LMFDB - Embedded newform 5239.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 9x^{5} + 12x^{4} + 22x^{3} - 18x^{2} - 13x - 1 $ x^7 - 2x^6 - 9x^5 + 12x^4 + 22x^3 - 18x^2 - 13x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.56423$ of defining polynomial
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.406064 q^{2} -0.564229 q^{3} -1.83511 q^{4} -2.08199 q^{5} +0.229113 q^{6} -4.31735 q^{7} +1.55730 q^{8} -2.68165 q^{9} +O(q^{10})$	\(q-0.406064 q^{2} -0.564229 q^{3} -1.83511 q^{4} -2.08199 q^{5} +0.229113 q^{6} -4.31735 q^{7} +1.55730 q^{8} -2.68165 q^{9} +0.845422 q^{10} -1.35737 q^{11} +1.03542 q^{12} +1.75312 q^{14} +1.17472 q^{15} +3.03786 q^{16} +3.04647 q^{17} +1.08892 q^{18} -4.46447 q^{19} +3.82069 q^{20} +2.43598 q^{21} +0.551178 q^{22} +5.93016 q^{23} -0.878675 q^{24} -0.665312 q^{25} +3.20575 q^{27} +7.92282 q^{28} +2.78072 q^{29} -0.477012 q^{30} -1.00000 q^{31} -4.34817 q^{32} +0.765866 q^{33} -1.23706 q^{34} +8.98869 q^{35} +4.92112 q^{36} -3.68286 q^{37} +1.81286 q^{38} -3.24229 q^{40} +0.350560 q^{41} -0.989162 q^{42} -11.3639 q^{43} +2.49092 q^{44} +5.58316 q^{45} -2.40802 q^{46} +11.0302 q^{47} -1.71405 q^{48} +11.6395 q^{49} +0.270159 q^{50} -1.71891 q^{51} -2.37177 q^{53} -1.30174 q^{54} +2.82603 q^{55} -6.72341 q^{56} +2.51899 q^{57} -1.12915 q^{58} +13.1961 q^{59} -2.15574 q^{60} +6.18275 q^{61} +0.406064 q^{62} +11.5776 q^{63} -4.31009 q^{64} -0.310991 q^{66} +2.80007 q^{67} -5.59061 q^{68} -3.34597 q^{69} -3.64998 q^{70} +11.5606 q^{71} -4.17613 q^{72} +13.9979 q^{73} +1.49548 q^{74} +0.375389 q^{75} +8.19281 q^{76} +5.86023 q^{77} +5.49553 q^{79} -6.32480 q^{80} +6.23616 q^{81} -0.142350 q^{82} -6.19615 q^{83} -4.47029 q^{84} -6.34272 q^{85} +4.61448 q^{86} -1.56896 q^{87} -2.11383 q^{88} -11.9670 q^{89} -2.26712 q^{90} -10.8825 q^{92} +0.564229 q^{93} -4.47898 q^{94} +9.29499 q^{95} +2.45336 q^{96} -3.24624 q^{97} -4.72639 q^{98} +3.63998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - 11 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - 11 * q^5 - 6 * q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	$ 7 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - 11 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 8 q^{11} - 3 q^{12} - 5 q^{14} + 2 q^{16} + 7 q^{17} + 9 q^{18} - q^{19} + 2 q^{21} + 6 q^{22} + 6 q^{23} - 5 q^{24} + 10 q^{25} + 11 q^{27} + 11 q^{28} - 2 q^{29} - 3 q^{30} - 7 q^{31} - 18 q^{32} - 6 q^{33} + 4 q^{34} - q^{35} - 20 q^{36} - 28 q^{37} - 8 q^{38} - 5 q^{40} - 3 q^{41} + 13 q^{42} - q^{43} - 12 q^{44} - 9 q^{45} + 37 q^{46} + q^{47} + 11 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} + 29 q^{53} - 2 q^{54} + 19 q^{55} - 20 q^{56} - 11 q^{57} - 3 q^{58} - 3 q^{59} + 43 q^{60} + 5 q^{61} + 2 q^{62} - q^{63} - 29 q^{64} - 29 q^{66} + 32 q^{67} + 38 q^{68} + 17 q^{69} + 23 q^{70} - 5 q^{71} + 17 q^{72} - q^{73} - 4 q^{74} - 7 q^{75} + 12 q^{76} - 5 q^{77} - 15 q^{79} + 11 q^{80} + 3 q^{81} - 36 q^{82} - 17 q^{83} - 2 q^{84} + q^{85} + 23 q^{86} - 42 q^{87} - 15 q^{88} - 26 q^{89} - 40 q^{90} - 24 q^{92} - 5 q^{93} + 18 q^{94} - 21 q^{95} + 4 q^{96} - 11 q^{97} - 6 q^{98} + 28 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - 11 * q^5 - 6 * q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 8 * q^11 - 3 * q^12 - 5 * q^14 + 2 * q^16 + 7 * q^17 + 9 * q^18 - q^19 + 2 * q^21 + 6 * q^22 + 6 * q^23 - 5 * q^24 + 10 * q^25 + 11 * q^27 + 11 * q^28 - 2 * q^29 - 3 * q^30 - 7 * q^31 - 18 * q^32 - 6 * q^33 + 4 * q^34 - q^35 - 20 * q^36 - 28 * q^37 - 8 * q^38 - 5 * q^40 - 3 * q^41 + 13 * q^42 - q^43 - 12 * q^44 - 9 * q^45 + 37 * q^46 + q^47 + 11 * q^48 - 19 * q^49 - 21 * q^50 - 30 * q^51 + 29 * q^53 - 2 * q^54 + 19 * q^55 - 20 * q^56 - 11 * q^57 - 3 * q^58 - 3 * q^59 + 43 * q^60 + 5 * q^61 + 2 * q^62 - q^63 - 29 * q^64 - 29 * q^66 + 32 * q^67 + 38 * q^68 + 17 * q^69 + 23 * q^70 - 5 * q^71 + 17 * q^72 - q^73 - 4 * q^74 - 7 * q^75 + 12 * q^76 - 5 * q^77 - 15 * q^79 + 11 * q^80 + 3 * q^81 - 36 * q^82 - 17 * q^83 - 2 * q^84 + q^85 + 23 * q^86 - 42 * q^87 - 15 * q^88 - 26 * q^89 - 40 * q^90 - 24 * q^92 - 5 * q^93 + 18 * q^94 - 21 * q^95 + 4 * q^96 - 11 * q^97 - 6 * q^98 + 28 * 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 $

$2$	−0.406064	−0.287131	−0.143565	−	0.989641i	$-0.545857\pi$
$2$	−0.406064	−0.287131	−0.143565	+	0.989641i	$0.545857\pi$
$3$	−0.564229	−0.325758	−0.162879	−	0.986646i	$-0.552078\pi$
$3$	−0.564229	−0.325758	−0.162879	+	0.986646i	$0.552078\pi$
$4$	−1.83511	−0.917556
$5$	−2.08199	−0.931095	−0.465547	−	0.885023i	$-0.654143\pi$
$5$	−2.08199	−0.931095	−0.465547	+	0.885023i	$0.654143\pi$
$6$	0.229113	0.0935351
$7$	−4.31735	−1.63180	−0.815902	−	0.578190i	$-0.803759\pi$
$7$	−4.31735	−1.63180	−0.815902	+	0.578190i	$0.803759\pi$
$8$	1.55730	0.550589
$9$	−2.68165	−0.893882
$10$	0.845422	0.267346
$11$	−1.35737	−0.409261	−0.204631	−	0.978839i	$-0.565599\pi$
$11$	−1.35737	−0.409261	−0.204631	+	0.978839i	$0.565599\pi$
$12$	1.03542	0.298901
$13$	0	0
$13$	0	0
$14$	1.75312	0.468541
$15$	1.17472	0.303312
$16$	3.03786	0.759465
$17$	3.04647	0.738877	0.369438	−	0.929255i	$-0.379550\pi$
$17$	3.04647	0.738877	0.369438	+	0.929255i	$0.379550\pi$
$18$	1.08892	0.256661
$19$	−4.46447	−1.02422	−0.512110	−	0.858920i	$-0.671136\pi$
$19$	−4.46447	−1.02422	−0.512110	+	0.858920i	$0.671136\pi$
$20$	3.82069	0.854332
$21$	2.43598	0.531574
$22$	0.551178	0.117511
$23$	5.93016	1.23652	0.618261	−	0.785973i	$-0.287837\pi$
$23$	5.93016	1.23652	0.618261	+	0.785973i	$0.287837\pi$
$24$	−0.878675	−0.179359
$25$	−0.665312	−0.133062
$26$	0	0
$27$	3.20575	0.616947
$28$	7.92282	1.49727
$29$	2.78072	0.516367	0.258183	−	0.966096i	$-0.416876\pi$
$29$	2.78072	0.516367	0.258183	+	0.966096i	$0.416876\pi$
$30$	−0.477012	−0.0870901
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.34817	−0.768655
$33$	0.765866	0.133320
$34$	−1.23706	−0.212154
$35$	8.98869	1.51937
$36$	4.92112	0.820187
$37$	−3.68286	−0.605458	−0.302729	−	0.953077i	$-0.597898\pi$
$37$	−3.68286	−0.605458	−0.302729	+	0.953077i	$0.597898\pi$
$38$	1.81286	0.294085
$39$	0	0
$40$	−3.24229	−0.512651
$41$	0.350560	0.0547483	0.0273742	−	0.999625i	$-0.491285\pi$
$41$	0.350560	0.0547483	0.0273742	+	0.999625i	$0.491285\pi$
$42$	−0.989162	−0.152631
$43$	−11.3639	−1.73298	−0.866492	−	0.499192i	$-0.833630\pi$
$43$	−11.3639	−1.73298	−0.866492	+	0.499192i	$0.833630\pi$
$44$	2.49092	0.375520
$45$	5.58316	0.832289
$46$	−2.40802	−0.355044
$47$	11.0302	1.60892	0.804462	−	0.594004i	$-0.202454\pi$
$47$	11.0302	1.60892	0.804462	+	0.594004i	$0.202454\pi$
$48$	−1.71405	−0.247402
$49$	11.6395	1.66279
$50$	0.270159	0.0382063
$51$	−1.71891	−0.240695
$52$	0	0
$53$	−2.37177	−0.325787	−0.162894	−	0.986644i	$-0.552083\pi$
$53$	−2.37177	−0.325787	−0.162894	+	0.986644i	$0.552083\pi$
$54$	−1.30174	−0.177144
$55$	2.82603	0.381061
$56$	−6.72341	−0.898454
$57$	2.51899	0.333648
$58$	−1.12915	−0.148265
$59$	13.1961	1.71798	0.858992	−	0.511990i	$-0.171091\pi$
$59$	13.1961	1.71798	0.858992	+	0.511990i	$0.171091\pi$
$60$	−2.15574	−0.278305
$61$	6.18275	0.791620	0.395810	−	0.918332i	$-0.370464\pi$
$61$	6.18275	0.791620	0.395810	+	0.918332i	$0.370464\pi$
$62$	0.406064	0.0515702
$63$	11.5776	1.45864
$64$	−4.31009	−0.538761
$65$	0	0
$66$	−0.310991	−0.0382803
$67$	2.80007	0.342082	0.171041	−	0.985264i	$-0.445287\pi$
$67$	2.80007	0.342082	0.171041	+	0.985264i	$0.445287\pi$
$68$	−5.59061	−0.677961
$69$	−3.34597	−0.402807
$70$	−3.64998	−0.436256
$71$	11.5606	1.37200	0.685998	−	0.727604i	$-0.259366\pi$
$71$	11.5606	1.37200	0.685998	+	0.727604i	$0.259366\pi$
$72$	−4.17613	−0.492162
$73$	13.9979	1.63833	0.819163	−	0.573560i	$-0.194438\pi$
$73$	13.9979	1.63833	0.819163	+	0.573560i	$0.194438\pi$
$74$	1.49548	0.173845
$75$	0.375389	0.0433462
$76$	8.19281	0.939779
$77$	5.86023	0.667835
$78$	0	0
$79$	5.49553	0.618295	0.309147	−	0.951014i	$-0.399956\pi$
$79$	5.49553	0.618295	0.309147	+	0.951014i	$0.399956\pi$
$80$	−6.32480	−0.707134
$81$	6.23616	0.692906
$82$	−0.142350	−0.0157199
$83$	−6.19615	−0.680116	−0.340058	−	0.940405i	$-0.610447\pi$
$83$	−6.19615	−0.680116	−0.340058	+	0.940405i	$0.610447\pi$
$84$	−4.47029	−0.487749
$85$	−6.34272	−0.687964
$86$	4.61448	0.497593
$87$	−1.56896	−0.168211
$88$	−2.11383	−0.225335
$89$	−11.9670	−1.26850	−0.634251	−	0.773127i	$-0.718691\pi$
$89$	−11.9670	−1.26850	−0.634251	+	0.773127i	$0.718691\pi$
$90$	−2.26712	−0.238976
$91$	0	0
$92$	−10.8825	−1.13458
$93$	0.564229	0.0585079
$94$	−4.47898	−0.461972
$95$	9.29499	0.953646
$96$	2.45336	0.250395
$97$	−3.24624	−0.329605	−0.164803	−	0.986327i	$-0.552699\pi$
$97$	−3.24624	−0.329605	−0.164803	+	0.986327i	$0.552699\pi$
$98$	−4.72639	−0.477437
$99$	3.63998	0.365831
$100$	1.22092	0.122092
$101$	−3.61159	−0.359367	−0.179684	−	0.983724i	$-0.557507\pi$
$101$	−3.61159	−0.359367	−0.179684	+	0.983724i	$0.557507\pi$
$102$	0.697986	0.0691109
$103$	−16.5588	−1.63159	−0.815794	−	0.578343i	$-0.803700\pi$
$103$	−16.5588	−1.63159	−0.815794	+	0.578343i	$0.803700\pi$
$104$	0	0
$105$	−5.07168	−0.494945
$106$	0.963089	0.0935434
$107$	20.2539	1.95802	0.979011	−	0.203810i	$-0.0653323\pi$
$107$	20.2539	1.95802	0.979011	+	0.203810i	$0.0653323\pi$
$108$	−5.88291	−0.566084
$109$	−3.84368	−0.368158	−0.184079	−	0.982911i	$-0.558930\pi$
$109$	−3.84368	−0.368158	−0.184079	+	0.982911i	$0.558930\pi$
$110$	−1.14755	−0.109414
$111$	2.07798	0.197233
$112$	−13.1155	−1.23930
$113$	12.6178	1.18699	0.593494	−	0.804839i	$-0.297748\pi$
$113$	12.6178	1.18699	0.593494	+	0.804839i	$0.297748\pi$
$114$	−1.02287	−0.0958006
$115$	−12.3465	−1.15132
$116$	−5.10293	−0.473795
$117$	0	0
$118$	−5.35845	−0.493286
$119$	−13.1527	−1.20570
$120$	1.82939	0.167000
$121$	−9.15756	−0.832505
$122$	−2.51059	−0.227298
$123$	−0.197796	−0.0178347
$124$	1.83511	0.164798
$125$	11.7951	1.05499
$126$	−4.70125	−0.418820
$127$	−21.8294	−1.93705	−0.968523	−	0.248923i	$-0.919923\pi$
$127$	−21.8294	−1.93705	−0.968523	+	0.248923i	$0.919923\pi$
$128$	10.4465	0.923349
$129$	6.41187	0.564533
$130$	0	0
$131$	−2.23229	−0.195036	−0.0975180	−	0.995234i	$-0.531090\pi$
$131$	−2.23229	−0.195036	−0.0975180	+	0.995234i	$0.531090\pi$
$132$	−1.40545	−0.122329
$133$	19.2747	1.67133
$134$	−1.13701	−0.0982223
$135$	−6.67435	−0.574436
$136$	4.74427	0.406818
$137$	−9.20030	−0.786034	−0.393017	−	0.919531i	$-0.628569\pi$
$137$	−9.20030	−0.786034	−0.393017	+	0.919531i	$0.628569\pi$
$138$	1.35868	0.115658
$139$	−11.0195	−0.934662	−0.467331	−	0.884082i	$-0.654784\pi$
$139$	−11.0195	−0.934662	−0.467331	+	0.884082i	$0.654784\pi$
$140$	−16.4952	−1.39410
$141$	−6.22358	−0.524120
$142$	−4.69436	−0.393942
$143$	0	0
$144$	−8.14646	−0.678872
$145$	−5.78943	−0.480786
$146$	−5.68403	−0.470414
$147$	−6.56736	−0.541666
$148$	6.75845	0.555541
$149$	8.55688	0.701007	0.350503	−	0.936561i	$-0.386010\pi$
$149$	8.55688	0.701007	0.350503	+	0.936561i	$0.386010\pi$
$150$	−0.152432	−0.0124460
$151$	−17.8160	−1.44985	−0.724923	−	0.688830i	$-0.758125\pi$
$151$	−17.8160	−1.44985	−0.724923	+	0.688830i	$0.758125\pi$
$152$	−6.95253	−0.563924
$153$	−8.16955	−0.660469
$154$	−2.37963	−0.191756
$155$	2.08199	0.167230
$156$	0	0
$157$	−4.06150	−0.324143	−0.162072	−	0.986779i	$-0.551818\pi$
$157$	−4.06150	−0.324143	−0.162072	+	0.986779i	$0.551818\pi$
$158$	−2.23154	−0.177531
$159$	1.33822	0.106128
$160$	9.05285	0.715690
$161$	−25.6026	−2.01776
$162$	−2.53228	−0.198955
$163$	16.0154	1.25442	0.627212	−	0.778849i	$-0.284196\pi$
$163$	16.0154	1.25442	0.627212	+	0.778849i	$0.284196\pi$
$164$	−0.643317	−0.0502347
$165$	−1.59453	−0.124134
$166$	2.51603	0.195282
$167$	3.82702	0.296143	0.148072	−	0.988977i	$-0.452693\pi$
$167$	3.82702	0.296143	0.148072	+	0.988977i	$0.452693\pi$
$168$	3.79355	0.292679
$169$	0	0
$170$	2.57555	0.197536
$171$	11.9721	0.915532
$172$	20.8541	1.59011
$173$	3.68973	0.280525	0.140263	−	0.990114i	$-0.455205\pi$
$173$	3.68973	0.280525	0.140263	+	0.990114i	$0.455205\pi$
$174$	0.637100	0.0482984
$175$	2.87239	0.217132
$176$	−4.12349	−0.310820
$177$	−7.44562	−0.559647
$178$	4.85938	0.364226
$179$	16.0592	1.20032	0.600162	−	0.799878i	$-0.295103\pi$
$179$	16.0592	1.20032	0.600162	+	0.799878i	$0.295103\pi$
$180$	−10.2457	−0.763671
$181$	−3.77686	−0.280732	−0.140366	−	0.990100i	$-0.544828\pi$
$181$	−3.77686	−0.280732	−0.140366	+	0.990100i	$0.544828\pi$
$182$	0	0
$183$	−3.48849	−0.257877
$184$	9.23504	0.680816
$185$	7.66767	0.563739
$186$	−0.229113	−0.0167994
$187$	−4.13517	−0.302394
$188$	−20.2417	−1.47628
$189$	−13.8404	−1.00674
$190$	−3.77436	−0.273821
$191$	−10.2320	−0.740362	−0.370181	−	0.928960i	$-0.620704\pi$
$191$	−10.2320	−0.740362	−0.370181	+	0.928960i	$0.620704\pi$
$192$	2.43188	0.175506
$193$	6.31774	0.454761	0.227381	−	0.973806i	$-0.426984\pi$
$193$	6.31774	0.454761	0.227381	+	0.973806i	$0.426984\pi$
$194$	1.31818	0.0946398
$195$	0	0
$196$	−21.3598	−1.52570
$197$	−12.0698	−0.859941	−0.429970	−	0.902843i	$-0.641476\pi$
$197$	−12.0698	−0.859941	−0.429970	+	0.902843i	$0.641476\pi$
$198$	−1.47806	−0.105041
$199$	−14.5115	−1.02869	−0.514346	−	0.857583i	$-0.671965\pi$
$199$	−14.5115	−1.02869	−0.514346	+	0.857583i	$0.671965\pi$
$200$	−1.03609	−0.0732627
$201$	−1.57988	−0.111436
$202$	1.46654	0.103185
$203$	−12.0053	−0.842610
$204$	3.15439	0.220851
$205$	−0.729864	−0.0509759
$206$	6.72394	0.468479
$207$	−15.9026	−1.10531
$208$	0	0
$209$	6.05992	0.419174
$210$	2.05943	0.142114
$211$	−5.92401	−0.407826	−0.203913	−	0.978989i	$-0.565366\pi$
$211$	−5.92401	−0.407826	−0.203913	+	0.978989i	$0.565366\pi$
$212$	4.35246	0.298928
$213$	−6.52285	−0.446939
$214$	−8.22439	−0.562208
$215$	23.6596	1.61357
$216$	4.99232	0.339684
$217$	4.31735	0.293081
$218$	1.56078	0.105709
$219$	−7.89801	−0.533698
$220$	−5.18607	−0.349645
$221$	0	0
$222$	−0.843791	−0.0566316
$223$	−1.36553	−0.0914427	−0.0457213	−	0.998954i	$-0.514559\pi$
$223$	−1.36553	−0.0914427	−0.0457213	+	0.998954i	$0.514559\pi$
$224$	18.7726	1.25429
$225$	1.78413	0.118942
$226$	−5.12365	−0.340820
$227$	−10.6877	−0.709370	−0.354685	−	0.934986i	$-0.615412\pi$
$227$	−10.6877	−0.709370	−0.354685	+	0.934986i	$0.615412\pi$
$228$	−4.62262	−0.306141
$229$	10.8669	0.718103	0.359052	−	0.933318i	$-0.383100\pi$
$229$	10.8669	0.718103	0.359052	+	0.933318i	$0.383100\pi$
$230$	5.01348	0.330579
$231$	−3.30651	−0.217553
$232$	4.33042	0.284306
$233$	0.962232	0.0630379	0.0315190	−	0.999503i	$-0.489966\pi$
$233$	0.962232	0.0630379	0.0315190	+	0.999503i	$0.489966\pi$
$234$	0	0
$235$	−22.9648	−1.49806
$236$	−24.2163	−1.57635
$237$	−3.10074	−0.201415
$238$	5.34083	0.346194
$239$	1.34770	0.0871752	0.0435876	−	0.999050i	$-0.486121\pi$
$239$	1.34770	0.0871752	0.0435876	+	0.999050i	$0.486121\pi$
$240$	3.56864	0.230355
$241$	−23.8634	−1.53718	−0.768589	−	0.639743i	$-0.779041\pi$
$241$	−23.8634	−1.53718	−0.768589	+	0.639743i	$0.779041\pi$
$242$	3.71855	0.239038
$243$	−13.1359	−0.842667
$244$	−11.3460	−0.726356
$245$	−24.2334	−1.54821
$246$	0.0803180	0.00512089
$247$	0	0
$248$	−1.55730	−0.0988887
$249$	3.49605	0.221553
$250$	−4.78958	−0.302920
$251$	26.5114	1.67339	0.836693	−	0.547672i	$-0.184486\pi$
$251$	26.5114	1.67339	0.836693	+	0.547672i	$0.184486\pi$
$252$	−21.2462	−1.33838
$253$	−8.04939	−0.506061
$254$	8.86414	0.556185
$255$	3.57875	0.224110
$256$	4.37822	0.273639
$257$	−22.8213	−1.42355	−0.711777	−	0.702405i	$-0.752110\pi$
$257$	−22.8213	−1.42355	−0.711777	+	0.702405i	$0.752110\pi$
$258$	−2.60363	−0.162095
$259$	15.9002	0.987989
$260$	0	0
$261$	−7.45690	−0.461571
$262$	0.906452	0.0560008
$263$	20.1810	1.24441	0.622207	−	0.782852i	$-0.286236\pi$
$263$	20.1810	1.24441	0.622207	+	0.782852i	$0.286236\pi$
$264$	1.19268	0.0734046
$265$	4.93800	0.303339
$266$	−7.82676	−0.479889
$267$	6.75215	0.413225
$268$	−5.13843	−0.313880
$269$	−6.47984	−0.395083	−0.197541	−	0.980295i	$-0.563296\pi$
$269$	−6.47984	−0.395083	−0.197541	+	0.980295i	$0.563296\pi$
$270$	2.71021	0.164938
$271$	23.1355	1.40538	0.702689	−	0.711497i	$-0.251982\pi$
$271$	23.1355	1.40538	0.702689	+	0.711497i	$0.251982\pi$
$272$	9.25474	0.561151
$273$	0	0
$274$	3.73591	0.225695
$275$	0.903073	0.0544573
$276$	6.14023	0.369598
$277$	−8.34538	−0.501425	−0.250713	−	0.968062i	$-0.580665\pi$
$277$	−8.34538	−0.501425	−0.250713	+	0.968062i	$0.580665\pi$
$278$	4.47462	0.268370
$279$	2.68165	0.160546
$280$	13.9981	0.836546
$281$	10.7239	0.639734	0.319867	−	0.947462i	$-0.396362\pi$
$281$	10.7239	0.639734	0.319867	+	0.947462i	$0.396362\pi$
$282$	2.52717	0.150491
$283$	30.5904	1.81841	0.909206	−	0.416346i	$-0.136690\pi$
$283$	30.5904	1.81841	0.909206	+	0.416346i	$0.136690\pi$
$284$	−21.2151	−1.25888
$285$	−5.24451	−0.310658
$286$	0	0
$287$	−1.51349	−0.0893386
$288$	11.6602	0.687086
$289$	−7.71903	−0.454061
$290$	2.35088	0.138048
$291$	1.83162	0.107372
$292$	−25.6877	−1.50326
$293$	−28.6619	−1.67445	−0.837224	−	0.546861i	$-0.815823\pi$
$293$	−28.6619	−1.67445	−0.837224	+	0.546861i	$0.815823\pi$
$294$	2.66677	0.155529
$295$	−27.4741	−1.59961
$296$	−5.73532	−0.333358
$297$	−4.35138	−0.252493
$298$	−3.47464	−0.201281
$299$	0	0
$300$	−0.688881	−0.0397725
$301$	49.0621	2.82789
$302$	7.23444	0.416295
$303$	2.03777	0.117067
$304$	−13.5624	−0.777859
$305$	−12.8724	−0.737074
$306$	3.31736	0.189641
$307$	−9.14856	−0.522136	−0.261068	−	0.965320i	$-0.584075\pi$
$307$	−9.14856	−0.522136	−0.261068	+	0.965320i	$0.584075\pi$
$308$	−10.7542	−0.612776
$309$	9.34297	0.531503
$310$	−0.845422	−0.0480167
$311$	13.1768	0.747191	0.373595	−	0.927592i	$-0.378125\pi$
$311$	13.1768	0.747191	0.373595	+	0.927592i	$0.378125\pi$
$312$	0	0
$313$	13.5935	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$313$	13.5935	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$314$	1.64923	0.0930715
$315$	−24.1045	−1.35813
$316$	−10.0849	−0.567320
$317$	−7.13123	−0.400530	−0.200265	−	0.979742i	$-0.564180\pi$
$317$	−7.13123	−0.400530	−0.200265	+	0.979742i	$0.564180\pi$
$318$	−0.543403	−0.0304725
$319$	−3.77446	−0.211329
$320$	8.97356	0.501637
$321$	−11.4279	−0.637841
$322$	10.3963	0.579362
$323$	−13.6009	−0.756773
$324$	−11.4440	−0.635780
$325$	0	0
$326$	−6.50328	−0.360183
$327$	2.16872	0.119930
$328$	0.545928	0.0301438
$329$	−47.6214	−2.62545
$330$	0.647480	0.0356426
$331$	27.8999	1.53352	0.766758	−	0.641936i	$-0.221869\pi$
$331$	27.8999	1.53352	0.766758	+	0.641936i	$0.221869\pi$
$332$	11.3706	0.624044
$333$	9.87611	0.541208
$334$	−1.55401	−0.0850318
$335$	−5.82971	−0.318511
$336$	7.40015	0.403712
$337$	−8.09521	−0.440974	−0.220487	−	0.975390i	$-0.570765\pi$
$337$	−8.09521	−0.440974	−0.220487	+	0.975390i	$0.570765\pi$
$338$	0	0
$339$	−7.11936	−0.386671
$340$	11.6396	0.631246
$341$	1.35737	0.0735055
$342$	−4.86145	−0.262877
$343$	−20.0304	−1.08154
$344$	−17.6971	−0.954162
$345$	6.96628	0.375052
$346$	−1.49827	−0.0805474
$347$	2.04686	0.109881	0.0549406	−	0.998490i	$-0.482503\pi$
$347$	2.04686	0.109881	0.0549406	+	0.998490i	$0.482503\pi$
$348$	2.87922	0.154343
$349$	−4.64066	−0.248409	−0.124204	−	0.992257i	$-0.539638\pi$
$349$	−4.64066	−0.248409	−0.124204	+	0.992257i	$0.539638\pi$
$350$	−1.16637	−0.0623453
$351$	0	0
$352$	5.90206	0.314581
$353$	5.00598	0.266442	0.133221	−	0.991086i	$-0.457468\pi$
$353$	5.00598	0.266442	0.133221	+	0.991086i	$0.457468\pi$
$354$	3.02340	0.160692
$355$	−24.0692	−1.27746
$356$	21.9608	1.16392
$357$	7.42112	0.392767
$358$	−6.52108	−0.344650
$359$	18.9931	1.00242	0.501209	−	0.865326i	$-0.332889\pi$
$359$	18.9931	1.00242	0.501209	+	0.865326i	$0.332889\pi$
$360$	8.69466	0.458249
$361$	0.931512	0.0490270
$362$	1.53365	0.0806067
$363$	5.16696	0.271195
$364$	0	0
$365$	−29.1434	−1.52544
$366$	1.41655	0.0740443
$367$	−17.5239	−0.914739	−0.457369	−	0.889277i	$-0.651208\pi$
$367$	−17.5239	−0.914739	−0.457369	+	0.889277i	$0.651208\pi$
$368$	18.0150	0.939096
$369$	−0.940078	−0.0489385
$370$	−3.11357	−0.161867
$371$	10.2397	0.531621
$372$	−1.03542	−0.0536842
$373$	14.5615	0.753968	0.376984	−	0.926220i	$-0.376961\pi$
$373$	14.5615	0.753968	0.376984	+	0.926220i	$0.376961\pi$
$374$	1.67915	0.0868265
$375$	−6.65516	−0.343671
$376$	17.1774	0.885856
$377$	0	0
$378$	5.62007	0.289065
$379$	19.9446	1.02449	0.512243	−	0.858840i	$-0.328815\pi$
$379$	19.9446	1.02449	0.512243	+	0.858840i	$0.328815\pi$
$380$	−17.0574	−0.875024
$381$	12.3168	0.631009
$382$	4.15485	0.212581
$383$	−9.56469	−0.488733	−0.244366	−	0.969683i	$-0.578580\pi$
$383$	−9.56469	−0.488733	−0.244366	+	0.969683i	$0.578580\pi$
$384$	−5.89423	−0.300789
$385$	−12.2009	−0.621818
$386$	−2.56541	−0.130576
$387$	30.4740	1.54908
$388$	5.95721	0.302431
$389$	2.92306	0.148205	0.0741025	−	0.997251i	$-0.476391\pi$
$389$	2.92306	0.148205	0.0741025	+	0.997251i	$0.476391\pi$
$390$	0	0
$391$	18.0660	0.913638
$392$	18.1262	0.915513
$393$	1.25952	0.0635345
$394$	4.90113	0.246915
$395$	−11.4416	−0.575691
$396$	−6.67976	−0.335671
$397$	3.61783	0.181574	0.0907869	−	0.995870i	$-0.471062\pi$
$397$	3.61783	0.181574	0.0907869	+	0.995870i	$0.471062\pi$
$398$	5.89259	0.295369
$399$	−10.8753	−0.544448
$400$	−2.02113	−0.101056
$401$	23.4418	1.17063	0.585315	−	0.810806i	$-0.300971\pi$
$401$	23.4418	1.17063	0.585315	+	0.810806i	$0.300971\pi$
$402$	0.641532	0.0319967
$403$	0	0
$404$	6.62768	0.329739
$405$	−12.9836	−0.645161
$406$	4.87494	0.241939
$407$	4.99898	0.247790
$408$	−2.67686	−0.132524
$409$	−21.1192	−1.04428	−0.522139	−	0.852860i	$-0.674866\pi$
$409$	−21.1192	−1.04428	−0.522139	+	0.852860i	$0.674866\pi$
$410$	0.296371	0.0146367
$411$	5.19108	0.256057
$412$	30.3873	1.49707
$413$	−56.9721	−2.80341
$414$	6.45746	0.317367
$415$	12.9003	0.633252
$416$	0	0
$417$	6.21753	0.304474
$418$	−2.46072	−0.120358
$419$	−9.42094	−0.460243	−0.230122	−	0.973162i	$-0.573912\pi$
$419$	−9.42094	−0.460243	−0.230122	+	0.973162i	$0.573912\pi$
$420$	9.30710	0.454140
$421$	18.3957	0.896553	0.448276	−	0.893895i	$-0.352038\pi$
$421$	18.3957	0.896553	0.448276	+	0.893895i	$0.352038\pi$
$422$	2.40553	0.117099
$423$	−29.5792	−1.43819
$424$	−3.69355	−0.179375
$425$	−2.02685	−0.0983168
$426$	2.64870	0.128330
$427$	−26.6931	−1.29177
$428$	−37.1682	−1.79659
$429$	0	0
$430$	−9.60732	−0.463306
$431$	−18.8823	−0.909529	−0.454764	−	0.890612i	$-0.650277\pi$
$431$	−18.8823	−0.909529	−0.454764	+	0.890612i	$0.650277\pi$
$432$	9.73862	0.468550
$433$	−2.71856	−0.130646	−0.0653228	−	0.997864i	$-0.520808\pi$
$433$	−2.71856	−0.130646	−0.0653228	+	0.997864i	$0.520808\pi$
$434$	−1.75312	−0.0841525
$435$	3.26657	0.156620
$436$	7.05358	0.337805
$437$	−26.4750	−1.26647
$438$	3.20710	0.153241
$439$	−0.993198	−0.0474027	−0.0237014	−	0.999719i	$-0.507545\pi$
$439$	−0.993198	−0.0474027	−0.0237014	+	0.999719i	$0.507545\pi$
$440$	4.40097	0.209808
$441$	−31.2130	−1.48634
$442$	0	0
$443$	5.71229	0.271399	0.135700	−	0.990750i	$-0.456672\pi$
$443$	5.71229	0.271399	0.135700	+	0.990750i	$0.456672\pi$
$444$	−3.81332	−0.180972
$445$	24.9152	1.18110
$446$	0.554493	0.0262560
$447$	−4.82804	−0.228359
$448$	18.6081	0.879152
$449$	17.8365	0.841757	0.420879	−	0.907117i	$-0.361722\pi$
$449$	17.8365	0.841757	0.420879	+	0.907117i	$0.361722\pi$
$450$	−0.724472	−0.0341519
$451$	−0.475839	−0.0224064
$452$	−23.1552	−1.08913
$453$	10.0523	0.472299
$454$	4.33991	0.203682
$455$	0	0
$456$	3.92282	0.183703
$457$	−24.9921	−1.16908	−0.584540	−	0.811365i	$-0.698725\pi$
$457$	−24.9921	−1.16908	−0.584540	+	0.811365i	$0.698725\pi$
$458$	−4.41265	−0.206189
$459$	9.76622	0.455848
$460$	22.6573	1.05640
$461$	4.01828	0.187150	0.0935750	−	0.995612i	$-0.470171\pi$
$461$	4.01828	0.187150	0.0935750	+	0.995612i	$0.470171\pi$
$462$	1.34266	0.0624660
$463$	31.1614	1.44819	0.724097	−	0.689698i	$-0.242257\pi$
$463$	31.1614	1.44819	0.724097	+	0.689698i	$0.242257\pi$
$464$	8.44744	0.392162
$465$	−1.17472	−0.0544764
$466$	−0.390728	−0.0181001
$467$	6.95026	0.321620	0.160810	−	0.986985i	$-0.448589\pi$
$467$	6.95026	0.321620	0.160810	+	0.986985i	$0.448589\pi$
$468$	0	0
$469$	−12.0889	−0.558212
$470$	9.32520	0.430139
$471$	2.29162	0.105592
$472$	20.5503	0.945903
$473$	15.4250	0.709243
$474$	1.25910	0.0578323
$475$	2.97027	0.136285
$476$	24.1366	1.10630
$477$	6.36023	0.291215
$478$	−0.547251	−0.0250307
$479$	22.8834	1.04557	0.522785	−	0.852465i	$-0.324893\pi$
$479$	22.8834	1.04557	0.522785	+	0.852465i	$0.324893\pi$
$480$	−5.10788	−0.233142
$481$	0	0
$482$	9.69008	0.441371
$483$	14.4457	0.657303
$484$	16.8051	0.763870
$485$	6.75864	0.306894
$486$	5.33401	0.241956
$487$	−13.9882	−0.633865	−0.316933	−	0.948448i	$-0.602653\pi$
$487$	−13.9882	−0.633865	−0.316933	+	0.948448i	$0.602653\pi$
$488$	9.62841	0.435857
$489$	−9.03636	−0.408638
$490$	9.84030	0.444539
$491$	2.26993	0.102441	0.0512203	−	0.998687i	$-0.483689\pi$
$491$	2.26993	0.102441	0.0512203	+	0.998687i	$0.483689\pi$
$492$	0.362979	0.0163643
$493$	8.47137	0.381531
$494$	0	0
$495$	−7.57840	−0.340624
$496$	−3.03786	−0.136404
$497$	−49.9113	−2.23883
$498$	−1.41962	−0.0636147
$499$	−1.87669	−0.0840120	−0.0420060	−	0.999117i	$-0.513375\pi$
$499$	−1.87669	−0.0840120	−0.0420060	+	0.999117i	$0.513375\pi$
$500$	−21.6454	−0.968011
$501$	−2.15931	−0.0964711
$502$	−10.7653	−0.480480
$503$	−31.3017	−1.39567	−0.697836	−	0.716257i	$-0.745854\pi$
$503$	−31.3017	−1.39567	−0.697836	+	0.716257i	$0.745854\pi$
$504$	18.0298	0.803112
$505$	7.51931	0.334605
$506$	3.26857	0.145306
$507$	0	0
$508$	40.0594	1.77735
$509$	−11.8274	−0.524241	−0.262120	−	0.965035i	$-0.584422\pi$
$509$	−11.8274	−0.524241	−0.262120	+	0.965035i	$0.584422\pi$
$510$	−1.45320	−0.0643488
$511$	−60.4337	−2.67343
$512$	−22.6709	−1.00192
$513$	−14.3120	−0.631890
$514$	9.26692	0.408746
$515$	34.4753	1.51916
$516$	−11.7665	−0.517991
$517$	−14.9721	−0.658471
$518$	−6.45649	−0.283682
$519$	−2.08186	−0.0913833
$520$	0	0
$521$	3.37548	0.147883	0.0739413	−	0.997263i	$-0.476442\pi$
$521$	3.37548	0.147883	0.0739413	+	0.997263i	$0.476442\pi$
$522$	3.02798	0.132531
$523$	2.01422	0.0880759	0.0440379	−	0.999030i	$-0.485978\pi$
$523$	2.01422	0.0880759	0.0440379	+	0.999030i	$0.485978\pi$
$524$	4.09650	0.178956
$525$	−1.62069	−0.0707325
$526$	−8.19479	−0.357310
$527$	−3.04647	−0.132706
$528$	2.32659	0.101252
$529$	12.1667	0.528989
$530$	−2.00514	−0.0870978
$531$	−35.3872	−1.53567
$532$	−35.3712	−1.53354
$533$	0	0
$534$	−2.74180	−0.118650
$535$	−42.1685	−1.82310
$536$	4.36054	0.188347
$537$	−9.06110	−0.391015
$538$	2.63123	0.113440
$539$	−15.7991	−0.680515
$540$	12.2482	0.527078
$541$	35.9908	1.54737	0.773683	−	0.633573i	$-0.218412\pi$
$541$	35.9908	1.54737	0.773683	+	0.633573i	$0.218412\pi$
$542$	−9.39448	−0.403527
$543$	2.13102	0.0914506
$544$	−13.2466	−0.567941
$545$	8.00251	0.342790
$546$	0	0
$547$	−27.1468	−1.16071	−0.580356	−	0.814363i	$-0.697087\pi$
$547$	−27.1468	−1.16071	−0.580356	+	0.814363i	$0.697087\pi$
$548$	16.8836	0.721230
$549$	−16.5799	−0.707615
$550$	−0.366705	−0.0156364
$551$	−12.4144	−0.528873
$552$	−5.21068	−0.221781
$553$	−23.7261	−1.00894
$554$	3.38876	0.143975
$555$	−4.32633	−0.183642
$556$	20.2220	0.857605
$557$	−23.7423	−1.00599	−0.502996	−	0.864289i	$-0.667769\pi$
$557$	−23.7423	−1.00599	−0.502996	+	0.864289i	$0.667769\pi$
$558$	−1.08892	−0.0460976
$559$	0	0
$560$	27.3064	1.15390
$561$	2.33319	0.0985072
$562$	−4.35459	−0.183687
$563$	43.1746	1.81959	0.909796	−	0.415055i	$-0.136238\pi$
$563$	43.1746	1.81959	0.909796	+	0.415055i	$0.136238\pi$
$564$	11.4210	0.480910
$565$	−26.2702	−1.10520
$566$	−12.4217	−0.522122
$567$	−26.9237	−1.13069
$568$	18.0034	0.755406
$569$	36.3142	1.52237	0.761186	−	0.648534i	$-0.224617\pi$
$569$	36.3142	1.52237	0.761186	+	0.648534i	$0.224617\pi$
$570$	2.12961	0.0891994
$571$	−38.0569	−1.59263	−0.796316	−	0.604880i	$-0.793221\pi$
$571$	−38.0569	−1.59263	−0.796316	+	0.604880i	$0.793221\pi$
$572$	0	0
$573$	5.77320	0.241179
$574$	0.614575	0.0256518
$575$	−3.94541	−0.164535
$576$	11.5581	0.481588
$577$	−19.8725	−0.827304	−0.413652	−	0.910435i	$-0.635747\pi$
$577$	−19.8725	−0.827304	−0.413652	+	0.910435i	$0.635747\pi$
$578$	3.13442	0.130375
$579$	−3.56466	−0.148142
$580$	10.6243	0.441148
$581$	26.7509	1.10982
$582$	−0.743756	−0.0308297
$583$	3.21936	0.133332
$584$	21.7989	0.902045
$585$	0	0
$586$	11.6386	0.480785
$587$	−18.8161	−0.776624	−0.388312	−	0.921528i	$-0.626942\pi$
$587$	−18.8161	−0.776624	−0.388312	+	0.921528i	$0.626942\pi$
$588$	12.0518	0.497009
$589$	4.46447	0.183955
$590$	11.1563	0.459296
$591$	6.81016	0.280133
$592$	−11.1880	−0.459824
$593$	15.0419	0.617698	0.308849	−	0.951111i	$-0.400056\pi$
$593$	15.0419	0.617698	0.308849	+	0.951111i	$0.400056\pi$
$594$	1.76694	0.0724984
$595$	27.3837	1.12262
$596$	−15.7028	−0.643213
$597$	8.18780	0.335104
$598$	0	0
$599$	−9.26937	−0.378736	−0.189368	−	0.981906i	$-0.560644\pi$
$599$	−9.26937	−0.378736	−0.189368	+	0.981906i	$0.560644\pi$
$600$	0.584593	0.0238659
$601$	31.5037	1.28506	0.642532	−	0.766259i	$-0.277884\pi$
$601$	31.5037	1.28506	0.642532	+	0.766259i	$0.277884\pi$
$602$	−19.9223	−0.811974
$603$	−7.50878	−0.305781
$604$	32.6944	1.33032
$605$	19.0660	0.775141
$606$	−0.827464	−0.0336134
$607$	11.4040	0.462873	0.231436	−	0.972850i	$-0.425657\pi$
$607$	11.4040	0.462873	0.231436	+	0.972850i	$0.425657\pi$
$608$	19.4123	0.787272
$609$	6.77377	0.274487
$610$	5.22703	0.211636
$611$	0	0
$612$	14.9920	0.606017
$613$	−43.8091	−1.76943	−0.884717	−	0.466129i	$-0.845648\pi$
$613$	−43.8091	−1.76943	−0.884717	+	0.466129i	$0.845648\pi$
$614$	3.71490	0.149921
$615$	0.411811	0.0166058
$616$	9.12614	0.367703
$617$	34.1160	1.37346	0.686728	−	0.726914i	$-0.259046\pi$
$617$	34.1160	1.37346	0.686728	+	0.726914i	$0.259046\pi$
$618$	−3.79384	−0.152611
$619$	−8.31433	−0.334181	−0.167090	−	0.985942i	$-0.553437\pi$
$619$	−8.31433	−0.334181	−0.167090	+	0.985942i	$0.553437\pi$
$620$	−3.82069	−0.153442
$621$	19.0106	0.762869
$622$	−5.35064	−0.214541
$623$	51.6658	2.06995
$624$	0	0
$625$	−21.2308	−0.849232
$626$	−5.51983	−0.220617
$627$	−3.41919	−0.136549
$628$	7.45331	0.297420
$629$	−11.2197	−0.447359
$630$	9.78796	0.389962
$631$	−25.1978	−1.00311	−0.501555	−	0.865126i	$-0.667239\pi$
$631$	−25.1978	−1.00311	−0.501555	+	0.865126i	$0.667239\pi$
$632$	8.55819	0.340426
$633$	3.34250	0.132852
$634$	2.89574	0.115004
$635$	45.4486	1.80357
$636$	−2.45578	−0.0973782
$637$	0	0
$638$	1.53267	0.0606790
$639$	−31.0015	−1.22640
$640$	−21.7495	−0.859726
$641$	−0.736830	−0.0291030	−0.0145515	−	0.999894i	$-0.504632\pi$
$641$	−0.736830	−0.0291030	−0.0145515	+	0.999894i	$0.504632\pi$
$642$	4.64044	0.183144
$643$	42.9484	1.69372	0.846860	−	0.531815i	$-0.178490\pi$
$643$	42.9484	1.69372	0.846860	+	0.531815i	$0.178490\pi$
$644$	46.9836	1.85141
$645$	−13.3494	−0.525634
$646$	5.52282	0.217293
$647$	−30.2305	−1.18848	−0.594242	−	0.804286i	$-0.702548\pi$
$647$	−30.2305	−1.18848	−0.594242	+	0.804286i	$0.702548\pi$
$648$	9.71157	0.381507
$649$	−17.9119	−0.703104
$650$	0	0
$651$	−2.43598	−0.0954734
$652$	−29.3901	−1.15100
$653$	48.1011	1.88234	0.941171	−	0.337932i	$-0.109727\pi$
$653$	48.1011	1.88234	0.941171	+	0.337932i	$0.109727\pi$
$654$	−0.880638	−0.0344357
$655$	4.64761	0.181597
$656$	1.06495	0.0415794
$657$	−37.5373	−1.46447
$658$	19.3373	0.753848
$659$	−30.5278	−1.18920	−0.594598	−	0.804023i	$-0.702689\pi$
$659$	−30.5278	−1.18920	−0.594598	+	0.804023i	$0.702689\pi$
$660$	2.92614	0.113900
$661$	−11.0833	−0.431090	−0.215545	−	0.976494i	$-0.569153\pi$
$661$	−11.0833	−0.431090	−0.215545	+	0.976494i	$0.569153\pi$
$662$	−11.3291	−0.440320
$663$	0	0
$664$	−9.64927	−0.374464
$665$	−40.1297	−1.55616
$666$	−4.01033	−0.155397
$667$	16.4901	0.638499
$668$	−7.02300	−0.271728
$669$	0.770472	0.0297882
$670$	2.36724	0.0914543
$671$	−8.39226	−0.323980
$672$	−10.5920	−0.408597
$673$	−31.2230	−1.20356	−0.601779	−	0.798663i	$-0.705541\pi$
$673$	−31.2230	−1.20356	−0.601779	+	0.798663i	$0.705541\pi$
$674$	3.28717	0.126617
$675$	−2.13283	−0.0820925
$676$	0	0
$677$	43.7708	1.68225	0.841125	−	0.540840i	$-0.181894\pi$
$677$	43.7708	1.68225	0.841125	+	0.540840i	$0.181894\pi$
$678$	2.89092	0.111025
$679$	14.0151	0.537852
$680$	−9.87752	−0.378786
$681$	6.03034	0.231083
$682$	−0.551178	−0.0211057
$683$	33.4334	1.27929	0.639646	−	0.768669i	$-0.279081\pi$
$683$	33.4334	1.27929	0.639646	+	0.768669i	$0.279081\pi$
$684$	−21.9702	−0.840052
$685$	19.1549	0.731872
$686$	8.13363	0.310543
$687$	−6.13141	−0.233928
$688$	−34.5220	−1.31614
$689$	0	0
$690$	−2.82875	−0.107689
$691$	2.27812	0.0866638	0.0433319	−	0.999061i	$-0.486203\pi$
$691$	2.27812	0.0866638	0.0433319	+	0.999061i	$0.486203\pi$
$692$	−6.77107	−0.257398
$693$	−15.7150	−0.596965
$694$	−0.831156	−0.0315503
$695$	22.9425	0.870259
$696$	−2.44335	−0.0926149
$697$	1.06797	0.0404523
$698$	1.88440	0.0713258
$699$	−0.542920	−0.0205351
$700$	−5.27115	−0.199231
$701$	26.4996	1.00088	0.500438	−	0.865773i	$-0.333172\pi$
$701$	26.4996	1.00088	0.500438	+	0.865773i	$0.333172\pi$
$702$	0	0
$703$	16.4420	0.620122
$704$	5.85037	0.220494
$705$	12.9574	0.488006
$706$	−2.03275	−0.0765036
$707$	15.5925	0.586417
$708$	13.6635	0.513507
$709$	−32.5888	−1.22390	−0.611949	−	0.790897i	$-0.709614\pi$
$709$	−32.5888	−1.22390	−0.611949	+	0.790897i	$0.709614\pi$
$710$	9.77362	0.366797
$711$	−14.7371	−0.552683
$712$	−18.6363	−0.698423
$713$	−5.93016	−0.222086
$714$	−3.01345	−0.112776
$715$	0	0
$716$	−29.4705	−1.10136
$717$	−0.760410	−0.0283980
$718$	−7.71243	−0.287825
$719$	−32.6893	−1.21911	−0.609553	−	0.792746i	$-0.708651\pi$
$719$	−32.6893	−1.21911	−0.609553	+	0.792746i	$0.708651\pi$
$720$	16.9609	0.632094
$721$	71.4902	2.66243
$722$	−0.378254	−0.0140771
$723$	13.4644	0.500748
$724$	6.93096	0.257587
$725$	−1.85005	−0.0687090
$726$	−2.09812	−0.0778685
$727$	17.6209	0.653523	0.326761	−	0.945107i	$-0.394043\pi$
$727$	17.6209	0.653523	0.326761	+	0.945107i	$0.394043\pi$
$728$	0	0
$729$	−11.2968	−0.418401
$730$	11.8341	0.438000
$731$	−34.6199	−1.28046
$732$	6.40177	0.236616
$733$	20.8867	0.771468	0.385734	−	0.922610i	$-0.373948\pi$
$733$	20.8867	0.771468	0.385734	+	0.922610i	$0.373948\pi$
$734$	7.11582	0.262650
$735$	13.6732	0.504343
$736$	−25.7853	−0.950459
$737$	−3.80071	−0.140001
$738$	0.381732	0.0140518
$739$	14.9613	0.550359	0.275180	−	0.961393i	$-0.411263\pi$
$739$	14.9613	0.550359	0.275180	+	0.961393i	$0.411263\pi$
$740$	−14.0710	−0.517262
$741$	0	0
$742$	−4.15799	−0.152645
$743$	31.3718	1.15092	0.575459	−	0.817830i	$-0.304823\pi$
$743$	31.3718	1.15092	0.575459	+	0.817830i	$0.304823\pi$
$744$	0.878675	0.0322138
$745$	−17.8153	−0.652704
$746$	−5.91292	−0.216487
$747$	16.6159	0.607943
$748$	7.58851	0.277463
$749$	−87.4433	−3.19511
$750$	2.70242	0.0986785
$751$	−6.57060	−0.239764	−0.119882	−	0.992788i	$-0.538252\pi$
$751$	−6.57060	−0.239764	−0.119882	+	0.992788i	$0.538252\pi$
$752$	33.5083	1.22192
$753$	−14.9585	−0.545119
$754$	0	0
$755$	37.0928	1.34994
$756$	25.3986	0.923738
$757$	−13.2323	−0.480937	−0.240468	−	0.970657i	$-0.577301\pi$
$757$	−13.2323	−0.480937	−0.240468	+	0.970657i	$0.577301\pi$
$758$	−8.09880	−0.294161
$759$	4.54171	0.164853
$760$	14.4751	0.525067
$761$	−42.4811	−1.53994	−0.769969	−	0.638081i	$-0.779728\pi$
$761$	−42.4811	−1.53994	−0.769969	+	0.638081i	$0.779728\pi$
$762$	−5.00141	−0.181182
$763$	16.5945	0.600762
$764$	18.7769	0.679324
$765$	17.0089	0.614959
$766$	3.88388	0.140330
$767$	0	0
$768$	−2.47032	−0.0891400
$769$	15.7669	0.568568	0.284284	−	0.958740i	$-0.408244\pi$
$769$	15.7669	0.568568	0.284284	+	0.958740i	$0.408244\pi$
$770$	4.95436	0.178543
$771$	12.8765	0.463734
$772$	−11.5938	−0.417269
$773$	−2.40323	−0.0864380	−0.0432190	−	0.999066i	$-0.513761\pi$
$773$	−2.40323	−0.0864380	−0.0432190	+	0.999066i	$0.513761\pi$
$774$	−12.3744	−0.444789
$775$	0.665312	0.0238987
$776$	−5.05537	−0.181477
$777$	−8.97135	−0.321845
$778$	−1.18695	−0.0425542
$779$	−1.56507	−0.0560743
$780$	0	0
$781$	−15.6920	−0.561505
$782$	−7.33596	−0.262334
$783$	8.91430	0.318571
$784$	35.3592	1.26283
$785$	8.45602	0.301808
$786$	−0.511447	−0.0182427
$787$	−21.6134	−0.770433	−0.385217	−	0.922826i	$-0.625873\pi$
$787$	−21.6134	−0.770433	−0.385217	+	0.922826i	$0.625873\pi$
$788$	22.1495	0.789044
$789$	−11.3867	−0.405378
$790$	4.64604	0.165299
$791$	−54.4757	−1.93693
$792$	5.66854	0.201423
$793$	0	0
$794$	−1.46907	−0.0521354
$795$	−2.78616	−0.0988150
$796$	26.6302	0.943882
$797$	27.3487	0.968742	0.484371	−	0.874863i	$-0.339048\pi$
$797$	27.3487	0.968742	0.484371	+	0.874863i	$0.339048\pi$
$798$	4.41609	0.156328
$799$	33.6032	1.18880
$800$	2.89289	0.102279
$801$	32.0913	1.13389
$802$	−9.51889	−0.336124
$803$	−19.0002	−0.670504
$804$	2.89926	0.102249
$805$	53.3043	1.87873
$806$	0	0
$807$	3.65611	0.128701
$808$	−5.62434	−0.197864
$809$	−37.7686	−1.32787	−0.663936	−	0.747789i	$-0.731115\pi$
$809$	−37.7686	−1.32787	−0.663936	+	0.747789i	$0.731115\pi$
$810$	5.27218	0.185246
$811$	−18.8166	−0.660739	−0.330369	−	0.943852i	$-0.607173\pi$
$811$	−18.8166	−0.660739	−0.330369	+	0.943852i	$0.607173\pi$
$812$	22.0311	0.773142
$813$	−13.0537	−0.457813
$814$	−2.02991	−0.0711482
$815$	−33.3439	−1.16799
$816$	−5.22180	−0.182800
$817$	50.7340	1.77496
$818$	8.57575	0.299844
$819$	0	0
$820$	1.33938	0.0467732
$821$	16.7626	0.585019	0.292510	−	0.956263i	$-0.405510\pi$
$821$	16.7626	0.585019	0.292510	+	0.956263i	$0.405510\pi$
$822$	−2.10791	−0.0735218
$823$	33.6286	1.17222	0.586109	−	0.810232i	$-0.300659\pi$
$823$	33.6286	1.17222	0.586109	+	0.810232i	$0.300659\pi$
$824$	−25.7870	−0.898334
$825$	−0.509540	−0.0177399
$826$	23.1343	0.804946
$827$	−28.0331	−0.974805	−0.487403	−	0.873177i	$-0.662056\pi$
$827$	−28.0331	−0.974805	−0.487403	+	0.873177i	$0.662056\pi$
$828$	29.1830	1.01418
$829$	40.8775	1.41973	0.709867	−	0.704336i	$-0.248755\pi$
$829$	40.8775	1.41973	0.709867	+	0.704336i	$0.248755\pi$
$830$	−5.23836	−0.181826
$831$	4.70871	0.163343
$832$	0	0
$833$	35.4594	1.22860
$834$	−2.52471	−0.0874237
$835$	−7.96781	−0.275738
$836$	−11.1206	−0.384615
$837$	−3.20575	−0.110807
$838$	3.82550	0.132150
$839$	17.4199	0.601401	0.300700	−	0.953719i	$-0.402780\pi$
$839$	17.4199	0.601401	0.300700	+	0.953719i	$0.402780\pi$
$840$	−7.89814	−0.272512
$841$	−21.2676	−0.733365
$842$	−7.46984	−0.257428
$843$	−6.05074	−0.208398
$844$	10.8712	0.374203
$845$	0	0
$846$	12.0110	0.412948
$847$	39.5364	1.35849
$848$	−7.20509	−0.247424
$849$	−17.2600	−0.592362
$850$	0.823032	0.0282298
$851$	−21.8399	−0.748662
$852$	11.9702	0.410091
$853$	−14.7377	−0.504609	−0.252304	−	0.967648i	$-0.581188\pi$
$853$	−14.7377	−0.504609	−0.252304	+	0.967648i	$0.581188\pi$
$854$	10.8391	0.370907
$855$	−24.9259	−0.852447
$856$	31.5415	1.07807
$857$	−27.9220	−0.953797	−0.476899	−	0.878958i	$-0.658239\pi$
$857$	−27.9220	−0.953797	−0.476899	+	0.878958i	$0.658239\pi$
$858$	0	0
$859$	−8.98897	−0.306700	−0.153350	−	0.988172i	$-0.549006\pi$
$859$	−8.98897	−0.306700	−0.153350	+	0.988172i	$0.549006\pi$
$860$	−43.4180	−1.48054
$861$	0.853957	0.0291028
$862$	7.66743	0.261154
$863$	53.9274	1.83571	0.917854	−	0.396917i	$-0.129920\pi$
$863$	53.9274	1.83571	0.917854	+	0.396917i	$0.129920\pi$
$864$	−13.9391	−0.474219
$865$	−7.68199	−0.261196
$866$	1.10391	0.0375124
$867$	4.35531	0.147914
$868$	−7.92282	−0.268918
$869$	−7.45944	−0.253044
$870$	−1.32644	−0.0449704
$871$	0	0
$872$	−5.98577	−0.202704
$873$	8.70525	0.294628
$874$	10.7506	0.363643
$875$	−50.9237	−1.72154
$876$	14.4937	0.489698
$877$	−27.4671	−0.927496	−0.463748	−	0.885967i	$-0.653496\pi$
$877$	−27.4671	−0.927496	−0.463748	+	0.885967i	$0.653496\pi$
$878$	0.403302	0.0136108
$879$	16.1719	0.545465
$880$	8.58507	0.289403
$881$	−35.5251	−1.19687	−0.598436	−	0.801171i	$-0.704211\pi$
$881$	−35.5251	−1.19687	−0.598436	+	0.801171i	$0.704211\pi$
$882$	12.6745	0.426772
$883$	13.7709	0.463427	0.231714	−	0.972784i	$-0.425567\pi$
$883$	13.7709	0.463427	0.231714	+	0.972784i	$0.425567\pi$
$884$	0	0
$885$	15.5017	0.521084
$886$	−2.31956	−0.0779270
$887$	33.4956	1.12467	0.562336	−	0.826909i	$-0.309903\pi$
$887$	33.4956	1.12467	0.562336	+	0.826909i	$0.309903\pi$
$888$	3.23603	0.108594
$889$	94.2452	3.16088
$890$	−10.1172	−0.339129
$891$	−8.46475	−0.283580
$892$	2.50590	0.0839038
$893$	−49.2442	−1.64789
$894$	1.96050	0.0655688
$895$	−33.4352	−1.11762
$896$	−45.1012	−1.50673
$897$	0	0
$898$	−7.24277	−0.241694
$899$	−2.78072	−0.0927422
$900$	−3.27408	−0.109136
$901$	−7.22551	−0.240717
$902$	0.193221	0.00643356
$903$	−27.6823	−0.921208
$904$	19.6498	0.653542
$905$	7.86339	0.261388
$906$	−4.08188	−0.135612
$907$	−4.40275	−0.146191	−0.0730955	−	0.997325i	$-0.523288\pi$
$907$	−4.40275	−0.146191	−0.0730955	+	0.997325i	$0.523288\pi$
$908$	19.6132	0.650887
$909$	9.68501	0.321232
$910$	0	0
$911$	55.0918	1.82527	0.912636	−	0.408774i	$-0.134044\pi$
$911$	55.0918	1.82527	0.912636	+	0.408774i	$0.134044\pi$
$912$	7.65233	0.253394
$913$	8.41044	0.278345
$914$	10.1484	0.335678
$915$	7.26301	0.240108
$916$	−19.9419	−0.658900
$917$	9.63757	0.318261
$918$	−3.96571	−0.130888
$919$	−25.7770	−0.850303	−0.425152	−	0.905122i	$-0.639779\pi$
$919$	−25.7770	−0.850303	−0.425152	+	0.905122i	$0.639779\pi$
$920$	−19.2273	−0.633904
$921$	5.16189	0.170090
$922$	−1.63168	−0.0537365
$923$	0	0
$924$	6.06782	0.199617
$925$	2.45025	0.0805637
$926$	−12.6535	−0.415821
$927$	44.4048	1.45845
$928$	−12.0910	−0.396908
$929$	−29.3272	−0.962196	−0.481098	−	0.876667i	$-0.659762\pi$
$929$	−29.3272	−0.962196	−0.481098	+	0.876667i	$0.659762\pi$
$930$	0.477012	0.0156418
$931$	−51.9643	−1.70306
$932$	−1.76580	−0.0578408
$933$	−7.43477	−0.243403
$934$	−2.82225	−0.0923468
$935$	8.60939	0.281557
$936$	0	0
$937$	−37.1240	−1.21279	−0.606393	−	0.795165i	$-0.707384\pi$
$937$	−37.1240	−1.21279	−0.606393	+	0.795165i	$0.707384\pi$
$938$	4.90885	0.160280
$939$	−7.66985	−0.250296
$940$	42.1431	1.37456
$941$	3.93774	0.128367	0.0641833	−	0.997938i	$-0.479556\pi$
$941$	3.93774	0.128367	0.0641833	+	0.997938i	$0.479556\pi$
$942$	−0.930545	−0.0303188
$943$	2.07888	0.0676976
$944$	40.0878	1.30475
$945$	28.8155	0.937368
$946$	−6.26355	−0.203645
$947$	32.6557	1.06117	0.530584	−	0.847632i	$-0.321973\pi$
$947$	32.6557	1.06117	0.530584	+	0.847632i	$0.321973\pi$
$948$	5.69020	0.184809
$949$	0	0
$950$	−1.20612	−0.0391317
$951$	4.02365	0.130476
$952$	−20.4827	−0.663847
$953$	−40.5066	−1.31214	−0.656069	−	0.754701i	$-0.727782\pi$
$953$	−40.5066	−1.31214	−0.656069	+	0.754701i	$0.727782\pi$
$954$	−2.58266	−0.0836168
$955$	21.3030	0.689347
$956$	−2.47317	−0.0799881
$957$	2.12966	0.0688421
$958$	−9.29213	−0.300215
$959$	39.7209	1.28265
$960$	−5.06315	−0.163412
$961$	1.00000	0.0322581
$962$	0	0
$963$	−54.3138	−1.75024
$964$	43.7921	1.41045
$965$	−13.1535	−0.423426
$966$	−5.86589	−0.188732
$967$	−60.9926	−1.96139	−0.980695	−	0.195545i	$-0.937353\pi$
$967$	−60.9926	−1.96139	−0.980695	+	0.195545i	$0.937353\pi$
$968$	−14.2611	−0.458368
$969$	7.67401	0.246525
$970$	−2.74444	−0.0881186
$971$	−7.43700	−0.238665	−0.119332	−	0.992854i	$-0.538075\pi$
$971$	−7.43700	−0.238665	−0.119332	+	0.992854i	$0.538075\pi$
$972$	24.1058	0.773194
$973$	47.5751	1.52519
$974$	5.68010	0.182002
$975$	0	0
$976$	18.7823	0.601208
$977$	−13.4473	−0.430218	−0.215109	−	0.976590i	$-0.569011\pi$
$977$	−13.4473	−0.430218	−0.215109	+	0.976590i	$0.569011\pi$
$978$	3.66934	0.117333
$979$	16.2436	0.519149
$980$	44.4709	1.42057
$981$	10.3074	0.329089
$982$	−0.921738	−0.0294138
$983$	−49.1221	−1.56675	−0.783376	−	0.621548i	$-0.786504\pi$
$983$	−49.1221	−1.56675	−0.783376	+	0.621548i	$0.786504\pi$
$984$	−0.308029	−0.00981960
$985$	25.1293	0.800687
$986$	−3.43992	−0.109549
$987$	26.8694	0.855262
$988$	0	0
$989$	−67.3899	−2.14287
$990$	3.07731	0.0978035
$991$	−16.4588	−0.522830	−0.261415	−	0.965226i	$-0.584189\pi$
$991$	−16.4588	−0.522830	−0.261415	+	0.965226i	$0.584189\pi$
$992$	4.34817	0.138054
$993$	−15.7419	−0.499555
$994$	20.2672	0.642836
$995$	30.2128	0.957809
$996$	−6.41564	−0.203287
$997$	6.71385	0.212630	0.106315	−	0.994333i	$-0.466095\pi$
$997$	6.71385	0.212630	0.106315	+	0.994333i	$0.466095\pi$
$998$	0.762055	0.0241224
$999$	−11.8063	−0.373535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.h.1.4		7
13.12	even	2		403.2.a.c.1.4	✓	7
39.38	odd	2		3627.2.a.n.1.4		7
52.51	odd	2		6448.2.a.ba.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.c.1.4	✓	7	13.12	even	2
3627.2.a.n.1.4		7	39.38	odd	2
5239.2.a.h.1.4		7	1.1	even	1	trivial
6448.2.a.ba.1.6		7	52.51	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-0.406064 q^{2} -0.564229 q^{3} -1.83511 q^{4} -2.08199 q^{5} +0.229113 q^{6} -4.31735 q^{7} +1.55730 q^{8} -2.68165 q^{9} +O(q^{10})\)	\(q-0.406064 q^{2} -0.564229 q^{3} -1.83511 q^{4} -2.08199 q^{5} +0.229113 q^{6} -4.31735 q^{7} +1.55730 q^{8} -2.68165 q^{9} +0.845422 q^{10} -1.35737 q^{11} +1.03542 q^{12} +1.75312 q^{14} +1.17472 q^{15} +3.03786 q^{16} +3.04647 q^{17} +1.08892 q^{18} -4.46447 q^{19} +3.82069 q^{20} +2.43598 q^{21} +0.551178 q^{22} +5.93016 q^{23} -0.878675 q^{24} -0.665312 q^{25} +3.20575 q^{27} +7.92282 q^{28} +2.78072 q^{29} -0.477012 q^{30} -1.00000 q^{31} -4.34817 q^{32} +0.765866 q^{33} -1.23706 q^{34} +8.98869 q^{35} +4.92112 q^{36} -3.68286 q^{37} +1.81286 q^{38} -3.24229 q^{40} +0.350560 q^{41} -0.989162 q^{42} -11.3639 q^{43} +2.49092 q^{44} +5.58316 q^{45} -2.40802 q^{46} +11.0302 q^{47} -1.71405 q^{48} +11.6395 q^{49} +0.270159 q^{50} -1.71891 q^{51} -2.37177 q^{53} -1.30174 q^{54} +2.82603 q^{55} -6.72341 q^{56} +2.51899 q^{57} -1.12915 q^{58} +13.1961 q^{59} -2.15574 q^{60} +6.18275 q^{61} +0.406064 q^{62} +11.5776 q^{63} -4.31009 q^{64} -0.310991 q^{66} +2.80007 q^{67} -5.59061 q^{68} -3.34597 q^{69} -3.64998 q^{70} +11.5606 q^{71} -4.17613 q^{72} +13.9979 q^{73} +1.49548 q^{74} +0.375389 q^{75} +8.19281 q^{76} +5.86023 q^{77} +5.49553 q^{79} -6.32480 q^{80} +6.23616 q^{81} -0.142350 q^{82} -6.19615 q^{83} -4.47029 q^{84} -6.34272 q^{85} +4.61448 q^{86} -1.56896 q^{87} -2.11383 q^{88} -11.9670 q^{89} -2.26712 q^{90} -10.8825 q^{92} +0.564229 q^{93} -4.47898 q^{94} +9.29499 q^{95} +2.45336 q^{96} -3.24624 q^{97} -4.72639 q^{98} +3.63998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - 11 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - 11 * q^5 - 6 * q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	\( 7 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - 11 q^{5} - 6 q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 8 q^{11} - 3 q^{12} - 5 q^{14} + 2 q^{16} + 7 q^{17} + 9 q^{18} - q^{19} + 2 q^{21} + 6 q^{22} + 6 q^{23} - 5 q^{24} + 10 q^{25} + 11 q^{27} + 11 q^{28} - 2 q^{29} - 3 q^{30} - 7 q^{31} - 18 q^{32} - 6 q^{33} + 4 q^{34} - q^{35} - 20 q^{36} - 28 q^{37} - 8 q^{38} - 5 q^{40} - 3 q^{41} + 13 q^{42} - q^{43} - 12 q^{44} - 9 q^{45} + 37 q^{46} + q^{47} + 11 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} + 29 q^{53} - 2 q^{54} + 19 q^{55} - 20 q^{56} - 11 q^{57} - 3 q^{58} - 3 q^{59} + 43 q^{60} + 5 q^{61} + 2 q^{62} - q^{63} - 29 q^{64} - 29 q^{66} + 32 q^{67} + 38 q^{68} + 17 q^{69} + 23 q^{70} - 5 q^{71} + 17 q^{72} - q^{73} - 4 q^{74} - 7 q^{75} + 12 q^{76} - 5 q^{77} - 15 q^{79} + 11 q^{80} + 3 q^{81} - 36 q^{82} - 17 q^{83} - 2 q^{84} + q^{85} + 23 q^{86} - 42 q^{87} - 15 q^{88} - 26 q^{89} - 40 q^{90} - 24 q^{92} - 5 q^{93} + 18 q^{94} - 21 q^{95} + 4 q^{96} - 11 q^{97} - 6 q^{98} + 28 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - 11 * q^5 - 6 * q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 8 * q^11 - 3 * q^12 - 5 * q^14 + 2 * q^16 + 7 * q^17 + 9 * q^18 - q^19 + 2 * q^21 + 6 * q^22 + 6 * q^23 - 5 * q^24 + 10 * q^25 + 11 * q^27 + 11 * q^28 - 2 * q^29 - 3 * q^30 - 7 * q^31 - 18 * q^32 - 6 * q^33 + 4 * q^34 - q^35 - 20 * q^36 - 28 * q^37 - 8 * q^38 - 5 * q^40 - 3 * q^41 + 13 * q^42 - q^43 - 12 * q^44 - 9 * q^45 + 37 * q^46 + q^47 + 11 * q^48 - 19 * q^49 - 21 * q^50 - 30 * q^51 + 29 * q^53 - 2 * q^54 + 19 * q^55 - 20 * q^56 - 11 * q^57 - 3 * q^58 - 3 * q^59 + 43 * q^60 + 5 * q^61 + 2 * q^62 - q^63 - 29 * q^64 - 29 * q^66 + 32 * q^67 + 38 * q^68 + 17 * q^69 + 23 * q^70 - 5 * q^71 + 17 * q^72 - q^73 - 4 * q^74 - 7 * q^75 + 12 * q^76 - 5 * q^77 - 15 * q^79 + 11 * q^80 + 3 * q^81 - 36 * q^82 - 17 * q^83 - 2 * q^84 + q^85 + 23 * q^86 - 42 * q^87 - 15 * q^88 - 26 * q^89 - 40 * q^90 - 24 * q^92 - 5 * q^93 + 18 * q^94 - 21 * q^95 + 4 * q^96 - 11 * q^97 - 6 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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