LMFDB - Embedded newform 6003.2.a.v.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6003,2,Mod(1,6003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6003, 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("6003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6003 = 3^{2} \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6003.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:	$47.9341963334$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33909 q^{2} -0.206831 q^{4} +0.887651 q^{5} -3.28671 q^{7} +2.95515 q^{8} +O(q^{10})$	\(q-1.33909 q^{2} -0.206831 q^{4} +0.887651 q^{5} -3.28671 q^{7} +2.95515 q^{8} -1.18865 q^{10} +3.91676 q^{11} -3.54751 q^{13} +4.40121 q^{14} -3.54356 q^{16} -3.14467 q^{17} -6.11207 q^{19} -0.183594 q^{20} -5.24490 q^{22} +1.00000 q^{23} -4.21208 q^{25} +4.75044 q^{26} +0.679794 q^{28} -1.00000 q^{29} -5.83045 q^{31} -1.16515 q^{32} +4.21100 q^{34} -2.91745 q^{35} +8.16140 q^{37} +8.18463 q^{38} +2.62314 q^{40} -6.59203 q^{41} +2.19714 q^{43} -0.810107 q^{44} -1.33909 q^{46} -1.28633 q^{47} +3.80245 q^{49} +5.64036 q^{50} +0.733735 q^{52} +1.04074 q^{53} +3.47671 q^{55} -9.71272 q^{56} +1.33909 q^{58} +6.63537 q^{59} +14.9349 q^{61} +7.80752 q^{62} +8.64736 q^{64} -3.14895 q^{65} -2.96633 q^{67} +0.650415 q^{68} +3.90673 q^{70} -5.53027 q^{71} +3.29584 q^{73} -10.9289 q^{74} +1.26417 q^{76} -12.8732 q^{77} -7.93748 q^{79} -3.14544 q^{80} +8.82734 q^{82} +12.6870 q^{83} -2.79137 q^{85} -2.94218 q^{86} +11.5746 q^{88} -0.999574 q^{89} +11.6596 q^{91} -0.206831 q^{92} +1.72251 q^{94} -5.42539 q^{95} +2.10158 q^{97} -5.09183 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - q^{2} + 37 q^{4} + 10 q^{7} - 6 q^{8}+O(q^{10}) $ 30 * q - q^2 + 37 * q^4 + 10 * q^7 - 6 * q^8	$ 30 q - q^{2} + 37 q^{4} + 10 q^{7} - 6 q^{8} + 8 q^{10} + 36 q^{13} - 7 q^{14} + 47 q^{16} - 18 q^{17} + 16 q^{19} + 25 q^{22} + 30 q^{23} + 56 q^{25} - 11 q^{26} + 27 q^{28} - 30 q^{29} + 14 q^{31} + 7 q^{32} + 3 q^{34} + 22 q^{35} + 40 q^{37} - 6 q^{38} + 30 q^{40} - 14 q^{41} + 34 q^{43} - 5 q^{44} - q^{46} + 2 q^{47} + 74 q^{49} + 21 q^{50} + 71 q^{52} - 16 q^{53} + 22 q^{55} - 14 q^{56} + q^{58} + 32 q^{59} + 46 q^{61} - 20 q^{62} + 68 q^{64} - 12 q^{65} + 14 q^{67} - 27 q^{68} + 32 q^{71} + 50 q^{73} + 26 q^{74} + 56 q^{76} - 34 q^{77} + 16 q^{79} - 2 q^{80} + 38 q^{82} + 14 q^{83} + 38 q^{85} - 10 q^{86} + 40 q^{88} + 2 q^{89} + 32 q^{91} + 37 q^{92} + 29 q^{94} + 28 q^{95} + 56 q^{97} - 8 q^{98}+O(q^{100}) $ 30 * q - q^2 + 37 * q^4 + 10 * q^7 - 6 * q^8 + 8 * q^10 + 36 * q^13 - 7 * q^14 + 47 * q^16 - 18 * q^17 + 16 * q^19 + 25 * q^22 + 30 * q^23 + 56 * q^25 - 11 * q^26 + 27 * q^28 - 30 * q^29 + 14 * q^31 + 7 * q^32 + 3 * q^34 + 22 * q^35 + 40 * q^37 - 6 * q^38 + 30 * q^40 - 14 * q^41 + 34 * q^43 - 5 * q^44 - q^46 + 2 * q^47 + 74 * q^49 + 21 * q^50 + 71 * q^52 - 16 * q^53 + 22 * q^55 - 14 * q^56 + q^58 + 32 * q^59 + 46 * q^61 - 20 * q^62 + 68 * q^64 - 12 * q^65 + 14 * q^67 - 27 * q^68 + 32 * q^71 + 50 * q^73 + 26 * q^74 + 56 * q^76 - 34 * q^77 + 16 * q^79 - 2 * q^80 + 38 * q^82 + 14 * q^83 + 38 * q^85 - 10 * q^86 + 40 * q^88 + 2 * q^89 + 32 * q^91 + 37 * q^92 + 29 * q^94 + 28 * q^95 + 56 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.33909	−0.946881	−0.473441	−	0.880826i	$-0.656988\pi$
$2$	−1.33909	−0.946881	−0.473441	+	0.880826i	$0.656988\pi$
$3$	0	0
$3$	0	0
$4$	−0.206831	−0.103416
$5$	0.887651	0.396970	0.198485	−	0.980104i	$-0.436398\pi$
$5$	0.887651	0.396970	0.198485	+	0.980104i	$0.436398\pi$
$6$	0	0
$7$	−3.28671	−1.24226	−0.621129	−	0.783708i	$-0.713326\pi$
$7$	−3.28671	−1.24226	−0.621129	+	0.783708i	$0.713326\pi$
$8$	2.95515	1.04480
$9$	0	0
$10$	−1.18865	−0.375883
$11$	3.91676	1.18095	0.590473	−	0.807057i	$-0.298941\pi$
$11$	3.91676	1.18095	0.590473	+	0.807057i	$0.298941\pi$
$12$	0	0
$13$	−3.54751	−0.983902	−0.491951	−	0.870623i	$-0.663716\pi$
$13$	−3.54751	−0.983902	−0.491951	+	0.870623i	$0.663716\pi$
$14$	4.40121	1.17627
$15$	0	0
$16$	−3.54356	−0.885890
$17$	−3.14467	−0.762694	−0.381347	−	0.924432i	$-0.624540\pi$
$17$	−3.14467	−0.762694	−0.381347	+	0.924432i	$0.624540\pi$
$18$	0	0
$19$	−6.11207	−1.40221	−0.701103	−	0.713060i	$-0.747309\pi$
$19$	−6.11207	−1.40221	−0.701103	+	0.713060i	$0.747309\pi$
$20$	−0.183594	−0.0410528
$21$	0	0
$22$	−5.24490	−1.11822
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−4.21208	−0.842415
$26$	4.75044	0.931638
$27$	0	0
$28$	0.679794	0.128469
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−5.83045	−1.04718	−0.523590	−	0.851970i	$-0.675408\pi$
$31$	−5.83045	−1.04718	−0.523590	+	0.851970i	$0.675408\pi$
$32$	−1.16515	−0.205971
$33$	0	0
$34$	4.21100	0.722181
$35$	−2.91745	−0.493139
$36$	0	0
$37$	8.16140	1.34173	0.670863	−	0.741581i	$-0.265924\pi$
$37$	8.16140	1.34173	0.670863	+	0.741581i	$0.265924\pi$
$38$	8.18463	1.32772
$39$	0	0
$40$	2.62314	0.414755
$41$	−6.59203	−1.02950	−0.514751	−	0.857340i	$-0.672116\pi$
$41$	−6.59203	−1.02950	−0.514751	+	0.857340i	$0.672116\pi$
$42$	0	0
$43$	2.19714	0.335061	0.167531	−	0.985867i	$-0.446421\pi$
$43$	2.19714	0.335061	0.167531	+	0.985867i	$0.446421\pi$
$44$	−0.810107	−0.122128
$45$	0	0
$46$	−1.33909	−0.197438
$47$	−1.28633	−0.187630	−0.0938151	−	0.995590i	$-0.529906\pi$
$47$	−1.28633	−0.187630	−0.0938151	+	0.995590i	$0.529906\pi$
$48$	0	0
$49$	3.80245	0.543207
$50$	5.64036	0.797667
$51$	0	0
$52$	0.733735	0.101751
$53$	1.04074	0.142957	0.0714785	−	0.997442i	$-0.477228\pi$
$53$	1.04074	0.142957	0.0714785	+	0.997442i	$0.477228\pi$
$54$	0	0
$55$	3.47671	0.468800
$56$	−9.71272	−1.29792
$57$	0	0
$58$	1.33909	0.175831
$59$	6.63537	0.863851	0.431926	−	0.901909i	$-0.357834\pi$
$59$	6.63537	0.863851	0.431926	+	0.901909i	$0.357834\pi$
$60$	0	0
$61$	14.9349	1.91222	0.956109	−	0.293011i	$-0.0946573\pi$
$61$	14.9349	1.91222	0.956109	+	0.293011i	$0.0946573\pi$
$62$	7.80752	0.991556
$63$	0	0
$64$	8.64736	1.08092
$65$	−3.14895	−0.390579
$66$	0	0
$67$	−2.96633	−0.362395	−0.181198	−	0.983447i	$-0.557997\pi$
$67$	−2.96633	−0.362395	−0.181198	+	0.983447i	$0.557997\pi$
$68$	0.650415	0.0788744
$69$	0	0
$70$	3.90673	0.466944
$71$	−5.53027	−0.656322	−0.328161	−	0.944622i	$-0.606429\pi$
$71$	−5.53027	−0.656322	−0.328161	+	0.944622i	$0.606429\pi$
$72$	0	0
$73$	3.29584	0.385749	0.192875	−	0.981223i	$-0.438219\pi$
$73$	3.29584	0.385749	0.192875	+	0.981223i	$0.438219\pi$
$74$	−10.9289	−1.27046
$75$	0	0
$76$	1.26417	0.145010
$77$	−12.8732	−1.46704
$78$	0	0
$79$	−7.93748	−0.893036	−0.446518	−	0.894775i	$-0.647336\pi$
$79$	−7.93748	−0.893036	−0.446518	+	0.894775i	$0.647336\pi$
$80$	−3.14544	−0.351671
$81$	0	0
$82$	8.82734	0.974817
$83$	12.6870	1.39258	0.696291	−	0.717760i	$-0.254832\pi$
$83$	12.6870	1.39258	0.696291	+	0.717760i	$0.254832\pi$
$84$	0	0
$85$	−2.79137	−0.302766
$86$	−2.94218	−0.317263
$87$	0	0
$88$	11.5746	1.23386
$89$	−0.999574	−0.105955	−0.0529773	−	0.998596i	$-0.516871\pi$
$89$	−0.999574	−0.105955	−0.0529773	+	0.998596i	$0.516871\pi$
$90$	0	0
$91$	11.6596	1.22226
$92$	−0.206831	−0.0215636
$93$	0	0
$94$	1.72251	0.177664
$95$	−5.42539	−0.556633
$96$	0	0
$97$	2.10158	0.213383	0.106691	−	0.994292i	$-0.465974\pi$
$97$	2.10158	0.213383	0.106691	+	0.994292i	$0.465974\pi$
$98$	−5.09183	−0.514352
$99$	0	0
$100$	0.871189	0.0871189
$101$	2.43909	0.242699	0.121349	−	0.992610i	$-0.461278\pi$
$101$	2.43909	0.242699	0.121349	+	0.992610i	$0.461278\pi$
$102$	0	0
$103$	−4.90445	−0.483250	−0.241625	−	0.970370i	$-0.577680\pi$
$103$	−4.90445	−0.483250	−0.241625	+	0.970370i	$0.577680\pi$
$104$	−10.4834	−1.02798
$105$	0	0
$106$	−1.39365	−0.135363
$107$	−12.5285	−1.21118	−0.605589	−	0.795777i	$-0.707062\pi$
$107$	−12.5285	−1.21118	−0.605589	+	0.795777i	$0.707062\pi$
$108$	0	0
$109$	−7.92090	−0.758684	−0.379342	−	0.925256i	$-0.623850\pi$
$109$	−7.92090	−0.758684	−0.379342	+	0.925256i	$0.623850\pi$
$110$	−4.65564	−0.443898
$111$	0	0
$112$	11.6466	1.10050
$113$	8.12384	0.764227	0.382113	−	0.924115i	$-0.375196\pi$
$113$	8.12384	0.764227	0.382113	+	0.924115i	$0.375196\pi$
$114$	0	0
$115$	0.887651	0.0827739
$116$	0.206831	0.0192038
$117$	0	0
$118$	−8.88537	−0.817965
$119$	10.3356	0.947463
$120$	0	0
$121$	4.34097	0.394634
$122$	−19.9992	−1.81064
$123$	0	0
$124$	1.20592	0.108295
$125$	−8.17711	−0.731383
$126$	0	0
$127$	−8.52190	−0.756196	−0.378098	−	0.925766i	$-0.623422\pi$
$127$	−8.52190	−0.756196	−0.378098	+	0.925766i	$0.623422\pi$
$128$	−9.24932	−0.817532
$129$	0	0
$130$	4.21673	0.369832
$131$	−2.59939	−0.227110	−0.113555	−	0.993532i	$-0.536224\pi$
$131$	−2.59939	−0.227110	−0.113555	+	0.993532i	$0.536224\pi$
$132$	0	0
$133$	20.0886	1.74190
$134$	3.97219	0.343145
$135$	0	0
$136$	−9.29297	−0.796865
$137$	1.97669	0.168880	0.0844398	−	0.996429i	$-0.473090\pi$
$137$	1.97669	0.168880	0.0844398	+	0.996429i	$0.473090\pi$
$138$	0	0
$139$	1.36684	0.115934	0.0579669	−	0.998319i	$-0.481538\pi$
$139$	1.36684	0.115934	0.0579669	+	0.998319i	$0.481538\pi$
$140$	0.603419	0.0509982
$141$	0	0
$142$	7.40554	0.621459
$143$	−13.8947	−1.16193
$144$	0	0
$145$	−0.887651	−0.0737154
$146$	−4.41344	−0.365259
$147$	0	0
$148$	−1.68803	−0.138755
$149$	5.71797	0.468434	0.234217	−	0.972184i	$-0.424747\pi$
$149$	5.71797	0.468434	0.234217	+	0.972184i	$0.424747\pi$
$150$	0	0
$151$	9.84368	0.801068	0.400534	−	0.916282i	$-0.368825\pi$
$151$	9.84368	0.801068	0.400534	+	0.916282i	$0.368825\pi$
$152$	−18.0621	−1.46503
$153$	0	0
$154$	17.2384	1.38911
$155$	−5.17541	−0.415699
$156$	0	0
$157$	−10.3417	−0.825357	−0.412678	−	0.910877i	$-0.635407\pi$
$157$	−10.3417	−0.825357	−0.412678	+	0.910877i	$0.635407\pi$
$158$	10.6290	0.845600
$159$	0	0
$160$	−1.03425	−0.0817643
$161$	−3.28671	−0.259029
$162$	0	0
$163$	−14.6337	−1.14620	−0.573099	−	0.819486i	$-0.694259\pi$
$163$	−14.6337	−1.14620	−0.573099	+	0.819486i	$0.694259\pi$
$164$	1.36344	0.106467
$165$	0	0
$166$	−16.9891	−1.31861
$167$	18.9539	1.46670	0.733349	−	0.679852i	$-0.237956\pi$
$167$	18.9539	1.46670	0.733349	+	0.679852i	$0.237956\pi$
$168$	0	0
$169$	−0.415191	−0.0319378
$170$	3.73790	0.286684
$171$	0	0
$172$	−0.454438	−0.0346506
$173$	−12.8377	−0.976029	−0.488015	−	0.872835i	$-0.662279\pi$
$173$	−12.8377	−0.976029	−0.488015	+	0.872835i	$0.662279\pi$
$174$	0	0
$175$	13.8439	1.04650
$176$	−13.8793	−1.04619
$177$	0	0
$178$	1.33852	0.100326
$179$	0.761921	0.0569486	0.0284743	−	0.999595i	$-0.490935\pi$
$179$	0.761921	0.0569486	0.0284743	+	0.999595i	$0.490935\pi$
$180$	0	0
$181$	−5.00493	−0.372014	−0.186007	−	0.982548i	$-0.559555\pi$
$181$	−5.00493	−0.372014	−0.186007	+	0.982548i	$0.559555\pi$
$182$	−15.6133	−1.15734
$183$	0	0
$184$	2.95515	0.217857
$185$	7.24448	0.532625
$186$	0	0
$187$	−12.3169	−0.900700
$188$	0.266053	0.0194039
$189$	0	0
$190$	7.26510	0.527065
$191$	21.0631	1.52408	0.762038	−	0.647533i	$-0.224199\pi$
$191$	21.0631	1.52408	0.762038	+	0.647533i	$0.224199\pi$
$192$	0	0
$193$	21.7205	1.56348	0.781738	−	0.623607i	$-0.214333\pi$
$193$	21.7205	1.56348	0.781738	+	0.623607i	$0.214333\pi$
$194$	−2.81420	−0.202048
$195$	0	0
$196$	−0.786464	−0.0561760
$197$	−12.9627	−0.923554	−0.461777	−	0.886996i	$-0.652788\pi$
$197$	−12.9627	−0.923554	−0.461777	+	0.886996i	$0.652788\pi$
$198$	0	0
$199$	17.4127	1.23435	0.617175	−	0.786826i	$-0.288277\pi$
$199$	17.4127	1.23435	0.617175	+	0.786826i	$0.288277\pi$
$200$	−12.4473	−0.880159
$201$	0	0
$202$	−3.26617	−0.229807
$203$	3.28671	0.230682
$204$	0	0
$205$	−5.85142	−0.408681
$206$	6.56751	0.457580
$207$	0	0
$208$	12.5708	0.871628
$209$	−23.9395	−1.65593
$210$	0	0
$211$	3.93404	0.270831	0.135415	−	0.990789i	$-0.456763\pi$
$211$	3.93404	0.270831	0.135415	+	0.990789i	$0.456763\pi$
$212$	−0.215258	−0.0147840
$213$	0	0
$214$	16.7769	1.14684
$215$	1.95030	0.133009
$216$	0	0
$217$	19.1630	1.30087
$218$	10.6068	0.718384
$219$	0	0
$220$	−0.719092	−0.0484812
$221$	11.1557	0.750416
$222$	0	0
$223$	−9.64189	−0.645669	−0.322834	−	0.946455i	$-0.604636\pi$
$223$	−9.64189	−0.645669	−0.322834	+	0.946455i	$0.604636\pi$
$224$	3.82951	0.255870
$225$	0	0
$226$	−10.8786	−0.723632
$227$	−13.4959	−0.895756	−0.447878	−	0.894095i	$-0.647820\pi$
$227$	−13.4959	−0.895756	−0.447878	+	0.894095i	$0.647820\pi$
$228$	0	0
$229$	23.2858	1.53877	0.769383	−	0.638788i	$-0.220564\pi$
$229$	23.2858	1.53877	0.769383	+	0.638788i	$0.220564\pi$
$230$	−1.18865	−0.0783770
$231$	0	0
$232$	−2.95515	−0.194015
$233$	−13.4769	−0.882902	−0.441451	−	0.897285i	$-0.645536\pi$
$233$	−13.4769	−0.882902	−0.441451	+	0.897285i	$0.645536\pi$
$234$	0	0
$235$	−1.14181	−0.0744835
$236$	−1.37240	−0.0893357
$237$	0	0
$238$	−13.8403	−0.897135
$239$	−4.00009	−0.258744	−0.129372	−	0.991596i	$-0.541296\pi$
$239$	−4.00009	−0.258744	−0.129372	+	0.991596i	$0.541296\pi$
$240$	0	0
$241$	17.5656	1.13150	0.565750	−	0.824577i	$-0.308587\pi$
$241$	17.5656	1.13150	0.565750	+	0.824577i	$0.308587\pi$
$242$	−5.81297	−0.373672
$243$	0	0
$244$	−3.08900	−0.197753
$245$	3.37524	0.215636
$246$	0	0
$247$	21.6826	1.37963
$248$	−17.2299	−1.09410
$249$	0	0
$250$	10.9499	0.692533
$251$	10.2267	0.645501	0.322750	−	0.946484i	$-0.395393\pi$
$251$	10.2267	0.645501	0.322750	+	0.946484i	$0.395393\pi$
$252$	0	0
$253$	3.91676	0.246244
$254$	11.4116	0.716028
$255$	0	0
$256$	−4.90903	−0.306814
$257$	23.0644	1.43872	0.719358	−	0.694640i	$-0.244436\pi$
$257$	23.0644	1.43872	0.719358	+	0.694640i	$0.244436\pi$
$258$	0	0
$259$	−26.8241	−1.66677
$260$	0.651301	0.0403920
$261$	0	0
$262$	3.48082	0.215046
$263$	25.6672	1.58271	0.791355	−	0.611357i	$-0.209376\pi$
$263$	25.6672	1.58271	0.791355	+	0.611357i	$0.209376\pi$
$264$	0	0
$265$	0.923816	0.0567495
$266$	−26.9005	−1.64937
$267$	0	0
$268$	0.613530	0.0374773
$269$	0.285422	0.0174025	0.00870124	−	0.999962i	$-0.497230\pi$
$269$	0.285422	0.0174025	0.00870124	+	0.999962i	$0.497230\pi$
$270$	0	0
$271$	0.277744	0.0168718	0.00843588	−	0.999964i	$-0.497315\pi$
$271$	0.277744	0.0168718	0.00843588	+	0.999964i	$0.497315\pi$
$272$	11.1433	0.675663
$273$	0	0
$274$	−2.64696	−0.159909
$275$	−16.4977	−0.994847
$276$	0	0
$277$	16.5888	0.996724	0.498362	−	0.866969i	$-0.333935\pi$
$277$	16.5888	0.996724	0.498362	+	0.866969i	$0.333935\pi$
$278$	−1.83033	−0.109776
$279$	0	0
$280$	−8.62150	−0.515233
$281$	−18.9390	−1.12981	−0.564903	−	0.825157i	$-0.691086\pi$
$281$	−18.9390	−1.12981	−0.564903	+	0.825157i	$0.691086\pi$
$282$	0	0
$283$	29.0335	1.72586	0.862932	−	0.505321i	$-0.168626\pi$
$283$	29.0335	1.72586	0.862932	+	0.505321i	$0.168626\pi$
$284$	1.14383	0.0678739
$285$	0	0
$286$	18.6063	1.10021
$287$	21.6661	1.27891
$288$	0	0
$289$	−7.11107	−0.418298
$290$	1.18865	0.0697997
$291$	0	0
$292$	−0.681683	−0.0398925
$293$	31.7227	1.85326	0.926629	−	0.375976i	$-0.122693\pi$
$293$	31.7227	1.85326	0.926629	+	0.375976i	$0.122693\pi$
$294$	0	0
$295$	5.88989	0.342923
$296$	24.1182	1.40184
$297$	0	0
$298$	−7.65689	−0.443552
$299$	−3.54751	−0.205158
$300$	0	0
$301$	−7.22137	−0.416233
$302$	−13.1816	−0.758516
$303$	0	0
$304$	21.6585	1.24220
$305$	13.2570	0.759092
$306$	0	0
$307$	8.19822	0.467897	0.233948	−	0.972249i	$-0.424835\pi$
$307$	8.19822	0.467897	0.233948	+	0.972249i	$0.424835\pi$
$308$	2.66259	0.151715
$309$	0	0
$310$	6.93035	0.393617
$311$	−21.3244	−1.20920	−0.604599	−	0.796530i	$-0.706667\pi$
$311$	−21.3244	−1.20920	−0.604599	+	0.796530i	$0.706667\pi$
$312$	0	0
$313$	16.8534	0.952609	0.476304	−	0.879281i	$-0.341976\pi$
$313$	16.8534	0.952609	0.476304	+	0.879281i	$0.341976\pi$
$314$	13.8485	0.781515
$315$	0	0
$316$	1.64172	0.0923539
$317$	−8.66758	−0.486820	−0.243410	−	0.969923i	$-0.578266\pi$
$317$	−8.66758	−0.486820	−0.243410	+	0.969923i	$0.578266\pi$
$318$	0	0
$319$	−3.91676	−0.219296
$320$	7.67584	0.429092
$321$	0	0
$322$	4.40121	0.245270
$323$	19.2204	1.06945
$324$	0	0
$325$	14.9424	0.828854
$326$	19.5959	1.08531
$327$	0	0
$328$	−19.4805	−1.07563
$329$	4.22778	0.233085
$330$	0	0
$331$	10.2467	0.563208	0.281604	−	0.959531i	$-0.409134\pi$
$331$	10.2467	0.563208	0.281604	+	0.959531i	$0.409134\pi$
$332$	−2.62407	−0.144015
$333$	0	0
$334$	−25.3811	−1.38879
$335$	−2.63307	−0.143860
$336$	0	0
$337$	−3.64596	−0.198608	−0.0993040	−	0.995057i	$-0.531662\pi$
$337$	−3.64596	−0.198608	−0.0993040	+	0.995057i	$0.531662\pi$
$338$	0.555979	0.0302413
$339$	0	0
$340$	0.577342	0.0313107
$341$	−22.8365	−1.23666
$342$	0	0
$343$	10.5094	0.567456
$344$	6.49289	0.350073
$345$	0	0
$346$	17.1908	0.924184
$347$	12.6714	0.680235	0.340118	−	0.940383i	$-0.389533\pi$
$347$	12.6714	0.680235	0.340118	+	0.940383i	$0.389533\pi$
$348$	0	0
$349$	−21.7480	−1.16414	−0.582071	−	0.813138i	$-0.697758\pi$
$349$	−21.7480	−1.16414	−0.582071	+	0.813138i	$0.697758\pi$
$350$	−18.5382	−0.990909
$351$	0	0
$352$	−4.56361	−0.243241
$353$	29.8696	1.58980	0.794900	−	0.606740i	$-0.207523\pi$
$353$	29.8696	1.58980	0.794900	+	0.606740i	$0.207523\pi$
$354$	0	0
$355$	−4.90895	−0.260540
$356$	0.206743	0.0109574
$357$	0	0
$358$	−1.02028	−0.0539236
$359$	7.19000	0.379474	0.189737	−	0.981835i	$-0.439237\pi$
$359$	7.19000	0.379474	0.189737	+	0.981835i	$0.439237\pi$
$360$	0	0
$361$	18.3574	0.966181
$362$	6.70207	0.352253
$363$	0	0
$364$	−2.41157	−0.126401
$365$	2.92556	0.153131
$366$	0	0
$367$	14.0990	0.735960	0.367980	−	0.929834i	$-0.380050\pi$
$367$	14.0990	0.735960	0.367980	+	0.929834i	$0.380050\pi$
$368$	−3.54356	−0.184721
$369$	0	0
$370$	−9.70102	−0.504332
$371$	−3.42061	−0.177589
$372$	0	0
$373$	−34.4989	−1.78629	−0.893143	−	0.449772i	$-0.851505\pi$
$373$	−34.4989	−1.78629	−0.893143	+	0.449772i	$0.851505\pi$
$374$	16.4935	0.852856
$375$	0	0
$376$	−3.80129	−0.196037
$377$	3.54751	0.182706
$378$	0	0
$379$	−15.6949	−0.806191	−0.403096	−	0.915158i	$-0.632066\pi$
$379$	−15.6949	−0.806191	−0.403096	+	0.915158i	$0.632066\pi$
$380$	1.12214	0.0575645
$381$	0	0
$382$	−28.2055	−1.44312
$383$	−8.75618	−0.447420	−0.223710	−	0.974656i	$-0.571817\pi$
$383$	−8.75618	−0.447420	−0.223710	+	0.974656i	$0.571817\pi$
$384$	0	0
$385$	−11.4269	−0.582370
$386$	−29.0858	−1.48043
$387$	0	0
$388$	−0.434671	−0.0220671
$389$	18.7625	0.951299	0.475649	−	0.879635i	$-0.342213\pi$
$389$	18.7625	0.951299	0.475649	+	0.879635i	$0.342213\pi$
$390$	0	0
$391$	−3.14467	−0.159033
$392$	11.2368	0.567544
$393$	0	0
$394$	17.3583	0.874496
$395$	−7.04571	−0.354508
$396$	0	0
$397$	−32.1562	−1.61387	−0.806936	−	0.590638i	$-0.798876\pi$
$397$	−32.1562	−1.61387	−0.806936	+	0.590638i	$0.798876\pi$
$398$	−23.3172	−1.16878
$399$	0	0
$400$	14.9257	0.746287
$401$	−13.3459	−0.666463	−0.333231	−	0.942845i	$-0.608139\pi$
$401$	−13.3459	−0.666463	−0.333231	+	0.942845i	$0.608139\pi$
$402$	0	0
$403$	20.6836	1.03032
$404$	−0.504480	−0.0250988
$405$	0	0
$406$	−4.40121	−0.218428
$407$	31.9662	1.58451
$408$	0	0
$409$	−23.8126	−1.17746	−0.588729	−	0.808330i	$-0.700372\pi$
$409$	−23.8126	−1.17746	−0.588729	+	0.808330i	$0.700372\pi$
$410$	7.83560	0.386973
$411$	0	0
$412$	1.01439	0.0499755
$413$	−21.8085	−1.07313
$414$	0	0
$415$	11.2616	0.552813
$416$	4.13338	0.202655
$417$	0	0
$418$	32.0572	1.56797
$419$	−11.8470	−0.578766	−0.289383	−	0.957213i	$-0.593450\pi$
$419$	−11.8470	−0.578766	−0.289383	+	0.957213i	$0.593450\pi$
$420$	0	0
$421$	29.3495	1.43041	0.715204	−	0.698915i	$-0.246334\pi$
$421$	29.3495	1.43041	0.715204	+	0.698915i	$0.246334\pi$
$422$	−5.26805	−0.256445
$423$	0	0
$424$	3.07555	0.149362
$425$	13.2456	0.642505
$426$	0	0
$427$	−49.0866	−2.37547
$428$	2.59129	0.125255
$429$	0	0
$430$	−2.61163	−0.125944
$431$	−25.1164	−1.20982	−0.604908	−	0.796295i	$-0.706790\pi$
$431$	−25.1164	−1.20982	−0.604908	+	0.796295i	$0.706790\pi$
$432$	0	0
$433$	34.2520	1.64605	0.823023	−	0.568008i	$-0.192286\pi$
$433$	34.2520	1.64605	0.823023	+	0.568008i	$0.192286\pi$
$434$	−25.6610	−1.23177
$435$	0	0
$436$	1.63829	0.0784598
$437$	−6.11207	−0.292380
$438$	0	0
$439$	−4.41781	−0.210850	−0.105425	−	0.994427i	$-0.533620\pi$
$439$	−4.41781	−0.210850	−0.105425	+	0.994427i	$0.533620\pi$
$440$	10.2742	0.489804
$441$	0	0
$442$	−14.9386	−0.710555
$443$	12.2202	0.580597	0.290298	−	0.956936i	$-0.406245\pi$
$443$	12.2202	0.580597	0.290298	+	0.956936i	$0.406245\pi$
$444$	0	0
$445$	−0.887273	−0.0420608
$446$	12.9114	0.611372
$447$	0	0
$448$	−28.4213	−1.34278
$449$	15.6942	0.740656	0.370328	−	0.928901i	$-0.379245\pi$
$449$	15.6942	0.740656	0.370328	+	0.928901i	$0.379245\pi$
$450$	0	0
$451$	−25.8194	−1.21579
$452$	−1.68026	−0.0790329
$453$	0	0
$454$	18.0723	0.848174
$455$	10.3497	0.485200
$456$	0	0
$457$	23.6308	1.10540	0.552702	−	0.833379i	$-0.313597\pi$
$457$	23.6308	1.10540	0.552702	+	0.833379i	$0.313597\pi$
$458$	−31.1818	−1.45703
$459$	0	0
$460$	−0.183594	−0.00856011
$461$	28.3970	1.32258	0.661290	−	0.750130i	$-0.270009\pi$
$461$	28.3970	1.32258	0.661290	+	0.750130i	$0.270009\pi$
$462$	0	0
$463$	17.7363	0.824277	0.412138	−	0.911121i	$-0.364782\pi$
$463$	17.7363	0.824277	0.412138	+	0.911121i	$0.364782\pi$
$464$	3.54356	0.164506
$465$	0	0
$466$	18.0468	0.836004
$467$	−13.4055	−0.620331	−0.310166	−	0.950683i	$-0.600384\pi$
$467$	−13.4055	−0.620331	−0.310166	+	0.950683i	$0.600384\pi$
$468$	0	0
$469$	9.74947	0.450188
$470$	1.52899	0.0705270
$471$	0	0
$472$	19.6085	0.902555
$473$	8.60567	0.395689
$474$	0	0
$475$	25.7445	1.18124
$476$	−2.13772	−0.0979824
$477$	0	0
$478$	5.35649	0.245000
$479$	−13.6060	−0.621674	−0.310837	−	0.950463i	$-0.600609\pi$
$479$	−13.6060	−0.621674	−0.310837	+	0.950463i	$0.600609\pi$
$480$	0	0
$481$	−28.9526	−1.32013
$482$	−23.5220	−1.07140
$483$	0	0
$484$	−0.897849	−0.0408113
$485$	1.86547	0.0847064
$486$	0	0
$487$	15.8742	0.719329	0.359665	−	0.933082i	$-0.382891\pi$
$487$	15.8742	0.719329	0.359665	+	0.933082i	$0.382891\pi$
$488$	44.1349	1.99789
$489$	0	0
$490$	−4.51977	−0.204182
$491$	−28.1153	−1.26883	−0.634413	−	0.772994i	$-0.718758\pi$
$491$	−28.1153	−1.26883	−0.634413	+	0.772994i	$0.718758\pi$
$492$	0	0
$493$	3.14467	0.141629
$494$	−29.0350	−1.30635
$495$	0	0
$496$	20.6606	0.927686
$497$	18.1764	0.815322
$498$	0	0
$499$	7.12120	0.318789	0.159394	−	0.987215i	$-0.449046\pi$
$499$	7.12120	0.318789	0.159394	+	0.987215i	$0.449046\pi$
$500$	1.69128	0.0756364
$501$	0	0
$502$	−13.6944	−0.611213
$503$	31.2925	1.39526	0.697631	−	0.716457i	$-0.254237\pi$
$503$	31.2925	1.39526	0.697631	+	0.716457i	$0.254237\pi$
$504$	0	0
$505$	2.16506	0.0963439
$506$	−5.24490	−0.233164
$507$	0	0
$508$	1.76259	0.0782024
$509$	−2.66312	−0.118041	−0.0590205	−	0.998257i	$-0.518798\pi$
$509$	−2.66312	−0.118041	−0.0590205	+	0.998257i	$0.518798\pi$
$510$	0	0
$511$	−10.8325	−0.479201
$512$	25.0723	1.10805
$513$	0	0
$514$	−30.8853	−1.36229
$515$	−4.35344	−0.191835
$516$	0	0
$517$	−5.03823	−0.221581
$518$	35.9200	1.57823
$519$	0	0
$520$	−9.30562	−0.408078
$521$	−23.8745	−1.04596	−0.522981	−	0.852344i	$-0.675180\pi$
$521$	−23.8745	−1.04596	−0.522981	+	0.852344i	$0.675180\pi$
$522$	0	0
$523$	29.0501	1.27027	0.635136	−	0.772400i	$-0.280944\pi$
$523$	29.0501	1.27027	0.635136	+	0.772400i	$0.280944\pi$
$524$	0.537635	0.0234867
$525$	0	0
$526$	−34.3708	−1.49864
$527$	18.3348	0.798678
$528$	0	0
$529$	1.00000	0.0434783
$530$	−1.23707	−0.0537351
$531$	0	0
$532$	−4.15495	−0.180140
$533$	23.3853	1.01293
$534$	0	0
$535$	−11.1210	−0.480801
$536$	−8.76596	−0.378632
$537$	0	0
$538$	−0.382206	−0.0164781
$539$	14.8933	0.641498
$540$	0	0
$541$	20.3331	0.874187	0.437094	−	0.899416i	$-0.356008\pi$
$541$	20.3331	0.874187	0.437094	+	0.899416i	$0.356008\pi$
$542$	−0.371925	−0.0159756
$543$	0	0
$544$	3.66401	0.157093
$545$	−7.03099	−0.301175
$546$	0	0
$547$	−0.644391	−0.0275522	−0.0137761	−	0.999905i	$-0.504385\pi$
$547$	−0.644391	−0.0275522	−0.0137761	+	0.999905i	$0.504385\pi$
$548$	−0.408840	−0.0174648
$549$	0	0
$550$	22.0919	0.942002
$551$	6.11207	0.260383
$552$	0	0
$553$	26.0882	1.10938
$554$	−22.2139	−0.943779
$555$	0	0
$556$	−0.282705	−0.0119894
$557$	−17.6952	−0.749771	−0.374885	−	0.927071i	$-0.622318\pi$
$557$	−17.6952	−0.749771	−0.374885	+	0.927071i	$0.622318\pi$
$558$	0	0
$559$	−7.79438	−0.329667
$560$	10.3382	0.436867
$561$	0	0
$562$	25.3611	1.06979
$563$	−1.15554	−0.0487000	−0.0243500	−	0.999703i	$-0.507752\pi$
$563$	−1.15554	−0.0487000	−0.0243500	+	0.999703i	$0.507752\pi$
$564$	0	0
$565$	7.21113	0.303375
$566$	−38.8786	−1.63419
$567$	0	0
$568$	−16.3428	−0.685728
$569$	−6.36563	−0.266861	−0.133431	−	0.991058i	$-0.542599\pi$
$569$	−6.36563	−0.266861	−0.133431	+	0.991058i	$0.542599\pi$
$570$	0	0
$571$	−17.6438	−0.738372	−0.369186	−	0.929356i	$-0.620363\pi$
$571$	−17.6438	−0.738372	−0.369186	+	0.929356i	$0.620363\pi$
$572$	2.87386	0.120162
$573$	0	0
$574$	−29.0129	−1.21097
$575$	−4.21208	−0.175656
$576$	0	0
$577$	−4.41303	−0.183717	−0.0918584	−	0.995772i	$-0.529281\pi$
$577$	−4.41303	−0.183717	−0.0918584	+	0.995772i	$0.529281\pi$
$578$	9.52238	0.396079
$579$	0	0
$580$	0.183594	0.00762332
$581$	−41.6985	−1.72995
$582$	0	0
$583$	4.07633	0.168824
$584$	9.73972	0.403032
$585$	0	0
$586$	−42.4796	−1.75482
$587$	10.5755	0.436496	0.218248	−	0.975893i	$-0.429966\pi$
$587$	10.5755	0.436496	0.218248	+	0.975893i	$0.429966\pi$
$588$	0	0
$589$	35.6362	1.46836
$590$	−7.88711	−0.324707
$591$	0	0
$592$	−28.9204	−1.18862
$593$	12.0082	0.493118	0.246559	−	0.969128i	$-0.420700\pi$
$593$	12.0082	0.493118	0.246559	+	0.969128i	$0.420700\pi$
$594$	0	0
$595$	9.17441	0.376114
$596$	−1.18265	−0.0484434
$597$	0	0
$598$	4.75044	0.194260
$599$	−0.0618119	−0.00252556	−0.00126278	−	0.999999i	$-0.500402\pi$
$599$	−0.0618119	−0.00252556	−0.00126278	+	0.999999i	$0.500402\pi$
$600$	0	0
$601$	−24.4635	−0.997887	−0.498944	−	0.866634i	$-0.666279\pi$
$601$	−24.4635	−0.997887	−0.498944	+	0.866634i	$0.666279\pi$
$602$	9.67008	0.394123
$603$	0	0
$604$	−2.03598	−0.0828429
$605$	3.85327	0.156658
$606$	0	0
$607$	−3.10992	−0.126228	−0.0631139	−	0.998006i	$-0.520103\pi$
$607$	−3.10992	−0.126228	−0.0631139	+	0.998006i	$0.520103\pi$
$608$	7.12148	0.288814
$609$	0	0
$610$	−17.7523	−0.718770
$611$	4.56326	0.184610
$612$	0	0
$613$	−36.3178	−1.46686	−0.733431	−	0.679764i	$-0.762082\pi$
$613$	−36.3178	−1.46686	−0.733431	+	0.679764i	$0.762082\pi$
$614$	−10.9782	−0.443043
$615$	0	0
$616$	−38.0423	−1.53277
$617$	41.2471	1.66055	0.830273	−	0.557357i	$-0.188185\pi$
$617$	41.2471	1.66055	0.830273	+	0.557357i	$0.188185\pi$
$618$	0	0
$619$	5.07953	0.204164	0.102082	−	0.994776i	$-0.467450\pi$
$619$	5.07953	0.204164	0.102082	+	0.994776i	$0.467450\pi$
$620$	1.07044	0.0429897
$621$	0	0
$622$	28.5554	1.14497
$623$	3.28531	0.131623
$624$	0	0
$625$	13.8020	0.552079
$626$	−22.5682	−0.902007
$627$	0	0
$628$	2.13898	0.0853548
$629$	−25.6649	−1.02333
$630$	0	0
$631$	−1.21558	−0.0483914	−0.0241957	−	0.999707i	$-0.507702\pi$
$631$	−1.21558	−0.0483914	−0.0241957	+	0.999707i	$0.507702\pi$
$632$	−23.4565	−0.933048
$633$	0	0
$634$	11.6067	0.460961
$635$	−7.56447	−0.300187
$636$	0	0
$637$	−13.4892	−0.534462
$638$	5.24490	0.207648
$639$	0	0
$640$	−8.21016	−0.324535
$641$	17.5431	0.692912	0.346456	−	0.938066i	$-0.387385\pi$
$641$	17.5431	0.692912	0.346456	+	0.938066i	$0.387385\pi$
$642$	0	0
$643$	−11.4715	−0.452390	−0.226195	−	0.974082i	$-0.572629\pi$
$643$	−11.4715	−0.452390	−0.226195	+	0.974082i	$0.572629\pi$
$644$	0.679794	0.0267876
$645$	0	0
$646$	−25.7379	−1.01265
$647$	36.2961	1.42695	0.713474	−	0.700682i	$-0.247121\pi$
$647$	36.2961	1.42695	0.713474	+	0.700682i	$0.247121\pi$
$648$	0	0
$649$	25.9891	1.02016
$650$	−20.0092	−0.784826
$651$	0	0
$652$	3.02670	0.118535
$653$	10.8263	0.423666	0.211833	−	0.977306i	$-0.432057\pi$
$653$	10.8263	0.423666	0.211833	+	0.977306i	$0.432057\pi$
$654$	0	0
$655$	−2.30735	−0.0901556
$656$	23.3593	0.912026
$657$	0	0
$658$	−5.66140	−0.220704
$659$	−6.10008	−0.237626	−0.118813	−	0.992917i	$-0.537909\pi$
$659$	−6.10008	−0.237626	−0.118813	+	0.992917i	$0.537909\pi$
$660$	0	0
$661$	36.5684	1.42235	0.711173	−	0.703017i	$-0.248164\pi$
$661$	36.5684	1.42235	0.711173	+	0.703017i	$0.248164\pi$
$662$	−13.7212	−0.533291
$663$	0	0
$664$	37.4921	1.45497
$665$	17.8317	0.691482
$666$	0	0
$667$	−1.00000	−0.0387202
$668$	−3.92026	−0.151679
$669$	0	0
$670$	3.52592	0.136218
$671$	58.4964	2.25823
$672$	0	0
$673$	13.4164	0.517164	0.258582	−	0.965989i	$-0.416745\pi$
$673$	13.4164	0.517164	0.258582	+	0.965989i	$0.416745\pi$
$674$	4.88228	0.188058
$675$	0	0
$676$	0.0858744	0.00330286
$677$	41.6134	1.59933	0.799666	−	0.600445i	$-0.205010\pi$
$677$	41.6134	1.59933	0.799666	+	0.600445i	$0.205010\pi$
$678$	0	0
$679$	−6.90726	−0.265076
$680$	−8.24891	−0.316331
$681$	0	0
$682$	30.5801	1.17097
$683$	13.5521	0.518558	0.259279	−	0.965803i	$-0.416515\pi$
$683$	13.5521	0.518558	0.259279	+	0.965803i	$0.416515\pi$
$684$	0	0
$685$	1.75461	0.0670401
$686$	−14.0731	−0.537313
$687$	0	0
$688$	−7.78571	−0.296827
$689$	−3.69204	−0.140656
$690$	0	0
$691$	15.1136	0.574950	0.287475	−	0.957788i	$-0.407184\pi$
$691$	15.1136	0.574950	0.287475	+	0.957788i	$0.407184\pi$
$692$	2.65523	0.100937
$693$	0	0
$694$	−16.9682	−0.644102
$695$	1.21328	0.0460222
$696$	0	0
$697$	20.7298	0.785195
$698$	29.1226	1.10231
$699$	0	0
$700$	−2.86334	−0.108224
$701$	−19.7858	−0.747298	−0.373649	−	0.927570i	$-0.621894\pi$
$701$	−19.7858	−0.747298	−0.373649	+	0.927570i	$0.621894\pi$
$702$	0	0
$703$	−49.8831	−1.88138
$704$	33.8696	1.27651
$705$	0	0
$706$	−39.9982	−1.50535
$707$	−8.01658	−0.301494
$708$	0	0
$709$	40.9653	1.53848	0.769241	−	0.638958i	$-0.220634\pi$
$709$	40.9653	1.53848	0.769241	+	0.638958i	$0.220634\pi$
$710$	6.57353	0.246700
$711$	0	0
$712$	−2.95389	−0.110702
$713$	−5.83045	−0.218352
$714$	0	0
$715$	−12.3337	−0.461253
$716$	−0.157589	−0.00588938
$717$	0	0
$718$	−9.62807	−0.359317
$719$	28.8560	1.07615	0.538075	−	0.842897i	$-0.319152\pi$
$719$	28.8560	1.07615	0.538075	+	0.842897i	$0.319152\pi$
$720$	0	0
$721$	16.1195	0.600321
$722$	−24.5823	−0.914859
$723$	0	0
$724$	1.03518	0.0384720
$725$	4.21208	0.156433
$726$	0	0
$727$	32.3858	1.20112	0.600561	−	0.799579i	$-0.294944\pi$
$727$	32.3858	1.20112	0.600561	+	0.799579i	$0.294944\pi$
$728$	34.4559	1.27702
$729$	0	0
$730$	−3.91760	−0.144997
$731$	−6.90928	−0.255549
$732$	0	0
$733$	22.4561	0.829434	0.414717	−	0.909950i	$-0.363881\pi$
$733$	22.4561	0.829434	0.414717	+	0.909950i	$0.363881\pi$
$734$	−18.8798	−0.696867
$735$	0	0
$736$	−1.16515	−0.0429480
$737$	−11.6184	−0.427969
$738$	0	0
$739$	14.8059	0.544645	0.272323	−	0.962206i	$-0.412208\pi$
$739$	14.8059	0.544645	0.272323	+	0.962206i	$0.412208\pi$
$740$	−1.49838	−0.0550817
$741$	0	0
$742$	4.58052	0.168156
$743$	−11.2091	−0.411222	−0.205611	−	0.978634i	$-0.565918\pi$
$743$	−11.2091	−0.411222	−0.205611	+	0.978634i	$0.565918\pi$
$744$	0	0
$745$	5.07556	0.185954
$746$	46.1973	1.69140
$747$	0	0
$748$	2.54752	0.0931465
$749$	41.1776	1.50460
$750$	0	0
$751$	13.9136	0.507713	0.253857	−	0.967242i	$-0.418301\pi$
$751$	13.9136	0.507713	0.253857	+	0.967242i	$0.418301\pi$
$752$	4.55818	0.166220
$753$	0	0
$754$	−4.75044	−0.173001
$755$	8.73775	0.317999
$756$	0	0
$757$	32.5191	1.18193	0.590963	−	0.806699i	$-0.298748\pi$
$757$	32.5191	1.18193	0.590963	+	0.806699i	$0.298748\pi$
$758$	21.0169	0.763368
$759$	0	0
$760$	−16.0328	−0.581572
$761$	47.7582	1.73123	0.865617	−	0.500707i	$-0.166926\pi$
$761$	47.7582	1.73123	0.865617	+	0.500707i	$0.166926\pi$
$762$	0	0
$763$	26.0337	0.942482
$764$	−4.35651	−0.157613
$765$	0	0
$766$	11.7253	0.423654
$767$	−23.5390	−0.849945
$768$	0	0
$769$	−8.04170	−0.289991	−0.144996	−	0.989432i	$-0.546317\pi$
$769$	−8.04170	−0.289991	−0.144996	+	0.989432i	$0.546317\pi$
$770$	15.3017	0.551436
$771$	0	0
$772$	−4.49248	−0.161688
$773$	−20.6949	−0.744345	−0.372172	−	0.928164i	$-0.621387\pi$
$773$	−20.6949	−0.744345	−0.372172	+	0.928164i	$0.621387\pi$
$774$	0	0
$775$	24.5583	0.882161
$776$	6.21047	0.222943
$777$	0	0
$778$	−25.1248	−0.900767
$779$	40.2910	1.44357
$780$	0	0
$781$	−21.6607	−0.775081
$782$	4.21100	0.150585
$783$	0	0
$784$	−13.4742	−0.481221
$785$	−9.17981	−0.327642
$786$	0	0
$787$	−0.137696	−0.00490832	−0.00245416	−	0.999997i	$-0.500781\pi$
$787$	−0.137696	−0.00490832	−0.00245416	+	0.999997i	$0.500781\pi$
$788$	2.68109	0.0955099
$789$	0	0
$790$	9.43486	0.335677
$791$	−26.7007	−0.949367
$792$	0	0
$793$	−52.9817	−1.88143
$794$	43.0601	1.52815
$795$	0	0
$796$	−3.60148	−0.127651
$797$	−45.6027	−1.61533	−0.807665	−	0.589642i	$-0.799269\pi$
$797$	−45.6027	−1.61533	−0.807665	+	0.589642i	$0.799269\pi$
$798$	0	0
$799$	4.04507	0.143104
$800$	4.90770	0.173513
$801$	0	0
$802$	17.8714	0.631061
$803$	12.9090	0.455549
$804$	0	0
$805$	−2.91745	−0.102827
$806$	−27.6972	−0.975593
$807$	0	0
$808$	7.20788	0.253572
$809$	−39.3261	−1.38263	−0.691315	−	0.722553i	$-0.742968\pi$
$809$	−39.3261	−1.38263	−0.691315	+	0.722553i	$0.742968\pi$
$810$	0	0
$811$	−24.3083	−0.853580	−0.426790	−	0.904351i	$-0.640356\pi$
$811$	−24.3083	−0.853580	−0.426790	+	0.904351i	$0.640356\pi$
$812$	−0.679794	−0.0238561
$813$	0	0
$814$	−42.8057	−1.50034
$815$	−12.9896	−0.455006
$816$	0	0
$817$	−13.4291	−0.469825
$818$	31.8873	1.11491
$819$	0	0
$820$	1.21026	0.0422640
$821$	−39.4621	−1.37724	−0.688619	−	0.725124i	$-0.741783\pi$
$821$	−39.4621	−1.37724	−0.688619	+	0.725124i	$0.741783\pi$
$822$	0	0
$823$	−18.7194	−0.652516	−0.326258	−	0.945281i	$-0.605788\pi$
$823$	−18.7194	−0.652516	−0.326258	+	0.945281i	$0.605788\pi$
$824$	−14.4934	−0.504901
$825$	0	0
$826$	29.2036	1.01612
$827$	15.8456	0.551006	0.275503	−	0.961300i	$-0.411156\pi$
$827$	15.8456	0.551006	0.275503	+	0.961300i	$0.411156\pi$
$828$	0	0
$829$	24.1768	0.839694	0.419847	−	0.907595i	$-0.362084\pi$
$829$	24.1768	0.839694	0.419847	+	0.907595i	$0.362084\pi$
$830$	−15.0804	−0.523448
$831$	0	0
$832$	−30.6766	−1.06352
$833$	−11.9574	−0.414300
$834$	0	0
$835$	16.8245	0.582235
$836$	4.95143	0.171249
$837$	0	0
$838$	15.8643	0.548023
$839$	19.5030	0.673317	0.336659	−	0.941627i	$-0.390703\pi$
$839$	19.5030	0.673317	0.336659	+	0.941627i	$0.390703\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−39.3017	−1.35443
$843$	0	0
$844$	−0.813683	−0.0280081
$845$	−0.368545	−0.0126783
$846$	0	0
$847$	−14.2675	−0.490238
$848$	−3.68793	−0.126644
$849$	0	0
$850$	−17.7371	−0.608376
$851$	8.16140	0.279769
$852$	0	0
$853$	12.8636	0.440441	0.220221	−	0.975450i	$-0.429322\pi$
$853$	12.8636	0.440441	0.220221	+	0.975450i	$0.429322\pi$
$854$	65.7316	2.24929
$855$	0	0
$856$	−37.0237	−1.26544
$857$	1.06558	0.0363996	0.0181998	−	0.999834i	$-0.494207\pi$
$857$	1.06558	0.0363996	0.0181998	+	0.999834i	$0.494207\pi$
$858$	0	0
$859$	31.7723	1.08406	0.542028	−	0.840360i	$-0.317657\pi$
$859$	31.7723	1.08406	0.542028	+	0.840360i	$0.317657\pi$
$860$	−0.403382	−0.0137552
$861$	0	0
$862$	33.6332	1.14555
$863$	−31.5043	−1.07242	−0.536209	−	0.844086i	$-0.680144\pi$
$863$	−31.5043	−1.07242	−0.536209	+	0.844086i	$0.680144\pi$
$864$	0	0
$865$	−11.3954	−0.387454
$866$	−45.8666	−1.55861
$867$	0	0
$868$	−3.96350	−0.134530
$869$	−31.0892	−1.05463
$870$	0	0
$871$	10.5231	0.356561
$872$	−23.4075	−0.792676
$873$	0	0
$874$	8.18463	0.276849
$875$	26.8758	0.908567
$876$	0	0
$877$	−44.5903	−1.50571	−0.752854	−	0.658188i	$-0.771323\pi$
$877$	−44.5903	−1.50571	−0.752854	+	0.658188i	$0.771323\pi$
$878$	5.91585	0.199650
$879$	0	0
$880$	−12.3199	−0.415305
$881$	−16.5635	−0.558038	−0.279019	−	0.960286i	$-0.590009\pi$
$881$	−16.5635	−0.558038	−0.279019	+	0.960286i	$0.590009\pi$
$882$	0	0
$883$	4.46642	0.150307	0.0751535	−	0.997172i	$-0.476055\pi$
$883$	4.46642	0.150307	0.0751535	+	0.997172i	$0.476055\pi$
$884$	−2.30735	−0.0776047
$885$	0	0
$886$	−16.3639	−0.549756
$887$	−21.7459	−0.730154	−0.365077	−	0.930977i	$-0.618957\pi$
$887$	−21.7459	−0.730154	−0.365077	+	0.930977i	$0.618957\pi$
$888$	0	0
$889$	28.0090	0.939391
$890$	1.18814	0.0398266
$891$	0	0
$892$	1.99424	0.0667722
$893$	7.86213	0.263096
$894$	0	0
$895$	0.676320	0.0226069
$896$	30.3998	1.01559
$897$	0	0
$898$	−21.0160	−0.701313
$899$	5.83045	0.194456
$900$	0	0
$901$	−3.27279	−0.109032
$902$	34.5745	1.15121
$903$	0	0
$904$	24.0072	0.798467
$905$	−4.44263	−0.147678
$906$	0	0
$907$	−33.9908	−1.12865	−0.564323	−	0.825554i	$-0.690863\pi$
$907$	−33.9908	−1.12865	−0.564323	+	0.825554i	$0.690863\pi$
$908$	2.79138	0.0926351
$909$	0	0
$910$	−13.8592	−0.459427
$911$	17.1945	0.569681	0.284840	−	0.958575i	$-0.408059\pi$
$911$	17.1945	0.569681	0.284840	+	0.958575i	$0.408059\pi$
$912$	0	0
$913$	49.6920	1.64456
$914$	−31.6439	−1.04669
$915$	0	0
$916$	−4.81622	−0.159132
$917$	8.54343	0.282129
$918$	0	0
$919$	13.6252	0.449455	0.224727	−	0.974422i	$-0.427851\pi$
$919$	13.6252	0.449455	0.224727	+	0.974422i	$0.427851\pi$
$920$	2.62314	0.0864824
$921$	0	0
$922$	−38.0262	−1.25233
$923$	19.6187	0.645756
$924$	0	0
$925$	−34.3764	−1.13029
$926$	−23.7506	−0.780493
$927$	0	0
$928$	1.16515	0.0382479
$929$	57.5779	1.88907	0.944535	−	0.328410i	$-0.106513\pi$
$929$	57.5779	1.88907	0.944535	+	0.328410i	$0.106513\pi$
$930$	0	0
$931$	−23.2408	−0.761687
$932$	2.78745	0.0913059
$933$	0	0
$934$	17.9512	0.587380
$935$	−10.9331	−0.357551
$936$	0	0
$937$	42.3053	1.38205	0.691026	−	0.722829i	$-0.257159\pi$
$937$	42.3053	1.38205	0.691026	+	0.722829i	$0.257159\pi$
$938$	−13.0554	−0.426275
$939$	0	0
$940$	0.236162	0.00770276
$941$	−18.9061	−0.616322	−0.308161	−	0.951334i	$-0.599714\pi$
$941$	−18.9061	−0.616322	−0.308161	+	0.951334i	$0.599714\pi$
$942$	0	0
$943$	−6.59203	−0.214666
$944$	−23.5128	−0.765277
$945$	0	0
$946$	−11.5238	−0.374671
$947$	−34.2972	−1.11451	−0.557255	−	0.830342i	$-0.688145\pi$
$947$	−34.2972	−1.11451	−0.557255	+	0.830342i	$0.688145\pi$
$948$	0	0
$949$	−11.6920	−0.379539
$950$	−34.4743	−1.11849
$951$	0	0
$952$	30.5433	0.989913
$953$	27.7360	0.898458	0.449229	−	0.893417i	$-0.351699\pi$
$953$	27.7360	0.898458	0.449229	+	0.893417i	$0.351699\pi$
$954$	0	0
$955$	18.6967	0.605011
$956$	0.827343	0.0267582
$957$	0	0
$958$	18.2197	0.588652
$959$	−6.49679	−0.209792
$960$	0	0
$961$	2.99418	0.0965865
$962$	38.7703	1.25000
$963$	0	0
$964$	−3.63312	−0.117015
$965$	19.2802	0.620652
$966$	0	0
$967$	−21.8567	−0.702864	−0.351432	−	0.936213i	$-0.614305\pi$
$967$	−21.8567	−0.702864	−0.351432	+	0.936213i	$0.614305\pi$
$968$	12.8282	0.412315
$969$	0	0
$970$	−2.49803	−0.0802069
$971$	−37.6803	−1.20922	−0.604608	−	0.796523i	$-0.706670\pi$
$971$	−37.6803	−1.20922	−0.604608	+	0.796523i	$0.706670\pi$
$972$	0	0
$973$	−4.49240	−0.144020
$974$	−21.2570	−0.681119
$975$	0	0
$976$	−52.9227	−1.69401
$977$	40.4037	1.29263	0.646315	−	0.763071i	$-0.276309\pi$
$977$	40.4037	1.29263	0.646315	+	0.763071i	$0.276309\pi$
$978$	0	0
$979$	−3.91509	−0.125127
$980$	−0.698106	−0.0223002
$981$	0	0
$982$	37.6490	1.20143
$983$	−21.5254	−0.686554	−0.343277	−	0.939234i	$-0.611537\pi$
$983$	−21.5254	−0.686554	−0.343277	+	0.939234i	$0.611537\pi$
$984$	0	0
$985$	−11.5064	−0.366623
$986$	−4.21100	−0.134106
$987$	0	0
$988$	−4.48464	−0.142676
$989$	2.19714	0.0698651
$990$	0	0
$991$	−30.0007	−0.953005	−0.476502	−	0.879173i	$-0.658096\pi$
$991$	−30.0007	−0.953005	−0.476502	+	0.879173i	$0.658096\pi$
$992$	6.79335	0.215689
$993$	0	0
$994$	−24.3398	−0.772013
$995$	15.4564	0.489999
$996$	0	0
$997$	50.1929	1.58962	0.794812	−	0.606856i	$-0.207569\pi$
$997$	50.1929	1.58962	0.794812	+	0.606856i	$0.207569\pi$
$998$	−9.53594	−0.301855
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6003.2.a.v.1.10	✓	30
3.2	odd	2		6003.2.a.w.1.21	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6003.2.a.v.1.10	✓	30	1.1	even	1	trivial
6003.2.a.w.1.21	yes	30	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6003.a (trivial)

\(f(q)\)	\(=\)	\(q-1.33909 q^{2} -0.206831 q^{4} +0.887651 q^{5} -3.28671 q^{7} +2.95515 q^{8} +O(q^{10})\)	\(q-1.33909 q^{2} -0.206831 q^{4} +0.887651 q^{5} -3.28671 q^{7} +2.95515 q^{8} -1.18865 q^{10} +3.91676 q^{11} -3.54751 q^{13} +4.40121 q^{14} -3.54356 q^{16} -3.14467 q^{17} -6.11207 q^{19} -0.183594 q^{20} -5.24490 q^{22} +1.00000 q^{23} -4.21208 q^{25} +4.75044 q^{26} +0.679794 q^{28} -1.00000 q^{29} -5.83045 q^{31} -1.16515 q^{32} +4.21100 q^{34} -2.91745 q^{35} +8.16140 q^{37} +8.18463 q^{38} +2.62314 q^{40} -6.59203 q^{41} +2.19714 q^{43} -0.810107 q^{44} -1.33909 q^{46} -1.28633 q^{47} +3.80245 q^{49} +5.64036 q^{50} +0.733735 q^{52} +1.04074 q^{53} +3.47671 q^{55} -9.71272 q^{56} +1.33909 q^{58} +6.63537 q^{59} +14.9349 q^{61} +7.80752 q^{62} +8.64736 q^{64} -3.14895 q^{65} -2.96633 q^{67} +0.650415 q^{68} +3.90673 q^{70} -5.53027 q^{71} +3.29584 q^{73} -10.9289 q^{74} +1.26417 q^{76} -12.8732 q^{77} -7.93748 q^{79} -3.14544 q^{80} +8.82734 q^{82} +12.6870 q^{83} -2.79137 q^{85} -2.94218 q^{86} +11.5746 q^{88} -0.999574 q^{89} +11.6596 q^{91} -0.206831 q^{92} +1.72251 q^{94} -5.42539 q^{95} +2.10158 q^{97} -5.09183 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - q^{2} + 37 q^{4} + 10 q^{7} - 6 q^{8}+O(q^{10}) \) 30 * q - q^2 + 37 * q^4 + 10 * q^7 - 6 * q^8	\( 30 q - q^{2} + 37 q^{4} + 10 q^{7} - 6 q^{8} + 8 q^{10} + 36 q^{13} - 7 q^{14} + 47 q^{16} - 18 q^{17} + 16 q^{19} + 25 q^{22} + 30 q^{23} + 56 q^{25} - 11 q^{26} + 27 q^{28} - 30 q^{29} + 14 q^{31} + 7 q^{32} + 3 q^{34} + 22 q^{35} + 40 q^{37} - 6 q^{38} + 30 q^{40} - 14 q^{41} + 34 q^{43} - 5 q^{44} - q^{46} + 2 q^{47} + 74 q^{49} + 21 q^{50} + 71 q^{52} - 16 q^{53} + 22 q^{55} - 14 q^{56} + q^{58} + 32 q^{59} + 46 q^{61} - 20 q^{62} + 68 q^{64} - 12 q^{65} + 14 q^{67} - 27 q^{68} + 32 q^{71} + 50 q^{73} + 26 q^{74} + 56 q^{76} - 34 q^{77} + 16 q^{79} - 2 q^{80} + 38 q^{82} + 14 q^{83} + 38 q^{85} - 10 q^{86} + 40 q^{88} + 2 q^{89} + 32 q^{91} + 37 q^{92} + 29 q^{94} + 28 q^{95} + 56 q^{97} - 8 q^{98}+O(q^{100}) \) 30 * q - q^2 + 37 * q^4 + 10 * q^7 - 6 * q^8 + 8 * q^10 + 36 * q^13 - 7 * q^14 + 47 * q^16 - 18 * q^17 + 16 * q^19 + 25 * q^22 + 30 * q^23 + 56 * q^25 - 11 * q^26 + 27 * q^28 - 30 * q^29 + 14 * q^31 + 7 * q^32 + 3 * q^34 + 22 * q^35 + 40 * q^37 - 6 * q^38 + 30 * q^40 - 14 * q^41 + 34 * q^43 - 5 * q^44 - q^46 + 2 * q^47 + 74 * q^49 + 21 * q^50 + 71 * q^52 - 16 * q^53 + 22 * q^55 - 14 * q^56 + q^58 + 32 * q^59 + 46 * q^61 - 20 * q^62 + 68 * q^64 - 12 * q^65 + 14 * q^67 - 27 * q^68 + 32 * q^71 + 50 * q^73 + 26 * q^74 + 56 * q^76 - 34 * q^77 + 16 * q^79 - 2 * q^80 + 38 * q^82 + 14 * q^83 + 38 * q^85 - 10 * q^86 + 40 * q^88 + 2 * q^89 + 32 * q^91 + 37 * q^92 + 29 * q^94 + 28 * q^95 + 56 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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