LMFDB - Embedded newform 7605.2.a.cp.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, 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("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.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:	$60.7262307372$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 $ x^9 - 17x^7 - 9x^6 + 59x^5 + 32x^4 - 44x^3 - 23x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 845)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.88295$ of defining polynomial
Character	$\chi$	$=$	7605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63597 q^{2} +4.94835 q^{4} -1.00000 q^{5} -3.28231 q^{7} -7.77176 q^{8} +O(q^{10})$	$q-2.63597 q^{2} +4.94835 q^{4} -1.00000 q^{5} -3.28231 q^{7} -7.77176 q^{8} +2.63597 q^{10} +3.22850 q^{11} +8.65206 q^{14} +10.5894 q^{16} +4.25510 q^{17} -2.87293 q^{19} -4.94835 q^{20} -8.51023 q^{22} -6.09907 q^{23} +1.00000 q^{25} -16.2420 q^{28} -5.77280 q^{29} -0.835435 q^{31} -12.3700 q^{32} -11.2163 q^{34} +3.28231 q^{35} -5.59588 q^{37} +7.57297 q^{38} +7.77176 q^{40} -2.18667 q^{41} +2.48711 q^{43} +15.9757 q^{44} +16.0770 q^{46} -10.5761 q^{47} +3.77353 q^{49} -2.63597 q^{50} +5.08351 q^{53} -3.22850 q^{55} +25.5093 q^{56} +15.2169 q^{58} +0.144765 q^{59} +6.06541 q^{61} +2.20218 q^{62} +11.4280 q^{64} +12.6133 q^{67} +21.0557 q^{68} -8.65206 q^{70} +9.02740 q^{71} -5.70395 q^{73} +14.7506 q^{74} -14.2163 q^{76} -10.5969 q^{77} +14.1043 q^{79} -10.5894 q^{80} +5.76401 q^{82} -7.41467 q^{83} -4.25510 q^{85} -6.55595 q^{86} -25.0911 q^{88} +13.0912 q^{89} -30.1803 q^{92} +27.8783 q^{94} +2.87293 q^{95} +2.97494 q^{97} -9.94691 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8}+O(q^{10}) $ 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8	$ 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8} + 3 q^{10} + 9 q^{11} + 2 q^{14} + 37 q^{16} + q^{17} - 4 q^{19} - 17 q^{20} + 12 q^{22} - 14 q^{23} + 9 q^{25} + 18 q^{28} - 12 q^{29} - 7 q^{31} - 22 q^{32} - 30 q^{34} - 7 q^{35} - 5 q^{37} + 47 q^{38} + 12 q^{40} + 10 q^{41} + 39 q^{43} + 25 q^{44} + 6 q^{46} - 36 q^{47} + 16 q^{49} - 3 q^{50} + 8 q^{53} - 9 q^{55} + 29 q^{56} + 21 q^{58} + 21 q^{59} - 3 q^{61} + 10 q^{62} + 34 q^{64} + q^{67} + 20 q^{68} - 2 q^{70} + q^{71} + 15 q^{74} - 5 q^{76} + 4 q^{77} + 39 q^{79} - 37 q^{80} - 4 q^{82} - 7 q^{83} - q^{85} + 24 q^{86} + 42 q^{88} + 19 q^{89} + 27 q^{92} + 16 q^{94} + 4 q^{95} - 34 q^{97} - 48 q^{98}+O(q^{100}) $ 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8 + 3 * q^10 + 9 * q^11 + 2 * q^14 + 37 * q^16 + q^17 - 4 * q^19 - 17 * q^20 + 12 * q^22 - 14 * q^23 + 9 * q^25 + 18 * q^28 - 12 * q^29 - 7 * q^31 - 22 * q^32 - 30 * q^34 - 7 * q^35 - 5 * q^37 + 47 * q^38 + 12 * q^40 + 10 * q^41 + 39 * q^43 + 25 * q^44 + 6 * q^46 - 36 * q^47 + 16 * q^49 - 3 * q^50 + 8 * q^53 - 9 * q^55 + 29 * q^56 + 21 * q^58 + 21 * q^59 - 3 * q^61 + 10 * q^62 + 34 * q^64 + q^67 + 20 * q^68 - 2 * q^70 + q^71 + 15 * q^74 - 5 * q^76 + 4 * q^77 + 39 * q^79 - 37 * q^80 - 4 * q^82 - 7 * q^83 - q^85 + 24 * q^86 + 42 * q^88 + 19 * q^89 + 27 * q^92 + 16 * q^94 + 4 * q^95 - 34 * q^97 - 48 * 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 $

$2$	−2.63597	−1.86391	−0.931957	−	0.362569i	$-0.881900\pi$
$2$	−2.63597	−1.86391	−0.931957	+	0.362569i	$0.881900\pi$
$3$	0	0
$3$	0	0
$4$	4.94835	2.47417
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−3.28231	−1.24059	−0.620297	−	0.784367i	$-0.712988\pi$
$7$	−3.28231	−1.24059	−0.620297	+	0.784367i	$0.712988\pi$
$8$	−7.77176	−2.74773
$9$	0	0
$10$	2.63597	0.833567
$11$	3.22850	0.973429	0.486715	−	0.873561i	$-0.338195\pi$
$11$	3.22850	0.973429	0.486715	+	0.873561i	$0.338195\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	8.65206	2.31236
$15$	0	0
$16$	10.5894	2.64736
$17$	4.25510	1.03201	0.516007	−	0.856584i	$-0.327418\pi$
$17$	4.25510	1.03201	0.516007	+	0.856584i	$0.327418\pi$
$18$	0	0
$19$	−2.87293	−0.659096	−0.329548	−	0.944139i	$-0.606896\pi$
$19$	−2.87293	−0.659096	−0.329548	+	0.944139i	$0.606896\pi$
$20$	−4.94835	−1.10648
$21$	0	0
$22$	−8.51023	−1.81439
$23$	−6.09907	−1.27174	−0.635872	−	0.771795i	$-0.719359\pi$
$23$	−6.09907	−1.27174	−0.635872	+	0.771795i	$0.719359\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−16.2420	−3.06945
$29$	−5.77280	−1.07198	−0.535991	−	0.844224i	$-0.680062\pi$
$29$	−5.77280	−1.07198	−0.535991	+	0.844224i	$0.680062\pi$
$30$	0	0
$31$	−0.835435	−0.150048	−0.0750242	−	0.997182i	$-0.523903\pi$
$31$	−0.835435	−0.150048	−0.0750242	+	0.997182i	$0.523903\pi$
$32$	−12.3700	−2.18672
$33$	0	0
$34$	−11.2163	−1.92358
$35$	3.28231	0.554811
$36$	0	0
$37$	−5.59588	−0.919957	−0.459978	−	0.887930i	$-0.652143\pi$
$37$	−5.59588	−0.919957	−0.459978	+	0.887930i	$0.652143\pi$
$38$	7.57297	1.22850
$39$	0	0
$40$	7.77176	1.22882
$41$	−2.18667	−0.341501	−0.170750	−	0.985314i	$-0.554619\pi$
$41$	−2.18667	−0.341501	−0.170750	+	0.985314i	$0.554619\pi$
$42$	0	0
$43$	2.48711	0.379280	0.189640	−	0.981854i	$-0.439268\pi$
$43$	2.48711	0.379280	0.189640	+	0.981854i	$0.439268\pi$
$44$	15.9757	2.40843
$45$	0	0
$46$	16.0770	2.37042
$47$	−10.5761	−1.54268	−0.771341	−	0.636422i	$-0.780414\pi$
$47$	−10.5761	−1.54268	−0.771341	+	0.636422i	$0.780414\pi$
$48$	0	0
$49$	3.77353	0.539075
$50$	−2.63597	−0.372783
$51$	0	0
$52$	0	0
$53$	5.08351	0.698273	0.349137	−	0.937072i	$-0.386475\pi$
$53$	5.08351	0.698273	0.349137	+	0.937072i	$0.386475\pi$
$54$	0	0
$55$	−3.22850	−0.435331
$56$	25.5093	3.40882
$57$	0	0
$58$	15.2169	1.99808
$59$	0.144765	0.0188468	0.00942338	−	0.999956i	$-0.497000\pi$
$59$	0.144765	0.0188468	0.00942338	+	0.999956i	$0.497000\pi$
$60$	0	0
$61$	6.06541	0.776596	0.388298	−	0.921534i	$-0.373063\pi$
$61$	6.06541	0.776596	0.388298	+	0.921534i	$0.373063\pi$
$62$	2.20218	0.279677
$63$	0	0
$64$	11.4280	1.42850
$65$	0	0
$66$	0	0
$67$	12.6133	1.54096	0.770482	−	0.637461i	$-0.220015\pi$
$67$	12.6133	1.54096	0.770482	+	0.637461i	$0.220015\pi$
$68$	21.0557	2.55338
$69$	0	0
$70$	−8.65206	−1.03412
$71$	9.02740	1.07136	0.535678	−	0.844423i	$-0.320056\pi$
$71$	9.02740	1.07136	0.535678	+	0.844423i	$0.320056\pi$
$72$	0	0
$73$	−5.70395	−0.667597	−0.333798	−	0.942644i	$-0.608331\pi$
$73$	−5.70395	−0.667597	−0.333798	+	0.942644i	$0.608331\pi$
$74$	14.7506	1.71472
$75$	0	0
$76$	−14.2163	−1.63072
$77$	−10.5969	−1.20763
$78$	0	0
$79$	14.1043	1.58686	0.793430	−	0.608662i	$-0.208293\pi$
$79$	14.1043	1.58686	0.793430	+	0.608662i	$0.208293\pi$
$80$	−10.5894	−1.18394
$81$	0	0
$82$	5.76401	0.636528
$83$	−7.41467	−0.813865	−0.406933	−	0.913458i	$-0.633402\pi$
$83$	−7.41467	−0.813865	−0.406933	+	0.913458i	$0.633402\pi$
$84$	0	0
$85$	−4.25510	−0.461531
$86$	−6.55595	−0.706946
$87$	0	0
$88$	−25.0911	−2.67472
$89$	13.0912	1.38766	0.693830	−	0.720138i	$-0.255922\pi$
$89$	13.0912	1.38766	0.693830	+	0.720138i	$0.255922\pi$
$90$	0	0
$91$	0	0
$92$	−30.1803	−3.14652
$93$	0	0
$94$	27.8783	2.87543
$95$	2.87293	0.294757
$96$	0	0
$97$	2.97494	0.302059	0.151030	−	0.988529i	$-0.451741\pi$
$97$	2.97494	0.302059	0.151030	+	0.988529i	$0.451741\pi$
$98$	−9.94691	−1.00479
$99$	0	0
$100$	4.94835	0.494835
$101$	−2.24007	−0.222896	−0.111448	−	0.993770i	$-0.535549\pi$
$101$	−2.24007	−0.222896	−0.111448	+	0.993770i	$0.535549\pi$
$102$	0	0
$103$	−12.6517	−1.24661	−0.623305	−	0.781979i	$-0.714210\pi$
$103$	−12.6517	−1.24661	−0.623305	+	0.781979i	$0.714210\pi$
$104$	0	0
$105$	0	0
$106$	−13.4000	−1.30152
$107$	−5.51892	−0.533534	−0.266767	−	0.963761i	$-0.585955\pi$
$107$	−5.51892	−0.533534	−0.266767	+	0.963761i	$0.585955\pi$
$108$	0	0
$109$	−7.12142	−0.682108	−0.341054	−	0.940044i	$-0.610784\pi$
$109$	−7.12142	−0.682108	−0.341054	+	0.940044i	$0.610784\pi$
$110$	8.51023	0.811419
$111$	0	0
$112$	−34.7578	−3.28430
$113$	−18.7572	−1.76453	−0.882264	−	0.470756i	$-0.843981\pi$
$113$	−18.7572	−1.76453	−0.882264	+	0.470756i	$0.843981\pi$
$114$	0	0
$115$	6.09907	0.568741
$116$	−28.5658	−2.65227
$117$	0	0
$118$	−0.381596	−0.0351287
$119$	−13.9665	−1.28031
$120$	0	0
$121$	−0.576790	−0.0524355
$122$	−15.9883	−1.44751
$123$	0	0
$124$	−4.13402	−0.371246
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	0.368129	0.0326661	0.0163331	−	0.999867i	$-0.494801\pi$
$127$	0.368129	0.0326661	0.0163331	+	0.999867i	$0.494801\pi$
$128$	−5.38392	−0.475875
$129$	0	0
$130$	0	0
$131$	−3.09282	−0.270221	−0.135110	−	0.990831i	$-0.543139\pi$
$131$	−3.09282	−0.270221	−0.135110	+	0.990831i	$0.543139\pi$
$132$	0	0
$133$	9.42984	0.817671
$134$	−33.2484	−2.87222
$135$	0	0
$136$	−33.0696	−2.83570
$137$	15.5865	1.33164	0.665822	−	0.746111i	$-0.268081\pi$
$137$	15.5865	1.33164	0.665822	+	0.746111i	$0.268081\pi$
$138$	0	0
$139$	18.7547	1.59075	0.795376	−	0.606116i	$-0.207273\pi$
$139$	18.7547	1.59075	0.795376	+	0.606116i	$0.207273\pi$
$140$	16.2420	1.37270
$141$	0	0
$142$	−23.7960	−1.99691
$143$	0	0
$144$	0	0
$145$	5.77280	0.479405
$146$	15.0355	1.24434
$147$	0	0
$148$	−27.6904	−2.27613
$149$	−13.1350	−1.07606	−0.538032	−	0.842925i	$-0.680832\pi$
$149$	−13.1350	−1.07606	−0.538032	+	0.842925i	$0.680832\pi$
$150$	0	0
$151$	1.66546	0.135533	0.0677665	−	0.997701i	$-0.478413\pi$
$151$	1.66546	0.135533	0.0677665	+	0.997701i	$0.478413\pi$
$152$	22.3278	1.81102
$153$	0	0
$154$	27.9332	2.25092
$155$	0.835435	0.0671037
$156$	0	0
$157$	−20.6056	−1.64450	−0.822251	−	0.569125i	$-0.807282\pi$
$157$	−20.6056	−1.64450	−0.822251	+	0.569125i	$0.807282\pi$
$158$	−37.1786	−2.95777
$159$	0	0
$160$	12.3700	0.977932
$161$	20.0190	1.57772
$162$	0	0
$163$	5.62628	0.440684	0.220342	−	0.975423i	$-0.429283\pi$
$163$	5.62628	0.440684	0.220342	+	0.975423i	$0.429283\pi$
$164$	−10.8204	−0.844933
$165$	0	0
$166$	19.5449	1.51697
$167$	−14.1216	−1.09276	−0.546381	−	0.837537i	$-0.683995\pi$
$167$	−14.1216	−1.09276	−0.546381	+	0.837537i	$0.683995\pi$
$168$	0	0
$169$	0	0
$170$	11.2163	0.860253
$171$	0	0
$172$	12.3071	0.938406
$173$	9.86557	0.750066	0.375033	−	0.927012i	$-0.377631\pi$
$173$	9.86557	0.750066	0.375033	+	0.927012i	$0.377631\pi$
$174$	0	0
$175$	−3.28231	−0.248119
$176$	34.1880	2.57702
$177$	0	0
$178$	−34.5079	−2.58648
$179$	−9.25334	−0.691627	−0.345813	−	0.938303i	$-0.612397\pi$
$179$	−9.25334	−0.691627	−0.345813	+	0.938303i	$0.612397\pi$
$180$	0	0
$181$	−21.6558	−1.60967	−0.804833	−	0.593501i	$-0.797745\pi$
$181$	−21.6558	−1.60967	−0.804833	+	0.593501i	$0.797745\pi$
$182$	0	0
$183$	0	0
$184$	47.4005	3.49441
$185$	5.59588	0.411417
$186$	0	0
$187$	13.7376	1.00459
$188$	−52.3342	−3.81686
$189$	0	0
$190$	−7.57297	−0.549401
$191$	21.3578	1.54539	0.772697	−	0.634775i	$-0.218907\pi$
$191$	21.3578	1.54539	0.772697	+	0.634775i	$0.218907\pi$
$192$	0	0
$193$	−5.77649	−0.415801	−0.207901	−	0.978150i	$-0.566663\pi$
$193$	−5.77649	−0.415801	−0.207901	+	0.978150i	$0.566663\pi$
$194$	−7.84186	−0.563013
$195$	0	0
$196$	18.6727	1.33377
$197$	12.4045	0.883787	0.441894	−	0.897067i	$-0.354307\pi$
$197$	12.4045	0.883787	0.441894	+	0.897067i	$0.354307\pi$
$198$	0	0
$199$	−6.03432	−0.427762	−0.213881	−	0.976860i	$-0.568610\pi$
$199$	−6.03432	−0.427762	−0.213881	+	0.976860i	$0.568610\pi$
$200$	−7.77176	−0.549547
$201$	0	0
$202$	5.90477	0.415458
$203$	18.9481	1.32989
$204$	0	0
$205$	2.18667	0.152724
$206$	33.3495	2.32357
$207$	0	0
$208$	0	0
$209$	−9.27526	−0.641583
$210$	0	0
$211$	−13.6840	−0.942049	−0.471024	−	0.882120i	$-0.656116\pi$
$211$	−13.6840	−0.942049	−0.471024	+	0.882120i	$0.656116\pi$
$212$	25.1550	1.72765
$213$	0	0
$214$	14.5477	0.994461
$215$	−2.48711	−0.169619
$216$	0	0
$217$	2.74215	0.186149
$218$	18.7719	1.27139
$219$	0	0
$220$	−15.9757	−1.07708
$221$	0	0
$222$	0	0
$223$	−18.6882	−1.25145	−0.625727	−	0.780042i	$-0.715198\pi$
$223$	−18.6882	−1.25145	−0.625727	+	0.780042i	$0.715198\pi$
$224$	40.6020	2.71284
$225$	0	0
$226$	49.4434	3.28893
$227$	11.5082	0.763828	0.381914	−	0.924198i	$-0.375265\pi$
$227$	11.5082	0.763828	0.381914	+	0.924198i	$0.375265\pi$
$228$	0	0
$229$	1.98065	0.130885	0.0654424	−	0.997856i	$-0.479154\pi$
$229$	1.98065	0.130885	0.0654424	+	0.997856i	$0.479154\pi$
$230$	−16.0770	−1.06008
$231$	0	0
$232$	44.8648	2.94552
$233$	−22.1334	−1.45001	−0.725005	−	0.688744i	$-0.758163\pi$
$233$	−22.1334	−1.45001	−0.725005	+	0.688744i	$0.758163\pi$
$234$	0	0
$235$	10.5761	0.689909
$236$	0.716346	0.0466302
$237$	0	0
$238$	36.8154	2.38639
$239$	−11.2846	−0.729942	−0.364971	−	0.931019i	$-0.618921\pi$
$239$	−11.2846	−0.729942	−0.364971	+	0.931019i	$0.618921\pi$
$240$	0	0
$241$	24.9029	1.60414	0.802068	−	0.597233i	$-0.203733\pi$
$241$	24.9029	1.60414	0.802068	+	0.597233i	$0.203733\pi$
$242$	1.52040	0.0977352
$243$	0	0
$244$	30.0138	1.92143
$245$	−3.77353	−0.241082
$246$	0	0
$247$	0	0
$248$	6.49280	0.412293
$249$	0	0
$250$	2.63597	0.166713
$251$	14.1454	0.892848	0.446424	−	0.894821i	$-0.352697\pi$
$251$	14.1454	0.892848	0.446424	+	0.894821i	$0.352697\pi$
$252$	0	0
$253$	−19.6908	−1.23795
$254$	−0.970377	−0.0608868
$255$	0	0
$256$	−8.66412	−0.541508
$257$	−3.53245	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$257$	−3.53245	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$258$	0	0
$259$	18.3674	1.14129
$260$	0	0
$261$	0	0
$262$	8.15259	0.503669
$263$	12.2296	0.754109	0.377055	−	0.926191i	$-0.376937\pi$
$263$	12.2296	0.754109	0.377055	+	0.926191i	$0.376937\pi$
$264$	0	0
$265$	−5.08351	−0.312277
$266$	−24.8568	−1.52407
$267$	0	0
$268$	62.4152	3.81261
$269$	22.4563	1.36919	0.684593	−	0.728926i	$-0.259980\pi$
$269$	22.4563	1.36919	0.684593	+	0.728926i	$0.259980\pi$
$270$	0	0
$271$	19.3264	1.17399	0.586997	−	0.809589i	$-0.300310\pi$
$271$	19.3264	1.17399	0.586997	+	0.809589i	$0.300310\pi$
$272$	45.0592	2.73211
$273$	0	0
$274$	−41.0855	−2.48207
$275$	3.22850	0.194686
$276$	0	0
$277$	−11.8931	−0.714587	−0.357294	−	0.933992i	$-0.616300\pi$
$277$	−11.8931	−0.714587	−0.357294	+	0.933992i	$0.616300\pi$
$278$	−49.4368	−2.96502
$279$	0	0
$280$	−25.5093	−1.52447
$281$	22.7024	1.35431	0.677157	−	0.735838i	$-0.263212\pi$
$281$	22.7024	1.35431	0.677157	+	0.735838i	$0.263212\pi$
$282$	0	0
$283$	−8.86050	−0.526702	−0.263351	−	0.964700i	$-0.584828\pi$
$283$	−8.86050	−0.526702	−0.263351	+	0.964700i	$0.584828\pi$
$284$	44.6707	2.65072
$285$	0	0
$286$	0	0
$287$	7.17733	0.423664
$288$	0	0
$289$	1.10589	0.0650525
$290$	−15.2169	−0.893569
$291$	0	0
$292$	−28.2251	−1.65175
$293$	−6.40308	−0.374072	−0.187036	−	0.982353i	$-0.559888\pi$
$293$	−6.40308	−0.374072	−0.187036	+	0.982353i	$0.559888\pi$
$294$	0	0
$295$	−0.144765	−0.00842853
$296$	43.4898	2.52780
$297$	0	0
$298$	34.6236	2.00569
$299$	0	0
$300$	0	0
$301$	−8.16345	−0.470533
$302$	−4.39010	−0.252622
$303$	0	0
$304$	−30.4228	−1.74487
$305$	−6.06541	−0.347304
$306$	0	0
$307$	25.8317	1.47429	0.737146	−	0.675733i	$-0.236173\pi$
$307$	25.8317	1.47429	0.737146	+	0.675733i	$0.236173\pi$
$308$	−52.4372	−2.98789
$309$	0	0
$310$	−2.20218	−0.125076
$311$	3.87202	0.219562	0.109781	−	0.993956i	$-0.464985\pi$
$311$	3.87202	0.219562	0.109781	+	0.993956i	$0.464985\pi$
$312$	0	0
$313$	4.13361	0.233645	0.116823	−	0.993153i	$-0.462729\pi$
$313$	4.13361	0.233645	0.116823	+	0.993153i	$0.462729\pi$
$314$	54.3157	3.06521
$315$	0	0
$316$	69.7931	3.92617
$317$	−24.9158	−1.39941	−0.699706	−	0.714431i	$-0.746686\pi$
$317$	−24.9158	−1.39941	−0.699706	+	0.714431i	$0.746686\pi$
$318$	0	0
$319$	−18.6375	−1.04350
$320$	−11.4280	−0.638844
$321$	0	0
$322$	−52.7695	−2.94073
$323$	−12.2246	−0.680196
$324$	0	0
$325$	0	0
$326$	−14.8307	−0.821397
$327$	0	0
$328$	16.9943	0.938353
$329$	34.7140	1.91384
$330$	0	0
$331$	−5.56860	−0.306078	−0.153039	−	0.988220i	$-0.548906\pi$
$331$	−5.56860	−0.306078	−0.153039	+	0.988220i	$0.548906\pi$
$332$	−36.6903	−2.01364
$333$	0	0
$334$	37.2241	2.03681
$335$	−12.6133	−0.689140
$336$	0	0
$337$	16.8799	0.919507	0.459753	−	0.888047i	$-0.347938\pi$
$337$	16.8799	0.919507	0.459753	+	0.888047i	$0.347938\pi$
$338$	0	0
$339$	0	0
$340$	−21.0557	−1.14191
$341$	−2.69720	−0.146062
$342$	0	0
$343$	10.5903	0.571821
$344$	−19.3292	−1.04216
$345$	0	0
$346$	−26.0054	−1.39806
$347$	12.4254	0.667031	0.333516	−	0.942745i	$-0.391765\pi$
$347$	12.4254	0.667031	0.333516	+	0.942745i	$0.391765\pi$
$348$	0	0
$349$	−2.73516	−0.146410	−0.0732050	−	0.997317i	$-0.523323\pi$
$349$	−2.73516	−0.146410	−0.0732050	+	0.997317i	$0.523323\pi$
$350$	8.65206	0.462472
$351$	0	0
$352$	−39.9364	−2.12862
$353$	−22.7460	−1.21065	−0.605323	−	0.795980i	$-0.706956\pi$
$353$	−22.7460	−1.21065	−0.605323	+	0.795980i	$0.706956\pi$
$354$	0	0
$355$	−9.02740	−0.479125
$356$	64.7796	3.43331
$357$	0	0
$358$	24.3915	1.28913
$359$	−11.5189	−0.607945	−0.303973	−	0.952681i	$-0.598313\pi$
$359$	−11.5189	−0.607945	−0.303973	+	0.952681i	$0.598313\pi$
$360$	0	0
$361$	−10.7463	−0.565592
$362$	57.0842	3.00028
$363$	0	0
$364$	0	0
$365$	5.70395	0.298558
$366$	0	0
$367$	14.0733	0.734622	0.367311	−	0.930098i	$-0.380279\pi$
$367$	14.0733	0.734622	0.367311	+	0.930098i	$0.380279\pi$
$368$	−64.5858	−3.36677
$369$	0	0
$370$	−14.7506	−0.766846
$371$	−16.6856	−0.866274
$372$	0	0
$373$	18.4780	0.956753	0.478377	−	0.878155i	$-0.341225\pi$
$373$	18.4780	0.956753	0.478377	+	0.878155i	$0.341225\pi$
$374$	−36.2119	−1.87247
$375$	0	0
$376$	82.1949	4.23888
$377$	0	0
$378$	0	0
$379$	−1.53391	−0.0787918	−0.0393959	−	0.999224i	$-0.512543\pi$
$379$	−1.53391	−0.0787918	−0.0393959	+	0.999224i	$0.512543\pi$
$380$	14.2163	0.729279
$381$	0	0
$382$	−56.2985	−2.88048
$383$	30.1620	1.54120	0.770602	−	0.637317i	$-0.219956\pi$
$383$	30.1620	1.54120	0.770602	+	0.637317i	$0.219956\pi$
$384$	0	0
$385$	10.5969	0.540069
$386$	15.2267	0.775017
$387$	0	0
$388$	14.7210	0.747348
$389$	−19.8405	−1.00595	−0.502976	−	0.864301i	$-0.667761\pi$
$389$	−19.8405	−1.00595	−0.502976	+	0.864301i	$0.667761\pi$
$390$	0	0
$391$	−25.9522	−1.31246
$392$	−29.3269	−1.48123
$393$	0	0
$394$	−32.6980	−1.64730
$395$	−14.1043	−0.709665
$396$	0	0
$397$	5.70766	0.286459	0.143230	−	0.989689i	$-0.454251\pi$
$397$	5.70766	0.286459	0.143230	+	0.989689i	$0.454251\pi$
$398$	15.9063	0.797311
$399$	0	0
$400$	10.5894	0.529472
$401$	−31.3372	−1.56491	−0.782454	−	0.622709i	$-0.786032\pi$
$401$	−31.3372	−1.56491	−0.782454	+	0.622709i	$0.786032\pi$
$402$	0	0
$403$	0	0
$404$	−11.0847	−0.551482
$405$	0	0
$406$	−49.9466	−2.47881
$407$	−18.0663	−0.895513
$408$	0	0
$409$	−19.2508	−0.951889	−0.475944	−	0.879475i	$-0.657894\pi$
$409$	−19.2508	−0.951889	−0.475944	+	0.879475i	$0.657894\pi$
$410$	−5.76401	−0.284664
$411$	0	0
$412$	−62.6050	−3.08433
$413$	−0.475162	−0.0233812
$414$	0	0
$415$	7.41467	0.363972
$416$	0	0
$417$	0	0
$418$	24.4493	1.19586
$419$	12.8466	0.627596	0.313798	−	0.949490i	$-0.398399\pi$
$419$	12.8466	0.627596	0.313798	+	0.949490i	$0.398399\pi$
$420$	0	0
$421$	−15.5491	−0.757819	−0.378910	−	0.925434i	$-0.623701\pi$
$421$	−15.5491	−0.757819	−0.378910	+	0.925434i	$0.623701\pi$
$422$	36.0708	1.75590
$423$	0	0
$424$	−39.5078	−1.91867
$425$	4.25510	0.206403
$426$	0	0
$427$	−19.9085	−0.963441
$428$	−27.3095	−1.32006
$429$	0	0
$430$	6.55595	0.316156
$431$	16.4219	0.791017	0.395509	−	0.918462i	$-0.370568\pi$
$431$	16.4219	0.791017	0.395509	+	0.918462i	$0.370568\pi$
$432$	0	0
$433$	−15.4378	−0.741895	−0.370948	−	0.928654i	$-0.620967\pi$
$433$	−15.4378	−0.741895	−0.370948	+	0.928654i	$0.620967\pi$
$434$	−7.22823	−0.346966
$435$	0	0
$436$	−35.2393	−1.68765
$437$	17.5222	0.838201
$438$	0	0
$439$	−39.6616	−1.89294	−0.946472	−	0.322785i	$-0.895381\pi$
$439$	−39.6616	−1.89294	−0.946472	+	0.322785i	$0.895381\pi$
$440$	25.0911	1.19617
$441$	0	0
$442$	0	0
$443$	−4.90611	−0.233097	−0.116548	−	0.993185i	$-0.537183\pi$
$443$	−4.90611	−0.233097	−0.116548	+	0.993185i	$0.537183\pi$
$444$	0	0
$445$	−13.0912	−0.620581
$446$	49.2615	2.33260
$447$	0	0
$448$	−37.5101	−1.77219
$449$	−28.2902	−1.33510	−0.667549	−	0.744566i	$-0.732657\pi$
$449$	−28.2902	−1.33510	−0.667549	+	0.744566i	$0.732657\pi$
$450$	0	0
$451$	−7.05967	−0.332427
$452$	−92.8171	−4.36575
$453$	0	0
$454$	−30.3354	−1.42371
$455$	0	0
$456$	0	0
$457$	32.3338	1.51251	0.756257	−	0.654275i	$-0.227026\pi$
$457$	32.3338	1.51251	0.756257	+	0.654275i	$0.227026\pi$
$458$	−5.22093	−0.243958
$459$	0	0
$460$	30.1803	1.40716
$461$	6.97401	0.324812	0.162406	−	0.986724i	$-0.448075\pi$
$461$	6.97401	0.324812	0.162406	+	0.986724i	$0.448075\pi$
$462$	0	0
$463$	33.1964	1.54277	0.771384	−	0.636370i	$-0.219565\pi$
$463$	33.1964	1.54277	0.771384	+	0.636370i	$0.219565\pi$
$464$	−61.1307	−2.83792
$465$	0	0
$466$	58.3431	2.70269
$467$	31.6108	1.46277	0.731386	−	0.681963i	$-0.238874\pi$
$467$	31.6108	1.46277	0.731386	+	0.681963i	$0.238874\pi$
$468$	0	0
$469$	−41.4008	−1.91171
$470$	−27.8783	−1.28593
$471$	0	0
$472$	−1.12508	−0.0517859
$473$	8.02963	0.369203
$474$	0	0
$475$	−2.87293	−0.131819
$476$	−69.1113	−3.16771
$477$	0	0
$478$	29.7460	1.36055
$479$	−10.3683	−0.473742	−0.236871	−	0.971541i	$-0.576122\pi$
$479$	−10.3683	−0.473742	−0.236871	+	0.971541i	$0.576122\pi$
$480$	0	0
$481$	0	0
$482$	−65.6433	−2.98997
$483$	0	0
$484$	−2.85416	−0.129734
$485$	−2.97494	−0.135085
$486$	0	0
$487$	34.9155	1.58217	0.791086	−	0.611705i	$-0.209516\pi$
$487$	34.9155	1.58217	0.791086	+	0.611705i	$0.209516\pi$
$488$	−47.1389	−2.13388
$489$	0	0
$490$	9.94691	0.449356
$491$	−17.5013	−0.789824	−0.394912	−	0.918719i	$-0.629225\pi$
$491$	−17.5013	−0.789824	−0.394912	+	0.918719i	$0.629225\pi$
$492$	0	0
$493$	−24.5638	−1.10630
$494$	0	0
$495$	0	0
$496$	−8.84679	−0.397233
$497$	−29.6307	−1.32912
$498$	0	0
$499$	−8.46542	−0.378964	−0.189482	−	0.981884i	$-0.560681\pi$
$499$	−8.46542	−0.378964	−0.189482	+	0.981884i	$0.560681\pi$
$500$	−4.94835	−0.221297
$501$	0	0
$502$	−37.2868	−1.66419
$503$	4.00003	0.178353	0.0891763	−	0.996016i	$-0.471577\pi$
$503$	4.00003	0.178353	0.0891763	+	0.996016i	$0.471577\pi$
$504$	0	0
$505$	2.24007	0.0996819
$506$	51.9045	2.30744
$507$	0	0
$508$	1.82163	0.0808217
$509$	18.2954	0.810927	0.405464	−	0.914111i	$-0.367110\pi$
$509$	18.2954	0.810927	0.405464	+	0.914111i	$0.367110\pi$
$510$	0	0
$511$	18.7221	0.828217
$512$	33.6062	1.48520
$513$	0	0
$514$	9.31144	0.410710
$515$	12.6517	0.557501
$516$	0	0
$517$	−34.1449	−1.50169
$518$	−48.4159	−2.12727
$519$	0	0
$520$	0	0
$521$	0.596886	0.0261500	0.0130750	−	0.999915i	$-0.495838\pi$
$521$	0.596886	0.0261500	0.0130750	+	0.999915i	$0.495838\pi$
$522$	0	0
$523$	34.0800	1.49021	0.745107	−	0.666945i	$-0.232398\pi$
$523$	34.0800	1.49021	0.745107	+	0.666945i	$0.232398\pi$
$524$	−15.3044	−0.668574
$525$	0	0
$526$	−32.2369	−1.40559
$527$	−3.55486	−0.154852
$528$	0	0
$529$	14.1986	0.617332
$530$	13.4000	0.582058
$531$	0	0
$532$	46.6621	2.02306
$533$	0	0
$534$	0	0
$535$	5.51892	0.238604
$536$	−98.0278	−4.23416
$537$	0	0
$538$	−59.1942	−2.55204
$539$	12.1828	0.524752
$540$	0	0
$541$	42.5430	1.82907	0.914534	−	0.404510i	$-0.132558\pi$
$541$	42.5430	1.82907	0.914534	+	0.404510i	$0.132558\pi$
$542$	−50.9438	−2.18822
$543$	0	0
$544$	−52.6355	−2.25673
$545$	7.12142	0.305048
$546$	0	0
$547$	42.0185	1.79658	0.898291	−	0.439401i	$-0.144809\pi$
$547$	42.0185	1.79658	0.898291	+	0.439401i	$0.144809\pi$
$548$	77.1274	3.29472
$549$	0	0
$550$	−8.51023	−0.362878
$551$	16.5849	0.706539
$552$	0	0
$553$	−46.2947	−1.96865
$554$	31.3499	1.33193
$555$	0	0
$556$	92.8047	3.93580
$557$	36.5703	1.54953	0.774767	−	0.632247i	$-0.217867\pi$
$557$	36.5703	1.54953	0.774767	+	0.632247i	$0.217867\pi$
$558$	0	0
$559$	0	0
$560$	34.7578	1.46879
$561$	0	0
$562$	−59.8430	−2.52433
$563$	−24.6898	−1.04055	−0.520277	−	0.853998i	$-0.674171\pi$
$563$	−24.6898	−1.04055	−0.520277	+	0.853998i	$0.674171\pi$
$564$	0	0
$565$	18.7572	0.789121
$566$	23.3560	0.981727
$567$	0	0
$568$	−70.1588	−2.94380
$569$	21.7107	0.910162	0.455081	−	0.890450i	$-0.349610\pi$
$569$	21.7107	0.910162	0.455081	+	0.890450i	$0.349610\pi$
$570$	0	0
$571$	30.8235	1.28992	0.644962	−	0.764215i	$-0.276873\pi$
$571$	30.8235	1.28992	0.644962	+	0.764215i	$0.276873\pi$
$572$	0	0
$573$	0	0
$574$	−18.9192	−0.789674
$575$	−6.09907	−0.254349
$576$	0	0
$577$	32.2437	1.34232	0.671161	−	0.741311i	$-0.265796\pi$
$577$	32.2437	1.34232	0.671161	+	0.741311i	$0.265796\pi$
$578$	−2.91510	−0.121252
$579$	0	0
$580$	28.5658	1.18613
$581$	24.3372	1.00968
$582$	0	0
$583$	16.4121	0.679720
$584$	44.3297	1.83438
$585$	0	0
$586$	16.8783	0.697238
$587$	7.71022	0.318235	0.159117	−	0.987260i	$-0.449135\pi$
$587$	7.71022	0.318235	0.159117	+	0.987260i	$0.449135\pi$
$588$	0	0
$589$	2.40015	0.0988964
$590$	0.381596	0.0157101
$591$	0	0
$592$	−59.2573	−2.43546
$593$	17.1507	0.704295	0.352147	−	0.935945i	$-0.385452\pi$
$593$	17.1507	0.704295	0.352147	+	0.935945i	$0.385452\pi$
$594$	0	0
$595$	13.9665	0.572572
$596$	−64.9967	−2.66237
$597$	0	0
$598$	0	0
$599$	14.8111	0.605163	0.302582	−	0.953123i	$-0.402151\pi$
$599$	14.8111	0.605163	0.302582	+	0.953123i	$0.402151\pi$
$600$	0	0
$601$	5.70203	0.232591	0.116295	−	0.993215i	$-0.462898\pi$
$601$	5.70203	0.232591	0.116295	+	0.993215i	$0.462898\pi$
$602$	21.5186	0.877033
$603$	0	0
$604$	8.24126	0.335332
$605$	0.576790	0.0234499
$606$	0	0
$607$	4.95359	0.201060	0.100530	−	0.994934i	$-0.467946\pi$
$607$	4.95359	0.201060	0.100530	+	0.994934i	$0.467946\pi$
$608$	35.5381	1.44126
$609$	0	0
$610$	15.9883	0.647345
$611$	0	0
$612$	0	0
$613$	20.0157	0.808427	0.404213	−	0.914665i	$-0.367545\pi$
$613$	20.0157	0.808427	0.404213	+	0.914665i	$0.367545\pi$
$614$	−68.0916	−2.74795
$615$	0	0
$616$	82.3567	3.31825
$617$	4.36915	0.175895	0.0879477	−	0.996125i	$-0.471969\pi$
$617$	4.36915	0.175895	0.0879477	+	0.996125i	$0.471969\pi$
$618$	0	0
$619$	29.2465	1.17552	0.587758	−	0.809037i	$-0.300011\pi$
$619$	29.2465	1.17552	0.587758	+	0.809037i	$0.300011\pi$
$620$	4.13402	0.166026
$621$	0	0
$622$	−10.2065	−0.409245
$623$	−42.9692	−1.72152
$624$	0	0
$625$	1.00000	0.0400000
$626$	−10.8961	−0.435495
$627$	0	0
$628$	−101.963	−4.06879
$629$	−23.8110	−0.949408
$630$	0	0
$631$	−2.37642	−0.0946038	−0.0473019	−	0.998881i	$-0.515062\pi$
$631$	−2.37642	−0.0946038	−0.0473019	+	0.998881i	$0.515062\pi$
$632$	−109.615	−4.36027
$633$	0	0
$634$	65.6774	2.60838
$635$	−0.368129	−0.0146087
$636$	0	0
$637$	0	0
$638$	49.1279	1.94499
$639$	0	0
$640$	5.38392	0.212818
$641$	28.9687	1.14419	0.572097	−	0.820186i	$-0.306130\pi$
$641$	28.9687	1.14419	0.572097	+	0.820186i	$0.306130\pi$
$642$	0	0
$643$	14.0697	0.554855	0.277427	−	0.960747i	$-0.410518\pi$
$643$	14.0697	0.554855	0.277427	+	0.960747i	$0.410518\pi$
$644$	99.0610	3.90355
$645$	0	0
$646$	32.2238	1.26783
$647$	−8.25026	−0.324351	−0.162176	−	0.986762i	$-0.551851\pi$
$647$	−8.25026	−0.324351	−0.162176	+	0.986762i	$0.551851\pi$
$648$	0	0
$649$	0.467373	0.0183460
$650$	0	0
$651$	0	0
$652$	27.8408	1.09033
$653$	13.2659	0.519136	0.259568	−	0.965725i	$-0.416420\pi$
$653$	13.2659	0.519136	0.259568	+	0.965725i	$0.416420\pi$
$654$	0	0
$655$	3.09282	0.120847
$656$	−23.1557	−0.904077
$657$	0	0
$658$	−91.5051	−3.56724
$659$	−28.0173	−1.09140	−0.545699	−	0.837981i	$-0.683736\pi$
$659$	−28.0173	−1.09140	−0.545699	+	0.837981i	$0.683736\pi$
$660$	0	0
$661$	−30.0308	−1.16806	−0.584031	−	0.811731i	$-0.698526\pi$
$661$	−30.0308	−1.16806	−0.584031	+	0.811731i	$0.698526\pi$
$662$	14.6787	0.570503
$663$	0	0
$664$	57.6250	2.23628
$665$	−9.42984	−0.365674
$666$	0	0
$667$	35.2087	1.36329
$668$	−69.8785	−2.70368
$669$	0	0
$670$	33.2484	1.28450
$671$	19.5822	0.755962
$672$	0	0
$673$	20.1701	0.777499	0.388749	−	0.921344i	$-0.372907\pi$
$673$	20.1701	0.777499	0.388749	+	0.921344i	$0.372907\pi$
$674$	−44.4949	−1.71388
$675$	0	0
$676$	0	0
$677$	28.5492	1.09723	0.548616	−	0.836074i	$-0.315155\pi$
$677$	28.5492	1.09723	0.548616	+	0.836074i	$0.315155\pi$
$678$	0	0
$679$	−9.76466	−0.374733
$680$	33.0696	1.26816
$681$	0	0
$682$	7.10974	0.272246
$683$	−12.4889	−0.477876	−0.238938	−	0.971035i	$-0.576799\pi$
$683$	−12.4889	−0.477876	−0.238938	+	0.971035i	$0.576799\pi$
$684$	0	0
$685$	−15.5865	−0.595529
$686$	−27.9157	−1.06582
$687$	0	0
$688$	26.3371	1.00409
$689$	0	0
$690$	0	0
$691$	−45.5955	−1.73453	−0.867267	−	0.497843i	$-0.834126\pi$
$691$	−45.5955	−1.73453	−0.867267	+	0.497843i	$0.834126\pi$
$692$	48.8183	1.85579
$693$	0	0
$694$	−32.7530	−1.24329
$695$	−18.7547	−0.711406
$696$	0	0
$697$	−9.30452	−0.352434
$698$	7.20981	0.272895
$699$	0	0
$700$	−16.2420	−0.613889
$701$	4.57596	0.172831	0.0864157	−	0.996259i	$-0.472459\pi$
$701$	4.57596	0.172831	0.0864157	+	0.996259i	$0.472459\pi$
$702$	0	0
$703$	16.0766	0.606340
$704$	36.8952	1.39054
$705$	0	0
$706$	59.9578	2.25654
$707$	7.35260	0.276523
$708$	0	0
$709$	−24.2827	−0.911957	−0.455979	−	0.889991i	$-0.650711\pi$
$709$	−24.2827	−0.911957	−0.455979	+	0.889991i	$0.650711\pi$
$710$	23.7960	0.893047
$711$	0	0
$712$	−101.741	−3.81292
$713$	5.09537	0.190823
$714$	0	0
$715$	0	0
$716$	−45.7887	−1.71120
$717$	0	0
$718$	30.3635	1.13316
$719$	13.0137	0.485329	0.242664	−	0.970110i	$-0.421979\pi$
$719$	13.0137	0.485329	0.242664	+	0.970110i	$0.421979\pi$
$720$	0	0
$721$	41.5267	1.54654
$722$	28.3268	1.05422
$723$	0	0
$724$	−107.161	−3.98259
$725$	−5.77280	−0.214396
$726$	0	0
$727$	11.5596	0.428722	0.214361	−	0.976755i	$-0.431233\pi$
$727$	11.5596	0.428722	0.214361	+	0.976755i	$0.431233\pi$
$728$	0	0
$729$	0	0
$730$	−15.0355	−0.556487
$731$	10.5829	0.391423
$732$	0	0
$733$	−13.7767	−0.508855	−0.254427	−	0.967092i	$-0.581887\pi$
$733$	−13.7767	−0.508855	−0.254427	+	0.967092i	$0.581887\pi$
$734$	−37.0969	−1.36927
$735$	0	0
$736$	75.4453	2.78095
$737$	40.7222	1.50002
$738$	0	0
$739$	5.83557	0.214665	0.107332	−	0.994223i	$-0.465769\pi$
$739$	5.83557	0.214665	0.107332	+	0.994223i	$0.465769\pi$
$740$	27.6904	1.01792
$741$	0	0
$742$	43.9828	1.61466
$743$	−12.1353	−0.445202	−0.222601	−	0.974910i	$-0.571455\pi$
$743$	−12.1353	−0.445202	−0.222601	+	0.974910i	$0.571455\pi$
$744$	0	0
$745$	13.1350	0.481230
$746$	−48.7074	−1.78331
$747$	0	0
$748$	67.9784	2.48554
$749$	18.1148	0.661900
$750$	0	0
$751$	45.3878	1.65622	0.828112	−	0.560563i	$-0.189415\pi$
$751$	45.3878	1.65622	0.828112	+	0.560563i	$0.189415\pi$
$752$	−111.995	−4.08404
$753$	0	0
$754$	0	0
$755$	−1.66546	−0.0606122
$756$	0	0
$757$	19.5260	0.709684	0.354842	−	0.934926i	$-0.384535\pi$
$757$	19.5260	0.709684	0.354842	+	0.934926i	$0.384535\pi$
$758$	4.04335	0.146861
$759$	0	0
$760$	−22.3278	−0.809913
$761$	28.1496	1.02042	0.510210	−	0.860050i	$-0.329568\pi$
$761$	28.1496	1.02042	0.510210	+	0.860050i	$0.329568\pi$
$762$	0	0
$763$	23.3747	0.846220
$764$	105.686	3.82357
$765$	0	0
$766$	−79.5061	−2.87267
$767$	0	0
$768$	0	0
$769$	−1.42110	−0.0512463	−0.0256232	−	0.999672i	$-0.508157\pi$
$769$	−1.42110	−0.0512463	−0.0256232	+	0.999672i	$0.508157\pi$
$770$	−27.9332	−1.00664
$771$	0	0
$772$	−28.5841	−1.02876
$773$	13.8186	0.497020	0.248510	−	0.968629i	$-0.420059\pi$
$773$	13.8186	0.497020	0.248510	+	0.968629i	$0.420059\pi$
$774$	0	0
$775$	−0.835435	−0.0300097
$776$	−23.1205	−0.829979
$777$	0	0
$778$	52.2989	1.87501
$779$	6.28217	0.225082
$780$	0	0
$781$	29.1450	1.04289
$782$	68.4092	2.44631
$783$	0	0
$784$	39.9596	1.42713
$785$	20.6056	0.735444
$786$	0	0
$787$	9.96442	0.355193	0.177597	−	0.984103i	$-0.443168\pi$
$787$	9.96442	0.355193	0.177597	+	0.984103i	$0.443168\pi$
$788$	61.3820	2.18664
$789$	0	0
$790$	37.1786	1.32275
$791$	61.5668	2.18906
$792$	0	0
$793$	0	0
$794$	−15.0452	−0.533935
$795$	0	0
$796$	−29.8599	−1.05836
$797$	10.0651	0.356523	0.178262	−	0.983983i	$-0.442953\pi$
$797$	10.0651	0.356523	0.178262	+	0.983983i	$0.442953\pi$
$798$	0	0
$799$	−45.0024	−1.59207
$800$	−12.3700	−0.437344
$801$	0	0
$802$	82.6041	2.91685
$803$	−18.4152	−0.649858
$804$	0	0
$805$	−20.0190	−0.705577
$806$	0	0
$807$	0	0
$808$	17.4093	0.612457
$809$	38.1107	1.33990	0.669950	−	0.742406i	$-0.266316\pi$
$809$	38.1107	1.33990	0.669950	+	0.742406i	$0.266316\pi$
$810$	0	0
$811$	3.57508	0.125538	0.0627690	−	0.998028i	$-0.480007\pi$
$811$	3.57508	0.125538	0.0627690	+	0.998028i	$0.480007\pi$
$812$	93.7617	3.29039
$813$	0	0
$814$	47.6222	1.66916
$815$	−5.62628	−0.197080
$816$	0	0
$817$	−7.14530	−0.249982
$818$	50.7445	1.77424
$819$	0	0
$820$	10.8204	0.377865
$821$	43.5678	1.52053	0.760263	−	0.649615i	$-0.225070\pi$
$821$	43.5678	1.52053	0.760263	+	0.649615i	$0.225070\pi$
$822$	0	0
$823$	−4.31879	−0.150544	−0.0752718	−	0.997163i	$-0.523982\pi$
$823$	−4.31879	−0.150544	−0.0752718	+	0.997163i	$0.523982\pi$
$824$	98.3260	3.42535
$825$	0	0
$826$	1.25251	0.0435805
$827$	23.6479	0.822320	0.411160	−	0.911563i	$-0.365124\pi$
$827$	23.6479	0.822320	0.411160	+	0.911563i	$0.365124\pi$
$828$	0	0
$829$	−49.9657	−1.73538	−0.867691	−	0.497105i	$-0.834397\pi$
$829$	−49.9657	−1.73538	−0.867691	+	0.497105i	$0.834397\pi$
$830$	−19.5449	−0.678412
$831$	0	0
$832$	0	0
$833$	16.0567	0.556333
$834$	0	0
$835$	14.1216	0.488698
$836$	−45.8972	−1.58739
$837$	0	0
$838$	−33.8632	−1.16978
$839$	14.7181	0.508125	0.254063	−	0.967188i	$-0.418233\pi$
$839$	14.7181	0.508125	0.254063	+	0.967188i	$0.418233\pi$
$840$	0	0
$841$	4.32519	0.149145
$842$	40.9871	1.41251
$843$	0	0
$844$	−67.7134	−2.33079
$845$	0	0
$846$	0	0
$847$	1.89320	0.0650512
$848$	53.8315	1.84858
$849$	0	0
$850$	−11.2163	−0.384717
$851$	34.1297	1.16995
$852$	0	0
$853$	−27.0196	−0.925134	−0.462567	−	0.886584i	$-0.653071\pi$
$853$	−27.0196	−0.925134	−0.462567	+	0.886584i	$0.653071\pi$
$854$	52.4783	1.79577
$855$	0	0
$856$	42.8917	1.46601
$857$	−33.1663	−1.13294	−0.566470	−	0.824083i	$-0.691691\pi$
$857$	−33.1663	−1.13294	−0.566470	+	0.824083i	$0.691691\pi$
$858$	0	0
$859$	−47.4781	−1.61993	−0.809966	−	0.586476i	$-0.800515\pi$
$859$	−47.4781	−1.61993	−0.809966	+	0.586476i	$0.800515\pi$
$860$	−12.3071	−0.419668
$861$	0	0
$862$	−43.2878	−1.47439
$863$	−3.65653	−0.124470	−0.0622349	−	0.998062i	$-0.519823\pi$
$863$	−3.65653	−0.124470	−0.0622349	+	0.998062i	$0.519823\pi$
$864$	0	0
$865$	−9.86557	−0.335440
$866$	40.6937	1.38283
$867$	0	0
$868$	13.5691	0.460566
$869$	45.5358	1.54470
$870$	0	0
$871$	0	0
$872$	55.3460	1.87425
$873$	0	0
$874$	−46.1881	−1.56234
$875$	3.28231	0.110962
$876$	0	0
$877$	7.26069	0.245176	0.122588	−	0.992458i	$-0.460881\pi$
$877$	7.26069	0.245176	0.122588	+	0.992458i	$0.460881\pi$
$878$	104.547	3.52828
$879$	0	0
$880$	−34.1880	−1.15248
$881$	39.7044	1.33767	0.668837	−	0.743409i	$-0.266792\pi$
$881$	39.7044	1.33767	0.668837	+	0.743409i	$0.266792\pi$
$882$	0	0
$883$	7.48855	0.252010	0.126005	−	0.992030i	$-0.459785\pi$
$883$	7.48855	0.252010	0.126005	+	0.992030i	$0.459785\pi$
$884$	0	0
$885$	0	0
$886$	12.9324	0.434472
$887$	3.24520	0.108963	0.0544816	−	0.998515i	$-0.482649\pi$
$887$	3.24520	0.108963	0.0544816	+	0.998515i	$0.482649\pi$
$888$	0	0
$889$	−1.20831	−0.0405254
$890$	34.5079	1.15671
$891$	0	0
$892$	−92.4757	−3.09631
$893$	30.3844	1.01678
$894$	0	0
$895$	9.25334	0.309305
$896$	17.6717	0.590369
$897$	0	0
$898$	74.5722	2.48851
$899$	4.82279	0.160849
$900$	0	0
$901$	21.6308	0.720628
$902$	18.6091	0.619615
$903$	0	0
$904$	145.776	4.84845
$905$	21.6558	0.719865
$906$	0	0
$907$	28.5229	0.947087	0.473544	−	0.880770i	$-0.342975\pi$
$907$	28.5229	0.947087	0.473544	+	0.880770i	$0.342975\pi$
$908$	56.9467	1.88984
$909$	0	0
$910$	0	0
$911$	49.2789	1.63268	0.816341	−	0.577570i	$-0.195999\pi$
$911$	49.2789	1.63268	0.816341	+	0.577570i	$0.195999\pi$
$912$	0	0
$913$	−23.9382	−0.792240
$914$	−85.2311	−2.81919
$915$	0	0
$916$	9.80092	0.323832
$917$	10.1516	0.335235
$918$	0	0
$919$	−9.83623	−0.324467	−0.162234	−	0.986752i	$-0.551870\pi$
$919$	−9.83623	−0.324467	−0.162234	+	0.986752i	$0.551870\pi$
$920$	−47.4005	−1.56275
$921$	0	0
$922$	−18.3833	−0.605421
$923$	0	0
$924$	0	0
$925$	−5.59588	−0.183991
$926$	−87.5048	−2.87559
$927$	0	0
$928$	71.4093	2.34413
$929$	27.6765	0.908037	0.454018	−	0.890992i	$-0.349990\pi$
$929$	27.6765	0.908037	0.454018	+	0.890992i	$0.349990\pi$
$930$	0	0
$931$	−10.8411	−0.355302
$932$	−109.524	−3.58758
$933$	0	0
$934$	−83.3251	−2.72648
$935$	−13.7376	−0.449267
$936$	0	0
$937$	−39.8796	−1.30281	−0.651406	−	0.758730i	$-0.725820\pi$
$937$	−39.8796	−1.30281	−0.651406	+	0.758730i	$0.725820\pi$
$938$	109.131	3.56327
$939$	0	0
$940$	52.3342	1.70695
$941$	2.58047	0.0841210	0.0420605	−	0.999115i	$-0.486608\pi$
$941$	2.58047	0.0841210	0.0420605	+	0.999115i	$0.486608\pi$
$942$	0	0
$943$	13.3367	0.434302
$944$	1.53298	0.0498942
$945$	0	0
$946$	−21.1659	−0.688162
$947$	5.28389	0.171703	0.0858517	−	0.996308i	$-0.472639\pi$
$947$	5.28389	0.171703	0.0858517	+	0.996308i	$0.472639\pi$
$948$	0	0
$949$	0	0
$950$	7.57297	0.245700
$951$	0	0
$952$	108.545	3.51795
$953$	−2.22577	−0.0720999	−0.0360499	−	0.999350i	$-0.511478\pi$
$953$	−2.22577	−0.0720999	−0.0360499	+	0.999350i	$0.511478\pi$
$954$	0	0
$955$	−21.3578	−0.691121
$956$	−55.8403	−1.80600
$957$	0	0
$958$	27.3307	0.883014
$959$	−51.1596	−1.65203
$960$	0	0
$961$	−30.3020	−0.977485
$962$	0	0
$963$	0	0
$964$	123.228	3.96891
$965$	5.77649	0.185952
$966$	0	0
$967$	−27.6359	−0.888712	−0.444356	−	0.895850i	$-0.646567\pi$
$967$	−27.6359	−0.888712	−0.444356	+	0.895850i	$0.646567\pi$
$968$	4.48268	0.144079
$969$	0	0
$970$	7.84186	0.251787
$971$	49.9320	1.60239	0.801197	−	0.598400i	$-0.204197\pi$
$971$	49.9320	1.60239	0.801197	+	0.598400i	$0.204197\pi$
$972$	0	0
$973$	−61.5586	−1.97348
$974$	−92.0363	−2.94903
$975$	0	0
$976$	64.2294	2.05593
$977$	35.2611	1.12810	0.564052	−	0.825739i	$-0.309242\pi$
$977$	35.2611	1.12810	0.564052	+	0.825739i	$0.309242\pi$
$978$	0	0
$979$	42.2648	1.35079
$980$	−18.6727	−0.596478
$981$	0	0
$982$	46.1330	1.47216
$983$	−20.6986	−0.660184	−0.330092	−	0.943949i	$-0.607080\pi$
$983$	−20.6986	−0.660184	−0.330092	+	0.943949i	$0.607080\pi$
$984$	0	0
$985$	−12.4045	−0.395242
$986$	64.7496	2.06205
$987$	0	0
$988$	0	0
$989$	−15.1690	−0.482348
$990$	0	0
$991$	12.6676	0.402400	0.201200	−	0.979550i	$-0.435516\pi$
$991$	12.6676	0.402400	0.201200	+	0.979550i	$0.435516\pi$
$992$	10.3343	0.328114
$993$	0	0
$994$	78.1056	2.47736
$995$	6.03432	0.191301
$996$	0	0
$997$	−47.7614	−1.51262	−0.756309	−	0.654214i	$-0.772999\pi$
$997$	−47.7614	−1.51262	−0.756309	+	0.654214i	$0.772999\pi$
$998$	22.3146	0.706356
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.cp.1.2		9
3.2	odd	2		845.2.a.o.1.8	yes	9
13.12	even	2		7605.2.a.cs.1.8		9
15.14	odd	2		4225.2.a.bs.1.2		9
39.2	even	12		845.2.m.j.316.17		36
39.5	even	4		845.2.c.h.506.2		18
39.8	even	4		845.2.c.h.506.17		18
39.11	even	12		845.2.m.j.316.2		36
39.17	odd	6		845.2.e.p.146.8		18
39.20	even	12		845.2.m.j.361.17		36
39.23	odd	6		845.2.e.p.191.8		18
39.29	odd	6		845.2.e.o.191.2		18
39.32	even	12		845.2.m.j.361.2		36
39.35	odd	6		845.2.e.o.146.2		18
39.38	odd	2		845.2.a.n.1.2	✓	9
195.194	odd	2		4225.2.a.bt.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.2	✓	9	39.38	odd	2
845.2.a.o.1.8	yes	9	3.2	odd	2
845.2.c.h.506.2		18	39.5	even	4
845.2.c.h.506.17		18	39.8	even	4
845.2.e.o.146.2		18	39.35	odd	6
845.2.e.o.191.2		18	39.29	odd	6
845.2.e.p.146.8		18	39.17	odd	6
845.2.e.p.191.8		18	39.23	odd	6
845.2.m.j.316.2		36	39.11	even	12
845.2.m.j.316.17		36	39.2	even	12
845.2.m.j.361.2		36	39.32	even	12
845.2.m.j.361.17		36	39.20	even	12
4225.2.a.bs.1.2		9	15.14	odd	2
4225.2.a.bt.1.8		9	195.194	odd	2
7605.2.a.cp.1.2		9	1.1	even	1	trivial
7605.2.a.cs.1.8		9	13.12	even	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:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63597 q^{2} +4.94835 q^{4} -1.00000 q^{5} -3.28231 q^{7} -7.77176 q^{8} +O(q^{10})\)	\(q-2.63597 q^{2} +4.94835 q^{4} -1.00000 q^{5} -3.28231 q^{7} -7.77176 q^{8} +2.63597 q^{10} +3.22850 q^{11} +8.65206 q^{14} +10.5894 q^{16} +4.25510 q^{17} -2.87293 q^{19} -4.94835 q^{20} -8.51023 q^{22} -6.09907 q^{23} +1.00000 q^{25} -16.2420 q^{28} -5.77280 q^{29} -0.835435 q^{31} -12.3700 q^{32} -11.2163 q^{34} +3.28231 q^{35} -5.59588 q^{37} +7.57297 q^{38} +7.77176 q^{40} -2.18667 q^{41} +2.48711 q^{43} +15.9757 q^{44} +16.0770 q^{46} -10.5761 q^{47} +3.77353 q^{49} -2.63597 q^{50} +5.08351 q^{53} -3.22850 q^{55} +25.5093 q^{56} +15.2169 q^{58} +0.144765 q^{59} +6.06541 q^{61} +2.20218 q^{62} +11.4280 q^{64} +12.6133 q^{67} +21.0557 q^{68} -8.65206 q^{70} +9.02740 q^{71} -5.70395 q^{73} +14.7506 q^{74} -14.2163 q^{76} -10.5969 q^{77} +14.1043 q^{79} -10.5894 q^{80} +5.76401 q^{82} -7.41467 q^{83} -4.25510 q^{85} -6.55595 q^{86} -25.0911 q^{88} +13.0912 q^{89} -30.1803 q^{92} +27.8783 q^{94} +2.87293 q^{95} +2.97494 q^{97} -9.94691 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8}+O(q^{10}) \) 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8	\( 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8} + 3 q^{10} + 9 q^{11} + 2 q^{14} + 37 q^{16} + q^{17} - 4 q^{19} - 17 q^{20} + 12 q^{22} - 14 q^{23} + 9 q^{25} + 18 q^{28} - 12 q^{29} - 7 q^{31} - 22 q^{32} - 30 q^{34} - 7 q^{35} - 5 q^{37} + 47 q^{38} + 12 q^{40} + 10 q^{41} + 39 q^{43} + 25 q^{44} + 6 q^{46} - 36 q^{47} + 16 q^{49} - 3 q^{50} + 8 q^{53} - 9 q^{55} + 29 q^{56} + 21 q^{58} + 21 q^{59} - 3 q^{61} + 10 q^{62} + 34 q^{64} + q^{67} + 20 q^{68} - 2 q^{70} + q^{71} + 15 q^{74} - 5 q^{76} + 4 q^{77} + 39 q^{79} - 37 q^{80} - 4 q^{82} - 7 q^{83} - q^{85} + 24 q^{86} + 42 q^{88} + 19 q^{89} + 27 q^{92} + 16 q^{94} + 4 q^{95} - 34 q^{97} - 48 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8 + 3 * q^10 + 9 * q^11 + 2 * q^14 + 37 * q^16 + q^17 - 4 * q^19 - 17 * q^20 + 12 * q^22 - 14 * q^23 + 9 * q^25 + 18 * q^28 - 12 * q^29 - 7 * q^31 - 22 * q^32 - 30 * q^34 - 7 * q^35 - 5 * q^37 + 47 * q^38 + 12 * q^40 + 10 * q^41 + 39 * q^43 + 25 * q^44 + 6 * q^46 - 36 * q^47 + 16 * q^49 - 3 * q^50 + 8 * q^53 - 9 * q^55 + 29 * q^56 + 21 * q^58 + 21 * q^59 - 3 * q^61 + 10 * q^62 + 34 * q^64 + q^67 + 20 * q^68 - 2 * q^70 + q^71 + 15 * q^74 - 5 * q^76 + 4 * q^77 + 39 * q^79 - 37 * q^80 - 4 * q^82 - 7 * q^83 - q^85 + 24 * q^86 + 42 * q^88 + 19 * q^89 + 27 * q^92 + 16 * q^94 + 4 * q^95 - 34 * q^97 - 48 * q^98

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