LMFDB - Embedded newform 9450.2.a.ed.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.a (trivial)

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:	yes
Analytic conductor:	$75.4586299101$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{73}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 18 $ x^2 - x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1890)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.77200$ of defining polynomial
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +4.77200 q^{11} +2.77200 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.77200 q^{17} +2.00000 q^{19} -4.77200 q^{22} -4.77200 q^{23} -2.77200 q^{26} -1.00000 q^{28} +3.00000 q^{29} +8.54400 q^{31} -1.00000 q^{32} -4.77200 q^{34} -0.227998 q^{37} -2.00000 q^{38} -1.77200 q^{41} -6.77200 q^{43} +4.77200 q^{44} +4.77200 q^{46} +12.5440 q^{47} +1.00000 q^{49} +2.77200 q^{52} +6.00000 q^{53} +1.00000 q^{56} -3.00000 q^{58} +1.77200 q^{59} -5.77200 q^{61} -8.54400 q^{62} +1.00000 q^{64} +7.54400 q^{67} +4.77200 q^{68} -1.77200 q^{71} -6.22800 q^{73} +0.227998 q^{74} +2.00000 q^{76} -4.77200 q^{77} +6.77200 q^{79} +1.77200 q^{82} +6.77200 q^{86} -4.77200 q^{88} +3.54400 q^{89} -2.77200 q^{91} -4.77200 q^{92} -12.5440 q^{94} +0.455996 q^{97} -1.00000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{7} - 2 q^{8} + q^{11} - 3 q^{13} + 2 q^{14} + 2 q^{16} + q^{17} + 4 q^{19} - q^{22} - q^{23} + 3 q^{26} - 2 q^{28} + 6 q^{29} - 2 q^{32} - q^{34} - 9 q^{37} - 4 q^{38} + 5 q^{41} - 5 q^{43} + q^{44} + q^{46} + 8 q^{47} + 2 q^{49} - 3 q^{52} + 12 q^{53} + 2 q^{56} - 6 q^{58} - 5 q^{59} - 3 q^{61} + 2 q^{64} - 2 q^{67} + q^{68} + 5 q^{71} - 21 q^{73} + 9 q^{74} + 4 q^{76} - q^{77} + 5 q^{79} - 5 q^{82} + 5 q^{86} - q^{88} - 10 q^{89} + 3 q^{91} - q^{92} - 8 q^{94} + 18 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^7 - 2 * q^8 + q^11 - 3 * q^13 + 2 * q^14 + 2 * q^16 + q^17 + 4 * q^19 - q^22 - q^23 + 3 * q^26 - 2 * q^28 + 6 * q^29 - 2 * q^32 - q^34 - 9 * q^37 - 4 * q^38 + 5 * q^41 - 5 * q^43 + q^44 + q^46 + 8 * q^47 + 2 * q^49 - 3 * q^52 + 12 * q^53 + 2 * q^56 - 6 * q^58 - 5 * q^59 - 3 * q^61 + 2 * q^64 - 2 * q^67 + q^68 + 5 * q^71 - 21 * q^73 + 9 * q^74 + 4 * q^76 - q^77 + 5 * q^79 - 5 * q^82 + 5 * q^86 - q^88 - 10 * q^89 + 3 * q^91 - q^92 - 8 * q^94 + 18 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	4.77200	1.43881	0.719406	−	0.694589i	$-0.244414\pi$
$11$	4.77200	1.43881	0.719406	+	0.694589i	$0.244414\pi$
$12$	0	0
$13$	2.77200	0.768815	0.384407	−	0.923164i	$-0.374406\pi$
$13$	2.77200	0.768815	0.384407	+	0.923164i	$0.374406\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.77200	1.15738	0.578690	−	0.815547i	$-0.303564\pi$
$17$	4.77200	1.15738	0.578690	+	0.815547i	$0.303564\pi$
$18$	0	0
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	0	0
$22$	−4.77200	−1.01739
$23$	−4.77200	−0.995031	−0.497516	−	0.867455i	$-0.665754\pi$
$23$	−4.77200	−0.995031	−0.497516	+	0.867455i	$0.665754\pi$
$24$	0	0
$25$	0	0
$26$	−2.77200	−0.543634
$27$	0	0
$28$	−1.00000	−0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	8.54400	1.53455	0.767274	−	0.641319i	$-0.221613\pi$
$31$	8.54400	1.53455	0.767274	+	0.641319i	$0.221613\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−4.77200	−0.818392
$35$	0	0
$36$	0	0
$37$	−0.227998	−0.0374827	−0.0187413	−	0.999824i	$-0.505966\pi$
$37$	−0.227998	−0.0374827	−0.0187413	+	0.999824i	$0.505966\pi$
$38$	−2.00000	−0.324443
$39$	0	0
$40$	0	0
$41$	−1.77200	−0.276740	−0.138370	−	0.990381i	$-0.544186\pi$
$41$	−1.77200	−0.276740	−0.138370	+	0.990381i	$0.544186\pi$
$42$	0	0
$43$	−6.77200	−1.03272	−0.516360	−	0.856371i	$-0.672713\pi$
$43$	−6.77200	−1.03272	−0.516360	+	0.856371i	$0.672713\pi$
$44$	4.77200	0.719406
$45$	0	0
$46$	4.77200	0.703593
$47$	12.5440	1.82973	0.914865	−	0.403759i	$-0.132296\pi$
$47$	12.5440	1.82973	0.914865	+	0.403759i	$0.132296\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	2.77200	0.384407
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.00000	−0.393919
$59$	1.77200	0.230695	0.115347	−	0.993325i	$-0.463202\pi$
$59$	1.77200	0.230695	0.115347	+	0.993325i	$0.463202\pi$
$60$	0	0
$61$	−5.77200	−0.739029	−0.369515	−	0.929225i	$-0.620476\pi$
$61$	−5.77200	−0.739029	−0.369515	+	0.929225i	$0.620476\pi$
$62$	−8.54400	−1.08509
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	7.54400	0.921647	0.460823	−	0.887492i	$-0.347554\pi$
$67$	7.54400	0.921647	0.460823	+	0.887492i	$0.347554\pi$
$68$	4.77200	0.578690
$69$	0	0
$70$	0	0
$71$	−1.77200	−0.210298	−0.105149	−	0.994456i	$-0.533532\pi$
$71$	−1.77200	−0.210298	−0.105149	+	0.994456i	$0.533532\pi$
$72$	0	0
$73$	−6.22800	−0.728932	−0.364466	−	0.931217i	$-0.618748\pi$
$73$	−6.22800	−0.728932	−0.364466	+	0.931217i	$0.618748\pi$
$74$	0.227998	0.0265042
$75$	0	0
$76$	2.00000	0.229416
$77$	−4.77200	−0.543820
$78$	0	0
$79$	6.77200	0.761910	0.380955	−	0.924594i	$-0.375595\pi$
$79$	6.77200	0.761910	0.380955	+	0.924594i	$0.375595\pi$
$80$	0	0
$81$	0	0
$82$	1.77200	0.195685
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	6.77200	0.730244
$87$	0	0
$88$	−4.77200	−0.508697
$89$	3.54400	0.375664	0.187832	−	0.982201i	$-0.439854\pi$
$89$	3.54400	0.375664	0.187832	+	0.982201i	$0.439854\pi$
$90$	0	0
$91$	−2.77200	−0.290585
$92$	−4.77200	−0.497516
$93$	0	0
$94$	−12.5440	−1.29382
$95$	0	0
$96$	0	0
$97$	0.455996	0.0462994	0.0231497	−	0.999732i	$-0.492631\pi$
$97$	0.455996	0.0462994	0.0231497	+	0.999732i	$0.492631\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	8.31601	0.827473	0.413737	−	0.910397i	$-0.364223\pi$
$101$	8.31601	0.827473	0.413737	+	0.910397i	$0.364223\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−2.77200	−0.271817
$105$	0	0
$106$	−6.00000	−0.582772
$107$	10.2280	0.988778	0.494389	−	0.869241i	$-0.335392\pi$
$107$	10.2280	0.988778	0.494389	+	0.869241i	$0.335392\pi$
$108$	0	0
$109$	17.5440	1.68041	0.840205	−	0.542268i	$-0.182434\pi$
$109$	17.5440	1.68041	0.840205	+	0.542268i	$0.182434\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	0.544004	0.0511756	0.0255878	−	0.999673i	$-0.491854\pi$
$113$	0.544004	0.0511756	0.0255878	+	0.999673i	$0.491854\pi$
$114$	0	0
$115$	0	0
$116$	3.00000	0.278543
$117$	0	0
$118$	−1.77200	−0.163126
$119$	−4.77200	−0.437449
$120$	0	0
$121$	11.7720	1.07018
$122$	5.77200	0.522572
$123$	0	0
$124$	8.54400	0.767274
$125$	0	0
$126$	0	0
$127$	−15.7720	−1.39954	−0.699769	−	0.714369i	$-0.746714\pi$
$127$	−15.7720	−1.39954	−0.699769	+	0.714369i	$0.746714\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	−7.54400	−0.651703
$135$	0	0
$136$	−4.77200	−0.409196
$137$	4.22800	0.361222	0.180611	−	0.983555i	$-0.442192\pi$
$137$	4.22800	0.361222	0.180611	+	0.983555i	$0.442192\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	0	0
$142$	1.77200	0.148703
$143$	13.2280	1.10618
$144$	0	0
$145$	0	0
$146$	6.22800	0.515433
$147$	0	0
$148$	−0.227998	−0.0187413
$149$	−14.3160	−1.17281	−0.586406	−	0.810017i	$-0.699458\pi$
$149$	−14.3160	−1.17281	−0.586406	+	0.810017i	$0.699458\pi$
$150$	0	0
$151$	−24.3160	−1.97881	−0.989404	−	0.145187i	$-0.953622\pi$
$151$	−24.3160	−1.97881	−0.989404	+	0.145187i	$0.953622\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	4.77200	0.384539
$155$	0	0
$156$	0	0
$157$	−10.3160	−0.823307	−0.411653	−	0.911340i	$-0.635049\pi$
$157$	−10.3160	−0.823307	−0.411653	+	0.911340i	$0.635049\pi$
$158$	−6.77200	−0.538752
$159$	0	0
$160$	0	0
$161$	4.77200	0.376086
$162$	0	0
$163$	−18.7720	−1.47034	−0.735168	−	0.677885i	$-0.762897\pi$
$163$	−18.7720	−1.47034	−0.735168	+	0.677885i	$0.762897\pi$
$164$	−1.77200	−0.138370
$165$	0	0
$166$	0	0
$167$	13.7720	1.06571	0.532855	−	0.846207i	$-0.321119\pi$
$167$	13.7720	1.06571	0.532855	+	0.846207i	$0.321119\pi$
$168$	0	0
$169$	−5.31601	−0.408924
$170$	0	0
$171$	0	0
$172$	−6.77200	−0.516360
$173$	7.77200	0.590894	0.295447	−	0.955359i	$-0.404531\pi$
$173$	7.77200	0.590894	0.295447	+	0.955359i	$0.404531\pi$
$174$	0	0
$175$	0	0
$176$	4.77200	0.359703
$177$	0	0
$178$	−3.54400	−0.265634
$179$	−15.5440	−1.16181	−0.580907	−	0.813970i	$-0.697302\pi$
$179$	−15.5440	−1.16181	−0.580907	+	0.813970i	$0.697302\pi$
$180$	0	0
$181$	−21.3160	−1.58441	−0.792203	−	0.610258i	$-0.791066\pi$
$181$	−21.3160	−1.58441	−0.792203	+	0.610258i	$0.791066\pi$
$182$	2.77200	0.205474
$183$	0	0
$184$	4.77200	0.351797
$185$	0	0
$186$	0	0
$187$	22.7720	1.66525
$188$	12.5440	0.914865
$189$	0	0
$190$	0	0
$191$	−19.0880	−1.38116	−0.690580	−	0.723256i	$-0.742645\pi$
$191$	−19.0880	−1.38116	−0.690580	+	0.723256i	$0.742645\pi$
$192$	0	0
$193$	−23.5440	−1.69473	−0.847367	−	0.531007i	$-0.821814\pi$
$193$	−23.5440	−1.69473	−0.847367	+	0.531007i	$0.821814\pi$
$194$	−0.455996	−0.0327386
$195$	0	0
$196$	1.00000	0.0714286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−0.316006	−0.0224010	−0.0112005	−	0.999937i	$-0.503565\pi$
$199$	−0.316006	−0.0224010	−0.0112005	+	0.999937i	$0.503565\pi$
$200$	0	0
$201$	0	0
$202$	−8.31601	−0.585112
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	8.00000	0.557386
$207$	0	0
$208$	2.77200	0.192204
$209$	9.54400	0.660173
$210$	0	0
$211$	−15.3160	−1.05440	−0.527199	−	0.849742i	$-0.676758\pi$
$211$	−15.3160	−1.05440	−0.527199	+	0.849742i	$0.676758\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	−10.2280	−0.699172
$215$	0	0
$216$	0	0
$217$	−8.54400	−0.580005
$218$	−17.5440	−1.18823
$219$	0	0
$220$	0	0
$221$	13.2280	0.889811
$222$	0	0
$223$	19.5440	1.30876	0.654382	−	0.756164i	$-0.272929\pi$
$223$	19.5440	1.30876	0.654382	+	0.756164i	$0.272929\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−0.544004	−0.0361866
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	0	0
$229$	11.5440	0.762849	0.381425	−	0.924400i	$-0.375434\pi$
$229$	11.5440	0.762849	0.381425	+	0.924400i	$0.375434\pi$
$230$	0	0
$231$	0	0
$232$	−3.00000	−0.196960
$233$	16.2280	1.06313	0.531566	−	0.847017i	$-0.321604\pi$
$233$	16.2280	1.06313	0.531566	+	0.847017i	$0.321604\pi$
$234$	0	0
$235$	0	0
$236$	1.77200	0.115347
$237$	0	0
$238$	4.77200	0.309323
$239$	20.8600	1.34932	0.674661	−	0.738128i	$-0.264290\pi$
$239$	20.8600	1.34932	0.674661	+	0.738128i	$0.264290\pi$
$240$	0	0
$241$	−11.2280	−0.723259	−0.361629	−	0.932322i	$-0.617779\pi$
$241$	−11.2280	−0.723259	−0.361629	+	0.932322i	$0.617779\pi$
$242$	−11.7720	−0.756733
$243$	0	0
$244$	−5.77200	−0.369515
$245$	0	0
$246$	0	0
$247$	5.54400	0.352757
$248$	−8.54400	−0.542545
$249$	0	0
$250$	0	0
$251$	10.7720	0.679923	0.339961	−	0.940439i	$-0.389586\pi$
$251$	10.7720	0.679923	0.339961	+	0.940439i	$0.389586\pi$
$252$	0	0
$253$	−22.7720	−1.43166
$254$	15.7720	0.989623
$255$	0	0
$256$	1.00000	0.0625000
$257$	−17.8600	−1.11408	−0.557038	−	0.830487i	$-0.688062\pi$
$257$	−17.8600	−1.11408	−0.557038	+	0.830487i	$0.688062\pi$
$258$	0	0
$259$	0.227998	0.0141671
$260$	0	0
$261$	0	0
$262$	−3.00000	−0.185341
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	0	0
$266$	2.00000	0.122628
$267$	0	0
$268$	7.54400	0.460823
$269$	−26.3160	−1.60452	−0.802258	−	0.596978i	$-0.796368\pi$
$269$	−26.3160	−1.60452	−0.802258	+	0.596978i	$0.796368\pi$
$270$	0	0
$271$	32.4040	1.96840	0.984202	−	0.177050i	$-0.0566555\pi$
$271$	32.4040	1.96840	0.984202	+	0.177050i	$0.0566555\pi$
$272$	4.77200	0.289345
$273$	0	0
$274$	−4.22800	−0.255423
$275$	0	0
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	10.0000	0.599760
$279$	0	0
$280$	0	0
$281$	8.45600	0.504442	0.252221	−	0.967670i	$-0.418839\pi$
$281$	8.45600	0.504442	0.252221	+	0.967670i	$0.418839\pi$
$282$	0	0
$283$	21.3160	1.26711	0.633553	−	0.773700i	$-0.281596\pi$
$283$	21.3160	1.26711	0.633553	+	0.773700i	$0.281596\pi$
$284$	−1.77200	−0.105149
$285$	0	0
$286$	−13.2280	−0.782188
$287$	1.77200	0.104598
$288$	0	0
$289$	5.77200	0.339530
$290$	0	0
$291$	0	0
$292$	−6.22800	−0.364466
$293$	−29.3160	−1.71266	−0.856330	−	0.516430i	$-0.827261\pi$
$293$	−29.3160	−1.71266	−0.856330	+	0.516430i	$0.827261\pi$
$294$	0	0
$295$	0	0
$296$	0.227998	0.0132521
$297$	0	0
$298$	14.3160	0.829304
$299$	−13.2280	−0.764995
$300$	0	0
$301$	6.77200	0.390332
$302$	24.3160	1.39923
$303$	0	0
$304$	2.00000	0.114708
$305$	0	0
$306$	0	0
$307$	7.68399	0.438549	0.219274	−	0.975663i	$-0.429631\pi$
$307$	7.68399	0.438549	0.219274	+	0.975663i	$0.429631\pi$
$308$	−4.77200	−0.271910
$309$	0	0
$310$	0	0
$311$	−25.0880	−1.42261	−0.711305	−	0.702883i	$-0.751896\pi$
$311$	−25.0880	−1.42261	−0.711305	+	0.702883i	$0.751896\pi$
$312$	0	0
$313$	0.455996	0.0257744	0.0128872	−	0.999917i	$-0.495898\pi$
$313$	0.455996	0.0257744	0.0128872	+	0.999917i	$0.495898\pi$
$314$	10.3160	0.582166
$315$	0	0
$316$	6.77200	0.380955
$317$	8.45600	0.474936	0.237468	−	0.971395i	$-0.423683\pi$
$317$	8.45600	0.474936	0.237468	+	0.971395i	$0.423683\pi$
$318$	0	0
$319$	14.3160	0.801542
$320$	0	0
$321$	0	0
$322$	−4.77200	−0.265933
$323$	9.54400	0.531043
$324$	0	0
$325$	0	0
$326$	18.7720	1.03969
$327$	0	0
$328$	1.77200	0.0978424
$329$	−12.5440	−0.691573
$330$	0	0
$331$	22.8600	1.25650	0.628250	−	0.778012i	$-0.283772\pi$
$331$	22.8600	1.25650	0.628250	+	0.778012i	$0.283772\pi$
$332$	0	0
$333$	0	0
$334$	−13.7720	−0.753570
$335$	0	0
$336$	0	0
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	5.31601	0.289153
$339$	0	0
$340$	0	0
$341$	40.7720	2.20793
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	6.77200	0.365122
$345$	0	0
$346$	−7.77200	−0.417825
$347$	11.3160	0.607475	0.303738	−	0.952756i	$-0.401765\pi$
$347$	11.3160	0.607475	0.303738	+	0.952756i	$0.401765\pi$
$348$	0	0
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	0	0
$351$	0	0
$352$	−4.77200	−0.254349
$353$	14.3160	0.761964	0.380982	−	0.924582i	$-0.375586\pi$
$353$	14.3160	0.761964	0.380982	+	0.924582i	$0.375586\pi$
$354$	0	0
$355$	0	0
$356$	3.54400	0.187832
$357$	0	0
$358$	15.5440	0.821526
$359$	−21.5440	−1.13705	−0.568525	−	0.822666i	$-0.692486\pi$
$359$	−21.5440	−1.13705	−0.568525	+	0.822666i	$0.692486\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	21.3160	1.12034
$363$	0	0
$364$	−2.77200	−0.145292
$365$	0	0
$366$	0	0
$367$	29.0880	1.51838	0.759191	−	0.650868i	$-0.225595\pi$
$367$	29.0880	1.51838	0.759191	+	0.650868i	$0.225595\pi$
$368$	−4.77200	−0.248758
$369$	0	0
$370$	0	0
$371$	−6.00000	−0.311504
$372$	0	0
$373$	−23.0000	−1.19089	−0.595447	−	0.803394i	$-0.703025\pi$
$373$	−23.0000	−1.19089	−0.595447	+	0.803394i	$0.703025\pi$
$374$	−22.7720	−1.17751
$375$	0	0
$376$	−12.5440	−0.646908
$377$	8.31601	0.428296
$378$	0	0
$379$	12.2280	0.628110	0.314055	−	0.949405i	$-0.398312\pi$
$379$	12.2280	0.628110	0.314055	+	0.949405i	$0.398312\pi$
$380$	0	0
$381$	0	0
$382$	19.0880	0.976627
$383$	8.31601	0.424928	0.212464	−	0.977169i	$-0.431851\pi$
$383$	8.31601	0.424928	0.212464	+	0.977169i	$0.431851\pi$
$384$	0	0
$385$	0	0
$386$	23.5440	1.19836
$387$	0	0
$388$	0.455996	0.0231497
$389$	3.00000	0.152106	0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000	0.152106	0.0760530	+	0.997104i	$0.475768\pi$
$390$	0	0
$391$	−22.7720	−1.15163
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−6.00000	−0.302276
$395$	0	0
$396$	0	0
$397$	37.4040	1.87725	0.938627	−	0.344934i	$-0.112099\pi$
$397$	37.4040	1.87725	0.938627	+	0.344934i	$0.112099\pi$
$398$	0.316006	0.0158399
$399$	0	0
$400$	0	0
$401$	28.6320	1.42981	0.714907	−	0.699219i	$-0.246469\pi$
$401$	28.6320	1.42981	0.714907	+	0.699219i	$0.246469\pi$
$402$	0	0
$403$	23.6840	1.17978
$404$	8.31601	0.413737
$405$	0	0
$406$	3.00000	0.148888
$407$	−1.08801	−0.0539305
$408$	0	0
$409$	−20.7720	−1.02711	−0.513555	−	0.858057i	$-0.671672\pi$
$409$	−20.7720	−1.02711	−0.513555	+	0.858057i	$0.671672\pi$
$410$	0	0
$411$	0	0
$412$	−8.00000	−0.394132
$413$	−1.77200	−0.0871945
$414$	0	0
$415$	0	0
$416$	−2.77200	−0.135909
$417$	0	0
$418$	−9.54400	−0.466812
$419$	3.00000	0.146560	0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000	0.146560	0.0732798	+	0.997311i	$0.476653\pi$
$420$	0	0
$421$	−0.455996	−0.0222239	−0.0111119	−	0.999938i	$-0.503537\pi$
$421$	−0.455996	−0.0222239	−0.0111119	+	0.999938i	$0.503537\pi$
$422$	15.3160	0.745571
$423$	0	0
$424$	−6.00000	−0.291386
$425$	0	0
$426$	0	0
$427$	5.77200	0.279327
$428$	10.2280	0.494389
$429$	0	0
$430$	0	0
$431$	35.3160	1.70111	0.850556	−	0.525884i	$-0.176266\pi$
$431$	35.3160	1.70111	0.850556	+	0.525884i	$0.176266\pi$
$432$	0	0
$433$	8.22800	0.395412	0.197706	−	0.980261i	$-0.436651\pi$
$433$	8.22800	0.395412	0.197706	+	0.980261i	$0.436651\pi$
$434$	8.54400	0.410125
$435$	0	0
$436$	17.5440	0.840205
$437$	−9.54400	−0.456552
$438$	0	0
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	0	0
$442$	−13.2280	−0.629192
$443$	−32.8600	−1.56123	−0.780613	−	0.625015i	$-0.785093\pi$
$443$	−32.8600	−1.56123	−0.780613	+	0.625015i	$0.785093\pi$
$444$	0	0
$445$	0	0
$446$	−19.5440	−0.925435
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	19.0880	0.900819	0.450409	−	0.892822i	$-0.351278\pi$
$449$	19.0880	0.900819	0.450409	+	0.892822i	$0.351278\pi$
$450$	0	0
$451$	−8.45600	−0.398177
$452$	0.544004	0.0255878
$453$	0	0
$454$	−24.0000	−1.12638
$455$	0	0
$456$	0	0
$457$	18.4560	0.863335	0.431668	−	0.902033i	$-0.357925\pi$
$457$	18.4560	0.863335	0.431668	+	0.902033i	$0.357925\pi$
$458$	−11.5440	−0.539416
$459$	0	0
$460$	0	0
$461$	33.5440	1.56230	0.781150	−	0.624343i	$-0.214633\pi$
$461$	33.5440	1.56230	0.781150	+	0.624343i	$0.214633\pi$
$462$	0	0
$463$	−19.3160	−0.897691	−0.448845	−	0.893609i	$-0.648165\pi$
$463$	−19.3160	−0.897691	−0.448845	+	0.893609i	$0.648165\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	−16.2280	−0.751747
$467$	−20.4560	−0.946591	−0.473295	−	0.880904i	$-0.656936\pi$
$467$	−20.4560	−0.946591	−0.473295	+	0.880904i	$0.656936\pi$
$468$	0	0
$469$	−7.54400	−0.348350
$470$	0	0
$471$	0	0
$472$	−1.77200	−0.0815630
$473$	−32.3160	−1.48589
$474$	0	0
$475$	0	0
$476$	−4.77200	−0.218724
$477$	0	0
$478$	−20.8600	−0.954115
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	−0.632011	−0.0288172
$482$	11.2280	0.511421
$483$	0	0
$484$	11.7720	0.535091
$485$	0	0
$486$	0	0
$487$	30.8600	1.39840	0.699200	−	0.714926i	$-0.253540\pi$
$487$	30.8600	1.39840	0.699200	+	0.714926i	$0.253540\pi$
$488$	5.77200	0.261286
$489$	0	0
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	14.3160	0.644760
$494$	−5.54400	−0.249437
$495$	0	0
$496$	8.54400	0.383637
$497$	1.77200	0.0794851
$498$	0	0
$499$	−22.4040	−1.00294	−0.501471	−	0.865175i	$-0.667207\pi$
$499$	−22.4040	−1.00294	−0.501471	+	0.865175i	$0.667207\pi$
$500$	0	0
$501$	0	0
$502$	−10.7720	−0.480778
$503$	1.22800	0.0547537	0.0273769	−	0.999625i	$-0.491285\pi$
$503$	1.22800	0.0547537	0.0273769	+	0.999625i	$0.491285\pi$
$504$	0	0
$505$	0	0
$506$	22.7720	1.01234
$507$	0	0
$508$	−15.7720	−0.699769
$509$	−27.4040	−1.21466	−0.607331	−	0.794449i	$-0.707760\pi$
$509$	−27.4040	−1.21466	−0.607331	+	0.794449i	$0.707760\pi$
$510$	0	0
$511$	6.22800	0.275510
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	17.8600	0.787771
$515$	0	0
$516$	0	0
$517$	59.8600	2.63264
$518$	−0.227998	−0.0100177
$519$	0	0
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	12.3160	0.538541	0.269271	−	0.963065i	$-0.413217\pi$
$523$	12.3160	0.538541	0.269271	+	0.963065i	$0.413217\pi$
$524$	3.00000	0.131056
$525$	0	0
$526$	−24.0000	−1.04645
$527$	40.7720	1.77606
$528$	0	0
$529$	−0.227998	−0.00991296
$530$	0	0
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	−4.91199	−0.212762
$534$	0	0
$535$	0	0
$536$	−7.54400	−0.325851
$537$	0	0
$538$	26.3160	1.13456
$539$	4.77200	0.205545
$540$	0	0
$541$	−26.6320	−1.14500	−0.572500	−	0.819905i	$-0.694026\pi$
$541$	−26.6320	−1.14500	−0.572500	+	0.819905i	$0.694026\pi$
$542$	−32.4040	−1.39187
$543$	0	0
$544$	−4.77200	−0.204598
$545$	0	0
$546$	0	0
$547$	−37.8600	−1.61878	−0.809389	−	0.587274i	$-0.800201\pi$
$547$	−37.8600	−1.61878	−0.809389	+	0.587274i	$0.800201\pi$
$548$	4.22800	0.180611
$549$	0	0
$550$	0	0
$551$	6.00000	0.255609
$552$	0	0
$553$	−6.77200	−0.287975
$554$	−22.0000	−0.934690
$555$	0	0
$556$	−10.0000	−0.424094
$557$	−8.45600	−0.358292	−0.179146	−	0.983822i	$-0.557333\pi$
$557$	−8.45600	−0.358292	−0.179146	+	0.983822i	$0.557333\pi$
$558$	0	0
$559$	−18.7720	−0.793971
$560$	0	0
$561$	0	0
$562$	−8.45600	−0.356695
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	0	0
$565$	0	0
$566$	−21.3160	−0.895979
$567$	0	0
$568$	1.77200	0.0743515
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	28.8600	1.20775	0.603877	−	0.797078i	$-0.293622\pi$
$571$	28.8600	1.20775	0.603877	+	0.797078i	$0.293622\pi$
$572$	13.2280	0.553090
$573$	0	0
$574$	−1.77200	−0.0739619
$575$	0	0
$576$	0	0
$577$	−35.9480	−1.49654	−0.748268	−	0.663397i	$-0.769114\pi$
$577$	−35.9480	−1.49654	−0.748268	+	0.663397i	$0.769114\pi$
$578$	−5.77200	−0.240084
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	28.6320	1.18582
$584$	6.22800	0.257716
$585$	0	0
$586$	29.3160	1.21103
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	0	0
$589$	17.0880	0.704099
$590$	0	0
$591$	0	0
$592$	−0.227998	−0.00937067
$593$	8.31601	0.341497	0.170749	−	0.985315i	$-0.445381\pi$
$593$	8.31601	0.341497	0.170749	+	0.985315i	$0.445381\pi$
$594$	0	0
$595$	0	0
$596$	−14.3160	−0.586406
$597$	0	0
$598$	13.2280	0.540933
$599$	2.86001	0.116857	0.0584284	−	0.998292i	$-0.481391\pi$
$599$	2.86001	0.116857	0.0584284	+	0.998292i	$0.481391\pi$
$600$	0	0
$601$	28.3160	1.15503	0.577517	−	0.816379i	$-0.304022\pi$
$601$	28.3160	1.15503	0.577517	+	0.816379i	$0.304022\pi$
$602$	−6.77200	−0.276006
$603$	0	0
$604$	−24.3160	−0.989404
$605$	0	0
$606$	0	0
$607$	−43.7200	−1.77454	−0.887270	−	0.461250i	$-0.847401\pi$
$607$	−43.7200	−1.77454	−0.887270	+	0.461250i	$0.847401\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	0	0
$611$	34.7720	1.40672
$612$	0	0
$613$	13.6840	0.552691	0.276346	−	0.961058i	$-0.410877\pi$
$613$	13.6840	0.552691	0.276346	+	0.961058i	$0.410877\pi$
$614$	−7.68399	−0.310101
$615$	0	0
$616$	4.77200	0.192269
$617$	29.1760	1.17458	0.587291	−	0.809376i	$-0.300194\pi$
$617$	29.1760	1.17458	0.587291	+	0.809376i	$0.300194\pi$
$618$	0	0
$619$	17.5440	0.705153	0.352577	−	0.935783i	$-0.385306\pi$
$619$	17.5440	0.705153	0.352577	+	0.935783i	$0.385306\pi$
$620$	0	0
$621$	0	0
$622$	25.0880	1.00594
$623$	−3.54400	−0.141988
$624$	0	0
$625$	0	0
$626$	−0.455996	−0.0182253
$627$	0	0
$628$	−10.3160	−0.411653
$629$	−1.08801	−0.0433817
$630$	0	0
$631$	4.45600	0.177390	0.0886952	−	0.996059i	$-0.471730\pi$
$631$	4.45600	0.177390	0.0886952	+	0.996059i	$0.471730\pi$
$632$	−6.77200	−0.269376
$633$	0	0
$634$	−8.45600	−0.335831
$635$	0	0
$636$	0	0
$637$	2.77200	0.109831
$638$	−14.3160	−0.566776
$639$	0	0
$640$	0	0
$641$	−16.6320	−0.656925	−0.328462	−	0.944517i	$-0.606530\pi$
$641$	−16.6320	−0.656925	−0.328462	+	0.944517i	$0.606530\pi$
$642$	0	0
$643$	−25.1760	−0.992845	−0.496423	−	0.868081i	$-0.665353\pi$
$643$	−25.1760	−0.992845	−0.496423	+	0.868081i	$0.665353\pi$
$644$	4.77200	0.188043
$645$	0	0
$646$	−9.54400	−0.375504
$647$	−36.4040	−1.43119	−0.715595	−	0.698516i	$-0.753844\pi$
$647$	−36.4040	−1.43119	−0.715595	+	0.698516i	$0.753844\pi$
$648$	0	0
$649$	8.45600	0.331927
$650$	0	0
$651$	0	0
$652$	−18.7720	−0.735168
$653$	1.08801	0.0425770	0.0212885	−	0.999773i	$-0.493223\pi$
$653$	1.08801	0.0425770	0.0212885	+	0.999773i	$0.493223\pi$
$654$	0	0
$655$	0	0
$656$	−1.77200	−0.0691850
$657$	0	0
$658$	12.5440	0.489016
$659$	−26.1760	−1.01967	−0.509836	−	0.860271i	$-0.670294\pi$
$659$	−26.1760	−1.01967	−0.509836	+	0.860271i	$0.670294\pi$
$660$	0	0
$661$	−27.3160	−1.06247	−0.531235	−	0.847225i	$-0.678272\pi$
$661$	−27.3160	−1.06247	−0.531235	+	0.847225i	$0.678272\pi$
$662$	−22.8600	−0.888479
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−14.3160	−0.554318
$668$	13.7720	0.532855
$669$	0	0
$670$	0	0
$671$	−27.5440	−1.06332
$672$	0	0
$673$	2.63201	0.101457	0.0507283	−	0.998712i	$-0.483846\pi$
$673$	2.63201	0.101457	0.0507283	+	0.998712i	$0.483846\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	−5.31601	−0.204462
$677$	−41.3160	−1.58790	−0.793952	−	0.607981i	$-0.791980\pi$
$677$	−41.3160	−1.58790	−0.793952	+	0.607981i	$0.791980\pi$
$678$	0	0
$679$	−0.455996	−0.0174995
$680$	0	0
$681$	0	0
$682$	−40.7720	−1.56124
$683$	31.7720	1.21572	0.607861	−	0.794044i	$-0.292028\pi$
$683$	31.7720	1.21572	0.607861	+	0.794044i	$0.292028\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−6.77200	−0.258180
$689$	16.6320	0.633629
$690$	0	0
$691$	6.91199	0.262945	0.131472	−	0.991320i	$-0.458030\pi$
$691$	6.91199	0.262945	0.131472	+	0.991320i	$0.458030\pi$
$692$	7.77200	0.295447
$693$	0	0
$694$	−11.3160	−0.429550
$695$	0	0
$696$	0	0
$697$	−8.45600	−0.320294
$698$	22.0000	0.832712
$699$	0	0
$700$	0	0
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	0	0
$703$	−0.455996	−0.0171982
$704$	4.77200	0.179852
$705$	0	0
$706$	−14.3160	−0.538790
$707$	−8.31601	−0.312756
$708$	0	0
$709$	35.5440	1.33488	0.667442	−	0.744662i	$-0.267389\pi$
$709$	35.5440	1.33488	0.667442	+	0.744662i	$0.267389\pi$
$710$	0	0
$711$	0	0
$712$	−3.54400	−0.132817
$713$	−40.7720	−1.52692
$714$	0	0
$715$	0	0
$716$	−15.5440	−0.580907
$717$	0	0
$718$	21.5440	0.804015
$719$	−10.6320	−0.396507	−0.198254	−	0.980151i	$-0.563527\pi$
$719$	−10.6320	−0.396507	−0.198254	+	0.980151i	$0.563527\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	15.0000	0.558242
$723$	0	0
$724$	−21.3160	−0.792203
$725$	0	0
$726$	0	0
$727$	13.5440	0.502319	0.251160	−	0.967946i	$-0.419188\pi$
$727$	13.5440	0.502319	0.251160	+	0.967946i	$0.419188\pi$
$728$	2.77200	0.102737
$729$	0	0
$730$	0	0
$731$	−32.3160	−1.19525
$732$	0	0
$733$	−22.4560	−0.829431	−0.414716	−	0.909951i	$-0.636119\pi$
$733$	−22.4560	−0.829431	−0.414716	+	0.909951i	$0.636119\pi$
$734$	−29.0880	−1.07366
$735$	0	0
$736$	4.77200	0.175898
$737$	36.0000	1.32608
$738$	0	0
$739$	15.7720	0.580182	0.290091	−	0.956999i	$-0.406314\pi$
$739$	15.7720	0.580182	0.290091	+	0.956999i	$0.406314\pi$
$740$	0	0
$741$	0	0
$742$	6.00000	0.220267
$743$	−38.3160	−1.40568	−0.702839	−	0.711349i	$-0.748085\pi$
$743$	−38.3160	−1.40568	−0.702839	+	0.711349i	$0.748085\pi$
$744$	0	0
$745$	0	0
$746$	23.0000	0.842090
$747$	0	0
$748$	22.7720	0.832627
$749$	−10.2280	−0.373723
$750$	0	0
$751$	27.2280	0.993564	0.496782	−	0.867875i	$-0.334515\pi$
$751$	27.2280	0.993564	0.496782	+	0.867875i	$0.334515\pi$
$752$	12.5440	0.457433
$753$	0	0
$754$	−8.31601	−0.302851
$755$	0	0
$756$	0	0
$757$	−0.367989	−0.0133748	−0.00668739	−	0.999978i	$-0.502129\pi$
$757$	−0.367989	−0.0133748	−0.00668739	+	0.999978i	$0.502129\pi$
$758$	−12.2280	−0.444141
$759$	0	0
$760$	0	0
$761$	4.22800	0.153265	0.0766324	−	0.997059i	$-0.475583\pi$
$761$	4.22800	0.153265	0.0766324	+	0.997059i	$0.475583\pi$
$762$	0	0
$763$	−17.5440	−0.635136
$764$	−19.0880	−0.690580
$765$	0	0
$766$	−8.31601	−0.300469
$767$	4.91199	0.177362
$768$	0	0
$769$	−44.7720	−1.61452	−0.807260	−	0.590196i	$-0.799050\pi$
$769$	−44.7720	−1.61452	−0.807260	+	0.590196i	$0.799050\pi$
$770$	0	0
$771$	0	0
$772$	−23.5440	−0.847367
$773$	26.8600	0.966087	0.483044	−	0.875596i	$-0.339531\pi$
$773$	26.8600	0.966087	0.483044	+	0.875596i	$0.339531\pi$
$774$	0	0
$775$	0	0
$776$	−0.455996	−0.0163693
$777$	0	0
$778$	−3.00000	−0.107555
$779$	−3.54400	−0.126977
$780$	0	0
$781$	−8.45600	−0.302579
$782$	22.7720	0.814325
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	23.6320	0.842390	0.421195	−	0.906970i	$-0.361611\pi$
$787$	23.6320	0.842390	0.421195	+	0.906970i	$0.361611\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	0	0
$791$	−0.544004	−0.0193425
$792$	0	0
$793$	−16.0000	−0.568177
$794$	−37.4040	−1.32742
$795$	0	0
$796$	−0.316006	−0.0112005
$797$	12.6840	0.449290	0.224645	−	0.974441i	$-0.427878\pi$
$797$	12.6840	0.449290	0.224645	+	0.974441i	$0.427878\pi$
$798$	0	0
$799$	59.8600	2.11769
$800$	0	0
$801$	0	0
$802$	−28.6320	−1.01103
$803$	−29.7200	−1.04880
$804$	0	0
$805$	0	0
$806$	−23.6840	−0.834233
$807$	0	0
$808$	−8.31601	−0.292556
$809$	41.7200	1.46680	0.733399	−	0.679799i	$-0.237933\pi$
$809$	41.7200	1.46680	0.733399	+	0.679799i	$0.237933\pi$
$810$	0	0
$811$	39.0880	1.37257	0.686283	−	0.727335i	$-0.259241\pi$
$811$	39.0880	1.37257	0.686283	+	0.727335i	$0.259241\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	1.08801	0.0381346
$815$	0	0
$816$	0	0
$817$	−13.5440	−0.473845
$818$	20.7720	0.726276
$819$	0	0
$820$	0	0
$821$	25.0880	0.875577	0.437789	−	0.899078i	$-0.355762\pi$
$821$	25.0880	0.875577	0.437789	+	0.899078i	$0.355762\pi$
$822$	0	0
$823$	34.4040	1.19925	0.599624	−	0.800282i	$-0.295317\pi$
$823$	34.4040	1.19925	0.599624	+	0.800282i	$0.295317\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	1.77200	0.0616558
$827$	−11.3160	−0.393496	−0.196748	−	0.980454i	$-0.563038\pi$
$827$	−11.3160	−0.393496	−0.196748	+	0.980454i	$0.563038\pi$
$828$	0	0
$829$	30.6320	1.06389	0.531947	−	0.846778i	$-0.321461\pi$
$829$	30.6320	1.06389	0.531947	+	0.846778i	$0.321461\pi$
$830$	0	0
$831$	0	0
$832$	2.77200	0.0961019
$833$	4.77200	0.165340
$834$	0	0
$835$	0	0
$836$	9.54400	0.330086
$837$	0	0
$838$	−3.00000	−0.103633
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0.455996	0.0157147
$843$	0	0
$844$	−15.3160	−0.527199
$845$	0	0
$846$	0	0
$847$	−11.7720	−0.404491
$848$	6.00000	0.206041
$849$	0	0
$850$	0	0
$851$	1.08801	0.0372964
$852$	0	0
$853$	−31.8600	−1.09087	−0.545433	−	0.838154i	$-0.683635\pi$
$853$	−31.8600	−1.09087	−0.545433	+	0.838154i	$0.683635\pi$
$854$	−5.77200	−0.197514
$855$	0	0
$856$	−10.2280	−0.349586
$857$	35.7200	1.22017	0.610086	−	0.792335i	$-0.291135\pi$
$857$	35.7200	1.22017	0.610086	+	0.792335i	$0.291135\pi$
$858$	0	0
$859$	38.0000	1.29654	0.648272	−	0.761409i	$-0.275492\pi$
$859$	38.0000	1.29654	0.648272	+	0.761409i	$0.275492\pi$
$860$	0	0
$861$	0	0
$862$	−35.3160	−1.20287
$863$	32.3160	1.10005	0.550025	−	0.835148i	$-0.314618\pi$
$863$	32.3160	1.10005	0.550025	+	0.835148i	$0.314618\pi$
$864$	0	0
$865$	0	0
$866$	−8.22800	−0.279599
$867$	0	0
$868$	−8.54400	−0.290002
$869$	32.3160	1.09625
$870$	0	0
$871$	20.9120	0.708576
$872$	−17.5440	−0.594115
$873$	0	0
$874$	9.54400	0.322831
$875$	0	0
$876$	0	0
$877$	−33.6320	−1.13567	−0.567836	−	0.823142i	$-0.692219\pi$
$877$	−33.6320	−1.13567	−0.567836	+	0.823142i	$0.692219\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	0	0
$881$	17.3160	0.583391	0.291696	−	0.956511i	$-0.405781\pi$
$881$	17.3160	0.583391	0.291696	+	0.956511i	$0.405781\pi$
$882$	0	0
$883$	35.0880	1.18081	0.590403	−	0.807109i	$-0.298969\pi$
$883$	35.0880	1.18081	0.590403	+	0.807109i	$0.298969\pi$
$884$	13.2280	0.444906
$885$	0	0
$886$	32.8600	1.10395
$887$	0.544004	0.0182659	0.00913293	−	0.999958i	$-0.497093\pi$
$887$	0.544004	0.0182659	0.00913293	+	0.999958i	$0.497093\pi$
$888$	0	0
$889$	15.7720	0.528976
$890$	0	0
$891$	0	0
$892$	19.5440	0.654382
$893$	25.0880	0.839538
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.0880	−0.636975
$899$	25.6320	0.854875
$900$	0	0
$901$	28.6320	0.953871
$902$	8.45600	0.281554
$903$	0	0
$904$	−0.544004	−0.0180933
$905$	0	0
$906$	0	0
$907$	29.2280	0.970500	0.485250	−	0.874376i	$-0.338729\pi$
$907$	29.2280	0.970500	0.485250	+	0.874376i	$0.338729\pi$
$908$	24.0000	0.796468
$909$	0	0
$910$	0	0
$911$	−6.68399	−0.221451	−0.110725	−	0.993851i	$-0.535317\pi$
$911$	−6.68399	−0.221451	−0.110725	+	0.993851i	$0.535317\pi$
$912$	0	0
$913$	0	0
$914$	−18.4560	−0.610470
$915$	0	0
$916$	11.5440	0.381425
$917$	−3.00000	−0.0990687
$918$	0	0
$919$	48.4920	1.59960	0.799802	−	0.600264i	$-0.204938\pi$
$919$	48.4920	1.59960	0.799802	+	0.600264i	$0.204938\pi$
$920$	0	0
$921$	0	0
$922$	−33.5440	−1.10471
$923$	−4.91199	−0.161680
$924$	0	0
$925$	0	0
$926$	19.3160	0.634763
$927$	0	0
$928$	−3.00000	−0.0984798
$929$	13.0880	0.429404	0.214702	−	0.976680i	$-0.431122\pi$
$929$	13.0880	0.429404	0.214702	+	0.976680i	$0.431122\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	16.2280	0.531566
$933$	0	0
$934$	20.4560	0.669341
$935$	0	0
$936$	0	0
$937$	48.8600	1.59619	0.798093	−	0.602534i	$-0.205842\pi$
$937$	48.8600	1.59619	0.798093	+	0.602534i	$0.205842\pi$
$938$	7.54400	0.246320
$939$	0	0
$940$	0	0
$941$	2.31601	0.0754996	0.0377498	−	0.999287i	$-0.487981\pi$
$941$	2.31601	0.0754996	0.0377498	+	0.999287i	$0.487981\pi$
$942$	0	0
$943$	8.45600	0.275365
$944$	1.77200	0.0576737
$945$	0	0
$946$	32.3160	1.05068
$947$	45.2640	1.47088	0.735442	−	0.677588i	$-0.236975\pi$
$947$	45.2640	1.47088	0.735442	+	0.677588i	$0.236975\pi$
$948$	0	0
$949$	−17.2640	−0.560414
$950$	0	0
$951$	0	0
$952$	4.77200	0.154661
$953$	33.6840	1.09113	0.545566	−	0.838068i	$-0.316315\pi$
$953$	33.6840	1.09113	0.545566	+	0.838068i	$0.316315\pi$
$954$	0	0
$955$	0	0
$956$	20.8600	0.674661
$957$	0	0
$958$	36.0000	1.16311
$959$	−4.22800	−0.136529
$960$	0	0
$961$	42.0000	1.35484
$962$	0.632011	0.0203769
$963$	0	0
$964$	−11.2280	−0.361629
$965$	0	0
$966$	0	0
$967$	−12.2280	−0.393226	−0.196613	−	0.980481i	$-0.562994\pi$
$967$	−12.2280	−0.393226	−0.196613	+	0.980481i	$0.562994\pi$
$968$	−11.7720	−0.378366
$969$	0	0
$970$	0	0
$971$	45.0000	1.44412	0.722059	−	0.691831i	$-0.243196\pi$
$971$	45.0000	1.44412	0.722059	+	0.691831i	$0.243196\pi$
$972$	0	0
$973$	10.0000	0.320585
$974$	−30.8600	−0.988818
$975$	0	0
$976$	−5.77200	−0.184757
$977$	−9.68399	−0.309818	−0.154909	−	0.987929i	$-0.549509\pi$
$977$	−9.68399	−0.309818	−0.154909	+	0.987929i	$0.549509\pi$
$978$	0	0
$979$	16.9120	0.540510
$980$	0	0
$981$	0	0
$982$	−12.0000	−0.382935
$983$	−5.86001	−0.186905	−0.0934526	−	0.995624i	$-0.529790\pi$
$983$	−5.86001	−0.186905	−0.0934526	+	0.995624i	$0.529790\pi$
$984$	0	0
$985$	0	0
$986$	−14.3160	−0.455914
$987$	0	0
$988$	5.54400	0.176378
$989$	32.3160	1.02759
$990$	0	0
$991$	−49.4040	−1.56937	−0.784685	−	0.619895i	$-0.787175\pi$
$991$	−49.4040	−1.56937	−0.784685	+	0.619895i	$0.787175\pi$
$992$	−8.54400	−0.271272
$993$	0	0
$994$	−1.77200	−0.0562045
$995$	0	0
$996$	0	0
$997$	−22.3160	−0.706755	−0.353377	−	0.935481i	$-0.614967\pi$
$997$	−22.3160	−0.706755	−0.353377	+	0.935481i	$0.614967\pi$
$998$	22.4040	0.709187
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.ed.1.2		2
3.2	odd	2		9450.2.a.eo.1.1		2
5.4	even	2		1890.2.a.bb.1.2	yes	2
15.14	odd	2		1890.2.a.z.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.z.1.1	✓	2	15.14	odd	2
1890.2.a.bb.1.2	yes	2	5.4	even	2
9450.2.a.ed.1.2		2	1.1	even	1	trivial
9450.2.a.eo.1.1		2	3.2	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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +4.77200 q^{11} +2.77200 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.77200 q^{17} +2.00000 q^{19} -4.77200 q^{22} -4.77200 q^{23} -2.77200 q^{26} -1.00000 q^{28} +3.00000 q^{29} +8.54400 q^{31} -1.00000 q^{32} -4.77200 q^{34} -0.227998 q^{37} -2.00000 q^{38} -1.77200 q^{41} -6.77200 q^{43} +4.77200 q^{44} +4.77200 q^{46} +12.5440 q^{47} +1.00000 q^{49} +2.77200 q^{52} +6.00000 q^{53} +1.00000 q^{56} -3.00000 q^{58} +1.77200 q^{59} -5.77200 q^{61} -8.54400 q^{62} +1.00000 q^{64} +7.54400 q^{67} +4.77200 q^{68} -1.77200 q^{71} -6.22800 q^{73} +0.227998 q^{74} +2.00000 q^{76} -4.77200 q^{77} +6.77200 q^{79} +1.77200 q^{82} +6.77200 q^{86} -4.77200 q^{88} +3.54400 q^{89} -2.77200 q^{91} -4.77200 q^{92} -12.5440 q^{94} +0.455996 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{7} - 2 q^{8} + q^{11} - 3 q^{13} + 2 q^{14} + 2 q^{16} + q^{17} + 4 q^{19} - q^{22} - q^{23} + 3 q^{26} - 2 q^{28} + 6 q^{29} - 2 q^{32} - q^{34} - 9 q^{37} - 4 q^{38} + 5 q^{41} - 5 q^{43} + q^{44} + q^{46} + 8 q^{47} + 2 q^{49} - 3 q^{52} + 12 q^{53} + 2 q^{56} - 6 q^{58} - 5 q^{59} - 3 q^{61} + 2 q^{64} - 2 q^{67} + q^{68} + 5 q^{71} - 21 q^{73} + 9 q^{74} + 4 q^{76} - q^{77} + 5 q^{79} - 5 q^{82} + 5 q^{86} - q^{88} - 10 q^{89} + 3 q^{91} - q^{92} - 8 q^{94} + 18 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^7 - 2 * q^8 + q^11 - 3 * q^13 + 2 * q^14 + 2 * q^16 + q^17 + 4 * q^19 - q^22 - q^23 + 3 * q^26 - 2 * q^28 + 6 * q^29 - 2 * q^32 - q^34 - 9 * q^37 - 4 * q^38 + 5 * q^41 - 5 * q^43 + q^44 + q^46 + 8 * q^47 + 2 * q^49 - 3 * q^52 + 12 * q^53 + 2 * q^56 - 6 * q^58 - 5 * q^59 - 3 * q^61 + 2 * q^64 - 2 * q^67 + q^68 + 5 * q^71 - 21 * q^73 + 9 * q^74 + 4 * q^76 - q^77 + 5 * q^79 - 5 * q^82 + 5 * q^86 - q^88 - 10 * q^89 + 3 * q^91 - q^92 - 8 * q^94 + 18 * q^97 - 2 * q^98

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