LMFDB - Embedded newform 1859.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.28561300.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 $ x^6 - 9x^4 - x^3 + 22x^2 + 4*x - 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.23039$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97462 q^{2} -0.571492 q^{3} +1.89914 q^{4} +1.23039 q^{5} -1.12848 q^{6} -2.55803 q^{7} -0.199164 q^{8} -2.67340 q^{9} +O(q^{10})$	\(q+1.97462 q^{2} -0.571492 q^{3} +1.89914 q^{4} +1.23039 q^{5} -1.12848 q^{6} -2.55803 q^{7} -0.199164 q^{8} -2.67340 q^{9} +2.42955 q^{10} -1.00000 q^{11} -1.08534 q^{12} -5.05115 q^{14} -0.703156 q^{15} -4.19155 q^{16} +5.97567 q^{17} -5.27895 q^{18} -5.32116 q^{19} +2.33667 q^{20} +1.46190 q^{21} -1.97462 q^{22} -3.26161 q^{23} +0.113821 q^{24} -3.48615 q^{25} +3.24230 q^{27} -4.85806 q^{28} -2.86469 q^{29} -1.38847 q^{30} +2.90456 q^{31} -7.87841 q^{32} +0.571492 q^{33} +11.7997 q^{34} -3.14737 q^{35} -5.07715 q^{36} -9.62343 q^{37} -10.5073 q^{38} -0.245048 q^{40} -3.47319 q^{41} +2.88669 q^{42} +4.53626 q^{43} -1.89914 q^{44} -3.28931 q^{45} -6.44045 q^{46} +0.858478 q^{47} +2.39544 q^{48} -0.456470 q^{49} -6.88383 q^{50} -3.41505 q^{51} -13.7446 q^{53} +6.40233 q^{54} -1.23039 q^{55} +0.509467 q^{56} +3.04100 q^{57} -5.65668 q^{58} +8.76048 q^{59} -1.33539 q^{60} +2.76304 q^{61} +5.73542 q^{62} +6.83863 q^{63} -7.17379 q^{64} +1.12848 q^{66} +3.64984 q^{67} +11.3486 q^{68} +1.86398 q^{69} -6.21487 q^{70} -7.31017 q^{71} +0.532443 q^{72} -5.63352 q^{73} -19.0026 q^{74} +1.99231 q^{75} -10.1056 q^{76} +2.55803 q^{77} +7.57221 q^{79} -5.15723 q^{80} +6.16724 q^{81} -6.85824 q^{82} -0.707087 q^{83} +2.77634 q^{84} +7.35238 q^{85} +8.95740 q^{86} +1.63715 q^{87} +0.199164 q^{88} +12.1474 q^{89} -6.49515 q^{90} -6.19425 q^{92} -1.65994 q^{93} +1.69517 q^{94} -6.54708 q^{95} +4.50245 q^{96} +3.45779 q^{97} -0.901356 q^{98} +2.67340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	$ 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} - 17 q^{12} + 12 q^{14} + 4 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 15 q^{20} - 12 q^{21} + 3 q^{23} - 14 q^{24} - 6 q^{25} + 10 q^{27} - 16 q^{28} + 3 q^{29} + 19 q^{30} - 5 q^{31} + q^{32} - q^{33} + 5 q^{34} - 13 q^{35} + 20 q^{36} - 25 q^{37} - 27 q^{38} - 8 q^{40} - 24 q^{41} + 13 q^{42} - 8 q^{43} - 8 q^{44} - 27 q^{45} - 18 q^{46} - 10 q^{47} - 28 q^{48} - q^{49} + 26 q^{50} - 17 q^{51} + 10 q^{53} - 47 q^{54} + 6 q^{55} + 15 q^{56} - 6 q^{58} + 4 q^{59} + 61 q^{60} - 21 q^{61} - 5 q^{62} - 6 q^{63} - 27 q^{64} + 12 q^{66} - 21 q^{67} + 14 q^{68} + 5 q^{69} - 31 q^{70} + 3 q^{71} + 50 q^{72} - 13 q^{73} - 38 q^{74} - 23 q^{75} - 8 q^{76} + 3 q^{77} - 4 q^{79} - 44 q^{80} + 34 q^{81} - 33 q^{82} - 8 q^{83} - 47 q^{84} + 13 q^{85} + 11 q^{86} - 51 q^{87} - 3 q^{88} + 9 q^{89} - 70 q^{90} + 15 q^{92} + 21 q^{93} + 10 q^{94} + 27 q^{95} + 19 q^{96} - 15 q^{97} - 21 q^{98} - 7 q^{99}+O(q^{100}) $ 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 - 17 * q^12 + 12 * q^14 + 4 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 15 * q^20 - 12 * q^21 + 3 * q^23 - 14 * q^24 - 6 * q^25 + 10 * q^27 - 16 * q^28 + 3 * q^29 + 19 * q^30 - 5 * q^31 + q^32 - q^33 + 5 * q^34 - 13 * q^35 + 20 * q^36 - 25 * q^37 - 27 * q^38 - 8 * q^40 - 24 * q^41 + 13 * q^42 - 8 * q^43 - 8 * q^44 - 27 * q^45 - 18 * q^46 - 10 * q^47 - 28 * q^48 - q^49 + 26 * q^50 - 17 * q^51 + 10 * q^53 - 47 * q^54 + 6 * q^55 + 15 * q^56 - 6 * q^58 + 4 * q^59 + 61 * q^60 - 21 * q^61 - 5 * q^62 - 6 * q^63 - 27 * q^64 + 12 * q^66 - 21 * q^67 + 14 * q^68 + 5 * q^69 - 31 * q^70 + 3 * q^71 + 50 * q^72 - 13 * q^73 - 38 * q^74 - 23 * q^75 - 8 * q^76 + 3 * q^77 - 4 * q^79 - 44 * q^80 + 34 * q^81 - 33 * q^82 - 8 * q^83 - 47 * q^84 + 13 * q^85 + 11 * q^86 - 51 * q^87 - 3 * q^88 + 9 * q^89 - 70 * q^90 + 15 * q^92 + 21 * q^93 + 10 * q^94 + 27 * q^95 + 19 * q^96 - 15 * q^97 - 21 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.97462	1.39627	0.698135	−	0.715966i	$-0.254014\pi$
$2$	1.97462	1.39627	0.698135	+	0.715966i	$0.254014\pi$
$3$	−0.571492	−0.329951	−0.164976	−	0.986298i	$-0.552755\pi$
$3$	−0.571492	−0.329951	−0.164976	+	0.986298i	$0.552755\pi$
$4$	1.89914	0.949569
$5$	1.23039	0.550246	0.275123	−	0.961409i	$-0.411281\pi$
$5$	1.23039	0.550246	0.275123	+	0.961409i	$0.411281\pi$
$6$	−1.12848	−0.460701
$7$	−2.55803	−0.966845	−0.483423	−	0.875387i	$-0.660607\pi$
$7$	−2.55803	−0.966845	−0.483423	+	0.875387i	$0.660607\pi$
$8$	−0.199164	−0.0704150
$9$	−2.67340	−0.891132
$10$	2.42955	0.768291
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.08534	−0.313312
$13$	0	0
$13$	0	0
$14$	−5.05115	−1.34998
$15$	−0.703156	−0.181554
$16$	−4.19155	−1.04789
$17$	5.97567	1.44931	0.724656	−	0.689111i	$-0.241999\pi$
$17$	5.97567	1.44931	0.724656	+	0.689111i	$0.241999\pi$
$18$	−5.27895	−1.24426
$19$	−5.32116	−1.22076	−0.610378	−	0.792110i	$-0.708983\pi$
$19$	−5.32116	−1.22076	−0.610378	+	0.792110i	$0.708983\pi$
$20$	2.33667	0.522496
$21$	1.46190	0.319012
$22$	−1.97462	−0.420991
$23$	−3.26161	−0.680093	−0.340046	−	0.940409i	$-0.610443\pi$
$23$	−3.26161	−0.680093	−0.340046	+	0.940409i	$0.610443\pi$
$24$	0.113821	0.0232335
$25$	−3.48615	−0.697230
$26$	0	0
$27$	3.24230	0.623981
$28$	−4.85806	−0.918087
$29$	−2.86469	−0.531959	−0.265979	−	0.963979i	$-0.585695\pi$
$29$	−2.86469	−0.531959	−0.265979	+	0.963979i	$0.585695\pi$
$30$	−1.38847	−0.253499
$31$	2.90456	0.521675	0.260838	−	0.965383i	$-0.416001\pi$
$31$	2.90456	0.521675	0.260838	+	0.965383i	$0.416001\pi$
$32$	−7.87841	−1.39272
$33$	0.571492	0.0994841
$34$	11.7997	2.02363
$35$	−3.14737	−0.532002
$36$	−5.07715	−0.846192
$37$	−9.62343	−1.58208	−0.791041	−	0.611764i	$-0.790460\pi$
$37$	−9.62343	−1.58208	−0.791041	+	0.611764i	$0.790460\pi$
$38$	−10.5073	−1.70451
$39$	0	0
$40$	−0.245048	−0.0387455
$41$	−3.47319	−0.542421	−0.271211	−	0.962520i	$-0.587424\pi$
$41$	−3.47319	−0.542421	−0.271211	+	0.962520i	$0.587424\pi$
$42$	2.88669	0.445427
$43$	4.53626	0.691773	0.345886	−	0.938276i	$-0.387578\pi$
$43$	4.53626	0.691773	0.345886	+	0.938276i	$0.387578\pi$
$44$	−1.89914	−0.286306
$45$	−3.28931	−0.490341
$46$	−6.44045	−0.949593
$47$	0.858478	0.125222	0.0626109	−	0.998038i	$-0.480057\pi$
$47$	0.858478	0.125222	0.0626109	+	0.998038i	$0.480057\pi$
$48$	2.39544	0.345752
$49$	−0.456470	−0.0652100
$50$	−6.88383	−0.973521
$51$	−3.41505	−0.478202
$52$	0	0
$53$	−13.7446	−1.88796	−0.943980	−	0.330003i	$-0.892950\pi$
$53$	−13.7446	−1.88796	−0.943980	+	0.330003i	$0.892950\pi$
$54$	6.40233	0.871246
$55$	−1.23039	−0.165905
$56$	0.509467	0.0680804
$57$	3.04100	0.402790
$58$	−5.65668	−0.742758
$59$	8.76048	1.14052	0.570259	−	0.821465i	$-0.306843\pi$
$59$	8.76048	1.14052	0.570259	+	0.821465i	$0.306843\pi$
$60$	−1.33539	−0.172398
$61$	2.76304	0.353771	0.176886	−	0.984231i	$-0.443398\pi$
$61$	2.76304	0.353771	0.176886	+	0.984231i	$0.443398\pi$
$62$	5.73542	0.728399
$63$	6.83863	0.861587
$64$	−7.17379	−0.896723
$65$	0	0
$66$	1.12848	0.138907
$67$	3.64984	0.445899	0.222950	−	0.974830i	$-0.428431\pi$
$67$	3.64984	0.445899	0.222950	+	0.974830i	$0.428431\pi$
$68$	11.3486	1.37622
$69$	1.86398	0.224397
$70$	−6.21487	−0.742819
$71$	−7.31017	−0.867558	−0.433779	−	0.901019i	$-0.642820\pi$
$71$	−7.31017	−0.867558	−0.433779	+	0.901019i	$0.642820\pi$
$72$	0.532443	0.0627491
$73$	−5.63352	−0.659353	−0.329677	−	0.944094i	$-0.606940\pi$
$73$	−5.63352	−0.659353	−0.329677	+	0.944094i	$0.606940\pi$
$74$	−19.0026	−2.20901
$75$	1.99231	0.230052
$76$	−10.1056	−1.15919
$77$	2.55803	0.291515
$78$	0	0
$79$	7.57221	0.851940	0.425970	−	0.904737i	$-0.359933\pi$
$79$	7.57221	0.851940	0.425970	+	0.904737i	$0.359933\pi$
$80$	−5.15723	−0.576595
$81$	6.16724	0.685249
$82$	−6.85824	−0.757366
$83$	−0.707087	−0.0776129	−0.0388065	−	0.999247i	$-0.512356\pi$
$83$	−0.707087	−0.0776129	−0.0388065	+	0.999247i	$0.512356\pi$
$84$	2.77634	0.302924
$85$	7.35238	0.797477
$86$	8.95740	0.965902
$87$	1.63715	0.175520
$88$	0.199164	0.0212309
$89$	12.1474	1.28762	0.643812	−	0.765183i	$-0.277352\pi$
$89$	12.1474	1.28762	0.643812	+	0.765183i	$0.277352\pi$
$90$	−6.49515	−0.684649
$91$	0	0
$92$	−6.19425	−0.645795
$93$	−1.65994	−0.172127
$94$	1.69517	0.174844
$95$	−6.54708	−0.671716
$96$	4.50245	0.459529
$97$	3.45779	0.351086	0.175543	−	0.984472i	$-0.443832\pi$
$97$	3.45779	0.351086	0.175543	+	0.984472i	$0.443832\pi$
$98$	−0.901356	−0.0910507
$99$	2.67340	0.268686
$100$	−6.62068	−0.662068
$101$	−17.7093	−1.76214	−0.881071	−	0.472984i	$-0.843177\pi$
$101$	−17.7093	−1.76214	−0.881071	+	0.472984i	$0.843177\pi$
$102$	−6.74343	−0.667699
$103$	15.6365	1.54071	0.770355	−	0.637616i	$-0.220079\pi$
$103$	15.6365	1.54071	0.770355	+	0.637616i	$0.220079\pi$
$104$	0	0
$105$	1.79870	0.175535
$106$	−27.1403	−2.63610
$107$	4.15886	0.402053	0.201026	−	0.979586i	$-0.435572\pi$
$107$	4.15886	0.402053	0.201026	+	0.979586i	$0.435572\pi$
$108$	6.15758	0.592514
$109$	−4.52071	−0.433006	−0.216503	−	0.976282i	$-0.569465\pi$
$109$	−4.52071	−0.433006	−0.216503	+	0.976282i	$0.569465\pi$
$110$	−2.42955	−0.231649
$111$	5.49971	0.522010
$112$	10.7221	1.01315
$113$	−6.36127	−0.598418	−0.299209	−	0.954188i	$-0.596723\pi$
$113$	−6.36127	−0.598418	−0.299209	+	0.954188i	$0.596723\pi$
$114$	6.00483	0.562404
$115$	−4.01304	−0.374218
$116$	−5.44043	−0.505132
$117$	0	0
$118$	17.2987	1.59247
$119$	−15.2859	−1.40126
$120$	0.140043	0.0127841
$121$	1.00000	0.0909091
$122$	5.45597	0.493960
$123$	1.98490	0.178973
$124$	5.51617	0.495367
$125$	−10.4412	−0.933893
$126$	13.5037	1.20301
$127$	21.7096	1.92642	0.963210	−	0.268750i	$-0.0866106\pi$
$127$	21.7096	1.92642	0.963210	+	0.268750i	$0.0866106\pi$
$128$	1.59128	0.140651
$129$	−2.59244	−0.228251
$130$	0	0
$131$	12.7296	1.11219	0.556097	−	0.831118i	$-0.312298\pi$
$131$	12.7296	1.11219	0.556097	+	0.831118i	$0.312298\pi$
$132$	1.08534	0.0944670
$133$	13.6117	1.18028
$134$	7.20707	0.622596
$135$	3.98929	0.343343
$136$	−1.19014	−0.102053
$137$	−9.57974	−0.818452	−0.409226	−	0.912433i	$-0.634201\pi$
$137$	−9.57974	−0.818452	−0.409226	+	0.912433i	$0.634201\pi$
$138$	3.68067	0.313319
$139$	8.55587	0.725700	0.362850	−	0.931848i	$-0.381804\pi$
$139$	8.55587	0.725700	0.362850	+	0.931848i	$0.381804\pi$
$140$	−5.97729	−0.505173
$141$	−0.490614	−0.0413171
$142$	−14.4348	−1.21135
$143$	0	0
$144$	11.2057	0.933806
$145$	−3.52467	−0.292708
$146$	−11.1241	−0.920635
$147$	0.260869	0.0215161
$148$	−18.2762	−1.50230
$149$	−6.92454	−0.567281	−0.283640	−	0.958931i	$-0.591542\pi$
$149$	−6.92454	−0.567281	−0.283640	+	0.958931i	$0.591542\pi$
$150$	3.93406	0.321214
$151$	−8.53083	−0.694229	−0.347115	−	0.937823i	$-0.612839\pi$
$151$	−8.53083	−0.694229	−0.347115	+	0.937823i	$0.612839\pi$
$152$	1.05978	0.0859596
$153$	−15.9753	−1.29153
$154$	5.05115	0.407033
$155$	3.57374	0.287049
$156$	0	0
$157$	−15.8805	−1.26740	−0.633701	−	0.773578i	$-0.718465\pi$
$157$	−15.8805	−1.26740	−0.633701	+	0.773578i	$0.718465\pi$
$158$	14.9523	1.18954
$159$	7.85491	0.622935
$160$	−9.69348	−0.766337
$161$	8.34330	0.657544
$162$	12.1780	0.956792
$163$	−23.4750	−1.83871	−0.919353	−	0.393435i	$-0.871287\pi$
$163$	−23.4750	−1.83871	−0.919353	+	0.393435i	$0.871287\pi$
$164$	−6.59607	−0.515066
$165$	0.703156	0.0547407
$166$	−1.39623	−0.108369
$167$	7.74766	0.599532	0.299766	−	0.954013i	$-0.403091\pi$
$167$	7.74766	0.599532	0.299766	+	0.954013i	$0.403091\pi$
$168$	−0.291157	−0.0224632
$169$	0	0
$170$	14.5182	1.11349
$171$	14.2256	1.08786
$172$	8.61498	0.656886
$173$	11.5028	0.874545	0.437273	−	0.899329i	$-0.355944\pi$
$173$	11.5028	0.874545	0.437273	+	0.899329i	$0.355944\pi$
$174$	3.23275	0.245074
$175$	8.91768	0.674113
$176$	4.19155	0.315950
$177$	−5.00655	−0.376315
$178$	23.9866	1.79787
$179$	15.7027	1.17367	0.586836	−	0.809706i	$-0.300373\pi$
$179$	15.7027	1.17367	0.586836	+	0.809706i	$0.300373\pi$
$180$	−6.24686	−0.465613
$181$	16.7002	1.24132	0.620659	−	0.784081i	$-0.286865\pi$
$181$	16.7002	1.24132	0.620659	+	0.784081i	$0.286865\pi$
$182$	0	0
$183$	−1.57906	−0.116727
$184$	0.649594	0.0478887
$185$	−11.8405	−0.870533
$186$	−3.27775	−0.240336
$187$	−5.97567	−0.436984
$188$	1.63037	0.118907
$189$	−8.29392	−0.603294
$190$	−12.9280	−0.937897
$191$	−6.83739	−0.494736	−0.247368	−	0.968922i	$-0.579566\pi$
$191$	−6.83739	−0.494736	−0.247368	+	0.968922i	$0.579566\pi$
$192$	4.09976	0.295875
$193$	11.0834	0.797804	0.398902	−	0.916994i	$-0.369391\pi$
$193$	11.0834	0.797804	0.398902	+	0.916994i	$0.369391\pi$
$194$	6.82784	0.490210
$195$	0	0
$196$	−0.866900	−0.0619214
$197$	−26.0214	−1.85395	−0.926975	−	0.375123i	$-0.877600\pi$
$197$	−26.0214	−1.85395	−0.926975	+	0.375123i	$0.877600\pi$
$198$	5.27895	0.375159
$199$	5.57241	0.395018	0.197509	−	0.980301i	$-0.436715\pi$
$199$	5.57241	0.395018	0.197509	+	0.980301i	$0.436715\pi$
$200$	0.694314	0.0490954
$201$	−2.08586	−0.147125
$202$	−34.9692	−2.46043
$203$	7.32796	0.514322
$204$	−6.48565	−0.454086
$205$	−4.27337	−0.298465
$206$	30.8762	2.15125
$207$	8.71957	0.606052
$208$	0	0
$209$	5.32116	0.368072
$210$	3.55175	0.245094
$211$	−6.08881	−0.419171	−0.209585	−	0.977790i	$-0.567211\pi$
$211$	−6.08881	−0.419171	−0.209585	+	0.977790i	$0.567211\pi$
$212$	−26.1028	−1.79275
$213$	4.17771	0.286252
$214$	8.21219	0.561374
$215$	5.58135	0.380645
$216$	−0.645749	−0.0439376
$217$	−7.42997	−0.504379
$218$	−8.92671	−0.604593
$219$	3.21951	0.217554
$220$	−2.33667	−0.157539
$221$	0	0
$222$	10.8599	0.728866
$223$	−9.78336	−0.655143	−0.327571	−	0.944826i	$-0.606230\pi$
$223$	−9.78336	−0.655143	−0.327571	+	0.944826i	$0.606230\pi$
$224$	20.1532	1.34654
$225$	9.31986	0.621324
$226$	−12.5611	−0.835553
$227$	12.5722	0.834446	0.417223	−	0.908804i	$-0.363003\pi$
$227$	12.5722	0.834446	0.417223	+	0.908804i	$0.363003\pi$
$228$	5.77528	0.382477
$229$	−13.6835	−0.904230	−0.452115	−	0.891960i	$-0.649330\pi$
$229$	−13.6835	−0.904230	−0.452115	+	0.891960i	$0.649330\pi$
$230$	−7.92424	−0.522509
$231$	−1.46190	−0.0961857
$232$	0.570541	0.0374579
$233$	−15.9817	−1.04700	−0.523499	−	0.852026i	$-0.675374\pi$
$233$	−15.9817	−1.04700	−0.523499	+	0.852026i	$0.675374\pi$
$234$	0	0
$235$	1.05626	0.0689028
$236$	16.6374	1.08300
$237$	−4.32746	−0.281099
$238$	−30.1840	−1.95654
$239$	−16.8419	−1.08941	−0.544707	−	0.838627i	$-0.683359\pi$
$239$	−16.8419	−1.08941	−0.544707	+	0.838627i	$0.683359\pi$
$240$	2.94732	0.190248
$241$	−9.06598	−0.583991	−0.291996	−	0.956420i	$-0.594319\pi$
$241$	−9.06598	−0.583991	−0.291996	+	0.956420i	$0.594319\pi$
$242$	1.97462	0.126934
$243$	−13.2514	−0.850080
$244$	5.24740	0.335930
$245$	−0.561634	−0.0358815
$246$	3.91943	0.249894
$247$	0	0
$248$	−0.578484	−0.0367338
$249$	0.404095	0.0256085
$250$	−20.6175	−1.30397
$251$	6.35232	0.400955	0.200477	−	0.979698i	$-0.435751\pi$
$251$	6.35232	0.400955	0.200477	+	0.979698i	$0.435751\pi$
$252$	12.9875	0.818136
$253$	3.26161	0.205056
$254$	42.8684	2.68980
$255$	−4.20183	−0.263129
$256$	17.4898	1.09311
$257$	24.2690	1.51386	0.756928	−	0.653498i	$-0.226699\pi$
$257$	24.2690	1.51386	0.756928	+	0.653498i	$0.226699\pi$
$258$	−5.11909	−0.318700
$259$	24.6170	1.52963
$260$	0	0
$261$	7.65844	0.474046
$262$	25.1362	1.55292
$263$	−7.83939	−0.483398	−0.241699	−	0.970351i	$-0.577705\pi$
$263$	−7.83939	−0.483398	−0.241699	+	0.970351i	$0.577705\pi$
$264$	−0.113821	−0.00700517
$265$	−16.9111	−1.03884
$266$	26.8780	1.64799
$267$	−6.94216	−0.424853
$268$	6.93156	0.423412
$269$	0.246971	0.0150581	0.00752905	−	0.999972i	$-0.497603\pi$
$269$	0.246971	0.0150581	0.00752905	+	0.999972i	$0.497603\pi$
$270$	7.87734	0.479399
$271$	−17.6629	−1.07295	−0.536473	−	0.843917i	$-0.680244\pi$
$271$	−17.6629	−1.07295	−0.536473	+	0.843917i	$0.680244\pi$
$272$	−25.0473	−1.51872
$273$	0	0
$274$	−18.9164	−1.14278
$275$	3.48615	0.210223
$276$	3.53997	0.213081
$277$	10.7868	0.648114	0.324057	−	0.946038i	$-0.394953\pi$
$277$	10.7868	0.648114	0.324057	+	0.946038i	$0.394953\pi$
$278$	16.8946	1.01327
$279$	−7.76505	−0.464882
$280$	0.626841	0.0374609
$281$	−25.4436	−1.51784	−0.758919	−	0.651185i	$-0.774272\pi$
$281$	−25.4436	−1.51784	−0.758919	+	0.651185i	$0.774272\pi$
$282$	−0.968777	−0.0576898
$283$	−31.0858	−1.84786	−0.923928	−	0.382566i	$-0.875040\pi$
$283$	−31.0858	−1.84786	−0.923928	+	0.382566i	$0.875040\pi$
$284$	−13.8830	−0.823806
$285$	3.74161	0.221634
$286$	0	0
$287$	8.88453	0.524437
$288$	21.0621	1.24110
$289$	18.7086	1.10051
$290$	−6.95990	−0.408699
$291$	−1.97610	−0.115841
$292$	−10.6988	−0.626102
$293$	−11.3869	−0.665232	−0.332616	−	0.943062i	$-0.607931\pi$
$293$	−11.3869	−0.665232	−0.332616	+	0.943062i	$0.607931\pi$
$294$	0.515118	0.0300423
$295$	10.7788	0.627565
$296$	1.91664	0.111402
$297$	−3.24230	−0.188137
$298$	−13.6734	−0.792077
$299$	0	0
$300$	3.78367	0.218450
$301$	−11.6039	−0.668837
$302$	−16.8452	−0.969331
$303$	10.1207	0.581421
$304$	22.3039	1.27922
$305$	3.39961	0.194661
$306$	−31.5453	−1.80332
$307$	−20.2057	−1.15320	−0.576600	−	0.817027i	$-0.695621\pi$
$307$	−20.2057	−1.15320	−0.576600	+	0.817027i	$0.695621\pi$
$308$	4.85806	0.276814
$309$	−8.93613	−0.508359
$310$	7.05679	0.400798
$311$	12.1332	0.688011	0.344005	−	0.938968i	$-0.388216\pi$
$311$	12.1332	0.688011	0.344005	+	0.938968i	$0.388216\pi$
$312$	0	0
$313$	19.4422	1.09894	0.549468	−	0.835514i	$-0.314830\pi$
$313$	19.4422	1.09894	0.549468	+	0.835514i	$0.314830\pi$
$314$	−31.3580	−1.76963
$315$	8.41416	0.474084
$316$	14.3807	0.808976
$317$	5.36260	0.301193	0.150597	−	0.988595i	$-0.451880\pi$
$317$	5.36260	0.301193	0.150597	+	0.988595i	$0.451880\pi$
$318$	15.5105	0.869785
$319$	2.86469	0.160392
$320$	−8.82653	−0.493418
$321$	−2.37676	−0.132658
$322$	16.4749	0.918109
$323$	−31.7974	−1.76926
$324$	11.7124	0.650691
$325$	0	0
$326$	−46.3543	−2.56733
$327$	2.58355	0.142871
$328$	0.691733	0.0381946
$329$	−2.19601	−0.121070
$330$	1.38847	0.0764327
$331$	15.9251	0.875322	0.437661	−	0.899140i	$-0.355807\pi$
$331$	15.9251	0.875322	0.437661	+	0.899140i	$0.355807\pi$
$332$	−1.34286	−0.0736988
$333$	25.7272	1.40984
$334$	15.2987	0.837108
$335$	4.49072	0.245354
$336$	−6.12761	−0.334289
$337$	7.71234	0.420118	0.210059	−	0.977689i	$-0.432634\pi$
$337$	7.71234	0.420118	0.210059	+	0.977689i	$0.432634\pi$
$338$	0	0
$339$	3.63542	0.197449
$340$	13.9632	0.757260
$341$	−2.90456	−0.157291
$342$	28.0901	1.51894
$343$	19.0739	1.02989
$344$	−0.903458	−0.0487112
$345$	2.29342	0.123474
$346$	22.7138	1.22110
$347$	−24.3767	−1.30861	−0.654305	−	0.756231i	$-0.727039\pi$
$347$	−24.3767	−1.30861	−0.654305	+	0.756231i	$0.727039\pi$
$348$	3.10917	0.166669
$349$	20.5401	1.09949	0.549743	−	0.835334i	$-0.314726\pi$
$349$	20.5401	1.09949	0.549743	+	0.835334i	$0.314726\pi$
$350$	17.6091	0.941244
$351$	0	0
$352$	7.87841	0.419920
$353$	11.4487	0.609355	0.304678	−	0.952456i	$-0.401451\pi$
$353$	11.4487	0.609355	0.304678	+	0.952456i	$0.401451\pi$
$354$	−9.88605	−0.525438
$355$	−8.99434	−0.477370
$356$	23.0696	1.22269
$357$	8.73580	0.462348
$358$	31.0068	1.63876
$359$	−12.2180	−0.644841	−0.322421	−	0.946596i	$-0.604497\pi$
$359$	−12.2180	−0.644841	−0.322421	+	0.946596i	$0.604497\pi$
$360$	0.655111	0.0345274
$361$	9.31470	0.490247
$362$	32.9766	1.73321
$363$	−0.571492	−0.0299956
$364$	0	0
$365$	−6.93140	−0.362806
$366$	−3.11804	−0.162983
$367$	−36.1839	−1.88878	−0.944391	−	0.328823i	$-0.893348\pi$
$367$	−36.1839	−1.88878	−0.944391	+	0.328823i	$0.893348\pi$
$368$	13.6712	0.712660
$369$	9.28521	0.483369
$370$	−23.3806	−1.21550
$371$	35.1590	1.82537
$372$	−3.15245	−0.163447
$373$	12.9241	0.669186	0.334593	−	0.942363i	$-0.391401\pi$
$373$	12.9241	0.669186	0.334593	+	0.942363i	$0.391401\pi$
$374$	−11.7997	−0.610148
$375$	5.96709	0.308139
$376$	−0.170978	−0.00881750
$377$	0	0
$378$	−16.3774	−0.842361
$379$	35.3528	1.81595	0.907975	−	0.419024i	$-0.137628\pi$
$379$	35.3528	1.81595	0.907975	+	0.419024i	$0.137628\pi$
$380$	−12.4338	−0.637841
$381$	−12.4069	−0.635625
$382$	−13.5013	−0.690786
$383$	1.52246	0.0777941	0.0388970	−	0.999243i	$-0.487616\pi$
$383$	1.52246	0.0777941	0.0388970	+	0.999243i	$0.487616\pi$
$384$	−0.909406	−0.0464079
$385$	3.14737	0.160405
$386$	21.8856	1.11395
$387$	−12.1272	−0.616461
$388$	6.56683	0.333380
$389$	33.3803	1.69245	0.846225	−	0.532826i	$-0.178870\pi$
$389$	33.3803	1.69245	0.846225	+	0.532826i	$0.178870\pi$
$390$	0	0
$391$	−19.4903	−0.985666
$392$	0.0909122	0.00459176
$393$	−7.27489	−0.366970
$394$	−51.3825	−2.58861
$395$	9.31674	0.468776
$396$	5.07715	0.255136
$397$	26.4193	1.32595	0.662974	−	0.748642i	$-0.269294\pi$
$397$	26.4193	1.32595	0.662974	+	0.748642i	$0.269294\pi$
$398$	11.0034	0.551551
$399$	−7.77898	−0.389436
$400$	14.6124	0.730618
$401$	15.8033	0.789179	0.394589	−	0.918858i	$-0.370887\pi$
$401$	15.8033	0.789179	0.394589	+	0.918858i	$0.370887\pi$
$402$	−4.11878	−0.205426
$403$	0	0
$404$	−33.6324	−1.67328
$405$	7.58809	0.377055
$406$	14.4700	0.718132
$407$	9.62343	0.477015
$408$	0.680153	0.0336726
$409$	−32.1554	−1.58998	−0.794992	−	0.606620i	$-0.792525\pi$
$409$	−32.1554	−1.58998	−0.794992	+	0.606620i	$0.792525\pi$
$410$	−8.43829	−0.416737
$411$	5.47475	0.270049
$412$	29.6959	1.46301
$413$	−22.4096	−1.10270
$414$	17.2179	0.846213
$415$	−0.869991	−0.0427062
$416$	0	0
$417$	−4.88962	−0.239445
$418$	10.5073	0.513928
$419$	6.35735	0.310577	0.155288	−	0.987869i	$-0.450369\pi$
$419$	6.35735	0.310577	0.155288	+	0.987869i	$0.450369\pi$
$420$	3.41597	0.166682
$421$	−4.90563	−0.239086	−0.119543	−	0.992829i	$-0.538143\pi$
$421$	−4.90563	−0.239086	−0.119543	+	0.992829i	$0.538143\pi$
$422$	−12.0231	−0.585275
$423$	−2.29505	−0.111589
$424$	2.73742	0.132941
$425$	−20.8321	−1.01050
$426$	8.24940	0.399685
$427$	−7.06795	−0.342042
$428$	7.89826	0.381777
$429$	0	0
$430$	11.0211	0.531483
$431$	15.9218	0.766928	0.383464	−	0.923556i	$-0.374731\pi$
$431$	15.9218	0.766928	0.383464	+	0.923556i	$0.374731\pi$
$432$	−13.5903	−0.653862
$433$	−25.1376	−1.20804	−0.604019	−	0.796970i	$-0.706435\pi$
$433$	−25.1376	−1.20804	−0.604019	+	0.796970i	$0.706435\pi$
$434$	−14.6714	−0.704249
$435$	2.01432	0.0965794
$436$	−8.58546	−0.411169
$437$	17.3555	0.830228
$438$	6.35733	0.303765
$439$	11.5138	0.549523	0.274761	−	0.961512i	$-0.411401\pi$
$439$	11.5138	0.549523	0.274761	+	0.961512i	$0.411401\pi$
$440$	0.245048	0.0116822
$441$	1.22033	0.0581107
$442$	0	0
$443$	−32.8533	−1.56091	−0.780453	−	0.625214i	$-0.785012\pi$
$443$	−32.8533	−1.56091	−0.780453	+	0.625214i	$0.785012\pi$
$444$	10.4447	0.495684
$445$	14.9460	0.708510
$446$	−19.3185	−0.914756
$447$	3.95732	0.187175
$448$	18.3508	0.866993
$449$	−9.56841	−0.451561	−0.225781	−	0.974178i	$-0.572493\pi$
$449$	−9.56841	−0.451561	−0.225781	+	0.974178i	$0.572493\pi$
$450$	18.4032	0.867536
$451$	3.47319	0.163546
$452$	−12.0809	−0.568239
$453$	4.87531	0.229062
$454$	24.8253	1.16511
$455$	0	0
$456$	−0.605657	−0.0283625
$457$	20.9620	0.980561	0.490281	−	0.871565i	$-0.336894\pi$
$457$	20.9620	0.980561	0.490281	+	0.871565i	$0.336894\pi$
$458$	−27.0197	−1.26255
$459$	19.3749	0.904344
$460$	−7.62132	−0.355346
$461$	−6.45806	−0.300782	−0.150391	−	0.988627i	$-0.548053\pi$
$461$	−6.45806	−0.300782	−0.150391	+	0.988627i	$0.548053\pi$
$462$	−2.88669	−0.134301
$463$	4.97086	0.231015	0.115508	−	0.993307i	$-0.463151\pi$
$463$	4.97086	0.231015	0.115508	+	0.993307i	$0.463151\pi$
$464$	12.0075	0.557433
$465$	−2.04236	−0.0947123
$466$	−31.5579	−1.46189
$467$	−9.95319	−0.460579	−0.230289	−	0.973122i	$-0.573967\pi$
$467$	−9.95319	−0.460579	−0.230289	+	0.973122i	$0.573967\pi$
$468$	0	0
$469$	−9.33642	−0.431116
$470$	2.08572	0.0962069
$471$	9.07558	0.418181
$472$	−1.74477	−0.0803095
$473$	−4.53626	−0.208577
$474$	−8.54510	−0.392489
$475$	18.5503	0.851148
$476$	−29.0301	−1.33059
$477$	36.7446	1.68242
$478$	−33.2565	−1.52111
$479$	−15.8258	−0.723097	−0.361549	−	0.932353i	$-0.617752\pi$
$479$	−15.8258	−0.723097	−0.361549	+	0.932353i	$0.617752\pi$
$480$	5.53975	0.252854
$481$	0	0
$482$	−17.9019	−0.815409
$483$	−4.76813	−0.216958
$484$	1.89914	0.0863245
$485$	4.25442	0.193183
$486$	−26.1666	−1.18694
$487$	20.8272	0.943771	0.471885	−	0.881660i	$-0.343574\pi$
$487$	20.8272	0.943771	0.471885	+	0.881660i	$0.343574\pi$
$488$	−0.550298	−0.0249108
$489$	13.4158	0.606683
$490$	−1.10902	−0.0501003
$491$	26.3130	1.18749	0.593744	−	0.804654i	$-0.297649\pi$
$491$	26.3130	1.18749	0.593744	+	0.804654i	$0.297649\pi$
$492$	3.76960	0.169947
$493$	−17.1184	−0.770974
$494$	0	0
$495$	3.28931	0.147844
$496$	−12.1746	−0.546657
$497$	18.6997	0.838795
$498$	0.797936	0.0357563
$499$	−30.9638	−1.38613	−0.693064	−	0.720876i	$-0.743740\pi$
$499$	−30.9638	−1.38613	−0.693064	+	0.720876i	$0.743740\pi$
$500$	−19.8294	−0.886796
$501$	−4.42773	−0.197816
$502$	12.5434	0.559841
$503$	−32.4429	−1.44656	−0.723279	−	0.690556i	$-0.757366\pi$
$503$	−32.4429	−1.44656	−0.723279	+	0.690556i	$0.757366\pi$
$504$	−1.36201	−0.0606686
$505$	−21.7893	−0.969611
$506$	6.44045	0.286313
$507$	0	0
$508$	41.2296	1.82927
$509$	−17.9485	−0.795551	−0.397776	−	0.917483i	$-0.630218\pi$
$509$	−17.9485	−0.795551	−0.397776	+	0.917483i	$0.630218\pi$
$510$	−8.29703	−0.367399
$511$	14.4107	0.637493
$512$	31.3531	1.38563
$513$	−17.2528	−0.761730
$514$	47.9221	2.11375
$515$	19.2389	0.847768
$516$	−4.92340	−0.216740
$517$	−0.858478	−0.0377558
$518$	48.6094	2.13577
$519$	−6.57379	−0.288557
$520$	0	0
$521$	−24.0093	−1.05187	−0.525934	−	0.850525i	$-0.676284\pi$
$521$	−24.0093	−1.05187	−0.525934	+	0.850525i	$0.676284\pi$
$522$	15.1225	0.661895
$523$	−26.5869	−1.16256	−0.581281	−	0.813703i	$-0.697448\pi$
$523$	−26.5869	−1.16256	−0.581281	+	0.813703i	$0.697448\pi$
$524$	24.1753	1.05610
$525$	−5.09639	−0.222425
$526$	−15.4798	−0.674953
$527$	17.3567	0.756070
$528$	−2.39544	−0.104248
$529$	−12.3619	−0.537474
$530$	−33.3931	−1.45050
$531$	−23.4202	−1.01635
$532$	25.8505	1.12076
$533$	0	0
$534$	−13.7082	−0.593210
$535$	5.11701	0.221228
$536$	−0.726916	−0.0313980
$537$	−8.97395	−0.387254
$538$	0.487675	0.0210252
$539$	0.456470	0.0196616
$540$	7.57621	0.326028
$541$	−7.65866	−0.329271	−0.164636	−	0.986354i	$-0.552645\pi$
$541$	−7.65866	−0.329271	−0.164636	+	0.986354i	$0.552645\pi$
$542$	−34.8776	−1.49812
$543$	−9.54405	−0.409574
$544$	−47.0787	−2.01848
$545$	−5.56222	−0.238260
$546$	0	0
$547$	32.5681	1.39251	0.696255	−	0.717794i	$-0.254848\pi$
$547$	32.5681	1.39251	0.696255	+	0.717794i	$0.254848\pi$
$548$	−18.1933	−0.777177
$549$	−7.38671	−0.315257
$550$	6.88383	0.293528
$551$	15.2434	0.649392
$552$	−0.371238	−0.0158009
$553$	−19.3699	−0.823694
$554$	21.2998	0.904941
$555$	6.76677	0.287234
$556$	16.2488	0.689102
$557$	−42.0379	−1.78120	−0.890601	−	0.454786i	$-0.849716\pi$
$557$	−42.0379	−1.78120	−0.890601	+	0.454786i	$0.849716\pi$
$558$	−15.3331	−0.649100
$559$	0	0
$560$	13.1924	0.557479
$561$	3.41505	0.144183
$562$	−50.2415	−2.11931
$563$	−6.16552	−0.259846	−0.129923	−	0.991524i	$-0.541473\pi$
$563$	−6.16552	−0.259846	−0.129923	+	0.991524i	$0.541473\pi$
$564$	−0.931743	−0.0392335
$565$	−7.82682	−0.329277
$566$	−61.3827	−2.58011
$567$	−15.7760	−0.662530
$568$	1.45592	0.0610891
$569$	2.68172	0.112424	0.0562119	−	0.998419i	$-0.482098\pi$
$569$	2.68172	0.112424	0.0562119	+	0.998419i	$0.482098\pi$
$570$	7.38826	0.309460
$571$	−21.1358	−0.884505	−0.442253	−	0.896891i	$-0.645821\pi$
$571$	−21.1358	−0.884505	−0.442253	+	0.896891i	$0.645821\pi$
$572$	0	0
$573$	3.90752	0.163239
$574$	17.5436	0.732256
$575$	11.3705	0.474181
$576$	19.1784	0.799099
$577$	8.09962	0.337192	0.168596	−	0.985685i	$-0.446077\pi$
$577$	8.09962	0.337192	0.168596	+	0.985685i	$0.446077\pi$
$578$	36.9424	1.53660
$579$	−6.33411	−0.263236
$580$	−6.69384	−0.277946
$581$	1.80875	0.0750397
$582$	−3.90206	−0.161746
$583$	13.7446	0.569241
$584$	1.12199	0.0464284
$585$	0	0
$586$	−22.4849	−0.928843
$587$	13.0544	0.538813	0.269406	−	0.963027i	$-0.413173\pi$
$587$	13.0544	0.538813	0.269406	+	0.963027i	$0.413173\pi$
$588$	0.495427	0.0204310
$589$	−15.4556	−0.636839
$590$	21.2840	0.876250
$591$	14.8710	0.611713
$592$	40.3371	1.65784
$593$	−0.674849	−0.0277127	−0.0138564	−	0.999904i	$-0.504411\pi$
$593$	−0.674849	−0.0277127	−0.0138564	+	0.999904i	$0.504411\pi$
$594$	−6.40233	−0.262691
$595$	−18.8076	−0.771037
$596$	−13.1507	−0.538672
$597$	−3.18459	−0.130337
$598$	0	0
$599$	−36.2030	−1.47922	−0.739608	−	0.673038i	$-0.764989\pi$
$599$	−36.2030	−1.47922	−0.739608	+	0.673038i	$0.764989\pi$
$600$	−0.396795	−0.0161991
$601$	−33.0688	−1.34890	−0.674451	−	0.738319i	$-0.735620\pi$
$601$	−33.0688	−1.34890	−0.674451	+	0.738319i	$0.735620\pi$
$602$	−22.9133	−0.933877
$603$	−9.75748	−0.397355
$604$	−16.2012	−0.659219
$605$	1.23039	0.0500223
$606$	19.9846	0.811821
$607$	18.8366	0.764554	0.382277	−	0.924048i	$-0.375140\pi$
$607$	18.8366	0.764554	0.382277	+	0.924048i	$0.375140\pi$
$608$	41.9222	1.70017
$609$	−4.18787	−0.169701
$610$	6.71295	0.271799
$611$	0	0
$612$	−30.3394	−1.22640
$613$	−36.5545	−1.47642	−0.738211	−	0.674570i	$-0.764329\pi$
$613$	−36.5545	−1.47642	−0.738211	+	0.674570i	$0.764329\pi$
$614$	−39.8986	−1.61018
$615$	2.44220	0.0984789
$616$	−0.509467	−0.0205270
$617$	2.77177	0.111587	0.0557936	−	0.998442i	$-0.482231\pi$
$617$	2.77177	0.111587	0.0557936	+	0.998442i	$0.482231\pi$
$618$	−17.6455	−0.709806
$619$	−38.3647	−1.54201	−0.771004	−	0.636830i	$-0.780245\pi$
$619$	−38.3647	−1.54201	−0.771004	+	0.636830i	$0.780245\pi$
$620$	6.78702	0.272573
$621$	−10.5751	−0.424365
$622$	23.9585	0.960649
$623$	−31.0735	−1.24493
$624$	0	0
$625$	4.58398	0.183359
$626$	38.3910	1.53441
$627$	−3.04100	−0.121446
$628$	−30.1593	−1.20349
$629$	−57.5064	−2.29293
$630$	16.6148	0.661950
$631$	−14.0166	−0.557994	−0.278997	−	0.960292i	$-0.590002\pi$
$631$	−14.0166	−0.557994	−0.278997	+	0.960292i	$0.590002\pi$
$632$	−1.50811	−0.0599893
$633$	3.47971	0.138306
$634$	10.5891	0.420547
$635$	26.7113	1.06000
$636$	14.9176	0.591520
$637$	0	0
$638$	5.65668	0.223950
$639$	19.5430	0.773109
$640$	1.95789	0.0773925
$641$	7.86006	0.310454	0.155227	−	0.987879i	$-0.450389\pi$
$641$	7.86006	0.310454	0.155227	+	0.987879i	$0.450389\pi$
$642$	−4.69321	−0.185226
$643$	24.1774	0.953463	0.476731	−	0.879049i	$-0.341821\pi$
$643$	24.1774	0.953463	0.476731	+	0.879049i	$0.341821\pi$
$644$	15.8451	0.624384
$645$	−3.18970	−0.125594
$646$	−62.7880	−2.47036
$647$	17.1838	0.675565	0.337782	−	0.941224i	$-0.390323\pi$
$647$	17.1838	0.675565	0.337782	+	0.941224i	$0.390323\pi$
$648$	−1.22829	−0.0482518
$649$	−8.76048	−0.343879
$650$	0	0
$651$	4.24617	0.166421
$652$	−44.5823	−1.74598
$653$	25.7432	1.00741	0.503705	−	0.863876i	$-0.331970\pi$
$653$	25.7432	1.00741	0.503705	+	0.863876i	$0.331970\pi$
$654$	5.10155	0.199486
$655$	15.6624	0.611979
$656$	14.5581	0.568396
$657$	15.0606	0.587571
$658$	−4.33630	−0.169047
$659$	13.2942	0.517869	0.258934	−	0.965895i	$-0.416629\pi$
$659$	13.2942	0.517869	0.258934	+	0.965895i	$0.416629\pi$
$660$	1.33539	0.0519800
$661$	8.72799	0.339480	0.169740	−	0.985489i	$-0.445707\pi$
$661$	8.72799	0.339480	0.169740	+	0.985489i	$0.445707\pi$
$662$	31.4461	1.22219
$663$	0	0
$664$	0.140826	0.00546511
$665$	16.7476	0.649446
$666$	50.8016	1.96852
$667$	9.34349	0.361781
$668$	14.7139	0.569297
$669$	5.59112	0.216165
$670$	8.86748	0.342581
$671$	−2.76304	−0.106666
$672$	−11.5174	−0.444294
$673$	−10.7132	−0.412965	−0.206483	−	0.978450i	$-0.566202\pi$
$673$	−10.7132	−0.412965	−0.206483	+	0.978450i	$0.566202\pi$
$674$	15.2290	0.586598
$675$	−11.3032	−0.435059
$676$	0	0
$677$	−4.57693	−0.175906	−0.0879528	−	0.996125i	$-0.528032\pi$
$677$	−4.57693	−0.175906	−0.0879528	+	0.996125i	$0.528032\pi$
$678$	7.17858	0.275692
$679$	−8.84515	−0.339446
$680$	−1.46433	−0.0561544
$681$	−7.18491	−0.275326
$682$	−5.73542	−0.219621
$683$	−38.0713	−1.45676	−0.728379	−	0.685174i	$-0.759726\pi$
$683$	−38.0713	−1.45676	−0.728379	+	0.685174i	$0.759726\pi$
$684$	27.0163	1.03299
$685$	−11.7868	−0.450350
$686$	37.6638	1.43801
$687$	7.82001	0.298352
$688$	−19.0140	−0.724900
$689$	0	0
$690$	4.52864	0.172403
$691$	−33.4726	−1.27336	−0.636679	−	0.771129i	$-0.719692\pi$
$691$	−33.4726	−1.27336	−0.636679	+	0.771129i	$0.719692\pi$
$692$	21.8455	0.830441
$693$	−6.83863	−0.259778
$694$	−48.1348	−1.82717
$695$	10.5270	0.399313
$696$	−0.326060	−0.0123593
$697$	−20.7546	−0.786137
$698$	40.5590	1.53518
$699$	9.13344	0.345459
$700$	16.9359	0.640117
$701$	9.43568	0.356381	0.178190	−	0.983996i	$-0.442976\pi$
$701$	9.43568	0.356381	0.178190	+	0.983996i	$0.442976\pi$
$702$	0	0
$703$	51.2077	1.93134
$704$	7.17379	0.270372
$705$	−0.603644	−0.0227346
$706$	22.6070	0.850825
$707$	45.3010	1.70372
$708$	−9.50813	−0.357337
$709$	−15.7263	−0.590613	−0.295307	−	0.955403i	$-0.595422\pi$
$709$	−15.7263	−0.590613	−0.295307	+	0.955403i	$0.595422\pi$
$710$	−17.7604	−0.666537
$711$	−20.2435	−0.759191
$712$	−2.41933	−0.0906681
$713$	−9.47355	−0.354787
$714$	17.2499	0.645562
$715$	0	0
$716$	29.8215	1.11448
$717$	9.62503	0.359453
$718$	−24.1260	−0.900373
$719$	−50.6347	−1.88836	−0.944178	−	0.329436i	$-0.893141\pi$
$719$	−50.6347	−1.88836	−0.944178	+	0.329436i	$0.893141\pi$
$720$	13.7873	0.513823
$721$	−39.9986	−1.48963
$722$	18.3930	0.684517
$723$	5.18114	0.192689
$724$	31.7160	1.17872
$725$	9.98672	0.370898
$726$	−1.12848	−0.0418819
$727$	−38.4164	−1.42478	−0.712392	−	0.701782i	$-0.752388\pi$
$727$	−38.4164	−1.42478	−0.712392	+	0.701782i	$0.752388\pi$
$728$	0	0
$729$	−10.9286	−0.404764
$730$	−13.6869	−0.506575
$731$	27.1072	1.00259
$732$	−2.99885	−0.110841
$733$	−10.8611	−0.401165	−0.200582	−	0.979677i	$-0.564283\pi$
$733$	−10.8611	−0.401165	−0.200582	+	0.979677i	$0.564283\pi$
$734$	−71.4495	−2.63725
$735$	0.320970	0.0118391
$736$	25.6963	0.947178
$737$	−3.64984	−0.134444
$738$	18.3348	0.674913
$739$	−42.5093	−1.56373	−0.781866	−	0.623447i	$-0.785732\pi$
$739$	−42.5093	−1.56373	−0.781866	+	0.623447i	$0.785732\pi$
$740$	−22.4868	−0.826632
$741$	0	0
$742$	69.4258	2.54870
$743$	−25.6654	−0.941574	−0.470787	−	0.882247i	$-0.656030\pi$
$743$	−25.6654	−0.941574	−0.470787	+	0.882247i	$0.656030\pi$
$744$	0.330599	0.0121203
$745$	−8.51986	−0.312144
$746$	25.5203	0.934364
$747$	1.89032	0.0691634
$748$	−11.3486	−0.414947
$749$	−10.6385	−0.388723
$750$	11.7828	0.430246
$751$	−37.6242	−1.37293	−0.686464	−	0.727164i	$-0.740838\pi$
$751$	−37.6242	−1.37293	−0.686464	+	0.727164i	$0.740838\pi$
$752$	−3.59835	−0.131218
$753$	−3.63030	−0.132296
$754$	0	0
$755$	−10.4962	−0.381997
$756$	−15.7513	−0.572869
$757$	17.2379	0.626521	0.313260	−	0.949667i	$-0.398579\pi$
$757$	17.2379	0.626521	0.313260	+	0.949667i	$0.398579\pi$
$758$	69.8084	2.53556
$759$	−1.86398	−0.0676584
$760$	1.30394	0.0472989
$761$	−8.83215	−0.320165	−0.160083	−	0.987104i	$-0.551176\pi$
$761$	−8.83215	−0.320165	−0.160083	+	0.987104i	$0.551176\pi$
$762$	−24.4990	−0.887504
$763$	11.5641	0.418650
$764$	−12.9852	−0.469787
$765$	−19.6558	−0.710658
$766$	3.00629	0.108622
$767$	0	0
$768$	−9.99526	−0.360673
$769$	13.5004	0.486837	0.243419	−	0.969921i	$-0.421731\pi$
$769$	13.5004	0.486837	0.243419	+	0.969921i	$0.421731\pi$
$770$	6.21487	0.223968
$771$	−13.8695	−0.499499
$772$	21.0490	0.757570
$773$	−10.4625	−0.376309	−0.188155	−	0.982139i	$-0.560251\pi$
$773$	−10.4625	−0.376309	−0.188155	+	0.982139i	$0.560251\pi$
$774$	−23.9467	−0.860746
$775$	−10.1257	−0.363728
$776$	−0.688667	−0.0247217
$777$	−14.0684	−0.504703
$778$	65.9136	2.36312
$779$	18.4814	0.662164
$780$	0	0
$781$	7.31017	0.261579
$782$	−38.4860	−1.37626
$783$	−9.28818	−0.331932
$784$	1.91332	0.0683327
$785$	−19.5391	−0.697382
$786$	−14.3652	−0.512388
$787$	−43.1408	−1.53781	−0.768903	−	0.639366i	$-0.779197\pi$
$787$	−43.1408	−1.53781	−0.768903	+	0.639366i	$0.779197\pi$
$788$	−49.4183	−1.76045
$789$	4.48015	0.159498
$790$	18.3971	0.654538
$791$	16.2723	0.578578
$792$	−0.532443	−0.0189196
$793$	0	0
$794$	52.1682	1.85138
$795$	9.66457	0.342767
$796$	10.5828	0.375097
$797$	25.8798	0.916710	0.458355	−	0.888769i	$-0.348439\pi$
$797$	25.8798	0.916710	0.458355	+	0.888769i	$0.348439\pi$
$798$	−15.3606	−0.543758
$799$	5.12998	0.181486
$800$	27.4653	0.971045
$801$	−32.4749	−1.14744
$802$	31.2055	1.10191
$803$	5.63352	0.198803
$804$	−3.96133	−0.139705
$805$	10.2655	0.361811
$806$	0	0
$807$	−0.141142	−0.00496844
$808$	3.52705	0.124081
$809$	18.8775	0.663696	0.331848	−	0.943333i	$-0.392328\pi$
$809$	18.8775	0.663696	0.331848	+	0.943333i	$0.392328\pi$
$810$	14.9836	0.526471
$811$	24.3009	0.853320	0.426660	−	0.904412i	$-0.359690\pi$
$811$	24.3009	0.853320	0.426660	+	0.904412i	$0.359690\pi$
$812$	13.9168	0.488384
$813$	10.0942	0.354020
$814$	19.0026	0.666042
$815$	−28.8833	−1.01174
$816$	14.3143	0.501102
$817$	−24.1381	−0.844486
$818$	−63.4949	−2.22005
$819$	0	0
$820$	−8.11571	−0.283413
$821$	−38.7547	−1.35255	−0.676274	−	0.736650i	$-0.736406\pi$
$821$	−38.7547	−1.35255	−0.676274	+	0.736650i	$0.736406\pi$
$822$	10.8106	0.377062
$823$	20.1615	0.702784	0.351392	−	0.936228i	$-0.385708\pi$
$823$	20.1615	0.702784	0.351392	+	0.936228i	$0.385708\pi$
$824$	−3.11422	−0.108489
$825$	−1.99231	−0.0693633
$826$	−44.2505	−1.53967
$827$	46.3998	1.61348	0.806740	−	0.590906i	$-0.201230\pi$
$827$	46.3998	1.61348	0.806740	+	0.590906i	$0.201230\pi$
$828$	16.5597	0.575489
$829$	−6.74133	−0.234136	−0.117068	−	0.993124i	$-0.537350\pi$
$829$	−6.74133	−0.234136	−0.117068	+	0.993124i	$0.537350\pi$
$830$	−1.71790	−0.0596293
$831$	−6.16455	−0.213846
$832$	0	0
$833$	−2.72771	−0.0945096
$834$	−9.65515	−0.334331
$835$	9.53262	0.329890
$836$	10.1056	0.349510
$837$	9.41748	0.325516
$838$	12.5534	0.433649
$839$	10.1387	0.350028	0.175014	−	0.984566i	$-0.444003\pi$
$839$	10.1387	0.350028	0.175014	+	0.984566i	$0.444003\pi$
$840$	−0.358235	−0.0123603
$841$	−20.7936	−0.717020
$842$	−9.68677	−0.333828
$843$	14.5408	0.500812
$844$	−11.5635	−0.398032
$845$	0	0
$846$	−4.53186	−0.155809
$847$	−2.55803	−0.0878950
$848$	57.6110	1.97837
$849$	17.7653	0.609703
$850$	−41.1355	−1.41094
$851$	31.3879	1.07596
$852$	7.93405	0.271816
$853$	13.8261	0.473395	0.236698	−	0.971583i	$-0.423935\pi$
$853$	13.8261	0.473395	0.236698	+	0.971583i	$0.423935\pi$
$854$	−13.9565	−0.477583
$855$	17.5029	0.598588
$856$	−0.828295	−0.0283105
$857$	21.5044	0.734576	0.367288	−	0.930107i	$-0.380286\pi$
$857$	21.5044	0.734576	0.367288	+	0.930107i	$0.380286\pi$
$858$	0	0
$859$	28.6851	0.978724	0.489362	−	0.872081i	$-0.337230\pi$
$859$	28.6851	0.978724	0.489362	+	0.872081i	$0.337230\pi$
$860$	10.5998	0.361449
$861$	−5.07744	−0.173039
$862$	31.4396	1.07084
$863$	22.3203	0.759791	0.379895	−	0.925029i	$-0.375960\pi$
$863$	22.3203	0.759791	0.379895	+	0.925029i	$0.375960\pi$
$864$	−25.5442	−0.869031
$865$	14.1529	0.481215
$866$	−49.6373	−1.68675
$867$	−10.6918	−0.363113
$868$	−14.1105	−0.478943
$869$	−7.57221	−0.256869
$870$	3.97753	0.134851
$871$	0	0
$872$	0.900362	0.0304901
$873$	−9.24405	−0.312864
$874$	34.2706	1.15922
$875$	26.7090	0.902930
$876$	6.11430	0.206583
$877$	0.127784	0.00431496	0.00215748	−	0.999998i	$-0.499313\pi$
$877$	0.127784	0.00431496	0.00215748	+	0.999998i	$0.499313\pi$
$878$	22.7354	0.767282
$879$	6.50755	0.219494
$880$	5.15723	0.173850
$881$	−34.7183	−1.16969	−0.584844	−	0.811146i	$-0.698844\pi$
$881$	−34.7183	−1.16969	−0.584844	+	0.811146i	$0.698844\pi$
$882$	2.40968	0.0811382
$883$	12.4010	0.417328	0.208664	−	0.977987i	$-0.433089\pi$
$883$	12.4010	0.417328	0.208664	+	0.977987i	$0.433089\pi$
$884$	0	0
$885$	−6.15999	−0.207066
$886$	−64.8729	−2.17945
$887$	24.5776	0.825234	0.412617	−	0.910905i	$-0.364615\pi$
$887$	24.5776	0.825234	0.412617	+	0.910905i	$0.364615\pi$
$888$	−1.09534	−0.0367573
$889$	−55.5340	−1.86255
$890$	29.5128	0.989271
$891$	−6.16724	−0.206610
$892$	−18.5800	−0.622103
$893$	−4.56809	−0.152865
$894$	7.81422	0.261347
$895$	19.3203	0.645807
$896$	−4.07055	−0.135988
$897$	0	0
$898$	−18.8940	−0.630501
$899$	−8.32066	−0.277510
$900$	17.6997	0.589990
$901$	−82.1329	−2.73624
$902$	6.85824	0.228355
$903$	6.63154	0.220684
$904$	1.26693	0.0421376
$905$	20.5477	0.683029
$906$	9.62689	0.319832
$907$	17.2563	0.572987	0.286494	−	0.958082i	$-0.407510\pi$
$907$	17.2563	0.572987	0.286494	+	0.958082i	$0.407510\pi$
$908$	23.8763	0.792364
$909$	47.3440	1.57030
$910$	0	0
$911$	6.76841	0.224247	0.112124	−	0.993694i	$-0.464235\pi$
$911$	6.76841	0.224247	0.112124	+	0.993694i	$0.464235\pi$
$912$	−12.7465	−0.422079
$913$	0.707087	0.0234012
$914$	41.3921	1.36913
$915$	−1.94285	−0.0642287
$916$	−25.9868	−0.858629
$917$	−32.5628	−1.07532
$918$	38.2582	1.26271
$919$	−4.80101	−0.158371	−0.0791853	−	0.996860i	$-0.525232\pi$
$919$	−4.80101	−0.158371	−0.0791853	+	0.996860i	$0.525232\pi$
$920$	0.799252	0.0263505
$921$	11.5474	0.380500
$922$	−12.7522	−0.419973
$923$	0	0
$924$	−2.77634	−0.0913350
$925$	33.5487	1.10307
$926$	9.81557	0.322560
$927$	−41.8025	−1.37298
$928$	22.5692	0.740869
$929$	46.0294	1.51018	0.755088	−	0.655624i	$-0.227594\pi$
$929$	46.0294	1.51018	0.755088	+	0.655624i	$0.227594\pi$
$930$	−4.03290	−0.132244
$931$	2.42895	0.0796055
$932$	−30.3515	−0.994198
$933$	−6.93403	−0.227010
$934$	−19.6538	−0.643092
$935$	−7.35238	−0.240448
$936$	0	0
$937$	47.2841	1.54470	0.772352	−	0.635195i	$-0.219080\pi$
$937$	47.2841	1.54470	0.772352	+	0.635195i	$0.219080\pi$
$938$	−18.4359	−0.601954
$939$	−11.1111	−0.362596
$940$	2.00598	0.0654280
$941$	23.6968	0.772494	0.386247	−	0.922395i	$-0.373771\pi$
$941$	23.6968	0.772494	0.386247	+	0.922395i	$0.373771\pi$
$942$	17.9209	0.583893
$943$	11.3282	0.368897
$944$	−36.7200	−1.19513
$945$	−10.2047	−0.331960
$946$	−8.95740	−0.291230
$947$	−25.5082	−0.828904	−0.414452	−	0.910071i	$-0.636027\pi$
$947$	−25.5082	−0.828904	−0.414452	+	0.910071i	$0.636027\pi$
$948$	−8.21844	−0.266923
$949$	0	0
$950$	36.6299	1.18843
$951$	−3.06468	−0.0993792
$952$	3.04441	0.0986697
$953$	−10.7323	−0.347655	−0.173827	−	0.984776i	$-0.555613\pi$
$953$	−10.7323	−0.347655	−0.173827	+	0.984776i	$0.555613\pi$
$954$	72.5568	2.34911
$955$	−8.41264	−0.272227
$956$	−31.9851	−1.03447
$957$	−1.63715	−0.0529214
$958$	−31.2499	−1.00964
$959$	24.5053	0.791317
$960$	5.04429	0.162804
$961$	−22.5635	−0.727855
$962$	0	0
$963$	−11.1183	−0.358282
$964$	−17.2176	−0.554540
$965$	13.6369	0.438988
$966$	−9.41527	−0.302931
$967$	−18.6494	−0.599724	−0.299862	−	0.953983i	$-0.596941\pi$
$967$	−18.6494	−0.599724	−0.299862	+	0.953983i	$0.596941\pi$
$968$	−0.199164	−0.00640136
$969$	18.1720	0.583769
$970$	8.40088	0.269736
$971$	29.4517	0.945151	0.472575	−	0.881290i	$-0.343324\pi$
$971$	29.4517	0.945151	0.472575	+	0.881290i	$0.343324\pi$
$972$	−25.1663	−0.807210
$973$	−21.8862	−0.701639
$974$	41.1259	1.31776
$975$	0	0
$976$	−11.5814	−0.370713
$977$	1.04992	0.0335898	0.0167949	−	0.999859i	$-0.494654\pi$
$977$	1.04992	0.0335898	0.0167949	+	0.999859i	$0.494654\pi$
$978$	26.4911	0.847093
$979$	−12.1474	−0.388233
$980$	−1.06662	−0.0340720
$981$	12.0857	0.385865
$982$	51.9582	1.65805
$983$	4.58788	0.146330	0.0731652	−	0.997320i	$-0.476690\pi$
$983$	4.58788	0.146330	0.0731652	+	0.997320i	$0.476690\pi$
$984$	−0.395320	−0.0126024
$985$	−32.0164	−1.02013
$986$	−33.8024	−1.07649
$987$	1.25501	0.0399473
$988$	0	0
$989$	−14.7955	−0.470470
$990$	6.49515	0.206429
$991$	−20.1109	−0.638845	−0.319423	−	0.947612i	$-0.603489\pi$
$991$	−20.1109	−0.638845	−0.319423	+	0.947612i	$0.603489\pi$
$992$	−22.8833	−0.726547
$993$	−9.10107	−0.288814
$994$	36.9248	1.17118
$995$	6.85622	0.217357
$996$	0.767432	0.0243170
$997$	4.50022	0.142523	0.0712617	−	0.997458i	$-0.477297\pi$
$997$	4.50022	0.142523	0.0712617	+	0.997458i	$0.477297\pi$
$998$	−61.1418	−1.93541
$999$	−31.2021	−0.987189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.k.1.5		6
13.3	even	3		143.2.e.c.100.2	✓	12
13.9	even	3		143.2.e.c.133.2	yes	12
13.12	even	2		1859.2.a.l.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.2	✓	12	13.3	even	3
143.2.e.c.133.2	yes	12	13.9	even	3
1859.2.a.k.1.5		6	1.1	even	1	trivial
1859.2.a.l.1.2		6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97462 q^{2} -0.571492 q^{3} +1.89914 q^{4} +1.23039 q^{5} -1.12848 q^{6} -2.55803 q^{7} -0.199164 q^{8} -2.67340 q^{9} +O(q^{10})\)	\(q+1.97462 q^{2} -0.571492 q^{3} +1.89914 q^{4} +1.23039 q^{5} -1.12848 q^{6} -2.55803 q^{7} -0.199164 q^{8} -2.67340 q^{9} +2.42955 q^{10} -1.00000 q^{11} -1.08534 q^{12} -5.05115 q^{14} -0.703156 q^{15} -4.19155 q^{16} +5.97567 q^{17} -5.27895 q^{18} -5.32116 q^{19} +2.33667 q^{20} +1.46190 q^{21} -1.97462 q^{22} -3.26161 q^{23} +0.113821 q^{24} -3.48615 q^{25} +3.24230 q^{27} -4.85806 q^{28} -2.86469 q^{29} -1.38847 q^{30} +2.90456 q^{31} -7.87841 q^{32} +0.571492 q^{33} +11.7997 q^{34} -3.14737 q^{35} -5.07715 q^{36} -9.62343 q^{37} -10.5073 q^{38} -0.245048 q^{40} -3.47319 q^{41} +2.88669 q^{42} +4.53626 q^{43} -1.89914 q^{44} -3.28931 q^{45} -6.44045 q^{46} +0.858478 q^{47} +2.39544 q^{48} -0.456470 q^{49} -6.88383 q^{50} -3.41505 q^{51} -13.7446 q^{53} +6.40233 q^{54} -1.23039 q^{55} +0.509467 q^{56} +3.04100 q^{57} -5.65668 q^{58} +8.76048 q^{59} -1.33539 q^{60} +2.76304 q^{61} +5.73542 q^{62} +6.83863 q^{63} -7.17379 q^{64} +1.12848 q^{66} +3.64984 q^{67} +11.3486 q^{68} +1.86398 q^{69} -6.21487 q^{70} -7.31017 q^{71} +0.532443 q^{72} -5.63352 q^{73} -19.0026 q^{74} +1.99231 q^{75} -10.1056 q^{76} +2.55803 q^{77} +7.57221 q^{79} -5.15723 q^{80} +6.16724 q^{81} -6.85824 q^{82} -0.707087 q^{83} +2.77634 q^{84} +7.35238 q^{85} +8.95740 q^{86} +1.63715 q^{87} +0.199164 q^{88} +12.1474 q^{89} -6.49515 q^{90} -6.19425 q^{92} -1.65994 q^{93} +1.69517 q^{94} -6.54708 q^{95} +4.50245 q^{96} +3.45779 q^{97} -0.901356 q^{98} +2.67340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} - 17 q^{12} + 12 q^{14} + 4 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 15 q^{20} - 12 q^{21} + 3 q^{23} - 14 q^{24} - 6 q^{25} + 10 q^{27} - 16 q^{28} + 3 q^{29} + 19 q^{30} - 5 q^{31} + q^{32} - q^{33} + 5 q^{34} - 13 q^{35} + 20 q^{36} - 25 q^{37} - 27 q^{38} - 8 q^{40} - 24 q^{41} + 13 q^{42} - 8 q^{43} - 8 q^{44} - 27 q^{45} - 18 q^{46} - 10 q^{47} - 28 q^{48} - q^{49} + 26 q^{50} - 17 q^{51} + 10 q^{53} - 47 q^{54} + 6 q^{55} + 15 q^{56} - 6 q^{58} + 4 q^{59} + 61 q^{60} - 21 q^{61} - 5 q^{62} - 6 q^{63} - 27 q^{64} + 12 q^{66} - 21 q^{67} + 14 q^{68} + 5 q^{69} - 31 q^{70} + 3 q^{71} + 50 q^{72} - 13 q^{73} - 38 q^{74} - 23 q^{75} - 8 q^{76} + 3 q^{77} - 4 q^{79} - 44 q^{80} + 34 q^{81} - 33 q^{82} - 8 q^{83} - 47 q^{84} + 13 q^{85} + 11 q^{86} - 51 q^{87} - 3 q^{88} + 9 q^{89} - 70 q^{90} + 15 q^{92} + 21 q^{93} + 10 q^{94} + 27 q^{95} + 19 q^{96} - 15 q^{97} - 21 q^{98} - 7 q^{99}+O(q^{100}) \) 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 - 17 * q^12 + 12 * q^14 + 4 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 15 * q^20 - 12 * q^21 + 3 * q^23 - 14 * q^24 - 6 * q^25 + 10 * q^27 - 16 * q^28 + 3 * q^29 + 19 * q^30 - 5 * q^31 + q^32 - q^33 + 5 * q^34 - 13 * q^35 + 20 * q^36 - 25 * q^37 - 27 * q^38 - 8 * q^40 - 24 * q^41 + 13 * q^42 - 8 * q^43 - 8 * q^44 - 27 * q^45 - 18 * q^46 - 10 * q^47 - 28 * q^48 - q^49 + 26 * q^50 - 17 * q^51 + 10 * q^53 - 47 * q^54 + 6 * q^55 + 15 * q^56 - 6 * q^58 + 4 * q^59 + 61 * q^60 - 21 * q^61 - 5 * q^62 - 6 * q^63 - 27 * q^64 + 12 * q^66 - 21 * q^67 + 14 * q^68 + 5 * q^69 - 31 * q^70 + 3 * q^71 + 50 * q^72 - 13 * q^73 - 38 * q^74 - 23 * q^75 - 8 * q^76 + 3 * q^77 - 4 * q^79 - 44 * q^80 + 34 * q^81 - 33 * q^82 - 8 * q^83 - 47 * q^84 + 13 * q^85 + 11 * q^86 - 51 * q^87 - 3 * q^88 + 9 * q^89 - 70 * q^90 + 15 * q^92 + 21 * q^93 + 10 * q^94 + 27 * q^95 + 19 * q^96 - 15 * q^97 - 21 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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