LMFDB - Embedded newform 7175.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7175,2,Mod(1,7175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7175, 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("7175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7175 = 5^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7175.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:	$57.2926634503$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.91223$ of defining polynomial
Character	$\chi$	$=$	7175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.91223 q^{2} -2.56885 q^{3} +1.65662 q^{4} -4.91223 q^{6} -1.00000 q^{7} -0.656620 q^{8} +3.59899 q^{9} +O(q^{10})$	\(q+1.91223 q^{2} -2.56885 q^{3} +1.65662 q^{4} -4.91223 q^{6} -1.00000 q^{7} -0.656620 q^{8} +3.59899 q^{9} -2.00000 q^{11} -4.25561 q^{12} -2.34338 q^{13} -1.91223 q^{14} -4.56885 q^{16} +3.22547 q^{17} +6.88209 q^{18} +2.08777 q^{19} +2.56885 q^{21} -3.82446 q^{22} +6.56885 q^{23} +1.68676 q^{24} -4.48108 q^{26} -1.53871 q^{27} -1.65662 q^{28} +7.82446 q^{29} +3.82446 q^{31} -7.42345 q^{32} +5.13770 q^{33} +6.16784 q^{34} +5.96216 q^{36} -4.28310 q^{37} +3.99230 q^{38} +6.01979 q^{39} -1.00000 q^{41} +4.91223 q^{42} -7.11021 q^{43} -3.31324 q^{44} +12.5611 q^{46} +8.79432 q^{47} +11.7367 q^{48} +1.00000 q^{49} -8.28575 q^{51} -3.88209 q^{52} +2.51122 q^{53} -2.94237 q^{54} +0.656620 q^{56} -5.36317 q^{57} +14.9622 q^{58} -4.00000 q^{59} -4.51122 q^{61} +7.31324 q^{62} -3.59899 q^{63} -5.05763 q^{64} +9.82446 q^{66} -6.51122 q^{67} +5.34338 q^{68} -16.8744 q^{69} -14.9622 q^{71} -2.36317 q^{72} +8.45094 q^{73} -8.19027 q^{74} +3.45864 q^{76} +2.00000 q^{77} +11.5112 q^{78} -1.13770 q^{79} -6.84425 q^{81} -1.91223 q^{82} +9.64892 q^{83} +4.25561 q^{84} -13.5963 q^{86} -20.0999 q^{87} +1.31324 q^{88} -16.9545 q^{89} +2.34338 q^{91} +10.8821 q^{92} -9.82446 q^{93} +16.8168 q^{94} +19.0697 q^{96} -16.3933 q^{97} +1.91223 q^{98} -7.19798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{3} + 3 q^{4} - 8 q^{6} - 3 q^{7} + 8 q^{9}+O(q^{10}) $ 3 * q - q^2 + q^3 + 3 * q^4 - 8 * q^6 - 3 * q^7 + 8 * q^9	$ 3 q - q^{2} + q^{3} + 3 q^{4} - 8 q^{6} - 3 q^{7} + 8 q^{9} - 6 q^{11} - 8 q^{12} - 9 q^{13} + q^{14} - 5 q^{16} - q^{17} + 8 q^{18} + 13 q^{19} - q^{21} + 2 q^{22} + 11 q^{23} + 9 q^{24} + 2 q^{26} + 10 q^{27} - 3 q^{28} + 10 q^{29} - 2 q^{31} - 6 q^{32} - 2 q^{33} + 7 q^{34} - 13 q^{36} - 3 q^{37} - 13 q^{38} - 12 q^{39} - 3 q^{41} + 8 q^{42} - 9 q^{43} - 6 q^{44} + 4 q^{46} + 7 q^{47} + 15 q^{48} + 3 q^{49} - 26 q^{51} + q^{52} - 2 q^{53} - 8 q^{54} + 12 q^{57} + 14 q^{58} - 12 q^{59} - 4 q^{61} + 18 q^{62} - 8 q^{63} - 16 q^{64} + 16 q^{66} - 10 q^{67} + 18 q^{68} - 13 q^{69} - 14 q^{71} + 21 q^{72} + 4 q^{73} + 6 q^{74} + 14 q^{76} + 6 q^{77} + 25 q^{78} + 14 q^{79} + 23 q^{81} + q^{82} + 2 q^{83} + 8 q^{84} - 27 q^{86} - 12 q^{87} + 5 q^{89} + 9 q^{91} + 20 q^{92} - 16 q^{93} + 12 q^{94} + 3 q^{96} - 27 q^{97} - q^{98} - 16 q^{99}+O(q^{100}) $ 3 * q - q^2 + q^3 + 3 * q^4 - 8 * q^6 - 3 * q^7 + 8 * q^9 - 6 * q^11 - 8 * q^12 - 9 * q^13 + q^14 - 5 * q^16 - q^17 + 8 * q^18 + 13 * q^19 - q^21 + 2 * q^22 + 11 * q^23 + 9 * q^24 + 2 * q^26 + 10 * q^27 - 3 * q^28 + 10 * q^29 - 2 * q^31 - 6 * q^32 - 2 * q^33 + 7 * q^34 - 13 * q^36 - 3 * q^37 - 13 * q^38 - 12 * q^39 - 3 * q^41 + 8 * q^42 - 9 * q^43 - 6 * q^44 + 4 * q^46 + 7 * q^47 + 15 * q^48 + 3 * q^49 - 26 * q^51 + q^52 - 2 * q^53 - 8 * q^54 + 12 * q^57 + 14 * q^58 - 12 * q^59 - 4 * q^61 + 18 * q^62 - 8 * q^63 - 16 * q^64 + 16 * q^66 - 10 * q^67 + 18 * q^68 - 13 * q^69 - 14 * q^71 + 21 * q^72 + 4 * q^73 + 6 * q^74 + 14 * q^76 + 6 * q^77 + 25 * q^78 + 14 * q^79 + 23 * q^81 + q^82 + 2 * q^83 + 8 * q^84 - 27 * q^86 - 12 * q^87 + 5 * q^89 + 9 * q^91 + 20 * q^92 - 16 * q^93 + 12 * q^94 + 3 * q^96 - 27 * q^97 - q^98 - 16 * q^99

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 $

$2$	1.91223	1.35215	0.676075	−	0.736833i	$-0.263679\pi$
$2$	1.91223	1.35215	0.676075	+	0.736833i	$0.263679\pi$
$3$	−2.56885	−1.48313	−0.741563	−	0.670883i	$-0.765915\pi$
$3$	−2.56885	−1.48313	−0.741563	+	0.670883i	$0.765915\pi$
$4$	1.65662	0.828310
$5$	0	0
$5$	0	0
$6$	−4.91223	−2.00541
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.656620	−0.232150
$9$	3.59899	1.19966
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−4.25561	−1.22849
$13$	−2.34338	−0.649937	−0.324968	−	0.945725i	$-0.605354\pi$
$13$	−2.34338	−0.649937	−0.324968	+	0.945725i	$0.605354\pi$
$14$	−1.91223	−0.511065
$15$	0	0
$16$	−4.56885	−1.14221
$17$	3.22547	0.782291	0.391146	−	0.920329i	$-0.372079\pi$
$17$	3.22547	0.782291	0.391146	+	0.920329i	$0.372079\pi$
$18$	6.88209	1.62212
$19$	2.08777	0.478967	0.239484	−	0.970900i	$-0.423022\pi$
$19$	2.08777	0.478967	0.239484	+	0.970900i	$0.423022\pi$
$20$	0	0
$21$	2.56885	0.560569
$22$	−3.82446	−0.815377
$23$	6.56885	1.36970	0.684850	−	0.728684i	$-0.259868\pi$
$23$	6.56885	1.36970	0.684850	+	0.728684i	$0.259868\pi$
$24$	1.68676	0.344308
$25$	0	0
$26$	−4.48108	−0.878812
$27$	−1.53871	−0.296125
$28$	−1.65662	−0.313072
$29$	7.82446	1.45297	0.726483	−	0.687185i	$-0.241154\pi$
$29$	7.82446	1.45297	0.726483	+	0.687185i	$0.241154\pi$
$30$	0	0
$31$	3.82446	0.686893	0.343446	−	0.939172i	$-0.388406\pi$
$31$	3.82446	0.686893	0.343446	+	0.939172i	$0.388406\pi$
$32$	−7.42345	−1.31229
$33$	5.13770	0.894359
$34$	6.16784	1.05778
$35$	0	0
$36$	5.96216	0.993693
$37$	−4.28310	−0.704138	−0.352069	−	0.935974i	$-0.614522\pi$
$37$	−4.28310	−0.704138	−0.352069	+	0.935974i	$0.614522\pi$
$38$	3.99230	0.647636
$39$	6.01979	0.963938
$40$	0	0
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	4.91223	0.757973
$43$	−7.11021	−1.08430	−0.542148	−	0.840283i	$-0.682389\pi$
$43$	−7.11021	−1.08430	−0.542148	+	0.840283i	$0.682389\pi$
$44$	−3.31324	−0.499490
$45$	0	0
$46$	12.5611	1.85204
$47$	8.79432	1.28278	0.641392	−	0.767214i	$-0.278357\pi$
$47$	8.79432	1.28278	0.641392	+	0.767214i	$0.278357\pi$
$48$	11.7367	1.69404
$49$	1.00000	0.142857
$50$	0	0
$51$	−8.28575	−1.16024
$52$	−3.88209	−0.538349
$53$	2.51122	0.344942	0.172471	−	0.985015i	$-0.444825\pi$
$53$	2.51122	0.344942	0.172471	+	0.985015i	$0.444825\pi$
$54$	−2.94237	−0.400406
$55$	0	0
$56$	0.656620	0.0877446
$57$	−5.36317	−0.710369
$58$	14.9622	1.96463
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	−4.51122	−0.577602	−0.288801	−	0.957389i	$-0.593257\pi$
$61$	−4.51122	−0.577602	−0.288801	+	0.957389i	$0.593257\pi$
$62$	7.31324	0.928783
$63$	−3.59899	−0.453430
$64$	−5.05763	−0.632204
$65$	0	0
$66$	9.82446	1.20931
$67$	−6.51122	−0.795472	−0.397736	−	0.917500i	$-0.630204\pi$
$67$	−6.51122	−0.795472	−0.397736	+	0.917500i	$0.630204\pi$
$68$	5.34338	0.647980
$69$	−16.8744	−2.03144
$70$	0	0
$71$	−14.9622	−1.77568	−0.887841	−	0.460151i	$-0.847795\pi$
$71$	−14.9622	−1.77568	−0.887841	+	0.460151i	$0.847795\pi$
$72$	−2.36317	−0.278502
$73$	8.45094	0.989108	0.494554	−	0.869147i	$-0.335331\pi$
$73$	8.45094	0.989108	0.494554	+	0.869147i	$0.335331\pi$
$74$	−8.19027	−0.952100
$75$	0	0
$76$	3.45864	0.396734
$77$	2.00000	0.227921
$78$	11.5112	1.30339
$79$	−1.13770	−0.128001	−0.0640006	−	0.997950i	$-0.520386\pi$
$79$	−1.13770	−0.128001	−0.0640006	+	0.997950i	$0.520386\pi$
$80$	0	0
$81$	−6.84425	−0.760472
$82$	−1.91223	−0.211170
$83$	9.64892	1.05911	0.529553	−	0.848277i	$-0.322360\pi$
$83$	9.64892	1.05911	0.529553	+	0.848277i	$0.322360\pi$
$84$	4.25561	0.464325
$85$	0	0
$86$	−13.5963	−1.46613
$87$	−20.0999	−2.15493
$88$	1.31324	0.139992
$89$	−16.9545	−1.79717	−0.898584	−	0.438801i	$-0.855403\pi$
$89$	−16.9545	−1.79717	−0.898584	+	0.438801i	$0.855403\pi$
$90$	0	0
$91$	2.34338	0.245653
$92$	10.8821	1.13454
$93$	−9.82446	−1.01875
$94$	16.8168	1.73452
$95$	0	0
$96$	19.0697	1.94629
$97$	−16.3933	−1.66449	−0.832244	−	0.554409i	$-0.812944\pi$
$97$	−16.3933	−1.66449	−0.832244	+	0.554409i	$0.812944\pi$
$98$	1.91223	0.193164
$99$	−7.19798	−0.723424
$100$	0	0
$101$	3.37087	0.335414	0.167707	−	0.985837i	$-0.446364\pi$
$101$	3.37087	0.335414	0.167707	+	0.985837i	$0.446364\pi$
$102$	−15.8442	−1.56881
$103$	−2.35108	−0.231659	−0.115830	−	0.993269i	$-0.536953\pi$
$103$	−2.35108	−0.231659	−0.115830	+	0.993269i	$0.536953\pi$
$104$	1.53871	0.150883
$105$	0	0
$106$	4.80202	0.466414
$107$	−16.0121	−1.54795	−0.773973	−	0.633218i	$-0.781734\pi$
$107$	−16.0121	−1.54795	−0.773973	+	0.633218i	$0.781734\pi$
$108$	−2.54906	−0.245283
$109$	−5.70919	−0.546842	−0.273421	−	0.961895i	$-0.588155\pi$
$109$	−5.70919	−0.546842	−0.273421	+	0.961895i	$0.588155\pi$
$110$	0	0
$111$	11.0026	1.04432
$112$	4.56885	0.431716
$113$	−17.5310	−1.64918	−0.824589	−	0.565732i	$-0.808594\pi$
$113$	−17.5310	−1.64918	−0.824589	+	0.565732i	$0.808594\pi$
$114$	−10.2556	−0.960526
$115$	0	0
$116$	12.9622	1.20351
$117$	−8.43380	−0.779705
$118$	−7.64892	−0.704140
$119$	−3.22547	−0.295678
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−8.62648	−0.781005
$123$	2.56885	0.231625
$124$	6.33568	0.568960
$125$	0	0
$126$	−6.88209	−0.613105
$127$	20.4432	1.81404	0.907022	−	0.421083i	$-0.138350\pi$
$127$	20.4432	1.81404	0.907022	+	0.421083i	$0.138350\pi$
$128$	5.17554	0.457458
$129$	18.2650	1.60815
$130$	0	0
$131$	0.962158	0.0840641	0.0420320	−	0.999116i	$-0.486617\pi$
$131$	0.962158	0.0840641	0.0420320	+	0.999116i	$0.486617\pi$
$132$	8.51122	0.740806
$133$	−2.08777	−0.181033
$134$	−12.4509	−1.07560
$135$	0	0
$136$	−2.11791	−0.181609
$137$	−3.37352	−0.288219	−0.144110	−	0.989562i	$-0.546032\pi$
$137$	−3.37352	−0.288219	−0.144110	+	0.989562i	$0.546032\pi$
$138$	−32.2677	−2.74681
$139$	14.7866	1.25418	0.627092	−	0.778945i	$-0.284245\pi$
$139$	14.7866	1.25418	0.627092	+	0.778945i	$0.284245\pi$
$140$	0	0
$141$	−22.5913	−1.90253
$142$	−28.6111	−2.40099
$143$	4.68676	0.391926
$144$	−16.4432	−1.37027
$145$	0	0
$146$	16.1601	1.33742
$147$	−2.56885	−0.211875
$148$	−7.09547	−0.583244
$149$	1.76418	0.144527	0.0722637	−	0.997386i	$-0.476978\pi$
$149$	1.76418	0.144527	0.0722637	+	0.997386i	$0.476978\pi$
$150$	0	0
$151$	−1.54906	−0.126061	−0.0630304	−	0.998012i	$-0.520076\pi$
$151$	−1.54906	−0.126061	−0.0630304	+	0.998012i	$0.520076\pi$
$152$	−1.37087	−0.111192
$153$	11.6084	0.938486
$154$	3.82446	0.308184
$155$	0	0
$156$	9.97251	0.798440
$157$	13.8520	1.10551	0.552753	−	0.833345i	$-0.313577\pi$
$157$	13.8520	1.10551	0.552753	+	0.833345i	$0.313577\pi$
$158$	−2.17554	−0.173077
$159$	−6.45094	−0.511593
$160$	0	0
$161$	−6.56885	−0.517698
$162$	−13.0878	−1.02827
$163$	24.3779	1.90942	0.954712	−	0.297531i	$-0.0961630\pi$
$163$	24.3779	1.90942	0.954712	+	0.297531i	$0.0961630\pi$
$164$	−1.65662	−0.129360
$165$	0	0
$166$	18.4509	1.43207
$167$	−12.1876	−0.943107	−0.471553	−	0.881837i	$-0.656307\pi$
$167$	−12.1876	−0.943107	−0.471553	+	0.881837i	$0.656307\pi$
$168$	−1.68676	−0.130136
$169$	−7.50857	−0.577582
$170$	0	0
$171$	7.51386	0.574599
$172$	−11.7789	−0.898134
$173$	−9.31324	−0.708073	−0.354036	−	0.935232i	$-0.615191\pi$
$173$	−9.31324	−0.708073	−0.354036	+	0.935232i	$0.615191\pi$
$174$	−38.4355	−2.91379
$175$	0	0
$176$	9.13770	0.688780
$177$	10.2754	0.772346
$178$	−32.4208	−2.43004
$179$	12.2754	0.917506	0.458753	−	0.888564i	$-0.348296\pi$
$179$	12.2754	0.917506	0.458753	+	0.888564i	$0.348296\pi$
$180$	0	0
$181$	13.7668	1.02328	0.511640	−	0.859200i	$-0.329038\pi$
$181$	13.7668	1.02328	0.511640	+	0.859200i	$0.329038\pi$
$182$	4.48108	0.332160
$183$	11.5886	0.856657
$184$	−4.31324	−0.317976
$185$	0	0
$186$	−18.7866	−1.37750
$187$	−6.45094	−0.471739
$188$	14.5688	1.06254
$189$	1.53871	0.111925
$190$	0	0
$191$	−9.31324	−0.673882	−0.336941	−	0.941526i	$-0.609392\pi$
$191$	−9.31324	−0.673882	−0.336941	+	0.941526i	$0.609392\pi$
$192$	12.9923	0.937638
$193$	−7.31324	−0.526419	−0.263209	−	0.964739i	$-0.584781\pi$
$193$	−7.31324	−0.526419	−0.263209	+	0.964739i	$0.584781\pi$
$194$	−31.3478	−2.25064
$195$	0	0
$196$	1.65662	0.118330
$197$	−16.4234	−1.17012	−0.585061	−	0.810989i	$-0.698929\pi$
$197$	−16.4234	−1.17012	−0.585061	+	0.810989i	$0.698929\pi$
$198$	−13.7642	−0.978178
$199$	−9.13000	−0.647208	−0.323604	−	0.946193i	$-0.604895\pi$
$199$	−9.13000	−0.647208	−0.323604	+	0.946193i	$0.604895\pi$
$200$	0	0
$201$	16.7263	1.17978
$202$	6.44588	0.453531
$203$	−7.82446	−0.549169
$204$	−13.7263	−0.961036
$205$	0	0
$206$	−4.49581	−0.313238
$207$	23.6412	1.64318
$208$	10.7065	0.742366
$209$	−4.17554	−0.288828
$210$	0	0
$211$	7.53365	0.518638	0.259319	−	0.965792i	$-0.416502\pi$
$211$	7.53365	0.518638	0.259319	+	0.965792i	$0.416502\pi$
$212$	4.16013	0.285719
$213$	38.4355	2.63356
$214$	−30.6188	−2.09306
$215$	0	0
$216$	1.01035	0.0687455
$217$	−3.82446	−0.259621
$218$	−10.9173	−0.739412
$219$	−21.7092	−1.46697
$220$	0	0
$221$	−7.55850	−0.508440
$222$	21.0396	1.41208
$223$	4.57149	0.306130	0.153065	−	0.988216i	$-0.451086\pi$
$223$	4.57149	0.306130	0.153065	+	0.988216i	$0.451086\pi$
$224$	7.42345	0.496000
$225$	0	0
$226$	−33.5233	−2.22994
$227$	0.351083	0.0233022	0.0116511	−	0.999932i	$-0.496291\pi$
$227$	0.351083	0.0233022	0.0116511	+	0.999932i	$0.496291\pi$
$228$	−8.88474	−0.588406
$229$	−6.90453	−0.456264	−0.228132	−	0.973630i	$-0.573262\pi$
$229$	−6.90453	−0.456264	−0.228132	+	0.973630i	$0.573262\pi$
$230$	0	0
$231$	−5.13770	−0.338036
$232$	−5.13770	−0.337306
$233$	−29.0070	−1.90031	−0.950157	−	0.311773i	$-0.899077\pi$
$233$	−29.0070	−1.90031	−0.950157	+	0.311773i	$0.899077\pi$
$234$	−16.1274	−1.05428
$235$	0	0
$236$	−6.62648	−0.431347
$237$	2.92258	0.189842
$238$	−6.16784	−0.399802
$239$	−28.4958	−1.84324	−0.921620	−	0.388093i	$-0.873134\pi$
$239$	−28.4958	−1.84324	−0.921620	+	0.388093i	$0.873134\pi$
$240$	0	0
$241$	20.9019	1.34641	0.673204	−	0.739457i	$-0.264917\pi$
$241$	20.9019	1.34641	0.673204	+	0.739457i	$0.264917\pi$
$242$	−13.3856	−0.860459
$243$	22.1980	1.42400
$244$	−7.47338	−0.478434
$245$	0	0
$246$	4.91223	0.313192
$247$	−4.89244	−0.311298
$248$	−2.51122	−0.159462
$249$	−24.7866	−1.57079
$250$	0	0
$251$	5.47338	0.345476	0.172738	−	0.984968i	$-0.444739\pi$
$251$	5.47338	0.345476	0.172738	+	0.984968i	$0.444739\pi$
$252$	−5.96216	−0.375581
$253$	−13.1377	−0.825960
$254$	39.0922	2.45286
$255$	0	0
$256$	20.0121	1.25076
$257$	−20.0422	−1.25020	−0.625100	−	0.780545i	$-0.714942\pi$
$257$	−20.0422	−1.25020	−0.625100	+	0.780545i	$0.714942\pi$
$258$	34.9270	2.17446
$259$	4.28310	0.266139
$260$	0	0
$261$	28.1601	1.74307
$262$	1.83987	0.113667
$263$	8.39066	0.517390	0.258695	−	0.965959i	$-0.416707\pi$
$263$	8.39066	0.517390	0.258695	+	0.965959i	$0.416707\pi$
$264$	−3.37352	−0.207626
$265$	0	0
$266$	−3.99230	−0.244783
$267$	43.5534	2.66543
$268$	−10.7866	−0.658897
$269$	23.1826	1.41347	0.706733	−	0.707480i	$-0.250168\pi$
$269$	23.1826	1.41347	0.706733	+	0.707480i	$0.250168\pi$
$270$	0	0
$271$	−20.3907	−1.23864	−0.619322	−	0.785137i	$-0.712593\pi$
$271$	−20.3907	−1.23864	−0.619322	+	0.785137i	$0.712593\pi$
$272$	−14.7367	−0.893543
$273$	−6.01979	−0.364334
$274$	−6.45094	−0.389716
$275$	0	0
$276$	−27.9545	−1.68266
$277$	−18.5534	−1.11477	−0.557384	−	0.830255i	$-0.688195\pi$
$277$	−18.5534	−1.11477	−0.557384	+	0.830255i	$0.688195\pi$
$278$	28.2754	1.69585
$279$	13.7642	0.824040
$280$	0	0
$281$	−15.8847	−0.947604	−0.473802	−	0.880631i	$-0.657119\pi$
$281$	−15.8847	−0.947604	−0.473802	+	0.880631i	$0.657119\pi$
$282$	−43.1997	−2.57251
$283$	−20.6265	−1.22612	−0.613059	−	0.790037i	$-0.710061\pi$
$283$	−20.6265	−1.22612	−0.613059	+	0.790037i	$0.710061\pi$
$284$	−24.7866	−1.47082
$285$	0	0
$286$	8.96216	0.529943
$287$	1.00000	0.0590281
$288$	−26.7169	−1.57431
$289$	−6.59634	−0.388020
$290$	0	0
$291$	42.1119	2.46865
$292$	14.0000	0.819288
$293$	−24.9468	−1.45740	−0.728702	−	0.684831i	$-0.759876\pi$
$293$	−24.9468	−1.45740	−0.728702	+	0.684831i	$0.759876\pi$
$294$	−4.91223	−0.286487
$295$	0	0
$296$	2.81237	0.163466
$297$	3.07742	0.178570
$298$	3.37352	0.195423
$299$	−15.3933	−0.890218
$300$	0	0
$301$	7.11021	0.409825
$302$	−2.96216	−0.170453
$303$	−8.65927	−0.497462
$304$	−9.53871	−0.547083
$305$	0	0
$306$	22.1980	1.26897
$307$	10.2204	0.583310	0.291655	−	0.956524i	$-0.405794\pi$
$307$	10.2204	0.583310	0.291655	+	0.956524i	$0.405794\pi$
$308$	3.31324	0.188789
$309$	6.03958	0.343580
$310$	0	0
$311$	−16.5387	−0.937824	−0.468912	−	0.883245i	$-0.655354\pi$
$311$	−16.5387	−0.937824	−0.468912	+	0.883245i	$0.655354\pi$
$312$	−3.95272	−0.223779
$313$	−16.4784	−0.931416	−0.465708	−	0.884938i	$-0.654200\pi$
$313$	−16.4784	−0.931416	−0.465708	+	0.884938i	$0.654200\pi$
$314$	26.4881	1.49481
$315$	0	0
$316$	−1.88474	−0.106025
$317$	−12.9019	−0.724642	−0.362321	−	0.932053i	$-0.618016\pi$
$317$	−12.9019	−0.724642	−0.362321	+	0.932053i	$0.618016\pi$
$318$	−12.3357	−0.691750
$319$	−15.6489	−0.876171
$320$	0	0
$321$	41.1326	2.29580
$322$	−12.5611	−0.700005
$323$	6.73404	0.374692
$324$	−11.3383	−0.629907
$325$	0	0
$326$	46.6161	2.58183
$327$	14.6661	0.811035
$328$	0.656620	0.0362558
$329$	−8.79432	−0.484847
$330$	0	0
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	15.9846	0.877268
$333$	−15.4148	−0.844728
$334$	−23.3055	−1.27522
$335$	0	0
$336$	−11.7367	−0.640289
$337$	4.39331	0.239319	0.119659	−	0.992815i	$-0.461820\pi$
$337$	4.39331	0.239319	0.119659	+	0.992815i	$0.461820\pi$
$338$	−14.3581	−0.780978
$339$	45.0345	2.44594
$340$	0	0
$341$	−7.64892	−0.414212
$342$	14.3682	0.776945
$343$	−1.00000	−0.0539949
$344$	4.66871	0.251720
$345$	0	0
$346$	−17.8091	−0.957421
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	−33.2978	−1.78495
$349$	18.9072	1.01208	0.506039	−	0.862511i	$-0.331109\pi$
$349$	18.9072	1.01208	0.506039	+	0.862511i	$0.331109\pi$
$350$	0	0
$351$	3.60578	0.192462
$352$	14.8469	0.791342
$353$	15.3735	0.818250	0.409125	−	0.912478i	$-0.365834\pi$
$353$	15.3735	0.818250	0.409125	+	0.912478i	$0.365834\pi$
$354$	19.6489	1.04433
$355$	0	0
$356$	−28.0871	−1.48861
$357$	8.28575	0.438528
$358$	23.4734	1.24061
$359$	−11.0851	−0.585051	−0.292525	−	0.956258i	$-0.594496\pi$
$359$	−11.0851	−0.585051	−0.292525	+	0.956258i	$0.594496\pi$
$360$	0	0
$361$	−14.6412	−0.770590
$362$	26.3253	1.38363
$363$	17.9819	0.943807
$364$	3.88209	0.203477
$365$	0	0
$366$	22.1601	1.15833
$367$	−8.57149	−0.447428	−0.223714	−	0.974655i	$-0.571818\pi$
$367$	−8.57149	−0.447428	−0.223714	+	0.974655i	$0.571818\pi$
$368$	−30.0121	−1.56449
$369$	−3.59899	−0.187356
$370$	0	0
$371$	−2.51122	−0.130376
$372$	−16.2754	−0.843840
$373$	16.4234	0.850374	0.425187	−	0.905106i	$-0.360208\pi$
$373$	16.4234	0.850374	0.425187	+	0.905106i	$0.360208\pi$
$374$	−12.3357	−0.637863
$375$	0	0
$376$	−5.77453	−0.297799
$377$	−18.3357	−0.944335
$378$	2.94237	0.151339
$379$	1.43115	0.0735133	0.0367566	−	0.999324i	$-0.488297\pi$
$379$	1.43115	0.0735133	0.0367566	+	0.999324i	$0.488297\pi$
$380$	0	0
$381$	−52.5156	−2.69046
$382$	−17.8091	−0.911190
$383$	−13.1953	−0.674250	−0.337125	−	0.941460i	$-0.609454\pi$
$383$	−13.1953	−0.674250	−0.337125	+	0.941460i	$0.609454\pi$
$384$	−13.2952	−0.678467
$385$	0	0
$386$	−13.9846	−0.711797
$387$	−25.5895	−1.30079
$388$	−27.1575	−1.37871
$389$	9.30554	0.471809	0.235905	−	0.971776i	$-0.424195\pi$
$389$	9.30554	0.471809	0.235905	+	0.971776i	$0.424195\pi$
$390$	0	0
$391$	21.1876	1.07150
$392$	−0.656620	−0.0331643
$393$	−2.47164	−0.124678
$394$	−31.4054	−1.58218
$395$	0	0
$396$	−11.9243	−0.599219
$397$	1.29783	0.0651364	0.0325682	−	0.999470i	$-0.489631\pi$
$397$	1.29783	0.0651364	0.0325682	+	0.999470i	$0.489631\pi$
$398$	−17.4586	−0.875123
$399$	5.36317	0.268494
$400$	0	0
$401$	6.22282	0.310753	0.155377	−	0.987855i	$-0.450341\pi$
$401$	6.22282	0.310753	0.155377	+	0.987855i	$0.450341\pi$
$402$	31.9846	1.59525
$403$	−8.96216	−0.446437
$404$	5.58426	0.277827
$405$	0	0
$406$	−14.9622	−0.742559
$407$	8.56620	0.424611
$408$	5.44059	0.269349
$409$	33.9846	1.68043	0.840215	−	0.542253i	$-0.182429\pi$
$409$	33.9846	1.68043	0.840215	+	0.542253i	$0.182429\pi$
$410$	0	0
$411$	8.66606	0.427465
$412$	−3.89485	−0.191886
$413$	4.00000	0.196827
$414$	45.2074	2.22182
$415$	0	0
$416$	17.3960	0.852907
$417$	−37.9846	−1.86011
$418$	−7.98459	−0.390539
$419$	33.3977	1.63158	0.815792	−	0.578345i	$-0.196301\pi$
$419$	33.3977	1.63158	0.815792	+	0.578345i	$0.196301\pi$
$420$	0	0
$421$	7.06201	0.344182	0.172091	−	0.985081i	$-0.444948\pi$
$421$	7.06201	0.344182	0.172091	+	0.985081i	$0.444948\pi$
$422$	14.4061	0.701277
$423$	31.6507	1.53891
$424$	−1.64892	−0.0800785
$425$	0	0
$426$	73.4975	3.56097
$427$	4.51122	0.218313
$428$	−26.5259	−1.28218
$429$	−12.0396	−0.581276
$430$	0	0
$431$	−31.2978	−1.50756	−0.753782	−	0.657125i	$-0.771772\pi$
$431$	−31.2978	−1.50756	−0.753782	+	0.657125i	$0.771772\pi$
$432$	7.03014	0.338238
$433$	26.7712	1.28654	0.643271	−	0.765638i	$-0.277577\pi$
$433$	26.7712	1.28654	0.643271	+	0.765638i	$0.277577\pi$
$434$	−7.31324	−0.351047
$435$	0	0
$436$	−9.45797	−0.452955
$437$	13.7143	0.656042
$438$	−41.5130	−1.98357
$439$	−15.7065	−0.749633	−0.374816	−	0.927099i	$-0.622294\pi$
$439$	−15.7065	−0.749633	−0.374816	+	0.927099i	$0.622294\pi$
$440$	0	0
$441$	3.59899	0.171380
$442$	−14.4536	−0.687487
$443$	−33.8168	−1.60668	−0.803341	−	0.595519i	$-0.796946\pi$
$443$	−33.8168	−1.60668	−0.803341	+	0.595519i	$0.796946\pi$
$444$	18.2272	0.865025
$445$	0	0
$446$	8.74175	0.413934
$447$	−4.53192	−0.214352
$448$	5.05763	0.238951
$449$	19.9270	0.940411	0.470206	−	0.882557i	$-0.344180\pi$
$449$	19.9270	0.940411	0.470206	+	0.882557i	$0.344180\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−29.0422	−1.36603
$453$	3.97930	0.186964
$454$	0.671352	0.0315081
$455$	0	0
$456$	3.52157	0.164912
$457$	−30.5662	−1.42983	−0.714913	−	0.699213i	$-0.753534\pi$
$457$	−30.5662	−1.42983	−0.714913	+	0.699213i	$0.753534\pi$
$458$	−13.2030	−0.616937
$459$	−4.96307	−0.231656
$460$	0	0
$461$	−32.3203	−1.50530	−0.752652	−	0.658418i	$-0.771226\pi$
$461$	−32.3203	−1.50530	−0.752652	+	0.658418i	$0.771226\pi$
$462$	−9.82446	−0.457075
$463$	−2.16013	−0.100390	−0.0501950	−	0.998739i	$-0.515984\pi$
$463$	−2.16013	−0.100390	−0.0501950	+	0.998739i	$0.515984\pi$
$464$	−35.7488	−1.65960
$465$	0	0
$466$	−55.4681	−2.56951
$467$	33.9692	1.57191	0.785953	−	0.618286i	$-0.212173\pi$
$467$	33.9692	1.57191	0.785953	+	0.618286i	$0.212173\pi$
$468$	−13.9716	−0.645837
$469$	6.51122	0.300660
$470$	0	0
$471$	−35.5836	−1.63960
$472$	2.62648	0.120894
$473$	14.2204	0.653855
$474$	5.58864	0.256695
$475$	0	0
$476$	−5.34338	−0.244913
$477$	9.03784	0.413814
$478$	−54.4905	−2.49234
$479$	−12.3779	−0.565561	−0.282780	−	0.959185i	$-0.591257\pi$
$479$	−12.3779	−0.565561	−0.282780	+	0.959185i	$0.591257\pi$
$480$	0	0
$481$	10.0369	0.457645
$482$	39.9692	1.82055
$483$	16.8744	0.767811
$484$	−11.5963	−0.527107
$485$	0	0
$486$	42.4476	1.92546
$487$	−18.4080	−0.834148	−0.417074	−	0.908873i	$-0.636944\pi$
$487$	−18.4080	−0.834148	−0.417074	+	0.908873i	$0.636944\pi$
$488$	2.96216	0.134091
$489$	−62.6232	−2.83192
$490$	0	0
$491$	14.3330	0.646841	0.323420	−	0.946255i	$-0.395167\pi$
$491$	14.3330	0.646841	0.323420	+	0.946255i	$0.395167\pi$
$492$	4.25561	0.191858
$493$	25.2376	1.13664
$494$	−9.35547	−0.420922
$495$	0	0
$496$	−17.4734	−0.784578
$497$	14.9622	0.671144
$498$	−47.3977	−2.12394
$499$	−17.8245	−0.797932	−0.398966	−	0.916966i	$-0.630631\pi$
$499$	−17.8245	−0.797932	−0.398966	+	0.916966i	$0.630631\pi$
$500$	0	0
$501$	31.3082	1.39875
$502$	10.4663	0.467136
$503$	−5.98195	−0.266722	−0.133361	−	0.991068i	$-0.542577\pi$
$503$	−5.98195	−0.266722	−0.133361	+	0.991068i	$0.542577\pi$
$504$	2.36317	0.105264
$505$	0	0
$506$	−25.1223	−1.11682
$507$	19.2884	0.856628
$508$	33.8667	1.50259
$509$	26.6791	1.18253	0.591264	−	0.806478i	$-0.298629\pi$
$509$	26.6791	1.18253	0.591264	+	0.806478i	$0.298629\pi$
$510$	0	0
$511$	−8.45094	−0.373848
$512$	27.9166	1.23375
$513$	−3.21248	−0.141834
$514$	−38.3253	−1.69046
$515$	0	0
$516$	30.2583	1.33205
$517$	−17.5886	−0.773547
$518$	8.19027	0.359860
$519$	23.9243	1.05016
$520$	0	0
$521$	−35.8115	−1.56893	−0.784464	−	0.620174i	$-0.787062\pi$
$521$	−35.8115	−1.56893	−0.784464	+	0.620174i	$0.787062\pi$
$522$	53.8486	2.35689
$523$	−32.2600	−1.41063	−0.705315	−	0.708894i	$-0.749195\pi$
$523$	−32.2600	−1.41063	−0.705315	+	0.708894i	$0.749195\pi$
$524$	1.59393	0.0696312
$525$	0	0
$526$	16.0449	0.699590
$527$	12.3357	0.537350
$528$	−23.4734	−1.02155
$529$	20.1498	0.876078
$530$	0	0
$531$	−14.3960	−0.624731
$532$	−3.45864	−0.149951
$533$	2.34338	0.101503
$534$	83.2842	3.60406
$535$	0	0
$536$	4.27540	0.184669
$537$	−31.5337	−1.36078
$538$	44.3304	1.91122
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	22.5233	0.968352	0.484176	−	0.874971i	$-0.339119\pi$
$541$	22.5233	0.968352	0.484176	+	0.874971i	$0.339119\pi$
$542$	−38.9916	−1.67483
$543$	−35.3649	−1.51765
$544$	−23.9441	−1.02660
$545$	0	0
$546$	−11.5112	−0.492635
$547$	−3.94501	−0.168677	−0.0843383	−	0.996437i	$-0.526878\pi$
$547$	−3.94501	−0.168677	−0.0843383	+	0.996437i	$0.526878\pi$
$548$	−5.58864	−0.238735
$549$	−16.2358	−0.692928
$550$	0	0
$551$	16.3357	0.695923
$552$	11.0801	0.471599
$553$	1.13770	0.0483799
$554$	−35.4784	−1.50733
$555$	0	0
$556$	24.4958	1.03885
$557$	1.08271	0.0458760	0.0229380	−	0.999737i	$-0.492698\pi$
$557$	1.08271	0.0458760	0.0229380	+	0.999737i	$0.492698\pi$
$558$	26.3203	1.11423
$559$	16.6619	0.704724
$560$	0	0
$561$	16.5715	0.699649
$562$	−30.3753	−1.28130
$563$	15.5568	0.655639	0.327820	−	0.944740i	$-0.393686\pi$
$563$	15.5568	0.655639	0.327820	+	0.944740i	$0.393686\pi$
$564$	−37.4252	−1.57588
$565$	0	0
$566$	−39.4426	−1.65789
$567$	6.84425	0.287431
$568$	9.82446	0.412225
$569$	23.7521	0.995740	0.497870	−	0.867252i	$-0.334116\pi$
$569$	23.7521	0.995740	0.497870	+	0.867252i	$0.334116\pi$
$570$	0	0
$571$	−43.5886	−1.82413	−0.912064	−	0.410048i	$-0.865512\pi$
$571$	−43.5886	−1.82413	−0.912064	+	0.410048i	$0.865512\pi$
$572$	7.76418	0.324637
$573$	23.9243	0.999453
$574$	1.91223	0.0798149
$575$	0	0
$576$	−18.2024	−0.758432
$577$	−36.0422	−1.50046	−0.750229	−	0.661178i	$-0.770057\pi$
$577$	−36.0422	−1.50046	−0.750229	+	0.661178i	$0.770057\pi$
$578$	−12.6137	−0.524662
$579$	18.7866	0.780745
$580$	0	0
$581$	−9.64892	−0.400305
$582$	80.5277	3.33798
$583$	−5.02243	−0.208008
$584$	−5.54906	−0.229622
$585$	0	0
$586$	−47.7039	−1.97063
$587$	−30.9347	−1.27681	−0.638405	−	0.769701i	$-0.720406\pi$
$587$	−30.9347	−1.27681	−0.638405	+	0.769701i	$0.720406\pi$
$588$	−4.25561	−0.175498
$589$	7.98459	0.328999
$590$	0	0
$591$	42.1894	1.73544
$592$	19.5688	0.804275
$593$	−20.2831	−0.832927	−0.416464	−	0.909152i	$-0.636731\pi$
$593$	−20.2831	−0.832927	−0.416464	+	0.909152i	$0.636731\pi$
$594$	5.88474	0.241454
$595$	0	0
$596$	2.92258	0.119713
$597$	23.4536	0.959891
$598$	−29.4355	−1.20371
$599$	5.71161	0.233370	0.116685	−	0.993169i	$-0.462773\pi$
$599$	5.71161	0.233370	0.116685	+	0.993169i	$0.462773\pi$
$600$	0	0
$601$	−17.3253	−0.706715	−0.353357	−	0.935488i	$-0.614960\pi$
$601$	−17.3253	−0.706715	−0.353357	+	0.935488i	$0.614960\pi$
$602$	13.5963	0.554146
$603$	−23.4338	−0.954298
$604$	−2.56620	−0.104417
$605$	0	0
$606$	−16.5585	−0.672643
$607$	−20.3753	−0.827006	−0.413503	−	0.910503i	$-0.635695\pi$
$607$	−20.3753	−0.827006	−0.413503	+	0.910503i	$0.635695\pi$
$608$	−15.4985	−0.628545
$609$	20.0999	0.814487
$610$	0	0
$611$	−20.6084	−0.833728
$612$	19.2308	0.777357
$613$	−3.25561	−0.131493	−0.0657464	−	0.997836i	$-0.520943\pi$
$613$	−3.25561	−0.131493	−0.0657464	+	0.997836i	$0.520943\pi$
$614$	19.5438	0.788722
$615$	0	0
$616$	−1.31324	−0.0529120
$617$	13.7970	0.555445	0.277722	−	0.960661i	$-0.410420\pi$
$617$	13.7970	0.555445	0.277722	+	0.960661i	$0.410420\pi$
$618$	11.5491	0.464571
$619$	36.2600	1.45741	0.728706	−	0.684827i	$-0.240122\pi$
$619$	36.2600	1.45741	0.728706	+	0.684827i	$0.240122\pi$
$620$	0	0
$621$	−10.1076	−0.405602
$622$	−31.6258	−1.26808
$623$	16.9545	0.679266
$624$	−27.5035	−1.10102
$625$	0	0
$626$	−31.5105	−1.25941
$627$	10.7263	0.428369
$628$	22.9474	0.915702
$629$	−13.8150	−0.550841
$630$	0	0
$631$	−39.0543	−1.55473	−0.777364	−	0.629051i	$-0.783444\pi$
$631$	−39.0543	−1.55473	−0.777364	+	0.629051i	$0.783444\pi$
$632$	0.747037	0.0297155
$633$	−19.3528	−0.769206
$634$	−24.6714	−0.979825
$635$	0	0
$636$	−10.6868	−0.423758
$637$	−2.34338	−0.0928481
$638$	−29.9243	−1.18471
$639$	−53.8486	−2.13022
$640$	0	0
$641$	−3.15311	−0.124540	−0.0622701	−	0.998059i	$-0.519834\pi$
$641$	−3.15311	−0.124540	−0.0622701	+	0.998059i	$0.519834\pi$
$642$	78.6550	3.10427
$643$	34.3521	1.35472	0.677358	−	0.735653i	$-0.263125\pi$
$643$	34.3521	1.35472	0.677358	+	0.735653i	$0.263125\pi$
$644$	−10.8821	−0.428814
$645$	0	0
$646$	12.8770	0.506640
$647$	−37.4681	−1.47302	−0.736511	−	0.676425i	$-0.763528\pi$
$647$	−37.4681	−1.47302	−0.736511	+	0.676425i	$0.763528\pi$
$648$	4.49407	0.176544
$649$	8.00000	0.314027
$650$	0	0
$651$	9.82446	0.385051
$652$	40.3849	1.58160
$653$	−43.9089	−1.71829	−0.859144	−	0.511734i	$-0.829003\pi$
$653$	−43.9089	−1.71829	−0.859144	+	0.511734i	$0.829003\pi$
$654$	28.0449	1.09664
$655$	0	0
$656$	4.56885	0.178384
$657$	30.4148	1.18660
$658$	−16.8168	−0.655585
$659$	11.1531	0.434463	0.217232	−	0.976120i	$-0.430297\pi$
$659$	11.1531	0.434463	0.217232	+	0.976120i	$0.430297\pi$
$660$	0	0
$661$	−20.7866	−0.808506	−0.404253	−	0.914647i	$-0.632468\pi$
$661$	−20.7866	−0.808506	−0.404253	+	0.914647i	$0.632468\pi$
$662$	42.0690	1.63506
$663$	19.4167	0.754080
$664$	−6.33568	−0.245872
$665$	0	0
$666$	−29.4767	−1.14220
$667$	51.3977	1.99013
$668$	−20.1903	−0.781185
$669$	−11.7435	−0.454029
$670$	0	0
$671$	9.02243	0.348307
$672$	−19.0697	−0.735630
$673$	−30.1548	−1.16238	−0.581192	−	0.813767i	$-0.697413\pi$
$673$	−30.1548	−1.16238	−0.581192	+	0.813767i	$0.697413\pi$
$674$	8.40101	0.323595
$675$	0	0
$676$	−12.4389	−0.478417
$677$	−21.1826	−0.814112	−0.407056	−	0.913403i	$-0.633445\pi$
$677$	−21.1826	−0.814112	−0.407056	+	0.913403i	$0.633445\pi$
$678$	86.1163	3.30728
$679$	16.3933	0.629117
$680$	0	0
$681$	−0.901880	−0.0345601
$682$	−14.6265	−0.560077
$683$	49.7435	1.90338	0.951691	−	0.307058i	$-0.0993446\pi$
$683$	49.7435	1.90338	0.951691	+	0.307058i	$0.0993446\pi$
$684$	12.4476	0.475947
$685$	0	0
$686$	−1.91223	−0.0730092
$687$	17.7367	0.676697
$688$	32.4855	1.23850
$689$	−5.88474	−0.224191
$690$	0	0
$691$	29.8168	1.13428	0.567141	−	0.823620i	$-0.308049\pi$
$691$	29.8168	1.13428	0.567141	+	0.823620i	$0.308049\pi$
$692$	−15.4285	−0.586504
$693$	7.19798	0.273429
$694$	34.4201	1.30657
$695$	0	0
$696$	13.1980	0.500268
$697$	−3.22547	−0.122173
$698$	36.1548	1.36848
$699$	74.5147	2.81840
$700$	0	0
$701$	−41.1696	−1.55495	−0.777477	−	0.628912i	$-0.783501\pi$
$701$	−41.1696	−1.55495	−0.777477	+	0.628912i	$0.783501\pi$
$702$	6.89508	0.260238
$703$	−8.94214	−0.337259
$704$	10.1153	0.381233
$705$	0	0
$706$	29.3977	1.10640
$707$	−3.37087	−0.126775
$708$	17.0224	0.639742
$709$	−31.8794	−1.19726	−0.598629	−	0.801027i	$-0.704288\pi$
$709$	−31.8794	−1.19726	−0.598629	+	0.801027i	$0.704288\pi$
$710$	0	0
$711$	−4.09457	−0.153558
$712$	11.1326	0.417213
$713$	25.1223	0.940837
$714$	15.8442	0.592956
$715$	0	0
$716$	20.3357	0.759980
$717$	73.2015	2.73376
$718$	−21.1973	−0.791076
$719$	43.2978	1.61474	0.807368	−	0.590048i	$-0.200891\pi$
$719$	43.2978	1.61474	0.807368	+	0.590048i	$0.200891\pi$
$720$	0	0
$721$	2.35108	0.0875589
$722$	−27.9974	−1.04195
$723$	−53.6938	−1.99689
$724$	22.8064	0.847593
$725$	0	0
$726$	34.3856	1.27617
$727$	−13.9672	−0.518015	−0.259008	−	0.965875i	$-0.583395\pi$
$727$	−13.9672	−0.518015	−0.259008	+	0.965875i	$0.583395\pi$
$728$	−1.53871	−0.0570284
$729$	−36.4905	−1.35150
$730$	0	0
$731$	−22.9338	−0.848236
$732$	19.1980	0.709578
$733$	3.38893	0.125173	0.0625864	−	0.998040i	$-0.480065\pi$
$733$	3.38893	0.125173	0.0625864	+	0.998040i	$0.480065\pi$
$734$	−16.3907	−0.604990
$735$	0	0
$736$	−48.7635	−1.79745
$737$	13.0224	0.479688
$738$	−6.88209	−0.253333
$739$	8.33809	0.306722	0.153361	−	0.988170i	$-0.450990\pi$
$739$	8.33809	0.306722	0.153361	+	0.988170i	$0.450990\pi$
$740$	0	0
$741$	12.5679	0.461695
$742$	−4.80202	−0.176288
$743$	42.7833	1.56957	0.784783	−	0.619770i	$-0.212774\pi$
$743$	42.7833	1.56957	0.784783	+	0.619770i	$0.212774\pi$
$744$	6.45094	0.236503
$745$	0	0
$746$	31.4054	1.14983
$747$	34.7263	1.27057
$748$	−10.6868	−0.390747
$749$	16.0121	0.585069
$750$	0	0
$751$	12.0396	0.439330	0.219665	−	0.975575i	$-0.429503\pi$
$751$	12.0396	0.439330	0.219665	+	0.975575i	$0.429503\pi$
$752$	−40.1799	−1.46521
$753$	−14.0603	−0.512385
$754$	−35.0620	−1.27688
$755$	0	0
$756$	2.54906	0.0927084
$757$	−2.35108	−0.0854516	−0.0427258	−	0.999087i	$-0.513604\pi$
$757$	−2.35108	−0.0854516	−0.0427258	+	0.999087i	$0.513604\pi$
$758$	2.73669	0.0994010
$759$	33.7488	1.22500
$760$	0	0
$761$	35.6938	1.29390	0.646949	−	0.762533i	$-0.276044\pi$
$761$	35.6938	1.29390	0.646949	+	0.762533i	$0.276044\pi$
$762$	−100.422	−3.63790
$763$	5.70919	0.206687
$764$	−15.4285	−0.558184
$765$	0	0
$766$	−25.2325	−0.911687
$767$	9.37352	0.338458
$768$	−51.4080	−1.85503
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	0	0
$771$	51.4855	1.85420
$772$	−12.1153	−0.436038
$773$	−25.9069	−0.931808	−0.465904	−	0.884835i	$-0.654271\pi$
$773$	−25.9069	−0.931808	−0.465904	+	0.884835i	$0.654271\pi$
$774$	−48.9331	−1.75886
$775$	0	0
$776$	10.7642	0.386412
$777$	−11.0026	−0.394718
$778$	17.7943	0.637957
$779$	−2.08777	−0.0748022
$780$	0	0
$781$	29.9243	1.07078
$782$	40.5156	1.44883
$783$	−12.0396	−0.430259
$784$	−4.56885	−0.163173
$785$	0	0
$786$	−4.72634	−0.168583
$787$	−8.11526	−0.289278	−0.144639	−	0.989484i	$-0.546202\pi$
$787$	−8.11526	−0.289278	−0.144639	+	0.989484i	$0.546202\pi$
$788$	−27.2074	−0.969224
$789$	−21.5544	−0.767355
$790$	0	0
$791$	17.5310	0.623331
$792$	4.72634	0.167943
$793$	10.5715	0.375405
$794$	2.48175	0.0880742
$795$	0	0
$796$	−15.1249	−0.536089
$797$	46.4302	1.64464	0.822322	−	0.569023i	$-0.192678\pi$
$797$	46.4302	1.64464	0.822322	+	0.569023i	$0.192678\pi$
$798$	10.2556	0.363045
$799$	28.3658	1.00351
$800$	0	0
$801$	−61.0189	−2.15600
$802$	11.8995	0.420185
$803$	−16.9019	−0.596454
$804$	27.7092	0.977228
$805$	0	0
$806$	−17.1377	−0.603650
$807$	−59.5525	−2.09635
$808$	−2.21338	−0.0778666
$809$	28.4958	1.00186	0.500930	−	0.865488i	$-0.332992\pi$
$809$	28.4958	1.00186	0.500930	+	0.865488i	$0.332992\pi$
$810$	0	0
$811$	−14.1755	−0.497771	−0.248885	−	0.968533i	$-0.580064\pi$
$811$	−14.1755	−0.497771	−0.248885	+	0.968533i	$0.580064\pi$
$812$	−12.9622	−0.454883
$813$	52.3805	1.83707
$814$	16.3805	0.574138
$815$	0	0
$816$	37.8563	1.32524
$817$	−14.8445	−0.519343
$818$	64.9863	2.27219
$819$	8.43380	0.294701
$820$	0	0
$821$	−3.92764	−0.137075	−0.0685377	−	0.997649i	$-0.521833\pi$
$821$	−3.92764	−0.137075	−0.0685377	+	0.997649i	$0.521833\pi$
$822$	16.5715	0.577997
$823$	12.5662	0.438030	0.219015	−	0.975721i	$-0.429716\pi$
$823$	12.5662	0.438030	0.219015	+	0.975721i	$0.429716\pi$
$824$	1.54377	0.0537798
$825$	0	0
$826$	7.64892	0.266140
$827$	13.5337	0.470611	0.235306	−	0.971921i	$-0.424391\pi$
$827$	13.5337	0.470611	0.235306	+	0.971921i	$0.424391\pi$
$828$	39.1645	1.36106
$829$	−46.3753	−1.61068	−0.805340	−	0.592814i	$-0.798017\pi$
$829$	−46.3753	−1.61068	−0.805340	+	0.592814i	$0.798017\pi$
$830$	0	0
$831$	47.6610	1.65334
$832$	11.8520	0.410892
$833$	3.22547	0.111756
$834$	−72.6352	−2.51515
$835$	0	0
$836$	−6.91729	−0.239239
$837$	−5.88474	−0.203406
$838$	63.8640	2.20615
$839$	39.8218	1.37480	0.687401	−	0.726278i	$-0.258752\pi$
$839$	39.8218	1.37480	0.687401	+	0.726278i	$0.258752\pi$
$840$	0	0
$841$	32.2221	1.11111
$842$	13.5042	0.465385
$843$	40.8055	1.40542
$844$	12.4804	0.429593
$845$	0	0
$846$	60.5233	2.08083
$847$	7.00000	0.240523
$848$	−11.4734	−0.393997
$849$	52.9863	1.81849
$850$	0	0
$851$	−28.1351	−0.964457
$852$	63.6731	2.18140
$853$	27.8245	0.952691	0.476346	−	0.879258i	$-0.341961\pi$
$853$	27.8245	0.952691	0.476346	+	0.879258i	$0.341961\pi$
$854$	8.62648	0.295192
$855$	0	0
$856$	10.5139	0.359356
$857$	−9.09812	−0.310786	−0.155393	−	0.987853i	$-0.549664\pi$
$857$	−9.09812	−0.310786	−0.155393	+	0.987853i	$0.549664\pi$
$858$	−23.0224	−0.785973
$859$	6.55080	0.223510	0.111755	−	0.993736i	$-0.464353\pi$
$859$	6.55080	0.223510	0.111755	+	0.993736i	$0.464353\pi$
$860$	0	0
$861$	−2.56885	−0.0875462
$862$	−59.8486	−2.03845
$863$	−2.04487	−0.0696082	−0.0348041	−	0.999394i	$-0.511081\pi$
$863$	−2.04487	−0.0696082	−0.0348041	+	0.999394i	$0.511081\pi$
$864$	11.4225	0.388603
$865$	0	0
$866$	51.1927	1.73960
$867$	16.9450	0.575483
$868$	−6.33568	−0.215047
$869$	2.27540	0.0771876
$870$	0	0
$871$	15.2583	0.517006
$872$	3.74877	0.126949
$873$	−58.9993	−1.99682
$874$	26.2248	0.887067
$875$	0	0
$876$	−35.9639	−1.21511
$877$	36.3625	1.22787	0.613937	−	0.789355i	$-0.289585\pi$
$877$	36.3625	1.22787	0.613937	+	0.789355i	$0.289585\pi$
$878$	−30.0345	−1.01362
$879$	64.0844	2.16151
$880$	0	0
$881$	−11.9344	−0.402081	−0.201041	−	0.979583i	$-0.564432\pi$
$881$	−11.9344	−0.402081	−0.201041	+	0.979583i	$0.564432\pi$
$882$	6.88209	0.231732
$883$	−27.6643	−0.930979	−0.465489	−	0.885053i	$-0.654122\pi$
$883$	−27.6643	−0.930979	−0.465489	+	0.885053i	$0.654122\pi$
$884$	−12.5216	−0.421146
$885$	0	0
$886$	−64.6654	−2.17248
$887$	−21.4811	−0.721264	−0.360632	−	0.932708i	$-0.617439\pi$
$887$	−21.4811	−0.721264	−0.360632	+	0.932708i	$0.617439\pi$
$888$	−7.22456	−0.242440
$889$	−20.4432	−0.685644
$890$	0	0
$891$	13.6885	0.458582
$892$	7.57323	0.253571
$893$	18.3605	0.614412
$894$	−8.66606	−0.289836
$895$	0	0
$896$	−5.17554	−0.172903
$897$	39.5431	1.32031
$898$	38.1049	1.27158
$899$	29.9243	0.998032
$900$	0	0
$901$	8.09986	0.269845
$902$	3.82446	0.127341
$903$	−18.2650	−0.607823
$904$	11.5112	0.382857
$905$	0	0
$906$	7.60934	0.252803
$907$	−14.3676	−0.477067	−0.238533	−	0.971134i	$-0.576667\pi$
$907$	−14.3676	−0.477067	−0.238533	+	0.971134i	$0.576667\pi$
$908$	0.581612	0.0193015
$909$	12.1317	0.402384
$910$	0	0
$911$	21.6161	0.716174	0.358087	−	0.933688i	$-0.383429\pi$
$911$	21.6161	0.716174	0.358087	+	0.933688i	$0.383429\pi$
$912$	24.5035	0.811392
$913$	−19.2978	−0.638665
$914$	−58.4496	−1.93334
$915$	0	0
$916$	−11.4382	−0.377928
$917$	−0.962158	−0.0317732
$918$	−9.49052	−0.313234
$919$	−27.4888	−0.906771	−0.453386	−	0.891314i	$-0.649784\pi$
$919$	−27.4888	−0.906771	−0.453386	+	0.891314i	$0.649784\pi$
$920$	0	0
$921$	−26.2547	−0.865122
$922$	−61.8038	−2.03540
$923$	35.0620	1.15408
$924$	−8.51122	−0.279998
$925$	0	0
$926$	−4.13067	−0.135742
$927$	−8.46152	−0.277913
$928$	−58.0844	−1.90672
$929$	10.3176	0.338510	0.169255	−	0.985572i	$-0.445864\pi$
$929$	10.3176	0.338510	0.169255	+	0.985572i	$0.445864\pi$
$930$	0	0
$931$	2.08777	0.0684239
$932$	−48.0536	−1.57405
$933$	42.4855	1.39091
$934$	64.9569	2.12545
$935$	0	0
$936$	5.53780	0.181009
$937$	32.8031	1.07163	0.535815	−	0.844335i	$-0.320004\pi$
$937$	32.8031	1.07163	0.535815	+	0.844335i	$0.320004\pi$
$938$	12.4509	0.406538
$939$	42.3306	1.38141
$940$	0	0
$941$	−13.0070	−0.424017	−0.212008	−	0.977268i	$-0.568000\pi$
$941$	−13.0070	−0.424017	−0.212008	+	0.977268i	$0.568000\pi$
$942$	−68.0440	−2.21699
$943$	−6.56885	−0.213911
$944$	18.2754	0.594814
$945$	0	0
$946$	27.1927	0.884110
$947$	16.4985	0.536128	0.268064	−	0.963401i	$-0.413616\pi$
$947$	16.4985	0.536128	0.268064	+	0.963401i	$0.413616\pi$
$948$	4.84160	0.157248
$949$	−19.8038	−0.642857
$950$	0	0
$951$	33.1430	1.07474
$952$	2.11791	0.0686418
$953$	13.6258	0.441383	0.220692	−	0.975344i	$-0.429169\pi$
$953$	13.6258	0.441383	0.220692	+	0.975344i	$0.429169\pi$
$954$	17.2824	0.559539
$955$	0	0
$956$	−47.2067	−1.52678
$957$	40.1997	1.29947
$958$	−23.6694	−0.764723
$959$	3.37352	0.108937
$960$	0	0
$961$	−16.3735	−0.528178
$962$	19.1929	0.618805
$963$	−57.6273	−1.85701
$964$	34.6265	1.11524
$965$	0	0
$966$	32.2677	1.03820
$967$	17.5182	0.563349	0.281674	−	0.959510i	$-0.409110\pi$
$967$	17.5182	0.563349	0.281674	+	0.959510i	$0.409110\pi$
$968$	4.59634	0.147732
$969$	−17.2987	−0.555716
$970$	0	0
$971$	59.6852	1.91539	0.957694	−	0.287788i	$-0.0929198\pi$
$971$	59.6852	1.91539	0.957694	+	0.287788i	$0.0929198\pi$
$972$	36.7736	1.17951
$973$	−14.7866	−0.474037
$974$	−35.2004	−1.12789
$975$	0	0
$976$	20.6111	0.659744
$977$	54.0295	1.72856	0.864278	−	0.503015i	$-0.167776\pi$
$977$	54.0295	1.72856	0.864278	+	0.503015i	$0.167776\pi$
$978$	−119.750	−3.82918
$979$	33.9089	1.08373
$980$	0	0
$981$	−20.5473	−0.656026
$982$	27.4080	0.874626
$983$	37.5337	1.19714	0.598569	−	0.801071i	$-0.295736\pi$
$983$	37.5337	1.19714	0.598569	+	0.801071i	$0.295736\pi$
$984$	−1.68676	−0.0537719
$985$	0	0
$986$	48.2600	1.53691
$987$	22.5913	0.719089
$988$	−8.10492	−0.257852
$989$	−46.7059	−1.48516
$990$	0	0
$991$	12.0242	0.381960	0.190980	−	0.981594i	$-0.438833\pi$
$991$	12.0242	0.381960	0.190980	+	0.981594i	$0.438833\pi$
$992$	−28.3907	−0.901404
$993$	−56.5147	−1.79344
$994$	28.6111	0.907488
$995$	0	0
$996$	−41.0620	−1.30110
$997$	−52.0114	−1.64722	−0.823609	−	0.567158i	$-0.808043\pi$
$997$	−52.0114	−1.64722	−0.823609	+	0.567158i	$0.808043\pi$
$998$	−34.0844	−1.07892
$999$	6.59046	0.208513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7175.2.a.k.1.3		3
5.4	even	2		287.2.a.c.1.1	✓	3
15.14	odd	2		2583.2.a.m.1.3		3
20.19	odd	2		4592.2.a.t.1.1		3
35.34	odd	2		2009.2.a.j.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.c.1.1	✓	3	5.4	even	2
2009.2.a.j.1.1		3	35.34	odd	2
2583.2.a.m.1.3		3	15.14	odd	2
4592.2.a.t.1.1		3	20.19	odd	2
7175.2.a.k.1.3		3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7175 = 5^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7175.a (trivial)

\(f(q)\)	\(=\)	\(q+1.91223 q^{2} -2.56885 q^{3} +1.65662 q^{4} -4.91223 q^{6} -1.00000 q^{7} -0.656620 q^{8} +3.59899 q^{9} +O(q^{10})\)	\(q+1.91223 q^{2} -2.56885 q^{3} +1.65662 q^{4} -4.91223 q^{6} -1.00000 q^{7} -0.656620 q^{8} +3.59899 q^{9} -2.00000 q^{11} -4.25561 q^{12} -2.34338 q^{13} -1.91223 q^{14} -4.56885 q^{16} +3.22547 q^{17} +6.88209 q^{18} +2.08777 q^{19} +2.56885 q^{21} -3.82446 q^{22} +6.56885 q^{23} +1.68676 q^{24} -4.48108 q^{26} -1.53871 q^{27} -1.65662 q^{28} +7.82446 q^{29} +3.82446 q^{31} -7.42345 q^{32} +5.13770 q^{33} +6.16784 q^{34} +5.96216 q^{36} -4.28310 q^{37} +3.99230 q^{38} +6.01979 q^{39} -1.00000 q^{41} +4.91223 q^{42} -7.11021 q^{43} -3.31324 q^{44} +12.5611 q^{46} +8.79432 q^{47} +11.7367 q^{48} +1.00000 q^{49} -8.28575 q^{51} -3.88209 q^{52} +2.51122 q^{53} -2.94237 q^{54} +0.656620 q^{56} -5.36317 q^{57} +14.9622 q^{58} -4.00000 q^{59} -4.51122 q^{61} +7.31324 q^{62} -3.59899 q^{63} -5.05763 q^{64} +9.82446 q^{66} -6.51122 q^{67} +5.34338 q^{68} -16.8744 q^{69} -14.9622 q^{71} -2.36317 q^{72} +8.45094 q^{73} -8.19027 q^{74} +3.45864 q^{76} +2.00000 q^{77} +11.5112 q^{78} -1.13770 q^{79} -6.84425 q^{81} -1.91223 q^{82} +9.64892 q^{83} +4.25561 q^{84} -13.5963 q^{86} -20.0999 q^{87} +1.31324 q^{88} -16.9545 q^{89} +2.34338 q^{91} +10.8821 q^{92} -9.82446 q^{93} +16.8168 q^{94} +19.0697 q^{96} -16.3933 q^{97} +1.91223 q^{98} -7.19798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{3} + 3 q^{4} - 8 q^{6} - 3 q^{7} + 8 q^{9}+O(q^{10}) \) 3 * q - q^2 + q^3 + 3 * q^4 - 8 * q^6 - 3 * q^7 + 8 * q^9	\( 3 q - q^{2} + q^{3} + 3 q^{4} - 8 q^{6} - 3 q^{7} + 8 q^{9} - 6 q^{11} - 8 q^{12} - 9 q^{13} + q^{14} - 5 q^{16} - q^{17} + 8 q^{18} + 13 q^{19} - q^{21} + 2 q^{22} + 11 q^{23} + 9 q^{24} + 2 q^{26} + 10 q^{27} - 3 q^{28} + 10 q^{29} - 2 q^{31} - 6 q^{32} - 2 q^{33} + 7 q^{34} - 13 q^{36} - 3 q^{37} - 13 q^{38} - 12 q^{39} - 3 q^{41} + 8 q^{42} - 9 q^{43} - 6 q^{44} + 4 q^{46} + 7 q^{47} + 15 q^{48} + 3 q^{49} - 26 q^{51} + q^{52} - 2 q^{53} - 8 q^{54} + 12 q^{57} + 14 q^{58} - 12 q^{59} - 4 q^{61} + 18 q^{62} - 8 q^{63} - 16 q^{64} + 16 q^{66} - 10 q^{67} + 18 q^{68} - 13 q^{69} - 14 q^{71} + 21 q^{72} + 4 q^{73} + 6 q^{74} + 14 q^{76} + 6 q^{77} + 25 q^{78} + 14 q^{79} + 23 q^{81} + q^{82} + 2 q^{83} + 8 q^{84} - 27 q^{86} - 12 q^{87} + 5 q^{89} + 9 q^{91} + 20 q^{92} - 16 q^{93} + 12 q^{94} + 3 q^{96} - 27 q^{97} - q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q - q^2 + q^3 + 3 * q^4 - 8 * q^6 - 3 * q^7 + 8 * q^9 - 6 * q^11 - 8 * q^12 - 9 * q^13 + q^14 - 5 * q^16 - q^17 + 8 * q^18 + 13 * q^19 - q^21 + 2 * q^22 + 11 * q^23 + 9 * q^24 + 2 * q^26 + 10 * q^27 - 3 * q^28 + 10 * q^29 - 2 * q^31 - 6 * q^32 - 2 * q^33 + 7 * q^34 - 13 * q^36 - 3 * q^37 - 13 * q^38 - 12 * q^39 - 3 * q^41 + 8 * q^42 - 9 * q^43 - 6 * q^44 + 4 * q^46 + 7 * q^47 + 15 * q^48 + 3 * q^49 - 26 * q^51 + q^52 - 2 * q^53 - 8 * q^54 + 12 * q^57 + 14 * q^58 - 12 * q^59 - 4 * q^61 + 18 * q^62 - 8 * q^63 - 16 * q^64 + 16 * q^66 - 10 * q^67 + 18 * q^68 - 13 * q^69 - 14 * q^71 + 21 * q^72 + 4 * q^73 + 6 * q^74 + 14 * q^76 + 6 * q^77 + 25 * q^78 + 14 * q^79 + 23 * q^81 + q^82 + 2 * q^83 + 8 * q^84 - 27 * q^86 - 12 * q^87 + 5 * q^89 + 9 * q^91 + 20 * q^92 - 16 * q^93 + 12 * q^94 + 3 * q^96 - 27 * q^97 - q^98 - 16 * q^99

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