LMFDB - Embedded newform 1805.2.b.h.1084.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, 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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.280944640000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 16x^{6} + 80x^{4} + 128x^{2} + 19 $ x^8 + 16x^6 + 80x^4 + 128*x^2 + 19
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1084.8
Root			$2.79913i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.h.1084.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79913i q^{2} +1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} -10.7350i q^{8} +1.74048 q^{9} +O(q^{10})$	$q+2.79913i q^{2} +1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} -10.7350i q^{8} +1.74048 q^{9} +6.25904i q^{10} +2.92978 q^{11} -6.54867i q^{12} -3.08876i q^{13} +2.50950i q^{15} +18.3785 q^{16} +4.87183i q^{18} -13.0477 q^{20} +8.20083i q^{22} +12.0477 q^{24} +5.00000 q^{25} +8.64583 q^{26} +5.32016i q^{27} -7.02443 q^{30} +29.9737i q^{32} +3.28804i q^{33} -10.1559 q^{36} +9.15124i q^{37} +3.46646 q^{39} -24.0042i q^{40} -17.0956 q^{44} +3.89183 q^{45} +20.6259i q^{48} +7.00000 q^{49} +13.9956i q^{50} +18.0233i q^{52} +13.6404i q^{53} -14.8918 q^{54} +6.55118 q^{55} -14.6433i q^{60} +1.11908 q^{61} -47.1432 q^{64} -6.90667i q^{65} -9.20366 q^{66} -13.7060i q^{67} -18.6841i q^{72} -25.6155 q^{74} +5.61142i q^{75} +9.70308i q^{78} +41.0955 q^{80} -0.749299 q^{81} -31.4512i q^{88} +10.8937i q^{90} -33.6390 q^{96} +15.8849i q^{97} +19.5939i q^{98} +5.09921 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} - 24 q^{9}+O(q^{10}) $ 8 * q - 16 * q^4 - 24 * q^9	$ 8 q - 16 q^{4} - 24 q^{9} + 32 q^{16} - 8 q^{24} + 40 q^{25} + 24 q^{26} - 40 q^{30} - 8 q^{36} - 72 q^{44} + 56 q^{49} - 88 q^{54} - 64 q^{64} + 104 q^{66} + 120 q^{80} + 72 q^{81} - 120 q^{96} - 32 q^{99}+O(q^{100}) $ 8 * q - 16 * q^4 - 24 * q^9 + 32 * q^16 - 8 * q^24 + 40 * q^25 + 24 * q^26 - 40 * q^30 - 8 * q^36 - 72 * q^44 + 56 * q^49 - 88 * q^54 - 64 * q^64 + 104 * q^66 + 120 * q^80 + 72 * q^81 - 120 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$	2.79913i	1.97928i	0.143559	+	0.989642i	$0.454145\pi$
$2$	2.79913i	1.97928i	−0.143559	+	0.989642i	$0.545855\pi$
$3$	1.12228i	0.647951i	0.946065	+	0.323976i	$0.105020\pi$
$3$	1.12228i	0.647951i	−0.946065	+	0.323976i	$0.894980\pi$
$4$	−5.83513	−2.91756
$5$	2.23607	1.00000
$5$	2.23607	1.00000
$6$	−3.14142	−1.28248
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	− 10.7350i	− 3.79540i
$9$	1.74048	0.580159
$10$	6.25904i	1.97928i
$11$	2.92978	0.883361	0.441680	−	0.897172i	$-0.354382\pi$
$11$	2.92978	0.883361	0.441680	+	0.897172i	$0.354382\pi$
$12$	− 6.54867i	− 1.89044i
$13$	− 3.08876i	− 0.856667i	−0.903621	−	0.428333i	$-0.859101\pi$
$13$	− 3.08876i	− 0.856667i	0.903621	−	0.428333i	$-0.140899\pi$
$14$	0	0
$15$	2.50950i	0.647951i
$16$	18.3785	4.59461
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	4.87183i	1.14830i
$19$	0	0
$19$	0	0
$20$	−13.0477	−2.91756
$21$	0	0
$22$	8.20083i	1.74842i
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	12.0477	2.45924
$25$	5.00000	1.00000
$26$	8.64583	1.69559
$27$	5.32016i	1.02387i
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−7.02443	−1.28248
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	29.9737i	5.29864i
$33$	3.28804i	0.572375i
$34$	0	0
$35$	0	0
$36$	−10.1559	−1.69265
$37$	9.15124i	1.50445i	0.658904	+	0.752227i	$0.271020\pi$
$37$	9.15124i	1.50445i	−0.658904	+	0.752227i	$0.728980\pi$
$38$	0	0
$39$	3.46646	0.555078
$40$	− 24.0042i	− 3.79540i
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−17.0956	−2.57726
$45$	3.89183	0.580159
$46$	0	0
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	20.6259i	2.97709i
$49$	7.00000	1.00000
$50$	13.9956i	1.97928i
$51$	0	0
$52$	18.0233i	2.49938i
$53$	13.6404i	1.87365i	0.349799	+	0.936825i	$0.386250\pi$
$53$	13.6404i	1.87365i	−0.349799	+	0.936825i	$0.613750\pi$
$54$	−14.8918	−2.02652
$55$	6.55118	0.883361
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	− 14.6433i	− 1.89044i
$61$	1.11908	0.143283	0.0716414	−	0.997430i	$-0.477176\pi$
$61$	1.11908	0.143283	0.0716414	+	0.997430i	$0.477176\pi$
$62$	0	0
$63$	0	0
$64$	−47.1432	−5.89290
$65$	− 6.90667i	− 0.856667i
$66$	−9.20366	−1.13289
$67$	− 13.7060i	− 1.67446i	−0.546853	−	0.837229i	$-0.684174\pi$
$67$	− 13.7060i	− 1.67446i	0.546853	−	0.837229i	$-0.315826\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	− 18.6841i	− 2.20194i
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−25.6155	−2.97774
$75$	5.61142i	0.647951i
$76$	0	0
$77$	0	0
$78$	9.70308i	1.09866i
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	41.0955	4.59461
$81$	−0.749299	−0.0832555
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	− 31.4512i	− 3.35271i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	10.8937i	1.14830i
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	−33.6390	−3.43326
$97$	15.8849i	1.61287i	0.591322	+	0.806436i	$0.298606\pi$
$97$	15.8849i	1.61287i	−0.591322	+	0.806436i	$0.701394\pi$
$98$	19.5939i	1.97928i
$99$	5.09921	0.512490
$100$	−29.1756	−2.91756
$101$	20.0810	1.99813	0.999067	−	0.0431977i	$-0.0137545\pi$
$101$	20.0810	1.99813	0.999067	+	0.0431977i	$0.0137545\pi$
$102$	0	0
$103$	− 19.8835i	− 1.95918i	−0.200999	−	0.979591i	$-0.564419\pi$
$103$	− 19.8835i	− 1.95918i	0.200999	−	0.979591i	$-0.435581\pi$
$104$	−33.1579	−3.25140
$105$	0	0
$106$	−38.1812	−3.70848
$107$	3.66801i	0.354600i	0.984157	+	0.177300i	$0.0567363\pi$
$107$	3.66801i	0.354600i	−0.984157	+	0.177300i	$0.943264\pi$
$108$	− 31.0438i	− 2.98719i
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	18.3376i	1.74842i
$111$	−10.2703	−0.974813
$112$	0	0
$113$	1.93025i	0.181583i	0.995870	+	0.0907914i	$0.0289396\pi$
$113$	1.93025i	0.181583i	−0.995870	+	0.0907914i	$0.971060\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	− 5.37591i	− 0.497003i
$118$	0	0
$119$	0	0
$120$	26.9396	2.45924
$121$	−2.41641	−0.219673
$122$	3.13244i	0.283597i
$123$	0	0
$124$	0	0
$125$	11.1803	1.00000
$126$	0	0
$127$	− 21.6693i	− 1.92284i	−0.275082	−	0.961421i	$-0.588705\pi$
$127$	− 21.6693i	− 1.92284i	0.275082	−	0.961421i	$-0.411295\pi$
$128$	− 72.0127i	− 6.36508i
$129$	0	0
$130$	19.3327	1.69559
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	− 19.1861i	− 1.66994i
$133$	0	0
$134$	38.3649	3.31423
$135$	11.8962i	1.02387i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	−21.8917	−1.85683	−0.928414	−	0.371546i	$-0.878828\pi$
$139$	−21.8917	−1.85683	−0.928414	+	0.371546i	$0.878828\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	− 9.04937i	− 0.756746i
$144$	31.9873	2.66561
$145$	0	0
$146$	0	0
$147$	7.85599i	0.647951i
$148$	− 53.3986i	− 4.38934i
$149$	−8.36188	−0.685032	−0.342516	−	0.939512i	$-0.611279\pi$
$149$	−8.36188	−0.685032	−0.342516	+	0.939512i	$0.611279\pi$
$150$	−15.7071	−1.28248
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	−20.2272	−1.61948
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	−15.3084	−1.21403
$160$	67.0231i	5.29864i
$161$	0	0
$162$	− 2.09739i	− 0.164786i
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	7.35229i	0.572375i
$166$	0	0
$167$	17.1802i	1.32944i	0.747091	+	0.664721i	$0.231450\pi$
$167$	17.1802i	1.32944i	−0.747091	+	0.664721i	$0.768550\pi$
$168$	0	0
$169$	3.45959	0.266122
$170$	0	0
$171$	0	0
$172$	0	0
$173$	13.1268i	0.998010i	0.866599	+	0.499005i	$0.166301\pi$
$173$	13.1268i	0.998010i	−0.866599	+	0.499005i	$0.833699\pi$
$174$	0	0
$175$	0	0
$176$	53.8448	4.05870
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	−22.7093	−1.69265
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	1.25592i	0.0928403i
$184$	0	0
$185$	20.4628i	1.50445i
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.94427	−0.647185	−0.323592	−	0.946197i	$-0.604891\pi$
$191$	−8.94427	−0.647185	−0.323592	+	0.946197i	$0.604891\pi$
$192$	− 52.9081i	− 3.81831i
$193$	− 2.41753i	− 0.174018i	−0.996208	−	0.0870089i	$-0.972269\pi$
$193$	− 2.41753i	− 0.174018i	0.996208	−	0.0870089i	$-0.0277309\pi$
$194$	−44.4640	−3.19233
$195$	7.75124	0.555078
$196$	−40.8459	−2.91756
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	14.2734i	1.01436i
$199$	26.8328	1.90213	0.951064	−	0.308994i	$-0.0999924\pi$
$199$	26.8328	1.90213	0.951064	+	0.308994i	$0.0999924\pi$
$200$	− 53.6751i	− 3.79540i
$201$	15.3821	1.08497
$202$	56.2093i	3.95487i
$203$	0	0
$204$	0	0
$205$	0	0
$206$	55.6566	3.87778
$207$	0	0
$208$	− 56.7666i	− 3.93605i
$209$	0	0
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	− 79.5933i	− 5.46649i
$213$	0	0
$214$	−10.2672	−0.701854
$215$	0	0
$216$	57.1121	3.88598
$217$	0	0
$218$	0	0
$219$	0	0
$220$	−38.2270	−2.57726
$221$	0	0
$222$	− 28.7479i	− 1.92943i
$223$	14.9356i	1.00016i	0.865978	+	0.500082i	$0.166697\pi$
$223$	14.9356i	1.00016i	−0.865978	+	0.500082i	$0.833303\pi$
$224$	0	0
$225$	8.70239	0.580159
$226$	−5.40302	−0.359404
$227$	− 18.7250i	− 1.24282i	−0.783484	−	0.621412i	$-0.786559\pi$
$227$	− 18.7250i	− 1.24282i	0.783484	−	0.621412i	$-0.213441\pi$
$228$	0	0
$229$	−29.5619	−1.95351	−0.976754	−	0.214362i	$-0.931233\pi$
$229$	−29.5619	−1.95351	−0.976754	+	0.214362i	$0.931233\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	15.0479	0.983711
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	46.1208i	2.97709i
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	− 6.76384i	− 0.434796i
$243$	15.1196i	0.969920i
$244$	−6.52995	−0.418037
$245$	15.6525	1.00000
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	31.2952i	1.97928i
$251$	17.8885	1.12911	0.564557	−	0.825394i	$-0.309047\pi$
$251$	17.8885	1.12911	0.564557	+	0.825394i	$0.309047\pi$
$252$	0	0
$253$	0	0
$254$	60.6553	3.80585
$255$	0	0
$256$	107.286	6.70540
$257$	− 20.3741i	− 1.27090i	−0.772142	−	0.635450i	$-0.780815\pi$
$257$	− 20.3741i	− 1.27090i	0.772142	−	0.635450i	$-0.219185\pi$
$258$	0	0
$259$	0	0
$260$	40.3013i	2.49938i
$261$	0	0
$262$	33.5896i	2.07517i
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	35.2972	2.17239
$265$	30.5008i	1.87365i
$266$	0	0
$267$	0	0
$268$	79.9764i	4.88534i
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	−33.2991	−2.02652
$271$	−24.1298	−1.46578	−0.732892	−	0.680345i	$-0.761830\pi$
$271$	−24.1298	−1.46578	−0.732892	+	0.680345i	$0.761830\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	14.6489	0.883361
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	− 61.2777i	− 3.67519i
$279$	0	0
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	25.3304	1.49781
$287$	0	0
$288$	52.1685i	3.07406i
$289$	17.0000	1.00000
$290$	0	0
$291$	−17.8274	−1.04506
$292$	0	0
$293$	0.172964i	0.0101047i	0.999987	+	0.00505234i	$0.00160822\pi$
$293$	0.172964i	0.0101047i	−0.999987	+	0.00505234i	$0.998392\pi$
$294$	−21.9899	−1.28248
$295$	0	0
$296$	98.2387	5.71001
$297$	15.5869i	0.904443i
$298$	− 23.4060i	− 1.35587i
$299$	0	0
$300$	− 32.7434i	− 1.89044i
$301$	0	0
$302$	0	0
$303$	22.5366i	1.29469i
$304$	0	0
$305$	2.50233	0.143283
$306$	0	0
$307$	1.35100i	0.0771055i	0.999257	+	0.0385528i	$0.0122748\pi$
$307$	1.35100i	0.0771055i	−0.999257	+	0.0385528i	$0.987725\pi$
$308$	0	0
$309$	22.3150	1.26945
$310$	0	0
$311$	−31.3726	−1.77898	−0.889490	−	0.456955i	$-0.848940\pi$
$311$	−31.3726	−1.77898	−0.889490	+	0.456955i	$0.848940\pi$
$312$	− 37.2125i	− 2.10675i
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	− 31.6593i	− 1.77816i	−0.457748	−	0.889082i	$-0.651344\pi$
$317$	− 31.6593i	− 1.77816i	0.457748	−	0.889082i	$-0.348656\pi$
$318$	− 42.8501i	− 2.40292i
$319$	0	0
$320$	−105.415	−5.89290
$321$	−4.11655	−0.229763
$322$	0	0
$323$	0	0
$324$	4.37226	0.242903
$325$	− 15.4438i	− 0.856667i
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	−20.5800	−1.13289
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	0	0
$333$	15.9275i	0.872823i
$334$	−48.0896	−2.63134
$335$	− 30.6476i	− 1.67446i
$336$	0	0
$337$	− 36.6783i	− 1.99800i	−0.0447653	−	0.998998i	$-0.514254\pi$
$337$	− 36.6783i	− 1.99800i	0.0447653	−	0.998998i	$-0.485746\pi$
$338$	9.68383i	0.526731i
$339$	−2.16629	−0.117657
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	−36.7435	−1.97534
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	−13.4164	−0.718164	−0.359082	−	0.933306i	$-0.616910\pi$
$349$	−13.4164	−0.718164	−0.359082	+	0.933306i	$0.616910\pi$
$350$	0	0
$351$	16.4327	0.877112
$352$	87.8161i	4.68061i
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−25.5131	−1.34653	−0.673265	−	0.739401i	$-0.735109\pi$
$359$	−25.5131	−1.34653	−0.673265	+	0.739401i	$0.735109\pi$
$360$	− 41.7789i	− 2.20194i
$361$	0	0
$362$	0	0
$363$	− 2.71190i	− 0.142338i
$364$	0	0
$365$	0	0
$366$	−3.51548	−0.183757
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	−57.2780	−2.97774
$371$	0	0
$372$	0	0
$373$	22.6186i	1.17115i	0.810619	+	0.585575i	$0.199131\pi$
$373$	22.6186i	1.17115i	−0.810619	+	0.585575i	$0.800869\pi$
$374$	0	0
$375$	12.5475i	0.647951i
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	24.3191	1.24591
$382$	− 25.0362i	− 1.28096i
$383$	29.9215i	1.52892i	0.644671	+	0.764460i	$0.276994\pi$
$383$	29.9215i	1.52892i	−0.644671	+	0.764460i	$0.723006\pi$
$384$	80.8187	4.12426
$385$	0	0
$386$	6.76699	0.344431
$387$	0	0
$388$	− 92.6907i	− 4.70566i
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	21.6967i	1.09866i
$391$	0	0
$392$	− 75.1451i	− 3.79540i
$393$	13.4674i	0.679341i
$394$	0	0
$395$	0	0
$396$	−29.7546	−1.49522
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	75.1085i	3.76485i
$399$	0	0
$400$	91.8923	4.59461
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	43.0564i	2.14746i
$403$	0	0
$404$	−117.175	−5.82968
$405$	−1.67548	−0.0832555
$406$	0	0
$407$	26.8111i	1.32898i
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	116.023i	5.71604i
$413$	0	0
$414$	0	0
$415$	0	0
$416$	92.5813	4.53917
$417$	− 24.5687i	− 1.20313i
$418$	0	0
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	0	0
$421$	0	0		−	1.00000i	$-0.5\pi$
$421$	0	0			1.00000i	$0.5\pi$
$422$	0	0
$423$	0	0
$424$	146.430	7.11125
$425$	0	0
$426$	0	0
$427$	0	0
$428$	− 21.4033i	− 1.03457i
$429$	10.1560	0.490334
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	97.7764i	4.70427i
$433$	− 18.1458i	− 0.872030i	−0.899939	−	0.436015i	$-0.856389\pi$
$433$	− 18.1458i	− 0.872030i	0.899939	−	0.436015i	$-0.143611\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	− 70.3270i	− 3.35271i
$441$	12.1833	0.580159
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	59.9284	2.84408
$445$	0	0
$446$	−41.8067	−1.97961
$447$	− 9.38441i	− 0.443867i
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	24.3591i	1.14830i
$451$	0	0
$452$	− 11.2633i	− 0.529779i
$453$	0	0
$454$	52.4138	2.45990
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	− 82.7477i	− 3.86655i
$459$	0	0
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	31.3691i	1.45004i
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	23.7408i	1.08702i
$478$	− 67.1791i	− 3.07270i
$479$	43.0918	1.96891	0.984456	−	0.175630i	$-0.0561962\pi$
$479$	43.0918	1.96891	0.984456	+	0.175630i	$0.0561962\pi$
$480$	−75.2190	−3.43326
$481$	28.2659	1.28882
$482$	0	0
$483$	0	0
$484$	14.1000	0.640911
$485$	35.5198i	1.61287i
$486$	−42.3216	−1.91975
$487$	32.2386i	1.46087i	0.682983	+	0.730434i	$0.260682\pi$
$487$	32.2386i	1.46087i	−0.682983	+	0.730434i	$0.739318\pi$
$488$	− 12.0133i	− 0.543816i
$489$	0	0
$490$	43.8133i	1.97928i
$491$	−35.7771	−1.61460	−0.807299	−	0.590143i	$-0.799071\pi$
$491$	−35.7771	−1.61460	−0.807299	+	0.590143i	$0.799071\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	11.4022	0.512490
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−4.31303	−0.193078	−0.0965389	−	0.995329i	$-0.530777\pi$
$499$	−4.31303	−0.193078	−0.0965389	+	0.995329i	$0.530777\pi$
$500$	−65.2387	−2.91756
$501$	−19.2811	−0.861414
$502$	50.0724i	2.23484i
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	44.9025	1.99813
$506$	0	0
$507$	3.88264i	0.172434i
$508$	126.443i	5.61001i
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	0	0
$512$	156.283i	6.90681i
$513$	0	0
$514$	57.0297	2.51547
$515$	− 44.4609i	− 1.95918i
$516$	0	0
$517$	0	0
$518$	0	0
$519$	−14.7320	−0.646661
$520$	−74.1432	−3.25140
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	39.9718i	1.74784i	0.486066	+	0.873922i	$0.338432\pi$
$523$	39.9718i	1.74784i	−0.486066	+	0.873922i	$0.661568\pi$
$524$	−70.0215	−3.05890
$525$	0	0
$526$	0	0
$527$	0	0
$528$	60.4291i	2.62984i
$529$	23.0000	1.00000
$530$	−85.3757	−3.70848
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	8.20192i	0.354600i
$536$	−147.134	−6.35524
$537$	0	0
$538$	0	0
$539$	20.5084	0.883361
$540$	− 69.4161i	− 2.98719i
$541$	−27.3238	−1.17474	−0.587371	−	0.809318i	$-0.699837\pi$
$541$	−27.3238	−1.17474	−0.587371	+	0.809318i	$0.699837\pi$
$542$	− 67.5426i	− 2.90120i
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	− 46.7055i	− 1.99698i	−0.0549052	−	0.998492i	$-0.517486\pi$
$547$	− 46.7055i	− 1.99698i	0.0549052	−	0.998492i	$-0.482514\pi$
$548$	0	0
$549$	1.94773	0.0831269
$550$	41.0041i	1.74842i
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−22.9651	−0.974813
$556$	127.741	5.41742
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	− 37.7272i	− 1.59001i	−0.606601	−	0.795007i	$-0.707467\pi$
$563$	− 37.7272i	− 1.59001i	0.606601	−	0.795007i	$-0.292533\pi$
$564$	0	0
$565$	4.31617i	0.181583i
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	−39.4704	−1.65178	−0.825891	−	0.563829i	$-0.809328\pi$
$571$	−39.4704	−1.65178	−0.825891	+	0.563829i	$0.809328\pi$
$572$	52.8042i	2.20785i
$573$	− 10.0380i	− 0.419344i
$574$	0	0
$575$	0	0
$576$	−82.0518	−3.41882
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	47.5852i	1.97928i
$579$	2.71316	0.112755
$580$	0	0
$581$	0	0
$582$	− 49.9013i	− 2.06847i
$583$	39.9632i	1.65511i
$584$	0	0
$585$	− 12.0209i	− 0.497003i
$586$	−0.484149	−0.0200000
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	− 45.8407i	− 1.89044i
$589$	0	0
$590$	0	0
$591$	0	0
$592$	168.186i	6.91239i
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	−43.6297	−1.79015
$595$	0	0
$596$	48.7926	1.99862
$597$	30.1140i	1.23249i
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	60.2387	2.45924
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	0	0
$603$	− 23.8550i	− 0.971452i
$604$	0	0
$605$	−5.40325	−0.219673
$606$	−63.0828	−2.56256
$607$	− 47.2956i	− 1.91967i	−0.280568	−	0.959834i	$-0.590523\pi$
$607$	− 47.2956i	− 1.91967i	0.280568	−	0.959834i	$-0.409477\pi$
$608$	0	0
$609$	0	0
$610$	7.00434i	0.283597i
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	−3.78162	−0.152614
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	62.4625i	2.51261i
$619$	34.9941	1.40653	0.703265	−	0.710928i	$-0.251725\pi$
$619$	34.9941	1.40653	0.703265	+	0.710928i	$0.251725\pi$
$620$	0	0
$621$	0	0
$622$	− 87.8161i	− 3.52111i
$623$	0	0
$624$	63.7082	2.55037
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	11.0275	0.438997	0.219499	−	0.975613i	$-0.429558\pi$
$631$	11.0275	0.438997	0.219499	+	0.975613i	$0.429558\pi$
$632$	0	0
$633$	0	0
$634$	88.6185	3.51949
$635$	− 48.4541i	− 1.92284i
$636$	89.3263	3.54202
$637$	− 21.6213i	− 0.856667i
$638$	0	0
$639$	0	0
$640$	− 161.025i	− 6.36508i
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	− 11.5228i	− 0.454767i
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	8.04374i	0.315988i
$649$	0	0
$650$	43.2291	1.69559
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	26.8328	1.04844
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	− 42.9015i	− 1.66994i
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−44.5832	−1.72756
$667$	0	0
$668$	− 100.249i	− 3.87873i
$669$	−16.7620	−0.648057
$670$	85.7866	3.31423
$671$	3.27864	0.126571
$672$	0	0
$673$	− 11.9683i	− 0.461343i	−0.973032	−	0.230671i	$-0.925908\pi$
$673$	− 11.9683i	− 0.461343i	0.973032	−	0.230671i	$-0.0740922\pi$
$674$	102.667	3.95460
$675$	26.6008i	1.02387i
$676$	−20.1871	−0.776428
$677$	− 27.1078i	− 1.04184i	−0.853607	−	0.520918i	$-0.825590\pi$
$677$	− 27.1078i	− 1.04184i	0.853607	−	0.520918i	$-0.174410\pi$
$678$	− 6.06373i	− 0.232876i
$679$	0	0
$680$	0	0
$681$	21.0148	0.805289
$682$	0	0
$683$	− 51.1946i	− 1.95891i	−0.201667	−	0.979454i	$-0.564636\pi$
$683$	− 51.1946i	− 1.95891i	0.201667	−	0.979454i	$-0.435364\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	− 33.1769i	− 1.26578i
$688$	0	0
$689$	42.1318	1.60509
$690$	0	0
$691$	52.5727	1.99996	0.999980	−	0.00630823i	$-0.00200798\pi$
$691$	52.5727	1.99996	0.999980	+	0.00630823i	$0.00200798\pi$
$692$	− 76.5964i	− 2.91176i
$693$	0	0
$694$	0	0
$695$	−48.9513	−1.85683
$696$	0	0
$697$	0	0
$698$	− 37.5543i	− 1.42145i
$699$	0	0
$700$	0	0
$701$	48.5239	1.83272	0.916360	−	0.400354i	$-0.131113\pi$
$701$	48.5239	1.83272	0.916360	+	0.400354i	$0.131113\pi$
$702$	45.9972i	1.73605i
$703$	0	0
$704$	−138.119	−5.20556
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	40.2492	1.51159	0.755796	−	0.654808i	$-0.227250\pi$
$709$	40.2492	1.51159	0.755796	+	0.654808i	$0.227250\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	− 20.2350i	− 0.756746i
$716$	0	0
$717$	− 26.9348i	− 1.00590i
$718$	− 71.4145i	− 2.66516i
$719$	13.7940	0.514429	0.257214	−	0.966354i	$-0.417195\pi$
$719$	13.7940	0.514429	0.257214	+	0.966354i	$0.417195\pi$
$720$	71.5258	2.66561
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	7.59095	0.281727
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	−19.2163	−0.711716
$730$	0	0
$731$	0	0
$732$	− 7.32845i	− 0.270867i
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	17.5665i	0.647951i
$736$	0	0
$737$	− 40.1556i	− 1.47915i
$738$	0	0
$739$	−53.6656	−1.97412	−0.987061	−	0.160345i	$-0.948739\pi$
$739$	−53.6656	−1.97412	−0.987061	+	0.160345i	$0.948739\pi$
$740$	− 119.403i	− 4.38934i
$741$	0	0
$742$	0	0
$743$	− 37.3813i	− 1.37139i	−0.727890	−	0.685693i	$-0.759499\pi$
$743$	− 37.3813i	− 1.37139i	0.727890	−	0.685693i	$-0.240501\pi$
$744$	0	0
$745$	−18.6977	−0.685032
$746$	−63.3125	−2.31804
$747$	0	0
$748$	0	0
$749$	0	0
$750$	−35.1221	−1.28248
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	20.0760i	0.731611i
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	54.3834	1.97140	0.985699	−	0.168518i	$-0.0538981\pi$
$761$	54.3834	1.97140	0.985699	+	0.168518i	$0.0538981\pi$
$762$	68.0724i	2.46600i
$763$	0	0
$764$	52.1910	1.88820
$765$	0	0
$766$	−83.7543	−3.02617
$767$	0	0
$768$	120.406i	4.34477i
$769$	−47.1406	−1.69993	−0.849967	−	0.526836i	$-0.823378\pi$
$769$	−47.1406	−1.69993	−0.849967	+	0.526836i	$0.823378\pi$
$770$	0	0
$771$	22.8655	0.823481
$772$	14.1066i	0.507708i
$773$	54.0523i	1.94413i	0.234717	+	0.972064i	$0.424584\pi$
$773$	54.0523i	1.94413i	−0.234717	+	0.972064i	$0.575416\pi$
$774$	0	0
$775$	0	0
$776$	170.525	6.12150
$777$	0	0
$778$	− 16.7948i	− 0.602122i
$779$	0	0
$780$	−45.2295	−1.61948
$781$	0	0
$782$	0	0
$783$	0	0
$784$	128.649	4.59461
$785$	0	0
$786$	−37.6970	−1.34461
$787$	53.4392i	1.90490i	0.304692	+	0.952451i	$0.401447\pi$
$787$	53.4392i	1.90490i	−0.304692	+	0.952451i	$0.598553\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	− 54.7402i	− 1.94511i
$793$	− 3.45655i	− 0.122746i
$794$	0	0
$795$	−34.2306	−1.21403
$796$	−156.573	−5.54958
$797$	− 54.7345i	− 1.93879i	−0.245499	−	0.969397i	$-0.578952\pi$
$797$	− 54.7345i	− 1.93879i	0.245499	−	0.969397i	$-0.421048\pi$
$798$	0	0
$799$	0	0
$800$	149.868i	5.29864i
$801$	0	0
$802$	0	0
$803$	0	0
$804$	−89.7562	−3.16546
$805$	0	0
$806$	0	0
$807$	0	0
$808$	− 215.570i	− 7.58372i
$809$	22.3607	0.786160	0.393080	−	0.919504i	$-0.371410\pi$
$809$	22.3607	0.786160	0.393080	+	0.919504i	$0.371410\pi$
$810$	− 4.68990i	− 0.164786i
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	0	0
$813$	− 27.0805i	− 0.949756i
$814$	−75.0477	−2.63042
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	−213.450	−7.43589
$825$	16.4402i	0.572375i
$826$	0	0
$827$	− 30.9935i	− 1.07775i	−0.842386	−	0.538875i	$-0.818849\pi$
$827$	− 30.9935i	− 1.07775i	0.842386	−	0.538875i	$-0.181151\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	145.614i	5.04825i
$833$	0	0
$834$	68.7710	2.38134
$835$	38.4161i	1.32944i
$836$	0	0
$837$	0	0
$838$	− 100.769i	− 3.48100i
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	7.73587	0.266122
$846$	0	0
$847$	0	0
$848$	250.689i	8.60870i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	39.3761	1.34585
$857$	− 48.0008i	− 1.63967i	−0.572597	−	0.819837i	$-0.694064\pi$
$857$	− 48.0008i	− 1.63967i	0.572597	−	0.819837i	$-0.305936\pi$
$858$	28.4278i	0.970511i
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	3.71278i	0.126385i	0.998001	+	0.0631923i	$0.0201281\pi$
$863$	3.71278i	0.126385i	−0.998001	+	0.0631923i	$0.979872\pi$
$864$	−159.465	−5.42510
$865$	29.3524i	0.998010i
$866$	50.7924	1.72600
$867$	19.0788i	0.647951i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−42.3346	−1.43445
$872$	0	0
$873$	27.6474i	0.935723i
$874$	0	0
$875$	0	0
$876$	0	0
$877$	− 59.2236i	− 1.99984i	−0.0127028	−	0.999919i	$-0.504044\pi$
$877$	− 59.2236i	− 1.99984i	0.0127028	−	0.999919i	$-0.495956\pi$
$878$	0	0
$879$	−0.194115	−0.00654733
$880$	120.401	4.05870
$881$	−9.21678	−0.310521	−0.155261	−	0.987874i	$-0.549622\pi$
$881$	−9.21678	−0.310521	−0.155261	+	0.987874i	$0.549622\pi$
$882$	34.1028i	1.14830i
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	− 52.3146i	− 1.75655i	−0.478154	−	0.878276i	$-0.658694\pi$
$887$	− 52.3146i	− 1.75655i	0.478154	−	0.878276i	$-0.341306\pi$
$888$	110.252i	3.69981i
$889$	0	0
$890$	0	0
$891$	−2.19528	−0.0735446
$892$	− 87.1513i	− 2.91804i
$893$	0	0
$894$	26.2682	0.878539
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	−50.7796	−1.69265
$901$	0	0
$902$	0	0
$903$	0	0
$904$	20.7213	0.689180
$905$	0	0
$906$	0	0
$907$	− 28.7630i	− 0.955061i	−0.878615	−	0.477531i	$-0.841532\pi$
$907$	− 28.7630i	− 0.955061i	0.878615	−	0.477531i	$-0.158468\pi$
$908$	109.263i	3.62602i
$909$	34.9505	1.15924
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	2.80832i	0.0928403i
$916$	172.498	5.69949
$917$	0	0
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	−1.51620	−0.0499606
$922$	50.3843i	1.65932i
$923$	0	0
$924$	0	0
$925$	45.7562i	1.50445i
$926$	0	0
$927$	− 34.6069i	− 1.13664i
$928$	0	0
$929$	31.3050	1.02708	0.513541	−	0.858065i	$-0.328333\pi$
$929$	31.3050	1.02708	0.513541	+	0.858065i	$0.328333\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	− 35.2090i	− 1.15269i
$934$	0	0
$935$	0	0
$936$	−57.7105	−1.88633
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	35.5307	1.15216
$952$	0	0
$953$	61.4682i	1.99115i	0.0939754	+	0.995575i	$0.470043\pi$
$953$	61.4682i	1.99115i	−0.0939754	+	0.995575i	$0.529957\pi$
$954$	−66.4535	−2.15151
$955$	−20.0000	−0.647185
$956$	140.043	4.52932
$957$	0	0
$958$	120.619i	3.89704i
$959$	0	0
$960$	− 118.306i	− 3.81831i
$961$	−31.0000	−1.00000
$962$	79.1200i	2.55093i
$963$	6.38409i	0.205724i
$964$	0	0
$965$	− 5.40577i	− 0.174018i
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	25.9402i	0.833749i
$969$	0	0
$970$	−99.4246	−3.19233
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	− 88.2246i	− 2.82980i
$973$	0	0
$974$	−90.2399	−2.89147
$975$	17.3323	0.555078
$976$	20.5669	0.658330
$977$	16.6023i	0.531154i	0.964090	+	0.265577i	$0.0855625\pi$
$977$	16.6023i	0.531154i	−0.964090	+	0.265577i	$0.914438\pi$
$978$	0	0
$979$	0	0
$980$	−91.3342	−2.91756
$981$	0	0
$982$	− 100.145i	− 3.19575i
$983$	− 0.192493i	− 0.00613957i	−0.999995	−	0.00306979i	$-0.999023\pi$
$983$	− 0.192493i	− 0.00613957i	0.999995	−	0.00306979i	$-0.000977145\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	31.9162i	1.01436i
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	60.0000	1.90213
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	− 12.0727i	− 0.382156i
$999$	−48.6861	−1.54036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.h.1084.8	yes	8
5.2	odd	4		9025.2.a.cb.1.1		8
5.3	odd	4		9025.2.a.cb.1.8		8
5.4	even	2	inner	1805.2.b.h.1084.1	✓	8
19.18	odd	2	inner	1805.2.b.h.1084.1	✓	8
95.18	even	4		9025.2.a.cb.1.1		8
95.37	even	4		9025.2.a.cb.1.8		8
95.94	odd	2	CM	1805.2.b.h.1084.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.h.1084.1	✓	8	5.4	even	2	inner
1805.2.b.h.1084.1	✓	8	19.18	odd	2	inner
1805.2.b.h.1084.8	yes	8	1.1	even	1	trivial
1805.2.b.h.1084.8	yes	8	95.94	odd	2	CM
9025.2.a.cb.1.1		8	5.2	odd	4
9025.2.a.cb.1.1		8	95.18	even	4
9025.2.a.cb.1.8		8	5.3	odd	4
9025.2.a.cb.1.8		8	95.37	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.79913i q^{2} +1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} -10.7350i q^{8} +1.74048 q^{9} +O(q^{10})\)	\(q+2.79913i q^{2} +1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} -10.7350i q^{8} +1.74048 q^{9} +6.25904i q^{10} +2.92978 q^{11} -6.54867i q^{12} -3.08876i q^{13} +2.50950i q^{15} +18.3785 q^{16} +4.87183i q^{18} -13.0477 q^{20} +8.20083i q^{22} +12.0477 q^{24} +5.00000 q^{25} +8.64583 q^{26} +5.32016i q^{27} -7.02443 q^{30} +29.9737i q^{32} +3.28804i q^{33} -10.1559 q^{36} +9.15124i q^{37} +3.46646 q^{39} -24.0042i q^{40} -17.0956 q^{44} +3.89183 q^{45} +20.6259i q^{48} +7.00000 q^{49} +13.9956i q^{50} +18.0233i q^{52} +13.6404i q^{53} -14.8918 q^{54} +6.55118 q^{55} -14.6433i q^{60} +1.11908 q^{61} -47.1432 q^{64} -6.90667i q^{65} -9.20366 q^{66} -13.7060i q^{67} -18.6841i q^{72} -25.6155 q^{74} +5.61142i q^{75} +9.70308i q^{78} +41.0955 q^{80} -0.749299 q^{81} -31.4512i q^{88} +10.8937i q^{90} -33.6390 q^{96} +15.8849i q^{97} +19.5939i q^{98} +5.09921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} - 24 q^{9}+O(q^{10}) \) 8 * q - 16 * q^4 - 24 * q^9	\( 8 q - 16 q^{4} - 24 q^{9} + 32 q^{16} - 8 q^{24} + 40 q^{25} + 24 q^{26} - 40 q^{30} - 8 q^{36} - 72 q^{44} + 56 q^{49} - 88 q^{54} - 64 q^{64} + 104 q^{66} + 120 q^{80} + 72 q^{81} - 120 q^{96} - 32 q^{99}+O(q^{100}) \) 8 * q - 16 * q^4 - 24 * q^9 + 32 * q^16 - 8 * q^24 + 40 * q^25 + 24 * q^26 - 40 * q^30 - 8 * q^36 - 72 * q^44 + 56 * q^49 - 88 * q^54 - 64 * q^64 + 104 * q^66 + 120 * q^80 + 72 * q^81 - 120 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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