3.13423	+	3.13423i	−0.382908	+	0.382908i	−0.872149	−	0.489241i	$-0.837274\pi$
$67$	−3.13423	+	3.13423i	−0.382908	+	0.382908i	0.489241	+	0.872149i	$0.337274\pi$
$68$		0			0
$69$	−10.8362	−	10.8362i	−1.30452	−	1.30452i
$70$		0			0
$71$	−2.44329	−	2.44329i	−0.289966	−	0.289966i	0.547101	−	0.837067i	$-0.315731\pi$
$71$	−2.44329	−	2.44329i	−0.289966	−	0.289966i	−0.837067	+	0.547101i	$0.815731\pi$
$72$		0			0
$73$			13.6735i			1.60036i	0.599759	+	0.800181i	$0.295263\pi$
$73$			13.6735i			1.60036i	−0.599759	+	0.800181i	$0.704737\pi$
$74$		0			0
$75$	−1.87834	−	1.87834i	−0.216893	−	0.216893i
$76$		0			0
$77$			5.50284i			0.627106i
$78$		0			0
$79$	−1.22940	−	1.22940i	−0.138318	−	0.138318i	0.634558	−	0.772876i	$-0.281182\pi$
$79$	−1.22940	−	1.22940i	−0.138318	−	0.138318i	−0.772876	+	0.634558i	$0.781182\pi$
$80$		0			0
$81$	9.40821			1.04536
$82$		0			0
$83$	6.98865			0.767104			0.383552	−	0.923519i	$-0.374701\pi$
$83$	6.98865			0.767104			0.383552	+	0.923519i	$0.374701\pi$
$84$		0			0
$85$	−3.50324	−	3.50324i	−0.379980	−	0.379980i
$86$		0			0
$87$		−	4.73018i		−	0.507129i
$88$		0			0
$89$	11.5345	+	11.5345i	1.22266	+	1.22266i	0.966683	+	0.255975i	$0.0823965\pi$
$89$	11.5345	+	11.5345i	1.22266	+	1.22266i	0.255975	+	0.966683i	$0.417603\pi$
$90$		0			0
$91$			3.33951i			0.350076i
$92$		0			0
$93$	11.5652	+	11.5652i	1.19925	+	1.19925i
$94$		0			0
$95$	−6.84417	−	6.84417i	−0.702197	−	0.702197i
$96$		0			0
$97$	11.0829	−	11.0829i	1.12530	−	1.12530i	0.134365	−	0.990932i	$-0.457100\pi$
$97$	11.0829	−	11.0829i	1.12530	−	1.12530i	0.990932	−	0.134365i	$-0.0428996\pi$
$98$		0			0
$99$	11.1173	−	11.1173i	1.11733	−	1.11733i
$100$		0			0
$101$	−2.96559	+	2.96559i	−0.295087	+	0.295087i	−0.839086	−	0.543999i	$-0.816910\pi$
$101$	−2.96559	+	2.96559i	−0.295087	+	0.295087i	0.543999	+	0.839086i	$0.316910\pi$
$102$		0			0
$103$		−	11.0539i		−	1.08918i	−0.838704	−	0.544588i	$-0.816686\pi$
$103$		−	11.0539i		−	1.08918i	0.838704	−	0.544588i	$-0.183314\pi$
$104$		0			0
$105$	−5.97616			−0.583213
$106$		0			0
$107$	−4.31574			−0.417218			−0.208609	−	0.977999i	$-0.566894\pi$
$107$	−4.31574			−0.417218			−0.208609	+	0.977999i	$0.566894\pi$
$108$		0			0
$109$	8.24007	−	8.24007i	0.789256	−	0.789256i	−0.192116	−	0.981372i	$-0.561535\pi$
$109$	8.24007	−	8.24007i	0.789256	−	0.789256i	0.981372	+	0.192116i	$0.0615350\pi$
$110$		0			0
$111$	1.25148	+	1.25148i	0.118785	+	0.118785i
$112$		0			0
$113$	14.0370			1.32049			0.660246	−	0.751049i	$-0.270452\pi$
$113$	14.0370			1.32049			0.660246	+	0.751049i	$0.270452\pi$
$114$		0			0
$115$			15.6361i			1.45808i
$116$		0			0
$117$	6.74678	−	6.74678i	0.623740	−	0.623740i
$118$		0			0
$119$	−2.00634			−0.183921
$120$		0			0
$121$			19.2812i			1.75284i
$122$		0			0
$123$	0.107159	+	15.4961i	0.00966217	+	1.39724i
$124$		0			0
$125$		−	9.63630i		−	0.861897i
$126$		0			0
$127$	−3.91790			−0.347657			−0.173829	−	0.984776i	$-0.555614\pi$
$127$	−3.91790			−0.347657			−0.173829	+	0.984776i	$0.555614\pi$
$128$		0			0
$129$	12.1996	−	12.1996i	1.07412	−	1.07412i
$130$		0			0
$131$			2.98844i			0.261102i	0.991442	+	0.130551i	$0.0416746\pi$
$131$			2.98844i			0.261102i	−0.991442	+	0.130551i	$0.958325\pi$
$132$		0			0
$133$	−3.91973			−0.339884
$134$		0			0
$135$	−0.603763	−	0.603763i	−0.0519637	−	0.0519637i
$136$		0			0
$137$	−6.46592	+	6.46592i	−0.552421	+	0.552421i	−0.927139	−	0.374718i	$-0.877740\pi$
$137$	−6.46592	+	6.46592i	−0.552421	+	0.552421i	0.374718	+	0.927139i	$0.377740\pi$
$138$		0			0
$139$	9.71747			0.824225			0.412113	−	0.911133i	$-0.364791\pi$
$139$	9.71747			0.824225			0.412113	+	0.911133i	$0.364791\pi$
$140$		0			0
$141$	−19.2030			−1.61718
$142$		0			0
$143$			18.3768i			1.53674i
$144$		0			0
$145$	−3.41272	+	3.41272i	−0.283411	+	0.283411i
$146$		0			0
$147$	−1.71130	+	1.71130i	−0.141146	+	0.141146i
$148$		0			0
$149$	−3.19072	+	3.19072i	−0.261394	+	0.261394i	−0.825620	−	0.564226i	$-0.809175\pi$
$149$	−3.19072	+	3.19072i	−0.261394	+	0.261394i	0.564226	+	0.825620i	$0.309175\pi$
$150$		0			0
$151$	14.8972	+	14.8972i	1.21232	+	1.21232i	0.970263	+	0.242054i	$0.0778212\pi$
$151$	14.8972	+	14.8972i	1.21232	+	1.21232i	0.242054	+	0.970263i	$0.422179\pi$
$152$		0			0
$153$	4.05340	+	4.05340i	0.327698	+	0.327698i
$154$		0			0
$155$		−	16.6880i		−	1.34041i
$156$		0			0
$157$	−7.35695	−	7.35695i	−0.587149	−	0.587149i	0.349710	−	0.936858i	$-0.386280\pi$
$157$	−7.35695	−	7.35695i	−0.587149	−	0.587149i	−0.936858	+	0.349710i	$0.886280\pi$
$158$		0			0
$159$			15.7684i			1.25051i
$160$		0			0
$161$	4.47749	+	4.47749i	0.352875	+	0.352875i
$162$		0			0
$163$	0.828390			0.0648845			0.0324422	−	0.999474i	$-0.489671\pi$
$163$	0.828390			0.0648845			0.0324422	+	0.999474i	$0.489671\pi$
$164$		0			0
$165$	−32.8858			−2.56016
$166$		0			0
$167$	−11.3713	−	11.3713i	−0.879941	−	0.879941i	0.113587	−	0.993528i	$-0.463766\pi$
$167$	−11.3713	−	11.3713i	−0.879941	−	0.879941i	−0.993528	+	0.113587i	$0.963766\pi$
$168$		0			0
$169$		−	1.84768i		−	0.142129i
$170$		0			0
$171$	7.91900	+	7.91900i	0.605581	+	0.605581i
$172$		0			0
$173$		−	8.39269i		−	0.638085i	−0.947740	−	0.319042i	$-0.896639\pi$
$173$		−	8.39269i		−	0.638085i	0.947740	−	0.319042i	$-0.103361\pi$
$174$		0			0
$175$	0.776127	+	0.776127i	0.0586697	+	0.0586697i
$176$		0			0
$177$	−17.4440	−	17.4440i	−1.31117	−	1.31117i
$178$		0			0
$179$	−11.4721	+	11.4721i	−0.857467	+	0.857467i	−0.991039	−	0.133572i	$-0.957355\pi$
$179$	−11.4721	+	11.4721i	−0.857467	+	0.857467i	0.133572	+	0.991039i	$0.457355\pi$
$180$		0			0
$181$	4.07525	−	4.07525i	0.302911	−	0.302911i	−0.539241	−	0.842152i	$-0.681289\pi$
$181$	4.07525	−	4.07525i	0.302911	−	0.302911i	0.842152	+	0.539241i	$0.181289\pi$
$182$		0			0
$183$	16.3857	−	16.3857i	1.21127	−	1.21127i
$184$		0			0
$185$		−	1.80583i		−	0.132767i
$186$		0			0
$187$	−11.0406			−0.807366
$188$		0			0
$189$	−0.345782			−0.0251519
$190$		0			0
$191$	9.19834	−	9.19834i	0.665568	−	0.665568i	−0.291119	−	0.956687i	$-0.594027\pi$
$191$	9.19834	−	9.19834i	0.665568	−	0.665568i	0.956687	+	0.291119i	$0.0940274\pi$
$192$		0			0
$193$	10.0353	+	10.0353i	0.722359	+	0.722359i	0.969085	−	0.246727i	$-0.0793550\pi$
$193$	10.0353	+	10.0353i	0.722359	+	0.722359i	−0.246727	+	0.969085i	$0.579355\pi$
$194$		0			0
$195$	−19.9574			−1.42918
$196$		0			0
$197$		−	6.58657i		−	0.469274i	−0.972083	−	0.234637i	$-0.924610\pi$
$197$		−	6.58657i		−	0.469274i	0.972083	−	0.234637i	$-0.0753901\pi$
$198$		0			0
$199$	0.494452	−	0.494452i	0.0350508	−	0.0350508i	−0.689364	−	0.724415i	$-0.742110\pi$
$199$	0.494452	−	0.494452i	0.0350508	−	0.0350508i	0.724415	+	0.689364i	$0.242110\pi$
$200$		0			0
$201$	−10.7273			−0.756642
$202$		0			0
$203$			1.95450i			0.137179i
$204$		0			0
$205$	11.1028	−	11.2574i	0.775454	−	0.786253i
$206$		0			0
$207$		−	18.0917i		−	1.25746i
$208$		0			0
$209$	−21.5696			−1.49200
$210$		0			0
$211$	17.2804	−	17.2804i	1.18963	−	1.18963i	0.212462	−	0.977169i	$-0.431852\pi$
$211$	17.2804	−	17.2804i	1.18963	−	1.18963i	0.977169	−	0.212462i	$-0.0681482\pi$
$212$		0			0
$213$		−	8.36244i		−	0.572985i
$214$		0			0
$215$	−17.6035			−1.20055
$216$		0			0
$217$	−4.77869	−	4.77869i	−0.324399	−	0.324399i
$218$		0			0
$219$	−23.3995	+	23.3995i	−1.58119	+	1.58119i
$220$		0			0
$221$	−6.70020			−0.450704
$222$		0			0
$223$	−19.6275			−1.31436			−0.657178	−	0.753736i	$-0.728250\pi$
$223$	−19.6275			−1.31436			−0.657178	+	0.753736i	$0.728250\pi$
$224$		0			0
$225$		−	3.13601i		−	0.209067i
$226$		0			0
$227$	5.16148	−	5.16148i	0.342579	−	0.342579i	−0.514757	−	0.857336i	$-0.672118\pi$
$227$	5.16148	−	5.16148i	0.342579	−	0.342579i	0.857336	+	0.514757i	$0.172118\pi$
$228$		0			0
$229$	−15.8018	+	15.8018i	−1.04421	+	1.04421i	−0.0452363	+	0.998976i	$0.514404\pi$
$229$	−15.8018	+	15.8018i	−1.04421	+	1.04421i	−0.998976	+	0.0452363i	$0.985596\pi$
$230$		0			0
$231$	−9.41703	+	9.41703i	−0.619595	+	0.619595i
$232$		0			0
$233$	−9.81829	−	9.81829i	−0.643218	−	0.643218i	0.308128	−	0.951345i	$-0.400298\pi$
$233$	−9.81829	−	9.81829i	−0.643218	−	0.643218i	−0.951345	+	0.308128i	$0.900298\pi$
$234$		0			0
$235$	13.8545	+	13.8545i	0.903770	+	0.903770i
$236$		0			0
$237$		−	4.20774i		−	0.273322i
$238$		0			0
$239$	14.0642	+	14.0642i	0.909736	+	0.909736i	0.996251	−	0.0865143i	$-0.0275728\pi$
$239$	14.0642	+	14.0642i	0.909736	+	0.909736i	−0.0865143	+	0.996251i	$0.527573\pi$
$240$		0			0
$241$		−	21.6985i		−	1.39773i	−0.715256	−	0.698863i	$-0.753690\pi$
$241$		−	21.6985i		−	1.39773i	0.715256	−	0.698863i	$-0.246310\pi$
$242$		0			0
$243$	15.3668	+	15.3668i	0.985781	+	0.985781i
$244$		0			0
$245$	2.46933			0.157760
$246$		0			0
$247$	−13.0900			−0.832895
$248$		0			0
$249$	11.9597	+	11.9597i	0.757916	+	0.757916i
$250$		0			0
$251$			28.9086i			1.82470i	0.409416	+	0.912348i	$0.365733\pi$
$251$			28.9086i			1.82470i	−0.409416	+	0.912348i	$0.634267\pi$
$252$		0			0
$253$	24.6389	+	24.6389i	1.54903	+	1.54903i
$254$		0			0
$255$		−	11.9902i		−	0.750856i
$256$		0			0
$257$	−17.7345	−	17.7345i	−1.10625	−	1.10625i	−0.993639	−	0.112611i	$-0.964079\pi$
$257$	−17.7345	−	17.7345i	−1.10625	−	1.10625i	−0.112611	−	0.993639i	$-0.535921\pi$
$258$		0			0
$259$	−0.517109	−	0.517109i	−0.0321316	−	0.0321316i
$260$		0			0
$261$	3.94866	−	3.94866i	0.244416	−	0.244416i
$262$		0			0
$263$	−5.62764	+	5.62764i	−0.347015	+	0.347015i	−0.858997	−	0.511981i	$-0.828912\pi$
$263$	−5.62764	+	5.62764i	−0.347015	+	0.347015i	0.511981	+	0.858997i	$0.328912\pi$
$264$		0			0
$265$	11.3765	−	11.3765i	0.698853	−	0.698853i
$266$		0			0
$267$			39.4782i			2.41603i
$268$		0			0
$269$	−9.20242			−0.561082			−0.280541	−	0.959842i	$-0.590514\pi$
$269$	−9.20242			−0.561082			−0.280541	+	0.959842i	$0.590514\pi$
$270$		0			0
$271$	4.97809			0.302398			0.151199	−	0.988503i	$-0.451687\pi$
$271$	4.97809			0.302398			0.151199	+	0.988503i	$0.451687\pi$
$272$		0			0
$273$	−5.71492	+	5.71492i	−0.345882	+	0.345882i
$274$		0			0
$275$	4.27090	+	4.27090i	0.257545	+	0.257545i
$276$		0			0
$277$	12.8880			0.774366			0.387183	−	0.922003i	$-0.373448\pi$
$277$	12.8880			0.774366			0.387183	+	0.922003i	$0.373448\pi$
$278$		0			0
$279$			19.3087i			1.15598i
$280$		0			0
$281$	7.70012	−	7.70012i	0.459351	−	0.459351i	−0.439091	−	0.898442i	$-0.644700\pi$
$281$	7.70012	−	7.70012i	0.459351	−	0.459351i	0.898442	+	0.439091i	$0.144700\pi$
$282$		0			0
$283$	−12.4347			−0.739166			−0.369583	−	0.929198i	$-0.620499\pi$
$283$	−12.4347			−0.739166			−0.369583	+	0.929198i	$0.620499\pi$
$284$		0			0
$285$		−	23.4249i		−	1.38757i
$286$		0			0
$287$	−0.0442777	−	6.40297i	−0.00261363	−	0.377955i
$288$		0			0
$289$			12.9746i			0.763211i
$290$		0			0
$291$	37.9324			2.22364
$292$		0			0
$293$	−0.813768	+	0.813768i	−0.0475409	+	0.0475409i	−0.730478	−	0.682937i	$-0.760702\pi$
$293$	−0.813768	+	0.813768i	−0.0475409	+	0.0475409i	0.682937	+	0.730478i	$0.260702\pi$
$294$		0			0
$295$			25.1709i			1.46551i
$296$		0			0
$297$	−1.90278			−0.110410
$298$		0			0
$299$	14.9526	+	14.9526i	0.864732	+	0.864732i
$300$		0			0
$301$	−5.04085	+	5.04085i	−0.290550	+	0.290550i
$302$		0			0
$303$	−10.1501			−0.583105
$304$		0			0
$305$	−23.6439			−1.35384
$306$		0			0
$307$			29.9471i			1.70917i	0.519310	+	0.854586i	$0.326189\pi$
$307$			29.9471i			1.70917i	−0.519310	+	0.854586i	$0.673811\pi$
$308$		0			0
$309$	18.9166	−	18.9166i	1.07613	−	1.07613i
$310$		0			0
$311$	0.623845	−	0.623845i	0.0353750	−	0.0353750i	−0.689198	−	0.724573i	$-0.742037\pi$
$311$	0.623845	−	0.623845i	0.0353750	−	0.0353750i	0.724573	+	0.689198i	$0.242037\pi$
$312$		0			0
$313$	−16.9142	+	16.9142i	−0.956046	+	0.956046i	−0.999074	−	0.0430274i	$-0.986300\pi$
$313$	−16.9142	+	16.9142i	−0.956046	+	0.956046i	0.0430274	+	0.999074i	$0.486300\pi$
$314$		0			0
$315$	−4.98877	−	4.98877i	−0.281086	−	0.281086i
$316$		0			0
$317$	13.1934	+	13.1934i	0.741016	+	0.741016i	0.972774	−	0.231757i	$-0.0744475\pi$
$317$	13.1934	+	13.1934i	0.741016	+	0.741016i	−0.231757	+	0.972774i	$0.574448\pi$
$318$		0			0
$319$			10.7553i			0.602181i
$320$		0			0
$321$	−7.38555	−	7.38555i	−0.412221	−	0.412221i
$322$		0			0
$323$		−	7.86432i		−	0.437582i
$324$		0			0
$325$	2.59188	+	2.59188i	0.143772	+	0.143772i
$326$		0			0
$327$	28.2025			1.55960
$328$		0			0
$329$	7.93464			0.437451
$330$		0			0
$331$	−1.16080	−	1.16080i	−0.0638035	−	0.0638035i	0.674485	−	0.738289i	$-0.264366\pi$
$331$	−1.16080	−	1.16080i	−0.0638035	−	0.0638035i	−0.738289	+	0.674485i	$0.764366\pi$
$332$		0			0
$333$			2.08942i			0.114500i
$334$		0			0
$335$	7.73947	+	7.73947i	0.422852	+	0.422852i
$336$		0			0
$337$		−	12.2758i		−	0.668703i	−0.942448	−	0.334352i	$-0.891483\pi$
$337$		−	12.2758i		−	0.668703i	0.942448	−	0.334352i	$-0.108517\pi$
$338$		0			0
$339$	24.0216	+	24.0216i	1.30468	+	1.30468i
$340$		0			0
$341$	−26.2964	−	26.2964i	−1.42403	−	1.42403i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−26.7582	+	26.7582i	−1.44061	+	1.44061i
$346$		0			0
$347$	4.90649	−	4.90649i	0.263394	−	0.263394i	−0.563037	−	0.826432i	$-0.690367\pi$
$347$	4.90649	−	4.90649i	0.263394	−	0.263394i	0.826432	+	0.563037i	$0.190367\pi$
$348$		0			0
$349$			14.8998i			0.797567i	0.917045	+	0.398784i	$0.130568\pi$
$349$			14.8998i			0.797567i	−0.917045	+	0.398784i	$0.869432\pi$
$350$		0			0
$351$	−1.15474			−0.0616355
$352$		0			0
$353$	32.5527			1.73260			0.866302	−	0.499521i	$-0.166491\pi$
$353$	32.5527			1.73260			0.866302	+	0.499521i	$0.166491\pi$
$354$		0			0
$355$	−6.03331	+	6.03331i	−0.320215	+	0.320215i
$356$		0			0
$357$	−3.43346	−	3.43346i	−0.181718	−	0.181718i
$358$		0			0
$359$	−22.4786			−1.18638			−0.593188	−	0.805064i	$-0.702131\pi$
$359$	−22.4786			−1.18638			−0.593188	+	0.805064i	$0.702131\pi$
$360$		0			0
$361$			3.63571i			0.191353i
$362$		0			0
$363$	−32.9960	+	32.9960i	−1.73184	+	1.73184i
$364$		0			0
$365$	33.7644			1.76731
$366$		0			0
$367$		−	20.8441i		−	1.08805i	−0.839068	−	0.544026i	$-0.816899\pi$
$367$		−	20.8441i		−	1.08805i	0.839068	−	0.544026i	$-0.183101\pi$
$368$		0			0
$369$	−12.8464	+	13.0253i	−0.668758	+	0.678071i
$370$		0			0
$371$		−	6.51545i		−	0.338265i
$372$		0			0
$373$	31.3888			1.62525			0.812626	−	0.582786i	$-0.198037\pi$
$373$	31.3888			1.62525			0.812626	+	0.582786i	$0.198037\pi$
$374$		0			0
$375$	16.4906	−	16.4906i	0.851573	−	0.851573i
$376$		0			0
$377$			6.52707i			0.336161i
$378$		0			0
$379$	7.34594			0.377335			0.188668	−	0.982041i	$-0.439583\pi$
$379$	7.34594			0.377335			0.188668	+	0.982041i	$0.439583\pi$
$380$		0			0
$381$	−6.70471	−	6.70471i	−0.343493	−	0.343493i
$382$		0			0
$383$	−0.758270	+	0.758270i	−0.0387458	+	0.0387458i	−0.726214	−	0.687468i	$-0.758722\pi$
$383$	−0.758270	+	0.758270i	−0.0387458	+	0.0387458i	0.687468	+	0.726214i	$0.258722\pi$
$384$		0			0
$385$	13.5883			0.692526
$386$		0			0
$387$	20.3680			1.03536
$388$		0			0
$389$		−	38.8495i		−	1.96975i	−0.173274	−	0.984874i	$-0.555435\pi$
$389$		−	38.8495i		−	1.96975i	0.173274	−	0.984874i	$-0.444565\pi$
$390$		0			0
$391$	−8.98337	+	8.98337i	−0.454308	+	0.454308i
$392$		0			0
$393$	−5.11414	+	5.11414i	−0.257974	+	0.257974i
$394$		0			0
$395$	−3.03579	+	3.03579i	−0.152747	+	0.152747i
$396$		0			0
$397$	−0.931306	−	0.931306i	−0.0467409	−	0.0467409i	0.683350	−	0.730091i	$-0.260522\pi$
$397$	−0.931306	−	0.931306i	−0.0467409	−	0.0467409i	−0.730091	+	0.683350i	$0.760522\pi$
$398$		0			0
$399$	−6.70785	−	6.70785i	−0.335813	−	0.335813i
$400$		0			0
$401$		−	5.00028i		−	0.249702i	−0.992175	−	0.124851i	$-0.960155\pi$
$401$		−	5.00028i		−	0.249702i	0.992175	−	0.124851i	$-0.0398453\pi$
$402$		0			0
$403$	−15.9585	−	15.9585i	−0.794949	−	0.794949i
$404$		0			0
$405$		−	23.2320i		−	1.15441i
$406$		0			0
$407$	−2.84557	−	2.84557i	−0.141050	−	0.141050i
$408$		0			0
$409$	20.2256			1.00009			0.500046	−	0.865999i	$-0.333316\pi$
$409$	20.2256			1.00009			0.500046	+	0.865999i	$0.333316\pi$
$410$		0			0
$411$	−22.1303			−1.09161
$412$		0			0
$413$	7.20782	+	7.20782i	0.354673	+	0.354673i
$414$		0			0
$415$		−	17.2573i		−	0.847128i
$416$		0			0
$417$	16.6295	+	16.6295i	0.814352	+	0.814352i
$418$		0			0
$419$			22.6402i			1.10605i	0.833165	+	0.553024i	$0.186526\pi$
$419$			22.6402i			1.10605i	−0.833165	+	0.553024i	$0.813474\pi$
$420$		0			0
$421$	1.01713	+	1.01713i	0.0495717	+	0.0495717i	0.731458	−	0.681886i	$-0.238840\pi$
$421$	1.01713	+	1.01713i	0.0495717	+	0.0495717i	−0.681886	+	0.731458i	$0.738840\pi$
$422$		0			0
$423$	−16.0303	−	16.0303i	−0.779419	−	0.779419i
$424$		0			0
$425$	−1.55718	+	1.55718i	−0.0755342	+	0.0755342i
$426$		0			0
$427$	−6.77055	+	6.77055i	−0.327650	+	0.327650i
$428$		0			0
$429$	−31.4483	+	31.4483i	−1.51834	+	1.51834i
$430$		0			0
$431$		−	11.1361i		−	0.536408i	−0.963362	−	0.268204i	$-0.913570\pi$
$431$		−	11.1361i		−	0.536408i	0.963362	−	0.268204i	$-0.0864300\pi$
$432$		0			0
$433$	10.4182			0.500668			0.250334	−	0.968160i	$-0.419460\pi$
$433$	10.4182			0.500668			0.250334	+	0.968160i	$0.419460\pi$
$434$		0			0
$435$	−11.6804			−0.560032
$436$		0			0
$437$	−17.5505	+	17.5505i	−0.839556	+	0.839556i
$438$		0			0
$439$	13.3721	+	13.3721i	0.638217	+	0.638217i	0.950115	−	0.311899i	$-0.100965\pi$
$439$	13.3721	+	13.3721i	0.638217	+	0.638217i	−0.311899	+	0.950115i	$0.600965\pi$
$440$		0			0
$441$	−2.85712			−0.136054
$442$		0			0
$443$		−	39.9456i		−	1.89787i	−0.315467	−	0.948937i	$-0.602161\pi$
$443$		−	39.9456i		−	1.89787i	0.315467	−	0.948937i	$-0.397839\pi$
$444$		0			0
$445$	28.4826	−	28.4826i	1.35021	−	1.35021i
$446$		0			0
$447$	−10.9206			−0.516526
$448$		0			0
$449$			11.3177i			0.534117i	0.963680	+	0.267059i	$0.0860517\pi$
$449$			11.3177i			0.534117i	−0.963680	+	0.267059i	$0.913948\pi$
$450$		0			0
$451$	−0.243653	−	35.2345i	−0.0114732	−	1.65913i
$452$		0			0
$453$			50.9873i			2.39559i
$454$		0			0
$455$	8.24636			0.386596
$456$		0			0
$457$	0.162747	−	0.162747i	0.00761300	−	0.00761300i	−0.703290	−	0.710903i	$-0.748286\pi$
$457$	0.162747	−	0.162747i	0.00761300	−	0.00761300i	0.710903	+	0.703290i	$0.248286\pi$
$458$		0			0
$459$		−	0.693756i		−	0.0323818i
$460$		0			0
$461$	5.70236			0.265585			0.132793	−	0.991144i	$-0.457606\pi$
$461$	5.70236			0.265585			0.132793	+	0.991144i	$0.457606\pi$
$462$		0			0
$463$	5.84943	+	5.84943i	0.271846	+	0.271846i	0.829843	−	0.557997i	$-0.188430\pi$
$463$	5.84943	+	5.84943i	0.271846	+	0.271846i	−0.557997	+	0.829843i	$0.688430\pi$
$464$		0			0
$465$	28.5582	−	28.5582i	1.32436	−	1.32436i
$466$		0			0
$467$	21.2083			0.981402			0.490701	−	0.871328i	$-0.336741\pi$
$467$	21.2083			0.981402			0.490701	+	0.871328i	$0.336741\pi$
$468$		0			0
$469$	4.43248			0.204673
$470$		0			0
$471$		−	25.1800i		−	1.16023i
$472$		0			0
$473$	−27.7390	+	27.7390i	−1.27544	+	1.27544i
$474$		0			0
$475$	−3.04221	+	3.04221i	−0.139586	+	0.139586i
$476$		0			0
$477$	−13.1631	+	13.1631i	−0.602697	+	0.602697i
$478$		0			0
$479$	−29.5963	−	29.5963i	−1.35229	−	1.35229i	−0.883094	−	0.469196i	$-0.844544\pi$
$479$	−29.5963	−	29.5963i	−1.35229	−	1.35229i	−0.469196	−	0.883094i	$-0.655456\pi$
$480$		0			0
$481$	−1.72689	−	1.72689i	−0.0787395	−	0.0787395i
$482$		0			0
$483$			15.3247i			0.697297i
$484$		0			0
$485$	−27.3674	−	27.3674i	−1.24269	−	1.24269i
$486$		0			0
$487$			12.1422i			0.550217i	0.961413	+	0.275109i	$0.0887138\pi$
$487$			12.1422i			0.550217i	−0.961413	+	0.275109i	$0.911286\pi$
$488$		0			0
$489$	1.41763	+	1.41763i	0.0641073	+	0.0641073i
$490$		0			0
$491$	24.9160			1.12444			0.562222	−	0.826986i	$-0.309947\pi$
$491$	24.9160			1.12444			0.562222	+	0.826986i	$0.309947\pi$
$492$		0			0
$493$	−3.92139			−0.176611
$494$		0			0
$495$	−27.4524	−	27.4524i	−1.23389	−	1.23389i
$496$		0			0
$497$			3.45534i			0.154993i
$498$		0			0
$499$	17.5105	+	17.5105i	0.783877	+	0.783877i	0.980483	−	0.196606i	$-0.0629920\pi$
$499$	17.5105	+	17.5105i	0.783877	+	0.783877i	−0.196606	+	0.980483i	$0.562992\pi$
$500$		0			0
$501$		−	38.9197i		−	1.73880i
$502$		0			0
$503$	9.02603	+	9.02603i	0.402451	+	0.402451i	0.879096	−	0.476645i	$-0.158147\pi$
$503$	9.02603	+	9.02603i	0.402451	+	0.402451i	−0.476645	+	0.879096i	$0.658147\pi$
$504$		0			0
$505$	7.32303	+	7.32303i	0.325871	+	0.325871i
$506$		0			0
$507$	3.16194	−	3.16194i	0.140426	−	0.140426i
$508$		0			0
$509$	−10.1880	+	10.1880i	−0.451575	+	0.451575i	−0.895877	−	0.444302i	$-0.853452\pi$
$509$	−10.1880	+	10.1880i	−0.451575	+	0.451575i	0.444302	+	0.895877i	$0.353452\pi$
$510$		0			0
$511$	9.66862	−	9.66862i	0.427715	−	0.427715i
$512$		0			0
$513$		−	1.35537i		−	0.0598411i
$514$		0			0
$515$	−27.2958			−1.20280
$516$		0			0
$517$	43.6630			1.92030
$518$		0			0
$519$	14.3624	−	14.3624i	0.630442	−	0.630442i
$520$		0			0
$521$	−1.30470	−	1.30470i	−0.0571600	−	0.0571600i	0.677949	−	0.735109i	$-0.262869\pi$
$521$	−1.30470	−	1.30470i	−0.0571600	−	0.0571600i	−0.735109	+	0.677949i	$0.762869\pi$
$522$		0			0
$523$	7.85916			0.343657			0.171828	−	0.985127i	$-0.445033\pi$
$523$	7.85916			0.343657			0.171828	+	0.985127i	$0.445033\pi$
$524$		0			0
$525$			2.65638i			0.115934i
$526$		0			0
$527$	9.58769	−	9.58769i	0.417647	−	0.417647i
$528$		0			0
$529$	17.0958			0.743295
$530$		0			0
$531$		−	29.1238i		−	1.26386i
$532$		0			0
$533$	−0.147866	−	21.3828i	−0.00640478	−	0.926191i
$534$		0			0
$535$			10.6570i			0.460743i
$536$		0			0
$537$	−39.2646			−1.69439
$538$		0			0
$539$	3.89109	−	3.89109i	0.167601	−	0.167601i
$540$		0			0
$541$			15.0287i			0.646134i	0.946376	+	0.323067i	$0.104714\pi$
$541$			15.0287i			0.646134i	−0.946376	+	0.323067i	$0.895286\pi$
$542$		0			0
$543$	13.9480			0.598565
$544$		0			0
$545$	−20.3475	−	20.3475i	−0.871591	−	0.871591i
$546$		0			0
$547$	−27.9351	+	27.9351i	−1.19442	+	1.19442i	−0.218608	+	0.975813i	$0.570152\pi$
$547$	−27.9351	+	27.9351i	−1.19442	+	1.19442i	−0.975813	+	0.218608i	$0.929848\pi$
$548$		0			0
$549$	27.3570			1.16757
$550$		0			0
$551$	−7.66111			−0.326374
$552$		0			0
$553$			1.73863i			0.0739340i
$554$		0			0
$555$	3.09033	−	3.09033i	0.131177	−	0.131177i
$556$		0			0
$557$	9.05263	−	9.05263i	0.383572	−	0.383572i	−0.488815	−	0.872387i	$-0.662571\pi$
$557$	9.05263	−	9.05263i	0.383572	−	0.383572i	0.872387	+	0.488815i	$0.162571\pi$
$558$		0			0
$559$	−16.8340	+	16.8340i	−0.712001	+	0.712001i
$560$		0			0
$561$	−18.8938	−	18.8938i	−0.797696	−	0.797696i
$562$		0			0
$563$	−23.5537	−	23.5537i	−0.992671	−	0.992671i	0.00730207	−	0.999973i	$-0.497676\pi$
$563$	−23.5537	−	23.5537i	−0.992671	−	0.992671i	−0.999973	+	0.00730207i	$0.997676\pi$
$564$		0			0
$565$		−	34.6621i		−	1.45825i
$566$		0			0
$567$	−6.65261	−	6.65261i	−0.279383	−	0.279383i
$568$		0			0
$569$		−	10.9470i		−	0.458924i	−0.973318	−	0.229462i	$-0.926303\pi$
$569$		−	10.9470i		−	0.458924i	0.973318	−	0.229462i	$-0.0736967\pi$
$570$		0			0
$571$	−10.3870	−	10.3870i	−0.434683	−	0.434683i	0.455535	−	0.890218i	$-0.349448\pi$
$571$	−10.3870	−	10.3870i	−0.434683	−	0.434683i	−0.890218	+	0.455535i	$0.849448\pi$
$572$		0			0
$573$	31.4823			1.31519
$574$		0			0
$575$	6.95020			0.289843
$576$		0			0
$577$	−23.6991	−	23.6991i	−0.986608	−	0.986608i	0.0133038	−	0.999912i	$-0.495765\pi$
$577$	−23.6991	−	23.6991i	−0.986608	−	0.986608i	−0.999912	+	0.0133038i	$0.995765\pi$
$578$		0			0
$579$			34.3470i			1.42741i
$580$		0			0
$581$	−4.94172	−	4.94172i	−0.205017	−	0.205017i
$582$		0			0
$583$		−	35.8534i		−	1.48490i
$584$		0			0
$585$	−16.6601	−	16.6601i	−0.688809	−	0.688809i
$586$		0			0
$587$	−31.4013	−	31.4013i	−1.29607	−	1.29607i	−0.930966	−	0.365106i	$-0.881033\pi$
$587$	−31.4013	−	31.4013i	−1.29607	−	1.29607i	−0.365106	−	0.930966i	$-0.618967\pi$
$588$		0			0
$589$	18.7312	−	18.7312i	0.771806	−	0.771806i
$590$		0			0
$591$	11.2716	−	11.2716i	0.463653	−	0.463653i
$592$		0			0
$593$	−30.3528	+	30.3528i	−1.24644	+	1.24644i	−0.289162	+	0.957280i	$0.593377\pi$
$593$	−30.3528	+	30.3528i	−1.24644	+	1.24644i	−0.957280	+	0.289162i	$0.906623\pi$
$594$		0			0
$595$			4.95433i			0.203108i
$596$		0			0
$597$	1.69231			0.0692618
$598$		0			0
$599$	34.4104			1.40597			0.702985	−	0.711204i	$-0.251850\pi$
$599$	34.4104			1.40597			0.702985	+	0.711204i	$0.251850\pi$
$600$		0			0
$601$	21.0421	−	21.0421i	0.858324	−	0.858324i	−0.132816	−	0.991141i	$-0.542402\pi$
$601$	21.0421	−	21.0421i	0.858324	−	0.858324i	0.991141	+	0.132816i	$0.0424021\pi$
$602$		0			0
$603$	−8.95489	−	8.95489i	−0.364671	−	0.364671i
$604$		0			0
$605$	47.6117			1.93569
$606$		0			0
$607$		−	20.5145i		−	0.832656i	−0.909214	−	0.416328i	$-0.863317\pi$
$607$		−	20.5145i		−	0.832656i	0.909214	−	0.416328i	$-0.136683\pi$
$608$		0			0
$609$	−3.34474	+	3.34474i	−0.135536	+	0.135536i
$610$		0			0
$611$	26.4978			1.07199
$612$		0			0
$613$		−	24.1384i		−	0.974941i	−0.873140	−	0.487470i	$-0.837920\pi$
$613$		−	24.1384i		−	0.974941i	0.873140	−	0.487470i	$-0.162080\pi$
$614$		0			0
$615$	38.2652	−	0.264611i	1.54300	−	0.0106701i
$616$		0			0
$617$			9.57610i			0.385519i	0.981246	+	0.192760i	$0.0617438\pi$
$617$			9.57610i			0.385519i	−0.981246	+	0.192760i	$0.938256\pi$
$618$		0			0
$619$	−2.76769			−0.111243			−0.0556215	−	0.998452i	$-0.517714\pi$
$619$	−2.76769			−0.111243			−0.0556215	+	0.998452i	$0.517714\pi$
$620$		0			0
$621$	−1.54823	+	1.54823i	−0.0621284	+	0.0621284i
$622$		0			0
$623$		−	16.3123i		−	0.653538i
$624$		0			0
$625$	−29.2833			−1.17133
$626$		0			0
$627$	−36.9122	−	36.9122i	−1.47413	−	1.47413i
$628$		0			0
$629$	1.03750	−	1.03750i	0.0413677	−	0.0413677i
$630$		0			0
$631$	8.64602			0.344193			0.172096	−	0.985080i	$-0.444946\pi$
$631$	8.64602			0.344193			0.172096	+	0.985080i	$0.444946\pi$
$632$		0			0
$633$	59.1440			2.35076
$634$		0			0
$635$			9.67460i			0.383925i
$636$		0			0
$637$	2.36139	−	2.36139i	0.0935617	−	0.0935617i
$638$		0			0
$639$	6.98079	−	6.98079i	0.276156	−	0.276156i
$640$		0			0
$641$	2.20348	−	2.20348i	0.0870323	−	0.0870323i	−0.662250	−	0.749283i	$-0.730398\pi$
$641$	2.20348	−	2.20348i	0.0870323	−	0.0870323i	0.749283	+	0.662250i	$0.230398\pi$
$642$		0			0
$643$	−10.6065	−	10.6065i	−0.418278	−	0.418278i	0.466332	−	0.884610i	$-0.345575\pi$
$643$	−10.6065	−	10.6065i	−0.418278	−	0.418278i	−0.884610	+	0.466332i	$0.845575\pi$
$644$		0			0
$645$	−30.1249	−	30.1249i	−1.18617	−	1.18617i
$646$		0			0
$647$			40.9173i			1.60863i	0.594206	+	0.804313i	$0.297466\pi$
$647$			40.9173i			1.60863i	−0.594206	+	0.804313i	$0.702534\pi$
$648$		0			0
$649$	39.6634	+	39.6634i	1.55693	+	1.55693i
$650$		0			0
$651$		−	16.3556i		−	0.641027i
$652$		0			0
$653$	−22.7064	−	22.7064i	−0.888569	−	0.888569i	0.105816	−	0.994386i	$-0.466254\pi$
$653$	−22.7064	−	22.7064i	−0.888569	−	0.888569i	−0.994386	+	0.105816i	$0.966254\pi$
$654$		0			0
$655$	7.37947			0.288340
$656$		0			0
$657$	−39.0669			−1.52414
$658$		0			0
$659$	4.10062	+	4.10062i	0.159737	+	0.159737i	0.782450	−	0.622713i	$-0.213970\pi$
$659$	4.10062	+	4.10062i	0.159737	+	0.159737i	−0.622713	+	0.782450i	$0.713970\pi$
$660$		0			0
$661$			5.07644i			0.197451i	0.995115	+	0.0987254i	$0.0314765\pi$
$661$			5.07644i			0.197451i	−0.995115	+	0.0987254i	$0.968523\pi$
$662$		0			0
$663$	−11.4661	−	11.4661i	−0.445305	−	0.445305i
$664$		0			0
$665$			9.67912i			0.375340i
$666$		0			0
$667$	8.75125	+	8.75125i	0.338850	+	0.338850i
$668$		0			0
$669$	−33.5886	−	33.5886i	−1.29861	−	1.29861i
$670$		0			0
$671$	−37.2572	+	37.2572i	−1.43830	+	1.43830i
$672$		0			0
$673$	−1.53374	+	1.53374i	−0.0591213	+	0.0591213i	−0.736049	−	0.676928i	$-0.763311\pi$
$673$	−1.53374	+	1.53374i	−0.0591213	+	0.0591213i	0.676928	+	0.736049i	$0.263311\pi$
$674$		0			0
$675$	−0.268371	+	0.268371i	−0.0103296	+	0.0103296i
$676$		0			0
$677$			16.1845i			0.622019i	0.950407	+	0.311010i	$0.100667\pi$
$677$			16.1845i			0.622019i	−0.950407	+	0.311010i	$0.899333\pi$
$678$		0			0
$679$	−15.6736			−0.601497
$680$		0			0
$681$	17.6657			0.676952
$682$		0			0
$683$	29.3842	−	29.3842i	1.12435	−	1.12435i	0.133275	−	0.991079i	$-0.457451\pi$
$683$	29.3842	−	29.3842i	1.12435	−	1.12435i	0.991079	−	0.133275i	$-0.0425495\pi$
$684$		0			0
$685$	15.9665	+	15.9665i	0.610049	+	0.610049i
$686$		0			0
$687$	−54.0834			−2.06341
$688$		0			0
$689$		−	21.7584i		−	0.828929i
$690$		0			0
$691$	−5.78735	+	5.78735i	−0.220161	+	0.220161i	−0.808566	−	0.588405i	$-0.799756\pi$
$691$	−5.78735	+	5.78735i	−0.220161	+	0.220161i	0.588405	+	0.808566i	$0.299756\pi$
$692$		0			0
$693$	−15.7223			−0.597240
$694$		0			0
$695$		−	23.9957i		−	0.910208i
$696$		0			0
$697$	12.8465	−	0.0888362i	0.486598	−	0.00336491i
$698$		0			0
$699$		−	33.6042i		−	1.27103i
$700$		0			0
$701$	46.6444			1.76173			0.880867	−	0.473364i	$-0.156960\pi$
$701$	46.6444			1.76173			0.880867	+	0.473364i	$0.156960\pi$
$702$		0			0
$703$	2.02693	−	2.02693i	0.0764471	−	0.0764471i
$704$		0			0
$705$			47.4186i			1.78589i
$706$		0			0
$707$	4.19398			0.157731
$708$		0			0
$709$	29.9441	+	29.9441i	1.12457	+	1.12457i	0.991045	+	0.133528i	$0.0426305\pi$
$709$	29.9441	+	29.9441i	1.12457	+	1.12457i	0.133528	+	0.991045i	$0.457369\pi$
$710$		0			0
$711$	3.51254	−	3.51254i	0.131730	−	0.131730i
$712$		0			0
$713$	−42.7931			−1.60261
$714$		0			0
$715$	45.3784			1.69706
$716$		0			0
$717$			48.1362i			1.79768i
$718$		0			0
$719$	−14.6174	+	14.6174i	−0.545135	+	0.545135i	−0.925030	−	0.379895i	$-0.875960\pi$
$719$	−14.6174	+	14.6174i	−0.545135	+	0.545135i	0.379895	+	0.925030i	$0.375960\pi$
$720$		0			0
$721$	−7.81631	+	7.81631i	−0.291094	+	0.291094i
$722$		0			0
$723$	37.1328	−	37.1328i	1.38098	−	1.38098i
$724$		0			0
$725$	1.51694	+	1.51694i	0.0563378	+	0.0563378i
$726$		0			0
$727$	−21.8827	−	21.8827i	−0.811585	−	0.811585i	0.173287	−	0.984871i	$-0.444561\pi$
$727$	−21.8827	−	21.8827i	−0.811585	−	0.811585i	−0.984871	+	0.173287i	$0.944561\pi$
$728$		0			0
$729$			24.3699i			0.902589i
$730$		0			0
$731$	−10.1137	−	10.1137i	−0.374067	−	0.374067i
$732$		0			0
$733$			47.8460i			1.76723i	0.468211	+	0.883617i	$0.344899\pi$
$733$			47.8460i			1.76723i	−0.468211	+	0.883617i	$0.655101\pi$
$734$		0			0
$735$	4.22578	+	4.22578i	0.155870	+	0.155870i
$736$		0			0
$737$	24.3912			0.898461
$738$		0			0
$739$	27.7356			1.02027			0.510135	−	0.860094i	$-0.329595\pi$
$739$	27.7356			1.02027			0.510135	+	0.860094i	$0.329595\pi$
$740$		0			0
$741$	−22.4009	−	22.4009i	−0.822919	−	0.822919i
$742$		0			0
$743$		−	7.35243i		−	0.269734i	−0.990864	−	0.134867i	$-0.956939\pi$
$743$		−	7.35243i		−	0.269734i	0.990864	−	0.134867i	$-0.0430608\pi$
$744$		0			0
$745$	7.87896	+	7.87896i	0.288663	+	0.288663i
$746$		0			0
$747$			19.9674i			0.730571i
$748$		0			0
$749$	3.05169	+	3.05169i	0.111506	+	0.111506i
$750$		0			0
$751$	19.9471	+	19.9471i	0.727881	+	0.727881i	0.970197	−	0.242316i	$-0.0779072\pi$
$751$	19.9471	+	19.9471i	0.727881	+	0.727881i	−0.242316	+	0.970197i	$0.577907\pi$
$752$		0			0
$753$	−49.4714	+	49.4714i	−1.80284	+	1.80284i
$754$		0			0
$755$	36.7862	−	36.7862i	1.33879	−	1.33879i
$756$		0			0
$757$	33.3190	−	33.3190i	1.21100	−	1.21100i	0.240301	−	0.970699i	$-0.422754\pi$
$757$	33.3190	−	33.3190i	1.21100	−	1.21100i	0.970699	−	0.240301i	$-0.0772460\pi$
$758$		0			0
$759$			84.3292i			3.06096i
$760$		0			0
$761$	35.1208			1.27313			0.636565	−	0.771223i	$-0.280355\pi$
$761$	35.1208			1.27313			0.636565	+	0.771223i	$0.280355\pi$
$762$		0			0
$763$	−11.6532			−0.421875
$764$		0			0
$765$	10.0092	−	10.0092i	0.361883	−	0.361883i
$766$		0			0
$767$	24.0706	+	24.0706i	0.869138	+	0.869138i
$768$		0			0
$769$	51.8614			1.87017			0.935085	−	0.354423i	$-0.115323\pi$
$769$	51.8614			1.87017			0.935085	+	0.354423i	$0.115323\pi$
$770$		0			0
$771$		−	60.6984i		−	2.18600i
$772$		0			0
$773$	7.18747	−	7.18747i	0.258515	−	0.258515i	−0.565935	−	0.824450i	$-0.691485\pi$
$773$	7.18747	−	7.18747i	0.258515	−	0.258515i	0.824450	+	0.565935i	$0.191485\pi$
$774$		0			0
$775$	−7.41775			−0.266454
$776$		0			0
$777$		−	1.76986i		−	0.0634935i
$778$		0			0
$779$	25.0979	−	0.173557i	0.899226	−	0.00621831i
$780$		0			0
$781$			19.0142i			0.680380i
$782$		0			0
$783$	−0.675830			−0.0241522
$784$		0			0
$785$	−18.1668	+	18.1668i	−0.648400	+	0.648400i
$786$		0			0
$787$			24.0153i			0.856052i	0.903767	+	0.428026i	$0.140791\pi$
$787$			24.0153i			0.856052i	−0.903767	+	0.428026i	$0.859209\pi$
$788$		0			0
$789$	−19.2612			−0.685718
$790$		0			0
$791$	−9.92568	−	9.92568i	−0.352916	−	0.352916i
$792$		0			0
$793$	−22.6103	+	22.6103i	−0.802915	+	0.802915i
$794$		0			0
$795$	38.9373			1.38097
$796$		0			0
$797$	−19.2773			−0.682836			−0.341418	−	0.939911i	$-0.610907\pi$
$797$	−19.2773			−0.682836			−0.341418	+	0.939911i	$0.610907\pi$
$798$		0			0
$799$			15.9196i			0.563195i
$800$		0			0
$801$	−32.9556	+	32.9556i	−1.16443	+	1.16443i
$802$		0			0
$803$	53.2048	−	53.2048i	1.87756	−	1.87756i
$804$		0			0
$805$	11.0564	−	11.0564i	0.389687	−	0.389687i
$806$		0			0
$807$	−15.7481	−	15.7481i	−0.554361	−	0.554361i
$808$		0			0
$809$	11.5212	+	11.5212i	0.405064	+	0.405064i	0.880013	−	0.474949i	$-0.157534\pi$
$809$	11.5212	+	11.5212i	0.405064	+	0.405064i	−0.474949	+	0.880013i	$0.657534\pi$
$810$		0			0
$811$			2.99712i			0.105243i	0.998615	+	0.0526216i	$0.0167577\pi$
$811$			2.99712i			0.105243i	−0.998615	+	0.0526216i	$0.983242\pi$
$812$		0			0
$813$	8.51903	+	8.51903i	0.298776	+	0.298776i
$814$		0			0
$815$		−	2.04557i		−	0.0716532i
$816$		0			0
$817$	−19.7588	−	19.7588i	−0.691272	−	0.691272i
$818$		0			0
$819$	−9.54139			−0.333403
$820$		0			0
$821$	−18.9692			−0.662030			−0.331015	−	0.943626i	$-0.607391\pi$
$821$	−18.9692			−0.662030			−0.331015	+	0.943626i	$0.607391\pi$
$822$		0			0
$823$	23.6015	+	23.6015i	0.822696	+	0.822696i	0.986494	−	0.163798i	$-0.0523746\pi$
$823$	23.6015	+	23.6015i	0.822696	+	0.822696i	−0.163798	+	0.986494i	$0.552375\pi$
$824$		0			0
$825$			14.6176i			0.508920i
$826$		0			0
$827$	14.5498	+	14.5498i	0.505945	+	0.505945i	0.913279	−	0.407334i	$-0.133542\pi$
$827$	14.5498	+	14.5498i	0.505945	+	0.505945i	−0.407334	+	0.913279i	$0.633542\pi$
$828$		0			0
$829$		−	31.8322i		−	1.10558i	−0.833321	−	0.552790i	$-0.813563\pi$
$829$		−	31.8322i		−	1.10558i	0.833321	−	0.552790i	$-0.186437\pi$
$830$		0			0
$831$	22.0553	+	22.0553i	0.765091	+	0.765091i
$832$		0			0
$833$	1.41870	+	1.41870i	0.0491550	+	0.0491550i
$834$		0			0
$835$	−28.0797	+	28.0797i	−0.971737	+	0.971737i
$836$		0			0
$837$	1.65238	−	1.65238i	0.0571148	−	0.0571148i
$838$		0			0
$839$	−18.5998	+	18.5998i	−0.642136	+	0.642136i	−0.951080	−	0.308944i	$-0.900024\pi$
$839$	−18.5998	+	18.5998i	−0.642136	+	0.642136i	0.308944	+	0.951080i	$0.400024\pi$
$840$		0			0
$841$		−	25.1799i		−	0.868273i
$842$		0			0
$843$	26.3545			0.907697
$844$		0			0
$845$	−4.56253			−0.156956
$846$		0			0
$847$	13.6339	−	13.6339i	0.468465	−	0.468465i
$848$		0			0
$849$	−21.2795	−	21.2795i	−0.730312	−	0.730312i
$850$		0			0
$851$	−4.63070			−0.158738
$852$		0			0
$853$			27.2260i			0.932200i	0.884732	+	0.466100i	$0.154341\pi$
$853$			27.2260i			0.932200i	−0.884732	+	0.466100i	$0.845659\pi$
$854$		0			0
$855$	19.5547	−	19.5547i	0.668755	−	0.668755i
$856$		0			0
$857$	−14.3110			−0.488856			−0.244428	−	0.969667i	$-0.578600\pi$
$857$	−14.3110			−0.488856			−0.244428	+	0.969667i	$0.578600\pi$
$858$		0			0
$859$		−	38.6603i		−	1.31907i	−0.751673	−	0.659536i	$-0.770753\pi$
$859$		−	38.6603i		−	1.31907i	0.751673	−	0.659536i	$-0.229247\pi$
$860$		0			0
$861$	10.8817	−	11.0332i	0.370846	−	0.376011i
$862$		0			0
$863$			24.3830i			0.830008i	0.909820	+	0.415004i	$0.136220\pi$
$863$			24.3830i			0.830008i	−0.909820	+	0.415004i	$0.863780\pi$
$864$		0			0
$865$	−20.7244			−0.704649
$866$		0			0
$867$	−22.2035	+	22.2035i	−0.754070	+	0.754070i
$868$		0			0
$869$			9.56739i			0.324552i
$870$		0			0
$871$	14.8023			0.501557
$872$		0			0
$873$	31.6652	+	31.6652i	1.07170	+	1.07170i
$874$		0			0
$875$	−6.81390	+	6.81390i	−0.230352	+	0.230352i
$876$		0			0
$877$	−40.5877			−1.37055			−0.685274	−	0.728285i	$-0.740318\pi$
$877$	−40.5877			−1.37055			−0.685274	+	0.728285i	$0.740318\pi$
$878$		0			0
$879$	−2.78521			−0.0939428
$880$		0			0
$881$		−	4.38861i		−	0.147856i	−0.997264	−	0.0739281i	$-0.976446\pi$
$881$		−	4.38861i		−	0.147856i	0.997264	−	0.0739281i	$-0.0235535\pi$
$882$		0			0
$883$	−25.3411	+	25.3411i	−0.852795	+	0.852795i	−0.990477	−	0.137682i	$-0.956035\pi$
$883$	−25.3411	+	25.3411i	−0.852795	+	0.852795i	0.137682	+	0.990477i	$0.456035\pi$
$884$		0			0
$885$	−43.0750	+	43.0750i	−1.44795	+	1.44795i
$886$		0			0
$887$	13.8091	−	13.8091i	0.463663	−	0.463663i	−0.436191	−	0.899854i	$-0.643673\pi$
$887$	13.8091	−	13.8091i	0.463663	−	0.463663i	0.899854	+	0.436191i	$0.143673\pi$
$888$		0			0
$889$	2.77037	+	2.77037i	0.0929153	+	0.0929153i
$890$		0			0
$891$	−36.6082	−	36.6082i	−1.22642	−	1.22642i
$892$		0			0
$893$			31.1016i			1.04078i
$894$		0			0
$895$	28.3285	+	28.3285i	0.946918	+	0.946918i
$896$		0			0
$897$			51.1769i			1.70875i
$898$		0			0
$899$	−9.33996	−	9.33996i	−0.311505	−	0.311505i
$900$		0			0
$901$	13.0722			0.435499
$902$		0			0
$903$	−17.2528			−0.574139
$904$		0			0
$905$	−10.0632	−	10.0632i	−0.334511	−	0.334511i
$906$		0			0
$907$		−	31.4661i		−	1.04482i	−0.852696	−	0.522408i	$-0.825034\pi$
$907$		−	31.4661i		−	1.04482i	0.852696	−	0.522408i	$-0.174966\pi$
$908$		0			0
$909$	−8.47306	−	8.47306i	−0.281034	−	0.281034i
$910$		0			0
$911$			21.7610i			0.720973i	0.932764	+	0.360486i	$0.117389\pi$
$911$			21.7610i			0.720973i	−0.932764	+	0.360486i	$0.882611\pi$
$912$		0			0
$913$	−27.1935	−	27.1935i	−0.899973	−	0.899973i
$914$		0			0
$915$	−40.4618	−	40.4618i	−1.33763	−	1.33763i
$916$		0			0
$917$	2.11315	−	2.11315i	0.0697823	−	0.0697823i
$918$		0			0
$919$	−6.08435	+	6.08435i	−0.200704	+	0.200704i	−0.800302	−	0.599597i	$-0.795327\pi$
$919$	−6.08435	+	6.08435i	−0.200704	+	0.200704i	0.599597	+	0.800302i	$0.295327\pi$
$920$		0			0
$921$	−51.2486	+	51.2486i	−1.68870	+	1.68870i
$922$		0			0
$923$			11.5391i			0.379815i
$924$		0			0
$925$	−0.802685			−0.0263921
$926$		0			0
$927$	31.5824			1.03730
$928$		0			0
$929$	−28.1311	+	28.1311i	−0.922952	+	0.922952i	−0.997237	−	0.0742849i	$-0.976333\pi$
$929$	−28.1311	+	28.1311i	−0.922952	+	0.922952i	0.0742849	+	0.997237i	$0.476333\pi$
$930$		0			0
$931$	2.77167	+	2.77167i	0.0908378	+	0.0908378i
$932$		0			0
$933$	2.13518			0.0699026
$934$		0			0
$935$			27.2629i			0.891591i
$936$		0			0
$937$	−23.1404	+	23.1404i	−0.755964	+	0.755964i	−0.975585	−	0.219621i	$-0.929518\pi$
$937$	−23.1404	+	23.1404i	−0.755964	+	0.755964i	0.219621	+	0.975585i	$0.429518\pi$
$938$		0			0
$939$	−57.8906			−1.88919
$940$		0			0
$941$		−	11.1328i		−	0.362919i	−0.983398	−	0.181460i	$-0.941918\pi$
$941$		−	11.1328i		−	0.362919i	0.983398	−	0.181460i	$-0.0580822\pi$
$942$		0			0
$943$	−28.8675	−	28.4710i	−0.940054	−	0.927142i
$944$		0			0
$945$			0.853850i			0.0277757i
$946$		0			0
$947$	46.4304			1.50878			0.754392	−	0.656424i	$-0.227932\pi$
$947$	46.4304			1.50878			0.754392	+	0.656424i	$0.227932\pi$
$948$		0			0
$949$	32.2885	−	32.2885i	1.04813	−	1.04813i
$950$		0			0
$951$			45.1559i			1.46428i
$952$		0			0
$953$	−8.04537			−0.260615			−0.130308	−	0.991474i	$-0.541596\pi$
$953$	−8.04537			−0.260615			−0.130308	+	0.991474i	$0.541596\pi$
$954$		0			0
$955$	−22.7138	−	22.7138i	−0.735000	−	0.735000i
$956$		0			0
$957$	−18.4056	+	18.4056i	−0.594968	+	0.594968i
$958$		0			0
$959$	9.14420			0.295281
$960$		0			0
$961$	14.6719			0.473285
$962$		0			0
$963$		−	12.3306i		−	0.397348i
$964$		0			0
$965$	24.7806	−	24.7806i	0.797715	−	0.797715i
$966$		0			0
$967$	−11.7657	+	11.7657i	−0.378360	+	0.378360i	−0.870510	−	0.492150i	$-0.836211\pi$
$967$	−11.7657	+	11.7657i	−0.378360	+	0.378360i	0.492150	+	0.870510i	$0.336211\pi$
$968$		0			0
$969$	13.4582	−	13.4582i	0.432341	−	0.432341i
$970$		0			0
$971$	−15.5066	−	15.5066i	−0.497631	−	0.497631i	0.413069	−	0.910700i	$-0.364457\pi$
$971$	−15.5066	−	15.5066i	−0.497631	−	0.497631i	−0.910700	+	0.413069i	$0.864457\pi$
$972$		0			0
$973$	−6.87129	−	6.87129i	−0.220283	−	0.220283i
$974$		0			0
$975$			8.87101i			0.284100i
$976$		0			0
$977$	6.88164	+	6.88164i	0.220163	+	0.220163i	0.808567	−	0.588404i	$-0.200243\pi$
$977$	6.88164	+	6.88164i	0.220163	+	0.220163i	−0.588404	+	0.808567i	$0.700243\pi$
$978$		0			0
$979$		−	89.7639i		−	2.86887i
$980$		0			0
$981$	23.5429	+	23.5429i	0.751667	+	0.751667i
$982$		0			0
$983$	−4.46548			−0.142427			−0.0712134	−	0.997461i	$-0.522687\pi$
$983$	−4.46548			−0.142427			−0.0712134	+	0.997461i	$0.522687\pi$
$984$		0			0
$985$	−16.2644			−0.518228
$986$		0			0
$987$	13.5786	+	13.5786i	0.432211	+	0.432211i
$988$		0			0
$989$			45.1407i			1.43539i
$990$		0			0
$991$	−38.7804	−	38.7804i	−1.23190	−	1.23190i	−0.963234	−	0.268665i	$-0.913418\pi$
$991$	−38.7804	−	38.7804i	−1.23190	−	1.23190i	−0.268665	−	0.963234i	$-0.586582\pi$
$992$		0			0
$993$		−	3.97297i		−	0.126078i
$994$		0			0
$995$	−1.22097	−	1.22097i	−0.0387072	−	0.0387072i
$996$		0			0
$997$	22.9295	+	22.9295i	0.726183	+	0.726183i	0.969857	−	0.243674i	$-0.0783526\pi$
$997$	22.9295	+	22.9295i	0.726183	+	0.726183i	−0.243674	+	0.969857i	$0.578353\pi$
$998$		0			0
$999$	0.178807	−	0.178807i	0.00565720	−	0.00565720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.16	✓	36
41.32	even	4	inner	1148.2.k.b.729.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.16	✓	36	1.1	even	1	trivial
1148.2.k.b.729.16	yes	36	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +O(q^{10})\)	\(q+(1.71130 + 1.71130i) q^{3} -2.46933i q^{5} +(-0.707107 - 0.707107i) q^{7} +2.85712i q^{9} +(-3.89109 - 3.89109i) q^{11} +(-2.36139 - 2.36139i) q^{13} +(4.22578 - 4.22578i) q^{15} +(1.41870 - 1.41870i) q^{17} +(2.77167 - 2.77167i) q^{19} -2.42015i q^{21} -6.33212 q^{23} -1.09761 q^{25} +(0.244504 - 0.244504i) q^{27} +(-1.38204 - 1.38204i) q^{29} +6.75810 q^{31} -13.3177i q^{33} +(-1.74608 + 1.74608i) q^{35} +0.731303 q^{37} -8.08211i q^{39} +(4.55889 + 4.49628i) q^{41} -7.12884i q^{43} +7.05519 q^{45} +(-5.61063 + 5.61063i) q^{47} +1.00000i q^{49} +4.85565 q^{51} +(4.60712 + 4.60712i) q^{53} +(-9.60841 + 9.60841i) q^{55} +9.48634 q^{57} -10.1934 q^{59} -9.57500i q^{61} +(2.02029 - 2.02029i) q^{63} +(-5.83106 + 5.83106i) q^{65} +(-3.13423 + 3.13423i) q^{67} +(-10.8362 - 10.8362i) q^{69} +(-2.44329 - 2.44329i) q^{71} +13.6735i q^{73} +(-1.87834 - 1.87834i) q^{75} +5.50284i q^{77} +(-1.22940 - 1.22940i) q^{79} +9.40821 q^{81} +6.98865 q^{83} +(-3.50324 - 3.50324i) q^{85} -4.73018i q^{87} +(11.5345 + 11.5345i) q^{89} +3.33951i q^{91} +(11.5652 + 11.5652i) q^{93} +(-6.84417 - 6.84417i) q^{95} +(11.0829 - 11.0829i) q^{97} +(11.1173 - 11.1173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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