LMFDB - Embedded newform 6017.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} +O(q^{10})$	\(q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} -3.08721 q^{10} +1.00000 q^{11} +2.91761 q^{12} +0.501016 q^{13} -10.6489 q^{14} +1.48935 q^{15} -1.86958 q^{16} -3.80935 q^{17} +4.12757 q^{18} -4.19367 q^{19} +3.91479 q^{20} +5.13728 q^{21} -2.18387 q^{22} -1.04856 q^{23} -1.77003 q^{24} -3.00163 q^{25} -1.09415 q^{26} -5.15191 q^{27} +13.5035 q^{28} +2.50838 q^{29} -3.25254 q^{30} -8.96340 q^{31} +7.44303 q^{32} +1.05356 q^{33} +8.31913 q^{34} +6.89309 q^{35} -5.23404 q^{36} +6.21728 q^{37} +9.15843 q^{38} +0.527848 q^{39} -2.37499 q^{40} +1.36683 q^{41} -11.2192 q^{42} -10.2419 q^{43} +2.76930 q^{44} -2.67181 q^{45} +2.28992 q^{46} -10.8797 q^{47} -1.96970 q^{48} +16.7767 q^{49} +6.55517 q^{50} -4.01336 q^{51} +1.38746 q^{52} +3.99296 q^{53} +11.2511 q^{54} +1.41364 q^{55} -8.19218 q^{56} -4.41826 q^{57} -5.47798 q^{58} -9.49024 q^{59} +4.12445 q^{60} -5.30877 q^{61} +19.5749 q^{62} -9.21600 q^{63} -12.5155 q^{64} +0.708255 q^{65} -2.30083 q^{66} -2.25286 q^{67} -10.5492 q^{68} -1.10471 q^{69} -15.0536 q^{70} -8.38292 q^{71} +3.17534 q^{72} +8.49245 q^{73} -13.5777 q^{74} -3.16238 q^{75} -11.6135 q^{76} +4.87614 q^{77} -1.15275 q^{78} -15.2896 q^{79} -2.64290 q^{80} +0.242242 q^{81} -2.98498 q^{82} -1.37370 q^{83} +14.2267 q^{84} -5.38503 q^{85} +22.3670 q^{86} +2.64272 q^{87} -1.68005 q^{88} +1.35696 q^{89} +5.83488 q^{90} +2.44302 q^{91} -2.90377 q^{92} -9.44344 q^{93} +23.7599 q^{94} -5.92832 q^{95} +7.84164 q^{96} -12.7861 q^{97} -36.6382 q^{98} -1.89002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.18387	−1.54423	−0.772116	−	0.635482i	$-0.780801\pi$
$2$	−2.18387	−1.54423	−0.772116	+	0.635482i	$0.780801\pi$
$3$	1.05356	0.608271	0.304135	−	0.952629i	$-0.401633\pi$
$3$	1.05356	0.608271	0.304135	+	0.952629i	$0.401633\pi$
$4$	2.76930	1.38465
$5$	1.41364	0.632198	0.316099	−	0.948726i	$-0.397627\pi$
$5$	1.41364	0.632198	0.316099	+	0.948726i	$0.397627\pi$
$6$	−2.30083	−0.939310
$7$	4.87614	1.84301	0.921504	−	0.388370i	$-0.126962\pi$
$7$	4.87614	1.84301	0.921504	+	0.388370i	$0.126962\pi$
$8$	−1.68005	−0.593989
$9$	−1.89002	−0.630007
$10$	−3.08721	−0.976260
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.91761	0.842242
$13$	0.501016	0.138957	0.0694784	−	0.997583i	$-0.477867\pi$
$13$	0.501016	0.138957	0.0694784	+	0.997583i	$0.477867\pi$
$14$	−10.6489	−2.84603
$15$	1.48935	0.384547
$16$	−1.86958	−0.467394
$17$	−3.80935	−0.923902	−0.461951	−	0.886905i	$-0.652850\pi$
$17$	−3.80935	−0.923902	−0.461951	+	0.886905i	$0.652850\pi$
$18$	4.12757	0.972876
$19$	−4.19367	−0.962093	−0.481046	−	0.876695i	$-0.659743\pi$
$19$	−4.19367	−0.962093	−0.481046	+	0.876695i	$0.659743\pi$
$20$	3.91479	0.875373
$21$	5.13728	1.12105
$22$	−2.18387	−0.465603
$23$	−1.04856	−0.218639	−0.109320	−	0.994007i	$-0.534867\pi$
$23$	−1.04856	−0.218639	−0.109320	+	0.994007i	$0.534867\pi$
$24$	−1.77003	−0.361306
$25$	−3.00163	−0.600326
$26$	−1.09415	−0.214581
$27$	−5.15191	−0.991485
$28$	13.5035	2.55192
$29$	2.50838	0.465795	0.232897	−	0.972501i	$-0.425179\pi$
$29$	2.50838	0.465795	0.232897	+	0.972501i	$0.425179\pi$
$30$	−3.25254	−0.593830
$31$	−8.96340	−1.60987	−0.804937	−	0.593361i	$-0.797801\pi$
$31$	−8.96340	−1.60987	−0.804937	+	0.593361i	$0.797801\pi$
$32$	7.44303	1.31575
$33$	1.05356	0.183400
$34$	8.31913	1.42672
$35$	6.89309	1.16515
$36$	−5.23404	−0.872339
$37$	6.21728	1.02211	0.511057	−	0.859547i	$-0.329254\pi$
$37$	6.21728	1.02211	0.511057	+	0.859547i	$0.329254\pi$
$38$	9.15843	1.48569
$39$	0.527848	0.0845233
$40$	−2.37499	−0.375519
$41$	1.36683	0.213463	0.106731	−	0.994288i	$-0.465961\pi$
$41$	1.36683	0.213463	0.106731	+	0.994288i	$0.465961\pi$
$42$	−11.2192	−1.73116
$43$	−10.2419	−1.56188	−0.780938	−	0.624608i	$-0.785259\pi$
$43$	−10.2419	−1.56188	−0.780938	+	0.624608i	$0.785259\pi$
$44$	2.76930	0.417488
$45$	−2.67181	−0.398289
$46$	2.28992	0.337630
$47$	−10.8797	−1.58697	−0.793483	−	0.608592i	$-0.791735\pi$
$47$	−10.8797	−1.58697	−0.793483	+	0.608592i	$0.791735\pi$
$48$	−1.96970	−0.284302
$49$	16.7767	2.39668
$50$	6.55517	0.927042
$51$	−4.01336	−0.561982
$52$	1.38746	0.192406
$53$	3.99296	0.548475	0.274238	−	0.961662i	$-0.411575\pi$
$53$	3.99296	0.548475	0.274238	+	0.961662i	$0.411575\pi$
$54$	11.2511	1.53108
$55$	1.41364	0.190615
$56$	−8.19218	−1.09473
$57$	−4.41826	−0.585213
$58$	−5.47798	−0.719295
$59$	−9.49024	−1.23552	−0.617762	−	0.786365i	$-0.711961\pi$
$59$	−9.49024	−1.23552	−0.617762	+	0.786365i	$0.711961\pi$
$60$	4.12445	0.532464
$61$	−5.30877	−0.679718	−0.339859	−	0.940476i	$-0.610379\pi$
$61$	−5.30877	−0.679718	−0.339859	+	0.940476i	$0.610379\pi$
$62$	19.5749	2.48602
$63$	−9.21600	−1.16111
$64$	−12.5155	−1.56443
$65$	0.708255	0.0878482
$66$	−2.30083	−0.283213
$67$	−2.25286	−0.275230	−0.137615	−	0.990486i	$-0.543944\pi$
$67$	−2.25286	−0.275230	−0.137615	+	0.990486i	$0.543944\pi$
$68$	−10.5492	−1.27928
$69$	−1.10471	−0.132992
$70$	−15.0536	−1.79925
$71$	−8.38292	−0.994869	−0.497435	−	0.867502i	$-0.665725\pi$
$71$	−8.38292	−0.994869	−0.497435	+	0.867502i	$0.665725\pi$
$72$	3.17534	0.374217
$73$	8.49245	0.993966	0.496983	−	0.867760i	$-0.334441\pi$
$73$	8.49245	0.993966	0.496983	+	0.867760i	$0.334441\pi$
$74$	−13.5777	−1.57838
$75$	−3.16238	−0.365160
$76$	−11.6135	−1.33216
$77$	4.87614	0.555688
$78$	−1.15275	−0.130523
$79$	−15.2896	−1.72022	−0.860109	−	0.510111i	$-0.829604\pi$
$79$	−15.2896	−1.72022	−0.860109	+	0.510111i	$0.829604\pi$
$80$	−2.64290	−0.295486
$81$	0.242242	0.0269158
$82$	−2.98498	−0.329636
$83$	−1.37370	−0.150784	−0.0753918	−	0.997154i	$-0.524021\pi$
$83$	−1.37370	−0.150784	−0.0753918	+	0.997154i	$0.524021\pi$
$84$	14.2267	1.55226
$85$	−5.38503	−0.584089
$86$	22.3670	2.41190
$87$	2.64272	0.283329
$88$	−1.68005	−0.179094
$89$	1.35696	0.143838	0.0719189	−	0.997410i	$-0.477088\pi$
$89$	1.35696	0.143838	0.0719189	+	0.997410i	$0.477088\pi$
$90$	5.83488	0.615051
$91$	2.44302	0.256098
$92$	−2.90377	−0.302739
$93$	−9.44344	−0.979239
$94$	23.7599	2.45064
$95$	−5.92832	−0.608233
$96$	7.84164	0.800334
$97$	−12.7861	−1.29823	−0.649114	−	0.760691i	$-0.724860\pi$
$97$	−12.7861	−1.29823	−0.649114	+	0.760691i	$0.724860\pi$
$98$	−36.6382	−3.70102
$99$	−1.89002	−0.189954
$100$	−8.31241	−0.831241
$101$	−4.01323	−0.399332	−0.199666	−	0.979864i	$-0.563986\pi$
$101$	−4.01323	−0.399332	−0.199666	+	0.979864i	$0.563986\pi$
$102$	8.76466	0.867831
$103$	2.42773	0.239211	0.119606	−	0.992821i	$-0.461837\pi$
$103$	2.42773	0.239211	0.119606	+	0.992821i	$0.461837\pi$
$104$	−0.841733	−0.0825387
$105$	7.26226	0.708724
$106$	−8.72011	−0.846972
$107$	1.81293	0.175263	0.0876315	−	0.996153i	$-0.472070\pi$
$107$	1.81293	0.175263	0.0876315	+	0.996153i	$0.472070\pi$
$108$	−14.2672	−1.37286
$109$	−20.1301	−1.92812	−0.964059	−	0.265689i	$-0.914401\pi$
$109$	−20.1301	−1.92812	−0.964059	+	0.265689i	$0.914401\pi$
$110$	−3.08721	−0.294353
$111$	6.55025	0.621722
$112$	−9.11632	−0.861411
$113$	11.9530	1.12444	0.562222	−	0.826986i	$-0.309947\pi$
$113$	11.9530	1.12444	0.562222	+	0.826986i	$0.309947\pi$
$114$	9.64892	0.903704
$115$	−1.48228	−0.138223
$116$	6.94646	0.644963
$117$	−0.946930	−0.0875437
$118$	20.7255	1.90794
$119$	−18.5749	−1.70276
$120$	−2.50218	−0.228417
$121$	1.00000	0.0909091
$122$	11.5937	1.04964
$123$	1.44003	0.129843
$124$	−24.8223	−2.22911
$125$	−11.3114	−1.01172
$126$	20.1266	1.79302
$127$	−10.5098	−0.932597	−0.466298	−	0.884627i	$-0.654413\pi$
$127$	−10.5098	−0.932597	−0.466298	+	0.884627i	$0.654413\pi$
$128$	12.4461	1.10009
$129$	−10.7904	−0.950043
$130$	−1.54674	−0.135658
$131$	−2.43365	−0.212629	−0.106314	−	0.994333i	$-0.533905\pi$
$131$	−2.43365	−0.212629	−0.106314	+	0.994333i	$0.533905\pi$
$132$	2.91761	0.253945
$133$	−20.4489	−1.77314
$134$	4.91995	0.425019
$135$	−7.28293	−0.626815
$136$	6.39991	0.548787
$137$	18.7767	1.60420	0.802100	−	0.597190i	$-0.203716\pi$
$137$	18.7767	1.60420	0.802100	+	0.597190i	$0.203716\pi$
$138$	2.41256	0.205370
$139$	−4.66596	−0.395761	−0.197881	−	0.980226i	$-0.563406\pi$
$139$	−4.66596	−0.395761	−0.197881	+	0.980226i	$0.563406\pi$
$140$	19.0890	1.61332
$141$	−11.4624	−0.965305
$142$	18.3072	1.53631
$143$	0.501016	0.0418970
$144$	3.53354	0.294462
$145$	3.54594	0.294474
$146$	−18.5464	−1.53491
$147$	17.6752	1.45783
$148$	17.2175	1.41527
$149$	−5.42490	−0.444426	−0.222213	−	0.974998i	$-0.571328\pi$
$149$	−5.42490	−0.444426	−0.222213	+	0.974998i	$0.571328\pi$
$150$	6.90624	0.563892
$151$	3.47722	0.282972	0.141486	−	0.989940i	$-0.454812\pi$
$151$	3.47722	0.282972	0.141486	+	0.989940i	$0.454812\pi$
$152$	7.04558	0.571472
$153$	7.19974	0.582065
$154$	−10.6489	−0.858110
$155$	−12.6710	−1.01776
$156$	1.46177	0.117035
$157$	19.6087	1.56495	0.782474	−	0.622684i	$-0.213958\pi$
$157$	19.6087	1.56495	0.782474	+	0.622684i	$0.213958\pi$
$158$	33.3906	2.65641
$159$	4.20680	0.333621
$160$	10.5217	0.831817
$161$	−5.11292	−0.402954
$162$	−0.529025	−0.0415642
$163$	−18.2826	−1.43200	−0.716002	−	0.698098i	$-0.754030\pi$
$163$	−18.2826	−1.43200	−0.716002	+	0.698098i	$0.754030\pi$
$164$	3.78516	0.295572
$165$	1.48935	0.115945
$166$	3.00000	0.232845
$167$	3.15255	0.243952	0.121976	−	0.992533i	$-0.461077\pi$
$167$	3.15255	0.243952	0.121976	+	0.992533i	$0.461077\pi$
$168$	−8.63091	−0.665889
$169$	−12.7490	−0.980691
$170$	11.7602	0.901969
$171$	7.92612	0.606125
$172$	−28.3629	−2.16265
$173$	−8.49595	−0.645935	−0.322968	−	0.946410i	$-0.604681\pi$
$173$	−8.49595	−0.645935	−0.322968	+	0.946410i	$0.604681\pi$
$174$	−5.77136	−0.437526
$175$	−14.6364	−1.10640
$176$	−1.86958	−0.140925
$177$	−9.99850	−0.751533
$178$	−2.96344	−0.222119
$179$	10.4457	0.780747	0.390374	−	0.920657i	$-0.372346\pi$
$179$	10.4457	0.780747	0.390374	+	0.920657i	$0.372346\pi$
$180$	−7.39903	−0.551491
$181$	20.8548	1.55012	0.775061	−	0.631886i	$-0.217719\pi$
$181$	20.8548	1.55012	0.775061	+	0.631886i	$0.217719\pi$
$182$	−5.33525	−0.395475
$183$	−5.59308	−0.413452
$184$	1.76163	0.129869
$185$	8.78898	0.646179
$186$	20.6233	1.51217
$187$	−3.80935	−0.278567
$188$	−30.1291	−2.19739
$189$	−25.1214	−1.82731
$190$	12.9467	0.939253
$191$	−2.97957	−0.215594	−0.107797	−	0.994173i	$-0.534380\pi$
$191$	−2.97957	−0.215594	−0.107797	+	0.994173i	$0.534380\pi$
$192$	−13.1857	−0.951599
$193$	15.2983	1.10120	0.550598	−	0.834771i	$-0.314400\pi$
$193$	15.2983	1.10120	0.550598	+	0.834771i	$0.314400\pi$
$194$	27.9231	2.00476
$195$	0.746186	0.0534355
$196$	46.4598	3.31856
$197$	13.9156	0.991444	0.495722	−	0.868481i	$-0.334904\pi$
$197$	13.9156	0.991444	0.495722	+	0.868481i	$0.334904\pi$
$198$	4.12757	0.293333
$199$	−14.8673	−1.05391	−0.526956	−	0.849893i	$-0.676667\pi$
$199$	−14.8673	−1.05391	−0.526956	+	0.849893i	$0.676667\pi$
$200$	5.04290	0.356587
$201$	−2.37351	−0.167414
$202$	8.76439	0.616660
$203$	12.2312	0.858463
$204$	−11.1142	−0.778149
$205$	1.93220	0.134951
$206$	−5.30186	−0.369398
$207$	1.98180	0.137744
$208$	−0.936687	−0.0649476
$209$	−4.19367	−0.290082
$210$	−15.8598	−1.09443
$211$	−17.0327	−1.17258	−0.586289	−	0.810102i	$-0.699412\pi$
$211$	−17.0327	−1.17258	−0.586289	+	0.810102i	$0.699412\pi$
$212$	11.0577	0.759446
$213$	−8.83187	−0.605150
$214$	−3.95922	−0.270647
$215$	−14.4783	−0.987415
$216$	8.65548	0.588931
$217$	−43.7068	−2.96701
$218$	43.9617	2.97746
$219$	8.94727	0.604600
$220$	3.91479	0.263935
$221$	−1.90854	−0.128382
$222$	−14.3049	−0.960082
$223$	6.88982	0.461376	0.230688	−	0.973028i	$-0.425902\pi$
$223$	6.88982	0.461376	0.230688	+	0.973028i	$0.425902\pi$
$224$	36.2932	2.42494
$225$	5.67314	0.378209
$226$	−26.1038	−1.73640
$227$	−13.8497	−0.919237	−0.459618	−	0.888117i	$-0.652014\pi$
$227$	−13.8497	−0.919237	−0.459618	+	0.888117i	$0.652014\pi$
$228$	−12.2355	−0.810315
$229$	29.4098	1.94346	0.971729	−	0.236100i	$-0.0758694\pi$
$229$	29.4098	1.94346	0.971729	+	0.236100i	$0.0758694\pi$
$230$	3.23711	0.213449
$231$	5.13728	0.338008
$232$	−4.21421	−0.276677
$233$	3.06208	0.200604	0.100302	−	0.994957i	$-0.468019\pi$
$233$	3.06208	0.200604	0.100302	+	0.994957i	$0.468019\pi$
$234$	2.06797	0.135188
$235$	−15.3799	−1.00328
$236$	−26.2813	−1.71077
$237$	−16.1085	−1.04636
$238$	40.5652	2.62945
$239$	5.50666	0.356196	0.178098	−	0.984013i	$-0.443006\pi$
$239$	5.50666	0.356196	0.178098	+	0.984013i	$0.443006\pi$
$240$	−2.78445	−0.179735
$241$	−24.4791	−1.57684	−0.788418	−	0.615140i	$-0.789100\pi$
$241$	−24.4791	−1.57684	−0.788418	+	0.615140i	$0.789100\pi$
$242$	−2.18387	−0.140385
$243$	15.7109	1.00786
$244$	−14.7016	−0.941171
$245$	23.7162	1.51517
$246$	−3.14484	−0.200508
$247$	−2.10109	−0.133689
$248$	15.0590	0.956247
$249$	−1.44727	−0.0917173
$250$	24.7027	1.56233
$251$	−12.0602	−0.761231	−0.380615	−	0.924733i	$-0.624288\pi$
$251$	−12.0602	−0.761231	−0.380615	+	0.924733i	$0.624288\pi$
$252$	−25.5219	−1.60773
$253$	−1.04856	−0.0659223
$254$	22.9521	1.44015
$255$	−5.67343	−0.355284
$256$	−2.14984	−0.134365
$257$	1.12981	0.0704757	0.0352379	−	0.999379i	$-0.488781\pi$
$257$	1.12981	0.0704757	0.0352379	+	0.999379i	$0.488781\pi$
$258$	23.5649	1.46709
$259$	30.3163	1.88376
$260$	1.96137	0.121639
$261$	−4.74089	−0.293454
$262$	5.31478	0.328348
$263$	17.0413	1.05081	0.525407	−	0.850851i	$-0.323913\pi$
$263$	17.0413	1.05081	0.525407	+	0.850851i	$0.323913\pi$
$264$	−1.77003	−0.108938
$265$	5.64460	0.346745
$266$	44.6578	2.73814
$267$	1.42964	0.0874923
$268$	−6.23883	−0.381097
$269$	29.3449	1.78919	0.894595	−	0.446877i	$-0.147464\pi$
$269$	29.3449	1.78919	0.894595	+	0.446877i	$0.147464\pi$
$270$	15.9050	0.967947
$271$	3.19145	0.193867	0.0969334	−	0.995291i	$-0.469097\pi$
$271$	3.19145	0.193867	0.0969334	+	0.995291i	$0.469097\pi$
$272$	7.12186	0.431826
$273$	2.57386	0.155777
$274$	−41.0059	−2.47726
$275$	−3.00163	−0.181005
$276$	−3.05929	−0.184147
$277$	−14.0288	−0.842909	−0.421455	−	0.906850i	$-0.638480\pi$
$277$	−14.0288	−0.842909	−0.421455	+	0.906850i	$0.638480\pi$
$278$	10.1899	0.611147
$279$	16.9410	1.01423
$280$	−11.5808	−0.692083
$281$	19.4628	1.16105	0.580527	−	0.814241i	$-0.302847\pi$
$281$	19.4628	1.16105	0.580527	+	0.814241i	$0.302847\pi$
$282$	25.0323	1.49065
$283$	22.0757	1.31227	0.656133	−	0.754645i	$-0.272191\pi$
$283$	22.0757	1.31227	0.656133	+	0.754645i	$0.272191\pi$
$284$	−23.2148	−1.37755
$285$	−6.24582	−0.369970
$286$	−1.09415	−0.0646987
$287$	6.66485	0.393414
$288$	−14.0675	−0.828934
$289$	−2.48889	−0.146405
$290$	−7.74389	−0.454737
$291$	−13.4708	−0.789674
$292$	23.5181	1.37630
$293$	25.9076	1.51354	0.756769	−	0.653683i	$-0.226777\pi$
$293$	25.9076	1.51354	0.756769	+	0.653683i	$0.226777\pi$
$294$	−38.6004	−2.25122
$295$	−13.4158	−0.781096
$296$	−10.4454	−0.607124
$297$	−5.15191	−0.298944
$298$	11.8473	0.686296
$299$	−0.525344	−0.0303814
$300$	−8.75758	−0.505619
$301$	−49.9410	−2.87855
$302$	−7.59380	−0.436974
$303$	−4.22816	−0.242902
$304$	7.84038	0.449677
$305$	−7.50467	−0.429716
$306$	−15.7233	−0.898842
$307$	24.4543	1.39568	0.697840	−	0.716254i	$-0.254145\pi$
$307$	24.4543	1.39568	0.697840	+	0.716254i	$0.254145\pi$
$308$	13.5035	0.769433
$309$	2.55775	0.145505
$310$	27.6718	1.57166
$311$	−16.5940	−0.940962	−0.470481	−	0.882410i	$-0.655920\pi$
$311$	−16.5940	−0.940962	−0.470481	+	0.882410i	$0.655920\pi$
$312$	−0.886813	−0.0502059
$313$	−14.3918	−0.813475	−0.406737	−	0.913545i	$-0.633334\pi$
$313$	−14.3918	−0.813475	−0.406737	+	0.913545i	$0.633334\pi$
$314$	−42.8230	−2.41664
$315$	−13.0281	−0.734050
$316$	−42.3416	−2.38190
$317$	−7.74596	−0.435056	−0.217528	−	0.976054i	$-0.569799\pi$
$317$	−7.74596	−0.435056	−0.217528	+	0.976054i	$0.569799\pi$
$318$	−9.18712	−0.515188
$319$	2.50838	0.140442
$320$	−17.6923	−0.989032
$321$	1.91003	0.106607
$322$	11.1660	0.622254
$323$	15.9751	0.888880
$324$	0.670840	0.0372689
$325$	−1.50386	−0.0834193
$326$	39.9269	2.21134
$327$	−21.2082	−1.17282
$328$	−2.29635	−0.126795
$329$	−53.0509	−2.92479
$330$	−3.25254	−0.179047
$331$	14.2007	0.780538	0.390269	−	0.920701i	$-0.372382\pi$
$331$	14.2007	0.780538	0.390269	+	0.920701i	$0.372382\pi$
$332$	−3.80420	−0.208783
$333$	−11.7508	−0.643939
$334$	−6.88477	−0.376718
$335$	−3.18472	−0.174000
$336$	−9.60454	−0.523971
$337$	−2.25049	−0.122592	−0.0612959	−	0.998120i	$-0.519523\pi$
$337$	−2.25049	−0.122592	−0.0612959	+	0.998120i	$0.519523\pi$
$338$	27.8422	1.51441
$339$	12.5932	0.683966
$340$	−14.9128	−0.808759
$341$	−8.96340	−0.485395
$342$	−17.3096	−0.935998
$343$	47.6727	2.57408
$344$	17.2070	0.927737
$345$	−1.56167	−0.0840773
$346$	18.5541	0.997474
$347$	−18.4841	−0.992281	−0.496140	−	0.868242i	$-0.665250\pi$
$347$	−18.4841	−0.992281	−0.496140	+	0.868242i	$0.665250\pi$
$348$	7.31848	0.392312
$349$	2.30388	0.123324	0.0616620	−	0.998097i	$-0.480360\pi$
$349$	2.30388	0.123324	0.0616620	+	0.998097i	$0.480360\pi$
$350$	31.9639	1.70854
$351$	−2.58119	−0.137774
$352$	7.44303	0.396715
$353$	24.8937	1.32496	0.662478	−	0.749082i	$-0.269505\pi$
$353$	24.8937	1.32496	0.662478	+	0.749082i	$0.269505\pi$
$354$	21.8354	1.16054
$355$	−11.8504	−0.628954
$356$	3.75784	0.199165
$357$	−19.5697	−1.03574
$358$	−22.8120	−1.20565
$359$	33.5314	1.76972	0.884860	−	0.465857i	$-0.154254\pi$
$359$	33.5314	1.76972	0.884860	+	0.465857i	$0.154254\pi$
$360$	4.48878	0.236579
$361$	−1.41317	−0.0743772
$362$	−45.5442	−2.39375
$363$	1.05356	0.0552973
$364$	6.76546	0.354606
$365$	12.0052	0.628383
$366$	12.2146	0.638466
$367$	18.7097	0.976637	0.488319	−	0.872665i	$-0.337610\pi$
$367$	18.7097	0.976637	0.488319	+	0.872665i	$0.337610\pi$
$368$	1.96036	0.102191
$369$	−2.58334	−0.134483
$370$	−19.1940	−0.997849
$371$	19.4702	1.01084
$372$	−26.1517	−1.35590
$373$	−23.0470	−1.19333	−0.596664	−	0.802491i	$-0.703508\pi$
$373$	−23.0470	−1.19333	−0.596664	+	0.802491i	$0.703508\pi$
$374$	8.31913	0.430172
$375$	−11.9172	−0.615401
$376$	18.2785	0.942640
$377$	1.25674	0.0647253
$378$	54.8620	2.82180
$379$	−15.0729	−0.774241	−0.387120	−	0.922029i	$-0.626530\pi$
$379$	−15.0729	−0.774241	−0.387120	+	0.922029i	$0.626530\pi$
$380$	−16.4173	−0.842190
$381$	−11.0727	−0.567271
$382$	6.50701	0.332928
$383$	16.1386	0.824643	0.412321	−	0.911038i	$-0.364718\pi$
$383$	16.1386	0.824643	0.412321	+	0.911038i	$0.364718\pi$
$384$	13.1127	0.669154
$385$	6.89309	0.351305
$386$	−33.4095	−1.70050
$387$	19.3574	0.983993
$388$	−35.4085	−1.79759
$389$	6.25842	0.317315	0.158657	−	0.987334i	$-0.449284\pi$
$389$	6.25842	0.317315	0.158657	+	0.987334i	$0.449284\pi$
$390$	−1.62957	−0.0825167
$391$	3.99432	0.202001
$392$	−28.1858	−1.42360
$393$	−2.56398	−0.129336
$394$	−30.3899	−1.53102
$395$	−21.6140	−1.08752
$396$	−5.23404	−0.263020
$397$	24.2095	1.21504	0.607520	−	0.794305i	$-0.292165\pi$
$397$	24.2095	1.21504	0.607520	+	0.794305i	$0.292165\pi$
$398$	32.4682	1.62748
$399$	−21.5440	−1.07855
$400$	5.61177	0.280589
$401$	15.0934	0.753728	0.376864	−	0.926269i	$-0.377002\pi$
$401$	15.0934	0.753728	0.376864	+	0.926269i	$0.377002\pi$
$402$	5.18344	0.258526
$403$	−4.49080	−0.223703
$404$	−11.1138	−0.552935
$405$	0.342442	0.0170161
$406$	−26.7114	−1.32567
$407$	6.21728	0.308179
$408$	6.74265	0.333811
$409$	−34.9246	−1.72691	−0.863455	−	0.504426i	$-0.831704\pi$
$409$	−34.9246	−1.72691	−0.863455	+	0.504426i	$0.831704\pi$
$410$	−4.21968	−0.208395
$411$	19.7823	0.975788
$412$	6.72312	0.331224
$413$	−46.2757	−2.27708
$414$	−4.32799	−0.212709
$415$	−1.94192	−0.0953252
$416$	3.72907	0.182833
$417$	−4.91585	−0.240730
$418$	9.15843	0.447954
$419$	18.2862	0.893340	0.446670	−	0.894699i	$-0.352610\pi$
$419$	18.2862	0.893340	0.446670	+	0.894699i	$0.352610\pi$
$420$	20.1114	0.981334
$421$	7.54789	0.367862	0.183931	−	0.982939i	$-0.441118\pi$
$421$	7.54789	0.367862	0.183931	+	0.982939i	$0.441118\pi$
$422$	37.1972	1.81073
$423$	20.5628	0.999800
$424$	−6.70839	−0.325788
$425$	11.4342	0.554642
$426$	19.2877	0.934491
$427$	−25.8863	−1.25272
$428$	5.02056	0.242678
$429$	0.527848	0.0254847
$430$	31.6189	1.52480
$431$	8.81633	0.424668	0.212334	−	0.977197i	$-0.431894\pi$
$431$	8.81633	0.424668	0.212334	+	0.977197i	$0.431894\pi$
$432$	9.63189	0.463414
$433$	14.0610	0.675728	0.337864	−	0.941195i	$-0.390296\pi$
$433$	14.0610	0.675728	0.337864	+	0.941195i	$0.390296\pi$
$434$	95.4500	4.58175
$435$	3.73585	0.179120
$436$	−55.7464	−2.66977
$437$	4.39730	0.210352
$438$	−19.5397	−0.933643
$439$	−30.5036	−1.45586	−0.727929	−	0.685652i	$-0.759517\pi$
$439$	−30.5036	−1.45586	−0.727929	+	0.685652i	$0.759517\pi$
$440$	−2.37499	−0.113223
$441$	−31.7084	−1.50992
$442$	4.16801	0.198252
$443$	19.5621	0.929422	0.464711	−	0.885462i	$-0.346158\pi$
$443$	19.5621	0.929422	0.464711	+	0.885462i	$0.346158\pi$
$444$	18.1396	0.860867
$445$	1.91825	0.0909340
$446$	−15.0465	−0.712471
$447$	−5.71544	−0.270331
$448$	−61.0272	−2.88326
$449$	−0.535403	−0.0252672	−0.0126336	−	0.999920i	$-0.504022\pi$
$449$	−0.535403	−0.0252672	−0.0126336	+	0.999920i	$0.504022\pi$
$450$	−12.3894	−0.584043
$451$	1.36683	0.0643615
$452$	33.1015	1.55696
$453$	3.66344	0.172123
$454$	30.2460	1.41951
$455$	3.45355	0.161905
$456$	7.42291	0.347610
$457$	0.633495	0.0296337	0.0148168	−	0.999890i	$-0.495283\pi$
$457$	0.633495	0.0296337	0.0148168	+	0.999890i	$0.495283\pi$
$458$	−64.2274	−3.00115
$459$	19.6254	0.916035
$460$	−4.10488	−0.191391
$461$	2.53078	0.117870	0.0589351	−	0.998262i	$-0.481229\pi$
$461$	2.53078	0.117870	0.0589351	+	0.998262i	$0.481229\pi$
$462$	−11.2192	−0.521963
$463$	−6.02308	−0.279916	−0.139958	−	0.990157i	$-0.544697\pi$
$463$	−6.02308	−0.279916	−0.139958	+	0.990157i	$0.544697\pi$
$464$	−4.68961	−0.217710
$465$	−13.3496	−0.619073
$466$	−6.68720	−0.309779
$467$	−10.2117	−0.472542	−0.236271	−	0.971687i	$-0.575925\pi$
$467$	−10.2117	−0.472542	−0.236271	+	0.971687i	$0.575925\pi$
$468$	−2.62233	−0.121217
$469$	−10.9852	−0.507251
$470$	33.5878	1.54929
$471$	20.6589	0.951911
$472$	15.9441	0.733888
$473$	−10.2419	−0.470923
$474$	35.1788	1.61582
$475$	12.5878	0.577569
$476$	−51.4395	−2.35772
$477$	−7.54678	−0.345543
$478$	−12.0258	−0.550049
$479$	12.6053	0.575949	0.287975	−	0.957638i	$-0.407018\pi$
$479$	12.6053	0.575949	0.287975	+	0.957638i	$0.407018\pi$
$480$	11.0852	0.505970
$481$	3.11495	0.142030
$482$	53.4592	2.43500
$483$	−5.38674	−0.245105
$484$	2.76930	0.125877
$485$	−18.0749	−0.820737
$486$	−34.3107	−1.55636
$487$	38.0829	1.72570	0.862849	−	0.505461i	$-0.168678\pi$
$487$	38.0829	1.72570	0.862849	+	0.505461i	$0.168678\pi$
$488$	8.91901	0.403745
$489$	−19.2617	−0.871046
$490$	−51.7932	−2.33978
$491$	−38.0827	−1.71865	−0.859323	−	0.511433i	$-0.829115\pi$
$491$	−38.0827	−1.71865	−0.859323	+	0.511433i	$0.829115\pi$
$492$	3.98788	0.179787
$493$	−9.55529	−0.430349
$494$	4.58852	0.206447
$495$	−2.67181	−0.120089
$496$	16.7578	0.752446
$497$	−40.8763	−1.83355
$498$	3.16066	0.141633
$499$	0.934781	0.0418465	0.0209233	−	0.999781i	$-0.493339\pi$
$499$	0.934781	0.0418465	0.0209233	+	0.999781i	$0.493339\pi$
$500$	−31.3247	−1.40088
$501$	3.32139	0.148389
$502$	26.3379	1.17552
$503$	1.90503	0.0849410	0.0424705	−	0.999098i	$-0.486477\pi$
$503$	1.90503	0.0849410	0.0424705	+	0.999098i	$0.486477\pi$
$504$	15.4834	0.689685
$505$	−5.67326	−0.252457
$506$	2.28992	0.101799
$507$	−13.4318	−0.596525
$508$	−29.1049	−1.29132
$509$	−10.5278	−0.466638	−0.233319	−	0.972400i	$-0.574959\pi$
$509$	−10.5278	−0.466638	−0.233319	+	0.972400i	$0.574959\pi$
$510$	12.3901	0.548641
$511$	41.4104	1.83189
$512$	−20.1973	−0.892602
$513$	21.6054	0.953901
$514$	−2.46737	−0.108831
$515$	3.43193	0.151229
$516$	−29.8819	−1.31548
$517$	−10.8797	−0.478488
$518$	−66.2070	−2.90897
$519$	−8.95096	−0.392904
$520$	−1.18991	−0.0521808
$521$	7.98725	0.349928	0.174964	−	0.984575i	$-0.444019\pi$
$521$	7.98725	0.349928	0.174964	+	0.984575i	$0.444019\pi$
$522$	10.3535	0.453161
$523$	−41.3774	−1.80931	−0.904654	−	0.426147i	$-0.859871\pi$
$523$	−41.3774	−1.80931	−0.904654	+	0.426147i	$0.859871\pi$
$524$	−6.73950	−0.294417
$525$	−15.4202	−0.672993
$526$	−37.2161	−1.62270
$527$	34.1447	1.48737
$528$	−1.96970	−0.0857203
$529$	−21.9005	−0.952197
$530$	−12.3271	−0.535454
$531$	17.9368	0.778389
$532$	−56.6291	−2.45518
$533$	0.684803	0.0296621
$534$	−3.12214	−0.135108
$535$	2.56283	0.110801
$536$	3.78492	0.163484
$537$	11.0051	0.474905
$538$	−64.0856	−2.76292
$539$	16.7767	0.722625
$540$	−20.1686	−0.867919
$541$	17.9121	0.770103	0.385052	−	0.922895i	$-0.374184\pi$
$541$	17.9121	0.770103	0.385052	+	0.922895i	$0.374184\pi$
$542$	−6.96972	−0.299375
$543$	21.9717	0.942894
$544$	−28.3531	−1.21563
$545$	−28.4567	−1.21895
$546$	−5.62098	−0.240556
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	51.9983	2.22126
$549$	10.0337	0.428227
$550$	6.55517	0.279514
$551$	−10.5193	−0.448138
$552$	1.85598	0.0789957
$553$	−74.5543	−3.17037
$554$	30.6371	1.30165
$555$	9.25968	0.393051
$556$	−12.9214	−0.547991
$557$	−15.8000	−0.669467	−0.334733	−	0.942313i	$-0.608646\pi$
$557$	−15.8000	−0.669467	−0.334733	+	0.942313i	$0.608646\pi$
$558$	−36.9970	−1.56621
$559$	−5.13136	−0.217033
$560$	−12.8872	−0.544582
$561$	−4.01336	−0.169444
$562$	−42.5043	−1.79294
$563$	−1.06041	−0.0446911	−0.0223455	−	0.999750i	$-0.507113\pi$
$563$	−1.06041	−0.0446911	−0.0223455	+	0.999750i	$0.507113\pi$
$564$	−31.7427	−1.33661
$565$	16.8972	0.710871
$566$	−48.2106	−2.02644
$567$	1.18120	0.0496059
$568$	14.0838	0.590941
$569$	−21.3551	−0.895252	−0.447626	−	0.894221i	$-0.647730\pi$
$569$	−21.3551	−0.895252	−0.447626	+	0.894221i	$0.647730\pi$
$570$	13.6401	0.571320
$571$	−30.3426	−1.26980	−0.634899	−	0.772595i	$-0.718958\pi$
$571$	−30.3426	−1.26980	−0.634899	+	0.772595i	$0.718958\pi$
$572$	1.38746	0.0580127
$573$	−3.13915	−0.131140
$574$	−14.5552	−0.607522
$575$	3.14738	0.131255
$576$	23.6545	0.985604
$577$	29.0193	1.20809	0.604044	−	0.796951i	$-0.293555\pi$
$577$	29.0193	1.20809	0.604044	+	0.796951i	$0.293555\pi$
$578$	5.43541	0.226083
$579$	16.1176	0.669825
$580$	9.81978	0.407744
$581$	−6.69838	−0.277895
$582$	29.4186	1.21944
$583$	3.99296	0.165371
$584$	−14.2678	−0.590405
$585$	−1.33862	−0.0553450
$586$	−56.5789	−2.33725
$587$	19.0132	0.784757	0.392378	−	0.919804i	$-0.371652\pi$
$587$	19.0132	0.784757	0.392378	+	0.919804i	$0.371652\pi$
$588$	48.9480	2.01858
$589$	37.5895	1.54885
$590$	29.2983	1.20619
$591$	14.6608	0.603066
$592$	−11.6237	−0.477730
$593$	16.6967	0.685653	0.342826	−	0.939399i	$-0.388616\pi$
$593$	16.6967	0.685653	0.342826	+	0.939399i	$0.388616\pi$
$594$	11.2511	0.461639
$595$	−26.2582	−1.07648
$596$	−15.0232	−0.615374
$597$	−15.6635	−0.641064
$598$	1.14728	0.0469160
$599$	−19.1336	−0.781779	−0.390889	−	0.920438i	$-0.627833\pi$
$599$	−19.1336	−0.781779	−0.390889	+	0.920438i	$0.627833\pi$
$600$	5.31297	0.216901
$601$	−14.2037	−0.579381	−0.289690	−	0.957120i	$-0.593552\pi$
$601$	−14.2037	−0.579381	−0.289690	+	0.957120i	$0.593552\pi$
$602$	109.065	4.44515
$603$	4.25794	0.173397
$604$	9.62946	0.391817
$605$	1.41364	0.0574726
$606$	9.23377	0.375096
$607$	12.6932	0.515201	0.257600	−	0.966252i	$-0.417068\pi$
$607$	12.6932	0.515201	0.257600	+	0.966252i	$0.417068\pi$
$608$	−31.2136	−1.26588
$609$	12.8863	0.522178
$610$	16.3892	0.663581
$611$	−5.45090	−0.220520
$612$	19.9382	0.805956
$613$	21.4708	0.867199	0.433599	−	0.901106i	$-0.357243\pi$
$613$	21.4708	0.867199	0.433599	+	0.901106i	$0.357243\pi$
$614$	−53.4050	−2.15525
$615$	2.03568	0.0820866
$616$	−8.19218	−0.330072
$617$	18.1322	0.729975	0.364988	−	0.931012i	$-0.381073\pi$
$617$	18.1322	0.729975	0.364988	+	0.931012i	$0.381073\pi$
$618$	−5.58580	−0.224694
$619$	−5.34304	−0.214755	−0.107378	−	0.994218i	$-0.534245\pi$
$619$	−5.34304	−0.214755	−0.107378	+	0.994218i	$0.534245\pi$
$620$	−35.0898	−1.40924
$621$	5.40208	0.216778
$622$	36.2393	1.45306
$623$	6.61674	0.265094
$624$	−0.986852	−0.0395057
$625$	−0.982089	−0.0392836
$626$	31.4299	1.25619
$627$	−4.41826	−0.176448
$628$	54.3025	2.16690
$629$	−23.6838	−0.944333
$630$	28.4517	1.13354
$631$	−7.44612	−0.296425	−0.148213	−	0.988956i	$-0.547352\pi$
$631$	−7.44612	−0.296425	−0.148213	+	0.988956i	$0.547352\pi$
$632$	25.6874	1.02179
$633$	−17.9449	−0.713245
$634$	16.9162	0.671828
$635$	−14.8571	−0.589586
$636$	11.6499	0.461949
$637$	8.40540	0.333034
$638$	−5.47798	−0.216875
$639$	15.8439	0.626774
$640$	17.5943	0.695477
$641$	−3.40029	−0.134303	−0.0671517	−	0.997743i	$-0.521391\pi$
$641$	−3.40029	−0.134303	−0.0671517	+	0.997743i	$0.521391\pi$
$642$	−4.17126	−0.164626
$643$	−16.3080	−0.643124	−0.321562	−	0.946889i	$-0.604208\pi$
$643$	−16.3080	−0.643124	−0.321562	+	0.946889i	$0.604208\pi$
$644$	−14.1592	−0.557951
$645$	−15.2537	−0.600615
$646$	−34.8876	−1.37264
$647$	24.9406	0.980516	0.490258	−	0.871577i	$-0.336903\pi$
$647$	24.9406	0.980516	0.490258	+	0.871577i	$0.336903\pi$
$648$	−0.406979	−0.0159877
$649$	−9.49024	−0.372525
$650$	3.28424	0.128819
$651$	−46.0475	−1.80474
$652$	−50.6300	−1.98282
$653$	17.1886	0.672641	0.336321	−	0.941748i	$-0.390817\pi$
$653$	17.1886	0.672641	0.336321	+	0.941748i	$0.390817\pi$
$654$	46.3160	1.81110
$655$	−3.44030	−0.134424
$656$	−2.55539	−0.0997713
$657$	−16.0509	−0.626206
$658$	115.856	4.51655
$659$	25.4227	0.990327	0.495164	−	0.868800i	$-0.335108\pi$
$659$	25.4227	0.990327	0.495164	+	0.868800i	$0.335108\pi$
$660$	4.12445	0.160544
$661$	14.1580	0.550684	0.275342	−	0.961346i	$-0.411209\pi$
$661$	14.1580	0.550684	0.275342	+	0.961346i	$0.411209\pi$
$662$	−31.0124	−1.20533
$663$	−2.01075	−0.0780912
$664$	2.30790	0.0895638
$665$	−28.9073	−1.12098
$666$	25.6622	0.994391
$667$	−2.63018	−0.101841
$668$	8.73036	0.337788
$669$	7.25880	0.280642
$670$	6.95503	0.268696
$671$	−5.30877	−0.204943
$672$	38.2369	1.47502
$673$	41.6177	1.60425	0.802123	−	0.597160i	$-0.203704\pi$
$673$	41.6177	1.60425	0.802123	+	0.597160i	$0.203704\pi$
$674$	4.91477	0.189310
$675$	15.4641	0.595214
$676$	−35.3058	−1.35791
$677$	−1.95263	−0.0750455	−0.0375227	−	0.999296i	$-0.511947\pi$
$677$	−1.95263	−0.0750455	−0.0375227	+	0.999296i	$0.511947\pi$
$678$	−27.5018	−1.05620
$679$	−62.3466	−2.39264
$680$	9.04715	0.346942
$681$	−14.5914	−0.559145
$682$	19.5749	0.749562
$683$	−5.53863	−0.211930	−0.105965	−	0.994370i	$-0.533793\pi$
$683$	−5.53863	−0.211930	−0.105965	+	0.994370i	$0.533793\pi$
$684$	21.9498	0.839271
$685$	26.5434	1.01417
$686$	−104.111	−3.97498
$687$	30.9849	1.18215
$688$	19.1480	0.730012
$689$	2.00053	0.0762143
$690$	3.41048	0.129835
$691$	−14.4895	−0.551208	−0.275604	−	0.961271i	$-0.588878\pi$
$691$	−14.4895	−0.551208	−0.275604	+	0.961271i	$0.588878\pi$
$692$	−23.5278	−0.894395
$693$	−9.21600	−0.350087
$694$	40.3670	1.53231
$695$	−6.59598	−0.250200
$696$	−4.43991	−0.168294
$697$	−5.20673	−0.197219
$698$	−5.03138	−0.190441
$699$	3.22607	0.122021
$700$	−40.5325	−1.53198
$701$	−36.6739	−1.38515	−0.692577	−	0.721344i	$-0.743525\pi$
$701$	−36.6739	−1.38515	−0.692577	+	0.721344i	$0.743525\pi$
$702$	5.63698	0.212754
$703$	−26.0732	−0.983369
$704$	−12.5155	−0.471694
$705$	−16.2036	−0.610264
$706$	−54.3646	−2.04604
$707$	−19.5691	−0.735971
$708$	−27.6888	−1.04061
$709$	18.8704	0.708691	0.354345	−	0.935115i	$-0.384704\pi$
$709$	18.8704	0.708691	0.354345	+	0.935115i	$0.384704\pi$
$710$	25.8798	0.971251
$711$	28.8977	1.08375
$712$	−2.27977	−0.0854381
$713$	9.39864	0.351982
$714$	42.7377	1.59942
$715$	0.708255	0.0264872
$716$	28.9272	1.08106
$717$	5.80157	0.216664
$718$	−73.2283	−2.73286
$719$	−6.81124	−0.254016	−0.127008	−	0.991902i	$-0.540537\pi$
$719$	−6.81124	−0.254016	−0.127008	+	0.991902i	$0.540537\pi$
$720$	4.99514	0.186158
$721$	11.8380	0.440869
$722$	3.08618	0.114856
$723$	−25.7901	−0.959143
$724$	57.7531	2.14638
$725$	−7.52923	−0.279628
$726$	−2.30083	−0.0853918
$727$	−42.6320	−1.58113	−0.790567	−	0.612375i	$-0.790214\pi$
$727$	−42.6320	−1.58113	−0.790567	+	0.612375i	$0.790214\pi$
$728$	−4.10441	−0.152119
$729$	15.8256	0.586134
$730$	−26.2179	−0.970369
$731$	39.0150	1.44302
$732$	−15.4889	−0.572487
$733$	−5.43901	−0.200895	−0.100447	−	0.994942i	$-0.532027\pi$
$733$	−5.43901	−0.200895	−0.100447	+	0.994942i	$0.532027\pi$
$734$	−40.8596	−1.50815
$735$	24.9864	0.921635
$736$	−7.80445	−0.287676
$737$	−2.25286	−0.0829850
$738$	5.64168	0.207673
$739$	−3.73867	−0.137529	−0.0687647	−	0.997633i	$-0.521906\pi$
$739$	−3.73867	−0.137529	−0.0687647	+	0.997633i	$0.521906\pi$
$740$	24.3393	0.894731
$741$	−2.21362	−0.0813193
$742$	−42.5205	−1.56098
$743$	−30.8466	−1.13165	−0.565826	−	0.824524i	$-0.691443\pi$
$743$	−30.8466	−1.13165	−0.565826	+	0.824524i	$0.691443\pi$
$744$	15.8655	0.581657
$745$	−7.66885	−0.280965
$746$	50.3317	1.84278
$747$	2.59633	0.0949948
$748$	−10.5492	−0.385718
$749$	8.84012	0.323011
$750$	26.0256	0.950322
$751$	−5.99027	−0.218588	−0.109294	−	0.994009i	$-0.534859\pi$
$751$	−5.99027	−0.218588	−0.109294	+	0.994009i	$0.534859\pi$
$752$	20.3404	0.741739
$753$	−12.7061	−0.463034
$754$	−2.74456	−0.0999508
$755$	4.91552	0.178894
$756$	−69.5688	−2.53019
$757$	−4.20580	−0.152863	−0.0764313	−	0.997075i	$-0.524353\pi$
$757$	−4.20580	−0.152863	−0.0764313	+	0.997075i	$0.524353\pi$
$758$	32.9172	1.19561
$759$	−1.10471	−0.0400986
$760$	9.95990	0.361284
$761$	−14.1484	−0.512878	−0.256439	−	0.966560i	$-0.582549\pi$
$761$	−14.1484	−0.512878	−0.256439	+	0.966560i	$0.582549\pi$
$762$	24.1814	0.875998
$763$	−98.1574	−3.55353
$764$	−8.25133	−0.298523
$765$	10.1778	0.367980
$766$	−35.2446	−1.27344
$767$	−4.75476	−0.171684
$768$	−2.26498	−0.0817304
$769$	−14.4585	−0.521386	−0.260693	−	0.965422i	$-0.583951\pi$
$769$	−14.4585	−0.521386	−0.260693	+	0.965422i	$0.583951\pi$
$770$	−15.0536	−0.542496
$771$	1.19032	0.0428683
$772$	42.3656	1.52477
$773$	−12.1996	−0.438789	−0.219394	−	0.975636i	$-0.570408\pi$
$773$	−12.1996	−0.438789	−0.219394	+	0.975636i	$0.570408\pi$
$774$	−42.2741	−1.51951
$775$	26.9048	0.966448
$776$	21.4813	0.771133
$777$	31.9399	1.14584
$778$	−13.6676	−0.490007
$779$	−5.73203	−0.205371
$780$	2.06641	0.0739894
$781$	−8.38292	−0.299964
$782$	−8.72309	−0.311937
$783$	−12.9229	−0.461828
$784$	−31.3654	−1.12019
$785$	27.7196	0.989357
$786$	5.59941	0.199724
$787$	−9.57506	−0.341314	−0.170657	−	0.985331i	$-0.554589\pi$
$787$	−9.57506	−0.341314	−0.170657	+	0.985331i	$0.554589\pi$
$788$	38.5364	1.37280
$789$	17.9540	0.639179
$790$	47.2022	1.67938
$791$	58.2845	2.07236
$792$	3.17534	0.112831
$793$	−2.65977	−0.0944514
$794$	−52.8704	−1.87630
$795$	5.94690	0.210915
$796$	−41.1719	−1.45930
$797$	−35.9353	−1.27289	−0.636446	−	0.771321i	$-0.719596\pi$
$797$	−35.9353	−1.27289	−0.636446	+	0.771321i	$0.719596\pi$
$798$	47.0495	1.66553
$799$	41.4445	1.46620
$800$	−22.3412	−0.789880
$801$	−2.56469	−0.0906188
$802$	−32.9620	−1.16393
$803$	8.49245	0.299692
$804$	−6.57296	−0.231810
$805$	−7.22781	−0.254747
$806$	9.80734	0.345449
$807$	30.9165	1.08831
$808$	6.74245	0.237198
$809$	−0.492652	−0.0173207	−0.00866037	−	0.999962i	$-0.502757\pi$
$809$	−0.492652	−0.0173207	−0.00866037	+	0.999962i	$0.502757\pi$
$810$	−0.747850	−0.0262768
$811$	2.60114	0.0913383	0.0456691	−	0.998957i	$-0.485458\pi$
$811$	2.60114	0.0913383	0.0456691	+	0.998957i	$0.485458\pi$
$812$	33.8719	1.18867
$813$	3.36237	0.117924
$814$	−13.5777	−0.475900
$815$	−25.8450	−0.905310
$816$	7.50328	0.262667
$817$	42.9511	1.50267
$818$	76.2709	2.66675
$819$	−4.61736	−0.161344
$820$	5.35085	0.186860
$821$	−31.7214	−1.10708	−0.553542	−	0.832821i	$-0.686724\pi$
$821$	−31.7214	−1.10708	−0.553542	+	0.832821i	$0.686724\pi$
$822$	−43.2020	−1.50684
$823$	−1.98973	−0.0693575	−0.0346788	−	0.999399i	$-0.511041\pi$
$823$	−1.98973	−0.0693575	−0.0346788	+	0.999399i	$0.511041\pi$
$824$	−4.07872	−0.142089
$825$	−3.16238	−0.110100
$826$	101.060	3.51634
$827$	−36.9343	−1.28433	−0.642166	−	0.766566i	$-0.721964\pi$
$827$	−36.9343	−1.28433	−0.642166	+	0.766566i	$0.721964\pi$
$828$	5.48819	0.190728
$829$	−15.5922	−0.541541	−0.270770	−	0.962644i	$-0.587278\pi$
$829$	−15.5922	−0.541541	−0.270770	+	0.962644i	$0.587278\pi$
$830$	4.24091	0.147204
$831$	−14.7801	−0.512717
$832$	−6.27044	−0.217389
$833$	−63.9084	−2.21429
$834$	10.7356	0.371743
$835$	4.45656	0.154226
$836$	−11.6135	−0.401662
$837$	46.1786	1.59617
$838$	−39.9347	−1.37952
$839$	−46.3569	−1.60042	−0.800209	−	0.599722i	$-0.795278\pi$
$839$	−46.3569	−1.60042	−0.800209	+	0.599722i	$0.795278\pi$
$840$	−12.2010	−0.420974
$841$	−22.7080	−0.783035
$842$	−16.4836	−0.568064
$843$	20.5052	0.706235
$844$	−47.1686	−1.62361
$845$	−18.0224	−0.619991
$846$	−44.9066	−1.54392
$847$	4.87614	0.167546
$848$	−7.46514	−0.256354
$849$	23.2580	0.798213
$850$	−24.9709	−0.856495
$851$	−6.51918	−0.223475
$852$	−24.4581	−0.837920
$853$	−18.5279	−0.634382	−0.317191	−	0.948362i	$-0.602740\pi$
$853$	−18.5279	−0.634382	−0.317191	+	0.948362i	$0.602740\pi$
$854$	56.5323	1.93450
$855$	11.2047	0.383191
$856$	−3.04583	−0.104104
$857$	39.3928	1.34563	0.672816	−	0.739810i	$-0.265085\pi$
$857$	39.3928	1.34563	0.672816	+	0.739810i	$0.265085\pi$
$858$	−1.15275	−0.0393543
$859$	−42.3995	−1.44665	−0.723325	−	0.690507i	$-0.757387\pi$
$859$	−42.3995	−1.44665	−0.723325	+	0.690507i	$0.757387\pi$
$860$	−40.0949	−1.36722
$861$	7.02179	0.239302
$862$	−19.2537	−0.655785
$863$	32.7692	1.11548	0.557738	−	0.830017i	$-0.311669\pi$
$863$	32.7692	1.11548	0.557738	+	0.830017i	$0.311669\pi$
$864$	−38.3458	−1.30455
$865$	−12.0102	−0.408359
$866$	−30.7074	−1.04348
$867$	−2.62218	−0.0890540
$868$	−121.037	−4.10827
$869$	−15.2896	−0.518665
$870$	−8.15861	−0.276603
$871$	−1.12872	−0.0382451
$872$	33.8197	1.14528
$873$	24.1659	0.817893
$874$	−9.60315	−0.324831
$875$	−55.1560	−1.86461
$876$	24.7777	0.837160
$877$	18.4330	0.622438	0.311219	−	0.950338i	$-0.399263\pi$
$877$	18.4330	0.622438	0.311219	+	0.950338i	$0.399263\pi$
$878$	66.6160	2.24818
$879$	27.2951	0.920640
$880$	−2.64290	−0.0890923
$881$	−35.8216	−1.20686	−0.603430	−	0.797416i	$-0.706200\pi$
$881$	−35.8216	−1.20686	−0.603430	+	0.797416i	$0.706200\pi$
$882$	69.2470	2.33167
$883$	−43.2725	−1.45623	−0.728117	−	0.685453i	$-0.759604\pi$
$883$	−43.2725	−1.45623	−0.728117	+	0.685453i	$0.759604\pi$
$884$	−5.28532	−0.177765
$885$	−14.1343	−0.475118
$886$	−42.7211	−1.43524
$887$	−9.88011	−0.331742	−0.165871	−	0.986147i	$-0.553043\pi$
$887$	−9.88011	−0.331742	−0.165871	+	0.986147i	$0.553043\pi$
$888$	−11.0048	−0.369296
$889$	−51.2474	−1.71878
$890$	−4.18922	−0.140423
$891$	0.242242	0.00811541
$892$	19.0800	0.638845
$893$	45.6258	1.52681
$894$	12.4818	0.417453
$895$	14.7664	0.493587
$896$	60.6891	2.02748
$897$	−0.553479	−0.0184801
$898$	1.16925	0.0390184
$899$	−22.4836	−0.749870
$900$	15.7106	0.523688
$901$	−15.2106	−0.506737
$902$	−2.98498	−0.0993890
$903$	−52.6156	−1.75094
$904$	−20.0817	−0.667907
$905$	29.4811	0.979985
$906$	−8.00049	−0.265798
$907$	0.859225	0.0285301	0.0142650	−	0.999898i	$-0.495459\pi$
$907$	0.859225	0.0285301	0.0142650	+	0.999898i	$0.495459\pi$
$908$	−38.3540	−1.27282
$909$	7.58509	0.251582
$910$	−7.54211	−0.250018
$911$	29.7435	0.985448	0.492724	−	0.870186i	$-0.336001\pi$
$911$	29.7435	0.985448	0.492724	+	0.870186i	$0.336001\pi$
$912$	8.26028	0.273525
$913$	−1.37370	−0.0454630
$914$	−1.38347	−0.0457612
$915$	−7.90659	−0.261384
$916$	81.4447	2.69101
$917$	−11.8668	−0.391876
$918$	−42.8594	−1.41457
$919$	45.5013	1.50095	0.750475	−	0.660899i	$-0.229825\pi$
$919$	45.5013	1.50095	0.750475	+	0.660899i	$0.229825\pi$
$920$	2.49031	0.0821032
$921$	25.7639	0.848951
$922$	−5.52691	−0.182019
$923$	−4.19997	−0.138244
$924$	14.2267	0.468023
$925$	−18.6620	−0.613601
$926$	13.1536	0.432255
$927$	−4.58846	−0.150705
$928$	18.6699	0.612871
$929$	−50.1197	−1.64437	−0.822186	−	0.569218i	$-0.807246\pi$
$929$	−50.1197	−1.64437	−0.822186	+	0.569218i	$0.807246\pi$
$930$	29.1538	0.955992
$931$	−70.3560	−2.30582
$932$	8.47983	0.277766
$933$	−17.4827	−0.572359
$934$	22.3011	0.729714
$935$	−5.38503	−0.176109
$936$	1.59089	0.0520000
$937$	−18.7886	−0.613798	−0.306899	−	0.951742i	$-0.599291\pi$
$937$	−18.7886	−0.613798	−0.306899	+	0.951742i	$0.599291\pi$
$938$	23.9904	0.783313
$939$	−15.1626	−0.494813
$940$	−42.5917	−1.38919
$941$	−27.6298	−0.900705	−0.450353	−	0.892851i	$-0.648702\pi$
$941$	−27.6298	−0.900705	−0.450353	+	0.892851i	$0.648702\pi$
$942$	−45.1164	−1.46997
$943$	−1.43320	−0.0466714
$944$	17.7427	0.577477
$945$	−35.5126	−1.15522
$946$	22.3670	0.727215
$947$	−21.5652	−0.700776	−0.350388	−	0.936605i	$-0.613950\pi$
$947$	−21.5652	−0.700776	−0.350388	+	0.936605i	$0.613950\pi$
$948$	−44.6092	−1.44884
$949$	4.25485	0.138118
$950$	−27.4902	−0.891900
$951$	−8.16080	−0.264632
$952$	31.2068	1.01142
$953$	−37.8932	−1.22748	−0.613741	−	0.789508i	$-0.710336\pi$
$953$	−37.8932	−1.22748	−0.613741	+	0.789508i	$0.710336\pi$
$954$	16.4812	0.533598
$955$	−4.21204	−0.136298
$956$	15.2496	0.493207
$957$	2.64272	0.0854269
$958$	−27.5283	−0.889399
$959$	91.5577	2.95655
$960$	−18.6399	−0.601599
$961$	49.3425	1.59169
$962$	−6.80266	−0.219327
$963$	−3.42648	−0.110417
$964$	−67.7899	−2.18337
$965$	21.6262	0.696174
$966$	11.7640	0.378499
$967$	4.75853	0.153024	0.0765120	−	0.997069i	$-0.475622\pi$
$967$	4.75853	0.153024	0.0765120	+	0.997069i	$0.475622\pi$
$968$	−1.68005	−0.0539990
$969$	16.8307	0.540679
$970$	39.4732	1.26741
$971$	22.1858	0.711978	0.355989	−	0.934490i	$-0.384144\pi$
$971$	22.1858	0.711978	0.355989	+	0.934490i	$0.384144\pi$
$972$	43.5083	1.39553
$973$	−22.7519	−0.729391
$974$	−83.1681	−2.66488
$975$	−1.58440	−0.0507415
$976$	9.92514	0.317696
$977$	−36.5605	−1.16967	−0.584837	−	0.811151i	$-0.698841\pi$
$977$	−36.5605	−1.16967	−0.584837	+	0.811151i	$0.698841\pi$
$978$	42.0652	1.34510
$979$	1.35696	0.0433687
$980$	65.6773	2.09799
$981$	38.0464	1.21473
$982$	83.1677	2.65399
$983$	30.6509	0.977613	0.488807	−	0.872392i	$-0.337432\pi$
$983$	30.6509	0.977613	0.488807	+	0.872392i	$0.337432\pi$
$984$	−2.41933	−0.0771254
$985$	19.6716	0.626789
$986$	20.8675	0.664558
$987$	−55.8921	−1.77906
$988$	−5.81855	−0.185113
$989$	10.7392	0.341488
$990$	5.83488	0.185445
$991$	5.31786	0.168927	0.0844637	−	0.996427i	$-0.473082\pi$
$991$	5.31786	0.168927	0.0844637	+	0.996427i	$0.473082\pi$
$992$	−66.7148	−2.11820
$993$	14.9612	0.474779
$994$	89.2686	2.83143
$995$	−21.0169	−0.666281
$996$	−4.00794	−0.126996
$997$	−43.3390	−1.37256	−0.686280	−	0.727338i	$-0.740757\pi$
$997$	−43.3390	−1.37256	−0.686280	+	0.727338i	$0.740757\pi$
$998$	−2.04144	−0.0646207
$999$	−32.0308	−1.01341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.16	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.16	✓	106	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} +O(q^{10})\)	\(q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} -3.08721 q^{10} +1.00000 q^{11} +2.91761 q^{12} +0.501016 q^{13} -10.6489 q^{14} +1.48935 q^{15} -1.86958 q^{16} -3.80935 q^{17} +4.12757 q^{18} -4.19367 q^{19} +3.91479 q^{20} +5.13728 q^{21} -2.18387 q^{22} -1.04856 q^{23} -1.77003 q^{24} -3.00163 q^{25} -1.09415 q^{26} -5.15191 q^{27} +13.5035 q^{28} +2.50838 q^{29} -3.25254 q^{30} -8.96340 q^{31} +7.44303 q^{32} +1.05356 q^{33} +8.31913 q^{34} +6.89309 q^{35} -5.23404 q^{36} +6.21728 q^{37} +9.15843 q^{38} +0.527848 q^{39} -2.37499 q^{40} +1.36683 q^{41} -11.2192 q^{42} -10.2419 q^{43} +2.76930 q^{44} -2.67181 q^{45} +2.28992 q^{46} -10.8797 q^{47} -1.96970 q^{48} +16.7767 q^{49} +6.55517 q^{50} -4.01336 q^{51} +1.38746 q^{52} +3.99296 q^{53} +11.2511 q^{54} +1.41364 q^{55} -8.19218 q^{56} -4.41826 q^{57} -5.47798 q^{58} -9.49024 q^{59} +4.12445 q^{60} -5.30877 q^{61} +19.5749 q^{62} -9.21600 q^{63} -12.5155 q^{64} +0.708255 q^{65} -2.30083 q^{66} -2.25286 q^{67} -10.5492 q^{68} -1.10471 q^{69} -15.0536 q^{70} -8.38292 q^{71} +3.17534 q^{72} +8.49245 q^{73} -13.5777 q^{74} -3.16238 q^{75} -11.6135 q^{76} +4.87614 q^{77} -1.15275 q^{78} -15.2896 q^{79} -2.64290 q^{80} +0.242242 q^{81} -2.98498 q^{82} -1.37370 q^{83} +14.2267 q^{84} -5.38503 q^{85} +22.3670 q^{86} +2.64272 q^{87} -1.68005 q^{88} +1.35696 q^{89} +5.83488 q^{90} +2.44302 q^{91} -2.90377 q^{92} -9.44344 q^{93} +23.7599 q^{94} -5.92832 q^{95} +7.84164 q^{96} -12.7861 q^{97} -36.6382 q^{98} -1.89002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more